LMFDB - Embedded newform 875.2.bb.a.857.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			857.9
Character	$\chi$	$=$	875.857
Dual form			875.2.bb.a.243.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0171512 - 0.000898858i) q^{2} +(-0.711812 + 0.879015i) q^{3} +(-1.98875 + 0.209026i) q^{4} +(-0.0114183 + 0.0157160i) q^{6} +(0.822022 + 2.51481i) q^{7} +(-0.0678483 + 0.0107461i) q^{8} +(0.357745 + 1.68306i) q^{9} +(-4.96090 - 1.05447i) q^{11} +(1.23188 - 1.89693i) q^{12} +(-0.286147 + 0.145799i) q^{13} +(0.0163592 + 0.0423932i) q^{14} +(3.91086 - 0.831279i) q^{16} +(1.33924 - 3.48884i) q^{17} +(0.00764859 + 0.0285449i) q^{18} +(-0.698358 + 6.64443i) q^{19} +(-2.79568 - 1.06750i) q^{21} +(-0.0860334 - 0.0136263i) q^{22} +(-0.178896 - 3.41354i) q^{23} +(0.0388492 - 0.0672888i) q^{24} +(-0.00477673 + 0.00275784i) q^{26} +(-4.75748 - 2.42406i) q^{27} +(-2.16046 - 4.82951i) q^{28} +(-1.99592 - 2.74715i) q^{29} +(0.305449 + 0.686049i) q^{31} +(0.199035 - 0.0533314i) q^{32} +(4.45813 - 3.61012i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-1.06327 - 3.27240i) q^{36} +(-2.76416 - 1.79507i) q^{37} +(-0.00600530 + 0.114588i) q^{38} +(0.0755233 - 0.355309i) q^{39} +(-7.88534 - 2.56210i) q^{41} +(-0.0489089 - 0.0157961i) q^{42} +(3.99562 - 3.99562i) q^{43} +(10.0864 + 1.06012i) q^{44} +(-0.00613657 - 0.0583856i) q^{46} +(5.87681 - 2.25590i) q^{47} +(-2.05309 + 4.02942i) q^{48} +(-5.64856 + 4.13446i) q^{49} +(2.11346 + 3.66061i) q^{51} +(0.538600 - 0.349771i) q^{52} +(-8.77763 - 7.10798i) q^{53} +(-0.0837755 - 0.0372993i) q^{54} +(-0.0827972 - 0.161792i) q^{56} +(-5.34345 - 5.34345i) q^{57} +(-0.0367018 - 0.0453229i) q^{58} +(-6.39870 - 7.10647i) q^{59} +(-2.03745 - 1.83453i) q^{61} +(0.00585548 + 0.0114920i) q^{62} +(-3.93850 + 2.28317i) q^{63} +(-7.60172 + 2.46995i) q^{64} +(0.0732173 - 0.0659252i) q^{66} +(6.09544 + 2.33982i) q^{67} +(-1.93416 + 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-3.66851 + 2.66533i) q^{71} +(-0.0423587 - 0.110348i) q^{72} +(-5.50292 - 8.47376i) q^{73} +(-0.0490223 - 0.0283030i) q^{74} -13.3601i q^{76} +(-1.42617 - 13.3425i) q^{77} +(0.000975946 - 0.00616188i) q^{78} +(-3.33735 + 7.49580i) q^{79} +(0.801517 - 0.356859i) q^{81} +(-0.137546 - 0.0368554i) q^{82} +(0.203179 + 1.28282i) q^{83} +(5.78305 + 1.53863i) q^{84} +(0.0649383 - 0.0721212i) q^{86} +(3.83550 + 0.201010i) q^{87} +(0.347920 + 0.0182337i) q^{88} +(0.663356 - 0.736732i) q^{89} +(-0.601877 - 0.599756i) q^{91} +(1.06930 + 6.75128i) q^{92} +(-0.820470 - 0.219844i) q^{93} +(0.0987668 - 0.0439738i) q^{94} +(-0.0947968 + 0.212917i) q^{96} +(1.94322 - 12.2690i) q^{97} +(-0.0931634 + 0.0759884i) q^{98} -8.72671i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.0171512		0.000898858i	0.0121278		0.000635588i	−0.0462711	−	0.998929i	$-0.514734\pi$
$2$	0.0171512		0.000898858i	0.0121278		0.000635588i	0.0583989	+	0.998293i	$0.481400\pi$
$3$	−0.711812	+	0.879015i	−0.410965	+	0.507499i	−0.940035	−	0.341079i	$-0.889208\pi$
$3$	−0.711812	+	0.879015i	−0.410965	+	0.507499i	0.529070	+	0.848578i	$0.322541\pi$
$4$	−1.98875	+	0.209026i	−0.994375	+	0.104513i
$5$		0			0
$5$		0			0
$6$	−0.0114183	+	0.0157160i	−0.00466152	+	0.00641603i
$7$	0.822022	+	2.51481i	0.310695	+	0.950510i
$7$	0.822022	+	2.51481i	0.310695	+	0.950510i
$8$	−0.0678483	+	0.0107461i	−0.0239880	+	0.00379932i
$9$	0.357745	+	1.68306i	0.119248	+	0.561019i
$10$		0			0
$11$	−4.96090	−	1.05447i	−1.49577	−	0.317935i	−0.613882	−	0.789398i	$-0.710393\pi$
$11$	−4.96090	−	1.05447i	−1.49577	−	0.317935i	−0.881886	+	0.471463i	$0.843726\pi$
$12$	1.23188	−	1.89693i	0.355613	−	0.547596i
$13$	−0.286147	+	0.145799i	−0.0793630	+	0.0404375i	−0.493222	−	0.869904i	$-0.664181\pi$
$13$	−0.286147	+	0.145799i	−0.0793630	+	0.0404375i	0.413859	+	0.910341i	$0.364181\pi$
$14$	0.0163592	+	0.0423932i	0.00437217	+	0.0113301i
$15$		0			0
$16$	3.91086	−	0.831279i	0.977715	−	0.207820i
$17$	1.33924	−	3.48884i	0.324814	−	0.846169i	−0.669802	−	0.742540i	$-0.733621\pi$
$17$	1.33924	−	3.48884i	0.324814	−	0.846169i	0.994616	−	0.103629i	$-0.0330455\pi$
$18$	0.00764859	+	0.0285449i	0.00180279	+	0.00672810i
$19$	−0.698358	+	6.64443i	−0.160214	+	1.52434i	0.558777	+	0.829318i	$0.311271\pi$
$19$	−0.698358	+	6.64443i	−0.160214	+	1.52434i	−0.718991	+	0.695019i	$0.755396\pi$
$20$		0			0
$21$	−2.79568	−	1.06750i	−0.610068	−	0.232948i
$22$	−0.0860334	−	0.0136263i	−0.0183424	−	0.00290515i
$23$	−0.178896	−	3.41354i	−0.0373024	−	0.711772i	−0.951714	−	0.306986i	$-0.900679\pi$
$23$	−0.178896	−	3.41354i	−0.0373024	−	0.711772i	0.914412	−	0.404786i	$-0.132654\pi$
$24$	0.0388492	−	0.0672888i	0.00793006	−	0.0137353i
$25$		0			0
$26$	−0.00477673	+	0.00275784i	−0.000936793	+	0.000540858i
$27$	−4.75748	−	2.42406i	−0.915577	−	0.466510i
$28$	−2.16046	−	4.82951i	−0.408288	−	0.912691i
$29$	−1.99592	−	2.74715i	−0.370633	−	0.510133i	0.582440	−	0.812874i	$-0.302098\pi$
$29$	−1.99592	−	2.74715i	−0.370633	−	0.510133i	−0.953073	+	0.302741i	$0.902098\pi$
$30$		0			0
$31$	0.305449	+	0.686049i	0.0548602	+	0.123218i	0.938896	−	0.344202i	$-0.111850\pi$
$31$	0.305449	+	0.686049i	0.0548602	+	0.123218i	−0.884036	+	0.467420i	$0.845184\pi$
$32$	0.199035	−	0.0533314i	0.0351848	−	0.00942775i
$33$	4.45813	−	3.61012i	0.776060	−	0.628441i
$34$	0.0198337	−	0.0610417i	0.00340145	−	0.0104686i
$35$		0			0
$36$	−1.06327	−	3.27240i	−0.177211	−	0.545400i
$37$	−2.76416	−	1.79507i	−0.454426	−	0.295107i	0.297058	−	0.954860i	$-0.403995\pi$
$37$	−2.76416	−	1.79507i	−0.454426	−	0.295107i	−0.751483	+	0.659752i	$0.770661\pi$
$38$	−0.00600530	+	0.114588i	−0.000974188	+	0.0185886i
$39$	0.0755233	−	0.355309i	0.0120934	−	0.0568950i
$40$		0			0
$41$	−7.88534	−	2.56210i	−1.23148	−	0.400133i	−0.380232	−	0.924891i	$-0.624156\pi$
$41$	−7.88534	−	2.56210i	−1.23148	−	0.400133i	−0.851252	+	0.524758i	$0.824156\pi$
$42$	−0.0489089	−	0.0157961i	−0.00754681	−	0.00243739i
$43$	3.99562	−	3.99562i	0.609326	−	0.609326i	−0.333444	−	0.942770i	$-0.608211\pi$
$43$	3.99562	−	3.99562i	0.609326	−	0.609326i	0.942770	+	0.333444i	$0.108211\pi$
$44$	10.0864	+	1.06012i	1.52058	+	0.159820i
$45$		0			0
$46$	−0.00613657	−	0.0583856i	−0.000904788	−	0.00860849i
$47$	5.87681	−	2.25590i	0.857221	−	0.329056i	0.110242	−	0.993905i	$-0.464837\pi$
$47$	5.87681	−	2.25590i	0.857221	−	0.329056i	0.746978	+	0.664849i	$0.231504\pi$
$48$	−2.05309	+	4.02942i	−0.296338	+	0.581596i
$49$	−5.64856	+	4.13446i	−0.806937	+	0.590638i
$50$		0			0
$51$	2.11346	+	3.66061i	0.295943	+	0.512588i
$52$	0.538600	−	0.349771i	0.0746903	−	0.0485045i
$53$	−8.77763	−	7.10798i	−1.20570	−	0.976356i	−0.205702	−	0.978615i	$-0.565948\pi$
$53$	−8.77763	−	7.10798i	−1.20570	−	0.976356i	−0.999997	+	0.00225825i	$0.999281\pi$
$54$	−0.0837755	−	0.0372993i	−0.0114004	−	0.00507579i
$55$		0			0
$56$	−0.0827972	−	0.161792i	−0.0110642	−	0.0216204i
$57$	−5.34345	−	5.34345i	−0.707757	−	0.707757i
$58$	−0.0367018	−	0.0453229i	−0.00481918	−	0.00595119i
$59$	−6.39870	−	7.10647i	−0.833039	−	0.925184i	0.165093	−	0.986278i	$-0.447208\pi$
$59$	−6.39870	−	7.10647i	−0.833039	−	0.925184i	−0.998132	+	0.0610943i	$0.980541\pi$
$60$		0			0
$61$	−2.03745	−	1.83453i	−0.260869	−	0.234887i	0.528309	−	0.849052i	$-0.322826\pi$
$61$	−2.03745	−	1.83453i	−0.260869	−	0.234887i	−0.789178	+	0.614165i	$0.789493\pi$
$62$	0.00585548	+	0.0114920i	0.000743647	+	0.00145949i
$63$	−3.93850	+	2.28317i	−0.496204	+	0.287652i
$64$	−7.60172	+	2.46995i	−0.950215	+	0.308744i
$65$		0			0
$66$	0.0732173	−	0.0659252i	0.00901243	−	0.00811483i
$67$	6.09544	+	2.33982i	0.744676	+	0.285854i	0.700971	−	0.713190i	$-0.252750\pi$
$67$	6.09544	+	2.33982i	0.744676	+	0.285854i	0.0437055	+	0.999044i	$0.486084\pi$
$68$	−1.93416	+	7.21837i	−0.234551	+	0.875357i
$69$	3.12789	+	2.27255i	0.376554	+	0.273582i
$70$		0			0
$71$	−3.66851	+	2.66533i	−0.435372	+	0.316316i	−0.783793	−	0.621022i	$-0.786718\pi$
$71$	−3.66851	+	2.66533i	−0.435372	+	0.316316i	0.348422	+	0.937338i	$0.386718\pi$
$72$	−0.0423587	−	0.110348i	−0.00499202	−	0.0130046i
$73$	−5.50292	−	8.47376i	−0.644069	−	0.991779i	−0.998394	−	0.0566564i	$-0.981956\pi$
$73$	−5.50292	−	8.47376i	−0.644069	−	0.991779i	0.354325	−	0.935122i	$-0.384711\pi$
$74$	−0.0490223	−	0.0283030i	−0.00569873	−	0.00329016i
$75$		0			0
$76$		−	13.3601i		−	1.53251i
$77$	−1.42617	−	13.3425i	−0.162528	−	1.52052i
$78$	0.000975946	−	0.00616188i	0.000110504	−	0.000697695i
$79$	−3.33735	+	7.49580i	−0.375481	+	0.843344i	0.622666	+	0.782488i	$0.286050\pi$
$79$	−3.33735	+	7.49580i	−0.375481	+	0.843344i	−0.998147	+	0.0608557i	$0.980617\pi$
$80$		0			0
$81$	0.801517	−	0.356859i	0.0890575	−	0.0396510i
$82$	−0.137546	−	0.0368554i	−0.0151894	−	0.00407000i
