LMFDB - Embedded newform 375.2.g.e.151.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 $ x^16 + 20x^14 + 156x^12 + 610x^10 + 1286x^8 + 1440x^6 + 761x^4 + 130*x^2 + 1
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:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			151.4
Root			$-1.35083i$ of defining polynomial
Character	$\chi$	$=$	375.151
Dual form			375.2.g.e.226.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.417429 + 1.28472i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.141788 - 0.103015i) q^{4} +(-1.09284 - 0.793998i) q^{6} -1.59580 q^{7} +(2.37722 + 1.72715i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.417429 + 1.28472i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.141788 - 0.103015i) q^{4} +(-1.09284 - 0.793998i) q^{6} -1.59580 q^{7} +(2.37722 + 1.72715i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.02988 + 3.16965i) q^{11} +(-0.0541581 + 0.166681i) q^{12} +(-2.17898 + 6.70620i) q^{13} +(-0.666132 - 2.05014i) q^{14} +(-1.11826 + 3.44165i) q^{16} +(3.31393 + 2.40771i) q^{17} +1.35083 q^{18} +(-0.459145 - 0.333589i) q^{19} +(1.29103 - 0.937986i) q^{21} +(-3.64220 + 2.64621i) q^{22} +(-1.94804 - 5.99546i) q^{23} -2.93840 q^{24} -9.52513 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.226264 + 0.164391i) q^{28} +(2.25196 - 1.63614i) q^{29} +(0.805639 + 0.585331i) q^{31} +0.988473 q^{32} +(-2.69627 - 1.95895i) q^{33} +(-1.70989 + 5.26251i) q^{34} +(-0.0541581 - 0.166681i) q^{36} +(1.09804 - 3.37943i) q^{37} +(0.236906 - 0.729121i) q^{38} +(-2.17898 - 6.70620i) q^{39} +(0.359364 - 1.10601i) q^{41} +(1.74396 + 1.26706i) q^{42} -0.117022 q^{43} +(0.472545 + 0.343324i) q^{44} +(6.88929 - 5.00536i) q^{46} +(6.18229 - 4.49170i) q^{47} +(-1.11826 - 3.44165i) q^{48} -4.45343 q^{49} -4.09625 q^{51} +(0.381886 + 1.17532i) q^{52} +(0.423629 - 0.307785i) q^{53} +(-1.09284 + 0.793998i) q^{54} +(-3.79356 - 2.75618i) q^{56} +0.567535 q^{57} +(3.04201 + 2.21015i) q^{58} +(0.304072 - 0.935838i) q^{59} +(3.27982 + 10.0942i) q^{61} +(-0.415686 + 1.27935i) q^{62} +(-0.493128 + 1.51769i) q^{63} +(2.64914 + 8.15321i) q^{64} +(1.39120 - 4.28166i) q^{66} +(-12.3099 - 8.94370i) q^{67} +0.717905 q^{68} +(5.10005 + 3.70540i) q^{69} +(8.62730 - 6.26810i) q^{71} +(2.37722 - 1.72715i) q^{72} +(-1.71761 - 5.28627i) q^{73} +4.79996 q^{74} -0.0994657 q^{76} +(-1.64348 - 5.05812i) q^{77} +(7.70599 - 5.59873i) q^{78} +(11.8091 - 8.57982i) q^{79} +(-0.809017 - 0.587785i) q^{81} +1.57091 q^{82} +(4.06448 + 2.95302i) q^{83} +(0.0864253 - 0.265990i) q^{84} +(-0.0488483 - 0.150339i) q^{86} +(-0.860172 + 2.64734i) q^{87} +(-3.02621 + 9.31372i) q^{88} +(0.872511 + 2.68531i) q^{89} +(3.47720 - 10.7017i) q^{91} +(-0.893830 - 0.649405i) q^{92} -0.995824 q^{93} +(8.35122 + 6.06752i) q^{94} +(-0.799691 + 0.581010i) q^{96} +(-1.38012 + 1.00271i) q^{97} +(-1.85899 - 5.72139i) q^{98} +3.33277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	$ 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * 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 $

$2$	0.417429	+	1.28472i	0.295167	+	0.908431i	0.983165	+	0.182719i	$0.0584897\pi$
$2$	0.417429	+	1.28472i	0.295167	+	0.908431i	−0.687998	+	0.725712i	$0.741510\pi$
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$3$	−0.809017	+	0.587785i	−0.467086	+	0.339358i
$4$	0.141788	−	0.103015i	0.0708938	−	0.0515074i
$5$		0			0
$5$		0			0
$6$	−1.09284	−	0.793998i	−0.446152	−	0.324148i
$7$	−1.59580			−0.603155			−0.301577	−	0.953442i	$-0.597513\pi$
$7$	−1.59580			−0.603155			−0.301577	+	0.953442i	$0.597513\pi$
$8$	2.37722	+	1.72715i	0.840474	+	0.610640i
$9$	0.309017	−	0.951057i	0.103006	−	0.317019i
$10$		0			0
$11$	1.02988	+	3.16965i	0.310521	+	0.955686i	0.977559	+	0.210662i	$0.0675619\pi$
$11$	1.02988	+	3.16965i	0.310521	+	0.955686i	−0.667038	+	0.745024i	$0.732438\pi$
$12$	−0.0541581	+	0.166681i	−0.0156341	+	0.0481168i
$13$	−2.17898	+	6.70620i	−0.604339	+	1.85997i	−0.103071	+	0.994674i	$0.532867\pi$
$13$	−2.17898	+	6.70620i	−0.604339	+	1.85997i	−0.501269	+	0.865292i	$0.667133\pi$
$14$	−0.666132	−	2.05014i	−0.178031	−	0.547924i
$15$		0			0
$16$	−1.11826	+	3.44165i	−0.279565	+	0.860413i
$17$	3.31393	+	2.40771i	0.803747	+	0.583957i	0.912011	−	0.410166i	$-0.134529\pi$
$17$	3.31393	+	2.40771i	0.803747	+	0.583957i	−0.108264	+	0.994122i	$0.534529\pi$
$18$	1.35083			0.318394
$19$	−0.459145	−	0.333589i	−0.105335	−	0.0765305i	0.533871	−	0.845566i	$-0.320737\pi$
$19$	−0.459145	−	0.333589i	−0.105335	−	0.0765305i	−0.639206	+	0.769036i	$0.720737\pi$
$20$		0			0
$21$	1.29103	−	0.937986i	0.281725	−	0.204685i
$22$	−3.64220	+	2.64621i	−0.776519	+	0.564174i
$23$	−1.94804	−	5.99546i	−0.406195	−	1.25014i	−0.919893	−	0.392169i	$-0.871725\pi$
$23$	−1.94804	−	5.99546i	−0.406195	−	1.25014i	0.513698	−	0.857971i	$-0.328275\pi$
$24$	−2.93840			−0.599799
$25$		0			0
$26$	−9.52513			−1.86803
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	−0.226264	+	0.164391i	−0.0427599	+	0.0310669i
$29$	2.25196	−	1.63614i	0.418178	−	0.303824i	−0.358726	−	0.933443i	$-0.616789\pi$
$29$	2.25196	−	1.63614i	0.418178	−	0.303824i	0.776904	+	0.629619i	$0.216789\pi$
$30$		0			0
$31$	0.805639	+	0.585331i	0.144697	+	0.105128i	0.657779	−	0.753211i	$-0.271496\pi$
$31$	0.805639	+	0.585331i	0.144697	+	0.105128i	−0.513082	+	0.858340i	$0.671496\pi$
$32$	0.988473			0.174739
$33$	−2.69627	−	1.95895i	−0.469360	−	0.341010i
$34$	−1.70989	+	5.26251i	−0.293244	+	0.902514i
$35$		0			0
$36$	−0.0541581	−	0.166681i	−0.00902634	−	0.0277802i
$37$	1.09804	−	3.37943i	0.180517	−	0.555574i	−0.819325	−	0.573329i	$-0.805652\pi$
$37$	1.09804	−	3.37943i	0.180517	−	0.555574i	0.999842	+	0.0177546i	$0.00565175\pi$
$38$	0.236906	−	0.729121i	0.0384312	−	0.118279i
$39$	−2.17898	−	6.70620i	−0.348916	−	1.07385i
$40$		0			0
$41$	0.359364	−	1.10601i	0.0561232	−	0.172729i	−0.919065	−	0.394105i	$-0.871055\pi$
$41$	0.359364	−	1.10601i	0.0561232	−	0.172729i	0.975189	+	0.221376i	$0.0710547\pi$
$42$	1.74396	+	1.26706i	0.269098	+	0.195511i
$43$	−0.117022			−0.0178456			−0.00892281	−	0.999960i	$-0.502840\pi$
$43$	−0.117022			−0.0178456			−0.00892281	+	0.999960i	$0.502840\pi$
$44$	0.472545	+	0.343324i	0.0712389	+	0.0517581i
$45$		0			0
$46$	6.88929	−	5.00536i	1.01577	−	0.738001i
$47$	6.18229	−	4.49170i	0.901780	−	0.655182i	−0.0371425	−	0.999310i	$-0.511826\pi$
$47$	6.18229	−	4.49170i	0.901780	−	0.655182i	0.938923	+	0.344128i	$0.111826\pi$
$48$	−1.11826	−	3.44165i	−0.161407	−	0.496760i
$49$	−4.45343			−0.636205
$50$		0			0
$51$	−4.09625			−0.573589
$52$	0.381886	+	1.17532i	0.0529580	+	0.162988i
$53$	0.423629	−	0.307785i	0.0581900	−	0.0422775i	−0.558310	−	0.829632i	$-0.688550\pi$
$53$	0.423629	−	0.307785i	0.0581900	−	0.0422775i	0.616500	+	0.787355i	$0.288550\pi$
$54$	−1.09284	+	0.793998i	−0.148717	+	0.108049i
$55$		0			0
$56$	−3.79356	−	2.75618i	−0.506936	−	0.368310i
$57$	0.567535			0.0751718
$58$	3.04201	+	2.21015i	0.399436	+	0.290207i
$59$	0.304072	−	0.935838i	0.0395868	−	0.121836i	−0.929310	−	0.369300i	$-0.879597\pi$
$59$	0.304072	−	0.935838i	0.0395868	−	0.121836i	0.968897	+	0.247465i	$0.0795974\pi$
$60$		0			0
$61$	3.27982	+	10.0942i	0.419937	+	1.29243i	0.907759	+	0.419491i	$0.137792\pi$
$61$	3.27982	+	10.0942i	0.419937	+	1.29243i	−0.487822	+	0.872943i	$0.662208\pi$
$62$	−0.415686	+	1.27935i	−0.0527922	+	0.162478i
$63$	−0.493128	+	1.51769i	−0.0621283	+	0.191211i
$64$	2.64914	+	8.15321i	0.331142	+	1.01915i
$65$		0			0
$66$	1.39120	−	4.28166i	0.171244	−	0.527036i
$67$	−12.3099	−	8.94370i	−1.50390	−	1.09265i	−0.968796	−	0.247861i	$-0.920272\pi$
$67$	−12.3099	−	8.94370i	−1.50390	−	1.09265i	−0.535104	−	0.844786i	$-0.679728\pi$
$68$	0.717905			0.0870588
$69$	5.10005	+	3.70540i	0.613973	+	0.446078i
$70$		0			0
$71$	8.62730	−	6.26810i	1.02387	−	0.743887i	0.0567995	−	0.998386i	$-0.481910\pi$
$71$	8.62730	−	6.26810i	1.02387	−	0.743887i	0.967073	+	0.254499i	$0.0819104\pi$
$72$	2.37722	−	1.72715i	0.280158	−	0.203547i
$73$	−1.71761	−	5.28627i	−0.201032	−	0.618711i	−0.999853	−	0.0171433i	$-0.994543\pi$
$73$	−1.71761	−	5.28627i	−0.201032	−	0.618711i	0.798821	−	0.601568i	$-0.205457\pi$
$74$	4.79996			0.557984
$75$		0			0
$76$	−0.0994657			−0.0114095
$77$	−1.64348	−	5.05812i	−0.187292	−	0.576426i
$78$	7.70599	−	5.59873i	0.872532	−	0.633931i
