LMFDB - Embedded newform 784.2.x.n.373.2

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			373.2
Character	$\chi$	$=$	784.373
Dual form			784.2.x.n.557.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41372 + 0.0372230i) q^{2} +(3.13308 + 0.839505i) q^{3} +(1.99723 - 0.105246i) q^{4} +(-2.74083 + 0.734404i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(6.51332 + 3.76047i) q^{9} +O(q^{10})$	\(q+(-1.41372 + 0.0372230i) q^{2} +(3.13308 + 0.839505i) q^{3} +(1.99723 - 0.105246i) q^{4} +(-2.74083 + 0.734404i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(6.51332 + 3.76047i) q^{9} +(3.84744 - 1.14027i) q^{10} +(-1.15955 + 4.32748i) q^{11} +(6.34583 + 1.34694i) q^{12} +(0.558438 - 0.558438i) q^{13} -9.20377 q^{15} +(3.97785 - 0.420401i) q^{16} +(1.09678 + 1.89967i) q^{17} +(-9.34802 - 5.07382i) q^{18} +(-0.684144 - 2.55326i) q^{19} +(-5.39678 + 1.75523i) q^{20} +(1.47820 - 6.16103i) q^{22} +(-0.647926 - 0.374080i) q^{23} +(-9.02138 - 1.66799i) q^{24} +(2.64268 - 1.52575i) q^{25} +(-0.768691 + 0.810264i) q^{26} +(10.3691 + 10.3691i) q^{27} +(-3.07468 + 3.07468i) q^{29} +(13.0116 - 0.342592i) q^{30} +(4.43398 + 7.67989i) q^{31} +(-5.60793 + 0.742397i) q^{32} +(-7.26589 + 12.5849i) q^{33} +(-1.62125 - 2.64479i) q^{34} +(13.4044 + 6.82502i) q^{36} +(-6.33730 + 1.69807i) q^{37} +(1.06223 + 3.58414i) q^{38} +(2.21844 - 1.28082i) q^{39} +(7.56421 - 2.68230i) q^{40} +0.267969i q^{41} +(4.53661 + 4.53661i) q^{43} +(-1.86043 + 8.76501i) q^{44} +(-20.6136 - 5.52341i) q^{45} +(0.929912 + 0.504728i) q^{46} +(3.74156 - 6.48057i) q^{47} +(12.8158 + 2.02228i) q^{48} +(-3.67923 + 2.25536i) q^{50} +(1.84150 + 6.87257i) q^{51} +(1.05656 - 1.17410i) q^{52} +(-1.16977 + 4.36564i) q^{53} +(-15.0450 - 14.2731i) q^{54} -12.7125i q^{55} -8.57391i q^{57} +(4.23229 - 4.46119i) q^{58} +(1.89585 - 7.07539i) q^{59} +(-18.3820 + 0.968660i) q^{60} +(-1.53730 - 5.73728i) q^{61} +(-6.55430 - 10.6922i) q^{62} +(7.90042 - 1.25829i) q^{64} +(-1.12047 + 1.94070i) q^{65} +(9.80352 - 18.0620i) q^{66} +(-5.53193 - 1.48228i) q^{67} +(2.39045 + 3.67865i) q^{68} +(-1.71596 - 1.71596i) q^{69} +9.37949i q^{71} +(-19.2041 - 9.14974i) q^{72} +(9.08221 - 5.24362i) q^{73} +(8.89598 - 2.63650i) q^{74} +(9.56061 - 2.56176i) q^{75} +(-1.63511 - 5.02744i) q^{76} +(-3.08859 + 1.89330i) q^{78} +(5.10952 - 8.84995i) q^{79} +(-10.5939 + 4.07359i) q^{80} +(12.5009 + 21.6521i) q^{81} +(-0.00997458 - 0.378833i) q^{82} +(-0.474267 + 0.474267i) q^{83} +(-4.40120 - 4.40120i) q^{85} +(-6.58238 - 6.24465i) q^{86} +(-12.2144 + 7.05199i) q^{87} +(2.30387 - 12.4606i) q^{88} +(12.5849 + 7.26589i) q^{89} +(29.3476 + 7.04127i) q^{90} +(-1.33343 - 0.678932i) q^{92} +(7.44471 + 27.7840i) q^{93} +(-5.04831 + 9.30101i) q^{94} +(3.75025 + 6.49562i) q^{95} +(-18.1933 - 2.38190i) 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 $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41372	+	0.0372230i	−0.999654	+	0.0263206i
$2$	−1.41372	+	0.0372230i	−0.999654	+	0.0263206i
$3$	3.13308	+	0.839505i	1.80888	+	0.484689i	0.995307	−	0.0967700i	$-0.0308511\pi$
$3$	3.13308	+	0.839505i	1.80888	+	0.484689i	0.813576	+	0.581459i	$0.197518\pi$
$4$	1.99723	−	0.105246i	0.998614	−	0.0526230i
$5$	−2.74083	+	0.734404i	−1.22574	+	0.328435i	−0.812918	−	0.582378i	$-0.802122\pi$
$5$	−2.74083	+	0.734404i	−1.22574	+	0.328435i	−0.412819	+	0.910813i	$0.635456\pi$
$6$	−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
$10$	3.84744	−	1.14027i	1.21667	−	0.360584i
$11$	−1.15955	+	4.32748i	−0.349616	+	1.30479i	0.537509	+	0.843258i	$0.319365\pi$
$11$	−1.15955	+	4.32748i	−0.349616	+	1.30479i	−0.887126	+	0.461528i	$0.847301\pi$
$12$	6.34583	+	1.34694i	1.83188	+	0.388828i
$13$	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
$16$	3.97785	−	0.420401i	0.994462	−	0.105100i
$17$	1.09678	+	1.89967i	0.266007	+	0.460738i	0.967827	−	0.251616i	$-0.0809622\pi$
$17$	1.09678	+	1.89967i	0.266007	+	0.460738i	−0.701820	+	0.712355i	$0.747629\pi$
$18$	−9.34802	−	5.07382i	−2.20335	−	1.19591i
$19$	−0.684144	−	2.55326i	−0.156954	−	0.585758i	−0.998930	−	0.0462445i	$-0.985275\pi$
$19$	−0.684144	−	2.55326i	−0.156954	−	0.585758i	0.841977	−	0.539514i	$-0.181392\pi$
$20$	−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	$-0.358187\pi$
$23$	−0.647926	−	0.374080i	−0.135102	−	0.0780011i	−0.566028	+	0.824386i	$0.691520\pi$
$24$	−9.02138	−	1.66799i	−1.84148	−	0.340477i
$25$	2.64268	−	1.52575i	0.528537	−	0.305151i
$26$	−0.768691	+	0.810264i	−0.150753	+	0.158906i
$27$	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	$0.382285\pi$
$30$	13.0116	−	0.342592i	2.37558	−	0.0625484i
$31$	4.43398	+	7.67989i	0.796367	+	1.37935i	0.921968	+	0.387267i	$0.126581\pi$
$31$	4.43398	+	7.67989i	0.796367	+	1.37935i	−0.125601	+	0.992081i	$0.540086\pi$
$32$	−5.60793	+	0.742397i	−0.991351	+	0.131239i
$33$	−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
$37$	−6.33730	+	1.69807i	−1.04185	+	0.279162i	−0.738878	−	0.673839i	$-0.764644\pi$
$37$	−6.33730	+	1.69807i	−1.04185	+	0.279162i	−0.302967	+	0.953001i	$0.597977\pi$
$38$	1.06223	+	3.58414i	0.172317	+	0.581424i
$39$	2.21844	−	1.28082i	0.355235	−	0.205095i
$40$	7.56421	−	2.68230i	1.19601	−	0.424109i
$41$			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	$0.587290\pi$
$44$	−1.86043	+	8.76501i	−0.280470	+	1.32138i
$45$	−20.6136	−	5.52341i	−3.07290	−	0.823381i
$46$	0.929912	+	0.504728i	0.137108	+	0.0744181i
$47$	3.74156	−	6.48057i	0.545763	−	0.945289i	−0.452796	−	0.891614i	$-0.649573\pi$
$47$	3.74156	−	6.48057i	0.545763	−	0.945289i	0.998558	−	0.0536746i	$-0.0170934\pi$
$48$	12.8158	+	2.02228i	1.84981	+	0.291890i
$49$		0			0
$50$	−3.67923	+	2.25536i	−0.520322	+	0.318956i
$51$	1.84150	+	6.87257i	0.257861	+	0.962352i
$52$	1.05656	−	1.17410i	0.146518	−	0.162819i
$53$	−1.16977	+	4.36564i	−0.160680	+	0.599667i	0.837871	+	0.545868i	$0.183800\pi$
$53$	−1.16977	+	4.36564i	−0.160680	+	0.599667i	−0.998552	+	0.0537996i	$0.982867\pi$
$54$	−15.0450	−	14.2731i	−2.04737	−	1.94232i
$55$		−	12.7125i		−	1.71415i
$56$		0			0
$57$		−	8.57391i		−	1.13564i
$58$	4.23229	−	4.46119i	0.555727	−	0.585783i
$59$	1.89585	−	7.07539i	0.246818	−	0.921137i	−0.725643	−	0.688071i	$-0.758458\pi$
$59$	1.89585	−	7.07539i	0.246818	−	0.921137i	0.972461	−	0.233066i	$-0.0748758\pi$
$60$	−18.3820	+	0.968660i	−2.37311	+	0.125053i
$61$	−1.53730	−	5.73728i	−0.196831	−	0.734583i	−0.991785	−	0.127914i	$-0.959172\pi$
$61$	−1.53730	−	5.73728i	−0.196831	−	0.734583i	0.794954	−	0.606669i	$-0.207495\pi$
$62$	−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
$66$	9.80352	−	18.0620i	1.20673	−	2.22328i
$67$	−5.53193	−	1.48228i	−0.675833	−	0.181089i	−0.0954519	−	0.995434i	$-0.530430\pi$
$67$	−5.53193	−	1.48228i	−0.675833	−	0.181089i	−0.580381	+	0.814345i	$0.697096\pi$
$68$	2.39045	+	3.67865i	0.289884	+	0.446102i
