LMFDB - Embedded newform 375.2.i.c.274.2

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} + 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:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			274.2
Root			$1.35083i$ of defining polynomial
Character	$\chi$	$=$	375.274
Dual form			375.2.i.c.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28472 - 0.417429i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.141788 - 0.103015i) q^{4} +(-1.09284 + 0.793998i) q^{6} +1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(-1.28472 - 0.417429i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.141788 - 0.103015i) q^{4} +(-1.09284 + 0.793998i) q^{6} +1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.02988 - 3.16965i) q^{11} +(-0.166681 + 0.0541581i) q^{12} +(6.70620 - 2.17898i) q^{13} +(0.666132 - 2.05014i) q^{14} +(-1.11826 - 3.44165i) q^{16} +(-2.40771 - 3.31393i) q^{17} +1.35083i q^{18} +(0.459145 - 0.333589i) q^{19} +(1.29103 + 0.937986i) q^{21} +(-2.64621 + 3.64220i) q^{22} +(-5.99546 - 1.94804i) q^{23} +2.93840 q^{24} -9.52513 q^{26} +(-0.951057 - 0.309017i) q^{27} +(0.164391 - 0.226264i) q^{28} +(-2.25196 - 1.63614i) q^{29} +(0.805639 - 0.585331i) q^{31} -0.988473i q^{32} +(-1.95895 - 2.69627i) q^{33} +(1.70989 + 5.26251i) q^{34} +(-0.0541581 + 0.166681i) q^{36} +(3.37943 - 1.09804i) q^{37} +(-0.729121 + 0.236906i) q^{38} +(2.17898 - 6.70620i) q^{39} +(0.359364 + 1.10601i) q^{41} +(-1.26706 - 1.74396i) q^{42} -0.117022i q^{43} +(-0.472545 + 0.343324i) q^{44} +(6.88929 + 5.00536i) q^{46} +(4.49170 - 6.18229i) q^{47} +(-3.44165 - 1.11826i) q^{48} +4.45343 q^{49} -4.09625 q^{51} +(-1.17532 - 0.381886i) q^{52} +(-0.307785 + 0.423629i) q^{53} +(1.09284 + 0.793998i) q^{54} +(-3.79356 + 2.75618i) q^{56} -0.567535i q^{57} +(2.21015 + 3.04201i) q^{58} +(-0.304072 - 0.935838i) q^{59} +(3.27982 - 10.0942i) q^{61} +(-1.27935 + 0.415686i) q^{62} +(1.51769 - 0.493128i) q^{63} +(-2.64914 + 8.15321i) q^{64} +(1.39120 + 4.28166i) q^{66} +(8.94370 + 12.3099i) q^{67} +0.717905i q^{68} +(-5.10005 + 3.70540i) q^{69} +(8.62730 + 6.26810i) q^{71} +(1.72715 - 2.37722i) q^{72} +(-5.28627 - 1.71761i) q^{73} -4.79996 q^{74} -0.0994657 q^{76} +(5.05812 + 1.64348i) q^{77} +(-5.59873 + 7.70599i) q^{78} +(-11.8091 - 8.57982i) q^{79} +(-0.809017 + 0.587785i) q^{81} -1.57091i q^{82} +(2.95302 + 4.06448i) q^{83} +(-0.0864253 - 0.265990i) q^{84} +(-0.0488483 + 0.150339i) q^{86} +(-2.64734 + 0.860172i) q^{87} +(9.31372 - 3.02621i) q^{88} +(-0.872511 + 2.68531i) q^{89} +(3.47720 + 10.7017i) q^{91} +(0.649405 + 0.893830i) q^{92} -0.995824i q^{93} +(-8.35122 + 6.06752i) q^{94} +(-0.799691 - 0.581010i) q^{96} +(-1.00271 + 1.38012i) q^{97} +(-5.72139 - 1.85899i) q^{98} -3.33277 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	$ 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) $ 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.28472	−	0.417429i	−0.908431	−	0.295167i	−0.182719	−	0.983165i	$-0.558490\pi$
$2$	−1.28472	−	0.417429i	−0.908431	−	0.295167i	−0.725712	+	0.687998i	$0.758490\pi$
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.141788	−	0.103015i	−0.0708938	−	0.0515074i
$5$		0			0
$5$		0			0
$6$	−1.09284	+	0.793998i	−0.446152	+	0.324148i
$7$			1.59580i			0.603155i	0.953442	+	0.301577i	$0.0975131\pi$
$7$			1.59580i			0.603155i	−0.953442	+	0.301577i	$0.902487\pi$
$8$	1.72715	+	2.37722i	0.610640	+	0.840474i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$		0			0
$11$	1.02988	−	3.16965i	0.310521	−	0.955686i	−0.667038	−	0.745024i	$-0.732438\pi$
$11$	1.02988	−	3.16965i	0.310521	−	0.955686i	0.977559	−	0.210662i	$-0.0675619\pi$
$12$	−0.166681	+	0.0541581i	−0.0481168	+	0.0156341i
$13$	6.70620	−	2.17898i	1.85997	−	0.604339i	0.865292	−	0.501269i	$-0.167133\pi$
$13$	6.70620	−	2.17898i	1.85997	−	0.604339i	0.994674	−	0.103071i	$-0.0328667\pi$
$14$	0.666132	−	2.05014i	0.178031	−	0.547924i
$15$		0			0
$16$	−1.11826	−	3.44165i	−0.279565	−	0.860413i
$17$	−2.40771	−	3.31393i	−0.583957	−	0.803747i	0.410166	−	0.912011i	$-0.365471\pi$
$17$	−2.40771	−	3.31393i	−0.583957	−	0.803747i	−0.994122	+	0.108264i	$0.965471\pi$
$18$			1.35083i			0.318394i
$19$	0.459145	−	0.333589i	0.105335	−	0.0765305i	−0.533871	−	0.845566i	$-0.679263\pi$
$19$	0.459145	−	0.333589i	0.105335	−	0.0765305i	0.639206	+	0.769036i	$0.279263\pi$
$20$		0			0
$21$	1.29103	+	0.937986i	0.281725	+	0.204685i
$22$	−2.64621	+	3.64220i	−0.564174	+	0.776519i
$23$	−5.99546	−	1.94804i	−1.25014	−	0.406195i	−0.392169	−	0.919893i	$-0.628275\pi$
$23$	−5.99546	−	1.94804i	−1.25014	−	0.406195i	−0.857971	+	0.513698i	$0.828275\pi$
$24$	2.93840			0.599799
$25$		0			0
$26$	−9.52513			−1.86803
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	0.164391	−	0.226264i	0.0310669	−	0.0427599i
$29$	−2.25196	−	1.63614i	−0.418178	−	0.303824i	0.358726	−	0.933443i	$-0.383211\pi$
$29$	−2.25196	−	1.63614i	−0.418178	−	0.303824i	−0.776904	+	0.629619i	$0.783211\pi$
$30$		0			0
$31$	0.805639	−	0.585331i	0.144697	−	0.105128i	−0.513082	−	0.858340i	$-0.671496\pi$
$31$	0.805639	−	0.585331i	0.144697	−	0.105128i	0.657779	+	0.753211i	$0.271496\pi$
$32$		−	0.988473i		−	0.174739i
$33$	−1.95895	−	2.69627i	−0.341010	−	0.469360i
$34$	1.70989	+	5.26251i	0.293244	+	0.902514i
$35$		0			0
$36$	−0.0541581	+	0.166681i	−0.00902634	+	0.0277802i
$37$	3.37943	−	1.09804i	0.555574	−	0.180517i	−0.0177546	−	0.999842i	$-0.505652\pi$
$37$	3.37943	−	1.09804i	0.555574	−	0.180517i	0.573329	+	0.819325i	$0.305652\pi$
$38$	−0.729121	+	0.236906i	−0.118279	+	0.0384312i
$39$	2.17898	−	6.70620i	0.348916	−	1.07385i
$40$		0			0
$41$	0.359364	+	1.10601i	0.0561232	+	0.172729i	0.975189	−	0.221376i	$-0.0710547\pi$
$41$	0.359364	+	1.10601i	0.0561232	+	0.172729i	−0.919065	+	0.394105i	$0.871055\pi$
$42$	−1.26706	−	1.74396i	−0.195511	−	0.269098i
$43$		−	0.117022i		−	0.0178456i	−0.999960	−	0.00892281i	$-0.997160\pi$
$43$		−	0.117022i		−	0.0178456i	0.999960	−	0.00892281i	$-0.00284026\pi$
$44$	−0.472545	+	0.343324i	−0.0712389	+	0.0517581i
$45$		0			0
$46$	6.88929	+	5.00536i	1.01577	+	0.738001i
$47$	4.49170	−	6.18229i	0.655182	−	0.901780i	−0.344128	−	0.938923i	$-0.611826\pi$
$47$	4.49170	−	6.18229i	0.655182	−	0.901780i	0.999310	+	0.0371425i	$0.0118256\pi$
$48$	−3.44165	−	1.11826i	−0.496760	−	0.161407i
$49$	4.45343			0.636205
$50$		0			0
$51$	−4.09625			−0.573589
$52$	−1.17532	−	0.381886i	−0.162988	−	0.0529580i
$53$	−0.307785	+	0.423629i	−0.0422775	+	0.0581900i	−0.829632	−	0.558310i	$-0.811450\pi$
$53$	−0.307785	+	0.423629i	−0.0422775	+	0.0581900i	0.787355	+	0.616500i	$0.211450\pi$
$54$	1.09284	+	0.793998i	0.148717	+	0.108049i
$55$		0			0
$56$	−3.79356	+	2.75618i	−0.506936	+	0.368310i
$57$		−	0.567535i		−	0.0751718i
$58$	2.21015	+	3.04201i	0.290207	+	0.399436i
$59$	−0.304072	−	0.935838i	−0.0395868	−	0.121836i	0.929310	−	0.369300i	$-0.120403\pi$
$59$	−0.304072	−	0.935838i	−0.0395868	−	0.121836i	−0.968897	+	0.247465i	$0.920403\pi$
$60$		0			0
$61$	3.27982	−	10.0942i	0.419937	−	1.29243i	−0.487822	−	0.872943i	$-0.662208\pi$
$61$	3.27982	−	10.0942i	0.419937	−	1.29243i	0.907759	−	0.419491i	$-0.137792\pi$
$62$	−1.27935	+	0.415686i	−0.162478	+	0.0527922i
$63$	1.51769	−	0.493128i	0.191211	−	0.0621283i
$64$	−2.64914	+	8.15321i	−0.331142	+	1.01915i
$65$		0			0
$66$	1.39120	+	4.28166i	0.171244	+	0.527036i
$67$	8.94370	+	12.3099i	1.09265	+	1.50390i	0.844786	+	0.535104i	$0.179728\pi$
$67$	8.94370	+	12.3099i	1.09265	+	1.50390i	0.247861	+	0.968796i	$0.420272\pi$
$68$			0.717905i			0.0870588i
$69$	−5.10005	+	3.70540i	−0.613973	+	0.446078i
$70$		0			0
$71$	8.62730	+	6.26810i	1.02387	+	0.743887i	0.967073	−	0.254499i	$-0.0819104\pi$
$71$	8.62730	+	6.26810i	1.02387	+	0.743887i	0.0567995	+	0.998386i	$0.481910\pi$
$72$	1.72715	−	2.37722i	0.203547	−	0.280158i
$73$	−5.28627	−	1.71761i	−0.618711	−	0.201032i	−0.0171433	−	0.999853i	$-0.505457\pi$
$73$	−5.28627	−	1.71761i	−0.618711	−	0.201032i	−0.601568	+	0.798821i	$0.705457\pi$
$74$	−4.79996			−0.557984
$75$		0			0
$76$	−0.0994657			−0.0114095
$77$	5.05812	+	1.64348i	0.576426	+	0.187292i
$78$	−5.59873	+	7.70599i	−0.633931	+	0.872532i
$79$	−11.8091	−	8.57982i	−1.32863	−	0.965305i	−0.999781	−	0.0209214i	$-0.993340\pi$
