LMFDB - Embedded newform 784.2.x.n.165.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.7
Character	$\chi$	$=$	784.165
Dual form			784.2.x.n.765.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.674626 - 1.24293i) q^{2} +(-0.839505 - 3.13308i) q^{3} +(-1.08976 - 1.67703i) q^{4} +(0.734404 - 2.74083i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(-6.51332 + 3.76047i) q^{9} +O(q^{10})$	\(q+(0.674626 - 1.24293i) q^{2} +(-0.839505 - 3.13308i) q^{3} +(-1.08976 - 1.67703i) q^{4} +(0.734404 - 2.74083i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(-6.51332 + 3.76047i) q^{9} +(-2.91122 - 2.76185i) q^{10} +(4.32748 - 1.15955i) q^{11} +(-4.33940 + 4.82218i) q^{12} +(0.558438 - 0.558438i) q^{13} -9.20377 q^{15} +(-1.62485 + 3.65512i) q^{16} +(1.09678 - 1.89967i) q^{17} +(0.279952 + 10.6325i) q^{18} +(2.55326 + 0.684144i) q^{19} +(-5.39678 + 1.75523i) q^{20} +(1.47820 - 6.16103i) q^{22} +(0.647926 - 0.374080i) q^{23} +(3.06617 + 8.64674i) q^{24} +(-2.64268 - 1.52575i) q^{25} +(-0.317364 - 1.07084i) q^{26} +(10.3691 + 10.3691i) q^{27} +(-3.07468 + 3.07468i) q^{29} +(-6.20910 + 11.4397i) q^{30} +(4.43398 - 7.67989i) q^{31} +(3.44690 + 4.48541i) q^{32} +(-7.26589 - 12.5849i) q^{33} +(-1.62125 - 2.64479i) q^{34} +(13.4044 + 6.82502i) q^{36} +(1.69807 - 6.33730i) q^{37} +(2.57284 - 2.71199i) q^{38} +(-2.21844 - 1.28082i) q^{39} +(-1.45917 + 7.89195i) q^{40} +0.267969i q^{41} +(4.53661 + 4.53661i) q^{43} +(-6.66051 - 5.99369i) q^{44} +(5.52341 + 20.6136i) q^{45} +(-0.0278487 - 1.05769i) q^{46} +(3.74156 + 6.48057i) q^{47} +(12.8158 + 2.02228i) q^{48} +(-3.67923 + 2.25536i) q^{50} +(-6.87257 - 1.84150i) q^{51} +(-1.54508 - 0.327953i) q^{52} +(4.36564 - 1.16977i) q^{53} +(19.8833 - 5.89282i) q^{54} -12.7125i q^{55} -8.57391i q^{57} +(1.74736 + 5.89587i) q^{58} +(-7.07539 + 1.89585i) q^{59} +(10.0299 + 15.4350i) q^{60} +(5.73728 + 1.53730i) q^{61} +(-6.55430 - 10.6922i) q^{62} +(7.90042 - 1.25829i) q^{64} +(-1.12047 - 1.94070i) q^{65} +(-20.5439 + 0.540916i) q^{66} +(1.48228 + 5.53193i) q^{67} +(-4.38103 + 0.230862i) q^{68} +(-1.71596 - 1.71596i) q^{69} +9.37949i q^{71} +(17.5260 - 12.0564i) q^{72} +(-9.08221 - 5.24362i) q^{73} +(-6.73127 - 6.38590i) q^{74} +(-2.56176 + 9.56061i) q^{75} +(-1.63511 - 5.02744i) q^{76} +(-3.08859 + 1.89330i) q^{78} +(5.10952 + 8.84995i) q^{79} +(8.82477 + 7.13776i) q^{80} +(12.5009 - 21.6521i) q^{81} +(0.333067 + 0.180778i) q^{82} +(-0.474267 + 0.474267i) q^{83} +(-4.40120 - 4.40120i) q^{85} +(8.69922 - 2.57819i) q^{86} +(12.2144 + 7.05199i) q^{87} +(-11.9431 + 4.23507i) q^{88} +(-12.5849 + 7.26589i) q^{89} +(29.3476 + 7.04127i) q^{90} +(-1.33343 - 0.678932i) q^{92} +(-27.7840 - 7.44471i) q^{93} +(10.5791 - 0.278544i) q^{94} +(3.75025 - 6.49562i) q^{95} +(11.1594 - 14.5649i) q^{96} -16.4976 q^{97} +(-23.8259 + 23.8259i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{4}+O(q^{10}) $ 40 * q + 8 * q^4	$ 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) $ 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.674626	−	1.24293i	0.477032	−	0.878886i
$2$	0.674626	−	1.24293i	0.477032	−	0.878886i
$3$	−0.839505	−	3.13308i	−0.484689	−	1.80888i	−0.581459	−	0.813576i	$-0.697518\pi$
$3$	−0.839505	−	3.13308i	−0.484689	−	1.80888i	0.0967700	−	0.995307i	$-0.469149\pi$
$4$	−1.08976	−	1.67703i	−0.544880	−	0.838514i
$5$	0.734404	−	2.74083i	0.328435	−	1.22574i	−0.582378	−	0.812918i	$-0.697878\pi$
$5$	0.734404	−	2.74083i	0.328435	−	1.22574i	0.910813	−	0.412819i	$-0.135456\pi$
$6$	−4.46055	−	1.07021i	−1.82101	−	0.436910i
$7$		0			0
$7$		0			0
$8$	−2.81961	+	0.223131i	−0.996883	+	0.0788889i
$9$	−6.51332	+	3.76047i	−2.17111	+	1.25349i
$10$	−2.91122	−	2.76185i	−0.920609	−	0.873374i
$11$	4.32748	−	1.15955i	1.30479	−	0.349616i	0.461528	−	0.887126i	$-0.347301\pi$
$11$	4.32748	−	1.15955i	1.30479	−	0.349616i	0.843258	+	0.537509i	$0.180635\pi$
$12$	−4.33940	+	4.82218i	−1.25268	+	1.39204i
$13$	0.558438	−	0.558438i	0.154883	−	0.154883i	−0.625412	−	0.780295i	$-0.715069\pi$
$13$	0.558438	−	0.558438i	0.154883	−	0.154883i	0.780295	+	0.625412i	$0.215069\pi$
$14$		0			0
$15$	−9.20377			−2.37640
$16$	−1.62485	+	3.65512i	−0.406211	+	0.913779i
$17$	1.09678	−	1.89967i	0.266007	−	0.460738i	−0.701820	−	0.712355i	$-0.747629\pi$
$17$	1.09678	−	1.89967i	0.266007	−	0.460738i	0.967827	+	0.251616i	$0.0809622\pi$
$18$	0.279952	+	10.6325i	0.0659852	+	2.50611i
$19$	2.55326	+	0.684144i	0.585758	+	0.156954i	0.539514	−	0.841977i	$-0.318608\pi$
$19$	2.55326	+	0.684144i	0.585758	+	0.156954i	0.0462445	+	0.998930i	$0.485275\pi$
$20$	−5.39678	+	1.75523i	−1.20676	+	0.392482i
$21$		0			0
$22$	1.47820	−	6.16103i	0.315152	−	1.31354i
$23$	0.647926	−	0.374080i	0.135102	−	0.0780011i	−0.430926	−	0.902387i	$-0.641813\pi$
$23$	0.647926	−	0.374080i	0.135102	−	0.0780011i	0.566028	+	0.824386i	$0.308480\pi$
$24$	3.06617	+	8.64674i	0.625879	+	1.76501i
$25$	−2.64268	−	1.52575i	−0.528537	−	0.305151i
$26$	−0.317364	−	1.07084i	−0.0622402	−	0.210009i
$27$	10.3691	+	10.3691i	1.99553	+	1.99553i
$28$		0			0
$29$	−3.07468	+	3.07468i	−0.570953	+	0.570953i	−0.932395	−	0.361442i	$-0.882285\pi$
$29$	−3.07468	+	3.07468i	−0.570953	+	0.570953i	0.361442	+	0.932395i	$0.382285\pi$
$30$	−6.20910	+	11.4397i	−1.13362	+	2.08859i
$31$	4.43398	−	7.67989i	0.796367	−	1.37935i	−0.125601	−	0.992081i	$-0.540086\pi$
$31$	4.43398	−	7.67989i	0.796367	−	1.37935i	0.921968	−	0.387267i	$-0.126581\pi$
$32$	3.44690	+	4.48541i	0.609331	+	0.792916i
$33$	−7.26589	−	12.5849i	−1.26483	−	2.19075i
$34$	−1.62125	−	2.64479i	−0.278042	−	0.453577i
$35$		0			0
$36$	13.4044	+	6.82502i	2.23406	+	1.13750i
$37$	1.69807	−	6.33730i	0.279162	−	1.04185i	−0.673839	−	0.738878i	$-0.735356\pi$
$37$	1.69807	−	6.33730i	0.279162	−	1.04185i	0.953001	−	0.302967i	$-0.0979773\pi$
$38$	2.57284	−	2.71199i	0.417370	−	0.439943i
$39$	−2.21844	−	1.28082i	−0.355235	−	0.205095i
$40$	−1.45917	+	7.89195i	−0.230715	+	1.24783i
$41$			0.267969i			0.0418497i	0.999781	+	0.0209248i	$0.00666107\pi$
$41$			0.267969i			0.0418497i	−0.999781	+	0.0209248i	$0.993339\pi$
$42$		0			0
$43$	4.53661	+	4.53661i	0.691827	+	0.691827i	0.962634	−	0.270807i	$-0.0872904\pi$
$43$	4.53661	+	4.53661i	0.691827	+	0.691827i	−0.270807	+	0.962634i	$0.587290\pi$
$44$	−6.66051	−	5.99369i	−1.00411	−	0.903582i
$45$	5.52341	+	20.6136i	0.823381	+	3.07290i
$46$	−0.0278487	−	1.05769i	−0.00410607	−	0.155948i
$47$	3.74156	+	6.48057i	0.545763	+	0.945289i	0.998558	+	0.0536746i	$0.0170934\pi$
$47$	3.74156	+	6.48057i	0.545763	+	0.945289i	−0.452796	+	0.891614i	$0.649573\pi$
$48$	12.8158	+	2.02228i	1.84981	+	0.291890i
$49$		0			0
$50$	−3.67923	+	2.25536i	−0.520322	+	0.318956i
$51$	−6.87257	−	1.84150i	−0.962352	−	0.257861i
$52$	−1.54508	−	0.327953i	−0.214264	−	0.0454789i
$53$	4.36564	−	1.16977i	0.599667	−	0.160680i	0.0537996	−	0.998552i	$-0.482867\pi$
$53$	4.36564	−	1.16977i	0.599667	−	0.160680i	0.545868	+	0.837871i	$0.316200\pi$
$54$	19.8833	−	5.89282i	2.70578	−	0.801912i
$55$		−	12.7125i		−	1.71415i
$56$		0			0
$57$		−	8.57391i		−	1.13564i
$58$	1.74736	+	5.89587i	0.229439	+	0.774166i
$59$	−7.07539	+	1.89585i	−0.921137	+	0.246818i	−0.688071	−	0.725643i	$-0.741542\pi$
$59$	−7.07539	+	1.89585i	−0.921137	+	0.246818i	−0.233066	+	0.972461i	$0.574876\pi$
$60$	10.0299	+	15.4350i	1.29486	+	1.99265i
$61$	5.73728	+	1.53730i	0.734583	+	0.196831i	0.606669	−	0.794954i	$-0.292505\pi$
$61$	5.73728	+	1.53730i	0.734583	+	0.196831i	0.127914	+	0.991785i	$0.459172\pi$
$62$	−6.55430	−	10.6922i	−0.832396	−	1.35791i
$63$		0			0
$64$	7.90042	−	1.25829i	0.987553	−	0.157286i
$65$	−1.12047	−	1.94070i	−0.138977	−	0.240715i
$66$	−20.5439	+	0.540916i	−2.52878	+	0.0665822i
$67$	1.48228	+	5.53193i	0.181089	+	0.675833i	0.995434	+	0.0954519i	$0.0304296\pi$
$67$	1.48228	+	5.53193i	0.181089	+	0.675833i	−0.814345	+	0.580381i	$0.802904\pi$
$68$	−4.38103	+	0.230862i	−0.531277	+	0.0279962i
$69$	−1.71596	−	1.71596i	−0.206577	−	0.206577i
$70$		0			0
$71$			9.37949i			1.11314i	0.830801	+	0.556570i	$0.187883\pi$
$71$			9.37949i			1.11314i	−0.830801	+	0.556570i	$0.812117\pi$
$72$	17.5260	−	12.0564i	2.06546	−	1.42086i
$73$	−9.08221	−	5.24362i	−1.06299	−	0.613719i	−0.136734	−	0.990608i	$-0.543661\pi$
$73$	−9.08221	−	5.24362i	−1.06299	−	0.613719i	−0.926258	+	0.376889i	$0.876994\pi$
$74$	−6.73127	−	6.38590i	−0.782494	−	0.742345i
$75$	−2.56176	+	9.56061i	−0.295806	+	1.10396i
$76$	−1.63511	−	5.02744i	−0.187560	−	0.576687i
$77$		0			0
$78$	−3.08859	+	1.89330i	−0.349714	+	0.214374i
$79$	5.10952	+	8.84995i	0.574866	+	0.995697i	0.996056	+	0.0887248i	$0.0282792\pi$
