LMFDB - Embedded newform 250.2.e.b.149.2

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			149.2
Root			$0.951057 + 0.309017i$ of defining polynomial
Character	$\chi$	$=$	250.149
Dual form			250.2.e.b.99.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(-0.224514 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{6} +3.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.881966 + 2.71441i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(-0.224514 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{6} +3.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.881966 + 2.71441i) q^{9} +(1.30902 - 4.02874i) q^{11} +(-0.363271 + 0.118034i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.673542 + 0.927051i) q^{17} +2.85410i q^{18} +(4.73607 - 3.44095i) q^{19} +(-0.927051 - 0.673542i) q^{21} +(2.48990 - 3.42705i) q^{22} +(-1.67760 - 0.545085i) q^{23} -0.381966 q^{24} -1.00000 q^{26} +(-2.12663 - 0.690983i) q^{27} +(-1.76336 + 2.42705i) q^{28} +(-7.66312 - 5.56758i) q^{29} +(0.190983 - 0.138757i) q^{31} +1.00000i q^{32} +(0.951057 + 1.30902i) q^{33} +(0.354102 + 1.08981i) q^{34} +(-0.881966 + 2.71441i) q^{36} +(-7.91872 + 2.57295i) q^{37} +(5.56758 - 1.80902i) q^{38} +(0.118034 - 0.363271i) q^{39} +(0.454915 + 1.40008i) q^{41} +(-0.673542 - 0.927051i) q^{42} -6.23607i q^{43} +(3.42705 - 2.48990i) q^{44} +(-1.42705 - 1.03681i) q^{46} +(7.02067 - 9.66312i) q^{47} +(-0.363271 - 0.118034i) q^{48} -2.00000 q^{49} -0.437694 q^{51} +(-0.951057 - 0.309017i) q^{52} +(6.15537 - 8.47214i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(-2.42705 + 1.76336i) q^{56} +2.23607i q^{57} +(-5.56758 - 7.66312i) q^{58} +(1.38197 + 4.25325i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(0.224514 - 0.0729490i) q^{62} +(-8.14324 + 2.64590i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.500000 + 1.53884i) q^{66} +(-6.01661 - 8.28115i) q^{67} +1.14590i q^{68} +(0.545085 - 0.396027i) q^{69} +(2.42705 + 1.76336i) q^{71} +(-1.67760 + 2.30902i) q^{72} +(7.33094 + 2.38197i) q^{73} -8.32624 q^{74} +5.85410 q^{76} +(12.0862 + 3.92705i) q^{77} +(0.224514 - 0.309017i) q^{78} +(-5.85410 - 4.25325i) q^{79} +(-6.23607 + 4.53077i) q^{81} +1.47214i q^{82} +(2.66141 + 3.66312i) q^{83} +(-0.354102 - 1.08981i) q^{84} +(1.92705 - 5.93085i) q^{86} +(3.44095 - 1.11803i) q^{87} +(4.02874 - 1.30902i) q^{88} +(-1.38197 + 4.25325i) q^{89} +(-0.927051 - 2.85317i) q^{91} +(-1.03681 - 1.42705i) q^{92} +0.0901699i q^{93} +(9.66312 - 7.02067i) q^{94} +(-0.309017 - 0.224514i) q^{96} +(-5.62058 + 7.73607i) q^{97} +(-1.90211 - 0.618034i) q^{98} +12.0902 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 $\left(\mathbb{Z}/250\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	−0.224514	+	0.309017i	−0.129623	+	0.178411i	−0.868895	−	0.494996i	$-0.835170\pi$
$3$	−0.224514	+	0.309017i	−0.129623	+	0.178411i	0.739272	+	0.673407i	$0.235170\pi$
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		0			0
$5$		0			0
$6$	−0.309017	+	0.224514i	−0.126156	+	0.0916575i
$7$			3.00000i			1.13389i	0.823754	+	0.566947i	$0.191875\pi$
$7$			3.00000i			1.13389i	−0.823754	+	0.566947i	$0.808125\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.881966	+	2.71441i	0.293989	+	0.904804i
$10$		0			0
$11$	1.30902	−	4.02874i	0.394683	−	1.21471i	−0.534524	−	0.845153i	$-0.679509\pi$
$11$	1.30902	−	4.02874i	0.394683	−	1.21471i	0.929208	−	0.369558i	$-0.120491\pi$
$12$	−0.363271	+	0.118034i	−0.104867	+	0.0340735i
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i	−0.437919	−	0.899014i	$-0.644284\pi$
$13$	−0.951057	+	0.309017i	−0.263776	+	0.0857059i	0.174143	+	0.984720i	$0.444284\pi$
$14$	−0.927051	+	2.85317i	−0.247765	+	0.762542i
$15$		0			0
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	0.673542	+	0.927051i	0.163358	+	0.224843i	0.882847	−	0.469661i	$-0.155624\pi$
$17$	0.673542	+	0.927051i	0.163358	+	0.224843i	−0.719489	+	0.694504i	$0.755624\pi$
$18$			2.85410i			0.672718i
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.107719	−	0.994181i	$-0.465645\pi$
$19$	4.73607	−	3.44095i	1.08653	−	0.789409i	0.978810	+	0.204772i	$0.0656454\pi$
$20$		0			0
$21$	−0.927051	−	0.673542i	−0.202299	−	0.146979i
$22$	2.48990	−	3.42705i	0.530848	−	0.730650i
$23$	−1.67760	−	0.545085i	−0.349804	−	0.113658i	0.128845	−	0.991665i	$-0.458873\pi$
$23$	−1.67760	−	0.545085i	−0.349804	−	0.113658i	−0.478648	+	0.878007i	$0.658873\pi$
$24$	−0.381966			−0.0779685
$25$		0			0
$26$	−1.00000			−0.196116
$27$	−2.12663	−	0.690983i	−0.409270	−	0.132980i
$28$	−1.76336	+	2.42705i	−0.333243	+	0.458670i
$29$	−7.66312	−	5.56758i	−1.42301	−	1.03387i	−0.991266	−	0.131875i	$-0.957900\pi$
$29$	−7.66312	−	5.56758i	−1.42301	−	1.03387i	−0.431739	−	0.901998i	$-0.642100\pi$
$30$		0			0
$31$	0.190983	−	0.138757i	0.0343016	−	0.0249215i	−0.570502	−	0.821296i	$-0.693251\pi$
$31$	0.190983	−	0.138757i	0.0343016	−	0.0249215i	0.604804	+	0.796374i	$0.293251\pi$
$32$			1.00000i			0.176777i
$33$	0.951057	+	1.30902i	0.165558	+	0.227871i
$34$	0.354102	+	1.08981i	0.0607280	+	0.186902i
$35$		0			0
$36$	−0.881966	+	2.71441i	−0.146994	+	0.452402i
$37$	−7.91872	+	2.57295i	−1.30183	+	0.422990i	−0.876218	−	0.481915i	$-0.839941\pi$
$37$	−7.91872	+	2.57295i	−1.30183	+	0.422990i	−0.425612	+	0.904906i	$0.639941\pi$
$38$	5.56758	−	1.80902i	0.903181	−	0.293461i
$39$	0.118034	−	0.363271i	0.0189006	−	0.0581700i
$40$		0			0
$41$	0.454915	+	1.40008i	0.0710458	+	0.218656i	0.980275	−	0.197640i	$-0.0633278\pi$
$41$	0.454915	+	1.40008i	0.0710458	+	0.218656i	−0.909229	+	0.416297i	$0.863328\pi$
$42$	−0.673542	−	0.927051i	−0.103930	−	0.143047i
$43$		−	6.23607i		−	0.950991i	−0.879718	−	0.475496i	$-0.842269\pi$
$43$		−	6.23607i		−	0.950991i	0.879718	−	0.475496i	$-0.157731\pi$
$44$	3.42705	−	2.48990i	0.516647	−	0.375366i
$45$		0			0
$46$	−1.42705	−	1.03681i	−0.210407	−	0.152870i
$47$	7.02067	−	9.66312i	1.02407	−	1.40951i	0.114759	−	0.993393i	$-0.463391\pi$
$47$	7.02067	−	9.66312i	1.02407	−	1.40951i	0.909311	−	0.416117i	$-0.136609\pi$
$48$	−0.363271	−	0.118034i	−0.0524337	−	0.0170367i
$49$	−2.00000			−0.285714
$50$		0			0
$51$	−0.437694			−0.0612894
$52$	−0.951057	−	0.309017i	−0.131888	−	0.0428529i
$53$	6.15537	−	8.47214i	0.845505	−	1.16374i	−0.139331	−	0.990246i	$-0.544495\pi$
$53$	6.15537	−	8.47214i	0.845505	−	1.16374i	0.984835	−	0.173491i	$-0.0555049\pi$
$54$	−1.80902	−	1.31433i	−0.246176	−	0.178857i
$55$		0			0
$56$	−2.42705	+	1.76336i	−0.324328	+	0.235638i
$57$			2.23607i			0.296174i
$58$	−5.56758	−	7.66312i	−0.731059	−	1.00622i
$59$	1.38197	+	4.25325i	0.179917	+	0.553727i	0.999824	−	0.0187700i	$-0.00597502\pi$
$59$	1.38197	+	4.25325i	0.179917	+	0.553727i	−0.819907	+	0.572496i	$0.805975\pi$
$60$		0			0
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	0.608357	+	0.793663i	$0.291829\pi$
$61$	−2.73607	+	8.42075i	−0.350318	+	1.07817i	−0.958675	+	0.284504i	$0.908171\pi$
$62$	0.224514	−	0.0729490i	0.0285133	−	0.00926453i
$63$	−8.14324	+	2.64590i	−1.02595	+	0.333352i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$		0			0
$66$	0.500000	+	1.53884i	0.0615457	+	0.189418i
$67$	−6.01661	−	8.28115i	−0.735046	−	1.01170i	−0.998888	−	0.0471381i	$-0.984990\pi$
$67$	−6.01661	−	8.28115i	−0.735046	−	1.01170i	0.263843	−	0.964566i	$-0.415010\pi$
$68$			1.14590i			0.138961i
$69$	0.545085	−	0.396027i	0.0656205	−	0.0476761i
$70$		0			0
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	0.722416	−	0.691459i	$-0.243032\pi$
$71$	2.42705	+	1.76336i	0.288038	+	0.209272i	−0.434378	+	0.900731i	$0.643032\pi$
$72$	−1.67760	+	2.30902i	−0.197707	+	0.272120i
$73$	7.33094	+	2.38197i	0.858021	+	0.278788i	0.704802	−	0.709404i	$-0.251036\pi$
$73$	7.33094	+	2.38197i	0.858021	+	0.278788i	0.153219	+	0.988192i	$0.451036\pi$
$74$	−8.32624			−0.967905
$75$		0			0
$76$	5.85410			0.671512
$77$	12.0862	+	3.92705i	1.37735	+	0.447529i
$78$	0.224514	−	0.309017i	0.0254212	−	0.0349893i
$79$	−5.85410	−	4.25325i	−0.658638	−	0.478528i	0.207565	−	0.978221i	$-0.433446\pi$
$79$	−5.85410	−	4.25325i	−0.658638	−	0.478528i	−0.866203	+	0.499693i	$0.833446\pi$
$80$		0			0
