LMFDB - Embedded newform 784.2.x.j.765.4

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:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 4 x^{14} + 4 x^{13} - 13 x^{12} + 32 x^{11} - 4 x^{10} - 34 x^{9} + 121 x^{8} + \cdots + 256 $ x^16 - 2x^15 + 4x^14 + 4x^13 - 13x^12 + 32x^11 - 4x^10 - 34x^9 + 121x^8 - 68x^7 - 16x^6 + 256x^5 - 208x^4 + 128x^3 + 256x^2 - 256*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			765.4
Root			$1.21641 - 0.721349i$ of defining polynomial
Character	$\chi$	$=$	784.765
Dual form			784.2.x.j.165.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.867450 - 1.11693i) q^{2} +(-0.442248 + 1.65049i) q^{3} +(-0.495063 - 1.93776i) q^{4} +(0.949390 + 3.54317i) q^{5} +(1.45986 + 1.92568i) q^{6} +(-2.59378 - 1.12796i) q^{8} +(0.0695300 + 0.0401432i) q^{9} +O(q^{10})$	\(q+(0.867450 - 1.11693i) q^{2} +(-0.442248 + 1.65049i) q^{3} +(-0.495063 - 1.93776i) q^{4} +(0.949390 + 3.54317i) q^{5} +(1.45986 + 1.92568i) q^{6} +(-2.59378 - 1.12796i) q^{8} +(0.0695300 + 0.0401432i) q^{9} +(4.78102 + 2.01312i) q^{10} +(1.47570 + 0.395412i) q^{11} +(3.41720 + 0.0398737i) q^{12} +(-2.97932 - 2.97932i) q^{13} -6.26785 q^{15} +(-3.50983 + 1.91862i) q^{16} +(3.59378 + 6.22461i) q^{17} +(0.105151 - 0.0428379i) q^{18} +(-3.08391 + 0.826331i) q^{19} +(6.39581 - 3.59378i) q^{20} +(1.72174 - 1.30525i) q^{22} +(3.02830 + 1.74839i) q^{23} +(3.00879 - 3.78218i) q^{24} +(-7.32261 + 4.22771i) q^{25} +(-5.91210 + 0.743280i) q^{26} +(-3.72174 + 3.72174i) q^{27} +(0.851361 + 0.851361i) q^{29} +(-5.43705 + 7.00075i) q^{30} +(-1.97932 - 3.42828i) q^{31} +(-0.901629 + 5.58454i) q^{32} +(-1.30525 + 2.26076i) q^{33} +(10.0699 + 1.38554i) q^{34} +(0.0433661 - 0.154606i) q^{36} +(2.17113 + 8.10278i) q^{37} +(-1.75218 + 4.16131i) q^{38} +(6.23495 - 3.59975i) q^{39} +(1.53404 - 10.2611i) q^{40} -2.67573i q^{41} +(-4.25592 + 4.25592i) q^{43} +(0.0356509 - 3.05530i) q^{44} +(-0.0762231 + 0.284468i) q^{45} +(4.57972 - 1.86576i) q^{46} +(1.17729 - 2.03913i) q^{47} +(-1.61446 - 6.64146i) q^{48} +(-1.62994 + 11.8462i) q^{50} +(-11.8630 + 3.17869i) q^{51} +(-4.29826 + 7.24816i) q^{52} +(4.66701 + 1.25052i) q^{53} +(0.928499 + 7.38535i) q^{54} +5.60406i q^{55} -5.45542i q^{57} +(1.68942 - 0.212397i) q^{58} +(5.27509 + 1.41346i) q^{59} +(3.10298 + 12.1456i) q^{60} +(1.92093 - 0.514711i) q^{61} +(-5.54611 - 0.763102i) q^{62} +(5.45542 + 5.85136i) q^{64} +(7.72771 - 13.3848i) q^{65} +(1.39287 + 3.41897i) q^{66} +(2.08734 - 7.79006i) q^{67} +(10.2827 - 10.0455i) q^{68} +(-4.22496 + 4.22496i) q^{69} -14.4738i q^{71} +(-0.135066 - 0.182550i) q^{72} +(2.88178 - 1.66380i) q^{73} +(10.9336 + 4.60375i) q^{74} +(-3.73940 - 13.9556i) q^{75} +(3.12796 + 5.56679i) q^{76} +(1.38784 - 10.0866i) q^{78} +(7.90931 - 13.6993i) q^{79} +(-10.1302 - 10.6144i) q^{80} +(-4.37635 - 7.58006i) q^{81} +(-2.98860 - 2.32106i) q^{82} +(-1.20825 - 1.20825i) q^{83} +(-18.6430 + 18.6430i) q^{85} +(1.06177 + 8.44535i) q^{86} +(-1.78168 + 1.02865i) q^{87} +(-3.38163 - 2.69014i) q^{88} +(10.9417 + 6.31718i) q^{89} +(0.251611 + 0.331898i) q^{90} +(1.88876 - 6.73368i) q^{92} +(6.53371 - 1.75070i) q^{93} +(-1.25632 - 3.08379i) q^{94} +(-5.85567 - 10.1423i) q^{95} +(-8.81850 - 3.95789i) q^{96} -1.08890 q^{97} +(0.0867323 + 0.0867323i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	$ 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) $ 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.867450	−	1.11693i	0.613379	−	0.789788i
$2$	0.867450	−	1.11693i	0.613379	−	0.789788i
$3$	−0.442248	+	1.65049i	−0.255332	+	0.952913i	0.712573	+	0.701598i	$0.247530\pi$
$3$	−0.442248	+	1.65049i	−0.255332	+	0.952913i	−0.967905	+	0.251315i	$0.919137\pi$
$4$	−0.495063	−	1.93776i	−0.247531	−	0.968880i
$5$	0.949390	+	3.54317i	0.424580	+	1.58456i	0.764838	+	0.644223i	$0.222819\pi$
$5$	0.949390	+	3.54317i	0.424580	+	1.58456i	−0.340258	+	0.940332i	$0.610514\pi$
$6$	1.45986	+	1.92568i	0.595984	+	0.786156i
$7$		0			0
$7$		0			0
$8$	−2.59378	−	1.12796i	−0.917041	−	0.398794i
$9$	0.0695300	+	0.0401432i	0.0231767	+	0.0133811i
$10$	4.78102	+	2.01312i	1.51189	+	0.636605i
$11$	1.47570	+	0.395412i	0.444940	+	0.119221i	0.474331	−	0.880347i	$-0.342690\pi$
$11$	1.47570	+	0.395412i	0.444940	+	0.119221i	−0.0293909	+	0.999568i	$0.509357\pi$
$12$	3.41720	+	0.0398737i	0.986461	+	0.0115105i
$13$	−2.97932	−	2.97932i	−0.826315	−	0.826315i	0.160690	−	0.987005i	$-0.448628\pi$
$13$	−2.97932	−	2.97932i	−0.826315	−	0.826315i	−0.987005	+	0.160690i	$0.948628\pi$
$14$		0			0
$15$	−6.26785			−1.61835
$16$	−3.50983	+	1.91862i	−0.877457	+	0.479656i
$17$	3.59378	+	6.22461i	0.871620	+	1.50969i	0.860320	+	0.509755i	$0.170264\pi$
$17$	3.59378	+	6.22461i	0.871620	+	1.50969i	0.0113004	+	0.999936i	$0.496403\pi$
$18$	0.105151	−	0.0428379i	0.0247843	−	0.0100970i
$19$	−3.08391	+	0.826331i	−0.707497	+	0.189573i	−0.594586	−	0.804032i	$-0.702684\pi$
$19$	−3.08391	+	0.826331i	−0.707497	+	0.189573i	−0.112911	+	0.993605i	$0.536017\pi$
$20$	6.39581	−	3.59378i	1.43015	−	0.803594i
$21$		0			0
$22$	1.72174	−	1.30525i	0.367077	−	0.278280i
$23$	3.02830	+	1.74839i	0.631444	+	0.364564i	0.781311	−	0.624142i	$-0.214551\pi$
$23$	3.02830	+	1.74839i	0.631444	+	0.364564i	−0.149867	+	0.988706i	$0.547885\pi$
$24$	3.00879	−	3.78218i	0.614166	−	0.772035i
$25$	−7.32261	+	4.22771i	−1.46452	+	0.845542i
$26$	−5.91210	+	0.743280i	−1.15946	+	0.145769i
$27$	−3.72174	+	3.72174i	−0.716250	+	0.716250i
$28$		0			0
$29$	0.851361	+	0.851361i	0.158094	+	0.158094i	0.781721	−	0.623628i	$-0.214342\pi$
$29$	0.851361	+	0.851361i	0.158094	+	0.158094i	−0.623628	+	0.781721i	$0.714342\pi$
$30$	−5.43705	+	7.00075i	−0.992664	+	1.27816i
$31$	−1.97932	−	3.42828i	−0.355496	−	0.615738i	0.631706	−	0.775208i	$-0.282355\pi$
$31$	−1.97932	−	3.42828i	−0.355496	−	0.615738i	−0.987203	+	0.159470i	$0.949021\pi$
$32$	−0.901629	+	5.58454i	−0.159387	+	0.987216i
$33$	−1.30525	+	2.26076i	−0.227215	+	0.393548i
$34$	10.0699	+	1.38554i	1.72697	+	0.237618i
$35$		0			0
$36$	0.0433661	−	0.154606i	0.00722769	−	0.0257676i
$37$	2.17113	+	8.10278i	0.356932	+	1.33209i	0.878036	+	0.478595i	$0.158854\pi$
$37$	2.17113	+	8.10278i	0.356932	+	1.33209i	−0.521103	+	0.853494i	$0.674479\pi$
$38$	−1.75218	+	4.16131i	−0.284242	+	0.675054i
$39$	6.23495	−	3.59975i	0.998391	−	0.576421i
$40$	1.53404	−	10.2611i	0.242553	−	1.62242i
$41$		−	2.67573i		−	0.417879i	−0.977929	−	0.208939i	$-0.932999\pi$
$41$		−	2.67573i		−	0.417879i	0.977929	−	0.208939i	$-0.0670011\pi$
$42$		0			0
$43$	−4.25592	+	4.25592i	−0.649021	+	0.649021i	−0.952757	−	0.303735i	$-0.901766\pi$
$43$	−4.25592	+	4.25592i	−0.649021	+	0.649021i	0.303735	+	0.952757i	$0.401766\pi$
$44$	0.0356509	−	3.05530i	0.00537457	−	0.460604i
$45$	−0.0762231	+	0.284468i	−0.0113627	+	0.0424061i
$46$	4.57972	−	1.86576i	0.675243	−	0.275091i
$47$	1.17729	−	2.03913i	0.171726	−	0.297438i	−0.767298	−	0.641291i	$-0.778399\pi$
$47$	1.17729	−	2.03913i	0.171726	−	0.297438i	0.939023	+	0.343854i	$0.111732\pi$
$48$	−1.61446	−	6.64146i	−0.233028	−	0.958612i
$49$		0			0
$50$	−1.62994	+	11.8462i	−0.230508	+	1.67530i
$51$	−11.8630	+	3.17869i	−1.66116	+	0.445106i
$52$	−4.29826	+	7.24816i	−0.596061	+	1.00514i
$53$	4.66701	+	1.25052i	0.641064	+	0.171772i	0.564685	−	0.825306i	$-0.308998\pi$
$53$	4.66701	+	1.25052i	0.641064	+	0.171772i	0.0763784	+	0.997079i	$0.475664\pi$
$54$	0.928499	+	7.38535i	0.126353	+	1.00502i
$55$			5.60406i			0.755651i
$56$		0			0
$57$		−	5.45542i		−	0.722588i
$58$	1.68942	−	0.212397i	0.221832	−	0.0278891i
$59$	5.27509	+	1.41346i	0.686758	+	0.184016i	0.585292	−	0.810823i	$-0.300980\pi$
$59$	5.27509	+	1.41346i	0.686758	+	0.184016i	0.101466	+	0.994839i	$0.467647\pi$
$60$	3.10298	+	12.1456i	0.400593	+	1.56799i
$61$	1.92093	−	0.514711i	0.245950	−	0.0659020i	−0.133738	−	0.991017i	$-0.542698\pi$
$61$	1.92093	−	0.514711i	0.245950	−	0.0659020i	0.379688	+	0.925115i	$0.376031\pi$
$62$	−5.54611	−	0.763102i	−0.704357	−	0.0969140i
$63$		0			0
$64$	5.45542	+	5.85136i	0.681927	+	0.731420i
$65$	7.72771	−	13.3848i	0.958504	−	1.66018i
$66$	1.39287	+	3.41897i	0.171451	+	0.420846i
$67$	2.08734	−	7.79006i	0.255009	−	0.951708i	−0.713076	−	0.701087i	$-0.752699\pi$
$67$	2.08734	−	7.79006i	0.255009	−	0.951708i	0.968085	−	0.250621i	$-0.0806348\pi$
$68$	10.2827	−	10.0455i	1.24696	−	1.21819i
$69$	−4.22496	+	4.22496i	−0.508626	+	0.508626i
$70$		0			0
$71$		−	14.4738i		−	1.71772i	−0.512207	−	0.858862i	$-0.671172\pi$
$71$		−	14.4738i		−	1.71772i	0.512207	−	0.858862i	$-0.328828\pi$
$72$	−0.135066	−	0.182550i	−0.0159177	−	0.0215137i
$73$	2.88178	−	1.66380i	0.337287	−	0.194733i	−0.321785	−	0.946813i	$-0.604283\pi$
$73$	2.88178	−	1.66380i	0.337287	−	0.194733i	0.659072	+	0.752080i	$0.270949\pi$
$74$	10.9336	+	4.60375i	1.27100	+	0.535175i
$75$	−3.73940	−	13.9556i	−0.431788	−	1.61146i
$76$	3.12796	+	5.56679i	0.358802	+	0.638555i
$77$		0			0
$78$	1.38784	−	10.0866i	0.157142	−	1.14208i