$79$	11.8091	−	8.57982i	1.32863	−	0.965305i	0.328847	−	0.944383i	$-0.393340\pi$
$79$	11.8091	−	8.57982i	1.32863	−	0.965305i	0.999781	−	0.0209214i	$-0.00665998\pi$
$80$		0			0
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	1.57091			0.173478
$83$	4.06448	+	2.95302i	0.446135	+	0.324136i	0.788068	−	0.615588i	$-0.211082\pi$
$83$	4.06448	+	2.95302i	0.446135	+	0.324136i	−0.341933	+	0.939724i	$0.611082\pi$
$84$	0.0864253	−	0.265990i	0.00942977	−	0.0290218i
$85$		0			0
$86$	−0.0488483	−	0.150339i	−0.00526744	−	0.0162115i
$87$	−0.860172	+	2.64734i	−0.0922201	+	0.283824i
$88$	−3.02621	+	9.31372i	−0.322595	+	0.992846i
$89$	0.872511	+	2.68531i	0.0924859	+	0.284642i	0.986590	−	0.163216i	$-0.0521868\pi$
$89$	0.872511	+	2.68531i	0.0924859	+	0.284642i	−0.894104	+	0.447859i	$0.852187\pi$
$90$		0			0
$91$	3.47720	−	10.7017i	0.364510	−	1.12185i
$92$	−0.893830	−	0.649405i	−0.0931882	−	0.0677052i
$93$	−0.995824			−0.103262
$94$	8.35122	+	6.06752i	0.861363	+	0.625817i
$95$		0			0
$96$	−0.799691	+	0.581010i	−0.0816182	+	0.0592991i
$97$	−1.38012	+	1.00271i	−0.140130	+	0.101810i	−0.655642	−	0.755072i	$-0.727602\pi$
$97$	−1.38012	+	1.00271i	−0.140130	+	0.101810i	0.515512	+	0.856882i	$0.327602\pi$
$98$	−1.85899	−	5.72139i	−0.187787	−	0.577948i
$99$	3.33277			0.334956
$100$		0			0
$101$	13.1747			1.31093			0.655464	−	0.755226i	$-0.272473\pi$
$101$	13.1747			1.31093			0.655464	+	0.755226i	$0.272473\pi$
$102$	−1.70989	−	5.26251i	−0.169305	−	0.521066i
$103$	8.79562	−	6.39039i	0.866658	−	0.629664i	−0.0630298	−	0.998012i	$-0.520076\pi$
$103$	8.79562	−	6.39039i	0.866658	−	0.629664i	0.929688	+	0.368347i	$0.120076\pi$
$104$	−16.7625	+	12.1787i	−1.64370	+	1.19422i
$105$		0			0
$106$	0.572251	+	0.415765i	0.0555819	+	0.0403826i
$107$	−9.37236			−0.906060			−0.453030	−	0.891495i	$-0.649657\pi$
$107$	−9.37236			−0.906060			−0.453030	+	0.891495i	$0.649657\pi$
$108$	0.141788	+	0.103015i	0.0136435	+	0.00991260i
$109$	−4.81755	+	14.8269i	−0.461438	+	1.42016i	0.401970	+	0.915653i	$0.368326\pi$
$109$	−4.81755	+	14.8269i	−0.461438	+	1.42016i	−0.863408	+	0.504506i	$0.831674\pi$
$110$		0			0
$111$	1.09804	+	3.37943i	0.104222	+	0.320761i
$112$	1.78452	−	5.49218i	0.168621	−	0.518962i
$113$	3.10503	−	9.55629i	0.292096	−	0.898980i	−0.692085	−	0.721816i	$-0.743308\pi$
$113$	3.10503	−	9.55629i	0.292096	−	0.898980i	0.984181	−	0.177164i	$-0.0566923\pi$
$114$	0.236906	+	0.729121i	0.0221883	+	0.0682884i
$115$		0			0
$116$	0.150753	−	0.463970i	0.0139971	−	0.0430785i
$117$	5.70464	+	4.14466i	0.527394	+	0.383174i
$118$	1.32921			0.122364
$119$	−5.28837	−	3.84222i	−0.484784	−	0.352216i
$120$		0			0
$121$	−0.0868453	+	0.0630968i	−0.00789503	+	0.00573608i
$122$	−11.5991	+	8.42726i	−1.05014	+	0.762968i
$123$	0.359364	+	1.10601i	0.0324027	+	0.0997253i
$124$	0.174527			0.0156730
$125$		0			0
$126$	−2.15565			−0.192041
$127$	−0.301843	−	0.928977i	−0.0267842	−	0.0824334i	0.936771	−	0.349943i	$-0.113799\pi$
$127$	−0.301843	−	0.928977i	−0.0267842	−	0.0824334i	−0.963555	+	0.267510i	$0.913799\pi$
$128$	−7.76934	+	5.64476i	−0.686719	+	0.498931i
$129$	0.0946725	−	0.0687836i	0.00833545	−	0.00605606i
$130$		0			0
$131$	−8.14001	−	5.91406i	−0.711196	−	0.516714i	0.172363	−	0.985033i	$-0.444860\pi$
$131$	−8.14001	−	5.91406i	−0.711196	−	0.516714i	−0.883559	+	0.468319i	$0.844860\pi$
$132$	−0.584098			−0.0508392
$133$	0.732703	+	0.532340i	0.0635334	+	0.0461597i
$134$	6.35158	−	19.5481i	0.548693	−	1.68870i
$135$		0			0
$136$	3.71946	+	11.4473i	0.318941	+	0.981600i
$137$	−1.50567	+	4.63397i	−0.128638	+	0.395907i	−0.994546	−	0.104296i	$-0.966741\pi$
$137$	−1.50567	+	4.63397i	−0.128638	+	0.395907i	0.865908	+	0.500203i	$0.166741\pi$
$138$	−2.63148	+	8.09885i	−0.224006	+	0.689420i
$139$	0.0574103	+	0.176691i	0.00486948	+	0.0149867i	0.953462	−	0.301514i	$-0.0974920\pi$
$139$	0.0574103	+	0.176691i	0.00486948	+	0.0149867i	−0.948592	+	0.316501i	$0.897492\pi$
$140$		0			0
$141$	−2.36143	+	7.26772i	−0.198868	+	0.612053i
$142$	11.6540	+	8.46714i	0.977984	+	0.710547i
$143$	−23.5004			−1.96520
$144$	2.92764	+	2.12706i	0.243970	+	0.177255i
$145$		0			0
$146$	6.07437	−	4.41329i	0.502719	−	0.365247i
$147$	3.60290	−	2.61766i	0.297162	−	0.215901i
$148$	−0.192442	−	0.592276i	−0.0158186	−	0.0486847i
$149$	3.88889			0.318590			0.159295	−	0.987231i	$-0.449078\pi$
$149$	3.88889			0.318590			0.159295	+	0.987231i	$0.449078\pi$
$150$		0			0
$151$	−22.1146			−1.79966			−0.899829	−	0.436242i	$-0.856309\pi$
$151$	−22.1146			−1.79966			−0.899829	+	0.436242i	$0.856309\pi$
$152$	−0.515331	−	1.58603i	−0.0417989	−	0.128644i
$153$	3.31393	−	2.40771i	0.267916	−	0.194652i
$154$	5.81221	−	4.22282i	0.468361	−	0.340284i
$155$		0			0
$156$	−0.999790	−	0.726390i	−0.0800472	−	0.0581577i
$157$	13.6058			1.08586			0.542931	−	0.839777i	$-0.317314\pi$
$157$	13.6058			1.08586			0.542931	+	0.839777i	$0.317314\pi$
$158$	15.9521	+	11.5899i	1.26908	+	0.922041i
$159$	−0.161812	+	0.498006i	−0.0128325	+	0.0394945i
$160$		0			0
$161$	3.10868	+	9.56754i	0.244999	+	0.754028i
$162$	0.417429	−	1.28472i	0.0327963	−	0.100937i
$163$	2.66649	−	8.20662i	0.208856	−	0.642792i	−0.790677	−	0.612233i	$-0.790271\pi$
$163$	2.66649	−	8.20662i	0.208856	−	0.642792i	0.999533	−	0.0305587i	$-0.00972864\pi$
$164$	−0.0629818	−	0.193838i	−0.00491805	−	0.0151362i
$165$		0			0
$166$	−2.09716	+	6.45438i	−0.162771	+	0.500957i
$167$	−5.33863	−	3.87874i	−0.413116	−	0.300146i	0.361746	−	0.932277i	$-0.382181\pi$
$167$	−5.33863	−	3.87874i	−0.413116	−	0.300146i	−0.774862	+	0.632131i	$0.782181\pi$
$168$	4.68910			0.361772
$169$	−29.7080	−	21.5841i	−2.28523	−	1.66032i
$170$		0			0
$171$	−0.459145	+	0.333589i	−0.0351117	+	0.0255102i
$172$	−0.0165922	+	0.0120550i	−0.00126514	+	0.000919182i
$173$	4.22102	+	12.9910i	0.320918	+	0.987685i	0.973249	+	0.229751i	$0.0737912\pi$
$173$	4.22102	+	12.9910i	0.320918	+	0.987685i	−0.652331	+	0.757934i	$0.726209\pi$
$174$	−3.76013			−0.285055
$175$		0			0
$176$	−12.0605			−0.909095
$177$	0.304072	+	0.935838i	0.0228555	+	0.0703419i
$178$	−3.08565	+	2.24186i	−0.231279	+	0.168034i
$179$	−7.95167	+	5.77722i	−0.594336	+	0.431810i	−0.843864	−	0.536557i	$-0.819724\pi$
$179$	−7.95167	+	5.77722i	−0.594336	+	0.431810i	0.249528	+	0.968368i	$0.419724\pi$
$180$		0			0
$181$	−14.4561	−	10.5030i	−1.07451	−	0.780679i	−0.0977940	−	0.995207i	$-0.531179\pi$
$181$	−14.4561	−	10.5030i	−1.07451	−	0.780679i	−0.976718	+	0.214528i	$0.931179\pi$
$182$	15.2002			1.12671
$183$	−8.58667	−	6.23858i	−0.634745	−	0.461169i
$184$	5.72414	−	17.6171i	0.421989	−	1.29875i
$185$		0			0
$186$	−0.415686	−	1.27935i	−0.0304796	−	0.0938065i
$187$	−4.21865	+	12.9837i	−0.308498	+	0.949461i
$188$	0.413862	−	1.27373i	0.0301840	−	0.0928967i
$189$	−0.493128	−	1.51769i	−0.0358698	−	0.110396i
$190$		0			0
$191$	0.100682	−	0.309867i	0.00728509	−	0.0224212i	−0.947348	−	0.320206i	$-0.896248\pi$
$191$	0.100682	−	0.309867i	0.00728509	−	0.0224212i	0.954633	+	0.297785i	$0.0962478\pi$
$192$	−6.93553	−	5.03896i	−0.500529	−	0.363656i
$193$	−2.90187			−0.208881			−0.104441	−	0.994531i	$-0.533305\pi$
$193$	−2.90187			−0.208881			−0.104441	+	0.994531i	$0.533305\pi$
$194$	−1.86430	−	1.35450i	−0.133849	−	0.0972471i
$195$		0			0
$196$	−0.631442	+	0.458769i	−0.0451030	+	0.0327692i
$197$	14.6610	−	10.6518i	1.04455	−	0.758911i	0.0733829	−	0.997304i	$-0.476620\pi$
$197$	14.6610	−	10.6518i	1.04455	−	0.758911i	0.971169	+	0.238393i	$0.0766205\pi$
$198$	1.39120	+	4.28166i	0.0988679	+	0.304284i
$199$	1.53256			0.108640			0.0543201	−	0.998524i	$-0.482701\pi$
$199$	1.53256			0.108640			0.0543201	+	0.998524i	$0.482701\pi$
$200$		0			0
$201$	15.2159			1.07325
$202$	5.49949	+	16.9257i	0.386943	+	1.19089i
$203$	−3.59367	+	2.61095i	−0.252226	+	0.183253i
$204$	−0.580797	+	0.421974i	−0.0406640	+	0.0295441i
$205$		0			0
$206$	11.8814	+	8.63233i	0.827816	+	0.601443i
$207$	−6.30400			−0.438158
$208$	−20.6437	−	14.9986i	−1.43139	−	1.03996i
$209$	0.584494	−	1.79889i	0.0404303	−	0.124432i
$210$		0			0
$211$	−3.51345	−	10.8133i	−0.241876	−	0.744418i	−0.996135	−	0.0878402i	$-0.972004\pi$
$211$	−3.51345	−	10.8133i	−0.241876	−	0.744418i	0.754259	−	0.656577i	$-0.227996\pi$
$212$	0.0283590	−	0.0872802i	0.00194771	−	0.00599443i
$213$	−3.29534	+	10.1420i	−0.225793	+	0.694919i
$214$	−3.91230	−	12.0408i	−0.267439	−	0.823093i
$215$		0			0
$216$	−0.908017	+	2.79459i	−0.0617827	+	0.190148i
