LMFDB - Embedded newform 110.4.g.d.91.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [110,4,Mod(31,110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(110, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("110.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 36 x^{14} + 201 x^{13} + 7402 x^{12} + 11076 x^{11} + 759461 x^{10} + 2416768 x^{9} + \cdots + 19847025 $ x^16 - x^15 + 36x^14 + 201x^13 + 7402x^12 + 11076x^11 + 759461x^10 + 2416768x^9 + 35264614x^8 + 89458413x^7 + 558214578x^6 + 1288789920x^5 + 4043254401x^4 + 6511836240x^3 + 5366285640x^2 - 535268250x + 19847025
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.4
Root			$2.44673 - 7.53026i$ of defining polynomial
Character	$\chi$	$=$	110.91
Dual form			110.4.g.d.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61803 + 1.17557i) q^{2} +(2.75575 + 8.48132i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.04508 - 2.93893i) q^{5} +(-14.4293 - 10.4835i) q^{6} +(-4.06895 + 12.5230i) q^{7} +(2.47214 + 7.60845i) q^{8} +(-42.4952 + 30.8746i) q^{9} +10.0000 q^{10} +(-22.6415 + 28.6070i) q^{11} +35.6711 q^{12} +(30.1829 - 21.9291i) q^{13} +(-8.13791 - 25.0459i) q^{14} +(13.7787 - 42.4066i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-89.8939 - 65.3118i) q^{17} +(32.4634 - 99.9122i) q^{18} +(4.51654 + 13.9005i) q^{19} +(-16.1803 + 11.7557i) q^{20} -117.424 q^{21} +(3.00517 - 72.9038i) q^{22} +115.962 q^{23} +(-57.7171 + 41.9339i) q^{24} +(7.72542 + 23.7764i) q^{25} +(-23.0577 + 70.9642i) q^{26} +(-184.168 - 133.806i) q^{27} +(42.6106 + 30.9584i) q^{28} +(-27.4099 + 84.3591i) q^{29} +(27.5575 + 84.8132i) q^{30} +(-187.286 + 136.071i) q^{31} +32.0000 q^{32} +(-305.020 - 113.196i) q^{33} +222.230 q^{34} +(53.2633 - 38.6980i) q^{35} +(64.9269 + 199.824i) q^{36} +(-35.0763 + 107.954i) q^{37} +(-23.6489 - 17.1819i) q^{38} +(269.164 + 195.559i) q^{39} +(12.3607 - 38.0423i) q^{40} +(-76.4263 - 235.216i) q^{41} +(189.996 - 138.040i) q^{42} +515.836 q^{43} +(80.8411 + 121.494i) q^{44} +262.635 q^{45} +(-187.630 + 136.321i) q^{46} +(140.825 + 433.414i) q^{47} +(44.0920 - 135.701i) q^{48} +(137.225 + 99.6997i) q^{49} +(-40.4508 - 29.3893i) q^{50} +(306.205 - 942.402i) q^{51} +(-46.1153 - 141.928i) q^{52} +(-423.785 + 307.897i) q^{53} +455.287 q^{54} +(175.661 - 49.1761i) q^{55} -105.339 q^{56} +(-105.448 + 76.6124i) q^{57} +(-54.8198 - 168.718i) q^{58} +(-205.805 + 633.404i) q^{59} +(-144.293 - 104.835i) q^{60} +(534.389 + 388.257i) q^{61} +(143.073 - 440.335i) q^{62} +(-213.730 - 657.792i) q^{63} +(-51.7771 + 37.6183i) q^{64} -186.540 q^{65} +(626.602 - 175.417i) q^{66} +250.611 q^{67} +(-359.576 + 261.247i) q^{68} +(319.561 + 983.508i) q^{69} +(-40.6895 + 125.230i) q^{70} +(-480.261 - 348.930i) q^{71} +(-339.961 - 246.996i) q^{72} +(-114.142 + 351.292i) q^{73} +(-70.1526 - 215.907i) q^{74} +(-180.366 + 131.044i) q^{75} +58.4633 q^{76} +(-266.117 - 399.939i) q^{77} -665.411 q^{78} +(-42.8752 + 31.1507i) q^{79} +(24.7214 + 76.0845i) q^{80} +(189.072 - 581.905i) q^{81} +(400.173 + 290.743i) q^{82} +(97.6363 + 70.9369i) q^{83} +(-145.144 + 446.708i) q^{84} +(171.682 + 528.383i) q^{85} +(-834.640 + 606.401i) q^{86} -791.011 q^{87} +(-273.628 - 101.546i) q^{88} -308.723 q^{89} +(-424.952 + 308.746i) q^{90} +(151.805 + 467.207i) q^{91} +(143.337 - 441.144i) q^{92} +(-1670.17 - 1213.45i) q^{93} +(-737.368 - 535.729i) q^{94} +(22.5827 - 69.5023i) q^{95} +(88.1839 + 271.402i) q^{96} +(1139.34 - 827.777i) q^{97} -339.239 q^{98} +(78.9262 - 1914.71i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 3 q^{3} - 16 q^{4} - 20 q^{5} - 16 q^{6} - 38 q^{7} - 32 q^{8} + 25 q^{9} + 160 q^{10} + 65 q^{11} + 88 q^{12} + 85 q^{13} - 76 q^{14} - 15 q^{15} - 64 q^{16} + 109 q^{17} - 280 q^{18}+ \cdots + 10702 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 3 * q^3 - 16 * q^4 - 20 * q^5 - 16 * q^6 - 38 * q^7 - 32 * q^8 + 25 * q^9 + 160 * q^10 + 65 * q^11 + 88 * q^12 + 85 * q^13 - 76 * q^14 - 15 * q^15 - 64 * q^16 + 109 * q^17 - 280 * q^18 + 12 * q^19 - 80 * q^20 - 36 * q^21 + 140 * q^22 + 432 * q^23 - 64 * q^24 - 100 * q^25 - 490 * q^26 - 507 * q^27 + 88 * q^28 + 369 * q^29 - 30 * q^30 - 334 * q^31 + 512 * q^32 - 280 * q^33 + 568 * q^34 + 110 * q^35 - 560 * q^36 - 360 * q^37 - 236 * q^38 + 279 * q^39 - 160 * q^40 - 595 * q^41 - 442 * q^42 + 612 * q^43 - 120 * q^44 + 1150 * q^45 - 206 * q^46 + 1066 * q^47 - 48 * q^48 - 1468 * q^49 - 200 * q^50 + 3404 * q^51 - 980 * q^52 - 533 * q^53 + 1556 * q^54 - 125 * q^55 + 256 * q^56 + 470 * q^57 + 738 * q^58 - 1842 * q^59 - 160 * q^60 + 1246 * q^61 - 178 * q^62 - 4622 * q^63 - 256 * q^64 + 1600 * q^65 + 920 * q^66 - 2200 * q^67 + 436 * q^68 + 4777 * q^69 - 380 * q^70 - 2158 * q^71 + 200 * q^72 - 55 * q^73 - 720 * q^74 - 200 * q^75 + 848 * q^76 + 3704 * q^77 - 1812 * q^78 + 1595 * q^79 - 320 * q^80 - 9487 * q^81 + 700 * q^82 - 486 * q^83 + 956 * q^84 - 1255 * q^85 - 1686 * q^86 - 1234 * q^87 - 640 * q^88 - 3512 * q^89 + 250 * q^90 + 3913 * q^91 - 452 * q^92 - 2423 * q^93 - 3748 * q^94 + 60 * q^95 - 96 * q^96 + 1101 * q^97 + 7224 * q^98 + 10702 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	2.75575	+	8.48132i	0.530344	+	1.63223i	0.753500	+	0.657448i	$0.228364\pi$
$3$	2.75575	+	8.48132i	0.530344	+	1.63223i	−0.223156	+	0.974783i	$0.571636\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	−4.04508	−	2.93893i	−0.361803	−	0.262866i
$5$	−4.04508	−	2.93893i	−0.361803	−	0.262866i
$6$	−14.4293	−	10.4835i	−0.981788	−	0.713311i
$7$	−4.06895	+	12.5230i	−0.219703	+	0.676176i	0.779083	+	0.626920i	$0.215685\pi$
$7$	−4.06895	+	12.5230i	−0.219703	+	0.676176i	−0.998786	+	0.0492555i	$0.984315\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	−42.4952	+	30.8746i	−1.57390	+	1.14350i
$10$	10.0000			0.316228
$11$	−22.6415	+	28.6070i	−0.620607	+	0.784122i
$11$	−22.6415	+	28.6070i	−0.620607	+	0.784122i
$12$	35.6711			0.858114
$13$	30.1829	−	21.9291i	0.643940	−	0.467850i	−0.217262	−	0.976113i	$-0.569712\pi$
$13$	30.1829	−	21.9291i	0.643940	−	0.467850i	0.861202	+	0.508264i	$0.169712\pi$
$14$	−8.13791	−	25.0459i	−0.155353	−	0.478129i
$15$	13.7787	−	42.4066i	0.237177	−	0.729956i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	−89.8939	−	65.3118i	−1.28250	−	0.931790i	−0.282873	−	0.959157i	$-0.591288\pi$
$17$	−89.8939	−	65.3118i	−1.28250	−	0.931790i	−0.999625	+	0.0273672i	$0.991288\pi$
$18$	32.4634	−	99.9122i	0.425095	−	1.30831i
$19$	4.51654	+	13.9005i	0.0545350	+	0.167841i	0.974614	−	0.223891i	$-0.0718759\pi$
$19$	4.51654	+	13.9005i	0.0545350	+	0.167841i	−0.920079	+	0.391732i	$0.871876\pi$
$20$	−16.1803	+	11.7557i	−0.180902	+	0.131433i
$21$	−117.424			−1.22019
$22$	3.00517	−	72.9038i	0.0291229	−	0.706507i
$23$	115.962			1.05129			0.525645	−	0.850704i	$-0.323824\pi$
$23$	115.962			1.05129			0.525645	+	0.850704i	$0.323824\pi$
$24$	−57.7171	+	41.9339i	−0.490894	+	0.356655i
$25$	7.72542	+	23.7764i	0.0618034	+	0.190211i
$26$	−23.0577	+	70.9642i	−0.173922	+	0.535278i
$27$	−184.168	−	133.806i	−1.31271	−	0.953737i
$28$	42.6106	+	30.9584i	0.287595	+	0.208950i
$29$	−27.4099	+	84.3591i	−0.175514	+	0.540175i	−0.999657	−	0.0262065i	$-0.991657\pi$
$29$	−27.4099	+	84.3591i	−0.175514	+	0.540175i	0.824143	+	0.566382i	$0.191657\pi$
$30$	27.5575	+	84.8132i	0.167709	+	0.516157i
$31$	−187.286	+	136.071i	−1.08508	+	0.788357i	−0.978562	−	0.205954i	$-0.933970\pi$
$31$	−187.286	+	136.071i	−1.08508	+	0.788357i	−0.106518	+	0.994311i	$0.533970\pi$
$32$	32.0000			0.176777
$33$	−305.020	−	113.196i	−1.60900	−	0.597119i
$34$	222.230			1.12095
$35$	53.2633	−	38.6980i	0.257233	−	0.186890i
$36$	64.9269	+	199.824i	0.300587	+	0.925113i
$37$	−35.0763	+	107.954i	−0.155851	+	0.479662i	−0.998246	−	0.0591995i	$-0.981145\pi$
$37$	−35.0763	+	107.954i	−0.155851	+	0.479662i	0.842395	+	0.538861i	$0.181145\pi$
$38$	−23.6489	−	17.1819i	−0.100957	−	0.0733494i
$39$	269.164	+	195.559i	1.10515	+	0.802937i
$40$	12.3607	−	38.0423i	0.0488599	−	0.150375i
$41$	−76.4263	−	235.216i	−0.291117	−	0.895965i	−0.984498	−	0.175394i	$-0.943880\pi$
$41$	−76.4263	−	235.216i	−0.291117	−	0.895965i	0.693382	−	0.720570i	$-0.256120\pi$
$42$	189.996	−	138.040i	0.698025	−	0.507145i
$43$	515.836			1.82940			0.914700	−	0.404134i	$-0.132427\pi$
$43$	515.836			1.82940			0.914700	+	0.404134i	$0.132427\pi$
$44$	80.8411	+	121.494i	0.276983	+	0.416270i
$45$	262.635			0.870028
$46$	−187.630	+	136.321i	−0.601403	+	0.436945i
$47$	140.825	+	433.414i	0.437051	+	1.34511i	0.890970	+	0.454062i	$0.150026\pi$
$47$	140.825	+	433.414i	0.437051	+	1.34511i	−0.453919	+	0.891043i	$0.649974\pi$
$48$	44.0920	−	135.701i	0.132586	−	0.408058i
$49$	137.225	+	99.6997i	0.400073	+	0.290670i
$50$	−40.4508	−	29.3893i	−0.114412	−	0.0831254i
$51$	306.205	−	942.402i	0.840731	−	2.58750i
$52$	−46.1153	−	141.928i	−0.122982	−	0.378498i
$53$	−423.785	+	307.897i	−1.09833	+	0.797981i	−0.980786	−	0.195088i	$-0.937501\pi$
$53$	−423.785	+	307.897i	−1.09833	+	0.797981i	−0.117540	+	0.993068i	$0.537501\pi$
$54$	455.287			1.14735
$55$	175.661	−	49.1761i	0.430656	−	0.120562i
$56$	−105.339			−0.251367
$57$	−105.448	+	76.6124i	−0.245034	+	0.178027i
