LMFDB - Embedded newform 968.2.o.i.245.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [968,2,Mod(245,968)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(968, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 8]))

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

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

chi := DirichletCharacter("968.245");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 968 = 2^{3} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	968.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.72951891566$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			245.8
Character	$\chi$	$=$	968.245
Dual form			968.2.o.i.565.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.25740 - 0.647266i) q^{2} +(-0.826127 + 0.268425i) q^{3} +(1.16209 - 1.62774i) q^{4} +(-2.15963 + 2.97247i) q^{5} +(-0.865027 + 0.872241i) q^{6} +(0.369362 - 1.13678i) q^{7} +(0.407629 - 2.79890i) q^{8} +(-1.81662 + 1.31985i) q^{9} +(-0.791527 + 5.13543i) q^{10} +(-0.523110 + 1.65665i) q^{12} +(-2.33969 - 3.22030i) q^{13} +(-0.271365 - 1.66846i) q^{14} +(0.986240 - 3.03533i) q^{15} +(-1.29908 - 3.78317i) q^{16} +(-2.57254 - 1.86906i) q^{17} +(-1.42991 + 2.83541i) q^{18} +(-4.09534 + 1.33066i) q^{19} +(2.32873 + 6.96960i) q^{20} +1.03827i q^{21} +2.46096 q^{23} +(0.414541 + 2.42166i) q^{24} +(-2.62651 - 8.08357i) q^{25} +(-5.02631 - 2.53480i) q^{26} +(2.67820 - 3.68622i) q^{27} +(-1.42115 - 1.92227i) q^{28} +(-3.65234 - 1.18672i) q^{29} +(-0.724575 - 4.45498i) q^{30} +(-7.40138 + 5.37742i) q^{31} +(-4.08218 - 3.91610i) q^{32} +(-4.44448 - 0.685031i) q^{34} +(2.58136 + 3.55294i) q^{35} +(0.0372960 + 4.49077i) q^{36} +(-5.06948 - 1.64717i) q^{37} +(-4.28818 + 4.32394i) q^{38} +(2.79729 + 2.03235i) q^{39} +(7.43932 + 7.25624i) q^{40} +(-0.164715 - 0.506940i) q^{41} +(0.672037 + 1.30552i) q^{42} -6.51729i q^{43} -8.25022i q^{45} +(3.09440 - 1.59290i) q^{46} +(0.110898 + 0.341309i) q^{47} +(2.08870 + 2.77667i) q^{48} +(4.50728 + 3.27473i) q^{49} +(-8.53478 - 8.46420i) q^{50} +(2.62694 + 0.853546i) q^{51} +(-7.96076 + 0.0661143i) q^{52} +(1.42471 + 1.96095i) q^{53} +(0.981589 - 6.36855i) q^{54} +(-3.03117 - 1.49719i) q^{56} +(3.02609 - 2.19858i) q^{57} +(-5.36056 + 0.871863i) q^{58} +(0.566526 + 0.184075i) q^{59} +(-3.79464 - 5.13268i) q^{60} +(-4.28455 + 5.89718i) q^{61} +(-5.82585 + 11.5522i) q^{62} +(0.829389 + 2.55260i) q^{63} +(-7.66768 - 2.28183i) q^{64} +14.6251 q^{65} +11.2692i q^{67} +(-6.03187 + 2.01541i) q^{68} +(-2.03306 + 0.660583i) q^{69} +(5.54549 + 2.79662i) q^{70} +(-4.52005 - 3.28401i) q^{71} +(2.95362 + 5.62254i) q^{72} +(0.825597 - 2.54093i) q^{73} +(-7.44051 + 1.21015i) q^{74} +(4.33966 + 5.97303i) q^{75} +(-2.59320 + 8.21250i) q^{76} +(4.83277 + 0.744878i) q^{78} +(-9.30369 + 6.75953i) q^{79} +(14.0509 + 4.30875i) q^{80} +(0.858601 - 2.64250i) q^{81} +(-0.535237 - 0.530810i) q^{82} +(0.589450 - 0.811308i) q^{83} +(1.69004 + 1.20657i) q^{84} +(11.1114 - 3.61033i) q^{85} +(-4.21843 - 8.19482i) q^{86} +3.33584 q^{87} +13.6469 q^{89} +(-5.34009 - 10.3738i) q^{90} +(-4.52497 + 1.47025i) q^{91} +(2.85986 - 4.00580i) q^{92} +(4.67105 - 6.42914i) q^{93} +(0.360360 + 0.357380i) q^{94} +(4.88906 - 15.0470i) q^{95} +(4.42358 + 2.13943i) q^{96} +(4.81420 - 3.49772i) q^{97} +(7.78706 + 1.20022i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/968\mathbb{Z}\right)^\times$.

$n$	$485$	$727$	$849$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.25740	−	0.647266i	0.889114	−	0.457686i
$2$	1.25740	−	0.647266i	0.889114	−	0.457686i
$3$	−0.826127	+	0.268425i	−0.476965	+	0.154975i	−0.537626	−	0.843183i	$-0.680679\pi$
$3$	−0.826127	+	0.268425i	−0.476965	+	0.154975i	0.0606618	+	0.998158i	$0.480679\pi$
$4$	1.16209	−	1.62774i	0.581046	−	0.813870i
$5$	−2.15963	+	2.97247i	−0.965814	+	1.32933i	−0.0216810	+	0.999765i	$0.506902\pi$
$5$	−2.15963	+	2.97247i	−0.965814	+	1.32933i	−0.944133	+	0.329564i	$0.893098\pi$
$6$	−0.865027	+	0.872241i	−0.353146	+	0.356091i
$7$	0.369362	−	1.13678i	0.139606	−	0.429662i	−0.856672	−	0.515861i	$-0.827472\pi$
$7$	0.369362	−	1.13678i	0.139606	−	0.429662i	0.996278	+	0.0861988i	$0.0274720\pi$
$8$	0.407629	−	2.79890i	0.144119	−	0.989560i
$9$	−1.81662	+	1.31985i	−0.605539	+	0.439950i
$10$	−0.791527	+	5.13543i	−0.250303	+	1.62396i
$11$		0			0
$11$		0			0
$12$	−0.523110	+	1.65665i	−0.151009	+	0.478235i
$13$	−2.33969	−	3.22030i	−0.648913	−	0.893152i	0.350139	−	0.936698i	$-0.386134\pi$
$13$	−2.33969	−	3.22030i	−0.648913	−	0.893152i	−0.999051	+	0.0435462i	$0.986134\pi$
$14$	−0.271365	−	1.66846i	−0.0725252	−	0.445914i
$15$	0.986240	−	3.03533i	0.254646	−	0.783720i
$16$	−1.29908	−	3.78317i	−0.324770	−	0.945793i
$17$	−2.57254	−	1.86906i	−0.623932	−	0.453313i	0.230361	−	0.973105i	$-0.426009\pi$
$17$	−2.57254	−	1.86906i	−0.623932	−	0.453313i	−0.854293	+	0.519792i	$0.826009\pi$
$18$	−1.42991	+	2.83541i	−0.337034	+	0.668313i
$19$	−4.09534	+	1.33066i	−0.939535	+	0.305273i	−0.738456	−	0.674302i	$-0.764445\pi$
$19$	−4.09534	+	1.33066i	−0.939535	+	0.305273i	−0.201079	+	0.979575i	$0.564445\pi$
$20$	2.32873	+	6.96960i	0.520719	+	1.55845i
$21$			1.03827i			0.226569i
$22$		0			0
$23$	2.46096			0.513145			0.256573	−	0.966525i	$-0.417407\pi$
$23$	2.46096			0.513145			0.256573	+	0.966525i	$0.417407\pi$
$24$	0.414541	+	2.42166i	0.0846177	+	0.494320i
$25$	−2.62651	−	8.08357i	−0.525302	−	1.61671i
$26$	−5.02631	−	2.53480i	−0.985741	−	0.497115i
$27$	2.67820	−	3.68622i	0.515420	−	0.709414i
$28$	−1.42115	−	1.92227i	−0.268572	−	0.363275i
$29$	−3.65234	−	1.18672i	−0.678223	−	0.220368i	−0.0504057	−	0.998729i	$-0.516051\pi$
$29$	−3.65234	−	1.18672i	−0.678223	−	0.220368i	−0.627817	+	0.778361i	$0.716051\pi$
$30$	−0.724575	−	4.45498i	−0.132289	−	0.813364i
$31$	−7.40138	+	5.37742i	−1.32933	+	0.965813i	−0.329563	+	0.944134i	$0.606901\pi$
$31$	−7.40138	+	5.37742i	−1.32933	+	0.965813i	−0.999765	+	0.0216793i	$0.993099\pi$
$32$	−4.08218	−	3.91610i	−0.721634	−	0.692274i
$33$		0			0
$34$	−4.44448	−	0.685031i	−0.762222	−	0.117482i
$35$	2.58136	+	3.55294i	0.436329	+	0.600556i
$36$	0.0372960	+	4.49077i	0.00621599	+	0.748462i
$37$	−5.06948	−	1.64717i	−0.833417	−	0.270794i	−0.138933	−	0.990302i	$-0.544367\pi$
$37$	−5.06948	−	1.64717i	−0.833417	−	0.270794i	−0.694484	+	0.719508i	$0.744367\pi$
$38$	−4.28818	+	4.32394i	−0.695634	+	0.701435i
$39$	2.79729	+	2.03235i	0.447925	+	0.325436i
$40$	7.43932	+	7.25624i	1.17626	+	1.14731i
$41$	−0.164715	−	0.506940i	−0.0257241	−	0.0791707i	0.937370	−	0.348335i	$-0.113253\pi$
$41$	−0.164715	−	0.506940i	−0.0257241	−	0.0791707i	−0.963094	+	0.269164i	$0.913253\pi$
$42$	0.672037	+	1.30552i	0.103698	+	0.201446i
$43$		−	6.51729i		−	0.993878i	−0.867785	−	0.496939i	$-0.834457\pi$
$43$		−	6.51729i		−	0.993878i	0.867785	−	0.496939i	$-0.165543\pi$
$44$		0			0
$45$		−	8.25022i		−	1.22987i
$46$	3.09440	−	1.59290i	0.456245	−	0.234860i
$47$	0.110898	+	0.341309i	0.0161761	+	0.0497850i	0.958819	−	0.284019i	$-0.0916678\pi$
$47$	0.110898	+	0.341309i	0.0161761	+	0.0497850i	−0.942643	+	0.333804i	$0.891668\pi$
$48$	2.08870	+	2.77667i	0.301478	+	0.400778i
$49$	4.50728	+	3.27473i	0.643897	+	0.467819i
$50$	−8.53478	−	8.46420i	−1.20700	−	1.19702i
$51$	2.62694	+	0.853546i	0.367846	+	0.119520i
$52$	−7.96076	+	0.0661143i	−1.10396	+	0.00916840i
$53$	1.42471	+	1.96095i	0.195700	+	0.269357i	0.895578	−	0.444905i	$-0.146762\pi$
$53$	1.42471	+	1.96095i	0.195700	+	0.269357i	−0.699878	+	0.714262i	$0.746762\pi$
$54$	0.981589	−	6.36855i	0.133577	−	0.866651i
$55$		0			0
$56$	−3.03117	−	1.49719i	−0.405057	−	0.200071i
$57$	3.02609	−	2.19858i	0.400815	−	0.291209i
$58$	−5.36056	+	0.871863i	−0.703877	+	0.114481i
$59$	0.566526	+	0.184075i	0.0737554	+	0.0239646i	0.345662	−	0.938359i	$-0.387654\pi$
$59$	0.566526	+	0.184075i	0.0737554	+	0.0239646i	−0.271907	+	0.962324i	$0.587654\pi$
$60$	−3.79464	−	5.13268i	−0.489885	−	0.662627i
$61$	−4.28455	+	5.89718i	−0.548580	+	0.755056i	−0.989819	−	0.142334i	$-0.954539\pi$
$61$	−4.28455	+	5.89718i	−0.548580	+	0.755056i	0.441238	+	0.897390i	$0.354539\pi$
$62$	−5.82585	+	11.5522i	−0.739884	+	1.46713i
$63$	0.829389	+	2.55260i	0.104493	+	0.321597i
$64$	−7.66768	−	2.28183i	−0.958460	−	0.285228i
$65$	14.6251			1.81402
$66$		0			0
$67$			11.2692i			1.37675i	0.725353	+	0.688377i	$0.241677\pi$
$67$			11.2692i			1.37675i	−0.725353	+	0.688377i	$0.758323\pi$
$68$	−6.03187	+	2.01541i	−0.731472	+	0.244404i
$69$	−2.03306	+	0.660583i	−0.244752	+	0.0795248i
$70$	5.54549	+	2.79662i	0.662813	+	0.334261i
$71$	−4.52005	−	3.28401i	−0.536432	−	0.389740i	0.286326	−	0.958132i	$-0.407566\pi$
$71$	−4.52005	−	3.28401i	−0.536432	−	0.389740i	−0.822758	+	0.568392i	$0.807566\pi$
$72$	2.95362	+	5.62254i	0.348087	+	0.662623i
$73$	0.825597	−	2.54093i	0.0966288	−	0.297393i	−0.891046	−	0.453913i	$-0.850028\pi$
$73$	0.825597	−	2.54093i	0.0966288	−	0.297393i	0.987675	+	0.156520i	$0.0500276\pi$
$74$	−7.44051	+	1.21015i	−0.864941	+	0.140677i
$75$	4.33966	+	5.97303i	0.501101	+	0.689706i
$76$	−2.59320	+	8.21250i	−0.297460	+	0.942038i
$77$		0			0