$79$	5.10952	+	8.84995i	0.574866	+	0.995697i	−0.421190	+	0.906972i	$0.638387\pi$
$80$	8.82477	+	7.13776i	0.986639	+	0.798026i
$81$	12.5009	−	21.6521i	1.38898	−	2.40579i
$82$	0.333067	+	0.180778i	0.0367811	+	0.0199636i
$83$	−0.474267	+	0.474267i	−0.0520576	+	0.0520576i	−0.732656	−	0.680599i	$-0.761720\pi$
$83$	−0.474267	+	0.474267i	−0.0520576	+	0.0520576i	0.680599	+	0.732656i	$0.261720\pi$
$84$		0			0
$85$	−4.40120	−	4.40120i	−0.477378	−	0.477378i
$86$	8.69922	−	2.57819i	0.938061	−	0.278013i
$87$	12.2144	+	7.05199i	1.30952	+	0.756053i
$88$	−11.9431	+	4.23507i	−1.27314	+	0.451460i
$89$	−12.5849	+	7.26589i	−1.33400	+	0.770183i	−0.985910	−	0.167279i	$-0.946502\pi$
$89$	−12.5849	+	7.26589i	−1.33400	+	0.770183i	−0.348087	+	0.937462i	$0.613169\pi$
$90$	29.3476	+	7.04127i	3.09351	+	0.742215i
$91$		0			0
$92$	−1.33343	−	0.678932i	−0.139019	−	0.0707835i
$93$	−27.7840	−	7.44471i	−2.88107	−	0.771980i
$94$	10.5791	−	0.278544i	1.09115	−	0.0287296i
$95$	3.75025	−	6.49562i	0.384768	−	0.666437i
$96$	11.1594	−	14.5649i	1.13896	−	1.48653i
$97$	−16.4976			−1.67507			−0.837537	−	0.546380i	$-0.816005\pi$
$97$	−16.4976			−1.67507			−0.837537	+	0.546380i	$0.816005\pi$
$98$		0			0
$99$	−23.8259	+	23.8259i	−2.39459	+	2.39459i
$100$	0.321159	+	6.09456i	0.0321159	+	0.609456i
$101$	−14.7659	+	3.95651i	−1.46926	+	0.393688i	−0.902679	−	0.430316i	$-0.858402\pi$
$101$	−14.7659	+	3.95651i	−1.46926	+	0.393688i	−0.566585	+	0.824003i	$0.691736\pi$
$102$	−6.92527	+	7.29981i	−0.685704	+	0.722789i
$103$	1.46459	−	0.845581i	0.144310	−	0.0833176i	−0.426106	−	0.904673i	$-0.640115\pi$
$103$	1.46459	−	0.845581i	0.144310	−	0.0833176i	0.570417	+	0.821355i	$0.306782\pi$
$104$	−1.44997	+	1.69918i	−0.142182	+	0.166619i
$105$		0			0
$106$	1.49123	−	6.21536i	0.144841	−	0.603689i
$107$	−0.692325	+	2.58379i	−0.0669296	+	0.249785i	−0.991282	−	0.131754i	$-0.957939\pi$
$107$	−0.692325	+	2.58379i	−0.0669296	+	0.249785i	0.924353	+	0.381539i	$0.124606\pi$
$108$	6.08944	−	28.6891i	0.585956	−	2.76061i
$109$	−2.03730	−	7.60329i	−0.195138	−	0.728264i	−0.992231	−	0.124408i	$-0.960297\pi$
$109$	−2.03730	−	7.60329i	−0.195138	−	0.728264i	0.797094	−	0.603856i	$-0.206370\pi$
$110$	−15.8008	−	8.57617i	−1.50654	−	0.817705i
$111$	−21.2808			−2.01988
$112$		0			0
$113$	7.18060			0.675494			0.337747	−	0.941237i	$-0.390335\pi$
$113$	7.18060			0.675494			0.337747	+	0.941237i	$0.390335\pi$
$114$	−10.6568	−	5.78418i	−0.998099	−	0.541738i
$115$	−0.549451	−	2.05058i	−0.0512366	−	0.191218i
$116$	8.50698	+	1.80566i	0.789853	+	0.167651i
$117$	−1.53730	+	5.73728i	−0.142123	+	0.530412i
$118$	−2.41683	+	10.0732i	−0.222488	+	0.927315i
$119$		0			0
$120$	25.9511	−	2.05365i	2.36900	−	0.187472i
$121$	7.85629	−	4.53583i	0.714209	−	0.412349i
$122$	5.78128	−	6.09395i	0.523412	−	0.551720i
$123$	0.839566	−	0.224961i	0.0757011	−	0.0202841i
$124$	−17.7114	+	0.933318i	−1.59053	+	0.0838144i
$125$	3.90951	−	3.90951i	0.349677	−	0.349677i
$126$		0			0
$127$	10.2378			0.908462			0.454231	−	0.890884i	$-0.349914\pi$
$127$	10.2378			0.908462			0.454231	+	0.890884i	$0.349914\pi$
$128$	3.76586	−	10.6686i	0.332858	−	0.942977i
$129$	10.4050	−	18.0221i	0.916113	−	1.58675i
$130$	−3.16806	+	0.0834141i	−0.277857	+	0.00731590i
$131$	3.87427	+	1.03811i	0.338496	+	0.0906998i	0.424063	−	0.905633i	$-0.360603\pi$
$131$	3.87427	+	1.03811i	0.338496	+	0.0906998i	−0.0855668	+	0.996332i	$0.527270\pi$
$132$	−13.1871	+	25.8996i	−1.14779	+	2.25427i
$133$		0			0
$134$	7.87579	+	1.88961i	0.680365	+	0.163238i
$135$	36.0351	−	20.8048i	3.10140	−	1.79060i
$136$	−2.66861	+	5.60106i	−0.228831	+	0.480287i
$137$	0.931953	+	0.538063i	0.0796221	+	0.0459698i	0.539282	−	0.842125i	$-0.318696\pi$
$137$	0.931953	+	0.538063i	0.0796221	+	0.0459698i	−0.459660	+	0.888095i	$0.652029\pi$
$138$	−3.29045	+	0.975190i	−0.280102	+	0.0830137i
$139$	−1.02686	−	1.02686i	−0.0870973	−	0.0870973i	0.662216	−	0.749313i	$-0.269616\pi$
$139$	−1.02686	−	1.02686i	−0.0870973	−	0.0870973i	−0.749313	+	0.662216i	$0.769616\pi$
$140$		0			0
$141$	17.1631	−	17.1631i	1.44539	−	1.44539i
$142$	11.6581	+	6.32764i	0.978323	+	0.531004i
$143$	1.76910	−	3.06417i	0.147939	−	0.256239i
$144$	−3.16181	−	29.9171i	−0.263484	−	2.49310i
$145$	6.16912	+	10.6852i	0.512317	+	0.887360i
$146$	−12.6446	+	7.75109i	−1.04647	+	0.641485i
$147$		0			0
$148$	−12.4783	+	4.05842i	−1.02571	+	0.333600i
$149$	0.151905	−	0.566917i	0.0124445	−	0.0464437i	−0.959424	−	0.281966i	$-0.909013\pi$
$149$	0.151905	−	0.566917i	0.0124445	−	0.0464437i	0.971869	+	0.235522i	$0.0756801\pi$
$150$	10.1550	+	9.63392i	0.829149	+	0.786606i
$151$	−9.36199	−	5.40515i	−0.761868	−	0.439865i	0.0680980	−	0.997679i	$-0.478307\pi$
$151$	−9.36199	−	5.40515i	−0.761868	−	0.439865i	−0.829966	+	0.557814i	$0.811640\pi$
$152$	−7.35186	−	1.35931i	−0.596315	−	0.110255i
$153$			16.4976i			1.33375i
$154$		0			0
$155$	−17.7929	−	17.7929i	−1.42916	−	1.42916i
$156$	0.269602	+	5.11617i	0.0215854	+	0.409622i
$157$	−2.35072	−	8.77302i	−0.187608	−	0.700163i	−0.994057	−	0.108859i	$-0.965280\pi$
$157$	−2.35072	−	8.77302i	−0.187608	−	0.700163i	0.806449	−	0.591304i	$-0.201387\pi$
$158$	14.4469	−	0.380383i	1.14933	−	0.0302616i
$159$	−7.32996	−	12.6959i	−0.581304	−	1.00685i
$160$	14.8252	−	6.15327i	1.17203	−	0.486459i
$161$		0			0
$162$	−18.4787	−	30.1448i	−1.45182	−	2.36840i
$163$	14.4844	+	3.88107i	1.13450	+	0.303989i	0.776739	−	0.629823i	$-0.216872\pi$
$163$	14.4844	+	3.88107i	1.13450	+	0.303989i	0.357764	+	0.933812i	$0.383539\pi$
$164$	0.449391	−	0.292021i	0.0350915	−	0.0228030i
$165$	−39.8292	+	10.6722i	−3.10070	+	0.830829i
$166$	0.269529	+	0.909434i	0.0209195	+	0.0705858i
$167$		−	17.7426i		−	1.37296i	−0.727147	−	0.686481i	$-0.759154\pi$
$167$		−	17.7426i		−	1.37296i	0.727147	−	0.686481i	$-0.240846\pi$
$168$		0			0
$169$			12.3763i			0.952023i
$170$	−8.43956	+	2.50123i	−0.647285	+	0.191836i
$171$	−19.2029	+	5.14541i	−1.46848	+	0.393479i
$172$	2.66421	−	12.5518i	0.203144	−	0.957069i
$173$	12.1355	+	3.25170i	0.922646	+	0.247222i	0.688716	−	0.725031i	$-0.258175\pi$
$173$	12.1355	+	3.25170i	0.922646	+	0.247222i	0.233930	+	0.972253i	$0.424841\pi$
$174$	17.0053	−	10.4242i	1.28917	−	0.790258i
$175$		0			0
$176$	−2.79322	+	17.7015i	−0.210547	+	1.33430i
$177$	11.8797	+	20.5762i	0.892930	+	1.54660i
$178$	0.540916	+	20.5439i	0.0405434	+	1.53983i
$179$	1.22964	+	4.58909i	0.0919079	+	0.343005i	0.996533	−	0.0832043i	$-0.0265154\pi$
$179$	1.22964	+	4.58909i	0.0919079	+	0.343005i	−0.904625	+	0.426209i	$0.859849\pi$
$180$	28.5504	−	31.7268i	2.12802	−	2.36478i
$181$	3.35107	+	3.35107i	0.249083	+	0.249083i	0.820594	−	0.571511i	$-0.193643\pi$
$181$	3.35107	+	3.35107i	0.249083	+	0.249083i	−0.571511	+	0.820594i	$0.693643\pi$
$182$		0			0
$183$		−	19.2659i		−	1.42418i
$184$	−1.74343	+	1.19933i	−0.128527	+	0.0884160i
$185$	−16.1224	−	9.30827i	−1.18534	−	0.684358i
$186$	−27.9971	+	29.5113i	−2.05285	+	2.16387i
$187$	2.54352	−	9.49256i	0.186001	−	0.694165i
$188$	6.79070	−	13.3370i	0.495263	−	0.972699i
$189$		0			0
$190$	−5.54360	−	9.04342i	−0.402175	−	0.656079i
$191$	−9.91610	−	17.1752i	−0.717504	−	1.24275i	−0.961986	−	0.273099i	$-0.911951\pi$
$191$	−9.91610	−	17.1752i	−0.717504	−	1.24275i	0.244482	−	0.969654i	$-0.421382\pi$
$192$	−10.5748	−	23.6963i	−0.763168	−	1.71013i
$193$	−1.81712	+	3.14734i	−0.130799	+	0.226551i	−0.923985	−	0.382429i	$-0.875088\pi$
$193$	−1.81712	+	3.14734i	−0.130799	+	0.226551i	0.793186	+	0.608980i	$0.208421\pi$
$194$	−11.1297	+	20.5054i	−0.799065	+	1.47220i
$195$	−5.13974	+	5.13974i	−0.368064	+	0.368064i
$196$		0			0
$197$	−9.84601	−	9.84601i	−0.701499	−	0.701499i	0.263233	−	0.964732i	$-0.415211\pi$
$197$	−9.84601	−	9.84601i	−0.701499	−	0.701499i	−0.964732	+	0.263233i	$0.915211\pi$
$198$	13.5404	+	45.6875i	0.962274	+	3.24687i
$199$	6.74009	+	3.89139i	0.477792	+	0.275854i	0.719496	−	0.694497i	$-0.244373\pi$
$199$	6.74009	+	3.89139i	0.477792	+	0.275854i	−0.241704	+	0.970350i	$0.577706\pi$
$200$	7.79178	+	3.71237i	0.550962	+	0.262504i
$201$	16.0876	−	9.28817i	1.13473	−	0.655137i
$202$	−5.04379	+	21.0222i	−0.354880	+	1.47912i
$203$		0			0
$204$	4.40120	+	13.5323i	0.308146	+	0.947449i
$205$	0.734457	+	0.196797i	0.0512967	+	0.0137449i
$206$	−0.0629501	−	2.39084i	−0.00438594	−	0.166578i
$207$	−2.81343	+	4.87301i	−0.195547	+	0.338698i
$208$	1.13378	+	2.94853i	0.0786136	+	0.204444i
$209$	11.8425			0.819163
$210$		0			0
$211$	3.04029	−	3.04029i	0.209302	−	0.209302i	−0.594669	−	0.803971i	$-0.702717\pi$
$211$	3.04029	−	3.04029i	0.209302	−	0.209302i	0.803971	+	0.594669i	$0.202717\pi$
$212$	−6.71924	−	6.04654i	−0.461480	−	0.415278i
$213$	29.3866	−	7.87413i	2.01354	−	0.539526i