$69$	−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	$0.812117\pi$
$72$	−19.2041	−	9.14974i	−2.26323	−	1.07831i
$73$	9.08221	−	5.24362i	1.06299	−	0.613719i	0.136734	−	0.990608i	$-0.456339\pi$
$73$	9.08221	−	5.24362i	1.06299	−	0.613719i	0.926258	+	0.376889i	$0.123006\pi$
$74$	8.89598	−	2.63650i	1.03414	−	0.306487i
$75$	9.56061	−	2.56176i	1.10396	−	0.295806i
$76$	−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	−0.421190	−	0.906972i	$-0.638387\pi$
$79$	5.10952	−	8.84995i	0.574866	−	0.995697i	0.996056	−	0.0887248i	$-0.0282792\pi$
$80$	−10.5939	+	4.07359i	−1.18443	+	0.455441i
$81$	12.5009	+	21.6521i	1.38898	+	2.40579i
$82$	−0.00997458	−	0.378833i	−0.00110151	−	0.0418352i
$83$	−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
$86$	−6.58238	−	6.24465i	−0.709797	−	0.673378i
$87$	−12.2144	+	7.05199i	−1.30952	+	0.756053i
$88$	2.30387	−	12.4606i	0.245594	−	1.32830i
$89$	12.5849	+	7.26589i	1.33400	+	0.770183i	0.985910	−	0.167279i	$-0.0534981\pi$
$89$	12.5849	+	7.26589i	1.33400	+	0.770183i	0.348087	+	0.937462i	$0.386831\pi$
$90$	29.3476	+	7.04127i	3.09351	+	0.742215i
$91$		0			0
$92$	−1.33343	−	0.678932i	−0.139019	−	0.0707835i
$93$	7.44471	+	27.7840i	0.771980	+	2.88107i
$94$	−5.04831	+	9.30101i	−0.520693	+	0.959326i
$95$	3.75025	+	6.49562i	0.384768	+	0.666437i
$96$	−18.1933	−	2.38190i	−1.85685	−	0.243101i
$97$	−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
$100$	5.11746	−	3.32541i	0.511746	−	0.332541i
$101$	3.95651	−	14.7659i	0.393688	−	1.46926i	−0.430316	−	0.902679i	$-0.641598\pi$
$101$	3.95651	−	14.7659i	0.393688	−	1.46926i	0.824003	−	0.566585i	$-0.191736\pi$
$102$	−2.85919	−	9.64736i	−0.283102	−	0.955231i
$103$	−1.46459	−	0.845581i	−0.144310	−	0.0833176i	0.426106	−	0.904673i	$-0.359885\pi$
$103$	−1.46459	−	0.845581i	−0.144310	−	0.0833176i	−0.570417	+	0.821355i	$0.693218\pi$
$104$	−1.44997	+	1.69918i	−0.142182	+	0.166619i
$105$		0			0
$106$	1.49123	−	6.21536i	0.144841	−	0.603689i
$107$	2.58379	−	0.692325i	0.249785	−	0.0669296i	−0.131754	−	0.991282i	$-0.542061\pi$
$107$	2.58379	−	0.692325i	0.249785	−	0.0669296i	0.381539	+	0.924353i	$0.375394\pi$
$108$	21.8008	+	19.6182i	2.09778	+	1.88776i
$109$	7.60329	+	2.03730i	0.728264	+	0.195138i	0.603856	−	0.797094i	$-0.293630\pi$
$109$	7.60329	+	2.03730i	0.728264	+	0.195138i	0.124408	+	0.992231i	$0.460297\pi$
$110$	0.473196	+	17.9719i	0.0451175	+	1.71356i
$111$	−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	$0.390335\pi$
$114$	0.319146	+	12.1211i	0.0298908	+	1.13525i
$115$	2.05058	+	0.549451i	0.191218	+	0.0512366i
$116$	−5.81724	+	6.46443i	−0.540117	+	0.600207i
$117$	5.73728	−	1.53730i	0.530412	−	0.142123i
$118$	−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
$122$	2.38687	+	8.05370i	0.216098	+	0.729148i
$123$	−0.224961	+	0.839566i	−0.0202841	+	0.0757011i
$124$	9.66396	+	14.8718i	0.867849	+	1.33553i
$125$	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	$0.349914\pi$
$128$	−11.1222	+	2.07295i	−0.983071	+	0.183225i
$129$	10.4050	+	18.0221i	0.916113	+	1.58675i
$130$	1.51179	−	2.78533i	0.132593	−	0.244289i
$131$	−1.03811	−	3.87427i	−0.0906998	−	0.338496i	0.905633	−	0.424063i	$-0.139397\pi$
$131$	−1.03811	−	3.87427i	−0.0906998	−	0.338496i	−0.996332	+	0.0855668i	$0.972730\pi$
$132$	−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
$136$	−3.51636	−	5.11161i	−0.301525	−	0.438317i
$137$	−0.931953	+	0.538063i	−0.0796221	+	0.0459698i	−0.539282	−	0.842125i	$-0.681304\pi$
$137$	−0.931953	+	0.538063i	−0.0796221	+	0.0459698i	0.459660	+	0.888095i	$0.347971\pi$
$138$	2.48976	+	2.36202i	0.211943	+	0.201068i
$139$	−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
$142$	−0.349132	−	13.2600i	−0.0292985	−	1.11275i
$143$	1.76910	+	3.06417i	0.147939	+	0.256239i
$144$	27.4899	+	12.2204i	2.29083	+	1.01836i
$145$	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
$149$	−0.566917	+	0.151905i	−0.0464437	+	0.0124445i	−0.281966	−	0.959424i	$-0.590987\pi$
$149$	−0.566917	+	0.151905i	−0.0464437	+	0.0124445i	0.235522	+	0.971869i	$0.424320\pi$
$150$	−13.4207	+	3.97749i	−1.09580	+	0.324761i
$151$	9.36199	−	5.40515i	0.761868	−	0.439865i	−0.0680980	−	0.997679i	$-0.521693\pi$
$151$	9.36199	−	5.40515i	0.761868	−	0.439865i	0.829966	+	0.557814i	$0.188360\pi$
$152$	2.49874	+	7.04655i	0.202674	+	0.571551i
$153$			16.4976i			1.33375i
$154$		0			0
$155$	−17.7929	−	17.7929i	−1.42916	−	1.42916i
$156$	4.29593	−	2.79157i	0.343950	−	0.223504i
$157$	8.77302	+	2.35072i	0.700163	+	0.187608i	0.591304	−	0.806449i	$-0.298613\pi$
$157$	8.77302	+	2.35072i	0.700163	+	0.187608i	0.108859	+	0.994057i	$0.465280\pi$
$158$	−6.89403	+	12.7016i	−0.548460	+	1.01048i
$159$	−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
$163$	−3.88107	−	14.4844i	−0.303989	−	1.13450i	−0.933812	−	0.357764i	$-0.883539\pi$
$163$	−3.88107	−	14.4844i	−0.303989	−	1.13450i	0.629823	−	0.776739i	$-0.283128\pi$
$164$	0.0282026	+	0.535195i	0.00220225	+	0.0417917i
$165$	10.6722	−	39.8292i	0.830829	−	3.10070i
$166$	0.652829	−	0.688136i	0.0506693	−	0.0534097i
$167$		−	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
$170$	6.38591	+	6.05826i	0.489777	+	0.464647i
$171$	5.14541	−	19.2029i	0.393479	−	1.46848i
$172$	9.53811	+	8.58319i	0.727274	+	0.654462i
$173$	−3.25170	−	12.1355i	−0.247222	−	0.922646i	−0.972253	−	0.233930i	$-0.924841\pi$
$173$	−3.25170	−	12.1355i	−0.247222	−	0.922646i	0.725031	−	0.688716i	$-0.241825\pi$
$174$	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
$178$	−18.0620	−	9.80352i	−1.35381	−	0.734805i
$179$	−4.58909	−	1.22964i	−0.343005	−	0.0919079i	0.0832043	−	0.996533i	$-0.473485\pi$
$179$	−4.58909	−	1.22964i	−0.343005	−	0.0919079i	−0.426209	+	0.904625i	$0.640151\pi$
$180$	−41.7515	−	8.86200i	−3.11197	−	0.660535i
$181$	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
$184$	1.91037	+	0.910188i	0.140834	+	0.0670999i
$185$	16.1224	−	9.30827i	1.18534	−	0.684358i
$186$	−11.5590	−	39.0018i	−0.847544	−	2.85975i
$187$	−9.49256	+	2.54352i	−0.694165	+	0.186001i
$188$	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	0.244482	+	0.969654i	$0.421382\pi$
$191$	−9.91610	+	17.1752i	−0.717504	+	1.24275i	−0.961986	+	0.273099i	$0.911951\pi$
$192$	25.8090	+	2.69013i	1.86260	+	0.194144i
$193$	−1.81712	−	3.14734i	−0.130799	−	0.226551i	0.793186	−	0.608980i	$-0.208421\pi$
$193$	−1.81712	−	3.14734i	−0.130799	−	0.226551i	−0.923985	+	0.382429i	$0.875088\pi$
$194$	23.3230	−	0.614088i	1.67449	−	0.0440890i
$195$	−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	$0.915211\pi$
$198$	32.7963	−	34.5701i	2.33073	−	2.45679i
$199$	−6.74009	+	3.89139i	−0.477792	+	0.275854i	−0.719496	−	0.694497i	$-0.755627\pi$
$199$	−6.74009	+	3.89139i	−0.477792	+	0.275854i	0.241704	+	0.970350i	$0.422294\pi$
$200$	−7.11090	+	4.89170i	−0.502816	+	0.345895i
$201$	−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
