LMFDB - Embedded newform 847.2.f.v.148.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
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} - 3 x^{15} + 14 x^{14} - 32 x^{13} + 86 x^{12} - 145 x^{11} + 245 x^{10} - 245 x^{9} + 640 x^{8} + \cdots + 25 $ x^16 - 3x^15 + 14x^14 - 32x^13 + 86x^12 - 145x^11 + 245x^10 - 245x^9 + 640x^8 - 1175x^7 + 2135x^6 - 2300x^5 + 1850x^4 - 925x^3 + 700x^2 - 200*x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			148.4
Root			$-1.38112 + 1.00344i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.v.372.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.527541 + 1.62360i) q^{2} +(-1.85391 - 1.34694i) q^{3} +(-0.739758 + 0.537466i) q^{4} +(1.25658 - 3.86735i) q^{5} +(1.20889 - 3.72058i) q^{6} +(0.809017 - 0.587785i) q^{7} +(1.49936 + 1.08935i) q^{8} +(0.695665 + 2.14104i) q^{9} +O(q^{10})$	\(q+(0.527541 + 1.62360i) q^{2} +(-1.85391 - 1.34694i) q^{3} +(-0.739758 + 0.537466i) q^{4} +(1.25658 - 3.86735i) q^{5} +(1.20889 - 3.72058i) q^{6} +(0.809017 - 0.587785i) q^{7} +(1.49936 + 1.08935i) q^{8} +(0.695665 + 2.14104i) q^{9} +6.94194 q^{10} +2.09538 q^{12} +(-1.01293 - 3.11749i) q^{13} +(1.38112 + 1.00344i) q^{14} +(-7.53867 + 5.47716i) q^{15} +(-1.54282 + 4.74831i) q^{16} +(0.408175 - 1.25623i) q^{17} +(-3.10921 + 2.25897i) q^{18} +(1.74889 + 1.27064i) q^{19} +(1.14900 + 3.53627i) q^{20} -2.29155 q^{21} -1.86611 q^{23} +(-1.31238 - 4.03909i) q^{24} +(-9.33231 - 6.78032i) q^{25} +(4.52720 - 3.28921i) q^{26} +(-0.530233 + 1.63189i) q^{27} +(-0.282562 + 0.869638i) q^{28} +(-0.197482 + 0.143479i) q^{29} +(-12.8697 - 9.35039i) q^{30} +(-2.12291 - 6.53364i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(-1.25658 - 3.86735i) q^{35} +(-1.66536 - 1.20995i) q^{36} +(-0.206800 + 0.150249i) q^{37} +(-1.14041 + 3.50982i) q^{38} +(-2.32119 + 7.14389i) q^{39} +(6.09694 - 4.42968i) q^{40} +(-4.63755 - 3.36938i) q^{41} +(-1.20889 - 3.72058i) q^{42} +8.01781 q^{43} +9.15429 q^{45} +(-0.984452 - 3.02983i) q^{46} +(3.29082 + 2.39092i) q^{47} +(9.25594 - 6.72484i) q^{48} +(0.309017 - 0.951057i) q^{49} +(6.08538 - 18.7289i) q^{50} +(-2.44879 + 1.77915i) q^{51} +(2.42487 + 1.76177i) q^{52} +(-1.54689 - 4.76085i) q^{53} -2.92926 q^{54} +1.85331 q^{56} +(-1.53080 - 4.71131i) q^{57} +(-0.337134 - 0.244942i) q^{58} +(0.795743 - 0.578141i) q^{59} +(2.63300 - 8.10355i) q^{60} +(-0.570665 + 1.75633i) q^{61} +(9.48813 - 6.89353i) q^{62} +(1.82128 + 1.32323i) q^{63} +(0.544649 + 