LMFDB - Embedded newform 375.2.g.b.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.26265625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 $ x^8 - 3x^7 + 2x^6 + x^4 + 8x^2 - 24x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.2
Root			$1.40799 + 0.132563i$ of defining polynomial
Character	$\chi$	$=$	375.151
Dual form			375.2.g.b.226.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.346820 + 1.06740i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.907987 + 0.659691i) q^{6} -1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.346820 + 1.06740i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.907987 + 0.659691i) q^{6} -1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.13412 + 3.49045i) q^{11} +(0.228786 - 0.704131i) q^{12} +(1.25215 - 3.85372i) q^{13} +(-0.386266 - 1.18880i) q^{14} +(-0.609110 + 1.87465i) q^{16} +(1.71700 + 1.24748i) q^{17} +1.12233 q^{18} +(3.28513 + 2.38678i) q^{19} +(-0.901030 + 0.654637i) q^{21} +(-3.33238 + 2.42112i) q^{22} +(-1.90799 - 5.87218i) q^{23} +3.07561 q^{24} +4.54774 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.667093 + 0.484672i) q^{28} +(1.82808 - 1.32818i) q^{29} +(-8.13227 - 5.90844i) q^{31} +3.93896 q^{32} +(2.96915 + 2.15722i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(-0.228786 - 0.704131i) q^{36} +(-2.27817 + 7.01149i) q^{37} +(-1.40831 + 4.33434i) q^{38} +(-1.25215 - 3.85372i) q^{39} +(-2.30902 + 7.10642i) q^{41} +(-1.01126 - 0.734721i) q^{42} -9.24998 q^{43} +(2.19826 + 1.59713i) q^{44} +(5.60625 - 4.07318i) q^{46} +(-2.53032 + 1.83839i) q^{47} +(0.609110 + 1.87465i) q^{48} -5.75960 q^{49} +2.12233 q^{51} +(-0.927051 - 2.85317i) q^{52} +(-2.83934 + 2.06290i) q^{53} +(0.907987 - 0.659691i) q^{54} +(-2.77121 - 2.01340i) q^{56} +4.06064 q^{57} +(2.05172 + 1.49066i) q^{58} +(-2.03760 + 6.27109i) q^{59} +(-2.81332 - 8.65850i) q^{61} +(3.48625 - 10.7296i) q^{62} +(-0.344163 + 1.05922i) q^{63} +(2.58433 + 7.95375i) q^{64} +(-1.27286 + 3.91745i) q^{66} +(2.12499 + 1.54390i) q^{67} +1.57131 q^{68} +(-4.99517 - 3.62921i) q^{69} +(-0.534620 + 0.388424i) q^{71} +(2.48822 - 1.80780i) q^{72} +(-2.31003 - 7.10955i) q^{73} -8.27420 q^{74} +3.00637 q^{76} +(-1.26310 - 3.88743i) q^{77} +(3.67920 - 2.67310i) q^{78} +(-6.90667 + 5.01799i) q^{79} +(-0.809017 - 0.587785i) q^{81} -8.38623 q^{82} +(9.92170 + 7.20854i) q^{83} +(-0.254807 + 0.784215i) q^{84} +(-3.20808 - 9.87345i) q^{86} +(0.698265 - 2.14904i) q^{87} +(-3.48809 + 10.7352i) q^{88} +(-4.72429 - 14.5399i) q^{89} +(-1.39456 + 4.29202i) q^{91} +(-3.69826 - 2.68695i) q^{92} -10.0520 q^{93} +(-2.83986 - 2.06328i) q^{94} +(3.18668 - 2.31526i) q^{96} +(10.9217 - 7.93508i) q^{97} +(-1.99754 - 6.14781i) q^{98} +3.67008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	$ 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) $ 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$1$

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 $

$2$	0.346820	+	1.06740i	0.245239	+	0.754768i	0.995597	+	0.0937362i	$0.0298810\pi$
$2$	0.346820	+	1.06740i	0.245239	+	0.754768i	−0.750358	+	0.661031i	$0.770119\pi$
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$3$	0.809017	−	0.587785i	0.467086	−	0.339358i
$4$	0.598970	−	0.435177i	0.299485	−	0.217589i
$5$		0			0
$5$		0			0
$6$	0.907987	+	0.659691i	0.370684	+	0.269318i
$7$	−1.11373			−0.420952			−0.210476	−	0.977599i	$-0.567501\pi$
$7$	−1.11373			−0.420952			−0.210476	+	0.977599i	$0.567501\pi$
$8$	2.48822	+	1.80780i	0.879718	+	0.639152i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	1.13412	+	3.49045i	0.341949	+	1.05241i	0.963197	+	0.268796i	$0.0866258\pi$
$11$	1.13412	+	3.49045i	0.341949	+	1.05241i	−0.621248	+	0.783614i	$0.713374\pi$
$12$	0.228786	−	0.704131i	0.0660449	−	0.203265i
$13$	1.25215	−	3.85372i	0.347284	−	1.06883i	−0.613066	−	0.790032i	$-0.710064\pi$
$13$	1.25215	−	3.85372i	0.347284	−	1.06883i	0.960350	−	0.278798i	$-0.0899360\pi$
$14$	−0.386266	−	1.18880i	−0.103234	−	0.317721i
$15$		0			0
$16$	−0.609110	+	1.87465i	−0.152277	+	0.468662i
$17$	1.71700	+	1.24748i	0.416435	+	0.302557i	0.776202	−	0.630485i	$-0.217144\pi$
$17$	1.71700	+	1.24748i	0.416435	+	0.302557i	−0.359767	+	0.933042i	$0.617144\pi$
$18$	1.12233			0.264537
$19$	3.28513	+	2.38678i	0.753660	+	0.547566i	0.896959	−	0.442113i	$-0.145771\pi$
$19$	3.28513	+	2.38678i	0.753660	+	0.547566i	−0.143299	+	0.989679i	$0.545771\pi$
$20$		0			0
$21$	−0.901030	+	0.654637i	−0.196621	+	0.142853i
$22$	−3.33238	+	2.42112i	−0.710466	+	0.516184i
$23$	−1.90799	−	5.87218i	−0.397843	−	1.22443i	−0.926725	−	0.375739i	$-0.877389\pi$
$23$	−1.90799	−	5.87218i	−0.397843	−	1.22443i	0.528883	−	0.848695i	$-0.322611\pi$
$24$	3.07561			0.627806
$25$		0			0
$26$	4.54774			0.891886
$27$	−0.309017	−	0.951057i	−0.0594703	−	0.183031i
$28$	−0.667093	+	0.484672i	−0.126069	+	0.0915943i
$29$	1.82808	−	1.32818i	0.339466	−	0.246637i	−0.404970	−	0.914330i	$-0.632718\pi$
$29$	1.82808	−	1.32818i	0.339466	−	0.246637i	0.744437	+	0.667693i	$0.232718\pi$
$30$		0			0
$31$	−8.13227	−	5.90844i	−1.46060	−	1.06119i	−0.983206	−	0.182498i	$-0.941582\pi$
$31$	−8.13227	−	5.90844i	−1.46060	−	1.06119i	−0.477393	−	0.878690i	$-0.658418\pi$
$32$	3.93896			0.696316
$33$	2.96915	+	2.15722i	0.516863	+	0.375523i
$34$	−0.736068	+	2.26538i	−0.126235	+	0.388510i
$35$		0			0
$36$	−0.228786	−	0.704131i	−0.0381310	−	0.117355i
$37$	−2.27817	+	7.01149i	−0.374529	+	1.15268i	0.569267	+	0.822153i	$0.307227\pi$
$37$	−2.27817	+	7.01149i	−0.374529	+	1.15268i	−0.943796	+	0.330529i	$0.892773\pi$
$38$	−1.40831	+	4.33434i	−0.228458	+	0.703123i
$39$	−1.25215	−	3.85372i	−0.200504	−	0.617089i
$40$		0			0
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	0.592078	+	0.805881i	$0.298308\pi$
$41$	−2.30902	+	7.10642i	−0.360608	+	1.10984i	−0.952686	+	0.303956i	$0.901692\pi$
$42$	−1.01126	−	0.734721i	−0.156040	−	0.113370i
$43$	−9.24998			−1.41061			−0.705304	−	0.708905i	$-0.749190\pi$
$43$	−9.24998			−1.41061			−0.705304	+	0.708905i	$0.749190\pi$
$44$	2.19826	+	1.59713i	0.331401	+	0.240777i
$45$		0			0
$46$	5.60625	−	4.07318i	0.826597	−	0.600558i
$47$	−2.53032	+	1.83839i	−0.369085	+	0.268156i	−0.756831	−	0.653610i	$-0.773254\pi$
$47$	−2.53032	+	1.83839i	−0.369085	+	0.268156i	0.387746	+	0.921766i	$0.373254\pi$
$48$	0.609110	+	1.87465i	0.0879174	+	0.270582i
$49$	−5.75960			−0.822799
$50$		0			0
$51$	2.12233			0.297186
$52$	−0.927051	−	2.85317i	−0.128559	−	0.395663i
$53$	−2.83934	+	2.06290i	−0.390013	+	0.283361i	−0.765461	−	0.643483i	$-0.777489\pi$
$53$	−2.83934	+	2.06290i	−0.390013	+	0.283361i	0.375448	+	0.926844i	$0.377489\pi$
$54$	0.907987	−	0.659691i	0.123561	−	0.0897726i
$55$		0			0
$56$	−2.77121	−	2.01340i	−0.370319	−	0.269053i
$57$	4.06064			0.537845
$58$	2.05172	+	1.49066i	0.269404	+	0.195733i
$59$	−2.03760	+	6.27109i	−0.265273	+	0.816427i	0.726357	+	0.687317i	$0.241212\pi$
$59$	−2.03760	+	6.27109i	−0.265273	+	0.816427i	−0.991630	+	0.129110i	$0.958788\pi$
$60$		0			0
$61$	−2.81332	−	8.65850i	−0.360208	−	1.10861i	−0.952928	−	0.303198i	$-0.901946\pi$
$61$	−2.81332	−	8.65850i	−0.360208	−	1.10861i	0.592719	−	0.805409i	$-0.298054\pi$
$62$	3.48625	−	10.7296i	0.442754	−	1.36266i
$63$	−0.344163	+	1.05922i	−0.0433604	+	0.133450i
$64$	2.58433	+	7.95375i	0.323041	+	0.994219i
$65$		0			0
$66$	−1.27286	+	3.91745i	−0.156678	+	0.482205i
$67$	2.12499	+	1.54390i	0.259609	+	0.188617i	0.709975	−	0.704227i	$-0.248706\pi$
$67$	2.12499	+	1.54390i	0.259609	+	0.188617i	−0.450366	+	0.892844i	$0.648706\pi$
$68$	1.57131			0.190549
$69$	−4.99517	−	3.62921i	−0.601348	−	0.436905i
$70$		0			0
$71$	−0.534620	+	0.388424i	−0.0634477	+	0.0460975i	−0.619057	−	0.785346i	$-0.712485\pi$
$71$	−0.534620	+	0.388424i	−0.0634477	+	0.0460975i	0.555609	+	0.831443i	$0.312485\pi$
$72$	2.48822	−	1.80780i	0.293239	−	0.213051i
$73$	−2.31003	−	7.10955i	−0.270369	−	0.832110i	−0.990408	−	0.138176i	$-0.955876\pi$
$73$	−2.31003	−	7.10955i	−0.270369	−	0.832110i	0.720039	−	0.693934i	$-0.244124\pi$
$74$	−8.27420			−0.961856
$75$		0			0
$76$	3.00637			0.344854
$77$	−1.26310	−	3.88743i	−0.143944	−	0.443014i
