LMFDB - Embedded newform 250.2.e.b.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [250,2,Mod(49,250)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(250, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("250.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 250 = 2 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	250.e (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:	$1.99626005053$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 50)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			49.2
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	250.49
Dual form			250.2.e.b.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(2.48990 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{6} +3.00000i q^{7} +(-0.951057 - 0.309017i) q^{8} +(3.11803 - 2.26538i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(2.48990 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{6} +3.00000i q^{7} +(-0.951057 - 0.309017i) q^{8} +(3.11803 - 2.26538i) q^{9} +(0.190983 + 0.138757i) q^{11} +(-1.53884 - 2.11803i) q^{12} +(-0.587785 - 0.809017i) q^{13} +(2.42705 + 1.76336i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-7.46969 - 2.42705i) q^{17} -3.85410i q^{18} +(0.263932 - 0.812299i) q^{19} +(2.42705 + 7.46969i) q^{21} +(0.224514 - 0.0729490i) q^{22} +(-3.66547 + 5.04508i) q^{23} -2.61803 q^{24} -1.00000 q^{26} +(1.31433 - 1.80902i) q^{27} +(2.85317 - 0.927051i) q^{28} +(0.163119 + 0.502029i) q^{29} +(1.30902 - 4.02874i) q^{31} +1.00000i q^{32} +(0.587785 + 0.190983i) q^{33} +(-6.35410 + 4.61653i) q^{34} +(-3.11803 - 2.26538i) q^{36} +(4.30625 + 5.92705i) q^{37} +(-0.502029 - 0.690983i) q^{38} +(-2.11803 - 1.53884i) q^{39} +(6.04508 - 4.39201i) q^{41} +(7.46969 + 2.42705i) q^{42} -1.76393i q^{43} +(0.0729490 - 0.224514i) q^{44} +(1.92705 + 5.93085i) q^{46} +(5.65334 - 1.83688i) q^{47} +(-1.53884 + 2.11803i) q^{48} -2.00000 q^{49} -20.5623 q^{51} +(-0.587785 + 0.809017i) q^{52} +(-1.45309 + 0.472136i) q^{53} +(-0.690983 - 2.12663i) q^{54} +(0.927051 - 2.85317i) q^{56} -2.23607i q^{57} +(0.502029 + 0.163119i) q^{58} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-2.48990 - 3.42705i) q^{62} +(6.79615 + 9.35410i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.500000 - 0.363271i) q^{66} +(5.48183 + 1.78115i) q^{67} +7.85410i q^{68} +(-5.04508 + 15.5272i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(-3.66547 + 1.19098i) q^{72} +(-3.35520 + 4.61803i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(-0.416272 + 0.572949i) q^{77} +(-2.48990 + 0.809017i) q^{78} +(0.854102 + 2.62866i) q^{79} +(-1.76393 + 5.42882i) q^{81} -7.47214i q^{82} +(-12.8128 - 4.16312i) q^{83} +(6.35410 - 4.61653i) q^{84} +(-1.42705 - 1.03681i) q^{86} +(0.812299 + 1.11803i) q^{87} +(-0.138757 - 0.190983i) q^{88} +(-3.61803 - 2.62866i) q^{89} +(2.42705 - 1.76336i) q^{91} +(5.93085 + 1.92705i) q^{92} -11.0902i q^{93} +(1.83688 - 5.65334i) q^{94} +(0.809017 + 2.48990i) q^{96} +(-10.0453 + 3.26393i) q^{97} +(-1.17557 + 1.61803i) q^{98} +0.909830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9}+O(q^{10}) $ 8 * q + 2 * q^4 + 2 * q^6 + 16 * q^9	$ 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9} + 6 q^{11} + 6 q^{14} - 2 q^{16} + 20 q^{19} + 6 q^{21} - 12 q^{24} - 8 q^{26} - 30 q^{29} + 6 q^{31} - 24 q^{34} - 16 q^{36} - 8 q^{39} + 26 q^{41} + 14 q^{44} + 2 q^{46} - 16 q^{49} - 84 q^{51} - 10 q^{54} - 6 q^{56} + 20 q^{59} - 4 q^{61} + 2 q^{64} + 4 q^{66} - 18 q^{69} + 6 q^{71} - 4 q^{74} + 20 q^{76} - 20 q^{79} - 32 q^{81} + 24 q^{84} + 2 q^{86} - 20 q^{89} + 6 q^{91} + 46 q^{94} + 2 q^{96} + 52 q^{99}+O(q^{100}) $ 8 * q + 2 * q^4 + 2 * q^6 + 16 * q^9 + 6 * q^11 + 6 * q^14 - 2 * q^16 + 20 * q^19 + 6 * q^21 - 12 * q^24 - 8 * q^26 - 30 * q^29 + 6 * q^31 - 24 * q^34 - 16 * q^36 - 8 * q^39 + 26 * q^41 + 14 * q^44 + 2 * q^46 - 16 * q^49 - 84 * q^51 - 10 * q^54 - 6 * q^56 + 20 * q^59 - 4 * q^61 + 2 * q^64 + 4 * q^66 - 18 * q^69 + 6 * q^71 - 4 * q^74 + 20 * q^76 - 20 * q^79 - 32 * q^81 + 24 * q^84 + 2 * q^86 - 20 * q^89 + 6 * q^91 + 46 * q^94 + 2 * q^96 + 52 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

$n$	$127$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	2.48990	−	0.809017i	1.43754	−	0.467086i	0.516413	−	0.856340i	$-0.327267\pi$
$3$	2.48990	−	0.809017i	1.43754	−	0.467086i	0.921131	+	0.389254i	$0.127267\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		0			0
$5$		0			0
$6$	0.809017	−	2.48990i	0.330280	−	1.01650i
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	3.11803	−	2.26538i	1.03934	−	0.755128i
$10$		0			0
$11$	0.190983	+	0.138757i	0.0575835	+	0.0418369i	0.616205	−	0.787586i	$-0.288669\pi$
$11$	0.190983	+	0.138757i	0.0575835	+	0.0418369i	−0.558621	+	0.829423i	$0.688669\pi$
$12$	−1.53884	−	2.11803i	−0.444225	−	0.611424i
$13$	−0.587785	−	0.809017i	−0.163022	−	0.224381i	0.719689	−	0.694297i	$-0.244284\pi$
$13$	−0.587785	−	0.809017i	−0.163022	−	0.224381i	−0.882711	+	0.469916i	$0.844284\pi$
$14$	2.42705	+	1.76336i	0.648657	+	0.471277i
$15$		0			0
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−7.46969	−	2.42705i	−1.81167	−	0.588646i	−0.999990	−	0.00454037i	$-0.998555\pi$
$17$	−7.46969	−	2.42705i	−1.81167	−	0.588646i	−0.811677	−	0.584106i	$-0.801445\pi$
$18$		−	3.85410i		−	0.908421i
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	−0.916206	−	0.400707i	$-0.868764\pi$
$19$	0.263932	−	0.812299i	0.0605502	−	0.186354i	0.976756	+	0.214353i	$0.0687644\pi$
$20$		0			0
$21$	2.42705	+	7.46969i	0.529626	+	1.63002i
$22$	0.224514	−	0.0729490i	0.0478665	−	0.0155528i
$23$	−3.66547	+	5.04508i	−0.764303	+	1.05197i	0.232541	+	0.972587i	$0.425296\pi$
$23$	−3.66547	+	5.04508i	−0.764303	+	1.05197i	−0.996844	+	0.0793863i	$0.974704\pi$
$24$	−2.61803			−0.534404
$25$		0			0
$26$	−1.00000			−0.196116
$27$	1.31433	−	1.80902i	0.252942	−	0.348145i
$28$	2.85317	−	0.927051i	0.539198	−	0.175196i
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	0.965059	−	0.262033i	$-0.0843931\pi$
$29$	0.163119	+	0.502029i	0.0302904	+	0.0932244i	−0.934768	+	0.355258i	$0.884393\pi$
$30$		0			0
$31$	1.30902	−	4.02874i	0.235106	−	0.723583i	−0.762001	−	0.647576i	$-0.775783\pi$
$31$	1.30902	−	4.02874i	0.235106	−	0.723583i	0.997107	−	0.0760071i	$-0.0242172\pi$
$32$			1.00000i			0.176777i
$33$	0.587785	+	0.190983i	0.102320	+	0.0332459i
$34$	−6.35410	+	4.61653i	−1.08972	+	0.791728i
$35$		0			0
$36$	−3.11803	−	2.26538i	−0.519672	−	0.377564i
$37$	4.30625	+	5.92705i	0.707944	+	0.974401i	0.999839	+	0.0179508i	$0.00571422\pi$
$37$	4.30625	+	5.92705i	0.707944	+	0.974401i	−0.291895	+	0.956450i	$0.594286\pi$
$38$	−0.502029	−	0.690983i	−0.0814398	−	0.112092i
$39$	−2.11803	−	1.53884i	−0.339157	−	0.246412i
$40$		0			0
$41$	6.04508	−	4.39201i	0.944084	−	0.685917i	−0.00531652	−	0.999986i	$-0.501692\pi$
$41$	6.04508	−	4.39201i	0.944084	−	0.685917i	0.949400	+	0.314069i	$0.101692\pi$
$42$	7.46969	+	2.42705i	1.15260	+	0.374502i
$43$		−	1.76393i		−	0.268997i	−0.990914	−	0.134499i	$-0.957058\pi$
$43$		−	1.76393i		−	0.268997i	0.990914	−	0.134499i	$-0.0429424\pi$
$44$	0.0729490	−	0.224514i	0.0109975	−	0.0338468i
$45$		0			0
$46$	1.92705	+	5.93085i	0.284128	+	0.874457i
$47$	5.65334	−	1.83688i	0.824624	−	0.267937i	0.133845	−	0.991002i	$-0.457268\pi$
$47$	5.65334	−	1.83688i	0.824624	−	0.267937i	0.690779	+	0.723066i	$0.257268\pi$
$48$	−1.53884	+	2.11803i	−0.222113	+	0.305712i
$49$	−2.00000			−0.285714
$50$		0			0
$51$	−20.5623			−2.87930
$52$	−0.587785	+	0.809017i	−0.0815111	+	0.112190i
$53$	−1.45309	+	0.472136i	−0.199597	+	0.0648529i	−0.407109	−	0.913379i	$-0.633463\pi$
$53$	−1.45309	+	0.472136i	−0.199597	+	0.0648529i	0.207513	+	0.978232i	$0.433463\pi$
$54$	−0.690983	−	2.12663i	−0.0940309	−	0.289397i
$55$		0			0
$56$	0.927051	−	2.85317i	0.123882	−	0.381271i
$57$		−	2.23607i		−	0.296174i
$58$	0.502029	+	0.163119i	0.0659196	+	0.0214186i
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	−0.326814	−	0.945089i	$-0.605975\pi$
$59$	3.61803	−	2.62866i	0.471028	−	0.342222i	0.797842	+	0.602867i	$0.205975\pi$
$60$		0			0
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	0.693353	−	0.720598i	$-0.256133\pi$
$61$	1.73607	+	1.26133i	0.222281	+	0.161496i	−0.471072	+	0.882095i	$0.656133\pi$
$62$	−2.48990	−	3.42705i	−0.316217	−	0.435236i
