LMFDB - Embedded newform 392.2.m.h.227.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(19,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-4,0,4,0,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.9640188644209402576896.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 4x^{14} + 6x^{12} + 8x^{10} + 20x^{8} + 32x^{6} + 96x^{4} + 256x^{2} + 256 $ x^16 + 4x^14 + 6x^12 + 8x^10 + 20x^8 + 32x^6 + 96x^4 + 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.4
Root			$1.33546 + 0.465333i$ of defining polynomial
Character	$\chi$	$=$	392.227
Dual form			392.2.m.h.19.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.10799 + 0.878843i) q^{2} +(0.662827 + 0.382683i) q^{3} +(0.455270 - 1.94749i) q^{4} +(-1.51423 - 2.62272i) q^{5} +(-1.07072 + 0.158513i) q^{6} +(1.20711 + 2.55791i) q^{8} +(-1.20711 - 2.09077i) q^{9} +(3.98271 + 1.57517i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(1.04704 - 1.11663i) q^{12} -3.02846 q^{13} -2.31788i q^{15} +(-3.58546 - 1.77327i) q^{16} +(-3.86324 - 2.23044i) q^{17} +(3.17492 + 1.25569i) q^{18} +(-2.92586 + 1.68925i) q^{19} +(-5.79712 + 1.75490i) q^{20} +(-0.878680 - 5.93531i) q^{22} +(-4.84616 + 2.79793i) q^{23} +(-0.178766 + 2.15739i) q^{24} +(-2.08579 + 3.61269i) q^{25} +(3.35549 - 2.66154i) q^{26} -4.14386i q^{27} +5.59587i q^{29} +(2.03706 + 2.56818i) q^{30} +(5.16991 - 8.95454i) q^{31} +(5.53107 - 1.18629i) q^{32} +(-2.81214 + 1.62359i) q^{33} +(6.24063 - 0.923880i) q^{34} +(-4.62132 + 1.39897i) q^{36} +(2.00735 - 1.15894i) q^{37} +(1.75723 - 4.44303i) q^{38} +(-2.00735 - 1.15894i) q^{39} +(4.88085 - 7.03917i) q^{40} -7.07401i q^{41} +2.58579 q^{43} +(6.18977 + 5.80403i) q^{44} +(-3.65568 + 6.33182i) q^{45} +(2.91054 - 7.35909i) q^{46} +(3.02846 + 5.24545i) q^{47} +(-1.69794 - 2.54747i) q^{48} +(-0.863961 - 5.83589i) q^{50} +(-1.70711 - 2.95680i) q^{51} +(-1.37877 + 5.89791i) q^{52} +(-2.83882 - 1.63899i) q^{53} +(3.64180 + 4.59134i) q^{54} +12.8487 q^{55} -2.58579 q^{57} +(-4.91789 - 6.20015i) q^{58} +(-9.32669 - 5.38476i) q^{59} +(-4.51406 - 1.05526i) q^{60} +(-3.65568 - 6.33182i) q^{61} +(2.14144 + 14.4650i) q^{62} +(-5.08579 + 6.17534i) q^{64} +(4.58579 + 7.94282i) q^{65} +(1.68893 - 4.27034i) q^{66} +(1.00000 - 1.73205i) q^{67} +(-6.10259 + 6.50818i) q^{68} -4.28289 q^{69} -14.4697i q^{71} +(3.89089 - 5.61145i) q^{72} +(2.92586 + 1.68925i) q^{73} +(-1.20559 + 3.04823i) q^{74} +(-2.76503 + 1.59639i) q^{75} +(1.95774 + 6.46716i) q^{76} +(3.24264 - 0.480049i) q^{78} +(9.69232 - 5.59587i) q^{79} +(0.778407 + 12.0888i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(6.21694 + 7.83791i) q^{82} +9.23880i q^{83} +13.5096i q^{85} +(-2.86502 + 2.27250i) q^{86} +(-2.14144 + 3.70909i) q^{87} +(-11.9590 - 0.990949i) q^{88} +(-2.14931 + 1.24090i) q^{89} +(-1.51423 - 10.2283i) q^{90} +(3.24264 + 10.7117i) q^{92} +(6.85351 - 3.95687i) q^{93} +(-7.96542 - 3.15035i) q^{94} +(8.86085 + 5.11582i) q^{95} +(4.12012 + 1.33034i) q^{96} +6.88830i q^{97} +10.2426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 8 q^{9} - 4 q^{16} + 4 q^{18} - 48 q^{22} - 56 q^{25} - 8 q^{30} + 36 q^{32} - 40 q^{36} + 64 q^{43} + 48 q^{44} + 40 q^{46} + 88 q^{50} - 16 q^{51} - 64 q^{57} - 40 q^{58}+ \cdots + 96 q^{99}+O(q^{100}) $ 16 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 8 * q^9 - 4 * q^16 + 4 * q^18 - 48 * q^22 - 56 * q^25 - 8 * q^30 + 36 * q^32 - 40 * q^36 + 64 * q^43 + 48 * q^44 + 40 * q^46 + 88 * q^50 - 16 * q^51 - 64 * q^57 - 40 * q^58 - 56 * q^60 - 104 * q^64 + 96 * q^65 + 16 * q^67 - 12 * q^72 + 8 * q^74 - 16 * q^78 + 24 * q^81 - 24 * q^86 - 24 * q^88 - 16 * q^92 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.10799	+	0.878843i	−0.783465	+	0.621436i
$2$	−1.10799	+	0.878843i	−0.783465	+	0.621436i
$3$	0.662827	+	0.382683i	0.382683	+	0.220942i	0.678985	−	0.734152i	$-0.262420\pi$
$3$	0.662827	+	0.382683i	0.382683	+	0.220942i	−0.296302	+	0.955094i	$0.595753\pi$
$4$	0.455270	−	1.94749i	0.227635	−	0.973746i
$5$	−1.51423	−	2.62272i	−0.677184	−	1.17292i	−0.975825	−	0.218552i	$-0.929867\pi$
$5$	−1.51423	−	2.62272i	−0.677184	−	1.17292i	0.298641	−	0.954366i	$-0.403467\pi$
$6$	−1.07072	+	0.158513i	−0.437121	+	0.0647125i
$7$		0			0
$7$		0			0
$8$	1.20711	+	2.55791i	0.426777	+	0.904357i
$9$	−1.20711	−	2.09077i	−0.402369	−	0.696923i
$10$	3.98271	+	1.57517i	1.25944	+	0.498114i
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	0.345918	+	0.938265i	$0.387568\pi$
$11$	−2.12132	+	3.67423i	−0.639602	+	1.10782i	−0.985520	+	0.169559i	$0.945766\pi$
$12$	1.04704	−	1.11663i	0.302254	−	0.322342i
$13$	−3.02846			−0.839944			−0.419972	−	0.907537i	$-0.637960\pi$
$13$	−3.02846			−0.839944			−0.419972	+	0.907537i	$0.637960\pi$
$14$		0			0
$15$		−	2.31788i		−	0.598475i
$16$	−3.58546	−	1.77327i	−0.896364	−	0.443318i
$17$	−3.86324	−	2.23044i	−0.936973	−	0.540962i	−0.0479630	−	0.998849i	$-0.515273\pi$
$17$	−3.86324	−	2.23044i	−0.936973	−	0.540962i	−0.889010	+	0.457887i	$0.848606\pi$
$18$	3.17492	+	1.25569i	0.748335	+	0.295969i
$19$	−2.92586	+	1.68925i	−0.671238	+	0.387540i	−0.796546	−	0.604578i	$-0.793342\pi$
$19$	−2.92586	+	1.68925i	−0.671238	+	0.387540i	0.125307	+	0.992118i	$0.460008\pi$
$20$	−5.79712	+	1.75490i	−1.29628	+	0.392409i
$21$		0			0
$22$	−0.878680	−	5.93531i	−0.187335	−	1.26541i
$23$	−4.84616	+	2.79793i	−1.01049	+	0.583409i	−0.911336	−	0.411662i	$-0.864948\pi$
$23$	−4.84616	+	2.79793i	−1.01049	+	0.583409i	−0.0991581	+	0.995072i	$0.531615\pi$
$24$	−0.178766	+	2.15739i	−0.0364904	+	0.440376i
$25$	−2.08579	+	3.61269i	−0.417157	+	0.722538i
$26$	3.35549	−	2.66154i	0.658067	−	0.521971i
$27$		−	4.14386i		−	0.797486i
$28$		0			0
$29$			5.59587i			1.03913i	0.854432	+	0.519563i	$0.173905\pi$
$29$			5.59587i			1.03913i	−0.854432	+	0.519563i	$0.826095\pi$
$30$	2.03706	+	2.56818i	0.371914	+	0.468884i
$31$	5.16991	−	8.95454i	0.928542	−	1.60828i	0.142780	−	0.989754i	$-0.454396\pi$
$31$	5.16991	−	8.95454i	0.928542	−	1.60828i	0.785763	−	0.618528i	$-0.212271\pi$
$32$	5.53107	−	1.18629i	0.977764	−	0.209709i
$33$	−2.81214	+	1.62359i	−0.489530	+	0.282630i
$34$	6.24063	−	0.923880i	1.07026	−	0.158444i
$35$		0			0
$36$	−4.62132	+	1.39897i	−0.770220	+	0.233161i
$37$	2.00735	−	1.15894i	0.330006	−	0.190529i	−0.325838	−	0.945426i	$-0.605646\pi$
$37$	2.00735	−	1.15894i	0.330006	−	0.190529i	0.655844	+	0.754897i	$0.272313\pi$
$38$	1.75723	−	4.44303i	0.285061	−	0.720755i
$39$	−2.00735	−	1.15894i	−0.321433	−	0.185579i
$40$	4.88085	−	7.03917i	0.771730	−	1.11299i
$41$		−	7.07401i		−	1.10477i	−0.833587	−	0.552387i	$-0.813717\pi$
$41$		−	7.07401i		−	1.10477i	0.833587	−	0.552387i	$-0.186283\pi$
$42$		0			0
$43$	2.58579			0.394329			0.197164	−	0.980370i	$-0.436827\pi$
$43$	2.58579			0.394329			0.197164	+	0.980370i	$0.436827\pi$
$44$	6.18977	+	5.80403i	0.933143	+	0.874990i
$45$	−3.65568	+	6.33182i	−0.544956	+	0.943891i
$46$	2.91054	−	7.35909i	0.429136	−	1.08504i
$47$	3.02846	+	5.24545i	0.441746	+	0.765127i	0.997819	−	0.0660064i	$-0.0210258\pi$
$47$	3.02846	+	5.24545i	0.441746	+	0.765127i	−0.556073	+	0.831134i	$0.687692\pi$
$48$	−1.69794	−	2.54747i	−0.245076	−	0.367695i
$49$		0			0
$50$	−0.863961	−	5.83589i	−0.122183	−	0.825319i
$51$	−1.70711	−	2.95680i	−0.239043	−	0.414034i
$52$	−1.37877	+	5.89791i	−0.191201	+	0.817892i
$53$	−2.83882	−	1.63899i	−0.389941	−	0.225133i	0.292193	−	0.956359i	$-0.405615\pi$
$53$	−2.83882	−	1.63899i	−0.389941	−	0.225133i	−0.682135	+	0.731227i	$0.738948\pi$
$54$	3.64180	+	4.59134i	0.495586	+	0.624803i
$55$	12.8487			1.73251
$56$		0			0
$57$	−2.58579			−0.342496
$58$	−4.91789	−	6.20015i	−0.645750	−	0.814119i
$59$	−9.32669	−	5.38476i	−1.21423	−	0.701037i	−0.250553	−	0.968103i	$-0.580612\pi$
$59$	−9.32669	−	5.38476i	−1.21423	−	0.701037i	−0.963678	+	0.267066i	$0.913946\pi$
$60$	−4.51406	−	1.05526i	−0.582763	−	0.136234i
$61$	−3.65568	−	6.33182i	−0.468061	−	0.810706i	0.531273	−	0.847201i	$-0.321714\pi$
$61$	−3.65568	−	6.33182i	−0.468061	−	0.810706i	−0.999334	+	0.0364951i	$0.988381\pi$
$62$	2.14144	+	14.4650i	0.271964	+	1.83706i
$63$		0			0
$64$	−5.08579	+	6.17534i	−0.635723	+	0.771917i
$65$	4.58579	+	7.94282i	0.568797	+	0.985185i
$66$	1.68893	−	4.27034i	0.207893	−	0.525643i
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	−6.10259	+	6.50818i	−0.740048	+	0.789233i
$69$	−4.28289			−0.515599
$70$		0			0
$71$		−	14.4697i		−	1.71724i	−0.512613	−	0.858619i	$-0.671323\pi$
$71$		−	14.4697i		−	1.71724i	0.512613	−	0.858619i	$-0.328677\pi$
