LMFDB - Embedded newform 575.2.r.b.168.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(7,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("575.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.r (of order $44$, degree $20$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	no (minimal twist has level 115)
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			168.7
Character	$\chi$	$=$	575.168
Dual form			575.2.r.b.332.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0452482 + 0.632652i) q^{2} +(1.67360 + 0.364069i) q^{3} +(1.58144 - 0.227377i) q^{4} +(-0.154602 + 1.07528i) q^{6} +(0.171765 + 0.0937908i) q^{7} +(0.485055 + 2.22976i) q^{8} +(-0.0605071 - 0.0276327i) q^{9} +(2.33306 - 2.02161i) q^{11} +(2.72948 + 0.195216i) q^{12} +(-0.0682068 - 0.124911i) q^{13} +(-0.0515649 + 0.112911i) q^{14} +(1.67726 - 0.492487i) q^{16} +(-0.702107 + 0.525590i) q^{17} +(0.0147440 - 0.0395303i) q^{18} +(1.07365 + 7.46738i) q^{19} +(0.253320 + 0.219503i) q^{21} +(1.38454 + 1.38454i) q^{22} +(-1.56765 - 4.53238i) q^{23} +3.90832i q^{24} +(0.0759392 - 0.0488032i) q^{26} +(-4.20456 - 3.14750i) q^{27} +(0.292962 + 0.109269i) q^{28} +(3.41800 + 0.491434i) q^{29} +(-0.282325 - 0.181439i) q^{31} +(1.98236 + 5.31490i) q^{32} +(4.64062 - 2.53397i) q^{33} +(-0.364285 - 0.420407i) q^{34} +(-0.101971 - 0.0299415i) q^{36} +(-7.03930 + 2.62552i) q^{37} +(-4.67567 + 1.01713i) q^{38} +(-0.0686744 - 0.233884i) q^{39} +(-3.88633 - 8.50988i) q^{41} +(-0.127407 + 0.170195i) q^{42} +(-0.170122 + 0.782038i) q^{43} +(3.22994 - 3.72754i) q^{44} +(2.79649 - 1.19686i) q^{46} +(4.49497 - 4.49497i) q^{47} +(2.98636 - 0.213588i) q^{48} +(-3.76378 - 5.85655i) q^{49} +(-1.36640 + 0.624012i) q^{51} +(-0.136267 - 0.182031i) q^{52} +(0.955623 - 1.75009i) q^{53} +(1.80102 - 2.80244i) q^{54} +(-0.125816 + 0.428489i) q^{56} +(-0.921788 + 12.8883i) q^{57} +(-0.156248 + 2.18464i) q^{58} +(-2.49768 + 8.50633i) q^{59} +(-5.60557 + 8.72243i) q^{61} +(0.102013 - 0.186823i) q^{62} +(-0.00780132 - 0.0104213i) q^{63} +(-0.0925946 + 0.0422865i) q^{64} +(1.81310 + 2.82124i) q^{66} +(-8.30923 + 0.594288i) q^{67} +(-0.990833 + 0.990833i) q^{68} +(-0.973521 - 8.15612i) q^{69} +(4.40447 - 5.08303i) q^{71} +(0.0322650 - 0.148320i) q^{72} +(-4.04711 + 5.40630i) q^{73} +(-1.97956 - 4.33463i) q^{74} +(3.39582 + 11.5651i) q^{76} +(0.590347 - 0.128422i) q^{77} +(0.144860 - 0.0540298i) q^{78} +(3.57517 + 1.04977i) q^{79} +(-5.76017 - 6.64759i) q^{81} +(5.20795 - 2.84375i) q^{82} +(3.02763 + 8.11740i) q^{83} +(0.450520 + 0.289532i) q^{84} +(-0.502456 - 0.0722422i) q^{86} +(5.54144 + 2.06685i) q^{87} +(5.63937 + 4.22158i) q^{88} +(-6.56977 + 4.22214i) q^{89} -0.0278526i q^{91} +(-3.50971 - 6.81125i) q^{92} +(-0.406442 - 0.406442i) q^{93} +(3.04714 + 2.64036i) q^{94} +(1.38268 + 9.61674i) q^{96} +(4.54643 - 12.1894i) q^{97} +(3.53486 - 2.64616i) q^{98} +(-0.197029 + 0.0578530i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q + 18 q^{2} + 14 q^{3} - 36 q^{6} + 22 q^{7} + 26 q^{8} - 44 q^{11} + 6 q^{12} + 26 q^{13} - 52 q^{16} + 22 q^{17} - 58 q^{18} - 44 q^{21} - 22 q^{23} - 28 q^{26} + 26 q^{27} - 66 q^{28} - 40 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) $ 200 * q + 18 * q^2 + 14 * q^3 - 36 * q^6 + 22 * q^7 + 26 * q^8 - 44 * q^11 + 6 * q^12 + 26 * q^13 - 52 * q^16 + 22 * q^17 - 58 * q^18 - 44 * q^21 - 22 * q^23 - 28 * q^26 + 26 * q^27 - 66 * q^28 - 40 * q^31 + 46 * q^32 - 12 * q^36 - 66 * q^37 + 22 * q^38 - 8 * q^41 - 198 * q^42 + 22 * q^43 - 76 * q^46 - 52 * q^47 - 18 * q^48 - 44 * q^51 - 158 * q^52 + 22 * q^53 + 88 * q^56 - 66 * q^57 + 58 * q^58 + 44 * q^61 - 38 * q^62 + 22 * q^63 + 132 * q^66 + 22 * q^67 + 132 * q^71 + 28 * q^72 - 34 * q^73 + 132 * q^76 + 10 * q^77 - 22 * q^78 - 48 * q^81 + 50 * q^82 + 22 * q^83 + 46 * q^87 + 110 * q^88 - 50 * q^92 + 36 * q^93 + 148 * q^96 + 88 * q^97 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$e\left(\frac{19}{22}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.0452482	+	0.632652i	0.0319953	+	0.447353i	0.988047	+	0.154154i	$0.0492652\pi$
$2$	0.0452482	+	0.632652i	0.0319953	+	0.447353i	−0.956052	+	0.293199i	$0.905280\pi$
$3$	1.67360	+	0.364069i	0.966253	+	0.210196i	0.667893	−	0.744258i	$-0.267197\pi$
$3$	1.67360	+	0.364069i	0.966253	+	0.210196i	0.298361	+	0.954453i	$0.403560\pi$
$4$	1.58144	−	0.227377i	0.790721	−	0.113688i
$5$		0			0
$5$		0			0
$6$	−0.154602	+	1.07528i	−0.0631160	+	0.438981i
$7$	0.171765	+	0.0937908i	0.0649211	+	0.0354496i	0.511382	−	0.859354i	$-0.329134\pi$
$7$	0.171765	+	0.0937908i	0.0649211	+	0.0354496i	−0.446461	+	0.894803i	$0.647316\pi$
$8$	0.485055	+	2.22976i	0.171493	+	0.788339i
$9$	−0.0605071	−	0.0276327i	−0.0201690	−	0.00921089i
$10$		0			0
$11$	2.33306	−	2.02161i	0.703445	−	0.609539i	−0.227897	−	0.973685i	$-0.573185\pi$
$11$	2.33306	−	2.02161i	0.703445	−	0.609539i	0.931342	+	0.364147i	$0.118639\pi$
$12$	2.72948	+	0.195216i	0.787933	+	0.0563541i
$13$	−0.0682068	−	0.124911i	−0.0189172	−	0.0346442i	0.868049	−	0.496478i	$-0.165374\pi$
$13$	−0.0682068	−	0.124911i	−0.0189172	−	0.0346442i	−0.886967	+	0.461834i	$0.847192\pi$
$14$	−0.0515649	+	0.112911i	−0.0137813	+	0.0301768i
$15$		0			0
$16$	1.67726	−	0.492487i	0.419314	−	0.123122i
$17$	−0.702107	+	0.525590i	−0.170286	+	0.127474i	−0.681022	−	0.732263i	$-0.738464\pi$
$17$	−0.702107	+	0.525590i	−0.170286	+	0.127474i	0.510736	+	0.859738i	$0.329373\pi$
$18$	0.0147440	−	0.0395303i	0.00347520	−	0.00931737i
$19$	1.07365	+	7.46738i	0.246311	+	1.71313i	0.619180	+	0.785249i	$0.287465\pi$
$19$	1.07365	+	7.46738i	0.246311	+	1.71313i	−0.372868	+	0.927884i	$0.621626\pi$
$20$		0			0
$21$	0.253320	+	0.219503i	0.0552789	+	0.0478994i
$22$	1.38454	+	1.38454i	0.295186	+	0.295186i
$23$	−1.56765	−	4.53238i	−0.326878	−	0.945067i
$23$	−1.56765	−	4.53238i	−0.326878	−	0.945067i
$24$			3.90832i			0.797782i
$25$		0			0
$26$	0.0759392	−	0.0488032i	0.0148929	−	0.00957109i
$27$	−4.20456	−	3.14750i	−0.809169	−	0.605736i
$28$	0.292962	+	0.109269i	0.0553647	+	0.0206500i
$29$	3.41800	+	0.491434i	0.634706	+	0.0912569i	0.452155	−	0.891939i	$-0.350655\pi$
$29$	3.41800	+	0.491434i	0.634706	+	0.0912569i	0.182551	+	0.983196i	$0.441565\pi$
$30$		0			0
$31$	−0.282325	−	0.181439i	−0.0507070	−	0.0325874i	0.515042	−	0.857165i	$-0.327776\pi$
$31$	−0.282325	−	0.181439i	−0.0507070	−	0.0325874i	−0.565749	+	0.824578i	$0.691413\pi$
$32$	1.98236	+	5.31490i	0.350434	+	0.939551i
$33$	4.64062	−	2.53397i	0.807828	−	0.441108i
$34$	−0.364285	−	0.420407i	−0.0624743	−	0.0720992i
$35$		0			0
$36$	−0.101971	−	0.0299415i	−0.0169952	−	0.00499025i
$37$	−7.03930	+	2.62552i	−1.15725	+	0.431633i	−0.853487	−	0.521113i	$-0.825517\pi$
$37$	−7.03930	+	2.62552i	−1.15725	+	0.431633i	−0.303766	+	0.952747i	$0.598244\pi$
$38$	−4.67567	+	1.01713i	−0.758494	+	0.165000i
$39$	−0.0686744	−	0.233884i	−0.0109967	−	0.0374514i
$40$		0			0
$41$	−3.88633	−	8.50988i	−0.606943	−	1.32902i	−0.924645	−	0.380830i	$-0.875638\pi$
$41$	−3.88633	−	8.50988i	−0.606943	−	1.32902i	0.317702	−	0.948191i	$-0.397089\pi$
$42$	−0.127407	+	0.170195i	−0.0196593	+	0.0262617i
$43$	−0.170122	+	0.782038i	−0.0259433	+	0.119260i	−0.988297	−	0.152539i	$-0.951255\pi$
$43$	−0.170122	+	0.782038i	−0.0259433	+	0.119260i	0.962354	+	0.271799i	$0.0876186\pi$
$44$	3.22994	−	3.72754i	0.486931	−	0.561948i
$45$		0			0
$46$	2.79649	−	1.19686i	0.412319	−	0.176467i
$47$	4.49497	−	4.49497i	0.655659	−	0.655659i	−0.298691	−	0.954350i	$-0.596550\pi$
$47$	4.49497	−	4.49497i	0.655659	−	0.655659i	0.954350	+	0.298691i	$0.0965501\pi$
$48$	2.98636	−	0.213588i	0.431043	−	0.0308288i
$49$	−3.76378	−	5.85655i	−0.537683	−	0.836651i
$50$		0			0
$51$	−1.36640	+	0.624012i	−0.191334	+	0.0873792i
$52$	−0.136267	−	0.182031i	−0.0188968	−	0.0252432i
$53$	0.955623	−	1.75009i	0.131265	−	0.240394i	−0.803777	−	0.594930i	$-0.797180\pi$
$53$	0.955623	−	1.75009i	0.131265	−	0.240394i	0.935042	+	0.354537i	$0.115361\pi$
$54$	1.80102	−	2.80244i	0.245088	−	0.381364i
$55$		0			0
$56$	−0.125816	+	0.428489i	−0.0168128	+	0.0572592i
$57$	−0.921788	+	12.8883i	−0.122094	+	1.70709i
$58$	−0.156248	+	2.18464i	−0.0205164	+	0.286857i
$59$	−2.49768	+	8.50633i	−0.325171	+	1.10743i	0.621013	+	0.783800i	$0.286721\pi$
$59$	−2.49768	+	8.50633i	−0.325171	+	1.10743i	−0.946184	+	0.323630i	$0.895097\pi$
$60$		0			0
$61$	−5.60557	+	8.72243i	−0.717719	+	1.11679i	0.270347	+	0.962763i	$0.412862\pi$
$61$	−5.60557	+	8.72243i	−0.717719	+	1.11679i	−0.988066	+	0.154030i	$0.950775\pi$
$62$	0.102013	−	0.186823i	0.0129557	−	0.0237266i
$63$	−0.00780132	−	0.0104213i	−0.000982873	−	0.00131297i
$64$	−0.0925946	+	0.0422865i	−0.0115743	+	0.00528582i
$65$		0			0
$66$	1.81310	+	2.82124i	0.223177	+	0.347271i
$67$	−8.30923	+	0.594288i	−1.01513	+	0.0726038i	−0.568979	−	0.822352i	$-0.692662\pi$
