LMFDB - Embedded newform 625.2.h.b.274.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

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

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			274.18
Character	$\chi$	$=$	625.274
Dual form			625.2.h.b.349.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415545 + 1.61844i) q^{2} +(1.28375 - 0.244888i) q^{3} +(-0.694058 + 0.381562i) q^{4} +(0.929792 + 1.97591i) q^{6} +(-0.910218 + 1.25281i) q^{7} +(1.38172 + 1.47138i) q^{8} +(-1.20129 + 0.475623i) q^{9} +O(q^{10})$	\(q+(0.415545 + 1.61844i) q^{2} +(1.28375 - 0.244888i) q^{3} +(-0.694058 + 0.381562i) q^{4} +(0.929792 + 1.97591i) q^{6} +(-0.910218 + 1.25281i) q^{7} +(1.38172 + 1.47138i) q^{8} +(-1.20129 + 0.475623i) q^{9} +(4.66011 - 1.19651i) q^{11} +(-0.797557 + 0.659796i) q^{12} +(0.940741 + 2.37604i) q^{13} +(-2.40583 - 0.952536i) q^{14} +(-2.65596 + 4.18512i) q^{16} +(0.100013 - 0.181923i) q^{17} +(-1.26896 - 1.74657i) q^{18} +(0.540545 - 2.83364i) q^{19} +(-0.861694 + 1.83119i) q^{21} +(3.87297 + 7.04491i) q^{22} +(3.38707 + 0.213096i) q^{23} +(2.13411 + 1.55052i) q^{24} +(-3.45456 + 2.50988i) q^{26} +(-4.73603 + 3.00558i) q^{27} +(0.153721 - 1.21683i) q^{28} +(-4.38410 - 0.553841i) q^{29} +(-7.06069 - 3.88165i) q^{31} +(-4.03772 - 1.31194i) q^{32} +(5.68941 - 2.67723i) q^{33} +(0.335991 + 0.0862678i) q^{34} +(0.652284 - 0.788475i) q^{36} +(9.09928 + 5.77458i) q^{37} +(4.81069 - 0.302663i) q^{38} +(1.78954 + 2.81986i) q^{39} +(0.203869 + 3.24041i) q^{41} +(-3.32175 - 0.633658i) q^{42} +(1.30432 - 0.423801i) q^{43} +(-2.77785 + 2.60857i) q^{44} +(1.06259 + 5.57031i) q^{46} +(4.98325 - 5.30662i) q^{47} +(-2.38470 + 6.02306i) q^{48} +(1.42209 + 4.37674i) q^{49} +(0.0838407 - 0.258035i) q^{51} +(-1.55953 - 1.29016i) q^{52} +(-9.10936 - 4.28654i) q^{53} +(-6.83238 - 6.41603i) q^{54} +(-3.10103 + 0.391751i) q^{56} -3.77005i q^{57} +(-0.925432 - 7.32555i) q^{58} +(1.73078 + 2.09215i) q^{59} +(0.932864 - 14.8274i) q^{61} +(3.34818 - 13.0403i) q^{62} +(0.497569 - 1.93790i) q^{63} +(-0.177039 + 2.81395i) q^{64} +(6.69714 + 8.09546i) q^{66} +(-0.647507 - 5.12554i) q^{67} +0.164426i q^{68} +(4.40033 - 0.555891i) q^{69} +(-5.63982 - 5.29615i) q^{71} +(-2.35967 - 1.11038i) q^{72} +(2.91466 + 2.41121i) q^{73} +(-5.56465 + 17.1262i) q^{74} +(0.706038 + 2.17296i) q^{76} +(-2.74272 + 6.92732i) q^{77} +(-3.82015 + 4.06804i) q^{78} +(-2.00895 - 10.5313i) q^{79} +(-2.51832 + 2.36486i) q^{81} +(-5.15970 + 1.67649i) q^{82} +(-2.44018 - 0.465489i) q^{83} +(-0.100647 - 1.59974i) q^{84} +(1.22790 + 1.93486i) q^{86} +(-5.76372 + 0.362622i) q^{87} +(8.19951 + 5.20357i) q^{88} +(5.29757 - 6.40366i) q^{89} +(-3.83300 - 0.984147i) q^{91} +(-2.43213 + 1.14447i) q^{92} +(-10.0147 - 3.25398i) q^{93} +(10.6592 + 5.85995i) q^{94} +(-5.50470 - 0.695406i) q^{96} +(0.189226 - 1.49787i) q^{97} +(-6.49255 + 4.12030i) q^{98} +(-5.02905 + 3.65382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	$ 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) $ 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	0.415545	+	1.61844i	0.293835	+	1.14441i	0.928412	+	0.371551i	$0.121174\pi$
$2$	0.415545	+	1.61844i	0.293835	+	1.14441i	−0.634578	+	0.772859i	$0.718826\pi$
$3$	1.28375	−	0.244888i	0.741173	−	0.141386i	0.197052	−	0.980393i	$-0.436863\pi$
$3$	1.28375	−	0.244888i	0.741173	−	0.141386i	0.544121	+	0.839007i	$0.316863\pi$
$4$	−0.694058	+	0.381562i	−0.347029	+	0.190781i
$5$		0			0
$5$		0			0
$6$	0.929792	+	1.97591i	0.379586	+	0.806662i
$7$	−0.910218	+	1.25281i	−0.344030	+	0.473517i	−0.945613	−	0.325293i	$-0.894537\pi$
$7$	−0.910218	+	1.25281i	−0.344030	+	0.473517i	0.601583	+	0.798810i	$0.294537\pi$
$8$	1.38172	+	1.47138i	0.488512	+	0.520213i
$9$	−1.20129	+	0.475623i	−0.400429	+	0.158541i
$10$		0			0
$11$	4.66011	−	1.19651i	1.40508	−	0.360763i	0.531339	−	0.847159i	$-0.321689\pi$
$11$	4.66011	−	1.19651i	1.40508	−	0.360763i	0.873738	+	0.486396i	$0.161689\pi$
$12$	−0.797557	+	0.659796i	−0.230235	+	0.190467i
$13$	0.940741	+	2.37604i	0.260915	+	0.658995i	0.999891	−	0.0147359i	$-0.00469075\pi$
$13$	0.940741	+	2.37604i	0.260915	+	0.658995i	−0.738977	+	0.673731i	$0.764691\pi$
$14$	−2.40583	−	0.952536i	−0.642985	−	0.254576i
$15$		0			0
$16$	−2.65596	+	4.18512i	−0.663989	+	1.04628i
$17$	0.100013	−	0.181923i	0.0242567	−	0.0441227i	−0.863901	−	0.503662i	$-0.831986\pi$
$17$	0.100013	−	0.181923i	0.0242567	−	0.0441227i	0.888157	+	0.459540i	$0.151986\pi$
$18$	−1.26896	−	1.74657i	−0.299096	−	0.411670i
$19$	0.540545	−	2.83364i	0.124010	−	0.650081i	−0.864946	−	0.501866i	$-0.832647\pi$
$19$	0.540545	−	2.83364i	0.124010	−	0.650081i	0.988955	−	0.148215i	$-0.0473528\pi$
$20$		0			0
$21$	−0.861694	+	1.83119i	−0.188037	+	0.399599i
$22$	3.87297	+	7.04491i	0.825721	+	1.50198i
$23$	3.38707	+	0.213096i	0.706252	+	0.0444336i	0.411855	−	0.911250i	$-0.364881\pi$
$23$	3.38707	+	0.213096i	0.706252	+	0.0444336i	0.294397	+	0.955683i	$0.404881\pi$
$24$	2.13411	+	1.55052i	0.435623	+	0.316499i
$25$		0			0
$26$	−3.45456	+	2.50988i	−0.677495	+	0.492229i
$27$	−4.73603	+	3.00558i	−0.911449	+	0.578423i
$28$	0.153721	−	1.21683i	0.0290505	−	0.229958i
$29$	−4.38410	−	0.553841i	−0.814107	−	0.102846i	−0.292755	−	0.956187i	$-0.594572\pi$
$29$	−4.38410	−	0.553841i	−0.814107	−	0.102846i	−0.521352	+	0.853342i	$0.674572\pi$
$30$		0			0
$31$	−7.06069	−	3.88165i	−1.26814	−	0.697165i	−0.301538	−	0.953454i	$-0.597500\pi$
$31$	−7.06069	−	3.88165i	−1.26814	−	0.697165i	−0.966600	+	0.256289i	$0.917500\pi$
$32$	−4.03772	−	1.31194i	−0.713775	−	0.231920i
$33$	5.68941	−	2.67723i	0.990399	−	0.466046i
$34$	0.335991	+	0.0862678i	0.0576219	+	0.0147948i
$35$		0			0
$36$	0.652284	−	0.788475i	0.108714	−	0.131413i
$37$	9.09928	+	5.77458i	1.49591	+	0.949335i	0.996555	+	0.0829394i	$0.0264308\pi$
$37$	9.09928	+	5.77458i	1.49591	+	0.949335i	0.499358	+	0.866396i	$0.333569\pi$
$38$	4.81069	−	0.302663i	0.780397	−	0.0490984i
$39$	1.78954	+	2.81986i	0.286556	+	0.451539i
$40$		0			0
$41$	0.203869	+	3.24041i	0.0318391	+	0.506067i	0.981337	+	0.192295i	$0.0615930\pi$
$41$	0.203869	+	3.24041i	0.0318391	+	0.506067i	−0.949498	+	0.313773i	$0.898407\pi$
$42$	−3.32175	−	0.633658i	−0.512557	−	0.0977755i
$43$	1.30432	−	0.423801i	0.198908	−	0.0646290i	−0.207869	−	0.978157i	$-0.566653\pi$
$43$	1.30432	−	0.423801i	0.198908	−	0.0646290i	0.406777	+	0.913528i	$0.366653\pi$
$44$	−2.77785	+	2.60857i	−0.418776	+	0.393257i
$45$		0			0
$46$	1.06259	+	5.57031i	0.156671	+	0.821298i
$47$	4.98325	−	5.30662i	0.726882	−	0.774050i	−0.254302	−	0.967125i	$-0.581846\pi$
$47$	4.98325	−	5.30662i	0.726882	−	0.774050i	0.981184	+	0.193074i	$0.0618459\pi$
$48$	−2.38470	+	6.02306i	−0.344201	+	0.869354i
$49$	1.42209	+	4.37674i	0.203156	+	0.625248i
$50$		0			0
$51$	0.0838407	−	0.258035i	0.0117400	−	0.0361321i
$52$	−1.55953	−	1.29016i	−0.216269	−	0.178913i
$53$	−9.10936	−	4.28654i	−1.25127	−	0.588801i	−0.318036	−	0.948079i	$-0.603023\pi$
$53$	−9.10936	−	4.28654i	−1.25127	−	0.588801i	−0.933231	+	0.359278i	$0.883023\pi$
$54$	−6.83238	−	6.41603i	−0.929769	−	0.873111i
$55$		0			0
$56$	−3.10103	+	0.391751i	−0.414392	+	0.0523499i
$57$		−	3.77005i		−	0.499356i
$58$	−0.925432	−	7.32555i	−0.121515	−	0.961892i
$59$	1.73078	+	2.09215i	0.225328	+	0.272375i	0.871046	−	0.491201i	$-0.163442\pi$
$59$	1.73078	+	2.09215i	0.225328	+	0.272375i	−0.645718	+	0.763576i	$0.723442\pi$
$60$		0			0
$61$	0.932864	−	14.8274i	0.119441	−	1.89846i	−0.248533	−	0.968623i	$-0.579948\pi$
$61$	0.932864	−	14.8274i	0.119441	−	1.89846i	0.367974	−	0.929836i	$-0.380052\pi$
$62$	3.34818	−	13.0403i	0.425220	−	1.65612i
$63$	0.497569	−	1.93790i	0.0626878	−	0.244153i
$64$	−0.177039	+	2.81395i	−0.0221298	+	0.351744i
$65$		0			0
$66$	6.69714	+	8.09546i	0.824361	+	0.996482i
$67$	−0.647507	−	5.12554i	−0.0791056	−	0.626185i	−0.980969	−	0.194164i	$-0.937801\pi$
$67$	−0.647507	−	5.12554i	−0.0791056	−	0.626185i	0.901864	−	0.432021i	$-0.142199\pi$
$68$			0.164426i			0.0199396i
$69$	4.40033	−	0.555891i	0.529737	−	0.0669214i
$70$		0			0
$71$	−5.63982	−	5.29615i	−0.669324	−	0.628537i	0.273483	−	0.961877i	$-0.411824\pi$
$71$	−5.63982	−	5.29615i	−0.669324	−	0.628537i	−0.942807	+	0.333340i	$0.891824\pi$
$72$	−2.35967	−	1.11038i	−0.278090	−	0.130859i
$73$	2.91466	+	2.41121i	0.341135	+	0.282211i	0.792177	−	0.610291i	$-0.208948\pi$
$73$	2.91466	+	2.41121i	0.341135	+	0.282211i	−0.451042	+	0.892503i	$0.648948\pi$
$74$	−5.56465	+	17.1262i	−0.646878	+	1.99089i
$75$		0			0
$76$	0.706038	+	2.17296i	0.0809881	+	0.249256i
$77$	−2.74272	+	6.92732i	−0.312562	+	0.789441i