$83$	0.203179	+	1.28282i	0.0223018	+	0.140808i	0.996327	−	0.0856324i	$-0.0272911\pi$
$83$	0.203179	+	1.28282i	0.0223018	+	0.140808i	−0.974025	+	0.226441i	$0.927291\pi$
$84$	5.78305	+	1.53863i	0.630983	+	0.167878i
$85$		0			0
$86$	0.0649383	−	0.0721212i	0.00700247	−	0.00777703i
$87$	3.83550	+	0.201010i	0.411209	+	0.0215506i
$88$	0.347920	+	0.0182337i	0.0370884	+	0.00194372i
$89$	0.663356	−	0.736732i	0.0703156	−	0.0780934i	−0.706960	−	0.707253i	$-0.749934\pi$
$89$	0.663356	−	0.736732i	0.0703156	−	0.0780934i	0.777276	+	0.629160i	$0.216601\pi$
$90$		0			0
$91$	−0.601877	−	0.599756i	−0.0630939	−	0.0628715i
$92$	1.06930	+	6.75128i	0.111482	+	0.703870i
$93$	−0.820470	−	0.219844i	−0.0850787	−	0.0227968i
$94$	0.0987668	−	0.0439738i	0.0101870	−	0.00453555i
$95$		0			0
$96$	−0.0947968	+	0.212917i	−0.00967515	+	0.0217308i
$97$	1.94322	−	12.2690i	0.197304	−	1.24573i	−0.667879	−	0.744270i	$-0.732798\pi$
$97$	1.94322	−	12.2690i	0.197304	−	1.24573i	0.865183	−	0.501457i	$-0.167202\pi$
$98$	−0.0931634	+	0.0759884i	−0.00941093	+	0.00767599i
$99$		−	8.72671i		−	0.877067i
$100$		0			0
$101$	10.1944	+	5.88575i	1.01438	+	0.585654i	0.912472	−	0.409139i	$-0.134171\pi$
$101$	10.1944	+	5.88575i	1.01438	+	0.585654i	0.101911	+	0.994794i	$0.467504\pi$
$102$	0.0395387	+	0.0608843i	0.00391492	+	0.00602845i
$103$	5.28346	+	13.7639i	0.520595	+	1.35620i	0.901979	+	0.431780i	$0.142114\pi$
$103$	5.28346	+	13.7639i	0.520595	+	1.35620i	−0.381384	+	0.924417i	$0.624552\pi$
$104$	0.0178478	−	0.0129672i	0.00175012	−	0.00127154i
$105$		0			0
$106$	−0.156936	−	0.114021i	−0.0152430	−	0.0110747i
$107$	−2.68589	+	10.0239i	−0.259655	+	0.969046i	0.705786	+	0.708425i	$0.250594\pi$
$107$	−2.68589	+	10.0239i	−0.259655	+	0.969046i	−0.965441	+	0.260621i	$0.916073\pi$
$108$	9.96813	+	3.82641i	0.959184	+	0.368196i
$109$	6.76285	−	6.08930i	0.647763	−	0.583249i	−0.278357	−	0.960478i	$-0.589790\pi$
$109$	6.76285	−	6.08930i	0.647763	−	0.583249i	0.926120	+	0.377229i	$0.123123\pi$
$110$		0			0
$111$	3.54546	−	1.15199i	0.336520	−	0.109342i
$112$	5.30532	+	9.15175i	0.501306	+	0.864759i
$113$	3.87378	+	7.60273i	0.364415	+	0.715204i	0.998304	−	0.0582196i	$-0.0185424\pi$
$113$	3.87378	+	7.60273i	0.364415	+	0.715204i	−0.633889	+	0.773424i	$0.718542\pi$
$114$	−0.0964498	−	0.0868438i	−0.00903335	−	0.00813366i
$115$		0			0
$116$	4.54361	+	5.04619i	0.421864	+	0.468527i
$117$	−0.347756	−	0.429443i	−0.0321501	−	0.0397020i
$118$	−0.116133	−	0.116133i	−0.0106909	−	0.0106909i
$119$	9.87467	+	0.500033i	0.905210	+	0.0458379i
$120$		0			0
$121$	13.4496	+	5.98816i	1.22269	+	0.544378i
$122$	−0.0365938	−	0.0296330i	−0.00331304	−	0.00268285i
$123$	7.86501	−	5.10760i	0.709164	−	0.460536i
$124$	−0.750864	−	1.30053i	−0.0674296	−	0.116791i
$125$		0			0
$126$	−0.0654978	+	0.0426993i	−0.00583501	+	0.00380396i
$127$	−7.32616	+	14.3784i	−0.650091	+	1.27588i	0.296989	+	0.954881i	$0.404017\pi$
$127$	−7.32616	+	14.3784i	−0.650091	+	1.27588i	−0.947081	+	0.320996i	$0.895983\pi$
$128$	−0.512900	+	0.196884i	−0.0453344	+	0.0174022i
$129$	0.668078	+	6.35633i	0.0588210	+	0.559644i
$130$		0			0
$131$	−2.96375	−	0.311503i	−0.258944	−	0.0272161i	−0.0258332	−	0.999666i	$-0.508224\pi$
$131$	−2.96375	−	0.311503i	−0.258944	−	0.0272161i	−0.233111	+	0.972450i	$0.574891\pi$
$132$	−8.11149	+	8.11149i	−0.706015	+	0.706015i
$133$	−17.2836	+	3.70563i	−1.49867	+	0.321319i
$134$	0.106647	+	0.0346518i	0.00921293	+	0.00299346i
$135$		0			0
$136$	−0.0533737	+	0.251104i	−0.00457676	+	0.0215320i
$137$	−0.809052	+	15.4376i	−0.0691220	+	1.31893i	0.715352	+	0.698764i	$0.246266\pi$
$137$	−0.809052	+	15.4376i	−0.0691220	+	1.31893i	−0.784474	+	0.620162i	$0.787067\pi$
$138$	0.0556899	+	0.0361654i	0.00474064	+	0.00307861i
$139$	−5.70394	−	17.5549i	−0.483801	−	1.48899i	−0.833709	−	0.552204i	$-0.813787\pi$
$139$	−5.70394	−	17.5549i	−0.483801	−	1.48899i	0.349908	−	0.936784i	$-0.386213\pi$
$140$		0			0
$141$	−2.20022	+	6.77157i	−0.185292	+	0.570269i
$142$	−0.0605237	+	0.0490111i	−0.00507903	+	0.00411292i
$143$	1.57329	−	0.421562i	0.131565	−	0.0352528i
$144$	2.79818	+	6.28481i	0.233182	+	0.523734i
$145$		0			0
$146$	−0.101999	−	0.140389i	−0.00844147	−	0.0116187i
$147$	0.386457	−	7.90813i	0.0318745	−	0.652251i
$148$	5.87245	+	2.99216i	0.482712	+	0.245954i
$149$	−12.7732	+	7.37458i	−1.04642	+	0.604149i	−0.921644	−	0.388036i	$-0.873154\pi$
$149$	−12.7732	+	7.37458i	−1.04642	+	0.604149i	−0.124773	+	0.992185i	$0.539820\pi$
$150$		0			0
$151$	−2.80622	+	4.86051i	−0.228367	+	0.395543i	−0.957324	−	0.289016i	$-0.906672\pi$
$151$	−2.80622	+	4.86051i	−0.228367	+	0.395543i	0.728957	+	0.684559i	$0.240005\pi$
$152$	−0.0240194	−	0.458318i	−0.00194823	−	0.0371745i
$153$	6.35103	+	1.00590i	0.513450	+	0.0813225i
$154$	−0.0364537	−	0.227559i	−0.00293752	−	0.0183372i
$155$		0			0
$156$	−0.0759281	+	0.722408i	−0.00607912	+	0.0578389i
$157$	−1.35782	−	5.06744i	−0.108366	−	0.404426i	0.890340	−	0.455297i	$-0.150467\pi$
$157$	−1.35782	−	5.06744i	−0.108366	−	0.404426i	−0.998705	+	0.0508712i	$0.983800\pi$
$158$	−0.0505019	+	0.131562i	−0.00401772	+	0.0104665i
$159$	12.4960	−	2.65612i	0.991000	−	0.210644i
$160$		0			0
$161$	8.43735	−	3.25590i	0.664957	−	0.256601i
$162$	0.0134262	−	0.00684101i	0.00105487	−	0.000537481i
$163$	9.67348	−	14.8958i	0.757685	−	1.16673i	−0.223695	−	0.974659i	$-0.571812\pi$
$163$	9.67348	−	14.8958i	0.757685	−	1.16673i	0.981381	−	0.192074i	$-0.0615212\pi$
$164$	16.2175	+	3.44714i	1.26638	+	0.269177i
$165$		0			0
$166$	0.00463785	+	0.0218194i	0.000359967	+	0.00169351i
$167$	5.68050	−	0.899703i	0.439571	−	0.0696211i	0.0672731	−	0.997735i	$-0.478570\pi$
$167$	5.68050	−	0.899703i	0.439571	−	0.0696211i	0.372297	+	0.928113i	$0.378570\pi$
$168$	0.201154	+	0.0423856i	0.0155193	+	0.00327012i
$169$	−7.58059	+	10.4338i	−0.583122	+	0.802599i
$170$		0			0
$171$	−11.4328	+	1.20163i	−0.874287	+	0.0918912i
$172$	−7.11110	+	8.78147i	−0.542216	+	0.669581i
$173$	2.25614	−	0.118239i	0.171531	−	0.00898956i	0.0336229	−	0.999435i	$-0.489295\pi$
$173$	2.25614	−	0.118239i	0.171531	−	0.00898956i	0.137908	+	0.990445i	$0.455962\pi$
$174$	0.0659643			0.00500074
$175$		0			0
$176$	−20.2779			−1.52851
$177$	10.8014	−	0.566075i	0.811880	−	0.0425488i
$178$	0.0107152	−	0.0132321i	0.000803135	−	0.000991789i
$179$	−23.0769	+	2.42548i	−1.72485	+	0.181289i	−0.914480	−	0.404631i	$-0.867400\pi$
$179$	−23.0769	+	2.42548i	−1.72485	+	0.181289i	−0.810369	+	0.585920i	$0.800733\pi$
$180$		0			0
$181$	−1.07470	+	1.47920i	−0.0798820	+	0.109948i	−0.847088	−	0.531453i	$-0.821646\pi$
$181$	−1.07470	+	1.47920i	−0.0798820	+	0.109948i	0.767206	+	0.641401i	$0.221646\pi$
$182$	−0.0108620	−	0.00974556i	−0.000805147	−	0.000722389i
$183$	3.06286	−	0.485109i	0.226413	−	0.0358603i
$184$	0.0488201	+	0.229680i	0.00359906	+	0.0169323i
$185$		0			0
$186$	−0.0142697	−	0.00303311i	−0.00104630	−	0.000222399i
$187$	−10.3227	+	15.8956i	−0.754873	+	1.16240i
$188$	−11.2160	+	5.71482i	−0.818008	+	0.416796i
$189$	2.18529	−	13.9568i	0.158957	−	1.01521i
$190$		0			0
$191$	0.720510	−	0.153149i	0.0521342	−	0.0110815i	−0.181771	−	0.983341i	$-0.558183\pi$
$191$	0.720510	−	0.153149i	0.0521342	−	0.0110815i	0.233905	+	0.972259i	$0.424850\pi$
$192$	3.23987	−	8.44016i	0.233818	−	0.609116i
$193$	3.73619	+	13.9437i	0.268937	+	1.00369i	0.959796	+	0.280697i	$0.0905656\pi$
$193$	3.73619	+	13.9437i	0.268937	+	1.00369i	−0.690860	+	0.722989i	$0.742768\pi$
$194$	0.0223005	−	0.212175i	0.00160108	−	0.0152333i
$195$		0			0
$196$	10.3694	−	9.40311i	0.740669	−	0.671651i
$197$	−9.93010	−	1.57277i	−0.707490	−	0.112055i	−0.207688	−	0.978195i	$-0.566594\pi$
$197$	−9.93010	−	1.57277i	−0.707490	−	0.112055i	−0.499802	+	0.866140i	$0.666594\pi$
$198$	−0.00784407	−	0.149674i	−0.000557454	−	0.0106368i
$199$	3.19046	−	5.52604i	0.226166	−	0.391731i	−0.730503	−	0.682910i	$-0.760714\pi$
$199$	3.19046	−	5.52604i	0.226166	−	0.391731i	0.956669	+	0.291179i	$0.0940475\pi$
$200$		0			0
$201$	−6.39554	+	3.69247i	−0.451107	+	0.260447i
$202$	0.180137	+	0.0917845i	0.0126744	+	0.00645794i
$203$	5.26787	−	7.27758i	0.369732	−	0.510786i
$204$	−4.96830	−	6.83828i	−0.347851	−	0.478775i
$205$		0			0
$206$	0.102990	+	0.231319i	0.00717563	+	0.0161167i
$207$	5.68118	−	1.52227i	0.394869	−	0.105805i
$208$	−0.997882	+	0.808069i	−0.0691907	+	0.0560295i
$209$	10.4708	−	32.2260i	0.724284	−	2.22912i
$210$		0			0
$211$	8.73583	+	26.8861i	0.601399	+	1.85092i	0.519868	+	0.854246i	$0.325981\pi$
$211$	8.73583	+	26.8861i	0.601399	+	1.85092i	0.0815311	+	0.996671i	$0.474019\pi$
$212$	18.9423	+	12.3012i	1.30096	+	0.844853i
$213$	0.268427	−	5.12188i	0.0183923	−	0.350946i
$214$	−0.0370563	+	0.174336i	−0.00253312	+	0.0119174i
