LMFDB - Embedded newform 115.2.l.a.33.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,2,Mod(7,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([11, 38])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			33.6
Character	$\chi$	$=$	115.33
Dual form			115.2.l.a.7.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.107969 - 0.00772212i) q^{2} +(0.390334 + 1.79434i) q^{3} +(-1.96805 - 0.282962i) q^{4} +(-2.08676 + 0.803398i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(2.36052 + 4.32296i) q^{7} +(0.421846 + 0.0917670i) q^{8} +(-0.338390 + 0.154538i) q^{9} +(0.231510 - 0.0706281i) q^{10} +(-0.599394 - 0.519378i) q^{11} +(-0.260466 - 3.64179i) q^{12} +(-2.17257 - 1.18632i) q^{13} +(-0.221481 - 0.484976i) q^{14} +(-2.25610 - 3.43075i) q^{15} +(3.77065 + 1.10716i) q^{16} +(3.16383 - 4.22639i) q^{17} +(0.0377291 - 0.0140722i) q^{18} +(-0.409398 + 2.84742i) q^{19} +(4.33416 - 0.990650i) q^{20} +(-6.83547 + 5.92297i) q^{21} +(0.0607055 + 0.0607055i) q^{22} +(4.72353 - 0.829644i) q^{23} +0.792754i q^{24} +(3.70910 - 3.35299i) q^{25} +(0.225410 + 0.144862i) q^{26} +(2.89199 + 3.86324i) q^{27} +(-3.42237 - 9.17573i) q^{28} +(-3.49570 + 0.502606i) q^{29} +(0.217097 + 0.387838i) q^{30} +(0.250636 - 0.161074i) q^{31} +(-1.20755 - 0.450393i) q^{32} +(0.697975 - 1.27825i) q^{33} +(-0.374233 + 0.431888i) q^{34} +(-8.39888 - 7.12454i) q^{35} +(0.709695 - 0.208385i) q^{36} +(-1.35219 + 3.62537i) q^{37} +(0.0661905 - 0.304273i) q^{38} +(1.28062 - 4.36139i) q^{39} +(-0.954015 + 0.147415i) q^{40} +(1.87241 - 4.10001i) q^{41} +(0.783758 - 0.586714i) q^{42} +(3.72300 - 0.809890i) q^{43} +(1.03267 + 1.19177i) q^{44} +(0.581983 - 0.594344i) q^{45} +(-0.516402 + 0.0531004i) q^{46} +(-3.24360 + 3.24360i) q^{47} +(-0.514810 + 7.19798i) q^{48} +(-9.33150 + 14.5201i) q^{49} +(-0.426362 + 0.333378i) q^{50} +(8.81852 + 4.02728i) q^{51} +(3.94004 + 2.94948i) q^{52} +(3.74531 - 2.04509i) q^{53} +(-0.282413 - 0.439444i) q^{54} +(1.66806 + 0.602264i) q^{55} +(0.599069 + 2.04024i) q^{56} +(-5.26904 + 0.376849i) q^{57} +(0.381310 - 0.0272718i) q^{58} +(-1.87184 - 6.37491i) q^{59} +(3.46933 + 7.39026i) q^{60} +(5.28454 + 8.22290i) q^{61} +(-0.0283048 + 0.0154556i) q^{62} +(-1.46684 - 1.09806i) q^{63} +(-7.02251 - 3.20707i) q^{64} +(5.48672 + 0.730110i) q^{65} +(-0.0852307 + 0.132622i) q^{66} +(0.550148 - 7.69208i) q^{67} +(-7.42247 + 7.42247i) q^{68} +(3.33241 + 8.15176i) q^{69} +(0.851805 + 0.834089i) q^{70} +(-10.1464 - 11.7096i) q^{71} +(-0.156930 + 0.0341380i) q^{72} +(-3.91486 + 2.93063i) q^{73} +(0.173991 - 0.380987i) q^{74} +(7.46419 + 5.34660i) q^{75} +(1.61143 - 5.48801i) q^{76} +(0.830373 - 3.81716i) q^{77} +(-0.171947 + 0.461007i) q^{78} +(13.6014 - 3.99372i) q^{79} +(-8.75792 + 0.718952i) q^{80} +(-6.53396 + 7.54059i) q^{81} +(-0.233824 + 0.428217i) q^{82} +(-4.21914 - 1.57366i) q^{83} +(15.1285 - 9.72249i) q^{84} +(-3.20668 + 11.3613i) q^{85} +(-0.408224 + 0.0586938i) q^{86} +(-2.26634 - 6.07629i) q^{87} +(-0.205190 - 0.274102i) q^{88} +(-5.37985 - 3.45742i) q^{89} +(-0.0674258 + 0.0596768i) q^{90} -12.1923i q^{91} +(-9.53087 + 0.296197i) q^{92} +(0.386853 + 0.386853i) q^{93} +(0.375256 - 0.325161i) q^{94} +(-1.43330 - 6.27079i) q^{95} +(0.336809 - 2.34255i) q^{96} +(3.64812 - 1.36068i) q^{97} +(1.11964 - 1.49567i) q^{98} +(0.283093 + 0.0831235i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.107969	−	0.00772212i	−0.0763458	−	0.00546036i	0.0331140	−	0.999452i	$-0.489458\pi$
$2$	−0.107969	−	0.00772212i	−0.0763458	−	0.00546036i	−0.109460	+	0.993991i	$0.534912\pi$
$3$	0.390334	+	1.79434i	0.225360	+	1.03596i	0.941240	+	0.337738i	$0.109662\pi$
$3$	0.390334	+	1.79434i	0.225360	+	1.03596i	−0.715880	+	0.698223i	$0.753974\pi$
$4$	−1.96805	−	0.282962i	−0.984023	−	0.141481i
$5$	−2.08676	+	0.803398i	−0.933226	+	0.359290i
$5$	−2.08676	+	0.803398i	−0.933226	+	0.359290i
$6$	−0.0282880	−	0.196748i	−0.0115485	−	0.0803218i
$7$	2.36052	+	4.32296i	0.892192	+	1.63393i	0.766862	+	0.641812i	$0.221817\pi$
$7$	2.36052	+	4.32296i	0.892192	+	1.63393i	0.125330	+	0.992115i	$0.460001\pi$
$8$	0.421846	+	0.0917670i	0.149145	+	0.0324445i
$9$	−0.338390	+	0.154538i	−0.112797	+	0.0515125i
$10$	0.231510	−	0.0706281i	0.0732097	−	0.0223346i
$11$	−0.599394	−	0.519378i	−0.180724	−	0.156598i	0.559801	−	0.828627i	$-0.310878\pi$
$11$	−0.599394	−	0.519378i	−0.180724	−	0.156598i	−0.740525	+	0.672029i	$0.765423\pi$
$12$	−0.260466	−	3.64179i	−0.0751900	−	1.05129i
$13$	−2.17257	−	1.18632i	−0.602564	−	0.329025i	0.148846	−	0.988860i	$-0.452444\pi$
$13$	−2.17257	−	1.18632i	−0.602564	−	0.329025i	−0.751410	+	0.659836i	$0.770626\pi$
$14$	−0.221481	−	0.484976i	−0.0591933	−	0.129615i
$15$	−2.25610	−	3.43075i	−0.582522	−	0.885816i
$16$	3.77065	+	1.10716i	0.942662	+	0.276791i
$17$	3.16383	−	4.22639i	0.767342	−	1.02505i	−0.231296	−	0.972883i	$-0.574297\pi$
$17$	3.16383	−	4.22639i	0.767342	−	1.02505i	0.998638	−	0.0521660i	$-0.0166125\pi$
$18$	0.0377291	−	0.0140722i	0.00889283	−	0.00331685i
$19$	−0.409398	+	2.84742i	−0.0939222	+	0.653244i	0.887418	+	0.460965i	$0.152497\pi$
$19$	−0.409398	+	2.84742i	−0.0939222	+	0.653244i	−0.981340	+	0.192278i	$0.938412\pi$
$20$	4.33416	−	0.990650i	0.969148	−	0.221516i
$21$	−6.83547	+	5.92297i	−1.49162	+	1.29250i
$22$	0.0607055	+	0.0607055i	0.0129424	+	0.0129424i
$23$	4.72353	−	0.829644i	0.984923	−	0.172993i
$23$	4.72353	−	0.829644i	0.984923	−	0.172993i
$24$			0.792754i			0.161820i
$25$	3.70910	−	3.35299i	0.741821	−	0.670598i
$26$	0.225410	+	0.144862i	0.0442066	+	0.0284099i
$27$	2.89199	+	3.86324i	0.556563	+	0.743482i
$28$	−3.42237	−	9.17573i	−0.646767	−	1.73405i
$29$	−3.49570	+	0.502606i	−0.649136	+	0.0933317i	−0.459014	−	0.888429i	$-0.651797\pi$
$29$	−3.49570	+	0.502606i	−0.649136	+	0.0933317i	−0.190122	+	0.981761i	$0.560888\pi$
$30$	0.217097	+	0.387838i	0.0396363	+	0.0708091i
$31$	0.250636	−	0.161074i	0.0450155	−	0.0289297i	−0.517940	−	0.855417i	$-0.673301\pi$
$31$	0.250636	−	0.161074i	0.0450155	−	0.0289297i	0.562955	+	0.826488i	$0.309664\pi$
$32$	−1.20755	−	0.450393i	−0.213467	−	0.0796189i
$33$	0.697975	−	1.27825i	0.121502	−	0.222514i
$34$	−0.374233	+	0.431888i	−0.0641805	+	0.0740683i
$35$	−8.39888	−	7.12454i	−1.41967	−	1.20427i
$36$	0.709695	−	0.208385i	0.118283	−	0.0347309i
$37$	−1.35219	+	3.62537i	−0.222299	+	0.596007i	−0.999445	−	0.0333136i	$-0.989394\pi$
$37$	−1.35219	+	3.62537i	−0.222299	+	0.596007i	0.777146	+	0.629321i	$0.216667\pi$
$38$	0.0661905	−	0.304273i	0.0107375	−	0.0493596i
$39$	1.28062	−	4.36139i	0.205063	−	0.698381i
$40$	−0.954015	+	0.147415i	−0.150843	+	0.0233083i
$41$	1.87241	−	4.10001i	0.292422	−	0.640315i	−0.705217	−	0.708991i	$-0.749150\pi$
$41$	1.87241	−	4.10001i	0.292422	−	0.640315i	0.997639	+	0.0686768i	$0.0218777\pi$
$42$	0.783758	−	0.586714i	0.120937	−	0.0905319i
$43$	3.72300	−	0.809890i	0.567753	−	0.123507i	0.0804789	−	0.996756i	$-0.474355\pi$
$43$	3.72300	−	0.809890i	0.567753	−	0.123507i	0.487274	+	0.873249i	$0.337991\pi$
$44$	1.03267	+	1.19177i	0.155681	+	0.179665i
$45$	0.581983	−	0.594344i	0.0867568	−	0.0885996i
$46$	−0.516402	+	0.0531004i	−0.0761394	+	0.00782923i
$47$	−3.24360	+	3.24360i	−0.473127	+	0.473127i	−0.902925	−	0.429798i	$-0.858585\pi$
$47$	−3.24360	+	3.24360i	−0.473127	+	0.473127i	0.429798	+	0.902925i	$0.358585\pi$
$48$	−0.514810	+	7.19798i	−0.0743064	+	1.03894i
$49$	−9.33150	+	14.5201i	−1.33307	+	2.07430i
$50$	−0.426362	+	0.333378i	−0.0602966	+	0.0471467i
$51$	8.81852	+	4.02728i	1.23484	+	0.563932i
$52$	3.94004	+	2.94948i	0.546385	+	0.409019i
$53$	3.74531	−	2.04509i	0.514458	−	0.280915i	−0.200975	−	0.979596i	$-0.564411\pi$
$53$	3.74531	−	2.04509i	0.514458	−	0.280915i	0.715433	+	0.698681i	$0.246229\pi$
$54$	−0.282413	−	0.439444i	−0.0384316	−	0.0598007i
$55$	1.66806	+	0.602264i	0.224921	+	0.0812092i
$56$	0.599069	+	2.04024i	0.0800540	+	0.272639i
$57$	−5.26904	+	0.376849i	−0.697901	+	0.0499149i
$58$	0.381310	−	0.0272718i	0.0500684	−	0.00358097i
$59$	−1.87184	−	6.37491i	−0.243693	−	0.829943i	−0.986962	−	0.160951i	$-0.948544\pi$
$59$	−1.87184	−	6.37491i	−0.243693	−	0.829943i	0.743269	−	0.668992i	$-0.233274\pi$
$60$	3.46933	+	7.39026i	0.447889	+	0.954079i
$61$	5.28454	+	8.22290i	0.676616	+	1.05283i	0.994503	+	0.104706i	$0.0333903\pi$
$61$	5.28454	+	8.22290i	0.676616	+	1.05283i	−0.317887	+	0.948128i	$0.602973\pi$
$62$	−0.0283048	+	0.0154556i	−0.00359471	+	0.00196286i
$63$	−1.46684	−	1.09806i	−0.184804	−	0.138343i
$64$	−7.02251	−	3.20707i	−0.877813	−	0.400884i
$65$	5.48672	+	0.730110i	0.680543	+	0.0905590i
$66$	−0.0852307	+	0.132622i	−0.0104912	+	0.0163246i
$67$	0.550148	−	7.69208i	0.0672113	−	0.939737i	−0.846243	−	0.532797i	$-0.821141\pi$
$67$	0.550148	−	7.69208i	0.0672113	−	0.939737i	0.913455	−	0.406941i	$-0.133404\pi$
$68$	−7.42247	+	7.42247i	−0.900107	+	0.900107i
$69$	3.33241	+	8.15176i	0.401176	+	0.981357i
$70$	0.851805	+	0.834089i	0.101810	+	0.0996927i
$71$	−10.1464	−	11.7096i	−1.20416	−	1.38967i	−0.899335	−	0.437260i	$-0.855949\pi$
$71$	−10.1464	−	11.7096i	−1.20416	−	1.38967i	−0.304820	−	0.952410i	$-0.598596\pi$
$72$	−0.156930	+	0.0341380i	−0.0184944	+	0.00402320i
$73$	−3.91486	+	2.93063i	−0.458200	+	0.343004i	−0.803313	−	0.595557i	$-0.796931\pi$
$73$	−3.91486	+	2.93063i	−0.458200	+	0.343004i	0.345113	+	0.938561i	$0.387841\pi$
$74$	0.173991	−	0.380987i	0.0202260	−	0.0442888i
$75$	7.46419	+	5.34660i	0.861890	+	0.617372i
$76$	1.61143	−	5.48801i	0.184843	−	0.629518i
$77$	0.830373	−	3.81716i	0.0946297	−	0.435006i