$78$	4.83277	+	0.744878i	0.547204	+	0.0843408i
$79$	−9.30369	+	6.75953i	−1.04675	+	0.760506i	−0.971591	−	0.236665i	$-0.923945\pi$
$79$	−9.30369	+	6.75953i	−1.04675	+	0.760506i	−0.0751561	+	0.997172i	$0.523945\pi$
$80$	14.0509	+	4.30875i	1.57094	+	0.481733i
$81$	0.858601	−	2.64250i	0.0954001	−	0.293611i
$82$	−0.535237	−	0.530810i	−0.0591070	−	0.0586182i
$83$	0.589450	−	0.811308i	0.0647006	−	0.0890527i	−0.775440	−	0.631421i	$-0.782472\pi$
$83$	0.589450	−	0.811308i	0.0647006	−	0.0890527i	0.840141	+	0.542368i	$0.182472\pi$
$84$	1.69004	+	1.20657i	0.184398	+	0.131647i
$85$	11.1114	−	3.61033i	1.20521	−	0.391595i
$86$	−4.21843	−	8.19482i	−0.454885	−	0.883671i
$87$	3.33584			0.357640
$88$		0			0
$89$	13.6469			1.44657			0.723283	−	0.690551i	$-0.242632\pi$
$89$	13.6469			1.44657			0.723283	+	0.690551i	$0.242632\pi$
$90$	−5.34009	−	10.3738i	−0.562895	−	1.09349i
$91$	−4.52497	+	1.47025i	−0.474346	+	0.154124i
$92$	2.85986	−	4.00580i	0.298161	−	0.417634i
$93$	4.67105	−	6.42914i	0.484365	−	0.666671i
$94$	0.360360	+	0.357380i	0.0371683	+	0.0368609i
$95$	4.88906	−	15.0470i	0.501607	−	1.54379i
$96$	4.42358	+	2.13943i	0.451479	+	0.218355i
$97$	4.81420	−	3.49772i	0.488808	−	0.355140i	−0.315918	−	0.948787i	$-0.602312\pi$
$97$	4.81420	−	3.49772i	0.488808	−	0.355140i	0.804726	+	0.593647i	$0.202312\pi$
$98$	7.78706	+	1.20022i	0.786612	+	0.121241i
$99$		0			0
$100$	−16.2102	−	5.11857i	−1.62102	−	0.511857i
$101$	3.51209	+	4.83398i	0.349466	+	0.480998i	0.947176	−	0.320714i	$-0.103923\pi$
$101$	3.51209	+	4.83398i	0.349466	+	0.480998i	−0.597710	+	0.801712i	$0.703923\pi$
$102$	3.85558	−	0.627087i	0.381760	−	0.0620909i
$103$	−1.21309	+	3.73350i	−0.119529	+	0.367873i	−0.992865	−	0.119246i	$-0.961952\pi$
$103$	−1.21309	+	3.73350i	−0.119529	+	0.367873i	0.873336	+	0.487119i	$0.161952\pi$
$104$	−9.96703	+	5.23586i	−0.977348	+	0.513418i
$105$	−3.08623	−	2.24228i	−0.301185	−	0.218824i
$106$	3.06069	+	1.54352i	0.297280	+	0.149920i
$107$	12.1838	−	3.95877i	1.17786	−	0.382709i	0.346287	−	0.938129i	$-0.387442\pi$
$107$	12.1838	−	3.95877i	1.17786	−	0.382709i	0.831570	+	0.555420i	$0.187442\pi$
$108$	−2.88790	−	8.64315i	−0.277889	−	0.831687i
$109$		−	5.65346i		−	0.541504i	−0.962649	−	0.270752i	$-0.912728\pi$
$109$		−	5.65346i		−	0.541504i	0.962649	−	0.270752i	$-0.0872723\pi$
$110$		0			0
$111$	4.63018			0.439477
$112$	−4.78046	+	0.0794092i	−0.451711	+	0.00750347i
$113$	−4.94390	−	15.2158i	−0.465083	−	1.43138i	−0.858878	−	0.512180i	$-0.828838\pi$
$113$	−4.94390	−	15.2158i	−0.465083	−	1.43138i	0.393796	−	0.919198i	$-0.371162\pi$
$114$	2.38192	−	4.72317i	0.223088	−	0.442366i
$115$	−5.31475	+	7.31513i	−0.495603	+	0.682139i
$116$	−6.17603	+	4.56599i	−0.573430	+	0.423942i
$117$	8.50064	+	2.76202i	0.785884	+	0.255349i
$118$	0.831493	−	0.135237i	0.0765452	−	0.0124496i
$119$	−3.07491	+	2.23405i	−0.281876	+	0.204795i
$120$	−8.09358	−	3.99768i	−0.738839	−	0.364936i
$121$		0			0
$122$	−1.57033	+	10.1883i	−0.142171	+	0.922408i
$123$	0.272150	+	0.374583i	0.0245390	+	0.0337750i
$124$	0.151954	+	18.2966i	0.0136458	+	1.64308i
$125$	12.2287	+	3.97334i	1.09377	+	0.355387i
$126$	2.69508	+	2.67279i	0.240097	+	0.238111i
$127$	7.48900	+	5.44108i	0.664541	+	0.482817i	0.868193	−	0.496226i	$-0.165281\pi$
$127$	7.48900	+	5.44108i	0.664541	+	0.482817i	−0.203652	+	0.979043i	$0.565281\pi$
$128$	−11.1183	+	2.09387i	−0.982725	+	0.185073i
$129$	1.74940	+	5.38411i	0.154026	+	0.474045i
$130$	18.3896	−	9.46634i	1.61287	−	0.830253i
$131$			13.3281i			1.16448i	0.813016	+	0.582241i	$0.197824\pi$
$131$			13.3281i			1.16448i	−0.813016	+	0.582241i	$0.802176\pi$
$132$		0			0
$133$			5.14699i			0.446301i
$134$	7.29419	+	14.1699i	0.630122	+	1.22409i
$135$	5.17328	+	15.9217i	0.445245	+	1.37032i
$136$	−6.27995	+	6.43839i	−0.538501	+	0.552088i
$137$	7.85466	+	5.70674i	0.671069	+	0.487560i	0.870383	−	0.492376i	$-0.163871\pi$
$137$	7.85466	+	5.70674i	0.671069	+	0.487560i	−0.199314	+	0.979936i	$0.563871\pi$
$138$	−2.12880	+	2.14655i	−0.181215	+	0.182726i
$139$	−21.1657	−	6.87716i	−1.79525	−	0.583313i	−0.795510	−	0.605941i	$-0.792797\pi$
$139$	−21.1657	−	6.87716i	−1.79525	−	0.583313i	−0.999744	+	0.0226274i	$0.992797\pi$
$140$	8.78304	−	0.0729434i	0.742302	−	0.00616484i
$141$	−0.183232	−	0.252197i	−0.0154309	−	0.0212388i
$142$	−7.80913	−	1.20363i	−0.655328	−	0.101006i
$143$		0			0
$144$	7.35315	+	5.15798i	0.612763	+	0.429832i
$145$	11.4152	−	8.29361i	0.947979	−	0.688747i
$146$	−0.606553	−	3.72933i	−0.0501987	−	0.308642i
$147$	−4.60260	−	1.49548i	−0.379616	−	0.123345i
$148$	−8.57238	+	6.33763i	−0.704645	+	0.520950i
$149$	7.40685	−	10.1947i	0.606793	−	0.835179i	−0.389516	−	0.921020i	$-0.627358\pi$
$149$	7.40685	−	10.1947i	0.606793	−	0.835179i	0.996309	+	0.0858410i	$0.0273577\pi$
$150$	9.32281	+	4.70155i	0.761205	+	0.383880i
$151$	4.68668	+	14.4241i	0.381397	+	1.17382i	0.939061	+	0.343751i	$0.111698\pi$
$151$	4.68668	+	14.4241i	0.381397	+	1.17382i	−0.557664	+	0.830067i	$0.688302\pi$
$152$	2.05499	+	12.0049i	0.166682	+	0.973722i
$153$	7.14020			0.577251
$154$		0			0
$155$		−	33.6136i		−	2.69991i
$156$	6.55885	−	2.19148i	0.525128	−	0.175459i
$157$	1.45191	−	0.471754i	0.115875	−	0.0376501i	−0.250506	−	0.968115i	$-0.580597\pi$
$157$	1.45191	−	0.471754i	0.115875	−	0.0376501i	0.366381	+	0.930465i	$0.380597\pi$
$158$	−7.32322	+	14.5214i	−0.582604	+	1.15526i
$159$	−1.70336	−	1.23757i	−0.135085	−	0.0981453i
$160$	20.4565	−	3.67686i	1.61723	−	0.290681i
$161$	0.908985	−	2.79757i	0.0716381	−	0.220479i
$162$	−0.630801	−	3.87842i	−0.0495604	−	0.304717i
$163$	−9.13195	−	12.5690i	−0.715269	−	0.984484i	−0.999668	−	0.0257776i	$-0.991794\pi$
$163$	−9.13195	−	12.5690i	−0.715269	−	0.984484i	0.284398	−	0.958706i	$-0.408206\pi$
$164$	−1.01658	−	0.320998i	−0.0793816	−	0.0250657i
$165$		0			0
$166$	0.216040	−	1.40167i	0.0167679	−	0.108791i
$167$	−6.79043	+	4.93353i	−0.525459	+	0.381768i	−0.818656	−	0.574284i	$-0.805281\pi$
$167$	−6.79043	+	4.93353i	−0.525459	+	0.381768i	0.293197	+	0.956052i	$0.405281\pi$
$168$	2.90601	+	0.423229i	0.224204	+	0.0326529i
$169$	−0.878998	+	2.70528i	−0.0676152	+	0.208098i
$170$	11.6346	−	11.7317i	0.892337	−	0.899778i
$171$	5.68340	−	7.82252i	0.434620	−	0.598203i
$172$	−10.6085	−	7.57370i	−0.808888	−	0.577489i
$173$	−23.6455	+	7.68290i	−1.79774	+	0.584120i	−0.999826	−	0.0186572i	$-0.994061\pi$
$173$	−23.6455	+	7.68290i	−1.79774	+	0.584120i	−0.797910	+	0.602777i	$0.794061\pi$
$174$	4.19448	−	2.15918i	0.317982	−	0.163687i
$175$	−10.1594			−0.767976
$176$		0			0
$177$	−0.517432			−0.0388926
$178$	17.1595	−	8.83317i	1.28616	−	0.662074i
$179$	15.6791	−	5.09444i	1.17191	−	0.380777i	0.342555	−	0.939498i	$-0.388708\pi$
$179$	15.6791	−	5.09444i	1.17191	−	0.380777i	0.829356	+	0.558721i	$0.188708\pi$
$180$	−13.4292	−	9.58752i	−1.00096	−	0.714612i
$181$	5.39531	−	7.42601i	0.401030	−	0.551971i	−0.559972	−	0.828512i	$-0.689188\pi$
$181$	5.39531	−	7.42601i	0.401030	−	0.551971i	0.961002	+	0.276541i	$0.0891880\pi$
$182$	−4.73804	+	4.77755i	−0.351207	+	0.354136i
$183$	1.95663	−	6.02189i	0.144638	−	0.445151i
$184$	1.00316	−	6.88798i	0.0739539	−	0.507788i
$185$	15.8444	−	11.5116i	1.16490	−	0.846350i
$186$	1.71199	−	11.1074i	0.125529	−	0.814434i
$187$		0			0
$188$	0.684436	+	0.216119i	0.0499176	+	0.0157621i
$189$	−3.20120	−	4.40607i	−0.232853	−	0.320495i
$190$	−3.59192	−	22.0846i	−0.260585	−	1.60218i
$191$	−0.763217	+	2.34894i	−0.0552244	+	0.169963i	−0.974864	−	0.222799i	$-0.928481\pi$
$191$	−0.763217	+	2.34894i	−0.0552244	+	0.169963i	0.919640	+	0.392763i	$0.128481\pi$
$192$	6.94697	−	0.173116i	0.501355	−	0.0124936i
$193$	−8.09515	−	5.88147i	−0.582702	−	0.423358i	0.256995	−	0.966413i	$-0.417268\pi$
$193$	−8.09515	−	5.88147i	−0.582702	−	0.423358i	−0.839697	+	0.543055i	$0.817268\pi$
$194$	3.78940	−	7.51409i	0.272063	−	0.539480i
$195$	−12.0822	+	3.92574i	−0.865224	+	0.281128i
$196$	10.5683	−	3.53114i	0.754878	−	0.252225i
$197$		−	11.7936i		−	0.840260i	−0.907464	−	0.420130i	$-0.861985\pi$
$197$		−	11.7936i		−	0.840260i	0.907464	−	0.420130i	$-0.138015\pi$
$198$		0			0
$199$	−14.7867			−1.04820			−0.524101	−	0.851656i	$-0.675598\pi$
$199$	−14.7867			−1.04820			−0.524101	+	0.851656i	$0.675598\pi$
$200$	−23.6957	+	4.05624i	−1.67554	+	0.286819i
$201$	−3.02494	−	9.30980i	−0.213363	−	0.656663i
$202$	7.54496	+	3.80497i	0.530861	+	0.267717i
$203$	−2.69807	+	3.71358i	−0.189368	+	0.260642i
$204$	4.44211	−	3.28409i	0.311010	−	0.229932i
$205$	1.86259	+	0.605191i	0.130089	+	0.0422684i
$206$	0.891238	+	5.47969i	0.0620955	+	0.381788i
$207$	−4.47062	+	3.24810i	−0.310730	+	0.225758i
$208$	−9.14352	+	13.0349i	−0.633989	+	0.903806i
$209$		0			0
$210$	−5.33196	−	0.821819i	−0.367940	−	0.0567109i
$211$	−4.99983	−	6.88168i	−0.344203	−	0.473754i	0.601460	−	0.798903i	$-0.294586\pi$
$211$	−4.99983	−	6.88168i	−0.344203	−	0.473754i	−0.945663	+	0.325148i	$0.894586\pi$
$212$	4.84757	−	0.0402592i	0.332932	−	0.00276501i
$213$	4.61565	+	1.49971i	0.316259	+	0.102759i
$214$	12.7575	−	12.8639i	0.872088	−	0.879361i
$215$	19.3725	+	14.0749i	1.32119	+	0.959902i
