LMFDB - Embedded newform 175.4.x.a.103.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			103.30
Character	$\chi$	$=$	175.103
Dual form			175.4.x.a.17.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.143226 + 0.00750617i) q^{2} +(-0.396770 - 0.489971i) q^{3} +(-7.93572 - 0.834078i) q^{4} +(-6.20528 + 9.30024i) q^{5} +(-0.0531501 - 0.0731549i) q^{6} +(-18.1483 - 3.69305i) q^{7} +(-2.26360 - 0.358519i) q^{8} +(5.53097 - 26.0212i) q^{9} +(-0.958568 + 1.28546i) q^{10} +(62.9213 - 13.3743i) q^{11} +(2.73998 + 4.21921i) q^{12} +(50.0770 + 25.5155i) q^{13} +(-2.57160 - 0.665166i) q^{14} +(7.01892 - 0.649656i) q^{15} +(62.1190 + 13.2038i) q^{16} +(7.31965 + 19.0683i) q^{17} +(0.987500 - 3.68540i) q^{18} +(7.32981 + 69.7385i) q^{19} +(57.0005 - 68.6284i) q^{20} +(5.39123 + 10.3574i) q^{21} +(9.11238 - 1.44326i) q^{22} +(2.91889 - 55.6957i) q^{23} +(0.722465 + 1.25135i) q^{24} +(-47.9890 - 115.421i) q^{25} +(6.98083 + 4.03038i) q^{26} +(-30.1116 + 15.3426i) q^{27} +(140.940 + 44.4441i) q^{28} +(56.0721 - 77.1766i) q^{29} +(1.01017 - 0.0403626i) q^{30} +(30.4126 - 68.3077i) q^{31} +(26.5077 + 7.10273i) q^{32} +(-31.5183 - 25.5231i) q^{33} +(0.905236 + 2.78603i) q^{34} +(146.962 - 145.867i) q^{35} +(-65.5959 + 201.883i) q^{36} +(126.443 - 82.1133i) q^{37} +(0.526352 + 10.0434i) q^{38} +(-7.36723 - 34.6601i) q^{39} +(17.3806 - 18.8273i) q^{40} +(-214.776 + 69.7848i) q^{41} +(0.694421 + 1.52392i) q^{42} +(269.498 + 269.498i) q^{43} +(-510.481 + 53.6537i) q^{44} +(207.682 + 212.908i) q^{45} +(0.836123 - 7.95518i) q^{46} +(-285.901 - 109.747i) q^{47} +(-18.1775 - 35.6753i) q^{48} +(315.723 + 134.045i) q^{49} +(-6.00692 - 16.8916i) q^{50} +(6.43871 - 11.1522i) q^{51} +(-376.115 - 244.252i) q^{52} +(326.272 - 264.210i) q^{53} +(-4.42793 + 1.97144i) q^{54} +(-266.060 + 668.175i) q^{55} +(39.7565 + 14.8661i) q^{56} +(31.2616 - 31.2616i) q^{57} +(8.61030 - 10.6328i) q^{58} +(420.752 - 467.292i) q^{59} +(-56.2420 - 0.698833i) q^{60} +(481.108 - 433.191i) q^{61} +(4.86861 - 9.55518i) q^{62} +(-196.475 + 451.814i) q^{63} +(-479.445 - 155.781i) q^{64} +(-548.043 + 307.398i) q^{65} +(-4.32267 - 3.89215i) q^{66} +(1.63055 - 0.625910i) q^{67} +(-42.1822 - 157.426i) q^{68} +(-28.4474 + 20.6682i) q^{69} +(22.1437 - 19.7889i) q^{70} +(663.379 + 481.973i) q^{71} +(-21.8490 + 56.9185i) q^{72} +(140.357 - 216.131i) q^{73} +(18.7264 - 10.8117i) q^{74} +(-37.5124 + 69.3089i) q^{75} -559.538i q^{76} +(-1191.31 + 10.3501i) q^{77} +(-0.795016 - 5.01953i) q^{78} +(-250.925 - 563.586i) q^{79} +(-508.264 + 495.788i) q^{80} +(-636.705 - 283.479i) q^{81} +(-31.2853 + 8.38288i) q^{82} +(-99.9493 + 631.055i) q^{83} +(-34.1444 - 86.6904i) q^{84} +(-222.761 - 50.2499i) q^{85} +(36.5763 + 40.6221i) q^{86} +(-60.0620 + 3.14772i) q^{87} +(-147.224 + 7.71566i) q^{88} +(628.670 + 698.208i) q^{89} +(28.1474 + 32.0529i) q^{90} +(-814.584 - 648.001i) q^{91} +(-69.6180 + 439.551i) q^{92} +(-45.5356 + 12.2012i) q^{93} +(-40.1247 - 17.8647i) q^{94} +(-694.068 - 364.578i) q^{95} +(-7.03736 - 15.8062i) q^{96} +(170.812 + 1078.46i) q^{97} +(44.2136 + 21.5687i) q^{98} -1711.26i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{20}\right)$

Coefficient data

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

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

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

$2$	0.143226	+	0.00750617i	0.0506381	+	0.00265383i	0.0776382	−	0.996982i	$-0.475262\pi$
$2$	0.143226	+	0.00750617i	0.0506381	+	0.00265383i	−0.0270001	+	0.999635i	$0.508595\pi$
$3$	−0.396770	−	0.489971i	−0.0763585	−	0.0942949i	0.737535	−	0.675309i	$-0.235990\pi$
$3$	−0.396770	−	0.489971i	−0.0763585	−	0.0942949i	−0.813894	+	0.581014i	$0.802656\pi$
$4$	−7.93572	−	0.834078i	−0.991965	−	0.104260i
$5$	−6.20528	+	9.30024i	−0.555017	+	0.831839i
$5$	−6.20528	+	9.30024i	−0.555017	+	0.831839i
$6$	−0.0531501	−	0.0731549i	−0.00361641	−	0.00497756i
$7$	−18.1483	−	3.69305i	−0.979917	−	0.199406i
$7$	−18.1483	−	3.69305i	−0.979917	−	0.199406i
$8$	−2.26360	−	0.358519i	−0.100038	−	0.0158444i
$9$	5.53097	−	26.0212i	0.204851	−	0.963747i
$10$	−0.958568	+	1.28546i	−0.0303126	+	0.0406499i
$11$	62.9213	−	13.3743i	1.72468	−	0.366592i	0.764209	−	0.644969i	$-0.223130\pi$
$11$	62.9213	−	13.3743i	1.72468	−	0.366592i	0.960472	+	0.278377i	$0.0897963\pi$
$12$	2.73998	+	4.21921i	0.0659138	+	0.101498i
$13$	50.0770	+	25.5155i	1.06837	+	0.544364i	0.897539	−	0.440935i	$-0.145353\pi$
$13$	50.0770	+	25.5155i	1.06837	+	0.544364i	0.170836	+	0.985299i	$0.445353\pi$
$14$	−2.57160	−	0.665166i	−0.0490920	−	0.0126981i
$15$	7.01892	−	0.649656i	0.120818	−	0.0111827i
$16$	62.1190	+	13.2038i	0.970609	+	0.206309i
$17$	7.31965	+	19.0683i	0.104428	+	0.272044i	0.975832	−	0.218522i	$-0.0701234\pi$
$17$	7.31965	+	19.0683i	0.104428	+	0.272044i	−0.871404	+	0.490566i	$0.836790\pi$
$18$	0.987500	−	3.68540i	0.0129309	−	0.0482587i
$19$	7.32981	+	69.7385i	0.0885039	+	0.842058i	0.945256	+	0.326330i	$0.105812\pi$
$19$	7.32981	+	69.7385i	0.0885039	+	0.842058i	−0.856752	+	0.515728i	$0.827521\pi$
$20$	57.0005	−	68.6284i	0.637285	−	0.767289i
$21$	5.39123	+	10.3574i	0.0560220	+	0.107627i
$22$	9.11238	−	1.44326i	0.0883075	−	0.0139865i
$23$	2.91889	−	55.6957i	0.0264622	−	0.504928i	−0.952959	−	0.303100i	$-0.901978\pi$
$23$	2.91889	−	55.6957i	0.0264622	−	0.504928i	0.979421	−	0.201828i	$-0.0646883\pi$
$24$	0.722465	+	1.25135i	0.00614469	+	0.0106429i
$25$	−47.9890	−	115.421i	−0.383912	−	0.923370i
$26$	6.98083	+	4.03038i	0.0526559	+	0.0304009i
$27$	−30.1116	+	15.3426i	−0.214629	+	0.109359i
$28$	140.940	+	44.4441i	0.951253	+	0.299970i
$29$	56.0721	−	77.1766i	0.359046	−	0.494184i	−0.590837	−	0.806791i	$-0.701202\pi$
$29$	56.0721	−	77.1766i	0.359046	−	0.494184i	0.949883	+	0.312607i	$0.101202\pi$
$30$	1.01017	−	0.0403626i	0.00614770	−	0.000245639i
$31$	30.4126	−	68.3077i	0.176202	−	0.395756i	−0.803756	−	0.594958i	$-0.797169\pi$
$31$	30.4126	−	68.3077i	0.176202	−	0.395756i	0.979958	+	0.199203i	$0.0638352\pi$
$32$	26.5077	+	7.10273i	0.146436	+	0.0392374i
$33$	−31.5183	−	25.5231i	−0.166262	−	0.134636i
$34$	0.905236	+	2.78603i	0.00456608	+	0.0140530i
$35$	146.962	−	145.867i	0.709744	−	0.704459i
$36$	−65.5959	+	201.883i	−0.303685	+	0.934646i
$37$	126.443	−	82.1133i	0.561816	−	0.364847i	−0.232272	−	0.972651i	$-0.574616\pi$
$37$	126.443	−	82.1133i	0.561816	−	0.364847i	0.794087	+	0.607804i	$0.207949\pi$
$38$	0.526352	+	10.0434i	0.00224699	+	0.0428751i
$39$	−7.36723	−	34.6601i	−0.0302487	−	0.142309i
$40$	17.3806	−	18.8273i	0.0687028	−	0.0744215i
$41$	−214.776	+	69.7848i	−0.818105	+	0.265819i	−0.688027	−	0.725685i	$-0.741523\pi$
$41$	−214.776	+	69.7848i	−0.818105	+	0.265819i	−0.130078	+	0.991504i	$0.541523\pi$
$42$	0.694421	+	1.52392i	0.00255123	+	0.00559873i
$43$	269.498	+	269.498i	0.955768	+	0.955768i	0.999062	−	0.0432941i	$-0.0137852\pi$
$43$	269.498	+	269.498i	0.955768	+	0.955768i	−0.0432941	+	0.999062i	$0.513785\pi$
$44$	−510.481	+	53.6537i	−1.74904	+	0.183832i
$45$	207.682	+	212.908i	0.687987	+	0.705299i
$46$	0.836123	−	7.95518i	0.00267999	−	0.0254984i
$47$	−285.901	−	109.747i	−0.887296	−	0.340601i	−0.128330	−	0.991732i	$-0.540962\pi$
$47$	−285.901	−	109.747i	−0.887296	−	0.340601i	−0.758966	+	0.651131i	$0.774295\pi$
$48$	−18.1775	−	35.6753i	−0.0546603	−	0.107277i
$49$	315.723	+	134.045i	0.920475	+	0.390803i
$50$	−6.00692	−	16.8916i	−0.0169901	−	0.0477766i
$51$	6.43871	−	11.1522i	0.0176784	−	0.0306199i