$81$	−6.23607	+	4.53077i	−0.692896	+	0.503419i
$82$			1.47214i			0.162570i
$83$	2.66141	+	3.66312i	0.292128	+	0.402080i	0.929704	−	0.368308i	$-0.120063\pi$
$83$	2.66141	+	3.66312i	0.292128	+	0.402080i	−0.637576	+	0.770387i	$0.720063\pi$
$84$	−0.354102	−	1.08981i	−0.0386357	−	0.118908i
$85$		0			0
$86$	1.92705	−	5.93085i	0.207799	−	0.639540i
$87$	3.44095	−	1.11803i	0.368909	−	0.119866i
$88$	4.02874	−	1.30902i	0.429465	−	0.139542i
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	−0.997199	−	0.0747893i	$-0.976172\pi$
$89$	−1.38197	+	4.25325i	−0.146488	+	0.450844i	0.850711	+	0.525633i	$0.176172\pi$
$90$		0			0
$91$	−0.927051	−	2.85317i	−0.0971813	−	0.299093i
$92$	−1.03681	−	1.42705i	−0.108095	−	0.148780i
$93$			0.0901699i			0.00935019i
$94$	9.66312	−	7.02067i	0.996675	−	0.724126i
$95$		0			0
$96$	−0.309017	−	0.224514i	−0.0315389	−	0.0229144i
$97$	−5.62058	+	7.73607i	−0.570684	+	0.785479i	−0.992635	−	0.121140i	$-0.961345\pi$
$97$	−5.62058	+	7.73607i	−0.570684	+	0.785479i	0.421952	+	0.906618i	$0.361345\pi$
$98$	−1.90211	−	0.618034i	−0.192142	−	0.0624309i
$99$	12.0902			1.21511
$100$		0			0
$101$	0.618034			0.0614967			0.0307483	−	0.999527i	$-0.490211\pi$
$101$	0.618034			0.0614967			0.0307483	+	0.999527i	$0.490211\pi$
$102$	−0.416272	−	0.135255i	−0.0412171	−	0.0133922i
$103$	−7.72696	+	10.6353i	−0.761360	+	1.04792i	0.235739	+	0.971816i	$0.424249\pi$
$103$	−7.72696	+	10.6353i	−0.761360	+	1.04792i	−0.997100	+	0.0761065i	$0.975751\pi$
$104$	−0.809017	−	0.587785i	−0.0793306	−	0.0576371i
$105$		0			0
$106$	8.47214	−	6.15537i	0.822887	−	0.597862i
$107$			1.09017i			0.105391i	0.998611	+	0.0526954i	$0.0167812\pi$
$107$			1.09017i			0.105391i	−0.998611	+	0.0526954i	$0.983219\pi$
$108$	−1.31433	−	1.80902i	−0.126471	−	0.174073i
$109$	4.63525	+	14.2658i	0.443977	+	1.36642i	0.883602	+	0.468239i	$0.155111\pi$
$109$	4.63525	+	14.2658i	0.443977	+	1.36642i	−0.439625	+	0.898181i	$0.644889\pi$
$110$		0			0
$111$	0.982779	−	3.02468i	0.0932813	−	0.287090i
$112$	−2.85317	+	0.927051i	−0.269599	+	0.0875981i
$113$	−3.57971	+	1.16312i	−0.336751	+	0.109417i	−0.472511	−	0.881325i	$-0.656652\pi$
$113$	−3.57971	+	1.16312i	−0.336751	+	0.109417i	0.135760	+	0.990742i	$0.456652\pi$
$114$	−0.690983	+	2.12663i	−0.0647165	+	0.199177i
$115$		0			0
$116$	−2.92705	−	9.00854i	−0.271770	−	0.836422i
$117$	−1.67760	−	2.30902i	−0.155094	−	0.213469i
$118$			4.47214i			0.411693i
$119$	−2.78115	+	2.02063i	−0.254948	+	0.185230i
$120$		0			0
$121$	−5.61803	−	4.08174i	−0.510730	−	0.371067i
$122$	−5.20431	+	7.16312i	−0.471176	+	0.648518i
$123$	−0.534785	−	0.173762i	−0.0482199	−	0.0156676i
$124$	0.236068			0.0211995
$125$		0			0
$126$	−8.56231			−0.762791
$127$	3.35520	+	1.09017i	0.297726	+	0.0967369i	0.454071	−	0.890966i	$-0.349971\pi$
$127$	3.35520	+	1.09017i	0.297726	+	0.0967369i	−0.156345	+	0.987702i	$0.549971\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	1.92705	+	1.40008i	0.169667	+	0.123271i
$130$		0			0
$131$	13.2812	−	9.64932i	1.16038	−	0.843065i	0.170554	−	0.985348i	$-0.445444\pi$
$131$	13.2812	−	9.64932i	1.16038	−	0.843065i	0.989826	+	0.142283i	$0.0454444\pi$
$132$			1.61803i			0.140832i
$133$	10.3229	+	14.2082i	0.895106	+	1.23201i
$134$	−3.16312	−	9.73508i	−0.273252	−	0.840983i
$135$		0			0
$136$	−0.354102	+	1.08981i	−0.0303640	+	0.0934508i
$137$	4.84104	−	1.57295i	0.413598	−	0.134386i	−0.0948243	−	0.995494i	$-0.530229\pi$
$137$	4.84104	−	1.57295i	0.413598	−	0.134386i	0.508422	+	0.861108i	$0.330229\pi$
$138$	0.640786	−	0.208204i	0.0545473	−	0.0177235i
$139$	1.64590	−	5.06555i	0.139603	−	0.429655i	−0.856674	−	0.515858i	$-0.827473\pi$
$139$	1.64590	−	5.06555i	0.139603	−	0.429655i	0.996278	+	0.0862030i	$0.0274734\pi$
$140$		0			0
$141$	1.40983	+	4.33901i	0.118729	+	0.365411i
$142$	1.76336	+	2.42705i	0.147978	+	0.203674i
$143$			4.23607i			0.354238i
$144$	−2.30902	+	1.67760i	−0.192418	+	0.139800i
$145$		0			0
$146$	6.23607	+	4.53077i	0.516101	+	0.374969i
$147$	0.449028	−	0.618034i	0.0370352	−	0.0509746i
$148$	−7.91872	−	2.57295i	−0.650915	−	0.211495i
$149$	−2.23607			−0.183186			−0.0915929	−	0.995797i	$-0.529196\pi$
$149$	−2.23607			−0.183186			−0.0915929	+	0.995797i	$0.529196\pi$
$150$		0			0
$151$	−9.70820			−0.790042			−0.395021	−	0.918672i	$-0.629263\pi$
$151$	−9.70820			−0.790042			−0.395021	+	0.918672i	$0.629263\pi$
$152$	5.56758	+	1.80902i	0.451591	+	0.146731i
$153$	−1.92236	+	2.64590i	−0.155413	+	0.213908i
$154$	10.2812	+	7.46969i	0.828479	+	0.601925i
$155$		0			0
$156$	0.309017	−	0.224514i	0.0247412	−	0.0179755i
$157$		−	4.56231i		−	0.364112i	−0.983288	−	0.182056i	$-0.941725\pi$
$157$		−	4.56231i		−	0.364112i	0.983288	−	0.182056i	$-0.0582752\pi$
$158$	−4.25325	−	5.85410i	−0.338371	−	0.465727i
$159$	1.23607	+	3.80423i	0.0980266	+	0.301695i
$160$		0			0
$161$	1.63525	−	5.03280i	0.128876	−	0.396640i
$162$	−7.33094	+	2.38197i	−0.575973	+	0.187145i
$163$	−1.76336	+	0.572949i	−0.138117	+	0.0448768i	−0.377260	−	0.926108i	$-0.623134\pi$
$163$	−1.76336	+	0.572949i	−0.138117	+	0.0448768i	0.239143	+	0.970984i	$0.423134\pi$
$164$	−0.454915	+	1.40008i	−0.0355229	+	0.109328i
$165$		0			0
$166$	1.39919	+	4.30625i	0.108598	+	0.334230i
$167$	7.86572	+	10.8262i	0.608668	+	0.837759i	0.996467	−	0.0839844i	$-0.0267646\pi$
$167$	7.86572	+	10.8262i	0.608668	+	0.837759i	−0.387799	+	0.921744i	$0.626765\pi$
$168$		−	1.14590i		−	0.0884080i
$169$	−9.70820	+	7.05342i	−0.746785	+	0.542571i
$170$		0			0
$171$	13.5172	+	9.82084i	1.03369	+	0.751018i
$172$	3.66547	−	5.04508i	0.279489	−	0.384684i
$173$	−1.17557	−	0.381966i	−0.0893770	−	0.0290403i	0.263987	−	0.964526i	$-0.414962\pi$
$173$	−1.17557	−	0.381966i	−0.0893770	−	0.0290403i	−0.353364	+	0.935486i	$0.614962\pi$
$174$	3.61803			0.274282
$175$		0			0
$176$	4.23607			0.319306
$177$	−1.62460	−	0.527864i	−0.122112	−	0.0396767i
$178$	−2.62866	+	3.61803i	−0.197026	+	0.271183i
$179$	9.04508	+	6.57164i	0.676061	+	0.491187i	0.872049	−	0.489419i	$-0.162791\pi$
$179$	9.04508	+	6.57164i	0.676061	+	0.491187i	−0.195987	+	0.980606i	$0.562791\pi$
$180$		0			0
$181$	−4.38197	+	3.18368i	−0.325709	+	0.236641i	−0.738608	−	0.674136i	$-0.764516\pi$
$181$	−4.38197	+	3.18368i	−0.325709	+	0.236641i	0.412899	+	0.910777i	$0.364516\pi$
$182$		−	3.00000i		−	0.222375i
$183$	−1.98787	−	2.73607i	−0.146948	−	0.202256i
$184$	−0.545085	−	1.67760i	−0.0401842	−	0.123674i
$185$		0			0
$186$	−0.0278640	+	0.0857567i	−0.00204309	+	0.00628799i
$187$	4.61653	−	1.50000i	0.337594	−	0.109691i
$188$	11.3597	−	3.69098i	0.828490	−	0.269193i
$189$	2.07295	−	6.37988i	0.150785	−	0.464068i
$190$		0			0
$191$	−4.21885	−	12.9843i	−0.305265	−	0.939509i	−0.979578	−	0.201064i	$-0.935560\pi$
$191$	−4.21885	−	12.9843i	−0.305265	−	0.939509i	0.674313	−	0.738446i	$-0.264440\pi$
$192$	−0.224514	−	0.309017i	−0.0162029	−	0.0223014i
$193$		−	14.6525i		−	1.05471i	−0.849646	−	0.527354i	$-0.823184\pi$
$193$		−	14.6525i		−	1.05471i	0.849646	−	0.527354i	$-0.176816\pi$
$194$	−7.73607	+	5.62058i	−0.555417	+	0.403534i
$195$		0			0
$196$	−1.61803	−	1.17557i	−0.115574	−	0.0839693i
$197$	−7.05342	+	9.70820i	−0.502536	+	0.691681i	−0.982638	−	0.185531i	$-0.940599\pi$
$197$	−7.05342	+	9.70820i	−0.502536	+	0.691681i	0.480103	+	0.877212i	$0.340599\pi$
$198$	11.4984	+	3.73607i	0.817158	+	0.265511i
$199$	−2.56231			−0.181637			−0.0908185	−	0.995867i	$-0.528948\pi$
$199$	−2.56231			−0.181637			−0.0908185	+	0.995867i	$0.528948\pi$
$200$		0			0
$201$	3.90983			0.275778
$202$	0.587785	+	0.190983i	0.0413564	+	0.0134375i
$203$	16.7027	−	22.9894i	1.17230	−	1.61354i
$204$	−0.354102	−	0.257270i	−0.0247921	−	0.0180125i
$205$		0			0
$206$	−10.6353	+	7.72696i	−0.740993	+	0.538363i
$207$		−	5.03444i		−	0.349918i
$208$	−0.587785	−	0.809017i	−0.0407556	−	0.0560952i
$209$	−7.66312	−	23.5847i	−0.530069	−	1.63138i
$210$		0			0
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	0.373830	+	0.927497i	$0.378044\pi$
$211$	−6.88197	+	21.1805i	−0.473774	+	1.45813i	−0.847604	+	0.530629i	$0.821956\pi$
$212$	9.95959	−	3.23607i	0.684028	−	0.222254i
$213$	−1.08981	+	0.354102i	−0.0746728	+	0.0242627i