$205$	−0.196797	−	0.734457i	−0.0137449	−	0.0512967i
$206$	2.10200	+	1.14090i	0.146453	+	0.0794904i
$207$	−2.81343	−	4.87301i	−0.195547	−	0.338698i
$208$	1.98661	−	2.45615i	0.137747	−	0.170303i
$209$	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	$0.202717\pi$
$212$	−1.87683	+	8.84230i	−0.128901	+	0.607292i
$213$	−7.87413	+	29.3866i	−0.539526	+	2.01354i
$214$	−3.62700	+	1.07493i	−0.247937	+	0.0734809i
$215$	−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
$219$	32.8573	−	8.80409i	2.22029	−	0.594925i
$220$	−1.33794	−	25.3897i	−0.0902037	−	1.71178i
$221$	1.67333	+	0.448368i	0.112560	+	0.0301605i
$222$	30.0851	−	0.792134i	2.01918	−	0.0531645i
$223$	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
$226$	−10.1514	+	0.267283i	−0.675260	+	0.0177794i
$227$	−21.2535	−	5.69486i	−1.41064	−	0.377981i	−0.528490	−	0.848940i	$-0.677241\pi$
$227$	−21.2535	−	5.69486i	−1.41064	−	0.377981i	−0.882155	+	0.470959i	$0.843908\pi$
$228$	−0.902369	−	17.1241i	−0.0597609	−	1.13407i
$229$	14.2547	−	3.81953i	0.941976	−	0.252402i	0.245022	−	0.969518i	$-0.421205\pi$
$229$	14.2547	−	3.81953i	0.941976	−	0.252402i	0.696954	+	0.717116i	$0.254538\pi$
$230$	−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	$-0.0673953\pi$
$233$	19.6072	+	11.3202i	1.28451	+	0.741611i	0.306839	+	0.951761i	$0.400729\pi$
$234$	−8.05370	+	2.38687i	−0.526487	+	0.156035i
$235$	−5.49563	+	20.5100i	−0.358496	+	1.33792i
$236$	3.04178	−	14.3307i	0.198003	−	0.932849i
$237$	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	$0.705241\pi$
$240$	−36.6112	+	3.86927i	−2.36324	+	0.249760i
$241$	−6.25821	−	10.8395i	−0.403126	−	0.698235i	0.590975	−	0.806690i	$-0.298743\pi$
$241$	−6.25821	−	10.8395i	−0.403126	−	0.698235i	−0.994101	+	0.108454i	$0.965410\pi$
$242$	11.2755	+	6.11998i	0.724814	+	0.393407i
$243$	9.60301	+	35.8389i	0.616033	+	2.29907i
$244$	−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
$248$	−14.2157	−	20.6649i	−0.902700	−	1.31222i
$249$	−1.88406	+	1.08777i	−0.119398	+	0.0689343i
$250$	−5.38144	+	5.67249i	−0.340352	+	0.358760i
$251$	−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
$254$	−14.4735	+	0.381083i	−0.908147	+	0.0239113i
$255$	−10.0945	−	17.4841i	−0.632141	−	1.09490i
$256$	15.6465	−	3.34458i	0.977908	−	0.209036i
$257$	11.3926	−	19.7326i	0.710653	−	1.23089i	−0.253959	−	0.967215i	$-0.581733\pi$
$257$	11.3926	−	19.7326i	0.710653	−	1.23089i	0.964612	−	0.263672i	$-0.0849337\pi$
$258$	−15.3807	−	25.0909i	−0.957560	−	1.56209i
$259$		0			0
$260$	−2.03358	+	3.99396i	−0.126117	+	0.247695i
$261$	−31.5886	+	8.46414i	−1.95528	+	0.523917i
$262$	1.61181	+	5.43850i	0.0995778	+	0.335992i
$263$	11.0752	−	6.39429i	0.682929	−	0.394289i	−0.118029	−	0.993010i	$-0.537658\pi$
$263$	11.0752	−	6.39429i	0.682929	−	0.394289i	0.800958	+	0.598721i	$0.204324\pi$
$264$	17.6789	−	37.1058i	1.08806	−	2.28370i
$265$		−	12.8246i		−	0.787808i
$266$		0			0
$267$	33.3297	+	33.3297i	2.03974	+	2.03974i
$268$	−11.2045	−	2.37823i	−0.684426	−	0.145274i
$269$	15.3998	+	4.12636i	0.938943	+	0.251589i	0.695664	−	0.718368i	$-0.255110\pi$
$269$	15.3998	+	4.12636i	0.938943	+	0.251589i	0.243279	+	0.969956i	$0.421777\pi$
$270$	51.7180	+	28.0710i	3.14746	+	1.70834i
$271$	−15.5305	+	26.8997i	−0.943412	+	1.63404i	−0.184513	+	0.982830i	$0.559071\pi$
$271$	−15.5305	+	26.8997i	−0.943412	+	1.63404i	−0.758899	+	0.651208i	$0.774263\pi$
$272$	5.16143	+	7.09552i	0.312958	+	0.430229i
$273$		0			0
$274$	1.29750	−	0.795363i	0.0783846	−	0.0480496i
$275$	3.53836	+	13.2054i	0.213371	+	0.796313i
$276$	−3.60776	−	3.24656i	−0.217162	−	0.195420i
$277$	−3.56302	+	13.2974i	−0.214081	+	0.798961i	0.772407	+	0.635128i	$0.219053\pi$
$277$	−3.56302	+	13.2974i	−0.214081	+	0.798961i	−0.986488	+	0.163833i	$0.947614\pi$
$278$	1.48992	+	1.41348i	0.0893596	+	0.0847747i
$279$			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	$-0.266800\pi$
$282$	−23.6250	+	24.9027i	−1.40685	+	1.48293i
$283$	−2.40640	+	8.98079i	−0.143045	+	0.533853i	0.856789	+	0.515667i	$0.172456\pi$
$283$	−2.40640	+	8.98079i	−0.143045	+	0.533853i	−0.999835	+	0.0181859i	$0.994211\pi$
$284$	0.987153	+	18.7330i	0.0585768	+	1.11160i
$285$	6.29671	+	23.4996i	0.372985	+	1.39200i
$286$	−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
$290$	−8.32369	+	15.3356i	−0.488784	+	0.900537i
$291$	−51.6882	−	13.8498i	−3.03001	−	0.811890i
$292$	17.5874	−	11.4286i	1.02922	−	0.668806i
$293$	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
$296$	17.4898	−	6.20196i	1.01658	−	0.360482i
$297$	−56.8955	+	32.8487i	−3.30141	+	1.90607i
$298$	0.795810	−	0.235854i	0.0461000	−	0.0136627i
$299$	−0.570727	+	0.152926i	−0.0330060	+	0.00884393i
$300$	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
$304$	−3.79481	−	9.86887i	−0.217648	−	0.566018i
$305$	8.42696	+	14.5959i	0.482526	+	0.835760i
$306$	−0.614088	−	23.3230i	−0.0351051	−	1.33329i
$307$	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
$310$	25.8166	+	24.4920i	1.46628	+	1.39105i
$311$	12.4797	−	7.20515i	0.707658	−	0.408566i	−0.102535	−	0.994729i	$-0.532695\pi$
$311$	12.4797	−	7.20515i	0.707658	−	0.408566i	0.810193	+	0.586163i	$0.199362\pi$
$312$	−5.96935	+	4.10641i	−0.337948	+	0.232480i
$313$	−9.04739	−	5.22352i	−0.511389	−	0.295251i	0.222015	−	0.975043i	$-0.428736\pi$
$313$	−9.04739	−	5.22352i	−0.511389	−	0.295251i	−0.733404	+	0.679793i	$0.762070\pi$
$314$	−12.4901	−	2.99672i	−0.704859	−	0.169114i
$315$		0			0
$316$	9.27346	−	18.2131i	0.521673	−	1.02457i
$317$	0.830548	+	3.09965i	0.0466482	+	0.174094i	0.985320	−	0.170719i	$-0.0546091\pi$
$317$	0.830548	+	3.09965i	0.0466482	+	0.174094i	−0.938672	+	0.344813i	$0.887942\pi$
$318$	9.88996	−	18.2213i	0.554602	−	1.02180i
$319$	−9.74039	−	16.8708i	−0.545357	−	0.944586i
$320$	−20.7296	+	9.25086i	−1.15882	+	0.517139i
$321$	8.67643			0.484271
$322$		0			0
$323$	4.10001	−	4.10001i	0.228130	−	0.228130i
$324$	27.2459	+	41.9286i	1.51366	+	2.32936i
$325$	0.623736	−	2.32781i	0.0345986	−	0.129124i
$326$	6.02592	+	20.3324i	0.333745	+	1.12611i
$327$	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
$331$	−17.7921	+	4.76739i	−0.977944	+	0.262039i	−0.712178	−	0.701998i	$-0.752291\pi$
$331$	−17.7921	+	4.76739i	−0.977944	+	0.262039i	−0.265765	+	0.964038i	$0.585625\pi$
$332$	−0.897305	+	0.997134i	−0.0492460	+	0.0547249i
$333$	−47.6624	−	12.7711i	−2.61189	−	0.699853i
$334$	0.660432	+	25.0831i	0.0361372	+	1.37249i
$335$	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	$0.353088\pi$
$338$	−0.460682	−	17.4967i	−0.0250578	−	0.951693i
$339$	22.4974	+	6.02816i	1.22189	+	0.327404i
$340$	−9.25342	−	8.32700i	−0.501837	−	0.451595i
$341$	−38.3760	+	10.2828i	−2.07818	+	0.556846i
$342$	−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
$346$	5.04873	+	17.0352i	0.271421	+	0.915820i