$214$	2.74442	+	2.60361i	0.187605	+	0.177979i
$215$	15.7658	−	9.10239i	1.07522	−	0.620778i
$216$	−31.5505	−	26.9232i	−2.14674	−	1.83189i
$217$		0			0
$218$	−10.8248	−	2.59716i	−0.733147	−	0.175902i
$219$	−8.80409	+	32.8573i	−0.594925	+	2.22029i
$220$	−21.3192	+	13.8536i	−1.43734	+	0.934006i
$221$	−0.448368	−	1.67333i	−0.0301605	−	0.112560i
$222$	−14.3566	+	26.4506i	−0.963550	+	1.77525i
$223$	21.2874			1.42551			0.712756	−	0.701412i	$-0.247447\pi$
$223$	21.2874			1.42551			0.712756	+	0.701412i	$0.247447\pi$
$224$		0			0
$225$	22.9502			1.53001
$226$	4.84422	−	8.92500i	0.322233	−	0.593682i
$227$	5.69486	+	21.2535i	0.377981	+	1.41064i	0.848940	+	0.528490i	$0.177241\pi$
$227$	5.69486	+	21.2535i	0.377981	+	1.41064i	−0.470959	+	0.882155i	$0.656092\pi$
$228$	−14.3787	+	9.34350i	−0.952252	+	0.618789i
$229$	−3.81953	+	14.2547i	−0.252402	+	0.941976i	0.717116	+	0.696954i	$0.245462\pi$
$229$	−3.81953	+	14.2547i	−0.252402	+	0.941976i	−0.969518	+	0.245022i	$0.921205\pi$
$230$	−2.91941	−	0.700444i	−0.192500	−	0.0461859i
$231$		0			0
$232$	7.98334	−	9.35545i	0.524132	−	0.614215i
$233$	−19.6072	+	11.3202i	−1.28451	+	0.741611i	−0.977669	−	0.210150i	$-0.932605\pi$
$233$	−19.6072	+	11.3202i	−1.28451	+	0.741611i	−0.306839	+	0.951761i	$0.599271\pi$
$234$	6.09395	+	5.78128i	0.398374	+	0.377934i
$235$	20.5100	−	5.49563i	1.33792	−	0.358496i
$236$	10.8899	+	9.79961i	0.708870	+	0.637900i
$237$	23.4381	−	23.4381i	1.52247	−	1.52247i
$238$		0			0
$239$	−18.5833			−1.20205			−0.601026	−	0.799230i	$-0.705241\pi$
$239$	−18.5833			−1.20205			−0.601026	+	0.799230i	$0.705241\pi$
$240$	14.9547	−	33.6409i	0.965322	−	2.17151i
$241$	−6.25821	+	10.8395i	−0.403126	+	0.698235i	−0.994101	−	0.108454i	$-0.965410\pi$
$241$	−6.25821	+	10.8395i	−0.403126	+	0.698235i	0.590975	+	0.806690i	$0.298743\pi$
$242$	−0.337674	−	12.8248i	−0.0217065	−	0.824411i
$243$	−35.8389	−	9.60301i	−2.29907	−	0.616033i
$244$	−3.67416	−	11.2969i	−0.235214	−	0.723208i
$245$		0			0
$246$	0.286782	−	1.19529i	0.0182845	−	0.0762088i
$247$	1.80789	−	1.04379i	0.115033	−	0.0664146i
$248$	−10.7885	+	22.6437i	−0.685070	+	1.43787i
$249$	1.88406	+	1.08777i	0.119398	+	0.0689343i
$250$	−2.22180	−	7.49671i	−0.140519	−	0.474134i
$251$	−8.79964	−	8.79964i	−0.555429	−	0.555429i	0.372574	−	0.928003i	$-0.378475\pi$
$251$	−8.79964	−	8.79964i	−0.555429	−	0.555429i	−0.928003	+	0.372574i	$0.878475\pi$
$252$		0			0
$253$	2.37012	−	2.37012i	0.149008	−	0.149008i
$254$	6.90672	−	12.7250i	0.433366	−	0.798434i
$255$	−10.0945	+	17.4841i	−0.632141	+	1.09490i
$256$	−10.7198	−	11.8780i	−0.669985	−	0.742375i
$257$	11.3926	+	19.7326i	0.710653	+	1.23089i	0.964612	+	0.263672i	$0.0849337\pi$
$257$	11.3926	+	19.7326i	0.710653	+	1.23089i	−0.253959	+	0.967215i	$0.581733\pi$
$258$	−15.3807	−	25.0909i	−0.957560	−	1.56209i
$259$		0			0
$260$	−2.03358	+	3.99396i	−0.126117	+	0.247695i
$261$	8.46414	−	31.5886i	0.523917	−	1.95528i
$262$	3.90398	−	4.11512i	0.241189	−	0.254233i
$263$	−11.0752	−	6.39429i	−0.682929	−	0.394289i	0.118029	−	0.993010i	$-0.462342\pi$
$263$	−11.0752	−	6.39429i	−0.682929	−	0.394289i	−0.800958	+	0.598721i	$0.795676\pi$
$264$	23.2951	+	33.8633i	1.43371	+	2.08414i
$265$		−	12.8246i		−	0.787808i
$266$		0			0
$267$	33.3297	+	33.3297i	2.03974	+	2.03974i
$268$	7.66188	−	8.51429i	0.468024	−	0.520093i
$269$	−4.12636	−	15.3998i	−0.251589	−	0.938943i	−0.969956	−	0.243279i	$-0.921777\pi$
$269$	−4.12636	−	15.3998i	−0.251589	−	0.938943i	0.718368	−	0.695664i	$-0.244890\pi$
$270$	−1.54884	−	58.8246i	−0.0942592	−	3.57995i
$271$	−15.5305	−	26.8997i	−0.943412	−	1.63404i	−0.758899	−	0.651208i	$-0.774263\pi$
$271$	−15.5305	−	26.8997i	−0.943412	−	1.63404i	−0.184513	−	0.982830i	$-0.559071\pi$
$272$	5.16143	+	7.09552i	0.312958	+	0.430229i
$273$		0			0
$274$	1.29750	−	0.795363i	0.0783846	−	0.0480496i
$275$	−13.2054	−	3.53836i	−0.796313	−	0.213371i
$276$	−1.00773	+	4.74769i	−0.0606581	+	0.285778i
$277$	13.2974	−	3.56302i	0.798961	−	0.214081i	0.163833	−	0.986488i	$-0.447614\pi$
$277$	13.2974	−	3.56302i	0.798961	−	0.214081i	0.635128	+	0.772407i	$0.280947\pi$
$278$	−1.96907	+	0.583572i	−0.118097	+	0.0350003i
$279$			66.6954i			3.99295i
$280$		0			0
$281$		−	24.9241i		−	1.48685i	−0.668820	−	0.743424i	$-0.733200\pi$
$281$		−	24.9241i		−	1.48685i	0.668820	−	0.743424i	$-0.266800\pi$
$282$	−9.75388	−	32.9112i	−0.580835	−	1.95983i
$283$	8.98079	−	2.40640i	0.533853	−	0.143045i	0.0181859	−	0.999835i	$-0.494211\pi$
$283$	8.98079	−	2.40640i	0.533853	−	0.143045i	0.515667	+	0.856789i	$0.327544\pi$
$284$	15.7297	−	10.2214i	0.933384	−	0.606528i
$285$	−23.4996	−	6.29671i	−1.39200	−	0.372985i
$286$	−2.61507	−	4.26603i	−0.154632	−	0.252256i
$287$		0			0
$288$	−39.3180	−	16.2530i	−2.31684	−	0.957715i
$289$	6.09417	+	10.5554i	0.358480	+	0.620906i
$290$	17.4429	−	0.459266i	1.02428	−	0.0269690i
$291$	13.8498	+	51.6882i	0.811890	+	3.03001i
$292$	1.10374	+	20.9454i	0.0645914	+	1.22574i
$293$	22.3389	+	22.3389i	1.30505	+	1.30505i	0.924939	+	0.380115i	$0.124115\pi$
$293$	22.3389	+	22.3389i	1.30505	+	1.30505i	0.380115	+	0.924939i	$0.375885\pi$
$294$		0			0
$295$			20.7848i			1.21014i
$296$	−3.37386	+	18.2476i	−0.196102	+	1.06062i
$297$	56.8955	+	32.8487i	3.30141	+	1.90607i
$298$	−0.602161	−	0.571265i	−0.0348822	−	0.0330925i
$299$	0.152926	−	0.570727i	0.00884393	−	0.0330060i
$300$	18.8251	−	6.12263i	1.08687	−	0.353490i
$301$		0			0
$302$	−13.0341	+	7.98987i	−0.750027	+	0.459765i
$303$	24.7921	+	42.9412i	1.42427	+	2.46691i
$304$	−6.64928	+	8.22084i	−0.381363	+	0.471498i
$305$	8.42696	−	14.5959i	0.482526	−	0.835760i
$306$	20.5054	+	11.1297i	1.17221	+	0.636242i
$307$	11.3960	−	11.3960i	0.650402	−	0.650402i	−0.302688	−	0.953090i	$-0.597884\pi$
$307$	11.3960	−	11.3960i	0.650402	−	0.650402i	0.953090	+	0.302688i	$0.0978840\pi$
$308$		0			0
$309$	−3.87880	−	3.87880i	−0.220657	−	0.220657i
$310$	−34.1190	+	10.1118i	−1.93783	+	0.574314i
$311$	−12.4797	−	7.20515i	−0.707658	−	0.408566i	0.102535	−	0.994729i	$-0.467305\pi$
$311$	−12.4797	−	7.20515i	−0.707658	−	0.408566i	−0.810193	+	0.586163i	$0.800638\pi$
$312$	6.54094	+	3.11641i	0.370308	+	0.176432i
$313$	9.04739	−	5.22352i	0.511389	−	0.295251i	−0.222015	−	0.975043i	$-0.571264\pi$
$313$	9.04739	−	5.22352i	0.511389	−	0.295251i	0.733404	+	0.679793i	$0.237930\pi$
$314$	−12.4901	−	2.99672i	−0.704859	−	0.169114i
$315$		0			0
$316$	9.27346	−	18.2131i	0.521673	−	1.02457i
$317$	−3.09965	−	0.830548i	−0.174094	−	0.0466482i	0.170719	−	0.985320i	$-0.445391\pi$
$317$	−3.09965	−	0.830548i	−0.174094	−	0.0466482i	−0.344813	+	0.938672i	$0.612058\pi$
$318$	−20.7251	+	0.545686i	−1.16221	+	0.0306005i
$319$	−9.74039	+	16.8708i	−0.545357	+	0.944586i
$320$	2.35334	−	22.5778i	0.131556	−	1.26214i
$321$	8.67643			0.484271
$322$		0			0
$323$	4.10001	−	4.10001i	0.228130	−	0.228130i
$324$	−49.9341	+	2.63133i	−2.77412	+	0.146185i
$325$	−2.32781	+	0.623736i	−0.129124	+	0.0345986i
$326$	14.5954	−	15.3848i	0.808367	−	0.852086i
$327$	−22.1114	+	12.7660i	−1.22276	+	0.705962i
$328$	−0.0597922	−	0.755567i	−0.00330147	−	0.0417192i
$329$		0			0
$330$	−13.6050	+	56.7047i	−0.748929	+	3.12149i
$331$	4.76739	−	17.7921i	0.262039	−	0.977944i	−0.701998	−	0.712178i	$-0.747709\pi$
$331$	4.76739	−	17.7921i	0.262039	−	0.977944i	0.964038	−	0.265765i	$-0.0856247\pi$
$332$	1.31220	+	0.278522i	0.0720161	+	0.0152859i
$333$	12.7711	+	47.6624i	0.699853	+	2.61189i
$334$	−22.0528	−	11.9696i	−1.20668	−	0.654948i
$335$	16.2507			0.887869
$336$		0			0
$337$	16.3502			0.890653			0.445326	−	0.895368i	$-0.353088\pi$
$337$	16.3502			0.890653			0.445326	+	0.895368i	$0.353088\pi$
$338$	15.3829	+	8.34937i	0.836719	+	0.454146i
$339$	−6.02816	−	22.4974i	−0.327404	−	1.22189i
$340$	−2.58469	+	12.1772i	−0.140174	+	0.660401i
$341$	10.2828	−	38.3760i	0.556846	−	2.07818i
$342$	−6.55940	+	27.3392i	−0.354692	+	1.47833i
$343$		0			0
$344$	−13.8037	−	11.7792i	−0.744248	−	0.635093i
$345$	−5.96336	+	3.44295i	−0.321056	+	0.185362i
$346$	12.2286	−	12.8899i	0.657412	−	0.692968i
$347$	−25.0090	+	6.70114i	−1.34255	+	0.359736i	−0.857381	−	0.514683i	$-0.827910\pi$
$347$	−25.0090	+	6.70114i	−1.34255	+	0.359736i	−0.485172	+	0.874419i	$0.661243\pi$
$348$	−1.48439	−	28.1689i	−0.0795715	−	1.51001i
$349$	−25.0101	+	25.0101i	−1.33876	+	1.33876i	−0.441494	+	0.897264i	$0.645552\pi$
$349$	−25.0101	+	25.0101i	−1.33876	+	1.33876i	−0.897264	+	0.441494i	$0.854448\pi$
$350$		0			0
$351$	11.5810			0.618148
$352$	20.1174	+	15.4137i	1.07226	+	0.821553i
$353$	3.57361	−	6.18968i	0.190204	−	0.329443i	−0.755114	−	0.655594i	$-0.772418\pi$
$353$	3.57361	−	6.18968i	0.190204	−	0.329443i	0.945318	+	0.326151i	$0.105752\pi$
