LMFDB - Embedded newform 375.2.i.c.349.2

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			349.2
Root			$-1.35083i$ of defining polynomial
Character	$\chi$	$=$	375.349
Dual form			375.2.i.c.274.2

$q$-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 $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$

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	−0.725712	−	0.687998i	$-0.758490\pi$
$2$	−1.28472	+	0.417429i	−0.908431	+	0.295167i	−0.182719	+	0.983165i	$0.558490\pi$
$3$	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	$-0.902487\pi$
$7$		−	1.59580i		−	0.603155i	0.953442	−	0.301577i	$-0.0975131\pi$
$8$	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	0.977559	+	0.210662i	$0.0675619\pi$
$11$	1.02988	+	3.16965i	0.310521	+	0.955686i	−0.667038	+	0.745024i	$0.732438\pi$
$12$	−0.166681	−	0.0541581i	−0.0481168	−	0.0156341i
$13$	6.70620	+	2.17898i	1.85997	+	0.604339i	0.994674	+	0.103071i	$0.0328667\pi$
$13$	6.70620	+	2.17898i	1.85997	+	0.604339i	0.865292	+	0.501269i	$0.167133\pi$
$14$	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	−0.994122	−	0.108264i	$-0.965471\pi$
$17$	−2.40771	+	3.31393i	−0.583957	+	0.803747i	0.410166	+	0.912011i	$0.365471\pi$
$18$		−	1.35083i		−	0.318394i
$19$	0.459145	+	0.333589i	0.105335	+	0.0765305i	0.639206	−	0.769036i	$-0.279263\pi$
$19$	0.459145	+	0.333589i	0.105335	+	0.0765305i	−0.533871	+	0.845566i	$0.679263\pi$
$20$		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	−0.857971	−	0.513698i	$-0.828275\pi$
$23$	−5.99546	+	1.94804i	−1.25014	+	0.406195i	−0.392169	+	0.919893i	$0.628275\pi$
$24$	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	−0.776904	−	0.629619i	$-0.783211\pi$
$29$	−2.25196	+	1.63614i	−0.418178	+	0.303824i	0.358726	+	0.933443i	$0.383211\pi$
$30$		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	$0.671496\pi$
$32$			0.988473i			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	0.573329	−	0.819325i	$-0.305652\pi$
$37$	3.37943	+	1.09804i	0.555574	+	0.180517i	−0.0177546	+	0.999842i	$0.505652\pi$
$38$	−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	−0.919065	−	0.394105i	$-0.871055\pi$
$41$	0.359364	−	1.10601i	0.0561232	−	0.172729i	0.975189	+	0.221376i	$0.0710547\pi$
$42$	−1.26706	+	1.74396i	−0.195511	+	0.269098i
$43$			0.117022i			0.0178456i	0.999960	+	0.00892281i	$0.00284026\pi$
$43$			0.117022i			0.0178456i	−0.999960	+	0.00892281i	$0.997160\pi$
$44$	−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	0.999310	−	0.0371425i	$-0.0118256\pi$
$47$	4.49170	+	6.18229i	0.655182	+	0.901780i	−0.344128	+	0.938923i	$0.611826\pi$
$48$	−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	0.787355	−	0.616500i	$-0.211450\pi$
$53$	−0.307785	−	0.423629i	−0.0422775	−	0.0581900i	−0.829632	+	0.558310i	$0.811450\pi$
$54$	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	−0.968897	−	0.247465i	$-0.920403\pi$
$59$	−0.304072	+	0.935838i	−0.0395868	+	0.121836i	0.929310	+	0.369300i	$0.120403\pi$
$60$		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	$0.662208\pi$
$62$	−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	0.247861	−	0.968796i	$-0.420272\pi$
$67$	8.94370	−	12.3099i	1.09265	−	1.50390i	0.844786	−	0.535104i	$-0.179728\pi$
$68$		−	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	0.0567995	−	0.998386i	$-0.481910\pi$
$71$	8.62730	−	6.26810i	1.02387	−	0.743887i	0.967073	+	0.254499i	$0.0819104\pi$
$72$	1.72715	+	2.37722i	0.203547	+	0.280158i
$73$	−5.28627	+	1.71761i	−0.618711	+	0.201032i	−0.601568	−	0.798821i	$-0.705457\pi$
$73$	−5.28627	+	1.71761i	−0.618711	+	0.201032i	−0.0171433	+	0.999853i	$0.505457\pi$