$79$	−11.8091	−	8.57982i	−1.32863	−	0.965305i	−0.328847	−	0.944383i	$-0.606660\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		−	1.57091i		−	0.173478i
$83$	2.95302	+	4.06448i	0.324136	+	0.446135i	0.939724	−	0.341933i	$-0.111082\pi$
$83$	2.95302	+	4.06448i	0.324136	+	0.446135i	−0.615588	+	0.788068i	$0.711082\pi$
$84$	−0.0864253	−	0.265990i	−0.00942977	−	0.0290218i
$85$		0			0
$86$	−0.0488483	+	0.150339i	−0.00526744	+	0.0162115i
$87$	−2.64734	+	0.860172i	−0.283824	+	0.0922201i
$88$	9.31372	−	3.02621i	0.992846	−	0.322595i
$89$	−0.872511	+	2.68531i	−0.0924859	+	0.284642i	−0.986590	−	0.163216i	$-0.947813\pi$
$89$	−0.872511	+	2.68531i	−0.0924859	+	0.284642i	0.894104	+	0.447859i	$0.147813\pi$
$90$		0			0
$91$	3.47720	+	10.7017i	0.364510	+	1.12185i
$92$	0.649405	+	0.893830i	0.0677052	+	0.0931882i
$93$		−	0.995824i		−	0.103262i
$94$	−8.35122	+	6.06752i	−0.861363	+	0.625817i
$95$		0			0
$96$	−0.799691	−	0.581010i	−0.0816182	−	0.0592991i
$97$	−1.00271	+	1.38012i	−0.101810	+	0.140130i	−0.856882	−	0.515512i	$-0.827602\pi$
$97$	−1.00271	+	1.38012i	−0.101810	+	0.140130i	0.755072	+	0.655642i	$0.227602\pi$
$98$	−5.72139	−	1.85899i	−0.577948	−	0.187787i
$99$	−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	$0.272473\pi$
$102$	5.26251	+	1.70989i	0.521066	+	0.169305i
$103$	−6.39039	+	8.79562i	−0.629664	+	0.866658i	−0.998012	−	0.0630298i	$-0.979924\pi$
$103$	−6.39039	+	8.79562i	−0.629664	+	0.866658i	0.368347	+	0.929688i	$0.379924\pi$
$104$	16.7625	+	12.1787i	1.64370	+	1.19422i
$105$		0			0
$106$	0.572251	−	0.415765i	0.0555819	−	0.0403826i
$107$			9.37236i			0.906060i	0.891495	+	0.453030i	$0.149657\pi$
$107$			9.37236i			0.906060i	−0.891495	+	0.453030i	$0.850343\pi$
$108$	0.103015	+	0.141788i	0.00991260	+	0.0136435i
$109$	4.81755	+	14.8269i	0.461438	+	1.42016i	0.863408	+	0.504506i	$0.168326\pi$
$109$	4.81755	+	14.8269i	0.461438	+	1.42016i	−0.401970	+	0.915653i	$0.631674\pi$
$110$		0			0
$111$	1.09804	−	3.37943i	0.104222	−	0.320761i
$112$	5.49218	−	1.78452i	0.518962	−	0.168621i
$113$	−9.55629	+	3.10503i	−0.898980	+	0.292096i	−0.721816	−	0.692085i	$-0.756692\pi$
$113$	−9.55629	+	3.10503i	−0.898980	+	0.292096i	−0.177164	+	0.984181i	$0.556692\pi$
$114$	−0.236906	+	0.729121i	−0.0221883	+	0.0682884i
$115$		0			0
$116$	0.150753	+	0.463970i	0.0139971	+	0.0430785i
$117$	−4.14466	−	5.70464i	−0.383174	−	0.527394i
$118$			1.32921i			0.122364i
$119$	5.28837	−	3.84222i	0.484784	−	0.352216i
$120$		0			0
$121$	−0.0868453	−	0.0630968i	−0.00789503	−	0.00573608i
$122$	−8.42726	+	11.5991i	−0.762968	+	1.05014i
$123$	1.10601	+	0.359364i	0.0997253	+	0.0324027i
$124$	−0.174527			−0.0156730
$125$		0			0
$126$	−2.15565			−0.192041
$127$	0.928977	+	0.301843i	0.0824334	+	0.0267842i	0.349943	−	0.936771i	$-0.386201\pi$
$127$	0.928977	+	0.301843i	0.0824334	+	0.0267842i	−0.267510	+	0.963555i	$0.586201\pi$
$128$	5.64476	−	7.76934i	0.498931	−	0.686719i
$129$	−0.0946725	−	0.0687836i	−0.00833545	−	0.00605606i
$130$		0			0
$131$	−8.14001	+	5.91406i	−0.711196	+	0.516714i	−0.883559	−	0.468319i	$-0.844860\pi$
$131$	−8.14001	+	5.91406i	−0.711196	+	0.516714i	0.172363	+	0.985033i	$0.444860\pi$
$132$			0.584098i			0.0508392i
$133$	0.532340	+	0.732703i	0.0461597	+	0.0635334i
$134$	−6.35158	−	19.5481i	−0.548693	−	1.68870i
$135$		0			0
$136$	3.71946	−	11.4473i	0.318941	−	0.981600i
$137$	−4.63397	+	1.50567i	−0.395907	+	0.128638i	−0.500203	−	0.865908i	$-0.666741\pi$
$137$	−4.63397	+	1.50567i	−0.395907	+	0.128638i	0.104296	+	0.994546i	$0.466741\pi$
$138$	8.09885	−	2.63148i	0.689420	−	0.224006i
$139$	−0.0574103	+	0.176691i	−0.00486948	+	0.0149867i	−0.953462	−	0.301514i	$-0.902508\pi$
$139$	−0.0574103	+	0.176691i	−0.00486948	+	0.0149867i	0.948592	+	0.316501i	$0.102508\pi$
$140$		0			0
$141$	−2.36143	−	7.26772i	−0.198868	−	0.612053i
$142$	−8.46714	−	11.6540i	−0.710547	−	0.977984i
$143$		−	23.5004i		−	1.96520i
$144$	−2.92764	+	2.12706i	−0.243970	+	0.177255i
$145$		0			0
$146$	6.07437	+	4.41329i	0.502719	+	0.365247i
$147$	2.61766	−	3.60290i	0.215901	−	0.297162i
$148$	−0.592276	−	0.192442i	−0.0486847	−	0.0158186i
$149$	−3.88889			−0.318590			−0.159295	−	0.987231i	$-0.550922\pi$
$149$	−3.88889			−0.318590			−0.159295	+	0.987231i	$0.550922\pi$
$150$		0			0
$151$	−22.1146			−1.79966			−0.899829	−	0.436242i	$-0.856309\pi$
$151$	−22.1146			−1.79966			−0.899829	+	0.436242i	$0.856309\pi$
$152$	1.58603	+	0.515331i	0.128644	+	0.0417989i
$153$	−2.40771	+	3.31393i	−0.194652	+	0.267916i
$154$	−5.81221	−	4.22282i	−0.468361	−	0.340284i
$155$		0			0
$156$	−0.999790	+	0.726390i	−0.0800472	+	0.0581577i
$157$		−	13.6058i		−	1.08586i	−0.839777	−	0.542931i	$-0.817314\pi$
$157$		−	13.6058i		−	1.08586i	0.839777	−	0.542931i	$-0.182686\pi$
$158$	11.5899	+	15.9521i	0.922041	+	1.26908i
$159$	0.161812	+	0.498006i	0.0128325	+	0.0394945i
$160$		0			0
$161$	3.10868	−	9.56754i	0.244999	−	0.754028i
$162$	1.28472	−	0.417429i	0.100937	−	0.0327963i
$163$	−8.20662	+	2.66649i	−0.642792	+	0.208856i	−0.612233	−	0.790677i	$-0.709729\pi$
$163$	−8.20662	+	2.66649i	−0.642792	+	0.208856i	−0.0305587	+	0.999533i	$0.509729\pi$
$164$	0.0629818	−	0.193838i	0.00491805	−	0.0151362i
$165$		0			0
$166$	−2.09716	−	6.45438i	−0.162771	−	0.500957i
$167$	3.87874	+	5.33863i	0.300146	+	0.413116i	0.932277	−	0.361746i	$-0.117819\pi$
$167$	3.87874	+	5.33863i	0.300146	+	0.413116i	−0.632131	+	0.774862i	$0.717819\pi$
$168$			4.68910i			0.361772i
$169$	29.7080	−	21.5841i	2.28523	−	1.66032i
$170$		0			0
$171$	−0.459145	−	0.333589i	−0.0351117	−	0.0255102i
$172$	−0.0120550	+	0.0165922i	−0.000919182	+	0.00126514i
$173$	12.9910	+	4.22102i	0.987685	+	0.320918i	0.757934	−	0.652331i	$-0.226209\pi$
$173$	12.9910	+	4.22102i	0.987685	+	0.320918i	0.229751	+	0.973249i	$0.426209\pi$
$174$	3.76013			0.285055
$175$		0			0
$176$	−12.0605			−0.909095
$177$	−0.935838	−	0.304072i	−0.0703419	−	0.0228555i
$178$	2.24186	−	3.08565i	0.168034	−	0.231279i
$179$	7.95167	+	5.77722i	0.594336	+	0.431810i	0.843864	−	0.536557i	$-0.180276\pi$
$179$	7.95167	+	5.77722i	0.594336	+	0.431810i	−0.249528	+	0.968368i	$0.580276\pi$
$180$		0			0
$181$	−14.4561	+	10.5030i	−1.07451	+	0.780679i	−0.976718	−	0.214528i	$-0.931179\pi$
$181$	−14.4561	+	10.5030i	−1.07451	+	0.780679i	−0.0977940	+	0.995207i	$0.531179\pi$
$182$		−	15.2002i		−	1.12671i
$183$	−6.23858	−	8.58667i	−0.461169	−	0.634745i
$184$	−5.72414	−	17.6171i	−0.421989	−	1.29875i
$185$		0			0
$186$	−0.415686	+	1.27935i	−0.0304796	+	0.0938065i
$187$	−12.9837	+	4.21865i	−0.949461	+	0.308498i
$188$	−1.27373	+	0.413862i	−0.0928967	+	0.0301840i
$189$	0.493128	−	1.51769i	0.0358698	−	0.110396i
$190$		0			0
$191$	0.100682	+	0.309867i	0.00728509	+	0.0224212i	0.954633	−	0.297785i	$-0.0962478\pi$
$191$	0.100682	+	0.309867i	0.00728509	+	0.0224212i	−0.947348	+	0.320206i	$0.896248\pi$
$192$	5.03896	+	6.93553i	0.363656	+	0.500529i
$193$		−	2.90187i		−	0.208881i	−0.994531	−	0.104441i	$-0.966695\pi$
$193$		−	2.90187i		−	0.208881i	0.994531	−	0.104441i	$-0.0333052\pi$
$194$	1.86430	−	1.35450i	0.133849	−	0.0972471i
$195$		0			0
$196$	−0.631442	−	0.458769i	−0.0451030	−	0.0327692i
$197$	10.6518	−	14.6610i	0.758911	−	1.04455i	−0.238393	−	0.971169i	$-0.576620\pi$
$197$	10.6518	−	14.6610i	0.758911	−	1.04455i	0.997304	−	0.0733829i	$-0.0233795\pi$
$198$	4.28166	+	1.39120i	0.304284	+	0.0988679i
$199$	−1.53256			−0.108640			−0.0543201	−	0.998524i	$-0.517299\pi$
$199$	−1.53256			−0.108640			−0.0543201	+	0.998524i	$0.517299\pi$
$200$		0			0
$201$	15.2159			1.07325
$202$	−16.9257	−	5.49949i	−1.19089	−	0.386943i
$203$	2.61095	−	3.59367i	0.183253	−	0.252226i
$204$	0.580797	+	0.421974i	0.0406640	+	0.0295441i
$205$		0			0
$206$	11.8814	−	8.63233i	0.827816	−	0.601443i
$207$			6.30400i			0.438158i
$208$	−14.9986	−	20.6437i	−1.03996	−	1.43139i
$209$	−0.584494	−	1.79889i	−0.0404303	−	0.124432i
$210$		0			0
$211$	−3.51345	+	10.8133i	−0.241876	+	0.744418i	0.754259	+	0.656577i	$0.227996\pi$
$211$	−3.51345	+	10.8133i	−0.241876	+	0.744418i	−0.996135	+	0.0878402i	$0.972004\pi$
$212$	0.0872802	−	0.0283590i	0.00599443	−	0.00194771i
$213$	10.1420	−	3.29534i	0.694919	−	0.225793i
$214$	3.91230	−	12.0408i	0.267439	−	0.823093i
$215$		0			0
$216$	−0.908017	−	2.79459i	−0.0617827	−	0.190148i
$217$	0.934069	+	1.28564i	0.0634087	+	0.0872746i
$218$		−	21.0593i		−	1.42632i