$72$	3.89089	−	5.61145i	0.458546	−	0.661316i
$73$	2.92586	+	1.68925i	0.342446	+	0.197711i	0.661353	−	0.750075i	$-0.269982\pi$
$73$	2.92586	+	1.68925i	0.342446	+	0.197711i	−0.318907	+	0.947786i	$0.603316\pi$
$74$	−1.20559	+	3.04823i	−0.140146	+	0.354350i
$75$	−2.76503	+	1.59639i	−0.319278	+	0.184335i
$76$	1.95774	+	6.46716i	0.224568	+	0.741834i
$77$		0			0
$78$	3.24264	−	0.480049i	0.367157	−	0.0543549i
$79$	9.69232	−	5.59587i	1.09047	−	0.629584i	0.156770	−	0.987635i	$-0.449892\pi$
$79$	9.69232	−	5.59587i	1.09047	−	0.629584i	0.933702	+	0.358051i	$0.116559\pi$
$80$	0.778407	+	12.0888i	0.0870286	+	1.35157i
$81$	−2.03553	+	3.52565i	−0.226170	+	0.391739i
$82$	6.21694	+	7.83791i	0.686547	+	0.865553i
$83$			9.23880i			1.01409i	0.861920	+	0.507045i	$0.169262\pi$
$83$			9.23880i			1.01409i	−0.861920	+	0.507045i	$0.830738\pi$
$84$		0			0
$85$			13.5096i			1.46532i
$86$	−2.86502	+	2.27250i	−0.308943	+	0.245050i
$87$	−2.14144	+	3.70909i	−0.229587	+	0.397656i
$88$	−11.9590	−	0.990949i	−1.27484	−	0.105635i
$89$	−2.14931	+	1.24090i	−0.227826	+	0.131536i	−0.609569	−	0.792733i	$-0.708657\pi$
$89$	−2.14931	+	1.24090i	−0.227826	+	0.131536i	0.381743	+	0.924269i	$0.375324\pi$
$90$	−1.51423	−	10.2283i	−0.159614	−	1.07816i
$91$		0			0
$92$	3.24264	+	10.7117i	0.338069	+	1.11677i
$93$	6.85351	−	3.95687i	0.710676	−	0.410309i
$94$	−7.96542	−	3.15035i	−0.821570	−	0.324933i
$95$	8.86085	+	5.11582i	0.909104	+	0.524872i
$96$	4.12012	+	1.33034i	0.420508	+	0.135777i
$97$			6.88830i			0.699401i	0.936862	+	0.349701i	$0.113717\pi$
$97$			6.88830i			0.699401i	−0.936862	+	0.349701i	$0.886283\pi$
$98$		0			0
$99$	10.2426			1.02942
$100$	6.08609	+	5.70680i	0.608609	+	0.570680i
$101$	−5.79712	+	10.0409i	−0.576835	+	0.999108i	0.419005	+	0.907984i	$0.362379\pi$
$101$	−5.79712	+	10.0409i	−0.576835	+	0.999108i	−0.995840	+	0.0911234i	$0.970954\pi$
$102$	4.49001	+	1.77581i	0.444577	+	0.175832i
$103$	2.14144	+	3.70909i	0.211003	+	0.365468i	0.952029	−	0.306009i	$-0.0989937\pi$
$103$	2.14144	+	3.70909i	0.211003	+	0.365468i	−0.741026	+	0.671477i	$0.765660\pi$
$104$	−3.65568	−	7.74652i	−0.358468	−	0.759609i
$105$		0			0
$106$	4.58579	−	0.678892i	0.445411	−	0.0659398i
$107$	1.65685	+	2.86976i	0.160174	+	0.277430i	0.934931	−	0.354830i	$-0.115461\pi$
$107$	1.65685	+	2.86976i	0.160174	+	0.277430i	−0.774757	+	0.632259i	$0.782128\pi$
$108$	−8.07014	−	1.88658i	−0.776549	−	0.181536i
$109$	−4.84616	−	2.79793i	−0.464178	−	0.267993i	0.249621	−	0.968344i	$-0.419694\pi$
$109$	−4.84616	−	2.79793i	−0.464178	−	0.267993i	−0.713799	+	0.700350i	$0.753027\pi$
$110$	−14.2362	+	11.2920i	−1.35736	+	1.07665i
$111$	1.77403			0.168384
$112$		0			0
$113$	−1.41421			−0.133038			−0.0665190	−	0.997785i	$-0.521189\pi$
$113$	−1.41421			−0.133038			−0.0665190	+	0.997785i	$0.521189\pi$
$114$	2.86502	−	2.27250i	0.268333	−	0.212839i
$115$	14.6764	+	8.47343i	1.36858	+	0.790151i
$116$	10.8979	+	2.54763i	1.01185	+	0.236542i
$117$	3.65568	+	6.33182i	0.337967	+	0.585377i
$118$	15.0662	−	2.23044i	1.38696	−	0.205329i
$119$		0			0
$120$	5.92893	−	2.79793i	0.541235	−	0.255415i
$121$	−3.50000	−	6.06218i	−0.318182	−	0.551107i
$122$	9.61511	+	3.80280i	0.870511	+	0.344290i
$123$	2.70711	−	4.68885i	0.244092	−	0.422779i
$124$	−15.0852	−	14.1451i	−1.35469	−	1.27027i
$125$	−2.50886			−0.224399
$126$		0			0
$127$			0.960099i			0.0851950i	0.999092	+	0.0425975i	$0.0135633\pi$
$127$			0.960099i			0.0851950i	−0.999092	+	0.0425975i	$0.986437\pi$
$128$	0.207835	−	11.3118i	0.0183702	−	0.999831i
$129$	1.71393	+	0.989538i	0.150903	+	0.0871239i
$130$	−12.0615	−	4.77035i	−1.05786	−	0.418387i
$131$	5.96544	−	3.44415i	0.521203	−	0.300917i	−0.216224	−	0.976344i	$-0.569374\pi$
$131$	5.96544	−	3.44415i	0.521203	−	0.300917i	0.737427	+	0.675427i	$0.236041\pi$
$132$	1.88164	+	6.21579i	0.163776	+	0.541015i
$133$		0			0
$134$	0.414214	+	2.79793i	0.0357826	+	0.241705i
$135$	−10.8682	+	6.27476i	−0.935386	+	0.540045i
$136$	1.04192	−	12.5742i	0.0893442	−	1.07823i
$137$	9.77817	−	16.9363i	0.835406	−	1.44697i	−0.0582937	−	0.998299i	$-0.518566\pi$
$137$	9.77817	−	16.9363i	0.835406	−	1.44697i	0.893700	−	0.448666i	$-0.148101\pi$
$138$	4.74539	−	3.76399i	0.403954	−	0.320412i
$139$		−	1.66205i		−	0.140973i	−0.997513	−	0.0704866i	$-0.977545\pi$
$139$		−	1.66205i		−	0.140973i	0.997513	−	0.0704866i	$-0.0224552\pi$
$140$		0			0
$141$			4.63577i			0.390402i
$142$	12.7166	+	16.0323i	1.06715	+	1.34540i
$143$	6.42433	−	11.1273i	0.537230	−	0.930509i
$144$	0.620527	+	9.63690i	0.0517106	+	0.803075i
$145$	14.6764	−	8.47343i	1.21881	−	0.703680i
$146$	−4.72640	+	0.699709i	−0.391159	+	0.0579083i
$147$		0			0
$148$	−1.34315	−	4.43692i	−0.110406	−	0.364713i
$149$	−4.01469	+	2.31788i	−0.328896	+	0.189888i	−0.655351	−	0.755324i	$-0.727479\pi$
$149$	−4.01469	+	2.31788i	−0.328896	+	0.189888i	0.326455	+	0.945213i	$0.394146\pi$
$150$	1.66064	−	4.19881i	0.135591	−	0.342831i
$151$	−8.86085	−	5.11582i	−0.721086	−	0.416319i	0.0940663	−	0.995566i	$-0.470013\pi$
$151$	−8.86085	−	5.11582i	−0.721086	−	0.416319i	−0.815152	+	0.579247i	$0.803347\pi$
$152$	−7.85276	−	5.44498i	−0.636943	−	0.441646i
$153$			10.7695i			0.870665i
$154$		0			0
$155$	−31.3137			−2.51518
$156$	−3.17092	+	3.38166i	−0.253876	+	0.270749i
$157$	3.65568	−	6.33182i	0.291755	−	0.505334i	−0.682470	−	0.730914i	$-0.739094\pi$
$157$	3.65568	−	6.33182i	0.291755	−	0.505334i	0.974225	+	0.225580i	$0.0724276\pi$
$158$	−5.82108	+	14.7182i	−0.463100	+	1.17092i
$159$	−1.25443	−	2.17274i	−0.0994827	−	0.172309i
$160$	−11.4866	−	12.7101i	−0.908098	−	1.00483i
$161$		0			0
$162$	−0.843146	−	5.69529i	−0.0662438	−	0.447464i
$163$	2.70711	+	4.68885i	0.212037	+	0.367259i	0.952352	−	0.305001i	$-0.0986569\pi$
$163$	2.70711	+	4.68885i	0.212037	+	0.367259i	−0.740315	+	0.672260i	$0.765324\pi$
$164$	−13.7766	−	3.22059i	−1.07577	−	0.251486i
$165$	8.51645	+	4.91697i	0.663005	+	0.382786i
$166$	−8.11945	−	10.2365i	−0.630192	−	0.794504i
$167$	−8.56578			−0.662840			−0.331420	−	0.943483i	$-0.607528\pi$
$167$	−8.56578			−0.662840			−0.331420	+	0.943483i	$0.607528\pi$
$168$		0			0
$169$	−3.82843			−0.294494
$170$	−11.8728	−	14.9685i	−0.910604	−	1.14803i
$171$	7.06365	+	4.07820i	0.540171	+	0.311868i
$172$	1.17723	−	5.03580i	0.0897631	−	0.383976i
$173$	4.91010	+	8.50455i	0.373308	+	0.646589i	0.990072	−	0.140559i	$-0.0448900\pi$
$173$	4.91010	+	8.50455i	0.373308	+	0.646589i	−0.616764	+	0.787148i	$0.711557\pi$
$174$	−0.887016	−	5.99162i	−0.0672445	−	0.454223i
$175$		0			0
$176$	14.1213	−	9.41214i	1.06443	−	0.709466i
$177$	−4.12132	−	7.13834i	−0.309777	−	0.536550i
$178$	1.29085	−	3.26381i	0.0967531	−	0.244633i
$179$	−1.17157	+	2.02922i	−0.0875675	+	0.151671i	−0.906482	−	0.422244i	$-0.861243\pi$
$179$	−1.17157	+	2.02922i	−0.0875675	+	0.151671i	0.818915	+	0.573915i	$0.194576\pi$
$180$	10.6668	+	10.0021i	0.795060	+	0.745512i
$181$	−9.08538			−0.675311			−0.337656	−	0.941270i	$-0.609634\pi$
$181$	−9.08538			−0.675311			−0.337656	+	0.941270i	$0.609634\pi$
$182$		0			0
$183$		−	5.59587i		−	0.413658i
$184$	−13.0067	−	9.01863i	−0.958866	−	0.664862i
$185$	−6.07917	−	3.50981i	−0.446949	−	0.258046i
$186$	−4.11613	+	10.4073i	−0.301809	+	0.763102i
$187$	16.3903	−	9.46297i	1.19858	−	0.692001i
$188$	11.5942	−	3.50981i	0.845597	−	0.255979i
$189$		0			0
$190$	−14.3137	+	2.11904i	−1.03843	+	0.153731i
$191$	−2.83882	+	1.63899i	−0.205409	+	0.118593i	−0.599176	−	0.800617i	$-0.704505\pi$
$191$	−2.83882	+	1.63899i	−0.205409	+	0.118593i	0.393767	+	0.919210i	$0.371172\pi$
$192$	−5.73420	+	2.14693i	−0.413830	+	0.154942i
$193$	4.70711	−	8.15295i	0.338825	−	0.586862i	−0.645387	−	0.763856i	$-0.723304\pi$
$193$	4.70711	−	8.15295i	0.338825	−	0.586862i	0.984212	+	0.176994i	$0.0566372\pi$
$194$	−6.05374	−	7.63215i	−0.434633	−	0.547956i
$195$			7.01962i			0.502685i
$196$		0			0
$197$		−	19.1055i		−	1.36121i	−0.732651	−	0.680605i	$-0.761717\pi$
$197$		−	19.1055i		−	1.36121i	0.732651	−	0.680605i	$-0.238283\pi$
$198$	−11.3487	+	9.00167i	−0.806518	+	0.639721i
$199$	−8.19837	+	14.2000i	−0.581167	+	1.00661i	0.414175	+	0.910197i	$0.364070\pi$
$199$	−8.19837	+	14.2000i	−0.581167	+	1.00661i	−0.995341	+	0.0964129i	$0.969263\pi$
$200$	−11.7587	−	0.974349i	−0.831465	−	0.0688969i
$201$	1.32565	−	0.765367i	0.0935044	−	0.0539848i
$202$	−2.40125	−	16.2200i	−0.168951	−	1.14123i
$203$		0			0
$204$	−6.53553	+	1.97844i	−0.457579	+	0.138518i
$205$	−18.5532	+	10.7117i	−1.29581	+	0.748136i
