LMFDB - Embedded newform 250.3.f.a.143.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,3,Mod(7,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([17]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("250.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	250.f (of order $20$, degree $8$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.81200660901$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			143.2
Root			$-1.64599i$ of defining polynomial
Character	$\chi$	$=$	250.143
Dual form			250.3.f.a.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26007 + 0.642040i) q^{2} +(3.59668 + 0.569657i) q^{3} +(1.17557 + 1.61803i) q^{4} +(4.16633 + 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(0.442463 + 2.79360i) q^{8} +(4.05206 + 1.31659i) q^{9} +O(q^{10})$	\(q+(1.26007 + 0.642040i) q^{2} +(3.59668 + 0.569657i) q^{3} +(1.17557 + 1.61803i) q^{4} +(4.16633 + 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(0.442463 + 2.79360i) q^{8} +(4.05206 + 1.31659i) q^{9} +(4.24327 + 13.0594i) q^{11} +(3.30642 + 6.48922i) q^{12} +(8.13219 - 4.14356i) q^{13} +(1.20932 - 0.392933i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(-5.81218 + 0.920559i) q^{17} +(4.26058 + 4.26058i) q^{18} +(18.5227 - 25.4943i) q^{19} +(2.64887 - 1.92451i) q^{21} +(-3.03784 + 19.1802i) q^{22} +(-14.0070 + 27.4902i) q^{23} +10.2997i q^{24} +12.9075 q^{26} +(-15.3775 - 7.83525i) q^{27} +(1.77612 + 0.281309i) q^{28} +(-33.4337 - 46.0176i) q^{29} +(-1.57058 - 1.14109i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.82225 + 49.3877i) q^{33} +(-7.91481 - 2.57168i) q^{34} +(2.63319 + 8.10411i) q^{36} +(5.33922 + 10.4788i) q^{37} +(39.7083 - 20.2324i) q^{38} +(31.6093 - 10.2705i) q^{39} +(20.6793 - 63.6443i) q^{41} +(4.57338 - 0.724353i) q^{42} +(-38.8107 - 38.8107i) q^{43} +(-16.1423 + 22.2180i) q^{44} +(-35.2996 + 25.6467i) q^{46} +(-7.80337 + 49.2685i) q^{47} +(-6.61284 + 12.9784i) q^{48} +48.1916i q^{49} -21.4289 q^{51} +(16.2644 + 8.28712i) q^{52} +(-35.9841 - 5.69932i) q^{53} +(-14.3463 - 19.7460i) q^{54} +(2.05742 + 1.49481i) q^{56} +(81.1431 - 81.1431i) q^{57} +(-12.5838 - 79.4513i) q^{58} +(57.8198 + 18.7868i) q^{59} +(4.37780 + 13.4735i) q^{61} +(-1.24642 - 2.44623i) q^{62} +(3.41328 - 1.73915i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(-21.8523 + 67.2544i) q^{66} +(-63.8194 + 10.1080i) q^{67} +(-8.32212 - 8.32212i) q^{68} +(-66.0385 + 90.8943i) q^{69} +(25.4392 - 18.4826i) q^{71} +(-1.88515 + 11.9024i) q^{72} +(31.4489 - 61.7220i) q^{73} +16.6321i q^{74} +63.0254 q^{76} +(11.0007 + 5.60513i) q^{77} +(46.4241 + 7.35285i) q^{78} +(-33.4082 - 45.9825i) q^{79} +(-81.8666 - 59.4796i) q^{81} +(66.9196 - 66.9196i) q^{82} +(6.33607 + 40.0044i) q^{83} +(6.22786 + 2.02355i) q^{84} +(-23.9863 - 73.8222i) q^{86} +(-94.0360 - 184.556i) q^{87} +(-34.6054 + 17.6323i) q^{88} +(57.1826 - 18.5798i) q^{89} +(2.53589 - 7.80467i) q^{91} +(-60.9463 + 9.65295i) q^{92} +(-4.99882 - 4.99882i) q^{93} +(-41.4652 + 57.0719i) q^{94} +(-16.6653 + 12.1081i) q^{96} +(1.94856 - 12.3027i) q^{97} +(-30.9409 + 60.7249i) q^{98} +58.5042i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9} + 32 q^{11} - 16 q^{12} - 8 q^{13} + 30 q^{14} + 16 q^{16} + 8 q^{17} - 16 q^{18} - 30 q^{19} - 68 q^{21} - 8 q^{22} + 42 q^{23} - 56 q^{26} - 40 q^{27} + 4 q^{28} - 100 q^{29} + 132 q^{31} - 64 q^{32} + 134 q^{33} - 100 q^{34} + 48 q^{36} - 82 q^{37} + 20 q^{38} + 320 q^{39} - 88 q^{41} - 128 q^{42} - 78 q^{43} - 40 q^{44} - 26 q^{46} + 168 q^{47} + 32 q^{48} - 168 q^{51} - 16 q^{52} - 518 q^{53} - 80 q^{54} + 48 q^{56} + 280 q^{57} + 80 q^{58} + 350 q^{59} + 372 q^{61} - 158 q^{62} + 142 q^{63} - 202 q^{66} + 158 q^{67} - 196 q^{68} + 30 q^{69} + 122 q^{71} + 68 q^{72} + 352 q^{73} + 40 q^{76} + 96 q^{77} + 158 q^{78} - 760 q^{79} - 144 q^{81} + 352 q^{82} + 32 q^{83} + 20 q^{84} + 264 q^{86} - 440 q^{87} - 244 q^{88} - 550 q^{89} - 798 q^{91} - 436 q^{92} + 54 q^{93} - 190 q^{94} - 16 q^{96} + 618 q^{97} + 336 q^{98}+O(q^{100}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9 + 32 * q^11 - 16 * q^12 - 8 * q^13 + 30 * q^14 + 16 * q^16 + 8 * q^17 - 16 * q^18 - 30 * q^19 - 68 * q^21 - 8 * q^22 + 42 * q^23 - 56 * q^26 - 40 * q^27 + 4 * q^28 - 100 * q^29 + 132 * q^31 - 64 * q^32 + 134 * q^33 - 100 * q^34 + 48 * q^36 - 82 * q^37 + 20 * q^38 + 320 * q^39 - 88 * q^41 - 128 * q^42 - 78 * q^43 - 40 * q^44 - 26 * q^46 + 168 * q^47 + 32 * q^48 - 168 * q^51 - 16 * q^52 - 518 * q^53 - 80 * q^54 + 48 * q^56 + 280 * q^57 + 80 * q^58 + 350 * q^59 + 372 * q^61 - 158 * q^62 + 142 * q^63 - 202 * q^66 + 158 * q^67 - 196 * q^68 + 30 * q^69 + 122 * q^71 + 68 * q^72 + 352 * q^73 + 40 * q^76 + 96 * q^77 + 158 * q^78 - 760 * q^79 - 144 * q^81 + 352 * q^82 + 32 * q^83 + 20 * q^84 + 264 * q^86 - 440 * q^87 - 244 * q^88 - 550 * q^89 - 798 * q^91 - 436 * q^92 + 54 * q^93 - 190 * q^94 - 16 * q^96 + 618 * q^97 + 336 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$3$	3.59668	+	0.569657i	1.19889	+	0.189886i	0.723774	−	0.690037i	$-0.242406\pi$
$3$	3.59668	+	0.569657i	1.19889	+	0.189886i	0.475117	+	0.879922i	$0.342406\pi$
$4$	1.17557	+	1.61803i	0.293893	+	0.404508i
$5$		0			0
$5$		0			0
$6$	4.16633	+	3.02702i	0.694389	+	0.504503i
$7$	0.635779	−	0.635779i	0.0908256	−	0.0908256i	−0.660234	−	0.751060i	$-0.729543\pi$
$7$	0.635779	−	0.635779i	0.0908256	−	0.0908256i	0.751060	+	0.660234i	$0.229543\pi$
$8$	0.442463	+	2.79360i	0.0553079	+	0.349201i
$9$	4.05206	+	1.31659i	0.450229	+	0.146288i
$10$		0			0
$11$	4.24327	+	13.0594i	0.385751	+	1.18722i	0.935934	+	0.352176i	$0.114558\pi$
$11$	4.24327	+	13.0594i	0.385751	+	1.18722i	−0.550182	+	0.835045i	$0.685442\pi$
$12$	3.30642	+	6.48922i	0.275535	+	0.540768i
$13$	8.13219	−	4.14356i	0.625553	−	0.318735i	−0.112323	−	0.993672i	$-0.535829\pi$
$13$	8.13219	−	4.14356i	0.625553	−	0.318735i	0.737876	+	0.674936i	$0.235829\pi$
$14$	1.20932	−	0.392933i	0.0863803	−	0.0280667i
$15$		0			0
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	−5.81218	+	0.920559i	−0.341893	+	0.0541505i	−0.325020	−	0.945707i	$-0.605371\pi$
$17$	−5.81218	+	0.920559i	−0.341893	+	0.0541505i	−0.0168729	+	0.999858i	$0.505371\pi$
$18$	4.26058	+	4.26058i	0.236699	+	0.236699i
$19$	18.5227	−	25.4943i	0.974878	−	1.34180i	0.0353349	−	0.999376i	$-0.488750\pi$
$19$	18.5227	−	25.4943i	0.974878	−	1.34180i	0.939544	−	0.342429i	$-0.111250\pi$
$20$		0			0
$21$	2.64887	−	1.92451i	0.126137	−	0.0916436i
$22$	−3.03784	+	19.1802i	−0.138084	+	0.871827i
$23$	−14.0070	+	27.4902i	−0.608999	+	1.19523i	0.356372	+	0.934344i	$0.384014\pi$
$23$	−14.0070	+	27.4902i	−0.608999	+	1.19523i	−0.965370	+	0.260883i	$0.915986\pi$
$24$			10.2997i			0.429156i
$25$		0			0
$26$	12.9075			0.496442
$27$	−15.3775	−	7.83525i	−0.569539	−	0.290194i
$28$	1.77612	+	0.281309i	0.0634327	+	0.0100468i
$29$	−33.4337	−	46.0176i	−1.15289	−	1.58681i	−0.734604	−	0.678496i	$-0.762632\pi$
$29$	−33.4337	−	46.0176i	−1.15289	−	1.58681i	−0.418282	−	0.908317i	$-0.637368\pi$
$30$		0			0
$31$	−1.57058	−	1.14109i	−0.0506637	−	0.0368093i	0.562165	−	0.827025i	$-0.309969\pi$
$31$	−1.57058	−	1.14109i	−0.0506637	−	0.0368093i	−0.612829	+	0.790216i	$0.709969\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	7.82225	+	49.3877i	0.237038	+	1.49660i
$34$	−7.91481	−	2.57168i	−0.232788	−	0.0756376i
$35$		0			0
$36$	2.63319	+	8.10411i	0.0731441	+	0.225114i
$37$	5.33922	+	10.4788i	0.144303	+	0.283211i	0.951834	−	0.306615i	$-0.0991964\pi$
$37$	5.33922	+	10.4788i	0.144303	+	0.283211i	−0.807530	+	0.589826i	$0.799196\pi$
$38$	39.7083	−	20.2324i	1.04496	−	0.532431i
$39$	31.6093	−	10.2705i	0.810494	−	0.263345i
$40$		0			0
$41$	20.6793	−	63.6443i	0.504373	−	1.55230i	−0.297449	−	0.954738i	$-0.596136\pi$
$41$	20.6793	−	63.6443i	0.504373	−	1.55230i	0.801822	−	0.597563i	$-0.203864\pi$
$42$	4.57338	−	0.724353i	0.108890	−	0.0172465i
$43$	−38.8107	−	38.8107i	−0.902573	−	0.902573i	0.0930849	−	0.995658i	$-0.470327\pi$
$43$	−38.8107	−	38.8107i	−0.902573	−	0.902573i	−0.995658	+	0.0930849i	$0.970327\pi$
$44$	−16.1423	+	22.2180i	−0.366871	+	0.504955i
$45$		0			0
$46$	−35.2996	+	25.6467i	−0.767383	+	0.557537i
$47$	−7.80337	+	49.2685i	−0.166029	+	1.04827i	0.754131	+	0.656724i	$0.228058\pi$
$47$	−7.80337	+	49.2685i	−0.166029	+	1.04827i	−0.920160	+	0.391542i	$0.871942\pi$
$48$	−6.61284	+	12.9784i	−0.137768	+	0.270384i
$49$			48.1916i			0.983501i
$50$		0			0
$51$	−21.4289			−0.420175
$52$	16.2644	+	8.28712i	0.312777	+	0.159368i
$53$	−35.9841	−	5.69932i	−0.678945	−	0.107534i	−0.192568	−	0.981284i	$-0.561682\pi$
$53$	−35.9841	−	5.69932i	−0.678945	−	0.107534i	−0.486377	+	0.873749i	$0.661682\pi$
$54$	−14.3463	−	19.7460i	−0.265672	−	0.365666i
$55$		0			0
