LMFDB - Embedded newform 875.2.h.d.701.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(176,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8, 0]))

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

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

chi := DirichletCharacter("875.176");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.h (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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{5})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			701.8
Character	$\chi$	$=$	875.701
Dual form			875.2.h.d.176.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.160894 - 0.116896i) q^{2} +(0.477493 + 1.46957i) q^{3} +(-0.605812 - 1.86450i) q^{4} +(0.0949619 - 0.292263i) q^{6} -1.00000 q^{7} +(-0.243394 + 0.749089i) q^{8} +(0.495409 - 0.359936i) q^{9} +O(q^{10})$	\(q+(-0.160894 - 0.116896i) q^{2} +(0.477493 + 1.46957i) q^{3} +(-0.605812 - 1.86450i) q^{4} +(0.0949619 - 0.292263i) q^{6} -1.00000 q^{7} +(-0.243394 + 0.749089i) q^{8} +(0.495409 - 0.359936i) q^{9} +(-2.54486 - 1.84895i) q^{11} +(2.45074 - 1.78057i) q^{12} +(-5.25890 + 3.82082i) q^{13} +(0.160894 + 0.116896i) q^{14} +(-3.04535 + 2.21257i) q^{16} +(-0.881886 + 2.71417i) q^{17} -0.121784 q^{18} +(-1.06144 + 3.26678i) q^{19} +(-0.477493 - 1.46957i) q^{21} +(0.193318 + 0.594971i) q^{22} +(0.469412 + 0.341048i) q^{23} -1.21706 q^{24} +1.29277 q^{26} +(4.51578 + 3.28091i) q^{27} +(0.605812 + 1.86450i) q^{28} +(0.343638 + 1.05761i) q^{29} +(-0.595158 + 1.83171i) q^{31} +2.32390 q^{32} +(1.50201 - 4.62272i) q^{33} +(0.459166 - 0.333604i) q^{34} +(-0.971225 - 0.705636i) q^{36} +(-2.04235 + 1.48385i) q^{37} +(0.552655 - 0.401527i) q^{38} +(-8.12605 - 5.90392i) q^{39} +(-4.17033 + 3.02992i) q^{41} +(-0.0949619 + 0.292263i) q^{42} -3.23994 q^{43} +(-1.90566 + 5.86501i) q^{44} +(-0.0356584 - 0.109745i) q^{46} +(1.09432 + 3.36797i) q^{47} +(-4.70567 - 3.41887i) q^{48} +1.00000 q^{49} -4.40975 q^{51} +(10.3098 + 7.49052i) q^{52} +(-0.220620 - 0.678998i) q^{53} +(-0.343036 - 1.05576i) q^{54} +(0.243394 - 0.749089i) q^{56} -5.30760 q^{57} +(0.0683414 - 0.210333i) q^{58} +(-8.59038 + 6.24127i) q^{59} +(-6.90849 - 5.01931i) q^{61} +(0.309878 - 0.225139i) q^{62} +(-0.495409 + 0.359936i) q^{63} +(5.71679 + 4.15349i) q^{64} +(-0.782044 + 0.568189i) q^{66} +(4.71139 - 14.5002i) q^{67} +5.59481 q^{68} +(-0.277053 + 0.852682i) q^{69} +(-3.64856 - 11.2291i) q^{71} +(0.149044 + 0.458712i) q^{72} +(-1.51347 - 1.09960i) q^{73} +0.502059 q^{74} +6.73394 q^{76} +(2.54486 + 1.84895i) q^{77} +(0.617287 + 1.89981i) q^{78} +(2.62230 + 8.07060i) q^{79} +(-2.09759 + 6.45571i) q^{81} +1.02517 q^{82} +(-3.67741 + 11.3179i) q^{83} +(-2.45074 + 1.78057i) q^{84} +(0.521288 + 0.378738i) q^{86} +(-1.39015 + 1.01000i) q^{87} +(2.00443 - 1.45631i) q^{88} +(-13.5558 - 9.84885i) q^{89} +(5.25890 - 3.82082i) q^{91} +(0.351507 - 1.08183i) q^{92} -2.97601 q^{93} +(0.217634 - 0.669808i) q^{94} +(1.10964 + 3.41513i) q^{96} +(-3.09402 - 9.52242i) q^{97} +(-0.160894 - 0.116896i) q^{98} -1.92625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	$ 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) $ 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

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 $

$2$	−0.160894	−	0.116896i	−0.113769	−	0.0826582i	0.529446	−	0.848344i	$-0.322400\pi$
$2$	−0.160894	−	0.116896i	−0.113769	−	0.0826582i	−0.643215	+	0.765686i	$0.722400\pi$
$3$	0.477493	+	1.46957i	0.275681	+	0.848458i	0.989039	+	0.147658i	$0.0471734\pi$
$3$	0.477493	+	1.46957i	0.275681	+	0.848458i	−0.713358	+	0.700800i	$0.752827\pi$
$4$	−0.605812	−	1.86450i	−0.302906	−	0.932249i
$5$		0			0
$5$		0			0
$6$	0.0949619	−	0.292263i	0.0387680	−	0.119316i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.243394	+	0.749089i	−0.0860526	+	0.264843i
$9$	0.495409	−	0.359936i	0.165136	−	0.119979i
$10$		0			0
$11$	−2.54486	−	1.84895i	−0.767305	−	0.557480i	0.133837	−	0.991003i	$-0.457270\pi$
$11$	−2.54486	−	1.84895i	−0.767305	−	0.557480i	−0.901142	+	0.433524i	$0.857270\pi$
$12$	2.45074	−	1.78057i	0.707468	−	0.514006i
$13$	−5.25890	+	3.82082i	−1.45856	+	1.05970i	−0.474822	+	0.880082i	$0.657488\pi$
$13$	−5.25890	+	3.82082i	−1.45856	+	1.05970i	−0.983736	+	0.179622i	$0.942512\pi$
$14$	0.160894	+	0.116896i	0.0430008	+	0.0312419i
$15$		0			0
$16$	−3.04535	+	2.21257i	−0.761336	+	0.553143i
$17$	−0.881886	+	2.71417i	−0.213889	+	0.658282i	0.785342	+	0.619062i	$0.212487\pi$
$17$	−0.881886	+	2.71417i	−0.213889	+	0.658282i	−0.999231	+	0.0392195i	$0.987513\pi$
$18$	−0.121784			−0.0287047
$19$	−1.06144	+	3.26678i	−0.243512	+	0.749451i	0.752366	+	0.658745i	$0.228912\pi$
$19$	−1.06144	+	3.26678i	−0.243512	+	0.749451i	−0.995878	+	0.0907063i	$0.971088\pi$
$20$		0			0
$21$	−0.477493	−	1.46957i	−0.104197	−	0.320687i
$22$	0.193318	+	0.594971i	0.0412155	+	0.126848i
$23$	0.469412	+	0.341048i	0.0978792	+	0.0711134i	0.635648	−	0.771979i	$-0.280733\pi$
$23$	0.469412	+	0.341048i	0.0978792	+	0.0711134i	−0.537769	+	0.843092i	$0.680733\pi$
$24$	−1.21706			−0.248431
$25$		0			0
$26$	1.29277			0.253532
$27$	4.51578	+	3.28091i	0.869063	+	0.631411i
$28$	0.605812	+	1.86450i	0.114488	+	0.352357i
$29$	0.343638	+	1.05761i	0.0638120	+	0.196393i	0.977880	−	0.209169i	$-0.0670758\pi$
$29$	0.343638	+	1.05761i	0.0638120	+	0.196393i	−0.914068	+	0.405562i	$0.867076\pi$
$30$		0			0
$31$	−0.595158	+	1.83171i	−0.106894	+	0.328985i	−0.990170	−	0.139868i	$-0.955332\pi$
$31$	−0.595158	+	1.83171i	−0.106894	+	0.328985i	0.883277	+	0.468852i	$0.155332\pi$
$32$	2.32390			0.410811
$33$	1.50201	−	4.62272i	0.261467	−	0.804712i
$34$	0.459166	−	0.333604i	0.0787464	−	0.0572126i
$35$		0			0
$36$	−0.971225	−	0.705636i	−0.161871	−	0.117606i
$37$	−2.04235	+	1.48385i	−0.335760	+	0.243944i	−0.742871	−	0.669435i	$-0.766536\pi$
$37$	−2.04235	+	1.48385i	−0.335760	+	0.243944i	0.407111	+	0.913379i	$0.366536\pi$
$38$	0.552655	−	0.401527i	0.0896525	−	0.0651363i
$39$	−8.12605	−	5.90392i	−1.30121	−	0.945384i
$40$		0			0
$41$	−4.17033	+	3.02992i	−0.651296	+	0.473194i	−0.863712	−	0.503985i	$-0.831867\pi$
$41$	−4.17033	+	3.02992i	−0.651296	+	0.473194i	0.212417	+	0.977179i	$0.431867\pi$
$42$	−0.0949619	+	0.292263i	−0.0146529	+	0.0450971i
$43$	−3.23994			−0.494086			−0.247043	−	0.969004i	$-0.579459\pi$
$43$	−3.23994			−0.494086			−0.247043	+	0.969004i	$0.579459\pi$
$44$	−1.90566	+	5.86501i	−0.287288	+	0.884183i
$45$		0			0
$46$	−0.0356584	−	0.109745i	−0.00525754	−	0.0161810i
$47$	1.09432	+	3.36797i	0.159623	+	0.491268i	0.998600	−	0.0528982i	$-0.0168459\pi$
$47$	1.09432	+	3.36797i	0.159623	+	0.491268i	−0.838977	+	0.544167i	$0.816846\pi$
$48$	−4.70567	−	3.41887i	−0.679204	−	0.493471i
$49$	1.00000			0.142857
$50$		0			0
$51$	−4.40975			−0.617489
$52$	10.3098	+	7.49052i	1.42971	+	1.03875i
$53$	−0.220620	−	0.678998i	−0.0303044	−	0.0932675i	0.934760	−	0.355279i	$-0.115614\pi$
$53$	−0.220620	−	0.678998i	−0.0303044	−	0.0932675i	−0.965065	+	0.262012i	$0.915614\pi$
$54$	−0.343036	−	1.05576i	−0.0466814	−	0.143670i
$55$		0			0
$56$	0.243394	−	0.749089i	0.0325248	−	0.100101i
$57$	−5.30760			−0.703009
$58$	0.0683414	−	0.210333i	0.00897366	−	0.0276181i
$59$	−8.59038	+	6.24127i	−1.11837	+	0.812545i	−0.983961	−	0.178381i	$-0.942914\pi$
$59$	−8.59038	+	6.24127i	−1.11837	+	0.812545i	−0.134410	+	0.990926i	$0.542914\pi$
$60$		0			0
$61$	−6.90849	−	5.01931i	−0.884541	−	0.642657i	0.0499078	−	0.998754i	$-0.484107\pi$
$61$	−6.90849	−	5.01931i	−0.884541	−	0.642657i	−0.934449	+	0.356097i	$0.884107\pi$
$62$	0.309878	−	0.225139i	0.0393545	−	0.0285927i
$63$	−0.495409	+	0.359936i	−0.0624157	+	0.0453477i
$64$	5.71679	+	4.15349i	0.714599	+	0.519186i
$65$		0			0
$66$	−0.782044	+	0.568189i	−0.0962630	+	0.0699392i
$67$	4.71139	−	14.5002i	0.575587	−	1.77148i	−0.0585831	−	0.998283i	$-0.518658\pi$
$67$	4.71139	−	14.5002i	0.575587	−	1.77148i	0.634171	−	0.773193i	$-0.281342\pi$
$68$	5.59481			0.678470
$69$	−0.277053	+	0.852682i	−0.0333533	+	0.102651i
$70$		0			0
$71$	−3.64856	−	11.2291i	−0.433004	−	1.33265i	−0.895118	−	0.445829i	$-0.852909\pi$
$71$	−3.64856	−	11.2291i	−0.433004	−	1.33265i	0.462114	−	0.886821i	$-0.347091\pi$
$72$	0.149044	+	0.458712i	0.0175651	+	0.0540597i
$73$	−1.51347	−	1.09960i	−0.177138	−	0.128698i	0.495683	−	0.868503i	$-0.334918\pi$