$67$	−8.30923	+	0.594288i	−1.01513	+	0.0726038i	−0.446155	+	0.894956i	$0.647207\pi$
$68$	−0.990833	+	0.990833i	−0.120156	+	0.120156i
$69$	−0.973521	−	8.15612i	−0.117198	−	0.981882i
$70$		0			0
$71$	4.40447	−	5.08303i	0.522714	−	0.603245i	−0.431594	−	0.902068i	$-0.642049\pi$
$71$	4.40447	−	5.08303i	0.522714	−	0.603245i	0.954308	+	0.298823i	$0.0965941\pi$
$72$	0.0322650	−	0.148320i	0.00380246	−	0.0174796i
$73$	−4.04711	+	5.40630i	−0.473678	+	0.632760i	−0.972210	−	0.234112i	$-0.924782\pi$
$73$	−4.04711	+	5.40630i	−0.473678	+	0.632760i	0.498532	+	0.866872i	$0.333873\pi$
$74$	−1.97956	−	4.33463i	−0.230119	−	0.503890i
$75$		0			0
$76$	3.39582	+	11.5651i	0.389527	+	1.32661i
$77$	0.590347	−	0.128422i	0.0672763	−	0.0146351i
$78$	0.144860	−	0.0540298i	0.0164021	−	0.00611767i
$79$	3.57517	+	1.04977i	0.402239	+	0.118108i	0.476593	−	0.879124i	$-0.341871\pi$
$79$	3.57517	+	1.04977i	0.402239	+	0.118108i	−0.0743546	+	0.997232i	$0.523690\pi$
$80$		0			0
$81$	−5.76017	−	6.64759i	−0.640019	−	0.738621i
$82$	5.20795	−	2.84375i	0.575121	−	0.314040i
$83$	3.02763	+	8.11740i	0.332326	+	0.891000i	0.990423	+	0.138067i	$0.0440890\pi$
$83$	3.02763	+	8.11740i	0.332326	+	0.891000i	−0.658097	+	0.752933i	$0.728638\pi$
$84$	0.450520	+	0.289532i	0.0491558	+	0.0315905i
$85$		0			0
$86$	−0.502456	−	0.0722422i	−0.0541812	−	0.00779008i
$87$	5.54144	+	2.06685i	0.594105	+	0.221590i
$88$	5.63937	+	4.22158i	0.601159	+	0.450022i
$89$	−6.56977	+	4.22214i	−0.696395	+	0.447546i	−0.840354	−	0.542038i	$-0.817653\pi$
$89$	−6.56977	+	4.22214i	−0.696395	+	0.447546i	0.143959	+	0.989584i	$0.454017\pi$
$90$		0			0
$91$		−	0.0278526i		−	0.00291974i
$92$	−3.50971	−	6.81125i	−0.365912	−	0.710121i
$93$	−0.406442	−	0.406442i	−0.0421461	−	0.0421461i
$94$	3.04714	+	2.64036i	0.314289	+	0.272333i
$95$		0			0
$96$	1.38268	+	9.61674i	0.141119	+	0.981504i
$97$	4.54643	−	12.1894i	0.461620	−	1.23765i	−0.472703	−	0.881222i	$-0.656722\pi$
$97$	4.54643	−	12.1894i	0.461620	−	1.23765i	0.934323	−	0.356428i	$-0.116006\pi$
$98$	3.53486	−	2.64616i	0.357075	−	0.267303i
$99$	−0.197029	+	0.0578530i	−0.0198022	+	0.00581445i
$100$		0			0
$101$	4.62209	−	10.1210i	0.459915	−	1.00707i	−0.527592	−	0.849498i	$-0.676905\pi$
$101$	4.62209	−	10.1210i	0.459915	−	1.00707i	0.987507	−	0.157575i	$-0.0503678\pi$
$102$	−0.456610	−	0.836218i	−0.0452111	−	0.0827979i
$103$	−5.63058	−	0.402707i	−0.554797	−	0.0396799i	−0.208874	−	0.977943i	$-0.566980\pi$
$103$	−5.63058	−	0.402707i	−0.554797	−	0.0396799i	−0.345924	+	0.938263i	$0.612434\pi$
$104$	0.245438	−	0.212674i	0.0240672	−	0.0208544i
$105$		0			0
$106$	1.15044	+	0.525389i	0.111741	+	0.0510303i
$107$	−3.70255	−	17.0203i	−0.357939	−	1.64542i	−0.706193	−	0.708019i	$-0.749589\pi$
$107$	−3.70255	−	17.0203i	−0.357939	−	1.64542i	0.348254	−	0.937400i	$-0.386775\pi$
$108$	−7.36494	−	4.02156i	−0.708692	−	0.386975i
$109$	−1.08276	+	7.53075i	−0.103709	+	0.721315i	0.869922	+	0.493189i	$0.164169\pi$
$109$	−1.08276	+	7.53075i	−0.103709	+	0.721315i	−0.973632	+	0.228126i	$0.926740\pi$
$110$		0			0
$111$	−12.7368	+	1.83128i	−1.20893	+	0.173817i
$112$	0.334285	+	0.0727192i	0.0315870	+	0.00687132i
$113$	−0.628483	−	8.78734i	−0.0591227	−	0.826644i	−0.937348	−	0.348396i	$-0.886727\pi$
$113$	−0.628483	−	8.78734i	−0.0591227	−	0.826644i	0.878225	−	0.478248i	$-0.158728\pi$
$114$	−8.19551			−0.767579
$115$		0			0
$116$	5.51710			0.512250
$117$	0.000675360		0.00944276i	6.24370e−5		0.000872983i
$118$	−5.49456	−	1.19527i	−0.505816	−	0.110033i
$119$	−0.169893	+	0.0244269i	−0.0155741	+	0.00223921i
$120$		0			0
$121$	−0.209189	+	1.45494i	−0.0190172	+	0.132268i
$122$	−5.77191	−	3.15170i	−0.522564	−	0.285341i
$123$	−3.40598	−	15.6570i	−0.307107	−	1.41175i
$124$	−0.487735	−	0.222741i	−0.0437999	−	0.0200028i
$125$		0			0
$126$	0.00624009	−	0.00540707i	0.000555911	−	0.000481700i
$127$	21.8775	+	1.56471i	1.94131	+	0.138845i	0.987080	−	0.160228i	$-0.0512229\pi$
$127$	21.8775	+	1.56471i	1.94131	+	0.138845i	0.954230	+	0.299073i	$0.0966775\pi$
$128$	5.40620	+	9.90071i	0.477845	+	0.875107i
$129$	−0.569432	+	1.24688i	−0.0501357	+	0.109782i
$130$		0			0
$131$	−17.6458	+	5.18128i	−1.54172	+	0.452691i	−0.938614	−	0.344968i	$-0.887890\pi$
$131$	−17.6458	+	5.18128i	−1.54172	+	0.452691i	−0.603109	+	0.797659i	$0.706071\pi$
$132$	6.76270	−	5.06250i	0.588618	−	0.440634i
$133$	−0.515956	+	1.38333i	−0.0447391	+	0.119950i
$134$	−0.751955	−	5.22996i	−0.0649590	−	0.451800i
$135$		0			0
$136$	−1.51250	−	1.31059i	−0.129696	−	0.112382i
$137$	5.31898	+	5.31898i	0.454431	+	0.454431i	0.896822	−	0.442391i	$-0.145870\pi$
$137$	5.31898	+	5.31898i	0.454431	+	0.454431i	−0.442391	+	0.896822i	$0.645870\pi$
$138$	5.11594	−	0.984950i	0.435498	−	0.0838445i
$139$		−	16.5816i		−	1.40643i	−0.710975	−	0.703217i	$-0.751746\pi$
$139$		−	16.5816i		−	1.40643i	0.710975	−	0.703217i	$-0.248254\pi$
$140$		0			0
$141$	9.15926	−	5.88630i	0.771349	−	0.495716i
$142$	3.41508	+	2.55650i	0.286587	+	0.214537i
$143$	−0.411653	−	0.153539i	−0.0344241	−	0.0128395i
$144$	−0.115095	−	0.0165481i	−0.00959122	−	0.00137901i
$145$		0			0
$146$	−3.60343	−	2.31579i	−0.298222	−	0.191656i
$147$	−4.16687	−	11.1718i	−0.343677	−	0.921435i
$148$	−10.5353	+	5.75268i	−0.865993	+	0.472868i
$149$	−8.33524	−	9.61937i	−0.682849	−	0.788050i	0.303480	−	0.952838i	$-0.401851\pi$
$149$	−8.33524	−	9.61937i	−0.682849	−	0.788050i	−0.986329	+	0.164788i	$0.947306\pi$
$150$		0			0
$151$	0.986154	+	0.289561i	0.0802521	+	0.0235641i	0.321612	−	0.946872i	$-0.395775\pi$
$151$	0.986154	+	0.289561i	0.0802521	+	0.0235641i	−0.241360	+	0.970436i	$0.577593\pi$
$152$	−16.1297	+	6.01606i	−1.30829	+	0.487967i
$153$	0.0570059	−	0.0124009i	0.00460865	−	0.00100255i
$154$	0.107959	+	0.367674i	0.00869956	+	0.0296280i
$155$		0			0
$156$	−0.161784	−	0.354258i	−0.0129531	−	0.0283634i
$157$	−10.2561	+	13.7006i	−0.818526	+	1.09342i	0.175521	+	0.984476i	$0.443839\pi$
$157$	−10.2561	+	13.7006i	−0.818526	+	1.09342i	−0.994048	+	0.108948i	$0.965252\pi$
$158$	−0.502366	+	2.30934i	−0.0399661	+	0.183721i
$159$	2.23649	−	2.58104i	0.177365	−	0.204690i
$160$		0			0
$161$	0.155828	−	0.925536i	0.0122810	−	0.0729425i
$162$	3.94497	−	3.94497i	0.309946	−	0.309946i
$163$	4.99602	−	0.357322i	0.391318	−	0.0279876i	0.125706	−	0.992068i	$-0.459880\pi$
$163$	4.99602	−	0.357322i	0.391318	−	0.0279876i	0.265612	+	0.964080i	$0.414426\pi$
$164$	−8.08096	−	12.5742i	−0.631017	−	0.981881i
$165$		0			0
$166$	−4.99849	+	2.28274i	−0.387958	+	0.177175i
$167$	−4.90538	−	6.55282i	−0.379590	−	0.507073i	0.569537	−	0.821965i	$-0.307122\pi$
$167$	−4.90538	−	6.55282i	−0.379590	−	0.507073i	−0.949127	+	0.314893i	$0.898031\pi$
$168$	−0.366565	+	0.671313i	−0.0282811	+	0.0517929i
$169$	7.01738	−	10.9193i	0.539798	−	0.839943i
$170$		0			0
$171$	0.141380	−	0.481497i	0.0108116	−	0.0368210i
$172$	−0.0912205	+	1.27543i	−0.00695550	+	0.0972505i
$173$	1.23899	−	17.3233i	0.0941985	−	1.31707i	−0.702063	−	0.712114i	$-0.747738\pi$
$173$	1.23899	−	17.3233i	0.0941985	−	1.31707i	0.796262	−	0.604952i	$-0.206808\pi$
$174$	−1.05686	+	3.59932i	−0.0801201	+	0.272864i
$175$		0			0
$176$	2.91753	−	4.53976i	0.219917	−	0.342198i
$177$	−7.27702	+	13.3269i	−0.546974	+	1.00171i
$178$	−2.96841	−	3.96534i	−0.222492	−	0.297215i
$179$	−11.4047	+	5.20834i	−0.852425	+	0.389290i	−0.793205	−	0.608955i	$-0.791589\pi$
$179$	−11.4047	+	5.20834i	−0.852425	+	0.389290i	−0.0592208	+	0.998245i	$0.518862\pi$
$180$		0			0
$181$	14.0743	+	21.9000i	1.04613	+	1.62782i	0.735812	+	0.677186i	$0.236801\pi$
$181$	14.0743	+	21.9000i	1.04613	+	1.62782i	0.310322	+	0.950631i	$0.399563\pi$
$182$	0.0176210	−	0.00126028i	0.00130616	−	9.34181e-5i
$183$	−12.5570	+	12.5570i	−0.928243	+	0.928243i
$184$	9.34572	−	5.69394i	0.688976	−	0.419763i
$185$		0			0
$186$	0.238746	−	0.275527i	0.0175057	−	0.0202026i
$187$	−0.575520	+	2.64562i	−0.0420862	+	0.193467i
$188$	6.08648	−	8.13058i	0.443902	−	0.592984i
$189$	−0.426991	−	0.934980i	−0.0310590	−	0.0680098i
$190$		0			0
$191$	3.50213	+	11.9272i	0.253406	+	0.863020i	0.983689	+	0.179876i	$0.0575697\pi$
$191$	3.50213	+	11.9272i	0.253406	+	0.863020i	−0.730284	+	0.683144i	$0.760612\pi$
$192$	−0.170362	+	0.0370599i	−0.0122948	+	0.00267457i
$193$	−10.6245	+	3.96275i	−0.764771	+	0.285245i	−0.701422	−	0.712747i	$-0.747451\pi$
$193$	−10.6245	+	3.96275i	−0.764771	+	0.285245i	−0.0633493	+	0.997991i	$0.520178\pi$
$194$	7.91739	+	2.32476i	0.568436	+	0.166908i
$195$		0			0
$196$	−7.28384	−	8.40600i	−0.520274	−	0.600429i
$197$	6.09462	−	3.32791i	0.434224	−	0.237104i	−0.247243	−	0.968954i	$-0.579524\pi$
$197$	6.09462	−	3.32791i	0.434224	−	0.237104i	0.681466	+	0.731850i	$0.261343\pi$
$198$	−0.0455161	−	0.122033i	−0.00323469	−	0.00867253i
$199$	−17.0426	−	10.9526i	−1.20812	−	0.776411i	−0.227777	−	0.973713i	$-0.573146\pi$