$215$		0			0
$216$	0.348836	+	0.113344i	0.0237353	+	0.00771206i
$217$	−1.47420	+	1.33209i	−0.100075	+	0.0904285i
$218$	0.110518	−	0.110518i	0.00748521	−	0.00748521i
$219$	11.3656	+	1.19457i	0.768017	+	0.0807218i
$220$		0			0
$221$	0.125451	+	1.19358i	0.00843873	+	0.0802891i
$222$	0.0597735	−	0.0229449i	0.00401173	−	0.00153996i
$223$	−9.61132	+	18.8633i	−0.643622	+	1.26318i	0.306670	+	0.951816i	$0.400785\pi$
$223$	−9.61132	+	18.8633i	−0.643622	+	1.26318i	−0.950291	+	0.311362i	$0.899215\pi$
$224$	0.297730	+	0.456697i	0.0198929	+	0.0305144i
$225$		0			0
$226$	0.0732739	+	0.126914i	0.00487411	+	0.00844220i
$227$	−16.7245	+	10.8610i	−1.11004	+	0.720872i	−0.963333	−	0.268308i	$-0.913536\pi$
$227$	−16.7245	+	10.8610i	−1.11004	+	0.720872i	−0.146712	+	0.989179i	$0.546869\pi$
$228$	11.7437	+	9.50987i	0.777746	+	0.629807i
$229$	−9.17427	−	4.08465i	−0.606253	−	0.269921i	0.0805667	−	0.996749i	$-0.474327\pi$
$229$	−9.17427	−	4.08465i	−0.606253	−	0.269921i	−0.686819	+	0.726828i	$0.740994\pi$
$230$		0			0
$231$	12.7434	+	8.24375i	0.838457	+	0.542399i
$232$	0.164941	+	0.164941i	0.0108289	+	0.0108289i
$233$	−1.75658	−	2.16919i	−0.115077	−	0.142108i	0.716352	−	0.697739i	$-0.245810\pi$
$233$	−1.75658	−	2.16919i	−0.115077	−	0.142108i	−0.831429	+	0.555630i	$0.812477\pi$
$234$	−0.00635045	−	0.00705289i	−0.000415142	−	0.000461062i
$235$		0			0
$236$	14.2108	+	12.7955i	0.925047	+	0.832916i
$237$	−4.21336	−	8.26918i	−0.273687	−	0.537141i
$238$	0.169812		0.000299749i	0.0110073		1.94298e-5i
$239$	3.96154	−	1.28718i	0.256251	−	0.0832609i	−0.178075	−	0.984017i	$-0.556987\pi$
$239$	3.96154	−	1.28718i	0.256251	−	0.0832609i	0.434325	+	0.900756i	$0.356987\pi$
$240$		0			0
$241$	5.27483	−	4.74948i	0.339782	−	0.305941i	−0.481520	−	0.876435i	$-0.659915\pi$
$241$	5.27483	−	4.74948i	0.339782	−	0.305941i	0.821301	+	0.570494i	$0.193248\pi$
$242$	0.236060	+	0.0906150i	0.0151745	+	0.00582495i
$243$	3.88900	−	14.5140i	0.249480	−	0.931071i
$244$	4.43544	+	3.22254i	0.283950	+	0.206302i
$245$		0			0
$246$	0.130304	−	0.0946711i	0.00830785	−	0.00603601i
$247$	−0.768920	−	2.00311i	−0.0489252	−	0.127455i
$248$	−0.0280965	−	0.0432649i	−0.00178413	−	0.00274732i
$249$	−1.27225	−	0.734532i	−0.0806254	−	0.0465491i
$250$		0			0
$251$		−	3.67076i		−	0.231697i	−0.993267	−	0.115848i	$-0.963041\pi$
$251$		−	3.67076i		−	0.231697i	0.993267	−	0.115848i	$-0.0369586\pi$
$252$	7.35544	−	5.36390i	0.463349	−	0.337894i
$253$	−2.71200	+	17.1229i	−0.170502	+	1.07651i
$254$	−0.112728	+	0.253192i	−0.00707321	+	0.0158867i
$255$		0			0
$256$	14.5952	−	6.49819i	0.912198	−	0.406137i
$257$	−5.31329	−	1.42369i	−0.331434	−	0.0888074i	0.0892647	−	0.996008i	$-0.471548\pi$
$257$	−5.31329	−	1.42369i	−0.331434	−	0.0888074i	−0.420698	+	0.907201i	$0.638215\pi$
$258$	0.0171718	+	0.108418i	0.00106907	+	0.00674984i
$259$	2.24206	−	8.42694i	0.139315	−	0.523624i
$260$		0			0
$261$	3.90958	−	4.34202i	0.241997	−	0.268765i
$262$	−0.0511120	−	0.00267867i	−0.00315771	−	0.000165489i
$263$	20.7708	+	1.08855i	1.28078	+	0.0671229i	0.680549	−	0.732703i	$-0.261741\pi$
$263$	20.7708	+	1.08855i	1.28078	+	0.0671229i	0.600232	+	0.799826i	$0.295075\pi$
$264$	−0.263681	+	0.292848i	−0.0162285	+	0.0180235i
$265$		0			0
$266$	−0.293103	+	0.0790916i	−0.0179713	+	0.00484942i
$267$	0.175413	+	1.10751i	0.0107351	+	0.0677788i
$268$	−12.6114	−	3.37921i	−0.770363	−	0.206418i
$269$	−0.143111	+	0.0637171i	−0.00872562	+	0.00388490i	−0.411095	−	0.911593i	$-0.634853\pi$
$269$	−0.143111	+	0.0637171i	−0.00872562	+	0.00388490i	0.402369	+	0.915477i	$0.368187\pi$
$270$		0			0
$271$	0.567128	−	1.27379i	0.0344506	−	0.0773772i	−0.895501	−	0.445060i	$-0.853182\pi$
$271$	0.567128	−	1.27379i	0.0344506	−	0.0773772i	0.929951	+	0.367683i	$0.119849\pi$
$272$	2.33738	−	14.7577i	0.141725	−	0.894814i
$273$	0.955618	−	0.102145i	0.0578366	−	0.00618212i
$274$			0.265502i			0.0160395i
$275$		0			0
$276$	−6.69562	−	3.86572i	−0.403029	−	0.232689i
$277$	−16.3574	−	25.1881i	−0.982819	−	1.51341i	−0.853027	−	0.521867i	$-0.825236\pi$
$277$	−16.3574	−	25.1881i	−0.982819	−	1.51341i	−0.129792	−	0.991541i	$-0.541431\pi$
$278$	−0.113609	−	0.295961i	−0.00681381	−	0.0177506i
$279$	−1.04539	+	0.759518i	−0.0625857	+	0.0454712i
$280$		0			0
$281$	−23.1092	−	16.7898i	−1.37858	−	1.00160i	−0.997011	−	0.0772549i	$-0.975384\pi$
$281$	−23.1092	−	16.7898i	−1.37858	−	1.00160i	−0.381567	−	0.924341i	$-0.624616\pi$
$282$	−0.0316498	+	0.118119i	−0.00188472	+	0.00703385i
$283$	−26.2719	−	10.0848i	−1.56170	−	0.599482i	−0.584426	−	0.811447i	$-0.698680\pi$
$283$	−26.2719	−	10.0848i	−1.56170	−	0.599482i	−0.977277	+	0.211965i	$0.932014\pi$
$284$	6.73862	−	6.06748i	0.399864	−	0.360039i
$285$		0			0
$286$	0.0266049	−	0.00864446i	0.00157318	−	0.000511158i
$287$	−0.0387214	−	21.9363i	−0.00228565	−	1.29486i
$288$	0.160964	+	0.315909i	0.00948487	+	0.0186151i
$289$	2.25500	+	2.03041i	0.132647	+	0.119436i
$290$		0			0
$291$	9.40141	+	10.4413i	0.551120	+	0.612081i
$292$	12.7152	+	15.7019i	0.744100	+	0.918887i
$293$	4.56757	+	4.56757i	0.266840	+	0.266840i	0.827826	−	0.560986i	$-0.189578\pi$
$293$	4.56757	+	4.56757i	0.266840	+	0.266840i	−0.560986	+	0.827826i	$0.689578\pi$
$294$	−0.000480065	−	0.135981i	−2.79979e−5	−	0.00793060i
$295$		0			0
$296$	0.206834	+	0.0920883i	0.0120220	+	0.00535252i
$297$	21.0453	+	17.0421i	1.22117	+	0.988885i
$298$	−0.212447	+	0.137964i	−0.0123067	+	0.00799207i
$299$	0.548882	+	0.950692i	0.0317427	+	0.0549799i
$300$		0			0
$301$	13.3327	+	6.76374i	0.768485	+	0.389855i
$302$	−0.0437612	+	0.0858861i	−0.00251817	+	0.00494219i
$303$	−12.4302	+	4.77150i	−0.714095	+	0.274115i
$304$	2.79219	+	26.5660i	0.160143	+	1.52366i
$305$		0			0
$306$	0.109832	+	0.0115438i	0.00627868	+	0.000659916i
$307$	−12.4946	+	12.4946i	−0.713104	+	0.713104i	−0.967183	−	0.254080i	$-0.918227\pi$
$307$	−12.4946	+	12.4946i	−0.713104	+	0.713104i	0.254080	+	0.967183i	$0.418227\pi$
$308$	5.62524	+	26.2369i	0.320528	+	1.49498i
$309$	−15.8595	−	5.15306i	−0.902215	−	0.293148i
$310$		0			0
$311$	1.55465	−	7.31407i	0.0881563	−	0.414743i	−0.911835	−	0.410557i	$-0.865334\pi$
$311$	1.55465	−	7.31407i	0.0881563	−	0.414743i	0.999991	−	0.00418591i	$-0.00133242\pi$
$312$	−0.00130593	+	0.0249187i	−7.39340e−5	+	0.00141074i
$313$	−23.3423	−	15.1587i	−1.31939	−	0.856819i	−0.323394	−	0.946264i	$-0.604824\pi$
$313$	−23.3423	−	15.1587i	−1.31939	−	0.856819i	−0.995992	+	0.0894451i	$0.971491\pi$
$314$	−0.0278431	−	0.0856923i	−0.00157128	−	0.00483590i
$315$		0			0
$316$	5.07033	−	15.6049i	0.285228	−	0.877843i
$317$	22.2075	−	17.9833i	1.24730	−	1.01004i	0.248150	−	0.968722i	$-0.420177\pi$
$317$	22.2075	−	17.9833i	1.24730	−	1.01004i	0.999146	−	0.0413185i	$-0.0131558\pi$
$318$	0.211935	−	0.0567878i	0.0118847	−	0.00318450i
$319$	7.00477	+	15.7330i	0.392192	+	0.880878i
$320$		0			0
$321$	−6.89929	−	9.49606i	−0.385081	−	0.530019i
$322$	0.141784	−	0.0634266i	0.00790134	−	0.00353463i
$323$	22.2461	+	11.3350i	1.23781	+	0.630694i
$324$	−1.51943	+	0.877241i	−0.0844125	+	0.0487356i
$325$		0			0
$326$	0.152523	−	0.264177i	0.00844745	−	0.0146314i
$327$	0.538704	+	10.2791i	0.0297904	+	0.568434i
$328$	0.562539	+	0.0890975i	0.0310610	+	0.00491959i
$329$	10.5040	+	12.9247i	0.579105	+	0.712560i
$330$		0			0
$331$	−1.74558	+	16.6081i	−0.0959457	+	0.912863i	0.835624	+	0.549301i	$0.185106\pi$
$331$	−1.74558	+	16.6081i	−0.0959457	+	0.912863i	−0.931570	+	0.363561i	$0.881561\pi$
$332$	−0.672217	−	2.50875i	−0.0368927	−	0.137685i
$333$	2.03234	−	5.29442i	0.111371	−	0.290132i
$334$	0.0966189	−	0.0205370i	0.00528675	−	0.00112373i
$335$		0			0
$336$	−11.8209	−	1.85087i	−0.644884	−	0.100973i
$337$	−21.2946	+	10.8501i	−1.15999	+	0.591044i	−0.924631	−	0.380865i	$-0.875626\pi$
$337$	−21.2946	+	10.8501i	−1.15999	+	0.591044i	−0.235358	+	0.971909i	$0.575626\pi$
$338$	−0.120638	+	0.185766i	−0.00656184	+	0.0101043i
$339$	−9.44031	−	2.00660i	−0.512728	−	0.108984i
$340$		0			0
$341$	−0.791882	−	3.72551i	−0.0428828	−	0.201748i
$342$	−0.195006	+	0.0308859i	−0.0105447	+	0.00167012i
$343$	−15.0406	−	10.8064i	−0.812118	−	0.583493i
$344$	−0.228158	+	0.314033i	−0.0123015	+	0.0169315i
$345$		0			0
$346$	0.0385893	−	0.00405590i	0.00207457	−	0.000218046i
$347$	2.31115	−	2.85404i	0.124069	−	0.153213i	−0.711326	−	0.702862i	$-0.751905\pi$
$347$	2.31115	−	2.85404i	0.124069	−	0.153213i	0.835396	+	0.549649i	$0.185239\pi$
$348$	−7.66988	+	0.401961i	−0.411149	+	0.0215474i
$349$	1.21897			0.0652497			0.0326249	−	0.999468i	$-0.489613\pi$
$349$	1.21897			0.0652497			0.0326249	+	0.999468i	$0.489613\pi$
$350$		0			0
$351$	1.71477			0.0915274
$352$	−1.04363	+	0.0546944i	−0.0556258	+	0.00291522i
