LMFDB - Embedded newform 875.2.bb.c.768.10

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 = [288,8] 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			768.10
Character	$\chi$	$=$	875.768
Dual form			875.2.bb.c.507.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0144040 + 0.00935405i) q^{2} +(-1.05595 + 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(0.0114183 - 0.0157160i) q^{6} +(0.822022 - 2.51481i) q^{7} +(-0.0107461 - 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +(3.39365 - 3.76903i) q^{11} +(0.118375 - 2.25873i) q^{12} +(0.145799 + 0.286147i) q^{13} +(0.0116833 + 0.0439125i) q^{14} +(-2.67534 - 2.97126i) q^{16} +(-2.90424 + 2.35181i) q^{17} +(0.00764859 - 0.0285449i) q^{18} +(6.10342 - 2.71742i) q^{19} +(0.151343 + 2.98873i) q^{21} +(-0.0136263 + 0.0860334i) q^{22} +(-1.86170 - 2.86676i) q^{23} +(0.0388492 + 0.0672888i) q^{24} +(-0.00477673 - 0.00275784i) q^{26} +(2.42406 - 4.75748i) q^{27} +(3.92552 + 3.54712i) q^{28} +(1.99592 + 2.74715i) q^{29} +(0.746861 + 0.0784982i) q^{31} +(0.199035 + 0.0533314i) q^{32} +(-2.05579 + 5.35552i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-1.06327 - 3.27240i) q^{36} +(3.29137 + 0.172493i) q^{37} +(-0.0624947 + 0.0962334i) q^{38} +(-0.269945 - 0.243060i) q^{39} +(7.88534 + 2.56210i) q^{41} +(-0.0301367 - 0.0416339i) q^{42} +(3.99562 + 3.99562i) q^{43} +(4.12511 + 9.26514i) q^{44} +(0.0536317 + 0.0238784i) q^{46} +(3.96152 - 4.89207i) q^{47} +(4.02942 + 2.05309i) q^{48} +(-5.64856 - 4.13446i) q^{49} +(2.11346 - 3.66061i) q^{51} +(-0.641326 + 0.0336105i) q^{52} +(4.04766 + 10.5445i) q^{53} +(0.00958565 + 0.0912013i) q^{54} +(-0.179459 - 0.0287484i) q^{56} +(-5.34345 + 5.34345i) q^{57} +(-0.0544462 - 0.0208999i) q^{58} +(9.35373 - 1.98820i) q^{59} +(0.570023 - 2.68175i) q^{61} +(-0.0114920 + 0.00585548i) q^{62} +(1.84430 + 4.16211i) q^{63} +(7.60172 - 2.46995i) q^{64} +(-0.0204842 - 0.0963707i) q^{66} +(4.10889 + 5.07406i) q^{67} +(-1.93416 - 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-3.66851 + 2.66533i) q^{71} +(0.0918577 + 0.0743849i) q^{72} +(-0.528792 - 10.0900i) q^{73} +(-0.0490223 + 0.0283030i) q^{74} +13.3601i q^{76} +(-6.68874 - 11.6326i) q^{77} +(0.00616188 + 0.000975946i) q^{78} +(-8.16023 + 0.857674i) q^{79} +(-0.0917101 + 0.872564i) q^{81} +(-0.137546 + 0.0368554i) q^{82} +(1.28282 - 0.203179i) q^{83} +(-5.58297 - 2.15442i) q^{84} +(-0.0949280 - 0.0201776i) q^{86} +(-3.22114 - 2.09183i) q^{87} +(-0.292191 - 0.189751i) q^{88} +(-0.969707 - 0.206118i) q^{89} +(0.839457 - 0.131438i) q^{91} +(6.75128 - 1.06930i) q^{92} +(-0.820470 + 0.219844i) q^{93} +(-0.0113010 + 0.107521i) q^{94} +(-0.231790 + 0.0243621i) q^{96} +(12.2690 + 1.94322i) q^{97} +(0.120036 + 0.00671581i) q^{98} +8.72671i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{3}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.0144040	+	0.00935405i	−0.0101851	+	0.00661431i	−0.549722	−	0.835348i	$-0.685266\pi$
$2$	−0.0144040	+	0.00935405i	−0.0101851	+	0.00661431i	0.539536	+	0.841962i	$0.318600\pi$
$3$	−1.05595	+	0.405343i	−0.609656	+	0.234025i	−0.643554	−	0.765400i	$-0.722541\pi$
$3$	−1.05595	+	0.405343i	−0.609656	+	0.234025i	0.0338987	+	0.999425i	$0.489208\pi$
$4$	−0.813353	+	1.82682i	−0.406677	+	0.913411i
$5$		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
$8$	−0.0107461	−	0.0678483i	−0.00379932	−	0.0239880i
$9$	−1.27870	+	1.15134i	−0.426232	+	0.383781i
$10$		0			0
$11$	3.39365	−	3.76903i	1.02322	−	1.13641i	0.0326443	−	0.999467i	$-0.489607\pi$
$11$	3.39365	−	3.76903i	1.02322	−	1.13641i	0.990580	−	0.136938i	$-0.0437262\pi$
$12$	0.118375	−	2.25873i	0.0341719	−	0.652039i
$13$	0.145799	+	0.286147i	0.0404375	+	0.0793630i	0.910341	−	0.413859i	$-0.135819\pi$
$13$	0.145799	+	0.286147i	0.0404375	+	0.0793630i	−0.869904	+	0.493222i	$0.835819\pi$
$14$	0.0116833	+	0.0439125i	0.00312249	+	0.0117361i
$15$		0			0
$16$	−2.67534	−	2.97126i	−0.668835	−	0.742816i
$17$	−2.90424	+	2.35181i	−0.704381	+	0.570397i	−0.913177	−	0.407562i	$-0.866379\pi$
$17$	−2.90424	+	2.35181i	−0.704381	+	0.570397i	0.208796	+	0.977959i	$0.433046\pi$
$18$	0.00764859	−	0.0285449i	0.00180279	−	0.00672810i
$19$	6.10342	−	2.71742i	1.40022	−	0.623419i	0.438822	−	0.898574i	$-0.355396\pi$
$19$	6.10342	−	2.71742i	1.40022	−	0.623419i	0.961400	+	0.275155i	$0.0887293\pi$
$20$		0			0
$21$	0.151343	+	2.98873i	0.0330257	+	0.652194i
$22$	−0.0136263	+	0.0860334i	−0.00290515	+	0.0183424i
$23$	−1.86170	−	2.86676i	−0.388191	−	0.597762i	0.589511	−	0.807761i	$-0.299321\pi$
$23$	−1.86170	−	2.86676i	−0.388191	−	0.597762i	−0.977702	+	0.209999i	$0.932654\pi$
$24$	0.0388492	+	0.0672888i	0.00793006	+	0.0137353i
$25$		0			0
$26$	−0.00477673	−	0.00275784i	−0.000936793	−	0.000540858i
$27$	2.42406	−	4.75748i	0.466510	−	0.915577i
$28$	3.92552	+	3.54712i	0.741853	+	0.670342i
$29$	1.99592	+	2.74715i	0.370633	+	0.510133i	0.953073	−	0.302741i	$-0.0979018\pi$
$29$	1.99592	+	2.74715i	0.370633	+	0.510133i	−0.582440	+	0.812874i	$0.697902\pi$
$30$		0			0
$31$	0.746861	+	0.0784982i	0.134140	+	0.0140987i	0.171361	−	0.985208i	$-0.445184\pi$
$31$	0.746861	+	0.0784982i	0.134140	+	0.0140987i	−0.0372204	+	0.999307i	$0.511850\pi$
$32$	0.199035	+	0.0533314i	0.0351848	+	0.00942775i
$33$	−2.05579	+	5.35552i	−0.357867	+	0.932276i
$34$	0.0198337	−	0.0610417i	0.00340145	−	0.0104686i
$35$		0			0
$36$	−1.06327	−	3.27240i	−0.177211	−	0.545400i
$37$	3.29137	+	0.172493i	0.541098	+	0.0283577i	0.320928	−	0.947104i	$-0.396005\pi$
$37$	3.29137	+	0.172493i	0.541098	+	0.0283577i	0.220170	+	0.975461i	$0.429339\pi$
$38$	−0.0624947	+	0.0962334i	−0.0101380	+	0.0156111i
$39$	−0.269945	−	0.243060i	−0.0432258	−	0.0389207i
$40$		0			0
$41$	7.88534	+	2.56210i	1.23148	+	0.400133i	0.851252	−	0.524758i	$-0.175844\pi$
$41$	7.88534	+	2.56210i	1.23148	+	0.400133i	0.380232	+	0.924891i	$0.375844\pi$
$42$	−0.0301367	−	0.0416339i	−0.00465019	−	0.00642425i
$43$	3.99562	+	3.99562i	0.609326	+	0.609326i	0.942770	−	0.333444i	$-0.108211\pi$
$43$	3.99562	+	3.99562i	0.609326	+	0.609326i	−0.333444	+	0.942770i	$0.608211\pi$
$44$	4.12511	+	9.26514i	0.621883	+	1.39677i
$45$		0			0
$46$	0.0536317	+	0.0238784i	0.00790756	+	0.00352067i
$47$	3.96152	−	4.89207i	0.577847	−	0.713581i	−0.401480	−	0.915868i	$-0.631504\pi$
$47$	3.96152	−	4.89207i	0.577847	−	0.713581i	0.979326	+	0.202287i	$0.0648373\pi$
$48$	4.02942	+	2.05309i	0.581596	+	0.296338i
$49$	−5.64856	−	4.13446i	−0.806937	−	0.590638i
$50$		0			0
$51$	2.11346	−	3.66061i	0.295943	−	0.512588i
$52$	−0.641326	+	0.0336105i	−0.0889360	+	0.00466094i
$53$	4.04766	+	10.5445i	0.555988	+	1.44840i	0.867152	+	0.498043i	$0.165948\pi$
$53$	4.04766	+	10.5445i	0.555988	+	1.44840i	−0.311164	+	0.950356i	$0.600719\pi$
$54$	0.00958565	+	0.0912013i	0.00130444	+	0.0124109i
$55$		0			0
$56$	−0.179459	−	0.0287484i	−0.0239812	−	0.00384166i
$57$	−5.34345	+	5.34345i	−0.707757	+	0.707757i
$58$	−0.0544462	−	0.0208999i	−0.00714913	−	0.00274429i
$59$	9.35373	−	1.98820i	1.21775	−	0.258841i	0.446157	−	0.894955i	$-0.352792\pi$
$59$	9.35373	−	1.98820i	1.21775	−	0.258841i	0.771595	+	0.636114i	$0.219459\pi$
$60$		0			0
$61$	0.570023	−	2.68175i	0.0729840	−	0.343363i	−0.926471	−	0.376365i	$-0.877174\pi$
$61$	0.570023	−	2.68175i	0.0729840	−	0.343363i	0.999455	+	0.0330028i	$0.0105070\pi$
$62$	−0.0114920	+	0.00585548i	−0.00145949	+	0.000743647i
$63$	1.84430	+	4.16211i	0.232359	+	0.524377i
$64$	7.60172	−	2.46995i	0.950215	−	0.308744i
$65$		0			0
$66$	−0.0204842	−	0.0963707i	−0.00252143	−	0.0118624i
$67$	4.10889	+	5.07406i	0.501981	+	0.619895i	0.963653	−	0.267155i	$-0.0860837\pi$
$67$	4.10889	+	5.07406i	0.501981	+	0.619895i	−0.461672	+	0.887051i	$0.652750\pi$
$68$	−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	$0.386718\pi$
$72$	0.0918577	+	0.0743849i	0.0108255	+	0.00876635i
$73$	−0.528792	−	10.0900i	−0.0618904	−	1.18094i	−0.836306	−	0.548263i	$-0.815289\pi$
$73$	−0.528792	−	10.0900i	−0.0618904	−	1.18094i	0.774416	−	0.632677i	$-0.218044\pi$
$74$	−0.0490223	+	0.0283030i	−0.00569873	+	0.00329016i
$75$		0			0
$76$			13.3601i			1.53251i
$77$	−6.68874	−	11.6326i	−0.762253	−	1.32566i
$78$	0.00616188		0.000975946i	0.000697695		0.000110504i
$79$	−8.16023	+	0.857674i	−0.918097	+	0.0964959i	−0.551776	−	0.833992i	$-0.686050\pi$
$79$	−8.16023	+	0.857674i	−0.918097	+	0.0964959i	−0.366321	+	0.930488i	$0.619383\pi$