$214$	−0.336881	+	1.03681i	−0.0230287	+	0.0708751i
$215$		0			0
$216$	−0.690983	−	2.12663i	−0.0470154	−	0.144699i
$217$	0.416272	+	0.572949i	0.0282584	+	0.0388943i
$218$			15.0000i			1.01593i
$219$	−2.38197	+	1.73060i	−0.160958	+	0.116943i
$220$		0			0
$221$	−0.927051	−	0.673542i	−0.0623602	−	0.0453073i
$222$	1.86936	−	2.57295i	0.125463	−	0.172685i
$223$	−8.55951	−	2.78115i	−0.573187	−	0.186240i	0.00805911	−	0.999968i	$-0.497435\pi$
$223$	−8.55951	−	2.78115i	−0.573187	−	0.186240i	−0.581246	+	0.813728i	$0.697435\pi$
$224$	−3.00000			−0.200446
$225$		0			0
$226$	−3.76393			−0.250373
$227$	−27.9237	−	9.07295i	−1.85336	−	0.602193i	−0.996195	−	0.0871483i	$-0.972225\pi$
$227$	−27.9237	−	9.07295i	−1.85336	−	0.602193i	−0.857163	−	0.515044i	$-0.827775\pi$
$228$	−1.31433	+	1.80902i	−0.0870435	+	0.119805i
$229$	−2.07295	−	1.50609i	−0.136984	−	0.0995249i	0.517183	−	0.855875i	$-0.326981\pi$
$229$	−2.07295	−	1.50609i	−0.136984	−	0.0995249i	−0.654167	+	0.756350i	$0.726981\pi$
$230$		0			0
$231$	−3.92705	+	2.85317i	−0.258381	+	0.187725i
$232$		−	9.47214i		−	0.621876i
$233$	−8.40051	−	11.5623i	−0.550336	−	0.757472i	0.439722	−	0.898134i	$-0.355077\pi$
$233$	−8.40051	−	11.5623i	−0.550336	−	0.757472i	−0.990058	+	0.140662i	$0.955077\pi$
$234$	−0.881966	−	2.71441i	−0.0576559	−	0.177447i
$235$		0			0
$236$	−1.38197	+	4.25325i	−0.0899583	+	0.276863i
$237$	2.62866	−	0.854102i	0.170750	−	0.0554799i
$238$	−3.26944	+	1.06231i	−0.211926	+	0.0688591i
$239$	2.13525	−	6.57164i	0.138118	−	0.425084i	−0.857944	−	0.513743i	$-0.828258\pi$
$239$	2.13525	−	6.57164i	0.138118	−	0.425084i	0.996062	+	0.0886595i	$0.0282583\pi$
$240$		0			0
$241$	4.82624	+	14.8536i	0.310885	+	0.956807i	0.977415	+	0.211328i	$0.0677789\pi$
$241$	4.82624	+	14.8536i	0.310885	+	0.956807i	−0.666530	+	0.745478i	$0.732221\pi$
$242$	−4.08174	−	5.61803i	−0.262384	−	0.361141i
$243$		−	9.65248i		−	0.619207i
$244$	−7.16312	+	5.20431i	−0.458572	+	0.333172i
$245$		0			0
$246$	−0.454915	−	0.330515i	−0.0290043	−	0.0210729i
$247$	−3.44095	+	4.73607i	−0.218943	+	0.301349i
$248$	0.224514	+	0.0729490i	0.0142567	+	0.00463227i
$249$	−1.72949			−0.109602
$250$		0			0
$251$	0.819660			0.0517365			0.0258682	−	0.999665i	$-0.491765\pi$
$251$	0.819660			0.0517365			0.0258682	+	0.999665i	$0.491765\pi$
$252$	−8.14324	−	2.64590i	−0.512976	−	0.166676i
$253$	−4.39201	+	6.04508i	−0.276123	+	0.380051i
$254$	2.85410	+	2.07363i	0.179082	+	0.130111i
$255$		0			0
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$		−	25.7426i		−	1.60578i	−0.596126	−	0.802891i	$-0.703294\pi$
$257$		−	25.7426i		−	1.60578i	0.596126	−	0.802891i	$-0.296706\pi$
$258$	1.40008	+	1.92705i	0.0871655	+	0.119973i
$259$	−7.71885	−	23.7562i	−0.479626	−	1.47614i
$260$		0			0
$261$	8.35410	−	25.7113i	0.517106	−	1.59149i
$262$	15.6129	−	5.07295i	0.964570	−	0.313408i
$263$	−4.39201	+	1.42705i	−0.270823	+	0.0879957i	−0.441280	−	0.897369i	$-0.645476\pi$
$263$	−4.39201	+	1.42705i	−0.270823	+	0.0879957i	0.170457	+	0.985365i	$0.445476\pi$
$264$	−0.500000	+	1.53884i	−0.0307729	+	0.0947092i
$265$		0			0
$266$	5.42705	+	16.7027i	0.332754	+	1.02411i
$267$	−1.00406	−	1.38197i	−0.0614473	−	0.0845749i
$268$		−	10.2361i		−	0.625267i
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	−0.539685	−	0.841867i	$-0.681457\pi$
$269$	1.54508	−	1.12257i	0.0942055	−	0.0684443i	0.633891	+	0.773422i	$0.281457\pi$
$270$		0			0
$271$	−23.0623	−	16.7557i	−1.40094	−	1.01784i	−0.994564	−	0.104131i	$-0.966794\pi$
$271$	−23.0623	−	16.7557i	−1.40094	−	1.01784i	−0.406372	−	0.913708i	$-0.633206\pi$
$272$	−0.673542	+	0.927051i	−0.0408395	+	0.0562107i
$273$	1.08981	+	0.354102i	0.0659585	+	0.0214312i
$274$	5.09017			0.307508
$275$		0			0
$276$	0.673762			0.0405557
$277$	−0.277515	−	0.0901699i	−0.0166742	−	0.00541779i	0.300668	−	0.953729i	$-0.402790\pi$
$277$	−0.277515	−	0.0901699i	−0.0166742	−	0.00541779i	−0.317342	+	0.948311i	$0.602790\pi$
$278$	3.13068	−	4.30902i	0.187766	−	0.258438i
$279$	0.545085	+	0.396027i	0.0326334	+	0.0237095i
$280$		0			0
$281$	−2.57295	+	1.86936i	−0.153489	+	0.111516i	−0.661879	−	0.749610i	$-0.730241\pi$
$281$	−2.57295	+	1.86936i	−0.153489	+	0.111516i	0.508390	+	0.861127i	$0.330241\pi$
$282$			4.56231i			0.271681i
$283$	7.22494	+	9.94427i	0.429478	+	0.591126i	0.967833	−	0.251592i	$-0.0809542\pi$
$283$	7.22494	+	9.94427i	0.429478	+	0.591126i	−0.538355	+	0.842718i	$0.680954\pi$
$284$	0.927051	+	2.85317i	0.0550104	+	0.169304i
$285$		0			0
$286$	−1.30902	+	4.02874i	−0.0774038	+	0.238224i
$287$	−4.20025	+	1.36475i	−0.247933	+	0.0805584i
$288$	−2.71441	+	0.881966i	−0.159948	+	0.0519703i
$289$	4.84752	−	14.9191i	0.285148	−	0.877597i
$290$		0			0
$291$	−1.12868	−	3.47371i	−0.0661642	−	0.203633i
$292$	4.53077	+	6.23607i	0.265143	+	0.364938i
$293$			8.56231i			0.500215i	0.968218	+	0.250108i	$0.0804660\pi$
$293$			8.56231i			0.500215i	−0.968218	+	0.250108i	$0.919534\pi$
$294$	0.618034	−	0.449028i	0.0360445	−	0.0261878i
$295$		0			0
$296$	−6.73607	−	4.89404i	−0.391526	−	0.284460i
$297$	−5.56758	+	7.66312i	−0.323064	+	0.444659i
$298$	−2.12663	−	0.690983i	−0.123192	−	0.0400276i
$299$	1.76393			0.102011
$300$		0			0
$301$	18.7082			1.07832
$302$	−9.23305	−	3.00000i	−0.531302	−	0.172631i
$303$	−0.138757	+	0.190983i	−0.00797140	+	0.0109717i
$304$	4.73607	+	3.44095i	0.271632	+	0.197352i
$305$		0			0
$306$	−2.64590	+	1.92236i	−0.151256	+	0.109894i
$307$			23.1246i			1.31979i	0.751357	+	0.659896i	$0.229400\pi$
$307$			23.1246i			1.31979i	−0.751357	+	0.659896i	$0.770600\pi$
$308$	7.46969	+	10.2812i	0.425625	+	0.585823i
$309$	−1.55166	−	4.77553i	−0.0882710	−	0.271670i
$310$		0			0
$311$	−3.06231	+	9.42481i	−0.173647	+	0.534432i	−0.999569	−	0.0293530i	$-0.990655\pi$
$311$	−3.06231	+	9.42481i	−0.173647	+	0.534432i	0.825922	+	0.563785i	$0.190655\pi$
$312$	0.363271	−	0.118034i	0.0205662	−	0.00668236i
$313$	15.7517	−	5.11803i	0.890338	−	0.289288i	0.172095	−	0.985080i	$-0.444946\pi$
$313$	15.7517	−	5.11803i	0.890338	−	0.289288i	0.718243	+	0.695792i	$0.244946\pi$
$314$	1.40983	−	4.33901i	0.0795613	−	0.244865i
$315$		0			0
$316$	−2.23607	−	6.88191i	−0.125789	−	0.387138i
$317$	4.92680	+	6.78115i	0.276716	+	0.380867i	0.924643	−	0.380835i	$-0.124364\pi$
$317$	4.92680	+	6.78115i	0.276716	+	0.380867i	−0.647926	+	0.761703i	$0.724364\pi$
$318$			4.00000i			0.224309i
$319$	−32.4615	+	23.5847i	−1.81749	+	1.32049i
$320$		0			0
$321$	−0.336881	−	0.244758i	−0.0188029	−	0.0136611i
$322$	3.11044	−	4.28115i	0.173338	−	0.238579i
$323$	6.37988	+	2.07295i	0.354986	+	0.115342i
$324$	−7.70820			−0.428234
$325$		0			0
$326$	−1.85410			−0.102689
$327$	−5.44907	−	1.77051i	−0.301334	−	0.0979094i
$328$	−0.865300	+	1.19098i	−0.0477782	+	0.0657610i
$329$	28.9894	+	21.0620i	1.59823	+	1.16119i
$330$		0			0
$331$	12.5902	−	9.14729i	0.692018	−	0.502781i	−0.185305	−	0.982681i	$-0.559327\pi$
$331$	12.5902	−	9.14729i	0.692018	−	0.502781i	0.877323	+	0.479900i	$0.159327\pi$
$332$			4.52786i			0.248499i
$333$	−13.9681	−	19.2254i	−0.765447	−	1.05355i
$334$	4.13525	+	12.7270i	0.226271	+	0.696391i
$335$		0			0
$336$	0.354102	−	1.08981i	0.0193178	−	0.0594542i
$337$	−4.35926	+	1.41641i	−0.237464	+	0.0771567i	−0.425331	−	0.905038i	$-0.639842\pi$
$337$	−4.35926	+	1.41641i	−0.237464	+	0.0771567i	0.187868	+	0.982194i	$0.439842\pi$
$338$	−11.4127	+	3.70820i	−0.620768	+	0.201700i
$339$	0.444272	−	1.36733i	0.0241295	−	0.0742631i
$340$		0			0
$341$	−0.309017	−	0.951057i	−0.0167342	−	0.0515026i
$342$	9.82084	+	13.5172i	0.531050	+	0.730928i
$343$			15.0000i			0.809924i
$344$	5.04508	−	3.66547i	0.272013	−	0.197629i
$345$		0			0
$346$	−1.00000	−	0.726543i	−0.0537603	−	0.0390592i
$347$	12.3965	−	17.0623i	0.665478	−	0.915953i	−0.334169	−	0.942513i	$-0.608456\pi$
$347$	12.3965	−	17.0623i	0.665478	−	0.915953i	0.999647	+	0.0265607i	$0.00845553\pi$
$348$	3.44095	+	1.11803i	0.184455	+	0.0599329i
$349$	17.7639			0.950881			0.475441	−	0.879748i	$-0.342289\pi$
$349$	17.7639			0.950881			0.475441	+	0.879748i	$0.342289\pi$
$350$		0			0
$351$	2.23607			0.119352
$352$	4.02874	+	1.30902i	0.214733	+	0.0697708i
$353$	−12.4822	+	17.1803i	−0.664363	+	0.914417i	−0.999616	−	0.0277109i	$-0.991178\pi$