$78$	−3.82015	+	4.06804i	−0.432546	+	0.460615i
$79$	−2.00895	−	10.5313i	−0.226025	−	1.18486i	−0.896539	−	0.442965i	$-0.853926\pi$
$79$	−2.00895	−	10.5313i	−0.226025	−	1.18486i	0.670514	−	0.741897i	$-0.266074\pi$
$80$		0			0
$81$	−2.51832	+	2.36486i	−0.279814	+	0.262763i
$82$	−5.15970	+	1.67649i	−0.569793	+	0.185137i
$83$	−2.44018	−	0.465489i	−0.267845	−	0.0510941i	0.0517093	−	0.998662i	$-0.483533\pi$
$83$	−2.44018	−	0.465489i	−0.267845	−	0.0510941i	−0.319554	+	0.947568i	$0.603533\pi$
$84$	−0.100647	−	1.59974i	−0.0109815	−	0.174546i
$85$		0			0
$86$	1.22790	+	1.93486i	0.132408	+	0.208642i
$87$	−5.76372	+	0.362622i	−0.617935	+	0.0388772i
$88$	8.19951	+	5.20357i	0.874071	+	0.554702i
$89$	5.29757	−	6.40366i	0.561541	−	0.678787i	−0.410968	−	0.911650i	$-0.634809\pi$
$89$	5.29757	−	6.40366i	0.561541	−	0.678787i	0.972510	+	0.232863i	$0.0748093\pi$
$90$		0			0
$91$	−3.83300	−	0.984147i	−0.401808	−	0.103167i
$92$	−2.43213	+	1.14447i	−0.253567	+	0.119320i
$93$	−10.0147	−	3.25398i	−1.03848	−	0.337422i
$94$	10.6592	+	5.85995i	1.09941	+	0.604408i
$95$		0			0
$96$	−5.50470	−	0.695406i	−0.561821	−	0.0709745i
$97$	0.189226	−	1.49787i	0.0192129	−	0.152086i	−0.979590	−	0.201008i	$-0.935578\pi$
$97$	0.189226	−	1.49787i	0.0192129	−	0.152086i	0.998803	+	0.0489215i	$0.0155784\pi$
$98$	−6.49255	+	4.12030i	−0.655846	+	0.416213i
$99$	−5.02905	+	3.65382i	−0.505438	+	0.367222i
$100$		0			0
$101$	−7.72911	−	5.61553i	−0.769076	−	0.558766i	0.132605	−	0.991169i	$-0.457666\pi$
$101$	−7.72911	−	5.61553i	−0.769076	−	0.558766i	−0.901681	+	0.432403i	$0.857666\pi$
$102$	0.452454	+	0.0284660i	0.0447996	+	0.00281855i
$103$	−8.37105	−	15.2269i	−0.824824	−	1.50035i	−0.865348	−	0.501171i	$-0.832903\pi$
$103$	−8.37105	−	15.2269i	−0.824824	−	1.50035i	0.0405240	−	0.999179i	$-0.487097\pi$
$104$	−2.19623	+	4.66722i	−0.215358	+	0.457658i
$105$		0			0
$106$	3.15216	−	16.5242i	0.306165	−	1.60497i
$107$	−3.66589	−	5.04566i	−0.354395	−	0.487782i	0.594182	−	0.804331i	$-0.297476\pi$
$107$	−3.66589	−	5.04566i	−0.354395	−	0.487782i	−0.948576	+	0.316548i	$0.897476\pi$
$108$	2.14027	−	3.89313i	0.205947	−	0.374617i
$109$	9.19096	−	14.4826i	0.880335	−	1.38719i	−0.0413081	−	0.999146i	$-0.513153\pi$
$109$	9.19096	−	14.4826i	0.880335	−	1.38719i	0.921643	−	0.388039i	$-0.126847\pi$
$110$		0			0
$111$	13.0953	+	5.18481i	1.24295	+	0.492120i
$112$	−2.82565	−	7.13678i	−0.266999	−	0.674362i
$113$	−5.67049	+	4.69104i	−0.533435	+	0.441296i	−0.864734	−	0.502230i	$-0.832513\pi$
$113$	−5.67049	+	4.69104i	−0.533435	+	0.441296i	0.331299	+	0.943526i	$0.392513\pi$
$114$	6.10161	−	1.56663i	0.571468	−	0.146728i
$115$		0			0
$116$	3.25415	−	1.28841i	0.302140	−	0.119626i
$117$	−2.26020	−	2.40687i	−0.208956	−	0.222515i
$118$	−2.66680	+	3.67054i	−0.245499	+	0.337901i
$119$	0.136881	+	0.290886i	0.0125478	+	0.0266655i
$120$		0			0
$121$	10.6457	−	5.85250i	0.967787	−	0.532045i
$122$	24.3850	−	4.65168i	2.20771	−	0.421144i
$123$	1.05526	+	4.10995i	0.0951492	+	0.370582i
$124$	6.38162			0.573087
$125$		0			0
$126$	3.34314			0.297831
$127$	4.84919	+	18.8864i	0.430296	+	1.67589i	0.700945	+	0.713215i	$0.252762\pi$
$127$	4.84919	+	18.8864i	0.430296	+	1.67589i	−0.270649	+	0.962678i	$0.587238\pi$
$128$	−12.9684	+	2.47386i	−1.14626	+	0.218660i
$129$	1.57064	−	0.863468i	0.138287	−	0.0760241i
$130$		0			0
$131$	3.30392	+	7.02118i	0.288665	+	0.613443i	0.995587	−	0.0938481i	$-0.0299168\pi$
$131$	3.30392	+	7.02118i	0.288665	+	0.613443i	−0.706922	+	0.707292i	$0.749917\pi$
$132$	−2.92725	+	4.02901i	−0.254784	+	0.350681i
$133$	3.05799	+	3.25643i	0.265161	+	0.282368i
$134$	8.02632	−	3.17785i	0.693368	−	0.274524i
$135$		0			0
$136$	0.405868	−	0.104209i	0.0348029	−	0.00893586i
$137$	−7.15228	+	5.91688i	−0.611060	+	0.505513i	−0.890700	−	0.454592i	$-0.849785\pi$
$137$	−7.15228	+	5.91688i	−0.611060	+	0.505513i	0.279640	+	0.960105i	$0.409785\pi$
$138$	2.72821	+	6.89067i	0.232241	+	0.586573i
$139$	0.891412	+	0.352935i	0.0756086	+	0.0299356i	0.405624	−	0.914040i	$-0.367054\pi$
$139$	0.891412	+	0.352935i	0.0756086	+	0.0299356i	−0.330016	+	0.943975i	$0.607054\pi$
$140$		0			0
$141$	5.09771	−	8.03271i	0.429305	−	0.676476i
$142$	6.22790	−	11.3285i	0.522634	−	0.950667i
$143$	7.22693	+	9.94701i	0.604346	+	0.831811i
$144$	1.20003	−	6.29077i	0.100002	−	0.524231i
$145$		0			0
$146$	−2.69123	+	5.71916i	−0.222728	+	0.473321i
$147$	2.89742	+	5.27038i	0.238975	+	0.434694i
$148$	−8.51879	−	0.535957i	−0.700240	−	0.0440554i
$149$	−4.44679	−	3.23079i	−0.364296	−	0.264676i	0.390546	−	0.920583i	$-0.372286\pi$
$149$	−4.44679	−	3.23079i	−0.364296	−	0.264676i	−0.754842	+	0.655907i	$0.772286\pi$
$150$		0			0
$151$	13.1967	−	9.58799i	1.07393	−	0.780259i	0.0973193	−	0.995253i	$-0.468973\pi$
$151$	13.1967	−	9.58799i	1.07393	−	0.780259i	0.976615	+	0.214994i	$0.0689732\pi$
$152$	4.91625	−	3.11995i	0.398761	−	0.253061i
$153$	−0.0336175	+	0.266110i	−0.00271781	+	0.0215137i
$154$	−12.3512	−	1.56032i	−0.995286	−	0.125734i
$155$		0			0
$156$	−2.31800	−	1.27433i	−0.185588	−	0.102028i
$157$	−1.75508	−	0.570260i	−0.140071	−	0.0455117i	0.238143	−	0.971230i	$-0.423461\pi$
$157$	−1.75508	−	0.570260i	−0.140071	−	0.0455117i	−0.378213	+	0.925718i	$0.623461\pi$
$158$	16.2094	−	7.62759i	1.28955	−	0.606818i
$159$	−12.7439	−	3.27207i	−1.01065	−	0.259492i
$160$		0			0
$161$	−3.34994	+	4.04938i	−0.264012	+	0.319136i
$162$	−4.87387	−	3.09305i	−0.382927	−	0.243013i
$163$	6.38274	−	0.401568i	0.499935	−	0.0314532i	0.189178	−	0.981943i	$-0.439418\pi$
$163$	6.38274	−	0.401568i	0.499935	−	0.0314532i	0.310756	+	0.950490i	$0.399418\pi$
$164$	−1.37791	−	2.17125i	−0.107597	−	0.169546i
$165$		0			0
$166$	−0.260638	−	4.14272i	−0.0202294	−	0.321537i
$167$	8.33697	+	1.59036i	0.645134	+	0.123066i	0.499557	−	0.866281i	$-0.333496\pi$
$167$	8.33697	+	1.59036i	0.645134	+	0.123066i	0.145577	+	0.989347i	$0.453496\pi$
$168$	−3.88501	+	1.26232i	−0.299735	+	0.0973898i
$169$	4.71602	−	4.42864i	0.362771	−	0.340664i
$170$		0			0
$171$	0.698394	+	3.66111i	0.0534075	+	0.279972i
$172$	−0.743571	+	0.791822i	−0.0566967	+	0.0603759i
$173$	0.244931	−	0.618626i	0.0186218	−	0.0470333i	−0.920168	−	0.391523i	$-0.871948\pi$
$173$	0.244931	−	0.618626i	0.0186218	−	0.0470333i	0.938790	+	0.344490i	$0.111948\pi$
$174$	−2.98196	−	9.17754i	−0.226062	−	0.695748i
$175$		0			0
$176$	−7.36951	+	22.6810i	−0.555498	+	1.70965i
$177$	2.73423	+	2.26195i	0.205517	+	0.170018i
$178$	12.5653	+	5.91279i	0.941811	+	0.443182i
$179$	13.4429	+	12.6238i	1.00477	+	0.943544i	0.998406	−	0.0564358i	$-0.0179736\pi$
$179$	13.4429	+	12.6238i	1.00477	+	0.943544i	0.00636599	+	0.999980i	$0.497974\pi$
$180$		0			0
$181$	−15.3964	+	1.94502i	−1.14441	+	0.144572i	−0.674591	−	0.738192i	$-0.735680\pi$
$181$	−15.3964	+	1.94502i	−1.14441	+	0.144572i	−0.469817	+	0.882764i	$0.655680\pi$
$182$		−	6.61244i		−	0.490147i
$183$	−2.43350	−	19.2632i	−0.179890	−	1.42397i
$184$	4.36643	+	5.27811i	0.321898	+	0.389108i
$185$		0			0
$186$	1.10481	−	17.5604i	0.0810085	−	1.28759i
$187$	0.248398	−	0.967447i	0.0181647	−	0.0707468i
$188$	−1.43386	+	5.58452i	−0.104575	+	0.407293i
$189$	0.545411	−	8.66906i	0.0396728	−	0.630582i
$190$		0			0
$191$	16.5862	+	20.0492i	1.20013	+	1.45071i	0.859971	+	0.510344i	$0.170482\pi$
$191$	16.5862	+	20.0492i	1.20013	+	1.45071i	0.340162	+	0.940367i	$0.389518\pi$
$192$	0.461830	+	3.65576i	0.0333297	+	0.263832i
$193$			20.4850i			1.47454i	0.675598	+	0.737270i	$0.263886\pi$
$193$			20.4850i			1.47454i	−0.675598	+	0.737270i	$0.736114\pi$
$194$	2.50285	−	0.316184i	0.179694	−	0.0227007i
$195$		0			0
$196$	−2.65701	−	2.49510i	−0.189786	−	0.178221i
$197$	−18.6518	−	8.77689i	−1.32889	−	0.625328i	−0.375430	−	0.926851i	$-0.622505\pi$
$197$	−18.6518	−	8.77689i	−1.32889	−	0.625328i	−0.953459	+	0.301523i	$0.902505\pi$
$198$	−8.00328	−	6.62089i	−0.568768	−	0.470526i
$199$	−0.212636	+	0.654427i	−0.0150734	+	0.0463911i	−0.958310	−	0.285730i	$-0.907764\pi$
$199$	−0.212636	+	0.654427i	−0.0150734	+	0.0463911i	0.943237	+	0.332121i	$0.107764\pi$
$200$		0			0
$201$	−2.08642	−	6.42135i	−0.147165	−	0.452927i
$202$	5.87661	−	14.8426i	0.413477	−	1.04432i
$203$	4.68434	−	4.98832i	0.328777	−	0.350111i
$204$	0.0402660	+	0.211082i	0.00281918	+	0.0147787i
$205$		0			0
$206$	21.1653	−	19.8755i	1.47465	−	1.38479i
$207$	−4.17019	+	1.35498i	−0.289848	+	0.0941774i
$208$	−12.4426	−	2.37355i	−0.862738	−	0.164576i
$209$	−0.871484	−	13.8518i	−0.0602818	−	0.958152i
$210$		0			0
$211$	4.12698	+	6.50307i	0.284113	+	0.447690i	0.956171	−	0.292808i	$-0.0945897\pi$