$58$	−54.8198	−	168.718i	−0.124107	−	0.381962i
$59$	−205.805	+	633.404i	−0.454129	+	1.39766i	0.418027	+	0.908435i	$0.362722\pi$
$59$	−205.805	+	633.404i	−0.454129	+	1.39766i	−0.872155	+	0.489229i	$0.837278\pi$
$60$	−144.293	−	104.835i	−0.310469	−	0.225569i
$61$	534.389	+	388.257i	1.12166	+	0.814937i	0.984461	−	0.175606i	$-0.0561884\pi$
$61$	534.389	+	388.257i	1.12166	+	0.814937i	0.137204	+	0.990543i	$0.456188\pi$
$62$	143.073	−	440.335i	0.293070	−	0.901977i
$63$	−213.730	−	657.792i	−0.427419	−	1.31546i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	−186.540			−0.355961
$66$	626.602	−	175.417i	1.16863	−	0.327156i
$67$	250.611			0.456971			0.228485	−	0.973547i	$-0.426623\pi$
$67$	250.611			0.456971			0.228485	+	0.973547i	$0.426623\pi$
$68$	−359.576	+	261.247i	−0.641249	+	0.465895i
$69$	319.561	+	983.508i	0.557545	+	1.71595i
$70$	−40.6895	+	125.230i	−0.0694761	+	0.213826i
$71$	−480.261	−	348.930i	−0.802767	−	0.583244i	0.108958	−	0.994046i	$-0.465249\pi$
$71$	−480.261	−	348.930i	−0.802767	−	0.583244i	−0.911725	+	0.410802i	$0.865249\pi$
$72$	−339.961	−	246.996i	−0.556456	−	0.404289i
$73$	−114.142	+	351.292i	−0.183004	+	0.563228i	−0.999908	−	0.0135454i	$-0.995688\pi$
$73$	−114.142	+	351.292i	−0.183004	+	0.563228i	0.816905	+	0.576773i	$0.195688\pi$
$74$	−70.1526	−	215.907i	−0.110204	−	0.339172i
$75$	−180.366	+	131.044i	−0.277692	+	0.201755i
$76$	58.4633			0.0882394
$77$	−266.117	−	399.939i	−0.393855	−	0.591913i
$78$	−665.411			−0.965935
$79$	−42.8752	+	31.1507i	−0.0610612	+	0.0443636i	−0.617897	−	0.786259i	$-0.712015\pi$
$79$	−42.8752	+	31.1507i	−0.0610612	+	0.0443636i	0.556836	+	0.830623i	$0.312015\pi$
$80$	24.7214	+	76.0845i	0.0345492	+	0.106331i
$81$	189.072	−	581.905i	0.259359	−	0.798223i
$82$	400.173	+	290.743i	0.538924	+	0.391551i
$83$	97.6363	+	70.9369i	0.129120	+	0.0938113i	0.650471	−	0.759531i	$-0.274572\pi$
$83$	97.6363	+	70.9369i	0.129120	+	0.0938113i	−0.521351	+	0.853343i	$0.674572\pi$
$84$	−145.144	+	446.708i	−0.188530	+	0.580236i
$85$	171.682	+	528.383i	0.219077	+	0.674250i
$86$	−834.640	+	606.401i	−1.04653	+	0.760348i
$87$	−791.011			−0.974773
$88$	−273.628	−	101.546i	−0.331464	−	0.123010i
$89$	−308.723			−0.367691			−0.183846	−	0.982955i	$-0.558855\pi$
$89$	−308.723			−0.367691			−0.183846	+	0.982955i	$0.558855\pi$
$90$	−424.952	+	308.746i	−0.497709	+	0.361607i
$91$	151.805	+	467.207i	0.174873	+	0.538205i
$92$	143.337	−	441.144i	0.162433	−	0.499918i
$93$	−1670.17	−	1213.45i	−1.86225	−	1.35300i
$94$	−737.368	−	535.729i	−0.809082	−	0.587832i
$95$	22.5827	−	69.5023i	0.0243888	−	0.0750610i
$96$	88.1839	+	271.402i	0.0937524	+	0.288540i
$97$	1139.34	−	827.777i	1.19260	−	0.866475i	0.199063	−	0.979987i	$-0.436210\pi$
$97$	1139.34	−	827.777i	1.19260	−	0.866475i	0.993537	+	0.113512i	$0.0362101\pi$
$98$	−339.239			−0.349676
$99$	78.9262	−	1914.71i	0.0801250	−	1.94379i
$100$	100.000			0.100000
$101$	907.129	−	659.068i	0.893690	−	0.649304i	−0.0431475	−	0.999069i	$-0.513739\pi$
$101$	907.129	−	659.068i	0.893690	−	0.649304i	0.936837	+	0.349765i	$0.113739\pi$
$102$	612.410	+	1884.80i	0.594486	+	1.82964i
$103$	41.5073	−	127.746i	0.0397071	−	0.122206i	−0.929238	−	0.369482i	$-0.879535\pi$
$103$	41.5073	−	127.746i	0.0397071	−	0.122206i	0.968945	+	0.247276i	$0.0795353\pi$
$104$	241.463	+	175.433i	0.227667	+	0.165410i
$105$	474.991	+	345.101i	0.441470	+	0.320747i
$106$	323.743	−	996.377i	0.296648	−	0.912988i
$107$	−219.360	−	675.122i	−0.198190	−	0.609968i	−0.999925	−	0.0122866i	$-0.996089\pi$
$107$	−219.360	−	675.122i	−0.198190	−	0.609968i	0.801734	−	0.597681i	$-0.203911\pi$
$108$	−736.670	+	535.222i	−0.656353	+	0.476869i
$109$	1489.08			1.30851			0.654257	−	0.756273i	$-0.272982\pi$
$109$	1489.08			1.30851			0.654257	+	0.756273i	$0.272982\pi$
$110$	−226.415	+	286.070i	−0.196253	+	0.247961i
$111$	−1012.25			−0.865573
$112$	170.443	−	123.834i	0.143797	−	0.104475i
$113$	225.947	+	695.393i	0.188100	+	0.578912i	0.999988	−	0.00490117i	$-0.00156010\pi$
$113$	225.947	+	695.393i	0.188100	+	0.578912i	−0.811888	+	0.583813i	$0.801560\pi$
$114$	80.5550	−	247.923i	0.0661813	−	0.203685i
$115$	−469.075	−	340.803i	−0.380360	−	0.276348i
$116$	287.040	+	208.547i	0.229750	+	0.166923i
$117$	−605.574	+	1863.76i	−0.478507	+	1.47269i
$118$	−411.611	−	1266.81i	−0.321117	−	0.988298i
$119$	1183.67	−	859.987i	0.911823	−	0.662478i
$120$	356.711			0.271360
$121$	−305.724	−	1295.41i	−0.229695	−	0.973263i
$122$	−1321.08			−0.980371
$123$	1784.33	−	1296.39i	1.30803	−	0.950339i
$124$	286.147	+	880.669i	0.207232	+	0.637794i
$125$	38.6271	−	118.882i	0.0276393	−	0.0850651i
$126$	1119.10	+	813.076i	0.791251	+	0.574877i
$127$	−1326.38	−	963.672i	−0.926750	−	0.673324i	0.0184446	−	0.999830i	$-0.494129\pi$
$127$	−1326.38	−	963.672i	−0.926750	−	0.673324i	−0.945195	+	0.326506i	$0.894129\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	1421.51	+	4374.97i	0.970211	+	2.98600i
$130$	301.829	−	219.291i	0.203632	−	0.147947i
$131$	−2250.95			−1.50127			−0.750636	−	0.660716i	$-0.770253\pi$
$131$	−2250.95			−1.50127			−0.750636	+	0.660716i	$0.770253\pi$
$132$	−807.649	+	1020.45i	−0.532552	+	0.672866i
$133$	−192.452			−0.125472
$134$	−405.498	+	294.611i	−0.261415	+	0.189929i
$135$	351.729	+	1082.51i	0.224237	+	0.690131i
$136$	274.691	−	845.413i	0.173196	−	0.533041i
$137$	1987.30	+	1443.86i	1.23932	+	0.900416i	0.997553	−	0.0699191i	$-0.0222741\pi$
$137$	1987.30	+	1443.86i	1.23932	+	0.900416i	0.241764	+	0.970335i	$0.422274\pi$
$138$	−1673.24	−	1215.68i	−1.03214	−	0.749897i
$139$	236.550	−	728.027i	0.144345	−	0.444248i	−0.852581	−	0.522595i	$-0.824964\pi$
$139$	236.550	−	728.027i	0.144345	−	0.444248i	0.996926	+	0.0783467i	$0.0249641\pi$
$140$	−81.3791	−	250.459i	−0.0491271	−	0.151198i
$141$	−3287.85	+	2388.76i	−1.96373	+	1.42674i
$142$	1187.27			0.701644
$143$	−56.0585	+	1359.95i	−0.0327822	+	0.795278i
$144$	840.431			0.486360
$145$	358.801	−	260.684i	0.205495	−	0.149301i
$146$	−228.283	−	702.584i	−0.129403	−	0.398262i
$147$	−467.428	+	1438.60i	−0.262264	+	0.807166i
$148$	367.324	+	266.876i	0.204012	+	0.148224i
$149$	−1106.10	−	803.625i	−0.608154	−	0.441849i	0.240610	−	0.970622i	$-0.422652\pi$
$149$	−1106.10	−	803.625i	−0.608154	−	0.441849i	−0.848764	+	0.528772i	$0.822652\pi$
$150$	137.787	−	424.066i	0.0750020	−	0.230832i
$151$	330.130	+	1016.03i	0.177918	+	0.547574i	0.999755	−	0.0221483i	$-0.00705061\pi$
$151$	330.130	+	1016.03i	0.177918	+	0.547574i	−0.821837	+	0.569723i	$0.807051\pi$
$152$	−94.5956	+	68.7277i	−0.0504784	+	0.0366747i
$153$	5836.53			3.08402
$154$	900.743	+	334.276i	0.471324	+	0.174914i
$155$	1157.49			0.599817
$156$	1076.66	−	782.237i	0.552574	−	0.401469i
$157$	−356.866	−	1098.32i	−0.181408	−	0.558315i	0.818460	−	0.574563i	$-0.194828\pi$
$157$	−356.866	−	1098.32i	−0.181408	−	0.558315i	−0.999868	+	0.0162476i	$0.994828\pi$
$158$	32.7537	−	100.806i	0.0164921	−	0.0507574i
$159$	−3779.22	−	2745.76i	−1.88498	−	1.36952i
$160$	−129.443	−	94.0456i	−0.0639584	−	0.0464685i
$161$	−471.843	+	1452.18i	−0.230972	+	0.710857i
$162$	378.145	+	1163.81i	0.183394	+	0.564429i
$163$	2581.10	−	1875.28i	1.24029	−	0.901125i	0.242675	−	0.970108i	$-0.421975\pi$
$163$	2581.10	−	1875.28i	1.24029	−	0.901125i	0.997618	+	0.0689825i	$0.0219753\pi$
$164$	−989.283			−0.471037
$165$	901.155	+	1354.32i	0.425181	+	0.638991i
$166$	−241.370			−0.112855
$167$	3416.08	−	2481.93i	1.58290	−	1.15004i	0.669622	−	0.742702i	$-0.266456\pi$
$167$	3416.08	−	2481.93i	1.58290	−	1.15004i	0.913276	−	0.407341i	$-0.133544\pi$
$168$	−290.289	−	893.416i	−0.133311	−	0.410289i
$169$	−248.792	+	765.703i	−0.113242	+	0.348522i
$170$	−898.939	−	653.118i	−0.405562	−	0.294658i
$171$	−621.102	−	451.257i	−0.277759	−	0.201804i
$172$	637.608	−	1962.36i	0.282658	−	0.869931i
$173$	−617.437	−	1900.28i	−0.271346	−	0.835117i	−0.990163	−	0.139918i	$-0.955316\pi$
$173$	−617.437	−	1900.28i	−0.271346	−	0.835117i	0.718817	−	0.695199i	$-0.244684\pi$
$174$	1279.88	−	929.889i	0.557630	−	0.405142i
$175$	−329.185			−0.142195
$176$	562.115	−	157.363i	0.240744	−	0.0673961i
$177$	−5939.25			−2.52215
$178$	499.524	−	362.925i	0.210342	−	0.152822i
$179$	−923.426	−	2842.01i	−0.385587	−	1.18672i	−0.936053	−	0.351858i	$-0.885550\pi$
$179$	−923.426	−	2842.01i	−0.385587	−	1.18672i	0.550466	−	0.834857i	$-0.314450\pi$
$180$	324.634	−	999.122i	0.134427	−	0.413723i
$181$	−432.634	−	314.327i	−0.177665	−	0.129081i	0.495398	−	0.868666i	$-0.335022\pi$
$181$	−432.634	−	314.327i	−0.177665	−	0.129081i	−0.673064	+	0.739584i	$0.735022\pi$
$182$	−794.860	−	577.500i	−0.323731	−	0.235204i
$183$	−1820.29	+	5602.26i	−0.735297	+	2.26301i
$184$	286.673	+	882.289i	0.114858	+	0.353496i
$185$	459.154	−	333.595i	0.182474	−	0.132575i
$186$	4128.89			1.62766
$187$	3903.71	−	1092.84i	1.52656	−	0.427360i
$188$	1822.87			0.707164
$189$	2425.01	−	1761.87i	0.933299	−	0.678082i
$190$	45.1654	+	139.005i	0.0172455	+	0.0530761i
$191$	−1200.12	+	3693.60i	−0.454649	+	1.39926i	0.416899	+	0.908953i	$0.363117\pi$
$191$	−1200.12	+	3693.60i	−0.454649	+	1.39926i	−0.871547	+	0.490311i	$0.836883\pi$
$192$	−461.737	−	335.472i	−0.173557	−	0.126097i
$193$	1949.53	+	1416.42i	0.727101	+	0.528270i	0.888645	−	0.458596i	$-0.151647\pi$