$353$	−12.4822	+	17.1803i	−0.664363	+	0.914417i	0.335253	+	0.942128i	$0.391178\pi$
$354$	−1.38197	−	1.00406i	−0.0734507	−	0.0533650i
$355$		0			0
$356$	−3.61803	+	2.62866i	−0.191755	+	0.139318i
$357$		−	1.31308i		−	0.0694957i
$358$	6.57164	+	9.04508i	0.347322	+	0.478048i
$359$	2.50000	+	7.69421i	0.131945	+	0.406085i	0.995102	−	0.0988502i	$-0.0315165\pi$
$359$	2.50000	+	7.69421i	0.131945	+	0.406085i	−0.863157	+	0.504935i	$0.831516\pi$
$360$		0			0
$361$	4.71885	−	14.5231i	0.248360	−	0.764375i
$362$	−5.15131	+	1.67376i	−0.270747	+	0.0879710i
$363$	2.52265	−	0.819660i	0.132405	−	0.0430210i
$364$	0.927051	−	2.85317i	0.0485907	−	0.149547i
$365$		0			0
$366$	−1.04508	−	3.21644i	−0.0546275	−	0.168126i
$367$	20.8905	+	28.7533i	1.09047	+	1.50091i	0.847440	+	0.530892i	$0.178143\pi$
$367$	20.8905	+	28.7533i	1.09047	+	1.50091i	0.243035	+	0.970018i	$0.421857\pi$
$368$		−	1.76393i		−	0.0919513i
$369$	−3.39919	+	2.46965i	−0.176955	+	0.128565i
$370$		0			0
$371$	25.4164	+	18.4661i	1.31955	+	0.958712i
$372$	−0.0530006	+	0.0729490i	−0.00274795	+	0.00378223i
$373$	−11.1882	−	3.63525i	−0.579301	−	0.188226i	0.00468631	−	0.999989i	$-0.498508\pi$
$373$	−11.1882	−	3.63525i	−0.579301	−	0.188226i	−0.583987	+	0.811763i	$0.698508\pi$
$374$	4.85410			0.251000
$375$		0			0
$376$	11.9443			0.615979
$377$	9.00854	+	2.92705i	0.463963	+	0.150751i
$378$	3.94298	−	5.42705i	0.202805	−	0.279137i
$379$	7.66312	+	5.56758i	0.393628	+	0.285987i	0.766941	−	0.641718i	$-0.221778\pi$
$379$	7.66312	+	5.56758i	0.393628	+	0.285987i	−0.373313	+	0.927706i	$0.621778\pi$
$380$		0			0
$381$	−1.09017	+	0.792055i	−0.0558511	+	0.0405782i
$382$		−	13.6525i		−	0.698521i
$383$	−6.65740	−	9.16312i	−0.340177	−	0.468214i	0.604316	−	0.796745i	$-0.293446\pi$
$383$	−6.65740	−	9.16312i	−0.340177	−	0.468214i	−0.944493	+	0.328531i	$0.893446\pi$
$384$	−0.118034	−	0.363271i	−0.00602340	−	0.0185381i
$385$		0			0
$386$	4.52786	−	13.9353i	0.230462	−	0.709290i
$387$	16.9273	−	5.50000i	0.860461	−	0.279581i
$388$	−9.09429	+	2.95492i	−0.461693	+	0.150013i
$389$	−5.62868	+	17.3233i	−0.285385	+	0.878326i	0.700898	+	0.713262i	$0.252783\pi$
$389$	−5.62868	+	17.3233i	−0.285385	+	0.878326i	−0.986283	+	0.165064i	$0.947217\pi$
$390$		0			0
$391$	−0.624612	−	1.92236i	−0.0315880	−	0.0972178i
$392$	−1.17557	−	1.61803i	−0.0593753	−	0.0817231i
$393$			6.27051i			0.316305i
$394$	−9.70820	+	7.05342i	−0.489092	+	0.355346i
$395$		0			0
$396$	9.78115	+	7.10642i	0.491521	+	0.357111i
$397$	6.01661	−	8.28115i	0.301965	−	0.415619i	−0.630889	−	0.775873i	$-0.717310\pi$
$397$	6.01661	−	8.28115i	0.301965	−	0.415619i	0.932854	+	0.360254i	$0.117310\pi$
$398$	−2.43690	−	0.791796i	−0.122151	−	0.0396892i
$399$	−6.70820			−0.335830
$400$		0			0
$401$	−14.1803			−0.708132			−0.354066	−	0.935220i	$-0.615201\pi$
$401$	−14.1803			−0.708132			−0.354066	+	0.935220i	$0.615201\pi$
$402$	3.71847	+	1.20820i	0.185460	+	0.0602597i
$403$	−0.138757	+	0.190983i	−0.00691199	+	0.00951354i
$404$	0.500000	+	0.363271i	0.0248759	+	0.0180734i
$405$		0			0
$406$	22.9894	−	16.7027i	1.14094	−	0.828943i
$407$			35.2705i			1.74829i
$408$	−0.257270	−	0.354102i	−0.0127368	−	0.0175307i
$409$	2.07295	+	6.37988i	0.102501	+	0.315465i	0.989136	−	0.147005i	$-0.0469634\pi$
$409$	2.07295	+	6.37988i	0.102501	+	0.315465i	−0.886635	+	0.462470i	$0.846963\pi$
$410$		0			0
$411$	−0.600813	+	1.84911i	−0.0296359	+	0.0912100i
$412$	−12.5025	+	4.06231i	−0.615954	+	0.200135i
$413$	−12.7598	+	4.14590i	−0.627867	+	0.204006i
$414$	1.55573	−	4.78804i	0.0764599	−	0.235319i
$415$		0			0
$416$	−0.309017	−	0.951057i	−0.0151508	−	0.0466294i
$417$	1.19581	+	1.64590i	0.0585593	+	0.0806000i
$418$		−	24.7984i		−	1.21293i
$419$	18.4164	−	13.3803i	0.899700	−	0.653671i	−0.0386886	−	0.999251i	$-0.512318\pi$
$419$	18.4164	−	13.3803i	0.899700	−	0.653671i	0.938389	+	0.345581i	$0.112318\pi$
$420$		0			0
$421$	−17.2082	−	12.5025i	−0.838677	−	0.609334i	0.0833241	−	0.996522i	$-0.473446\pi$
$421$	−17.2082	−	12.5025i	−0.838677	−	0.609334i	−0.922001	+	0.387188i	$0.873446\pi$
$422$	−13.0903	+	18.0172i	−0.637225	+	0.877065i
$423$	32.4217	+	10.5344i	1.57640	+	0.512202i
$424$	10.4721			0.508572
$425$		0			0
$426$	−1.14590			−0.0555189
$427$	−25.2623	−	8.20820i	−1.22253	−	0.397223i
$428$	−0.640786	+	0.881966i	−0.0309736	+	0.0426314i
$429$	−1.30902	−	0.951057i	−0.0631999	−	0.0459174i
$430$		0			0
$431$	−21.0902	+	15.3229i	−1.01588	+	0.738078i	−0.965434	−	0.260649i	$-0.916064\pi$
$431$	−21.0902	+	15.3229i	−1.01588	+	0.738078i	−0.0504440	+	0.998727i	$0.516064\pi$
$432$		−	2.23607i		−	0.107583i
$433$	12.5555	+	17.2812i	0.603378	+	0.830479i	0.996012	−	0.0892157i	$-0.0284360\pi$
$433$	12.5555	+	17.2812i	0.603378	+	0.830479i	−0.392634	+	0.919695i	$0.628436\pi$
$434$	0.218847	+	0.673542i	0.0105050	+	0.0323310i
$435$		0			0
$436$	−4.63525	+	14.2658i	−0.221988	+	0.683210i
$437$	−9.82084	+	3.19098i	−0.469794	+	0.152645i
$438$	−2.80017	+	0.909830i	−0.133797	+	0.0434734i
$439$	−7.92705	+	24.3970i	−0.378338	+	1.16440i	0.562862	+	0.826551i	$0.309700\pi$
$439$	−7.92705	+	24.3970i	−0.378338	+	1.16440i	−0.941199	+	0.337852i	$0.890300\pi$
$440$		0			0
$441$	−1.76393	−	5.42882i	−0.0839968	−	0.258515i
$442$	−0.673542	−	0.927051i	−0.0320371	−	0.0440953i
$443$			19.4164i			0.922501i	0.887270	+	0.461251i	$0.152599\pi$
$443$			19.4164i			0.922501i	−0.887270	+	0.461251i	$0.847401\pi$
$444$	2.57295	−	1.86936i	0.122107	−	0.0887158i
$445$		0			0
$446$	−7.28115	−	5.29007i	−0.344773	−	0.250492i
$447$	0.502029	−	0.690983i	0.0237451	−	0.0326824i
$448$	−2.85317	−	0.927051i	−0.134800	−	0.0437990i
$449$	3.94427			0.186142			0.0930709	−	0.995659i	$-0.470332\pi$
$449$	3.94427			0.186142			0.0930709	+	0.995659i	$0.470332\pi$
$450$		0			0
$451$	6.23607			0.293645
$452$	−3.57971	−	1.16312i	−0.168375	−	0.0547085i
$453$	2.17963	−	3.00000i	0.102408	−	0.140952i
$454$	−23.7533	−	17.2578i	−1.11480	−	0.809947i
$455$		0			0
$456$	−1.80902	+	1.31433i	−0.0847150	+	0.0615490i
$457$		−	40.2148i		−	1.88117i	−0.339561	−	0.940584i	$-0.610278\pi$
$457$		−	40.2148i		−	1.88117i	0.339561	−	0.940584i	$-0.389722\pi$
$458$	−1.50609	−	2.07295i	−0.0703748	−	0.0968625i
$459$	−0.791796	−	2.43690i	−0.0369579	−	0.113745i
$460$		0			0
$461$	1.79837	−	5.53483i	0.0837586	−	0.257783i	−0.900403	−	0.435057i	$-0.856728\pi$
$461$	1.79837	−	5.53483i	0.0837586	−	0.257783i	0.984161	+	0.177275i	$0.0567281\pi$
$462$	−4.61653	+	1.50000i	−0.214780	+	0.0697863i
$463$	33.2667	−	10.8090i	1.54604	−	0.502338i	0.593002	−	0.805201i	$-0.297943\pi$
$463$	33.2667	−	10.8090i	1.54604	−	0.502338i	0.953034	+	0.302863i	$0.0979425\pi$
$464$	2.92705	−	9.00854i	0.135885	−	0.418211i
$465$		0			0
$466$	−4.41641	−	13.5923i	−0.204586	−	0.629651i
$467$	−11.2739	−	15.5172i	−0.521695	−	0.718051i	0.464142	−	0.885761i	$-0.346363\pi$
$467$	−11.2739	−	15.5172i	−0.521695	−	0.718051i	−0.985836	+	0.167710i	$0.946363\pi$
$468$		−	2.85410i		−	0.131931i
$469$	24.8435	−	18.0498i	1.14716	−	0.833464i
$470$		0			0
$471$	1.40983	+	1.02430i	0.0649615	+	0.0471973i
$472$	−2.62866	+	3.61803i	−0.120994	+	0.166534i
$473$	−25.1235	−	8.16312i	−1.15518	−	0.375341i
$474$	2.76393			0.126952
$475$		0			0
$476$	−3.43769			−0.157566
$477$	28.4257	+	9.23607i	1.30152	+	0.422891i
$478$	4.06150	−	5.59017i	0.185769	−	0.255688i
$479$	−12.2984	−	8.93529i	−0.561927	−	0.408264i	0.270237	−	0.962794i	$-0.412898\pi$
$479$	−12.2984	−	8.93529i	−0.561927	−	0.408264i	−0.832164	+	0.554530i	$0.812898\pi$
$480$		0			0
$481$	6.73607	−	4.89404i	0.307138	−	0.223149i
$482$			15.6180i			0.711382i
$483$	1.18808	+	1.63525i	0.0540596	+	0.0744067i
$484$	−2.14590	−	6.60440i	−0.0975408	−	0.300200i
$485$		0			0
$486$	2.98278	−	9.18005i	0.135302	−	0.416416i
$487$	21.0418	−	6.83688i	0.953493	−	0.309809i	0.209359	−	0.977839i	$-0.432862\pi$
$487$	21.0418	−	6.83688i	0.953493	−	0.309809i	0.744134	+	0.668030i	$0.232862\pi$
$488$	−8.42075	+	2.73607i	−0.381190	+	0.123856i
$489$	0.218847	−	0.673542i	0.00989661	−	0.0304586i
$490$		0			0
$491$	5.94427	+	18.2946i	0.268261	+	0.825623i	0.990924	+	0.134423i	$0.0429179\pi$