$217$	−1.28564	−	0.934069i	−0.0872746	−	0.0634087i
$218$	−21.0593			−1.42632
$219$	4.49677	+	3.26710i	0.303864	+	0.220770i
$220$		0			0
$221$	−23.3676	+	16.9776i	−1.57188	+	1.14203i
$222$	−3.88325	+	2.82134i	−0.260626	+	0.189356i
$223$	5.23804	+	16.1210i	0.350765	+	1.07954i	0.958424	+	0.285347i	$0.0921087\pi$
$223$	5.23804	+	16.1210i	0.350765	+	1.07954i	−0.607659	+	0.794198i	$0.707891\pi$
$224$	−1.57740			−0.105395
$225$		0			0
$226$	13.5732			0.902878
$227$	4.36076	+	13.4210i	0.289434	+	0.890785i	0.985035	+	0.172357i	$0.0551382\pi$
$227$	4.36076	+	13.4210i	0.289434	+	0.890785i	−0.695601	+	0.718428i	$0.744862\pi$
$228$	0.0804694	−	0.0584645i	0.00532922	−	0.00387190i
$229$	−0.0501546	+	0.0364394i	−0.00331431	+	0.00240799i	−0.589441	−	0.807811i	$-0.700652\pi$
$229$	−0.0501546	+	0.0364394i	−0.00331431	+	0.00240799i	0.586127	+	0.810219i	$0.300652\pi$
$230$		0			0
$231$	4.30269	+	3.12609i	0.283096	+	0.205682i
$232$	8.17927			0.536995
$233$	21.0499	+	15.2936i	1.37902	+	1.00192i	0.996971	+	0.0777775i	$0.0247824\pi$
$233$	21.0499	+	15.2936i	1.37902	+	1.00192i	0.382052	+	0.924141i	$0.375218\pi$
$234$	−2.94343	+	9.05894i	−0.192418	+	0.592201i
$235$		0			0
$236$	−0.0532914	−	0.164014i	−0.00346898	−	0.0106764i
$237$	−4.51068	+	13.8824i	−0.293000	+	0.901761i
$238$	2.72864	−	8.39790i	0.176872	−	0.544355i
$239$	6.02491	+	18.5428i	0.389719	+	1.19943i	0.932998	+	0.359881i	$0.117183\pi$
$239$	6.02491	+	18.5428i	0.389719	+	1.19943i	−0.543279	+	0.839552i	$0.682817\pi$
$240$		0			0
$241$	−1.26654	+	3.89800i	−0.0815848	+	0.251092i	−0.983526	−	0.180767i	$-0.942142\pi$
$241$	−1.26654	+	3.89800i	−0.0815848	+	0.251092i	0.901941	+	0.431859i	$0.142142\pi$
$242$	−0.117313	−	0.0852331i	−0.00754118	−	0.00547899i
$243$	1.00000			0.0641500
$244$	1.50489	+	1.09337i	0.0963409	+	0.0699957i
$245$		0			0
$246$	−1.27090	+	0.923360i	−0.0810294	+	0.0588713i
$247$	3.23758	−	2.35224i	0.206002	−	0.149669i
$248$	0.904225	+	2.78292i	0.0574184	+	0.176716i
$249$	−5.02398			−0.318382
$250$		0			0
$251$	−1.02933			−0.0649704			−0.0324852	−	0.999472i	$-0.510342\pi$
$251$	−1.02933			−0.0649704			−0.0324852	+	0.999472i	$0.510342\pi$
$252$	0.0864253	+	0.265990i	0.00544428	+	0.0167558i
$253$	16.9973	−	12.3492i	1.06861	−	0.776390i
$254$	1.06747	−	0.775565i	0.0669792	−	0.0486633i
$255$		0			0
$256$	3.37601	+	2.45281i	0.211001	+	0.153301i
$257$	−18.5597			−1.15772			−0.578862	−	0.815426i	$-0.696503\pi$
$257$	−18.5597			−1.15772			−0.578862	+	0.815426i	$0.696503\pi$
$258$	0.127886	+	0.0929149i	0.00796186	+	0.00578463i
$259$	−1.75225	+	5.39288i	−0.108880	+	0.335097i
$260$		0			0
$261$	−0.860172	−	2.64734i	−0.0532433	−	0.163866i
$262$	4.20001	−	12.9263i	0.259477	−	0.798589i
$263$	3.82988	−	11.7872i	0.236161	−	0.726827i	−0.760805	−	0.648981i	$-0.775196\pi$
$263$	3.82988	−	11.7872i	0.236161	−	0.726827i	0.996965	−	0.0778466i	$-0.0248044\pi$
$264$	−3.02621	−	9.31372i	−0.186250	−	0.573220i
$265$		0			0
$266$	−0.378053	+	1.16353i	−0.0231799	+	0.0713405i
$267$	−2.28426	−	1.65961i	−0.139795	−	0.101567i
$268$	−2.66673			−0.162897
$269$	4.28805	+	3.11545i	0.261447	+	0.189952i	0.710785	−	0.703410i	$-0.248340\pi$
$269$	4.28805	+	3.11545i	0.261447	+	0.189952i	−0.449338	+	0.893362i	$0.648340\pi$
$270$		0			0
$271$	−0.645132	+	0.468716i	−0.0391890	+	0.0284725i	−0.607207	−	0.794543i	$-0.707710\pi$
$271$	−0.645132	+	0.468716i	−0.0391890	+	0.0284725i	0.568018	+	0.823016i	$0.307710\pi$
$272$	−11.9924	+	8.71295i	−0.727143	+	0.528300i
$273$	3.47720	+	10.7017i	0.210450	+	0.647698i
$274$	−6.58184			−0.397624
$275$		0			0
$276$	1.10483			0.0665032
$277$	−1.46605	−	4.51205i	−0.0880867	−	0.271103i	0.897304	−	0.441414i	$-0.145523\pi$
$277$	−1.46605	−	4.51205i	−0.0880867	−	0.271103i	−0.985390	+	0.170311i	$0.945523\pi$
$278$	−0.203033	+	0.147512i	−0.0121771	+	0.00884717i
$279$	0.805639	−	0.585331i	0.0482323	−	0.0350428i
$280$		0			0
$281$	15.1608	+	11.0150i	0.904418	+	0.657098i	0.939597	−	0.342283i	$-0.111200\pi$
$281$	15.1608	+	11.0150i	0.904418	+	0.657098i	−0.0351791	+	0.999381i	$0.511200\pi$
$282$	−10.3227			−0.614707
$283$	−9.51501	−	6.91306i	−0.565608	−	0.410939i	0.267899	−	0.963447i	$-0.413671\pi$
$283$	−9.51501	−	6.91306i	−0.565608	−	0.410939i	−0.833507	+	0.552508i	$0.813671\pi$
$284$	0.577538	−	1.77748i	0.0342706	−	0.105474i
$285$		0			0
$286$	−9.80976	−	30.1913i	−0.580063	−	1.78525i
$287$	−0.573471	+	1.76496i	−0.0338509	+	0.104182i
$288$	0.305455	−	0.940094i	0.0179991	−	0.0553956i
$289$	−0.0682154	−	0.209945i	−0.00401267	−	0.0123497i
$290$		0			0
$291$	0.527158	−	1.62242i	0.0309025	−	0.0951082i
$292$	−0.788101	−	0.572589i	−0.0461201	−	0.0335082i
$293$	22.2819			1.30172			0.650860	−	0.759198i	$-0.274408\pi$
$293$	22.2819			1.30172			0.650860	+	0.759198i	$0.274408\pi$
$294$	4.86691	+	3.53602i	0.283844	+	0.206225i
$295$		0			0
$296$	8.44707	−	6.13715i	0.490976	−	0.356715i
$297$	−2.69627	+	1.95895i	−0.156453	+	0.113670i
$298$	1.62333	+	4.99611i	0.0940373	+	0.289417i
$299$	44.4515			2.57070
$300$		0			0
$301$	0.186743			0.0107637
$302$	−9.23127	−	28.4109i	−0.531200	−	1.63487i
$303$	−10.6585	+	7.74387i	−0.612316	+	0.444874i
$304$	1.66154	−	1.20718i	0.0952958	−	0.0692365i
$305$		0			0
$306$	4.47656	+	3.25241i	0.255908	+	0.185928i
$307$	−15.3063			−0.873574			−0.436787	−	0.899565i	$-0.643884\pi$
$307$	−15.3063			−0.873574			−0.436787	+	0.899565i	$0.643884\pi$
$308$	−0.754087	−	0.547876i	−0.0429681	−	0.0312181i
$309$	−3.35963	+	10.3399i	−0.191123	+	0.588215i
$310$		0			0
$311$	−3.97226	−	12.2254i	−0.225246	−	0.693237i	−0.998267	−	0.0588556i	$-0.981255\pi$
$311$	−3.97226	−	12.2254i	−0.225246	−	0.693237i	0.773020	−	0.634382i	$-0.218745\pi$
$312$	6.40272	−	19.7055i	0.362482	−	1.11561i
$313$	−3.24690	+	9.99293i	−0.183526	+	0.564834i	−0.999920	−	0.0126612i	$-0.995970\pi$
$313$	−3.24690	+	9.99293i	−0.183526	+	0.564834i	0.816394	+	0.577495i	$0.195970\pi$
$314$	5.67947	+	17.4796i	0.320511	+	0.986431i
$315$		0			0
$316$	0.790537	−	2.43302i	0.0444712	−	0.136868i
$317$	15.7602	+	11.4504i	0.885179	+	0.643120i	0.934617	−	0.355657i	$-0.115743\pi$
$317$	15.7602	+	11.4504i	0.885179	+	0.643120i	−0.0494374	+	0.998777i	$0.515743\pi$
$318$	−0.707341			−0.0396657
$319$	7.50526	+	5.45289i	0.420214	+	0.305303i
$320$		0			0
$321$	7.58240	−	5.50893i	0.423208	−	0.307479i
$322$	−10.9939	+	7.98754i	−0.612667	+	0.445128i
$323$	−0.718392	−	2.21098i	−0.0399724	−	0.123022i
$324$	−0.175259			−0.00973662
$325$		0			0
$326$	11.6562			0.645579
$327$	−4.81755	−	14.8269i	−0.266411	−	0.819929i
$328$	2.76453	−	2.00855i	0.152646	−	0.110903i
$329$	−9.86568	+	7.16784i	−0.543913	+	0.395176i
$330$		0			0
$331$	11.7247	+	8.51846i	0.644446	+	0.468217i	0.861375	−	0.507970i	$-0.169604\pi$
$331$	11.7247	+	8.51846i	0.644446	+	0.468217i	−0.216929	+	0.976187i	$0.569604\pi$
$332$	0.880498			0.0483236
$333$	−2.87471	−	2.08860i	−0.157533	−	0.114455i
$334$	2.75458	−	8.47772i	0.150724	−	0.463880i
$335$		0			0
$336$	1.78452	+	5.49218i	0.0973533	+	0.299623i
$337$	2.88382	−	8.87550i	0.157092	−	0.483479i	−0.841275	−	0.540608i	$-0.818194\pi$
$337$	2.88382	−	8.87550i	0.157092	−	0.483479i	0.998367	+	0.0571283i	$0.0181944\pi$
$338$	15.3285	−	47.1761i	0.833758	−	2.56604i
$339$	3.10503	+	9.55629i	0.168642	+	0.519026i
$340$		0			0
$341$	−1.02558	+	3.15641i	−0.0555383	+	0.170929i
$342$	−0.620227	−	0.450621i	−0.0335380	−	0.0243668i
$343$	18.2774			0.986884
$344$	−0.278186	−	0.202114i	−0.0149988	−	0.0108973i
$345$		0			0
$346$	−14.9277	+	10.8456i	−0.802519	+	0.583064i
$347$	0.852225	−	0.619178i	0.0457498	−	0.0332392i	−0.564675	−	0.825313i	$-0.690999\pi$
$347$	0.852225	−	0.619178i	0.0457498	−	0.0332392i	0.610425	+	0.792074i	$0.290999\pi$
$348$	0.150753	+	0.463970i	0.00808121	+	0.0248714i
$349$	−13.0715			−0.699700			−0.349850	−	0.936806i	$-0.613767\pi$
$349$	−13.0715			−0.699700			−0.349850	+	0.936806i	$0.613767\pi$
$350$		0			0
$351$	−7.05132			−0.376371
$352$	1.01801	+	3.13311i	0.0542602	+	0.166996i
$353$	−27.4639	+	19.9537i	−1.46176	+	1.06203i	−0.478855	+	0.877894i	$0.658948\pi$
$353$	−27.4639	+	19.9537i	−1.46176	+	1.06203i	−0.982901	+	0.184134i	$0.941052\pi$
$354$	−1.07536	+	0.781292i	−0.0571546	+	0.0415252i
$355$		0			0
$356$	0.400338	+	0.290863i	0.0212179	+	0.0154157i
$357$	6.53678			0.345963
$358$	−10.7413	−	7.80405i	−0.567698	−	0.412457i
