LMFDB - Embedded newform 375.2.i.b.274.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, 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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 $ x^16 + 5x^14 + 6x^12 - 20x^10 - 79x^8 - 80x^6 + 96x^4 + 320*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			274.3
Root			$0.720348 + 1.21700i$ of defining polynomial
Character	$\chi$	$=$	375.274
Dual form			375.2.i.b.349.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06740 + 0.346820i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.598970 - 0.435177i) q^{4} +(0.907987 - 0.659691i) q^{6} -1.11373i q^{7} +(-1.80780 - 2.48822i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(1.06740 + 0.346820i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.598970 - 0.435177i) q^{4} +(0.907987 - 0.659691i) q^{6} -1.11373i q^{7} +(-1.80780 - 2.48822i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.13412 - 3.49045i) q^{11} +(-0.704131 + 0.228786i) q^{12} +(3.85372 - 1.25215i) q^{13} +(0.386266 - 1.18880i) q^{14} +(-0.609110 - 1.87465i) q^{16} +(1.24748 + 1.71700i) q^{17} -1.12233i q^{18} +(-3.28513 + 2.38678i) q^{19} +(-0.901030 - 0.654637i) q^{21} +(2.42112 - 3.33238i) q^{22} +(5.87218 + 1.90799i) q^{23} -3.07561 q^{24} +4.54774 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-0.484672 + 0.667093i) q^{28} +(-1.82808 - 1.32818i) q^{29} +(-8.13227 + 5.90844i) q^{31} +3.93896i q^{32} +(-2.15722 - 2.96915i) q^{33} +(0.736068 + 2.26538i) q^{34} +(-0.228786 + 0.704131i) q^{36} +(7.01149 - 2.27817i) q^{37} +(-4.33434 + 1.40831i) q^{38} +(1.25215 - 3.85372i) q^{39} +(-2.30902 - 7.10642i) q^{41} +(-0.734721 - 1.01126i) q^{42} +9.24998i q^{43} +(-2.19826 + 1.59713i) q^{44} +(5.60625 + 4.07318i) q^{46} +(1.83839 - 2.53032i) q^{47} +(-1.87465 - 0.609110i) q^{48} +5.75960 q^{49} +2.12233 q^{51} +(-2.85317 - 0.927051i) q^{52} +(-2.06290 + 2.83934i) q^{53} +(-0.907987 - 0.659691i) q^{54} +(-2.77121 + 2.01340i) q^{56} +4.06064i q^{57} +(-1.49066 - 2.05172i) q^{58} +(2.03760 + 6.27109i) q^{59} +(-2.81332 + 8.65850i) q^{61} +(-10.7296 + 3.48625i) q^{62} +(-1.05922 + 0.344163i) q^{63} +(-2.58433 + 7.95375i) q^{64} +(-1.27286 - 3.91745i) q^{66} +(1.54390 + 2.12499i) q^{67} -1.57131i q^{68} +(4.99517 - 3.62921i) q^{69} +(-0.534620 - 0.388424i) q^{71} +(-1.80780 + 2.48822i) q^{72} +(7.10955 + 2.31003i) q^{73} +8.27420 q^{74} +3.00637 q^{76} +(-3.88743 - 1.26310i) q^{77} +(2.67310 - 3.67920i) q^{78} +(6.90667 + 5.01799i) q^{79} +(-0.809017 + 0.587785i) q^{81} -8.38623i q^{82} +(-7.20854 - 9.92170i) q^{83} +(0.254807 + 0.784215i) q^{84} +(-3.20808 + 9.87345i) q^{86} +(-2.14904 + 0.698265i) q^{87} +(-10.7352 + 3.48809i) q^{88} +(4.72429 - 14.5399i) q^{89} +(-1.39456 - 4.29202i) q^{91} +(-2.68695 - 3.69826i) q^{92} +10.0520i q^{93} +(2.83986 - 2.06328i) q^{94} +(3.18668 + 2.31526i) q^{96} +(-7.93508 + 10.9217i) q^{97} +(6.14781 + 1.99754i) q^{98} -3.67008 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	$ 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) $ 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	1.06740	+	0.346820i	0.754768	+	0.245239i	0.661031	−	0.750358i	$-0.270119\pi$
$2$	1.06740	+	0.346820i	0.754768	+	0.245239i	0.0937362	+	0.995597i	$0.470119\pi$
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.598970	−	0.435177i	−0.299485	−	0.217589i
$5$		0			0
$5$		0			0
$6$	0.907987	−	0.659691i	0.370684	−	0.269318i
$7$		−	1.11373i		−	0.420952i	−0.977599	−	0.210476i	$-0.932499\pi$
$7$		−	1.11373i		−	0.420952i	0.977599	−	0.210476i	$-0.0675014\pi$
$8$	−1.80780	−	2.48822i	−0.639152	−	0.879718i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	1.13412	−	3.49045i	0.341949	−	1.05241i	−0.621248	−	0.783614i	$-0.713374\pi$
$11$	1.13412	−	3.49045i	0.341949	−	1.05241i	0.963197	−	0.268796i	$-0.0866258\pi$
$12$	−0.704131	+	0.228786i	−0.203265	+	0.0660449i
$13$	3.85372	−	1.25215i	1.06883	−	0.347284i	0.278798	−	0.960350i	$-0.410064\pi$
$13$	3.85372	−	1.25215i	1.06883	−	0.347284i	0.790032	+	0.613066i	$0.210064\pi$
$14$	0.386266	−	1.18880i	0.103234	−	0.317721i
$15$		0			0
$16$	−0.609110	−	1.87465i	−0.152277	−	0.468662i
$17$	1.24748	+	1.71700i	0.302557	+	0.416435i	0.933042	−	0.359767i	$-0.117144\pi$
$17$	1.24748	+	1.71700i	0.302557	+	0.416435i	−0.630485	+	0.776202i	$0.717144\pi$
$18$		−	1.12233i		−	0.264537i
$19$	−3.28513	+	2.38678i	−0.753660	+	0.547566i	−0.896959	−	0.442113i	$-0.854229\pi$
$19$	−3.28513	+	2.38678i	−0.753660	+	0.547566i	0.143299	+	0.989679i	$0.454229\pi$
$20$		0			0
$21$	−0.901030	−	0.654637i	−0.196621	−	0.142853i
$22$	2.42112	−	3.33238i	0.516184	−	0.710466i
$23$	5.87218	+	1.90799i	1.22443	+	0.397843i	0.848695	−	0.528883i	$-0.177389\pi$
$23$	5.87218	+	1.90799i	1.22443	+	0.397843i	0.375739	+	0.926725i	$0.377389\pi$
$24$	−3.07561			−0.627806
$25$		0			0
$26$	4.54774			0.891886
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−0.484672	+	0.667093i	−0.0915943	+	0.126069i
$29$	−1.82808	−	1.32818i	−0.339466	−	0.246637i	0.404970	−	0.914330i	$-0.367282\pi$
$29$	−1.82808	−	1.32818i	−0.339466	−	0.246637i	−0.744437	+	0.667693i	$0.767282\pi$
$30$		0			0
$31$	−8.13227	+	5.90844i	−1.46060	+	1.06119i	−0.477393	+	0.878690i	$0.658418\pi$
$31$	−8.13227	+	5.90844i	−1.46060	+	1.06119i	−0.983206	+	0.182498i	$0.941582\pi$
$32$			3.93896i			0.696316i
$33$	−2.15722	−	2.96915i	−0.375523	−	0.516863i
$34$	0.736068	+	2.26538i	0.126235	+	0.388510i
$35$		0			0
$36$	−0.228786	+	0.704131i	−0.0381310	+	0.117355i
$37$	7.01149	−	2.27817i	1.15268	−	0.374529i	0.330529	−	0.943796i	$-0.392773\pi$
$37$	7.01149	−	2.27817i	1.15268	−	0.374529i	0.822153	+	0.569267i	$0.192773\pi$
$38$	−4.33434	+	1.40831i	−0.703123	+	0.228458i
$39$	1.25215	−	3.85372i	0.200504	−	0.617089i
$40$		0			0
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	−0.952686	−	0.303956i	$-0.901692\pi$
$41$	−2.30902	−	7.10642i	−0.360608	−	1.10984i	0.592078	−	0.805881i	$-0.298308\pi$
$42$	−0.734721	−	1.01126i	−0.113370	−	0.156040i
$43$			9.24998i			1.41061i	0.708905	+	0.705304i	$0.249190\pi$
$43$			9.24998i			1.41061i	−0.708905	+	0.705304i	$0.750810\pi$
$44$	−2.19826	+	1.59713i	−0.331401	+	0.240777i
$45$		0			0
$46$	5.60625	+	4.07318i	0.826597	+	0.600558i
$47$	1.83839	−	2.53032i	0.268156	−	0.369085i	−0.653610	−	0.756831i	$-0.726746\pi$
$47$	1.83839	−	2.53032i	0.268156	−	0.369085i	0.921766	+	0.387746i	$0.126746\pi$
$48$	−1.87465	−	0.609110i	−0.270582	−	0.0879174i
$49$	5.75960			0.822799
$50$		0			0
$51$	2.12233			0.297186
$52$	−2.85317	−	0.927051i	−0.395663	−	0.128559i
$53$	−2.06290	+	2.83934i	−0.283361	+	0.390013i	−0.926844	−	0.375448i	$-0.877489\pi$
$53$	−2.06290	+	2.83934i	−0.283361	+	0.390013i	0.643483	+	0.765461i	$0.277489\pi$
$54$	−0.907987	−	0.659691i	−0.123561	−	0.0897726i
$55$		0			0
$56$	−2.77121	+	2.01340i	−0.370319	+	0.269053i
$57$			4.06064i			0.537845i
$58$	−1.49066	−	2.05172i	−0.195733	−	0.269404i
$59$	2.03760	+	6.27109i	0.265273	+	0.816427i	0.991630	+	0.129110i	$0.0412119\pi$
$59$	2.03760	+	6.27109i	0.265273	+	0.816427i	−0.726357	+	0.687317i	$0.758788\pi$
$60$		0			0
$61$	−2.81332	+	8.65850i	−0.360208	+	1.10861i	0.592719	+	0.805409i	$0.298054\pi$
$61$	−2.81332	+	8.65850i	−0.360208	+	1.10861i	−0.952928	+	0.303198i	$0.901946\pi$
$62$	−10.7296	+	3.48625i	−1.36266	+	0.442754i
$63$	−1.05922	+	0.344163i	−0.133450	+	0.0433604i
$64$	−2.58433	+	7.95375i	−0.323041	+	0.994219i
$65$		0			0
$66$	−1.27286	−	3.91745i	−0.156678	−	0.482205i
$67$	1.54390	+	2.12499i	0.188617	+	0.259609i	0.892844	−	0.450366i	$-0.148706\pi$
$67$	1.54390	+	2.12499i	0.188617	+	0.259609i	−0.704227	+	0.709975i	$0.748706\pi$
$68$		−	1.57131i		−	0.190549i
$69$	4.99517	−	3.62921i	0.601348	−	0.436905i
$70$		0			0
$71$	−0.534620	−	0.388424i	−0.0634477	−	0.0460975i	0.555609	−	0.831443i	$-0.312485\pi$
$71$	−0.534620	−	0.388424i	−0.0634477	−	0.0460975i	−0.619057	+	0.785346i	$0.712485\pi$
$72$	−1.80780	+	2.48822i	−0.213051	+	0.293239i
$73$	7.10955	+	2.31003i	0.832110	+	0.270369i	0.693934	−	0.720039i	$-0.255876\pi$
$73$	7.10955	+	2.31003i	0.832110	+	0.270369i	0.138176	+	0.990408i	$0.455876\pi$
$74$	8.27420			0.961856
$75$		0			0