$219$	−4.49677	+	3.26710i	−0.303864	+	0.220770i
$220$		0			0
$221$	−23.3676	−	16.9776i	−1.57188	−	1.14203i
$222$	−2.82134	+	3.88325i	−0.189356	+	0.260626i
$223$	16.1210	+	5.23804i	1.07954	+	0.350765i	0.794198	−	0.607659i	$-0.207891\pi$
$223$	16.1210	+	5.23804i	1.07954	+	0.350765i	0.285347	+	0.958424i	$0.407891\pi$
$224$	1.57740			0.105395
$225$		0			0
$226$	13.5732			0.902878
$227$	−13.4210	−	4.36076i	−0.890785	−	0.289434i	−0.172357	−	0.985035i	$-0.555138\pi$
$227$	−13.4210	−	4.36076i	−0.890785	−	0.289434i	−0.718428	+	0.695601i	$0.755138\pi$
$228$	−0.0584645	+	0.0804694i	−0.00387190	+	0.00532922i
$229$	0.0501546	+	0.0364394i	0.00331431	+	0.00240799i	0.589441	−	0.807811i	$-0.299348\pi$
$229$	0.0501546	+	0.0364394i	0.00331431	+	0.00240799i	−0.586127	+	0.810219i	$0.699348\pi$
$230$		0			0
$231$	4.30269	−	3.12609i	0.283096	−	0.205682i
$232$		−	8.17927i		−	0.536995i
$233$	15.2936	+	21.0499i	1.00192	+	1.37902i	0.924141	+	0.382052i	$0.124782\pi$
$233$	15.2936	+	21.0499i	1.00192	+	1.37902i	0.0777775	+	0.996971i	$0.475218\pi$
$234$	2.94343	+	9.05894i	0.192418	+	0.592201i
$235$		0			0
$236$	−0.0532914	+	0.164014i	−0.00346898	+	0.0106764i
$237$	−13.8824	+	4.51068i	−0.901761	+	0.293000i
$238$	−8.39790	+	2.72864i	−0.544355	+	0.176872i
$239$	−6.02491	+	18.5428i	−0.389719	+	1.19943i	0.543279	+	0.839552i	$0.317183\pi$
$239$	−6.02491	+	18.5428i	−0.389719	+	1.19943i	−0.932998	+	0.359881i	$0.882817\pi$
$240$		0			0
$241$	−1.26654	−	3.89800i	−0.0815848	−	0.251092i	0.901941	−	0.431859i	$-0.142142\pi$
$241$	−1.26654	−	3.89800i	−0.0815848	−	0.251092i	−0.983526	+	0.180767i	$0.942142\pi$
$242$	0.0852331	+	0.117313i	0.00547899	+	0.00754118i
$243$			1.00000i			0.0641500i
$244$	−1.50489	+	1.09337i	−0.0963409	+	0.0699957i
$245$		0			0
$246$	−1.27090	−	0.923360i	−0.0810294	−	0.0588713i
$247$	2.35224	−	3.23758i	0.149669	−	0.206002i
$248$	2.78292	+	0.904225i	0.176716	+	0.0574184i
$249$	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	$0.510342\pi$
$252$	−0.265990	−	0.0864253i	−0.0167558	−	0.00544428i
$253$	−12.3492	+	16.9973i	−0.776390	+	1.06861i
$254$	−1.06747	−	0.775565i	−0.0669792	−	0.0486633i
$255$		0			0
$256$	3.37601	−	2.45281i	0.211001	−	0.153301i
$257$			18.5597i			1.15772i	0.815426	+	0.578862i	$0.196503\pi$
$257$			18.5597i			1.15772i	−0.815426	+	0.578862i	$0.803497\pi$
$258$	0.0929149	+	0.127886i	0.00578463	+	0.00796186i
$259$	1.75225	+	5.39288i	0.108880	+	0.335097i
$260$		0			0
$261$	−0.860172	+	2.64734i	−0.0532433	+	0.163866i
$262$	12.9263	−	4.20001i	0.798589	−	0.259477i
$263$	−11.7872	+	3.82988i	−0.726827	+	0.236161i	−0.648981	−	0.760805i	$-0.724804\pi$
$263$	−11.7872	+	3.82988i	−0.726827	+	0.236161i	−0.0778466	+	0.996965i	$0.524804\pi$
$264$	3.02621	−	9.31372i	0.186250	−	0.573220i
$265$		0			0
$266$	−0.378053	−	1.16353i	−0.0231799	−	0.0713405i
$267$	1.65961	+	2.28426i	0.101567	+	0.139795i
$268$		−	2.66673i		−	0.162897i
$269$	−4.28805	+	3.11545i	−0.261447	+	0.189952i	−0.710785	−	0.703410i	$-0.751660\pi$
$269$	−4.28805	+	3.11545i	−0.261447	+	0.189952i	0.449338	+	0.893362i	$0.351660\pi$
$270$		0			0
$271$	−0.645132	−	0.468716i	−0.0391890	−	0.0284725i	0.568018	−	0.823016i	$-0.307710\pi$
$271$	−0.645132	−	0.468716i	−0.0391890	−	0.0284725i	−0.607207	+	0.794543i	$0.707710\pi$
$272$	−8.71295	+	11.9924i	−0.528300	+	0.727143i
$273$	10.7017	+	3.47720i	0.647698	+	0.210450i
$274$	6.58184			0.397624
$275$		0			0
$276$	1.10483			0.0665032
$277$	4.51205	+	1.46605i	0.271103	+	0.0880867i	0.441414	−	0.897304i	$-0.354477\pi$
$277$	4.51205	+	1.46605i	0.271103	+	0.0880867i	−0.170311	+	0.985390i	$0.554477\pi$
$278$	0.147512	−	0.203033i	0.00884717	−	0.0121771i
$279$	−0.805639	−	0.585331i	−0.0482323	−	0.0350428i
$280$		0			0
$281$	15.1608	−	11.0150i	0.904418	−	0.657098i	−0.0351791	−	0.999381i	$-0.511200\pi$
$281$	15.1608	−	11.0150i	0.904418	−	0.657098i	0.939597	+	0.342283i	$0.111200\pi$
$282$			10.3227i			0.614707i
$283$	−6.91306	−	9.51501i	−0.410939	−	0.565608i	0.552508	−	0.833507i	$-0.313671\pi$
$283$	−6.91306	−	9.51501i	−0.410939	−	0.565608i	−0.963447	+	0.267899i	$0.913671\pi$
$284$	−0.577538	−	1.77748i	−0.0342706	−	0.105474i
$285$		0			0
$286$	−9.80976	+	30.1913i	−0.580063	+	1.78525i
$287$	−1.76496	+	0.573471i	−0.104182	+	0.0338509i
$288$	−0.940094	+	0.305455i	−0.0553956	+	0.0179991i
$289$	0.0682154	−	0.209945i	0.00401267	−	0.0123497i
$290$		0			0
$291$	0.527158	+	1.62242i	0.0309025	+	0.0951082i
$292$	0.572589	+	0.788101i	0.0335082	+	0.0461201i
$293$			22.2819i			1.30172i	0.759198	+	0.650860i	$0.225592\pi$
$293$			22.2819i			1.30172i	−0.759198	+	0.650860i	$0.774408\pi$
$294$	−4.86691	+	3.53602i	−0.283844	+	0.206225i
$295$		0			0
$296$	8.44707	+	6.13715i	0.490976	+	0.356715i
$297$	−1.95895	+	2.69627i	−0.113670	+	0.156453i
$298$	4.99611	+	1.62333i	0.289417	+	0.0940373i
$299$	−44.4515			−2.57070
$300$		0			0
$301$	0.186743			0.0107637
$302$	28.4109	+	9.23127i	1.63487	+	0.531200i
$303$	7.74387	−	10.6585i	0.444874	−	0.612316i
$304$	−1.66154	−	1.20718i	−0.0952958	−	0.0692365i
$305$		0			0
$306$	4.47656	−	3.25241i	0.255908	−	0.185928i
$307$			15.3063i			0.873574i	0.899565	+	0.436787i	$0.143884\pi$
$307$			15.3063i			0.873574i	−0.899565	+	0.436787i	$0.856116\pi$
$308$	−0.547876	−	0.754087i	−0.0312181	−	0.0429681i
$309$	3.35963	+	10.3399i	0.191123	+	0.588215i
$310$		0			0
$311$	−3.97226	+	12.2254i	−0.225246	+	0.693237i	0.773020	+	0.634382i	$0.218745\pi$
$311$	−3.97226	+	12.2254i	−0.225246	+	0.693237i	−0.998267	+	0.0588556i	$0.981255\pi$
$312$	19.7055	−	6.40272i	1.11561	−	0.362482i
$313$	9.99293	−	3.24690i	0.564834	−	0.183526i	−0.0126612	−	0.999920i	$-0.504030\pi$
$313$	9.99293	−	3.24690i	0.564834	−	0.183526i	0.577495	+	0.816394i	$0.304030\pi$
$314$	−5.67947	+	17.4796i	−0.320511	+	0.986431i
$315$		0			0
$316$	0.790537	+	2.43302i	0.0444712	+	0.136868i
$317$	−11.4504	−	15.7602i	−0.643120	−	0.885179i	0.355657	−	0.934617i	$-0.384257\pi$
$317$	−11.4504	−	15.7602i	−0.643120	−	0.885179i	−0.998777	+	0.0494374i	$0.984257\pi$
$318$		−	0.707341i		−	0.0396657i
$319$	−7.50526	+	5.45289i	−0.420214	+	0.305303i
$320$		0			0
$321$	7.58240	+	5.50893i	0.423208	+	0.307479i
$322$	−7.98754	+	10.9939i	−0.445128	+	0.612667i
$323$	−2.21098	−	0.718392i	−0.123022	−	0.0399724i
$324$	0.175259			0.00973662
$325$		0			0
$326$	11.6562			0.645579
$327$	14.8269	+	4.81755i	0.819929	+	0.266411i
$328$	−2.00855	+	2.76453i	−0.110903	+	0.152646i
$329$	9.86568	+	7.16784i	0.543913	+	0.395176i
$330$		0			0
$331$	11.7247	−	8.51846i	0.644446	−	0.468217i	−0.216929	−	0.976187i	$-0.569604\pi$
$331$	11.7247	−	8.51846i	0.644446	−	0.468217i	0.861375	+	0.507970i	$0.169604\pi$
$332$		−	0.880498i		−	0.0483236i
$333$	−2.08860	−	2.87471i	−0.114455	−	0.157533i
$334$	−2.75458	−	8.47772i	−0.150724	−	0.463880i
$335$		0			0
$336$	1.78452	−	5.49218i	0.0973533	−	0.299623i
$337$	8.87550	−	2.88382i	0.483479	−	0.157092i	−0.0571283	−	0.998367i	$-0.518194\pi$
$337$	8.87550	−	2.88382i	0.483479	−	0.157092i	0.540608	+	0.841275i	$0.318194\pi$
$338$	−47.1761	+	15.3285i	−2.56604	+	0.833758i
$339$	−3.10503	+	9.55629i	−0.168642	+	0.519026i
$340$		0			0
$341$	−1.02558	−	3.15641i	−0.0555383	−	0.170929i
$342$	0.450621	+	0.620227i	0.0243668	+	0.0335380i
$343$			18.2774i			0.986884i
$344$	0.278186	−	0.202114i	0.0149988	−	0.0108973i
$345$		0			0
$346$	−14.9277	−	10.8456i	−0.802519	−	0.583064i
$347$	0.619178	−	0.852225i	0.0332392	−	0.0457498i	−0.792074	−	0.610425i	$-0.790999\pi$
$347$	0.619178	−	0.852225i	0.0332392	−	0.0457498i	0.825313	+	0.564675i	$0.190999\pi$
$348$	0.463970	+	0.150753i	0.0248714	+	0.00808121i
$349$	13.0715			0.699700			0.349850	−	0.936806i	$-0.386233\pi$
$349$	13.0715			0.699700			0.349850	+	0.936806i	$0.386233\pi$
$350$		0			0
$351$	−7.05132			−0.376371
$352$	−3.13311	−	1.01801i	−0.166996	−	0.0542602i
$353$	19.9537	−	27.4639i	1.06203	−	1.46176i	0.184134	−	0.982901i	$-0.441052\pi$
$353$	19.9537	−	27.4639i	1.06203	−	1.46176i	0.877894	−	0.478855i	$-0.158948\pi$
$354$	1.07536	+	0.781292i	0.0571546	+	0.0415252i
$355$		0			0
$356$	0.400338	−	0.290863i	0.0212179	−	0.0154157i
$357$		−	6.53678i		−	0.345963i
$358$	−7.80405	−	10.7413i	−0.412457	−	0.567698i
$359$	1.88331	+	5.79622i	0.0993971	+	0.305913i	0.988375	−	0.152038i	$-0.0485836\pi$
