LMFDB - Embedded newform 1176.2.c.e.589.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1176,2,Mod(589,1176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1176, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("1176.589");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1176 = 2^{3} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1176.c (of order $2$, degree $1$, 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:	$9.39040727770$
Analytic rank:	$0$
Dimension:	$16$
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} + x^{14} - 2 x^{13} - 2 x^{12} - 4 x^{11} - 2 x^{10} + 16 x^{9} + 8 x^{8} + 32 x^{7} - 8 x^{6} + \cdots + 256 $ x^16 + x^14 - 2x^13 - 2x^12 - 4x^11 - 2x^10 + 16x^9 + 8x^8 + 32x^7 - 8x^6 - 32x^5 - 32x^4 - 64x^3 + 64x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			589.6
Root			$-0.865014 - 1.11882i$ of defining polynomial
Character	$\chi$	$=$	1176.589
Dual form			1176.2.c.e.589.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11882 + 0.865014i) q^{2} -1.00000i q^{3} +(0.503501 - 1.93558i) q^{4} -3.57776i q^{5} +(0.865014 + 1.11882i) q^{6} +(1.11098 + 2.60110i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-1.11882 + 0.865014i) q^{2} -1.00000i q^{3} +(0.503501 - 1.93558i) q^{4} -3.57776i q^{5} +(0.865014 + 1.11882i) q^{6} +(1.11098 + 2.60110i) q^{8} -1.00000 q^{9} +(3.09481 + 4.00286i) q^{10} -0.941967i q^{11} +(-1.93558 - 0.503501i) q^{12} -6.15117i q^{13} -3.57776 q^{15} +(-3.49297 - 1.94914i) q^{16} -3.78375 q^{17} +(1.11882 - 0.865014i) q^{18} -2.41460i q^{19} +(-6.92506 - 1.80141i) q^{20} +(0.814815 + 1.05389i) q^{22} +2.98743 q^{23} +(2.60110 - 1.11098i) q^{24} -7.80037 q^{25} +(5.32085 + 6.88203i) q^{26} +1.00000i q^{27} +2.68125i q^{29} +(4.00286 - 3.09481i) q^{30} +10.7137 q^{31} +(5.59403 - 0.840746i) q^{32} -0.941967 q^{33} +(4.23332 - 3.27300i) q^{34} +(-0.503501 + 1.93558i) q^{36} +1.70724i q^{37} +(2.08866 + 2.70149i) q^{38} -6.15117 q^{39} +(9.30611 - 3.97483i) q^{40} -4.56000 q^{41} -3.50672i q^{43} +(-1.82326 - 0.474281i) q^{44} +3.57776i q^{45} +(-3.34238 + 2.58417i) q^{46} -6.84583 q^{47} +(-1.94914 + 3.49297i) q^{48} +(8.72718 - 6.74743i) q^{50} +3.78375i q^{51} +(-11.9061 - 3.09712i) q^{52} +7.59176i q^{53} +(-0.865014 - 1.11882i) q^{54} -3.37013 q^{55} -2.41460 q^{57} +(-2.31932 - 2.99983i) q^{58} +0.116189i q^{59} +(-1.80141 + 6.92506i) q^{60} +8.15432i q^{61} +(-11.9867 + 9.26752i) q^{62} +(-5.53143 + 5.77955i) q^{64} -22.0074 q^{65} +(1.05389 - 0.814815i) q^{66} -3.97580i q^{67} +(-1.90512 + 7.32377i) q^{68} -2.98743i q^{69} -3.92572 q^{71} +(-1.11098 - 2.60110i) q^{72} +6.22876 q^{73} +(-1.47678 - 1.91008i) q^{74} +7.80037i q^{75} +(-4.67365 - 1.21575i) q^{76} +(6.88203 - 5.32085i) q^{78} -5.47255 q^{79} +(-6.97354 + 12.4970i) q^{80} +1.00000 q^{81} +(5.10180 - 3.94446i) q^{82} +1.19560i q^{83} +13.5373i q^{85} +(3.03337 + 3.92338i) q^{86} +2.68125 q^{87} +(2.45015 - 1.04651i) q^{88} -1.82102 q^{89} +(-3.09481 - 4.00286i) q^{90} +(1.50417 - 5.78242i) q^{92} -10.7137i q^{93} +(7.65923 - 5.92174i) q^{94} -8.63884 q^{95} +(-0.840746 - 5.59403i) q^{96} +12.0241 q^{97} +0.941967i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9	$ 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9} - 6 q^{10} + 10 q^{16} + 2 q^{18} - 20 q^{20} - 6 q^{22} + 8 q^{23} + 6 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{30} + 24 q^{31} + 8 q^{32} - 12 q^{34} - 2 q^{36} + 26 q^{38} + 6 q^{40} - 20 q^{44} - 16 q^{46} + 24 q^{47} - 8 q^{48} + 26 q^{50} - 44 q^{52} - 32 q^{55} - 8 q^{57} - 34 q^{58} + 22 q^{60} + 50 q^{62} - 10 q^{64} - 12 q^{66} - 16 q^{68} - 40 q^{71} + 8 q^{72} - 8 q^{73} - 10 q^{74} - 16 q^{76} + 6 q^{78} - 8 q^{79} + 56 q^{80} + 16 q^{81} + 22 q^{86} - 24 q^{87} - 50 q^{88} + 6 q^{90} + 32 q^{92} + 48 q^{94} - 24 q^{95} - 10 q^{96} - 24 q^{97}+O(q^{100}) $ 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9 - 6 * q^10 + 10 * q^16 + 2 * q^18 - 20 * q^20 - 6 * q^22 + 8 * q^23 + 6 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^30 + 24 * q^31 + 8 * q^32 - 12 * q^34 - 2 * q^36 + 26 * q^38 + 6 * q^40 - 20 * q^44 - 16 * q^46 + 24 * q^47 - 8 * q^48 + 26 * q^50 - 44 * q^52 - 32 * q^55 - 8 * q^57 - 34 * q^58 + 22 * q^60 + 50 * q^62 - 10 * q^64 - 12 * q^66 - 16 * q^68 - 40 * q^71 + 8 * q^72 - 8 * q^73 - 10 * q^74 - 16 * q^76 + 6 * q^78 - 8 * q^79 + 56 * q^80 + 16 * q^81 + 22 * q^86 - 24 * q^87 - 50 * q^88 + 6 * q^90 + 32 * q^92 + 48 * q^94 - 24 * q^95 - 10 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times$.

$n$	$295$	$589$	$785$	$1081$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.11882	+	0.865014i	−0.791123	+	0.611657i
$2$	−1.11882	+	0.865014i	−0.791123	+	0.611657i
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	0.503501	−	1.93558i	0.251750	−	0.967792i
$5$		−	3.57776i		−	1.60002i	−0.599985	−	0.800012i	$-0.704827\pi$
$5$		−	3.57776i		−	1.60002i	0.599985	−	0.800012i	$-0.295173\pi$
$6$	0.865014	+	1.11882i	0.353141	+	0.456755i
$7$		0			0
$7$		0			0
$8$	1.11098	+	2.60110i	0.392792	+	0.919627i
$9$	−1.00000			−0.333333
$10$	3.09481	+	4.00286i	0.978666	+	1.26581i
$11$		−	0.941967i		−	0.284014i	−0.989866	−	0.142007i	$-0.954644\pi$
$11$		−	0.941967i		−	0.284014i	0.989866	−	0.142007i	$-0.0453555\pi$
$12$	−1.93558	−	0.503501i	−0.558755	−	0.145348i
$13$		−	6.15117i		−	1.70603i	−0.521889	−	0.853013i	$-0.674772\pi$
$13$		−	6.15117i		−	1.70603i	0.521889	−	0.853013i	$-0.325228\pi$
$14$		0			0
$15$	−3.57776			−0.923774
$16$	−3.49297	−	1.94914i	−0.873243	−	0.487284i
$17$	−3.78375			−0.917694			−0.458847	−	0.888515i	$-0.651737\pi$
$17$	−3.78375			−0.917694			−0.458847	+	0.888515i	$0.651737\pi$
$18$	1.11882	−	0.865014i	0.263708	−	0.203886i
$19$		−	2.41460i		−	0.553946i	−0.960878	−	0.276973i	$-0.910669\pi$
$19$		−	2.41460i		−	0.553946i	0.960878	−	0.276973i	$-0.0893313\pi$
$20$	−6.92506	−	1.80141i	−1.54849	−	0.402806i
$21$		0			0
$22$	0.814815	+	1.05389i	0.173719	+	0.224690i
$23$	2.98743			0.622922			0.311461	−	0.950259i	$-0.399182\pi$
$23$	2.98743			0.622922			0.311461	+	0.950259i	$0.399182\pi$
$24$	2.60110	−	1.11098i	0.530947	−	0.226778i
$25$	−7.80037			−1.56007
$26$	5.32085	+	6.88203i	1.04350	+	1.34968i
$27$			1.00000i			0.192450i
$28$		0			0
$29$			2.68125i			0.497897i	0.968517	+	0.248948i	$0.0800849\pi$
$29$			2.68125i			0.497897i	−0.968517	+	0.248948i	$0.919915\pi$
$30$	4.00286	−	3.09481i	0.730818	−	0.565033i
$31$	10.7137			1.92424			0.962120	−	0.272625i	$-0.0878919\pi$
$31$	10.7137			1.92424			0.962120	+	0.272625i	$0.0878919\pi$
$32$	5.59403	−	0.840746i	0.988894	−	0.148624i
$33$	−0.941967			−0.163975
$34$	4.23332	−	3.27300i	0.726009	−	0.561314i
$35$		0			0
$36$	−0.503501	+	1.93558i	−0.0839168	+	0.322597i
$37$			1.70724i			0.280668i	0.990104	+	0.140334i	$0.0448176\pi$
$37$			1.70724i			0.280668i	−0.990104	+	0.140334i	$0.955182\pi$
$38$	2.08866	+	2.70149i	0.338825	+	0.438239i
$39$	−6.15117			−0.984975
$40$	9.30611	−	3.97483i	1.47143	−	0.628476i
$41$	−4.56000			−0.712152			−0.356076	−	0.934457i	$-0.615886\pi$
$41$	−4.56000			−0.712152			−0.356076	+	0.934457i	$0.615886\pi$
$42$		0			0
$43$		−	3.50672i		−	0.534770i	−0.963590	−	0.267385i	$-0.913840\pi$
$43$		−	3.50672i		−	0.534770i	0.963590	−	0.267385i	$-0.0861596\pi$
$44$	−1.82326	−	0.474281i	−0.274866	−	0.0715006i
$45$			3.57776i			0.533341i
$46$	−3.34238	+	2.58417i	−0.492808	+	0.381015i
$47$	−6.84583			−0.998567			−0.499284	−	0.866439i	$-0.666403\pi$
$47$	−6.84583			−0.998567			−0.499284	+	0.866439i	$0.666403\pi$
$48$	−1.94914	+	3.49297i	−0.281334	+	0.504167i
$49$		0			0
$50$	8.72718	−	6.74743i	1.23421	−	0.954231i
$51$			3.78375i			0.529831i
$52$	−11.9061	−	3.09712i	−1.65108	−	0.429493i