$211$	4.12698	+	6.50307i	0.284113	+	0.447690i	−0.672059	+	0.740498i	$0.734590\pi$
$212$	7.95800	−	0.500675i	0.546558	−	0.0343865i
$213$	−8.53709	−	5.41780i	−0.584951	−	0.371222i
$214$	6.64276	−	8.02972i	0.454090	−	0.548900i
$215$		0			0
$216$	−10.9662	−	2.81565i	−0.746157	−	0.191581i
$217$	11.2897	−	5.31255i	0.766397	−	0.360639i
$218$	27.2586	+	8.85684i	1.84618	+	0.599861i
$219$	4.33217	+	2.38163i	0.292741	+	0.160936i
$220$		0			0
$221$	0.526342	+	0.0664924i	0.0354056	+	0.00447276i
$222$	−2.94960	+	23.3485i	−0.197964	+	1.56705i
$223$	−4.93151	+	3.12963i	−0.330238	+	0.209576i	−0.690600	−	0.723237i	$-0.742653\pi$
$223$	−4.93151	+	3.12963i	−0.330238	+	0.209576i	0.360361	+	0.932813i	$0.382653\pi$
$224$	5.31881	−	3.86434i	0.355378	−	0.258197i
$225$		0			0
$226$	−9.94851	−	7.22801i	−0.661765	−	0.480800i
$227$	−20.3560	−	1.28069i	−1.35107	−	0.0850024i	−0.629317	−	0.777149i	$-0.716665\pi$
$227$	−20.3560	−	1.28069i	−1.35107	−	0.0850024i	−0.721757	+	0.692146i	$0.756665\pi$
$228$	1.43851	+	2.61664i	0.0952675	+	0.173291i
$229$	2.54363	−	5.40549i	0.168088	−	0.357205i	−0.802981	−	0.596005i	$-0.796754\pi$
$229$	2.54363	−	5.40549i	0.168088	−	0.357205i	0.971069	+	0.238800i	$0.0767539\pi$
$230$		0			0
$231$	−1.82454	+	9.56460i	−0.120046	+	0.629304i
$232$	−5.24269	−	7.21595i	−0.344200	−	0.473750i
$233$	−11.5523	+	21.0136i	−0.756817	+	1.37665i	0.163925	+	0.986473i	$0.447585\pi$
$233$	−11.5523	+	21.0136i	−0.756817	+	1.37665i	−0.920742	+	0.390172i	$0.872415\pi$
$234$	2.95616	−	4.65816i	0.193250	−	0.304513i
$235$		0			0
$236$	−1.99954	−	0.791675i	−0.130159	−	0.0515337i
$237$	−5.15798	−	13.0276i	−0.335047	−	0.846231i
$238$	−0.413902	+	0.342409i	−0.0268293	+	0.0221951i
$239$	−12.1569	+	3.12135i	−0.786362	+	0.201903i	−0.620459	−	0.784239i	$-0.713054\pi$
$239$	−12.1569	+	3.12135i	−0.786362	+	0.201903i	−0.165903	+	0.986142i	$0.553054\pi$
$240$		0			0
$241$	21.7269	−	8.60227i	1.39955	−	0.554121i	0.457385	−	0.889269i	$-0.348786\pi$
$241$	21.7269	−	8.60227i	1.39955	−	0.554121i	0.942166	+	0.335148i	$0.108786\pi$
$242$	13.8957	+	14.7974i	0.893247	+	0.951211i
$243$	7.23730	−	9.96129i	0.464273	−	0.639017i
$244$	5.01012	+	10.6471i	0.320740	+	0.681608i
$245$		0			0
$246$	−6.21320	+	3.41574i	−0.396139	+	0.217780i
$247$	7.24135	−	1.38136i	0.460756	−	0.0878939i
$248$	−4.04452	−	15.7524i	−0.256827	−	1.00028i
$249$	−3.24657			−0.205743
$250$		0			0
$251$	−24.8717			−1.56989			−0.784945	−	0.619565i	$-0.787309\pi$
$251$	−24.8717			−1.56989			−0.784945	+	0.619565i	$0.787309\pi$
$252$	0.394088	+	1.53487i	0.0248252	+	0.0966878i
$253$	16.0391	−	3.05962i	1.00837	−	0.192357i
$254$	−28.5514	+	15.6963i	−1.79147	+	0.984871i
$255$		0			0
$256$	−6.99176	−	14.8582i	−0.436985	−	0.928640i
$257$	1.25505	−	1.72743i	0.0782880	−	0.107754i	−0.768077	−	0.640358i	$-0.778786\pi$
$257$	1.25505	−	1.72743i	0.0782880	−	0.107754i	0.846365	+	0.532603i	$0.178786\pi$
$258$	2.05014	+	2.18318i	0.127636	+	0.135919i
$259$	−15.5168	+	6.14352i	−0.964165	+	0.381740i
$260$		0			0
$261$	5.52998	−	1.41986i	0.342297	−	0.0878870i
$262$	−9.99044	+	8.26481i	−0.617211	+	0.510602i
$263$	−7.68667	−	19.4143i	−0.473980	−	1.19714i	−0.948467	−	0.316875i	$-0.897366\pi$
$263$	−7.68667	−	19.4143i	−0.473980	−	1.19714i	0.474487	−	0.880263i	$-0.342634\pi$
$264$	11.8004	+	4.67211i	0.726265	+	0.287549i
$265$		0			0
$266$	−3.99960	+	6.30236i	−0.245231	+	0.386423i
$267$	5.23257	−	9.51801i	0.320228	−	0.582493i
$268$	2.40512	+	3.31036i	0.146916	+	0.202213i
$269$	−5.14025	+	26.9461i	−0.313407	+	1.64294i	0.381886	+	0.924209i	$0.375275\pi$
$269$	−5.14025	+	26.9461i	−0.313407	+	1.64294i	−0.695293	+	0.718726i	$0.744725\pi$
$270$		0			0
$271$	−9.63819	+	20.4822i	−0.585478	+	1.24421i	0.364300	+	0.931282i	$0.381308\pi$
$271$	−9.63819	+	20.4822i	−0.585478	+	1.24421i	−0.949778	+	0.312923i	$0.898692\pi$
$272$	0.495738	+	0.901745i	0.0300586	+	0.0546763i
$273$	−5.16162	−	0.324742i	−0.312395	−	0.0196542i
$274$	−12.5482	−	9.11681i	−0.758065	−	0.550766i
$275$		0			0
$276$	−2.84198	+	2.06482i	−0.171067	+	0.124287i
$277$	−14.9761	+	9.50413i	−0.899828	+	0.571048i	−0.903330	−	0.428946i	$-0.858885\pi$
$277$	−14.9761	+	9.50413i	−0.899828	+	0.571048i	0.00350262	+	0.999994i	$0.498885\pi$
$278$	−0.200783	+	1.58936i	−0.0120421	+	0.0953234i
$279$	10.3281	+	1.30475i	0.618329	+	0.0781131i
$280$		0			0
$281$	−3.35186	−	1.84270i	−0.199955	−	0.109926i	0.378631	−	0.925548i	$-0.376395\pi$
$281$	−3.35186	−	1.84270i	−0.199955	−	0.109926i	−0.578586	+	0.815622i	$0.696395\pi$
$282$	15.1188	+	4.91239i	0.900311	+	0.292529i
$283$	13.3907	−	6.30117i	0.795993	−	0.374566i	0.0156181	−	0.999878i	$-0.495028\pi$
$283$	13.3907	−	6.30117i	0.795993	−	0.374566i	0.780375	+	0.625312i	$0.215028\pi$
$284$	5.93517	+	1.52389i	0.352188	+	0.0904264i
$285$		0			0
$286$	−13.0955	+	15.8298i	−0.774355	+	0.936034i
$287$	−4.24518	−	2.69407i	−0.250585	−	0.159026i
$288$	5.47445	−	0.344423i	0.322585	−	0.0202953i
$289$	9.08596	+	14.3172i	0.534468	+	0.842187i
$290$		0			0
$291$	−0.123894	−	1.96924i	−0.00726278	−	0.115439i
$292$	−2.94297	−	0.561401i	−0.172224	−	0.0328535i
$293$	−9.13755	+	2.96897i	−0.533821	+	0.173449i	−0.563509	−	0.826110i	$-0.690549\pi$
$293$	−9.13755	+	2.96897i	−0.533821	+	0.173449i	0.0296873	+	0.999559i	$0.490549\pi$
$294$	−7.32579	+	6.87938i	−0.427249	+	0.401213i
$295$		0			0
$296$	4.07605	+	21.3674i	0.236916	+	1.24195i
$297$	−18.4742	+	19.6731i	−1.07198	+	1.14155i
$298$	3.38099	−	8.53941i	0.195856	−	0.494675i
$299$	2.68003	+	8.24827i	0.154990	+	0.477010i
$300$		0			0
$301$	−0.656279	+	2.01982i	−0.0378273	+	0.116420i
$302$	21.0014	+	17.3739i	1.20850	+	0.999755i
$303$	−11.2974	−	5.31616i	−0.649020	−	0.305406i
$304$	10.4234	+	9.78827i	0.597826	+	0.561396i
$305$		0			0
$306$	−0.444652	+	0.0561727i	−0.0254191	+	0.00321118i
$307$			10.4232i			0.594883i	0.954740	+	0.297442i	$0.0961334\pi$
$307$			10.4232i			0.594883i	−0.954740	+	0.297442i	$0.903867\pi$
$308$	−0.739593	−	5.85448i	−0.0421422	−	0.333590i
$309$	−14.4752	−	17.4975i	−0.823466	−	0.995400i
$310$		0			0
$311$	−0.758648	+	12.0584i	−0.0430190	+	0.683767i	0.916133	+	0.400875i	$0.131294\pi$
$311$	−0.758648	+	12.0584i	−0.0430190	+	0.683767i	−0.959152	+	0.282892i	$0.908706\pi$
$312$	−1.67646	+	6.52937i	−0.0949106	+	0.369653i
$313$	3.73968	−	14.5651i	0.211379	−	0.823268i	−0.771072	−	0.636748i	$-0.780279\pi$
$313$	3.73968	−	14.5651i	0.211379	−	0.823268i	0.982451	−	0.186520i	$-0.0597210\pi$
$314$	0.193617	−	3.07746i	0.0109265	−	0.173671i
$315$		0			0
$316$	5.41266	+	6.54279i	0.304486	+	0.368060i
$317$	−0.222923	−	1.76462i	−0.0125206	−	0.0991109i	0.984616	−	0.174732i	$-0.0559060\pi$
$317$	−0.222923	−	1.76462i	−0.0125206	−	0.0991109i	−0.997137	+	0.0756214i	$0.975906\pi$
$318$		−	21.9849i		−	1.23285i
$319$	−21.0931	+	2.66468i	−1.18099	+	0.149193i
$320$		0			0
$321$	−5.94170	−	5.57963i	−0.331634	−	0.311425i
$322$	−7.94573	−	3.73897i	−0.442798	−	0.208365i
$323$	−0.461441	−	0.381737i	−0.0256753	−	0.0212404i
$324$	0.845522	−	2.60225i	0.0469734	−	0.144569i
$325$		0			0
$326$	3.30223	+	10.1632i	0.182893	+	0.562888i
$327$	8.25227	−	20.8428i	0.456351	−	1.15261i
$328$	−4.48620	+	4.77732i	−0.247709	+	0.263783i
$329$	2.11233	+	11.0732i	0.116457	+	0.610487i
$330$		0			0
$331$	13.7320	−	12.8952i	0.754778	−	0.708784i	−0.208282	−	0.978069i	$-0.566787\pi$
$331$	13.7320	−	12.8952i	0.754778	−	0.708784i	0.963061	+	0.269285i	$0.0867873\pi$
$332$	1.87124	−	0.608003i	0.102698	−	0.0333685i
$333$	−13.6774	−	2.60910i	−0.749516	−	0.142978i
$334$	0.890478	+	14.1537i	0.0487248	+	0.774459i
$335$		0			0
$336$	−5.37514	−	8.46986i	−0.293238	−	0.462069i
$337$	3.07601	−	0.193526i	0.167561	−	0.0105420i	0.0212116	−	0.999775i	$-0.493248\pi$
$337$	3.07601	−	0.193526i	0.167561	−	0.0105420i	0.146349	+	0.989233i	$0.453248\pi$
$338$	9.12720	+	5.79230i	0.496454	+	0.315060i
$339$	−6.13071	+	7.41075i	−0.332974	+	0.402497i
$340$		0			0
$341$	−37.5481	−	9.64071i	−2.03334	−	0.522074i
$342$	−5.63507	+	2.65166i	−0.304710	+	0.143386i
$343$	−17.0870	−	5.55189i	−0.922610	−	0.299774i
$344$	2.42579	+	1.33359i	0.130790	+	0.0719022i
$345$		0			0
$346$	1.10299	+	0.139340i	0.0592971	+	0.00749096i
$347$	0.752614	−	5.95755i	0.0404024	−	0.319818i	−0.958942	−	0.283604i	$-0.908470\pi$
$347$	0.752614	−	5.95755i	0.0404024	−	0.319818i	0.999344	−	0.0362146i	$-0.0115300\pi$
$348$	3.86199	−	2.45089i	0.207024	−	0.131382i
$349$	−11.9227	+	8.66235i	−0.638208	+	0.463685i	−0.859234	−	0.511583i	$-0.829059\pi$
$349$	−11.9227	+	8.66235i	−0.638208	+	0.463685i	0.221026	+	0.975268i	$0.429059\pi$
$350$		0			0
$351$	−11.5967	−	8.42553i	−0.618988	−	0.449721i