$79$	7.90931	−	13.6993i	0.889867	−	1.54129i	0.0498344	−	0.998757i	$-0.484131\pi$
$79$	7.90931	−	13.6993i	0.889867	−	1.54129i	0.840032	−	0.542537i	$-0.182536\pi$
$80$	−10.1302	−	10.6144i	−1.13259	−	1.18673i
$81$	−4.37635	−	7.58006i	−0.486261	−	0.842228i
$82$	−2.98860	−	2.32106i	−0.330036	−	0.256318i
$83$	−1.20825	−	1.20825i	−0.132622	−	0.132622i	0.637680	−	0.770302i	$-0.279894\pi$
$83$	−1.20825	−	1.20825i	−0.132622	−	0.132622i	−0.770302	+	0.637680i	$0.779894\pi$
$84$		0			0
$85$	−18.6430	+	18.6430i	−2.02212	+	2.02212i
$86$	1.06177	+	8.44535i	0.114493	+	0.910686i
$87$	−1.78168	+	1.02865i	−0.191016	+	0.110283i
$88$	−3.38163	−	2.69014i	−0.360483	−	0.286770i
$89$	10.9417	+	6.31718i	1.15982	+	0.669620i	0.951260	−	0.308390i	$-0.0997902\pi$
$89$	10.9417	+	6.31718i	1.15982	+	0.669620i	0.208556	+	0.978010i	$0.433124\pi$
$90$	0.251611	+	0.331898i	0.0265222	+	0.0349851i
$91$		0			0
$92$	1.88876	−	6.73368i	0.196917	−	0.702034i
$93$	6.53371	−	1.75070i	0.677514	−	0.181539i
$94$	−1.25632	−	3.08379i	−0.129580	−	0.318069i
$95$	−5.85567	−	10.1423i	−0.600779	−	1.04058i
$96$	−8.81850	−	3.95789i	−0.900035	−	0.403950i
$97$	−1.08890			−0.110561			−0.0552805	−	0.998471i	$-0.517605\pi$
$97$	−1.08890			−0.110561			−0.0552805	+	0.998471i	$0.517605\pi$
$98$		0			0
$99$	0.0867323	+	0.0867323i	0.00871692	+	0.00871692i
$100$	11.8174	+	12.0965i	1.18174	+	1.20965i
$101$	3.93505	+	1.05439i	0.391552	+	0.104916i	0.449223	−	0.893420i	$-0.351701\pi$
$101$	3.93505	+	1.05439i	0.391552	+	0.104916i	−0.0576713	+	0.998336i	$0.518368\pi$
$102$	−6.74021	+	16.0075i	−0.667380	+	1.58498i
$103$	−0.724259	−	0.418151i	−0.0713633	−	0.0412016i	0.463894	−	0.885891i	$-0.346452\pi$
$103$	−0.724259	−	0.418151i	−0.0713633	−	0.0412016i	−0.535257	+	0.844689i	$0.679785\pi$
$104$	4.36716	+	11.0883i	0.428235	+	1.08729i
$105$		0			0
$106$	5.44514	−	4.12796i	0.528879	−	0.400943i
$107$	−2.29419	−	8.56204i	−0.221788	−	0.827724i	−0.983666	−	0.180004i	$-0.942389\pi$
$107$	−2.29419	−	8.56204i	−0.221788	−	0.827724i	0.761878	−	0.647721i	$-0.224278\pi$
$108$	9.05434	+	5.36935i	0.871254	+	0.516666i
$109$	−2.62095	+	9.78152i	−0.251042	+	0.936900i	0.719208	+	0.694795i	$0.244505\pi$
$109$	−2.62095	+	9.78152i	−0.251042	+	0.936900i	−0.970250	+	0.242106i	$0.922162\pi$
$110$	6.25933	+	4.86124i	0.596804	+	0.463501i
$111$	−14.3338			−1.36050
$112$		0			0
$113$	3.37756			0.317735			0.158867	−	0.987300i	$-0.449216\pi$
$113$	3.37756			0.317735			0.158867	+	0.987300i	$0.449216\pi$
$114$	−6.09332	−	4.73230i	−0.570691	−	0.443220i
$115$	−3.31981	+	12.3897i	−0.309574	+	1.15534i
$116$	1.22826	−	2.07121i	0.114041	−	0.192307i
$117$	−0.0875528	−	0.326752i	−0.00809426	−	0.0302082i
$118$	6.15461	−	4.66580i	0.566577	−	0.429522i
$119$		0			0
$120$	16.2574	+	7.06988i	1.48409	+	0.645389i
$121$	−7.50494	−	4.33298i	−0.682268	−	0.393907i
$122$	1.09141	−	2.59203i	0.0988118	−	0.234671i
$123$	4.41627	+	1.18334i	0.398202	+	0.106698i
$124$	−5.66330	+	5.53266i	−0.508579	+	0.496848i
$125$	−8.96260	−	8.96260i	−0.801639	−	0.801639i
$126$		0			0
$127$	16.5443			1.46807			0.734035	−	0.679111i	$-0.237635\pi$
$127$	16.5443			1.46807			0.734035	+	0.679111i	$0.237635\pi$
$128$	11.2679	−	1.01756i	0.995947	−	0.0899400i
$129$	−5.14219	−	8.90654i	−0.452745	−	0.784177i
$130$	−8.24646	−	20.2419i	−0.723262	−	1.77533i
$131$	−14.0707	+	3.77023i	−1.22936	+	0.329407i	−0.814331	−	0.580400i	$-0.802896\pi$
$131$	−14.0707	+	3.77023i	−1.22936	+	0.329407i	−0.415031	+	0.909807i	$0.636229\pi$
$132$	5.02699	+	1.41004i	0.437544	+	0.122729i
$133$		0			0
$134$	−6.89029	−	9.08890i	−0.595230	−	0.785161i
$135$	−16.7202	−	9.65339i	−1.43904	−	0.830831i
$136$	−2.30038	−	20.1989i	−0.197256	−	1.73204i
$137$	−8.40280	+	4.85136i	−0.717900	+	0.414480i	−0.813979	−	0.580894i	$-0.802703\pi$
$137$	−8.40280	+	4.85136i	−0.717900	+	0.414480i	0.0960793	+	0.995374i	$0.469370\pi$
$138$	1.05404	+	8.38393i	0.0897261	+	0.713688i
$139$	7.04920	−	7.04920i	0.597905	−	0.597905i	−0.341849	−	0.939755i	$-0.611053\pi$
$139$	7.04920	−	7.04920i	0.597905	−	0.597905i	0.939755	+	0.341849i	$0.111053\pi$
$140$		0			0
$141$	2.84492	+	2.84492i	0.239585	+	0.239585i
$142$	−16.1662	−	12.5553i	−1.35664	−	1.05362i
$143$	−3.21852	−	5.57464i	−0.269146	−	0.466175i
$144$	−0.321058	−	0.00749357i	−0.0267548	−	0.000624464i
$145$	−2.20825	+	3.82479i	−0.183385	+	0.317632i
$146$	0.641455	−	4.66200i	0.0530872	−	0.385830i
$147$		0			0
$148$	14.6264	−	8.21852i	1.20228	−	0.675558i
$149$	2.45652	+	9.16785i	0.201246	+	0.751060i	0.990561	+	0.137072i	$0.0437691\pi$
$149$	2.45652	+	9.16785i	0.201246	+	0.751060i	−0.789315	+	0.613988i	$0.789564\pi$
$150$	−18.8312	−	7.92915i	−1.53756	−	0.647412i
$151$	0.971374	−	0.560823i	0.0790493	−	0.0456391i	−0.459954	−	0.887943i	$-0.652134\pi$
$151$	0.971374	−	0.560823i	0.0790493	−	0.0456391i	0.539004	+	0.842303i	$0.318801\pi$
$152$	8.93106	+	1.33520i	0.724404	+	0.108299i
$153$			0.577063i			0.0466528i
$154$		0			0
$155$	10.2679	−	10.2679i	0.824734	−	0.824734i
$156$	−10.0621	−	10.2997i	−0.805616	−	0.824639i
$157$	5.47519	−	20.4337i	0.436968	−	1.63079i	−0.299344	−	0.954145i	$-0.596768\pi$
$157$	5.47519	−	20.4337i	0.436968	−	1.63079i	0.736312	−	0.676642i	$-0.236565\pi$
$158$	−8.44025	−	20.7176i	−0.671470	−	1.64820i
$159$	−4.12796	+	7.14983i	−0.327368	+	0.567019i
$160$	−20.6430	+	2.10728i	−1.63197	+	0.166595i
$161$		0			0
$162$	−12.2626	−	1.68725i	−0.963445	−	0.132563i
$163$	15.4290	−	4.13420i	1.20850	−	0.323816i	0.402324	−	0.915497i	$-0.368202\pi$
$163$	15.4290	−	4.13420i	1.20850	−	0.323816i	0.806172	+	0.591682i	$0.201536\pi$
$164$	−5.18492	+	1.32465i	−0.404874	+	0.103438i
$165$	−9.24946	−	2.47839i	−0.720069	−	0.192942i
$166$	−2.39762	+	0.301433i	−0.186091	+	0.0233957i
$167$		−	16.8535i		−	1.30417i	−0.758148	−	0.652083i	$-0.773896\pi$
$167$		−	16.8535i		−	1.30417i	0.758148	−	0.652083i	$-0.226104\pi$
$168$		0			0
$169$			4.75270i			0.365592i
$170$	4.65105	+	36.9947i	0.356719	+	2.83737i
$171$	−0.247596	−	0.0663431i	−0.0189341	−	0.00507338i
$172$	10.3539	+	6.14000i	0.789477	+	0.468171i
$173$	2.88628	−	0.773375i	0.219439	−	0.0587986i	−0.147424	−	0.989073i	$-0.547098\pi$
$173$	2.88628	−	0.773375i	0.219439	−	0.0587986i	0.366864	+	0.930275i	$0.380432\pi$
$174$	−0.396584	+	2.88231i	−0.0300650	+	0.218508i
$175$		0			0
$176$	−5.93809	+	1.44348i	−0.447601	+	0.108807i
$177$	−4.66580	+	8.08141i	−0.350703	+	0.607436i
$178$	16.5472	−	6.74125i	1.24027	−	0.505278i
$179$	−5.39897	+	20.1492i	−0.403538	+	1.50602i	0.403198	+	0.915113i	$0.367898\pi$
$179$	−5.39897	+	20.1492i	−0.403538	+	1.50602i	−0.806736	+	0.590912i	$0.798768\pi$
$180$	0.588967	+	0.00687237i	0.0438990	+	0.000512236i
$181$	2.01672	−	2.01672i	0.149902	−	0.149902i	−0.628173	−	0.778074i	$-0.716197\pi$
$181$	2.01672	−	2.01672i	0.149902	−	0.149902i	0.778074	+	0.628173i	$0.216197\pi$
$182$		0			0
$183$			3.39811i			0.251196i
$184$	−5.88264	−	7.95074i	−0.433674	−	0.586136i
$185$	−26.6483	+	15.3854i	−1.95922	+	1.13116i
$186$	3.71225	−	8.81634i	0.272196	−	0.646445i
$187$	2.84205	+	10.6067i	0.207831	+	0.775637i
$188$	−4.53418	−	1.27181i	−0.330689	−	0.0927565i
$189$		0			0
$190$	−16.4077	−	2.25758i	−1.19034	−	0.163782i
$191$	−5.18757	+	8.98513i	−0.375359	+	0.650141i	−0.990381	−	0.138369i	$-0.955814\pi$
$191$	−5.18757	+	8.98513i	−0.375359	+	0.650141i	0.615022	+	0.788510i	$0.289147\pi$
$192$	−12.0703	+	6.41638i	−0.871098	+	0.463062i
$193$	−0.230931	−	0.399985i	−0.0166228	−	0.0287916i	0.857594	−	0.514327i	$-0.171958\pi$
$193$	−0.230931	−	0.399985i	−0.0166228	−	0.0287916i	−0.874217	+	0.485535i	$0.838625\pi$
$194$	−0.944565	+	1.21622i	−0.0678158	+	0.0873198i
$195$	18.6739	+	18.6739i	1.33727	+	1.33727i
$196$		0			0
$197$	4.80599	−	4.80599i	0.342413	−	0.342413i	−0.514861	−	0.857274i	$-0.672157\pi$
$197$	4.80599	−	4.80599i	0.342413	−	0.342413i	0.857274	+	0.514861i	$0.172157\pi$
$198$	0.172110	−	0.0216379i	0.0122313	−	0.00153774i
$199$	11.5211	−	6.65173i	0.816711	−	0.471529i	−0.0325697	−	0.999469i	$-0.510369\pi$
$199$	11.5211	−	6.65173i	0.816711	−	0.471529i	0.849281	+	0.527941i	$0.177036\pi$
$200$	23.7619	−	2.70616i	1.68022	−	0.191354i
$201$	11.9343	+	6.89029i	0.841783	+	0.486003i
$202$	4.59114	−	3.48054i	0.323031	−	0.244890i
$203$		0			0
$204$	12.0325	+	21.4141i	0.842442	+	1.49928i
$205$	9.48057	−	2.54031i	0.662152	−	0.177423i
$206$	−1.09530	+	0.446221i	−0.0763134	+	0.0310897i
$207$	0.140372	+	0.243131i	0.00975651	+	0.0168988i
$208$	16.1731	+	4.74070i	1.12140	+	0.328708i
$209$	−4.87766			−0.337395
$210$		0			0
$211$	−8.83298	−	8.83298i	−0.608088	−	0.608088i	0.334358	−	0.942446i	$-0.391480\pi$
$211$	−8.83298	−	8.83298i	−0.608088	−	0.608088i	−0.942446	+	0.334358i	$0.891480\pi$
$212$	0.112749	−	9.66264i	0.00774361	−	0.663633i
$213$	23.8889	+	6.40101i	1.63684	+	0.438590i
$214$	−11.5533	−	4.86469i	−0.789767	−	0.332543i
$215$	−19.1200	−	11.0389i	−1.30397	−	0.752849i
$216$	13.8514	−	5.45542i	0.942466	−	0.371194i