$63$	6.79615	+	9.35410i	0.856235	+	1.17851i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$		0			0
$66$	0.500000	−	0.363271i	0.0615457	−	0.0447156i
$67$	5.48183	+	1.78115i	0.669712	+	0.217602i	0.624085	−	0.781356i	$-0.285472\pi$
$67$	5.48183	+	1.78115i	0.669712	+	0.217602i	0.0456261	+	0.998959i	$0.485472\pi$
$68$			7.85410i			0.952450i
$69$	−5.04508	+	15.5272i	−0.607357	+	1.86925i
$70$		0			0
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	0.880855	−	0.473386i	$-0.156968\pi$
$71$	−0.927051	−	2.85317i	−0.110021	−	0.338609i	−0.990876	+	0.134777i	$0.956968\pi$
$72$	−3.66547	+	1.19098i	−0.431980	+	0.140359i
$73$	−3.35520	+	4.61803i	−0.392696	+	0.540500i	−0.958892	−	0.283771i	$-0.908415\pi$
$73$	−3.35520	+	4.61803i	−0.392696	+	0.540500i	0.566196	+	0.824271i	$0.308415\pi$
$74$	7.32624			0.851658
$75$		0			0
$76$	−0.854102			−0.0979722
$77$	−0.416272	+	0.572949i	−0.0474386	+	0.0652936i
$78$	−2.48990	+	0.809017i	−0.281925	+	0.0916031i
$79$	0.854102	+	2.62866i	0.0960940	+	0.295747i	0.987537	−	0.157385i	$-0.0503065\pi$
$79$	0.854102	+	2.62866i	0.0960940	+	0.295747i	−0.891443	+	0.453132i	$0.850307\pi$
$80$		0			0
$81$	−1.76393	+	5.42882i	−0.195992	+	0.603203i
$82$		−	7.47214i		−	0.825159i
$83$	−12.8128	−	4.16312i	−1.40638	−	0.456962i	−0.495134	−	0.868817i	$-0.664881\pi$
$83$	−12.8128	−	4.16312i	−1.40638	−	0.456962i	−0.911249	+	0.411855i	$0.864881\pi$
$84$	6.35410	−	4.61653i	0.693289	−	0.503704i
$85$		0			0
$86$	−1.42705	−	1.03681i	−0.153883	−	0.111802i
$87$	0.812299	+	1.11803i	0.0870876	+	0.119866i
$88$	−0.138757	−	0.190983i	−0.0147916	−	0.0203589i
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	0.379280	−	0.925282i	$-0.376172\pi$
$89$	−3.61803	−	2.62866i	−0.383511	−	0.278637i	−0.762791	+	0.646645i	$0.776172\pi$
$90$		0			0
$91$	2.42705	−	1.76336i	0.254424	−	0.184850i
$92$	5.93085	+	1.92705i	0.618334	+	0.200909i
$93$		−	11.0902i		−	1.15000i
$94$	1.83688	−	5.65334i	0.189460	−	0.583097i
$95$		0			0
$96$	0.809017	+	2.48990i	0.0825700	+	0.254124i
$97$	−10.0453	+	3.26393i	−1.01995	+	0.331402i	−0.770810	−	0.637065i	$-0.780148\pi$
$97$	−10.0453	+	3.26393i	−1.01995	+	0.331402i	−0.249141	+	0.968467i	$0.580148\pi$
$98$	−1.17557	+	1.61803i	−0.118751	+	0.163446i
$99$	0.909830			0.0914414
$100$		0			0
$101$	−1.61803			−0.161000			−0.0805002	−	0.996755i	$-0.525652\pi$
$101$	−1.61803			−0.161000			−0.0805002	+	0.996755i	$0.525652\pi$
$102$	−12.0862	+	16.6353i	−1.19671	+	1.64714i
$103$	18.8824	−	6.13525i	1.86054	−	0.604525i	0.866010	−	0.500026i	$-0.166676\pi$
$103$	18.8824	−	6.13525i	1.86054	−	0.604525i	0.994525	−	0.104499i	$-0.0333238\pi$
$104$	0.309017	+	0.951057i	0.0303016	+	0.0932588i
$105$		0			0
$106$	−0.472136	+	1.45309i	−0.0458579	+	0.141136i
$107$		−	10.0902i		−	0.975454i	−0.872996	−	0.487727i	$-0.837826\pi$
$107$		−	10.0902i		−	0.975454i	0.872996	−	0.487727i	$-0.162174\pi$
$108$	−2.12663	−	0.690983i	−0.204635	−	0.0664899i
$109$	−12.1353	+	8.81678i	−1.16235	+	0.844494i	−0.990073	−	0.140555i	$-0.955111\pi$
$109$	−12.1353	+	8.81678i	−1.16235	+	0.844494i	−0.172274	+	0.985049i	$0.555111\pi$
$110$		0			0
$111$	15.5172	+	11.2739i	1.47283	+	1.07007i
$112$	−1.76336	−	2.42705i	−0.166621	−	0.229335i
$113$	−4.84104	−	6.66312i	−0.455407	−	0.626814i	0.518142	−	0.855295i	$-0.326624\pi$
$113$	−4.84104	−	6.66312i	−0.455407	−	0.626814i	−0.973548	+	0.228481i	$0.926624\pi$
$114$	−1.80902	−	1.31433i	−0.169430	−	0.123098i
$115$		0			0
$116$	0.427051	−	0.310271i	0.0396507	−	0.0288079i
$117$	−3.66547	−	1.19098i	−0.338873	−	0.110106i
$118$		−	4.47214i		−	0.411693i
$119$	7.28115	−	22.4091i	0.667462	−	2.05424i
$120$		0			0
$121$	−3.38197	−	10.4086i	−0.307451	−	0.946238i
$122$	2.04087	−	0.663119i	0.184772	−	0.0600360i
$123$	11.4984	−	15.8262i	1.03678	−	1.42700i
$124$	−4.23607			−0.380410
$125$		0			0
$126$	11.5623			1.03005
$127$	7.33094	−	10.0902i	0.650516	−	0.895358i	−0.348606	−	0.937269i	$-0.613345\pi$
$127$	7.33094	−	10.0902i	0.650516	−	0.895358i	0.999121	+	0.0419116i	$0.0133448\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−1.42705	−	4.39201i	−0.125645	−	0.386695i
$130$		0			0
$131$	3.21885	−	9.90659i	0.281232	−	0.865543i	−0.706271	−	0.707942i	$-0.749624\pi$
$131$	3.21885	−	9.90659i	0.281232	−	0.865543i	0.987503	−	0.157601i	$-0.0503761\pi$
$132$		−	0.618034i		−	0.0537930i
$133$	2.43690	+	0.791796i	0.211306	+	0.0686574i
$134$	4.66312	−	3.38795i	0.402832	−	0.292675i
$135$		0			0
$136$	6.35410	+	4.61653i	0.544860	+	0.395864i
$137$	−3.57971	−	4.92705i	−0.305835	−	0.420946i	0.628241	−	0.778018i	$-0.283775\pi$
$137$	−3.57971	−	4.92705i	−0.305835	−	0.420946i	−0.934077	+	0.357072i	$0.883775\pi$
$138$	9.59632	+	13.2082i	0.816893	+	1.12436i
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	0.882717	−	0.469905i	$-0.155712\pi$
$139$	8.35410	+	6.06961i	0.708586	+	0.514818i	−0.174131	+	0.984722i	$0.555712\pi$
$140$		0			0
$141$	12.5902	−	9.14729i	1.06028	−	0.770341i
$142$	−2.85317	−	0.927051i	−0.239433	−	0.0777964i
$143$		−	0.236068i		−	0.0197410i
$144$	−1.19098	+	3.66547i	−0.0992486	+	0.305456i
$145$		0			0
$146$	1.76393	+	5.42882i	0.145984	+	0.449293i
$147$	−4.97980	+	1.61803i	−0.410727	+	0.133453i
$148$	4.30625	−	5.92705i	0.353972	−	0.487201i
$149$	2.23607			0.183186			0.0915929	−	0.995797i	$-0.470804\pi$
$149$	2.23607			0.183186			0.0915929	+	0.995797i	$0.470804\pi$
$150$		0			0
$151$	3.70820			0.301769			0.150885	−	0.988551i	$-0.451788\pi$
$151$	3.70820			0.301769			0.150885	+	0.988551i	$0.451788\pi$
$152$	−0.502029	+	0.690983i	−0.0407199	+	0.0560461i
$153$	−28.7890	+	9.35410i	−2.32745	+	0.756234i
$154$	0.218847	+	0.673542i	0.0176352	+	0.0542756i
$155$		0			0
$156$	−0.809017	+	2.48990i	−0.0647732	+	0.199351i
$157$			15.5623i			1.24201i	0.783808	+	0.621004i	$0.213275\pi$
$157$			15.5623i			1.24201i	−0.783808	+	0.621004i	$0.786725\pi$
$158$	2.62866	+	0.854102i	0.209125	+	0.0679487i
$159$	−3.23607	+	2.35114i	−0.256637	+	0.186458i
$160$		0			0
$161$	−15.1353	−	10.9964i	−1.19283	−	0.866638i
$162$	3.35520	+	4.61803i	0.263609	+	0.362827i
$163$	2.85317	+	3.92705i	0.223477	+	0.307590i	0.906003	−	0.423271i	$-0.139118\pi$
$163$	2.85317	+	3.92705i	0.223477	+	0.307590i	−0.682525	+	0.730862i	$0.739118\pi$
$164$	−6.04508	−	4.39201i	−0.472042	−	0.342958i
$165$		0			0
$166$	−10.8992	+	7.91872i	−0.845941	+	0.614612i
$167$	−14.8536	−	4.82624i	−1.14941	−	0.373466i	−0.328488	−	0.944508i	$-0.606539\pi$
$167$	−14.8536	−	4.82624i	−1.14941	−	0.373466i	−0.820920	+	0.571043i	$0.806539\pi$
$168$		−	7.85410i		−	0.605957i
$169$	3.70820	−	11.4127i	0.285246	−	0.877898i
$170$		0			0
$171$	−1.01722	−	3.13068i	−0.0777888	−	0.239409i
$172$	−1.67760	+	0.545085i	−0.127916	+	0.0415623i
$173$	1.90211	−	2.61803i	0.144615	−	0.199045i	−0.730565	−	0.682843i	$-0.760743\pi$
$173$	1.90211	−	2.61803i	0.144615	−	0.199045i	0.875180	+	0.483798i	$0.160743\pi$
$174$	1.38197			0.104767
$175$		0			0
$176$	−0.236068			−0.0177943
$177$	6.88191	−	9.47214i	0.517276	−	0.711969i
$178$	−4.25325	+	1.38197i	−0.318795	+	0.103583i
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	0.993176	+	0.116629i	$0.0372089\pi$
$179$	3.45492	+	10.6331i	0.258232	+	0.794758i	−0.734943	+	0.678129i	$0.762791\pi$
$180$		0			0
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	0.329796	+	0.944052i	$0.393020\pi$
$181$	−6.61803	+	20.3682i	−0.491915	+	1.51396i	−0.821710	+	0.569905i	$0.806980\pi$
$182$		−	3.00000i		−	0.222375i
$183$	5.34307	+	1.73607i	0.394971	+	0.128334i
$184$	5.04508	−	3.66547i	0.371929	−	0.270222i
$185$		0			0
$186$	−8.97214	−	6.51864i	−0.657869	−	0.477970i
$187$	−1.08981	−	1.50000i	−0.0796951	−	0.109691i
$188$	−3.49396	−	4.80902i	−0.254823	−	0.350734i
$189$	5.42705	+	3.94298i	0.394760	+	0.286810i
$190$		0			0
$191$	−14.2812	+	10.3759i	−1.03335	+	0.750771i	−0.968976	−	0.247155i	$-0.920504\pi$
$191$	−14.2812	+	10.3759i	−1.03335	+	0.750771i	−0.0643719	+	0.997926i	$0.520504\pi$
$192$	2.48990	+	0.809017i	0.179693	+	0.0583858i
$193$			16.6525i			1.19867i	0.800498	+	0.599336i	$0.204569\pi$
$193$			16.6525i			1.19867i	−0.800498	+	0.599336i	$0.795431\pi$
$194$	−3.26393	+	10.0453i	−0.234337	+	0.721214i
$195$		0			0
$196$	0.618034	+	1.90211i	0.0441453	+	0.135865i
$197$	11.4127	−	3.70820i	0.813120	−	0.264199i	0.127201	−	0.991877i	$-0.459401\pi$
$197$	11.4127	−	3.70820i	0.813120	−	0.264199i	0.685919	+	0.727678i	$0.259401\pi$
$198$	0.534785	−	0.736068i	0.0380055	−	0.0523101i