$354$	33.5891	−	0.884392i	1.78524	−	0.0470049i
$355$	25.7076	+	6.88833i	1.36442	+	0.365595i
$356$	25.8996	+	13.1871i	1.37268	+	0.698917i
$357$		0			0
$358$	6.53348	+	1.56756i	0.345305	+	0.0828480i
$359$	18.5075	−	10.6853i	0.976790	−	0.563950i	0.0754905	−	0.997147i	$-0.475948\pi$
$359$	18.5075	−	10.6853i	0.976790	−	0.563950i	0.901299	+	0.433197i	$0.142614\pi$
$360$	−20.1734	−	56.8900i	−1.06323	−	2.99837i
$361$	−10.4034	−	6.00640i	−0.547547	−	0.316126i
$362$	6.42587	−	1.90444i	0.337736	−	0.100095i
$363$	−20.8065	−	20.8065i	−1.09206	−	1.09206i
$364$		0			0
$365$	−21.0419	+	21.0419i	−1.10138	+	1.10138i
$366$	−23.9462	−	12.9973i	−1.25169	−	0.679379i
$367$	−5.90009	+	10.2193i	−0.307982	+	0.533441i	−0.977921	−	0.208976i	$-0.932987\pi$
$367$	−5.90009	+	10.2193i	−0.307982	+	0.533441i	0.669939	+	0.742416i	$0.266320\pi$
$368$	0.314527	+	2.97607i	0.0163958	+	0.155138i
$369$	−1.00769	−	1.74537i	−0.0524581	−	0.0908601i
$370$	−22.4461	+	13.7594i	−1.16692	+	0.715319i
$371$		0			0
$372$	17.7929	+	54.7075i	0.922521	+	2.83645i
$373$	5.33914	−	19.9259i	0.276450	−	1.03173i	−0.678413	−	0.734680i	$-0.737332\pi$
$373$	5.33914	−	19.9259i	0.276450	−	1.03173i	0.954863	−	0.297045i	$-0.0960012\pi$
$374$	−10.0827	−	9.56535i	−0.521363	−	0.494613i
$375$	−15.5309	−	8.96674i	−0.802010	−	0.463041i
$376$	−11.9958	−	17.4378i	−0.618635	−	0.899288i
$377$			3.43403i			0.176862i
$378$		0			0
$379$	12.1075	+	12.1075i	0.621921	+	0.621921i	0.946022	−	0.324102i	$-0.105062\pi$
$379$	12.1075	+	12.1075i	0.621921	+	0.621921i	−0.324102	+	0.946022i	$0.605062\pi$
$380$	−14.9802	+	0.789397i	−0.768469	+	0.0404952i
$381$	−8.59473	−	32.0760i	−0.440321	−	1.64330i
$382$	−28.0372	+	0.738213i	−1.43451	+	0.0377703i
$383$	6.35291	+	11.0036i	0.324619	+	0.562256i	0.981435	−	0.191794i	$-0.0614307\pi$
$383$	6.35291	+	11.0036i	0.324619	+	0.562256i	−0.656816	+	0.754051i	$0.728097\pi$
$384$	−36.5869	−	2.84242i	−1.86707	−	0.145052i
$385$		0			0
$386$	2.68606	+	4.38183i	0.136717	+	0.223029i
$387$	−46.6082	−	12.4886i	−2.36923	−	0.634833i
$388$	17.9784	+	27.6669i	0.912715	+	1.40457i
$389$	18.2083	−	4.87891i	0.923199	−	0.247371i	0.234247	−	0.972177i	$-0.424738\pi$
$389$	18.2083	−	4.87891i	0.923199	−	0.247371i	0.688952	+	0.724807i	$0.258071\pi$
$390$	2.92095	+	9.85574i	0.147908	+	0.499065i
$391$		−	1.64113i		−	0.0829954i
$392$		0			0
$393$		−	13.0099i		−	0.656261i
$394$	−18.8803	+	5.59555i	−0.951175	+	0.281900i
$395$	28.0087	−	7.50490i	1.40927	−	0.377613i
$396$	65.9211	+	13.9922i	3.31266	+	0.703133i
$397$	−1.94725	−	0.521765i	−0.0977299	−	0.0261866i	0.209623	−	0.977782i	$-0.432776\pi$
$397$	−1.94725	−	0.521765i	−0.0977299	−	0.0261866i	−0.307353	+	0.951596i	$0.599443\pi$
$398$	9.38378	−	5.75224i	0.470366	−	0.288334i
$399$		0			0
$400$	9.87076	−	7.18020i	0.493538	−	0.359010i
$401$	6.75679	+	11.7031i	0.337418	+	0.584425i	0.983946	−	0.178465i	$-0.0571131\pi$
$401$	6.75679	+	11.7031i	0.337418	+	0.584425i	−0.646528	+	0.762890i	$0.723780\pi$
$402$	−0.691466	−	26.2618i	−0.0344872	−	1.30982i
$403$	−1.81264	−	6.76485i	−0.0902938	−	0.336981i
$404$	22.7265	+	20.4512i	1.13069	+	1.01749i
$405$	−50.1641	−	50.1641i	−2.49268	−	2.49268i
$406$		0			0
$407$		−	29.3936i		−	1.45698i
$408$	19.7889	+	3.65883i	0.979695	+	0.181139i
$409$	−26.1114	−	15.0754i	−1.29113	−	0.745432i	−0.312273	−	0.949993i	$-0.601090\pi$
$409$	−26.1114	−	15.0754i	−1.29113	−	0.745432i	−0.978854	+	0.204560i	$0.934424\pi$
$410$	0.740089	−	0.780115i	0.0365504	−	0.0385272i
$411$	0.903414	−	3.37159i	0.0445621	−	0.166308i
$412$	−3.01412	−	1.53468i	−0.148495	−	0.0756081i
$413$		0			0
$414$	4.15880	+	6.78436i	0.204394	+	0.333433i
$415$	0.951583	+	1.64819i	0.0467114	+	0.0809064i
$416$	4.42970	+	0.579944i	0.217184	+	0.0284341i
$417$	−2.35518	+	4.07929i	−0.115334	+	0.199764i
$418$	7.98925	−	14.7194i	0.390767	−	0.719950i
$419$	−20.8065	+	20.8065i	−1.01646	+	1.01646i	−0.0166027	+	0.999862i	$0.505285\pi$
$419$	−20.8065	+	20.8065i	−1.01646	+	1.01646i	−0.999862	+	0.0166027i	$0.994715\pi$
$420$		0			0
$421$	27.7151	+	27.7151i	1.35075	+	1.35075i	0.884823	+	0.465928i	$0.154279\pi$
$421$	27.7151	+	27.7151i	1.35075	+	1.35075i	0.465928	+	0.884823i	$0.345721\pi$
$422$	−1.72782	−	5.82994i	−0.0841088	−	0.283797i
$423$	−48.7400	−	28.1401i	−2.36982	−	1.36822i
$424$	−12.0484	+	4.27241i	−0.585123	+	0.207487i
$425$	−5.79686	+	3.34682i	−0.281189	+	0.162345i
$426$	10.0380	−	41.8377i	0.486342	−	2.02704i
$427$		0			0
$428$	5.08756	−	1.65467i	0.245917	−	0.0799813i
$429$	−11.0854	−	2.97033i	−0.535210	−	0.143409i
$430$	−0.677636	−	25.7365i	−0.0326785	−	1.24113i
$431$	1.17780	−	2.04001i	0.0567328	−	0.0982641i	−0.836264	−	0.548327i	$-0.815265\pi$
$431$	1.17780	−	2.04001i	0.0567328	−	0.0982641i	0.892997	+	0.450063i	$0.148598\pi$
$432$	−54.7484	+	21.0521i	−2.63409	+	1.01287i
$433$	8.53525			0.410178			0.205089	−	0.978743i	$-0.434252\pi$
$433$	8.53525			0.410178			0.205089	+	0.978743i	$0.434252\pi$
$434$		0			0
$435$	28.2986	−	28.2986i	1.35681	−	1.35681i
$436$	−10.5308	+	11.7024i	−0.504333	+	0.560442i
$437$	1.91025	−	0.511850i	0.0913796	−	0.0244851i
$438$	34.8999	+	33.1093i	1.66758	+	1.58202i
$439$	0.346478	−	0.200039i	0.0165365	−	0.00954735i	−0.491709	−	0.870760i	$-0.663628\pi$
$439$	0.346478	−	0.200039i	0.0165365	−	0.00954735i	0.508245	+	0.861212i	$0.330294\pi$
$440$	2.83655	+	35.8443i	0.135227	+	1.70881i
$441$		0			0
$442$	−2.38232	−	0.571582i	−0.113315	−	0.0271874i
$443$	4.16746	−	15.5532i	0.198002	−	0.738953i	−0.793468	−	0.608613i	$-0.791726\pi$
$443$	4.16746	−	15.5532i	0.198002	−	0.738953i	0.991469	−	0.130340i	$-0.0416070\pi$
$444$	23.1909	+	35.6885i	1.10059	+	1.69370i
$445$	10.6722	+	39.8292i	0.505911	+	1.88808i
$446$	14.3611	−	26.4588i	0.680016	−	1.25286i
$447$	−1.90372			−0.0900429
$448$		0			0
$449$	4.33298			0.204486			0.102243	−	0.994759i	$-0.467398\pi$
$449$	4.33298			0.204486			0.102243	+	0.994759i	$0.467398\pi$
$450$	15.4828	−	28.5255i	0.729866	−	1.34471i
$451$	0.310722	+	1.15963i	0.0146313	+	0.0546048i
$452$	−7.82514	−	12.0421i	−0.368063	−	0.566411i
$453$	−9.07530	+	33.8695i	−0.426395	+	1.59133i
$454$	30.2586	+	7.25984i	1.42010	+	0.340721i
$455$		0			0
$456$	1.91311	+	24.1751i	0.0895895	+	1.13210i
$457$	9.00399	−	5.19846i	0.421189	−	0.243174i	−0.274397	−	0.961617i	$-0.588478\pi$
$457$	9.00399	−	5.19846i	0.421189	−	0.243174i	0.695586	+	0.718443i	$0.255145\pi$
$458$	15.1408	+	14.3640i	0.707485	+	0.671185i
$459$	31.0705	−	8.32530i	1.45024	−	0.388592i
$460$	−2.84011	+	3.15609i	−0.132421	+	0.147153i
$461$	−14.6872	+	14.6872i	−0.684052	+	0.684052i	−0.960911	−	0.276859i	$-0.910707\pi$
$461$	−14.6872	+	14.6872i	−0.684052	+	0.684052i	0.276859	+	0.960911i	$0.410707\pi$
$462$		0			0
$463$	17.0456			0.792176			0.396088	−	0.918213i	$-0.370368\pi$
$463$	17.0456			0.792176			0.396088	+	0.918213i	$0.370368\pi$
$464$	−6.24243	−	16.2342i	−0.289797	−	0.753653i
$465$	−40.8094	+	70.6839i	−1.89249	+	3.27789i
$466$	0.842743	+	32.0073i	0.0390393	+	1.48271i
$467$	14.4921	+	3.88314i	0.670614	+	0.179690i	0.578031	−	0.816015i	$-0.303821\pi$
$467$	14.4921	+	3.88314i	0.670614	+	0.179690i	0.0925825	+	0.995705i	$0.470488\pi$
$468$	11.2969	−	3.67416i	0.522198	−	0.169838i
$469$		0			0
$470$	7.00586	−	29.2000i	0.323156	−	1.34690i
$471$	−25.5131	+	14.7300i	−1.17558	+	0.678722i
$472$	19.5268	−	6.92429i	0.898795	−	0.318716i
$473$	24.8925	+	14.3717i	1.14456	+	0.660812i
$474$	−13.3200	−	44.9439i	−0.611809	−	2.06434i
$475$	−5.70363	−	5.70363i	−0.261700	−	0.261700i
$476$		0			0
$477$	−24.0360	+	24.0360i	−1.10053	+	1.10053i
$478$	−12.5367	+	23.0977i	−0.573417	+	1.05647i
$479$	13.1436	−	22.7654i	0.600547	−	1.04018i	−0.392191	−	0.919884i	$-0.628283\pi$
$479$	13.1436	−	22.7654i	0.600547	−	1.04018i	0.992738	−	0.120294i	$-0.0383838\pi$
$480$	−31.7245	−	41.2827i	−1.44802	−	1.88429i
$481$	−2.59072	−	4.48726i	−0.118127	−	0.204601i
$482$	9.25085	+	15.0911i	0.421365	+	0.687383i
$483$		0			0
$484$	−16.1682	−	8.23225i	−0.734918	−	0.374193i
$485$	−12.1159	+	45.2171i	−0.550154	+	2.05320i
$486$	−36.1138	+	38.0669i	−1.63815	+	1.72675i
$487$	17.8122	+	10.2839i	0.807146	+	0.466006i	0.845964	−	0.533240i	$-0.179026\pi$
$487$	17.8122	+	10.2839i	0.807146	+	0.466006i	−0.0388179	+	0.999246i	$0.512359\pi$
$488$	−16.5199	−	3.05442i	−0.747822	−	0.138267i
$489$		−	48.6388i		−	2.19952i
$490$		0			0
$491$	−11.2818	−	11.2818i	−0.509139	−	0.509139i	0.405123	−	0.914262i	$-0.367229\pi$
$491$	−11.2818	−	11.2818i	−0.509139	−	0.509139i	−0.914262	+	0.405123i	$0.867229\pi$
$492$	−1.29219	−	1.16282i	−0.0582565	−	0.0524241i
$493$	2.46864	+	9.21311i	0.111182	+	0.414937i
$494$	−0.0777057	−	2.95125i	−0.00349614	−	0.132783i