$359$	1.88331	+	5.79622i	0.0993971	+	0.305913i	−0.888978	+	0.457951i	$0.848584\pi$
$360$		0			0
$361$	−5.77179	+	17.7637i	−0.303778	+	0.934934i
$362$	22.9562	−	7.45892i	1.20655	−	0.392032i
$363$	−0.102093	+	0.0331720i	−0.00535848	+	0.00174108i
$364$	0.609412	−	1.87558i	0.0319419	−	0.0983070i
$365$		0			0
$366$	4.43047	+	13.6356i	0.231585	+	0.712744i
$367$	−12.8511	−	17.6881i	−0.670823	−	0.923309i	0.328955	−	0.944345i	$-0.393303\pi$
$367$	−12.8511	−	17.6881i	−0.670823	−	0.923309i	−0.999779	+	0.0210364i	$0.993303\pi$
$368$			22.8127i			1.18919i
$369$	0.940826	−	0.683550i	0.0489775	−	0.0355842i
$370$		0			0
$371$	−0.676026	−	0.491162i	−0.0350975	−	0.0254999i
$372$	−0.102585	+	0.141196i	−0.00531876	+	0.00732065i
$373$	−23.2590	−	7.55730i	−1.20430	−	0.391302i	−0.362961	−	0.931804i	$-0.618234\pi$
$373$	−23.2590	−	7.55730i	−1.20430	−	0.391302i	−0.841343	+	0.540502i	$0.818234\pi$
$374$	18.4413			0.953578
$375$		0			0
$376$	22.4545			1.15800
$377$	−18.6672	−	6.06534i	−0.961410	−	0.312381i
$378$	−1.26706	+	1.74396i	−0.0651705	+	0.0896995i
$379$	−5.07918	−	3.69024i	−0.260900	−	0.189555i	0.449644	−	0.893208i	$-0.351551\pi$
$379$	−5.07918	−	3.69024i	−0.260900	−	0.189555i	−0.710544	+	0.703653i	$0.751551\pi$
$380$		0			0
$381$	0.790235	−	0.574140i	0.0404850	−	0.0294141i
$382$		−	0.440118i		−	0.0225184i
$383$	−14.5110	−	19.9727i	−0.741477	−	1.02056i	−0.998532	−	0.0541589i	$-0.982752\pi$
$383$	−14.5110	−	19.9727i	−0.741477	−	1.02056i	0.257055	−	0.966397i	$-0.417248\pi$
$384$	−2.96762	−	9.13341i	−0.151441	−	0.466087i
$385$		0			0
$386$	−1.21133	+	3.72808i	−0.0616549	+	0.189754i
$387$	−0.111294	+	0.0361617i	−0.00565740	+	0.00183820i
$388$	0.284345	−	0.0923892i	0.0144354	−	0.00469035i
$389$	3.99360	−	12.2910i	0.202484	−	0.623181i	−0.797324	−	0.603552i	$-0.793752\pi$
$389$	3.99360	−	12.2910i	0.202484	−	0.623181i	0.999807	−	0.0196288i	$-0.00624845\pi$
$390$		0			0
$391$	7.97967	+	24.5589i	0.403549	+	1.24200i
$392$	7.69175	+	10.5868i	0.388492	+	0.534713i
$393$			10.0616i			0.507541i
$394$	−19.8045	+	14.3888i	−0.997736	+	0.724897i
$395$		0			0
$396$	0.472545	+	0.343324i	0.0237463	+	0.0172527i
$397$	17.0584	−	23.4788i	0.856135	−	1.17837i	−0.126342	−	0.991987i	$-0.540324\pi$
$397$	17.0584	−	23.4788i	0.856135	−	1.17837i	0.982477	−	0.186383i	$-0.0596764\pi$
$398$	1.96890	+	0.639734i	0.0986921	+	0.0320670i
$399$	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	$0.301454\pi$
$402$	−19.5481	−	6.35158i	−0.974973	−	0.316788i
$403$	4.12735	−	5.68081i	0.205598	−	0.282981i
$404$	−1.86800	−	1.35719i	−0.0929367	−	0.0675225i
$405$		0			0
$406$	−4.85443	+	3.52695i	−0.240921	+	0.175040i
$407$		−	11.8425i		−	0.587009i
$408$	−7.07484	−	9.73768i	−0.350257	−	0.482087i
$409$	4.94173	+	15.2091i	0.244353	+	0.752040i	0.995742	+	0.0921815i	$0.0293840\pi$
$409$	4.94173	+	15.2091i	0.244353	+	0.752040i	−0.751389	+	0.659859i	$0.770616\pi$
$410$		0			0
$411$	−1.50567	+	4.63397i	−0.0742691	+	0.228577i
$412$	1.81216	−	0.588806i	0.0892786	−	0.0290084i
$413$	1.49341	−	0.485237i	0.0734858	−	0.0238770i
$414$	2.63148	−	8.09885i	0.129330	−	0.398037i
$415$		0			0
$416$	−2.15386	−	6.62890i	−0.105602	−	0.325008i
$417$	0.109201	+	0.150302i	0.00534759	+	0.00736033i
$418$			2.55504i			0.124971i
$419$	26.1935	−	19.0307i	1.27964	−	0.929710i	0.280094	−	0.959973i	$-0.409634\pi$
$419$	26.1935	−	19.0307i	1.27964	−	0.929710i	0.999542	+	0.0302627i	$0.00963440\pi$
$420$		0			0
$421$	−14.6044	−	10.6107i	−0.711774	−	0.517134i	0.171972	−	0.985102i	$-0.444986\pi$
$421$	−14.6044	−	10.6107i	−0.711774	−	0.517134i	−0.883745	+	0.467968i	$0.844986\pi$
$422$	9.02757	−	12.4254i	0.439455	−	0.604858i
$423$	−7.26772	−	2.36143i	−0.353369	−	0.114816i
$424$	−1.53865			−0.0747235
$425$		0			0
$426$	−14.4052			−0.697932
$427$	16.1084	+	5.23392i	0.779538	+	0.253287i
$428$	0.965491	−	1.32888i	0.0466688	−	0.0642340i
$429$	−19.0122	−	13.8132i	−0.917919	−	0.666907i
$430$		0			0
$431$	−26.8070	+	19.4764i	−1.29125	+	0.938146i	−0.999830	−	0.0184500i	$-0.994127\pi$
$431$	−26.8070	+	19.4764i	−1.29125	+	0.938146i	−0.291417	+	0.956596i	$0.594127\pi$
$432$			3.61877i			0.174108i
$433$	13.3223	+	18.3366i	0.640230	+	0.881201i	0.998628	−	0.0523682i	$-0.0166770\pi$
$433$	13.3223	+	18.3366i	0.640230	+	0.881201i	−0.358398	+	0.933569i	$0.616677\pi$
$434$	−0.663351	−	2.04158i	−0.0318419	−	0.0979991i
$435$		0			0
$436$	0.844320	−	2.59855i	0.0404356	−	0.124448i
$437$	−3.40263	+	1.10558i	−0.162770	+	0.0528872i
$438$	7.14085	−	2.32020i	0.341203	−	0.110864i
$439$	2.62799	−	8.08812i	0.125427	−	0.386025i	−0.868551	−	0.495599i	$-0.834949\pi$
$439$	2.62799	−	8.08812i	0.125427	−	0.386025i	0.993979	+	0.109574i	$0.0349486\pi$
$440$		0			0
$441$	−1.37619	−	4.23547i	−0.0655327	−	0.201689i
$442$	22.9338	+	31.5657i	1.09085	+	1.50142i
$443$			6.35768i			0.302063i	0.988529	+	0.151031i	$0.0482594\pi$
$443$			6.35768i			0.302063i	−0.988529	+	0.151031i	$0.951741\pi$
$444$	−0.503820	+	0.366046i	−0.0239102	+	0.0173718i
$445$		0			0
$446$	−18.5244	−	13.4588i	−0.877157	−	0.637292i
$447$	−2.28583	+	3.14617i	−0.108116	+	0.148809i
$448$	−13.0109	−	4.22749i	−0.614706	−	0.199730i
$449$	6.25726			0.295298			0.147649	−	0.989040i	$-0.452829\pi$
$449$	6.25726			0.295298			0.147649	+	0.989040i	$0.452829\pi$
$450$		0			0
$451$	3.87576			0.182502
$452$	1.67483	+	0.544184i	0.0787772	+	0.0255963i
$453$	−12.9986	+	17.8911i	−0.610729	+	0.840596i
$454$	15.4219	+	11.2047i	0.723786	+	0.525861i
$455$		0			0
$456$	1.34915	−	0.980218i	0.0631800	−	0.0459029i
$457$			11.0441i			0.516620i	0.966062	+	0.258310i	$0.0831657\pi$
$457$			11.0441i			0.516620i	−0.966062	+	0.258310i	$0.916834\pi$
$458$	−0.0492235	−	0.0677503i	−0.00230006	−	0.00316576i
$459$	1.26581	+	3.89576i	0.0590830	+	0.181839i
$460$		0			0
$461$	−7.31202	+	22.5041i	−0.340555	+	1.04812i	0.623366	+	0.781930i	$0.285765\pi$
$461$	−7.31202	+	22.5041i	−0.340555	+	1.04812i	−0.963921	+	0.266189i	$0.914235\pi$
$462$	−6.83266	+	2.22007i	−0.317884	+	0.103287i
$463$	5.91977	−	1.92345i	0.275115	−	0.0893903i	−0.168210	−	0.985751i	$-0.553799\pi$
$463$	5.91977	−	1.92345i	0.275115	−	0.0893903i	0.443325	+	0.896361i	$0.353799\pi$
$464$	−3.11276	+	9.58009i	−0.144506	+	0.444744i
$465$		0			0
$466$	−10.8611	−	33.4271i	−0.503132	−	1.54848i
$467$	2.90765	+	4.00204i	0.134550	+	0.185192i	0.870976	−	0.491326i	$-0.163488\pi$
$467$	2.90765	+	4.00204i	0.134550	+	0.185192i	−0.736425	+	0.676519i	$0.763488\pi$
$468$			1.23581i			0.0571252i
$469$	−19.6442	+	14.2723i	−0.907084	+	0.659035i
$470$		0			0
$471$	−11.0073	−	7.99730i	−0.507191	−	0.368496i
$472$	1.69951	−	2.33918i	0.0782264	−	0.107669i
$473$	−0.370918	−	0.120518i	−0.0170548	−	0.00554144i
$474$	19.7179			0.905671
$475$		0			0
$476$	−1.14563			−0.0525099
$477$	0.498006	+	0.161812i	0.0228021	+	0.00740886i
$478$	15.4806	−	21.3072i	0.708066	−	0.974569i
$479$	−24.3432	−	17.6863i	−1.11227	−	0.808109i	−0.129248	−	0.991612i	$-0.541256\pi$
$479$	−24.3432	−	17.6863i	−1.11227	−	0.808109i	−0.983019	+	0.183503i	$0.941256\pi$
$480$		0			0
$481$	20.2705	−	14.7274i	0.924256	−	0.671511i
$482$			5.53651i			0.252181i
$483$	−5.91307	−	8.13864i	−0.269054	−	0.370321i
$484$	0.00581369	+	0.0178927i	0.000264259	+	0.000813305i
$485$		0			0
$486$	0.417429	−	1.28472i	0.0189350	−	0.0582759i
$487$	−32.5736	+	10.5838i	−1.47605	+	0.479598i	−0.932930	−	0.360057i	$-0.882757\pi$
$487$	−32.5736	+	10.5838i	−1.47605	+	0.479598i	−0.543120	+	0.839655i	$0.682757\pi$
$488$	29.6609	−	9.63743i	1.34269	−	0.436266i
$489$	−2.66649	+	8.20662i	−0.120583	+	0.371116i
$490$		0			0
$491$	−3.21975	−	9.90938i	−0.145305	−	0.447204i	0.851745	−	0.523957i	$-0.175545\pi$
$491$	−3.21975	−	9.90938i	−0.145305	−	0.447204i	−0.997050	+	0.0767530i	$0.975545\pi$
$492$	−0.119798	−	0.164888i	−0.00540093	−	0.00743374i
$493$			11.4022i			0.513530i
$494$	−4.37342	+	3.17747i	−0.196769	+	0.142961i
$495$		0			0
$496$	−2.91542	−	2.11817i	−0.130906	−	0.0951088i
$497$	−10.0026	+	13.7674i	−0.448679	+	0.617553i
$498$	−6.45438	−	2.09716i	−0.289228	−	0.0939758i
$499$	−8.83514			−0.395515			−0.197757	−	0.980251i	$-0.563366\pi$
$499$	−8.83514			−0.395515			−0.197757	+	0.980251i	$0.563366\pi$
$500$		0			0
$501$	6.59891			0.294818
$502$	1.32239	+	0.429671i	0.0590211	+	0.0191771i
$503$	12.5630	−	17.2915i	0.560156	−	0.770988i	−0.431190	−	0.902261i	$-0.641906\pi$