$199$	17.5623			1.24496			0.622479	−	0.782636i	$-0.286125\pi$
$199$	17.5623			1.24496			0.622479	+	0.782636i	$0.286125\pi$
$200$		0			0
$201$	15.0902			1.06438
$202$	−0.951057	+	1.30902i	−0.0669161	+	0.0921021i
$203$	−1.50609	+	0.489357i	−0.105706	+	0.0343461i
$204$	6.35410	+	19.5559i	0.444876	+	1.36919i
$205$		0			0
$206$	6.13525	−	18.8824i	0.427463	−	1.31560i
$207$			24.0344i			1.67051i
$208$	0.951057	+	0.309017i	0.0659439	+	0.0214265i
$209$	0.163119	−	0.118513i	0.0112832	−	0.00819771i
$210$		0			0
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	0.898056	+	1.23607i	0.0616787	+	0.0848935i
$213$	−4.61653	−	6.35410i	−0.316319	−	0.435376i
$214$	−8.16312	−	5.93085i	−0.558019	−	0.405425i
$215$		0			0
$216$	−1.80902	+	1.31433i	−0.123088	+	0.0894287i
$217$	12.0862	+	3.92705i	0.820466	+	0.266586i
$218$			15.0000i			1.01593i
$219$	−4.61803	+	14.2128i	−0.312058	+	0.960415i
$220$		0			0
$221$	2.42705	+	7.46969i	0.163261	+	0.502466i
$222$	18.2416	−	5.92705i	1.22430	−	0.397798i
$223$	−5.29007	+	7.28115i	−0.354249	+	0.487582i	−0.948535	−	0.316672i	$-0.897435\pi$
$223$	−5.29007	+	7.28115i	−0.354249	+	0.487582i	0.594286	+	0.804254i	$0.297435\pi$
$224$	−3.00000			−0.200446
$225$		0			0
$226$	−8.23607			−0.547855
$227$	9.02878	−	12.4271i	0.599261	−	0.824812i	−0.396379	−	0.918087i	$-0.629733\pi$
$227$	9.02878	−	12.4271i	0.599261	−	0.824812i	0.995640	+	0.0932746i	$0.0297334\pi$
$228$	−2.12663	+	0.690983i	−0.140839	+	0.0457615i
$229$	−5.42705	−	16.7027i	−0.358630	−	1.10375i	−0.953875	−	0.300204i	$-0.902945\pi$
$229$	−5.42705	−	16.7027i	−0.358630	−	1.10375i	0.595245	−	0.803544i	$-0.297055\pi$
$230$		0			0
$231$	−0.572949	+	1.76336i	−0.0376973	+	0.116020i
$232$		−	0.527864i		−	0.0346560i
$233$	26.3521	+	8.56231i	1.72638	+	0.560935i	0.992919	−	0.118795i	$-0.0379030\pi$
$233$	26.3521	+	8.56231i	1.72638	+	0.560935i	0.733463	+	0.679730i	$0.237903\pi$
$234$	−3.11803	+	2.26538i	−0.203832	+	0.148093i
$235$		0			0
$236$	−3.61803	−	2.62866i	−0.235514	−	0.171111i
$237$	4.25325	+	5.85410i	0.276279	+	0.380265i
$238$	−13.8496	−	19.0623i	−0.897735	−	1.23563i
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	0.00334240	−	0.999994i	$-0.498936\pi$
$239$	−14.6353	−	10.6331i	−0.946676	−	0.687800i	−0.950018	+	0.312194i	$0.898936\pi$
$240$		0			0
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	−0.879078	−	0.476679i	$-0.841841\pi$
$241$	−10.8262	+	7.86572i	−0.697379	+	0.506676i	0.181698	+	0.983354i	$0.441841\pi$
$242$	−10.4086	−	3.38197i	−0.669092	−	0.217401i
$243$			21.6525i			1.38901i
$244$	0.663119	−	2.04087i	0.0424518	−	0.130653i
$245$		0			0
$246$	−6.04508	−	18.6049i	−0.385421	−	1.18620i
$247$	−0.812299	+	0.263932i	−0.0516854	+	0.0167936i
$248$	−2.48990	+	3.42705i	−0.158109	+	0.217618i
$249$	−35.2705			−2.23518
$250$		0			0
$251$	23.1803			1.46313			0.731565	−	0.681772i	$-0.238790\pi$
$251$	23.1803			1.46313			0.731565	+	0.681772i	$0.238790\pi$
$252$	6.79615	−	9.35410i	0.428117	−	0.589253i
$253$	−1.40008	+	0.454915i	−0.0880226	+	0.0286003i
$254$	−3.85410	−	11.8617i	−0.241828	−	0.744270i
$255$		0			0
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$			16.7426i			1.04438i	0.852830	+	0.522189i	$0.174884\pi$
$257$			16.7426i			1.04438i	−0.852830	+	0.522189i	$0.825116\pi$
$258$	−4.39201	−	1.42705i	−0.273435	−	0.0888443i
$259$	−17.7812	+	12.9188i	−1.10487	+	0.802733i
$260$		0			0
$261$	1.64590	+	1.19581i	0.101879	+	0.0740191i
$262$	−6.12261	−	8.42705i	−0.378256	−	0.520625i
$263$	−1.40008	−	1.92705i	−0.0863329	−	0.118827i	0.763666	−	0.645612i	$-0.223397\pi$
$263$	−1.40008	−	1.92705i	−0.0863329	−	0.118827i	−0.849999	+	0.526785i	$0.823397\pi$
$264$	−0.500000	−	0.363271i	−0.0307729	−	0.0223578i
$265$		0			0
$266$	2.07295	−	1.50609i	0.127101	−	0.0923440i
$267$	−11.1352	−	3.61803i	−0.681461	−	0.221420i
$268$		−	5.76393i		−	0.352088i
$269$	−4.04508	+	12.4495i	−0.246633	+	0.759059i	0.748730	+	0.662875i	$0.230664\pi$
$269$	−4.04508	+	12.4495i	−0.246633	+	0.759059i	−0.995364	+	0.0961842i	$0.969336\pi$
$270$		0			0
$271$	−2.93769	−	9.04129i	−0.178452	−	0.549219i	0.821322	−	0.570465i	$-0.193237\pi$
$271$	−2.93769	−	9.04129i	−0.178452	−	0.549219i	−0.999774	+	0.0212453i	$0.993237\pi$
$272$	7.46969	−	2.42705i	0.452917	−	0.147162i
$273$	4.61653	−	6.35410i	0.279405	−	0.384568i
$274$	−6.09017			−0.367921
$275$		0			0
$276$	16.3262			0.982724
$277$	−8.05748	+	11.0902i	−0.484127	+	0.666344i	−0.979291	−	0.202456i	$-0.935108\pi$
$277$	−8.05748	+	11.0902i	−0.484127	+	0.666344i	0.495164	+	0.868799i	$0.335108\pi$
$278$	9.82084	−	3.19098i	0.589015	−	0.191382i
$279$	−5.04508	−	15.5272i	−0.302041	−	0.929588i
$280$		0			0
$281$	−5.92705	+	18.2416i	−0.353578	+	1.08820i	0.603251	+	0.797551i	$0.293872\pi$
$281$	−5.92705	+	18.2416i	−0.353578	+	1.08820i	−0.956829	+	0.290651i	$0.906128\pi$
$282$		−	15.5623i		−	0.926722i
$283$	−24.4500	−	7.94427i	−1.45340	−	0.472238i	−0.527352	−	0.849647i	$-0.676815\pi$
$283$	−24.4500	−	7.94427i	−1.45340	−	0.472238i	−0.926047	+	0.377409i	$0.876815\pi$
$284$	−2.42705	+	1.76336i	−0.144019	+	0.104636i
$285$		0			0
$286$	−0.190983	−	0.138757i	−0.0112931	−	0.00820489i
$287$	13.1760	+	18.1353i	0.777757	+	1.07049i
$288$	2.26538	+	3.11803i	0.133489	+	0.183732i
$289$	36.1525	+	26.2663i	2.12662	+	1.54508i
$290$		0			0
$291$	−22.3713	+	16.2537i	−1.31143	+	0.952810i
$292$	5.42882	+	1.76393i	0.317698	+	0.103226i
$293$		−	11.5623i		−	0.675477i	−0.941240	−	0.337739i	$-0.890338\pi$
$293$		−	11.5623i		−	0.675477i	0.941240	−	0.337739i	$-0.109662\pi$
$294$	−1.61803	+	4.97980i	−0.0943657	+	0.290428i
$295$		0			0
$296$	−2.26393	−	6.96767i	−0.131588	−	0.404987i
$297$	0.502029	−	0.163119i	0.0291307	−	0.00946512i
$298$	1.31433	−	1.80902i	0.0761370	−	0.104794i
$299$	6.23607			0.360641
$300$		0			0
$301$	5.29180			0.305014
$302$	2.17963	−	3.00000i	0.125423	−	0.172631i
$303$	−4.02874	+	1.30902i	−0.231445	+	0.0752011i
$304$	0.263932	+	0.812299i	0.0151375	+	0.0465886i
$305$		0			0
$306$	−9.35410	+	28.7890i	−0.534738	+	1.64576i
$307$		−	17.1246i		−	0.977353i	−0.872465	−	0.488677i	$-0.837480\pi$
$307$		−	17.1246i		−	0.977353i	0.872465	−	0.488677i	$-0.162520\pi$
$308$	0.673542	+	0.218847i	0.0383786	+	0.0124700i
$309$	42.0517	−	30.5523i	2.39224	−	1.73806i
$310$		0			0
$311$	17.0623	+	12.3965i	0.967515	+	0.702941i	0.954884	−	0.296980i	$-0.0959794\pi$
$311$	17.0623	+	12.3965i	0.967515	+	0.702941i	0.0126308	+	0.999920i	$0.495979\pi$
$312$	1.53884	+	2.11803i	0.0871198	+	0.119910i
$313$	−2.09387	−	2.88197i	−0.118353	−	0.162898i	0.745730	−	0.666248i	$-0.232101\pi$
$313$	−2.09387	−	2.88197i	−0.118353	−	0.162898i	−0.864083	+	0.503350i	$0.832101\pi$
$314$	12.5902	+	9.14729i	0.710504	+	0.516212i
$315$		0			0
$316$	2.23607	−	1.62460i	0.125789	−	0.0913908i
$317$	−10.0984	−	3.28115i	−0.567180	−	0.184288i	0.0113694	−	0.999935i	$-0.496381\pi$
$317$	−10.0984	−	3.28115i	−0.567180	−	0.184288i	−0.578549	+	0.815647i	$0.696381\pi$
$318$			4.00000i			0.224309i
$319$	−0.0385072	+	0.118513i	−0.00215599	+	0.00663545i
$320$		0			0
$321$	−8.16312	−	25.1235i	−0.455621	−	1.40226i
$322$	−17.7926	+	5.78115i	−0.991541	+	0.322171i
$323$	−3.94298	+	5.42705i	−0.219393	+	0.301969i
$324$	5.70820			0.317122
$325$		0			0
$326$	4.85410			0.268844
$327$	−23.0826	+	31.7705i	−1.27647	+	1.75691i
$328$	−7.10642	+	2.30902i	−0.392387	+	0.127494i
$329$	5.51064	+	16.9600i	0.303812	+	0.935036i
$330$		0			0
$331$	1.40983	−	4.33901i	0.0774913	−	0.238494i	−0.904805	−	0.425825i	$-0.859984\pi$
$331$	1.40983	−	4.33901i	0.0774913	−	0.238494i	0.982297	+	0.187332i	$0.0599839\pi$
$332$			13.4721i			0.739380i
$333$	26.8541	+	8.72542i	1.47160	+	0.478150i
$334$	−12.6353	+	9.18005i	−0.691370	+	0.502310i
$335$		0			0
$336$	−6.35410	−	4.61653i	−0.346645	−	0.251852i
$337$	−18.4661	−	25.4164i	−1.00591	−	1.38452i	−0.921626	−	0.388078i	$-0.873139\pi$
$337$	−18.4661	−	25.4164i	−1.00591	−	1.38452i	−0.0842863	−	0.996442i	$-0.526861\pi$
$338$	−7.05342	−	9.70820i	−0.383656	−	0.528057i
$339$	−17.4443	−	12.6740i	−0.947443	−	0.688357i
$340$		0			0
$341$	0.809017	−	0.587785i	0.0438107	−	0.0318304i
$342$	−3.13068	−	1.01722i	−0.169288	−	0.0550050i
$343$			15.0000i			0.809924i
$344$	−0.545085	+	1.67760i	−0.0293890	+	0.0904501i
$345$		0			0
$346$	−1.00000	−	3.07768i	−0.0537603	−	0.165457i
$347$	−9.42481	+	3.06231i	−0.505950	+	0.164393i	−0.550860	−	0.834598i	$-0.685700\pi$