$52$	−376.115	−	244.252i	−1.00303	−	0.651379i
$53$	326.272	−	264.210i	0.845603	−	0.684756i	−0.105234	−	0.994447i	$-0.533559\pi$
$53$	326.272	−	264.210i	0.845603	−	0.684756i	0.950837	+	0.309692i	$0.100226\pi$
$54$	−4.42793	+	1.97144i	−0.0111586	+	0.00496814i
$55$	−266.060	+	668.175i	−0.652282	+	1.63812i
$56$	39.7565	+	14.8661i	0.0948693	+	0.0354744i
$57$	31.2616	−	31.2616i	0.0726437	−	0.0726437i
$58$	8.61030	−	10.6328i	0.0194929	−	0.0240717i
$59$	420.752	−	467.292i	0.928428	−	1.03112i	−0.0710059	−	0.997476i	$-0.522621\pi$
$59$	420.752	−	467.292i	0.928428	−	1.03112i	0.999434	−	0.0336477i	$-0.0107124\pi$
$60$	−56.2420	−	0.698833i	−0.121014	−	0.00150365i
$61$	481.108	−	433.191i	1.00983	−	0.909253i	0.0139453	−	0.999903i	$-0.495561\pi$
$61$	481.108	−	433.191i	1.00983	−	0.909253i	0.995883	+	0.0906494i	$0.0288943\pi$
$62$	4.86861	−	9.55518i	0.00997280	−	0.0195727i
$63$	−196.475	+	451.814i	−0.392914	+	0.903544i
$64$	−479.445	−	155.781i	−0.936415	−	0.304260i
$65$	−548.043	+	307.398i	−1.04579	+	0.586584i
$66$	−4.32267	−	3.89215i	−0.00806189	−	0.00725895i
$67$	1.63055	−	0.625910i	0.00297319	−	0.00114130i	−0.356881	−	0.934150i	$-0.616160\pi$
$67$	1.63055	−	0.625910i	0.00297319	−	0.00114130i	0.359854	+	0.933009i	$0.382826\pi$
$68$	−42.1822	−	157.426i	−0.0752257	−	0.280746i
$69$	−28.4474	+	20.6682i	−0.0496328	+	0.0360603i
$70$	22.1437	−	19.7889i	0.0378096	−	0.0337890i
$71$	663.379	+	481.973i	1.10885	+	0.805629i	0.982483	−	0.186354i	$-0.0596672\pi$
$71$	663.379	+	481.973i	1.10885	+	0.805629i	0.126370	+	0.991983i	$0.459667\pi$
$72$	−21.8490	+	56.9185i	−0.0357629	+	0.0931655i
$73$	140.357	−	216.131i	0.225035	−	0.346523i	−0.708061	−	0.706151i	$-0.750430\pi$
$73$	140.357	−	216.131i	0.225035	−	0.346523i	0.933096	+	0.359628i	$0.117096\pi$
$74$	18.7264	−	10.8117i	0.0294175	−	0.0169842i
$75$	−37.5124	+	69.3089i	−0.0577541	+	0.106708i
$76$		−	559.538i		−	0.844519i
$77$	−1191.31	+	10.3501i	−1.76314	+	0.0153183i
$78$	−0.795016	−	5.01953i	−0.00115408	−	0.00728654i
$79$	−250.925	−	563.586i	−0.357357	−	0.802638i	−0.999354	−	0.0359305i	$-0.988561\pi$
$79$	−250.925	−	563.586i	−0.357357	−	0.802638i	0.641997	−	0.766707i	$-0.278106\pi$
$80$	−508.264	+	495.788i	−0.710321	+	0.692885i
$81$	−636.705	−	283.479i	−0.873395	−	0.388861i
$82$	−31.2853	+	8.38288i	−0.0421328	+	0.0112894i
$83$	−99.9493	+	631.055i	−0.132179	+	0.834546i	0.829126	+	0.559061i	$0.188838\pi$
$83$	−99.9493	+	631.055i	−0.132179	+	0.834546i	−0.961306	+	0.275485i	$0.911162\pi$
$84$	−34.1444	−	86.6904i	−0.0443507	−	0.112604i
$85$	−222.761	−	50.2499i	−0.284256	−	0.0641219i
$86$	36.5763	+	40.6221i	0.0458619	+	0.0509348i
$87$	−60.0620	+	3.14772i	−0.0740152	+	0.00387897i
$88$	−147.224	+	7.71566i	−0.178342	+	0.00934650i
$89$	628.670	+	698.208i	0.748751	+	0.831572i	0.990319	−	0.138812i	$-0.0443283\pi$
$89$	628.670	+	698.208i	0.748751	+	0.831572i	−0.241568	+	0.970384i	$0.577662\pi$
$90$	28.1474	+	32.0529i	0.0329666	+	0.0375408i
$91$	−814.584	−	648.001i	−0.938369	−	0.746472i
$92$	−69.6180	+	439.551i	−0.0788932	+	0.498112i
$93$	−45.5356	+	12.2012i	−0.0507723	+	0.0136044i
$94$	−40.1247	−	17.8647i	−0.0440271	−	0.0196021i
$95$	−694.068	−	364.578i	−0.749578	−	0.393736i
$96$	−7.03736	−	15.8062i	−0.00748174	−	0.0168043i
$97$	170.812	+	1078.46i	0.178797	+	1.12888i	0.899914	+	0.436067i	$0.143629\pi$
$97$	170.812	+	1078.46i	0.178797	+	1.12888i	−0.721117	+	0.692813i	$0.756371\pi$
$98$	44.2136	+	21.5687i	0.0455740	+	0.0222323i
$99$		−	1711.26i		−	1.73725i
$100$	284.557	+	955.977i	0.284557	+	0.955977i
$101$	938.483	−	541.833i	0.924580	−	0.533806i	0.0394865	−	0.999220i	$-0.487428\pi$
$101$	938.483	−	541.833i	0.924580	−	0.533806i	0.885093	+	0.465414i	$0.154094\pi$
$102$	1.00590	−	1.54895i	0.000976462	−	0.00150362i
$103$	−494.917	+	1289.30i	−0.473453	+	1.23339i	0.464174	+	0.885744i	$0.346351\pi$
$103$	−494.917	+	1289.30i	−0.473453	+	1.23339i	−0.937627	+	0.347643i	$0.886982\pi$
$104$	−104.207	−	75.7105i	−0.0982528	−	0.0713849i
$105$	−129.781	−	14.1310i	−0.120622	−	0.0131338i
$106$	48.7140	−	35.3928i	0.0446370	−	0.0324307i
$107$	348.876	+	1302.02i	0.315206	+	1.17637i	0.923797	+	0.382882i	$0.125068\pi$
$107$	348.876	+	1302.02i	0.315206	+	1.17637i	−0.608591	+	0.793484i	$0.708265\pi$
$108$	251.754	−	96.6392i	0.224306	−	0.0861029i
$109$	−348.345	−	313.652i	−0.306105	−	0.275618i	0.501733	−	0.865022i	$-0.332696\pi$
$109$	−348.345	−	313.652i	−0.306105	−	0.275618i	−0.807838	+	0.589404i	$0.799363\pi$
$110$	−43.1222	+	93.7031i	−0.0373776	+	0.0812204i
$111$	−90.4021	−	29.3734i	−0.0773026	−	0.0251171i
$112$	−1078.59	−	469.035i	−0.909977	−	0.395711i
$113$	−133.351	+	261.716i	−0.111014	+	0.217878i	−0.939829	−	0.341646i	$-0.889016\pi$
$113$	−133.351	+	261.716i	−0.111014	+	0.217878i	0.828815	+	0.559523i	$0.189016\pi$
$114$	4.71213	−	4.24282i	0.00387133	−	0.00348576i
$115$	499.871	+	372.754i	0.405332	+	0.302256i
$116$	−509.344	+	565.683i	−0.407684	+	0.452779i
$117$	940.919	−	1161.94i	0.743487	−	0.918130i
$118$	63.7703	−	63.7703i	0.0497503	−	0.0497503i
$119$	−62.4190	−	373.090i	−0.0480835	−	0.287404i
$120$	−16.1209	−	1.04585i	−0.0122636	−	0.000795607i
$121$	2564.29	−	1141.70i	1.92659	−	0.857773i
$122$	72.1589	−	58.4331i	0.0535488	−	0.0433630i
$123$	119.409	+	77.5452i	0.0875346	+	0.0568456i
$124$	−298.319	+	516.705i	−0.216047	+	0.374205i
$125$	1371.23	+	269.911i	0.981173	+	0.193133i
$126$	−31.5318	+	63.2369i	−0.0222943	+	0.0447110i
$127$	−459.344	−	901.513i	−0.320946	−	0.629893i	0.673014	−	0.739629i	$-0.264999\pi$
$127$	−459.344	−	901.513i	−0.320946	−	0.629893i	−0.993961	+	0.109737i	$0.964999\pi$
$128$	−272.461	−	104.588i	−0.188143	−	0.0722214i
$129$	25.1173	−	238.975i	0.0171430	−	0.163105i
$130$	−80.8015	+	39.9137i	−0.0545135	+	0.0269282i
$131$	1439.59	−	151.307i	0.960132	−	0.100914i	0.388522	−	0.921440i	$-0.372986\pi$
$131$	1439.59	−	151.307i	0.960132	−	0.100914i	0.571610	+	0.820526i	$0.306319\pi$
$132$	228.832	+	228.832i	0.150889	+	0.150889i
$133$	124.524	−	1292.71i	0.0811850	−	0.842795i
$134$	0.238236	−	0.0774075i	0.000153585	−	4.99029e-5i
$135$	44.1607	−	375.250i	0.0281537	−	0.239232i
$136$	−9.73240	−	45.7873i	−0.00613637	−	0.0288693i
$137$	2.52633	+	48.2053i	0.00157547	+	0.0300617i	0.999304	−	0.0372992i	$-0.0118755\pi$
$137$	2.52633	+	48.2053i	0.00157547	+	0.0300617i	−0.997729	+	0.0673609i	$0.978542\pi$
$138$	−4.22955	+	2.74670i	−0.00260901	+	0.00169431i
$139$	43.3662	−	133.467i	0.0264624	−	0.0814429i	−0.936953	−	0.349455i	$-0.886367\pi$
$139$	43.3662	−	133.467i	0.0264624	−	0.0814429i	0.963416	+	0.268012i	$0.0863667\pi$
$140$	−1287.91	+	1034.98i	−0.777488	+	0.624801i
$141$	59.6641	+	183.627i	0.0356356	+	0.109675i
$142$	91.3955	+	74.0106i	0.0540122	+	0.0437382i
$143$	3492.17	+	935.723i	2.04217	+	0.547197i
$144$	687.156	−	1543.38i	0.397660	−	0.893159i
$145$	369.818	+	1000.39i	0.211805	+	0.572949i
$146$	21.7251	−	29.9021i	0.0123150	−	0.0169501i
$147$	−59.5912	−	207.880i	−0.0334354	−	0.116637i
$148$	−1071.91	+	546.165i	−0.595340	+	0.303341i
$149$	−2213.95	−	1278.23i	−1.21728	−	0.702795i	−0.252942	−	0.967481i	$-0.581398\pi$
$149$	−2213.95	−	1278.23i	−1.21728	−	0.702795i	−0.964334	+	0.264687i	$0.914731\pi$
$150$	−5.89300	+	9.64528i	−0.00320774	+	0.00525023i
$151$	−860.075	−	1489.69i	−0.463523	−	0.802845i	0.535611	−	0.844465i	$-0.320081\pi$
$151$	−860.075	−	1489.69i	−0.463523	−	0.802845i	−0.999134	+	0.0416200i	$0.986748\pi$
$152$	8.41081	−	160.488i	0.00448820	−	0.0856400i
$153$	536.666	−	84.9995i	0.283574	−	0.0449137i