$359$	−1.88331	+	5.79622i	−0.0993971	+	0.305913i	−0.988375	−	0.152038i	$-0.951416\pi$
$359$	−1.88331	+	5.79622i	−0.0993971	+	0.305913i	0.888978	+	0.457951i	$0.151416\pi$
$360$		0			0
$361$	−5.77179	−	17.7637i	−0.303778	−	0.934934i
$362$	7.45892	−	22.9562i	0.392032	−	1.20655i
$363$	0.0331720	−	0.102093i	0.00174108	−	0.00535848i
$364$	−0.609412	−	1.87558i	−0.0319419	−	0.0983070i
$365$		0			0
$366$	4.43047	−	13.6356i	0.231585	−	0.712744i
$367$	17.6881	+	12.8511i	0.923309	+	0.670823i	0.944345	−	0.328955i	$-0.106697\pi$
$367$	17.6881	+	12.8511i	0.923309	+	0.670823i	−0.0210364	+	0.999779i	$0.506697\pi$
$368$	22.8127			1.18919
$369$	−0.940826	−	0.683550i	−0.0489775	−	0.0355842i
$370$		0			0
$371$	−0.676026	+	0.491162i	−0.0350975	+	0.0254999i
$372$	−0.141196	+	0.102585i	−0.00732065	+	0.00531876i
$373$	−7.55730	−	23.2590i	−0.391302	−	1.20430i	−0.931804	−	0.362961i	$-0.881766\pi$
$373$	−7.55730	−	23.2590i	−0.391302	−	1.20430i	0.540502	−	0.841343i	$-0.318234\pi$
$374$	−18.4413			−0.953578
$375$		0			0
$376$	22.4545			1.15800
$377$	6.06534	+	18.6672i	0.312381	+	0.961410i
$378$	1.74396	−	1.26706i	0.0896995	−	0.0651705i
$379$	5.07918	−	3.69024i	0.260900	−	0.189555i	−0.449644	−	0.893208i	$-0.648449\pi$
$379$	5.07918	−	3.69024i	0.260900	−	0.189555i	0.710544	+	0.703653i	$0.248449\pi$
$380$		0			0
$381$	0.790235	+	0.574140i	0.0404850	+	0.0294141i
$382$	0.440118			0.0225184
$383$	−19.9727	−	14.5110i	−1.02056	−	0.741477i	−0.0541589	−	0.998532i	$-0.517248\pi$
$383$	−19.9727	−	14.5110i	−1.02056	−	0.741477i	−0.966397	+	0.257055i	$0.917248\pi$
$384$	2.96762	−	9.13341i	0.151441	−	0.466087i
$385$		0			0
$386$	−1.21133	−	3.72808i	−0.0616549	−	0.189754i
$387$	−0.0361617	+	0.111294i	−0.00183820	+	0.00565740i
$388$	−0.0923892	+	0.284345i	−0.00469035	+	0.0144354i
$389$	−3.99360	−	12.2910i	−0.202484	−	0.623181i	−0.999807	−	0.0196288i	$-0.993752\pi$
$389$	−3.99360	−	12.2910i	−0.202484	−	0.623181i	0.797324	−	0.603552i	$-0.206248\pi$
$390$		0			0
$391$	7.97967	−	24.5589i	0.403549	−	1.24200i
$392$	−10.5868	−	7.69175i	−0.534713	−	0.388492i
$393$	10.0616			0.507541
$394$	19.8045	+	14.3888i	0.997736	+	0.724897i
$395$		0			0
$396$	0.472545	−	0.343324i	0.0237463	−	0.0172527i
$397$	23.4788	−	17.0584i	1.17837	−	0.856135i	0.186383	−	0.982477i	$-0.440324\pi$
$397$	23.4788	−	17.0584i	1.17837	−	0.856135i	0.991987	+	0.126342i	$0.0403236\pi$
$398$	0.639734	+	1.96890i	0.0320670	+	0.0986921i
$399$	−0.905670			−0.0453402
$400$		0			0
$401$	23.3926			1.16817			0.584084	−	0.811693i	$-0.301454\pi$
$401$	23.3926			1.16817			0.584084	+	0.811693i	$0.301454\pi$
$402$	6.35158	+	19.5481i	0.316788	+	0.974973i
$403$	−5.68081	+	4.12735i	−0.282981	+	0.205598i
$404$	1.86800	−	1.35719i	0.0929367	−	0.0675225i
$405$		0			0
$406$	−4.85443	−	3.52695i	−0.240921	−	0.175040i
$407$	11.8425			0.587009
$408$	−9.73768	−	7.07484i	−0.482087	−	0.350257i
$409$	−4.94173	+	15.2091i	−0.244353	+	0.752040i	0.751389	+	0.659859i	$0.229384\pi$
$409$	−4.94173	+	15.2091i	−0.244353	+	0.752040i	−0.995742	+	0.0921815i	$0.970616\pi$
$410$		0			0
$411$	−1.50567	−	4.63397i	−0.0742691	−	0.228577i
$412$	0.588806	−	1.81216i	0.0290084	−	0.0892786i
$413$	−0.485237	+	1.49341i	−0.0238770	+	0.0734858i
$414$	−2.63148	−	8.09885i	−0.129330	−	0.398037i
$415$		0			0
$416$	−2.15386	+	6.62890i	−0.105602	+	0.325008i
$417$	−0.150302	−	0.109201i	−0.00736033	−	0.00534759i
$418$	2.55504			0.124971
$419$	−26.1935	−	19.0307i	−1.27964	−	0.929710i	−0.280094	−	0.959973i	$-0.590366\pi$
$419$	−26.1935	−	19.0307i	−1.27964	−	0.929710i	−0.999542	+	0.0302627i	$0.990366\pi$
$420$		0			0
$421$	−14.6044	+	10.6107i	−0.711774	+	0.517134i	−0.883745	−	0.467968i	$-0.844986\pi$
$421$	−14.6044	+	10.6107i	−0.711774	+	0.517134i	0.171972	+	0.985102i	$0.444986\pi$
$422$	12.4254	−	9.02757i	0.604858	−	0.439455i
$423$	−2.36143	−	7.26772i	−0.114816	−	0.353369i
$424$	1.53865			0.0747235
$425$		0			0
$426$	−14.4052			−0.697932
$427$	−5.23392	−	16.1084i	−0.253287	−	0.779538i
$428$	−1.32888	+	0.965491i	−0.0642340	+	0.0466688i
$429$	19.0122	−	13.8132i	0.917919	−	0.666907i
$430$		0			0
$431$	−26.8070	−	19.4764i	−1.29125	−	0.938146i	−0.291417	−	0.956596i	$-0.594127\pi$
$431$	−26.8070	−	19.4764i	−1.29125	−	0.938146i	−0.999830	+	0.0184500i	$0.994127\pi$
$432$	−3.61877			−0.174108
$433$	18.3366	+	13.3223i	0.881201	+	0.640230i	0.933569	−	0.358398i	$-0.116677\pi$
$433$	18.3366	+	13.3223i	0.881201	+	0.640230i	−0.0523682	+	0.998628i	$0.516677\pi$
$434$	0.663351	−	2.04158i	0.0318419	−	0.0979991i
$435$		0			0
$436$	0.844320	+	2.59855i	0.0404356	+	0.124448i
$437$	−1.10558	+	3.40263i	−0.0528872	+	0.162770i
$438$	−2.32020	+	7.14085i	−0.110864	+	0.341203i
$439$	−2.62799	−	8.08812i	−0.125427	−	0.386025i	0.868551	−	0.495599i	$-0.165051\pi$
$439$	−2.62799	−	8.08812i	−0.125427	−	0.386025i	−0.993979	+	0.109574i	$0.965051\pi$
$440$		0			0
$441$	−1.37619	+	4.23547i	−0.0655327	+	0.201689i
$442$	−31.5657	−	22.9338i	−1.50142	−	1.09085i
$443$	6.35768			0.302063			0.151031	−	0.988529i	$-0.451741\pi$
$443$	6.35768			0.302063			0.151031	+	0.988529i	$0.451741\pi$
$444$	0.503820	+	0.366046i	0.0239102	+	0.0173718i
$445$		0			0
$446$	−18.5244	+	13.4588i	−0.877157	+	0.637292i
$447$	−3.14617	+	2.28583i	−0.148809	+	0.108116i
$448$	−4.22749	−	13.0109i	−0.199730	−	0.614706i
$449$	−6.25726			−0.295298			−0.147649	−	0.989040i	$-0.547171\pi$
$449$	−6.25726			−0.295298			−0.147649	+	0.989040i	$0.547171\pi$
$450$		0			0
$451$	3.87576			0.182502
$452$	−0.544184	−	1.67483i	−0.0255963	−	0.0787772i
$453$	17.8911	−	12.9986i	0.840596	−	0.610729i
$454$	−15.4219	+	11.2047i	−0.723786	+	0.525861i
$455$		0			0
$456$	1.34915	+	0.980218i	0.0631800	+	0.0459029i
$457$	−11.0441			−0.516620			−0.258310	−	0.966062i	$-0.583166\pi$
$457$	−11.0441			−0.516620			−0.258310	+	0.966062i	$0.583166\pi$
$458$	−0.0677503	−	0.0492235i	−0.00316576	−	0.00230006i
$459$	−1.26581	+	3.89576i	−0.0590830	+	0.181839i
$460$		0			0
$461$	−7.31202	−	22.5041i	−0.340555	−	1.04812i	−0.963921	−	0.266189i	$-0.914235\pi$
$461$	−7.31202	−	22.5041i	−0.340555	−	1.04812i	0.623366	−	0.781930i	$-0.285765\pi$
$462$	−2.22007	+	6.83266i	−0.103287	+	0.317884i
$463$	−1.92345	+	5.91977i	−0.0893903	+	0.275115i	−0.985751	−	0.168210i	$-0.946201\pi$
$463$	−1.92345	+	5.91977i	−0.0893903	+	0.275115i	0.896361	+	0.443325i	$0.146201\pi$
$464$	3.11276	+	9.58009i	0.144506	+	0.444744i
$465$		0			0
$466$	−10.8611	+	33.4271i	−0.503132	+	1.54848i
$467$	−4.00204	−	2.90765i	−0.185192	−	0.134550i	0.491326	−	0.870976i	$-0.336512\pi$
$467$	−4.00204	−	2.90765i	−0.185192	−	0.134550i	−0.676519	+	0.736425i	$0.736512\pi$
$468$	1.23581			0.0571252
$469$	19.6442	+	14.2723i	0.907084	+	0.659035i
$470$		0			0
$471$	−11.0073	+	7.99730i	−0.507191	+	0.368496i
$472$	2.33918	−	1.69951i	0.107669	−	0.0782264i
$473$	−0.120518	−	0.370918i	−0.00554144	−	0.0170548i
$474$	−19.7179			−0.905671
$475$		0			0
$476$	−1.14563			−0.0525099
$477$	−0.161812	−	0.498006i	−0.00740886	−	0.0228021i
$478$	−21.3072	+	15.4806i	−0.974569	+	0.708066i
$479$	24.3432	−	17.6863i	1.11227	−	0.808109i	0.129248	−	0.991612i	$-0.458744\pi$
$479$	24.3432	−	17.6863i	1.11227	−	0.808109i	0.983019	+	0.183503i	$0.0587436\pi$
$480$		0			0
$481$	20.2705	+	14.7274i	0.924256	+	0.671511i
$482$	−5.53651			−0.252181
$483$	−8.13864	−	5.91307i	−0.370321	−	0.269054i
$484$	−0.00581369	+	0.0178927i	−0.000264259	+	0.000813305i
$485$		0			0
$486$	0.417429	+	1.28472i	0.0189350	+	0.0582759i
$487$	−10.5838	+	32.5736i	−0.479598	+	1.47605i	0.360057	+	0.932930i	$0.382757\pi$
$487$	−10.5838	+	32.5736i	−0.479598	+	1.47605i	−0.839655	+	0.543120i	$0.817243\pi$
$488$	−9.63743	+	29.6609i	−0.436266	+	1.34269i
$489$	2.66649	+	8.20662i	0.120583	+	0.371116i
$490$		0			0
$491$	−3.21975	+	9.90938i	−0.145305	+	0.447204i	−0.997050	−	0.0767530i	$-0.975545\pi$
$491$	−3.21975	+	9.90938i	−0.145305	+	0.447204i	0.851745	+	0.523957i	$0.175545\pi$
$492$	0.164888	+	0.119798i	0.00743374	+	0.00540093i
$493$	11.4022			0.513530
$494$	4.37342	+	3.17747i	0.196769	+	0.142961i
$495$		0			0
$496$	−2.91542	+	2.11817i	−0.130906	+	0.0951088i
$497$	−13.7674	+	10.0026i	−0.617553	+	0.448679i
$498$	−2.09716	−	6.45438i	−0.0939758	−	0.289228i
$499$	8.83514			0.395515			0.197757	−	0.980251i	$-0.436634\pi$
$499$	8.83514			0.395515			0.197757	+	0.980251i	$0.436634\pi$
$500$		0			0
$501$	6.59891			0.294818
$502$	−0.429671	−	1.32239i	−0.0191771	−	0.0590211i