$193$	1949.53	+	1416.42i	0.727101	+	0.528270i	−0.161544	+	0.986865i	$0.551647\pi$
$194$	−870.376	+	2678.74i	−0.322110	+	0.991353i
$195$	−514.058	−	1582.11i	−0.188782	−	0.581011i
$196$	548.900	−	398.799i	0.200036	−	0.145335i
$197$	1603.00			0.579742			0.289871	−	0.957066i	$-0.406388\pi$
$197$	1603.00			0.579742			0.289871	+	0.957066i	$0.406388\pi$
$198$	2123.17	+	3190.84i	0.762055	+	1.14527i
$199$	−2028.13			−0.722464			−0.361232	−	0.932476i	$-0.617644\pi$
$199$	−2028.13			−0.722464			−0.361232	+	0.932476i	$0.617644\pi$
$200$	−161.803	+	117.557i	−0.0572061	+	0.0415627i
$201$	690.622	+	2125.52i	0.242352	+	0.745882i
$202$	−692.985	+	2132.79i	−0.241377	+	0.742883i
$203$	−944.895	−	686.506i	−0.326693	−	0.237356i
$204$	−3206.62	−	2329.75i	−1.10053	−	0.799582i
$205$	−382.131	+	1176.08i	−0.130191	+	0.400688i
$206$	83.0145	+	255.492i	0.0280772	+	0.0864126i
$207$	−4927.81	+	3580.26i	−1.65462	+	1.20215i
$208$	−596.929			−0.198988
$209$	−499.912	−	185.523i	−0.165453	−	0.0614014i
$210$	−1174.24			−0.385859
$211$	1942.72	−	1411.47i	0.633850	−	0.460519i	−0.223882	−	0.974616i	$-0.571873\pi$
$211$	1942.72	−	1411.47i	0.633850	−	0.460519i	0.857732	+	0.514097i	$0.171873\pi$
$212$	647.485	+	1992.75i	0.209762	+	0.645580i
$213$	1635.91	−	5034.81i	0.526247	−	1.61962i
$214$	1148.59	+	834.497i	0.366896	+	0.266566i
$215$	−2086.60	−	1516.00i	−0.661883	−	0.480886i
$216$	562.766	−	1732.02i	0.177275	−	0.545596i
$217$	−941.953	−	2899.03i	−0.294673	−	0.906909i
$218$	−2409.38	+	1750.52i	−0.748550	+	0.543853i
$219$	−3293.96			−1.01637
$220$	30.0517	−	729.038i	0.00920948	−	0.223417i
$221$	−4145.49			−1.26179
$222$	1637.86	−	1189.97i	0.495161	−	0.359756i
$223$	1654.73	+	5092.73i	0.496900	+	1.52930i	0.813974	+	0.580901i	$0.197300\pi$
$223$	1654.73	+	5092.73i	0.496900	+	1.52930i	−0.317074	+	0.948401i	$0.602700\pi$
$224$	−130.207	+	400.734i	−0.0388383	+	0.119532i
$225$	−1062.38	−	771.864i	−0.314779	−	0.228700i
$226$	−1183.07	−	859.553i	−0.348216	−	0.252994i
$227$	−603.683	+	1857.94i	−0.176510	+	0.543243i	−0.999699	−	0.0245248i	$-0.992193\pi$
$227$	−603.683	+	1857.94i	−0.176510	+	0.543243i	0.823189	+	0.567768i	$0.192193\pi$
$228$	161.110	+	495.846i	0.0467972	+	0.144027i
$229$	−3264.56	+	2371.84i	−0.942044	+	0.684435i	−0.948912	−	0.315541i	$-0.897814\pi$
$229$	−3264.56	+	2371.84i	−0.942044	+	0.684435i	0.00686776	+	0.999976i	$0.497814\pi$
$230$	1159.62			0.332447
$231$	2658.66	−	3359.16i	0.757260	−	0.956780i
$232$	−709.603			−0.200809
$233$	−2815.20	+	2045.36i	−0.791544	+	0.575090i	−0.908421	−	0.418056i	$-0.862711\pi$
$233$	−2815.20	+	2045.36i	−0.791544	+	0.575090i	0.116878	+	0.993146i	$0.462711\pi$
$234$	−1211.15	−	3727.53i	−0.338356	−	1.04135i
$235$	704.124	−	2167.07i	0.195455	−	0.601549i
$236$	2155.22	+	1565.86i	0.594462	+	0.431902i
$237$	−382.352	−	277.795i	−0.104795	−	0.0761381i
$238$	−904.244	+	2782.98i	−0.246275	+	0.757956i
$239$	1102.95	+	3394.53i	0.298510	+	0.918719i	0.982020	+	0.188778i	$0.0604525\pi$
$239$	1102.95	+	3394.53i	0.298510	+	0.918719i	−0.683510	+	0.729941i	$0.739547\pi$
$240$	−577.171	+	419.339i	−0.155234	+	0.112784i
$241$	−3290.24			−0.879433			−0.439716	−	0.898137i	$-0.644921\pi$
$241$	−3290.24			−0.879433			−0.439716	+	0.898137i	$0.644921\pi$
$242$	2017.52	+	1736.62i	0.535914	+	0.461299i
$243$	−690.023			−0.182160
$244$	2137.56	−	1553.03i	0.560832	−	0.407468i
$245$	−262.076	−	806.588i	−0.0683406	−	0.210331i
$246$	−1363.11	+	4195.21i	−0.353287	+	1.08730i
$247$	441.147	+	320.512i	0.113642	+	0.0825656i
$248$	−1498.28	−	1088.57i	−0.383634	−	0.278726i
$249$	−332.578	+	1023.57i	−0.0846436	+	0.260506i
$250$	77.2542	+	237.764i	0.0195440	+	0.0601501i
$251$	5670.81	−	4120.09i	1.42605	−	1.03609i	0.435315	−	0.900278i	$-0.356637\pi$
$251$	5670.81	−	4120.09i	1.42605	−	1.03609i	0.990735	−	0.135808i	$-0.0433631\pi$
$252$	−2766.57			−0.691579
$253$	−2625.55	+	3317.32i	−0.652438	+	0.824340i
$254$	3278.99			0.810010
$255$	−4008.27	+	2912.18i	−0.984345	+	0.715168i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	2526.59	−	7776.05i	0.613247	−	1.88738i	0.188484	−	0.982076i	$-0.439642\pi$
$257$	2526.59	−	7776.05i	0.613247	−	1.88738i	0.424763	−	0.905305i	$-0.360358\pi$
$258$	−7443.14	−	5407.76i	−1.79608	−	1.30493i
$259$	−1209.18	−	878.517i	−0.290095	−	0.210766i
$260$	−230.577	+	709.642i	−0.0549990	+	0.169270i
$261$	−1439.76	−	4431.12i	−0.341451	−	1.05088i
$262$	3642.12	−	2646.15i	0.858820	−	0.623969i
$263$	3740.41			0.876972			0.438486	−	0.898738i	$-0.355515\pi$
$263$	3740.41			0.876972			0.438486	+	0.898738i	$0.355515\pi$
$264$	107.198	−	2600.56i	0.0249908	−	0.606264i
$265$	2619.13			0.607140
$266$	311.395	−	226.241i	0.0717776	−	0.0521495i
$267$	−850.762	−	2618.38i	−0.195003	−	0.600157i
$268$	309.773	−	953.382i	0.0706059	−	0.217303i
$269$	515.124	+	374.259i	0.116757	+	0.0848290i	0.644631	−	0.764493i	$-0.277011\pi$
$269$	515.124	+	374.259i	0.116757	+	0.0848290i	−0.527874	+	0.849322i	$0.677011\pi$
$270$	−1841.68	−	1338.06i	−0.415114	−	0.301598i
$271$	845.375	−	2601.80i	0.189494	−	0.583202i	−0.810503	−	0.585735i	$-0.800806\pi$
$271$	845.375	−	2601.80i	0.189494	−	0.583202i	0.999997	+	0.00253235i	$0.000806073\pi$
$272$	549.383	+	1690.83i	0.122468	+	0.376917i
$273$	−3544.20	+	2575.01i	−0.785731	+	0.570867i
$274$	−4912.87			−1.08320
$275$	−855.088	−	317.333i	−0.187504	−	0.0695850i
$276$	4136.49			0.902128
$277$	−3652.26	+	2653.52i	−0.792213	+	0.575577i	−0.908619	−	0.417625i	$-0.862863\pi$
$277$	−3652.26	+	2653.52i	−0.792213	+	0.575577i	0.116406	+	0.993202i	$0.462863\pi$
$278$	473.101	+	1456.05i	0.102067	+	0.314131i
$279$	3757.60	−	11564.7i	0.806315	−	2.48158i
$280$	426.106	+	309.584i	0.0909454	+	0.0660757i
$281$	513.424	+	373.024i	0.108998	+	0.0791914i	0.640949	−	0.767584i	$-0.278541\pi$
$281$	513.424	+	373.024i	0.108998	+	0.0791914i	−0.531951	+	0.846775i	$0.678541\pi$
$282$	2511.69	−	7730.19i	0.530387	−	1.63236i
$283$	524.670	+	1614.77i	0.110206	+	0.339180i	0.990917	−	0.134474i	$-0.0429346\pi$
$283$	524.670	+	1614.77i	0.110206	+	0.339180i	−0.880711	+	0.473654i	$0.842935\pi$
$284$	−1921.04	+	1395.72i	−0.401383	+	0.291622i
$285$	651.704			0.135451
$286$	−1508.01	−	2266.35i	−0.311786	−	0.468573i
$287$	3256.57			0.669789
$288$	−1359.85	+	987.986i	−0.278228	+	0.202144i
$289$	2297.09	+	7069.72i	0.467554	+	1.43898i
$290$	−274.099	+	843.591i	−0.0555023	+	0.170818i
$291$	10160.4	+	7381.94i	2.04677	+	1.48707i
$292$	1195.31	+	868.441i	0.239555	+	0.174047i
$293$	−1262.46	+	3885.44i	−0.251718	+	0.774710i	0.742740	+	0.669580i	$0.233526\pi$
$293$	−1262.46	+	3885.44i	−0.251718	+	0.774710i	−0.994458	+	0.105130i	$0.966474\pi$
$294$	−934.856	−	2877.19i	−0.185449	−	0.570752i
$295$	2694.03	−	1957.33i	0.531703	−	0.386305i
$296$	−908.074			−0.178313
$297$	7997.61	−	2238.93i	1.56252	−	0.437426i
$298$	2734.42			0.531546
$299$	3500.06	−	2542.94i	0.676968	−	0.491846i
$300$	275.575	+	848.132i	0.0530344	+	0.163223i
$301$	−2098.91	+	6459.78i	−0.401924	+	1.23700i
$302$	−1728.58	−	1255.89i	−0.329367	−	0.239299i
$303$	8089.58	+	5877.42i	1.53378	+	1.11435i
$304$	72.2646	−	222.408i	0.0136337	−	0.0419603i
$305$	−1020.59	−	3141.06i	−0.191603	−	0.589694i
$306$	−9443.70	+	6861.25i	−1.76425	+	1.28180i
$307$	−6741.77			−1.25333			−0.626666	−	0.779288i	$-0.715581\pi$
$307$	−6741.77			−1.25333			−0.626666	+	0.779288i	$0.715581\pi$
$308$	−1850.40	+	518.017i	−0.342325	+	0.0958337i
$309$	1197.84			0.220527
$310$	−1872.86	+	1360.71i	−0.343132	+	0.249300i
$311$	2455.92	+	7558.55i	0.447789	+	1.37815i	0.879396	+	0.476092i	$0.157947\pi$
$311$	2455.92	+	7558.55i	0.447789	+	1.37815i	−0.431606	+	0.902062i	$0.642053\pi$
$312$	−822.493	+	2531.37i	−0.149245	+	0.459329i
$313$	−2835.85	−	2060.36i	−0.512113	−	0.372072i	0.301511	−	0.953463i	$-0.402509\pi$
$313$	−2835.85	−	2060.36i	−0.512113	−	0.372072i	−0.813625	+	0.581391i	$0.802509\pi$
$314$	1868.57	+	1357.60i	0.335827	+	0.243993i
$315$	−1068.65	+	3288.96i	−0.191148	+	0.588292i
$316$	65.5075	+	201.611i	0.0116617	+	0.0358909i
$317$	−1490.12	+	1082.63i	−0.264016	+	0.191819i	−0.711916	−	0.702265i	$-0.752172\pi$
$317$	−1490.12	+	1082.63i	−0.264016	+	0.191819i	0.447899	+	0.894084i	$0.352172\pi$
$318$	9342.75			1.64753
$319$	−1792.66	−	2694.13i	−0.314638	−	0.472861i
$320$	320.000			0.0559017
$321$	5121.42	−	3720.93i	0.890499	−	0.646985i
$322$	−943.685	−	2904.36i	−0.163322	−	0.502652i
$323$	501.855	−	1544.55i	0.0864519	−	0.266072i
$324$	−1979.99	−	1438.55i	−0.339505	−	0.246665i
$325$	754.572	+	548.228i	0.128788	+	0.0935700i
$326$	−1971.79	+	6068.54i	−0.334992	+	1.03100i
$327$	4103.53	+	12629.4i	0.693962	+	2.13580i
$328$	1600.69	−	1162.97i	0.269462	−	0.195775i
$329$	−6000.63			−1.00555
$330$	−3050.20	−	1131.96i	−0.508811	−	0.188826i
$331$	2810.69			0.466736			0.233368	−	0.972389i	$-0.425025\pi$
$331$	2810.69			0.466736			0.233368	+	0.972389i	$0.425025\pi$
$332$	390.545	−	283.748i	0.0645601	−	0.0469056i
$333$	−1842.45	−	5670.48i	−0.303200	−	0.933154i
$334$	−2609.65	+	8031.68i	−0.427526	+	1.31579i
$335$	−1013.74	−	736.528i	−0.165334	−	0.120122i
$336$	1519.97	+	1104.32i	0.246789	+	0.179303i
$337$	1637.54	−	5039.84i	0.264697	−	0.814652i	−0.727067	−	0.686567i	$-0.759117\pi$