$154$	−170.704	−	7.45975i	−0.0893230	−	0.00390340i
$155$	446.560	+	706.713i	0.231410	+	0.366223i
$156$	29.5550	+	281.197i	0.0151686	+	0.144319i
$157$	232.452	−	867.521i	0.118163	−	0.440992i	−0.881341	−	0.472481i	$-0.843358\pi$
$157$	232.452	−	867.521i	0.118163	−	0.440992i	0.999504	+	0.0314895i	$0.0100251\pi$
$158$	−31.7086	−	82.6038i	−0.0159658	−	0.0415924i
$159$	−258.910	−	55.0331i	−0.129138	−	0.0274491i
$160$	−230.545	+	202.454i	−0.113914	+	0.100034i
$161$	−258.660	+	1000.00i	−0.126616	+	0.489511i
$162$	−89.0651	−	45.3809i	−0.0431951	−	0.0220090i
$163$	1852.48	+	2852.56i	0.890166	+	1.37074i	0.928445	+	0.371469i	$0.121146\pi$
$163$	1852.48	+	2852.56i	0.890166	+	1.37074i	−0.0382791	+	0.999267i	$0.512188\pi$
$164$	1762.60	−	374.653i	0.839246	−	0.178387i
$165$	432.951	−	134.751i	0.204274	−	0.0635777i
$166$	−19.0522	+	89.6334i	−0.00890804	+	0.0419091i
$167$	−3260.66	−	516.437i	−1.51088	−	0.239300i	−0.654666	−	0.755918i	$-0.727191\pi$
$167$	−3260.66	−	516.437i	−1.51088	−	0.239300i	−0.856216	+	0.516618i	$0.827191\pi$
$168$	−8.49024	−	25.3779i	−0.00389903	−	0.0116545i
$169$	565.304	+	778.074i	0.257307	+	0.354153i
$170$	−31.5280	−	8.86918i	−0.0142240	−	0.00400138i
$171$	1855.22	+	194.991i	0.829661	+	0.0872009i
$172$	−1913.88	−	2363.44i	−0.848440	−	1.04774i
$173$	1573.23	+	82.4494i	0.691389	+	0.0362342i	0.394795	−	0.918769i	$-0.370816\pi$
$173$	1573.23	+	82.4494i	0.691389	+	0.0362342i	0.296595	+	0.955003i	$0.404149\pi$
$174$	−8.62609			−0.00375829
$175$	444.664	+	2271.93i	0.192077	+	0.981380i
$176$	4085.20			1.74962
$177$	−395.901	−	20.7483i	−0.168123	−	0.00881095i
$178$	84.8011	+	104.721i	0.0357085	+	0.0440963i
$179$	588.003	+	61.8016i	0.245527	+	0.0258060i	0.226493	−	0.974013i	$-0.427274\pi$
$179$	588.003	+	61.8016i	0.245527	+	0.0258060i	0.0190346	+	0.999819i	$0.493941\pi$
$180$	−1470.52	−	1862.80i	−0.608924	−	0.771361i
$181$	1005.74	+	1384.28i	0.413017	+	0.568470i	0.963951	−	0.266079i	$-0.0857283\pi$
$181$	1005.74	+	1384.28i	0.413017	+	0.568470i	−0.550934	+	0.834549i	$0.685728\pi$
$182$	−111.806	−	98.9252i	−0.0455363	−	0.0402902i
$183$	−403.140	−	63.8511i	−0.162847	−	0.0257924i
$184$	−26.5751	+	125.026i	−0.0106475	+	0.0500927i
$185$	−20.9430	+	1685.49i	−0.00832303	+	0.669837i
$186$	−6.61348	+	1.40574i	−0.00260712	+	0.000554160i
$187$	715.589	+	1101.91i	0.279834	+	0.430907i
$188$	2177.29	+	1109.38i	0.844655	+	0.430373i
$189$	603.135	−	167.239i	0.232125	−	0.0643643i
$190$	−96.6722	−	57.4269i	−0.0369123	−	0.0219273i
$191$	−1644.39	−	349.526i	−0.622952	−	0.132413i	−0.114387	−	0.993436i	$-0.536490\pi$
$191$	−1644.39	−	349.526i	−0.622952	−	0.132413i	−0.508565	+	0.861024i	$0.669824\pi$
$192$	113.901	+	296.723i	0.0428131	+	0.111532i
$193$	1320.91	−	4929.69i	0.492647	−	1.83858i	−0.0501806	−	0.998740i	$-0.515980\pi$
$193$	1320.91	−	4929.69i	0.492647	−	1.83858i	0.542828	−	0.839844i	$-0.317354\pi$
$194$	16.3696	+	155.747i	0.00605809	+	0.0576389i
$195$	368.063	+	146.558i	0.135167	+	0.0538219i
$196$	−2393.68	−	1327.08i	−0.872333	−	0.483631i
$197$	−377.247	+	59.7501i	−0.136435	+	0.0216092i	−0.224279	−	0.974525i	$-0.572003\pi$
$197$	−377.247	+	59.7501i	−0.136435	+	0.0216092i	0.0878433	+	0.996134i	$0.472003\pi$
$198$	12.8450	−	245.097i	0.00461038	−	0.0879713i
$199$	−2196.84	−	3805.03i	−0.782561	−	1.35543i	−0.930446	−	0.366430i	$-0.880580\pi$
$199$	−2196.84	−	3805.03i	−0.782561	−	1.35543i	0.147885	−	0.989005i	$-0.452753\pi$
$200$	67.2472	+	278.472i	0.0237755	+	0.0984548i
$201$	−0.953631	−	0.550579i	−0.000334647	−	0.000193208i
$202$	138.483	−	70.5604i	0.0482356	−	0.0245773i
$203$	−1302.63	+	1193.55i	−0.450378	+	0.412663i
$204$	−60.3975	+	83.1301i	−0.0207288	+	0.0285307i
$205$	683.727	−	2430.50i	0.232944	−	0.828066i
$206$	−80.5629	+	180.947i	−0.0272480	+	0.0611999i
$207$	−1433.12	−	384.004i	−0.481202	−	0.128938i
$208$	2773.83	+	2246.21i	0.924667	+	0.748780i
$209$	1393.91	+	4290.01i	0.461333	+	1.41984i
$210$	−18.4819	−	2.99809i	−0.00607321	−	0.000985181i
$211$	869.976	−	2677.51i	0.283846	−	0.873589i	−0.702896	−	0.711293i	$-0.748110\pi$
$211$	869.976	−	2677.51i	0.283846	−	0.873589i	0.986742	−	0.162296i	$-0.0518901\pi$
$212$	−2809.58	+	1824.56i	−0.910201	+	0.591091i
$213$	−27.0565	−	516.268i	−0.00870366	−	0.166076i
$214$	40.1950	+	189.102i	0.0128396	+	0.0604055i
$215$	−4178.70	+	834.086i	−1.32551	+	0.264578i
$216$	73.6611	−	23.9340i	0.0232037	−	0.00753935i
$217$	−804.201	+	1127.36i	−0.251579	+	0.352672i
$218$	−47.5379	−	47.5379i	−0.0147691	−	0.0147691i
$219$	−161.587	+	16.9835i	−0.0498587	+	0.00524036i
$220$	2668.68	−	5080.53i	0.817830	−	1.55695i
$221$	−119.992	+	1141.65i	−0.0365229	+	0.347492i
$222$	−12.7275	−	4.88562i	−0.00384780	−	0.00147703i
$223$	−1927.14	−	3782.23i	−0.578705	−	1.13577i	−0.975937	−	0.218054i	$-0.930029\pi$
$223$	−1927.14	−	3782.23i	−0.578705	−	1.13577i	0.397232	−	0.917718i	$-0.369971\pi$
$224$	−454.840	−	226.797i	−0.135671	−	0.0676496i
$225$	−3268.82	+	610.339i	−0.968540	+	0.180841i
$226$	−21.0639	+	36.4837i	−0.00619977	+	0.0107383i
$227$	1170.61	+	760.205i	0.342275	+	0.222276i	0.704316	−	0.709886i	$-0.251254\pi$
$227$	1170.61	+	760.205i	0.342275	+	0.222276i	−0.362042	+	0.932162i	$0.617920\pi$
$228$	−274.157	+	222.008i	−0.0796338	+	0.0644862i
$229$	−1437.23	+	639.897i	−0.414738	+	0.184653i	−0.603488	−	0.797372i	$-0.706223\pi$
$229$	−1437.23	+	639.897i	−0.414738	+	0.184653i	0.188750	+	0.982025i	$0.439556\pi$
$230$	68.7967	+	57.1402i	0.0197231	+	0.0163814i
$231$	477.747	+	579.599i	0.136075	+	0.165086i
$232$	−154.594	+	154.594i	−0.0437482	+	0.0437482i
$233$	−2506.16	+	3094.84i	−0.704651	+	0.870172i	−0.996264	−	0.0863648i	$-0.972475\pi$
$233$	−2506.16	+	3094.84i	−0.704651	+	0.870172i	0.291612	+	0.956537i	$0.405808\pi$
$234$	143.486	−	159.357i	0.0400854	−	0.0445193i
$235$	2794.77	−	1977.93i	0.775789	−	0.549048i
$236$	−3728.73	+	3357.36i	−1.02847	+	0.926041i
$237$	−176.581	+	346.560i	−0.0483974	+	0.0949852i
$238$	−6.13956	−	53.9049i	−0.00167214	−	0.0146812i
$239$	774.801	+	251.748i	0.209698	+	0.0681349i	0.411982	−	0.911192i	$-0.364837\pi$
$239$	774.801	+	251.748i	0.209698	+	0.0681349i	−0.202285	+	0.979327i	$0.564837\pi$
$240$	444.586	+	52.3204i	0.119575	+	0.0140719i
$241$	−310.967	−	279.996i	−0.0831168	−	0.0748387i	0.626525	−	0.779401i	$-0.284477\pi$
$241$	−310.967	−	279.996i	−0.0831168	−	0.0748387i	−0.709642	+	0.704563i	$0.751143\pi$
$242$	375.843	−	144.273i	0.0998352	−	0.0383232i
$243$	349.893	+	1305.82i	0.0923688	+	0.344725i
$244$	−4179.25	+	3036.40i	−1.09651	+	0.796663i
$245$	−3205.80	+	2104.51i	−0.835964	+	0.548784i
$246$	16.5205	+	12.0028i	0.00428173	+	0.00311086i
$247$	−1412.36	+	3679.32i	−0.363831	+	0.947812i
$248$	−93.3315	+	143.718i	−0.0238974	+	0.0367988i
$249$	348.855	−	201.412i	0.0887864	−	0.0512608i
$250$	194.370	+	48.9511i	0.0491722	+	0.0123838i
$251$			2253.80i			0.566767i	0.959007	+	0.283384i	$0.0914570\pi$
$251$			2253.80i			0.566767i	−0.959007	+	0.283384i	$0.908543\pi$
$252$	1936.02	−	3421.60i	0.483960	−	0.855318i
$253$	−561.233	−	3543.48i	−0.139464	−	0.880541i
$254$	−59.0232	−	132.568i	−0.0145805	−	0.0327483i
$255$	63.7639	+	129.084i	0.0156590	+	0.0317002i
$256$	3646.04	+	1623.32i	0.890146	+	0.396319i
$257$	6641.62	−	1779.62i	1.61204	−	0.431944i	0.663387	−	0.748276i	$-0.269118\pi$
$257$	6641.62	−	1779.62i	1.61204	−	0.431944i	0.948648	+	0.316333i	$0.102452\pi$
$258$	5.39124	−	34.0389i	0.00130094	−	0.00821384i
$259$	−2597.98	+	1023.26i	−0.623285	+	0.245491i
$260$	4605.51	−	1982.31i	1.09854	−	0.472837i