$352$	−20.3860	−	1.28258i	−1.08658	−	0.0683617i
$353$	15.1307	+	27.5227i	0.805328	+	1.46489i	0.883747	+	0.467966i	$0.155013\pi$
$353$	15.1307	+	27.5227i	0.805328	+	1.46489i	−0.0784185	+	0.996921i	$0.524987\pi$
$354$	−2.52464	+	5.36512i	−0.134183	+	0.285153i
$355$		0			0
$356$	−1.23343	+	6.46586i	−0.0653716	+	0.342690i
$357$	0.246955	+	0.339905i	0.0130702	+	0.0179897i
$358$	−14.8447	+	27.0023i	−0.784564	+	1.42712i
$359$	−7.32605	+	11.5440i	−0.386654	+	0.609269i	−0.980783	−	0.195100i	$-0.937497\pi$
$359$	−7.32605	+	11.5440i	−0.386654	+	0.609269i	0.594129	+	0.804370i	$0.297497\pi$
$360$		0			0
$361$	9.92844	+	3.93095i	0.522550	+	0.206892i
$362$	−9.54581	−	24.1100i	−0.501717	−	1.26719i
$363$	12.2331	−	10.1201i	0.642073	−	0.531169i
$364$	3.03584	−	0.779471i	0.159121	−	0.0408554i
$365$		0			0
$366$	30.1651	−	11.9432i	1.57675	−	0.624281i
$367$	14.2334	+	15.1571i	0.742979	+	0.791192i	0.983779	−	0.179382i	$-0.0574099\pi$
$367$	14.2334	+	15.1571i	0.742979	+	0.791192i	−0.240800	+	0.970575i	$0.577410\pi$
$368$	−9.88774	+	13.6093i	−0.515434	+	0.709434i
$369$	−1.78612	−	3.79570i	−0.0929818	−	0.197596i
$370$		0			0
$371$	13.6617	−	7.51059i	0.709281	−	0.389930i
$372$	8.19240	−	1.56278i	0.424756	−	0.0810266i
$373$	1.78761	+	6.96230i	0.0925591	+	0.360494i	0.997944	−	0.0640987i	$-0.0204173\pi$
$373$	1.78761	+	6.96230i	0.0925591	+	0.360494i	−0.905384	+	0.424593i	$0.860417\pi$
$374$	1.66898			0.0863007
$375$		0			0
$376$	14.6935			0.757762
$377$	−2.80835	−	10.9378i	−0.144638	−	0.563326i
$378$	14.2570	−	2.71967i	0.733301	−	0.139885i
$379$	18.9872	−	10.4383i	0.975309	−	0.536181i	0.0873868	−	0.996174i	$-0.472148\pi$
$379$	18.9872	−	10.4383i	0.975309	−	0.536181i	0.887922	+	0.459994i	$0.152148\pi$
$380$		0			0
$381$	10.8502	+	23.0578i	0.555872	+	1.18129i
$382$	−25.5562	+	35.1751i	−1.30757	+	1.79971i
$383$	23.5786	+	25.1087i	1.20481	+	1.28299i	0.948639	+	0.316361i	$0.102461\pi$
$383$	23.5786	+	25.1087i	1.20481	+	1.28299i	0.256171	+	0.966632i	$0.417539\pi$
$384$	−16.0424	+	6.35162i	−0.818658	+	0.324130i
$385$		0			0
$386$	−33.1537	+	8.51242i	−1.68748	+	0.433271i
$387$	−1.36530	+	1.12947i	−0.0694020	+	0.0574144i
$388$	0.440198	+	1.11181i	0.0223477	+	0.0564438i
$389$	−16.1497	−	6.39413i	−0.818824	−	0.324195i	−0.0788972	−	0.996883i	$-0.525140\pi$
$389$	−16.1497	−	6.39413i	−0.818824	−	0.324195i	−0.739927	+	0.672687i	$0.765140\pi$
$390$		0			0
$391$	0.377517	−	0.594872i	0.0190919	−	0.0300840i
$392$	−4.47493	+	8.13987i	−0.226018	+	0.411126i
$393$	5.96081	+	8.20435i	0.300683	+	0.413855i
$394$	6.45420	−	33.8341i	0.325158	−	1.70454i
$395$		0			0
$396$	2.09629	−	4.45485i	0.105343	−	0.223865i
$397$	−11.6539	−	21.1984i	−0.584893	−	1.06392i	−0.988818	−	0.149125i	$-0.952354\pi$
$397$	−11.6539	−	21.1984i	−0.584893	−	1.06392i	0.403925	−	0.914792i	$-0.367646\pi$
$398$	−1.14751	−	0.0721953i	−0.0575196	−	0.00361882i
$399$	4.72315	+	3.43157i	0.236453	+	0.171793i
$400$		0			0
$401$	2.12829	−	1.54630i	0.106282	−	0.0772184i	−0.533375	−	0.845879i	$-0.679076\pi$
$401$	2.12829	−	1.54630i	0.106282	−	0.0772184i	0.639657	+	0.768661i	$0.279076\pi$
$402$	9.52557	−	6.04511i	0.475092	−	0.301503i
$403$	2.58067	−	20.4281i	0.128552	−	1.01760i
$404$	7.50713	+	0.948371i	0.373493	+	0.0471832i
$405$		0			0
$406$	10.0199	+	5.50846i	0.497277	+	0.273380i
$407$	49.3131	+	16.0228i	2.44436	+	0.794220i
$408$	0.495513	−	0.233171i	0.0245316	−	0.0115437i
$409$	−24.1142	−	6.19148i	−1.19237	−	0.306149i	−0.400188	−	0.916433i	$-0.631055\pi$
$409$	−24.1142	−	6.19148i	−1.19237	−	0.306149i	−0.792183	+	0.610284i	$0.791055\pi$
$410$		0			0
$411$	−7.73276	+	9.34730i	−0.381429	+	0.461068i
$412$	11.6200	+	7.37427i	0.572476	+	0.363304i
$413$	−4.19645	+	0.264018i	−0.206494	+	0.0129915i
$414$	−3.92585	−	6.18615i	−0.192945	−	0.304033i
$415$		0			0
$416$	−0.681239	−	10.8280i	−0.0334005	−	0.530886i
$417$	1.23078	+	0.234784i	0.0602716	+	0.0114974i
$418$	22.0562	−	7.16651i	1.07881	−	0.350525i
$419$	−2.82586	+	2.65366i	−0.138052	+	0.129640i	−0.750497	−	0.660873i	$-0.770186\pi$
$419$	−2.82586	+	2.65366i	−0.138052	+	0.129640i	0.612445	+	0.790513i	$0.290186\pi$
$420$		0			0
$421$	3.96494	+	20.7849i	0.193239	+	1.01300i	0.938254	+	0.345947i	$0.112442\pi$
$421$	3.96494	+	20.7849i	0.193239	+	1.01300i	−0.745015	+	0.667048i	$0.767558\pi$
$422$	−8.80989	+	9.38158i	−0.428859	+	0.456688i
$423$	−3.46236	+	8.74493i	−0.168346	+	0.425193i
$424$	−6.27945	−	19.3262i	−0.304957	−	0.938561i
$425$		0			0
$426$	5.22084	−	16.0681i	0.252951	−	0.778502i
$427$	17.7268	+	14.6649i	0.857861	+	0.709685i
$428$	4.46957	+	2.10322i	0.216045	+	0.101663i
$429$	11.7135	+	10.9997i	0.565531	+	0.531069i
$430$		0			0
$431$	7.93340	−	1.00222i	0.382138	−	0.0482753i	0.0680822	−	0.997680i	$-0.478312\pi$
$431$	7.93340	−	1.00222i	0.382138	−	0.0482753i	0.314056	+	0.949404i	$0.398312\pi$
$432$		−	27.8035i		−	1.33770i
$433$	−2.29403	−	18.1591i	−0.110244	−	0.872670i	−0.946134	−	0.323774i	$-0.895048\pi$
$433$	−2.29403	−	18.1591i	−0.110244	−	0.872670i	0.835891	−	0.548896i	$-0.184952\pi$
$434$	13.2894	+	16.0642i	0.637913	+	0.771104i
$435$		0			0
$436$	−0.853042	+	13.5587i	−0.0408533	+	0.649345i
$437$	2.43470	−	9.48252i	0.116467	−	0.453611i
$438$	−2.05431	+	8.00103i	−0.0981589	+	0.382304i
$439$	0.324337	−	5.15519i	0.0154798	−	0.246044i	−0.982676	−	0.185334i	$-0.940663\pi$
$439$	0.324337	−	5.15519i	0.0154798	−	0.246044i	0.998155	−	0.0607103i	$-0.0193366\pi$
$440$		0			0
$441$	−3.79002	−	4.58134i	−0.180477	−	0.218159i
$442$	0.111105	+	0.879483i	0.00528471	+	0.0418327i
$443$			16.7609i			0.796333i	0.917313	+	0.398167i	$0.130353\pi$
$443$			16.7609i			0.796333i	−0.917313	+	0.398167i	$0.869647\pi$
$444$	−11.0672	+	1.39812i	−0.525228	+	0.0663517i
$445$		0			0
$446$	−7.11438	−	6.68085i	−0.336876	−	0.316347i
$447$	−6.49975	−	3.05855i	−0.307428	−	0.144664i
$448$	−3.36419	−	2.78310i	−0.158943	−	0.131489i
$449$	7.70898	−	23.7258i	0.363809	−	1.11969i	−0.586914	−	0.809649i	$-0.699657\pi$
$449$	7.70898	−	23.7258i	0.363809	−	1.11969i	0.950723	−	0.310041i	$-0.100343\pi$
$450$		0			0
$451$	4.82725	+	14.8568i	0.227307	+	0.699577i
$452$	2.14573	−	5.41949i	0.100927	−	0.254912i
$453$	14.5933	−	15.5403i	0.685653	−	0.730147i
$454$	−6.38611	−	33.4771i	−0.299715	−	1.57116i
$455$		0			0
$456$	5.54719	−	5.20916i	0.259771	−	0.243941i
$457$	−37.6798	+	12.2429i	−1.76259	+	0.572699i	−0.997463	−	0.0711837i	$-0.977322\pi$
$457$	−37.6798	+	12.2429i	−1.76259	+	0.572699i	−0.765124	+	0.643883i	$0.777322\pi$
$458$	9.80546	+	1.87049i	0.458179	+	0.0874023i
$459$	0.0731186	+	1.16219i	0.00341288	+	0.0542463i
$460$		0			0
$461$	−15.4963	−	24.4183i	−0.721736	−	1.13727i	−0.985001	−	0.172551i	$-0.944799\pi$
$461$	−15.4963	−	24.4183i	−0.721736	−	1.13727i	0.263264	−	0.964724i	$-0.415201\pi$
$462$	−16.2379	+	1.02160i	−0.755456	+	0.0475293i
$463$	0.653744	+	0.414879i	0.0303821	+	0.0192810i	0.550931	−	0.834551i	$-0.314273\pi$
$463$	0.653744	+	0.414879i	0.0303821	+	0.0192810i	−0.520549	+	0.853832i	$0.674273\pi$
$464$	13.9619	−	16.8770i	0.648164	−	0.783496i
$465$		0			0
$466$	−38.8097	−	9.96464i	−1.79783	−	0.461603i
$467$	−12.7158	+	5.98361i	−0.588418	+	0.276888i	−0.696852	−	0.717215i	$-0.745416\pi$
$467$	−12.7158	+	5.98361i	−0.588418	+	0.276888i	0.108434	+	0.994104i	$0.465416\pi$
$468$	2.48708	+	0.808101i	0.114965	+	0.0373545i
$469$	7.01070	+	3.85416i	0.323724	+	0.177969i
$470$		0			0
$471$	−2.39273	−	0.302273i	−0.110251	−	0.0139280i
$472$	−0.686904	+	5.43740i	−0.0316173	+	0.250277i
$473$	5.57122	−	3.53560i	0.256165	−	0.162567i
$474$	18.9410	−	13.7614i	0.869987	−	0.632083i
$475$		0			0
$476$	−0.205994	−	0.149664i	−0.00944173	−	0.00685982i
$477$	12.9817	+	0.816741i	0.594393	+	0.0373960i
$478$	−10.1034	−	18.3781i	−0.462121	−	0.840594i
$479$	9.46448	−	20.1130i	0.432443	−	0.918988i	−0.563251	−	0.826286i	$-0.690450\pi$
$479$	9.46448	−	20.1130i	0.432443	−	0.918988i	0.995694	−	0.0927022i	$-0.0295504\pi$
$480$		0			0
$481$	−5.16057	+	27.0526i	−0.235302	+	1.23349i
$482$	22.9508	+	31.5890i	1.04538	+	1.43884i
$483$	−3.30883	+	6.01875i	−0.150557	+	0.273862i
$484$	−5.15561	+	8.12395i	−0.234346	+	0.369270i
$485$		0			0
$486$	19.1292	+	7.57377i	0.867717	+	0.343553i
$487$	13.9195	+	35.1567i	0.630753	+	1.59310i	0.794951	+	0.606674i	$0.207496\pi$
$487$	13.9195	+	35.1567i	0.630753	+	1.59310i	−0.164198	+	0.986427i	$0.552504\pi$
$488$	23.1058	−	19.1148i	1.04595	−	0.865286i
$489$	8.09550	−	2.07857i	0.366091	−	0.0939962i
$490$		0			0
$491$	−2.47845	+	0.981286i	−0.111851	+	0.0442848i	−0.423383	−	0.905951i	$-0.639158\pi$