$216$	−9.22566	−	8.99862i	−0.627727	−	0.612279i
$217$	3.37915	+	10.4000i	0.229392	+	0.705995i
$218$	−3.65930	−	7.10865i	−0.247839	−	0.481458i
$219$			2.32074i			0.156821i
$220$		0			0
$221$			12.6574i			0.851427i
$222$	5.82197	−	2.99696i	0.390745	−	0.201143i
$223$	1.55218	+	4.77711i	0.103941	+	0.319899i	0.989481	−	0.144666i	$-0.0462108\pi$
$223$	1.55218	+	4.77711i	0.103941	+	0.319899i	−0.885539	+	0.464565i	$0.846211\pi$
$224$	−5.95954	+	3.19408i	−0.398189	+	0.213414i
$225$	15.4405	+	11.2181i	1.02936	+	0.747877i
$226$	−16.0651	−	15.9322i	−1.06863	−	1.05980i
$227$	17.1881	+	5.58475i	1.14081	+	0.370673i	0.817676	−	0.575679i	$-0.195262\pi$
$227$	17.1881	+	5.58475i	1.14081	+	0.370673i	0.323138	+	0.946352i	$0.395262\pi$
$228$	−0.0621269	−	7.48064i	−0.00411445	−	0.495418i
$229$	−2.34091	−	3.22199i	−0.154692	−	0.212915i	0.724636	−	0.689132i	$-0.242008\pi$
$229$	−2.34091	−	3.22199i	−0.154692	−	0.212915i	−0.879328	+	0.476217i	$0.842008\pi$
$230$	−1.94791	+	12.6381i	−0.128442	+	0.833330i
$231$		0			0
$232$	−4.81031	+	9.73880i	−0.315812	+	0.639383i
$233$	9.93905	−	7.22114i	0.651129	−	0.473073i	−0.212527	−	0.977155i	$-0.568169\pi$
$233$	9.93905	−	7.22114i	0.651129	−	0.473073i	0.863656	+	0.504082i	$0.168169\pi$
$234$	12.4764	−	2.02922i	0.815610	−	0.132654i
$235$	−1.25403	−	0.407459i	−0.0818038	−	0.0265797i
$236$	0.957982	−	0.708245i	0.0623593	−	0.0461028i
$237$	5.87160	−	8.08157i	0.381402	−	0.524954i
$238$	−2.42035	+	4.79937i	−0.156888	+	0.311097i
$239$	−6.47271	−	19.9210i	−0.418685	−	1.28858i	−0.908913	−	0.416985i	$-0.863087\pi$
$239$	−6.47271	−	19.9210i	−0.418685	−	1.28858i	0.490228	−	0.871594i	$-0.336913\pi$
$240$	−12.7644	+	0.212032i	−0.823938	+	0.0136866i
$241$	−17.4490			−1.12399			−0.561996	−	0.827140i	$-0.689966\pi$
$241$	−17.4490			−1.12399			−0.561996	+	0.827140i	$0.689966\pi$
$242$		0			0
$243$			16.0828i			1.03171i
$244$	4.62003	+	13.8272i	0.295767	+	0.885196i
$245$	−19.4681	+	6.32556i	−1.24377	+	0.404125i
$246$	0.584656	+	0.294846i	0.0372763	+	0.0187987i
$247$	13.8669	+	10.0749i	0.882332	+	0.641051i
$248$	12.0338	+	22.9077i	0.764149	+	1.45464i
$249$	−0.269185	+	0.828467i	−0.0170589	+	0.0525019i
$250$	17.9481	−	2.91915i	1.13514	−	0.184623i
$251$	3.50218	+	4.82034i	0.221056	+	0.304257i	0.905113	−	0.425171i	$-0.139786\pi$
$251$	3.50218	+	4.82034i	0.221056	+	0.304257i	−0.684057	+	0.729428i	$0.739786\pi$
$252$	5.11879	+	1.61632i	0.322454	+	0.101819i
$253$		0			0
$254$	12.9385	+	1.99421i	0.811832	+	0.125128i
$255$	−8.21036	+	5.96517i	−0.514153	+	0.373554i
$256$	−12.6248	+	9.82930i	−0.789048	+	0.614331i
$257$	−4.37822	+	13.4748i	−0.273106	+	0.840533i	0.716609	+	0.697476i	$0.245693\pi$
$257$	−4.37822	+	13.4748i	−0.273106	+	0.840533i	−0.989714	+	0.143058i	$0.954307\pi$
$258$	5.68465	+	5.63763i	0.353911	+	0.350984i
$259$	−3.74495	+	5.15448i	−0.232700	+	0.320284i
$260$	16.9957	−	23.8059i	1.05403	−	1.47638i
$261$	8.20120	−	2.66473i	0.507641	−	0.164943i
$262$	8.62684	+	16.7587i	0.532968	+	1.03536i
$263$	−11.0152			−0.679225			−0.339612	−	0.940566i	$-0.610296\pi$
$263$	−11.0152			−0.679225			−0.339612	+	0.940566i	$0.610296\pi$
$264$		0			0
$265$	−8.90572			−0.547074
$266$	3.33147	+	6.47181i	0.204266	+	0.396812i
$267$	−11.2741	+	3.66316i	−0.689961	+	0.224182i
$268$	18.3434	+	13.0959i	1.12050	+	0.799958i
$269$	−1.45964	+	2.00902i	−0.0889959	+	0.122492i	−0.851193	−	0.524852i	$-0.824121\pi$
$269$	−1.45964	+	2.00902i	−0.0889959	+	0.122492i	0.762197	+	0.647345i	$0.224121\pi$
$270$	16.8105	+	16.6714i	1.02305	+	1.01459i
$271$	−0.0950935	+	0.292668i	−0.00577652	+	0.0177783i	−0.953903	−	0.300114i	$-0.902975\pi$
$271$	−0.0950935	+	0.292668i	−0.00577652	+	0.0177783i	0.948127	+	0.317893i	$0.102975\pi$
$272$	−3.72903	+	12.1604i	−0.226106	+	0.737333i
$273$	3.34355	−	2.42923i	0.202361	−	0.147024i
$274$	13.5702	+	2.09158i	0.819806	+	0.126357i
$275$		0			0
$276$	−1.28735	+	4.07696i	−0.0774895	+	0.245404i
$277$	1.46947	+	2.02255i	0.0882919	+	0.121523i	0.850878	−	0.525363i	$-0.176071\pi$
$277$	1.46947	+	2.02255i	0.0882919	+	0.121523i	−0.762586	+	0.646887i	$0.776071\pi$
$278$	−31.0651	+	5.05254i	−1.86316	+	0.303031i
$279$	6.34809	−	19.5374i	0.380051	−	1.16968i
$280$	10.9966	−	5.77669i	0.657170	−	0.345223i
$281$	−1.00572	−	0.730699i	−0.0599963	−	0.0435899i	0.557383	−	0.830256i	$-0.311806\pi$
$281$	−1.00572	−	0.730699i	−0.0599963	−	0.0435899i	−0.617379	+	0.786666i	$0.711806\pi$
$282$	−0.393633	−	0.198512i	−0.0234405	−	0.0118212i
$283$	13.1263	−	4.26500i	0.780279	−	0.253528i	0.108320	−	0.994116i	$-0.465453\pi$
$283$	13.1263	−	4.26500i	0.780279	−	0.253528i	0.671959	+	0.740588i	$0.265453\pi$
$284$	−10.5982	+	3.54115i	−0.628890	+	0.210129i
$285$			13.7431i			0.814069i
$286$		0			0
$287$	−0.637118			−0.0376079
$288$	12.5844	+	1.72618i	0.741544	+	0.101716i
$289$	−2.12871	−	6.55151i	−0.125219	−	0.385383i
$290$	8.98523	−	17.8170i	0.527631	−	1.04625i
$291$	−3.03826	+	4.18181i	−0.178106	+	0.245142i
$292$	−3.17655	−	4.29665i	−0.185894	−	0.251442i
$293$	−14.1561	−	4.59959i	−0.827007	−	0.268711i	−0.135223	−	0.990815i	$-0.543175\pi$
$293$	−14.1561	−	4.59959i	−0.827007	−	0.268711i	−0.691784	+	0.722104i	$0.743175\pi$
$294$	−6.75527	+	1.09870i	−0.393975	+	0.0640777i
$295$	−1.77064	+	1.28645i	−0.103091	+	0.0748998i
$296$	−6.67674	+	13.5175i	−0.388078	+	0.785690i
$297$		0			0
$298$	2.71469	−	17.6129i	0.157258	−	1.02029i
$299$	−5.75788	−	7.92504i	−0.332987	−	0.458317i
$300$	14.7656	−	0.122629i	0.852494	−	0.00707998i
$301$	−7.40873	−	2.40724i	−0.427032	−	0.138751i
$302$	15.2293	+	15.1033i	0.876345	+	0.869097i
$303$	−4.19899	−	3.05074i	−0.241226	−	0.175261i
$304$	10.3543	+	13.7647i	0.593859	+	0.789462i
$305$	−8.27616	−	25.4714i	−0.473891	−	1.45849i
$306$	8.97806	−	4.62161i	0.513241	−	0.264200i
$307$			8.40361i			0.479619i	0.970820	+	0.239810i	$0.0770850\pi$
$307$			8.40361i			0.479619i	−0.970820	+	0.239810i	$0.922915\pi$
$308$		0			0
$309$		−	3.40997i		−	0.193986i
$310$	−21.7570	−	42.2656i	−1.23571	−	2.40053i
$311$	7.92512	+	24.3910i	0.449392	+	1.38309i	0.877594	+	0.479404i	$0.159147\pi$
$311$	7.92512	+	24.3910i	0.449392	+	1.38309i	−0.428202	+	0.903683i	$0.640853\pi$
$312$	6.82860	−	7.00088i	0.386593	−	0.396347i
$313$	−15.2762	−	11.0988i	−0.863460	−	0.627340i	0.0653641	−	0.997861i	$-0.479179\pi$
$313$	−15.2762	−	11.0988i	−0.863460	−	0.627340i	−0.928824	+	0.370521i	$0.879179\pi$
$314$	1.52028	−	1.53295i	0.0857941	−	0.0865096i
$315$	−9.37869	−	3.04732i	−0.528429	−	0.171697i
$316$	0.191009	+	22.9992i	0.0107451	+	1.29381i
$317$	−11.7338	−	16.1502i	−0.659037	−	0.907087i	0.340412	−	0.940276i	$-0.389434\pi$
$317$	−11.7338	−	16.1502i	−0.659037	−	0.907087i	−0.999449	+	0.0331895i	$0.989434\pi$
$318$	−2.94284	−	0.453581i	−0.165026	−	0.0254356i
$319$		0			0
$320$	23.3420	−	17.8640i	1.30486	−	0.998631i
$321$	−9.00277	+	6.54089i	−0.502485	+	0.365077i
$322$	−0.667817	−	4.10601i	−0.0372160	−	0.228819i
$323$	13.0225	+	4.23126i	0.724591	+	0.235434i
$324$	−3.30353	−	4.46841i	−0.183530	−	0.248245i
$325$	−19.8863	+	27.3712i	−1.10309	+	1.51828i
$326$	−19.6180	−	9.89348i	−1.08654	−	0.547949i
$327$	1.51753	+	4.67048i	0.0839196	+	0.258278i
$328$	−1.48602	+	0.254376i	−0.0820515	+	0.0140456i
$329$	0.428955			0.0236490
$330$		0			0
$331$			18.8624i			1.03677i	0.855147	+	0.518386i	$0.173467\pi$
$331$			18.8624i			1.03677i	−0.855147	+	0.518386i	$0.826533\pi$
$332$	−0.635604	−	1.90229i	−0.0348833	−	0.104402i
$333$	11.3833	−	3.69867i	0.623803	−	0.202686i
$334$	−5.34495	+	10.5986i	−0.292463	+	0.579931i
$335$	−33.4974	−	24.3373i	−1.83016	−	1.32969i
$336$	3.92795	−	1.34880i	0.214287	−	0.0735829i
$337$	−6.57702	+	20.2420i	−0.358273	+	1.10265i	0.595814	+	0.803123i	$0.296830\pi$
$337$	−6.57702	+	20.2420i	−0.358273	+	1.10265i	−0.954087	+	0.299529i	$0.903170\pi$
$338$	0.645786	+	3.97055i	0.0351261	+	0.215970i
$339$	8.16857	+	11.2431i	0.443656	+	0.610640i
$340$	7.03585	−	22.2821i	0.381572	−	1.20842i
$341$		0			0
$342$	2.08303	−	13.5147i	0.112637	−	0.730791i
$343$	12.1565	−	8.83220i	0.656388	−	0.476894i
$344$	−18.2413	−	2.65664i	−0.983502	−	0.143236i
$345$	2.42710	−	7.46983i	0.130670	−	0.402162i
$346$	−24.7589	+	24.9654i	−1.33105	+	1.34215i
$347$	−3.20169	+	4.40674i	−0.171876	+	0.236566i	−0.886261	−	0.463186i	$-0.846706\pi$
$347$	−3.20169	+	4.40674i	−0.171876	+	0.236566i	0.714386	+	0.699752i	$0.246706\pi$
$348$	3.87656	−	5.42989i	0.207805	−	0.291072i
$349$	9.70881	−	3.15458i	0.519701	−	0.168861i	−0.0374088	−	0.999300i	$-0.511910\pi$
$349$	9.70881	−	3.15458i	0.519701	−	0.168861i	0.557109	+	0.830439i	$0.311910\pi$
$350$	−12.7744	+	6.57582i	−0.682818	+	0.351492i
$351$	−18.1369			−0.968077
$352$		0			0
$353$	5.11121			0.272042			0.136021	−	0.990706i	$-0.456569\pi$
$353$	5.11121			0.272042			0.136021	+	0.990706i	$0.456569\pi$
$354$	−0.650618	+	0.334917i	−0.0345799	+	0.0178006i
$355$	19.5233	−	6.34349i	1.03619	−	0.336677i
$356$	15.8589	−	22.2136i	0.840522	−	1.17732i
$357$	1.94059	−	2.67099i	0.102707	−	0.141364i
$358$	16.4174	−	16.5543i	0.867685	−	0.874921i
$359$	−6.48321	+	19.9533i	−0.342171	+	1.05309i	0.620910	+	0.783882i	$0.286763\pi$