$503$	12.5630	−	17.2915i	0.560156	−	0.770988i	0.991346	+	0.131273i	$0.0419063\pi$
$504$	3.79356	+	2.75618i	0.168979	+	0.122770i
$505$		0			0
$506$	22.9604	−	16.6817i	1.02072	−	0.741593i
$507$		−	36.7211i		−	1.63084i
$508$	−0.100623	−	0.138496i	−0.00446443	−	0.00614477i
$509$	5.18529	+	15.9587i	0.229834	+	0.707356i	0.997765	+	0.0668236i	$0.0212865\pi$
$509$	5.18529	+	15.9587i	0.229834	+	0.707356i	−0.767931	+	0.640533i	$0.778714\pi$
$510$		0			0
$511$	2.74096	−	8.43582i	0.121253	−	0.373179i
$512$	−23.6279	+	7.67717i	−1.04422	+	0.339286i
$513$	−0.539758	+	0.175378i	−0.0238309	+	0.00774312i
$514$	7.74737	−	23.8440i	0.341722	−	1.05171i
$515$		0			0
$516$	0.00633766	+	0.0195053i	0.000279000	+	0.000858674i
$517$	−14.9698	−	20.6042i	−0.658371	−	0.906170i
$518$		−	7.65976i		−	0.336550i
$519$	11.0508	−	8.02886i	0.485075	−	0.352428i
$520$		0			0
$521$	3.72559	+	2.70680i	0.163221	+	0.118587i	0.666397	−	0.745597i	$-0.267835\pi$
$521$	3.72559	+	2.70680i	0.163221	+	0.118587i	−0.503176	+	0.864184i	$0.667835\pi$
$522$	2.21015	−	3.04201i	0.0967357	−	0.133145i
$523$	12.3290	+	4.00592i	0.539108	+	0.175167i	0.565899	−	0.824474i	$-0.308529\pi$
$523$	12.3290	+	4.00592i	0.539108	+	0.175167i	−0.0267915	+	0.999641i	$0.508529\pi$
$524$	1.76339			0.0770340
$525$		0			0
$526$	16.7418			0.729979
$527$	−3.87949	−	1.26052i	−0.168993	−	0.0549093i
$528$	−7.08899	+	9.75716i	−0.308509	+	0.424626i
$529$	13.5433	+	9.83979i	0.588840	+	0.427817i
$530$		0			0
$531$	−0.796071	+	0.578380i	−0.0345465	+	0.0250995i
$532$		−	0.158727i		−	0.00688169i
$533$	4.81993	+	6.63406i	0.208774	+	0.287353i
$534$	−1.17861	−	3.62740i	−0.0510036	−	0.156973i
$535$		0			0
$536$	−13.8163	+	42.5223i	−0.596774	+	1.83668i
$537$	9.34775	−	3.03727i	0.403385	−	0.131068i
$538$	6.80940	−	2.21251i	0.293574	−	0.0953880i
$539$	4.58651	−	14.1158i	0.197555	−	0.608012i
$540$		0			0
$541$	−8.45597	−	26.0248i	−0.363551	−	1.11889i	−0.950884	−	0.309548i	$-0.899822\pi$
$541$	−8.45597	−	26.0248i	−0.363551	−	1.11889i	0.587333	−	0.809345i	$-0.300178\pi$
$542$	0.633156	+	0.871464i	0.0271964	+	0.0374326i
$543$			17.8687i			0.766819i
$544$	−3.27573	+	2.37996i	−0.140446	+	0.102040i
$545$		0			0
$546$	−12.2972	−	8.93444i	−0.526271	−	0.382359i
$547$	−16.2495	+	22.3656i	−0.694779	+	0.956282i	0.305213	+	0.952284i	$0.401272\pi$
$547$	−16.2495	+	22.3656i	−0.694779	+	0.956282i	−0.999992	+	0.00399765i	$0.998728\pi$
$548$	0.812146	+	0.263882i	0.0346931	+	0.0112725i
$549$	−10.6137			−0.452982
$550$		0			0
$551$	−1.57978			−0.0673007
$552$	−17.6171	−	5.72414i	−0.749833	−	0.243636i
$553$	13.6916	−	18.8449i	0.582228	−	0.801368i
$554$	−5.18473	−	3.76692i	−0.220278	−	0.160041i
$555$		0			0
$556$	0.0263418	−	0.0191385i	0.00111714	−	0.000811652i
$557$			6.17333i			0.261572i	0.991411	+	0.130786i	$0.0417501\pi$
$557$			6.17333i			0.261572i	−0.991411	+	0.130786i	$0.958250\pi$
$558$	0.790682	+	1.08828i	0.0334722	+	0.0460706i
$559$	−0.254987	−	0.784770i	−0.0107848	−	0.0331923i
$560$		0			0
$561$	−4.21865	+	12.9837i	−0.178112	+	0.548171i
$562$	−24.0753	+	7.82254i	−1.01555	+	0.329974i
$563$	−5.42039	+	1.76119i	−0.228442	+	0.0742254i	−0.421001	−	0.907060i	$-0.638321\pi$
$563$	−5.42039	+	1.76119i	−0.228442	+	0.0742254i	0.192559	+	0.981285i	$0.438321\pi$
$564$	−0.413862	+	1.27373i	−0.0174267	+	0.0536339i
$565$		0			0
$566$	4.90947	+	15.1098i	0.206360	+	0.635112i
$567$	−0.937986	−	1.29103i	−0.0393917	−	0.0542180i
$568$			31.3350i			1.31479i
$569$	16.3185	−	11.8561i	0.684109	−	0.497034i	−0.190610	−	0.981666i	$-0.561046\pi$
$569$	16.3185	−	11.8561i	0.684109	−	0.497034i	0.874718	+	0.484632i	$0.161046\pi$
$570$		0			0
$571$	12.7464	+	9.26077i	0.533418	+	0.387551i	0.821635	−	0.570014i	$-0.193062\pi$
$571$	12.7464	+	9.26077i	0.533418	+	0.387551i	−0.288217	+	0.957565i	$0.593062\pi$
$572$	−2.42089	+	3.33207i	−0.101222	+	0.139321i
$573$	0.309867	+	0.100682i	0.0129449	+	0.00420605i
$574$	2.50686			0.104634
$575$		0			0
$576$	8.57279			0.357200
$577$	15.3179	+	4.97709i	0.637692	+	0.207199i	0.609980	−	0.792417i	$-0.291178\pi$
$577$	15.3179	+	4.97709i	0.637692	+	0.207199i	0.0277128	+	0.999616i	$0.491178\pi$
$578$	−0.175275	+	0.241245i	−0.00729047	+	0.0100345i
$579$	−2.34766	−	1.70568i	−0.0975656	−	0.0708855i
$580$		0			0
$581$	−6.48609	+	4.71242i	−0.269088	+	0.195504i
$582$		−	2.30441i		−	0.0955207i
$583$	1.02578	+	1.41186i	0.0424833	+	0.0584732i
$584$	−5.04705	−	15.5332i	−0.208848	−	0.642769i
$585$		0			0
$586$	9.30110	−	28.6258i	0.384225	−	1.18252i
$587$	1.90280	−	0.618257i	0.0785369	−	0.0255182i	−0.269485	−	0.963005i	$-0.586853\pi$
$587$	1.90280	−	0.618257i	0.0785369	−	0.0255182i	0.348022	+	0.937486i	$0.386853\pi$
$588$	−0.742304	+	0.241189i	−0.0306121	+	0.00994648i
$589$	0.174646	−	0.537504i	0.00719614	−	0.0221475i
$590$		0			0
$591$	−5.60000	−	17.2350i	−0.230353	−	0.708954i
$592$	−7.55816	−	10.4029i	−0.310638	−	0.427557i
$593$		−	26.8231i		−	1.10149i	−0.834672	−	0.550747i	$-0.814343\pi$
$593$		−	26.8231i		−	1.10149i	0.834672	−	0.550747i	$-0.185657\pi$
$594$	3.64220	−	2.64621i	0.149441	−	0.108575i
$595$		0			0
$596$	0.551396	+	0.400613i	0.0225861	+	0.0164097i
$597$	−0.900815	+	1.23987i	−0.0368679	+	0.0507443i
$598$	57.1076	+	18.5554i	2.33530	+	0.758786i
$599$	44.8025			1.83058			0.915290	−	0.402796i	$-0.131962\pi$
$599$	44.8025			1.83058			0.915290	+	0.402796i	$0.131962\pi$
$600$		0			0
$601$	−14.2298			−0.580446			−0.290223	−	0.956959i	$-0.593729\pi$
$601$	−14.2298			−0.580446			−0.290223	+	0.956959i	$0.593729\pi$
$602$	−0.239911	−	0.0779519i	−0.00977805	−	0.00317708i
$603$	8.94370	−	12.3099i	0.364216	−	0.501300i
$604$	3.13557	+	2.27813i	0.127585	+	0.0926957i
$605$		0			0
$606$	−14.3979	+	10.4607i	−0.584873	+	0.424935i
$607$			20.3346i			0.825356i	0.910877	+	0.412678i	$0.135406\pi$
$607$			20.3346i			0.825356i	−0.910877	+	0.412678i	$0.864594\pi$
$608$	−0.329743	−	0.453853i	−0.0133729	−	0.0184062i
$609$	−1.37266	−	4.22461i	−0.0556230	−	0.171190i
$610$		0			0
$611$	16.6512	−	51.2470i	0.673634	−	2.07323i
$612$	0.682768	−	0.221845i	0.0275993	−	0.00896755i
$613$	19.7744	−	6.42510i	0.798681	−	0.259507i	0.118885	−	0.992908i	$-0.462068\pi$
$613$	19.7744	−	6.42510i	0.798681	−	0.259507i	0.679797	+	0.733401i	$0.262068\pi$
$614$	6.38928	−	19.6642i	0.257850	−	0.793582i
$615$		0			0
$616$	4.82922	+	14.8628i	0.194575	+	0.598839i
$617$	2.90738	+	4.00167i	0.117047	+	0.161101i	0.863520	−	0.504314i	$-0.168255\pi$
$617$	2.90738	+	4.00167i	0.117047	+	0.161101i	−0.746474	+	0.665415i	$0.768255\pi$
$618$		−	14.6862i		−	0.590766i
$619$	−37.1765	+	27.0103i	−1.49425	+	1.08564i	−0.521650	+	0.853160i	$0.674683\pi$
$619$	−37.1765	+	27.0103i	−1.49425	+	1.08564i	−0.972602	+	0.232477i	$0.925317\pi$
$620$		0			0
$621$	5.10005	+	3.70540i	0.204658	+	0.148693i
$622$	10.2065	−	14.0480i	0.409242	−	0.563273i
$623$	−4.28521	−	1.39235i	−0.171683	−	0.0557833i
$624$	−25.5171			−1.02150
$625$		0			0
$626$	−14.1934			−0.567283
$627$	−1.79889	−	0.584494i	−0.0718407	−	0.0233424i
$628$	−1.40160	+	1.92914i	−0.0559299	+	0.0769810i
$629$	−11.7755	−	8.55543i	−0.469521	−	0.341127i
$630$		0			0
$631$	17.5262	−	12.7335i	0.697707	−	0.506914i	−0.181477	−	0.983395i	$-0.558088\pi$
$631$	17.5262	−	12.7335i	0.697707	−	0.506914i	0.879185	+	0.476481i	$0.158088\pi$
$632$		−	42.8915i		−	1.70613i
$633$	6.68298	+	9.19833i	0.265625	+	0.365601i
$634$	8.13179	+	25.0271i	0.322955	+	0.993952i
$635$		0			0
$636$	0.0283590	−	0.0872802i	0.00112451	−	0.00346088i
$637$	29.8656	−	9.70393i	1.18332	−	0.384484i
$638$	11.9183	−	3.87249i	0.471851	−	0.153314i
$639$	3.29534	−	10.1420i	0.130362	−	0.401211i
$640$		0			0
$641$	11.2442	+	34.6061i	0.444119	+	1.36686i	0.883447	+	0.468531i	$0.155217\pi$
$641$	11.2442	+	34.6061i	0.444119	+	1.36686i	−0.439328	+	0.898327i	$0.644783\pi$
$642$	−7.44163	−	10.2425i	−0.293698	−	0.404240i
$643$		−	1.01349i		−	0.0399682i	−0.999800	−	0.0199841i	$-0.993638\pi$
$643$		−	1.01349i		−	0.0399682i	0.999800	−	0.0199841i	$-0.00636156\pi$
$644$	−1.42637	+	1.03632i	−0.0562069	+	0.0408367i
$645$		0			0
$646$	2.54060	+	1.84586i	0.0999587	+	0.0726243i
$647$	−8.05306	+	11.0841i	−0.316598	+	0.435760i	−0.937425	−	0.348188i	$-0.886797\pi$
$647$	−8.05306	+	11.0841i	−0.316598	+	0.435760i	0.620826	+	0.783948i	$0.286797\pi$
$648$	−2.79459	−	0.908017i	−0.109782	−	0.0356703i