1.67626i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(0.373231 + 1.14869i) q^{68} +(3.45960 + 2.51355i) q^{69} +(5.61615 - 4.08037i) q^{70} +(2.00132 - 6.15944i) q^{71} +(-1.28928 + 3.96800i) q^{72} +(-7.80834 + 5.67309i) q^{73} +(-0.353041 - 0.256499i) q^{74} +(8.16853 + 25.1401i) q^{75} -1.97668 q^{76} -12.8234 q^{78} +(1.71025 + 5.26362i) q^{79} +(16.4247 + 11.9332i) q^{80} +(8.64489 - 6.28088i) q^{81} +(3.02404 - 9.30704i) q^{82} +(-0.639735 + 1.96890i) q^{83} +(1.69520 - 1.23163i) q^{84} +(-4.34539 - 3.15711i) q^{85} +(4.22973 + 13.0178i) q^{86} +0.559372 q^{87} +16.6306 q^{89} +(4.82927 + 14.8630i) q^{90} +(-2.65189 - 1.92671i) q^{91} +(1.38047 - 1.00297i) q^{92} +(-4.86476 + 14.9722i) q^{93} +(-2.14587 + 6.60430i) q^{94} +(7.11164 - 5.16691i) q^{95} +(8.92965 + 6.48777i) q^{96} +(-0.798992 - 2.45904i) q^{97} +1.70716 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.527541	+	1.62360i	0.373028	+	1.14806i	0.944800	+	0.327649i	$0.106256\pi$
$2$	0.527541	+	1.62360i	0.373028	+	1.14806i	−0.571772	+	0.820413i	$0.693744\pi$
$3$	−1.85391	−	1.34694i	−1.07035	−	0.777657i	−0.0943775	−	0.995536i	$-0.530086\pi$
$3$	−1.85391	−	1.34694i	−1.07035	−	0.777657i	−0.975976	+	0.217879i	$0.930086\pi$
$4$	−0.739758	+	0.537466i	−0.369879	+	0.268733i
$5$	1.25658	−	3.86735i	0.561959	−	1.72953i	−0.114861	−	0.993382i	$-0.536642\pi$
$5$	1.25658	−	3.86735i	0.561959	−	1.72953i	0.676820	−	0.736149i	$-0.263358\pi$
$6$	1.20889	−	3.72058i	0.493527	−	1.51892i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$7$	0.809017	−	0.587785i	0.305780	−	0.222162i
$8$	1.49936	+	1.08935i	0.530103	+	0.385142i
$9$	0.695665	+	2.14104i	0.231888	+	0.713679i
$10$	6.94194			2.19523
$11$		0			0
$11$		0			0
$12$	2.09538			0.604883
$13$	−1.01293	−	3.11749i	−0.280937	−	0.864636i	−0.987587	−	0.157072i	$-0.949794\pi$
$13$	−1.01293	−	3.11749i	−0.280937	−	0.864636i	0.706650	−	0.707563i	$-0.250206\pi$
$14$	1.38112	+	1.00344i	0.369120	+	0.268181i
$15$	−7.53867	+	5.47716i	−1.94648	+	1.41420i
$16$	−1.54282	+	4.74831i	−0.385705	+	1.18708i
$17$	0.408175	−	1.25623i	0.0989969	−	0.304681i	−0.889278	−	0.457367i	$-0.848792\pi$
$17$	0.408175	−	1.25623i	0.0989969	−	0.304681i	0.988275	+	0.152686i	$0.0487924\pi$
$18$	−3.10921	+	2.25897i	−0.732847	+	0.532444i
$19$	1.74889	+	1.27064i	0.401223	+	0.291506i	0.770039	−	0.637997i	$-0.220237\pi$
$19$	1.74889	+	1.27064i	0.401223	+	0.291506i	−0.368816	+	0.929502i	$0.620237\pi$
$20$	1.14900	+	3.53627i	0.256925	+	0.790734i