$80$		0			0
$81$	−0.0917101	+	0.872564i	−0.0101900	+	0.0969515i
$82$	−0.137546	+	0.0368554i	−0.0151894	+	0.00407000i
$83$	1.28282	−	0.203179i	0.140808	−	0.0223018i	−0.0856324	−	0.996327i	$-0.527291\pi$
$83$	1.28282	−	0.203179i	0.140808	−	0.0223018i	0.226441	+	0.974025i	$0.427291\pi$
$84$	−5.58297	−	2.15442i	−0.609152	−	0.235066i
$85$		0			0
$86$	−0.0949280	−	0.0201776i	−0.0102363	−	0.00217580i
$87$	−3.22114	−	2.09183i	−0.345342	−	0.224268i
$88$	−0.292191	−	0.189751i	−0.0311476	−	0.0202275i
$89$	−0.969707	−	0.206118i	−0.102789	−	0.0218484i	0.156230	−	0.987721i	$-0.450066\pi$
$89$	−0.969707	−	0.206118i	−0.102789	−	0.0218484i	−0.259019	+	0.965872i	$0.583399\pi$
$90$		0			0
$91$	0.839457	−	0.131438i	0.0879990	−	0.0137785i
$92$	6.75128	−	1.06930i	0.703870	−	0.111482i
$93$	−0.820470	+	0.219844i	−0.0850787	+	0.0227968i
$94$	−0.0113010	+	0.107521i	−0.00116560	+	0.0110900i
$95$		0			0
$96$	−0.231790	+	0.0243621i	−0.0236570	+	0.00248645i
$97$	12.2690	+	1.94322i	1.24573	+	0.197304i	0.744270	−	0.667879i	$-0.232798\pi$
$97$	12.2690	+	1.94322i	1.24573	+	0.197304i	0.501457	+	0.865183i	$0.332798\pi$
$98$	0.120036	+	0.00671581i	0.0121254	+	0.000678400i
$99$			8.72671i			0.877067i
$100$		0			0
$101$	10.1944	−	5.88575i	1.01438	−	0.585654i	0.101911	−	0.994794i	$-0.467504\pi$
$101$	10.1944	−	5.88575i	1.01438	−	0.585654i	0.912472	+	0.409139i	$0.134171\pi$
$102$	0.00379939	+	0.0724967i	0.000376196	+	0.00717825i
$103$	−11.4576	−	9.27815i	−1.12895	−	0.914203i	−0.131920	−	0.991260i	$-0.542114\pi$
$103$	−11.4576	−	9.27815i	−1.12895	−	0.914203i	−0.997027	+	0.0770569i	$0.975448\pi$
$104$	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	−0.965441	−	0.260621i	$-0.916073\pi$
$107$	−2.68589	−	10.0239i	−0.259655	−	0.969046i	0.705786	−	0.708425i	$-0.250594\pi$
$108$	6.71945	+	8.29783i	0.646579	+	0.798459i
$109$	−1.89206	−	8.90145i	−0.181227	−	0.852604i	−0.970976	−	0.239175i	$-0.923123\pi$
$109$	−1.89206	−	8.90145i	−0.181227	−	0.852604i	0.789750	−	0.613429i	$-0.210210\pi$
$110$		0			0
$111$	−3.54546	+	1.15199i	−0.336520	+	0.109342i
$112$	−9.67136	+	4.28553i	−0.913857	+	0.404944i
$113$	−7.60273	+	3.87378i	−0.715204	+	0.364415i	−0.773424	−	0.633889i	$-0.781458\pi$
$113$	−7.60273	+	3.87378i	−0.715204	+	0.364415i	0.0582196	+	0.998304i	$0.481458\pi$
$114$	0.0269840	−	0.126950i	0.00252729	−	0.0118899i
$115$		0			0
$116$	−6.64194	+	1.41179i	−0.616689	+	0.131081i
$117$	−0.515887	−	0.198031i	−0.0476938	−	0.0183079i
$118$	−0.116133	+	0.116133i	−0.0106909	+	0.0106909i
$119$	3.52700	+	9.23685i	0.323320	+	0.846741i
$120$		0			0
$121$	−1.53891	−	14.6418i	−0.139901	−	1.33107i
$122$	0.0168746	+	0.0439598i	0.00152775	+	0.00397994i
$123$	−9.36510	+	0.490804i	−0.844422	+	0.0442543i
$124$	−0.750864	+	1.30053i	−0.0674296	+	0.116791i
$125$		0			0
$126$	−0.0654978	−	0.0426993i	−0.00583501	−	0.00380396i
$127$	14.3784	+	7.32616i	1.27588	+	0.650091i	0.954881	−	0.296989i	$-0.0959826\pi$
$127$	14.3784	+	7.32616i	1.27588	+	0.650091i	0.320996	+	0.947081i	$0.395983\pi$
$128$	−0.345742	+	0.426956i	−0.0305596	+	0.0377379i
$129$	−5.83879	−	2.59960i	−0.514076	−	0.228882i
$130$		0			0
$131$	−1.21211	−	2.72244i	−0.105902	−	0.237860i	0.852820	−	0.522205i	$-0.174891\pi$
$131$	−1.21211	−	2.72244i	−0.105902	−	0.237860i	−0.958722	+	0.284345i	$0.908224\pi$
$132$	−8.11149	−	8.11149i	−0.706015	−	0.706015i
$133$	−1.81665	−	17.5827i	−0.157523	−	1.52462i
$134$	−0.106647	−	0.0346518i	−0.00921293	−	0.00299346i
$135$		0			0
$136$	0.190775	+	0.171775i	0.0163588	+	0.0147296i
$137$	−8.41948	+	12.9649i	−0.719324	+	1.10766i	0.270131	+	0.962824i	$0.412933\pi$
$137$	−8.41948	+	12.9649i	−0.719324	+	1.10766i	−0.989455	+	0.144839i	$0.953734\pi$
$138$	−0.0663116	−	0.00347524i	−0.00564482	−	0.000295832i
$139$	−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
$142$	0.0279095	−	0.0727067i	0.00234211	−	0.00610141i
$143$	1.57329	+	0.421562i	0.131565	+	0.0352528i
$144$	6.84189	+	0.719112i	0.570158	+	0.0599260i
$145$		0			0
$146$	0.101999	+	0.140389i	0.00844147	+	0.0116187i
$147$	7.64050	+	2.07620i	0.630178	+	0.171242i
$148$	−2.99216	+	5.87245i	−0.245954	+	0.482712i
$149$	−12.7732	−	7.37458i	−1.04642	−	0.604149i	−0.124773	−	0.992185i	$-0.539820\pi$
$149$	−12.7732	−	7.37458i	−1.04642	−	0.604149i	−0.921644	+	0.388036i	$0.873154\pi$
$150$		0			0
$151$	−2.80622	−	4.86051i	−0.228367	−	0.395543i	0.728957	−	0.684559i	$-0.240005\pi$
$151$	−2.80622	−	4.86051i	−0.228367	−	0.395543i	−0.957324	+	0.289016i	$0.906672\pi$
$152$	−0.249960	−	0.384905i	−0.0202745	−	0.0312199i
$153$	1.00590	−	6.35103i	0.0813225	−	0.513450i
$154$	0.205157	+	0.104989i	0.0165320	+	0.00846026i
$155$		0			0
$156$	0.663588	−	0.295448i	0.0531295	−	0.0236548i
$157$	−1.35782	+	5.06744i	−0.108366	+	0.404426i	−0.998705	−	0.0508712i	$-0.983800\pi$
$157$	−1.35782	+	5.06744i	−0.108366	+	0.404426i	0.890340	+	0.455297i	$0.150467\pi$
$158$	0.109517	−	0.0886851i	0.00871270	−	0.00705541i
$159$	−8.54828	−	9.49383i	−0.677923	−	0.752910i
$160$		0			0
$161$	−8.73973	+	2.32528i	−0.688787	+	0.183257i
$162$	−0.00684101	−	0.0134262i	−0.000537481	−	0.00105487i
$163$	0.929553	−	17.7369i	0.0728082	−	1.38926i	−0.681055	−	0.732232i	$-0.738479\pi$
$163$	0.929553	−	17.7369i	0.0728082	−	1.38926i	0.753864	−	0.657031i	$-0.228188\pi$
$164$	−11.0941	+	12.3212i	−0.866302	+	0.962126i
$165$		0			0
$166$	−0.0165772	+	0.0149262i	−0.00128664	+	0.00115850i
$167$	0.899703	+	5.68050i	0.0696211	+	0.439571i	0.997735	+	0.0672731i	$0.0214299\pi$
$167$	0.899703	+	5.68050i	0.0696211	+	0.439571i	−0.928113	+	0.372297i	$0.878570\pi$
$168$	0.201154	−	0.0423856i	0.0155193	−	0.00327012i
$169$	7.58059	−	10.4338i	0.583122	−	0.802599i
$170$		0			0
$171$	−4.67575	+	10.5019i	−0.357563	+	0.803100i
$172$	−10.5491	+	4.04943i	−0.804363	+	0.308766i
$173$	−1.89475	+	1.23047i	−0.144055	+	0.0935507i	−0.614654	−	0.788797i	$-0.710705\pi$
$173$	−1.89475	+	1.23047i	−0.144055	+	0.0935507i	0.470599	+	0.882347i	$0.344038\pi$
$174$	0.0659643			0.00500074
$175$		0			0
$176$	−20.2779			−1.52851
$177$	−9.07122	+	5.89092i	−0.681834	+	0.442788i
$178$	0.0158957	−	0.00610177i	0.00119143	−	0.000457347i
$179$	−9.43793	+	21.1979i	−0.705424	+	1.58441i	0.102237	+	0.994760i	$0.467400\pi$
$179$	−9.43793	+	21.1979i	−0.705424	+	1.58441i	−0.807661	+	0.589648i	$0.799267\pi$
$180$		0			0
$181$	1.07470	−	1.47920i	0.0798820	−	0.109948i	−0.767206	−	0.641401i	$-0.778354\pi$
$181$	1.07470	−	1.47920i	0.0798820	−	0.109948i	0.847088	+	0.531453i	$0.178354\pi$
$182$	−0.0108620	+	0.00974556i	−0.000805147	+	0.000722389i
$183$	0.485109	+	3.06286i	0.0358603	+	0.226413i
$184$	−0.174499	+	0.157120i	−0.0128642	+	0.0115830i
$185$		0			0
$186$	0.00976159	−	0.0108413i	0.000715754	−	0.000794926i
$187$	−0.991941	+	18.9274i	−0.0725379	+	1.38411i
$188$	5.71482	+	11.2160i	0.416796	+	0.818008i
$189$	−9.97154	−	10.0068i	−0.725322	−	0.727888i
$190$		0			0
$191$	−0.492886	−	0.547405i	−0.0356640	−	0.0396088i	0.725049	−	0.688697i	$-0.241817\pi$
$191$	−0.492886	−	0.547405i	−0.0356640	−	0.0396088i	−0.760713	+	0.649089i	$0.775150\pi$
$192$	−7.02590	+	5.68946i	−0.507050	+	0.410601i
$193$	3.73619	−	13.9437i	0.268937	−	1.00369i	−0.690860	−	0.722989i	$-0.742768\pi$
$193$	3.73619	−	13.9437i	0.268937	−	1.00369i	0.959796	−	0.280697i	$-0.0905656\pi$
$194$	−0.194899	+	0.0867746i	−0.0139929	+	0.00623006i
$195$		0			0
$196$	12.1472	−	6.95613i	0.867657	−	0.496866i
$197$	−1.57277	+	9.93010i	−0.112055	+	0.707490i	0.866140	+	0.499802i	$0.166594\pi$
$197$	−1.57277	+	9.93010i	−0.112055	+	0.707490i	−0.978195	+	0.207688i	$0.933406\pi$
$198$	−0.0816300	−	0.125699i	−0.00580119	−	0.00893306i
$199$	3.19046	+	5.52604i	0.226166	+	0.391731i	0.956669	−	0.291179i	$-0.0940475\pi$
$199$	3.19046	+	5.52604i	0.226166	+	0.391731i	−0.730503	+	0.682910i	$0.760714\pi$
$200$		0			0
$201$	−6.39554	−	3.69247i	−0.451107	−	0.260447i
$202$	−0.0917845	+	0.180137i	−0.00645794	+	0.0126744i
$203$	8.54926	−	2.76115i	0.600040	−	0.193795i
$204$	4.96830	+	6.83828i	0.347851	+	0.478775i
$205$		0			0
$206$	0.251823	+	0.0264676i	0.0175453	+	0.00184409i
$207$	5.68118	+	1.52227i	0.394869	+	0.105805i
$208$	0.460157	−	1.19875i	0.0319061	−	0.0831183i
$209$	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	$0.474019\pi$
$212$	−22.5551	−	1.18206i	−1.54909	−	0.0811844i