$649$	−3.27944			−0.128729
$650$		0			0
$651$	1.58913			0.0622830
$652$	1.43829	+	0.467327i	0.0563276	+	0.0183019i
$653$	−14.0112	+	19.2847i	−0.548299	+	0.754669i	−0.989780	−	0.142601i	$-0.954453\pi$
$653$	−14.0112	+	19.2847i	−0.548299	+	0.754669i	0.441481	+	0.897271i	$0.354453\pi$
$654$	−17.0374	−	12.3784i	−0.666213	−	0.484032i
$655$		0			0
$656$	3.40463	−	2.47361i	0.132928	−	0.0965782i
$657$			5.55832i			0.216851i
$658$	−9.68253	−	13.3269i	−0.377464	−	0.519535i
$659$	−4.56597	−	14.0526i	−0.177865	−	0.547412i	0.821888	−	0.569649i	$-0.192921\pi$
$659$	−4.56597	−	14.0526i	−0.177865	−	0.547412i	−0.999753	+	0.0222376i	$0.992921\pi$
$660$		0			0
$661$	2.33453	−	7.18496i	0.0908029	−	0.279463i	−0.895334	−	0.445395i	$-0.853063\pi$
$661$	2.33453	−	7.18496i	0.0908029	−	0.279463i	0.986137	+	0.165932i	$0.0530633\pi$
$662$	−18.6187	+	6.04958i	−0.723637	+	0.235124i
$663$	−27.4703	+	8.92563i	−1.06686	+	0.346643i
$664$	−4.56186	+	14.0399i	−0.177034	+	0.544856i
$665$		0			0
$666$	1.48327	+	4.56503i	0.0574755	+	0.176891i
$667$	10.3143	+	14.1964i	0.399369	+	0.549685i
$668$		−	1.15652i		−	0.0447471i
$669$	13.7134	−	9.96335i	0.530190	−	0.385205i
$670$		0			0
$671$	−28.6174	−	20.7917i	−1.10476	−	0.802656i
$672$	0.927174	−	1.27615i	0.0357665	−	0.0492284i
$673$	−11.5978	−	3.76836i	−0.447063	−	0.145259i	0.0768292	−	0.997044i	$-0.475520\pi$
$673$	−11.5978	−	3.76836i	−0.447063	−	0.145259i	−0.523892	+	0.851785i	$0.675520\pi$
$674$	−12.6063			−0.485576
$675$		0			0
$676$	−6.43571			−0.247527
$677$	−17.0721	−	5.54706i	−0.656134	−	0.213191i	−0.0380172	−	0.999277i	$-0.512104\pi$
$677$	−17.0721	−	5.54706i	−0.656134	−	0.213191i	−0.618117	+	0.786086i	$0.712104\pi$
$678$	7.97815	−	10.9810i	0.306399	−	0.421722i
$679$	−2.20239	−	1.60013i	−0.0845198	−	0.0614073i
$680$		0			0
$681$	−11.4166	+	8.29466i	−0.437486	+	0.317852i
$682$			4.48320i			0.171671i
$683$	−5.89391	−	8.11227i	−0.225524	−	0.310407i	0.681228	−	0.732071i	$-0.261446\pi$
$683$	−5.89391	−	8.11227i	−0.225524	−	0.310407i	−0.906752	+	0.421664i	$0.861446\pi$
$684$	0.0307366	+	0.0945975i	0.00117524	+	0.00361703i
$685$		0			0
$686$	7.62950	−	23.4812i	0.291296	−	0.896516i
$687$	0.0589602	−	0.0191573i	0.00224947	−	0.000730898i
$688$	−0.402748	+	0.130861i	−0.0153546	+	0.00498901i
$689$	−1.14099	+	3.51160i	−0.0434682	+	0.133781i
$690$		0			0
$691$	5.91136	+	18.1933i	0.224879	+	0.692105i	0.998304	+	0.0582177i	$0.0185418\pi$
$691$	5.91136	+	18.1933i	0.224879	+	0.692105i	−0.773425	+	0.633887i	$0.781458\pi$
$692$	−1.40713	−	1.93675i	−0.0534911	−	0.0736242i
$693$		−	5.31842i		−	0.202030i
$694$	−1.15121	+	0.836404i	−0.0436994	+	0.0317494i
$695$		0			0
$696$	−6.61716	−	4.80765i	−0.250823	−	0.182234i
$697$	2.79999	−	3.85386i	0.106057	−	0.145975i
$698$	−16.7931	−	5.45642i	−0.635629	−	0.206528i
$699$	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	$0.522978\pi$
$702$	9.05894	+	2.94343i	0.341907	+	0.111092i
$703$	1.18535	−	1.63150i	0.0447065	−	0.0615332i
$704$	23.1145	+	16.7937i	0.871162	+	0.632936i
$705$		0			0
$706$	−37.0991	+	26.9540i	−1.39624	+	1.01443i
$707$			21.0241i			0.790692i
$708$	0.101366	+	0.139519i	0.00380958	+	0.00524344i
$709$	−11.7592	−	36.1911i	−0.441626	−	1.35918i	−0.886142	−	0.463413i	$-0.846625\pi$
$709$	−11.7592	−	36.1911i	−0.441626	−	1.35918i	0.444517	−	0.895771i	$-0.353375\pi$
$710$		0			0
$711$	−4.51068	+	13.8824i	−0.169164	+	0.520632i
$712$	−7.89053	+	2.56379i	−0.295710	+	0.0960821i
$713$	−5.97043	+	1.93991i	−0.223594	+	0.0726502i
$714$	−2.72864	+	8.39790i	−0.102117	+	0.314284i
$715$		0			0
$716$	−0.532309	−	1.63828i	−0.0198933	−	0.0612253i
$717$	11.4601	+	15.7734i	0.427984	+	0.589070i
$718$		−	8.23264i		−	0.307239i
$719$	15.7224	−	11.4230i	0.586348	−	0.426007i	−0.254659	−	0.967031i	$-0.581963\pi$
$719$	15.7224	−	11.4230i	0.586348	−	0.426007i	0.841007	+	0.541024i	$0.181963\pi$
$720$		0			0
$721$	−14.0360	−	10.1978i	−0.522729	−	0.379785i
$722$	14.8302	−	20.4120i	0.551923	−	0.759657i
$723$	−3.89800	−	1.26654i	−0.144968	−	0.0471030i
$724$	3.13165			0.116387
$725$		0			0
$726$	0.145007			0.00538172
$727$	36.2104	+	11.7655i	1.34297	+	0.436358i	0.890322	−	0.455331i	$-0.150479\pi$
$727$	36.2104	+	11.7655i	1.34297	+	0.436358i	0.452649	+	0.891689i	$0.350479\pi$
$728$	−19.4347	+	26.7496i	−0.720298	+	0.991406i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$		0			0
$731$	−0.387802	+	0.281755i	−0.0143434	+	0.0104211i
$732$			1.86015i			0.0687531i
$733$	−9.96833	−	13.7202i	−0.368189	−	0.506768i	0.584219	−	0.811596i	$-0.301401\pi$
$733$	−9.96833	−	13.7202i	−0.368189	−	0.506768i	−0.952407	+	0.304828i	$0.901401\pi$
$734$	9.12653	+	28.0886i	0.336866	+	1.03677i
$735$		0			0
$736$	−1.92559	+	5.92635i	−0.0709781	+	0.218448i
$737$	48.2292	−	15.6706i	1.77655	−	0.577235i
$738$	−1.49403	+	0.485439i	−0.0549959	+	0.0178693i
$739$	−4.08025	+	12.5577i	−0.150095	+	0.461944i	−0.997631	−	0.0687937i	$-0.978085\pi$
$739$	−4.08025	+	12.5577i	−0.150095	+	0.461944i	0.847536	+	0.530737i	$0.178085\pi$
$740$		0			0
$741$	−1.23665	−	3.80600i	−0.0454293	−	0.139817i
$742$	0.663476	+	0.913197i	0.0243570	+	0.0335245i
$743$			42.2364i			1.54950i	0.632265	+	0.774752i	$0.282125\pi$
$743$			42.2364i			1.54950i	−0.632265	+	0.774752i	$0.717875\pi$
$744$	2.36729	−	1.71994i	0.0867891	−	0.0630560i
$745$		0			0
$746$	26.7265	+	19.4180i	0.978528	+	0.710942i
$747$	2.95302	−	4.06448i	0.108045	−	0.148712i
$748$	2.27551	+	0.739358i	0.0832008	+	0.0270336i
$749$	−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	$0.506087\pi$
$752$	−26.3002	−	8.54545i	−0.959069	−	0.311620i
$753$	−0.605022	+	0.832742i	−0.0220482	+	0.0303468i
$754$	21.4502	+	15.5845i	0.781170	+	0.567553i
$755$		0			0
$756$	−0.226264	+	0.164391i	−0.00822915	+	0.00597883i
$757$		−	17.0074i		−	0.618146i	−0.951038	−	0.309073i	$-0.899981\pi$
$757$		−	17.0074i		−	0.618146i	0.951038	−	0.309073i	$-0.100019\pi$
$758$	4.98488	+	6.86110i	0.181059	+	0.249207i
$759$	6.49238	+	19.9815i	0.235658	+	0.725282i
$760$		0			0
$761$	−7.45484	+	22.9436i	−0.270238	+	0.831706i	0.720203	+	0.693764i	$0.244049\pi$
$761$	−7.45484	+	22.9436i	−0.270238	+	0.831706i	−0.990440	+	0.137942i	$0.955951\pi$
$762$	−1.25489	+	0.407738i	−0.0454599	+	0.0147708i
$763$	−23.6607	+	7.68783i	−0.856575	+	0.278318i
$764$	0.0176454	−	0.0543070i	0.000638389	−	0.00196476i
$765$		0			0
$766$	10.3053	+	31.7165i	0.372346	+	1.14596i
$767$	−4.07834	−	5.61335i	−0.147260	−	0.202686i
$768$		−	4.17298i		−	0.150579i
$769$	40.2744	−	29.2611i	1.45233	−	1.05518i	0.467053	−	0.884230i	$-0.345316\pi$
$769$	40.2744	−	29.2611i	1.45233	−	1.05518i	0.985279	−	0.170952i	$-0.0546841\pi$
$770$		0			0
$771$	15.0151	+	10.9091i	0.540757	+	0.392883i
$772$	−0.298936	+	0.411450i	−0.0107589	+	0.0148084i
$773$	−29.9338	−	9.72608i	−1.07664	−	0.349823i	−0.283572	−	0.958951i	$-0.591520\pi$
$773$	−29.9338	−	9.72608i	−1.07664	−	0.349823i	−0.793072	+	0.609128i	$0.791520\pi$
$774$	0.158076			0.00568193
$775$		0			0
$776$	−5.01268			−0.179945
$777$	5.39288	+	1.75225i	0.193468	+	0.0628617i
$778$	−10.2613	+	14.1235i	−0.367885	+	0.506350i
$779$	0.533952	+	0.387939i	0.0191308	+	0.0138993i
$780$		0			0
$781$	28.7528	−	20.8901i	1.02886	−	0.747508i
$782$		−	34.8822i		−	1.24738i
$783$	1.63614	+	2.25196i	0.0584710	+	0.0804784i
$784$	−4.98010	−	15.3272i	−0.177861	−	0.547399i
$785$		0			0
$786$	4.20001	−	12.9263i	0.149809	−	0.461066i
$787$	−18.2047	+	5.91505i	−0.648926	+	0.210849i	−0.614941	−	0.788573i	$-0.710820\pi$
$787$	−18.2047	+	5.91505i	−0.648926	+	0.210849i	−0.0339855	+	0.999422i	$0.510820\pi$
$788$	−3.02060	+	0.981451i	−0.107604	+	0.0349627i
$789$	−3.82988	+	11.7872i	−0.136347	+	0.419634i
$790$		0			0
$791$	−4.95499	−	15.2499i	−0.176179	−	0.542224i
$792$	−5.75619	−	7.92272i	−0.204537	−	0.281522i
$793$		−	74.8406i		−	2.65767i
$794$	−31.7159	+	23.0430i	−1.12556	+	0.817764i
$795$		0			0
$796$	0.217298	+	0.157876i	0.00770191	+	0.00559577i
$797$	4.24050	−	5.83655i	0.150206	−	0.206741i	−0.727283	−	0.686338i	$-0.759217\pi$
$797$	4.24050	−	5.83655i	0.150206	−	0.206741i	0.877489	+	0.479597i	$0.159217\pi$
$798$	−1.16353	−	0.378053i	−0.0411885	−	0.0133829i
$799$	−31.3024			−1.10740
$800$		0			0
$801$	2.82350			0.0997636
$802$	−30.0528	−	9.76474i	−1.06120	−	0.344805i
