LMFDB - Embedded newform 175.4.x.a.17.30

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			17.30
Character	$\chi$	$=$	175.17
Dual form			175.4.x.a.103.30

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{20}\right)$

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	−0.0270001	−	0.999635i	$-0.508595\pi$
$2$	0.143226	−	0.00750617i	0.0506381	−	0.00265383i	0.0776382	+	0.996982i	$0.475262\pi$
$3$	−0.396770	+	0.489971i	−0.0763585	+	0.0942949i	−0.813894	−	0.581014i	$-0.802656\pi$
$3$	−0.396770	+	0.489971i	−0.0763585	+	0.0942949i	0.737535	+	0.675309i	$0.235990\pi$
$4$	−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	0.960472	−	0.278377i	$-0.0897963\pi$
$11$	62.9213	+	13.3743i	1.72468	+	0.366592i	0.764209	+	0.644969i	$0.223130\pi$
$12$	2.73998	−	4.21921i	0.0659138	−	0.101498i
$13$	50.0770	−	25.5155i	1.06837	−	0.544364i	0.170836	−	0.985299i	$-0.445353\pi$
$13$	50.0770	−	25.5155i	1.06837	−	0.544364i	0.897539	+	0.440935i	$0.145353\pi$
$14$	−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	−0.871404	−	0.490566i	$-0.836790\pi$
$17$	7.31965	−	19.0683i	0.104428	−	0.272044i	0.975832	+	0.218522i	$0.0701234\pi$
$18$	0.987500	+	3.68540i	0.0129309	+	0.0482587i
$19$	7.32981	−	69.7385i	0.0885039	−	0.842058i	−0.856752	−	0.515728i	$-0.827521\pi$
$19$	7.32981	−	69.7385i	0.0885039	−	0.842058i	0.945256	−	0.326330i	$-0.105812\pi$
$20$	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	0.979421	+	0.201828i	$0.0646883\pi$
$23$	2.91889	+	55.6957i	0.0264622	+	0.504928i	−0.952959	+	0.303100i	$0.901978\pi$
$24$	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	0.949883	−	0.312607i	$-0.101202\pi$
$29$	56.0721	+	77.1766i	0.359046	+	0.494184i	−0.590837	+	0.806791i	$0.701202\pi$
$30$	1.01017	+	0.0403626i	0.00614770	+	0.000245639i
$31$	30.4126	+	68.3077i	0.176202	+	0.395756i	0.979958	−	0.199203i	$-0.0638352\pi$
$31$	30.4126	+	68.3077i	0.176202	+	0.395756i	−0.803756	+	0.594958i	$0.797169\pi$
$32$	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	0.794087	−	0.607804i	$-0.207949\pi$
$37$	126.443	+	82.1133i	0.561816	+	0.364847i	−0.232272	+	0.972651i	$0.574616\pi$
$38$	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	−0.130078	−	0.991504i	$-0.541523\pi$
$41$	−214.776	−	69.7848i	−0.818105	−	0.265819i	−0.688027	+	0.725685i	$0.741523\pi$
$42$	0.694421	−	1.52392i	0.00255123	−	0.00559873i
$43$	269.498	−	269.498i	0.955768	−	0.955768i	−0.0432941	−	0.999062i	$-0.513785\pi$
$43$	269.498	−	269.498i	0.955768	−	0.955768i	0.999062	+	0.0432941i	$0.0137852\pi$
$44$	−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	−0.758966	−	0.651131i	$-0.774295\pi$
$47$	−285.901	+	109.747i	−0.887296	+	0.340601i	−0.128330	+	0.991732i	$0.540962\pi$
$48$	−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	0.950837	−	0.309692i	$-0.100226\pi$
$53$	326.272	+	264.210i	0.845603	+	0.684756i	−0.105234	+	0.994447i	$0.533559\pi$
$54$	−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	0.999434	+	0.0336477i	$0.0107124\pi$
$59$	420.752	+	467.292i	0.928428	+	1.03112i	−0.0710059	+	0.997476i	$0.522621\pi$
$60$	−56.2420	+	0.698833i	−0.121014	+	0.00150365i
$61$	481.108	+	433.191i	1.00983	+	0.909253i	0.995883	−	0.0906494i	$-0.0288943\pi$
$61$	481.108	+	433.191i	1.00983	+	0.909253i	0.0139453	+	0.999903i	$0.495561\pi$
$62$	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	0.359854	−	0.933009i	$-0.382826\pi$
$67$	1.63055	+	0.625910i	0.00297319	+	0.00114130i	−0.356881	+	0.934150i	$0.616160\pi$
$68$	−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	0.126370	−	0.991983i	$-0.459667\pi$
$71$	663.379	−	481.973i	1.10885	−	0.805629i	0.982483	+	0.186354i	$0.0596672\pi$
$72$	−21.8490	−	56.9185i	−0.0357629	−	0.0931655i
$73$	140.357	+	216.131i	0.225035	+	0.346523i	0.933096	−	0.359628i	$-0.117096\pi$
$73$	140.357	+	216.131i	0.225035	+	0.346523i	−0.708061	+	0.706151i	$0.750430\pi$
$74$	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	0.641997	+	0.766707i	$0.278106\pi$
$79$	−250.925	+	563.586i	−0.357357	+	0.802638i	−0.999354	+	0.0359305i	$0.988561\pi$
$80$	−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	−0.961306	−	0.275485i	$-0.911162\pi$
$83$	−99.9493	−	631.055i	−0.132179	−	0.834546i	0.829126	−	0.559061i	$-0.188838\pi$
$84$	−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	−0.241568	−	0.970384i	$-0.577662\pi$
$89$	628.670	−	698.208i	0.748751	−	0.831572i	0.990319	+	0.138812i	$0.0443283\pi$
$90$	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	−0.721117	−	0.692813i	$-0.756371\pi$
$97$	170.812	−	1078.46i	0.178797	−	1.12888i	0.899914	−	0.436067i	$-0.143629\pi$
$98$	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	0.885093	−	0.465414i	$-0.154094\pi$
$101$	938.483	+	541.833i	0.924580	+	0.533806i	0.0394865	+	0.999220i	$0.487428\pi$
$102$	1.00590	+	1.54895i	0.000976462	+	0.00150362i
$103$	−494.917	−	1289.30i	−0.473453	−	1.23339i	−0.937627	−	0.347643i	$-0.886982\pi$
$103$	−494.917	−	1289.30i	−0.473453	−	1.23339i	0.464174	−	0.885744i	$-0.346351\pi$
$104$	−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	−0.608591	−	0.793484i	$-0.708265\pi$