$76$	3.00637			0.344854
$77$	−3.88743	−	1.26310i	−0.443014	−	0.143944i
$78$	2.67310	−	3.67920i	0.302668	−	0.416587i
$79$	6.90667	+	5.01799i	0.777061	+	0.564568i	0.904096	−	0.427330i	$-0.140546\pi$
$79$	6.90667	+	5.01799i	0.777061	+	0.564568i	−0.127034	+	0.991898i	$0.540546\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		−	8.38623i		−	0.926104i
$83$	−7.20854	−	9.92170i	−0.791240	−	1.08905i	−0.993953	−	0.109810i	$-0.964976\pi$
$83$	−7.20854	−	9.92170i	−0.791240	−	1.08905i	0.202713	−	0.979238i	$-0.435024\pi$
$84$	0.254807	+	0.784215i	0.0278017	+	0.0855649i
$85$		0			0
$86$	−3.20808	+	9.87345i	−0.345936	+	1.06468i
$87$	−2.14904	+	0.698265i	−0.230401	+	0.0748618i
$88$	−10.7352	+	3.48809i	−1.14438	+	0.371832i
$89$	4.72429	−	14.5399i	0.500773	−	1.54122i	−0.306989	−	0.951713i	$-0.599321\pi$
$89$	4.72429	−	14.5399i	0.500773	−	1.54122i	0.807762	−	0.589509i	$-0.200679\pi$
$90$		0			0
$91$	−1.39456	−	4.29202i	−0.146190	−	0.449926i
$92$	−2.68695	−	3.69826i	−0.280134	−	0.385571i
$93$			10.0520i			1.04235i
$94$	2.83986	−	2.06328i	0.292910	−	0.212811i
$95$		0			0
$96$	3.18668	+	2.31526i	0.325240	+	0.236300i
$97$	−7.93508	+	10.9217i	−0.805685	+	1.10893i	0.186290	+	0.982495i	$0.440354\pi$
$97$	−7.93508	+	10.9217i	−0.805685	+	1.10893i	−0.991975	+	0.126436i	$0.959646\pi$
$98$	6.14781	+	1.99754i	0.621022	+	0.201782i
$99$	−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	$0.382938\pi$
$102$	2.26538	+	0.736068i	0.224306	+	0.0728816i
$103$	3.10203	−	4.26957i	0.305652	−	0.420693i	−0.628367	−	0.777917i	$-0.716277\pi$
$103$	3.10203	−	4.26957i	0.305652	−	0.420693i	0.934019	+	0.357223i	$0.116277\pi$
$104$	−10.0824	−	7.32526i	−0.988657	−	0.718301i
$105$		0			0
$106$	−3.18668	+	2.31526i	−0.309518	+	0.224878i
$107$		−	5.46682i		−	0.528498i	−0.964455	−	0.264249i	$-0.914876\pi$
$107$		−	5.46682i		−	0.528498i	0.964455	−	0.264249i	$-0.0851240\pi$
$108$	0.435177	+	0.598970i	0.0418749	+	0.0576359i
$109$	−3.50410	−	10.7845i	−0.335632	−	1.03297i	−0.966410	−	0.257005i	$-0.917264\pi$
$109$	−3.50410	−	10.7845i	−0.335632	−	1.03297i	0.630778	−	0.775963i	$-0.282736\pi$
$110$		0			0
$111$	2.27817	−	7.01149i	0.216234	−	0.665501i
$112$	−2.08786	+	0.678387i	−0.197284	+	0.0641015i
$113$	−4.59855	+	1.49416i	−0.432595	+	0.140559i	−0.517217	−	0.855854i	$-0.673032\pi$
$113$	−4.59855	+	1.49416i	−0.432595	+	0.140559i	0.0846215	+	0.996413i	$0.473032\pi$
$114$	−1.40831	+	4.33434i	−0.131900	+	0.405948i
$115$		0			0
$116$	0.516973	+	1.59108i	0.0479997	+	0.147728i
$117$	−2.38173	−	3.27817i	−0.220191	−	0.303067i
$118$			7.40046i			0.681268i
$119$	1.91229	−	1.38936i	0.175299	−	0.127362i
$120$		0			0
$121$	−1.99783	−	1.45151i	−0.181621	−	0.131955i
$122$	−6.00588	+	8.26639i	−0.543747	+	0.748404i
$123$	−7.10642	−	2.30902i	−0.640765	−	0.208197i
$124$	7.44220			0.668330
$125$		0			0
$126$	−1.24998			−0.111357
$127$	−0.722418	−	0.234728i	−0.0641043	−	0.0208287i	0.276789	−	0.960931i	$-0.410730\pi$
$127$	−0.722418	−	0.234728i	−0.0641043	−	0.0208287i	−0.340894	+	0.940102i	$0.610730\pi$
$128$	−0.886518	+	1.22019i	−0.0783578	+	0.107850i
$129$	7.48339	+	5.43700i	0.658876	+	0.478701i
$130$		0			0
$131$	−11.8562	+	8.61406i	−1.03588	+	0.752614i	−0.969478	−	0.245179i	$-0.921153\pi$
$131$	−11.8562	+	8.61406i	−1.03588	+	0.752614i	−0.0664061	+	0.997793i	$0.521153\pi$
$132$			2.71720i			0.236502i
$133$	2.65824	+	3.65876i	0.230499	+	0.317255i
$134$	0.910969	+	2.80367i	0.0786958	+	0.242201i
$135$		0			0
$136$	2.01710	−	6.20799i	0.172965	−	0.532330i
$137$	11.6898	−	3.79825i	0.998728	−	0.324506i	0.236371	−	0.971663i	$-0.424042\pi$
$137$	11.6898	−	3.79825i	0.998728	−	0.324506i	0.762357	+	0.647157i	$0.224042\pi$
$138$	6.59054	−	2.14140i	0.561024	−	0.182288i
$139$	−4.55306	+	14.0129i	−0.386185	+	1.18856i	0.549432	+	0.835539i	$0.314844\pi$
$139$	−4.55306	+	14.0129i	−0.386185	+	1.18856i	−0.935617	+	0.353017i	$0.885156\pi$
$140$		0			0
$141$	−0.966496	−	2.97457i	−0.0813937	−	0.250504i
$142$	−0.435941	−	0.600022i	−0.0365834	−	0.0503527i
$143$		−	14.8713i		−	1.24360i
$144$	−1.59467	+	1.15860i	−0.132889	+	0.0965497i
$145$		0			0
$146$	6.78758	+	4.93147i	0.561744	+	0.408131i
$147$	3.38541	−	4.65961i	0.279224	−	0.384318i
$148$	−5.19108	−	1.68668i	−0.426704	−	0.138645i
$149$	−15.6498			−1.28208			−0.641041	−	0.767507i	$-0.721497\pi$
$149$	−15.6498			−1.28208			−0.641041	+	0.767507i	$0.721497\pi$
$150$		0			0
$151$	3.95819			0.322113			0.161056	−	0.986945i	$-0.448510\pi$
$151$	3.95819			0.322113			0.161056	+	0.986945i	$0.448510\pi$
$152$	11.8777	+	3.85929i	0.963407	+	0.313030i
$153$	1.24748	−	1.71700i	0.100852	−	0.138812i
$154$	−3.71139	−	2.69648i	−0.299072	−	0.217289i
$155$		0			0
$156$	−2.42705	+	1.76336i	−0.194320	+	0.141181i
$157$			4.50061i			0.359188i	0.983741	+	0.179594i	$0.0574784\pi$
$157$			4.50061i			0.359188i	−0.983741	+	0.179594i	$0.942522\pi$
$158$	5.63186	+	7.75159i	0.448047	+	0.616683i
$159$	1.08453	+	3.33784i	0.0860089	+	0.264708i
$160$		0			0
$161$	2.12499	−	6.54005i	0.167473	−	0.515428i
$162$	−1.06740	+	0.346820i	−0.0838631	+	0.0272488i
$163$	2.33378	−	0.758292i	0.182796	−	0.0593940i	−0.216189	−	0.976352i	$-0.569363\pi$
$163$	2.33378	−	0.758292i	0.182796	−	0.0593940i	0.398985	+	0.916958i	$0.369363\pi$
$164$	−1.70952	+	5.26137i	−0.133491	+	0.410844i
$165$		0			0
$166$	−4.25337	−	13.0905i	−0.330125	−	1.01602i
$167$	−1.80055	−	2.47824i	−0.139331	−	0.191772i	0.733649	−	0.679528i	$-0.237816\pi$
$167$	−1.80055	−	2.47824i	−0.139331	−	0.191772i	−0.872980	+	0.487756i	$0.837816\pi$
$168$			3.42541i			0.264276i
$169$	2.76606	−	2.00966i	0.212774	−	0.154589i
$170$		0			0
$171$	3.28513	+	2.38678i	0.251220	+	0.182522i
$172$	4.02538	−	5.54046i	0.306932	−	0.422456i
$173$	10.7085	+	3.47942i	0.814156	+	0.264535i	0.686357	−	0.727265i	$-0.259209\pi$
$173$	10.7085	+	3.47942i	0.814156	+	0.264535i	0.127799	+	0.991800i	$0.459209\pi$
$174$	−2.53606			−0.192258
$175$		0			0
$176$	−7.23416			−0.545296
$177$	6.27109	+	2.03760i	0.471364	+	0.153156i
$178$	10.0854	−	13.8814i	0.755935	−	1.04046i
$179$	8.13657	+	5.91157i	0.608156	+	0.441851i	0.848764	−	0.528771i	$-0.177347\pi$
$179$	8.13657	+	5.91157i	0.608156	+	0.441851i	−0.240609	+	0.970622i	$0.577347\pi$
$180$		0			0
$181$	15.7503	−	11.4433i	1.17071	−	0.850571i	0.179617	−	0.983737i	$-0.442514\pi$
$181$	15.7503	−	11.4433i	1.17071	−	0.850571i	0.991094	+	0.133165i	$0.0425141\pi$
$182$		−	5.06498i		−	0.375441i
$183$	5.35125	+	7.36536i	0.395575	+	0.544463i
$184$	−5.86822	−	18.0605i	−0.432611	−	1.33144i
$185$		0			0
$186$	−3.48625	+	10.7296i	−0.255624	+	0.786731i
$187$	7.40790	−	2.40697i	0.541719	−	0.176015i
$188$	−2.20227	+	0.715563i	−0.160617	+	0.0521878i
$189$	−0.344163	+	1.05922i	−0.0250342	+	0.0770472i
$190$		0			0
$191$	−3.58739	−	11.0408i	−0.259574	−	0.798888i	−0.992894	−	0.119003i	$-0.962030\pi$
$191$	−3.58739	−	11.0408i	−0.259574	−	0.798888i	0.733320	−	0.679884i	$-0.237970\pi$
$192$	4.91569	+	6.76586i	0.354759	+	0.488284i
$193$		−	3.38156i		−	0.243410i	−0.992566	−	0.121705i	$-0.961164\pi$
$193$		−	3.38156i		−	0.243410i	0.992566	−	0.121705i	$-0.0388362\pi$
$194$	−12.2578	+	8.90581i	−0.880058	+	0.639400i
$195$		0			0
$196$	−3.44982	−	2.50644i	−0.246416	−	0.179032i
$197$	10.3380	−	14.2291i	0.736554	−	1.01378i	−0.262256	−	0.964998i	$-0.584466\pi$
$197$	10.3380	−	14.2291i	0.736554	−	1.01378i	0.998809	−	0.0487811i	$-0.0155337\pi$
$198$	−3.91745	−	1.27286i	−0.278401	−	0.0904579i
$199$	−20.0102			−1.41849			−0.709244	−	0.704963i	$-0.750963\pi$
$199$	−20.0102			−1.41849			−0.709244	+	0.704963i	$0.750963\pi$
$200$		0			0
$201$	2.62663			0.185268
$202$	7.71350	+	2.50627i	0.542720	+	0.176340i
$203$	−1.47924	+	2.03600i	−0.103822	+	0.142899i
$204$	−1.27121	−	0.923591i	−0.0890028	−	0.0646643i
$205$		0			0
$206$	4.79188	−	3.48151i	0.333866	−	0.242568i
$207$		−	6.17438i		−	0.429149i
$208$	−4.69468	−	6.46167i	−0.325517	−	0.448036i
$209$	4.60524	+	14.1735i	0.318551	+	0.980399i
$210$		0			0
$211$	0.754807	−	2.32306i	0.0519631	−	0.159926i	−0.921707	−	0.387886i	$-0.873206\pi$
$211$	0.754807	−	2.32306i	0.0519631	−	0.159926i	0.973671	+	0.227960i	$0.0732055\pi$
$212$	2.47123	−	0.802951i	0.169725	−	0.0551469i