$359$	−6.48321	+	19.9533i	−0.342171	+	1.05309i	−0.963081	+	0.269212i	$0.913237\pi$
$360$	−23.0915	−	3.36303i	−1.21703	−	0.177247i
$361$	−0.370174	+	0.268947i	−0.0194828	+	0.0141551i
$362$	1.97744	−	12.8296i	0.103932	−	0.674311i
$363$		0			0
$364$	−2.86524	+	9.07405i	−0.150180	+	0.475609i
$365$	5.76985	+	7.94152i	0.302008	+	0.415678i
$366$	−1.43751	−	8.83837i	−0.0751397	−	0.461989i
$367$	−9.74300	+	29.9859i	−0.508580	+	1.56525i	0.286086	+	0.958204i	$0.407646\pi$
$367$	−9.74300	+	29.9859i	−0.508580	+	1.56525i	−0.794667	+	0.607046i	$0.792354\pi$
$368$	−3.19699	−	9.31023i	−0.166654	−	0.485329i
$369$	0.968308	+	0.703517i	0.0504081	+	0.0366236i
$370$	12.4716	−	24.7302i	0.648366	−	1.28566i
$371$	2.75540	−	0.895285i	0.143053	−	0.0464809i
$372$	−5.03679	−	15.0745i	−0.261146	−	0.781577i
$373$			24.8244i			1.28536i	0.766136	+	0.642678i	$0.222177\pi$
$373$			24.8244i			1.28536i	−0.766136	+	0.642678i	$0.777823\pi$
$374$		0			0
$375$	−11.1690			−0.576765
$376$	1.00049	−	0.171265i	0.0515966	−	0.00883230i
$377$	4.72375	+	14.5382i	0.243285	+	0.748755i
$378$	−6.87708	−	3.46815i	−0.353719	−	0.178383i
$379$	21.0081	−	28.9152i	1.07911	−	1.48527i	0.218620	−	0.975810i	$-0.429844\pi$
$379$	21.0081	−	28.9152i	1.07911	−	1.48527i	0.860493	−	0.509462i	$-0.170156\pi$
$380$	−18.8111	−	25.4441i	−0.964987	−	1.30526i
$381$	−7.64738	−	2.48479i	−0.391787	−	0.127299i
$382$	0.560723	+	3.44755i	0.0286891	+	0.176392i
$383$	15.4018	−	11.1901i	0.786997	−	0.571787i	−0.120073	−	0.992765i	$-0.538313\pi$
$383$	15.4018	−	11.1901i	0.786997	−	0.571787i	0.907071	+	0.420978i	$0.138313\pi$
$384$	8.62305	−	4.71422i	0.440043	−	0.240571i
$385$		0			0
$386$	−13.9857	−	2.15562i	−0.711853	−	0.109718i
$387$	8.60185	+	11.8394i	0.437257	+	0.601832i
$388$	−0.0988377	−	11.9009i	−0.00501772	−	0.604179i
$389$	−30.9758	−	10.0646i	−1.57053	−	0.510297i	−0.610938	−	0.791679i	$-0.709207\pi$
$389$	−30.9758	−	10.0646i	−1.57053	−	0.510297i	−0.959596	+	0.281381i	$0.909207\pi$
$390$	−12.6511	+	12.7566i	−0.640614	+	0.645956i
$391$	−6.33091	−	4.59968i	−0.320168	−	0.232616i
$392$	11.0029	−	11.2805i	0.555732	−	0.569754i
$393$	−3.57760	−	11.0107i	−0.180466	−	0.555417i
$394$	−7.63360	−	14.8292i	−0.384575	−	0.747086i
$395$		−	42.2530i		−	2.12598i
$396$		0			0
$397$		−	13.0143i		−	0.653167i	−0.945168	−	0.326584i	$-0.894103\pi$
$397$		−	13.0143i		−	0.653167i	0.945168	−	0.326584i	$-0.105897\pi$
$398$	−18.5927	+	9.57093i	−0.931970	+	0.479747i
$399$	−1.38158	−	4.25207i	−0.0691655	−	0.212870i
$400$	−27.1695	+	20.4377i	−1.35847	+	1.02189i
$401$	−16.6284	−	12.0813i	−0.830384	−	0.603310i	0.0892837	−	0.996006i	$-0.471542\pi$
$401$	−16.6284	−	12.0813i	−0.830384	−	0.603310i	−0.919668	+	0.392697i	$0.871542\pi$
$402$	−9.82947	−	9.74818i	−0.490249	−	0.486195i
$403$	34.6339	+	11.2532i	1.72523	+	0.560563i
$404$	11.9498	−	0.0992436i	0.594526	−	0.00493756i
$405$	6.00050	+	8.25898i	0.298167	+	0.410392i
$406$	−0.988874	+	6.41581i	−0.0490770	+	0.318412i
$407$		0			0
$408$	3.45981	−	7.00462i	0.171286	−	0.346781i
$409$	7.97764	−	5.79610i	0.394469	−	0.286598i	−0.372815	−	0.927906i	$-0.621608\pi$
$409$	7.97764	−	5.79610i	0.394469	−	0.286598i	0.767284	+	0.641307i	$0.221608\pi$
$410$	2.73373	−	0.444624i	0.135009	−	0.0219584i
$411$	−8.02078	−	2.60611i	−0.395636	−	0.128550i
$412$	4.66746	+	6.31327i	0.229949	+	0.311033i
$413$	0.418506	−	0.576025i	0.0205934	−	0.0283443i
$414$	−3.51896	+	6.97783i	−0.172947	+	0.342942i
$415$	1.13860	+	3.50425i	0.0558916	+	0.172017i
$416$	−3.05999	+	22.3083i	−0.150028	+	1.09375i
$417$	19.3316			0.946671
$418$		0			0
$419$		−	0.169087i		−	0.00826046i	−0.999991	−	0.00413023i	$-0.998685\pi$
$419$		−	0.169087i		−	0.00826046i	0.999991	−	0.00413023i	$-0.00131470\pi$
$420$	−7.23633	+	2.41785i	−0.353097	+	0.117979i
$421$	22.3620	−	7.26586i	1.08986	−	0.354116i	0.291666	−	0.956520i	$-0.405790\pi$
$421$	22.3620	−	7.26586i	1.08986	−	0.354116i	0.798192	+	0.602404i	$0.205790\pi$
$422$	−10.7411	−	5.41678i	−0.522866	−	0.263685i
$423$	−0.651936	−	0.473659i	−0.0316982	−	0.0230301i
$424$	6.06926	−	3.18829i	0.294749	−	0.154837i
$425$	−8.35186	+	25.7044i	−0.405125	+	1.24685i
$426$	6.77441	−	1.10182i	0.328221	−	0.0533832i
$427$	5.12124	+	7.04878i	0.247834	+	0.341114i
$428$	7.71490	−	24.4326i	0.372914	−	1.18099i
$429$		0			0
$430$	33.4691	+	5.15861i	1.61402	+	0.248770i
$431$	−5.89994	+	4.28656i	−0.284190	+	0.206476i	−0.720743	−	0.693202i	$-0.756199\pi$
$431$	−5.89994	+	4.28656i	−0.284190	+	0.206476i	0.436553	+	0.899679i	$0.356199\pi$
$432$	−17.4248	−	5.34338i	−0.838352	−	0.257083i
$433$	0.722575	−	2.22386i	0.0347247	−	0.106872i	−0.932192	−	0.361965i	$-0.882106\pi$
$433$	0.722575	−	2.22386i	0.0347247	−	0.106872i	0.966917	+	0.255093i	$0.0821061\pi$
$434$	10.9805	+	10.8897i	0.527080	+	0.522720i
$435$	−7.20417	+	9.91569i	−0.345414	+	0.475421i
$436$	−9.20237	−	6.56985i	−0.440714	−	0.314639i
$437$	−10.0785	+	3.27469i	−0.482118	+	0.156650i
$438$	1.50214	+	2.91809i	0.0717748	+	0.139432i
$439$	1.21401			0.0579413			0.0289707	−	0.999580i	$-0.490777\pi$
$439$	1.21401			0.0579413			0.0289707	+	0.999580i	$0.490777\pi$
$440$		0			0
$441$	−12.5102			−0.595722
$442$	8.19269	+	15.9153i	0.389687	+	0.757015i
$443$	−4.39270	+	1.42728i	−0.208704	+	0.0678119i	−0.411503	−	0.911408i	$-0.634996\pi$
$443$	−4.39270	+	1.42728i	−0.208704	+	0.0678119i	0.202799	+	0.979220i	$0.434996\pi$
$444$	5.38069	−	7.53673i	0.255356	−	0.357677i
$445$	−29.4722	+	40.5650i	−1.39711	+	1.92296i
$446$	5.04376	+	5.00205i	0.238829	+	0.236854i
$447$	−3.38250	+	10.4103i	−0.159987	+	0.492388i
$448$	−5.42609	+	7.87364i	−0.256358	+	0.371994i
$449$	−4.74796	+	3.44960i	−0.224070	+	0.162797i	−0.694157	−	0.719824i	$-0.744223\pi$
$449$	−4.74796	+	3.44960i	−0.224070	+	0.162797i	0.470087	+	0.882620i	$0.344223\pi$
$450$	26.6759	+	4.11157i	1.25751	+	0.193821i
$451$		0			0
$452$	−30.5126	−	9.63473i	−1.43519	−	0.453180i
$453$	−7.74358	−	10.6581i	−0.363825	−	0.500762i
$454$	25.2271	−	4.10303i	1.18397	−	0.192565i
$455$	5.40196	−	16.6255i	0.253248	−	0.779417i
$456$	−4.92009	−	9.36592i	−0.230404	−	0.438599i
$457$	−19.8188	−	14.3992i	−0.927084	−	0.673566i	0.0181932	−	0.999834i	$-0.494209\pi$
$457$	−19.8188	−	14.3992i	−0.927084	−	0.673566i	−0.945277	+	0.326269i	$0.894209\pi$
$458$	−5.02893	−	2.53612i	−0.234987	−	0.118505i
$459$	−13.7795	+	4.47724i	−0.643174	+	0.208980i
$460$	5.73090	+	17.1519i	0.267205	+	0.799711i
$461$		−	6.59878i		−	0.307336i	−0.988123	−	0.153668i	$-0.950891\pi$
$461$		−	6.59878i		−	0.307336i	0.988123	−	0.153668i	$-0.0491086\pi$
$462$		0			0
$463$	−14.4202			−0.670163			−0.335081	−	0.942189i	$-0.608764\pi$
$463$	−14.4202			−0.670163			−0.335081	+	0.942189i	$0.608764\pi$
$464$	0.255133	+	15.3591i	0.0118442	+	0.713027i
$465$	9.02273	+	27.7691i	0.418419	+	1.28776i
$466$	7.82333	−	15.5131i	0.362409	−	0.718628i
$467$	−3.22623	+	4.44053i	−0.149292	+	0.205483i	−0.877113	−	0.480285i	$-0.840533\pi$
$467$	−3.22623	+	4.44053i	−0.149292	+	0.205483i	0.727821	+	0.685768i	$0.240533\pi$
$468$	14.3744	−	10.6271i	0.664456	−	0.491238i
$469$	12.8106	+	4.16242i	0.591540	+	0.192203i
$470$	−1.84055	+	0.299353i	−0.0848980	+	0.0138081i
$471$	−1.07283	+	0.779457i	−0.0494334	+	0.0359155i
$472$	0.746141	−	1.51061i	0.0343439	−	0.0695316i
$473$		0			0
$474$	2.15201	−	13.9622i	0.0988450	−	0.641307i
$475$	21.5129	+	29.6100i	0.987079	+	1.35860i
$476$	0.0631292	+	7.60133i	0.00289352	+	0.348406i
$477$	−5.17632	−	1.68189i	−0.237007	−	0.0770084i
$478$	−21.0329	−	20.8590i	−0.962024	−	0.954067i
$479$	−24.1603	−	17.5535i	−1.10391	−	0.802039i	−0.122217	−	0.992503i	$-0.539001\pi$
$479$	−24.1603	−	17.5535i	−1.10391	−	0.802039i	−0.981694	+	0.190465i	$0.939001\pi$
$480$	−15.9127	+	8.52857i	−0.726311	+	0.389274i
$481$	6.55660	+	20.1791i	0.298955	+	0.920090i
$482$	−21.9404	+	11.2942i	−0.999356	+	0.514436i
$483$			2.55514i			0.116263i
$484$		0			0
$485$			21.8638i			0.992786i
$486$	10.4098	+	20.2224i	0.472200	+	0.917308i
$487$	−0.920108	−	2.83180i	−0.0416941	−	0.128321i	0.928043	−	0.372474i	$-0.121490\pi$
$487$	−0.920108	−	2.83180i	−0.0416941	−	0.128321i	−0.969737	+	0.244152i	$0.921490\pi$
$488$	14.7591	+	14.3959i	0.668113	+	0.651671i
$489$	10.9180	+	7.93238i	0.493729	+	0.358715i
$490$	−20.3848	+	20.5548i	−0.920890	+	0.928570i
$491$	−2.83468	−	0.921042i	−0.127927	−	0.0415661i	0.244354	−	0.969686i	$-0.421424\pi$
$491$	−2.83468	−	0.921042i	−0.127927	−	0.0415661i	−0.372281	+	0.928120i	$0.621424\pi$
$492$	0.925988	−	0.00769035i	0.0417468	−	0.000346708i
$493$	7.17774	+	9.87932i	0.323269	+	0.444942i
$494$	23.9574	+	3.69257i	1.07789	+	0.166136i
$495$		0			0
$496$	29.9587	+	21.0150i	1.34519	+	0.943601i
$497$	−5.40273	+	3.92532i	−0.242346	+	0.176075i
$498$	0.197766	+	1.21595i	0.00886211	+	0.0544878i
$499$	14.4506	+	4.69530i	0.646900	+	0.210190i	0.614047	−	0.789270i	$-0.289541\pi$
$499$	14.4506	+	4.69530i	0.646900	+	0.210190i	0.0328530	+	0.999460i	$0.489541\pi$
$500$	20.6785	−	15.2878i	0.924769	−	0.683689i
$501$	4.28547	−	5.89844i	0.191461	−	0.263523i
$502$	7.52368	+	3.79424i	0.335798	+	0.169345i