$53$			7.59176i			1.04281i	0.853310	+	0.521404i	$0.174592\pi$
$53$			7.59176i			1.04281i	−0.853310	+	0.521404i	$0.825408\pi$
$54$	−0.865014	−	1.11882i	−0.117714	−	0.152252i
$55$	−3.37013			−0.454429
$56$		0			0
$57$	−2.41460			−0.319821
$58$	−2.31932	−	2.99983i	−0.304542	−	0.393897i
$59$			0.116189i			0.0151266i	0.999971	+	0.00756328i	$0.00240749\pi$
$59$			0.116189i			0.0151266i	−0.999971	+	0.00756328i	$0.997593\pi$
$60$	−1.80141	+	6.92506i	−0.232560	+	0.894021i
$61$			8.15432i			1.04405i	0.852929	+	0.522027i	$0.174824\pi$
$61$			8.15432i			1.04405i	−0.852929	+	0.522027i	$0.825176\pi$
$62$	−11.9867	+	9.26752i	−1.52231	+	1.17698i
$63$		0			0
$64$	−5.53143	+	5.77955i	−0.691429	+	0.722444i
$65$	−22.0074			−2.72968
$66$	1.05389	−	0.814815i	0.129725	−	0.100297i
$67$		−	3.97580i		−	0.485721i	−0.970061	−	0.242861i	$-0.921914\pi$
$67$		−	3.97580i		−	0.485721i	0.970061	−	0.242861i	$-0.0780857\pi$
$68$	−1.90512	+	7.32377i	−0.231030	+	0.888137i
$69$		−	2.98743i		−	0.359644i
$70$		0			0
$71$	−3.92572			−0.465897			−0.232949	−	0.972489i	$-0.574837\pi$
$71$	−3.92572			−0.465897			−0.232949	+	0.972489i	$0.574837\pi$
$72$	−1.11098	−	2.60110i	−0.130931	−	0.306542i
$73$	6.22876			0.729022			0.364511	−	0.931199i	$-0.381236\pi$
$73$	6.22876			0.729022			0.364511	+	0.931199i	$0.381236\pi$
$74$	−1.47678	−	1.91008i	−0.171673	−	0.222043i
$75$			7.80037i			0.900709i
$76$	−4.67365	−	1.21575i	−0.536105	−	0.139456i
$77$		0			0
$78$	6.88203	−	5.32085i	0.779236	−	0.602467i
$79$	−5.47255			−0.615710			−0.307855	−	0.951433i	$-0.599611\pi$
$79$	−5.47255			−0.615710			−0.307855	+	0.951433i	$0.599611\pi$
$80$	−6.97354	+	12.4970i	−0.779666	+	1.39721i
$81$	1.00000			0.111111
$82$	5.10180	−	3.94446i	0.563400	−	0.435593i
$83$			1.19560i			0.131234i	0.997845	+	0.0656172i	$0.0209016\pi$
$83$			1.19560i			0.131234i	−0.997845	+	0.0656172i	$0.979098\pi$
$84$		0			0
$85$			13.5373i			1.46833i
$86$	3.03337	+	3.92338i	0.327096	+	0.423069i
$87$	2.68125			0.287461
$88$	2.45015	−	1.04651i	0.261187	−	0.111558i
$89$	−1.82102			−0.193028			−0.0965138	−	0.995332i	$-0.530769\pi$
$89$	−1.82102			−0.193028			−0.0965138	+	0.995332i	$0.530769\pi$
$90$	−3.09481	−	4.00286i	−0.326222	−	0.421938i
$91$		0			0
$92$	1.50417	−	5.78242i	0.156821	−	0.602859i
$93$		−	10.7137i		−	1.11096i
$94$	7.65923	−	5.92174i	0.789989	−	0.610781i
$95$	−8.63884			−0.886327
$96$	−0.840746	−	5.59403i	−0.0858082	−	0.570938i
$97$	12.0241			1.22086			0.610431	−	0.792069i	$-0.290996\pi$
$97$	12.0241			1.22086			0.610431	+	0.792069i	$0.290996\pi$
$98$		0			0
$99$			0.941967i			0.0946713i
$100$	−3.92749	+	15.0983i	−0.392749	+	1.50983i
$101$			1.78101i			0.177217i	0.996067	+	0.0886085i	$0.0282420\pi$
$101$			1.78101i			0.177217i	−0.996067	+	0.0886085i	$0.971758\pi$
$102$	−3.27300	−	4.23332i	−0.324075	−	0.419161i
$103$	−12.4230			−1.22407			−0.612037	−	0.790829i	$-0.709650\pi$
$103$	−12.4230			−1.22407			−0.612037	+	0.790829i	$0.709650\pi$
$104$	15.9998	−	6.83384i	1.56891	−	0.670113i
$105$		0			0
$106$	−6.56698	−	8.49379i	−0.637842	−	0.824990i
$107$		−	9.71411i		−	0.939098i	−0.882906	−	0.469549i	$-0.844417\pi$
$107$		−	9.71411i		−	0.939098i	0.882906	−	0.469549i	$-0.155583\pi$
$108$	1.93558	+	0.503501i	0.186252	+	0.0484494i
$109$		−	14.2775i		−	1.36753i	−0.729700	−	0.683767i	$-0.760340\pi$
$109$		−	14.2775i		−	1.36753i	0.729700	−	0.683767i	$-0.239660\pi$
$110$	3.77056	−	2.91521i	0.359509	−	0.277955i
$111$	1.70724			0.162044
$112$		0			0
$113$	−13.8775			−1.30549			−0.652743	−	0.757580i	$-0.726382\pi$
$113$	−13.8775			−1.30549			−0.652743	+	0.757580i	$0.726382\pi$
$114$	2.70149	−	2.08866i	0.253018	−	0.195621i
$115$		−	10.6883i		−	0.996690i
$116$	5.18980	+	1.35001i	0.481860	+	0.125346i
$117$			6.15117i			0.568676i
$118$	−0.100505	−	0.129995i	−0.00925228	−	0.0119670i
$119$		0			0
$120$	−3.97483	−	9.30611i	−0.362851	−	0.849528i
$121$	10.1127			0.919336
$122$	−7.05360	−	9.12318i	−0.638603	−	0.825974i
$123$			4.56000i			0.411161i
$124$	5.39437	−	20.7373i	0.484428	−	1.86227i
$125$			10.0191i			0.896131i
$126$		0			0
$127$	7.77389			0.689822			0.344911	−	0.938635i	$-0.387909\pi$
$127$	7.77389			0.689822			0.344911	+	0.938635i	$0.387909\pi$
$128$	1.18926	−	11.2510i	0.105117	−	0.994460i
$129$	−3.50672			−0.308750
$130$	24.6222	−	19.0367i	2.15951	−	1.66963i
$131$			7.04522i			0.615543i	0.951460	+	0.307772i	$0.0995833\pi$
$131$			7.04522i			0.615543i	−0.951460	+	0.307772i	$0.900417\pi$
$132$	−0.474281	+	1.82326i	−0.0412809	+	0.158694i
$133$		0			0
$134$	3.43912	+	4.44819i	0.297095	+	0.384265i
$135$	3.57776			0.307925
$136$	−4.20368	−	9.84191i	−0.360463	−	0.843937i
$137$	−18.1076			−1.54704			−0.773518	−	0.633775i	$-0.781505\pi$
$137$	−18.1076			−1.54704			−0.773518	+	0.633775i	$0.781505\pi$
$138$	2.58417	+	3.34238i	0.219979	+	0.284523i
$139$		−	8.32721i		−	0.706305i	−0.935566	−	0.353152i	$-0.885110\pi$
$139$		−	8.32721i		−	0.706305i	0.935566	−	0.353152i	$-0.114890\pi$
$140$		0			0
$141$			6.84583i			0.576523i
$142$	4.39216	−	3.39580i	0.368582	−	0.284969i
$143$	−5.79420			−0.484535
$144$	3.49297	+	1.94914i	0.291081	+	0.162428i
$145$	9.59289			0.796646
$146$	−6.96884	+	5.38797i	−0.576746	+	0.445911i
$147$		0			0
$148$	3.30450	+	0.859595i	0.271628	+	0.0706582i
$149$			20.7056i			1.69627i	0.529782	+	0.848134i	$0.322274\pi$
$149$			20.7056i			1.69627i	−0.529782	+	0.848134i	$0.677726\pi$
$150$	−6.74743	−	8.72718i	−0.550925	−	0.712572i
$151$	3.95566			0.321907			0.160954	−	0.986962i	$-0.448543\pi$
$151$	3.95566			0.321907			0.160954	+	0.986962i	$0.448543\pi$
$152$	6.28060	−	2.68257i	0.509424	−	0.217585i
$153$	3.78375			0.305898
$154$		0			0
$155$		−	38.3311i		−	3.07883i
$156$	−3.09712	+	11.9061i	−0.247968	+	0.953251i
$157$			11.8706i			0.947381i	0.880691	+	0.473690i	$0.157078\pi$
$157$			11.8706i			0.947381i	−0.880691	+	0.473690i	$0.842922\pi$
$158$	6.12278	−	4.73383i	0.487102	−	0.376604i
$159$	7.59176			0.602066
$160$	−3.00799	−	20.0141i	−0.237802	−	1.58225i
$161$		0			0
$162$	−1.11882	+	0.865014i	−0.0879025	+	0.0679619i
$163$		−	17.0530i		−	1.33569i	−0.744299	−	0.667846i	$-0.767216\pi$
$163$		−	17.0530i		−	1.33569i	0.744299	−	0.667846i	$-0.232784\pi$
$164$	−2.29596	+	8.82626i	−0.179285	+	0.689215i
$165$			3.37013i			0.262365i
$166$	−1.03421	−	1.33766i	−0.0802705	−	0.103823i
$167$	10.4339			0.807396			0.403698	−	0.914892i	$-0.367725\pi$
$167$	10.4339			0.807396			0.403698	+	0.914892i	$0.367725\pi$
$168$		0			0
$169$	−24.8369			−1.91053
$170$	−11.7100	−	15.1458i	−0.898116	−	1.16163i
$171$			2.41460i			0.184649i
$172$	−6.78756	−	1.76564i	−0.517547	−	0.134629i
$173$		−	14.5742i		−	1.10805i	−0.832499	−	0.554027i	$-0.813091\pi$
$173$		−	14.5742i		−	1.10805i	0.832499	−	0.554027i	$-0.186909\pi$
$174$	−2.99983	+	2.31932i	−0.227417	+	0.175827i
$175$		0			0
$176$	−1.83602	+	3.29027i	−0.138395	+	0.248013i
$177$	0.116189			0.00873333
$178$	2.03738	−	1.57521i	0.152708	−	0.118067i
$179$			3.77961i			0.282501i	0.989974	+	0.141251i	$0.0451123\pi$
$179$			3.77961i			0.282501i	−0.989974	+	0.141251i	$0.954888\pi$
$180$	6.92506	+	1.80141i	0.516163	+	0.134269i
$181$			1.12363i			0.0835189i	0.999128	+	0.0417595i	$0.0132963\pi$
$181$			1.12363i			0.0835189i	−0.999128	+	0.0417595i	$0.986704\pi$
$182$		0			0
$183$	8.15432			0.602784
$184$	3.31898	+	7.77060i	0.244679	+	0.572856i
$185$	6.10808			0.449075
$186$	9.26752	+	11.9867i	0.679527	+	0.878906i
$187$			3.56417i			0.260638i
$188$	−3.44688	+	13.2507i	−0.251390	+	0.966406i
$189$		0			0
$190$	9.66528	−	7.47272i	0.701193	−	0.542128i
$191$	14.0300			1.01518			0.507589	−	0.861600i	$-0.330537\pi$
$191$	14.0300			1.01518			0.507589	+	0.861600i	$0.330537\pi$
$192$	5.77955	+	5.53143i	0.417103	+	0.399197i
$193$	0.780195			0.0561597			0.0280798	−	0.999606i	$-0.491061\pi$