$213$	−0.628483	+	0.204207i	−0.0430630	+	0.0139920i
$214$	1.89600	−	5.83530i	0.129608	−	0.398893i
$215$		0			0
$216$	0.950415	+	2.92508i	0.0646675	+	0.199026i
$217$	6.58044	+	9.05719i	0.446709	+	0.614842i
$218$		−	12.7267i		−	0.861961i
$219$	6.04774	−	4.39394i	0.408669	−	0.296915i
$220$		0			0
$221$	6.95737	+	5.05483i	0.468003	+	0.340024i
$222$	4.86345	−	6.69397i	0.326413	−	0.449270i
$223$	−24.3821	−	7.92223i	−1.63275	−	0.530511i	−0.657846	−	0.753153i	$-0.728532\pi$
$223$	−24.3821	−	7.92223i	−1.63275	−	0.530511i	−0.974900	+	0.222641i	$0.928532\pi$
$224$	4.38695			0.293116
$225$		0			0
$226$	−5.42671			−0.360979
$227$	−6.24212	−	2.02819i	−0.414304	−	0.134616i	0.0944455	−	0.995530i	$-0.469892\pi$
$227$	−6.24212	−	2.02819i	−0.414304	−	0.134616i	−0.508750	+	0.860914i	$0.669892\pi$
$228$	1.76710	−	2.43220i	0.117029	−	0.161076i
$229$	−6.44293	−	4.68106i	−0.425761	−	0.309333i	0.354191	−	0.935173i	$-0.384756\pi$
$229$	−6.44293	−	4.68106i	−0.425761	−	0.309333i	−0.779952	+	0.625840i	$0.784756\pi$
$230$		0			0
$231$	−3.30685	+	2.40257i	−0.217575	+	0.158077i
$232$			6.94974i			0.456273i
$233$	5.53757	+	7.62181i	0.362778	+	0.499321i	0.950920	−	0.309436i	$-0.100140\pi$
$233$	5.53757	+	7.62181i	0.362778	+	0.499321i	−0.588142	+	0.808758i	$0.700140\pi$
$234$	−1.40533	−	4.32516i	−0.0918693	−	0.282745i
$235$		0			0
$236$	1.50857	−	4.64291i	0.0981998	−	0.302228i
$237$	8.11928	−	2.63811i	0.527404	−	0.171364i
$238$	2.52304	−	0.819784i	0.163544	−	0.0531387i
$239$	3.46814	−	10.6738i	0.224335	−	0.690433i	−0.774023	−	0.633157i	$-0.781759\pi$
$239$	3.46814	−	10.6738i	0.224335	−	0.690433i	0.998358	−	0.0572756i	$-0.0182414\pi$
$240$		0			0
$241$	7.00879	+	21.5708i	0.451476	+	1.38950i	0.875223	+	0.483719i	$0.160714\pi$
$241$	7.00879	+	21.5708i	0.451476	+	1.38950i	−0.423748	+	0.905780i	$0.639286\pi$
$242$	−1.62908	−	2.24223i	−0.104721	−	0.144136i
$243$			1.00000i			0.0641500i
$244$	5.45307	−	3.96189i	0.349097	−	0.253634i
$245$		0			0
$246$	−6.78460	−	4.92930i	−0.432570	−	0.314281i
$247$	−9.67135	+	13.3115i	−0.615373	+	0.846989i
$248$	29.4030	+	9.55361i	1.86709	+	0.606655i
$249$	−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	$0.568520\pi$
$252$	0.784215	+	0.254807i	0.0494009	+	0.0160513i
$253$	13.3195	−	18.3327i	0.837387	−	1.15257i
$254$	−0.689703	−	0.501098i	−0.0432758	−	0.0314417i
$255$		0			0
$256$	12.1623	−	8.83640i	0.760142	−	0.552275i
$257$			14.7934i			0.922786i	0.887196	+	0.461393i	$0.152650\pi$
$257$			14.7934i			0.922786i	−0.887196	+	0.461393i	$0.847350\pi$
$258$	6.10213	+	8.39886i	0.379902	+	0.522890i
$259$	−2.53728	−	7.80894i	−0.157659	−	0.485224i
$260$		0			0
$261$	−0.698265	+	2.14904i	−0.0432215	+	0.133022i
$262$	−15.6429	+	5.08269i	−0.966422	+	0.314009i
$263$	−18.9915	+	6.17070i	−1.17106	+	0.380502i	−0.829040	−	0.559189i	$-0.811113\pi$
$263$	−18.9915	+	6.17070i	−1.17106	+	0.380502i	−0.342024	+	0.939691i	$0.611113\pi$
$264$	−3.48809	+	10.7352i	−0.214677	+	0.660709i
$265$		0			0
$266$	1.56849	+	4.82730i	0.0961700	+	0.295981i
$267$	−8.98613	−	12.3683i	−0.549942	−	0.756930i
$268$		−	1.94467i		−	0.118790i
$269$	−8.28280	+	6.01780i	−0.505011	+	0.366912i	−0.810928	−	0.585146i	$-0.801037\pi$
$269$	−8.28280	+	6.01780i	−0.505011	+	0.366912i	0.305917	+	0.952058i	$0.401037\pi$
$270$		0			0
$271$	−9.95701	−	7.23419i	−0.604845	−	0.439446i	0.242750	−	0.970089i	$-0.421950\pi$
$271$	−9.95701	−	7.23419i	−0.604845	−	0.439446i	−0.847595	+	0.530643i	$0.821950\pi$
$272$	2.45893	−	3.38442i	0.149094	−	0.205211i
$273$	−4.29202	−	1.39456i	−0.259765	−	0.0844028i
$274$	13.7950			0.833389
$275$		0			0
$276$	−4.57131			−0.275160
$277$	−30.0077	−	9.75011i	−1.80299	−	0.585827i	−0.803041	−	0.595923i	$-0.796786\pi$
$277$	−30.0077	−	9.75011i	−1.80299	−	0.585827i	−0.999949	+	0.0100963i	$0.996786\pi$
$278$	−9.71989	+	13.3783i	−0.582960	+	0.802376i
$279$	8.13227	+	5.90844i	0.486866	+	0.353729i
$280$		0			0
$281$	17.2417	−	12.5268i	1.02855	−	0.747288i	0.0605353	−	0.998166i	$-0.480719\pi$
$281$	17.2417	−	12.5268i	1.02855	−	0.747288i	0.968019	+	0.250878i	$0.0807192\pi$
$282$		−	3.51026i		−	0.209033i
$283$	0.508083	+	0.699317i	0.0302024	+	0.0415701i	0.823851	−	0.566806i	$-0.191821\pi$
$283$	0.508083	+	0.699317i	0.0302024	+	0.0415701i	−0.793649	+	0.608376i	$0.791821\pi$
$284$	0.151188	+	0.465309i	0.00897135	+	0.0276110i
$285$		0			0
$286$	5.15767	−	15.8737i	0.304979	−	0.938629i
$287$	−7.91467	+	2.57163i	−0.467188	+	0.151799i
$288$	3.74617	−	1.21720i	0.220745	−	0.0717245i
$289$	3.86138	−	11.8841i	0.227140	−	0.699066i
$290$		0			0
$291$	4.17172	+	12.8392i	0.244550	+	0.752649i
$292$	−3.25313	−	4.47755i	−0.190375	−	0.262029i
$293$			3.17701i			0.185603i	0.995685	+	0.0928014i	$0.0295822\pi$
$293$			3.17701i			0.185603i	−0.995685	+	0.0928014i	$0.970418\pi$
$294$	5.22964	−	3.79955i	0.304999	−	0.221594i
$295$		0			0
$296$	−18.3439	−	13.3276i	−1.06622	−	0.774653i
$297$	−2.15722	+	2.96915i	−0.125174	+	0.172288i
$298$	−16.7046	−	5.42766i	−0.967673	−	0.314416i
$299$	25.0188			1.44688
$300$		0			0
$301$	10.3020			0.593799
$302$	4.22498	+	1.37278i	0.243120	+	0.0789945i
$303$	4.24758	−	5.84629i	0.244017	−	0.335861i
$304$	6.47538	+	4.70464i	0.371389	+	0.269830i
$305$		0			0
$306$	1.92705	−	1.40008i	0.110162	−	0.0800375i
$307$			0.507986i			0.0289923i	0.999895	+	0.0144961i	$0.00461443\pi$
$307$			0.507986i			0.0289923i	−0.999895	+	0.0144961i	$0.995386\pi$
$308$	1.77878	+	2.44828i	0.101356	+	0.139504i
$309$	−1.63083	−	5.01918i	−0.0927747	−	0.285531i
$310$		0			0
$311$	−4.52519	+	13.9271i	−0.256600	+	0.789734i	0.736910	+	0.675991i	$0.236284\pi$
$311$	−4.52519	+	13.9271i	−0.256600	+	0.789734i	−0.993510	+	0.113743i	$0.963716\pi$
$312$	−11.8525	+	3.85112i	−0.671017	+	0.218027i
$313$	14.2241	−	4.62171i	0.803996	−	0.261234i	0.121943	−	0.992537i	$-0.461087\pi$
$313$	14.2241	−	4.62171i	0.803996	−	0.261234i	0.682053	+	0.731303i	$0.261087\pi$
$314$	−1.56090	+	4.80397i	−0.0880869	+	0.271103i
$315$		0			0
$316$	−1.95317	−	6.01125i	−0.109875	−	0.338159i
$317$	10.6501	+	14.6586i	0.598170	+	0.823310i	0.995539	−	0.0943487i	$-0.0300769\pi$
$317$	10.6501	+	14.6586i	0.598170	+	0.823310i	−0.397369	+	0.917659i	$0.630077\pi$
$318$			3.93896i			0.220886i
$319$	−6.70920	+	4.87452i	−0.375643	+	0.272921i
$320$		0			0
$321$	−4.42275	−	3.21332i	−0.246854	−	0.179350i
$322$	4.53644	−	6.24388i	0.252806	−	0.347958i
$323$	−8.19624	−	2.66312i	−0.456051	−	0.148180i
$324$	0.740367			0.0411315
$325$		0			0
$326$	2.75408			0.152534
$327$	−10.7845	−	3.50410i	−0.596385	−	0.193777i
$328$	−13.5081	+	18.5923i	−0.745860	+	1.02659i
$329$	−2.81811	−	2.04747i	−0.155367	−	0.112881i
$330$		0			0
$331$	−21.3188	+	15.4890i	−1.17178	+	0.851351i	−0.991221	−	0.132212i	$-0.957792\pi$
$331$	−21.3188	+	15.4890i	−1.17178	+	0.851351i	−0.180563	+	0.983563i	$0.557792\pi$
$332$			9.07979i			0.498318i
$333$	−4.33334	−	5.96433i	−0.237465	−	0.326843i
$334$	−1.06241	−	3.26975i	−0.0581322	−	0.178913i
$335$		0			0
$336$	−0.678387	+	2.08786i	−0.0370090	+	0.113902i
$337$	−10.1714	+	3.30488i	−0.554070	+	0.180028i	−0.572651	−	0.819799i	$-0.694085\pi$
$337$	−10.1714	+	3.30488i	−0.554070	+	0.180028i	0.0185811	+	0.999827i	$0.494085\pi$
$338$	3.64949	−	1.18579i	0.198506	−	0.0644986i
$339$	−1.49416	+	4.59855i	−0.0811516	+	0.249759i
$340$		0			0
$341$	11.4002	+	35.0861i	0.617354	+	1.90002i
$342$	2.67877	+	3.68701i	0.144851	+	0.199371i
$343$		−	14.2108i		−	0.767311i
$344$	23.0160	−	16.7221i	1.24094	−	0.901594i
$345$		0			0
$346$	10.2236	+	7.42788i	0.549624	+	0.399325i
$347$	−9.50682	+	13.0850i	−0.510353	+	0.702441i	−0.983979	−	0.178286i	$-0.942945\pi$
$347$	−9.50682	+	13.0850i	−0.510353	+	0.702441i	0.473626	+	0.880726i	$0.342945\pi$
$348$	1.59108	+	0.516973i	0.0852907	+	0.0277126i
$349$	−15.2383			−0.815688			−0.407844	−	0.913052i	$-0.633719\pi$
$349$	−15.2383			−0.815688			−0.407844	+	0.913052i	$0.633719\pi$
$350$		0			0
$351$	−4.05204			−0.216282
$352$	13.7487	+	4.46723i	0.732810	+	0.238104i
$353$	−17.3622	+	23.8970i	−0.924097	+	1.27191i	0.0380214	+	0.999277i	$0.487894\pi$
$353$	−17.3622	+	23.8970i	−0.924097	+	1.27191i	−0.962118	+	0.272633i	$0.912106\pi$