$217$		0			0
$218$	8.65173	+	11.4124i	0.585969	+	0.772945i
$219$	1.47162	+	5.49217i	0.0994430	+	0.371126i
$220$	10.8593	−	2.77436i	0.732135	−	0.187047i
$221$	7.83809	−	29.2521i	0.527247	−	1.96771i
$222$	−12.4338	+	16.0098i	−0.834504	+	1.07451i
$223$	−10.4370			−0.698916			−0.349458	−	0.936952i	$-0.613634\pi$
$223$	−10.4370			−0.698916			−0.349458	+	0.936952i	$0.613634\pi$
$224$		0			0
$225$	−0.678855			−0.0452570
$226$	2.92987	−	3.77250i	0.194892	−	0.250943i
$227$	−6.88634	+	25.7002i	−0.457062	+	1.70578i	0.224891	+	0.974384i	$0.427798\pi$
$227$	−6.88634	+	25.7002i	−0.457062	+	1.70578i	−0.681953	+	0.731396i	$0.738869\pi$
$228$	−10.5713	+	2.70077i	−0.700101	+	0.178863i
$229$	−1.19932	−	4.47592i	−0.0792532	−	0.295777i	0.914911	−	0.403656i	$-0.132261\pi$
$229$	−1.19932	−	4.47592i	−0.0792532	−	0.295777i	−0.994164	+	0.107879i	$0.965594\pi$
$230$	10.9586	+	14.4554i	0.722591	+	0.953162i
$231$		0			0
$232$	−1.24795	−	3.16855i	−0.0819316	−	0.208025i
$233$	12.6599	+	7.30921i	0.829379	+	0.478842i	0.853640	−	0.520863i	$-0.174390\pi$
$233$	12.6599	+	7.30921i	0.829379	+	0.478842i	−0.0242608	+	0.999706i	$0.507723\pi$
$234$	−0.440906	−	0.185650i	−0.0288229	−	0.0121363i
$235$	8.34270	+	2.23542i	0.544218	+	0.145823i
$236$	0.127439	−	10.9216i	0.00829557	−	0.710936i
$237$	19.1128	+	19.1128i	1.24151	+	1.24151i
$238$		0			0
$239$	7.92589			0.512683			0.256342	−	0.966586i	$-0.417483\pi$
$239$	7.92589			0.512683			0.256342	+	0.966586i	$0.417483\pi$
$240$	21.9991	−	12.0257i	1.42003	−	0.776253i
$241$	−2.15891	−	3.73935i	−0.139068	−	0.240872i	0.788076	−	0.615578i	$-0.211077\pi$
$241$	−2.15891	−	3.73935i	−0.139068	−	0.240872i	−0.927144	+	0.374705i	$0.877744\pi$
$242$	−11.3498	+	4.62385i	−0.729592	+	0.297232i
$243$	−0.805712	+	0.215890i	−0.0516864	+	0.0138493i
$244$	−1.94837	−	3.46748i	−0.124731	−	0.221983i
$245$		0			0
$246$	5.15260	−	3.90618i	0.328518	−	0.249049i
$247$	11.6499	+	6.72605i	0.741263	+	0.427968i
$248$	1.26696	+	11.1248i	0.0804523	+	0.706426i
$249$	2.52855	−	1.45986i	0.160240	−	0.0925147i
$250$	−17.7852	+	2.23599i	−1.12483	+	0.141416i
$251$	−8.13989	+	8.13989i	−0.513785	+	0.513785i	−0.915684	−	0.401899i	$-0.868350\pi$
$251$	−8.13989	+	8.13989i	−0.513785	+	0.513785i	0.401899	+	0.915684i	$0.368350\pi$
$252$		0			0
$253$	3.77752	+	3.77752i	0.237491	+	0.237491i
$254$	14.3514	−	18.4788i	0.900484	−	1.15947i
$255$	−22.5253	−	39.0150i	−1.41059	−	2.44321i
$256$	8.63776	−	13.4681i	0.539860	−	0.841755i
$257$	−2.61446	+	4.52838i	−0.163086	+	0.282473i	−0.935974	−	0.352070i	$-0.885478\pi$
$257$	−2.61446	+	4.52838i	−0.163086	+	0.282473i	0.772888	+	0.634542i	$0.218811\pi$
$258$	−14.4086	−	1.98251i	−0.897038	−	0.123426i
$259$		0			0
$260$	−29.7622	−	8.34814i	−1.84577	−	0.517730i
$261$	0.0250188	+	0.0933715i	0.00154863	+	0.00577955i
$262$	−7.99454	+	18.9865i	−0.493904	+	1.17299i
$263$	−6.75620	+	3.90069i	−0.416605	+	0.240527i	−0.693624	−	0.720337i	$-0.743987\pi$
$263$	−6.75620	+	3.90069i	−0.416605	+	0.240527i	0.277019	+	0.960865i	$0.410654\pi$
$264$	5.93558	−	4.39165i	0.365310	−	0.270288i
$265$			17.7233i			1.08873i
$266$		0			0
$267$	−15.2654	+	15.2654i	−0.934228	+	0.934228i
$268$	−16.1286	−	0.188197i	−0.985213	−	0.0114960i
$269$	4.47436	−	16.6986i	0.272807	−	1.01813i	−0.684490	−	0.729022i	$-0.739975\pi$
$269$	4.47436	−	16.6986i	0.272807	−	1.01813i	0.957297	−	0.289107i	$-0.0933582\pi$
$270$	−25.2860	+	10.3014i	−1.53886	+	0.626924i
$271$	1.70981	−	2.96147i	0.103863	−	0.179897i	−0.809410	−	0.587244i	$-0.800213\pi$
$271$	1.70981	−	2.96147i	0.103863	−	0.179897i	0.913273	+	0.407347i	$0.133546\pi$
$272$	−24.5563	−	14.9522i	−1.48894	−	0.906610i
$273$		0			0
$274$	−1.87038	+	13.5936i	−0.112994	+	0.821222i
$275$	−12.4776	+	3.34338i	−0.752430	+	0.201613i
$276$	10.2786	+	6.09534i	0.618698	+	0.366897i
$277$	7.06124	+	1.89205i	0.424269	+	0.113682i	0.464635	−	0.885503i	$-0.346186\pi$
$277$	7.06124	+	1.89205i	0.424269	+	0.113682i	−0.0403659	+	0.999185i	$0.512852\pi$
$278$	−1.75863	−	13.9883i	−0.105476	−	0.838961i
$279$		−	0.317825i		−	0.0190277i
$280$		0			0
$281$		−	15.8438i		−	0.945160i	−0.881288	−	0.472580i	$-0.843323\pi$
$281$		−	15.8438i		−	0.945160i	0.881288	−	0.472580i	$-0.156677\pi$
$282$	5.64539	−	0.709749i	0.336178	−	0.0422649i
$283$	−18.8311	−	5.04577i	−1.11939	−	0.299940i	−0.348754	−	0.937214i	$-0.613395\pi$
$283$	−18.8311	−	5.04577i	−1.11939	−	0.299940i	−0.770637	+	0.637274i	$0.780062\pi$
$284$	−28.0467	+	7.16543i	−1.66427	+	0.425190i
$285$	19.3295	−	5.17932i	1.14498	−	0.306796i
$286$	−9.01838	−	1.24086i	−0.533268	−	0.0733735i
$287$		0			0
$288$	−0.286871	+	0.352099i	−0.0169041	+	0.0207476i
$289$	−17.3305	+	30.0174i	−1.01944	+	1.76573i
$290$	2.35648	+	5.78427i	0.138377	+	0.339664i
$291$	0.481564	−	1.79722i	0.0282298	−	0.105355i
$292$	−4.65070	−	4.76051i	−0.272161	−	0.278588i
$293$	19.5117	−	19.5117i	1.13989	−	1.13989i	0.151416	−	0.988470i	$-0.451617\pi$
$293$	19.5117	−	19.5117i	1.13989	−	1.13989i	0.988470	−	0.151416i	$-0.0483832\pi$
$294$		0			0
$295$			20.0325i			1.16634i
$296$	3.50816	−	23.4658i	0.203907	−	1.36392i
$297$	−6.96379	+	4.02055i	−0.404080	+	0.233296i
$298$	12.3708	+	5.20889i	0.716618	+	0.301743i
$299$	−3.81326	−	14.2313i	−0.220526	−	0.823016i
$300$	−25.1914	+	14.1550i	−1.45443	+	0.817237i
$301$		0			0
$302$	0.216218	−	1.57144i	0.0124420	−	0.0904263i
$303$	−3.48054	+	6.02847i	−0.199952	+	0.346326i
$304$	9.23857	−	8.81714i	0.529868	−	0.505698i
$305$	3.64742	+	6.31752i	0.208851	+	0.361740i
$306$	0.644539	+	0.500573i	0.0368458	+	0.0286159i
$307$	−2.94441	−	2.94441i	−0.168046	−	0.168046i	0.618074	−	0.786120i	$-0.287913\pi$
$307$	−2.94441	−	2.94441i	−0.168046	−	0.168046i	−0.786120	+	0.618074i	$0.787913\pi$
$308$		0			0
$309$	1.01046	−	1.01046i	0.0574830	−	0.0574830i
$310$	−2.56162	−	20.3753i	−0.145490	−	1.15724i
$311$	−9.56059	+	5.51981i	−0.542131	+	0.313000i	−0.745942	−	0.666011i	$-0.768001\pi$
$311$	−9.56059	+	5.51981i	−0.542131	+	0.313000i	0.203811	+	0.979010i	$0.434667\pi$
$312$	−20.2325	+	2.30420i	−1.14544	+	0.130450i
$313$	29.8948	+	17.2597i	1.68975	+	0.975578i	0.954701	+	0.297566i	$0.0961748\pi$
$313$	29.8948	+	17.2597i	1.68975	+	0.975578i	0.735050	+	0.678013i	$0.237159\pi$
$314$	−18.0735	−	23.8406i	−1.01995	−	1.34540i
$315$		0			0
$316$	−30.4616	−	8.54432i	−1.71360	−	0.480655i
$317$	−7.39906	+	1.98257i	−0.415573	+	0.111352i	−0.460546	−	0.887636i	$-0.652346\pi$
$317$	−7.39906	+	1.98257i	−0.415573	+	0.111352i	0.0449733	+	0.998988i	$0.485680\pi$
$318$	4.40506	+	10.8128i	0.247024	+	0.606349i
$319$	0.919714	+	1.59299i	0.0514941	+	0.0891904i
$320$	−15.5531	+	24.8847i	−0.869443	+	1.39110i
$321$	15.1462			0.845379
$322$		0			0
$323$	−16.2265	−	16.2265i	−0.902866	−	0.902866i
$324$	−12.5218	+	12.2329i	−0.695653	+	0.679606i
$325$	34.4121	+	9.22069i	1.90884	+	0.511472i
$326$	8.76631	−	20.8194i	0.485521	−	1.15308i
$327$	−14.9852	−	8.65173i	−0.828685	−	0.478442i
$328$	−3.01811	+	6.94026i	−0.166647	+	0.383212i
$329$		0			0
$330$	−10.7916	+	8.18112i	−0.594059	+	0.450356i
$331$	4.37717	+	16.3358i	0.240591	+	0.897897i	0.975549	+	0.219784i	$0.0705353\pi$
$331$	4.37717	+	16.3358i	0.240591	+	0.897897i	−0.734958	+	0.678113i	$0.762798\pi$
$332$	−1.74313	+	2.93945i	−0.0956668	+	0.161323i
$333$	−0.174312	+	0.650543i	−0.00955226	+	0.0356495i
$334$	−18.8242	−	14.6196i	−1.03001	−	0.799948i
$335$	29.5832			1.61631
$336$		0			0
$337$	29.2992			1.59603			0.798014	−	0.602639i	$-0.205884\pi$
$337$	29.2992			1.59603			0.798014	+	0.602639i	$0.205884\pi$
$338$	5.30842	+	4.12272i	0.288740	+	0.224247i
$339$	−1.49372	+	5.57465i	−0.0811279	+	0.302773i
$340$	45.3551	+	26.8962i	2.45972	+	1.45865i
$341$	−1.56529	−	5.84176i	−0.0847655	−	0.316349i
$342$	−0.288877	+	0.218998i	−0.0156207	+	0.0118420i
$343$		0			0
$344$	15.8394	−	6.23843i	0.854005	−	0.336353i
$345$	−18.9809	−	10.9586i	−1.02190	−	0.589993i
$346$	1.63989	−	3.89463i	0.0881612	−	0.209377i
$347$	31.8657	+	8.53839i	1.71064	+	0.458365i	0.975582	−	0.219637i	$-0.0704874\pi$
$347$	31.8657	+	8.53839i	1.71064	+	0.458365i	0.735060	+	0.678002i	$0.237154\pi$
$348$	2.87532	+	2.94322i	0.154134	+	0.157773i
$349$	−10.6143	−	10.6143i	−0.568172	−	0.568172i	0.363444	−	0.931616i	$-0.381601\pi$
$349$	−10.6143	−	10.6143i	−0.568172	−	0.568172i	−0.931616	+	0.363444i	$0.881601\pi$
$350$		0			0
$351$	22.1765			1.18369
$352$	−3.53873	+	7.88458i	−0.188615	+	0.420250i
$353$	−16.8410	−	29.1694i	−0.896354	−	1.55253i	−0.832120	−	0.554595i	$-0.812873\pi$
$353$	−16.8410	−	29.1694i	−0.896354	−	1.55253i	−0.0642331	−	0.997935i	$-0.520460\pi$
$354$	4.97901	+	12.2216i	0.264631	+	0.649570i
$355$	51.2832	−	13.7413i	2.72183	−	0.729312i
$356$	6.82437	−	24.3298i	0.361691	−	1.28947i
$357$		0			0
$358$	17.8219	+	23.5087i	0.941919	+	1.24247i
$359$	−19.4841	−	11.2492i	−1.02833	−	0.593709i	−0.111827	−	0.993728i	$-0.535670\pi$
$359$	−19.4841	−	11.2492i	−1.02833	−	0.593709i	−0.916507	+	0.400019i	$0.869004\pi$