$347$	6.70114	−	25.0090i	0.359736	−	1.34255i	−0.514683	−	0.857381i	$-0.672090\pi$
$347$	6.70114	−	25.0090i	0.359736	−	1.34255i	0.874419	−	0.485172i	$-0.161243\pi$
$348$	−23.6528	+	15.3700i	−1.26792	+	0.823916i
$349$	−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
$352$	3.28994	−	25.1291i	0.175354	−	1.33938i
$353$	3.57361	+	6.18968i	0.190204	+	0.329443i	0.945318	−	0.326151i	$-0.105752\pi$
$353$	3.57361	+	6.18968i	0.190204	+	0.329443i	−0.755114	+	0.655594i	$0.772418\pi$
$354$	−16.0286	+	29.5312i	−0.851913	+	1.56957i
$355$	−6.88833	−	25.7076i	−0.365595	−	1.36442i
$356$	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	$-0.524052\pi$
$359$	−18.5075	−	10.6853i	−0.976790	−	0.563950i	−0.901299	+	0.433197i	$0.857386\pi$
$360$	59.3549	+	10.9743i	3.12828	+	0.578397i
$361$	10.4034	−	6.00640i	0.547547	−	0.316126i
$362$	−4.86223	−	4.61275i	−0.255553	−	0.242441i
$363$	−20.8065	−	20.8065i	−1.09206	−	1.09206i
$364$		0			0
$365$	−21.0419	+	21.0419i	−1.10138	+	1.10138i
$366$	0.717134	+	27.2367i	0.0374852	+	1.42368i
$367$	−5.90009	−	10.2193i	−0.307982	−	0.533441i	0.669939	−	0.742416i	$-0.266320\pi$
$367$	−5.90009	−	10.2193i	−0.307982	−	0.533441i	−0.977921	+	0.208976i	$0.932987\pi$
$368$	−2.73461	−	1.21564i	−0.142552	−	0.0633699i
$369$	−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
$373$	−19.9259	+	5.33914i	−1.03173	+	0.276450i	−0.734680	−	0.678413i	$-0.762668\pi$
$373$	−19.9259	+	5.33914i	−1.03173	+	0.276450i	−0.297045	+	0.954863i	$0.596001\pi$
$374$	13.3252	−	3.94918i	0.689029	−	0.204207i
$375$	15.5309	−	8.96674i	0.802010	−	0.463041i
$376$	−9.10373	+	19.1076i	−0.469489	+	0.985397i
$377$			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	$0.605062\pi$
$380$	8.17375	+	12.5785i	0.419304	+	0.645266i
$381$	32.0760	+	8.59473i	1.64330	+	0.440321i
$382$	13.3793	−	24.6501i	0.684545	−	1.26121i
$383$	6.35291	−	11.0036i	0.324619	−	0.562256i	−0.656816	−	0.754051i	$-0.728097\pi$
$383$	6.35291	−	11.0036i	0.324619	−	0.562256i	0.981435	+	0.191794i	$0.0614307\pi$
$384$	−36.5869	−	2.84242i	−1.86707	−	0.145052i
$385$		0			0
$386$	2.68606	+	4.38183i	0.136717	+	0.223029i
$387$	12.4886	+	46.6082i	0.634833	+	2.36923i
$388$	−32.9494	+	1.73630i	−1.67275	+	0.0881474i
$389$	−4.87891	+	18.2083i	−0.247371	+	0.923199i	0.724807	+	0.688952i	$0.241929\pi$
$389$	−4.87891	+	18.2083i	−0.247371	+	0.923199i	−0.972177	+	0.234247i	$0.924738\pi$
$390$	7.07485	−	7.45749i	0.358249	−	0.377624i
$391$		−	1.64113i		−	0.0829954i
$392$		0			0
$393$		−	13.0099i		−	0.656261i
$394$	14.2860	+	13.5530i	0.719720	+	0.682792i
$395$	−7.50490	+	28.0087i	−0.377613	+	1.40927i
$396$	−45.0781	+	50.0933i	−2.26526	+	2.51728i
$397$	0.521765	+	1.94725i	0.0261866	+	0.0977299i	0.977782	−	0.209623i	$-0.0672236\pi$
$397$	0.521765	+	1.94725i	0.0261866	+	0.0977299i	−0.951596	+	0.307353i	$0.900557\pi$
$398$	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	−0.646528	−	0.762890i	$-0.723780\pi$
$401$	6.75679	−	11.7031i	0.337418	−	0.584425i	0.983946	+	0.178465i	$0.0571131\pi$
$402$	23.0891	+	12.5321i	1.15158	+	0.625043i
$403$	6.76485	+	1.81264i	0.336981	+	0.0902938i
$404$	6.34801	−	29.9073i	0.315825	−	1.48794i
$405$	−50.1641	−	50.1641i	−2.49268	−	2.49268i
$406$		0			0
$407$		−	29.3936i		−	1.45698i
$408$	−6.72580	−	18.9671i	−0.332977	−	0.939010i
$409$	26.1114	−	15.0754i	1.29113	−	0.745432i	0.312273	−	0.949993i	$-0.398910\pi$
$409$	26.1114	−	15.0754i	1.29113	−	0.745432i	0.978854	+	0.204560i	$0.0655765\pi$
$410$	0.305555	+	1.03099i	0.0150903	+	0.0509171i
$411$	−3.37159	+	0.903414i	−0.166308	+	0.0445621i
$412$	−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
$416$	−2.71710	+	3.54626i	−0.133217	+	0.173870i
$417$	−2.35518	−	4.07929i	−0.115334	−	0.199764i
$418$	−16.7420	+	0.440813i	−0.818879	+	0.0215609i
$419$	−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	$0.345721\pi$
$422$	−4.18497	+	4.41130i	−0.203721	+	0.214739i
$423$	48.7400	−	28.1401i	2.36982	−	1.36822i
$424$	2.32419	−	12.5704i	0.112873	−	0.610474i
$425$	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
$429$	2.97033	+	11.0854i	0.143409	+	0.535210i
$430$	22.6273	+	12.2814i	1.09119	+	0.592262i
$431$	1.17780	+	2.04001i	0.0567328	+	0.0982641i	0.892997	−	0.450063i	$-0.148598\pi$
$431$	1.17780	+	2.04001i	0.0567328	+	0.0982641i	−0.836264	+	0.548327i	$0.815265\pi$
$432$	45.6059	+	36.8875i	2.19421	+	1.77475i
$433$	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
$436$	15.3999	+	3.26873i	0.737523	+	0.156544i
$437$	−0.511850	+	1.91025i	−0.0244851	+	0.0913796i
$438$	−46.1234	+	13.6696i	−2.20386	+	0.653158i
$439$	−0.346478	−	0.200039i	−0.0165365	−	0.00954735i	0.491709	−	0.870760i	$-0.336372\pi$
$439$	−0.346478	−	0.200039i	−0.0165365	−	0.00954735i	−0.508245	+	0.861212i	$0.669706\pi$
$440$	2.83655	+	35.8443i	0.135227	+	1.70881i
$441$		0			0
$442$	−2.38232	−	0.571582i	−0.113315	−	0.0271874i
$443$	−15.5532	+	4.16746i	−0.738953	+	0.198002i	−0.608613	−	0.793468i	$-0.708274\pi$
$443$	−15.5532	+	4.16746i	−0.738953	+	0.198002i	−0.130340	+	0.991469i	$0.541607\pi$
$444$	−42.5026	+	2.23972i	−2.01708	+	0.106292i
$445$	−39.8292	−	10.6722i	−1.88808	−	0.505911i
$446$	−30.0946	+	0.792381i	−1.42502	+	0.0375203i
$447$	−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	$0.467398\pi$
$450$	−32.4452	+	0.854275i	−1.52948	+	0.0402709i
$451$	−1.15963	−	0.310722i	−0.0546048	−	0.0146313i
$452$	14.3413	−	0.755729i	0.674558	−	0.0355465i
$453$	33.8695	−	9.07530i	1.59133	−	0.426395i
$454$	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	$-0.411522\pi$
$457$	−9.00399	−	5.19846i	−0.421189	−	0.243174i	−0.695586	+	0.718443i	$0.744855\pi$
$458$	−20.0100	+	5.93036i	−0.935006	+	0.277108i
$459$	−8.32530	+	31.0705i	−0.388592	+	1.45024i
$460$	4.15331	+	0.881565i	0.193649	+	0.0411032i
$461$	−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	$0.370368\pi$
$464$	−10.9380	+	13.5232i	−0.507784	+	0.627798i
$465$	−40.8094	−	70.6839i	−1.89249	−	3.27789i
$466$	−28.1405	−	15.2738i	−1.30358	−	0.707545i
$467$	−3.88314	−	14.4921i	−0.179690	−	0.670614i	−0.995705	−	0.0925825i	$-0.970488\pi$
$467$	−3.88314	−	14.4921i	−0.179690	−	0.670614i	0.816015	−	0.578031i	$-0.196179\pi$
$468$	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
$472$	−3.76681	+	20.3729i	−0.173381	+	0.937738i
$473$	−24.8925	+	14.3717i	−1.14456	+	0.660812i
$474$	−32.2626	+	34.0074i	−1.48187	+	1.56201i
$475$	−5.70363	−	5.70363i	−0.261700	−	0.261700i
$476$		0			0
$477$	−24.0360	+	24.0360i	−1.10053	+	1.10053i
$478$	26.2716	−	0.691724i	1.20163	−	0.0316387i
$479$	13.1436	+	22.7654i	0.600547	+	1.04018i	0.992738	+	0.120294i	$0.0383838\pi$
$479$	13.1436	+	22.7654i	0.600547	+	1.04018i	−0.392191	+	0.919884i	$0.628283\pi$
$480$	51.6141	−	6.83286i	2.35585	−	0.311876i
$481$	−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
$485$	45.2171	−	12.1159i	2.05320	−	0.550154i
$486$	−14.9100	−	50.3089i	−0.676333	−	2.28206i
