LMFDB - Embedded newform 875.2.bb.b.607.9

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			607.9
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.b.493.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.00935405 + 0.0144040i) q^{2} +(-0.405343 - 1.05595i) q^{3} +(0.813353 - 1.82682i) q^{4} +(0.0114183 - 0.0157160i) q^{6} +(-2.51481 - 0.822022i) q^{7} +(0.0678483 - 0.0107461i) q^{8} +(1.27870 - 1.15134i) q^{9} +(3.39365 - 3.76903i) q^{11} +(-2.25873 - 0.118375i) q^{12} +(-0.286147 + 0.145799i) q^{13} +(-0.0116833 - 0.0439125i) q^{14} +(-2.67534 - 2.97126i) q^{16} +(2.35181 + 2.90424i) q^{17} +(0.0285449 + 0.00764859i) q^{18} +(-6.10342 + 2.71742i) q^{19} +(0.151343 + 2.98873i) q^{21} +(0.0860334 + 0.0136263i) q^{22} +(2.86676 - 1.86170i) q^{23} +(-0.0388492 - 0.0672888i) q^{24} +(-0.00477673 - 0.00275784i) q^{26} +(-4.75748 - 2.42406i) q^{27} +(-3.54712 + 3.92552i) q^{28} +(-1.99592 - 2.74715i) q^{29} +(0.746861 + 0.0784982i) q^{31} +(0.0533314 - 0.199035i) q^{32} +(-5.35552 - 2.05579i) q^{33} +(-0.0198337 + 0.0610417i) q^{34} +(-1.06327 - 3.27240i) q^{36} +(0.172493 - 3.29137i) q^{37} +(-0.0962334 - 0.0624947i) q^{38} +(0.269945 + 0.243060i) q^{39} +(7.88534 + 2.56210i) q^{41} +(-0.0416339 + 0.0301367i) q^{42} +(-3.99562 + 3.99562i) q^{43} +(-4.12511 - 9.26514i) q^{44} +(0.0536317 + 0.0238784i) q^{46} +(-4.89207 - 3.96152i) q^{47} +(-2.05309 + 4.02942i) q^{48} +(5.64856 + 4.13446i) q^{49} +(2.11346 - 3.66061i) q^{51} +(0.0336105 + 0.641326i) q^{52} +(-10.5445 + 4.04766i) q^{53} +(-0.00958565 - 0.0912013i) q^{54} +(-0.179459 - 0.0287484i) q^{56} +(5.34345 + 5.34345i) q^{57} +(0.0208999 - 0.0544462i) q^{58} +(-9.35373 + 1.98820i) q^{59} +(0.570023 - 2.68175i) q^{61} +(0.00585548 + 0.0114920i) q^{62} +(-4.16211 + 1.84430i) q^{63} +(-7.60172 + 2.46995i) q^{64} +(-0.0204842 - 0.0963707i) q^{66} +(5.07406 - 4.10889i) q^{67} +(7.21837 - 1.93416i) q^{68} +(-3.12789 - 2.27255i) q^{69} +(-3.66851 + 2.66533i) q^{71} +(0.0743849 - 0.0918577i) q^{72} +(10.0900 - 0.528792i) q^{73} +(0.0490223 - 0.0283030i) q^{74} +13.3601i q^{76} +(-11.6326 + 6.68874i) q^{77} +(-0.000975946 + 0.00616188i) q^{78} +(8.16023 - 0.857674i) q^{79} +(-0.0917101 + 0.872564i) q^{81} +(0.0368554 + 0.137546i) q^{82} +(0.203179 + 1.28282i) q^{83} +(5.58297 + 2.15442i) q^{84} +(-0.0949280 - 0.0201776i) q^{86} +(-2.09183 + 3.22114i) q^{87} +(0.189751 - 0.292191i) q^{88} +(0.969707 + 0.206118i) q^{89} +(0.839457 - 0.131438i) q^{91} +(-1.06930 - 6.75128i) q^{92} +(-0.219844 - 0.820470i) q^{93} +(0.0113010 - 0.107521i) q^{94} +(-0.231790 + 0.0243621i) q^{96} +(1.94322 - 12.2690i) q^{97} +(-0.00671581 + 0.120036i) 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 $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{13}{20}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.00935405	+	0.0144040i	0.00661431	+	0.0101851i	0.841962	−	0.539536i	$-0.181400\pi$
$2$	0.00935405	+	0.0144040i	0.00661431	+	0.0101851i	−0.835348	+	0.549722i	$0.814734\pi$
$3$	−0.405343	−	1.05595i	−0.234025	−	0.609656i	0.765400	−	0.643554i	$-0.222541\pi$
$3$	−0.405343	−	1.05595i	−0.234025	−	0.609656i	−0.999425	+	0.0338987i	$0.989208\pi$
$4$	0.813353	−	1.82682i	0.406677	−	0.913411i
$5$		0			0
$5$		0			0
$6$	0.0114183	−	0.0157160i	0.00466152	−	0.00641603i
$7$	−2.51481	−	0.822022i	−0.950510	−	0.310695i
$7$	−2.51481	−	0.822022i	−0.950510	−	0.310695i
$8$	0.0678483	−	0.0107461i	0.0239880	−	0.00379932i
$9$	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	$-0.0437262\pi$
$12$	−2.25873	−	0.118375i	−0.652039	−	0.0341719i
$13$	−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	$0.364181\pi$
$14$	−0.0116833	−	0.0439125i	−0.00312249	−	0.0117361i
$15$		0			0
$16$	−2.67534	−	2.97126i	−0.668835	−	0.742816i
$17$	2.35181	+	2.90424i	0.570397	+	0.704381i	0.977959	−	0.208796i	$-0.0669545\pi$
$17$	2.35181	+	2.90424i	0.570397	+	0.704381i	−0.407562	+	0.913177i	$0.633621\pi$
$18$	0.0285449	+	0.00764859i	0.00672810	+	0.00180279i
$19$	−6.10342	+	2.71742i	−1.40022	+	0.623419i	−0.961400	−	0.275155i	$-0.911271\pi$
$19$	−6.10342	+	2.71742i	−1.40022	+	0.623419i	−0.438822	+	0.898574i	$0.644604\pi$
$20$		0			0
$21$	0.151343	+	2.98873i	0.0330257	+	0.652194i
$22$	0.0860334	+	0.0136263i	0.0183424	+	0.00290515i
$23$	2.86676	−	1.86170i	0.597762	−	0.388191i	−0.209999	−	0.977702i	$-0.567346\pi$
$23$	2.86676	−	1.86170i	0.597762	−	0.388191i	0.807761	+	0.589511i	$0.200679\pi$
$24$	−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
$28$	−3.54712	+	3.92552i	−0.670342	+	0.741853i
$29$	−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
$31$	0.746861	+	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	$0.511850\pi$
$32$	0.0533314	−	0.199035i	0.00942775	−	0.0351848i
$33$	−5.35552	−	2.05579i	−0.932276	−	0.357867i
$34$	−0.0198337	+	0.0610417i	−0.00340145	+	0.0104686i
$35$		0			0
$36$	−1.06327	−	3.27240i	−0.177211	−	0.545400i
$37$	0.172493	−	3.29137i	0.0283577	−	0.541098i	−0.947104	−	0.320928i	$-0.896005\pi$
$37$	0.172493	−	3.29137i	0.0283577	−	0.541098i	0.975461	−	0.220170i	$-0.0706613\pi$
$38$	−0.0962334	−	0.0624947i	−0.0156111	−	0.0101380i
$39$	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	$0.375844\pi$
$42$	−0.0416339	+	0.0301367i	−0.00642425	+	0.00465019i
$43$	−3.99562	+	3.99562i	−0.609326	+	0.609326i	−0.942770	−	0.333444i	$-0.891789\pi$
$43$	−3.99562	+	3.99562i	−0.609326	+	0.609326i	0.333444	+	0.942770i	$0.391789\pi$
$44$	−4.12511	−	9.26514i	−0.621883	−	1.39677i
$45$		0			0
$46$	0.0536317	+	0.0238784i	0.00790756	+	0.00352067i
$47$	−4.89207	−	3.96152i	−0.713581	−	0.577847i	0.202287	−	0.979326i	$-0.435163\pi$
$47$	−4.89207	−	3.96152i	−0.713581	−	0.577847i	−0.915868	+	0.401480i	$0.868496\pi$
$48$	−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
$52$	0.0336105	+	0.641326i	0.00466094	+	0.0889360i
$53$	−10.5445	+	4.04766i	−1.44840	+	0.555988i	−0.950356	−	0.311164i	$-0.899281\pi$
$53$	−10.5445	+	4.04766i	−1.44840	+	0.555988i	−0.498043	+	0.867152i	$0.665948\pi$
$54$	−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
$58$	0.0208999	−	0.0544462i	0.00274429	−	0.00714913i
$59$	−9.35373	+	1.98820i	−1.21775	+	0.258841i	−0.771595	−	0.636114i	$-0.780541\pi$
$59$	−9.35373	+	1.98820i	−1.21775	+	0.258841i	−0.446157	+	0.894955i	$0.647208\pi$
$60$		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	$0.0105070\pi$
$62$	0.00585548	+	0.0114920i	0.000743647	+	0.00145949i
$63$	−4.16211	+	1.84430i	−0.524377	+	0.232359i
$64$	−7.60172	+	2.46995i	−0.950215	+	0.308744i
$65$		0			0
$66$	−0.0204842	−	0.0963707i	−0.00252143	−	0.0118624i
$67$	5.07406	−	4.10889i	0.619895	−	0.501981i	−0.267155	−	0.963653i	$-0.586084\pi$
$67$	5.07406	−	4.10889i	0.619895	−	0.501981i	0.887051	+	0.461672i	$0.152750\pi$
$68$	7.21837	−	1.93416i	0.875357	−	0.234551i
$69$	−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	$0.386718\pi$
$72$	0.0743849	−	0.0918577i	0.00876635	−	0.0108255i
$73$	10.0900	−	0.528792i	1.18094	−	0.0618904i	0.548263	−	0.836306i	$-0.315289\pi$