$495$	47.8049	+	82.8005i	2.14867	+	3.72161i
$496$	20.8663	+	28.6854i	0.936926	+	1.28801i
$497$		0			0
$498$	2.62306	−	1.60793i	0.117542	−	0.0720531i
$499$	−12.9636	−	3.47358i	−0.580329	−	0.155499i	−0.0432996	−	0.999062i	$-0.513787\pi$
$499$	−12.9636	−	3.47358i	−0.580329	−	0.155499i	−0.537030	+	0.843563i	$0.680454\pi$
$500$	−10.8168	−	2.29593i	−0.483741	−	0.102677i
$501$	−55.5889	+	14.8950i	−2.48353	+	0.665459i
$502$	−16.8738	+	5.00089i	−0.753116	+	0.223201i
$503$		−	24.1272i		−	1.07578i	−0.843015	−	0.537890i	$-0.819222\pi$
$503$		−	24.1272i		−	1.07578i	0.843015	−	0.537890i	$-0.180778\pi$
$504$		0			0
$505$			43.3766i			1.93023i
$506$	−1.34696	−	4.54485i	−0.0598795	−	0.202043i
$507$	38.7759	−	10.3900i	1.72210	−	0.461435i
$508$	−11.1568	−	17.1692i	−0.495003	−	0.761758i
$509$	−33.1419	−	8.88035i	−1.46899	−	0.393615i	−0.566405	−	0.824127i	$-0.691666\pi$
$509$	−33.1419	−	8.88035i	−1.46899	−	0.393615i	−0.902585	+	0.430512i	$0.858333\pi$
$510$	14.9216	+	24.3420i	0.660740	+	1.07788i
$511$		0			0
$512$	−21.9954	+	5.31072i	−0.972067	+	0.234703i
$513$	19.3811	+	33.5690i	0.855695	+	1.48211i
$514$	32.2121	−	0.848135i	1.42081	−	0.0374096i
$515$	−1.24200	−	4.63519i	−0.0547289	−	0.204251i
$516$	−41.5625	+	2.19018i	−1.82969	+	0.0964172i
$517$	23.7061	+	23.7061i	1.04259	+	1.04259i
$518$		0			0
$519$		−	40.7513i		−	1.78878i
$520$	3.59231	+	5.22202i	0.157533	+	0.229001i
$521$	20.4408	+	11.8015i	0.895527	+	0.517033i	0.875746	−	0.482772i	$-0.160370\pi$
$521$	20.4408	+	11.8015i	0.895527	+	0.517033i	0.0197804	+	0.999804i	$0.493703\pi$
$522$	−33.5523	−	31.8308i	−1.46855	−	1.39320i
$523$	−2.60866	+	9.73565i	−0.114069	+	0.425710i	−0.999216	−	0.0396015i	$-0.987391\pi$
$523$	−2.60866	+	9.73565i	−0.114069	+	0.425710i	0.885147	+	0.465312i	$0.154058\pi$
$524$	−2.48109	−	7.62854i	−0.108387	−	0.333254i
$525$		0			0
$526$	−15.4193	+	9.45202i	−0.672314	+	0.412128i
$527$	−9.72617	−	16.8462i	−0.423679	−	0.733833i
$528$	57.8052	−	6.10917i	2.51565	−	0.265868i
$529$	−11.2201	+	19.4338i	−0.487832	+	0.844949i
$530$	−15.9401	−	8.65179i	−0.692393	−	0.375810i
$531$	38.9550	−	38.9550i	1.69051	−	1.69051i
$532$		0			0
$533$	0.149644	+	0.149644i	0.00648180	+	0.00648180i
$534$	63.9116	−	18.9415i	2.76573	−	0.819678i
$535$	6.57330	+	3.79509i	0.284188	+	0.164076i
$536$	−5.41379	−	15.2672i	−0.233840	−	0.659441i
$537$	13.3457	−	7.70514i	0.575909	−	0.332501i
$538$	−21.9247	−	5.26031i	−0.945239	−	0.226788i
$539$		0			0
$540$	−74.1599	−	37.7595i	−3.19133	−	1.62491i
$541$	25.3552	+	6.79390i	1.09010	+	0.292092i	0.758729	−	0.651407i	$-0.225821\pi$
$541$	25.3552	+	6.79390i	1.09010	+	0.292092i	0.331375	+	0.943499i	$0.392487\pi$
$542$	−43.9117	+	1.15618i	−1.88617	+	0.0496624i
$543$	7.68592	−	13.3124i	0.329835	−	0.571290i
$544$	12.3013	−	1.62849i	0.527413	−	0.0698208i
$545$	−22.3356			−0.956750
$546$		0			0
$547$	−30.2973	+	30.2973i	−1.29542	+	1.29542i	−0.364032	+	0.931387i	$0.618600\pi$
$547$	−30.2973	+	30.2973i	−1.29542	+	1.29542i	−0.931387	+	0.364032i	$0.881400\pi$
$548$	−0.113258	−	2.14927i	−0.00483814	−	0.0918123i
$549$	−43.1497	+	11.5619i	−1.84159	+	0.493451i
$550$	−13.3066	+	14.0263i	−0.567396	+	0.598083i
$551$	−9.95398	+	5.74693i	−0.424054	+	0.244827i
$552$	5.22122	+	4.45545i	0.222230	+	0.189637i
$553$		0			0
$554$	4.54215	−	18.9314i	0.192978	−	0.804319i
$555$	−15.6287	+	58.3270i	−0.663401	+	2.47585i
$556$	−0.603043	+	2.84111i	−0.0255747	+	0.120490i
$557$	−9.41584	−	35.1404i	−0.398962	−	1.48895i	−0.814926	−	0.579565i	$-0.803223\pi$
$557$	−9.41584	−	35.1404i	−0.398962	−	1.48895i	0.415965	−	0.909381i	$-0.363444\pi$
$558$	82.8979	+	44.9945i	3.50935	+	1.90477i
$559$	5.06684			0.214304
$560$		0			0
$561$	−31.8762			−1.34582
$562$	−30.9790	−	16.8145i	−1.30677	−	0.709275i
$563$	7.25375	+	27.0714i	0.305709	+	1.14092i	0.932333	+	0.361600i	$0.117769\pi$
$563$	7.25375	+	27.0714i	0.305709	+	1.14092i	−0.626624	+	0.779322i	$0.715564\pi$
$564$	−47.4866	−	10.0793i	−1.99955	−	0.424416i
$565$	5.27346	−	19.6808i	0.221856	−	0.827979i
$566$	3.06769	−	12.7859i	0.128945	−	0.537433i
$567$		0			0
$568$	−2.09286	−	26.4465i	−0.0878144	−	1.10967i
$569$	−4.17102	+	2.40814i	−0.174858	+	0.100954i	−0.584875	−	0.811124i	$-0.698856\pi$
$569$	−4.17102	+	2.40814i	−0.174858	+	0.100954i	0.410016	+	0.912078i	$0.365523\pi$
$570$	−23.6798	+	24.9605i	−0.991840	+	1.04548i
$571$	18.1409	−	4.86083i	0.759172	−	0.203419i	0.141589	−	0.989926i	$-0.454779\pi$
$571$	18.1409	−	4.86083i	0.759172	−	0.203419i	0.617582	+	0.786506i	$0.288112\pi$
$572$	−7.06659	+	0.372381i	−0.295469	+	0.0155700i
$573$	−45.4866	+	45.4866i	−1.90023	+	1.90023i
$574$		0			0
$575$	−2.28302			−0.0952083
$576$	−46.7263	+	37.9049i	−1.94693	+	1.57937i
$577$	−6.23120	+	10.7928i	−0.259408	+	0.449309i	−0.966084	−	0.258230i	$-0.916861\pi$
$577$	−6.23120	+	10.7928i	−0.259408	+	0.449309i	0.706675	+	0.707538i	$0.250194\pi$
$578$	17.2309	−	0.453686i	0.716712	−	0.0188708i
$579$	11.3863	+	3.05096i	0.473200	+	0.126794i
$580$	11.1966	−	21.9901i	0.464912	−	0.913090i
$581$		0			0
$582$	73.5883	+	17.6558i	3.05033	+	0.731857i
$583$	17.5359	−	10.1243i	0.726261	−	0.419307i
$584$	26.7783	+	12.7584i	1.10809	+	0.527948i
$585$	14.5959	+	8.42696i	0.603467	+	0.348412i
$586$	42.8362	−	12.6954i	1.76955	−	0.524440i
$587$	−16.7157	−	16.7157i	−0.689932	−	0.689932i	0.272285	−	0.962217i	$-0.412221\pi$
$587$	−16.7157	−	16.7157i	−0.689932	−	0.689932i	−0.962217	+	0.272285i	$0.912221\pi$
$588$		0			0
$589$	16.5753	−	16.5753i	0.682972	−	0.682972i
$590$	25.8341	+	14.0219i	1.06357	+	0.577274i
$591$	−22.5825	+	39.1141i	−0.928921	+	1.60894i
$592$	20.4045	+	16.5038i	0.838618	+	0.678302i
$593$	−1.44134	−	2.49647i	−0.0591886	−	0.102518i	0.834913	−	0.550382i	$-0.185518\pi$
$593$	−1.44134	−	2.49647i	−0.0591886	−	0.102518i	−0.894101	+	0.447865i	$0.852185\pi$
$594$	79.2119	−	48.5567i	3.25010	−	1.99231i
$595$		0			0
$596$	−1.11628	+	0.363055i	−0.0457245	+	0.0148713i
$597$	6.53369	−	24.3841i	0.267406	−	0.997974i
$598$	−0.606207	−	0.575104i	−0.0247897	−	0.0235177i
$599$	4.25846	+	2.45862i	0.173996	+	0.100457i	0.584469	−	0.811416i	$-0.301303\pi$
$599$	4.25846	+	2.45862i	0.173996	+	0.100457i	−0.410473	+	0.911873i	$0.634636\pi$
$600$	5.08989	−	27.5288i	0.207794	−	1.12386i
$601$			18.3142i			0.747051i	0.927620	+	0.373526i	$0.121851\pi$
$601$			18.3142i			0.747051i	−0.927620	+	0.373526i	$0.878149\pi$
$602$		0			0
$603$	−30.4572	−	30.4572i	−1.24031	−	1.24031i
$604$	1.13774	+	21.5906i	0.0462940	+	0.878510i
$605$	−6.66227	−	24.8639i	−0.270860	−	1.01086i
$606$	70.0984	−	1.84567i	2.84755	−	0.0749753i
$607$	−5.07953	−	8.79800i	−0.206172	−	0.357100i	0.744334	−	0.667808i	$-0.232767\pi$
$607$	−5.07953	−	8.79800i	−0.206172	−	0.357100i	−0.950505	+	0.310708i	$0.899434\pi$
$608$	5.73217	+	13.8106i	0.232470	+	0.560094i
$609$		0			0
$610$	−12.4567	−	20.3209i	−0.504357	−	0.822770i
$611$	5.70843	+	1.52957i	0.230938	+	0.0618798i
$612$	27.6669	−	17.9784i	1.11837	−	0.726734i
$613$	−17.9784	+	4.81729i	−0.726140	+	0.194569i	−0.602910	−	0.797810i	$-0.705992\pi$
$613$	−17.9784	+	4.81729i	−0.726140	+	0.194569i	−0.123230	+	0.992378i	$0.539325\pi$
$614$	−6.47640	−	21.8524i	−0.261366	−	0.881892i
$615$		−	2.46632i		−	0.0994517i
$616$		0			0
$617$			14.2380i			0.573202i	0.958050	+	0.286601i	$0.0925253\pi$
$617$			14.2380i			0.573202i	−0.958050	+	0.286601i	$0.907475\pi$
$618$	−7.43783	+	2.20435i	−0.299193	+	0.0886719i
$619$	32.0464	−	8.58680i	1.28805	−	0.345133i	0.451132	−	0.892457i	$-0.351020\pi$
$619$	32.0464	−	8.58680i	1.28805	−	0.345133i	0.836920	+	0.547325i	$0.184354\pi$
$620$	−10.4492	+	49.2293i	−0.419651	+	1.97710i
$621$	10.5973	+	2.83953i	0.425254	+	0.113946i
$622$	−17.3746	+	10.6506i	−0.696659	+	0.427051i
$623$		0			0
$624$	8.28616	−	6.02753i	0.331712	−	0.241294i
$625$	−15.4729	−	26.7999i	−0.618917	−	1.07200i
$626$	−0.388869	−	14.7692i	−0.0155423	−	0.590297i
$627$	−9.94184	−	37.1035i	−0.397039	−	1.48177i
$628$	−12.1509	+	13.5027i	−0.484873	+	0.538817i
$629$	−10.1764	−	10.1764i	−0.405759	−	0.405759i
$630$		0			0
$631$			24.6875i			0.982795i	0.870935	+	0.491397i	$0.163514\pi$
$631$			24.6875i			0.982795i	−0.870935	+	0.491397i	$0.836486\pi$
$632$	−16.3816	−	23.8133i	−0.651624	−	0.947243i
$633$	−12.0778	−	6.97313i	−0.480050	−	0.277157i
$634$	−3.12342	+	3.29234i	−0.124047	+	0.130756i
$635$	7.51871	−	28.0602i	0.298371	−	1.11354i
$636$	−13.3034	+	26.1280i	−0.527515	+	1.03604i
$637$		0			0
$638$	14.3982	+	23.4881i	0.570030	+	0.929904i
$639$	−35.2713	−	61.0916i	−1.39531	−	2.41675i
$640$	−26.4751	−	18.1566i	−1.04652	−	0.717704i
$641$	24.6259	−	42.6533i	0.972663	−	1.68470i	0.285223	−	0.958461i	$-0.407932\pi$