$503$	−17.2915	+	12.5630i	−0.770988	+	0.560156i	−0.902261	−	0.431190i	$-0.858094\pi$
$503$	−17.2915	+	12.5630i	−0.770988	+	0.560156i	0.131273	+	0.991346i	$0.458094\pi$
$504$	−3.79356	+	2.75618i	−0.168979	+	0.122770i
$505$		0			0
$506$	22.9604	+	16.6817i	1.02072	+	0.741593i
$507$	36.7211			1.63084
$508$	−0.138496	−	0.100623i	−0.00614477	−	0.00446443i
$509$	−5.18529	+	15.9587i	−0.229834	+	0.707356i	0.767931	+	0.640533i	$0.221286\pi$
$509$	−5.18529	+	15.9587i	−0.229834	+	0.707356i	−0.997765	+	0.0668236i	$0.978714\pi$
$510$		0			0
$511$	2.74096	+	8.43582i	0.121253	+	0.373179i
$512$	−7.67717	+	23.6279i	−0.339286	+	1.04422i
$513$	0.175378	−	0.539758i	0.00774312	−	0.0238309i
$514$	−7.74737	−	23.8440i	−0.341722	−	1.05171i
$515$		0			0
$516$	0.00633766	−	0.0195053i	0.000279000	−	0.000858674i
$517$	20.6042	+	14.9698i	0.906170	+	0.658371i
$518$	−7.65976			−0.336550
$519$	−11.0508	−	8.02886i	−0.485075	−	0.352428i
$520$		0			0
$521$	3.72559	−	2.70680i	0.163221	−	0.118587i	−0.503176	−	0.864184i	$-0.667835\pi$
$521$	3.72559	−	2.70680i	0.163221	−	0.118587i	0.666397	+	0.745597i	$0.267835\pi$
$522$	3.04201	−	2.21015i	0.133145	−	0.0967357i
$523$	4.00592	+	12.3290i	0.175167	+	0.539108i	0.999641	−	0.0267915i	$-0.00852902\pi$
$523$	4.00592	+	12.3290i	0.175167	+	0.539108i	−0.824474	+	0.565899i	$0.808529\pi$
$524$	−1.76339			−0.0770340
$525$		0			0
$526$	16.7418			0.729979
$527$	1.26052	+	3.87949i	0.0549093	+	0.168993i
$528$	9.75716	−	7.08899i	0.424626	−	0.308509i
$529$	−13.5433	+	9.83979i	−0.588840	+	0.427817i
$530$		0			0
$531$	−0.796071	−	0.578380i	−0.0345465	−	0.0250995i
$532$	0.158727			0.00688169
$533$	6.63406	+	4.81993i	0.287353	+	0.208774i
$534$	1.17861	−	3.62740i	0.0510036	−	0.156973i
$535$		0			0
$536$	−13.8163	−	42.5223i	−0.596774	−	1.83668i
$537$	3.03727	−	9.34775i	0.131068	−	0.403385i
$538$	−2.21251	+	6.80940i	−0.0953880	+	0.293574i
$539$	−4.58651	−	14.1158i	−0.197555	−	0.608012i
$540$		0			0
$541$	−8.45597	+	26.0248i	−0.363551	+	1.11889i	0.587333	+	0.809345i	$0.300178\pi$
$541$	−8.45597	+	26.0248i	−0.363551	+	1.11889i	−0.950884	+	0.309548i	$0.899822\pi$
$542$	−0.871464	−	0.633156i	−0.0374326	−	0.0271964i
$543$	17.8687			0.766819
$544$	3.27573	+	2.37996i	0.140446	+	0.102040i
$545$		0			0
$546$	−12.2972	+	8.93444i	−0.526271	+	0.382359i
$547$	−22.3656	+	16.2495i	−0.956282	+	0.694779i	−0.952284	−	0.305213i	$-0.901272\pi$
$547$	−22.3656	+	16.2495i	−0.956282	+	0.694779i	−0.00399765	+	0.999992i	$0.501272\pi$
$548$	0.263882	+	0.812146i	0.0112725	+	0.0346931i
$549$	10.6137			0.452982
$550$		0			0
$551$	−1.57978			−0.0673007
$552$	5.72414	+	17.6171i	0.243636	+	0.749833i
$553$	−18.8449	+	13.6916i	−0.801368	+	0.582228i
$554$	5.18473	−	3.76692i	0.220278	−	0.160041i
$555$		0			0
$556$	0.0263418	+	0.0191385i	0.00111714	+	0.000811652i
$557$	−6.17333			−0.261572			−0.130786	−	0.991411i	$-0.541750\pi$
$557$	−6.17333			−0.261572			−0.130786	+	0.991411i	$0.541750\pi$
$558$	1.08828	+	0.790682i	0.0460706	+	0.0334722i
$559$	0.254987	−	0.784770i	0.0107848	−	0.0331923i
$560$		0			0
$561$	−4.21865	−	12.9837i	−0.178112	−	0.548171i
$562$	−7.82254	+	24.0753i	−0.329974	+	1.01555i
$563$	1.76119	−	5.42039i	0.0742254	−	0.228442i	−0.907060	−	0.421001i	$-0.861679\pi$
$563$	1.76119	−	5.42039i	0.0742254	−	0.228442i	0.981285	+	0.192559i	$0.0616787\pi$
$564$	0.413862	+	1.27373i	0.0174267	+	0.0536339i
$565$		0			0
$566$	4.90947	−	15.1098i	0.206360	−	0.635112i
$567$	1.29103	+	0.937986i	0.0542180	+	0.0393917i
$568$	31.3350			1.31479
$569$	−16.3185	−	11.8561i	−0.684109	−	0.497034i	0.190610	−	0.981666i	$-0.438954\pi$
$569$	−16.3185	−	11.8561i	−0.684109	−	0.497034i	−0.874718	+	0.484632i	$0.838954\pi$
$570$		0			0
$571$	12.7464	−	9.26077i	0.533418	−	0.387551i	−0.288217	−	0.957565i	$-0.593062\pi$
$571$	12.7464	−	9.26077i	0.533418	−	0.387551i	0.821635	+	0.570014i	$0.193062\pi$
$572$	−3.33207	+	2.42089i	−0.139321	+	0.101222i
$573$	0.100682	+	0.309867i	0.00420605	+	0.0129449i
$574$	−2.50686			−0.104634
$575$		0			0
$576$	8.57279			0.357200
$577$	−4.97709	−	15.3179i	−0.207199	−	0.637692i	−0.999616	−	0.0277128i	$-0.991178\pi$
$577$	−4.97709	−	15.3179i	−0.207199	−	0.637692i	0.792417	−	0.609980i	$-0.208822\pi$
$578$	0.241245	−	0.175275i	0.0100345	−	0.00729047i
$579$	2.34766	−	1.70568i	0.0975656	−	0.0708855i
$580$		0			0
$581$	−6.48609	−	4.71242i	−0.269088	−	0.195504i
$582$	2.30441			0.0955207
$583$	1.41186	+	1.02578i	0.0584732	+	0.0424833i
$584$	5.04705	−	15.5332i	0.208848	−	0.642769i
$585$		0			0
$586$	9.30110	+	28.6258i	0.384225	+	1.18252i
$587$	0.618257	−	1.90280i	0.0255182	−	0.0785369i	−0.937486	−	0.348022i	$-0.886853\pi$
$587$	0.618257	−	1.90280i	0.0255182	−	0.0785369i	0.963005	+	0.269485i	$0.0868535\pi$
$588$	0.241189	−	0.742304i	0.00994648	−	0.0306121i
$589$	−0.174646	−	0.537504i	−0.00719614	−	0.0221475i
$590$		0			0
$591$	−5.60000	+	17.2350i	−0.230353	+	0.708954i
$592$	10.4029	+	7.55816i	0.427557	+	0.310638i
$593$	−26.8231			−1.10149			−0.550747	−	0.834672i	$-0.685657\pi$
$593$	−26.8231			−1.10149			−0.550747	+	0.834672i	$0.685657\pi$
$594$	−3.64220	−	2.64621i	−0.149441	−	0.108575i
$595$		0			0
$596$	0.551396	−	0.400613i	0.0225861	−	0.0164097i
$597$	−1.23987	+	0.900815i	−0.0507443	+	0.0368679i
$598$	18.5554	+	57.1076i	0.758786	+	2.33530i
$599$	−44.8025			−1.83058			−0.915290	−	0.402796i	$-0.868038\pi$
$599$	−44.8025			−1.83058			−0.915290	+	0.402796i	$0.868038\pi$
$600$		0			0
$601$	−14.2298			−0.580446			−0.290223	−	0.956959i	$-0.593729\pi$
$601$	−14.2298			−0.580446			−0.290223	+	0.956959i	$0.593729\pi$
$602$	0.0779519	+	0.239911i	0.00317708	+	0.00977805i
$603$	−12.3099	+	8.94370i	−0.501300	+	0.364216i
$604$	−3.13557	+	2.27813i	−0.127585	+	0.0926957i
$605$		0			0
$606$	−14.3979	−	10.4607i	−0.584873	−	0.424935i
$607$	−20.3346			−0.825356			−0.412678	−	0.910877i	$-0.635406\pi$
$607$	−20.3346			−0.825356			−0.412678	+	0.910877i	$0.635406\pi$
$608$	−0.453853	−	0.329743i	−0.0184062	−	0.0133729i
$609$	1.37266	−	4.22461i	0.0556230	−	0.171190i
$610$		0			0
$611$	16.6512	+	51.2470i	0.673634	+	2.07323i
$612$	0.221845	−	0.682768i	0.00896755	−	0.0275993i
$613$	−6.42510	+	19.7744i	−0.259507	+	0.798681i	0.733401	+	0.679797i	$0.237932\pi$
$613$	−6.42510	+	19.7744i	−0.259507	+	0.798681i	−0.992908	+	0.118885i	$0.962068\pi$
$614$	−6.38928	−	19.6642i	−0.257850	−	0.793582i
$615$		0			0
$616$	4.82922	−	14.8628i	0.194575	−	0.598839i
$617$	−4.00167	−	2.90738i	−0.161101	−	0.117047i	0.504314	−	0.863520i	$-0.331745\pi$
$617$	−4.00167	−	2.90738i	−0.161101	−	0.117047i	−0.665415	+	0.746474i	$0.731745\pi$
$618$	−14.6862			−0.590766
$619$	37.1765	+	27.0103i	1.49425	+	1.08564i	0.972602	+	0.232477i	$0.0746832\pi$
$619$	37.1765	+	27.0103i	1.49425	+	1.08564i	0.521650	+	0.853160i	$0.325317\pi$
$620$		0			0
$621$	5.10005	−	3.70540i	0.204658	−	0.148693i
$622$	14.0480	−	10.2065i	0.563273	−	0.409242i
$623$	−1.39235	−	4.28521i	−0.0557833	−	0.171683i
$624$	25.5171			1.02150
$625$		0			0
$626$	−14.1934			−0.567283
$627$	0.584494	+	1.79889i	0.0233424	+	0.0718407i
$628$	1.92914	−	1.40160i	0.0769810	−	0.0559299i
$629$	11.7755	−	8.55543i	0.469521	−	0.341127i
$630$		0			0
$631$	17.5262	+	12.7335i	0.697707	+	0.506914i	0.879185	−	0.476481i	$-0.158088\pi$
$631$	17.5262	+	12.7335i	0.697707	+	0.506914i	−0.181477	+	0.983395i	$0.558088\pi$
$632$	42.8915			1.70613
$633$	9.19833	+	6.68298i	0.365601	+	0.265625i
$634$	−8.13179	+	25.0271i	−0.322955	+	0.993952i
$635$		0			0
$636$	0.0283590	+	0.0872802i	0.00112451	+	0.00346088i
$637$	9.70393	−	29.8656i	0.384484	−	1.18332i
$638$	−3.87249	+	11.9183i	−0.153314	+	0.471851i
$639$	−3.29534	−	10.1420i	−0.130362	−	0.401211i
$640$		0			0
$641$	11.2442	−	34.6061i	0.444119	−	1.36686i	−0.439328	−	0.898327i	$-0.644783\pi$
$641$	11.2442	−	34.6061i	0.444119	−	1.36686i	0.883447	−	0.468531i	$-0.155217\pi$
$642$	10.2425	+	7.44163i	0.404240	+	0.293698i
$643$	−1.01349			−0.0399682			−0.0199841	−	0.999800i	$-0.506362\pi$
$643$	−1.01349			−0.0399682			−0.0199841	+	0.999800i	$0.506362\pi$
$644$	1.42637	+	1.03632i	0.0562069	+	0.0408367i
$645$		0			0
$646$	2.54060	−	1.84586i	0.0999587	−	0.0726243i
$647$	−11.0841	+	8.05306i	−0.435760	+	0.316598i	−0.783948	−	0.620826i	$-0.786797\pi$
$647$	−11.0841	+	8.05306i	−0.435760	+	0.316598i	0.348188	+	0.937425i	$0.386797\pi$
$648$	−0.908017	−	2.79459i	−0.0356703	−	0.109782i