$73$	−1.51347	−	1.09960i	−0.177138	−	0.128698i	−0.672821	+	0.739805i	$0.734918\pi$
$74$	0.502059			0.0583631
$75$		0			0
$76$	6.73394			0.772436
$77$	2.54486	+	1.84895i	0.290014	+	0.210708i
$78$	0.617287	+	1.89981i	0.0698940	+	0.215111i
$79$	2.62230	+	8.07060i	0.295031	+	0.908013i	0.983211	+	0.182473i	$0.0584101\pi$
$79$	2.62230	+	8.07060i	0.295031	+	0.908013i	−0.688180	+	0.725540i	$0.741590\pi$
$80$		0			0
$81$	−2.09759	+	6.45571i	−0.233065	+	0.717301i
$82$	1.02517			0.113211
$83$	−3.67741	+	11.3179i	−0.403648	+	1.24230i	0.518370	+	0.855156i	$0.326539\pi$
$83$	−3.67741	+	11.3179i	−0.403648	+	1.24230i	−0.922019	+	0.387146i	$0.873461\pi$
$84$	−2.45074	+	1.78057i	−0.267398	+	0.194276i
$85$		0			0
$86$	0.521288	+	0.378738i	0.0562119	+	0.0408403i
$87$	−1.39015	+	1.01000i	−0.149039	+	0.108284i
$88$	2.00443	−	1.45631i	0.213673	−	0.155243i
$89$	−13.5558	−	9.84885i	−1.43691	−	1.04398i	−0.988677	−	0.150060i	$-0.952053\pi$
$89$	−13.5558	−	9.84885i	−1.43691	−	1.04398i	−0.448233	−	0.893917i	$-0.647947\pi$
$90$		0			0
$91$	5.25890	−	3.82082i	0.551283	−	0.400530i
$92$	0.351507	−	1.08183i	0.0366472	−	0.112788i
$93$	−2.97601			−0.308598
$94$	0.217634	−	0.669808i	0.0224472	−	0.0690854i
$95$		0			0
$96$	1.10964	+	3.41513i	0.113253	+	0.348556i
$97$	−3.09402	−	9.52242i	−0.314150	−	0.966855i	−0.976103	−	0.217309i	$-0.930272\pi$
$97$	−3.09402	−	9.52242i	−0.314150	−	0.966855i	0.661953	−	0.749546i	$-0.269728\pi$
$98$	−0.160894	−	0.116896i	−0.0162528	−	0.0118083i
$99$	−1.92625			−0.193596
$100$		0			0
$101$	18.6057			1.85133			0.925667	−	0.378339i	$-0.123505\pi$
$101$	18.6057			1.85133			0.925667	+	0.378339i	$0.123505\pi$
$102$	0.709504	+	0.515485i	0.0702513	+	0.0510406i
$103$	2.10824	+	6.48850i	0.207731	+	0.639331i	0.999590	+	0.0286269i	$0.00911348\pi$
$103$	2.10824	+	6.48850i	0.207731	+	0.639331i	−0.791859	+	0.610704i	$0.790887\pi$
$104$	−1.58215	−	4.86935i	−0.155142	−	0.477479i
$105$		0			0
$106$	−0.0438760	+	0.135036i	−0.00426161	+	0.0131159i
$107$	−11.2305			−1.08570			−0.542848	−	0.839831i	$-0.682654\pi$
$107$	−11.2305			−1.08570			−0.542848	+	0.839831i	$0.682654\pi$
$108$	3.38153	−	10.4073i	0.325388	−	1.00144i
$109$	14.6006	−	10.6079i	1.39848	−	1.01606i	0.403608	−	0.914932i	$-0.367756\pi$
$109$	14.6006	−	10.6079i	1.39848	−	1.01606i	0.994874	−	0.101124i	$-0.0322439\pi$
$110$		0			0
$111$	−3.15583	−	2.29285i	−0.299538	−	0.217627i
$112$	3.04535	−	2.21257i	0.287758	−	0.209069i
$113$	−8.82526	+	6.41192i	−0.830210	+	0.603183i	−0.919619	−	0.392812i	$-0.871502\pi$
$113$	−8.82526	+	6.41192i	−0.830210	+	0.603183i	0.0894084	+	0.995995i	$0.471502\pi$
$114$	0.853962	+	0.620440i	0.0799809	+	0.0581095i
$115$		0			0
$116$	1.76373	−	1.28142i	0.163758	−	0.118977i
$117$	−1.23006	+	3.78574i	−0.113719	+	0.349992i
$118$	2.11172			0.194400
$119$	0.881886	−	2.71417i	0.0808423	−	0.248807i
$120$		0			0
$121$	−0.341479	−	1.05096i	−0.0310436	−	0.0955423i
$122$	0.524796	+	1.61515i	0.0475128	+	0.146229i
$123$	−6.44398	−	4.68183i	−0.581035	−	0.422146i
$124$	3.77577			0.339074
$125$		0			0
$126$	0.121784			0.0108494
$127$	−10.0747	−	7.31970i	−0.893986	−	0.649519i	0.0429283	−	0.999078i	$-0.486331\pi$
$127$	−10.0747	−	7.31970i	−0.893986	−	0.649519i	−0.936914	+	0.349559i	$0.886331\pi$
$128$	−1.87052	−	5.75686i	−0.165332	−	0.508839i
$129$	−1.54705	−	4.76133i	−0.136210	−	0.419211i
$130$		0			0
$131$	−0.769069	+	2.36695i	−0.0671939	+	0.206802i	−0.979016	−	0.203784i	$-0.934676\pi$
$131$	−0.769069	+	2.36695i	−0.0671939	+	0.206802i	0.911822	+	0.410586i	$0.134676\pi$
$132$	−9.52899			−0.829392
$133$	1.06144	−	3.26678i	0.0920387	−	0.283266i
$134$	−2.45305	+	1.78225i	−0.211911	+	0.153963i
$135$		0			0
$136$	−1.81851	−	1.32122i	−0.155936	−	0.113294i
$137$	−8.17703	+	5.94096i	−0.698611	+	0.507571i	−0.879480	−	0.475937i	$-0.842109\pi$
$137$	−8.17703	+	5.94096i	−0.698611	+	0.507571i	0.180868	+	0.983507i	$0.442109\pi$
$138$	0.144252	−	0.104805i	0.0122795	−	0.00892160i
$139$	14.8897	+	10.8180i	1.26293	+	0.917574i	0.998898	−	0.0469397i	$-0.0149469\pi$
$139$	14.8897	+	10.8180i	1.26293	+	0.917574i	0.264034	+	0.964513i	$0.414947\pi$
$140$		0			0
$141$	−4.42694	+	3.21636i	−0.372816	+	0.270866i
$142$	−0.725611	+	2.23320i	−0.0608919	+	0.187406i
$143$	20.4477			1.70992
$144$	−0.712308	+	2.19226i	−0.0593590	+	0.182688i
$145$		0			0
$146$	0.114969	+	0.353838i	0.00951490	+	0.0292838i
$147$	0.477493	+	1.46957i	0.0393829	+	0.121208i
$148$	4.00392	+	2.90902i	0.329120	+	0.239120i
$149$	20.1992			1.65479			0.827393	−	0.561623i	$-0.189823\pi$
$149$	20.1992			1.65479			0.827393	+	0.561623i	$0.189823\pi$
$150$		0			0
$151$	11.8668			0.965706			0.482853	−	0.875701i	$-0.339601\pi$
$151$	11.8668			0.965706			0.482853	+	0.875701i	$0.339601\pi$
$152$	−2.18876	−	1.59023i	−0.177532	−	0.128985i
$153$	0.540031	+	1.66205i	0.0436589	+	0.134368i
$154$	−0.193318	−	0.594971i	−0.0155780	−	0.0479441i
$155$		0			0
$156$	−6.08499	+	18.7277i	−0.487189	+	1.49941i
$157$	16.5799			1.32322			0.661608	−	0.749850i	$-0.269874\pi$
$157$	16.5799			1.32322			0.661608	+	0.749850i	$0.269874\pi$
$158$	0.521512	−	1.60505i	0.0414893	−	0.127691i
$159$	0.892491	−	0.648433i	0.0707792	−	0.0514241i
$160$		0			0
$161$	−0.469412	−	0.341048i	−0.0369948	−	0.0268783i
$162$	1.09214	−	0.793485i	0.0858065	−	0.0623421i
$163$	−15.6328	+	11.3579i	−1.22446	+	0.889620i	−0.996462	−	0.0840429i	$-0.973217\pi$
$163$	−15.6328	+	11.3579i	−1.22446	+	0.889620i	−0.227994	+	0.973663i	$0.573217\pi$
$164$	8.17571	+	5.94000i	0.638416	+	0.463836i
$165$		0			0
$166$	1.91470	−	1.39111i	0.148609	−	0.107971i
$167$	−0.473525	+	1.45736i	−0.0366425	+	0.112774i	−0.967705	−	0.252086i	$-0.918883\pi$
$167$	−0.473525	+	1.45736i	−0.0366425	+	0.112774i	0.931062	+	0.364860i	$0.118883\pi$
$168$	1.21706			0.0938981
$169$	9.04020	−	27.8229i	0.695400	−	2.14022i
$170$		0			0
$171$	0.649984	+	2.00045i	0.0497056	+	0.152978i
$172$	1.96280	+	6.04086i	0.149662	+	0.460611i
$173$	3.74051	+	2.71764i	0.284386	+	0.206618i	0.720828	−	0.693114i	$-0.243762\pi$
$173$	3.74051	+	2.71764i	0.284386	+	0.206618i	−0.436442	+	0.899732i	$0.643762\pi$
$174$	0.341732			0.0259066
$175$		0			0
$176$	11.8409			0.892544
$177$	−13.2738	−	9.64401i	−0.997723	−	0.724888i
$178$	1.02975	+	3.16924i	0.0771830	+	0.237545i
$179$	0.568958	+	1.75107i	0.0425259	+	0.130881i	0.970065	−	0.242844i	$-0.0780803\pi$
$179$	0.568958	+	1.75107i	0.0425259	+	0.130881i	−0.927539	+	0.373725i	$0.878080\pi$
$180$		0			0
$181$	−0.648662	+	1.99638i	−0.0482146	+	0.148389i	−0.972265	−	0.233881i	$-0.924858\pi$
$181$	−0.648662	+	1.99638i	−0.0482146	+	0.148389i	0.924051	+	0.382270i	$0.124858\pi$
$182$	−1.29277			−0.0958262
$183$	4.07748	−	12.5492i	0.301416	−	0.927664i
$184$	−0.369727	+	0.268622i	−0.0272566	+	0.0198031i
$185$		0			0
$186$	0.478823	+	0.347885i	0.0351090	+	0.0255082i
$187$	7.26264	−	5.27662i	0.531097	−	0.385864i
$188$	5.61661	−	4.08071i	0.409634	−	0.297616i
$189$	−4.51578	−	3.28091i	−0.328475	−	0.238651i
$190$		0			0
$191$	−17.0257	+	12.3699i	−1.23194	+	0.895056i	−0.997034	−	0.0769630i	$-0.975478\pi$
$191$	−17.0257	+	12.3699i	−1.23194	+	0.895056i	−0.234904	+	0.972019i	$0.575478\pi$
$192$	−3.37413	+	10.3845i	−0.243507	+	0.749436i
$193$	22.4099			1.61310			0.806548	−	0.591168i	$-0.201333\pi$
$193$	22.4099			1.61310			0.806548	+	0.591168i	$0.201333\pi$
$194$	−0.615327	+	1.89378i	−0.0441779	+	0.135966i
$195$		0			0
$196$	−0.605812	−	1.86450i	−0.0432723	−	0.133178i
$197$	3.83414	+	11.8003i	0.273171	+	0.840734i	0.989697	+	0.143174i	$0.0457309\pi$
$197$	3.83414	+	11.8003i	0.273171	+	0.840734i	−0.716526	+	0.697560i	$0.754269\pi$
$198$	0.309923	+	0.225172i	0.0220253	+	0.0160023i
$199$	−16.7681			−1.18866			−0.594329	−	0.804222i	$-0.702582\pi$
$199$	−16.7681			−1.18866			−0.594329	+	0.804222i	$0.702582\pi$
$200$		0			0
$201$	23.5587			1.66170
$202$	−2.99354	−	2.17494i	−0.210625	−	0.153028i
$203$	−0.343638	−	1.05761i	−0.0241187	−	0.0742296i
$204$	2.67148	+	8.22198i	0.187041	+	0.575653i
$205$		0			0
$206$	0.419279	−	1.29041i	0.0292125	−	0.0899069i
$207$	0.355306			0.0246955
$208$	7.56134	−	23.2714i	0.524285	−	1.61358i
$209$	8.74135	−	6.35096i	0.604652	−	0.439305i
$210$		0			0
$211$	7.43639	+	5.40286i	0.511943	+	0.371948i	0.813560	−	0.581481i	$-0.197527\pi$
$211$	7.43639	+	5.40286i	0.511943	+	0.371948i	−0.301617	+	0.953429i	$0.597527\pi$