$347$	−9.42481	+	3.06231i	−0.505950	+	0.164393i	0.0449095	+	0.998991i	$0.485700\pi$
$348$	0.812299	−	1.11803i	0.0435438	−	0.0599329i
$349$	22.2361			1.19027			0.595135	−	0.803626i	$-0.297099\pi$
$349$	22.2361			1.19027			0.595135	+	0.803626i	$0.297099\pi$
$350$		0			0
$351$	−2.23607			−0.119352
$352$	−0.138757	+	0.190983i	−0.00739579	+	0.0101794i
$353$	15.9434	−	5.18034i	0.848584	−	0.275722i	0.147731	−	0.989028i	$-0.452803\pi$
$353$	15.9434	−	5.18034i	0.848584	−	0.275722i	0.700853	+	0.713306i	$0.252803\pi$
$354$	−3.61803	−	11.1352i	−0.192296	−	0.591827i
$355$		0			0
$356$	−1.38197	+	4.25325i	−0.0732441	+	0.225422i
$357$		−	61.6869i		−	3.26482i
$358$	10.6331	+	3.45492i	0.561979	+	0.182598i
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	−0.519855	−	0.854254i	$-0.674014\pi$
$359$	2.50000	−	1.81636i	0.131945	−	0.0958636i	0.651800	+	0.758391i	$0.274014\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	12.5882	+	17.3262i	0.661624	+	0.910647i
$363$	−16.8415	−	23.1803i	−0.883950	−	1.21665i
$364$	−2.42705	−	1.76336i	−0.127212	−	0.0924250i
$365$		0			0
$366$	4.54508	−	3.30220i	0.237575	−	0.172609i
$367$	29.9973	+	9.74671i	1.56585	+	0.508774i	0.958362	−	0.285557i	$-0.0921788\pi$
$367$	29.9973	+	9.74671i	1.56585	+	0.508774i	0.607484	+	0.794332i	$0.292179\pi$
$368$		−	6.23607i		−	0.325078i
$369$	8.89919	−	27.3889i	0.463273	−	1.42581i
$370$		0			0
$371$	−1.41641	−	4.35926i	−0.0735362	−	0.226321i
$372$	−10.5474	+	3.42705i	−0.546856	+	0.177684i
$373$	−9.54332	+	13.1353i	−0.494134	+	0.680118i	−0.981144	−	0.193279i	$-0.938088\pi$
$373$	−9.54332	+	13.1353i	−0.494134	+	0.680118i	0.487009	+	0.873397i	$0.338088\pi$
$374$	−1.85410			−0.0958733
$375$		0			0
$376$	−5.94427			−0.306552
$377$	0.310271	−	0.427051i	0.0159798	−	0.0219942i
$378$	6.37988	−	2.07295i	0.328146	−	0.106621i
$379$	−0.163119	−	0.502029i	−0.00837886	−	0.0257875i	0.946780	−	0.321882i	$-0.104316\pi$
$379$	−0.163119	−	0.502029i	−0.00837886	−	0.0257875i	−0.955159	+	0.296095i	$0.904316\pi$
$380$		0			0
$381$	10.0902	−	31.0543i	0.516935	−	1.59096i
$382$			17.6525i			0.903179i
$383$	−4.11450	−	1.33688i	−0.210241	−	0.0683114i	0.202003	−	0.979385i	$-0.435255\pi$
$383$	−4.11450	−	1.33688i	−0.210241	−	0.0683114i	−0.412244	+	0.911073i	$0.635255\pi$
$384$	2.11803	−	1.53884i	0.108085	−	0.0785287i
$385$		0			0
$386$	13.4721	+	9.78808i	0.685714	+	0.498200i
$387$	−3.99598	−	5.50000i	−0.203127	−	0.279581i
$388$	6.20837	+	8.54508i	0.315182	+	0.433811i
$389$	−26.8713	−	19.5232i	−1.36243	−	0.989863i	−0.998286	−	0.0585208i	$-0.981362\pi$
$389$	−26.8713	−	19.5232i	−1.36243	−	0.989863i	−0.364144	−	0.931343i	$-0.618638\pi$
$390$		0			0
$391$	39.6246	−	28.7890i	2.00390	−	1.45592i
$392$	1.90211	+	0.618034i	0.0960712	+	0.0312154i
$393$		−	27.2705i		−	1.37562i
$394$	3.70820	−	11.4127i	0.186817	−	0.574962i
$395$		0			0
$396$	−0.281153	−	0.865300i	−0.0141285	−	0.0434830i
$397$	−5.48183	+	1.78115i	−0.275125	+	0.0893935i	−0.443330	−	0.896359i	$-0.646203\pi$
$397$	−5.48183	+	1.78115i	−0.275125	+	0.0893935i	0.168205	+	0.985752i	$0.446203\pi$
$398$	10.3229	−	14.2082i	0.517438	−	0.712193i
$399$	6.70820			0.335830
$400$		0			0
$401$	8.18034			0.408507			0.204253	−	0.978918i	$-0.434523\pi$
$401$	8.18034			0.408507			0.204253	+	0.978918i	$0.434523\pi$
$402$	8.86978	−	12.2082i	0.442384	−	0.608890i
$403$	−4.02874	+	1.30902i	−0.200686	+	0.0652068i
$404$	0.500000	+	1.53884i	0.0248759	+	0.0765602i
$405$		0			0
$406$	−0.489357	+	1.50609i	−0.0242864	+	0.0747458i
$407$			1.72949i			0.0857276i
$408$	19.5559	+	6.35410i	0.968162	+	0.314575i
$409$	5.42705	−	3.94298i	0.268350	−	0.194968i	−0.445470	−	0.895297i	$-0.646963\pi$
$409$	5.42705	−	3.94298i	0.268350	−	0.194968i	0.713820	+	0.700329i	$0.246963\pi$
$410$		0			0
$411$	−12.8992	−	9.37181i	−0.636270	−	0.462277i
$412$	−11.6699	−	16.0623i	−0.574937	−	0.791333i
$413$	7.88597	+	10.8541i	0.388043	+	0.534095i
$414$	19.4443	+	14.1271i	0.955634	+	0.694309i
$415$		0			0
$416$	0.809017	−	0.587785i	0.0396653	−	0.0288185i
$417$	25.7113	+	8.35410i	1.25909	+	0.409102i
$418$		−	0.201626i		−	0.00986186i
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	0.504465	+	0.863432i	$0.331690\pi$
$419$	−8.41641	+	25.9030i	−0.411168	+	1.26545i	−0.915633	+	0.402014i	$0.868310\pi$
$420$		0			0
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	0.815144	−	0.579258i	$-0.196658\pi$
$421$	−3.79180	−	11.6699i	−0.184801	−	0.568758i	−0.999945	+	0.0104998i	$0.996658\pi$
$422$	−10.7189	+	3.48278i	−0.521787	+	0.169539i
$423$	13.4661	−	18.5344i	0.654742	−	0.901175i
$424$	1.52786			0.0741996
$425$		0			0
$426$	−7.85410			−0.380532
$427$	−3.78398	+	5.20820i	−0.183120	+	0.252043i
$428$	−9.59632	+	3.11803i	−0.463856	+	0.150716i
$429$	−0.190983	−	0.587785i	−0.00922075	−	0.0283785i
$430$		0			0
$431$	−9.90983	+	30.4993i	−0.477340	+	1.46910i	0.365436	+	0.930836i	$0.380920\pi$
$431$	−9.90983	+	30.4993i	−0.477340	+	1.46910i	−0.842776	+	0.538264i	$0.819080\pi$
$432$			2.23607i			0.107583i
$433$	22.2173	+	7.21885i	1.06770	+	0.346916i	0.789590	−	0.613635i	$-0.210293\pi$
$433$	22.2173	+	7.21885i	1.06770	+	0.346916i	0.278106	+	0.960550i	$0.410293\pi$
$434$	10.2812	−	7.46969i	0.493511	−	0.358557i
$435$		0			0
$436$	12.1353	+	8.81678i	0.581173	+	0.422247i
$437$	3.13068	+	4.30902i	0.149761	+	0.206128i
$438$	8.78402	+	12.0902i	0.419717	+	0.577691i
$439$	−4.57295	−	3.32244i	−0.218255	−	0.158572i	0.473286	−	0.880909i	$-0.343068\pi$
$439$	−4.57295	−	3.32244i	−0.218255	−	0.158572i	−0.691541	+	0.722337i	$0.743068\pi$
$440$		0			0
$441$	−6.23607	+	4.53077i	−0.296956	+	0.215751i
$442$	7.46969	+	2.42705i	0.355297	+	0.115443i
$443$		−	7.41641i		−	0.352364i	−0.984358	−	0.176182i	$-0.943625\pi$
$443$		−	7.41641i		−	0.352364i	0.984358	−	0.176182i	$-0.0563748\pi$
$444$	5.92705	−	18.2416i	0.281285	−	0.865707i
$445$		0			0
$446$	2.78115	+	8.55951i	0.131691	+	0.405304i
$447$	5.56758	−	1.80902i	0.263338	−	0.0855636i
$448$	−1.76336	+	2.42705i	−0.0833107	+	0.114667i
$449$	−13.9443			−0.658071			−0.329035	−	0.944318i	$-0.606724\pi$
$449$	−13.9443			−0.658071			−0.329035	+	0.944318i	$0.606724\pi$
$450$		0			0
$451$	1.76393			0.0830603
$452$	−4.84104	+	6.66312i	−0.227703	+	0.313407i
$453$	9.23305	−	3.00000i	0.433807	−	0.140952i
$454$	−4.74671	−	14.6089i	−0.222774	−	0.685628i
$455$		0			0
$456$	−0.690983	+	2.12663i	−0.0323582	+	0.0995884i
$457$			11.2148i			0.524605i	0.964986	+	0.262303i	$0.0844819\pi$
$457$			11.2148i			0.524605i	−0.964986	+	0.262303i	$0.915518\pi$
$458$	−16.7027	−	5.42705i	−0.780468	−	0.253589i
$459$	−14.2082	+	10.3229i	−0.663182	+	0.481830i
$460$		0			0
$461$	−22.7984	−	16.5640i	−1.06183	−	0.771462i	−0.0874008	−	0.996173i	$-0.527856\pi$
$461$	−22.7984	−	16.5640i	−1.06183	−	0.771462i	−0.974425	+	0.224711i	$0.927856\pi$
$462$	1.08981	+	1.50000i	0.0507027	+	0.0697863i
$463$	−7.04091	−	9.69098i	−0.327219	−	0.450378i	0.613435	−	0.789745i	$-0.289787\pi$
$463$	−7.04091	−	9.69098i	−0.327219	−	0.450378i	−0.940654	+	0.339367i	$0.889787\pi$
$464$	−0.427051	−	0.310271i	−0.0198253	−	0.0144040i
$465$		0			0
$466$	22.4164	−	16.2865i	1.03842	−	0.754456i
$467$	−3.02468	−	0.982779i	−0.139966	−	0.0454776i	0.238196	−	0.971217i	$-0.423444\pi$
$467$	−3.02468	−	0.982779i	−0.139966	−	0.0454776i	−0.378162	+	0.925739i	$0.623444\pi$
$468$			3.85410i			0.178156i
$469$	−5.34346	+	16.4455i	−0.246738	+	0.759381i
$470$		0			0
$471$	12.5902	+	38.7486i	0.580124	+	1.78544i
$472$	−4.25325	+	1.38197i	−0.195772	+	0.0636101i
$473$	0.244758	−	0.336881i	0.0112540	−	0.0154898i
$474$	7.23607			0.332364
$475$		0			0
$476$	−23.5623			−1.07998
$477$	−3.46120	+	4.76393i	−0.158477	+	0.218125i
$478$	−17.2048	+	5.59017i	−0.786928	+	0.255688i
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	0.676910	+	0.736066i	$0.263319\pi$
$479$	12.2984	+	37.8505i	0.561927	+	1.72943i	−0.114983	+	0.993368i	$0.536681\pi$
$480$		0			0
$481$	2.26393	−	6.96767i	0.103226	−	0.317698i
$482$			13.3820i			0.609532i
$483$	−46.5815	−	15.1353i	−2.11953	−	0.688678i
$484$	−8.85410	+	6.43288i	−0.402459	+	0.292404i
$485$		0			0
$486$	17.5172	+	12.7270i	0.794597	+	0.577309i
$487$	−10.6534	−	14.6631i	−0.482751	−	0.664449i	0.496280	−	0.868163i	$-0.334699\pi$
$487$	−10.6534	−	14.6631i	−0.482751	−	0.664449i	−0.979031	+	0.203713i	$0.934699\pi$
$488$	−1.26133	−	1.73607i	−0.0570976	−	0.0785881i
$489$	10.2812	+	7.46969i	0.464930	+	0.337791i