$78$	−0.171947	+	0.461007i	−0.0194691	+	0.0521988i
$79$	13.6014	−	3.99372i	1.53027	−	0.449329i	0.595139	−	0.803623i	$-0.297097\pi$
$79$	13.6014	−	3.99372i	1.53027	−	0.449329i	0.935134	+	0.354294i	$0.115279\pi$
$80$	−8.75792	+	0.718952i	−0.979165	+	0.0803813i
$81$	−6.53396	+	7.54059i	−0.725996	+	0.837844i
$82$	−0.233824	+	0.428217i	−0.0258215	+	0.0472886i
$83$	−4.21914	−	1.57366i	−0.463111	−	0.172731i	0.107068	−	0.994252i	$-0.465854\pi$
$83$	−4.21914	−	1.57366i	−0.463111	−	0.172731i	−0.570179	+	0.821520i	$0.693126\pi$
$84$	15.1285	−	9.72249i	1.65065	−	1.06081i
$85$	−3.20668	+	11.3613i	−0.347813	+	1.23230i
$86$	−0.408224	+	0.0586938i	−0.0440199	+	0.00632911i
$87$	−2.26634	−	6.07629i	−0.242977	−	0.651447i
$88$	−0.205190	−	0.274102i	−0.0218734	−	0.0292194i
$89$	−5.37985	−	3.45742i	−0.570263	−	0.366486i	0.223508	−	0.974702i	$-0.428249\pi$
$89$	−5.37985	−	3.45742i	−0.570263	−	0.366486i	−0.793771	+	0.608216i	$0.791885\pi$
$90$	−0.0674258	+	0.0596768i	−0.00710731	+	0.00629048i
$91$		−	12.1923i		−	1.27810i
$92$	−9.53087	+	0.296197i	−0.993662	+	0.0308807i
$93$	0.386853	+	0.386853i	0.0401148	+	0.0401148i
$94$	0.375256	−	0.325161i	0.0387047	−	0.0335378i
$95$	−1.43330	−	6.27079i	−0.147053	−	0.643369i
$96$	0.336809	−	2.34255i	0.0343754	−	0.239086i
$97$	3.64812	−	1.36068i	0.370411	−	0.138156i	−0.157364	−	0.987541i	$-0.550299\pi$
$97$	3.64812	−	1.36068i	0.370411	−	0.138156i	0.527774	+	0.849385i	$0.323027\pi$
$98$	1.11964	−	1.49567i	0.113101	−	0.151085i
$99$	0.283093	+	0.0831235i	0.0284519	+	0.00835422i
$100$	−8.24845	+	5.54930i	−0.824845	+	0.554930i
$101$	1.09056	+	2.38800i	0.108515	+	0.237615i	0.956097	−	0.293049i	$-0.0946700\pi$
$101$	1.09056	+	2.38800i	0.108515	+	0.237615i	−0.847582	+	0.530664i	$0.821943\pi$
$102$	−0.921030	−	0.502920i	−0.0911955	−	0.0497965i
$103$	0.810011	+	11.3254i	0.0798128	+	1.11593i	0.866699	+	0.498831i	$0.166237\pi$
$103$	0.810011	+	11.3254i	0.0798128	+	1.11593i	−0.786886	+	0.617098i	$0.788308\pi$
$104$	−0.807627	−	0.699813i	−0.0791944	−	0.0686223i
$105$	9.50546	−	17.8514i	0.927638	−	1.74212i
$106$	−0.420171	+	0.191886i	−0.0408106	+	0.0186376i
$107$	9.64444	+	2.09802i	0.932363	+	0.202823i	0.652996	−	0.757361i	$-0.273512\pi$
$107$	9.64444	+	2.09802i	0.932363	+	0.202823i	0.279367	+	0.960184i	$0.409875\pi$
$108$	−4.59841	−	8.42136i	−0.442482	−	0.810346i
$109$	−2.53793	−	17.6517i	−0.243090	−	1.69073i	−0.636430	−	0.771334i	$-0.719590\pi$
$109$	−2.53793	−	17.6517i	−0.243090	−	1.69073i	0.393340	−	0.919393i	$-0.371319\pi$
$110$	−0.175448	−	0.0779069i	−0.0167283	−	0.00742813i
$111$	−7.03294	−	1.01118i	−0.667537	−	0.0959774i
$112$	4.11446	+	18.9139i	0.388780	+	1.78719i
$113$	16.2938	+	1.16536i	1.53280	+	0.109628i	0.812057	−	0.583578i	$-0.198348\pi$
$113$	16.2938	+	1.16536i	1.53280	+	0.109628i	0.720739	+	0.693206i	$0.243802\pi$
$114$	0.571804			0.0535544
$115$	−9.19031	+	5.52613i	−0.857001	+	0.515315i
$116$	7.02192			0.651969
$117$	0.918508	+	0.0656930i	0.0849161	+	0.00607332i
$118$	0.152874	+	0.702749i	0.0140732	+	0.0646933i
$119$	25.7388	+	3.70068i	2.35947	+	0.339241i
$120$	−0.636897	−	1.65428i	−0.0581404	−	0.151015i
$121$	−1.47594	−	10.2654i	−0.134177	−	0.933219i
$122$	−0.507070	−	0.928629i	−0.0459079	−	0.0840741i
$123$	8.08768	+	1.75937i	0.729241	+	0.158637i
$124$	−0.538841	+	0.246080i	−0.0483893	+	0.0220987i
$125$	−5.04621	+	9.97676i	−0.451347	+	0.892348i
$126$	0.149894	+	0.129884i	0.0133536	+	0.0115710i
$127$	−0.709390	−	9.91857i	−0.0629482	−	0.880131i	−0.926602	−	0.376045i	$-0.877284\pi$
$127$	−0.709390	−	9.91857i	−0.0629482	−	0.880131i	0.863653	−	0.504086i	$-0.168171\pi$
$128$	2.99577	+	1.63581i	0.264791	+	0.144587i
$129$	2.90643	+	6.36420i	0.255897	+	0.560336i
$130$	−0.586759	−	0.121199i	−0.0514621	−	0.0106298i
$131$	−11.5421	−	3.38907i	−1.00844	−	0.296105i	−0.264525	−	0.964379i	$-0.585215\pi$
$131$	−11.5421	−	3.38907i	−1.00844	−	0.296105i	−0.743915	+	0.668274i	$0.767033\pi$
$132$	−1.73534	+	2.31815i	−0.151042	+	0.201769i
$133$	−13.2757	+	4.95158i	−1.15115	+	0.429356i
$134$	−0.118798	+	0.826260i	−0.0102626	+	0.0713780i
$135$	−9.13859	−	5.73823i	−0.786525	−	0.493868i
$136$	1.72249	−	1.49255i	0.147703	−	0.127985i
$137$	−8.24135	−	8.24135i	−0.704106	−	0.704106i	0.261184	−	0.965289i	$-0.415887\pi$
$137$	−8.24135	−	8.24135i	−0.704106	−	0.704106i	−0.965289	+	0.261184i	$0.915887\pi$
$138$	−0.296850	−	0.905873i	−0.0252695	−	0.0771130i
$139$		−	10.2903i		−	0.872812i	−0.899750	−	0.436406i	$-0.856251\pi$
$139$		−	10.2903i		−	0.872812i	0.899750	−	0.436406i	$-0.143749\pi$
$140$	14.5134	+	16.3980i	1.22661	+	1.38588i
$141$	−7.08619	−	4.55402i	−0.596765	−	0.383518i
$142$	1.00508	+	1.34262i	0.0843441	+	0.112671i
$143$	0.686082	+	1.83946i	0.0573731	+	0.153823i
$144$	−1.44705	+	0.208054i	−0.120587	+	0.0173378i
$145$	6.89089	−	3.85726i	0.572257	−	0.320328i
$146$	0.445316	−	0.286187i	0.0368546	−	0.0236850i
$147$	−29.6963	−	11.0762i	−2.44931	−	0.913547i
$148$	3.68702	−	6.75227i	0.303071	−	0.555033i
$149$	−5.87592	+	6.78117i	−0.481374	+	0.555535i	−0.943540	−	0.331258i	$-0.892527\pi$
$149$	−5.87592	+	6.78117i	−0.481374	+	0.555535i	0.462166	+	0.886793i	$0.347072\pi$
$150$	−0.764616	−	0.634908i	−0.0624306	−	0.0518400i
$151$	−4.52333	+	1.32817i	−0.368103	+	0.108085i	−0.460552	−	0.887633i	$-0.652349\pi$
$151$	−4.52333	+	1.32817i	−0.368103	+	0.108085i	0.0924491	+	0.995717i	$0.470530\pi$
$152$	−0.434002	+	1.16360i	−0.0352022	+	0.0943808i
$153$	−0.417474	+	1.91910i	−0.0337508	+	0.155150i
$154$	−0.119131	+	0.405724i	−0.00959987	+	0.0326942i
$155$	−0.393610	+	0.537482i	−0.0316155	+	0.0431716i
$156$	−3.75443	+	8.22105i	−0.300595	+	0.658210i
$157$	1.06265	−	0.795493i	0.0848091	−	0.0634873i	−0.556032	−	0.831161i	$-0.687677\pi$
$157$	1.06265	−	0.795493i	0.0848091	−	0.0634873i	0.640841	+	0.767674i	$0.278586\pi$
$158$	−1.49937	+	0.326168i	−0.119283	+	0.0259485i
$159$	5.13151	+	5.92208i	0.406955	+	0.469652i
$160$	2.88171	−	0.0302825i	0.227819	−	0.00239404i
$161$	14.7365	+	18.4612i	1.16140	+	1.45495i
$162$	0.763696	−	0.763696i	0.0600016	−	0.0600016i
$163$	0.159208	−	2.22602i	0.0124702	−	0.174356i	−0.987400	−	0.158244i	$-0.949417\pi$
$163$	0.159208	−	2.22602i	0.0124702	−	0.174356i	0.999870	−	0.0161116i	$-0.00512871\pi$
$164$	−4.84514	+	7.53919i	−0.378342	+	0.588712i
$165$	−0.429565	+	3.22814i	−0.0334416	+	0.251310i
$166$	0.443386	+	0.202487i	0.0344134	+	0.0157161i
$167$	12.4948	+	9.35351i	0.966878	+	0.723796i	0.961104	−	0.276187i	$-0.0890710\pi$
$167$	12.4948	+	9.35351i	0.966878	+	0.723796i	0.00577449	+	0.999983i	$0.498162\pi$
$168$	−3.42705	+	1.87131i	−0.264402	+	0.144375i
$169$	−3.71560	−	5.78158i	−0.285815	−	0.444737i
$170$	0.433956	−	1.20190i	0.0332829	−	0.0921818i
$171$	−0.301498	−	1.02681i	−0.0230561	−	0.0785219i
$172$	−7.55621	+	0.540431i	−0.576155	+	0.0412074i
$173$	−3.66026	+	0.261787i	−0.278285	+	0.0199033i	−0.209784	−	0.977748i	$-0.567276\pi$
$173$	−3.66026	+	0.261787i	−0.278285	+	0.0199033i	−0.0685006	+	0.997651i	$0.521822\pi$
$174$	0.197773	+	0.673554i	0.0149931	+	0.0510620i
$175$	23.2503	+	8.11954i	1.75755	+	0.613779i
$176$	−1.68507	−	2.62202i	−0.127017	−	0.197642i
$177$	10.7081	−	5.84707i	0.804870	−	0.439492i
$178$	0.554160	+	0.414839i	0.0415361	+	0.0310935i
$179$	9.98011	+	4.55776i	0.745949	+	0.340663i	0.751863	−	0.659319i	$-0.229155\pi$
$179$	9.98011	+	4.55776i	0.745949	+	0.340663i	−0.00591453	+	0.999983i	$0.501883\pi$
$180$	−1.31354	+	1.00502i	−0.0979059	+	0.0749095i
$181$	−1.60058	+	2.49055i	−0.118970	+	0.185121i	−0.895631	−	0.444798i	$-0.853276\pi$
$181$	−1.60058	+	2.49055i	−0.118970	+	0.185121i	0.776661	+	0.629919i	$0.216912\pi$
$182$	−0.0941502	+	1.31639i	−0.00697888	+	0.0975774i
$183$	−12.6919	+	12.6919i	−0.938214	+	0.938214i
$184$	2.06873	+	0.0834818i	0.152509	+	0.00615436i
$185$	−0.0909157	−	8.65161i	−0.00668426	−	0.636079i
$186$	−0.0387809	−	0.0447555i	−0.00284355	−	0.00328163i
$187$	−4.09148	+	0.890046i	−0.299198	+	0.0650866i
$188$	7.30136	−	5.46573i	0.532506	−	0.398629i
$189$	−9.87408	+	21.6212i	−0.718233	+	1.57271i
$190$	0.106329	+	0.688120i	0.00771389	+	0.0499215i
$191$	−5.69734	+	19.4034i	−0.412245	+	1.40398i	0.447971	+	0.894048i	$0.352147\pi$
$191$	−5.69734	+	19.4034i	−0.412245	+	1.40398i	−0.860216	+	0.509929i	$0.829672\pi$
$192$	3.01344	−	13.8526i	0.217477	−	0.999724i
$193$	−5.12298	+	13.7353i	−0.368760	+	0.988685i	0.611547	+	0.791208i	$0.290547\pi$
$193$	−5.12298	+	13.7353i	−0.368760	+	0.988685i	−0.980308	+	0.197477i	$0.936725\pi$
$194$	−0.404392	+	0.118740i	−0.0290337	+	0.00852506i
$195$	0.831589	+	10.1300i	0.0595513	+	0.725425i
$196$	22.4734	−	25.9357i	1.60525	−	1.85255i
$197$	−4.13395	+	7.57076i	−0.294531	+	0.539394i	−0.982481	−	0.186365i	$-0.940329\pi$
$197$	−4.13395	+	7.57076i	−0.294531	+	0.539394i	0.687949	+	0.725759i	$0.258511\pi$
$198$	−0.0299234	−	0.0111609i	−0.00212656	−	0.000793167i
$199$	−5.12646	+	3.29457i	−0.363405	+	0.233546i	−0.709582	−	0.704623i	$-0.751116\pi$
$199$	−5.12646	+	3.29457i	−0.363405	+	0.233546i	0.346177	+	0.938169i	$0.387480\pi$
$200$	1.87236	−	1.07407i	0.132396	−	0.0759484i
$201$	14.0169	−	2.01533i	0.988678	−	0.142150i
$202$	−0.0993068	−	0.266252i	−0.00698720	−	0.0187334i
$203$	−10.4244	−	13.9254i	−0.731651	−	0.977371i
$204$	−16.2157	−	10.4212i	−1.13532	−	0.729628i
$205$	−0.613330	+	10.0600i	−0.0428368	+	0.702622i
$206$		−	1.22905i		−	0.0856323i
$207$	−1.47018	+	1.01071i	−0.102185	+	0.0702489i
$208$	−6.87857	−	6.87857i	−0.476943	−	0.476943i
$209$	1.72428	−	1.49410i	0.119271	−	0.103349i
$210$	−1.16415	+	1.85400i	−0.0803338	+	0.127938i