$212$	−1.13234	+	0.822690i	−0.0777691	+	0.0565026i
$213$	14.7598	−	10.7236i	1.01133	−	0.734772i
$214$	1.80693	+	1.31281i	0.123519	+	0.0897418i
$215$		0			0
$216$	−3.55680	+	2.58417i	−0.242010	+	0.175830i
$217$	0.595158	−	1.83171i	0.0404020	−	0.124344i
$218$	−3.58918			−0.243090
$219$	0.893269	−	2.74920i	0.0603616	−	0.185774i
$220$		0			0
$221$	−5.73258	−	17.6431i	−0.385615	−	1.18680i
$222$	0.239729	+	0.737811i	0.0160896	+	0.0495186i
$223$	−14.8206	−	10.7678i	−0.992460	−	0.721064i	−0.0320016	−	0.999488i	$-0.510188\pi$
$223$	−14.8206	−	10.7678i	−0.992460	−	0.721064i	−0.960458	+	0.278423i	$0.910188\pi$
$224$	−2.32390			−0.155272
$225$		0			0
$226$	2.16946			0.144311
$227$	−13.9235	−	10.1160i	−0.924137	−	0.671424i	0.0204137	−	0.999792i	$-0.493502\pi$
$227$	−13.9235	−	10.1160i	−0.924137	−	0.671424i	−0.944550	+	0.328367i	$0.893502\pi$
$228$	3.21541	+	9.89601i	0.212946	+	0.655379i
$229$	0.727716	+	2.23968i	0.0480889	+	0.148002i	0.972218	−	0.234079i	$-0.0752074\pi$
$229$	0.727716	+	2.23968i	0.0480889	+	0.148002i	−0.924129	+	0.382081i	$0.875207\pi$
$230$		0			0
$231$	−1.50201	+	4.62272i	−0.0988252	+	0.304153i
$232$	−0.875882			−0.0575045
$233$	0.429855	−	1.32296i	0.0281608	−	0.0866699i	−0.935988	−	0.352031i	$-0.885491\pi$
$233$	0.429855	−	1.32296i	0.0281608	−	0.0866699i	0.964149	+	0.265361i	$0.0854912\pi$
$234$	0.640449	−	0.465313i	0.0418674	−	0.0304185i
$235$		0			0
$236$	16.8410	+	12.2357i	1.09625	+	0.796476i
$237$	−10.6082	+	7.70730i	−0.689076	+	0.500643i
$238$	−0.459166	+	0.333604i	−0.0297633	+	0.0216243i
$239$	8.49728	+	6.17364i	0.549644	+	0.399339i	0.827654	−	0.561239i	$-0.189675\pi$
$239$	8.49728	+	6.17364i	0.549644	+	0.399339i	−0.278010	+	0.960578i	$0.589675\pi$
$240$		0			0
$241$	10.3506	−	7.52017i	0.666742	−	0.484417i	−0.202191	−	0.979346i	$-0.564806\pi$
$241$	10.3506	−	7.52017i	0.666742	−	0.484417i	0.868933	+	0.494930i	$0.164806\pi$
$242$	−0.0679120	+	0.209012i	−0.00436555	+	0.0134358i
$243$	6.25673			0.401370
$244$	−5.17325	+	15.9216i	−0.331183	+	1.01928i
$245$		0			0
$246$	0.489510	+	1.50656i	0.0312100	+	0.0960546i
$247$	−6.89976	−	21.2353i	−0.439021	−	1.35117i
$248$	−1.22725	−	0.891652i	−0.0779307	−	0.0566200i
$249$	−18.3884			−1.16532
$250$		0			0
$251$	−12.7027			−0.801789			−0.400894	−	0.916124i	$-0.631301\pi$
$251$	−12.7027			−0.801789			−0.400894	+	0.916124i	$0.631301\pi$
$252$	0.971225	+	0.705636i	0.0611814	+	0.0444509i
$253$	−0.564009	−	1.73584i	−0.0354589	−	0.109131i
$254$	0.765314	+	2.35539i	0.0480201	+	0.147791i
$255$		0			0
$256$	3.99524	−	12.2961i	0.249702	−	0.768505i
$257$	20.2119			1.26079			0.630393	−	0.776276i	$-0.282894\pi$
$257$	20.2119			1.26079			0.630393	+	0.776276i	$0.282894\pi$
$258$	−0.307671	+	0.946914i	−0.0191548	+	0.0589523i
$259$	2.04235	−	1.48385i	0.126905	−	0.0922021i
$260$		0			0
$261$	0.550913	+	0.400262i	0.0341007	+	0.0247756i
$262$	0.400427	−	0.290927i	0.0247385	−	0.0179735i
$263$	1.29573	−	0.941404i	0.0798983	−	0.0580495i	−0.547119	−	0.837055i	$-0.684276\pi$
$263$	1.29573	−	0.941404i	0.0798983	−	0.0580495i	0.627017	+	0.779005i	$0.284276\pi$
$264$	3.09725	+	2.25028i	0.190622	+	0.138495i
$265$		0			0
$266$	−0.552655	+	0.401527i	−0.0338855	+	0.0246192i
$267$	8.00081	−	24.6239i	0.489641	−	1.50696i
$268$	−29.8897			−1.82580
$269$	6.08709	−	18.7341i	0.371136	−	1.14224i	−0.574912	−	0.818215i	$-0.694964\pi$
$269$	6.08709	−	18.7341i	0.371136	−	1.14224i	0.946049	−	0.324025i	$-0.105036\pi$
$270$		0			0
$271$	−8.23911	−	25.3574i	−0.500490	−	1.54035i	−0.808222	−	0.588878i	$-0.799570\pi$
$271$	−8.23911	−	25.3574i	−0.500490	−	1.54035i	0.307732	−	0.951473i	$-0.400430\pi$
$272$	−3.31964	−	10.2168i	−0.201283	−	0.619485i
$273$	8.12605	+	5.90392i	0.491811	+	0.357322i
$274$	2.01011			0.121435
$275$		0			0
$276$	1.75767			0.105799
$277$	−2.74918	−	1.99739i	−0.165182	−	0.120012i	0.502123	−	0.864796i	$-0.332552\pi$
$277$	−2.74918	−	1.99739i	−0.165182	−	0.120012i	−0.667305	+	0.744784i	$0.732552\pi$
$278$	−1.13108	−	3.48112i	−0.0678379	−	0.208783i
$279$	0.364451	+	1.12166i	0.0218191	+	0.0671523i
$280$		0			0
$281$	−10.2397	+	31.5144i	−0.610847	+	1.87999i	−0.160806	+	0.986986i	$0.551409\pi$
$281$	−10.2397	+	31.5144i	−0.610847	+	1.87999i	−0.450041	+	0.893008i	$0.648591\pi$
$282$	1.08825			0.0648043
$283$	−2.72669	+	8.39189i	−0.162085	+	0.498846i	−0.998810	−	0.0487777i	$-0.984467\pi$
$283$	−2.72669	+	8.39189i	−0.162085	+	0.498846i	0.836725	+	0.547624i	$0.184467\pi$
$284$	−18.7263	+	13.6055i	−1.11120	+	0.807335i
$285$		0			0
$286$	−3.28991	−	2.39026i	−0.194537	−	0.141339i
$287$	4.17033	−	3.02992i	0.246167	−	0.178850i
$288$	1.15128	−	0.836454i	0.0678398	−	0.0492885i
$289$	7.16432	+	5.20518i	0.421430	+	0.306187i
$290$		0			0
$291$	12.5165	−	9.09377i	0.733730	−	0.533086i
$292$	−1.13332	+	3.48801i	−0.0663227	+	0.204120i
$293$	16.0205			0.935929			0.467965	−	0.883747i	$-0.344987\pi$
$293$	16.0205			0.935929			0.467965	+	0.883747i	$0.344987\pi$
$294$	0.0949619	−	0.292263i	0.00553829	−	0.0170451i
$295$		0			0
$296$	−0.614442	−	1.89106i	−0.0357137	−	0.109916i
$297$	−5.42581	−	16.6989i	−0.314837	−	0.968970i
$298$	−3.24994	−	2.36122i	−0.188264	−	0.136782i
$299$	−3.77167			−0.218122
$300$		0			0
$301$	3.23994			0.186747
$302$	−1.90930	−	1.38719i	−0.109868	−	0.0798236i
$303$	8.88408	+	27.3424i	0.510377	+	1.57078i
$304$	−3.99554	−	12.2970i	−0.229160	−	0.705281i
$305$		0			0
$306$	0.107399	−	0.330541i	0.00613961	−	0.0188958i
$307$	−13.9199			−0.794452			−0.397226	−	0.917721i	$-0.630027\pi$
$307$	−13.9199			−0.794452			−0.397226	+	0.917721i	$0.630027\pi$
$308$	1.90566	−	5.86501i	0.108585	−	0.334190i
$309$	−8.52865	+	6.19642i	−0.485178	+	0.352502i
$310$		0			0
$311$	−17.1323	−	12.4473i	−0.971481	−	0.705822i	−0.0156926	−	0.999877i	$-0.504995\pi$
$311$	−17.1323	−	12.4473i	−0.971481	−	0.705822i	−0.955789	+	0.294054i	$0.904995\pi$
$312$	6.40039	−	4.65016i	0.362351	−	0.263263i
$313$	−9.62791	+	6.99509i	−0.544202	+	0.395386i	−0.825643	−	0.564193i	$-0.809188\pi$
$313$	−9.62791	+	6.99509i	−0.544202	+	0.395386i	0.281441	+	0.959578i	$0.409188\pi$
$314$	−2.66760	−	1.93813i	−0.150541	−	0.109375i
$315$		0			0
$316$	13.4590	−	9.77853i	0.757127	−	0.550085i
$317$	−4.88635	+	15.0386i	−0.274445	+	0.844653i	0.714921	+	0.699205i	$0.246463\pi$
$317$	−4.88635	+	15.0386i	−0.274445	+	0.844653i	−0.989366	+	0.145448i	$0.953537\pi$
$318$	−0.219396			−0.0123031
$319$	1.08096	−	3.32684i	0.0605219	−	0.186267i
$320$		0			0
$321$	−5.36250	−	16.5041i	−0.299305	−	0.921167i
$322$	0.0356584	+	0.109745i	0.00198716	+	0.00611586i
$323$	−7.93052	−	5.76186i	−0.441266	−	0.320598i
$324$	13.3074			0.739300
$325$		0			0
$326$	3.84293			0.212840
$327$	22.5608	+	16.3914i	1.24761	+	0.906445i
$328$	−1.25465	−	3.86141i	−0.0692763	−	0.213211i
$329$	−1.09432	−	3.36797i	−0.0603318	−	0.185682i
$330$		0			0
$331$	0.154570	−	0.475716i	0.00849591	−	0.0261477i	−0.946719	−	0.322062i	$-0.895624\pi$
$331$	0.154570	−	0.475716i	0.00849591	−	0.0261477i	0.955215	+	0.295914i	$0.0956242\pi$
$332$	23.3300			1.28040
$333$	−0.477706	+	1.47023i	−0.0261781	+	0.0805680i
$334$	0.246548	−	0.179127i	0.0134905	−	0.00980142i
$335$		0			0
$336$	4.70567	+	3.41887i	0.256715	+	0.186514i
$337$	−12.9844	+	9.43372i	−0.707305	+	0.513887i	−0.882303	−	0.470681i	$-0.844008\pi$
$337$	−12.9844	+	9.43372i	−0.707305	+	0.513887i	0.174998	+	0.984569i	$0.444008\pi$
$338$	−4.70691	+	3.41977i	−0.256022	+	0.186011i
$339$	−13.6368	−	9.90770i	−0.740648	−	0.538112i
$340$		0			0
$341$	4.90134	−	3.56103i	0.265422	−	0.192841i
$342$	0.129266	−	0.397841i	0.00698992	−	0.0215128i
$343$	−1.00000			−0.0539949
$344$	0.788581	−	2.42700i	0.0425175	−	0.130855i
$345$		0			0
$346$	−0.284144	−	0.874504i	−0.0152757	−	0.0470136i
$347$	9.18549	+	28.2700i	0.493103	+	1.51761i	0.819893	+	0.572517i	$0.194033\pi$
$347$	9.18549	+	28.2700i	0.493103	+	1.51761i	−0.326790	+	0.945097i	$0.605967\pi$
$348$	2.72531	+	1.98006i	0.146092	+	0.106142i
$349$	4.77252			0.255467			0.127734	−	0.991809i	$-0.459230\pi$
$349$	4.77252			0.255467			0.127734	+	0.991809i	$0.459230\pi$
$350$		0			0
$351$	−36.2838			−1.93669
$352$	−5.91400	−	4.29677i	−0.315217	−	0.229019i
$353$	−4.59978	−	14.1567i	−0.244821	−	0.753483i	−0.995666	−	0.0930035i	$-0.970353\pi$
$353$	−4.59978	−	14.1567i	−0.244821	−	0.753483i	0.750844	−	0.660479i	$-0.229647\pi$
$354$	1.00833	+	3.10333i	0.0535923	+	0.164940i