$261$	−1698.09	−	1885.92i	−0.402718	−	0.447263i
$262$	207.322	−	10.8653i	0.0488871	−	0.00256206i
$263$	−7889.09	+	413.450i	−1.84967	+	0.0969369i	−0.944578	−	0.328288i	$-0.893528\pi$
$263$	−7889.09	+	413.450i	−1.84967	+	0.0969369i	−0.905088	+	0.425225i	$0.860195\pi$
$264$	62.1944	+	69.0739i	0.0144992	+	0.0161030i
$265$	432.607	+	4673.91i	0.100282	+	1.08346i
$266$	27.5384	−	184.215i	0.00634769	−	0.0424621i
$267$	92.6641	−	585.058i	0.0212395	−	0.134101i
$268$	−13.4616	+	3.60704i	−0.00306829	+	0.000822145i
$269$	1614.23	+	718.703i	0.365879	+	0.162900i	0.581438	−	0.813591i	$-0.302490\pi$
$269$	1614.23	+	718.703i	0.365879	+	0.162900i	−0.215558	+	0.976491i	$0.569157\pi$
$270$	9.14166	−	53.4142i	0.00206053	−	0.0120396i
$271$	−1622.02	−	3643.12i	−0.363582	−	0.816620i	−0.999011	−	0.0444600i	$-0.985843\pi$
$271$	−1622.02	−	3643.12i	−0.363582	−	0.816620i	0.635429	−	0.772160i	$-0.280823\pi$
$272$	202.915	+	1281.15i	0.0452335	+	0.285593i
$273$	5.70135	+	656.230i	0.00126396	+	0.145483i
$274$			6.92322i			0.00152645i
$275$	−4563.21	−	6620.63i	−1.00063	−	1.45178i
$276$	242.989	−	140.290i	0.0529936	−	0.0305959i
$277$	−524.427	+	807.546i	−0.113754	+	0.175165i	−0.890962	−	0.454078i	$-0.849969\pi$
$277$	−524.427	+	807.546i	−0.113754	+	0.175165i	0.777208	+	0.629244i	$0.216635\pi$
$278$	7.21301	−	18.7905i	0.00155614	−	0.00405389i
$279$	−1609.24	−	1169.18i	−0.345314	−	0.250885i
$280$	−384.958	+	277.497i	−0.0821631	+	0.0592271i
$281$	−4464.18	+	3243.42i	−0.947725	+	0.688562i	−0.950268	−	0.311434i	$-0.899191\pi$
$281$	−4464.18	+	3243.42i	−0.947725	+	0.688562i	0.00254280	+	0.999997i	$0.499191\pi$
$282$	7.16713	+	26.7481i	0.00151346	+	0.00564832i
$283$	−5114.36	+	1963.22i	−1.07427	+	0.412372i	−0.830246	−	0.557398i	$-0.811800\pi$
$283$	−5114.36	+	1963.22i	−1.07427	+	0.412372i	−0.244021	+	0.969770i	$0.578467\pi$
$284$	−4862.38	−	4378.11i	−1.01595	−	0.914764i
$285$	96.7533	+	484.727i	0.0201094	+	0.100746i
$286$	493.146	+	160.233i	0.101959	+	0.0331286i
$287$	4155.54	−	473.300i	0.854681	−	0.0973450i
$288$	331.435	−	650.478i	0.0678125	−	0.133089i
$289$	3341.05	−	3008.29i	0.680042	−	0.612313i
$290$	45.4586	+	146.058i	0.00920490	+	0.0295752i
$291$	460.643	−	511.595i	0.0927950	−	0.103059i
$292$	−1294.10	+	1598.08i	−0.259355	+	0.320277i
$293$	−6356.80	+	6356.80i	−1.26747	+	1.26747i	−0.320078	+	0.947391i	$0.603709\pi$
$293$	−6356.80	+	6356.80i	−1.26747	+	1.26747i	−0.947391	+	0.320078i	$0.896291\pi$
$294$	−6.97464	−	30.2212i	−0.00138357	−	0.00599502i
$295$	1735.05	+	6812.78i	0.342435	+	1.34459i
$296$	−315.656	+	140.539i	−0.0619837	+	0.0275969i
$297$	−1689.46	+	1368.10i	−0.330076	+	0.267290i
$298$	−307.502	−	199.694i	−0.0597755	−	0.0388187i
$299$	1567.27	−	2714.60i	0.303136	−	0.525048i
$300$	355.497	−	518.728i	0.0684154	−	0.0998292i
$301$	−3895.66	−	5886.20i	−0.745988	−	1.12716i
$302$	−112.003	−	219.819i	−0.0213413	−	0.0418847i
$303$	−637.845	−	244.846i	−0.120935	−	0.0464225i
$304$	−465.492	+	4428.86i	−0.0878218	+	0.835568i
$305$	1043.38	+	7162.49i	0.195881	+	1.34467i
$306$	77.5026	−	8.14585i	0.0144789	−	0.00152179i
$307$	−4948.22	−	4948.22i	−0.919901	−	0.919901i	0.0771208	−	0.997022i	$-0.475427\pi$
$307$	−4948.22	−	4948.22i	−0.919901	−	0.919901i	−0.997022	+	0.0771208i	$0.975427\pi$
$308$	9462.52	+	911.508i	1.75057	+	0.168630i
$309$	828.089	−	269.062i	0.152454	−	0.0495354i
$310$	58.6544	+	104.572i	0.0107463	+	0.0191590i
$311$	−368.077	−	1731.67i	−0.0671118	−	0.315736i	0.931768	−	0.363054i	$-0.118266\pi$
$311$	−368.077	−	1731.67i	−0.0671118	−	0.315736i	−0.998880	+	0.0473179i	$0.984933\pi$
$312$	4.25016	+	81.0978i	0.000771211	+	0.0147156i
$313$	7374.77	−	4789.23i	1.33178	−	0.864866i	0.334780	−	0.942296i	$-0.391338\pi$
$313$	7374.77	−	4789.23i	1.33178	−	0.864866i	0.996998	+	0.0774300i	$0.0246714\pi$
$314$	39.8049	−	122.507i	0.00715389	−	0.0220174i
$315$	−2982.80	−	4630.90i	−0.533529	−	0.828323i
$316$	1521.19	+	4681.75i	0.270803	+	0.833446i
$317$	5874.06	+	4756.72i	1.04076	+	0.842788i	0.987787	−	0.155808i	$-0.0497981\pi$
$317$	5874.06	+	4756.72i	1.04076	+	0.842788i	0.0529693	+	0.998596i	$0.483131\pi$
$318$	−36.6697	−	9.82561i	−0.00646646	−	0.00173268i
$319$	2495.94	−	5605.98i	0.438075	−	0.983933i
$320$	4423.89	−	3492.29i	0.772822	−	0.610077i
$321$	499.529	−	687.542i	0.0868566	−	0.119548i
$322$	−44.5531	+	141.285i	−0.00771070	+	0.0244519i
$323$	−1276.15	+	650.229i	−0.219835	+	0.112011i
$324$	4816.27	+	2780.67i	0.825835	+	0.476796i
$325$	541.885	−	7004.42i	0.0924873	−	1.19549i
$326$	243.911	+	422.467i	0.0414387	+	0.0717739i
$327$	−15.4669	+	295.127i	−0.00261567	+	0.0499099i
$328$	511.185	−	80.9638i	0.0860533	−	0.0136295i
$329$	4783.31	+	3047.57i	0.801558	+	0.510693i
$330$	63.0214	−	16.0500i	0.0105128	−	0.00267735i
$331$	413.143	+	3930.79i	0.0686054	+	0.652737i	0.973748	+	0.227629i	$0.0730973\pi$
$331$	413.143	+	3930.79i	0.0686054	+	0.652737i	−0.905143	+	0.425108i	$0.860236\pi$
$332$	1319.52	−	4924.51i	0.218126	−	0.814059i
$333$	−1437.33	−	3744.37i	−0.236532	−	0.616187i
$334$	−463.135	−	98.4425i	−0.0758732	−	0.0161273i
$335$	−4.29691	+	19.0485i	−0.000700792	+	0.00310665i
$336$	198.140	+	714.578i	0.0321709	+	0.116022i
$337$	5993.96	+	3054.08i	0.968878	+	0.493668i	0.865465	−	0.500970i	$-0.167023\pi$
$337$	5993.96	+	3054.08i	0.968878	+	0.493668i	0.103414	+	0.994638i	$0.467023\pi$
$338$	75.1260	+	115.684i	0.0120897	+	0.0186165i
$339$	181.143	−	38.5031i	0.0290216	−	0.00616874i
$340$	1725.85	+	584.569i	0.275287	+	0.0932432i
$341$	1000.03	−	4704.76i	0.158811	−	0.747147i
$342$	264.252	+	41.8535i	0.0417811	+	0.00661747i
$343$	−5234.80	−	3598.68i	−0.824060	−	0.566502i
$344$	−513.415	−	706.655i	−0.0804694	−	0.110757i
$345$	−15.6956	−	392.820i	−0.00244934	−	0.0613006i
$346$	224.709	+	23.6179i	0.0349145	+	0.00366966i
$347$	−614.351	−	758.660i	−0.0950435	−	0.117369i	0.727405	−	0.686208i	$-0.240726\pi$
$347$	−614.351	−	758.660i	−0.0950435	−	0.117369i	−0.822449	+	0.568839i	$0.807393\pi$
$348$	479.261	+	25.1170i	0.0738249	+	0.00386900i
$349$	12324.8			1.89034			0.945171	−	0.326577i	$-0.105895\pi$
$349$	12324.8			1.89034			0.945171	+	0.326577i	$0.105895\pi$
$350$	46.6340	+	328.737i	0.00712198	+	0.0502050i
$351$	−1899.37			−0.288835
$352$	1762.90	+	92.3895i	0.266939	+	0.0139897i
$353$	941.068	+	1162.12i	0.141892	+	0.175222i	0.843138	−	0.537697i	$-0.180706\pi$
$353$	941.068	+	1162.12i	0.141892	+	0.175222i	−0.701246	+	0.712920i	$0.747372\pi$
$354$	−56.5477	−	5.94341i	−0.00849005	−	0.000892341i
$355$	−8598.91	+	3178.81i	−1.28559	+	0.475249i
$356$	−4406.58	−	6065.14i	−0.656035	−	0.902955i
$357$	−158.037	+	178.615i	−0.0234292	+	0.0264798i
$358$	83.7536	+	13.2653i	0.0123646	+	0.00195835i
$359$	−313.348	+	1474.19i	−0.0460665	+	0.216726i	−0.995160	−	0.0982690i	$-0.968669\pi$
$359$	−313.348	+	1474.19i	−0.0460665	+	0.216726i	0.949093	+	0.314995i	$0.102003\pi$
$360$	−393.777	−	556.396i	−0.0576497	−	0.0814574i
$361$	1899.39	−	403.727i	0.276919	−	0.0588609i
$362$	133.658	+	205.815i	0.0194058	+	0.0298823i
$363$	−1576.83	−	803.436i	−0.227995	−	0.116169i
$364$	5923.83	+	5821.78i	0.853002	+	0.838308i
$365$	1139.11	+	2646.51i	0.163353	+	0.379519i
$366$	−57.2610	−	12.1712i	−0.00817781	−	0.00173825i
$367$	4321.45	+	11257.8i	0.614654	+	1.60123i	0.787524	+	0.616284i	$0.211363\pi$
$367$	4321.45	+	11257.8i	0.614654	+	1.60123i	−0.172870	+	0.984945i	$0.555304\pi$
$368$	916.713	−	3421.22i	0.129856	−	0.484629i
$369$	627.965	+	5974.69i	0.0885923	+	0.842900i
$370$	−15.6512	+	241.249i	−0.00219910	+	0.0338972i
