LMFDB - Embedded newform 375.2.g.c.226.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (of order $5$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			226.2
Root			$0.199632 + 0.145041i$ of defining polynomial
Character	$\chi$	$=$	375.226
Dual form			375.2.g.c.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0762527 + 0.234682i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.56877 + 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(-0.0762527 + 0.234682i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.56877 + 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.794084 - 2.44394i) q^{11} +(-0.599218 - 1.84420i) q^{12} +(1.44659 + 4.45215i) q^{13} +(-0.0950687 + 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(4.72397 - 3.43216i) q^{17} -0.246759 q^{18} +(-3.37244 + 2.45022i) q^{19} +(-1.00865 - 0.732827i) q^{21} +(0.512997 + 0.372714i) q^{22} +(-0.496117 + 1.52689i) q^{23} +0.972011 q^{24} -1.15514 q^{26} +(0.309017 - 0.951057i) q^{27} +(1.95588 + 1.42103i) q^{28} +(2.60158 + 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182 q^{32} +(-2.07894 + 1.51044i) q^{33} +(0.445250 + 1.37034i) q^{34} +(-0.599218 + 1.84420i) q^{36} +(0.394857 + 1.21524i) q^{37} +(-0.317865 - 0.978287i) q^{38} +(1.44659 - 4.45215i) q^{39} +(2.68719 + 8.27031i) q^{41} +(0.248893 - 0.180832i) q^{42} +3.88086 q^{43} +(4.03129 - 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(-2.59656 - 1.88651i) q^{47} +(1.12432 - 3.46029i) q^{48} -5.44559 q^{49} -5.83914 q^{51} +(-2.80510 + 8.63320i) q^{52} +(-10.7877 - 7.83770i) q^{53} +(0.199632 + 0.145041i) q^{54} +(-0.980418 + 0.712315i) q^{56} +4.16857 q^{57} +(-0.641964 + 0.466414i) q^{58} +(-1.97548 - 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(0.701000 + 2.15746i) q^{62} +(0.385270 + 1.18574i) q^{63} +(-2.03194 + 6.25366i) q^{64} +(-0.195947 - 0.603064i) q^{66} +(-8.19034 + 5.95063i) q^{67} +11.3227 q^{68} +(1.29885 - 0.943670i) q^{69} +(-11.2284 - 8.15794i) q^{71} +(-0.786373 - 0.571334i) q^{72} +(3.51704 - 10.8243i) q^{73} -0.315305 q^{74} -8.08332 q^{76} +(0.990032 - 3.04700i) q^{77} +(0.934531 + 0.678976i) q^{78} +(-9.29008 - 6.74964i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.14580 q^{82} +(-2.29137 + 1.66478i) q^{83} +(-0.747080 - 2.29928i) q^{84} +(-0.295926 + 0.910766i) q^{86} +(-0.993717 - 3.05835i) q^{87} +(0.771858 + 2.37554i) q^{88} +(-0.426682 + 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-2.51861 + 1.82988i) q^{92} -9.19312 q^{93} +(0.640724 - 0.465513i) q^{94} +(2.29908 + 1.67038i) q^{96} +(0.0246815 + 0.0179322i) q^{97} +(0.415241 - 1.27798i) q^{98} +2.56971 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.0762527	+	0.234682i	−0.0539188	+	0.165945i	−0.974390	−	0.224866i	$-0.927805\pi$
$2$	−0.0762527	+	0.234682i	−0.0539188	+	0.165945i	0.920471	+	0.390811i	$0.127805\pi$
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$3$	−0.809017	−	0.587785i	−0.467086	−	0.339358i
$4$	1.56877	+	1.13978i	0.784386	+	0.569890i
$5$		0			0
$5$		0			0
$6$	0.199632	−	0.145041i	0.0814995	−	0.0592129i
$7$	1.24676			0.471231			0.235615	−	0.971846i	$-0.424289\pi$
$7$	1.24676			0.471231			0.235615	+	0.971846i	$0.424289\pi$
$8$	−0.786373	+	0.571334i	−0.278025	+	0.201997i
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	0.794084	−	2.44394i	0.239425	−	0.736876i	−0.757078	−	0.653324i	$-0.773374\pi$
$11$	0.794084	−	2.44394i	0.239425	−	0.736876i	0.996503	−	0.0835513i	$-0.0266262\pi$
$12$	−0.599218	−	1.84420i	−0.172979	−	0.532376i
$13$	1.44659	+	4.45215i	0.401212	+	1.23480i	0.924017	+	0.382351i	$0.124885\pi$
$13$	1.44659	+	4.45215i	0.401212	+	1.23480i	−0.522805	+	0.852452i	$0.675115\pi$
$14$	−0.0950687	+	0.292592i	−0.0254082	+	0.0781984i
$15$		0			0
$16$	1.12432	+	3.46029i	0.281079	+	0.865073i
$17$	4.72397	−	3.43216i	1.14573	−	0.832422i	0.157823	−	0.987467i	$-0.449553\pi$
$17$	4.72397	−	3.43216i	1.14573	−	0.832422i	0.987907	+	0.155046i	$0.0495526\pi$
$18$	−0.246759			−0.0581616
$19$	−3.37244	+	2.45022i	−0.773692	+	0.562120i	−0.903079	−	0.429474i	$-0.858699\pi$
$19$	−3.37244	+	2.45022i	−0.773692	+	0.562120i	0.129387	+	0.991594i	$0.458699\pi$
$20$		0			0
$21$	−1.00865	−	0.732827i	−0.220105	−	0.159916i
$22$	0.512997	+	0.372714i	0.109371	+	0.0794629i
$23$	−0.496117	+	1.52689i	−0.103447	+	0.318379i	−0.989363	−	0.145468i	$-0.953531\pi$
$23$	−0.496117	+	1.52689i	−0.103447	+	0.318379i	0.885915	+	0.463847i	$0.153531\pi$
$24$	0.972011			0.198411
$25$		0			0
$26$	−1.15514			−0.226542
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	1.95588	+	1.42103i	0.369627	+	0.268550i
$29$	2.60158	+	1.89016i	0.483102	+	0.350994i	0.802525	−	0.596618i	$-0.203489\pi$
$29$	2.60158	+	1.89016i	0.483102	+	0.350994i	−0.319423	+	0.947612i	$0.603489\pi$
$30$		0			0
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.336207	−	0.941788i	$-0.390856\pi$
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.999587	−	0.0287236i	$-0.00914425\pi$
$32$	−2.84182			−0.502368
$33$	−2.07894	+	1.51044i	−0.361897	+	0.262934i
$34$	0.445250	+	1.37034i	0.0763598	+	0.235011i
$35$		0			0
$36$	−0.599218	+	1.84420i	−0.0998697	+	0.307367i
$37$	0.394857	+	1.21524i	0.0649141	+	0.199785i	0.978253	−	0.207415i	$-0.0665051\pi$
$37$	0.394857	+	1.21524i	0.0649141	+	0.199785i	−0.913339	+	0.407200i	$0.866505\pi$
$38$	−0.317865	−	0.978287i	−0.0515645	−	0.158699i
$39$	1.44659	−	4.45215i	0.231640	−	0.712914i
$40$		0			0
$41$	2.68719	+	8.27031i	0.419668	+	1.29161i	0.908008	+	0.418953i	$0.137603\pi$
$41$	2.68719	+	8.27031i	0.419668	+	1.29161i	−0.488340	+	0.872654i	$0.662397\pi$
$42$	0.248893	−	0.180832i	0.0384051	−	0.0279029i
$43$	3.88086			0.591825			0.295913	−	0.955215i	$-0.404376\pi$
$43$	3.88086			0.591825			0.295913	+	0.955215i	$0.404376\pi$
$44$	4.03129	−	2.92891i	0.607740	−	0.441549i
$45$		0			0
$46$	−0.320503	−	0.232859i	−0.0472556	−	0.0343332i
$47$	−2.59656	−	1.88651i	−0.378747	−	0.275176i	0.382082	−	0.924129i	$-0.375207\pi$
$47$	−2.59656	−	1.88651i	−0.378747	−	0.275176i	−0.760829	+	0.648953i	$0.775207\pi$
$48$	1.12432	−	3.46029i	0.162281	−	0.499450i
$49$	−5.44559			−0.777942
$50$		0			0
$51$	−5.83914			−0.817643
$52$	−2.80510	+	8.63320i	−0.388997	+	1.19721i
$53$	−10.7877	−	7.83770i	−1.48180	−	1.07659i	−0.976971	−	0.213371i	$-0.931556\pi$
$53$	−10.7877	−	7.83770i	−1.48180	−	1.07659i	−0.504829	−	0.863219i	$-0.668444\pi$
$54$	0.199632	+	0.145041i	0.0271665	+	0.0197376i
$55$		0			0
$56$	−0.980418	+	0.712315i	−0.131014	+	0.0951871i
$57$	4.16857			0.552141
$58$	−0.641964	+	0.466414i	−0.0842940	+	0.0612432i
$59$	−1.97548	−	6.07990i	−0.257186	−	0.791536i	−0.993391	−	0.114778i	$-0.963384\pi$
$59$	−1.97548	−	6.07990i	−0.257186	−	0.791536i	0.736206	−	0.676758i	$-0.236616\pi$
$60$		0			0
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	−0.846366	−	0.532602i	$-0.821214\pi$
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	0.997780	+	0.0665973i	$0.0212143\pi$
$62$	0.701000	+	2.15746i	0.0890271	+	0.273997i
$63$	0.385270	+	1.18574i	0.0485394	+	0.149389i
$64$	−2.03194	+	6.25366i	−0.253992	+	0.781708i
$65$		0			0
$66$	−0.195947	−	0.603064i	−0.0241195	−	0.0742321i
$67$	−8.19034	+	5.95063i	−1.00061	+	0.726985i	−0.962219	−	0.272277i	$-0.912223\pi$
$67$	−8.19034	+	5.95063i	−1.00061	+	0.726985i	−0.0383907	+	0.999263i	$0.512223\pi$
$68$	11.3227			1.37308
$69$	1.29885	−	0.943670i	0.156363	−	0.113605i
$70$		0			0
$71$	−11.2284	−	8.15794i	−1.33257	−	0.968169i	−0.999682	−	0.0252028i	$-0.991977\pi$
$71$	−11.2284	−	8.15794i	−1.33257	−	0.968169i	−0.332888	−	0.942966i	$-0.608023\pi$
$72$	−0.786373	−	0.571334i	−0.0926750	−	0.0673323i
$73$	3.51704	−	10.8243i	0.411638	−	1.26689i	−0.503585	−	0.863946i	$-0.667986\pi$
$73$	3.51704	−	10.8243i	0.411638	−	1.26689i	0.915223	−	0.402947i	$-0.132014\pi$
$74$	−0.315305			−0.0366534
$75$		0			0
$76$	−8.08332			−0.927220
$77$	0.990032	−	3.04700i	0.112825	−	0.347238i
$78$	0.934531	+	0.678976i	0.105815	+	0.0768789i
$79$	−9.29008	−	6.74964i	−1.04522	−	0.759394i	−0.0739188	−	0.997264i	$-0.523551\pi$