$107$	348.876	−	1302.02i	0.315206	−	1.17637i	0.923797	−	0.382882i	$-0.125068\pi$
$108$	251.754	+	96.6392i	0.224306	+	0.0861029i
$109$	−348.345	+	313.652i	−0.306105	+	0.275618i	−0.807838	−	0.589404i	$-0.799363\pi$
$109$	−348.345	+	313.652i	−0.306105	+	0.275618i	0.501733	+	0.865022i	$0.332696\pi$
$110$	−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	0.828815	−	0.559523i	$-0.189016\pi$
$113$	−133.351	−	261.716i	−0.111014	−	0.217878i	−0.939829	+	0.341646i	$0.889016\pi$
$114$	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	−0.993961	−	0.109737i	$-0.964999\pi$
$127$	−459.344	+	901.513i	−0.320946	+	0.629893i	0.673014	+	0.739629i	$0.264999\pi$
$128$	−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	0.571610	−	0.820526i	$-0.306319\pi$
$131$	1439.59	+	151.307i	0.960132	+	0.100914i	0.388522	+	0.921440i	$0.372986\pi$
$132$	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	−0.997729	−	0.0673609i	$-0.978542\pi$
$137$	2.52633	−	48.2053i	0.00157547	−	0.0300617i	0.999304	+	0.0372992i	$0.0118755\pi$
$138$	−4.22955	−	2.74670i	−0.00260901	−	0.00169431i
$139$	43.3662	+	133.467i	0.0264624	+	0.0814429i	0.963416	−	0.268012i	$-0.0863667\pi$
$139$	43.3662	+	133.467i	0.0264624	+	0.0814429i	−0.936953	+	0.349455i	$0.886367\pi$
$140$	−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	−0.964334	−	0.264687i	$-0.914731\pi$
$149$	−2213.95	+	1278.23i	−1.21728	+	0.702795i	−0.252942	+	0.967481i	$0.581398\pi$
$150$	−5.89300	−	9.64528i	−0.00320774	−	0.00525023i
$151$	−860.075	+	1489.69i	−0.463523	+	0.802845i	−0.999134	−	0.0416200i	$-0.986748\pi$
$151$	−860.075	+	1489.69i	−0.463523	+	0.802845i	0.535611	+	0.844465i	$0.320081\pi$
$152$	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	0.999504	−	0.0314895i	$-0.0100251\pi$
$157$	232.452	+	867.521i	0.118163	+	0.440992i	−0.881341	+	0.472481i	$0.843358\pi$
$158$	−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	−0.0382791	−	0.999267i	$-0.512188\pi$
$163$	1852.48	−	2852.56i	0.890166	−	1.37074i	0.928445	−	0.371469i	$-0.121146\pi$
$164$	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	−0.856216	−	0.516618i	$-0.827191\pi$
$167$	−3260.66	+	516.437i	−1.51088	+	0.239300i	−0.654666	+	0.755918i	$0.727191\pi$
$168$	−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	0.296595	−	0.955003i	$-0.404149\pi$
$173$	1573.23	−	82.4494i	0.691389	−	0.0362342i	0.394795	+	0.918769i	$0.370816\pi$
$174$	−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	0.0190346	−	0.999819i	$-0.493941\pi$
$179$	588.003	−	61.8016i	0.245527	−	0.0258060i	0.226493	+	0.974013i	$0.427274\pi$
$180$	−1470.52	+	1862.80i	−0.608924	+	0.771361i
$181$	1005.74	−	1384.28i	0.413017	−	0.568470i	−0.550934	−	0.834549i	$-0.685728\pi$
$181$	1005.74	−	1384.28i	0.413017	−	0.568470i	0.963951	+	0.266079i	$0.0857283\pi$
$182$	−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	−0.508565	−	0.861024i	$-0.669824\pi$
$191$	−1644.39	+	349.526i	−0.622952	+	0.132413i	−0.114387	+	0.993436i	$0.536490\pi$
$192$	113.901	−	296.723i	0.0428131	−	0.111532i
$193$	1320.91	+	4929.69i	0.492647	+	1.83858i	0.542828	+	0.839844i	$0.317354\pi$
$193$	1320.91	+	4929.69i	0.492647	+	1.83858i	−0.0501806	+	0.998740i	$0.515980\pi$
$194$	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	0.0878433	−	0.996134i	$-0.472003\pi$
$197$	−377.247	−	59.7501i	−0.136435	−	0.0216092i	−0.224279	+	0.974525i	$0.572003\pi$
$198$	12.8450	+	245.097i	0.00461038	+	0.0879713i
$199$	−2196.84	+	3805.03i	−0.782561	+	1.35543i	0.147885	+	0.989005i	$0.452753\pi$
$199$	−2196.84	+	3805.03i	−0.782561	+	1.35543i	−0.930446	+	0.366430i	$0.880580\pi$
$200$	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	0.986742	+	0.162296i	$0.0518901\pi$
$211$	869.976	+	2677.51i	0.283846	+	0.873589i	−0.702896	+	0.711293i	$0.748110\pi$
$212$	−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	0.397232	+	0.917718i	$0.369971\pi$
$223$	−1927.14	+	3782.23i	−0.578705	+	1.13577i	−0.975937	+	0.218054i	$0.930029\pi$
$224$	−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	−0.362042	−	0.932162i	$-0.617920\pi$
$227$	1170.61	−	760.205i	0.342275	−	0.222276i	0.704316	+	0.709886i	$0.251254\pi$
$228$	−274.157	−	222.008i	−0.0796338	−	0.0644862i
$229$	−1437.23	−	639.897i	−0.414738	−	0.184653i	0.188750	−	0.982025i	$-0.439556\pi$
$229$	−1437.23	−	639.897i	−0.414738	−	0.184653i	−0.603488	+	0.797372i	$0.706223\pi$
$230$	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	0.291612	−	0.956537i	$-0.405808\pi$
$233$	−2506.16	−	3094.84i	−0.704651	−	0.870172i	−0.996264	+	0.0863648i	$0.972475\pi$
$234$	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	−0.202285	−	0.979327i	$-0.564837\pi$
$239$	774.801	−	251.748i	0.209698	−	0.0681349i	0.411982	+	0.911192i	$0.364837\pi$
$240$	444.586	−	52.3204i	0.119575	−	0.0140719i
$241$	−310.967	+	279.996i	−0.0831168	+	0.0748387i	−0.709642	−	0.704563i	$-0.751143\pi$
$241$	−310.967	+	279.996i	−0.0831168	+	0.0748387i	0.626525	+	0.779401i	$0.284477\pi$
$242$	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	$-0.908543\pi$
$251$		−	2253.80i		−	0.566767i	0.959007	−	0.283384i	$-0.0914570\pi$