$199$	−17.0426	−	10.9526i	−1.20812	−	0.776411i	−0.980343	+	0.197302i	$0.936782\pi$
$200$		0			0
$201$	−14.1227	−	2.03054i	−0.996138	−	0.143223i
$202$	6.61219	+	2.46622i	0.465232	+	0.173523i
$203$	0.541000	+	0.404988i	0.0379708	+	0.0284246i
$204$	−2.01899	+	1.29753i	−0.141358	+	0.0908450i
$205$		0			0
$206$		−	3.58042i		−	0.249460i
$207$	−0.0303877	+	0.317560i	−0.00211209	+	0.0220719i
$208$	−0.175917	−	0.175917i	−0.0121977	−	0.0121977i
$209$	17.6010	+	15.2514i	1.21749	+	1.05496i
$210$		0			0
$211$	−0.733595	−	5.10227i	−0.0505028	−	0.351255i	−0.999367	−	0.0355706i	$-0.988675\pi$
$211$	−0.733595	−	5.10227i	−0.0505028	−	0.351255i	0.948864	−	0.315684i	$-0.102234\pi$
$212$	1.11333	−	2.98496i	0.0764639	−	0.205008i
$213$	9.22189	−	6.90342i	0.631874	−	0.473015i
$214$	10.6004	−	3.11257i	0.724630	−	0.212771i
$215$		0			0
$216$	4.97872	−	10.9019i	0.338759	−	0.741779i
$217$	−0.0314762	−	0.0576444i	−0.00213674	−	0.00391316i
$218$	−4.81334	−	0.344257i	−0.326000	−	0.0233160i
$219$	−8.74151	+	7.57456i	−0.590696	+	0.511841i
$220$		0			0
$221$	0.113541	+	0.0518523i	0.00763757	+	0.00348796i
$222$	−1.73488	−	7.97513i	−0.116438	−	0.535255i
$223$	10.7757	+	5.88395i	0.721591	+	0.394019i	0.797679	−	0.603083i	$-0.206061\pi$
$223$	10.7757	+	5.88395i	0.721591	+	0.394019i	−0.0760877	+	0.997101i	$0.524243\pi$
$224$	−0.157990	+	1.09884i	−0.0105561	+	0.0734195i
$225$		0			0
$226$	5.53089	−	0.795223i	0.367910	−	0.0528974i
$227$	−5.04440	−	1.09734i	−0.334808	−	0.0728331i	0.0420184	−	0.999117i	$-0.486621\pi$
$227$	−5.04440	−	1.09734i	−0.334808	−	0.0728331i	−0.376827	+	0.926284i	$0.622985\pi$
$228$	1.47274	+	20.5917i	0.0975349	+	1.36372i
$229$	16.5896			1.09627			0.548137	−	0.836389i	$-0.315337\pi$
$229$	16.5896			1.09627			0.548137	+	0.836389i	$0.315337\pi$
$230$		0			0
$231$	1.03476			0.0680822
$232$	0.562136	+	7.85968i	0.0369060	+	0.516013i
$233$	9.08066	+	1.97538i	0.594894	+	0.129411i	0.499924	−	0.866069i	$-0.333361\pi$
$233$	9.08066	+	1.97538i	0.594894	+	0.129411i	0.0949691	+	0.995480i	$0.469725\pi$
$234$	−0.00594342		0.000854535i	−0.000388534		5.58627e-5i
$235$		0			0
$236$	−2.01580	+	14.0202i	−0.131217	+	0.912636i
$237$	5.60122	+	3.05850i	0.363838	+	0.198671i
$238$	−0.0231411	−	0.106378i	−0.00150001	−	0.00689545i
$239$	3.59581	+	1.64215i	0.232594	+	0.106222i	0.528303	−	0.849056i	$-0.322829\pi$
$239$	3.59581	+	1.64215i	0.232594	+	0.106222i	−0.295709	+	0.955278i	$0.595556\pi$
$240$		0			0
$241$	4.61704	−	4.00069i	0.297409	−	0.257707i	−0.493354	−	0.869829i	$-0.664229\pi$
$241$	4.61704	−	4.00069i	0.297409	−	0.257707i	0.790763	+	0.612122i	$0.209684\pi$
$242$	−0.929939	−	0.0665106i	−0.0597788	−	0.00427546i
$243$	0.331233	+	0.606607i	0.0212486	+	0.0389139i
$244$	−6.88160	+	15.0686i	−0.440549	+	0.964668i
$245$		0			0
$246$	9.75134	−	2.86325i	0.621723	−	0.182554i
$247$	0.859530	−	0.643436i	0.0546906	−	0.0409409i
$248$	0.267623	−	0.717525i	0.0169941	−	0.0455629i
$249$	2.11175	+	14.6875i	0.133827	+	0.930785i
$250$		0			0
$251$	4.28686	+	3.71459i	0.270584	+	0.234463i	0.779574	−	0.626310i	$-0.215436\pi$
$251$	4.28686	+	3.71459i	0.270584	+	0.234463i	−0.508990	+	0.860772i	$0.669981\pi$
$252$	−0.0147069	−	0.0147069i	−0.000926447	−	0.000926447i
$253$	−12.8201	−	7.40515i	−0.805995	−	0.465558i
$254$			13.9116i			0.872893i
$255$		0			0
$256$	−6.19035	+	3.97830i	−0.386897	+	0.248644i
$257$	18.5185	+	13.8628i	1.15515	+	0.864737i	0.992536	−	0.121952i	$-0.0389154\pi$
$257$	18.5185	+	13.8628i	1.15515	+	0.864737i	0.162618	+	0.986689i	$0.448006\pi$
$258$	−0.814608	−	0.303833i	−0.0507153	−	0.0189158i
$259$	−1.45536	−	0.209249i	−0.0904314	−	0.0130021i
$260$		0			0
$261$	−0.193233	−	0.124184i	−0.0119608	−	0.00768677i
$262$	−4.07639	−	10.9292i	−0.251840	−	0.675210i
$263$	22.9578	−	12.5359i	1.41564	−	0.772998i	0.424451	−	0.905451i	$-0.360467\pi$
$263$	22.9578	−	12.5359i	1.41564	−	0.772998i	0.991189	+	0.132453i	$0.0422854\pi$
$264$	7.90110	+	9.11836i	0.486279	+	0.561196i
$265$		0			0
$266$	−0.898514	−	0.263828i	−0.0550915	−	0.0161763i
$267$	−12.5323	+	4.67431i	−0.766966	+	0.286063i
$268$	−13.0054	+	2.82916i	−0.794433	+	0.172818i
$269$	5.70242	+	19.4206i	0.347683	+	1.18410i	0.928894	+	0.370345i	$0.120761\pi$
$269$	5.70242	+	19.4206i	0.347683	+	1.18410i	−0.581212	+	0.813752i	$0.697421\pi$
$270$		0			0
$271$	3.29990	+	7.22577i	0.200455	+	0.438934i	0.982987	−	0.183676i	$-0.0587996\pi$
$271$	3.29990	+	7.22577i	0.200455	+	0.438934i	−0.782532	+	0.622610i	$0.786072\pi$
$272$	−0.918766	+	1.22733i	−0.0557084	+	0.0744177i
$273$	0.0101403	−	0.0466141i	0.000613717	−	0.00282121i
$274$	−3.12439	+	3.60574i	−0.188751	+	0.217831i
$275$		0			0
$276$	−3.39408	−	12.6771i	−0.204300	−	0.763070i
$277$	−2.42021	+	2.42021i	−0.145416	+	0.145416i	−0.776067	−	0.630651i	$-0.782788\pi$
$277$	−2.42021	+	2.42021i	−0.145416	+	0.145416i	0.630651	+	0.776067i	$0.282788\pi$
$278$	10.4904	−	0.750288i	0.629172	−	0.0449993i
$279$	0.0120690	+	0.0187797i	0.000722553	+	0.00112431i
$280$		0			0
$281$	0.296073	−	0.135212i	0.0176623	−	0.00806608i	−0.406564	−	0.913622i	$-0.633273\pi$
$281$	0.296073	−	0.135212i	0.0176623	−	0.00806608i	0.424227	+	0.905556i	$0.360546\pi$
$282$	4.13842	+	5.52828i	0.246439	+	0.329204i
$283$	−12.8604	+	23.5521i	−0.764471	+	1.40002i	0.147201	+	0.989107i	$0.452974\pi$
$283$	−12.8604	+	23.5521i	−0.764471	+	1.40002i	−0.911672	+	0.410918i	$0.865208\pi$
$284$	5.80965	−	9.03999i	0.344739	−	0.536425i
$285$		0			0
$286$	0.0785100	−	0.267380i	0.00464239	−	0.0158105i
$287$	0.130613	−	1.82620i	0.00770982	−	0.107797i
$288$	0.0269183	−	0.376367i	0.00158618	−	0.0221776i
$289$	−4.57275	+	15.5733i	−0.268985	+	0.916079i
$290$		0			0
$291$	12.0467	−	18.7450i	0.706190	−	1.09885i
$292$	−5.17100	+	9.46997i	−0.302610	+	0.554188i
$293$	5.21528	+	6.96681i	0.304680	+	0.407005i	0.926584	−	0.376089i	$-0.122731\pi$
$293$	5.21528	+	6.96681i	0.304680	+	0.407005i	−0.621903	+	0.783094i	$0.713640\pi$
$294$	6.87932	−	3.14168i	0.401210	−	0.183227i
$295$		0			0
$296$	−9.26873	−	14.4224i	−0.538734	−	0.838287i
$297$	−16.1725	+	1.15668i	−0.938425	+	0.0671175i
$298$	5.70856	−	5.70856i	0.330688	−	0.330688i
$299$	−0.459221	+	0.504957i	−0.0265575	+	0.0292024i
$300$		0			0
$301$	−0.102569	+	0.118371i	−0.00591198	+	0.00682279i
$302$	−0.138570	+	0.636994i	−0.00797379	+	0.0366549i
$303$	11.4203	−	15.2557i	0.656077	−	0.876416i
$304$	5.47837	+	11.9959i	0.314206	+	0.688015i
$305$		0			0
$306$	0.0104248	+	0.0355038i	0.000595949	+	0.00202962i
$307$	21.2410	−	4.62069i	1.21229	−	0.263717i	0.439418	−	0.898283i	$-0.355185\pi$
$307$	21.2410	−	4.62069i	1.21229	−	0.263717i	0.772869	+	0.634566i	$0.218821\pi$
$308$	0.904400	−	0.337324i	0.0515330	−	0.0192208i
$309$	−9.27672	−	2.72389i	−0.527734	−	0.154957i
$310$		0			0
$311$	11.0480	+	12.7501i	0.626474	+	0.722990i	0.976923	−	0.213592i	$-0.0685164\pi$
$311$	11.0480	+	12.7501i	0.626474	+	0.722990i	−0.350449	+	0.936582i	$0.613971\pi$
$312$	0.488194	−	0.266574i	0.0276385	−	0.0150918i
$313$	8.81628	+	23.6374i	0.498326	+	1.33606i	0.906132	+	0.422994i	$0.139021\pi$
$313$	8.81628	+	23.6374i	0.498326	+	1.33606i	−0.407807	+	0.913068i	$0.633706\pi$
$314$	−9.13175	−	5.86862i	−0.515335	−	0.331186i
$315$		0			0
$316$	5.89262	+	0.847231i	0.331486	+	0.0476605i
$317$	−22.9628	−	8.56468i	−1.28972	−	0.481040i	−0.391334	−	0.920249i	$-0.627986\pi$
$317$	−22.9628	−	8.56468i	−1.28972	−	0.481040i	−0.898385	+	0.439208i	$0.855259\pi$
$318$	1.73410	+	1.29813i	0.0972434	+	0.0727955i
$319$	8.96789	−	5.76331i	0.502105	−	0.322683i
$320$		0			0
$321$		−	29.8332i		−	1.66513i
$322$	0.592593	+	0.0567060i	0.0330239	+	0.00316010i
$323$	−4.67859	−	4.67859i	−0.260324	−	0.260324i
$324$	−10.6209	−	9.20304i	−0.590049	−	0.511280i
$325$		0			0
$326$	0.452121	+	3.14457i	0.0250407	+	0.174162i
$327$	−4.55382	+	12.2093i	−0.251827	+	0.675174i
$328$	17.0899	−	12.7933i	0.943633	−	0.706395i
$329$	1.19367	−	0.350492i	0.0658089	−	0.0193232i
$330$		0			0
$331$	0.362741	−	0.794293i	0.0199381	−	0.0436583i	−0.899401	−	0.437125i	$-0.855997\pi$
$331$	0.362741	−	0.794293i	0.0199381	−	0.0436583i	0.919339	+	0.393466i	$0.128724\pi$
$332$	6.63373	+	12.1488i	0.364073	+	0.666751i
$333$	0.498478	+	0.0356518i	0.0273164	+	0.00195371i
$334$	3.92370	−	3.39990i	0.214695	−	0.186034i
$335$		0			0
$336$	0.532984	+	0.243406i	0.0290767	+	0.0132789i
$337$	−1.37093	−	6.30208i	−0.0746795	−	0.343296i	0.924613	−	0.380908i	$-0.124389\pi$
$337$	−1.37093	−	6.30208i	−0.0746795	−	0.343296i	−0.999292	+	0.0376120i	$0.988025\pi$
$338$	7.22561	+	3.94548i	0.393022	+	0.214606i
$339$	2.14737	−	14.9353i	0.116629	−	0.811174i
$340$		0			0
$341$	−1.02548	+	0.147442i	−0.0555329	+	0.00798443i
$342$	0.311017	+	0.0676577i	0.0168179	+	0.00365851i
$343$	−0.194924	−	2.72540i	−0.0105249	−	0.147158i