$211$	2.23555	−	15.5486i	0.153901	−	1.07041i	−0.755698	−	0.654921i	$-0.772702\pi$
$211$	2.23555	−	15.5486i	0.153901	−	1.07041i	0.909599	−	0.415487i	$-0.136389\pi$
$212$	−7.94963	+	2.96506i	−0.545983	+	0.203641i
$213$	17.0504	−	22.7767i	1.16828	−	1.56063i
$214$	−1.02510	−	0.300997i	−0.0700745	−	0.0205757i
$215$	−7.11834	+	4.68109i	−0.485467	+	0.319248i
$216$	0.865455	+	1.89508i	0.0588868	+	0.128944i
$217$	1.28795	+	0.703272i	0.0874316	+	0.0477412i
$218$	0.137710	+	1.92544i	0.00932691	+	0.130407i
$219$	−6.78664	−	5.88066i	−0.458599	−	0.397378i
$220$	−3.11239	−	1.65728i	−0.209838	−	0.111734i
$221$	−11.8875	+	5.42883i	−0.799639	+	0.365183i
$222$	0.751533	+	0.163486i	0.0504396	+	0.0109725i
$223$	4.03383	+	7.38740i	0.270125	+	0.494697i	0.977166	−	0.212475i	$-0.0681524\pi$
$223$	4.03383	+	7.38740i	0.270125	+	0.494697i	−0.707042	+	0.707172i	$0.749971\pi$
$224$	−0.903410	−	6.28335i	−0.0603616	−	0.419824i
$225$	−0.736961	+	1.70781i	−0.0491308	+	0.113854i
$226$	−1.75024	−	0.251646i	−0.116424	−	0.0167392i
$227$	1.18769	+	5.45972i	0.0788298	+	0.362375i	0.999617	−	0.0276918i	$-0.00881571\pi$
$227$	1.18769	+	5.45972i	0.0788298	+	0.362375i	−0.920787	+	0.390066i	$0.872452\pi$
$228$	10.4763	+	0.749283i	0.693813	+	0.0496225i
$229$	17.9294			1.18481			0.592406	−	0.805640i	$-0.298178\pi$
$229$	17.9294			1.18481			0.592406	+	0.805640i	$0.298178\pi$
$230$	1.03494	−	0.525684i	0.0682422	−	0.0346626i
$231$	7.17340			0.471975
$232$	−1.52077	−	0.108768i	−0.0998436	−	0.00714095i
$233$	−4.15019	−	19.0781i	−0.271888	−	1.24985i	−0.887133	−	0.461513i	$-0.847307\pi$
$233$	−4.15019	−	19.0781i	−0.271888	−	1.24985i	0.615245	−	0.788336i	$-0.289057\pi$
$234$	−0.0986633	−	0.0141856i	−0.00644982	−	0.000927345i
$235$	4.16270	−	9.37449i	0.271544	−	0.611524i
$236$	1.88001	+	13.0758i	0.122378	+	0.851161i
$237$	12.4752	+	22.8465i	0.810349	+	1.48404i
$238$	−2.75042	−	0.598318i	−0.178283	−	0.0387832i
$239$	5.20394	−	2.37656i	0.336615	−	0.153727i	−0.239935	−	0.970789i	$-0.577126\pi$
$239$	5.20394	−	2.37656i	0.336615	−	0.153727i	0.576550	+	0.817062i	$0.304399\pi$
$240$	−4.70856	−	15.4340i	−0.303936	−	0.996262i
$241$	−11.1657	−	9.67514i	−0.719246	−	0.623230i	0.216344	−	0.976317i	$-0.430587\pi$
$241$	−11.1657	−	9.67514i	−0.719246	−	0.623230i	−0.935591	+	0.353087i	$0.885132\pi$
$242$	0.0800858	+	1.11975i	0.00514811	+	0.0719800i
$243$	−3.37431	−	1.84251i	−0.216462	−	0.118197i
$244$	−8.07344	−	17.6784i	−0.516849	−	1.13174i
$245$	7.80715	−	37.7968i	0.498781	−	2.41475i
$246$	−0.859634	−	0.252411i	−0.0548083	−	0.0160932i
$247$	4.26739	−	5.70056i	0.271527	−	0.362718i
$248$	0.120511	−	0.0449483i	0.00765246	−	0.00285422i
$249$	1.17680	−	8.18482i	0.0745766	−	0.518692i
$250$	0.621878	−	1.03822i	0.0393310	−	0.0656625i
$251$	−11.2092	+	9.71281i	−0.707517	+	0.613067i	−0.932446	−	0.361308i	$-0.882330\pi$
$251$	−11.2092	+	9.71281i	−0.707517	+	0.613067i	0.224930	+	0.974375i	$0.427785\pi$
$252$	2.57609	+	2.57609i	0.162278	+	0.162278i
$253$	−3.26215	−	1.95601i	−0.205090	−	0.122973i
$254$			1.07638i			0.0675380i
$255$	−21.6376	−	1.31918i	−1.35500	−	0.0826103i
$256$	12.6784	+	8.14792i	0.792401	+	0.509245i
$257$	8.50171	+	11.3570i	0.530322	+	0.708427i	0.983074	−	0.183209i	$-0.0586486\pi$
$257$	8.50171	+	11.3570i	0.530322	+	0.708427i	−0.452752	+	0.891637i	$0.649558\pi$
$258$	−0.264660	−	0.709581i	−0.0164770	−	0.0441766i
$259$	−18.8642	+	2.71226i	−1.17217	+	0.168532i
$260$	−10.5915	−	2.98942i	−0.656858	−	0.185396i
$261$	1.10524	−	0.710295i	0.0684127	−	0.0439661i
$262$	1.22002	+	0.455045i	0.0753733	+	0.0281128i
$263$	−8.25499	+	15.1179i	−0.509024	+	0.932209i	0.489173	+	0.872187i	$0.337299\pi$
$263$	−8.25499	+	15.1179i	−0.509024	+	0.932209i	−0.998197	+	0.0600217i	$0.980883\pi$
$264$	0.411739	−	0.475172i	0.0253408	−	0.0292448i
$265$	−6.17253	+	7.27659i	−0.379175	+	0.446997i
$266$	1.47160	−	0.432102i	0.0902298	−	0.0264939i
$267$	4.10384	−	11.0028i	0.251151	−	0.673362i
$268$	−3.25928	+	14.9827i	−0.199093	+	0.915213i
$269$	−1.46335	+	4.98370i	−0.0892218	+	0.303862i	−0.991999	−	0.126247i	$-0.959707\pi$
$269$	−1.46335	+	4.98370i	−0.0892218	+	0.303862i	0.902777	+	0.430109i	$0.141525\pi$
$270$	0.942376	+	0.690122i	0.0573512	+	0.0419995i
$271$	0.696019	−	1.52407i	0.0422801	−	0.0925806i	−0.887313	−	0.461167i	$-0.847431\pi$
$271$	0.696019	−	1.52407i	0.0422801	−	0.0925806i	0.929593	+	0.368586i	$0.120158\pi$
$272$	16.6090	−	12.4333i	1.00707	−	0.753882i
$273$	21.8771	−	4.75906i	1.32406	−	0.288032i
$274$	0.826171	+	0.953453i	0.0499108	+	0.0576002i
$275$	−3.96469	+	0.0833353i	−0.239080	+	0.00502531i
$276$	−4.25170	−	16.9860i	−0.255922	−	1.02244i
$277$	−15.8354	+	15.8354i	−0.951459	+	0.951459i	−0.998875	−	0.0474157i	$-0.984901\pi$
$277$	−15.8354	+	15.8354i	−0.951459	+	0.951459i	0.0474157	+	0.998875i	$0.484901\pi$
$278$	−0.0794629	+	1.11104i	−0.00476587	+	0.0666356i
$279$	−0.0599207	+	0.0932385i	−0.00358736	+	0.00558204i
$280$	−2.88924	−	3.77620i	−0.172665	−	0.225671i
$281$	−1.97290	−	0.900995i	−0.117694	−	0.0537488i	0.355698	−	0.934601i	$-0.384243\pi$
$281$	−1.97290	−	0.900995i	−0.117694	−	0.0537488i	−0.473392	+	0.880852i	$0.656970\pi$
$282$	0.729924	+	0.546415i	0.0434664	+	0.0325385i
$283$	21.9077	−	11.9625i	1.30228	−	0.711099i	0.329792	−	0.944053i	$-0.393021\pi$
$283$	21.9077	−	11.9625i	1.30228	−	0.711099i	0.972488	+	0.232955i	$0.0748394\pi$
$284$	16.6552	+	25.9160i	0.988304	+	1.53783i
$285$	10.6924	−	5.01953i	0.633366	−	0.297331i
$286$	−0.0598713	−	0.203903i	−0.00354026	−	0.0120570i
$287$	22.1441	−	1.58378i	1.30712	−	0.0934873i
$288$	0.478225	−	0.0342034i	0.0281797	−	0.00201545i
$289$	−3.06305	−	10.4318i	−0.180179	−	0.613635i
$290$	−0.773791	+	0.363253i	−0.0454386	+	0.0213310i
$291$	3.86550	+	6.01484i	0.226600	+	0.352596i
$292$	8.53389	−	4.65985i	0.499408	−	0.272697i
$293$	1.22235	+	0.915037i	0.0714102	+	0.0534570i	0.634386	−	0.773016i	$-0.281253\pi$
$293$	1.22235	+	0.915037i	0.0714102	+	0.0534570i	−0.562976	+	0.826473i	$0.690344\pi$
$294$	3.12076	+	1.42520i	0.182007	+	0.0831196i
$295$	9.02767	+	11.7991i	0.525611	+	0.686968i
$296$	−0.903106	+	1.40526i	−0.0524920	+	0.0816791i
$297$	0.273043	−	3.81764i	0.0158436	−	0.221522i
$298$	0.686784	−	0.686784i	0.0397843	−	0.0397843i
$299$	−11.2464	−	3.80113i	−0.650398	−	0.219825i
$300$	−13.1770	−	12.6344i	−0.760773	−	0.729449i
$301$	12.2893	+	14.1827i	0.708346	+	0.817475i
$302$	0.498637	−	0.108472i	0.0286933	−	0.00624185i
$303$	−3.85919	+	2.88895i	−0.221705	+	0.165966i
$304$	−4.69625	+	10.2834i	−0.269349	+	0.589791i
$305$	−17.6338	−	12.9136i	−1.00971	−	0.739431i
$306$	0.0598939	−	0.203980i	0.00342391	−	0.0116608i
$307$	−1.32106	+	6.07281i	−0.0753968	+	0.346594i	−0.999355	−	0.0358989i	$-0.988571\pi$
$307$	−1.32106	+	6.07281i	−0.0753968	+	0.346594i	0.923959	+	0.382492i	$0.124934\pi$
$308$	−2.71432	+	7.27738i	−0.154663	+	0.414667i
$309$	−20.0055	+	5.87414i	−1.13807	+	0.334168i
$310$	0.0466483	−	0.0549921i	0.00264944	−	0.00312334i
$311$	2.69973	−	3.11566i	0.153088	−	0.176673i	−0.674025	−	0.738708i	$-0.735436\pi$
$311$	2.69973	−	3.11566i	0.153088	−	0.176673i	0.827113	+	0.562035i	$0.189982\pi$
$312$	0.940456	−	1.72232i	0.0532428	−	0.0975070i
$313$	4.78149	+	1.78340i	0.270266	+	0.100804i	0.480943	−	0.876752i	$-0.340294\pi$
$313$	4.78149	+	1.78340i	0.270266	+	0.100804i	−0.210677	+	0.977556i	$0.567567\pi$
$314$	−0.120877	+	0.0776829i	−0.00682148	+	0.00438390i
$315$	3.94311	+	1.11293i	0.222169	+	0.0627065i
$316$	−27.8982	+	4.01115i	−1.56939	+	0.225645i
$317$	−10.9358	−	29.3201i	−0.614218	−	1.64678i	−0.754213	−	0.656630i	$-0.771982\pi$
$317$	−10.9358	−	29.3201i	−0.614218	−	1.64678i	0.139995	−	0.990152i	$-0.455291\pi$
$318$	−0.508315	−	0.679029i	−0.0285049	−	0.0380781i
$319$	2.35635	+	1.51433i	0.131930	+	0.0847864i
$320$	17.2308	+	1.05051i	0.963232	+	0.0587254i
$321$			18.1243i			1.01160i
$322$	−1.44853	−	2.10704i	−0.0807233	−	0.117421i
$323$	10.7390	+	10.7390i	0.597536	+	0.597536i
$324$	14.9928	−	12.9914i	0.832935	−	0.721742i
$325$	−12.0360	+	2.88445i	−0.667638	+	0.160001i
$326$	−0.0343792	+	0.239113i	−0.00190409	+	0.0132432i
$327$	30.6825	−	11.4440i	1.69675	−	0.632853i
$328$	1.16612	−	1.55775i	0.0643880	−	0.0860123i
$329$	−21.6785	−	6.36539i	−1.19518	−	0.350935i
$330$	0.0713078	−	0.345223i	0.00392537	−	0.0190039i
$331$	8.14271	+	17.8300i	0.447564	+	0.980028i	0.990148	+	0.140026i	$0.0447187\pi$
$331$	8.14271	+	17.8300i	0.447564	+	0.980028i	−0.542584	+	0.840002i	$0.682554\pi$
$332$	7.85818	+	4.29089i	0.431273	+	0.235493i
$333$	−0.102687	−	1.43575i	−0.00562722	−	0.0786788i
$334$	−1.27683	−	1.10638i	−0.0698649	−	0.0605383i
$335$	5.03177	+	16.4935i	0.274915	+	0.901135i
$336$	−32.3318	+	14.7655i	−1.76385	+	0.805522i
$337$	−13.3225	−	2.89813i	−0.725722	−	0.157871i	−0.165495	−	0.986211i	$-0.552922\pi$
$337$	−13.3225	−	2.89813i	−0.725722	−	0.157871i	−0.560226	+	0.828340i	$0.689286\pi$
$338$	0.356524	+	0.652925i	0.0193924	+	0.0355145i
$339$	4.26900	+	29.6915i	0.231860	+	1.61262i
$340$	9.52570	−	21.4521i	0.516604	−	1.16340i
$341$	−0.233888	−	0.0336280i	−0.0126657	−	0.00182106i
$342$	0.0246234	+	0.113192i	0.00133148	+	0.00612071i
$343$	−50.4067	−	3.60516i	−2.72171	−	0.194660i
$344$	1.64486			0.0886846
$345$	−13.5030	−	14.3335i	−0.726979	−	0.771689i
$346$	0.397217			0.0213545
$347$	−24.0519	−	1.72022i	−1.29117	−	0.0923465i	−0.591205	−	0.806521i	$-0.701348\pi$
$347$	−24.0519	−	1.72022i	−1.29117	−	0.0923465i	−0.699967	+	0.714175i	$0.746802\pi$
$348$	2.74090	+	12.5997i	0.146928	+	0.675415i