$491$	−2.47845	+	0.981286i	−0.111851	+	0.0442848i	0.311533	+	0.950235i	$0.399158\pi$
$492$	−2.30061	−	2.44990i	−0.103719	−	0.110450i
$493$	−0.539223	+	0.742176i	−0.0242854	+	0.0334259i
$494$	5.24475	+	11.1457i	0.235973	+	0.501467i
$495$		0			0
$496$	34.9981	−	19.2404i	1.57146	−	0.863917i
$497$	11.7685	−	2.24497i	0.527891	−	0.100701i
$498$	−1.34910	−	5.25439i	−0.0604545	−	0.235455i
$499$	13.9992			0.626691			0.313346	−	0.949639i	$-0.398550\pi$
$499$	13.9992			0.626691			0.313346	+	0.949639i	$0.398550\pi$
$500$		0			0
$501$	11.0920			0.495556
$502$	−10.3353	−	40.2534i	−0.461288	−	1.79660i
$503$	−9.15345	+	1.74611i	−0.408132	+	0.0778554i	−0.387359	−	0.921929i	$-0.626613\pi$
$503$	−9.15345	+	1.74611i	−0.408132	+	0.0778554i	−0.0207729	+	0.999784i	$0.506613\pi$
$504$	3.53890	−	1.94553i	0.157635	−	0.0866607i
$505$		0			0
$506$	11.6168	+	24.6869i	0.516428	+	1.09747i
$507$	4.96967	−	6.84016i	0.220711	−	0.303782i
$508$	−10.5719	−	11.2580i	−0.469054	−	0.499491i
$509$	23.5949	−	9.34187i	1.04582	−	0.414071i	0.218524	−	0.975832i	$-0.429876\pi$
$509$	23.5949	−	9.34187i	1.04582	−	0.414071i	0.827300	+	0.561761i	$0.189876\pi$
$510$		0			0
$511$	−5.67376	+	1.45677i	−0.250992	+	0.0644439i
$512$	0.796776	−	0.659151i	0.0352129	−	0.0291306i
$513$	5.95667	+	15.0448i	0.262993	+	0.664246i
$514$	3.31728	+	1.31340i	0.146319	+	0.0579317i
$515$		0			0
$516$	−0.760650	+	1.19859i	−0.0334858	+	0.0527651i
$517$	16.8731	−	30.6920i	0.742077	−	1.34983i
$518$	−16.3908	−	22.5601i	−0.720172	−	0.991232i
$519$	0.162936	−	0.854142i	0.00715211	−	0.0374927i
$520$		0			0
$521$	9.30442	−	19.7729i	0.407634	−	0.866266i	−0.590606	−	0.806960i	$-0.701111\pi$
$521$	9.30442	−	19.7729i	0.407634	−	0.866266i	0.998240	−	0.0593061i	$-0.0188888\pi$
$522$	4.59591	+	8.35993i	0.201158	+	0.365904i
$523$	18.2842	+	1.15035i	0.799514	+	0.0503012i	0.457291	−	0.889317i	$-0.348820\pi$
$523$	18.2842	+	1.15035i	0.799514	+	0.0503012i	0.342224	+	0.939619i	$0.388820\pi$
$524$	−4.97212	−	3.61246i	−0.217208	−	0.157811i
$525$		0			0
$526$	28.2267	−	20.5079i	1.23074	−	0.894188i
$527$	−1.41232	+	0.896286i	−0.0615216	+	0.0390428i
$528$	−3.90629	+	30.9215i	−0.169999	+	1.34568i
$529$	−11.3918	−	1.43912i	−0.495297	−	0.0625706i
$530$		0			0
$531$	−3.07424	−	1.69007i	−0.133410	−	0.0733430i
$532$	−3.36495	−	1.09334i	−0.145889	−	0.0474022i
$533$	−7.50756	+	3.53279i	−0.325189	+	0.153022i
$534$	17.5787	+	4.51344i	0.760705	+	0.195316i
$535$		0			0
$536$	6.64697	−	8.03481i	0.287105	−	0.347051i
$537$	20.3488	+	12.9137i	0.878114	+	0.557268i
$538$	−45.7467	+	2.87814i	−1.97228	+	0.124085i
$539$	11.8639	+	18.6946i	0.511015	+	0.805232i
$540$		0			0
$541$	−0.944947	−	15.0195i	−0.0406265	−	0.645739i	−0.964672	−	0.263456i	$-0.915138\pi$
$541$	−0.944947	−	15.0195i	−0.0406265	−	0.645739i	0.924045	−	0.382284i	$-0.124862\pi$
$542$	−37.1543	−	7.08757i	−1.59591	−	0.304437i
$543$	−19.2889	+	6.26733i	−0.827764	+	0.268957i
$544$	−0.642495	+	0.603343i	−0.0275468	+	0.0258681i
$545$		0			0
$546$	−1.61931	−	8.48872i	−0.0693000	−	0.363284i
$547$	17.2149	−	18.3320i	0.736057	−	0.783821i	−0.246627	−	0.969111i	$-0.579322\pi$
$547$	17.2149	−	18.3320i	0.736057	−	0.783821i	0.982684	+	0.185289i	$0.0593222\pi$
$548$	2.70644	−	6.83569i	0.115613	−	0.292006i
$549$	5.93164	+	18.2557i	0.253156	+	0.779135i
$550$		0			0
$551$	−3.93919	+	12.1236i	−0.167815	+	0.516482i
$552$	6.89796	+	5.70649i	0.293596	+	0.242884i
$553$	15.0223	+	7.06894i	0.638811	+	0.300602i
$554$	−21.6051	−	20.2886i	−0.917913	−	0.861978i
$555$		0			0
$556$	−0.753359	+	0.0951713i	−0.0319495	+	0.00403616i
$557$		−	23.8005i		−	1.00846i	−0.863569	−	0.504230i	$-0.831776\pi$
$557$		−	23.8005i		−	1.00846i	0.863569	−	0.504230i	$-0.168224\pi$
$558$	2.18015	+	17.2576i	0.0922930	+	0.730574i
$559$	2.23400	+	2.70044i	0.0944881	+	0.114216i
$560$		0			0
$561$	0.0819646	−	1.30279i	0.00346055	−	0.0550038i
$562$	1.58945	−	6.19050i	0.0670469	−	0.261131i
$563$	1.03003	−	4.01170i	0.0434105	−	0.169073i	−0.943182	−	0.332277i	$-0.892183\pi$
$563$	1.03003	−	4.01170i	0.0434105	−	0.169073i	0.986592	+	0.163204i	$0.0521830\pi$
$564$	−0.473135	+	7.52026i	−0.0199226	+	0.316660i
$565$		0			0
$566$	15.7625	+	19.0536i	0.662547	+	0.800882i
$567$	−0.670495	−	5.30752i	−0.0281582	−	0.222895i
$568$		−	15.6161i		−	0.655239i
$569$	4.88375	−	0.616961i	0.204737	−	0.0258643i	−0.0222956	−	0.999751i	$-0.507098\pi$
$569$	4.88375	−	0.616961i	0.204737	−	0.0258643i	0.227033	+	0.973887i	$0.427098\pi$
$570$		0			0
$571$	8.35346	+	7.84442i	0.349581	+	0.328279i	0.839368	−	0.543564i	$-0.182925\pi$
$571$	8.35346	+	7.84442i	0.349581	+	0.328279i	−0.489787	+	0.871842i	$0.662925\pi$
$572$	−8.81130	−	4.14628i	−0.368419	−	0.173365i
$573$	26.2023	+	21.6764i	1.09462	+	0.905545i
$574$	2.59613	−	7.99008i	0.108361	−	0.333499i
$575$		0			0
$576$	−1.12571	−	3.46457i	−0.0469044	−	0.144357i
$577$	8.54570	−	21.5840i	0.355762	−	0.898552i	−0.636143	−	0.771571i	$-0.719471\pi$
$577$	8.54570	−	21.5840i	0.355762	−	0.898552i	0.991905	−	0.126981i	$-0.0405288\pi$
$578$	−19.3959	+	20.6545i	−0.806762	+	0.859115i
$579$	5.01653	+	26.2976i	0.208480	+	1.09289i
$580$		0			0
$581$	2.80427	−	2.63338i	0.116341	−	0.109251i
$582$	3.13561	−	1.01882i	0.129975	−	0.0422315i
$583$	−47.5796	−	9.07629i	−1.97054	−	0.375901i
$584$	0.479423	+	7.62020i	0.0198386	+	0.315326i
$585$		0			0
$586$	−8.60216	−	13.5548i	−0.355352	−	0.559945i
$587$	2.99653	−	0.188526i	0.123680	−	0.00778129i	−0.000829801	−	1.00000i	$-0.500264\pi$
$587$	2.99653	−	0.188526i	0.123680	−	0.00778129i	0.124510	+	0.992218i	$0.460264\pi$
$588$	−4.02195	−	2.55241i	−0.165863	−	0.105260i
$589$	−14.8158	+	17.9092i	−0.610475	+	0.737937i
$590$		0			0
$591$	−26.0937	−	6.69971i	−1.07335	−	0.275589i
$592$	−48.3346	+	22.7445i	−1.98654	+	0.934795i
$593$	−5.01637	−	1.62992i	−0.205998	−	0.0669327i	0.204201	−	0.978929i	$-0.434541\pi$
$593$	−5.01637	−	1.62992i	−0.205998	−	0.0669327i	−0.410198	+	0.911996i	$0.634541\pi$
$594$	−39.5165	−	21.7244i	−1.62138	−	0.891363i
$595$		0			0
$596$	4.31908	+	0.545626i	0.176916	+	0.0223497i
$597$	−0.112710	+	0.892193i	−0.00461292	+	0.0365150i
$598$	−12.2357	+	7.76499i	−0.500353	+	0.317534i
$599$	6.31463	−	4.58785i	0.258009	−	0.187454i	−0.451260	−	0.892393i	$-0.649025\pi$
$599$	6.31463	−	4.58785i	0.258009	−	0.187454i	0.709269	+	0.704938i	$0.249025\pi$
$600$		0			0
$601$	−35.0698	−	25.4797i	−1.43053	−	1.03934i	−0.989918	−	0.141642i	$-0.954762\pi$
$601$	−35.0698	−	25.4797i	−1.43053	−	1.03934i	−0.440611	−	0.897698i	$-0.645238\pi$
$602$	−3.54167	−	0.222823i	−0.144348	−	0.00908159i
$603$	3.21567	+	5.84928i	0.130952	+	0.238201i
$604$	−5.50089	+	11.6900i	−0.223828	+	0.475659i
$605$		0			0
$606$	3.90931	−	20.4933i	0.158805	−	0.832484i
$607$	4.44997	+	6.12486i	0.180619	+	0.248600i	0.889720	−	0.456506i	$-0.150899\pi$
$607$	4.44997	+	6.12486i	0.180619	+	0.248600i	−0.709102	+	0.705106i	$0.750899\pi$
$608$	−5.90012	+	10.7323i	−0.239282	+	0.435252i
$609$	4.79194	−	7.55089i	0.194179	−	0.305978i
$610$		0			0
$611$	17.2967	+	6.84824i	0.699749	+	0.277050i
$612$	−0.0782048	−	0.197523i	−0.00316124	−	0.00798439i
$613$	−32.0779	+	26.5371i	−1.29561	+	1.07182i	−0.302688	+	0.953090i	$0.597884\pi$
$613$	−32.0779	+	26.5371i	−1.29561	+	1.07182i	−0.992926	+	0.118735i	$0.962116\pi$
$614$	−16.8693	+	4.33131i	−0.680791	+	0.174797i
$615$		0			0
$616$	−13.9824	+	5.53603i	−0.563368	+	0.223053i
$617$	12.6187	+	13.4376i	0.508010	+	0.540976i	0.930933	−	0.365190i	$-0.118996\pi$
$617$	12.6187	+	13.4376i	0.508010	+	0.540976i	−0.422923	+	0.906166i	$0.638996\pi$
$618$	22.3036	−	30.6983i	0.897183	−	1.23487i
$619$	−4.65698	−	9.89659i	−0.187180	−	0.397777i	0.789108	−	0.614255i	$-0.210543\pi$
$619$	−4.65698	−	9.89659i	−0.187180	−	0.397777i	−0.976288	+	0.216477i	$0.930543\pi$
$620$		0			0
$621$	−16.6817	+	9.17085i	−0.669414	+	0.368014i
$622$	−19.8310	+	3.78296i	−0.795150	+	0.151683i
$623$	3.20061	+	12.4656i	0.128230	+	0.499422i
$624$	−16.5544			−0.662707
$625$		0			0
$626$	25.1268			1.00427
$627$	−4.51092	−	17.5689i	−0.180149	−	0.701633i
$628$	1.43572	−	0.273878i	0.0572914	−	0.0109289i
$629$	1.96057	−	1.07783i	0.0781731	−	0.0429760i
$630$		0			0
$631$	6.45961	+	13.7274i	0.257153	+	0.546478i	0.991161	−	0.132662i	$-0.0423526\pi$
$631$	6.45961	+	13.7274i	0.257153	+	0.546478i	−0.734008	+	0.679141i	$0.762353\pi$
$632$	12.7198	−	17.5072i	0.505965	−	0.696401i
$633$	6.89053	+	7.33767i	0.273874	+	0.291646i
$634$	2.76330	−	1.09407i	0.109744	−	0.0434509i
$635$		0			0
$636$	10.0935	−	2.59156i	0.400232	−	0.102762i
$637$	−9.06149	+	7.49632i	−0.359029	+	0.297015i