$21$	−2.29155			−0.500058
$22$		0			0
$23$	−1.86611			−0.389112			−0.194556	−	0.980891i	$-0.562327\pi$
$23$	−1.86611			−0.389112			−0.194556	+	0.980891i	$0.562327\pi$
$24$	−1.31238	−	4.03909i	−0.267889	−	0.824476i
$25$	−9.33231	−	6.78032i	−1.86646	−	1.35606i
$26$	4.52720	−	3.28921i	0.887858	−	0.645067i
$27$	−0.530233	+	1.63189i	−0.102043	+	0.314057i
$28$	−0.282562	+	0.869638i	−0.0533993	+	0.164346i
$29$	−0.197482	+	0.143479i	−0.0366716	+	0.0266435i	−0.605970	−	0.795487i	$-0.707215\pi$
$29$	−0.197482	+	0.143479i	−0.0366716	+	0.0266435i	0.569298	+	0.822131i	$0.307215\pi$
$30$	−12.8697	−	9.35039i	−2.34968	−	1.70714i
$31$	−2.12291	−	6.53364i	−0.381286	−	1.17348i	−0.939139	−	0.343537i	$-0.888375\pi$
$31$	−2.12291	−	6.53364i	−0.381286	−	1.17348i	0.557853	−	0.829940i	$-0.311625\pi$
$32$	−4.81667			−0.851475
$33$		0			0
$34$	2.25495			0.386721
$35$	−1.25658	−	3.86735i	−0.212400	−	0.653701i
$36$	−1.66536	−	1.20995i	−0.277560	−	0.201659i
$37$	−0.206800	+	0.150249i	−0.0339978	+	0.0247008i	−0.604654	−	0.796488i	$-0.706689\pi$
$37$	−0.206800	+	0.150249i	−0.0339978	+	0.0247008i	0.570657	+	0.821189i	$0.306689\pi$
$38$	−1.14041	+	3.50982i	−0.184999	+	0.569368i
$39$	−2.32119	+	7.14389i	−0.371688	+	1.14394i
$40$	6.09694	−	4.42968i	0.964011	−	0.700395i
$41$	−4.63755	−	3.36938i	−0.724264	−	0.526208i	0.163480	−	0.986547i	$-0.447728\pi$
$41$	−4.63755	−	3.36938i	−0.724264	−	0.526208i	−0.887744	+	0.460338i	$0.847728\pi$
$42$	−1.20889	−	3.72058i	−0.186536	−	0.574098i
$43$	8.01781			1.22270			0.611352	−	0.791358i	$-0.290626\pi$
$43$	8.01781			1.22270			0.611352	+	0.791358i	$0.290626\pi$
$44$		0			0
$45$	9.15429			1.36464
$46$	−0.984452	−	3.02983i	−0.145150	−	0.446724i
$47$	3.29082	+	2.39092i	0.480015	+	0.348752i	0.801332	−	0.598220i	$-0.204125\pi$
$47$	3.29082	+	2.39092i	0.480015	+	0.348752i	−0.321316	+	0.946972i	$0.604125\pi$
$48$	9.25594	−	6.72484i	1.33598	−	0.970647i
$49$	0.309017	−	0.951057i	0.0441453	−	0.135865i
$50$	6.08538	−	18.7289i	0.860603	−	2.64866i
$51$	−2.44879	+	1.77915i	−0.342899	+	0.249131i
$52$	2.42487	+	1.76177i	0.336269	+	0.244314i
$53$	−1.54689	−	4.76085i	−0.212482	−	0.653953i	−0.999323	−	0.0367965i	$-0.988285\pi$
$53$	−1.54689	−	4.76085i	−0.212482	−	0.653953i	0.786841	−	0.617156i	$-0.211715\pi$
$54$	−2.92926			−0.398622
$55$		0			0
$56$	1.85331			0.247658
$57$	−1.53080	−	4.71131i	−0.202759	−	0.624028i
$58$	−0.337134	−	0.244942i	−0.0442679	−	0.0321625i
$59$	0.795743	−	0.578141i	0.103597	−	0.0752676i	−0.534781	−	0.844991i	$-0.679606\pi$