$349$	−16.4605	−	2.36666i	−0.881108	−	0.126684i	−0.313113	−	0.949716i	$-0.601372\pi$
$349$	−16.4605	−	2.36666i	−0.881108	−	0.126684i	−0.567996	+	0.823032i	$0.692281\pi$
$350$	−2.44761	−	1.05620i	−0.130830	−	0.0564564i
$351$	−1.70003	−	11.8240i	−0.0907411	−	0.631118i
$352$	0.489874	+	0.897137i	0.0261104	+	0.0478176i
$353$	−3.24562	−	0.706041i	−0.172747	−	0.0375787i	0.125360	−	0.992111i	$-0.459991\pi$
$353$	−3.24562	−	0.706041i	−0.172747	−	0.0375787i	−0.298107	+	0.954533i	$0.596355\pi$
$354$	−1.20130	+	0.548614i	−0.0638483	+	0.0291585i
$355$	30.5805	+	16.2834i	1.62304	+	0.864234i
$356$	9.60947	+	8.32666i	0.509301	+	0.441312i
$357$	3.40647	+	47.6286i	0.180289	+	2.52077i
$358$	−1.04235	−	0.569166i	−0.0550899	−	0.0300814i
$359$	12.7982	+	28.0241i	0.675462	+	1.47906i	0.867380	+	0.497646i	$0.165802\pi$
$359$	12.7982	+	28.0241i	0.675462	+	1.47906i	−0.191918	+	0.981411i	$0.561471\pi$
$360$	0.300048	−	0.197315i	0.0158139	−	0.0103994i
$361$	10.2902	+	3.02146i	0.541587	+	0.159024i
$362$	0.192046	−	0.256543i	0.0100937	−	0.0134836i
$363$	17.8435	−	6.65528i	0.936541	−	0.349312i
$364$	−3.44995	+	23.9950i	−0.180827	+	1.25768i
$365$	5.81491	−	9.26070i	0.304366	−	0.484727i
$366$	1.46835	−	1.27233i	0.0767517	−	0.0665057i
$367$	−19.6376	−	19.6376i	−1.02508	−	1.02508i	−0.999677	−	0.0253980i	$-0.991915\pi$
$367$	−19.6376	−	19.6376i	−1.02508	−	1.02508i	−0.0253980	−	0.999677i	$-0.508085\pi$
$368$	18.7293	+	2.10142i	0.976333	+	0.109544i
$369$			1.67676i			0.0872888i
$370$	−0.0569926	+	0.934810i	−0.00296291	+	0.0485985i
$371$	17.6817	+	11.3634i	0.917990	+	0.589957i
$372$	−0.651879	−	0.870808i	−0.0337984	−	0.0451493i
$373$	−2.50161	−	6.70708i	−0.129529	−	0.347280i	0.855955	−	0.517050i	$-0.172970\pi$
$373$	−2.50161	−	6.70708i	−0.129529	−	0.347280i	−0.985484	+	0.169771i	$0.945697\pi$
$374$	0.448627	−	0.0645028i	0.0231979	−	0.00333536i
$375$	−19.8714	−	5.16034i	−1.02615	−	0.266479i
$376$	−1.66595	+	1.07064i	−0.0859150	+	0.0552142i
$377$	8.19093	+	3.05506i	0.421854	+	0.157343i
$378$	1.23306	−	2.25818i	0.0634217	−	0.116148i
$379$	8.34078	−	9.62577i	0.428437	−	0.494443i	−0.499952	−	0.866053i	$-0.666649\pi$
$379$	8.34078	−	9.62577i	0.428437	−	0.494443i	0.928389	+	0.371611i	$0.121194\pi$
$380$	1.04640	+	12.7468i	0.0536793	+	0.653895i
$381$	17.5204	−	5.14444i	0.897595	−	0.263558i
$382$	0.764972	−	2.05097i	0.0391394	−	0.104937i
$383$	−4.27550	+	19.6542i	−0.218468	+	1.00428i	0.729020	+	0.684492i	$0.239976\pi$
$383$	−4.27550	+	19.6542i	−0.218468	+	1.00428i	−0.947489	+	0.319790i	$0.896388\pi$
$384$	−1.76585	+	6.01394i	−0.0901133	+	0.306898i
$385$	1.33391	+	8.63260i	0.0679825	+	0.439958i
$386$	0.659190	−	1.44342i	0.0335519	−	0.0734684i
$387$	−1.13467	+	0.849403i	−0.0576785	+	0.0431776i
$388$	−7.56469	+	1.64560i	−0.384039	+	0.0835426i
$389$	−14.8609	−	17.1504i	−0.753477	−	0.869559i	0.241423	−	0.970420i	$-0.422386\pi$
$389$	−14.8609	−	17.1504i	−0.753477	−	0.869559i	−0.994901	+	0.100861i	$0.967840\pi$
$390$	−0.0115610	−	1.10015i	−0.000585413	−	0.0557083i
$391$	11.4381	−	22.5883i	0.578447	−	1.14234i
$392$	−5.26892	+	5.26892i	−0.266121	+	0.266121i
$393$	1.57586	−	22.0333i	0.0794914	−	1.11143i
$394$	0.504801	−	0.785486i	0.0254315	−	0.0395722i
$395$	−25.1742	+	19.2612i	−1.26665	+	0.969137i
$396$	−0.533618	−	0.243695i	−0.0268153	−	0.0122461i
$397$	14.4410	+	10.8104i	0.724775	+	0.542560i	0.896748	−	0.442542i	$-0.145923\pi$
$397$	14.4410	+	10.8104i	0.724775	+	0.542560i	−0.171973	+	0.985102i	$0.555014\pi$
$398$	0.578941	−	0.316126i	0.0290197	−	0.0158459i
$399$	−14.0668	−	21.8883i	−0.704219	−	1.09579i
$400$	17.6980	−	8.53637i	0.884902	−	0.426818i
$401$	−5.90383	−	20.1066i	−0.294823	−	1.00408i	−0.965082	−	0.261948i	$-0.915635\pi$
$401$	−5.90383	−	20.1066i	−0.294823	−	1.00408i	0.670259	−	0.742128i	$-0.266183\pi$
$402$	−1.52896	+	0.109353i	−0.0762576	+	0.00545405i
$403$	−0.735609	+	0.0526118i	−0.0366433	+	0.00262078i
$404$	−1.47056	−	5.00828i	−0.0731632	−	0.249171i
$405$	7.57669	−	20.9847i	0.376489	−	1.04274i
$406$	1.01798	+	1.58401i	0.0505217	+	0.0786133i
$407$	2.69343	−	1.47073i	0.133509	−	0.0729012i
$408$	3.35048	+	2.50814i	0.165874	+	0.124172i
$409$	−6.64652	−	3.03536i	−0.328649	−	0.150089i	0.244256	−	0.969711i	$-0.421456\pi$
$409$	−6.64652	−	3.03536i	−0.328649	−	0.150089i	−0.572905	+	0.819622i	$0.694184\pi$
$410$	0.143905	−	1.08144i	0.00710698	−	0.0534084i
$411$	11.5709	−	18.0046i	0.570749	−	0.888103i
$412$	1.61053	−	22.5182i	0.0793452	−	1.10939i
$413$	23.1400	−	23.1400i	1.13865	−	1.13865i
$414$	0.166539	−	0.0977722i	0.00818496	−	0.00480524i
$415$	10.0686	−	0.105806i	0.494248	−	0.00519382i
$416$	2.08918	+	2.41105i	0.102431	+	0.118211i
$417$	18.4643	−	4.01666i	0.904200	−	0.196697i
$418$	−0.197707	+	0.148001i	−0.00967015	+	0.00723899i
$419$	9.29391	−	20.3508i	0.454037	−	0.994203i	−0.534769	−	0.844998i	$-0.679601\pi$
$419$	9.29391	−	20.3508i	0.454037	−	0.994203i	0.988806	−	0.149205i	$-0.0476713\pi$
$420$	−23.7584	+	32.4426i	−1.15929	+	1.58304i
$421$	9.30346	−	31.6847i	0.453423	−	1.54422i	−0.342916	−	0.939366i	$-0.611415\pi$
$421$	9.30346	−	31.6847i	0.453423	−	1.54422i	0.796339	−	0.604851i	$-0.206767\pi$
$422$	−0.361438	+	1.66150i	−0.0175945	+	0.0808808i
$423$	0.596343	−	1.59886i	0.0289952	−	0.0777392i
$424$	1.76762	−	0.519019i	0.0858431	−	0.0252058i
$425$	−2.43604	−	26.2844i	−0.118165	−	1.27498i
$426$	−2.01681	+	2.32752i	−0.0977146	+	0.112769i
$427$	−23.0731	+	42.2552i	−1.11658	+	2.04487i
$428$	−18.3870	−	6.85801i	−0.888770	−	0.331494i
$429$	−3.03281	+	1.94907i	−0.146425	+	0.0941018i
$430$	0.804710	−	0.450446i	0.0388065	−	0.0217224i
$431$	−4.45996	+	0.641246i	−0.214829	+	0.0308877i	−0.248889	−	0.968532i	$-0.580065\pi$
$431$	−4.45996	+	0.641246i	−0.214829	+	0.0308877i	0.0340599	+	0.999420i	$0.489156\pi$
$432$	6.62743	+	17.7688i	0.318863	+	0.854904i
$433$	−6.83477	−	9.13018i	−0.328458	−	0.438768i	0.605665	−	0.795720i	$-0.292907\pi$
$433$	−6.83477	−	9.13018i	−0.328458	−	0.438768i	−0.934123	+	0.356951i	$0.883816\pi$
$434$	−0.133628	−	0.0858775i	−0.00641435	−	0.00412225i
$435$	9.61097	+	10.8590i	0.460811	+	0.520648i
$436$			35.4575i			1.69811i
$437$	0.428546	+	13.7895i	0.0205001	+	0.659643i
$438$	0.687338	+	0.687338i	0.0328423	+	0.0328423i
$439$	3.81470	−	3.30545i	0.182066	−	0.157761i	−0.559060	−	0.829127i	$-0.688838\pi$
$439$	3.81470	−	3.30545i	0.182066	−	0.157761i	0.741125	+	0.671367i	$0.234292\pi$
$440$	0.648395	+	0.407135i	0.0309110	+	0.0194094i
$441$	0.913786	−	6.35552i	0.0435136	−	0.302644i
$442$	1.32541	−	0.494351i	0.0630431	−	0.0235139i
$443$	−4.43442	+	5.92369i	−0.210686	+	0.281443i	−0.893419	−	0.449225i	$-0.851700\pi$
$443$	−4.43442	+	5.92369i	−0.210686	+	0.281443i	0.682733	+	0.730668i	$0.260791\pi$
$444$	13.5550	+	3.98011i	0.643293	+	0.188888i
$445$	14.0041	+	2.89264i	0.663859	+	0.137124i
$446$	−0.378483	−	0.828762i	−0.0179217	−	0.0392430i
$447$	−14.4613	−	7.89646i	−0.683995	−	0.373490i
$448$	−2.71269	−	37.9284i	−0.128163	−	1.79195i
$449$	−3.25668	−	2.82193i	−0.153692	−	0.133175i	0.574620	−	0.818420i	$-0.305150\pi$
$449$	−3.25668	−	2.82193i	−0.153692	−	0.133175i	−0.728313	+	0.685245i	$0.759695\pi$
$450$	0.0927571	−	0.178701i	0.00437261	−	0.00842403i
$451$	−3.25177	+	1.48503i	−0.153120	+	0.0699275i
$452$	−31.7373	−	6.90402i	−1.49280	−	0.324738i
$453$	−4.14879	−	7.59795i	−0.194927	−	0.356983i
$454$	−0.0860734	−	0.598654i	−0.00403963	−	0.0280962i
$455$	9.79525	+	25.4423i	0.459208	+	1.19275i
$456$	−2.25731	−	0.324552i	−0.105708	−	0.0151985i
$457$	2.98247	+	13.7102i	0.139514	+	0.641335i	0.992789	+	0.119874i	$0.0382491\pi$
$457$	2.98247	+	13.7102i	0.139514	+	0.641335i	−0.853275	+	0.521461i	$0.825387\pi$
$458$	−1.93583	−	0.138453i	−0.0904554	−	0.00646949i
$459$	25.4773			1.18918
$460$	19.6506	−	8.27517i	0.916216	−	0.385832i
$461$	−14.1608			−0.659534			−0.329767	−	0.944062i	$-0.606970\pi$
$461$	−14.1608			−0.659534			−0.329767	+	0.944062i	$0.606970\pi$
$462$	−0.774507	−	0.0553938i	−0.0360333	−	0.00257715i
$463$	−3.19035	−	14.6658i	−0.148268	−	0.681578i	−0.989928	−	0.141570i	$-0.954785\pi$
$463$	−3.19035	−	14.6658i	−0.148268	−	0.681578i	0.841660	−	0.540008i	$-0.181579\pi$
$464$	−13.7375	−	1.97516i	−0.637750	−	0.0916945i
$465$	−1.11806	−	0.496471i	−0.0518490	−	0.0230233i
$466$	0.300770	+	2.09190i	0.0139329	+	0.0969054i
$467$	−7.25468	−	13.2860i	−0.335707	−	0.614801i	0.654233	−	0.756293i	$-0.272992\pi$
$467$	−7.25468	−	13.2860i	−0.335707	−	0.614801i	−0.989939	+	0.141493i	$0.954810\pi$
$468$	−1.78908	−	0.389190i	−0.0827001	−	0.0179903i
$469$	34.5512	−	15.7790i	1.59543	−	0.728607i
$470$	−0.521834	+	0.980012i	−0.0240704	+	0.0452046i
$471$	1.84217	+	1.59625i	0.0848829	+	0.0735514i
$472$	−0.204623	−	2.86101i	−0.00941854	−	0.131688i
$473$	−2.65219	−	1.44820i	−0.121948	−	0.0665884i
$474$	−1.17051	−	2.56306i	−0.0537633	−	0.117725i
$475$	8.02888	+	11.9341i	0.368390	+	0.547574i
$476$	−49.6080	−	14.5662i	−2.27378	−	0.667641i
$477$	−0.951332	+	1.27083i	−0.0435585	+	0.0581874i
$478$	−0.580218	+	0.216410i	−0.0265385	+	0.00989837i
$479$	−0.160132	+	1.11374i	−0.00731661	+	0.0508881i	−0.993153	−	0.116824i	$-0.962729\pi$
$479$	−0.160132	+	1.11374i	−0.00731661	+	0.0508881i	0.985836	+	0.167712i	$0.0536378\pi$
$480$	1.17917	+	5.15893i	0.0538213	+	0.235472i
$481$	7.23857	−	6.27225i	0.330050	−	0.285990i
$482$	1.13084	+	1.13084i	0.0515084	+	0.0515084i
$483$	−27.3736	+	33.6483i	−1.24554	+	1.53105i
$484$			20.6204i			0.937292i
$485$	−6.51958	+	5.77030i	−0.296039	+	0.262016i
$486$	0.350094	+	0.224992i	0.0158806	+	0.0102058i