$344$	−1.82628			−0.0984662
$345$		0			0
$346$	11.0157			0.592207
$347$	1.02315	+	14.3054i	0.0549253	+	0.767956i	0.948045	+	0.318137i	$0.103057\pi$
$347$	1.02315	+	14.3054i	0.0549253	+	0.767956i	−0.893120	+	0.449819i	$0.851488\pi$
$348$	9.23342	+	2.00861i	0.494963	+	0.107673i
$349$	26.0154	−	3.74046i	1.39257	−	0.200222i	0.595138	−	0.803624i	$-0.297098\pi$
$349$	26.0154	−	3.74046i	1.39257	−	0.200222i	0.797437	+	0.603402i	$0.206188\pi$
$350$		0			0
$351$	−0.106378	+	0.739879i	−0.00567806	+	0.0394918i
$352$	15.3696	+	8.39245i	0.819204	+	0.447319i
$353$	3.12048	+	14.3446i	0.166086	+	0.763486i	0.982536	+	0.186070i	$0.0595752\pi$
$353$	3.12048	+	14.3446i	0.166086	+	0.763486i	−0.816450	+	0.577416i	$0.804061\pi$
$354$	−8.76054	−	4.00080i	−0.465617	−	0.212640i
$355$		0			0
$356$	−9.42970	+	8.17088i	−0.499773	+	0.433056i
$357$	−0.293226	−	0.0209719i	−0.0155192	−	0.00110995i
$358$	−3.81111	−	6.97952i	−0.201423	−	0.368879i
$359$	−6.34071	+	13.8842i	−0.334650	+	0.732781i	−0.999904	−	0.0138356i	$-0.995596\pi$
$359$	−6.34071	+	13.8842i	−0.334650	+	0.732781i	0.665254	+	0.746617i	$0.268323\pi$
$360$		0			0
$361$	−36.3786	+	10.6817i	−1.91466	+	0.562196i
$362$	−13.2183	+	9.89507i	−0.694737	+	0.520073i
$363$	−0.879800	+	2.35883i	−0.0461775	+	0.123807i
$364$	−0.00633304	−	0.0440472i	−0.000331941	−	0.00230870i
$365$		0			0
$366$	−8.51242	−	7.37606i	−0.444951	−	0.385553i
$367$	−10.4062	−	10.4062i	−0.543199	−	0.543199i	0.381266	−	0.924465i	$-0.375488\pi$
$367$	−10.4062	−	10.4062i	−0.543199	−	0.543199i	−0.924465	+	0.381266i	$0.875488\pi$
$368$	−4.86149	−	6.82992i	−0.253423	−	0.356034i
$369$			0.622298i			0.0323955i
$370$		0			0
$371$	0.328285	−	0.210976i	0.0170437	−	0.0109533i
$372$	−0.735180	−	0.550349i	−0.0381173	−	0.0285343i
$373$	17.1142	+	6.38327i	0.886140	+	0.330513i	0.750991	−	0.660312i	$-0.229576\pi$
$373$	17.1142	+	6.38327i	0.886140	+	0.330513i	0.135149	+	0.990825i	$0.456849\pi$
$374$	−1.69980	−	0.244394i	−0.0878945	−	0.0126373i
$375$		0			0
$376$	12.2030	+	7.84240i	0.629322	+	0.404441i
$377$	−0.171745	−	0.460466i	−0.00884531	−	0.0237152i
$378$	0.572196	−	0.312443i	0.0294306	−	0.0160703i
$379$	2.12189	+	2.44879i	0.108994	+	0.125786i	0.807625	−	0.589696i	$-0.200752\pi$
$379$	2.12189	+	2.44879i	0.108994	+	0.125786i	−0.698631	+	0.715482i	$0.746207\pi$
$380$		0			0
$381$	36.0444	+	10.5836i	1.84661	+	0.542214i
$382$	−7.38729	+	2.75532i	−0.377967	+	0.140974i
$383$	−24.7699	+	5.38836i	−1.26568	+	0.275332i	−0.794804	−	0.606866i	$-0.792427\pi$
$383$	−24.7699	+	5.38836i	−1.26568	+	0.275332i	−0.470878	+	0.882198i	$0.656063\pi$
$384$	5.44326	+	18.5380i	0.277775	+	0.946016i
$385$		0			0
$386$	−2.98778	−	6.54233i	−0.152074	−	0.332996i
$387$	0.0319034	−	0.0426179i	0.00162174	−	0.00216639i
$388$	4.41831	−	20.3106i	0.224306	−	1.03112i
$389$	−8.46700	+	9.77144i	−0.429294	+	0.495432i	−0.928646	−	0.370968i	$-0.879026\pi$
$389$	−8.46700	+	9.77144i	−0.429294	+	0.495432i	0.499352	+	0.866399i	$0.333572\pi$
$390$		0			0
$391$	3.48283	+	2.35827i	0.176134	+	0.119263i
$392$	11.2331	−	11.2331i	0.567356	−	0.567356i
$393$	−31.4184	+	2.24709i	−1.58485	+	0.113351i
$394$	2.38118	+	3.70519i	0.119962	+	0.186665i
$395$		0			0
$396$	−0.298436	+	0.136291i	−0.0149970	+	0.00684889i
$397$	13.2178	+	17.6569i	0.663382	+	0.886174i	0.998429	−	0.0560269i	$-0.0178433\pi$
$397$	13.2178	+	17.6569i	0.663382	+	0.886174i	−0.335047	+	0.942201i	$0.608752\pi$
$398$	6.15806	−	11.2776i	0.308675	−	0.565297i
$399$	−1.36713	+	2.12730i	−0.0684423	+	0.106498i
$400$		0			0
$401$	6.39755	−	21.7880i	0.319478	−	1.08804i	−0.630620	−	0.776092i	$-0.717199\pi$
$401$	6.39755	−	21.7880i	0.319478	−	1.08804i	0.950098	−	0.311951i	$-0.100982\pi$
$402$	0.645597	−	9.02663i	0.0321995	−	0.450207i
$403$	−0.00340735	+	0.0476410i	−0.000169732	+	0.00237317i
$404$	5.00829	−	17.0567i	0.249172	−	0.848601i
$405$		0			0
$406$	−0.231737	+	0.360590i	−0.0115009	+	0.0178958i
$407$	−11.1153	+	20.3562i	−0.550967	+	1.00902i
$408$	−2.05417	−	2.74406i	−0.101697	−	0.135851i
$409$	9.91080	−	4.52611i	0.490058	−	0.223802i	−0.155031	−	0.987910i	$-0.549548\pi$
$409$	9.91080	−	4.52611i	0.490058	−	0.223802i	0.645089	+	0.764108i	$0.276820\pi$
$410$		0			0
$411$	6.96537	+	10.8383i	0.343576	+	0.534615i
$412$	−8.99600	+	0.643407i	−0.443201	+	0.0316984i
$413$	−1.22683	+	1.22683i	−0.0603684	+	0.0603684i
$414$	−0.202280	−	0.00485584i	−0.00994150	−	0.000238651i
$415$		0			0
$416$	0.528682	−	0.610131i	0.0259208	−	0.0299142i
$417$	6.03686	−	27.7510i	0.295626	−	1.35897i
$418$	−8.85239	+	11.8254i	−0.432985	+	0.578400i
$419$	−13.3850	−	29.3090i	−0.653898	−	1.43184i	−0.888101	−	0.459649i	$-0.847975\pi$
$419$	−13.3850	−	29.3090i	−0.653898	−	1.43184i	0.234203	−	0.972188i	$-0.424752\pi$
$420$		0			0
$421$	3.93444	+	13.3995i	0.191753	+	0.653050i	0.998100	+	0.0616082i	$0.0196229\pi$
$421$	3.93444	+	13.3995i	0.191753	+	0.653050i	−0.806348	+	0.591442i	$0.798559\pi$
$422$	3.19477	−	0.694979i	0.155519	−	0.0338310i
$423$	−0.396185	+	0.147770i	−0.0192632	+	0.00718480i
$424$	4.36582	+	1.28192i	0.212023	+	0.0622555i
$425$		0			0
$426$	4.78474	+	5.52188i	0.231821	+	0.267536i
$427$	−1.78092	+	0.972458i	−0.0861850	+	0.0470606i
$428$	−9.72540	−	26.0748i	−0.470095	−	1.26037i
$429$	−0.633043	−	0.406832i	−0.0305636	−	0.0196420i
$430$		0			0
$431$	2.74180	+	0.394211i	0.132068	+	0.0189885i	0.208032	−	0.978122i	$-0.433294\pi$
$431$	2.74180	+	0.394211i	0.132068	+	0.0189885i	−0.0759639	+	0.997111i	$0.524203\pi$
$432$	−8.60223	−	3.20847i	−0.413875	−	0.154367i
$433$	−9.75986	−	7.30614i	−0.469029	−	0.351111i	0.338473	−	0.940976i	$-0.390090\pi$
$433$	−9.75986	−	7.30614i	−0.469029	−	0.351111i	−0.807501	+	0.589866i	$0.799181\pi$
$434$	0.0350446	−	0.0225218i	0.00168219	−	0.00108108i
$435$		0			0
$436$			12.1556i			0.582149i
$437$	32.1619	−	16.5724i	1.53851	−	0.792766i
$438$	−5.18760	−	5.18760i	−0.247873	−	0.247873i
$439$	−16.0315	−	13.8914i	−0.765140	−	0.662998i	0.182187	−	0.983264i	$-0.441682\pi$
$439$	−16.0315	−	13.8914i	−0.765140	−	0.662998i	−0.947328	+	0.320266i	$0.896228\pi$
$440$		0			0
$441$	0.0659031	+	0.458366i	0.00313824	+	0.0218270i
$442$	−0.0276669	+	0.0741780i	−0.00131598	+	0.00352829i
$443$	−18.3197	+	13.7140i	−0.870397	+	0.651571i	−0.938187	−	0.346129i	$-0.887496\pi$
$443$	−18.3197	+	13.7140i	−0.870397	+	0.651571i	0.0677903	+	0.997700i	$0.478405\pi$
$444$	−19.7262	+	5.79213i	−0.936163	+	0.274882i
$445$		0			0
$446$	−3.23492	+	7.08348i	−0.153178	+	0.335412i
$447$	−10.4477	−	19.1336i	−0.494161	−	0.904987i
$448$	−0.0198706	−	0.00142117i	−0.000938798	−	6.71442e-5i
$449$	21.0185	−	18.2126i	0.991925	−	0.859508i	0.00184293	−	0.999998i	$-0.499413\pi$
$449$	21.0185	−	18.2126i	0.991925	−	0.859508i	0.990082	+	0.140490i	$0.0448679\pi$
$450$		0			0
$451$	−26.2707	−	11.9974i	−1.23704	−	0.564937i
$452$	−2.99195	−	13.7538i	−0.140729	−	0.646923i
$453$	1.54501	+	0.843637i	0.0725907	+	0.0396375i
$454$	0.465986	−	3.24100i	0.0218698	−	0.152108i
$455$		0			0
$456$	−29.1849	+	4.19615i	−1.36671	+	0.196503i
$457$	39.4237	+	8.57611i	1.84416	+	0.401173i	0.992431	−	0.122802i	$-0.0391881\pi$
$457$	39.4237	+	8.57611i	1.84416	+	0.401173i	0.851733	+	0.523976i	$0.175552\pi$
$458$	0.750651	+	10.4955i	0.0350756	+	0.490421i
$459$	4.60635			0.215006
$460$		0			0
$461$	9.74476			0.453859			0.226929	−	0.973911i	$-0.427131\pi$
$461$	9.74476			0.453859			0.226929	+	0.973911i	$0.427131\pi$
$462$	0.0468210	+	0.654643i	0.00217831	+	0.0304567i
$463$	−9.37152	−	2.03865i	−0.435531	−	0.0947440i	−0.0105462	−	0.999944i	$-0.503357\pi$
$463$	−9.37152	−	2.03865i	−0.435531	−	0.0947440i	−0.424985	+	0.905200i	$0.639721\pi$
$464$	5.97488	−	0.859058i	0.277377	−	0.0398808i
$465$		0			0
$466$	−0.838843	+	5.83428i	−0.0388586	+	0.270268i
$467$	5.69780	+	3.11123i	0.263663	+	0.143971i	0.605643	−	0.795736i	$-0.292916\pi$
$467$	5.69780	+	3.11123i	0.263663	+	0.143971i	−0.341981	+	0.939707i	$0.611098\pi$
$468$	0.00321511	+	0.0147796i	0.000148618	+	0.000683188i
$469$	−1.48297	−	0.677252i	−0.0684774	−	0.0312726i
$470$		0			0
$471$	−22.1526	+	19.1953i	−1.02074	+	0.884473i
$472$	−20.1786	−	1.44320i	−0.928795	−	0.0664287i
$473$	1.18407	+	2.16846i	0.0544436	+	0.0997061i
$474$	−1.68152	+	3.68202i	−0.0772348	+	0.169121i
$475$		0			0
$476$	−0.263122	+	0.0772595i	−0.0120602	+	0.00354118i
$477$	−0.106182	+	0.0794867i	−0.00486173	+	0.00363944i
$478$	−0.876207	+	2.34920i	−0.0400768	+	0.107450i
$479$	1.67535	+	11.6523i	0.0765487	+	0.532408i	0.991627	+	0.129132i	$0.0412192\pi$
$479$	1.67535	+	11.6523i	0.0765487	+	0.532408i	−0.915079	+	0.403275i	$0.867872\pi$
$480$		0			0
$481$	0.808086	+	0.700210i	0.0368455	+	0.0319268i
$482$	2.73995	+	2.73995i	0.124802	+	0.124802i
$483$	0.597753	−	1.49224i	0.0271987	−	0.0678995i
$484$			2.34847i			0.106749i
$485$		0			0