$59$	0.795743	−	0.578141i	0.103597	−	0.0752676i	0.638378	+	0.769723i	$0.279606\pi$
$60$	2.63300	−	8.10355i	0.339919	−	1.04616i
$61$	−0.570665	+	1.75633i	−0.0730661	+	0.224874i	−0.980920	−	0.194413i	$-0.937720\pi$
$61$	−0.570665	+	1.75633i	−0.0730661	+	0.224874i	0.907854	+	0.419287i	$0.137720\pi$
$62$	9.48813	−	6.89353i	1.20499	−	0.875479i
$63$	1.82128	+	1.32323i	0.229459	+	0.166712i
$64$	0.544649	+	1.67626i	0.0680812	+	0.209532i
$65$	−13.3292			−1.65329
$66$		0			0
$67$	−3.00700			−0.367364			−0.183682	−	0.982986i	$-0.558802\pi$
$67$	−3.00700			−0.367364			−0.183682	+	0.982986i	$0.558802\pi$
$68$	0.373231	+	1.14869i	0.0452610	+	0.139299i
$69$	3.45960	+	2.51355i	0.416487	+	0.302595i
$70$	5.61615	−	4.08037i	0.671258	−	0.487697i
$71$	2.00132	−	6.15944i	0.237513	−	0.730991i	−0.759265	−	0.650782i	$-0.774441\pi$
$71$	2.00132	−	6.15944i	0.237513	−	0.730991i	0.996778	−	0.0802090i	$-0.0255588\pi$
$72$	−1.28928	+	3.96800i	−0.151943	+	0.467633i
$73$	−7.80834	+	5.67309i	−0.913897	+	0.663985i	−0.941998	−	0.335620i	$-0.891054\pi$
$73$	−7.80834	+	5.67309i	−0.913897	+	0.663985i	0.0281002	+	0.999605i	$0.491054\pi$
$74$	−0.353041	−	0.256499i	−0.0410402	−	0.0298175i
$75$	8.16853	+	25.1401i	0.943220	+	2.90293i
$76$	−1.97668			−0.226741
$77$		0			0
$78$	−12.8234			−1.45196
$79$	1.71025	+	5.26362i	0.192419	+	0.592204i	0.999997	+	0.00244345i	$0.000777776\pi$
$79$	1.71025	+	5.26362i	0.192419	+	0.592204i	−0.807578	+	0.589760i	$0.799222\pi$
$80$	16.4247	+	11.9332i	1.83634	+	1.33418i
$81$	8.64489	−	6.28088i	0.960543	−	0.697875i
$82$	3.02404	−	9.30704i	0.333949	−	1.02779i
$83$	−0.639735	+	1.96890i	−0.0702201	+	0.216115i	−0.980008	−	0.198958i	$-0.936244\pi$
$83$	−0.639735	+	1.96890i	−0.0702201	+	0.216115i	0.909788	+	0.415074i	$0.136244\pi$
$84$	1.69520	−	1.23163i	0.184961	−	0.134382i
$85$	−4.34539	−	3.15711i	−0.471323	−	0.342436i
$86$	4.22973	+	13.0178i	0.456103	+	1.40374i
$87$	0.559372			0.0599710
$88$		0			0
$89$	16.6306			1.76284			0.881421	−	0.472331i	$-0.156587\pi$
$89$	16.6306			1.76284			0.881421	+	0.472331i	$0.156587\pi$
$90$	4.82927	+	14.8630i	0.509049	+	1.56669i
$91$	−2.65189	−	1.92671i	−0.277994	−	0.201975i
$92$	1.38047	−	1.00297i	0.143924	−	0.104567i
$93$	−4.86476	+	14.9722i	−0.504452	+	1.55254i
$94$	−2.14587	+	6.60430i	−0.221329	+	0.681181i
$95$	7.11164	−	5.16691i	0.729638	−	0.530113i
$96$	8.92965	+	6.48777i	0.911379	+	0.662156i
$97$	−0.798992	−	2.45904i	−0.0811253	−	0.249678i	0.902265	−	0.431182i	$-0.141903\pi$