$56$	2.05742	+	1.49481i	0.0367397	+	0.0266930i
$57$	81.1431	−	81.1431i	1.42356	−	1.42356i
$58$	−12.5838	−	79.4513i	−0.216963	−	1.36985i
$59$	57.8198	+	18.7868i	0.979997	+	0.318420i	0.754845	−	0.655904i	$-0.227712\pi$
$59$	57.8198	+	18.7868i	0.979997	+	0.318420i	0.225152	+	0.974324i	$0.427712\pi$
$60$		0			0
$61$	4.37780	+	13.4735i	0.0717672	+	0.220877i	0.980506	−	0.196488i	$-0.0629537\pi$
$61$	4.37780	+	13.4735i	0.0717672	+	0.220877i	−0.908739	+	0.417365i	$0.862954\pi$
$62$	−1.24642	−	2.44623i	−0.0201035	−	0.0394553i
$63$	3.41328	−	1.73915i	0.0541790	−	0.0276056i
$64$	−7.60845	+	2.47214i	−0.118882	+	0.0386271i
$65$		0			0
$66$	−21.8523	+	67.2544i	−0.331095	+	1.01901i
$67$	−63.8194	+	10.1080i	−0.952528	+	0.150866i	−0.613310	−	0.789842i	$-0.710162\pi$
$67$	−63.8194	+	10.1080i	−0.952528	+	0.150866i	−0.339218	+	0.940708i	$0.610162\pi$
$68$	−8.32212	−	8.32212i	−0.122384	−	0.122384i
$69$	−66.0385	+	90.8943i	−0.957080	+	1.31731i
$70$		0			0
$71$	25.4392	−	18.4826i	0.358298	−	0.260319i	−0.394044	−	0.919092i	$-0.628924\pi$
$71$	25.4392	−	18.4826i	0.358298	−	0.260319i	0.752342	+	0.658773i	$0.228924\pi$
$72$	−1.88515	+	11.9024i	−0.0261827	+	0.165311i
$73$	31.4489	−	61.7220i	0.430807	−	0.845506i	−0.568926	−	0.822389i	$-0.692641\pi$
$73$	31.4489	−	61.7220i	0.430807	−	0.845506i	0.999733	−	0.0231175i	$-0.00735918\pi$
$74$			16.6321i			0.224757i
$75$		0			0
$76$	63.0254			0.829281
$77$	11.0007	+	5.60513i	0.142866	+	0.0727939i
$78$	46.4241	+	7.35285i	0.595180	+	0.0942673i
$79$	−33.4082	−	45.9825i	−0.422889	−	0.582057i	0.543414	−	0.839465i	$-0.317132\pi$
$79$	−33.4082	−	45.9825i	−0.422889	−	0.582057i	−0.966303	+	0.257408i	$0.917132\pi$
$80$		0			0
$81$	−81.8666	−	59.4796i	−1.01070	−	0.734316i
$82$	66.9196	−	66.9196i	0.816093	−	0.816093i
$83$	6.33607	+	40.0044i	0.0763382	+	0.481981i	0.996006	+	0.0892838i	$0.0284578\pi$
$83$	6.33607	+	40.0044i	0.0763382	+	0.481981i	−0.919668	+	0.392697i	$0.871542\pi$
$84$	6.22786	+	2.02355i	0.0741412	+	0.0240899i
$85$		0			0
$86$	−23.9863	−	73.8222i	−0.278910	−	0.858398i
$87$	−94.0360	−	184.556i	−1.08087	−	2.12133i
$88$	−34.6054	+	17.6323i	−0.393243	+	0.200367i
$89$	57.1826	−	18.5798i	0.642501	−	0.208761i	0.0303965	−	0.999538i	$-0.490323\pi$
$89$	57.1826	−	18.5798i	0.642501	−	0.208761i	0.612105	+	0.790777i	$0.290323\pi$
$90$		0			0
$91$	2.53589	−	7.80467i	0.0278669	−	0.0857656i
$92$	−60.9463	+	9.65295i	−0.662460	+	0.104923i
$93$	−4.99882	−	4.99882i	−0.0537507	−	0.0537507i
$94$	−41.4652	+	57.0719i	−0.441119	+	0.607148i
$95$		0			0
$96$	−16.6653	+	12.1081i	−0.173597	+	0.126126i
$97$	1.94856	−	12.3027i	0.0200882	−	0.126832i	−0.975606	−	0.219528i	$-0.929548\pi$
$97$	1.94856	−	12.3027i	0.0200882	−	0.126832i	0.995694	+	0.0926957i	$0.0295484\pi$
$98$	−30.9409	+	60.7249i	−0.315723	+	0.619642i
$99$			58.5042i			0.590952i
$100$		0			0
$101$	−66.0665			−0.654124			−0.327062	−	0.945003i	$-0.606059\pi$
$101$	−66.0665			−0.654124			−0.327062	+	0.945003i	$0.606059\pi$
$102$	−27.0020	−	13.7582i	−0.264726	−	0.134884i
$103$	−10.0920	−	1.59842i	−0.0979807	−	0.0155186i	0.107252	−	0.994232i	$-0.465795\pi$
$103$	−10.0920	−	1.59842i	−0.0979807	−	0.0155186i	−0.205232	+	0.978713i	$0.565795\pi$
$104$	15.1737	+	20.8848i	0.145901	+	0.200815i
$105$		0			0
$106$	−41.6834	−	30.2848i	−0.393240	−	0.285705i
$107$	28.4807	−	28.4807i	0.266175	−	0.266175i	−0.561382	−	0.827557i	$-0.689730\pi$
$107$	28.4807	−	28.4807i	0.266175	−	0.266175i	0.827557	+	0.561382i	$0.189730\pi$
$108$	−5.39969	−	34.0923i	−0.0499971	−	0.315669i
$109$	−50.7034	−	16.4745i	−0.465169	−	0.151142i	0.0670496	−	0.997750i	$-0.478641\pi$
$109$	−50.7034	−	16.4745i	−0.465169	−	0.151142i	−0.532218	+	0.846607i	$0.678641\pi$
$110$		0			0
$111$	13.2341	+	40.7304i	0.119226	+	0.366940i
$112$	1.63278	+	3.20451i	0.0145784	+	0.0286117i
$113$	−95.9600	+	48.8940i	−0.849203	+	0.432691i	−0.823728	−	0.566985i	$-0.808110\pi$
$113$	−95.9600	+	48.8940i	−0.849203	+	0.432691i	−0.0254749	+	0.999675i	$0.508110\pi$
$114$	154.343	−	50.1492i	1.35389	−	0.439905i
$115$		0			0
$116$	35.1543	−	108.194i	0.303054	−	0.932705i
$117$	38.4075	−	6.08315i	0.328269	−	0.0519927i
$118$	60.7953	+	60.7953i	0.515215	+	0.515215i
$119$	−3.10999	+	4.28053i	−0.0261344	+	0.0359709i
$120$		0			0
$121$	−54.6524	+	39.7073i	−0.451672	+	0.328159i
$122$	−3.13416	+	19.7883i	−0.0256898	+	0.162199i
$123$	110.632	−	217.128i	0.899449	−	1.76527i
$124$		−	3.88268i		−	0.0313119i
$125$		0			0
$126$	5.41758			0.0429967
$127$	78.6966	+	40.0979i	0.619658	+	0.315732i	0.735488	−	0.677537i	$-0.236953\pi$
$127$	78.6966	+	40.0979i	0.619658	+	0.315732i	−0.115830	+	0.993269i	$0.536953\pi$
$128$	−11.1744	−	1.76985i	−0.0873001	−	0.0138270i
$129$	−117.481	−	161.698i	−0.910702	−	1.25347i
$130$		0			0
$131$	77.7492	+	56.4881i	0.593505	+	0.431207i	0.843568	−	0.537023i	$-0.180451\pi$
$131$	77.7492	+	56.4881i	0.593505	+	0.431207i	−0.250062	+	0.968230i	$0.580451\pi$
$132$	−70.7154	+	70.7154i	−0.535723	+	0.535723i
$133$	−4.43240	−	27.9851i	−0.0333263	−	0.210414i
$134$	−86.9069	−	28.2377i	−0.648559	−	0.210729i
$135$		0			0
$136$	−5.14335	−	15.8296i	−0.0378188	−	0.116394i
$137$	108.715	+	213.366i	0.793542	+	1.55741i	0.829793	+	0.558071i	$0.188458\pi$
$137$	108.715	+	213.366i	0.793542	+	1.55741i	−0.0362512	+	0.999343i	$0.511542\pi$
$138$	−141.571	+	72.1341i	−1.02588	+	0.522711i
$139$	132.664	−	43.1053i	0.954420	−	0.310110i	0.209910	−	0.977721i	$-0.432683\pi$
$139$	132.664	−	43.1053i	0.954420	−	0.310110i	0.744510	+	0.667611i	$0.232683\pi$
$140$		0			0
$141$	−56.1324	+	172.758i	−0.398102	+	1.22523i
$142$	43.9218	−	6.95653i	0.309308	−	0.0489896i
$143$	88.6196	+	88.6196i	0.619717	+	0.619717i
$144$	−10.0172	+	13.7875i	−0.0695641	+	0.0957468i
$145$		0			0
$146$	79.2559	−	57.5828i	0.542849	−	0.394403i
$147$	−27.4527	+	173.329i	−0.186753	+	1.17911i
$148$	−10.6784	+	20.9576i	−0.0721516	+	0.141605i
$149$			187.994i			1.26170i	0.775903	+	0.630852i	$0.217295\pi$
$149$			187.994i			1.26170i	−0.775903	+	0.630852i	$0.782705\pi$
$150$		0			0
$151$	160.259			1.06132			0.530660	−	0.847585i	$-0.321944\pi$
$151$	160.259			1.06132			0.530660	+	0.847585i	$0.321944\pi$
$152$	79.4166	+	40.4648i	0.522478	+	0.266216i
$153$	−24.7633	−	3.92212i	−0.161852	−	0.0256348i
$154$	10.2630	+	14.1258i	0.0666426	+	0.0917257i
$155$		0			0
$156$	53.7769	+	39.0712i	0.344724	+	0.250456i
$157$	−88.0051	+	88.0051i	−0.560542	+	0.560542i	−0.929461	−	0.368919i	$-0.879728\pi$
$157$	−88.0051	+	88.0051i	−0.560542	+	0.560542i	0.368919	+	0.929461i	$0.379728\pi$
$158$	−12.5743	−	79.3907i	−0.0795839	−	0.502473i
$159$	−126.176	−	40.9972i	−0.793562	−	0.257844i
$160$		0			0
$161$	8.57237	+	26.3831i	0.0532446	+	0.163870i
$162$	−64.9697	−	127.510i	−0.401048	−	0.787100i
$163$	162.119	−	82.6039i	0.994597	−	0.506772i	0.120599	−	0.992701i	$-0.461519\pi$
$163$	162.119	−	82.6039i	0.994597	−	0.506772i	0.873998	+	0.485929i	$0.161519\pi$
$164$	127.289	−	41.3586i	0.776150	−	0.252186i
$165$		0			0
$166$	−17.7005	+	54.4765i	−0.106629	+	0.328172i
$167$	−179.271	+	28.3937i	−1.07348	+	0.170022i	−0.668059	−	0.744109i	$-0.732874\pi$
$167$	−179.271	+	28.3937i	−1.07348	+	0.170022i	−0.405419	+	0.914131i	$0.632874\pi$
$168$	6.54836	+	6.54836i	0.0389783	+	0.0389783i
$169$	−50.3722	+	69.3314i	−0.298061	+	0.410245i
$170$		0			0
$171$	108.621	−	78.9175i	0.635208	−	0.461506i
$172$	17.1723	−	108.422i	0.0998389	−	0.630358i
$173$	−100.701	+	197.637i	−0.582086	+	1.14241i	0.392783	+	0.919631i	$0.371512\pi$
$173$	−100.701	+	197.637i	−0.582086	+	1.14241i	−0.974869	+	0.222777i	$0.928488\pi$
$174$		−	292.929i		−	1.68350i
$175$		0			0
$176$	−54.9260			−0.312079
$177$	197.257	+	100.507i	1.11445	+	0.567839i
$178$	83.9833	+	13.3016i	0.471816	+	0.0747283i
$179$	38.1969	+	52.5735i	0.213391	+	0.293707i	0.902272	−	0.431167i	$-0.141898\pi$
$179$	38.1969	+	52.5735i	0.213391	+	0.293707i	−0.688882	+	0.724874i	$0.741898\pi$
$180$		0			0
$181$	171.558	+	124.644i	0.947832	+	0.688641i	0.950293	−	0.311356i	$-0.100783\pi$
$181$	171.558	+	124.644i	0.947832	+	0.688641i	−0.00246082	+	0.999997i	$0.500783\pi$
$182$	8.20631	−	8.20631i	0.0450896	−	0.0450896i
$183$	8.07025	+	50.9536i	0.0440997	+	0.278435i
$184$	−82.9944	−	26.9665i	−0.451057	−	0.146557i
$185$		0			0
$186$	−3.08944	−	9.50832i	−0.0166099	−	0.0511200i
$187$	−36.6846	−	71.9976i	−0.196174	−	0.385014i
$188$	−88.8916	+	45.2925i	−0.472827	+	0.240918i
$189$	−14.7582	+	4.79523i	−0.0780858	+	0.0253716i
$190$		0			0
$191$	28.5061	−	87.7327i	0.149247	−	0.459334i	−0.848286	−	0.529538i	$-0.822365\pi$
$191$	28.5061	−	87.7327i	0.149247	−	0.459334i	0.997533	+	0.0702046i	$0.0223652\pi$
$192$	−28.7734	+	4.55726i	−0.149861	+	0.0237357i
$193$	151.113	+	151.113i	0.782967	+	0.782967i	0.980330	−	0.197363i	$-0.0632378\pi$