$353$	15.9851	−	19.7399i	0.850799	−	1.05065i	−0.147304	−	0.989091i	$-0.547060\pi$
$353$	15.9851	−	19.7399i	0.850799	−	1.05065i	0.998103	−	0.0615584i	$-0.0196070\pi$
$354$	0.184748	−	0.0194178i	0.00981924	−	0.00103204i
$355$		0			0
$356$	−1.16525	+	1.60383i	−0.0617583	+	0.0850031i
$357$	−7.46845	+	8.32405i	−0.395272	+	0.440556i
$358$	−0.393617	+	0.0623428i	−0.0208033	+	0.00329492i
$359$	2.33682	+	10.9939i	0.123333	+	0.580235i	0.995799	+	0.0915616i	$0.0291858\pi$
$359$	2.33682	+	10.9939i	0.123333	+	0.580235i	−0.872467	+	0.488674i	$0.837481\pi$
$360$		0			0
$361$	−25.0759	−	5.33005i	−1.31979	−	0.280529i
$362$	−0.0171029	+	0.0263361i	−0.000898908	+	0.00138420i
$363$	−14.8373	+	7.55997i	−0.778755	+	0.396796i
$364$	1.32235	+	1.06696i	0.0693099	+	0.0559238i
$365$		0			0
$366$	0.0520958	−	0.0110733i	0.00272309	−	0.000578810i
$367$	−2.58488	+	6.73383i	−0.134929	+	0.351503i	−0.984353	−	0.176209i	$-0.943617\pi$
$367$	−2.58488	+	6.73383i	−0.134929	+	0.351503i	0.849423	+	0.527712i	$0.176950\pi$
$368$	−3.53724	−	13.2012i	−0.184391	−	0.688158i
$369$	1.49122	−	14.1881i	0.0776301	−	0.738601i
$370$		0			0
$371$	10.6598	−	27.9170i	0.553431	−	1.44938i
$372$	1.67766	+	0.265716i	0.0869827	+	0.0137767i
$373$	−0.204078	−	3.89404i	−0.0105667	−	0.201626i	−0.998811	−	0.0487442i	$-0.984478\pi$
$373$	−0.204078	−	3.89404i	−0.0105667	−	0.201626i	0.988245	−	0.152881i	$-0.0488552\pi$
$374$	−0.162760	+	0.281908i	−0.00841610	+	0.0145771i
$375$		0			0
$376$	−0.374489	+	0.216211i	−0.0193128	+	0.0111503i
$377$	0.971660	+	0.495085i	0.0500430	+	0.0254982i
$378$	0.0249353	−	0.241340i	0.00128253	−	0.0124132i
$379$	2.70772	+	3.72686i	0.139086	+	0.191436i	0.872878	−	0.487939i	$-0.162251\pi$
$379$	2.70772	+	3.72686i	0.139086	+	0.191436i	−0.733792	+	0.679375i	$0.762251\pi$
$380$		0			0
$381$	−7.42397	−	16.6745i	−0.380342	−	0.854261i
$382$	0.0122200	−	0.00327433i	0.000625228	−	0.000167529i
$383$	22.1000	−	17.8962i	1.12926	−	0.914454i	0.132208	−	0.991222i	$-0.457793\pi$
$383$	22.1000	−	17.8962i	1.12926	−	0.914454i	0.997049	+	0.0767678i	$0.0244600\pi$
$384$	0.192024	−	0.590991i	0.00979921	−	0.0301589i
$385$		0			0
$386$	0.0766136	+	0.235792i	0.00389953	+	0.0120015i
$387$	8.15426	+	5.29544i	0.414504	+	0.269182i
$388$	−1.30003	+	24.8061i	−0.0659992	+	1.25934i
$389$	−6.09298	+	28.6652i	−0.308926	+	1.45338i	0.500282	+	0.865863i	$0.333230\pi$
$389$	−6.09298	+	28.6652i	−0.308926	+	1.45338i	−0.809208	+	0.587522i	$0.800104\pi$
$390$		0			0
$391$	−12.1489	−	3.94741i	−0.614396	−	0.199629i
$392$	0.338815	−	0.341216i	0.0171128	−	0.0172340i
$393$	2.38345	−	2.38345i	0.120229	−	0.120229i
$394$	−0.171727	−	0.0180493i	−0.00865149	−	0.000909308i
$395$		0			0
$396$	1.82411	+	17.3552i	0.0916649	+	0.872134i
$397$	1.04017	−	0.399283i	0.0522045	−	0.0200394i	−0.332126	−	0.943235i	$-0.607766\pi$
$397$	1.04017	−	0.399283i	0.0522045	−	0.0200394i	0.384330	+	0.923196i	$0.374432\pi$
$398$	0.0497532	−	0.0976462i	0.00249390	−	0.00489456i
$399$	9.04534	−	17.8302i	0.452833	−	0.892627i
$400$		0			0
$401$	−4.29812	−	7.44456i	−0.214638	−	0.371764i	0.738523	−	0.674229i	$-0.235524\pi$
$401$	−4.29812	−	7.44456i	−0.214638	−	0.371764i	−0.953160	+	0.302465i	$0.902190\pi$
$402$	−0.106372	+	0.0690790i	−0.00530537	+	0.00344535i
$403$	−0.187429	−	0.151777i	−0.00933650	−	0.00756055i
$404$	−21.5044	−	9.57439i	−1.06989	−	0.476344i
$405$		0			0
$406$	0.0838090	−	0.129555i	0.00415937	−	0.00642969i
$407$	11.8199	+	11.8199i	0.585890	+	0.585890i
$408$	−0.182732	−	0.225655i	−0.00904657	−	0.0111716i
$409$	10.3987	+	11.5490i	0.514185	+	0.571060i	0.943195	−	0.332240i	$-0.107804\pi$
$409$	10.3987	+	11.5490i	0.514185	+	0.571060i	−0.429010	+	0.903300i	$0.641138\pi$
$410$		0			0
$411$	−12.9940	−	11.6999i	−0.640947	−	0.577112i
$412$	−13.3845	−	26.2686i	−0.659407	−	1.29416i
$413$	12.6116	−	21.9332i	0.620575	−	1.07926i
$414$	0.0960709	−	0.0312153i	0.00472163	−	0.00153415i
$415$		0			0
$416$	−0.0491778	+	0.0442799i	−0.00241114	+	0.00217100i
$417$	19.4912	+	7.48195i	0.954486	+	0.366393i
$418$	0.150621	−	0.562127i	0.00736713	−	0.0274945i
$419$	−5.12758	−	3.72540i	−0.250499	−	0.181998i	0.455449	−	0.890262i	$-0.349479\pi$
$419$	−5.12758	−	3.72540i	−0.250499	−	0.181998i	−0.705948	+	0.708264i	$0.749479\pi$
$420$		0			0
$421$	−17.9408	+	13.0347i	−0.874380	+	0.635274i	−0.931759	−	0.363079i	$-0.881726\pi$
$421$	−17.9408	+	13.0347i	−0.874380	+	0.635274i	0.0573790	+	0.998352i	$0.481726\pi$
$422$	0.173997	+	0.453278i	0.00847004	+	0.0220652i
$423$	5.89920	+	9.08396i	0.286829	+	0.441677i
$424$	0.671930	+	0.387939i	0.0326318	+	0.0188400i
$425$		0			0
$426$		−	0.0880879i		−	0.00426787i
$427$	2.93866	−	6.63183i	0.142212	−	0.320937i
$428$	3.24632	−	20.4964i	0.156917	−	0.990732i
$429$	−0.749328	+	1.68302i	−0.0361779	+	0.0812568i
$430$		0			0
$431$	−8.89080	+	3.95844i	−0.428255	+	0.190671i	−0.609533	−	0.792761i	$-0.708643\pi$
$431$	−8.89080	+	3.95844i	−0.428255	+	0.190671i	0.181279	+	0.983432i	$0.441976\pi$
$432$	−20.6209	−	5.52535i	−0.992123	−	0.265839i
$433$	−1.94672	−	12.2911i	−0.0935535	−	0.590674i	−0.989276	−	0.146060i	$-0.953341\pi$
$433$	−1.94672	−	12.2911i	−0.0935535	−	0.590674i	0.895722	−	0.444614i	$-0.146659\pi$
$434$	−0.0240870	+	0.0241722i	−0.00115621	+	0.00116030i
$435$		0			0
$436$	−12.1768	+	13.5237i	−0.583163	+	0.647668i
$437$	22.8060	+	1.19521i	1.09096	+	0.0571746i
$438$	0.196008	+	0.0102723i	0.00936562	+	0.000490831i
$439$	−16.4159	+	18.2318i	−0.783490	+	0.870154i	−0.994217	−	0.107391i	$-0.965750\pi$
$439$	−16.4159	+	18.2318i	−0.783490	+	0.870154i	0.210727	+	0.977545i	$0.432417\pi$
$440$		0			0
$441$	−8.97928	−	8.02776i	−0.427585	−	0.382274i
$442$	0.00322450	+	0.0203587i	0.000153374	+	0.000968363i
$443$	6.76871	+	1.81367i	0.321591	+	0.0861701i	0.416003	−	0.909363i	$-0.363430\pi$
$443$	6.76871	+	1.81367i	0.321591	+	0.0861701i	−0.0944121	+	0.995533i	$0.530097\pi$
$444$	−6.81023	+	3.03211i	−0.323199	+	0.143898i
$445$		0			0
$446$	−0.147891	+	0.332168i	−0.00700282	+	0.0157286i
$447$	2.60972	−	16.4771i	0.123435	−	0.779340i
$448$	−12.4602	−	17.0865i	−0.588691	−	0.807263i
$449$			11.3776i			0.536943i	0.963288	+	0.268472i	$0.0865186\pi$
$449$			11.3776i			0.536943i	−0.963288	+	0.268472i	$0.913481\pi$
$450$		0			0
$451$	36.4167	+	21.0252i	1.71480	+	0.990039i
$452$	−9.29316	−	14.3102i	−0.437113	−	0.673095i
$453$	−2.27496	−	5.92648i	−0.106887	−	0.278450i
$454$	−0.277083	+	0.201313i	−0.0130042	+	0.00944808i
$455$		0			0
$456$	0.419965	+	0.305123i	0.0196667	+	0.0142887i
$457$	1.77469	−	6.62325i	0.0830167	−	0.309822i	−0.911915	−	0.410380i	$-0.865396\pi$
$457$	1.77469	−	6.62325i	0.0830167	−	0.309822i	0.994931	+	0.100558i	$0.0320627\pi$
$458$	−0.161021	−	0.0618104i	−0.00752404	−	0.00288821i
$459$	−14.8286	+	13.3517i	−0.692138	+	0.623204i
$460$		0			0
$461$	6.19822	−	2.01392i	0.288680	−	0.0937978i	−0.161097	−	0.986939i	$-0.551503\pi$
$461$	6.19822	−	2.01392i	0.288680	−	0.0937978i	0.449777	+	0.893141i	$0.351503\pi$
$462$	0.225976	+	0.129936i	0.0105133	+	0.00604516i
$463$	2.03589	+	3.99566i	0.0946158	+	0.185694i	0.933464	−	0.358672i	$-0.116770\pi$
$463$	2.03589	+	3.99566i	0.0946158	+	0.185694i	−0.838848	+	0.544366i	$0.816770\pi$
$464$	−10.0894	−	9.08455i	−0.468389	−	0.421740i
$465$		0			0
$466$	−0.0320772	−	0.0356254i	−0.00148595	−	0.00165031i
$467$	−25.2819	−	31.2205i	−1.16991	−	1.44471i	−0.871583	−	0.490248i	$-0.836906\pi$
$467$	−25.2819	−	31.2205i	−1.16991	−	1.44471i	−0.298322	−	0.954465i	$-0.596427\pi$
$468$	0.781365	+	0.781365i	0.0361186	+	0.0361186i
$469$	−0.873619	+	17.2523i	−0.0403400	+	0.796636i
$470$		0			0
$471$	5.42086	+	2.41352i	0.249780	+	0.111209i
$472$	0.510507	+	0.413401i	0.0234980	+	0.0190283i
$473$	−24.0351	+	15.6086i	−1.10514	+	0.717684i
$474$	−0.0796971	−	0.138039i	−0.00366061	−	0.00634036i
$475$		0			0
$476$	−19.7428	+	1.06962i	−0.904909	+	0.0490261i
$477$	8.82298	−	17.3161i	0.403977	−	0.792849i
$478$	0.0667882	−	0.0256376i	0.00305482	−	0.00117264i
$479$	−2.16757	−	20.6230i	−0.0990386	−	0.942290i	−0.925360	−	0.379090i	$-0.876237\pi$
$479$	−2.16757	−	20.6230i	−0.0990386	−	0.942290i	0.826321	−	0.563199i	$-0.190430\pi$
$480$		0			0
$481$	1.05268	+	0.110641i	0.0479980	+	0.00504479i
$482$	0.0862007	−	0.0862007i	0.00392633	−	0.00392633i
$483$	−3.14383	+	9.73414i	−0.143049	+	0.442919i
$484$	−27.9996	−	9.09763i	−1.27271	−	0.413529i
$485$		0			0
$486$	0.0536552	−	0.252428i	0.00243385	−	0.0114504i
$487$	−0.389033	+	7.42319i	−0.0176288	+	0.336377i	0.975550	+	0.219777i	$0.0705329\pi$
$487$	−0.389033	+	7.42319i	−0.0176288	+	0.336377i	−0.993179	+	0.116600i	$0.962800\pi$
$488$	0.157952	+	0.102575i	0.00715013	+	0.00464335i
$489$	6.20797	+	19.1062i	0.280734	+	0.864011i
$490$		0			0