$487$	−17.8122	+	10.2839i	−0.807146	+	0.466006i	−0.845964	−	0.533240i	$-0.820974\pi$
$487$	−17.8122	+	10.2839i	−0.807146	+	0.466006i	0.0388179	+	0.999246i	$0.487641\pi$
$488$	5.61476	+	15.8339i	0.254168	+	0.716766i
$489$		−	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	$0.867229\pi$
$492$	−0.360938	+	1.70048i	−0.0162723	+	0.0766636i
$493$	−9.21311	−	2.46864i	−0.414937	−	0.111182i
$494$	2.59471	+	1.40833i	0.116742	+	0.0633638i
$495$	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
$499$	3.47358	+	12.9636i	0.155499	+	0.580329i	0.999062	+	0.0432996i	$0.0137870\pi$
$499$	3.47358	+	12.9636i	0.155499	+	0.580329i	−0.843563	+	0.537030i	$0.819546\pi$
$500$	7.39673	−	8.21965i	0.330792	−	0.367594i
$501$	14.8950	−	55.5889i	0.665459	−	2.48353i
$502$	12.7678	+	12.1127i	0.569855	+	0.540617i
$503$		−	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
$506$	−3.26248	+	3.43892i	−0.145035	+	0.152879i
$507$	−10.3900	+	38.7759i	−0.461435	+	1.72210i
$508$	20.4473	−	1.07749i	0.907203	−	0.0478060i
$509$	8.88035	+	33.1419i	0.393615	+	1.46899i	0.824127	+	0.566405i	$0.191666\pi$
$509$	8.88035	+	33.1419i	0.393615	+	1.46899i	−0.430512	+	0.902585i	$0.641667\pi$
$510$	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
$514$	−15.3715	+	28.3205i	−0.678009	+	1.24917i
$515$	4.63519	+	1.24200i	0.204251	+	0.0547289i
$516$	22.6780	+	34.8991i	0.998344	+	1.53635i
$517$	23.7061	+	23.7061i	1.04259	+	1.04259i
$518$		0			0
$519$		−	40.7513i		−	1.78878i
$520$	2.72625	−	5.72204i	0.119554	−	0.250928i
$521$	−20.4408	+	11.8015i	−0.895527	+	0.517033i	−0.875746	−	0.482772i	$-0.839630\pi$
$521$	−20.4408	+	11.8015i	−0.895527	+	0.517033i	−0.0197804	+	0.999804i	$0.506297\pi$
$522$	44.3425	−	13.1418i	1.94082	−	0.575200i
$523$	9.73565	−	2.60866i	0.425710	−	0.114069i	−0.0396015	−	0.999216i	$-0.512609\pi$
$523$	9.73565	−	2.60866i	0.425710	−	0.114069i	0.465312	+	0.885147i	$0.345942\pi$
$524$	−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
$528$	−23.6119	+	53.1154i	−1.02758	+	2.31155i
$529$	−11.2201	−	19.4338i	−0.487832	−	0.844949i
$530$	0.477369	+	18.1304i	0.0207356	+	0.787535i
$531$	38.9550	−	38.9550i	1.69051	−	1.69051i
$532$		0			0
$533$	0.149644	+	0.149644i	0.00648180	+	0.00648180i
$534$	−48.3596	−	45.8783i	−2.09272	−	1.98535i
$535$	−6.57330	+	3.79509i	−0.284188	+	0.164076i
$536$	15.9286	+	2.94510i	0.688012	+	0.127209i
$537$	−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
$541$	−6.79390	−	25.3552i	−0.292092	−	1.09010i	−0.943499	−	0.331375i	$-0.892487\pi$
$541$	−6.79390	−	25.3552i	−0.292092	−	1.09010i	0.651407	−	0.758729i	$-0.274179\pi$
$542$	20.9546	−	38.6068i	0.900077	−	1.65830i
$543$	7.68592	+	13.3124i	0.329835	+	0.571290i
$544$	−7.56095	−	9.83898i	−0.324173	−	0.421843i
$545$	−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	$0.881400\pi$
$548$	−1.80469	+	1.17272i	−0.0770927	+	0.0500961i
$549$	11.5619	−	43.1497i	0.493451	−	1.84159i
$550$	−5.49381	−	18.5370i	−0.234257	−	0.790421i
$551$	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
$555$	58.3270	−	15.6287i	2.47585	−	0.663401i
$556$	−2.15895	−	1.94281i	−0.0915600	−	0.0823933i
$557$	35.1404	+	9.41584i	1.48895	+	0.398962i	0.909381	−	0.415965i	$-0.136556\pi$
$557$	35.1404	+	9.41584i	1.48895	+	0.398962i	0.579565	+	0.814926i	$0.303223\pi$
$558$	−2.48260	−	94.2889i	−0.105097	−	3.99157i
$559$	5.06684			0.214304
$560$		0			0
$561$	−31.8762			−1.34582
$562$	0.927750	+	35.2358i	0.0391348	+	1.48633i
$563$	−27.0714	−	7.25375i	−1.14092	−	0.305709i	−0.361600	−	0.932333i	$-0.617769\pi$
$563$	−27.0714	−	7.25375i	−1.14092	−	0.305709i	−0.779322	+	0.626624i	$0.784436\pi$
$564$	32.4722	−	36.0849i	1.36733	−	1.51945i
$565$	−19.6808	+	5.27346i	−0.827979	+	0.221856i
$566$	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	$-0.301144\pi$
$569$	4.17102	+	2.40814i	0.174858	+	0.100954i	−0.410016	+	0.912078i	$0.634477\pi$
$570$	−9.77653	−	32.9876i	−0.409494	−	1.38170i
$571$	−4.86083	+	18.1409i	−0.203419	+	0.759172i	0.786506	+	0.617582i	$0.211888\pi$
$571$	−4.86083	+	18.1409i	−0.203419	+	0.759172i	−0.989926	+	0.141589i	$0.954779\pi$
$572$	3.85578	+	5.93365i	0.161218	+	0.248099i
$573$	−45.4866	+	45.4866i	−1.90023	+	1.90023i
$574$		0			0
$575$	−2.28302			−0.0952083
$576$	56.1898	+	21.5137i	2.34124	+	0.896403i
$577$	−6.23120	−	10.7928i	−0.259408	−	0.449309i	0.706675	−	0.707538i	$-0.250194\pi$
$577$	−6.23120	−	10.7928i	−0.259408	−	0.449309i	−0.966084	+	0.258230i	$0.916861\pi$
$578$	−8.22256	+	15.1493i	−0.342013	+	0.630126i
$579$	−3.05096	−	11.3863i	−0.126794	−	0.473200i
$580$	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
$584$	−24.4383	+	16.8115i	−1.01126	+	0.695664i
$585$	−14.5959	+	8.42696i	−0.603467	+	0.348412i
$586$	−32.4126	−	30.7495i	−1.33895	−	1.27025i
$587$	−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
$590$	−0.773671	−	29.3839i	−0.0318515	−	1.20972i
$591$	−22.5825	−	39.1141i	−0.928921	−	1.60894i
$592$	−24.4949	+	9.41888i	−1.00674	+	0.387114i
$593$	−1.44134	+	2.49647i	−0.0591886	+	0.102518i	−0.894101	−	0.447865i	$-0.852185\pi$
$593$	−1.44134	+	2.49647i	−0.0591886	+	0.102518i	0.834913	+	0.550382i	$0.185518\pi$
$594$	79.2119	−	48.5567i	3.25010	−	1.99231i
$595$		0			0
$596$	−1.11628	+	0.363055i	−0.0457245	+	0.0148713i
$597$	−24.3841	+	6.53369i	−0.997974	+	0.267406i
$598$	0.801158	−	0.237439i	0.0327618	−	0.00970960i
$599$	−4.25846	+	2.45862i	−0.173996	+	0.100457i	−0.584469	−	0.811416i	$-0.698697\pi$
$599$	−4.25846	+	2.45862i	−0.173996	+	0.100457i	0.410473	+	0.911873i	$0.365364\pi$
$600$	−26.3856	+	9.35643i	−1.07719	+	0.381975i
$601$			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
$604$	18.1292	−	11.7806i	0.737665	−	0.479347i
$605$	24.8639	+	6.66227i	1.01086	+	0.270860i
$606$	−33.4508	+	61.6299i	−1.35885	+	2.50354i
$607$	−5.07953	+	8.79800i	−0.206172	+	0.357100i	−0.950505	−	0.310708i	$-0.899434\pi$
$607$	−5.07953	+	8.79800i	−0.206172	+	0.357100i	0.744334	+	0.667808i	$0.232767\pi$
$608$	5.73217	+	13.8106i	0.232470	+	0.560094i
$609$		0			0
$610$	−12.4567	−	20.3209i	−0.504357	−	0.822770i
$611$	−1.52957	−	5.70843i	−0.0618798	−	0.230938i
$612$	1.73630	+	32.9494i	0.0701859	+	1.33190i
$613$	4.81729	−	17.9784i	0.194569	−	0.726140i	−0.797810	−	0.602910i	$-0.794008\pi$
$613$	4.81729	−	17.9784i	0.194569	−	0.726140i	0.992378	−	0.123230i	$-0.0393254\pi$
$614$	−15.6865	+	16.5349i	−0.633057	+	0.667295i
$615$		−	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	$0.907475\pi$
$618$	5.62794	+	5.33917i	0.226389	+	0.214773i
$619$	−8.58680	+	32.0464i	−0.345133	+	1.28805i	0.547325	+	0.836920i	$0.315646\pi$
$619$	−8.58680	+	32.0464i	−0.345133	+	1.28805i	−0.892457	+	0.451132i	$0.851020\pi$
$620$	−37.4092	−	33.6639i	−1.50239	−	1.35198i
$621$	−2.83953	−	10.5973i	−0.113946	−	0.425254i
$622$	−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