$252$	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	0.948648	−	0.316333i	$-0.102452\pi$
$257$	6641.62	+	1779.62i	1.61204	+	0.431944i	0.663387	+	0.748276i	$0.269118\pi$
$258$	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	−0.905088	−	0.425225i	$-0.860195\pi$
$263$	−7889.09	−	413.450i	−1.84967	−	0.0969369i	−0.944578	+	0.328288i	$0.893528\pi$
$264$	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	−0.215558	−	0.976491i	$-0.569157\pi$
$269$	1614.23	−	718.703i	0.365879	−	0.162900i	0.581438	+	0.813591i	$0.302490\pi$
$270$	9.14166	+	53.4142i	0.00206053	+	0.0120396i
$271$	−1622.02	+	3643.12i	−0.363582	+	0.816620i	0.635429	+	0.772160i	$0.280823\pi$
$271$	−1622.02	+	3643.12i	−0.363582	+	0.816620i	−0.999011	+	0.0444600i	$0.985843\pi$
$272$	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	0.777208	−	0.629244i	$-0.216635\pi$
$277$	−524.427	−	807.546i	−0.113754	−	0.175165i	−0.890962	+	0.454078i	$0.849969\pi$
$278$	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	0.00254280	−	0.999997i	$-0.499191\pi$
$281$	−4464.18	−	3243.42i	−0.947725	−	0.688562i	−0.950268	+	0.311434i	$0.899191\pi$
$282$	7.16713	−	26.7481i	0.00151346	−	0.00564832i
$283$	−5114.36	−	1963.22i	−1.07427	−	0.412372i	−0.244021	−	0.969770i	$-0.578467\pi$
$283$	−5114.36	−	1963.22i	−1.07427	−	0.412372i	−0.830246	+	0.557398i	$0.811800\pi$
$284$	−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	−0.947391	−	0.320078i	$-0.896291\pi$
$293$	−6356.80	−	6356.80i	−1.26747	−	1.26747i	−0.320078	−	0.947391i	$-0.603709\pi$
$294$	−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	−0.997022	−	0.0771208i	$-0.975427\pi$
$307$	−4948.22	+	4948.22i	−0.919901	+	0.919901i	0.0771208	+	0.997022i	$0.475427\pi$
$308$	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	−0.998880	−	0.0473179i	$-0.984933\pi$
$311$	−368.077	+	1731.67i	−0.0671118	+	0.315736i	0.931768	+	0.363054i	$0.118266\pi$
$312$	4.25016	−	81.0978i	0.000771211	−	0.0147156i
$313$	7374.77	+	4789.23i	1.33178	+	0.864866i	0.996998	−	0.0774300i	$-0.0246714\pi$
$313$	7374.77	+	4789.23i	1.33178	+	0.864866i	0.334780	+	0.942296i	$0.391338\pi$
$314$	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	0.0529693	−	0.998596i	$-0.483131\pi$
$317$	5874.06	−	4756.72i	1.04076	−	0.842788i	0.987787	+	0.155808i	$0.0497981\pi$
$318$	−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	−0.905143	−	0.425108i	$-0.860236\pi$
$331$	413.143	−	3930.79i	0.0686054	−	0.652737i	0.973748	−	0.227629i	$-0.0730973\pi$
$332$	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	0.103414	−	0.994638i	$-0.467023\pi$
$337$	5993.96	−	3054.08i	0.968878	−	0.493668i	0.865465	+	0.500970i	$0.167023\pi$
$338$	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	−0.822449	−	0.568839i	$-0.807393\pi$
$347$	−614.351	+	758.660i	−0.0950435	+	0.117369i	0.727405	+	0.686208i	$0.240726\pi$
$348$	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	−0.701246	−	0.712920i	$-0.747372\pi$
$353$	941.068	−	1162.12i	0.141892	−	0.175222i	0.843138	+	0.537697i	$0.180706\pi$
$354$	−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	0.949093	−	0.314995i	$-0.102003\pi$
$359$	−313.348	−	1474.19i	−0.0460665	−	0.216726i	−0.995160	+	0.0982690i	$0.968669\pi$
$360$	−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	−0.172870	−	0.984945i	$-0.555304\pi$
$367$	4321.45	−	11257.8i	0.614654	−	1.60123i	0.787524	−	0.616284i	$-0.211363\pi$
$368$	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	0.936366	+	0.351025i	$0.114167\pi$
$373$	301.275	+	5748.68i	0.0418216	+	0.798003i	−0.894545	+	0.446979i	$0.852500\pi$
$374$	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	−0.805411	−	0.592717i	$-0.798055\pi$
$379$	−8265.46	−	11376.4i	−1.12023	−	1.54187i	−0.314821	−	0.949151i	$-0.601945\pi$
$380$	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	−0.962948	−	0.269687i	$-0.913080\pi$
$383$	−6741.13	+	5458.86i	−0.899362	+	0.728289i	0.0635860	+	0.997976i	$0.479746\pi$
$384$	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	−0.688429	−	0.725304i	$-0.741699\pi$
$389$	1806.74	−	8500.06i	0.235490	−	1.10789i	0.923919	−	0.382589i	$-0.124967\pi$
$390$	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	−0.350606	−	0.936523i	$-0.614024\pi$
$397$	122.607	−	47.0643i	0.0154999	−	0.00594984i	0.366106	+	0.930573i	$0.380691\pi$
$398$	−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	−0.998914	−	0.0465982i	$-0.985162\pi$
$401$	−4334.70	−	7507.92i	−0.539812	−	0.934982i	0.459102	−	0.888384i	$-0.348171\pi$
$402$	−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	0.655187	−	0.755467i	$-0.272590\pi$
$409$	−1361.71	−	1512.33i	−0.164627	−	0.182836i	−0.819814	+	0.572630i	$0.805923\pi$
$410$	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	0.682698	−	0.730700i	$-0.260806\pi$
$419$	1704.42	+	1238.33i	0.198726	+	0.144383i	−0.483972	+	0.875084i	$0.660806\pi$
$420$	1018.12	−	220.387i	0.118283	−	0.0256043i
$421$	−2910.63	+	2114.70i	−0.336949	+	0.244808i	−0.743373	−	0.668877i	$-0.766775\pi$
$421$	−2910.63	+	2114.70i	−0.336949	+	0.244808i	0.406425	+	0.913684i	$0.366775\pi$
$422$	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	−0.715041	−	0.699083i	$-0.753592\pi$