$360$	0.518575	−	0.651873i	0.0273313	−	0.0343567i
$361$	−7.62681	+	4.40334i	−0.401411	+	0.231755i
$362$	−0.503131	−	4.00194i	−0.0264440	−	0.210337i
$363$	10.4706	−	10.4706i	0.549564	−	0.549564i
$364$		0			0
$365$	8.63105	+	8.63105i	0.451770	+	0.451770i
$366$	3.79545	+	2.94769i	0.198391	+	0.154078i
$367$	8.46978	+	14.6701i	0.442119	+	0.765773i	0.997847	−	0.0655918i	$-0.0208935\pi$
$367$	8.46978	+	14.6701i	0.442119	+	0.765773i	−0.555727	+	0.831365i	$0.687560\pi$
$368$	−13.9833	−	0.326373i	−0.728930	−	0.0170134i
$369$	0.107412	−	0.186044i	0.00559166	−	0.00968504i
$370$	−5.93165	+	43.1103i	−0.308372	+	2.24120i
$371$		0			0
$372$	−6.62704	−	11.7941i	−0.343596	−	0.611493i
$373$	−3.36961	−	12.5756i	−0.174472	−	0.651138i	−0.996641	−	0.0818944i	$-0.973903\pi$
$373$	−3.36961	−	12.5756i	−0.174472	−	0.651138i	0.822169	−	0.569243i	$-0.192764\pi$
$374$	14.3122	+	6.02639i	0.740069	+	0.311617i
$375$	18.7564	−	10.8290i	0.968577	−	0.559208i
$376$	−5.35369	+	3.96112i	−0.276096	+	0.204279i
$377$		−	5.07295i		−	0.261270i
$378$		0			0
$379$	0.491289	−	0.491289i	0.0252358	−	0.0252358i	−0.694376	−	0.719612i	$-0.744320\pi$
$379$	0.491289	−	0.491289i	0.0252358	−	0.0252358i	0.719612	+	0.694376i	$0.244320\pi$
$380$	−16.7544	+	16.3680i	−0.859485	+	0.839658i
$381$	−7.31670	+	27.3063i	−0.374846	+	1.39894i
$382$	5.53580	+	13.5883i	0.283236	+	0.695237i
$383$	−3.73202	+	6.46404i	−0.190697	+	0.330297i	−0.945481	−	0.325676i	$-0.894408\pi$
$383$	−3.73202	+	6.46404i	−0.190697	+	0.330297i	0.754784	+	0.655973i	$0.227741\pi$
$384$	−3.30372	+	19.0475i	−0.168592	+	0.972016i
$385$		0			0
$386$	−0.647076	−	0.0890327i	−0.0329353	−	0.00453164i
$387$	−0.466760	+	0.125068i	−0.0237268	+	0.00635756i
$388$	0.539073	+	2.11003i	0.0273673	+	0.107120i
$389$	13.9445	+	3.73643i	0.707016	+	0.189444i	0.594371	−	0.804191i	$-0.297401\pi$
$389$	13.9445	+	3.73643i	0.707016	+	0.189444i	0.112645	+	0.993635i	$0.464068\pi$
$390$	37.0562	−	4.65877i	1.87641	−	0.235906i
$391$			25.1333i			1.27105i
$392$		0			0
$393$		−	24.8910i		−	1.25558i
$394$	−1.19900	−	9.53690i	−0.0604046	−	0.480462i
$395$	56.0481	+	15.0180i	2.82009	+	0.755640i
$396$	0.125128	−	0.211004i	0.00628794	−	0.0106034i
$397$	−30.2771	+	8.11273i	−1.51957	+	0.407166i	−0.919599	−	0.392858i	$-0.871486\pi$
$397$	−30.2771	+	8.11273i	−1.51957	+	0.407166i	−0.599967	+	0.800025i	$0.704820\pi$
$398$	2.56449	−	18.6383i	0.128546	−	0.934255i
$399$		0			0
$400$	17.5897	−	28.8879i	0.879484	−	1.44439i
$401$	6.51072	−	11.2769i	0.325130	−	0.563141i	−0.656409	−	0.754405i	$-0.727925\pi$
$401$	6.51072	−	11.2769i	0.325130	−	0.563141i	0.981539	+	0.191264i	$0.0612587\pi$
$402$	18.0484	−	7.35282i	0.900172	−	0.366726i
$403$	−4.31692	+	16.1110i	−0.215041	+	0.802545i
$404$	0.0950654	−	8.14717i	0.00472968	−	0.405337i
$405$	22.7026	−	22.7026i	1.12810	−	1.12810i
$406$		0			0
$407$			12.8158i			0.635253i
$408$	34.3556	+	5.13618i	1.70085	+	0.254279i
$409$	3.34970	−	1.93395i	0.165632	−	0.0956276i	−0.414893	−	0.909870i	$-0.636181\pi$
$409$	3.34970	−	1.93395i	0.165632	−	0.0956276i	0.580524	+	0.814243i	$0.302848\pi$
$410$	5.38657	−	12.7927i	0.266024	−	0.631787i
$411$	−4.29101	−	16.0143i	−0.211660	−	0.789926i
$412$	−0.451723	+	1.61045i	−0.0222548	+	0.0793412i
$413$		0			0
$414$	0.393326	+	0.0541185i	0.0193309	+	0.00265978i
$415$	3.13393	−	5.42812i	0.153838	−	0.266456i
$416$	19.3244	−	13.9519i	0.947455	−	0.684047i
$417$	8.51716	+	14.7522i	0.417087	+	0.722416i
$418$	−4.23113	+	5.44800i	−0.206951	+	0.266471i
$419$	−1.29097	−	1.29097i	−0.0630678	−	0.0630678i	0.674869	−	0.737937i	$-0.264200\pi$
$419$	−1.29097	−	1.29097i	−0.0630678	−	0.0630678i	−0.737937	+	0.674869i	$0.764200\pi$
$420$		0			0
$421$	3.80050	−	3.80050i	0.185225	−	0.185225i	−0.608403	−	0.793628i	$-0.708190\pi$
$421$	3.80050	−	3.80050i	0.185225	−	0.185225i	0.793628	+	0.608403i	$0.208190\pi$
$422$	−17.5280	+	2.20365i	−0.853249	+	0.107272i
$423$	0.163714	−	0.0945205i	0.00796006	−	0.00459574i
$424$	−10.6947	−	8.50778i	−0.519380	−	0.413174i
$425$	−52.6317	−	30.3869i	−2.55301	−	1.47398i
$426$	27.8719	−	21.1297i	1.35040	−	1.02374i
$427$		0			0
$428$	−15.4554	+	8.68434i	−0.747066	+	0.419774i
$429$	10.6243	−	2.84677i	0.512946	−	0.137443i
$430$	−28.9153	+	11.7800i	−1.39442	+	0.568080i
$431$	0.206239	+	0.357217i	0.00993420	+	0.0172065i	0.870950	−	0.491372i	$-0.163504\pi$
$431$	0.206239	+	0.357217i	0.00993420	+	0.0172065i	−0.861016	+	0.508579i	$0.830171\pi$
$432$	5.92204	−	20.2033i	0.284924	−	0.972031i
$433$	5.11277			0.245704			0.122852	−	0.992425i	$-0.460796\pi$
$433$	5.11277			0.245704			0.122852	+	0.992425i	$0.460796\pi$
$434$		0			0
$435$	−5.33620	−	5.33620i	−0.255851	−	0.255851i
$436$	20.2518	+	0.236308i	0.969884	+	0.0113171i
$437$	−10.7837	−	2.88950i	−0.515856	−	0.138223i
$438$	7.41092	+	3.12048i	0.354108	+	0.149102i
$439$	26.2547	+	15.1581i	1.25307	+	0.723459i	0.971717	−	0.236147i	$-0.0758846\pi$
$439$	26.2547	+	15.1581i	1.25307	+	0.723459i	0.281350	+	0.959605i	$0.409218\pi$
$440$	6.32115	−	14.5357i	0.301349	−	0.692962i
$441$		0			0
$442$	−25.8734	−	34.1294i	−1.23067	−	1.62337i
$443$	9.23265	+	34.4567i	0.438656	+	1.63709i	0.732162	+	0.681130i	$0.238511\pi$
$443$	9.23265	+	34.4567i	0.438656	+	1.63709i	−0.293506	+	0.955957i	$0.594822\pi$
$444$	7.09611	+	27.7754i	0.336767	+	1.31816i
$445$	−11.9949	+	44.7658i	−0.568615	+	2.12210i
$446$	−9.05360	+	11.6574i	−0.428701	+	0.551995i
$447$	−16.2179			−0.767079
$448$		0			0
$449$	−32.8741			−1.55142			−0.775712	−	0.631087i	$-0.782609\pi$
$449$	−32.8741			−1.55142			−0.775712	+	0.631087i	$0.782609\pi$
$450$	−0.588872	+	0.758233i	−0.0277597	+	0.0357434i
$451$	1.05802	−	3.94857i	0.0498200	−	0.185931i
$452$	−1.67211	−	6.54491i	−0.0786492	−	0.307847i
$453$	0.496046	+	1.85127i	0.0233063	+	0.0869803i
$454$	22.7317	+	29.9852i	1.06685	+	1.40727i
$455$		0			0
$456$	−6.15349	+	14.1502i	−0.288163	+	0.662642i
$457$	6.79262	+	3.92172i	0.317745	+	0.183450i	0.650387	−	0.759603i	$-0.274607\pi$
$457$	6.79262	+	3.92172i	0.317745	+	0.183450i	−0.332642	+	0.943053i	$0.607940\pi$
$458$	−6.03963	−	2.54308i	−0.282213	−	0.118830i
$459$	−36.5415	−	9.79128i	−1.70561	−	0.457018i
$460$	25.6517	+	0.299318i	1.19602	+	0.0139558i
$461$	11.5635	+	11.5635i	0.538564	+	0.538564i	0.923107	−	0.384543i	$-0.125641\pi$
$461$	11.5635	+	11.5635i	0.538564	+	0.538564i	−0.384543	+	0.923107i	$0.625641\pi$
$462$		0			0
$463$	7.72659			0.359085			0.179543	−	0.983750i	$-0.442538\pi$
$463$	7.72659			0.359085			0.179543	+	0.983750i	$0.442538\pi$
$464$	−4.62157	−	1.35469i	−0.214551	−	0.0628898i
$465$	12.4061	+	21.4880i	0.575318	+	0.996481i
$466$	19.1457	−	7.79987i	0.886908	−	0.361322i
$467$	2.32823	−	0.623847i	0.107738	−	0.0288682i	−0.204547	−	0.978857i	$-0.565572\pi$
$467$	2.32823	−	0.623847i	0.107738	−	0.0288682i	0.312285	+	0.949988i	$0.398906\pi$
$468$	−0.589822	+	0.331419i	−0.0272645	+	0.0153198i
$469$		0			0
$470$	9.73368	−	7.37909i	0.448981	−	0.340372i
$471$	31.3043	+	18.0735i	1.44243	+	0.832785i
$472$	−12.0881	−	9.61628i	−0.556401	−	0.442625i
$473$	−7.96329	+	4.59761i	−0.366153	+	0.211398i
$474$	37.9270	−	4.76825i	1.74204	−	0.219013i
$475$	19.0888	−	19.0888i	0.875853	−	0.875853i
$476$		0			0
$477$	0.274298	+	0.274298i	0.0125592	+	0.0125592i
$478$	6.87531	−	8.85266i	0.314469	−	0.404911i
$479$	−4.67075	−	8.08997i	−0.213412	−	0.369640i	0.739368	−	0.673301i	$-0.235124\pi$
$479$	−4.67075	−	8.08997i	−0.213412	−	0.369640i	−0.952780	+	0.303661i	$0.901791\pi$
$480$	5.65128	−	35.0031i	0.257944	−	1.59766i
$481$	17.6723	−	30.6093i	0.805786	−	1.39566i
$482$	−6.04933	−	0.832341i	−0.275540	−	0.0379121i
$483$		0			0
$484$	−4.68086	+	16.6879i	−0.212766	+	0.758540i
$485$	−1.03379	−	3.85816i	−0.0469420	−	0.175190i
$486$	−0.457781	+	1.08720i	−0.0207653	+	0.0493162i
$487$	−25.6273	+	14.7959i	−1.16128	+	0.670467i	−0.951611	−	0.307304i	$-0.900573\pi$
$487$	−25.6273	+	14.7959i	−1.16128	+	0.670467i	−0.209672	+	0.977772i	$0.567240\pi$
$488$	−5.56304	−	0.831680i	−0.251827	−	0.0376484i
$489$			27.2939i			1.23427i
$490$		0			0
$491$	4.11589	−	4.11589i	0.185748	−	0.185748i	−0.608107	−	0.793855i	$-0.708071\pi$
$491$	4.11589	−	4.11589i	0.185748	−	0.185748i	0.793855	+	0.608107i	$0.208071\pi$
$492$	0.106691	−	9.14351i	0.00481001	−	0.412221i
$493$	−2.23979	+	8.35900i	−0.100875	+	0.376470i
$494$	17.6182	−	7.17756i	0.792680	−	0.322934i
$495$	−0.224965	+	0.389650i	−0.0101114	+	0.0175135i
$496$	13.5247	+	8.23510i	0.607275	+	0.369767i
$497$		0			0
$498$	0.562829	−	4.09056i	0.0252210	−	0.183302i
$499$	−35.1223	+	9.41100i	−1.57229	+	0.421294i	−0.936529	−	0.350590i	$-0.885981\pi$
$499$	−35.1223	+	9.41100i	−1.57229	+	0.421294i	−0.635763	+	0.771885i	$0.719314\pi$
$500$	−12.9303	+	21.8044i	−0.578261	+	0.975123i
$501$	27.8166	+	7.45345i	1.24276	+	0.332995i
$502$	2.03074	+	16.1526i	0.0906363	+	0.720927i
$503$		−	21.6898i		−	0.967102i	−0.875316	−	0.483551i	$-0.839347\pi$