$337$	1637.54	−	5039.84i	0.264697	−	0.814652i	0.991763	−	0.128085i	$-0.0408831\pi$
$338$	−497.584	−	1531.41i	−0.0800740	−	0.246442i
$339$	−5275.20	+	3832.65i	−0.845160	+	0.614045i
$340$	2222.30			0.354474
$341$	347.845	−	8438.53i	0.0552400	−	1.34009i
$342$	1535.45			0.242771
$343$	−5460.76	+	3967.47i	−0.859630	+	0.624558i
$344$	1275.22	+	3924.71i	0.199869	+	0.615134i
$345$	1597.81	−	4917.54i	0.249342	−	0.767396i
$346$	3232.94	+	2348.87i	0.502324	+	0.364960i
$347$	708.845	+	515.006i	0.109662	+	0.0796743i	0.641265	−	0.767320i	$-0.278410\pi$
$347$	708.845	+	515.006i	0.109662	+	0.0796743i	−0.531603	+	0.846994i	$0.678410\pi$
$348$	−977.743	+	3009.18i	−0.150611	+	0.463532i
$349$	−3438.09	−	10581.4i	−0.527326	−	1.62294i	−0.759669	−	0.650310i	$-0.774639\pi$
$349$	−3438.09	−	10581.4i	−0.527326	−	1.62294i	0.232343	−	0.972634i	$-0.425361\pi$
$350$	532.633	−	386.980i	0.0813441	−	0.0590999i
$351$	−8492.95			−1.29151
$352$	−724.529	+	915.425i	−0.109709	+	0.138614i
$353$	6910.71			1.04198			0.520992	−	0.853562i	$-0.325562\pi$
$353$	6910.71			1.04198			0.520992	+	0.853562i	$0.325562\pi$
$354$	9609.91	−	6982.01i	1.44283	−	1.04828i
$355$	917.216	+	2822.90i	0.137129	+	0.422040i
$356$	−381.602	+	1174.45i	−0.0568114	+	0.174848i
$357$	10555.7	+	7669.18i	1.56490	+	1.13696i
$358$	4835.12	+	3512.92i	0.713810	+	0.518614i
$359$	−320.713	+	987.054i	−0.0471493	+	0.145111i	−0.971860	−	0.235561i	$-0.924307\pi$
$359$	−320.713	+	987.054i	−0.0471493	+	0.145111i	0.924710	+	0.380672i	$0.124307\pi$
$360$	649.269	+	1998.24i	0.0950540	+	0.292546i
$361$	5376.22	−	3906.06i	0.783820	−	0.569479i
$362$	1069.53			0.155285
$363$	10144.3	−	6162.77i	1.46677	−	0.891079i
$364$	1965.00			0.282951
$365$	1494.13	−	1085.55i	0.214264	−	0.155672i
$366$	−3640.57	−	11204.5i	−0.519934	−	1.60019i
$367$	−426.294	+	1312.00i	−0.0606332	+	0.186610i	−0.976785	−	0.214221i	$-0.931279\pi$
$367$	−426.294	+	1312.00i	−0.0606332	+	0.186610i	0.916152	+	0.400831i	$0.131279\pi$
$368$	−1501.04	−	1090.57i	−0.212628	−	0.154483i
$369$	10509.9	+	7635.91i	1.48272	+	1.07726i
$370$	−350.763	+	1079.54i	−0.0492846	+	0.151682i
$371$	−2131.43	−	6559.85i	−0.298270	−	0.917980i
$372$	−6680.69	+	4853.80i	−0.931123	+	0.676500i
$373$	5503.51			0.763971			0.381985	−	0.924168i	$-0.375240\pi$
$373$	5503.51			0.763971			0.381985	+	0.924168i	$0.375240\pi$
$374$	−5031.62	+	6357.34i	−0.695666	+	0.878958i
$375$	1114.72			0.153504
$376$	−2949.47	+	2142.92i	−0.404541	+	0.293916i
$377$	1022.61	+	3147.27i	0.139701	+	0.429955i
$378$	−1852.54	+	5701.54i	−0.252076	+	0.775809i
$379$	−5229.64	−	3799.55i	−0.708782	−	0.514960i	0.173998	−	0.984746i	$-0.444331\pi$
$379$	−5229.64	−	3799.55i	−0.708782	−	0.514960i	−0.882781	+	0.469786i	$0.844331\pi$
$380$	−236.489	−	171.819i	−0.0319253	−	0.0231951i
$381$	4518.04	−	13905.1i	0.607523	−	1.86976i
$382$	−2400.25	−	7387.20i	−0.321485	−	0.989429i
$383$	10074.2	−	7319.36i	1.34405	−	0.976506i	0.344760	−	0.938691i	$-0.387960\pi$
$383$	10074.2	−	7319.36i	1.34405	−	0.976506i	0.999285	−	0.0378152i	$-0.0120398\pi$
$384$	1141.48			0.151695
$385$	−98.9258	+	2399.89i	−0.0130954	+	0.317687i
$386$	−4819.51			−0.635510
$387$	−21920.5	+	15926.2i	−2.87928	+	2.09192i
$388$	−1740.75	−	5357.49i	−0.227766	−	0.700993i
$389$	608.074	−	1871.46i	0.0792560	−	0.243925i	−0.903576	−	0.428428i	$-0.859068\pi$
$389$	608.074	−	1871.46i	0.0792560	−	0.243925i	0.982832	+	0.184503i	$0.0590676\pi$
$390$	2691.64	+	1955.59i	0.349479	+	0.253911i
$391$	−10424.3	−	7573.66i	−1.34828	−	0.979582i
$392$	−419.322	+	1290.54i	−0.0540280	+	0.166281i
$393$	−6203.06	−	19091.0i	−0.796190	−	2.45042i
$394$	−2593.71	+	1884.44i	−0.331648	+	0.240956i
$395$	264.983			0.0337538
$396$	−7186.42	−	2666.96i	−0.911948	−	0.338434i
$397$	−5489.87			−0.694027			−0.347013	−	0.937860i	$-0.612804\pi$
$397$	−5489.87			−0.694027			−0.347013	+	0.937860i	$0.612804\pi$
$398$	3281.58	−	2384.21i	0.413294	−	0.300276i
$399$	−530.351	−	1632.25i	−0.0665432	−	0.204799i
$400$	123.607	−	380.423i	0.0154508	−	0.0475528i
$401$	1628.97	+	1183.51i	0.202859	+	0.147386i	0.684577	−	0.728940i	$-0.259987\pi$
$401$	1628.97	+	1183.51i	0.202859	+	0.147386i	−0.481718	+	0.876327i	$0.659987\pi$
$402$	−3616.14	−	2627.28i	−0.448649	−	0.325962i
$403$	−2668.90	+	8214.02i	−0.329894	+	1.01531i
$404$	−1385.97	−	4265.58i	−0.170680	−	0.525298i
$405$	−2474.99	+	1798.18i	−0.303662	+	0.220624i
$406$	2335.91			0.285540
$407$	−2294.05	−	3447.66i	−0.279391	−	0.419888i
$408$	7927.20			0.961899
$409$	−4665.17	+	3389.45i	−0.564005	+	0.409773i	−0.832922	−	0.553390i	$-0.813334\pi$
$409$	−4665.17	+	3389.45i	−0.564005	+	0.409773i	0.268918	+	0.963163i	$0.413334\pi$
$410$	−764.263	−	2352.16i	−0.0920591	−	0.283329i
$411$	−6769.32	+	20833.8i	−0.812423	+	2.50038i
$412$	−434.670	−	315.806i	−0.0519773	−	0.0377637i
$413$	−7094.68	−	5154.58i	−0.845293	−	0.614142i
$414$	3764.51	−	11586.0i	0.446898	−	1.37541i
$415$	−186.469	−	573.892i	−0.0220564	−	0.0678825i
$416$	965.852	−	701.732i	0.113834	−	0.0827049i
$417$	6826.50			0.801668
$418$	1026.97	−	287.500i	0.120169	−	0.0336413i
$419$	6853.60			0.799094			0.399547	−	0.916713i	$-0.369167\pi$
$419$	6853.60			0.799094			0.399547	+	0.916713i	$0.369167\pi$
$420$	1899.96	−	1380.40i	0.220735	−	0.160373i
$421$	2230.65	+	6865.24i	0.258231	+	0.794753i	0.993176	+	0.116626i	$0.0372080\pi$
$421$	2230.65	+	6865.24i	0.258231	+	0.794753i	−0.734945	+	0.678127i	$0.762792\pi$
$422$	−1484.11	+	4567.61i	−0.171197	+	0.526890i
$423$	−19365.8	−	14070.1i	−2.22600	−	1.61729i
$424$	−3390.28	−	2463.18i	−0.388317	−	0.282129i
$425$	858.411	−	2641.92i	0.0979742	−	0.301534i
$426$	3271.82	+	10069.6i	0.372113	+	1.14524i
$427$	−7036.52	+	5112.33i	−0.797474	+	0.579398i
$428$	−2839.46			−0.320679
$429$	−11688.7	+	3272.23i	−1.31546	+	0.368263i
$430$	5158.36			0.578507
$431$	−10069.3	+	7315.77i	−1.12534	+	0.817606i	−0.985010	−	0.172499i	$-0.944816\pi$
$431$	−10069.3	+	7315.77i	−1.12534	+	0.817606i	−0.140329	+	0.990105i	$0.544816\pi$
$432$	1125.53	+	3464.03i	0.125352	+	0.385795i
$433$	−4337.62	+	13349.8i	−0.481415	+	1.48164i	0.355692	+	0.934603i	$0.384245\pi$
$433$	−4337.62	+	13349.8i	−0.481415	+	1.48164i	−0.837107	+	0.547040i	$0.815755\pi$
$434$	4932.13	+	3583.40i	0.545507	+	0.396334i
$435$	3199.71	+	2324.72i	0.352676	+	0.256234i
$436$	1840.60	−	5664.80i	0.202176	−	0.622235i
$437$	523.745	+	1611.92i	0.0573321	+	0.176450i
$438$	5329.75	−	3872.29i	0.581427	−	0.422432i
$439$	8289.51			0.901223			0.450611	−	0.892720i	$-0.351206\pi$
$439$	8289.51			0.901223			0.450611	+	0.892720i	$0.351206\pi$
$440$	808.411	+	1214.94i	0.0875898	+	0.131636i
$441$	−8909.58			−0.962054
$442$	6707.54	−	4873.31i	0.721821	−	0.524434i
$443$	−3386.55	−	10422.7i	−0.363205	−	1.11783i	−0.951097	−	0.308891i	$-0.900042\pi$
$443$	−3386.55	−	10422.7i	−0.363205	−	1.11783i	0.587892	−	0.808939i	$-0.299958\pi$
$444$	−1251.21	+	3850.83i	−0.133738	+	0.411605i
$445$	1248.81	+	907.313i	0.133032	+	0.0966534i
$446$	−8664.26	−	6294.96i	−0.919876	−	0.668329i
$447$	3767.68	−	11595.7i	0.398670	−	1.22698i
$448$	−260.413	−	801.469i	−0.0274629	−	0.0845220i
$449$	4902.38	−	3561.79i	0.515273	−	0.374368i	−0.299547	−	0.954082i	$-0.596836\pi$
$449$	4902.38	−	3561.79i	0.515273	−	0.374368i	0.814820	+	0.579714i	$0.196836\pi$
$450$	2626.35			0.275127
$451$	8459.23	+	3139.32i	0.883215	+	0.327771i
$452$	2924.72			0.304352
$453$	−7707.56	+	5599.87i	−0.799410	+	0.580805i
$454$	−1207.37	−	3715.89i	−0.124812	−	0.384131i
$455$	759.024	−	2336.04i	0.0782057	−	0.240692i
$456$	−843.583	−	612.899i	−0.0866325	−	0.0629422i
$457$	−7888.56	−	5731.37i	−0.807464	−	0.586657i	0.105630	−	0.994405i	$-0.466314\pi$
$457$	−7888.56	−	5731.37i	−0.807464	−	0.586657i	−0.913094	+	0.407749i	$0.866314\pi$
$458$	2493.90	−	7675.44i	0.254437	−	0.783078i
$459$	7816.47	+	24056.6i	0.794862	+	2.44633i
$460$	−1876.30	+	1363.21i	−0.190180	+	0.138174i
$461$	−13314.3			−1.34514			−0.672570	−	0.740034i	$-0.734810\pi$
$461$	−13314.3			−1.34514			−0.672570	+	0.740034i	$0.734810\pi$
$462$	−352.880	+	8560.67i	−0.0355356	+	0.862075i
$463$	−5092.01			−0.511114			−0.255557	−	0.966794i	$-0.582259\pi$
$463$	−5092.01			−0.511114			−0.255557	+	0.966794i	$0.582259\pi$
$464$	1148.16	−	834.188i	0.114875	−	0.0834617i
$465$	3189.75	+	9817.03i	0.318109	+	0.979040i
$466$	2150.62	−	6618.92i	0.213789	−	0.657974i
$467$	7638.91	+	5549.99i	0.756930	+	0.549942i	0.897967	−	0.440062i	$-0.145044\pi$
$467$	7638.91	+	5549.99i	0.756930	+	0.549942i	−0.141037	+	0.990004i	$0.545044\pi$
$468$	6341.65	+	4607.48i	0.626374	+	0.455087i
$469$	−1019.73	+	3138.39i	−0.100398	+	0.308993i
$470$	1408.25	+	4334.14i	0.138208	+	0.425360i
$471$	8331.77	−	6053.39i	0.815091	−	0.592198i
$472$	−5328.00			−0.519579
$473$	−11679.3	+	14756.5i	−1.13534	+	1.43447i
$474$	945.226			0.0915942
$475$	−295.611	+	214.774i	−0.0285549	+	0.0207463i
$476$	−1808.49	−	5565.95i	−0.174143	−	0.535956i
$477$	8502.60	−	26168.3i	0.816158	−	2.51188i
$478$	−5775.12	−	4195.87i	−0.552610	−	0.401495i
$479$	6527.94	+	4742.83i	0.622691	+	0.452412i	0.853861	−	0.520502i	$-0.174255\pi$
$479$	6527.94	+	4742.83i	0.622691	+	0.452412i	−0.231169	+	0.972914i	$0.574255\pi$
$480$	440.920	−	1357.01i	0.0419274	−	0.129039i