$487$	−16.4884	−	22.0259i	−0.747160	−	0.998089i	−0.999536	−	0.0304601i	$-0.990303\pi$
$487$	−16.4884	−	22.0259i	−0.747160	−	0.998089i	0.252376	−	0.967629i	$-0.418788\pi$
$488$	1.47467	+	3.95374i	0.0667552	+	0.178978i
$489$	4.05638	−	0.583220i	0.183436	−	0.0263741i
$490$	−1.13480	+	4.02061i	−0.0512652	+	0.181632i
$491$	21.9542	−	14.1091i	0.990779	−	0.636735i	0.0584288	−	0.998292i	$-0.481391\pi$
$491$	21.9542	−	14.1091i	0.990779	−	0.636735i	0.932350	+	0.361557i	$0.117755\pi$
$492$	−15.4191	−	5.75102i	−0.695146	−	0.259276i
$493$	−8.93562	+	16.3644i	−0.402440	+	0.737014i
$494$	−0.504767	+	0.582532i	−0.0227105	+	0.0262094i
$495$	−0.657526	+	0.0539774i	−0.0295536	+	0.00242610i
$496$	1.12340	−	0.329859i	0.0504419	−	0.0148111i
$497$	26.6693	−	71.5031i	1.19628	−	3.20735i
$498$	−0.190262	+	0.874621i	−0.00852586	+	0.0391927i
$499$	−3.59093	+	12.2296i	−0.160752	+	0.547471i	0.839241	+	0.543760i	$0.183000\pi$
$499$	−3.59093	+	12.2296i	−0.160752	+	0.547471i	−0.999993	+	0.00371164i	$0.998819\pi$
$500$	12.7542	−	18.2068i	0.570386	−	0.814234i
$501$	−11.9062	+	26.0709i	−0.531929	+	1.16476i
$502$	1.28525	−	0.962126i	0.0573635	−	0.0429418i
$503$	23.8331	−	5.18456i	1.06266	−	0.231168i	0.352938	−	0.935647i	$-0.385183\pi$
$503$	23.8331	−	5.18456i	1.06266	−	0.231168i	0.709725	+	0.704478i	$0.248819\pi$
$504$	−0.518013	−	0.597819i	−0.0230742	−	0.0266290i
$505$	−4.19425	−	4.10701i	−0.186642	−	0.182760i
$506$	0.337108	+	0.236380i	0.0149863	+	0.0105084i
$507$	8.92378	−	8.92378i	0.396319	−	0.396319i
$508$	−1.41047	+	19.7209i	−0.0625794	+	0.874974i
$509$	15.5147	−	24.1413i	0.687677	−	1.07005i	−0.305359	−	0.952237i	$-0.598777\pi$
$509$	15.5147	−	24.1413i	0.687677	−	1.07005i	0.993036	−	0.117809i	$-0.0375870\pi$
$510$	2.32601	+	0.309519i	0.102997	+	0.0137057i
$511$	−21.9101	−	10.0060i	−0.969246	−	0.442640i
$512$	−6.77092	−	5.06864i	−0.299235	−	0.224005i
$513$	−12.1843	+	6.65311i	−0.537948	+	0.293742i
$514$	−0.830224	−	1.29185i	−0.0366196	−	0.0569812i
$515$	−10.7891	−	22.9827i	−0.475426	−	1.01274i
$516$	−3.91916	−	13.3474i	−0.172531	−	0.587588i
$517$	3.62885	−	0.259540i	0.159596	−	0.0114146i
$518$	2.05770	−	0.147170i	0.0904102	−	0.00646626i
$519$	−1.89846	−	6.46556i	−0.0833331	−	0.283807i
$520$	2.24755	+	0.811493i	0.0985615	+	0.0355863i
$521$	13.3721	+	20.8074i	0.585842	+	0.911588i	0.999999	+	0.00138259i	$0.000440093\pi$
$521$	13.3721	+	20.8074i	0.585842	+	0.911588i	−0.414157	+	0.910205i	$0.635924\pi$
$522$	−0.124817	+	0.0681552i	−0.00546309	+	0.00298307i
$523$	8.59201	+	6.43190i	0.375702	+	0.281247i	0.770396	−	0.637565i	$-0.220058\pi$
$523$	8.59201	+	6.43190i	0.375702	+	0.281247i	−0.394694	+	0.918813i	$0.629149\pi$
$524$	21.7564	+	9.93583i	0.950434	+	0.434049i
$525$	−5.49382	+	44.8882i	−0.239770	+	1.95908i
$526$	1.00803	−	1.56852i	0.0439521	−	0.0683908i
$527$	0.112210	−	1.56890i	0.00488793	−	0.0683422i
$528$	4.04705	−	4.04705i	0.176125	−	0.176125i
$529$	21.6234	−	7.83768i	0.940147	−	0.340769i
$530$	0.722634	−	0.737983i	0.0313892	−	0.0320559i
$531$	1.61858	+	1.86794i	0.0702403	+	0.0810616i
$532$	27.5283	−	5.98841i	1.19350	−	0.259631i
$533$	−8.93187	+	6.68631i	−0.386882	+	0.289616i
$534$	−0.528054	+	1.15628i	−0.0228511	+	0.0500370i
$535$	−21.8111	+	3.37026i	−0.942977	+	0.145709i
$536$	0.937957	−	3.19439i	0.0405136	−	0.137977i
$537$	−4.28259	+	19.6867i	−0.184807	+	0.849546i
$538$	0.196481	−	0.526786i	0.00847090	−	0.0227114i
$539$	13.1347	−	3.85668i	0.565750	−	0.166119i
$540$	16.3615	+	13.8790i	0.704085	+	0.597256i
$541$	−0.956634	+	1.10401i	−0.0411289	+	0.0474653i	−0.775941	−	0.630805i	$-0.782725\pi$
$541$	−0.956634	+	1.10401i	−0.0411289	+	0.0474653i	0.734812	+	0.678270i	$0.237270\pi$
$542$	−0.0869177	+	0.159178i	−0.00373344	+	0.00683728i
$543$	−5.09365	−	1.89983i	−0.218589	−	0.0815296i
$544$	−5.72402	+	3.67860i	−0.245415	+	0.157719i
$545$	19.4774	+	34.7958i	0.834320	+	1.49049i
$546$	−2.39880	+	0.344895i	−0.102659	+	0.0147602i
$547$	10.7508	+	28.8241i	0.459673	+	1.23243i	0.935636	+	0.352966i	$0.114827\pi$
$547$	10.7508	+	28.8241i	0.459673	+	1.23243i	−0.475963	+	0.879465i	$0.657900\pi$
$548$	13.8874	+	18.5513i	0.593238	+	0.792473i
$549$	−3.05898	−	1.96589i	−0.130554	−	0.0839021i
$550$	0.428708	+	0.0216181i	0.0182802	+	0.000921799i
$551$		−	10.1595i		−	0.432810i
$552$	0.657703	+	3.74459i	0.0279937	+	0.159380i
$553$	49.3710	+	49.3710i	2.09947	+	2.09947i
$554$	1.83202	−	1.58746i	0.0778353	−	0.0674446i
$555$	15.4884	−	3.54015i	0.657447	−	0.150271i
$556$	−2.91177	+	20.2518i	−0.123486	+	0.858867i
$557$	−31.2219	+	11.6452i	−1.32292	+	0.493422i	−0.908963	−	0.416876i	$-0.863125\pi$
$557$	−31.2219	+	11.6452i	−1.32292	+	0.493422i	−0.413953	+	0.910298i	$0.635852\pi$
$558$	0.00718960	−	0.00960418i	0.000304360	−	0.000406577i
$559$	−9.04928	−	2.65711i	−0.382744	−	0.112384i
$560$	−23.7812	−	36.1631i	−1.00494	−	1.52817i
$561$	−3.19409	−	6.99407i	−0.134854	−	0.295290i
$562$	0.206055	+	0.112515i	0.00869192	+	0.00474615i
$563$	1.39146	+	19.4551i	0.0586429	+	0.819935i	0.938627	+	0.344933i	$0.112098\pi$
$563$	1.39146	+	19.4551i	0.0586429	+	0.819935i	−0.879985	+	0.475002i	$0.842447\pi$
$564$	12.6573	+	10.9676i	0.532970	+	0.461821i
$565$	−34.9375	+	10.6586i	−1.46983	+	0.448411i
$566$	−2.45774	+	1.12241i	−0.103306	+	0.0471785i
$567$	−48.0212	−	10.4464i	−2.01670	−	0.438707i
$568$	−3.20567	−	5.87074i	−0.134507	−	0.246331i
$569$	3.68129	+	25.6039i	0.154328	+	1.07337i	0.908857	+	0.417107i	$0.136956\pi$
$569$	3.68129	+	25.6039i	0.154328	+	1.07337i	−0.754530	+	0.656266i	$0.772135\pi$
$570$	−1.19322	+	0.459386i	−0.0499783	+	0.0192416i
$571$	−12.1361	−	1.74491i	−0.507881	−	0.0730223i	−0.116389	−	0.993204i	$-0.537132\pi$
$571$	−12.1361	−	1.74491i	−0.507881	−	0.0730223i	−0.391492	+	0.920181i	$0.628041\pi$
$572$	−0.829744	−	3.81427i	−0.0346933	−	0.159483i
$573$	−37.0400	−	2.64916i	−1.54737	−	0.110670i
$574$	−2.40311			−0.100304
$575$	14.7383	−	18.9152i	0.614628	−	0.788817i
$576$	2.87196			0.119665
$577$	40.1338	+	2.87042i	1.67079	+	0.119497i	0.874374	−	0.485252i	$-0.161272\pi$
$577$	40.1338	+	2.87042i	1.67079	+	0.119497i	0.796416	+	0.604749i	$0.206727\pi$
$578$	0.250160	+	1.14997i	0.0104053	+	0.0478323i
$579$	−26.6454	−	3.83102i	−1.10734	−	0.159212i
$580$	−14.6530	+	5.64140i	−0.608435	+	0.234246i
$581$	−3.15649	−	21.9539i	−0.130953	−	0.910799i
$582$	−0.370908	−	0.679268i	−0.0153746	−	0.0281566i
$583$	−3.30710	−	0.719415i	−0.136966	−	0.0297951i
$584$	−1.92040	+	0.877019i	−0.0794669	+	0.0362913i
$585$	−1.96948	+	0.600842i	−0.0814280	+	0.0248417i
$586$	−0.124910	−	0.108235i	−0.00515998	−	0.00447114i
$587$	1.31646	+	18.4064i	0.0543359	+	0.759715i	0.949458	+	0.313894i	$0.101634\pi$
$587$	1.31646	+	18.4064i	0.0543359	+	0.759715i	−0.895122	+	0.445821i	$0.852912\pi$
$588$	55.3096	+	30.2013i	2.28093	+	1.24548i
$589$	0.356036	+	0.779610i	0.0146702	+	0.0321233i
$590$	−0.883597	−	1.34365i	−0.0363771	−	0.0553171i
$591$	−15.1981	−	4.46257i	−0.625167	−	0.183566i
$592$	−9.11252	+	12.1729i	−0.374522	+	0.500303i
$593$	−24.0905	+	8.98529i	−0.989278	+	0.368982i	−0.791436	−	0.611252i	$-0.790666\pi$
$593$	−24.0905	+	8.98529i	−0.989278	+	0.368982i	−0.197842	+	0.980234i	$0.563393\pi$
$594$	−0.0589605	+	0.410079i	−0.00241918	+	0.0168258i
$595$	−56.6837	+	12.9561i	−2.32381	+	0.531147i
$596$	13.4829	−	11.6830i	0.552280	−	0.478554i
$597$	−7.91261	−	7.91261i	−0.323841	−	0.323841i
$598$	1.18492	+	0.497251i	0.0484548	+	0.0203341i
$599$		−	27.1547i		−	1.10951i	−0.832013	−	0.554756i	$-0.812812\pi$
$599$		−	27.1547i		−	1.10951i	0.832013	−	0.554756i	$-0.187188\pi$
$600$	2.65810	+	2.94041i	0.108516	+	0.120042i
$601$	−12.7595	−	8.20004i	−0.520471	−	0.334487i	0.253887	−	0.967234i	$-0.418291\pi$
$601$	−12.7595	−	8.20004i	−0.520471	−	0.334487i	−0.774358	+	0.632747i	$0.781927\pi$
$602$	−1.21735	−	1.62619i	−0.0496155	−	0.0662786i
$603$	1.00255	+	2.68794i	0.0408270	+	0.109461i
$604$	9.27794	−	1.33397i	0.377514	−	0.0542783i
$605$	11.3271	+	20.2356i	0.460514	+	0.822696i
$606$	0.438983	−	0.282117i	0.0178325	−	0.0114602i
$607$	−20.2793	−	7.56379i	−0.823111	−	0.307005i	−0.0976093	−	0.995225i	$-0.531120\pi$
$607$	−20.2793	−	7.56379i	−0.823111	−	0.307005i	−0.725502	+	0.688220i	$0.758392\pi$
$608$	1.77683	−	3.25401i	0.0720598	−	0.131968i
$609$	20.9179	−	24.1405i	0.847634	−	0.978222i
$610$	1.80419	+	1.53044i	0.0730495	+	0.0619658i
$611$	10.8949	−	3.19903i	0.440760	−	0.129419i
$612$	1.36464	−	3.65874i	0.0551623	−	0.147896i
$613$	−0.539989	+	2.48229i	−0.0218100	+	0.100259i	−0.986765	−	0.162156i	$-0.948155\pi$
$613$	−0.539989	+	2.48229i	−0.0218100	+	0.100259i	0.964955	+	0.262415i	$0.0845189\pi$
$614$	0.189529	−	0.645476i	0.00764876	−	0.0260493i
$615$	−18.2905	+	2.82625i	−0.737543	+	0.113965i
$616$	0.700579	−	1.53405i	0.0282271	−	0.0618088i
$617$	−6.03199	+	4.51549i	−0.242839	+	0.181787i	−0.713764	−	0.700386i	$-0.753011\pi$
$617$	−6.03199	+	4.51549i	−0.242839	+	0.181787i	0.470925	+	0.882173i	$0.343920\pi$
$618$	2.20534	−	0.479742i	0.0887117	−	0.0192981i
$619$	4.64039	+	5.35530i	0.186513	+	0.215248i	0.841304	−	0.540563i	$-0.181789\pi$
$619$	4.64039	+	5.35530i	0.186513	+	0.215248i	−0.654791	+	0.755810i	$0.727243\pi$
$620$	0.926729	−	0.946413i	0.0372183	−	0.0380089i
$621$	16.8655	+	15.8488i	0.676789	+	0.635991i
$622$	−0.315548	+	0.315548i	−0.0126523	+	0.0126523i
$623$	2.24708	−	31.4182i	0.0900272	−	1.25874i
$624$	9.65754	−	15.0274i	0.386611	−	0.601578i
$625$	2.51492	−	24.8732i	0.100597	−	0.994927i
$626$	−0.502483	−	0.229476i	−0.0200832	−	0.00917171i