$503$		−	21.6898i		−	0.967102i	0.875316	−	0.483551i	$-0.160653\pi$
$504$		0			0
$505$			14.9436i			0.664981i
$506$	7.49603	−	0.942415i	0.333239	−	0.0418955i
$507$	−7.84429	−	2.10187i	−0.348377	−	0.0933474i
$508$	−8.19047	−	32.0589i	−0.363393	−	1.42238i
$509$	−1.97114	+	0.528166i	−0.0873694	+	0.0234105i	−0.302239	−	0.953232i	$-0.597734\pi$
$509$	−1.97114	+	0.528166i	−0.0873694	+	0.0234105i	0.214870	+	0.976643i	$0.431067\pi$
$510$	−63.1165	−	8.68434i	−2.79485	−	0.384549i
$511$		0			0
$512$	−7.55007	−	21.3306i	−0.333669	−	0.942690i
$513$	8.40212	−	14.5529i	0.370963	−	0.642526i
$514$	2.78997	+	6.84831i	0.123060	+	0.302066i
$515$	0.793977	−	2.96316i	0.0349868	−	0.130573i
$516$	−14.7130	+	14.3736i	−0.647705	+	0.632764i
$517$	2.54362	−	2.54362i	0.111868	−	0.111868i
$518$		0			0
$519$			5.10580i			0.224120i
$520$	−35.1415	+	26.0007i	−1.54106	+	1.14021i
$521$	−31.8651	+	18.3973i	−1.39604	+	0.806002i	−0.993975	−	0.109611i	$-0.965040\pi$
$521$	−31.8651	+	18.3973i	−1.39604	+	0.806002i	−0.402062	+	0.915613i	$0.631706\pi$
$522$	0.125992	+	0.0530508i	0.00551452	+	0.00232197i
$523$	5.09469	+	19.0136i	0.222775	+	0.831408i	0.983284	+	0.182080i	$0.0582830\pi$
$523$	5.09469	+	19.0136i	0.222775	+	0.831408i	−0.760509	+	0.649328i	$0.775050\pi$
$524$	14.2717	+	25.3991i	0.623461	+	1.10957i
$525$		0			0
$526$	−1.50386	+	10.9299i	−0.0655715	+	0.476564i
$527$	14.2265	−	24.6410i	0.619716	−	1.07338i
$528$	0.243652	−	10.4392i	0.0106036	−	0.454306i
$529$	−5.38628	−	9.32930i	−0.234186	−	0.405622i
$530$	19.7956	+	15.3740i	0.859868	+	0.667806i
$531$	0.310037	+	0.310037i	0.0134544	+	0.0134544i
$532$		0			0
$533$	−7.97185	+	7.97185i	−0.345299	+	0.345299i
$534$	3.80841	+	30.2924i	0.164806	+	1.31088i
$535$	28.1587	−	16.2574i	1.21741	−	0.702871i
$536$	−14.2010	+	17.8513i	−0.613389	+	0.771059i
$537$	−30.8685	−	17.8219i	−1.33207	−	0.769073i
$538$	−14.7698	−	19.4827i	−0.636772	−	0.839959i
$539$		0			0
$540$	−10.4284	+	37.1787i	−0.448768	+	1.59992i
$541$	−25.2151	+	6.75637i	−1.08408	+	0.290479i	−0.756267	−	0.654263i	$-0.772979\pi$
$541$	−25.2151	+	6.75637i	−1.08408	+	0.290479i	−0.327815	+	0.944742i	$0.606312\pi$
$542$	−1.82459	−	4.47866i	−0.0783727	−	0.192375i
$543$	2.43669	+	4.22047i	0.104568	+	0.181118i
$544$	−38.0019	+	14.4573i	−1.62932	+	0.619853i
$545$	−37.1459			−1.59116
$546$		0			0
$547$	13.1422	+	13.1422i	0.561920	+	0.561920i	0.929852	−	0.367933i	$-0.119934\pi$
$547$	13.1422	+	13.1422i	0.561920	+	0.561920i	−0.367933	+	0.929852i	$0.619934\pi$
$548$	13.5607	+	13.8809i	0.579284	+	0.592962i
$549$	0.154224	+	0.0413243i	0.00658213	+	0.00176368i
$550$	−7.08942	+	16.8369i	−0.302294	+	0.717926i
$551$	−3.32903	−	1.92201i	−0.141821	−	0.0818806i
$552$	15.7242	−	6.19305i	0.669268	−	0.263594i
$553$		0			0
$554$	8.23856	−	6.24564i	0.350023	−	0.265352i
$555$	−13.6083	−	50.7870i	−0.577642	−	2.15579i
$556$	−17.1495	−	10.1699i	−0.727299	−	0.431298i
$557$	9.04934	−	33.7726i	0.383433	−	1.43099i	−0.457189	−	0.889370i	$-0.651144\pi$
$557$	9.04934	−	33.7726i	0.383433	−	1.43099i	0.840622	−	0.541622i	$-0.182190\pi$
$558$	−0.354988	−	0.275697i	−0.0150278	−	0.0116712i
$559$	25.3595			1.07259
$560$		0			0
$561$	−18.7632			−0.792181
$562$	−17.6964	−	13.7437i	−0.746476	−	0.579741i
$563$	−0.630250	+	2.35212i	−0.0265619	+	0.0991302i	−0.977934	−	0.208913i	$-0.933007\pi$
$563$	−0.630250	+	2.35212i	−0.0265619	+	0.0991302i	0.951372	+	0.308043i	$0.0996741\pi$
$564$	4.10435	−	6.92117i	0.172824	−	0.291434i
$565$	3.20663	+	11.9673i	0.134904	+	0.503468i
$566$	−21.9708	+	16.6560i	−0.923501	+	0.700105i
$567$		0			0
$568$	−16.3258	+	37.5419i	−0.685017	+	1.57522i
$569$	2.17879	+	1.25792i	0.0913396	+	0.0527349i	0.544974	−	0.838453i	$-0.316539\pi$
$569$	2.17879	+	1.25792i	0.0913396	+	0.0527349i	−0.453634	+	0.891188i	$0.649873\pi$
$570$	10.9824	−	26.0825i	0.460003	−	1.09247i
$571$	−35.1889	−	9.42882i	−1.47261	−	0.394584i	−0.568783	−	0.822487i	$-0.692586\pi$
$571$	−35.1889	−	9.42882i	−1.47261	−	0.394584i	−0.903824	+	0.427903i	$0.859252\pi$
$572$	−9.20894	+	8.99651i	−0.385045	+	0.376163i
$573$	−12.5357	−	12.5357i	−0.523687	−	0.523687i
$574$		0			0
$575$	−29.5667			−1.23302
$576$	0.144423	+	0.625843i	0.00601763	+	0.0260768i
$577$	12.2878	+	21.2830i	0.511546	+	0.886024i	0.999910	+	0.0133840i	$0.00426038\pi$
$577$	12.2878	+	21.2830i	0.511546	+	0.886024i	−0.488364	+	0.872640i	$0.662406\pi$
$578$	18.4939	+	45.3956i	0.769246	+	1.88821i
$579$	0.762302	−	0.204258i	0.0316802	−	0.00848868i
$580$	8.50475	+	2.38554i	0.353141	+	0.0990540i
$581$		0			0
$582$	−1.58964	−	2.09687i	−0.0658926	−	0.0869182i
$583$	6.39263	+	3.69079i	0.264756	+	0.152857i
$584$	−9.35140	+	1.06500i	−0.386964	+	0.0440699i
$585$	1.07462	−	0.620430i	0.0444299	−	0.0256516i
$586$	−4.86778	−	38.7186i	−0.201086	−	1.59945i
$587$	−2.31949	+	2.31949i	−0.0957354	+	0.0957354i	−0.753352	−	0.657617i	$-0.771565\pi$
$587$	−2.31949	+	2.31949i	−0.0957354	+	0.0957354i	0.657617	+	0.753352i	$0.271565\pi$
$588$		0			0
$589$	8.93694	+	8.93694i	0.368240	+	0.368240i
$590$	22.3749	+	17.3772i	0.921159	+	0.715407i
$591$	5.80681	+	10.0577i	0.238860	+	0.413718i
$592$	−23.1665	−	24.2738i	−0.952137	−	0.997645i
$593$	1.48420	−	2.57072i	0.0609489	−	0.105567i	−0.833941	−	0.551854i	$-0.813921\pi$
$593$	1.48420	−	2.57072i	0.0609489	−	0.105567i	0.894890	+	0.446287i	$0.147254\pi$
$594$	−1.55007	+	11.2657i	−0.0636002	+	0.462237i
$595$		0			0
$596$	16.5490	−	9.29881i	0.677872	−	0.380894i
$597$	5.88343	+	21.9573i	0.240793	+	0.898651i
$598$	−19.2031	−	8.08577i	−0.785275	−	0.330652i
$599$	25.4696	−	14.7049i	1.04066	−	0.600825i	0.120640	−	0.992696i	$-0.461505\pi$
$599$	25.4696	−	14.7049i	1.04066	−	0.600825i	0.920020	+	0.391871i	$0.128172\pi$
$600$	−6.04218	+	40.4157i	−0.246671	+	1.64996i
$601$		−	8.63437i		−	0.352203i	−0.984372	−	0.176102i	$-0.943651\pi$
$601$		−	8.63437i		−	0.352203i	0.984372	−	0.176102i	$-0.0563487\pi$
$602$		0			0
$603$	0.457851	−	0.457851i	0.0186451	−	0.0186451i
$604$	−1.56763	−	1.60465i	−0.0637860	−	0.0652922i
$605$	8.22738	−	30.7050i	0.334491	−	1.24834i
$606$	3.71418	+	9.11690i	0.150878	+	0.370349i
$607$	−15.1272	+	26.2011i	−0.613994	+	1.06347i	0.376567	+	0.926390i	$0.377105\pi$
$607$	−15.1272	+	26.2011i	−0.613994	+	1.06347i	−0.990560	+	0.137078i	$0.956229\pi$
$608$	−1.83413	−	17.9673i	−0.0743840	−	0.728668i
$609$		0			0
$610$	10.2202	+	1.40622i	0.413803	+	0.0569361i
$611$	−9.58275	+	2.56769i	−0.387677	+	0.103878i
$612$	1.11821	−	0.285682i	0.0452010	−	0.0115480i
$613$	−15.8263	−	4.24065i	−0.639219	−	0.171278i	−0.0753696	−	0.997156i	$-0.524014\pi$
$613$	−15.8263	−	4.24065i	−0.639219	−	0.171278i	−0.563850	+	0.825877i	$0.690680\pi$
$614$	−5.84282	+	0.734570i	−0.235797	+	0.0296448i
$615$			16.7711i			0.676275i
$616$		0			0
$617$			35.7651i			1.43985i	0.694054	+	0.719923i	$0.255823\pi$
$617$			35.7651i			1.43985i	−0.694054	+	0.719923i	$0.744177\pi$
$618$	−0.252089	−	2.00513i	−0.0101405	−	0.0806582i
$619$	17.2261	+	4.61572i	0.692375	+	0.185521i	0.587813	−	0.808997i	$-0.299989\pi$
$619$	17.2261	+	4.61572i	0.692375	+	0.185521i	0.104562	+	0.994518i	$0.466656\pi$
$620$	−24.9799	−	14.8134i	−1.00322	−	0.594921i
$621$	−17.7776	+	4.76349i	−0.713390	+	0.191152i
$622$	−2.12809	+	15.4667i	−0.0853287	+	0.620157i
$623$		0			0
$624$	−14.9770	+	24.5970i	−0.599561	+	0.984669i
$625$	2.10850	−	3.65202i	0.0843398	−	0.146081i
$626$	45.2101	−	18.4184i	1.80696	−	0.736146i
$627$	2.15714	−	8.05055i	0.0861478	−	0.321508i
$628$	−42.3062	−	0.493650i	−1.68820	−	0.0196988i
$629$	−42.6341	+	42.6341i	−1.69993	+	1.69993i
$630$		0			0
$631$		−	9.56602i		−	0.380817i	−0.981705	−	0.190409i	$-0.939019\pi$
$631$		−	9.56602i		−	0.380817i	0.981705	−	0.190409i	$-0.0609813\pi$
$632$	−35.9673	+	26.6117i	−1.43070	+	1.05856i
$633$	18.4852	−	10.6724i	0.734719	−	0.424190i
$634$	−4.20392	+	9.98401i	−0.166959	+	0.396516i
$635$	15.7070	+	58.6194i	0.623314	+	2.32624i
$636$	15.8983	+	4.45938i	0.630407	+	0.176826i
$637$		0			0
$638$	2.57706	+	0.354584i	0.102027	+	0.0140381i
$639$	0.581024	−	1.00636i	0.0229850	−	0.0398111i
$640$	14.3030	+	38.9579i	0.565374	+	1.53995i
$641$	−0.135586	−	0.234842i	−0.00535533	−	0.00927571i	0.863335	−	0.504631i	$-0.168371\pi$
$641$	−0.135586	−	0.234842i	−0.00535533	−	0.00927571i	−0.868691	+	0.495355i	$0.835038\pi$
$642$	13.1386	−	16.9172i	0.518538	−	0.667670i
$643$	−16.8473	−	16.8473i	−0.664391	−	0.664391i	0.292021	−	0.956412i	$-0.405672\pi$
$643$	−16.8473	−	16.8473i	−0.664391	−	0.664391i	−0.956412	+	0.292021i	$0.905672\pi$
$644$		0			0
$645$	26.6755	−	26.6755i	1.05035	−	1.05035i
$646$	−32.1995	+	4.04818i	−1.26687	+	0.159274i
$647$	−13.4490	+	7.76476i	−0.528733	+	0.305264i	−0.740500	−	0.672056i	$-0.765411\pi$
$647$	−13.4490	+	7.76476i	−0.528733	+	0.305264i	0.211767	+	0.977320i	$0.432078\pi$
$648$	2.80130	+	24.5974i	0.110046	+	0.966276i
$649$	7.22555	+	4.17167i	0.283627	+	0.163752i
$650$	40.1496	−	30.4374i	1.57480	−	1.19385i
$651$		0			0
$652$	−15.6494	−	27.8511i	−0.612879	−	1.09073i