$193$	0.780195			0.0561597			0.0280798	+	0.999606i	$0.491061\pi$
$194$	−13.4528	+	10.4010i	−0.965852	+	0.746750i
$195$			22.0074i			1.57598i
$196$		0			0
$197$			2.37637i			0.169309i	0.996410	+	0.0846545i	$0.0269787\pi$
$197$			2.37637i			0.169309i	−0.996410	+	0.0846545i	$0.973021\pi$
$198$	−0.814815	−	1.05389i	−0.0579064	−	0.0748966i
$199$	−13.5839			−0.962938			−0.481469	−	0.876463i	$-0.659897\pi$
$199$	−13.5839			−0.962938			−0.481469	+	0.876463i	$0.659897\pi$
$200$	−8.66608	−	20.2895i	−0.612784	−	1.43469i
$201$	−3.97580			−0.280431
$202$	−1.54060	−	1.99262i	−0.108396	−	0.140200i
$203$		0			0
$204$	7.32377	+	1.90512i	0.512766	+	0.133385i
$205$			16.3146i			1.13946i
$206$	13.8991	−	10.7461i	0.968393	−	0.748714i
$207$	−2.98743			−0.207641
$208$	−11.9895	+	21.4859i	−0.831320	+	1.48978i
$209$	−2.27447			−0.157328
$210$		0			0
$211$			14.1932i			0.977103i	0.872535	+	0.488551i	$0.162474\pi$
$211$			14.1932i			0.977103i	−0.872535	+	0.488551i	$0.837526\pi$
$212$	14.6945	+	3.82246i	1.00922	+	0.262528i
$213$			3.92572i			0.268986i
$214$	8.40284	+	10.8683i	0.574406	+	0.742942i
$215$	−12.5462			−0.855645
$216$	−2.60110	+	1.11098i	−0.176982	+	0.0755928i
$217$		0			0
$218$	12.3502	+	15.9739i	0.836462	+	1.08189i
$219$		−	6.22876i		−	0.420901i
$220$	−1.69687	+	6.52318i	−0.114403	+	0.439793i
$221$			23.2745i			1.56561i
$222$	−1.91008	+	1.47678i	−0.128196	+	0.0991152i
$223$	−0.198178			−0.0132710			−0.00663548	−	0.999978i	$-0.502112\pi$
$223$	−0.198178			−0.0132710			−0.00663548	+	0.999978i	$0.502112\pi$
$224$		0			0
$225$	7.80037			0.520025
$226$	15.5264	−	12.0042i	1.03280	−	0.798510i
$227$		−	25.7560i		−	1.70949i	−0.519050	−	0.854744i	$-0.673714\pi$
$227$		−	25.7560i		−	1.70949i	0.519050	−	0.854744i	$-0.326286\pi$
$228$	−1.21575	+	4.67365i	−0.0805151	+	0.309520i
$229$		−	16.1617i		−	1.06800i	−0.845485	−	0.533999i	$-0.820689\pi$
$229$		−	16.1617i		−	1.06800i	0.845485	−	0.533999i	$-0.179311\pi$
$230$	9.24554	+	11.9583i	0.609633	+	0.788504i
$231$		0			0
$232$	−6.97421	+	2.97883i	−0.457879	+	0.195570i
$233$	25.1239			1.64592			0.822959	−	0.568100i	$-0.192321\pi$
$233$	25.1239			1.64592			0.822959	+	0.568100i	$0.192321\pi$
$234$	−5.32085	−	6.88203i	−0.347835	−	0.449892i
$235$			24.4927i			1.59773i
$236$	0.224894	+	0.0585014i	0.0146394	+	0.00380812i
$237$			5.47255i			0.355480i
$238$		0			0
$239$	16.0389			1.03747			0.518736	−	0.854935i	$-0.326403\pi$
$239$	16.0389			1.03747			0.518736	+	0.854935i	$0.326403\pi$
$240$	12.4970	+	6.97354i	0.806679	+	0.450140i
$241$	−13.1691			−0.848293			−0.424147	−	0.905594i	$-0.639426\pi$
$241$	−13.1691			−0.848293			−0.424147	+	0.905594i	$0.639426\pi$
$242$	−11.3143	+	8.74763i	−0.727308	+	0.562319i
$243$		−	1.00000i		−	0.0641500i
$244$	15.7834	+	4.10570i	1.01043	+	0.262841i
$245$		0			0
$246$	−3.94446	−	5.10180i	−0.251490	−	0.325279i
$247$	−14.8526			−0.945047
$248$	11.9028	+	27.8674i	0.755826	+	1.76958i
$249$	1.19560			0.0757683
$250$	−8.66662	−	11.2095i	−0.548125	−	0.708950i
$251$		−	8.64704i		−	0.545796i	−0.962043	−	0.272898i	$-0.912018\pi$
$251$		−	8.64704i		−	0.545796i	0.962043	−	0.272898i	$-0.0879822\pi$
$252$		0			0
$253$		−	2.81406i		−	0.176918i
$254$	−8.69756	+	6.72453i	−0.545733	+	0.421934i
$255$	13.5373			0.847742
$256$	8.40173	+	13.6166i	0.525108	+	0.851035i
$257$	−14.4651			−0.902307			−0.451154	−	0.892446i	$-0.648987\pi$
$257$	−14.4651			−0.902307			−0.451154	+	0.892446i	$0.648987\pi$
$258$	3.92338	−	3.03337i	0.244259	−	0.188849i
$259$		0			0
$260$	−11.0807	+	42.5972i	−0.687199	+	2.64177i
$261$		−	2.68125i		−	0.165966i
$262$	−6.09421	−	7.88230i	−0.376502	−	0.486970i
$263$	19.8967			1.22688			0.613440	−	0.789741i	$-0.289785\pi$
$263$	19.8967			1.22688			0.613440	+	0.789741i	$0.289785\pi$
$264$	−1.04651	−	2.45015i	−0.0644082	−	0.150796i
$265$	27.1615			1.66852
$266$		0			0
$267$			1.82102i			0.111444i
$268$	−7.69549	−	2.00182i	−0.470077	−	0.122280i
$269$		−	16.9660i		−	1.03443i	−0.855854	−	0.517217i	$-0.826968\pi$
$269$		−	16.9660i		−	1.03443i	0.855854	−	0.517217i	$-0.173032\pi$
$270$	−4.00286	+	3.09481i	−0.243606	+	0.188344i
$271$	1.07637			0.0653849			0.0326925	−	0.999465i	$-0.489592\pi$
$271$	1.07637			0.0653849			0.0326925	+	0.999465i	$0.489592\pi$
$272$	13.2165	+	7.37504i	0.801370	+	0.447178i
$273$		0			0
$274$	20.2591	−	15.6633i	1.22390	−	0.946256i
$275$			7.34769i			0.443083i
$276$	−5.78242	−	1.50417i	−0.348061	−	0.0905406i
$277$		−	4.89143i		−	0.293898i	−0.989144	−	0.146949i	$-0.953055\pi$
$277$		−	4.89143i		−	0.293898i	0.989144	−	0.146949i	$-0.0469453\pi$
$278$	7.20315	+	9.31662i	0.432016	+	0.558774i
$279$	−10.7137			−0.641414
$280$		0			0
$281$	−0.754188			−0.0449911			−0.0224956	−	0.999747i	$-0.507161\pi$
$281$	−0.754188			−0.0449911			−0.0224956	+	0.999747i	$0.507161\pi$
$282$	−5.92174	−	7.65923i	−0.352635	−	0.456101i
$283$		−	19.4302i		−	1.15501i	−0.816389	−	0.577503i	$-0.804027\pi$
$283$		−	19.4302i		−	1.15501i	0.816389	−	0.577503i	$-0.195973\pi$
$284$	−1.97660	+	7.59856i	−0.117290	+	0.450892i
$285$			8.63884i			0.511721i
$286$	6.48265	−	5.01206i	0.383327	−	0.296370i
$287$		0			0
$288$	−5.59403	+	0.840746i	−0.329631	+	0.0495414i
$289$	−2.68324			−0.157838
$290$	−10.7327	+	8.29798i	−0.630245	+	0.487274i
$291$		−	12.0241i		−	0.704865i
$292$	3.13619	−	12.0563i	0.183531	−	0.705541i
$293$		−	21.9433i		−	1.28194i	−0.767564	−	0.640972i	$-0.778532\pi$
$293$		−	21.9433i		−	1.28194i	0.767564	−	0.640972i	$-0.221468\pi$
$294$		0			0
$295$	0.415698			0.0242029
$296$	−4.44069	+	1.89671i	−0.258110	+	0.110244i
$297$	0.941967			0.0546585
$298$	−17.9106	−	23.1658i	−1.03753	−	1.34196i
$299$		−	18.3762i		−	1.06272i
$300$	15.0983	+	3.92749i	0.871699	+	0.226754i
$301$		0			0
$302$	−4.42566	+	3.42170i	−0.254668	+	0.196897i
$303$	1.78101			0.102316
$304$	−4.70638	+	8.43412i	−0.269929	+	0.483730i
$305$	29.1742			1.67051
$306$	−4.23332	+	3.27300i	−0.242003	+	0.187105i
$307$		−	2.18555i		−	0.124736i	−0.998053	−	0.0623679i	$-0.980135\pi$
$307$		−	2.18555i		−	0.124736i	0.998053	−	0.0623679i	$-0.0198652\pi$
$308$		0			0
$309$			12.4230i			0.706720i
$310$	33.1570	+	42.8855i	1.88319	+	2.43573i
$311$	27.2685			1.54626			0.773129	−	0.634249i	$-0.218691\pi$
$311$	27.2685			1.54626			0.773129	+	0.634249i	$0.218691\pi$
$312$	−6.83384	−	15.9998i	−0.386890	−	0.905810i
$313$	−1.36654			−0.0772412			−0.0386206	−	0.999254i	$-0.512296\pi$
$313$	−1.36654			−0.0772412			−0.0386206	+	0.999254i	$0.512296\pi$
$314$	−10.2683	−	13.2811i	−0.579472	−	0.749494i
$315$		0			0
$316$	−2.75543	+	10.5926i	−0.155005	+	0.595879i
$317$			8.19107i			0.460056i	0.973184	+	0.230028i	$0.0738819\pi$
$317$			8.19107i			0.460056i	−0.973184	+	0.230028i	$0.926118\pi$
$318$	−8.49379	+	6.56698i	−0.476308	+	0.368258i
$319$	2.52565			0.141410
$320$	20.6779	+	19.7901i	1.15593	+	1.10630i
$321$	−9.71411			−0.542189
$322$		0			0
$323$			9.13622i			0.508353i
$324$	0.503501	−	1.93558i	0.0279723	−	0.107532i
$325$			47.9814i			2.66153i
$326$	14.7511	+	19.0792i	0.816987	+	1.05670i
$327$	−14.2775			−0.789546
$328$	−5.06608	−	11.8610i	−0.279727	−	0.654914i
$329$		0			0
$330$	−2.91521	−	3.77056i	−0.160477	−	0.207563i
$331$			15.4318i			0.848208i	0.905613	+	0.424104i	$0.139411\pi$
$331$			15.4318i			0.848208i	−0.905613	+	0.424104i	$0.860589\pi$
$332$	2.31419	+	0.601987i	0.127008	+	0.0330383i
$333$		−	1.70724i		−	0.0935559i
$334$	−11.6736	+	9.02543i	−0.638749	+	0.493850i
$335$	−14.2245			−0.777165
$336$		0			0
$337$	−0.543923			−0.0296294			−0.0148147	−	0.999890i	$-0.504716\pi$
$337$	−0.543923			−0.0296294			−0.0148147	+	0.999890i	$0.504716\pi$
$338$	27.7879	−	21.4842i	1.51146	−	1.16859i
$339$			13.8775i			0.753722i
$340$	26.2027	+	6.81607i	1.42104	+	0.369653i
$341$		−	10.0920i		−	0.546511i