$354$	5.98710	+	4.34988i	0.318211	+	0.231194i
$355$		0			0
$356$	−9.15712	+	6.65304i	−0.485326	+	0.352610i
$357$		−	2.36372i		−	0.125101i
$358$	6.63475	+	9.13195i	0.350657	+	0.482638i
$359$	4.06875	+	12.5223i	0.214740	+	0.660903i	0.999172	+	0.0406876i	$0.0129549\pi$
$359$	4.06875	+	12.5223i	0.214740	+	0.660903i	−0.784431	+	0.620216i	$0.787045\pi$
$360$		0			0
$361$	−0.776002	+	2.38829i	−0.0408422	+	0.125699i
$362$	20.7807	−	6.75205i	1.09221	−	0.354880i
$363$	−2.34859	+	0.763104i	−0.123269	+	0.0400526i
$364$	−1.03249	+	3.17767i	−0.0541171	+	0.166555i
$365$		0			0
$366$	3.15748	+	9.71772i	0.165044	+	0.507953i
$367$	−2.28586	−	3.14622i	−0.119321	−	0.164232i	0.745178	−	0.666865i	$-0.232364\pi$
$367$	−2.28586	−	3.14622i	−0.119321	−	0.164232i	−0.864499	+	0.502634i	$0.832364\pi$
$368$		−	12.1704i		−	0.634428i
$369$	−6.04508	+	4.39201i	−0.314695	+	0.228639i
$370$		0			0
$371$	3.16227	+	2.29752i	0.164177	+	0.119281i
$372$	4.37442	−	6.02087i	0.226803	−	0.312168i
$373$	−7.74470	−	2.51641i	−0.401006	−	0.130295i	0.101569	−	0.994829i	$-0.467614\pi$
$373$	−7.74470	−	2.51641i	−0.401006	−	0.130295i	−0.502575	+	0.864534i	$0.667614\pi$
$374$	8.74200			0.452038
$375$		0			0
$376$	−9.61941			−0.496083
$377$	−8.70799	−	2.82940i	−0.448484	−	0.145721i
$378$	−0.734721	+	1.01126i	−0.0377900	+	0.0520134i
$379$	8.01509	+	5.82330i	0.411708	+	0.299123i	0.774293	−	0.632828i	$-0.218106\pi$
$379$	8.01509	+	5.82330i	0.411708	+	0.299123i	−0.362585	+	0.931951i	$0.618106\pi$
$380$		0			0
$381$	−0.614526	+	0.446479i	−0.0314831	+	0.0228738i
$382$		−	13.0292i		−	0.666632i
$383$	3.06951	+	4.22481i	0.156844	+	0.215878i	0.880206	−	0.474591i	$-0.157404\pi$
$383$	3.06951	+	4.22481i	0.156844	+	0.215878i	−0.723362	+	0.690469i	$0.757404\pi$
$384$	0.466070	+	1.43442i	0.0237840	+	0.0731997i
$385$		0			0
$386$	1.17279	−	3.60949i	0.0596937	−	0.183718i
$387$	8.79726	−	2.85840i	0.447190	−	0.145301i
$388$	9.50575	−	3.08860i	0.482581	−	0.156800i
$389$	1.15255	−	3.54719i	0.0584367	−	0.179850i	−0.917577	−	0.397557i	$-0.869858\pi$
$389$	1.15255	−	3.54719i	0.0584367	−	0.179850i	0.976014	+	0.217708i	$0.0698579\pi$
$390$		0			0
$391$	4.04938	+	12.4627i	0.204786	+	0.630267i
$392$	−10.4122	−	14.3311i	−0.525894	−	0.723831i
$393$			14.6551i			0.739253i
$394$	15.9698	−	11.6027i	0.804545	−	0.584536i
$395$		0			0
$396$	2.19826	+	1.59713i	0.110467	+	0.0802589i
$397$	−2.36032	+	3.24870i	−0.118461	+	0.163048i	−0.864130	−	0.503270i	$-0.832130\pi$
$397$	−2.36032	+	3.24870i	−0.118461	+	0.163048i	0.745668	+	0.666317i	$0.232130\pi$
$398$	−21.3590	−	6.93995i	−1.07063	−	0.347868i
$399$	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	$0.714471\pi$
$402$	2.80367	+	0.910969i	0.139835	+	0.0454350i
$403$	−23.9413	+	32.9523i	−1.19260	+	1.64147i
$404$	−4.32841	−	3.14477i	−0.215346	−	0.156458i
$405$		0			0
$406$	−2.28507	+	1.66020i	−0.113406	+	0.0823943i
$407$		−	27.0570i		−	1.34116i
$408$	−3.83675	−	5.28083i	−0.189947	−	0.261440i
$409$	7.84186	+	24.1348i	0.387755	+	1.19339i	0.934462	+	0.356063i	$0.115881\pi$
$409$	7.84186	+	24.1348i	0.387755	+	1.19339i	−0.546707	+	0.837324i	$0.684119\pi$
$410$		0			0
$411$	3.79825	−	11.6898i	0.187354	−	0.576616i
$412$	−3.71604	+	1.20741i	−0.183076	+	0.0594850i
$413$	6.98433	−	2.26935i	0.343677	−	0.111667i
$414$	2.14140	−	6.59054i	0.105244	−	0.323908i
$415$		0			0
$416$	4.93216	+	15.1796i	0.241819	+	0.744243i
$417$	8.66043	+	11.9201i	0.424103	+	0.583728i
$418$			16.7260i			0.818094i
$419$	−24.9354	+	18.1166i	−1.21817	+	0.885056i	−0.995947	−	0.0899392i	$-0.971333\pi$
$419$	−24.9354	+	18.1166i	−1.21817	+	0.885056i	−0.222227	+	0.974995i	$0.571333\pi$
$420$		0			0
$421$	−6.91425	−	5.02350i	−0.336980	−	0.244830i	0.406406	−	0.913692i	$-0.366782\pi$
$421$	−6.91425	−	5.02350i	−0.336980	−	0.244830i	−0.743387	+	0.668862i	$0.766782\pi$
$422$	1.61137	−	2.21785i	0.0784401	−	0.107963i
$423$	−2.97457	−	0.966496i	−0.144629	−	0.0469927i
$424$	10.7942			0.524212
$425$		0			0
$426$	−0.741668			−0.0359339
$427$	9.64327	+	3.13329i	0.466670	+	0.151630i
$428$	−2.37904	+	3.27446i	−0.114995	+	0.158277i
$429$	−12.0311	−	8.74113i	−0.580869	−	0.422026i
$430$		0			0
$431$	21.3431	−	15.5067i	1.02806	−	0.746929i	0.0601403	−	0.998190i	$-0.480845\pi$
$431$	21.3431	−	15.5067i	1.02806	−	0.746929i	0.967919	+	0.251261i	$0.0808452\pi$
$432$			1.97112i			0.0948356i
$433$	5.50914	+	7.58269i	0.264753	+	0.364401i	0.920609	−	0.390485i	$-0.127693\pi$
$433$	5.50914	+	7.58269i	0.264753	+	0.364401i	−0.655857	+	0.754885i	$0.727693\pi$
$434$	3.88276	+	11.9499i	0.186378	+	0.573613i
$435$		0			0
$436$	−2.59432	+	7.98450i	−0.124245	+	0.382388i
$437$	−23.8448	+	7.74765i	−1.14065	+	0.370620i
$438$	7.97928	−	2.59263i	0.381265	−	0.123880i
$439$	0.159447	−	0.490727i	0.00760998	−	0.0234211i	−0.947179	−	0.320704i	$-0.896080\pi$
$439$	0.159447	−	0.490727i	0.00760998	−	0.0234211i	0.954789	+	0.297283i	$0.0960805\pi$
$440$		0			0
$441$	−1.77981	−	5.47770i	−0.0847530	−	0.260843i
$442$	5.67320	+	7.80849i	0.269847	+	0.371412i
$443$		−	17.8348i		−	0.847357i	−0.905813	−	0.423678i	$-0.860739\pi$
$443$		−	17.8348i		−	0.847357i	0.905813	−	0.423678i	$-0.139261\pi$
$444$	−4.41579	+	3.20826i	−0.209564	+	0.152257i
$445$		0			0
$446$	−23.2779	−	16.9124i	−1.10224	−	0.800826i
$447$	−9.19872	+	12.6610i	−0.435084	+	0.598842i
$448$	8.85836	+	2.87826i	0.418518	+	0.135985i
$449$	4.16533			0.196574			0.0982870	−	0.995158i	$-0.468664\pi$
$449$	4.16533			0.196574			0.0982870	+	0.995158i	$0.468664\pi$
$450$		0			0
$451$	−27.4233			−1.29131
$452$	3.40462	+	1.10623i	0.160140	+	0.0520325i
$453$	2.32656	−	3.20224i	0.109311	−	0.150454i
$454$	−5.95944	−	4.32979i	−0.279691	−	0.203207i
$455$		0			0
$456$	10.1038	−	7.34081i	0.473152	−	0.343765i
$457$			17.6734i			0.826725i	0.910567	+	0.413362i	$0.135646\pi$
$457$			17.6734i			0.826725i	−0.910567	+	0.413362i	$0.864354\pi$
$458$	−5.25371	−	7.23112i	−0.245490	−	0.337888i
$459$	−0.655837	−	2.01846i	−0.0306119	−	0.0942136i
$460$		0			0
$461$	−0.0633350	+	0.194925i	−0.00294981	+	0.00907857i	−0.952521	−	0.304474i	$-0.901519\pi$
$461$	−0.0633350	+	0.194925i	−0.00294981	+	0.00907857i	0.949571	+	0.313553i	$0.101519\pi$
$462$	−4.36300	+	1.41762i	−0.202985	+	0.0659538i
$463$	12.1902	−	3.96084i	0.566528	−	0.184076i	−0.0117286	−	0.999931i	$-0.503733\pi$
$463$	12.1902	−	3.96084i	0.566528	−	0.184076i	0.578256	+	0.815855i	$0.303733\pi$
$464$	−1.37636	+	4.23601i	−0.0638961	+	0.196652i
$465$		0			0
$466$	3.26742	+	10.0561i	0.151360	+	0.465839i
$467$	0.654637	+	0.901030i	0.0302930	+	0.0416947i	0.823895	−	0.566743i	$-0.191797\pi$
$467$	0.654637	+	0.901030i	0.0302930	+	0.0416947i	−0.793602	+	0.608437i	$0.791797\pi$
$468$			3.00000i			0.138675i
$469$	2.36668	−	1.71949i	0.109283	−	0.0793987i
$470$		0			0
$471$	3.64107	+	2.64539i	0.167772	+	0.121893i
$472$	11.9203	−	16.4069i	0.548675	−	0.755187i
$473$	32.2866	+	10.4905i	1.48454	+	0.482356i
$474$	9.58149			0.440092
$475$		0			0
$476$	−1.75002			−0.0802120
$477$	3.33784	+	1.08453i	0.152829	+	0.0496572i
$478$	7.40380	−	10.1905i	0.338642	−	0.466101i
$479$	−20.3670	−	14.7975i	−0.930590	−	0.676113i	0.0155470	−	0.999879i	$-0.495051\pi$
$479$	−20.3670	−	14.7975i	−0.930590	−	0.676113i	−0.946137	+	0.323766i	$0.895051\pi$
$480$		0			0
$481$	24.1677	−	17.5589i	1.10195	−	0.800615i
$482$			25.4555i			1.15947i
$483$	−4.04197	−	5.56330i	−0.183916	−	0.253139i
$484$	0.564977	+	1.73882i	0.0256808	+	0.0790373i
$485$		0			0
$486$	−0.346820	+	1.06740i	−0.0157321	+	0.0484184i
$487$	9.85274	−	3.20135i	0.446470	−	0.145067i	−0.0771487	−	0.997020i	$-0.524582\pi$
$487$	9.85274	−	3.20135i	0.446470	−	0.145067i	0.523619	+	0.851953i	$0.324582\pi$
$488$	26.6301	−	8.65265i	1.20549	−	0.391687i
$489$	0.758292	−	2.33378i	0.0342912	−	0.105537i
$490$		0			0
$491$	−4.83831	−	14.8908i	−0.218350	−	0.672012i	−0.998899	−	0.0469170i	$-0.985060\pi$
$491$	−4.83831	−	14.8908i	−0.218350	−	0.672012i	0.780549	−	0.625095i	$-0.214940\pi$
$492$	3.25170	+	4.47558i	0.146598	+	0.201775i
$493$		−	4.79569i		−	0.215987i
$494$	−14.9399	+	10.8545i	−0.672178	+	0.488366i
$495$		0			0
$496$	16.0297	+	11.6463i	0.719754	+	0.522932i
$497$	−0.432601	+	0.595425i	−0.0194048	+	0.0267084i