$431$	−6030.61	+	2685.00i	−0.673977	+	0.300074i	0.0410639	+	0.999157i	$0.486925\pi$
$432$	−2073.08	−	555.480i	−0.230882	−	0.0618647i
$433$	696.794	+	4399.39i	0.0773344	+	0.488270i	0.995708	+	0.0925548i	$0.0295033\pi$
$433$	696.794	+	4399.39i	0.0773344	+	0.488270i	−0.918373	+	0.395715i	$0.870497\pi$
$434$	−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	−0.451277	−	0.892384i	$-0.649032\pi$
$439$	4446.25	−	4938.06i	0.483389	−	0.536858i	0.934666	+	0.355526i	$0.115698\pi$
$440$	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	0.194210	−	0.980960i	$-0.437786\pi$
$443$	−1194.22	−	319.991i	−0.128079	−	0.0343188i	−0.322289	+	0.946641i	$0.604452\pi$
$444$	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	$0.260354\pi$
$449$			13885.5i			1.45946i	−0.683737	+	0.729728i	$0.739646\pi$
$450$	−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	−0.947992	−	0.318295i	$-0.896890\pi$
$457$	314.000	−	1171.86i	0.0321407	−	0.119951i	0.980132	+	0.198344i	$0.0635564\pi$
$458$	−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	0.390536	−	0.920588i	$-0.372290\pi$
$461$	12348.8	−	4012.37i	1.24759	−	0.405368i	0.857058	+	0.515220i	$0.172290\pi$
$462$	64.0753	−	86.5999i	0.00645250	−	0.00872076i
$463$	3402.16	+	6677.11i	0.341494	+	0.670220i	0.996334	−	0.0855478i	$-0.0272640\pi$
$463$	3402.16	+	6677.11i	0.341494	+	0.670220i	−0.654840	+	0.755767i	$0.727264\pi$
$464$	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	0.636089	−	0.771615i	$-0.280551\pi$
$467$	−2532.22	−	3127.03i	−0.250915	−	0.309854i	−0.887004	+	0.461761i	$0.847218\pi$
$468$	−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	−0.854813	−	0.518936i	$-0.826328\pi$
$479$	−1326.91	−	12624.8i	−0.126573	−	1.20426i	0.728240	−	0.685322i	$-0.240338\pi$
$480$	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	−0.0528431	−	0.998603i	$-0.516828\pi$
$487$	1118.70	−	21346.1i	0.104093	−	1.98621i	0.156936	−	0.987609i	$-0.449838\pi$
$488$	−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	−0.750078	−	0.661350i	$-0.769984\pi$
$491$	2670.78	−	8219.81i	0.245480	−	0.755509i	0.995557	−	0.0941587i	$-0.0300161\pi$
$492$	−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	−0.961750	−	0.273929i	$-0.911677\pi$
$499$	−13436.3	+	7757.46i	−1.20539	+	0.695935i	−0.243645	+	0.969864i	$0.578343\pi$
$500$	−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	−0.191719	−	0.981450i	$-0.561406\pi$
$503$	−7641.15	−	1210.24i	−0.677340	−	0.107280i	−0.485620	+	0.874170i	$0.661406\pi$
$504$	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	−0.485095	−	0.874461i	$-0.661215\pi$
$509$	−6575.21	+	1397.60i	−0.572576	+	0.121705i	−0.0874809	+	0.996166i	$0.527882\pi$
$510$	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	−0.919748	−	0.392509i	$-0.871607\pi$
$521$	−20665.9	+	2172.07i	−1.73779	+	0.182649i	−0.818042	+	0.575158i	$0.804940\pi$
$522$	−229.055	+	282.860i	−0.0192059	+	0.0237173i
$523$	−17558.1	+	920.183i	−1.46800	+	0.0769346i	−0.769486	−	0.638663i	$-0.779488\pi$
$523$	−17558.1	+	920.183i	−1.46800	+	0.0769346i	−0.698513	+	0.715598i	$0.746154\pi$
$524$	−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	−0.303056	−	0.952973i	$-0.598007\pi$
$541$	−2419.82	+	514.348i	−0.192303	+	0.0408753i	0.110753	+	0.993848i	$0.464674\pi$
$542$	−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	0.908232	−	0.418466i	$-0.137432\pi$
$547$	21015.5	+	3328.52i	1.64270	+	0.260178i	0.734467	+	0.678644i	$0.237432\pi$
$548$	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	0.569588	−	0.821930i	$-0.307103\pi$
$557$	19374.5	−	5191.38i	1.47383	−	0.394912i	0.904243	+	0.427018i	$0.140436\pi$
$558$	−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	0.926542	+	0.376192i	$0.122767\pi$
$563$	−457.495	+	8729.52i	−0.0342471	+	0.653473i	−0.960789	+	0.277281i	$0.910567\pi$
$564$	−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	0.387675	−	0.921796i	$-0.373278\pi$
$569$	7807.41	+	820.592i	0.575226	+	0.0604587i	0.187551	+	0.982255i	$0.439945\pi$
$570$	10.2192	−	70.1518i	0.000750937	−	0.00515498i
$571$	−192.563	−	1832.11i	−0.0141129	−	0.134276i	0.985197	−	0.171428i	$-0.0548380\pi$
$571$	−192.563	−	1832.11i	−0.0141129	−	0.134276i	−0.999310	+	0.0371522i	$0.988171\pi$
$572$	−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	−0.710569	−	0.703628i	$-0.751562\pi$
$577$	−4945.07	+	3211.37i	−0.356787	+	0.231700i	0.353782	+	0.935328i	$0.384896\pi$
$578$	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	0.995086	−	0.0990178i	$-0.0315701\pi$
$587$	4694.39	+	9213.25i	0.330082	+	0.647822i	−0.665004	+	0.746840i	$0.731570\pi$
$588$	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	0.660493	+	0.750832i	$0.270347\pi$
$593$	−4143.36	+	15463.2i	−0.286927	+	1.07082i	−0.947420	+	0.319993i	$0.896319\pi$
$594$	−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	0.344693	−	0.938716i	$-0.387983\pi$
$599$	−4338.14	−	2504.62i	−0.295912	−	0.170845i	−0.640605	+	0.767871i	$0.721316\pi$
$600$	109.762	+	143.439i	0.00746833	+	0.00975977i
$601$			11001.0i			0.746656i	0.927699	+	0.373328i	$0.121783\pi$