$653$	0.548366	−	0.146934i	0.0214592	−	0.00574998i	−0.248073	−	0.968741i	$-0.579797\pi$
$653$	0.548366	−	0.146934i	0.0214592	−	0.00574998i	0.269533	+	0.962991i	$0.413131\pi$
$654$	−22.6623	+	9.23251i	−0.886166	+	0.361020i
$655$	−26.7172	−	46.2755i	−1.04393	−	1.80813i
$656$	5.13372	+	9.39134i	0.200438	+	0.366670i
$657$	0.267160			0.0104229
$658$		0			0
$659$	−7.69079	−	7.69079i	−0.299591	−	0.299591i	0.541263	−	0.840853i	$-0.317946\pi$
$659$	−7.69079	−	7.69079i	−0.299591	−	0.299591i	−0.840853	+	0.541263i	$0.817946\pi$
$660$	−0.223454	+	19.1502i	−0.00869795	+	0.745420i
$661$	−43.5171	−	11.6604i	−1.69262	−	0.453536i	−0.721555	−	0.692357i	$-0.756572\pi$
$661$	−43.5171	−	11.6604i	−1.69262	−	0.453536i	−0.971063	+	0.238822i	$0.923239\pi$
$662$	22.0429	+	9.28150i	0.856722	+	0.360736i
$663$	44.8141	+	25.8734i	1.74044	+	1.00484i
$664$	1.77107	+	4.49678i	0.0687310	+	0.174509i
$665$		0			0
$666$	0.575403	+	0.759008i	0.0222964	+	0.0294109i
$667$	1.08966	+	4.06668i	0.0421920	+	0.157463i
$668$	−32.6581	+	8.34355i	−1.26358	+	0.322822i
$669$	4.61576	−	17.2263i	0.178456	−	0.666006i
$670$	25.6620	−	33.0424i	0.991408	−	1.27654i
$671$	3.03823			0.117290
$672$		0			0
$673$	−43.2191			−1.66597			−0.832987	−	0.553293i	$-0.813371\pi$
$673$	−43.2191			−1.66597			−0.832987	+	0.553293i	$0.813371\pi$
$674$	25.4156	−	32.7251i	0.978971	−	1.26052i
$675$	11.5184	−	42.9873i	0.443344	−	1.65458i
$676$	9.20958	−	2.35288i	0.354215	−	0.0904954i
$677$	−6.50674	−	24.2835i	−0.250074	−	0.933290i	−0.970765	−	0.240033i	$-0.922842\pi$
$677$	−6.50674	−	24.2835i	−0.250074	−	0.933290i	0.720690	−	0.693257i	$-0.243825\pi$
$678$	4.93076	+	6.50411i	0.189365	+	0.249789i
$679$		0			0
$680$	69.3844	−	27.3273i	2.66077	−	1.04796i
$681$	−39.3725	−	22.7317i	−1.50876	−	0.871081i
$682$	−7.88265	−	3.31911i	−0.301842	−	0.127095i
$683$	41.2947	+	11.0649i	1.58010	+	0.423386i	0.938956	−	0.344037i	$-0.111795\pi$
$683$	41.2947	+	11.0649i	1.58010	+	0.423386i	0.641141	+	0.767423i	$0.278461\pi$
$684$	−0.00598158	+	0.512625i	−0.000228711	+	0.0196007i
$685$	−25.1668	−	25.1668i	−0.961572	−	0.961572i
$686$		0			0
$687$	7.91787			0.302086
$688$	6.77202	−	23.1030i	0.258181	−	0.880795i
$689$	−10.1788	−	17.6302i	−0.387782	−	0.671658i
$690$	−28.7050	+	11.6943i	−1.09278	+	0.445194i
$691$	−15.1521	+	4.05999i	−0.576412	+	0.154449i	−0.535236	−	0.844703i	$-0.679777\pi$
$691$	−15.1521	+	4.05999i	−0.576412	+	0.154449i	−0.0411763	+	0.999152i	$0.513111\pi$
$692$	−2.92750	−	5.21004i	−0.111287	−	0.198056i
$693$		0			0
$694$	37.1787	−	28.1851i	1.41128	−	1.06989i
$695$	31.6690	+	18.2841i	1.20127	+	0.693555i
$696$	5.78157	−	0.658441i	0.219150	−	0.0249581i
$697$	16.6554	−	9.61599i	0.630868	−	0.364232i
$698$	−21.0629	+	2.64806i	−0.797241	+	0.100231i
$699$	−17.6626	+	17.6626i	−0.668062	+	0.668062i
$700$		0			0
$701$	−17.3503	−	17.3503i	−0.655312	−	0.655312i	0.298955	−	0.954267i	$-0.403362\pi$
$701$	−17.3503	−	17.3503i	−0.655312	−	0.655312i	−0.954267	+	0.298955i	$0.903362\pi$
$702$	19.2370	−	24.7696i	0.726054	−	0.934869i
$703$	−13.3912	−	23.1942i	−0.505057	−	0.874785i
$704$	5.73685	+	10.7920i	0.216216	+	0.406738i
$705$	−7.37909	+	12.7810i	−0.277913	+	0.481359i
$706$	−47.1888	−	6.49282i	−1.77597	−	0.244360i
$707$		0			0
$708$	17.9697	+	5.04040i	0.675342	+	0.189430i
$709$	2.34745	+	8.76082i	0.0881605	+	0.329020i	0.995894	−	0.0905279i	$-0.0288554\pi$
$709$	2.34745	+	8.76082i	0.0881605	+	0.329020i	−0.907733	+	0.419547i	$0.862189\pi$
$710$	29.1375	−	69.1995i	1.09351	−	2.59701i
$711$	1.09987	−	0.635009i	0.0412483	−	0.0238147i
$712$	−21.2548	−	28.7272i	−0.796558	−	1.07660i
$713$		−	13.8425i		−	0.518405i
$714$		0			0
$715$	16.6963	−	16.6963i	0.624405	−	0.624405i
$716$	41.7172	+	0.486778i	1.55904	+	0.0181918i
$717$	−3.50521	+	13.0816i	−0.130905	+	0.488543i
$718$	−29.4661	+	12.0043i	−1.09966	+	0.447997i
$719$	17.4013	−	30.1399i	0.648959	−	1.12403i	−0.334413	−	0.942427i	$-0.608538\pi$
$719$	17.4013	−	30.1399i	0.648959	−	1.12403i	0.983372	−	0.181603i	$-0.0581286\pi$
$720$	−0.278258	−	1.14468i	−0.0103701	−	0.0426596i
$721$		0			0
$722$	−1.69765	+	12.3383i	−0.0631801	+	0.459183i
$723$	7.12654	−	1.90955i	0.265039	−	0.0710170i
$724$	−4.90632	−	2.90952i	−0.182342	−	0.108131i
$725$	−9.83349	−	2.63487i	−0.365207	−	0.0978568i
$726$	−2.61221	−	20.7777i	−0.0969481	−	0.771131i
$727$			22.4368i			0.832134i	0.909334	+	0.416067i	$0.136592\pi$
$727$			22.4368i			0.832134i	−0.909334	+	0.416067i	$0.863408\pi$
$728$		0			0
$729$		−	27.6834i		−	1.02531i
$730$	17.1273	−	2.15327i	0.633909	−	0.0796962i
$731$	−41.7863	−	11.1966i	−1.54552	−	0.414121i
$732$	6.58472	−	1.68228i	0.243378	−	0.0621788i
$733$	−7.05722	+	1.89098i	−0.260664	+	0.0698448i	−0.386784	−	0.922170i	$-0.626414\pi$
$733$	−7.05722	+	1.89098i	−0.260664	+	0.0698448i	0.126120	+	0.992015i	$0.459748\pi$
$734$	23.7326	+	3.26542i	0.875985	+	0.120529i
$735$		0			0
$736$	−12.4943	+	15.3352i	−0.460548	+	0.565265i
$737$	6.16057	−	10.6704i	0.226928	−	0.393050i
$738$	−0.114623	−	0.281355i	−0.00421932	−	0.0103568i
$739$	−2.56129	+	9.55885i	−0.0942185	+	0.351628i	−0.996900	−	0.0786816i	$-0.974929\pi$
$739$	−2.56129	+	9.55885i	−0.0942185	+	0.351628i	0.902681	+	0.430310i	$0.141596\pi$
$740$	43.0058	+	44.0213i	1.58092	+	1.61825i
$741$	−16.2534	+	16.2534i	−0.597085	+	0.597085i
$742$		0			0
$743$			10.5142i			0.385729i	0.981225	+	0.192864i	$0.0617777\pi$
$743$			10.5142i			0.385729i	−0.981225	+	0.192864i	$0.938222\pi$
$744$	−18.9217	−	2.82882i	−0.693705	−	0.103709i
$745$	−30.1511	+	17.4077i	−1.10465	+	0.637770i
$746$	−16.9690	−	7.14504i	−0.621278	−	0.261599i
$747$	−0.0355065	−	0.132512i	−0.00129912	−	0.00484837i
$748$	19.1462	−	10.7582i	0.700055	−	0.393358i
$749$		0			0
$750$	4.17499	−	30.3432i	0.152449	−	1.10798i
$751$	14.4208	−	24.9776i	0.526222	−	0.911444i	−0.473311	−	0.880895i	$-0.656941\pi$
$751$	14.4208	−	24.9776i	0.526222	−	0.911444i	0.999533	−	0.0305484i	$-0.00972538\pi$
$752$	−0.219766	+	9.41577i	−0.00801405	+	0.343358i
$753$	−9.83499	−	17.0347i	−0.358407	−	0.620779i
$754$	−5.66613	−	4.40053i	−0.206348	−	0.160258i
$755$	2.90931	+	2.90931i	0.105881	+	0.105881i
$756$		0			0
$757$	−6.34883	+	6.34883i	−0.230752	+	0.230752i	−0.813007	−	0.582254i	$-0.802171\pi$
$757$	−6.34883	+	6.34883i	−0.230752	+	0.230752i	0.582254	+	0.813007i	$0.302171\pi$
$758$	−0.122567	−	0.974904i	−0.00445183	−	0.0354101i
$759$	−7.90538	+	4.56417i	−0.286947	+	0.165669i
$760$	3.74821	+	32.9119i	0.135962	+	1.19384i
$761$	−14.2696	−	8.23856i	−0.517273	−	0.298648i	0.218545	−	0.975827i	$-0.429869\pi$
$761$	−14.2696	−	8.23856i	−0.517273	−	0.298648i	−0.735818	+	0.677179i	$0.763202\pi$
$762$	24.1523	+	31.8591i	0.874947	+	1.15413i
$763$		0			0
$764$	19.9792	+	5.60406i	0.722822	+	0.202748i
$765$	−2.04464	+	0.547858i	−0.0739240	+	0.0198079i
$766$	3.98254	+	9.77563i	0.143895	+	0.353208i
$767$	−11.5050	−	19.9273i	−0.415423	−	0.719534i
$768$	18.4089	+	20.2128i	0.664276	+	0.729367i
$769$	20.1524			0.726714			0.363357	−	0.931650i	$-0.381631\pi$
$769$	20.1524			0.726714			0.363357	+	0.931650i	$0.381631\pi$
$770$		0			0
$771$	−6.31782	−	6.31782i	−0.227531	−	0.227531i
$772$	−0.660749	+	0.645507i	−0.0237809	+	0.0232323i
$773$	−1.09150	−	0.292467i	−0.0392587	−	0.0105193i	0.239136	−	0.970986i	$-0.423136\pi$
$773$	−1.09150	−	0.292467i	−0.0392587	−	0.0105193i	−0.278395	+	0.960467i	$0.589802\pi$
$774$	−0.265199	+	0.629828i	−0.00953237	+	0.0226387i
$775$	28.9876	+	16.7360i	1.04126	+	0.601174i
$776$	2.82437	+	1.22823i	0.101389	+	0.0440910i
$777$		0			0
$778$	16.2695	−	12.3339i	0.583290	−	0.442192i
$779$	2.21104	+	8.25171i	0.0792187	+	0.295648i
$780$	26.9408	−	45.4304i	0.964637	−	1.62667i
$781$	5.72312	−	21.3590i	0.204789	−	0.764284i
$782$	28.0721	+	21.8019i	1.00386	+	0.779634i
$783$	−6.33709			−0.226469
$784$		0			0
$785$	77.5982			2.76960
$786$	−27.8015	−	21.5917i	−0.991645	−	0.770149i
$787$	8.16066	−	30.4560i	0.290896	−	1.08564i	−0.653526	−	0.756904i	$-0.726711\pi$
$787$	8.16066	−	30.4560i	0.290896	−	1.08564i	0.944422	−	0.328735i	$-0.106622\pi$
$788$	−11.6921	−	6.93359i	−0.416514	−	0.246999i
$789$	−3.45015	−	12.8761i	−0.122829	−	0.458403i
$790$	65.3930	−	49.5744i	2.32658	−	1.76378i
$791$		0			0
$792$	−0.127134	−	0.322795i	−0.00451752	−	0.0114700i
$793$	−7.25655	−	4.18957i	−0.257688	−	0.148776i
$794$	−17.2025	+	40.8548i	−0.610495	+	1.44988i
$795$	−29.2521	−	7.83809i	−1.03747	−	0.277988i
$796$	−18.5931	−	19.0322i	−0.659016	−	0.674577i
$797$	28.3719	+	28.3719i	1.00498	+	1.00498i	0.999988	+	0.00499575i	$0.00159020\pi$
$797$	28.3719	+	28.3719i	1.00498	+	1.00498i	0.00499575	+	0.999988i	$0.498410\pi$
$798$		0			0
$799$	16.9237			0.598718
$800$	−17.0075	−	44.7052i	−0.601307	−	1.58057i
$801$	0.507184	+	0.878468i	0.0179205	+	0.0310391i
$802$	−6.94777	−	17.0541i	−0.245334	−	0.602203i
$803$	4.91052	−	1.31577i	0.173289	−	0.0464325i
$804$	7.44348	−	26.5370i	0.262511	−	0.935887i
$805$		0			0