$503$	−10.1733	−	31.3103i	−0.453607	−	1.39606i	−0.872763	−	0.488144i	$-0.837674\pi$
$503$	−10.1733	−	31.3103i	−0.453607	−	1.39606i	0.419156	−	0.907914i	$-0.362326\pi$
$504$	7.48254	−	1.28086i	0.333299	−	0.0570542i
$505$	−21.9536			−0.976924
$506$		0			0
$507$		−	2.47085i		−	0.109734i
$508$	17.5596	−	5.86712i	0.779080	−	0.260311i
$509$	−12.8194	+	4.16527i	−0.568209	+	0.184622i	−0.579011	−	0.815319i	$-0.696561\pi$
$509$	−12.8194	+	4.16527i	−0.568209	+	0.184622i	0.0108026	+	0.999942i	$0.496561\pi$
$510$	−6.46262	+	12.8149i	−0.286170	+	0.567452i
$511$	−2.58353	−	1.87704i	−0.114289	−	0.0830356i
$512$	−9.51218	+	20.5309i	−0.420383	+	0.907347i
$513$	−6.06303	+	18.6601i	−0.267689	+	0.823863i
$514$	3.21661	+	19.7770i	0.141879	+	0.872326i
$515$	−8.47791	−	11.6688i	−0.373581	−	0.514191i
$516$	10.7969	+	3.40926i	0.475307	+	0.150084i
$517$		0			0
$518$	−1.37256	+	8.90520i	−0.0603070	+	0.391272i
$519$	17.4719	−	12.6941i	0.766932	−	0.557209i
$520$	5.96162	−	40.9342i	0.261435	−	1.79508i
$521$	2.87587	−	8.85103i	0.125994	−	0.387771i	−0.868087	−	0.496413i	$-0.834650\pi$
$521$	2.87587	−	8.85103i	0.125994	−	0.387771i	0.994081	+	0.108642i	$0.0346503\pi$
$522$	8.58737	−	8.65898i	0.375859	−	0.378993i
$523$	8.42368	−	11.5942i	0.368342	−	0.506979i	−0.584107	−	0.811676i	$-0.698555\pi$
$523$	8.42368	−	11.5942i	0.368342	−	0.506979i	0.952449	+	0.304697i	$0.0985554\pi$
$524$	21.6947	+	15.4885i	0.947738	+	0.676618i
$525$	8.39293	−	2.72703i	0.366297	−	0.119017i
$526$	−13.8504	+	7.12975i	−0.603908	+	0.310872i
$527$	29.0911			1.26723
$528$		0			0
$529$	−16.9437			−0.736682
$530$	−11.1980	+	5.76437i	−0.486411	+	0.250388i
$531$	−1.27211	+	0.413334i	−0.0552050	+	0.0179372i
$532$	8.37797	+	5.98128i	0.363231	+	0.259321i
$533$	−1.24712	+	1.71651i	−0.0540187	+	0.0743504i
$534$	−11.8049	+	11.9034i	−0.510849	+	0.515109i
$535$	−14.5452	+	44.7656i	−0.628845	+	1.93538i
$536$	31.5414	+	4.59367i	1.36238	+	0.198416i
$537$	−11.5854	+	8.41731i	−0.499949	+	0.363234i
$538$	−0.534975	+	3.47092i	−0.0230644	+	0.149642i
$539$		0			0
$540$	31.9283	+	10.0818i	1.37398	+	0.433850i
$541$	−13.5920	−	18.7077i	−0.584364	−	0.804308i	0.409801	−	0.912175i	$-0.365598\pi$
$541$	−13.5920	−	18.7077i	−0.584364	−	0.804308i	−0.994165	+	0.107867i	$0.965598\pi$
$542$	0.0698637	+	0.429550i	0.00300090	+	0.0184508i
$543$	−2.46389	+	7.58306i	−0.105735	+	0.325420i
$544$	3.18215	+	17.7041i	0.136434	+	0.759059i
$545$	16.8048	+	12.2094i	0.719836	+	0.522992i
$546$	2.63181	−	5.21867i	0.112631	−	0.223338i
$547$	−8.59894	+	2.79397i	−0.367664	+	0.119461i	−0.487021	−	0.873390i	$-0.661917\pi$
$547$	−8.59894	+	2.79397i	−0.367664	+	0.119461i	0.119357	+	0.992851i	$0.461917\pi$
$548$	18.4169	−	6.15359i	0.786733	−	0.262868i
$549$		−	16.3679i		−	0.698564i
$550$		0			0
$551$	16.5367			0.704487
$552$	1.02017	+	5.95962i	0.0434212	+	0.253658i
$553$	4.24766	+	13.0730i	0.180629	+	0.555919i
$554$	3.15684	+	1.59201i	0.134121	+	0.0676381i
$555$	−9.99945	+	13.7631i	−0.424453	+	0.584209i
$556$	−35.7908	+	26.4604i	−1.51787	+	1.12217i
$557$	26.4461	+	8.59286i	1.12056	+	0.364091i	0.809980	−	0.586457i	$-0.199478\pi$
$557$	26.4461	+	8.59286i	1.12056	+	0.364091i	0.310577	+	0.950548i	$0.399478\pi$
$558$	−4.66385	−	28.6752i	−0.197436	−	1.21392i
$559$	−20.9877	+	15.2484i	−0.887684	+	0.644940i
$560$	10.0880	−	14.3813i	0.426295	−	0.607720i
$561$		0			0
$562$	−1.73755	−	0.267809i	−0.0732940	−	0.0112969i
$563$	−20.7692	−	28.5863i	−0.875316	−	1.20477i	−0.977696	−	0.210024i	$-0.932646\pi$
$563$	−20.7692	−	28.5863i	−0.875316	−	1.20477i	0.102380	−	0.994745i	$-0.467354\pi$
$564$	−0.623443	+	0.00517771i	−0.0262517	+	0.000218021i
$565$	55.9053	+	18.1647i	2.35196	+	0.764197i
$566$	13.7444	−	13.8590i	0.577720	−	0.582538i
$567$	−2.68681	−	1.95208i	−0.112835	−	0.0819797i
$568$	−11.0341	+	11.3125i	−0.462982	+	0.474663i
$569$	−10.1065	−	31.1047i	−0.423687	−	1.30398i	−0.904246	−	0.427013i	$-0.859566\pi$
$569$	−10.1065	−	31.1047i	−0.423687	−	1.30398i	0.480558	−	0.876963i	$-0.340434\pi$
$570$	8.89542	+	17.2805i	0.372588	+	0.723800i
$571$			32.0987i			1.34329i	0.740874	+	0.671644i	$0.234412\pi$
$571$			32.0987i			1.34329i	−0.740874	+	0.671644i	$0.765588\pi$
$572$		0			0
$573$		−	2.14539i		−	0.0896249i
$574$	−0.801110	+	0.412385i	−0.0334377	+	0.0172126i
$575$	−6.46373	−	19.8933i	−0.269556	−	0.829609i
$576$	16.9409	−	5.97497i	0.705871	−	0.248957i
$577$	−17.1459	−	12.4572i	−0.713794	−	0.518602i	0.170601	−	0.985340i	$-0.445429\pi$
$577$	−17.1459	−	12.4572i	−0.713794	−	0.518602i	−0.884396	+	0.466738i	$0.845429\pi$
$578$	−6.91721	−	6.86000i	−0.287718	−	0.285338i
$579$	8.26636	+	2.68590i	0.343538	+	0.111622i
$580$	−0.234359	−	28.2189i	−0.00973121	−	1.17173i
$581$	−0.704558	−	0.969742i	−0.0292300	−	0.0402317i
$582$	−1.11356	+	7.22476i	−0.0461584	+	0.299476i
$583$		0			0
$584$	−6.77526	−	3.34652i	−0.280362	−	0.138480i
$585$	−26.5682	+	19.3029i	−1.09846	+	0.798079i
$586$	−20.7770	+	3.37924i	−0.858288	+	0.139595i
$587$	6.43150	+	2.08972i	0.265457	+	0.0862521i	0.438721	−	0.898623i	$-0.355432\pi$
$587$	6.43150	+	2.08972i	0.265457	+	0.0862521i	−0.173265	+	0.984875i	$0.555432\pi$
$588$	−7.78290	+	5.75396i	−0.320961	+	0.237289i
$589$	23.1557	−	31.8710i	0.954113	−	1.31322i
$590$	−1.39373	+	2.76365i	−0.0573788	+	0.113778i
$591$	3.16570	+	9.74301i	0.130219	+	0.400774i
$592$	0.354126	+	21.3185i	0.0145545	+	0.876186i
$593$	−8.93648			−0.366977			−0.183489	−	0.983022i	$-0.558739\pi$
$593$	−8.93648			−0.366977			−0.183489	+	0.983022i	$0.558739\pi$
$594$		0			0
$595$		−	13.9648i		−	0.572500i
$596$	−7.98681	−	23.9036i	−0.327153	−	0.979128i
$597$	12.2157	−	3.96912i	0.499955	−	0.162445i
$598$	−12.3695	−	6.23804i	−0.505828	−	0.255092i
$599$	4.58215	+	3.32913i	0.187222	+	0.136025i	0.677448	−	0.735571i	$-0.263086\pi$
$599$	4.58215	+	3.32913i	0.187222	+	0.136025i	−0.490226	+	0.871595i	$0.663086\pi$
$600$	18.4869	−	9.71149i	0.754724	−	0.396470i
$601$	10.6085	−	32.6495i	0.432729	−	1.33180i	−0.462668	−	0.886532i	$-0.653108\pi$
$601$	10.6085	−	32.6495i	0.432729	−	1.33180i	0.895396	−	0.445270i	$-0.146892\pi$
$602$	−10.8738	+	1.76856i	−0.443185	+	0.0720812i
$603$	−14.8737	−	20.4719i	−0.605703	−	0.833679i
$604$	28.9251	+	9.13346i	1.17694	+	0.371635i
$605$		0			0
$606$	−7.25444	−	1.11813i	−0.294691	−	0.0454210i
$607$	−32.7211	+	23.7733i	−1.32811	+	0.964929i	−0.328318	+	0.944567i	$0.606482\pi$
$607$	−32.7211	+	23.7733i	−1.32811	+	0.964929i	−0.999793	+	0.0203611i	$0.993518\pi$
$608$	21.9289	+	10.6058i	0.889334	+	0.430120i
$609$	1.23213	−	3.79212i	0.0499286	−	0.153664i
$610$	−26.8932	−	26.6708i	−1.08887	−	1.07987i
$611$	0.839652	−	1.15568i	0.0339687	−	0.0467539i
$612$	8.29757	−	11.6224i	0.335409	−	0.469807i
$613$	−13.7906	+	4.48085i	−0.556998	+	0.180980i	−0.573970	−	0.818876i	$-0.694597\pi$
$613$	−13.7906	+	4.48085i	−0.556998	+	0.180980i	0.0169719	+	0.999856i	$0.494597\pi$
$614$	5.43937	+	10.5667i	0.219515	+	0.426436i
$615$	−1.70118			−0.0685982
$616$		0			0
$617$	−17.5018			−0.704595			−0.352297	−	0.935888i	$-0.614599\pi$
$617$	−17.5018			−0.704595			−0.352297	+	0.935888i	$0.614599\pi$
$618$	−2.20716	−	4.28769i	−0.0887850	−	0.172476i
$619$	−26.6998	+	8.67528i	−1.07315	+	0.348689i	−0.791715	−	0.610890i	$-0.790812\pi$
$619$	−26.6998	+	8.67528i	−1.07315	+	0.348689i	−0.281439	+	0.959579i	$0.590812\pi$
$620$	−54.7142	−	39.0621i	−2.19738	−	1.56877i
$621$	6.59094	−	9.07165i	0.264485	−	0.364033i
$622$	25.7525	+	25.5395i	1.03258	+	1.02404i
$623$	5.04064	−	15.5135i	0.201949	−	0.621535i
$624$	4.05482	−	13.2228i	0.162323	−	0.529336i
$625$	−3.83860	+	2.78891i	−0.153544	+	0.111556i
$626$	−26.3921	−	4.06783i	−1.05484	−	0.162583i
$627$		0			0
$628$	0.919360	−	2.91155i	0.0366864	−	0.116184i
$629$	9.96277	+	13.7126i	0.397242	+	0.546756i
$630$	−13.7652	+	2.23882i	−0.548417	+	0.0891967i
$631$	5.53882	−	17.0467i	0.220497	−	0.678620i	−0.778221	−	0.627991i	$-0.783877\pi$
$631$	5.53882	−	17.0467i	0.220497	−	0.678620i	0.998718	−	0.0506287i	$-0.0161225\pi$
$632$	15.1268	+	28.7955i	0.601711	+	1.14542i
$633$	5.97771	+	4.34306i	0.237593	+	0.172621i
$634$	−25.2076	−	12.7123i	−1.00112	−	0.504871i
$635$	−32.3469	+	10.5101i	−1.28365	+	0.417082i
$636$	−3.99390	+	1.33447i	−0.158368	+	0.0529151i
$637$		−	22.1767i		−	0.878671i
$638$		0			0
$639$	12.5456			0.496297
$640$	17.7873	−	37.5707i	0.703106	−	1.48511i
$641$	1.09534	+	3.37112i	0.0432634	+	0.133151i	0.970355	−	0.241683i	$-0.0776995\pi$
$641$	1.09534	+	3.37112i	0.0432634	+	0.133151i	−0.927092	+	0.374835i	$0.877700\pi$
$642$	−7.08635	+	14.0517i	−0.279676	+	0.554576i
$643$	−9.19302	+	12.6531i	−0.362537	+	0.498990i	−0.950854	−	0.309641i	$-0.899791\pi$
$643$	−9.19302	+	12.6531i	−0.362537	+	0.498990i	0.588316	+	0.808631i	$0.299791\pi$
$644$	−3.49739	−	4.73063i	−0.137817	−	0.186413i
$645$	−19.7822	−	6.42762i	−0.778922	−	0.253087i
$646$	19.1132	−	3.10864i	0.751998	−	0.122308i
$647$	22.4391	−	16.3030i	0.882174	−	0.640937i	−0.0516518	−	0.998665i	$-0.516449\pi$
$647$	22.4391	−	16.3030i	0.882174	−	0.640937i	0.933826	+	0.357728i	$0.116449\pi$
$648$	−7.04611	−	3.48030i	−0.276797	−	0.136719i