$342$	−2.08866	−	2.70149i	−0.112942	−	0.146080i
$343$		0			0
$344$	9.12134	−	3.89591i	0.491790	−	0.210053i
$345$	−10.6883			−0.575439
$346$	12.6069	+	16.3058i	0.677749	+	0.876606i
$347$		−	11.4632i		−	0.615375i	−0.951487	−	0.307688i	$-0.900445\pi$
$347$		−	11.4632i		−	0.615375i	0.951487	−	0.307688i	$-0.0995552\pi$
$348$	1.35001	−	5.18980i	0.0723684	−	0.278202i
$349$			1.23092i			0.0658899i	0.999457	+	0.0329449i	$0.0104886\pi$
$349$			1.23092i			0.0658899i	−0.999457	+	0.0329449i	$0.989511\pi$
$350$		0			0
$351$	6.15117			0.328325
$352$	−0.791955	−	5.26939i	−0.0422113	−	0.280860i
$353$	−34.2183			−1.82126			−0.910628	−	0.413228i	$-0.864401\pi$
$353$	−34.2183			−1.82126			−0.910628	+	0.413228i	$0.864401\pi$
$354$	−0.129995	+	0.100505i	−0.00690913	+	0.00534180i
$355$			14.0453i			0.745446i
$356$	−0.916884	+	3.52473i	−0.0485948	+	0.186811i
$357$		0			0
$358$	−3.26941	−	4.22869i	−0.172794	−	0.223493i
$359$	33.9072			1.78955			0.894777	−	0.446513i	$-0.147334\pi$
$359$	33.9072			1.78955			0.894777	+	0.446513i	$0.147334\pi$
$360$	−9.30611	+	3.97483i	−0.490475	+	0.209492i
$361$	13.1697			0.693144
$362$	−0.971958	−	1.25714i	−0.0510850	−	0.0660737i
$363$		−	10.1127i		−	0.530779i
$364$		0			0
$365$		−	22.2850i		−	1.16645i
$366$	−9.12318	+	7.05360i	−0.476876	+	0.368697i
$367$	−19.2447			−1.00456			−0.502282	−	0.864704i	$-0.667506\pi$
$367$	−19.2447			−1.00456			−0.502282	+	0.864704i	$0.667506\pi$
$368$	−10.4350	−	5.82291i	−0.543963	−	0.303540i
$369$	4.56000			0.237384
$370$	−6.83382	+	5.28358i	−0.355273	+	0.274680i
$371$		0			0
$372$	−20.7373	−	5.39437i	−1.07518	−	0.279685i
$373$			14.8337i			0.768061i	0.923320	+	0.384030i	$0.125464\pi$
$373$			14.8337i			0.768061i	−0.923320	+	0.384030i	$0.874536\pi$
$374$	−3.08306	−	3.98765i	−0.159421	−	0.206196i
$375$	10.0191			0.517382
$376$	−7.60560	−	17.8067i	−0.392229	−	0.918310i
$377$	16.4928			0.849425
$378$		0			0
$379$			11.7500i			0.603555i	0.953378	+	0.301778i	$0.0975800\pi$
$379$			11.7500i			0.603555i	−0.953378	+	0.301778i	$0.902420\pi$
$380$	−4.34966	+	16.7212i	−0.223133	+	0.857780i
$381$		−	7.77389i		−	0.398269i
$382$	−15.6970	+	12.1362i	−0.803130	+	0.620941i
$383$	19.0655			0.974200			0.487100	−	0.873346i	$-0.338055\pi$
$383$	19.0655			0.974200			0.487100	+	0.873346i	$0.338055\pi$
$384$	−11.2510	−	1.18926i	−0.574152	−	0.0606894i
$385$		0			0
$386$	−0.872895	+	0.674880i	−0.0444292	+	0.0343505i
$387$			3.50672i			0.178257i
$388$	6.05415	−	23.2737i	0.307353	−	1.18154i
$389$			2.00331i			0.101572i	0.998710	+	0.0507859i	$0.0161726\pi$
$389$			2.00331i			0.101572i	−0.998710	+	0.0507859i	$0.983827\pi$
$390$	−19.0367	−	24.6222i	−0.963962	−	1.24680i
$391$	−11.3037			−0.571652
$392$		0			0
$393$	7.04522			0.355384
$394$	−2.05559	−	2.65872i	−0.103559	−	0.133944i
$395$			19.5795i			0.985150i
$396$	1.82326	+	0.474281i	0.0916221	+	0.0238335i
$397$		−	8.48379i		−	0.425789i	−0.977075	−	0.212895i	$-0.931711\pi$
$397$		−	8.48379i		−	0.425789i	0.977075	−	0.212895i	$-0.0682891\pi$
$398$	15.1979	−	11.7503i	0.761802	−	0.588988i
$399$		0			0
$400$	27.2465	+	15.2040i	1.36232	+	0.760199i
$401$	−14.0926			−0.703753			−0.351876	−	0.936046i	$-0.614456\pi$
$401$	−14.0926			−0.703753			−0.351876	+	0.936046i	$0.614456\pi$
$402$	4.44819	−	3.43912i	0.221855	−	0.171528i
$403$		−	65.9019i		−	3.28281i
$404$	3.44729	+	0.896739i	0.171509	+	0.0446144i
$405$		−	3.57776i		−	0.177780i
$406$		0			0
$407$	1.60816			0.0797135
$408$	−9.84191	+	4.20368i	−0.487247	+	0.208113i
$409$	30.3577			1.50109			0.750547	−	0.660817i	$-0.229790\pi$
$409$	30.3577			1.50109			0.750547	+	0.660817i	$0.229790\pi$
$410$	−14.1123	−	18.2530i	−0.696959	−	0.901452i
$411$			18.1076i			0.893181i
$412$	−6.25499	+	24.0458i	−0.308161	+	1.18465i
$413$		0			0
$414$	3.34238	−	2.58417i	0.164269	−	0.127005i
$415$	4.27758			0.209978
$416$	−5.17157	−	34.4098i	−0.253557	−	1.68708i
$417$	−8.32721			−0.407785
$418$	2.54471	−	1.96745i	0.124466	−	0.0962311i
$419$			30.8896i			1.50905i	0.656269	+	0.754527i	$0.272134\pi$
$419$			30.8896i			1.50905i	−0.656269	+	0.754527i	$0.727866\pi$
$420$		0			0
$421$			20.0940i			0.979321i	0.871913	+	0.489661i	$0.162879\pi$
$421$			20.0940i			0.979321i	−0.871913	+	0.489661i	$0.837121\pi$
$422$	−12.2774	−	15.8796i	−0.597652	−	0.773008i
$423$	6.84583			0.332856
$424$	−19.7469	+	8.43432i	−0.958996	+	0.409607i
$425$	29.5146			1.43167
$426$	−3.39580	−	4.39216i	−0.164527	−	0.212801i
$427$		0			0
$428$	−18.8025	−	4.89106i	−0.908852	−	0.236418i
$429$			5.79420i			0.279747i
$430$	14.0369	−	10.8527i	0.676920	−	0.523362i
$431$	8.01747			0.386188			0.193094	−	0.981180i	$-0.438148\pi$
$431$	8.01747			0.386188			0.193094	+	0.981180i	$0.438148\pi$
$432$	1.94914	−	3.49297i	0.0937779	−	0.168056i
$433$	−26.9812			−1.29663			−0.648316	−	0.761371i	$-0.724527\pi$
$433$	−26.9812			−1.29663			−0.648316	+	0.761371i	$0.724527\pi$
$434$		0			0
$435$		−	9.59289i		−	0.459944i
$436$	−27.6353	−	7.18872i	−1.32349	−	0.344277i
$437$		−	7.21343i		−	0.345065i
$438$	5.38797	+	6.96884i	0.257447	+	0.332984i
$439$	36.5152			1.74278			0.871388	−	0.490594i	$-0.163220\pi$
$439$	36.5152			1.74278			0.871388	+	0.490594i	$0.163220\pi$
$440$	−3.74416	−	8.76605i	−0.178496	−	0.417905i
$441$		0			0
$442$	−20.1328	−	26.0399i	−0.957617	−	1.23859i
$443$			0.219929i			0.0104491i	0.999986	+	0.00522457i	$0.00166304\pi$
$443$			0.219929i			0.0104491i	−0.999986	+	0.00522457i	$0.998337\pi$
$444$	0.859595	−	3.30450i	0.0407946	−	0.156825i
$445$			6.51517i			0.308848i
$446$	0.221725	−	0.171427i	0.0104990	−	0.00811728i
$447$	20.7056			0.979341
$448$		0			0
$449$	20.6799			0.975946			0.487973	−	0.872859i	$-0.337736\pi$
$449$	20.6799			0.975946			0.487973	+	0.872859i	$0.337736\pi$
$450$	−8.72718	+	6.74743i	−0.411403	+	0.318077i
$451$			4.29537i			0.202261i
$452$	−6.98733	+	26.8611i	−0.328656	+	1.26344i
$453$		−	3.95566i		−	0.185853i
$454$	22.2793	+	28.8163i	1.04562	+	1.35242i
$455$		0			0
$456$	−2.68257	−	6.28060i	−0.125623	−	0.294116i
$457$	−8.58418			−0.401551			−0.200776	−	0.979637i	$-0.564346\pi$
$457$	−8.58418			−0.401551			−0.200776	+	0.979637i	$0.564346\pi$
$458$	13.9801	+	18.0820i	0.653249	+	0.844917i
$459$		−	3.78375i		−	0.176610i
$460$	−20.6881	−	5.38157i	−0.964588	−	0.250917i
$461$		−	13.8203i		−	0.643676i	−0.946795	−	0.321838i	$-0.895699\pi$
$461$		−	13.8203i		−	0.643676i	0.946795	−	0.321838i	$-0.104301\pi$
$462$		0			0
$463$	28.8694			1.34168			0.670838	−	0.741604i	$-0.265935\pi$
$463$	28.8694			1.34168			0.670838	+	0.741604i	$0.265935\pi$
$464$	5.22613	−	9.36555i	0.242617	−	0.434785i
$465$	−38.3311			−1.77756
$466$	−28.1090	+	21.7325i	−1.30212	+	1.00674i
$467$		−	12.4341i		−	0.575381i	−0.957723	−	0.287691i	$-0.907112\pi$
$467$		−	12.4341i		−	0.575381i	0.957723	−	0.287691i	$-0.0928875\pi$
$468$	11.9061	+	3.09712i	0.550360	+	0.143164i
$469$		0			0
$470$	−21.1866	−	27.4029i	−0.977264	−	1.26400i
$471$	11.8706			0.546970
$472$	−0.302220	+	0.129084i	−0.0139108	+	0.00594159i
$473$	−3.30322			−0.151882
$474$	−4.73383	−	6.12278i	−0.217432	−	0.281229i
$475$			18.8347i			0.864197i
$476$		0			0
$477$		−	7.59176i		−	0.347603i
$478$	−17.9446	+	13.8739i	−0.820767	+	0.634577i
$479$	38.2820			1.74915			0.874575	−	0.484891i	$-0.161141\pi$
$479$	38.2820			1.74915			0.874575	+	0.484891i	$0.161141\pi$
$480$	−20.0141	+	3.00799i	−0.913514	+	0.137295i
$481$	10.5015			0.478827
$482$	14.7338	−	11.3914i	0.671104	−	0.518865i
$483$		0			0
$484$	5.09175	−	19.5740i	0.231443	−	0.889726i
$485$		−	43.0194i		−	1.95341i
$486$	0.865014	+	1.11882i	0.0392378	+	0.0507505i
$487$	−1.80458			−0.0817733			−0.0408867	−	0.999164i	$-0.513018\pi$
$487$	−1.80458			−0.0817733			−0.0408867	+	0.999164i	$0.513018\pi$
$488$	−21.2102	+	9.05930i	−0.960140	+	0.410095i