$74$	−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	−0.328847	+	0.944383i	$0.606660\pi$
$79$	−11.8091	+	8.57982i	−1.32863	+	0.965305i	−0.999781	+	0.0209214i	$0.993340\pi$
$80$		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	−0.615588	−	0.788068i	$-0.711082\pi$
$83$	2.95302	−	4.06448i	0.324136	−	0.446135i	0.939724	+	0.341933i	$0.111082\pi$
$84$	−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	0.894104	−	0.447859i	$-0.147813\pi$
$89$	−0.872511	−	2.68531i	−0.0924859	−	0.284642i	−0.986590	+	0.163216i	$0.947813\pi$
$90$		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	0.755072	−	0.655642i	$-0.227602\pi$
$97$	−1.00271	−	1.38012i	−0.101810	−	0.140130i	−0.856882	+	0.515512i	$0.827602\pi$
$98$	−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	0.368347	−	0.929688i	$-0.379924\pi$
$103$	−6.39039	−	8.79562i	−0.629664	−	0.866658i	−0.998012	+	0.0630298i	$0.979924\pi$
$104$	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	$-0.850343\pi$
$107$		−	9.37236i		−	0.906060i	0.891495	−	0.453030i	$-0.149657\pi$
$108$	0.103015	−	0.141788i	0.00991260	−	0.0136435i
$109$	4.81755	−	14.8269i	0.461438	−	1.42016i	−0.401970	−	0.915653i	$-0.631674\pi$
$109$	4.81755	−	14.8269i	0.461438	−	1.42016i	0.863408	−	0.504506i	$-0.168326\pi$
$110$		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	−0.177164	−	0.984181i	$-0.556692\pi$
$113$	−9.55629	−	3.10503i	−0.898980	−	0.292096i	−0.721816	+	0.692085i	$0.756692\pi$
$114$	−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	−0.267510	−	0.963555i	$-0.586201\pi$
$127$	0.928977	−	0.301843i	0.0824334	−	0.0267842i	0.349943	+	0.936771i	$0.386201\pi$
$128$	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	0.172363	−	0.985033i	$-0.444860\pi$
$131$	−8.14001	−	5.91406i	−0.711196	−	0.516714i	−0.883559	+	0.468319i	$0.844860\pi$
$132$		−	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	0.104296	−	0.994546i	$-0.466741\pi$
$137$	−4.63397	−	1.50567i	−0.395907	−	0.128638i	−0.500203	+	0.865908i	$0.666741\pi$
$138$	8.09885	+	2.63148i	0.689420	+	0.224006i
$139$	−0.0574103	−	0.176691i	−0.00486948	−	0.0149867i	0.948592	−	0.316501i	$-0.102508\pi$
$139$	−0.0574103	−	0.176691i	−0.00486948	−	0.0149867i	−0.953462	+	0.301514i	$0.902508\pi$
$140$		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	$0.182686\pi$
$157$			13.6058i			1.08586i	−0.839777	+	0.542931i	$0.817314\pi$
$158$	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	−0.0305587	−	0.999533i	$-0.509729\pi$
$163$	−8.20662	−	2.66649i	−0.642792	−	0.208856i	−0.612233	+	0.790677i	$0.709729\pi$
$164$	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	−0.632131	−	0.774862i	$-0.717819\pi$
$167$	3.87874	−	5.33863i	0.300146	−	0.413116i	0.932277	+	0.361746i	$0.117819\pi$
$168$		−	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	0.229751	−	0.973249i	$-0.426209\pi$
$173$	12.9910	−	4.22102i	0.987685	−	0.320918i	0.757934	+	0.652331i	$0.226209\pi$
$174$	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	−0.249528	−	0.968368i	$-0.580276\pi$
$179$	7.95167	−	5.77722i	0.594336	−	0.431810i	0.843864	+	0.536557i	$0.180276\pi$
$180$		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	$0.931179\pi$
$182$			15.2002i			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	−0.947348	−	0.320206i	$-0.896248\pi$
$191$	0.100682	−	0.309867i	0.00728509	−	0.0224212i	0.954633	+	0.297785i	$0.0962478\pi$
$192$	5.03896	−	6.93553i	0.363656	−	0.500529i
$193$			2.90187i			0.208881i	0.994531	+	0.104441i	$0.0333052\pi$
$193$			2.90187i			0.208881i	−0.994531	+	0.104441i	$0.966695\pi$