$806$	14.2501	+	18.7972i	0.501939	+	0.662102i
$807$	25.5821	+	14.7698i	0.900532	+	0.519922i
$808$	−9.01734	−	7.17344i	−0.317229	−	0.252361i
$809$	16.0708	−	9.27847i	0.565019	−	0.326214i	−0.190139	−	0.981757i	$-0.560894\pi$
$809$	16.0708	−	9.27847i	0.565019	−	0.326214i	0.755157	+	0.655544i	$0.227560\pi$
$810$	−5.66384	−	45.0505i	−0.199007	−	1.58291i
$811$	10.1065	−	10.1065i	0.354886	−	0.354886i	−0.507038	−	0.861924i	$-0.669260\pi$
$811$	10.1065	−	10.1065i	0.354886	−	0.354886i	0.861924	+	0.507038i	$0.169260\pi$
$812$		0			0
$813$	4.13174	+	4.13174i	0.144906	+	0.144906i
$814$	14.3143	+	11.1170i	0.501716	+	0.389651i
$815$	29.2964	+	50.7428i	1.02621	+	1.77744i
$816$	35.5385	−	33.9174i	1.24410	−	1.18734i
$817$	9.60807	−	16.6417i	0.336144	−	0.582218i
$818$	0.745609	−	5.41898i	0.0260696	−	0.189470i
$819$		0			0
$820$	−9.61599	−	17.1135i	−0.335805	−	0.597628i
$821$	−4.06555	−	15.1728i	−0.141889	−	0.529535i	−0.999874	−	0.0158616i	$-0.994951\pi$
$821$	−4.06555	−	15.1728i	−0.141889	−	0.529535i	0.857986	−	0.513674i	$-0.171716\pi$
$822$	−21.6091	−	9.09882i	−0.753703	−	0.317358i
$823$	−32.9472	+	19.0221i	−1.14847	+	0.663068i	−0.948513	−	0.316737i	$-0.897413\pi$
$823$	−32.9472	+	19.0221i	−1.14847	+	0.663068i	−0.199954	+	0.979805i	$0.564079\pi$
$824$	1.40691	+	1.90153i	0.0490121	+	0.0662428i
$825$		−	22.0729i		−	0.768479i
$826$		0			0
$827$	−30.4616	+	30.4616i	−1.05925	+	1.05925i	−0.0611233	+	0.998130i	$0.519468\pi$
$827$	−30.4616	+	30.4616i	−1.05925	+	1.05925i	−0.998130	+	0.0611233i	$0.980532\pi$
$828$	0.401637	−	0.392372i	0.0139578	−	0.0136359i
$829$	−4.73303	+	17.6639i	−0.164385	+	0.613493i	0.833733	+	0.552168i	$0.186199\pi$
$829$	−4.73303	+	17.6639i	−0.164385	+	0.613493i	−0.998118	+	0.0613249i	$0.980467\pi$
$830$	−3.34430	−	8.20899i	−0.116082	−	0.284938i
$831$	−6.24564	+	10.8178i	−0.216659	+	0.375264i
$832$	1.17964	−	33.6865i	0.0408968	−	1.16787i
$833$		0			0
$834$	23.8653	+	3.28368i	0.826389	+	0.113705i
$835$	59.7150	−	16.0006i	2.06652	−	0.553723i
$836$	2.41475	+	9.45174i	0.0835158	+	0.326895i
$837$	20.1257	+	5.39267i	0.695646	+	0.186398i
$838$	−2.56176	+	0.322070i	−0.0884947	+	0.0111257i
$839$		−	33.9776i		−	1.17304i	−0.809935	−	0.586519i	$-0.800498\pi$
$839$		−	33.9776i		−	1.17304i	0.809935	−	0.586519i	$-0.199502\pi$
$840$		0			0
$841$		−	27.5504i		−	0.950013i
$842$	−0.948148	−	7.54163i	−0.0326754	−	0.259902i
$843$	26.1500	+	7.00688i	0.900655	+	0.241330i
$844$	−12.7433	+	21.4891i	−0.438643	+	0.739684i
$845$	−16.8396	+	4.51216i	−0.579301	+	0.155223i
$846$	0.0364412	−	0.264849i	0.00125287	−	0.00910570i
$847$		0			0
$848$	−18.7797	+	4.56513i	−0.644897	+	0.156767i
$849$	16.6560	−	28.8491i	0.571634	−	0.990099i
$850$	−79.5954	+	32.4268i	−2.73010	+	1.11223i
$851$	−7.59197	+	28.3336i	−0.260249	+	0.971264i
$852$	0.577124	−	49.4599i	0.0197719	−	1.69447i
$853$	−19.2350	+	19.2350i	−0.658593	+	0.658593i	−0.955047	−	0.296454i	$-0.904196\pi$
$853$	−19.2350	+	19.2350i	−0.658593	+	0.658593i	0.296454	+	0.955047i	$0.404196\pi$
$854$		0			0
$855$		−	0.940260i		−	0.0321562i
$856$	−3.70700	+	24.7958i	−0.126703	+	0.847504i
$857$	36.7583	−	21.2224i	1.25564	−	0.724943i	0.283415	−	0.958997i	$-0.408533\pi$
$857$	36.7583	−	21.2224i	1.25564	−	0.724943i	0.972224	+	0.234054i	$0.0751993\pi$
$858$	6.03640	−	14.3360i	0.206079	−	0.489423i
$859$	−2.04656	−	7.63785i	−0.0698276	−	0.260600i	0.922183	−	0.386753i	$-0.126404\pi$
$859$	−2.04656	−	7.63785i	−0.0698276	−	0.260600i	−0.992011	+	0.126153i	$0.959737\pi$
$860$	−11.9252	+	42.5149i	−0.406646	+	1.44975i
$861$		0			0
$862$	0.577888	+	0.0795129i	0.0196830	+	0.00270822i
$863$	−14.1517	+	24.5115i	−0.481729	+	0.834380i	−0.999780	−	0.0209703i	$-0.993324\pi$
$863$	−14.1517	+	24.5115i	−0.481729	+	0.834380i	0.518051	+	0.855350i	$0.326658\pi$
$864$	−17.4286	−	24.1398i	−0.592932	−	0.821254i
$865$	5.48040	+	9.49234i	0.186339	+	0.322749i
$866$	4.43507	−	5.71060i	0.150710	−	0.194054i
$867$	−41.8791	−	41.8791i	−1.42229	−	1.42229i
$868$		0			0
$869$	17.0886	−	17.0886i	0.579692	−	0.579692i
$870$	−10.5891	+	1.33128i	−0.359002	+	0.0451345i
$871$	−29.4279	+	16.9902i	−0.997128	+	0.575692i
$872$	17.8313	−	22.4148i	0.603845	−	0.759062i
$873$	−0.0757112	−	0.0437119i	−0.00256244	−	0.00147942i
$874$	−12.5817	+	9.53819i	−0.425583	+	0.322634i
$875$		0			0
$876$	9.91396	−	5.57062i	0.334962	−	0.188214i
$877$	31.2052	−	8.36140i	1.05372	−	0.282344i	0.309934	−	0.950758i	$-0.399693\pi$
$877$	31.2052	−	8.36140i	1.05372	−	0.282344i	0.743790	+	0.668414i	$0.233026\pi$
$878$	39.7052	−	16.1757i	1.33998	−	0.545903i
$879$	23.5749	+	40.8330i	0.795162	+	1.37726i
$880$	−10.7521	−	19.6693i	−0.362453	−	0.663051i
$881$	−25.4754			−0.858287			−0.429144	−	0.903236i	$-0.641185\pi$
$881$	−25.4754			−0.858287			−0.429144	+	0.903236i	$0.641185\pi$
$882$		0			0
$883$	23.7113	+	23.7113i	0.797950	+	0.797950i	0.982772	−	0.184822i	$-0.0591709\pi$
$883$	23.7113	+	23.7113i	0.797950	+	0.797950i	−0.184822	+	0.982772i	$0.559171\pi$
$884$	−60.5640	−	0.706692i	−2.03699	−	0.0237686i
$885$	−33.0635	−	8.85933i	−1.11142	−	0.297803i
$886$	46.4946	+	19.5772i	1.56202	+	0.657710i
$887$	−10.7238	−	6.19139i	−0.360070	−	0.207887i	0.309041	−	0.951049i	$-0.399992\pi$
$887$	−10.7238	−	6.19139i	−0.360070	−	0.207887i	−0.669112	+	0.743162i	$0.733325\pi$
$888$	37.1787	+	16.1679i	1.24764	+	0.542559i
$889$		0			0
$890$	39.5952	+	52.2295i	1.32723	+	1.75074i
$891$	−3.46092	−	12.9163i	−0.115945	−	0.432714i
$892$	5.16699	+	20.2245i	0.173003	+	0.677165i
$893$	−1.94567	+	7.26132i	−0.0651092	+	0.242991i
$894$	−14.0682	+	18.1142i	−0.470511	+	0.605830i
$895$	−76.5179			−2.55771
$896$		0			0
$897$	25.1750			0.840570
$898$	−28.5166	+	36.7180i	−0.951611	+	1.22530i
$899$	1.23359	−	4.60382i	0.0411425	−	0.153546i
$900$	0.336075	+	1.31546i	0.0112025	+	0.0438486i
$901$	8.98821	+	33.5445i	0.299441	+	1.11753i
$902$	−3.49250	−	4.60691i	−0.116287	−	0.153393i
$903$		0			0
$904$	−8.76067	−	3.80975i	−0.291375	−	0.126711i
$905$	9.06024	+	5.23093i	0.301173	+	0.173882i
$906$	2.49803	+	1.05183i	0.0829916	+	0.0349449i
$907$	−0.280381	−	0.0751280i	−0.00930991	−	0.00249458i	0.254161	−	0.967162i	$-0.418201\pi$
$907$	−0.280381	−	0.0751280i	−0.00930991	−	0.00249458i	−0.263471	+	0.964667i	$0.584867\pi$
$908$	53.2099	+	0.620881i	1.76583	+	0.0206047i
$909$	0.231277	+	0.231277i	0.00767098	+	0.00767098i
$910$		0			0
$911$	−42.6222			−1.41214			−0.706068	−	0.708144i	$-0.749533\pi$
$911$	−42.6222			−1.41214			−0.706068	+	0.708144i	$0.749533\pi$
$912$	10.4669	+	19.1476i	0.346594	+	0.634039i
$913$	−1.30525	−	2.26076i	−0.0431975	−	0.0748203i
$914$	10.2725	−	4.18498i	0.339785	−	0.138427i
$915$	−12.0401	+	3.22613i	−0.398033	+	0.106653i
$916$	−8.07951	+	4.53985i	−0.266955	+	0.150001i
$917$		0			0
$918$	−42.6341	+	32.3209i	−1.40714	+	1.06675i
$919$	−41.1186	−	23.7399i	−1.35638	−	0.783106i	−0.367245	−	0.930124i	$-0.619699\pi$
$919$	−41.1186	−	23.7399i	−1.35638	−	0.783106i	−0.989134	+	0.147019i	$0.953032\pi$
$920$	22.5859	−	28.3915i	0.744636	−	0.936042i
$921$	6.16188	−	3.55756i	0.203041	−	0.117226i
$922$	22.9463	−	2.88485i	0.755696	−	0.0950076i
$923$	−43.1221	+	43.1221i	−1.41938	+	1.41938i
$924$		0			0
$925$	−50.1546	−	50.1546i	−1.64907	−	1.64907i
$926$	6.70243	−	8.63005i	0.220255	−	0.283601i
$927$	−0.0335718	−	0.0581481i	−0.00110264	−	0.00190983i
$928$	−5.52207	+	3.98685i	−0.181271	+	0.130875i
$929$	−19.8966	+	34.4619i	−0.652786	+	1.13066i	0.329658	+	0.944101i	$0.393067\pi$
$929$	−19.8966	+	34.4619i	−0.652786	+	1.13066i	−0.982444	+	0.186558i	$0.940267\pi$
$930$	34.7622	+	4.78301i	1.13990	+	0.156841i
$931$		0			0
$932$	7.89604	−	28.1504i	0.258643	−	0.922097i
$933$	−4.88225	−	18.2208i	−0.159838	−	0.596523i
$934$	1.32283	−	3.14162i	0.0432843	−	0.102797i
$935$	−34.8831	+	20.1398i	−1.14080	+	0.658641i
$936$	−0.141469	+	0.946278i	−0.00462407	+	0.0309301i
$937$			27.4306i			0.896118i	0.894004	+	0.448059i	$0.147885\pi$
$937$			27.4306i			0.896118i	−0.894004	+	0.448059i	$0.852115\pi$
$938$		0			0
$939$	−41.7080	+	41.7080i	−1.36109	+	1.36109i
$940$	0.201548	−	17.2728i	0.00657378	−	0.563377i
$941$	5.63479	−	21.0293i	0.183689	−	0.685536i	−0.811219	−	0.584743i	$-0.801195\pi$
$941$	5.63479	−	21.0293i	0.183689	−	0.685536i	0.994907	−	0.100793i	$-0.0321380\pi$
$942$	47.3418	−	19.2868i	1.54248	−	0.628398i
$943$	4.67821	−	8.10291i	0.152344	−	0.263867i
$944$	−21.2265	+	5.15993i	−0.690865	+	0.167942i
$945$		0			0
$946$	−1.77255	+	12.8826i	−0.0576306	+	0.418851i
$947$	1.85336	−	0.496605i	0.0602260	−	0.0161375i	−0.228580	−	0.973525i	$-0.573408\pi$
$947$	1.85336	−	0.496605i	0.0602260	−	0.0161375i	0.288806	+	0.957388i	$0.406742\pi$
$948$	27.5739	−	46.4980i	0.895560	−	1.51018i
$949$	−13.5427	−	3.62876i	−0.439615	−	0.117795i
$950$	−4.76226	−	37.8793i	−0.154508	−	1.22897i
$951$		−	13.0889i		−	0.424437i
$952$		0			0
$953$		−	22.5056i		−	0.729027i	−0.931198	−	0.364514i	$-0.881235\pi$
$953$		−	22.5056i		−	0.729027i	0.931198	−	0.364514i	$-0.118765\pi$
