LMFDB - Embedded newform 875.2.bb.a.607.10

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,-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			607.10
Character	$\chi$	$=$	875.607
Dual form			875.2.bb.a.493.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.00935405 - 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	0.835348	−	0.549722i	$-0.185266\pi$
$2$	−0.00935405	−	0.0144040i	−0.00661431	−	0.0101851i	−0.841962	+	0.539536i	$0.818600\pi$
$3$	0.405343	+	1.05595i	0.234025	+	0.609656i	0.999425	−	0.0338987i	$-0.0107924\pi$
$3$	0.405343	+	1.05595i	0.234025	+	0.609656i	−0.765400	+	0.643554i	$0.777459\pi$
$4$	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	−0.413859	−	0.910341i	$-0.635819\pi$
$13$	0.286147	−	0.145799i	0.0793630	−	0.0404375i	0.493222	+	0.869904i	$0.335819\pi$
$14$	−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	0.407562	−	0.913177i	$-0.366379\pi$
$17$	−2.35181	−	2.90424i	−0.570397	−	0.704381i	−0.977959	+	0.208796i	$0.933046\pi$
$18$	−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	−0.807761	−	0.589511i	$-0.799321\pi$
$23$	−2.86676	+	1.86170i	−0.597762	+	0.388191i	0.209999	+	0.977702i	$0.432654\pi$
$24$	−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	$0.103995\pi$
$37$	−0.172493	+	3.29137i	−0.0283577	+	0.541098i	−0.975461	+	0.220170i	$0.929339\pi$
$38$	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	−0.333444	−	0.942770i	$-0.608211\pi$
$43$	3.99562	−	3.99562i	0.609326	−	0.609326i	0.942770	+	0.333444i	$0.108211\pi$
$44$	−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	0.915868	−	0.401480i	$-0.131504\pi$
$47$	4.89207	+	3.96152i	0.713581	+	0.577847i	−0.202287	+	0.979326i	$0.564837\pi$
$48$	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	0.498043	−	0.867152i	$-0.334052\pi$
$53$	10.5445	−	4.04766i	1.44840	−	0.555988i	0.950356	+	0.311164i	$0.100719\pi$
$54$	−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	−0.887051	−	0.461672i	$-0.847250\pi$
$67$	−5.07406	+	4.10889i	−0.619895	+	0.501981i	0.267155	+	0.963653i	$0.413916\pi$
$68$	−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	−0.632677	−	0.774416i	$-0.718044\pi$
$73$	−10.0900	+	0.528792i	−1.18094	+	0.0618904i	−0.548263	+	0.836306i	$0.684711\pi$
$74$	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	0.974025	−	0.226441i	$-0.0727089\pi$
$83$	−0.203179	−	1.28282i	−0.0223018	−	0.140808i	−0.996327	+	0.0856324i	$0.972709\pi$
$84$	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	$0.267202\pi$
$97$	−1.94322	+	12.2690i	−0.197304	+	1.24573i	−0.865183	+	0.501457i	$0.832798\pi$
$98$	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	$0.475448\pi$
$103$	−9.27815	+	11.4576i	−0.914203	+	1.12895i	−0.991260	+	0.131920i	$0.957886\pi$
$104$	−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	0.260621	−	0.965441i	$-0.416073\pi$
$107$	10.0239	−	2.68589i	0.969046	−	0.259655i	0.708425	+	0.705786i	$0.249406\pi$
$108$	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	0.998304	−	0.0582196i	$-0.0185424\pi$
$113$	3.87378	+	7.60273i	0.364415	+	0.715204i	−0.633889	+	0.773424i	$0.718542\pi$
$114$	−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	$0.404017\pi$
$127$	−7.32616	+	14.3784i	−0.650091	+	1.27588i	−0.947081	+	0.320996i	$0.895983\pi$
$128$	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	−0.144839	−	0.989455i	$-0.546266\pi$