$803$	−10.8885	+	14.9867i	−0.384246	+	0.528869i
$804$	−2.15743	−	1.56747i	−0.0760867	−	0.0552802i
$805$		0			0
$806$	−7.67381	+	5.57535i	−0.270298	+	0.196383i
$807$			5.30032i			0.186580i
$808$	22.7546	+	31.3191i	0.800505	+	1.10180i
$809$	−0.327376	−	1.00756i	−0.0115099	−	0.0354239i	0.945137	−	0.326675i	$-0.105928\pi$
$809$	−0.327376	−	1.00756i	−0.0115099	−	0.0354239i	−0.956647	+	0.291251i	$0.905928\pi$
$810$		0			0
$811$	6.68712	−	20.5808i	0.234817	−	0.722691i	−0.762329	−	0.647190i	$-0.775944\pi$
$811$	6.68712	−	20.5808i	0.234817	−	0.722691i	0.997146	−	0.0755016i	$-0.0240558\pi$
$812$	−0.740402	+	0.240571i	−0.0259830	+	0.00844239i
$813$	−0.758399	+	0.246419i	−0.0265982	+	0.00864228i
$814$	−4.94339	+	15.2142i	−0.173266	+	0.533257i
$815$		0			0
$816$	4.58067	+	14.0979i	0.160356	+	0.493524i
$817$	−0.0390371	−	0.0537299i	−0.00136573	−	0.00187977i
$818$		−	21.6022i		−	0.755302i
$819$	9.10344	−	6.61404i	0.318100	−	0.231113i
$820$		0			0
$821$	18.7553	+	13.6265i	0.654564	+	0.475568i	0.864823	−	0.502077i	$-0.167431\pi$
$821$	18.7553	+	13.6265i	0.654564	+	0.475568i	−0.210259	+	0.977646i	$0.567431\pi$
$822$	3.86871	−	5.32482i	0.134937	−	0.185724i
$823$	−26.6076	−	8.64534i	−0.927483	−	0.301358i	−0.193950	−	0.981011i	$-0.562130\pi$
$823$	−26.6076	−	8.64534i	−0.927483	−	0.301358i	−0.733533	+	0.679654i	$0.762130\pi$
$824$	−31.9463			−1.11290
$825$		0			0
$826$	−2.12116			−0.0738044
$827$	39.2829	+	12.7638i	1.36600	+	0.443841i	0.898042	−	0.439909i	$-0.144989\pi$
$827$	39.2829	+	12.7638i	1.36600	+	0.443841i	0.467959	+	0.883750i	$0.344989\pi$
$828$	0.649405	−	0.893830i	0.0225684	−	0.0310627i
$829$	38.4838	+	27.9602i	1.33660	+	0.971096i	0.999562	+	0.0296051i	$0.00942497\pi$
$829$	38.4838	+	27.9602i	1.33660	+	0.971096i	0.337038	+	0.941491i	$0.390575\pi$
$830$		0			0
$831$	3.83818	−	2.78860i	0.133145	−	0.0967355i
$832$			60.4495i			2.09571i
$833$	−10.7226	−	14.7584i	−0.371516	−	0.511348i
$834$	−0.0775516	−	0.238679i	−0.00268539	−	0.00826478i
$835$		0			0
$836$	−0.102438	+	0.315272i	−0.00354289	+	0.0109039i
$837$	−0.947085	+	0.307727i	−0.0327360	+	0.0106366i
$838$	−41.5951	+	13.5151i	−1.43688	+	0.466871i
$839$	−15.1518	+	46.6324i	−0.523097	+	1.60993i	0.244950	+	0.969536i	$0.421228\pi$
$839$	−15.1518	+	46.6324i	−0.523097	+	1.60993i	−0.768048	+	0.640393i	$0.778772\pi$
$840$		0			0
$841$	−6.56714	−	20.2116i	−0.226453	−	0.696951i
$842$	14.3332	+	19.7280i	0.493956	+	0.679872i
$843$		−	18.7398i		−	0.645433i
$844$	1.61209	−	1.17125i	0.0554905	−	0.0403162i
$845$		0			0
$846$	8.35122	+	6.06752i	0.287121	+	0.208606i
$847$	0.100690	−	0.138588i	0.00345974	−	0.00476192i
$848$	1.80217	+	0.585560i	0.0618867	+	0.0201082i
$849$	−11.7612			−0.403643
$850$		0			0
$851$	−22.4003			−0.767871
$852$	−1.77748	−	0.577538i	−0.0608954	−	0.0197861i
$853$	−19.1251	+	26.3235i	−0.654832	+	0.901299i	−0.999297	−	0.0375002i	$-0.988061\pi$
$853$	−19.1251	+	26.3235i	−0.654832	+	0.901299i	0.344464	+	0.938799i	$0.388061\pi$
$854$	−18.5099	−	13.4482i	−0.633394	−	0.460188i
$855$		0			0
$856$	−22.2801	+	16.1875i	−0.761520	+	0.553276i
$857$			30.4813i			1.04122i	0.853794	+	0.520610i	$0.174296\pi$
$857$			30.4813i			1.04122i	−0.853794	+	0.520610i	$0.825704\pi$
$858$	18.6593	+	25.6823i	0.637017	+	0.876779i
$859$	−1.27382	−	3.92040i	−0.0434620	−	0.133762i	0.926971	−	0.375133i	$-0.122403\pi$
$859$	−1.27382	−	3.92040i	−0.0434620	−	0.133762i	−0.970433	+	0.241371i	$0.922403\pi$
$860$		0			0
$861$	−0.573471	+	1.76496i	−0.0195439	+	0.0601498i
$862$	42.5694	−	13.8316i	1.44992	−	0.471107i
$863$	17.5169	−	5.69159i	0.596283	−	0.193744i	0.00470109	−	0.999989i	$-0.498504\pi$
$863$	17.5169	−	5.69159i	0.596283	−	0.193744i	0.591582	+	0.806245i	$0.298504\pi$
$864$	−0.305455	+	0.940094i	−0.0103918	+	0.0319826i
$865$		0			0
$866$	−9.46115	−	29.1184i	−0.321503	−	0.989485i
$867$	−0.129753	−	0.178590i	−0.00440666	−	0.00606524i
$868$		−	0.278510i		−	0.00945325i
$869$	−39.3570	+	28.5945i	−1.33510	+	0.970003i
$870$		0			0
$871$	86.8013	+	63.0649i	2.94115	+	2.13687i
$872$	−26.9261	+	37.0607i	−0.911834	+	1.25503i
$873$	1.62242	+	0.527158i	0.0549108	+	0.0178416i
$874$	4.83292			0.163476
$875$		0			0
$876$	0.974146			0.0329133
$877$	17.9870	+	5.84432i	0.607377	+	0.197349i	0.596528	−	0.802593i	$-0.296547\pi$
$877$	17.9870	+	5.84432i	0.607377	+	0.197349i	0.0108490	+	0.999941i	$0.496547\pi$
$878$	−6.75244	+	9.29394i	−0.227884	+	0.313655i
$879$	18.0264	+	13.0969i	0.608015	+	0.441749i
$880$		0			0
$881$	−28.0192	+	20.3571i	−0.943990	+	0.685849i	−0.949378	−	0.314137i	$-0.898285\pi$
$881$	−28.0192	+	20.3571i	−0.943990	+	0.685849i	0.00538802	+	0.999985i	$0.498285\pi$
$882$			6.01583i			0.202563i
$883$	19.2132	+	26.4447i	0.646575	+	0.889934i	0.998945	−	0.0459269i	$-0.0146241\pi$
$883$	19.2132	+	26.4447i	0.646575	+	0.889934i	−0.352370	+	0.935861i	$0.614624\pi$
$884$	1.56430	+	4.81442i	0.0526131	+	0.161926i
$885$		0			0
$886$	2.65388	−	8.16781i	0.0891589	−	0.274403i
$887$	46.4037	−	15.0775i	1.55809	−	0.506253i	0.601790	−	0.798655i	$-0.294455\pi$
$887$	46.4037	−	15.0775i	1.55809	−	0.506253i	0.956296	+	0.292402i	$0.0944545\pi$
$888$	9.93012	−	3.22649i	0.333233	−	0.108274i
$889$	−0.481680	+	1.48246i	−0.0161550	+	0.0497201i
$890$		0			0
$891$	1.02988	+	3.16965i	0.0345024	+	0.106187i
$892$	−1.74617	−	2.40340i	−0.0584661	−	0.0804716i
$893$		−	4.33695i		−	0.145131i
$894$	4.24995	−	3.08777i	0.142139	−	0.103270i
$895$		0			0
$896$	12.3983	+	9.00789i	0.414198	+	0.300932i
$897$	−26.1280	+	35.9620i	−0.872387	+	1.20074i
$898$	−8.03879	−	2.61196i	−0.268258	−	0.0871623i
$899$	−2.77195			−0.0924497
$900$		0			0
$901$	2.14494			0.0714582
$902$	−4.97925	−	1.61786i	−0.165791	−	0.0538687i
$903$	0.109765	−	0.151078i	0.00365274	−	0.00502756i
$904$	−23.8865	−	17.3545i	−0.794452	−	0.577203i
$905$		0			0
$906$	24.1678	−	17.5589i	0.802921	−	0.583356i
$907$		−	45.0367i		−	1.49542i	−0.664025	−	0.747710i	$-0.731153\pi$
$907$		−	45.0367i		−	1.49542i	0.664025	−	0.747710i	$-0.268847\pi$
$908$	1.45371	+	2.00087i	0.0482432	+	0.0664011i
$909$	−4.07120	−	12.5299i	−0.135033	−	0.415589i
$910$		0			0
$911$	4.00018	−	12.3113i	0.132532	−	0.407891i	−0.862666	−	0.505774i	$-0.831207\pi$
$911$	4.00018	−	12.3113i	0.132532	−	0.407891i	0.995198	+	0.0978826i	$0.0312070\pi$
$912$	−1.95326	+	0.634652i	−0.0646788	+	0.0210154i
$913$	15.9243	−	5.17410i	0.527016	−	0.171238i
$914$	4.61012	−	14.1885i	0.152489	−	0.469314i
$915$		0			0
$916$	−0.00335750	−	0.0103333i	−0.000110935	−	0.000341423i
$917$	−9.43764	−	12.9898i	−0.311658	−	0.428961i
$918$		−	5.53333i		−	0.182627i
$919$	11.7889	−	8.56513i	0.388880	−	0.282538i	−0.376117	−	0.926572i	$-0.622741\pi$
$919$	11.7889	−	8.56513i	0.388880	−	0.282538i	0.764996	+	0.644035i	$0.222741\pi$
$920$		0			0
$921$	12.3830	+	8.99679i	0.408034	+	0.296454i
$922$	18.7877	−	25.8591i	0.618741	−	0.851623i
$923$	71.5145	+	23.2365i	2.35393	+	0.764838i
$924$	−0.932102			−0.0306639
$925$		0			0
$926$	−8.40813			−0.276308
$927$	10.3399	+	3.35963i	0.339606	+	0.110345i
$928$	−1.61728	+	2.22600i	−0.0530899	+	0.0730720i
$929$	−25.3701	−	18.4324i	−0.832365	−	0.604749i	0.0878623	−	0.996133i	$-0.471996\pi$
$929$	−25.3701	−	18.4324i	−0.832365	−	0.604749i	−0.920227	+	0.391384i	$0.871996\pi$
$930$		0			0
$931$	2.04477	−	1.48561i	0.0670147	−	0.0486890i
$932$		−	4.56008i		−	0.149370i
$933$	7.55569	+	10.3995i	0.247362	+	0.340465i
$934$	−2.06494	−	6.35522i	−0.0675668	−	0.207949i
$935$		0			0
$936$	6.40272	−	19.7055i	0.209279	−	0.644095i
$937$	−46.3855	+	15.0716i	−1.51535	+	0.492367i	−0.944450	−	0.328654i	$-0.893405\pi$
$937$	−46.3855	+	15.0716i	−1.51535	+	0.492367i	−0.570898	+	0.821021i	$0.693405\pi$
$938$	31.1949	−	10.1358i	1.01855	−	0.330946i
$939$	3.24690	−	9.99293i	0.105959	−	0.326107i
$940$		0			0
$941$	−9.96145	−	30.6582i	−0.324734	−	0.999429i	−0.971561	−	0.236791i	$-0.923904\pi$
$941$	−9.96145	−	30.6582i	−0.324734	−	0.999429i	0.646827	−	0.762637i	$-0.276096\pi$
$942$	10.8030	+	14.8690i	0.351980	+	0.484460i
$943$		−	7.33108i		−	0.238733i
$944$	−2.88080	+	2.09302i	−0.0937619	+	0.0681220i
$945$		0			0
$946$	0.426216	+	0.309664i	0.0138575	+	0.0100680i
$947$	30.5199	−	42.0070i	0.991763	−	1.36505i	0.0615183	−	0.998106i	$-0.480406\pi$
$947$	30.5199	−	42.0070i	0.991763	−	1.36505i	0.930245	−	0.366939i	$-0.119594\pi$