$193$	151.113	+	151.113i	0.782967	+	0.782967i	−0.197363	+	0.980330i	$0.563238\pi$
$194$	10.3541	−	14.2513i	0.0533719	−	0.0734601i
$195$		0			0
$196$	−77.9756	+	56.6526i	−0.397835	+	0.289044i
$197$	−10.5979	+	66.9124i	−0.0537964	+	0.339657i	0.946080	+	0.323933i	$0.105005\pi$
$197$	−10.5979	+	66.9124i	−0.0537964	+	0.339657i	−0.999876	+	0.0157239i	$0.994995\pi$
$198$	−37.5620	+	73.7196i	−0.189707	+	0.372321i
$199$		−	113.482i		−	0.570260i	−0.958489	−	0.285130i	$-0.907963\pi$
$199$		−	113.482i		−	0.570260i	0.958489	−	0.285130i	$-0.0920368\pi$
$200$		0			0
$201$	−235.296			−1.17063
$202$	−83.2487	−	42.4173i	−0.412122	−	0.209987i
$203$	−50.5135	−	8.00055i	−0.248835	−	0.0394116i
$204$	−25.1912	−	34.6727i	−0.123486	−	0.169964i
$205$		0			0
$206$	−11.6904	−	8.49360i	−0.0567497	−	0.0412311i
$207$	−92.9505	+	92.9505i	−0.449036	+	0.449036i
$208$	5.71109	+	36.0584i	0.0274572	+	0.173358i
$209$	411.538	+	133.717i	1.96908	+	0.639793i
$210$		0			0
$211$	−3.50834	−	10.7976i	−0.0166272	−	0.0511733i	0.942399	−	0.334492i	$-0.108565\pi$
$211$	−3.50834	−	10.7976i	−0.0166272	−	0.0511733i	−0.959026	+	0.283319i	$0.908565\pi$
$212$	−33.0801	−	64.9234i	−0.156038	−	0.306243i
$213$	102.025	−	51.9844i	0.478991	−	0.244058i
$214$	54.1736	−	17.6021i	0.253148	−	0.0822526i
$215$		0			0
$216$	15.0846	−	46.4256i	0.0698361	−	0.214933i
$217$	−1.72402	+	0.273058i	−0.00794479	+	0.00125833i
$218$	−53.3127	−	53.3127i	−0.244554	−	0.244554i
$219$	148.272	−	204.079i	0.677041	−	0.931867i
$220$		0			0
$221$	−43.4514	+	31.5693i	−0.196613	+	0.142847i
$222$	−9.47457	+	59.8201i	−0.0426783	+	0.269460i
$223$	66.5421	−	130.596i	0.298395	−	0.585633i	−0.692320	−	0.721591i	$-0.743411\pi$
$223$	66.5421	−	130.596i	0.298395	−	0.585633i	0.990715	+	0.135958i	$0.0434111\pi$
$224$			5.08623i			0.0227064i
$225$		0			0
$226$	−152.309			−0.673931
$227$	187.668	+	95.6214i	0.826729	+	0.421240i	0.815542	−	0.578698i	$-0.196439\pi$
$227$	187.668	+	95.6214i	0.826729	+	0.421240i	0.0111872	+	0.999937i	$0.496439\pi$
$228$	226.682	+	35.9029i	0.994218	+	0.157469i
$229$	−111.799	−	153.877i	−0.488203	−	0.671954i	0.491852	−	0.870679i	$-0.336320\pi$
$229$	−111.799	−	153.877i	−0.488203	−	0.671954i	−0.980055	+	0.198725i	$0.936320\pi$
$230$		0			0
$231$	36.3729	+	26.4265i	0.157459	+	0.114400i
$232$	113.762	−	113.762i	0.490352	−	0.490352i
$233$	69.4571	+	438.535i	0.298099	+	1.88212i	0.448935	+	0.893565i	$0.351804\pi$
$233$	69.4571	+	438.535i	0.298099	+	1.88212i	−0.150836	+	0.988559i	$0.548196\pi$
$234$	52.3019	+	16.9939i	0.223512	+	0.0726236i
$235$		0			0
$236$	37.5736	+	115.640i	0.159210	+	0.489998i
$237$	−93.9643	−	184.415i	−0.396474	−	0.778124i
$238$	−6.66709	+	3.39705i	−0.0280130	+	0.0142733i
$239$	−245.647	+	79.8157i	−1.02781	+	0.333957i	−0.773925	−	0.633277i	$-0.781710\pi$
$239$	−245.647	+	79.8157i	−1.02781	+	0.333957i	−0.253888	+	0.967234i	$0.581710\pi$
$240$		0			0
$241$	−50.4176	+	155.169i	−0.209202	+	0.643857i	0.790313	+	0.612703i	$0.209918\pi$
$241$	−50.4176	+	155.169i	−0.209202	+	0.643857i	−0.999515	+	0.0311532i	$0.990082\pi$
$242$	−94.3596	+	14.9451i	−0.389916	+	0.0617566i
$243$	−150.731	−	150.731i	−0.620294	−	0.620294i
$244$	−16.6541	+	22.9224i	−0.0682546	+	0.0939444i
$245$		0			0
$246$	278.809	−	202.567i	1.13337	−	0.823442i
$247$	44.9930	−	284.074i	0.182158	−	1.15010i
$248$	2.49283	−	4.89246i	0.0100517	−	0.0197276i
$249$			147.492i			0.592338i
$250$		0			0
$251$	269.305			1.07293			0.536463	−	0.843924i	$-0.319760\pi$
$251$	269.305			1.07293			0.536463	+	0.843924i	$0.319760\pi$
$252$	6.82655	+	3.47830i	0.0270895	+	0.0138028i
$253$	−418.442	−	66.2747i	−1.65392	−	0.261955i
$254$	73.4191	+	101.053i	0.289051	+	0.397845i
$255$		0			0
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	61.4130	−	61.4130i	0.238961	−	0.238961i	−0.577459	−	0.816420i	$-0.695956\pi$
$257$	61.4130	−	61.4130i	0.238961	−	0.238961i	0.816420	+	0.577459i	$0.195956\pi$
$258$	−44.2176	−	279.179i	−0.171386	−	1.08209i
$259$	10.0568	+	3.26764i	0.0388292	+	0.0126164i
$260$		0			0
$261$	−74.8889	−	230.484i	−0.286931	−	0.883082i
$262$	61.7021	+	121.097i	0.235504	+	0.462203i
$263$	324.035	−	165.104i	1.23207	−	0.627773i	0.288039	−	0.957619i	$-0.406997\pi$
$263$	324.035	−	165.104i	1.23207	−	0.627773i	0.944035	+	0.329846i	$0.106997\pi$
$264$	−134.509	+	43.7045i	−0.509503	+	0.165548i
$265$		0			0
$266$	12.3824	−	38.1090i	0.0465503	−	0.143267i
$267$	216.251	−	34.2509i	0.809931	−	0.128280i
$268$	−91.3793	−	91.3793i	−0.340967	−	0.340967i
$269$	−184.825	+	254.390i	−0.687082	+	0.945687i	−0.999992	−	0.00409606i	$-0.998696\pi$
$269$	−184.825	+	254.390i	−0.687082	+	0.945687i	0.312910	+	0.949783i	$0.398696\pi$
$270$		0			0
$271$	−196.495	+	142.762i	−0.725073	+	0.526797i	−0.888001	−	0.459841i	$-0.847906\pi$
$271$	−196.495	+	142.762i	−0.725073	+	0.526797i	0.162928	+	0.986638i	$0.447906\pi$
$272$	3.68224	−	23.2487i	0.0135376	−	0.0854732i
$273$	13.5668	−	26.6263i	0.0496951	−	0.0975321i
$274$			338.656i			1.23597i
$275$		0			0
$276$	−224.703			−0.814141
$277$	−382.219	−	194.750i	−1.37985	−	0.703070i	−0.402646	−	0.915356i	$-0.631909\pi$
$277$	−382.219	−	194.750i	−1.37985	−	0.703070i	−0.977208	+	0.212286i	$0.931909\pi$
$278$	194.842	+	30.8600i	0.700871	+	0.111007i
$279$	−4.86171	−	6.69157i	−0.0174255	−	0.0239841i
$280$		0			0
$281$	−180.948	−	131.467i	−0.643944	−	0.467852i	0.217259	−	0.976114i	$-0.430288\pi$
$281$	−180.948	−	131.467i	−0.643944	−	0.467852i	−0.861203	+	0.508262i	$0.830288\pi$
$282$	−181.648	+	181.648i	−0.644142	+	0.644142i
$283$	−55.7689	−	352.111i	−0.197063	−	1.24421i	−0.865679	−	0.500600i	$-0.833113\pi$
$283$	−55.7689	−	352.111i	−0.197063	−	1.24421i	0.668615	−	0.743608i	$-0.266887\pi$
$284$	59.8111	+	19.4338i	0.210602	+	0.0684288i
$285$		0			0
$286$	54.7699	+	168.564i	0.191503	+	0.589386i
$287$	−27.3163	−	53.6112i	−0.0951786	−	0.186799i
$288$	−21.4746	+	10.9419i	−0.0745646	+	0.0379926i
$289$	−241.921	+	78.6050i	−0.837098	+	0.271990i
$290$		0			0
$291$	14.0166	−	43.1388i	0.0481672	−	0.148243i
$292$	136.839	−	21.6731i	0.468626	−	0.0742230i
$293$	−331.758	−	331.758i	−1.13228	−	1.13228i	−0.989797	−	0.142481i	$-0.954492\pi$
$293$	−331.758	−	331.758i	−1.13228	−	1.13228i	−0.142481	−	0.989797i	$-0.545508\pi$
$294$	−145.877	+	200.782i	−0.496179	+	0.682932i
$295$		0			0
$296$	−26.9112	+	19.5522i	−0.0909163	+	0.0660546i
$297$	37.0729	−	234.069i	0.124825	−	0.788111i
$298$	−120.700	+	236.886i	−0.405032	+	0.794920i
$299$			281.595i			0.941788i
$300$		0			0
$301$	−49.3500			−0.163954
$302$	201.938	+	102.893i	0.668670	+	0.340705i
$303$	−237.620	−	37.6353i	−0.784224	−	0.124209i
$304$	74.0908	+	101.977i	0.243720	+	0.335451i
$305$		0			0
$306$	−28.6854	−	20.8412i	−0.0937431	−	0.0681084i
$307$	5.33327	−	5.33327i	0.0173722	−	0.0173722i	−0.698367	−	0.715740i	$-0.746090\pi$
$307$	5.33327	−	5.33327i	0.0173722	−	0.0173722i	0.715740	+	0.698367i	$0.246090\pi$
$308$	3.86279	+	24.3887i	0.0125415	+	0.0791842i
$309$	−35.3872	−	11.4980i	−0.114522	−	0.0372103i
$310$		0			0
$311$	−78.3745	−	241.212i	−0.252008	−	0.775601i	−0.994404	−	0.105640i	$-0.966311\pi$
$311$	−78.3745	−	241.212i	−0.252008	−	0.775601i	0.742396	−	0.669961i	$-0.233689\pi$
$312$	42.6776	+	83.7595i	0.136787	+	0.268460i
$313$	118.104	−	60.1772i	0.377330	−	0.192259i	−0.255031	−	0.966933i	$-0.582086\pi$
$313$	118.104	−	60.1772i	0.377330	−	0.192259i	0.632362	+	0.774673i	$0.282086\pi$
$314$	−167.396	+	54.3901i	−0.533107	+	0.173217i
$315$		0			0
$316$	35.1275	−	108.111i	0.111163	−	0.342125i
$317$	222.037	−	35.1671i	0.700431	−	0.110937i	0.203945	−	0.978982i	$-0.434624\pi$
$317$	222.037	−	35.1671i	0.700431	−	0.110937i	0.496486	+	0.868045i	$0.334624\pi$
$318$	−132.670	−	132.670i	−0.417200	−	0.417200i
$319$	459.095	−	631.890i	1.43917	−	1.98085i
$320$		0			0
$321$	118.660	−	86.2117i	0.369658	−	0.268572i
$322$	−6.13714	+	38.7484i	−0.0190594	+	0.120337i
$323$	−84.1882	+	165.229i	−0.260645	+	0.511544i
$324$		−	202.385i		−	0.624646i
$325$		0			0
$326$	257.317			0.789317
$327$	−172.979	−	88.1371i	−0.528987	−	0.269532i
$328$	186.947	+	29.6095i	0.569960	+	0.0902728i
$329$	26.3627	+	36.2851i	0.0801297	+	0.110289i
$330$		0			0
$331$	−340.878	−	247.662i	−1.02984	−	0.748225i	−0.0615656	−	0.998103i	$-0.519609\pi$
$331$	−340.878	−	247.662i	−1.02984	−	0.748225i	−0.968277	+	0.249878i	$0.919609\pi$
$332$	−57.2800	+	57.2800i	−0.172530	+	0.172530i
$333$	7.83849	+	49.4903i	0.0235390	+	0.148619i
$334$	−244.124	−	79.3208i	−0.730911	−	0.237487i
$335$		0			0
$336$	4.04711	+	12.4557i	0.0120450	+	0.0370706i
$337$	158.905	+	311.868i	0.471527	+	0.925423i	0.997203	+	0.0747388i	$0.0238123\pi$
$337$	158.905	+	311.868i	0.471527	+	0.925423i	−0.525676	+	0.850685i	$0.676188\pi$
$338$	−107.986	+	55.0217i	−0.319486	+	0.162786i
$339$	−372.990	+	121.192i	−1.10026	+	0.357498i