$641$	24.6259	−	42.6533i	0.972663	−	1.68470i	0.687440	−	0.726241i	$-0.258734\pi$
$642$	5.85335	−	10.7842i	0.231013	−	0.425619i
$643$	−9.26033	+	9.26033i	−0.365192	+	0.365192i	−0.865720	−	0.500528i	$-0.833139\pi$
$643$	−9.26033	+	9.26033i	−0.365192	+	0.365192i	0.500528	+	0.865720i	$0.333139\pi$
$644$		0			0
$645$	−41.7540	−	41.7540i	−1.64406	−	1.64406i
$646$	−2.33006	−	7.86200i	−0.0916749	−	0.309326i
$647$	18.5542	+	10.7123i	0.729442	+	0.421144i	0.818218	−	0.574908i	$-0.194962\pi$
$647$	18.5542	+	10.7123i	0.729442	+	0.421144i	−0.0887760	+	0.996052i	$0.528296\pi$
$648$	−30.4163	+	63.8399i	−1.19486	+	2.50787i
$649$	−28.4203	+	16.4085i	−1.11560	+	0.644089i
$650$	−0.795142	+	3.31410i	−0.0311880	+	0.129990i
$651$		0			0
$652$	−9.27582	−	28.5201i	−0.363269	−	1.11693i
$653$	−7.07682	−	1.89623i	−0.276937	−	0.0742051i	0.117677	−	0.993052i	$-0.462455\pi$
$653$	−7.07682	−	1.89623i	−0.276937	−	0.0742051i	−0.394615	+	0.918847i	$0.629122\pi$
$654$	0.950378	+	36.0952i	0.0371627	+	1.41144i
$655$	5.69055	−	9.85633i	0.222348	−	0.385119i
$656$	−0.979456	−	0.435408i	−0.0382413	−	0.0169998i
$657$	78.8738			3.07716
$658$		0			0
$659$	−2.05464	+	2.05464i	−0.0800374	+	0.0800374i	−0.745992	−	0.665955i	$-0.768024\pi$
$659$	−2.05464	+	2.05464i	−0.0800374	+	0.0800374i	0.665955	+	0.745992i	$0.268024\pi$
$660$	61.3018	+	55.1645i	2.38617	+	2.14728i
$661$	16.9833	−	4.55066i	0.660573	−	0.177000i	0.0870687	−	0.996202i	$-0.472250\pi$
$661$	16.9833	−	4.55066i	0.660573	−	0.177000i	0.573505	+	0.819202i	$0.305583\pi$
$662$	−18.8982	−	17.9286i	−0.734500	−	0.696814i
$663$	−4.86627	+	2.80954i	−0.188990	+	0.109114i
$664$	1.23143	−	1.44307i	0.0477886	−	0.0560021i
$665$		0			0
$666$	67.8569	+	16.2807i	2.62940	+	0.630864i
$667$	−0.841987	+	3.14234i	−0.0326018	+	0.121672i
$668$	−29.7548	+	19.3352i	−1.15125	+	0.748100i
$669$	−17.8709	−	66.6952i	−0.690930	−	2.57858i
$670$	10.9631	−	20.1985i	0.423542	−	0.780336i
$671$	26.6106			1.02729
$672$		0			0
$673$	−35.1315			−1.35422			−0.677109	−	0.735883i	$-0.736768\pi$
$673$	−35.1315			−1.35422			−0.677109	+	0.735883i	$0.736768\pi$
$674$	11.0303	−	20.3222i	0.424870	−	0.782782i
$675$	−11.5815	−	43.2229i	−0.445774	−	1.66365i
$676$	20.7554	−	13.4872i	0.798284	−	0.518738i
$677$	8.04169	−	30.0120i	0.309067	−	1.15345i	−0.620320	−	0.784349i	$-0.712997\pi$
$677$	8.04169	−	30.0120i	0.309067	−	1.15345i	0.929387	−	0.369106i	$-0.120336\pi$
$678$	−32.0295	−	7.68473i	−1.23008	−	0.295130i
$679$		0			0
$680$	13.3917	+	11.4276i	0.513550	+	0.438230i
$681$	61.8080	−	35.6849i	2.36849	−	1.36745i
$682$	−40.7617	−	38.6703i	−1.56085	−	1.48076i
$683$	−34.0128	+	9.11370i	−1.30146	+	0.348726i	−0.842003	−	0.539472i	$-0.818624\pi$
$683$	−34.0128	+	9.11370i	−1.30146	+	0.348726i	−0.459460	+	0.888198i	$0.651957\pi$
$684$	29.5556	+	26.5966i	1.13009	+	1.01695i
$685$	2.15917	−	2.15917i	0.0824977	−	0.0824977i
$686$		0			0
$687$	47.8675			1.82626
$688$	−23.9531	+	9.21055i	−0.913205	+	0.351149i
$689$	1.78470	−	3.09119i	0.0679916	−	0.117765i
$690$	0.256313	+	9.73475i	0.00975768	+	0.370596i
$691$	31.2778	+	8.38087i	1.18987	+	0.318823i	0.798833	−	0.601553i	$-0.205451\pi$
$691$	31.2778	+	8.38087i	1.18987	+	0.318823i	0.391033	+	0.920377i	$0.372118\pi$
$692$	−7.77161	−	23.8952i	−0.295432	−	0.908358i
$693$		0			0
$694$	−8.54265	+	35.6052i	−0.324274	+	1.35156i
$695$	−3.56859	+	2.06033i	−0.135364	+	0.0781526i
$696$	−36.0134	−	17.1585i	−1.36508	−	0.650390i
$697$	0.509052	+	0.293901i	0.0192817	+	0.0111323i
$698$	14.2134	+	47.9583i	0.537984	+	1.81525i
$699$	51.9274	+	51.9274i	1.96407	+	1.96407i
$700$		0			0
$701$	25.3450	−	25.3450i	0.957266	−	0.957266i	−0.0418577	−	0.999124i	$-0.513328\pi$
$701$	25.3450	−	25.3450i	0.957266	−	0.957266i	0.999124	+	0.0418577i	$0.0133276\pi$
$702$	7.81284	−	14.3944i	0.294877	−	0.543281i
$703$	8.67125	−	15.0191i	0.327043	−	0.566454i
$704$	32.7299	−	14.6061i	1.23356	−	0.550489i
$705$	−34.4365	−	59.6457i	−1.29695	−	2.24639i
$706$	−5.28250	−	8.61747i	−0.198809	−	0.324323i
$707$		0			0
$708$	21.5608	−	42.3456i	0.810306	−	1.59145i
$709$	6.51377	−	24.3097i	0.244630	−	0.912971i	−0.728939	−	0.684578i	$-0.759986\pi$
$709$	6.51377	−	24.3097i	0.244630	−	0.912971i	0.973569	−	0.228393i	$-0.0733470\pi$
$710$	25.9047	−	27.3057i	0.972187	−	1.02477i
$711$	−66.5599	−	38.4284i	−2.49619	−	1.44118i
$712$	33.8633	−	23.2951i	1.26908	−	0.873020i
$713$		−	6.63466i		−	0.248470i
$714$		0			0
$715$	−7.09914	−	7.09914i	−0.265493	−	0.265493i
$716$	6.35602	−	7.06316i	0.237536	−	0.263963i
$717$	15.6007	+	58.2228i	0.582620	+	2.17437i
$718$	−0.795479	−	30.2122i	−0.0296870	−	1.12751i
$719$	−14.7568	−	25.5596i	−0.550337	−	0.953212i	−0.998250	−	0.0591349i	$-0.981166\pi$
$719$	−14.7568	−	25.5596i	−0.550337	−	0.953212i	0.447913	−	0.894077i	$-0.352168\pi$
$720$	−84.3199	−	13.3053i	−3.14242	−	0.495858i
$721$		0			0
$722$	−14.4839	+	8.87863i	−0.539037	+	0.330429i
$723$	39.2149	+	10.5076i	1.45842	+	0.390782i
$724$	1.96798	−	9.27171i	0.0731393	−	0.344580i
$725$	12.8166	−	3.43420i	0.475996	−	0.127543i
$726$	−39.8977	+	11.8245i	−1.48074	+	0.438847i
$727$		−	6.61420i		−	0.245307i	−0.992450	−	0.122654i	$-0.960860\pi$
$727$		−	6.61420i		−	0.245307i	0.992450	−	0.122654i	$-0.0391404\pi$
$728$		0			0
$729$			45.3428i			1.67936i
$730$	11.9582	+	40.3490i	0.442594	+	1.49338i
$731$	13.5937	−	3.64243i	0.502782	−	0.134720i
$732$	−32.3095	+	20.9952i	−1.19419	+	0.776006i
$733$	2.54074	+	0.680788i	0.0938442	+	0.0251455i	0.305436	−	0.952213i	$-0.401198\pi$
$733$	2.54074	+	0.680788i	0.0938442	+	0.0251455i	−0.211591	+	0.977358i	$0.567865\pi$
$734$	8.72149	+	14.2276i	0.321916	+	0.525150i
$735$		0			0
$736$	3.91124	+	1.61680i	0.144170	+	0.0595959i
$737$	12.8291	+	22.2206i	0.472564	+	0.818505i
$738$	−2.84918	+	0.0750182i	−0.104880	+	0.00276146i
$739$	−5.96130	−	22.2479i	−0.219290	−	0.818402i	−0.984612	−	0.174754i	$-0.944087\pi$
$739$	−5.96130	−	22.2479i	−0.219290	−	0.818402i	0.765322	−	0.643647i	$-0.222580\pi$
$740$	1.95932	+	37.1815i	0.0720259	+	1.36682i
$741$	−4.78800	−	4.78800i	−0.175892	−	0.175892i
$742$		0			0
$743$		−	34.4705i		−	1.26460i	−0.774723	−	0.632300i	$-0.782111\pi$
$743$		−	34.4705i		−	1.26460i	0.774723	−	0.632300i	$-0.217889\pi$
$744$	80.0013	+	14.7917i	2.93299	+	0.542290i
$745$	−1.44227	−	0.832692i	−0.0528405	−	0.0305075i
$746$	−21.1647	−	20.0787i	−0.774893	−	0.735135i
$747$	1.30559	−	4.87252i	0.0477690	−	0.178276i
$748$	−18.6911	+	6.07905i	−0.683415	+	0.222272i
$749$		0			0
$750$	−21.6226	+	13.2546i	−0.789544	+	0.483989i
$751$	−1.35839	−	2.35281i	−0.0495685	−	0.0858552i	0.840177	−	0.542313i	$-0.182451\pi$
$751$	−1.35839	−	2.35281i	−0.0495685	−	0.0858552i	−0.889745	+	0.456458i	$0.849118\pi$
$752$	−29.7667	+	3.14591i	−1.08548	+	0.114719i
$753$	−20.1826	+	34.9573i	−0.735495	+	1.27392i
$754$	4.26827	+	2.31669i	0.155441	+	0.0843688i
$755$	−21.6901	+	21.6901i	−0.789383	+	0.789383i
$756$		0			0
$757$	−20.1791	−	20.1791i	−0.733420	−	0.733420i	0.237875	−	0.971296i	$-0.423549\pi$
$757$	−20.1791	−	20.1791i	−0.733420	−	0.733420i	−0.971296	+	0.237875i	$0.923549\pi$
$758$	23.2168	−	6.88077i	0.843273	−	0.249921i
$759$	−9.41552	−	5.43605i	−0.341762	−	0.197316i
$760$	−9.12487	+	19.1519i	−0.330994	+	0.694714i
$761$	−46.8585	+	27.0538i	−1.69862	+	0.980699i	−0.751549	+	0.659677i	$0.770693\pi$
$761$	−46.8585	+	27.0538i	−1.69862	+	0.980699i	−0.947072	+	0.321022i	$0.895974\pi$
$762$	−45.6665	−	10.9566i	−1.65432	−	0.396916i
$763$		0			0
$764$	−17.9971	+	35.3464i	−0.651112	+	1.27879i
$765$	45.2171	+	12.1159i	1.63483	+	0.438050i
$766$	17.9625	−	0.472949i	0.649013	−	0.0170883i
$767$	−2.89246	+	5.00988i	−0.104441	+	0.180896i
$768$	−28.2154	+	43.5575i	−1.01814	+	1.57174i
$769$	−26.9334			−0.971244			−0.485622	−	0.874169i	$-0.661407\pi$
$769$	−26.9334			−0.971244			−0.485622	+	0.874169i	$0.661407\pi$
$770$		0			0
$771$	52.2596	−	52.2596i	1.88208	−	1.88208i
$772$	7.25840	−	0.382489i	0.261236	−	0.0137661i
$773$	−11.5879	+	3.10496i	−0.416787	+	0.111678i	−0.461117	−	0.887339i	$-0.652551\pi$
$773$	−11.5879	+	3.10496i	−0.416787	+	0.111678i	0.0443301	+	0.999017i	$0.485885\pi$
$774$	−46.9656	+	49.5057i	−1.68815	+	1.77945i
$775$	−23.4352	+	13.5303i	−0.841818	+	0.486024i
$776$	46.5167	−	3.68113i	1.66985	−	0.132145i
$777$		0			0
$778$	6.21966	−	25.9232i	0.222986	−	0.929390i
$779$	−0.183329	+	0.684194i	−0.00656845	+	0.0245138i
$780$	14.2206	+	3.01840i	0.509178	+	0.108076i
$781$	10.8759	+	40.5896i	0.389172	+	1.45241i
$782$	−2.03981	−	1.10715i	−0.0729435	−	0.0395915i
$783$	−63.7632			−2.27871
$784$		0			0
$785$	−25.7717			−0.919833
$786$	−16.1704	−	8.77680i	−0.576779	−	0.313058i