$481$	1308.63	+	4027.54i	0.124051	+	0.381788i
$482$	5323.73	−	3867.91i	0.503090	−	0.365516i
$483$	−13616.7			−1.28278
$484$	−5305.94	−	438.177i	−0.498304	−	0.0411511i
$485$	−7041.49			−0.659253
$486$	1116.48	−	811.171i	0.104207	−	0.0757108i
$487$	−322.392	−	992.222i	−0.0299979	−	0.0923241i	0.934937	−	0.354815i	$-0.115456\pi$
$487$	−322.392	−	992.222i	−0.0299979	−	0.0923241i	−0.964935	+	0.262491i	$0.915456\pi$
$488$	−1632.95	+	5025.70i	−0.151476	+	0.466194i
$489$	23017.7	+	16723.4i	2.12863	+	1.54654i
$490$	1372.25	+	996.997i	0.126514	+	0.0919178i
$491$	330.465	−	1017.07i	0.0303741	−	0.0934818i	−0.934720	−	0.355384i	$-0.884350\pi$
$491$	330.465	−	1017.07i	0.0303741	−	0.0934818i	0.965094	+	0.261903i	$0.0843499\pi$
$492$	−2726.21	−	8390.42i	−0.249811	−	0.768840i
$493$	7973.62	−	5793.18i	0.728426	−	0.529232i
$494$	−1090.58			−0.0993266
$495$	−5946.45	+	7513.19i	−0.539945	+	0.682208i
$496$	3703.96			0.335308
$497$	6323.79	−	4594.50i	0.570746	−	0.414671i
$498$	−665.155	−	2047.14i	−0.0598520	−	0.184206i
$499$	719.282	−	2213.72i	0.0645280	−	0.198597i	−0.913594	−	0.406627i	$-0.866705\pi$
$499$	719.282	−	2213.72i	0.0645280	−	0.198597i	0.978123	+	0.208030i	$0.0667050\pi$
$500$	−404.508	−	293.893i	−0.0361803	−	0.0262866i
$501$	30463.9	+	22133.3i	2.71662	+	1.97374i
$502$	−4332.12	+	13332.9i	−0.385163	+	1.18541i
$503$	−395.305	−	1216.62i	−0.0350413	−	0.107846i	0.932006	−	0.362443i	$-0.118057\pi$
$503$	−395.305	−	1216.62i	−0.0350413	−	0.107846i	−0.967047	+	0.254597i	$0.918057\pi$
$504$	4476.41	−	3252.30i	0.395625	−	0.287439i
$505$	−5606.36			−0.494020
$506$	348.485	−	8454.05i	0.0306167	−	0.742744i
$507$	−7179.78			−0.628925
$508$	−5305.52	+	3854.69i	−0.463375	+	0.336662i
$509$	−554.075	−	1705.27i	−0.0482494	−	0.148496i	0.924029	−	0.382322i	$-0.124875\pi$
$509$	−554.075	−	1705.27i	−0.0482494	−	0.148496i	−0.972279	+	0.233826i	$0.924875\pi$
$510$	3062.05	−	9424.02i	0.265862	−	0.818240i
$511$	−3934.77	−	2858.78i	−0.340634	−	0.247485i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	1028.16	−	3164.35i	0.0884881	−	0.272339i
$514$	5053.19	+	15552.1i	0.433631	+	1.33458i
$515$	−543.337	+	394.758i	−0.0464899	+	0.0337769i
$516$	18400.4			1.56983
$517$	−15587.2	−	5784.57i	−1.32596	−	0.492080i
$518$	2989.25			0.253552
$519$	14415.3	−	10473.4i	1.21920	−	0.885799i
$520$	−461.153	−	1419.28i	−0.0388902	−	0.119692i
$521$	5905.86	−	18176.4i	0.496623	−	1.52845i	−0.317790	−	0.948161i	$-0.602941\pi$
$521$	5905.86	−	18176.4i	0.496623	−	1.52845i	0.814413	−	0.580286i	$-0.197059\pi$
$522$	7538.68	+	5477.17i	0.632105	+	0.459251i
$523$	3148.37	+	2287.42i	0.263229	+	0.191247i	0.711569	−	0.702616i	$-0.247985\pi$
$523$	3148.37	+	2287.42i	0.263229	+	0.191247i	−0.448341	+	0.893863i	$0.647985\pi$
$524$	−2782.33	+	8563.13i	−0.231959	+	0.713897i
$525$	−907.152	−	2791.93i	−0.0754121	−	0.232095i
$526$	−6052.11	+	4397.12i	−0.501682	+	0.364493i
$527$	25722.9			2.12620
$528$	2883.70	+	4333.82i	0.237683	+	0.357207i
$529$	1280.11			0.105212
$530$	−4237.85	+	3078.97i	−0.347321	+	0.252344i
$531$	−10810.3	−	33270.8i	−0.883481	−	2.71907i
$532$	−237.884	+	732.133i	−0.0193865	+	0.0596654i
$533$	−7464.85	−	5423.53i	−0.606639	−	0.440749i
$534$	4454.65	+	3236.49i	0.360995	+	0.262278i
$535$	−1096.80	+	3375.61i	−0.0886335	+	0.272786i
$536$	619.545	+	1906.76i	0.0499259	+	0.153656i
$537$	21559.3	−	15663.7i	1.73250	−	1.25873i
$538$	−1273.46			−0.102049
$539$	−5959.09	+	1668.24i	−0.476208	+	0.133314i
$540$	4552.87			0.362823
$541$	−699.242	+	508.029i	−0.0555689	+	0.0403731i	−0.615223	−	0.788353i	$-0.710934\pi$
$541$	−699.242	+	508.029i	−0.0555689	+	0.0403731i	0.559654	+	0.828726i	$0.310934\pi$
$542$	1690.75	+	5203.59i	0.133992	+	0.412386i
$543$	1473.68	−	4535.51i	0.116467	−	0.358448i
$544$	−2876.61	−	2089.98i	−0.226716	−	0.164719i
$545$	−6023.45	−	4376.29i	−0.473425	−	0.343963i
$546$	2707.53	−	8332.91i	0.212219	−	0.653142i
$547$	2413.70	+	7428.61i	0.188670	+	0.580667i	0.999992	−	0.00393263i	$-0.00125180\pi$
$547$	2413.70	+	7428.61i	0.188670	+	0.580667i	−0.811322	+	0.584599i	$0.801252\pi$
$548$	7949.19	−	5775.43i	0.619658	−	0.450208i
$549$	−34696.2			−2.69726
$550$	1756.61	−	491.761i	0.136185	−	0.0381250i
$551$	−1296.43			−0.100235
$552$	−6692.98	+	4862.73i	−0.516072	+	0.374949i
$553$	−215.641	−	663.675i	−0.0165823	−	0.0510349i
$554$	2790.08	−	8586.98i	0.213970	−	0.658530i
$555$	4094.64	+	2974.93i	0.313167	+	0.227529i
$556$	−2477.19	−	1799.78i	−0.188950	−	0.137280i
$557$	399.566	−	1229.74i	0.0303952	−	0.0935469i	−0.934708	−	0.355416i	$-0.884339\pi$
$557$	399.566	−	1229.74i	0.0303952	−	0.0935469i	0.965103	+	0.261870i	$0.0843390\pi$
$558$	7515.21	+	23129.4i	0.570151	+	1.75474i
$559$	15569.4	−	11311.8i	1.17802	−	0.855884i
$560$	−1053.39			−0.0794892
$561$	20026.4	+	30097.0i	1.50716	+	2.26506i
$562$	−1269.25			−0.0952674
$563$	−6478.23	+	4706.71i	−0.484947	+	0.352334i	−0.803238	−	0.595659i	$-0.796891\pi$
$563$	−6478.23	+	4706.71i	−0.484947	+	0.352334i	0.318291	+	0.947993i	$0.396891\pi$
$564$	5023.38	+	15460.4i	0.375040	+	1.15425i
$565$	1129.73	−	3476.96i	0.0841208	−	0.258897i
$566$	−2747.21	−	1995.96i	−0.204017	−	0.148227i
$567$	6517.84	+	4735.49i	0.482758	+	0.350744i
$568$	1467.55	−	4516.64i	0.108410	−	0.333652i
$569$	−1663.74	−	5120.46i	−0.122579	−	0.377260i	0.870873	−	0.491508i	$-0.163554\pi$
$569$	−1663.74	−	5120.46i	−0.122579	−	0.377260i	−0.993452	+	0.114248i	$0.963554\pi$
$570$	−1054.48	+	766.124i	−0.0774864	+	0.0562972i
$571$	3495.65			0.256197			0.128098	−	0.991761i	$-0.459113\pi$
$571$	3495.65			0.256197			0.128098	+	0.991761i	$0.459113\pi$
$572$	5104.27	+	1894.25i	0.373112	+	0.138466i
$573$	−34633.8			−2.52504
$574$	−5269.24	+	3828.33i	−0.383160	+	0.278382i
$575$	895.853	+	2757.15i	0.0649733	+	0.199967i
$576$	1038.83	−	3197.19i	0.0751468	−	0.231278i
$577$	13265.8	+	9638.13i	0.957124	+	0.695391i	0.952481	−	0.304598i	$-0.0985221\pi$
$577$	13265.8	+	9638.13i	0.957124	+	0.695391i	0.00464297	+	0.999989i	$0.498522\pi$
$578$	−12027.7	−	8738.66i	−0.865550	−	0.628859i
$579$	−6640.68	+	20437.9i	−0.476645	+	1.46696i
$580$	−548.198	−	1687.18i	−0.0392460	−	0.120787i
$581$	−1285.62	+	934.055i	−0.0918010	+	0.0666973i
$582$	−25117.8			−1.78895
$583$	787.094	−	19094.5i	0.0559144	−	1.35645i
$584$	−2954.96			−0.209379
$585$	7927.07	−	5759.35i	0.560246	−	0.407042i
$586$	−2524.91	−	7770.88i	−0.177992	−	0.547803i
$587$	−3188.39	+	9812.85i	−0.224189	+	0.689983i	0.774184	+	0.632961i	$0.218160\pi$
$587$	−3188.39	+	9812.85i	−0.224189	+	0.689983i	−0.998373	+	0.0570219i	$0.981840\pi$
$588$	4894.97	+	3556.40i	0.343308	+	0.249428i
$589$	−2737.33	−	1988.79i	−0.191494	−	0.139128i
$590$	−2058.05	+	6334.04i	−0.143608	+	0.441980i
$591$	4417.47	+	13595.6i	0.307462	+	0.946272i
$592$	1469.29	−	1067.50i	0.102006	−	0.0741118i
$593$	23386.5			1.61951			0.809753	−	0.586771i	$-0.199601\pi$
$593$	23386.5			1.61951			0.809753	+	0.586771i	$0.199601\pi$
$594$	−10308.4	+	13024.4i	−0.712052	+	0.899660i
$595$	−7315.49			−0.504043
$596$	−4424.38	+	3214.50i	−0.304077	+	0.220925i
$597$	−5589.02	−	17201.2i	−0.383155	−	1.17923i
$598$	−2673.80	+	8229.12i	−0.182843	+	0.562732i
$599$	5680.23	+	4126.93i	0.387459	+	0.281505i	0.764413	−	0.644727i	$-0.223029\pi$
$599$	5680.23	+	4126.93i	0.387459	+	0.281505i	−0.376955	+	0.926232i	$0.623029\pi$
$600$	−1442.93	−	1048.35i	−0.0981788	−	0.0713311i
$601$	−1552.71	+	4778.76i	−0.105385	+	0.324342i	−0.989821	−	0.142320i	$-0.954544\pi$
$601$	−1552.71	+	4778.76i	−0.105385	+	0.324342i	0.884436	+	0.466662i	$0.154544\pi$
$602$	−4197.82	−	12919.6i	−0.284203	−	0.874688i
$603$	−10649.8	+	7737.51i	−0.719225	+	0.522547i
$604$	4273.29			0.287877
$605$	−2570.44	+	6138.55i	−0.172733	+	0.412509i
$606$	−19998.5			−1.34057
$607$	−9551.25	+	6939.39i	−0.638671	+	0.464022i	−0.859393	−	0.511315i	$-0.829159\pi$
$607$	−9551.25	+	6939.39i	−0.638671	+	0.464022i	0.220722	+	0.975337i	$0.429159\pi$
$608$	144.529	+	444.815i	0.00964051	+	0.0296704i
$609$	3218.59	−	9905.79i	0.214160	−	0.659118i
$610$	5343.89	+	3882.57i	0.354701	+	0.257706i
$611$	13754.9	+	9993.51i	0.910742	+	0.661693i
$612$	7214.35	−	22203.5i	0.476508	−	1.46654i
$613$	4412.76	+	13581.1i	0.290750	+	0.894837i	0.984616	+	0.174732i	$0.0559060\pi$
$613$	4412.76	+	13581.1i	0.290750	+	0.894837i	−0.693866	+	0.720104i	$0.744094\pi$
$614$	10908.4	−	7925.43i	0.716983	−	0.520919i
$615$	−11027.8			−0.723061
$616$	2385.04	−	3013.44i	0.156000	−	0.197102i
$617$	−14756.0			−0.962813			−0.481407	−	0.876497i	$-0.659874\pi$
$617$	−14756.0			−0.962813			−0.481407	+	0.876497i	$0.659874\pi$
$618$	−1938.15	+	1408.15i	−0.126155	+	0.0916568i
$619$	−2810.63	−	8650.22i	−0.182502	−	0.561683i	0.817395	−	0.576078i	$-0.195418\pi$
$619$	−2810.63	−	8650.22i	−0.182502	−	0.561683i	−0.999896	+	0.0143954i	$0.995418\pi$
$620$	1430.73	−	4403.35i	0.0926769	−	0.285230i
$621$	−21356.4	−	15516.3i	−1.38004	−	1.00265i
$622$	−12859.4	−	9342.88i	−0.828961	−	0.602275i
$623$	1256.18	−	3866.12i	0.0807828	−	0.248624i
$624$	−1644.99	−	5062.75i	−0.105532	−	0.324795i
$625$	−505.636	+	367.366i	−0.0323607	+	0.0235114i
$626$	7010.59			0.447603
$627$	195.848	−	4751.17i	0.0124744	−	0.302621i
$628$	−4619.37			−0.293524