$79$	−9.29008	−	6.74964i	−1.04522	−	0.759394i	−0.971297	+	0.237871i	$0.923551\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	−2.14580			−0.236964
$83$	−2.29137	+	1.66478i	−0.251511	+	0.182733i	−0.706396	−	0.707817i	$-0.749680\pi$
$83$	−2.29137	+	1.66478i	−0.251511	+	0.182733i	0.454885	+	0.890550i	$0.349680\pi$
$84$	−0.747080	−	2.29928i	−0.0815131	−	0.250872i
$85$		0			0
$86$	−0.295926	+	0.910766i	−0.0319105	+	0.0982105i
$87$	−0.993717	−	3.05835i	−0.106538	−	0.327889i
$88$	0.771858	+	2.37554i	0.0822804	+	0.253233i
$89$	−0.426682	+	1.31319i	−0.0452282	+	0.139198i	−0.971121	−	0.238589i	$-0.923315\pi$
$89$	−0.426682	+	1.31319i	−0.0452282	+	0.139198i	0.925892	+	0.377788i	$0.123315\pi$
$90$		0			0
$91$	1.80355	+	5.55075i	0.189063	+	0.581877i
$92$	−2.51861	+	1.82988i	−0.262584	+	0.190778i
$93$	−9.19312			−0.953282
$94$	0.640724	−	0.465513i	0.0660857	−	0.0480140i
$95$		0			0
$96$	2.29908	+	1.67038i	0.234649	+	0.170483i
$97$	0.0246815	+	0.0179322i	0.00250603	+	0.00182074i	0.589038	−	0.808106i	$-0.299507\pi$
$97$	0.0246815	+	0.0179322i	0.00250603	+	0.00182074i	−0.586532	+	0.809926i	$0.699507\pi$
$98$	0.415241	−	1.27798i	0.0419457	−	0.129096i
$99$	2.56971			0.258266
$100$		0			0
$101$	−11.2308			−1.11750			−0.558751	−	0.829336i	$-0.688719\pi$
$101$	−11.2308			−1.11750			−0.558751	+	0.829336i	$0.688719\pi$
$102$	0.445250	−	1.37034i	0.0440864	−	0.135684i
$103$	−0.583288	−	0.423783i	−0.0574730	−	0.0417566i	0.558678	−	0.829385i	$-0.311309\pi$
$103$	−0.583288	−	0.423783i	−0.0574730	−	0.0417566i	−0.616151	+	0.787628i	$0.711309\pi$
$104$	−3.68122	−	2.67456i	−0.360973	−	0.262262i
$105$		0			0
$106$	2.66195	−	1.93402i	0.258552	−	0.187849i
$107$	−2.11668			−0.204627			−0.102313	−	0.994752i	$-0.532624\pi$
$107$	−2.11668			−0.204627			−0.102313	+	0.994752i	$0.532624\pi$
$108$	1.56877	−	1.13978i	0.150955	−	0.109675i
$109$	0.690602	+	2.12545i	0.0661477	+	0.203582i	0.978667	−	0.205451i	$-0.0658662\pi$
$109$	0.690602	+	2.12545i	0.0661477	+	0.203582i	−0.912520	+	0.409033i	$0.865866\pi$
$110$		0			0
$111$	0.394857	−	1.21524i	0.0374782	−	0.115346i
$112$	1.40175	+	4.31415i	0.132453	+	0.407649i
$113$	0.973217	+	2.99525i	0.0915526	+	0.281770i	0.986340	−	0.164723i	$-0.0526729\pi$
$113$	0.973217	+	2.99525i	0.0915526	+	0.281770i	−0.894787	+	0.446493i	$0.852673\pi$
$114$	−0.317865	+	0.978287i	−0.0297708	+	0.0916250i
$115$		0			0
$116$	1.92693	+	5.93047i	0.178911	+	0.550630i
$117$	−3.78722	+	2.75158i	−0.350129	+	0.254383i
$118$	1.57748			0.145219
$119$	5.88965	−	4.27908i	0.539903	−	0.392262i
$120$		0			0
$121$	3.55691	+	2.58425i	0.323356	+	0.234932i
$122$	0.763975	+	0.555061i	0.0691671	+	0.0502528i
$123$	2.68719	−	8.27031i	0.242296	−	0.745709i
$124$	17.8265			1.60086
$125$		0			0
$126$	−0.307649			−0.0274075
$127$	4.83929	−	14.8938i	0.429418	−	1.32161i	−0.469282	−	0.883048i	$-0.655487\pi$
$127$	4.83929	−	14.8938i	0.429418	−	1.32161i	0.898700	−	0.438564i	$-0.144513\pi$
$128$	−5.91084	−	4.29448i	−0.522450	−	0.379582i
$129$	−3.13968	−	2.28111i	−0.276433	−	0.200841i
$130$		0			0
$131$	12.1000	−	8.79116i	1.05718	−	0.768087i	0.0836161	−	0.996498i	$-0.473353\pi$
$131$	12.1000	−	8.79116i	1.05718	−	0.768087i	0.973565	+	0.228411i	$0.0733530\pi$
$132$	−4.98295			−0.433710
$133$	−4.20463	+	3.05484i	−0.364587	+	0.264888i
$134$	−0.771969	−	2.37588i	−0.0666879	−	0.205244i
$135$		0			0
$136$	−1.75389	+	5.39792i	−0.150395	+	0.462868i
$137$	3.24300	+	9.98092i	0.277068	+	0.852727i	0.988665	+	0.150139i	$0.0479723\pi$
$137$	3.24300	+	9.98092i	0.277068	+	0.852727i	−0.711597	+	0.702588i	$0.752028\pi$
$138$	0.122421	+	0.376774i	0.0104212	+	0.0320731i
$139$	3.84749	−	11.8414i	0.326340	−	1.00437i	−0.644492	−	0.764611i	$-0.722931\pi$
$139$	3.84749	−	11.8414i	0.326340	−	1.00437i	0.970832	−	0.239761i	$-0.0770690\pi$
$140$		0			0
$141$	0.991798	+	3.05244i	0.0835244	+	0.257062i
$142$	2.77072	−	2.01304i	0.232513	−	0.168931i
$143$	12.0295			1.00596
$144$	−2.94350	+	2.13858i	−0.245292	+	0.178215i
$145$		0			0
$146$	2.27209	+	1.65077i	0.188039	+	0.136619i
$147$	4.40558	+	3.20084i	0.363366	+	0.264001i
$148$	−0.765671	+	2.35649i	−0.0629378	+	0.193703i
$149$	−17.0680			−1.39826			−0.699131	−	0.714994i	$-0.746430\pi$
$149$	−17.0680			−1.39826			−0.699131	+	0.714994i	$0.746430\pi$
$150$		0			0
$151$	−1.57516			−0.128185			−0.0640923	−	0.997944i	$-0.520415\pi$
$151$	−1.57516			−0.128185			−0.0640923	+	0.997944i	$0.520415\pi$
$152$	1.25210	−	3.85358i	0.101559	−	0.312567i
$153$	4.72397	+	3.43216i	0.381910	+	0.277474i
$154$	0.639584	+	0.464685i	0.0515391	+	0.0374454i
$155$		0			0
$156$	7.34384	−	5.33561i	0.587978	−	0.427191i
$157$	9.20058			0.734286			0.367143	−	0.930164i	$-0.380336\pi$
$157$	9.20058			0.734286			0.367143	+	0.930164i	$0.380336\pi$
$158$	2.29241	−	1.66553i	0.182374	−	0.132503i
$159$	4.12052	+	12.6817i	0.326779	+	1.00572i
$160$		0			0
$161$	−0.618538	+	1.90366i	−0.0487476	+	0.150030i
$162$	−0.0762527	−	0.234682i	−0.00599098	−	0.0184383i
$163$	1.41553	+	4.35656i	0.110873	+	0.341232i	0.991064	−	0.133388i	$-0.0425855\pi$
$163$	1.41553	+	4.35656i	0.110873	+	0.341232i	−0.880191	+	0.474620i	$0.842586\pi$
$164$	−5.21075	+	16.0370i	−0.406891	+	1.25228i
$165$		0			0
$166$	−0.215970	−	0.664687i	−0.0167625	−	0.0515897i
$167$	0.115310	−	0.0837776i	0.00892296	−	0.00648291i	−0.583315	−	0.812246i	$-0.698245\pi$
$167$	0.115310	−	0.0837776i	0.00892296	−	0.00648291i	0.592238	+	0.805763i	$0.298245\pi$
$168$	1.21186			0.0934973
$169$	−7.21176	+	5.23965i	−0.554751	+	0.403050i
$170$		0			0
$171$	−3.37244	−	2.45022i	−0.257897	−	0.187373i
$172$	6.08819	+	4.42333i	0.464220	+	0.337275i
$173$	−7.60885	+	23.4176i	−0.578490	+	1.78041i	0.0454831	+	0.998965i	$0.485517\pi$
$173$	−7.60885	+	23.4176i	−0.578490	+	1.78041i	−0.623974	+	0.781445i	$0.714483\pi$
$174$	0.793511			0.0601559
$175$		0			0
$176$	9.34955			0.704749
$177$	−1.97548	+	6.07990i	−0.148486	+	0.456993i
$178$	−0.275647	−	0.200269i	−0.0206606	−	0.0150108i
$179$	19.5420	+	14.1981i	1.46064	+	1.06122i	0.983195	+	0.182557i	$0.0584373\pi$
$179$	19.5420	+	14.1981i	1.46064	+	1.06122i	0.477446	+	0.878661i	$0.341563\pi$
$180$		0			0
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	−0.645384	−	0.763858i	$-0.723303\pi$
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	0.527038	+	0.849842i	$0.323303\pi$
$182$	−1.44019			−0.106754
$183$	−3.09604	+	2.24940i	−0.228866	+	0.166281i
$184$	−0.482231	−	1.48415i	−0.0355505	−	0.109413i
$185$		0			0
$186$	0.701000	−	2.15746i	0.0513998	−	0.158192i
$187$	−4.63677	−	14.2705i	−0.339074	−	1.04356i
$188$	−1.92320	−	5.91901i	−0.140264	−	0.431689i
$189$	0.385270	−	1.18574i	0.0280242	−	0.0862498i
$190$		0			0
$191$	−2.40061	−	7.38832i	−0.173702	−	0.534600i	0.825870	−	0.563861i	$-0.190685\pi$
$191$	−2.40061	−	7.38832i	−0.173702	−	0.534600i	−0.999572	+	0.0292607i	$0.990685\pi$
$192$	5.31968	−	3.86498i	0.383915	−	0.278931i
$193$	−14.3458			−1.03264			−0.516318	−	0.856397i	$-0.672698\pi$
$193$	−14.3458			−1.03264			−0.516318	+	0.856397i	$0.672698\pi$
$194$	−0.00609039	+	0.00442493i	−0.000437265	+	0.000317691i
$195$		0			0
$196$	−8.54290	−	6.20678i	−0.610207	−	0.443341i
$197$	0.132307	+	0.0961264i	0.00942645	+	0.00684872i	0.592489	−	0.805579i	$-0.298146\pi$
$197$	0.132307	+	0.0961264i	0.00942645	+	0.00684872i	−0.583062	+	0.812428i	$0.698146\pi$
$198$	−0.195947	+	0.603064i	−0.0139254	+	0.0428579i
$199$	4.96974			0.352295			0.176148	−	0.984364i	$-0.443636\pi$
$199$	4.96974			0.352295			0.176148	+	0.984364i	$0.443636\pi$
$200$		0			0
$201$	10.1238			0.714079
$202$	0.856375	−	2.63565i	0.0602543	−	0.185444i
$203$	3.24355	+	2.35658i	0.227652	+	0.165399i
$204$	−9.16029	−	6.65534i	−0.641348	−	0.465967i
$205$		0			0
$206$	0.143931	−	0.104572i	0.0100282	−	0.00728590i
$207$	−1.60547			−0.111588
$208$	−13.7793	+	10.0112i	−0.955423	+	0.694155i
$209$	3.31020	+	10.1877i	0.228971	+	0.704701i
$210$		0			0
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	−0.909888	−	0.414853i	$-0.863833\pi$
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	0.979960	+	0.199196i	$0.0638330\pi$
$212$	−7.99015	−	24.5911i	−0.548766	−	1.68893i