$787$	3.70513	+	13.8277i	0.132074	+	0.492905i	0.999993	−	0.00380017i	$-0.00120964\pi$
$787$	3.70513	+	13.8277i	0.132074	+	0.492905i	−0.867919	+	0.496705i	$0.834543\pi$
$788$	−5.78224	+	27.2418i	−0.205984	+	0.970449i
$789$	−10.7361	+	40.0676i	−0.382215	+	1.42645i
$790$	9.56729	−	39.8759i	0.340389	−	1.41872i
$791$		0			0
$792$	61.8634	−	72.4960i	2.19822	−	2.57603i
$793$	4.06240	−	2.34543i	0.144260	−	0.0832886i
$794$	−1.96219	+	2.06831i	−0.0696354	+	0.0734015i
$795$	−40.1804	+	10.7663i	−1.42505	+	0.381841i
$796$	−0.819107	−	15.5440i	−0.0290325	−	0.550943i
$797$	−3.21815	+	3.21815i	−0.113993	+	0.113993i	−0.761802	−	0.647810i	$-0.775685\pi$
$797$	−3.21815	+	3.21815i	−0.113993	+	0.113993i	0.647810	+	0.761802i	$0.275685\pi$
$798$		0			0
$799$	16.4146			0.580707
$800$	−2.26543	−	17.1126i	−0.0800951	−	0.605023i
$801$	54.6463	−	94.6502i	1.93083	−	3.34430i
$802$	19.1045	−	0.503015i	0.674602	−	0.0177621i
$803$	−45.3833	−	12.1604i	−1.60154	−	0.429132i
$804$	−33.1081	−	16.8574i	−1.16763	−	0.594516i
$805$		0			0
$806$	−9.63110	−	2.31076i	−0.339241	−	0.0813930i
$807$	−44.7847	+	25.8564i	−1.57649	+	0.910190i
$808$	40.7513	−	14.4506i	1.43363	−	0.508370i
$809$	0.173970	+	0.100441i	0.00611645	+	0.00353133i	0.503055	−	0.864254i	$-0.332209\pi$
$809$	0.173970	+	0.100441i	0.00611645	+	0.00353133i	−0.496939	+	0.867786i	$0.665543\pi$
$810$	−96.1926	+	28.5086i	−3.37986	+	1.00169i
$811$	10.7615	+	10.7615i	0.377886	+	0.377886i	0.870339	−	0.492453i	$-0.163900\pi$
$811$	10.7615	+	10.7615i	0.377886	+	0.377886i	−0.492453	+	0.870339i	$0.663900\pi$
$812$		0			0
$813$	−71.2407	+	71.2407i	−2.49852	+	2.49852i
$814$	−36.5342	−	19.8296i	−1.28052	−	0.695029i
$815$	21.2747	−	36.8489i	0.745222	−	1.29076i
$816$	17.8978	−	22.1279i	0.626547	−	0.774631i
$817$	8.47946	+	14.6869i	0.296659	+	0.513828i
$818$	−36.3532	+	22.2844i	−1.27106	+	0.779157i
$819$		0			0
$820$	−0.470347	−	1.44617i	−0.0164252	−	0.0505023i
$821$	−5.97882	+	22.3132i	−0.208662	+	0.778737i	0.779640	+	0.626228i	$0.215402\pi$
$821$	−5.97882	+	22.3132i	−0.208662	+	0.778737i	−0.988302	+	0.152509i	$0.951265\pi$
$822$	−3.58119	−	3.39744i	−0.124908	−	0.118499i
$823$	29.9668	+	17.3013i	1.04458	+	0.603087i	0.921126	−	0.389264i	$-0.127271\pi$
$823$	29.9668	+	17.3013i	1.04458	+	0.603087i	0.123451	+	0.992351i	$0.460604\pi$
$824$	−3.94090	+	2.71101i	−0.137288	+	0.0944424i
$825$			44.3439i			1.54385i
$826$		0			0
$827$	25.9781	+	25.9781i	0.903348	+	0.903348i	0.995724	−	0.0923762i	$-0.0294463\pi$
$827$	25.9781	+	25.9781i	0.903348	+	0.903348i	−0.0923762	+	0.995724i	$0.529446\pi$
$828$	11.2381	−	0.592205i	0.390552	−	0.0205805i
$829$	−8.51045	−	31.7614i	−0.295580	−	1.10312i	−0.940756	−	0.339086i	$-0.889882\pi$
$829$	−8.51045	−	31.7614i	−0.295580	−	1.10312i	0.645175	−	0.764034i	$-0.276784\pi$
$830$	2.69055	−	0.0708414i	0.0933903	−	0.00245894i
$831$	−22.3264	−	38.6705i	−0.774494	−	1.34146i
$832$	3.70922	−	5.11458i	0.128594	−	0.177316i
$833$		0			0
$834$	3.48142	+	5.67933i	0.120552	+	0.196659i
$835$	−48.6294	−	13.0302i	−1.68289	−	0.450929i
$836$	−12.9055	−	19.8602i	−0.446345	−	0.686879i
$837$	125.610	−	33.6571i	4.34171	−	1.16336i
$838$	11.8245	+	39.8977i	0.408470	+	1.37824i
$839$			0.706396i			0.0243875i	0.999926	+	0.0121938i	$0.00388149\pi$
$839$			0.706396i			0.0243875i	−0.999926	+	0.0121938i	$0.996119\pi$
$840$		0			0
$841$			10.0927i			0.348025i
$842$	53.1453	−	15.7507i	1.83151	−	0.542803i
$843$	−78.0892	+	20.9239i	−2.68953	+	0.720659i
$844$	−8.41185	−	1.78547i	−0.289548	−	0.0614583i
$845$	33.9213	+	9.08920i	1.16693	+	0.312678i
$846$	−67.8574	+	41.5965i	−2.33299	+	1.43012i
$847$		0			0
$848$	−2.81785	+	17.8576i	−0.0967654	+	0.613234i
$849$	−15.0788	−	26.1173i	−0.517505	−	0.896344i
$850$	0.249157	+	9.46296i	0.00854602	+	0.324577i
$851$	−1.27043	−	4.74131i	−0.0435498	−	0.162530i
$852$	−45.2295	−	40.7013i	−1.54954	−	1.39440i
$853$	40.1092	+	40.1092i	1.37331	+	1.37331i	0.855482	+	0.517832i	$0.173261\pi$
$853$	40.1092	+	40.1092i	1.37331	+	1.37331i	0.517832	+	0.855482i	$0.326739\pi$
$854$		0			0
$855$			56.4108i			1.92921i
$856$	1.37556	−	7.43977i	0.0470158	−	0.254286i
$857$	−12.3231	−	7.11472i	−0.420947	−	0.243034i	0.274535	−	0.961577i	$-0.411476\pi$
$857$	−12.3231	−	7.11472i	−0.420947	−	0.243034i	−0.695483	+	0.718543i	$0.744809\pi$
$858$	−11.1704	+	11.7746i	−0.381353	+	0.401978i
$859$	5.65962	−	21.1220i	0.193104	−	0.720673i	−0.799646	−	0.600472i	$-0.794979\pi$
$859$	5.65962	−	21.1220i	0.193104	−	0.720673i	0.992750	−	0.120201i	$-0.0383540\pi$
$860$	−32.4459	−	16.5203i	−1.10640	−	0.563336i
$861$		0			0
$862$	−1.74102	−	2.84018i	−0.0592995	−	0.0967368i
$863$	8.97968	+	15.5533i	0.305672	+	0.529439i	0.977411	−	0.211349i	$-0.0677856\pi$
$863$	8.97968	+	15.5533i	0.305672	+	0.529439i	−0.671739	+	0.740788i	$0.734452\pi$
$864$	−10.7684	+	82.2509i	−0.366349	+	2.79823i
$865$	17.8247	−	30.8734i	0.606059	−	1.04973i
$866$	5.75810	−	10.6087i	0.195668	−	0.360500i
$867$	27.9548	−	27.9548i	0.949395	−	0.949395i
$868$		0			0
$869$	32.3733	+	32.3733i	1.09819	+	1.09819i
$870$	−16.0823	−	54.2642i	−0.545240	−	1.83973i
$871$	3.91700	+	2.26148i	0.132722	+	0.0766274i
$872$	7.44092	+	20.9838i	0.251981	+	0.710600i
$873$	107.454	−	62.0386i	3.63677	−	2.09969i
$874$	0.652509	−	2.71962i	0.0220714	−	0.0919924i
$875$		0			0
$876$	64.6970	−	21.0419i	2.18591	−	0.710939i
$877$	−16.3939	−	4.39274i	−0.553583	−	0.148332i	−0.0288266	−	0.999584i	$-0.509177\pi$
$877$	−16.3939	−	4.39274i	−0.553583	−	0.148332i	−0.524757	+	0.851252i	$0.675844\pi$
$878$	−0.0148921	−	0.565600i	−0.000502584	−	0.0190881i
$879$	51.2359	−	88.7432i	1.72814	−	2.99323i
$880$	46.4656	+	20.6558i	1.56636	+	0.696308i
$881$	−2.43251			−0.0819533			−0.0409766	−	0.999160i	$-0.513047\pi$
$881$	−2.43251			−0.0819533			−0.0409766	+	0.999160i	$0.513047\pi$
$882$		0			0
$883$	−12.6792	+	12.6792i	−0.426691	+	0.426691i	−0.887499	−	0.460809i	$-0.847559\pi$
$883$	−12.6792	+	12.6792i	−0.426691	+	0.426691i	0.460809	+	0.887499i	$0.347559\pi$
$884$	−2.31761	+	2.57545i	−0.0779496	+	0.0866219i
$885$	65.1203	−	17.4489i	2.18899	−	0.586539i
$886$	−16.5200	−	15.6724i	−0.555002	−	0.526525i
$887$	23.8413	−	13.7648i	0.800511	−	0.462175i	−0.0431388	−	0.999069i	$-0.513736\pi$
$887$	23.8413	−	13.7648i	0.800511	−	0.462175i	0.843650	+	0.536894i	$0.180402\pi$
$888$	60.0036	−	4.74841i	2.01359	−	0.159346i
$889$		0			0
$890$	56.7047	+	13.6050i	1.90075	+	0.456040i
$891$	28.9906	−	108.195i	0.971223	−	3.62465i
$892$	−23.1982	−	35.6996i	−0.776733	−	1.19531i
$893$	5.11954	+	19.1064i	0.171319	+	0.639370i
$894$	−1.28430	+	2.36620i	−0.0429534	+	0.0791374i
$895$	13.4810			0.450620
$896$		0			0
$897$	−1.91651			−0.0639905
$898$	2.92314	−	5.38559i	0.0975464	−	0.179720i
$899$	9.98010	+	37.2462i	0.332855	+	1.24223i
$900$	−25.0102	−	38.4881i	−0.833674	−	1.28294i
$901$	2.56595	−	9.57627i	0.0854843	−	0.319032i
$902$	1.65096	+	0.396110i	0.0549710	+	0.0131890i
$903$		0			0
$904$	−20.2465	+	1.60222i	−0.673389	+	0.0532890i
$905$	11.6458	−	6.72369i	0.387118	−	0.223503i
$906$	35.9750	+	34.1292i	1.19519	+	1.13387i
$907$	34.4073	−	9.21942i	1.14248	−	0.306126i	0.362530	−	0.931972i	$-0.381913\pi$
$907$	34.4073	−	9.21942i	1.14248	−	0.306126i	0.779946	+	0.625846i	$0.215246\pi$
$908$	29.4367	−	32.7117i	0.976891	−	1.08557i
$909$	81.2968	−	81.2968i	2.69645	−	2.69645i
$910$		0			0
$911$	−34.9979			−1.15953			−0.579766	−	0.814783i	$-0.696856\pi$
$911$	−34.9979			−1.15953			−0.579766	+	0.814783i	$0.696856\pi$
$912$	31.3386	+	13.9313i	1.03773	+	0.461311i
$913$	−1.50245	+	2.60232i	−0.0497238	+	0.0861241i
$914$	−0.387004	−	14.6984i	−0.0128010	−	0.486179i
$915$	−52.8046	−	14.1490i	−1.74567	−	0.467750i
$916$	28.0679	−	9.12872i	0.927389	−	0.301622i
$917$		0			0
$918$	10.6131	−	44.2349i	0.350286	−	1.45997i
$919$	−13.4271	+	7.75216i	−0.442920	+	0.255720i	−0.704836	−	0.709371i	$-0.748979\pi$
$919$	−13.4271	+	7.75216i	−0.442920	+	0.255720i	0.261915	+	0.965091i	$0.415646\pi$
$920$	2.00679	+	5.65924i	0.0661619	+	0.186580i
$921$	−45.2714	−	26.1374i	−1.49174	−	0.861258i
$922$	8.34684	+	28.1636i	0.274888	+	0.927518i
$923$	5.23786	+	5.23786i	0.172406	+	0.172406i
$924$		0			0
$925$	−14.1566	+	14.1566i	−0.465467	+	0.465467i
$926$	11.4994	−	21.1865i	0.377893	−	0.696232i
$927$	−6.35957	+	11.0151i	−0.208876	+	0.361783i
$928$	−24.3893	−	3.19308i	−0.800617	−	0.104818i
$929$	14.6486	+	25.3721i	0.480604	+	0.832431i	0.999752	−	0.0222533i	$-0.00708402\pi$
$929$	14.6486	+	25.3721i	0.480604	+	0.832431i	−0.519148	+	0.854684i	$0.673751\pi$
$930$	60.3242	+	98.4085i	1.97811	+	3.22694i
$931$		0			0
$932$	40.3514	+	20.5455i	1.32175	+	0.672989i
$933$	−12.0975	+	45.1486i	−0.396055	+	1.47810i