$355$		0			0
$356$	−10.1509	+	31.2413i	−0.537997	+	1.65578i
$357$	4.40975			0.233389
$358$	0.113152	−	0.348246i	0.00598028	−	0.0184054i
$359$	1.22879	−	0.892771i	0.0648532	−	0.0471186i	−0.554886	−	0.831926i	$-0.687238\pi$
$359$	1.22879	−	0.892771i	0.0648532	−	0.0471186i	0.619740	+	0.784808i	$0.287238\pi$
$360$		0			0
$361$	5.82611	+	4.23292i	0.306637	+	0.222785i
$362$	0.337735	−	0.245379i	0.0177510	−	0.0128968i
$363$	1.38141	−	1.00366i	0.0725055	−	0.0526783i
$364$	−10.3098	−	7.49052i	−0.540381	−	0.392610i
$365$		0			0
$366$	−2.12300	+	1.54245i	−0.110971	+	0.0806251i
$367$	−0.346453	+	1.06627i	−0.0180847	+	0.0556589i	−0.959692	−	0.281055i	$-0.909316\pi$
$367$	−0.346453	+	1.06627i	−0.0180847	+	0.0556589i	0.941607	+	0.336714i	$0.109316\pi$
$368$	−2.18411			−0.113855
$369$	−0.975442	+	3.00210i	−0.0507795	+	0.156283i
$370$		0			0
$371$	0.220620	+	0.678998i	0.0114540	+	0.0352518i
$372$	1.80290	+	5.54876i	0.0934761	+	0.287690i
$373$	−16.7488	−	12.1687i	−0.867217	−	0.630070i	0.0626214	−	0.998037i	$-0.480054\pi$
$373$	−16.7488	−	12.1687i	−0.867217	−	0.630070i	−0.929839	+	0.367967i	$0.880054\pi$
$374$	−1.78533			−0.0923174
$375$		0			0
$376$	−2.78926			−0.143845
$377$	−5.84809	−	4.24889i	−0.301192	−	0.218829i
$378$	0.343036	+	1.05576i	0.0176439	+	0.0543023i
$379$	3.43439	+	10.5700i	0.176413	+	0.542942i	0.999695	−	0.0246897i	$-0.00785978\pi$
$379$	3.43439	+	10.5700i	0.176413	+	0.542942i	−0.823283	+	0.567632i	$0.807860\pi$
$380$		0			0
$381$	5.94623	−	18.3006i	0.304635	−	0.937569i
$382$	4.18534			0.214140
$383$	−6.76503	+	20.8206i	−0.345677	+	1.06388i	0.615543	+	0.788103i	$0.288937\pi$
$383$	−6.76503	+	20.8206i	−0.345677	+	1.06388i	−0.961220	+	0.275782i	$0.911063\pi$
$384$	7.56696	−	5.49772i	0.386150	−	0.280554i
$385$		0			0
$386$	−3.60561	−	2.61963i	−0.183521	−	0.133336i
$387$	−1.60510	+	1.16617i	−0.0815917	+	0.0592798i
$388$	−15.8801	+	11.5376i	−0.806191	+	0.585732i
$389$	26.3164	+	19.1200i	1.33429	+	0.969422i	0.999633	+	0.0270833i	$0.00862194\pi$
$389$	26.3164	+	19.1200i	1.33429	+	0.969422i	0.334661	+	0.942338i	$0.391378\pi$
$390$		0			0
$391$	−1.33963	+	0.973297i	−0.0677479	+	0.0492217i
$392$	−0.243394	+	0.749089i	−0.0122932	+	0.0378347i
$393$	−3.84563			−0.193986
$394$	0.762519	−	2.34679i	0.0384151	−	0.118230i
$395$		0			0
$396$	1.16695	+	3.59149i	0.0586413	+	0.180479i
$397$	−2.57008	−	7.90989i	−0.128989	−	0.396986i	0.865618	−	0.500705i	$-0.166926\pi$
$397$	−2.57008	−	7.90989i	−0.128989	−	0.396986i	−0.994607	+	0.103719i	$0.966926\pi$
$398$	2.69789	+	1.96013i	0.135233	+	0.0982524i
$399$	5.30760			0.265712
$400$		0			0
$401$	0.343282			0.0171427			0.00857134	−	0.999963i	$-0.497272\pi$
$401$	0.343282			0.0171427			0.00857134	+	0.999963i	$0.497272\pi$
$402$	−3.79045	−	2.75392i	−0.189051	−	0.137353i
$403$	−3.86874	−	11.9068i	−0.192716	−	0.593118i
$404$	−11.2715	−	34.6902i	−0.560780	−	1.72590i
$405$		0			0
$406$	−0.0683414	+	0.210333i	−0.00339173	+	0.0104387i
$407$	7.94107			0.393624
$408$	1.07331	−	3.30330i	0.0531366	−	0.163538i
$409$	13.6719	−	9.93319i	0.676030	−	0.491165i	−0.196008	−	0.980602i	$-0.562798\pi$
$409$	13.6719	−	9.93319i	0.676030	−	0.491165i	0.872038	+	0.489438i	$0.162798\pi$
$410$		0			0
$411$	−12.6351	−	9.17997i	−0.623246	−	0.452815i
$412$	10.8206	−	7.86162i	0.533092	−	0.387314i
$413$	8.59038	−	6.24127i	0.422705	−	0.307113i
$414$	−0.0571667	−	0.0415341i	−0.00280959	−	0.00204129i
$415$		0			0
$416$	−12.2212	+	8.87919i	−0.599191	+	0.435338i
$417$	−8.78813	+	27.0471i	−0.430357	+	1.32450i
$418$	−2.14884			−0.105103
$419$	−8.47434	+	26.0813i	−0.413999	+	1.27416i	0.499145	+	0.866519i	$0.333648\pi$
$419$	−8.47434	+	26.0813i	−0.413999	+	1.27416i	−0.913143	+	0.407639i	$0.866352\pi$
$420$		0			0
$421$	3.84570	+	11.8358i	0.187428	+	0.576843i	0.999982	−	0.00604268i	$-0.00192346\pi$
$421$	3.84570	+	11.8358i	0.187428	+	0.576843i	−0.812554	+	0.582886i	$0.801923\pi$
$422$	−0.564898	−	1.73858i	−0.0274988	−	0.0846325i
$423$	1.75439	+	1.27464i	0.0853013	+	0.0619750i
$424$	0.562327			0.0273090
$425$		0			0
$426$	−3.62832			−0.175793
$427$	6.90849	+	5.01931i	0.334325	+	0.242901i
$428$	6.80359	+	20.9393i	0.328864	+	1.01214i
$429$	9.76363	+	30.0494i	0.471392	+	1.45080i
$430$		0			0
$431$	−5.58749	+	17.1965i	−0.269140	+	0.828327i	0.721571	+	0.692341i	$0.243420\pi$
$431$	−5.58749	+	17.1965i	−0.269140	+	0.828327i	−0.990711	+	0.135987i	$0.956580\pi$
$432$	−21.0114			−1.01091
$433$	−4.90270	+	15.0890i	−0.235609	+	0.725130i	0.761431	+	0.648246i	$0.224497\pi$
$433$	−4.90270	+	15.0890i	−0.235609	+	0.725130i	−0.997040	+	0.0768839i	$0.975503\pi$
$434$	−0.309878	+	0.225139i	−0.0148746	+	0.0108070i
$435$		0			0
$436$	−28.6237	−	20.7963i	−1.37083	−	0.995963i
$437$	−1.61238	+	1.17146i	−0.0771307	+	0.0560387i
$438$	−0.465093	+	0.337910i	−0.0222230	+	0.0161460i
$439$	−16.8115	−	12.2143i	−0.802370	−	0.582956i	0.109238	−	0.994016i	$-0.465159\pi$
$439$	−16.8115	−	12.2143i	−0.802370	−	0.582956i	−0.911609	+	0.411059i	$0.865159\pi$
$440$		0			0
$441$	0.495409	−	0.359936i	0.0235909	−	0.0171398i
$442$	−1.14007	+	3.50878i	−0.0542277	+	0.166896i
$443$	−17.1519			−0.814913			−0.407456	−	0.913225i	$-0.633584\pi$
$443$	−17.1519			−0.814913			−0.407456	+	0.913225i	$0.633584\pi$
$444$	−2.36317	+	7.27308i	−0.112151	+	0.345165i
$445$		0			0
$446$	1.12583	+	3.46495i	0.0533096	+	0.164070i
$447$	9.64499	+	29.6842i	0.456192	+	1.40402i
$448$	−5.71679	−	4.15349i	−0.270093	−	0.196234i
$449$	−40.9515			−1.93262			−0.966311	−	0.257378i	$-0.917141\pi$
$449$	−40.9515			−1.93262			−0.966311	+	0.257378i	$0.917141\pi$
$450$		0			0
$451$	16.2151			0.763538
$452$	17.3015	+	12.5702i	0.813792	+	0.591255i
$453$	5.66631	+	17.4391i	0.266226	+	0.819360i
$454$	1.05768	+	3.25522i	0.0496396	+	0.152775i
$455$		0			0
$456$	1.29184	−	3.97586i	0.0604958	−	0.186187i
$457$	2.15047			0.100595			0.0502974	−	0.998734i	$-0.483983\pi$
$457$	2.15047			0.100595			0.0502974	+	0.998734i	$0.483983\pi$
$458$	0.144725	−	0.445419i	0.00676257	−	0.0208131i
$459$	−12.8873	+	9.36320i	−0.601529	+	0.437037i
$460$		0			0
$461$	15.1567	+	11.0120i	0.705919	+	0.512880i	0.881855	−	0.471521i	$-0.156295\pi$
$461$	15.1567	+	11.0120i	0.705919	+	0.512880i	−0.175935	+	0.984402i	$0.556295\pi$
$462$	0.782044	−	0.568189i	0.0363840	−	0.0264345i
$463$	−7.57799	+	5.50573i	−0.352179	+	0.255873i	−0.749783	−	0.661684i	$-0.769842\pi$
$463$	−7.57799	+	5.50573i	−0.352179	+	0.255873i	0.397604	+	0.917557i	$0.369842\pi$
$464$	−3.38653	−	2.46046i	−0.157216	−	0.114224i
$465$		0			0
$466$	−0.223810	+	0.162608i	−0.0103678	+	0.00753266i
$467$	−5.31635	+	16.3621i	−0.246012	+	0.757146i	0.749457	+	0.662053i	$0.230315\pi$
$467$	−5.31635	+	16.3621i	−0.246012	+	0.757146i	−0.995468	+	0.0950926i	$0.969685\pi$
$468$	7.80368			0.360725
$469$	−4.71139	+	14.5002i	−0.217552	+	0.669555i
$470$		0			0
$471$	7.91676	+	24.3653i	0.364785	+	1.12269i
$472$	−2.58442	−	7.95404i	−0.118958	−	0.366114i
$473$	8.24521	+	5.99049i	0.379115	+	0.275443i
$474$	2.60775			0.119778
$475$		0			0
$476$	−5.59481			−0.256438
$477$	−0.353693	−	0.256973i	−0.0161945	−	0.0117660i
$478$	−0.645487	−	1.98660i	−0.0295239	−	0.0908651i
$479$	−0.493255	−	1.51808i	−0.0225374	−	0.0693630i	0.939155	−	0.343493i	$-0.111610\pi$
$479$	−0.493255	−	1.51808i	−0.0225374	−	0.0693630i	−0.961693	+	0.274130i	$0.911610\pi$
$480$		0			0
$481$	5.07098	−	15.6069i	0.231217	−	0.711612i
$482$	−2.54444			−0.115896
$483$	0.277053	−	0.852682i	0.0126064	−	0.0387984i
$484$	−1.75265	+	1.27337i	−0.0796659	+	0.0578806i
$485$		0			0
$486$	−1.00667	−	0.731390i	−0.0456635	−	0.0331765i
$487$	29.8809	−	21.7097i	1.35403	−	0.983761i	0.355231	−	0.934779i	$-0.384402\pi$
$487$	29.8809	−	21.7097i	1.35403	−	0.983761i	0.998800	−	0.0489823i	$-0.0155978\pi$
$488$	5.44139	−	3.95340i	0.246320	−	0.178962i
$489$	−24.1558	−	17.5502i	−1.09236	−	0.793648i
$490$		0			0
$491$	−11.5175	+	8.36798i	−0.519779	+	0.377642i	−0.816521	−	0.577316i	$-0.804100\pi$
$491$	−11.5175	+	8.36798i	−0.519779	+	0.377642i	0.296742	+	0.954958i	$0.404100\pi$
$492$	−4.82541	+	14.8511i	−0.217546	+	0.669539i
$493$	−3.17358			−0.142931
$494$	−1.37220	+	4.22319i	−0.0617381	+	0.190010i
$495$		0			0
$496$	−2.24033	−	6.89502i	−0.100594	−	0.309595i
$497$	3.64856	+	11.2291i	0.163660	+	0.503694i
$498$	2.95859	+	2.14954i	0.132577	+	0.0963232i