$78$	3.67920	−	2.67310i	0.416587	−	0.302668i
$79$	−6.90667	+	5.01799i	−0.777061	+	0.564568i	−0.904096	−	0.427330i	$-0.859454\pi$
$79$	−6.90667	+	5.01799i	−0.777061	+	0.564568i	0.127034	+	0.991898i	$0.459454\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	−8.38623			−0.926104
$83$	9.92170	+	7.20854i	1.08905	+	0.791240i	0.979238	−	0.202713i	$-0.0649758\pi$
$83$	9.92170	+	7.20854i	1.08905	+	0.791240i	0.109810	+	0.993953i	$0.464976\pi$
$84$	−0.254807	+	0.784215i	−0.0278017	+	0.0855649i
$85$		0			0
$86$	−3.20808	−	9.87345i	−0.345936	−	1.06468i
$87$	0.698265	−	2.14904i	0.0748618	−	0.230401i
$88$	−3.48809	+	10.7352i	−0.371832	+	1.14438i
$89$	−4.72429	−	14.5399i	−0.500773	−	1.54122i	−0.807762	−	0.589509i	$-0.799321\pi$
$89$	−4.72429	−	14.5399i	−0.500773	−	1.54122i	0.306989	−	0.951713i	$-0.400679\pi$
$90$		0			0
$91$	−1.39456	+	4.29202i	−0.146190	+	0.449926i
$92$	−3.69826	−	2.68695i	−0.385571	−	0.280134i
$93$	−10.0520			−1.04235
$94$	−2.83986	−	2.06328i	−0.292910	−	0.212811i
$95$		0			0
$96$	3.18668	−	2.31526i	0.325240	−	0.236300i
$97$	10.9217	−	7.93508i	1.10893	−	0.805685i	0.126436	−	0.991975i	$-0.459646\pi$
$97$	10.9217	−	7.93508i	1.10893	−	0.805685i	0.982495	+	0.186290i	$0.0596463\pi$
$98$	−1.99754	−	6.14781i	−0.201782	−	0.621022i
$99$	3.67008			0.368856
$100$		0			0
$101$	7.22642			0.719055			0.359528	−	0.933134i	$-0.382938\pi$
$101$	7.22642			0.719055			0.359528	+	0.933134i	$0.382938\pi$
$102$	0.736068	+	2.26538i	0.0728816	+	0.224306i
$103$	4.26957	−	3.10203i	0.420693	−	0.305652i	−0.357223	−	0.934019i	$-0.616277\pi$
$103$	4.26957	−	3.10203i	0.420693	−	0.305652i	0.777917	+	0.628367i	$0.216277\pi$
$104$	10.0824	−	7.32526i	0.988657	−	0.718301i
$105$		0			0
$106$	−3.18668	−	2.31526i	−0.309518	−	0.224878i
$107$	−5.46682			−0.528498			−0.264249	−	0.964455i	$-0.585124\pi$
$107$	−5.46682			−0.528498			−0.264249	+	0.964455i	$0.585124\pi$
$108$	−0.598970	−	0.435177i	−0.0576359	−	0.0418749i
$109$	3.50410	−	10.7845i	0.335632	−	1.03297i	−0.630778	−	0.775963i	$-0.717264\pi$
$109$	3.50410	−	10.7845i	0.335632	−	1.03297i	0.966410	−	0.257005i	$-0.0827358\pi$
$110$		0			0
$111$	2.27817	+	7.01149i	0.216234	+	0.665501i
$112$	0.678387	−	2.08786i	0.0641015	−	0.197284i
$113$	−1.49416	+	4.59855i	−0.140559	+	0.432595i	−0.996413	−	0.0846215i	$-0.973032\pi$
$113$	−1.49416	+	4.59855i	−0.140559	+	0.432595i	0.855854	+	0.517217i	$0.173032\pi$
$114$	1.40831	+	4.33434i	0.131900	+	0.405948i
$115$		0			0
$116$	0.516973	−	1.59108i	0.0479997	−	0.147728i
$117$	−3.27817	−	2.38173i	−0.303067	−	0.220191i
$118$	−7.40046			−0.681268
$119$	−1.91229	−	1.38936i	−0.175299	−	0.127362i
$120$		0			0
$121$	−1.99783	+	1.45151i	−0.181621	+	0.131955i
$122$	8.26639	−	6.00588i	0.748404	−	0.543747i
$123$	2.30902	+	7.10642i	0.208197	+	0.640765i
$124$	−7.44220			−0.668330
$125$		0			0
$126$	−1.24998			−0.111357
$127$	−0.234728	−	0.722418i	−0.0208287	−	0.0641043i	0.940102	−	0.340894i	$-0.110730\pi$
$127$	−0.234728	−	0.722418i	−0.0208287	−	0.0641043i	−0.960931	+	0.276789i	$0.910730\pi$
$128$	−1.22019	+	0.886518i	−0.107850	+	0.0783578i
$129$	−7.48339	+	5.43700i	−0.658876	+	0.478701i
$130$		0			0
$131$	−11.8562	−	8.61406i	−1.03588	−	0.752614i	−0.0664061	−	0.997793i	$-0.521153\pi$
$131$	−11.8562	−	8.61406i	−1.03588	−	0.752614i	−0.969478	+	0.245179i	$0.921153\pi$
$132$	2.71720			0.236502
$133$	−3.65876	−	2.65824i	−0.317255	−	0.230499i
$134$	−0.910969	+	2.80367i	−0.0786958	+	0.242201i
$135$		0			0
$136$	2.01710	+	6.20799i	0.172965	+	0.532330i
$137$	−3.79825	+	11.6898i	−0.324506	+	0.998728i	0.647157	+	0.762357i	$0.275958\pi$
$137$	−3.79825	+	11.6898i	−0.324506	+	0.998728i	−0.971663	+	0.236371i	$0.924042\pi$
$138$	2.14140	−	6.59054i	0.182288	−	0.561024i
$139$	4.55306	+	14.0129i	0.386185	+	1.18856i	0.935617	+	0.353017i	$0.114844\pi$
$139$	4.55306	+	14.0129i	0.386185	+	1.18856i	−0.549432	+	0.835539i	$0.685156\pi$
$140$		0			0
$141$	−0.966496	+	2.97457i	−0.0813937	+	0.250504i
$142$	−0.600022	−	0.435941i	−0.0503527	−	0.0365834i
$143$	14.8713			1.24360
$144$	1.59467	+	1.15860i	0.132889	+	0.0965497i
$145$		0			0
$146$	6.78758	−	4.93147i	0.561744	−	0.408131i
$147$	−4.65961	+	3.38541i	−0.384318	+	0.279224i
$148$	1.68668	+	5.19108i	0.138645	+	0.426704i
$149$	15.6498			1.28208			0.641041	−	0.767507i	$-0.278503\pi$
$149$	15.6498			1.28208			0.641041	+	0.767507i	$0.278503\pi$
$150$		0			0
$151$	3.95819			0.322113			0.161056	−	0.986945i	$-0.448510\pi$
$151$	3.95819			0.322113			0.161056	+	0.986945i	$0.448510\pi$
$152$	3.85929	+	11.8777i	0.313030	+	0.963407i
$153$	1.71700	−	1.24748i	0.138812	−	0.100852i
$154$	3.71139	−	2.69648i	0.299072	−	0.217289i
$155$		0			0
$156$	−2.42705	−	1.76336i	−0.194320	−	0.141181i
$157$	4.50061			0.359188			0.179594	−	0.983741i	$-0.442522\pi$
$157$	4.50061			0.359188			0.179594	+	0.983741i	$0.442522\pi$
$158$	−7.75159	−	5.63186i	−0.616683	−	0.448047i
$159$	−1.08453	+	3.33784i	−0.0860089	+	0.264708i
$160$		0			0
$161$	2.12499	+	6.54005i	0.167473	+	0.515428i
$162$	0.346820	−	1.06740i	0.0272488	−	0.0838631i
$163$	0.758292	−	2.33378i	0.0593940	−	0.182796i	−0.916958	−	0.398985i	$-0.869363\pi$
$163$	0.758292	−	2.33378i	0.0593940	−	0.182796i	0.976352	+	0.216189i	$0.0693626\pi$
$164$	1.70952	+	5.26137i	0.133491	+	0.410844i
$165$		0			0
$166$	−4.25337	+	13.0905i	−0.330125	+	1.01602i
$167$	−2.47824	−	1.80055i	−0.191772	−	0.139331i	0.487756	−	0.872980i	$-0.337816\pi$
$167$	−2.47824	−	1.80055i	−0.191772	−	0.139331i	−0.679528	+	0.733649i	$0.737816\pi$
$168$	−3.42541			−0.264276
$169$	−2.76606	−	2.00966i	−0.212774	−	0.154589i
$170$		0			0
$171$	3.28513	−	2.38678i	0.251220	−	0.182522i
$172$	−5.54046	+	4.02538i	−0.422456	+	0.306932i
$173$	−3.47942	−	10.7085i	−0.264535	−	0.814156i	−0.991800	−	0.127799i	$-0.959209\pi$
$173$	−3.47942	−	10.7085i	−0.264535	−	0.814156i	0.727265	−	0.686357i	$-0.240791\pi$
$174$	2.53606			0.192258
$175$		0			0
$176$	−7.23416			−0.545296
$177$	2.03760	+	6.27109i	0.153156	+	0.471364i
$178$	13.8814	−	10.0854i	1.04046	−	0.755935i
$179$	−8.13657	+	5.91157i	−0.608156	+	0.441851i	−0.848764	−	0.528771i	$-0.822653\pi$
$179$	−8.13657	+	5.91157i	−0.608156	+	0.441851i	0.240609	+	0.970622i	$0.422653\pi$
$180$		0			0
$181$	15.7503	+	11.4433i	1.17071	+	0.850571i	0.991094	−	0.133165i	$-0.0425141\pi$
$181$	15.7503	+	11.4433i	1.17071	+	0.850571i	0.179617	+	0.983737i	$0.442514\pi$
$182$	−5.06498			−0.375441
$183$	−7.36536	−	5.35125i	−0.544463	−	0.395575i
$184$	5.86822	−	18.0605i	0.432611	−	1.33144i
$185$		0			0
$186$	−3.48625	−	10.7296i	−0.255624	−	0.786731i
$187$	−2.40697	+	7.40790i	−0.176015	+	0.541719i
$188$	−0.715563	+	2.20227i	−0.0521878	+	0.160617i
$189$	0.344163	+	1.05922i	0.0250342	+	0.0770472i
$190$		0			0
$191$	−3.58739	+	11.0408i	−0.259574	+	0.798888i	0.733320	+	0.679884i	$0.237970\pi$
$191$	−3.58739	+	11.0408i	−0.259574	+	0.798888i	−0.992894	+	0.119003i	$0.962030\pi$
$192$	6.76586	+	4.91569i	0.488284	+	0.354759i
$193$	3.38156			0.243410			0.121705	−	0.992566i	$-0.461164\pi$
$193$	3.38156			0.243410			0.121705	+	0.992566i	$0.461164\pi$
$194$	12.2578	+	8.90581i	0.880058	+	0.639400i
$195$		0			0
$196$	−3.44982	+	2.50644i	−0.246416	+	0.179032i
$197$	−14.2291	+	10.3380i	−1.01378	+	0.736554i	−0.964998	−	0.262256i	$-0.915534\pi$
$197$	−14.2291	+	10.3380i	−1.01378	+	0.736554i	−0.0487811	+	0.998809i	$0.515534\pi$
$198$	1.27286	+	3.91745i	0.0904579	+	0.278401i
$199$	20.0102			1.41849			0.709244	−	0.704963i	$-0.249037\pi$
$199$	20.0102			1.41849			0.709244	+	0.704963i	$0.249037\pi$
$200$		0			0
$201$	2.62663			0.185268
$202$	2.50627	+	7.71350i	0.176340	+	0.542720i
$203$	−2.03600	+	1.47924i	−0.142899	+	0.103822i
$204$	1.27121	−	0.923591i	0.0890028	−	0.0646643i
$205$		0			0
$206$	4.79188	+	3.48151i	0.333866	+	0.242568i
$207$	−6.17438			−0.429149
$208$	6.46167	+	4.69468i	0.448036	+	0.325517i
$209$	−4.60524	+	14.1735i	−0.318551	+	0.980399i
$210$		0			0
$211$	0.754807	+	2.32306i	0.0519631	+	0.159926i	0.973671	−	0.227960i	$-0.0732055\pi$
$211$	0.754807	+	2.32306i	0.0519631	+	0.159926i	−0.921707	+	0.387886i	$0.873206\pi$
$212$	−0.802951	+	2.47123i	−0.0551469	+	0.169725i