$489$	−17.0530			−0.771163
$490$		0			0
$491$		−	4.10278i		−	0.185156i	−0.995705	−	0.0925780i	$-0.970489\pi$
$491$		−	4.10278i		−	0.185156i	0.995705	−	0.0925780i	$-0.0295108\pi$
$492$	8.82626	+	2.29596i	0.397918	+	0.103510i
$493$		−	10.1452i		−	0.456917i
$494$	16.6173	−	12.8477i	0.747648	−	0.578045i
$495$	3.37013			0.151476
$496$	−37.4227	−	20.8825i	−1.68033	−	0.937652i
$497$		0			0
$498$	−1.33766	+	1.03421i	−0.0599420	+	0.0463442i
$499$		−	44.4007i		−	1.98765i	−0.110961	−	0.993825i	$-0.535393\pi$
$499$		−	44.4007i		−	1.98765i	0.110961	−	0.993825i	$-0.464607\pi$
$500$	19.3927	+	5.04460i	0.867269	+	0.225601i
$501$		−	10.4339i		−	0.466150i
$502$	7.47981	+	9.67445i	0.333840	+	0.431792i
$503$	8.88976			0.396375			0.198187	−	0.980164i	$-0.436495\pi$
$503$	8.88976			0.396375			0.198187	+	0.980164i	$0.436495\pi$
$504$		0			0
$505$	6.37202			0.283551
$506$	2.43420	+	3.14842i	0.108213	+	0.139964i
$507$			24.8369i			1.10304i
$508$	3.91416	−	15.0470i	0.173663	−	0.667604i
$509$		−	11.0463i		−	0.489621i	−0.969571	−	0.244810i	$-0.921274\pi$
$509$		−	11.0463i		−	0.489621i	0.969571	−	0.244810i	$-0.0787257\pi$
$510$	−15.1458	+	11.7100i	−0.670668	+	0.518527i
$511$		0			0
$512$	−21.1785	−	7.96682i	−0.935967	−	0.352087i
$513$	2.41460			0.106607
$514$	16.1838	−	12.5125i	0.713836	−	0.551903i
$515$			44.4465i			1.95855i
$516$	−1.76564	+	6.78756i	−0.0777279	+	0.298806i
$517$			6.44855i			0.283607i
$518$		0			0
$519$	−14.5742			−0.639735
$520$	−24.4498	−	57.2434i	−1.07220	−	2.51029i
$521$	−33.9951			−1.48935			−0.744675	−	0.667427i	$-0.767396\pi$
$521$	−33.9951			−1.48935			−0.744675	+	0.667427i	$0.767396\pi$
$522$	2.31932	+	2.99983i	0.101514	+	0.131299i
$523$			18.2103i			0.796282i	0.917324	+	0.398141i	$0.130345\pi$
$523$			18.2103i			0.796282i	−0.917324	+	0.398141i	$0.869655\pi$
$524$	13.6366	+	3.54727i	0.595718	+	0.154963i
$525$		0			0
$526$	−22.2607	+	17.2109i	−0.970613	+	0.750430i
$527$	−40.5380			−1.76586
$528$	3.29027	+	1.83602i	0.143190	+	0.0799026i
$529$	−14.0753			−0.611968
$530$	−30.3887	+	23.4951i	−1.32000	+	1.02056i
$531$		−	0.116189i		−	0.00504219i
$532$		0			0
$533$			28.0493i			1.21495i
$534$	−1.57521	−	2.03738i	−0.0681658	−	0.0881663i
$535$	−34.7547			−1.50258
$536$	10.3414	−	4.41704i	0.446682	−	0.190787i
$537$	3.77961			0.163102
$538$	14.6758	+	18.9818i	0.632720	+	0.818365i
$539$		0			0
$540$	1.80141	−	6.92506i	0.0775201	−	0.298007i
$541$		−	30.1308i		−	1.29542i	−0.761886	−	0.647712i	$-0.775726\pi$
$541$		−	30.1308i		−	1.29542i	0.761886	−	0.647712i	$-0.224274\pi$
$542$	−1.20426	+	0.931077i	−0.0517275	+	0.0399932i
$543$	1.12363			0.0482197
$544$	−21.1664	+	3.18117i	−0.907502	+	0.136392i
$545$	−51.0814			−2.18809
$546$		0			0
$547$		−	36.0927i		−	1.54321i	−0.636101	−	0.771606i	$-0.719454\pi$
$547$		−	36.0927i		−	1.54321i	0.636101	−	0.771606i	$-0.280546\pi$
$548$	−9.11719	+	35.0488i	−0.389467	+	1.49721i
$549$		−	8.15432i		−	0.348018i
$550$	−6.35586	−	8.22072i	−0.271015	−	0.350533i
$551$	6.47415			0.275808
$552$	7.77060	−	3.31898i	0.330739	−	0.141265i
$553$		0			0
$554$	4.23116	+	5.47262i	0.179765	+	0.232509i
$555$		−	6.10808i		−	0.259274i
$556$	−16.1180	−	4.19276i	−0.683556	−	0.177812i
$557$		−	42.4146i		−	1.79717i	−0.438804	−	0.898583i	$-0.644598\pi$
$557$		−	42.4146i		−	1.79717i	0.438804	−	0.898583i	$-0.355402\pi$
$558$	11.9867	−	9.26752i	0.507437	−	0.392325i
$559$	−21.5704			−0.912333
$560$		0			0
$561$	3.56417			0.150479
$562$	0.843798	−	0.652384i	0.0355935	−	0.0275191i
$563$		−	11.8537i		−	0.499574i	−0.968301	−	0.249787i	$-0.919639\pi$
$563$		−	11.8537i		−	0.499574i	0.968301	−	0.249787i	$-0.0803606\pi$
$564$	13.2507	+	3.44688i	0.557955	+	0.145140i
$565$			49.6504i			2.08881i
$566$	16.8074	+	21.7388i	0.706468	+	0.913751i
$567$		0			0
$568$	−4.36141	−	10.2112i	−0.183001	−	0.428452i
$569$	5.42414			0.227392			0.113696	−	0.993516i	$-0.463731\pi$
$569$	5.42414			0.227392			0.113696	+	0.993516i	$0.463731\pi$
$570$	−7.47272	−	9.66528i	−0.312998	−	0.404834i
$571$			19.5852i			0.819617i	0.912172	+	0.409809i	$0.134404\pi$
$571$			19.5852i			0.819617i	−0.912172	+	0.409809i	$0.865596\pi$
$572$	−2.91738	+	11.2152i	−0.121982	+	0.468929i
$573$		−	14.0300i		−	0.586113i
$574$		0			0
$575$	−23.3031			−0.971804
$576$	5.53143	−	5.77955i	0.230476	−	0.240815i
$577$	6.22349			0.259087			0.129544	−	0.991574i	$-0.458649\pi$
$577$	6.22349			0.259087			0.129544	+	0.991574i	$0.458649\pi$
$578$	3.00205	−	2.32104i	0.124869	−	0.0965426i
$579$		−	0.780195i		−	0.0324238i
$580$	4.83003	−	18.5678i	0.200556	−	0.770988i
$581$		0			0
$582$	10.4010	+	13.4528i	0.431136	+	0.557635i
$583$	7.15119			0.296172
$584$	6.92005	+	16.2016i	0.286354	+	0.670428i
$585$	22.0074			0.909894
$586$	18.9813	+	24.5506i	0.784110	+	1.01417i
$587$		−	0.894279i		−	0.0369108i	−0.999830	−	0.0184554i	$-0.994125\pi$
$587$		−	0.894279i		−	0.0369108i	0.999830	−	0.0184554i	$-0.00587487\pi$
$588$		0			0
$589$		−	25.8693i		−	1.06593i
$590$	−0.465089	+	0.359584i	−0.0191474	+	0.0148039i
$591$	2.37637			0.0977506
$592$	3.32764	−	5.96333i	0.136765	−	0.245091i
$593$	−22.6996			−0.932161			−0.466080	−	0.884742i	$-0.654334\pi$
$593$	−22.6996			−0.932161			−0.466080	+	0.884742i	$0.654334\pi$
$594$	−1.05389	+	0.814815i	−0.0432416	+	0.0334323i
$595$		0			0
$596$	40.0774	+	10.4253i	1.64163	+	0.427036i
$597$			13.5839i			0.555953i
$598$	15.8957	+	20.5596i	0.650022	+	0.840743i
$599$	−39.0356			−1.59495			−0.797476	−	0.603351i	$-0.793832\pi$
$599$	−39.0356			−1.59495			−0.797476	+	0.603351i	$0.793832\pi$
$600$	−20.2895	+	8.66608i	−0.828317	+	0.353791i
$601$	−0.397117			−0.0161987			−0.00809936	−	0.999967i	$-0.502578\pi$
$601$	−0.397117			−0.0161987			−0.00809936	+	0.999967i	$0.502578\pi$
$602$		0			0
$603$			3.97580i			0.161907i
$604$	1.99168	−	7.65652i	0.0810403	−	0.311539i
$605$		−	36.1808i		−	1.47096i
$606$	−1.99262	+	1.54060i	−0.0809447	+	0.0625825i
$607$	21.8315			0.886112			0.443056	−	0.896494i	$-0.353894\pi$
$607$	21.8315			0.886112			0.443056	+	0.896494i	$0.353894\pi$
$608$	−2.03006	−	13.5073i	−0.0823298	−	0.547794i
$609$		0			0
$610$	−32.6406	+	25.2361i	−1.32158	+	1.02178i
$611$			42.1099i			1.70358i
$612$	1.90512	−	7.32377i	0.0770099	−	0.296046i
$613$			24.9947i			1.00953i	0.863258	+	0.504763i	$0.168420\pi$
$613$			24.9947i			1.00953i	−0.863258	+	0.504763i	$0.831580\pi$
$614$	1.89053	+	2.44523i	0.0762955	+	0.0986813i
$615$	16.3146			0.657867
$616$		0			0
$617$	−17.0538			−0.686560			−0.343280	−	0.939233i	$-0.611538\pi$
$617$	−17.0538			−0.686560			−0.343280	+	0.939233i	$0.611538\pi$
$618$	−10.7461	−	13.8991i	−0.432270	−	0.559102i
$619$			4.98901i			0.200525i	0.994961	+	0.100263i	$0.0319683\pi$
$619$			4.98901i			0.200525i	−0.994961	+	0.100263i	$0.968032\pi$
$620$	−74.1931	−	19.2998i	−2.97967	−	0.775097i
$621$			2.98743i			0.119881i
$622$	−30.5085	+	23.5877i	−1.22328	+	0.945780i
$623$		0			0
$624$	21.4859	+	11.9895i	0.860123	+	0.479963i
$625$	−3.15608			−0.126243
$626$	1.52890	−	1.18207i	0.0611073	−	0.0472452i
$627$			2.27447i			0.0908336i
$628$	22.9766	+	5.97688i	0.916868	+	0.238503i
$629$		−	6.45975i		−	0.257567i
$630$		0			0
$631$	15.7236			0.625947			0.312973	−	0.949762i	$-0.398675\pi$
$631$	15.7236			0.625947			0.312973	+	0.949762i	$0.398675\pi$
$632$	−6.07991	−	14.2346i	−0.241846	−	0.566224i
$633$	14.1932			0.564130
$634$	−7.08539	−	9.16431i	−0.281397	−	0.363961i
$635$		−	27.8131i		−	1.10373i
$636$	3.82246	−	14.6945i	0.151570	−	0.582675i
$637$		0			0
$638$	−2.82574	+	2.18473i	−0.111872	+	0.0864942i
$639$	3.92572			0.155299
$640$	−40.2535	−	4.25490i	−1.59116	−	0.168190i
$641$	24.6707			0.974433			0.487216	−	0.873281i	$-0.338012\pi$
$641$	24.6707			0.974433			0.487216	+	0.873281i	$0.338012\pi$
$642$	10.8683	−	8.40284i	0.428938	−	0.331634i