$626$	12.9850	+	7.04784i	0.518983	+	0.281688i
$627$	37.1035	+	9.94184i	1.48177	+	0.397039i
$628$	17.7691	+	3.77161i	0.709066	+	0.150504i
$629$	−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	$0.836486\pi$
$632$	−12.4322	+	26.0935i	−0.494525	+	1.03794i
$633$	12.0778	−	6.97313i	0.480050	−	0.277157i
$634$	−1.28954	−	4.35113i	−0.0512143	−	0.172805i
$635$	−28.0602	+	7.51871i	−1.11354	+	0.298371i
$636$	−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
$640$	28.9616	−	13.8498i	1.14481	−	0.547460i
$641$	24.6259	+	42.6533i	0.972663	+	1.68470i	0.687440	+	0.726241i	$0.258734\pi$
$641$	24.6259	+	42.6533i	0.972663	+	1.68470i	0.285223	+	0.958461i	$0.407932\pi$
$642$	−12.2661	+	0.322963i	−0.484103	+	0.0127463i
$643$	−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
$646$	−5.64366	+	5.94889i	−0.222047	+	0.234056i
$647$	−18.5542	+	10.7123i	−0.729442	+	0.421144i	−0.818218	−	0.574908i	$-0.805038\pi$
$647$	−18.5542	+	10.7123i	−0.729442	+	0.421144i	0.0887760	+	0.996052i	$0.471704\pi$
$648$	−40.0788	−	58.2612i	−1.57445	−	2.28872i
$649$	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
$653$	1.89623	+	7.07682i	0.0742051	+	0.276937i	0.993052	−	0.117677i	$-0.0375448\pi$
$653$	1.89623	+	7.07682i	0.0742051	+	0.276937i	−0.918847	+	0.394615i	$0.870878\pi$
$654$	−31.7346	−	17.2246i	−1.24092	−	0.673534i
$655$	5.69055	+	9.85633i	0.222348	+	0.385119i
$656$	0.112654	+	1.06594i	0.00439840	+	0.0416179i
$657$	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	$0.268024\pi$
$660$	17.1230	−	80.6712i	0.666510	−	3.14012i
$661$	−4.55066	+	16.9833i	−0.177000	+	0.660573i	0.819202	+	0.573505i	$0.194417\pi$
$661$	−4.55066	+	16.9833i	−0.177000	+	0.660573i	−0.996202	+	0.0870687i	$0.972250\pi$
$662$	24.9757	−	7.40204i	0.970708	−	0.287689i
$663$	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
$667$	3.14234	−	0.841987i	0.121672	−	0.0326018i
$668$	−1.86734	−	35.4360i	−0.0722494	−	1.37106i
$669$	66.6952	+	17.8709i	2.57858	+	0.690930i
$670$	−22.9740	+	0.604898i	−0.887562	+	0.0233693i
$671$	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	$0.736768\pi$
$674$	−23.1147	+	0.608603i	−0.890344	+	0.0234425i
$675$	43.2229	+	11.5815i	1.66365	+	0.445774i
$676$	1.30255	+	24.7183i	0.0500983	+	0.950704i
$677$	−30.0120	+	8.04169i	−1.15345	+	0.309067i	−0.784349	−	0.620320i	$-0.787003\pi$
$677$	−30.0120	+	8.04169i	−1.15345	+	0.309067i	−0.369106	+	0.929387i	$0.620336\pi$
$678$	−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
$682$	53.8703	−	15.9655i	2.06280	−	0.611352i
$683$	9.11370	−	34.0128i	0.348726	−	1.30146i	−0.539472	−	0.842003i	$-0.681376\pi$
$683$	9.11370	−	34.0128i	0.348726	−	1.30146i	0.888198	−	0.459460i	$-0.151957\pi$
$684$	8.25553	−	38.8942i	0.315658	−	1.48716i
$685$	2.15917	−	2.15917i	0.0824977	−	0.0824977i
$686$		0			0
$687$	47.8675			1.82626
$688$	19.9531	+	16.1388i	0.760707	+	0.615284i
$689$	1.78470	+	3.09119i	0.0679916	+	0.117765i
$690$	−8.55870	−	4.64540i	−0.325824	−	0.176847i
$691$	−8.38087	−	31.2778i	−0.318823	−	1.18987i	−0.920377	−	0.391033i	$-0.872118\pi$
$691$	−8.38087	−	31.2778i	−0.318823	−	1.18987i	0.601553	−	0.798833i	$-0.294549\pi$
$692$	−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
$696$	32.8664	−	22.6093i	1.24580	−	0.857003i
$697$	−0.509052	+	0.293901i	−0.0192817	+	0.0111323i
$698$	34.4264	−	36.2883i	1.30306	−	1.37353i
$699$	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	$0.0133276\pi$
$702$	−16.3723	+	0.431079i	−0.617934	+	0.0162700i
$703$	8.67125	+	15.0191i	0.327043	+	0.566454i
$704$	−3.71568	+	35.6480i	−0.140040	+	1.34353i
$705$	−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
$709$	−24.3097	+	6.51377i	−0.912971	+	0.244630i	−0.684578	−	0.728939i	$-0.740014\pi$
$709$	−24.3097	+	6.51377i	−0.912971	+	0.244630i	−0.228393	+	0.973569i	$0.573347\pi$
$710$	10.6951	+	36.0870i	0.401380	+	1.35432i
$711$	66.5599	−	38.4284i	2.49619	−	1.44118i
$712$	−37.1058	−	17.6789i	−1.39060	−	0.662545i
$713$		−	6.63466i		−	0.248470i
$714$		0			0
$715$	−7.09914	−	7.09914i	−0.265493	−	0.265493i
$716$	−9.29488	−	1.97290i	−0.347366	−	0.0737306i
$717$	−58.2228	−	15.6007i	−2.17437	−	0.582620i
$718$	26.5623	+	14.4172i	0.991295	+	0.538045i
$719$	−14.7568	+	25.5596i	−0.550337	+	0.953212i	0.447913	+	0.894077i	$0.352168\pi$
$719$	−14.7568	+	25.5596i	−0.550337	+	0.953212i	−0.998250	+	0.0591349i	$0.981166\pi$
$720$	−84.3199	−	13.3053i	−3.14242	−	0.495858i
$721$		0			0
$722$	−14.4839	+	8.87863i	−0.539037	+	0.330429i
$723$	−10.5076	−	39.2149i	−0.390782	−	1.45842i
$724$	7.04554	+	6.34017i	0.261846	+	0.235631i
$725$	−3.43420	+	12.8166i	−0.127543	+	0.475996i
$726$	30.1891	+	28.6402i	1.12042	+	1.06294i
$727$		−	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
$730$	28.9642	−	30.5306i	1.07201	−	1.12999i
$731$	−3.64243	+	13.5937i	−0.134720	+	0.502782i
$732$	−2.02766	−	38.4784i	−0.0749444	−	1.42220i
$733$	−0.680788	−	2.54074i	−0.0251455	−	0.0938442i	0.952213	−	0.305436i	$-0.0988021\pi$
$733$	−0.680788	−	2.54074i	−0.0251455	−	0.0938442i	−0.977358	+	0.211591i	$0.932135\pi$
$734$	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
$738$	1.35962	−	2.50497i	0.0500485	−	0.0922094i
$739$	22.2479	+	5.96130i	0.818402	+	0.219290i	0.643647	−	0.765322i	$-0.277420\pi$
$739$	22.2479	+	5.96130i	0.818402	+	0.219290i	0.174754	+	0.984612i	$0.444087\pi$
$740$	31.2205	−	20.2876i	1.14769	−	0.745786i
$741$	−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	$-0.217889\pi$
$744$	−27.1907	−	76.6790i	−0.996858	−	2.81119i
$745$	1.44227	−	0.832692i	0.0528405	−	0.0305075i
$746$	27.9710	−	8.28977i	1.02409	−	0.303510i
$747$	−4.87252	+	1.30559i	−0.178276	+	0.0477690i
$748$	−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	−0.889745	−	0.456458i	$-0.849118\pi$
$751$	−1.35839	+	2.35281i	−0.0495685	+	0.0858552i	0.840177	+	0.542313i	$0.182451\pi$
$752$	12.1589	−	27.3517i	0.443390	−	0.997413i
$753$	−20.1826	−	34.9573i	−0.735495	−	1.27392i
$754$	−0.127825	−	4.85477i	−0.00465511	−	0.176800i
$755$	−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	$0.923549\pi$
$758$	−17.5673	−	16.6660i	−0.638074	−	0.605336i
$759$	9.41552	−	5.43605i	0.341762	−	0.197316i
$760$	−12.0236	−	17.4783i	−0.436143	−	0.634006i
$761$	46.8585	+	27.0538i	1.69862	+	0.980699i	0.947072	+	0.321022i	$0.104026\pi$
$761$	46.8585	+	27.0538i	1.69862	+	0.980699i	0.751549	+	0.659677i	$0.229307\pi$
$762$	−45.6665	−	10.9566i	−1.65432	−	0.396916i
$763$		0			0
$764$	−17.9971	+	35.3464i	−0.651112	+	1.27879i
$765$	−12.1159	−	45.2171i	−0.438050	−	1.63483i
$766$	−8.57168	+	15.7925i	−0.309707	+	0.570606i
$767$	−2.89246	−	5.00988i	−0.104441	−	0.180896i
$768$	51.8296	+	2.65652i	1.87024	+	0.0958591i
$769$	−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
$772$	−3.96045	−	6.09472i	−0.142540	−	0.219354i
$773$	3.10496	−	11.5879i	0.111678	−	0.416787i	−0.887339	−	0.461117i	$-0.847449\pi$