$97$	−0.798992	−	2.45904i	−0.0811253	−	0.249678i	−0.983390	+	0.181504i	$0.941903\pi$
$98$	1.70716			0.172449
$99$		0			0
$100$	10.5478			1.05478
$101$	−3.26588	−	10.0513i	−0.324967	−	1.00015i	−0.971456	−	0.237222i	$-0.923763\pi$
$101$	−3.26588	−	10.0513i	−0.324967	−	1.00015i	0.646489	−	0.762924i	$-0.276237\pi$
$102$	−4.18047	−	3.03729i	−0.413929	−	0.300737i
$103$	−11.2040	+	8.14017i	−1.10396	+	0.802075i	−0.981702	−	0.190423i	$-0.939014\pi$
$103$	−11.2040	+	8.14017i	−1.10396	+	0.802075i	−0.122259	+	0.992498i	$0.539014\pi$
$104$	1.87728	−	5.77766i	0.184082	−	0.566546i
$105$	−2.87952	+	8.86224i	−0.281012	+	0.864866i
$106$	6.91368	−	5.02309i	0.671516	−	0.487885i
$107$	10.0550	+	7.30538i	0.972052	+	0.706237i	0.955918	−	0.293633i	$-0.0948642\pi$
$107$	10.0550	+	7.30538i	0.972052	+	0.706237i	0.0161339	+	0.999870i	$0.494864\pi$
$108$	−0.484840	−	1.49219i	−0.0466538	−	0.143586i
$109$	7.36748			0.705676			0.352838	−	0.935684i	$-0.385217\pi$
$109$	7.36748			0.705676			0.352838	+	0.935684i	$0.385217\pi$
$110$		0			0
$111$	0.585766			0.0555984
$112$	1.54282	+	4.74831i	0.145783	+	0.448673i
$113$	−9.22949	−	6.70562i	−0.868237	−	0.630811i	0.0618761	−	0.998084i	$-0.480292\pi$
$113$	−9.22949	−	6.70562i	−0.868237	−	0.630811i	−0.930113	+	0.367273i	$0.880292\pi$
$114$	6.84174	−	4.97082i	0.640788	−	0.465560i
$115$	−2.34492	+	7.21691i	−0.218665	+	0.672981i
$116$	0.0689740	−	0.212280i	0.00640407	−	0.0197097i
$117$	5.97000	−	4.33746i	0.551926	−	0.400998i
$118$	1.35846	+	0.986979i	0.125056	+	0.0908587i
$119$	−0.408175	−	1.25623i	−0.0374173	−	0.115159i
$120$	−17.2697			−1.57650
$121$		0			0
$122$	−3.15263			−0.285425
$123$	4.05923	+	12.4930i	0.366008	+	1.12646i
$124$	5.08205	+	3.69232i	0.456381	+	0.331581i
$125$	−21.4998	+	15.6205i	−1.92300	+	1.39714i
$126$	−1.18761	+	3.65509i	−0.105801	+	0.325621i
$127$	2.70342	−	8.32027i	0.239890	−	0.738305i	−0.756545	−	0.653941i	$-0.773114\pi$
$127$	2.70342	−	8.32027i	0.239890	−	0.738305i	0.996435	−	0.0843635i	$-0.0268857\pi$
$128$	−10.2278	+	7.43092i	−0.904018	+	0.656807i
$129$	−14.8643	−	10.7995i	−1.30873	−	0.950845i
$130$	−7.03172	−	21.6414i	−0.616723	−	1.89808i
$131$	12.5516			1.09664			0.548319	−	0.836269i	$-0.315268\pi$
$131$	12.5516			1.09664			0.548319	+	0.836269i	$0.315268\pi$
$132$		0			0
$133$	2.16175			0.187447
$134$	−1.58632	−	4.88218i	−0.137037	−	0.421756i
$135$	5.64480	+	4.10119i	0.485827	+	0.352974i
$136$	1.98047	−	1.43890i	0.169824	−	0.123384i