$627$	3.35396	+	2.51074i	0.133944	+	0.100269i
$628$	−2.31645	+	1.26488i	−0.0924363	+	0.0504740i
$629$	11.0441	+	17.1850i	0.440357	+	0.685209i
$630$	−0.417140	−	0.150611i	−0.0166193	−	0.00600050i
$631$	2.60088	+	8.85780i	0.103540	+	0.352623i	0.994925	−	0.100624i	$-0.0320838\pi$
$631$	2.60088	+	8.85780i	0.103540	+	0.352623i	−0.891385	+	0.453247i	$0.850266\pi$
$632$	6.10417	−	0.436579i	0.242811	−	0.0173662i
$633$	28.7720	−	2.05781i	1.14358	−	0.0817907i
$634$	0.954321	+	3.25012i	0.0379009	+	0.129079i
$635$	9.44888	+	20.1277i	0.374967	+	0.798744i
$636$	−8.42332	−	13.1069i	−0.334007	−	0.519724i
$637$	37.4988	−	20.4759i	1.48576	−	0.811284i
$638$	−0.242719	−	0.181697i	−0.00960935	−	0.00719347i
$639$	5.24301	+	2.39440i	0.207410	+	0.0947211i
$640$	−7.56565	−	1.00675i	−0.299059	−	0.0397954i
$641$	−4.64508	+	7.22789i	−0.183470	+	0.285485i	−0.920790	−	0.390059i	$-0.872455\pi$
$641$	−4.64508	+	7.22789i	−0.183470	+	0.285485i	0.737320	+	0.675544i	$0.236091\pi$
$642$	0.139958	−	1.95687i	0.00552370	−	0.0772314i
$643$	−12.0118	+	12.0118i	−0.473699	+	0.473699i	−0.903109	−	0.429410i	$-0.858721\pi$
$643$	−12.0118	+	12.0118i	−0.473699	+	0.473699i	0.429410	+	0.903109i	$0.358721\pi$
$644$	−23.7782	−	40.5024i	−0.936994	−	1.59602i
$645$	−11.1780	−	10.9455i	−0.440133	−	0.430979i
$646$	−1.07656	−	1.24241i	−0.0423566	−	0.0488822i
$647$	−16.7084	+	3.63470i	−0.656876	+	0.142895i	−0.528636	−	0.848848i	$-0.677296\pi$
$647$	−16.7084	+	3.63470i	−0.656876	+	0.142895i	−0.128240	+	0.991743i	$0.540933\pi$
$648$	−3.44830	+	2.58137i	−0.135462	+	0.101406i
$649$	−2.18902	+	4.79328i	−0.0859265	+	0.188153i
$650$	1.32179	−	0.218489i	0.0518450	−	0.00856983i
$651$	−0.759178	+	2.58552i	−0.0297545	+	0.101335i
$652$	−0.943210	+	4.33586i	−0.0369389	+	0.169806i
$653$	3.83932	−	10.2936i	0.150244	−	0.402820i	−0.839924	−	0.542705i	$-0.817400\pi$
$653$	3.83932	−	10.2936i	0.150244	−	0.402820i	0.990168	+	0.139884i	$0.0446731\pi$
$654$	−3.40114	+	0.998664i	−0.132995	+	0.0390508i
$655$	26.8084	−	2.20074i	1.04749	−	0.0859901i
$656$	11.5996	−	13.3866i	0.452888	−	0.522661i
$657$	0.871859	−	1.59669i	0.0340144	−	0.0622928i
$658$	2.29146	+	0.854670i	0.0893304	+	0.0333185i
$659$	−28.3720	+	18.2336i	−1.10522	+	0.710280i	−0.960246	−	0.279156i	$-0.909945\pi$
$659$	−28.3720	+	18.2336i	−1.10522	+	0.710280i	−0.144972	+	0.989436i	$0.546309\pi$
$660$	1.75884	−	6.23158i	0.0684629	−	0.242564i
$661$	16.6437	−	2.39301i	0.647366	−	0.0930771i	0.189192	−	0.981940i	$-0.439413\pi$
$661$	16.6437	−	2.39301i	0.647366	−	0.0930771i	0.458173	+	0.888863i	$0.348504\pi$
$662$	−0.741477	−	1.98798i	−0.0288183	−	0.0772649i
$663$	−14.3813	−	19.2111i	−0.558522	−	0.746098i
$664$	−1.63542	−	1.05102i	−0.0634665	−	0.0407875i
$665$	23.7251	−	20.9984i	0.920018	−	0.814283i
$666$			0.155810i			0.00603752i
$667$	−16.0951	+	5.27426i	−0.623203	+	0.204220i
$668$	−21.9437	−	21.9437i	−0.849027	−	0.849027i
$669$	−11.6809	+	10.1216i	−0.451612	+	0.391324i
$670$	−0.415912	−	1.81965i	−0.0160681	−	0.0702990i
$671$	1.10327	−	7.67343i	0.0425914	−	0.296230i
$672$	10.9218	−	4.07363i	0.421319	−	0.157144i
$673$	−0.958077	+	1.27984i	−0.0369311	+	0.0493342i	−0.818627	−	0.574326i	$-0.805264\pi$
$673$	−0.958077	+	1.27984i	−0.0369311	+	0.0493342i	0.781696	+	0.623660i	$0.214355\pi$
$674$	1.41604	+	0.415786i	0.0545438	+	0.0160155i
$675$	23.6801	+	4.63237i	0.911448	+	0.178300i
$676$	5.67649	+	12.4298i	0.218327	+	0.478069i
$677$	−0.0810392	−	0.0442508i	−0.00311459	−	0.00170070i	0.477691	−	0.878528i	$-0.341474\pi$
$677$	−0.0810392	−	0.0442508i	−0.00311459	−	0.00170070i	−0.480806	+	0.876827i	$0.659656\pi$
$678$	−0.231639	−	3.23874i	−0.00889605	−	0.124383i
$679$	14.4936	+	12.5588i	0.556214	+	0.481962i
$680$	−2.39531	+	4.49843i	−0.0918561	+	0.172507i
$681$	−9.33299	+	4.26223i	−0.357641	+	0.163329i
$682$	0.0249930	+	0.00543690i	0.000957033	+	0.000208190i
$683$	−16.0729	−	29.4354i	−0.615013	−	1.12631i	−0.980690	−	0.195571i	$-0.937344\pi$
$683$	−16.0729	−	29.4354i	−0.615013	−	1.12631i	0.365676	−	0.930742i	$-0.380838\pi$
$684$	0.302814	+	2.10612i	0.0115784	+	0.0805293i
$685$	23.8188	+	10.5766i	0.910068	+	0.404111i
$686$	5.41454	+	0.778493i	0.206728	+	0.0297230i
$687$	6.99848	+	32.1715i	0.267009	+	1.22742i
$688$	14.9348	+	1.06816i	0.569385	+	0.0407232i
$689$	−10.5631			−0.402422
$690$	1.34723	+	1.65185i	0.0512881	+	0.0628848i
$691$	27.8807			1.06063			0.530315	−	0.847801i	$-0.322074\pi$
$691$	27.8807			1.06063			0.530315	+	0.847801i	$0.322074\pi$
$692$	7.27764	+	0.520507i	0.276654	+	0.0197867i
$693$	0.308905	+	1.42001i	0.0117343	+	0.0539418i
$694$	2.58358	+	0.371463i	0.0980714	+	0.0141005i
$695$	8.26721	+	21.4734i	0.313593	+	0.814531i
$696$	−0.398443	−	2.77123i	−0.0151030	−	0.105043i
$697$	−11.4042	−	20.8853i	−0.431966	−	0.791087i
$698$	1.75895	+	0.382636i	0.0665772	+	0.0144830i
$699$	32.6126	−	14.8937i	1.23352	−	0.563331i
$700$	−43.4600	−	22.5586i	−1.64264	−	0.852634i
$701$	3.17607	+	2.75208i	0.119958	+	0.103945i	0.712774	−	0.701393i	$-0.247438\pi$
$701$	3.17607	+	2.75208i	0.119958	+	0.103945i	−0.592816	+	0.805338i	$0.701984\pi$
$702$	0.0922451	+	1.28976i	0.00348157	+	0.0486787i
$703$	−9.76937	−	5.33448i	−0.368459	−	0.201194i
$704$	2.54357	+	5.56964i	0.0958643	+	0.209914i
$705$	18.4458	+	3.81010i	0.694711	+	0.143497i
$706$	0.344975	+	0.101294i	0.0129833	+	0.00381224i
$707$	−7.74894	+	10.3514i	−0.291429	+	0.389303i
$708$	−22.7285	+	8.47730i	−0.854190	+	0.318597i
$709$	3.48761	−	24.2569i	0.130980	−	0.910985i	−0.813301	−	0.581844i	$-0.802332\pi$
$709$	3.48761	−	24.2569i	0.130980	−	0.910985i	0.944281	−	0.329142i	$-0.106759\pi$
$710$	−3.17601	−	1.99426i	−0.119194	−	0.0748431i
$711$	−3.98539	+	3.45336i	−0.149464	+	0.129511i
$712$	−1.95219	−	1.95219i	−0.0731615	−	0.0731615i
$713$	1.05025	−	0.968775i	0.0393322	−	0.0362809i
$714$		−	5.16873i		−	0.193435i
$715$	−2.90950	−	3.28730i	−0.108809	−	0.122938i
$716$	−18.3516	−	11.7939i	−0.685833	−	0.440758i
$717$	6.29563	+	8.40997i	0.235115	+	0.314076i
$718$	−1.16541	−	3.12457i	−0.0434925	−	0.116608i
$719$	−22.1084	+	3.17870i	−0.824503	+	0.118546i	−0.541635	−	0.840613i	$-0.682195\pi$
$719$	−22.1084	+	3.17870i	−0.824503	+	0.118546i	−0.282867	+	0.959159i	$0.591286\pi$
$720$	2.85249	−	1.59671i	0.106306	−	0.0595060i
$721$	−47.0474	+	30.2356i	−1.75214	+	1.12603i
$722$	−1.08769	−	0.405687i	−0.0404796	−	0.0150981i
$723$	13.0021	−	23.8116i	0.483553	−	0.885562i
$724$	3.85474	−	4.44861i	0.143260	−	0.165331i
$725$	−11.2807	+	13.5853i	−0.418955	+	0.504545i
$726$	−1.97794	+	0.580776i	−0.0734083	+	0.0215546i
$727$	3.98054	−	10.6722i	0.147630	−	0.395811i	−0.841995	−	0.539485i	$-0.818619\pi$
$727$	3.98054	−	10.6722i	0.147630	−	0.395811i	0.989625	+	0.143674i	$0.0458916\pi$
$728$	1.11885	−	5.14326i	0.0414673	−	0.190622i
$729$	−6.44409	+	21.9466i	−0.238670	+	0.812835i
$730$	−0.699343	+	0.954968i	−0.0258839	+	0.0353450i
$731$	8.35605	−	18.2972i	0.309060	−	0.676747i
$732$	28.5696	−	21.3869i	1.05596	−	0.790484i
$733$	−36.8954	+	8.02610i	−1.36276	+	0.296451i	−0.833740	−	0.552157i	$-0.813805\pi$
$733$	−36.8954	+	8.02610i	−1.36276	+	0.296451i	−0.529022	+	0.848608i	$0.677441\pi$
$734$	1.96862	+	2.27190i	0.0726629	+	0.0838575i
$735$	70.8676	−	0.744715i	2.61399	−	0.0274692i
$736$	−6.07756	−	1.12561i	−0.224022	−	0.0414904i
$737$	−4.32485	+	4.32485i	−0.159308	+	0.159308i
$738$	0.0129482	−	0.181039i	0.000476628	−	0.00666413i
$739$	19.2459	−	29.9472i	0.707972	−	1.10163i	−0.281870	−	0.959453i	$-0.590955\pi$
$739$	19.2459	−	29.9472i	0.707972	−	1.10163i	0.989842	−	0.142173i	$-0.0454091\pi$
$740$	−2.26915	+	17.0525i	−0.0834157	+	0.626862i
$741$	11.8944	+	5.43201i	0.436953	+	0.199550i
$742$	−1.82134	−	1.36344i	−0.0668633	−	0.0500533i
$743$	−13.7642	+	7.51580i	−0.504958	+	0.275728i	−0.711470	−	0.702716i	$-0.751970\pi$
$743$	−13.7642	+	7.51580i	−0.504958	+	0.275728i	0.206512	+	0.978444i	$0.433789\pi$
$744$	0.127692	+	0.198693i	0.00468142	+	0.00728442i
$745$	6.81363	−	18.8713i	0.249632	−	0.691393i
$746$	0.218305	+	0.743477i	0.00799270	+	0.0272206i
$747$	1.67091	−	0.119506i	0.0611352	−	0.00437248i
$748$	8.30406	−	0.593918i	0.303626	−	0.0217158i
$749$	13.6962	+	46.6450i	0.500448	+	1.70437i
$750$	2.10565	+	0.710607i	0.0768875	+	0.0259477i
$751$	19.3947	+	30.1788i	0.707724	+	1.10124i	0.989885	+	0.141873i	$0.0453123\pi$
$751$	19.3947	+	30.1788i	0.707724	+	1.10124i	−0.282161	+	0.959367i	$0.591051\pi$
$752$	−15.8217	+	8.63928i	−0.576956	+	0.315042i
$753$	−21.8034	−	16.3218i	−0.794559	−	0.594800i
$754$	−0.860777	−	0.393104i	−0.0313476	−	0.0143160i
$755$	8.37204	−	6.40560i	0.304690	−	0.233124i
$756$	25.5506	−	39.7575i	0.929267	−	1.44597i
$757$	−1.02360	+	14.3117i	−0.0372032	+	0.520169i	0.944345	+	0.328956i	$0.106697\pi$
$757$	−1.02360	+	14.3117i	−0.0372032	+	0.520169i	−0.981549	+	0.191213i	$0.938758\pi$
$758$	−0.974879	+	0.974879i	−0.0354092	+	0.0354092i
$759$	2.23642	−	6.61690i	0.0811767	−	0.240178i
$760$	−0.0291805	−	2.77684i	−0.00105849	−	0.100726i
$761$	−27.4199	−	31.6442i	−0.993970	−	1.14710i	−0.989120	−	0.147114i	$-0.953002\pi$
$761$	−27.4199	−	31.6442i	−0.993970	−	1.14710i	−0.00485031	−	0.999988i	$-0.501544\pi$
$762$	−1.93139	+	0.420147i	−0.0699668	+	0.0152203i
$763$	70.3169	−	52.6386i	2.54564	−	1.90564i
$764$	16.7030	−	36.5745i	0.604295	−	1.32322i
$765$	−0.670632	−	4.34009i	−0.0242467	−	0.156916i
$766$	0.613395	−	2.08903i	0.0221629	−	0.0754798i
$767$	−3.49594	+	16.0706i	−0.126231	+	0.580275i
$768$	−9.67130	+	25.9298i	−0.348983	+	0.935660i
$769$	−47.9122	+	14.0683i	−1.72776	+	0.507316i	−0.986480	−	0.163881i	$-0.947599\pi$