$194$	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	0.997304	+	0.0733829i	$0.0233795\pi$
$197$	10.6518	+	14.6610i	0.758911	+	1.04455i	−0.238393	+	0.971169i	$0.576620\pi$
$198$	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	−0.996135	−	0.0878402i	$-0.972004\pi$
$211$	−3.51345	−	10.8133i	−0.241876	−	0.744418i	0.754259	−	0.656577i	$-0.227996\pi$
$212$	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	0.285347	−	0.958424i	$-0.407891\pi$
$223$	16.1210	−	5.23804i	1.07954	−	0.350765i	0.794198	+	0.607659i	$0.207891\pi$
$224$	1.57740			0.105395
$225$		0			0
$226$	13.5732			0.902878
$227$	−13.4210	+	4.36076i	−0.890785	+	0.289434i	−0.718428	−	0.695601i	$-0.755138\pi$
$227$	−13.4210	+	4.36076i	−0.890785	+	0.289434i	−0.172357	+	0.985035i	$0.555138\pi$
$228$	−0.0584645	−	0.0804694i	−0.00387190	−	0.00532922i
$229$	0.0501546	−	0.0364394i	0.00331431	−	0.00240799i	−0.586127	−	0.810219i	$-0.699348\pi$
$229$	0.0501546	−	0.0364394i	0.00331431	−	0.00240799i	0.589441	+	0.807811i	$0.299348\pi$
$230$		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	0.0777775	−	0.996971i	$-0.475218\pi$
$233$	15.2936	−	21.0499i	1.00192	−	1.37902i	0.924141	−	0.382052i	$-0.124782\pi$
$234$	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	−0.932998	−	0.359881i	$-0.882817\pi$
$239$	−6.02491	−	18.5428i	−0.389719	−	1.19943i	0.543279	−	0.839552i	$-0.317183\pi$
$240$		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	$0.142142\pi$
$242$	0.0852331	−	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	$-0.803497\pi$
$257$		−	18.5597i		−	1.15772i	0.815426	−	0.578862i	$-0.196503\pi$
$258$	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	−0.0778466	−	0.996965i	$-0.524804\pi$
$263$	−11.7872	−	3.82988i	−0.726827	−	0.236161i	−0.648981	+	0.760805i	$0.724804\pi$
$264$	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	0.449338	−	0.893362i	$-0.351660\pi$
$269$	−4.28805	−	3.11545i	−0.261447	−	0.189952i	−0.710785	+	0.703410i	$0.751660\pi$
$270$		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	$0.307710\pi$
$272$	−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	−0.170311	−	0.985390i	$-0.554477\pi$
$277$	4.51205	−	1.46605i	0.271103	−	0.0880867i	0.441414	+	0.897304i	$0.354477\pi$
$278$	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	0.939597	−	0.342283i	$-0.111200\pi$
$281$	15.1608	+	11.0150i	0.904418	+	0.657098i	−0.0351791	+	0.999381i	$0.511200\pi$
$282$		−	10.3227i		−	0.614707i
$283$	−6.91306	+	9.51501i	−0.410939	+	0.565608i	−0.963447	−	0.267899i	$-0.913671\pi$
$283$	−6.91306	+	9.51501i	−0.410939	+	0.565608i	0.552508	+	0.833507i	$0.313671\pi$
$284$	−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	$-0.774408\pi$
$293$		−	22.2819i		−	1.30172i	0.759198	−	0.650860i	$-0.225592\pi$
$294$	−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	$-0.856116\pi$
$307$		−	15.3063i		−	0.873574i	0.899565	−	0.436787i	$-0.143884\pi$
$308$	−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	−0.998267	−	0.0588556i	$-0.981255\pi$
$311$	−3.97226	−	12.2254i	−0.225246	−	0.693237i	0.773020	−	0.634382i	$-0.218745\pi$
$312$	19.7055	+	6.40272i	1.11561	+	0.362482i
$313$	9.99293	+	3.24690i	0.564834	+	0.183526i	0.577495	−	0.816394i	$-0.304030\pi$
$313$	9.99293	+	3.24690i	0.564834	+	0.183526i	−0.0126612	+	0.999920i	$0.504030\pi$
$314$	−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	−0.998777	−	0.0494374i	$-0.984257\pi$
$317$	−11.4504	+	15.7602i	−0.643120	+	0.885179i	0.355657	+	0.934617i	$0.384257\pi$
$318$			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	0.861375	−	0.507970i	$-0.169604\pi$