$213$	2.79341	−	4.30147i	0.191401	−	0.294732i
$214$	0.132451	+	0.119260i	0.00905419	+	0.00815243i
$215$		0			0
$216$	−0.348836	−	0.113344i	−0.0237353	−	0.00771206i
$217$	0.811344	−	1.81369i	0.0550776	−	0.123121i
$218$	0.110518	+	0.110518i	0.00748521	+	0.00748521i
$219$	4.64827	+	10.4402i	0.314101	+	0.705483i
$220$		0			0
$221$	−1.09640	−	0.488148i	−0.0737518	−	0.0328364i
$222$	0.0402929	−	0.0497576i	0.00270428	−	0.00333951i
$223$	18.8633	+	9.61132i	1.26318	+	0.643622i	0.951816	−	0.306670i	$-0.0992147\pi$
$223$	18.8633	+	9.61132i	1.26318	+	0.643622i	0.311362	+	0.950291i	$0.399215\pi$
$224$	0.297730	−	0.456697i	0.0198929	−	0.0305144i
$225$		0			0
$226$	0.0732739	−	0.126914i	0.00487411	−	0.00844220i
$227$	19.9144	−	1.04367i	1.32176	−	0.0692707i	0.621646	−	0.783299i	$-0.286464\pi$
$227$	19.9144	−	1.04367i	1.32176	−	0.0692707i	0.700117	+	0.714028i	$0.253131\pi$
$228$	−5.41542	−	14.1076i	−0.358645	−	0.934302i
$229$	1.04973	+	9.98747i	0.0693678	+	0.659991i	0.972861	+	0.231389i	$0.0743270\pi$
$229$	1.04973	+	9.98747i	0.0693678	+	0.659991i	−0.903493	+	0.428602i	$0.859006\pi$
$230$		0			0
$231$	11.7782	+	9.57228i	0.774949	+	0.629810i
$232$	0.164941	−	0.164941i	0.0108289	−	0.0108289i
$233$	−2.60583	−	1.00029i	−0.170714	−	0.0655309i	0.271510	−	0.962436i	$-0.412477\pi$
$233$	−2.60583	−	1.00029i	−0.170714	−	0.0655309i	−0.442224	+	0.896905i	$0.645810\pi$
$234$	0.00928321	−	0.00197321i	0.000606863	−	0.000128993i
$235$		0			0
$236$	−3.97581	+	18.7047i	−0.258803	+	1.21757i
$237$	8.26918	−	4.21336i	0.537141	−	0.273687i
$238$	−0.137205	−	0.100056i	−0.00889366	−	0.00648564i
$239$	−3.96154	+	1.28718i	−0.256251	+	0.0832609i	−0.434325	−	0.900756i	$-0.643013\pi$
$239$	−3.96154	+	1.28718i	−0.256251	+	0.0832609i	0.178075	+	0.984017i	$0.443013\pi$
$240$		0			0
$241$	−1.47575	−	6.94288i	−0.0950617	−	0.447230i	−0.999775	−	0.0212092i	$-0.993248\pi$
$241$	−1.47575	−	6.94288i	−0.0950617	−	0.447230i	0.904713	−	0.426021i	$-0.140085\pi$
$242$	0.159127	+	0.196505i	0.0102290	+	0.0126318i
$243$	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
$247$	1.66746	+	1.35028i	0.106098	+	0.0859163i
$248$	−0.00269988	−	0.0515167i	−0.000171442	−	0.00327132i
$249$	−1.27225	+	0.734532i	−0.0806254	+	0.0465491i
$250$		0			0
$251$			3.67076i			0.231697i	0.993267	+	0.115848i	$0.0369586\pi$
$251$			3.67076i			0.231697i	−0.993267	+	0.115848i	$0.963041\pi$
$252$	−9.10350	−	0.0160693i	−0.573467	−	0.00101227i
$253$	−17.1229	−	2.71200i	−1.07651	−	0.170502i
$254$	−0.275635	+	0.0289704i	−0.0172949	+	0.00181777i
$255$		0			0
$256$	−1.66999	+	15.8889i	−0.104374	+	0.993055i
$257$	−5.31329	+	1.42369i	−0.331434	+	0.0888074i	−0.420698	−	0.907201i	$-0.638215\pi$
$257$	−5.31329	+	1.42369i	−0.331434	+	0.0888074i	0.0892647	+	0.996008i	$0.471548\pi$
$258$	0.108418	−	0.0171718i	0.00674984	−	0.00106907i
$259$	3.13937	−	8.13538i	0.195071	−	0.505508i
$260$		0			0
$261$	−5.71509	−	1.21478i	−0.353755	−	0.0751930i
$262$	0.0429249	+	0.0278758i	0.00265191	+	0.00172217i
$263$	−17.4437	−	11.3281i	−1.07563	−	0.698521i	−0.119904	−	0.992786i	$-0.538259\pi$
$263$	−17.4437	−	11.3281i	−1.07563	−	0.698521i	−0.955724	+	0.294265i	$0.904925\pi$
$264$	0.385454	+	0.0819308i	0.0237231	+	0.00504249i
$265$		0			0
$266$	0.190637	+	0.236268i	0.0116887	+	0.0144865i
$267$	1.10751	−	0.175413i	0.0677788	−	0.0107351i
$268$	−12.6114	+	3.37921i	−0.770363	+	0.206418i
$269$	0.0163748	−	0.155796i	0.000998391	−	0.00949906i	−0.994011	−	0.109277i	$-0.965147\pi$
$269$	0.0163748	−	0.155796i	0.000998391	−	0.00949906i	0.995010	+	0.0997777i	$0.0318132\pi$
$270$		0			0
$271$	1.38670	−	0.145748i	0.0842359	−	0.00885355i	−0.0623167	−	0.998056i	$-0.519849\pi$
$271$	1.38670	−	0.145748i	0.0842359	−	0.00885355i	0.146553	+	0.989203i	$0.453182\pi$
$272$	14.7577	+	2.33738i	0.894814	+	0.141725i
$273$	−0.833151	+	0.479061i	−0.0504246	+	0.0289941i
$274$		−	0.265502i		−	0.0160395i
$275$		0			0
$276$	−6.69562	+	3.86572i	−0.403029	+	0.232689i
$277$	−1.57183	−	29.9922i	−0.0944419	−	1.80206i	−0.477809	−	0.878464i	$-0.658569\pi$
$277$	−1.57183	−	29.9922i	−0.0944419	−	1.80206i	0.383367	−	0.923596i	$-0.374764\pi$
$278$	0.246369	+	0.199506i	0.0147762	+	0.0119655i
$279$	−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
$283$	−17.7097	−	21.8697i	−1.05273	−	1.30002i	−0.952329	−	0.305071i	$-0.901320\pi$
$283$	−17.7097	−	21.8697i	−1.05273	−	1.30002i	−0.100404	−	0.994947i	$-0.532014\pi$
$284$	−1.88528	−	8.86956i	−0.111871	−	0.526312i
$285$		0			0
$286$	−0.0266049	+	0.00864446i	−0.00157318	+	0.000511158i
$287$	12.9251	−	17.7240i	0.762947	−	1.04622i
$288$	−0.315909	+	0.160964i	−0.0186151	+	0.00948487i
$289$	−0.630888	+	2.96810i	−0.0371111	+	0.174594i
$290$		0			0
$291$	−13.7432	+	2.92120i	−0.805638	+	0.171244i
$292$	18.8626	+	7.24069i	1.10385	+	0.423729i
$293$	4.56757	−	4.56757i	0.266840	−	0.266840i	−0.560986	−	0.827826i	$-0.689578\pi$
$293$	4.56757	−	4.56757i	0.266840	−	0.266840i	0.827826	+	0.560986i	$0.189578\pi$
$294$	−0.129474	+	0.0415640i	−0.00755110	+	0.00242406i
$295$		0			0
$296$	−0.0236660	−	0.225167i	−0.00137556	−	0.0130876i
$297$	−9.70468	−	25.2816i	−0.563123	−	1.46698i
$298$	0.252966	−	0.0132574i	0.0146539	−	0.000767981i
$299$	0.548882	−	0.950692i	0.0317427	−	0.0549799i
$300$		0			0
$301$	13.3327	−	6.76374i	0.768485	−	0.389855i
$302$	0.0858861	+	0.0437612i	0.00494219	+	0.00251817i
$303$	−8.37910	+	10.3473i	−0.481367	+	0.594438i
$304$	−24.4029	−	10.8649i	−1.39960	−	0.623143i
$305$		0			0
$306$	0.0449188	+	0.100889i	0.00256784	+	0.00576746i
$307$	−12.4946	−	12.4946i	−0.713104	−	0.713104i	0.254080	−	0.967183i	$-0.418227\pi$
$307$	−12.4946	−	12.4946i	−0.713104	−	0.713104i	−0.967183	+	0.254080i	$0.918227\pi$
$308$	26.6910	−	2.75771i	1.52086	−	0.157135i
$309$	15.8595	+	5.15306i	0.902215	+	0.293148i
$310$		0			0
$311$	−5.55685	−	5.00341i	−0.315100	−	0.283717i	0.496371	−	0.868111i	$-0.334666\pi$
$311$	−5.55685	−	5.00341i	−0.315100	−	0.283717i	−0.811470	+	0.584394i	$0.801332\pi$
$312$	−0.0135903	+	0.0209273i	−0.000769401	+	0.00118477i
$313$	27.7944	+	1.45664i	1.57103	+	0.0823343i	0.817832	−	0.575458i	$-0.195176\pi$
$313$	27.7944	+	1.45664i	1.57103	+	0.0823343i	0.753200	+	0.657792i	$0.228509\pi$
$314$	−0.0278431	−	0.0856923i	−0.00157128	−	0.00483590i
$315$		0			0
$316$	5.07033	−	15.6049i	0.285228	−	0.877843i
$317$	−10.2406	+	26.6777i	−0.575170	+	1.49837i	0.269457	+	0.963012i	$0.413156\pi$
$317$	−10.2406	+	26.6777i	−0.575170	+	1.49837i	−0.844627	+	0.535356i	$0.820177\pi$
$318$	0.211935	+	0.0567878i	0.0118847	+	0.00318450i
$319$	17.1275	+	1.80018i	0.958958	+	0.100791i
$320$		0			0
$321$	6.89929	+	9.49606i	0.385081	+	0.530019i
$322$	0.104136	−	0.115245i	0.00580328	−	0.00642236i
$323$	−11.3350	+	22.2461i	−0.630694	+	1.23781i
$324$	−1.51943	−	0.877241i	−0.0844125	−	0.0487356i
$325$		0			0
$326$	0.152523	+	0.264177i	0.00844745	+	0.0146314i
$327$	5.60607	+	8.63259i	0.310016	+	0.477383i
$328$	0.0890975	−	0.562539i	0.00491959	−	0.0310610i
$329$	−9.04617	−	13.9839i	−0.498732	−	0.770955i
$330$		0			0
$331$	15.2558	−	6.79232i	0.838535	−	0.373340i	0.0578965	−	0.998323i	$-0.481561\pi$
$331$	15.2558	−	6.79232i	0.838535	−	0.373340i	0.780639	+	0.624983i	$0.214894\pi$
$332$	−0.672217	+	2.50875i	−0.0368927	+	0.137685i
$333$	−4.40726	+	3.56893i	−0.241517	+	0.195576i
$334$	−0.0660950	−	0.0734059i	−0.00361656	−	0.00401659i
$335$		0			0
$336$	8.47541	−	8.44554i	0.462371	−	0.460742i
$337$	10.8501	+	21.2946i	0.591044	+	1.15999i	0.971909	+	0.235358i	$0.0756263\pi$
$337$	10.8501	+	21.2946i	0.591044	+	1.15999i	−0.380865	+	0.924631i	$0.624374\pi$
$338$	−0.0115924	+	0.221197i	−0.000630546	+	0.0120315i
$339$	6.45792	−	7.17225i	0.350746	−	0.389543i
$340$		0			0
$341$	2.83045	−	2.54854i	0.153277	−	0.138011i
$342$	−0.0308859	−	0.195006i	−0.00167012	−	0.0105447i
$343$	−15.0406	+	10.8064i	−0.812118	+	0.583493i
$344$	0.228158	−	0.314033i	0.0123015	−	0.0169315i
$345$		0			0
$346$	0.0157821	−	0.0354472i	0.000848452	−	0.00190566i
$347$	3.42854	−	1.31609i	0.184053	−	0.0706515i	−0.264596	−	0.964359i	$-0.585239\pi$
$347$	3.42854	−	1.31609i	0.184053	−	0.0706515i	0.448649	+	0.893708i	$0.351905\pi$
$348$	6.44133	−	4.18305i	0.345291	−	0.224235i
$349$	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
$352$	0.876464	−	0.569183i	0.0467157	−	0.0303375i
$353$	23.7134	−	9.10273i	1.26214	−	0.484490i	0.366976	−	0.930230i	$-0.380393\pi$