$206$	−5.63240	−	2.22763i	−0.392428	−	0.155206i
$207$	11.6997	+	6.75481i	0.813183	+	0.469492i
$208$	10.8584	+	5.37028i	0.752896	+	0.372362i
$209$		−	14.3337i		−	0.991485i
$210$		0			0
$211$	18.9706			1.30599			0.652994	−	0.757363i	$-0.273513\pi$
$211$	18.9706			1.30599			0.652994	+	0.757363i	$0.273513\pi$
$212$	−4.48435	+	4.78239i	−0.307987	+	0.328456i
$213$	5.53732	−	9.59092i	0.379411	−	0.657159i
$214$	−4.35784	−	1.72354i	−0.297896	−	0.117819i
$215$	−3.91548	−	6.78180i	−0.267033	−	0.462515i
$216$	10.5996	−	5.00208i	0.721212	−	0.340349i
$217$		0			0
$218$	7.82843	−	1.15894i	0.530208	−	0.0784934i
$219$	1.29289	+	2.23936i	0.0873656	+	0.151322i
$220$	5.84962	−	25.0227i	0.394381	−	1.68703i
$221$	11.6997	+	6.75481i	0.787005	+	0.454377i
$222$	−1.96560	+	1.55909i	−0.131923	+	0.104640i
$223$	−4.28289			−0.286804			−0.143402	−	0.989665i	$-0.545804\pi$
$223$	−4.28289			−0.286804			−0.143402	+	0.989665i	$0.545804\pi$
$224$		0			0
$225$	10.0711			0.671405
$226$	1.56693	−	1.24287i	0.104231	−	0.0826746i
$227$	4.09069	+	2.36176i	0.271508	+	0.156755i	0.629573	−	0.776941i	$-0.283230\pi$
$227$	4.09069	+	2.36176i	0.271508	+	0.156755i	−0.358065	+	0.933697i	$0.616563\pi$
$228$	−1.17723	+	5.03580i	−0.0779641	+	0.333504i
$229$	−12.2215	−	21.1682i	−0.807616	−	1.39883i	−0.914510	−	0.404562i	$-0.867424\pi$
$229$	−12.2215	−	21.1682i	−0.807616	−	1.39883i	0.106894	−	0.994270i	$-0.465909\pi$
$230$	−23.7081	+	3.50981i	−1.56326	+	0.231430i
$231$		0			0
$232$	−14.3137	+	6.75481i	−0.939741	+	0.443475i
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	0.981364	−	0.192158i	$-0.0615485\pi$
$233$	4.94975	+	8.57321i	0.324269	+	0.561650i	−0.657095	+	0.753807i	$0.728215\pi$
$234$	−9.61511	−	3.80280i	−0.628559	−	0.248597i
$235$	9.17157	−	15.8856i	0.598287	−	1.03626i
$236$	−14.7330	+	15.7121i	−0.959034	+	1.02277i
$237$	8.56578			0.556407
$238$		0			0
$239$			18.1454i			1.17373i	0.809686	+	0.586864i	$0.199638\pi$
$239$			18.1454i			1.17373i	−0.809686	+	0.586864i	$0.800362\pi$
$240$	−4.11024	+	8.31067i	−0.265315	+	0.536452i
$241$	15.9550	+	9.21160i	1.02775	+	0.593371i	0.916339	−	0.400403i	$-0.131130\pi$
$241$	15.9550	+	9.21160i	1.02775	+	0.593371i	0.111410	+	0.993775i	$0.464463\pi$
$242$	9.20566	+	3.64086i	0.591762	+	0.234044i
$243$	−13.4645	+	7.77372i	−0.863747	+	0.498684i
$244$	−13.9955	+	4.23671i	−0.895969	+	0.271228i
$245$		0			0
$246$	1.12132	+	7.57430i	0.0714928	+	0.482920i
$247$	8.86085	−	5.11582i	0.563803	−	0.325512i
$248$	29.1455	+	2.41506i	1.85074	+	0.153356i
$249$	−3.53553	+	6.12372i	−0.224055	+	0.388075i
$250$	2.77978	−	2.20489i	0.175809	−	0.139450i
$251$		−	21.4077i		−	1.35124i	−0.737248	−	0.675622i	$-0.763875\pi$
$251$		−	21.4077i		−	1.35124i	0.737248	−	0.675622i	$-0.236125\pi$
$252$		0			0
$253$		−	23.7412i		−	1.49260i
$254$	−0.843776	−	1.06378i	−0.0529432	−	0.0667473i
$255$	−5.16991	+	8.95454i	−0.323752	+	0.560755i
$256$	9.71102	+	12.7160i	0.606939	+	0.794749i
$257$	9.48751	−	5.47762i	0.591815	−	0.341684i	−0.174000	−	0.984746i	$-0.555669\pi$
$257$	9.48751	−	5.47762i	0.591815	−	0.341684i	0.765815	+	0.643061i	$0.222336\pi$
$258$	−2.76866	+	0.409880i	−0.172369	+	0.0255180i
$259$		0			0
$260$	17.5563	−	5.31466i	1.08880	−	0.329601i
$261$	11.6997	−	6.75481i	0.724191	−	0.418112i
$262$	−3.58277	+	9.05876i	−0.221344	+	0.559652i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$	−7.54754	−	5.23334i	−0.464519	−	0.322090i
$265$			9.92724i			0.609825i
$266$		0			0
$267$	−1.89949			−0.116247
$268$	−2.91789	−	2.73604i	−0.178238	−	0.167131i
$269$	2.76866	−	4.79546i	0.168808	−	0.292384i	−0.769193	−	0.639017i	$-0.779341\pi$
$269$	2.76866	−	4.79546i	0.168808	−	0.292384i	0.938001	+	0.346632i	$0.112675\pi$
$270$	6.52730	−	16.5038i	0.397239	−	1.00439i
$271$	−0.887016	−	1.53636i	−0.0538824	−	0.0933270i	0.837826	−	0.545937i	$-0.183826\pi$
$271$	−0.887016	−	1.53636i	−0.0538824	−	0.0933270i	−0.891708	+	0.452610i	$0.850493\pi$
$272$	9.89630	+	14.8477i	0.600052	+	0.900276i
$273$		0			0
$274$	4.05025	+	27.3587i	0.244685	+	1.65280i
$275$	−8.84924	−	15.3273i	−0.533629	−	0.924273i
$276$	−1.94987	+	8.34090i	−0.117369	+	0.502063i
$277$	−8.51645	−	4.91697i	−0.511704	−	0.295432i	0.221830	−	0.975085i	$-0.428797\pi$
$277$	−8.51645	−	4.91697i	−0.511704	−	0.295432i	−0.733534	+	0.679653i	$0.762130\pi$
$278$	1.46068	+	1.84153i	0.0876058	+	0.110448i
$279$	−24.9625			−1.49447
$280$		0			0
$281$	−11.0711			−0.660445			−0.330222	−	0.943903i	$-0.607124\pi$
$281$	−11.0711			−0.660445			−0.330222	+	0.943903i	$0.607124\pi$
$282$	−4.07411	−	5.13637i	−0.242610	−	0.305866i
$283$	−22.3558	−	12.9071i	−1.32891	−	0.767248i	−0.343782	−	0.939050i	$-0.611708\pi$
$283$	−22.3558	−	12.9071i	−1.32891	−	0.767248i	−0.985132	+	0.171801i	$0.945041\pi$
$284$	−28.1797	−	6.58763i	−1.67216	−	0.390904i
$285$	3.91548	+	6.78180i	0.231933	+	0.401719i
$286$	2.66105	+	17.9749i	0.157351	+	1.06288i
$287$		0			0
$288$	−9.15685	−	10.1322i	−0.539573	−	0.597046i
$289$	1.44975	+	2.51104i	0.0852793	+	0.147708i
$290$	−8.81446	+	22.2867i	−0.517603	+	1.30872i
$291$	−2.63604	+	4.56575i	−0.154527	+	0.267649i
$292$	4.62185	−	4.92903i	0.270473	−	0.288450i
$293$	29.7650			1.73889			0.869445	−	0.494030i	$-0.164477\pi$
$293$	29.7650			1.73889			0.869445	+	0.494030i	$0.164477\pi$
$294$		0			0
$295$			32.6151i			1.89892i
$296$	5.38755	+	3.73564i	0.313145	+	0.217130i
$297$	15.2255	+	8.79045i	0.883474	+	0.510074i
$298$	2.41117	−	6.09647i	0.139675	−	0.353159i
$299$	14.6764	−	8.47343i	0.848759	−	0.490031i
$300$	1.85012	+	6.11167i	0.106817	+	0.352857i
$301$		0			0
$302$	14.3137	−	2.11904i	0.823661	−	0.121937i
$303$	−7.68498	+	4.43692i	−0.441490	+	0.254895i
$304$	13.4860	−	0.868376i	0.773478	−	0.0498048i
$305$	−11.0711	+	19.1757i	−0.633927	+	1.09799i
$306$	−9.46472	−	11.9325i	−0.541062	−	0.682136i
$307$			23.2011i			1.32416i	0.749434	+	0.662079i	$0.230326\pi$
$307$			23.2011i			1.32416i	−0.749434	+	0.662079i	$0.769674\pi$
$308$		0			0
$309$			3.27798i			0.186478i
$310$	34.6952	−	27.5198i	1.97055	−	1.56302i
$311$	1.77403	−	3.07271i	0.100596	−	0.174238i	−0.811334	−	0.584582i	$-0.801258\pi$
$311$	1.77403	−	3.07271i	0.100596	−	0.174238i	0.911930	+	0.410345i	$0.134592\pi$
$312$	0.541385	−	6.53357i	0.0306499	−	0.369891i
$313$	−30.0823	+	17.3680i	−1.70035	+	0.981698i	−0.754952	+	0.655781i	$0.772340\pi$
$313$	−30.0823	+	17.3680i	−1.70035	+	0.981698i	−0.945398	+	0.325917i	$0.894327\pi$
$314$	1.51423	+	10.2283i	0.0854530	+	0.577218i
$315$		0			0
$316$	−6.48528	−	21.4234i	−0.364826	−	1.20516i
$317$	13.7070	−	7.91375i	0.769863	−	0.444480i	−0.0629630	−	0.998016i	$-0.520055\pi$
$317$	13.7070	−	7.91375i	0.769863	−	0.444480i	0.832826	+	0.553535i	$0.186722\pi$
$318$	3.29938	+	1.30492i	0.185020	+	0.0731761i
$319$	−20.5605	−	11.8706i	−1.15117	−	0.664627i
$320$	23.8973	+	3.98773i	1.33590	+	0.222921i
$321$			2.53620i			0.141557i
$322$		0			0
$323$	15.0711			0.838577
$324$	5.93946	+	5.56931i	0.329970	+	0.309406i
$325$	6.31672	−	10.9409i	0.350389	−	0.606891i
$326$	−7.12020	−	2.81606i	−0.394351	−	0.155967i
$327$	−2.14144	−	3.70909i	−0.118422	−	0.205113i
$328$	18.0947	−	8.53909i	0.999111	−	0.471492i
$329$		0			0
$330$	−13.7574	+	2.03668i	−0.757318	+	0.112115i
$331$	1.53553	+	2.65962i	0.0844006	+	0.146186i	0.905136	−	0.425123i	$-0.139769\pi$
$331$	1.53553	+	2.65962i	0.0844006	+	0.146186i	−0.820735	+	0.571309i	$0.806436\pi$
$332$	17.9925	+	4.20615i	0.987466	+	0.230842i
$333$	−4.84616	−	2.79793i	−0.265568	−	0.153326i
$334$	9.49077	−	7.52797i	0.519312	−	0.411912i
$335$	−6.05692			−0.330925
$336$		0			0
$337$	14.1421			0.770371			0.385186	−	0.922839i	$-0.374137\pi$
$337$	14.1421			0.770371			0.385186	+	0.922839i	$0.374137\pi$
$338$	4.24185	−	3.36459i	0.230726	−	0.183009i
$339$	−0.937379	−	0.541196i	−0.0509114	−	0.0293937i
$340$	26.3099	+	6.15053i	1.42685	+	0.333559i
$341$	21.9341	+	37.9909i	1.18780	+	2.05732i
$342$	−11.4105	+	1.68925i	−0.617011	+	0.0913440i
$343$		0			0
$344$	3.12132	+	6.61420i	0.168290	+	0.356614i
$345$	6.48528	+	11.2328i	0.349156	+	0.604756i
$346$	−12.9145	−	5.10772i	−0.694288	−	0.274593i
$347$	−1.87868	+	3.25397i	−0.100853	+	0.174682i	−0.912036	−	0.410110i	$-0.865490\pi$
$347$	−1.87868	+	3.25397i	−0.100853	+	0.174682i	0.811183	+	0.584792i	$0.198824\pi$
$348$	6.24849	+	5.85909i	0.334954	+	0.314080i
$349$	5.53732			0.296406			0.148203	−	0.988957i	$-0.452651\pi$
$349$	5.53732			0.296406			0.148203	+	0.988957i	$0.452651\pi$
$350$		0			0
$351$			12.5495i			0.669844i