$649$		0			0
$650$	−7.28856	+	47.2882i	−0.285881	+	1.85480i
$651$	−5.58321	−	7.68464i	−0.218823	−	0.301185i
$652$	−31.0713	+	0.258048i	−1.21685	+	0.0101059i
$653$	−4.21888	−	1.37080i	−0.165098	−	0.0536434i	0.225302	−	0.974289i	$-0.427663\pi$
$653$	−4.21888	−	1.37080i	−0.165098	−	0.0536434i	−0.390400	+	0.920646i	$0.627663\pi$
$654$	4.93118	+	4.89040i	0.192824	+	0.191230i
$655$	−39.6174	−	28.7837i	−1.54798	−	1.12467i
$656$	−1.70386	+	1.28170i	−0.0665246	+	0.0500420i
$657$	1.85385	+	5.70556i	0.0723255	+	0.222595i
$658$	0.539366	−	0.277648i	0.0210267	−	0.0108238i
$659$			14.0037i			0.545506i	0.962084	+	0.272753i	$0.0879341\pi$
$659$			14.0037i			0.545506i	−0.962084	+	0.272753i	$0.912066\pi$
$660$		0			0
$661$		−	33.4719i		−	1.30191i	−0.759118	−	0.650953i	$-0.774369\pi$
$661$		−	33.4719i		−	1.30191i	0.759118	−	0.650953i	$-0.225631\pi$
$662$	12.2090	+	23.7175i	0.474516	+	0.921808i
$663$	−3.39755	−	10.4566i	−0.131950	−	0.406100i
$664$	−2.03049	−	1.98052i	−0.0787984	−	0.0768593i
$665$	−15.2993	−	11.1156i	−0.593281	−	0.431044i
$666$	11.9193	−	12.0187i	0.461865	−	0.465717i
$667$	−8.98826	−	2.92046i	−0.348027	−	0.113081i
$668$	0.139410	+	16.7863i	0.00539395	+	0.649481i
$669$	−2.56459	−	3.52985i	−0.0991527	−	0.136472i
$670$	−57.8723	−	8.91989i	−2.23580	−	0.344605i
$671$		0			0
$672$	4.06597	−	4.23841i	0.156848	−	0.163500i
$673$	−0.817162	+	0.593703i	−0.0314993	+	0.0228856i	−0.603423	−	0.797421i	$-0.706197\pi$
$673$	−0.817162	+	0.593703i	−0.0314993	+	0.0228856i	0.571924	+	0.820306i	$0.306197\pi$
$674$	4.83204	+	29.7093i	0.186123	+	1.14436i
$675$	−36.8322	−	11.9675i	−1.41767	−	0.460629i
$676$	3.38201	+	4.57457i	0.130077	+	0.175945i
$677$	−18.3934	+	25.3163i	−0.706915	+	0.972985i	0.292943	+	0.956130i	$0.405365\pi$
$677$	−18.3934	+	25.3163i	−0.706915	+	0.972985i	−0.999858	+	0.0168552i	$0.994635\pi$
$678$	17.5484	+	8.84976i	0.673942	+	0.339873i
$679$	−2.19796	−	6.76461i	−0.0843498	−	0.259602i
$680$	−5.57559	−	32.5715i	−0.213814	−	1.24906i
$681$	−15.6986			−0.601573
$682$		0			0
$683$			12.2698i			0.469491i	0.972057	+	0.234745i	$0.0754256\pi$
$683$			12.2698i			0.469491i	−0.972057	+	0.234745i	$0.924574\pi$
$684$	−6.12841	−	18.3416i	−0.234326	−	0.701308i
$685$	−33.9263	+	11.0233i	−1.29626	+	0.421179i
$686$	9.56873	−	18.9741i	0.365336	−	0.724433i
$687$	2.79875	+	2.03341i	0.106779	+	0.0775794i
$688$	−24.6560	+	8.46650i	−0.940003	+	0.322782i
$689$	2.98147	−	9.17603i	0.113585	−	0.349579i
$690$	−1.78315	−	10.9635i	−0.0678833	−	0.417374i
$691$	6.17353	+	8.49714i	0.234852	+	0.323246i	0.910134	−	0.414313i	$-0.135978\pi$
$691$	6.17353	+	8.49714i	0.234852	+	0.323246i	−0.675282	+	0.737559i	$0.735978\pi$
$692$	−14.9725	+	47.4170i	−0.569170	+	1.80252i
$693$		0			0
$694$	−1.17345	+	7.61337i	−0.0445437	+	0.288999i
$695$	66.1522	−	48.0624i	2.50930	−	1.82311i
$696$	1.35979	−	9.33668i	0.0515426	−	0.353906i
$697$	−0.523765	+	1.61198i	−0.0198390	+	0.0610582i
$698$	10.1660	−	10.2507i	0.384788	−	0.387997i
$699$	−6.27258	+	8.63347i	−0.237251	+	0.326548i
$700$	−11.8061	+	16.5368i	−0.446230	+	0.625033i
$701$	−5.50999	+	1.79030i	−0.208109	+	0.0676188i	−0.411217	−	0.911538i	$-0.634896\pi$
$701$	−5.50999	+	1.79030i	−0.208109	+	0.0676188i	0.203107	+	0.979157i	$0.434896\pi$
$702$	−22.8053	+	11.7394i	−0.860730	+	0.443076i
$703$	22.9531			0.865691
$704$		0			0
$705$	1.14536			0.0431367
$706$	6.42681	−	3.30831i	0.241876	−	0.124510i
$707$	6.79240	−	2.20698i	0.255454	−	0.0830022i
$708$	−0.601304	+	0.842246i	−0.0225984	+	0.0316535i
$709$	26.7781	−	36.8569i	1.00567	−	1.38419i	0.0838916	−	0.996475i	$-0.473265\pi$
$709$	26.7781	−	36.8569i	1.00567	−	1.38419i	0.921780	−	0.387713i	$-0.126735\pi$
$710$	20.4425	−	20.6130i	0.767195	−	0.773593i
$711$	7.97969	−	24.5590i	0.299262	−	0.921033i
$712$	5.56287	−	38.1963i	0.208477	−	1.43147i
$713$	−18.2145	+	13.2336i	−0.682138	+	0.495603i
$714$	0.711247	−	4.61457i	0.0266177	−	0.172696i
$715$		0			0
$716$	9.92812	−	31.4417i	0.371031	−	1.17503i
$717$	10.6946	+	14.7198i	0.399396	+	0.549721i
$718$	4.76312	+	29.2856i	0.177758	+	1.09293i
$719$	0.905713	−	2.78750i	0.0337774	−	0.103956i	−0.932746	−	0.360533i	$-0.882595\pi$
$719$	0.905713	−	2.78750i	0.0337774	−	0.103956i	0.966524	+	0.256577i	$0.0825947\pi$
$720$	−31.2120	+	10.7177i	−1.16320	+	0.399426i
$721$	3.79610	+	2.75803i	0.141374	+	0.102714i
$722$	−0.291375	+	0.577774i	−0.0108439	+	0.0215025i
$723$	14.4151	−	4.68376i	0.536104	−	0.174191i
$724$	−5.81777	−	17.4119i	−0.216216	−	0.647108i
$725$			32.6409i			1.21225i
$726$		0			0
$727$	−24.5751			−0.911438			−0.455719	−	0.890124i	$-0.650618\pi$
$727$	−24.5751			−0.911438			−0.455719	+	0.890124i	$0.650618\pi$
$728$	2.27058	+	13.2643i	0.0841531	+	0.491606i
$729$	−1.74122	−	5.35891i	−0.0644895	−	0.198478i
$730$	12.3953	+	6.25101i	0.458769	+	0.231360i
$731$	−12.1812	+	16.7660i	−0.450538	+	0.620113i
$732$	−7.52830	−	10.1829i	−0.278254	−	0.376370i
$733$	19.7862	+	6.42893i	0.730820	+	0.237458i	0.650708	−	0.759328i	$-0.274472\pi$
$733$	19.7862	+	6.42893i	0.730820	+	0.237458i	0.0801122	+	0.996786i	$0.474472\pi$
$734$	7.15803	+	44.0105i	0.264208	+	1.62446i
$735$	14.3852	−	10.4514i	0.530605	−	0.385507i
$736$	−10.0461	−	9.63735i	−0.370303	−	0.355237i
$737$		0			0
$738$	1.67291	+	0.257847i	0.0615807	+	0.00949147i
$739$	−1.61711	−	2.22575i	−0.0594862	−	0.0818757i	0.778237	−	0.627970i	$-0.216114\pi$
$739$	−1.61711	−	2.22575i	−0.0594862	−	0.0818757i	−0.837724	+	0.546094i	$0.816114\pi$
$740$	−0.325292	−	39.1681i	−0.0119580	−	1.43985i
$741$	−14.1602	−	4.60093i	−0.520188	−	0.169019i
$742$	2.88515	−	2.90921i	0.105917	−	0.106800i
$743$	36.3879	+	26.4374i	1.33494	+	0.969894i	0.999614	+	0.0277933i	$0.00884801\pi$
$743$	36.3879	+	26.4374i	1.33494	+	0.969894i	0.335331	+	0.942101i	$0.391152\pi$
$744$	−16.0905	−	15.6945i	−0.589905	−	0.575388i
$745$	14.3073	+	44.0333i	0.524178	+	1.61325i
$746$	16.0680	+	31.2141i	0.588290	+	1.14283i
$747$			2.25182i			0.0823899i
$748$		0			0
$749$		−	15.3126i		−	0.559509i
$750$	−14.0439	+	7.22932i	−0.512809	+	0.263977i
$751$	−10.9010	−	33.5497i	−0.397782	−	1.22425i	−0.926774	−	0.375619i	$-0.877430\pi$
$751$	−10.9010	−	33.5497i	−0.397782	−	1.22425i	0.528992	−	0.848627i	$-0.322570\pi$
$752$	1.14716	−	0.862934i	0.0418328	−	0.0314680i
$753$	−4.18715	−	3.04214i	−0.152588	−	0.110862i
$754$	15.3497	+	15.2228i	0.559003	+	0.554380i
$755$	−52.9967	−	17.2197i	−1.92875	−	0.626688i
$756$	−10.8920	+	0.0904587i	−0.396140	+	0.00328995i
$757$	27.5638	+	37.9383i	1.00182	+	1.37889i	0.924201	+	0.381906i	$0.124732\pi$
$757$	27.5638	+	37.9383i	1.00182	+	1.37889i	0.0776206	+	0.996983i	$0.475268\pi$
$758$	7.69970	−	49.9557i	0.279666	−	1.81447i
$759$		0			0
$760$	−40.1221	−	19.8176i	−1.45538	−	0.718860i
$761$	3.57793	−	2.59952i	0.129700	−	0.0942324i	−0.521044	−	0.853530i	$-0.674457\pi$
$761$	3.57793	−	2.59952i	0.129700	−	0.0942324i	0.650744	+	0.759297i	$0.274457\pi$
$762$	−11.2241	+	1.82553i	−0.406607	+	0.0661321i
$763$	−6.42674	−	2.08818i	−0.232664	−	0.0755970i
$764$	2.93654	+	3.97200i	0.106240	+	0.143702i
$765$	−15.4202	+	21.2240i	−0.557517	+	0.767356i
$766$	12.1233	−	24.0395i	0.438031	−	0.868582i
$767$	−0.732715	−	2.25506i	−0.0264568	−	0.0814256i
$768$	7.79124	−	11.5090i	0.281142	−	0.415297i
$769$	−53.6158			−1.93344			−0.966718	−	0.255844i	$-0.917647\pi$
$769$	−53.6158			−1.93344			−0.966718	+	0.255844i	$0.917647\pi$
$770$		0			0
$771$		−	12.3071i		−	0.443229i
$772$	−18.9808	+	6.34200i	−0.683135	+	0.228253i
$773$	40.8810	−	13.2830i	1.47039	−	0.477758i	0.539161	−	0.842202i	$-0.318741\pi$
$773$	40.8810	−	13.2830i	1.47039	−	0.477758i	0.931225	+	0.364445i	$0.118741\pi$
$774$	18.4792	+	9.31917i	0.664221	+	0.334971i
$775$	62.9085	+	45.7057i	2.25974	+	1.64180i
$776$	−7.82736	−	14.9002i	−0.280986	−	0.534887i
$777$	1.71021	−	5.26349i	0.0613535	−	0.188827i
$778$	−45.4633	+	7.39433i	−1.62994	+	0.265100i
$779$	1.34912	+	1.85691i	0.0483374	+	0.0665307i
$780$	−7.65054	+	24.2288i	−0.273933	+	0.867529i
$781$		0			0
$782$	−10.9377	−	1.68583i	−0.391131	−	0.0602852i
$783$	−14.1562	+	10.2851i	−0.505901	+	0.367559i
$784$	6.53354	−	21.3060i	0.233341	−	0.760927i
$785$	−1.73331	+	5.33457i	−0.0618644	+	0.190399i
$786$	−11.6253	−	11.5292i	−0.414661	−	0.411232i
$787$	8.95616	−	12.3271i	0.319253	−	0.439414i	−0.618986	−	0.785402i	$-0.712456\pi$
$787$	8.95616	−	12.3271i	0.319253	−	0.439414i	0.938239	+	0.345988i	$0.112456\pi$
$788$	−19.1969	−	13.7053i	−0.683863	−	0.488230i
$789$	9.09993	−	2.95675i	0.323966	−	0.105263i
$790$	−27.3489	−	53.1288i	−0.973032	−	1.89024i
$791$	−19.1230			−0.679937
$792$		0			0
$793$	29.0152			1.03036
$794$	−8.42370	−	16.3641i	−0.298946	−	0.580740i
$795$	7.35725	−	2.39052i	0.260935	−	0.0847829i
$796$	−17.1835	+	24.0689i	−0.609053	+	0.853100i
$797$	18.9900	−	26.1375i	0.672660	−	0.925837i	−0.327157	−	0.944970i	$-0.606091\pi$
$797$	18.9900	−	26.1375i	0.672660	−	0.925837i	0.999817	+	0.0191333i	$0.00609068\pi$
$798$	−4.48941	−	4.45228i	−0.158924	−	0.157609i
$799$	0.352637	−	1.08531i	0.0124754	−	0.0383953i
$800$	−20.9341	+	43.2842i	−0.740133	+	1.53033i