$629$	10203.8	−	7413.49i	0.646823	−	0.469945i
$630$	−2137.30	−	6577.92i	−0.135162	−	0.415985i
$631$	−4400.95	+	13544.7i	−0.277653	+	0.854528i	0.710852	+	0.703341i	$0.248309\pi$
$631$	−4400.95	+	13544.7i	−0.277653	+	0.854528i	−0.988505	+	0.151186i	$0.951691\pi$
$632$	−343.002	−	249.205i	−0.0215884	−	0.0156849i
$633$	17324.8	+	12587.2i	1.08783	+	0.790356i
$634$	1138.35	−	3503.47i	0.0713084	−	0.219465i
$635$	2533.16	+	7796.27i	0.158308	+	0.487222i
$636$	−15116.9	+	10983.1i	−0.942489	+	0.684759i
$637$	6328.17			0.393613
$638$	6067.73	+	2251.80i	0.376526	+	0.139733i
$639$	31181.8			1.93041
$640$	−517.771	+	376.183i	−0.0319792	+	0.0232343i
$641$	3339.99	+	10279.4i	0.205806	+	0.633407i	0.999679	+	0.0253231i	$0.00806145\pi$
$641$	3339.99	+	10279.4i	0.205806	+	0.633407i	−0.793873	+	0.608084i	$0.791939\pi$
$642$	−3912.42	+	12041.2i	−0.240515	+	0.740230i
$643$	6763.22	+	4913.77i	0.414799	+	0.301369i	0.775542	−	0.631296i	$-0.217477\pi$
$643$	6763.22	+	4913.77i	0.414799	+	0.301369i	−0.360743	+	0.932665i	$0.617477\pi$
$644$	4941.20	+	3589.99i	0.302346	+	0.219667i
$645$	7107.56	−	21874.8i	0.433892	−	1.33538i
$646$	1003.71	+	3089.10i	0.0611307	+	0.188141i
$647$	15018.0	−	10911.2i	0.912546	−	0.663003i	−0.0291115	−	0.999576i	$-0.509268\pi$
$647$	15018.0	−	10911.2i	0.912546	−	0.663003i	0.941657	+	0.336573i	$0.109268\pi$
$648$	4894.81			0.296738
$649$	−13460.1	−	20228.7i	−0.814104	−	1.22349i
$650$	−1865.40			−0.112565
$651$	21991.8	−	15978.0i	1.32401	−	0.961947i
$652$	−3943.58	−	12137.1i	−0.236875	−	0.729026i
$653$	−4958.44	+	15260.5i	−0.297150	+	0.914532i	0.685341	+	0.728222i	$0.259653\pi$
$653$	−4958.44	+	15260.5i	−0.297150	+	0.914532i	−0.982491	+	0.186310i	$0.940347\pi$
$654$	−21486.3	−	15610.7i	−1.28468	−	0.933377i
$655$	9105.29	+	6615.38i	0.543165	+	0.394633i
$656$	−1222.82	+	3763.45i	−0.0727791	+	0.223991i
$657$	−5995.51	−	18452.3i	−0.356023	−	1.09573i
$658$	9709.23	−	7054.17i	0.575236	−	0.417933i
$659$	16099.2			0.951645			0.475822	−	0.879541i	$-0.342151\pi$
$659$	16099.2			0.951645			0.475822	+	0.879541i	$0.342151\pi$
$660$	6266.02	−	1754.17i	0.369552	−	0.103456i
$661$	−17086.4			−1.00542			−0.502711	−	0.864454i	$-0.667664\pi$
$661$	−17086.4			−1.00542			−0.502711	+	0.864454i	$0.667664\pi$
$662$	−4547.79	+	3304.17i	−0.267002	+	0.193988i
$663$	−11423.9	−	35159.2i	−0.669183	−	2.05953i
$664$	−298.350	+	918.226i	−0.0174371	+	0.0536658i
$665$	778.487	+	565.604i	0.0453961	+	0.0329822i
$666$	9647.19	+	7009.09i	0.561293	+	0.407803i
$667$	−3178.50	+	9782.42i	−0.184516	+	0.567881i
$668$	−5219.30	−	16063.4i	−0.302307	−	0.930404i
$669$	−38633.0	+	28068.5i	−2.23264	+	1.62211i
$670$	2506.11			0.144507
$671$	−23206.2	+	6496.57i	−1.33512	+	0.373766i
$672$	−3757.57			−0.215702
$673$	13407.5	−	9741.12i	0.767936	−	0.557938i	−0.133398	−	0.991063i	$-0.542589\pi$
$673$	13407.5	−	9741.12i	0.767936	−	0.557938i	0.901334	+	0.433124i	$0.142589\pi$
$674$	3275.09	+	10079.7i	0.187169	+	0.576046i
$675$	1758.64	−	5412.55i	0.100282	−	0.308636i
$676$	2605.38	+	1892.92i	0.148235	+	0.107699i
$677$	18150.1	+	13186.8i	1.03038	+	0.748612i	0.968384	−	0.249464i	$-0.0802545\pi$
$677$	18150.1	+	13186.8i	1.03038	+	0.748612i	0.0619925	+	0.998077i	$0.480255\pi$
$678$	4029.89	−	12402.7i	0.228270	−	0.702543i
$679$	5730.30	+	17636.1i	0.323872	+	0.996774i
$680$	−3595.76	+	2612.47i	−0.202781	+	0.147329i
$681$	−17421.4			−0.980309
$682$	9357.26	+	14062.7i	0.525379	+	0.789575i
$683$	4461.39			0.249942			0.124971	−	0.992160i	$-0.460116\pi$
$683$	4461.39			0.249942			0.124971	+	0.992160i	$0.460116\pi$
$684$	−2484.41	+	1805.03i	−0.138880	+	0.100902i
$685$	−3795.40	−	11681.0i	−0.211701	−	0.651547i
$686$	4171.65	−	12839.0i	0.232178	−	0.714571i
$687$	−29112.6	−	21151.6i	−1.61676	−	1.17465i
$688$	−6677.12	−	4851.21i	−0.370004	−	0.268824i
$689$	−6039.11	+	18586.5i	−0.333921	+	1.02770i
$690$	3195.61	+	9835.08i	0.176311	+	0.542631i
$691$	27297.1	−	19832.5i	1.50280	−	1.09184i	0.533544	−	0.845772i	$-0.320860\pi$
$691$	27297.1	−	19832.5i	1.50280	−	1.09184i	0.969251	−	0.246073i	$-0.0791402\pi$
$692$	−7992.27			−0.439047
$693$	23656.6	+	8779.24i	1.29674	+	0.481235i
$694$	−1752.36			−0.0958484
$695$	−3096.48	+	2249.73i	−0.169002	+	0.122787i
$696$	−1955.49	−	6018.37i	−0.106498	−	0.327767i
$697$	−8492.11	+	26136.0i	−0.461494	+	1.42033i
$698$	18002.1	+	13079.3i	0.976202	+	0.709252i
$699$	−25105.3	−	18240.1i	−1.35847	−	0.986986i
$700$	−406.895	+	1252.30i	−0.0219703	+	0.0676176i
$701$	−2045.60	−	6295.69i	−0.110216	−	0.339208i	0.880704	−	0.473668i	$-0.157070\pi$
$701$	−2045.60	−	6295.69i	−0.110216	−	0.339208i	−0.990919	+	0.134459i	$0.957070\pi$
$702$	13741.9	−	9984.06i	0.738823	−	0.536786i
$703$	−1659.03			−0.0890064
$704$	96.1654	−	2332.92i	0.00514825	−	0.124894i
$705$	20320.0			1.08553
$706$	−11181.8	+	8124.03i	−0.596078	+	0.433076i
$707$	4562.41	+	14041.6i	0.242697	+	0.746945i
$708$	−7341.32	+	22594.2i	−0.389694	+	1.19936i
$709$	11330.0	+	8231.74i	0.600152	+	0.436036i	0.845933	−	0.533289i	$-0.179044\pi$
$709$	11330.0	+	8231.74i	0.600152	+	0.436036i	−0.245781	+	0.969325i	$0.579044\pi$
$710$	−4802.61	−	3489.30i	−0.253857	−	0.184438i
$711$	860.227	−	2647.51i	0.0453742	−	0.139647i
$712$	−763.204	−	2348.90i	−0.0401718	−	0.123636i
$713$	−21717.9	+	15779.0i	−1.14073	+	0.828792i
$714$	−26095.2			−1.36777
$715$	4223.56	−	5336.36i	0.220912	−	0.279117i
$716$	−11953.1			−0.623893
$717$	−25750.6	+	18708.9i	−1.34125	+	0.974474i
$718$	−641.426	−	1974.11i	−0.0333396	−	0.102609i
$719$	3763.15	−	11581.8i	0.195190	−	0.600734i	−0.804784	−	0.593568i	$-0.797719\pi$
$719$	3763.15	−	11581.8i	0.195190	−	0.600734i	0.999974	−	0.00716651i	$-0.00228119\pi$
$720$	−3399.61	−	2469.96i	−0.175967	−	0.127847i
$721$	1430.87	+	1039.59i	0.0739089	+	0.0536980i
$722$	−4107.07	+	12640.3i	−0.211703	+	0.651554i
$723$	−9067.08	−	27905.6i	−0.466402	−	1.43544i
$724$	−1730.54	+	1257.31i	−0.0888327	+	0.0645407i
$725$	−2217.51			−0.113595
$726$	−9169.07	+	21896.9i	−0.468728	+	1.11938i
$727$	2934.33			0.149695			0.0748475	−	0.997195i	$-0.476153\pi$
$727$	2934.33			0.149695			0.0748475	+	0.997195i	$0.476153\pi$
$728$	−3179.44	+	2310.00i	−0.161865	+	0.117602i
$729$	−7006.48	−	21563.7i	−0.355966	−	1.09555i
$730$	−1141.42	+	3512.92i	−0.0578709	+	0.178108i
$731$	−46370.5	−	33690.1i	−2.34620	−	1.70462i
$732$	19062.3	+	13849.6i	0.962517	+	0.699309i
$733$	3366.47	−	10360.9i	0.169636	−	0.522087i	−0.829712	−	0.558192i	$-0.811495\pi$
$733$	3366.47	−	10360.9i	0.169636	−	0.522087i	0.999348	+	0.0361053i	$0.0114952\pi$
$734$	−852.588	−	2624.00i	−0.0428741	−	0.131953i
$735$	6118.71	−	4445.50i	0.307064	−	0.223095i
$736$	3710.77			0.185844
$737$	−5674.22	+	7169.25i	−0.283599	+	0.358321i
$738$	−25982.0			−1.29595
$739$	1132.52	−	822.823i	0.0563740	−	0.0409581i	−0.559241	−	0.829005i	$-0.688908\pi$
$739$	1132.52	−	822.823i	0.0563740	−	0.0409581i	0.615615	+	0.788047i	$0.288908\pi$
$740$	−701.526	−	2159.07i	−0.0348495	−	0.107256i
$741$	−1502.68	+	4624.76i	−0.0744969	+	0.229278i
$742$	11160.3	+	8108.42i	0.552166	+	0.401172i
$743$	29439.4	+	21389.0i	1.45360	+	1.05610i	0.984973	+	0.172709i	$0.0552519\pi$
$743$	29439.4	+	21389.0i	1.45360	+	1.05610i	0.468629	+	0.883395i	$0.344748\pi$
$744$	5103.59	−	15707.2i	0.251488	−	0.773999i
$745$	2112.45	+	6501.47i	0.103885	+	0.319725i
$746$	−8904.87	+	6469.77i	−0.437038	+	0.317527i
$747$	−6339.22			−0.310495
$748$	667.839	−	16201.4i	0.0326452	−	0.791955i
$749$	9347.09			0.455988
$750$	−1803.66	+	1310.44i	−0.0878138	+	0.0638005i
$751$	2954.88	+	9094.18i	0.143575	+	0.441879i	0.996825	−	0.0796233i	$-0.0253717\pi$
$751$	2954.88	+	9094.18i	0.143575	+	0.441879i	−0.853250	+	0.521502i	$0.825372\pi$
$752$	2253.20	−	6934.62i	0.109263	−	0.336276i
$753$	50571.1	+	36742.1i	2.44743	+	1.77816i
$754$	−5354.46	−	3890.24i	−0.258618	−	0.187897i
$755$	1650.65	−	5080.17i	0.0795672	−	0.244883i
$756$	−3705.09	−	11403.1i	−0.178244	−	0.548580i
$757$	−8509.39	+	6182.44i	−0.408559	+	0.296835i	−0.773018	−	0.634384i	$-0.781254\pi$
$757$	−8509.39	+	6182.44i	−0.408559	+	0.296835i	0.364459	+	0.931219i	$0.381254\pi$
$758$	12928.4			0.619498
$759$	−35370.6	−	13126.4i	−1.69153	−	0.627746i
$760$	584.633			0.0279038
$761$	−6609.22	+	4801.88i	−0.314828	+	0.228736i	−0.733965	−	0.679187i	$-0.762333\pi$
$761$	−6609.22	+	4801.88i	−0.314828	+	0.228736i	0.419137	+	0.907923i	$0.362333\pi$
$762$	9036.08	+	27810.2i	0.429584	+	1.32212i
$763$	−6059.00	+	18647.7i	−0.287484	+	0.884785i
$764$	12567.9	+	9131.08i	0.595143	+	0.432396i
$765$	−23609.3	−	17153.1i	−1.11581	−	0.810683i
$766$	−7696.03	+	23685.9i	−0.363014	+	1.11724i
$767$	7678.20	+	23631.1i	0.361465	+	1.11248i
$768$	−1846.95	+	1341.89i	−0.0867786	+	0.0630484i
$769$	−26522.3			−1.24372			−0.621858	−	0.783130i	$-0.713622\pi$
$769$	−26522.3			−1.24372			−0.621858	+	0.783130i	$0.713622\pi$
$770$	−2661.17	−	3999.39i	−0.124548	−	0.187179i
$771$	72913.8			3.40587
$772$	7798.13	−	5665.68i	0.363550	−	0.264135i
$773$	−587.486	−	1808.09i	−0.0273356	−	0.0841302i	0.936458	−	0.350780i	$-0.114083\pi$
$773$	−587.486	−	1808.09i	−0.0273356	−	0.0841302i	−0.963794	+	0.266649i	$0.914083\pi$
$774$	16745.8	−	51538.2i	0.777668	−	2.39342i
$775$	−4682.14	−	3401.77i	−0.217016	−	0.157671i