$352$	−7.37445	+	22.8389i	−0.393060	+	1.21732i
$353$	−18.9279	−	10.9280i	−1.00743	−	0.581641i	−0.0969930	−	0.995285i	$-0.530922\pi$
$353$	−18.9279	−	10.9280i	−1.00743	−	0.581641i	−0.910439	+	0.413644i	$0.864256\pi$
$354$	10.8398	+	4.28719i	0.576131	+	0.227862i
$355$	−37.9501	+	21.9105i	−2.01418	+	1.16289i
$356$	1.43814	+	4.75071i	0.0762211	+	0.251787i
$357$		0			0
$358$	−0.485281	−	3.27798i	−0.0256479	−	0.173247i
$359$	15.7144	−	9.07269i	0.829372	−	0.478838i	−0.0242655	−	0.999706i	$-0.507725\pi$
$359$	15.7144	−	9.07269i	0.829372	−	0.478838i	0.853638	+	0.520867i	$0.174391\pi$
$360$	−20.6090	−	1.70770i	−1.08619	−	0.0900039i
$361$	−3.79289	+	6.56948i	−0.199626	+	0.345762i
$362$	10.0665	−	7.98462i	0.529083	−	0.419662i
$363$		−	5.35757i		−	0.281199i
$364$		0			0
$365$		−	10.2316i		−	0.535548i
$366$	4.91789	+	6.20015i	0.257062	+	0.324087i
$367$	−18.0186	+	31.2091i	−0.940562	+	1.62910i	−0.176160	+	0.984362i	$0.556367\pi$
$367$	−18.0186	+	31.2091i	−0.940562	+	1.62910i	−0.764402	+	0.644739i	$0.776966\pi$
$368$	22.3372	−	1.43831i	1.16441	−	0.0749771i
$369$	−14.7901	+	8.53909i	−0.769944	+	0.444527i
$370$	9.82021	−	1.45381i	0.510528	−	0.0755800i
$371$		0			0
$372$	−4.58579	−	15.1486i	−0.237762	−	0.785419i
$373$	−27.4140	+	15.8275i	−1.41944	+	0.819517i	−0.996250	−	0.0865220i	$-0.972425\pi$
$373$	−27.4140	+	15.8275i	−1.41944	+	0.819517i	−0.423195	+	0.906039i	$0.639091\pi$
$374$	−9.84382	+	24.8894i	−0.509012	+	1.28700i
$375$	−1.66294	−	0.960099i	−0.0858738	−	0.0495793i
$376$	−9.76170	+	14.0783i	−0.503421	+	0.726035i
$377$		−	16.9469i		−	0.872808i
$378$		0			0
$379$	−26.3848			−1.35529			−0.677647	−	0.735387i	$-0.737000\pi$
$379$	−26.3848			−1.35529			−0.677647	+	0.735387i	$0.737000\pi$
$380$	13.9971	−	14.9274i	0.718036	−	0.765758i
$381$	−0.367414	+	0.636379i	−0.0188232	+	0.0326027i
$382$	1.70496	−	4.31085i	0.0872331	−	0.220562i
$383$	−4.80249	−	8.31816i	−0.245396	−	0.425038i	0.716847	−	0.697231i	$-0.245585\pi$
$383$	−4.80249	−	8.31816i	−0.245396	−	0.425038i	−0.962243	+	0.272192i	$0.912251\pi$
$384$	4.46660	−	7.41823i	0.227935	−	0.378560i
$385$		0			0
$386$	1.94975	+	13.1702i	0.0992395	+	0.670344i
$387$	−3.12132	−	5.40629i	−0.158666	−	0.274817i
$388$	13.4149	+	3.13604i	0.681039	+	0.159208i
$389$	0.831470	+	0.480049i	0.0421572	+	0.0243395i	0.520930	−	0.853599i	$-0.325585\pi$
$389$	0.831470	+	0.480049i	0.0421572	+	0.0243395i	−0.478773	+	0.877939i	$0.658918\pi$
$390$	−6.16914	−	7.77765i	−0.312387	−	0.393836i
$391$	24.9625			1.26241
$392$		0			0
$393$	5.27208			0.265941
$394$	16.7907	+	21.1686i	0.845904	+	1.06646i
$395$	−29.3528	−	16.9469i	−1.47690	−	0.852689i
$396$	4.66317	−	19.9475i	0.234333	−	1.00240i
$397$	−1.88164	−	3.25910i	−0.0944370	−	0.163570i	0.814936	−	0.579550i	$-0.196772\pi$
$397$	−1.88164	−	3.25910i	−0.0944370	−	0.163570i	−0.909374	+	0.415981i	$0.863438\pi$
$398$	−3.39587	−	22.9385i	−0.170220	−	1.14980i
$399$		0			0
$400$	13.8848	−	9.25448i	0.694239	−	0.462724i
$401$	−8.07107	−	13.9795i	−0.403050	−	0.698103i	0.591042	−	0.806640i	$-0.298717\pi$
$401$	−8.07107	−	13.9795i	−0.403050	−	0.698103i	−0.994092	+	0.108538i	$0.965383\pi$
$402$	−0.796170	+	2.01306i	−0.0397094	+	0.100402i
$403$	−15.6569	+	27.1185i	−0.779923	+	1.35087i
$404$	16.9153	+	15.8612i	0.841570	+	0.789123i
$405$	12.3291			0.612636
$406$		0			0
$407$			9.83395i			0.487451i
$408$	5.50255	−	7.93579i	0.272417	−	0.392880i
$409$	−22.2892	−	12.8687i	−1.10213	−	0.636314i	−0.165349	−	0.986235i	$-0.552875\pi$
$409$	−22.2892	−	12.8687i	−1.10213	−	0.636314i	−0.936779	+	0.349921i	$0.886208\pi$
$410$	11.1428	−	28.1737i	0.550303	−	1.39140i
$411$	12.9625	−	7.48389i	0.639392	−	0.369153i
$412$	8.19837	−	2.48181i	0.403904	−	0.122270i
$413$		0			0
$414$	−18.8995	+	2.79793i	−0.928860	+	0.137511i
$415$	24.2308	−	13.9897i	1.18944	−	0.686726i
$416$	−16.7506	+	3.59264i	−0.821267	+	0.176144i
$417$	0.636039	−	1.10165i	0.0311470	−	0.0539481i
$418$	12.5971	+	15.8816i	0.616144	+	0.776794i
$419$		−	24.0209i		−	1.17350i	−0.809770	−	0.586748i	$-0.800408\pi$
$419$		−	24.0209i		−	1.17350i	0.809770	−	0.586748i	$-0.199592\pi$
$420$		0			0
$421$		−	30.2972i		−	1.47660i	−0.674475	−	0.738298i	$-0.735630\pi$
$421$		−	30.2972i		−	1.47660i	0.674475	−	0.738298i	$-0.264370\pi$
$422$	−21.0191	+	16.6721i	−1.02320	+	0.811587i
$423$	7.31135	−	12.6636i	0.355490	−	0.615727i
$424$	0.765634	−	9.23987i	0.0371825	−	0.448728i
$425$	16.1158	−	9.30445i	0.781730	−	0.451332i
$426$	2.29363	+	15.4930i	0.111127	+	0.750641i
$427$		0			0
$428$	6.34315	−	1.92020i	0.306608	−	0.0928162i
$429$	8.51645	−	4.91697i	0.411178	−	0.237394i
$430$	10.2984	+	4.07306i	0.496635	+	0.196420i
$431$	−17.3773	−	10.0328i	−0.837035	−	0.483262i	0.0192202	−	0.999815i	$-0.493882\pi$
$431$	−17.3773	−	10.0328i	−0.837035	−	0.483262i	−0.856255	+	0.516553i	$0.827215\pi$
$432$	−7.34819	+	14.8576i	−0.353540	+	0.714838i
$433$			3.19278i			0.153435i	0.997053	+	0.0767177i	$0.0244440\pi$
$433$			3.19278i			0.153435i	−0.997053	+	0.0767177i	$0.975556\pi$
$434$		0			0
$435$	12.9706			0.621891
$436$	−7.65527	+	8.16405i	−0.366621	+	0.390987i
$437$	9.45280	−	16.3727i	0.452189	−	0.783213i
$438$	−3.40055	−	1.34493i	−0.162485	−	0.0642632i
$439$	2.66105	+	4.60907i	0.127005	+	0.219979i	0.922515	−	0.385962i	$-0.126130\pi$
$439$	2.66105	+	4.60907i	0.127005	+	0.219979i	−0.795510	+	0.605940i	$0.792797\pi$
$440$	15.5097	+	32.8657i	0.739397	+	1.56681i
$441$		0			0
$442$	−18.8995	+	2.79793i	−0.898957	+	0.133084i
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	0.897444	+	0.441129i	$0.145422\pi$
$443$	17.4853	+	30.2854i	0.830751	+	1.43890i	−0.0666929	+	0.997774i	$0.521245\pi$
$444$	0.807664	−	3.45491i	0.0383300	−	0.163963i
$445$	6.50910	+	3.75803i	0.308561	+	0.178148i
$446$	4.74539	−	3.76399i	0.224701	−	0.178230i
$447$	−3.54806			−0.167818
$448$		0			0
$449$	−20.2843			−0.957274			−0.478637	−	0.878013i	$-0.658869\pi$
$449$	−20.2843			−0.957274			−0.478637	+	0.878013i	$0.658869\pi$
$450$	−11.1586	+	8.85089i	−0.526022	+	0.417235i
$451$	25.9916	+	15.0062i	1.22390	+	0.706616i
$452$	−0.643849	+	2.75417i	−0.0302841	+	0.129545i
$453$	−3.91548	−	6.78180i	−0.183965	−	0.318637i
$454$	−6.60804	+	0.978272i	−0.310131	+	0.0459126i
$455$		0			0
$456$	−3.12132	−	6.61420i	−0.146169	−	0.309738i
$457$	−12.0208	−	20.8207i	−0.562310	−	0.973950i	−0.997294	−	0.0735115i	$-0.976579\pi$
$457$	−12.0208	−	20.8207i	−0.562310	−	0.973950i	0.434984	−	0.900438i	$-0.356754\pi$
$458$	32.1447	+	12.7133i	1.50202	+	0.594055i
$459$	−9.24264	+	16.0087i	−0.431410	+	0.747223i
$460$	23.1837	−	24.7245i	1.08094	−	1.15279i
$461$	14.1031			0.656847			0.328423	−	0.944531i	$-0.393483\pi$
$461$	14.1031			0.656847			0.328423	+	0.944531i	$0.393483\pi$
$462$		0			0
$463$		−	23.7412i		−	1.10335i	−0.834059	−	0.551675i	$-0.813989\pi$
$463$		−	23.7412i		−	1.10335i	0.834059	−	0.551675i	$-0.186011\pi$
$464$	9.92299	−	20.0637i	0.460663	−	0.931436i
$465$	−20.7556	−	11.9832i	−0.962517	−	0.555709i
$466$	−13.0188	−	5.14896i	−0.603083	−	0.238521i
$467$	−4.57317	+	2.64032i	−0.211621	+	0.122180i	−0.602065	−	0.798447i	$-0.705655\pi$
$467$	−4.57317	+	2.64032i	−0.211621	+	0.122180i	0.390443	+	0.920627i	$0.372322\pi$
$468$	13.9955	−	4.23671i	0.646942	−	0.195842i
$469$		0			0
$470$	3.79899	+	25.6614i	0.175234	+	1.18367i
$471$	4.84616	−	2.79793i	0.223299	−	0.128922i
$472$	2.51543	−	30.3568i	0.115782	−	1.39728i
$473$	−5.48528	+	9.50079i	−0.252214	+	0.436847i
$474$	−9.49077	+	7.52797i	−0.435926	+	0.345771i
$475$		−	14.0936i		−	0.646660i
$476$		0			0
$477$			7.91375i			0.362346i
$478$	−15.9469	−	20.1048i	−0.729396	−	0.919574i
$479$	−9.45280	+	16.3727i	−0.431909	+	0.748089i	−0.997038	−	0.0769142i	$-0.975493\pi$
$479$	−9.45280	+	16.3727i	−0.431909	+	0.748089i	0.565128	+	0.825003i	$0.308827\pi$
$480$	−2.74969	−	12.8204i	−0.125505	−	0.585167i
$481$	−6.07917	+	3.50981i	−0.277186	+	0.160034i
$482$	−25.7734	+	3.81557i	−1.17395	+	0.173794i
$483$		0			0
$484$	−13.3995	+	4.05630i	−0.609068	+	0.184377i
$485$	18.0661	−	10.4305i	0.820340	−	0.473623i
$486$	8.08659	−	20.4463i	0.366815	−	0.927465i
$487$	29.4214	+	16.9864i	1.33321	+	0.769729i	0.985790	−	0.167981i	$-0.0537247\pi$
$487$	29.4214	+	16.9864i	1.33321	+	0.769729i	0.347420	+	0.937710i	$0.387058\pi$
$488$	11.7834	−	16.9941i	0.533410	−	0.769285i
$489$			4.14386i			0.187392i
$490$		0			0
$491$	−26.0000			−1.17336			−0.586682	−	0.809818i	$-0.699566\pi$
$491$	−26.0000			−1.17336			−0.586682	+	0.809818i	$0.699566\pi$
$492$	−7.89903	−	7.40676i	−0.356116	−	0.333923i