$213$	−0.204207	+	0.628483i	−0.0139920	+	0.0430630i
$214$	−1.89600	−	5.83530i	−0.129608	−	0.398893i
$215$		0			0
$216$	0.950415	−	2.92508i	0.0646675	−	0.199026i
$217$	9.05719	+	6.58044i	0.614842	+	0.446709i
$218$	12.7267			0.861961
$219$	−6.04774	−	4.39394i	−0.408669	−	0.296915i
$220$		0			0
$221$	6.95737	−	5.05483i	0.468003	−	0.340024i
$222$	−6.69397	+	4.86345i	−0.449270	+	0.326413i
$223$	7.92223	+	24.3821i	0.530511	+	1.63275i	0.753153	+	0.657846i	$0.228532\pi$
$223$	7.92223	+	24.3821i	0.530511	+	1.63275i	−0.222641	+	0.974900i	$0.571468\pi$
$224$	−4.38695			−0.293116
$225$		0			0
$226$	−5.42671			−0.360979
$227$	−2.02819	−	6.24212i	−0.134616	−	0.414304i	0.860914	−	0.508750i	$-0.169892\pi$
$227$	−2.02819	−	6.24212i	−0.134616	−	0.414304i	−0.995530	+	0.0944455i	$0.969892\pi$
$228$	2.43220	−	1.76710i	0.161076	−	0.117029i
$229$	6.44293	−	4.68106i	0.425761	−	0.309333i	−0.354191	−	0.935173i	$-0.615244\pi$
$229$	6.44293	−	4.68106i	0.425761	−	0.309333i	0.779952	+	0.625840i	$0.215244\pi$
$230$		0			0
$231$	−3.30685	−	2.40257i	−0.217575	−	0.158077i
$232$	6.94974			0.456273
$233$	−7.62181	−	5.53757i	−0.499321	−	0.362778i	0.309436	−	0.950920i	$-0.399860\pi$
$233$	−7.62181	−	5.53757i	−0.499321	−	0.362778i	−0.808758	+	0.588142i	$0.799860\pi$
$234$	1.40533	−	4.32516i	0.0918693	−	0.282745i
$235$		0			0
$236$	1.50857	+	4.64291i	0.0981998	+	0.302228i
$237$	−2.63811	+	8.11928i	−0.171364	+	0.527404i
$238$	0.819784	−	2.52304i	0.0531387	−	0.163544i
$239$	−3.46814	−	10.6738i	−0.224335	−	0.690433i	−0.998358	−	0.0572756i	$-0.981759\pi$
$239$	−3.46814	−	10.6738i	−0.224335	−	0.690433i	0.774023	−	0.633157i	$-0.218241\pi$
$240$		0			0
$241$	7.00879	−	21.5708i	0.451476	−	1.38950i	−0.423748	−	0.905780i	$-0.639286\pi$
$241$	7.00879	−	21.5708i	0.451476	−	1.38950i	0.875223	−	0.483719i	$-0.160714\pi$
$242$	−2.24223	−	1.62908i	−0.144136	−	0.104721i
$243$	−1.00000			−0.0641500
$244$	−5.45307	−	3.96189i	−0.349097	−	0.253634i
$245$		0			0
$246$	−6.78460	+	4.92930i	−0.432570	+	0.314281i
$247$	13.3115	−	9.67135i	0.846989	−	0.615373i
$248$	−9.55361	−	29.4030i	−0.606655	−	1.86709i
$249$	12.2639			0.777193
$250$		0			0
$251$	−6.76819			−0.427205			−0.213602	−	0.976921i	$-0.568520\pi$
$251$	−6.76819			−0.427205			−0.213602	+	0.976921i	$0.568520\pi$
$252$	0.254807	+	0.784215i	0.0160513	+	0.0494009i
$253$	18.3327	−	13.3195i	1.15257	−	0.837387i
$254$	0.689703	−	0.501098i	0.0432758	−	0.0314417i
$255$		0			0
$256$	12.1623	+	8.83640i	0.760142	+	0.552275i
$257$	14.7934			0.922786			0.461393	−	0.887196i	$-0.347350\pi$
$257$	14.7934			0.922786			0.461393	+	0.887196i	$0.347350\pi$
$258$	−8.39886	−	6.10213i	−0.522890	−	0.379902i
$259$	2.53728	−	7.80894i	0.157659	−	0.485224i
$260$		0			0
$261$	−0.698265	−	2.14904i	−0.0432215	−	0.133022i
$262$	5.08269	−	15.6429i	0.314009	−	0.966422i
$263$	−6.17070	+	18.9915i	−0.380502	+	1.17106i	0.559189	+	0.829040i	$0.311113\pi$
$263$	−6.17070	+	18.9915i	−0.380502	+	1.17106i	−0.939691	+	0.342024i	$0.888887\pi$
$264$	3.48809	+	10.7352i	0.214677	+	0.660709i
$265$		0			0
$266$	1.56849	−	4.82730i	0.0961700	−	0.295981i
$267$	−12.3683	−	8.98613i	−0.756930	−	0.549942i
$268$	1.94467			0.118790
$269$	8.28280	+	6.01780i	0.505011	+	0.366912i	0.810928	−	0.585146i	$-0.198963\pi$
$269$	8.28280	+	6.01780i	0.505011	+	0.366912i	−0.305917	+	0.952058i	$0.598963\pi$
$270$		0			0
$271$	−9.95701	+	7.23419i	−0.604845	+	0.439446i	−0.847595	−	0.530643i	$-0.821950\pi$
$271$	−9.95701	+	7.23419i	−0.604845	+	0.439446i	0.242750	+	0.970089i	$0.421950\pi$
$272$	−3.38442	+	2.45893i	−0.205211	+	0.149094i
$273$	1.39456	+	4.29202i	0.0844028	+	0.259765i
$274$	−13.7950			−0.833389
$275$		0			0
$276$	−4.57131			−0.275160
$277$	−9.75011	−	30.0077i	−0.585827	−	1.80299i	−0.595923	−	0.803041i	$-0.703214\pi$
$277$	−9.75011	−	30.0077i	−0.585827	−	1.80299i	0.0100963	−	0.999949i	$-0.496786\pi$
$278$	−13.3783	+	9.71989i	−0.802376	+	0.582960i
$279$	−8.13227	+	5.90844i	−0.486866	+	0.353729i
$280$		0			0
$281$	17.2417	+	12.5268i	1.02855	+	0.747288i	0.968019	−	0.250878i	$-0.0807192\pi$
$281$	17.2417	+	12.5268i	1.02855	+	0.747288i	0.0605353	+	0.998166i	$0.480719\pi$
$282$	−3.51026			−0.209033
$283$	−0.699317	−	0.508083i	−0.0415701	−	0.0302024i	0.566806	−	0.823851i	$-0.308179\pi$
$283$	−0.699317	−	0.508083i	−0.0415701	−	0.0302024i	−0.608376	+	0.793649i	$0.708179\pi$
$284$	−0.151188	+	0.465309i	−0.00897135	+	0.0276110i
$285$		0			0
$286$	5.15767	+	15.8737i	0.304979	+	0.938629i
$287$	2.57163	−	7.91467i	0.151799	−	0.467188i
$288$	1.21720	−	3.74617i	0.0717245	−	0.220745i
$289$	−3.86138	−	11.8841i	−0.227140	−	0.699066i
$290$		0			0
$291$	4.17172	−	12.8392i	0.244550	−	0.752649i
$292$	−4.47755	−	3.25313i	−0.262029	−	0.190375i
$293$	−3.17701			−0.185603			−0.0928014	−	0.995685i	$-0.529582\pi$
$293$	−3.17701			−0.185603			−0.0928014	+	0.995685i	$0.529582\pi$
$294$	−5.22964	−	3.79955i	−0.304999	−	0.221594i
$295$		0			0
$296$	−18.3439	+	13.3276i	−1.06622	+	0.774653i
$297$	2.96915	−	2.15722i	0.172288	−	0.125174i
$298$	5.42766	+	16.7046i	0.314416	+	0.967673i
$299$	−25.0188			−1.44688
$300$		0			0
$301$	10.3020			0.593799
$302$	1.37278	+	4.22498i	0.0789945	+	0.243120i
$303$	5.84629	−	4.24758i	0.335861	−	0.244017i
$304$	−6.47538	+	4.70464i	−0.371389	+	0.269830i
$305$		0			0
$306$	1.92705	+	1.40008i	0.110162	+	0.0800375i
$307$	0.507986			0.0289923			0.0144961	−	0.999895i	$-0.495386\pi$
$307$	0.507986			0.0289923			0.0144961	+	0.999895i	$0.495386\pi$
$308$	−2.44828	−	1.77878i	−0.139504	−	0.101356i
$309$	1.63083	−	5.01918i	0.0927747	−	0.285531i
$310$		0			0
$311$	−4.52519	−	13.9271i	−0.256600	−	0.789734i	−0.993510	−	0.113743i	$-0.963716\pi$
$311$	−4.52519	−	13.9271i	−0.256600	−	0.789734i	0.736910	−	0.675991i	$-0.236284\pi$
$312$	3.85112	−	11.8525i	0.218027	−	0.671017i
$313$	4.62171	−	14.2241i	0.261234	−	0.803996i	−0.731303	−	0.682053i	$-0.761087\pi$
$313$	4.62171	−	14.2241i	0.261234	−	0.803996i	0.992537	−	0.121943i	$-0.0389127\pi$
$314$	1.56090	+	4.80397i	0.0880869	+	0.271103i
$315$		0			0
$316$	−1.95317	+	6.01125i	−0.109875	+	0.338159i
$317$	14.6586	+	10.6501i	0.823310	+	0.598170i	0.917659	−	0.397369i	$-0.130077\pi$
$317$	14.6586	+	10.6501i	0.823310	+	0.598170i	−0.0943487	+	0.995539i	$0.530077\pi$
$318$	−3.93896			−0.220886
$319$	6.70920	+	4.87452i	0.375643	+	0.272921i
$320$		0			0
$321$	−4.42275	+	3.21332i	−0.246854	+	0.179350i
$322$	−6.24388	+	4.53644i	−0.347958	+	0.252806i
$323$	2.66312	+	8.19624i	0.148180	+	0.456051i
$324$	−0.740367			−0.0411315
$325$		0			0
$326$	2.75408			0.152534
$327$	−3.50410	−	10.7845i	−0.193777	−	0.596385i
$328$	−18.5923	+	13.5081i	−1.02659	+	0.745860i
$329$	2.81811	−	2.04747i	0.155367	−	0.112881i
$330$		0			0
$331$	−21.3188	−	15.4890i	−1.17178	−	0.851351i	−0.180563	−	0.983563i	$-0.557792\pi$
$331$	−21.3188	−	15.4890i	−1.17178	−	0.851351i	−0.991221	+	0.132212i	$0.957792\pi$
$332$	9.07979			0.498318
$333$	5.96433	+	4.33334i	0.326843	+	0.237465i
$334$	1.06241	−	3.26975i	0.0581322	−	0.178913i
$335$		0			0
$336$	−0.678387	−	2.08786i	−0.0370090	−	0.113902i
$337$	3.30488	−	10.1714i	0.180028	−	0.554070i	−0.819799	−	0.572651i	$-0.805915\pi$
$337$	3.30488	−	10.1714i	0.180028	−	0.554070i	0.999827	+	0.0185811i	$0.00591487\pi$
$338$	1.18579	−	3.64949i	0.0644986	−	0.198506i
$339$	1.49416	+	4.59855i	0.0811516	+	0.249759i
$340$		0			0
$341$	11.4002	−	35.0861i	0.617354	−	1.90002i
$342$	3.68701	+	2.67877i	0.199371	+	0.144851i
$343$	14.2108			0.767311
$344$	−23.0160	−	16.7221i	−1.24094	−	0.901594i
$345$		0			0
$346$	10.2236	−	7.42788i	0.549624	−	0.399325i
$347$	13.0850	−	9.50682i	0.702441	−	0.510353i	−0.178286	−	0.983979i	$-0.557055\pi$
$347$	13.0850	−	9.50682i	0.702441	−	0.510353i	0.880726	+	0.473626i	$0.157055\pi$
$348$	−0.516973	−	1.59108i	−0.0277126	−	0.0852907i
$349$	15.2383			0.815688			0.407844	−	0.913052i	$-0.366281\pi$
$349$	15.2383			0.815688			0.407844	+	0.913052i	$0.366281\pi$
$350$		0			0
$351$	−4.05204			−0.216282
$352$	4.46723	+	13.7487i	0.238104	+	0.732810i
$353$	−23.8970	+	17.3622i	−1.27191	+	0.924097i	−0.999277	−	0.0380214i	$-0.987894\pi$
$353$	−23.8970	+	17.3622i	−1.27191	+	0.924097i	−0.272633	+	0.962118i	$0.587894\pi$