$499$	8.62876			0.386276			0.193138	−	0.981172i	$-0.438133\pi$
$499$	8.62876			0.386276			0.193138	+	0.981172i	$0.438133\pi$
$500$		0			0
$501$	−2.36780			−0.105786
$502$	2.04379	+	1.48490i	0.0912190	+	0.0662745i
$503$	−1.73953	−	5.35372i	−0.0775618	−	0.238711i	0.904757	−	0.425929i	$-0.140053\pi$
$503$	−1.73953	−	5.35372i	−0.0775618	−	0.238711i	−0.982318	+	0.187219i	$0.940053\pi$
$504$	−0.149044	−	0.458712i	−0.00663897	−	0.0204326i
$505$		0			0
$506$	−0.112168	+	0.345217i	−0.00498647	+	0.0153468i
$507$	45.2044			2.00760
$508$	−7.54419	+	23.2186i	−0.334719	+	1.03016i
$509$	−13.1848	+	9.57934i	−0.584407	+	0.424597i	−0.840310	−	0.542106i	$-0.817627\pi$
$509$	−13.1848	+	9.57934i	−0.584407	+	0.424597i	0.255903	+	0.966702i	$0.417627\pi$
$510$		0			0
$511$	1.51347	+	1.09960i	0.0669519	+	0.0486434i
$512$	−11.8743	+	8.62721i	−0.524776	+	0.381272i
$513$	−15.5113	+	11.2696i	−0.684839	+	0.497565i
$514$	−3.25198	−	2.36270i	−0.143439	−	0.104214i
$515$		0			0
$516$	−7.94026	+	5.76894i	−0.349550	+	0.253963i
$517$	3.44232	−	10.5944i	0.151393	−	0.465939i
$518$	−0.502059			−0.0220592
$519$	−2.20770	+	6.79460i	−0.0969072	+	0.298250i
$520$		0			0
$521$	0.0730238	+	0.224744i	0.00319923	+	0.00984623i	0.952643	−	0.304090i	$-0.0983523\pi$
$521$	0.0730238	+	0.224744i	0.00319923	+	0.00984623i	−0.949444	+	0.313936i	$0.898352\pi$
$522$	−0.0418495	−	0.128800i	−0.00183170	−	0.00563740i
$523$	6.20767	+	4.51014i	0.271443	+	0.197215i	0.715176	−	0.698944i	$-0.246346\pi$
$523$	6.20767	+	4.51014i	0.271443	+	0.197215i	−0.443734	+	0.896159i	$0.646346\pi$
$524$	4.87909			0.213144
$525$		0			0
$526$	−0.318522			−0.0138882
$527$	−4.44670	−	3.23071i	−0.193701	−	0.140732i
$528$	5.65396	+	17.4011i	0.246057	+	0.757285i
$529$	−7.00336	−	21.5541i	−0.304494	−	0.937135i
$530$		0			0
$531$	−2.00929	+	6.18397i	−0.0871959	+	0.268361i
$532$	−6.73394			−0.291953
$533$	10.3546	−	31.8681i	0.448507	−	1.38036i
$534$	−4.16573	+	3.02658i	−0.180269	+	0.130973i
$535$		0			0
$536$	9.71518	+	7.05849i	0.419632	+	0.304880i
$537$	−2.30165	+	1.67225i	−0.0993237	+	0.0721629i
$538$	−3.16933	+	2.30265i	−0.136639	+	0.0992744i
$539$	−2.54486	−	1.84895i	−0.109615	−	0.0796400i
$540$		0			0
$541$	−1.06900	+	0.776676i	−0.0459600	+	0.0333919i	−0.610528	−	0.791995i	$-0.709043\pi$
$541$	−1.06900	+	0.776676i	−0.0459600	+	0.0333919i	0.564568	+	0.825387i	$0.309043\pi$
$542$	−1.63856	+	5.04298i	−0.0703823	+	0.216614i
$543$	−3.24355			−0.139194
$544$	−2.04941	+	6.30744i	−0.0878678	+	0.270429i
$545$		0			0
$546$	−0.617287	−	1.89981i	−0.0264174	−	0.0813045i
$547$	10.6660	+	32.8266i	0.456046	+	1.40357i	0.869903	+	0.493224i	$0.164182\pi$
$547$	10.6660	+	32.8266i	0.456046	+	1.40357i	−0.413856	+	0.910342i	$0.635818\pi$
$548$	16.0307	+	11.6469i	0.684795	+	0.497533i
$549$	−5.22916			−0.223175
$550$		0			0
$551$	−3.81973			−0.162726
$552$	−0.571302	−	0.415075i	−0.0243162	−	0.0176668i
$553$	−2.62230	−	8.07060i	−0.111511	−	0.343197i
$554$	0.208838	+	0.642738i	0.00887269	+	0.0273073i
$555$		0			0
$556$	11.1498	−	34.3156i	0.472857	−	1.45530i
$557$	−39.5507			−1.67582			−0.837909	−	0.545810i	$-0.816222\pi$
$557$	−39.5507			−1.67582			−0.837909	+	0.545810i	$0.816222\pi$
$558$	0.0724805	−	0.223072i	0.00306835	−	0.00944340i
$559$	17.0385	−	12.3792i	0.720654	−	0.523585i
$560$		0			0
$561$	11.2222	+	8.15342i	0.473803	+	0.344238i
$562$	5.33143	−	3.87351i	0.224893	−	0.163394i
$563$	3.94887	−	2.86902i	0.166425	−	0.120915i	−0.501455	−	0.865184i	$-0.667202\pi$
$563$	3.94887	−	2.86902i	0.166425	−	0.120915i	0.667880	+	0.744269i	$0.267202\pi$
$564$	8.67879	+	6.30551i	0.365443	+	0.265510i
$565$		0			0
$566$	1.41969	−	1.03147i	0.0596740	−	0.0433557i
$567$	2.09759	−	6.45571i	0.0880904	−	0.271114i
$568$	9.29963			0.390204
$569$	−3.15196	+	9.70074i	−0.132137	+	0.406676i	−0.995134	−	0.0985334i	$-0.968585\pi$
$569$	−3.15196	+	9.70074i	−0.132137	+	0.406676i	0.862997	+	0.505210i	$0.168585\pi$
$570$		0			0
$571$	3.82386	+	11.7686i	0.160024	+	0.492502i	0.998635	−	0.0522276i	$-0.0166321\pi$
$571$	3.82386	+	11.7686i	0.160024	+	0.492502i	−0.838611	+	0.544730i	$0.816632\pi$
$572$	−12.3875	−	38.1247i	−0.517946	−	1.59407i
$573$	−26.3081	−	19.1140i	−1.09904	−	0.798498i
$574$	−1.02517			−0.0427897
$575$		0			0
$576$	4.32714			0.180298
$577$	−20.4264	−	14.8406i	−0.850362	−	0.617824i	0.0748839	−	0.997192i	$-0.476141\pi$
$577$	−20.4264	−	14.8406i	−0.850362	−	0.617824i	−0.925246	+	0.379368i	$0.876141\pi$
$578$	−0.544229	−	1.67497i	−0.0226370	−	0.0696694i
$579$	10.7005	+	32.9329i	0.444699	+	1.36864i
$580$		0			0
$581$	3.67741	−	11.3179i	0.152565	−	0.469546i
$582$	−3.07686			−0.127540
$583$	−0.693987	+	2.13587i	−0.0287420	+	0.0884587i
$584$	1.19207	−	0.866086i	0.0493280	−	0.0358389i
$585$		0			0
$586$	−2.57761	−	1.87274i	−0.106480	−	0.0773623i
$587$	20.5017	−	14.8953i	0.846194	−	0.614796i	−0.0778996	−	0.996961i	$-0.524821\pi$
$587$	20.5017	−	14.8953i	0.846194	−	0.614796i	0.924094	+	0.382165i	$0.124821\pi$
$588$	2.45074	−	1.78057i	0.101067	−	0.0734294i
$589$	−5.35207	−	3.88850i	−0.220528	−	0.160223i
$590$		0			0
$591$	−15.5106	+	11.2691i	−0.638019	+	0.463548i
$592$	2.93652	−	9.03769i	0.120690	−	0.371447i
$593$	−22.4503			−0.921924			−0.460962	−	0.887420i	$-0.652495\pi$
$593$	−22.4503			−0.921924			−0.460962	+	0.887420i	$0.652495\pi$
$594$	−1.07906	+	3.32102i	−0.0442745	+	0.136263i
$595$		0			0
$596$	−12.2369	−	37.6614i	−0.501244	−	1.54267i
$597$	−8.00664	−	24.6419i	−0.327690	−	1.00853i
$598$	0.606840	+	0.440895i	0.0248155	+	0.0180295i
$599$	−19.6210			−0.801691			−0.400845	−	0.916146i	$-0.631284\pi$
$599$	−19.6210			−0.801691			−0.400845	+	0.916146i	$0.631284\pi$
$600$		0			0
$601$	−10.6423			−0.434109			−0.217055	−	0.976159i	$-0.569645\pi$
$601$	−10.6423			−0.434109			−0.217055	+	0.976159i	$0.569645\pi$
$602$	−0.521288	−	0.378738i	−0.0212461	−	0.0154362i
$603$	−2.88506	−	8.87931i	−0.117489	−	0.361593i
$604$	−7.18904	−	22.1256i	−0.292518	−	0.900278i
$605$		0			0
$606$	1.76683	−	5.43774i	0.0717726	−	0.220893i
$607$	0.0394412			0.00160087			0.000800435	−	1.00000i	$-0.499745\pi$
$607$	0.0394412			0.00160087			0.000800435		1.00000i	$0.499745\pi$
$608$	−2.46668	+	7.59167i	−0.100037	+	0.307883i
$609$	1.39015	−	1.01000i	0.0563316	−	0.0409273i
$610$		0			0
$611$	−18.6233	−	13.5306i	−0.753418	−	0.547390i
$612$	2.77172	−	2.01377i	0.112040	−	0.0814020i
$613$	10.9840	−	7.98031i	0.443638	−	0.322322i	−0.343441	−	0.939174i	$-0.611593\pi$
$613$	10.9840	−	7.98031i	0.443638	−	0.322322i	0.787079	+	0.616853i	$0.211593\pi$
$614$	2.23963	+	1.62719i	0.0903843	+	0.0656680i
$615$		0			0
$616$	−2.00443	+	1.45631i	−0.0807609	+	0.0586762i
$617$	13.2111	−	40.6595i	0.531858	−	1.63689i	−0.218484	−	0.975840i	$-0.570111\pi$
$617$	13.2111	−	40.6595i	0.531858	−	1.63689i	0.750342	−	0.661050i	$-0.229889\pi$
$618$	2.09655			0.0843356
$619$	−0.536195	+	1.65024i	−0.0215515	+	0.0663287i	−0.961254	−	0.275665i	$-0.911102\pi$
$619$	−0.536195	+	1.65024i	−0.0215515	+	0.0663287i	0.939702	+	0.341993i	$0.111102\pi$
$620$		0			0
$621$	1.00082	+	3.08020i	0.0401614	+	0.123604i
$622$	1.30143	+	4.00540i	0.0521827	+	0.160602i
$623$	13.5558	+	9.84885i	0.543101	+	0.394586i
$624$	37.8095			1.51359
$625$		0			0
$626$	2.36678			0.0945954
$627$	13.5071	+	9.81350i	0.539423	+	0.391913i
$628$	−10.0443	−	30.9131i	−0.400810	−	1.23357i
$629$	−2.22630	−	6.85186i	−0.0887685	−	0.273201i
$630$		0			0
$631$	3.77123	−	11.6066i	0.150130	−	0.462053i	−0.847505	−	0.530788i	$-0.821896\pi$
$631$	3.77123	−	11.6066i	0.150130	−	0.462053i	0.997635	+	0.0687345i	$0.0218961\pi$
$632$	−6.68384			−0.265869
$633$	−4.38906	+	13.5081i	−0.174450	+	0.536900i
$634$	2.54415	−	1.84843i	0.101041	−	0.0734105i
$635$		0			0
$636$	−1.74968	−	1.27122i	−0.0693795	−	0.0504071i
$637$	−5.25890	+	3.82082i	−0.208365	+	0.151386i
$638$	−0.562815	+	0.408909i	−0.0222821	+	0.0161889i
$639$	−5.84929	−	4.24976i	−0.231394	−	0.168118i
$640$		0			0
$641$	5.04063	−	3.66223i	0.199093	−	0.144650i	−0.483772	−	0.875194i	$-0.660734\pi$
$641$	5.04063	−	3.66223i	0.199093	−	0.144650i	0.682865	+	0.730544i	$0.260734\pi$
$642$	−1.06647	+	3.28226i	−0.0420903	+	0.129541i
$643$	−11.8383			−0.466857			−0.233429	−	0.972374i	$-0.574995\pi$
$643$	−11.8383			−0.466857			−0.233429	+	0.972374i	$0.574995\pi$
$644$	−0.351507	+	1.08183i	−0.0138513	+	0.0426300i
$645$		0			0
$646$	0.602433	+	1.85410i	0.0237024	+	0.0729485i