$371$	−6897.04	+	3590.03i	−0.965165	+	0.502386i
$372$	371.534	−	58.8453i	0.0517827	−	0.00820157i
$373$	301.275	−	5748.68i	0.0418216	−	0.798003i	−0.894545	−	0.446979i	$-0.852500\pi$
$373$	301.275	−	5748.68i	0.0418216	−	0.798003i	0.936366	−	0.351025i	$-0.114167\pi$
$374$	94.2200	+	163.194i	0.0130267	+	0.0225630i
$375$	−411.815	−	778.955i	−0.0567094	−	0.107267i
$376$	607.818	+	350.924i	0.0833665	+	0.0481317i
$377$	4777.13	−	2434.07i	0.652612	−	0.332522i
$378$	87.6401	−	19.4258i	0.0119252	−	0.00264327i
$379$	−8265.46	+	11376.4i	−1.12023	+	1.54187i	−0.314821	+	0.949151i	$0.601945\pi$
$379$	−8265.46	+	11376.4i	−1.12023	+	1.54187i	−0.805411	+	0.592717i	$0.798055\pi$
$380$	5203.84	+	3472.09i	0.702504	+	0.468723i
$381$	−259.461	+	582.759i	−0.0348887	+	0.0783612i
$382$	−232.896	−	62.4044i	−0.0311937	−	0.00835834i
$383$	−6741.13	−	5458.86i	−0.899362	−	0.728289i	0.0635860	−	0.997976i	$-0.479746\pi$
$383$	−6741.13	−	5458.86i	−0.899362	−	0.728289i	−0.962948	+	0.269687i	$0.913080\pi$
$384$	56.8593	+	174.995i	0.00755622	+	0.0232557i
$385$	7296.14	−	11143.7i	0.965833	−	1.47515i
$386$	226.192	−	696.146i	0.0298260	−	0.0917951i
$387$	8503.24	−	5522.07i	1.11691	−	0.725329i
$388$	−455.993	−	8700.86i	−0.0596637	−	1.13845i
$389$	1806.74	+	8500.06i	0.235490	+	1.10789i	0.923919	+	0.382589i	$0.124967\pi$
$389$	1806.74	+	8500.06i	0.235490	+	1.10789i	−0.688429	+	0.725304i	$0.741699\pi$
$390$	51.6162	+	23.7538i	0.00670176	+	0.00308415i
$391$	1083.39	−	352.015i	0.140126	−	0.0455298i
$392$	−666.612	−	416.617i	−0.0858903	−	0.0536795i
$393$	−645.321	−	645.321i	−0.0828299	−	0.0828299i
$394$	−54.4802	+	5.72610i	−0.00696617	+	0.000732174i
$395$	6798.54	+	1163.55i	0.866005	+	0.148214i
$396$	−1427.32	+	13580.1i	−0.181125	+	1.72329i
$397$	122.607	+	47.0643i	0.0154999	+	0.00594984i	0.366106	−	0.930573i	$-0.380691\pi$
$397$	122.607	+	47.0643i	0.0154999	+	0.00594984i	−0.350606	+	0.936523i	$0.614024\pi$
$398$	−286.083	−	561.470i	−0.0360303	−	0.0707135i
$399$	−682.795	+	451.894i	−0.0856704	+	0.0566992i
$400$	−1457.03	−	7803.48i	−0.182129	−	0.975435i
$401$	−4334.70	+	7507.92i	−0.539812	+	0.934982i	0.459102	+	0.888384i	$0.348171\pi$
$401$	−4334.70	+	7507.92i	−0.539812	+	0.934982i	−0.998914	+	0.0465982i	$0.985162\pi$
$402$	−0.132452	−	0.0860155i	−1.64331e−5	−	1.06718e-5i
$403$	3265.88	−	2644.66i	0.403685	−	0.326898i
$404$	−7899.47	+	3517.07i	−0.972805	+	0.433121i
$405$	6587.36	−	4162.44i	0.808219	−	0.510700i
$406$	−195.530	+	161.170i	−0.0239015	+	0.0197013i
$407$	6857.78	−	6857.78i	0.835202	−	0.835202i
$408$	−18.5729	+	22.9356i	−0.00225367	+	0.00278305i
$409$	−1361.71	+	1512.33i	−0.164627	+	0.182836i	−0.819814	−	0.572630i	$-0.805923\pi$
$409$	−1361.71	+	1512.33i	−0.164627	+	0.182836i	0.655187	+	0.755467i	$0.272590\pi$
$410$	116.171	−	342.979i	0.0139934	−	0.0413135i
$411$	22.6168	−	20.3642i	0.00271436	−	0.00244402i
$412$	5002.90	−	9818.75i	0.598241	−	1.17411i
$413$	−9361.67	+	6926.71i	−1.11539	+	0.825281i
$414$	−202.378	−	65.7567i	−0.0240250	−	0.00780620i
$415$	−5248.75	−	4845.43i	−0.620846	−	0.573139i
$416$	1146.20	+	1032.04i	0.135089	+	0.121635i
$417$	−82.6015	+	31.7077i	−0.00970027	+	0.00372359i
$418$	167.443	+	624.904i	0.0195930	+	0.0731222i
$419$	1704.42	−	1238.33i	0.198726	−	0.144383i	−0.483972	−	0.875084i	$-0.660806\pi$
$419$	1704.42	−	1238.33i	0.198726	−	0.144383i	0.682698	+	0.730700i	$0.260806\pi$
$420$	1018.12	+	220.387i	0.118283	+	0.0256043i
$421$	−2910.63	−	2114.70i	−0.336949	−	0.244808i	0.406425	−	0.913684i	$-0.366775\pi$
$421$	−2910.63	−	2114.70i	−0.336949	−	0.244808i	−0.743373	+	0.668877i	$0.766775\pi$
$422$	144.701	−	376.960i	0.0166918	−	0.0434837i
$423$	−4437.05	+	6832.46i	−0.510016	+	0.785356i
$424$	−833.274	+	481.091i	−0.0954419	+	0.0551034i
$425$	1849.63	−	1759.91i	0.211106	−	0.200867i
$426$		−	74.1463i		−	0.00843286i
$427$	−10331.1	+	6084.94i	−1.17086	+	0.689627i
$428$	−1682.59	−	10623.5i	−0.190026	−	1.19978i
$429$	−927.111	−	2082.33i	−0.104339	−	0.234349i
$430$	−604.761	+	88.0969i	−0.0678237	+	0.00988003i
$431$	−6030.61	−	2685.00i	−0.673977	−	0.300074i	0.0410639	−	0.999157i	$-0.486925\pi$
$431$	−6030.61	−	2685.00i	−0.673977	−	0.300074i	−0.715041	+	0.699083i	$0.753592\pi$
$432$	−2073.08	+	555.480i	−0.230882	+	0.0618647i
$433$	696.794	−	4399.39i	0.0773344	−	0.488270i	−0.918373	−	0.395715i	$-0.870497\pi$
$433$	696.794	−	4399.39i	0.0773344	−	0.488270i	0.995708	−	0.0925548i	$-0.0295033\pi$
$434$	−123.645	+	155.430i	−0.0136754	+	0.0171910i
$435$	343.427	−	578.124i	0.0378530	−	0.0637216i
$436$	2502.76	+	2779.60i	0.274909	+	0.305318i
$437$	3905.53	−	204.680i	0.427521	−	0.0224054i
$438$	−23.2710	+	1.21958i	−0.00253866	+	0.000133045i
$439$	4446.25	+	4938.06i	0.483389	+	0.536858i	0.934666	−	0.355526i	$-0.115698\pi$
$439$	4446.25	+	4938.06i	0.483389	+	0.536858i	−0.451277	+	0.892384i	$0.649032\pi$
$440$	841.806	−	1417.09i	0.0912080	−	0.153539i
$441$	5234.27	−	7474.08i	0.565195	−	0.807048i
$442$	−25.7555	+	162.614i	−0.00277164	+	0.0174994i
$443$	−1194.22	+	319.991i	−0.128079	+	0.0343188i	−0.322289	−	0.946641i	$-0.604452\pi$
$443$	−1194.22	+	319.991i	−0.128079	+	0.0343188i	0.194210	+	0.980960i	$0.437786\pi$
$444$	692.906	+	308.502i	0.0740628	+	0.0329749i
$445$	−10394.6	+	1514.20i	−1.10730	+	0.161304i
$446$	−247.628	−	556.181i	−0.0262904	−	0.0590491i
$447$	252.138	+	1591.93i	0.0266794	+	0.168447i
$448$	8125.81	+	4597.78i	0.856938	+	0.484876i
$449$		−	13885.5i		−	1.45946i	−0.683737	−	0.729728i	$-0.739646\pi$
$449$		−	13885.5i		−	1.45946i	0.683737	−	0.729728i	$-0.260354\pi$
$450$	−472.762	+	62.8803i	−0.0495250	+	0.00658712i
$451$	−12580.6	+	7263.44i	−1.31352	+	0.758363i
$452$	1276.53	−	1965.68i	0.132838	−	0.204553i
$453$	−388.654	+	1012.48i	−0.0403103	+	0.105012i
$454$	161.956	+	117.668i	0.0167423	+	0.0121640i
$455$	11081.3	−	3554.80i	1.14176	−	0.366267i
$456$	−81.9715	+	59.5558i	−0.00841813	+	0.00611613i
$457$	314.000	+	1171.86i	0.0321407	+	0.119951i	0.980132	−	0.198344i	$-0.0635564\pi$
$457$	314.000	+	1171.86i	0.0321407	+	0.119951i	−0.947992	+	0.318295i	$0.896890\pi$
$458$	−210.653	+	80.8619i	−0.0214916	+	0.00824985i
$459$	−512.964	−	461.875i	−0.0521637	−	0.0469684i
$460$	−3655.93	−	3375.00i	−0.370562	−	0.342087i
$461$	12348.8	+	4012.37i	1.24759	+	0.405368i	0.857058	−	0.515220i	$-0.172290\pi$
$461$	12348.8	+	4012.37i	1.24759	+	0.405368i	0.390536	+	0.920588i	$0.372290\pi$
$462$	64.0753	+	86.5999i	0.00645250	+	0.00872076i
$463$	3402.16	−	6677.11i	0.341494	−	0.670220i	−0.654840	−	0.755767i	$-0.727264\pi$
$463$	3402.16	−	6677.11i	0.341494	−	0.670220i	0.996334	+	0.0855478i	$0.0272640\pi$
$464$	4502.16	−	4053.77i	0.450448	−	0.405585i
$465$	169.087	−	499.204i	0.0168628	−	0.0497850i
$466$	−382.178	+	424.451i	−0.0379915	+	0.0421938i
$467$	−2532.22	+	3127.03i	−0.250915	+	0.309854i	−0.887004	−	0.461761i	$-0.847218\pi$
$467$	−2532.22	+	3127.03i	−0.250915	+	0.309854i	0.636089	+	0.771615i	$0.280551\pi$
$468$	−8436.01	+	8436.01i	−0.833237	+	0.833237i
$469$	−31.9033	+	5.33750i	−0.00314106	+	0.000525507i
$470$	415.131	−	262.314i	0.0407416	−	0.0257439i
$471$	−517.290	+	230.312i	−0.0506061	+	0.0225313i
$472$	−1119.95	+	906.915i	−0.109216	+	0.0884410i
$473$	20561.5	+	13352.8i	1.99877	+	1.29802i
$474$	−27.8924	+	48.3110i	−0.00270283	+	0.00468143i
$475$	7697.55	−	4192.70i	0.743553	−	0.404998i
$476$	184.153	+	3012.80i	0.0177325	+	0.290108i
$477$	−5070.46	−	9951.33i	−0.486709	−	0.955220i
$478$	109.082	+	41.8727i	0.0104379	+	0.00400673i