$213$	4.28888	+	13.1998i	0.293869	+	0.904437i
$214$	0.161402	−	0.496745i	0.0110332	−	0.0339568i
$215$		0			0
$216$	0.300368	+	0.924437i	0.0204374	+	0.0629000i
$217$	9.27263	−	6.73696i	0.629467	−	0.457335i
$218$	−0.551465			−0.0373500
$219$	−9.20773	+	6.68981i	−0.622201	+	0.452055i
$220$		0			0
$221$	22.1141	+	16.0669i	1.48756	+	1.08077i
$222$	0.255087	+	0.185331i	0.0171203	+	0.0124386i
$223$	4.87419	−	15.0012i	0.326400	−	1.00456i	−0.644404	−	0.764685i	$-0.722895\pi$
$223$	4.87419	−	15.0012i	0.326400	−	1.00456i	0.970805	−	0.239872i	$-0.0771053\pi$
$224$	−3.54307			−0.236731
$225$		0			0
$226$	−0.777142			−0.0516947
$227$	−4.18427	+	12.8779i	−0.277720	+	0.854734i	0.710767	+	0.703428i	$0.248348\pi$
$227$	−4.18427	+	12.8779i	−0.277720	+	0.854734i	−0.988487	+	0.151307i	$0.951652\pi$
$228$	6.53954	+	4.75125i	0.433092	+	0.314660i
$229$	11.9596	+	8.68915i	0.790312	+	0.574195i	0.908056	−	0.418849i	$-0.137566\pi$
$229$	11.9596	+	8.68915i	0.790312	+	0.574195i	−0.117744	+	0.993044i	$0.537566\pi$
$230$		0			0
$231$	−2.59194	+	1.88315i	−0.170537	+	0.123902i
$232$	−3.12573			−0.205214
$233$	0.419864	−	0.305049i	0.0275062	−	0.0199844i	−0.573947	−	0.818892i	$-0.694589\pi$
$233$	0.419864	−	0.305049i	0.0275062	−	0.0199844i	0.601453	+	0.798908i	$0.294589\pi$
$234$	−0.356959	−	1.09861i	−0.0233351	−	0.0718182i
$235$		0			0
$236$	3.83067	−	11.7896i	0.249356	−	0.767438i
$237$	3.54849	+	10.9211i	0.230500	+	0.709405i
$238$	0.555120	+	1.70848i	0.0359831	+	0.110745i
$239$	2.54331	−	7.82750i	0.164513	−	0.506319i	−0.834487	−	0.551027i	$-0.814236\pi$
$239$	2.54331	−	7.82750i	0.164513	−	0.506319i	0.999000	+	0.0447086i	$0.0142359\pi$
$240$		0			0
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	0.937495	−	0.347998i	$-0.113138\pi$
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	−0.962998	+	0.269509i	$0.913138\pi$
$242$	−0.877700	+	0.637686i	−0.0564207	+	0.0409920i
$243$	1.00000			0.0641500
$244$	6.00356	−	4.36184i	0.384339	−	0.279238i
$245$		0			0
$246$	1.73599	+	1.26127i	0.110682	+	0.0804155i
$247$	−15.7873	−	11.4701i	−1.00452	−	0.729828i
$248$	−2.76132	+	8.49846i	−0.175344	+	0.539653i
$249$	2.83229			0.179489
$250$		0			0
$251$	4.63494			0.292555			0.146277	−	0.989244i	$-0.453271\pi$
$251$	4.63494			0.292555			0.146277	+	0.989244i	$0.453271\pi$
$252$	−0.747080	+	2.29928i	−0.0470616	+	0.144841i
$253$	3.33767	+	2.42496i	0.209837	+	0.152456i
$254$	3.12630	+	2.27139i	0.196161	+	0.142519i
$255$		0			0
$256$	−9.18081	+	6.67025i	−0.573801	+	0.416891i
$257$	18.3001			1.14153			0.570766	−	0.821113i	$-0.306647\pi$
$257$	18.3001			1.14153			0.570766	+	0.821113i	$0.306647\pi$
$258$	0.774744	−	0.562885i	0.0482335	−	0.0350437i
$259$	0.492291	+	1.51512i	0.0305895	+	0.0941448i
$260$		0			0
$261$	−0.993717	+	3.05835i	−0.0615095	+	0.189307i
$262$	1.14047	+	3.51000i	0.0704583	+	0.216848i
$263$	−5.15027	−	15.8509i	−0.317579	−	0.977409i	−0.974680	−	0.223606i	$-0.928217\pi$
$263$	−5.15027	−	15.8509i	−0.317579	−	0.977409i	0.657100	−	0.753803i	$-0.271783\pi$
$264$	0.771858	−	2.37554i	0.0475046	−	0.146204i
$265$		0			0
$266$	−0.396301	−	1.21969i	−0.0242988	−	0.0747839i
$267$	1.11707	−	0.811598i	0.0683635	−	0.0496690i
$268$	−19.6312			−1.19917
$269$	−2.12942	+	1.54712i	−0.129833	+	0.0943294i	−0.650807	−	0.759244i	$-0.725569\pi$
$269$	−2.12942	+	1.54712i	−0.129833	+	0.0943294i	0.520973	+	0.853573i	$0.325569\pi$
$270$		0			0
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	0.469978	−	0.882678i	$-0.344262\pi$
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	−0.694246	+	0.719738i	$0.744262\pi$
$272$	17.1875	+	12.4875i	1.04215	+	0.757164i
$273$	1.80355	−	5.55075i	0.109156	−	0.335947i
$274$	−2.58963			−0.156445
$275$		0			0
$276$	3.11318			0.187391
$277$	−0.389132	+	1.19762i	−0.0233807	+	0.0719583i	−0.962066	−	0.272817i	$-0.912045\pi$
$277$	−0.389132	+	1.19762i	−0.0233807	+	0.0719583i	0.938685	+	0.344775i	$0.112045\pi$
$278$	2.48557	+	1.80587i	0.149075	+	0.108309i
$279$	7.43739	+	5.40358i	0.445265	+	0.323504i
$280$		0			0
$281$	−10.8543	+	7.88611i	−0.647513	+	0.470446i	−0.862423	−	0.506188i	$-0.831054\pi$
$281$	−10.8543	+	7.88611i	−0.647513	+	0.470446i	0.214910	+	0.976634i	$0.431054\pi$
$282$	−0.791979			−0.0471617
$283$	19.4884	−	14.1591i	1.15846	−	0.841674i	0.168882	−	0.985636i	$-0.445984\pi$
$283$	19.4884	−	14.1591i	1.15846	−	0.841674i	0.989583	+	0.143962i	$0.0459844\pi$
$284$	−8.31661	−	25.5959i	−0.493500	−	1.51884i
$285$		0			0
$286$	−0.917281	+	2.82310i	−0.0542400	+	0.166934i
$287$	3.35028	+	10.3111i	0.197761	+	0.608644i
$288$	−0.878171	−	2.70273i	−0.0517467	−	0.159260i
$289$	5.28283	−	16.2589i	0.310754	−	0.956404i
$290$		0			0
$291$	−0.00942751	−	0.0290149i	−0.000552651	−	0.00170088i
$292$	17.8548	−	12.9723i	1.04487	−	0.759145i
$293$	32.1727			1.87955			0.939776	−	0.341792i	$-0.111034\pi$
$293$	32.1727			1.87955			0.939776	+	0.341792i	$0.111034\pi$
$294$	−1.08712	+	0.789836i	−0.0634019	+	0.0460641i
$295$		0			0
$296$	−1.00481	−	0.730041i	−0.0584037	−	0.0424328i
$297$	−2.07894	−	1.51044i	−0.120632	−	0.0876445i
$298$	1.30148	−	4.00554i	0.0753926	−	0.232035i
$299$	−7.51561			−0.434639
$300$		0			0
$301$	4.83849			0.278886
$302$	0.120110	−	0.369661i	0.00691156	−	0.0212716i
$303$	9.08587	+	6.60127i	0.521970	+	0.379233i
$304$	−12.2702	−	8.91482i	−0.703744	−	0.511300i
$305$		0			0
$306$	−1.16568	+	0.846917i	−0.0666375	+	0.0484150i
$307$	−20.2962			−1.15837			−0.579183	−	0.815198i	$-0.696628\pi$
$307$	−20.2962			−1.15837			−0.579183	+	0.815198i	$0.696628\pi$
$308$	5.02605	−	3.65164i	0.286386	−	0.208071i
$309$	0.222796	+	0.685696i	0.0126744	+	0.0390079i
$310$		0			0
$311$	−5.78554	+	17.8061i	−0.328068	+	1.00969i	0.641969	+	0.766731i	$0.278118\pi$
$311$	−5.78554	+	17.8061i	−0.328068	+	1.00969i	−0.970037	+	0.242959i	$0.921882\pi$
$312$	1.40610	+	4.32753i	0.0796048	+	0.244998i
$313$	−7.68955	−	23.6660i	−0.434639	−	1.33768i	−0.893456	−	0.449151i	$-0.851726\pi$
$313$	−7.68955	−	23.6660i	−0.434639	−	1.33768i	0.458817	−	0.888531i	$-0.348274\pi$
$314$	−0.701569	+	2.15921i	−0.0395919	+	0.121851i
$315$		0			0
$316$	−6.88092	−	21.1773i	−0.387082	−	1.19132i
$317$	−20.3775	+	14.8052i	−1.14452	+	0.831540i	−0.987742	−	0.156094i	$-0.950110\pi$
$317$	−20.3775	+	14.8052i	−1.14452	+	0.831540i	−0.156775	+	0.987634i	$0.550110\pi$
$318$	−3.29036			−0.184514
$319$	6.68532	−	4.85717i	0.374306	−	0.271949i
$320$		0			0
$321$	1.71243	+	1.24415i	0.0955783	+	0.0694417i
$322$	−0.399590	−	0.290319i	−0.0222683	−	0.0161788i
$323$	−7.52174	+	23.1496i	−0.418521	+	1.28808i
$324$	−1.93911			−0.107728
$325$		0			0
$326$	−1.13034			−0.0626039
$327$	0.690602	−	2.12545i	0.0381904	−	0.117538i
$328$	−6.83824	−	4.96827i	−0.377579	−	0.274327i
$329$	−3.23728	−	2.35202i	−0.178477	−	0.129671i
$330$		0			0
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.353797	+	0.935322i	$0.615110\pi$
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.998874	+	0.0474508i	$0.984890\pi$
$332$	−5.49212			−0.301419
$333$	−1.03375	+	0.751062i	−0.0566491	+	0.0411580i
$334$	0.0108684	+	0.0334494i	0.000594691	+	0.00183027i
$335$		0			0
$336$	1.40175	−	4.31415i	0.0764719	−	0.235356i
$337$	1.41361	+	4.35066i	0.0770045	+	0.236995i	0.982148	−	0.188111i	$-0.0602366\pi$
$337$	1.41361	+	4.35066i	0.0770045	+	0.236995i	−0.905143	+	0.425107i	$0.860237\pi$
$338$	−0.679734	−	2.09200i	−0.0369726	−	0.113790i
$339$	0.973217	−	2.99525i	0.0528579	−	0.162680i
$340$		0			0
$341$	−7.30011	−	22.4674i	−0.395323	−	1.21668i
$342$	0.832181	−	0.604615i	0.0449992	−	0.0326938i
$343$	−15.5167			−0.837821
$344$	−3.05180	+	2.21726i	−0.164542	+	0.119547i
$345$		0			0
$346$	−4.91550	−	3.57132i	−0.264259	−	0.191995i
$347$	−13.6038	−	9.88377i	−0.730293	−	0.530589i	0.159363	−	0.987220i	$-0.449056\pi$
$347$	−13.6038	−	9.88377i	−0.730293	−	0.530589i	−0.889656	+	0.456631i	$0.849056\pi$
$348$	1.92693	−	5.93047i	0.103294	−	0.317906i
$349$	0.373581			0.0199973			0.00999866	−	0.999950i	$-0.496817\pi$
$349$	0.373581			0.0199973			0.00999866	+	0.999950i	$0.496817\pi$
$350$		0			0
$351$	4.68126			0.249867