$776$	9114.70	+	6622.22i	0.421648	+	0.306345i
$777$	4118.80	−	12676.4i	0.190169	−	0.585280i
$778$	1216.15	+	3742.92i	0.0560425	+	0.172481i
$779$	2924.43	−	2124.72i	0.134504	−	0.0977228i
$780$	−6654.11			−0.305456
$781$	20855.7	−	5838.53i	0.955537	−	0.267502i
$782$	25770.2			1.17844
$783$	16335.7	−	11868.6i	0.745583	−	0.541698i
$784$	−838.644	−	2581.08i	−0.0382035	−	0.117578i
$785$	−1784.33	+	5491.60i	−0.0811280	+	0.249686i
$786$	32479.6	+	23597.8i	1.47393	+	1.07087i
$787$	−29966.0	−	21771.5i	−1.35727	−	0.986114i	−0.998613	−	0.0526445i	$-0.983235\pi$
$787$	−29966.0	−	21771.5i	−1.35727	−	0.986114i	−0.358656	−	0.933470i	$-0.616765\pi$
$788$	1981.42	−	6098.18i	0.0895750	−	0.275683i
$789$	10307.6	+	31723.6i	0.465097	+	1.43142i
$790$	−428.752	+	311.507i	−0.0193093	+	0.0140290i
$791$	−9627.74			−0.432772
$792$	14763.1	−	4132.91i	0.662352	−	0.185425i
$793$	24643.5			1.10355
$794$	8882.79	−	6453.73i	0.397026	−	0.288456i
$795$	7217.67	+	22213.7i	0.321993	+	0.990992i
$796$	−2506.91	+	7715.47i	−0.111627	+	0.343552i
$797$	−2291.10	−	1664.58i	−0.101825	−	0.0739804i	0.535708	−	0.844404i	$-0.320045\pi$
$797$	−2291.10	−	1664.58i	−0.101825	−	0.0739804i	−0.637533	+	0.770423i	$0.720045\pi$
$798$	2776.95	+	2017.57i	0.123187	+	0.0895004i
$799$	15647.7	−	48158.8i	0.692838	−	2.13234i
$800$	247.214	+	760.845i	0.0109254	+	0.0336249i
$801$	13119.2	−	9531.67i	0.578708	−	0.420456i
$802$	−4027.02			−0.177306
$803$	−7465.08	−	11219.0i	−0.328066	−	0.493040i
$804$	8939.60			0.392133
$805$	6176.50	−	4487.49i	0.270426	−	0.196476i
$806$	−5337.79	−	16428.0i	−0.233270	−	0.717932i
$807$	−1754.66	+	5400.29i	−0.0765391	+	0.235563i
$808$	7257.03	+	5272.54i	0.315967	+	0.229564i
$809$	−34633.9	−	25163.0i	−1.50515	−	1.09355i	−0.968274	−	0.249891i	$-0.919605\pi$
$809$	−34633.9	−	25163.0i	−1.50515	−	1.09355i	−0.536873	−	0.843663i	$-0.680395\pi$
$810$	1890.72	−	5819.05i	0.0820164	−	0.252420i
$811$	−3995.43	−	12296.7i	−0.172994	−	0.532422i	0.826542	−	0.562875i	$-0.190305\pi$
$811$	−3995.43	−	12296.7i	−0.172994	−	0.532422i	−0.999536	+	0.0304535i	$0.990305\pi$
$812$	−3779.58	+	2746.02i	−0.163346	+	0.118678i
$813$	24396.3			1.05242
$814$	7764.83	+	2881.61i	0.334345	+	0.124079i
$815$	−15952.1			−0.685617
$816$	−12826.5	+	9318.98i	−0.550265	+	0.399791i
$817$	2329.79	+	7170.36i	0.0997663	+	0.307049i
$818$	3563.88	−	10968.5i	0.152332	−	0.468831i
$819$	−20875.8	−	15167.1i	−0.890670	−	0.647110i
$820$	4001.73	+	2907.43i	0.170423	+	0.123819i
$821$	−13166.6	+	40522.7i	−0.559706	+	1.72260i	0.123474	+	0.992348i	$0.460596\pi$
$821$	−13166.6	+	40522.7i	−0.559706	+	1.72260i	−0.683180	+	0.730250i	$0.739404\pi$
$822$	−13538.6	−	41667.6i	−0.574470	−	1.76804i
$823$	−9967.00	+	7241.45i	−0.422148	+	0.306709i	−0.778502	−	0.627643i	$-0.784020\pi$
$823$	−9967.00	+	7241.45i	−0.422148	+	0.306709i	0.356353	+	0.934351i	$0.384020\pi$
$824$	1074.56			0.0454298
$825$	334.993	−	8126.76i	0.0141369	−	0.342955i
$826$	17539.0			0.738813
$827$	−4427.29	+	3216.61i	−0.186157	+	0.135251i	−0.676961	−	0.736019i	$-0.736703\pi$
$827$	−4427.29	+	3216.61i	−0.186157	+	0.135251i	0.490804	+	0.871270i	$0.336703\pi$
$828$	7529.03	+	23172.0i	0.316005	+	0.972562i
$829$	10644.6	−	32760.8i	0.445963	−	1.37253i	−0.435462	−	0.900207i	$-0.643415\pi$
$829$	10644.6	−	32760.8i	0.445963	−	1.37253i	0.881424	−	0.472325i	$-0.156585\pi$
$830$	976.363	+	709.369i	0.0408314	+	0.0296657i
$831$	−32570.1	−	23663.6i	−1.35962	−	0.987821i
$832$	−737.845	+	2270.85i	−0.0307454	+	0.0946246i
$833$	−5824.12	−	17924.8i	−0.242249	−	0.745567i
$834$	−11045.5	+	8025.04i	−0.458603	+	0.333195i
$835$	−21112.5			−0.875005
$836$	−1323.70	+	1672.46i	−0.0547620	+	0.0691905i
$837$	52699.0			2.17628
$838$	−11089.4	+	8056.89i	−0.457131	+	0.332125i
$839$	9078.19	+	27939.8i	0.373556	+	1.14969i	0.944447	+	0.328662i	$0.106598\pi$
$839$	9078.19	+	27939.8i	0.373556	+	1.14969i	−0.570891	+	0.821026i	$0.693402\pi$
$840$	−1451.44	+	4467.08i	−0.0596185	+	0.183487i
$841$	13366.0	+	9710.94i	0.548033	+	0.398169i
$842$	−11679.8	−	8485.90i	−0.478045	−	0.347320i
$843$	−1748.87	+	5382.48i	−0.0714524	+	0.219908i
$844$	−2968.21	−	9135.22i	−0.121055	−	0.372568i
$845$	3256.73	−	2366.15i	0.132586	−	0.0963291i
$846$	47875.0			1.94560
$847$	17466.4	+	1442.41i	0.708561	+	0.0585147i
$848$	8381.22			0.339401
$849$	−12249.5	+	8899.79i	−0.495173	+	0.359764i
$850$	1716.82	+	5283.83i	0.0692782	+	0.213216i
$851$	−4067.50	+	12518.5i	−0.163845	+	0.504264i
$852$	−17131.4	−	12446.7i	−0.688866	−	0.500490i
$853$	−7735.24	−	5619.98i	−0.310492	−	0.225585i	0.421616	−	0.906775i	$-0.361463\pi$
$853$	−7735.24	−	5619.98i	−0.310492	−	0.225585i	−0.732107	+	0.681189i	$0.761463\pi$
$854$	5375.43	−	16543.9i	0.215390	−	0.662903i
$855$	1186.20	+	3650.74i	0.0474470	+	0.146027i
$856$	4594.35	−	3337.99i	0.183448	−	0.133283i
$857$	43615.6			1.73848			0.869241	−	0.494389i	$-0.164608\pi$
$857$	43615.6			1.73848			0.869241	+	0.494389i	$0.164608\pi$
$858$	15065.9	−	19035.4i	0.599466	−	0.757411i
$859$	37037.9			1.47115			0.735574	−	0.677444i	$-0.236912\pi$
$859$	37037.9			1.47115			0.735574	+	0.677444i	$0.236912\pi$
$860$	−8346.40	+	6064.01i	−0.330942	+	0.240443i
$861$	8974.29	+	27620.0i	0.355218	+	1.09325i
$862$	7692.26	−	23674.3i	0.303943	−	0.935442i
$863$	33836.3	+	24583.5i	1.33465	+	0.969679i	0.999623	+	0.0274696i	$0.00874495\pi$
$863$	33836.3	+	24583.5i	1.33465	+	0.969679i	0.335026	+	0.942209i	$0.391255\pi$
$864$	−5893.36	−	4281.78i	−0.232056	−	0.168598i
$865$	−3087.18	+	9501.38i	−0.121350	+	0.373476i
$866$	−8675.24	−	26699.6i	−0.340412	−	1.04768i
$867$	−53630.4	+	38964.7i	−2.10079	+	1.52631i
$868$	−12192.9			−0.476790
$869$	79.6320	−	1931.83i	0.00310855	−	0.0754118i
$870$	−7910.11			−0.308250
$871$	7564.17	−	5495.69i	0.294262	−	0.213794i
$872$	3681.21	+	11329.6i	0.142960	+	0.439987i
$873$	−22859.1	+	70353.1i	−0.886212	+	2.72748i
$874$	−2742.37	−	1992.44i	−0.106135	−	0.0771115i
$875$	1331.58	+	967.451i	0.0514465	+	0.0373781i
$876$	−4071.56	+	12531.0i	−0.157038	+	0.483314i
$877$	243.776	+	750.267i	0.00938625	+	0.0288879i	0.955640	−	0.294537i	$-0.0951656\pi$
$877$	243.776	+	750.267i	0.00938625	+	0.0288879i	−0.946254	+	0.323425i	$0.895166\pi$
$878$	−13412.7	+	9744.90i	−0.515555	+	0.374572i
$879$	−36432.7			−1.39800
$880$	−2736.28	−	1015.46i	−0.104818	−	0.0388992i
$881$	−7477.50			−0.285952			−0.142976	−	0.989726i	$-0.545667\pi$
$881$	−7477.50			−0.285952			−0.142976	+	0.989726i	$0.545667\pi$
$882$	14416.0	−	10473.8i	0.550354	−	0.399855i
$883$	−6661.32	−	20501.4i	−0.253875	−	0.781346i	−0.994049	−	0.108931i	$-0.965257\pi$
$883$	−6661.32	−	20501.4i	−0.253875	−	0.781346i	0.740175	−	0.672415i	$-0.234743\pi$
$884$	−5124.10	+	15770.4i	−0.194957	+	0.600017i
$885$	24024.8	+	17455.0i	0.912524	+	0.662988i
$886$	17732.2	+	12883.2i	0.672376	+	0.488510i
$887$	−7958.25	+	24493.0i	−0.301254	+	0.927163i	0.679795	+	0.733402i	$0.262069\pi$
$887$	−7958.25	+	24493.0i	−0.301254	+	0.927163i	−0.981049	+	0.193761i	$0.937931\pi$
$888$	−2502.42	−	7701.66i	−0.0945673	−	0.291048i
$889$	17465.0	−	12689.1i	0.658895	−	0.478715i
$890$	−3087.23			−0.116274
$891$	12365.7	+	18584.0i	0.464945	+	0.698752i
$892$	21419.2			0.804001
$893$	−5388.62	+	3915.06i	−0.201930	+	0.146711i
$894$	7535.37	+	23191.5i	0.281902	+	0.867605i
$895$	−4617.13	+	14210.1i	−0.172440	+	0.530715i
$896$	1363.54	+	990.670i	0.0508401	+	0.0369375i
$897$	31212.7	+	22677.4i	1.16183	+	0.844120i
$898$	−3745.09	+	11526.2i	−0.139171	+	0.428323i
$899$	−6345.33	−	19528.9i	−0.235405	−	0.724501i
$900$	−4249.52	+	3087.46i	−0.157390	+	0.114350i
$901$	58205.0			2.15215
$902$	−17377.8	+	4864.91i	−0.641483	+	0.179583i
$903$	−60571.6			−2.23222
$904$	−4732.29	+	3438.21i	−0.174108	+	0.126497i
$905$	826.258	+	2542.96i	0.0303489	+	0.0934042i
$906$	5888.05	−	18121.6i	0.215913	−	0.664513i
$907$	−24654.1	−	17912.3i	−0.902566	−	0.655753i	0.0365577	−	0.999332i	$-0.488361\pi$
$907$	−24654.1	−	17912.3i	−0.902566	−	0.655753i	−0.939124	+	0.343579i	$0.888361\pi$
$908$	6321.85	+	4593.09i	0.231055	+	0.167871i
$909$	−18200.2	+	56014.4i	−0.664094	+	2.04387i
$910$	1518.05	+	4672.07i	0.0552998	+	0.170195i
$911$	−23414.7	+	17011.8i	−0.851552	+	0.618689i	−0.925574	−	0.378568i	$-0.876417\pi$
$911$	−23414.7	+	17011.8i	−0.851552	+	0.618689i	0.0740212	+	0.997257i	$0.476417\pi$
$912$	2085.45			0.0757195
$913$	−4239.93	+	1186.96i	−0.153692	+	0.0430260i
$914$	19501.6			0.705749
$915$	23827.8	−	17311.9i	0.860901	−	0.625481i
$916$	4987.80	+	15350.9i	0.179914	+	0.553720i
$917$	9159.02	−	28188.6i	0.329834	−	1.01512i
$918$	−40927.6	−	29735.6i	−1.47147	−	1.06909i
$919$	15000.0	+	10898.1i	0.538416	+	0.391182i	0.823496	−	0.567322i	$-0.192020\pi$
$919$	15000.0	+	10898.1i	0.538416	+	0.391182i	−0.285080	+	0.958504i	$0.592020\pi$
$920$	1433.37	−	4411.44i	0.0513659	−	0.158088i
$921$	−18578.6	−	57179.1i	−0.664697	−	2.04573i
$922$	21543.0	−	15651.9i	0.769503	−	0.559076i
$923$	−22147.4			−0.789805
$924$	−9492.70	−	14266.3i	−0.337973	−	0.507929i
$925$	−2837.73			−0.100869
$926$	8239.05	−	5986.02i	0.292389	−	0.212433i
$927$	2180.25	+	6710.12i	0.0772479	+	0.237744i
$928$	−877.117	+	2699.49i	−0.0310267	+	0.0954904i