$490$		0			0
$491$	−11.9443	+	8.67802i	−0.539037	+	0.391634i	−0.823727	−	0.566986i	$-0.808109\pi$
$491$	−11.9443	+	8.67802i	−0.539037	+	0.391634i	0.284690	+	0.958620i	$0.408109\pi$
$492$	−18.6049	−	6.04508i	−0.838772	−	0.272533i
$493$		−	4.14590i		−	0.186722i
$494$	−0.263932	+	0.812299i	−0.0118749	+	0.0365471i
$495$		0			0
$496$	1.30902	+	4.02874i	0.0587766	+	0.180896i
$497$	8.55951	−	2.78115i	0.383946	−	0.124752i
$498$	−20.7315	+	28.5344i	−0.929000	+	1.27866i
$499$	−40.8541			−1.82888			−0.914440	−	0.404721i	$-0.867369\pi$
$499$	−40.8541			−1.82888			−0.914440	+	0.404721i	$0.867369\pi$
$500$		0			0
$501$	−40.8885			−1.82677
$502$	13.6251	−	18.7533i	0.608116	−	0.837000i
$503$	−7.13918	+	2.31966i	−0.318320	+	0.103429i	−0.463819	−	0.885930i	$-0.653521\pi$
$503$	−7.13918	+	2.31966i	−0.318320	+	0.103429i	0.145499	+	0.989358i	$0.453521\pi$
$504$	−3.57295	−	10.9964i	−0.159152	−	0.489819i
$505$		0			0
$506$	−0.454915	+	1.40008i	−0.0202234	+	0.0622413i
$507$		−	31.4164i		−	1.39525i
$508$	−11.8617	−	3.85410i	−0.526278	−	0.170998i
$509$	−10.5902	+	7.69421i	−0.469401	+	0.341040i	−0.797208	−	0.603705i	$-0.793690\pi$
$509$	−10.5902	+	7.69421i	−0.469401	+	0.341040i	0.327807	+	0.944745i	$0.393690\pi$
$510$		0			0
$511$	−13.8541	−	10.0656i	−0.612869	−	0.445276i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	−1.12257	−	1.54508i	−0.0495627	−	0.0682172i
$514$	13.5451	+	9.84108i	0.597448	+	0.434071i
$515$		0			0
$516$	−3.73607	+	2.71441i	−0.164471	+	0.119495i
$517$	1.33457	+	0.433629i	0.0586944	+	0.0190710i
$518$			21.9787i			0.965689i
$519$	2.61803	−	8.05748i	0.114919	−	0.353684i
$520$		0			0
$521$	10.0279	+	30.8626i	0.439329	+	1.35211i	0.888585	+	0.458712i	$0.151689\pi$
$521$	10.0279	+	30.8626i	0.439329	+	1.35211i	−0.449256	+	0.893403i	$0.648311\pi$
$522$	1.93487	−	0.628677i	0.0846869	−	0.0275164i
$523$	15.6659	−	21.5623i	0.685023	−	0.942854i	−0.314957	−	0.949106i	$-0.601990\pi$
$523$	15.6659	−	21.5623i	0.685023	−	0.942854i	0.999980	+	0.00625211i	$0.00199012\pi$
$524$	−10.4164			−0.455043
$525$		0			0
$526$	−2.38197			−0.103859
$527$	−19.5559	+	26.9164i	−0.851869	+	1.17250i
$528$	−0.587785	+	0.190983i	−0.0255801	+	0.00831147i
$529$	−4.90983	−	15.1109i	−0.213471	−	0.656996i
$530$		0			0
$531$	5.32624	−	16.3925i	0.231139	−	0.711373i
$532$		−	2.56231i		−	0.111090i
$533$	−7.10642	−	2.30902i	−0.307813	−	0.100015i
$534$	−9.47214	+	6.88191i	−0.409899	+	0.297809i
$535$		0			0
$536$	−4.66312	−	3.38795i	−0.201416	−	0.146337i
$537$	17.2048	+	23.6803i	0.742441	+	1.02188i
$538$	7.69421	+	10.5902i	0.331721	+	0.456575i
$539$	−0.381966	−	0.277515i	−0.0164524	−	0.0119534i
$540$		0			0
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.961774	−	0.273843i	$-0.911705\pi$
$541$	−23.2254	+	16.8743i	−0.998539	+	0.725481i	−0.0367646	+	0.999324i	$0.511705\pi$
$542$	−9.04129	−	2.93769i	−0.388357	−	0.126185i
$543$			56.0689i			2.40615i
$544$	2.42705	−	7.46969i	0.104059	−	0.320261i
$545$		0			0
$546$	−2.42705	−	7.46969i	−0.103868	−	0.319673i
$547$	10.0984	−	3.28115i	0.431774	−	0.140292i	−0.0850631	−	0.996376i	$-0.527109\pi$
$547$	10.0984	−	3.28115i	0.431774	−	0.140292i	0.516837	+	0.856084i	$0.327109\pi$
$548$	−3.57971	+	4.92705i	−0.152918	+	0.210473i
$549$	8.27051			0.352977
$550$		0			0
$551$	0.450850			0.0192068
$552$	9.59632	−	13.2082i	0.408447	−	0.562178i
$553$	−7.88597	+	2.56231i	−0.335345	+	0.108960i
$554$	4.23607	+	13.0373i	0.179973	+	0.553901i
$555$		0			0
$556$	3.19098	−	9.82084i	0.135328	−	0.416496i
$557$			10.8885i			0.461362i	0.973029	+	0.230681i	$0.0740954\pi$
$557$			10.8885i			0.461362i	−0.973029	+	0.230681i	$0.925905\pi$
$558$	−15.5272	−	5.04508i	−0.657318	−	0.213575i
$559$	−1.42705	+	1.03681i	−0.0603578	+	0.0438525i
$560$		0			0
$561$	−3.92705	−	2.85317i	−0.165800	−	0.120461i
$562$	11.2739	+	15.5172i	0.475562	+	0.654554i
$563$	20.4867	+	28.1976i	0.863413	+	1.18839i	0.980745	+	0.195293i	$0.0625657\pi$
$563$	20.4867	+	28.1976i	0.863413	+	1.18839i	−0.117332	+	0.993093i	$0.537434\pi$
$564$	−12.5902	−	9.14729i	−0.530142	−	0.385171i
$565$		0			0
$566$	−20.7984	+	15.1109i	−0.874221	+	0.635159i
$567$	−16.2865	−	5.29180i	−0.683968	−	0.222235i
$568$			3.00000i			0.125877i
$569$	−6.87132	+	21.1478i	−0.288061	+	0.886560i	0.697404	+	0.716679i	$0.254339\pi$
$569$	−6.87132	+	21.1478i	−0.288061	+	0.886560i	−0.985464	+	0.169882i	$0.945661\pi$
$570$		0			0
$571$	0.517221	+	1.59184i	0.0216450	+	0.0666165i	0.961296	−	0.275519i	$-0.0888497\pi$
$571$	0.517221	+	1.59184i	0.0216450	+	0.0666165i	−0.939651	+	0.342136i	$0.888850\pi$
$572$	−0.224514	+	0.0729490i	−0.00938740	+	0.00305015i
$573$	−27.1644	+	37.3885i	−1.13481	+	1.56193i
$574$	22.4164			0.935643
$575$		0			0
$576$	3.85410			0.160588
$577$	25.2748	−	34.7877i	1.05220	−	1.44823i	0.165318	−	0.986240i	$-0.447135\pi$
$577$	25.2748	−	34.7877i	1.05220	−	1.44823i	0.886884	−	0.461992i	$-0.152865\pi$
$578$	42.4998	−	13.8090i	1.76776	−	0.574379i
$579$	13.4721	+	41.4630i	0.559883	+	1.72314i
$580$		0			0
$581$	12.4894	−	38.4383i	0.518146	−	1.59469i
$582$			27.6525i			1.14623i
$583$	−0.343027	−	0.111456i	−0.0142067	−	0.00461604i
$584$	4.61803	−	3.35520i	0.191096	−	0.138839i
$585$		0			0
$586$	−9.35410	−	6.79615i	−0.386414	−	0.280746i
$587$	−6.94742	−	9.56231i	−0.286751	−	0.394679i	0.641205	−	0.767370i	$-0.278435\pi$
$587$	−6.94742	−	9.56231i	−0.286751	−	0.394679i	−0.927955	+	0.372691i	$0.878435\pi$
$588$	3.07768	+	4.23607i	0.126922	+	0.174692i
$589$	−2.92705	−	2.12663i	−0.120607	−	0.0876261i
$590$		0			0
$591$	25.4164	−	18.4661i	1.04549	−	0.759594i
$592$	−6.96767	−	2.26393i	−0.286369	−	0.0930470i
$593$		−	47.0132i		−	1.93060i	−0.261145	−	0.965299i	$-0.584100\pi$
$593$		−	47.0132i		−	1.93060i	0.261145	−	0.965299i	$-0.415900\pi$
$594$	0.163119	−	0.502029i	0.00669285	−	0.0205985i
$595$		0			0
$596$	−0.690983	−	2.12663i	−0.0283038	−	0.0871100i
$597$	43.7284	−	14.2082i	1.78968	−	0.581503i
$598$	3.66547	−	5.04508i	0.149892	−	0.206309i
$599$	8.94427			0.365453			0.182727	−	0.983164i	$-0.441508\pi$
$599$	8.94427			0.365453			0.182727	+	0.983164i	$0.441508\pi$
$600$		0			0
$601$	−14.8328			−0.605043			−0.302522	−	0.953143i	$-0.597828\pi$
$601$	−14.8328			−0.605043			−0.302522	+	0.953143i	$0.597828\pi$
$602$	3.11044	−	4.28115i	0.126772	−	0.174487i
$603$	21.1275	−	6.86475i	0.860379	−	0.279554i
$604$	−1.14590	−	3.52671i	−0.0466259	−	0.143500i
$605$		0			0
$606$	−1.30902	+	4.02874i	−0.0531752	+	0.163656i
$607$			27.1459i			1.10182i	0.834565	+	0.550909i	$0.185719\pi$
$607$			27.1459i			1.10182i	−0.834565	+	0.550909i	$0.814281\pi$
$608$	0.812299	+	0.263932i	0.0329431	+	0.0107039i
$609$	−3.35410	+	2.43690i	−0.135915	+	0.0987481i
$610$		0			0
$611$	−4.80902	−	3.49396i	−0.194552	−	0.141350i
$612$	17.7926	+	24.4894i	0.719222	+	0.989924i
$613$	24.4297	+	33.6246i	0.986707	+	1.35809i	0.933137	+	0.359521i	$0.117060\pi$
$613$	24.4297	+	33.6246i	0.986707	+	1.35809i	0.0535698	+	0.998564i	$0.482940\pi$
$614$	−13.8541	−	10.0656i	−0.559106	−	0.406214i
$615$		0			0
$616$	0.572949	−	0.416272i	0.0230848	−	0.0167721i
$617$	28.8747	+	9.38197i	1.16245	+	0.377704i	0.825821	−	0.563933i	$-0.190712\pi$
$617$	28.8747	+	9.38197i	1.16245	+	0.377704i	0.336632	+	0.941636i	$0.390712\pi$
$618$		−	51.9787i		−	2.09089i
$619$	14.5106	−	44.6592i	0.583232	−	1.79500i	−0.0230252	−	0.999735i	$-0.507330\pi$
$619$	14.5106	−	44.6592i	0.583232	−	1.79500i	0.606257	−	0.795269i	$-0.292670\pi$
$620$		0			0
$621$	4.30902	+	13.2618i	0.172915	+	0.532177i
$622$	20.0579	−	6.51722i	0.804250	−	0.261317i
$623$	7.88597	−	10.8541i	0.315945	−	0.434860i
$624$	2.61803			0.104805
$625$		0			0
$626$	−3.56231			−0.142378
$627$	0.310271	−	0.427051i	0.0123910	−	0.0170548i
$628$	14.8006	−	4.80902i	0.590610	−	0.191901i
$629$	−17.7812	−	54.7248i	−0.708981	−	2.18202i
$630$		0			0
$631$	2.72949	−	8.40051i	0.108659	−	0.334419i	−0.881913	−	0.471413i	$-0.843744\pi$
$631$	2.72949	−	8.40051i	0.108659	−	0.334419i	0.990572	+	0.136994i	$0.0437441\pi$
$632$		−	2.76393i		−	0.109943i
$633$	−28.0624	−	9.11803i	−1.11538	−	0.362409i
$634$	−8.59017	+	6.24112i	−0.341159	+	0.247867i
$635$		0			0
$636$	3.23607	+	2.35114i	0.128318	+	0.0932288i
$637$	1.17557	+	1.61803i	0.0465778	+	0.0641088i
$638$	0.0732450	+	0.100813i	0.00289980	+	0.00399123i
$639$	−9.35410	−	6.79615i	−0.370043	−	0.268852i
$640$		0			0
$641$	−11.6180	+	8.44100i	−0.458885	+	0.333399i	−0.793094	−	0.609100i	$-0.791531\pi$