$352$	−2.25665	+	6.94524i	−0.120280	+	0.370183i
$353$	−19.3909	−	14.0883i	−1.03208	−	0.749847i	−0.0633526	−	0.997991i	$-0.520179\pi$
$353$	−19.3909	−	14.0883i	−1.03208	−	0.749847i	−0.968723	+	0.248144i	$0.920179\pi$
$354$	−1.27621	−	0.927218i	−0.0678296	−	0.0492811i
$355$		0			0
$356$	−2.16612	+	1.57378i	−0.114804	+	0.0834101i
$357$	−7.28000			−0.385299
$358$	−4.82218	+	3.50352i	−0.254860	+	0.185167i
$359$	−1.46789	−	4.51771i	−0.0774724	−	0.238435i	0.904819	−	0.425797i	$-0.140006\pi$
$359$	−1.46789	−	4.51771i	−0.0774724	−	0.238435i	−0.982291	+	0.187362i	$0.940006\pi$
$360$		0			0
$361$	−0.501540	+	1.54358i	−0.0263969	+	0.0812412i
$362$	−0.150069	−	0.461865i	−0.00788744	−	0.0242751i
$363$	−1.35862	−	4.18140i	−0.0713090	−	0.219467i
$364$	−3.49728	+	10.7635i	−0.183307	+	0.564162i
$365$		0			0
$366$	−0.291813	−	0.898107i	−0.0152533	−	0.0469448i
$367$	−14.0526	+	10.2098i	−0.733540	+	0.532948i	−0.890681	−	0.454628i	$-0.849772\pi$
$367$	−14.0526	+	10.2098i	−0.733540	+	0.532948i	0.157141	+	0.987576i	$0.449772\pi$
$368$	−5.84128			−0.304498
$369$	−7.03515	+	5.11134i	−0.366235	+	0.266085i
$370$		0			0
$371$	−13.4496	−	9.77172i	−0.698270	−	0.507323i
$372$	−14.4219	−	10.4781i	−0.747742	−	0.543266i
$373$	−0.651645	+	2.00556i	−0.0337409	+	0.103844i	−0.966509	−	0.256634i	$-0.917386\pi$
$373$	−0.651645	+	2.00556i	−0.0337409	+	0.103844i	0.932768	+	0.360478i	$0.117386\pi$
$374$	3.70260			0.191457
$375$		0			0
$376$	3.11969			0.160886
$377$	−4.65185	+	14.3169i	−0.239582	+	0.737359i
$378$	0.248893	+	0.180832i	0.0128017	+	0.00930097i
$379$	−10.0391	−	7.29380i	−0.515671	−	0.374657i	0.299299	−	0.954159i	$-0.403247\pi$
$379$	−10.0391	−	7.29380i	−0.515671	−	0.374657i	−0.814971	+	0.579502i	$0.803247\pi$
$380$		0			0
$381$	−12.6694	+	9.20488i	−0.649075	+	0.471580i
$382$	1.91696			0.0980801
$383$	26.9448	−	19.5766i	1.37682	−	1.00032i	0.379646	−	0.925132i	$-0.376046\pi$
$383$	26.9448	−	19.5766i	1.37682	−	1.00032i	0.997170	−	0.0751836i	$-0.0239543\pi$
$384$	2.25774	+	6.94861i	0.115215	+	0.354595i
$385$		0			0
$386$	1.09391	−	3.36671i	0.0556785	−	0.171361i
$387$	1.19925	+	3.69092i	0.0609614	+	0.187620i
$388$	0.0182810	+	0.0562631i	0.000928076	+	0.00285633i
$389$	−5.24639	+	16.1467i	−0.266002	+	0.818671i	0.725459	+	0.688266i	$0.241628\pi$
$389$	−5.24639	+	16.1467i	−0.266002	+	0.818671i	−0.991461	+	0.130405i	$0.958372\pi$
$390$		0			0
$391$	2.89690	+	8.91573i	0.146502	+	0.450888i
$392$	4.28227	−	3.11125i	0.216287	−	0.157142i
$393$	−14.9564			−0.754451
$394$	−0.0326478	+	0.0237200i	−0.00164477	+	0.00119500i
$395$		0			0
$396$	4.03129	+	2.92891i	0.202580	+	0.147183i
$397$	−0.701070	−	0.509357i	−0.0351857	−	0.0255639i	0.570053	−	0.821608i	$-0.306922\pi$
$397$	−0.701070	−	0.509357i	−0.0351857	−	0.0255639i	−0.605239	+	0.796044i	$0.706922\pi$
$398$	−0.378956	+	1.16631i	−0.0189953	+	0.0584617i
$399$	5.19720			0.260186
$400$		0			0
$401$	9.68680			0.483736			0.241868	−	0.970309i	$-0.422240\pi$
$401$	9.68680			0.483736			0.241868	+	0.970309i	$0.422240\pi$
$402$	−0.771969	+	2.37588i	−0.0385023	+	0.118498i
$403$	34.8164	+	25.2956i	1.73433	+	1.26006i
$404$	−17.6185	−	12.8006i	−0.876553	−	0.636853i
$405$		0			0
$406$	−0.800374	+	0.581506i	−0.0397219	+	0.0288597i
$407$	3.28353			0.162759
$408$	4.59174	−	3.33610i	0.227325	−	0.165161i
$409$	0.469043	+	1.44357i	0.0231927	+	0.0713797i	0.961983	−	0.273109i	$-0.0880521\pi$
$409$	0.469043	+	1.44357i	0.0231927	+	0.0713797i	−0.938790	+	0.344489i	$0.888052\pi$
$410$		0			0
$411$	3.24300	−	9.98092i	0.159965	−	0.492322i
$412$	−0.432026	−	1.32964i	−0.0212844	−	0.0655066i
$413$	−2.46295	−	7.58017i	−0.121194	−	0.372996i
$414$	0.122421	−	0.376774i	0.00601667	−	0.0185174i
$415$		0			0
$416$	−4.11095	−	12.6522i	−0.201556	−	0.620325i
$417$	−10.0729	+	7.31837i	−0.493271	+	0.358382i
$418$	−2.64329			−0.129287
$419$	24.7252	−	17.9639i	1.20790	−	0.877594i	0.212866	−	0.977081i	$-0.431720\pi$
$419$	24.7252	−	17.9639i	1.20790	−	0.877594i	0.995039	+	0.0994875i	$0.0317203\pi$
$420$		0			0
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	0.716683	−	0.697399i	$-0.245659\pi$
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	−0.441799	+	0.897114i	$0.645659\pi$
$422$	0.657551	+	0.477739i	0.0320091	+	0.0232560i
$423$	0.991798	−	3.05244i	0.0482228	−	0.148415i
$424$	12.9611			0.629445
$425$		0			0
$426$	−3.42480			−0.165932
$427$	1.47439	−	4.53772i	0.0713510	−	0.219596i
$428$	−3.32058	−	2.41255i	−0.160506	−	0.116615i
$429$	−9.73206	−	7.07076i	−0.469868	−	0.341379i
$430$		0			0
$431$	−8.85650	+	6.43463i	−0.426603	+	0.309945i	−0.780289	−	0.625419i	$-0.784928\pi$
$431$	−8.85650	+	6.43463i	−0.426603	+	0.309945i	0.353686	+	0.935364i	$0.384928\pi$
$432$	3.63837			0.175051
$433$	8.44561	−	6.13609i	0.405870	−	0.294882i	−0.366058	−	0.930592i	$-0.619293\pi$
$433$	8.44561	−	6.13609i	0.405870	−	0.294882i	0.771928	+	0.635710i	$0.219293\pi$
$434$	0.873978	+	2.68983i	0.0419523	+	0.129116i
$435$		0			0
$436$	−1.33915	+	4.12149i	−0.0641338	+	0.197384i
$437$	−2.06810	−	6.36495i	−0.0989305	−	0.304477i
$438$	−0.867861	−	2.67100i	−0.0414680	−	0.127625i
$439$	4.76917	−	14.6780i	0.227620	−	0.700543i	−0.770395	−	0.637567i	$-0.779941\pi$
$439$	4.76917	−	14.6780i	0.227620	−	0.700543i	0.998015	−	0.0629758i	$-0.0200591\pi$
$440$		0			0
$441$	−1.68278	−	5.17907i	−0.0801324	−	0.246622i
$442$	−5.45686	+	3.96464i	−0.259556	+	0.188579i
$443$	−18.9105			−0.898463			−0.449231	−	0.893415i	$-0.648302\pi$
$443$	−18.9105			−0.898463			−0.449231	+	0.893415i	$0.648302\pi$
$444$	2.00455	−	1.45639i	0.0951318	−	0.0691173i
$445$		0			0
$446$	3.14884	+	2.28777i	0.149102	+	0.108329i
$447$	13.8083	+	10.0323i	0.653109	+	0.474511i
$448$	−2.53334	+	7.79681i	−0.119689	+	0.368365i
$449$	−11.4152			−0.538714			−0.269357	−	0.963040i	$-0.586811\pi$
$449$	−11.4152			−0.538714			−0.269357	+	0.963040i	$0.586811\pi$
$450$		0			0
$451$	22.3460			1.05223
$452$	−1.88717	+	5.80813i	−0.0887652	+	0.273191i
$453$	1.27433	+	0.925855i	0.0598733	+	0.0435005i
$454$	−2.70314	−	1.96395i	−0.126865	−	0.0921725i
$455$		0			0
$456$	−3.27805	+	2.38164i	−0.153509	+	0.111531i
$457$	33.9739			1.58923			0.794616	−	0.607112i	$-0.207672\pi$
$457$	33.9739			1.58923			0.794616	+	0.607112i	$0.207672\pi$
$458$	−2.95114	+	2.14413i	−0.137898	+	0.100188i
$459$	−1.80439	−	5.55335i	−0.0842219	−	0.259208i
$460$		0			0
$461$	−7.62985	+	23.4823i	−0.355358	+	1.09368i	0.600444	+	0.799667i	$0.294991\pi$
$461$	−7.62985	+	23.4823i	−0.355358	+	1.09368i	−0.955802	+	0.294012i	$0.905009\pi$
$462$	−0.244299	−	0.751876i	−0.0113658	−	0.0349804i
$463$	4.21237	+	12.9643i	0.195765	+	0.602504i	0.999967	+	0.00814689i	$0.00259326\pi$
$463$	4.21237	+	12.9643i	0.195765	+	0.602504i	−0.804202	+	0.594357i	$0.797407\pi$
$464$	−3.61551	+	11.1274i	−0.167846	+	0.516576i
$465$		0			0
$466$	0.0395737	+	0.121795i	0.00183321	+	0.00564205i
$467$	7.66232	−	5.56700i	0.354570	−	0.257610i	−0.396214	−	0.918158i	$-0.629676\pi$
$467$	7.66232	−	5.56700i	0.354570	−	0.257610i	0.750784	+	0.660548i	$0.229676\pi$
$468$	−9.07748			−0.419607
$469$	−10.2114	+	7.41900i	−0.471518	+	0.342578i
$470$		0			0
$471$	−7.44343	−	5.40797i	−0.342975	−	0.249186i
$472$	5.02712	+	3.65241i	0.231392	+	0.168116i
$473$	3.08173	−	9.48459i	0.141698	−	0.436102i
$474$	−2.83358			−0.130150
$475$		0			0
$476$	14.1167			0.647039
$477$	4.12052	−	12.6817i	0.188666	−	0.580654i
$478$	1.64304	+	1.19374i	0.0751508	+	0.0546002i
$479$	20.8149	+	15.1229i	0.951055	+	0.690982i	0.951056	−	0.309018i	$-0.100000\pi$
$479$	20.8149	+	15.1229i	0.951055	+	0.690982i	−1.08775e−6		1.00000i	$0.500000\pi$
$480$		0			0
$481$	−4.83925	+	3.51592i	−0.220651	+	0.160312i
$482$	0.316142			0.0143999
$483$	1.61935	−	1.17653i	0.0736831	−	0.0535339i
$484$	2.63451	+	8.10820i	0.119751	+	0.368554i
$485$		0			0
$486$	−0.0762527	+	0.234682i	−0.00345889	+	0.0106454i
$487$	8.77751	+	27.0144i	0.397747	+	1.22414i	0.926802	+	0.375551i	$0.122547\pi$
$487$	8.77751	+	27.0144i	0.397747	+	1.22414i	−0.529055	+	0.848588i	$0.677453\pi$
$488$	1.14948	+	3.53774i	0.0520346	+	0.160146i