$353$	23.7134	−	9.10273i	1.26214	−	0.484490i	0.895162	+	0.445741i	$0.147060\pi$
$354$	0.0755576	−	0.169705i	0.00401584	−	0.00901973i
$355$		0			0
$356$	1.16525	−	1.60383i	0.0617583	−	0.0850031i
$357$	−7.46845	−	8.32405i	−0.395272	−	0.440556i
$358$	−0.0623428	−	0.393617i	−0.00329492	−	0.0208033i
$359$	−8.35258	+	7.52069i	−0.440832	+	0.396927i	−0.859437	−	0.511241i	$-0.829186\pi$
$359$	−8.35258	+	7.52069i	−0.440832	+	0.396927i	0.418605	+	0.908168i	$0.362519\pi$
$360$		0			0
$361$	17.1539	−	19.0514i	0.902838	−	1.00270i
$362$	−0.00164347	+	0.0313592i	−8.63787e−5	+	0.00164820i
$363$	7.55997	+	14.8373i	0.396796	+	0.778755i
$364$	−0.442661	+	1.64044i	−0.0232017	+	0.0859826i
$365$		0			0
$366$	−0.0356376	−	0.0395796i	−0.00186281	−	0.00206886i
$367$	5.60548	−	4.53923i	0.292604	−	0.236946i	−0.471766	−	0.881724i	$-0.656383\pi$
$367$	5.60548	−	4.53923i	0.292604	−	0.236946i	0.764370	+	0.644778i	$0.223050\pi$
$368$	−3.53724	+	13.2012i	−0.184391	+	0.688158i
$369$	−13.0328	+	5.80259i	−0.678462	+	0.302071i
$370$		0			0
$371$	29.8447	−	1.51127i	1.54946	−	0.0784614i
$372$	0.265716	−	1.67766i	0.0137767	−	0.0869827i
$373$	−2.12375	−	3.27030i	−0.109964	−	0.169329i	0.779404	−	0.626521i	$-0.215522\pi$
$373$	−2.12375	−	3.27030i	−0.109964	−	0.169329i	−0.889368	+	0.457192i	$0.848855\pi$
$374$	−0.162760	−	0.281908i	−0.00841610	−	0.0145771i
$375$		0			0
$376$	−0.374489	−	0.216211i	−0.0193128	−	0.0111503i
$377$	−0.495085	+	0.971660i	−0.0254982	+	0.0500430i
$378$	0.237234	+	0.0508634i	0.0122020	+	0.00261613i
$379$	−2.70772	−	3.72686i	−0.139086	−	0.191436i	0.733792	−	0.679375i	$-0.237749\pi$
$379$	−2.70772	−	3.72686i	−0.139086	−	0.191436i	−0.872878	+	0.487939i	$0.837749\pi$
$380$		0			0
$381$	−18.1525	−	1.90791i	−0.929983	−	0.0977451i
$382$	0.0122200	+	0.00327433i	0.000625228	+	0.000167529i
$383$	−10.1910	+	26.5486i	−0.520738	+	1.35657i	0.381116	+	0.924527i	$0.375540\pi$
$383$	−10.1910	+	26.5486i	−0.520738	+	1.35657i	−0.901854	+	0.432042i	$0.857793\pi$
$384$	0.192024	−	0.590991i	0.00979921	−	0.0301589i
$385$		0			0
$386$	0.0766136	+	0.235792i	0.00389953	+	0.0120015i
$387$	−9.70951	−	0.508854i	−0.493562	−	0.0258665i
$388$	−13.5289	+	20.8327i	−0.686827	+	1.05762i
$389$	21.7783	+	19.6093i	1.10420	+	0.994230i	1.00000		0.000325536i	$-0.000103621\pi$
$389$	21.7783	+	19.6093i	1.10420	+	0.994230i	0.104205	+	0.994556i	$0.466770\pi$
$390$		0			0
$391$	12.1489	+	3.94741i	0.614396	+	0.199629i
$392$	−0.219816	+	0.427674i	−0.0111024	+	0.0216008i
$393$	2.38345	+	2.38345i	0.120229	+	0.120229i
$394$	−0.0702325	−	0.157745i	−0.00353826	−	0.00794706i
$395$		0			0
$396$	−15.9421	−	7.09790i	−0.801122	−	0.356683i
$397$	0.701171	−	0.865873i	0.0351907	−	0.0434569i	−0.759247	−	0.650803i	$-0.774432\pi$
$397$	0.701171	−	0.865873i	0.0351907	−	0.0434569i	0.794438	+	0.607346i	$0.207766\pi$
$398$	−0.0976462	−	0.0497532i	−0.00489456	−	0.00249390i
$399$	9.04534	+	17.8302i	0.452833	+	0.892627i
$400$		0			0
$401$	−4.29812	+	7.44456i	−0.214638	+	0.371764i	−0.953160	−	0.302465i	$-0.902190\pi$
$401$	−4.29812	+	7.44456i	−0.214638	+	0.371764i	0.738523	+	0.674229i	$0.235524\pi$
$402$	0.126661	−	0.00663801i	0.00631726	−	0.000331074i
$403$	0.0864297	+	0.225157i	0.00430537	+	0.0112159i
$404$	2.46055	+	23.4106i	0.122417	+	1.16472i
$405$		0			0
$406$	−0.0973153	+	0.119742i	−0.00482968	+	0.00594268i
$407$	11.8199	−	11.8199i	0.585890	−	0.585890i
$408$	−0.271078	−	0.104057i	−0.0134203	−	0.00515159i
$409$	−15.2011	+	3.23109i	−0.751645	+	0.159767i	−0.567775	−	0.823184i	$-0.692196\pi$
$409$	−15.2011	+	3.23109i	−0.751645	+	0.159767i	−0.183869	+	0.982951i	$0.558862\pi$
$410$		0			0
$411$	3.63537	−	17.1031i	0.179320	−	0.843633i
$412$	26.2686	−	13.3845i	1.29416	−	0.659407i
$413$	2.68904	−	25.1572i	0.132319	−	1.23791i
$414$	−0.0960709	+	0.0312153i	−0.00472163	+	0.00153415i
$415$		0			0
$416$	0.0137586	+	0.0647291i	0.000674571	+	0.00317361i
$417$	13.1389	+	16.2251i	0.643413	+	0.794548i
$418$	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	$0.481726\pi$
$422$	−0.377325	−	0.305552i	−0.0183679	−	0.0148740i
$423$	0.566871	+	10.8165i	0.0275622	+	0.525918i
$424$	0.671930	−	0.387939i	0.0326318	−	0.0188400i
$425$		0			0
$426$			0.0880879i			0.00426787i
$427$	−6.27552	−	3.63796i	−0.303694	−	0.176053i
$428$	20.4964	+	3.24632i	0.990732	+	0.156917i
$429$	−1.83220	+	0.192572i	−0.0884594	+	0.00929746i
$430$		0			0
$431$	1.01729	−	9.67888i	0.0490012	−	0.466215i	−0.942316	−	0.334724i	$-0.891357\pi$
$431$	1.01729	−	9.67888i	0.0490012	−	0.466215i	0.991317	−	0.131491i	$-0.0419764\pi$
$432$	−20.6209	+	5.52535i	−0.992123	+	0.265839i
$433$	−12.2911	+	1.94672i	−0.590674	+	0.0935535i	−0.444614	−	0.895722i	$-0.646659\pi$
$433$	−12.2911	+	1.94672i	−0.590674	+	0.0935535i	−0.146060	+	0.989276i	$0.546659\pi$
$434$	0.00527873	+	0.0337136i	0.000253387	+	0.00161831i
$435$		0			0
$436$	17.8003	+	3.78356i	0.852478	+	0.181200i
$437$	−19.1529	−	12.4381i	−0.916209	−	0.594993i
$438$	−0.164612	−	0.106900i	−0.00786545	−	0.00510788i
$439$	23.9971	+	5.10075i	1.14532	+	0.243445i	0.741215	−	0.671267i	$-0.234250\pi$
$439$	23.9971	+	5.10075i	1.14532	+	0.243445i	0.404105	+	0.914713i	$0.367583\pi$
$440$		0			0
$441$	11.9830	−	1.21671i	0.570618	−	0.0579384i
$442$	0.0203587	−	0.00322450i	0.000968363	−	0.000153374i
$443$	6.76871	−	1.81367i	0.321591	−	0.0861701i	−0.0944121	−	0.995533i	$-0.530097\pi$
$443$	6.76871	−	1.81367i	0.321591	−	0.0861701i	0.416003	+	0.909363i	$0.363430\pi$
$444$	0.779231	−	7.41389i	0.0369807	−	0.351848i
$445$		0			0
$446$	−0.361611	+	0.0380068i	−0.0171228	+	0.00179968i
$447$	16.4771	+	2.60972i	0.779340	+	0.123435i
$448$	0.0373287	−	21.1472i	0.00176361	−	0.999114i
$449$		−	11.3776i		−	0.536943i	−0.963288	−	0.268472i	$-0.913481\pi$
$449$		−	11.3776i		−	0.536943i	0.963288	−	0.268472i	$-0.0865186\pi$
$450$		0			0
$451$	36.4167	−	21.0252i	1.71480	−	0.990039i
$452$	−0.893007	−	17.0396i	−0.0420035	−	0.801474i
$453$	4.93341	+	3.99500i	0.231792	+	0.187701i
$454$	−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	0.994931	−	0.100558i	$-0.0320627\pi$
$457$	1.77469	+	6.62325i	0.0830167	+	0.309822i	−0.911915	+	0.410380i	$0.865396\pi$
$458$	−0.108544	−	0.134040i	−0.00507191	−	0.00626328i
$459$	4.14863	+	19.5178i	0.193641	+	0.911011i
$460$		0			0
$461$	−6.19822	+	2.01392i	−0.288680	+	0.0937978i	−0.449777	−	0.893141i	$-0.648497\pi$
$461$	−6.19822	+	2.01392i	−0.288680	+	0.0937978i	0.161097	+	0.986939i	$0.448497\pi$
$462$	−0.259193	−	0.0277049i	−0.0120587	−	0.00128895i
$463$	−3.99566	+	2.03589i	−0.185694	+	0.0946158i	−0.544366	−	0.838848i	$-0.683230\pi$
$463$	−3.99566	+	2.03589i	−0.185694	+	0.0946158i	0.358672	+	0.933464i	$0.383230\pi$
$464$	2.82274	−	13.2800i	0.131043	−	0.616507i
$465$		0			0
$466$	0.0468911	−	0.00996701i	0.00217219	−	0.000461713i
$467$	−37.5050	−	14.3968i	−1.73552	−	0.666205i	−0.735587	−	0.677430i	$-0.763094\pi$
$467$	−37.5050	−	14.3968i	−1.73552	−	0.666205i	−0.999937	+	0.0112245i	$0.996427\pi$
$468$	0.781365	−	0.781365i	0.0361186	−	0.0361186i
$469$	16.1379	−	6.16210i	0.745180	−	0.284539i
$470$		0			0
$471$	−0.620259	−	5.90137i	−0.0285800	−	0.271921i
$472$	−0.235412	−	0.613269i	−0.0108357	−	0.0282280i
$473$	28.6193	−	1.49988i	1.31592	−	0.0689643i
$474$	−0.0796971	+	0.138039i	−0.00366061	+	0.00634036i
$475$		0			0
$476$	−19.7428	−	1.06962i	−0.904909	−	0.0490261i
$477$	−17.3161	−	8.82298i	−0.792849	−	0.403977i
$478$	0.0450215	−	0.0555969i	0.00205924	−	0.00254294i
$479$	18.9438	+	8.43434i	0.865566	+	0.385375i	0.790982	−	0.611840i	$-0.209570\pi$
$479$	18.9438	+	8.43434i	0.865566	+	0.385375i	0.0745845	+	0.997215i	$0.476237\pi$
$480$		0			0
$481$	0.430521	+	0.966966i	0.0196301	+	0.0440898i
$482$	0.0862007	+	0.0862007i	0.00392633	+	0.00392633i
$483$	8.28622	−	5.99797i	0.377036	−	0.272917i
$484$	27.9996	+	9.09763i	1.27271	+	0.413529i
$485$		0			0
$486$	−0.191781	−	0.172681i	−0.00869938	−	0.00783296i
$487$	−4.04851	+	6.23415i	−0.183455	+	0.282496i	−0.918418	−	0.395611i	$-0.870533\pi$
$487$	−4.04851	+	6.23415i	−0.183455	+	0.282496i	0.734963	+	0.678107i	$0.237200\pi$
$488$	−0.188077	−	0.00985672i	−0.00851387	−	0.000446193i
$489$	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	$0.948518\pi$
$492$	6.72052	−	17.5076i	0.302984	−	0.789302i
$493$	−12.2574	−	3.28436i	−0.552045	−	0.147920i