$601$			11001.0i			0.746656i	−0.927699	+	0.373328i	$0.878217\pi$
$602$	−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	0.796407	−	0.604761i	$-0.206731\pi$
$607$	17702.6	+	4743.40i	1.18374	+	0.317181i	0.387328	+	0.921942i	$0.373398\pi$
$608$	−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	0.00213957	−	0.999998i	$-0.499319\pi$
$613$	−1521.68	−	79.7476i	−0.100261	−	0.00525445i	−0.102400	+	0.994743i	$0.532652\pi$
$614$	−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	−0.734601	−	0.678499i	$-0.762631\pi$
$617$	−3764.39	−	23767.4i	−0.245622	−	1.55079i	0.488979	−	0.872295i	$-0.337369\pi$
$618$	120.624	+	32.3210i	0.00785145	+	0.00210379i
$619$	3861.07	−	1719.06i	0.250710	−	0.111623i	−0.277534	−	0.960716i	$-0.589517\pi$
$619$	3861.07	−	1719.06i	0.250710	−	0.111623i	0.528244	+	0.849092i	$0.322851\pi$
$620$	−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	0.919081	−	0.394069i	$-0.128933\pi$
$631$	13129.2	+	9538.91i	0.828311	+	0.601803i	−0.0907699	+	0.995872i	$0.528933\pi$
$632$	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	0.959731	−	0.280922i	$-0.0906402\pi$
$641$	9413.18	+	10454.4i	0.580029	+	0.644187i	−0.379702	+	0.925109i	$0.623974\pi$
$642$	76.7065	+	94.7246i	0.00471552	+	0.00582318i
$643$	−1218.63	−	1218.63i	−0.0747406	−	0.0747406i	0.668748	−	0.743489i	$-0.266830\pi$
$643$	−1218.63	−	1218.63i	−0.0747406	−	0.0747406i	−0.743489	+	0.668748i	$0.766830\pi$
$644$	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	−0.0376678	−	0.999290i	$-0.511993\pi$
$647$	−16835.0	−	13632.7i	−1.02295	−	0.828371i	−0.985285	+	0.170919i	$0.945326\pi$
$648$	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	0.443155	−	0.896445i	$-0.353859\pi$
$653$	22899.5	−	8790.30i	1.37232	−	0.526785i	0.929167	+	0.369659i	$0.120526\pi$
$654$	−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	0.0149371	−	0.999888i	$-0.495245\pi$
$659$	−9485.44	−	3082.01i	−0.560698	−	0.182182i	−0.575635	+	0.817707i	$0.695245\pi$
$660$	−3548.17	−	708.228i	−0.209261	−	0.0417693i
$661$	1796.71	−	8452.84i	0.105724	−	0.497394i	−0.893141	−	0.449776i	$-0.851504\pi$
$661$	1796.71	−	8452.84i	0.105724	−	0.497394i	0.998866	−	0.0476176i	$-0.0151629\pi$
$662$	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	0.344359	−	0.938838i	$-0.388096\pi$
$673$	−3714.74	−	1892.75i	−0.212768	−	0.108411i	−0.557127	+	0.830427i	$0.688096\pi$
$674$	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	0.998836	−	0.0482284i	$-0.0153575\pi$
$677$	7.58314	+	144.695i	0.000430493	+	0.00821429i	−0.998406	+	0.0564427i	$0.982024\pi$
$678$	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	−0.603545	−	0.797329i	$-0.706246\pi$
$683$	6756.00	−	17600.0i	0.378493	−	0.986009i	0.982039	−	0.188680i	$-0.0604210\pi$
$684$	−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	−0.978211	−	0.207615i	$-0.933430\pi$
$691$	−3070.04	−	14443.4i	−0.169015	−	0.795155i	0.809195	−	0.587540i	$-0.199904\pi$
$692$	−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	0.972281	+	0.233816i	$0.0751213\pi$
$709$	3382.28	+	15912.4i	0.179160	+	0.842879i	−0.793121	+	0.609064i	$0.791545\pi$
$710$	−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	0.604733	+	0.796428i	$0.293280\pi$
$719$	−2937.64	+	27949.8i	−0.152372	+	1.44972i	−0.757105	+	0.653293i	$0.773387\pi$
$720$	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	0.360405	−	0.932796i	$-0.382639\pi$
$727$	−3575.46	−	1821.79i	−0.182402	−	0.0929386i	−0.542807	+	0.839857i	$0.682639\pi$
$728$	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	−0.537087	−	0.843527i	$-0.680475\pi$
$733$	3499.49	−	2833.83i	0.176339	−	0.142797i	0.713427	+	0.700730i	$0.247142\pi$
$734$	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	−0.820365	−	0.571841i	$-0.806230\pi$
$739$	3247.74	−	15279.4i	0.161664	−	0.760570i	0.982029	−	0.188730i	$-0.0604371\pi$
$740$	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	−0.905581	−	0.424172i	$-0.860565\pi$
$743$	−9749.84	+	9749.84i	−0.481409	+	0.481409i	0.424172	+	0.905581i	$0.360565\pi$
$744$	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	0.926180	−	0.377082i	$-0.123072\pi$
$751$	2809.83	+	4866.77i	0.136528	+	0.236473i	−0.789652	+	0.613554i	$0.789739\pi$
$752$	−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	0.998296	−	0.0583588i	$-0.0185867\pi$
$757$	19576.8	+	19576.8i	0.939937	+	0.939937i	−0.0583588	+	0.998296i	$0.518587\pi$
$758$	−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	0.584700	−	0.811250i	$-0.301212\pi$
$761$	−3379.65	−	3043.05i	−0.160988	−	0.144955i	−0.745688	+	0.666295i	$0.767879\pi$
$762$	−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	1.55322	+	0.596224i
$768$	−651.261	+	2430.54i	−0.0305994	+	0.114199i
$769$	−33309.3	−	24200.6i	−1.56198	−	1.13485i	−0.934361	−	0.356327i	$-0.884029\pi$
$769$	−33309.3	−	24200.6i	−1.56198	−	1.13485i	−0.627621	−	0.778519i	$-0.715971\pi$
$770$	1128.65	+	1541.30i	0.0528228	+	0.0721359i
$771$	−3507.16	+	2548.10i	−0.163823	+	0.119024i
$772$	−14594.1	−	38018.9i	−0.680379	−	1.77245i
$773$	−9771.31	−	15046.5i	−0.454657	−	0.700110i	0.534794	−	0.844983i	$-0.320389\pi$