$649$	3.27944			0.128729
$650$		0			0
$651$	1.58913			0.0622830
$652$	−0.467327	−	1.43829i	−0.0183019	−	0.0563276i
$653$	19.2847	−	14.0112i	0.754669	−	0.548299i	−0.142601	−	0.989780i	$-0.545547\pi$
$653$	19.2847	−	14.0112i	0.754669	−	0.548299i	0.897271	+	0.441481i	$0.145547\pi$
$654$	17.0374	−	12.3784i	0.666213	−	0.484032i
$655$		0			0
$656$	3.40463	+	2.47361i	0.132928	+	0.0965782i
$657$	−5.55832			−0.216851
$658$	−13.3269	−	9.68253i	−0.519535	−	0.377464i
$659$	4.56597	−	14.0526i	0.177865	−	0.547412i	−0.821888	−	0.569649i	$-0.807079\pi$
$659$	4.56597	−	14.0526i	0.177865	−	0.547412i	0.999753	+	0.0222376i	$0.00707903\pi$
$660$		0			0
$661$	2.33453	+	7.18496i	0.0908029	+	0.279463i	0.986137	−	0.165932i	$-0.0530633\pi$
$661$	2.33453	+	7.18496i	0.0908029	+	0.279463i	−0.895334	+	0.445395i	$0.853063\pi$
$662$	−6.04958	+	18.6187i	−0.235124	+	0.723637i
$663$	8.92563	−	27.4703i	0.346643	−	1.06686i
$664$	4.56186	+	14.0399i	0.177034	+	0.544856i
$665$		0			0
$666$	1.48327	−	4.56503i	0.0574755	−	0.176891i
$667$	−14.1964	−	10.3143i	−0.549685	−	0.399369i
$668$	−1.15652			−0.0447471
$669$	−13.7134	−	9.96335i	−0.530190	−	0.385205i
$670$		0			0
$671$	−28.6174	+	20.7917i	−1.10476	+	0.802656i
$672$	1.27615	−	0.927174i	0.0492284	−	0.0357665i
$673$	−3.76836	−	11.5978i	−0.145259	−	0.447063i	0.851785	−	0.523892i	$-0.175520\pi$
$673$	−3.76836	−	11.5978i	−0.145259	−	0.447063i	−0.997044	+	0.0768292i	$0.975520\pi$
$674$	12.6063			0.485576
$675$		0			0
$676$	−6.43571			−0.247527
$677$	5.54706	+	17.0721i	0.213191	+	0.656134i	0.999277	+	0.0380172i	$0.0121042\pi$
$677$	5.54706	+	17.0721i	0.213191	+	0.656134i	−0.786086	+	0.618117i	$0.787896\pi$
$678$	−10.9810	+	7.97815i	−0.421722	+	0.306399i
$679$	2.20239	−	1.60013i	0.0845198	−	0.0614073i
$680$		0			0
$681$	−11.4166	−	8.29466i	−0.437486	−	0.317852i
$682$	−4.48320			−0.171671
$683$	−8.11227	−	5.89391i	−0.310407	−	0.225524i	0.421664	−	0.906752i	$-0.361446\pi$
$683$	−8.11227	−	5.89391i	−0.310407	−	0.225524i	−0.732071	+	0.681228i	$0.761446\pi$
$684$	−0.0307366	+	0.0945975i	−0.00117524	+	0.00361703i
$685$		0			0
$686$	7.62950	+	23.4812i	0.291296	+	0.896516i
$687$	0.0191573	−	0.0589602i	0.000730898	−	0.00224947i
$688$	0.130861	−	0.402748i	0.00498901	−	0.0153546i
$689$	1.14099	+	3.51160i	0.0434682	+	0.133781i
$690$		0			0
$691$	5.91136	−	18.1933i	0.224879	−	0.692105i	−0.773425	−	0.633887i	$-0.781458\pi$
$691$	5.91136	−	18.1933i	0.224879	−	0.692105i	0.998304	−	0.0582177i	$-0.0185418\pi$
$692$	1.93675	+	1.40713i	0.0736242	+	0.0534911i
$693$	−5.31842			−0.202030
$694$	1.15121	+	0.836404i	0.0436994	+	0.0317494i
$695$		0			0
$696$	−6.61716	+	4.80765i	−0.250823	+	0.182234i
$697$	3.85386	−	2.79999i	0.145975	−	0.106057i
$698$	−5.45642	−	16.7931i	−0.206528	−	0.635629i
$699$	−26.0191			−0.984131
$700$		0			0
$701$	−3.81920			−0.144249			−0.0721246	−	0.997396i	$-0.522978\pi$
$701$	−3.81920			−0.144249			−0.0721246	+	0.997396i	$0.522978\pi$
$702$	−2.94343	−	9.05894i	−0.111092	−	0.341907i
$703$	−1.63150	+	1.18535i	−0.0615332	+	0.0447065i
$704$	−23.1145	+	16.7937i	−0.871162	+	0.632936i
$705$		0			0
$706$	−37.0991	−	26.9540i	−1.39624	−	1.01443i
$707$	−21.0241			−0.790692
$708$	0.139519	+	0.101366i	0.00524344	+	0.00380958i
$709$	11.7592	−	36.1911i	0.441626	−	1.35918i	−0.444517	−	0.895771i	$-0.646625\pi$
$709$	11.7592	−	36.1911i	0.441626	−	1.35918i	0.886142	−	0.463413i	$-0.153375\pi$
$710$		0			0
$711$	−4.51068	−	13.8824i	−0.169164	−	0.520632i
$712$	−2.56379	+	7.89053i	−0.0960821	+	0.295710i
$713$	1.93991	−	5.97043i	0.0726502	−	0.223594i
$714$	2.72864	+	8.39790i	0.102117	+	0.314284i
$715$		0			0
$716$	−0.532309	+	1.63828i	−0.0198933	+	0.0612253i
$717$	−15.7734	−	11.4601i	−0.589070	−	0.427984i
$718$	−8.23264			−0.307239
$719$	−15.7224	−	11.4230i	−0.586348	−	0.426007i	0.254659	−	0.967031i	$-0.418037\pi$
$719$	−15.7224	−	11.4230i	−0.586348	−	0.426007i	−0.841007	+	0.541024i	$0.818037\pi$
$720$		0			0
$721$	−14.0360	+	10.1978i	−0.522729	+	0.379785i
$722$	20.4120	−	14.8302i	0.759657	−	0.551923i
$723$	−1.26654	−	3.89800i	−0.0471030	−	0.144968i
$724$	−3.13165			−0.116387
$725$		0			0
$726$	0.145007			0.00538172
$727$	−11.7655	−	36.2104i	−0.436358	−	1.34297i	−0.891689	−	0.452649i	$-0.850479\pi$
$727$	−11.7655	−	36.2104i	−0.436358	−	1.34297i	0.455331	−	0.890322i	$-0.349521\pi$
$728$	26.7496	−	19.4347i	0.991406	−	0.720298i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$		0			0
$731$	−0.387802	−	0.281755i	−0.0143434	−	0.0104211i
$732$	−1.86015			−0.0687531
$733$	−13.7202	−	9.96833i	−0.506768	−	0.368189i	0.304828	−	0.952407i	$-0.401401\pi$
$733$	−13.7202	−	9.96833i	−0.506768	−	0.368189i	−0.811596	+	0.584219i	$0.801401\pi$
$734$	−9.12653	+	28.0886i	−0.336866	+	1.03677i
$735$		0			0
$736$	−1.92559	−	5.92635i	−0.0709781	−	0.218448i
$737$	15.6706	−	48.2292i	0.577235	−	1.77655i
$738$	0.485439	−	1.49403i	0.0178693	−	0.0549959i
$739$	4.08025	+	12.5577i	0.150095	+	0.461944i	0.997631	−	0.0687937i	$-0.0219150\pi$
$739$	4.08025	+	12.5577i	0.150095	+	0.461944i	−0.847536	+	0.530737i	$0.821915\pi$
$740$		0			0
$741$	−1.23665	+	3.80600i	−0.0454293	+	0.139817i
$742$	−0.913197	−	0.663476i	−0.0335245	−	0.0243570i
$743$	42.2364			1.54950			0.774752	−	0.632265i	$-0.217875\pi$
$743$	42.2364			1.54950			0.774752	+	0.632265i	$0.217875\pi$
$744$	−2.36729	−	1.71994i	−0.0867891	−	0.0630560i
$745$		0			0
$746$	26.7265	−	19.4180i	0.978528	−	0.710942i
$747$	4.06448	−	2.95302i	0.148712	−	0.108045i
$748$	0.739358	+	2.27551i	0.0270336	+	0.0832008i
$749$	14.9564			0.546494
$750$		0			0
$751$	−1.04801			−0.0382426			−0.0191213	−	0.999817i	$-0.506087\pi$
$751$	−1.04801			−0.0382426			−0.0191213	+	0.999817i	$0.506087\pi$
$752$	8.54545	+	26.3002i	0.311620	+	0.959069i
$753$	0.832742	−	0.605022i	0.0303468	−	0.0220482i
$754$	−21.4502	+	15.5845i	−0.781170	+	0.567553i
$755$		0			0
$756$	−0.226264	−	0.164391i	−0.00822915	−	0.00597883i
$757$	17.0074			0.618146			0.309073	−	0.951038i	$-0.399981\pi$
$757$	17.0074			0.618146			0.309073	+	0.951038i	$0.399981\pi$
$758$	6.86110	+	4.98488i	0.249207	+	0.181059i
$759$	−6.49238	+	19.9815i	−0.235658	+	0.725282i
$760$		0			0
$761$	−7.45484	−	22.9436i	−0.270238	−	0.831706i	−0.990440	−	0.137942i	$-0.955951\pi$
$761$	−7.45484	−	22.9436i	−0.270238	−	0.831706i	0.720203	−	0.693764i	$-0.244049\pi$
$762$	−0.407738	+	1.25489i	−0.0147708	+	0.0454599i
$763$	7.68783	−	23.6607i	0.278318	−	0.856575i
$764$	−0.0176454	−	0.0543070i	−0.000638389	−	0.00196476i
$765$		0			0
$766$	10.3053	−	31.7165i	0.372346	−	1.14596i
$767$	5.61335	+	4.07834i	0.202686	+	0.147260i
$768$	−4.17298			−0.150579
$769$	−40.2744	−	29.2611i	−1.45233	−	1.05518i	−0.985279	−	0.170952i	$-0.945316\pi$
$769$	−40.2744	−	29.2611i	−1.45233	−	1.05518i	−0.467053	−	0.884230i	$-0.654684\pi$
$770$		0			0
$771$	15.0151	−	10.9091i	0.540757	−	0.392883i
$772$	−0.411450	+	0.298936i	−0.0148084	+	0.0107589i
$773$	−9.72608	−	29.9338i	−0.349823	−	1.07664i	−0.958951	−	0.283572i	$-0.908480\pi$
$773$	−9.72608	−	29.9338i	−0.349823	−	1.07664i	0.609128	−	0.793072i	$-0.291520\pi$
$774$	−0.158076			−0.00568193
$775$		0			0
$776$	−5.01268			−0.179945
$777$	−1.75225	−	5.39288i	−0.0628617	−	0.193468i
$778$	14.1235	−	10.2613i	0.506350	−	0.367885i
$779$	−0.533952	+	0.387939i	−0.0191308	+	0.0138993i
$780$		0			0
$781$	28.7528	+	20.8901i	1.02886	+	0.747508i
$782$	34.8822			1.24738
$783$	2.25196	+	1.63614i	0.0804784	+	0.0584710i
$784$	4.98010	−	15.3272i	0.177861	−	0.547399i
$785$		0			0
$786$	4.20001	+	12.9263i	0.149809	+	0.461066i
$787$	−5.91505	+	18.2047i	−0.210849	+	0.648926i	0.788573	+	0.614941i	$0.210820\pi$
$787$	−5.91505	+	18.2047i	−0.210849	+	0.648926i	−0.999422	+	0.0339855i	$0.989180\pi$
$788$	0.981451	−	3.02060i	0.0349627	−	0.107604i
$789$	3.82988	+	11.7872i	0.136347	+	0.419634i
$790$		0			0
$791$	−4.95499	+	15.2499i	−0.176179	+	0.542224i
$792$	7.92272	+	5.75619i	0.281522	+	0.204537i
$793$	−74.8406			−2.65767
$794$	31.7159	+	23.0430i	1.12556	+	0.817764i
$795$		0			0
$796$	0.217298	−	0.157876i	0.00770191	−	0.00559577i
$797$	5.83655	−	4.24050i	0.206741	−	0.150206i	−0.479597	−	0.877489i	$-0.659217\pi$
$797$	5.83655	−	4.24050i	0.206741	−	0.150206i	0.686338	+	0.727283i	$0.259217\pi$
$798$	−0.378053	−	1.16353i	−0.0133829	−	0.0411885i
$799$	31.3024			1.10740
$800$		0			0
$801$	2.82350			0.0997636