$73$	10.0900	−	0.528792i	1.18094	−	0.0618904i	0.632677	+	0.774416i	$0.281956\pi$
$74$	0.0490223	−	0.0283030i	0.00569873	−	0.00329016i
$75$		0			0
$76$			13.3601i			1.53251i
$77$	−11.6326	+	6.68874i	−1.32566	+	0.762253i
$78$	−0.000975946		0.00616188i	−0.000110504		0.000697695i
$79$	8.16023	−	0.857674i	0.918097	−	0.0964959i	0.366321	−	0.930488i	$-0.380617\pi$
$79$	8.16023	−	0.857674i	0.918097	−	0.0964959i	0.551776	+	0.833992i	$0.313950\pi$
$80$		0			0
$81$	−0.0917101	+	0.872564i	−0.0101900	+	0.0969515i
$82$	0.0368554	+	0.137546i	0.00407000	+	0.0151894i
$83$	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	$0.927291\pi$
$84$	5.58297	+	2.15442i	0.609152	+	0.235066i
$85$		0			0
$86$	−0.0949280	−	0.0201776i	−0.0102363	−	0.00217580i
$87$	−2.09183	+	3.22114i	−0.224268	+	0.345342i
$88$	0.189751	−	0.292191i	0.0202275	−	0.0311476i
$89$	0.969707	+	0.206118i	0.102789	+	0.0218484i	0.259019	−	0.965872i	$-0.416601\pi$
$89$	0.969707	+	0.206118i	0.102789	+	0.0218484i	−0.156230	+	0.987721i	$0.549934\pi$
$90$		0			0
$91$	0.839457	−	0.131438i	0.0879990	−	0.0137785i
$92$	−1.06930	−	6.75128i	−0.111482	−	0.703870i
$93$	−0.219844	−	0.820470i	−0.0227968	−	0.0850787i
$94$	0.0113010	−	0.107521i	0.00116560	−	0.0110900i
$95$		0			0
$96$	−0.231790	+	0.0243621i	−0.0236570	+	0.00248645i
$97$	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	$-0.167202\pi$
$98$	−0.00671581	+	0.120036i	−0.000678400	+	0.0121254i
$99$		−	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	$0.134171\pi$
$102$	0.0724967	−	0.00379939i	0.00717825	−	0.000376196i
$103$	9.27815	−	11.4576i	0.914203	−	1.12895i	−0.0770569	−	0.997027i	$-0.524552\pi$
$103$	9.27815	−	11.4576i	0.914203	−	1.12895i	0.991260	−	0.131920i	$-0.0421143\pi$
$104$	−0.0178478	+	0.0129672i	−0.00175012	+	0.00127154i
$105$		0			0
$106$	−0.156936	−	0.114021i	−0.0152430	−	0.0110747i
$107$	−10.0239	+	2.68589i	−0.969046	+	0.259655i	−0.708425	−	0.705786i	$-0.750594\pi$
$107$	−10.0239	+	2.68589i	−0.969046	+	0.259655i	−0.260621	+	0.965441i	$0.583927\pi$
$108$	−8.29783	+	6.71945i	−0.798459	+	0.646579i
$109$	1.89206	+	8.90145i	0.181227	+	0.852604i	0.970976	+	0.239175i	$0.0768770\pi$
$109$	1.89206	+	8.90145i	0.181227	+	0.852604i	−0.789750	+	0.613429i	$0.789790\pi$
$110$		0			0
$111$	−3.54546	+	1.15199i	−0.336520	+	0.109342i
$112$	4.28553	+	9.67136i	0.404944	+	0.913857i
$113$	−3.87378	−	7.60273i	−0.364415	−	0.715204i	0.633889	−	0.773424i	$-0.281458\pi$
$113$	−3.87378	−	7.60273i	−0.364415	−	0.715204i	−0.998304	+	0.0582196i	$0.981458\pi$
$114$	−0.0269840	+	0.126950i	−0.00252729	+	0.0118899i
$115$		0			0
$116$	−6.64194	+	1.41179i	−0.616689	+	0.131081i
$117$	−0.198031	+	0.515887i	−0.0183079	+	0.0476938i
$118$	−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
$122$	0.0439598	−	0.0168746i	0.00397994	−	0.00152775i
$123$	−0.490804	−	9.36510i	−0.0442543	−	0.844422i
$124$	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	$-0.595983\pi$
$127$	7.32616	−	14.3784i	0.650091	−	1.27588i	0.947081	−	0.320996i	$-0.104017\pi$
$128$	−0.426956	−	0.345742i	−0.0377379	−	0.0305596i
$129$	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
$133$	17.5827	−	1.81665i	1.52462	−	0.157523i
$134$	0.106647	+	0.0346518i	0.00921293	+	0.00299346i
$135$		0			0
$136$	0.190775	+	0.171775i	0.0163588	+	0.0147296i
$137$	12.9649	+	8.41948i	1.10766	+	0.719324i	0.962824	−	0.270131i	$-0.0870670\pi$
$137$	12.9649	+	8.41948i	1.10766	+	0.719324i	0.144839	+	0.989455i	$0.453734\pi$
$138$	0.00347524	−	0.0663116i	0.000295832	−	0.00564482i
$139$	5.70394	+	17.5549i	0.483801	+	1.48899i	0.833709	+	0.552204i	$0.186213\pi$
$139$	5.70394	+	17.5549i	0.483801	+	1.48899i	−0.349908	+	0.936784i	$0.613787\pi$
$140$		0			0
$141$	−2.20022	+	6.77157i	−0.185292	+	0.570269i
$142$	−0.0727067	−	0.0279095i	−0.00610141	−	0.00234211i
$143$	−0.421562	+	1.57329i	−0.0352528	+	0.131565i
$144$	−6.84189	−	0.719112i	−0.570158	−	0.0599260i
$145$		0			0
$146$	0.101999	+	0.140389i	0.00844147	+	0.0116187i
$147$	2.07620	−	7.64050i	0.171242	−	0.630178i
$148$	−5.87245	−	2.99216i	−0.482712	−	0.245954i
$149$	12.7732	+	7.37458i	1.04642	+	0.604149i	0.921644	−	0.388036i	$-0.126846\pi$
$149$	12.7732	+	7.37458i	1.04642	+	0.604149i	0.124773	+	0.992185i	$0.460180\pi$
$150$		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	$0.906672\pi$
$152$	−0.384905	+	0.249960i	−0.0312199	+	0.0202745i
$153$	6.35103	+	1.00590i	0.513450	+	0.0813225i
$154$	−0.205157	−	0.104989i	−0.0165320	−	0.00846026i
$155$		0			0
$156$	0.663588	−	0.295448i	0.0531295	−	0.0236548i
$157$	5.06744	+	1.35782i	0.404426	+	0.108366i	0.455297	−	0.890340i	$-0.349533\pi$
$157$	5.06744	+	1.35782i	0.404426	+	0.108366i	−0.0508712	+	0.998705i	$0.516200\pi$
$158$	0.0886851	+	0.109517i	0.00705541	+	0.00871270i
$159$	8.54828	+	9.49383i	0.677923	+	0.752910i
$160$		0			0
$161$	−8.73973	+	2.32528i	−0.688787	+	0.183257i
$162$	−0.0134262	+	0.00684101i	−0.00105487	+	0.000537481i
$163$	17.7369	+	0.929553i	1.38926	+	0.0728082i	0.732232	−	0.681055i	$-0.238479\pi$
$163$	17.7369	+	0.929553i	1.38926	+	0.0728082i	0.657031	+	0.753864i	$0.271812\pi$
$164$	11.0941	−	12.3212i	0.866302	−	0.962126i
$165$		0			0
$166$	−0.0165772	+	0.0149262i	−0.00128664	+	0.00115850i
$167$	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	$0.378570\pi$
$168$	0.0423856	+	0.201154i	0.00327012	+	0.0155193i
$169$	−7.58059	+	10.4338i	−0.583122	+	0.802599i
$170$		0			0
$171$	−4.67575	+	10.5019i	−0.357563	+	0.803100i
$172$	4.04943	+	10.5491i	0.308766	+	0.804363i
$173$	−1.23047	−	1.89475i	−0.0935507	−	0.144055i	0.788797	−	0.614654i	$-0.210705\pi$
$173$	−1.23047	−	1.89475i	−0.0935507	−	0.144055i	−0.882347	+	0.470599i	$0.844038\pi$
$174$	−0.0659643			−0.00500074
$175$		0			0
$176$	−20.2779			−1.52851
$177$	5.89092	+	9.07122i	0.442788	+	0.681834i
$178$	0.00610177	+	0.0158957i	0.000457347	+	0.00119143i
$179$	9.43793	−	21.1979i	0.705424	−	1.58441i	−0.102237	−	0.994760i	$-0.532600\pi$
$179$	9.43793	−	21.1979i	0.705424	−	1.58441i	0.807661	−	0.589648i	$-0.200733\pi$
$180$		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	$0.178354\pi$
$182$	0.00974556	+	0.0108620i	0.000722389	+	0.000805147i
$183$	−3.06286	+	0.485109i	−0.226413	+	0.0358603i
$184$	0.174499	−	0.157120i	0.0128642	−	0.0115830i
$185$		0			0
$186$	0.00976159	−	0.0108413i	0.000715754	−	0.000794926i
$187$	18.9274	+	0.991941i	1.38411	+	0.0725379i
$188$	−11.2160	+	5.71482i	−0.818008	+	0.416796i
$189$	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	$0.775150\pi$
$192$	5.68946	+	7.02590i	0.410601	+	0.507050i
$193$	13.9437	+	3.73619i	1.00369	+	0.268937i	0.722989	−	0.690860i	$-0.242768\pi$
$193$	13.9437	+	3.73619i	1.00369	+	0.268937i	0.280697	+	0.959796i	$0.409434\pi$
$194$	0.194899	−	0.0867746i	0.0139929	−	0.00623006i
$195$		0			0
$196$	12.1472	−	6.95613i	0.867657	−	0.496866i
$197$	9.93010	+	1.57277i	0.707490	+	0.112055i	0.499802	−	0.866140i	$-0.333406\pi$
$197$	9.93010	+	1.57277i	0.707490	+	0.112055i	0.207688	+	0.978195i	$0.433406\pi$
$198$	0.125699	−	0.0816300i	0.00893306	−	0.00580119i