$486$	−0.368784	+	0.237003i	−0.0167284	+	0.0107507i
$487$	12.8124	+	9.59126i	0.580586	+	0.434621i	0.848782	−	0.528743i	$-0.177337\pi$
$487$	12.8124	+	9.59126i	0.580586	+	0.434621i	−0.268196	+	0.963364i	$0.586427\pi$
$488$	−22.1679	−	8.26821i	−1.00350	−	0.374284i
$489$	8.49142	+	1.22088i	0.383996	+	0.0552102i
$490$		0			0
$491$	−4.32259	−	2.77796i	−0.195076	−	0.125368i	0.439457	−	0.898264i	$-0.355171\pi$
$491$	−4.32259	−	2.77796i	−0.195076	−	0.125368i	−0.634533	+	0.772896i	$0.718807\pi$
$492$	−8.94640	−	23.9862i	−0.403335	−	1.08138i
$493$	−2.65809	+	1.45143i	−0.119714	+	0.0653690i
$494$	0.445964	+	0.514669i	0.0200648	+	0.0231561i
$495$		0			0
$496$	−0.562888	−	0.165279i	−0.0252744	−	0.00742123i
$497$	1.23328	−	0.459988i	0.0553200	−	0.0206333i
$498$	−9.19655	+	2.00059i	−0.412107	+	0.0896485i
$499$	−9.59724	−	32.6852i	−0.429631	−	1.46319i	−0.835618	−	0.549311i	$-0.814890\pi$
$499$	−9.59724	−	32.6852i	−0.429631	−	1.46319i	0.405986	−	0.913879i	$-0.366928\pi$
$500$		0			0
$501$	−5.82396	−	12.7527i	−0.260196	−	0.569749i
$502$	−2.15607	+	2.88017i	−0.0962300	+	0.128548i
$503$	−0.334058	+	1.53564i	−0.0148949	+	0.0684709i	−0.983994	−	0.178199i	$-0.942973\pi$
$503$	−0.334058	+	1.53564i	−0.0148949	+	0.0684709i	0.969099	+	0.246670i	$0.0793364\pi$
$504$	0.0194530	−	0.0224500i	0.000866506	−	0.00100000i
$505$		0			0
$506$	4.10479	−	8.44576i	0.182480	−	0.375460i
$507$	15.7196	−	15.7196i	0.698134	−	0.698134i
$508$	34.9537	−	2.49994i	1.55082	−	0.110917i
$509$	10.9905	+	17.1015i	0.487145	+	0.758012i	0.994613	−	0.103659i	$-0.0330549\pi$
$509$	10.9905	+	17.1015i	0.487145	+	0.758012i	−0.507468	+	0.861670i	$0.669419\pi$
$510$		0			0
$511$	−1.20221	+	0.549032i	−0.0531828	+	0.0242878i
$512$	10.7234	+	14.3248i	0.473911	+	0.633072i
$513$	18.9893	−	34.7764i	0.838399	−	1.53541i
$514$	−7.93239	+	12.3430i	−0.349883	+	0.544428i
$515$		0			0
$516$	−0.617011	+	2.10135i	−0.0271624	+	0.0925066i
$517$	1.39997	−	19.5741i	0.0615706	−	0.860869i
$518$	0.0665294	−	0.930202i	0.00292313	−	0.0408707i
$519$	8.38045	−	28.5412i	0.367861	−	1.25282i
$520$		0			0
$521$	19.6254	−	30.5377i	0.859804	−	1.33788i	−0.0802212	−	0.996777i	$-0.525563\pi$
$521$	19.6254	−	30.5377i	0.859804	−	1.33788i	0.940025	−	0.341104i	$-0.110801\pi$
$522$	0.0698215	−	0.127869i	0.00305600	−	0.00559666i
$523$	−1.45985	−	1.95013i	−0.0638346	−	0.0852730i	0.767488	−	0.641064i	$-0.221507\pi$
$523$	−1.45985	−	1.95013i	−0.0638346	−	0.0852730i	−0.831322	+	0.555791i	$0.812416\pi$
$524$	−26.7277	+	12.2061i	−1.16761	+	0.533228i
$525$		0			0
$526$	8.96968	+	13.9571i	0.391096	+	0.608558i
$527$	0.293585	−	0.0209976i	0.0127888	−	0.000914670i
$528$	6.53556	−	6.53556i	0.284424	−	0.284424i
$529$	−18.0849	+	14.2104i	−0.786302	+	0.617843i
$530$		0			0
$531$	0.386180	−	0.445676i	0.0167588	−	0.0193407i
$532$	−0.501417	+	2.30498i	−0.0217392	+	0.0999334i
$533$	−0.797907	+	1.06588i	−0.0345612	+	0.0461683i
$534$	−3.52428	−	7.71709i	−0.152510	−	0.333951i
$535$		0			0
$536$	−5.35555	−	18.2393i	−0.231325	−	0.787819i
$537$	−20.9831	+	4.56458i	−0.905486	+	0.196976i
$538$	−12.0285	+	4.48640i	−0.518585	+	0.193422i
$539$	−20.6208	−	6.05482i	−0.888201	−	0.260799i
$540$		0			0
$541$	23.9206	+	27.6058i	1.02843	+	1.18687i	0.982181	+	0.187937i	$0.0601800\pi$
$541$	23.9206	+	27.6058i	1.02843	+	1.18687i	0.0462450	+	0.998930i	$0.485275\pi$
$542$	−4.42208	+	2.41464i	−0.189945	+	0.103718i
$543$	15.5816	+	41.7759i	0.668671	+	1.79278i
$544$	−4.18529	−	2.68972i	−0.179443	−	0.115321i
$545$		0			0
$546$	0.0299493	+	0.00430606i	0.00128171	+	0.000184282i
$547$	−38.6516	−	14.4163i	−1.65262	−	0.616396i	−0.661571	−	0.749883i	$-0.730110\pi$
$547$	−38.6516	−	14.4163i	−1.65262	−	0.616396i	−0.991051	+	0.133487i	$0.957383\pi$
$548$	9.62107	+	7.20225i	0.410992	+	0.307665i
$549$	0.580200	−	0.372872i	0.0247624	−	0.0159138i
$550$		0			0
$551$			26.0511i			1.10981i
$552$	17.7140	−	6.12688i	0.753957	−	0.260777i
$553$	0.515632	+	0.515632i	0.0219269	+	0.0219269i
$554$	−1.64066	−	1.42164i	−0.0697050	−	0.0603997i
$555$		0			0
$556$	−3.77028	−	26.2229i	−0.159895	−	1.11210i
$557$	−4.73958	+	12.7073i	−0.200822	+	0.538426i	−0.997852	−	0.0655152i	$-0.979131\pi$
$557$	−4.73958	+	12.7073i	−0.200822	+	0.538426i	0.797029	+	0.603941i	$0.206404\pi$
$558$	−0.0113349	+	0.00848523i	−0.000479846	+	0.000359208i
$559$	0.109289	−	0.0320901i	0.00462243	−	0.00135727i
$560$		0			0
$561$	−1.92638	+	4.21818i	−0.0813318	+	0.178092i
$562$	0.0989391	+	0.181193i	0.00417349	+	0.00764318i
$563$	21.1473	+	1.51248i	0.891251	+	0.0637435i	0.509449	−	0.860501i	$-0.329849\pi$
$563$	21.1473	+	1.51248i	0.891251	+	0.0637435i	0.381802	+	0.924244i	$0.375304\pi$
$564$	13.1464	−	11.3914i	0.553564	−	0.479666i
$565$		0			0
$566$	−15.4822	−	7.07047i	−0.650764	−	0.297194i
$567$	−0.365913	−	1.68207i	−0.0153669	−	0.0706405i
$568$	13.4703	+	7.35537i	0.565203	+	0.308624i
$569$	0.120169	−	0.835792i	0.00503773	−	0.0350382i	−0.987148	−	0.159812i	$-0.948911\pi$
$569$	0.120169	−	0.835792i	0.00503773	−	0.0350382i	0.992185	+	0.124773i	$0.0398204\pi$
$570$		0			0
$571$	−25.5215	+	3.66943i	−1.06804	+	0.153561i	−0.653846	−	0.756628i	$-0.726846\pi$
$571$	−25.5215	+	3.66943i	−1.06804	+	0.153561i	−0.414194	+	0.910189i	$0.635937\pi$
$572$	−0.685916	−	0.149212i	−0.0286796	−	0.00623886i
$573$	1.51885	+	21.2363i	0.0634510	+	0.887161i
$574$	1.16126			0.0484701
$575$		0			0
$576$	0.00677112			0.000282130
$577$	−1.51556	−	21.1902i	−0.0630934	−	0.882161i	−0.926174	−	0.377096i	$-0.876923\pi$
$577$	−1.51556	−	21.1902i	−0.0630934	−	0.882161i	0.863081	−	0.505066i	$-0.168532\pi$
$578$	−10.0594	−	2.18829i	−0.418416	−	0.0910209i
$579$	−19.2239	+	2.76398i	−0.798919	+	0.114867i
$580$		0			0
$581$	−0.241296	+	1.67825i	−0.0100106	+	0.0696255i
$582$	12.4042	+	6.77319i	0.514170	+	0.280758i
$583$	−1.30848	−	6.01498i	−0.0541916	−	0.249115i
$584$	−14.0178	−	6.40173i	−0.580062	−	0.264905i
$585$		0			0
$586$	−4.17158	+	3.61470i	−0.172326	+	0.149322i
$587$	−1.93346	−	0.138284i	−0.0798026	−	0.00570759i	0.0313808	−	0.999508i	$-0.490010\pi$
$587$	−1.93346	−	0.138284i	−0.0798026	−	0.00570759i	−0.111183	+	0.993800i	$0.535464\pi$
$588$	−9.12987	−	16.7201i	−0.376509	−	0.689526i
$589$	1.05176	−	2.30303i	0.0433369	−	0.0948946i
$590$		0			0
$591$	11.4115	−	3.35073i	0.469408	−	0.137831i
$592$	−10.5137	+	7.87044i	−0.432109	+	0.323473i
$593$	−1.30615	+	3.50192i	−0.0536371	+	0.143807i	−0.961005	−	0.276530i	$-0.910815\pi$
$593$	−1.30615	+	3.50192i	−0.0536371	+	0.143807i	0.907368	+	0.420337i	$0.138088\pi$
$594$	−1.46355	−	10.1792i	−0.0600504	−	0.417660i
$595$		0			0
$596$	−15.3689	−	13.3172i	−0.629535	−	0.545495i
$597$	−24.5350	−	24.5350i	−1.00415	−	1.00415i
$598$	−0.340241	−	0.267679i	−0.0139135	−	0.0109462i
$599$		−	30.7152i		−	1.25499i	−0.778622	−	0.627494i	$-0.784081\pi$
$599$		−	30.7152i		−	1.25499i	0.778622	−	0.627494i	$-0.215919\pi$
$600$		0			0
$601$	−5.73269	+	3.68418i	−0.233841	+	0.150281i	−0.652314	−	0.757949i	$-0.726202\pi$
$601$	−5.73269	+	3.68418i	−0.233841	+	0.150281i	0.418473	+	0.908229i	$0.362565\pi$
$602$	−0.0795287	−	0.0595344i	−0.00324135	−	0.00242644i
$603$	0.519189	+	0.193648i	0.0211430	+	0.00788594i
$604$	1.62538	+	0.233695i	0.0661359	+	0.00950891i
$605$		0			0
$606$	10.1683	+	6.53476i	0.413058	+	0.265456i
$607$	−5.35178	−	14.3487i	−0.217222	−	0.582395i	0.781939	−	0.623355i	$-0.214231\pi$
$607$	−5.35178	−	14.3487i	−0.217222	−	0.582395i	−0.999161	+	0.0409605i	$0.986958\pi$
$608$	−37.5600	+	20.5093i	−1.52326	+	0.831763i
$609$	0.757974	+	0.874749i	0.0307147	+	0.0354466i
$610$		0			0
$611$	−0.868060	−	0.254885i	−0.0351180	−	0.0103116i
$612$	0.0873318	−	0.0325731i	0.00353018	−	0.00131669i
$613$	44.8300	−	9.75216i	1.81066	−	0.393886i	0.825348	−	0.564624i	$-0.190979\pi$
$613$	44.8300	−	9.75216i	1.81066	−	0.393886i	0.985316	+	0.170738i	$0.0546152\pi$
$614$	3.88441	+	13.2291i	0.156762	+	0.533882i
$615$		0			0
$616$	0.572702	+	1.25404i	0.0230748	+	0.0505268i
$617$	−16.2881	+	21.7584i	−0.655736	+	0.875961i	−0.997972	−	0.0636532i	$-0.979725\pi$
$617$	−16.2881	+	21.7584i	−0.655736	+	0.875961i	0.342236	+	0.939614i	$0.388816\pi$
$618$	1.30352	−	5.99219i	0.0524353	−	0.241041i
$619$	−6.85826	+	7.91486i	−0.275657	+	0.318125i	−0.876650	−	0.481130i	$-0.840227\pi$
$619$	−6.85826	+	7.91486i	−0.275657	+	0.318125i	0.600993	+	0.799255i	$0.294772\pi$
$620$		0			0
$621$	−7.67436	+	23.9909i	−0.307961	+	0.962720i
$622$	−7.56645	+	7.56645i	−0.303387	+	0.303387i
$623$	−1.52446	+	0.109031i	−0.0610760	+	0.00436824i
$624$	−0.230369	−	0.358462i	−0.00922215	−	0.0143499i
$625$		0			0
$626$	−14.5553	+	6.64719i	−0.581747	+	0.265675i
$627$	23.9045	+	31.9327i	0.954653	+	1.27527i
$628$	−13.1042	+	23.9986i	−0.522916	+	0.957649i
$629$	3.56239	−	5.54318i	0.142042	−	0.221021i
$630$		0			0