$773$	−9771.31	−	15046.5i	−0.454657	−	0.700110i	−0.989450	+	0.144873i	$0.953723\pi$
$774$	1259.34	+	727.078i	0.0584831	+	0.0337652i
$775$	−9343.63	+	232.234i	−0.433075	+	0.0107640i
$776$			2502.45i			0.115764i
$777$	1532.17	−	866.938i	0.0707416	−	0.0400273i
$778$	194.970	−	1230.99i	0.00898460	−	0.0567265i
$779$	−6440.95	+	14466.6i	−0.296240	+	0.665366i
$780$	−2798.60	+	1470.04i	−0.128469	+	0.0674819i
$781$	48186.7	−	21454.1i	2.20775	−	0.982956i
$782$	157.812	+	42.2856i	0.00721656	+	0.00193367i
$783$	−504.328	−	3184.20i	−0.0230181	−	0.145331i
$784$	17842.5	−	12495.5i	0.812794	−	0.569219i
$785$	6625.73	−	7545.07i	0.301252	−	0.343051i
$786$	−87.5830	+	97.2708i	−0.00397453	+	0.00441417i
$787$	−31289.2	−	1639.80i	−1.41720	−	0.0742725i	−0.671725	−	0.740801i	$-0.734446\pi$
$787$	−31289.2	−	1639.80i	−1.41720	−	0.0742725i	−0.745480	+	0.666528i	$0.767780\pi$
$788$	3043.56	+	159.506i	0.137592	+	0.00721089i
$789$	3332.73	−	3701.38i	0.150378	−	0.167012i
$790$	964.996	−	217.682i	0.0434595	−	0.00980350i
$791$	3386.63	+	4257.24i	0.152231	+	0.191365i
$792$	−613.519	−	3873.61i	−0.0275258	−	0.173791i
$793$	35145.6	+	9417.22i	1.57384	+	0.421709i
$794$	17.2072	−	7.66115i	0.000769095	−	0.000342423i
$795$	2118.43	+	2066.43i	0.0945070	+	0.0921872i
$796$	14259.8	−	32028.0i	0.634955	−	1.42613i
$797$	−395.612	+	2497.80i	−0.0175826	+	0.111012i	−0.994919	−	0.100681i	$-0.967898\pi$
$797$	−395.612	+	2497.80i	−0.0175826	+	0.111012i	0.977336	+	0.211693i	$0.0678978\pi$
$798$	−101.186	−	59.5979i	−0.00448866	−	0.00264379i
$799$			6254.96i			0.276952i
$800$	−452.275	+	3400.41i	−0.0199879	+	0.150278i
$801$	21645.4	+	12497.0i	0.954808	+	0.551258i
$802$	−677.199	−	1042.79i	−0.0298164	−	0.0459132i
$803$	5940.84	+	15476.4i	0.261081	+	0.680138i
$804$	7.10852	−	5.16464i	0.000311814	−	0.000226546i
$805$	−7695.22	+	8610.90i	−0.336920	+	0.377012i
$806$	487.611	+	354.270i	0.0213094	+	0.0154822i
$807$	−288.337	+	1076.09i	−0.0125774	+	0.0469393i
$808$	−2318.61	−	890.030i	−0.100951	−	0.0387514i
$809$	−26831.8	+	24159.4i	−1.16607	+	1.04994i	−0.168136	+	0.985764i	$0.553775\pi$
$809$	−26831.8	+	24159.4i	−1.16607	+	1.04994i	−0.997939	+	0.0641743i	$0.979559\pi$
$810$	974.727	+	546.726i	0.0422820	+	0.0237160i
$811$	14171.4	−	4604.58i	0.613597	−	0.199370i	0.0143014	−	0.999898i	$-0.495448\pi$
$811$	14171.4	−	4604.58i	0.613597	−	0.199370i	0.599295	+	0.800528i	$0.295448\pi$
$812$	11332.8	+	8385.17i	0.489783	+	0.362391i
$813$	−1141.45	−	2240.23i	−0.0492404	−	0.0966398i
$814$	1033.69	+	930.738i	0.0445096	+	0.0400766i
$815$	−38024.7	+	472.474i	−1.63429	+	0.0203068i
$816$	547.217	+	607.746i	0.0234760	+	0.0260727i
$817$	−16819.0	−	20769.7i	−0.720223	−	0.889402i
$818$	−206.385	−	206.385i	−0.00882160	−	0.00882160i
$819$	−21367.2	−	17612.4i	−0.911636	−	0.751435i
$820$	−7453.09	−	18717.5i	−0.317406	−	0.797125i
$821$	−32819.6	−	14612.2i	−1.39514	−	0.621158i	−0.434941	−	0.900459i	$-0.643231\pi$
$821$	−32819.6	−	14612.2i	−1.39514	−	0.621158i	−0.960204	+	0.279301i	$0.909897\pi$
$822$	3.39217	+	2.74693i	0.000143936	+	0.000116557i
$823$	−35820.7	+	23262.2i	−1.51717	+	0.985262i	−0.526322	+	0.850285i	$0.676429\pi$
$823$	−35820.7	+	23262.2i	−1.51717	+	0.985262i	−0.990849	+	0.134977i	$0.956904\pi$
$824$	1582.53	+	2741.03i	0.0669055	+	0.115884i
$825$	−1433.37	−	4862.71i	−0.0604890	−	0.205210i
$826$	−1392.83	−	921.817i	−0.0586717	−	0.0388306i
$827$	−10078.5	+	19780.3i	−0.423779	+	0.831713i	0.576118	+	0.817367i	$0.304567\pi$
$827$	−10078.5	+	19780.3i	−0.423779	+	0.831713i	−0.999897	+	0.0143468i	$0.995433\pi$
$828$	11052.6	−	4242.68i	0.463893	−	0.178072i
$829$	−19.0617	−	181.360i	−0.000798602	−	0.00759819i	0.994115	−	0.108327i	$-0.0345493\pi$
$829$	−19.0617	−	181.360i	−0.000798602	−	0.00759819i	−0.994914	+	0.100729i	$0.967883\pi$
$830$	−715.389	+	733.390i	−0.0299175	+	0.0306703i
$831$	603.751	+	63.4568i	0.0252032	+	0.00264897i
$832$	−20034.3	+	20034.3i	−0.834815	+	0.834815i
$833$	−245.041	−	7001.48i	−0.0101923	−	0.291221i
$834$	−12.0687	−	3.92136i	−0.000501085	−	0.000162813i
$835$	25036.3	+	27120.3i	1.03762	+	1.12399i
$836$	−7483.46	+	35206.9i	−0.309594	+	1.45653i
$837$	132.249	−	2523.46i	0.00546140	−	0.104210i
$838$	253.413	+	164.568i	0.0104463	+	0.00678391i
$839$	−14006.0	−	43106.0i	−0.576330	−	1.77376i	−0.631606	−	0.775290i	$-0.717604\pi$
$839$	−14006.0	−	43106.0i	−0.576330	−	1.77376i	0.0552759	−	0.998471i	$-0.482396\pi$
$840$	288.705	−	78.5159i	0.0118587	−	0.00322506i
$841$	4724.47	−	14540.4i	0.193713	−	0.596187i
$842$	−401.005	+	324.728i	−0.0164128	+	0.0132908i
$843$	3360.43	−	900.425i	0.137295	−	0.0367880i
$844$	−9137.13	−	20522.3i	−0.372646	−	0.836976i
$845$	−10744.2	−	429.297i	−0.437408	−	0.0174772i
$846$	−686.788	−	945.283i	−0.0279105	−	0.0384155i
$847$	−50753.9	−	11249.8i	−2.05894	−	0.456373i
$848$	23756.3	+	12104.4i	0.962021	+	0.490174i
$849$	2991.15	−	1726.94i	0.120914	−	0.0698097i
$850$	278.126	+	238.182i	0.0112231	+	0.00961128i
$851$	−4204.28	+	7282.03i	−0.169355	+	0.293331i
$852$	−215.895	−	4119.53i	−0.00868128	−	0.165649i
$853$	−31986.5	−	5066.16i	−1.28393	−	0.203355i	−0.523083	−	0.852282i	$-0.675218\pi$