$137$	−1.95552	+	6.01847i	−0.167071	+	0.514192i	−0.999183	−	0.0404157i	$-0.987132\pi$
$137$	−1.95552	+	6.01847i	−0.167071	+	0.514192i	0.832112	+	0.554608i	$0.187132\pi$
$138$	−2.25592	+	6.94302i	−0.192037	+	0.591029i
$139$	11.6846	−	8.48935i	0.991073	−	0.720057i	0.0309175	−	0.999522i	$-0.490157\pi$
$139$	11.6846	−	8.48935i	0.991073	−	0.720057i	0.960156	+	0.279465i	$0.0901571\pi$
$140$	3.00813	+	2.18553i	0.254233	+	0.184711i
$141$	−2.88044	−	8.86509i	−0.242577	−	0.746575i
$142$	11.0563			0.927822
$143$		0			0
$144$	−11.2396			−0.936633
$145$	0.306733	+	0.944026i	0.0254728	+	0.0783971i
$146$	−13.3301	−	9.68487i	−1.10321	−	0.801526i
$147$	−1.85391	+	1.34694i	−0.152908	+	0.111094i
$148$	0.0722284	−	0.222296i	0.00593714	−	0.0182726i
$149$	−7.43471	+	22.8817i	−0.609075	+	1.87454i	−0.143188	+	0.989696i	$0.545735\pi$
$149$	−7.43471	+	22.8817i	−0.609075	+	1.87454i	−0.465887	+	0.884844i	$0.654265\pi$
$150$	−36.5084	+	26.5249i	−2.98090	+	2.16575i
$151$	−1.07129	−	0.778335i	−0.0871800	−	0.0633400i	0.543341	−	0.839512i	$-0.317159\pi$
$151$	−1.07129	−	0.778335i	−0.0871800	−	0.0633400i	−0.630521	+	0.776172i	$0.717159\pi$
$152$	1.23804	+	3.81029i	0.100418	+	0.309056i
$153$	2.97359			0.240401
$154$		0			0
$155$	−27.9355			−2.24383
$156$	−2.12248	−	6.53231i	−0.169934	−	0.523004i
$157$	−11.8230	−	8.58994i	−0.943581	−	0.685552i	0.00569912	−	0.999984i	$-0.498186\pi$
$157$	−11.8230	−	8.58994i	−0.943581	−	0.685552i	−0.949280	+	0.314432i	$0.898186\pi$
$158$	−7.64381	+	5.55355i	−0.608109	+	0.441817i
$159$	−3.54479	+	10.9097i	−0.281120	+	0.865199i
$160$	−6.05252	+	18.6277i	−0.478494	+	1.47265i
$161$	−1.50972	+	1.09687i	−0.118982	+	0.0864458i
$162$	14.7582	+	10.7225i	1.15951	+	0.842436i
$163$	−6.46509	−	19.8975i	−0.506385	−	1.55849i	−0.798429	−	0.602089i	$-0.794335\pi$
$163$	−6.46509	−	19.8975i	−0.506385	−	1.55849i	0.292044	−	0.956405i	$-0.405665\pi$
$164$	5.24159			0.409300
$165$		0			0
$166$	−3.53421			−0.274308
$167$	−1.51831	−	4.67287i	−0.117490	−	0.361598i	0.874968	−	0.484181i	$-0.160882\pi$
$167$	−1.51831	−	4.67287i	−0.117490	−	0.361598i	−0.992458	+	0.122583i	$0.960882\pi$
$168$	−3.43586	−	2.49630i	−0.265082	−	0.192593i
$169$	1.82452	−	1.32559i	0.140348	−	0.101969i
$170$	2.83352	−	8.72069i	0.217321	−	0.668847i
$171$	−1.50385	+	4.62838i	−0.115002	+	0.353941i
$172$	−5.93124	+	4.30930i	−0.452253	+	0.328581i
$173$	15.9035	+	11.5546i	1.20912	+	0.878479i	0.995151	−	0.0983612i	$-0.0313600\pi$
$173$	15.9035	+	11.5546i	1.20912	+	0.878479i	0.213971	+	0.976840i	$0.431360\pi$