$199$	−3.19046	−	5.52604i	−0.226166	−	0.391731i	0.730503	−	0.682910i	$-0.239286\pi$
$199$	−3.19046	−	5.52604i	−0.226166	−	0.391731i	−0.956669	+	0.291179i	$0.905952\pi$
$200$		0			0
$201$	−6.39554	−	3.69247i	−0.451107	−	0.260447i
$202$	0.180137	+	0.0917845i	0.0126744	+	0.00645794i
$203$	2.76115	+	8.54926i	0.193795	+	0.600040i
$204$	−4.96830	−	6.83828i	−0.347851	−	0.478775i
$205$		0			0
$206$	0.251823	+	0.0264676i	0.0175453	+	0.00184409i
$207$	1.52227	−	5.68118i	0.105805	−	0.394869i
$208$	1.19875	+	0.460157i	0.0831183	+	0.0319061i
$209$	−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	$0.474019\pi$
$212$	−1.18206	+	22.5551i	−0.0811844	+	1.54909i
$213$	4.30147	+	2.79341i	0.294732	+	0.191401i
$214$	−0.132451	−	0.119260i	−0.00905419	−	0.00815243i
$215$		0			0
$216$	−0.348836	−	0.113344i	−0.0237353	−	0.00771206i
$217$	−1.81369	−	0.811344i	−0.123121	−	0.0550776i
$218$	−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
$222$	−0.0497576	−	0.0402929i	−0.00333951	−	0.00270428i
$223$	−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
$227$	−1.04367	−	19.9144i	−0.0692707	−	1.32176i	−0.783299	−	0.621646i	$-0.786464\pi$
$227$	−1.04367	−	19.9144i	−0.0692707	−	1.32176i	0.714028	−	0.700117i	$-0.246869\pi$
$228$	14.1076	−	5.41542i	0.934302	−	0.358645i
$229$	−1.04973	−	9.98747i	−0.0693678	−	0.659991i	−0.972861	−	0.231389i	$-0.925673\pi$
$229$	−1.04973	−	9.98747i	−0.0693678	−	0.659991i	0.903493	−	0.428602i	$-0.140994\pi$
$230$		0			0
$231$	11.7782	+	9.57228i	0.774949	+	0.629810i
$232$	−0.164941	−	0.164941i	−0.0108289	−	0.0108289i
$233$	1.00029	−	2.60583i	0.0655309	−	0.170714i	−0.896905	−	0.442224i	$-0.854190\pi$
$233$	1.00029	−	2.60583i	0.0655309	−	0.170714i	0.962436	+	0.271510i	$0.0875230\pi$
$234$	−0.00928321	+	0.00197321i	−0.000606863	+	0.000128993i
$235$		0			0
$236$	−3.97581	+	18.7047i	−0.258803	+	1.21757i
$237$	−4.21336	−	8.26918i	−0.273687	−	0.537141i
$238$	0.100056	−	0.137205i	0.00648564	−	0.00889366i
$239$	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
$241$	−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	$-0.140085\pi$
$242$	0.196505	−	0.159127i	0.0126318	−	0.0102290i
$243$	−14.5140	+	3.88900i	−0.931071	+	0.249480i
$244$	−4.43544	−	3.22254i	−0.283950	−	0.206302i
$245$		0			0
$246$	0.130304	−	0.0946711i	0.00830785	−	0.00603601i
$247$	1.35028	−	1.66746i	0.0859163	−	0.106098i
$248$	0.0515167	−	0.00269988i	0.00327132	−	0.000171442i
$249$	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	$0.963041\pi$
$252$	−0.0160693	+	9.10350i	−0.00101227	+	0.573467i
$253$	2.71200	−	17.1229i	0.170502	−	1.07651i
$254$	0.275635	−	0.0289704i	0.0172949	−	0.00181777i
$255$		0			0
$256$	−1.66999	+	15.8889i	−0.104374	+	0.993055i
$257$	1.42369	+	5.31329i	0.0888074	+	0.331434i	0.996008	−	0.0892647i	$-0.0284517\pi$
$257$	1.42369	+	5.31329i	0.0888074	+	0.331434i	−0.907201	+	0.420698i	$0.861785\pi$
$258$	0.0171718	+	0.108418i	0.00106907	+	0.00674984i
$259$	−3.13937	+	8.13538i	−0.195071	+	0.505508i
$260$		0			0
$261$	−5.71509	−	1.21478i	−0.353755	−	0.0751930i
$262$	0.0278758	−	0.0429249i	0.00172217	−	0.00265191i
$263$	11.3281	−	17.4437i	0.698521	−	1.07563i	−0.294265	−	0.955724i	$-0.595075\pi$
$263$	11.3281	−	17.4437i	0.698521	−	1.07563i	0.992786	−	0.119904i	$-0.0382585\pi$
$264$	−0.385454	−	0.0819308i	−0.0237231	−	0.00504249i
$265$		0			0
$266$	0.190637	+	0.236268i	0.0116887	+	0.0144865i
$267$	−0.175413	−	1.10751i	−0.0107351	−	0.0677788i
$268$	−3.37921	−	12.6114i	−0.206418	−	0.770363i
$269$	−0.0163748	+	0.155796i	−0.000998391	+	0.00949906i	−0.995010	−	0.0997777i	$-0.968187\pi$
$269$	−0.0163748	+	0.155796i	−0.000998391	+	0.00949906i	0.994011	+	0.109277i	$0.0348535\pi$
$270$		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	$0.453182\pi$
$272$	2.33738	−	14.7577i	0.141725	−	0.894814i
$273$	−0.479061	−	0.833151i	−0.0289941	−	0.0504246i
$274$			0.265502i			0.0160395i
$275$		0			0
$276$	−6.69562	+	3.86572i	−0.403029	+	0.232689i
$277$	−29.9922	+	1.57183i	−1.80206	+	0.0944419i	−0.923596	−	0.383367i	$-0.874764\pi$
$277$	−29.9922	+	1.57183i	−1.80206	+	0.0944419i	−0.878464	+	0.477809i	$0.841431\pi$
$278$	−0.199506	+	0.246369i	−0.0119655	+	0.0147762i
$279$	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	$-0.624616\pi$
$282$	−0.118119	+	0.0316498i	−0.00703385	+	0.00188472i
$283$	21.8697	−	17.7097i	1.30002	−	1.05273i	0.305071	−	0.952329i	$-0.401320\pi$
$283$	21.8697	−	17.7097i	1.30002	−	1.05273i	0.994947	−	0.100404i	$-0.0320137\pi$
$284$	1.88528	+	8.86956i	0.111871	+	0.526312i
$285$		0			0
$286$	−0.0266049	+	0.00864446i	−0.00157318	+	0.000511158i
$287$	−17.7240	−	12.9251i	−1.04622	−	0.762947i
$288$	−0.160964	−	0.315909i	−0.00948487	−	0.0186151i
$289$	0.630888	−	2.96810i	0.0371111	−	0.174594i
$290$		0			0
$291$	−13.7432	+	2.92120i	−0.805638	+	0.171244i
$292$	7.24069	−	18.8626i	0.423729	−	1.10385i
$293$	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	$0.689578\pi$
$294$	0.129474	−	0.0415640i	0.00755110	−	0.00242406i
$295$		0			0
$296$	−0.0236660	−	0.225167i	−0.00137556	−	0.0130876i
$297$	−25.2816	+	9.70468i	−1.46698	+	0.563123i
$298$	0.0132574	+	0.252966i	0.000767981	+	0.0146539i
$299$	−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
$303$	−10.3473	−	8.37910i	−0.594438	−	0.481367i
$304$	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	−0.967183	−	0.254080i	$-0.918227\pi$
$307$	−12.4946	+	12.4946i	−0.713104	+	0.713104i	0.254080	+	0.967183i	$0.418227\pi$
$308$	2.75771	+	26.6910i	0.157135	+	1.52086i
$309$	−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	$0.801332\pi$
$312$	0.0209273	+	0.0135903i	0.00118477	+	0.000769401i
$313$	−1.45664	+	27.7944i	−0.0823343	+	1.57103i	0.575458	+	0.817832i	$0.304824\pi$
$313$	−1.45664	+	27.7944i	−0.0823343	+	1.57103i	−0.657792	+	0.753200i	$0.728509\pi$
$314$	0.0278431	+	0.0856923i	0.00157128	+	0.00483590i
$315$		0			0
$316$	5.07033	−	15.6049i	0.285228	−	0.877843i
$317$	26.6777	+	10.2406i	1.49837	+	0.575170i	0.963012	−	0.269457i	$-0.0868442\pi$
$317$	26.6777	+	10.2406i	1.49837	+	0.575170i	0.535356	+	0.844627i	$0.320177\pi$
$318$	−0.0567878	+	0.211935i	−0.00318450	+	0.0118847i
$319$	−17.1275	−	1.80018i	−0.958958	−	0.100791i
$320$		0			0
$321$	6.89929	+	9.49606i	0.385081	+	0.530019i
$322$	−0.115245	−	0.104136i	−0.00642236	−	0.00580328i
$323$	−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
$327$	8.63259	−	5.60607i	0.477383	−	0.310016i
$328$	0.562539	+	0.0890975i	0.0310610	+	0.00491959i
$329$	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	$0.214894\pi$
$332$	2.50875	+	0.672217i	0.137685	+	0.0368927i
$333$	−3.56893	−	4.40726i	−0.195576	−	0.241517i
$334$	0.0660950	+	0.0734059i	0.00361656	+	0.00401659i
$335$		0			0
$336$	8.47541	−	8.44554i	0.462371	−	0.460742i
$337$	21.2946	−	10.8501i	1.15999	−	0.591044i	0.235358	−	0.971909i	$-0.424374\pi$
$337$	21.2946	−	10.8501i	1.15999	−	0.591044i	0.924631	+	0.380865i	$0.124374\pi$
$338$	−0.221197	−	0.0115924i	−0.0120315	−	0.000630546i