$491$	−6.27403	+	19.3095i	−0.283143	+	0.871425i	0.703806	+	0.710392i	$0.251482\pi$
$491$	−6.27403	+	19.3095i	−0.283143	+	0.871425i	−0.986949	+	0.161033i	$0.948518\pi$
$492$	−14.5739	+	11.8017i	−0.657043	+	0.532063i
$493$	−12.2574	+	3.28436i	−0.552045	+	0.147920i
$494$	−0.0149884	−	0.0336646i	−0.000674362	−	0.00151464i
$495$		0			0
$496$	1.76487	+	2.42913i	0.0792448	+	0.109071i
$497$	−9.71839	−	7.03465i	−0.435929	−	0.315547i
$498$	−0.0224808	−	0.0114546i	−0.00100739	−	0.000513291i
$499$	−7.97198	+	4.60262i	−0.356875	+	0.206042i	−0.667709	−	0.744422i	$-0.732725\pi$
$499$	−7.97198	+	4.60262i	−0.356875	+	0.206042i	0.310834	+	0.950464i	$0.399392\pi$
$500$		0			0
$501$	−3.25260	+	5.63367i	−0.145315	+	0.251694i
$502$	−0.00329950	−	0.0629581i	−0.000147264	−	0.00280996i
$503$	−20.6686	−	3.27358i	−0.921565	−	0.145962i	−0.322415	−	0.946598i	$-0.604495\pi$
$503$	−20.6686	−	3.27358i	−0.921565	−	0.145962i	−0.599150	+	0.800637i	$0.704495\pi$
$504$	0.242685	−	0.197233i	0.0108100	−	0.00878544i
$505$		0			0
$506$	−0.0311230	+	0.296116i	−0.00138359	+	0.0131640i
$507$	−3.77549	−	14.0903i	−0.167676	−	0.625774i
$508$	11.5644	−	30.1264i	0.513089	−	1.33664i
$509$	−6.93922	+	1.47498i	−0.307575	+	0.0653772i	−0.359114	−	0.933294i	$-0.616921\pi$
$509$	−6.93922	+	1.47498i	−0.307575	+	0.0653772i	0.0515382	+	0.998671i	$0.483588\pi$
$510$		0			0
$511$	16.7864	−	20.8044i	0.742586	−	0.920334i
$512$	1.22350	−	0.623407i	0.0540718	−	0.0275509i
$513$	19.4289	−	29.9179i	0.857807	−	1.32091i
$514$	−0.0924091	−	0.0196422i	−0.00407599	−	0.000866379i
$515$		0			0
$516$	−2.65728	−	12.5015i	−0.116980	−	0.550349i
$517$	−31.5330	+	4.99434i	−1.38682	+	0.219651i
$518$	0.0308794	−	0.146548i	0.00135676	−	0.00643893i
$519$	−1.50201	+	2.06734i	−0.0659310	+	0.0907463i
$520$		0			0
$521$	−15.1966	+	1.59723i	−0.665775	+	0.0699757i	−0.431386	−	0.902167i	$-0.641975\pi$
$521$	−15.1966	+	1.59723i	−0.665775	+	0.0699757i	−0.234388	+	0.972143i	$0.575309\pi$
$522$	0.0631512	−	0.0779852i	0.00276405	−	0.00341332i
$523$	−4.63114	+	0.242708i	−0.202506	+	0.0106129i	−0.153319	−	0.988177i	$-0.548996\pi$
$523$	−4.63114	+	0.242708i	−0.202506	+	0.0106129i	−0.0491867	+	0.998790i	$0.515663\pi$
$524$	5.95927			0.260332
$525$		0			0
$526$	0.357223			0.0155757
$527$	2.80259	−	0.146877i	0.122083	−	0.00639808i
$528$	14.4341	−	17.8246i	0.628163	−	0.775717i
$529$	11.2538	−	1.18282i	0.489294	−	0.0514268i
$530$		0			0
$531$	9.67149	−	13.3117i	0.419707	−	0.577677i
$532$	33.5981	−	10.9823i	1.45666	−	0.476143i
$533$	2.62992	−	0.416539i	0.113915	−	0.0180423i
$534$	0.00400405	+	0.0188376i	0.000173272	+	0.000815181i
$535$		0			0
$536$	−0.438709	−	0.0932504i	−0.0189493	−	0.00402781i
$537$	14.2944	−	22.0114i	0.616848	−	0.949863i
$538$	−0.00239725	+	0.00122146i	−0.000103353	+	5.26610e-5i
$539$	32.3816	−	14.5544i	1.39477	−	0.626903i
$540$		0			0
$541$	−24.8117	+	5.27390i	−1.06674	+	0.226743i	−0.707652	−	0.706561i	$-0.750246\pi$
$541$	−24.8117	+	5.27390i	−1.06674	+	0.226743i	−0.359088	+	0.933304i	$0.616912\pi$
$542$	0.00858198	−	0.0223568i	0.000368628	−	0.000960308i
$543$	−0.535254	−	1.99759i	−0.0229699	−	0.0857249i
$544$	0.0804917	−	0.765827i	0.00345105	−	0.0328346i
$545$		0			0
$546$	0.0162982	−	0.00261088i	0.000697499	−	0.000111735i
$547$	8.90589	+	1.41055i	0.380788	+	0.0603110i	0.343895	−	0.939008i	$-0.388254\pi$
$547$	8.90589	+	1.41055i	0.380788	+	0.0603110i	0.0368938	+	0.999319i	$0.488254\pi$
$548$	−1.61787	−	30.8707i	−0.0691118	−	1.31873i
$549$	2.35873	−	4.08544i	0.100668	−	0.174362i
$550$		0			0
$551$	19.6471	−	11.3433i	0.836995	−	0.483239i
$552$	−0.236643	−	0.120576i	−0.0100722	−	0.00513204i
$553$	−21.5939	−	2.23108i	−0.918266	−	0.0948752i
$554$	−0.303190	−	0.417305i	−0.0128813	−	0.0177296i
$555$		0			0
$556$	15.0131	+	33.7201i	0.636699	+	1.43005i
$557$	16.3666	−	4.38542i	0.693475	−	0.185816i	0.105169	−	0.994454i	$-0.466462\pi$
$557$	16.3666	−	4.38542i	0.693475	−	0.185816i	0.588306	+	0.808638i	$0.299795\pi$
$558$	−0.0172470	+	0.0139663i	−0.000730123	+	0.000591242i
$559$	−0.560777	+	1.72589i	−0.0237183	+	0.0729975i
$560$		0			0
$561$	−6.62463	−	20.3885i	−0.279692	−	0.860804i
$562$	−0.411443	−	0.267194i	−0.0173557	−	0.0112709i
$563$	−2.26896	+	43.2943i	−0.0956252	+	1.82464i	0.358310	+	0.933603i	$0.383353\pi$
$563$	−2.26896	+	43.2943i	−0.0956252	+	1.82464i	−0.453935	+	0.891035i	$0.649980\pi$
$564$	2.96025	−	13.9269i	0.124649	−	0.586427i
$565$		0			0
$566$	−0.459661	−	0.149353i	−0.0193210	−	0.00627776i
$567$	1.55630	+	1.72232i	0.0653584	+	0.0723306i
$568$	0.220260	−	0.220260i	0.00924190	−	0.00924190i
$569$	9.81623	+	1.03173i	0.411518	+	0.0432522i	0.308026	−	0.951378i	$-0.400332\pi$
$569$	9.81623	+	1.03173i	0.411518	+	0.0432522i	0.103492	+	0.994630i	$0.466998\pi$
$570$		0			0
$571$	0.152474	+	1.45070i	0.00638085	+	0.0607098i	0.997249	−	0.0741249i	$-0.0236163\pi$
$571$	0.152474	+	1.45070i	0.00638085	+	0.0607098i	−0.990868	+	0.134835i	$0.956950\pi$
$572$	−3.04076	+	1.16724i	−0.127141	+	0.0488047i
$573$	−0.378247	+	0.742352i	−0.0158015	+	0.0310122i
$574$	−0.0203817	−	0.376199i	−0.000850716	−	0.0157022i
$575$		0			0
$576$	−6.87654	−	11.9105i	−0.286522	−	0.496271i
$577$	−4.72112	+	3.06593i	−0.196543	+	0.127636i	−0.639159	−	0.769075i	$-0.720717\pi$
$577$	−4.72112	+	3.06593i	−0.196543	+	0.127636i	0.442616	+	0.896711i	$0.354051\pi$
$578$	0.0405011	+	0.0327972i	0.00168462	+	0.00136418i
$579$	−14.9161	−	6.64109i	−0.619894	−	0.275994i
$580$		0			0
$581$	−3.05904	+	1.56547i	−0.126911	+	0.0649466i
$582$	0.170631	+	0.170631i	0.00707288	+	0.00707288i
$583$	36.0498	+	44.5177i	1.49303	+	1.84374i
$584$	0.464424	+	0.515795i	0.0192180	+	0.0213437i
$585$		0			0
$586$	0.0824450	+	0.0742338i	0.00340577	+	0.00306657i
$587$	9.42678	+	18.5011i	0.389085	+	0.763622i	0.999597	−	0.0283850i	$-0.00903644\pi$
$587$	9.42678	+	18.5011i	0.389085	+	0.763622i	−0.610512	+	0.792007i	$0.709036\pi$
$588$	0.884438	+	15.8081i	0.0364736	+	0.651914i
$589$	−4.77172	+	1.55043i	−0.196615	+	0.0638842i
$590$		0			0
$591$	8.45086	−	7.60919i	0.347622	−	0.313000i
$592$	−12.3025	−	4.72247i	−0.505628	−	0.194092i
$593$	−3.80233	+	14.1905i	−0.156143	+	0.582733i	0.842862	+	0.538130i	$0.180869\pi$
$593$	−3.80233	+	14.1905i	−0.156143	+	0.582733i	−0.999005	+	0.0446033i	$0.985798\pi$
$594$	0.376271	+	0.273377i	0.0154386	+	0.0112168i
$595$		0			0
$596$	23.8611	−	17.3361i	0.977390	−	0.710116i
$597$	2.58646	+	6.73797i	0.105857	+	0.275767i
$598$	0.0102685	+	0.0158122i	0.000419912	+	0.000646608i
$599$	−8.74982	−	5.05171i	−0.357508	−	0.206407i	0.310479	−	0.950580i	$-0.399511\pi$
$599$	−8.74982	−	5.05171i	−0.357508	−	0.206407i	−0.667987	+	0.744173i	$0.732844\pi$
$600$		0			0
$601$		−	22.6515i		−	0.923974i	−0.886887	−	0.461987i	$-0.847137\pi$
$601$		−	22.6515i		−	0.923974i	0.886887	−	0.461987i	$-0.152863\pi$
$602$	0.234752	+	0.104022i	0.00956778	+	0.00423963i
$603$	−1.75744	+	11.0960i	−0.0715684	+	0.451865i
$604$	4.56489	−	10.2529i	0.185743	−	0.417185i
$605$		0			0
$606$	−0.208904	+	0.0930100i	−0.00848614	+	0.00377827i
$607$	19.2701	+	5.16341i	0.782150	+	0.209576i	0.627732	−	0.778429i	$-0.283983\pi$
$607$	19.2701	+	5.16341i	0.782150	+	0.209576i	0.154418	+	0.988006i	$0.450650\pi$
$608$	0.215359	+	1.35972i	0.00873395	+	0.0551440i
$609$	2.64737	+	9.81081i	0.107277	+	0.397554i
$610$		0			0
$611$	−1.35272	+	1.50235i	−0.0547254	+	0.0607787i
$612$	−12.8409	−	0.672961i	−0.519061	−	0.0272028i
$613$	−38.3266	−	2.00861i	−1.54800	−	0.0811272i	−0.740929	−	0.671584i	$-0.765614\pi$
$613$	−38.3266	−	2.00861i	−1.54800	−	0.0811272i	−0.807070	+	0.590456i	$0.798948\pi$
$614$	−0.203067	+	0.225528i	−0.00819510	+	0.00910158i
$615$		0			0
$616$	0.240144	+	0.889942i	0.00967566	+	0.0358568i
$617$	0.0933065	+	0.589114i	0.00375638	+	0.0237168i	0.989495	−	0.144565i	$-0.0461782\pi$
$617$	0.0933065	+	0.589114i	0.00375638	+	0.0237168i	−0.985739	+	0.168282i	$0.946178\pi$
$618$	−0.276642	−	0.0741259i	−0.0111282	−	0.00298178i
$619$	−2.53843	+	1.13018i	−0.102028	+	0.0454258i	−0.457116	−	0.889407i	$-0.651118\pi$
$619$	−2.53843	+	1.13018i	−0.102028	+	0.0454258i	0.355088	+	0.934833i	$0.384451\pi$
$620$		0			0
$621$	−7.42352	+	16.6735i	−0.297896	+	0.669084i
$622$	0.0200899	−	0.126843i	0.000805532	−	0.00508593i
$623$	2.39804	+	1.06261i	0.0960753	+	0.0425724i
$624$		−	1.45235i		−	0.0581404i
$625$		0			0
$626$	−0.413975	−	0.239009i	−0.0165458	−	0.00955270i
$627$	20.8738	+	32.1429i	0.833620	+	1.28366i
$628$	3.75958	+	9.79405i	0.150024	+	0.390825i
$629$	−9.96459	+	7.23970i	−0.397314	+	0.288666i
$630$		0			0
$631$	22.3034	+	16.2043i	0.887883	+	0.645085i	0.935325	−	0.353789i	$-0.115107\pi$
$631$	22.3034	+	16.2043i	0.887883	+	0.645085i	−0.0474420	+	0.998874i	$0.515107\pi$