$631$	1.07019	−	3.64475i	0.0426037	−	0.145095i	−0.935445	−	0.353474i	$-0.885000\pi$
$631$	1.07019	−	3.64475i	0.0426037	−	0.145095i	0.978048	+	0.208379i	$0.0668186\pi$
$632$	−0.606571	+	8.48098i	−0.0241281	+	0.337355i
$633$	0.629834	−	8.80623i	0.0250337	−	0.350016i
$634$	4.37944	−	14.9150i	0.173930	−	0.592350i
$635$		0			0
$636$	2.95000	−	4.59029i	0.116975	−	0.182017i
$637$	−0.474835	+	0.869596i	−0.0188137	+	0.0344546i
$638$	4.05195	+	5.41277i	0.160418	+	0.214294i
$639$	−0.406959	+	0.185852i	−0.0160991	+	0.00735220i
$640$		0			0
$641$	−6.36323	−	9.90138i	−0.251333	−	0.391081i	0.692546	−	0.721374i	$-0.256489\pi$
$641$	−6.36323	−	9.90138i	−0.251333	−	0.391081i	−0.943879	+	0.330293i	$0.892853\pi$
$642$	18.8741	−	1.34990i	0.744900	−	0.0532763i
$643$	−12.7726	+	12.7726i	−0.503701	+	0.503701i	−0.912586	−	0.408885i	$-0.865918\pi$
$643$	−12.7726	+	12.7726i	−0.503701	+	0.503701i	0.408885	+	0.912586i	$0.365918\pi$
$644$	0.0359870	−	1.49911i	0.00141809	−	0.0590733i
$645$		0			0
$646$	2.74823	−	3.17162i	0.108127	−	0.124786i
$647$	5.54103	−	25.4717i	0.217840	−	1.00140i	−0.730197	−	0.683237i	$-0.760572\pi$
$647$	5.54103	−	25.4717i	0.217840	−	1.00140i	0.948037	−	0.318160i	$-0.103065\pi$
$648$	12.0285	−	16.0682i	0.472525	−	0.631220i
$649$	11.3692	+	24.8952i	0.446282	+	0.977220i
$650$		0			0
$651$	−0.0316920	−	0.107933i	−0.00124211	−	0.00423023i
$652$	7.81966	−	1.70106i	0.306242	−	0.0666188i
$653$	−29.1500	+	10.8724i	−1.14073	+	0.425469i	−0.847617	−	0.530609i	$-0.821963\pi$
$653$	−29.1500	+	10.8724i	−1.14073	+	0.425469i	−0.293111	+	0.956079i	$0.594690\pi$
$654$	−7.93027	−	2.32854i	−0.310098	−	0.0910530i
$655$		0			0
$656$	−10.7094	−	12.3593i	−0.418131	−	0.482549i
$657$	0.394269	−	0.215287i	0.0153819	−	0.00839916i
$658$	0.275751	+	0.739316i	0.0107499	+	0.0288215i
$659$	0.0162657	+	0.0104533i	0.000633622	+	0.000407204i	0.540958	−	0.841050i	$-0.318062\pi$
$659$	0.0162657	+	0.0104533i	0.000633622	+	0.000407204i	−0.540324	+	0.841457i	$0.681698\pi$
$660$		0			0
$661$	35.4326	+	5.09444i	1.37817	+	0.198151i	0.791248	−	0.611495i	$-0.209432\pi$
$661$	35.4326	+	5.09444i	1.37817	+	0.198151i	0.586919	+	0.809646i	$0.300341\pi$
$662$	0.518924	+	0.193549i	0.0201686	+	0.00752249i
$663$	0.171144	+	0.128117i	0.00664667	+	0.00497564i
$664$	−16.6313	+	10.6883i	−0.645419	+	0.414786i
$665$		0			0
$666$			0.316976i			0.0122826i
$667$	−3.13086	−	16.2621i	−0.121228	−	0.629669i
$668$	−9.24754	−	9.24754i	−0.357798	−	0.357798i
$669$	15.8920	+	13.7705i	0.614419	+	0.532397i
$670$		0			0
$671$	4.55522	+	31.6823i	0.175852	+	1.22308i
$672$	−0.664466	+	1.78150i	−0.0256323	+	0.0687229i
$673$	20.0631	−	15.0190i	0.773374	−	0.578940i	−0.138042	−	0.990426i	$-0.544081\pi$
$673$	20.0631	−	15.0190i	0.773374	−	0.578940i	0.911416	+	0.411486i	$0.134990\pi$
$674$	3.92499	−	1.15248i	0.151185	−	0.0443919i
$675$		0			0
$676$	8.61479	−	18.8638i	0.331338	−	0.725529i
$677$	16.1282	+	29.5365i	0.619856	+	1.13518i	0.979376	+	0.202044i	$0.0647583\pi$
$677$	16.1282	+	29.5365i	0.619856	+	1.13518i	−0.359521	+	0.933137i	$0.617060\pi$
$678$	9.54602	+	0.682745i	0.366613	+	0.0262207i
$679$	1.92418	−	1.66731i	0.0738431	−	0.0639854i
$680$		0			0
$681$	−8.04279	−	3.67302i	−0.308201	−	0.140750i
$682$	−0.139681	−	0.642101i	−0.00534865	−	0.0245873i
$683$	−17.8768	−	9.76146i	−0.684036	−	0.373512i	0.0993455	−	0.995053i	$-0.468325\pi$
$683$	−17.8768	−	9.76146i	−0.684036	−	0.373512i	−0.783382	+	0.621541i	$0.786507\pi$
$684$	0.114103	−	0.793606i	0.00436285	−	0.0303443i
$685$		0			0
$686$	1.71541	−	0.246638i	0.0654946	−	0.00941670i
$687$	27.7644	+	6.03978i	1.05928	+	0.230432i
$688$	0.0998053	+	1.39546i	0.00380504	+	0.0532014i
$689$	−0.283787			−0.0108114
$690$		0			0
$691$	−9.06622			−0.344895			−0.172448	−	0.985019i	$-0.555168\pi$
$691$	−9.06622			−0.344895			−0.172448	+	0.985019i	$0.555168\pi$
$692$	−1.97953	−	27.6775i	−0.0752506	−	1.05214i
$693$	−0.0392689	−	0.00854242i	−0.00149170	−	0.000324500i
$694$	−9.00407	+	1.29459i	−0.341790	+	0.0491420i
$695$		0			0
$696$	−1.92068	+	13.3586i	−0.0728032	+	0.506357i
$697$	7.20133	+	3.93222i	0.272770	+	0.148944i
$698$	3.54356	+	16.2895i	0.134126	+	0.616566i
$699$	14.4782	+	6.61198i	0.547616	+	0.250088i
$700$		0			0
$701$	−2.88463	+	2.49955i	−0.108951	+	0.0944066i	−0.707633	−	0.706580i	$-0.750237\pi$
$701$	−2.88463	+	2.49955i	−0.108951	+	0.0944066i	0.598682	+	0.800987i	$0.295691\pi$
$702$	−0.472899	−	0.0338224i	−0.0178484	−	0.00127654i
$703$	−27.1635	−	49.7462i	−1.02449	−	1.87621i
$704$	−0.130542	+	0.285847i	−0.00491999	+	0.0107733i
$705$		0			0
$706$	−8.93395	+	2.62324i	−0.336234	+	0.0987271i
$707$	1.74317	−	1.30492i	0.0655585	−	0.0490765i
$708$	−8.47796	+	22.7303i	−0.318621	+	0.854256i
$709$	−0.496317	−	3.45196i	−0.0186396	−	0.129641i	0.978377	−	0.206830i	$-0.0663147\pi$
$709$	−0.496317	−	3.45196i	−0.0186396	−	0.129641i	−0.997016	+	0.0771888i	$0.975406\pi$
$710$		0			0
$711$	−0.187316	−	0.162310i	−0.00702488	−	0.00608710i
$712$	−12.6011	−	12.6011i	−0.472244	−	0.472244i
$713$	−0.379764	+	1.56404i	−0.0142223	+	0.0585736i
$714$		−	0.186459i		−	0.00697805i
$715$		0			0
$716$	−16.8516	+	10.8298i	−0.629773	+	0.404730i
$717$	5.42009	+	4.05743i	0.202417	+	0.151528i
$718$	−9.07079	−	3.38323i	−0.338519	−	0.126261i
$719$	−1.41127	−	0.202910i	−0.0526314	−	0.00756725i	0.115949	−	0.993255i	$-0.463009\pi$
$719$	−1.41127	−	0.202910i	−0.0526314	−	0.00756725i	−0.168580	+	0.985688i	$0.553918\pi$
$720$		0			0
$721$	−0.929367	−	0.597268i	−0.0346114	−	0.0222434i
$722$	−8.40388	−	22.5317i	−0.312760	−	0.838542i
$723$	9.18360	−	5.01462i	0.341542	−	0.186496i
$724$	27.2372	+	31.4335i	1.01226	+	1.16822i
$725$		0			0
$726$	−1.53213	−	0.449874i	−0.0568627	−	0.0166964i
$727$	−6.16192	+	2.29828i	−0.228533	+	0.0852384i	−0.461122	−	0.887337i	$-0.652553\pi$
$727$	−6.16192	+	2.29828i	−0.228533	+	0.0852384i	0.232589	+	0.972575i	$0.425280\pi$
$728$	0.0621046	−	0.0135100i	0.00230175	−	0.000500715i
$729$	7.76788	+	26.4550i	0.287699	+	0.979814i
$730$		0			0
$731$	−0.291588	−	0.638488i	−0.0107848	−	0.0236153i
$732$	−17.0030	+	22.7134i	−0.628451	+	0.839512i
$733$	2.58919	−	11.9023i	0.0956338	−	0.439621i	−0.904286	−	0.426928i	$-0.859596\pi$
$733$	2.58919	−	11.9023i	0.0956338	−	0.439621i	0.999919	−	0.0126935i	$-0.00404057\pi$
$734$	6.11264	−	7.05436i	0.225622	−	0.260381i
$735$		0			0
$736$	20.9815	−	17.3167i	0.773389	−	0.638302i
$737$	−18.1845	+	18.1845i	−0.669836	+	0.669836i
$738$	−0.393698	+	0.0281578i	−0.0144922	+	0.00103650i
$739$	7.74807	+	12.0562i	0.285017	+	0.443496i	0.954011	−	0.299773i	$-0.0969108\pi$
$739$	7.74807	+	12.0562i	0.285017	+	0.443496i	−0.668993	+	0.743269i	$0.733274\pi$
$740$		0			0
$741$	1.67276	−	0.763926i	0.0614506	−	0.0280635i
$742$	0.148329	+	0.198144i	0.00544533	+	0.00727410i
$743$	9.02949	−	16.5363i	0.331260	−	0.606657i	−0.657967	−	0.753047i	$-0.728583\pi$
$743$	9.02949	−	16.5363i	0.331260	−	0.606657i	0.989227	+	0.146389i	$0.0467652\pi$
$744$	0.709122	−	1.10342i	0.0259977	−	0.0404532i
$745$		0			0
$746$	−3.26400	+	11.1162i	−0.119504	+	0.406992i
$747$	0.0411121	−	0.574822i	0.00150421	−	0.0210316i
$748$	−0.308597	+	4.31476i	−0.0112834	+	0.157763i
$749$	0.960384	−	3.27077i	0.0350917	−	0.119511i
$750$		0			0
$751$	15.9579	−	24.8310i	0.582313	−	0.906096i	−0.417684	−	0.908592i	$-0.637158\pi$
$751$	15.9579	−	24.8310i	0.582313	−	0.906096i	0.999997	+	0.00249615i	$0.000794549\pi$
$752$	5.32550	−	9.75293i	0.194201	−	0.355653i
$753$	5.82212	+	7.77744i	0.212170	+	0.283426i
$754$	0.283543	−	0.129490i	0.0103260	−	0.00471575i
$755$		0			0
$756$	−0.887854	−	1.38153i	−0.0322909	−	0.0502457i
$757$	21.7294	−	1.55412i	0.789770	−	0.0564854i	0.329374	−	0.944199i	$-0.393162\pi$
$757$	21.7294	−	1.55412i	0.789770	−	0.0564854i	0.460395	+	0.887714i	$0.347708\pi$
$758$	−1.45322	+	1.45322i	−0.0527834	+	0.0527834i
$759$	−18.7598	−	17.0607i	−0.680937	−	0.619263i
$760$		0			0
$761$	−12.8439	+	14.8227i	−0.465593	+	0.537323i	−0.939180	−	0.343424i	$-0.888413\pi$
$761$	−12.8439	+	14.8227i	−0.465593	+	0.537323i	0.473588	+	0.880747i	$0.342959\pi$
$762$	−5.06479	+	23.2825i	−0.183478	+	0.843435i
$763$	−0.892296	+	1.19197i	−0.0323033	+	0.0431521i
$764$	8.25039	+	18.0658i	0.298488	+	0.653599i
$765$		0			0
$766$	−4.52975	−	15.4269i	−0.163667	−	0.557397i
$767$	1.23290	−	0.268200i	0.0445173	−	0.00968415i
$768$	−11.8085	+	4.40436i	−0.426104	+	0.158929i
$769$	−0.293488	−	0.0861757i	−0.0105834	−	0.00310758i	0.276437	−	0.961032i	$-0.410846\pi$
$769$	−0.293488	−	0.0861757i	−0.0105834	−	0.00310758i	−0.287020	+	0.957925i	$0.592665\pi$
$770$		0			0
$771$	25.9456	+	29.9428i	0.934407	+	1.07836i
$772$	−15.9010	+	8.68263i	−0.572291	+	0.312495i
$773$	7.03246	+	18.8547i	0.252940	+	0.678158i	0.999912	+	0.0133021i	$0.00423432\pi$
$773$	7.03246	+	18.8547i	0.252940	+	0.678158i	−0.746972	+	0.664856i	$0.768493\pi$