$354$	−5.98710	+	4.34988i	−0.318211	+	0.231194i
$355$		0			0
$356$	−9.15712	−	6.65304i	−0.485326	−	0.352610i
$357$	−2.36372			−0.125101
$358$	−9.13195	−	6.63475i	−0.482638	−	0.350657i
$359$	−4.06875	+	12.5223i	−0.214740	+	0.660903i	0.784431	+	0.620216i	$0.212955\pi$
$359$	−4.06875	+	12.5223i	−0.214740	+	0.660903i	−0.999172	+	0.0406876i	$0.987045\pi$
$360$		0			0
$361$	−0.776002	−	2.38829i	−0.0408422	−	0.125699i
$362$	−6.75205	+	20.7807i	−0.354880	+	1.09221i
$363$	−0.763104	+	2.34859i	−0.0400526	+	0.123269i
$364$	1.03249	+	3.17767i	0.0541171	+	0.166555i
$365$		0			0
$366$	3.15748	−	9.71772i	0.165044	−	0.507953i
$367$	−3.14622	−	2.28586i	−0.164232	−	0.119321i	0.502634	−	0.864499i	$-0.332364\pi$
$367$	−3.14622	−	2.28586i	−0.164232	−	0.119321i	−0.666865	+	0.745178i	$0.732364\pi$
$368$	12.1704			0.634428
$369$	6.04508	+	4.39201i	0.314695	+	0.228639i
$370$		0			0
$371$	3.16227	−	2.29752i	0.164177	−	0.119281i
$372$	−6.02087	+	4.37442i	−0.312168	+	0.226803i
$373$	2.51641	+	7.74470i	0.130295	+	0.401006i	0.994829	−	0.101569i	$-0.0323862\pi$
$373$	2.51641	+	7.74470i	0.130295	+	0.401006i	−0.864534	+	0.502575i	$0.832386\pi$
$374$	−8.74200			−0.452038
$375$		0			0
$376$	−9.61941			−0.496083
$377$	−2.82940	−	8.70799i	−0.145721	−	0.448484i
$378$	−1.01126	+	0.734721i	−0.0520134	+	0.0377900i
$379$	−8.01509	+	5.82330i	−0.411708	+	0.299123i	−0.774293	−	0.632828i	$-0.781894\pi$
$379$	−8.01509	+	5.82330i	−0.411708	+	0.299123i	0.362585	+	0.931951i	$0.381894\pi$
$380$		0			0
$381$	−0.614526	−	0.446479i	−0.0314831	−	0.0228738i
$382$	−13.0292			−0.666632
$383$	−4.22481	−	3.06951i	−0.215878	−	0.156844i	0.474591	−	0.880206i	$-0.342596\pi$
$383$	−4.22481	−	3.06951i	−0.215878	−	0.156844i	−0.690469	+	0.723362i	$0.742596\pi$
$384$	−0.466070	+	1.43442i	−0.0237840	+	0.0731997i
$385$		0			0
$386$	1.17279	+	3.60949i	0.0596937	+	0.183718i
$387$	−2.85840	+	8.79726i	−0.145301	+	0.447190i
$388$	3.08860	−	9.50575i	0.156800	−	0.482581i
$389$	−1.15255	−	3.54719i	−0.0584367	−	0.179850i	0.917577	−	0.397557i	$-0.130142\pi$
$389$	−1.15255	−	3.54719i	−0.0584367	−	0.179850i	−0.976014	+	0.217708i	$0.930142\pi$
$390$		0			0
$391$	4.04938	−	12.4627i	0.204786	−	0.630267i
$392$	−14.3311	−	10.4122i	−0.723831	−	0.525894i
$393$	−14.6551			−0.739253
$394$	−15.9698	−	11.6027i	−0.804545	−	0.584536i
$395$		0			0
$396$	2.19826	−	1.59713i	0.110467	−	0.0802589i
$397$	3.24870	−	2.36032i	0.163048	−	0.118461i	−0.503270	−	0.864130i	$-0.667870\pi$
$397$	3.24870	−	2.36032i	0.163048	−	0.118461i	0.666317	+	0.745668i	$0.267870\pi$
$398$	6.93995	+	21.3590i	0.347868	+	1.07063i
$399$	−4.52248			−0.226407
$400$		0			0
$401$	−24.9890			−1.24789			−0.623945	−	0.781468i	$-0.714471\pi$
$401$	−24.9890			−1.24789			−0.623945	+	0.781468i	$0.714471\pi$
$402$	0.910969	+	2.80367i	0.0454350	+	0.139835i
$403$	−32.9523	+	23.9413i	−1.64147	+	1.19260i
$404$	4.32841	−	3.14477i	0.215346	−	0.156458i
$405$		0			0
$406$	−2.28507	−	1.66020i	−0.113406	−	0.0823943i
$407$	−27.0570			−1.34116
$408$	5.28083	+	3.83675i	0.261440	+	0.189947i
$409$	−7.84186	+	24.1348i	−0.387755	+	1.19339i	0.546707	+	0.837324i	$0.315881\pi$
$409$	−7.84186	+	24.1348i	−0.387755	+	1.19339i	−0.934462	+	0.356063i	$0.884119\pi$
$410$		0			0
$411$	3.79825	+	11.6898i	0.187354	+	0.576616i
$412$	1.20741	−	3.71604i	0.0594850	−	0.183076i
$413$	2.26935	−	6.98433i	0.111667	−	0.343677i
$414$	−2.14140	−	6.59054i	−0.105244	−	0.323908i
$415$		0			0
$416$	4.93216	−	15.1796i	0.241819	−	0.744243i
$417$	11.9201	+	8.66043i	0.583728	+	0.424103i
$418$	−16.7260			−0.818094
$419$	24.9354	+	18.1166i	1.21817	+	0.885056i	0.995947	−	0.0899392i	$-0.0286673\pi$
$419$	24.9354	+	18.1166i	1.21817	+	0.885056i	0.222227	+	0.974995i	$0.428667\pi$
$420$		0			0
$421$	−6.91425	+	5.02350i	−0.336980	+	0.244830i	−0.743387	−	0.668862i	$-0.766782\pi$
$421$	−6.91425	+	5.02350i	−0.336980	+	0.244830i	0.406406	+	0.913692i	$0.366782\pi$
$422$	−2.21785	+	1.61137i	−0.107963	+	0.0784401i
$423$	0.966496	+	2.97457i	0.0469927	+	0.144629i
$424$	−10.7942			−0.524212
$425$		0			0
$426$	−0.741668			−0.0359339
$427$	3.13329	+	9.64327i	0.151630	+	0.466670i
$428$	−3.27446	+	2.37904i	−0.158277	+	0.114995i
$429$	12.0311	−	8.74113i	0.580869	−	0.422026i
$430$		0			0
$431$	21.3431	+	15.5067i	1.02806	+	0.746929i	0.967919	−	0.251261i	$-0.0808452\pi$
$431$	21.3431	+	15.5067i	1.02806	+	0.746929i	0.0601403	+	0.998190i	$0.480845\pi$
$432$	1.97112			0.0948356
$433$	−7.58269	−	5.50914i	−0.364401	−	0.264753i	0.390485	−	0.920609i	$-0.372307\pi$
$433$	−7.58269	−	5.50914i	−0.364401	−	0.264753i	−0.754885	+	0.655857i	$0.772307\pi$
$434$	−3.88276	+	11.9499i	−0.186378	+	0.573613i
$435$		0			0
$436$	−2.59432	−	7.98450i	−0.124245	−	0.382388i
$437$	7.74765	−	23.8448i	0.370620	−	1.14065i
$438$	2.59263	−	7.97928i	0.123880	−	0.381265i
$439$	−0.159447	−	0.490727i	−0.00760998	−	0.0234211i	0.947179	−	0.320704i	$-0.103920\pi$
$439$	−0.159447	−	0.490727i	−0.00760998	−	0.0234211i	−0.954789	+	0.297283i	$0.903920\pi$
$440$		0			0
$441$	−1.77981	+	5.47770i	−0.0847530	+	0.260843i
$442$	7.80849	+	5.67320i	0.371412	+	0.269847i
$443$	17.8348			0.847357			0.423678	−	0.905813i	$-0.360739\pi$
$443$	17.8348			0.847357			0.423678	+	0.905813i	$0.360739\pi$
$444$	4.41579	+	3.20826i	0.209564	+	0.152257i
$445$		0			0
$446$	−23.2779	+	16.9124i	−1.10224	+	0.800826i
$447$	12.6610	−	9.19872i	0.598842	−	0.435084i
$448$	−2.87826	−	8.85836i	−0.135985	−	0.418518i
$449$	−4.16533			−0.196574			−0.0982870	−	0.995158i	$-0.531336\pi$
$449$	−4.16533			−0.196574			−0.0982870	+	0.995158i	$0.531336\pi$
$450$		0			0
$451$	−27.4233			−1.29131
$452$	1.10623	+	3.40462i	0.0520325	+	0.160140i
$453$	3.20224	−	2.32656i	0.150454	−	0.109311i
$454$	5.95944	−	4.32979i	0.279691	−	0.203207i
$455$		0			0
$456$	10.1038	+	7.34081i	0.473152	+	0.343765i
$457$	17.6734			0.826725			0.413362	−	0.910567i	$-0.364354\pi$
$457$	17.6734			0.826725			0.413362	+	0.910567i	$0.364354\pi$
$458$	7.23112	+	5.25371i	0.337888	+	0.245490i
$459$	0.655837	−	2.01846i	0.0306119	−	0.0942136i
$460$		0			0
$461$	−0.0633350	−	0.194925i	−0.00294981	−	0.00907857i	0.949571	−	0.313553i	$-0.101519\pi$
$461$	−0.0633350	−	0.194925i	−0.00294981	−	0.00907857i	−0.952521	+	0.304474i	$0.901519\pi$
$462$	1.41762	−	4.36300i	0.0659538	−	0.202985i
$463$	3.96084	−	12.1902i	0.184076	−	0.566528i	−0.815855	−	0.578256i	$-0.803733\pi$
$463$	3.96084	−	12.1902i	0.184076	−	0.566528i	0.999931	+	0.0117286i	$0.00373342\pi$
$464$	1.37636	+	4.23601i	0.0638961	+	0.196652i
$465$		0			0
$466$	3.26742	−	10.0561i	0.151360	−	0.465839i
$467$	0.901030	+	0.654637i	0.0416947	+	0.0302930i	0.608437	−	0.793602i	$-0.291797\pi$
$467$	0.901030	+	0.654637i	0.0416947	+	0.0302930i	−0.566743	+	0.823895i	$0.691797\pi$
$468$	−3.00000			−0.138675
$469$	−2.36668	−	1.71949i	−0.109283	−	0.0793987i
$470$		0			0
$471$	3.64107	−	2.64539i	0.167772	−	0.121893i
$472$	−16.4069	+	11.9203i	−0.755187	+	0.548675i
$473$	−10.4905	−	32.2866i	−0.482356	−	1.48454i
$474$	−9.58149			−0.440092
$475$		0			0
$476$	−1.75002			−0.0802120
$477$	1.08453	+	3.33784i	0.0496572	+	0.152829i
$478$	10.1905	−	7.40380i	0.466101	−	0.338642i
$479$	20.3670	−	14.7975i	0.930590	−	0.676113i	−0.0155470	−	0.999879i	$-0.504949\pi$
$479$	20.3670	−	14.7975i	0.930590	−	0.676113i	0.946137	+	0.323766i	$0.104949\pi$
$480$		0			0
$481$	24.1677	+	17.5589i	1.10195	+	0.800615i
$482$	25.4555			1.15947
$483$	5.56330	+	4.04197i	0.253139	+	0.183916i
$484$	−0.564977	+	1.73882i	−0.0256808	+	0.0790373i
$485$		0			0
$486$	−0.346820	−	1.06740i	−0.0157321	−	0.0484184i
$487$	−3.20135	+	9.85274i	−0.145067	+	0.446470i	−0.997020	−	0.0771487i	$-0.975418\pi$
$487$	−3.20135	+	9.85274i	−0.145067	+	0.446470i	0.851953	+	0.523619i	$0.175418\pi$
$488$	8.65265	−	26.6301i	0.391687	−	1.20549i
$489$	−0.758292	−	2.33378i	−0.0342912	−	0.105537i
$490$		0			0
$491$	−4.83831	+	14.8908i	−0.218350	+	0.672012i	0.780549	+	0.625095i	$0.214940\pi$
$491$	−4.83831	+	14.8908i	−0.218350	+	0.672012i	−0.998899	+	0.0469170i	$0.985060\pi$
$492$	4.47558	+	3.25170i	0.201775	+	0.146598i
$493$	4.79569			0.215987