$137$	−12.9649	−	8.41948i	−1.10766	−	0.719324i	−0.962824	+	0.270131i	$0.912933\pi$
$138$	−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	0.0508712	−	0.998705i	$-0.483800\pi$
$157$	−5.06744	−	1.35782i	−0.404426	−	0.108366i	−0.455297	+	0.890340i	$0.650467\pi$
$158$	−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	−0.657031	−	0.753864i	$-0.728188\pi$
$163$	−17.7369	−	0.929553i	−1.38926	−	0.0728082i	−0.732232	+	0.681055i	$0.761521\pi$
$164$	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	−0.372297	−	0.928113i	$-0.621430\pi$
$167$	−5.68050	+	0.899703i	−0.439571	+	0.0696211i	−0.0672731	+	0.997735i	$0.521430\pi$
$168$	−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	0.882347	−	0.470599i	$-0.155962\pi$
$173$	1.23047	+	1.89475i	0.0935507	+	0.144055i	−0.788797	+	0.614654i	$0.789295\pi$
$174$	−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	−0.280697	−	0.959796i	$-0.590566\pi$
$193$	−13.9437	−	3.73619i	−1.00369	−	0.268937i	−0.722989	+	0.690860i	$0.757232\pi$
$194$	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	−0.207688	−	0.978195i	$-0.566594\pi$
$197$	−9.93010	−	1.57277i	−0.707490	−	0.112055i	−0.499802	+	0.866140i	$0.666594\pi$
$198$	−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	$-0.599215\pi$
$223$	9.61132	−	18.8633i	0.643622	−	1.26318i	0.950291	−	0.311362i	$-0.100785\pi$
$224$	−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	$0.213536\pi$
$227$	1.04367	+	19.9144i	0.0692707	+	1.32176i	−0.714028	+	0.700117i	$0.753131\pi$
$228$	−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	−0.962436	−	0.271510i	$-0.912477\pi$
$233$	−1.00029	+	2.60583i	−0.0655309	+	0.170714i	0.896905	+	0.442224i	$0.145810\pi$
$234$	−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	0.907201	−	0.420698i	$-0.138215\pi$
$257$	−1.42369	−	5.31329i	−0.0888074	−	0.331434i	−0.996008	+	0.0892647i	$0.971548\pi$
$258$	−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	$0.404925\pi$
$263$	−11.3281	+	17.4437i	−0.698521	+	1.07563i	−0.992786	+	0.119904i	$0.961741\pi$
$264$	−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	0.878464	−	0.477809i	$-0.158569\pi$
$277$	29.9922	−	1.57183i	1.80206	−	0.0944419i	0.923596	+	0.383367i	$0.125236\pi$
$278$	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	$0.598680\pi$
$283$	−21.8697	+	17.7097i	−1.30002	+	1.05273i	−0.994947	+	0.100404i	$0.967986\pi$
$284$	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	0.560986	−	0.827826i	$-0.310422\pi$
$293$	−4.56757	−	4.56757i	−0.266840	−	0.266840i	−0.827826	+	0.560986i	$0.810422\pi$
$294$	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	−0.254080	−	0.967183i	$-0.581773\pi$
$307$	12.4946	−	12.4946i	0.713104	−	0.713104i	0.967183	+	0.254080i	$0.0817725\pi$
$308$	−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	$-0.695176\pi$
$313$	1.45664	−	27.7944i	0.0823343	−	1.57103i	0.657792	−	0.753200i	$-0.271491\pi$
$314$	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	−0.535356	−	0.844627i	$-0.679823\pi$
$317$	−26.6777	−	10.2406i	−1.49837	−	0.575170i	−0.963012	+	0.269457i	$0.913156\pi$
$318$	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	−0.924631	−	0.380865i	$-0.875626\pi$
$337$	−21.2946	+	10.8501i	−1.15999	+	0.591044i	−0.235358	+	0.971909i	$0.575626\pi$
$338$	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	0.964359	−	0.264596i	$-0.0852386\pi$