$331$	11.7247	+	8.51846i	0.644446	+	0.468217i	−0.216929	+	0.976187i	$0.569604\pi$
$332$			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	0.540608	−	0.841275i	$-0.318194\pi$
$337$	8.87550	+	2.88382i	0.483479	+	0.157092i	−0.0571283	+	0.998367i	$0.518194\pi$
$338$	−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	0.825313	−	0.564675i	$-0.190999\pi$
$347$	0.619178	+	0.852225i	0.0332392	+	0.0457498i	−0.792074	+	0.610425i	$0.790999\pi$
$348$	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	0.877894	+	0.478855i	$0.158948\pi$
$353$	19.9537	+	27.4639i	1.06203	+	1.46176i	0.184134	+	0.982901i	$0.441052\pi$
$354$	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	−0.888978	−	0.457951i	$-0.848584\pi$
$359$	1.88331	−	5.79622i	0.0993971	−	0.305913i	0.988375	+	0.152038i	$0.0485836\pi$
$360$		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	−0.999779	−	0.0210364i	$-0.993303\pi$
$367$	−12.8511	+	17.6881i	−0.670823	+	0.923309i	0.328955	+	0.944345i	$0.393303\pi$
$368$		−	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	−0.841343	−	0.540502i	$-0.818234\pi$
$373$	−23.2590	+	7.55730i	−1.20430	+	0.391302i	−0.362961	+	0.931804i	$0.618234\pi$
$374$	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	−0.710544	−	0.703653i	$-0.751551\pi$
$379$	−5.07918	+	3.69024i	−0.260900	+	0.189555i	0.449644	+	0.893208i	$0.351551\pi$
$380$		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	0.257055	+	0.966397i	$0.417248\pi$
$383$	−14.5110	+	19.9727i	−0.741477	+	1.02056i	−0.998532	+	0.0541589i	$0.982752\pi$
$384$	−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	0.999807	+	0.0196288i	$0.00624845\pi$
$389$	3.99360	+	12.2910i	0.202484	+	0.623181i	−0.797324	+	0.603552i	$0.793752\pi$
$390$		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	0.982477	+	0.186383i	$0.0596764\pi$
$397$	17.0584	+	23.4788i	0.856135	+	1.17837i	−0.126342	+	0.991987i	$0.540324\pi$
$398$	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	−0.751389	−	0.659859i	$-0.770616\pi$
$409$	4.94173	−	15.2091i	0.244353	−	0.752040i	0.995742	−	0.0921815i	$-0.0293840\pi$
$410$		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	0.999542	−	0.0302627i	$-0.00963440\pi$
$419$	26.1935	+	19.0307i	1.27964	+	0.929710i	0.280094	+	0.959973i	$0.409634\pi$
$420$		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	$0.444986\pi$
$422$	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	−0.291417	−	0.956596i	$-0.594127\pi$
$431$	−26.8070	−	19.4764i	−1.29125	−	0.938146i	−0.999830	+	0.0184500i	$0.994127\pi$
$432$		−	3.61877i		−	0.174108i
$433$	13.3223	−	18.3366i	0.640230	−	0.881201i	−0.358398	−	0.933569i	$-0.616677\pi$
$433$	13.3223	−	18.3366i	0.640230	−	0.881201i	0.998628	+	0.0523682i	$0.0166770\pi$
$434$	−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	0.993979	−	0.109574i	$-0.0349486\pi$
$439$	2.62799	+	8.08812i	0.125427	+	0.386025i	−0.868551	+	0.495599i	$0.834949\pi$
$440$		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	$-0.951741\pi$
$443$		−	6.35768i		−	0.302063i	0.988529	−	0.151031i	$-0.0482594\pi$
$444$	−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	$-0.916834\pi$
$457$		−	11.0441i		−	0.516620i	0.966062	−	0.258310i	$-0.0831657\pi$
$458$	−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	−0.963921	−	0.266189i	$-0.914235\pi$
$461$	−7.31202	−	22.5041i	−0.340555	−	1.04812i	0.623366	−	0.781930i	$-0.285765\pi$
$462$	−6.83266	−	2.22007i	−0.317884	−	0.103287i
$463$	5.91977	+	1.92345i	0.275115	+	0.0893903i	0.443325	−	0.896361i	$-0.353799\pi$
$463$	5.91977	+	1.92345i	0.275115	+	0.0893903i	−0.168210	+	0.985751i	$0.553799\pi$