$494$	−0.0366486	−	0.00385192i	−0.00164890	−	0.000173306i
$495$		0			0
$496$	−1.76487	−	2.42913i	−0.0792448	−	0.109071i
$497$	3.68720	+	11.4166i	0.165393	+	0.512103i
$498$	0.0114546	−	0.0224808i	0.000513291	−	0.00100739i
$499$	−7.97198	−	4.60262i	−0.356875	−	0.206042i	0.310834	−	0.950464i	$-0.399392\pi$
$499$	−7.97198	−	4.60262i	−0.356875	−	0.206042i	−0.667709	+	0.744422i	$0.732725\pi$
$500$		0			0
$501$	−3.25260	−	5.63367i	−0.145315	−	0.251694i
$502$	−0.0343365	−	0.0528736i	−0.00153251	−	0.00235986i
$503$	−3.27358	+	20.6686i	−0.145962	+	0.921565i	0.800637	+	0.599150i	$0.204495\pi$
$503$	−3.27358	+	20.6686i	−0.145962	+	0.921565i	−0.946598	+	0.322415i	$0.895505\pi$
$504$	0.262573	−	0.169859i	0.0116959	−	0.00756611i
$505$		0			0
$506$	0.272005	−	0.121105i	0.0120921	−	0.00538376i
$507$	−3.77549	+	14.0903i	−0.167676	+	0.625774i
$508$	−25.0783	+	20.3080i	−1.11267	+	0.901022i
$509$	4.74698	+	5.27205i	0.210406	+	0.233680i	0.839105	−	0.543969i	$-0.183079\pi$
$509$	4.74698	+	5.27205i	0.210406	+	0.233680i	−0.628699	+	0.777648i	$0.716412\pi$
$510$		0			0
$511$	−25.8090	−	6.96436i	−1.14172	−	0.308085i
$512$	−0.623407	−	1.22350i	−0.0275509	−	0.0540718i
$513$	1.86698	−	35.6241i	0.0824291	−	1.57284i
$514$	0.0632152	−	0.0702076i	0.00278830	−	0.00309672i
$515$		0			0
$516$	9.49799	−	8.55203i	0.418126	−	0.376482i
$517$	−4.99434	−	31.5330i	−0.219651	−	1.38682i
$518$	0.0308794	+	0.146548i	0.00135676	+	0.00643893i
$519$	1.50201	−	2.06734i	0.0659310	−	0.0907463i
$520$		0			0
$521$	−6.21506	+	13.9592i	−0.272287	+	0.611566i	−0.996993	−	0.0774921i	$-0.975309\pi$
$521$	−6.21506	+	13.9592i	−0.272287	+	0.611566i	0.724706	+	0.689058i	$0.241975\pi$
$522$	0.0936831	−	0.0359616i	0.00410040	−	0.00157400i
$523$	3.88934	−	2.52576i	0.170069	−	0.110444i	−0.456798	−	0.889571i	$-0.651004\pi$
$523$	3.88934	−	2.52576i	0.170069	−	0.110444i	0.626867	+	0.779127i	$0.284337\pi$
$524$	5.95927			0.260332
$525$		0			0
$526$	0.357223			0.0155757
$527$	−2.35367	+	1.52849i	−0.102528	+	0.0665822i
$528$	21.4126	−	8.21952i	0.931863	−	0.357709i
$529$	4.60253	−	10.3374i	0.200110	−	0.449454i
$530$		0			0
$531$	−9.67149	+	13.3117i	−0.419707	+	0.577677i
$532$	33.5981	+	10.9823i	1.45666	+	0.476143i
$533$	0.416539	+	2.62992i	0.0180423	+	0.113915i
$534$	−0.0143118	+	0.0128864i	−0.000619332	+	0.000557649i
$535$		0			0
$536$	0.300112	−	0.333308i	0.0129628	−	0.0143967i
$537$	1.37359	−	26.2097i	0.0592748	−	1.13103i
$538$	0.00122146	+	0.00239725i	5.26610e−5	+	0.000103353i
$539$	−34.7521	+	7.25866i	−1.49688	+	0.312653i
$540$		0			0
$541$	16.9732	+	18.8507i	0.729735	+	0.810453i	0.987809	−	0.155672i	$-0.0497544\pi$
$541$	16.9732	+	18.8507i	0.729735	+	0.810453i	−0.258074	+	0.966125i	$0.583088\pi$
$542$	−0.0186106	+	0.0150706i	−0.000799395	+	0.000647337i
$543$	−0.535254	+	1.99759i	−0.0229699	+	0.0857249i
$544$	−0.703472	+	0.313206i	−0.0301611	+	0.0134286i
$545$		0			0
$546$	0.00751952	−	0.0146937i	0.000321806	−	0.000628833i
$547$	1.41055	−	8.90589i	0.0603110	−	0.380788i	−0.939008	−	0.343895i	$-0.888254\pi$
$547$	1.41055	−	8.90589i	0.0603110	−	0.380788i	0.999319	−	0.0368938i	$-0.0117463\pi$
$548$	−16.8365	−	25.9259i	−0.719218	−	1.10750i
$549$	2.35873	+	4.08544i	0.100668	+	0.174362i
$550$		0			0
$551$	19.6471	+	11.3433i	0.836995	+	0.483239i
$552$	0.120576	−	0.236643i	0.00513204	−	0.0100722i
$553$	−4.55100	+	21.2265i	−0.193528	+	0.902641i
$554$	0.303190	+	0.417305i	0.0128813	+	0.0177296i
$555$		0			0
$556$	36.7090	+	3.85827i	1.55681	+	0.163627i
$557$	16.3666	+	4.38542i	0.693475	+	0.185816i	0.588306	−	0.808638i	$-0.299795\pi$
$557$	16.3666	+	4.38542i	0.693475	+	0.185816i	0.105169	+	0.994454i	$0.466462\pi$
$558$	0.00795316	−	0.0207187i	0.000336684	−	0.000877092i
$559$	−0.560777	+	1.72589i	−0.0237183	+	0.0729975i
$560$		0			0
$561$	−6.62463	−	20.3885i	−0.279692	−	0.860804i
$562$	0.489917	+	0.0256755i	0.0206659	+	0.00108305i
$563$	−23.6121	+	36.3595i	−0.995133	+	1.53237i	−0.156496	+	0.987679i	$0.550020\pi$
$563$	−23.6121	+	36.3595i	−0.995133	+	1.53237i	−0.838637	+	0.544691i	$0.816647\pi$
$564$	−10.5809	−	9.52709i	−0.445536	−	0.401163i
$565$		0			0
$566$	0.459661	+	0.149353i	0.0193210	+	0.00627776i
$567$	2.11895	+	0.947901i	0.0889874	+	0.0398081i
$568$	0.220260	+	0.220260i	0.00924190	+	0.00924190i
$569$	4.01461	+	9.01696i	0.168301	+	0.378011i	0.977930	−	0.208931i	$-0.0669984\pi$
$569$	4.01461	+	9.01696i	0.168301	+	0.378011i	−0.809629	+	0.586942i	$0.800332\pi$
$570$		0			0
$571$	−1.33258	−	0.593302i	−0.0557666	−	0.0248289i	0.378664	−	0.925534i	$-0.376384\pi$
$571$	−1.33258	−	0.593302i	−0.0557666	−	0.0248289i	−0.434430	+	0.900705i	$0.643050\pi$
$572$	−2.04976	+	2.53124i	−0.0857047	+	0.105836i
$573$	0.742352	+	0.378247i	0.0310122	+	0.0158015i
$574$	−0.0203817	+	0.376199i	−0.000850716	+	0.0157022i
$575$		0			0
$576$	−6.87654	+	11.9105i	−0.286522	+	0.496271i
$577$	5.62157	−	0.294614i	0.234029	−	0.0122649i	0.0650391	−	0.997883i	$-0.479283\pi$
$577$	5.62157	−	0.294614i	0.234029	−	0.0122649i	0.168990	+	0.985618i	$0.445949\pi$
$578$	−0.0186764	−	0.0486537i	−0.000776837	−	0.00202373i
$579$	1.70671	+	16.2383i	0.0709286	+	0.674841i
$580$		0			0
$581$	0.543552	−	3.39308i	0.0225504	−	0.140769i
$582$	0.170631	−	0.170631i	0.00707288	−	0.00707288i
$583$	53.4789	+	20.5286i	2.21487	+	0.850209i
$584$	−0.678903	+	0.144305i	−0.0280932	+	0.00597140i
$585$		0			0
$586$	−0.0230659	+	0.108516i	−0.000952842	+	0.00448277i
$587$	−18.5011	+	9.42678i	−0.763622	+	0.389085i	−0.792007	−	0.610512i	$-0.790964\pi$
$587$	−18.5011	+	9.42678i	−0.763622	+	0.389085i	0.0283850	+	0.999597i	$0.490964\pi$
$588$	−10.0073	+	12.2691i	−0.412693	+	0.505971i
$589$	4.77172	−	1.55043i	0.196615	−	0.0638842i
$590$		0			0
$591$	−2.36432	−	11.1232i	−0.0972551	−	0.457549i
$592$	−8.29300	−	10.2410i	−0.340840	−	0.420903i
$593$	−3.80233	−	14.1905i	−0.156143	−	0.582733i	−0.999005	−	0.0446033i	$-0.985798\pi$
$593$	−3.80233	−	14.1905i	−0.156143	−	0.582733i	0.842862	−	0.538130i	$-0.180869\pi$
$594$	0.376271	+	0.273377i	0.0154386	+	0.0112168i
$595$		0			0
$596$	23.8611	−	17.3361i	0.977390	−	0.710116i
$597$	−5.60893	−	4.54202i	−0.229558	−	0.185892i
$598$	0.000986734		0.0188280i	4.03506e−5		0.000769935i
$599$	−8.74982	+	5.05171i	−0.357508	+	0.206407i	−0.667987	−	0.744173i	$-0.732844\pi$
$599$	−8.74982	+	5.05171i	−0.357508	+	0.206407i	0.310479	+	0.950580i	$0.399511\pi$
$600$		0			0
$601$			22.6515i			0.923974i	0.886887	+	0.461987i	$0.152863\pi$
$601$			22.6515i			0.923974i	−0.886887	+	0.461987i	$0.847137\pi$
$602$	−0.128776	+	0.222140i	−0.00524850	+	0.00905373i
$603$	−11.0960	−	1.75744i	−0.451865	−	0.0715684i
$604$	11.1617	−	1.17315i	0.454165	−	0.0477346i
$605$		0			0
$606$	0.0239029	−	0.227421i	0.000970990	−	0.00923835i
$607$	19.2701	−	5.16341i	0.782150	−	0.209576i	0.154418	−	0.988006i	$-0.450650\pi$
$607$	19.2701	−	5.16341i	0.782150	−	0.209576i	0.627732	+	0.778429i	$0.283983\pi$
$608$	1.35972	−	0.215359i	0.0551440	−	0.00873395i
$609$	−7.90841	+	6.38103i	−0.320465	+	0.258572i
$610$		0			0
$611$	1.97744	+	0.420317i	0.0799986	+	0.0170042i
$612$	10.7840	+	7.00323i	0.435919	+	0.283089i
$613$	32.1875	+	20.9028i	1.30004	+	0.844257i	0.994171	−	0.107815i	$-0.0343856\pi$
$613$	32.1875	+	20.9028i	1.30004	+	0.844257i	0.305871	+	0.952073i	$0.401052\pi$
$614$	0.296847	+	0.0630967i	0.0119798	+	0.00254638i
$615$		0			0
$616$	−0.717375	+	0.578825i	−0.0289039	+	0.0233215i
$617$	0.589114	−	0.0933065i	0.0237168	−	0.00375638i	−0.144565	−	0.989495i	$-0.546178\pi$
$617$	0.589114	−	0.0933065i	0.0237168	−	0.00375638i	0.168282	+	0.985739i	$0.446178\pi$
$618$	−0.276642	+	0.0741259i	−0.0111282	+	0.00298178i
$619$	0.290449	−	2.76344i	0.0116741	−	0.111072i	−0.987133	−	0.159901i	$-0.948882\pi$
$619$	0.290449	−	2.76344i	0.0116741	−	0.111072i	0.998807	+	0.0488294i	$0.0155491\pi$
$620$		0			0
$621$	−18.1514	+	1.90779i	−0.728392	+	0.0765571i
$622$	0.126843	+	0.0200899i	0.00508593	+	0.000805532i
$623$	−1.31547	+	2.26920i	−0.0527031	+	0.0909134i
$624$			1.45235i			0.0581404i
$625$		0			0
$626$	−0.413975	+	0.239009i	−0.0165458	+	0.00955270i
$627$	2.00583	+	38.2734i	0.0801050	+	1.52849i
$628$	−8.15292	−	6.60211i	−0.325337	−	0.263453i
$629$	−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
$633$	−20.1227	−	24.8495i	−0.799807	−	0.987680i
$634$	−0.102039	−	0.480056i	−0.00405249	−	0.0190655i
$635$		0			0