$489$	1.41553	−	4.35656i	0.0640126	−	0.197010i
$490$		0			0
$491$	−1.88593	−	5.80429i	−0.0851107	−	0.261944i	0.899440	−	0.437045i	$-0.143975\pi$
$491$	−1.88593	−	5.80429i	−0.0851107	−	0.261944i	−0.984551	+	0.175101i	$0.943975\pi$
$492$	13.6419	−	9.91144i	0.615026	−	0.446842i
$493$	18.7771			0.845679
$494$	3.89566	−	2.83036i	0.175274	−	0.127344i
$495$		0			0
$496$	27.0600	+	19.6602i	1.21503	+	0.882770i
$497$	−13.9992	−	10.1710i	−0.627948	−	0.456231i
$498$	−0.215970	+	0.664687i	−0.00967784	+	0.0297853i
$499$	−20.3163			−0.909481			−0.454740	−	0.890624i	$-0.650268\pi$
$499$	−20.3163			−0.909481			−0.454740	+	0.890624i	$0.650268\pi$
$500$		0			0
$501$	−0.142531			−0.00636782
$502$	−0.353426	+	1.08773i	−0.0157742	+	0.0485480i
$503$	11.8332	+	8.59734i	0.527617	+	0.383336i	0.819466	−	0.573128i	$-0.194270\pi$
$503$	11.8332	+	8.59734i	0.527617	+	0.383336i	−0.291848	+	0.956465i	$0.594270\pi$
$504$	−0.980418	−	0.712315i	−0.0436713	−	0.0317290i
$505$		0			0
$506$	−0.823600	+	0.598380i	−0.0366135	+	0.0266012i
$507$	8.91422			0.395894
$508$	24.5674	−	17.8493i	1.09000	−	0.791934i
$509$	−1.33058	−	4.09510i	−0.0589768	−	0.181512i	0.917228	−	0.398363i	$-0.130422\pi$
$509$	−1.33058	−	4.09510i	−0.0589768	−	0.181512i	−0.976205	+	0.216851i	$0.930422\pi$
$510$		0			0
$511$	4.38490	−	13.4953i	0.193977	−	0.596999i
$512$	−5.38081	−	16.5604i	−0.237800	−	0.731874i
$513$	1.28816	+	3.96455i	0.0568736	+	0.175039i
$514$	−1.39543	+	4.29471i	−0.0615500	+	0.189431i
$515$		0			0
$516$	−2.32548	−	7.15709i	−0.102374	−	0.315073i
$517$	−6.67241	+	4.84779i	−0.293452	+	0.213205i
$518$	−0.393109			−0.0172722
$519$	19.9202	−	14.4729i	0.874401	−	0.635290i
$520$		0			0
$521$	32.0705	+	23.3006i	1.40503	+	1.02082i	0.994021	+	0.109186i	$0.0348243\pi$
$521$	32.0705	+	23.3006i	1.40503	+	1.02082i	0.411011	+	0.911630i	$0.365176\pi$
$522$	−0.641964	−	0.466414i	−0.0280980	−	0.0204144i
$523$	−11.2134	+	34.5114i	−0.490329	+	1.50908i	0.333782	+	0.942650i	$0.391675\pi$
$523$	−11.2134	+	34.5114i	−0.490329	+	1.50908i	−0.824111	+	0.566428i	$0.808325\pi$
$524$	29.0021			1.26696
$525$		0			0
$526$	4.11264			0.179320
$527$	16.5880	−	51.0526i	0.722585	−	2.22389i
$528$	−7.56395	−	5.49553i	−0.329179	−	0.239162i
$529$	16.5221	+	12.0040i	0.718353	+	0.521914i
$530$		0			0
$531$	5.17187	−	3.75759i	0.224440	−	0.163065i
$532$	−10.0779			−0.436934
$533$	−32.9334	+	23.9275i	−1.42650	+	1.03642i
$534$	0.105288	+	0.324042i	0.00455625	+	0.0140227i
$535$		0			0
$536$	3.04087	−	9.35883i	0.131346	−	0.404240i
$537$	−7.46440	−	22.9731i	−0.322113	−	0.991360i
$538$	−0.200706	−	0.617709i	−0.00865304	−	0.0266313i
$539$	−4.32426	+	13.3087i	−0.186259	+	0.573246i
$540$		0			0
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	−0.787096	−	0.616830i	$-0.788417\pi$
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	0.274211	−	0.961670i	$-0.411583\pi$
$542$	0.911014	−	0.661890i	0.0391314	−	0.0284306i
$543$	1.96805			0.0844570
$544$	−13.4247	+	9.75359i	−0.575578	+	0.418182i
$545$		0			0
$546$	1.16513	+	0.846520i	0.0498632	+	0.0362277i
$547$	8.38303	+	6.09063i	0.358433	+	0.260416i	0.752398	−	0.658709i	$-0.228897\pi$
$547$	8.38303	+	6.09063i	0.358433	+	0.260416i	−0.393965	+	0.919125i	$0.628897\pi$
$548$	−6.28853	+	19.3541i	−0.268633	+	0.826766i
$549$	3.82692			0.163329
$550$		0			0
$551$	−13.4050			−0.571073
$552$	−0.482231	+	1.48415i	−0.0205251	+	0.0631698i
$553$	−11.5825	−	8.41517i	−0.492538	−	0.357850i
$554$	−0.251388	−	0.182644i	−0.0106805	−	0.00775981i
$555$		0			0
$556$	19.5324	−	14.1911i	0.828359	−	0.601838i
$557$	−12.6830			−0.537398			−0.268699	−	0.963224i	$-0.586594\pi$
$557$	−12.6830			−0.537398			−0.268699	+	0.963224i	$0.586594\pi$
$558$	−1.83524	+	1.33338i	−0.0776920	+	0.0564465i
$559$	5.61401	+	17.2781i	0.237447	+	0.730788i
$560$		0			0
$561$	−4.63677	+	14.2705i	−0.195765	+	0.602502i
$562$	−1.02306	−	3.14864i	−0.0431550	−	0.132817i
$563$	−4.04480	−	12.4486i	−0.170468	−	0.524646i	0.828930	−	0.559353i	$-0.188950\pi$
$563$	−4.04480	−	12.4486i	−0.170468	−	0.524646i	−0.999398	+	0.0347068i	$0.988950\pi$
$564$	−1.92320	+	5.91901i	−0.0809815	+	0.249235i
$565$		0			0
$566$	1.83685	+	5.65324i	0.0772086	+	0.237624i
$567$	−1.00865	+	0.732827i	−0.0423593	+	0.0307758i
$568$	13.4906			0.566055
$569$	2.09376	−	1.52120i	0.0877748	−	0.0637721i	−0.543032	−	0.839712i	$-0.682724\pi$
$569$	2.09376	−	1.52120i	0.0877748	−	0.0637721i	0.630807	+	0.775940i	$0.282724\pi$
$570$		0			0
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	0.752236	−	0.658893i	$-0.228975\pi$
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	−0.394191	+	0.919029i	$0.628975\pi$
$572$	18.8715	+	13.7110i	0.789059	+	0.573285i
$573$	−2.40061	+	7.38832i	−0.100287	+	0.308652i
$574$	−2.67529			−0.111665
$575$		0			0
$576$	−6.57549			−0.273979
$577$	0.00441597	−	0.0135910i	0.000183839	−	0.000565800i	−0.950965	−	0.309300i	$-0.899905\pi$
$577$	0.00441597	−	0.0135910i	0.000183839	−	0.000565800i	0.951148	+	0.308734i	$0.0999053\pi$
$578$	3.41283	+	2.47957i	0.141955	+	0.103136i
$579$	11.6060	+	8.43227i	0.482330	+	0.350433i
$580$		0			0
$581$	−2.85679	+	2.07558i	−0.118519	+	0.0861094i
$582$	0.00752814			0.000312051
$583$	−27.7212	+	20.1406i	−1.14809	+	0.834139i
$584$	3.41860	+	10.5214i	0.141463	+	0.435377i
$585$		0			0
$586$	−2.45326	+	7.55035i	−0.101343	+	0.311902i
$587$	6.99581	+	21.5309i	0.288748	+	0.888675i	0.985250	+	0.171120i	$0.0547387\pi$
$587$	6.99581	+	21.5309i	0.288748	+	0.888675i	−0.696502	+	0.717555i	$0.745261\pi$
$588$	3.26310	+	10.0428i	0.134568	+	0.414157i
$589$	−11.8422	+	36.4465i	−0.487949	+	1.50175i
$590$		0			0
$591$	−0.0505366	−	0.155536i	−0.00207880	−	0.00639788i
$592$	−3.76116	+	2.73264i	−0.154583	+	0.112311i
$593$	−12.7423			−0.523264			−0.261632	−	0.965168i	$-0.584261\pi$
$593$	−12.7423			−0.523264			−0.261632	+	0.965168i	$0.584261\pi$
$594$	0.512997	−	0.372714i	0.0210485	−	0.0152926i
$595$		0			0
$596$	−26.7758	−	19.4537i	−1.09678	−	0.796856i
$597$	−4.02060	−	2.92114i	−0.164552	−	0.119554i
$598$	0.573086	−	1.76378i	0.0234352	−	0.0721262i
$599$	−6.83599			−0.279311			−0.139656	−	0.990200i	$-0.544600\pi$
$599$	−6.83599			−0.279311			−0.139656	+	0.990200i	$0.544600\pi$
$600$		0			0
$601$	31.8422			1.29887			0.649435	−	0.760417i	$-0.275005\pi$
$601$	31.8422			1.29887			0.649435	+	0.760417i	$0.275005\pi$
$602$	−0.368948	+	1.13551i	−0.0150372	+	0.0462798i
$603$	−8.19034	−	5.95063i	−0.333537	−	0.242328i
$604$	−2.47107	−	1.79534i	−0.100546	−	0.0730511i
$605$		0			0
$606$	−2.24202	+	1.62892i	−0.0910758	+	0.0661705i
$607$	−27.7763			−1.12741			−0.563703	−	0.825977i	$-0.690624\pi$
$607$	−27.7763			−1.12741			−0.563703	+	0.825977i	$0.690624\pi$
$608$	9.58388	−	6.96310i	0.388678	−	0.282391i
$609$	−1.23892	−	3.81302i	−0.0502038	−	0.154511i
$610$		0			0
$611$	4.64286	−	14.2893i	0.187830	−	0.578082i
$612$	3.49892	+	10.7686i	0.141435	+	0.435293i
$613$	1.11769	+	3.43991i	0.0451433	+	0.138937i	0.971088	−	0.238723i	$-0.0767289\pi$
$613$	1.11769	+	3.43991i	0.0451433	+	0.138937i	−0.925944	+	0.377660i	$0.876729\pi$
$614$	1.54764	−	4.76315i	0.0624577	−	0.192225i
$615$		0			0
$616$	0.962321	+	2.96172i	0.0387730	+	0.119331i
$617$	36.1166	−	26.2402i	1.45400	−	1.05639i	0.469122	−	0.883133i	$-0.344570\pi$
$617$	36.1166	−	26.2402i	1.45400	−	1.05639i	0.984876	−	0.173259i	$-0.0554297\pi$
$618$	−0.177909			−0.00715655
$619$	−16.5917	+	12.0546i	−0.666878	+	0.484515i	−0.868979	−	0.494850i	$-0.835223\pi$
$619$	−16.5917	+	12.0546i	−0.666878	+	0.484515i	0.202101	+	0.979365i	$0.435223\pi$
$620$		0			0
$621$	1.29885	+	0.943670i	0.0521211	+	0.0378682i
$622$	−3.73760	−	2.71552i	−0.149864	−	0.108883i
$623$	−0.531970	+	1.63724i	−0.0213129	+	0.0655945i
$624$	17.0322			0.681832
$625$		0			0
$626$	6.14033			0.245417
$627$	3.31020	−	10.1877i	0.132197	−	0.406859i
$628$	14.4336	+	10.4866i	0.575964	+	0.418463i
$629$	6.03621	+	4.38556i	0.240679	+	0.174864i
$630$		0			0
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.219629	−	0.975583i	$-0.429515\pi$
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.995704	+	0.0925923i	$0.0295153\pi$