$769$	−47.9122	+	14.0683i	−1.72776	+	0.507316i	−0.741279	+	0.671197i	$0.765781\pi$
$770$	−0.0773596	−	0.942357i	−0.00278785	−	0.0339602i
$771$	−17.0597	+	19.6879i	−0.614390	+	0.709044i
$772$	13.9688	−	25.5820i	0.502749	−	0.920716i
$773$	−42.2821	−	15.7704i	−1.52078	−	0.567223i	−0.556210	−	0.831042i	$-0.687745\pi$
$773$	−42.2821	−	15.7704i	−1.52078	−	0.567223i	−0.964572	+	0.263819i	$0.915018\pi$
$774$	0.129069	−	0.0829473i	0.00463927	−	0.00298148i
$775$	0.389556	−	1.43782i	0.0139933	−	0.0516480i
$776$	1.66381	−	0.239220i	0.0597273	−	0.00858749i
$777$	−12.2301	−	32.7901i	−0.438751	−	1.17634i
$778$	1.47208	+	1.96647i	0.0527767	+	0.0705015i
$779$	10.9079	+	7.01009i	0.390816	+	0.251163i
$780$	1.22980	−	20.1716i	0.0440341	−	0.722260i
$781$			12.2885i			0.439716i
$782$	−1.40939	+	2.35052i	−0.0503996	+	0.0840543i
$783$	−12.0512	−	12.0512i	−0.430676	−	0.430676i
$784$	−51.2619	+	44.4187i	−1.83078	+	1.58638i
$785$	−1.57840	+	2.51373i	−0.0563356	+	0.0897190i
$786$	−0.340288	+	2.36675i	−0.0121377	+	0.0844193i
$787$	8.45004	−	3.15170i	0.301211	−	0.112346i	−0.194314	−	0.980939i	$-0.562248\pi$
$787$	8.45004	−	3.15170i	0.301211	−	0.112346i	0.495526	+	0.868593i	$0.334975\pi$
$788$	10.2780	−	13.7298i	0.366140	−	0.489105i
$789$	−30.3488	−	8.91121i	−1.08045	−	0.317247i
$790$	2.86678	−	1.88522i	0.101995	−	0.0670732i
$791$	33.4241	+	73.1886i	1.18842	+	2.60229i
$792$	0.111793	+	0.0610438i	0.00397241	+	0.00216910i
$793$	−1.72610	−	24.1340i	−0.0612955	−	0.857023i
$794$	−1.47571	−	1.27871i	−0.0523710	−	0.0453797i
$795$	−15.4660	−	8.23530i	−0.548523	−	0.292076i
$796$	11.0213	−	5.03328i	0.390641	−	0.178400i
$797$	−19.3514	−	4.20965i	−0.685464	−	0.149113i	−0.143671	−	0.989626i	$-0.545891\pi$
$797$	−19.3514	−	4.20965i	−0.685464	−	0.149113i	−0.541793	+	0.840512i	$0.682254\pi$
$798$	1.34975	+	2.47189i	0.0477808	+	0.0875040i
$799$	3.44649	+	23.9709i	0.121928	+	0.848029i
$800$	−5.98909	+	2.37835i	−0.211746	+	0.0840873i
$801$	2.35479	+	0.338568i	0.0832024	+	0.0119627i
$802$	0.482167	+	2.21649i	0.0170259	+	0.0782668i
$803$	3.86865	+	0.276691i	0.136522	+	0.00976423i
$804$	−28.1562			−0.992993
$805$	−45.5832	−	26.6849i	−1.60660	−	0.940518i
$806$	0.0798295			0.00281187
$807$	−9.51363	−	0.680428i	−0.334896	−	0.0239522i
$808$	0.240910	+	1.10744i	0.00847518	+	0.0389598i
$809$	−35.1251	−	5.05023i	−1.23493	−	0.177557i	−0.506238	−	0.862394i	$-0.668964\pi$
$809$	−35.1251	−	5.05023i	−1.23493	−	0.177557i	−0.728696	+	0.684837i	$0.759873\pi$
$810$	−0.980096	+	2.20720i	−0.0344371	+	0.0775531i
$811$	−6.00846	−	41.7898i	−0.210986	−	1.46744i	−0.769875	−	0.638195i	$-0.779682\pi$
$811$	−6.00846	−	41.7898i	−0.210986	−	1.46744i	0.558890	−	0.829242i	$-0.311228\pi$
$812$	16.5754	+	30.3555i	0.581682	+	1.06527i
$813$	3.00637	+	0.653997i	0.105438	+	0.0229367i
$814$	−0.302165	+	0.137994i	−0.0105909	+	0.00483669i
$815$	1.45615	+	4.77308i	0.0510068	+	0.167194i
$816$	28.7927	+	24.9490i	1.00795	+	0.873390i
$817$	0.781910	+	10.9325i	0.0273556	+	0.382481i
$818$	0.694180	+	0.379051i	0.0242714	+	0.0132532i
$819$	1.88417	+	4.12575i	0.0658381	+	0.144165i
$820$	4.05367	−	19.6250i	0.141560	−	0.685336i
$821$	42.0954	+	12.3603i	1.46914	+	0.431379i	0.915820	−	0.401589i	$-0.131542\pi$
$821$	42.0954	+	12.3603i	1.46914	+	0.431379i	0.553321	+	0.832968i	$0.313360\pi$
$822$	−1.38833	+	1.85460i	−0.0484237	+	0.0646865i
$823$	39.3016	−	14.6587i	1.36997	−	0.510971i	0.446546	−	0.894761i	$-0.352654\pi$
$823$	39.3016	−	14.6587i	1.36997	−	0.510971i	0.923420	+	0.383790i	$0.125381\pi$
$824$	−0.697601	+	4.85192i	−0.0243021	+	0.169025i
$825$	−1.69708	−	7.08145i	−0.0590849	−	0.246545i
$826$	−2.67710	+	2.31972i	−0.0931482	+	0.0807134i
$827$	26.1573	+	26.1573i	0.909578	+	0.909578i	0.996238	−	0.0866596i	$-0.0276192\pi$
$827$	26.1573	+	26.1573i	0.909578	+	0.909578i	−0.0866596	+	0.996238i	$0.527619\pi$
$828$	3.17938	−	1.57311i	0.110491	−	0.0546693i
$829$		−	7.75893i		−	0.269479i	−0.990881	−	0.134739i	$-0.956980\pi$
$829$		−	7.75893i		−	0.269479i	0.990881	−	0.134739i	$-0.0430197\pi$
$830$	−1.08792	−	0.0663270i	−0.0377621	−	0.00230225i
$831$	−34.5952	−	22.2330i	−1.20010	−	0.771255i
$832$	11.4523	+	15.2985i	0.397038	+	0.530380i
$833$	31.8442	+	85.3777i	1.10334	+	2.95816i
$834$	−2.02459	+	0.291092i	−0.0701059	+	0.0100797i
$835$	−33.5882	−	9.48018i	−1.16237	−	0.328075i
$836$	−3.81623	+	2.45254i	−0.131987	+	0.0848230i
$837$	1.34710	+	0.502444i	0.0465627	+	0.0173670i
$838$	−1.16061	+	2.12550i	−0.0400925	+	0.0734240i
$839$	−30.0770	+	34.7107i	−1.03837	+	1.19835i	−0.0585894	+	0.998282i	$0.518660\pi$
$839$	−30.0770	+	34.7107i	−1.03837	+	1.19835i	−0.979783	+	0.200063i	$0.935885\pi$
$840$	5.64801	−	6.65825i	0.194875	−	0.229731i
$841$	−15.8580	+	4.65632i	−0.546826	+	0.160563i
$842$	−1.24916	+	3.34913i	−0.0430489	+	0.115419i
$843$	0.846597	−	3.89174i	0.0291583	−	0.134039i
$844$	−8.79931	+	29.9677i	−0.302885	+	1.03153i
$845$	12.3985	+	9.07965i	0.426520	+	0.312349i
$846$	−0.0767333	+	0.168023i	−0.00263815	+	0.00577673i
$847$	40.8930	−	30.6121i	1.40510	−	1.05185i
$848$	16.3865	−	3.56467i	0.562715	−	0.122411i
$849$	30.0162	+	34.6405i	1.03015	+	1.18886i
$850$	0.0600465	+	2.85672i	0.00205958	+	0.0979847i
$851$	−3.37935	+	18.2464i	−0.115843	+	0.625477i
$852$	−40.0010	+	40.0010i	−1.37041	+	1.37041i
$853$	−2.62080	+	36.6436i	−0.0897345	+	1.25465i	0.730615	+	0.682790i	$0.239234\pi$
$853$	−2.62080	+	36.6436i	−0.0897345	+	1.25465i	−0.820349	+	0.571863i	$0.806221\pi$
$854$	2.81748	−	4.38409i	0.0964123	−	0.150020i
$855$	1.45409	+	1.90047i	0.0497287	+	0.0649948i
$856$	3.87594	+	1.77008i	0.132477	+	0.0605001i
$857$	44.2949	+	33.1587i	1.51308	+	1.13268i	0.952482	+	0.304596i	$0.0985213\pi$
$857$	44.2949	+	33.1587i	1.51308	+	1.13268i	0.560603	+	0.828085i	$0.310570\pi$
$858$	0.342501	−	0.187020i	0.0116928	−	0.00638474i
$859$	−7.98822	−	12.4299i	−0.272555	−	0.424103i	0.677812	−	0.735235i	$-0.262928\pi$
$859$	−7.98822	−	12.4299i	−0.272555	−	0.424103i	−0.950367	+	0.311132i	$0.899292\pi$
$860$	15.3338	−	7.19838i	0.522878	−	0.245463i
$861$	11.4854	+	39.1158i	0.391422	+	1.33306i
$862$	0.486491	−	0.0347945i	0.0165699	−	0.00118511i
$863$	36.9504	−	2.64275i	1.25781	−	0.0899602i	0.573532	−	0.819183i	$-0.305573\pi$
$863$	36.9504	−	2.64275i	1.25781	−	0.0899602i	0.684276	+	0.729223i	$0.260118\pi$
$864$	−1.75224	−	5.96759i	−0.0596125	−	0.203021i
$865$	7.42776	−	3.48693i	0.252551	−	0.118559i
$866$	0.667441	+	1.03856i	0.0226806	+	0.0352916i
$867$	17.5225	−	9.56803i	0.595097	−	0.324947i
$868$	−2.33574	−	1.74851i	−0.0792801	−	0.0593484i
$869$	−10.2268	−	4.67044i	−0.346921	−	0.158434i
$870$	−0.953836	−	1.24665i	−0.0323381	−	0.0422655i
$871$	−10.3205	+	16.0590i	−0.349696	+	0.544137i
$872$	0.549227	−	7.67920i	0.0185992	−	0.260051i
$873$	−1.02421	+	1.02421i	−0.0346643	+	0.0346643i
$874$	0.0602145	−	1.49215i	0.00203679	−	0.0504729i
$875$	−55.0409	+	1.73571i	−1.86072	+	0.0586776i
$876$	11.6924	+	13.4938i	0.395050	+	0.455912i
$877$	−11.7842	+	2.56350i	−0.397925	+	0.0865634i	−0.407075	−	0.913395i	$-0.633451\pi$
$877$	−11.7842	+	2.56350i	−0.397925	+	0.0865634i	0.00914951	+	0.999958i	$0.497088\pi$
$878$	−0.437395	+	0.327430i	−0.0147614	+	0.0110502i
$879$	−1.16476	+	2.55047i	−0.0392864	+	0.0860253i
$880$	5.62285	+	4.11773i	0.189546	+	0.138809i
$881$	7.53089	−	25.6479i	0.253722	−	0.864099i	−0.729854	−	0.683603i	$-0.760412\pi$
$881$	7.53089	−	25.6479i	0.253722	−	0.864099i	0.983576	−	0.180495i	$-0.0577700\pi$
$882$	−0.147739	+	0.679145i	−0.00497463	+	0.0228680i
$883$	−9.99980	+	26.8105i	−0.336520	+	0.902245i	0.652936	+	0.757413i	$0.273537\pi$
$883$	−9.99980	+	26.8105i	−0.336520	+	0.902245i	−0.989456	+	0.144832i	$0.953736\pi$
$884$	24.9313	−	7.32048i	0.838529	−	0.246214i
$885$	−17.6477	+	20.8043i	−0.593220	+	0.699328i
$886$	0.524525	−	0.605334i	0.0176217	−	0.0203366i
$887$	13.5556	−	24.8252i	0.455152	−	0.833549i	−0.544835	−	0.838543i	$-0.683408\pi$
$887$	13.5556	−	24.8252i	0.455152	−	0.833549i	0.999988	+	0.00499390i	$0.00158962\pi$
$888$	−2.87403	−	1.07196i	−0.0964460	−	0.0359725i
$889$	41.2031	−	26.4796i	1.38191	−	0.888098i
$890$	−1.48968	−	0.420457i	−0.0499341	−	0.0140938i
$891$	7.83284	−	1.12619i	0.262410	−	0.0377288i
$892$	−5.84840	−	15.6802i	−0.195819	−	0.525010i
$893$	−7.90797	−	10.5638i	−0.264630	−	0.353504i
$894$	1.50040	+	0.964246i	0.0501808	+	0.0322492i
$895$	−24.4878	−	1.49295i	−0.818536	−	0.0499037i
$896$			16.8120i			0.561649i
$897$	2.43064	−	21.6636i	0.0811567	−	0.723326i
$898$	0.329830	+	0.329830i	0.0110066	+	0.0110066i
$899$	−0.795192	+	0.689038i	−0.0265212	+	0.0229807i
$900$	1.93362	−	3.15252i	0.0644540	−	0.105084i
$901$	3.20618	−	22.2995i	0.106813	−	0.742903i
$902$	0.362559	−	0.135228i	0.0120719	−	0.00450258i
$903$	−20.6515	+	27.5872i	−0.687239	+	0.918044i
$904$	6.76655	+	1.98684i	0.225052	+	0.0660813i
$905$	1.33912	−	6.48307i	0.0445138	−	0.215505i
$906$	0.389270	+	0.852382i	0.0129326	+	0.0283185i
$907$	4.71412	+	2.57411i	0.156530	+	0.0854718i	0.555605	−	0.831447i	$-0.312487\pi$
$907$	4.71412	+	2.57411i	0.156530	+	0.0854718i	−0.399075	+	0.916918i	$0.630669\pi$
$908$	−0.792532	−	11.0811i	−0.0263011	−	0.367738i
$909$	−0.738071	−	0.639542i	−0.0244803	−	0.0212123i
$910$	−0.861117	−	2.82263i	−0.0285458	−	0.0935692i
$911$	28.7911	−	13.1485i	0.953892	−	0.435628i	0.123214	−	0.992380i	$-0.460680\pi$
$911$	28.7911	−	13.1485i	0.953892	−	0.435628i	0.830679	+	0.556752i	$0.187953\pi$
$912$	−20.2849	−	4.41272i	−0.671701	−	0.146120i
$913$	1.71161	+	3.13457i	0.0566459	+	0.103739i