$934$	14.6032	−	15.3930i	0.477832	−	0.503675i
$935$	−24.1495	−	13.9427i	−0.789774	−	0.455976i
$936$	3.05442	−	16.5199i	0.0998368	−	0.539971i
$937$		−	50.5492i		−	1.65137i	−0.564131	−	0.825685i	$-0.690789\pi$
$937$		−	50.5492i		−	1.65137i	0.564131	−	0.825685i	$-0.309211\pi$
$938$		0			0
$939$	−23.9610	−	23.9610i	−0.781938	−	0.781938i
$940$	−31.5673	−	28.4069i	−1.02961	−	0.926531i
$941$	14.1591	+	52.8424i	0.461573	+	1.72261i	0.668010	+	0.744153i	$0.267146\pi$
$941$	14.1591	+	52.8424i	0.461573	+	1.72261i	−0.206437	+	0.978460i	$0.566187\pi$
$942$	1.09659	+	41.6483i	0.0357288	+	1.35697i
$943$	0.100242	+	0.173624i	0.00326432	+	0.00565397i
$944$	4.56688	−	28.9418i	0.148639	−	0.941976i
$945$		0			0
$946$	34.6562	−	21.2442i	1.12677	−	0.690709i
$947$	18.2814	+	4.89848i	0.594064	+	0.159179i	0.543310	−	0.839532i	$-0.317171\pi$
$947$	18.2814	+	4.89848i	0.594064	+	0.159179i	0.0507543	+	0.998711i	$0.483837\pi$
$948$	−64.8483	−	13.7644i	−2.10617	−	0.447048i
$949$	−8.00009	+	2.14362i	−0.259694	+	0.0695848i
$950$	−10.9370	+	3.24141i	−0.354844	+	0.105165i
$951$			10.4087i			0.337525i
$952$		0			0
$953$		−	23.1169i		−	0.748830i	−0.927261	−	0.374415i	$-0.877844\pi$
$953$		−	23.1169i		−	0.748830i	0.927261	−	0.374415i	$-0.122156\pi$
$954$	13.6598	+	46.0904i	0.442252	+	1.49223i
$955$	−54.3567	+	14.5648i	−1.75894	+	0.471307i
$956$	20.2513	+	31.1646i	0.654974	+	1.00794i
$957$	61.0347	+	16.3542i	1.97297	+	0.528657i
$958$	−19.4288	−	31.6948i	−0.627717	−	1.02401i
$959$		0			0
$960$	−72.7137	+	11.5810i	−2.34682	+	0.373775i
$961$	−23.8204	−	41.2582i	−0.768401	−	1.33091i
$962$	−7.32512	+	0.192869i	−0.236171	+	0.00621833i
$963$	−5.20694	−	19.4326i	−0.167791	−	0.626205i
$964$	24.9981	−	1.31730i	0.805136	−	0.0424274i
$965$	7.29184	+	7.29184i	0.234733	+	0.234733i
$966$		0			0
$967$		−	20.7758i		−	0.668105i	−0.942555	−	0.334052i	$-0.891584\pi$
$967$		−	20.7758i		−	0.668105i	0.942555	−	0.334052i	$-0.108416\pi$
$968$	−21.1396	+	14.5423i	−0.679453	+	0.467407i
$969$	−16.2876	−	9.40366i	−0.523233	−	0.302089i
$970$	48.0281	+	45.5638i	1.54209	+	1.46297i
$971$	−6.54826	+	24.4384i	−0.210144	+	0.784267i	0.777676	+	0.628665i	$0.216398\pi$
$971$	−6.54826	+	24.4384i	−0.210144	+	0.784267i	−0.987820	+	0.155602i	$0.950268\pi$
$972$	22.9513	+	70.5679i	0.736164	+	2.26347i
$973$		0			0
$974$	24.7987	−	15.2015i	0.794601	−	0.487089i
$975$	3.90843	+	6.76959i	0.125170	+	0.216800i
$976$	−14.9412	+	18.4725i	−0.478256	+	0.591292i
$977$	−16.8040	+	29.1053i	−0.537607	+	0.931162i	0.461426	+	0.887179i	$0.347338\pi$
$977$	−16.8040	+	29.1053i	−0.537607	+	0.931162i	−0.999032	+	0.0439831i	$0.985995\pi$
$978$	−60.4547	−	32.8130i	−1.93313	−	1.04924i
$979$	−46.0358	+	46.0358i	−1.47131	+	1.47131i
$980$		0			0
$981$	41.8615	+	41.8615i	1.33654	+	1.33654i
$982$	−21.6334	+	6.41150i	−0.690351	+	0.204599i
$983$	4.11952	+	2.37841i	0.131392	+	0.0758594i	0.564255	−	0.825600i	$-0.309163\pi$
$983$	4.11952	+	2.37841i	0.131392	+	0.0758594i	−0.432863	+	0.901460i	$0.642497\pi$
$984$	−2.31705	+	0.821637i	−0.0738650	+	0.0261928i
$985$	−34.2172	+	19.7553i	−1.09025	+	0.629456i
$986$	13.1167	+	3.14704i	0.417720	+	0.100222i
$987$		0			0
$988$	−3.72063	−	1.89441i	−0.118369	−	0.0602691i
$989$	4.63644	+	1.24233i	0.147430	+	0.0395038i
$990$	135.166	−	3.55888i	4.29585	−	0.113109i
$991$	−14.5579	+	25.2150i	−0.462446	+	0.800979i	−0.999082	−	0.0428342i	$-0.986361\pi$
$991$	−14.5579	+	25.2150i	−0.462446	+	0.800979i	0.536637	+	0.843813i	$0.319695\pi$
$992$	49.7309	−	6.58356i	1.57896	−	0.209028i
$993$	−59.7464			−1.89599
$994$		0			0
$995$	15.6156	−	15.6156i	0.495048	−	0.495048i
$996$	−0.228966	−	4.34503i	−0.00725506	−	0.137678i
$997$	−9.97995	+	2.67412i	−0.316068	+	0.0846902i	−0.413366	−	0.910565i	$-0.635647\pi$
$997$	−9.97995	+	2.67412i	−0.316068	+	0.0846902i	0.0972974	+	0.995255i	$0.468980\pi$
$998$	−13.0630	+	13.7695i	−0.413502	+	0.435865i
$999$	83.3196	−	48.1046i	2.63611	−	1.52196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.n.165.7		40
7.2	even	3	inner	784.2.x.n.373.2		40
7.3	odd	6		784.2.m.i.197.8	yes	20
7.4	even	3		784.2.m.i.197.7	✓	20
7.5	odd	6	inner	784.2.x.n.373.1		40
7.6	odd	2	inner	784.2.x.n.165.8		40
16.13	even	4	inner	784.2.x.n.557.2		40
112.13	odd	4	inner	784.2.x.n.557.1		40
112.45	odd	12		784.2.m.i.589.8	yes	20
112.61	odd	12	inner	784.2.x.n.765.8		40
112.93	even	12	inner	784.2.x.n.765.7		40
112.109	even	12		784.2.m.i.589.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.i.197.7	✓	20	7.4	even	3
784.2.m.i.197.8	yes	20	7.3	odd	6
784.2.m.i.589.7	yes	20	112.109	even	12
784.2.m.i.589.8	yes	20	112.45	odd	12
784.2.x.n.165.7		40	1.1	even	1	trivial
784.2.x.n.165.8		40	7.6	odd	2	inner
784.2.x.n.373.1		40	7.5	odd	6	inner
784.2.x.n.373.2		40	7.2	even	3	inner
784.2.x.n.557.1		40	112.13	odd	4	inner
784.2.x.n.557.2		40	16.13	even	4	inner
784.2.x.n.765.7		40	112.93	even	12	inner
784.2.x.n.765.8		40	112.61	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.674626 - 1.24293i) q^{2} +(-0.839505 - 3.13308i) q^{3} +(-1.08976 - 1.67703i) q^{4} +(0.734404 - 2.74083i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(-6.51332 + 3.76047i) q^{9} +O(q^{10})\)	\(q+(0.674626 - 1.24293i) q^{2} +(-0.839505 - 3.13308i) q^{3} +(-1.08976 - 1.67703i) q^{4} +(0.734404 - 2.74083i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(-6.51332 + 3.76047i) q^{9} +(-2.91122 - 2.76185i) q^{10} +(4.32748 - 1.15955i) q^{11} +(-4.33940 + 4.82218i) q^{12} +(0.558438 - 0.558438i) q^{13} -9.20377 q^{15} +(-1.62485 + 3.65512i) q^{16} +(1.09678 - 1.89967i) q^{17} +(0.279952 + 10.6325i) q^{18} +(2.55326 + 0.684144i) q^{19} +(-5.39678 + 1.75523i) q^{20} +(1.47820 - 6.16103i) q^{22} +(0.647926 - 0.374080i) q^{23} +(3.06617 + 8.64674i) q^{24} +(-2.64268 - 1.52575i) q^{25} +(-0.317364 - 1.07084i) q^{26} +(10.3691 + 10.3691i) q^{27} +(-3.07468 + 3.07468i) q^{29} +(-6.20910 + 11.4397i) q^{30} +(4.43398 - 7.67989i) q^{31} +(3.44690 + 4.48541i) q^{32} +(-7.26589 - 12.5849i) q^{33} +(-1.62125 - 2.64479i) q^{34} +(13.4044 + 6.82502i) q^{36} +(1.69807 - 6.33730i) q^{37} +(2.57284 - 2.71199i) q^{38} +(-2.21844 - 1.28082i) q^{39} +(-1.45917 + 7.89195i) q^{40} +0.267969i q^{41} +(4.53661 + 4.53661i) q^{43} +(-6.66051 - 5.99369i) q^{44} +(5.52341 + 20.6136i) q^{45} +(-0.0278487 - 1.05769i) q^{46} +(3.74156 + 6.48057i) q^{47} +(12.8158 + 2.02228i) q^{48} +(-3.67923 + 2.25536i) q^{50} +(-6.87257 - 1.84150i) q^{51} +(-1.54508 - 0.327953i) q^{52} +(4.36564 - 1.16977i) q^{53} +(19.8833 - 5.89282i) q^{54} -12.7125i q^{55} -8.57391i q^{57} +(1.74736 + 5.89587i) q^{58} +(-7.07539 + 1.89585i) q^{59} +(10.0299 + 15.4350i) q^{60} +(5.73728 + 1.53730i) q^{61} +(-6.55430 - 10.6922i) q^{62} +(7.90042 - 1.25829i) q^{64} +(-1.12047 - 1.94070i) q^{65} +(-20.5439 + 0.540916i) q^{66} +(1.48228 + 5.53193i) q^{67} +(-4.38103 + 0.230862i) q^{68} +(-1.71596 - 1.71596i) q^{69} +9.37949i q^{71} +(17.5260 - 12.0564i) q^{72} +(-9.08221 - 5.24362i) q^{73} +(-6.73127 - 6.38590i) q^{74} +(-2.56176 + 9.56061i) q^{75} +(-1.63511 - 5.02744i) q^{76} +(-3.08859 + 1.89330i) q^{78} +(5.10952 + 8.84995i) q^{79} +(8.82477 + 7.13776i) q^{80} +(12.5009 - 21.6521i) q^{81} +(0.333067 + 0.180778i) q^{82} +(-0.474267 + 0.474267i) q^{83} +(-4.40120 - 4.40120i) q^{85} +(8.69922 - 2.57819i) q^{86} +(12.2144 + 7.05199i) q^{87} +(-11.9431 + 4.23507i) q^{88} +(-12.5849 + 7.26589i) q^{89} +(29.3476 + 7.04127i) q^{90} +(-1.33343 - 0.678932i) q^{92} +(-27.7840 - 7.44471i) q^{93} +(10.5791 - 0.278544i) q^{94} +(3.75025 - 6.49562i) q^{95} +(11.1594 - 14.5649i) q^{96} -16.4976 q^{97} +(-23.8259 + 23.8259i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{4}+O(q^{10}) \) 40 * q + 8 * q^4	\( 40 q + 8 q^{4} - 4 q^{11} - 32 q^{15} - 16 q^{18} - 8 q^{29} - 8 q^{30} + 40 q^{32} + 80 q^{36} + 20 q^{37} + 120 q^{43} - 56 q^{44} + 64 q^{46} - 112 q^{50} + 16 q^{51} - 28 q^{53} + 72 q^{58} + 24 q^{60} - 64 q^{64} - 16 q^{65} - 12 q^{67} - 16 q^{72} + 16 q^{74} - 176 q^{78} + 72 q^{79} - 12 q^{81} + 64 q^{85} + 40 q^{86} - 80 q^{88} - 48 q^{92} - 48 q^{93} - 64 q^{95} - 216 q^{99}+O(q^{100}) \) 40 * q + 8 * q^4 - 4 * q^11 - 32 * q^15 - 16 * q^18 - 8 * q^29 - 8 * q^30 + 40 * q^32 + 80 * q^36 + 20 * q^37 + 120 * q^43 - 56 * q^44 + 64 * q^46 - 112 * q^50 + 16 * q^51 - 28 * q^53 + 72 * q^58 + 24 * q^60 - 64 * q^64 - 16 * q^65 - 12 * q^67 - 16 * q^72 + 16 * q^74 - 176 * q^78 + 72 * q^79 - 12 * q^81 + 64 * q^85 + 40 * q^86 - 80 * q^88 - 48 * q^92 - 48 * q^93 - 64 * q^95 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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