$340$		0			0
$341$	8.23761	−	25.3528i	0.0241572	−	0.0743483i
$342$	187.538	−	29.7031i	0.548357	−	0.0868512i
$343$	61.7924	+	61.7924i	0.180153	+	0.180153i
$344$	91.2493	−	125.594i	0.265260	−	0.365099i
$345$		0			0
$346$	−253.781	+	184.383i	−0.733471	+	0.532898i
$347$	25.8523	−	163.225i	0.0745022	−	0.470388i	−0.922026	−	0.387129i	$-0.873467\pi$
$347$	25.8523	−	163.225i	0.0745022	−	0.470388i	0.996528	−	0.0832597i	$-0.0265331\pi$
$348$	188.072	−	369.112i	0.540437	−	1.06067i
$349$		−	541.612i		−	1.55190i	−0.630796	−	0.775949i	$-0.717272\pi$
$349$		−	541.612i		−	1.55190i	0.630796	−	0.775949i	$-0.282728\pi$
$350$		0			0
$351$	−157.519			−0.448772
$352$	−69.2108	−	35.2647i	−0.196622	−	0.100184i
$353$	−5.62039	−	0.890182i	−0.0159218	−	0.00252176i	0.148468	−	0.988917i	$-0.452566\pi$
$353$	−5.62039	−	0.890182i	−0.0159218	−	0.00252176i	−0.164390	+	0.986395i	$0.552566\pi$
$354$	184.029	+	253.294i	0.519855	+	0.715519i
$355$		0			0
$356$	97.2849	+	70.6816i	0.273272	+	0.198544i
$357$	−13.6241	+	13.6241i	−0.0381626	+	0.0381626i
$358$	14.3766	+	90.7704i	0.0401582	+	0.253549i
$359$	46.7523	+	15.1908i	0.130229	+	0.0423141i	0.373407	−	0.927668i	$-0.378190\pi$
$359$	46.7523	+	15.1908i	0.130229	+	0.0423141i	−0.243177	+	0.969982i	$0.578190\pi$
$360$		0			0
$361$	−195.314	−	601.114i	−0.541036	−	1.66514i
$362$	136.149	+	267.207i	0.376102	+	0.738142i
$363$	−219.186	+	111.681i	−0.603819	+	0.307661i
$364$	15.6093	−	5.07178i	0.0428828	−	0.0139335i
$365$		0			0
$366$	−22.5451	+	69.3866i	−0.0615986	+	0.189581i
$367$	−353.395	+	55.9723i	−0.962929	+	0.152513i	−0.618054	−	0.786136i	$-0.712079\pi$
$367$	−353.395	+	55.9723i	−0.962929	+	0.152513i	−0.344875	+	0.938649i	$0.612079\pi$
$368$	−87.2655	−	87.2655i	−0.237134	−	0.237134i
$369$	167.587	−	230.664i	0.454166	−	0.625106i
$370$		0			0
$371$	−26.5014	+	19.2544i	−0.0714324	+	0.0518987i
$372$	2.21180	−	13.9647i	0.00594569	−	0.0375396i
$373$	−75.0714	+	147.336i	−0.201264	+	0.395003i	−0.969474	−	0.245196i	$-0.921148\pi$
$373$	−75.0714	+	147.336i	−0.201264	+	0.395003i	0.768210	+	0.640198i	$0.221148\pi$
$374$		−	114.275i		−	0.305549i
$375$		0			0
$376$	−141.089			−0.375238
$377$	−462.566	−	235.689i	−1.22697	−	0.625170i
$378$	−21.6752	−	3.43301i	−0.0573417	−	0.00908203i
$379$	346.461	+	476.863i	0.914145	+	1.25821i	0.965731	+	0.259544i	$0.0835723\pi$
$379$	346.461	+	476.863i	0.914145	+	1.25821i	−0.0515863	+	0.998669i	$0.516428\pi$
$380$		0			0
$381$	260.204	+	189.049i	0.682950	+	0.496193i
$382$	92.2477	−	92.2477i	0.241486	−	0.241486i
$383$	106.883	+	674.830i	0.279067	+	1.76196i	0.586080	+	0.810253i	$0.300670\pi$
$383$	106.883	+	674.830i	0.279067	+	1.76196i	−0.307013	+	0.951705i	$0.599330\pi$
$384$	−39.1825	−	12.7312i	−0.102038	−	0.0331541i
$385$		0			0
$386$	93.3928	+	287.433i	0.241950	+	0.744646i
$387$	−106.165	−	208.361i	−0.274329	−	0.538400i
$388$	22.1968	−	11.3099i	0.0572084	−	0.0291491i
$389$	−149.313	+	48.5147i	−0.383837	+	0.124716i	−0.494579	−	0.869133i	$-0.664678\pi$
$389$	−149.313	+	48.5147i	−0.383837	+	0.124716i	0.110741	+	0.993849i	$0.464678\pi$
$390$		0			0
$391$	56.1047	−	172.672i	0.143490	−	0.441617i
$392$	−134.628	+	21.3230i	−0.343439	+	0.0543954i
$393$	247.460	+	247.460i	0.629669	+	0.629669i
$394$	−56.3145	+	77.5103i	−0.142930	+	0.196727i
$395$		0			0
$396$	−94.6618	+	68.7758i	−0.239045	+	0.173676i
$397$	27.1282	−	171.281i	0.0683331	−	0.431438i	−0.929677	−	0.368377i	$-0.879914\pi$
$397$	27.1282	−	171.281i	0.0683331	−	0.431438i	0.998010	−	0.0630614i	$-0.0200864\pi$
$398$	72.8598	−	142.995i	0.183065	−	0.359285i
$399$		−	103.178i		−	0.258592i
$400$		0			0
$401$	410.229			1.02302			0.511508	−	0.859278i	$-0.329087\pi$
$401$	410.229			1.02302			0.511508	+	0.859278i	$0.329087\pi$
$402$	−296.490	−	151.069i	−0.737537	−	0.375794i
$403$	−17.5004	−	2.77179i	−0.0434253	−	0.00687789i
$404$	−77.6659	−	106.898i	−0.192242	−	0.264599i
$405$		0			0
$406$	−58.5140	−	42.5129i	−0.144123	−	0.104712i
$407$	−114.191	+	114.191i	−0.280569	+	0.280569i
$408$	−9.48152	−	59.8639i	−0.0232390	−	0.146725i
$409$	−38.3159	−	12.4496i	−0.0936820	−	0.0304391i	0.261801	−	0.965122i	$-0.415684\pi$
$409$	−38.3159	−	12.4496i	−0.0936820	−	0.0304391i	−0.355483	+	0.934683i	$0.615684\pi$
$410$		0			0
$411$	269.468	+	829.338i	0.655640	+	2.01785i
$412$	−9.27758	−	18.2083i	−0.0225184	−	0.0441948i
$413$	48.7049	−	24.8164i	0.117929	−	0.0600881i
$414$	−176.802	+	57.4466i	−0.427059	+	0.138760i
$415$		0			0
$416$	−15.9545	+	49.1030i	−0.0383522	+	0.118036i
$417$	501.706	−	79.4624i	1.20313	−	0.190557i
$418$	432.716	+	432.716i	1.03521	+	1.03521i
$419$	256.242	−	352.687i	0.611556	−	0.841735i	−0.385148	−	0.922855i	$-0.625850\pi$
$419$	256.242	−	352.687i	0.611556	−	0.841735i	0.996704	+	0.0811197i	$0.0258496\pi$
$420$		0			0
$421$	140.600	−	102.152i	0.333967	−	0.242641i	−0.408145	−	0.912917i	$-0.633824\pi$
$421$	140.600	−	102.152i	0.333967	−	0.242641i	0.742112	+	0.670276i	$0.233824\pi$
$422$	2.51169	−	15.8582i	0.00595188	−	0.0375787i
$423$	−96.4863	+	189.365i	−0.228100	+	0.447671i
$424$		−	103.047i		−	0.243035i
$425$		0			0
$426$	161.935			0.380130
$427$	11.3495	+	5.78284i	0.0265795	+	0.0135430i
$428$	79.5639	+	12.6017i	0.185897	+	0.0294432i
$429$	268.253	+	369.219i	0.625299	+	0.860650i
$430$		0			0
$431$	−98.9485	−	71.8903i	−0.229579	−	0.166799i	0.467049	−	0.884231i	$-0.345317\pi$
$431$	−98.9485	−	71.8903i	−0.229579	−	0.166799i	−0.696628	+	0.717433i	$0.745317\pi$
$432$	48.8148	−	48.8148i	0.112997	−	0.112997i
$433$	−46.0011	−	290.440i	−0.106238	−	0.670761i	−0.982123	−	0.188241i	$-0.939721\pi$
$433$	−46.0011	−	290.440i	−0.106238	−	0.670761i	0.875885	−	0.482520i	$-0.160279\pi$
$434$	−2.34771	−	0.762816i	−0.00540946	−	0.00175764i
$435$		0			0
$436$	−32.9491	−	101.407i	−0.0755712	−	0.232584i
$437$	441.397	+	866.291i	1.01006	+	1.98236i
$438$	317.860	−	161.958i	0.725708	−	0.369767i
$439$	−135.892	+	44.1541i	−0.309550	+	0.100579i	−0.459672	−	0.888089i	$-0.652033\pi$
$439$	−135.892	+	44.1541i	−0.309550	+	0.100579i	0.150123	+	0.988667i	$0.452033\pi$
$440$		0			0
$441$	−63.4487	+	195.275i	−0.143875	+	0.442800i
$442$	−75.0206	+	11.8821i	−0.169730	+	0.0268826i
$443$	13.7393	+	13.7393i	0.0310143	+	0.0310143i	0.722444	−	0.691430i	$-0.243019\pi$
$443$	13.7393	+	13.7393i	0.0310143	+	0.0310143i	−0.691430	+	0.722444i	$0.743019\pi$
$444$	−50.3455	+	69.2947i	−0.113391	+	0.156069i
$445$		0			0
$446$	167.696	−	121.838i	0.376000	−	0.273180i
$447$	−107.092	+	676.154i	−0.239580	+	1.51265i
$448$	−3.26556	+	6.40903i	−0.00728920	+	0.0143059i
$449$		−	313.808i		−	0.698904i	−0.936954	−	0.349452i	$-0.886368\pi$
$449$		−	313.808i		−	0.698904i	0.936954	−	0.349452i	$-0.113632\pi$
$450$		0			0
$451$	918.906			2.03749
$452$	−191.920	−	97.7881i	−0.424602	−	0.216345i
$453$	576.401	+	91.2929i	1.27241	+	0.201530i
$454$	175.082	+	240.980i	0.385644	+	0.530793i
$455$		0			0
$456$	262.585	+	190.779i	0.575844	+	0.418375i
$457$	−36.5102	+	36.5102i	−0.0798911	+	0.0798911i	−0.745923	−	0.666032i	$-0.767991\pi$
$457$	−36.5102	+	36.5102i	−0.0798911	+	0.0798911i	0.666032	+	0.745923i	$0.267991\pi$
$458$	−42.0789	−	265.676i	−0.0918754	−	0.580079i
$459$	96.5899	+	31.3839i	0.210435	+	0.0683746i
$460$		0			0
$461$	252.310	+	776.530i	0.547310	+	1.68445i	0.715434	+	0.698680i	$0.246229\pi$
$461$	252.310	+	776.530i	0.547310	+	1.68445i	−0.168124	+	0.985766i	$0.553771\pi$
$462$	28.8657	+	56.6522i	0.0624799	+	0.122624i
$463$	−490.040	+	249.688i	−1.05840	+	0.539283i	−0.894442	−	0.447184i	$-0.852427\pi$
$463$	−490.040	+	249.688i	−1.05840	+	0.539283i	−0.163960	+	0.986467i	$0.552427\pi$
$464$	216.388	−	70.3086i	0.466353	−	0.151527i
$465$		0			0
$466$	−194.036	+	597.180i	−0.416385	+	1.28150i
$467$	581.328	−	92.0733i	1.24481	−	0.197159i	0.500941	−	0.865481i	$-0.332987\pi$
$467$	581.328	−	92.0733i	1.24481	−	0.197159i	0.743872	+	0.668322i	$0.232987\pi$
$468$	54.9935	+	54.9935i	0.117507	+	0.117507i
$469$	−34.1486	+	47.0015i	−0.0728115	+	0.100216i
$470$		0			0
$471$	−366.659	+	266.393i	−0.778468	+	0.565590i
$472$	−26.8997	+	169.838i	−0.0569909	+	0.359827i
$473$	342.161	−	671.529i	0.723385	−	1.41972i
$474$		−	292.706i		−	0.617523i
$475$		0			0
$476$	−10.5821			−0.0222312
$477$	−138.306	−	70.4704i	−0.289949	−	0.147737i
$478$	−360.779	−	57.1417i	−0.754767	−	0.119543i
$479$	122.812	+	169.037i	0.256393	+	0.352895i	0.917737	−	0.397188i	$-0.130014\pi$
$479$	122.812	+	169.037i	0.256393	+	0.352895i	−0.661344	+	0.750083i	$0.730014\pi$
$480$		0			0
$481$	86.8391	+	63.0923i	0.180539	+	0.131169i
$482$	−163.155	+	163.155i	−0.338495	+	0.338495i
$483$	15.8027	+	99.7746i	0.0327179	+	0.206573i
$484$	−128.495	−	41.7507i	−0.265486	−	0.0862617i
$485$		0			0
$486$	−93.1571	−	286.708i	−0.191681	−	0.589935i