$632$	0.145882	−	0.544441i	0.00580289	−	0.0216567i
$633$	−29.8516	−	11.4589i	−1.18649	−	0.455452i
$634$	0.364721	−	0.328396i	0.0144849	−	0.0130423i
$635$		0			0
$636$	−24.2963	+	7.89435i	−0.963411	+	0.313031i
$637$	1.01352	−	2.00662i	0.0401570	−	0.0795052i
$638$	0.134282	+	0.263544i	0.00531628	+	0.0104338i
$639$	−5.79828	−	5.22080i	−0.229377	−	0.206532i
$640$		0			0
$641$	1.01518	+	1.12747i	0.0400971	+	0.0445323i	0.762860	−	0.646564i	$-0.223795\pi$
$641$	1.01518	+	1.12747i	0.0400971	+	0.0445323i	−0.722763	+	0.691096i	$0.757128\pi$
$642$	−0.126867	−	0.156668i	−0.00500704	−	0.00618318i
$643$	18.1864	+	18.1864i	0.717201	+	0.717201i	0.968031	−	0.250830i	$-0.0807034\pi$
$643$	18.1864	+	18.1864i	0.717201	+	0.717201i	−0.250830	+	0.968031i	$0.580703\pi$
$644$	−16.0992	+	8.23879i	−0.634398	+	0.324654i
$645$		0			0
$646$	0.391737	+	0.174412i	0.0154127	+	0.00686216i
$647$	−5.86608	−	4.75026i	−0.230620	−	0.186752i	0.507045	−	0.861920i	$-0.330738\pi$
$647$	−5.86608	−	4.75026i	−0.230620	−	0.186752i	−0.737664	+	0.675168i	$0.764071\pi$
$648$	−0.0505467	+	0.0328254i	−0.00198566	+	0.00128950i
$649$	24.2497	+	42.0017i	0.951885	+	1.64871i
$650$		0			0
$651$	−0.121578	−	2.24404i	−0.00476501	−	0.0879510i
$652$	−16.1245	+	31.6461i	−0.631484	+	1.23936i
$653$	−32.2034	+	12.3617i	−1.26022	+	0.483751i	−0.894539	−	0.446990i	$-0.852496\pi$
$653$	−32.2034	+	12.3617i	−1.26022	+	0.483751i	−0.365677	+	0.930742i	$0.619162\pi$
$654$	0.0184789	+	0.175815i	0.000722581	+	0.00687489i
$655$		0			0
$656$	−32.9683	−	3.46511i	−1.28720	−	0.135290i
$657$	12.2932	−	12.2932i	0.479602	−	0.479602i
$658$	0.191774	+	0.212232i	0.00747614	+	0.00827368i
$659$	16.9511	+	5.50773i	0.660319	+	0.214551i	0.619959	−	0.784634i	$-0.287149\pi$
$659$	16.9511	+	5.50773i	0.660319	+	0.214551i	0.0403605	+	0.999185i	$0.487149\pi$
$660$		0			0
$661$	8.15962	−	38.3880i	0.317372	−	1.49312i	−0.473311	−	0.880895i	$-0.656941\pi$
$661$	8.15962	−	38.3880i	0.317372	−	1.49312i	0.790684	−	0.612225i	$-0.209725\pi$
$662$	−0.0150105	+	0.286418i	−0.000583401	+	0.0111320i
$663$	−1.13847	−	0.739334i	−0.0442147	−	0.0287134i
$664$	−0.0275707	−	0.0848540i	−0.00106995	−	0.00329297i
$665$		0			0
$666$	0.0300981	−	0.0926326i	0.00116628	−	0.00358944i
$667$	−9.02044	+	7.30461i	−0.349273	+	0.282836i
$668$	−11.1090	+	2.97666i	−0.429822	+	0.115170i
$669$	−9.73964	−	21.8756i	−0.376556	−	0.845760i
$670$		0			0
$671$	8.17313	+	11.2493i	0.315520	+	0.434276i
$672$	−0.613371	−	0.0633735i	−0.0236613	−	0.00244468i
$673$	15.3295	+	7.81076i	0.590908	+	0.301083i	0.723759	−	0.690053i	$-0.242413\pi$
$673$	15.3295	+	7.81076i	0.590908	+	0.301083i	−0.132850	+	0.991136i	$0.542413\pi$
$674$	−0.355475	+	0.205234i	−0.0136924	+	0.00790531i
$675$		0			0
$676$	12.8950	−	22.3347i	0.495960	−	0.859028i
$677$	0.0333362	+	0.636093i	0.00128122	+	0.0244470i	0.999195	−	0.0401085i	$-0.0127704\pi$
$677$	0.0333362	+	0.636093i	0.00128122	+	0.0244470i	−0.997914	+	0.0645556i	$0.979437\pi$
$678$	−0.163717	−	0.0259302i	−0.00628750	−	0.000995842i
$679$	32.4515	−	5.19856i	1.24538	−	0.199502i
$680$		0			0
$681$	2.35771	−	22.4321i	0.0903476	−	0.859600i
$682$	−0.0169304	−	0.0631853i	−0.000648300	−	0.00241949i
$683$	6.51343	−	16.9681i	0.249229	−	0.649265i	−0.750706	−	0.660637i	$-0.770286\pi$
$683$	6.51343	−	16.9681i	0.249229	−	0.649265i	0.999935	+	0.0113716i	$0.00361978\pi$
$684$	22.4858	−	4.77950i	0.859765	−	0.182749i
$685$		0			0
$686$	−0.267679	−	0.171824i	−0.0102200	−	0.00656028i
$687$	10.1208	−	5.15681i	0.386133	−	0.196745i
$688$	12.3048	−	18.9478i	0.469117	−	0.722377i
$689$	3.54803	+	0.754158i	0.135169	+	0.0287311i
$690$		0			0
$691$	5.16326	+	24.2912i	0.196420	+	0.924081i	0.960353	+	0.278786i	$0.0899322\pi$
$691$	5.16326	+	24.2912i	0.196420	+	0.924081i	−0.763934	+	0.645295i	$0.776735\pi$
$692$	−4.46218	+	0.706740i	−0.169627	+	0.0268662i
$693$	21.9460	−	7.17355i	0.833661	−	0.272501i
$694$	0.0370737	−	0.0510276i	0.00140730	−	0.00193698i
$695$		0			0
$696$	−0.262392	+	0.0275786i	−0.00994596	+	0.00104536i
$697$	−19.4992	+	24.0795i	−0.738583	+	0.912074i
$698$	0.0209068	−	0.00109568i	0.000791333	−	4.14720e-5i
$699$	3.15710			0.119413
$700$		0			0
$701$	−7.79098			−0.294261			−0.147131	−	0.989117i	$-0.547004\pi$
$701$	−7.79098			−0.294261			−0.147131	+	0.989117i	$0.547004\pi$
$702$	0.0294103	−	0.00154133i	0.00111002	−	5.81738e-5i
$703$	13.8576	−	17.1127i	0.522648	−	0.645417i
$704$	40.3159	−	4.23737i	1.51946	−	0.159702i
$705$		0			0
$706$	0.256420	−	0.352932i	0.00965050	−	0.0132828i
$707$	−6.42152	+	30.4753i	−0.241506	+	1.14614i
$708$	−21.3629	+	3.38355i	−0.802866	+	0.127162i
$709$	9.38432	+	44.1498i	0.352436	+	1.65808i	0.695319	+	0.718701i	$0.255263\pi$
$709$	9.38432	+	44.1498i	0.352436	+	1.65808i	−0.342884	+	0.939378i	$0.611404\pi$
$710$		0			0
$711$	−13.8098	−	2.93536i	−0.517907	−	0.110085i
$712$	−0.0370906	+	0.0571145i	−0.00139003	+	0.00214046i
$713$	2.28721	−	1.16539i	0.0856568	−	0.0436443i
$714$	−0.120611	+	0.149481i	−0.00451375	+	0.00559418i
$715$		0			0
$716$	45.3872	−	9.64735i	1.69620	−	0.360539i
$717$	−1.68842	+	4.39848i	−0.0630552	+	0.164264i
$718$	0.0499613	+	0.186458i	0.00186454	+	0.00695856i
$719$	3.25147	−	30.9356i	0.121259	−	1.15370i	−0.749503	−	0.662001i	$-0.769708\pi$
$719$	3.25147	−	30.9356i	0.121259	−	1.15370i	0.870762	−	0.491704i	$-0.163626\pi$
$720$		0			0
$721$	−30.2705	+	24.6012i	−1.12733	+	0.916195i
$722$	−0.434874	−	0.0688773i	−0.0161843	−	0.00256335i
$723$	0.420174	+	8.01739i	0.0156264	+	0.298170i
$724$	1.82812	−	3.16640i	0.0679417	−	0.117678i
$725$		0			0
$726$	−0.247682	+	0.142999i	−0.00919235	+	0.00530721i
$727$	19.4572	+	9.91394i	0.721628	+	0.367688i	0.775915	−	0.630838i	$-0.217289\pi$
$727$	19.4572	+	9.91394i	0.721628	+	0.367688i	−0.0542869	+	0.998525i	$0.517289\pi$
$728$	0.0472814	+	0.0342246i	0.00175236	+	0.00126845i
$729$	11.5369	+	15.8791i	0.427291	+	0.588116i
$730$		0			0
$731$	−8.58899	−	19.2912i	−0.317675	−	0.713510i
$732$	−5.98986	+	1.60498i	−0.221392	+	0.0593217i
$733$	−0.175122	+	0.141811i	−0.00646830	+	0.00523792i	−0.632549	−	0.774520i	$-0.717991\pi$
$733$	−0.175122	+	0.141811i	−0.00646830	+	0.00523792i	0.626081	+	0.779758i	$0.284658\pi$
$734$	−0.0382810	+	0.117817i	−0.00141298	+	0.00434870i
$735$		0			0
$736$	−0.217655	−	0.669875i	−0.00802289	−	0.0246919i
$737$	−27.7716	−	18.0351i	−1.02298	−	0.664331i
$738$	0.0128233	−	0.244683i	0.000472032	−	0.00900691i
$739$	8.38752	−	39.4602i	0.308540	−	1.45157i	−0.501483	−	0.865167i	$-0.667212\pi$
$739$	8.38752	−	39.4602i	0.308540	−	1.45157i	0.810023	−	0.586398i	$-0.199455\pi$
$740$		0			0
$741$	2.30809	+	0.749943i	0.0847897	+	0.0275498i
$742$	0.157736	−	0.488393i	0.00579066	−	0.0179295i
$743$	1.97911	−	1.97911i	0.0726064	−	0.0726064i	−0.669871	−	0.742477i	$-0.733651\pi$
$743$	1.97911	−	1.97911i	0.0726064	−	0.0726064i	0.742477	+	0.669871i	$0.233651\pi$
$744$	0.0580299	+	0.00609919i	0.00212748	+	0.000223607i
$745$		0			0
$746$	−0.00700037	−	0.0666041i	−0.000256302	−	0.00243855i
$747$	−2.08638	+	0.800886i	−0.0763366	+	0.0293029i
$748$	17.2067	−	33.7701i	0.629141	−	1.23476i
$749$	−27.4161	+	1.48535i	−1.00176	+	0.0542734i
$750$		0			0
$751$	14.9793	+	25.9449i	0.546602	+	0.946743i	0.998504	+	0.0546754i	$0.0174124\pi$
$751$	14.9793	+	25.9449i	0.546602	+	0.946743i	−0.451902	+	0.892068i	$0.649254\pi$
$752$	21.1081	−	13.7078i	0.769733	−	0.499870i
$753$	3.22666	+	2.61289i	0.117586	+	0.0952192i
$754$	0.0171102	+	0.00761794i	0.000623116	+	0.000277429i
$755$		0			0
$756$	−1.42867	+	28.2134i	−0.0519601	+	1.02611i
$757$	−29.2442	−	29.2442i	−1.06290	−	1.06290i	−0.997884	−	0.0650131i	$-0.979291\pi$
$757$	−29.2442	−	29.2442i	−1.06290	−	1.06290i	−0.0650131	−	0.997884i	$-0.520709\pi$
$758$	0.0497906	+	0.0614863i	0.00180848	+	0.00223328i
$759$	−13.1208	−	14.5721i	−0.476256	−	0.528936i
$760$		0			0
$761$	35.3614	+	31.8396i	1.28185	+	1.15418i	0.979601	+	0.200954i	$0.0644043\pi$
$761$	35.3614	+	31.8396i	1.28185	+	1.15418i	0.302250	+	0.953229i	$0.402262\pi$
$762$	−0.142318	−	0.279315i	−0.00515565	−	0.0101185i
$763$	20.8726	+	12.0018i	0.755641	+	0.434493i
$764$	−1.40090	+	0.455180i	−0.0506828	+	0.0164679i
$765$		0			0
$766$	0.362956	−	0.326807i	0.0131141	−	0.0118080i
$767$	2.86709	+	1.10057i	0.103525	+	0.0397394i
$768$	−4.67702	+	17.4549i	−0.168767	+	0.629848i
$769$	−30.0966	−	21.8665i	−1.08531	−	0.788525i	−0.106710	−	0.994290i	$-0.534032\pi$
$769$	−30.0966	−	21.8665i	−1.08531	−	0.788525i	−0.978601	+	0.205765i	$0.934032\pi$
$770$		0			0
$771$	5.03351	−	3.65706i	0.181277	−	0.131706i
$772$	−10.3449	−	26.9495i	−0.372322	−	0.969933i
$773$	0.188996	+	0.291029i	0.00679773	+	0.0104676i	0.842053	−	0.539395i	$-0.181347\pi$