$773$	3.10496	−	11.5879i	0.111678	−	0.416787i	0.999017	+	0.0443301i	$0.0141153\pi$
$774$	−19.3904	−	65.4263i	−0.696973	−	2.35170i
$775$	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
$779$	0.684194	−	0.183329i	0.0245138	−	0.00656845i
$780$	−9.72430	+	10.8062i	−0.348186	+	0.386923i
$781$	−40.5896	−	10.8759i	−1.45241	−	0.389172i
$782$	0.0610876	+	2.32010i	0.00218449	+	0.0829666i
$783$	−63.7632			−2.27871
$784$		0			0
$785$	−25.7717			−0.919833
$786$	0.484266	+	18.3924i	0.0172732	+	0.656034i
$787$	−13.8277	−	3.70513i	−0.492905	−	0.132074i	0.00380017	−	0.999993i	$-0.498790\pi$
$787$	−13.8277	−	3.70513i	−0.492905	−	0.132074i	−0.496705	+	0.867919i	$0.665457\pi$
$788$	−20.7010	−	18.6285i	−0.737442	−	0.663612i
$789$	40.0676	−	10.7361i	1.42645	−	0.382215i
$790$	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
$794$	−0.810114	−	2.73346i	−0.0287499	−	0.0970068i
$795$	10.7663	−	40.1804i	0.381841	−	1.42505i
$796$	−13.0520	+	8.48137i	−0.462614	+	0.300614i
$797$	−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
$800$	−13.6873	+	10.5182i	−0.483918	+	0.371876i
$801$	54.6463	+	94.6502i	1.93083	+	3.34430i
$802$	−9.11661	+	16.7965i	−0.321919	+	0.593104i
$803$	12.1604	+	45.3833i	0.429132	+	1.60154i
$804$	−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
$808$	−7.86110	+	42.5170i	−0.276552	+	1.49574i
$809$	−0.173970	+	0.100441i	−0.00611645	+	0.00353133i	−0.503055	−	0.864254i	$-0.667791\pi$
$809$	−0.173970	+	0.100441i	−0.00611645	+	0.00353133i	0.496939	+	0.867786i	$0.334457\pi$
$810$	72.7855	+	69.0510i	2.55742	+	2.42620i
$811$	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
$814$	1.09412	+	41.5544i	0.0383487	+	1.45648i
$815$	21.2747	+	36.8489i	0.745222	+	1.29076i
$816$	10.2144	+	26.5638i	0.357577	+	0.929921i
$817$	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
$821$	22.3132	−	5.97882i	0.778737	−	0.208662i	0.152509	−	0.988302i	$-0.451265\pi$
$821$	22.3132	−	5.97882i	0.778737	−	0.208662i	0.626228	+	0.779640i	$0.284598\pi$
$822$	4.73286	−	1.40268i	0.165078	−	0.0489240i
$823$	−29.9668	+	17.3013i	−1.04458	+	0.603087i	−0.921126	−	0.389264i	$-0.872729\pi$
$823$	−29.9668	+	17.3013i	−1.04458	+	0.603087i	−0.123451	+	0.992351i	$0.539396\pi$
$824$	4.31825	+	2.05742i	0.150433	+	0.0716735i
$825$			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	$0.529446\pi$
$828$	−6.13193	−	9.43641i	−0.213099	−	0.327938i
$829$	31.7614	+	8.51045i	1.10312	+	0.295580i	0.764034	−	0.645175i	$-0.223216\pi$
$829$	31.7614	+	8.51045i	1.10312	+	0.295580i	0.339086	+	0.940756i	$0.389882\pi$
$830$	−1.28392	+	2.36551i	−0.0445657	+	0.0821079i
$831$	−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
$835$	13.0302	+	48.6294i	0.450929	+	1.68289i
$836$	23.6522	−	1.24638i	0.818028	−	0.0431068i
$837$	−33.6571	+	125.610i	−1.16336	+	4.34171i
$838$	28.6402	−	30.1891i	0.989359	−	1.04287i
$839$			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
$842$	−40.2131	−	38.1498i	−1.38584	−	1.31473i
$843$	20.9239	−	78.0892i	0.720659	−	2.68953i
$844$	5.75218	−	6.39214i	0.197998	−	0.220027i
$845$	−9.08920	−	33.9213i	−0.312678	−	1.16693i
$846$	−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
$850$	−8.31974	−	4.51570i	−0.285365	−	0.154887i
$851$	4.74131	+	1.27043i	0.162530	+	0.0435498i
$852$	−12.6336	+	59.5206i	−0.432820	+	2.03914i
$853$	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
$856$	−7.13081	+	2.52861i	−0.243726	+	0.0864263i
$857$	12.3231	−	7.11472i	0.420947	−	0.243034i	−0.274535	−	0.961577i	$-0.588524\pi$
$857$	12.3231	−	7.11472i	0.420947	−	0.243034i	0.695483	+	0.718543i	$0.255191\pi$
$858$	−4.61186	−	15.5612i	−0.157446	−	0.531250i
$859$	−21.1220	+	5.65962i	−0.720673	+	0.193104i	−0.600472	−	0.799646i	$-0.705021\pi$
$859$	−21.1220	+	5.65962i	−0.720673	+	0.193104i	−0.120201	+	0.992750i	$0.538354\pi$
$860$	−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	−0.671739	−	0.740788i	$-0.734452\pi$
$863$	8.97968	−	15.5533i	0.305672	−	0.529439i	0.977411	+	0.211349i	$0.0677856\pi$
$864$	−65.8471	−	50.4511i	−2.24016	−	1.71638i
$865$	17.8247	+	30.8734i	0.606059	+	1.04973i
$866$	−12.0665	+	0.317707i	−0.410036	+	0.0107961i
$867$	27.9548	−	27.9548i	0.949395	−	0.949395i
$868$		0			0
$869$	32.3733	+	32.3733i	1.09819	+	1.09819i
$870$	−38.9531	+	41.0598i	−1.32063	+	1.39206i
$871$	−3.91700	+	2.26148i	−0.132722	+	0.0766274i
$872$	−21.8929	−	4.04785i	−0.741388	−	0.137078i
$873$	−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
$877$	4.39274	+	16.3939i	0.148332	+	0.553583i	0.999584	+	0.0288266i	$0.00917705\pi$
$877$	4.39274	+	16.3939i	0.148332	+	0.553583i	−0.851252	+	0.524757i	$0.824156\pi$
$878$	0.497270	+	0.269903i	0.0167821	+	0.00910879i
$879$	51.2359	+	88.7432i	1.72814	+	2.99323i
$880$	−5.34433	−	50.5683i	−0.180157	−	1.70466i
$881$	−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	$0.347559\pi$
$884$	3.38921	+	0.719381i	0.113992	+	0.0241954i
$885$	−17.4489	+	65.1203i	−0.586539	+	2.18899i
$886$	21.8327	−	6.47057i	0.733485	−	0.217383i
$887$	−23.8413	−	13.7648i	−0.800511	−	0.462175i	0.0431388	−	0.999069i	$-0.486264\pi$
$887$	−23.8413	−	13.7648i	−0.800511	−	0.462175i	−0.843650	+	0.536894i	$0.819598\pi$
$888$	60.0036	−	4.74841i	2.01359	−	0.159346i
$889$		0			0
$890$	56.7047	+	13.6050i	1.90075	+	0.456040i
$891$	−108.195	+	28.9906i	−3.62465	+	0.971223i
$892$	42.5159	−	2.24042i	1.42354	−	0.0750147i
$893$	−19.1064	−	5.11954i	−0.639370	−	0.171319i
$894$	2.69133	−	0.0708621i	0.0900117	−	0.00236998i
$895$	13.4810			0.450620
$896$		0			0
$897$	−1.91651			−0.0639905
$898$	−6.12563	+	0.161286i	−0.204415	+	0.00538219i
$899$	−37.2462	−	9.98010i	−1.24223	−	0.332855i
$900$	45.8368	−	2.41542i	1.52789	−	0.0805139i
$901$	−9.57627	+	2.56595i	−0.319032	+	0.0854843i
$902$	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
$906$	−47.5443	+	14.0907i	−1.57955	+	0.468132i
$907$	−9.21942	+	34.4073i	−0.306126	+	1.14248i	0.625846	+	0.779946i	$0.284754\pi$
$907$	−9.21942	+	34.4073i	−0.306126	+	1.14248i	−0.931972	+	0.362530i	$0.881913\pi$
$908$	−43.0475	−	9.13709i	−1.42858	−	0.303225i
$909$	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	$0.696856\pi$
$912$	−3.60448	−	34.1057i	−0.119356	−	1.12935i
$913$	−1.50245	−	2.60232i	−0.0497238	−	0.0861241i
$914$	12.9227	+	7.01403i	0.427444	+	0.232003i
$915$	14.1490	+	52.8046i	0.467750	+	1.74567i
$916$	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	$-0.251021\pi$
$919$	13.4271	+	7.75216i	0.442920	+	0.255720i	−0.261915	+	0.965091i	$0.584354\pi$
$920$	−5.90444	−	1.09169i	−0.194664	−	0.0359920i
$921$	45.2714	−	26.1374i	1.49174	−	0.861258i
$922$	20.2170	−	21.3104i	0.665810	−	0.701819i
$923$	5.23786	+	5.23786i	0.172406	+	0.172406i
$924$		0			0
$925$	−14.1566	+	14.1566i	−0.465467	+	0.465467i
$926$	−24.0977	+	0.634487i	−0.791901	+	0.0208505i
$927$	−6.35957	−	11.0151i	−0.208876	−	0.361783i