$802$	9.76474	+	30.0528i	0.344805	+	1.06120i
$803$	14.9867	−	10.8885i	0.528869	−	0.384246i
$804$	2.15743	−	1.56747i	0.0760867	−	0.0552802i
$805$		0			0
$806$	−7.67381	−	5.57535i	−0.270298	−	0.196383i
$807$	−5.30032			−0.186580
$808$	31.3191	+	22.7546i	1.10180	+	0.800505i
$809$	0.327376	−	1.00756i	0.0115099	−	0.0354239i	−0.945137	−	0.326675i	$-0.894072\pi$
$809$	0.327376	−	1.00756i	0.0115099	−	0.0354239i	0.956647	+	0.291251i	$0.0940716\pi$
$810$		0			0
$811$	6.68712	+	20.5808i	0.234817	+	0.722691i	0.997146	+	0.0755016i	$0.0240558\pi$
$811$	6.68712	+	20.5808i	0.234817	+	0.722691i	−0.762329	+	0.647190i	$0.775944\pi$
$812$	−0.240571	+	0.740402i	−0.00844239	+	0.0259830i
$813$	0.246419	−	0.758399i	0.00864228	−	0.0265982i
$814$	4.94339	+	15.2142i	0.173266	+	0.533257i
$815$		0			0
$816$	4.58067	−	14.0979i	0.160356	−	0.493524i
$817$	0.0537299	+	0.0390371i	0.00187977	+	0.00136573i
$818$	−21.6022			−0.755302
$819$	−9.10344	−	6.61404i	−0.318100	−	0.231113i
$820$		0			0
$821$	18.7553	−	13.6265i	0.654564	−	0.475568i	−0.210259	−	0.977646i	$-0.567431\pi$
$821$	18.7553	−	13.6265i	0.654564	−	0.475568i	0.864823	+	0.502077i	$0.167431\pi$
$822$	5.32482	−	3.86871i	0.185724	−	0.134937i
$823$	−8.64534	−	26.6076i	−0.301358	−	0.927483i	−0.981011	−	0.193950i	$-0.937870\pi$
$823$	−8.64534	−	26.6076i	−0.301358	−	0.927483i	0.679654	−	0.733533i	$-0.262130\pi$
$824$	31.9463			1.11290
$825$		0			0
$826$	−2.12116			−0.0738044
$827$	−12.7638	−	39.2829i	−0.443841	−	1.36600i	−0.883750	−	0.467959i	$-0.844989\pi$
$827$	−12.7638	−	39.2829i	−0.443841	−	1.36600i	0.439909	−	0.898042i	$-0.355011\pi$
$828$	−0.893830	+	0.649405i	−0.0310627	+	0.0225684i
$829$	−38.4838	+	27.9602i	−1.33660	+	0.971096i	−0.337038	+	0.941491i	$0.609425\pi$
$829$	−38.4838	+	27.9602i	−1.33660	+	0.971096i	−0.999562	+	0.0296051i	$0.990575\pi$
$830$		0			0
$831$	3.83818	+	2.78860i	0.133145	+	0.0967355i
$832$	−60.4495			−2.09571
$833$	−14.7584	−	10.7226i	−0.511348	−	0.371516i
$834$	0.0775516	−	0.238679i	0.00268539	−	0.00826478i
$835$		0			0
$836$	−0.102438	−	0.315272i	−0.00354289	−	0.0109039i
$837$	−0.307727	+	0.947085i	−0.0106366	+	0.0327360i
$838$	13.5151	−	41.5951i	0.466871	−	1.43688i
$839$	15.1518	+	46.6324i	0.523097	+	1.60993i	0.768048	+	0.640393i	$0.221228\pi$
$839$	15.1518	+	46.6324i	0.523097	+	1.60993i	−0.244950	+	0.969536i	$0.578772\pi$
$840$		0			0
$841$	−6.56714	+	20.2116i	−0.226453	+	0.696951i
$842$	−19.7280	−	14.3332i	−0.679872	−	0.493956i
$843$	−18.7398			−0.645433
$844$	−1.61209	−	1.17125i	−0.0554905	−	0.0403162i
$845$		0			0
$846$	8.35122	−	6.06752i	0.287121	−	0.208606i
$847$	0.138588	−	0.100690i	0.00476192	−	0.00345974i
$848$	0.585560	+	1.80217i	0.0201082	+	0.0618867i
$849$	11.7612			0.403643
$850$		0			0
$851$	−22.4003			−0.767871
$852$	0.577538	+	1.77748i	0.0197861	+	0.0608954i
$853$	26.3235	−	19.1251i	0.901299	−	0.654832i	−0.0375002	−	0.999297i	$-0.511939\pi$
$853$	26.3235	−	19.1251i	0.901299	−	0.654832i	0.938799	+	0.344464i	$0.111939\pi$
$854$	18.5099	−	13.4482i	0.633394	−	0.460188i
$855$		0			0
$856$	−22.2801	−	16.1875i	−0.761520	−	0.553276i
$857$	−30.4813			−1.04122			−0.520610	−	0.853794i	$-0.674296\pi$
$857$	−30.4813			−1.04122			−0.520610	+	0.853794i	$0.674296\pi$
$858$	25.6823	+	18.6593i	0.876779	+	0.637017i
$859$	1.27382	−	3.92040i	0.0434620	−	0.133762i	−0.926971	−	0.375133i	$-0.877597\pi$
$859$	1.27382	−	3.92040i	0.0434620	−	0.133762i	0.970433	+	0.241371i	$0.0775970\pi$
$860$		0			0
$861$	−0.573471	−	1.76496i	−0.0195439	−	0.0601498i
$862$	13.8316	−	42.5694i	0.471107	−	1.44992i
$863$	−5.69159	+	17.5169i	−0.193744	+	0.596283i	0.806245	+	0.591582i	$0.201496\pi$
$863$	−5.69159	+	17.5169i	−0.193744	+	0.596283i	−0.999989	+	0.00470109i	$0.998504\pi$
$864$	0.305455	+	0.940094i	0.0103918	+	0.0319826i
$865$		0			0
$866$	−9.46115	+	29.1184i	−0.321503	+	0.989485i
$867$	0.178590	+	0.129753i	0.00606524	+	0.00440666i
$868$	−0.278510			−0.00945325
$869$	39.3570	+	28.5945i	1.33510	+	0.970003i
$870$		0			0
$871$	86.8013	−	63.0649i	2.94115	−	2.13687i
$872$	−37.0607	+	26.9261i	−1.25503	+	0.911834i
$873$	0.527158	+	1.62242i	0.0178416	+	0.0549108i
$874$	−4.83292			−0.163476
$875$		0			0
$876$	0.974146			0.0329133
$877$	−5.84432	−	17.9870i	−0.197349	−	0.607377i	−0.999941	−	0.0108490i	$-0.996547\pi$
$877$	−5.84432	−	17.9870i	−0.197349	−	0.607377i	0.802593	−	0.596528i	$-0.203453\pi$
$878$	9.29394	−	6.75244i	0.313655	−	0.227884i
$879$	−18.0264	+	13.0969i	−0.608015	+	0.441749i
$880$		0			0
$881$	−28.0192	−	20.3571i	−0.943990	−	0.685849i	0.00538802	−	0.999985i	$-0.498285\pi$
$881$	−28.0192	−	20.3571i	−0.943990	−	0.685849i	−0.949378	+	0.314137i	$0.898285\pi$
$882$	−6.01583			−0.202563
$883$	26.4447	+	19.2132i	0.889934	+	0.646575i	0.935861	−	0.352370i	$-0.114624\pi$
$883$	26.4447	+	19.2132i	0.889934	+	0.646575i	−0.0459269	+	0.998945i	$0.514624\pi$
$884$	−1.56430	+	4.81442i	−0.0526131	+	0.161926i
$885$		0			0
$886$	2.65388	+	8.16781i	0.0891589	+	0.274403i
$887$	15.0775	−	46.4037i	0.506253	−	1.55809i	−0.292402	−	0.956296i	$-0.594455\pi$
$887$	15.0775	−	46.4037i	0.506253	−	1.55809i	0.798655	−	0.601790i	$-0.205545\pi$
$888$	−3.22649	+	9.93012i	−0.108274	+	0.333233i
$889$	0.481680	+	1.48246i	0.0161550	+	0.0497201i
$890$		0			0
$891$	1.02988	−	3.16965i	0.0345024	−	0.106187i
$892$	2.40340	+	1.74617i	0.0804716	+	0.0584661i
$893$	−4.33695			−0.145131
$894$	−4.24995	−	3.08777i	−0.142139	−	0.103270i
$895$		0			0
$896$	12.3983	−	9.00789i	0.414198	−	0.300932i
$897$	−35.9620	+	26.1280i	−1.20074	+	0.872387i
$898$	−2.61196	−	8.03879i	−0.0871623	−	0.268258i
$899$	2.77195			0.0924497
$900$		0			0
$901$	2.14494			0.0714582
$902$	1.61786	+	4.97925i	0.0538687	+	0.165791i
$903$	−0.151078	+	0.109765i	−0.00502756	+	0.00365274i
$904$	23.8865	−	17.3545i	0.794452	−	0.577203i
$905$		0			0
$906$	24.1678	+	17.5589i	0.802921	+	0.583356i
$907$	45.0367			1.49542			0.747710	−	0.664025i	$-0.231153\pi$
$907$	45.0367			1.49542			0.747710	+	0.664025i	$0.231153\pi$
$908$	2.00087	+	1.45371i	0.0664011	+	0.0482432i
$909$	4.07120	−	12.5299i	0.135033	−	0.415589i
$910$		0			0
$911$	4.00018	+	12.3113i	0.132532	+	0.407891i	0.995198	−	0.0978826i	$-0.0312070\pi$
$911$	4.00018	+	12.3113i	0.132532	+	0.407891i	−0.862666	+	0.505774i	$0.831207\pi$
$912$	−0.634652	+	1.95326i	−0.0210154	+	0.0646788i
$913$	−5.17410	+	15.9243i	−0.171238	+	0.527016i
$914$	−4.61012	−	14.1885i	−0.152489	−	0.469314i
$915$		0			0
$916$	−0.00335750	+	0.0103333i	−0.000110935	+	0.000341423i
$917$	12.9898	+	9.43764i	0.428961	+	0.311658i
$918$	−5.53333			−0.182627
$919$	−11.7889	−	8.56513i	−0.388880	−	0.282538i	0.376117	−	0.926572i	$-0.377259\pi$
$919$	−11.7889	−	8.56513i	−0.388880	−	0.282538i	−0.764996	+	0.644035i	$0.777259\pi$
$920$		0			0
$921$	12.3830	−	8.99679i	0.408034	−	0.296454i
$922$	25.8591	−	18.7877i	0.851623	−	0.618741i
$923$	23.2365	+	71.5145i	0.764838	+	2.35393i
$924$	0.932102			0.0306639
$925$		0			0
$926$	−8.40813			−0.276308
$927$	−3.35963	−	10.3399i	−0.110345	−	0.339606i
$928$	2.22600	−	1.61728i	0.0730720	−	0.0530899i
$929$	25.3701	−	18.4324i	0.832365	−	0.604749i	−0.0878623	−	0.996133i	$-0.528004\pi$
$929$	25.3701	−	18.4324i	0.832365	−	0.604749i	0.920227	+	0.391384i	$0.128004\pi$
$930$		0			0
$931$	2.04477	+	1.48561i	0.0670147	+	0.0486890i
$932$	4.56008			0.149370
$933$	10.3995	+	7.55569i	0.340465	+	0.247362i
$934$	2.06494	−	6.35522i	0.0675668	−	0.207949i
$935$		0			0
$936$	6.40272	+	19.7055i	0.209279	+	0.644095i
$937$	−15.0716	+	46.3855i	−0.492367	+	1.51535i	0.328654	+	0.944450i	$0.393405\pi$
$937$	−15.0716	+	46.3855i	−0.492367	+	1.51535i	−0.821021	+	0.570898i	$0.806595\pi$
$938$	−10.1358	+	31.1949i	−0.330946	+	1.01855i
$939$	−3.24690	−	9.99293i	−0.105959	−	0.326107i
$940$		0			0
$941$	−9.96145	+	30.6582i	−0.324734	+	0.999429i	0.646827	+	0.762637i	$0.276096\pi$
$941$	−9.96145	+	30.6582i	−0.324734	+	0.999429i	−0.971561	+	0.236791i	$0.923904\pi$
$942$	−14.8690	−	10.8030i	−0.484460	−	0.351980i
$943$	−7.33108			−0.238733
$944$	2.88080	+	2.09302i	0.0937619	+	0.0681220i
$945$		0			0
$946$	0.426216	−	0.309664i	0.0138575	−	0.0100680i
$947$	42.0070	−	30.5199i	1.36505	−	0.991763i	0.366939	−	0.930245i	$-0.380406\pi$
$947$	42.0070	−	30.5199i	1.36505	−	0.991763i	0.998106	−	0.0615183i	$-0.0195942\pi$
$948$	0.790537	+	2.43302i	0.0256755	+	0.0790209i
$949$	39.1935			1.27227
$950$		0			0