$498$	−13.0905	−	4.25337i	−0.586600	−	0.190598i
$499$	−35.7864			−1.60202			−0.801010	−	0.598651i	$-0.795704\pi$
$499$	−35.7864			−1.60202			−0.801010	+	0.598651i	$0.795704\pi$
$500$		0			0
$501$	−3.06328			−0.136857
$502$	−7.22439	−	2.34735i	−0.322440	−	0.104767i
$503$	−6.92356	+	9.52947i	−0.308706	+	0.424898i	−0.934977	−	0.354708i	$-0.884580\pi$
$503$	−6.92356	+	9.52947i	−0.308706	+	0.424898i	0.626271	+	0.779606i	$0.284580\pi$
$504$	2.77121	+	2.01340i	0.123440	+	0.0896842i
$505$		0			0
$506$	20.5754	−	14.9489i	0.914687	−	0.664559i
$507$		−	3.41904i		−	0.151845i
$508$	0.330559	+	0.454975i	0.0146662	+	0.0201862i
$509$	−10.3986	−	32.0037i	−0.460912	−	1.41854i	−0.864052	−	0.503402i	$-0.832082\pi$
$509$	−10.3986	−	32.0037i	−0.460912	−	1.41854i	0.403141	−	0.915138i	$-0.367918\pi$
$510$		0			0
$511$	2.57276	−	7.91815i	0.113812	−	0.350278i
$512$	18.9155	−	6.14602i	0.835955	−	0.271618i
$513$	3.86190	−	1.25481i	0.170507	−	0.0554011i
$514$	−5.13064	+	15.7905i	−0.226303	+	0.696489i
$515$		0			0
$516$	−2.11627	−	6.51320i	−0.0931635	−	0.286728i
$517$	−6.74701	−	9.28647i	−0.296733	−	0.408418i
$518$		−	9.21526i		−	0.404895i
$519$	9.10923	−	6.61825i	0.399851	−	0.290509i
$520$		0			0
$521$	9.58263	+	6.96219i	0.419823	+	0.305019i	0.777566	−	0.628801i	$-0.216454\pi$
$521$	9.58263	+	6.96219i	0.419823	+	0.305019i	−0.357744	+	0.933820i	$0.616454\pi$
$522$	−1.49066	+	2.05172i	−0.0652444	+	0.0898012i
$523$	3.89642	+	1.26602i	0.170379	+	0.0553593i	0.392964	−	0.919554i	$-0.371450\pi$
$523$	3.89642	+	1.26602i	0.170379	+	0.0553593i	−0.222586	+	0.974913i	$0.571450\pi$
$524$	10.8502			0.473992
$525$		0			0
$526$	−22.4117			−0.977195
$527$	−20.2896	−	6.59250i	−0.883830	−	0.287174i
$528$	−4.25213	+	5.85256i	−0.185050	+	0.254700i
$529$	12.2347	+	8.88902i	0.531943	+	0.386479i
$530$		0			0
$531$	5.33451	−	3.87575i	0.231498	−	0.168193i
$532$		−	3.34829i		−	0.145167i
$533$	−17.7966	−	24.4949i	−0.770857	−	1.06099i
$534$	−5.30222	−	16.3186i	−0.229450	−	0.706174i
$535$		0			0
$536$	2.49639	−	7.68310i	0.107828	−	0.331859i
$537$	9.56511	−	3.10789i	0.412765	−	0.134116i
$538$	−10.9282	+	3.55078i	−0.471147	+	0.153085i
$539$	6.53205	−	20.1036i	0.281355	−	0.865922i
$540$		0			0
$541$	4.31332	+	13.2750i	0.185444	+	0.570738i	0.999956	−	0.00940920i	$-0.00299509\pi$
$541$	4.31332	+	13.2750i	0.185444	+	0.570738i	−0.814512	+	0.580147i	$0.802995\pi$
$542$	−8.11917	−	11.1751i	−0.348748	−	0.480011i
$543$		−	19.4684i		−	0.835471i
$544$	−6.76321	+	4.91376i	−0.289970	+	0.210676i
$545$		0			0
$546$	−4.09765	−	2.97712i	−0.175363	−	0.127409i
$547$	15.5789	−	21.4426i	0.666107	−	0.916818i	−0.333557	−	0.942730i	$-0.608249\pi$
$547$	15.5789	−	21.4426i	0.666107	−	0.916818i	0.999664	+	0.0259119i	$0.00824893\pi$
$548$	−8.65476	−	2.81210i	−0.369713	−	0.120127i
$549$	9.10408			0.388553
$550$		0			0
$551$	9.17556			0.390892
$552$	−18.0605	−	5.86822i	−0.768706	−	0.249768i
$553$	5.58871	−	7.69220i	0.237656	−	0.327105i
$554$	−28.6488	−	20.8146i	−1.21717	−	0.884327i
$555$		0			0
$556$	8.82522	−	6.41190i	0.374273	−	0.271925i
$557$		−	10.6860i		−	0.452781i	−0.974037	−	0.226391i	$-0.927307\pi$
$557$		−	10.6860i		−	0.452781i	0.974037	−	0.226391i	$-0.0726926\pi$
$558$	6.63124	+	9.12712i	0.280723	+	0.386382i
$559$	11.5824	+	35.6468i	0.489882	+	1.50770i
$560$		0			0
$561$	2.40697	−	7.40790i	0.101622	−	0.312762i
$562$	22.7484	−	7.39140i	0.959583	−	0.311788i
$563$	24.3232	−	7.90310i	1.02510	−	0.333076i	0.252250	−	0.967662i	$-0.418829\pi$
$563$	24.3232	−	7.90310i	1.02510	−	0.333076i	0.772852	+	0.634586i	$0.218829\pi$
$564$	−0.715563	+	2.20227i	−0.0301306	+	0.0927325i
$565$		0			0
$566$	0.299792	+	0.922666i	0.0126012	+	0.0387825i
$567$	0.654637	+	0.901030i	0.0274922	+	0.0378397i
$568$			2.03244i			0.0852794i
$569$	4.93670	−	3.58672i	0.206957	−	0.150363i	−0.479479	−	0.877554i	$-0.659174\pi$
$569$	4.93670	−	3.58672i	0.206957	−	0.150363i	0.686436	+	0.727190i	$0.259174\pi$
$570$		0			0
$571$	−19.2058	−	13.9538i	−0.803737	−	0.583949i	0.108271	−	0.994121i	$-0.465468\pi$
$571$	−19.2058	−	13.9538i	−0.803737	−	0.583949i	−0.912008	+	0.410173i	$0.865468\pi$
$572$	−6.47165	+	8.90746i	−0.270593	+	0.372440i
$573$	−11.0408	−	3.58739i	−0.461238	−	0.149865i
$574$	−9.34003			−0.389845
$575$		0			0
$576$	8.36307			0.348461
$577$	42.0024	+	13.6474i	1.74858	+	0.568149i	0.995919	−	0.0902565i	$-0.0287687\pi$
$577$	42.0024	+	13.6474i	1.74858	+	0.568149i	0.752664	+	0.658405i	$0.228769\pi$
$578$	8.24330	−	11.3459i	0.342876	−	0.471929i
$579$	−2.73574	−	1.98763i	−0.113694	−	0.0826032i
$580$		0			0
$581$	−11.0501	+	8.02840i	−0.458437	+	0.333074i
$582$			15.1515i			0.628048i
$583$	7.57100	+	10.4206i	0.313559	+	0.431576i
$584$	−7.10475	−	21.8662i	−0.293997	−	0.904828i
$585$		0			0
$586$	−1.10185	+	3.39115i	−0.0455170	+	0.140087i
$587$	0.486909	−	0.158206i	0.0200969	−	0.00652987i	−0.298951	−	0.954268i	$-0.596637\pi$
$587$	0.486909	−	0.158206i	0.0200969	−	0.00652987i	0.319048	+	0.947738i	$0.396637\pi$
$588$	−4.05551	+	1.31772i	−0.167246	+	0.0543417i
$589$	12.6134	−	38.8200i	0.519725	−	1.59955i
$590$		0			0
$591$	−5.43502	−	16.7273i	−0.223567	−	0.688068i
$592$	−8.54153	−	11.7564i	−0.351055	−	0.483186i
$593$		−	18.8405i		−	0.773687i	−0.922145	−	0.386844i	$-0.873565\pi$
$593$		−	18.8405i		−	0.773687i	0.922145	−	0.386844i	$-0.126435\pi$
$594$	−3.33238	+	2.42112i	−0.136729	+	0.0993396i
$595$		0			0
$596$	9.37376	+	6.81043i	0.383964	+	0.278966i
$597$	−11.7617	+	16.1886i	−0.481375	+	0.662556i
$598$	26.7052	+	8.67703i	1.09206	+	0.354830i
$599$	−6.20712			−0.253616			−0.126808	−	0.991927i	$-0.540473\pi$
$599$	−6.20712			−0.253616			−0.126808	+	0.991927i	$0.540473\pi$
$600$		0			0
$601$	34.0303			1.38813			0.694063	−	0.719915i	$-0.255819\pi$
$601$	34.0303			1.38813			0.694063	+	0.719915i	$0.255819\pi$
$602$	10.9964	+	3.57295i	0.448180	+	0.145623i
$603$	1.54390	−	2.12499i	0.0628723	−	0.0865363i
$604$	−2.37083	−	1.72251i	−0.0964679	−	0.0700880i
$605$		0			0
$606$	6.56149	−	4.76720i	0.266542	−	0.193654i
$607$		−	16.2488i		−	0.659518i	−0.944065	−	0.329759i	$-0.893032\pi$
$607$		−	16.2488i		−	0.659518i	0.944065	−	0.329759i	$-0.106968\pi$
$608$	−9.40144	−	12.9400i	−0.381279	−	0.524785i
$609$	0.777682	+	2.39346i	0.0315132	+	0.0969878i
$610$		0			0
$611$	3.91628	−	12.0531i	0.158436	−	0.487615i
$612$	−1.49440	+	0.485560i	−0.0604076	+	0.0196276i
$613$	0.0646578	−	0.0210086i	0.00261150	−	0.000848529i	−0.307711	−	0.951480i	$-0.599563\pi$
$613$	0.0646578	−	0.0210086i	0.00261150	−	0.000848529i	0.310322	+	0.950631i	$0.399563\pi$
$614$	−0.176180	+	0.542225i	−0.00711004	+	0.0218824i
$615$		0			0
$616$	3.88481	+	11.9562i	0.156523	+	0.481730i
$617$	19.2857	+	26.5445i	0.776413	+	1.06864i	0.995669	+	0.0929733i	$0.0296371\pi$
$617$	19.2857	+	26.5445i	0.776413	+	1.06864i	−0.219256	+	0.975667i	$0.570363\pi$
$618$		−	5.92309i		−	0.238262i
$619$	−5.48280	+	3.98349i	−0.220372	+	0.160110i	−0.692494	−	0.721423i	$-0.743488\pi$
$619$	−5.48280	+	3.98349i	−0.220372	+	0.160110i	0.472122	+	0.881533i	$0.343488\pi$
$620$		0			0
$621$	−4.99517	−	3.62921i	−0.200449	−	0.145635i
$622$	−9.66040	+	13.2964i	−0.387347	+	0.533137i
$623$	−16.1935	−	5.26160i	−0.648780	−	0.210802i
$624$	−7.98706			−0.319738
$625$		0			0
$626$	16.7858			0.670895
$627$	14.1735	+	4.60524i	0.566034	+	0.183915i
$628$	1.95856	−	2.69573i	0.0781552	−	0.107571i
$629$	12.6583	+	9.19679i	0.504719	+	0.366700i
$630$		0			0
$631$	6.20352	−	4.50712i	0.246958	−	0.179426i	−0.457419	−	0.889251i	$-0.651226\pi$
$631$	6.20352	−	4.50712i	0.246958	−	0.179426i	0.704378	+	0.709825i	$0.251226\pi$
$632$		−	26.2568i		−	1.04444i
$633$	−1.43573	−	1.97611i	−0.0570651	−	0.0785433i
$634$	6.28405	+	19.3403i	0.249572	+	0.768102i
$635$		0			0
$636$	0.802951	−	2.47123i	0.0318391	−	0.0979906i
$637$	22.1959	−	7.21188i	0.879432	−	0.285745i
$638$	−8.85199	+	2.87619i	−0.350454	+	0.113869i
$639$	−0.204207	+	0.628483i	−0.00807829	+	0.0248624i
$640$		0			0
$641$	−7.32096	−	22.5316i	−0.289161	−	0.889945i	−0.985121	−	0.171864i	$-0.945021\pi$
$641$	−7.32096	−	22.5316i	−0.289161	−	0.889945i	0.695960	−	0.718081i	$-0.254979\pi$
$642$	−3.60641	−	4.96380i	−0.142334	−	0.195906i