$643$		−	47.6908i		−	1.88074i	−0.340150	−	0.940371i	$-0.610478\pi$
$643$		−	47.6908i		−	1.88074i	0.340150	−	0.940371i	$-0.389522\pi$
$644$		0			0
$645$			12.5462i			0.494007i
$646$	−7.90296	−	10.2218i	−0.310938	−	0.402170i
$647$	−19.2945			−0.758547			−0.379273	−	0.925285i	$-0.623826\pi$
$647$	−19.2945			−0.758547			−0.379273	+	0.925285i	$0.623826\pi$
$648$	1.11098	+	2.60110i	0.0436435	+	0.102181i
$649$	0.109447			0.00429615
$650$	−41.5046	−	53.6824i	−1.62794	−	2.10560i
$651$		0			0
$652$	−33.0075	−	8.58619i	−1.29267	−	0.336261i
$653$		−	41.5457i		−	1.62581i	−0.582396	−	0.812905i	$-0.697885\pi$
$653$		−	41.5457i		−	1.62581i	0.582396	−	0.812905i	$-0.302115\pi$
$654$	15.9739	−	12.3502i	0.624628	−	0.482932i
$655$	25.2061			0.984884
$656$	15.9280	+	8.88806i	0.621882	+	0.347020i
$657$	−6.22876			−0.243007
$658$		0			0
$659$		−	21.7026i		−	0.845414i	−0.906266	−	0.422707i	$-0.861080\pi$
$659$		−	21.7026i		−	0.845414i	0.906266	−	0.422707i	$-0.138920\pi$
$660$	6.52318	+	1.69687i	0.253914	+	0.0660504i
$661$		−	14.7670i		−	0.574368i	−0.957875	−	0.287184i	$-0.907281\pi$
$661$		−	14.7670i		−	0.574368i	0.957875	−	0.287184i	$-0.0927191\pi$
$662$	−13.3487	−	17.2653i	−0.518813	−	0.671037i
$663$	23.2745			0.903906
$664$	−3.10988	+	1.32829i	−0.120687	+	0.0515478i
$665$		0			0
$666$	1.47678	+	1.91008i	0.0572242	+	0.0740142i
$667$			8.01006i			0.310151i
$668$	5.25345	−	20.1956i	0.203262	−	0.781391i
$669$			0.198178i			0.00766200i
$670$	15.9146	−	12.3044i	0.614833	−	0.475359i
$671$	7.68110			0.296526
$672$		0			0
$673$	3.09088			0.119145			0.0595724	−	0.998224i	$-0.481026\pi$
$673$	3.09088			0.119145			0.0595724	+	0.998224i	$0.481026\pi$
$674$	0.608550	−	0.470501i	0.0234405	−	0.0181230i
$675$		−	7.80037i		−	0.300236i
$676$	−12.5054	+	48.0738i	−0.480976	+	1.84899i
$677$		−	38.8018i		−	1.49128i	−0.666351	−	0.745638i	$-0.732145\pi$
$677$		−	38.8018i		−	1.49128i	0.666351	−	0.745638i	$-0.267855\pi$
$678$	−12.0042	−	15.5264i	−0.461020	−	0.596287i
$679$		0			0
$680$	−35.2120	+	15.0398i	−1.35032	+	0.576749i
$681$	−25.7560			−0.986973
$682$	8.72970	+	11.2911i	0.334277	+	0.432357i
$683$		−	26.0073i		−	0.995140i	−0.867424	−	0.497570i	$-0.834226\pi$
$683$		−	26.0073i		−	0.995140i	0.867424	−	0.497570i	$-0.165774\pi$
$684$	4.67365	+	1.21575i	0.178702	+	0.0464854i
$685$			64.7846i			2.47529i
$686$		0			0
$687$	−16.1617			−0.616609
$688$	−6.83509	+	12.2489i	−0.260585	+	0.466985i
$689$	46.6982			1.77906
$690$	11.9583	−	9.24554i	0.455243	−	0.351972i
$691$		−	9.94014i		−	0.378141i	−0.981964	−	0.189070i	$-0.939453\pi$
$691$		−	9.94014i		−	0.378141i	0.981964	−	0.189070i	$-0.0605475\pi$
$692$	−28.2095	−	7.33810i	−1.07237	−	0.278953i
$693$		0			0
$694$	9.91581	+	12.8252i	0.376399	+	0.486837i
$695$	−29.7928			−1.13010
$696$	2.97883	+	6.97421i	0.112912	+	0.264357i
$697$	17.2539			0.653538
$698$	−1.06477	−	1.37718i	−0.0403020	−	0.0521270i
$699$		−	25.1239i		−	0.950272i
$700$		0			0
$701$		−	32.3250i		−	1.22090i	−0.792056	−	0.610449i	$-0.790989\pi$
$701$		−	32.3250i		−	1.22090i	0.792056	−	0.610449i	$-0.209011\pi$
$702$	−6.88203	+	5.32085i	−0.259745	+	0.200822i
$703$	4.12228			0.155475
$704$	5.44415	+	5.21043i	0.205184	+	0.196375i
$705$	24.4927			0.922450
$706$	38.2840	−	29.5993i	1.44084	−	1.11398i
$707$		0			0
$708$	0.0585014	−	0.224894i	0.00219862	−	0.00845205i
$709$			44.1160i			1.65681i	0.560128	+	0.828406i	$0.310752\pi$
$709$			44.1160i			1.65681i	−0.560128	+	0.828406i	$0.689248\pi$
$710$	−12.1494	−	15.7141i	−0.455958	−	0.589739i
$711$	5.47255			0.205237
$712$	−2.02312	−	4.73665i	−0.0758196	−	0.177513i
$713$	32.0065			1.19865
$714$		0			0
$715$			20.7303i			0.775268i
$716$	7.31575	+	1.90303i	0.273402	+	0.0711198i
$717$		−	16.0389i		−	0.598984i
$718$	−37.9360	+	29.3302i	−1.41576	+	1.09459i
$719$	−6.45859			−0.240865			−0.120432	−	0.992722i	$-0.538428\pi$
$719$	−6.45859			−0.240865			−0.120432	+	0.992722i	$0.538428\pi$
$720$	6.97354	−	12.4970i	0.259889	−	0.465737i
$721$		0			0
$722$	−14.7345	+	11.3920i	−0.548362	+	0.423966i
$723$			13.1691i			0.489762i
$724$	2.17488	+	0.565750i	0.0808290	+	0.0210259i
$725$		−	20.9148i		−	0.776755i
$726$	8.74763	+	11.3143i	0.324655	+	0.419911i
$727$	−25.6040			−0.949600			−0.474800	−	0.880094i	$-0.657480\pi$
$727$	−25.6040			−0.949600			−0.474800	+	0.880094i	$0.657480\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	19.2769	+	24.9329i	0.713469	+	0.922806i
$731$			13.2686i			0.490756i
$732$	4.10570	−	15.7834i	0.151751	−	0.583370i
$733$			10.3299i			0.381544i	0.981634	+	0.190772i	$0.0610991\pi$
$733$			10.3299i			0.381544i	−0.981634	+	0.190772i	$0.938901\pi$
$734$	21.5313	−	16.6469i	0.794734	−	0.614449i
$735$		0			0
$736$	16.7118	−	2.51167i	0.616004	−	0.0925813i
$737$	−3.74507			−0.137951
$738$	−5.10180	+	3.94446i	−0.187800	+	0.145198i
$739$			46.3422i			1.70472i	0.522952	+	0.852362i	$0.324831\pi$
$739$			46.3422i			1.70472i	−0.522952	+	0.852362i	$0.675169\pi$
$740$	3.07542	−	11.8227i	0.113055	−	0.434611i
$741$			14.8526i			0.545623i
$742$		0			0
$743$	−38.1002			−1.39776			−0.698880	−	0.715239i	$-0.746318\pi$
$743$	−38.1002			−1.39776			−0.698880	+	0.715239i	$0.746318\pi$
$744$	27.8674	−	11.9028i	1.02167	−	0.436376i
$745$	74.0796			2.71407
$746$	−12.8314	−	16.5962i	−0.469790	−	0.607631i
$747$		−	1.19560i		−	0.0437448i
$748$	6.89875	+	1.79456i	0.252243	+	0.0656157i
$749$		0			0
$750$	−11.2095	+	8.66662i	−0.409312	+	0.316460i
$751$	−7.51999			−0.274408			−0.137204	−	0.990543i	$-0.543812\pi$
$751$	−7.51999			−0.274408			−0.137204	+	0.990543i	$0.543812\pi$
$752$	23.9123	+	13.3435i	0.871992	+	0.486586i
$753$	−8.64704			−0.315116
$754$	−18.4525	+	14.2665i	−0.671999	+	0.519557i
$755$		−	14.1524i		−	0.515059i
$756$		0			0
$757$		−	41.2006i		−	1.49746i	−0.662873	−	0.748731i	$-0.730663\pi$
$757$		−	41.2006i		−	1.49746i	0.662873	−	0.748731i	$-0.269337\pi$
$758$	−10.1639	−	13.1461i	−0.369169	−	0.477486i
$759$	−2.81406			−0.102144
$760$	−9.59761	−	22.4705i	−0.348142	−	0.815090i
$761$	28.6212			1.03752			0.518759	−	0.854920i	$-0.326394\pi$
$761$	28.6212			1.03752			0.518759	+	0.854920i	$0.326394\pi$
$762$	6.72453	+	8.69756i	0.243604	+	0.315079i
$763$		0			0
$764$	7.06413	−	27.1563i	0.255571	−	0.982481i
$765$		−	13.5373i		−	0.489444i
$766$	−21.3308	+	16.4919i	−0.770712	+	0.595877i
$767$	0.714700			0.0258063
$768$	13.6166	−	8.40173i	0.491346	−	0.303171i
$769$	−14.6303			−0.527581			−0.263791	−	0.964580i	$-0.584973\pi$
$769$	−14.6303			−0.527581			−0.263791	+	0.964580i	$0.584973\pi$
$770$		0			0
$771$			14.4651i			0.520947i
$772$	0.392829	−	1.51013i	0.0141382	−	0.0543509i
$773$			42.4716i			1.52760i	0.645455	+	0.763798i	$0.276668\pi$
$773$			42.4716i			1.52760i	−0.645455	+	0.763798i	$0.723332\pi$
$774$	−3.03337	−	3.92338i	−0.109032	−	0.141023i
$775$	−83.5710			−3.00196
$776$	13.3586	+	31.2759i	0.479545	+	1.12274i
$777$		0			0
$778$	−1.73289	−	2.24134i	−0.0621271	−	0.0803558i
$779$			11.0105i			0.394494i
$780$	42.5972	+	11.0807i	1.52522	+	0.396754i
$781$			3.69790i			0.132321i
$782$	12.6467	−	9.77785i	0.452247	−	0.349655i
$783$	−2.68125			−0.0958202
$784$		0			0
$785$	42.4703			1.51583
$786$	−7.88230	+	6.09421i	−0.281153	+	0.217373i
$787$			7.56670i			0.269724i	0.990864	+	0.134862i	$0.0430591\pi$
$787$			7.56670i			0.269724i	−0.990864	+	0.134862i	$0.956941\pi$
$788$	4.59966	+	1.19650i	0.163856	+	0.0426236i
$789$		−	19.8967i		−	0.708340i
$790$	−16.9365	−	21.9058i	−0.602575	−	0.779375i
$791$		0			0
$792$	−2.45015	+	1.04651i	−0.0870623	+	0.0371861i
$793$	50.1586			1.78118
$794$	7.33860	+	9.49181i	0.260437	+	0.336852i
$795$		−	27.1615i		−	0.963320i
$796$	−6.83951	+	26.2928i	−0.242420	+	0.931924i
$797$		−	11.4622i		−	0.406013i	−0.979177	−	0.203007i	$-0.934929\pi$