$491$	5.94427	+	18.2946i	0.268261	+	0.825623i	−0.722663	+	0.691201i	$0.757082\pi$
$492$	−0.330515	−	0.454915i	−0.0149008	−	0.0205092i
$493$		−	10.8541i		−	0.488844i
$494$	−4.73607	+	3.44095i	−0.213086	+	0.154816i
$495$		0			0
$496$	0.190983	+	0.138757i	0.00857539	+	0.00623039i
$497$	−5.29007	+	7.28115i	−0.237292	+	0.326604i
$498$	−1.64484	−	0.534442i	−0.0737072	−	0.0239489i
$499$	−34.1459			−1.52858			−0.764290	−	0.644873i	$-0.776910\pi$
$499$	−34.1459			−1.52858			−0.764290	+	0.644873i	$0.776910\pi$
$500$		0			0
$501$	−5.11146			−0.228363
$502$	0.779543	+	0.253289i	0.0347927	+	0.0113048i
$503$	−17.9313	+	24.6803i	−0.799518	+	1.10044i	0.193339	+	0.981132i	$0.438068\pi$
$503$	−17.9313	+	24.6803i	−0.799518	+	1.10044i	−0.992857	+	0.119310i	$0.961932\pi$
$504$	−6.92705	−	5.03280i	−0.308555	−	0.224179i
$505$		0			0
$506$	−6.04508	+	4.39201i	−0.268737	+	0.195249i
$507$		−	4.58359i		−	0.203564i
$508$	2.07363	+	2.85410i	0.0920023	+	0.126630i
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	0.963284	−	0.268486i	$-0.0865232\pi$
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	−0.937125	+	0.348994i	$0.886523\pi$
$510$		0			0
$511$	−7.14590	+	21.9928i	−0.316116	+	0.972905i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−12.4495	+	4.04508i	−0.549658	+	0.178595i
$514$	7.95492	−	24.4827i	0.350876	−	1.07989i
$515$		0			0
$516$	0.736068	+	2.26538i	0.0324036	+	0.0997280i
$517$	−29.7400	−	40.9336i	−1.30796	−	1.80026i
$518$		−	24.9787i		−	1.09750i
$519$	0.381966	−	0.277515i	0.0167664	−	0.0121815i
$520$		0			0
$521$	18.9721	+	13.7841i	0.831184	+	0.603891i	0.919894	−	0.392167i	$-0.128274\pi$
$521$	18.9721	+	13.7841i	0.831184	+	0.603891i	−0.0887098	+	0.996058i	$0.528274\pi$
$522$	15.8904	−	21.8713i	0.695506	−	0.957282i
$523$	−4.42477	−	1.43769i	−0.193482	−	0.0628660i	0.210673	−	0.977557i	$-0.432434\pi$
$523$	−4.42477	−	1.43769i	−0.193482	−	0.0628660i	−0.404155	+	0.914691i	$0.632434\pi$
$524$	16.4164			0.717154
$525$		0			0
$526$	−4.61803			−0.201356
$527$	0.257270	+	0.0835921i	0.0112069	+	0.00364133i
$528$	−0.951057	+	1.30902i	−0.0413894	+	0.0569677i
$529$	−16.0902	−	11.6902i	−0.699573	−	0.508269i
$530$		0			0
$531$	−10.3262	+	7.50245i	−0.448121	+	0.325579i
$532$			17.5623i			0.761423i
$533$	−0.865300	−	1.19098i	−0.0374803	−	0.0515872i
$534$	−0.527864	−	1.62460i	−0.0228429	−	0.0703033i
$535$		0			0
$536$	3.16312	−	9.73508i	0.136626	−	0.420491i
$537$	−4.06150	+	1.31966i	−0.175266	+	0.0569475i
$538$	1.81636	−	0.590170i	0.0783087	−	0.0254440i
$539$	−2.61803	+	8.05748i	−0.112767	+	0.347060i
$540$		0			0
$541$	4.72542	+	14.5434i	0.203162	+	0.625268i	0.999784	+	0.0207902i	$0.00661819\pi$
$541$	4.72542	+	14.5434i	0.203162	+	0.625268i	−0.796622	+	0.604478i	$0.793382\pi$
$542$	−16.7557	−	23.0623i	−0.719721	−	0.990611i
$543$		−	2.06888i		−	0.0887843i
$544$	−0.927051	+	0.673542i	−0.0397470	+	0.0288779i
$545$		0			0
$546$	0.927051	+	0.673542i	0.0396741	+	0.0288249i
$547$	−4.92680	+	6.78115i	−0.210655	+	0.289941i	−0.901249	−	0.433301i	$-0.857349\pi$
$547$	−4.92680	+	6.78115i	−0.210655	+	0.289941i	0.690595	+	0.723242i	$0.257349\pi$
$548$	4.84104	+	1.57295i	0.206799	+	0.0671931i
$549$	−25.2705			−1.07852
$550$		0			0
$551$	−55.4508			−2.36229
$552$	0.640786	+	0.208204i	0.0272737	+	0.00886175i
$553$	12.7598	−	17.5623i	0.542600	−	0.746825i
$554$	−0.236068	−	0.171513i	−0.0100296	−	0.00728691i
$555$		0			0
$556$	4.30902	−	3.13068i	0.182743	−	0.132771i
$557$		−	24.8885i		−	1.05456i	−0.849691	−	0.527281i	$-0.823212\pi$
$557$		−	24.8885i		−	1.05456i	0.849691	−	0.527281i	$-0.176788\pi$
$558$	0.396027	+	0.545085i	0.0167652	+	0.0230753i
$559$	1.92705	+	5.93085i	0.0815056	+	0.250848i
$560$		0			0
$561$	−0.572949	+	1.76336i	−0.0241899	+	0.0744489i
$562$	−3.02468	+	0.982779i	−0.127589	+	0.0414560i
$563$	26.7683	−	8.69756i	1.12815	−	0.366558i	0.315278	−	0.948999i	$-0.397902\pi$
$563$	26.7683	−	8.69756i	1.12815	−	0.366558i	0.812873	+	0.582441i	$0.197902\pi$
$564$	−1.40983	+	4.33901i	−0.0593646	+	0.182705i
$565$		0			0
$566$	3.79837	+	11.6902i	0.159658	+	0.491375i
$567$	−13.5923	−	18.7082i	−0.570823	−	0.785671i
$568$			3.00000i			0.125877i
$569$	14.3713	−	10.4414i	0.602477	−	0.437725i	−0.244280	−	0.969705i	$-0.578552\pi$
$569$	14.3713	−	10.4414i	0.602477	−	0.437725i	0.846757	+	0.531979i	$0.178552\pi$
$570$		0			0
$571$	−14.0172	−	10.1841i	−0.586602	−	0.426192i	0.254496	−	0.967074i	$-0.418090\pi$
$571$	−14.0172	−	10.1841i	−0.586602	−	0.426192i	−0.841098	+	0.540882i	$0.818090\pi$
$572$	−2.48990	+	3.42705i	−0.104108	+	0.143292i
$573$	4.95955	+	1.61146i	0.207188	+	0.0673195i
$574$	−4.41641			−0.184337
$575$		0			0
$576$	−2.85410			−0.118921
$577$	40.8954	+	13.2877i	1.70250	+	0.553175i	0.989056	−	0.147538i	$-0.0471349\pi$
$577$	40.8954	+	13.2877i	1.70250	+	0.553175i	0.713443	+	0.700714i	$0.247135\pi$
$578$	9.22054	−	12.6910i	0.383524	−	0.527875i
$579$	4.52786	+	3.28969i	0.188172	+	0.136715i
$580$		0			0
$581$	−10.9894	+	7.98424i	−0.455915	+	0.331242i
$582$		−	3.65248i		−	0.151400i
$583$	−26.0746	−	35.8885i	−1.07990	−	1.48635i
$584$	2.38197	+	7.33094i	0.0985665	+	0.303356i
$585$		0			0
$586$	−2.64590	+	8.14324i	−0.109301	+	0.336394i
$587$	−32.5074	+	10.5623i	−1.34173	+	0.435953i	−0.889901	−	0.456154i	$-0.849227\pi$
$587$	−32.5074	+	10.5623i	−1.34173	+	0.435953i	−0.451824	+	0.892107i	$0.649227\pi$
$588$	0.726543	−	0.236068i	0.0299621	−	0.00973528i
$589$	0.427051	−	1.31433i	0.0175963	−	0.0541559i
$590$		0			0
$591$	−1.41641	−	4.35926i	−0.0582632	−	0.179316i
$592$	−4.89404	−	6.73607i	−0.201144	−	0.276851i
$593$			29.0132i			1.19143i	0.803197	+	0.595714i	$0.203131\pi$
$593$			29.0132i			1.19143i	−0.803197	+	0.595714i	$0.796869\pi$
$594$	−7.66312	+	5.56758i	−0.314422	+	0.228441i
$595$		0			0
$596$	−1.80902	−	1.31433i	−0.0741002	−	0.0538370i
$597$	0.575274	−	0.791796i	0.0235444	−	0.0324061i
$598$	1.67760	+	0.545085i	0.0686021	+	0.0222902i
$599$	−8.94427			−0.365453			−0.182727	−	0.983164i	$-0.558492\pi$
$599$	−8.94427			−0.365453			−0.182727	+	0.983164i	$0.558492\pi$
$600$		0			0
$601$	38.8328			1.58402			0.792012	−	0.610506i	$-0.209034\pi$
$601$	38.8328			1.58402			0.792012	+	0.610506i	$0.209034\pi$
$602$	17.7926	+	5.78115i	0.725171	+	0.235622i
$603$	17.1720	−	23.6353i	0.699299	−	0.962502i
$604$	−7.85410	−	5.70634i	−0.319579	−	0.232188i
$605$		0			0
$606$	−0.190983	+	0.138757i	−0.00775815	+	0.00563663i
$607$			33.8541i			1.37410i	0.726612	+	0.687048i	$0.241094\pi$
$607$			33.8541i			1.37410i	−0.726612	+	0.687048i	$0.758906\pi$
$608$	3.44095	+	4.73607i	0.139549	+	0.192073i
$609$	3.35410	+	10.3229i	0.135915	+	0.418304i
$610$		0			0
$611$	−3.69098	+	11.3597i	−0.149321	+	0.459563i
$612$	−3.11044	+	1.01064i	−0.125732	+	0.0408528i
$613$	20.3885	−	6.62461i	0.823482	−	0.267566i	0.133185	−	0.991091i	$-0.457480\pi$
$613$	20.3885	−	6.62461i	0.823482	−	0.267566i	0.690297	+	0.723526i	$0.257480\pi$
$614$	−7.14590	+	21.9928i	−0.288385	+	0.887558i
$615$		0			0
$616$	3.92705	+	12.0862i	0.158225	+	0.486968i
$617$	8.44100	+	11.6180i	0.339822	+	0.467724i	0.944389	−	0.328829i	$-0.106654\pi$
$617$	8.44100	+	11.6180i	0.339822	+	0.467724i	−0.604568	+	0.796554i	$0.706654\pi$
$618$		−	5.02129i		−	0.201986i
$619$	37.9894	−	27.6009i	1.52692	−	1.10937i	0.569002	−	0.822336i	$-0.307330\pi$
$619$	37.9894	−	27.6009i	1.52692	−	1.10937i	0.957920	−	0.287037i	$-0.0926702\pi$
$620$		0			0
$621$	3.19098	+	2.31838i	0.128050	+	0.0930336i
$622$	−5.82485	+	8.01722i	−0.233555	+	0.321461i
$623$	−12.7598	−	4.14590i	−0.511209	−	0.166102i
$624$	0.381966			0.0152909
$625$		0			0
$626$	16.5623			0.661963
$627$	9.00854	+	2.92705i	0.359766	+	0.116895i
$628$	2.68166	−	3.69098i	0.107010	−	0.147286i
$629$	−7.71885	−	5.60807i	−0.307771	−	0.223608i
$630$		0			0
$631$	36.2705	−	26.3521i	1.44391	−	1.04906i	0.456698	−	0.889622i	$-0.349032\pi$
$631$	36.2705	−	26.3521i	1.44391	−	1.04906i	0.987208	−	0.159438i	$-0.0509681\pi$
$632$		−	7.23607i		−	0.287835i
$633$	−5.00004	−	6.88197i	−0.198734	−	0.273534i
$634$	2.59017	+	7.97172i	0.102869	+	0.316598i
$635$		0			0
$636$	−1.23607	+	3.80423i	−0.0490133	+	0.150847i