$643$			2.16861i			0.0855218i	0.999085	+	0.0427609i	$0.0136154\pi$
$643$			2.16861i			0.0855218i	−0.999085	+	0.0427609i	$0.986385\pi$
$644$	−4.11889	+	2.99255i	−0.162307	+	0.117923i
$645$		0			0
$646$	−7.82506	−	5.68524i	−0.307873	−	0.223683i
$647$	−1.50203	+	2.06737i	−0.0590510	+	0.0812767i	−0.837521	−	0.546405i	$-0.815996\pi$
$647$	−1.50203	+	2.06737i	−0.0590510	+	0.0812767i	0.778470	+	0.627682i	$0.215996\pi$
$648$	2.92508	+	0.950415i	0.114908	+	0.0373358i
$649$	24.1998			0.949926
$650$		0			0
$651$	11.1953			0.438779
$652$	−1.72786	−	0.561415i	−0.0676681	−	0.0219867i
$653$	19.0523	−	26.2233i	0.745575	−	1.02620i	−0.252704	−	0.967544i	$-0.581320\pi$
$653$	19.0523	−	26.2233i	0.745575	−	1.02620i	0.998279	−	0.0586517i	$-0.0186801\pi$
$654$	−10.2961	−	7.48057i	−0.402610	−	0.292513i
$655$		0			0
$656$	−11.9156	+	8.65719i	−0.465226	+	0.338006i
$657$		−	7.47542i		−	0.291644i
$658$	−2.29795	−	3.16285i	−0.0895833	−	0.123301i
$659$	−0.139043	−	0.427929i	−0.00541633	−	0.0166697i	0.948312	−	0.317340i	$-0.102790\pi$
$659$	−0.139043	−	0.427929i	−0.00541633	−	0.0166697i	−0.953728	+	0.300670i	$0.902790\pi$
$660$		0			0
$661$	−8.33812	+	25.6621i	−0.324315	+	0.998140i	0.647433	+	0.762122i	$0.275842\pi$
$661$	−8.33812	+	25.6621i	−0.324315	+	0.998140i	−0.971749	+	0.236018i	$0.924158\pi$
$662$	−28.1276	+	9.13921i	−1.09321	+	0.355205i
$663$	8.17888	−	2.65748i	0.317641	−	0.103208i
$664$	−11.6558	+	35.8728i	−0.452332	+	1.39214i
$665$		0			0
$666$	−2.55687	−	7.86923i	−0.0990766	−	0.304926i
$667$	−8.20067	−	11.2873i	−0.317531	−	0.437044i
$668$			2.26795i			0.0877496i
$669$	−20.7407	+	15.0690i	−0.801880	+	0.582600i
$670$		0			0
$671$	27.0314	+	19.6395i	1.04354	+	0.758174i
$672$	2.57859	−	3.54912i	0.0994711	−	0.136910i
$673$	16.7599	+	5.44561i	0.646046	+	0.209913i	0.613670	−	0.789563i	$-0.289693\pi$
$673$	16.7599	+	5.44561i	0.646046	+	0.209913i	0.0323758	+	0.999476i	$0.489693\pi$
$674$	−12.0032			−0.462344
$675$		0			0
$676$	−2.53135			−0.0973595
$677$	18.4014	+	5.97899i	0.707225	+	0.229791i	0.640476	−	0.767978i	$-0.278737\pi$
$677$	18.4014	+	5.97899i	0.707225	+	0.229791i	0.0667494	+	0.997770i	$0.478737\pi$
$678$	−3.18974	+	4.39030i	−0.122501	+	0.168608i
$679$	12.1639	+	8.83757i	0.466807	+	0.339155i
$680$		0			0
$681$	−5.30987	+	3.85784i	−0.203475	+	0.147833i
$682$			41.4049i			1.58547i
$683$	17.6018	+	24.2268i	0.673515	+	0.927015i	0.999834	−	0.0182455i	$-0.00580805\pi$
$683$	17.6018	+	24.2268i	0.673515	+	0.927015i	−0.326318	+	0.945260i	$0.605808\pi$
$684$	−0.929018	−	2.85922i	−0.0355219	−	0.109325i
$685$		0			0
$686$	4.92859	−	15.1686i	0.188175	−	0.579142i
$687$	−7.57412	+	2.46098i	−0.288971	+	0.0938923i
$688$	17.3405	−	5.63426i	0.661099	−	0.214804i
$689$	−4.39456	+	13.5251i	−0.167419	+	0.515264i
$690$		0			0
$691$	−6.16024	−	18.9593i	−0.234346	−	0.721244i	−0.997207	−	0.0746817i	$-0.976206\pi$
$691$	−6.16024	−	18.9593i	−0.234346	−	0.721244i	0.762861	−	0.646563i	$-0.223794\pi$
$692$	−4.89993	−	6.74418i	−0.186268	−	0.256375i
$693$			4.08749i			0.155271i
$694$	−14.6858	+	10.6698i	−0.557464	+	0.405021i
$695$		0			0
$696$	5.62246	+	4.08495i	0.213119	+	0.154840i
$697$	9.32131	−	12.8297i	0.353070	−	0.485959i
$698$	−16.2654	−	5.28495i	−0.615655	−	0.200038i
$699$	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	$0.876469\pi$
$702$	−4.32516	−	1.40533i	−0.163243	−	0.0530407i
$703$	−17.5961	+	24.2190i	−0.663651	+	0.913437i
$704$	24.8312	+	18.0409i	0.935862	+	0.679944i
$705$		0			0
$706$	−26.8204	+	19.4862i	−1.00940	+	0.733372i
$707$		−	8.04831i		−	0.302688i
$708$	−2.86948	−	3.94950i	−0.107842	−	0.148431i
$709$	1.48744	+	4.57788i	0.0558621	+	0.171926i	0.975095	−	0.221789i	$-0.0711897\pi$
$709$	1.48744	+	4.57788i	0.0558621	+	0.171926i	−0.919233	+	0.393715i	$0.871190\pi$
$710$		0			0
$711$	2.63811	−	8.11928i	0.0989370	−	0.304497i
$712$	−44.7189	+	14.5300i	−1.67591	+	0.544536i
$713$	−59.0274	+	19.1792i	−2.21059	+	0.718265i
$714$	0.819784	−	2.52304i	0.0306797	−	0.0944223i
$715$		0			0
$716$	−2.30098	−	7.08170i	−0.0859918	−	0.264656i
$717$	−6.59679	−	9.07970i	−0.246362	−	0.339088i
$718$			14.7775i			0.551491i
$719$	26.0917	−	18.9568i	0.973058	−	0.706968i	0.0169113	−	0.999857i	$-0.494617\pi$
$719$	26.0917	−	18.9568i	0.973058	−	0.706968i	0.956146	+	0.292889i	$0.0946167\pi$
$720$		0			0
$721$	−4.75517	−	3.45483i	−0.177092	−	0.128665i
$722$	−1.65661	+	2.28013i	−0.0616528	+	0.0848578i
$723$	21.5708	+	7.00879i	0.802228	+	0.260660i
$724$	−14.4138			−0.535685
$725$		0			0
$726$	−2.77155			−0.102862
$727$	27.7468	+	9.01548i	1.02907	+	0.334366i	0.774423	−	0.632668i	$-0.218040\pi$
$727$	27.7468	+	9.01548i	1.02907	+	0.334366i	0.254648	+	0.967034i	$0.418040\pi$
$728$	−8.15840	+	11.2291i	−0.302370	+	0.416177i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	−15.8823	+	11.5391i	−0.587426	+	0.426790i
$732$		−	6.74037i		−	0.249131i
$733$	−3.05708	−	4.20771i	−0.112916	−	0.155415i	0.748818	−	0.662775i	$-0.230622\pi$
$733$	−3.05708	−	4.20771i	−0.112916	−	0.155415i	−0.861734	+	0.507360i	$0.830622\pi$
$734$	−1.34876	−	4.15107i	−0.0497838	−	0.153219i
$735$		0			0
$736$	−7.51548	+	23.1303i	−0.277024	+	0.852593i
$737$	9.16813	−	2.97891i	0.337712	−	0.109729i
$738$	−7.97578	+	2.59149i	−0.293592	+	0.0953940i
$739$	5.04334	−	15.5218i	0.185522	−	0.570979i	−0.814435	−	0.580255i	$-0.802953\pi$
$739$	5.04334	−	15.5218i	0.185522	−	0.570979i	0.999957	+	0.00927620i	$0.00295275\pi$
$740$		0			0
$741$	5.08453	+	15.6486i	0.186785	+	0.574865i
$742$	2.57859	+	3.54912i	0.0946629	+	0.130292i
$743$			53.4487i			1.96084i	0.196914	+	0.980421i	$0.436908\pi$
$743$			53.4487i			1.96084i	−0.196914	+	0.980421i	$0.563092\pi$
$744$	25.0117	−	18.1720i	0.916972	−	0.666219i
$745$		0			0
$746$	−7.39398	−	5.37204i	−0.270713	−	0.196684i
$747$	−7.20854	+	9.92170i	−0.263747	+	0.363016i
$748$	−5.48457	−	1.78204i	−0.200536	−	0.0651580i
$749$	−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	$0.503293\pi$
$752$	−5.86324	−	1.90508i	−0.213810	−	0.0694712i
$753$	−3.97824	+	5.47558i	−0.144975	+	0.199541i
$754$	−8.31364	−	6.04021i	−0.302765	−	0.219972i
$755$		0			0
$756$	0.667093	−	0.484672i	0.0242620	−	0.0176273i
$757$		−	53.0708i		−	1.92889i	−0.264282	−	0.964445i	$-0.585135\pi$
$757$		−	53.0708i		−	1.92889i	0.264282	−	0.964445i	$-0.414865\pi$
$758$	6.53569	+	8.99560i	0.237387	+	0.326735i
$759$	−7.00246	−	21.5513i	−0.254173	−	0.782264i
$760$		0			0
$761$	−8.49970	+	26.1594i	−0.308114	+	0.948277i	0.670383	+	0.742015i	$0.266130\pi$
$761$	−8.49970	+	26.1594i	−0.308114	+	0.948277i	−0.978497	+	0.206262i	$0.933870\pi$
$762$	−0.810794	+	0.263443i	−0.0293720	+	0.00954353i
$763$	−12.0111	+	3.90264i	−0.434830	+	0.141285i
$764$	−2.65599	+	8.17428i	−0.0960902	+	0.295735i
$765$		0			0
$766$	1.81115	+	5.57414i	0.0654394	+	0.201402i
$767$	15.7047	+	21.6157i	0.567064	+	0.780496i
$768$		−	15.0334i		−	0.542471i
$769$	12.1123	−	8.80007i	0.436779	−	0.317339i	−0.347575	−	0.937652i	$-0.612995\pi$
$769$	12.1123	−	8.80007i	0.436779	−	0.317339i	0.784354	+	0.620314i	$0.212995\pi$
$770$		0			0
$771$	11.9681	+	8.69533i	0.431021	+	0.313155i
$772$	−1.47158	+	2.02546i	−0.0529633	+	0.0728977i
$773$	−1.95373	−	0.634806i	−0.0702708	−	0.0228324i	0.273671	−	0.961823i	$-0.411762\pi$
$773$	−1.95373	−	0.634806i	−0.0702708	−	0.0228324i	−0.343941	+	0.938991i	$0.611762\pi$
$774$	10.3816			0.373158
$775$		0			0
$776$	41.5206			1.49050
$777$	−7.80894	−	2.53728i	−0.280144	−	0.0910243i
$778$	2.46048	−	3.38655i	0.0882123	−	0.121414i
$779$	24.5469	+	17.8344i	0.879485	+	0.638983i
$780$		0			0
$781$	−1.96210	+	1.42555i	−0.0702093	+	0.0510100i
$782$			14.7072i			0.525927i
$783$	1.32818	+	1.82808i	0.0474652	+	0.0653303i
$784$	−3.50823	−	10.7972i	−0.125294	−	0.385615i
$785$		0			0
$786$	−5.08269	+	15.6429i	−0.181293	+	0.557964i
$787$	−16.0034	+	5.19981i	−0.570458	+	0.185353i	−0.580022	−	0.814601i	$-0.696956\pi$
$787$	−16.0034	+	5.19981i	−0.570458	+	0.185353i	0.00956327	+	0.999954i	$0.496956\pi$
$788$	−12.3843	+	4.02391i	−0.441174	+	0.143346i
$789$	−6.17070	+	18.9915i	−0.219683	+	0.676114i
$790$		0			0
$791$	1.66410	+	5.12156i	0.0591685	+	0.182102i
$792$	6.63475	+	9.13195i	0.235756	+	0.324490i