$801$	−24.7912	+	18.0118i	−0.875953	+	0.636417i
$802$	−28.7283	−	4.42792i	−1.01443	−	0.156355i
$803$		0			0
$804$	−18.6692	−	5.89504i	−0.658412	−	0.207902i
$805$	6.35262	+	8.74363i	0.223901	+	0.308173i
$806$	50.8323	−	8.26756i	1.79049	−	0.291213i
$807$	0.666577	−	2.05151i	0.0234646	−	0.0722167i
$808$	14.9614	−	7.85951i	0.526342	−	0.276497i
$809$	40.7382	+	29.5981i	1.43228	+	1.04061i	0.989587	+	0.143939i	$0.0459769\pi$
$809$	40.7382	+	29.5981i	1.43228	+	1.04061i	0.442693	+	0.896673i	$0.354023\pi$
$810$	12.8908	+	6.50089i	0.452935	+	0.228418i
$811$	41.5216	−	13.4912i	1.45802	−	0.473739i	0.530555	−	0.847650i	$-0.321984\pi$
$811$	41.5216	−	13.4912i	1.45802	−	0.473739i	0.927464	+	0.373911i	$0.121984\pi$
$812$	2.90933	+	8.70729i	0.102098	+	0.305566i
$813$		−	0.267306i		−	0.00937483i
$814$		0			0
$815$	57.0827			1.99952
$816$	−0.183504	−	11.0470i	−0.00642393	−	0.386723i
$817$	8.67228	+	26.6905i	0.303405	+	0.933783i
$818$	6.27944	−	12.4516i	0.219556	−	0.435362i
$819$	6.27963	−	8.64316i	0.219428	−	0.302017i
$820$	3.14959	−	2.32852i	0.109988	−	0.0813154i
$821$	18.0688	+	5.87092i	0.630607	+	0.204897i	0.606844	−	0.794821i	$-0.292435\pi$
$821$	18.0688	+	5.87092i	0.630607	+	0.204897i	0.0237628	+	0.999718i	$0.492435\pi$
$822$	−11.7721	+	1.91467i	−0.410601	+	0.0667817i
$823$	10.6891	−	7.76610i	0.372599	−	0.270709i	−0.385689	−	0.922629i	$-0.626036\pi$
$823$	10.6891	−	7.76610i	0.372599	−	0.270709i	0.758288	+	0.651920i	$0.226036\pi$
$824$	9.95521	+	4.91720i	0.346806	+	0.171299i
$825$		0			0
$826$	0.153387	−	0.995176i	0.00533702	−	0.0346266i
$827$	−10.4334	−	14.3603i	−0.362804	−	0.499357i	0.588123	−	0.808771i	$-0.299867\pi$
$827$	−10.4334	−	14.3603i	−0.362804	−	0.499357i	−0.950927	+	0.309415i	$0.899867\pi$
$828$	0.0917838	+	11.0516i	0.00318971	+	0.384070i
$829$	−8.14454	−	2.64632i	−0.282872	−	0.0919106i	0.164145	−	0.986436i	$-0.447514\pi$
$829$	−8.14454	−	2.64632i	−0.282872	−	0.0919106i	−0.447017	+	0.894526i	$0.647514\pi$
$830$	3.69985	+	3.66925i	0.128424	+	0.127362i
$831$	−1.75687	−	1.27644i	−0.0609452	−	0.0442793i
$832$	10.5918	+	30.0310i	0.367204	+	1.04114i
$833$	−5.47449	−	16.8487i	−0.189680	−	0.583774i
$834$	24.3075	−	12.5127i	0.841699	−	0.433279i
$835$		−	30.8389i		−	1.06723i
$836$		0			0
$837$			41.6850i			1.44084i
$838$	−0.109445	−	0.212610i	−0.00378070	−	0.00734449i
$839$	−11.7633	−	36.2037i	−0.406114	−	1.24989i	−0.919962	−	0.392008i	$-0.871780\pi$
$839$	−11.7633	−	36.2037i	−0.406114	−	1.24989i	0.513848	−	0.857881i	$-0.328220\pi$
$840$	−7.53394	+	7.72402i	−0.259946	+	0.266504i
$841$	−11.5302	−	8.37718i	−0.397593	−	0.288868i
$842$	23.4150	−	23.6102i	0.806933	−	0.813663i
$843$	1.02699	+	0.333690i	0.0353715	+	0.0114929i
$844$	−17.0119	+	0.141284i	−0.585572	+	0.00486319i
$845$	−6.14305	−	8.45519i	−0.211327	−	0.290867i
$846$	−1.12633	−	0.173601i	−0.0387239	−	0.00596853i
$847$		0			0
$848$	5.56779	−	7.93737i	0.191199	−	0.272571i
$849$	−9.69917	+	7.04686i	−0.332875	+	0.241848i
$850$	6.13598	+	37.7265i	0.210462	+	1.29401i
$851$	−12.4758	−	4.05363i	−0.427664	−	0.138957i
$852$	7.80496	−	5.77027i	0.267393	−	0.197686i
$853$	20.1305	−	27.7072i	0.689254	−	0.948677i	−0.310744	−	0.950493i	$-0.600578\pi$
$853$	20.1305	−	27.7072i	0.689254	−	0.948677i	0.999998	+	0.00181694i	$0.000578350\pi$
$854$	11.0019	+	5.54831i	0.376476	+	0.189859i
$855$	10.9782	+	33.7875i	0.375447	+	1.15551i
$856$	−6.11371	−	35.7151i	−0.208962	−	1.22072i
$857$	52.8215			1.80435			0.902174	−	0.431371i	$-0.141970\pi$
$857$	52.8215			1.80435			0.902174	+	0.431371i	$0.141970\pi$
$858$		0			0
$859$			8.91497i			0.304175i	0.988367	+	0.152087i	$0.0485995\pi$
$859$			8.91497i			0.304175i	−0.988367	+	0.152087i	$0.951400\pi$
$860$	45.4229	−	15.1770i	1.54891	−	0.517531i
$861$	0.526340	−	0.171018i	0.0179376	−	0.00582829i
$862$	−4.64402	+	9.20874i	−0.158176	+	0.313651i
$863$	0.848339	+	0.616354i	0.0288778	+	0.0209809i	0.602131	−	0.798398i	$-0.294319\pi$
$863$	0.848339	+	0.616354i	0.0288778	+	0.0209809i	−0.573253	+	0.819379i	$0.694319\pi$
$864$	−25.3685	+	4.55975i	−0.863054	+	0.155126i
$865$	28.2283	−	86.8778i	0.959791	−	2.95393i
$866$	−0.530864	−	3.26397i	−0.0180395	−	0.110914i
$867$	3.51718	+	4.84098i	0.119450	+	0.164408i
$868$	20.8553	+	6.58533i	0.707876	+	0.223521i
$869$		0			0
$870$	−2.64041	+	17.1310i	−0.0895182	+	0.580794i
$871$	36.2903	−	26.3665i	1.22965	−	0.893393i
$872$	−15.8235	−	2.30452i	−0.535851	−	0.0780408i
$873$	−4.12909	+	12.7080i	−0.139749	+	0.430102i
$874$	−10.5530	+	10.6410i	−0.356961	+	0.359938i
$875$	9.03364	−	12.4337i	0.305393	−	0.420337i
$876$	3.77756	+	2.69691i	0.127632	+	0.0911203i
$877$	11.4920	−	3.73397i	0.388056	−	0.126087i	−0.108490	−	0.994098i	$-0.534601\pi$
$877$	11.4920	−	3.73397i	0.388056	−	0.126087i	0.496546	+	0.868010i	$0.334601\pi$
$878$	1.52649	−	0.785785i	0.0515164	−	0.0265190i
$879$	12.9294			0.436096
$880$		0			0
$881$	11.8356			0.398752			0.199376	−	0.979923i	$-0.436109\pi$
$881$	11.8356			0.398752			0.199376	+	0.979923i	$0.436109\pi$
$882$	−15.7302	+	8.09740i	−0.529664	+	0.272654i
$883$	−48.6275	+	15.8000i	−1.63645	+	0.531713i	−0.975740	−	0.218932i	$-0.929743\pi$
$883$	−48.6275	+	15.8000i	−1.63645	+	0.531713i	−0.660705	+	0.750645i	$0.729743\pi$
$884$	20.6029	+	14.7090i	0.692951	+	0.494718i
$885$	1.11746	−	1.53805i	0.0375630	−	0.0517011i
$886$	−4.59954	+	4.63790i	−0.154525	+	0.155813i
$887$	−5.24892	+	16.1545i	−0.176242	+	0.542416i	−0.999688	−	0.0249781i	$-0.992048\pi$
$887$	−5.24892	+	16.1545i	−0.176242	+	0.542416i	0.823446	+	0.567394i	$0.192048\pi$
$888$	1.88740	−	12.9594i	0.0633369	−	0.434889i
$889$	8.95146	−	6.50362i	0.300222	−	0.218124i
$890$	−10.8019	+	70.0826i	−0.362080	+	2.34917i
$891$		0			0
$892$	9.57966	+	3.02490i	0.320751	+	0.101281i
$893$	−0.908329	−	1.25021i	−0.0303961	−	0.0418366i
$894$	2.48507	+	15.2792i	0.0831131	+	0.511013i
$895$	−18.7179	+	57.6077i	−0.625670	+	1.92561i
$896$	−1.72640	+	13.4124i	−0.0576750	+	0.448077i
$897$	6.88401	+	5.00153i	0.229850	+	0.166996i
$898$	−3.73726	+	7.41071i	−0.124714	+	0.247299i
$899$	33.4139	−	10.8568i	1.11441	−	0.362095i
$900$	36.2035	−	12.0965i	1.20678	−	0.403218i
$901$		−	7.70750i		−	0.256774i
$902$		0			0
$903$	6.76671			0.225182
$904$	−44.6026	+	7.63508i	−1.48346	+	0.253939i
$905$	10.4217	+	32.0748i	0.346430	+	1.06620i
$906$	−16.6354	−	8.38933i	−0.552674	−	0.278717i
$907$	8.46620	−	11.6527i	0.281116	−	0.386922i	−0.644987	−	0.764193i	$-0.723137\pi$
$907$	8.46620	−	11.6527i	0.281116	−	0.386922i	0.926103	+	0.377271i	$0.123137\pi$
$908$	29.0647	−	21.4878i	0.964545	−	0.713097i
$909$	−12.7602	−	4.14605i	−0.423231	−	0.137516i
$910$	−3.96874	−	24.4014i	−0.131562	−	0.808898i
$911$	32.3517	−	23.5049i	1.07186	−	0.778751i	0.0956137	−	0.995419i	$-0.469519\pi$
$911$	32.3517	−	23.5049i	1.07186	−	0.778751i	0.976246	+	0.216667i	$0.0695187\pi$
$912$	−12.2487	−	8.59207i	−0.405596	−	0.284512i
$913$		0			0
$914$	−34.2402	−	5.27746i	−1.13256	−	0.174563i
$915$	13.6743	+	18.8211i	0.452059	+	0.622205i
$916$	−7.96491	+	0.0661488i	−0.263168	+	0.00218562i
$917$	15.1511	+	4.92290i	0.500334	+	0.162568i
$918$	−14.4284	+	14.5487i	−0.476207	+	0.480179i
$919$	−5.72709	−	4.16097i	−0.188919	−	0.137258i	0.489305	−	0.872112i	$-0.337250\pi$
$919$	−5.72709	−	4.16097i	−0.188919	−	0.137258i	−0.678225	+	0.734855i	$0.737250\pi$
$920$	18.3079	+	17.8573i	0.603592	+	0.588738i
$921$	−2.25574	−	6.94245i	−0.0743291	−	0.228761i
$922$	−4.27117	−	8.29728i	−0.140663	−	0.273256i
$923$			22.2395i			0.732022i
$924$		0			0
$925$			45.3058i			1.48965i
$926$	−18.1319	+	9.33370i	−0.595851	+	0.306724i
$927$	−2.72395	−	8.38345i	−0.0894661	−	0.275348i
$928$	10.2622	+	19.1473i	0.336874	+	0.628541i
$929$	31.0156	+	22.5341i	1.01759	+	0.739320i	0.965787	−	0.259337i	$-0.0835040\pi$
$929$	31.0156	+	22.5341i	1.01759	+	0.739320i	0.0518005	+	0.998657i	$0.483504\pi$
$930$	29.3191	+	29.0767i	0.961413	+	0.953461i
$931$	−22.8164	−	7.41349i	−0.747776	−	0.242967i
$932$	−0.204053	−	24.5698i	−0.00668398	−	0.804812i
$933$	−13.0943	−	18.0228i	−0.428688	−	0.590039i
$934$	−1.18245	+	7.67174i	−0.0386909	+	0.251027i
$935$		0			0
$936$	11.1957	−	22.6665i	0.365944	−	0.740879i
$937$	−46.9358	+	34.1009i	−1.53333	+	1.11403i	−0.578973	+	0.815346i	$0.696546\pi$
$937$	−46.9358	+	34.1009i	−1.53333	+	1.11403i	−0.954353	+	0.298680i	$0.903454\pi$
$938$	18.8022	−	3.05807i	0.613915	−	0.0998494i
$939$	15.5992	+	5.06850i	0.509062	+	0.165404i
$940$	−2.12053	+	1.56773i	−0.0691642	+	0.0511337i
$941$	6.48795	−	8.92990i	0.211501	−	0.291106i	−0.690065	−	0.723747i	$-0.742418\pi$
$941$	6.48795	−	8.92990i	0.211501	−	0.291106i	0.901566	+	0.432641i	$0.142418\pi$
$942$	−0.844457	+	1.67449i	−0.0275139	+	0.0545580i
$943$	−0.405356	−	1.24756i	−0.0132002	−	0.0406261i
$944$	−0.0395744	−	2.38239i	−0.00128804	−	0.0775403i
$945$	20.0103			0.650936
$946$		0			0
$947$			15.5478i			0.505235i	0.967566	+	0.252617i	$0.0812914\pi$
$947$			15.5478i			0.505235i	−0.967566	+	0.252617i	$0.918709\pi$
$948$	−6.33136	−	18.9490i	−0.205633	−	0.615434i
$949$	−10.1142	+	3.28630i	−0.328321	+	0.106678i
$950$	46.2158	+	23.3069i	1.49944	+	0.756175i