$948$	2.43302	+	0.790537i	0.0790209	+	0.0256755i
$949$	−39.1935			−1.27227
$950$		0			0
$951$	−19.4806			−0.631703
$952$	18.2676	+	5.93551i	0.592057	+	0.192371i
$953$	−23.3814	+	32.1817i	−0.757398	+	1.04247i	0.240028	+	0.970766i	$0.422843\pi$
$953$	−23.3814	+	32.1817i	−0.757398	+	1.04247i	−0.997426	+	0.0717028i	$0.977157\pi$
$954$	−0.572251	−	0.415765i	−0.0185273	−	0.0134609i
$955$		0			0
$956$	2.76444	−	2.00848i	0.0894083	−	0.0649590i
$957$			9.27701i			0.299883i
$958$	23.8912	+	32.8835i	0.771891	+	1.06242i
$959$	−2.40274	−	7.39487i	−0.0775885	−	0.238793i
$960$		0			0
$961$	−9.27309	+	28.5396i	−0.299132	+	0.920633i
$962$	−32.1895	+	10.4590i	−1.03783	+	0.337211i
$963$	8.91364	−	2.89622i	0.287238	−	0.0933293i
$964$	−0.221972	+	0.683160i	−0.00714924	+	0.0220031i
$965$		0			0
$966$	4.19930	+	12.9241i	0.135110	+	0.415827i
$967$	−11.6862	−	16.0847i	−0.375802	−	0.517248i	0.578664	−	0.815566i	$-0.303574\pi$
$967$	−11.6862	−	16.0847i	−0.375802	−	0.517248i	−0.954466	+	0.298318i	$0.903574\pi$
$968$		−	0.315428i		−	0.0101382i
$969$	−1.88077	+	1.36646i	−0.0604191	+	0.0438971i
$970$		0			0
$971$	33.4804	+	24.3250i	1.07444	+	0.780625i	0.976705	−	0.214588i	$-0.0688407\pi$
$971$	33.4804	+	24.3250i	1.07444	+	0.780625i	0.0977335	+	0.995213i	$0.468841\pi$
$972$	0.103015	−	0.141788i	0.00330420	−	0.00454784i
$973$	−0.281963	−	0.0916152i	−0.00903931	−	0.00293705i
$974$	46.2658			1.48245
$975$		0			0
$976$	−38.4085			−1.22943
$977$	3.44274	+	1.11861i	0.110143	+	0.0357876i	0.363570	−	0.931567i	$-0.381558\pi$
$977$	3.44274	+	1.11861i	0.110143	+	0.0357876i	−0.253427	+	0.967355i	$0.581558\pi$
$978$	6.85137	−	9.43010i	0.219083	−	0.301541i
$979$	7.61292	+	5.53111i	0.243310	+	0.176775i
$980$		0			0
$981$	12.6125	−	9.16353i	0.402686	−	0.292569i
$982$			14.0747i			0.449143i
$983$	−11.8203	−	16.2692i	−0.377008	−	0.518907i	0.577781	−	0.816192i	$-0.303919\pi$
$983$	−11.8203	−	16.2692i	−0.377008	−	0.518907i	−0.954789	+	0.297285i	$0.903919\pi$
$984$	1.05596	+	3.24990i	0.0336626	+	0.103603i
$985$		0			0
$986$	4.75962	−	14.6486i	0.151577	−	0.466506i
$987$	11.5978	−	3.76836i	0.369162	−	0.119948i
$988$	−0.667037	+	0.216733i	−0.0212213	+	0.00689521i
$989$	−0.227963	+	0.701599i	−0.00724881	+	0.0223095i
$990$		0			0
$991$	2.29905	+	7.07576i	0.0730319	+	0.224769i	0.980909	−	0.194467i	$-0.0622978\pi$
$991$	2.29905	+	7.07576i	0.0730319	+	0.224769i	−0.907877	+	0.419236i	$0.862298\pi$
$992$	−0.578584	−	0.796352i	−0.0183700	−	0.0252842i
$993$		−	14.4925i		−	0.459905i
$994$	18.5974	−	13.5118i	0.589875	−	0.428569i
$995$		0			0
$996$	−0.712338	−	0.517544i	−0.0225713	−	0.0163990i
$997$	−27.1246	+	37.3338i	−0.859045	+	1.18237i	0.122751	+	0.992438i	$0.460828\pi$
$997$	−27.1246	+	37.3338i	−0.859045	+	1.18237i	−0.981796	+	0.189937i	$0.939172\pi$
$998$	11.3506	+	3.68804i	0.359298	+	0.116743i
$999$	−3.55334			−0.112423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.c.274.2		16
5.2	odd	4		375.2.g.e.226.4		16
5.3	odd	4		375.2.g.d.226.1		16
5.4	even	2		75.2.i.a.4.3	✓	16
15.14	odd	2		225.2.m.b.154.2		16
25.6	even	5		75.2.i.a.19.3	yes	16
25.8	odd	20		375.2.g.d.151.1		16
25.9	even	10		1875.2.b.h.1249.12		16
25.12	odd	20		1875.2.a.m.1.7		8
25.13	odd	20		1875.2.a.p.1.2		8
25.16	even	5		1875.2.b.h.1249.5		16
25.17	odd	20		375.2.g.e.151.4		16
25.19	even	10	inner	375.2.i.c.349.2		16
75.38	even	20		5625.2.a.t.1.7		8
75.56	odd	10		225.2.m.b.19.2		16
75.62	even	20		5625.2.a.bd.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.3	✓	16	5.4	even	2
75.2.i.a.19.3	yes	16	25.6	even	5
225.2.m.b.19.2		16	75.56	odd	10
225.2.m.b.154.2		16	15.14	odd	2
375.2.g.d.151.1		16	25.8	odd	20
375.2.g.d.226.1		16	5.3	odd	4
375.2.g.e.151.4		16	25.17	odd	20
375.2.g.e.226.4		16	5.2	odd	4
375.2.i.c.274.2		16	1.1	even	1	trivial
375.2.i.c.349.2		16	25.19	even	10	inner
1875.2.a.m.1.7		8	25.12	odd	20
1875.2.a.p.1.2		8	25.13	odd	20
1875.2.b.h.1249.5		16	25.16	even	5
1875.2.b.h.1249.12		16	25.9	even	10
5625.2.a.t.1.7		8	75.38	even	20
5625.2.a.bd.1.2		8	75.62	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)

\(f(q)\)	\(=\)	\(q+(-1.28472 - 0.417429i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.141788 - 0.103015i) q^{4} +(-1.09284 + 0.793998i) q^{6} +1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(-1.28472 - 0.417429i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.141788 - 0.103015i) q^{4} +(-1.09284 + 0.793998i) q^{6} +1.59580i q^{7} +(1.72715 + 2.37722i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.02988 - 3.16965i) q^{11} +(-0.166681 + 0.0541581i) q^{12} +(6.70620 - 2.17898i) q^{13} +(0.666132 - 2.05014i) q^{14} +(-1.11826 - 3.44165i) q^{16} +(-2.40771 - 3.31393i) q^{17} +1.35083i q^{18} +(0.459145 - 0.333589i) q^{19} +(1.29103 + 0.937986i) q^{21} +(-2.64621 + 3.64220i) q^{22} +(-5.99546 - 1.94804i) q^{23} +2.93840 q^{24} -9.52513 q^{26} +(-0.951057 - 0.309017i) q^{27} +(0.164391 - 0.226264i) q^{28} +(-2.25196 - 1.63614i) q^{29} +(0.805639 - 0.585331i) q^{31} -0.988473i q^{32} +(-1.95895 - 2.69627i) q^{33} +(1.70989 + 5.26251i) q^{34} +(-0.0541581 + 0.166681i) q^{36} +(3.37943 - 1.09804i) q^{37} +(-0.729121 + 0.236906i) q^{38} +(2.17898 - 6.70620i) q^{39} +(0.359364 + 1.10601i) q^{41} +(-1.26706 - 1.74396i) q^{42} -0.117022i q^{43} +(-0.472545 + 0.343324i) q^{44} +(6.88929 + 5.00536i) q^{46} +(4.49170 - 6.18229i) q^{47} +(-3.44165 - 1.11826i) q^{48} +4.45343 q^{49} -4.09625 q^{51} +(-1.17532 - 0.381886i) q^{52} +(-0.307785 + 0.423629i) q^{53} +(1.09284 + 0.793998i) q^{54} +(-3.79356 + 2.75618i) q^{56} -0.567535i q^{57} +(2.21015 + 3.04201i) q^{58} +(-0.304072 - 0.935838i) q^{59} +(3.27982 - 10.0942i) q^{61} +(-1.27935 + 0.415686i) q^{62} +(1.51769 - 0.493128i) q^{63} +(-2.64914 + 8.15321i) q^{64} +(1.39120 + 4.28166i) q^{66} +(8.94370 + 12.3099i) q^{67} +0.717905i q^{68} +(-5.10005 + 3.70540i) q^{69} +(8.62730 + 6.26810i) q^{71} +(1.72715 - 2.37722i) q^{72} +(-5.28627 - 1.71761i) q^{73} -4.79996 q^{74} -0.0994657 q^{76} +(5.05812 + 1.64348i) q^{77} +(-5.59873 + 7.70599i) q^{78} +(-11.8091 - 8.57982i) q^{79} +(-0.809017 + 0.587785i) q^{81} -1.57091i q^{82} +(2.95302 + 4.06448i) q^{83} +(-0.0864253 - 0.265990i) q^{84} +(-0.0488483 + 0.150339i) q^{86} +(-2.64734 + 0.860172i) q^{87} +(9.31372 - 3.02621i) q^{88} +(-0.872511 + 2.68531i) q^{89} +(3.47720 + 10.7017i) q^{91} +(0.649405 + 0.893830i) q^{92} -0.995824i q^{93} +(-8.35122 + 6.06752i) q^{94} +(-0.799691 - 0.581010i) q^{96} +(-1.00271 + 1.38012i) q^{97} +(-5.72139 - 1.85899i) q^{98} -3.33277 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9}+O(q^{10}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9	\( 16 q + 2 q^{4} + 2 q^{6} + 30 q^{8} + 4 q^{9} - 6 q^{11} - 12 q^{14} - 10 q^{16} - 10 q^{17} - 2 q^{19} + 4 q^{21} + 30 q^{22} + 20 q^{23} + 24 q^{24} + 12 q^{26} - 30 q^{28} + 16 q^{29} + 6 q^{31} - 10 q^{33} - 36 q^{34} - 2 q^{36} + 10 q^{37} - 30 q^{38} - 8 q^{39} - 14 q^{41} + 10 q^{42} + 26 q^{44} + 16 q^{46} - 40 q^{47} - 32 q^{51} - 40 q^{52} - 10 q^{53} - 2 q^{54} - 10 q^{58} + 12 q^{59} + 10 q^{62} + 10 q^{63} + 8 q^{64} + 16 q^{66} + 40 q^{67} - 12 q^{69} - 8 q^{71} + 30 q^{72} + 20 q^{73} - 52 q^{74} - 32 q^{76} + 40 q^{77} - 20 q^{79} - 4 q^{81} - 10 q^{83} + 12 q^{84} - 36 q^{86} - 40 q^{87} + 40 q^{88} + 18 q^{89} + 26 q^{91} - 10 q^{92} - 38 q^{94} - 26 q^{96} - 40 q^{97} - 60 q^{98} - 4 q^{99}+O(q^{100}) \) 16 * q + 2 * q^4 + 2 * q^6 + 30 * q^8 + 4 * q^9 - 6 * q^11 - 12 * q^14 - 10 * q^16 - 10 * q^17 - 2 * q^19 + 4 * q^21 + 30 * q^22 + 20 * q^23 + 24 * q^24 + 12 * q^26 - 30 * q^28 + 16 * q^29 + 6 * q^31 - 10 * q^33 - 36 * q^34 - 2 * q^36 + 10 * q^37 - 30 * q^38 - 8 * q^39 - 14 * q^41 + 10 * q^42 + 26 * q^44 + 16 * q^46 - 40 * q^47 - 32 * q^51 - 40 * q^52 - 10 * q^53 - 2 * q^54 - 10 * q^58 + 12 * q^59 + 10 * q^62 + 10 * q^63 + 8 * q^64 + 16 * q^66 + 40 * q^67 - 12 * q^69 - 8 * q^71 + 30 * q^72 + 20 * q^73 - 52 * q^74 - 32 * q^76 + 40 * q^77 - 20 * q^79 - 4 * q^81 - 10 * q^83 + 12 * q^84 - 36 * q^86 - 40 * q^87 + 40 * q^88 + 18 * q^89 + 26 * q^91 - 10 * q^92 - 38 * q^94 - 26 * q^96 - 40 * q^97 - 60 * q^98 - 4 * q^99

Introduction

L-functions

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Database

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