$636$	24.2963	−	7.89435i	0.963411	−	0.313031i
$637$	0.359510	−	2.21912i	0.0142443	−	0.0879248i
$638$	−0.263544	+	0.134282i	−0.0104338	+	0.00531628i
$639$	1.62220	−	7.63186i	0.0641733	−	0.301912i
$640$		0			0
$641$	−1.48400	+	0.315435i	−0.0586146	+	0.0124589i	−0.237126	−	0.971479i	$-0.576205\pi$
$641$	−1.48400	+	0.315435i	−0.0586146	+	0.0124589i	0.178511	+	0.983938i	$0.442872\pi$
$642$	−0.188204	−	0.0722447i	−0.00742781	−	0.00285127i
$643$	18.1864	−	18.1864i	0.717201	−	0.717201i	−0.250830	−	0.968031i	$-0.580703\pi$
$643$	18.1864	−	18.1864i	0.717201	−	0.717201i	0.968031	+	0.250830i	$0.0807034\pi$
$644$	2.86062	−	17.8572i	0.112724	−	0.703672i
$645$		0			0
$646$	−0.0448227	−	0.426460i	−0.00176353	−	0.0167788i
$647$	2.70505	+	7.04689i	0.106346	+	0.277042i	0.976420	−	0.215880i	$-0.0692621\pi$
$647$	2.70505	+	7.04689i	0.106346	+	0.277042i	−0.870073	+	0.492922i	$0.835929\pi$
$648$	0.0601875	−	0.00315429i	0.00236439	−	0.000123912i
$649$	24.2497	−	42.0017i	0.951885	−	1.64871i
$650$		0			0
$651$	−0.121578	+	2.24404i	−0.00476501	+	0.0879510i
$652$	31.6461	+	16.1245i	1.23936	+	0.631484i
$653$	−21.7081	+	26.8073i	−0.849503	+	1.04905i	0.148686	+	0.988885i	$0.452496\pi$
$653$	−21.7081	+	26.8073i	−0.849503	+	1.04905i	−0.998188	+	0.0601643i	$0.980838\pi$
$654$	−0.161499	−	0.0719041i	−0.00631512	−	0.00281167i
$655$		0			0
$656$	−13.4833	−	30.2839i	−0.526433	−	1.18239i
$657$	12.2932	+	12.2932i	0.479602	+	0.479602i
$658$	0.261107	+	0.116805i	0.0101790	+	0.00455353i
$659$	−16.9511	−	5.50773i	−0.660319	−	0.214551i	−0.0403605	−	0.999185i	$-0.512851\pi$
$659$	−16.9511	−	5.50773i	−0.660319	−	0.214551i	−0.619959	+	0.784634i	$0.712851\pi$
$660$		0			0
$661$	−29.1652	−	26.2604i	−1.13439	−	1.02141i	−0.999533	−	0.0305478i	$-0.990275\pi$
$661$	−29.1652	−	26.2604i	−1.13439	−	1.02141i	−0.134860	−	0.990865i	$-0.543059\pi$
$662$	−0.156209	+	0.240540i	−0.00607122	+	0.00934885i
$663$	1.35562	+	0.0710448i	0.0526477	+	0.00275915i
$664$	−0.0275707	−	0.0848540i	−0.00106995	−	0.00329297i
$665$		0			0
$666$	0.0300981	−	0.0926326i	0.00116628	−	0.00358944i
$667$	4.15963	−	10.8362i	0.161061	−	0.419579i
$668$	−11.1090	−	2.97666i	−0.429822	−	0.115170i
$669$	−23.8146	−	2.50302i	−0.920727	−	0.0967724i
$670$		0			0
$671$	−8.17313	−	11.2493i	−0.315520	−	0.434276i
$672$	−0.129270	+	0.602934i	−0.00498672	+	0.0232587i
$673$	−7.81076	+	15.3295i	−0.301083	+	0.590908i	−0.991136	−	0.132850i	$-0.957587\pi$
$673$	−7.81076	+	15.3295i	−0.301083	+	0.590908i	0.690053	+	0.723759i	$0.257587\pi$
$674$	−0.355475	−	0.205234i	−0.0136924	−	0.00790531i
$675$		0			0
$676$	12.8950	+	22.3347i	0.495960	+	0.859028i
$677$	0.346917	+	0.534205i	0.0133331	+	0.0205312i	0.845274	−	0.534333i	$-0.179437\pi$
$677$	0.346917	+	0.534205i	0.0133331	+	0.0205312i	−0.831941	+	0.554864i	$0.812770\pi$
$678$	−0.0259302	+	0.163717i	−0.000995842	+	0.00628750i
$679$	14.9722	−	29.2568i	0.574580	−	1.12277i
$680$		0			0
$681$	−20.6056	+	9.17421i	−0.789609	+	0.351557i
$682$	−0.0169304	+	0.0631853i	−0.000648300	+	0.00241949i
$683$	−14.1248	+	11.4381i	−0.540471	+	0.437665i	−0.860284	−	0.509816i	$-0.829714\pi$
$683$	−14.1248	+	11.4381i	−0.540471	+	0.437665i	0.319812	+	0.947481i	$0.396380\pi$
$684$	−15.3821	−	17.0835i	−0.588148	−	0.653204i
$685$		0			0
$686$	0.115561	−	0.296347i	0.00441214	−	0.0113146i
$687$	−5.15681	−	10.1208i	−0.196745	−	0.386133i
$688$	1.18241	−	22.5617i	0.0450788	−	0.860155i
$689$	−2.42714	+	2.69561i	−0.0924665	+	0.102694i
$690$		0			0
$691$	−18.4552	+	16.6171i	−0.702068	+	0.632145i	−0.940809	−	0.338938i	$-0.889932\pi$
$691$	−18.4552	+	16.6171i	−0.702068	+	0.632145i	0.238740	+	0.971083i	$0.423265\pi$
$692$	−0.706740	−	4.46218i	−0.0268662	−	0.169627i
$693$	21.9460	+	7.17355i	0.833661	+	0.272501i
$694$	−0.0370737	+	0.0510276i	−0.00140730	+	0.00193698i
$695$		0			0
$696$	−0.107312	+	0.241028i	−0.00406767	+	0.00913613i
$697$	−28.9265	+	11.1038i	−1.09567	+	0.420588i
$698$	−0.0175580	+	0.0114023i	−0.000664578	+	0.000431582i
$699$	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	$0.547004\pi$
$702$	−0.0246994	+	0.0160400i	−0.000932220	+	0.000605391i
$703$	20.5574	−	7.89123i	0.775335	−	0.297623i
$704$	16.4883	−	37.0332i	0.621425	−	1.39574i
$705$		0			0
$706$	−0.256420	+	0.352932i	−0.00965050	+	0.0132828i
$707$	−6.42152	−	30.4753i	−0.241506	−	1.14614i
$708$	−3.38355	−	21.3629i	−0.127162	−	0.802866i
$709$	−33.5426	+	30.2019i	−1.25972	+	1.13426i	−0.274754	+	0.961515i	$0.588596\pi$
$709$	−33.5426	+	30.2019i	−1.25972	+	1.13426i	−0.984967	+	0.172743i	$0.944737\pi$
$710$		0			0
$711$	9.44698	−	10.4919i	0.354289	−	0.393478i
$712$	−0.00356414	+	0.0680079i	−0.000133572	+	0.00254870i
$713$	−1.16539	−	2.28721i	−0.0436443	−	0.0856568i
$714$	0.185439	+	0.0500392i	0.00693988	+	0.00187267i
$715$		0			0
$716$	−31.0485	−	34.4828i	−1.16034	−	1.28868i
$717$	3.66145	−	2.96499i	0.136740	−	0.110729i
$718$	0.0499613	−	0.186458i	0.00186454	−	0.00695856i
$719$	−28.4168	+	12.6520i	−1.05977	+	0.471839i	−0.861209	−	0.508250i	$-0.830292\pi$
$719$	−28.4168	+	12.6520i	−1.05977	+	0.471839i	−0.198558	+	0.980089i	$0.563626\pi$
$720$		0			0
$721$	−32.7512	+	21.1868i	−1.21972	+	0.789036i
$722$	−0.0688773	+	0.434874i	−0.00256335	+	0.0161843i
$723$	4.37258	+	6.73318i	0.162618	+	0.250409i
$724$	1.82812	+	3.16640i	0.0679417	+	0.117678i
$725$		0			0
$726$	−0.247682	−	0.142999i	−0.00919235	−	0.00530721i
$727$	−9.91394	+	19.4572i	−0.367688	+	0.721628i	−0.998525	−	0.0542869i	$-0.982711\pi$
$727$	−9.91394	+	19.4572i	−0.367688	+	0.721628i	0.630838	+	0.775915i	$0.282711\pi$
$728$	−0.0179388	−	0.0555432i	−0.000664855	−	0.00205857i
$729$	−11.5369	−	15.8791i	−0.427291	−	0.588116i
$730$		0			0
$731$	−21.0011	−	2.20731i	−0.776755	−	0.0816403i
$732$	−5.98986	−	1.60498i	−0.221392	−	0.0593217i
$733$	0.0807548	−	0.210373i	0.00298275	−	0.00777032i	−0.932081	−	0.362250i	$-0.882009\pi$
$733$	0.0807548	−	0.210373i	0.00298275	−	0.00777032i	0.935064	+	0.354480i	$0.115342\pi$
$734$	−0.0382810	+	0.117817i	−0.00141298	+	0.00434870i
$735$		0			0
$736$	−0.217655	−	0.669875i	−0.00802289	−	0.0246919i
$737$	33.0684	+	1.73304i	1.21809	+	0.0638375i
$738$	0.133447	−	0.205490i	0.00491224	−	0.00756419i
$739$	−29.9797	−	26.9939i	−1.10282	−	0.992986i	−0.102824	−	0.994700i	$-0.532788\pi$
$739$	−29.9797	−	26.9939i	−1.10282	−	0.992986i	−0.999999	+	0.00171350i	$0.999455\pi$
$740$		0			0
$741$	−2.30809	−	0.749943i	−0.0847897	−	0.0275498i
$742$	−0.415746	+	0.300937i	−0.0152625	+	0.0110478i
$743$	1.97911	+	1.97911i	0.0726064	+	0.0726064i	0.742477	−	0.669871i	$-0.233651\pi$
$743$	1.97911	+	1.97911i	0.0726064	+	0.0726064i	−0.669871	+	0.742477i	$0.733651\pi$
$744$	0.0237329	+	0.0533050i	0.000870090	+	0.00195426i
$745$		0			0
$746$	0.0611810	+	0.0272395i	0.00224000	+	0.000997310i
$747$	−1.40641	+	1.73678i	−0.0514580	+	0.0635454i
$748$	−33.7701	−	17.2067i	−1.23476	−	0.629141i
$749$	−27.4161	−	1.48535i	−1.00176	−	0.0542734i
$750$		0			0
$751$	14.9793	−	25.9449i	0.546602	−	0.946743i	−0.451902	−	0.892068i	$-0.649254\pi$
$751$	14.9793	−	25.9449i	0.546602	−	0.946743i	0.998504	−	0.0546754i	$-0.0174124\pi$
$752$	−25.1340	+	1.31722i	−0.916543	+	0.0480340i
$753$	−1.48792	−	3.87616i	−0.0542228	−	0.141255i
$754$	−0.00195776	−	0.0186268i	−7.12973e−5	−	0.000678349i
$755$		0			0
$756$	26.3910	−	10.0771i	0.959832	−	0.366502i
$757$	−29.2442	+	29.2442i	−1.06290	+	1.06290i	−0.0650131	+	0.997884i	$0.520709\pi$
$757$	−29.2442	+	29.2442i	−1.06290	+	1.06290i	−0.997884	+	0.0650131i	$0.979291\pi$
$758$	0.0738631	+	0.0283534i	0.00268283	+	0.00102984i
$759$	19.1803	−	4.07689i	0.696199	−	0.147982i
$760$		0			0
$761$	−9.89316	+	46.5437i	−0.358627	+	1.68721i	0.315769	+	0.948836i	$0.397738\pi$
$761$	−9.89316	+	46.5437i	−0.358627	+	1.68721i	−0.674396	+	0.738370i	$0.735596\pi$
$762$	0.279315	−	0.142318i	0.0101185	−	0.00515565i
$763$	−23.9408	−	2.55901i	−0.866714	−	0.0926424i
$764$	1.40090	−	0.455180i	0.0506828	−	0.0164679i
$765$		0			0
$766$	−0.101545	−	0.477733i	−0.00366898	−	0.0172612i
$767$	1.93269	+	2.38667i	0.0697852	+	0.0861776i
$768$	−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
$772$	22.4337	+	18.1665i	0.807407	+	0.653825i
$773$	0.0181612	+	0.346537i	0.000653213	+	0.0124641i	0.998937	−	0.0461029i	$-0.0146802\pi$
$773$	0.0181612	+	0.346537i	0.000653213	+	0.0124641i	−0.998283	+	0.0585670i	$0.981347\pi$