$339$	−6.45792	+	7.17225i	−0.350746	+	0.389543i
$340$		0			0
$341$	2.83045	−	2.54854i	0.153277	−	0.138011i
$342$	−0.195006	+	0.0308859i	−0.0105447	+	0.00167012i
$343$	−10.8064	−	15.0406i	−0.583493	−	0.812118i
$344$	−0.228158	+	0.314033i	−0.0123015	+	0.0169315i
$345$		0			0
$346$	0.0157821	−	0.0354472i	0.000848452	−	0.00190566i
$347$	−1.31609	−	3.42854i	−0.0706515	−	0.184053i	0.893708	−	0.448649i	$-0.148095\pi$
$347$	−1.31609	−	3.42854i	−0.0706515	−	0.184053i	−0.964359	+	0.264596i	$0.914761\pi$
$348$	4.18305	+	6.44133i	0.224235	+	0.345291i
$349$	−1.21897			−0.0652497			−0.0326249	−	0.999468i	$-0.510387\pi$
$349$	−1.21897			−0.0652497			−0.0326249	+	0.999468i	$0.510387\pi$
$350$		0			0
$351$	1.71477			0.0915274
$352$	−0.569183	−	0.876464i	−0.0303375	−	0.0467157i
$353$	9.10273	+	23.7134i	0.484490	+	1.26214i	0.930230	+	0.366976i	$0.119607\pi$
$353$	9.10273	+	23.7134i	0.484490	+	1.26214i	−0.445741	+	0.895162i	$0.647060\pi$
$354$	−0.0755576	+	0.169705i	−0.00401584	+	0.00901973i
$355$		0			0
$356$	1.16525	−	1.60383i	0.0617583	−	0.0850031i
$357$	−8.32405	+	7.46845i	−0.440556	+	0.395272i
$358$	0.393617	−	0.0623428i	0.0208033	−	0.00329492i
$359$	8.35258	−	7.52069i	0.440832	−	0.396927i	−0.418605	−	0.908168i	$-0.637481\pi$
$359$	8.35258	−	7.52069i	0.440832	−	0.396927i	0.859437	+	0.511241i	$0.170814\pi$
$360$		0			0
$361$	17.1539	−	19.0514i	0.902838	−	1.00270i
$362$	0.0313592	+	0.00164347i	0.00164820	+	8.63787e-5i
$363$	−14.8373	+	7.55997i	−0.778755	+	0.396796i
$364$	0.442661	−	1.64044i	0.0232017	−	0.0859826i
$365$		0			0
$366$	−0.0356376	−	0.0395796i	−0.00186281	−	0.00206886i
$367$	−4.53923	−	5.60548i	−0.236946	−	0.292604i	0.644778	−	0.764370i	$-0.276950\pi$
$367$	−4.53923	−	5.60548i	−0.236946	−	0.292604i	−0.881724	+	0.471766i	$0.843617\pi$
$368$	−13.2012	−	3.53724i	−0.688158	−	0.184391i
$369$	13.0328	−	5.80259i	0.678462	−	0.302071i
$370$		0			0
$371$	29.8447	−	1.51127i	1.54946	−	0.0784614i
$372$	−1.67766	−	0.265716i	−0.0869827	−	0.0137767i
$373$	3.27030	−	2.12375i	0.169329	−	0.109964i	−0.457192	−	0.889368i	$-0.651145\pi$
$373$	3.27030	−	2.12375i	0.169329	−	0.109964i	0.626521	+	0.779404i	$0.284478\pi$
$374$	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
$378$	−0.0508634	+	0.237234i	−0.00261613	+	0.0122020i
$379$	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
$381$	−18.1525	−	1.90791i	−0.929983	−	0.0977451i
$382$	0.00327433	−	0.0122200i	0.000167529	−	0.000625228i
$383$	−26.5486	−	10.1910i	−1.35657	−	0.520738i	−0.432042	−	0.901854i	$-0.642207\pi$
$383$	−26.5486	−	10.1910i	−1.35657	−	0.520738i	−0.924527	+	0.381116i	$0.875540\pi$
$384$	−0.192024	+	0.590991i	−0.00979921	+	0.0301589i
$385$		0			0
$386$	0.0766136	+	0.235792i	0.00389953	+	0.0120015i
$387$	−0.508854	+	9.70951i	−0.0258665	+	0.493562i
$388$	−20.8327	−	13.5289i	−1.05762	−	0.686827i
$389$	−21.7783	−	19.6093i	−1.10420	−	0.994230i	−0.104205	−	0.994556i	$-0.533230\pi$
$389$	−21.7783	−	19.6093i	−1.10420	−	0.994230i	−1.00000		0.000325536i	$0.999896\pi$
$390$		0			0
$391$	12.1489	+	3.94741i	0.614396	+	0.199629i
$392$	0.427674	+	0.219816i	0.0216008	+	0.0111024i
$393$	−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
$397$	−0.865873	−	0.701171i	−0.0434569	−	0.0351907i	0.607346	−	0.794438i	$-0.292234\pi$
$397$	−0.865873	−	0.701171i	−0.0434569	−	0.0351907i	−0.650803	+	0.759247i	$0.725568\pi$
$398$	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	−0.953160	−	0.302465i	$-0.902190\pi$
$401$	−4.29812	+	7.44456i	−0.214638	+	0.371764i	0.738523	+	0.674229i	$0.235524\pi$
$402$	−0.00663801	−	0.126661i	−0.000331074	−	0.00631726i
$403$	−0.225157	+	0.0864297i	−0.0112159	+	0.00430537i
$404$	−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
$408$	0.104057	−	0.271078i	0.00515159	−	0.0134203i
$409$	15.2011	−	3.23109i	0.751645	−	0.159767i	0.183869	−	0.982951i	$-0.441138\pi$
$409$	15.2011	−	3.23109i	0.751645	−	0.159767i	0.567775	+	0.823184i	$0.307804\pi$
$410$		0			0
$411$	3.63537	−	17.1031i	0.179320	−	0.843633i
$412$	−13.3845	−	26.2686i	−0.659407	−	1.29416i
$413$	25.1572	+	2.68904i	1.23791	+	0.132319i
$414$	0.0960709	−	0.0312153i	0.00472163	−	0.00153415i
$415$		0			0
$416$	0.0137586	+	0.0647291i	0.000674571	+	0.00317361i
$417$	16.2251	−	13.1389i	0.794548	−	0.643413i
$418$	−0.562127	+	0.150621i	−0.0274945	+	0.00736713i
$419$	5.12758	+	3.72540i	0.250499	+	0.181998i	0.705948	−	0.708264i	$-0.250521\pi$
$419$	5.12758	+	3.72540i	0.250499	+	0.181998i	−0.455449	+	0.890262i	$0.650521\pi$
$420$		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	$0.481726\pi$
$422$	−0.305552	+	0.377325i	−0.0148740	+	0.0183679i
$423$	−10.8165	+	0.566871i	−0.525918	+	0.0275622i
$424$	−0.671930	+	0.387939i	−0.0326318	+	0.0188400i
$425$		0			0
$426$			0.0880879i			0.00426787i
$427$	−3.63796	+	6.27552i	−0.176053	+	0.303694i
$428$	−3.24632	+	20.4964i	−0.156917	+	0.990732i
$429$	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	$-0.0419764\pi$
$432$	5.52535	+	20.6209i	0.265839	+	0.992123i
$433$	−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	$-0.146659\pi$
$434$	−0.00527873	−	0.0337136i	−0.000253387	−	0.00161831i
$435$		0			0
$436$	17.8003	+	3.78356i	0.852478	+	0.181200i
$437$	−12.4381	+	19.1529i	−0.594993	+	0.916209i
$438$	0.106900	−	0.164612i	0.00510788	−	0.00786545i
$439$	−23.9971	−	5.10075i	−1.14532	−	0.243445i	−0.404105	−	0.914713i	$-0.632417\pi$
$439$	−23.9971	−	5.10075i	−1.14532	−	0.243445i	−0.741215	+	0.671267i	$0.765750\pi$
$440$		0			0
$441$	11.9830	−	1.21671i	0.570618	−	0.0579384i
$442$	−0.00322450	−	0.0203587i	−0.000153374	−	0.000968363i
$443$	1.81367	+	6.76871i	0.0861701	+	0.321591i	0.995533	−	0.0944121i	$-0.0300971\pi$
$443$	1.81367	+	6.76871i	0.0861701	+	0.321591i	−0.909363	+	0.416003i	$0.863430\pi$
$444$	−0.779231	+	7.41389i	−0.0369807	+	0.351848i
$445$		0			0
$446$	−0.361611	+	0.0380068i	−0.0171228	+	0.00179968i
$447$	2.60972	−	16.4771i	0.123435	−	0.779340i
$448$	21.1472	+	0.0373287i	0.999114	+	0.00176361i
$449$			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
$452$	−17.0396	+	0.893007i	−0.801474	+	0.0420035i
$453$	−3.99500	+	4.93341i	−0.187701	+	0.231792i
$454$	0.277083	−	0.201313i	0.0130042	−	0.00944808i
$455$		0			0
$456$	0.419965	+	0.305123i	0.0196667	+	0.0142887i
$457$	6.62325	−	1.77469i	0.309822	−	0.0830167i	−0.100558	−	0.994931i	$-0.532063\pi$
$457$	6.62325	−	1.77469i	0.309822	−	0.0830167i	0.410380	+	0.911915i	$0.365396\pi$
$458$	0.134040	−	0.108544i	0.00626328	−	0.00507191i
$459$	−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	$0.448497\pi$
$462$	−0.0277049	+	0.259193i	−0.00128895	+	0.0120587i
$463$	−2.03589	−	3.99566i	−0.0946158	−	0.185694i	0.838848	−	0.544366i	$-0.183230\pi$
$463$	−2.03589	−	3.99566i	−0.0946158	−	0.185694i	−0.933464	+	0.358672i	$0.883230\pi$
$464$	−2.82274	+	13.2800i	−0.131043	+	0.616507i
$465$		0			0
$466$	0.0468911	−	0.00996701i	0.00217219	−	0.000461713i
$467$	−14.3968	+	37.5050i	−0.666205	+	1.73552i	0.0112245	+	0.999937i	$0.496427\pi$
$467$	−14.3968	+	37.5050i	−0.666205	+	1.73552i	−0.677430	+	0.735587i	$0.736906\pi$