$641$	−11.6180	+	8.44100i	−0.458885	+	0.333399i	0.334209	+	0.942499i	$0.391531\pi$
$642$	−25.1235	−	8.16312i	−0.991545	−	0.322173i
$643$		−	36.2361i		−	1.42901i	−0.699630	−	0.714506i	$-0.746652\pi$
$643$		−	36.2361i		−	1.42901i	0.699630	−	0.714506i	$-0.253348\pi$
$644$	−5.78115	+	17.7926i	−0.227809	+	0.701125i
$645$		0			0
$646$	2.07295	+	6.37988i	0.0815591	+	0.251013i
$647$	7.27794	−	2.36475i	0.286125	−	0.0929677i	−0.162438	−	0.986719i	$-0.551936\pi$
$647$	7.27794	−	2.36475i	0.286125	−	0.0929677i	0.448563	+	0.893751i	$0.351936\pi$
$648$	3.35520	−	4.61803i	0.131805	−	0.181414i
$649$	1.05573			0.0414410
$650$		0			0
$651$	33.2705			1.30397
$652$	2.85317	−	3.92705i	0.111739	−	0.153795i
$653$	−38.6098	+	12.5451i	−1.51092	+	0.490927i	−0.943180	−	0.332282i	$-0.892181\pi$
$653$	−38.6098	+	12.5451i	−1.51092	+	0.490927i	−0.567738	+	0.823209i	$0.692181\pi$
$654$	12.1353	+	37.3485i	0.474526	+	1.46044i
$655$		0			0
$656$	−2.30902	+	7.10642i	−0.0901520	+	0.277459i
$657$			22.0000i			0.858302i
$658$	16.9600	+	5.51064i	0.661170	+	0.214827i
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	−0.495144	−	0.868811i	$-0.664885\pi$
$659$	4.57295	−	3.32244i	0.178137	−	0.129424i	0.673281	+	0.739387i	$0.264885\pi$
$660$		0			0
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	0.484741	−	0.874658i	$-0.338914\pi$
$661$	−5.07295	−	3.68571i	−0.197315	−	0.143358i	−0.682056	+	0.731300i	$0.738914\pi$
$662$	−2.68166	−	3.69098i	−0.104226	−	0.143454i
$663$	12.0862	+	16.6353i	0.469390	+	0.646060i
$664$	10.8992	+	7.91872i	0.422970	+	0.307306i
$665$		0			0
$666$	22.8435	−	16.5967i	0.885166	−	0.643111i
$667$	−3.13068	−	1.01722i	−0.121221	−	0.0393870i
$668$			15.6180i			0.604280i
$669$	−7.28115	+	22.4091i	−0.281506	+	0.866385i
$670$		0			0
$671$	0.156541	+	0.481784i	0.00604320	+	0.0185991i
$672$	−7.46969	+	2.42705i	−0.288150	+	0.0936255i
$673$	−0.726543	+	1.00000i	−0.0280062	+	0.0385472i	−0.822790	−	0.568345i	$-0.807584\pi$
$673$	−0.726543	+	1.00000i	−0.0280062	+	0.0385472i	0.794784	+	0.606892i	$0.207584\pi$
$674$	−31.4164			−1.21011
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−6.24112	+	8.59017i	−0.239866	+	0.330147i	−0.911930	−	0.410346i	$-0.865408\pi$
$677$	−6.24112	+	8.59017i	−0.239866	+	0.330147i	0.672064	+	0.740493i	$0.265408\pi$
$678$	−20.5070	+	6.66312i	−0.787565	+	0.255896i
$679$	−9.79180	−	30.1360i	−0.375775	−	1.15652i
$680$		0			0
$681$	12.4271	−	38.2465i	0.476206	−	1.46561i
$682$		−	1.00000i		−	0.0382920i
$683$	31.7279	+	10.3090i	1.21403	+	0.394464i	0.844906	−	0.534915i	$-0.179656\pi$
$683$	31.7279	+	10.3090i	1.21403	+	0.394464i	0.369128	+	0.929379i	$0.379656\pi$
$684$	−2.66312	+	1.93487i	−0.101827	+	0.0739816i
$685$		0			0
$686$	12.1353	+	8.81678i	0.463326	+	0.336626i
$687$	−27.0256	−	37.1976i	−1.03109	−	1.41918i
$688$	1.03681	+	1.42705i	0.0395281	+	0.0544058i
$689$	1.23607	+	0.898056i	0.0470904	+	0.0342132i
$690$		0			0
$691$	−1.02786	+	0.746787i	−0.0391018	+	0.0284091i	−0.607164	−	0.794576i	$-0.707693\pi$
$691$	−1.02786	+	0.746787i	−0.0391018	+	0.0284091i	0.568063	+	0.822985i	$0.307693\pi$
$692$	−3.07768	−	1.00000i	−0.116996	−	0.0380143i
$693$			2.72949i			0.103685i
$694$	−3.06231	+	9.42481i	−0.116244	+	0.357761i
$695$		0			0
$696$	−0.427051	−	1.31433i	−0.0161873	−	0.0498195i
$697$	−55.8146	+	18.1353i	−2.11413	+	0.686922i
$698$	13.0700	−	17.9894i	0.494708	−	0.680907i
$699$	72.5410			2.74375
$700$		0			0
$701$	−4.18034			−0.157889			−0.0789446	−	0.996879i	$-0.525155\pi$
$701$	−4.18034			−0.157889			−0.0789446	+	0.996879i	$0.525155\pi$
$702$	−1.31433	+	1.80902i	−0.0496061	+	0.0682769i
$703$	5.95110	−	1.93363i	0.224450	−	0.0729282i
$704$	0.0729490	+	0.224514i	0.00274937	+	0.00846169i
$705$		0			0
$706$	5.18034	−	15.9434i	0.194965	−	0.600040i
$707$		−	4.85410i		−	0.182557i
$708$	−11.1352	−	3.61803i	−0.418485	−	0.135974i
$709$	6.28115	−	4.56352i	0.235894	−	0.171387i	−0.463558	−	0.886066i	$-0.653428\pi$
$709$	6.28115	−	4.56352i	0.235894	−	0.171387i	0.699452	+	0.714680i	$0.253428\pi$
$710$		0			0
$711$	8.61803	+	6.26137i	0.323202	+	0.234820i
$712$	2.62866	+	3.61803i	0.0985130	+	0.135592i
$713$	15.5272	+	21.3713i	0.581497	+	0.800362i
$714$	−49.9058	−	36.2587i	−1.86768	−	1.35695i
$715$		0			0
$716$	9.04508	−	6.57164i	0.338031	−	0.245594i
$717$	−45.0427	−	14.6353i	−1.68215	−	0.546564i
$718$		−	3.09017i		−	0.115324i
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	−0.674028	−	0.738705i	$-0.735438\pi$
$719$	8.19098	−	25.2093i	0.305472	−	0.940147i	0.979501	−	0.201441i	$-0.0645625\pi$
$720$		0			0
$721$	18.4058	+	56.6471i	0.685466	+	2.10965i
$722$	17.3763	−	5.64590i	0.646678	−	0.210119i
$723$	−20.5927	+	28.3435i	−0.765852	+	1.05410i
$724$	21.4164			0.795935
$725$		0			0
$726$	−28.6525			−1.06339
$727$	16.8415	−	23.1803i	0.624617	−	0.859711i	−0.373062	−	0.927806i	$-0.621692\pi$
$727$	16.8415	−	23.1803i	0.624617	−	0.859711i	0.997679	+	0.0680952i	$0.0216922\pi$
$728$	−2.85317	+	0.927051i	−0.105745	+	0.0343588i
$729$	12.2254	+	37.6260i	0.452794	+	1.39356i
$730$		0			0
$731$	−4.28115	+	13.1760i	−0.158344	+	0.487333i
$732$		−	5.61803i		−	0.207649i
$733$	−37.8303	−	12.2918i	−1.39729	−	0.454008i	−0.488978	−	0.872296i	$-0.662630\pi$
$733$	−37.8303	−	12.2918i	−1.39729	−	0.454008i	−0.908314	+	0.418288i	$0.862630\pi$
$734$	25.5172	−	18.5393i	0.941858	−	0.684300i
$735$		0			0
$736$	−5.04508	−	3.66547i	−0.185964	−	0.135111i
$737$	0.799788	+	1.10081i	0.0294606	+	0.0405490i
$738$	−16.9273	−	23.2984i	−0.623101	−	0.857625i
$739$	24.2705	+	17.6336i	0.892805	+	0.648661i	0.936608	−	0.350379i	$-0.113947\pi$
$739$	24.2705	+	17.6336i	0.892805	+	0.648661i	−0.0438028	+	0.999040i	$0.513947\pi$
$740$		0			0
$741$	−1.80902	+	1.31433i	−0.0664559	+	0.0482830i
$742$	−4.35926	−	1.41641i	−0.160033	−	0.0519980i
$743$		−	18.2705i		−	0.670280i	−0.942168	−	0.335140i	$-0.891216\pi$
$743$		−	18.2705i		−	0.670280i	0.942168	−	0.335140i	$-0.108784\pi$
$744$	−3.42705	+	10.5474i	−0.125642	+	0.386686i
$745$		0			0
$746$	5.01722	+	15.4414i	0.183694	+	0.565350i
$747$	−49.3817	+	16.0451i	−1.80678	+	0.587059i
$748$	−1.08981	+	1.50000i	−0.0398475	+	0.0548454i
$749$	30.2705			1.10606
$750$		0			0
$751$	1.14590			0.0418144			0.0209072	−	0.999781i	$-0.493345\pi$
$751$	1.14590			0.0418144			0.0209072	+	0.999781i	$0.493345\pi$
$752$	−3.49396	+	4.80902i	−0.127411	+	0.175367i
$753$	57.7167	−	18.7533i	2.10331	−	0.683408i
$754$	−0.163119	−	0.502029i	−0.00594044	−	0.0182828i
$755$		0			0
$756$	2.07295	−	6.37988i	0.0753924	−	0.232034i
$757$		−	10.4164i		−	0.378591i	−0.981920	−	0.189295i	$-0.939380\pi$
$757$		−	10.4164i		−	0.378591i	0.981920	−	0.189295i	$-0.0606204\pi$
$758$	−0.502029	−	0.163119i	−0.0182345	−	0.00592475i
$759$	−3.11803	+	2.26538i	−0.113177	+	0.0822282i
$760$		0			0
$761$	30.6803	+	22.2906i	1.11216	+	0.808033i	0.983003	−	0.183591i	$-0.0587723\pi$
$761$	30.6803	+	22.2906i	1.11216	+	0.808033i	0.129159	+	0.991624i	$0.458772\pi$
$762$	−19.1926	−	26.4164i	−0.695276	−	0.956965i
$763$	−26.4503	−	36.4058i	−0.957566	−	1.31798i
$764$	14.2812	+	10.3759i	0.516674	+	0.375386i
$765$		0			0
$766$	−3.50000	+	2.54290i	−0.126460	+	0.0918787i
$767$	−4.25325	−	1.38197i	−0.153576	−	0.0498999i
$768$		−	2.61803i		−	0.0944702i
$769$	7.23607	−	22.2703i	0.260939	−	0.803089i	−0.731662	−	0.681668i	$-0.761255\pi$
$769$	7.23607	−	22.2703i	0.260939	−	0.803089i	0.992601	−	0.121421i	$-0.0387450\pi$
$770$		0			0
$771$	13.5451	+	41.6875i	0.487814	+	1.50134i
$772$	15.8374	−	5.14590i	0.570002	−	0.185205i
$773$	3.64522	−	5.01722i	0.131110	−	0.180457i	−0.738415	−	0.674347i	$-0.764425\pi$
$773$	3.64522	−	5.01722i	0.131110	−	0.180457i	0.869525	+	0.493890i	$0.164425\pi$
$774$	−6.79837			−0.244363
$775$		0			0
$776$	10.5623			0.379165
$777$	−33.8218	+	46.5517i	−1.21335	+	1.67003i
$778$	−31.5891	+	10.2639i	−1.13253	+	0.367980i
$779$	−1.97214	−	6.06961i	−0.0706591	−	0.217466i
$780$		0			0
$781$	0.218847	−	0.673542i	0.00783096	−	0.0241012i
$782$		−	48.9787i		−	1.75148i
$783$	1.12257	+	0.364745i	0.0401174	+	0.0130349i
$784$	1.61803	−	1.17557i	0.0577869	−	0.0419847i
$785$		0			0
$786$	−22.0623	−	16.0292i	−0.786936	−	0.571743i
$787$	9.06154	+	12.4721i	0.323009	+	0.444584i	0.939383	−	0.342870i	$-0.111399\pi$
$787$	9.06154	+	12.4721i	0.323009	+	0.444584i	−0.616374	+	0.787454i	$0.711399\pi$
$788$	−7.05342	−	9.70820i	−0.251268	−	0.345840i