$774$	0.144615	−	0.0834938i	0.00519809	−	0.00300112i
$775$		0			0
$776$		−	0.853311i		−	0.0306321i
$777$	−0.0174102	+	9.86311i	−0.000624586	+	0.353837i
$778$	−0.497121	−	0.0787362i	−0.0178226	−	0.00282283i
$779$	55.0899	−	5.79018i	1.97380	−	0.207455i
$780$		0			0
$781$	−2.40393	+	22.8719i	−0.0860195	+	0.818421i
$782$	−0.211917	+	0.0567829i	−0.00757812	+	0.00203055i
$783$	17.9077	−	2.83631i	0.639970	−	0.101361i
$784$	2.82722	+	27.8444i	0.100972	+	0.994445i
$785$		0			0
$786$	−0.0566260	−	0.0120362i	−0.00201978	−	0.000429318i
$787$	8.11239	+	5.26825i	0.289175	+	0.187793i	0.681072	−	0.732217i	$-0.261514\pi$
$787$	8.11239	+	5.26825i	0.289175	+	0.187793i	−0.391896	+	0.920009i	$0.628181\pi$
$788$	−16.8613	−	10.9499i	−0.600659	−	0.390073i
$789$	23.0116	+	4.89126i	0.819234	+	0.174133i
$790$		0			0
$791$	3.49222	+	22.3038i	0.124169	+	0.793031i
$792$	0.592092	−	0.0937781i	0.0210391	−	0.00333226i
$793$	0.850484	−	0.227886i	0.0302016	−	0.00809249i
$794$	−0.00200022	+	0.0190308i	−7.09851e−5	+	0.000675378i
$795$		0			0
$796$	−12.6901	+	1.33378i	−0.449787	+	0.0472746i
$797$	−47.4366	−	7.51322i	−1.68029	−	0.266132i	−0.757895	−	0.652377i	$-0.773772\pi$
$797$	−47.4366	−	7.51322i	−1.68029	−	0.266132i	−0.922396	+	0.386245i	$0.873772\pi$
$798$	−0.297073	−	0.172215i	−0.0105163	−	0.00609636i
$799$			23.5245i			0.832235i
$800$		0			0
$801$	1.47727	−	0.852904i	0.0521969	−	0.0301359i
$802$	−0.00772680	−	0.147436i	−0.000272843	−	0.00520615i
$803$	−39.8239	−	32.2487i	−1.40535	−	1.13803i
$804$	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
$808$	−0.508888	−	0.628425i	−0.0179026	−	0.0221079i
$809$	6.71500	+	31.5916i	0.236087	+	1.11070i	0.923250	+	0.384199i	$0.125522\pi$
$809$	6.71500	+	31.5916i	0.236087	+	1.11070i	−0.687163	+	0.726503i	$0.741144\pi$
$810$		0			0
$811$	−25.8661	+	8.40440i	−0.908281	+	0.295118i	−0.725651	−	0.688063i	$-0.758461\pi$
$811$	−25.8661	+	8.40440i	−0.908281	+	0.295118i	−0.182630	+	0.983182i	$0.558461\pi$
$812$	−1.90944	+	17.8638i	−0.0670083	+	0.626895i
$813$	−1.40521	+	0.715992i	−0.0492830	+	0.0251109i
$814$	−0.0596895	+	0.280817i	−0.00209212	+	0.00984263i
$815$		0			0
$816$	−16.5309	+	3.51374i	−0.578696	+	0.123006i
$817$	35.2447	+	13.5292i	1.23306	+	0.473326i
$818$	0.188732	−	0.188732i	0.00659886	−	0.00659886i
$819$	−0.922080	+	1.13457i	−0.0322201	+	0.0396452i
$820$		0			0
$821$	−0.0494968	−	0.470930i	−0.00172745	−	0.0164356i	0.993624	−	0.112743i	$-0.0359636\pi$
$821$	−0.0494968	−	0.470930i	−0.00172745	−	0.0164356i	−0.995352	+	0.0963071i	$0.969297\pi$
$822$	0.107619	+	0.280358i	0.00375365	+	0.00977860i
$823$	16.1570	−	0.846752i	0.563197	−	0.0295159i	0.231387	−	0.972862i	$-0.425674\pi$
$823$	16.1570	−	0.846752i	0.563197	−	0.0295159i	0.331811	+	0.943346i	$0.392340\pi$
$824$	−0.506382	+	0.877080i	−0.0176407	+	0.0305545i
$825$		0			0
$826$	0.196589	+	0.387517i	0.00684021	+	0.0134835i
$827$	−12.0127	−	6.12078i	−0.417723	−	0.212841i	0.232480	−	0.972601i	$-0.425316\pi$
$827$	−12.0127	−	6.12078i	−0.417723	−	0.212841i	−0.650203	+	0.759761i	$0.725316\pi$
$828$	−7.40172	+	9.14036i	−0.257227	+	0.317649i
$829$	3.14458	+	1.40006i	0.109216	+	0.0486259i	0.460617	−	0.887599i	$-0.347628\pi$
$829$	3.14458	+	1.40006i	0.109216	+	0.0486259i	−0.351402	+	0.936225i	$0.614295\pi$
$830$		0			0
$831$	13.8169	+	31.0333i	0.479304	+	1.07653i
$832$	1.81509	+	1.81509i	0.0629271	+	0.0629271i
$833$	26.1282	−	1.27684i	0.905289	−	0.0442400i
$834$	−0.341022	−	0.110805i	−0.0118086	−	0.00383686i
$835$		0			0
$836$	50.3546	+	45.3395i	1.74155	+	1.56810i
$837$	2.18389	−	3.36289i	0.0754861	−	0.116238i
$838$	0.108705	+	0.00569699i	0.00375516	+	0.000196799i
$839$	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
$842$	0.136491	−	0.355571i	0.00470378	−	0.0122538i
$843$	31.2079	+	8.36213i	1.07486	+	0.288007i
$844$	−56.2215	−	5.90911i	−1.93522	−	0.203400i
$845$		0			0
$846$	−0.109344	−	0.150499i	−0.00375931	−	0.00517425i
$847$	−38.0864	−	8.16580i	−1.30866	−	0.280580i
$848$	20.5017	−	40.2368i	0.704030	−	1.38174i
$849$	27.5654	+	15.9149i	0.946042	+	0.546198i
$850$		0			0
$851$	−5.63304	−	9.75671i	−0.193098	−	0.334456i
$852$	5.58599	+	8.60167i	0.191373	+	0.294688i
$853$	4.81360	−	30.3919i	0.164815	−	1.04060i	−0.757126	−	0.653268i	$-0.773397\pi$
$853$	4.81360	−	30.3919i	0.164815	−	1.04060i	0.921941	−	0.387330i	$-0.126603\pi$
$854$	0.124422	−	0.00630047i	0.00425764	−	0.000215598i
$855$		0			0
$856$	−0.651240	+	0.289951i	−0.0222589	+	0.00991032i
$857$	1.08695	−	4.05654i	0.0371294	−	0.138569i	−0.944873	−	0.327437i	$-0.893815\pi$
$857$	1.08695	−	4.05654i	0.0371294	−	0.138569i	0.982002	+	0.188868i	$0.0604818\pi$
$858$	0.0245896	−	0.0199123i	0.000839476	−	0.000679794i
$859$	−4.81200	−	5.34427i	−0.164183	−	0.182344i	0.655439	−	0.755248i	$-0.272484\pi$
$859$	−4.81200	−	5.34427i	−0.164183	−	0.182344i	−0.819623	+	0.572904i	$0.805817\pi$
$860$		0			0
$861$	−6.46404	+	23.9549i	−0.220294	+	0.816381i
$862$	0.0758837	+	0.148930i	0.00258461	+	0.00507258i
$863$	0.516497	−	9.85535i	0.0175818	−	0.335480i	−0.975650	−	0.219332i	$-0.929612\pi$
$863$	0.516497	−	9.85535i	0.0175818	−	0.335480i	0.993232	−	0.116148i	$-0.0370546\pi$
$864$	0.736196	−	0.817629i	0.0250459	−	0.0278163i
$865$		0			0
$866$	0.158831	−	0.143012i	0.00539730	−	0.00485975i
$867$	−0.536908	−	3.38990i	−0.0182343	−	0.115127i
$868$	2.65337	+	2.95735i	0.0900613	+	0.100379i
$869$	−24.4604	+	33.6668i	−0.829761	+	1.14207i
$870$		0			0
$871$	−0.852855	+	1.91554i	−0.0288979	+	0.0649057i
$872$	−0.583615	+	0.224029i	−0.0197637	+	0.00758658i
$873$	−17.9256	+	11.6410i	−0.606690	+	0.393989i
$874$	0.392224			0.0132672
$875$		0			0
$876$	−22.8531			−0.772133
$877$	−27.4507	+	17.8267i	−0.926944	+	0.601965i	−0.917390	−	0.397990i	$-0.869708\pi$
$877$	−27.4507	+	17.8267i	−0.926944	+	0.601965i	−0.00955443	+	0.999954i	$0.503041\pi$
$878$	−0.393367	+	0.150999i	−0.0132755	+	0.00509598i
$879$	−2.97171	+	6.67457i	−0.100233	+	0.225128i
$880$		0			0
$881$	11.3837	−	15.6683i	0.383527	−	0.527880i	−0.572988	−	0.819564i	$-0.694216\pi$
$881$	11.3837	−	15.6683i	0.383527	−	0.527880i	0.956515	+	0.291684i	$0.0942157\pi$
$882$	−0.161221	+	0.129615i	−0.00542861	+	0.00436436i
$883$	−5.72089	−	36.1203i	−0.192523	−	1.21554i	−0.874813	−	0.484461i	$-0.839016\pi$
$883$	−5.72089	−	36.1203i	−0.192523	−	1.21554i	0.682289	−	0.731082i	$-0.260984\pi$
$884$	1.78352	−	1.60589i	0.0599863	−	0.0540119i
$885$		0			0
$886$	−0.0805312	+	0.0894389i	−0.00270550	+	0.00300476i
$887$	0.598808	−	11.4259i	0.0201060	−	0.383645i	−0.969980	−	0.243184i	$-0.921808\pi$
$887$	0.598808	−	11.4259i	0.0201060	−	0.383645i	0.990086	−	0.140461i	$-0.0448586\pi$
$888$	0.116260	+	0.228174i	0.00390144	+	0.00765701i
$889$	30.2433	−	30.1367i	1.01433	−	1.01075i
$890$		0			0
$891$	2.97749	+	3.30683i	0.0997496	+	0.110783i
$892$	−32.9007	+	26.6424i	−1.10160	+	0.892055i
$893$	10.8850	−	40.6235i	0.364253	−	1.35941i
$894$	−0.261747	+	0.116537i	−0.00875414	+	0.00389759i
$895$		0			0
$896$	0.789507	+	1.22044i	0.0263756	+	0.0407722i
$897$	−0.194238	+	1.22637i	−0.00648543	+	0.0409474i
$898$	0.106427	+	0.163883i	0.00355151	+	0.00546885i
$899$	1.27503	+	2.20841i	0.0425246	+	0.0736547i
$900$		0			0
$901$	−36.5540	−	21.1045i	−1.21779	−	0.703091i
$902$	−0.327875	+	0.643490i	−0.0109170	+	0.0214259i
$903$	−11.3371	+	12.5465i	−0.377275	+	0.417522i
$904$	0.344529	+	0.474204i	0.0114589	+	0.0157718i
$905$		0			0
$906$	−0.108430	−	0.0113965i	−0.00360235	−	0.000378622i
$907$	0.668595	+	0.179150i	0.0222003	+	0.00594856i	0.269902	−	0.962888i	$-0.413009\pi$
$907$	0.668595	+	0.179150i	0.0222003	+	0.00594856i	−0.247702	+	0.968836i	$0.579675\pi$
$908$	−14.2908	+	37.2289i	−0.474258	+	1.23548i
$909$	−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	$0.771900\pi$
$912$	30.1723	+	1.58127i	0.999106	+	0.0523609i
$913$	3.58767	−	5.52452i	0.118734	−	0.182835i
$914$	−0.0875168	−	0.0788005i	−0.00289480	−	0.00260649i
$915$		0			0
$916$	−19.0991	−	6.20568i	−0.631053	−	0.205042i
$917$	−7.84279	+	0.810316i	−0.258992	+	0.0267590i
$918$	−0.242327	−	0.242327i	−0.00799798	−	0.00799798i
$919$	−3.16025	−	7.09803i	−0.104247	−	0.234142i	0.853890	−	0.520454i	$-0.174237\pi$
$919$	−3.16025	−	7.09803i	−0.104247	−	0.234142i	−0.958137	+	0.286312i	$0.907571\pi$
$920$		0			0
$921$	18.2583	+	8.12912i	0.601632	+	0.267864i
$922$	0.0704407	−	0.0869870i	0.00231984	−	0.00286476i