$637$	1.90211	−	0.618034i	0.0753645	−	0.0244874i
$638$	−38.1608	+	12.3992i	−1.51080	+	0.490889i
$639$	−2.64590	+	8.14324i	−0.104670	+	0.322141i
$640$		0			0
$641$	−9.38197	−	28.8747i	−0.370565	−	1.14048i	−0.946422	−	0.322932i	$-0.895331\pi$
$641$	−9.38197	−	28.8747i	−0.370565	−	1.14048i	0.575857	−	0.817551i	$-0.304669\pi$
$642$	−0.244758	−	0.336881i	−0.00965984	−	0.0132956i
$643$		−	31.7639i		−	1.25265i	−0.779563	−	0.626324i	$-0.784559\pi$
$643$		−	31.7639i		−	1.25265i	0.779563	−	0.626324i	$-0.215441\pi$
$644$	4.28115	−	3.11044i	0.168701	−	0.122568i
$645$		0			0
$646$	5.42705	+	3.94298i	0.213524	+	0.155135i
$647$	13.9026	−	19.1353i	0.546567	−	0.752284i	−0.442975	−	0.896534i	$-0.646077\pi$
$647$	13.9026	−	19.1353i	0.546567	−	0.752284i	0.989541	+	0.144250i	$0.0460768\pi$
$648$	−7.33094	−	2.38197i	−0.287986	−	0.0935725i
$649$	18.9443			0.743628
$650$		0			0
$651$	−0.270510			−0.0106021
$652$	−1.76336	−	0.572949i	−0.0690583	−	0.0224384i
$653$	−5.05304	+	6.95492i	−0.197741	+	0.272167i	−0.896360	−	0.443327i	$-0.853798\pi$
$653$	−5.05304	+	6.95492i	−0.197741	+	0.272167i	0.698619	+	0.715494i	$0.253798\pi$
$654$	−4.63525	−	3.36771i	−0.181253	−	0.131688i
$655$		0			0
$656$	−1.19098	+	0.865300i	−0.0465001	+	0.0337843i
$657$			22.0000i			0.858302i
$658$	21.0620	+	28.9894i	0.821082	+	1.13012i
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	0.978234	+	0.207504i	$0.0665341\pi$
$659$	7.92705	+	24.3970i	0.308794	+	0.950370i	−0.669440	+	0.742866i	$0.733466\pi$
$660$		0			0
$661$	−8.42705	+	25.9358i	−0.327774	+	1.00879i	0.642398	+	0.766371i	$0.277939\pi$
$661$	−8.42705	+	25.9358i	−0.327774	+	1.00879i	−0.970173	+	0.242415i	$0.922061\pi$
$662$	14.8006	−	4.80902i	0.575243	−	0.186908i
$663$	0.416272	−	0.135255i	0.0161667	−	0.00525287i
$664$	−1.39919	+	4.30625i	−0.0542990	+	0.167115i
$665$		0			0
$666$	−7.34346	−	22.6008i	−0.284553	−	0.875765i
$667$	9.82084	+	13.5172i	0.380264	+	0.523389i
$668$			13.3820i			0.517764i
$669$	2.78115	−	2.02063i	0.107526	−	0.0781219i
$670$		0			0
$671$	30.3435	+	22.0458i	1.17140	+	0.851069i
$672$	0.673542	−	0.927051i	0.0259824	−	0.0357618i
$673$	3.07768	+	1.00000i	0.118636	+	0.0385472i	0.367733	−	0.929931i	$-0.380134\pi$
$673$	3.07768	+	1.00000i	0.118636	+	0.0385472i	−0.249097	+	0.968478i	$0.580134\pi$
$674$	−4.58359			−0.176553
$675$		0			0
$676$	−12.0000			−0.461538
$677$	−7.97172	−	2.59017i	−0.306378	−	0.0995483i	0.151793	−	0.988412i	$-0.451495\pi$
$677$	−7.97172	−	2.59017i	−0.306378	−	0.0995483i	−0.458171	+	0.888864i	$0.651495\pi$
$678$	0.845055	−	1.16312i	0.0324542	−	0.0446693i
$679$	−23.2082	−	16.8617i	−0.890649	−	0.647094i
$680$		0			0
$681$	9.07295	−	6.59188i	0.347676	−	0.252602i
$682$		−	1.00000i		−	0.0382920i
$683$	6.67764	+	9.19098i	0.255513	+	0.351683i	0.917432	−	0.397892i	$-0.130258\pi$
$683$	6.67764	+	9.19098i	0.255513	+	0.351683i	−0.661920	+	0.749575i	$0.730258\pi$
$684$	5.16312	+	15.8904i	0.197417	+	0.607586i
$685$		0			0
$686$	−4.63525	+	14.2658i	−0.176975	+	0.544673i
$687$	0.930812	−	0.302439i	0.0355127	−	0.0115388i
$688$	5.93085	−	1.92705i	0.226112	−	0.0734681i
$689$	−3.23607	+	9.95959i	−0.123284	+	0.379430i
$690$		0			0
$691$	−9.97214	−	30.6911i	−0.379358	−	1.16754i	−0.940491	−	0.339818i	$-0.889634\pi$
$691$	−9.97214	−	30.6911i	−0.379358	−	1.16754i	0.561133	−	0.827725i	$-0.310366\pi$
$692$	−0.726543	−	1.00000i	−0.0276190	−	0.0380143i
$693$			36.2705i			1.37780i
$694$	17.0623	−	12.3965i	0.647676	−	0.470564i
$695$		0			0
$696$	2.92705	+	2.12663i	0.110950	+	0.0806096i
$697$	−0.991545	+	1.36475i	−0.0375575	+	0.0516934i
$698$	16.8945	+	5.48936i	0.639466	+	0.207775i
$699$	5.45898			0.206478
$700$		0			0
$701$	18.1803			0.686662			0.343331	−	0.939214i	$-0.388445\pi$
$701$	18.1803			0.686662			0.343331	+	0.939214i	$0.388445\pi$
$702$	2.12663	+	0.690983i	0.0802644	+	0.0260795i
$703$	−28.6502	+	39.4336i	−1.08056	+	1.48727i
$704$	3.42705	+	2.48990i	0.129162	+	0.0938416i
$705$		0			0
$706$	−17.1803	+	12.4822i	−0.646591	+	0.469776i
$707$			1.85410i			0.0697307i
$708$	−1.00406	−	1.38197i	−0.0377348	−	0.0519375i
$709$	−3.78115	−	11.6372i	−0.142004	−	0.437044i	0.854609	−	0.519271i	$-0.173797\pi$
$709$	−3.78115	−	11.6372i	−0.142004	−	0.437044i	−0.996614	+	0.0822274i	$0.973797\pi$
$710$		0			0
$711$	6.38197	−	19.6417i	0.239342	−	0.736620i
$712$	−4.25325	+	1.38197i	−0.159397	+	0.0517914i
$713$	−0.396027	+	0.128677i	−0.0148313	+	0.00481900i
$714$	0.405765	−	1.24882i	0.0151854	−	0.0467357i
$715$		0			0
$716$	3.45492	+	10.6331i	0.129116	+	0.397379i
$717$	1.55135	+	2.13525i	0.0579364	+	0.0797426i
$718$			8.09017i			0.301922i
$719$	9.30902	−	6.76340i	0.347168	−	0.252232i	−0.400512	−	0.916291i	$-0.631168\pi$
$719$	9.30902	−	6.76340i	0.347168	−	0.252232i	0.747680	+	0.664059i	$0.231168\pi$
$720$		0			0
$721$	−31.9058	−	23.1809i	−1.18823	−	0.863302i
$722$	8.97578	−	12.3541i	0.334044	−	0.459772i
$723$	−5.67358	−	1.84346i	−0.211003	−	0.0685590i
$724$	−5.41641			−0.201299
$725$		0			0
$726$	2.65248			0.0984426
$727$	−2.52265	−	0.819660i	−0.0935601	−	0.0303995i	0.261863	−	0.965105i	$-0.415663\pi$
$727$	−2.52265	−	0.819660i	−0.0935601	−	0.0303995i	−0.355423	+	0.934706i	$0.615663\pi$
$728$	1.76336	−	2.42705i	0.0653543	−	0.0899525i
$729$	−15.7254	−	11.4252i	−0.582423	−	0.423155i
$730$		0			0
$731$	5.78115	−	4.20025i	0.213824	−	0.155352i
$732$		−	3.38197i		−	0.125001i
$733$	−18.6781	−	25.7082i	−0.689891	−	0.949554i	0.310108	−	0.950701i	$-0.399635\pi$
$733$	−18.6781	−	25.7082i	−0.689891	−	0.949554i	−0.999999	+	0.00114721i	$0.999635\pi$
$734$	10.9828	+	33.8015i	0.405382	+	1.24764i
$735$		0			0
$736$	0.545085	−	1.67760i	0.0200921	−	0.0618371i
$737$	−41.2385	+	13.3992i	−1.51904	+	0.493565i
$738$	−3.99598	+	1.29837i	−0.147094	+	0.0477938i
$739$	−9.27051	+	28.5317i	−0.341021	+	1.04956i	0.622658	+	0.782494i	$0.286053\pi$
$739$	−9.27051	+	28.5317i	−0.341021	+	1.04956i	−0.963679	+	0.267062i	$0.913947\pi$
$740$		0			0
$741$	−0.690983	−	2.12663i	−0.0253839	−	0.0781236i
$742$	18.4661	+	25.4164i	0.677912	+	0.933066i
$743$			15.2705i			0.560221i	0.959968	+	0.280110i	$0.0903711\pi$
$743$			15.2705i			0.560221i	−0.959968	+	0.280110i	$0.909629\pi$
$744$	−0.0729490	+	0.0530006i	−0.00267444	+	0.00194309i
$745$		0			0
$746$	−9.51722	−	6.91467i	−0.348450	−	0.253164i
$747$	−7.59594	+	10.4549i	−0.277921	+	0.382525i
$748$	4.61653	+	1.50000i	0.168797	+	0.0548454i
$749$	−3.27051			−0.119502
$750$		0			0
$751$	7.85410			0.286600			0.143300	−	0.989679i	$-0.454229\pi$
$751$	7.85410			0.286600			0.143300	+	0.989679i	$0.454229\pi$
$752$	11.3597	+	3.69098i	0.414245	+	0.134596i
$753$	−0.184025	+	0.253289i	−0.00670625	+	0.00923036i
$754$	7.66312	+	5.56758i	0.279074	+	0.202759i
$755$		0			0
$756$	5.42705	−	3.94298i	0.197380	−	0.143405i
$757$			16.4164i			0.596664i	0.954462	+	0.298332i	$0.0964303\pi$
$757$			16.4164i			0.596664i	−0.954462	+	0.298332i	$0.903570\pi$
$758$	5.56758	+	7.66312i	0.202224	+	0.278337i
$759$	−0.881966	−	2.71441i	−0.0320133	−	0.0985269i
$760$		0			0
$761$	8.31966	−	25.6053i	0.301587	−	0.928191i	−0.679341	−	0.733823i	$-0.737734\pi$
$761$	8.31966	−	25.6053i	0.301587	−	0.928191i	0.980929	−	0.194368i	$-0.0622656\pi$
$762$	−1.28157	+	0.416408i	−0.0464264	+	0.0150849i
$763$	−42.7975	+	13.9058i	−1.54938	+	0.503422i
$764$	4.21885	−	12.9843i	0.152633	−	0.469755i
$765$		0			0
$766$	−3.50000	−	10.7719i	−0.126460	−	0.389204i
$767$	−2.62866	−	3.61803i	−0.0949153	−	0.130640i
$768$		−	0.381966i		−	0.0137830i
$769$	2.76393	−	2.00811i	0.0996699	−	0.0724144i	−0.536834	−	0.843688i	$-0.680380\pi$
$769$	2.76393	−	2.00811i	0.0996699	−	0.0724144i	0.636504	+	0.771273i	$0.280380\pi$
$770$		0			0
$771$	7.95492	+	5.77958i	0.286489	+	0.208147i
$772$	8.61251	−	11.8541i	0.309971	−	0.426638i
$773$	29.2910	+	9.51722i	1.05352	+	0.342311i	0.784050	−	0.620697i	$-0.213150\pi$
$773$	29.2910	+	9.51722i	1.05352	+	0.342311i	0.269473	+	0.963008i	$0.413150\pi$
$774$	17.7984			0.639749
$775$		0			0
$776$	−9.56231			−0.343267
$777$	9.07405	+	2.94834i	0.325530	+	0.105771i
$778$	−10.7064	+	14.7361i	−0.383842	+	0.528314i
$779$	6.97214	+	5.06555i	0.249803	+	0.181492i