$468$	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
$472$	−0.613269	+	0.235412i	−0.0282280	+	0.0108357i
$473$	1.49988	+	28.6193i	0.0689643	+	1.31592i
$474$	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
$478$	0.0555969	+	0.0450215i	0.00254294	+	0.00205924i
$479$	−18.9438	−	8.43434i	−0.865566	−	0.385375i	−0.0745845	−	0.997215i	$-0.523763\pi$
$479$	−18.9438	−	8.43434i	−0.865566	−	0.385375i	−0.790982	+	0.611840i	$0.790430\pi$
$480$		0			0
$481$	0.430521	+	0.966966i	0.0196301	+	0.0440898i
$482$	0.0862007	−	0.0862007i	0.00392633	−	0.00392633i
$483$	5.99797	+	8.28622i	0.272917	+	0.377036i
$484$	−27.9996	−	9.09763i	−1.27271	−	0.413529i
$485$		0			0
$486$	−0.191781	−	0.172681i	−0.00869938	−	0.00783296i
$487$	6.23415	+	4.04851i	0.282496	+	0.183455i	0.678107	−	0.734963i	$-0.262800\pi$
$487$	6.23415	+	4.04851i	0.282496	+	0.183455i	−0.395611	+	0.918418i	$0.629467\pi$
$488$	0.00985672	−	0.188077i	0.000446193	−	0.00851387i
$489$	−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	$0.948518\pi$
$492$	−17.5076	−	6.72052i	−0.789302	−	0.302984i
$493$	3.28436	−	12.2574i	0.147920	−	0.552045i
$494$	0.0366486	+	0.00385192i	0.00164890	+	0.000173306i
$495$		0			0
$496$	−1.76487	−	2.42913i	−0.0792448	−	0.109071i
$497$	11.4166	−	3.68720i	0.512103	−	0.165393i
$498$	0.0224808	+	0.0114546i	0.00100739	+	0.000513291i
$499$	7.97198	+	4.60262i	0.356875	+	0.206042i	0.667709	−	0.744422i	$-0.267275\pi$
$499$	7.97198	+	4.60262i	0.356875	+	0.206042i	−0.310834	+	0.950464i	$0.600608\pi$
$500$		0			0
$501$	−3.25260	−	5.63367i	−0.145315	−	0.251694i
$502$	−0.0528736	+	0.0343365i	−0.00235986	+	0.00153251i
$503$	−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	$0.704495\pi$
$504$	−0.262573	+	0.169859i	−0.0116959	+	0.00756611i
$505$		0			0
$506$	0.272005	−	0.121105i	0.0120921	−	0.00538376i
$507$	14.0903	+	3.77549i	0.625774	+	0.167676i
$508$	−20.3080	−	25.0783i	−0.901022	−	1.11267i
$509$	−4.74698	−	5.27205i	−0.210406	−	0.233680i	0.628699	−	0.777648i	$-0.283588\pi$
$509$	−4.74698	−	5.27205i	−0.210406	−	0.233680i	−0.839105	+	0.543969i	$0.816921\pi$
$510$		0			0
$511$	−25.8090	−	6.96436i	−1.14172	−	0.308085i
$512$	−1.22350	+	0.623407i	−0.0540718	+	0.0275509i
$513$	35.6241	+	1.86698i	1.57284	+	0.0824291i
$514$	−0.0632152	+	0.0702076i	−0.00278830	+	0.00309672i
$515$		0			0
$516$	9.49799	−	8.55203i	0.418126	−	0.376482i
$517$	−31.5330	+	4.99434i	−1.38682	+	0.219651i
$518$	−0.146548	+	0.0308794i	−0.00643893	+	0.00135676i
$519$	−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	$0.241975\pi$
$522$	−0.0359616	−	0.0936831i	−0.00157400	−	0.00410040i
$523$	2.52576	+	3.88934i	0.110444	+	0.170069i	0.889571	−	0.456798i	$-0.151004\pi$
$523$	2.52576	+	3.88934i	0.110444	+	0.170069i	−0.779127	+	0.626867i	$0.784337\pi$
$524$	−5.95927			−0.260332
$525$		0			0
$526$	0.357223			0.0155757
$527$	1.52849	+	2.35367i	0.0665822	+	0.102528i
$528$	8.21952	+	21.4126i	0.357709	+	0.931863i
$529$	−4.60253	+	10.3374i	−0.200110	+	0.449454i
$530$		0			0
$531$	−9.67149	+	13.3117i	−0.419707	+	0.577677i
$532$	10.9823	−	33.5981i	0.476143	−	1.45666i
$533$	−2.62992	+	0.416539i	−0.113915	+	0.0180423i
$534$	0.0143118	−	0.0128864i	0.000619332	−	0.000557649i
$535$		0			0
$536$	0.300112	−	0.333308i	0.0129628	−	0.0143967i
$537$	−26.2097	−	1.37359i	−1.13103	−	0.0592748i
$538$	−0.00239725	+	0.00122146i	−0.000103353	+	5.26610e-5i
$539$	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	$0.583088\pi$
$542$	0.0150706	+	0.0186106i	0.000647337	+	0.000799395i
$543$	−1.99759	−	0.535254i	−0.0857249	−	0.0229699i
$544$	0.703472	−	0.313206i	0.0301611	−	0.0134286i
$545$		0			0
$546$	0.00751952	−	0.0146937i	0.000321806	−	0.000628833i
$547$	−8.90589	−	1.41055i	−0.380788	−	0.0603110i	−0.0368938	−	0.999319i	$-0.511746\pi$
$547$	−8.90589	−	1.41055i	−0.380788	−	0.0603110i	−0.343895	+	0.939008i	$0.611746\pi$
$548$	25.9259	−	16.8365i	1.10750	−	0.719218i
$549$	−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
$553$	−21.2265	−	4.55100i	−0.902641	−	0.193528i
$554$	−0.303190	−	0.417305i	−0.0128813	−	0.0177296i
$555$		0			0
$556$	36.7090	+	3.85827i	1.55681	+	0.163627i
$557$	4.38542	−	16.3666i	0.185816	−	0.693475i	−0.808638	−	0.588306i	$-0.799795\pi$
$557$	4.38542	−	16.3666i	0.185816	−	0.693475i	0.994454	−	0.105169i	$-0.0335383\pi$
$558$	0.0207187	+	0.00795316i	0.000877092	+	0.000336684i
$559$	0.560777	−	1.72589i	0.0237183	−	0.0729975i
$560$		0			0
$561$	−6.62463	−	20.3885i	−0.279692	−	0.860804i
$562$	0.0256755	−	0.489917i	0.00108305	−	0.0206659i
$563$	−36.3595	−	23.6121i	−1.53237	−	0.995133i	−0.987679	−	0.156496i	$-0.949980\pi$
$563$	−36.3595	−	23.6121i	−1.53237	−	0.995133i	−0.544691	−	0.838637i	$-0.683353\pi$
$564$	10.5809	+	9.52709i	0.445536	+	0.401163i
$565$		0			0
$566$	0.459661	+	0.149353i	0.0193210	+	0.00627776i
$567$	0.947901	−	2.11895i	0.0398081	−	0.0889874i
$568$	−0.220260	+	0.220260i	−0.00924190	+	0.00924190i
$569$	−4.01461	−	9.01696i	−0.168301	−	0.378011i	0.809629	−	0.586942i	$-0.199668\pi$
$569$	−4.01461	−	9.01696i	−0.168301	−	0.378011i	−0.977930	+	0.208931i	$0.933002\pi$
$570$		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	$0.643050\pi$
$572$	2.53124	+	2.04976i	0.105836	+	0.0857047i
$573$	−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
$577$	−0.294614	−	5.62157i	−0.0122649	−	0.234029i	−0.997883	−	0.0650391i	$-0.979283\pi$
$577$	−0.294614	−	5.62157i	−0.0122649	−	0.234029i	0.985618	−	0.168990i	$-0.0540506\pi$
$578$	0.0486537	−	0.0186764i	0.00202373	−	0.000776837i
$579$	−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
$583$	−20.5286	+	53.4789i	−0.850209	+	2.21487i
$584$	0.678903	−	0.144305i	0.0280932	−	0.00597140i
$585$		0			0
$586$	−0.0230659	+	0.108516i	−0.000952842	+	0.00448277i
$587$	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	$0.709036\pi$
$588$	−12.2691	−	10.0073i	−0.505971	−	0.412693i
$589$	−4.77172	+	1.55043i	−0.196615	+	0.0638842i
$590$		0			0
$591$	−2.36432	−	11.1232i	−0.0972551	−	0.457549i
$592$	−10.2410	+	8.29300i	−0.420903	+	0.340840i
$593$	14.1905	−	3.80233i	0.582733	−	0.156143i	0.0446033	−	0.999005i	$-0.485798\pi$
$593$	14.1905	−	3.80233i	0.582733	−	0.156143i	0.538130	+	0.842862i	$0.319131\pi$
$594$	−0.376271	−	0.273377i	−0.0154386	−	0.0112168i
$595$		0			0
$596$	23.8611	−	17.3361i	0.977390	−	0.710116i
$597$	−4.54202	+	5.60893i	−0.185892	+	0.229558i
$598$	−0.0188280		0.000986734i	−0.000769935		4.03506e-5i
$599$	8.74982	−	5.05171i	0.357508	−	0.206407i	−0.310479	−	0.950580i	$-0.600489\pi$
$599$	8.74982	−	5.05171i	0.357508	−	0.206407i	0.667987	+	0.744173i	$0.267156\pi$
$600$		0			0
$601$			22.6515i			0.923974i	0.886887	+	0.461987i	$0.152863\pi$
$601$			22.6515i			0.923974i	−0.886887	+	0.461987i	$0.847137\pi$
$602$	0.222140	+	0.128776i	0.00905373	+	0.00524850i
$603$	1.75744	−	11.0960i	0.0715684	−	0.451865i
$604$	−11.1617	+	1.17315i	−0.454165	+	0.0477346i
$605$		0			0
$606$	0.0239029	−	0.227421i	0.000970990	−	0.00923835i