$464$	−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	−0.736425	−	0.676519i	$-0.763488\pi$
$467$	2.90765	−	4.00204i	0.134550	−	0.185192i	0.870976	+	0.491326i	$0.163488\pi$
$468$		−	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	−0.983019	−	0.183503i	$-0.941256\pi$
$479$	−24.3432	+	17.6863i	−1.11227	+	0.808109i	−0.129248	+	0.991612i	$0.541256\pi$
$480$		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	−0.543120	−	0.839655i	$-0.682757\pi$
$487$	−32.5736	−	10.5838i	−1.47605	−	0.479598i	−0.932930	+	0.360057i	$0.882757\pi$
$488$	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	−0.997050	−	0.0767530i	$-0.975545\pi$
$491$	−3.21975	+	9.90938i	−0.145305	+	0.447204i	0.851745	+	0.523957i	$0.175545\pi$
$492$	−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	0.991346	−	0.131273i	$-0.0419063\pi$
$503$	12.5630	+	17.2915i	0.560156	+	0.770988i	−0.431190	+	0.902261i	$0.641906\pi$
$504$	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	−0.767931	−	0.640533i	$-0.778714\pi$
$509$	5.18529	−	15.9587i	0.229834	−	0.707356i	0.997765	−	0.0668236i	$-0.0212865\pi$
$510$		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	−0.503176	−	0.864184i	$-0.667835\pi$
$521$	3.72559	−	2.70680i	0.163221	−	0.118587i	0.666397	+	0.745597i	$0.267835\pi$
$522$	2.21015	+	3.04201i	0.0967357	+	0.133145i
$523$	12.3290	−	4.00592i	0.539108	−	0.175167i	−0.0267915	−	0.999641i	$-0.508529\pi$
$523$	12.3290	−	4.00592i	0.539108	−	0.175167i	0.565899	+	0.824474i	$0.308529\pi$
$524$	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	0.587333	+	0.809345i	$0.300178\pi$
$541$	−8.45597	+	26.0248i	−0.363551	+	1.11889i	−0.950884	+	0.309548i	$0.899822\pi$
$542$	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	−0.999992	−	0.00399765i	$-0.998728\pi$
$547$	−16.2495	−	22.3656i	−0.694779	−	0.956282i	0.305213	−	0.952284i	$-0.401272\pi$
$548$	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	$-0.958250\pi$
$557$		−	6.17333i		−	0.261572i	0.991411	−	0.130786i	$-0.0417501\pi$
$558$	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	0.192559	−	0.981285i	$-0.438321\pi$
$563$	−5.42039	−	1.76119i	−0.228442	−	0.0742254i	−0.421001	+	0.907060i	$0.638321\pi$
$564$	−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	0.874718	−	0.484632i	$-0.161046\pi$
$569$	16.3185	+	11.8561i	0.684109	+	0.497034i	−0.190610	+	0.981666i	$0.561046\pi$
$570$		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	$0.193062\pi$
$572$	−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	0.0277128	−	0.999616i	$-0.491178\pi$
$577$	15.3179	−	4.97709i	0.637692	−	0.207199i	0.609980	+	0.792417i	$0.291178\pi$
$578$	−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	0.348022	−	0.937486i	$-0.386853\pi$
$587$	1.90280	+	0.618257i	0.0785369	+	0.0255182i	−0.269485	+	0.963005i	$0.586853\pi$
$588$	−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	$0.185657\pi$
$593$			26.8231i			1.10149i	−0.834672	+	0.550747i	$0.814343\pi$
$594$	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	$-0.864594\pi$
$607$		−	20.3346i		−	0.825356i	0.910877	−	0.412678i	$-0.135406\pi$
$608$	−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	0.679797	−	0.733401i	$-0.262068\pi$
$613$	19.7744	+	6.42510i	0.798681	+	0.259507i	0.118885	+	0.992908i	$0.462068\pi$
$614$	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	−0.746474	−	0.665415i	$-0.768255\pi$
$617$	2.90738	−	4.00167i	0.117047	−	0.161101i	0.863520	+	0.504314i	$0.168255\pi$
$618$			14.6862i			0.590766i
$619$	−37.1765	−	27.0103i	−1.49425	−	1.08564i	−0.972602	−	0.232477i	$-0.925317\pi$