$780$		0			0
$781$	10.2812	−	7.46969i	0.367889	−	0.267287i
$782$		−	2.02129i		−	0.0722810i
$783$	12.4495	+	17.1353i	0.444909	+	0.612364i
$784$	−0.618034	−	1.90211i	−0.0220726	−	0.0679326i
$785$		0			0
$786$	−1.93769	+	5.96361i	−0.0691153	+	0.212715i
$787$	−10.8576	+	3.52786i	−0.387033	+	0.125755i	−0.496069	−	0.868283i	$-0.665224\pi$
$787$	−10.8576	+	3.52786i	−0.387033	+	0.125755i	0.109036	+	0.994038i	$0.465224\pi$
$788$	−11.4127	+	3.70820i	−0.406560	+	0.132099i
$789$	0.545085	−	1.67760i	0.0194055	−	0.0597241i
$790$		0			0
$791$	−3.48936	−	10.7391i	−0.124067	−	0.381840i
$792$	7.10642	+	9.78115i	0.252516	+	0.347558i
$793$		−	8.85410i		−	0.314418i
$794$	8.28115	−	6.01661i	0.293887	−	0.213521i
$795$		0			0
$796$	−2.07295	−	1.50609i	−0.0734737	−	0.0533818i
$797$	−3.30220	+	4.54508i	−0.116970	+	0.160995i	−0.863487	−	0.504371i	$-0.831724\pi$
$797$	−3.30220	+	4.54508i	−0.116970	+	0.160995i	0.746517	+	0.665366i	$0.231724\pi$
$798$	−6.37988	−	2.07295i	−0.225845	−	0.0733816i
$799$	13.6869			0.484208
$800$		0			0
$801$	−12.7639			−0.450991
$802$	−13.4863	−	4.38197i	−0.476218	−	0.154733i
$803$	19.1926	−	26.4164i	0.677294	−	0.932215i
$804$	3.16312	+	2.29814i	0.111555	+	0.0810492i
$805$		0			0
$806$	−0.190983	+	0.138757i	−0.00672709	+	0.00488752i
$807$			0.729490i			0.0256793i
$808$	0.363271	+	0.500000i	0.0127798	+	0.0175899i
$809$	0.690983	+	2.12663i	0.0242937	+	0.0747682i	0.962468	−	0.271394i	$-0.0874847\pi$
$809$	0.690983	+	2.12663i	0.0242937	+	0.0747682i	−0.938175	+	0.346162i	$0.887485\pi$
$810$		0			0
$811$	12.6525	−	38.9403i	0.444289	−	1.36738i	−0.438974	−	0.898500i	$-0.644658\pi$
$811$	12.6525	−	38.9403i	0.444289	−	1.36738i	0.883262	−	0.468880i	$-0.155342\pi$
$812$	27.0256	−	8.78115i	0.948413	−	0.308158i
$813$	10.3556	−	3.36475i	0.363187	−	0.118007i
$814$	−10.8992	+	33.5442i	−0.382016	+	1.17573i
$815$		0			0
$816$	−0.135255	−	0.416272i	−0.00473487	−	0.0145724i
$817$	−21.4580	−	29.5344i	−0.750721	−	1.03328i
$818$			6.70820i			0.234547i
$819$	6.92705	−	5.03280i	0.242051	−	0.175860i
$820$		0			0
$821$	−31.6803	−	23.0171i	−1.10565	−	0.803303i	−0.123678	−	0.992322i	$-0.539469\pi$
$821$	−31.6803	−	23.0171i	−1.10565	−	0.803303i	−0.981973	+	0.189020i	$0.939469\pi$
$822$	−1.14281	+	1.57295i	−0.0398602	+	0.0548629i
$823$	−19.8132	−	6.43769i	−0.690644	−	0.224404i	−0.0573946	−	0.998352i	$-0.518279\pi$
$823$	−19.8132	−	6.43769i	−0.690644	−	0.224404i	−0.633250	+	0.773948i	$0.718279\pi$
$824$	−13.1459			−0.457959
$825$		0			0
$826$	−13.4164			−0.466817
$827$	4.78804	+	1.55573i	0.166496	+	0.0540980i	0.391079	−	0.920357i	$-0.372102\pi$
$827$	4.78804	+	1.55573i	0.166496	+	0.0540980i	−0.224583	+	0.974455i	$0.572102\pi$
$828$	2.95917	−	4.07295i	0.102838	−	0.141545i
$829$	43.2148	+	31.3974i	1.50091	+	1.09048i	0.970017	+	0.243038i	$0.0781440\pi$
$829$	43.2148	+	31.3974i	1.50091	+	1.09048i	0.530895	+	0.847438i	$0.321856\pi$
$830$		0			0
$831$	0.0901699	−	0.0655123i	0.00312796	−	0.00227260i
$832$		−	1.00000i		−	0.0346688i
$833$	−1.34708	−	1.85410i	−0.0466737	−	0.0642408i
$834$	0.628677	+	1.93487i	0.0217693	+	0.0669990i
$835$		0			0
$836$	7.66312	−	23.5847i	0.265035	−	0.815692i
$837$	−0.502029	+	0.163119i	−0.0173526	+	0.00563822i
$838$	21.6498	−	7.03444i	0.747879	−	0.243001i
$839$	17.0729	−	52.5451i	0.589424	−	1.81406i	0.00869515	−	0.999962i	$-0.497232\pi$
$839$	17.0729	−	52.5451i	0.589424	−	1.81406i	0.580729	−	0.814097i	$-0.302768\pi$
$840$		0			0
$841$	18.7639	+	57.7494i	0.647032	+	1.99136i
$842$	−12.5025	−	17.2082i	−0.430864	−	0.593034i
$843$		−	1.21478i		−	0.0418393i
$844$	−18.0172	+	13.0903i	−0.620178	+	0.450586i
$845$		0			0
$846$	27.5795	+	20.0377i	0.948204	+	0.688910i
$847$	12.2452	−	16.8541i	0.420751	−	0.579114i
$848$	9.95959	+	3.23607i	0.342014	+	0.111127i
$849$	−4.69505			−0.161134
$850$		0			0
$851$	14.6869			0.503461
$852$	−1.08981	−	0.354102i	−0.0373364	−	0.0121313i
$853$	−10.6659	+	14.6803i	−0.365193	+	0.502645i	−0.951586	−	0.307381i	$-0.900547\pi$
$853$	−10.6659	+	14.6803i	−0.365193	+	0.502645i	0.586393	+	0.810026i	$0.300547\pi$
$854$	−21.4894	−	15.6129i	−0.735351	−	0.534264i
$855$		0			0
$856$	−0.881966	+	0.640786i	−0.0301450	+	0.0219016i
$857$			56.3394i			1.92452i	0.272137	+	0.962259i	$0.412270\pi$
$857$			56.3394i			1.92452i	−0.272137	+	0.962259i	$0.587730\pi$
$858$	−0.951057	−	1.30902i	−0.0324685	−	0.0446891i
$859$	−10.6287	−	32.7117i	−0.362646	−	1.11611i	−0.951442	−	0.307828i	$-0.900398\pi$
$859$	−10.6287	−	32.7117i	−0.362646	−	1.11611i	0.588796	−	0.808281i	$-0.299602\pi$
$860$		0			0
$861$	0.521286	−	1.60435i	0.0177654	−	0.0546762i
$862$	−24.7930	+	8.05573i	−0.844452	+	0.274379i
$863$	10.6861	−	3.47214i	0.363760	−	0.118193i	−0.121433	−	0.992600i	$-0.538749\pi$
$863$	10.6861	−	3.47214i	0.363760	−	0.118193i	0.485194	+	0.874407i	$0.338749\pi$
$864$	0.690983	−	2.12663i	0.0235077	−	0.0723493i
$865$		0			0
$866$	6.60081	+	20.3152i	0.224305	+	0.690339i
$867$	3.52193	+	4.84752i	0.119611	+	0.164631i
$868$			0.708204i			0.0240380i
$869$	−24.7984	+	18.0171i	−0.841227	+	0.611187i
$870$		0			0
$871$	8.28115	+	6.01661i	0.280596	+	0.203865i
$872$	−8.81678	+	12.1353i	−0.298574	+	0.410952i
$873$	−25.9560	−	8.43363i	−0.878479	−	0.285435i
$874$	−10.3262			−0.349290
$875$		0			0
$876$	−2.94427			−0.0994777
$877$	−4.22050	−	1.37132i	−0.142516	−	0.0463063i	0.236890	−	0.971536i	$-0.423872\pi$
$877$	−4.22050	−	1.37132i	−0.142516	−	0.0463063i	−0.379406	+	0.925230i	$0.623872\pi$
$878$	−15.0781	+	20.7533i	−0.508863	+	0.700390i
$879$	−2.64590	−	1.92236i	−0.0892439	−	0.0648395i
$880$		0			0
$881$	−30.8885	+	22.4418i	−1.04066	+	0.756085i	−0.970415	−	0.241445i	$-0.922379\pi$
$881$	−30.8885	+	22.4418i	−1.04066	+	0.756085i	−0.0702469	+	0.997530i	$0.522379\pi$
$882$		−	5.70820i		−	0.192205i
$883$	24.5030	+	33.7254i	0.824590	+	1.13495i	0.988906	+	0.148543i	$0.0474584\pi$
$883$	24.5030	+	33.7254i	0.824590	+	1.13495i	−0.164316	+	0.986408i	$0.552542\pi$
$884$	−0.354102	−	1.08981i	−0.0119097	−	0.0366544i
$885$		0			0
$886$	−6.00000	+	18.4661i	−0.201574	+	0.620381i
$887$	31.5564	−	10.2533i	1.05956	−	0.344272i	0.273146	−	0.961973i	$-0.411936\pi$
$887$	31.5564	−	10.2533i	1.05956	−	0.344272i	0.786413	+	0.617701i	$0.211936\pi$
$888$	3.02468	−	0.982779i	0.101502	−	0.0329799i
$889$	−3.27051	+	10.0656i	−0.109689	+	0.337589i
$890$		0			0
$891$	10.0902	+	31.0543i	0.338033	+	1.04036i
$892$	−5.29007	−	7.28115i	−0.177125	−	0.243791i
$893$		−	69.9230i		−	2.33988i
$894$	0.690983	−	0.502029i	0.0231099	−	0.0167903i
$895$		0			0
$896$	−2.42705	−	1.76336i	−0.0810821	−	0.0589096i
$897$	−0.396027	+	0.545085i	−0.0132230	+	0.0181999i
$898$	3.75123	+	1.21885i	0.125180	+	0.0406735i
$899$	−2.23607			−0.0745770
$900$		0			0
$901$	12.0000			0.399778
$902$	5.93085	+	1.92705i	0.197476	+	0.0641638i
$903$	−4.20025	+	5.78115i	−0.139776	+	0.192385i
$904$	−3.04508	−	2.21238i	−0.101278	−	0.0735828i
$905$		0			0
$906$	3.00000	−	2.17963i	0.0996683	−	0.0724133i
$907$		−	25.6180i		−	0.850633i	−0.905045	−	0.425316i	$-0.860163\pi$
$907$		−	25.6180i		−	0.850633i	0.905045	−	0.425316i	$-0.139837\pi$
$908$	−17.2578	−	23.7533i	−0.572719	−	0.788281i
$909$	0.545085	+	1.67760i	0.0180793	+	0.0556424i
$910$		0			0
$911$	−5.07295	+	15.6129i	−0.168074	+	0.517280i	−0.999250	−	0.0387308i	$-0.987669\pi$
$911$	−5.07295	+	15.6129i	−0.168074	+	0.517280i	0.831175	+	0.556010i	$0.187669\pi$
$912$	−2.12663	+	0.690983i	−0.0704197	+	0.0228807i
$913$	18.2416	−	5.92705i	0.603708	−	0.196157i
$914$	12.4271	−	38.2465i	0.411050	−	1.26508i
$915$		0			0
$916$	−0.791796	−	2.43690i	−0.0261617	−	0.0805174i
$917$	28.9480	+	39.8435i	0.955946	+	1.31575i
$918$		−	2.56231i		−	0.0845687i
$919$	−4.57295	+	3.32244i	−0.150848	+	0.109597i	−0.660649	−	0.750695i	$-0.729719\pi$
$919$	−4.57295	+	3.32244i	−0.150848	+	0.109597i	0.509801	+	0.860292i	$0.329719\pi$
$920$		0			0
$921$	−7.14590	−	5.19180i	−0.235465	−	0.171076i
$922$	3.42071	−	4.70820i	0.112655	−	0.155056i
$923$	−2.85317	−	0.927051i	−0.0939132	−	0.0305143i
$924$	−4.85410			−0.159688
$925$		0			0
$926$	34.9787			1.14947
$927$	−35.6834	−	11.5942i	−1.17200	−	0.380805i