$797$		−	11.4622i		−	0.406013i	0.979177	−	0.203007i	$-0.0650713\pi$
$798$		0			0
$799$	25.9029			0.916379
$800$	−43.6355	+	6.55813i	−1.54275	+	0.231865i
$801$	1.82102			0.0643425
$802$	15.7671	−	12.1903i	0.556755	−	0.430456i
$803$		−	5.86729i		−	0.207052i
$804$	−2.00182	+	7.69549i	−0.0705987	+	0.271399i
$805$		0			0
$806$	57.0061	+	73.7321i	2.00795	+	2.59710i
$807$	−16.9660			−0.597231
$808$	−4.63258	+	1.97867i	−0.162974	+	0.0696093i
$809$	17.0821			0.600573			0.300287	−	0.953849i	$-0.402918\pi$
$809$	17.0821			0.600573			0.300287	+	0.953849i	$0.402918\pi$
$810$	3.09481	+	4.00286i	0.108741	+	0.140646i
$811$			16.6693i			0.585338i	0.956214	+	0.292669i	$0.0945434\pi$
$811$			16.6693i			0.585338i	−0.956214	+	0.292669i	$0.905457\pi$
$812$		0			0
$813$		−	1.07637i		−	0.0377500i
$814$	−1.79924	+	1.39108i	−0.0630632	+	0.0487574i
$815$	−61.0115			−2.13714
$816$	7.37504	−	13.2165i	0.258178	−	0.462671i
$817$	−8.46732			−0.296234
$818$	−33.9647	+	26.2599i	−1.18755	+	0.918155i
$819$		0			0
$820$	31.5782	+	8.21440i	1.10276	+	0.286859i
$821$			43.0233i			1.50152i	0.660572	+	0.750762i	$0.270314\pi$
$821$			43.0233i			1.50152i	−0.660572	+	0.750762i	$0.729686\pi$
$822$	−15.6633	−	20.2591i	−0.546321	−	0.706616i
$823$	34.6509			1.20786			0.603928	−	0.797039i	$-0.293602\pi$
$823$	34.6509			1.20786			0.603928	+	0.797039i	$0.293602\pi$
$824$	−13.8017	−	32.3135i	−0.480806	−	1.12569i
$825$	7.34769			0.255814
$826$		0			0
$827$			36.5937i			1.27249i	0.771489	+	0.636243i	$0.219513\pi$
$827$			36.5937i			1.27249i	−0.771489	+	0.636243i	$0.780487\pi$
$828$	−1.50417	+	5.78242i	−0.0522736	+	0.200953i
$829$			7.55875i			0.262526i	0.991348	+	0.131263i	$0.0419033\pi$
$829$			7.55875i			0.262526i	−0.991348	+	0.131263i	$0.958097\pi$
$830$	−4.78583	+	3.70017i	−0.166119	+	0.128435i
$831$	−4.89143			−0.169682
$832$	35.5510	+	34.0248i	1.23251	+	1.17960i
$833$		0			0
$834$	9.31662	−	7.20315i	0.322608	−	0.249425i
$835$		−	37.3298i		−	1.29185i
$836$	−1.14520	+	4.40243i	−0.0396075	+	0.152261i
$837$			10.7137i			0.370320i
$838$	−26.7199	−	34.5598i	−0.923024	−	1.19385i
$839$	−33.3899			−1.15275			−0.576374	−	0.817186i	$-0.695533\pi$
$839$	−33.3899			−1.15275			−0.576374	+	0.817186i	$0.695533\pi$
$840$		0			0
$841$	21.8109			0.752099
$842$	−17.3816	−	22.4815i	−0.599009	−	0.774763i
$843$			0.754188i			0.0259756i
$844$	27.4722	+	7.14631i	0.945632	+	0.245986i
$845$			88.8603i			3.05689i
$846$	−7.65923	+	5.92174i	−0.263330	+	0.203594i
$847$		0			0
$848$	14.7974	−	26.5178i	0.508144	−	0.910626i
$849$	−19.4302			−0.666843
$850$	−33.0215	+	25.5306i	−1.13263	+	0.875692i
$851$			5.10025i			0.174834i
$852$	7.59856	+	1.97660i	0.260322	+	0.0677173i
$853$			18.6855i			0.639779i	0.947455	+	0.319889i	$0.103646\pi$
$853$			18.6855i			0.639779i	−0.947455	+	0.319889i	$0.896354\pi$
$854$		0			0
$855$	8.63884			0.295442
$856$	25.2674	−	10.7922i	0.863620	−	0.368870i
$857$	−30.8881			−1.05512			−0.527559	−	0.849518i	$-0.676893\pi$
$857$	−30.8881			−1.05512			−0.527559	+	0.849518i	$0.676893\pi$
$858$	−5.01206	−	6.48265i	−0.171109	−	0.221314i
$859$		−	40.8604i		−	1.39414i	−0.717004	−	0.697069i	$-0.754487\pi$
$859$		−	40.8604i		−	1.39414i	0.717004	−	0.697069i	$-0.245513\pi$
$860$	−6.31703	+	24.2843i	−0.215409	+	0.828087i
$861$		0			0
$862$	−8.97007	+	6.93522i	−0.305522	+	0.236215i
$863$	3.75352			0.127771			0.0638857	−	0.997957i	$-0.479651\pi$
$863$	3.75352			0.127771			0.0638857	+	0.997957i	$0.479651\pi$
$864$	0.840746	+	5.59403i	0.0286027	+	0.190313i
$865$	−52.1429			−1.77291
$866$	30.1870	−	23.3391i	1.02580	−	0.793095i
$867$			2.68324i			0.0911277i
$868$		0			0
$869$			5.15496i			0.174870i
$870$	8.29798	+	10.7327i	0.281328	+	0.363872i
$871$	−24.4558			−0.828653
$872$	37.1371	−	15.8620i	1.25762	−	0.537156i
$873$	−12.0241			−0.406954
$874$	6.23972	+	8.07051i	0.211062	+	0.272989i
$875$		0			0
$876$	−12.0563	−	3.13619i	−0.407345	−	0.105962i
$877$		−	30.0472i		−	1.01462i	−0.861763	−	0.507311i	$-0.830639\pi$
$877$		−	30.0472i		−	1.01462i	0.861763	−	0.507311i	$-0.169361\pi$
$878$	−40.8538	+	31.5862i	−1.37875	+	1.06598i
$879$	−21.9433			−0.740130
$880$	11.7718	+	6.56885i	0.396827	+	0.221436i
$881$	42.4160			1.42903			0.714516	−	0.699619i	$-0.246647\pi$
$881$	42.4160			1.42903			0.714516	+	0.699619i	$0.246647\pi$
$882$		0			0
$883$			20.3124i			0.683568i	0.939779	+	0.341784i	$0.111031\pi$
$883$			20.3124i			0.683568i	−0.939779	+	0.341784i	$0.888969\pi$
$884$	45.0497	+	11.7187i	1.51519	+	0.394143i
$885$		−	0.415698i		−	0.0139735i
$886$	−0.190242	−	0.246060i	−0.00639129	−	0.00826655i
$887$	17.3844			0.583711			0.291855	−	0.956462i	$-0.405727\pi$
$887$	17.3844			0.583711			0.291855	+	0.956462i	$0.405727\pi$
$888$	1.89671	+	4.44069i	0.0636494	+	0.149020i
$889$		0			0
$890$	−5.63571	−	7.28928i	−0.188909	−	0.244337i
$891$		−	0.941967i		−	0.0315571i
$892$	−0.0997827	+	0.383590i	−0.00334097	+	0.0128435i
$893$			16.5299i			0.553152i
$894$	−23.1658	+	17.9106i	−0.774779	+	0.599021i
$895$	13.5225			0.452008
$896$		0			0
$897$	−18.3762			−0.613563
$898$	−23.1370	+	17.8884i	−0.772093	+	0.596945i
$899$			28.7262i			0.958073i
$900$	3.92749	−	15.0983i	0.130916	−	0.503276i
$901$		−	28.7253i		−	0.956980i
$902$	−3.71555	−	4.80573i	−0.123714	−	0.160013i
$903$		0			0
$904$	−15.4177	−	36.0967i	−0.512784	−	1.20056i
$905$	4.02009			0.133632
$906$	3.42170	+	4.42566i	0.113679	+	0.147033i
$907$			21.8203i			0.724533i	0.932075	+	0.362266i	$0.117997\pi$
$907$			21.8203i			0.724533i	−0.932075	+	0.362266i	$0.882003\pi$
$908$	−49.8530	−	12.9682i	−1.65443	−	0.430364i
$909$		−	1.78101i		−	0.0590723i
$910$		0			0
$911$	11.9139			0.394727			0.197363	−	0.980330i	$-0.436762\pi$
$911$	11.9139			0.394727			0.197363	+	0.980330i	$0.436762\pi$
$912$	8.43412	+	4.70638i	0.279282	+	0.155844i
$913$	1.12622			0.0372724
$914$	9.60412	−	7.42544i	0.317676	−	0.245612i
$915$		−	29.1742i		−	0.964469i
$916$	−31.2824	−	8.13745i	−1.03360	−	0.268869i
$917$		0			0
$918$	3.27300	+	4.23332i	0.108025	+	0.139720i
$919$	−37.7665			−1.24580			−0.622900	−	0.782301i	$-0.714046\pi$
$919$	−37.7665			−1.24580			−0.622900	+	0.782301i	$0.714046\pi$
$920$	27.8013	−	11.8745i	0.916583	−	0.391491i
$921$	−2.18555			−0.0720162
$922$	11.9548	+	15.4624i	0.393709	+	0.509226i
$923$			24.1477i			0.794833i
$924$		0			0
$925$		−	13.3171i		−	0.437863i
$926$	−32.2996	+	24.9724i	−1.06143	+	0.820645i
$927$	12.4230			0.408025
$928$	2.25425	+	14.9990i	0.0739995	+	0.492367i
$929$	−34.5094			−1.13222			−0.566108	−	0.824331i	$-0.691552\pi$
$929$	−34.5094			−1.13222			−0.566108	+	0.824331i	$0.691552\pi$
$930$	42.8855	−	33.1570i	1.40627	−	1.08726i
$931$		0			0
$932$	12.6499	−	48.6294i	0.414361	−	1.59291i
$933$		−	27.2685i		−	0.892732i
$934$	10.7557	+	13.9115i	0.351936	+	0.455197i
$935$	12.7517			0.417026
$936$	−15.9998	+	6.83384i	−0.522970	+	0.223371i
$937$	2.63475			0.0860735			0.0430367	−	0.999073i	$-0.486297\pi$
$937$	2.63475			0.0860735			0.0430367	+	0.999073i	$0.486297\pi$
$938$		0			0
$939$			1.36654i			0.0445952i
$940$	47.4078	+	12.3321i	1.54627	+	0.402229i
$941$			20.5159i			0.668799i	0.942431	+	0.334399i	$0.108533\pi$
$941$			20.5159i			0.668799i	−0.942431	+	0.334399i	$0.891467\pi$
$942$	−13.2811	+	10.2683i	−0.432721	+	0.334559i
$943$	−13.6227			−0.443615
$944$	0.226469	−	0.405846i	0.00737094	−	0.0132092i
$945$		0			0
$946$	3.69570	−	2.85733i	0.120157	−	0.0928999i
$947$			31.4487i			1.02194i	0.859597	+	0.510972i	$0.170714\pi$
$947$			31.4487i			1.02194i	−0.859597	+	0.510972i	$0.829286\pi$
$948$	10.5926	+	2.75543i	0.344031	+	0.0894923i
$949$		−	38.3142i		−	1.24373i
$950$	−16.2923	−	21.0726i	−0.528592	−	0.683686i
$951$	8.19107			0.265614
$952$		0			0
$953$	7.69660			0.249317			0.124659	−	0.992200i	$-0.460216\pi$