$773$	0.188996	+	0.291029i	0.00679773	+	0.0104676i	−0.835255	+	0.549862i	$0.814680\pi$
$774$	0.144615	+	0.0834938i	0.00519809	+	0.00300112i
$775$		0			0
$776$			0.853311i			0.0306321i
$777$	5.81148	+	7.96919i	0.208486	+	0.285893i
$778$	−0.0787362	+	0.497121i	−0.00282283	+	0.0178226i
$779$	22.5305	−	50.6043i	0.807239	−	1.81309i
$780$		0			0
$781$	21.0096	−	9.35408i	0.751783	−	0.334715i
$782$	−0.211917	−	0.0567829i	−0.00757812	−	0.00203055i
$783$	2.83631	+	17.9077i	0.101361	+	0.639970i
$784$	−18.6538	+	20.8648i	−0.666208	+	0.745173i
$785$		0			0
$786$	0.0387367	−	0.0430215i	0.00138169	−	0.00153453i
$787$	−9.65966	−	0.506241i	−0.344330	−	0.0180456i	−0.120613	−	0.992700i	$-0.538486\pi$
$787$	−9.65966	−	0.506241i	−0.344330	−	0.0180456i	−0.223717	+	0.974654i	$0.571819\pi$
$788$	20.0772	+	1.05220i	0.715222	+	0.0374832i
$789$	−15.7417	+	17.4830i	−0.560421	+	0.622410i
$790$		0			0
$791$	−15.9351	+	15.9914i	−0.566587	+	0.568590i
$792$	0.0937781	+	0.592092i	0.00333226	+	0.0210391i
$793$	0.850484	+	0.227886i	0.0302016	+	0.00809249i
$794$	0.0174813	−	0.00778316i	0.000620387	−	0.000276214i
$795$		0			0
$796$	−5.18995	+	11.6568i	−0.183953	+	0.413165i
$797$	−7.51322	+	47.4366i	−0.266132	+	1.68029i	0.386245	+	0.922396i	$0.373772\pi$
$797$	−7.51322	+	47.4366i	−0.266132	+	1.68029i	−0.652377	+	0.757895i	$0.726228\pi$
$798$	0.139112	−	0.313941i	0.00492451	−	0.0111134i
$799$		−	23.5245i		−	0.832235i
$800$		0			0
$801$	1.47727	+	0.852904i	0.0521969	+	0.0301359i
$802$	−0.0804096	−	0.123820i	−0.00283936	−	0.00437224i
$803$	18.3641	+	47.8402i	0.648056	+	1.68824i
$804$	11.9473	−	8.68023i	0.421349	−	0.306128i
$805$		0			0
$806$	−0.00335106	−	0.00243469i	−0.000118036	−	8.57583e-5i
$807$	0.0458598	−	0.171151i	0.00161434	−	0.00602480i
$808$	−0.754923	−	0.289788i	−0.0265581	−	0.0101947i
$809$	−24.0016	+	21.6112i	−0.843852	+	0.759808i	−0.972752	−	0.231850i	$-0.925522\pi$
$809$	−24.0016	+	21.6112i	−0.843852	+	0.759808i	0.128899	+	0.991658i	$0.458856\pi$
$810$		0			0
$811$	25.8661	−	8.40440i	0.908281	−	0.295118i	0.182630	−	0.983182i	$-0.441539\pi$
$811$	25.8661	−	8.40440i	0.908281	−	0.295118i	0.725651	+	0.688063i	$0.241539\pi$
$812$	−8.95528	+	15.5744i	−0.314269	+	0.546555i
$813$	0.715992	+	1.40521i	0.0251109	+	0.0492830i
$814$	0.213350	+	0.192101i	0.00747791	+	0.00673314i
$815$		0			0
$816$	11.3084	+	12.5593i	0.395874	+	0.439663i
$817$	23.7582	+	29.3390i	0.831195	+	1.02644i
$818$	0.188732	+	0.188732i	0.00659886	+	0.00659886i
$819$	0.794105	−	1.22755i	0.0277483	−	0.0428942i
$820$		0			0
$821$	0.432586	+	0.192600i	0.0150974	+	0.00672177i	0.414271	−	0.910153i	$-0.364036\pi$
$821$	0.432586	+	0.192600i	0.0150974	+	0.00672177i	−0.399174	+	0.916875i	$0.630703\pi$
$822$	−0.233380	−	0.188987i	−0.00814006	−	0.00659169i
$823$	−13.5690	+	8.81180i	−0.472985	+	0.307160i	−0.759030	−	0.651056i	$-0.774326\pi$
$823$	−13.5690	+	8.81180i	−0.472985	+	0.307160i	0.286044	+	0.958216i	$0.407660\pi$
$824$	−0.506382	−	0.877080i	−0.0176407	−	0.0305545i
$825$		0			0
$826$	0.196589	−	0.387517i	0.00684021	−	0.0134835i
$827$	6.12078	−	12.0127i	0.212841	−	0.417723i	−0.759761	−	0.650203i	$-0.774684\pi$
$827$	6.12078	−	12.0127i	0.212841	−	0.417723i	0.972601	+	0.232480i	$0.0746839\pi$
$828$	−10.9803	+	4.21492i	−0.381590	+	0.146479i
$829$	−0.359804	−	3.42331i	−0.0124965	−	0.118896i	0.986495	−	0.163790i	$-0.0523719\pi$
$829$	−0.359804	−	3.42331i	−0.0124965	−	0.118896i	−0.998992	+	0.0448933i	$0.985705\pi$
$830$		0			0
$831$	33.7841	+	3.55085i	1.17196	+	0.123178i
$832$	1.81509	−	1.81509i	0.0629271	−	0.0629271i
$833$	6.85971	+	25.2440i	0.237675	+	0.874652i
$834$	0.341022	+	0.110805i	0.0118086	+	0.00383686i
$835$		0			0
$836$	−14.0878	+	66.2781i	−0.487238	+	2.29227i
$837$	0.209856	−	4.00429i	0.00725368	−	0.138409i
$838$	−0.0912929	−	0.0592863i	−0.00315366	−	0.00204801i
$839$	8.56984	+	26.3753i	0.295864	+	0.910575i	0.982930	+	0.183980i	$0.0588982\pi$
$839$	8.56984	+	26.3753i	0.295864	+	0.910575i	−0.687066	+	0.726595i	$0.741102\pi$
$840$		0			0
$841$	5.39836	−	16.6145i	0.186150	−	0.572912i
$842$	−0.295990	+	0.239688i	−0.0102005	+	0.00826019i
$843$	31.2079	−	8.36213i	1.07486	−	0.288007i
$844$	−22.9933	−	51.6438i	−0.791462	−	1.77765i
$845$		0			0
$846$	0.109344	+	0.150499i	0.00375931	+	0.00517425i
$847$	−4.00320	+	38.7457i	−0.137552	+	1.33132i
$848$	−40.2368	−	20.5017i	−1.38174	−	0.704030i
$849$	27.5654	−	15.9149i	0.946042	−	0.546198i
$850$		0			0
$851$	−5.63304	+	9.75671i	−0.193098	+	0.334456i
$852$	0.536774	+	10.2423i	0.0183896	+	0.350894i
$853$	30.3919	+	4.81360i	1.04060	+	0.164815i	0.653268	−	0.757126i	$-0.273397\pi$
$853$	30.3919	+	4.81360i	1.04060	+	0.164815i	0.387330	+	0.921941i	$0.373397\pi$
$854$	0.0444406	−	0.116385i	0.00152073	−	0.00398263i
$855$		0			0
$856$	0.0745154	−	0.708966i	0.00254688	−	0.0242320i
$857$	1.08695	+	4.05654i	0.0371294	+	0.138569i	0.982002	−	0.188868i	$-0.0604818\pi$
$857$	1.08695	+	4.05654i	0.0371294	+	0.138569i	−0.944873	+	0.327437i	$0.893815\pi$
$858$	−0.0113391	+	0.0295394i	−0.000387110	+	0.00100846i
$859$	7.03428	−	1.49518i	0.240006	−	0.0510149i	−0.0863379	−	0.996266i	$-0.527516\pi$
$859$	7.03428	−	1.49518i	0.240006	−	0.0510149i	0.326344	+	0.945251i	$0.394183\pi$
$860$		0			0
$861$	19.3099	+	15.5805i	0.658078	+	0.530981i
$862$	−0.148930	+	0.0758837i	−0.00507258	+	0.00258461i
$863$	5.37498	−	8.27674i	0.182966	−	0.281743i	−0.735272	−	0.677773i	$-0.762945\pi$
$863$	5.37498	−	8.27674i	0.182966	−	0.281743i	0.918238	+	0.396029i	$0.129612\pi$
$864$	−1.07619	−	0.228750i	−0.0366126	−	0.00778224i
$865$		0			0
$866$	−0.0444367	−	0.209058i	−0.00151002	−	0.00710408i
$867$	−3.38990	+	0.536908i	−0.115127	+	0.0182343i
$868$	2.65337	−	2.95735i	0.0900613	−	0.100379i
$869$	24.4604	−	33.6668i	0.829761	−	1.14207i
$870$		0			0
$871$	−2.08534	+	0.219178i	−0.0706589	+	0.00742655i
$872$	−0.393411	+	0.485822i	−0.0133226	+	0.0164520i
$873$	21.3446	−	1.11862i	0.722404	−	0.0378596i
$874$	0.392224			0.0132672
$875$		0			0
$876$	−22.8531			−0.772133
$877$	32.6864	−	1.71302i	1.10374	−	0.0578445i	0.508252	−	0.861209i	$-0.330292\pi$
$877$	32.6864	−	1.71302i	1.10374	−	0.0578445i	0.595488	+	0.803364i	$0.296959\pi$
$878$	−0.265166	+	0.327453i	−0.00894891	+	0.0110510i
$879$	−7.26621	+	0.763709i	−0.245083	+	0.0257593i
$880$		0			0
$881$	−11.3837	+	15.6683i	−0.383527	+	0.527880i	−0.956515	−	0.291684i	$-0.905784\pi$
$881$	−11.3837	+	15.6683i	−0.383527	+	0.527880i	0.572988	+	0.819564i	$0.305784\pi$
$882$	−0.161221	−	0.129615i	−0.00542861	−	0.00436436i
$883$	−36.1203	+	5.72089i	−1.21554	+	0.192523i	−0.731082	−	0.682289i	$-0.760984\pi$
$883$	−36.1203	+	5.72089i	−1.21554	+	0.192523i	−0.484461	+	0.874813i	$0.660984\pi$
$884$	−0.498980	−	2.34752i	−0.0167825	−	0.0789556i
$885$		0			0
$886$	0.117722	+	0.0250226i	0.00395495	+	0.000840650i
$887$	6.23155	−	9.59574i	0.209235	−	0.322194i	−0.718435	−	0.695594i	$-0.755141\pi$
$887$	6.23155	−	9.59574i	0.209235	−	0.322194i	0.927670	+	0.373400i	$0.121808\pi$
$888$	−0.228174	+	0.116260i	−0.00765701	+	0.00390144i
$889$	−42.1812	−	6.60455i	−1.41471	−	0.221509i
$890$		0			0
$891$	−4.35255	+	0.925162i	−0.145816	+	0.0309941i
$892$	15.1716	−	39.5234i	0.507983	−	1.32334i
$893$	10.8850	+	40.6235i	0.364253	+	1.35941i
$894$	0.0299493	−	0.284948i	0.00100165	−	0.00953010i
$895$		0			0
$896$	−0.916741	−	1.12800i	−0.0306262	−	0.0376839i
$897$	−1.22637	−	0.194238i	−0.0409474	−	0.00648543i
$898$	0.0102269	+	0.195140i	0.000341275	+	0.00651192i
$899$	1.27503	−	2.20841i	0.0425246	−	0.0736547i
$900$		0			0
$901$	−36.5540	+	21.1045i	−1.21779	+	0.703091i
$902$	0.643490	+	0.327875i	0.0214259	+	0.0109170i
$903$	−15.4358	+	6.90514i	−0.513672	+	0.229789i
$904$	−0.344529	−	0.474204i	−0.0114589	−	0.0157718i
$905$		0			0
$906$	−0.0443454	−	0.0996015i	−0.00147328	−	0.00330904i
$907$	0.668595	−	0.179150i	0.0222003	−	0.00594856i	−0.247702	−	0.968836i	$-0.579675\pi$
$907$	0.668595	−	0.179150i	0.0222003	−	0.00594856i	0.269902	+	0.962888i	$0.413009\pi$
$908$	30.9906	−	25.0957i	1.02846	−	0.832831i
$909$	−6.25905	+	19.2634i	−0.207600	+	0.638926i
$910$		0			0
$911$	7.30607	+	22.4858i	0.242061	+	0.744987i	0.996106	+	0.0881643i	$0.0281000\pi$
$911$	7.30607	+	22.4858i	0.242061	+	0.744987i	−0.754045	+	0.656823i	$0.771900\pi$
$912$	−25.3394	−	16.4556i	−0.839071	−	0.544899i
$913$	0.344749	−	6.57821i	0.0114095	−	0.217707i
$914$	0.0244848	−	0.115192i	0.000809886	−	0.00381021i
$915$		0			0
$916$	19.0991	+	6.20568i	0.631053	+	0.205042i
$917$	−1.65290	−	7.70934i	−0.0545835	−	0.254585i
$918$	−0.242327	+	0.242327i	−0.00799798	+	0.00799798i
$919$	−7.72720	−	0.812161i	−0.254897	−	0.0267907i	−0.0237818	−	0.999717i	$-0.507571\pi$