$853$	−31986.5	−	5066.16i	−1.28393	−	0.203355i	−0.760851	+	0.648926i	$0.775218\pi$
$854$	−1525.36	−	793.976i	−0.0611202	−	0.0318142i
$855$	−13325.6	−	16044.0i	−0.533013	−	0.641747i
$856$	−322.915	+	3072.33i	−0.0128937	+	0.122675i
$857$	9481.97	+	35387.2i	0.377944	+	1.41051i	0.848995	+	0.528401i	$0.177208\pi$
$857$	9481.97	+	35387.2i	0.377944	+	1.41051i	−0.471051	+	0.882106i	$0.656125\pi$
$858$	−117.156	+	305.203i	−0.00466160	+	0.0121439i
$859$	19849.6	−	4219.17i	0.788429	−	0.167586i	0.203936	−	0.978984i	$-0.434627\pi$
$859$	19849.6	−	4219.17i	0.788429	−	0.167586i	0.584493	+	0.811399i	$0.301293\pi$
$860$	33856.7	+	3133.71i	1.34245	+	0.124254i
$861$	−1880.70	+	1848.30i	−0.0744413	+	0.0731589i
$862$	−843.587	+	429.829i	−0.0333326	+	0.0169838i
$863$	2294.21	−	3532.78i	0.0904935	−	0.139348i	−0.790525	−	0.612430i	$-0.790192\pi$
$863$	2294.21	−	3532.78i	0.0904935	−	0.139348i	0.881018	+	0.473082i	$0.156859\pi$
$864$	−907.164	−	192.824i	−0.0357203	−	0.00759259i
$865$	−10529.1	−	14119.8i	−0.413874	−	0.555014i
$866$	132.822	+	624.878i	0.00521186	+	0.0245199i
$867$	−2799.60	+	443.413i	−0.109665	+	0.0173692i
$868$	7322.21	+	8275.61i	0.286327	+	0.323609i
$869$	−23326.1	+	32105.6i	−0.910568	+	1.25329i
$870$	53.5273	+	80.2247i	0.00208591	+	0.00312629i
$871$	97.6235	−	10.2606i	0.00379776	−	0.000399161i
$872$	676.064	−	834.870i	0.0262551	−	0.0324223i
$873$	29007.7	−	1520.23i	1.12458	−	0.0589369i
$874$	560.910			0.0217083
$875$	−23888.7	+	9962.46i	−0.922956	+	0.384906i
$876$	1296.48			0.0500044
$877$	−44881.2	+	2352.12i	−1.72808	+	0.0905651i	−0.890282	−	0.455409i	$-0.849493\pi$
$877$	−44881.2	+	2352.12i	−1.72808	+	0.0905651i	−0.837802	+	0.545974i	$0.816160\pi$
$878$	599.753	−	740.634i	0.0230532	−	0.0284683i
$879$	5636.84	−	592.456i	0.216298	−	0.0227338i
$880$	−25349.8	−	37993.3i	−0.971070	−	1.45540i
$881$	−7903.80	+	10878.6i	−0.302254	+	0.416017i	−0.932946	−	0.360016i	$-0.882771\pi$
$881$	−7903.80	+	10878.6i	−0.302254	+	0.416017i	0.630692	+	0.776033i	$0.282771\pi$
$882$	805.787	+	1031.19i	0.0307622	+	0.0393675i
$883$	−18987.9	+	3007.39i	−0.723663	+	0.114617i	−0.507391	−	0.861716i	$-0.669390\pi$
$883$	−18987.9	+	3007.39i	−0.723663	+	0.114617i	−0.216273	+	0.976333i	$0.569390\pi$
$884$	1904.45	+	8959.74i	0.0724589	+	0.340892i
$885$	2649.64	+	3553.23i	0.100640	+	0.134961i
$886$	−173.446	−	36.8671i	−0.00657678	−	0.00139794i
$887$	8774.80	−	13512.0i	0.332164	−	0.511487i	−0.632644	−	0.774442i	$-0.718031\pi$
$887$	8774.80	−	13512.0i	0.332164	−	0.511487i	0.964808	+	0.262955i	$0.0846972\pi$
$888$	194.103	−	98.9006i	0.00733522	−	0.00373748i
$889$	5006.98	−	18057.3i	0.188896	−	0.681241i
$890$	−1500.14	−	138.850i	−0.0564999	−	0.00522951i
$891$	−43853.7	+	9321.39i	−1.64888	+	0.350481i
$892$	12138.6	−	31622.1i	0.455639	−	1.18698i
$893$	5557.99	+	20742.7i	0.208277	+	0.777299i
$894$	24.1634	−	229.899i	0.000903966	−	0.00860066i
$895$	−4223.49	−	5085.07i	−0.157738	−	0.189916i
$896$	4558.45	−	2904.30i	0.169963	−	0.108288i
$897$	−1951.92	−	309.154i	−0.0726564	−	0.0115076i
$898$	104.227	+	1988.77i	0.00387315	+	0.0739042i
$899$	−3566.46	+	6177.30i	−0.132312	+	0.229171i
$900$	26449.5	+	2117.03i	0.979612	+	0.0784085i
$901$	7426.25	−	4287.55i	0.274589	−	0.158534i
$902$	−1856.40	−	945.882i	−0.0685270	−	0.0349162i
$903$	−1338.38	−	4244.23i	−0.0493229	−	0.156411i
$904$	395.684	+	544.612i	0.0145578	+	0.0200371i
$905$	−19115.1	−	763.768i	−0.702107	−	0.0280536i
$906$	−63.2653	−	142.096i	−0.00231992	−	0.00521063i
$907$	−37148.8	+	9953.99i	−1.35998	+	0.364407i	−0.863810	−	0.503817i	$-0.831929\pi$
$907$	−37148.8	+	9953.99i	−1.35998	+	0.364407i	−0.496173	+	0.868224i	$0.665262\pi$
$908$	−8655.58	+	7009.15i	−0.316350	+	0.256175i
$909$	−8908.42	+	27417.3i	−0.325053	+	1.00041i
$910$	1613.81	+	425.963i	0.0587884	+	0.0155171i
$911$	267.901	+	824.515i	0.00974310	+	0.0299862i	0.955810	−	0.293986i	$-0.0949817\pi$
$911$	267.901	+	824.515i	0.00974310	+	0.0299862i	−0.946067	+	0.323972i	$0.894982\pi$
$912$	2354.71	+	1529.16i	0.0854957	+	0.0555216i
$913$	2151.00	−	41043.6i	0.0779713	−	1.48778i
$914$	36.1768	−	170.199i	0.00130922	−	0.00615937i
$915$	3095.43	+	3353.09i	0.111838	+	0.121147i
$916$	11939.2	+	3879.28i	0.430657	+	0.139929i
$917$	−26684.8	+	2570.50i	−0.960972	+	0.0925687i
$918$	−70.0031	+	70.0031i	−0.00251683	+	0.00251683i
$919$	20369.8	+	2140.95i	0.731162	+	0.0768482i	0.462791	−	0.886467i	$-0.346848\pi$
$919$	20369.8	+	2140.95i	0.731162	+	0.0768482i	0.268371	+	0.963316i	$0.413515\pi$
$920$	−997.868	+	1022.98i	−0.0357595	+	0.0366593i
$921$	−461.175	−	4387.79i	−0.0164997	−	0.156984i
$922$	1738.55	−	667.368i	0.0621000	−	0.0238380i
$923$	20922.3	−	41062.2i	0.746115	−	1.46433i
$924$	−3307.83	+	4998.01i	−0.117770	+	0.177947i
$925$	−15545.5	+	10653.7i	−0.552577	+	0.378694i
$926$	537.398	+	930.801i	0.0190713	+	0.0330324i
$927$	30811.8	−	20009.4i	1.09169	−	0.708949i
$928$	2034.51	+	1647.51i	0.0719677	+	0.0582783i
$929$	−17359.2	−	7728.82i	−0.613065	−	0.272954i	0.0766236	−	0.997060i	$-0.475586\pi$
$929$	−17359.2	−	7728.82i	−0.613065	−	0.272954i	−0.689689	+	0.724106i	$0.742253\pi$