$914$	−0.216143	−	1.50331i	−0.00714938	−	0.0497250i
$915$	16.2883	−	36.6816i	0.538474	−	1.21266i
$916$	−35.2860	−	5.07335i	−1.16588	−	0.167628i
$917$	−12.5945	−	57.8962i	−0.415908	−	1.91190i
$918$	−2.75077	−	0.196739i	−0.0907889	−	0.00649335i
$919$	−30.2174			−0.996779			−0.498389	−	0.866953i	$-0.666075\pi$
$919$	−30.2174			−0.996779			−0.498389	+	0.866953i	$0.666075\pi$
$920$	−4.38401	+	1.48781i	−0.144537	+	0.0490516i
$921$	−11.4123			−0.376049
$922$	1.52893	+	0.109351i	0.0503526	+	0.00360129i
$923$	8.15256	+	37.4767i	0.268345	+	1.23356i
$924$	−14.1176	−	2.02980i	−0.464434	−	0.0667755i
$925$	7.14040	+	17.9808i	0.234775	+	0.591204i
$926$	0.231209	+	1.60809i	0.00759799	+	0.0528452i
$927$	−2.02431	−	3.70724i	−0.0664869	−	0.121762i
$928$	4.44761	+	0.967518i	0.146000	+	0.0317603i
$929$	−47.3922	+	21.6433i	−1.55489	+	0.710093i	−0.993109	−	0.117195i	$-0.962610\pi$
$929$	−47.3922	+	21.6433i	−1.55489	+	0.710093i	−0.561778	+	0.827288i	$0.689882\pi$
$930$	0.116883	+	0.0622374i	0.00383274	+	0.00204085i
$931$	−37.5246	−	32.5152i	−1.22982	−	1.06564i
$932$	2.76938	+	38.7210i	0.0907140	+	1.26835i
$933$	6.64434	+	3.62809i	0.217526	+	0.118778i
$934$	0.680687	+	1.49050i	0.0222728	+	0.0487705i
$935$	7.82285	−	5.14439i	0.255835	−	0.168240i
$936$	0.381440	+	0.112001i	0.0124678	+	0.00366087i
$937$	−16.6386	+	22.2265i	−0.543558	+	0.726108i	−0.985262	−	0.171053i	$-0.945283\pi$
$937$	−16.6386	+	22.2265i	−0.543558	+	0.726108i	0.441704	+	0.897161i	$0.354374\pi$
$938$	−3.85232	+	1.43684i	−0.125783	+	0.0469145i
$939$	−1.33365	+	9.27573i	−0.0435220	+	0.302702i
$940$	−10.8450	+	17.2715i	−0.353725	+	0.563335i
$941$	−40.6073	+	35.1864i	−1.32376	+	1.14704i	−0.345787	+	0.938313i	$0.612388\pi$
$941$	−40.6073	+	35.1864i	−1.32376	+	1.14704i	−0.977973	+	0.208731i	$0.933067\pi$
$942$	−0.186572	−	0.186572i	−0.00607883	−	0.00607883i
$943$	5.44284	−	20.9200i	0.177243	−	0.681247i
$944$		−	26.1100i		−	0.849808i
$945$	3.23436	−	53.0510i	0.105214	−	1.72575i
$946$	0.275171	+	0.176842i	0.00894659	+	0.00574963i
$947$	18.0908	+	24.1664i	0.587871	+	0.785303i	0.991568	−	0.129589i	$-0.0413659\pi$
$947$	18.0908	+	24.1664i	0.587871	+	0.785303i	−0.403697	+	0.914893i	$0.632275\pi$
$948$	−18.0870	−	48.4930i	−0.587437	−	1.57498i
$949$	11.9820	−	1.72275i	0.388952	−	0.0559228i
$950$	−0.774716	−	1.35052i	−0.0251351	−	0.0438165i
$951$	48.3415	−	31.0672i	1.56758	−	1.00742i
$952$	10.5182	+	3.92309i	0.340897	+	0.127148i
$953$	9.43451	−	17.2780i	0.305614	−	0.559690i	−0.679063	−	0.734080i	$-0.737614\pi$
$953$	9.43451	−	17.2780i	0.305614	−	0.559690i	0.984677	+	0.174390i	$0.0557954\pi$
$954$	0.112528	−	0.129864i	0.00364323	−	0.00420452i
$955$	−3.69965	−	45.0673i	−0.119718	−	1.45834i
$956$	−10.9141	+	3.20466i	−0.352986	+	0.103646i
$957$	−1.79746	+	4.81918i	−0.0581037	+	0.155782i
$958$	0.0258898	−	0.119013i	0.000836460	−	0.00384514i
$959$	16.1732	−	55.0809i	0.522260	−	1.77865i
$960$	4.84080	+	31.3280i	0.156236	+	1.01111i
$961$	−12.8410	+	28.1179i	−0.414226	+	0.907027i
$962$	−0.829978	+	0.621314i	−0.0267596	+	0.0200320i
$963$	−3.58780	+	0.780479i	−0.115615	+	0.0251506i
$964$	19.2369	+	22.2006i	0.619579	+	0.715032i
$965$	−0.344448	−	32.7779i	−0.0110882	−	1.05516i
$966$	3.21534	−	3.42160i	0.103452	−	0.110088i
$967$	16.8032	−	16.8032i	0.540355	−	0.540355i	−0.383278	−	0.923633i	$-0.625205\pi$
$967$	16.8032	−	16.8032i	0.540355	−	0.540355i	0.923633	+	0.383278i	$0.125205\pi$
$968$	0.319405	−	4.46587i	0.0102661	−	0.143538i
$969$	−15.0777	+	23.4613i	−0.484364	+	0.753685i
$970$	0.748473	−	0.572670i	0.0240320	−	0.0183873i
$971$	−34.9478	−	15.9601i	−1.12153	−	0.512185i	−0.233677	−	0.972314i	$-0.575076\pi$
$971$	−34.9478	−	15.9601i	−1.12153	−	0.512185i	−0.887852	+	0.460129i	$0.847803\pi$
$972$	6.11944	+	4.58095i	0.196281	+	0.146934i
$973$	44.4846	−	24.2904i	1.42611	−	0.778716i
$974$	1.61015	+	2.50545i	0.0515926	+	0.0802797i
$975$	−9.87375	−	20.4708i	−0.316213	−	0.655589i
$976$	10.8221	+	36.8565i	0.346405	+	1.17975i
$977$	49.3040	−	3.52629i	1.57737	−	0.112816i	0.745013	−	0.667049i	$-0.232443\pi$
$977$	49.3040	−	3.52629i	1.57737	−	0.112816i	0.832361	+	0.554233i	$0.186988\pi$
$978$	−0.442468	+	0.0316460i	−0.0141486	+	0.00101193i
$979$	1.42894	+	4.86654i	0.0456692	+	0.155535i
$980$	−26.0599	+	72.1767i	−0.832453	+	2.30560i
$981$	3.58666	+	5.58096i	0.114513	+	0.178186i
$982$	−2.47933	+	1.35382i	−0.0791186	+	0.0432020i
$983$	9.35296	+	7.00154i	0.298313	+	0.223314i	0.737940	−	0.674866i	$-0.235799\pi$
$983$	9.35296	+	7.00154i	0.298313	+	0.223314i	−0.439627	+	0.898180i	$0.644889\pi$
$984$	3.25030	+	1.48436i	0.103616	+	0.0473198i
$985$	2.54421	−	19.1195i	0.0810653	−	0.609199i
$986$	1.09114	−	1.69785i	0.0347490	−	0.0540705i
$987$	2.95979	−	41.3832i	0.0942110	−	1.31724i
$988$	−10.0115	+	10.0115i	−0.318507	+	0.318507i
$989$	16.9138	−	6.91430i	0.537827	−	0.219862i
$990$	0.0714095		0.000750409i	0.00226954		2.38496e-5i
$991$	8.60417	+	9.92974i	0.273320	+	0.315429i	0.875770	−	0.482728i	$-0.160354\pi$
$991$	8.60417	+	9.92974i	0.273320	+	0.315429i	−0.602450	+	0.798157i	$0.705809\pi$
$992$	−0.375202	+	0.0816202i	−0.0119127	+	0.00259144i
$993$	−28.8147	+	21.5704i	−0.914408	+	0.684517i
$994$	−3.43162	+	7.51420i	−0.108844	+	0.238336i
$995$	8.05081	−	10.9936i	0.255228	−	0.348519i
$996$	−4.63199	+	15.7751i	−0.146770	+	0.499853i
$997$	−3.52027	+	16.1824i	−0.111488	+	0.512503i	0.887204	+	0.461377i	$0.152645\pi$
$997$	−3.52027	+	16.1824i	−0.111488	+	0.512503i	−0.998692	+	0.0511256i	$0.983719\pi$
$998$	0.482148	−	1.29269i	0.0152621	−	0.0409194i
$999$	−17.9162	+	5.26067i	−0.566844	+	0.166440i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.33.6	yes	200
5.2	odd	4	inner	115.2.l.a.102.5	yes	200
5.3	odd	4		575.2.r.b.332.6		200
5.4	even	2		575.2.r.b.493.5		200
23.7	odd	22	inner	115.2.l.a.53.5	yes	200
115.7	even	44	inner	115.2.l.a.7.6	✓	200
115.53	even	44		575.2.r.b.7.5		200
115.99	odd	22		575.2.r.b.168.6		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.6	✓	200	115.7	even	44	inner
115.2.l.a.33.6	yes	200	1.1	even	1	trivial
115.2.l.a.53.5	yes	200	23.7	odd	22	inner
115.2.l.a.102.5	yes	200	5.2	odd	4	inner
575.2.r.b.7.5		200	115.53	even	44
575.2.r.b.168.6		200	115.99	odd	22
575.2.r.b.332.6		200	5.3	odd	4
575.2.r.b.493.5		200	5.4	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.107969 - 0.00772212i) q^{2} +(0.390334 + 1.79434i) q^{3} +(-1.96805 - 0.282962i) q^{4} +(-2.08676 + 0.803398i) q^{5} +(-0.0282880 - 0.196748i) q^{6} +(2.36052 + 4.32296i) q^{7} +(0.421846 + 0.0917670i) q^{8} +(-0.338390 + 0.154538i) q^{9} +(0.231510 - 0.0706281i) q^{10} +(-0.599394 - 0.519378i) q^{11} +(-0.260466 - 3.64179i) q^{12} +(-2.17257 - 1.18632i) q^{13} +(-0.221481 - 0.484976i) q^{14} +(-2.25610 - 3.43075i) q^{15} +(3.77065 + 1.10716i) q^{16} +(3.16383 - 4.22639i) q^{17} +(0.0377291 - 0.0140722i) q^{18} +(-0.409398 + 2.84742i) q^{19} +(4.33416 - 0.990650i) q^{20} +(-6.83547 + 5.92297i) q^{21} +(0.0607055 + 0.0607055i) q^{22} +(4.72353 - 0.829644i) q^{23} +0.792754i q^{24} +(3.70910 - 3.35299i) q^{25} +(0.225410 + 0.144862i) q^{26} +(2.89199 + 3.86324i) q^{27} +(-3.42237 - 9.17573i) q^{28} +(-3.49570 + 0.502606i) q^{29} +(0.217097 + 0.387838i) q^{30} +(0.250636 - 0.161074i) q^{31} +(-1.20755 - 0.450393i) q^{32} +(0.697975 - 1.27825i) q^{33} +(-0.374233 + 0.431888i) q^{34} +(-8.39888 - 7.12454i) q^{35} +(0.709695 - 0.208385i) q^{36} +(-1.35219 + 3.62537i) q^{37} +(0.0661905 - 0.304273i) q^{38} +(1.28062 - 4.36139i) q^{39} +(-0.954015 + 0.147415i) q^{40} +(1.87241 - 4.10001i) q^{41} +(0.783758 - 0.586714i) q^{42} +(3.72300 - 0.809890i) q^{43} +(1.03267 + 1.19177i) q^{44} +(0.581983 - 0.594344i) q^{45} +(-0.516402 + 0.0531004i) q^{46} +(-3.24360 + 3.24360i) q^{47} +(-0.514810 + 7.19798i) q^{48} +(-9.33150 + 14.5201i) q^{49} +(-0.426362 + 0.333378i) q^{50} +(8.81852 + 4.02728i) q^{51} +(3.94004 + 2.94948i) q^{52} +(3.74531 - 2.04509i) q^{53} +(-0.282413 - 0.439444i) q^{54} +(1.66806 + 0.602264i) q^{55} +(0.599069 + 2.04024i) q^{56} +(-5.26904 + 0.376849i) q^{57} +(0.381310 - 0.0272718i) q^{58} +(-1.87184 - 6.37491i) q^{59} +(3.46933 + 7.39026i) q^{60} +(5.28454 + 8.22290i) q^{61} +(-0.0283048 + 0.0154556i) q^{62} +(-1.46684 - 1.09806i) q^{63} +(-7.02251 - 3.20707i) q^{64} +(5.48672 + 0.730110i) q^{65} +(-0.0852307 + 0.132622i) q^{66} +(0.550148 - 7.69208i) q^{67} +(-7.42247 + 7.42247i) q^{68} +(3.33241 + 8.15176i) q^{69} +(0.851805 + 0.834089i) q^{70} +(-10.1464 - 11.7096i) q^{71} +(-0.156930 + 0.0341380i) q^{72} +(-3.91486 + 2.93063i) q^{73} +(0.173991 - 0.380987i) q^{74} +(7.46419 + 5.34660i) q^{75} +(1.61143 - 5.48801i) q^{76} +(0.830373 - 3.81716i) q^{77} +(-0.171947 + 0.461007i) q^{78} +(13.6014 - 3.99372i) q^{79} +(-8.75792 + 0.718952i) q^{80} +(-6.53396 + 7.54059i) q^{81} +(-0.233824 + 0.428217i) q^{82} +(-4.21914 - 1.57366i) q^{83} +(15.1285 - 9.72249i) q^{84} +(-3.20668 + 11.3613i) q^{85} +(-0.408224 + 0.0586938i) q^{86} +(-2.26634 - 6.07629i) q^{87} +(-0.205190 - 0.274102i) q^{88} +(-5.37985 - 3.45742i) q^{89} +(-0.0674258 + 0.0596768i) q^{90} -12.1923i q^{91} +(-9.53087 + 0.296197i) q^{92} +(0.386853 + 0.386853i) q^{93} +(0.375256 - 0.325161i) q^{94} +(-1.43330 - 6.27079i) q^{95} +(0.336809 - 2.34255i) q^{96} +(3.64812 - 1.36068i) q^{97} +(1.11964 - 1.49567i) q^{98} +(0.283093 + 0.0831235i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23}+ \cdots - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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