$479$	−1326.91	+	12624.8i	−0.126573	+	1.20426i	0.728240	+	0.685322i	$0.240338\pi$
$479$	−1326.91	+	12624.8i	−0.126573	+	1.20426i	−0.854813	+	0.518936i	$0.826328\pi$
$480$	190.670	+	32.6325i	0.0181309	+	0.00310305i
$481$	8427.08	−	885.722i	0.798840	−	0.0839614i
$482$	−42.4370	−	42.4370i	−0.00401027	−	0.00401027i
$483$	592.601	−	270.036i	0.0558266	−	0.0254390i
$484$	−21301.7	+	6921.35i	−2.00054	+	0.650015i
$485$	−11089.9	−	5103.58i	−1.03828	−	0.477818i
$486$	40.3121	+	189.654i	0.00376254	+	0.0177014i
$487$	1118.70	+	21346.1i	0.104093	+	1.98621i	0.156936	+	0.987609i	$0.449838\pi$
$487$	1118.70	+	21346.1i	0.104093	+	1.98621i	−0.0528431	+	0.998603i	$0.516828\pi$
$488$	−1244.34	+	808.085i	−0.115428	+	0.0749596i
$489$	662.664	−	2039.47i	0.0612816	−	0.188605i
$490$	−474.952	+	277.358i	−0.0437880	+	0.0255709i
$491$	2670.78	+	8219.81i	0.245480	+	0.755509i	0.995557	+	0.0941587i	$0.0300161\pi$
$491$	2670.78	+	8219.81i	0.245480	+	0.755509i	−0.750078	+	0.661350i	$0.769984\pi$
$492$	−882.918	−	714.973i	−0.0809045	−	0.0655152i
$493$	1882.06	+	504.296i	0.171934	+	0.0460697i
$494$	−229.905	+	516.374i	−0.0209391	+	0.0470299i
$495$	15915.1	+	10618.8i	1.44511	+	0.964205i
$496$	2791.12	−	3841.64i	0.252671	−	0.347772i
$497$	−10259.3	−	11196.9i	−0.925937	−	1.01056i
$498$	51.4771	−	26.2289i	0.00463201	−	0.00236013i
$499$	−13436.3	−	7757.46i	−1.20539	−	0.695935i	−0.243645	−	0.969864i	$-0.578343\pi$
$499$	−13436.3	−	7757.46i	−1.20539	−	0.695935i	−0.961750	+	0.273929i	$0.911677\pi$
$500$	−10656.6	−	3285.65i	−0.953153	−	0.293878i
$501$	1040.69	+	1802.53i	0.0928039	+	0.160741i
$502$	−16.9174	+	322.803i	−0.00150411	+	0.0287000i
$503$	−7641.15	+	1210.24i	−0.677340	+	0.107280i	−0.485620	−	0.874170i	$-0.661406\pi$
$503$	−7641.15	+	1210.24i	−0.677340	+	0.107280i	−0.191719	+	0.981450i	$0.561406\pi$
$504$	606.725	−	952.286i	0.0536224	−	0.0841631i
$505$	−784.367	+	12090.3i	−0.0691166	+	1.06537i
$506$	−53.7853	−	511.733i	−0.00472539	−	0.0449591i
$507$	156.938	−	585.699i	0.0137472	−	0.0513054i
$508$	2893.29	+	7537.28i	0.252695	+	0.658293i
$509$	−6575.21	−	1397.60i	−0.572576	−	0.121705i	−0.0874809	−	0.996166i	$-0.527882\pi$
$509$	−6575.21	−	1397.60i	−0.572576	−	0.121705i	−0.485095	+	0.874461i	$0.661215\pi$
$510$	8.16374	+	18.9668i	0.000708817	+	0.00164679i
$511$	−3345.42	+	3404.06i	−0.289614	+	0.294691i
$512$	2590.31	+	1319.83i	0.223587	+	0.113923i
$513$	−1290.68	−	1987.48i	−0.111082	−	0.171051i
$514$	964.613	−	205.035i	0.0827768	−	0.0175947i
$515$	−8919.73	−	12603.3i	−0.763205	−	1.07839i
$516$	−398.647	+	1875.49i	−0.0340106	+	0.160007i
$517$	−19457.0	−	3081.69i	−1.65516	−	0.262152i
$518$	−379.780	+	127.056i	−0.0322135	+	0.0107771i
$519$	−583.813	−	803.549i	−0.0493768	−	0.0679613i
$520$	1350.76	−	499.341i	0.113913	−	0.0421107i
$521$	−20665.9	−	2172.07i	−1.73779	−	0.182649i	−0.818042	−	0.575158i	$-0.804940\pi$
$521$	−20665.9	−	2172.07i	−1.73779	−	0.182649i	−0.919748	+	0.392509i	$0.871607\pi$
$522$	−229.055	−	282.860i	−0.0192059	−	0.0237173i
$523$	−17558.1	−	920.183i	−1.46800	−	0.0769346i	−0.698513	−	0.715598i	$-0.746154\pi$
$523$	−17558.1	−	920.183i	−1.46800	−	0.0769346i	−0.769486	+	0.638663i	$0.779488\pi$
$524$	−11550.4			−0.962938
$525$	936.748	−	1119.31i	0.0778724	−	0.0930485i
$526$	−1133.03			−0.0939209
$527$	1525.13	+	79.9284i	0.126064	+	0.00660671i
$528$	−1620.89	−	2001.63i	−0.133598	−	0.164980i
$529$	9006.86	+	946.659i	0.740269	+	0.0778055i
$530$	26.8776	+	672.674i	0.00220281	+	0.0551304i
$531$	−9832.33	−	13533.0i	−0.803553	−	1.10600i
$532$	−2066.40	+	10154.7i	−0.168402	+	0.827559i
$533$	−12535.9	−	1985.50i	−1.01875	−	0.161353i
$534$	17.6635	−	83.1001i	0.00143141	−	0.00673426i
$535$	−14274.0	−	4834.78i	−1.15349	−	0.390702i
$536$	−3.91531	+	0.832225i	−0.000315514	+	6.70647e-5i
$537$	−203.021	−	312.625i	−0.0163147	−	0.0251225i
$538$	225.806	+	115.054i	0.0180951	+	0.00921993i
$539$	21658.5	+	4211.72i	1.73079	+	0.336571i
$540$	−663.434	+	2941.04i	−0.0528698	+	0.234375i
$541$	−2419.82	−	514.348i	−0.192303	−	0.0408753i	0.110753	−	0.993848i	$-0.464674\pi$
$541$	−2419.82	−	514.348i	−0.192303	−	0.0408753i	−0.303056	+	0.952973i	$0.598007\pi$
$542$	−204.970	−	533.966i	−0.0162440	−	0.0423170i
$543$	279.210	−	1042.03i	0.0220664	−	0.0823529i
$544$	58.5902	+	557.448i	0.00461771	+	0.0439346i
$545$	5078.62	−	1293.40i	0.399163	−	0.101657i
$546$	−4.10919	+	94.0321i	−0.000322083	+	0.00737034i
$547$	21015.5	−	3328.52i	1.64270	−	0.260178i	0.734467	−	0.678644i	$-0.237432\pi$
$547$	21015.5	−	3328.52i	1.64270	−	0.260178i	0.908232	+	0.418466i	$0.137432\pi$
$548$	20.1587	−	384.650i	0.00157142	−	0.0299844i
$549$	−8611.15	−	14915.0i	−0.669426	−	1.15948i
$550$	−603.877	−	982.501i	−0.0468171	−	0.0761709i
$551$	5793.18	+	3344.69i	0.447909	+	0.258600i
$552$	71.8034	−	36.5857i	0.00553651	−	0.00282099i
$553$	2472.51	+	11154.8i	0.190130	+	0.857777i
$554$	−81.1733	+	111.725i	−0.00622513	+	0.00856816i
$555$	834.151	−	658.491i	0.0637977	−	0.0503629i
$556$	−455.464	+	1022.99i	−0.0347410	+	0.0780295i
$557$	19374.5	+	5191.38i	1.47383	+	0.394912i	0.904243	−	0.427018i	$-0.140436\pi$
$557$	19374.5	+	5191.38i	1.47383	+	0.394912i	0.569588	+	0.821930i	$0.307103\pi$
$558$	−221.709	−	179.536i	−0.0168202	−	0.0136208i
$559$	6619.28	+	20372.0i	0.500833	+	1.54140i
$560$	11055.1	−	7120.68i	0.834221	−	0.537328i
$561$	255.979	−	787.823i	0.0192646	−	0.0592904i
$562$	−663.734	+	431.034i	−0.0498184	+	0.0323524i
$563$	−457.495	−	8729.52i	−0.0342471	−	0.653473i	−0.960789	−	0.277281i	$-0.910567\pi$
$563$	−457.495	−	8729.52i	−0.0342471	−	0.653473i	0.926542	−	0.376192i	$-0.122767\pi$
$564$	−320.318	−	1506.98i	−0.0239146	−	0.112509i
$565$	−1606.54	−	2864.22i	−0.119624	−	0.213272i
$566$	−747.248	+	242.795i	−0.0554932	+	0.0180308i
$567$	10508.2	+	7496.06i	0.778314	+	0.555211i
$568$	−1328.83	−	1328.83i	−0.0981626	−	0.0981626i
$569$	7807.41	−	820.592i	0.575226	−	0.0604587i	0.187551	−	0.982255i	$-0.439945\pi$
$569$	7807.41	−	820.592i	0.575226	−	0.0604587i	0.387675	+	0.921796i	$0.373278\pi$
$570$	10.2192	+	70.1518i	0.000750937	+	0.00515498i
$571$	−192.563	+	1832.11i	−0.0141129	+	0.134276i	−0.999310	−	0.0371522i	$-0.988171\pi$
$571$	−192.563	+	1832.11i	−0.0141129	+	0.134276i	0.985197	+	0.171428i	$0.0548380\pi$
$572$	−26932.4	−	10338.4i	−1.96871	−	0.755715i
$573$	481.188	+	944.384i	0.0350819	+	0.0688520i
$574$	598.735	−	36.5968i	0.0435378	−	0.00266119i
$575$	−6568.54	+	2335.88i	−0.476395	+	0.169414i
$576$	−6705.40	+	11614.1i	−0.485055	+	0.840140i
$577$	−4945.07	−	3211.37i	−0.356787	−	0.231700i	0.353782	−	0.935328i	$-0.384896\pi$
$577$	−4945.07	−	3211.37i	−0.356787	−	0.231700i	−0.710569	+	0.703628i	$0.751562\pi$
$578$	501.106	−	405.788i	0.0360610	−	0.0292016i
$579$	−2939.50	+	1308.75i	−0.210987	+	0.0939374i
$580$	−2100.37	−	8247.24i	−0.150368	−	0.590428i
$581$	4144.43	−	11083.5i	0.295938	−	0.791428i
$582$	69.8162	−	69.8162i	0.00497247	−	0.00497247i
$583$	16995.9	−	20988.1i	1.20737	−	1.49098i
$584$	−395.199	+	438.913i	−0.0280025	+	0.0310999i
$585$	4967.64	+	15960.9i	0.351088	+	1.12804i
$586$	−958.177	+	862.746i	−0.0675459	+	0.0608186i
$587$	4694.39	−	9213.25i	0.330082	−	0.647822i	−0.665004	−	0.746840i	$-0.731570\pi$
$587$	4694.39	−	9213.25i	0.330082	−	0.647822i	0.995086	+	0.0990178i	$0.0315701\pi$
$588$	299.511	+	1699.38i	0.0210061	+	0.119186i
$589$	4986.60	+	1620.24i	0.348844	+	0.113346i
$590$	197.367	+	988.792i	0.0137720	+	0.0689965i
$591$	178.956	+	161.133i	0.0124556	+	0.0112151i
$592$	8938.74	−	3431.26i	0.620575	−	0.238216i