$347$	1.31609	+	3.42854i	0.0706515	+	0.184053i	−0.893708	+	0.448649i	$0.851905\pi$
$348$	−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	$-0.880393\pi$
$353$	−9.10273	−	23.7134i	−0.484490	−	1.26214i	0.445741	−	0.895162i	$-0.352940\pi$
$354$	−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	0.881724	−	0.471766i	$-0.156383\pi$
$367$	4.53923	+	5.60548i	0.236946	+	0.292604i	−0.644778	+	0.764370i	$0.723050\pi$
$368$	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	−0.626521	−	0.779404i	$-0.715522\pi$
$373$	−3.27030	+	2.12375i	−0.169329	+	0.109964i	0.457192	+	0.889368i	$0.348855\pi$
$374$	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	0.924527	−	0.381116i	$-0.124460\pi$
$383$	26.5486	+	10.1910i	1.35657	+	0.520738i	0.432042	+	0.901854i	$0.357793\pi$
$384$	−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	0.650803	−	0.759247i	$-0.274432\pi$
$397$	0.865873	+	0.701171i	0.0434569	+	0.0351907i	−0.607346	+	0.794438i	$0.707766\pi$
$398$	−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	$0.0466591\pi$
$433$	1.94672	+	12.2911i	0.0935535	+	0.590674i	−0.895722	+	0.444614i	$0.853341\pi$
$434$	−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	0.909363	−	0.416003i	$-0.136570\pi$
$443$	−1.81367	−	6.76871i	−0.0861701	−	0.321591i	−0.995533	+	0.0944121i	$0.969903\pi$
$444$	−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	−0.410380	−	0.911915i	$-0.634604\pi$
$457$	−6.62325	+	1.77469i	−0.309822	+	0.0830167i	0.100558	+	0.994931i	$0.467937\pi$
$458$	−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	0.933464	−	0.358672i	$-0.116770\pi$
$463$	2.03589	+	3.99566i	0.0946158	+	0.185694i	−0.838848	+	0.544366i	$0.816770\pi$
$464$	−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	$-0.503573\pi$
$467$	14.3968	−	37.5050i	0.666205	−	1.73552i	0.677430	−	0.735587i	$-0.263094\pi$
$468$	−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	0.395611	−	0.918418i	$-0.370533\pi$
$487$	−6.23415	−	4.04851i	−0.282496	−	0.183455i	−0.678107	+	0.734963i	$0.737200\pi$
$488$	−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	0.599150	−	0.800637i	$-0.295505\pi$
$503$	20.6686	+	3.27358i	0.921565	+	0.145962i	0.322415	+	0.946598i	$0.395505\pi$
$504$	−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	0.779127	−	0.626867i	$-0.215663\pi$
$523$	−2.52576	−	3.88934i	−0.110444	−	0.170069i	−0.889571	+	0.456798i	$0.848996\pi$
$524$	−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	0.343895	−	0.939008i	$-0.388254\pi$
$547$	8.90589	+	1.41055i	0.380788	+	0.0603110i	0.0368938	+	0.999319i	$0.488254\pi$
$548$	−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	$0.200205\pi$
$557$	−4.38542	+	16.3666i	−0.185816	+	0.693475i	−0.994454	+	0.105169i	$0.966462\pi$
$558$	−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	$0.0500198\pi$
$563$	36.3595	+	23.6121i	1.53237	+	0.995133i	0.544691	+	0.838637i	$0.316647\pi$
$564$	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	$0.0207172\pi$
$577$	0.294614	+	5.62157i	0.0122649	+	0.234029i	−0.985618	+	0.168990i	$0.945949\pi$
$578$	−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	0.610512	−	0.792007i	$-0.290964\pi$
$587$	−9.42678	−	18.5011i	−0.389085	−	0.763622i	−0.999597	+	0.0283850i	$0.990964\pi$
$588$	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	−0.538130	−	0.842862i	$-0.680869\pi$