$929$	−37135.9	−	26980.8i	−1.31151	−	0.952866i	−0.999997	−	0.00262392i	$-0.999165\pi$
$929$	−37135.9	−	26980.8i	−1.31151	−	0.952866i	−0.311511	−	0.950242i	$-0.600835\pi$
$930$	−16701.7	−	12134.5i	−0.588894	−	0.427856i
$931$	−766.092	+	2357.79i	−0.0269685	+	0.0830004i
$932$	4301.24	+	13237.8i	0.151171	+	0.465258i
$933$	−57338.6	+	41658.9i	−2.01198	+	1.46179i
$934$	−18884.4			−0.661581
$935$	−19002.6	−	7052.08i	−0.664655	−	0.246661i
$936$	−15677.4			−0.547471
$937$	−13281.2	+	9649.33i	−0.463049	+	0.336425i	−0.794726	−	0.606968i	$-0.792385\pi$
$937$	−13281.2	+	9649.33i	−0.463049	+	0.336425i	0.331677	+	0.943393i	$0.392385\pi$
$938$	−2039.45	−	6276.79i	−0.0709920	−	0.218491i
$939$	9659.72	−	29729.5i	0.335711	−	1.03321i
$940$	−7373.68	−	5357.29i	−0.255854	−	0.185889i
$941$	−24120.9	−	17524.9i	−0.835621	−	0.607114i	0.0855232	−	0.996336i	$-0.472744\pi$
$941$	−24120.9	−	17524.9i	−0.835621	−	0.607114i	−0.921144	+	0.389222i	$0.872744\pi$
$942$	−6364.91	+	19589.2i	−0.220149	+	0.677548i
$943$	−8862.52	−	27276.0i	−0.306048	−	0.941919i
$944$	8620.89	−	6263.44i	0.297231	−	0.215951i
$945$	−14987.4			−0.515915
$946$	1550.17	−	37606.4i	0.0532775	−	1.29248i
$947$	763.316			0.0261927			0.0130963	−	0.999914i	$-0.495831\pi$
$947$	763.316			0.0261927			0.0130963	+	0.999914i	$0.495831\pi$
$948$	−1529.41	+	1111.18i	−0.0523975	+	0.0380690i
$949$	4258.41	+	13106.0i	0.145662	+	0.448303i
$950$	225.827	−	695.023i	0.00771241	−	0.0237364i
$951$	−13288.5	−	9654.68i	−0.453113	−	0.329206i
$952$	9469.36	+	6879.89i	0.322378	+	0.234221i
$953$	15970.6	−	49152.5i	0.542853	−	1.67073i	−0.183188	−	0.983078i	$-0.558642\pi$
$953$	15970.6	−	49152.5i	0.542853	−	1.67073i	0.726041	−	0.687651i	$-0.241358\pi$
$954$	17005.2	+	52336.6i	0.577111	+	1.77616i
$955$	15709.8	−	11413.9i	0.532312	−	0.386747i
$956$	14276.9			0.482999
$957$	17909.7	−	22628.5i	0.604951	−	0.764341i
$958$	−16138.0			−0.544252
$959$	−26167.6	+	19011.9i	−0.881121	+	0.640172i
$960$	881.839	+	2714.02i	0.0296471	+	0.0912445i
$961$	7354.65	−	22635.3i	0.246875	−	0.759803i
$962$	−6852.07	−	4978.32i	−0.229646	−	0.166848i
$963$	30165.9	+	21916.8i	1.00943	+	0.733394i
$964$	−4066.97	+	12516.8i	−0.135880	+	0.418195i
$965$	−3723.28	−	11459.1i	−0.124204	−	0.382260i
$966$	22032.3	−	16007.4i	0.733827	−	0.533157i
$967$	−15749.8			−0.523765			−0.261883	−	0.965100i	$-0.584343\pi$
$967$	−15749.8			−0.523765			−0.261883	+	0.965100i	$0.584343\pi$
$968$	9100.30	−	5528.52i	0.302164	−	0.183567i
$969$	14482.8			0.480139
$970$	11393.4	−	8277.77i	0.377133	−	0.274003i
$971$	−9339.59	−	28744.3i	−0.308673	−	0.949999i	−0.978281	−	0.207284i	$-0.933538\pi$
$971$	−9339.59	−	28744.3i	−0.308673	−	0.949999i	0.669608	−	0.742715i	$-0.266462\pi$
$972$	−852.915	+	2625.00i	−0.0281453	+	0.0866224i
$973$	8154.54	+	5924.62i	0.268677	+	0.195205i
$974$	1688.07	+	1226.45i	0.0555331	+	0.0403471i
$975$	−2570.29	+	7910.54i	−0.0844258	+	0.259836i
$976$	−3265.90	−	10051.4i	−0.107109	−	0.329649i
$977$	−16624.7	+	12078.5i	−0.544392	+	0.395524i	−0.825714	−	0.564090i	$-0.809227\pi$
$977$	−16624.7	+	12078.5i	−0.544392	+	0.395524i	0.281322	+	0.959614i	$0.409227\pi$
$978$	−56903.0			−1.86049
$979$	6989.95	−	8831.63i	0.228192	−	0.288315i
$980$	−3392.39			−0.110577
$981$	−63278.7	+	45974.7i	−2.05946	+	1.49629i
$982$	660.930	+	2034.13i	0.0214777	+	0.0661016i
$983$	−6321.65	+	19456.0i	−0.205116	+	0.631283i	0.794592	+	0.607143i	$0.207685\pi$
$983$	−6321.65	+	19456.0i	−0.205116	+	0.631283i	−0.999709	+	0.0241395i	$0.992315\pi$
$984$	14274.6	+	10371.1i	0.462458	+	0.335996i
$985$	−6484.27	−	4711.10i	−0.209752	−	0.152394i
$986$	−6091.31	+	18747.1i	−0.196741	+	0.605507i
$987$	−16536.2	−	50893.3i	−0.533287	−	1.64129i
$988$	1764.59	−	1282.05i	0.0568209	−	0.0412828i
$989$	59817.2			1.92323
$990$	789.262	−	19147.1i	0.0253378	−	0.614681i
$991$	−43831.3			−1.40499			−0.702497	−	0.711687i	$-0.747931\pi$
$991$	−43831.3			−1.40499			−0.702497	+	0.711687i	$0.747931\pi$
$992$	−5993.14	+	4354.27i	−0.191817	+	0.139363i
$993$	7745.56	+	23838.4i	0.247531	+	0.761821i
$994$	−4830.95	+	14868.1i	−0.154153	+	0.474435i
$995$	8203.96	+	5960.53i	0.261390	+	0.189911i
$996$	3482.80	+	2530.40i	0.110800	+	0.0805008i
$997$	9180.40	−	28254.4i	0.291621	−	0.897517i	−0.692715	−	0.721212i	$-0.743585\pi$
$997$	9180.40	−	28254.4i	0.291621	−	0.897517i	0.984336	−	0.176305i	$-0.0564145\pi$
$998$	1438.56	+	4427.45i	0.0456282	+	0.140429i
$999$	20904.7	−	15188.2i	0.662058	−	0.481013i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.g.d.91.4	yes	16
11.2	odd	10		1210.4.a.bi.1.7		8
11.4	even	5	inner	110.4.g.d.81.4	✓	16
11.9	even	5		1210.4.a.bj.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.g.d.81.4	✓	16	11.4	even	5	inner
110.4.g.d.91.4	yes	16	1.1	even	1	trivial
1210.4.a.bi.1.7		8	11.2	odd	10
1210.4.a.bj.1.7		8	11.9	even	5

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(2.75575 + 8.48132i) q^{3} +(1.23607 - 3.80423i) q^{4} +(-4.04508 - 2.93893i) q^{5} +(-14.4293 - 10.4835i) q^{6} +(-4.06895 + 12.5230i) q^{7} +(2.47214 + 7.60845i) q^{8} +(-42.4952 + 30.8746i) q^{9} +10.0000 q^{10} +(-22.6415 + 28.6070i) q^{11} +35.6711 q^{12} +(30.1829 - 21.9291i) q^{13} +(-8.13791 - 25.0459i) q^{14} +(13.7787 - 42.4066i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(-89.8939 - 65.3118i) q^{17} +(32.4634 - 99.9122i) q^{18} +(4.51654 + 13.9005i) q^{19} +(-16.1803 + 11.7557i) q^{20} -117.424 q^{21} +(3.00517 - 72.9038i) q^{22} +115.962 q^{23} +(-57.7171 + 41.9339i) q^{24} +(7.72542 + 23.7764i) q^{25} +(-23.0577 + 70.9642i) q^{26} +(-184.168 - 133.806i) q^{27} +(42.6106 + 30.9584i) q^{28} +(-27.4099 + 84.3591i) q^{29} +(27.5575 + 84.8132i) q^{30} +(-187.286 + 136.071i) q^{31} +32.0000 q^{32} +(-305.020 - 113.196i) q^{33} +222.230 q^{34} +(53.2633 - 38.6980i) q^{35} +(64.9269 + 199.824i) q^{36} +(-35.0763 + 107.954i) q^{37} +(-23.6489 - 17.1819i) q^{38} +(269.164 + 195.559i) q^{39} +(12.3607 - 38.0423i) q^{40} +(-76.4263 - 235.216i) q^{41} +(189.996 - 138.040i) q^{42} +515.836 q^{43} +(80.8411 + 121.494i) q^{44} +262.635 q^{45} +(-187.630 + 136.321i) q^{46} +(140.825 + 433.414i) q^{47} +(44.0920 - 135.701i) q^{48} +(137.225 + 99.6997i) q^{49} +(-40.4508 - 29.3893i) q^{50} +(306.205 - 942.402i) q^{51} +(-46.1153 - 141.928i) q^{52} +(-423.785 + 307.897i) q^{53} +455.287 q^{54} +(175.661 - 49.1761i) q^{55} -105.339 q^{56} +(-105.448 + 76.6124i) q^{57} +(-54.8198 - 168.718i) q^{58} +(-205.805 + 633.404i) q^{59} +(-144.293 - 104.835i) q^{60} +(534.389 + 388.257i) q^{61} +(143.073 - 440.335i) q^{62} +(-213.730 - 657.792i) q^{63} +(-51.7771 + 37.6183i) q^{64} -186.540 q^{65} +(626.602 - 175.417i) q^{66} +250.611 q^{67} +(-359.576 + 261.247i) q^{68} +(319.561 + 983.508i) q^{69} +(-40.6895 + 125.230i) q^{70} +(-480.261 - 348.930i) q^{71} +(-339.961 - 246.996i) q^{72} +(-114.142 + 351.292i) q^{73} +(-70.1526 - 215.907i) q^{74} +(-180.366 + 131.044i) q^{75} +58.4633 q^{76} +(-266.117 - 399.939i) q^{77} -665.411 q^{78} +(-42.8752 + 31.1507i) q^{79} +(24.7214 + 76.0845i) q^{80} +(189.072 - 581.905i) q^{81} +(400.173 + 290.743i) q^{82} +(97.6363 + 70.9369i) q^{83} +(-145.144 + 446.708i) q^{84} +(171.682 + 528.383i) q^{85} +(-834.640 + 606.401i) q^{86} -791.011 q^{87} +(-273.628 - 101.546i) q^{88} -308.723 q^{89} +(-424.952 + 308.746i) q^{90} +(151.805 + 467.207i) q^{91} +(143.337 - 441.144i) q^{92} +(-1670.17 - 1213.45i) q^{93} +(-737.368 - 535.729i) q^{94} +(22.5827 - 69.5023i) q^{95} +(88.1839 + 271.402i) q^{96} +(1139.34 - 827.777i) q^{97} -339.239 q^{98} +(78.9262 - 1914.71i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 3 q^{3} - 16 q^{4} - 20 q^{5} - 16 q^{6} - 38 q^{7} - 32 q^{8} + 25 q^{9} + 160 q^{10} + 65 q^{11} + 88 q^{12} + 85 q^{13} - 76 q^{14} - 15 q^{15} - 64 q^{16} + 109 q^{17} - 280 q^{18}+ \cdots + 10702 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 3 * q^3 - 16 * q^4 - 20 * q^5 - 16 * q^6 - 38 * q^7 - 32 * q^8 + 25 * q^9 + 160 * q^10 + 65 * q^11 + 88 * q^12 + 85 * q^13 - 76 * q^14 - 15 * q^15 - 64 * q^16 + 109 * q^17 - 280 * q^18 + 12 * q^19 - 80 * q^20 - 36 * q^21 + 140 * q^22 + 432 * q^23 - 64 * q^24 - 100 * q^25 - 490 * q^26 - 507 * q^27 + 88 * q^28 + 369 * q^29 - 30 * q^30 - 334 * q^31 + 512 * q^32 - 280 * q^33 + 568 * q^34 + 110 * q^35 - 560 * q^36 - 360 * q^37 - 236 * q^38 + 279 * q^39 - 160 * q^40 - 595 * q^41 - 442 * q^42 + 612 * q^43 - 120 * q^44 + 1150 * q^45 - 206 * q^46 + 1066 * q^47 - 48 * q^48 - 1468 * q^49 - 200 * q^50 + 3404 * q^51 - 980 * q^52 - 533 * q^53 + 1556 * q^54 - 125 * q^55 + 256 * q^56 + 470 * q^57 + 738 * q^58 - 1842 * q^59 - 160 * q^60 + 1246 * q^61 - 178 * q^62 - 4622 * q^63 - 256 * q^64 + 1600 * q^65 + 920 * q^66 - 2200 * q^67 + 436 * q^68 + 4777 * q^69 - 380 * q^70 - 2158 * q^71 + 200 * q^72 - 55 * q^73 - 720 * q^74 - 200 * q^75 + 848 * q^76 + 3704 * q^77 - 1812 * q^78 + 1595 * q^79 - 320 * q^80 - 9487 * q^81 + 700 * q^82 - 486 * q^83 + 956 * q^84 - 1255 * q^85 - 1686 * q^86 - 1234 * q^87 - 640 * q^88 - 3512 * q^89 + 250 * q^90 + 3913 * q^91 - 452 * q^92 - 2423 * q^93 - 3748 * q^94 + 60 * q^95 - 96 * q^96 + 1101 * q^97 + 7224 * q^98 + 10702 * q^99

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