$930$	27.9648	+	70.2299i	0.000986022	+	0.00247627i
$931$	−7033.93	−	23000.6i	−0.247613	−	0.809681i
$932$	22469.5	+	22469.5i	0.789713	+	0.789713i
$933$	−702.424	−	867.422i	−0.0246477	−	0.0304374i
$934$	−386.153	−	428.866i	−0.0135282	−	0.0150245i
$935$	−14688.5	+	182.511i	−0.513758	+	0.00638368i
$936$	−2546.44	−	2292.82i	−0.0889241	−	0.0800676i
$937$	30.6895	+	60.2316i	0.00106999	+	0.00209998i	0.891541	−	0.452940i	$-0.149625\pi$
$937$	30.6895	+	60.2316i	0.00106999	+	0.00209998i	−0.890471	+	0.455040i	$0.849625\pi$
$938$	−4.60945	−	0.524999i	−0.000160452	−	1.82749e-5i
$939$	−5272.67	+	1713.19i	−0.183245	+	0.0595399i
$940$	−23828.2	−	13365.3i	−0.826799	−	0.463752i
$941$	5653.89	−	5090.78i	0.195868	−	0.176360i	−0.565361	−	0.824844i	$-0.691263\pi$
$941$	5653.89	−	5090.78i	0.195868	−	0.176360i	0.761229	+	0.648484i	$0.224596\pi$
$942$	−75.8182	−	29.1039i	−0.00262239	−	0.00100664i
$943$	3259.81	−	12165.8i	0.112570	−	0.420119i
$944$	32306.7	+	23472.2i	1.11387	+	0.809274i
$945$	−2187.26	−	6647.07i	−0.0752927	−	0.228814i
$946$	2844.72	−	2066.81i	0.0977694	−	0.0710336i
$947$	−6224.32	−	16214.9i	−0.213583	−	0.556403i	0.784374	−	0.620288i	$-0.212984\pi$
$947$	−6224.32	−	16214.9i	−0.213583	−	0.556403i	−0.997957	+	0.0638851i	$0.979651\pi$
$948$	1690.36	+	2602.92i	0.0579116	+	0.0891760i
$949$	12543.4	+	7241.91i	0.429056	+	0.247716i
$950$	1133.96	+	542.725i	0.0387269	+	0.0185351i
$951$			4765.44i			0.162492i
$952$	7.53170	−	866.905i	0.000256412	−	0.0295132i
$953$	−397.858	+	2511.98i	−0.0135235	+	0.0853839i	−0.993527	−	0.113596i	$-0.963763\pi$
$953$	−397.858	+	2511.98i	−0.0135235	+	0.0853839i	0.980004	+	0.198980i	$0.0637630\pi$
$954$	−651.526	+	1463.35i	−0.0221110	+	0.0496622i
$955$	13454.6	+	13124.3i	0.455895	+	0.444705i
$956$	−5938.63	+	2644.05i	−0.200909	+	0.0894504i
$957$	−3737.08	−	1001.35i	−0.126231	−	0.0338234i
$958$	−284.813	−	1798.24i	−0.00960530	−	0.0606455i
$959$	132.176	+	884.174i	0.00445066	+	0.0297721i
$960$	−3466.39	+	781.940i	−0.116539	+	0.0262885i
$961$	16193.0	−	17984.2i	0.543555	−	0.603679i
$962$	1213.63	+	63.6035i	0.0406746	+	0.00213166i
$963$	35809.8	+	1876.71i	1.19829	+	0.0627997i
$964$	2234.21	−	2481.34i	0.0746463	−	0.0829031i
$965$	37650.7	−	42874.8i	1.25598	−	1.43025i
$966$	86.9029	+	34.2281i	0.00289447	+	0.00114003i
$967$	8024.05	+	50661.8i	0.266842	+	1.68477i	0.649089	+	0.760712i	$0.275150\pi$
$967$	8024.05	+	50661.8i	0.266842	+	1.68477i	−0.382248	+	0.924060i	$0.624850\pi$
$968$	−6213.84	−	1664.99i	−0.206323	−	0.0552840i
$969$	824.930	−	367.282i	0.0273484	−	0.0121763i
$970$	−1550.06	+	814.209i	−0.0513086	+	0.0269512i
$971$	−744.912	+	1673.10i	−0.0246193	+	0.0552959i	−0.925437	−	0.378902i	$-0.876302\pi$
$971$	−744.912	+	1673.10i	−0.0246193	+	0.0552959i	0.900817	+	0.434198i	$0.142968\pi$
$972$	−1687.50	+	10654.4i	−0.0556857	+	0.351585i
$973$	−1279.93	−	2262.05i	−0.0421711	−	0.0745305i
$974$		−	3065.72i		−	0.100854i
$975$	−3646.96	−	2513.64i	−0.119791	−	0.0825650i
$976$	35605.7	+	20556.9i	1.16774	+	0.674192i
$977$	13356.4	+	20567.0i	0.437367	+	0.673487i	0.986780	−	0.162064i	$-0.0518152\pi$
$977$	13356.4	+	20567.0i	0.437367	+	0.673487i	−0.549413	+	0.835551i	$0.685149\pi$
$978$	110.220	+	287.132i	0.00360371	+	0.00938800i
$979$	48894.8	−	35524.1i	1.59620	−	1.15971i
$980$	27195.7	+	14026.9i	0.886463	+	0.457217i
$981$	−10088.3	−	7329.56i	−0.328332	−	0.238547i
$982$	320.826	−	1197.34i	0.0104256	−	0.0389090i
$983$	44913.4	+	17240.6i	1.45729	+	0.559401i	0.952687	−	0.303952i	$-0.0983062\pi$
$983$	44913.4	+	17240.6i	1.45729	+	0.559401i	0.504601	+	0.863353i	$0.331640\pi$
$984$	−242.493	+	218.342i	−0.00785609	+	0.00707366i
$985$	1785.23	+	3879.26i	0.0577485	+	0.125486i
$986$	265.775	−	86.3555i	0.00858418	−	0.00278917i
$987$	−404.658	+	3552.87i	−0.0130501	+	0.114579i
$988$	14276.9	+	28020.0i	0.459726	+	0.902263i
$989$	15796.5	+	14223.2i	0.507886	+	0.457303i
$990$	2199.76	−	1640.36i	0.0706191	−	0.0526606i
$991$	−6087.89	−	6761.28i	−0.195144	−	0.216730i	0.637629	−	0.770343i	$-0.279915\pi$
$991$	−6087.89	−	6761.28i	−0.195144	−	0.216730i	−0.832774	+	0.553614i	$0.813248\pi$
$992$	1291.34	+	1594.67i	0.0413307	+	0.0510392i
$993$	1762.05	+	1762.05i	0.0563112	+	0.0563112i
$994$	−1385.35	+	1680.70i	−0.0442058	+	0.0536302i
$995$	49019.7	−	3180.18i	1.56184	−	0.101325i
$996$	−2936.41	−	1307.37i	−0.0934174	−	0.0415921i
$997$	6806.47	+	5511.77i	0.216212	+	0.175085i	0.731308	−	0.682048i	$-0.238910\pi$
$997$	6806.47	+	5511.77i	0.216212	+	0.175085i	−0.515096	+	0.857133i	$0.672244\pi$
$998$	−1866.20	+	1211.93i	−0.0591921	+	0.0384398i
$999$	−2547.58	−	4412.53i	−0.0806825	−	0.139746i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.17.30	yes	928
7.5	odd	6	inner	175.4.x.a.117.29	yes	928
25.3	odd	20	inner	175.4.x.a.3.29	✓	928
175.103	even	60	inner	175.4.x.a.103.30	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.29	✓	928	25.3	odd	20	inner
175.4.x.a.17.30	yes	928	1.1	even	1	trivial
175.4.x.a.103.30	yes	928	175.103	even	60	inner
175.4.x.a.117.29	yes	928	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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