$793$			36.8901i			1.31001i
$794$	−3.64613	+	2.64907i	−0.129396	+	0.0940118i
$795$		0			0
$796$	11.9855	+	8.70799i	0.424816	+	0.308647i
$797$	0.122783	−	0.168996i	0.00434920	−	0.00598616i	−0.806837	−	0.590774i	$-0.798822\pi$
$797$	0.122783	−	0.168996i	0.00434920	−	0.00598616i	0.811186	+	0.584788i	$0.198822\pi$
$798$	4.82730	+	1.56849i	0.170885	+	0.0555238i
$799$	6.63791			0.234832
$800$		0			0
$801$	−15.2881			−0.540179
$802$	−26.6733	−	8.66668i	−0.941867	−	0.306031i
$803$	16.1261	−	22.1957i	0.569078	−	0.783268i
$804$	−1.57327	−	1.14305i	−0.0554851	−	0.0403123i
$805$		0			0
$806$	−36.9835	+	26.8701i	−1.30269	+	0.946458i
$807$			10.2381i			0.360398i
$808$	−13.0639	−	17.9809i	−0.459586	−	0.632566i
$809$	5.24264	+	16.1352i	0.184321	+	0.567283i	0.999936	−	0.0113128i	$-0.00360104\pi$
$809$	5.24264	+	16.1352i	0.184321	+	0.567283i	−0.815615	+	0.578595i	$0.803601\pi$
$810$		0			0
$811$	−6.32508	+	19.4666i	−0.222103	+	0.683564i	0.776469	+	0.630155i	$0.217009\pi$
$811$	−6.32508	+	19.4666i	−0.222103	+	0.683564i	−0.998573	+	0.0534090i	$0.982991\pi$
$812$	1.77204	−	0.575770i	0.0621864	−	0.0202056i
$813$	−11.7052	+	3.80324i	−0.410518	+	0.133385i
$814$	9.38390	−	28.8807i	0.328905	−	1.01227i
$815$		0			0
$816$	−1.29273	−	3.97863i	−0.0452548	−	0.139280i
$817$	−22.0777	−	30.3874i	−0.772401	−	1.06312i
$818$			28.4812i			0.995822i
$819$	−3.65101	+	2.65262i	−0.127577	+	0.0926899i
$820$		0			0
$821$	−31.0368	−	22.5496i	−1.08319	−	0.786985i	−0.104955	−	0.994477i	$-0.533470\pi$
$821$	−31.0368	−	22.5496i	−1.08319	−	0.786985i	−0.978237	+	0.207492i	$0.933470\pi$
$822$	8.10852	−	11.1604i	0.282817	−	0.389265i
$823$	−27.5899	−	8.96451i	−0.961725	−	0.312483i	−0.214254	−	0.976778i	$-0.568732\pi$
$823$	−27.5899	−	8.96451i	−0.961725	−	0.312483i	−0.747471	+	0.664295i	$0.768732\pi$
$824$	−16.2315			−0.565449
$825$		0			0
$826$	8.24215			0.286781
$827$	−13.6541	−	4.43648i	−0.474799	−	0.154271i	0.0618356	−	0.998086i	$-0.480305\pi$
$827$	−13.6541	−	4.43648i	−0.474799	−	0.154271i	−0.536634	+	0.843815i	$0.680305\pi$
$828$	−2.68695	+	3.69826i	−0.0933779	+	0.128524i
$829$	3.75031	+	2.72476i	0.130254	+	0.0946347i	0.651004	−	0.759074i	$-0.274348\pi$
$829$	3.75031	+	2.72476i	0.130254	+	0.0946347i	−0.520751	+	0.853709i	$0.674348\pi$
$830$		0			0
$831$	−25.5261	+	18.5458i	−0.885491	+	0.643347i
$832$			33.8875i			1.17484i
$833$	7.18496	+	9.88925i	0.248944	+	0.342642i
$834$	5.11005	+	15.7271i	0.176946	+	0.544585i
$835$		0			0
$836$	3.40957	−	10.4936i	0.117922	−	0.362928i
$837$	9.56006	−	3.10625i	0.330444	−	0.107368i
$838$	−32.8993	+	10.6896i	−1.13649	+	0.369268i
$839$	−1.52235	+	4.68531i	−0.0525573	+	0.161755i	−0.973890	−	0.227020i	$-0.927102\pi$
$839$	−1.52235	+	4.68531i	−0.0525573	+	0.161755i	0.921333	+	0.388775i	$0.127102\pi$
$840$		0			0
$841$	−7.38367	−	22.7246i	−0.254609	−	0.783607i
$842$	−5.63804	−	7.76010i	−0.194300	−	0.267431i
$843$		−	21.3119i		−	0.734022i
$844$	−1.46305	+	1.06297i	−0.0503602	+	0.0365888i
$845$		0			0
$846$	−2.83986	−	2.06328i	−0.0976365	−	0.0709371i
$847$	−1.61660	+	2.22505i	−0.0555469	+	0.0764538i
$848$	6.57929	+	2.13774i	0.225934	+	0.0734103i
$849$	0.864403			0.0296662
$850$		0			0
$851$	45.5194			1.56039
$852$	0.465309	+	0.151188i	0.0159412	+	0.00517961i
$853$	31.5333	−	43.4018i	1.07968	−	1.48605i	0.219805	−	0.975544i	$-0.429458\pi$
$853$	31.5333	−	43.4018i	1.07968	−	1.48605i	0.859874	−	0.510507i	$-0.170542\pi$
$854$	9.20656	+	6.68896i	0.315042	+	0.228891i
$855$		0			0
$856$	−13.6026	+	9.88290i	−0.464929	+	0.337790i
$857$			27.1144i			0.926210i	0.886303	+	0.463105i	$0.153265\pi$
$857$			27.1144i			0.926210i	−0.886303	+	0.463105i	$0.846735\pi$
$858$	−9.81046	−	13.5029i	−0.334924	−	0.460983i
$859$	−3.21966	−	9.90910i	−0.109853	−	0.338094i	0.880985	−	0.473143i	$-0.156881\pi$
$859$	−3.21966	−	9.90910i	−0.109853	−	0.338094i	−0.990839	+	0.135049i	$0.956881\pi$
$860$		0			0
$861$	−2.57163	+	7.91467i	−0.0876410	+	0.269731i
$862$	28.1597	−	9.14963i	0.959122	−	0.311638i
$863$	41.5072	−	13.4865i	1.41292	−	0.459086i	0.499575	−	0.866271i	$-0.333490\pi$
$863$	41.5072	−	13.4865i	1.41292	−	0.459086i	0.913346	+	0.407185i	$0.133490\pi$
$864$	1.21720	−	3.74617i	0.0414101	−	0.127447i
$865$		0			0
$866$	3.25065	+	10.0045i	0.110461	+	0.339965i
$867$	−7.34479	−	10.1092i	−0.249442	−	0.343328i
$868$		−	8.28864i		−	0.281335i
$869$	25.3480	−	18.4164i	0.859872	−	0.624734i
$870$		0			0
$871$	8.61055	+	6.25593i	0.291757	+	0.211974i
$872$	−20.4995	+	28.2151i	−0.694201	+	0.955485i
$873$	12.8392	+	4.17172i	0.434542	+	0.141191i
$874$	−28.1391			−0.951818
$875$		0			0
$876$	−5.53456			−0.186995
$877$	−51.0180	−	16.5767i	−1.72275	−	0.559757i	−0.730383	−	0.683038i	$-0.760658\pi$
$877$	−51.0180	−	16.5767i	−1.72275	−	0.559757i	−0.992372	+	0.123281i	$0.960658\pi$
$878$	0.340388	−	0.468503i	0.0114875	−	0.0158112i
$879$	2.57025	+	1.86740i	0.0866925	+	0.0629858i
$880$		0			0
$881$	44.4110	−	32.2665i	1.49625	−	1.08709i	0.524398	−	0.851473i	$-0.324290\pi$
$881$	44.4110	−	32.2665i	1.49625	−	1.08709i	0.971847	−	0.235613i	$-0.0757097\pi$
$882$		−	6.46419i		−	0.217661i
$883$	11.2239	+	15.4483i	0.377713	+	0.519877i	0.954977	−	0.296681i	$-0.0958796\pi$
$883$	11.2239	+	15.4483i	0.377713	+	0.519877i	−0.577264	+	0.816558i	$0.695880\pi$
$884$	−1.96751	−	6.05538i	−0.0661746	−	0.203664i
$885$		0			0
$886$	6.18547	−	19.0369i	0.207805	−	0.639558i
$887$	−10.6672	+	3.46598i	−0.358170	+	0.116376i	−0.482574	−	0.875855i	$-0.660298\pi$
$887$	−10.6672	+	3.46598i	−0.358170	+	0.116376i	0.124404	+	0.992232i	$0.460298\pi$
$888$	−21.5646	+	7.00676i	−0.723660	+	0.235131i
$889$	−0.261425	+	0.804582i	−0.00876790	+	0.0269848i
$890$		0			0
$891$	1.13412	+	3.49045i	0.0379943	+	0.116934i
$892$	11.1566	+	15.3557i	0.373550	+	0.514147i
$893$			12.7003i			0.424998i
$894$	−14.2098	+	10.3240i	−0.475247	+	0.345287i
$895$		0			0
$896$	1.35896	+	0.987345i	0.0453998	+	0.0329849i
$897$	14.7057	−	20.2407i	0.491009	−	0.675816i
$898$	4.44608	+	1.44462i	0.148368	+	0.0482076i
$899$	22.7139			0.757552
$900$		0			0
$901$	−7.44857			−0.248148
$902$	−29.2717	−	9.51095i	−0.974641	−	0.316680i
$903$	6.05538	−	8.33451i	0.201510	−	0.277355i
$904$	12.0310	+	8.74106i	0.400146	+	0.290723i
$905$		0			0
$906$	3.59398	−	2.61118i	0.119402	−	0.0867506i
$907$			36.4513i			1.21034i	0.796095	+	0.605172i	$0.206896\pi$
$907$			36.4513i			1.21034i	−0.796095	+	0.605172i	$0.793104\pi$
$908$	2.85622	+	3.93125i	0.0947871	+	0.130463i
$909$	−2.23309	−	6.87273i	−0.0740668	−	0.227954i
$910$		0			0
$911$	0.360106	−	1.10829i	0.0119309	−	0.0367194i	−0.944914	−	0.327319i	$-0.893855\pi$
$911$	0.360106	−	1.10829i	0.0119309	−	0.0367194i	0.956845	+	0.290600i	$0.0938548\pi$
$912$	7.61227	−	2.47338i	0.252067	−	0.0819017i
$913$	−42.8065	+	13.9087i	−1.41669	+	0.460310i
$914$	−6.12948	+	18.8646i	−0.202745	+	0.623985i
$915$		0			0
$916$	1.82203	+	5.60763i	0.0602016	+	0.185281i
$917$	9.59377	+	13.2047i	0.316814	+	0.436057i
$918$		−	2.38197i		−	0.0786166i
$919$	35.5543	−	25.8317i	1.17283	−	0.852109i	0.181482	−	0.983394i	$-0.441911\pi$
$919$	35.5543	−	25.8317i	1.17283	−	0.852109i	0.991345	+	0.131286i	$0.0419105\pi$
$920$		0			0
$921$	0.410969	+	0.298587i	0.0135419	+	0.00983876i
$922$	−0.135208	+	0.186098i	−0.00445283	+	0.00612880i
$923$	−2.54664	−	0.827454i	−0.0838237	−	0.0272360i
$924$	3.02624			0.0995561
$925$		0			0
$926$	14.3856			0.472739
$927$	−5.01918	−	1.63083i	−0.164852	−	0.0535635i
$928$	5.23164	−	7.20073i	0.171737	−	0.236376i
$929$	25.2512	+	18.3460i	0.828464	+	0.601914i	0.919124	−	0.393968i	$-0.128898\pi$
$929$	25.2512	+	18.3460i	0.828464	+	0.601914i	−0.0906606	+	0.995882i	$0.528898\pi$
$930$		0			0
$931$	−18.9210	+	13.7469i	−0.620111	+	0.450537i
$932$		−	6.97506i		−	0.228476i
$933$	8.60743	+	11.8471i	0.281795	+	0.387857i
$934$	0.386266	+	1.18880i	0.0126390	+	0.0388988i
$935$		0			0
$936$	−3.85112	+	11.8525i	−0.125878	+	0.387412i
$937$	−42.8983	+	13.9385i	−1.40143	+	0.455351i	−0.909652	−	0.415371i	$-0.863652\pi$
$937$	−42.8983	+	13.9385i	−1.40143	+	0.455351i	−0.491775	+	0.870722i	$0.663652\pi$
$938$	3.12255	−	1.01458i	0.101955	−	0.0331271i
$939$	4.62171	−	14.2241i	0.150824	−	0.464188i