$593$	−14.1905	+	3.80233i	−0.582733	+	0.156143i	−0.0446033	+	0.999005i	$0.514202\pi$
$594$	−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	$0.0493501\pi$
$607$	5.16341	+	19.2701i	0.209576	+	0.782150i	−0.778429	+	0.627732i	$0.783983\pi$
$608$	−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	$-0.534386\pi$
$613$	20.9028	−	32.1875i	0.844257	−	1.30004i	0.952073	−	0.305871i	$-0.0989478\pi$
$614$	−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	0.989495	−	0.144565i	$-0.0461782\pi$
$617$	0.0933065	+	0.589114i	0.00375638	+	0.0237168i	−0.985739	+	0.168282i	$0.946178\pi$
$618$	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	0.250830	−	0.968031i	$-0.419297\pi$
$643$	−18.1864	−	18.1864i	−0.717201	−	0.717201i	−0.968031	+	0.250830i	$0.919297\pi$
$644$	−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	−0.492922	−	0.870073i	$-0.664071\pi$
$647$	−7.04689	+	2.70505i	−0.277042	+	0.106346i	0.215880	+	0.976420i	$0.430738\pi$
$648$	−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	0.988885	−	0.148686i	$-0.0475042\pi$
$653$	26.8073	+	21.7081i	1.04905	+	0.849503i	0.0601643	+	0.998188i	$0.480838\pi$
$654$	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	0.723759	−	0.690053i	$-0.242413\pi$
$673$	15.3295	+	7.81076i	0.590908	+	0.301083i	−0.132850	+	0.991136i	$0.542413\pi$
$674$	0.355475	+	0.205234i	0.0136924	+	0.00790531i
$675$		0			0
$676$	12.8950	+	22.3347i	0.495960	+	0.859028i
$677$	−0.534205	+	0.346917i	−0.0205312	+	0.0133331i	−0.554864	−	0.831941i	$-0.687230\pi$
$677$	−0.534205	+	0.346917i	−0.0205312	+	0.0133331i	0.534333	+	0.845274i	$0.320563\pi$
$678$	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	0.947481	−	0.319812i	$-0.103620\pi$
$683$	11.4381	+	14.1248i	0.437665	+	0.540471i	−0.509816	+	0.860284i	$0.670286\pi$
$684$	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	0.0542869	−	0.998525i	$-0.482711\pi$
$727$	−19.4572	−	9.91394i	−0.721628	−	0.367688i	−0.775915	+	0.630838i	$0.782711\pi$
$728$	−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	0.354480	−	0.935064i	$-0.384658\pi$
$733$	−0.210373	−	0.0807548i	−0.00777032	−	0.00298275i	−0.362250	+	0.932081i	$0.617991\pi$
$734$	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	−0.669871	−	0.742477i	$-0.733651\pi$
$743$	1.97911	−	1.97911i	0.0726064	−	0.0726064i	0.742477	+	0.669871i	$0.233651\pi$
$744$	−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	$-0.979291\pi$
$757$	−29.2442	−	29.2442i	−1.06290	−	1.06290i	−0.0650131	−	0.997884i	$-0.520709\pi$
$758$	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	−0.0461029	−	0.998937i	$-0.514680\pi$
$773$	0.346537	−	0.0181612i	0.0124641	−	0.000653213i	0.0585670	+	0.998283i	$0.481347\pi$
$774$	−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	−0.920009	−	0.391896i	$-0.871819\pi$
$787$	−5.26825	+	8.11239i	−0.187793	+	0.289175i	0.732217	+	0.681072i	$0.238486\pi$
$788$	−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	$-0.626228\pi$
$797$	7.51322	−	47.4366i	0.266132	−	1.68029i	0.652377	−	0.757895i	$-0.273772\pi$
$798$	−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	$-0.925674\pi$
$823$	−0.846752	−	16.1570i	−0.0295159	−	0.563197i	0.943346	−	0.331811i	$-0.107660\pi$
$824$	0.506382	−	0.877080i	0.0176407	−	0.0305545i
$825$		0			0
$826$	0.196589	+	0.387517i	0.00684021	+	0.0134835i