$789$	−5.04508	−	3.66547i	−0.179610	−	0.130494i
$790$		0			0
$791$	19.9894	−	14.5231i	0.710740	−	0.516383i
$792$	−0.865300	−	0.281153i	−0.0307471	−	0.00999034i
$793$		−	2.14590i		−	0.0762031i
$794$	−1.78115	+	5.48183i	−0.0632108	+	0.194543i
$795$		0			0
$796$	−5.42705	−	16.7027i	−0.192357	−	0.592013i
$797$	3.21644	−	1.04508i	0.113932	−	0.0370188i	−0.251496	−	0.967858i	$-0.580923\pi$
$797$	3.21644	−	1.04508i	0.113932	−	0.0370188i	0.365428	+	0.930840i	$0.380923\pi$
$798$	3.94298	−	5.42705i	0.139580	−	0.192116i
$799$	−46.6869			−1.65166
$800$		0			0
$801$	−17.2361			−0.609007
$802$	4.80828	−	6.61803i	0.169786	−	0.233691i
$803$	−1.28157	+	0.416408i	−0.0452257	+	0.0146947i
$804$	−4.66312	−	14.3516i	−0.164456	−	0.506142i
$805$		0			0
$806$	−1.30902	+	4.02874i	−0.0461082	+	0.141906i
$807$			34.2705i			1.20638i
$808$	1.53884	+	0.500000i	0.0541363	+	0.0175899i
$809$	1.80902	−	1.31433i	0.0636017	−	0.0462093i	−0.555530	−	0.831496i	$-0.687485\pi$
$809$	1.80902	−	1.31433i	0.0636017	−	0.0462093i	0.619132	+	0.785287i	$0.287485\pi$
$810$		0			0
$811$	−18.6525	−	13.5518i	−0.654977	−	0.475869i	0.209986	−	0.977704i	$-0.432658\pi$
$811$	−18.6525	−	13.5518i	−0.654977	−	0.475869i	−0.864963	+	0.501836i	$0.832658\pi$
$812$	0.930812	+	1.28115i	0.0326651	+	0.0449597i
$813$	−14.6291	−	20.1353i	−0.513066	−	0.706174i
$814$	1.39919	+	1.01657i	0.0490415	+	0.0356307i
$815$		0			0
$816$	16.6353	−	12.0862i	0.582350	−	0.423102i
$817$	−1.43284	−	0.465558i	−0.0501287	−	0.0162878i
$818$		−	6.70820i		−	0.234547i
$819$	3.57295	−	10.9964i	0.124849	−	0.384246i
$820$		0			0
$821$	−9.31966	−	28.6830i	−0.325258	−	1.00104i	−0.971324	−	0.237760i	$-0.923587\pi$
$821$	−9.31966	−	28.6830i	−0.325258	−	1.00104i	0.646065	−	0.763282i	$-0.276413\pi$
$822$	−15.1639	+	4.92705i	−0.528902	+	0.171851i
$823$	19.2986	−	26.5623i	0.672708	−	0.925904i	−0.327109	−	0.944986i	$-0.606075\pi$
$823$	19.2986	−	26.5623i	0.672708	−	0.925904i	0.999818	+	0.0190827i	$0.00607458\pi$
$824$	−19.8541			−0.691650
$825$		0			0
$826$	13.4164			0.466817
$827$	−14.1271	+	19.4443i	−0.491247	+	0.676144i	−0.980617	−	0.195932i	$-0.937227\pi$
$827$	−14.1271	+	19.4443i	−0.491247	+	0.676144i	0.489370	+	0.872076i	$0.337227\pi$
$828$	22.8581	−	7.42705i	0.794374	−	0.258108i
$829$	−8.21478	−	25.2825i	−0.285311	−	0.878097i	−0.986305	−	0.164930i	$-0.947260\pi$
$829$	−8.21478	−	25.2825i	−0.285311	−	0.878097i	0.700994	−	0.713167i	$-0.252740\pi$
$830$		0			0
$831$	−11.0902	+	34.1320i	−0.384714	+	1.18403i
$832$		−	1.00000i		−	0.0346688i
$833$	14.9394	+	4.85410i	0.517619	+	0.168185i
$834$	21.8713	−	15.8904i	0.757342	−	0.550241i
$835$		0			0
$836$	−0.163119	−	0.118513i	−0.00564159	−	0.00409885i
$837$	−5.56758	−	7.66312i	−0.192444	−	0.264876i
$838$	16.0090	+	22.0344i	0.553020	+	0.761167i
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	0.881628	−	0.471945i	$-0.156448\pi$
$839$	20.4271	+	14.8411i	0.705220	+	0.512372i	−0.176408	+	0.984317i	$0.556448\pi$
$840$		0			0
$841$	23.2361	−	16.8820i	0.801244	−	0.582138i
$842$	−11.6699	−	3.79180i	−0.402173	−	0.130674i
$843$			50.2148i			1.72949i
$844$	−3.48278	+	10.7189i	−0.119882	+	0.368959i
$845$		0			0
$846$	−7.07953	−	21.7885i	−0.243399	−	0.749106i
$847$	31.2259	−	10.1459i	1.07293	−	0.348617i
$848$	0.898056	−	1.23607i	0.0308394	−	0.0424467i
$849$	−67.3050			−2.30990
$850$		0			0
$851$	−45.6869			−1.56613
$852$	−4.61653	+	6.35410i	−0.158160	+	0.217688i
$853$	23.6377	−	7.68034i	0.809338	−	0.262970i	0.125021	−	0.992154i	$-0.460100\pi$
$853$	23.6377	−	7.68034i	0.809338	−	0.262970i	0.684317	+	0.729184i	$0.260100\pi$
$854$	1.98936	+	6.12261i	0.0680744	+	0.209511i
$855$		0			0
$856$	−3.11803	+	9.59632i	−0.106572	+	0.327996i
$857$		−	35.3394i		−	1.20717i	−0.797298	−	0.603585i	$-0.793738\pi$
$857$		−	35.3394i		−	1.20717i	0.797298	−	0.603585i	$-0.206262\pi$
$858$	−0.587785	−	0.190983i	−0.0200667	−	0.00652005i
$859$	−31.8713	+	23.1559i	−1.08744	+	0.790068i	−0.978964	−	0.204031i	$-0.934596\pi$
$859$	−31.8713	+	23.1559i	−1.08744	+	0.790068i	−0.108471	+	0.994100i	$0.534596\pi$
$860$		0			0
$861$	47.4787	+	34.4953i	1.61807	+	1.17560i
$862$	18.8496	+	25.9443i	0.642020	+	0.883665i
$863$	3.97574	+	5.47214i	0.135336	+	0.186274i	0.871306	−	0.490740i	$-0.163274\pi$
$863$	3.97574	+	5.47214i	0.135336	+	0.186274i	−0.735970	+	0.677014i	$0.763274\pi$
$864$	1.80902	+	1.31433i	0.0615440	+	0.0447143i
$865$		0			0
$866$	18.8992	−	13.7311i	0.642221	−	0.466601i
$867$	111.266	+	36.1525i	3.77879	+	1.22780i
$868$		−	12.7082i		−	0.431345i
$869$	−0.201626	+	0.620541i	−0.00683970	+	0.0210504i
$870$		0			0
$871$	−1.78115	−	5.48183i	−0.0603521	−	0.185745i
$872$	14.2658	−	4.63525i	0.483103	−	0.156970i
$873$	−23.9277	+	32.9336i	−0.809829	+	1.11463i
$874$	5.32624			0.180163
$875$		0			0
$876$	14.9443			0.504920
$877$	−14.4374	+	19.8713i	−0.487515	+	0.671007i	−0.979927	−	0.199355i	$-0.936115\pi$
$877$	−14.4374	+	19.8713i	−0.487515	+	0.671007i	0.492412	+	0.870362i	$0.336115\pi$
$878$	−5.37582	+	1.74671i	−0.181425	+	0.0589486i
$879$	−9.35410	−	28.7890i	−0.315506	−	0.971028i
$880$		0			0
$881$	4.88854	−	15.0454i	0.164699	−	0.506892i	−0.834315	−	0.551288i	$-0.814136\pi$
$881$	4.88854	−	15.0454i	0.164699	−	0.506892i	0.999014	+	0.0443963i	$0.0141364\pi$
$882$			7.70820i			0.259549i
$883$	17.7723	+	5.77458i	0.598086	+	0.194330i	0.592387	−	0.805654i	$-0.298186\pi$
$883$	17.7723	+	5.77458i	0.598086	+	0.194330i	0.00569940	+	0.999984i	$0.498186\pi$
$884$	6.35410	−	4.61653i	0.213712	−	0.155271i
$885$		0			0
$886$	−6.00000	−	4.35926i	−0.201574	−	0.146452i
$887$	6.35964	+	8.75329i	0.213536	+	0.293907i	0.902326	−	0.431054i	$-0.141858\pi$
$887$	6.35964	+	8.75329i	0.213536	+	0.293907i	−0.688791	+	0.724960i	$0.741858\pi$
$888$	−11.2739	−	15.5172i	−0.378328	−	0.520724i
$889$	30.2705	+	21.9928i	1.01524	+	0.737615i
$890$		0			0
$891$	−1.09017	+	0.792055i	−0.0365221	+	0.0265348i
$892$	8.55951	+	2.78115i	0.286594	+	0.0931199i
$893$		−	5.07701i		−	0.169896i
$894$	1.80902	−	5.56758i	0.0605026	−	0.186208i
$895$		0			0
$896$	0.927051	+	2.85317i	0.0309706	+	0.0953177i
$897$	15.5272	−	5.04508i	0.518437	−	0.168450i
$898$	−8.19624	+	11.2812i	−0.273512	+	0.376457i
$899$	2.23607			0.0745770
$900$		0			0
$901$	12.0000			0.399778
$902$	1.03681	−	1.42705i	0.0345221	−	0.0475156i
$903$	13.1760	−	4.28115i	0.438471	−	0.142468i
$904$	2.54508	+	7.83297i	0.0846483	+	0.260521i
$905$		0			0
$906$	3.00000	−	9.23305i	0.0996683	−	0.306748i
$907$		−	23.3820i		−	0.776385i	−0.921578	−	0.388193i	$-0.873099\pi$
$907$		−	23.3820i		−	0.776385i	0.921578	−	0.388193i	$-0.126901\pi$
$908$	−14.6089	−	4.74671i	−0.484813	−	0.157525i
$909$	−5.04508	+	3.66547i	−0.167335	+	0.121576i
$910$		0			0
$911$	−8.42705	−	6.12261i	−0.279201	−	0.202851i	0.439368	−	0.898307i	$-0.355202\pi$
$911$	−8.42705	−	6.12261i	−0.279201	−	0.202851i	−0.718569	+	0.695456i	$0.755202\pi$
$912$	1.31433	+	1.80902i	0.0435217	+	0.0599025i
$913$	−1.86936	−	2.57295i	−0.0618667	−	0.0851522i
$914$	9.07295	+	6.59188i	0.300106	+	0.218040i
$915$		0			0
$916$	−14.2082	+	10.3229i	−0.469452	+	0.341077i
$917$	29.7198	+	9.65654i	0.981434	+	0.318887i
$918$			17.5623i			0.579642i
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	0.730992	+	0.682386i	$0.239058\pi$
$919$	−7.92705	+	24.3970i	−0.261489	+	0.804781i	−0.992481	+	0.122395i	$0.960942\pi$
$920$		0			0
$921$	−13.8541	−	42.6385i	−0.456508	−	1.40499i
$922$	−26.8011	+	8.70820i	−0.882647	+	0.286789i
$923$	−1.76336	+	2.42705i	−0.0580416	+	0.0798874i
$924$	1.85410			0.0609955
$925$		0			0
$926$	−11.9787			−0.393645
$927$	44.9772	−	61.9058i	1.47724	−	2.03325i
$928$	−0.502029	+	0.163119i	−0.0164799	+	0.00535464i
$929$	5.28773	+	16.2740i	0.173485	+	0.533931i	0.999561	−	0.0296271i	$-0.00943197\pi$
$929$	5.28773	+	16.2740i	0.173485	+	0.533931i	−0.826076	+	0.563558i	$0.809432\pi$
$930$		0			0
$931$	−0.527864	+	1.62460i	−0.0173000	+	0.0532441i
$932$		−	27.7082i		−	0.907612i
$933$	52.5124	+	17.0623i	1.71918	+	0.558595i
$934$	−2.57295	+	1.86936i	−0.0841895	+	0.0611672i
$935$		0			0
$936$	3.11803	+	2.26538i	0.101916	+	0.0740464i
$937$	−13.4738	−	18.5451i	−0.440170	−	0.605842i	0.530080	−	0.847948i	$-0.322162\pi$
$937$	−13.4738	−	18.5451i	−0.440170	−	0.605842i	−0.970250	+	0.242106i	$0.922162\pi$
$938$	10.1639	+	13.9894i	0.331862	+	0.456769i
$939$	−7.54508	−	5.48183i	−0.246225	−	0.178893i