$940$		0			0
$941$	−12.0931	−	37.2187i	−0.394224	−	1.21330i	−0.929565	−	0.368659i	$-0.879817\pi$
$941$	−12.0931	−	37.2187i	−0.394224	−	1.21330i	0.535341	−	0.844636i	$-0.320183\pi$
$942$	2.96901	+	4.08650i	0.0967357	+	0.133145i
$943$		−	46.1358i		−	1.50239i
$944$	10.5150	−	7.63957i	0.342233	−	0.248647i
$945$		0			0
$946$	30.8245	+	22.3953i	1.00219	+	0.728133i
$947$	28.7155	−	39.5235i	0.933128	−	1.28434i	−0.0254991	−	0.999675i	$-0.508117\pi$
$947$	28.7155	−	39.5235i	0.933128	−	1.28434i	0.958627	−	0.284665i	$-0.0918825\pi$
$948$	−6.01125	−	1.95317i	−0.195236	−	0.0634361i
$949$	30.2907			0.983278
$950$		0			0
$951$	18.1190			0.587550
$952$	−6.91405	−	2.24651i	−0.224086	−	0.0728098i
$953$	13.3912	−	18.4314i	0.433783	−	0.597051i	−0.535034	−	0.844831i	$-0.679701\pi$
$953$	13.3912	−	18.4314i	0.433783	−	0.597051i	0.968816	+	0.247780i	$0.0797010\pi$
$954$	3.18668	+	2.31526i	0.103173	+	0.0749593i
$955$		0			0
$956$	−6.72232	+	4.88405i	−0.217415	+	0.157961i
$957$			8.29302i			0.268075i
$958$	−16.6077	−	22.8585i	−0.536570	−	0.738525i
$959$	−4.23024	−	13.0193i	−0.136602	−	0.420417i
$960$		0			0
$961$	21.6446	−	66.6154i	0.698214	−	2.14888i
$962$	31.8864	−	10.3605i	1.02806	−	0.334037i
$963$	−5.19926	+	1.68934i	−0.167544	+	0.0544382i
$964$	5.18908	−	15.9703i	0.167129	−	0.514370i
$965$		0			0
$966$	−2.38495	−	7.34012i	−0.0767345	−	0.236164i
$967$	25.3880	+	34.9436i	0.816425	+	1.12371i	0.990300	+	0.138944i	$0.0443709\pi$
$967$	25.3880	+	34.9436i	0.816425	+	1.12371i	−0.173876	+	0.984768i	$0.555629\pi$
$968$			7.59507i			0.244115i
$969$	−6.97214	+	5.06555i	−0.223977	+	0.162729i
$970$		0			0
$971$	25.9089	+	18.8239i	0.831457	+	0.604089i	0.919971	−	0.391986i	$-0.128212\pi$
$971$	25.9089	+	18.8239i	0.831457	+	0.604089i	−0.0885142	+	0.996075i	$0.528212\pi$
$972$	0.435177	−	0.598970i	0.0139583	−	0.0192120i
$973$	15.6066	+	5.07090i	0.500325	+	0.162565i
$974$	11.6271			0.372557
$975$		0			0
$976$	17.9452			0.574413
$977$	6.91428	+	2.24659i	0.221208	+	0.0718747i	0.417524	−	0.908666i	$-0.362898\pi$
$977$	6.91428	+	2.24659i	0.221208	+	0.0718747i	−0.196316	+	0.980541i	$0.562898\pi$
$978$	1.61881	−	2.22810i	0.0517637	−	0.0712467i
$979$	−45.3927	−	32.9798i	−1.45076	−	1.05404i
$980$		0			0
$981$	−9.17385	+	6.66519i	−0.292898	+	0.212803i
$982$		−	17.5725i		−	0.560760i
$983$	2.99274	+	4.11915i	0.0954535	+	0.131380i	0.854072	−	0.520154i	$-0.174126\pi$
$983$	2.99274	+	4.11915i	0.0954535	+	0.131380i	−0.758619	+	0.651535i	$0.774126\pi$
$984$	7.10163	+	21.8566i	0.226392	+	0.696762i
$985$		0			0
$986$	1.66324	−	5.11894i	0.0529685	−	0.163020i
$987$	−3.31288	+	1.07642i	−0.105450	+	0.0342628i
$988$	11.5857	−	3.76442i	0.368590	−	0.119762i
$989$	−17.6488	+	54.3176i	−0.561201	+	1.72720i
$990$		0			0
$991$	−19.1826	−	59.0380i	−0.609356	−	1.87540i	−0.463497	−	0.886098i	$-0.653406\pi$
$991$	−19.1826	−	59.0380i	−0.609356	−	1.87540i	−0.145859	−	0.989305i	$-0.546594\pi$
$992$	−23.2731	−	32.0327i	−0.738922	−	1.01704i
$993$			26.3514i			0.836237i
$994$	−0.668265	+	0.485523i	−0.0211961	+	0.0153999i
$995$		0			0
$996$	7.34570	+	5.33697i	0.232758	+	0.169108i
$997$	−1.50999	+	2.07832i	−0.0478219	+	0.0658212i	−0.832258	−	0.554388i	$-0.812952\pi$
$997$	−1.50999	+	2.07832i	−0.0478219	+	0.0658212i	0.784436	+	0.620209i	$0.212952\pi$
$998$	−38.1985	−	12.4114i	−1.20915	−	0.392878i
$999$	−7.37232			−0.233250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.b.274.3		16
5.2	odd	4		75.2.g.b.46.1	yes	8
5.3	odd	4		375.2.g.b.226.2		8
5.4	even	2	inner	375.2.i.b.274.2		16
15.2	even	4		225.2.h.c.46.2		8
25.6	even	5	inner	375.2.i.b.349.2		16
25.8	odd	20		375.2.g.b.151.2		8
25.9	even	10		1875.2.b.c.1249.4		8
25.12	odd	20		1875.2.a.h.1.2		4
25.13	odd	20		1875.2.a.e.1.3		4
25.16	even	5		1875.2.b.c.1249.5		8
25.17	odd	20		75.2.g.b.31.1	✓	8
25.19	even	10	inner	375.2.i.b.349.3		16
75.17	even	20		225.2.h.c.181.2		8
75.38	even	20		5625.2.a.n.1.2		4
75.62	even	20		5625.2.a.i.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.b.31.1	✓	8	25.17	odd	20
75.2.g.b.46.1	yes	8	5.2	odd	4
225.2.h.c.46.2		8	15.2	even	4
225.2.h.c.181.2		8	75.17	even	20
375.2.g.b.151.2		8	25.8	odd	20
375.2.g.b.226.2		8	5.3	odd	4
375.2.i.b.274.2		16	5.4	even	2	inner
375.2.i.b.274.3		16	1.1	even	1	trivial
375.2.i.b.349.2		16	25.6	even	5	inner
375.2.i.b.349.3		16	25.19	even	10	inner
1875.2.a.e.1.3		4	25.13	odd	20
1875.2.a.h.1.2		4	25.12	odd	20
1875.2.b.c.1249.4		8	25.9	even	10
1875.2.b.c.1249.5		8	25.16	even	5
5625.2.a.i.1.3		4	75.62	even	20
5625.2.a.n.1.2		4	75.38	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.06740 + 0.346820i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.598970 - 0.435177i) q^{4} +(0.907987 - 0.659691i) q^{6} -1.11373i q^{7} +(-1.80780 - 2.48822i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(1.06740 + 0.346820i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.598970 - 0.435177i) q^{4} +(0.907987 - 0.659691i) q^{6} -1.11373i q^{7} +(-1.80780 - 2.48822i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.13412 - 3.49045i) q^{11} +(-0.704131 + 0.228786i) q^{12} +(3.85372 - 1.25215i) q^{13} +(0.386266 - 1.18880i) q^{14} +(-0.609110 - 1.87465i) q^{16} +(1.24748 + 1.71700i) q^{17} -1.12233i q^{18} +(-3.28513 + 2.38678i) q^{19} +(-0.901030 - 0.654637i) q^{21} +(2.42112 - 3.33238i) q^{22} +(5.87218 + 1.90799i) q^{23} -3.07561 q^{24} +4.54774 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-0.484672 + 0.667093i) q^{28} +(-1.82808 - 1.32818i) q^{29} +(-8.13227 + 5.90844i) q^{31} +3.93896i q^{32} +(-2.15722 - 2.96915i) q^{33} +(0.736068 + 2.26538i) q^{34} +(-0.228786 + 0.704131i) q^{36} +(7.01149 - 2.27817i) q^{37} +(-4.33434 + 1.40831i) q^{38} +(1.25215 - 3.85372i) q^{39} +(-2.30902 - 7.10642i) q^{41} +(-0.734721 - 1.01126i) q^{42} +9.24998i q^{43} +(-2.19826 + 1.59713i) q^{44} +(5.60625 + 4.07318i) q^{46} +(1.83839 - 2.53032i) q^{47} +(-1.87465 - 0.609110i) q^{48} +5.75960 q^{49} +2.12233 q^{51} +(-2.85317 - 0.927051i) q^{52} +(-2.06290 + 2.83934i) q^{53} +(-0.907987 - 0.659691i) q^{54} +(-2.77121 + 2.01340i) q^{56} +4.06064i q^{57} +(-1.49066 - 2.05172i) q^{58} +(2.03760 + 6.27109i) q^{59} +(-2.81332 + 8.65850i) q^{61} +(-10.7296 + 3.48625i) q^{62} +(-1.05922 + 0.344163i) q^{63} +(-2.58433 + 7.95375i) q^{64} +(-1.27286 - 3.91745i) q^{66} +(1.54390 + 2.12499i) q^{67} -1.57131i q^{68} +(4.99517 - 3.62921i) q^{69} +(-0.534620 - 0.388424i) q^{71} +(-1.80780 + 2.48822i) q^{72} +(7.10955 + 2.31003i) q^{73} +8.27420 q^{74} +3.00637 q^{76} +(-3.88743 - 1.26310i) q^{77} +(2.67310 - 3.67920i) q^{78} +(6.90667 + 5.01799i) q^{79} +(-0.809017 + 0.587785i) q^{81} -8.38623i q^{82} +(-7.20854 - 9.92170i) q^{83} +(0.254807 + 0.784215i) q^{84} +(-3.20808 + 9.87345i) q^{86} +(-2.14904 + 0.698265i) q^{87} +(-10.7352 + 3.48809i) q^{88} +(4.72429 - 14.5399i) q^{89} +(-1.39456 - 4.29202i) q^{91} +(-2.68695 - 3.69826i) q^{92} +10.0520i q^{93} +(2.83986 - 2.06328i) q^{94} +(3.18668 + 2.31526i) q^{96} +(-7.93508 + 10.9217i) q^{97} +(6.14781 + 1.99754i) q^{98} -3.67008 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9	\( 16 q - 2 q^{4} - 2 q^{6} + 4 q^{9} + 32 q^{11} + 16 q^{14} - 34 q^{16} + 10 q^{19} - 22 q^{21} - 60 q^{24} + 12 q^{26} - 10 q^{29} - 38 q^{31} - 24 q^{34} - 18 q^{36} + 16 q^{39} - 28 q^{41} + 6 q^{44} + 32 q^{46} - 32 q^{49} + 8 q^{51} + 2 q^{54} - 30 q^{56} - 60 q^{59} - 28 q^{61} + 88 q^{64} - 14 q^{66} + 16 q^{69} + 42 q^{71} + 76 q^{74} + 160 q^{76} + 60 q^{79} - 4 q^{81} - 16 q^{84} - 68 q^{86} + 42 q^{91} + 66 q^{94} + 68 q^{96} + 28 q^{99}+O(q^{100}) \) 16 * q - 2 * q^4 - 2 * q^6 + 4 * q^9 + 32 * q^11 + 16 * q^14 - 34 * q^16 + 10 * q^19 - 22 * q^21 - 60 * q^24 + 12 * q^26 - 10 * q^29 - 38 * q^31 - 24 * q^34 - 18 * q^36 + 16 * q^39 - 28 * q^41 + 6 * q^44 + 32 * q^46 - 32 * q^49 + 8 * q^51 + 2 * q^54 - 30 * q^56 - 60 * q^59 - 28 * q^61 + 88 * q^64 - 14 * q^66 + 16 * q^69 + 42 * q^71 + 76 * q^74 + 160 * q^76 + 60 * q^79 - 4 * q^81 - 16 * q^84 - 68 * q^86 + 42 * q^91 + 66 * q^94 + 68 * q^96 + 28 * q^99

Introduction

L-functions

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