$174$	0.295092	+	0.908199i	0.0223709	+	0.0688504i
$175$	−11.5354			−0.871992
$176$		0			0
$177$	−2.25395			−0.169418
$178$	8.77334	+	27.0016i	0.657590	+	2.02385i
$179$	20.5157	+	14.9056i	1.53342	+	1.11409i	0.954300	+	0.298850i	$0.0966030\pi$
$179$	20.5157	+	14.9056i	1.53342	+	1.11409i	0.579118	+	0.815244i	$0.303397\pi$
$180$	−6.77196	+	4.92012i	−0.504752	+	0.366724i
$181$	−0.610521	+	1.87899i	−0.0453797	+	0.139664i	−0.971179	−	0.238351i	$-0.923393\pi$
$181$	−0.610521	+	1.87899i	−0.0453797	+	0.139664i	0.925799	+	0.378015i	$0.123393\pi$
$182$	1.72924	−	5.32205i	0.128180	−	0.394496i
$183$	3.42363	−	2.48741i	0.253082	−	0.183875i
$184$	−2.79797	−	2.03284i	−0.206269	−	0.149863i
$185$	0.321206	+	0.988569i	0.0236155	+	0.0726810i
$186$	−26.8753			−1.97059
$187$		0			0
$188$	−3.71945			−0.271269
$189$	0.530233	+	1.63189i	0.0385688	+	0.118702i
$190$	12.1407	+	8.82073i	0.880778	+	0.639923i
$191$	−0.787170	+	0.571912i	−0.0569576	+	0.0413821i	−0.615900	−	0.787825i	$-0.711207\pi$
$191$	−0.787170	+	0.571912i	−0.0569576	+	0.0413821i	0.558942	+	0.829207i	$0.311207\pi$
$192$	1.24809	−	3.84124i	0.0900734	−	0.277217i
$193$	7.14838	−	22.0004i	0.514551	−	1.58363i	−0.269545	−	0.962988i	$-0.586873\pi$
$193$	7.14838	−	22.0004i	0.514551	−	1.58363i	0.784097	−	0.620639i	$-0.213127\pi$
$194$	3.57101	−	2.59449i	0.256384	−	0.186274i
$195$	24.7112	+	17.9537i	1.76960	+	1.28569i
$196$	0.282562	+	0.869638i	0.0201830	+	0.0621170i
$197$	9.91237			0.706227			0.353114	−	0.935580i	$-0.385123\pi$
$197$	9.91237			0.706227			0.353114	+	0.935580i	$0.385123\pi$
$198$		0			0
$199$	10.3847			0.736154			0.368077	−	0.929795i	$-0.380016\pi$
$199$	10.3847			0.736154			0.368077	+	0.929795i	$0.380016\pi$
$200$	−6.60634	−	20.3322i	−0.467139	−	1.43771i
$201$	5.57470	+	4.05025i	0.393209	+	0.285683i
$202$	14.5965	−	10.6050i	1.02701	−	0.746164i
$203$	−0.0754316	+	0.232155i	−0.00529426	+	0.0162941i
$204$	0.855280	−	2.63228i	0.0598816	−	0.184297i
$205$	−18.8580	+	13.7011i	−1.31710	+	0.956929i
$206$	−19.1270	−	13.8966i	−1.33264	−	0.968219i
$207$	−1.29819	−	3.99542i	−0.0902305	−	0.277701i
$208$	16.3656			1.13475
$209$		0			0
$210$	−15.9078			−1.09774
$211$	4.01462	+	12.3557i	0.276378	+	0.850604i	0.988852	+	0.148905i	$0.0475749\pi$
$211$	4.01462	+	12.3557i	0.276378	+	0.850604i	−0.712474	+	0.701699i	$0.752425\pi$
$212$	3.70312	+	2.69047i	0.254331	+	0.184782i
$213$	−12.0067	+	8.72336i	−0.822684	+	0.597715i
$214$	−6.55662	+	20.1792i	−0.448201	+	1.37942i