$593$	−4143.36	−	15463.2i	−0.286927	−	1.07082i	−0.947420	−	0.319993i	$-0.896319\pi$
$593$	−4143.36	−	15463.2i	−0.286927	−	1.07082i	0.660493	−	0.750832i	$-0.270347\pi$
$594$	−252.245	+	183.266i	−0.0174238	+	0.0126591i
$595$	3857.16	+	1734.62i	0.265761	+	0.119517i
$596$	16503.2	+	11990.3i	1.13422	+	0.824060i
$597$	−992.714	+	2586.11i	−0.0680554	+	0.177290i
$598$	244.851	−	377.038i	0.0167437	−	0.0257830i
$599$	−4338.14	+	2504.62i	−0.295912	+	0.170845i	−0.640605	−	0.767871i	$-0.721316\pi$
$599$	−4338.14	+	2504.62i	−0.295912	+	0.170845i	0.344693	+	0.938716i	$0.387983\pi$
$600$	109.762	−	143.439i	0.00746833	−	0.00975977i
$601$		−	11001.0i		−	0.746656i	−0.927699	−	0.373328i	$-0.878217\pi$
$601$		−	11001.0i		−	0.746656i	0.927699	−	0.373328i	$-0.121783\pi$
$602$	−513.778	−	872.300i	−0.0347841	−	0.0590570i
$603$	−7.26838	−	45.8907i	−0.000490864	−	0.00309919i
$604$	5582.79	+	12539.2i	0.376094	+	0.844721i
$605$	−5294.09	+	30933.1i	−0.355761	+	2.07869i
$606$	−89.5183	−	39.8561i	−0.00600071	−	0.00267169i
$607$	17702.6	−	4743.40i	1.18374	−	0.317181i	0.387328	−	0.921942i	$-0.373398\pi$
$607$	17702.6	−	4743.40i	1.18374	−	0.317181i	0.796407	+	0.604761i	$0.206731\pi$
$608$	−301.037	+	1900.67i	−0.0200800	+	0.126780i
$609$	1101.65	+	164.686i	0.0733023	+	0.0109580i
$610$	95.6760	+	1033.69i	0.00635051	+	0.0686112i
$611$	−11516.8	−	12790.7i	−0.762553	−	0.846901i
$612$	−4329.72	+	226.911i	−0.285978	+	0.0149875i
$613$	−1521.68	+	79.7476i	−0.100261	+	0.00525445i	−0.102400	−	0.994743i	$-0.532652\pi$
$613$	−1521.68	+	79.7476i	−0.100261	+	0.00525445i	0.00213957	+	0.999998i	$0.499319\pi$
$614$	−671.572	−	745.857i	−0.0441408	−	0.0490233i
$615$	−1462.16	+	629.344i	−0.0958696	+	0.0412644i
$616$	2700.35	+	403.678i	0.176624	+	0.0264036i
$617$	−3764.39	+	23767.4i	−0.245622	+	1.55079i	0.488979	+	0.872295i	$0.337369\pi$
$617$	−3764.39	+	23767.4i	−0.245622	+	1.55079i	−0.734601	+	0.678499i	$0.762631\pi$
$618$	120.624	−	32.3210i	0.00785145	−	0.00210379i
$619$	3861.07	+	1719.06i	0.250710	+	0.111623i	0.528244	−	0.849092i	$-0.322851\pi$
$619$	3861.07	+	1719.06i	0.250710	+	0.111623i	−0.277534	+	0.960716i	$0.589517\pi$
$620$	−2954.32	−	5980.74i	−0.191368	−	0.387407i
$621$	766.625	+	1721.87i	0.0495388	+	0.111266i
$622$	−39.7202	−	250.783i	−0.00256050	−	0.0161664i
$623$	−8830.78	−	14993.0i	−0.567893	−	0.964177i
$624$		−	2250.32i		−	0.144367i
$625$	−11019.1	+	11077.9i	−0.705223	+	0.708986i
$626$	1092.21	−	630.587i	0.0697339	−	0.0402609i
$627$	1548.92	−	2385.12i	0.0986566	−	0.151918i
$628$	−2568.25	+	6690.52i	−0.163192	+	0.425129i
$629$	2491.29	+	1810.03i	0.157924	+	0.114738i
$630$	−392.455	−	685.656i	−0.0248187	−	0.0433606i
$631$	13129.2	−	9538.91i	0.828311	−	0.601803i	−0.0907699	−	0.995872i	$-0.528933\pi$
$631$	13129.2	−	9538.91i	0.828311	−	0.601803i	0.919081	+	0.394069i	$0.128933\pi$
$632$	365.937	+	1365.69i	0.0230319	+	0.0859563i
$633$	−1657.08	+	636.094i	−0.104049	+	0.0399407i
$634$	805.614	+	725.379i	0.0504654	+	0.0454392i
$635$	11234.6	+	1322.13i	0.702100	+	0.0826255i
$636$	2008.74	+	652.679i	0.125238	+	0.0406924i
$637$	12390.2	+	14768.4i	0.770673	+	0.918597i
$638$	399.564	−	784.189i	0.0247945	−	0.0486620i
$639$	16210.6	−	14596.1i	1.00357	−	0.903620i
$640$	2663.39	−	1884.95i	0.164499	−	0.116421i
$641$	9413.18	−	10454.4i	0.580029	−	0.644187i	−0.379702	−	0.925109i	$-0.623974\pi$
$641$	9413.18	−	10454.4i	0.580029	−	0.644187i	0.959731	+	0.280922i	$0.0906402\pi$
$642$	76.7065	−	94.7246i	0.00471552	−	0.00582318i
$643$	−1218.63	+	1218.63i	−0.0747406	+	0.0747406i	−0.743489	−	0.668748i	$-0.766830\pi$
$643$	−1218.63	+	1218.63i	−0.0747406	+	0.0747406i	0.668748	+	0.743489i	$0.266830\pi$
$644$	2886.73	−	7720.00i	0.176635	−	0.472377i
$645$	2066.66	+	1716.50i	0.126162	+	0.104786i
$646$	−187.658	+	83.5509i	−0.0114293	+	0.00508865i
$647$	−16835.0	+	13632.7i	−1.02295	+	0.828371i	−0.985285	−	0.170919i	$-0.945326\pi$
$647$	−16835.0	+	13632.7i	−1.02295	+	0.828371i	−0.0376678	+	0.999290i	$0.511993\pi$
$648$	1339.61	+	869.955i	0.0812114	+	0.0527393i
$649$	20224.5	−	35029.9i	1.22324	−	2.11871i
$650$	130.189	−	999.149i	0.00785602	−	0.0602921i
$651$	871.454	−	53.2664i	0.0524654	−	0.00320688i
$652$	−12321.5	−	24182.2i	−0.740101	−	1.45253i
$653$	22899.5	+	8790.30i	1.37232	+	0.526785i	0.929167	−	0.369659i	$-0.120526\pi$
$653$	22899.5	+	8790.30i	1.37232	+	0.526785i	0.443155	+	0.896445i	$0.353859\pi$
$654$	−4.43054	+	42.1538i	−0.000264905	+	0.00252040i
$655$	−7525.85	+	14327.4i	−0.448945	+	0.854684i
$656$	−14263.1	+	1499.11i	−0.848901	+	0.0892231i
$657$	−4847.67	−	4847.67i	−0.287862	−	0.287862i
$658$	662.221	+	472.396i	0.0392341	+	0.0279877i
$659$	−9485.44	+	3082.01i	−0.560698	+	0.182182i	−0.575635	−	0.817707i	$-0.695245\pi$
$659$	−9485.44	+	3082.01i	−0.560698	+	0.182182i	0.0149371	+	0.999888i	$0.495245\pi$
$660$	−3548.17	+	708.228i	−0.209261	+	0.0417693i
$661$	1796.71	+	8452.84i	0.105724	+	0.497394i	0.998866	+	0.0476176i	$0.0151629\pi$
$661$	1796.71	+	8452.84i	0.105724	+	0.497394i	−0.893141	+	0.449776i	$0.851504\pi$
$662$	29.6677	+	566.094i	0.00174180	+	0.0332355i
$663$	606.985	−	394.181i	0.0355556	−	0.0230901i
$664$	452.490	−	1392.62i	0.0264458	−	0.0813919i
$665$	11249.8	+	9179.70i	0.656011	+	0.535299i
$666$	−177.758	−	547.082i	−0.0103423	−	0.0318303i
$667$	−4134.74	−	3348.24i	−0.240026	−	0.194370i
$668$	25444.9	+	6817.94i	1.47379	+	0.394901i
$669$	−1088.55	+	2444.92i	−0.0629084	+	0.141295i
$670$	−0.758411	+	2.69599i	−4.37313e−5	+	0.000155455i
$671$	24478.3	−	33691.5i	1.40831	−	1.93837i
$672$	69.3432	+	312.845i	0.00398062	+	0.0179587i
$673$	−3714.74	+	1892.75i	−0.212768	+	0.108411i	−0.557127	−	0.830427i	$-0.688096\pi$
$673$	−3714.74	+	1892.75i	−0.212768	+	0.108411i	0.344359	+	0.938838i	$0.388096\pi$
$674$	835.569	+	482.416i	0.0477521	+	0.0275697i
$675$	3215.89	+	2739.24i	0.183377	+	0.156197i
$676$	−3837.12	−	6646.09i	−0.218316	−	0.378134i
$677$	7.58314	−	144.695i	0.000430493	−	0.00821429i	−0.998406	−	0.0564427i	$-0.982024\pi$
$677$	7.58314	−	144.695i	0.000430493	−	0.00821429i	0.998836	+	0.0482284i	$0.0153575\pi$
$678$	26.2335	−	4.15497i	0.00148597	−	0.000235355i
$679$	882.873	−	20203.1i	0.0498992	−	1.14186i
$680$	486.225	+	193.609i	0.0274204	+	0.0109185i
$681$	−91.9865	−	875.193i	−0.00517611	−	0.0492474i
$682$	178.545	−	666.339i	0.0100247	−	0.0374127i
$683$	6756.00	+	17600.0i	0.378493	+	0.986009i	0.982039	+	0.188680i	$0.0604210\pi$
$683$	6756.00	+	17600.0i	0.378493	+	0.986009i	−0.603545	+	0.797329i	$0.706246\pi$
$684$	−14559.8	−	3094.79i	−0.813903	−	0.173000i
$685$	−463.997	−	275.632i	−0.0258809	−	0.0153742i
$686$	−722.749	−	554.718i	−0.0402255	−	0.0308735i
$687$	883.782	+	450.309i	0.0490806	+	0.0250078i
$688$	13182.5	+	20299.3i	0.730493	+	1.12486i
$689$	23080.2	−	4905.85i	1.27618	−	0.271260i
$690$	0.700546	−	56.3799i	3.86512e−5	−	0.00311065i
$691$	−3070.04	+	14443.4i	−0.169015	+	0.795155i	0.809195	+	0.587540i	$0.199904\pi$
$691$	−3070.04	+	14443.4i	−0.169015	+	0.795155i	−0.978211	+	0.207615i	$0.933430\pi$
$692$	−12415.9	−	1966.49i	−0.682056	−	0.108027i
$693$	−6319.77	+	31056.5i	−0.346419	+	1.70236i
$694$	−82.2966	−	113.271i	−0.00450135	−	0.00619557i
$695$	972.180	+	1231.52i	0.0530603	+	0.0672146i
$696$	137.085	+	14.4082i	0.00746579	+	0.000784686i
$697$	−2902.76	−	3584.62i	−0.157748	−	0.194802i
$698$	1765.23	+	92.5117i	0.0957234	+	0.00501665i
$699$	2510.75			0.135859
$700$	−1633.76	−	18400.3i	−0.0882148	−	0.993520i
$701$	30294.7			1.63226			0.816132	−	0.577866i	$-0.196114\pi$