$638$	−13.0777	−	33.0306i	−0.517753	−	1.30769i
$639$	9.29402	+	3.67976i	0.367666	+	0.145569i
$640$		0			0
$641$	4.39935	−	6.93227i	0.173764	−	0.273808i	−0.746273	−	0.665640i	$-0.768159\pi$
$641$	4.39935	−	6.93227i	0.173764	−	0.273808i	0.920037	+	0.391832i	$0.128159\pi$
$642$	6.56125	−	11.9349i	0.258952	−	0.471032i
$643$	−4.08765	−	5.62617i	−0.161201	−	0.221874i	0.720774	−	0.693170i	$-0.243786\pi$
$643$	−4.08765	−	5.62617i	−0.161201	−	0.221874i	−0.881975	+	0.471296i	$0.843786\pi$
$644$	0.779963	−	4.08871i	0.0307349	−	0.161118i
$645$		0			0
$646$	0.426070	−	0.905444i	0.0167635	−	0.0356242i
$647$	−10.6232	−	19.3236i	−0.417643	−	0.759690i	0.580882	−	0.813988i	$-0.302708\pi$
$647$	−10.6232	−	19.3236i	−0.417643	−	0.759690i	−0.998525	+	0.0542983i	$0.982708\pi$
$648$	−6.95924	−	0.437838i	−0.273385	−	0.0171999i
$649$	10.5689	+	7.67876i	0.414866	+	0.301418i
$650$		0			0
$651$	13.1922	−	9.58470i	0.517043	−	0.375654i
$652$	−4.27677	+	2.71412i	−0.167491	+	0.106293i
$653$	−2.53764	+	20.0875i	−0.0993053	+	0.786083i	0.861286	+	0.508120i	$0.169659\pi$
$653$	−2.53764	+	20.0875i	−0.0993053	+	0.786083i	−0.960592	+	0.277963i	$0.910341\pi$
$654$	37.1621	+	4.69466i	1.45315	+	0.183576i
$655$		0			0
$656$	−14.1030	−	7.75318i	−0.550629	−	0.302711i
$657$	−4.64817	−	1.51028i	−0.181342	−	0.0589217i
$658$	−17.0436	+	8.02011i	−0.664429	+	0.312657i
$659$	33.3974	+	8.57500i	1.30098	+	0.334035i	0.834750	−	0.550629i	$-0.185612\pi$
$659$	33.3974	+	8.57500i	1.30098	+	0.334035i	0.466229	+	0.884664i	$0.345612\pi$
$660$		0			0
$661$	4.90244	−	5.92604i	0.190683	−	0.230496i	−0.666504	−	0.745501i	$-0.732210\pi$
$661$	4.90244	−	5.92604i	0.190683	−	0.230496i	0.857187	+	0.515005i	$0.172210\pi$
$662$	26.5764	+	16.8659i	1.03292	+	0.655511i
$663$	0.691974	−	0.0435353i	0.0268740	−	0.00169077i
$664$	−2.68674	−	4.23362i	−0.104266	−	0.164296i
$665$		0			0
$666$	−1.46089	−	23.2202i	−0.0566084	−	0.899765i
$667$	−14.7312	−	2.81013i	−0.570395	−	0.108809i
$668$	−6.39316	+	2.07726i	−0.247359	+	0.0803717i
$669$	−5.56441	+	5.22533i	−0.215133	+	0.202023i
$670$		0			0
$671$	−13.3940	−	70.2138i	−0.517069	−	2.71057i
$672$	5.88169	−	6.26336i	0.226891	−	0.241615i
$673$	5.49852	−	13.8877i	0.211952	−	0.535330i	−0.784439	−	0.620206i	$-0.787049\pi$
$673$	5.49852	−	13.8877i	0.211952	−	0.535330i	0.996392	+	0.0848752i	$0.0270492\pi$
$674$	1.59143	+	4.89792i	0.0612997	+	0.188661i
$675$		0			0
$676$	−1.58339	+	4.87318i	−0.0608998	+	0.187430i
$677$	−16.3724	−	13.5444i	−0.629241	−	0.520553i	0.267243	−	0.963629i	$-0.413887\pi$
$677$	−16.3724	−	13.5444i	−0.629241	−	0.520553i	−0.896484	+	0.443076i	$0.853887\pi$
$678$	−14.5414	−	6.84268i	−0.558461	−	0.262792i
$679$	1.70431	+	1.60046i	0.0654055	+	0.0614199i
$680$		0			0
$681$	−26.4456	+	3.34086i	−1.01340	+	0.128022i
$682$		−	64.7755i		−	2.48038i
$683$	2.37979	+	18.8380i	0.0910603	+	0.720816i	0.969866	+	0.243637i	$0.0783407\pi$
$683$	2.37979	+	18.8380i	0.0910603	+	0.720816i	−0.878806	+	0.477179i	$0.841659\pi$
$684$	−1.88166	−	2.27454i	−0.0719472	−	0.0869693i
$685$		0			0
$686$	1.88501	−	29.9613i	0.0719698	−	1.14393i
$687$	1.94164	−	7.56220i	0.0740783	−	0.288516i
$688$	−1.69057	+	6.58435i	−0.0644525	+	0.251026i
$689$	1.61544	−	25.6767i	0.0615434	−	0.978205i
$690$		0			0
$691$	20.1754	+	24.3878i	0.767507	+	0.927757i	0.998983	−	0.0450840i	$-0.0143555\pi$
$691$	20.1754	+	24.3878i	0.767507	+	0.927757i	−0.231476	+	0.972841i	$0.574356\pi$
$692$	0.0660474	+	0.522819i	0.00251075	+	0.0198746i
$693$		−	9.62620i		−	0.365669i
$694$	9.95469	−	1.25757i	0.377875	−	0.0477367i
$695$		0			0
$696$	−8.49741	−	7.97960i	−0.322093	−	0.302466i
$697$	0.609894	+	0.286994i	0.0231014	+	0.0108707i
$698$	−18.9739	−	15.6966i	−0.718174	−	0.594125i
$699$	−9.68429	+	29.8052i	−0.366294	+	1.12734i
$700$		0			0
$701$	5.97474	+	18.3884i	0.225663	+	0.694519i	0.998224	+	0.0595783i	$0.0189756\pi$
$701$	5.97474	+	18.3884i	0.225663	+	0.694519i	−0.772561	+	0.634941i	$0.781024\pi$
$702$	8.81725	−	22.2698i	0.332785	−	0.840520i
$703$	21.2816	−	22.6626i	0.802652	−	0.854738i
$704$	2.54191	+	13.3252i	0.0958018	+	0.502211i
$705$		0			0
$706$	−38.2564	+	35.9251i	−1.43980	+	1.35206i
$707$	14.0704	−	4.57174i	0.529170	−	0.171938i
$708$	−2.76078	−	0.526648i	−0.103757	−	0.0197926i
$709$	1.82461	+	29.0014i	0.0685248	+	1.08917i	0.870614	+	0.491966i	$0.163722\pi$
$709$	1.82461	+	29.0014i	0.0685248	+	1.08917i	−0.802090	+	0.597204i	$0.796278\pi$
$710$		0			0
$711$	7.42225	+	11.6956i	0.278356	+	0.438619i
$712$	16.7420	−	1.05332i	0.627433	−	0.0394748i
$713$	−23.0879	−	14.6520i	−0.864647	−	0.548722i
$714$	−0.447494	+	0.540928i	−0.0167471	+	0.0202437i
$715$		0			0
$716$	−14.1469	−	3.63231i	−0.528695	−	0.135746i
$717$	−14.8420	+	6.98410i	−0.554284	+	0.260826i
$718$	−21.7276	−	7.05972i	−0.810866	−	0.263466i
$719$	−6.29814	−	3.46243i	−0.234881	−	0.129127i	0.359967	−	0.932965i	$-0.382788\pi$
$719$	−6.29814	−	3.46243i	−0.234881	−	0.129127i	−0.594848	+	0.803838i	$0.702788\pi$
$720$		0			0
$721$	26.6958	+	3.37247i	0.994205	+	0.125597i
$722$	−2.23629	+	17.7021i	−0.0832262	+	0.658803i
$723$	25.7852	−	16.3638i	0.958964	−	0.608577i
$724$	9.94388	−	7.22465i	0.369561	−	0.268502i
$725$		0			0
$726$	21.4623	+	15.5932i	0.796539	+	0.578719i
$727$	−9.87667	−	0.621387i	−0.366305	−	0.0230460i	−0.121428	−	0.992600i	$-0.538748\pi$
$727$	−9.87667	−	0.621387i	−0.366305	−	0.0230460i	−0.244877	+	0.969554i	$0.578748\pi$
$728$	−3.84808	−	6.99963i	−0.142619	−	0.259424i
$729$	11.2642	−	23.9377i	0.417193	−	0.886581i
$730$		0			0
$731$	0.0533502	−	0.279672i	0.00197323	−	0.0103440i
$732$	9.03908	+	12.4412i	0.334094	+	0.459841i
$733$	16.1852	−	29.4408i	0.597814	−	1.08742i	−0.388329	−	0.921521i	$-0.626947\pi$
$733$	16.1852	−	29.4408i	0.597814	−	1.08742i	0.986143	−	0.165899i	$-0.0530525\pi$
$734$	−18.6162	+	29.3344i	−0.687136	+	1.08275i
$735$		0			0
$736$	−13.3965	−	5.30404i	−0.493800	−	0.195509i
$737$	−9.15024	−	23.1109i	−0.337054	−	0.851300i
$738$	5.40090	−	4.46801i	0.198810	−	0.164470i
$739$	−41.6755	+	10.7004i	−1.53306	+	0.393622i	−0.918555	−	0.395294i	$-0.870643\pi$
$739$	−41.6755	+	10.7004i	−1.53306	+	0.393622i	−0.614502	+	0.788916i	$0.710643\pi$
$740$		0			0
$741$	8.95780	−	3.54664i	0.329073	−	0.130289i
$742$	17.8325	+	18.9897i	0.654651	+	0.697133i
$743$	−12.0200	+	16.5440i	−0.440969	+	0.606942i	−0.970427	−	0.241394i	$-0.922395\pi$
$743$	−12.0200	+	16.5440i	−0.440969	+	0.606942i	0.529458	+	0.848336i	$0.322395\pi$
$744$	−9.04971	−	19.2316i	−0.331779	−	0.705065i
$745$		0			0
$746$	−10.5252	+	5.78629i	−0.385356	+	0.211851i
$747$	3.15276	−	0.601420i	0.115353	−	0.0220048i
$748$	0.196738	+	0.766244i	0.00719345	+	0.0280167i
$749$	9.65800			0.352896
$750$		0			0
$751$	9.16712			0.334513			0.167256	−	0.985913i	$-0.446509\pi$
$751$	9.16712			0.334513			0.167256	+	0.985913i	$0.446509\pi$
$752$	8.97355	+	34.9497i	0.327232	+	1.27448i
$753$	−31.9291	+	6.09080i	−1.16356	+	0.221961i
$754$	16.5352	−	9.09031i	0.602177	−	0.331049i
$755$		0			0
$756$	2.92924	+	6.22494i	0.106535	+	0.226399i
$757$	13.7158	−	18.8782i	0.498509	−	0.686139i	−0.483420	−	0.875389i	$-0.660605\pi$
$757$	13.7158	−	18.8782i	0.498509	−	0.686139i	0.981929	+	0.189249i	$0.0606055\pi$
$758$	24.7839	+	26.3921i	0.900190	+	0.958605i
$759$	19.8409	−	7.85557i	0.720179	−	0.285139i
$760$		0			0
$761$	−3.47812	+	0.893029i	−0.126082	+	0.0323723i	−0.311203	−	0.950343i	$-0.600732\pi$
$761$	−3.47812	+	0.893029i	−0.126082	+	0.0323723i	0.185122	+	0.982716i	$0.440732\pi$
$762$	−32.8090	+	27.1420i	−1.18854	+	0.983250i
$763$	9.77819	+	24.6969i	0.353994	+	0.894087i
$764$	−19.1618	−	7.58668i	−0.693249	−	0.274477i
$765$		0			0
$766$	−30.8389	+	48.5943i	−1.11425	+	1.75578i
$767$	−3.34282	+	6.08056i	−0.120702	+	0.219556i
$768$	−12.6143	−	17.3621i	−0.455179	−	0.626500i
$769$	1.76522	−	9.25360i	0.0636554	−	0.333693i	−0.936186	−	0.351505i	$-0.885670\pi$
$769$	1.76522	−	9.25360i	0.0636554	−	0.333693i	0.999841	+	0.0178119i	$0.00567000\pi$
$770$		0			0
$771$	1.18815	−	2.52494i	0.0427900	−	0.0909334i
$772$	−7.81628	−	14.2178i	−0.281314	−	0.511708i
$773$	20.6820	+	1.30120i	0.743879	+	0.0468009i	0.430207	−	0.902730i	$-0.358441\pi$
$773$	20.6820	+	1.30120i	0.743879	+	0.0468009i	0.313672	+	0.949531i	$0.398441\pi$
$774$	−2.39533	−	1.74031i	−0.0860983	−	0.0625541i
$775$		0			0
$776$	2.46541	−	1.79122i	0.0885029	−	0.0643011i
$777$	−18.4152	+	11.6866i	−0.660640	+	0.419255i
$778$	3.63758	−	28.7944i	0.130414	−	1.03233i
$779$	9.29235	+	1.17390i	0.332933	+	0.0420592i
$780$		0			0
$781$	−32.6191	−	17.9325i	−1.16720	−	0.641676i
$782$	1.11964	+	0.363793i	0.0400382	+	0.0130092i