$619$	−37.1765	−	27.0103i	−1.49425	−	1.08564i	−0.521650	−	0.853160i	$-0.674683\pi$
$620$		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	0.879185	−	0.476481i	$-0.158088\pi$
$631$	17.5262	+	12.7335i	0.697707	+	0.506914i	−0.181477	+	0.983395i	$0.558088\pi$
$632$			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	−0.439328	−	0.898327i	$-0.644783\pi$
$641$	11.2442	−	34.6061i	0.444119	−	1.36686i	0.883447	−	0.468531i	$-0.155217\pi$
$642$	−7.44163	+	10.2425i	−0.293698	+	0.404240i
$643$			1.01349i			0.0399682i	0.999800	+	0.0199841i	$0.00636156\pi$
$643$			1.01349i			0.0399682i	−0.999800	+	0.0199841i	$0.993638\pi$
$644$	−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	0.620826	−	0.783948i	$-0.286797\pi$
$647$	−8.05306	−	11.0841i	−0.316598	−	0.435760i	−0.937425	+	0.348188i	$0.886797\pi$
$648$	−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	0.441481	−	0.897271i	$-0.354453\pi$
$653$	−14.0112	−	19.2847i	−0.548299	−	0.754669i	−0.989780	+	0.142601i	$0.954453\pi$
$654$	−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	−0.999753	−	0.0222376i	$-0.992921\pi$
$659$	−4.56597	+	14.0526i	−0.177865	+	0.547412i	0.821888	+	0.569649i	$0.192921\pi$
$660$		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	$0.853063\pi$
$662$	−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	−0.523892	−	0.851785i	$-0.675520\pi$
$673$	−11.5978	+	3.76836i	−0.447063	+	0.145259i	0.0768292	+	0.997044i	$0.475520\pi$
$674$	−12.6063			−0.485576
$675$		0			0
$676$	−6.43571			−0.247527
$677$	−17.0721	+	5.54706i	−0.656134	+	0.213191i	−0.618117	−	0.786086i	$-0.712104\pi$
$677$	−17.0721	+	5.54706i	−0.656134	+	0.213191i	−0.0380172	+	0.999277i	$0.512104\pi$
$678$	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	−0.906752	−	0.421664i	$-0.861446\pi$
$683$	−5.89391	+	8.11227i	−0.225524	+	0.310407i	0.681228	+	0.732071i	$0.261446\pi$
$684$	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	−0.773425	−	0.633887i	$-0.781458\pi$
$691$	5.91136	−	18.1933i	0.224879	−	0.692105i	0.998304	−	0.0582177i	$-0.0185418\pi$
$692$	−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	0.444517	+	0.895771i	$0.353375\pi$
$709$	−11.7592	+	36.1911i	−0.441626	+	1.35918i	−0.886142	+	0.463413i	$0.846625\pi$
$710$		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	0.841007	−	0.541024i	$-0.181963\pi$
$719$	15.7224	+	11.4230i	0.586348	+	0.426007i	−0.254659	+	0.967031i	$0.581963\pi$
$720$		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	0.452649	−	0.891689i	$-0.350479\pi$
$727$	36.2104	−	11.7655i	1.34297	−	0.436358i	0.890322	+	0.455331i	$0.150479\pi$
$728$	−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	−0.952407	−	0.304828i	$-0.901401\pi$
$733$	−9.96833	+	13.7202i	−0.368189	+	0.506768i	0.584219	+	0.811596i	$0.301401\pi$
$734$	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	0.847536	−	0.530737i	$-0.178085\pi$
$739$	−4.08025	−	12.5577i	−0.150095	−	0.461944i	−0.997631	+	0.0687937i	$0.978085\pi$
$740$		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	$-0.717875\pi$
$743$		−	42.2364i		−	1.54950i	0.632265	−	0.774752i	$-0.282125\pi$
$744$	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	$0.100019\pi$
$757$			17.0074i			0.618146i	−0.951038	+	0.309073i	$0.899981\pi$
$758$	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	−0.990440	−	0.137942i	$-0.955951\pi$
$761$	−7.45484	−	22.9436i	−0.270238	−	0.831706i	0.720203	−	0.693764i	$-0.244049\pi$
$762$	−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	0.985279	+	0.170952i	$0.0546841\pi$
$769$	40.2744	+	29.2611i	1.45233	+	1.05518i	0.467053	+	0.884230i	$0.345316\pi$