$647$	−1.25127	−	3.85100i	−0.0491923	−	0.151398i	0.923443	−	0.383736i	$-0.125363\pi$
$647$	−1.25127	−	3.85100i	−0.0491923	−	0.151398i	−0.972635	+	0.232337i	$0.925363\pi$
$648$	−4.32536	−	3.14256i	−0.169916	−	0.123451i
$649$	33.4011			1.31111
$650$		0			0
$651$	2.97601			0.116639
$652$	30.6473	+	22.2666i	1.20024	+	0.872027i
$653$	−6.61410	−	20.3561i	−0.258830	−	0.796596i	−0.993051	−	0.117685i	$-0.962453\pi$
$653$	−6.61410	−	20.3561i	−0.258830	−	0.796596i	0.734221	−	0.678910i	$-0.237547\pi$
$654$	−1.71381	−	5.27455i	−0.0670151	−	0.206251i
$655$		0			0
$656$	5.99617	−	18.4543i	0.234111	−	0.720520i
$657$	−1.14557			−0.0446930
$658$	−0.217634	+	0.669808i	−0.00848425	+	0.0261118i
$659$	−12.3162	+	8.94823i	−0.479770	+	0.348573i	−0.801237	−	0.598348i	$-0.795824\pi$
$659$	−12.3162	+	8.94823i	−0.479770	+	0.348573i	0.321467	+	0.946921i	$0.395824\pi$
$660$		0			0
$661$	10.1057	+	7.34222i	0.393066	+	0.285579i	0.766711	−	0.641993i	$-0.221892\pi$
$661$	10.1057	+	7.34222i	0.393066	+	0.285579i	−0.373645	+	0.927572i	$0.621892\pi$
$662$	−0.0804788	+	0.0584713i	−0.00312790	+	0.00227255i
$663$	23.1905	−	16.8489i	0.900644	−	0.654356i
$664$	−7.58306	−	5.50941i	−0.294280	−	0.213807i
$665$		0			0
$666$	0.248725	−	0.180709i	0.00963788	−	0.00700233i
$667$	−0.199387	+	0.613651i	−0.00772031	+	0.0237607i
$668$	3.00411			0.116233
$669$	8.74731	−	26.9215i	0.338191	−	1.04084i
$670$		0			0
$671$	8.30070	+	25.5469i	0.320445	+	0.986228i
$672$	−1.10964	−	3.41513i	−0.0428054	−	0.131742i
$673$	13.2376	+	9.61769i	0.510273	+	0.370735i	0.812927	−	0.582366i	$-0.197873\pi$
$673$	13.2376	+	9.61769i	0.510273	+	0.370735i	−0.302654	+	0.953100i	$0.597873\pi$
$674$	3.19188			0.122947
$675$		0			0
$676$	−57.3524			−2.20586
$677$	18.0175	+	13.0905i	0.692470	+	0.503109i	0.877471	−	0.479630i	$-0.159229\pi$
$677$	18.0175	+	13.0905i	0.692470	+	0.503109i	−0.185001	+	0.982738i	$0.559229\pi$
$678$	1.03590	+	3.18818i	0.0397836	+	0.122441i
$679$	3.09402	+	9.52242i	0.118738	+	0.365437i
$680$		0			0
$681$	8.21785	−	25.2919i	0.314909	−	0.969189i
$682$	−1.20487			−0.0461368
$683$	3.12674	−	9.62312i	0.119641	−	0.368219i	−0.873245	−	0.487281i	$-0.837989\pi$
$683$	3.12674	−	9.62312i	0.119641	−	0.368219i	0.992887	+	0.119062i	$0.0379888\pi$
$684$	3.33606	−	2.42379i	0.127557	−	0.0926759i
$685$		0			0
$686$	0.160894	+	0.116896i	0.00614297	+	0.00446313i
$687$	−2.94389	+	2.13886i	−0.112316	+	0.0816027i
$688$	9.86674	−	7.16861i	0.376166	−	0.273301i
$689$	3.75454	+	2.72784i	0.143037	+	0.103922i
$690$		0			0
$691$	−10.9145	+	7.92983i	−0.415206	+	0.301665i	−0.775706	−	0.631094i	$-0.782606\pi$
$691$	−10.9145	+	7.92983i	−0.415206	+	0.301665i	0.360500	+	0.932759i	$0.382606\pi$
$692$	2.80099	−	8.62055i	0.106477	−	0.327704i
$693$	1.92625			0.0731723
$694$	1.82677	−	5.62223i	0.0693434	−	0.213417i
$695$		0			0
$696$	−0.418227	−	1.28717i	−0.0158529	−	0.0487901i
$697$	−4.54595	−	13.9910i	−0.172190	−	0.529947i
$698$	−0.767870	−	0.557890i	−0.0290643	−	0.0211165i
$699$	2.14944			0.0812991
$700$		0			0
$701$	12.7883			0.483007			0.241503	−	0.970400i	$-0.422360\pi$
$701$	12.7883			0.483007			0.241503	+	0.970400i	$0.422360\pi$
$702$	5.83785	+	4.24145i	0.220336	+	0.160083i
$703$	−2.67959	−	8.24693i	−0.101063	−	0.311039i
$704$	−6.86885	−	21.1401i	−0.258879	−	0.796749i
$705$		0			0
$706$	−0.914785	+	2.81542i	−0.0344284	+	0.105960i
$707$	−18.6057			−0.699739
$708$	−9.93978	+	30.5915i	−0.373560	+	1.14970i
$709$	20.2329	−	14.7001i	0.759864	−	0.552073i	−0.139005	−	0.990292i	$-0.544390\pi$
$709$	20.2329	−	14.7001i	0.759864	−	0.552073i	0.898868	+	0.438218i	$0.144390\pi$
$710$		0			0
$711$	4.20401	+	3.05439i	0.157663	+	0.114549i
$712$	10.6771	−	7.75733i	0.400140	−	0.290718i
$713$	−0.904074	+	0.656848i	−0.0338578	+	0.0245992i
$714$	−0.709504	−	0.515485i	−0.0265525	−	0.0192915i
$715$		0			0
$716$	2.92019	−	2.12164i	0.109133	−	0.0792895i
$717$	−5.01521	+	15.4352i	−0.187297	+	0.576439i
$718$	−0.302067			−0.0112731
$719$	2.24894	−	6.92151i	0.0838712	−	0.258129i	−0.900323	−	0.435223i	$-0.856670\pi$
$719$	2.24894	−	6.92151i	0.0838712	−	0.258129i	0.984194	+	0.177094i	$0.0566696\pi$
$720$		0			0
$721$	−2.10824	−	6.48850i	−0.0785150	−	0.241644i
$722$	−0.442574	−	1.36210i	−0.0164709	−	0.0506922i
$723$	15.9938	+	11.6202i	0.594815	+	0.432158i
$724$	4.11520			0.152940
$725$		0			0
$726$	−0.339585			−0.0126032
$727$	18.8077	+	13.6646i	0.697540	+	0.506792i	0.879130	−	0.476582i	$-0.158124\pi$
$727$	18.8077	+	13.6646i	0.697540	+	0.506792i	−0.181590	+	0.983374i	$0.558124\pi$
$728$	1.58215	+	4.86935i	0.0586383	+	0.180470i
$729$	9.28031	+	28.5618i	0.343715	+	1.05785i
$730$		0			0
$731$	2.85726	−	8.79374i	0.105680	−	0.325248i
$732$	−25.8681			−0.956114
$733$	10.8631	−	33.4330i	0.401236	−	1.23488i	−0.522761	−	0.852479i	$-0.675098\pi$
$733$	10.8631	−	33.4330i	0.401236	−	1.23488i	0.923997	−	0.382399i	$-0.124902\pi$
$734$	0.180386	−	0.131058i	0.00665815	−	0.00483743i
$735$		0			0
$736$	1.09086	+	0.792560i	0.0402098	+	0.0292141i
$737$	−38.7999	+	28.1898i	−1.42921	+	1.03838i
$738$	0.507878	−	0.368995i	0.0186952	−	0.0135829i
$739$	−14.1676	−	10.2934i	−0.521164	−	0.378648i	0.295878	−	0.955226i	$-0.404388\pi$
$739$	−14.1676	−	10.2934i	−0.521164	−	0.378648i	−0.817042	+	0.576578i	$0.804388\pi$
$740$		0			0
$741$	27.9122	−	20.2794i	1.02538	−	0.744982i
$742$	0.0438760	−	0.135036i	0.00161074	−	0.00495734i
$743$	−12.5993			−0.462223			−0.231111	−	0.972927i	$-0.574236\pi$
$743$	−12.5993			−0.462223			−0.231111	+	0.972927i	$0.574236\pi$
$744$	0.724342	−	2.22930i	0.0265557	−	0.0817299i
$745$		0			0
$746$	1.27230	+	3.91574i	0.0465822	+	0.143365i
$747$	2.25190	+	6.93063i	0.0823927	+	0.253579i
$748$	−14.2380	−	10.3445i	−0.520594	−	0.378234i
$749$	11.2305			0.410355
$750$		0			0
$751$	9.86802			0.360089			0.180045	−	0.983658i	$-0.442376\pi$
$751$	9.86802			0.360089			0.180045	+	0.983658i	$0.442376\pi$
$752$	−10.7845	−	7.83536i	−0.393269	−	0.285726i
$753$	−6.06546	−	18.6676i	−0.221038	−	0.680284i
$754$	0.444244	+	1.36724i	0.0161784	+	0.0497920i
$755$		0			0
$756$	−3.38153	+	10.4073i	−0.122985	+	0.378509i
$757$	−37.0730			−1.34744			−0.673721	−	0.738986i	$-0.735305\pi$
$757$	−37.0730			−1.34744			−0.673721	+	0.738986i	$0.735305\pi$
$758$	0.683017	−	2.10211i	0.0248083	−	0.0763521i
$759$	2.28163	−	1.65770i	0.0828180	−	0.0601708i
$760$		0			0
$761$	23.8906	+	17.3575i	0.866032	+	0.629209i	0.929519	−	0.368774i	$-0.120222\pi$
$761$	23.8906	+	17.3575i	0.866032	+	0.629209i	−0.0634873	+	0.997983i	$0.520222\pi$
$762$	−3.09599	+	2.24937i	−0.112156	+	0.0814860i
$763$	−14.6006	+	10.6079i	−0.528576	+	0.384033i
$764$	33.3781	+	24.2506i	1.20758	+	0.877355i
$765$		0			0
$766$	3.52231	−	2.55911i	0.127266	−	0.0924644i
$767$	21.3292	−	65.6445i	0.770153	−	2.37029i
$768$	19.9777			0.720882
$769$	−7.81095	+	24.0396i	−0.281670	+	0.866891i	0.705707	+	0.708504i	$0.250629\pi$
$769$	−7.81095	+	24.0396i	−0.281670	+	0.866891i	−0.987377	+	0.158387i	$0.949371\pi$
$770$		0			0
$771$	9.65105	+	29.7029i	0.347574	+	1.06972i
$772$	−13.5762	−	41.7831i	−0.488617	−	1.50381i
$773$	−3.46722	−	2.51909i	−0.124707	−	0.0906052i	0.523683	−	0.851913i	$-0.324558\pi$
$773$	−3.46722	−	2.51909i	−0.124707	−	0.0906052i	−0.648391	+	0.761308i	$0.724558\pi$
$774$	0.394572			0.0141826
$775$		0			0
$776$	7.88620			0.283098
$777$	3.15583	+	2.29285i	0.113215	+	0.0822554i
$778$	−1.99910	−	6.15259i	−0.0716711	−	0.220581i
$779$	−5.47153	−	16.8396i	−0.196038	−	0.603343i
$780$		0			0
$781$	−11.4770	+	35.3226i	−0.410679	+	1.26394i
$782$	0.329313			0.0117762
$783$	−1.91812	+	5.90338i	−0.0685482	+	0.210970i
$784$	−3.04535	+	2.21257i	−0.108762	+	0.0790205i
$785$		0			0
$786$	0.618739	+	0.449540i	0.0220697	+	0.0160346i
$787$	−37.0174	+	26.8947i	−1.31953	+	0.958693i	−0.319590	+	0.947556i	$0.603545\pi$
$787$	−37.0174	+	26.8947i	−1.31953	+	0.958693i	−0.999938	+	0.0111376i	$0.996455\pi$
$788$	19.6788	−	14.2975i	0.701028	−	0.509327i
$789$	2.00216	+	1.45466i	0.0712789	+	0.0517872i
$790$		0			0
$791$	8.82526	−	6.41192i	0.313790	−	0.227982i
$792$	0.468838	−	1.44293i	0.0166594	−	0.0512724i
$793$	55.5089			1.97118
$794$	−0.511127	+	1.57309i	−0.0181392	+	0.0558268i
$795$		0			0
$796$	10.1583	+	31.2641i	0.360052	+	1.10813i
$797$	8.24078	+	25.3625i	0.291903	+	0.898386i	0.984244	+	0.176816i	$0.0565796\pi$