$493$	12.4813	−	21.6182i	0.562127	−	0.973633i
$494$	−5.32171	+	13.4556i	−0.239435	+	0.605394i
$495$	−15.5097	−	26.8636i	−0.697110	−	1.20743i
$496$	−34.4153	+	22.9385i	−1.54529	+	1.02997i
$497$		0			0
$498$	−1.46447	−	9.89219i	−0.0656243	−	0.443279i
$499$	−2.31371	−	4.00746i	−0.103576	−	0.179399i	0.809580	−	0.587010i	$-0.199695\pi$
$499$	−2.31371	−	4.00746i	−0.103576	−	0.179399i	−0.913155	+	0.407611i	$0.866362\pi$
$500$	−1.14221	+	4.88598i	−0.0510811	+	0.218508i
$501$	−5.67763	−	3.27798i	−0.253658	−	0.146449i
$502$	18.8140	+	23.7195i	0.839712	+	1.05865i
$503$	−15.3575			−0.684758			−0.342379	−	0.939562i	$-0.611233\pi$
$503$	−15.3575			−0.684758			−0.342379	+	0.939562i	$0.611233\pi$
$504$		0			0
$505$	35.1127			1.56249
$506$	20.8648	+	26.3050i	0.927555	+	1.16940i
$507$	−2.53759	−	1.46508i	−0.112698	−	0.0650663i
$508$	1.86979	+	0.437104i	0.0829583	+	0.0193934i
$509$	−6.68414	−	11.5773i	−0.296269	−	0.513153i	0.679010	−	0.734129i	$-0.262409\pi$
$509$	−6.68414	−	11.5773i	−0.296269	−	0.513153i	−0.975279	+	0.220976i	$0.929076\pi$
$510$	−2.14144	−	14.4650i	−0.0948248	−	0.640523i
$511$		0			0
$512$	−21.9350	−	5.55468i	−0.969400	−	0.245485i
$513$	7.00000	+	12.1244i	0.309058	+	0.535303i
$514$	−5.69808	+	14.4072i	−0.251331	+	0.635473i
$515$	6.48528	−	11.2328i	0.285776	−	0.494978i
$516$	2.70742	−	2.88736i	0.119187	−	0.127109i
$517$	−25.6973			−1.13017
$518$		0			0
$519$			7.51606i			0.329919i
$520$	−14.7815	+	21.3178i	−0.648210	+	0.934849i
$521$	8.84420	+	5.10620i	0.387471	+	0.223707i	0.681064	−	0.732224i	$-0.261518\pi$
$521$	8.84420	+	5.10620i	0.387471	+	0.223707i	−0.293593	+	0.955931i	$0.594851\pi$
$522$	−7.02667	+	17.7664i	−0.307549	+	0.777615i
$523$	−5.18889	+	2.99581i	−0.226894	+	0.130998i	−0.609139	−	0.793064i	$-0.708485\pi$
$523$	−5.18889	+	2.99581i	−0.226894	+	0.130998i	0.382244	+	0.924061i	$0.375151\pi$
$524$	−3.99157	−	13.1857i	−0.174373	−	0.576019i
$525$		0			0
$526$		0			0
$527$	−39.9452	+	23.0624i	−1.74004	+	1.00461i
$528$	12.9619	−	0.834624i	0.564093	−	0.0363224i
$529$	4.15685	−	7.19988i	0.180733	−	0.313038i
$530$	−8.72448	−	10.9993i	−0.378967	−	0.477777i
$531$			25.9999i			1.12830i
$532$		0			0
$533$			21.4234i			0.927949i
$534$	2.10462	−	1.66936i	0.0910756	−	0.0722402i
$535$	5.01772	−	8.69094i	0.216935	−	0.375742i
$536$	5.63753	+	0.467138i	0.243504	+	0.0201773i
$537$	−1.55310	+	0.896683i	−0.0670212	+	0.0386947i
$538$	1.14682	+	7.74652i	0.0494428	+	0.333976i
$539$		0			0
$540$	7.27208	+	24.0225i	0.312940	+	1.03376i
$541$	−26.2382	+	15.1486i	−1.12807	+	0.651289i	−0.943448	−	0.331521i	$-0.892438\pi$
$541$	−26.2382	+	15.1486i	−1.12807	+	0.651289i	−0.184618	+	0.982810i	$0.559105\pi$
$542$	2.33302	+	0.922715i	0.100212	+	0.0396340i
$543$	−6.02204	−	3.47682i	−0.258430	−	0.149205i
$544$	−24.0138	−	7.75380i	−1.02958	−	0.332441i
$545$			16.9469i			0.725924i
$546$		0			0
$547$	34.5858			1.47878			0.739391	−	0.673277i	$-0.235114\pi$
$547$	34.5858			1.47878			0.739391	+	0.673277i	$0.235114\pi$
$548$	−28.5316	−	26.7535i	−1.21881	−	1.14285i
$549$	−8.82558	+	15.2864i	−0.376667	+	0.652406i
$550$	23.2752	+	9.20540i	0.992456	+	0.392519i
$551$	−9.45280	−	16.3727i	−0.402703	−	0.697501i
$552$	−5.16991	−	10.9552i	−0.220046	−	0.466286i
$553$		0			0
$554$	13.7574	−	2.03668i	0.584494	−	0.0865301i
$555$	−2.68629	−	4.65279i	−0.114027	−	0.197500i
$556$	−3.23683	−	0.756682i	−0.137272	−	0.0320905i
$557$	−26.2382	−	15.1486i	−1.11175	−	0.641867i	−0.172465	−	0.985016i	$-0.555173\pi$
$557$	−26.2382	−	15.1486i	−1.11175	−	0.641867i	−0.939281	+	0.343149i	$0.888507\pi$
$558$	27.6581	−	21.9381i	1.17086	−	0.928715i
$559$	−7.83095			−0.331214
$560$		0			0
$561$	14.4853			0.611569
$562$	12.2666	−	9.72973i	0.517435	−	0.410424i
$563$	21.5126	+	12.4203i	0.906649	+	0.523454i	0.879351	−	0.476174i	$-0.157977\pi$
$563$	21.5126	+	12.4203i	0.906649	+	0.523454i	0.0272973	+	0.999627i	$0.491310\pi$
$564$	9.02812	+	2.11053i	0.380153	+	0.0888692i
$565$	2.14144	+	3.70909i	0.0900913	+	0.156043i
$566$	36.1132	−	5.34630i	1.51795	−	0.224722i
$567$		0			0
$568$	37.0122	−	17.4665i	1.55300	−	0.732878i
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	0.598394	−	0.801202i	$-0.295806\pi$
$569$	−9.41421	−	16.3059i	−0.394664	−	0.683579i	−0.993058	+	0.117623i	$0.962472\pi$
$570$	−10.2984	−	4.07306i	−0.431354	−	0.170602i
$571$	−1.19239	+	2.06528i	−0.0498999	+	0.0864291i	−0.889896	−	0.456163i	$-0.849224\pi$
$571$	−1.19239	+	2.06528i	−0.0498999	+	0.0864291i	0.839997	+	0.542592i	$0.182557\pi$
$572$	−18.7455	−	17.5773i	−0.783788	−	0.734942i
$573$	−2.50886			−0.104809
$574$		0			0
$575$		−	23.3436i		−	0.973494i
$576$	19.0503	+	3.17892i	0.793762	+	0.132455i
$577$	28.1409	+	16.2471i	1.17152	+	0.676378i	0.954038	−	0.299687i	$-0.0968821\pi$
$577$	28.1409	+	16.2471i	1.17152	+	0.676378i	0.217483	+	0.976064i	$0.430215\pi$
$578$	−3.81311	−	1.50810i	−0.158604	−	0.0627285i
$579$	6.24000	−	3.60266i	0.259325	−	0.149722i
$580$	−9.82021	−	32.4399i	−0.407762	−	1.34699i
$581$		0			0
$582$	−1.09188	−	7.37546i	−0.0452600	−	0.305723i
$583$	12.0441	−	6.95365i	0.498815	−	0.287991i
$584$	−0.789111	+	9.52318i	−0.0326536	+	0.394072i
$585$	11.0711	−	19.1757i	0.457732	−	0.792816i
$586$	−32.9792	+	26.1588i	−1.36236	+	1.08061i
$587$		−	38.8799i		−	1.60474i	−0.596824	−	0.802372i	$-0.703571\pi$
$587$		−	38.8799i		−	1.60474i	0.596824	−	0.802372i	$-0.296429\pi$
$588$		0			0
$589$			34.9330i			1.43939i
$590$	−28.6635	−	36.1371i	−1.18006	−	1.48774i
$591$	7.31135	−	12.6636i	0.300749	−	0.520912i
$592$	−9.25237	+	0.595767i	−0.380270	+	0.0244859i
$593$	−16.5983	+	9.58302i	−0.681609	+	0.393527i	−0.800461	−	0.599385i	$-0.795412\pi$
$593$	−16.5983	+	9.58302i	−0.681609	+	0.393527i	0.118852	+	0.992912i	$0.462079\pi$
$594$	−24.5951	+	3.64113i	−1.00915	+	0.149397i
$595$		0			0
$596$	2.68629	+	8.87385i	0.110035	+	0.363487i
$597$	−10.8682	+	6.27476i	−0.444806	+	0.256809i
$598$	−8.81446	+	22.2867i	−0.360450	+	0.911371i
$599$	26.2382	+	15.1486i	1.07206	+	0.618955i	0.928744	−	0.370722i	$-0.120890\pi$
$599$	26.2382	+	15.1486i	1.07206	+	0.618955i	0.143318	+	0.989677i	$0.454223\pi$
$600$	−7.42111	−	5.14568i	−0.302966	−	0.210072i
$601$		−	43.5809i		−	1.77770i	−0.458198	−	0.888850i	$-0.651505\pi$
$601$		−	43.5809i		−	1.77770i	0.458198	−	0.888850i	$-0.348495\pi$
$602$		0			0
$603$	−4.82843			−0.196629
$604$	−13.9971	+	14.9274i	−0.569534	+	0.607386i
$605$	−10.5996	+	18.3591i	−0.430935	+	0.746402i
$606$	4.61550	−	11.6699i	0.187492	−	0.474059i
$607$	20.1600	+	34.9182i	0.818270	+	1.41729i	0.906956	+	0.421226i	$0.138400\pi$
$607$	20.1600	+	34.9182i	0.818270	+	1.41729i	−0.0886860	+	0.996060i	$0.528267\pi$
$608$	−14.1792	+	12.8143i	−0.575042	+	0.519687i
$609$		0			0
$610$	−4.58579	−	30.9761i	−0.185673	−	1.25419i
$611$	−9.17157	−	15.8856i	−0.371042	−	0.642664i
$612$	20.9736	+	4.90305i	0.847807	+	0.198194i
$613$	36.7619	+	21.2245i	1.48480	+	0.857250i	0.999850	−	0.0172913i	$-0.00550427\pi$
$613$	36.7619	+	21.2245i	1.48480	+	0.857250i	0.484951	+	0.874542i	$0.338838\pi$
$614$	−20.3901	−	25.7065i	−0.822879	−	1.03743i
$615$	−16.3967			−0.661180
$616$		0			0
$617$	−28.8284			−1.16059			−0.580294	−	0.814407i	$-0.697063\pi$
$617$	−28.8284			−1.16059			−0.580294	+	0.814407i	$0.697063\pi$
$618$	−2.88083	−	3.63196i	−0.115884	−	0.146099i
$619$	−17.6689	−	10.2011i	−0.710173	−	0.410018i	0.100952	−	0.994891i	$-0.467811\pi$
$619$	−17.6689	−	10.2011i	−0.710173	−	0.410018i	−0.811125	+	0.584873i	$0.801144\pi$
$620$	−14.2562	+	60.9832i	−0.572543	+	2.44915i
$621$	11.5942	+	20.0818i	0.465261	+	0.805855i
$622$	0.734828	+	4.96362i	0.0294639	+	0.199023i
$623$		0			0
$624$	5.14214	+	7.71491i	0.205850	+	0.308843i
$625$	14.2279	+	24.6435i	0.569117	+	0.985739i
$626$	18.0670	−	45.6811i	0.722103	−	1.82578i
$627$	5.48528	−	9.50079i	0.219061	−	0.379425i
$628$	−10.6668	−	10.0021i	−0.425653	−	0.399127i
$629$	−10.3398			−0.412275
$630$		0			0
$631$			17.1853i			0.684135i	0.939675	+	0.342068i	$0.111127\pi$
$631$			17.1853i			0.684135i	−0.939675	+	0.342068i	$0.888873\pi$
$632$	26.0134	+	18.0373i	1.03476	+	0.717484i
$633$	12.5742	+	7.25972i	0.499780	+	0.288548i
$634$	−8.23225	+	20.8146i	−0.326944	+	0.826655i
$635$	2.51807	−	1.45381i	0.0999267	−	0.0576927i
$636$	−4.80249	+	1.45381i	−0.190431	+	0.0576473i
$637$		0			0
$638$	33.2132	−	4.91697i	1.31492	−	0.194665i
$639$	−30.2528	+	17.4665i	−1.19678	+	0.690964i
$640$	−29.9824	+	16.5836i	−1.18516	+	0.655523i