$487$	75.5860	+	148.346i	0.155207	+	0.304611i	0.955496	−	0.295003i	$-0.0953206\pi$
$487$	75.5860	+	148.346i	0.155207	+	0.304611i	−0.800289	+	0.599614i	$0.795321\pi$
$488$	−35.7025	+	18.1914i	−0.0731609	+	0.0372774i
$489$	630.146	−	204.747i	1.28864	−	0.418705i
$490$		0			0
$491$	91.4686	−	281.511i	0.186290	−	0.573343i	−0.813678	−	0.581316i	$-0.802538\pi$
$491$	91.4686	−	281.511i	0.186290	−	0.573343i	0.999968	+	0.00797308i	$0.00253794\pi$
$492$	481.376	−	76.2425i	0.978407	−	0.154964i
$493$	236.685	+	236.685i	0.480091	+	0.480091i
$494$	239.081	−	329.067i	0.483970	−	0.666128i
$495$		0			0
$496$	6.28230	−	4.56436i	0.0126659	−	0.00920234i
$497$	4.42282	−	27.9246i	0.00889903	−	0.0561862i
$498$	−94.6958	+	185.851i	−0.190152	+	0.373195i
$499$		−	459.459i		−	0.920759i	−0.887722	−	0.460380i	$-0.847713\pi$
$499$		−	459.459i		−	0.920759i	0.887722	−	0.460380i	$-0.152287\pi$
$500$		0			0
$501$	−660.954			−1.31927
$502$	339.344	+	172.904i	0.675983	+	0.344431i
$503$	230.666	+	36.5339i	0.458580	+	0.0726319i	0.381451	−	0.924389i	$-0.375425\pi$
$503$	230.666	+	36.5339i	0.458580	+	0.0726319i	0.0771293	+	0.997021i	$0.475425\pi$
$504$	6.36875	+	8.76583i	0.0126364	+	0.0173925i
$505$		0			0
$506$	−484.717	−	352.167i	−0.957938	−	0.695983i
$507$	−220.668	+	220.668i	−0.435242	+	0.435242i
$508$	27.6336	+	174.472i	0.0543969	+	0.343448i
$509$	−241.356	−	78.4213i	−0.474177	−	0.154069i	0.0621728	−	0.998065i	$-0.480197\pi$
$509$	−241.356	−	78.4213i	−0.474177	−	0.154069i	−0.536349	+	0.843996i	$0.680197\pi$
$510$		0			0
$511$	−19.2470	−	59.2361i	−0.0376653	−	0.115922i
$512$	−10.2726	−	20.1612i	−0.0200637	−	0.0393773i
$513$	−484.588	+	246.910i	−0.944615	+	0.481306i
$514$	116.815	−	37.9553i	0.227266	−	0.0738431i
$515$		0			0
$516$	123.526	−	380.175i	0.239392	−	0.736773i
$517$	−676.531	+	107.152i	−1.30857	+	0.207257i
$518$	10.5743	+	10.5743i	0.0204137	+	0.0204137i
$519$	−474.774	+	653.470i	−0.914785	+	1.25909i
$520$		0			0
$521$	260.762	−	189.454i	0.500502	−	0.363636i	−0.308707	−	0.951157i	$-0.599896\pi$
$521$	260.762	−	189.454i	0.500502	−	0.363636i	0.809209	+	0.587521i	$0.199896\pi$
$522$	53.6146	−	338.509i	0.102710	−	0.648485i
$523$	62.4913	−	122.646i	0.119486	−	0.234505i	−0.823515	−	0.567295i	$-0.807990\pi$
$523$	62.4913	−	122.646i	0.119486	−	0.234505i	0.943001	+	0.332790i	$0.107990\pi$
$524$			192.207i			0.366806i
$525$		0			0
$526$	514.312			0.977780
$527$	10.1789	+	5.18641i	0.0193148	+	0.00984139i
$528$	−197.551	−	31.2890i	−0.374150	−	0.0592595i
$529$	−248.579	−	342.140i	−0.469904	−	0.646767i
$530$		0			0
$531$	209.555	+	152.250i	0.394641	+	0.286724i
$532$	40.0702	−	40.0702i	0.0753199	−	0.0753199i
$533$	−95.5460	−	603.254i	−0.179261	−	1.13181i
$534$	294.483	+	95.6834i	0.551467	+	0.179182i
$535$		0			0
$536$	−56.4755	−	173.814i	−0.105365	−	0.324279i
$537$	107.433	+	210.849i	0.200061	+	0.392643i
$538$	−396.221	+	201.885i	−0.736471	+	0.375251i
$539$	−629.354	+	204.490i	−1.16763	+	0.379387i
$540$		0			0
$541$	195.153	−	600.618i	0.360726	−	1.11020i	−0.591889	−	0.806020i	$-0.701617\pi$
$541$	195.153	−	600.618i	0.360726	−	1.11020i	0.952614	−	0.304180i	$-0.0983825\pi$
$542$	−339.257	+	53.7330i	−0.625935	+	0.0991383i
$543$	546.033	+	546.033i	1.00559	+	1.00559i
$544$	19.5665	−	26.9310i	0.0359678	−	0.0495054i
$545$		0			0
$546$	34.1902	−	24.8407i	0.0626195	−	0.0454957i
$547$	15.5855	−	98.4028i	0.0284926	−	0.179895i	−0.969338	−	0.245732i	$-0.920972\pi$
$547$	15.5855	−	98.4028i	0.0284926	−	0.179895i	0.997830	+	0.0658367i	$0.0209717\pi$
$548$	−217.430	+	426.731i	−0.396771	+	0.778707i
$549$			60.3591i			0.109944i
$550$		0			0
$551$	−1792.47			−3.25312
$552$	−283.142	−	144.268i	−0.512939	−	0.261355i
$553$	−50.4750	−	7.99445i	−0.0912748	−	0.0144565i
$554$	−356.587	−	490.800i	−0.643659	−	0.885920i
$555$		0			0
$556$	225.702	+	163.982i	0.405939	+	0.294932i
$557$	557.960	−	557.960i	1.00172	−	1.00172i	0.00172416	−	0.999999i	$-0.499451\pi$
$557$	557.960	−	557.960i	1.00172	−	1.00172i	0.999999	−	0.00172416i	$-0.000548818\pi$
$558$	−1.82986	−	11.5533i	−0.00327932	−	0.0207048i
$559$	−476.430	−	154.801i	−0.852290	−	0.276926i
$560$		0			0
$561$	−90.9286	−	279.850i	−0.162083	−	0.498841i
$562$	−143.601	−	281.833i	−0.255518	−	0.501483i
$563$	−99.2730	+	50.5821i	−0.176329	+	0.0898439i	−0.539927	−	0.841712i	$-0.681548\pi$
$563$	−99.2730	+	50.5821i	−0.176329	+	0.0898439i	0.363598	+	0.931556i	$0.381548\pi$
$564$	−345.515	+	112.265i	−0.612616	+	0.199051i
$565$		0			0
$566$	155.796	−	479.492i	0.275258	−	0.847158i
$567$	−89.8649	+	14.2332i	−0.158492	+	0.0251027i
$568$	62.8891	+	62.8891i	0.110720	+	0.110720i
$569$	−1.68455	+	2.31858i	−0.00296054	+	0.00407483i	−0.810495	−	0.585746i	$-0.800802\pi$
$569$	−1.68455	+	2.31858i	−0.00296054	+	0.00407483i	0.807534	+	0.589821i	$0.200802\pi$
$570$		0			0
$571$	−144.753	+	105.169i	−0.253507	+	0.184184i	−0.707280	−	0.706934i	$-0.750078\pi$
$571$	−144.753	+	105.169i	−0.253507	+	0.184184i	0.453773	+	0.891118i	$0.350078\pi$
$572$	−39.2109	+	247.568i	−0.0685506	+	0.432811i
$573$	152.505	−	299.308i	0.266151	−	0.522352i
$574$		−	85.0922i		−	0.148244i
$575$		0			0
$576$	−34.0847			−0.0591748
$577$	−426.909	−	217.521i	−0.739878	−	0.376987i	0.0430716	−	0.999072i	$-0.486286\pi$
$577$	−426.909	−	217.521i	−0.739878	−	0.376987i	−0.782949	+	0.622085i	$0.786286\pi$
$578$	−355.306	−	56.2750i	−0.614717	−	0.0973615i
$579$	457.421	+	629.586i	0.790019	+	1.08737i
$580$		0			0
$581$	29.4623	+	21.4056i	0.0507096	+	0.0368427i
$582$	45.3588	−	45.3588i	0.0779361	−	0.0779361i
$583$	−78.2602	−	494.115i	−0.134237	−	0.847539i
$584$	186.342	+	60.5461i	0.319078	+	0.103675i
$585$		0			0
$586$	−205.038	−	631.041i	−0.349893	−	1.07686i
$587$	−390.539	−	766.476i	−0.665313	−	1.30575i	−0.938995	−	0.343931i	$-0.888241\pi$
$587$	−390.539	−	766.476i	−0.665313	−	1.30575i	0.273682	−	0.961820i	$-0.411759\pi$
$588$	−312.725	+	159.342i	−0.531846	+	0.270989i
$589$	−58.1826	+	18.9047i	−0.0987819	+	0.0320962i
$590$		0			0
$591$	−76.2343	+	234.625i	−0.128992	+	0.396997i
$592$	−46.4634	+	7.35908i	−0.0784854	+	0.0124309i
$593$	−735.093	−	735.093i	−1.23962	−	1.23962i	−0.960158	−	0.279459i	$-0.909845\pi$
$593$	−735.093	−	735.093i	−1.23962	−	1.23962i	−0.279459	−	0.960158i	$-0.590155\pi$
$594$	196.996	−	271.142i	0.331643	−	0.456468i
$595$		0			0
$596$	−304.181	+	221.000i	−0.510370	+	0.370806i
$597$	64.6457	−	408.157i	0.108284	−	0.683680i
$598$	−180.795	+	354.830i	−0.302332	+	0.593361i
$599$		−	515.872i		−	0.861222i	−0.902538	−	0.430611i	$-0.858298\pi$
$599$		−	515.872i		−	0.861222i	0.902538	−	0.430611i	$-0.141702\pi$
$600$		0			0
$601$	707.544			1.17728			0.588639	−	0.808396i	$-0.299664\pi$
$601$	707.544			1.17728			0.588639	+	0.808396i	$0.299664\pi$
$602$	−62.1846	−	31.6847i	−0.103297	−	0.0526323i
$603$	−271.908	−	43.0660i	−0.450925	−	0.0714195i
$604$	188.396	+	259.305i	0.311914	+	0.429313i
$605$		0			0
$606$	−275.255	−	199.985i	−0.454217	−	0.330008i
$607$	−422.828	+	422.828i	−0.696587	+	0.696587i	−0.963673	−	0.267086i	$-0.913939\pi$
$607$	−422.828	+	422.828i	−0.696587	+	0.696587i	0.267086	+	0.963673i	$0.413939\pi$
$608$	27.8864	+	176.068i	0.0458658	+	0.289585i
$609$	−177.123	−	57.5507i	−0.290842	−	0.0945004i
$610$		0			0
$611$	140.689	+	432.995i	0.230259	+	0.708666i
$612$	−22.7649	−	44.6786i	−0.0371975	−	0.0730042i
$613$	879.227	−	447.989i	1.43430	−	0.730813i	0.447734	−	0.894167i	$-0.352231\pi$
$613$	879.227	−	447.989i	1.43430	−	0.730813i	0.986568	+	0.163353i	$0.0522310\pi$
$614$	10.1445	−	3.29614i	0.0165219	−	0.00536831i
$615$		0			0
$616$	−10.7911	+	33.2117i	−0.0175181	+	0.0539150i
$617$	−601.071	+	95.2002i	−0.974182	+	0.154295i	−0.623179	−	0.782079i	$-0.714159\pi$
$617$	−601.071	+	95.2002i	−0.974182	+	0.154295i	−0.351003	+	0.936374i	$0.614159\pi$
$618$	−37.2083	−	37.2083i	−0.0602075	−	0.0602075i
$619$	−716.320	+	985.930i	−1.15722	+	1.59278i	−0.436227	+	0.899836i	$0.643686\pi$
$619$	−716.320	+	985.930i	−1.15722	+	1.59278i	−0.720994	+	0.692942i	$0.756314\pi$
$620$		0			0
$621$	430.786	−	312.984i	0.693697	−	0.504000i
$622$	56.1099	−	354.264i	0.0902089	−	0.569557i
$623$	24.5429	−	48.1681i	0.0393947	−	0.0773164i
$624$			132.944i			0.213051i
$625$		0			0
$626$	187.456			0.299451
$627$	1403.99	+	715.371i	2.23923	+	1.14094i
$628$	−245.851	−	38.9390i	−0.391483	−	0.0620048i
$629$	−40.6788	−	55.9896i	−0.0646723	−	0.0890137i
$630$		0			0
$631$	−694.007	−	504.226i	−1.09985	−	0.799090i	−0.118817	−	0.992916i	$-0.537910\pi$
$631$	−694.007	−	504.226i	−1.09985	−	0.799090i	−0.981036	+	0.193827i	$0.937910\pi$
$632$	113.675	−	113.675i	0.179865	−	0.179865i
$633$	−6.46745	−	40.8339i	−0.0102171	−	0.0645085i
$634$	302.361	+	98.2430i	0.476910	+	0.154957i
$635$		0			0
$636$	−81.9944	−	252.353i	−0.128922	−	0.396781i
$637$	199.685	+	391.903i	0.313477	+	0.615233i