$928$	5.56758	−	7.66312i	0.182765	−	0.251554i
$929$	−42.7877	−	31.0871i	−1.40382	−	1.01993i	−0.994185	−	0.107685i	$-0.965656\pi$
$929$	−42.7877	−	31.0871i	−1.40382	−	1.01993i	−0.409635	−	0.912250i	$-0.634344\pi$
$930$		0			0
$931$	−9.47214	+	6.88191i	−0.310437	+	0.225545i
$932$		−	14.2918i		−	0.468143i
$933$	−2.22490	−	3.06231i	−0.0728398	−	0.100255i
$934$	−5.92705	−	18.2416i	−0.193939	−	0.596883i
$935$		0			0
$936$	0.881966	−	2.71441i	0.0288280	−	0.0887233i
$937$	39.8711	−	12.9549i	1.30253	−	0.423219i	0.426071	−	0.904690i	$-0.359897\pi$
$937$	39.8711	−	12.9549i	1.30253	−	0.423219i	0.876462	+	0.481471i	$0.159897\pi$
$938$	29.2052	−	9.48936i	0.953585	−	0.309838i
$939$	−1.95492	+	6.01661i	−0.0637962	+	0.196345i
$940$		0			0
$941$	−2.89919	−	8.92278i	−0.0945108	−	0.290874i	0.892615	−	0.450820i	$-0.148868\pi$
$941$	−2.89919	−	8.92278i	−0.0945108	−	0.290874i	−0.987126	+	0.159945i	$0.948868\pi$
$942$	1.02430	+	1.40983i	0.0333735	+	0.0459347i
$943$		−	2.59675i		−	0.0845617i
$944$	−3.61803	+	2.62866i	−0.117757	+	0.0855555i
$945$		0			0
$946$	−21.3713	−	15.5272i	−0.694842	−	0.504832i
$947$	23.1481	−	31.8607i	0.752213	−	1.03533i	−0.245609	−	0.969369i	$-0.578988\pi$
$947$	23.1481	−	31.8607i	0.752213	−	1.03533i	0.997822	−	0.0659639i	$-0.0210122\pi$
$948$	2.62866	+	0.854102i	0.0853748	+	0.0277399i
$949$	−7.70820			−0.250219
$950$		0			0
$951$	−3.20163			−0.103820
$952$	−3.26944	−	1.06231i	−0.105963	−	0.0344295i
$953$	26.2258	−	36.0967i	0.849538	−	1.16929i	−0.134427	−	0.990924i	$-0.542919\pi$
$953$	26.2258	−	36.0967i	0.849538	−	1.16929i	0.983964	−	0.178365i	$-0.0570807\pi$
$954$	24.1803	+	17.5680i	0.782867	+	0.568786i
$955$		0			0
$956$	5.59017	−	4.06150i	0.180799	−	0.131358i
$957$		−	15.3262i		−	0.495427i
$958$	−8.93529	−	12.2984i	−0.288686	−	0.397342i
$959$	4.71885	+	14.5231i	0.152380	+	0.468976i
$960$		0			0
$961$	−9.56231	+	29.4298i	−0.308461	+	0.949347i
$962$	7.91872	−	2.57295i	0.255310	−	0.0829552i
$963$	−2.95917	+	0.961493i	−0.0953579	+	0.0309837i
$964$	−4.82624	+	14.8536i	−0.155443	+	0.478403i
$965$		0			0
$966$	0.624612	+	1.92236i	0.0200966	+	0.0618508i
$967$	−7.71445	−	10.6180i	−0.248080	−	0.341453i	0.666758	−	0.745275i	$-0.267682\pi$
$967$	−7.71445	−	10.6180i	−0.248080	−	0.341453i	−0.914838	+	0.403822i	$0.867682\pi$
$968$		−	6.94427i		−	0.223197i
$969$	−2.07295	+	1.50609i	−0.0665927	+	0.0483824i
$970$		0			0
$971$	−4.90983	−	3.56720i	−0.157564	−	0.114477i	0.506210	−	0.862410i	$-0.331046\pi$
$971$	−4.90983	−	3.56720i	−0.157564	−	0.114477i	−0.663774	+	0.747934i	$0.731046\pi$
$972$	5.67358	−	7.80902i	0.181980	−	0.250474i
$973$	15.1967	+	4.93769i	0.487183	+	0.158295i
$974$	22.1246			0.708918
$975$		0			0
$976$	−8.85410			−0.283413
$977$	−47.5653	−	15.4549i	−1.52175	−	0.494447i	−0.575478	−	0.817817i	$-0.695184\pi$
$977$	−47.5653	−	15.4549i	−1.52175	−	0.494447i	−0.946272	+	0.323371i	$0.895184\pi$
$978$	0.416272	−	0.572949i	0.0133109	−	0.0183209i
$979$	15.3262	+	11.1352i	0.489829	+	0.355881i
$980$		0			0
$981$	−34.6353	+	25.1640i	−1.10582	+	0.803424i
$982$			19.2361i			0.613848i
$983$	−22.6211	−	31.1353i	−0.721501	−	0.993060i	−0.999473	−	0.0324712i	$-0.989662\pi$
$983$	−22.6211	−	31.1353i	−0.721501	−	0.993060i	0.277972	−	0.960589i	$-0.410338\pi$
$984$	−0.173762	−	0.534785i	−0.00553933	−	0.0170483i
$985$		0			0
$986$	3.35410	−	10.3229i	0.106816	−	0.328747i
$987$	−13.0170	+	4.22949i	−0.414337	+	0.134626i
$988$	−5.56758	+	1.80902i	−0.177128	+	0.0575525i
$989$	−3.39919	+	10.4616i	−0.108088	+	0.332660i
$990$		0			0
$991$	−1.06637	−	3.28195i	−0.0338744	−	0.104255i	0.932690	−	0.360680i	$-0.117455\pi$
$991$	−1.06637	−	3.28195i	−0.0338744	−	0.104255i	−0.966564	+	0.256425i	$0.917455\pi$
$992$	0.138757	+	0.190983i	0.00440555	+	0.00606372i
$993$			5.94427i			0.188636i
$994$	−7.28115	+	5.29007i	−0.230944	+	0.167791i
$995$		0			0
$996$	−1.39919	−	1.01657i	−0.0443349	−	0.0322112i
$997$	−16.0167	+	22.0451i	−0.507254	+	0.698175i	−0.983453	−	0.181162i	$-0.942014\pi$
$997$	−16.0167	+	22.0451i	−0.507254	+	0.698175i	0.476199	+	0.879337i	$0.342014\pi$
$998$	−32.4747	−	10.5517i	−1.02797	−	0.334007i
$999$	18.6180			0.589049

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	250.2.e.b.149.2		8
5.2	odd	4		50.2.d.a.21.1	✓	4
5.3	odd	4		250.2.d.a.101.1		4
5.4	even	2	inner	250.2.e.b.149.1		8
15.2	even	4		450.2.h.a.271.1		4
20.7	even	4		400.2.u.c.321.1		4
25.6	even	5	inner	250.2.e.b.99.1		8
25.8	odd	20		250.2.d.a.151.1		4
25.9	even	10		1250.2.b.b.1249.1		4
25.12	odd	20		1250.2.a.a.1.2		2
25.13	odd	20		1250.2.a.d.1.1		2
25.16	even	5		1250.2.b.b.1249.4		4
25.17	odd	20		50.2.d.a.31.1	yes	4
25.19	even	10	inner	250.2.e.b.99.2		8
75.17	even	20		450.2.h.a.181.1		4
100.63	even	20		10000.2.a.a.1.2		2
100.67	even	20		400.2.u.c.81.1		4
100.87	even	20		10000.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.2.d.a.21.1	✓	4	5.2	odd	4
50.2.d.a.31.1	yes	4	25.17	odd	20
250.2.d.a.101.1		4	5.3	odd	4
250.2.d.a.151.1		4	25.8	odd	20
250.2.e.b.99.1		8	25.6	even	5	inner
250.2.e.b.99.2		8	25.19	even	10	inner
250.2.e.b.149.1		8	5.4	even	2	inner
250.2.e.b.149.2		8	1.1	even	1	trivial
400.2.u.c.81.1		4	100.67	even	20
400.2.u.c.321.1		4	20.7	even	4
450.2.h.a.181.1		4	75.17	even	20
450.2.h.a.271.1		4	15.2	even	4
1250.2.a.a.1.2		2	25.12	odd	20
1250.2.a.d.1.1		2	25.13	odd	20
1250.2.b.b.1249.1		4	25.9	even	10
1250.2.b.b.1249.4		4	25.16	even	5
10000.2.a.a.1.2		2	100.63	even	20
10000.2.a.n.1.1		2	100.87	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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.224514 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{6} +3.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.881966 + 2.71441i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(-0.224514 + 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{6} +3.00000i q^{7} +(0.587785 + 0.809017i) q^{8} +(0.881966 + 2.71441i) q^{9} +(1.30902 - 4.02874i) q^{11} +(-0.363271 + 0.118034i) q^{12} +(-0.951057 + 0.309017i) q^{13} +(-0.927051 + 2.85317i) q^{14} +(0.309017 + 0.951057i) q^{16} +(0.673542 + 0.927051i) q^{17} +2.85410i q^{18} +(4.73607 - 3.44095i) q^{19} +(-0.927051 - 0.673542i) q^{21} +(2.48990 - 3.42705i) q^{22} +(-1.67760 - 0.545085i) q^{23} -0.381966 q^{24} -1.00000 q^{26} +(-2.12663 - 0.690983i) q^{27} +(-1.76336 + 2.42705i) q^{28} +(-7.66312 - 5.56758i) q^{29} +(0.190983 - 0.138757i) q^{31} +1.00000i q^{32} +(0.951057 + 1.30902i) q^{33} +(0.354102 + 1.08981i) q^{34} +(-0.881966 + 2.71441i) q^{36} +(-7.91872 + 2.57295i) q^{37} +(5.56758 - 1.80902i) q^{38} +(0.118034 - 0.363271i) q^{39} +(0.454915 + 1.40008i) q^{41} +(-0.673542 - 0.927051i) q^{42} -6.23607i q^{43} +(3.42705 - 2.48990i) q^{44} +(-1.42705 - 1.03681i) q^{46} +(7.02067 - 9.66312i) q^{47} +(-0.363271 - 0.118034i) q^{48} -2.00000 q^{49} -0.437694 q^{51} +(-0.951057 - 0.309017i) q^{52} +(6.15537 - 8.47214i) q^{53} +(-1.80902 - 1.31433i) q^{54} +(-2.42705 + 1.76336i) q^{56} +2.23607i q^{57} +(-5.56758 - 7.66312i) q^{58} +(1.38197 + 4.25325i) q^{59} +(-2.73607 + 8.42075i) q^{61} +(0.224514 - 0.0729490i) q^{62} +(-8.14324 + 2.64590i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(0.500000 + 1.53884i) q^{66} +(-6.01661 - 8.28115i) q^{67} +1.14590i q^{68} +(0.545085 - 0.396027i) q^{69} +(2.42705 + 1.76336i) q^{71} +(-1.67760 + 2.30902i) q^{72} +(7.33094 + 2.38197i) q^{73} -8.32624 q^{74} +5.85410 q^{76} +(12.0862 + 3.92705i) q^{77} +(0.224514 - 0.309017i) q^{78} +(-5.85410 - 4.25325i) q^{79} +(-6.23607 + 4.53077i) q^{81} +1.47214i q^{82} +(2.66141 + 3.66312i) q^{83} +(-0.354102 - 1.08981i) q^{84} +(1.92705 - 5.93085i) q^{86} +(3.44095 - 1.11803i) q^{87} +(4.02874 - 1.30902i) q^{88} +(-1.38197 + 4.25325i) q^{89} +(-0.927051 - 2.85317i) q^{91} +(-1.03681 - 1.42705i) q^{92} +0.0901699i q^{93} +(9.66312 - 7.02067i) q^{94} +(-0.309017 - 0.224514i) q^{96} +(-5.62058 + 7.73607i) q^{97} +(-1.90211 - 0.618034i) q^{98} +12.0902 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

Modular forms

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Representations

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