$928$	14.9599	−	19.5252i	0.491084	−	0.640946i
$929$	14.6486	−	25.3721i	0.480604	−	0.832431i	−0.519148	−	0.854684i	$-0.673751\pi$
$929$	14.6486	−	25.3721i	0.480604	−	0.832431i	0.999752	+	0.0222533i	$0.00708402\pi$
$930$	60.3242	+	98.4085i	1.97811	+	3.22694i
$931$		0			0
$932$	40.3514	+	20.5455i	1.32175	+	0.672989i
$933$	45.1486	−	12.0975i	1.47810	−	0.396055i
$934$	6.02913	+	20.3433i	0.197279	+	0.665652i
$935$	24.1495	−	13.9427i	0.789774	−	0.455976i
$936$	−15.8339	+	5.61476i	−0.517547	+	0.183524i
$937$		−	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
$940$	−8.81744	+	41.5415i	−0.287593	+	1.35493i
$941$	−52.8424	−	14.1591i	−1.72261	−	0.461573i	−0.744153	−	0.668010i	$-0.767146\pi$
$941$	−52.8424	−	14.1591i	−1.72261	−	0.461573i	−0.978460	+	0.206437i	$0.933813\pi$
$942$	−36.6168	−	19.8745i	−1.19304	−	0.647545i
$943$	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
$947$	−4.89848	−	18.2814i	−0.159179	−	0.594064i	−0.998711	−	0.0507543i	$-0.983837\pi$
$947$	−4.89848	−	18.2814i	−0.159179	−	0.594064i	0.839532	−	0.543310i	$-0.182829\pi$
$948$	44.3445	−	49.2780i	1.44024	−	1.60048i
$949$	2.14362	−	8.00009i	0.0695848	−	0.259694i
$950$	8.27566	+	7.85104i	0.268498	+	0.254722i
$951$			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	$-0.122156\pi$
$954$	33.0855	−	34.8749i	1.07118	−	1.12912i
$955$	14.5648	−	54.3567i	0.471307	−	1.75894i
$956$	−37.1150	+	1.95581i	−1.20039	+	0.0632555i
$957$	−16.3542	−	61.0347i	−0.528657	−	1.97297i
$958$	−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
$962$	3.49553	−	6.44018i	0.112701	−	0.207640i
$963$	19.4326	+	5.20694i	0.626205	+	0.167791i
$964$	−13.6399	−	20.9904i	−0.439311	−	0.676054i
$965$	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	$-0.108416\pi$
$968$	23.1638	+	11.0363i	0.744512	+	0.354720i
$969$	16.2876	−	9.40366i	0.523233	−	0.302089i
$970$	−63.4734	+	18.8116i	−2.03801	+	0.604004i
$971$	24.4384	−	6.54826i	0.784267	−	0.210144i	0.155602	−	0.987820i	$-0.450268\pi$
$971$	24.4384	−	6.54826i	0.784267	−	0.210144i	0.628665	+	0.777676i	$0.283602\pi$
$972$	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
$976$	−8.52710	−	22.1757i	−0.272946	−	0.709828i
$977$	−16.8040	−	29.1053i	−0.537607	−	0.931162i	−0.999032	−	0.0439831i	$-0.985995\pi$
$977$	−16.8040	−	29.1053i	−0.537607	−	0.931162i	0.461426	−	0.887179i	$-0.347338\pi$
$978$	1.81048	+	68.7619i	0.0578928	+	2.19876i
$979$	−46.0358	+	46.0358i	−1.47131	+	1.47131i
$980$		0			0
$981$	41.8615	+	41.8615i	1.33654	+	1.33654i
$982$	16.3692	+	15.5294i	0.522363	+	0.495562i
$983$	−4.11952	+	2.37841i	−0.131392	+	0.0758594i	−0.564255	−	0.825600i	$-0.690837\pi$
$983$	−4.11952	+	2.37841i	−0.131392	+	0.0758594i	0.432863	+	0.901460i	$0.357503\pi$
$984$	0.446969	−	2.41745i	0.0142489	−	0.0770654i
$985$	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
$989$	−1.24233	−	4.63644i	−0.0395038	−	0.147430i
$990$	−64.5008	+	118.836i	−2.04997	+	3.77687i
$991$	−14.5579	−	25.2150i	−0.462446	−	0.800979i	0.536637	−	0.843813i	$-0.319695\pi$
$991$	−14.5579	−	25.2150i	−0.462446	−	0.800979i	−0.999082	+	0.0428342i	$0.986361\pi$
$992$	−30.5670	−	39.7765i	−0.970503	−	1.26290i
$993$	−59.7464			−1.89599
$994$		0			0
$995$	15.6156	−	15.6156i	0.495048	−	0.495048i
$996$	−3.64843	+	2.37081i	−0.115605	+	0.0751219i
$997$	2.67412	−	9.97995i	0.0846902	−	0.316068i	−0.910565	−	0.413366i	$-0.864353\pi$
$997$	2.67412	−	9.97995i	0.0846902	−	0.316068i	0.995255	+	0.0972974i	$0.0310198\pi$
$998$	−5.39322	−	18.1976i	−0.170720	−	0.576035i
$999$	−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.373.2		40
7.2	even	3		784.2.m.i.197.7	✓	20
7.3	odd	6	inner	784.2.x.n.165.8		40
7.4	even	3	inner	784.2.x.n.165.7		40
7.5	odd	6		784.2.m.i.197.8	yes	20
7.6	odd	2	inner	784.2.x.n.373.1		40
16.13	even	4	inner	784.2.x.n.765.7		40
112.13	odd	4	inner	784.2.x.n.765.8		40
112.45	odd	12	inner	784.2.x.n.557.1		40
112.61	odd	12		784.2.m.i.589.8	yes	20
112.93	even	12		784.2.m.i.589.7	yes	20
112.109	even	12	inner	784.2.x.n.557.2		40

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

\(f(q)\)	\(=\)	\(q+(-1.41372 + 0.0372230i) q^{2} +(3.13308 + 0.839505i) q^{3} +(1.99723 - 0.105246i) q^{4} +(-2.74083 + 0.734404i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(6.51332 + 3.76047i) q^{9} +O(q^{10})\)	\(q+(-1.41372 + 0.0372230i) q^{2} +(3.13308 + 0.839505i) q^{3} +(1.99723 - 0.105246i) q^{4} +(-2.74083 + 0.734404i) q^{5} +(-4.46055 - 1.07021i) q^{6} +(-2.81961 + 0.223131i) q^{8} +(6.51332 + 3.76047i) q^{9} +(3.84744 - 1.14027i) q^{10} +(-1.15955 + 4.32748i) q^{11} +(6.34583 + 1.34694i) q^{12} +(0.558438 - 0.558438i) q^{13} -9.20377 q^{15} +(3.97785 - 0.420401i) q^{16} +(1.09678 + 1.89967i) q^{17} +(-9.34802 - 5.07382i) q^{18} +(-0.684144 - 2.55326i) q^{19} +(-5.39678 + 1.75523i) q^{20} +(1.47820 - 6.16103i) q^{22} +(-0.647926 - 0.374080i) q^{23} +(-9.02138 - 1.66799i) q^{24} +(2.64268 - 1.52575i) q^{25} +(-0.768691 + 0.810264i) q^{26} +(10.3691 + 10.3691i) q^{27} +(-3.07468 + 3.07468i) q^{29} +(13.0116 - 0.342592i) q^{30} +(4.43398 + 7.67989i) q^{31} +(-5.60793 + 0.742397i) q^{32} +(-7.26589 + 12.5849i) q^{33} +(-1.62125 - 2.64479i) q^{34} +(13.4044 + 6.82502i) q^{36} +(-6.33730 + 1.69807i) q^{37} +(1.06223 + 3.58414i) q^{38} +(2.21844 - 1.28082i) q^{39} +(7.56421 - 2.68230i) q^{40} +0.267969i q^{41} +(4.53661 + 4.53661i) q^{43} +(-1.86043 + 8.76501i) q^{44} +(-20.6136 - 5.52341i) q^{45} +(0.929912 + 0.504728i) q^{46} +(3.74156 - 6.48057i) q^{47} +(12.8158 + 2.02228i) q^{48} +(-3.67923 + 2.25536i) q^{50} +(1.84150 + 6.87257i) q^{51} +(1.05656 - 1.17410i) q^{52} +(-1.16977 + 4.36564i) q^{53} +(-15.0450 - 14.2731i) q^{54} -12.7125i q^{55} -8.57391i q^{57} +(4.23229 - 4.46119i) q^{58} +(1.89585 - 7.07539i) q^{59} +(-18.3820 + 0.968660i) q^{60} +(-1.53730 - 5.73728i) q^{61} +(-6.55430 - 10.6922i) q^{62} +(7.90042 - 1.25829i) q^{64} +(-1.12047 + 1.94070i) q^{65} +(9.80352 - 18.0620i) q^{66} +(-5.53193 - 1.48228i) q^{67} +(2.39045 + 3.67865i) q^{68} +(-1.71596 - 1.71596i) q^{69} +9.37949i q^{71} +(-19.2041 - 9.14974i) q^{72} +(9.08221 - 5.24362i) q^{73} +(8.89598 - 2.63650i) q^{74} +(9.56061 - 2.56176i) q^{75} +(-1.63511 - 5.02744i) q^{76} +(-3.08859 + 1.89330i) q^{78} +(5.10952 - 8.84995i) q^{79} +(-10.5939 + 4.07359i) q^{80} +(12.5009 + 21.6521i) q^{81} +(-0.00997458 - 0.378833i) q^{82} +(-0.474267 + 0.474267i) q^{83} +(-4.40120 - 4.40120i) q^{85} +(-6.58238 - 6.24465i) q^{86} +(-12.2144 + 7.05199i) q^{87} +(2.30387 - 12.4606i) q^{88} +(12.5849 + 7.26589i) q^{89} +(29.3476 + 7.04127i) q^{90} +(-1.33343 - 0.678932i) q^{92} +(7.44471 + 27.7840i) q^{93} +(-5.04831 + 9.30101i) q^{94} +(3.75025 + 6.49562i) q^{95} +(-18.1933 - 2.38190i) 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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