$607$	−5.16341	−	19.2701i	−0.209576	−	0.782150i	−0.988006	−	0.154418i	$-0.950650\pi$
$607$	−5.16341	−	19.2701i	−0.209576	−	0.782150i	0.778429	−	0.627732i	$-0.216017\pi$
$608$	0.215359	+	1.35972i	0.00873395	+	0.0551440i
$609$	7.90841	−	6.38103i	0.320465	−	0.258572i
$610$		0			0
$611$	1.97744	+	0.420317i	0.0799986	+	0.0170042i
$612$	7.00323	−	10.7840i	0.283089	−	0.435919i
$613$	−20.9028	+	32.1875i	−0.844257	+	1.30004i	0.107815	+	0.994171i	$0.465614\pi$
$613$	−20.9028	+	32.1875i	−0.844257	+	1.30004i	−0.952073	+	0.305871i	$0.901052\pi$
$614$	−0.296847	−	0.0630967i	−0.0119798	−	0.00254638i
$615$		0			0
$616$	−0.717375	+	0.578825i	−0.0289039	+	0.0233215i
$617$	−0.0933065	−	0.589114i	−0.00375638	−	0.0237168i	0.985739	−	0.168282i	$-0.0538218\pi$
$617$	−0.0933065	−	0.589114i	−0.00375638	−	0.0237168i	−0.989495	+	0.144565i	$0.953822\pi$
$618$	−0.0741259	−	0.276642i	−0.00298178	−	0.0111282i
$619$	−0.290449	+	2.76344i	−0.0116741	+	0.111072i	−0.998807	−	0.0488294i	$-0.984451\pi$
$619$	−0.290449	+	2.76344i	−0.0116741	+	0.111072i	0.987133	+	0.159901i	$0.0511176\pi$
$620$		0			0
$621$	−18.1514	+	1.90779i	−0.728392	+	0.0765571i
$622$	0.0200899	−	0.126843i	0.000805532	−	0.00508593i
$623$	−2.26920	−	1.31547i	−0.0909134	−	0.0527031i
$624$		−	1.45235i		−	0.0581404i
$625$		0			0
$626$	−0.413975	+	0.239009i	−0.0165458	+	0.00955270i
$627$	38.2734	−	2.00583i	1.52849	−	0.0801050i
$628$	6.60211	−	8.15292i	0.263453	−	0.325337i
$629$	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	$0.515107\pi$
$632$	0.544441	−	0.145882i	0.0216567	−	0.00580289i
$633$	24.8495	−	20.1227i	0.987680	−	0.799807i
$634$	0.102039	+	0.480056i	0.00405249	+	0.0190655i
$635$		0			0
$636$	24.2963	−	7.89435i	0.963411	−	0.313031i
$637$	−2.21912	−	0.359510i	−0.0879248	−	0.0142443i
$638$	−0.134282	−	0.263544i	−0.00531628	−	0.0104338i
$639$	−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	$0.442872\pi$
$642$	−0.0722447	+	0.188204i	−0.00285127	+	0.00742781i
$643$	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	$0.580703\pi$
$644$	−2.86062	+	17.8572i	−0.112724	+	0.703672i
$645$		0			0
$646$	−0.0448227	−	0.426460i	−0.00176353	−	0.0167788i
$647$	7.04689	−	2.70505i	0.277042	−	0.106346i	−0.215880	−	0.976420i	$-0.569262\pi$
$647$	7.04689	−	2.70505i	0.277042	−	0.106346i	0.492922	+	0.870073i	$0.335929\pi$
$648$	0.00315429	+	0.0601875i	0.000123912	+	0.00236439i
$649$	−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
$653$	−26.8073	−	21.7081i	−1.04905	−	0.849503i	−0.0601643	−	0.998188i	$-0.519162\pi$
$653$	−26.8073	−	21.7081i	−1.04905	−	0.849503i	−0.988885	+	0.148686i	$0.952496\pi$
$654$	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
$658$	−0.116805	+	0.261107i	−0.00455353	+	0.0101790i
$659$	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
$661$	−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	$-0.543059\pi$
$662$	0.240540	+	0.156209i	0.00934885	+	0.00607122i
$663$	−0.0710448	+	1.35562i	−0.00275915	+	0.0526477i
$664$	0.0275707	+	0.0848540i	0.00106995	+	0.00329297i
$665$		0			0
$666$	0.0300981	−	0.0926326i	0.00116628	−	0.00358944i
$667$	−10.8362	−	4.15963i	−0.419579	−	0.161061i
$668$	2.97666	−	11.1090i	0.115170	−	0.429822i
$669$	23.8146	+	2.50302i	0.920727	+	0.0967724i
$670$		0			0
$671$	−8.17313	−	11.2493i	−0.315520	−	0.434276i
$672$	0.602934	+	0.129270i	0.0232587	+	0.00498672i
$673$	−15.3295	−	7.81076i	−0.590908	−	0.301083i	0.132850	−	0.991136i	$-0.457587\pi$
$673$	−15.3295	−	7.81076i	−0.590908	−	0.301083i	−0.723759	+	0.690053i	$0.757587\pi$
$674$	0.355475	+	0.205234i	0.0136924	+	0.00790531i
$675$		0			0
$676$	12.8950	+	22.3347i	0.495960	+	0.859028i
$677$	0.534205	−	0.346917i	0.0205312	−	0.0133331i	−0.534333	−	0.845274i	$-0.679437\pi$
$677$	0.534205	−	0.346917i	0.0205312	−	0.0133331i	0.554864	+	0.831941i	$0.312770\pi$
$678$	−0.163717	−	0.0259302i	−0.00628750	−	0.000995842i
$679$	−14.9722	+	29.2568i	−0.574580	+	1.12277i
$680$		0			0
$681$	−20.6056	+	9.17421i	−0.789609	+	0.351557i
$682$	0.0631853	+	0.0169304i	0.00241949	+	0.000648300i
$683$	−11.4381	−	14.1248i	−0.437665	−	0.540471i	0.509816	−	0.860284i	$-0.329714\pi$
$683$	−11.4381	−	14.1248i	−0.437665	−	0.540471i	−0.947481	+	0.319812i	$0.896380\pi$
$684$	15.3821	+	17.0835i	0.588148	+	0.653204i
$685$		0			0
$686$	0.115561	−	0.296347i	0.00441214	−	0.0113146i
$687$	−10.1208	+	5.15681i	−0.386133	+	0.196745i
$688$	22.5617	+	1.18241i	0.860155	+	0.0450788i
$689$	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	$0.423265\pi$
$692$	−4.46218	+	0.706740i	−0.169627	+	0.0268662i
$693$	−7.17355	+	21.9460i	−0.272501	+	0.833661i
$694$	0.0370737	−	0.0510276i	0.00140730	−	0.00193698i
$695$		0			0
$696$	−0.107312	+	0.241028i	−0.00406767	+	0.00913613i
$697$	11.1038	+	28.9265i	0.420588	+	1.09567i
$698$	−0.0114023	−	0.0175580i	−0.000431582	−	0.000664578i
$699$	−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	$0.547004\pi$
$702$	0.0160400	+	0.0246994i	0.000605391	+	0.000932220i
$703$	7.89123	+	20.5574i	0.297623	+	0.775335i
$704$	−16.4883	+	37.0332i	−0.621425	+	1.39574i
$705$		0			0
$706$	−0.256420	+	0.352932i	−0.00965050	+	0.0132828i
$707$	−30.4753	+	6.42152i	−1.14614	+	0.241506i
$708$	21.3629	−	3.38355i	0.802866	−	0.127162i
$709$	33.5426	−	30.2019i	1.25972	−	1.13426i	0.274754	−	0.961515i	$-0.411404\pi$
$709$	33.5426	−	30.2019i	1.25972	−	1.13426i	0.984967	−	0.172743i	$-0.0552629\pi$
$710$		0			0
$711$	9.44698	−	10.4919i	0.354289	−	0.393478i
$712$	0.0680079	+	0.00356414i	0.00254870	+	0.000133572i
$713$	2.28721	−	1.16539i	0.0856568	−	0.0436443i
$714$	−0.185439	−	0.0500392i	−0.00693988	−	0.00187267i
$715$		0			0
$716$	−31.0485	−	34.4828i	−1.16034	−	1.28868i
$717$	−2.96499	−	3.66145i	−0.110729	−	0.136740i
$718$	0.186458	+	0.0499613i	0.00695856	+	0.00186454i
$719$	28.4168	−	12.6520i	1.05977	−	0.471839i	0.198558	−	0.980089i	$-0.436374\pi$
$719$	28.4168	−	12.6520i	1.05977	−	0.471839i	0.861209	+	0.508250i	$0.169708\pi$
$720$		0			0
$721$	−32.7512	+	21.1868i	−1.21972	+	0.789036i
$722$	0.434874	+	0.0688773i	0.0161843	+	0.00256335i
$723$	−6.73318	+	4.37258i	−0.250409	+	0.162618i
$724$	−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	$0.517289\pi$
$728$	0.0555432	−	0.0179388i	0.00205857	−	0.000664855i
$729$	11.5369	+	15.8791i	0.427291	+	0.588116i
$730$		0			0
$731$	−21.0011	−	2.20731i	−0.776755	−	0.0816403i
$732$	−1.60498	+	5.98986i	−0.0593217	+	0.221392i
$733$	0.210373	+	0.0807548i	0.00777032	+	0.00298275i	0.362250	−	0.932081i	$-0.382009\pi$
$733$	0.210373	+	0.0807548i	0.00777032	+	0.00298275i	−0.354480	+	0.935064i	$0.615342\pi$
$734$	0.0382810	−	0.117817i	0.00141298	−	0.00434870i
$735$		0			0
$736$	−0.217655	−	0.669875i	−0.00802289	−	0.0246919i
$737$	1.73304	−	33.0684i	0.0638375	−	1.21809i
$738$	0.205490	+	0.133447i	0.00756419	+	0.00491224i
$739$	29.9797	+	26.9939i	1.10282	+	0.992986i	0.999999	−	0.00171350i	$-0.000545424\pi$
$739$	29.9797	+	26.9939i	1.10282	+	0.992986i	0.102824	+	0.994700i	$0.467212\pi$
$740$		0			0
$741$	−2.30809	−	0.749943i	−0.0847897	−	0.0275498i