$641$	3.07107	−	5.31925i	0.121300	−	0.210098i	−0.798981	−	0.601357i	$-0.794627\pi$
$641$	3.07107	−	5.31925i	0.121300	−	0.210098i	0.920281	+	0.391259i	$0.127960\pi$
$642$	−2.22892	−	2.81008i	−0.0879686	−	0.110905i
$643$			49.3324i			1.94548i	0.231901	+	0.972739i	$0.425505\pi$
$643$			49.3324i			1.94548i	−0.231901	+	0.972739i	$0.574495\pi$
$644$		0			0
$645$		−	5.99355i		−	0.235996i
$646$	−16.6985	+	13.2451i	−0.656996	+	0.521122i
$647$	17.2837	−	29.9363i	0.679494	−	1.17692i	−0.295639	−	0.955300i	$-0.595533\pi$
$647$	17.2837	−	29.9363i	0.679494	−	1.17692i	0.975133	−	0.221619i	$-0.0711341\pi$
$648$	−11.4754	−	0.950875i	−0.450796	−	0.0373539i
$649$	39.5698	−	22.8456i	1.55325	−	0.896769i
$650$	2.61647	+	17.6738i	0.102626	+	0.693222i
$651$		0			0
$652$	10.3640	−	3.13738i	0.405884	−	0.122869i
$653$	−3.67029	+	2.11904i	−0.143629	+	0.0829245i	−0.570093	−	0.821580i	$-0.693093\pi$
$653$	−3.67029	+	2.11904i	−0.143629	+	0.0829245i	0.426463	+	0.904505i	$0.359759\pi$
$654$	5.63240	+	2.22763i	0.220244	+	0.0871073i
$655$	−18.0661	−	10.4305i	−0.705901	−	0.407552i
$656$	−12.5441	+	25.3636i	−0.489766	+	0.990281i
$657$		−	8.15640i		−	0.318212i
$658$		0			0
$659$	25.6985			1.00107			0.500535	−	0.865716i	$-0.333137\pi$
$659$	25.6985			1.00107			0.500535	+	0.865716i	$0.333137\pi$
$660$	13.4531	−	14.3472i	0.523659	−	0.558463i
$661$	−9.71260	+	16.8227i	−0.377776	+	0.654328i	−0.990738	−	0.135785i	$-0.956644\pi$
$661$	−9.71260	+	16.8227i	−0.377776	+	0.654328i	0.612962	+	0.790112i	$0.289978\pi$
$662$	−4.03874	−	1.59733i	−0.156970	−	0.0620822i
$663$	5.16991	+	8.95454i	0.200782	+	0.347765i
$664$	−23.6320	+	11.1522i	−0.917099	+	0.432790i
$665$		0			0
$666$	7.82843	−	1.15894i	0.303345	−	0.0449081i
$667$	−15.6569	−	27.1185i	−0.606236	−	1.05003i
$668$	−3.89975	+	16.6818i	−0.150886	+	0.645438i
$669$	−2.83882	−	1.63899i	−0.109755	−	0.0633671i
$670$	6.71099	−	5.32308i	0.259268	−	0.205649i
$671$	31.0194			1.19749
$672$		0			0
$673$	−29.8995			−1.15254			−0.576270	−	0.817259i	$-0.695492\pi$
$673$	−29.8995			−1.15254			−0.576270	+	0.817259i	$0.695492\pi$
$674$	−15.6693	+	12.4287i	−0.603559	+	0.478736i
$675$	14.9705	+	8.64321i	0.576214	+	0.332677i
$676$	−1.74297	+	7.45583i	−0.0670373	+	0.286763i
$677$	−21.6743	−	37.5409i	−0.833009	−	1.44281i	−0.895641	−	0.444777i	$-0.853283\pi$
$677$	−21.6743	−	37.5409i	−0.833009	−	1.44281i	0.0626320	−	0.998037i	$-0.480051\pi$
$678$	1.51423	−	0.224171i	0.0581537	−	0.00860923i
$679$		0			0
$680$	−34.5563	+	16.3075i	−1.32518	+	0.625366i
$681$	1.80761	+	3.13088i	0.0692678	+	0.119975i
$682$	−57.6907	−	22.8168i	−2.20909	−	0.873701i
$683$	25.4853	−	44.1418i	0.975167	−	1.68904i	0.295785	−	0.955255i	$-0.404419\pi$
$683$	25.4853	−	44.1418i	0.975167	−	1.68904i	0.679382	−	0.733785i	$-0.262248\pi$
$684$	11.1581	−	11.8997i	0.426642	−	0.454998i
$685$	−59.2256			−2.26290
$686$		0			0
$687$		−	18.7078i		−	0.713747i
$688$	−9.27123	−	4.58530i	−0.353462	−	0.174813i
$689$	8.59724	+	4.96362i	0.327529	+	0.189099i
$690$	−17.0575	−	6.74629i	−0.649368	−	0.256827i
$691$	26.0387	−	15.0334i	0.990558	−	0.571899i	0.0851170	−	0.996371i	$-0.472874\pi$
$691$	26.0387	−	15.0334i	0.990558	−	0.571899i	0.905441	+	0.424472i	$0.139540\pi$
$692$	18.7980	−	5.69052i	0.714592	−	0.216321i
$693$		0			0
$694$	−0.778175	−	5.25642i	−0.0295391	−	0.199531i
$695$	−4.35910	+	2.51673i	−0.165350	+	0.0954649i
$696$	−12.0725	−	1.00035i	−0.457606	−	0.0379182i
$697$	−15.7782	+	27.3286i	−0.597641	+	1.03514i
$698$	−6.13528	+	4.86643i	−0.232224	+	0.184197i
$699$			7.57675i			0.286579i
$700$		0			0
$701$		−	16.7876i		−	0.634059i	−0.948416	−	0.317029i	$-0.897315\pi$
$701$		−	16.7876i		−	0.634059i	0.948416	−	0.317029i	$-0.102685\pi$
$702$	−11.0291	−	13.9047i	−0.416265	−	0.524799i
$703$	−3.91548	+	6.78180i	−0.147675	+	0.255781i
$704$	−11.9011	−	31.7862i	−0.448538	−	1.19799i
$705$	12.1583	−	7.01962i	0.457909	−	0.264374i
$706$	30.5759	−	4.52654i	1.15074	−	0.170359i
$707$		0			0
$708$	−15.7782	+	4.77637i	−0.592980	+	0.179507i
$709$	9.34792	−	5.39702i	0.351068	−	0.202689i	−0.314087	−	0.949394i	$-0.601698\pi$
$709$	9.34792	−	5.39702i	0.351068	−	0.202689i	0.665156	+	0.746705i	$0.268365\pi$
$710$	22.7923	−	57.6287i	0.855380	−	2.16277i
$711$	−23.3993	−	13.5096i	−0.877544	−	0.506650i
$712$	−5.76857	−	3.99983i	−0.216186	−	0.149900i
$713$			57.8602i			2.16688i
$714$		0			0
$715$	−38.9117			−1.45521
$716$	3.41852	+	3.20548i	0.127756	+	0.119794i
$717$	−6.94394	+	12.0273i	−0.259326	+	0.449166i
$718$	−9.43784	+	23.8629i	−0.352217	+	0.890555i
$719$	6.05692	+	10.4909i	0.225885	+	0.391244i	0.956585	−	0.291455i	$-0.0941393\pi$
$719$	6.05692	+	10.4909i	0.225885	+	0.391244i	−0.730700	+	0.682699i	$0.760806\pi$
$720$	24.3353	−	16.2200i	0.906923	−	0.604482i
$721$		0			0
$722$	−1.57107	−	10.6123i	−0.0584691	−	0.394947i
$723$	7.05025	+	12.2114i	0.262202	+	0.454147i
$724$	−4.13630	+	17.6937i	−0.153725	+	0.657582i
$725$	−20.2161	−	11.6718i	−0.750808	−	0.433479i
$726$	4.70846	+	5.93612i	0.174747	+	0.220310i
$727$	38.8504			1.44088			0.720441	−	0.693517i	$-0.243940\pi$
$727$	38.8504			1.44088			0.720441	+	0.693517i	$0.243940\pi$
$728$		0			0
$729$	0.313708			0.0116188
$730$	8.99200	+	11.3365i	0.332809	+	0.419583i
$731$	−9.98951	−	5.76745i	−0.369475	−	0.213317i
$732$	−10.8979	−	2.54763i	−0.402798	−	0.0941632i
$733$	−13.6281	−	23.6045i	−0.503364	−	0.871853i	−0.999992	−	0.00388916i	$-0.998762\pi$
$733$	−13.6281	−	23.6045i	−0.503364	−	0.871853i	0.496628	−	0.867963i	$-0.334571\pi$
$734$	−7.46354	−	50.4148i	−0.275484	−	1.86084i
$735$		0			0
$736$	−23.4853	+	21.2245i	−0.865679	+	0.782346i
$737$	4.24264	+	7.34847i	0.156280	+	0.270684i
$738$	8.88276	−	22.4594i	0.326979	−	0.826742i
$739$	12.1213	−	20.9947i	0.445890	−	0.772304i	−0.552224	−	0.833696i	$-0.686221\pi$
$739$	12.1213	−	20.9947i	0.445890	−	0.772304i	0.998114	+	0.0613918i	$0.0195539\pi$
$740$	−9.60299	+	10.2412i	−0.353013	+	0.376475i
$741$	7.83095			0.287677
$742$		0			0
$743$		−	38.6086i		−	1.41641i	−0.706005	−	0.708207i	$-0.749504\pi$
$743$		−	38.6086i		−	1.41641i	0.706005	−	0.708207i	$-0.250496\pi$
$744$	18.3942	+	12.7543i	0.674365	+	0.467594i
$745$	12.1583	+	7.01962i	0.445447	+	0.257179i
$746$	16.4645	−	41.6293i	0.602808	−	1.52416i
$747$	19.3162	−	11.1522i	0.706743	−	0.408038i
$748$	−10.9670	−	36.2283i	−0.400994	−	1.32464i
$749$		0			0
$750$	2.68629	−	0.397686i	0.0980895	−	0.0145214i
$751$	32.7473	−	18.9066i	1.19496	−	0.689913i	0.235536	−	0.971866i	$-0.424315\pi$
$751$	32.7473	−	18.9066i	1.19496	−	0.689913i	0.959428	+	0.281953i	$0.0909821\pi$
$752$	−1.55681	−	24.1776i	−0.0567712	−	0.881667i
$753$	8.19239	−	14.1896i	0.298547	−	0.517099i
$754$	14.8936	+	18.7769i	0.542394	+	0.683814i
$755$			30.9861i			1.12770i
$756$		0			0
$757$			27.4169i			0.996485i	0.867038	+	0.498242i	$0.166021\pi$
$757$			27.4169i			0.996485i	−0.867038	+	0.498242i	$0.833979\pi$
$758$	29.2340	−	23.1881i	1.06183	−	0.842229i
$759$	9.08538	−	15.7363i	0.329778	−	0.571193i
$760$	−2.38979	+	28.8406i	−0.0866868	+	1.04616i
$761$	12.0446	−	6.95396i	0.436617	−	0.252081i	−0.265545	−	0.964099i	$-0.585552\pi$
$761$	12.0446	−	6.95396i	0.436617	−	0.252081i	0.702162	+	0.712018i	$0.252218\pi$
$762$	−0.152188	−	1.02800i	−0.00551318	−	0.0372405i
$763$		0			0
$764$	1.89949	+	6.27476i	0.0687213	+	0.227013i
$765$	28.2455	−	16.3075i	1.02122	−	0.589601i
$766$	12.6315	+	4.99578i	0.456393	+	0.180505i
$767$	28.2455	+	16.3075i	1.01989	+	0.588831i
$768$	1.57053	+	12.1447i	0.0566716	+	0.438236i
$769$			1.21371i			0.0437674i	0.999761	+	0.0218837i	$0.00696636\pi$
$769$			1.21371i			0.0437674i	−0.999761	+	0.0218837i	$0.993034\pi$
$770$		0			0
$771$	8.38478			0.301970
$772$	−13.7348	−	12.8789i	−0.494326	−	0.463520i
$773$	−8.82558	+	15.2864i	−0.317434	+	0.549812i	−0.979952	−	0.199234i	$-0.936155\pi$
$773$	−8.82558	+	15.2864i	−0.317434	+	0.549812i	0.662518	+	0.749046i	$0.269488\pi$
$774$	8.20966	+	3.24694i	0.295090	+	0.116709i
$775$	21.5666	+	37.3545i	0.774696	+	1.34181i
$776$	−17.6196	+	8.31492i	−0.632508	+	0.298488i
$777$		0			0
$778$	−1.34315	+	0.198843i	−0.0481541	+	0.00712887i
$779$	11.9497	+	20.6976i	0.428144	+	0.741567i
$780$	13.6707	+	3.19582i	0.489488	+	0.114429i
$781$	53.1651	+	30.6949i	1.90240	+	1.09835i
$782$	−27.6581	+	21.9381i	−0.989053	+	0.784506i
$783$	23.1885			0.828689
$784$		0			0
$785$	−22.1421			−0.790287
$786$	−5.84139	+	4.63333i	−0.208356	+	0.165265i
$787$	5.57717	+	3.21998i	0.198805	+	0.114780i	0.596098	−	0.802912i	$-0.296717\pi$