$774$	0.0284059	+	0.0182554i	0.00102103	+	0.000656175i
$775$		0			0
$776$	29.3848	+	4.22490i	1.05485	+	0.151665i
$777$	−2.35950	−	0.880049i	−0.0846467	−	0.0315716i
$778$	−6.56504	−	4.91453i	−0.235368	−	0.176194i
$779$	59.3739	−	38.1573i	2.12729	−	1.36713i
$780$		0			0
$781$		−	20.7632i		−	0.742964i
$782$	−1.33437	+	2.31013i	−0.0477171	+	0.0826101i
$783$	−12.8244	−	12.8244i	−0.458306	−	0.458306i
$784$	−9.19710	−	7.96933i	−0.328468	−	0.284619i
$785$		0			0
$786$	−2.84325	−	19.7752i	−0.101415	−	0.705359i
$787$	−7.36810	+	19.7546i	−0.262644	+	0.704177i	0.736957	+	0.675940i	$0.236262\pi$
$787$	−7.36810	+	19.7546i	−0.262644	+	0.704177i	−0.999601	+	0.0282370i	$0.991011\pi$
$788$	8.88159	−	6.64868i	0.316394	−	0.236849i
$789$	42.9861	−	12.6219i	1.53035	−	0.449351i
$790$		0			0
$791$	0.716221	−	1.56830i	0.0254659	−	0.0557625i
$792$	−0.224568	−	0.411266i	−0.00797969	−	0.0146137i
$793$	1.47187	+	0.105270i	0.0522676	+	0.00373825i
$794$	−10.5726	+	9.16121i	−0.375207	+	0.325119i
$795$		0			0
$796$	−29.4423	−	13.4458i	−1.04355	−	0.476575i
$797$	−4.78441	−	21.9936i	−0.169472	−	0.779052i	−0.980887	−	0.194580i	$-0.937666\pi$
$797$	−4.78441	−	21.9936i	−0.169472	−	0.779052i	0.811414	−	0.584471i	$-0.198698\pi$
$798$	−1.40770	−	0.768663i	−0.0498321	−	0.0272104i
$799$	−0.793435	+	5.51846i	−0.0280697	+	0.195229i
$800$		0			0
$801$	0.514187	−	0.0739289i	0.0181679	−	0.00261215i
$802$	14.0737	+	3.06155i	0.496961	+	0.108107i
$803$	1.48728	+	20.7949i	0.0524850	+	0.733837i
$804$	−22.7959			−0.803949
$805$		0			0
$806$	−0.0302943			−0.00106707
$807$	2.47310	+	34.5785i	0.0870573	+	1.21722i
$808$	24.8093	+	5.39693i	0.872788	+	0.189863i
$809$	−36.4611	+	5.24231i	−1.28190	+	0.184310i	−0.749400	−	0.662118i	$-0.769658\pi$
$809$	−36.4611	+	5.24231i	−1.28190	+	0.184310i	−0.532504	+	0.846428i	$0.678749\pi$
$810$		0			0
$811$	2.23766	−	15.5633i	0.0785750	−	0.546501i	−0.912070	−	0.410035i	$-0.865516\pi$
$811$	2.23766	−	15.5633i	0.0785750	−	0.546501i	0.990645	−	0.136466i	$-0.0435744\pi$
$812$	0.947645	+	0.517454i	0.0332558	+	0.0181591i
$813$	2.89203	+	13.2944i	0.101428	+	0.466256i
$814$	−13.3814	−	6.11106i	−0.469017	−	0.214193i
$815$		0			0
$816$	−1.98448	+	1.71956i	−0.0694707	+	0.0601967i
$817$	−6.02242	−	0.430732i	−0.210698	−	0.0150694i
$818$	3.31190	+	6.06529i	0.115798	+	0.212068i
$819$	−0.000769641		0.00168528i	−2.68934e−5		5.88884e-5i
$820$		0			0
$821$	18.5294	−	5.44073i	0.646682	−	0.189883i	0.0580876	−	0.998311i	$-0.481500\pi$
$821$	18.5294	−	5.44073i	0.646682	−	0.189883i	0.588594	+	0.808429i	$0.299682\pi$
$822$	−6.54172	+	4.89707i	−0.228169	+	0.170805i
$823$	5.33967	−	14.3162i	0.186129	−	0.499032i	−0.810050	−	0.586360i	$-0.800560\pi$
$823$	5.33967	−	14.3162i	0.186129	−	0.499032i	0.996180	+	0.0873287i	$0.0278330\pi$
$824$	−1.83320	−	12.7502i	−0.0638625	−	0.444173i
$825$		0			0
$826$	−0.831669	−	0.720645i	−0.0289375	−	0.0250745i
$827$	−15.0227	−	15.0227i	−0.522391	−	0.522391i	0.395902	−	0.918293i	$-0.370432\pi$
$827$	−15.0227	−	15.0227i	−0.522391	−	0.522391i	−0.918293	+	0.395902i	$0.870432\pi$
$828$	0.0241494	+	0.509111i	0.000839249	+	0.0176928i
$829$		−	37.7158i		−	1.30992i	−0.755661	−	0.654962i	$-0.772684\pi$
$829$		−	37.7158i		−	1.30992i	0.755661	−	0.654962i	$-0.227316\pi$
$830$		0			0
$831$	−4.93159	+	3.16934i	−0.171075	+	0.109943i
$832$	0.0115977	+	0.00868189i	0.000402076	+	0.000300991i
$833$	5.72072	+	2.13372i	0.198211	+	0.0739290i
$834$	17.8299	+	2.56355i	0.617398	+	0.0887685i
$835$		0			0
$836$	31.3028	+	20.1171i	1.08263	+	0.695764i
$837$	0.615974	+	1.65149i	0.0212912	+	0.0570838i
$838$	17.9367	−	9.79420i	0.619614	−	0.338335i
$839$	15.5246	+	17.9164i	0.535970	+	0.618543i	0.957556	−	0.288246i	$-0.0930720\pi$
$839$	15.5246	+	17.9164i	0.535970	+	0.618543i	−0.421586	+	0.906788i	$0.638527\pi$
$840$		0			0
$841$	−16.3841	−	4.81081i	−0.564969	−	0.165890i
$842$	−8.29918	+	3.09543i	−0.286008	+	0.106676i
$843$	0.544735	−	0.118500i	0.0187617	−	0.00408135i
$844$	−2.32028	−	7.90214i	−0.0798672	−	0.272003i
$845$		0			0
$846$	−0.111413	−	0.243961i	−0.00383047	−	0.00838756i
$847$	−0.172392	+	0.230289i	−0.00592346	+	0.00791281i
$848$	0.740927	−	3.40599i	0.0254435	−	0.116962i
$849$	−30.0977	+	34.7346i	−1.03295	+	1.19209i
$850$		0			0
$851$	22.9350	+	27.7889i	0.786203	+	0.952590i
$852$	13.0142	−	13.0142i	0.445859	−	0.445859i
$853$	−2.98919	+	0.213791i	−0.102348	+	0.00732006i	−0.122419	−	0.992478i	$-0.539065\pi$
$853$	−2.98919	+	0.213791i	−0.102348	+	0.00732006i	0.0200713	+	0.999799i	$0.493611\pi$
$854$	−0.695811	−	1.08270i	−0.0238102	−	0.0370494i
$855$		0			0
$856$	36.1554	−	16.5116i	1.23576	−	0.564355i
$857$	31.6373	+	42.2625i	1.08071	+	1.44366i	0.886517	+	0.462696i	$0.153118\pi$
$857$	31.6373	+	42.2625i	1.08071	+	1.44366i	0.194193	+	0.980963i	$0.437791\pi$
$858$	0.228739	−	0.418905i	0.00780903	−	0.0143012i
$859$	−28.8098	+	44.8289i	−0.982977	+	1.52954i	−0.141014	+	0.990008i	$0.545036\pi$
$859$	−28.8098	+	44.8289i	−0.982977	+	1.52954i	−0.841963	+	0.539535i	$0.818600\pi$
$860$		0			0
$861$	0.883458	−	3.00878i	0.0301082	−	0.102539i
$862$	−0.125337	+	1.75244i	−0.00426900	+	0.0596884i
$863$	3.32241	−	46.4534i	0.113096	−	1.58129i	−0.551555	−	0.834139i	$-0.685965\pi$
$863$	3.32241	−	46.4534i	0.113096	−	1.58129i	0.664651	−	0.747154i	$-0.268580\pi$
$864$	8.39370	−	28.5863i	0.285559	−	0.972526i
$865$		0			0
$866$	4.18063	−	6.50518i	0.142064	−	0.221055i
$867$	−13.3227	+	24.3987i	−0.452463	+	0.828625i
$868$	−0.0628848	−	0.0840043i	−0.00213445	−	0.00285129i
$869$	10.4633	−	4.77844i	0.354944	−	0.162097i
$870$		0			0
$871$	0.640979	+	0.997383i	0.0217188	+	0.0337950i
$872$	−17.3170	+	1.23853i	−0.586426	+	0.0419420i
$873$	−0.611918	+	0.611918i	−0.0207103	+	0.0207103i
$874$	11.9398	+	19.5974i	0.403871	+	0.662892i
$875$		0			0
$876$	−12.1019	+	13.9663i	−0.408885	+	0.471879i
$877$	−7.42725	+	34.1425i	−0.250801	+	1.15291i	0.663596	+	0.748091i	$0.269030\pi$
$877$	−7.42725	+	34.1425i	−0.250801	+	1.15291i	−0.914396	+	0.404820i	$0.867334\pi$
$878$	8.06300	−	10.7709i	0.272113	−	0.363500i
$879$	6.19190	+	13.5584i	0.208848	+	0.457312i
$880$		0			0
$881$	2.81610	+	9.59077i	0.0948769	+	0.323121i	0.993232	−	0.116149i	$-0.0370551\pi$
$881$	2.81610	+	9.59077i	0.0948769	+	0.323121i	−0.898355	+	0.439271i	$0.855237\pi$
$882$	−0.287004	+	0.0624340i	−0.00966394	+	0.00210226i
$883$	−19.9409	+	7.43756i	−0.671064	+	0.250294i	−0.661819	−	0.749664i	$-0.730215\pi$
$883$	−19.9409	+	7.43756i	−0.671064	+	0.250294i	−0.00924435	+	0.999957i	$0.502943\pi$
$884$	0.191348	+	0.0561848i	0.00643573	+	0.00188970i
$885$		0			0
$886$	−9.50511	−	10.9695i	−0.319331	−	0.368527i
$887$	15.3253	−	8.36823i	0.514572	−	0.280978i	−0.200909	−	0.979610i	$-0.564390\pi$
$887$	15.3253	−	8.36823i	0.514572	−	0.280978i	0.715481	+	0.698632i	$0.246208\pi$
$888$	−10.2614	−	27.5118i	−0.344349	−	0.923236i
$889$	3.61103	+	2.32067i	0.121110	+	0.0778327i
$890$		0			0
$891$	−26.8777	−	3.86443i	−0.900436	−	0.129463i
$892$	18.3789	+	6.85499i	0.615372	+	0.229522i
$893$	38.3916	+	28.7396i	1.28473	+	0.961734i
$894$	11.6322	−	7.47554i	0.389038	−	0.250019i
$895$		0			0
$896$			2.20765i			0.0737523i
$897$	−0.952392	+	0.677907i	−0.0317994	+	0.0226346i
$898$	12.4733	+	12.4733i	0.416240	+	0.416240i
$899$	−0.875820	−	0.758902i	−0.0292102	−	0.0253108i
$900$		0			0
$901$	0.248883	+	1.73102i	0.00829149	+	0.0576686i
$902$	6.40150	−	17.1631i	0.213147	−	0.571469i
$903$	−0.214755	+	0.160763i	−0.00714659	+	0.00534987i
$904$	19.2888	−	5.66371i	0.641537	−	0.188372i
$905$		0			0
$906$	−0.463820	+	1.01562i	−0.0154094	+	0.0337419i
$907$	−21.4410	−	39.2663i	−0.711938	−	1.30382i	−0.943622	−	0.331026i	$-0.892605\pi$
$907$	−21.4410	−	39.2663i	−0.711938	−	1.30382i	0.231683	−	0.972791i	$-0.425577\pi$
$908$	−8.22693	−	0.588402i	−0.273020	−	0.0195268i
$909$	−0.559338	+	0.484669i	−0.0185521	+	0.0160755i
$910$		0			0
$911$	−22.6399	−	10.3393i	−0.750095	−	0.342557i	0.00341443	−	0.999994i	$-0.498913\pi$
$911$	−22.6399	−	10.3393i	−0.750095	−	0.342557i	−0.753509	+	0.657437i	$0.771640\pi$
$912$	4.80123	+	22.0709i	0.158985	+	0.730841i
$913$	23.4739	+	12.8177i	0.776872	+	0.424204i
$914$	−3.64184	+	25.3296i	−0.120461	+	0.837827i
$915$		0			0
$916$	26.2355	−	3.77210i	0.866847	−	0.124634i
$917$	−3.51689	−	0.765053i	−0.116138	−	0.0252643i
$918$	0.208429	+	2.91421i	0.00687917	+	0.0961834i
$919$	−24.9235			−0.822150			−0.411075	−	0.911602i	$-0.634847\pi$
$919$	−24.9235			−0.822150			−0.411075	+	0.911602i	$0.634847\pi$
$920$		0			0
$921$	37.2311			1.22681
$922$	0.440932	+	6.16504i	0.0145213	+	0.203035i
$923$	−0.935343	−	0.203471i	−0.0307872	−	0.00669734i
$924$	1.63641	−	0.235281i	0.0538340	−	0.00774016i
$925$		0			0
$926$	0.865711	−	6.02115i	0.0284490	−	0.197867i