$494$	14.9399	+	10.8545i	0.672178	+	0.488366i
$495$		0			0
$496$	16.0297	−	11.6463i	0.719754	−	0.522932i
$497$	0.595425	−	0.432601i	0.0267084	−	0.0194048i
$498$	4.25337	+	13.0905i	0.190598	+	0.586600i
$499$	35.7864			1.60202			0.801010	−	0.598651i	$-0.204296\pi$
$499$	35.7864			1.60202			0.801010	+	0.598651i	$0.204296\pi$
$500$		0			0
$501$	−3.06328			−0.136857
$502$	−2.34735	−	7.22439i	−0.104767	−	0.322440i
$503$	−9.52947	+	6.92356i	−0.424898	+	0.308706i	−0.779606	−	0.626271i	$-0.784580\pi$
$503$	−9.52947	+	6.92356i	−0.424898	+	0.308706i	0.354708	+	0.934977i	$0.384580\pi$
$504$	−2.77121	+	2.01340i	−0.123440	+	0.0896842i
$505$		0			0
$506$	20.5754	+	14.9489i	0.914687	+	0.664559i
$507$	−3.41904			−0.151845
$508$	−0.454975	−	0.330559i	−0.0201862	−	0.0146662i
$509$	10.3986	−	32.0037i	0.460912	−	1.41854i	−0.403141	−	0.915138i	$-0.632082\pi$
$509$	10.3986	−	32.0037i	0.460912	−	1.41854i	0.864052	−	0.503402i	$-0.167918\pi$
$510$		0			0
$511$	2.57276	+	7.91815i	0.113812	+	0.350278i
$512$	−6.14602	+	18.9155i	−0.271618	+	0.835955i
$513$	1.25481	−	3.86190i	0.0554011	−	0.170507i
$514$	5.13064	+	15.7905i	0.226303	+	0.696489i
$515$		0			0
$516$	−2.11627	+	6.51320i	−0.0931635	+	0.286728i
$517$	−9.28647	−	6.74701i	−0.408418	−	0.296733i
$518$	9.21526			0.404895
$519$	−9.10923	−	6.61825i	−0.399851	−	0.290509i
$520$		0			0
$521$	9.58263	−	6.96219i	0.419823	−	0.305019i	−0.357744	−	0.933820i	$-0.616454\pi$
$521$	9.58263	−	6.96219i	0.419823	−	0.305019i	0.777566	+	0.628801i	$0.216454\pi$
$522$	2.05172	−	1.49066i	0.0898012	−	0.0652444i
$523$	−1.26602	−	3.89642i	−0.0553593	−	0.170379i	0.919554	−	0.392964i	$-0.128550\pi$
$523$	−1.26602	−	3.89642i	−0.0553593	−	0.170379i	−0.974913	+	0.222586i	$0.928550\pi$
$524$	−10.8502			−0.473992
$525$		0			0
$526$	−22.4117			−0.977195
$527$	−6.59250	−	20.2896i	−0.287174	−	0.883830i
$528$	−5.85256	+	4.25213i	−0.254700	+	0.185050i
$529$	−12.2347	+	8.88902i	−0.531943	+	0.386479i
$530$		0			0
$531$	5.33451	+	3.87575i	0.231498	+	0.168193i
$532$	−3.34829			−0.145167
$533$	24.4949	+	17.7966i	1.06099	+	0.770857i
$534$	5.30222	−	16.3186i	0.229450	−	0.706174i
$535$		0			0
$536$	2.49639	+	7.68310i	0.107828	+	0.331859i
$537$	−3.10789	+	9.56511i	−0.134116	+	0.412765i
$538$	−3.55078	+	10.9282i	−0.153085	+	0.471147i
$539$	−6.53205	−	20.1036i	−0.281355	−	0.865922i
$540$		0			0
$541$	4.31332	−	13.2750i	0.185444	−	0.570738i	−0.814512	−	0.580147i	$-0.802995\pi$
$541$	4.31332	−	13.2750i	0.185444	−	0.570738i	0.999956	+	0.00940920i	$0.00299509\pi$
$542$	−11.1751	−	8.11917i	−0.480011	−	0.348748i
$543$	19.4684			0.835471
$544$	6.76321	+	4.91376i	0.289970	+	0.210676i
$545$		0			0
$546$	−4.09765	+	2.97712i	−0.175363	+	0.127409i
$547$	−21.4426	+	15.5789i	−0.916818	+	0.666107i	−0.942730	−	0.333557i	$-0.891751\pi$
$547$	−21.4426	+	15.5789i	−0.916818	+	0.666107i	0.0259119	+	0.999664i	$0.491751\pi$
$548$	2.81210	+	8.65476i	0.120127	+	0.369713i
$549$	−9.10408			−0.388553
$550$		0			0
$551$	9.17556			0.390892
$552$	−5.86822	−	18.0605i	−0.249768	−	0.768706i
$553$	7.69220	−	5.58871i	0.327105	−	0.237656i
$554$	28.6488	−	20.8146i	1.21717	−	0.884327i
$555$		0			0
$556$	8.82522	+	6.41190i	0.374273	+	0.271925i
$557$	−10.6860			−0.452781			−0.226391	−	0.974037i	$-0.572693\pi$
$557$	−10.6860			−0.452781			−0.226391	+	0.974037i	$0.572693\pi$
$558$	−9.12712	−	6.63124i	−0.386382	−	0.280723i
$559$	−11.5824	+	35.6468i	−0.489882	+	1.50770i
$560$		0			0
$561$	2.40697	+	7.40790i	0.101622	+	0.312762i
$562$	−7.39140	+	22.7484i	−0.311788	+	0.959583i
$563$	7.90310	−	24.3232i	0.333076	−	1.02510i	−0.634586	−	0.772852i	$-0.718829\pi$
$563$	7.90310	−	24.3232i	0.333076	−	1.02510i	0.967662	−	0.252250i	$-0.0811706\pi$
$564$	0.715563	+	2.20227i	0.0301306	+	0.0927325i
$565$		0			0
$566$	0.299792	−	0.922666i	0.0126012	−	0.0387825i
$567$	0.901030	+	0.654637i	0.0378397	+	0.0274922i
$568$	−2.03244			−0.0852794
$569$	−4.93670	−	3.58672i	−0.206957	−	0.150363i	0.479479	−	0.877554i	$-0.340826\pi$
$569$	−4.93670	−	3.58672i	−0.206957	−	0.150363i	−0.686436	+	0.727190i	$0.740826\pi$
$570$		0			0
$571$	−19.2058	+	13.9538i	−0.803737	+	0.583949i	−0.912008	−	0.410173i	$-0.865468\pi$
$571$	−19.2058	+	13.9538i	−0.803737	+	0.583949i	0.108271	+	0.994121i	$0.465468\pi$
$572$	8.90746	−	6.47165i	0.372440	−	0.270593i
$573$	3.58739	+	11.0408i	0.149865	+	0.461238i
$574$	9.34003			0.389845
$575$		0			0
$576$	8.36307			0.348461
$577$	13.6474	+	42.0024i	0.568149	+	1.74858i	0.658405	+	0.752664i	$0.271231\pi$
$577$	13.6474	+	42.0024i	0.568149	+	1.74858i	−0.0902565	+	0.995919i	$0.528769\pi$
$578$	11.3459	−	8.24330i	0.471929	−	0.342876i
$579$	2.73574	−	1.98763i	0.113694	−	0.0826032i
$580$		0			0
$581$	−11.0501	−	8.02840i	−0.458437	−	0.333074i
$582$	15.1515			0.628048
$583$	−10.4206	−	7.57100i	−0.431576	−	0.313559i
$584$	7.10475	−	21.8662i	0.293997	−	0.904828i
$585$		0			0
$586$	−1.10185	−	3.39115i	−0.0455170	−	0.140087i
$587$	−0.158206	+	0.486909i	−0.00652987	+	0.0200969i	−0.954268	−	0.298951i	$-0.903363\pi$
$587$	−0.158206	+	0.486909i	−0.00652987	+	0.0200969i	0.947738	+	0.319048i	$0.103363\pi$
$588$	−1.31772	+	4.05551i	−0.0543417	+	0.167246i
$589$	−12.6134	−	38.8200i	−0.519725	−	1.59955i
$590$		0			0
$591$	−5.43502	+	16.7273i	−0.223567	+	0.688068i
$592$	−11.7564	−	8.54153i	−0.483186	−	0.351055i
$593$	18.8405			0.773687			0.386844	−	0.922145i	$-0.373565\pi$
$593$	18.8405			0.773687			0.386844	+	0.922145i	$0.373565\pi$
$594$	3.33238	+	2.42112i	0.136729	+	0.0993396i
$595$		0			0
$596$	9.37376	−	6.81043i	0.383964	−	0.278966i
$597$	16.1886	−	11.7617i	0.662556	−	0.481375i
$598$	−8.67703	−	26.7052i	−0.354830	−	1.09206i
$599$	6.20712			0.253616			0.126808	−	0.991927i	$-0.459527\pi$
$599$	6.20712			0.253616			0.126808	+	0.991927i	$0.459527\pi$
$600$		0			0
$601$	34.0303			1.38813			0.694063	−	0.719915i	$-0.255819\pi$
$601$	34.0303			1.38813			0.694063	+	0.719915i	$0.255819\pi$
$602$	3.57295	+	10.9964i	0.145623	+	0.448180i
$603$	2.12499	−	1.54390i	0.0865363	−	0.0628723i
$604$	2.37083	−	1.72251i	0.0964679	−	0.0700880i
$605$		0			0
$606$	6.56149	+	4.76720i	0.266542	+	0.193654i
$607$	−16.2488			−0.659518			−0.329759	−	0.944065i	$-0.606968\pi$
$607$	−16.2488			−0.659518			−0.329759	+	0.944065i	$0.606968\pi$
$608$	12.9400	+	9.40144i	0.524785	+	0.381279i
$609$	−0.777682	+	2.39346i	−0.0315132	+	0.0969878i
$610$		0			0
$611$	3.91628	+	12.0531i	0.158436	+	0.487615i
$612$	0.485560	−	1.49440i	0.0196276	−	0.0604076i
$613$	0.0210086	−	0.0646578i	0.000848529	−	0.00261150i	−0.950631	−	0.310322i	$-0.899563\pi$
$613$	0.0210086	−	0.0646578i	0.000848529	−	0.00261150i	0.951480	+	0.307711i	$0.0995630\pi$
$614$	0.176180	+	0.542225i	0.00711004	+	0.0218824i
$615$		0			0
$616$	3.88481	−	11.9562i	0.156523	−	0.481730i
$617$	26.5445	+	19.2857i	1.06864	+	0.776413i	0.975667	−	0.219256i	$-0.0703629\pi$
$617$	26.5445	+	19.2857i	1.06864	+	0.776413i	0.0929733	+	0.995669i	$0.470363\pi$
$618$	5.92309			0.238262
$619$	5.48280	+	3.98349i	0.220372	+	0.160110i	0.692494	−	0.721423i	$-0.256512\pi$
$619$	5.48280	+	3.98349i	0.220372	+	0.160110i	−0.472122	+	0.881533i	$0.656512\pi$
$620$		0			0
$621$	−4.99517	+	3.62921i	−0.200449	+	0.145635i
$622$	13.2964	−	9.66040i	0.533137	−	0.387347i
$623$	5.26160	+	16.1935i	0.210802	+	0.648780i
$624$	7.98706			0.319738
$625$		0			0
$626$	16.7858			0.670895
$627$	4.60524	+	14.1735i	0.183915	+	0.566034i
$628$	2.69573	−	1.95856i	0.107571	−	0.0781552i
$629$	−12.6583	+	9.19679i	−0.504719	+	0.366700i
$630$		0			0
$631$	6.20352	+	4.50712i	0.246958	+	0.179426i	0.704378	−	0.709825i	$-0.251226\pi$
$631$	6.20352	+	4.50712i	0.246958	+	0.179426i	−0.457419	+	0.889251i	$0.651226\pi$
$632$	−26.2568			−1.04444
$633$	1.97611	+	1.43573i	0.0785433	+	0.0570651i
$634$	−6.28405	+	19.3403i	−0.249572	+	0.768102i
$635$		0			0
$636$	0.802951	+	2.47123i	0.0318391	+	0.0979906i
$637$	−7.21188	+	22.1959i	−0.285745	+	0.879432i
$638$	−2.87619	+	8.85199i	−0.113869	+	0.350454i
$639$	0.204207	+	0.628483i	0.00807829	+	0.0248624i
$640$		0			0
$641$	−7.32096	+	22.5316i	−0.289161	+	0.889945i	0.695960	+	0.718081i	$0.254979\pi$
$641$	−7.32096	+	22.5316i	−0.289161	+	0.889945i	−0.985121	+	0.171864i	$0.945021\pi$