$951$	−19.4806			−0.631703
$952$	−5.93551	−	18.2676i	−0.192371	−	0.592057i
$953$	32.1817	−	23.3814i	1.04247	−	0.757398i	0.0717028	−	0.997426i	$-0.477157\pi$
$953$	32.1817	−	23.3814i	1.04247	−	0.757398i	0.970766	+	0.240028i	$0.0771567\pi$
$954$	0.572251	−	0.415765i	0.0185273	−	0.0134609i
$955$		0			0
$956$	2.76444	+	2.00848i	0.0894083	+	0.0649590i
$957$	−9.27701			−0.299883
$958$	32.8835	+	23.8912i	1.06242	+	0.771891i
$959$	2.40274	−	7.39487i	0.0775885	−	0.238793i
$960$		0			0
$961$	−9.27309	−	28.5396i	−0.299132	−	0.920633i
$962$	−10.4590	+	32.1895i	−0.337211	+	1.03783i
$963$	−2.89622	+	8.91364i	−0.0933293	+	0.287238i
$964$	0.221972	+	0.683160i	0.00714924	+	0.0220031i
$965$		0			0
$966$	4.19930	−	12.9241i	0.135110	−	0.415827i
$967$	16.0847	+	11.6862i	0.517248	+	0.375802i	0.815566	−	0.578664i	$-0.196426\pi$
$967$	16.0847	+	11.6862i	0.517248	+	0.375802i	−0.298318	+	0.954466i	$0.596426\pi$
$968$	−0.315428			−0.0101382
$969$	1.88077	+	1.36646i	0.0604191	+	0.0438971i
$970$		0			0
$971$	33.4804	−	24.3250i	1.07444	−	0.780625i	0.0977335	−	0.995213i	$-0.468841\pi$
$971$	33.4804	−	24.3250i	1.07444	−	0.780625i	0.976705	+	0.214588i	$0.0688407\pi$
$972$	0.141788	−	0.103015i	0.00454784	−	0.00330420i
$973$	−0.0916152	−	0.281963i	−0.00293705	−	0.00903931i
$974$	−46.2658			−1.48245
$975$		0			0
$976$	−38.4085			−1.22943
$977$	−1.11861	−	3.44274i	−0.0357876	−	0.110143i	0.931567	−	0.363570i	$-0.118442\pi$
$977$	−1.11861	−	3.44274i	−0.0357876	−	0.110143i	−0.967355	+	0.253427i	$0.918442\pi$
$978$	−9.43010	+	6.85137i	−0.301541	+	0.219083i
$979$	−7.61292	+	5.53111i	−0.243310	+	0.176775i
$980$		0			0
$981$	12.6125	+	9.16353i	0.402686	+	0.292569i
$982$	−14.0747			−0.449143
$983$	−16.2692	−	11.8203i	−0.518907	−	0.377008i	0.297285	−	0.954789i	$-0.403919\pi$
$983$	−16.2692	−	11.8203i	−0.518907	−	0.377008i	−0.816192	+	0.577781i	$0.803919\pi$
$984$	−1.05596	+	3.24990i	−0.0336626	+	0.103603i
$985$		0			0
$986$	4.75962	+	14.6486i	0.151577	+	0.466506i
$987$	3.76836	−	11.5978i	0.119948	−	0.369162i
$988$	0.216733	−	0.667037i	0.00689521	−	0.0212213i
$989$	0.227963	+	0.701599i	0.00724881	+	0.0223095i
$990$		0			0
$991$	2.29905	−	7.07576i	0.0730319	−	0.224769i	−0.907877	−	0.419236i	$-0.862298\pi$
$991$	2.29905	−	7.07576i	0.0730319	−	0.224769i	0.980909	+	0.194467i	$0.0622978\pi$
$992$	0.796352	+	0.578584i	0.0252842	+	0.0183700i
$993$	−14.4925			−0.459905
$994$	−18.5974	−	13.5118i	−0.589875	−	0.428569i
$995$		0			0
$996$	−0.712338	+	0.517544i	−0.0225713	+	0.0163990i
$997$	−37.3338	+	27.1246i	−1.18237	+	0.859045i	−0.992438	−	0.122751i	$-0.960828\pi$
$997$	−37.3338	+	27.1246i	−1.18237	+	0.859045i	−0.189937	+	0.981796i	$0.560828\pi$
$998$	3.68804	+	11.3506i	0.116743	+	0.359298i
$999$	3.55334			0.112423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.e.151.4		16
5.2	odd	4		375.2.i.c.349.2		16
5.3	odd	4		75.2.i.a.19.3	yes	16
5.4	even	2		375.2.g.d.151.1		16
15.8	even	4		225.2.m.b.19.2		16
25.2	odd	20		1875.2.b.h.1249.12		16
25.3	odd	20		375.2.i.c.274.2		16
25.4	even	10		375.2.g.d.226.1		16
25.11	even	5		1875.2.a.m.1.7		8
25.14	even	10		1875.2.a.p.1.2		8
25.21	even	5	inner	375.2.g.e.226.4		16
25.22	odd	20		75.2.i.a.4.3	✓	16
25.23	odd	20		1875.2.b.h.1249.5		16
75.11	odd	10		5625.2.a.bd.1.2		8
75.14	odd	10		5625.2.a.t.1.7		8
75.47	even	20		225.2.m.b.154.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.3	✓	16	25.22	odd	20
75.2.i.a.19.3	yes	16	5.3	odd	4
225.2.m.b.19.2		16	15.8	even	4
225.2.m.b.154.2		16	75.47	even	20
375.2.g.d.151.1		16	5.4	even	2
375.2.g.d.226.1		16	25.4	even	10
375.2.g.e.151.4		16	1.1	even	1	trivial
375.2.g.e.226.4		16	25.21	even	5	inner
375.2.i.c.274.2		16	25.3	odd	20
375.2.i.c.349.2		16	5.2	odd	4
1875.2.a.m.1.7		8	25.11	even	5
1875.2.a.p.1.2		8	25.14	even	10
1875.2.b.h.1249.5		16	25.23	odd	20
1875.2.b.h.1249.12		16	25.2	odd	20
5625.2.a.t.1.7		8	75.14	odd	10
5625.2.a.bd.1.2		8	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)

\(f(q)\)	\(=\)	\(q+(0.417429 + 1.28472i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.141788 - 0.103015i) q^{4} +(-1.09284 - 0.793998i) q^{6} -1.59580 q^{7} +(2.37722 + 1.72715i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.417429 + 1.28472i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(0.141788 - 0.103015i) q^{4} +(-1.09284 - 0.793998i) q^{6} -1.59580 q^{7} +(2.37722 + 1.72715i) q^{8} +(0.309017 - 0.951057i) q^{9} +(1.02988 + 3.16965i) q^{11} +(-0.0541581 + 0.166681i) q^{12} +(-2.17898 + 6.70620i) q^{13} +(-0.666132 - 2.05014i) q^{14} +(-1.11826 + 3.44165i) q^{16} +(3.31393 + 2.40771i) q^{17} +1.35083 q^{18} +(-0.459145 - 0.333589i) q^{19} +(1.29103 - 0.937986i) q^{21} +(-3.64220 + 2.64621i) q^{22} +(-1.94804 - 5.99546i) q^{23} -2.93840 q^{24} -9.52513 q^{26} +(0.309017 + 0.951057i) q^{27} +(-0.226264 + 0.164391i) q^{28} +(2.25196 - 1.63614i) q^{29} +(0.805639 + 0.585331i) q^{31} +0.988473 q^{32} +(-2.69627 - 1.95895i) q^{33} +(-1.70989 + 5.26251i) q^{34} +(-0.0541581 - 0.166681i) q^{36} +(1.09804 - 3.37943i) q^{37} +(0.236906 - 0.729121i) q^{38} +(-2.17898 - 6.70620i) q^{39} +(0.359364 - 1.10601i) q^{41} +(1.74396 + 1.26706i) q^{42} -0.117022 q^{43} +(0.472545 + 0.343324i) q^{44} +(6.88929 - 5.00536i) q^{46} +(6.18229 - 4.49170i) q^{47} +(-1.11826 - 3.44165i) q^{48} -4.45343 q^{49} -4.09625 q^{51} +(0.381886 + 1.17532i) q^{52} +(0.423629 - 0.307785i) q^{53} +(-1.09284 + 0.793998i) q^{54} +(-3.79356 - 2.75618i) q^{56} +0.567535 q^{57} +(3.04201 + 2.21015i) q^{58} +(0.304072 - 0.935838i) q^{59} +(3.27982 + 10.0942i) q^{61} +(-0.415686 + 1.27935i) q^{62} +(-0.493128 + 1.51769i) q^{63} +(2.64914 + 8.15321i) q^{64} +(1.39120 - 4.28166i) q^{66} +(-12.3099 - 8.94370i) q^{67} +0.717905 q^{68} +(5.10005 + 3.70540i) q^{69} +(8.62730 - 6.26810i) q^{71} +(2.37722 - 1.72715i) q^{72} +(-1.71761 - 5.28627i) q^{73} +4.79996 q^{74} -0.0994657 q^{76} +(-1.64348 - 5.05812i) q^{77} +(7.70599 - 5.59873i) q^{78} +(11.8091 - 8.57982i) q^{79} +(-0.809017 - 0.587785i) q^{81} +1.57091 q^{82} +(4.06448 + 2.95302i) q^{83} +(0.0864253 - 0.265990i) q^{84} +(-0.0488483 - 0.150339i) q^{86} +(-0.860172 + 2.64734i) q^{87} +(-3.02621 + 9.31372i) q^{88} +(0.872511 + 2.68531i) q^{89} +(3.47720 - 10.7017i) q^{91} +(-0.893830 - 0.649405i) q^{92} -0.995824 q^{93} +(8.35122 + 6.06752i) q^{94} +(-0.799691 + 0.581010i) q^{96} +(-1.38012 + 1.00271i) q^{97} +(-1.85899 - 5.72139i) q^{98} +3.33277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9	\( 16 q + 2 q^{2} - 4 q^{3} - 2 q^{4} + 2 q^{6} - 16 q^{7} + 6 q^{8} - 4 q^{9} - 6 q^{11} - 2 q^{12} + 8 q^{13} + 12 q^{14} - 10 q^{16} + 8 q^{17} - 8 q^{18} + 2 q^{19} + 4 q^{21} - 4 q^{22} + 2 q^{23} - 24 q^{24} + 12 q^{26} - 4 q^{27} + 28 q^{28} - 16 q^{29} + 6 q^{31} + 4 q^{32} + 4 q^{33} + 36 q^{34} - 2 q^{36} + 24 q^{37} - 38 q^{38} + 8 q^{39} - 14 q^{41} - 18 q^{42} - 40 q^{43} - 26 q^{44} + 16 q^{46} - 10 q^{47} - 10 q^{48} - 32 q^{51} + 48 q^{52} + 12 q^{53} + 2 q^{54} - 28 q^{57} + 44 q^{58} - 12 q^{59} + 28 q^{62} + 4 q^{63} - 8 q^{64} + 16 q^{66} - 12 q^{67} + 4 q^{68} + 12 q^{69} - 8 q^{71} + 6 q^{72} - 8 q^{73} + 52 q^{74} - 32 q^{76} + 18 q^{77} + 32 q^{78} + 20 q^{79} - 4 q^{81} - 32 q^{82} + 6 q^{83} - 12 q^{84} - 36 q^{86} + 14 q^{87} + 16 q^{88} - 18 q^{89} + 26 q^{91} - 36 q^{92} - 44 q^{93} + 38 q^{94} - 26 q^{96} + 8 q^{97} - 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 - 4 * q^3 - 2 * q^4 + 2 * q^6 - 16 * q^7 + 6 * q^8 - 4 * q^9 - 6 * q^11 - 2 * q^12 + 8 * q^13 + 12 * q^14 - 10 * q^16 + 8 * q^17 - 8 * q^18 + 2 * q^19 + 4 * q^21 - 4 * q^22 + 2 * q^23 - 24 * q^24 + 12 * q^26 - 4 * q^27 + 28 * q^28 - 16 * q^29 + 6 * q^31 + 4 * q^32 + 4 * q^33 + 36 * q^34 - 2 * q^36 + 24 * q^37 - 38 * q^38 + 8 * q^39 - 14 * q^41 - 18 * q^42 - 40 * q^43 - 26 * q^44 + 16 * q^46 - 10 * q^47 - 10 * q^48 - 32 * q^51 + 48 * q^52 + 12 * q^53 + 2 * q^54 - 28 * q^57 + 44 * q^58 - 12 * q^59 + 28 * q^62 + 4 * q^63 - 8 * q^64 + 16 * q^66 - 12 * q^67 + 4 * q^68 + 12 * q^69 - 8 * q^71 + 6 * q^72 - 8 * q^73 + 52 * q^74 - 32 * q^76 + 18 * q^77 + 32 * q^78 + 20 * q^79 - 4 * q^81 - 32 * q^82 + 6 * q^83 - 12 * q^84 - 36 * q^86 + 14 * q^87 + 16 * q^88 - 18 * q^89 + 26 * q^91 - 36 * q^92 - 44 * q^93 + 38 * q^94 - 26 * q^96 + 8 * q^97 - 18 * q^98 + 4 * q^99

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