$632$	11.1618			0.443991
$633$	−2.66475	+	1.93605i	−0.105914	+	0.0769512i
$634$	−1.92066	−	5.91117i	−0.0762790	−	0.234763i
$635$		0			0
$636$	−7.99015	+	24.5911i	−0.316830	+	0.975102i
$637$	−7.87754	−	24.2446i	−0.312119	−	0.960605i
$638$	0.630115	+	1.93929i	0.0249465	+	0.0767774i
$639$	4.28888	−	13.1998i	0.169666	−	0.522177i
$640$		0			0
$641$	−2.83865	−	8.73646i	−0.112120	−	0.345070i	0.879216	−	0.476424i	$-0.158067\pi$
$641$	−2.83865	−	8.73646i	−0.112120	−	0.345070i	−0.991335	+	0.131355i	$0.958067\pi$
$642$	−0.422557	+	0.307005i	−0.0166770	+	0.0121165i
$643$	−3.42111			−0.134915			−0.0674577	−	0.997722i	$-0.521489\pi$
$643$	−3.42111			−0.134915			−0.0674577	+	0.997722i	$0.521489\pi$
$644$	−3.14010	+	2.28142i	−0.123737	+	0.0899005i
$645$		0			0
$646$	−4.85922	−	3.53043i	−0.191184	−	0.138903i
$647$	2.64334	+	1.92050i	0.103920	+	0.0755027i	0.638532	−	0.769595i	$-0.279542\pi$
$647$	2.64334	+	1.92050i	0.103920	+	0.0755027i	−0.534611	+	0.845098i	$0.679542\pi$
$648$	0.300368	−	0.924437i	0.0117996	−	0.0363153i
$649$	−16.4276			−0.644840
$650$		0			0
$651$	−11.4616			−0.449216
$652$	−2.74487	+	8.44785i	−0.107498	+	0.330843i
$653$	10.2229	+	7.42740i	0.400054	+	0.290656i	0.769563	−	0.638571i	$-0.220474\pi$
$653$	10.2229	+	7.42740i	0.400054	+	0.290656i	−0.369509	+	0.929227i	$0.620474\pi$
$654$	0.446145	+	0.324143i	0.0174456	+	0.0126750i
$655$		0			0
$656$	−25.5965	+	18.5969i	−0.999374	+	0.726088i
$657$	11.3814			0.444030
$658$	0.798829	−	0.580383i	0.0311416	−	0.0226257i
$659$	−2.82719	−	8.70118i	−0.110131	−	0.338950i	0.880769	−	0.473546i	$-0.157026\pi$
$659$	−2.82719	−	8.70118i	−0.110131	−	0.338950i	−0.990901	+	0.134596i	$0.957026\pi$
$660$		0			0
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	−0.905275	−	0.424825i	$-0.860336\pi$
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	0.982089	+	0.188417i	$0.0603356\pi$
$662$	−2.31955	−	7.13884i	−0.0901519	−	0.277459i
$663$	−8.44684	−	25.9967i	−0.328048	−	1.00963i
$664$	0.850729	−	2.61827i	0.0330147	−	0.101609i
$665$		0			0
$666$	−0.0974345	−	0.299872i	−0.00377551	−	0.0116198i
$667$	−4.17676	+	3.03459i	−0.161725	+	0.117500i
$668$	0.276383			0.0106936
$669$	−12.7608	+	9.27127i	−0.493361	+	0.358448i
$670$		0			0
$671$	−7.95593	−	5.78032i	−0.307135	−	0.223147i
$672$	2.86640	+	2.08256i	0.110574	+	0.0803366i
$673$	10.4158	−	32.0566i	0.401500	−	1.23569i	−0.522282	−	0.852773i	$-0.674919\pi$
$673$	10.4158	−	32.0566i	0.401500	−	1.23569i	0.923782	−	0.382918i	$-0.125081\pi$
$674$	−1.12881			−0.0434802
$675$		0			0
$676$	−17.2857			−0.664833
$677$	−2.84401	+	8.75295i	−0.109304	+	0.336403i	−0.990716	−	0.135944i	$-0.956593\pi$
$677$	−2.84401	+	8.75295i	−0.109304	+	0.336403i	0.881412	+	0.472347i	$0.156593\pi$
$678$	0.628721	+	0.456792i	0.0241459	+	0.0175430i
$679$	0.0307719	+	0.0223571i	0.00118092	+	0.000857988i
$680$		0			0
$681$	10.9546	−	7.95896i	0.419780	−	0.304988i
$682$	5.82935			0.223217
$683$	22.0227	−	16.0005i	0.842677	−	0.612241i	−0.0804402	−	0.996759i	$-0.525633\pi$
$683$	22.0227	−	16.0005i	0.842677	−	0.612241i	0.923117	+	0.384519i	$0.125633\pi$
$684$	−2.49788	−	7.68769i	−0.0955089	−	0.293946i
$685$		0			0
$686$	1.18319	−	3.64147i	0.0451743	−	0.139032i
$687$	−4.56816	−	14.0593i	−0.174286	−	0.536397i
$688$	4.36332	+	13.4289i	0.166350	+	0.511972i
$689$	19.2892	−	59.3662i	0.734862	−	2.26167i
$690$		0			0
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	0.958519	+	0.285028i	$0.0920028\pi$
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	−0.607923	+	0.793996i	$0.707997\pi$
$692$	−38.6275	+	28.0645i	−1.46840	+	1.06685i
$693$	3.20381			0.121703
$694$	3.35687	−	2.43891i	0.127425	−	0.0925797i
$695$		0			0
$696$	2.52877	+	1.83726i	0.0958527	+	0.0696410i
$697$	41.0792	+	29.8458i	1.55599	+	1.13049i
$698$	−0.0284865	+	0.0876726i	−0.00107823	+	0.00331846i
$699$	−0.518980			−0.0196296
$700$		0			0
$701$	−19.1081			−0.721704			−0.360852	−	0.932623i	$-0.617514\pi$
$701$	−19.1081			−0.721704			−0.360852	+	0.932623i	$0.617514\pi$
$702$	−0.356959	+	1.09861i	−0.0134725	+	0.0414642i
$703$	−4.30925	−	3.13086i	−0.162527	−	0.118082i
$704$	13.6700	+	9.93187i	0.515209	+	0.374322i
$705$		0			0
$706$	4.78489	−	3.47642i	0.180082	−	0.130837i
$707$	−14.0020			−0.526601
$708$	−10.0288	+	7.28637i	−0.376907	+	0.273839i
$709$	4.48525	+	13.8042i	0.168447	+	0.518427i	0.999274	−	0.0381042i	$-0.0121319\pi$
$709$	4.48525	+	13.8042i	0.168447	+	0.518427i	−0.830827	+	0.556531i	$0.812132\pi$
$710$		0			0
$711$	3.54849	−	10.9211i	0.133079	−	0.409575i
$712$	−0.414740	−	1.27644i	−0.0155430	−	0.0478365i
$713$	4.56086	+	14.0369i	0.170806	+	0.525685i
$714$	0.555120	−	1.70848i	0.0207748	−	0.0639384i
$715$		0			0
$716$	14.4743	+	44.5473i	0.540930	+	1.66481i
$717$	−6.65847	+	4.83766i	−0.248665	+	0.180666i
$718$	1.17215			0.0437444
$719$	−28.1139	+	20.4260i	−1.04847	+	0.761760i	−0.971921	−	0.235306i	$-0.924391\pi$
$719$	−28.1139	+	20.4260i	−1.04847	+	0.761760i	−0.0765512	+	0.997066i	$0.524391\pi$
$720$		0			0
$721$	−0.727219	−	0.528356i	−0.0270831	−	0.0196770i
$722$	−0.324007	−	0.235405i	−0.0120583	−	0.00876086i
$723$	−0.395906	+	1.21847i	−0.0147239	+	0.0453155i
$724$	−3.81626			−0.141830
$725$		0			0
$726$	1.08490			0.0402643
$727$	−13.1727	+	40.5415i	−0.488550	+	1.50360i	0.338223	+	0.941066i	$0.390174\pi$
$727$	−13.1727	+	40.5415i	−0.488550	+	1.50360i	−0.826773	+	0.562536i	$0.809826\pi$
$728$	−4.58959	−	3.33453i	−0.170102	−	0.123586i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	18.3330	−	13.3197i	0.678072	−	0.492648i
$732$	−7.42081			−0.274281
$733$	1.58754	−	1.15341i	0.0586370	−	0.0426023i	−0.558081	−	0.829787i	$-0.688462\pi$
$733$	1.58754	−	1.15341i	0.0586370	−	0.0426023i	0.616718	+	0.787184i	$0.288462\pi$
$734$	−1.32451	−	4.07642i	−0.0488885	−	0.150463i
$735$		0			0
$736$	1.40987	−	4.33915i	0.0519687	−	0.159943i
$737$	8.03917	+	24.7420i	0.296127	+	0.911384i
$738$	−0.663088	−	2.04077i	−0.0244086	−	0.0751219i
$739$	3.81947	−	11.7551i	0.140501	−	0.432419i	−0.855904	−	0.517135i	$-0.826998\pi$
$739$	3.81947	−	11.7551i	0.140501	−	0.432419i	0.996405	+	0.0847164i	$0.0269984\pi$
$740$		0			0
$741$	6.03021	+	18.5591i	0.221525	+	0.681785i
$742$	3.31881	−	2.41126i	0.121838	−	0.0885201i
$743$	−8.63742			−0.316876			−0.158438	−	0.987369i	$-0.550646\pi$
$743$	−8.63742			−0.316876			−0.158438	+	0.987369i	$0.550646\pi$
$744$	7.22922	−	5.25234i	0.265036	−	0.192560i
$745$		0			0
$746$	−0.420978	−	0.305858i	−0.0154131	−	0.0111983i
$747$	−2.29137	−	1.66478i	−0.0838369	−	0.0609110i
$748$	8.99121	−	27.6721i	0.328751	−	1.01179i
$749$	−2.63898			−0.0964264
$750$		0			0
$751$	−24.3654			−0.889105			−0.444552	−	0.895753i	$-0.646637\pi$
$751$	−24.3654			−0.889105			−0.444552	+	0.895753i	$0.646637\pi$
$752$	3.60852	−	11.1059i	0.131589	−	0.404990i
$753$	−3.74974	−	2.72435i	−0.136648	−	0.0992807i
$754$	−3.00520	−	2.18341i	−0.109443	−	0.0795150i
$755$		0			0
$756$	1.95588	−	1.42103i	0.0711347	−	0.0516824i
$757$	5.18352			0.188398			0.0941991	−	0.995553i	$-0.469971\pi$
$757$	5.18352			0.188398			0.0941991	+	0.995553i	$0.469971\pi$
$758$	2.47723	−	1.79981i	0.0899769	−	0.0653720i
$759$	−1.27488	−	3.92367i	−0.0462751	−	0.142420i
$760$		0			0
$761$	9.66099	−	29.7335i	0.350211	−	1.07784i	−0.608524	−	0.793535i	$-0.708238\pi$
$761$	9.66099	−	29.7335i	0.350211	−	1.07784i	0.958735	−	0.284302i	$-0.0917618\pi$
$762$	−1.19414	−	3.67518i	−0.0432591	−	0.133138i
$763$	0.861014	+	2.64993i	0.0311708	+	0.0959339i
$764$	4.65505	−	14.3268i	0.168414	−	0.518324i
$765$		0			0
$766$	2.53964	+	7.81622i	0.0917611	+	0.282412i
$767$	24.2109	−	17.5903i	0.874205	−	0.635147i
$768$	11.3481			0.409490
$769$	35.7497	−	25.9737i	1.28917	−	0.936636i	0.289380	−	0.957214i	$-0.406551\pi$
$769$	35.7497	−	25.9737i	1.28917	−	0.936636i	0.999788	+	0.0205786i	$0.00655083\pi$
$770$		0			0
$771$	−14.8051	−	10.7566i	−0.533193	−	0.387388i
$772$	−22.5054	−	16.3511i	−0.809986	−	0.588489i
$773$	6.67110	−	20.5315i	0.239943	−	0.738468i	−0.756484	−	0.654012i	$-0.773085\pi$
$773$	6.67110	−	20.5315i	0.239943	−	0.738468i	0.996427	−	0.0844563i	$-0.0269153\pi$