$642$	−4.96380	−	3.60641i	−0.195906	−	0.142334i
$643$	−2.16861			−0.0855218			−0.0427609	−	0.999085i	$-0.513615\pi$
$643$	−2.16861			−0.0855218			−0.0427609	+	0.999085i	$0.513615\pi$
$644$	4.11889	+	2.99255i	0.162307	+	0.117923i
$645$		0			0
$646$	−7.82506	+	5.68524i	−0.307873	+	0.223683i
$647$	2.06737	−	1.50203i	0.0812767	−	0.0590510i	−0.546405	−	0.837521i	$-0.684004\pi$
$647$	2.06737	−	1.50203i	0.0812767	−	0.0590510i	0.627682	+	0.778470i	$0.284004\pi$
$648$	−0.950415	−	2.92508i	−0.0373358	−	0.114908i
$649$	−24.1998			−0.949926
$650$		0			0
$651$	11.1953			0.438779
$652$	−0.561415	−	1.72786i	−0.0219867	−	0.0676681i
$653$	26.2233	−	19.0523i	1.02620	−	0.745575i	0.0586517	−	0.998279i	$-0.481320\pi$
$653$	26.2233	−	19.0523i	1.02620	−	0.745575i	0.967544	+	0.252704i	$0.0813199\pi$
$654$	10.2961	−	7.48057i	0.402610	−	0.292513i
$655$		0			0
$656$	−11.9156	−	8.65719i	−0.465226	−	0.338006i
$657$	−7.47542			−0.291644
$658$	3.16285	+	2.29795i	0.123301	+	0.0895833i
$659$	0.139043	−	0.427929i	0.00541633	−	0.0166697i	−0.948312	−	0.317340i	$-0.897210\pi$
$659$	0.139043	−	0.427929i	0.00541633	−	0.0166697i	0.953728	+	0.300670i	$0.0972104\pi$
$660$		0			0
$661$	−8.33812	−	25.6621i	−0.324315	−	0.998140i	−0.971749	−	0.236018i	$-0.924158\pi$
$661$	−8.33812	−	25.6621i	−0.324315	−	0.998140i	0.647433	−	0.762122i	$-0.275842\pi$
$662$	9.13921	−	28.1276i	0.355205	−	1.09321i
$663$	2.65748	−	8.17888i	0.103208	−	0.317641i
$664$	11.6558	+	35.8728i	0.452332	+	1.39214i
$665$		0			0
$666$	−2.55687	+	7.86923i	−0.0990766	+	0.304926i
$667$	−11.2873	−	8.20067i	−0.437044	−	0.317531i
$668$	−2.26795			−0.0877496
$669$	20.7407	+	15.0690i	0.801880	+	0.582600i
$670$		0			0
$671$	27.0314	−	19.6395i	1.04354	−	0.758174i
$672$	−3.54912	+	2.57859i	−0.136910	+	0.0994711i
$673$	−5.44561	−	16.7599i	−0.209913	−	0.646046i	−0.999476	−	0.0323758i	$-0.989693\pi$
$673$	−5.44561	−	16.7599i	−0.209913	−	0.646046i	0.789563	−	0.613670i	$-0.210307\pi$
$674$	12.0032			0.462344
$675$		0			0
$676$	−2.53135			−0.0973595
$677$	5.97899	+	18.4014i	0.229791	+	0.707225i	0.997770	+	0.0667494i	$0.0212628\pi$
$677$	5.97899	+	18.4014i	0.229791	+	0.707225i	−0.767978	+	0.640476i	$0.778737\pi$
$678$	−4.39030	+	3.18974i	−0.168608	+	0.122501i
$679$	−12.1639	+	8.83757i	−0.466807	+	0.339155i
$680$		0			0
$681$	−5.30987	−	3.85784i	−0.203475	−	0.147833i
$682$	41.4049			1.58547
$683$	−24.2268	−	17.6018i	−0.927015	−	0.673515i	0.0182455	−	0.999834i	$-0.494192\pi$
$683$	−24.2268	−	17.6018i	−0.927015	−	0.673515i	−0.945260	+	0.326318i	$0.894192\pi$
$684$	0.929018	−	2.85922i	0.0355219	−	0.109325i
$685$		0			0
$686$	4.92859	+	15.1686i	0.188175	+	0.579142i
$687$	2.46098	−	7.57412i	0.0938923	−	0.288971i
$688$	5.63426	−	17.3405i	0.214804	−	0.661099i
$689$	4.39456	+	13.5251i	0.167419	+	0.515264i
$690$		0			0
$691$	−6.16024	+	18.9593i	−0.234346	+	0.721244i	0.762861	+	0.646563i	$0.223794\pi$
$691$	−6.16024	+	18.9593i	−0.234346	+	0.721244i	−0.997207	+	0.0746817i	$0.976206\pi$
$692$	−6.74418	−	4.89993i	−0.256375	−	0.186268i
$693$	−4.08749			−0.155271
$694$	14.6858	+	10.6698i	0.557464	+	0.405021i
$695$		0			0
$696$	5.62246	−	4.08495i	0.213119	−	0.154840i
$697$	−12.8297	+	9.32131i	−0.485959	+	0.353070i
$698$	5.28495	+	16.2654i	0.200038	+	0.615655i
$699$	−9.42107			−0.356338
$700$		0			0
$701$	−49.0150			−1.85127			−0.925636	−	0.378415i	$-0.876469\pi$
$701$	−49.0150			−1.85127			−0.925636	+	0.378415i	$0.876469\pi$
$702$	−1.40533	−	4.32516i	−0.0530407	−	0.163243i
$703$	−24.2190	+	17.5961i	−0.913437	+	0.663651i
$704$	−24.8312	+	18.0409i	−0.935862	+	0.679944i
$705$		0			0
$706$	−26.8204	−	19.4862i	−1.00940	−	0.733372i
$707$	−8.04831			−0.302688
$708$	3.94950	+	2.86948i	0.148431	+	0.107842i
$709$	−1.48744	+	4.57788i	−0.0558621	+	0.171926i	−0.975095	−	0.221789i	$-0.928810\pi$
$709$	−1.48744	+	4.57788i	−0.0558621	+	0.171926i	0.919233	+	0.393715i	$0.128810\pi$
$710$		0			0
$711$	2.63811	+	8.11928i	0.0989370	+	0.304497i
$712$	14.5300	−	44.7189i	0.544536	−	1.67591i
$713$	−19.1792	+	59.0274i	−0.718265	+	2.21059i
$714$	−0.819784	−	2.52304i	−0.0306797	−	0.0944223i
$715$		0			0
$716$	−2.30098	+	7.08170i	−0.0859918	+	0.264656i
$717$	−9.07970	−	6.59679i	−0.339088	−	0.246362i
$718$	−14.7775			−0.551491
$719$	−26.0917	−	18.9568i	−0.973058	−	0.706968i	−0.0169113	−	0.999857i	$-0.505383\pi$
$719$	−26.0917	−	18.9568i	−0.973058	−	0.706968i	−0.956146	+	0.292889i	$0.905383\pi$
$720$		0			0
$721$	−4.75517	+	3.45483i	−0.177092	+	0.128665i
$722$	2.28013	−	1.65661i	0.0848578	−	0.0616528i
$723$	−7.00879	−	21.5708i	−0.260660	−	0.802228i
$724$	14.4138			0.535685
$725$		0			0
$726$	−2.77155			−0.102862
$727$	9.01548	+	27.7468i	0.334366	+	1.02907i	0.967034	+	0.254648i	$0.0819598\pi$
$727$	9.01548	+	27.7468i	0.334366	+	1.02907i	−0.632668	+	0.774423i	$0.718040\pi$
$728$	−11.2291	+	8.15840i	−0.416177	+	0.302370i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−15.8823	−	11.5391i	−0.587426	−	0.426790i
$732$	−6.74037			−0.249131
$733$	4.20771	+	3.05708i	0.155415	+	0.112916i	0.662775	−	0.748818i	$-0.269378\pi$
$733$	4.20771	+	3.05708i	0.155415	+	0.112916i	−0.507360	+	0.861734i	$0.669378\pi$
$734$	1.34876	−	4.15107i	0.0497838	−	0.153219i
$735$		0			0
$736$	−7.51548	−	23.1303i	−0.277024	−	0.852593i
$737$	−2.97891	+	9.16813i	−0.109729	+	0.337712i
$738$	−2.59149	+	7.97578i	−0.0953940	+	0.293592i
$739$	−5.04334	−	15.5218i	−0.185522	−	0.570979i	0.814435	−	0.580255i	$-0.197047\pi$
$739$	−5.04334	−	15.5218i	−0.185522	−	0.570979i	−0.999957	+	0.00927620i	$0.997047\pi$
$740$		0			0
$741$	5.08453	−	15.6486i	0.186785	−	0.574865i
$742$	3.54912	+	2.57859i	0.130292	+	0.0946629i
$743$	−53.4487			−1.96084			−0.980421	−	0.196914i	$-0.936908\pi$
$743$	−53.4487			−1.96084			−0.980421	+	0.196914i	$0.936908\pi$
$744$	−25.0117	−	18.1720i	−0.916972	−	0.666219i
$745$		0			0
$746$	−7.39398	+	5.37204i	−0.270713	+	0.196684i
$747$	9.92170	−	7.20854i	0.363016	−	0.263747i
$748$	1.78204	+	5.48457i	0.0651580	+	0.200536i
$749$	6.08859			0.222472
$750$		0			0
$751$	−0.566970			−0.0206890			−0.0103445	−	0.999946i	$-0.503293\pi$
$751$	−0.566970			−0.0206890			−0.0103445	+	0.999946i	$0.503293\pi$
$752$	−1.90508	−	5.86324i	−0.0694712	−	0.213810i
$753$	−5.47558	+	3.97824i	−0.199541	+	0.144975i
$754$	8.31364	−	6.04021i	0.302765	−	0.219972i
$755$		0			0
$756$	0.667093	+	0.484672i	0.0242620	+	0.0176273i
$757$	−53.0708			−1.92889			−0.964445	−	0.264282i	$-0.914865\pi$
$757$	−53.0708			−1.92889			−0.964445	+	0.264282i	$0.914865\pi$
$758$	−8.99560	−	6.53569i	−0.326735	−	0.237387i
$759$	7.00246	−	21.5513i	0.254173	−	0.782264i
$760$		0			0
$761$	−8.49970	−	26.1594i	−0.308114	−	0.948277i	−0.978497	−	0.206262i	$-0.933870\pi$
$761$	−8.49970	−	26.1594i	−0.308114	−	0.948277i	0.670383	−	0.742015i	$-0.266130\pi$
$762$	0.263443	−	0.810794i	0.00954353	−	0.0293720i
$763$	−3.90264	+	12.0111i	−0.141285	+	0.434830i
$764$	2.65599	+	8.17428i	0.0960902	+	0.295735i
$765$		0			0
$766$	1.81115	−	5.57414i	0.0654394	−	0.201402i
$767$	21.6157	+	15.7047i	0.780496	+	0.567064i
$768$	15.0334			0.542471
$769$	−12.1123	−	8.80007i	−0.436779	−	0.317339i	0.347575	−	0.937652i	$-0.387005\pi$
$769$	−12.1123	−	8.80007i	−0.436779	−	0.317339i	−0.784354	+	0.620314i	$0.787005\pi$
$770$		0			0
$771$	11.9681	−	8.69533i	0.431021	−	0.313155i
$772$	2.02546	−	1.47158i	0.0728977	−	0.0529633i
$773$	0.634806	+	1.95373i	0.0228324	+	0.0702708i	0.961823	−	0.273671i	$-0.0882378\pi$
$773$	0.634806	+	1.95373i	0.0228324	+	0.0702708i	−0.938991	+	0.343941i	$0.888238\pi$
$774$	−10.3816			−0.373158
$775$		0			0
$776$	41.5206			1.49050
$777$	−2.53728	−	7.80894i	−0.0910243	−	0.280144i
$778$	3.38655	−	2.46048i	0.121414	−	0.0882123i
$779$	−24.5469	+	17.8344i	−0.879485	+	0.638983i
$780$		0			0
$781$	−1.96210	−	1.42555i	−0.0702093	−	0.0510100i
$782$	14.7072			0.525927
$783$	−1.82808	−	1.32818i	−0.0653303	−	0.0474652i
$784$	3.50823	−	10.7972i	0.125294	−	0.385615i
$785$		0			0
$786$	−5.08269	−	15.6429i	−0.181293	−	0.557964i
$787$	5.19981	−	16.0034i	0.185353	−	0.570458i	−0.814601	−	0.580022i	$-0.803044\pi$