$783$	22.4278	−	10.5537i	0.801506	−	0.377160i
$784$	−22.0942	−	5.67282i	−0.789078	−	0.202601i
$785$		0			0
$786$	−10.8013	+	13.0565i	−0.385268	+	0.465709i
$787$	19.0223	+	12.0719i	0.678073	+	0.430318i	0.829768	−	0.558109i	$-0.188473\pi$
$787$	19.0223	+	12.0719i	0.678073	+	0.430318i	−0.151694	+	0.988427i	$0.548473\pi$
$788$	16.2944	−	1.02516i	0.580464	−	0.0365197i
$789$	−14.6221	−	23.0407i	−0.520560	−	0.820272i
$790$		0			0
$791$	−0.715585	−	11.3739i	−0.0254433	−	0.404409i
$792$	−12.3249	−	2.35110i	−0.437947	−	0.0835428i
$793$	36.1082	−	11.7323i	1.28224	−	0.416625i
$794$	29.4656	−	27.6701i	1.04570	−	0.981974i
$795$		0			0
$796$	−0.102122	−	0.535345i	−0.00361963	−	0.0189748i
$797$	13.5782	−	14.4593i	0.480964	−	0.512174i	−0.442024	−	0.897003i	$-0.645739\pi$
$797$	13.5782	−	14.4593i	0.480964	−	0.512174i	0.922988	+	0.384829i	$0.125739\pi$
$798$	−3.59111	+	9.07011i	−0.127124	+	0.321078i
$799$	−0.467006	−	1.43730i	−0.0165215	−	0.0508479i
$800$		0			0
$801$	−3.31817	+	10.2123i	−0.117242	+	0.360833i
$802$	3.38699	+	2.80196i	0.119599	+	0.0989407i
$803$	16.4677	+	7.74910i	0.581132	+	0.273460i
$804$	3.89824	+	3.66069i	0.137480	+	0.129103i
$805$		0			0
$806$	34.1341	−	4.31214i	1.20232	−	0.151889i
$807$			35.8509i			1.26201i
$808$	−2.41688	−	19.1316i	−0.0850256	−	0.673047i
$809$	13.1712	+	15.9213i	0.463076	+	0.559763i	0.949422	−	0.314004i	$-0.101670\pi$
$809$	13.1712	+	15.9213i	0.463076	+	0.559763i	−0.486346	+	0.873767i	$0.661670\pi$
$810$		0			0
$811$	−2.29773	+	36.5214i	−0.0806842	+	1.28244i	0.724442	+	0.689335i	$0.242097\pi$
$811$	−2.29773	+	36.5214i	−0.0806842	+	1.28244i	−0.805127	+	0.593103i	$0.797903\pi$
$812$	−1.34786	+	5.24955i	−0.0473005	+	0.184223i
$813$	−7.35717	+	28.6543i	−0.258027	+	1.00495i
$814$	−5.44013	+	86.4684i	−0.190677	+	3.03072i
$815$		0			0
$816$	0.857230	+	1.03621i	0.0300091	+	0.0362747i
$817$	−0.495851	−	3.92506i	−0.0173476	−	0.137321i
$818$		−	41.6002i		−	1.45452i
$819$	5.07262	−	0.640821i	0.177252	−	0.0223921i
$820$		0			0
$821$	−19.8294	−	18.6211i	−0.692052	−	0.649880i	0.256484	−	0.966548i	$-0.417436\pi$
$821$	−19.8294	−	18.6211i	−0.692052	−	0.649880i	−0.948536	+	0.316668i	$0.897436\pi$
$822$	−18.3413	−	8.63078i	−0.639728	−	0.301033i
$823$	20.2385	+	16.7427i	0.705468	+	0.583614i	0.919442	−	0.393225i	$-0.128641\pi$
$823$	20.2385	+	16.7427i	0.705468	+	0.583614i	−0.213974	+	0.976839i	$0.568641\pi$
$824$	10.8381	−	33.3563i	0.377564	−	1.16202i
$825$		0			0
$826$	−2.17111	−	6.68199i	−0.0755425	−	0.232496i
$827$	−3.84862	+	9.72051i	−0.133830	+	0.338015i	−0.981202	−	0.192984i	$-0.938183\pi$
$827$	−3.84862	+	9.72051i	−0.133830	+	0.338015i	0.847372	+	0.531000i	$0.178183\pi$
$828$	2.37735	−	2.53162i	0.0826186	−	0.0879798i
$829$	0.489169	+	2.56431i	0.0169895	+	0.0890623i	0.989772	−	0.142658i	$-0.0455648\pi$
$829$	0.489169	+	2.56431i	0.0169895	+	0.0890623i	−0.972783	+	0.231720i	$0.925565\pi$
$830$		0			0
$831$	−16.8981	+	15.8684i	−0.586190	+	0.550469i
$832$	−6.85260	+	2.22655i	−0.237571	+	0.0771916i
$833$	0.938455	+	0.179020i	0.0325155	+	0.00620267i
$834$	0.131461	+	2.08951i	0.00455211	+	0.0723537i
$835$		0			0
$836$	5.89019	+	9.28146i	0.203717	+	0.321006i
$837$	45.1062	−	2.83784i	1.55910	−	0.0980903i
$838$	−5.46906	−	3.47077i	−0.188926	−	0.119896i
$839$	−24.9515	+	30.1611i	−0.861420	+	1.04128i	0.137291	+	0.990531i	$0.456160\pi$
$839$	−24.9515	+	30.1611i	−0.861420	+	1.04128i	−0.998712	+	0.0507473i	$0.983840\pi$
$840$		0			0
$841$	−9.17531	−	2.35582i	−0.316390	−	0.0812352i
$842$	−31.9916	+	15.0541i	−1.10250	+	0.518798i
$843$	−4.75420	−	1.54473i	−0.163743	−	0.0532034i
$844$	−5.34569	−	2.93882i	−0.184006	−	0.101158i
$845$		0			0
$846$	−15.5919	−	1.96972i	−0.536061	−	0.0677202i
$847$	−2.35781	+	18.6640i	−0.0810154	+	0.641303i
$848$	42.1337	−	26.7389i	1.44688	−	0.918217i
$849$	15.6472	−	11.3683i	0.537010	−	0.390160i
$850$		0			0
$851$	29.5893	+	21.4979i	1.01431	+	0.736939i
$852$	7.99246	+	0.502843i	0.273817	+	0.0172271i
$853$	18.2248	+	33.1508i	0.624006	+	1.13506i	0.979702	+	0.200461i	$0.0642438\pi$
$853$	18.2248	+	33.1508i	0.624006	+	1.13506i	−0.355696	+	0.934602i	$0.615756\pi$
$854$	−16.3680	+	34.7837i	−0.560101	+	1.19028i
$855$		0			0
$856$	2.35887	−	12.3656i	0.0806245	−	0.422648i
$857$	−10.7430	−	14.7865i	−0.366974	−	0.505096i	0.585101	−	0.810960i	$-0.301055\pi$
$857$	−10.7430	−	14.7865i	−0.366974	−	0.505096i	−0.952075	+	0.305864i	$0.901055\pi$
$858$	−12.9349	+	23.5284i	−0.441589	+	0.803247i
$859$	2.61605	−	4.12224i	0.0892585	−	0.140649i	−0.796765	−	0.604289i	$-0.793457\pi$
$859$	2.61605	−	4.12224i	0.0892585	−	0.140649i	0.886023	+	0.463641i	$0.153457\pi$
$860$		0			0
$861$	−6.10949	−	2.41892i	−0.208211	−	0.0824366i
$862$	4.91872	+	12.4233i	0.167532	+	0.423138i
$863$	−26.3113	+	21.7666i	−0.895648	+	0.740944i	−0.966534	−	0.256540i	$-0.917417\pi$
$863$	−26.3113	+	21.7666i	−0.895648	+	0.740944i	0.0708857	+	0.997484i	$0.477417\pi$
$864$	23.0659	−	5.92232i	0.784718	−	0.201481i
$865$		0			0
$866$	28.4361	−	11.2587i	0.966299	−	0.382585i
$867$	15.1702	+	16.1546i	0.515207	+	0.548640i
$868$	−5.80867	+	7.99495i	−0.197159	+	0.271366i
$869$	−21.9628	−	46.6733i	−0.745036	−	1.58328i
$870$		0			0
$871$	11.5694	−	6.36031i	0.392013	−	0.215511i
$872$	34.0089	−	6.48754i	1.15169	−	0.219696i
$873$	0.485110	+	1.88938i	0.0164185	+	0.0639458i
$874$	16.3586			0.553339
$875$		0			0
$876$	−3.91551			−0.132293
$877$	5.14188	+	20.0263i	0.173629	+	0.676240i	0.994464	+	0.105075i	$0.0335084\pi$
$877$	5.14188	+	20.0263i	0.173629	+	0.676240i	−0.820835	+	0.571165i	$0.806492\pi$
$878$	8.47815	−	1.61729i	0.286124	−	0.0545810i
$879$	−11.0033	+	6.04909i	−0.371131	+	0.204031i
$880$		0			0
$881$	−1.91010	−	4.05917i	−0.0643529	−	0.136757i	0.870063	−	0.492940i	$-0.164078\pi$
$881$	−1.91010	−	4.05917i	−0.0643529	−	0.136757i	−0.934416	+	0.356183i	$0.884078\pi$
$882$	5.83971	−	8.03767i	0.196633	−	0.270642i
$883$	−2.09194	−	2.22769i	−0.0703994	−	0.0749678i	0.692805	−	0.721125i	$-0.256375\pi$
$883$	−2.09194	−	2.22769i	−0.0703994	−	0.0749678i	−0.763204	+	0.646158i	$0.776375\pi$
$884$	−0.390683	+	0.154682i	−0.0131401	+	0.00520253i
$885$		0			0
$886$	−27.1265	+	6.96489i	−0.911332	+	0.233990i
$887$	−16.6458	+	13.7706i	−0.558911	+	0.462372i	−0.873478	−	0.486864i	$-0.838141\pi$
$887$	−16.6458	+	13.7706i	−0.558911	+	0.462372i	0.314567	+	0.949235i	$0.398141\pi$
$888$	10.4653	+	26.4322i	0.351191	+	0.887007i
$889$	−28.0748	−	11.1156i	−0.941599	−	0.372805i
$890$		0			0
$891$	−8.90609	+	14.0337i	−0.298365	+	0.470148i
$892$	2.22861	−	4.05382i	0.0746193	−	0.135732i
$893$	−12.3434	−	16.9892i	−0.413055	−	0.568522i
$894$	2.24914	−	11.7904i	0.0752226	−	0.394331i
$895$		0			0
$896$	8.70481	−	18.4987i	0.290807	−	0.617997i
$897$	5.46039	+	9.93240i	0.182317	+	0.331633i
$898$	41.6022	+	2.61739i	1.38828	+	0.0873435i
$899$	28.8050	+	20.9280i	0.960700	+	0.697989i
$900$		0			0
$901$	−1.69087	+	1.22849i	−0.0563311	+	0.0409269i
$902$	−22.0388	+	13.9863i	−0.733813	+	0.465692i
$903$	−0.347868	+	2.75366i	−0.0115763	+	0.0916359i
$904$	−14.7374	−	1.86176i	−0.490157	−	0.0619212i
$905$		0			0
$906$	31.2152	+	17.1607i	1.03706	+	0.570126i
$907$	25.9358	+	8.42705i	0.861184	+	0.279816i	0.706123	−	0.708089i	$-0.250443\pi$
$907$	25.9358	+	8.42705i	0.861184	+	0.279816i	0.155061	+	0.987905i	$0.450443\pi$
$908$	14.6169	−	6.87819i	0.485079	−	0.228261i
$909$	11.9558	+	3.06972i	0.396548	+	0.101816i
$910$		0			0
$911$	3.05467	−	3.69247i	0.101206	−	0.122337i	−0.717478	−	0.696581i	$-0.754704\pi$
$911$	3.05467	−	3.69247i	0.101206	−	0.122337i	0.818684	+	0.574244i	$0.194704\pi$
$912$	15.7781	+	10.0131i	0.522466	+	0.331567i
$913$	−11.9285	+	0.750477i	−0.394775	+	0.0248372i
$914$	−35.4721	−	55.8950i	−1.17331	−	1.84884i
$915$		0			0
$916$	0.297101	+	4.72228i	0.00981648	+	0.156028i
$917$	−11.8035	−	2.25163i	−0.389785	−	0.0743555i
$918$	−1.85055	+	0.601279i	−0.0610771	+	0.0198452i
$919$	−3.73994	+	3.51204i	−0.123369	+	0.115851i	−0.743777	−	0.668428i	$-0.766967\pi$
$919$	−3.73994	+	3.51204i	−0.123369	+	0.115851i	0.620407	+	0.784280i	$0.286967\pi$
$920$		0			0
$921$	2.55252	+	13.3808i	0.0841084	+	0.440912i
$922$	33.0802	−	35.2268i	1.08944	−	1.16013i
$923$	7.27825	−	18.3828i	0.239566	−	0.605076i
$924$	−2.38314	−	7.33456i	−0.0783997	−	0.241289i
$925$		0			0
$926$	−0.399796	+	1.23045i	−0.0131381	+	0.0404350i
$927$	17.2983	+	14.3104i	0.568151	+	0.470015i
$928$	16.9752	+	7.98792i	0.557238	+	0.262216i
$929$	−36.4443	−	34.2235i	−1.19570	−	1.12284i	−0.989531	−	0.144320i	$-0.953901\pi$
$929$	−36.4443	−	34.2235i	−1.19570	−	1.12284i	−0.206168	−	0.978517i	$-0.566099\pi$