$638$	984.192	−	501.471i	1.54262	−	0.786004i
$639$	127.415	−	41.3997i	0.199398	−	0.0647882i
$640$		0			0
$641$	−263.656	+	811.451i	−0.411321	+	1.26591i	0.504180	+	0.863598i	$0.331795\pi$
$641$	−263.656	+	811.451i	−0.411321	+	1.26591i	−0.915501	+	0.402316i	$0.868205\pi$
$642$	204.872	−	32.4485i	0.319115	−	0.0505429i
$643$	−382.594	−	382.594i	−0.595015	−	0.595015i	0.343967	−	0.938982i	$-0.388229\pi$
$643$	−382.594	−	382.594i	−0.595015	−	0.595015i	−0.938982	+	0.343967i	$0.888229\pi$
$644$	−32.6112	+	44.8855i	−0.0506386	+	0.0696980i
$645$		0			0
$646$	−212.167	+	154.148i	−0.328431	+	0.238619i
$647$	36.6956	−	231.687i	0.0567165	−	0.358094i	−0.942966	−	0.332890i	$-0.891976\pi$
$647$	36.6956	−	231.687i	0.0567165	−	0.358094i	0.999682	−	0.0252045i	$-0.00802368\pi$
$648$	129.939	−	255.020i	0.200524	−	0.393550i
$649$			834.811i			1.28630i
$650$		0			0
$651$	−6.35629			−0.00976389
$652$	324.239	+	165.208i	0.497298	+	0.253386i
$653$	344.513	+	54.5654i	0.527584	+	0.0835612i	0.414544	−	0.910029i	$-0.363941\pi$
$653$	344.513	+	54.5654i	0.527584	+	0.0835612i	0.113040	+	0.993590i	$0.463941\pi$
$654$	−161.379	−	222.118i	−0.246756	−	0.339631i
$655$		0			0
$656$	216.556	+	157.337i	0.330116	+	0.239844i
$657$	208.696	−	208.696i	0.317649	−	0.317649i
$658$	9.92244	+	62.6478i	0.0150797	+	0.0952094i
$659$	130.784	+	42.4942i	0.198458	+	0.0644829i	0.406559	−	0.913624i	$-0.366728\pi$
$659$	130.784	+	42.4942i	0.198458	+	0.0644829i	−0.208101	+	0.978107i	$0.566728\pi$
$660$		0			0
$661$	60.3829	+	185.840i	0.0913509	+	0.281149i	0.986286	−	0.165048i	$-0.0527780\pi$
$661$	60.3829	+	185.840i	0.0913509	+	0.281149i	−0.894935	+	0.446197i	$0.852778\pi$
$662$	−270.522	−	530.930i	−0.408644	−	0.802009i
$663$	−174.264	+	88.7920i	−0.262842	+	0.133925i
$664$	−108.953	+	35.4010i	−0.164086	+	0.0533147i
$665$		0			0
$666$	−21.8976	+	67.3940i	−0.0328793	+	0.101192i
$667$	1733.34	−	274.534i	2.59871	−	0.411595i
$668$	−256.687	−	256.687i	−0.384263	−	0.384263i
$669$	313.726	−	431.806i	0.468947	−	0.645450i
$670$		0			0
$671$	−157.380	+	114.343i	−0.234545	+	0.170407i
$672$	−2.89741	+	18.2935i	−0.00431162	+	0.0272225i
$673$	−79.6810	+	156.383i	−0.118397	+	0.232367i	−0.942598	−	0.333931i	$-0.891625\pi$
$673$	−79.6810	+	156.383i	−0.118397	+	0.232367i	0.824201	+	0.566298i	$0.191625\pi$
$674$			494.999i			0.734420i
$675$		0			0
$676$	−171.397			−0.253545
$677$	−430.607	−	219.405i	−0.636051	−	0.324084i	0.106061	−	0.994360i	$-0.466176\pi$
$677$	−430.607	−	219.405i	−0.636051	−	0.324084i	−0.742112	+	0.670275i	$0.766176\pi$
$678$	−547.804	−	86.7637i	−0.807971	−	0.127970i
$679$	−6.58295	−	9.06065i	−0.00969506	−	0.0133441i
$680$		0			0
$681$	620.508	+	450.825i	0.911172	+	0.662005i
$682$	26.6575	−	26.6575i	0.0390872	−	0.0390872i
$683$	−42.2070	−	266.484i	−0.0617964	−	0.390167i	−0.999129	−	0.0417309i	$-0.986713\pi$
$683$	−42.2070	−	266.484i	−0.0617964	−	0.390167i	0.937332	−	0.348436i	$-0.113287\pi$
$684$	255.382	+	82.9788i	0.373366	+	0.121314i
$685$		0			0
$686$	38.1898	+	117.536i	0.0556702	+	0.171335i
$687$	−314.446	−	617.134i	−0.457708	−	0.898303i
$688$	195.617	−	99.6719i	0.284327	−	0.144872i
$689$	−316.245	+	102.754i	−0.458991	+	0.149135i
$690$		0			0
$691$	−39.1934	+	120.625i	−0.0567198	+	0.174565i	−0.975403	−	0.220430i	$-0.929254\pi$
$691$	−39.1934	+	120.625i	−0.0567198	+	0.174565i	0.918683	+	0.394996i	$0.129254\pi$
$692$	−438.164	+	69.3983i	−0.633185	+	0.100287i
$693$	37.1958	+	37.1958i	0.0536735	+	0.0536735i
$694$	137.373	−	189.077i	0.197943	−	0.272445i
$695$		0			0
$696$	473.969	−	344.359i	0.680990	−	0.494768i
$697$	−61.6034	+	388.949i	−0.0883837	+	0.558033i
$698$	347.736	−	682.471i	0.498190	−	0.977752i
$699$			1616.83i			2.31307i
$700$		0			0
$701$	−988.792			−1.41054			−0.705272	−	0.708937i	$-0.749175\pi$
$701$	−988.792			−1.41054			−0.705272	+	0.708937i	$0.749175\pi$
$702$	−198.485	−	101.133i	−0.282743	−	0.144065i
$703$	366.046	+	57.9761i	0.520692	+	0.0824695i
$704$	−64.5694	−	88.8721i	−0.0917179	−	0.126239i
$705$		0			0
$706$	−6.51057	−	4.73020i	−0.00922177	−	0.00670001i
$707$	−42.0037	+	42.0037i	−0.0594112	+	0.0594112i
$708$	69.2650	+	437.322i	0.0978320	+	0.617687i
$709$	1071.72	+	348.224i	1.51160	+	0.491148i	0.943375	−	0.331728i	$-0.107631\pi$
$709$	1071.72	+	348.224i	1.51160	+	0.491148i	0.568222	+	0.822875i	$0.307631\pi$
$710$		0			0
$711$	−74.8319	−	230.309i	−0.105249	−	0.323922i
$712$	77.2057	+	151.525i	0.108435	+	0.212816i
$713$	53.3678	−	27.1923i	0.0748497	−	0.0381378i
$714$	−25.9145	+	8.42014i	−0.0362948	+	0.0117929i
$715$		0			0
$716$	−40.1626	+	123.608i	−0.0560930	+	0.172637i
$717$	−928.982	+	147.136i	−1.29565	+	0.205211i
$718$	49.1583	+	49.1583i	0.0684656	+	0.0684656i
$719$	52.6231	−	72.4294i	0.0731892	−	0.100736i	−0.770853	−	0.637013i	$-0.780170\pi$
$719$	52.6231	−	72.4294i	0.0731892	−	0.100736i	0.844042	+	0.536277i	$0.180170\pi$
$720$		0			0
$721$	−7.43253	+	5.40005i	−0.0103086	+	0.00748967i
$722$	139.829	−	882.848i	0.193669	−	1.22278i
$723$	−269.729	+	529.373i	−0.373069	+	0.732190i
$724$			424.114i			0.585793i
$725$		0			0
$726$	−347.895			−0.479194
$727$	596.168	+	303.763i	0.820038	+	0.417830i	0.813085	−	0.582145i	$-0.197787\pi$
$727$	596.168	+	303.763i	0.820038	+	0.417830i	0.00695359	+	0.999976i	$0.497787\pi$
$728$	22.9252	+	3.63099i	0.0314906	+	0.00498763i
$729$	79.0493	+	108.802i	0.108435	+	0.149248i
$730$		0			0
$731$	261.302	+	189.847i	0.357458	+	0.259709i
$732$	−72.9574	+	72.9574i	−0.0996686	+	0.0996686i
$733$	38.0021	+	239.936i	0.0518446	+	0.327334i	0.999956	+	0.00939532i	$0.00299067\pi$
$733$	38.0021	+	239.936i	0.0518446	+	0.327334i	−0.948111	+	0.317939i	$0.897009\pi$
$734$	−481.240	−	156.364i	−0.655641	−	0.213031i
$735$		0			0
$736$	−53.9330	−	165.989i	−0.0732786	−	0.225528i
$737$	−402.807	−	790.554i	−0.546550	−	1.07266i
$738$	359.268	−	183.056i	0.486813	−	0.248044i
$739$	1232.20	−	400.367i	1.66739	−	0.541769i	0.684993	−	0.728550i	$-0.259805\pi$
$739$	1232.20	−	400.367i	1.66739	−	0.541769i	0.982402	+	0.186781i	$0.0598054\pi$
$740$		0			0
$741$	323.650	−	996.093i	0.436775	−	1.34425i
$742$	−45.7559	+	7.24702i	−0.0616656	+	0.00976687i
$743$	−560.204	−	560.204i	−0.753976	−	0.753976i	0.221243	−	0.975219i	$-0.428989\pi$
$743$	−560.204	−	560.204i	−0.753976	−	0.753976i	−0.975219	+	0.221243i	$0.928989\pi$
$744$	11.7529	−	16.1765i	0.0157969	−	0.0217426i
$745$		0			0
$746$	−189.191	+	137.455i	−0.253607	+	0.184257i
$747$	−26.9954	+	170.442i	−0.0361384	+	0.228169i
$748$	73.3692	−	143.995i	0.0980872	−	0.192507i
$749$		−	36.2149i		−	0.0483510i
$750$		0			0
$751$	1236.03			1.64585			0.822926	−	0.568149i	$-0.192340\pi$
$751$	1236.03			1.64585			0.822926	+	0.568149i	$0.192340\pi$
$752$	−177.783	−	90.5850i	−0.236414	−	0.120459i
$753$	968.601	+	153.411i	1.28632	+	0.203734i
$754$	−431.545	−	593.971i	−0.572341	−	0.787760i
$755$		0			0
$756$	−25.1082	−	18.2422i	−0.0332119	−	0.0241298i
$757$	−212.988	+	212.988i	−0.281358	+	0.281358i	−0.833650	−	0.552293i	$-0.813753\pi$
$757$	−212.988	+	212.988i	−0.281358	+	0.281358i	0.552293	+	0.833650i	$0.313753\pi$
$758$	130.402	+	823.324i	0.172034	+	1.08618i
$759$	−1467.25	−	476.737i	−1.93313	−	0.628112i
$760$		0			0
$761$	−93.0421	−	286.354i	−0.122263	−	0.376287i	0.871129	−	0.491053i	$-0.163388\pi$
$761$	−93.0421	−	286.354i	−0.122263	−	0.376287i	−0.993392	+	0.114767i	$0.963388\pi$
$762$	206.499	+	405.277i	0.270996	+	0.531860i
$763$	−42.7103	+	21.7620i	−0.0559768	+	0.0285216i
$764$	175.465	−	57.0122i	0.229667	−	0.0746233i
$765$		0			0
$766$	−298.588	+	918.958i	−0.389801	+	1.19968i
$767$	548.046	−	86.8019i	0.714532	−	0.113171i
$768$	−41.1990	−	41.1990i	−0.0536445	−	0.0536445i
$769$	−191.979	+	264.237i	−0.249648	+	0.343611i	−0.915388	−	0.402573i	$-0.868116\pi$
$769$	−191.979	+	264.237i	−0.249648	+	0.343611i	0.665740	+	0.746184i	$0.268116\pi$
$770$		0			0
$771$	255.867	−	185.898i	0.331864	−	0.241113i
$772$	−66.8618	+	422.149i	−0.0866086	+	0.546825i
$773$	−484.917	+	951.703i	−0.627318	+	1.23118i	0.330500	+	0.943806i	$0.392783\pi$
$773$	−484.917	+	951.703i	−0.627318	+	1.23118i	−0.957818	+	0.287375i	$0.907217\pi$
$774$		−	330.712i		−	0.427277i
$775$		0			0
$776$	35.2310			0.0454008
$777$	34.3095	+	17.4816i	0.0441564	+	0.0224988i
$778$	−219.293	−	34.7327i	−0.281868	−	0.0446435i
$779$	−1239.53	−	1706.07i	−1.59118	−	2.19007i
$780$		0			0
$781$	349.318	+	253.794i	0.447270	+	0.324961i
$782$	181.558	−	181.558i	0.232172	−	0.232172i
$783$	153.569	+	969.599i	0.196129	+	1.23831i
$784$	−183.332	−	59.5681i	−0.233841	−	0.0759797i
$785$		0			0
$786$	152.939	+	470.696i	0.194578	+	0.598850i
$787$	205.111	+	402.553i	0.260624	+	0.511503i	0.983825	−	0.179135i	$-0.0573298\pi$
$787$	205.111	+	402.553i	0.260624	+	0.511503i	−0.723201	+	0.690638i	$0.757330\pi$