$742$	0.300937	+	0.415746i	0.0110478	+	0.0152625i
$743$	−1.97911	+	1.97911i	−0.0726064	+	0.0726064i	−0.742477	−	0.669871i	$-0.766349\pi$
$743$	−1.97911	+	1.97911i	−0.0726064	+	0.0726064i	0.669871	+	0.742477i	$0.266349\pi$
$744$	−0.0237329	−	0.0533050i	−0.000870090	−	0.00195426i
$745$		0			0
$746$	0.0611810	+	0.0272395i	0.00224000	+	0.000997310i
$747$	1.73678	+	1.40641i	0.0635454	+	0.0514580i
$748$	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	−0.451902	−	0.892068i	$-0.649254\pi$
$751$	14.9793	−	25.9449i	0.546602	−	0.946743i	0.998504	−	0.0546754i	$-0.0174124\pi$
$752$	1.31722	+	25.1340i	0.0480340	+	0.916543i
$753$	3.87616	−	1.48792i	0.141255	−	0.0542228i
$754$	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	0.997884	+	0.0650131i	$0.0207089\pi$
$757$	29.2442	+	29.2442i	1.06290	+	1.06290i	0.0650131	+	0.997884i	$0.479291\pi$
$758$	−0.0283534	+	0.0738631i	−0.00102984	+	0.00268283i
$759$	−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	$0.735596\pi$
$762$	−0.142318	−	0.279315i	−0.00515565	−	0.0101185i
$763$	2.55901	−	23.9408i	0.0926424	−	0.866714i
$764$	−1.40090	+	0.455180i	−0.0506828	+	0.0164679i
$765$		0			0
$766$	−0.101545	−	0.477733i	−0.00366898	−	0.0172612i
$767$	2.38667	−	1.93269i	0.0861776	−	0.0697852i
$768$	17.4549	−	4.67702i	0.629848	−	0.168767i
$769$	30.0966	+	21.8665i	1.08531	+	0.788525i	0.978601	−	0.205765i	$-0.0659683\pi$
$769$	30.0966	+	21.8665i	1.08531	+	0.788525i	0.106710	+	0.994290i	$0.465968\pi$
$770$		0			0
$771$	5.03351	−	3.65706i	0.181277	−	0.131706i
$772$	18.1665	−	22.4337i	0.653825	−	0.807407i
$773$	−0.346537	+	0.0181612i	−0.0124641	+	0.000653213i	−0.0585670	−	0.998283i	$-0.518653\pi$
$773$	−0.346537	+	0.0181612i	−0.0124641	+	0.000653213i	0.0461029	+	0.998937i	$0.485320\pi$
$774$	−0.144615	+	0.0834938i	−0.00519809	+	0.00300112i
$775$		0			0
$776$		−	0.853311i		−	0.0306321i
$777$	9.86311	+	0.0174102i	0.353837	+	0.000624586i
$778$	0.0787362	−	0.497121i	0.00282283	−	0.0178226i
$779$	−55.0899	+	5.79018i	−1.97380	+	0.207455i
$780$		0			0
$781$	−2.40393	+	22.8719i	−0.0860195	+	0.818421i
$782$	0.0567829	+	0.211917i	0.00203055	+	0.00757812i
$783$	2.83631	+	17.9077i	0.101361	+	0.639970i
$784$	−2.82722	−	27.8444i	−0.100972	−	0.994445i
$785$		0			0
$786$	−0.0566260	−	0.0120362i	−0.00201978	−	0.000429318i
$787$	5.26825	−	8.11239i	0.187793	−	0.289175i	−0.732217	−	0.681072i	$-0.761514\pi$
$787$	5.26825	−	8.11239i	0.187793	−	0.289175i	0.920009	+	0.391896i	$0.128181\pi$
$788$	10.9499	−	16.8613i	0.390073	−	0.600659i
$789$	−23.0116	−	4.89126i	−0.819234	−	0.174133i
$790$		0			0
$791$	3.49222	+	22.3038i	0.124169	+	0.793031i
$792$	−0.0937781	−	0.592092i	−0.00333226	−	0.0210391i
$793$	0.227886	+	0.850484i	0.00809249	+	0.0302016i
$794$	0.00200022	−	0.0190308i	7.09851e−5	−	0.000675378i
$795$		0			0
$796$	−12.6901	+	1.33378i	−0.449787	+	0.0472746i
$797$	−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	$0.726228\pi$
$798$	0.172215	−	0.297073i	0.00609636	−	0.0105163i
$799$		−	23.5245i		−	0.832235i
$800$		0			0
$801$	1.47727	−	0.852904i	0.0521969	−	0.0301359i
$802$	−0.147436	+	0.00772680i	−0.00520615	+	0.000272843i
$803$	32.2487	−	39.8239i	1.13803	−	1.40535i
$804$	−11.9473	+	8.68023i	−0.421349	+	0.306128i
$805$		0			0
$806$	−0.00335106	−	0.00243469i	−0.000118036	−	8.57583e-5i
$807$	0.171151	−	0.0458598i	0.00602480	−	0.00161434i
$808$	0.628425	−	0.508888i	0.0221079	−	0.0179026i
$809$	−6.71500	−	31.5916i	−0.236087	−	1.11070i	−0.923250	−	0.384199i	$-0.874478\pi$
$809$	−6.71500	−	31.5916i	−0.236087	−	1.11070i	0.687163	−	0.726503i	$-0.258856\pi$
$810$		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	$0.558461\pi$
$812$	17.8638	+	1.90944i	0.626895	+	0.0670083i
$813$	−0.715992	−	1.40521i	−0.0251109	−	0.0492830i
$814$	0.0596895	−	0.280817i	0.00209212	−	0.00984263i
$815$		0			0
$816$	−16.5309	+	3.51374i	−0.578696	+	0.123006i
$817$	13.5292	−	35.2447i	0.473326	−	1.23306i
$818$	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	$0.969297\pi$
$822$	0.280358	−	0.107619i	0.00977860	−	0.00375365i
$823$	0.846752	+	16.1570i	0.0295159	+	0.563197i	0.972862	+	0.231387i	$0.0743262\pi$
$823$	0.846752	+	16.1570i	0.0295159	+	0.563197i	−0.943346	+	0.331811i	$0.892340\pi$
$824$	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	−0.972601	−	0.232480i	$-0.925316\pi$
$827$	−6.12078	+	12.0127i	−0.212841	+	0.417723i	0.759761	+	0.650203i	$0.225316\pi$
$828$	−9.14036	−	7.40172i	−0.317649	−	0.257227i
$829$	−3.14458	−	1.40006i	−0.109216	−	0.0486259i	0.351402	−	0.936225i	$-0.385705\pi$
$829$	−3.14458	−	1.40006i	−0.109216	−	0.0486259i	−0.460617	+	0.887599i	$0.652372\pi$
$830$		0			0
$831$	13.8169	+	31.0333i	0.479304	+	1.07653i
$832$	1.81509	−	1.81509i	0.0629271	−	0.0629271i
$833$	1.27684	+	26.1282i	0.0442400	+	0.905289i
$834$	0.341022	+	0.110805i	0.0118086	+	0.00383686i
$835$		0			0
$836$	50.3546	+	45.3395i	1.74155	+	1.56810i
$837$	−3.36289	−	2.18389i	−0.116238	−	0.0754861i
$838$	−0.00569699	+	0.108705i	−0.000196799	+	0.00375516i
$839$	−8.56984	−	26.3753i	−0.295864	−	0.910575i	−0.982930	−	0.183980i	$-0.941102\pi$
$839$	−8.56984	−	26.3753i	−0.295864	−	0.910575i	0.687066	−	0.726595i	$-0.258898\pi$
$840$		0			0
$841$	5.39836	−	16.6145i	0.186150	−	0.572912i
$842$	−0.355571	−	0.136491i	−0.0122538	−	0.00470378i
$843$	−8.36213	+	31.2079i	−0.288007	+	1.07486i
$844$	56.2215	+	5.90911i	1.93522	+	0.203400i
$845$		0			0
$846$	−0.109344	−	0.150499i	−0.00375931	−	0.00517425i
$847$	−8.16580	+	38.0864i	−0.280580	+	1.30866i
$848$	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
$852$	8.60167	−	5.58599i	0.294688	−	0.191373i
$853$	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	$0.373397\pi$
$854$	−0.124422	+	0.00630047i	−0.00425764	+	0.000215598i
$855$		0			0
$856$	−0.651240	+	0.289951i	−0.0222589	+	0.00991032i
$857$	−4.05654	−	1.08695i	−0.138569	−	0.0371294i	0.188868	−	0.982002i	$-0.439518\pi$
$857$	−4.05654	−	1.08695i	−0.138569	−	0.0371294i	−0.327437	+	0.944873i	$0.606185\pi$
$858$	0.0199123	+	0.0245896i	0.000679794	+	0.000839476i
$859$	4.81200	+	5.34427i	0.164183	+	0.182344i	0.819623	−	0.572904i	$-0.194183\pi$
$859$	4.81200	+	5.34427i	0.164183	+	0.182344i	−0.655439	+	0.755248i	$0.727516\pi$
$860$		0			0
$861$	−6.46404	+	23.9549i	−0.220294	+	0.816381i
$862$	0.148930	−	0.0758837i	0.00507258	−	0.00258461i
$863$	9.85535	+	0.516497i	0.335480	+	0.0175818i	0.219332	−	0.975650i	$-0.429612\pi$
$863$	9.85535	+	0.516497i	0.335480	+	0.0175818i	0.116148	+	0.993232i	$0.462945\pi$
$864$	−0.736196	+	0.817629i	−0.0250459	+	0.0278163i
$865$		0			0
$866$	0.158831	−	0.143012i	0.00539730	−	0.00485975i
$867$	−3.38990	+	0.536908i	−0.115127	+	0.0182343i
$868$	−2.95735	+	2.65337i	−0.100379	+	0.0900613i
$869$	24.4604	−	33.6668i	0.829761	−	1.14207i
$870$		0			0
$871$	−0.852855	+	1.91554i	−0.0288979	+	0.0649057i
$872$	0.224029	+	0.583615i	0.00758658	+	0.0197637i
$873$	−11.6410	−	17.9256i	−0.393989	−	0.606690i
$874$	−0.392224			−0.0132672
$875$		0			0
$876$	−22.8531			−0.772133