$787$	5.19981	−	16.0034i	0.185353	−	0.570458i	0.999954	+	0.00956327i	$0.00304413\pi$
$788$	−4.02391	+	12.3843i	−0.143346	+	0.441174i
$789$	6.17070	+	18.9915i	0.219683	+	0.676114i
$790$		0			0
$791$	1.66410	−	5.12156i	0.0591685	−	0.182102i
$792$	9.13195	+	6.63475i	0.324490	+	0.235756i
$793$	−36.8901			−1.31001
$794$	3.64613	+	2.64907i	0.129396	+	0.0940118i
$795$		0			0
$796$	11.9855	−	8.70799i	0.424816	−	0.308647i
$797$	−0.168996	+	0.122783i	−0.00598616	+	0.00434920i	−0.590774	−	0.806837i	$-0.701178\pi$
$797$	−0.168996	+	0.122783i	−0.00598616	+	0.00434920i	0.584788	+	0.811186i	$0.301178\pi$
$798$	−1.56849	−	4.82730i	−0.0555238	−	0.170885i
$799$	−6.63791			−0.234832
$800$		0			0
$801$	−15.2881			−0.540179
$802$	−8.66668	−	26.6733i	−0.306031	−	0.941867i
$803$	22.1957	−	16.1261i	0.783268	−	0.569078i
$804$	1.57327	−	1.14305i	0.0554851	−	0.0403123i
$805$		0			0
$806$	−36.9835	−	26.8701i	−1.30269	−	0.946458i
$807$	10.2381			0.360398
$808$	17.9809	+	13.0639i	0.632566	+	0.459586i
$809$	−5.24264	+	16.1352i	−0.184321	+	0.567283i	−0.999936	−	0.0113128i	$-0.996399\pi$
$809$	−5.24264	+	16.1352i	−0.184321	+	0.567283i	0.815615	+	0.578595i	$0.196399\pi$
$810$		0			0
$811$	−6.32508	−	19.4666i	−0.222103	−	0.683564i	−0.998573	−	0.0534090i	$-0.982991\pi$
$811$	−6.32508	−	19.4666i	−0.222103	−	0.683564i	0.776469	−	0.630155i	$-0.217009\pi$
$812$	−0.575770	+	1.77204i	−0.0202056	+	0.0621864i
$813$	−3.80324	+	11.7052i	−0.133385	+	0.410518i
$814$	−9.38390	−	28.8807i	−0.328905	−	1.01227i
$815$		0			0
$816$	−1.29273	+	3.97863i	−0.0452548	+	0.139280i
$817$	−30.3874	−	22.0777i	−1.06312	−	0.772401i
$818$	−28.4812			−0.995822
$819$	3.65101	+	2.65262i	0.127577	+	0.0926899i
$820$		0			0
$821$	−31.0368	+	22.5496i	−1.08319	+	0.786985i	−0.978237	−	0.207492i	$-0.933470\pi$
$821$	−31.0368	+	22.5496i	−1.08319	+	0.786985i	−0.104955	+	0.994477i	$0.533470\pi$
$822$	−11.1604	+	8.10852i	−0.389265	+	0.282817i
$823$	8.96451	+	27.5899i	0.312483	+	0.961725i	0.976778	+	0.214254i	$0.0687320\pi$
$823$	8.96451	+	27.5899i	0.312483	+	0.961725i	−0.664295	+	0.747471i	$0.731268\pi$
$824$	16.2315			0.565449
$825$		0			0
$826$	8.24215			0.286781
$827$	−4.43648	−	13.6541i	−0.154271	−	0.474799i	0.843815	−	0.536634i	$-0.180305\pi$
$827$	−4.43648	−	13.6541i	−0.154271	−	0.474799i	−0.998086	+	0.0618356i	$0.980305\pi$
$828$	−3.69826	+	2.68695i	−0.128524	+	0.0933779i
$829$	−3.75031	+	2.72476i	−0.130254	+	0.0946347i	−0.651004	−	0.759074i	$-0.725652\pi$
$829$	−3.75031	+	2.72476i	−0.130254	+	0.0946347i	0.520751	+	0.853709i	$0.325652\pi$
$830$		0			0
$831$	−25.5261	−	18.5458i	−0.885491	−	0.643347i
$832$	33.8875			1.17484
$833$	−9.88925	−	7.18496i	−0.342642	−	0.248944i
$834$	−5.11005	+	15.7271i	−0.176946	+	0.544585i
$835$		0			0
$836$	3.40957	+	10.4936i	0.117922	+	0.362928i
$837$	−3.10625	+	9.56006i	−0.107368	+	0.330444i
$838$	−10.6896	+	32.8993i	−0.369268	+	1.13649i
$839$	1.52235	+	4.68531i	0.0525573	+	0.161755i	0.973890	−	0.227020i	$-0.0728983\pi$
$839$	1.52235	+	4.68531i	0.0525573	+	0.161755i	−0.921333	+	0.388775i	$0.872898\pi$
$840$		0			0
$841$	−7.38367	+	22.7246i	−0.254609	+	0.783607i
$842$	−7.76010	−	5.63804i	−0.267431	−	0.194300i
$843$	21.3119			0.734022
$844$	1.46305	+	1.06297i	0.0503602	+	0.0365888i
$845$		0			0
$846$	−2.83986	+	2.06328i	−0.0976365	+	0.0709371i
$847$	2.22505	−	1.61660i	0.0764538	−	0.0555469i
$848$	−2.13774	−	6.57929i	−0.0734103	−	0.225934i
$849$	−0.864403			−0.0296662
$850$		0			0
$851$	45.5194			1.56039
$852$	0.151188	+	0.465309i	0.00517961	+	0.0159412i
$853$	43.4018	−	31.5333i	1.48605	−	1.07968i	0.510507	−	0.859874i	$-0.329458\pi$
$853$	43.4018	−	31.5333i	1.48605	−	1.07968i	0.975544	−	0.219805i	$-0.0705422\pi$
$854$	−9.20656	+	6.68896i	−0.315042	+	0.228891i
$855$		0			0
$856$	−13.6026	−	9.88290i	−0.464929	−	0.337790i
$857$	27.1144			0.926210			0.463105	−	0.886303i	$-0.346735\pi$
$857$	27.1144			0.926210			0.463105	+	0.886303i	$0.346735\pi$
$858$	13.5029	+	9.81046i	0.460983	+	0.334924i
$859$	3.21966	−	9.90910i	0.109853	−	0.338094i	−0.880985	−	0.473143i	$-0.843119\pi$
$859$	3.21966	−	9.90910i	0.109853	−	0.338094i	0.990839	+	0.135049i	$0.0431193\pi$
$860$		0			0
$861$	−2.57163	−	7.91467i	−0.0876410	−	0.269731i
$862$	−9.14963	+	28.1597i	−0.311638	+	0.959122i
$863$	13.4865	−	41.5072i	0.459086	−	1.41292i	−0.407185	−	0.913346i	$-0.633490\pi$
$863$	13.4865	−	41.5072i	0.459086	−	1.41292i	0.866271	−	0.499575i	$-0.166510\pi$
$864$	−1.21720	−	3.74617i	−0.0414101	−	0.127447i
$865$		0			0
$866$	3.25065	−	10.0045i	0.110461	−	0.339965i
$867$	−10.1092	−	7.34479i	−0.343328	−	0.249442i
$868$	8.28864			0.281335
$869$	−25.3480	−	18.4164i	−0.859872	−	0.624734i
$870$		0			0
$871$	8.61055	−	6.25593i	0.291757	−	0.211974i
$872$	28.2151	−	20.4995i	0.955485	−	0.694201i
$873$	−4.17172	−	12.8392i	−0.141191	−	0.434542i
$874$	28.1391			0.951818
$875$		0			0
$876$	−5.53456			−0.186995
$877$	−16.5767	−	51.0180i	−0.559757	−	1.72275i	−0.683038	−	0.730383i	$-0.739342\pi$
$877$	−16.5767	−	51.0180i	−0.559757	−	1.72275i	0.123281	−	0.992372i	$-0.460658\pi$
$878$	0.468503	−	0.340388i	0.0158112	−	0.0114875i
$879$	−2.57025	+	1.86740i	−0.0866925	+	0.0629858i
$880$		0			0
$881$	44.4110	+	32.2665i	1.49625	+	1.08709i	0.971847	+	0.235613i	$0.0757097\pi$
$881$	44.4110	+	32.2665i	1.49625	+	1.08709i	0.524398	+	0.851473i	$0.324290\pi$
$882$	−6.46419			−0.217661
$883$	−15.4483	−	11.2239i	−0.519877	−	0.377713i	0.296681	−	0.954977i	$-0.404120\pi$
$883$	−15.4483	−	11.2239i	−0.519877	−	0.377713i	−0.816558	+	0.577264i	$0.804120\pi$
$884$	1.96751	−	6.05538i	0.0661746	−	0.203664i
$885$		0			0
$886$	6.18547	+	19.0369i	0.207805	+	0.639558i
$887$	3.46598	−	10.6672i	0.116376	−	0.358170i	−0.875855	−	0.482574i	$-0.839702\pi$
$887$	3.46598	−	10.6672i	0.116376	−	0.358170i	0.992232	+	0.124404i	$0.0397020\pi$
$888$	−7.00676	+	21.5646i	−0.235131	+	0.723660i
$889$	0.261425	+	0.804582i	0.00876790	+	0.0269848i
$890$		0			0
$891$	1.13412	−	3.49045i	0.0379943	−	0.116934i
$892$	15.3557	+	11.1566i	0.514147	+	0.373550i
$893$	−12.7003			−0.424998
$894$	14.2098	+	10.3240i	0.475247	+	0.345287i
$895$		0			0
$896$	1.35896	−	0.987345i	0.0453998	−	0.0329849i
$897$	−20.2407	+	14.7057i	−0.675816	+	0.491009i
$898$	−1.44462	−	4.44608i	−0.0482076	−	0.148368i
$899$	−22.7139			−0.757552
$900$		0			0
$901$	−7.44857			−0.248148
$902$	−9.51095	−	29.2717i	−0.316680	−	0.974641i
$903$	8.33451	−	6.05538i	0.277355	−	0.201510i
$904$	−12.0310	+	8.74106i	−0.400146	+	0.290723i
$905$		0			0
$906$	3.59398	+	2.61118i	0.119402	+	0.0867506i
$907$	36.4513			1.21034			0.605172	−	0.796095i	$-0.293104\pi$
$907$	36.4513			1.21034			0.605172	+	0.796095i	$0.293104\pi$
$908$	−3.93125	−	2.85622i	−0.130463	−	0.0947871i
$909$	2.23309	−	6.87273i	0.0740668	−	0.227954i
$910$		0			0
$911$	0.360106	+	1.10829i	0.0119309	+	0.0367194i	0.956845	−	0.290600i	$-0.0938548\pi$
$911$	0.360106	+	1.10829i	0.0119309	+	0.0367194i	−0.944914	+	0.327319i	$0.893855\pi$
$912$	−2.47338	+	7.61227i	−0.0819017	+	0.252067i
$913$	−13.9087	+	42.8065i	−0.460310	+	1.41669i
$914$	6.12948	+	18.8646i	0.202745	+	0.623985i
$915$		0			0
$916$	1.82203	−	5.60763i	0.0602016	−	0.185281i
$917$	13.2047	+	9.59377i	0.436057	+	0.316814i
$918$	2.38197			0.0786166
$919$	−35.5543	−	25.8317i	−1.17283	−	0.852109i	−0.181482	−	0.983394i	$-0.558089\pi$
$919$	−35.5543	−	25.8317i	−1.17283	−	0.852109i	−0.991345	+	0.131286i	$0.958089\pi$
$920$		0			0
$921$	0.410969	−	0.298587i	0.0135419	−	0.00983876i
$922$	0.186098	−	0.135208i	0.00612880	−	0.00445283i
$923$	0.827454	+	2.54664i	0.0272360	+	0.0838237i
$924$	−3.02624			−0.0995561
$925$		0			0
$926$	14.3856			0.472739
$927$	−1.63083	−	5.01918i	−0.0535635	−	0.164852i
$928$	7.20073	−	5.23164i	0.236376	−	0.171737i
$929$	−25.2512	+	18.3460i	−0.828464	+	0.601914i	−0.919124	−	0.393968i	$-0.871102\pi$
$929$	−25.2512	+	18.3460i	−0.828464	+	0.601914i	0.0906606	+	0.995882i	$0.471102\pi$
$930$		0			0
$931$	−18.9210	−	13.7469i	−0.620111	−	0.450537i
$932$	−6.97506			−0.228476
$933$	−11.8471	−	8.60743i	−0.387857	−	0.281795i
$934$	−0.386266	+	1.18880i	−0.0126390	+	0.0388988i
$935$		0			0
$936$	−3.85112	−	11.8525i	−0.125878	−	0.387412i