$788$	−120.725	+	61.5125i	−0.153205	+	0.0780616i
$789$	1259.50	−	409.237i	1.59633	−	0.518679i
$790$		0			0
$791$	−29.9235	+	92.0952i	−0.0378300	+	0.116429i
$792$	−163.438	+	25.8860i	−0.206361	+	0.0326843i
$793$	91.4292	+	91.4292i	0.115295	+	0.115295i
$794$	144.153	−	198.409i	0.181553	−	0.249886i
$795$		0			0
$796$	183.617	−	133.406i	0.230675	−	0.167595i
$797$	−8.61487	+	54.3922i	−0.0108091	+	0.0682461i	−0.992503	−	0.122218i	$-0.960999\pi$
$797$	−8.61487	+	54.3922i	−0.0108091	+	0.0682461i	0.981694	+	0.190464i	$0.0609993\pi$
$798$	66.2445	−	130.012i	0.0830131	−	0.162922i
$799$		−	293.541i		−	0.367385i
$800$		0			0
$801$	256.169			0.319812
$802$	516.919	+	263.384i	0.644538	+	0.328408i
$803$	939.500	+	148.802i	1.16999	+	0.185308i
$804$	−276.607	−	380.716i	−0.344038	−	0.473528i
$805$		0			0
$806$	−20.2722	−	14.7286i	−0.0251516	−	0.0182737i
$807$	−809.670	+	809.670i	−1.00331	+	1.00331i
$808$	−29.2320	−	184.564i	−0.0361783	−	0.228421i
$809$	−33.7918	−	10.9796i	−0.0417698	−	0.0135718i	0.288058	−	0.957613i	$-0.406991\pi$
$809$	−33.7918	−	10.9796i	−0.0417698	−	0.0135718i	−0.329827	+	0.944041i	$0.606991\pi$
$810$		0			0
$811$	−392.037	−	1206.57i	−0.483400	−	1.48775i	−0.834285	−	0.551333i	$-0.814119\pi$
$811$	−392.037	−	1206.57i	−0.483400	−	1.48775i	0.350885	−	0.936419i	$-0.385881\pi$
$812$	−46.4370	−	91.1377i	−0.0571884	−	0.112239i
$813$	−788.054	+	401.533i	−0.969316	+	0.493891i
$814$	−217.205	+	70.5742i	−0.266837	+	0.0867005i
$815$		0			0
$816$	26.4876	−	81.5205i	0.0324603	−	0.0999026i
$817$	−1708.33	+	270.573i	−2.09098	+	0.331178i
$818$	−40.2878	−	40.2878i	−0.0492515	−	0.0492515i
$819$	20.5511	−	28.2862i	0.0250930	−	0.0345375i
$820$		0			0
$821$	739.680	−	537.409i	0.900950	−	0.654578i	−0.0377601	−	0.999287i	$-0.512022\pi$
$821$	739.680	−	537.409i	0.900950	−	0.654578i	0.938710	+	0.344709i	$0.112022\pi$
$822$	−192.918	+	1218.04i	−0.234693	+	1.48180i
$823$	−464.929	+	912.475i	−0.564920	+	1.10872i	0.415091	+	0.909780i	$0.363750\pi$
$823$	−464.929	+	912.475i	−0.564920	+	1.10872i	−0.980012	+	0.198939i	$0.936250\pi$
$824$		−	28.9003i		−	0.0350732i
$825$		0			0
$826$	77.3048			0.0935894
$827$	311.391	+	158.662i	0.376531	+	0.191852i	0.632006	−	0.774963i	$-0.282232\pi$
$827$	311.391	+	158.662i	0.376531	+	0.191852i	−0.255475	+	0.966816i	$0.582232\pi$
$828$	−259.667	−	41.1272i	−0.313607	−	0.0496705i
$829$	−46.1567	−	63.5292i	−0.0556775	−	0.0766336i	0.780270	−	0.625442i	$-0.215081\pi$
$829$	−46.1567	−	63.5292i	−0.0556775	−	0.0766336i	−0.835948	+	0.548809i	$0.815081\pi$
$830$		0			0
$831$	−1263.78	−	918.188i	−1.52079	−	1.10492i
$832$	−51.6300	+	51.6300i	−0.0620552	+	0.0620552i
$833$	−44.3632	−	280.098i	−0.0532571	−	0.336252i
$834$	683.204	+	221.987i	0.819190	+	0.266171i
$835$		0			0
$836$	267.433	+	823.075i	0.319896	+	0.984540i
$837$	15.2109	+	29.8530i	0.0181731	+	0.0356667i
$838$	549.323	−	279.894i	0.655517	−	0.334002i
$839$	251.975	−	81.8717i	0.300328	−	0.0975824i	−0.154977	−	0.987918i	$-0.549530\pi$
$839$	251.975	−	81.8717i	0.300328	−	0.0975824i	0.455305	+	0.890336i	$0.349530\pi$
$840$		0			0
$841$	−739.920	+	2277.24i	−0.879809	+	2.70777i
$842$	242.752	−	38.4482i	0.288304	−	0.0456629i
$843$	−575.921	−	575.921i	−0.683180	−	0.683180i
$844$	13.3465	−	18.3699i	0.0158134	−	0.0217653i
$845$		0			0
$846$	−243.160	+	176.666i	−0.287423	+	0.208825i
$847$	−9.50178	+	59.9919i	−0.0112182	+	0.0708287i
$848$	66.1603	−	129.847i	0.0780192	−	0.153121i
$849$		−	1298.20i		−	1.52909i
$850$		0			0
$851$	−362.851			−0.426382
$852$	204.050	+	103.969i	0.239496	+	0.122029i
$853$	−753.921	−	119.409i	−0.883846	−	0.139987i	−0.302021	−	0.953301i	$-0.597661\pi$
$853$	−753.921	−	119.409i	−0.883846	−	0.139987i	−0.581825	+	0.813314i	$0.697661\pi$
$854$	10.5883	+	14.5736i	0.0123985	+	0.0170651i
$855$		0			0
$856$	92.1656	+	66.9622i	0.107670	+	0.0782269i
$857$	326.208	−	326.208i	0.380639	−	0.380639i	−0.490693	−	0.871332i	$-0.663256\pi$
$857$	326.208	−	326.208i	0.380639	−	0.380639i	0.871332	+	0.490693i	$0.163256\pi$
$858$	100.966	+	637.472i	0.117676	+	0.742974i
$859$	1286.41	+	417.979i	1.49756	+	0.486588i	0.939306	−	0.343080i	$-0.111470\pi$
$859$	1286.41	+	417.979i	1.49756	+	0.486588i	0.558257	+	0.829668i	$0.311470\pi$
$860$		0			0
$861$	−67.7077	−	208.383i	−0.0786385	−	0.242024i
$862$	−78.5260	−	154.116i	−0.0910974	−	0.178789i
$863$	295.874	−	150.755i	0.342843	−	0.174687i	−0.274088	−	0.961705i	$-0.588376\pi$
$863$	295.874	−	150.755i	0.342843	−	0.174687i	0.616931	+	0.787017i	$0.288376\pi$
$864$	92.8512	−	30.1692i	0.107467	−	0.0349180i
$865$		0			0
$866$	128.509	−	395.510i	0.148394	−	0.456709i
$867$	−914.890	+	144.904i	−1.05524	+	0.167133i
$868$	−2.46852	−	2.46852i	−0.00284392	−	0.00284392i
$869$	458.745	−	631.409i	0.527900	−	0.726592i
$870$		0			0
$871$	−477.108	+	346.640i	−0.547771	+	0.397979i
$872$	23.5889	−	148.935i	0.0270515	−	0.170797i
$873$	24.0933	−	47.2858i	0.0275983	−	0.0541647i
$874$			1374.98i			1.57321i
$875$		0			0
$876$	504.511			0.575925
$877$	973.819	+	496.185i	1.11040	+	0.565776i	0.910279	−	0.413996i	$-0.135867\pi$
$877$	973.819	+	496.185i	1.11040	+	0.565776i	0.200119	+	0.979772i	$0.435867\pi$
$878$	−199.583	−	31.6108i	−0.227316	−	0.0360032i
$879$	−1004.24	−	1382.21i	−1.14248	−	1.57248i
$880$		0			0
$881$	489.612	+	355.724i	0.555745	+	0.403773i	0.829899	−	0.557913i	$-0.188398\pi$
$881$	489.612	+	355.724i	0.555745	+	0.403773i	−0.274154	+	0.961686i	$0.588398\pi$
$882$	−205.324	+	205.324i	−0.232794	+	0.232794i
$883$	−181.570	−	1146.39i	−0.205628	−	1.29829i	−0.847221	−	0.531241i	$-0.821726\pi$
$883$	−181.570	−	1146.39i	−0.205628	−	1.29829i	0.641592	−	0.767046i	$-0.278274\pi$
$884$	−102.160	−	33.1939i	−0.115566	−	0.0375497i
$885$		0			0
$886$	8.49138	+	26.1338i	0.00958395	+	0.0294964i
$887$	−309.274	−	606.984i	−0.348674	−	0.684311i	0.648355	−	0.761338i	$-0.275457\pi$
$887$	−309.274	−	606.984i	−0.348674	−	0.684311i	−0.997029	+	0.0770268i	$0.975457\pi$
$888$	−107.929	+	54.9926i	−0.121542	+	0.0619286i
$889$	75.5271	−	24.5402i	0.0849574	−	0.0276043i
$890$		0			0
$891$	429.387	−	1321.52i	0.481916	−	1.48319i
$892$	289.534	−	45.8577i	0.324590	−	0.0514100i
$893$	1111.53	+	1111.53i	1.24471	+	1.24471i
$894$	−569.061	+	783.246i	−0.636534	+	0.876114i
$895$		0			0
$896$	−8.22970	+	5.97923i	−0.00918493	+	0.00667324i
$897$	−160.412	+	1012.80i	−0.178832	+	1.12910i
$898$	201.477	−	395.421i	0.224362	−	0.440335i
$899$			110.425i			0.122831i
$900$		0			0
$901$	214.393			0.237950
$902$	1157.89	+	589.974i	1.28369	+	0.654073i
$903$	−177.496	−	28.1126i	−0.196563	−	0.0311324i
$904$	−179.049	−	246.440i	−0.198063	−	0.272611i
$905$		0			0
$906$	667.693	+	485.108i	0.736968	+	0.535439i
$907$	911.088	−	911.088i	1.00451	−	1.00451i	0.00451769	−	0.999990i	$-0.498562\pi$
$907$	911.088	−	911.088i	1.00451	−	1.00451i	0.999990	−	0.00451769i	$-0.00143803\pi$
$908$	65.8978	+	416.062i	0.0725746	+	0.458218i
$909$	−267.705	−	86.9828i	−0.294505	−	0.0956906i
$910$		0			0
$911$	315.739	+	971.745i	0.346585	+	1.06668i	0.960730	+	0.277486i	$0.0895011\pi$
$911$	315.739	+	971.745i	0.346585	+	1.06668i	−0.614145	+	0.789193i	$0.710499\pi$
$912$	208.388	+	408.985i	0.228496	+	0.448449i
$913$	−495.549	+	252.495i	−0.542770	+	0.276555i
$914$	−69.4466	+	22.5646i	−0.0759810	+	0.0246877i
$915$		0			0
$916$	117.552	−	361.788i	0.128332	−	0.394965i
$917$	85.3453	−	13.5174i	0.0930701	−	0.0147409i
$918$	101.561	+	101.561i	0.110632	+	0.110632i
$919$	−713.919	+	982.625i	−0.776843	+	1.06923i	0.218780	+	0.975774i	$0.429792\pi$
$919$	−713.919	+	982.625i	−0.776843	+	1.06923i	−0.995623	+	0.0934584i	$0.970208\pi$
$920$		0			0
$921$	22.2202	−	16.1439i	0.0241261	−	0.0175287i
$922$	−180.634	+	1140.48i	−0.195915	+	1.23696i
$923$	130.292	−	255.713i	0.141162	−	0.277045i
$924$			89.9188i			0.0973147i
$925$		0			0
$926$	−777.796			−0.839953
$927$	−38.7890	−	19.7640i	−0.0418435	−	0.0213203i
$928$	317.805	+	50.3354i	0.342462	+	0.0542407i
$929$	317.570	+	437.097i	0.341840	+	0.470503i	0.944978	−	0.327134i	$-0.106083\pi$
$929$	317.570	+	437.097i	0.341840	+	0.470503i	−0.603137	+	0.797637i	$0.706083\pi$
$930$		0			0
$931$	1228.61	+	892.637i	1.31967	+	0.958794i
$932$	−627.912	+	627.912i	−0.673726	+	0.673726i
$933$	−144.479	−	912.208i	−0.154855	−	0.977714i
$934$	791.630	+	257.216i	0.847570	+	0.275392i
$935$		0			0
$936$	33.9878	+	104.604i	0.0363118	+	0.111756i
$937$	−300.755	−	590.265i	−0.320976	−	0.629952i	0.672988	−	0.739653i	$-0.265011\pi$
$937$	−300.755	−	590.265i	−0.320976	−	0.629952i	−0.993965	+	0.109701i	$0.965011\pi$
$938$	−73.2065	+	37.3006i	−0.0780453	+	0.0397661i
$939$	459.064	−	149.159i	0.488886	−	0.158849i
$940$		0			0
$941$	17.8066	−	54.8030i	0.0189230	−	0.0582391i	−0.941149	−	0.337992i	$-0.890252\pi$