$927$	0.329562	+	0.179955i	0.0108242	+	0.00591048i
$928$	4.16376	+	19.1405i	0.136682	+	0.628318i
$929$	−0.933878	−	0.426488i	−0.0306395	−	0.0139926i	0.400036	−	0.916499i	$-0.368998\pi$
$929$	−0.933878	−	0.426488i	−0.0306395	−	0.0139926i	−0.430676	+	0.902507i	$0.641725\pi$
$930$		0			0
$931$	39.6921	−	34.3934i	1.30086	−	1.12720i
$932$	14.8097	+	1.05921i	0.485107	+	0.0346956i
$933$	13.8480	+	25.3607i	0.453363	+	0.830273i
$934$	−1.71051	+	3.74550i	−0.0559697	+	0.122557i
$935$		0			0
$936$	−0.0207275	+	0.00608614i	−0.000677500	+	0.000198932i
$937$	−7.34182	+	5.49602i	−0.239847	+	0.179547i	−0.712439	−	0.701734i	$-0.752409\pi$
$937$	−7.34182	+	5.49602i	−0.239847	+	0.179547i	0.472592	+	0.881281i	$0.343318\pi$
$938$	0.361363	−	0.968851i	0.0117989	−	0.0316341i
$939$	6.14929	+	42.7692i	0.200674	+	1.39572i
$940$		0			0
$941$	−11.2095	−	9.71311i	−0.365420	−	0.316638i	0.452725	−	0.891650i	$-0.350452\pi$
$941$	−11.2095	−	9.71311i	−0.365420	−	0.316638i	−0.818145	+	0.575012i	$0.804997\pi$
$942$	−13.1463	−	13.1463i	−0.428330	−	0.428330i
$943$	−32.4776	+	30.9549i	−1.05762	+	1.00803i
$944$			15.4974i			0.504397i
$945$		0			0
$946$	−1.31831	+	0.847224i	−0.0428618	+	0.0275456i
$947$	−3.87889	−	2.90370i	−0.126047	−	0.0943577i	0.534394	−	0.845235i	$-0.320540\pi$
$947$	−3.87889	−	2.90370i	−0.126047	−	0.0943577i	−0.660441	+	0.750878i	$0.729631\pi$
$948$	9.55344	+	3.56325i	0.310281	+	0.115729i
$949$	0.951349	+	0.136783i	0.0308821	+	0.00444017i
$950$		0			0
$951$	−35.3124	−	22.6939i	−1.14508	−	0.735900i
$952$	−0.136874	−	0.366972i	−0.00443610	−	0.0118936i
$953$	22.1425	−	12.0907i	0.717267	−	0.391658i	−0.0787799	−	0.996892i	$-0.525102\pi$
$953$	22.1425	−	12.0907i	0.717267	−	0.391658i	0.796047	+	0.605234i	$0.206921\pi$
$954$	−0.0550919	−	0.0635795i	−0.00178367	−	0.00205846i
$955$		0			0
$956$	6.05996	+	1.77936i	0.195993	+	0.0575487i
$957$	17.1069	−	6.38054i	0.552987	−	0.206254i
$958$	−7.29605	+	1.58716i	−0.235725	+	0.0512788i
$959$	0.414744	+	1.41249i	0.0133928	+	0.0456116i
$960$		0			0
$961$	−12.8311	−	28.0961i	−0.413906	−	0.906327i
$962$	−0.406425	+	0.542920i	−0.0131037	+	0.0175045i
$963$	−0.246287	+	1.13216i	−0.00793649	+	0.0364834i
$964$	6.39191	−	7.37666i	0.205870	−	0.237586i
$965$		0			0
$966$	0.971119	+	0.310648i	0.0312452	+	0.00999494i
$967$	31.6406	−	31.6406i	1.01749	−	1.01749i	0.0176482	−	0.999844i	$-0.494382\pi$
$967$	31.6406	−	31.6406i	1.01749	−	1.01749i	0.999844	−	0.0176482i	$-0.00561789\pi$
$968$	−3.34565	+	0.239285i	−0.107533	+	0.00769092i
$969$	−6.12676	−	9.53343i	−0.196820	−	0.306258i
$970$		0			0
$971$	3.89604	−	1.77926i	0.125030	−	0.0570993i	−0.351918	−	0.936031i	$-0.614470\pi$
$971$	3.89604	−	1.77926i	0.125030	−	0.0570993i	0.476948	+	0.878932i	$0.341743\pi$
$972$	0.661753	+	0.883999i	0.0212257	+	0.0283543i
$973$	1.55520	−	2.84814i	0.0498575	−	0.0913073i
$974$	−5.48819	+	8.53979i	−0.175853	+	0.273633i
$975$		0			0
$976$	−5.10629	+	17.3904i	−0.163448	+	0.556654i
$977$	0.917337	−	12.8260i	0.0293482	−	0.410342i	−0.961449	−	0.274984i	$-0.911327\pi$
$977$	0.917337	−	12.8260i	0.0293482	−	0.410342i	0.990797	−	0.135357i	$-0.0432182\pi$
$978$	−0.388172	+	5.42736i	−0.0124124	+	0.173548i
$979$	−6.79218	+	23.1320i	−0.217079	+	0.739303i
$980$		0			0
$981$	0.273609	−	0.425744i	0.00873567	−	0.0135930i
$982$	1.56189	−	2.86040i	0.0498420	−	0.0912789i
$983$	3.07935	+	4.11353i	0.0982159	+	0.131201i	0.846957	−	0.531662i	$-0.178432\pi$
$983$	3.07935	+	4.11353i	0.0982159	+	0.131201i	−0.748741	+	0.662863i	$0.769341\pi$
$984$	33.2593	−	15.1890i	1.06027	−	0.484209i
$985$		0			0
$986$	−1.03852	−	1.61597i	−0.0330733	−	0.0514630i
$987$	2.12532	−	0.152006i	0.0676497	−	0.00483840i
$988$	1.21299	−	1.21299i	0.0385905	−	0.0385905i
$989$	3.81118	−	0.454906i	0.121189	−	0.0144652i
$990$		0			0
$991$	2.02548	−	2.33753i	0.0643416	−	0.0742541i	−0.722666	−	0.691197i	$-0.757084\pi$
$991$	2.02548	−	2.33753i	0.0643416	−	0.0742541i	0.787008	+	0.616943i	$0.211629\pi$
$992$	0.404663	−	1.86021i	0.0128481	−	0.0590616i
$993$	0.896261	−	1.19726i	0.0284420	−	0.0379940i
$994$	0.346816	+	0.759421i	0.0110003	+	0.0240874i
$995$		0			0
$996$	6.67922	+	22.7473i	0.211639	+	0.720777i
$997$	−35.3791	+	7.69626i	−1.12047	+	0.243743i	−0.734393	−	0.678724i	$-0.762533\pi$
$997$	−35.3791	+	7.69626i	−1.12047	+	0.243743i	−0.386075	+	0.922467i	$0.626170\pi$
$998$	20.2441	−	7.55066i	0.640816	−	0.239012i
$999$	37.8610	+	11.1170i	1.19787	+	0.351726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.r.b.168.7		200
5.2	odd	4	inner	575.2.r.b.7.4		200
5.3	odd	4		115.2.l.a.7.7	✓	200
5.4	even	2		115.2.l.a.53.4	yes	200
23.10	odd	22	inner	575.2.r.b.493.4		200
115.33	even	44		115.2.l.a.102.4	yes	200
115.79	odd	22		115.2.l.a.33.7	yes	200
115.102	even	44	inner	575.2.r.b.332.7		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.7	✓	200	5.3	odd	4
115.2.l.a.33.7	yes	200	115.79	odd	22
115.2.l.a.53.4	yes	200	5.4	even	2
115.2.l.a.102.4	yes	200	115.33	even	44
575.2.r.b.7.4		200	5.2	odd	4	inner
575.2.r.b.168.7		200	1.1	even	1	trivial
575.2.r.b.332.7		200	115.102	even	44	inner
575.2.r.b.493.4		200	23.10	odd	22	inner

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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.r (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0452482 + 0.632652i) q^{2} +(1.67360 + 0.364069i) q^{3} +(1.58144 - 0.227377i) q^{4} +(-0.154602 + 1.07528i) q^{6} +(0.171765 + 0.0937908i) q^{7} +(0.485055 + 2.22976i) q^{8} +(-0.0605071 - 0.0276327i) q^{9} +(2.33306 - 2.02161i) q^{11} +(2.72948 + 0.195216i) q^{12} +(-0.0682068 - 0.124911i) q^{13} +(-0.0515649 + 0.112911i) q^{14} +(1.67726 - 0.492487i) q^{16} +(-0.702107 + 0.525590i) q^{17} +(0.0147440 - 0.0395303i) q^{18} +(1.07365 + 7.46738i) q^{19} +(0.253320 + 0.219503i) q^{21} +(1.38454 + 1.38454i) q^{22} +(-1.56765 - 4.53238i) q^{23} +3.90832i q^{24} +(0.0759392 - 0.0488032i) q^{26} +(-4.20456 - 3.14750i) q^{27} +(0.292962 + 0.109269i) q^{28} +(3.41800 + 0.491434i) q^{29} +(-0.282325 - 0.181439i) q^{31} +(1.98236 + 5.31490i) q^{32} +(4.64062 - 2.53397i) q^{33} +(-0.364285 - 0.420407i) q^{34} +(-0.101971 - 0.0299415i) q^{36} +(-7.03930 + 2.62552i) q^{37} +(-4.67567 + 1.01713i) q^{38} +(-0.0686744 - 0.233884i) q^{39} +(-3.88633 - 8.50988i) q^{41} +(-0.127407 + 0.170195i) q^{42} +(-0.170122 + 0.782038i) q^{43} +(3.22994 - 3.72754i) q^{44} +(2.79649 - 1.19686i) q^{46} +(4.49497 - 4.49497i) q^{47} +(2.98636 - 0.213588i) q^{48} +(-3.76378 - 5.85655i) q^{49} +(-1.36640 + 0.624012i) q^{51} +(-0.136267 - 0.182031i) q^{52} +(0.955623 - 1.75009i) q^{53} +(1.80102 - 2.80244i) q^{54} +(-0.125816 + 0.428489i) q^{56} +(-0.921788 + 12.8883i) q^{57} +(-0.156248 + 2.18464i) q^{58} +(-2.49768 + 8.50633i) q^{59} +(-5.60557 + 8.72243i) q^{61} +(0.102013 - 0.186823i) q^{62} +(-0.00780132 - 0.0104213i) q^{63} +(-0.0925946 + 0.0422865i) q^{64} +(1.81310 + 2.82124i) q^{66} +(-8.30923 + 0.594288i) q^{67} +(-0.990833 + 0.990833i) q^{68} +(-0.973521 - 8.15612i) q^{69} +(4.40447 - 5.08303i) q^{71} +(0.0322650 - 0.148320i) q^{72} +(-4.04711 + 5.40630i) q^{73} +(-1.97956 - 4.33463i) q^{74} +(3.39582 + 11.5651i) q^{76} +(0.590347 - 0.128422i) q^{77} +(0.144860 - 0.0540298i) q^{78} +(3.57517 + 1.04977i) q^{79} +(-5.76017 - 6.64759i) q^{81} +(5.20795 - 2.84375i) q^{82} +(3.02763 + 8.11740i) q^{83} +(0.450520 + 0.289532i) q^{84} +(-0.502456 - 0.0722422i) q^{86} +(5.54144 + 2.06685i) q^{87} +(5.63937 + 4.22158i) q^{88} +(-6.56977 + 4.22214i) q^{89} -0.0278526i q^{91} +(-3.50971 - 6.81125i) q^{92} +(-0.406442 - 0.406442i) q^{93} +(3.04714 + 2.64036i) q^{94} +(1.38268 + 9.61674i) q^{96} +(4.54643 - 12.1894i) q^{97} +(3.53486 - 2.64616i) q^{98} +(-0.197029 + 0.0578530i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q + 18 q^{2} + 14 q^{3} - 36 q^{6} + 22 q^{7} + 26 q^{8} - 44 q^{11} + 6 q^{12} + 26 q^{13} - 52 q^{16} + 22 q^{17} - 58 q^{18} - 44 q^{21} - 22 q^{23} - 28 q^{26} + 26 q^{27} - 66 q^{28} - 40 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) \) 200 * q + 18 * q^2 + 14 * q^3 - 36 * q^6 + 22 * q^7 + 26 * q^8 - 44 * q^11 + 6 * q^12 + 26 * q^13 - 52 * q^16 + 22 * q^17 - 58 * q^18 - 44 * q^21 - 22 * q^23 - 28 * q^26 + 26 * q^27 - 66 * q^28 - 40 * q^31 + 46 * q^32 - 12 * q^36 - 66 * q^37 + 22 * q^38 - 8 * q^41 - 198 * q^42 + 22 * q^43 - 76 * q^46 - 52 * q^47 - 18 * q^48 - 44 * q^51 - 158 * q^52 + 22 * q^53 + 88 * q^56 - 66 * q^57 + 58 * q^58 + 44 * q^61 - 38 * q^62 + 22 * q^63 + 132 * q^66 + 22 * q^67 + 132 * q^71 + 28 * q^72 - 34 * q^73 + 132 * q^76 + 10 * q^77 - 22 * q^78 - 48 * q^81 + 50 * q^82 + 22 * q^83 + 46 * q^87 + 110 * q^88 - 50 * q^92 + 36 * q^93 + 148 * q^96 + 88 * q^97 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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