$797$	8.24078	+	25.3625i	0.291903	+	0.898386i	−0.692341	+	0.721571i	$0.743420\pi$
$798$	−0.853962	−	0.620440i	−0.0302299	−	0.0219633i
$799$	−10.1063			−0.357535
$800$		0			0
$801$	−10.2606			−0.362541
$802$	−0.0552320	−	0.0401284i	−0.00195031	−	0.00141698i
$803$	1.81846	+	5.59666i	0.0641722	+	0.197502i
$804$	−14.2721	−	43.9251i	−0.503339	−	1.54912i
$805$		0			0
$806$	−0.769400	+	2.36797i	−0.0271010	+	0.0834082i
$807$	30.4377			1.07146
$808$	−4.52850	+	13.9373i	−0.159312	+	0.490313i
$809$	7.26466	−	5.27808i	0.255412	−	0.185568i	−0.452710	−	0.891658i	$-0.649543\pi$
$809$	7.26466	−	5.27808i	0.255412	−	0.185568i	0.708122	+	0.706090i	$0.249543\pi$
$810$		0			0
$811$	25.2348	+	18.3341i	0.886113	+	0.643799i	0.934862	−	0.355012i	$-0.115523\pi$
$811$	25.2348	+	18.3341i	0.886113	+	0.643799i	−0.0487484	+	0.998811i	$0.515523\pi$
$812$	−1.76373	+	1.28142i	−0.0618948	+	0.0449692i
$813$	33.3304	−	24.2159i	1.16895	−	0.849290i
$814$	−1.27767	−	0.928282i	−0.0447823	−	0.0325363i
$815$		0			0
$816$	13.4292	−	9.75690i	0.470117	−	0.341560i
$817$	3.43901	−	10.5842i	0.120316	−	0.370294i
$818$	−3.36088			−0.117510
$819$	1.23006	−	3.78574i	0.0429818	−	0.132284i
$820$		0			0
$821$	6.28513	+	19.3437i	0.219353	+	0.675098i	0.998816	+	0.0486501i	$0.0154919\pi$
$821$	6.28513	+	19.3437i	0.219353	+	0.675098i	−0.779463	+	0.626448i	$0.784508\pi$
$822$	0.959815	+	2.95401i	0.0334774	+	0.103033i
$823$	11.3083	+	8.21599i	0.394184	+	0.286391i	0.767168	−	0.641446i	$-0.221665\pi$
$823$	11.3083	+	8.21599i	0.394184	+	0.286391i	−0.372984	+	0.927838i	$0.621665\pi$
$824$	−5.37359			−0.187198
$825$		0			0
$826$	−2.11172			−0.0734762
$827$	−27.6754	−	20.1073i	−0.962367	−	0.699200i	−0.00866736	−	0.999962i	$-0.502759\pi$
$827$	−27.6754	−	20.1073i	−0.962367	−	0.699200i	−0.953699	+	0.300762i	$0.902759\pi$
$828$	−0.215249	−	0.662468i	−0.00748041	−	0.0230223i
$829$	13.7578	+	42.3423i	0.477829	+	1.47061i	0.842103	+	0.539316i	$0.181317\pi$
$829$	13.7578	+	42.3423i	0.477829	+	1.47061i	−0.364274	+	0.931292i	$0.618683\pi$
$830$		0			0
$831$	1.62260	−	4.99385i	0.0562874	−	0.173235i
$832$	−45.9338			−1.59247
$833$	−0.881886	+	2.71417i	−0.0305555	+	0.0940403i
$834$	4.57567	−	3.32442i	0.158442	−	0.115115i
$835$		0			0
$836$	−17.1370	−	12.4507i	−0.592694	−	0.430618i
$837$	−8.69727	+	6.31894i	−0.300622	+	0.218414i
$838$	4.41229	−	3.20572i	0.152420	−	0.110740i
$839$	28.4507	+	20.6706i	0.982227	+	0.713630i	0.958205	−	0.286082i	$-0.0923529\pi$
$839$	28.4507	+	20.6706i	0.982227	+	0.713630i	0.0240218	+	0.999711i	$0.492353\pi$
$840$		0			0
$841$	22.4610	−	16.3189i	0.774519	−	0.562721i
$842$	0.764817	−	2.35386i	0.0263573	−	0.0811195i
$843$	−51.2021			−1.76349
$844$	5.56856	−	17.1383i	0.191678	−	0.589923i
$845$		0			0
$846$	−0.133270	−	0.410163i	−0.00458192	−	0.0141017i
$847$	0.341479	+	1.05096i	0.0117334	+	0.0361116i
$848$	2.17420	+	1.57965i	0.0746622	+	0.0542452i
$849$	−13.6345			−0.467933
$850$		0			0
$851$	−1.46477			−0.0502116
$852$	−28.9359	−	21.0231i	−0.991327	−	0.720241i
$853$	5.60038	+	17.2362i	0.191753	+	0.590156i	0.999999	+	0.00131102i	$0.000417310\pi$
$853$	5.60038	+	17.2362i	0.191753	+	0.590156i	−0.808246	+	0.588845i	$0.799583\pi$
$854$	−0.524796	−	1.61515i	−0.0179581	−	0.0552695i
$855$		0			0
$856$	2.73344	−	8.41266i	0.0934271	−	0.287539i
$857$	34.1832			1.16767			0.583837	−	0.811871i	$-0.301551\pi$
$857$	34.1832			1.16767			0.583837	+	0.811871i	$0.301551\pi$
$858$	1.94175	−	5.97610i	0.0662903	−	0.204021i
$859$	16.6058	−	12.0648i	0.566584	−	0.411647i	−0.267279	−	0.963619i	$-0.586125\pi$
$859$	16.6058	−	12.0648i	0.566584	−	0.411647i	0.833863	+	0.551972i	$0.186125\pi$
$860$		0			0
$861$	6.44398	+	4.68183i	0.219610	+	0.159556i
$862$	2.90921	−	2.11366i	0.0990880	−	0.0719916i
$863$	23.7550	−	17.2590i	0.808630	−	0.587504i	−0.104803	−	0.994493i	$-0.533421\pi$
$863$	23.7550	−	17.2590i	0.808630	−	0.587504i	0.913433	+	0.406989i	$0.133421\pi$
$864$	10.4942	+	7.62449i	0.357020	+	0.259391i
$865$		0			0
$866$	2.55266	−	1.85462i	0.0867430	−	0.0630225i
$867$	−4.22848	+	13.0139i	−0.143607	+	0.441976i
$868$	−3.77577			−0.128158
$869$	8.24876	−	25.3871i	0.279820	−	0.861197i
$870$		0			0
$871$	30.6257	+	94.2563i	1.03771	+	3.19375i
$872$	4.39260	+	13.5190i	0.148752	+	0.457812i
$873$	−4.96027	−	3.60385i	−0.167880	−	0.121972i
$874$	0.396363			0.0134072
$875$		0			0
$876$	−5.66703			−0.191471
$877$	23.4416	+	17.0313i	0.791568	+	0.575108i	0.908428	−	0.418041i	$-0.137283\pi$
$877$	23.4416	+	17.0313i	0.791568	+	0.575108i	−0.116861	+	0.993148i	$0.537283\pi$
$878$	1.27707	+	3.93041i	0.0430990	+	0.132645i
$879$	7.64969	+	23.5433i	0.258017	+	0.794096i
$880$		0			0
$881$	15.8830	−	48.8829i	0.535112	−	1.64691i	−0.208294	−	0.978066i	$-0.566791\pi$
$881$	15.8830	−	48.8829i	0.535112	−	1.64691i	0.743407	−	0.668840i	$-0.233209\pi$
$882$	−0.121784			−0.00410067
$883$	−7.65007	+	23.5445i	−0.257445	+	0.792335i	0.735893	+	0.677098i	$0.236763\pi$
$883$	−7.65007	+	23.5445i	−0.257445	+	0.792335i	−0.993338	+	0.115237i	$0.963237\pi$
$884$	−29.4226	+	21.3768i	−0.989588	+	0.718978i
$885$		0			0
$886$	2.75965	+	2.00500i	0.0927121	+	0.0673593i
$887$	−20.3908	+	14.8148i	−0.684658	+	0.497433i	−0.874900	−	0.484304i	$-0.839073\pi$
$887$	−20.3908	+	14.8148i	−0.684658	+	0.497433i	0.190242	+	0.981737i	$0.439073\pi$
$888$	2.48566	−	1.80593i	0.0834131	−	0.0606032i
$889$	10.0747	+	7.31970i	0.337895	+	0.245495i
$890$		0			0
$891$	17.2744	−	12.5506i	0.578713	−	0.420460i
$892$	−11.0980	+	34.1562i	−0.371589	+	1.14363i
$893$	−12.1640			−0.407052
$894$	1.91816	−	5.90348i	0.0641528	−	0.197442i
$895$		0			0
$896$	1.87052	+	5.75686i	0.0624896	+	0.192323i
$897$	−1.80095	−	5.54274i	−0.0601319	−	0.185067i
$898$	6.58886	+	4.78709i	0.219873	+	0.159747i
$899$	−2.14175			−0.0714314
$900$		0			0
$901$	2.03747			0.0678781
$902$	−2.60891	−	1.89549i	−0.0868673	−	0.0631128i
$903$	1.54705	+	4.76133i	0.0514826	+	0.158447i
$904$	−2.65509	−	8.17152i	−0.0883069	−	0.271781i
$905$		0			0
$906$	1.12689	−	3.46822i	0.0374385	−	0.115224i
$907$	9.04710			0.300404			0.150202	−	0.988655i	$-0.452008\pi$
$907$	9.04710			0.300404			0.150202	+	0.988655i	$0.452008\pi$
$908$	−10.4263	+	32.0888i	−0.346008	+	1.06490i
$909$	9.21743	−	6.69685i	0.305723	−	0.222121i
$910$		0			0
$911$	4.94024	+	3.58929i	0.163677	+	0.118919i	0.666609	−	0.745408i	$-0.267745\pi$
$911$	4.94024	+	3.58929i	0.163677	+	0.118919i	−0.502931	+	0.864326i	$0.667745\pi$
$912$	16.1635	−	11.7435i	0.535226	−	0.388865i
$913$	30.2848	−	22.0032i	1.00228	−	0.728199i
$914$	−0.345998	−	0.251382i	−0.0114446	−	0.00831498i
$915$		0			0
$916$	3.73502	−	2.71365i	0.123409	−	0.0896615i
$917$	0.769069	−	2.36695i	0.0253969	−	0.0781636i
$918$	3.16802			0.104560
$919$	−0.955985	+	2.94222i	−0.0315350	+	0.0970548i	−0.965585	−	0.260087i	$-0.916249\pi$
$919$	−0.955985	+	2.94222i	−0.0315350	+	0.0970548i	0.934050	+	0.357142i	$0.116249\pi$
$920$		0			0
$921$	−6.64666	−	20.4563i	−0.219015	−	0.674059i
$922$	−1.15136	−	3.54353i	−0.0379182	−	0.116700i
$923$	62.0918	+	45.1123i	2.04378	+	1.48489i
$924$	9.52899			0.313481
$925$		0			0
$926$	1.86285			0.0612172
$927$	3.37989	+	2.45563i	0.111010	+	0.0806535i
$928$	0.798579	+	2.45777i	0.0262147	+	0.0806804i
$929$	−2.76439	−	8.50791i	−0.0906966	−	0.279135i	0.895412	−	0.445239i	$-0.146881\pi$
$929$	−2.76439	−	8.50791i	−0.0906966	−	0.279135i	−0.986108	+	0.166104i	$0.946881\pi$
$930$		0			0
$931$	−1.06144	+	3.26678i	−0.0347874	+	0.107064i
$932$	−2.72706			−0.0893280
$933$	10.1117	−	31.1206i	0.331042	−	1.01884i
$934$	2.76804	−	2.01110i	0.0905729	−	0.0658051i
$935$		0			0
$936$	−2.53646	−	1.84285i	−0.0829069	−	0.0602354i
$937$	14.1455	−	10.2773i	0.462113	−	0.335745i	−0.332247	−	0.943193i	$-0.607807\pi$
$937$	14.1455	−	10.2773i	0.462113	−	0.335745i	0.794360	+	0.607448i	$0.207807\pi$
$938$	2.45305	−	1.78225i	0.0800949	−	0.0581924i
$939$	−14.8770	−	10.8088i	−0.485494	−	0.352732i
$940$		0			0
$941$	−35.2364	+	25.6007i	−1.14867	+	0.834561i	−0.988304	−	0.152496i	$-0.951269\pi$
$941$	−35.2364	+	25.6007i	−1.14867	+	0.834561i	−0.160370	+	0.987057i	$0.551269\pi$
$942$	1.57445	−	4.84567i	0.0512985	−	0.157880i
$943$	−2.99095			−0.0973987
$944$	12.3514	−	38.0137i	0.402003	−	1.23724i
$945$		0			0
$946$	−0.626338	−	1.92767i	−0.0203640	−	0.0626740i
$947$	16.0885	+	49.5152i	0.522805	+	1.60903i	0.768616	+	0.639711i	$0.220946\pi$