$770$		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	−0.793072	−	0.609128i	$-0.791520\pi$
$773$	−29.9338	+	9.72608i	−1.07664	+	0.349823i	−0.283572	+	0.958951i	$0.591520\pi$
$774$	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	−0.0339855	−	0.999422i	$-0.510820\pi$
$787$	−18.2047	−	5.91505i	−0.648926	−	0.210849i	−0.614941	+	0.788573i	$0.710820\pi$
$788$	−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	0.877489	−	0.479597i	$-0.159217\pi$
$797$	4.24050	+	5.83655i	0.150206	+	0.206741i	−0.727283	+	0.686338i	$0.759217\pi$
$798$	−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	−0.956647	−	0.291251i	$-0.905928\pi$
$809$	−0.327376	+	1.00756i	−0.0115099	+	0.0354239i	0.945137	+	0.326675i	$0.105928\pi$
$810$		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	$0.775944\pi$
$812$	−0.740402	−	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	−0.210259	−	0.977646i	$-0.567431\pi$
$821$	18.7553	−	13.6265i	0.654564	−	0.475568i	0.864823	+	0.502077i	$0.167431\pi$
$822$	3.86871	+	5.32482i	0.134937	+	0.185724i
$823$	−26.6076	+	8.64534i	−0.927483	+	0.301358i	−0.733533	−	0.679654i	$-0.762130\pi$
$823$	−26.6076	+	8.64534i	−0.927483	+	0.301358i	−0.193950	+	0.981011i	$0.562130\pi$
$824$	−31.9463			−1.11290
$825$		0			0
$826$	−2.12116			−0.0738044
$827$	39.2829	−	12.7638i	1.36600	−	0.443841i	0.467959	−	0.883750i	$-0.344989\pi$
$827$	39.2829	−	12.7638i	1.36600	−	0.443841i	0.898042	+	0.439909i	$0.144989\pi$
$828$	0.649405	+	0.893830i	0.0225684	+	0.0310627i
$829$	38.4838	−	27.9602i	1.33660	−	0.971096i	0.337038	−	0.941491i	$-0.390575\pi$
$829$	38.4838	−	27.9602i	1.33660	−	0.971096i	0.999562	−	0.0296051i	$-0.00942497\pi$
$830$		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	−0.768048	−	0.640393i	$-0.778772\pi$
$839$	−15.1518	−	46.6324i	−0.523097	−	1.60993i	0.244950	−	0.969536i	$-0.421228\pi$
$840$		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	0.344464	−	0.938799i	$-0.388061\pi$
$853$	−19.1251	−	26.3235i	−0.654832	−	0.901299i	−0.999297	+	0.0375002i	$0.988061\pi$
$854$	−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	$-0.825704\pi$
$857$		−	30.4813i		−	1.04122i	0.853794	−	0.520610i	$-0.174296\pi$
$858$	18.6593	−	25.6823i	0.637017	−	0.876779i
$859$	−1.27382	+	3.92040i	−0.0434620	+	0.133762i	−0.970433	−	0.241371i	$-0.922403\pi$
$859$	−1.27382	+	3.92040i	−0.0434620	+	0.133762i	0.926971	+	0.375133i	$0.122403\pi$
$860$		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	0.591582	−	0.806245i	$-0.298504\pi$
$863$	17.5169	+	5.69159i	0.596283	+	0.193744i	0.00470109	+	0.999989i	$0.498504\pi$
$864$	−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	0.0108490	−	0.999941i	$-0.496547\pi$
$877$	17.9870	−	5.84432i	0.607377	−	0.197349i	0.596528	+	0.802593i	$0.296547\pi$
$878$	−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	0.00538802	−	0.999985i	$-0.498285\pi$
$881$	−28.0192	−	20.3571i	−0.943990	−	0.685849i	−0.949378	+	0.314137i	$0.898285\pi$
$882$		−	6.01583i		−	0.202563i
$883$	19.2132	−	26.4447i	0.646575	−	0.889934i	−0.352370	−	0.935861i	$-0.614624\pi$
$883$	19.2132	−	26.4447i	0.646575	−	0.889934i	0.998945	+	0.0459269i	$0.0146241\pi$
$884$	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	0.956296	−	0.292402i	$-0.0944545\pi$
$887$	46.4037	+	15.0775i	1.55809	+	0.506253i	0.601790	+	0.798655i	$0.294455\pi$
$888$	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	$0.268847\pi$
$907$			45.0367i			1.49542i	−0.664025	+	0.747710i	$0.731153\pi$
$908$	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	0.995198	−	0.0978826i	$-0.0312070\pi$