$787$	5.57717	+	3.21998i	0.198805	+	0.114780i	−0.397293	+	0.917692i	$0.630050\pi$
$788$	−37.2078	−	8.69816i	−1.32547	−	0.309859i
$789$		0			0
$790$	47.4162	−	7.01962i	1.68699	−	0.249747i
$791$		0			0
$792$	12.3640	+	26.1997i	0.439334	+	0.930967i
$793$	11.0711	+	19.1757i	0.393145	+	0.680947i
$794$	4.94908	+	1.95737i	0.175636	+	0.0694646i
$795$	−3.79899	+	6.58004i	−0.134736	+	0.233370i
$796$	23.9219	+	22.4311i	0.847889	+	0.795049i
$797$	23.7081			0.839783			0.419892	−	0.907574i	$-0.362068\pi$
$797$	23.7081			0.839783			0.419892	+	0.907574i	$0.362068\pi$
$798$		0			0
$799$		−	27.0192i		−	0.955872i
$800$	−7.25092	+	22.4564i	−0.256359	+	0.793953i
$801$	5.18889	+	2.99581i	0.183341	+	0.105852i
$802$	21.2284	+	8.39590i	0.749602	+	0.296470i
$803$	−12.4134	+	7.16687i	−0.438058	+	0.252913i
$804$	−0.887016	−	2.93015i	−0.0312826	−	0.103338i
$805$		0			0
$806$	−6.48528	−	43.8068i	−0.228434	−	1.54303i
$807$	3.67029	−	2.11904i	0.129200	−	0.0745938i
$808$	−32.6815	−	2.70805i	−1.14973	−	0.0952690i
$809$	17.5355	−	30.3724i	0.616517	−	1.06784i	−0.373600	−	0.927590i	$-0.621877\pi$
$809$	17.5355	−	30.3724i	0.616517	−	1.06784i	0.990116	−	0.140248i	$-0.0447900\pi$
$810$	−13.6604	+	10.8353i	−0.479979	+	0.380714i
$811$		−	32.6800i		−	1.14755i	−0.819013	−	0.573775i	$-0.805478\pi$
$811$		−	32.6800i		−	1.14755i	0.819013	−	0.573775i	$-0.194522\pi$
$812$		0			0
$813$		−	1.35778i		−	0.0476196i
$814$	−8.64249	−	10.8959i	−0.302919	−	0.381901i
$815$	8.19837	−	14.2000i	0.287176	−	0.497404i
$816$	0.877558	+	13.6286i	0.0307207	+	0.477097i
$817$	−7.56565	+	4.36803i	−0.264689	+	0.152818i
$818$	36.0056	−	5.33037i	1.25891	−	0.186372i
$819$		0			0
$820$	12.4142	+	41.0089i	0.433523	+	1.43209i
$821$	25.0623	−	14.4697i	0.874680	−	0.504996i	0.00577905	−	0.999983i	$-0.498160\pi$
$821$	25.0623	−	14.4697i	0.874680	−	0.504996i	0.868900	+	0.494987i	$0.164827\pi$
$822$	−7.78509	+	19.6840i	−0.271536	+	0.686560i
$823$	22.2235	+	12.8307i	0.774661	+	0.447251i	0.834535	−	0.550955i	$-0.185736\pi$
$823$	22.2235	+	12.8307i	0.774661	+	0.447251i	−0.0598737	+	0.998206i	$0.519070\pi$
$824$	−6.90256	+	9.95489i	−0.240462	+	0.346795i
$825$		−	13.5458i		−	0.471605i
$826$		0			0
$827$	−1.65685			−0.0576145			−0.0288072	−	0.999585i	$-0.509171\pi$
$827$	−1.65685			−0.0576145			−0.0288072	+	0.999585i	$0.509171\pi$
$828$	18.4815	−	19.7098i	0.642275	−	0.684962i
$829$	−13.4759	+	23.3409i	−0.468037	+	0.810664i	−0.999333	−	0.0365227i	$-0.988372\pi$
$829$	−13.4759	+	23.3409i	−0.468037	+	0.810664i	0.531296	+	0.847186i	$0.321705\pi$
$830$	−14.5527	+	36.7954i	−0.505132	+	1.27719i
$831$	−3.76329	−	6.51821i	−0.130547	−	0.226114i
$832$	15.4021	−	18.7018i	0.533972	−	0.648367i
$833$		0			0
$834$	0.263456	+	1.77959i	0.00912273	+	0.0616223i
$835$	12.9706	+	22.4657i	0.448865	+	0.777457i
$836$	−27.9148	−	6.52572i	−0.965455	−	0.225697i
$837$	−37.1064	−	21.4234i	−1.28258	−	0.740500i
$838$	21.1106	+	26.6148i	0.729253	+	0.919393i
$839$	−16.3967			−0.566078			−0.283039	−	0.959108i	$-0.591343\pi$
$839$	−16.3967			−0.566078			−0.283039	+	0.959108i	$0.591343\pi$
$840$		0			0
$841$	−2.31371			−0.0797831
$842$	26.6265	+	33.5689i	0.917609	+	1.15686i
$843$	−7.33820	−	4.23671i	−0.252741	−	0.145920i
$844$	8.63673	−	36.9450i	0.297289	−	1.27170i
$845$	5.79712	+	10.0409i	0.199427	+	0.345418i
$846$	3.02846	+	20.4567i	0.104121	+	0.703315i
$847$		0			0
$848$	7.27208	+	10.9105i	0.249724	+	0.374669i
$849$	−9.87868	−	17.1104i	−0.339035	−	0.587227i
$850$	−9.67893	+	24.4725i	−0.331985	+	0.839398i
$851$	−6.48528	+	11.2328i	−0.222313	+	0.385057i
$852$	−16.1573	−	15.1504i	−0.553539	−	0.519042i
$853$	−19.4252			−0.665106			−0.332553	−	0.943085i	$-0.607910\pi$
$853$	−19.4252			−0.665106			−0.332553	+	0.943085i	$0.607910\pi$
$854$		0			0
$855$		−	24.7013i		−	0.844768i
$856$	−5.34057	+	7.70218i	−0.182537	+	0.263255i
$857$	−33.5101	−	19.3471i	−1.14468	−	0.660884i	−0.197098	−	0.980384i	$-0.563152\pi$
$857$	−33.5101	−	19.3471i	−1.14468	−	0.660884i	−0.947586	+	0.319500i	$0.896485\pi$
$858$	−5.11487	+	12.9326i	−0.174619	+	0.441510i
$859$	−2.60420	+	1.50354i	−0.0888543	+	0.0513000i	−0.543769	−	0.839235i	$-0.683003\pi$
$859$	−2.60420	+	1.50354i	−0.0888543	+	0.0513000i	0.454915	+	0.890535i	$0.349670\pi$
$860$	−14.9901	+	4.53781i	−0.511159	+	0.154738i
$861$		0			0
$862$	28.0711	−	4.15572i	0.956104	−	0.141544i
$863$	−29.0770	+	16.7876i	−0.989792	+	0.571456i	−0.905212	−	0.424960i	$-0.860288\pi$
$863$	−29.0770	+	16.7876i	−0.989792	+	0.571456i	−0.0845796	+	0.996417i	$0.526955\pi$
$864$	−4.91583	−	22.9200i	−0.167240	−	0.779753i
$865$	14.8701	−	25.7557i	0.505597	−	0.875720i
$866$	−2.80596	−	3.53756i	−0.0953502	−	0.120211i
$867$			2.21918i			0.0753672i
$868$		0			0
$869$			47.4825i			1.61073i
$870$	−14.3712	+	11.3991i	−0.487230	+	0.386465i
$871$	−3.02846	+	5.24545i	−0.102615	+	0.177735i
$872$	1.30702	−	15.7734i	0.0442613	−	0.534156i
$873$	14.4019	−	8.31492i	0.487429	−	0.281417i
$874$	3.91548	+	26.4483i	0.132443	+	0.894627i
$875$		0			0
$876$	4.94975	−	1.49839i	0.167236	−	0.0506258i
$877$	24.2308	−	13.9897i	0.818216	−	0.472397i	−0.0315847	−	0.999501i	$-0.510055\pi$
$877$	24.2308	−	13.9897i	0.818216	−	0.472397i	0.849801	+	0.527104i	$0.176722\pi$
$878$	−6.99905	−	2.76815i	−0.236207	−	0.0934204i
$879$	19.7291	+	11.3906i	0.665444	+	0.384195i
$880$	−46.0684	−	22.7842i	−1.55296	−	0.768055i
$881$			4.19825i			0.141443i	0.997496	+	0.0707214i	$0.0225301\pi$
$881$			4.19825i			0.141443i	−0.997496	+	0.0707214i	$0.977470\pi$
$882$		0			0
$883$	−13.6569			−0.459590			−0.229795	−	0.973239i	$-0.573806\pi$
$883$	−13.6569			−0.459590			−0.229795	+	0.973239i	$0.573806\pi$
$884$	18.4815	−	19.7098i	0.621598	−	0.662911i
$885$	−12.4813	+	21.6182i	−0.419553	+	0.726687i
$886$	−45.9896	−	18.1890i	−1.54505	−	0.611072i
$887$	13.3683	+	23.1545i	0.448863	+	0.777453i	0.998312	−	0.0580740i	$-0.0184959\pi$
$887$	13.3683	+	23.1545i	0.448863	+	0.777453i	−0.549450	+	0.835527i	$0.685163\pi$
$888$	2.14144	+	4.53781i	0.0718622	+	0.152279i
$889$		0			0
$890$	−10.5147	+	1.55663i	−0.352454	+	0.0521783i
$891$	−8.63604	−	14.9581i	−0.289318	−	0.501114i
$892$	−1.94987	+	8.34090i	−0.0652866	+	0.279274i
$893$	−17.7217	−	10.2316i	−0.593034	−	0.342389i
$894$	3.93121	−	3.11819i	0.131479	−	0.104288i
$895$	7.09612			0.237197
$896$		0			0
$897$	12.9706			0.433074
$898$	22.4747	−	17.8267i	0.749991	−	0.594884i
$899$	50.1084	+	28.9301i	1.67121	+	0.964873i
$900$	4.58506	−	19.6133i	0.152835	−	0.653778i
$901$	7.31135	+	12.6636i	0.243576	+	0.421887i
$902$	−41.9865	+	6.21579i	−1.39800	+	0.206963i
$903$		0			0
$904$	−1.70711	−	3.61743i	−0.0567775	−	0.120314i
$905$	13.7574	+	23.8284i	0.457310	+	0.792084i
$906$	10.2984	+	4.07306i	0.342143	+	0.135318i
$907$	−18.4853	+	32.0174i	−0.613794	+	1.06312i	0.376801	+	0.926294i	$0.377024\pi$
$907$	−18.4853	+	32.0174i	−0.613794	+	1.06312i	−0.990595	+	0.136828i	$0.956309\pi$
$908$	6.46188	−	6.89134i	0.214445	−	0.228697i
$909$	27.9910			0.928402
$910$		0			0
$911$			27.9793i			0.926996i	0.886098	+	0.463498i	$0.153406\pi$
$911$			27.9793i			0.926996i	−0.886098	+	0.463498i	$0.846594\pi$
$912$	9.27123	+	4.58530i	0.307001	+	0.151835i
$913$	−33.9455	−	19.5984i	−1.12343	−	0.648614i
$914$	31.6170	+	12.5046i	1.04580	+	0.413616i
$915$	−14.6764	+	8.47343i	−0.485187	+	0.280123i
$916$	−46.7889	+	14.1640i	−1.54595	+	0.467990i
$917$		0			0
$918$	−3.82843	−	25.8603i	−0.126357	−	0.853517i
$919$	−12.5311	+	7.23486i	−0.413364	+	0.238656i	−0.692234	−	0.721673i	$-0.743373\pi$
$919$	−12.5311	+	7.23486i	−0.413364	+	0.238656i	0.278870	+	0.960329i	$0.410040\pi$
$920$	−3.95826	+	47.7692i	−0.130500	+	1.57491i
$921$	−8.87868	+	15.3783i	−0.292562	+	0.506733i
$922$	−15.6261	+	12.3944i	−0.514617	+	0.408188i
$923$			43.8210i			1.44238i
$924$		0			0
$925$			9.66922i			0.317922i
$926$	20.8648	+	26.3050i	0.685661	+	0.864436i
$927$	5.16991	−	8.95454i	0.169802	−	0.294106i
$928$	6.63833	+	30.9511i	0.217914	+	1.01602i
$929$	6.51455	−	3.76118i	0.213735	−	0.123400i	−0.389311	−	0.921106i	$-0.627287\pi$
$929$	6.51455	−	3.76118i	0.213735	−	0.123400i	0.603046	+	0.797706i	$0.293953\pi$
$930$	33.5283	−	4.96362i	1.09944	−	0.162763i
$931$		0			0
$932$	18.9497	−	5.73647i	0.620720	−	0.187904i
$933$	2.35175	−	1.35778i	0.0769929	−	0.0444519i
$934$	2.74659	−	6.94454i	0.0898711	−	0.227232i
$935$	−49.6375	−	28.6582i	−1.62332	−	0.937224i
$936$	−11.7834	+	16.9941i	−0.385153	+	0.555468i
$937$			12.0376i			0.393252i	0.980479	+	0.196626i	$0.0629985\pi$