$947$	16.0885	+	49.5152i	0.522805	+	1.60903i	−0.245811	+	0.969318i	$0.579054\pi$
$948$	20.7968	+	15.1098i	0.675449	+	0.490742i
$949$	12.1606			0.394748
$950$		0			0
$951$	−24.4335			−0.792312
$952$	1.81851	+	1.32122i	0.0589381	+	0.0428210i
$953$	−4.33482	−	13.3412i	−0.140419	−	0.432164i	0.855975	−	0.517018i	$-0.172958\pi$
$953$	−4.33482	−	13.3412i	−0.140419	−	0.432164i	−0.996393	+	0.0848534i	$0.972958\pi$
$954$	0.0268679	+	0.0826908i	0.000869880	+	0.00267721i
$955$		0			0
$956$	6.36297	−	19.5832i	0.205793	−	0.633367i
$957$	5.40518			0.174725
$958$	−0.0980967	+	0.301911i	−0.00316936	+	0.00975429i
$959$	8.17703	−	5.94096i	0.264050	−	0.191844i
$960$		0			0
$961$	22.0786	+	16.0410i	0.712212	+	0.517453i
$962$	−2.64028	+	1.91827i	−0.0851260	+	0.0618477i
$963$	−5.56371	+	4.04227i	−0.179288	+	0.130260i
$964$	−20.2919	−	14.7429i	−0.653557	−	0.474837i
$965$		0			0
$966$	−0.144252	+	0.104805i	−0.00464122	+	0.00337205i
$967$	5.81641	−	17.9011i	0.187043	−	0.575659i	−0.812935	−	0.582355i	$-0.802131\pi$
$967$	5.81641	−	17.9011i	0.187043	−	0.575659i	0.999978	+	0.00669587i	$0.00213138\pi$
$968$	0.870380			0.0279751
$969$	4.68070	−	14.4057i	0.150366	−	0.462778i
$970$		0			0
$971$	5.79293	+	17.8288i	0.185904	+	0.572153i	0.999963	−	0.00862896i	$-0.00274672\pi$
$971$	5.79293	+	17.8288i	0.185904	+	0.572153i	−0.814059	+	0.580782i	$0.802747\pi$
$972$	−3.79040	−	11.6657i	−0.121577	−	0.374176i
$973$	−14.8897	−	10.8180i	−0.477343	−	0.346810i
$974$	−7.34544			−0.235363
$975$		0			0
$976$	32.1443			1.02891
$977$	−36.8251	−	26.7550i	−1.17814	−	0.855968i	−0.186178	−	0.982516i	$-0.559610\pi$
$977$	−36.8251	−	26.7550i	−1.17814	−	0.855968i	−0.991960	+	0.126548i	$0.959610\pi$
$978$	1.83497	+	5.64745i	0.0586758	+	0.180586i
$979$	16.2876	+	50.1280i	0.520553	+	1.60210i
$980$		0			0
$981$	3.41508	−	10.5105i	0.109035	−	0.335576i
$982$	2.83129			0.0903501
$983$	3.52908	−	10.8614i	0.112560	−	0.346424i	−0.878870	−	0.477061i	$-0.841702\pi$
$983$	3.52908	−	10.8614i	0.112560	−	0.346424i	0.991430	+	0.130637i	$0.0417021\pi$
$984$	5.07553	−	3.68759i	0.161802	−	0.117556i
$985$		0			0
$986$	0.510610	+	0.370980i	0.0162611	+	0.0118144i
$987$	4.42694	−	3.21636i	0.140911	−	0.102378i
$988$	−35.4132	+	25.7292i	−1.12664	+	0.818554i
$989$	−1.52087	−	1.10497i	−0.0483608	−	0.0351362i
$990$		0			0
$991$	−7.23921	+	5.25959i	−0.229961	+	0.167076i	−0.696799	−	0.717266i	$-0.745393\pi$
$991$	−7.23921	+	5.25959i	−0.229961	+	0.167076i	0.466838	+	0.884343i	$0.345393\pi$
$992$	−1.38309	+	4.25670i	−0.0439130	+	0.135150i
$993$	0.772905			0.0245274
$994$	0.725611	−	2.23320i	0.0230150	−	0.0708328i
$995$		0			0
$996$	11.1399	+	34.2851i	0.352982	+	1.08637i
$997$	−11.1261	−	34.2425i	−0.352366	−	1.08447i	−0.957521	−	0.288363i	$-0.906889\pi$
$997$	−11.1261	−	34.2425i	−0.352366	−	1.08447i	0.605155	−	0.796108i	$-0.293111\pi$
$998$	−1.38832	−	1.00867i	−0.0439464	−	0.0319289i
$999$	−14.0912			−0.445825

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.h.d.701.8		56
5.2	odd	4		175.2.n.a.134.8	yes	56
5.3	odd	4		875.2.n.c.799.7		56
5.4	even	2		875.2.h.e.701.7		56
25.2	odd	20		875.2.n.c.449.7		56
25.6	even	5		4375.2.a.p.1.13		28
25.11	even	5	inner	875.2.h.d.176.8		56
25.14	even	10		875.2.h.e.176.7		56
25.19	even	10		4375.2.a.o.1.16		28
25.23	odd	20		175.2.n.a.64.8	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.n.a.64.8	✓	56	25.23	odd	20
175.2.n.a.134.8	yes	56	5.2	odd	4
875.2.h.d.176.8		56	25.11	even	5	inner
875.2.h.d.701.8		56	1.1	even	1	trivial
875.2.h.e.176.7		56	25.14	even	10
875.2.h.e.701.7		56	5.4	even	2
875.2.n.c.449.7		56	25.2	odd	20
875.2.n.c.799.7		56	5.3	odd	4
4375.2.a.o.1.16		28	25.19	even	10
4375.2.a.p.1.13		28	25.6	even	5

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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.h (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.160894 - 0.116896i) q^{2} +(0.477493 + 1.46957i) q^{3} +(-0.605812 - 1.86450i) q^{4} +(0.0949619 - 0.292263i) q^{6} -1.00000 q^{7} +(-0.243394 + 0.749089i) q^{8} +(0.495409 - 0.359936i) q^{9} +O(q^{10})\)	\(q+(-0.160894 - 0.116896i) q^{2} +(0.477493 + 1.46957i) q^{3} +(-0.605812 - 1.86450i) q^{4} +(0.0949619 - 0.292263i) q^{6} -1.00000 q^{7} +(-0.243394 + 0.749089i) q^{8} +(0.495409 - 0.359936i) q^{9} +(-2.54486 - 1.84895i) q^{11} +(2.45074 - 1.78057i) q^{12} +(-5.25890 + 3.82082i) q^{13} +(0.160894 + 0.116896i) q^{14} +(-3.04535 + 2.21257i) q^{16} +(-0.881886 + 2.71417i) q^{17} -0.121784 q^{18} +(-1.06144 + 3.26678i) q^{19} +(-0.477493 - 1.46957i) q^{21} +(0.193318 + 0.594971i) q^{22} +(0.469412 + 0.341048i) q^{23} -1.21706 q^{24} +1.29277 q^{26} +(4.51578 + 3.28091i) q^{27} +(0.605812 + 1.86450i) q^{28} +(0.343638 + 1.05761i) q^{29} +(-0.595158 + 1.83171i) q^{31} +2.32390 q^{32} +(1.50201 - 4.62272i) q^{33} +(0.459166 - 0.333604i) q^{34} +(-0.971225 - 0.705636i) q^{36} +(-2.04235 + 1.48385i) q^{37} +(0.552655 - 0.401527i) q^{38} +(-8.12605 - 5.90392i) q^{39} +(-4.17033 + 3.02992i) q^{41} +(-0.0949619 + 0.292263i) q^{42} -3.23994 q^{43} +(-1.90566 + 5.86501i) q^{44} +(-0.0356584 - 0.109745i) q^{46} +(1.09432 + 3.36797i) q^{47} +(-4.70567 - 3.41887i) q^{48} +1.00000 q^{49} -4.40975 q^{51} +(10.3098 + 7.49052i) q^{52} +(-0.220620 - 0.678998i) q^{53} +(-0.343036 - 1.05576i) q^{54} +(0.243394 - 0.749089i) q^{56} -5.30760 q^{57} +(0.0683414 - 0.210333i) q^{58} +(-8.59038 + 6.24127i) q^{59} +(-6.90849 - 5.01931i) q^{61} +(0.309878 - 0.225139i) q^{62} +(-0.495409 + 0.359936i) q^{63} +(5.71679 + 4.15349i) q^{64} +(-0.782044 + 0.568189i) q^{66} +(4.71139 - 14.5002i) q^{67} +5.59481 q^{68} +(-0.277053 + 0.852682i) q^{69} +(-3.64856 - 11.2291i) q^{71} +(0.149044 + 0.458712i) q^{72} +(-1.51347 - 1.09960i) q^{73} +0.502059 q^{74} +6.73394 q^{76} +(2.54486 + 1.84895i) q^{77} +(0.617287 + 1.89981i) q^{78} +(2.62230 + 8.07060i) q^{79} +(-2.09759 + 6.45571i) q^{81} +1.02517 q^{82} +(-3.67741 + 11.3179i) q^{83} +(-2.45074 + 1.78057i) q^{84} +(0.521288 + 0.378738i) q^{86} +(-1.39015 + 1.01000i) q^{87} +(2.00443 - 1.45631i) q^{88} +(-13.5558 - 9.84885i) q^{89} +(5.25890 - 3.82082i) q^{91} +(0.351507 - 1.08183i) q^{92} -2.97601 q^{93} +(0.217634 - 0.669808i) q^{94} +(1.10964 + 3.41513i) q^{96} +(-3.09402 - 9.52242i) q^{97} +(-0.160894 - 0.116896i) q^{98} -1.92625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9}+O(q^{10}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9	\( 56 q - 4 q^{2} - 4 q^{3} - 12 q^{4} - 56 q^{7} - 12 q^{8} - 6 q^{9} + 8 q^{11} - 12 q^{12} - 8 q^{13} + 4 q^{14} - 32 q^{16} - 20 q^{17} + 48 q^{18} - 12 q^{19} + 4 q^{21} - 8 q^{22} - 16 q^{23} + 28 q^{24} + 12 q^{26} - 16 q^{27} + 12 q^{28} + 2 q^{29} + 12 q^{31} + 112 q^{32} - 14 q^{33} - 14 q^{36} - 16 q^{37} - 20 q^{38} + 4 q^{39} + 4 q^{41} + 32 q^{43} - 22 q^{44} - 4 q^{46} - 18 q^{47} - 48 q^{48} + 56 q^{49} - 44 q^{51} + 16 q^{52} - 20 q^{53} - 54 q^{54} + 12 q^{56} + 152 q^{57} + 32 q^{58} + 6 q^{59} - 4 q^{61} + 18 q^{62} + 6 q^{63} - 24 q^{64} - 74 q^{66} - 32 q^{67} + 124 q^{68} + 78 q^{69} - 8 q^{71} - 100 q^{72} - 48 q^{73} - 60 q^{74} + 52 q^{76} - 8 q^{77} + 124 q^{78} - 72 q^{81} + 44 q^{82} + 10 q^{83} + 12 q^{84} - 20 q^{86} + 26 q^{87} - 88 q^{88} - 38 q^{89} + 8 q^{91} - 96 q^{92} + 96 q^{93} - 88 q^{94} - 28 q^{96} - 90 q^{97} - 4 q^{98} - 60 q^{99}+O(q^{100}) \) 56 * q - 4 * q^2 - 4 * q^3 - 12 * q^4 - 56 * q^7 - 12 * q^8 - 6 * q^9 + 8 * q^11 - 12 * q^12 - 8 * q^13 + 4 * q^14 - 32 * q^16 - 20 * q^17 + 48 * q^18 - 12 * q^19 + 4 * q^21 - 8 * q^22 - 16 * q^23 + 28 * q^24 + 12 * q^26 - 16 * q^27 + 12 * q^28 + 2 * q^29 + 12 * q^31 + 112 * q^32 - 14 * q^33 - 14 * q^36 - 16 * q^37 - 20 * q^38 + 4 * q^39 + 4 * q^41 + 32 * q^43 - 22 * q^44 - 4 * q^46 - 18 * q^47 - 48 * q^48 + 56 * q^49 - 44 * q^51 + 16 * q^52 - 20 * q^53 - 54 * q^54 + 12 * q^56 + 152 * q^57 + 32 * q^58 + 6 * q^59 - 4 * q^61 + 18 * q^62 + 6 * q^63 - 24 * q^64 - 74 * q^66 - 32 * q^67 + 124 * q^68 + 78 * q^69 - 8 * q^71 - 100 * q^72 - 48 * q^73 - 60 * q^74 + 52 * q^76 - 8 * q^77 + 124 * q^78 - 72 * q^81 + 44 * q^82 + 10 * q^83 + 12 * q^84 - 20 * q^86 + 26 * q^87 - 88 * q^88 - 38 * q^89 + 8 * q^91 - 96 * q^92 + 96 * q^93 - 88 * q^94 - 28 * q^96 - 90 * q^97 - 4 * q^98 - 60 * q^99

Introduction

L-functions

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