$937$	13.9385	−	42.8983i	0.455351	−	1.40143i	−0.415371	−	0.909652i	$-0.636348\pi$
$937$	13.9385	−	42.8983i	0.455351	−	1.40143i	0.870722	−	0.491775i	$-0.163652\pi$
$938$	1.01458	−	3.12255i	0.0331271	−	0.101955i
$939$	−4.62171	−	14.2241i	−0.150824	−	0.464188i
$940$		0			0
$941$	−12.0931	+	37.2187i	−0.394224	+	1.21330i	0.535341	+	0.844636i	$0.320183\pi$
$941$	−12.0931	+	37.2187i	−0.394224	+	1.21330i	−0.929565	+	0.368659i	$0.879817\pi$
$942$	4.08650	+	2.96901i	0.133145	+	0.0967357i
$943$	46.1358			1.50239
$944$	−10.5150	−	7.63957i	−0.342233	−	0.248647i
$945$		0			0
$946$	30.8245	−	22.3953i	1.00219	−	0.728133i
$947$	−39.5235	+	28.7155i	−1.28434	+	0.933128i	−0.999675	−	0.0254991i	$-0.991883\pi$
$947$	−39.5235	+	28.7155i	−1.28434	+	0.933128i	−0.284665	+	0.958627i	$0.591883\pi$
$948$	1.95317	+	6.01125i	0.0634361	+	0.195236i
$949$	−30.2907			−0.983278
$950$		0			0
$951$	18.1190			0.587550
$952$	−2.24651	−	6.91405i	−0.0728098	−	0.224086i
$953$	18.4314	−	13.3912i	0.597051	−	0.433783i	−0.247780	−	0.968816i	$-0.579701\pi$
$953$	18.4314	−	13.3912i	0.597051	−	0.433783i	0.844831	+	0.535034i	$0.179701\pi$
$954$	−3.18668	+	2.31526i	−0.103173	+	0.0749593i
$955$		0			0
$956$	−6.72232	−	4.88405i	−0.217415	−	0.157961i
$957$	8.29302			0.268075
$958$	22.8585	+	16.6077i	0.738525	+	0.536570i
$959$	4.23024	−	13.0193i	0.136602	−	0.420417i
$960$		0			0
$961$	21.6446	+	66.6154i	0.698214	+	2.14888i
$962$	−10.3605	+	31.8864i	−0.334037	+	1.02806i
$963$	−1.68934	+	5.19926i	−0.0544382	+	0.167544i
$964$	−5.18908	−	15.9703i	−0.167129	−	0.514370i
$965$		0			0
$966$	−2.38495	+	7.34012i	−0.0767345	+	0.236164i
$967$	34.9436	+	25.3880i	1.12371	+	0.816425i	0.984768	−	0.173876i	$-0.0556291\pi$
$967$	34.9436	+	25.3880i	1.12371	+	0.816425i	0.138944	+	0.990300i	$0.455629\pi$
$968$	−7.59507			−0.244115
$969$	6.97214	+	5.06555i	0.223977	+	0.162729i
$970$		0			0
$971$	25.9089	−	18.8239i	0.831457	−	0.604089i	−0.0885142	−	0.996075i	$-0.528212\pi$
$971$	25.9089	−	18.8239i	0.831457	−	0.604089i	0.919971	+	0.391986i	$0.128212\pi$
$972$	−0.598970	+	0.435177i	−0.0192120	+	0.0139583i
$973$	−5.07090	−	15.6066i	−0.162565	−	0.500325i
$974$	−11.6271			−0.372557
$975$		0			0
$976$	17.9452			0.574413
$977$	2.24659	+	6.91428i	0.0718747	+	0.221208i	0.980541	−	0.196316i	$-0.0628980\pi$
$977$	2.24659	+	6.91428i	0.0718747	+	0.221208i	−0.908666	+	0.417524i	$0.862898\pi$
$978$	2.22810	−	1.61881i	0.0712467	−	0.0517637i
$979$	45.3927	−	32.9798i	1.45076	−	1.05404i
$980$		0			0
$981$	−9.17385	−	6.66519i	−0.292898	−	0.212803i
$982$	−17.5725			−0.560760
$983$	−4.11915	−	2.99274i	−0.131380	−	0.0954535i	0.520154	−	0.854072i	$-0.325874\pi$
$983$	−4.11915	−	2.99274i	−0.131380	−	0.0954535i	−0.651535	+	0.758619i	$0.725874\pi$
$984$	−7.10163	+	21.8566i	−0.226392	+	0.696762i
$985$		0			0
$986$	1.66324	+	5.11894i	0.0529685	+	0.163020i
$987$	1.07642	−	3.31288i	0.0342628	−	0.105450i
$988$	3.76442	−	11.5857i	0.119762	−	0.368590i
$989$	17.6488	+	54.3176i	0.561201	+	1.72720i
$990$		0			0
$991$	−19.1826	+	59.0380i	−0.609356	+	1.87540i	−0.145859	+	0.989305i	$0.546594\pi$
$991$	−19.1826	+	59.0380i	−0.609356	+	1.87540i	−0.463497	+	0.886098i	$0.653406\pi$
$992$	−32.0327	−	23.2731i	−1.01704	−	0.738922i
$993$	−26.3514			−0.836237
$994$	0.668265	+	0.485523i	0.0211961	+	0.0153999i
$995$		0			0
$996$	7.34570	−	5.33697i	0.232758	−	0.169108i
$997$	2.07832	−	1.50999i	0.0658212	−	0.0478219i	−0.554388	−	0.832258i	$-0.687048\pi$
$997$	2.07832	−	1.50999i	0.0658212	−	0.0478219i	0.620209	+	0.784436i	$0.287048\pi$
$998$	12.4114	+	38.1985i	0.392878	+	1.20915i
$999$	7.37232			0.233250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.b.151.2		8
5.2	odd	4		375.2.i.b.349.2		16
5.3	odd	4		375.2.i.b.349.3		16
5.4	even	2		75.2.g.b.31.1	✓	8
15.14	odd	2		225.2.h.c.181.2		8
25.2	odd	20		1875.2.b.c.1249.5		8
25.3	odd	20		375.2.i.b.274.2		16
25.4	even	10		75.2.g.b.46.1	yes	8
25.11	even	5		1875.2.a.e.1.3		4
25.14	even	10		1875.2.a.h.1.2		4
25.21	even	5	inner	375.2.g.b.226.2		8
25.22	odd	20		375.2.i.b.274.3		16
25.23	odd	20		1875.2.b.c.1249.4		8
75.11	odd	10		5625.2.a.n.1.2		4
75.14	odd	10		5625.2.a.i.1.3		4
75.29	odd	10		225.2.h.c.46.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.1	✓	8	5.4	even	2
75.2.g.b.46.1	yes	8	25.4	even	10
225.2.h.c.46.2		8	75.29	odd	10
225.2.h.c.181.2		8	15.14	odd	2
375.2.g.b.151.2		8	1.1	even	1	trivial
375.2.g.b.226.2		8	25.21	even	5	inner
375.2.i.b.274.2		16	25.3	odd	20
375.2.i.b.274.3		16	25.22	odd	20
375.2.i.b.349.2		16	5.2	odd	4
375.2.i.b.349.3		16	5.3	odd	4
1875.2.a.e.1.3		4	25.11	even	5
1875.2.a.h.1.2		4	25.14	even	10
1875.2.b.c.1249.4		8	25.23	odd	20
1875.2.b.c.1249.5		8	25.2	odd	20
5625.2.a.i.1.3		4	75.14	odd	10
5625.2.a.n.1.2		4	75.11	odd	10

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.346820 + 1.06740i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.907987 + 0.659691i) q^{6} -1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.346820 + 1.06740i) q^{2} +(0.809017 - 0.587785i) q^{3} +(0.598970 - 0.435177i) q^{4} +(0.907987 + 0.659691i) q^{6} -1.11373 q^{7} +(2.48822 + 1.80780i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.13412 + 3.49045i) q^{11} +(0.228786 - 0.704131i) q^{12} +(1.25215 - 3.85372i) q^{13} +(-0.386266 - 1.18880i) q^{14} +(-0.609110 + 1.87465i) q^{16} +(1.71700 + 1.24748i) q^{17} +1.12233 q^{18} +(3.28513 + 2.38678i) q^{19} +(-0.901030 + 0.654637i) q^{21} +(-3.33238 + 2.42112i) q^{22} +(-1.90799 - 5.87218i) q^{23} +3.07561 q^{24} +4.54774 q^{26} +(-0.309017 - 0.951057i) q^{27} +(-0.667093 + 0.484672i) q^{28} +(1.82808 - 1.32818i) q^{29} +(-8.13227 - 5.90844i) q^{31} +3.93896 q^{32} +(2.96915 + 2.15722i) q^{33} +(-0.736068 + 2.26538i) q^{34} +(-0.228786 - 0.704131i) q^{36} +(-2.27817 + 7.01149i) q^{37} +(-1.40831 + 4.33434i) q^{38} +(-1.25215 - 3.85372i) q^{39} +(-2.30902 + 7.10642i) q^{41} +(-1.01126 - 0.734721i) q^{42} -9.24998 q^{43} +(2.19826 + 1.59713i) q^{44} +(5.60625 - 4.07318i) q^{46} +(-2.53032 + 1.83839i) q^{47} +(0.609110 + 1.87465i) q^{48} -5.75960 q^{49} +2.12233 q^{51} +(-0.927051 - 2.85317i) q^{52} +(-2.83934 + 2.06290i) q^{53} +(0.907987 - 0.659691i) q^{54} +(-2.77121 - 2.01340i) q^{56} +4.06064 q^{57} +(2.05172 + 1.49066i) q^{58} +(-2.03760 + 6.27109i) q^{59} +(-2.81332 - 8.65850i) q^{61} +(3.48625 - 10.7296i) q^{62} +(-0.344163 + 1.05922i) q^{63} +(2.58433 + 7.95375i) q^{64} +(-1.27286 + 3.91745i) q^{66} +(2.12499 + 1.54390i) q^{67} +1.57131 q^{68} +(-4.99517 - 3.62921i) q^{69} +(-0.534620 + 0.388424i) q^{71} +(2.48822 - 1.80780i) q^{72} +(-2.31003 - 7.10955i) q^{73} -8.27420 q^{74} +3.00637 q^{76} +(-1.26310 - 3.88743i) q^{77} +(3.67920 - 2.67310i) q^{78} +(-6.90667 + 5.01799i) q^{79} +(-0.809017 - 0.587785i) q^{81} -8.38623 q^{82} +(9.92170 + 7.20854i) q^{83} +(-0.254807 + 0.784215i) q^{84} +(-3.20808 - 9.87345i) q^{86} +(0.698265 - 2.14904i) q^{87} +(-3.48809 + 10.7352i) q^{88} +(-4.72429 - 14.5399i) q^{89} +(-1.39456 + 4.29202i) q^{91} +(-3.69826 - 2.68695i) q^{92} -10.0520 q^{93} +(-2.83986 - 2.06328i) q^{94} +(3.18668 - 2.31526i) q^{96} +(10.9217 - 7.93508i) q^{97} +(-1.99754 - 6.14781i) q^{98} +3.67008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 - q^6 - 4 * q^7 - 2 * q^9 + 16 * q^11 + 9 * q^12 + 8 * q^13 - 8 * q^14 - 17 * q^16 + q^17 - 4 * q^18 - 5 * q^19 - 11 * q^21 - 13 * q^22 - 7 * q^23 + 30 * q^24 + 6 * q^26 + 2 * q^27 + 17 * q^28 + 5 * q^29 - 19 * q^31 - 24 * q^32 + 9 * q^33 + 12 * q^34 - 9 * q^36 + q^37 + 10 * q^38 - 8 * q^39 - 14 * q^41 + 8 * q^42 - 32 * q^43 - 3 * q^44 + 16 * q^46 + q^47 + 17 * q^48 + 16 * q^49 + 4 * q^51 + 6 * q^52 + 3 * q^53 - q^54 - 15 * q^56 - 10 * q^57 - 5 * q^58 + 30 * q^59 - 14 * q^61 + 17 * q^62 - 9 * q^63 - 44 * q^64 - 7 * q^66 - 4 * q^67 + 22 * q^68 - 8 * q^69 + 21 * q^71 - 2 * q^73 - 38 * q^74 + 80 * q^76 + 37 * q^77 + 14 * q^78 - 30 * q^79 - 2 * q^81 + 12 * q^82 - 2 * q^83 + 8 * q^84 - 34 * q^86 - 15 * q^87 - 70 * q^88 + 21 * q^91 - 9 * q^92 - 46 * q^93 - 33 * q^94 + 34 * q^96 + 6 * q^97 - 73 * q^98 - 14 * q^99

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