$774$	−0.957636			−0.0344215
$775$		0			0
$776$	−0.0296542			−0.00106452
$777$	0.492291	−	1.51512i	0.0176609	−	0.0543545i
$778$	−3.38929	−	2.46246i	−0.121512	−	0.0882835i
$779$	−29.3265	−	21.3070i	−1.05073	−	0.763401i
$780$		0			0
$781$	−28.8538	+	20.9635i	−1.03247	+	0.750135i
$782$	−2.31325			−0.0827218
$783$	2.60158	−	1.89016i	0.0929730	−	0.0675488i
$784$	−6.12257	−	18.8433i	−0.218663	−	0.672977i
$785$		0			0
$786$	1.14047	−	3.51000i	0.0406791	−	0.125197i
$787$	−4.45638	−	13.7153i	−0.158853	−	0.488899i	0.839678	−	0.543085i	$-0.182744\pi$
$787$	−4.45638	−	13.7153i	−0.158853	−	0.488899i	−0.998531	+	0.0541857i	$0.982744\pi$
$788$	0.0979961	+	0.301601i	0.00349097	+	0.0107441i
$789$	−5.15027	+	15.8509i	−0.183355	+	0.564307i
$790$		0			0
$791$	1.21337	+	3.73436i	0.0431424	+	0.132779i
$792$	−2.02075	+	1.46816i	−0.0718043	+	0.0521689i
$793$	17.9148			0.636173
$794$	0.172995	−	0.125688i	0.00613937	−	0.00446052i
$795$		0			0
$796$	7.79639	+	5.66441i	0.276336	+	0.200770i
$797$	−31.9211	−	23.1921i	−1.13070	−	0.821505i	−0.144907	−	0.989445i	$-0.546288\pi$
$797$	−31.9211	−	23.1921i	−1.13070	−	0.821505i	−0.985797	+	0.167941i	$0.946288\pi$
$798$	−0.396301	+	1.21969i	−0.0140289	+	0.0431765i
$799$	−18.7409			−0.663004
$800$		0			0
$801$	−1.38077			−0.0487872
$802$	−0.738645	+	2.27332i	−0.0260825	+	0.0802736i
$803$	−23.6612	−	17.1909i	−0.834986	−	0.606653i
$804$	15.8820	+	11.5389i	0.560114	+	0.406947i
$805$		0			0
$806$	−8.59125	+	6.24191i	−0.302614	+	0.219862i
$807$	2.63211			0.0926547
$808$	8.83156	−	6.41650i	0.310693	−	0.225732i
$809$	−1.84237	−	5.67024i	−0.0647744	−	0.199355i	0.913431	−	0.406993i	$-0.133423\pi$
$809$	−1.84237	−	5.67024i	−0.0647744	−	0.199355i	−0.978206	+	0.207638i	$0.933423\pi$
$810$		0			0
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	0.477788	+	0.878475i	$0.341439\pi$
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	−0.902893	+	0.429865i	$0.858561\pi$
$812$	2.40241	+	7.39386i	0.0843081	+	0.259474i
$813$	1.41019	+	4.34011i	0.0494574	+	0.152214i
$814$	−0.250378	+	0.770586i	−0.00877576	+	0.0270090i
$815$		0			0
$816$	−6.56505	−	20.2051i	−0.229823	−	0.707322i
$817$	−13.0880	+	9.50897i	−0.457890	+	0.332677i
$818$	−0.374544			−0.0130956
$819$	−4.72175	+	3.43055i	−0.164991	+	0.119873i
$820$		0			0
$821$	−16.6923	−	12.1277i	−0.582567	−	0.423260i	0.257082	−	0.966390i	$-0.417239\pi$
$821$	−16.6923	−	12.1277i	−0.582567	−	0.423260i	−0.839649	+	0.543130i	$0.817239\pi$
$822$	2.09505	+	1.52214i	0.0730733	+	0.0530909i
$823$	−12.0567	+	37.1066i	−0.420269	+	1.29345i	0.487183	+	0.873300i	$0.338024\pi$
$823$	−12.0567	+	37.1066i	−0.420269	+	1.29345i	−0.907452	+	0.420155i	$0.861976\pi$
$824$	0.700803			0.0244136
$825$		0			0
$826$	1.96673			0.0684314
$827$	−6.05598	+	18.6384i	−0.210587	+	0.648120i	0.788850	+	0.614585i	$0.210677\pi$
$827$	−6.05598	+	18.6384i	−0.210587	+	0.648120i	−0.999438	+	0.0335352i	$0.989323\pi$
$828$	−2.51861	−	1.82988i	−0.0875279	−	0.0635927i
$829$	7.01831	+	5.09910i	0.243756	+	0.177099i	0.702955	−	0.711234i	$-0.251864\pi$
$829$	7.01831	+	5.09910i	0.243756	+	0.177099i	−0.459199	+	0.888333i	$0.651864\pi$
$830$		0			0
$831$	1.01876	−	0.740173i	0.0353404	−	0.0256763i
$832$	−30.7816			−1.06716
$833$	−25.7248	+	18.6902i	−0.891311	+	0.647575i
$834$	−0.949404	−	2.92196i	−0.0328752	−	0.101179i
$835$		0			0
$836$	−6.41884	+	19.7551i	−0.222000	+	0.683246i
$837$	−2.84083	−	8.74318i	−0.0981935	−	0.302208i
$838$	2.33044	+	7.17235i	0.0805036	+	0.247765i
$839$	−1.19256	+	3.67033i	−0.0411718	+	0.126714i	−0.969530	−	0.244974i	$-0.921221\pi$
$839$	−1.19256	+	3.67033i	−0.0411718	+	0.126714i	0.928358	+	0.371687i	$0.121221\pi$
$840$		0			0
$841$	−5.76596	−	17.7458i	−0.198826	−	0.611925i
$842$	−1.39176	+	1.01117i	−0.0479632	+	0.0348473i
$843$	13.4167			0.462094
$844$	5.16724	−	3.75422i	0.177864	−	0.129226i
$845$		0			0
$846$	0.640724	+	0.465513i	0.0220286	+	0.0160047i
$847$	4.43461	+	3.22193i	0.152375	+	0.110707i
$848$	14.9920	−	46.1406i	0.514827	−	1.58447i
$849$	−24.0890			−0.826732
$850$		0			0
$851$	−2.05144			−0.0703224
$852$	−8.31661	+	25.5959i	−0.284922	+	0.876901i
$853$	−24.1004	−	17.5100i	−0.825183	−	0.599531i	0.0930093	−	0.995665i	$-0.470351\pi$
$853$	−24.1004	−	17.5100i	−0.825183	−	0.599531i	−0.918192	+	0.396135i	$0.870351\pi$
$854$	0.952493	+	0.692027i	0.0325936	+	0.0236807i
$855$		0			0
$856$	1.66450	−	1.20933i	0.0568913	−	0.0413340i
$857$	−36.2041			−1.23671			−0.618354	−	0.785899i	$-0.712200\pi$
$857$	−36.2041			−1.23671			−0.618354	+	0.785899i	$0.712200\pi$
$858$	2.40147	−	1.74477i	0.0819850	−	0.0595656i
$859$	−11.6355	−	35.8104i	−0.396998	−	1.22184i	−0.927394	−	0.374086i	$-0.877957\pi$
$859$	−11.6355	−	35.8104i	−0.396998	−	1.22184i	0.530396	−	0.847750i	$-0.322043\pi$
$860$		0			0
$861$	3.35028	−	10.3111i	0.114177	−	0.351401i
$862$	−0.834757	−	2.56912i	−0.0284319	−	0.0875045i
$863$	0.772275	+	2.37682i	0.0262885	+	0.0809078i	0.963340	−	0.268283i	$-0.0864564\pi$
$863$	0.772275	+	2.37682i	0.0262885	+	0.0809078i	−0.937051	+	0.349191i	$0.886456\pi$
$864$	−0.878171	+	2.70273i	−0.0298760	+	0.0919488i
$865$		0			0
$866$	0.796028	+	2.44992i	0.0270501	+	0.0832518i
$867$	−13.8306	+	10.0485i	−0.469712	+	0.341266i
$868$	22.2253			0.754376
$869$	−23.8728	+	17.3446i	−0.809830	+	0.588376i
$870$		0			0
$871$	−38.3411	−	27.8565i	−1.29914	−	0.943881i
$872$	−1.75741	−	1.27684i	−0.0595136	−	0.0432391i
$873$	−0.00942751	+	0.0290149i	−0.000319073	+	0.000982006i
$874$	1.65143			0.0558606
$875$		0			0
$876$	−22.0697			−0.745668
$877$	10.0273	−	30.8609i	0.338599	−	1.04210i	−0.626323	−	0.779563i	$-0.715441\pi$
$877$	10.0273	−	30.8609i	0.338599	−	1.04210i	0.964922	−	0.262537i	$-0.0845590\pi$
$878$	3.08100	+	2.23847i	0.103979	+	0.0755449i
$879$	−26.0283	−	18.9107i	−0.877912	−	0.637841i
$880$		0			0
$881$	26.9099	−	19.5512i	0.906619	−	0.658697i	−0.0335388	−	0.999437i	$-0.510678\pi$
$881$	26.9099	−	19.5512i	0.906619	−	0.658697i	0.940157	+	0.340740i	$0.110678\pi$
$882$	1.34375			0.0452464
$883$	−8.87730	+	6.44974i	−0.298745	+	0.217051i	−0.727052	−	0.686582i	$-0.759110\pi$
$883$	−8.87730	+	6.44974i	−0.298745	+	0.217051i	0.428307	+	0.903633i	$0.359110\pi$
$884$	16.3794	+	50.4105i	0.550897	+	1.69549i
$885$		0			0
$886$	1.44197	−	4.43794i	0.0484440	−	0.149095i
$887$	8.03604	+	24.7324i	0.269824	+	0.830432i	0.990543	+	0.137205i	$0.0438118\pi$
$887$	8.03604	+	24.7324i	0.269824	+	0.830432i	−0.720719	+	0.693227i	$0.756188\pi$
$888$	0.383805	+	1.18123i	0.0128797	+	0.0396395i
$889$	6.03343	−	18.5690i	0.202355	−	0.622784i
$890$		0			0
$891$	0.794084	+	2.44394i	0.0266028	+	0.0818751i
$892$	24.7446	−	17.9780i	0.828511	−	0.601948i
$893$	13.3791			0.447715
$894$	−3.40731	+	2.47556i	−0.113958	+	0.0827951i
$895$		0			0
$896$	−7.36940	−	5.35418i	−0.246194	−	0.178871i
$897$	6.08026	+	4.41757i	0.203014	+	0.147498i
$898$	0.870436	−	2.67893i	0.0290468	−	0.0893970i
$899$	29.5626			0.985969
$900$		0			0
$901$	−77.8608			−2.59392
$902$	−1.70394	+	5.24420i	−0.0567351	+	0.174613i
$903$	−3.91442	−	2.84400i	−0.130264	−	0.0946423i
$904$	−2.47660	−	1.79936i	−0.0823705	−	0.0598457i
$905$		0			0
$906$	−0.314452	+	0.228463i	−0.0104470	+	0.00759018i
$907$	55.0108			1.82660			0.913302	−	0.407283i	$-0.133524\pi$
$907$	55.0108			1.82660			0.913302	+	0.407283i	$0.133524\pi$
$908$	−21.2421	+	15.4333i	−0.704944	+	0.512172i
$909$	−3.47049	−	10.6811i	−0.115109	−	0.354269i
$910$		0			0
$911$	−3.74142	+	11.5149i	−0.123959	+	0.381506i	−0.993710	−	0.111985i	$-0.964279\pi$
$911$	−3.74142	+	11.5149i	−0.123959	+	0.381506i	0.869751	+	0.493490i	$0.164279\pi$
$912$	4.68680	+	14.4245i	0.155195	+	0.477642i
$913$	2.24908	+	6.92195i	0.0744336	+	0.229083i
$914$	−2.59060	+	7.97306i	−0.0856895	+	0.263725i
$915$		0			0
$916$	8.85816	+	27.2626i	0.292682	+	0.900782i
$917$	15.0858	−	10.9605i	0.498176	−	0.361946i
$918$	1.44086			0.0475555
$919$	−4.83138	+	3.51020i	−0.159372	+	0.115791i	−0.664613	−	0.747188i	$-0.731404\pi$
$919$	−4.83138	+	3.51020i	−0.159372	+	0.115791i	0.505241	+	0.862978i	$0.331404\pi$
$920$		0			0