$923$	−1.29754	−	0.661131i	−0.0427091	−	0.0217614i
$924$	−27.0667	+	13.7310i	−0.890429	+	0.451718i
$925$		0			0
$926$	0.0385095	−	0.0667005i	0.00126550	−	0.00219191i
$927$	25.3331	−	1.32765i	0.832048	−	0.0436058i
$928$	0.250750	+	0.653225i	0.00823126	+	0.0214432i
$929$	−5.76695	−	54.8689i	−0.189208	−	1.80019i	−0.517573	−	0.855639i	$-0.673164\pi$
$929$	−5.76695	−	54.8689i	−0.189208	−	1.80019i	0.328365	−	0.944551i	$-0.393502\pi$
$930$		0			0
$931$	−45.7106	−	9.88488i	−1.49810	−	0.323964i
$932$	3.94681	−	3.94681i	0.129282	−	0.129282i
$933$	7.89587	+	3.03094i	0.258499	+	0.0992286i
$934$	0.674889	−	0.143452i	0.0220831	−	0.00469390i
$935$		0			0
$936$	−0.00789225	+	0.0371301i	−0.000257966	+	0.00121364i
$937$	−30.2515	+	15.4139i	−0.988274	+	0.503551i	−0.871915	−	0.489657i	$-0.837122\pi$
$937$	−30.2515	+	15.4139i	−0.988274	+	0.503551i	−0.116358	+	0.993207i	$0.537122\pi$
$938$	−0.174809	+	0.239714i	−0.00570773	+	0.00782693i
$939$	−29.9400	+	9.72811i	−0.977057	+	0.317465i
$940$		0			0
$941$	4.83848	+	22.7633i	0.157730	+	0.742061i	0.983911	+	0.178657i	$0.0571753\pi$
$941$	4.83848	+	22.7633i	0.157730	+	0.742061i	−0.826181	+	0.563404i	$0.809491\pi$
$942$	0.0641359	+	0.0792012i	0.00208966	+	0.00258051i
$943$	−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
$947$	−25.0666	−	20.2986i	−0.814556	−	0.659615i	0.128699	−	0.991684i	$-0.458920\pi$
$947$	−25.0666	−	20.2986i	−0.814556	−	0.659615i	−0.943255	+	0.332069i	$0.892253\pi$
$948$	0.971287	+	18.5333i	0.0315459	+	0.601932i
$949$	2.81012	−	1.62242i	0.0912202	−	0.0526660i
$950$		0			0
$951$		−	32.3214i		−	1.04809i
$952$	0.588803	−	0.338561i	0.0190832	−	0.0109728i
$953$	28.1170	+	4.45329i	0.910797	+	0.144256i	0.594213	−	0.804308i	$-0.297464\pi$
$953$	28.1170	+	4.45329i	0.910797	+	0.144256i	0.316585	+	0.948564i	$0.397464\pi$
$954$	0.331951	−	0.0348895i	0.0107473	−	0.00112959i
$955$		0			0
$956$	0.870679	−	8.28396i	0.0281598	−	0.267922i
$957$	−18.8156	+	5.04162i	−0.608222	+	0.162973i
$958$	−0.351762	+	0.0557136i	−0.0113649	+	0.00180002i
$959$	25.6832	+	31.8308i	0.829353	+	1.02787i
$960$		0			0
$961$	−29.7709	−	6.32801i	−0.960353	−	0.204129i
$962$	−0.0152463	−	0.00990103i	−0.000491559	−	0.000319222i
$963$	14.9754	+	9.72513i	0.482575	+	0.313388i
$964$	13.8837	+	2.95107i	0.447164	+	0.0950476i
$965$		0			0
$966$	−0.0632492	+	0.163904i	−0.00203501	+	0.00527354i
$967$	−21.0805	+	3.33883i	−0.677904	+	0.107369i	−0.485886	−	0.874022i	$-0.661503\pi$
$967$	−21.0805	+	3.33883i	−0.677904	+	0.107369i	−0.192018	+	0.981391i	$0.561503\pi$
$968$	−0.976883	+	0.261755i	−0.0313982	+	0.00841312i
$969$	2.95190	−	28.0854i	0.0948286	−	0.902234i
$970$		0			0
$971$	52.9519	−	5.56547i	1.69931	−	0.178604i	0.795328	−	0.606179i	$-0.207299\pi$
$971$	52.9519	−	5.56547i	1.69931	−	0.178604i	0.903980	+	0.427575i	$0.140632\pi$
$972$	−29.6775	−	4.70046i	−0.951908	−	0.150767i
$973$	−48.8361	−	0.0862044i	−1.56561	−	0.00276359i
$974$		−	0.127666i		−	0.00409070i
$975$		0			0
$976$	−9.49319	+	5.48089i	−0.303870	+	0.175439i
$977$	1.94719	+	37.1545i	0.0622960	+	1.18868i	0.833658	+	0.552282i	$0.186243\pi$
$977$	1.94719	+	37.1545i	0.0622960	+	1.18868i	−0.771362	+	0.636397i	$0.780424\pi$
$978$	−0.268139	−	0.217135i	−0.00857416	−	0.00694321i
$979$	−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
$983$	−12.6142	−	15.5773i	−0.402331	−	0.496838i	0.535206	−	0.844721i	$-0.320234\pi$
$983$	−12.6142	−	15.5773i	−0.402331	−	0.496838i	−0.937538	+	0.347883i	$0.886900\pi$
$984$	0.133939	+	0.630131i	0.00426980	+	0.0200879i
$985$		0			0
$986$	0.207277	−	0.0673484i	0.00660105	−	0.00214481i
$987$	15.2206	+	11.0995i	0.484477	+	0.353302i
$988$	−3.82295	+	1.94789i	−0.121624	+	0.0619707i
$989$	4.01586	−	18.8931i	0.127697	−	0.600766i
$990$		0			0
$991$	38.8742	−	8.26297i	1.23488	−	0.262482i	0.456185	−	0.889885i	$-0.349215\pi$
$991$	38.8742	−	8.26297i	1.23488	−	0.262482i	0.778695	+	0.627403i	$0.215882\pi$
$992$	0.144465	+	0.0554550i	0.00458678	+	0.00176070i
$993$	−13.3562	+	13.3562i	−0.423847	+	0.423847i
$994$	−0.159901	−	0.129954i	−0.00507176	−	0.00412188i
$995$		0			0
$996$	−0.307073	−	2.92160i	−0.00972997	−	0.0925745i
$997$	4.08061	+	10.6304i	0.129234	+	0.336667i	0.982896	−	0.184161i	$-0.0589567\pi$
$997$	4.08061	+	10.6304i	0.129234	+	0.336667i	−0.853662	+	0.520828i	$0.825623\pi$
$998$	0.157881	−	0.00827421i	0.00499764	−	0.000261915i
$999$	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.c.768.10		288
5.2	odd	4		875.2.bb.a.607.10		288
5.3	odd	4		875.2.bb.b.607.9		288
5.4	even	2		175.2.x.a.33.9	✓	288
7.3	odd	6	inner	875.2.bb.c.143.10		288
25.3	odd	20		175.2.x.a.47.9	yes	288
25.4	even	10		875.2.bb.b.243.10		288
25.21	even	5		875.2.bb.a.243.9		288
25.22	odd	20	inner	875.2.bb.c.257.10		288
35.3	even	12		875.2.bb.b.857.10		288
35.17	even	12		875.2.bb.a.857.9		288
35.24	odd	6		175.2.x.a.108.9	yes	288
175.3	even	60		175.2.x.a.122.9	yes	288
175.122	even	60	inner	875.2.bb.c.507.10		288
175.129	odd	30		875.2.bb.b.493.9		288
175.171	odd	30		875.2.bb.a.493.10		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.9	✓	288	5.4	even	2
175.2.x.a.47.9	yes	288	25.3	odd	20
175.2.x.a.108.9	yes	288	35.24	odd	6
175.2.x.a.122.9	yes	288	175.3	even	60
875.2.bb.a.243.9		288	25.21	even	5
875.2.bb.a.493.10		288	175.171	odd	30
875.2.bb.a.607.10		288	5.2	odd	4
875.2.bb.a.857.9		288	35.17	even	12
875.2.bb.b.243.10		288	25.4	even	10
875.2.bb.b.493.9		288	175.129	odd	30
875.2.bb.b.607.9		288	5.3	odd	4
875.2.bb.b.857.10		288	35.3	even	12
875.2.bb.c.143.10		288	7.3	odd	6	inner
875.2.bb.c.257.10		288	25.22	odd	20	inner
875.2.bb.c.507.10		288	175.122	even	60	inner
875.2.bb.c.768.10		288	1.1	even	1	trivial

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+(-0.0144040 + 0.00935405i) q^{2} +(-1.05595 + 0.405343i) q^{3} +(-0.813353 + 1.82682i) q^{4} +(0.0114183 - 0.0157160i) q^{6} +(0.822022 - 2.51481i) q^{7} +(-0.0107461 - 0.0678483i) q^{8} +(-1.27870 + 1.15134i) q^{9} +(3.39365 - 3.76903i) q^{11} +(0.118375 - 2.25873i) q^{12} +(0.145799 + 0.286147i) q^{13} +(0.0116833 + 0.0439125i) q^{14} +(-2.67534 - 2.97126i) q^{16} +(-2.90424 + 2.35181i) q^{17} +(0.00764859 - 0.0285449i) q^{18} +(6.10342 - 2.71742i) q^{19} +(0.151343 + 2.98873i) q^{21} +(-0.0136263 + 0.0860334i) q^{22} +(-1.86170 - 2.86676i) q^{23} +(0.0388492 + 0.0672888i) q^{24} +(-0.00477673 - 0.00275784i) q^{26} +(2.42406 - 4.75748i) q^{27} +(3.92552 + 3.54712i) q^{28} +(1.99592 + 2.74715i) q^{29} +(0.746861 + 0.0784982i) q^{31} +(0.199035 + 0.0533314i) q^{32} +(-2.05579 + 5.35552i) q^{33} +(0.0198337 - 0.0610417i) q^{34} +(-1.06327 - 3.27240i) q^{36} +(3.29137 + 0.172493i) q^{37} +(-0.0624947 + 0.0962334i) q^{38} +(-0.269945 - 0.243060i) q^{39} +(7.88534 + 2.56210i) q^{41} +(-0.0301367 - 0.0416339i) q^{42} +(3.99562 + 3.99562i) q^{43} +(4.12511 + 9.26514i) q^{44} +(0.0536317 + 0.0238784i) q^{46} +(3.96152 - 4.89207i) q^{47} +(4.02942 + 2.05309i) q^{48} +(-5.64856 - 4.13446i) q^{49} +(2.11346 - 3.66061i) q^{51} +(-0.641326 + 0.0336105i) q^{52} +(4.04766 + 10.5445i) q^{53} +(0.00958565 + 0.0912013i) q^{54} +(-0.179459 - 0.0287484i) q^{56} +(-5.34345 + 5.34345i) q^{57} +(-0.0544462 - 0.0208999i) q^{58} +(9.35373 - 1.98820i) q^{59} +(0.570023 - 2.68175i) q^{61} +(-0.0114920 + 0.00585548i) q^{62} +(1.84430 + 4.16211i) q^{63} +(7.60172 - 2.46995i) q^{64} +(-0.0204842 - 0.0963707i) q^{66} +(4.10889 + 5.07406i) q^{67} +(-1.93416 - 7.21837i) q^{68} +(3.12789 + 2.27255i) q^{69} +(-3.66851 + 2.66533i) q^{71} +(0.0918577 + 0.0743849i) q^{72} +(-0.528792 - 10.0900i) q^{73} +(-0.0490223 + 0.0283030i) q^{74} +13.3601i q^{76} +(-6.68874 - 11.6326i) q^{77} +(0.00616188 + 0.000975946i) q^{78} +(-8.16023 + 0.857674i) q^{79} +(-0.0917101 + 0.872564i) q^{81} +(-0.137546 + 0.0368554i) q^{82} +(1.28282 - 0.203179i) q^{83} +(-5.58297 - 2.15442i) q^{84} +(-0.0949280 - 0.0201776i) q^{86} +(-3.22114 - 2.09183i) q^{87} +(-0.292191 - 0.189751i) q^{88} +(-0.969707 - 0.206118i) q^{89} +(0.839457 - 0.131438i) q^{91} +(6.75128 - 1.06930i) q^{92} +(-0.820470 + 0.219844i) q^{93} +(-0.0113010 + 0.107521i) q^{94} +(-0.231790 + 0.0243621i) q^{96} +(12.2690 + 1.94322i) q^{97} +(0.120036 + 0.00671581i) q^{98} +8.72671i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

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