$954$	0.544310	−	0.0684317i	0.0176227	−	0.00221556i
$955$	−36.7609	−	9.85005i	−1.18955	−	0.318740i
$956$	−3.92381	−	15.3585i	−0.126905	−	0.496729i
$957$	−3.03596	+	0.813484i	−0.0981388	+	0.0262962i
$958$	−13.0876	−	1.80075i	−0.422840	−	0.0581795i
$959$		0			0
$960$	−34.1937	−	36.6755i	−1.10360	−	1.18370i
$961$	7.66458	−	13.2755i	0.247245	−	0.428240i
$962$	−18.8586	−	46.2907i	−0.608026	−	1.49247i
$963$	0.184192	−	0.687415i	0.00593552	−	0.0221516i
$964$	−6.17716	+	6.03466i	−0.198953	+	0.194363i
$965$	1.19797	−	1.19797i	0.0385641	−	0.0385641i
$966$		0			0
$967$		−	10.5320i		−	0.338685i	−0.985557	−	0.169342i	$-0.945836\pi$
$967$		−	10.5320i		−	0.338685i	0.985557	−	0.169342i	$-0.0541644\pi$
$968$	14.5788	+	19.7041i	0.468579	+	0.633313i
$969$	33.9579	−	19.6056i	1.09088	−	0.629822i
$970$	−5.20605	−	2.19209i	−0.167156	−	0.0703837i
$971$	−4.48075	−	16.7224i	−0.143794	−	0.536647i	−0.999806	−	0.0196909i	$-0.993732\pi$
$971$	−4.48075	−	16.7224i	−0.143794	−	0.536647i	0.856012	−	0.516956i	$-0.172935\pi$
$972$	0.817220	+	1.45440i	0.0262124	+	0.0466498i
$973$		0			0
$974$	−5.70438	+	41.4586i	−0.182780	+	1.32842i
$975$	−30.4374	+	52.7191i	−0.974776	+	1.68836i
$976$	−5.75459	+	5.49209i	−0.184200	+	0.175797i
$977$	−17.4561	−	30.2349i	−0.558470	−	0.967299i	−0.997624	−	0.0688873i	$-0.978055\pi$
$977$	−17.4561	−	30.2349i	−0.558470	−	0.967299i	0.439154	−	0.898412i	$-0.355278\pi$
$978$	30.4853	+	23.6761i	0.974814	+	0.757077i
$979$	13.6487	+	13.6487i	0.436216	+	0.436216i
$980$		0			0
$981$	−0.574896	+	0.574896i	−0.0183550	+	0.0183550i
$982$	−1.02683	−	8.16749i	−0.0327675	−	0.260635i
$983$	19.7630	−	11.4102i	0.630342	−	0.363928i	−0.150542	−	0.988604i	$-0.548102\pi$
$983$	19.7630	−	11.4102i	0.630342	−	0.363928i	0.780885	+	0.624675i	$0.214769\pi$
$984$	−10.1201	−	8.05070i	−0.322617	−	0.256647i
$985$	21.5912	+	12.4657i	0.687953	+	0.397190i
$986$	7.39351	+	9.75270i	0.235457	+	0.310589i
$987$		0			0
$988$	7.26606	−	25.9044i	0.231164	−	0.824130i
$989$	−20.3292	+	5.44719i	−0.646430	+	0.173211i
$990$	0.240066	+	0.589271i	0.00762981	+	0.0187283i
$991$	24.1898	+	41.8979i	0.768414	+	1.33093i	0.938423	+	0.345489i	$0.112287\pi$
$991$	24.1898	+	41.8979i	0.768414	+	1.33093i	−0.170009	+	0.985443i	$0.554380\pi$
$992$	20.9300	−	7.96255i	0.664528	−	0.252811i
$993$	−28.8979			−0.917048
$994$		0			0
$995$	34.5063	+	34.5063i	1.09392	+	1.09392i
$996$	−4.08064	−	4.17699i	−0.129300	−	0.132353i
$997$	30.0904	+	8.06270i	0.952972	+	0.255348i	0.701623	−	0.712548i	$-0.252459\pi$
$997$	30.0904	+	8.06270i	0.952972	+	0.255348i	0.251349	+	0.967896i	$0.419126\pi$
$998$	−19.9554	+	47.3927i	−0.631678	+	1.50019i
$999$	−38.2369	−	22.0761i	−1.20976	−	0.698456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.j.765.4		16
7.2	even	3		784.2.m.g.589.1		8
7.3	odd	6		784.2.x.k.557.3		16
7.4	even	3	inner	784.2.x.j.557.3		16
7.5	odd	6		112.2.m.c.29.1	✓	8
7.6	odd	2		784.2.x.k.765.4		16
16.5	even	4	inner	784.2.x.j.373.3		16
28.19	even	6		448.2.m.c.337.2		8
56.5	odd	6		896.2.m.e.673.2		8
56.19	even	6		896.2.m.f.673.3		8
112.5	odd	12		112.2.m.c.85.1	yes	8
112.19	even	12		896.2.m.f.225.3		8
112.37	even	12		784.2.m.g.197.1		8
112.53	even	12	inner	784.2.x.j.165.4		16
112.61	odd	12		896.2.m.e.225.2		8
112.69	odd	4		784.2.x.k.373.3		16
112.75	even	12		448.2.m.c.113.2		8
112.101	odd	12		784.2.x.k.165.4		16
224.5	odd	24		7168.2.a.bc.1.3		8
224.75	even	24		7168.2.a.bd.1.3		8
224.117	odd	24		7168.2.a.bc.1.6		8
224.187	even	24		7168.2.a.bd.1.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.m.c.29.1	✓	8	7.5	odd	6
112.2.m.c.85.1	yes	8	112.5	odd	12
448.2.m.c.113.2		8	112.75	even	12
448.2.m.c.337.2		8	28.19	even	6
784.2.m.g.197.1		8	112.37	even	12
784.2.m.g.589.1		8	7.2	even	3
784.2.x.j.165.4		16	112.53	even	12	inner
784.2.x.j.373.3		16	16.5	even	4	inner
784.2.x.j.557.3		16	7.4	even	3	inner
784.2.x.j.765.4		16	1.1	even	1	trivial
784.2.x.k.165.4		16	112.101	odd	12
784.2.x.k.373.3		16	112.69	odd	4
784.2.x.k.557.3		16	7.3	odd	6
784.2.x.k.765.4		16	7.6	odd	2
896.2.m.e.225.2		8	112.61	odd	12
896.2.m.e.673.2		8	56.5	odd	6
896.2.m.f.225.3		8	112.19	even	12
896.2.m.f.673.3		8	56.19	even	6
7168.2.a.bc.1.3		8	224.5	odd	24
7168.2.a.bc.1.6		8	224.117	odd	24
7168.2.a.bd.1.3		8	224.75	even	24
7168.2.a.bd.1.6		8	224.187	even	24

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)

\(f(q)\)	\(=\)	\(q+(0.867450 - 1.11693i) q^{2} +(-0.442248 + 1.65049i) q^{3} +(-0.495063 - 1.93776i) q^{4} +(0.949390 + 3.54317i) q^{5} +(1.45986 + 1.92568i) q^{6} +(-2.59378 - 1.12796i) q^{8} +(0.0695300 + 0.0401432i) q^{9} +O(q^{10})\)	\(q+(0.867450 - 1.11693i) q^{2} +(-0.442248 + 1.65049i) q^{3} +(-0.495063 - 1.93776i) q^{4} +(0.949390 + 3.54317i) q^{5} +(1.45986 + 1.92568i) q^{6} +(-2.59378 - 1.12796i) q^{8} +(0.0695300 + 0.0401432i) q^{9} +(4.78102 + 2.01312i) q^{10} +(1.47570 + 0.395412i) q^{11} +(3.41720 + 0.0398737i) q^{12} +(-2.97932 - 2.97932i) q^{13} -6.26785 q^{15} +(-3.50983 + 1.91862i) q^{16} +(3.59378 + 6.22461i) q^{17} +(0.105151 - 0.0428379i) q^{18} +(-3.08391 + 0.826331i) q^{19} +(6.39581 - 3.59378i) q^{20} +(1.72174 - 1.30525i) q^{22} +(3.02830 + 1.74839i) q^{23} +(3.00879 - 3.78218i) q^{24} +(-7.32261 + 4.22771i) q^{25} +(-5.91210 + 0.743280i) q^{26} +(-3.72174 + 3.72174i) q^{27} +(0.851361 + 0.851361i) q^{29} +(-5.43705 + 7.00075i) q^{30} +(-1.97932 - 3.42828i) q^{31} +(-0.901629 + 5.58454i) q^{32} +(-1.30525 + 2.26076i) q^{33} +(10.0699 + 1.38554i) q^{34} +(0.0433661 - 0.154606i) q^{36} +(2.17113 + 8.10278i) q^{37} +(-1.75218 + 4.16131i) q^{38} +(6.23495 - 3.59975i) q^{39} +(1.53404 - 10.2611i) q^{40} -2.67573i q^{41} +(-4.25592 + 4.25592i) q^{43} +(0.0356509 - 3.05530i) q^{44} +(-0.0762231 + 0.284468i) q^{45} +(4.57972 - 1.86576i) q^{46} +(1.17729 - 2.03913i) q^{47} +(-1.61446 - 6.64146i) q^{48} +(-1.62994 + 11.8462i) q^{50} +(-11.8630 + 3.17869i) q^{51} +(-4.29826 + 7.24816i) q^{52} +(4.66701 + 1.25052i) q^{53} +(0.928499 + 7.38535i) q^{54} +5.60406i q^{55} -5.45542i q^{57} +(1.68942 - 0.212397i) q^{58} +(5.27509 + 1.41346i) q^{59} +(3.10298 + 12.1456i) q^{60} +(1.92093 - 0.514711i) q^{61} +(-5.54611 - 0.763102i) q^{62} +(5.45542 + 5.85136i) q^{64} +(7.72771 - 13.3848i) q^{65} +(1.39287 + 3.41897i) q^{66} +(2.08734 - 7.79006i) q^{67} +(10.2827 - 10.0455i) q^{68} +(-4.22496 + 4.22496i) q^{69} -14.4738i q^{71} +(-0.135066 - 0.182550i) q^{72} +(2.88178 - 1.66380i) q^{73} +(10.9336 + 4.60375i) q^{74} +(-3.73940 - 13.9556i) q^{75} +(3.12796 + 5.56679i) q^{76} +(1.38784 - 10.0866i) q^{78} +(7.90931 - 13.6993i) q^{79} +(-10.1302 - 10.6144i) q^{80} +(-4.37635 - 7.58006i) q^{81} +(-2.98860 - 2.32106i) q^{82} +(-1.20825 - 1.20825i) q^{83} +(-18.6430 + 18.6430i) q^{85} +(1.06177 + 8.44535i) q^{86} +(-1.78168 + 1.02865i) q^{87} +(-3.38163 - 2.69014i) q^{88} +(10.9417 + 6.31718i) q^{89} +(0.251611 + 0.331898i) q^{90} +(1.88876 - 6.73368i) q^{92} +(6.53371 - 1.75070i) q^{93} +(-1.25632 - 3.08379i) q^{94} +(-5.85567 - 10.1423i) q^{95} +(-8.81850 - 3.95789i) q^{96} -1.08890 q^{97} +(0.0867323 + 0.0867323i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8}+O(q^{10}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8	\( 16 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 32 q^{6} - 8 q^{8} + 12 q^{10} - 12 q^{12} - 16 q^{15} - 8 q^{16} + 24 q^{17} - 6 q^{18} - 12 q^{19} + 16 q^{20} - 8 q^{22} + 8 q^{26} - 24 q^{27} - 32 q^{29} - 20 q^{30} + 16 q^{31} + 28 q^{32} - 24 q^{33} + 24 q^{34} + 48 q^{36} - 16 q^{37} - 16 q^{38} + 28 q^{40} - 64 q^{43} + 32 q^{44} - 8 q^{45} - 20 q^{46} + 24 q^{47} - 40 q^{48} - 28 q^{50} - 8 q^{51} + 32 q^{52} + 8 q^{53} - 16 q^{54} - 12 q^{58} - 28 q^{59} + 28 q^{60} + 28 q^{61} - 40 q^{62} - 64 q^{64} + 48 q^{65} - 16 q^{66} + 28 q^{68} - 88 q^{69} - 44 q^{72} + 4 q^{74} + 28 q^{75} + 48 q^{76} + 24 q^{78} + 24 q^{79} - 12 q^{80} - 40 q^{81} + 4 q^{82} - 80 q^{85} + 40 q^{88} + 32 q^{90} + 72 q^{92} - 16 q^{93} + 28 q^{94} - 16 q^{95} + 8 q^{96} + 64 q^{97} + 96 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 4 * q^4 - 4 * q^5 + 32 * q^6 - 8 * q^8 + 12 * q^10 - 12 * q^12 - 16 * q^15 - 8 * q^16 + 24 * q^17 - 6 * q^18 - 12 * q^19 + 16 * q^20 - 8 * q^22 + 8 * q^26 - 24 * q^27 - 32 * q^29 - 20 * q^30 + 16 * q^31 + 28 * q^32 - 24 * q^33 + 24 * q^34 + 48 * q^36 - 16 * q^37 - 16 * q^38 + 28 * q^40 - 64 * q^43 + 32 * q^44 - 8 * q^45 - 20 * q^46 + 24 * q^47 - 40 * q^48 - 28 * q^50 - 8 * q^51 + 32 * q^52 + 8 * q^53 - 16 * q^54 - 12 * q^58 - 28 * q^59 + 28 * q^60 + 28 * q^61 - 40 * q^62 - 64 * q^64 + 48 * q^65 - 16 * q^66 + 28 * q^68 - 88 * q^69 - 44 * q^72 + 4 * q^74 + 28 * q^75 + 48 * q^76 + 24 * q^78 + 24 * q^79 - 12 * q^80 - 40 * q^81 + 4 * q^82 - 80 * q^85 + 40 * q^88 + 32 * q^90 + 72 * q^92 - 16 * q^93 + 28 * q^94 - 16 * q^95 + 8 * q^96 + 64 * q^97 + 96 * q^99

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