$921$	16.4200	+	11.9298i	0.541056	+	0.393100i
$922$	−4.92906	−	3.58117i	−0.162330	−	0.117940i
$923$	20.0774	−	61.7918i	0.660855	−	2.03390i
$924$	−6.21254			−0.204378
$925$		0			0
$926$	−3.36370			−0.110538
$927$	0.222796	−	0.685696i	0.00731758	−	0.0225212i
$928$	−7.39324	−	5.37150i	−0.242695	−	0.176328i
$929$	−37.9232	−	27.5528i	−1.24422	−	0.903979i	−0.246348	−	0.969182i	$-0.579230\pi$
$929$	−37.9232	−	27.5528i	−1.24422	−	0.903979i	−0.997872	+	0.0652030i	$0.979230\pi$
$930$		0			0
$931$	18.3650	−	13.3429i	0.601887	−	0.437297i
$932$	1.00636			0.0329644
$933$	15.1468	−	11.0048i	0.495882	−	0.360280i
$934$	0.722201	+	2.22271i	0.0236311	+	0.0727291i
$935$		0			0
$936$	1.40610	−	4.32753i	0.0459598	−	0.141450i
$937$	6.00528	+	18.4823i	0.196184	+	0.603792i	0.999961	+	0.00886093i	$0.00282056\pi$
$937$	6.00528	+	18.4823i	0.196184	+	0.603792i	−0.803777	+	0.594931i	$0.797179\pi$
$938$	−0.962459	−	2.96214i	−0.0314254	−	0.0967174i
$939$	−7.68955	+	23.6660i	−0.250939	+	0.772311i
$940$		0			0
$941$	6.70867	+	20.6472i	0.218696	+	0.673078i	0.998870	+	0.0475159i	$0.0151305\pi$
$941$	6.70867	+	20.6472i	0.218696	+	0.673078i	−0.780174	+	0.625563i	$0.784870\pi$
$942$	1.83673	−	1.33446i	0.0598440	−	0.0434792i
$943$	−13.9610			−0.454633
$944$	18.8172	−	13.6715i	0.612447	−	0.444969i
$945$		0			0
$946$	1.99087	+	1.44645i	0.0647287	+	0.0470282i
$947$	−5.10943	−	3.71222i	−0.166034	−	0.120631i	0.501665	−	0.865062i	$-0.332721\pi$
$947$	−5.10943	−	3.71222i	−0.166034	−	0.120631i	−0.667699	+	0.744431i	$0.732721\pi$
$948$	−6.88092	+	21.1773i	−0.223482	+	0.687807i
$949$	53.2792			1.72952
$950$		0			0
$951$	25.1880			0.816778
$952$	−2.18668	+	6.72990i	−0.0708707	+	0.218117i
$953$	17.6380	+	12.8147i	0.571350	+	0.415110i	0.835595	−	0.549345i	$-0.185123\pi$
$953$	17.6380	+	12.8147i	0.571350	+	0.415110i	−0.264245	+	0.964455i	$0.585123\pi$
$954$	2.66195	+	1.93402i	0.0861839	+	0.0626163i
$955$		0			0
$956$	12.9115	−	9.38076i	0.417588	−	0.303395i
$957$	−8.26351			−0.267121
$958$	−5.13625	+	3.73171i	−0.165945	+	0.120566i
$959$	4.04324	+	12.4438i	0.130563	+	0.401831i
$960$		0			0
$961$	16.5366	−	50.8943i	0.533437	−	1.64175i
$962$	−0.456116	−	1.40378i	−0.0147058	−	0.0452597i
$963$	−0.654089	−	2.01308i	−0.0210777	−	0.0648705i
$964$	0.767705	−	2.36275i	0.0247261	−	0.0760992i
$965$		0			0
$966$	0.152630	+	0.469746i	0.00491078	+	0.0151138i
$967$	−5.67338	+	4.12195i	−0.182444	+	0.132553i	−0.675259	−	0.737581i	$-0.735968\pi$
$967$	−5.67338	+	4.12195i	−0.182444	+	0.132553i	0.492815	+	0.870134i	$0.335968\pi$
$968$	−4.27353			−0.137356
$969$	19.6922	−	14.3072i	0.632604	−	0.459614i
$970$		0			0
$971$	−5.99504	−	4.35565i	−0.192390	−	0.139779i	0.487420	−	0.873167i	$-0.337938\pi$
$971$	−5.99504	−	4.35565i	−0.192390	−	0.139779i	−0.679810	+	0.733388i	$0.737938\pi$
$972$	1.56877	+	1.13978i	0.0503184	+	0.0365585i
$973$	4.79690	−	14.7633i	0.153781	−	0.473291i
$974$	−7.00909			−0.224586
$975$		0			0
$976$	13.9237			0.445688
$977$	−12.1315	+	37.3370i	−0.388122	+	1.19452i	0.546068	+	0.837741i	$0.316124\pi$
$977$	−12.1315	+	37.3370i	−0.388122	+	1.19452i	−0.934190	+	0.356776i	$0.883876\pi$
$978$	0.914467	+	0.664399i	0.0292414	+	0.0212451i
$979$	2.87054	+	2.08557i	0.0917430	+	0.0666552i
$980$		0			0
$981$	−1.80802	+	1.31360i	−0.0577256	+	0.0419401i
$982$	1.50597			0.0480573
$983$	−14.8719	+	10.8051i	−0.474341	+	0.344629i	−0.799131	−	0.601158i	$-0.794706\pi$
$983$	−14.8719	+	10.8051i	−0.474341	+	0.344629i	0.324790	+	0.945786i	$0.394706\pi$
$984$	2.61198	+	8.03883i	0.0832667	+	0.256269i
$985$		0			0
$986$	−1.43181	+	4.40665i	−0.0455980	+	0.140336i
$987$	1.23653	+	3.80566i	0.0393593	+	0.121135i
$988$	−11.6932	−	35.9881i	−0.372012	−	1.14493i
$989$	−1.92536	+	5.92564i	−0.0612228	+	0.188424i
$990$		0			0
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	0.783250	+	0.621707i	$0.213560\pi$
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	−0.268233	+	0.963354i	$0.586440\pi$
$992$	−21.1357	+	15.3560i	−0.671060	+	0.487554i
$993$	30.4193			0.965326
$994$	3.45442	−	2.50978i	0.109567	−	0.0796054i
$995$		0			0
$996$	4.44322	+	3.22819i	0.140789	+	0.102289i
$997$	−29.4256	−	21.3789i	−0.931917	−	0.677077i	0.0145444	−	0.999894i	$-0.495370\pi$
$997$	−29.4256	−	21.3789i	−0.931917	−	0.677077i	−0.946461	+	0.322817i	$0.895370\pi$
$998$	1.54917	−	4.76785i	0.0490381	−	0.150924i
$999$	1.27778			0.0404273

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.226.2		12
5.2	odd	4		375.2.i.d.274.3		24
5.3	odd	4		375.2.i.d.274.4		24
5.4	even	2		75.2.g.c.46.2	yes	12
15.14	odd	2		225.2.h.d.46.2		12
25.6	even	5	inner	375.2.g.c.151.2		12
25.8	odd	20		375.2.i.d.349.3		24
25.9	even	10		1875.2.a.j.1.4		6
25.12	odd	20		1875.2.b.f.1249.5		12
25.13	odd	20		1875.2.b.f.1249.8		12
25.16	even	5		1875.2.a.k.1.3		6
25.17	odd	20		375.2.i.d.349.4		24
25.19	even	10		75.2.g.c.31.2	✓	12
75.41	odd	10		5625.2.a.q.1.4		6
75.44	odd	10		225.2.h.d.181.2		12
75.59	odd	10		5625.2.a.p.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	25.19	even	10
75.2.g.c.46.2	yes	12	5.4	even	2
225.2.h.d.46.2		12	15.14	odd	2
225.2.h.d.181.2		12	75.44	odd	10
375.2.g.c.151.2		12	25.6	even	5	inner
375.2.g.c.226.2		12	1.1	even	1	trivial
375.2.i.d.274.3		24	5.2	odd	4
375.2.i.d.274.4		24	5.3	odd	4
375.2.i.d.349.3		24	25.8	odd	20
375.2.i.d.349.4		24	25.17	odd	20
1875.2.a.j.1.4		6	25.9	even	10
1875.2.a.k.1.3		6	25.16	even	5
1875.2.b.f.1249.5		12	25.12	odd	20
1875.2.b.f.1249.8		12	25.13	odd	20
5625.2.a.p.1.3		6	75.59	odd	10
5625.2.a.q.1.4		6	75.41	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0762527 + 0.234682i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.56877 + 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(-0.0762527 + 0.234682i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(1.56877 + 1.13978i) q^{4} +(0.199632 - 0.145041i) q^{6} +1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(0.309017 + 0.951057i) q^{9} +(0.794084 - 2.44394i) q^{11} +(-0.599218 - 1.84420i) q^{12} +(1.44659 + 4.45215i) q^{13} +(-0.0950687 + 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(4.72397 - 3.43216i) q^{17} -0.246759 q^{18} +(-3.37244 + 2.45022i) q^{19} +(-1.00865 - 0.732827i) q^{21} +(0.512997 + 0.372714i) q^{22} +(-0.496117 + 1.52689i) q^{23} +0.972011 q^{24} -1.15514 q^{26} +(0.309017 - 0.951057i) q^{27} +(1.95588 + 1.42103i) q^{28} +(2.60158 + 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182 q^{32} +(-2.07894 + 1.51044i) q^{33} +(0.445250 + 1.37034i) q^{34} +(-0.599218 + 1.84420i) q^{36} +(0.394857 + 1.21524i) q^{37} +(-0.317865 - 0.978287i) q^{38} +(1.44659 - 4.45215i) q^{39} +(2.68719 + 8.27031i) q^{41} +(0.248893 - 0.180832i) q^{42} +3.88086 q^{43} +(4.03129 - 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(-2.59656 - 1.88651i) q^{47} +(1.12432 - 3.46029i) q^{48} -5.44559 q^{49} -5.83914 q^{51} +(-2.80510 + 8.63320i) q^{52} +(-10.7877 - 7.83770i) q^{53} +(0.199632 + 0.145041i) q^{54} +(-0.980418 + 0.712315i) q^{56} +4.16857 q^{57} +(-0.641964 + 0.466414i) q^{58} +(-1.97548 - 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(0.701000 + 2.15746i) q^{62} +(0.385270 + 1.18574i) q^{63} +(-2.03194 + 6.25366i) q^{64} +(-0.195947 - 0.603064i) q^{66} +(-8.19034 + 5.95063i) q^{67} +11.3227 q^{68} +(1.29885 - 0.943670i) q^{69} +(-11.2284 - 8.15794i) q^{71} +(-0.786373 - 0.571334i) q^{72} +(3.51704 - 10.8243i) q^{73} -0.315305 q^{74} -8.08332 q^{76} +(0.990032 - 3.04700i) q^{77} +(0.934531 + 0.678976i) q^{78} +(-9.29008 - 6.74964i) q^{79} +(-0.809017 + 0.587785i) q^{81} -2.14580 q^{82} +(-2.29137 + 1.66478i) q^{83} +(-0.747080 - 2.29928i) q^{84} +(-0.295926 + 0.910766i) q^{86} +(-0.993717 - 3.05835i) q^{87} +(0.771858 + 2.37554i) q^{88} +(-0.426682 + 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-2.51861 + 1.82988i) q^{92} -9.19312 q^{93} +(0.640724 - 0.465513i) q^{94} +(2.29908 + 1.67038i) q^{96} +(0.0246815 + 0.0179322i) q^{97} +(0.415241 - 1.27798i) q^{98} +2.56971 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

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