$911$	4.00018	+	12.3113i	0.132532	+	0.407891i	−0.862666	+	0.505774i	$0.831207\pi$
$912$	−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	0.764996	−	0.644035i	$-0.222741\pi$
$919$	11.7889	+	8.56513i	0.388880	+	0.282538i	−0.376117	+	0.926572i	$0.622741\pi$
$920$		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	−0.920227	−	0.391384i	$-0.871996\pi$
$929$	−25.3701	+	18.4324i	−0.832365	+	0.604749i	0.0878623	+	0.996133i	$0.471996\pi$
$930$		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	−0.570898	−	0.821021i	$-0.693405\pi$
$937$	−46.3855	−	15.0716i	−1.51535	−	0.492367i	−0.944450	+	0.328654i	$0.893405\pi$
$938$	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	0.646827	+	0.762637i	$0.276096\pi$
$941$	−9.96145	+	30.6582i	−0.324734	+	0.999429i	−0.971561	+	0.236791i	$0.923904\pi$
$942$	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	0.930245	+	0.366939i	$0.119594\pi$
$947$	30.5199	+	42.0070i	0.991763	+	1.36505i	0.0615183	+	0.998106i	$0.480406\pi$
$948$	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	−0.997426	−	0.0717028i	$-0.977157\pi$
$953$	−23.3814	−	32.1817i	−0.757398	−	1.04247i	0.240028	−	0.970766i	$-0.422843\pi$
$954$	−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	−0.954466	−	0.298318i	$-0.903574\pi$
$967$	−11.6862	+	16.0847i	−0.375802	+	0.517248i	0.578664	+	0.815566i	$0.303574\pi$
$968$			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	0.0977335	−	0.995213i	$-0.468841\pi$
$971$	33.4804	−	24.3250i	1.07444	−	0.780625i	0.976705	+	0.214588i	$0.0688407\pi$
$972$	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	−0.253427	−	0.967355i	$-0.581558\pi$
$977$	3.44274	−	1.11861i	0.110143	−	0.0357876i	0.363570	+	0.931567i	$0.381558\pi$
$978$	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	−0.954789	−	0.297285i	$-0.903919\pi$
$983$	−11.8203	+	16.2692i	−0.377008	+	0.518907i	0.577781	+	0.816192i	$0.303919\pi$
$984$	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	−0.907877	−	0.419236i	$-0.862298\pi$
$991$	2.29905	−	7.07576i	0.0730319	−	0.224769i	0.980909	+	0.194467i	$0.0622978\pi$
$992$	−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	−0.981796	−	0.189937i	$-0.939172\pi$
$997$	−27.1246	−	37.3338i	−0.859045	−	1.18237i	0.122751	−	0.992438i	$-0.460828\pi$
$998$	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.349.2		16
5.2	odd	4		375.2.g.d.151.1		16
5.3	odd	4		375.2.g.e.151.4		16
5.4	even	2		75.2.i.a.19.3	yes	16
15.14	odd	2		225.2.m.b.19.2		16
25.2	odd	20		1875.2.a.p.1.2		8
25.3	odd	20		375.2.g.e.226.4		16
25.4	even	10	inner	375.2.i.c.274.2		16
25.11	even	5		1875.2.b.h.1249.12		16
25.14	even	10		1875.2.b.h.1249.5		16
25.21	even	5		75.2.i.a.4.3	✓	16
25.22	odd	20		375.2.g.d.226.1		16
25.23	odd	20		1875.2.a.m.1.7		8
75.2	even	20		5625.2.a.t.1.7		8
75.23	even	20		5625.2.a.bd.1.2		8
75.71	odd	10		225.2.m.b.154.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.i.a.4.3	✓	16	25.21	even	5
75.2.i.a.19.3	yes	16	5.4	even	2
225.2.m.b.19.2		16	15.14	odd	2
225.2.m.b.154.2		16	75.71	odd	10
375.2.g.d.151.1		16	5.2	odd	4
375.2.g.d.226.1		16	25.22	odd	20
375.2.g.e.151.4		16	5.3	odd	4
375.2.g.e.226.4		16	25.3	odd	20
375.2.i.c.274.2		16	25.4	even	10	inner
375.2.i.c.349.2		16	1.1	even	1	trivial
1875.2.a.m.1.7		8	25.23	odd	20
1875.2.a.p.1.2		8	25.2	odd	20
1875.2.b.h.1249.5		16	25.14	even	10
1875.2.b.h.1249.12		16	25.11	even	5
5625.2.a.t.1.7		8	75.2	even	20
5625.2.a.bd.1.2		8	75.23	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

Modular forms

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Database

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