$877$	17.8267	+	27.4507i	0.601965	+	0.926944i	0.999954	+	0.00955443i	$0.00304131\pi$
$877$	17.8267	+	27.4507i	0.601965	+	0.926944i	−0.397990	+	0.917390i	$0.630292\pi$
$878$	−0.150999	−	0.393367i	−0.00509598	−	0.0132755i
$879$	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	$0.0942157\pi$
$882$	0.129615	+	0.161221i	0.00436436	+	0.00542861i
$883$	36.1203	−	5.72089i	1.21554	−	0.192523i	0.484461	−	0.874813i	$-0.339016\pi$
$883$	36.1203	−	5.72089i	1.21554	−	0.192523i	0.731082	+	0.682289i	$0.239016\pi$
$884$	−1.78352	+	1.60589i	−0.0599863	+	0.0540119i
$885$		0			0
$886$	−0.0805312	+	0.0894389i	−0.00270550	+	0.00300476i
$887$	−11.4259	−	0.598808i	−0.383645	−	0.0201060i	−0.140461	−	0.990086i	$-0.544859\pi$
$887$	−11.4259	−	0.598808i	−0.383645	−	0.0201060i	−0.243184	+	0.969980i	$0.578192\pi$
$888$	−0.228174	+	0.116260i	−0.00765701	+	0.00390144i
$889$	−30.2433	+	30.1367i	−1.01433	+	1.01075i
$890$		0			0
$891$	2.97749	+	3.30683i	0.0997496	+	0.110783i
$892$	26.6424	+	32.9007i	0.892055	+	1.10160i
$893$	40.6235	+	10.8850i	1.35941	+	0.364253i
$894$	0.261747	−	0.116537i	0.00875414	−	0.00389759i
$895$		0			0
$896$	0.789507	+	1.22044i	0.0263756	+	0.0407722i
$897$	1.22637	+	0.194238i	0.0409474	+	0.00648543i
$898$	−0.163883	+	0.106427i	−0.00546885	+	0.00355151i
$899$	−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
$903$	−12.5465	−	11.3371i	−0.417522	−	0.377275i
$904$	−0.344529	−	0.474204i	−0.0114589	−	0.0157718i
$905$		0			0
$906$	−0.108430	−	0.0113965i	−0.00360235	−	0.000378622i
$907$	0.179150	−	0.668595i	0.00594856	−	0.0222003i	−0.962888	−	0.269902i	$-0.913009\pi$
$907$	0.179150	−	0.668595i	0.00594856	−	0.0222003i	0.968836	+	0.247702i	$0.0796753\pi$
$908$	−37.2289	−	14.2908i	−1.23548	−	0.474258i
$909$	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	$0.771900\pi$
$912$	1.58127	−	30.1723i	0.0523609	−	0.999106i
$913$	5.52452	+	3.58767i	0.182835	+	0.118734i
$914$	0.0875168	+	0.0788005i	0.00289480	+	0.00260649i
$915$		0			0
$916$	−19.0991	−	6.20568i	−0.631053	−	0.205042i
$917$	0.810316	+	7.84279i	0.0267590	+	0.258992i
$918$	0.242327	−	0.242327i	0.00799798	−	0.00799798i
$919$	3.16025	+	7.09803i	0.104247	+	0.234142i	0.958137	−	0.286312i	$-0.0924293\pi$
$919$	3.16025	+	7.09803i	0.104247	+	0.234142i	−0.853890	+	0.520454i	$0.825763\pi$
$920$		0			0
$921$	18.2583	+	8.12912i	0.601632	+	0.267864i
$922$	−0.0869870	−	0.0704407i	−0.00286476	−	0.00231984i
$923$	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
$927$	−1.32765	−	25.3331i	−0.0436058	−	0.832048i
$928$	−0.653225	+	0.250750i	−0.0214432	+	0.00823126i
$929$	5.76695	+	54.8689i	0.189208	+	1.80019i	0.517573	+	0.855639i	$0.326836\pi$
$929$	5.76695	+	54.8689i	0.189208	+	1.80019i	−0.328365	+	0.944551i	$0.606498\pi$
$930$		0			0
$931$	−45.7106	−	9.88488i	−1.49810	−	0.323964i
$932$	−3.94681	−	3.94681i	−0.129282	−	0.129282i
$933$	−3.03094	+	7.89587i	−0.0992286	+	0.258499i
$934$	−0.674889	+	0.143452i	−0.0220831	+	0.00469390i
$935$		0			0
$936$	−0.00789225	+	0.0371301i	−0.000257966	+	0.00121364i
$937$	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	$0.662878\pi$
$938$	−0.239714	−	0.174809i	−0.00782693	−	0.00570773i
$939$	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	$0.809491\pi$
$942$	0.0792012	−	0.0641359i	0.00258051	−	0.00208966i
$943$	27.3753	−	7.33518i	0.891462	−	0.238866i
$944$	30.9319	+	22.4733i	1.00675	+	0.731444i
$945$		0			0
$946$	−0.398202	+	0.289311i	−0.0129467	+	0.00940630i
$947$	−20.2986	+	25.0666i	−0.659615	+	0.814556i	−0.991684	−	0.128699i	$-0.958920\pi$
$947$	−20.2986	+	25.0666i	−0.659615	+	0.814556i	0.332069	+	0.943255i	$0.392253\pi$
$948$	−18.5333	+	0.971287i	−0.601932	+	0.0315459i
$949$	−2.81012	+	1.62242i	−0.0912202	+	0.0526660i
$950$		0			0
$951$		−	32.3214i		−	1.04809i
$952$	−0.338561	−	0.588803i	−0.0109728	−	0.0190832i
$953$	−4.45329	+	28.1170i	−0.144256	+	0.910797i	0.804308	+	0.594213i	$0.202536\pi$
$953$	−4.45329	+	28.1170i	−0.144256	+	0.910797i	−0.948564	+	0.316585i	$0.897464\pi$
$954$	−0.331951	+	0.0348895i	−0.0107473	+	0.00112959i
$955$		0			0
$956$	0.870679	−	8.28396i	0.0281598	−	0.267922i
$957$	5.04162	+	18.8156i	0.162973	+	0.608222i
$958$	−0.0557136	−	0.351762i	−0.00180002	−	0.0113649i
$959$	−25.6832	−	31.8308i	−0.829353	−	1.02787i
$960$		0			0
$961$	−29.7709	−	6.32801i	−0.960353	−	0.204129i
$962$	−0.00990103	+	0.0152463i	−0.000319222	+	0.000491559i
$963$	−9.72513	+	14.9754i	−0.313388	+	0.482575i
$964$	−13.8837	−	2.95107i	−0.447164	−	0.0950476i
$965$		0			0
$966$	−0.0632492	+	0.163904i	−0.00203501	+	0.00527354i
$967$	3.33883	+	21.0805i	0.107369	+	0.677904i	0.981391	+	0.192018i	$0.0615031\pi$
$967$	3.33883	+	21.0805i	0.107369	+	0.677904i	−0.874022	+	0.485886i	$0.838497\pi$
$968$	−0.261755	−	0.976883i	−0.00841312	−	0.0313982i
$969$	−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	$0.140632\pi$
$972$	−4.70046	+	29.6775i	−0.150767	+	0.951908i
$973$	0.0862044	−	48.8361i	0.00276359	−	1.56561i
$974$			0.127666i			0.00409070i
$975$		0			0
$976$	−9.49319	+	5.48089i	−0.303870	+	0.175439i
$977$	37.1545	−	1.94719i	1.18868	−	0.0622960i	0.552282	−	0.833658i	$-0.313757\pi$
$977$	37.1545	−	1.94719i	1.18868	−	0.0622960i	0.636397	+	0.771362i	$0.280424\pi$
$978$	0.217135	−	0.268139i	0.00694321	−	0.00857416i
$979$	4.06771	−	2.95536i	0.130005	−	0.0944538i
$980$		0			0
$981$	12.6680	+	9.20384i	0.404458	+	0.293856i
$982$	−0.336821	+	0.0902509i	−0.0107484	+	0.00288002i
$983$	15.5773	−	12.6142i	0.496838	−	0.402331i	−0.347883	−	0.937538i	$-0.613100\pi$
$983$	15.5773	−	12.6142i	0.496838	−	0.402331i	0.844721	+	0.535206i	$0.179766\pi$
$984$	−0.133939	−	0.630131i	−0.00426980	−	0.0200879i
$985$		0			0
$986$	0.207277	−	0.0673484i	0.00660105	−	0.00214481i
$987$	11.0995	−	15.2206i	0.353302	−	0.484477i
$988$	−1.94789	−	3.82295i	−0.0619707	−	0.121624i
$989$	−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	$0.215882\pi$
$992$	0.0554550	−	0.144465i	0.00176070	−	0.00458678i
$993$	−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
$997$	10.6304	−	4.08061i	0.336667	−	0.129234i	−0.184161	−	0.982896i	$-0.558957\pi$
$997$	10.6304	−	4.08061i	0.336667	−	0.129234i	0.520828	+	0.853662i	$0.325623\pi$
$998$	0.00827421	+	0.157881i	0.000261915	+	0.00499764i
$999$	−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.b.607.9		288
5.2	odd	4		875.2.bb.c.768.10		288
5.3	odd	4		175.2.x.a.33.9	✓	288
5.4	even	2		875.2.bb.a.607.10		288
7.3	odd	6	inner	875.2.bb.b.857.10		288
25.3	odd	20	inner	875.2.bb.b.243.10		288
25.4	even	10		875.2.bb.c.257.10		288
25.21	even	5		175.2.x.a.47.9	yes	288
25.22	odd	20		875.2.bb.a.243.9		288
35.3	even	12		175.2.x.a.108.9	yes	288
35.17	even	12		875.2.bb.c.143.10		288
35.24	odd	6		875.2.bb.a.857.9		288
175.3	even	60	inner	875.2.bb.b.493.9		288
175.122	even	60		875.2.bb.a.493.10		288
175.129	odd	30		875.2.bb.c.507.10		288
175.171	odd	30		175.2.x.a.122.9	yes	288

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

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

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