$941$	17.8066	−	54.8030i	0.0189230	−	0.0582391i	0.960072	+	0.279753i	$0.0902524\pi$
$942$	−633.052	+	100.266i	−0.672029	+	0.106439i
$943$	1459.94	+	1459.94i	1.54819	+	1.54819i
$944$	−142.938	+	196.738i	−0.151418	+	0.208409i
$945$		0			0
$946$	862.296	−	626.495i	0.911518	−	0.662257i
$947$	16.9962	−	107.310i	0.0179474	−	0.113316i	−0.977088	−	0.212835i	$-0.931730\pi$
$947$	16.9962	−	107.310i	0.0179474	−	0.113316i	0.995036	+	0.0995191i	$0.0317304\pi$
$948$	187.929	−	368.831i	0.198237	−	0.389062i
$949$		−	632.245i		−	0.666223i
$950$		0			0
$951$	818.627			0.860806
$952$	−13.3342	−	6.79410i	−0.0140065	−	0.00713666i
$953$	69.0176	+	10.9313i	0.0724214	+	0.0114704i	0.192540	−	0.981289i	$-0.438327\pi$
$953$	69.0176	+	10.9313i	0.0724214	+	0.0114704i	−0.120119	+	0.992760i	$0.538327\pi$
$954$	−129.031	−	177.596i	−0.135252	−	0.186159i
$955$		0			0
$956$	−417.920	−	303.637i	−0.437155	−	0.317612i
$957$	2011.18	−	2011.18i	2.10154	−	2.10154i
$958$	46.2244	+	291.849i	0.0482509	+	0.304644i
$959$	204.772	+	66.5346i	0.213527	+	0.0693791i
$960$		0			0
$961$	−295.801	−	910.381i	−0.307805	−	0.947327i
$962$	68.9159	+	135.255i	0.0716381	+	0.140598i
$963$	152.903	−	77.9080i	0.158778	−	0.0809014i
$964$	−310.339	+	100.835i	−0.321928	+	0.104601i
$965$		0			0
$966$	−44.1466	+	135.869i	−0.0457004	+	0.140651i
$967$	382.375	−	60.5623i	0.395424	−	0.0626290i	0.0444438	−	0.999012i	$-0.485848\pi$
$967$	382.375	−	60.5623i	0.395424	−	0.0626290i	0.350980	+	0.936383i	$0.385848\pi$
$968$	−135.108	−	135.108i	−0.139574	−	0.139574i
$969$	−396.921	+	546.315i	−0.409620	+	0.563793i
$970$		0			0
$971$	−801.968	+	582.664i	−0.825920	+	0.600066i	−0.918402	−	0.395648i	$-0.870520\pi$
$971$	−801.968	+	582.664i	−0.825920	+	0.600066i	0.0924822	+	0.995714i	$0.470520\pi$
$972$	66.6932	−	421.084i	0.0686144	−	0.433214i
$973$	56.9398	−	111.751i	0.0585198	−	0.114852i
$974$			235.456i			0.241741i
$975$		0			0
$976$	−56.6674			−0.0580608
$977$	−813.120	−	414.305i	−0.832262	−	0.424059i	−0.0146951	−	0.999892i	$-0.504678\pi$
$977$	−813.120	−	414.305i	−0.832262	−	0.424059i	−0.817567	+	0.575833i	$0.804678\pi$
$978$	925.486	+	146.583i	0.946305	+	0.149880i
$979$	485.282	+	667.934i	0.495692	+	0.682261i
$980$		0			0
$981$	−183.763	−	133.511i	−0.187322	−	0.136097i
$982$	295.999	−	295.999i	0.301424	−	0.301424i
$983$	93.2715	+	588.893i	0.0948846	+	0.599078i	0.988614	+	0.150472i	$0.0480793\pi$
$983$	93.2715	+	588.893i	0.0948846	+	0.599078i	−0.893730	+	0.448606i	$0.851921\pi$
$984$	655.520	+	212.991i	0.666179	+	0.216455i
$985$		0			0
$986$	146.279	+	450.201i	0.148356	+	0.456593i
$987$	74.1479	+	145.523i	0.0751245	+	0.147440i
$988$	512.534	−	261.149i	0.518759	−	0.264321i
$989$	1610.53	−	523.294i	1.62845	−	0.529114i
$990$		0			0
$991$	146.456	−	450.746i	0.147786	−	0.454840i	−0.849572	−	0.527472i	$-0.823140\pi$
$991$	146.456	−	450.746i	0.147786	−	0.454840i	0.997359	+	0.0726323i	$0.0231400\pi$
$992$	10.8467	−	1.71794i	0.0109341	−	0.00173180i
$993$	−1084.94	−	1084.94i	−1.09259	−	1.09259i
$994$	23.5017	−	32.3474i	0.0236436	−	0.0325426i
$995$		0			0
$996$	−238.647	+	173.387i	−0.239606	+	0.174084i
$997$	−162.004	+	1022.85i	−0.162492	+	1.02593i	0.762789	+	0.646648i	$0.223830\pi$
$997$	−162.004	+	1022.85i	−0.162492	+	1.02593i	−0.925280	+	0.379284i	$0.876170\pi$
$998$	294.991	−	578.952i	0.295582	−	0.580112i
$999$		−	202.972i		−	0.203176i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.3.f.a.143.2		16
5.2	odd	4		50.3.f.a.17.2	yes	16
5.3	odd	4		250.3.f.b.107.1		16
5.4	even	2		250.3.f.c.143.1		16
20.7	even	4		400.3.bg.a.17.1		16
25.3	odd	20		250.3.f.c.7.1		16
25.4	even	10		250.3.f.b.243.1		16
25.21	even	5		50.3.f.a.3.2	✓	16
25.22	odd	20	inner	250.3.f.a.7.2		16
100.71	odd	10		400.3.bg.a.353.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.3.2	✓	16	25.21	even	5
50.3.f.a.17.2	yes	16	5.2	odd	4
250.3.f.a.7.2		16	25.22	odd	20	inner
250.3.f.a.143.2		16	1.1	even	1	trivial
250.3.f.b.107.1		16	5.3	odd	4
250.3.f.b.243.1		16	25.4	even	10
250.3.f.c.7.1		16	25.3	odd	20
250.3.f.c.143.1		16	5.4	even	2
400.3.bg.a.17.1		16	20.7	even	4
400.3.bg.a.353.1		16	100.71	odd	10

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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	250.f (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.26007 + 0.642040i) q^{2} +(3.59668 + 0.569657i) q^{3} +(1.17557 + 1.61803i) q^{4} +(4.16633 + 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(0.442463 + 2.79360i) q^{8} +(4.05206 + 1.31659i) q^{9} +O(q^{10})\)	\(q+(1.26007 + 0.642040i) q^{2} +(3.59668 + 0.569657i) q^{3} +(1.17557 + 1.61803i) q^{4} +(4.16633 + 3.02702i) q^{6} +(0.635779 - 0.635779i) q^{7} +(0.442463 + 2.79360i) q^{8} +(4.05206 + 1.31659i) q^{9} +(4.24327 + 13.0594i) q^{11} +(3.30642 + 6.48922i) q^{12} +(8.13219 - 4.14356i) q^{13} +(1.20932 - 0.392933i) q^{14} +(-1.23607 + 3.80423i) q^{16} +(-5.81218 + 0.920559i) q^{17} +(4.26058 + 4.26058i) q^{18} +(18.5227 - 25.4943i) q^{19} +(2.64887 - 1.92451i) q^{21} +(-3.03784 + 19.1802i) q^{22} +(-14.0070 + 27.4902i) q^{23} +10.2997i q^{24} +12.9075 q^{26} +(-15.3775 - 7.83525i) q^{27} +(1.77612 + 0.281309i) q^{28} +(-33.4337 - 46.0176i) q^{29} +(-1.57058 - 1.14109i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(7.82225 + 49.3877i) q^{33} +(-7.91481 - 2.57168i) q^{34} +(2.63319 + 8.10411i) q^{36} +(5.33922 + 10.4788i) q^{37} +(39.7083 - 20.2324i) q^{38} +(31.6093 - 10.2705i) q^{39} +(20.6793 - 63.6443i) q^{41} +(4.57338 - 0.724353i) q^{42} +(-38.8107 - 38.8107i) q^{43} +(-16.1423 + 22.2180i) q^{44} +(-35.2996 + 25.6467i) q^{46} +(-7.80337 + 49.2685i) q^{47} +(-6.61284 + 12.9784i) q^{48} +48.1916i q^{49} -21.4289 q^{51} +(16.2644 + 8.28712i) q^{52} +(-35.9841 - 5.69932i) q^{53} +(-14.3463 - 19.7460i) q^{54} +(2.05742 + 1.49481i) q^{56} +(81.1431 - 81.1431i) q^{57} +(-12.5838 - 79.4513i) q^{58} +(57.8198 + 18.7868i) q^{59} +(4.37780 + 13.4735i) q^{61} +(-1.24642 - 2.44623i) q^{62} +(3.41328 - 1.73915i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(-21.8523 + 67.2544i) q^{66} +(-63.8194 + 10.1080i) q^{67} +(-8.32212 - 8.32212i) q^{68} +(-66.0385 + 90.8943i) q^{69} +(25.4392 - 18.4826i) q^{71} +(-1.88515 + 11.9024i) q^{72} +(31.4489 - 61.7220i) q^{73} +16.6321i q^{74} +63.0254 q^{76} +(11.0007 + 5.60513i) q^{77} +(46.4241 + 7.35285i) q^{78} +(-33.4082 - 45.9825i) q^{79} +(-81.8666 - 59.4796i) q^{81} +(66.9196 - 66.9196i) q^{82} +(6.33607 + 40.0044i) q^{83} +(6.22786 + 2.02355i) q^{84} +(-23.9863 - 73.8222i) q^{86} +(-94.0360 - 184.556i) q^{87} +(-34.6054 + 17.6323i) q^{88} +(57.1826 - 18.5798i) q^{89} +(2.53589 - 7.80467i) q^{91} +(-60.9463 + 9.65295i) q^{92} +(-4.99882 - 4.99882i) q^{93} +(-41.4652 + 57.0719i) q^{94} +(-16.6653 + 12.1081i) q^{96} +(1.94856 - 12.3027i) q^{97} +(-30.9409 + 60.7249i) q^{98} +58.5042i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} + 40 q^{9} + 32 q^{11} - 16 q^{12} - 8 q^{13} + 30 q^{14} + 16 q^{16} + 8 q^{17} - 16 q^{18} - 30 q^{19} - 68 q^{21} - 8 q^{22} + 42 q^{23} - 56 q^{26} - 40 q^{27} + 4 q^{28} - 100 q^{29} + 132 q^{31} - 64 q^{32} + 134 q^{33} - 100 q^{34} + 48 q^{36} - 82 q^{37} + 20 q^{38} + 320 q^{39} - 88 q^{41} - 128 q^{42} - 78 q^{43} - 40 q^{44} - 26 q^{46} + 168 q^{47} + 32 q^{48} - 168 q^{51} - 16 q^{52} - 518 q^{53} - 80 q^{54} + 48 q^{56} + 280 q^{57} + 80 q^{58} + 350 q^{59} + 372 q^{61} - 158 q^{62} + 142 q^{63} - 202 q^{66} + 158 q^{67} - 196 q^{68} + 30 q^{69} + 122 q^{71} + 68 q^{72} + 352 q^{73} + 40 q^{76} + 96 q^{77} + 158 q^{78} - 760 q^{79} - 144 q^{81} + 352 q^{82} + 32 q^{83} + 20 q^{84} + 264 q^{86} - 440 q^{87} - 244 q^{88} - 550 q^{89} - 798 q^{91} - 436 q^{92} + 54 q^{93} - 190 q^{94} - 16 q^{96} + 618 q^{97} + 336 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 + 40 * q^9 + 32 * q^11 - 16 * q^12 - 8 * q^13 + 30 * q^14 + 16 * q^16 + 8 * q^17 - 16 * q^18 - 30 * q^19 - 68 * q^21 - 8 * q^22 + 42 * q^23 - 56 * q^26 - 40 * q^27 + 4 * q^28 - 100 * q^29 + 132 * q^31 - 64 * q^32 + 134 * q^33 - 100 * q^34 + 48 * q^36 - 82 * q^37 + 20 * q^38 + 320 * q^39 - 88 * q^41 - 128 * q^42 - 78 * q^43 - 40 * q^44 - 26 * q^46 + 168 * q^47 + 32 * q^48 - 168 * q^51 - 16 * q^52 - 518 * q^53 - 80 * q^54 + 48 * q^56 + 280 * q^57 + 80 * q^58 + 350 * q^59 + 372 * q^61 - 158 * q^62 + 142 * q^63 - 202 * q^66 + 158 * q^67 - 196 * q^68 + 30 * q^69 + 122 * q^71 + 68 * q^72 + 352 * q^73 + 40 * q^76 + 96 * q^77 + 158 * q^78 - 760 * q^79 - 144 * q^81 + 352 * q^82 + 32 * q^83 + 20 * q^84 + 264 * q^86 - 440 * q^87 - 244 * q^88 - 550 * q^89 - 798 * q^91 - 436 * q^92 + 54 * q^93 - 190 * q^94 - 16 * q^96 + 618 * q^97 + 336 * q^98

Introduction

L-functions

Modular forms

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