$827$	6.12078	−	12.0127i	0.212841	−	0.417723i	−0.759761	−	0.650203i	$-0.774684\pi$
$827$	6.12078	−	12.0127i	0.212841	−	0.417723i	0.972601	+	0.232480i	$0.0746839\pi$
$828$	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	−0.387330	−	0.921941i	$-0.626603\pi$
$853$	−30.3919	−	4.81360i	−1.04060	−	0.164815i	−0.653268	+	0.757126i	$0.726603\pi$
$854$	−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	0.327437	−	0.944873i	$-0.393815\pi$
$857$	4.05654	+	1.08695i	0.138569	+	0.0371294i	−0.188868	+	0.982002i	$0.560482\pi$
$858$	−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	−0.116148	−	0.993232i	$-0.537055\pi$
$863$	−9.85535	−	0.516497i	−0.335480	−	0.0175818i	−0.219332	+	0.975650i	$0.570388\pi$
$864$	−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	$-0.996959\pi$
$877$	−17.8267	−	27.4507i	−0.601965	−	0.926944i	0.397990	−	0.917390i	$-0.369708\pi$
$878$	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	−0.731082	−	0.682289i	$-0.760984\pi$
$883$	−36.1203	+	5.72089i	−1.21554	+	0.192523i	−0.484461	+	0.874813i	$0.660984\pi$
$884$	−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	0.243184	−	0.969980i	$-0.421808\pi$
$887$	11.4259	+	0.598808i	0.383645	+	0.0201060i	0.140461	+	0.990086i	$0.455141\pi$
$888$	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	−0.968836	−	0.247702i	$-0.920325\pi$
$907$	−0.179150	+	0.668595i	−0.00594856	+	0.0222003i	0.962888	+	0.269902i	$0.0869913\pi$
$908$	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	$-0.962878\pi$
$937$	−15.4139	−	30.2515i	−0.503551	−	0.988274i	0.489657	−	0.871915i	$-0.337122\pi$
$938$	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	−0.332069	−	0.943255i	$-0.607747\pi$
$947$	20.2986	−	25.0666i	0.659615	−	0.814556i	0.991684	+	0.128699i	$0.0410800\pi$
$948$	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	$-0.797464\pi$
$953$	4.45329	−	28.1170i	0.144256	−	0.910797i	0.948564	−	0.316585i	$-0.102536\pi$
$954$	−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	$-0.938497\pi$
$967$	−3.33883	−	21.0805i	−0.107369	−	0.677904i	0.874022	−	0.485886i	$-0.161503\pi$
$968$	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	−0.636397	−	0.771362i	$-0.719576\pi$
$977$	−37.1545	+	1.94719i	−1.18868	+	0.0622960i	−0.552282	+	0.833658i	$0.686243\pi$
$978$	−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	−0.844721	−	0.535206i	$-0.820234\pi$
$983$	−15.5773	+	12.6142i	−0.496838	+	0.402331i	0.347883	+	0.937538i	$0.386900\pi$
$984$	−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	−0.520828	−	0.853662i	$-0.674377\pi$
$997$	−10.6304	+	4.08061i	−0.336667	+	0.129234i	0.184161	+	0.982896i	$0.441043\pi$
$998$	−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.a.607.10		288
5.2	odd	4		175.2.x.a.33.9	✓	288
5.3	odd	4		875.2.bb.c.768.10		288
5.4	even	2		875.2.bb.b.607.9		288
7.3	odd	6	inner	875.2.bb.a.857.9		288
25.3	odd	20	inner	875.2.bb.a.243.9		288
25.4	even	10		175.2.x.a.47.9	yes	288
25.21	even	5		875.2.bb.c.257.10		288
25.22	odd	20		875.2.bb.b.243.10		288
35.3	even	12		875.2.bb.c.143.10		288
35.17	even	12		175.2.x.a.108.9	yes	288
35.24	odd	6		875.2.bb.b.857.10		288
175.3	even	60	inner	875.2.bb.a.493.10		288
175.122	even	60		875.2.bb.b.493.9		288
175.129	odd	30		175.2.x.a.122.9	yes	288
175.171	odd	30		875.2.bb.c.507.10		288

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more