$930$		0			0
$931$	13.1708	−	1.66386i	0.431655	−	0.0545307i
$932$		−	18.9926i		−	0.622122i
$933$	1.97904	+	15.6657i	0.0647908	+	0.512872i
$934$	−14.9681	−	18.0933i	−0.489771	−	0.592032i
$935$		0			0
$936$	0.418461	−	6.65124i	0.0136778	−	0.217403i
$937$	−4.66106	+	18.1536i	−0.152270	+	0.593053i	0.845942	+	0.533276i	$0.179039\pi$
$937$	−4.66106	+	18.1536i	−0.152270	+	0.593053i	−0.998212	+	0.0597775i	$0.980961\pi$
$938$	−3.32447	+	12.9480i	−0.108548	+	0.422766i
$939$	1.23399	−	19.6137i	0.0402698	−	0.640070i
$940$		0			0
$941$	15.9059	+	19.2269i	0.518517	+	0.626780i	0.963160	−	0.268928i	$-0.0866694\pi$
$941$	15.9059	+	19.2269i	0.518517	+	0.626780i	−0.444643	+	0.895708i	$0.646669\pi$
$942$	−0.505078	−	3.99810i	−0.0164563	−	0.130265i
$943$			11.0189i			0.358826i
$944$	−13.3528	+	1.68685i	−0.434596	+	0.0549022i
$945$		0			0
$946$	8.03725	+	7.54748i	0.261314	+	0.245390i
$947$	−24.0610	−	11.3222i	−0.781877	−	0.367923i	−0.00695112	−	0.999976i	$-0.502213\pi$
$947$	−24.0610	−	11.3222i	−0.781877	−	0.367923i	−0.774925	+	0.632053i	$0.782213\pi$
$948$	8.55075	+	7.07380i	0.277716	+	0.229746i
$949$	−2.98720	+	9.19367i	−0.0969687	+	0.298439i
$950$		0			0
$951$	−0.718312	−	2.21074i	−0.0232929	−	0.0716881i
$952$	−0.238874	+	0.603328i	−0.00774196	+	0.0195540i
$953$	−21.7238	+	23.1335i	−0.703703	+	0.749368i	−0.977157	−	0.212517i	$-0.931834\pi$
$953$	−21.7238	+	23.1335i	−0.703703	+	0.749368i	0.273454	+	0.961885i	$0.411834\pi$
$954$	4.07264	+	21.3496i	0.131857	+	0.691217i
$955$		0			0
$956$	7.24658	−	6.80499i	0.234371	−	0.220089i
$957$	−26.4257	+	8.58623i	−0.854221	+	0.277553i
$958$	36.4847	+	6.95982i	1.17877	+	0.224862i
$959$	−0.902579	−	14.3461i	−0.0291458	−	0.463259i
$960$		0			0
$961$	18.1756	+	28.6401i	0.586309	+	0.923875i
$962$	−45.9275	+	2.88952i	−1.48076	+	0.0931617i
$963$	6.80362	+	4.31771i	0.219243	+	0.139136i
$964$	−11.7974	+	14.2606i	−0.379969	+	0.459304i
$965$		0			0
$966$	−11.1160	−	2.85409i	−0.357650	−	0.0918289i
$967$	−24.1547	+	11.3663i	−0.776763	+	0.365517i	−0.772943	−	0.634476i	$-0.781216\pi$
$967$	−24.1547	+	11.3663i	−0.776763	+	0.365517i	−0.00382046	+	0.999993i	$0.501216\pi$
$968$	23.3206	+	7.57732i	0.749552	+	0.243544i
$969$	−0.685858	−	0.377054i	−0.0220329	−	0.0121127i
$970$		0			0
$971$	−48.5515	−	6.13349i	−1.55809	−	0.196833i	−0.701441	−	0.712728i	$-0.747460\pi$
$971$	−48.5515	−	6.13349i	−1.55809	−	0.196833i	−0.856652	+	0.515895i	$0.827460\pi$
$972$	−1.22226	+	9.67519i	−0.0392040	+	0.310332i
$973$	−1.25354	+	0.795521i	−0.0401866	+	0.0255032i
$974$	−51.1148	+	37.1371i	−1.63782	+	1.18995i
$975$		0			0
$976$	59.5770	+	43.2852i	1.90701	+	1.38553i
$977$	−4.26646	−	0.268423i	−0.136496	−	0.00858760i	−0.00560448	−	0.999984i	$-0.501784\pi$
$977$	−4.26646	−	0.268423i	−0.136496	−	0.00858760i	−0.130892	+	0.991397i	$0.541784\pi$
$978$	6.72808	+	12.2383i	0.215140	+	0.391339i
$979$	17.0252	−	36.1804i	0.544128	−	1.15633i
$980$		0			0
$981$	−4.15271	+	21.7693i	−0.132586	+	0.695039i
$982$	−2.61806	−	3.60345i	−0.0835456	−	0.114991i
$983$	25.3837	−	46.1728i	0.809614	−	1.47268i	−0.0702870	−	0.997527i	$-0.522391\pi$
$983$	25.3837	−	46.1728i	0.809614	−	1.47268i	0.879901	−	0.475156i	$-0.157609\pi$
$984$	−4.58925	+	7.23150i	−0.146300	+	0.230532i
$985$		0			0
$986$	−1.42524	−	0.564292i	−0.0453889	−	0.0179707i
$987$	5.42341	+	13.6980i	0.172629	+	0.436011i
$988$	−4.49884	+	3.72177i	−0.143127	+	0.118405i
$989$	4.50814	−	1.15749i	0.143351	−	0.0368062i
$990$		0			0
$991$	32.9189	−	13.0335i	1.04570	−	0.414024i	0.218449	−	0.975848i	$-0.429900\pi$
$991$	32.9189	−	13.0335i	1.04570	−	0.414024i	0.827256	+	0.561825i	$0.189900\pi$
$992$	23.4167	+	24.9362i	0.743480	+	0.791725i
$993$	14.4705	−	19.9170i	0.459209	−	0.632047i
$994$	8.52370	+	18.1138i	0.270355	+	0.574534i
$995$		0			0
$996$	2.25331	−	1.23877i	0.0713989	−	0.0392519i
$997$	−19.1230	+	3.64791i	−0.605633	+	0.115531i	−0.481072	−	0.876681i	$-0.659752\pi$
$997$	−19.1230	+	3.64791i	−0.605633	+	0.115531i	−0.124561	+	0.992212i	$0.539752\pi$
$998$	5.81731	+	22.6569i	0.184144	+	0.717192i
$999$	−60.4504			−1.91257

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.b.274.18		440
5.2	odd	4		125.2.g.a.21.3	yes	220
5.3	odd	4		625.2.g.a.351.9		220
5.4	even	2	inner	625.2.h.b.274.5		440
125.6	even	25	inner	625.2.h.b.349.5		440
125.33	odd	100		625.2.g.a.276.9		220
125.92	odd	100		125.2.g.a.6.3	✓	220
125.119	even	50	inner	625.2.h.b.349.18		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.6.3	✓	220	125.92	odd	100
125.2.g.a.21.3	yes	220	5.2	odd	4
625.2.g.a.276.9		220	125.33	odd	100
625.2.g.a.351.9		220	5.3	odd	4
625.2.h.b.274.5		440	5.4	even	2	inner
625.2.h.b.274.18		440	1.1	even	1	trivial
625.2.h.b.349.5		440	125.6	even	25	inner
625.2.h.b.349.18		440	125.119	even	50	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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.415545 + 1.61844i) q^{2} +(1.28375 - 0.244888i) q^{3} +(-0.694058 + 0.381562i) q^{4} +(0.929792 + 1.97591i) q^{6} +(-0.910218 + 1.25281i) q^{7} +(1.38172 + 1.47138i) q^{8} +(-1.20129 + 0.475623i) q^{9} +O(q^{10})\)	\(q+(0.415545 + 1.61844i) q^{2} +(1.28375 - 0.244888i) q^{3} +(-0.694058 + 0.381562i) q^{4} +(0.929792 + 1.97591i) q^{6} +(-0.910218 + 1.25281i) q^{7} +(1.38172 + 1.47138i) q^{8} +(-1.20129 + 0.475623i) q^{9} +(4.66011 - 1.19651i) q^{11} +(-0.797557 + 0.659796i) q^{12} +(0.940741 + 2.37604i) q^{13} +(-2.40583 - 0.952536i) q^{14} +(-2.65596 + 4.18512i) q^{16} +(0.100013 - 0.181923i) q^{17} +(-1.26896 - 1.74657i) q^{18} +(0.540545 - 2.83364i) q^{19} +(-0.861694 + 1.83119i) q^{21} +(3.87297 + 7.04491i) q^{22} +(3.38707 + 0.213096i) q^{23} +(2.13411 + 1.55052i) q^{24} +(-3.45456 + 2.50988i) q^{26} +(-4.73603 + 3.00558i) q^{27} +(0.153721 - 1.21683i) q^{28} +(-4.38410 - 0.553841i) q^{29} +(-7.06069 - 3.88165i) q^{31} +(-4.03772 - 1.31194i) q^{32} +(5.68941 - 2.67723i) q^{33} +(0.335991 + 0.0862678i) q^{34} +(0.652284 - 0.788475i) q^{36} +(9.09928 + 5.77458i) q^{37} +(4.81069 - 0.302663i) q^{38} +(1.78954 + 2.81986i) q^{39} +(0.203869 + 3.24041i) q^{41} +(-3.32175 - 0.633658i) q^{42} +(1.30432 - 0.423801i) q^{43} +(-2.77785 + 2.60857i) q^{44} +(1.06259 + 5.57031i) q^{46} +(4.98325 - 5.30662i) q^{47} +(-2.38470 + 6.02306i) q^{48} +(1.42209 + 4.37674i) q^{49} +(0.0838407 - 0.258035i) q^{51} +(-1.55953 - 1.29016i) q^{52} +(-9.10936 - 4.28654i) q^{53} +(-6.83238 - 6.41603i) q^{54} +(-3.10103 + 0.391751i) q^{56} -3.77005i q^{57} +(-0.925432 - 7.32555i) q^{58} +(1.73078 + 2.09215i) q^{59} +(0.932864 - 14.8274i) q^{61} +(3.34818 - 13.0403i) q^{62} +(0.497569 - 1.93790i) q^{63} +(-0.177039 + 2.81395i) q^{64} +(6.69714 + 8.09546i) q^{66} +(-0.647507 - 5.12554i) q^{67} +0.164426i q^{68} +(4.40033 - 0.555891i) q^{69} +(-5.63982 - 5.29615i) q^{71} +(-2.35967 - 1.11038i) q^{72} +(2.91466 + 2.41121i) q^{73} +(-5.56465 + 17.1262i) q^{74} +(0.706038 + 2.17296i) q^{76} +(-2.74272 + 6.92732i) q^{77} +(-3.82015 + 4.06804i) q^{78} +(-2.00895 - 10.5313i) q^{79} +(-2.51832 + 2.36486i) q^{81} +(-5.15970 + 1.67649i) q^{82} +(-2.44018 - 0.465489i) q^{83} +(-0.100647 - 1.59974i) q^{84} +(1.22790 + 1.93486i) q^{86} +(-5.76372 + 0.362622i) q^{87} +(8.19951 + 5.20357i) q^{88} +(5.29757 - 6.40366i) q^{89} +(-3.83300 - 0.984147i) q^{91} +(-2.43213 + 1.14447i) q^{92} +(-10.0147 - 3.25398i) q^{93} +(10.6592 + 5.85995i) q^{94} +(-5.50470 - 0.695406i) q^{96} +(0.189226 - 1.49787i) q^{97} +(-6.49255 + 4.12030i) q^{98} +(-5.02905 + 3.65382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9}+O(q^{10}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9	\( 440 q + 40 q^{4} - 40 q^{6} + 40 q^{9} - 30 q^{11} + 20 q^{14} + 20 q^{19} - 10 q^{21} - 30 q^{24} + 30 q^{26} + 20 q^{29} - 20 q^{31} - 10 q^{34} - 420 q^{36} - 10 q^{41} - 30 q^{44} + 40 q^{49} + 50 q^{51} - 120 q^{54} - 210 q^{56} - 10 q^{59} - 90 q^{64} + 110 q^{66} - 80 q^{69} - 170 q^{71} - 70 q^{74} + 70 q^{76} + 110 q^{81} - 230 q^{84} + 80 q^{86} - 110 q^{89} - 210 q^{91} - 120 q^{94} + 270 q^{96} - 90 q^{99}+O(q^{100}) \) 440 * q + 40 * q^4 - 40 * q^6 + 40 * q^9 - 30 * q^11 + 20 * q^14 + 20 * q^19 - 10 * q^21 - 30 * q^24 + 30 * q^26 + 20 * q^29 - 20 * q^31 - 10 * q^34 - 420 * q^36 - 10 * q^41 - 30 * q^44 + 40 * q^49 + 50 * q^51 - 120 * q^54 - 210 * q^56 - 10 * q^59 - 90 * q^64 + 110 * q^66 - 80 * q^69 - 170 * q^71 - 70 * q^74 + 70 * q^76 + 110 * q^81 - 230 * q^84 + 80 * q^86 - 110 * q^89 - 210 * q^91 - 120 * q^94 + 270 * q^96 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more