$953$	7.69660			0.249317			0.124659	+	0.992200i	$0.460216\pi$
$954$	6.56698	+	8.49379i	0.212614	+	0.274997i
$955$		−	50.1961i		−	1.62431i
$956$	8.07561	−	31.0447i	0.261184	−	1.00406i
$957$		−	2.52565i		−	0.0816428i
$958$	−42.8305	+	33.1145i	−1.38379	+	1.06988i
$959$		0			0
$960$	19.7901	−	20.6779i	0.638724	−	0.667375i
$961$	83.7838			2.70270
$962$	−11.7492	+	9.08394i	−0.378811	+	0.292878i
$963$			9.71411i			0.313033i
$964$	−6.63063	+	25.4898i	−0.213558	+	0.820972i
$965$		−	2.79135i		−	0.0898568i
$966$		0			0
$967$	−58.4850			−1.88075			−0.940375	−	0.340140i	$-0.889526\pi$
$967$	−58.4850			−1.88075			−0.940375	+	0.340140i	$0.889526\pi$
$968$	11.2350	+	26.3041i	0.361108	+	0.845447i
$969$	9.13622			0.293498
$970$	37.2124	+	48.1308i	1.19482	+	1.54539i
$971$			46.6300i			1.49643i	0.663457	+	0.748215i	$0.269089\pi$
$971$			46.6300i			1.49643i	−0.663457	+	0.748215i	$0.730911\pi$
$972$	−1.93558	−	0.503501i	−0.0620839	−	0.0161498i
$973$		0			0
$974$	2.01899	−	1.56099i	0.0646927	−	0.0500173i
$975$	47.9814			1.53663
$976$	15.8939	−	28.4828i	0.508751	−	0.911713i
$977$	−1.50961			−0.0482967			−0.0241484	−	0.999708i	$-0.507687\pi$
$977$	−1.50961			−0.0482967			−0.0241484	+	0.999708i	$0.507687\pi$
$978$	19.0792	−	14.7511i	0.610084	−	0.471687i
$979$			1.71534i			0.0548225i
$980$		0			0
$981$			14.2775i			0.455845i
$982$	3.54897	+	4.59026i	0.113252	+	0.146481i
$983$	22.1661			0.706988			0.353494	−	0.935437i	$-0.384993\pi$
$983$	22.1661			0.706988			0.353494	+	0.935437i	$0.384993\pi$
$984$	−11.8610	+	5.06608i	−0.378115	+	0.161501i
$985$	8.50207			0.270898
$986$	8.77574	+	11.3506i	0.279476	+	0.361477i
$987$		0			0
$988$	−7.47829	+	28.7484i	−0.237916	+	0.914609i
$989$		−	10.4761i		−	0.333120i
$990$	−3.77056	+	2.91521i	−0.119836	+	0.0926516i
$991$	−57.8841			−1.83875			−0.919374	−	0.393384i	$-0.871304\pi$
$991$	−57.8841			−1.83875			−0.919374	+	0.393384i	$0.871304\pi$
$992$	59.9328	−	9.00751i	1.90287	−	0.285989i
$993$	15.4318			0.489713
$994$		0			0
$995$			48.6000i			1.54072i
$996$	0.601987	−	2.31419i	0.0190747	−	0.0733279i
$997$			50.9825i			1.61463i	0.590118	+	0.807317i	$0.299081\pi$
$997$			50.9825i			1.61463i	−0.590118	+	0.807317i	$0.700919\pi$
$998$	38.4073	+	49.6763i	1.21576	+	1.57247i
$999$	−1.70724			−0.0540145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1176.2.c.e.589.6		16
4.3	odd	2		4704.2.c.e.2353.9		16
7.2	even	3		168.2.bc.a.109.15	yes	32
7.4	even	3		168.2.bc.a.37.7	✓	32
7.6	odd	2		1176.2.c.f.589.6		16
8.3	odd	2		4704.2.c.e.2353.8		16
8.5	even	2	inner	1176.2.c.e.589.5		16
21.2	odd	6		504.2.cj.e.109.2		32
21.11	odd	6		504.2.cj.e.37.10		32
28.11	odd	6		672.2.bk.a.625.16		32
28.23	odd	6		672.2.bk.a.529.1		32
28.27	even	2		4704.2.c.f.2353.8		16
56.11	odd	6		672.2.bk.a.625.1		32
56.13	odd	2		1176.2.c.f.589.5		16
56.27	even	2		4704.2.c.f.2353.9		16
56.37	even	6		168.2.bc.a.109.7	yes	32
56.51	odd	6		672.2.bk.a.529.16		32
56.53	even	6		168.2.bc.a.37.15	yes	32
84.11	even	6		2016.2.cr.e.1297.1		32
84.23	even	6		2016.2.cr.e.1873.16		32
168.11	even	6		2016.2.cr.e.1297.16		32
168.53	odd	6		504.2.cj.e.37.2		32
168.107	even	6		2016.2.cr.e.1873.1		32
168.149	odd	6		504.2.cj.e.109.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.bc.a.37.7	✓	32	7.4	even	3
168.2.bc.a.37.15	yes	32	56.53	even	6
168.2.bc.a.109.7	yes	32	56.37	even	6
168.2.bc.a.109.15	yes	32	7.2	even	3
504.2.cj.e.37.2		32	168.53	odd	6
504.2.cj.e.37.10		32	21.11	odd	6
504.2.cj.e.109.2		32	21.2	odd	6
504.2.cj.e.109.10		32	168.149	odd	6
672.2.bk.a.529.1		32	28.23	odd	6
672.2.bk.a.529.16		32	56.51	odd	6
672.2.bk.a.625.1		32	56.11	odd	6
672.2.bk.a.625.16		32	28.11	odd	6
1176.2.c.e.589.5		16	8.5	even	2	inner
1176.2.c.e.589.6		16	1.1	even	1	trivial
1176.2.c.f.589.5		16	56.13	odd	2
1176.2.c.f.589.6		16	7.6	odd	2
2016.2.cr.e.1297.1		32	84.11	even	6
2016.2.cr.e.1297.16		32	168.11	even	6
2016.2.cr.e.1873.1		32	168.107	even	6
2016.2.cr.e.1873.16		32	84.23	even	6
4704.2.c.e.2353.8		16	8.3	odd	2
4704.2.c.e.2353.9		16	4.3	odd	2
4704.2.c.f.2353.8		16	28.27	even	2
4704.2.c.f.2353.9		16	56.27	even	2

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:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11882 + 0.865014i) q^{2} -1.00000i q^{3} +(0.503501 - 1.93558i) q^{4} -3.57776i q^{5} +(0.865014 + 1.11882i) q^{6} +(1.11098 + 2.60110i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-1.11882 + 0.865014i) q^{2} -1.00000i q^{3} +(0.503501 - 1.93558i) q^{4} -3.57776i q^{5} +(0.865014 + 1.11882i) q^{6} +(1.11098 + 2.60110i) q^{8} -1.00000 q^{9} +(3.09481 + 4.00286i) q^{10} -0.941967i q^{11} +(-1.93558 - 0.503501i) q^{12} -6.15117i q^{13} -3.57776 q^{15} +(-3.49297 - 1.94914i) q^{16} -3.78375 q^{17} +(1.11882 - 0.865014i) q^{18} -2.41460i q^{19} +(-6.92506 - 1.80141i) q^{20} +(0.814815 + 1.05389i) q^{22} +2.98743 q^{23} +(2.60110 - 1.11098i) q^{24} -7.80037 q^{25} +(5.32085 + 6.88203i) q^{26} +1.00000i q^{27} +2.68125i q^{29} +(4.00286 - 3.09481i) q^{30} +10.7137 q^{31} +(5.59403 - 0.840746i) q^{32} -0.941967 q^{33} +(4.23332 - 3.27300i) q^{34} +(-0.503501 + 1.93558i) q^{36} +1.70724i q^{37} +(2.08866 + 2.70149i) q^{38} -6.15117 q^{39} +(9.30611 - 3.97483i) q^{40} -4.56000 q^{41} -3.50672i q^{43} +(-1.82326 - 0.474281i) q^{44} +3.57776i q^{45} +(-3.34238 + 2.58417i) q^{46} -6.84583 q^{47} +(-1.94914 + 3.49297i) q^{48} +(8.72718 - 6.74743i) q^{50} +3.78375i q^{51} +(-11.9061 - 3.09712i) q^{52} +7.59176i q^{53} +(-0.865014 - 1.11882i) q^{54} -3.37013 q^{55} -2.41460 q^{57} +(-2.31932 - 2.99983i) q^{58} +0.116189i q^{59} +(-1.80141 + 6.92506i) q^{60} +8.15432i q^{61} +(-11.9867 + 9.26752i) q^{62} +(-5.53143 + 5.77955i) q^{64} -22.0074 q^{65} +(1.05389 - 0.814815i) q^{66} -3.97580i q^{67} +(-1.90512 + 7.32377i) q^{68} -2.98743i q^{69} -3.92572 q^{71} +(-1.11098 - 2.60110i) q^{72} +6.22876 q^{73} +(-1.47678 - 1.91008i) q^{74} +7.80037i q^{75} +(-4.67365 - 1.21575i) q^{76} +(6.88203 - 5.32085i) q^{78} -5.47255 q^{79} +(-6.97354 + 12.4970i) q^{80} +1.00000 q^{81} +(5.10180 - 3.94446i) q^{82} +1.19560i q^{83} +13.5373i q^{85} +(3.03337 + 3.92338i) q^{86} +2.68125 q^{87} +(2.45015 - 1.04651i) q^{88} -1.82102 q^{89} +(-3.09481 - 4.00286i) q^{90} +(1.50417 - 5.78242i) q^{92} -10.7137i q^{93} +(7.65923 - 5.92174i) q^{94} -8.63884 q^{95} +(-0.840746 - 5.59403i) q^{96} +12.0241 q^{97} +0.941967i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9	\( 16 q - 2 q^{2} + 2 q^{4} - 8 q^{8} - 16 q^{9} - 6 q^{10} + 10 q^{16} + 2 q^{18} - 20 q^{20} - 6 q^{22} + 8 q^{23} + 6 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{30} + 24 q^{31} + 8 q^{32} - 12 q^{34} - 2 q^{36} + 26 q^{38} + 6 q^{40} - 20 q^{44} - 16 q^{46} + 24 q^{47} - 8 q^{48} + 26 q^{50} - 44 q^{52} - 32 q^{55} - 8 q^{57} - 34 q^{58} + 22 q^{60} + 50 q^{62} - 10 q^{64} - 12 q^{66} - 16 q^{68} - 40 q^{71} + 8 q^{72} - 8 q^{73} - 10 q^{74} - 16 q^{76} + 6 q^{78} - 8 q^{79} + 56 q^{80} + 16 q^{81} + 22 q^{86} - 24 q^{87} - 50 q^{88} + 6 q^{90} + 32 q^{92} + 48 q^{94} - 24 q^{95} - 10 q^{96} - 24 q^{97}+O(q^{100}) \) 16 * q - 2 * q^2 + 2 * q^4 - 8 * q^8 - 16 * q^9 - 6 * q^10 + 10 * q^16 + 2 * q^18 - 20 * q^20 - 6 * q^22 + 8 * q^23 + 6 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^30 + 24 * q^31 + 8 * q^32 - 12 * q^34 - 2 * q^36 + 26 * q^38 + 6 * q^40 - 20 * q^44 - 16 * q^46 + 24 * q^47 - 8 * q^48 + 26 * q^50 - 44 * q^52 - 32 * q^55 - 8 * q^57 - 34 * q^58 + 22 * q^60 + 50 * q^62 - 10 * q^64 - 12 * q^66 - 16 * q^68 - 40 * q^71 + 8 * q^72 - 8 * q^73 - 10 * q^74 - 16 * q^76 + 6 * q^78 - 8 * q^79 + 56 * q^80 + 16 * q^81 + 22 * q^86 - 24 * q^87 - 50 * q^88 + 6 * q^90 + 32 * q^92 + 48 * q^94 - 24 * q^95 - 10 * q^96 - 24 * q^97

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