$701$	30294.7			1.63226			0.816132	+	0.577866i	$0.196114\pi$
$702$	−272.040	−	14.2570i	−0.0146261	−	0.000766519i
$703$	6653.27	+	8216.10i	0.356945	+	0.440791i
$704$	−32250.8	−	3389.69i	−1.72656	−	0.181468i
$705$	−2078.01	−	584.568i	−0.111010	−	0.0312285i
$706$	126.063	+	173.510i	0.00672015	+	0.00924950i
$707$	−19032.9	+	6367.50i	−1.01246	+	0.338719i
$708$	3124.46	+	494.865i	0.165853	+	0.0262686i
$709$	3382.28	−	15912.4i	0.179160	−	0.842879i	−0.793121	−	0.609064i	$-0.791545\pi$
$709$	3382.28	−	15912.4i	0.179160	−	0.842879i	0.972281	−	0.233816i	$-0.0751213\pi$
$710$	−1255.45	+	390.744i	−0.0663609	+	0.0206540i
$711$	−16053.0	+	3412.18i	−0.846745	+	0.179981i
$712$	−1172.74	−	1805.85i	−0.0617277	−	0.0950523i
$713$	−3715.68	−	1893.23i	−0.195166	−	0.0994419i
$714$	−23.9758	+	24.3961i	−0.00125668	+	0.00127871i
$715$	−30372.3	+	26671.6i	−1.58862	+	1.39505i
$716$	−4614.68	−	980.880i	−0.240864	−	0.0511972i
$717$	−184.069	−	479.516i	−0.00958742	−	0.0249761i
$718$	−55.9451	+	208.790i	−0.00290787	+	0.0108523i
$719$	−2937.64	−	27949.8i	−0.152372	−	1.44972i	−0.757105	−	0.653293i	$-0.773387\pi$
$719$	−2937.64	−	27949.8i	−0.152372	−	1.44972i	0.604733	−	0.796428i	$-0.293280\pi$
$720$	10089.8	+	15967.8i	0.522256	+	0.826507i
$721$	13743.4	−	21570.9i	0.709889	−	1.11421i
$722$	275.072	−	43.5672i	0.0141789	−	0.00224571i
$723$	−13.8073	+	263.459i	−0.000710233	+	0.0135521i
$724$	−6826.68	−	11824.2i	−0.350430	−	0.606963i
$725$	−11598.7	−	2768.28i	−0.594157	−	0.141809i
$726$	−219.813	−	126.909i	−0.0112369	−	0.00648765i
$727$	−3575.46	+	1821.79i	−0.182402	+	0.0929386i	−0.542807	−	0.839857i	$-0.682639\pi$
$727$	−3575.46	+	1821.79i	−0.182402	+	0.0929386i	0.360405	+	0.932796i	$0.382639\pi$
$728$	1611.57	+	1758.86i	0.0820450	+	0.0895434i
$729$	−10559.9	+	14534.5i	−0.536500	+	0.738428i
$730$	143.286	+	387.600i	0.00726473	+	0.0196516i
$731$	−3166.25	+	7111.51i	−0.160202	+	0.359820i
$732$	3145.95	+	842.955i	0.158849	+	0.0425635i
$733$	3499.49	+	2833.83i	0.176339	+	0.142797i	0.713427	−	0.700730i	$-0.247142\pi$
$733$	3499.49	+	2833.83i	0.176339	+	0.142797i	−0.537087	+	0.843527i	$0.680475\pi$
$734$	534.443	+	1644.85i	0.0268755	+	0.0827144i
$735$	2303.11	+	735.741i	0.115581	+	0.0369228i
$736$	472.964	−	1455.63i	0.0236871	−	0.0729014i
$737$	94.2252	−	61.1906i	0.00470940	−	0.00305832i
$738$	45.0941	+	860.447i	0.00224924	+	0.0429180i
$739$	3247.74	+	15279.4i	0.161664	+	0.760570i	0.982029	+	0.188730i	$0.0604371\pi$
$739$	3247.74	+	15279.4i	0.161664	+	0.760570i	−0.820365	+	0.571841i	$0.806230\pi$
$740$	1572.03	−	13358.1i	0.0780931	−	0.663587i
$741$	2363.14	−	767.831i	0.117155	−	0.0380661i
$742$	−1014.78	+	462.416i	−0.0502074	+	0.0228785i
$743$	−9749.84	−	9749.84i	−0.481409	−	0.481409i	0.424172	−	0.905581i	$-0.360565\pi$
$743$	−9749.84	−	9749.84i	−0.481409	−	0.481409i	−0.905581	+	0.424172i	$0.860565\pi$
$744$	107.449	−	11.2933i	0.00529470	−	0.000556496i
$745$	25626.0	−	12658.6i	1.26022	−	0.622515i
$746$	86.3011	−	821.100i	0.00423553	−	0.0402984i
$747$	15868.0	+	6091.15i	0.777214	+	0.298345i
$748$	−4759.63	−	9341.30i	−0.232660	−	0.456620i
$749$	−1523.07	−	24917.9i	−0.0743016	−	1.21560i
$750$	−53.1358	−	114.658i	−0.00258699	−	0.00558229i
$751$	2809.83	−	4866.77i	0.136528	−	0.236473i	−0.789652	−	0.613554i	$-0.789739\pi$
$751$	2809.83	−	4866.77i	0.136528	−	0.236473i	0.926180	+	0.377082i	$0.123072\pi$
$752$	−16310.8	−	10592.3i	−0.790948	−	0.513647i
$753$	1104.30	−	894.241i	0.0534433	−	0.0432775i
$754$	702.481	−	312.765i	0.0339295	−	0.0151064i
$755$	19191.5	+	1245.06i	0.925101	+	0.0600164i
$756$	−4925.80	+	824.100i	−0.236970	+	0.0396458i
$757$	19576.8	−	19576.8i	0.939937	−	0.939937i	−0.0583588	−	0.998296i	$-0.518587\pi$
$757$	19576.8	−	19576.8i	0.939937	−	0.939937i	0.998296	+	0.0583588i	$0.0185867\pi$
$758$	−1269.22	+	1567.36i	−0.0608183	+	0.0751044i
$759$	−1513.52	+	1680.94i	−0.0723813	+	0.0803875i
$760$	1440.38	+	1074.09i	0.0687477	+	0.0512651i
$761$	−3379.65	+	3043.05i	−0.160988	+	0.144955i	−0.745688	−	0.666295i	$-0.767879\pi$
$761$	−3379.65	+	3043.05i	−0.160988	+	0.144955i	0.584700	+	0.811250i	$0.301212\pi$
$762$	−41.5359	+	81.5188i	−0.00197465	+	0.00387548i
$763$	5163.55	+	6978.71i	0.244998	+	0.331122i
$764$	12757.9	+	4145.29i	0.604141	+	0.196297i
$765$	−2539.64	+	5518.56i	−0.120027	+	0.260816i
$766$	−924.532	−	832.452i	−0.0436093	−	0.0392659i
$767$	32993.2	−	12664.9i	1

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.143226 + 0.00750617i) q^{2} +(-0.396770 - 0.489971i) q^{3} +(-7.93572 - 0.834078i) q^{4} +(-6.20528 + 9.30024i) q^{5} +(-0.0531501 - 0.0731549i) q^{6} +(-18.1483 - 3.69305i) q^{7} +(-2.26360 - 0.358519i) q^{8} +(5.53097 - 26.0212i) q^{9} +(-0.958568 + 1.28546i) q^{10} +(62.9213 - 13.3743i) q^{11} +(2.73998 + 4.21921i) q^{12} +(50.0770 + 25.5155i) q^{13} +(-2.57160 - 0.665166i) q^{14} +(7.01892 - 0.649656i) q^{15} +(62.1190 + 13.2038i) q^{16} +(7.31965 + 19.0683i) q^{17} +(0.987500 - 3.68540i) q^{18} +(7.32981 + 69.7385i) q^{19} +(57.0005 - 68.6284i) q^{20} +(5.39123 + 10.3574i) q^{21} +(9.11238 - 1.44326i) q^{22} +(2.91889 - 55.6957i) q^{23} +(0.722465 + 1.25135i) q^{24} +(-47.9890 - 115.421i) q^{25} +(6.98083 + 4.03038i) q^{26} +(-30.1116 + 15.3426i) q^{27} +(140.940 + 44.4441i) q^{28} +(56.0721 - 77.1766i) q^{29} +(1.01017 - 0.0403626i) q^{30} +(30.4126 - 68.3077i) q^{31} +(26.5077 + 7.10273i) q^{32} +(-31.5183 - 25.5231i) q^{33} +(0.905236 + 2.78603i) q^{34} +(146.962 - 145.867i) q^{35} +(-65.5959 + 201.883i) q^{36} +(126.443 - 82.1133i) q^{37} +(0.526352 + 10.0434i) q^{38} +(-7.36723 - 34.6601i) q^{39} +(17.3806 - 18.8273i) q^{40} +(-214.776 + 69.7848i) q^{41} +(0.694421 + 1.52392i) q^{42} +(269.498 + 269.498i) q^{43} +(-510.481 + 53.6537i) q^{44} +(207.682 + 212.908i) q^{45} +(0.836123 - 7.95518i) q^{46} +(-285.901 - 109.747i) q^{47} +(-18.1775 - 35.6753i) q^{48} +(315.723 + 134.045i) q^{49} +(-6.00692 - 16.8916i) q^{50} +(6.43871 - 11.1522i) q^{51} +(-376.115 - 244.252i) q^{52} +(326.272 - 264.210i) q^{53} +(-4.42793 + 1.97144i) q^{54} +(-266.060 + 668.175i) q^{55} +(39.7565 + 14.8661i) q^{56} +(31.2616 - 31.2616i) q^{57} +(8.61030 - 10.6328i) q^{58} +(420.752 - 467.292i) q^{59} +(-56.2420 - 0.698833i) q^{60} +(481.108 - 433.191i) q^{61} +(4.86861 - 9.55518i) q^{62} +(-196.475 + 451.814i) q^{63} +(-479.445 - 155.781i) q^{64} +(-548.043 + 307.398i) q^{65} +(-4.32267 - 3.89215i) q^{66} +(1.63055 - 0.625910i) q^{67} +(-42.1822 - 157.426i) q^{68} +(-28.4474 + 20.6682i) q^{69} +(22.1437 - 19.7889i) q^{70} +(663.379 + 481.973i) q^{71} +(-21.8490 + 56.9185i) q^{72} +(140.357 - 216.131i) q^{73} +(18.7264 - 10.8117i) q^{74} +(-37.5124 + 69.3089i) q^{75} -559.538i q^{76} +(-1191.31 + 10.3501i) q^{77} +(-0.795016 - 5.01953i) q^{78} +(-250.925 - 563.586i) q^{79} +(-508.264 + 495.788i) q^{80} +(-636.705 - 283.479i) q^{81} +(-31.2853 + 8.38288i) q^{82} +(-99.9493 + 631.055i) q^{83} +(-34.1444 - 86.6904i) q^{84} +(-222.761 - 50.2499i) q^{85} +(36.5763 + 40.6221i) q^{86} +(-60.0620 + 3.14772i) q^{87} +(-147.224 + 7.71566i) q^{88} +(628.670 + 698.208i) q^{89} +(28.1474 + 32.0529i) q^{90} +(-814.584 - 648.001i) q^{91} +(-69.6180 + 439.551i) q^{92} +(-45.5356 + 12.2012i) q^{93} +(-40.1247 - 17.8647i) q^{94} +(-694.068 - 364.578i) q^{95} +(-7.03736 - 15.8062i) q^{96} +(170.812 + 1078.46i) q^{97} +(44.2136 + 21.5687i) q^{98} -1711.26i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

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