$940$		0			0
$941$	9.39919	−	6.82891i	0.306405	−	0.222616i	−0.423948	−	0.905687i	$-0.639356\pi$
$941$	9.39919	−	6.82891i	0.306405	−	0.222616i	0.730352	+	0.683071i	$0.239356\pi$
$942$	38.7486	+	12.5902i	1.26250	+	0.410210i
$943$			46.5967i			1.51740i
$944$	−1.38197	+	4.25325i	−0.0449792	+	0.138432i
$945$		0			0
$946$	−0.128677	−	0.396027i	−0.00418365	−	0.0128760i
$947$	−39.5811	+	12.8607i	−1.28621	+	0.417916i	−0.870764	−	0.491701i	$-0.836375\pi$
$947$	−39.5811	+	12.8607i	−1.28621	+	0.417916i	−0.415449	+	0.909617i	$0.636375\pi$
$948$	4.25325	−	5.85410i	0.138139	−	0.190132i
$949$	5.70820			0.185296
$950$		0			0
$951$	−27.7984			−0.901424
$952$	−13.8496	+	19.0623i	−0.448867	+	0.617813i
$953$	−40.3076	+	13.0967i	−1.30569	+	0.424245i	−0.877558	−	0.479470i	$-0.840829\pi$
$953$	−40.3076	+	13.0967i	−1.30569	+	0.424245i	−0.428134	+	0.903715i	$0.640829\pi$
$954$	1.81966	+	5.60034i	0.0589137	+	0.181318i
$955$		0			0
$956$	−5.59017	+	17.2048i	−0.180799	+	0.556442i
$957$			0.326238i			0.0105458i
$958$	37.8505	+	12.2984i	1.22289	+	0.397342i
$959$	14.7812	−	10.7391i	0.477308	−	0.346785i
$960$		0			0
$961$	10.5623	+	7.67396i	0.340720	+	0.247547i
$962$	−4.30625	−	5.92705i	−0.138839	−	0.191096i
$963$	−22.8581	−	31.4615i	−0.736592	−	1.01383i
$964$	10.8262	+	7.86572i	0.348690	+	0.253338i
$965$		0			0
$966$	−39.6246	+	28.7890i	−1.27490	+	0.926270i
$967$	−25.7970	−	8.38197i	−0.829577	−	0.269546i	−0.136710	−	0.990611i	$-0.543653\pi$
$967$	−25.7970	−	8.38197i	−0.829577	−	0.269546i	−0.692867	+	0.721065i	$0.743653\pi$
$968$			10.9443i			0.351762i
$969$	−5.42705	+	16.7027i	−0.174342	+	0.536569i
$970$		0			0
$971$	−16.0902	−	49.5205i	−0.516358	−	1.58919i	−0.780797	−	0.624785i	$-0.785187\pi$
$971$	−16.0902	−	49.5205i	−0.516358	−	1.58919i	0.264439	−	0.964402i	$-0.414813\pi$
$972$	20.5927	−	6.69098i	0.660512	−	0.214613i
$973$	−18.2088	+	25.0623i	−0.583748	+	0.803461i
$974$	−18.1246			−0.580750
$975$		0			0
$976$	−2.14590			−0.0686885
$977$	15.2901	−	21.0451i	0.489175	−	0.673292i	−0.491060	−	0.871126i	$-0.663391\pi$
$977$	15.2901	−	21.0451i	0.489175	−	0.673292i	0.980236	+	0.197834i	$0.0633906\pi$
$978$	12.0862	−	3.92705i	0.386475	−	0.125573i
$979$	−0.326238	−	1.00406i	−0.0104266	−	0.0320898i
$980$		0			0
$981$	−17.8647	+	54.9820i	−0.570377	+	1.75544i
$982$			14.7639i			0.471136i
$983$	−44.2101	−	14.3647i	−1.41008	−	0.458164i	−0.497647	−	0.867380i	$-0.665802\pi$
$983$	−44.2101	−	14.3647i	−1.41008	−	0.458164i	−0.912438	+	0.409216i	$0.865802\pi$
$984$	−15.8262	+	11.4984i	−0.504522	+	0.366557i
$985$		0			0
$986$	−3.35410	−	2.43690i	−0.106816	−	0.0776066i
$987$	27.4419	+	37.7705i	0.873485	+	1.20225i
$988$	0.502029	+	0.690983i	0.0159717	+	0.0219831i
$989$	8.89919	+	6.46564i	0.282978	+	0.205595i
$990$		0			0
$991$	−42.4336	+	30.8298i	−1.34795	+	0.979342i	−0.348838	+	0.937183i	$0.613424\pi$
$991$	−42.4336	+	30.8298i	−1.34795	+	0.979342i	−0.999111	+	0.0421589i	$0.986576\pi$
$992$	4.02874	+	1.30902i	0.127913	+	0.0415613i
$993$		−	11.9443i		−	0.379040i
$994$	2.78115	−	8.55951i	0.0882128	−	0.271491i
$995$		0			0
$996$	10.8992	+	33.5442i	0.345354	+	1.06289i
$997$	−50.6430	+	16.4549i	−1.60388	+	0.521132i	−0.968063	−	0.250707i	$-0.919337\pi$
$997$	−50.6430	+	16.4549i	−1.60388	+	0.521132i	−0.635818	+	0.771839i	$0.719337\pi$
$998$	−24.0134	+	33.0517i	−0.760132	+	1.04623i
$999$	16.3820			0.518302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.b.49.2		8
5.2	odd	4		50.2.d.a.41.1	yes	4
5.3	odd	4		250.2.d.a.201.1		4
5.4	even	2	inner	250.2.e.b.49.1		8
15.2	even	4		450.2.h.a.91.1		4
20.7	even	4		400.2.u.c.241.1		4
25.2	odd	20		50.2.d.a.11.1	✓	4
25.6	even	5		1250.2.b.b.1249.3		4
25.8	odd	20		1250.2.a.d.1.2		2
25.11	even	5	inner	250.2.e.b.199.1		8
25.14	even	10	inner	250.2.e.b.199.2		8
25.17	odd	20		1250.2.a.a.1.1		2
25.19	even	10		1250.2.b.b.1249.2		4
25.23	odd	20		250.2.d.a.51.1		4
75.2	even	20		450.2.h.a.361.1		4
100.27	even	20		400.2.u.c.161.1		4
100.67	even	20		10000.2.a.n.1.2		2
100.83	even	20		10000.2.a.a.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.11.1	✓	4	25.2	odd	20
50.2.d.a.41.1	yes	4	5.2	odd	4
250.2.d.a.51.1		4	25.23	odd	20
250.2.d.a.201.1		4	5.3	odd	4
250.2.e.b.49.1		8	5.4	even	2	inner
250.2.e.b.49.2		8	1.1	even	1	trivial
250.2.e.b.199.1		8	25.11	even	5	inner
250.2.e.b.199.2		8	25.14	even	10	inner
400.2.u.c.161.1		4	100.27	even	20
400.2.u.c.241.1		4	20.7	even	4
450.2.h.a.91.1		4	15.2	even	4
450.2.h.a.361.1		4	75.2	even	20
1250.2.a.a.1.1		2	25.17	odd	20
1250.2.a.d.1.2		2	25.8	odd	20
1250.2.b.b.1249.2		4	25.19	even	10
1250.2.b.b.1249.3		4	25.6	even	5
10000.2.a.a.1.1		2	100.83	even	20
10000.2.a.n.1.2		2	100.67	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:	\( N \)	\(=\)	\( 250 = 2 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	250.e (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(2.48990 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{6} +3.00000i q^{7} +(-0.951057 - 0.309017i) q^{8} +(3.11803 - 2.26538i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(2.48990 - 0.809017i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(0.809017 - 2.48990i) q^{6} +3.00000i q^{7} +(-0.951057 - 0.309017i) q^{8} +(3.11803 - 2.26538i) q^{9} +(0.190983 + 0.138757i) q^{11} +(-1.53884 - 2.11803i) q^{12} +(-0.587785 - 0.809017i) q^{13} +(2.42705 + 1.76336i) q^{14} +(-0.809017 + 0.587785i) q^{16} +(-7.46969 - 2.42705i) q^{17} -3.85410i q^{18} +(0.263932 - 0.812299i) q^{19} +(2.42705 + 7.46969i) q^{21} +(0.224514 - 0.0729490i) q^{22} +(-3.66547 + 5.04508i) q^{23} -2.61803 q^{24} -1.00000 q^{26} +(1.31433 - 1.80902i) q^{27} +(2.85317 - 0.927051i) q^{28} +(0.163119 + 0.502029i) q^{29} +(1.30902 - 4.02874i) q^{31} +1.00000i q^{32} +(0.587785 + 0.190983i) q^{33} +(-6.35410 + 4.61653i) q^{34} +(-3.11803 - 2.26538i) q^{36} +(4.30625 + 5.92705i) q^{37} +(-0.502029 - 0.690983i) q^{38} +(-2.11803 - 1.53884i) q^{39} +(6.04508 - 4.39201i) q^{41} +(7.46969 + 2.42705i) q^{42} -1.76393i q^{43} +(0.0729490 - 0.224514i) q^{44} +(1.92705 + 5.93085i) q^{46} +(5.65334 - 1.83688i) q^{47} +(-1.53884 + 2.11803i) q^{48} -2.00000 q^{49} -20.5623 q^{51} +(-0.587785 + 0.809017i) q^{52} +(-1.45309 + 0.472136i) q^{53} +(-0.690983 - 2.12663i) q^{54} +(0.927051 - 2.85317i) q^{56} -2.23607i q^{57} +(0.502029 + 0.163119i) q^{58} +(3.61803 - 2.62866i) q^{59} +(1.73607 + 1.26133i) q^{61} +(-2.48990 - 3.42705i) q^{62} +(6.79615 + 9.35410i) q^{63} +(0.809017 + 0.587785i) q^{64} +(0.500000 - 0.363271i) q^{66} +(5.48183 + 1.78115i) q^{67} +7.85410i q^{68} +(-5.04508 + 15.5272i) q^{69} +(-0.927051 - 2.85317i) q^{71} +(-3.66547 + 1.19098i) q^{72} +(-3.35520 + 4.61803i) q^{73} +7.32624 q^{74} -0.854102 q^{76} +(-0.416272 + 0.572949i) q^{77} +(-2.48990 + 0.809017i) q^{78} +(0.854102 + 2.62866i) q^{79} +(-1.76393 + 5.42882i) q^{81} -7.47214i q^{82} +(-12.8128 - 4.16312i) q^{83} +(6.35410 - 4.61653i) q^{84} +(-1.42705 - 1.03681i) q^{86} +(0.812299 + 1.11803i) q^{87} +(-0.138757 - 0.190983i) q^{88} +(-3.61803 - 2.62866i) q^{89} +(2.42705 - 1.76336i) q^{91} +(5.93085 + 1.92705i) q^{92} -11.0902i q^{93} +(1.83688 - 5.65334i) q^{94} +(0.809017 + 2.48990i) q^{96} +(-10.0453 + 3.26393i) q^{97} +(-1.17557 + 1.61803i) q^{98} +0.909830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9}+O(q^{10}) \) 8 * q + 2 * q^4 + 2 * q^6 + 16 * q^9	\( 8 q + 2 q^{4} + 2 q^{6} + 16 q^{9} + 6 q^{11} + 6 q^{14} - 2 q^{16} + 20 q^{19} + 6 q^{21} - 12 q^{24} - 8 q^{26} - 30 q^{29} + 6 q^{31} - 24 q^{34} - 16 q^{36} - 8 q^{39} + 26 q^{41} + 14 q^{44} + 2 q^{46} - 16 q^{49} - 84 q^{51} - 10 q^{54} - 6 q^{56} + 20 q^{59} - 4 q^{61} + 2 q^{64} + 4 q^{66} - 18 q^{69} + 6 q^{71} - 4 q^{74} + 20 q^{76} - 20 q^{79} - 32 q^{81} + 24 q^{84} + 2 q^{86} - 20 q^{89} + 6 q^{91} + 46 q^{94} + 2 q^{96} + 52 q^{99}+O(q^{100}) \) 8 * q + 2 * q^4 + 2 * q^6 + 16 * q^9 + 6 * q^11 + 6 * q^14 - 2 * q^16 + 20 * q^19 + 6 * q^21 - 12 * q^24 - 8 * q^26 - 30 * q^29 + 6 * q^31 - 24 * q^34 - 16 * q^36 - 8 * q^39 + 26 * q^41 + 14 * q^44 + 2 * q^46 - 16 * q^49 - 84 * q^51 - 10 * q^54 - 6 * q^56 + 20 * q^59 - 4 * q^61 + 2 * q^64 + 4 * q^66 - 18 * q^69 + 6 * q^71 - 4 * q^74 + 20 * q^76 - 20 * q^79 - 32 * q^81 + 24 * q^84 + 2 * q^86 - 20 * q^89 + 6 * q^91 + 46 * q^94 + 2 * q^96 + 52 * q^99

Introduction

L-functions

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