$919$	−7.72720	−	0.812161i	−0.254897	−	0.0267907i	−0.231115	+	0.972926i	$0.574237\pi$
$920$		0			0
$921$	−2.08913	−	19.8767i	−0.0688391	−	0.654960i
$922$	0.104497	−	0.0401126i	0.00344142	−	0.00132104i
$923$	0.661131	−	1.29754i	0.0217614	−	0.0427091i
$924$	−27.0667	−	13.7310i	−0.890429	−	0.451718i
$925$		0			0
$926$	0.0385095	+	0.0667005i	0.00126550	+	0.00219191i
$927$	−21.2753	+	13.8163i	−0.698772	+	0.453788i
$928$	−0.543768	−	0.440335i	−0.0178501	−	0.0144547i
$929$	50.4013	+	22.4401i	1.65361	+	0.736236i	0.999792	−	0.0204117i	$-0.00649769\pi$
$929$	50.4013	+	22.4401i	1.65361	+	0.736236i	0.653822	+	0.756648i	$0.273164\pi$
$930$		0			0
$931$	−23.5264	−	40.4188i	−0.771048	−	1.32467i
$932$	3.94681	+	3.94681i	0.129282	+	0.129282i
$933$	5.32256	+	6.57281i	0.174253	+	0.215184i
$934$	−0.461678	−	0.512745i	−0.0151066	−	0.0167775i
$935$		0			0
$936$	0.0282095	+	0.0253999i	0.000922056	+	0.000830223i
$937$	15.4139	+	30.2515i	0.503551	+	0.988274i	0.993207	+	0.116358i	$0.0371221\pi$
$937$	15.4139	+	30.2515i	0.503551	+	0.988274i	−0.489657	+	0.871915i	$0.662878\pi$
$938$	0.000523698		0.296683i	1.70994e−5		0.00968704i
$939$	29.9400	−	9.72811i	0.977057	−	0.317465i
$940$		0			0
$941$	−17.2943	+	15.5719i	−0.563779	+	0.507629i	−0.901013	−	0.433792i	$-0.857175\pi$
$941$	−17.2943	+	15.5719i	−0.563779	+	0.507629i	0.337234	+	0.941421i	$0.390509\pi$
$942$	0.0951439	+	0.0365223i	0.00309995	+	0.00118996i
$943$	−7.33518	+	27.3753i	−0.238866	+	0.891462i
$944$	−30.9319	−	22.4733i	−1.00675	−	0.731444i
$945$		0			0
$946$	−0.398202	+	0.289311i	−0.0129467	+	0.00940630i
$947$	11.5591	+	30.1124i	0.375619	+	0.978521i	0.982917	+	0.184047i	$0.0589200\pi$
$947$	11.5591	+	30.1124i	0.375619	+	0.978521i	−0.607298	+	0.794474i	$0.707747\pi$
$948$	10.1078	+	15.5646i	0.328286	+	0.505516i
$949$	2.81012	+	1.62242i	0.0912202	+	0.0526660i
$950$		0			0
$951$			32.3214i			1.04809i
$952$	−0.675353	+	0.0721879i	−0.0218883	+	0.00233962i
$953$	4.45329	−	28.1170i	0.144256	−	0.910797i	−0.804308	−	0.594213i	$-0.797464\pi$
$953$	4.45329	−	28.1170i	0.144256	−	0.910797i	0.948564	−	0.316585i	$-0.102536\pi$
$954$	0.135760	−	0.304923i	0.00439540	−	0.00987224i
$955$		0			0
$956$	−7.60946	+	3.38795i	−0.246107	+	0.109574i
$957$	−18.8156	−	5.04162i	−0.608222	−	0.162973i
$958$	−0.0557136	−	0.351762i	−0.00180002	−	0.0113649i
$959$	−39.4878	+	10.6555i	−1.27513	+	0.344083i
$960$		0			0
$961$	20.3657	−	22.6184i	0.656958	−	0.729625i
$962$	0.0181542		0.000951419i	0.000585314		3.06750e-5i
$963$	−17.8316	−	0.934516i	−0.574616	−	0.0301144i
$964$	−9.49755	+	10.5481i	−0.305896	+	0.339732i
$965$		0			0
$966$	−0.0451709	+	0.169778i	−0.00145335	+	0.00546253i
$967$	−3.33883	−	21.0805i	−0.107369	−	0.677904i	−0.981391	−	0.192018i	$-0.938497\pi$
$967$	−3.33883	−	21.0805i	−0.107369	−	0.677904i	0.874022	−	0.485886i	$-0.161503\pi$
$968$	−0.976883	−	0.261755i	−0.0313982	−	0.00841312i
$969$	−25.7986	+	11.4863i	−0.828772	+	0.368993i
$970$		0			0
$971$	21.6561	−	48.6404i	0.694978	−	1.56095i	−0.127302	−	0.991864i	$-0.540632\pi$
$971$	21.6561	−	48.6404i	0.694978	−	1.56095i	0.822281	−	0.569082i	$-0.192701\pi$
$972$	−4.70046	+	29.6775i	−0.150767	+	0.951908i
$973$	39.4585	−	28.7749i	1.26498	−	0.922479i
$974$			0.127666i			0.00409070i
$975$		0			0
$976$	−9.49319	−	5.48089i	−0.303870	−	0.175439i
$977$	20.2636	+	31.2032i	0.648289	+	0.998278i	0.998109	+	0.0614611i	$0.0195760\pi$
$977$	20.2636	+	31.2032i	0.648289	+	0.998278i	−0.349820	+	0.936817i	$0.613757\pi$
$978$	0.123648	+	0.322114i	0.00395383	+	0.0103001i
$979$	−4.06771	+	2.95536i	−0.130005	+	0.0944538i
$980$		0			0
$981$	12.6680	+	9.20384i	0.404458	+	0.293856i
$982$	−0.0902509	+	0.336821i	−0.00288002	+	0.0107484i
$983$	−18.7129	−	7.18320i	−0.596848	−	0.229109i	0.0411417	−	0.999153i	$-0.486900\pi$
$983$	−18.7129	−	7.18320i	−0.596848	−	0.229109i	−0.637990	+	0.770045i	$0.720234\pi$
$984$	−0.478740	+	0.431060i	−0.0152617	+	0.0137417i
$985$		0			0
$986$	−0.207277	+	0.0673484i	−0.00660105	+	0.00214481i
$987$	−18.8379	+	0.0332522i	−0.599616	+	0.00105843i
$988$	1.94789	+	3.82295i	0.0619707	+	0.121624i
$989$	−14.3540	−	12.9244i	−0.456431	−	0.410972i
$990$		0			0
$991$	−26.5931	−	29.5346i	−0.844756	−	0.938197i	0.153999	−	0.988071i	$-0.450785\pi$
$991$	−26.5931	−	29.5346i	−0.844756	−	0.938197i	−0.998756	+	0.0498742i	$0.984118\pi$
$992$	0.0973831	+	0.120258i	0.00309192	+	0.00381820i
$993$	−13.3562	−	13.3562i	−0.423847	−	0.423847i
$994$	−0.173005	−	0.111917i	−0.00548740	−	0.00354980i
$995$		0			0
$996$	2.68372	+	1.19487i	0.0850369	+	0.0378609i
$997$	−8.84910	−	7.16586i	−0.280254	−	0.226945i	0.478879	−	0.877881i	$-0.341043\pi$
$997$	−8.84910	−	7.16586i	−0.280254	−	0.226945i	−0.759133	+	0.650936i	$0.774377\pi$
$998$	−0.132592	+	0.0861063i	−0.00419713	+	0.00272565i
$999$	8.79910	+	15.2405i	0.278391	+	0.482188i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.857.9		288
5.2	odd	4		175.2.x.a.108.9	yes	288
5.3	odd	4		875.2.bb.c.143.10		288
5.4	even	2		875.2.bb.b.857.10		288
7.5	odd	6	inner	875.2.bb.a.607.10		288
25.3	odd	20	inner	875.2.bb.a.493.10		288
25.4	even	10		175.2.x.a.122.9	yes	288
25.21	even	5		875.2.bb.c.507.10		288
25.22	odd	20		875.2.bb.b.493.9		288
35.12	even	12		175.2.x.a.33.9	✓	288
35.19	odd	6		875.2.bb.b.607.9		288
35.33	even	12		875.2.bb.c.768.10		288
175.47	even	60		875.2.bb.b.243.10		288
175.54	odd	30		175.2.x.a.47.9	yes	288
175.96	odd	30		875.2.bb.c.257.10		288
175.103	even	60	inner	875.2.bb.a.243.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.9	✓	288	35.12	even	12
175.2.x.a.47.9	yes	288	175.54	odd	30
175.2.x.a.108.9	yes	288	5.2	odd	4
175.2.x.a.122.9	yes	288	25.4	even	10
875.2.bb.a.243.9		288	175.103	even	60	inner
875.2.bb.a.493.10		288	25.3	odd	20	inner
875.2.bb.a.607.10		288	7.5	odd	6	inner
875.2.bb.a.857.9		288	1.1	even	1	trivial
875.2.bb.b.243.10		288	175.47	even	60
875.2.bb.b.493.9		288	25.22	odd	20
875.2.bb.b.607.9		288	35.19	odd	6
875.2.bb.b.857.10		288	5.4	even	2
875.2.bb.c.143.10		288	5.3	odd	4
875.2.bb.c.257.10		288	175.96	odd	30
875.2.bb.c.507.10		288	25.21	even	5
875.2.bb.c.768.10		288	35.33	even	12

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0171512 - 0.000898858i) q^{2} +(-0.711812 + 0.879015i) q^{3} +(-1.98875 + 0.209026i) q^{4} +(-0.0114183 + 0.0157160i) q^{6} +(0.822022 + 2.51481i) q^{7} +(-0.0678483 + 0.0107461i) q^{8} +(0.357745 + 1.68306i) q^{9} +(-4.96090 - 1.05447i) q^{11} +(1.23188 - 1.89693i) q^{12} +(-0.286147 + 0.145799i) q^{13} +(0.0163592 + 0.0423932i) q^{14} +(3.91086 - 0.831279i) q^{16} +(1.33924 - 3.48884i) q^{17} +(0.00764859 + 0.0285449i) q^{18} +(-0.698358 + 6.64443i) q^{19} +(-2.79568 - 1.06750i) q^{21} +(-0.0860334 - 0.0136263i) q^{22} +(-0.178896 - 3.41354i) q^{23} +(0.0388492 - 0.0672888i) q^{24} +(-0.00477673 + 0.00275784i) q^{26} +(-4.75748 - 2.42406i) q^{27} +(-2.16046 - 4.82951i) q^{28} +(-1.99592 - 2.74715i) q^{29} +(0.305449 + 0.686049i) q^{31} +(0.199035 - 0.0533314i) q^{32} +(4.45813 - 3.61012i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-1.06327 - 3.27240i) q^{36} +(-2.76416 - 1.79507i) q^{37} +(-0.00600530 + 0.114588i) q^{38} +(0.0755233 - 0.355309i) q^{39} +(-7.88534 - 2.56210i) q^{41} +(-0.0489089 - 0.0157961i) q^{42} +(3.99562 - 3.99562i) q^{43} +(10.0864 + 1.06012i) q^{44} +(-0.00613657 - 0.0583856i) q^{46} +(5.87681 - 2.25590i) q^{47} +(-2.05309 + 4.02942i) q^{48} +(-5.64856 + 4.13446i) q^{49} +(2.11346 + 3.66061i) q^{51} +(0.538600 - 0.349771i) q^{52} +(-8.77763 - 7.10798i) q^{53} +(-0.0837755 - 0.0372993i) q^{54} +(-0.0827972 - 0.161792i) q^{56} +(-5.34345 - 5.34345i) q^{57} +(-0.0367018 - 0.0453229i) q^{58} +(-6.39870 - 7.10647i) q^{59} +(-2.03745 - 1.83453i) q^{61} +(0.00585548 + 0.0114920i) q^{62} +(-3.93850 + 2.28317i) q^{63} +(-7.60172 + 2.46995i) q^{64} +(0.0732173 - 0.0659252i) q^{66} +(6.09544 + 2.33982i) q^{67} +(-1.93416 + 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-3.66851 + 2.66533i) q^{71} +(-0.0423587 - 0.110348i) q^{72} +(-5.50292 - 8.47376i) q^{73} +(-0.0490223 - 0.0283030i) q^{74} -13.3601i q^{76} +(-1.42617 - 13.3425i) q^{77} +(0.000975946 - 0.00616188i) q^{78} +(-3.33735 + 7.49580i) q^{79} +(0.801517 - 0.356859i) q^{81} +(-0.137546 - 0.0368554i) q^{82} +(0.203179 + 1.28282i) q^{83} +(5.78305 + 1.53863i) q^{84} +(0.0649383 - 0.0721212i) q^{86} +(3.83550 + 0.201010i) q^{87} +(0.347920 + 0.0182337i) q^{88} +(0.663356 - 0.736732i) q^{89} +(-0.601877 - 0.599756i) q^{91} +(1.06930 + 6.75128i) q^{92} +(-0.820470 - 0.219844i) q^{93} +(0.0987668 - 0.0439738i) q^{94} +(-0.0947968 + 0.212917i) q^{96} +(1.94322 - 12.2690i) q^{97} +(-0.0931634 + 0.0759884i) q^{98} -8.72671i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more