$937$			12.0376i			0.393252i	−0.980479	+	0.196626i	$0.937001\pi$
$938$		0			0
$939$	−26.5858			−0.867594
$940$	−26.7616	−	25.0938i	−0.872867	−	0.818470i
$941$	−8.30598	+	14.3864i	−0.270767	+	0.468983i	−0.969058	−	0.246831i	$-0.920611\pi$
$941$	−8.30598	+	14.3864i	−0.270767	+	0.468983i	0.698291	+	0.715814i	$0.253944\pi$
$942$	−2.91054	+	7.35909i	−0.0948305	+	0.239772i
$943$	19.7926	+	34.2818i	0.644536	+	1.11637i
$944$	23.8918	+	35.8456i	0.777612	+	1.16667i
$945$		0			0
$946$	−2.27208	−	15.3474i	−0.0738716	−	0.498989i
$947$	−8.60660	−	14.9071i	−0.279677	−	0.484415i	0.691627	−	0.722254i	$-0.256894\pi$
$947$	−8.60660	−	14.9071i	−0.279677	−	0.484415i	−0.971304	+	0.237840i	$0.923561\pi$
$948$	3.89975	−	16.6818i	0.126658	−	0.541800i
$949$	−8.86085	−	5.11582i	−0.287635	−	0.166066i
$950$	12.3861	+	15.6156i	0.401858	+	0.506636i
$951$	12.1138			0.392818
$952$		0			0
$953$	50.6274			1.63998			0.819991	−	0.572376i	$-0.193978\pi$
$953$	50.6274			1.63998			0.819991	+	0.572376i	$0.193978\pi$
$954$	−6.95494	−	8.76833i	−0.225175	−	0.283885i
$955$	8.59724	+	4.96362i	0.278200	+	0.160619i
$956$	35.3380	+	8.26105i	1.14291	+	0.267182i
$957$	−9.08538	−	15.7363i	−0.293689	−	0.508684i
$958$	−3.91548	−	26.4483i	−0.126503	−	0.854505i
$959$		0			0
$960$	14.3137	+	11.7883i	0.461973	+	0.380464i
$961$	−37.9558	−	65.7415i	−1.22438	−	2.12069i
$962$	3.65107	−	9.23146i	0.117715	−	0.297634i
$963$	4.00000	−	6.92820i	0.128898	−	0.223258i
$964$	25.2033	−	26.8784i	0.811745	−	0.865695i
$965$	−28.5106			−0.917788
$966$		0			0
$967$		−	16.7876i		−	0.539853i	−0.962881	−	0.269926i	$-0.913001\pi$
$967$		−	16.7876i		−	0.539853i	0.962881	−	0.269926i	$-0.0869994\pi$
$968$	11.2816	−	16.2704i	0.362605	−	0.522950i
$969$	9.98951	+	5.76745i	0.320909	+	0.185277i
$970$	−10.8503	+	27.4341i	−0.348381	+	0.880856i
$971$	−1.27855	+	0.738170i	−0.0410306	+	0.0236890i	−0.520375	−	0.853938i	$-0.674208\pi$
$971$	−1.27855	+	0.738170i	−0.0410306	+	0.0236890i	0.479344	+	0.877627i	$0.340874\pi$
$972$	9.00929	+	29.7611i	0.288973	+	0.954588i
$973$		0			0
$974$	−47.5269	+	7.03601i	−1.52286	+	0.225448i
$975$	8.37379	−	4.83461i	0.268176	−	0.154831i
$976$	1.87924	+	29.1850i	0.0601531	+	0.934188i
$977$	−6.12132	+	10.6024i	−0.195838	+	0.339202i	−0.947175	−	0.320717i	$-0.896076\pi$
$977$	−6.12132	+	10.6024i	−0.195838	+	0.339202i	0.751337	+	0.659919i	$0.229409\pi$
$978$	−3.64180	−	4.59134i	−0.116452	−	0.146815i
$979$		−	10.5294i		−	0.336522i
$980$		0			0
$981$			13.5096i			0.431329i
$982$	28.8077	−	22.8499i	0.919289	−	0.729170i
$983$	−5.16991	+	8.95454i	−0.164894	+	0.285605i	−0.936618	−	0.350353i	$-0.886062\pi$
$983$	−5.16991	+	8.95454i	−0.164894	+	0.285605i	0.771723	+	0.635958i	$0.219395\pi$
$984$	15.2614	+	1.26459i	0.486516	+	0.0403137i
$985$	−50.1084	+	28.9301i	−1.59659	+	0.921789i
$986$	5.16991	+	34.9217i	0.164643	+	1.11213i
$987$		0			0
$988$	−5.92893	−	19.5855i	−0.188624	−	0.623099i
$989$	−12.5311	+	7.23486i	−0.398467	+	0.230055i
$990$	40.7935	+	16.1339i	1.29650	+	0.512770i
$991$	−18.2088	−	10.5128i	−0.578421	−	0.333951i	0.182085	−	0.983283i	$-0.441715\pi$
$991$	−18.2088	−	10.5128i	−0.578421	−	0.333951i	−0.760505	+	0.649332i	$0.775049\pi$
$992$	17.9724	−	55.6612i	0.570624	−	1.76724i
$993$			2.35049i			0.0745907i
$994$		0			0
$995$	49.6569			1.57423
$996$	10.3163	+	9.67338i	0.326884	+	0.306513i
$997$	13.1085	−	22.7045i	0.415149	−	0.719060i	−0.580295	−	0.814407i	$-0.697063\pi$
$997$	13.1085	−	22.7045i	0.415149	−	0.719060i	0.995444	+	0.0953467i	$0.0303960\pi$
$998$	6.08549	+	2.40683i	0.192633	+	0.0761868i
$999$	−4.80249	−	8.31816i	−0.151944	−	0.263175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.m.h.227.4		16
4.3	odd	2		1568.2.q.h.815.3		16
7.2	even	3	inner	392.2.m.h.19.7		16
7.3	odd	6		392.2.e.d.195.2	yes	8
7.4	even	3		392.2.e.d.195.1	✓	8
7.5	odd	6	inner	392.2.m.h.19.8		16
7.6	odd	2	inner	392.2.m.h.227.3		16
8.3	odd	2	inner	392.2.m.h.227.8		16
8.5	even	2		1568.2.q.h.815.4		16
28.3	even	6		1568.2.e.d.783.3		8
28.11	odd	6		1568.2.e.d.783.6		8
28.19	even	6		1568.2.q.h.1391.4		16
28.23	odd	6		1568.2.q.h.1391.5		16
28.27	even	2		1568.2.q.h.815.6		16
56.3	even	6		392.2.e.d.195.4	yes	8
56.5	odd	6		1568.2.q.h.1391.3		16
56.11	odd	6		392.2.e.d.195.3	yes	8
56.13	odd	2		1568.2.q.h.815.5		16
56.19	even	6	inner	392.2.m.h.19.4		16
56.27	even	2	inner	392.2.m.h.227.7		16
56.37	even	6		1568.2.q.h.1391.6		16
56.45	odd	6		1568.2.e.d.783.4		8
56.51	odd	6	inner	392.2.m.h.19.3		16
56.53	even	6		1568.2.e.d.783.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
392.2.e.d.195.1	✓	8	7.4	even	3
392.2.e.d.195.2	yes	8	7.3	odd	6
392.2.e.d.195.3	yes	8	56.11	odd	6
392.2.e.d.195.4	yes	8	56.3	even	6
392.2.m.h.19.3		16	56.51	odd	6	inner
392.2.m.h.19.4		16	56.19	even	6	inner
392.2.m.h.19.7		16	7.2	even	3	inner
392.2.m.h.19.8		16	7.5	odd	6	inner
392.2.m.h.227.3		16	7.6	odd	2	inner
392.2.m.h.227.4		16	1.1	even	1	trivial
392.2.m.h.227.7		16	56.27	even	2	inner
392.2.m.h.227.8		16	8.3	odd	2	inner
1568.2.e.d.783.3		8	28.3	even	6
1568.2.e.d.783.4		8	56.45	odd	6
1568.2.e.d.783.5		8	56.53	even	6
1568.2.e.d.783.6		8	28.11	odd	6
1568.2.q.h.815.3		16	4.3	odd	2
1568.2.q.h.815.4		16	8.5	even	2
1568.2.q.h.815.5		16	56.13	odd	2
1568.2.q.h.815.6		16	28.27	even	2
1568.2.q.h.1391.3		16	56.5	odd	6
1568.2.q.h.1391.4		16	28.19	even	6
1568.2.q.h.1391.5		16	28.23	odd	6
1568.2.q.h.1391.6		16	56.37	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.10799 + 0.878843i) q^{2} +(0.662827 + 0.382683i) q^{3} +(0.455270 - 1.94749i) q^{4} +(-1.51423 - 2.62272i) q^{5} +(-1.07072 + 0.158513i) q^{6} +(1.20711 + 2.55791i) q^{8} +(-1.20711 - 2.09077i) q^{9} +(3.98271 + 1.57517i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(1.04704 - 1.11663i) q^{12} -3.02846 q^{13} -2.31788i q^{15} +(-3.58546 - 1.77327i) q^{16} +(-3.86324 - 2.23044i) q^{17} +(3.17492 + 1.25569i) q^{18} +(-2.92586 + 1.68925i) q^{19} +(-5.79712 + 1.75490i) q^{20} +(-0.878680 - 5.93531i) q^{22} +(-4.84616 + 2.79793i) q^{23} +(-0.178766 + 2.15739i) q^{24} +(-2.08579 + 3.61269i) q^{25} +(3.35549 - 2.66154i) q^{26} -4.14386i q^{27} +5.59587i q^{29} +(2.03706 + 2.56818i) q^{30} +(5.16991 - 8.95454i) q^{31} +(5.53107 - 1.18629i) q^{32} +(-2.81214 + 1.62359i) q^{33} +(6.24063 - 0.923880i) q^{34} +(-4.62132 + 1.39897i) q^{36} +(2.00735 - 1.15894i) q^{37} +(1.75723 - 4.44303i) q^{38} +(-2.00735 - 1.15894i) q^{39} +(4.88085 - 7.03917i) q^{40} -7.07401i q^{41} +2.58579 q^{43} +(6.18977 + 5.80403i) q^{44} +(-3.65568 + 6.33182i) q^{45} +(2.91054 - 7.35909i) q^{46} +(3.02846 + 5.24545i) q^{47} +(-1.69794 - 2.54747i) q^{48} +(-0.863961 - 5.83589i) q^{50} +(-1.70711 - 2.95680i) q^{51} +(-1.37877 + 5.89791i) q^{52} +(-2.83882 - 1.63899i) q^{53} +(3.64180 + 4.59134i) q^{54} +12.8487 q^{55} -2.58579 q^{57} +(-4.91789 - 6.20015i) q^{58} +(-9.32669 - 5.38476i) q^{59} +(-4.51406 - 1.05526i) q^{60} +(-3.65568 - 6.33182i) q^{61} +(2.14144 + 14.4650i) q^{62} +(-5.08579 + 6.17534i) q^{64} +(4.58579 + 7.94282i) q^{65} +(1.68893 - 4.27034i) q^{66} +(1.00000 - 1.73205i) q^{67} +(-6.10259 + 6.50818i) q^{68} -4.28289 q^{69} -14.4697i q^{71} +(3.89089 - 5.61145i) q^{72} +(2.92586 + 1.68925i) q^{73} +(-1.20559 + 3.04823i) q^{74} +(-2.76503 + 1.59639i) q^{75} +(1.95774 + 6.46716i) q^{76} +(3.24264 - 0.480049i) q^{78} +(9.69232 - 5.59587i) q^{79} +(0.778407 + 12.0888i) q^{80} +(-2.03553 + 3.52565i) q^{81} +(6.21694 + 7.83791i) q^{82} +9.23880i q^{83} +13.5096i q^{85} +(-2.86502 + 2.27250i) q^{86} +(-2.14144 + 3.70909i) q^{87} +(-11.9590 - 0.990949i) q^{88} +(-2.14931 + 1.24090i) q^{89} +(-1.51423 - 10.2283i) q^{90} +(3.24264 + 10.7117i) q^{92} +(6.85351 - 3.95687i) q^{93} +(-7.96542 - 3.15035i) q^{94} +(8.86085 + 5.11582i) q^{95} +(4.12012 + 1.33034i) q^{96} +6.88830i q^{97} +10.2426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 4 q^{4} + 8 q^{8} - 8 q^{9} - 4 q^{16} + 4 q^{18} - 48 q^{22} - 56 q^{25} - 8 q^{30} + 36 q^{32} - 40 q^{36} + 64 q^{43} + 48 q^{44} + 40 q^{46} + 88 q^{50} - 16 q^{51} - 64 q^{57} - 40 q^{58}+ \cdots + 96 q^{99}+O(q^{100}) \) 16 * q - 4 * q^2 + 4 * q^4 + 8 * q^8 - 8 * q^9 - 4 * q^16 + 4 * q^18 - 48 * q^22 - 56 * q^25 - 8 * q^30 + 36 * q^32 - 40 * q^36 + 64 * q^43 + 48 * q^44 + 40 * q^46 + 88 * q^50 - 16 * q^51 - 64 * q^57 - 40 * q^58 - 56 * q^60 - 104 * q^64 + 96 * q^65 + 16 * q^67 - 12 * q^72 + 8 * q^74 - 16 * q^78 + 24 * q^81 - 24 * q^86 - 24 * q^88 - 16 * q^92 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more