$951$	14.0287	+	10.1925i	0.454913	+	0.330514i
$952$	4.99946	+	9.51702i	0.162033	+	0.308448i
$953$	−2.41825	+	7.44259i	−0.0783346	+	0.241089i	−0.982554	−	0.185980i	$-0.940454\pi$
$953$	−2.41825	+	7.44259i	−0.0783346	+	0.241089i	0.904219	+	0.427069i	$0.140454\pi$
$954$	−7.59732	+	1.23566i	−0.245972	+	0.0400059i
$955$	−5.33389	−	7.34147i	−0.172601	−	0.237564i
$956$	−39.9480	−	12.6141i	−1.29201	−	0.407969i
$957$		0			0
$958$	−41.7408	−	6.43354i	−1.34858	−	0.207858i
$959$	9.38853	−	6.82116i	0.303171	−	0.220267i
$960$	−14.4883	+	21.0235i	−0.467607	+	0.678532i
$961$	16.2843	−	50.1179i	0.525300	−	1.61671i
$962$	21.3055	+	21.1293i	0.686918	+	0.681237i
$963$	−16.9084	+	23.2724i	−0.544866	+	0.749943i
$964$	−20.2774	+	28.4025i	−0.653091	+	0.914784i
$965$	34.9650	−	11.3608i	1.12556	−	0.365718i
$966$	1.65386	+	3.21283i	0.0532120	+	0.103371i
$967$	47.0564			1.51323			0.756615	−	0.653860i	$-0.226852\pi$
$967$	47.0564			1.51323			0.756615	+	0.653860i	$0.226852\pi$
$968$		0			0
$969$	−11.8940			−0.382090
$970$	14.1517	+	27.4915i	0.454385	+	0.882699i
$971$	36.8899	−	11.9863i	1.18385	−	0.384657i	0.350057	−	0.936729i	$-0.386162\pi$
$971$	36.8899	−	11.9863i	1.18385	−	0.384657i	0.833797	+	0.552071i	$0.186162\pi$
$972$	26.1786	+	18.6897i	0.839679	+	0.599472i
$973$	−15.6356	+	21.5206i	−0.501256	+	0.689919i
$974$	−2.98987	−	2.96514i	−0.0958016	−	0.0950093i
$975$	9.08152	−	27.9500i	0.290841	−	0.895118i
$976$	27.8760	+	8.54827i	0.892289	+	0.273624i
$977$	31.5826	−	22.9461i	1.01042	−	0.734111i	0.0461207	−	0.998936i	$-0.485314\pi$
$977$	31.5826	−	22.9461i	1.01042	−	0.734111i	0.964297	+	0.264825i	$0.0853141\pi$
$978$	18.8626	+	2.90731i	0.603160	+	0.0929654i
$979$		0			0
$980$	−12.3273	+	39.0399i	−0.393782	+	1.24708i
$981$	7.46172	+	10.2702i	0.238234	+	0.327902i
$982$	−4.16047	+	0.676675i	−0.132766	+	0.0215936i
$983$	1.73793	−	5.34880i	0.0554314	−	0.170600i	−0.919508	−	0.393072i	$-0.871412\pi$
$983$	1.73793	−	5.34880i	0.0554314	−	0.170600i	0.974939	+	0.222471i	$0.0714124\pi$
$984$	1.15936	−	0.609031i	0.0369589	−	0.0194152i
$985$	35.0561	+	25.4698i	1.11698	+	0.811535i
$986$	15.4198	+	7.77631i	0.491067	+	0.247648i
$987$	−0.354371	+	0.115142i	−0.0112797	+	0.00366501i
$988$	32.5140	−	10.8638i	1.03441	−	0.345623i
$989$		−	16.0388i		−	0.510004i
$990$		0			0
$991$	7.34032			0.233173			0.116586	−	0.993181i	$-0.462805\pi$
$991$	7.34032			0.233173			0.116586	+	0.993181i	$0.462805\pi$
$992$	51.2723	+	7.03293i	1.62790	+	0.223296i
$993$	−5.06314	−	15.5827i	−0.160674	−	0.494503i
$994$	−4.25266	+	8.43269i	−0.134886	+	0.267469i
$995$	31.9337	−	43.9530i	1.01237	−	1.39340i
$996$	1.03571	+	1.40092i	0.0328178	+	0.0443898i
$997$	−54.1523	−	17.5952i	−1.71502	−	0.557244i	−0.723864	−	0.689942i	$-0.757636\pi$
$997$	−54.1523	−	17.5952i	−1.71502	−	0.557244i	−0.991156	+	0.132698i	$0.957636\pi$
$998$	21.2093	−	3.44956i	0.671369	−	0.109194i
$999$	−19.6489	+	14.2758i	−0.621665	+	0.451666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	968.2.o.i.245.8		40
8.5	even	2	inner	968.2.o.i.245.7		40
11.2	odd	10		968.2.c.h.485.20		20
11.3	even	5		968.2.o.d.269.5		40
11.4	even	5	inner	968.2.o.i.565.7		40
11.5	even	5		968.2.o.d.493.4		40
11.6	odd	10		968.2.o.j.493.7		40
11.7	odd	10		88.2.o.a.37.4	yes	40
11.8	odd	10		968.2.o.j.269.6		40
11.9	even	5		968.2.c.i.485.1		20
11.10	odd	2		88.2.o.a.69.3	yes	40
33.29	even	10		792.2.br.b.37.7		40
33.32	even	2		792.2.br.b.685.8		40
44.7	even	10		352.2.w.a.81.4		40
44.31	odd	10		3872.2.c.i.1937.7		20
44.35	even	10		3872.2.c.h.1937.7		20
44.43	even	2		352.2.w.a.113.7		40
88.5	even	10		968.2.o.d.493.5		40
88.13	odd	10		968.2.c.h.485.19		20
88.21	odd	2		88.2.o.a.69.4	yes	40
88.29	odd	10		88.2.o.a.37.3	✓	40
88.35	even	10		3872.2.c.h.1937.14		20
88.37	even	10	inner	968.2.o.i.565.8		40
88.43	even	2		352.2.w.a.113.4		40
88.51	even	10		352.2.w.a.81.7		40
88.53	even	10		968.2.c.i.485.2		20
88.61	odd	10		968.2.o.j.493.6		40
88.69	even	10		968.2.o.d.269.4		40
88.75	odd	10		3872.2.c.i.1937.14		20
88.85	odd	10		968.2.o.j.269.7		40
264.29	even	10		792.2.br.b.37.8		40
264.197	even	2		792.2.br.b.685.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.3	✓	40	88.29	odd	10
88.2.o.a.37.4	yes	40	11.7	odd	10
88.2.o.a.69.3	yes	40	11.10	odd	2
88.2.o.a.69.4	yes	40	88.21	odd	2
352.2.w.a.81.4		40	44.7	even	10
352.2.w.a.81.7		40	88.51	even	10
352.2.w.a.113.4		40	88.43	even	2
352.2.w.a.113.7		40	44.43	even	2
792.2.br.b.37.7		40	33.29	even	10
792.2.br.b.37.8		40	264.29	even	10
792.2.br.b.685.7		40	264.197	even	2
792.2.br.b.685.8		40	33.32	even	2
968.2.c.h.485.19		20	88.13	odd	10
968.2.c.h.485.20		20	11.2	odd	10
968.2.c.i.485.1		20	11.9	even	5
968.2.c.i.485.2		20	88.53	even	10
968.2.o.d.269.4		40	88.69	even	10
968.2.o.d.269.5		40	11.3	even	5
968.2.o.d.493.4		40	11.5	even	5
968.2.o.d.493.5		40	88.5	even	10
968.2.o.i.245.7		40	8.5	even	2	inner
968.2.o.i.245.8		40	1.1	even	1	trivial
968.2.o.i.565.7		40	11.4	even	5	inner
968.2.o.i.565.8		40	88.37	even	10	inner
968.2.o.j.269.6		40	11.8	odd	10
968.2.o.j.269.7		40	88.85	odd	10
968.2.o.j.493.6		40	88.61	odd	10
968.2.o.j.493.7		40	11.6	odd	10
3872.2.c.h.1937.7		20	44.35	even	10
3872.2.c.h.1937.14		20	88.35	even	10
3872.2.c.i.1937.7		20	44.31	odd	10
3872.2.c.i.1937.14		20	88.75	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.25740 - 0.647266i) q^{2} +(-0.826127 + 0.268425i) q^{3} +(1.16209 - 1.62774i) q^{4} +(-2.15963 + 2.97247i) q^{5} +(-0.865027 + 0.872241i) q^{6} +(0.369362 - 1.13678i) q^{7} +(0.407629 - 2.79890i) q^{8} +(-1.81662 + 1.31985i) q^{9} +(-0.791527 + 5.13543i) q^{10} +(-0.523110 + 1.65665i) q^{12} +(-2.33969 - 3.22030i) q^{13} +(-0.271365 - 1.66846i) q^{14} +(0.986240 - 3.03533i) q^{15} +(-1.29908 - 3.78317i) q^{16} +(-2.57254 - 1.86906i) q^{17} +(-1.42991 + 2.83541i) q^{18} +(-4.09534 + 1.33066i) q^{19} +(2.32873 + 6.96960i) q^{20} +1.03827i q^{21} +2.46096 q^{23} +(0.414541 + 2.42166i) q^{24} +(-2.62651 - 8.08357i) q^{25} +(-5.02631 - 2.53480i) q^{26} +(2.67820 - 3.68622i) q^{27} +(-1.42115 - 1.92227i) q^{28} +(-3.65234 - 1.18672i) q^{29} +(-0.724575 - 4.45498i) q^{30} +(-7.40138 + 5.37742i) q^{31} +(-4.08218 - 3.91610i) q^{32} +(-4.44448 - 0.685031i) q^{34} +(2.58136 + 3.55294i) q^{35} +(0.0372960 + 4.49077i) q^{36} +(-5.06948 - 1.64717i) q^{37} +(-4.28818 + 4.32394i) q^{38} +(2.79729 + 2.03235i) q^{39} +(7.43932 + 7.25624i) q^{40} +(-0.164715 - 0.506940i) q^{41} +(0.672037 + 1.30552i) q^{42} -6.51729i q^{43} -8.25022i q^{45} +(3.09440 - 1.59290i) q^{46} +(0.110898 + 0.341309i) q^{47} +(2.08870 + 2.77667i) q^{48} +(4.50728 + 3.27473i) q^{49} +(-8.53478 - 8.46420i) q^{50} +(2.62694 + 0.853546i) q^{51} +(-7.96076 + 0.0661143i) q^{52} +(1.42471 + 1.96095i) q^{53} +(0.981589 - 6.36855i) q^{54} +(-3.03117 - 1.49719i) q^{56} +(3.02609 - 2.19858i) q^{57} +(-5.36056 + 0.871863i) q^{58} +(0.566526 + 0.184075i) q^{59} +(-3.79464 - 5.13268i) q^{60} +(-4.28455 + 5.89718i) q^{61} +(-5.82585 + 11.5522i) q^{62} +(0.829389 + 2.55260i) q^{63} +(-7.66768 - 2.28183i) q^{64} +14.6251 q^{65} +11.2692i q^{67} +(-6.03187 + 2.01541i) q^{68} +(-2.03306 + 0.660583i) q^{69} +(5.54549 + 2.79662i) q^{70} +(-4.52005 - 3.28401i) q^{71} +(2.95362 + 5.62254i) q^{72} +(0.825597 - 2.54093i) q^{73} +(-7.44051 + 1.21015i) q^{74} +(4.33966 + 5.97303i) q^{75} +(-2.59320 + 8.21250i) q^{76} +(4.83277 + 0.744878i) q^{78} +(-9.30369 + 6.75953i) q^{79} +(14.0509 + 4.30875i) q^{80} +(0.858601 - 2.64250i) q^{81} +(-0.535237 - 0.530810i) q^{82} +(0.589450 - 0.811308i) q^{83} +(1.69004 + 1.20657i) q^{84} +(11.1114 - 3.61033i) q^{85} +(-4.21843 - 8.19482i) q^{86} +3.33584 q^{87} +13.6469 q^{89} +(-5.34009 - 10.3738i) q^{90} +(-4.52497 + 1.47025i) q^{91} +(2.85986 - 4.00580i) q^{92} +(4.67105 - 6.42914i) q^{93} +(0.360360 + 0.357380i) q^{94} +(4.88906 - 15.0470i) q^{95} +(4.42358 + 2.13943i) q^{96} +(4.81420 - 3.49772i) q^{97} +(7.78706 + 1.20022i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} - q^{4} + 7 q^{6} + 10 q^{7} + 5 q^{8} + 20 q^{10} - 6 q^{12} + 2 q^{14} - 18 q^{15} + 15 q^{16} + 6 q^{17} + 20 q^{18} + 8 q^{20} - 8 q^{23} - 25 q^{24} - 4 q^{25} - 10 q^{26} - 32 q^{28}+ \cdots + 144 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 - q^4 + 7 * q^6 + 10 * q^7 + 5 * q^8 + 20 * q^10 - 6 * q^12 + 2 * q^14 - 18 * q^15 + 15 * q^16 + 6 * q^17 + 20 * q^18 + 8 * q^20 - 8 * q^23 - 25 * q^24 - 4 * q^25 - 10 * q^26 - 32 * q^28 + 28 * q^30 - 6 * q^31 - 20 * q^32 + 10 * q^34 + 18 * q^36 + 12 * q^38 + 34 * q^39 - 10 * q^40 + 14 * q^41 + 40 * q^42 - 18 * q^46 - 6 * q^47 + 18 * q^48 - 4 * q^49 - 61 * q^50 - 20 * q^52 - 108 * q^54 - 32 * q^56 + 26 * q^57 + 4 * q^58 - 46 * q^60 - 48 * q^62 - 60 * q^63 - 49 * q^64 + 36 * q^65 + 42 * q^68 - 8 * q^70 + 22 * q^71 + 101 * q^72 + 6 * q^73 - 54 * q^74 + 134 * q^76 - 12 * q^78 - 74 * q^79 - 44 * q^80 - 4 * q^81 - 31 * q^82 + 28 * q^84 - 15 * q^86 - 68 * q^87 - 16 * q^89 + 84 * q^90 - 4 * q^92 + 100 * q^94 - 66 * q^95 + 30 * q^96 + 10 * q^97 + 144 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more