$215$	10.0750	−	31.0077i	0.687109	−	2.11471i
$216$	−2.57270	+	1.86918i	−0.175050	+	0.127181i
$217$	−5.55785	−	4.03801i	−0.377291	−	0.274118i
$218$	3.88665	+	11.9619i	0.263237	+	0.810160i
$219$	22.1173			1.49455
$220$		0			0
$221$	−4.32975			−0.291250
$222$	0.309015	+	0.951052i	0.0207398	+	0.0638304i
$223$	11.6116	+	8.43630i	0.777568	+	0.564936i	0.904248	−	0.427008i	$-0.140432\pi$
$223$	11.6116	+	8.43630i	0.777568	+	0.564936i	−0.126680	+	0.991944i	$0.540432\pi$
$224$	−3.89677	+	2.83117i	−0.260364	+	0.189165i
$225$	8.02475	−	24.6977i	0.534984	−	1.64651i
$226$	6.01833	−	18.5225i	0.400334	−	1.23210i
$227$	5.15732	−	3.74701i	0.342303	−	0.248698i	−0.403330	−	0.915055i	$-0.632147\pi$
$227$	5.15732	−	3.74701i	0.342303	−	0.248698i	0.745633	+	0.666357i	$0.232147\pi$
$228$	3.66458	+	2.66248i	0.242693	+	0.176327i
$229$	−2.47287	−	7.61071i	−0.163412	−	0.502930i	0.835504	−	0.549484i	$-0.185176\pi$
$229$	−2.47287	−	7.61071i	−0.163412	−	0.502930i	−0.998916	+	0.0465547i	$0.985176\pi$
$230$	−12.9545			−0.854191
$231$		0			0
$232$	−0.452395			−0.0297012
$233$	3.33806	+	10.2735i	0.218684	+	0.673039i	0.998872	+	0.0474937i	$0.0151234\pi$
$233$	3.33806	+	10.2735i	0.218684	+	0.673039i	−0.780188	+	0.625545i	$0.784877\pi$
$234$	10.1917	+	7.40473i	0.666254	+	0.484062i
$235$	13.3817	−	9.72237i	0.872925	−	0.634217i
$236$	−0.277926	+	0.855369i	−0.0180915	+	0.0556798i
$237$	3.91914	−	12.0619i	0.254576	−	0.783503i
$238$	1.82430	−	1.32543i	0.118252	−	0.0859148i
$239$	20.3535	+	14.7877i	1.31656	+	0.956534i	0.999968	+	0.00797061i	$0.00253715\pi$
$239$	20.3535	+	14.7877i	1.31656	+	0.956534i	0.316588	+	0.948563i	$0.397463\pi$
$240$	−14.3765	−	44.2462i	−0.927997	−	2.85608i
$241$	18.2462			1.17534			0.587669	−	0.809101i	$-0.300046\pi$
$241$	18.2462			1.17534			0.587669	+	0.809101i	$0.300046\pi$
$242$		0			0
$243$	−19.3392			−1.24061
$244$	−0.521811	−	1.60597i	−0.0334055	−	0.102812i
$245$	−3.28976	−	2.39015i	−0.210175	−	0.152701i
$246$	−18.1423	+	13.1812i	−1.15671	+	0.840400i
$247$	2.18971	−	6.73922i	0.139328	−	0.428806i
$248$	3.93440	−	12.1088i	0.249835	−	0.768912i
$249$	3.83801	−	2.78848i	0.243224	−	0.176712i
$250$	−36.7036	−	26.6667i	−2.32134	−	1.68655i
$251$	4.73674	+	14.5782i	0.298980	+	0.920166i	0.981855	+	0.189631i	$0.0607292\pi$
$251$	4.73674	+	14.5782i	0.298980	+	0.920166i	−0.682875	+	0.730535i	$0.739271\pi$
$252$	−2.05850			−0.129673
$253$		0			0
$254$	14.9350			0.937105
$255$	3.80350	+	11.7060i	0.238184	+	0.733056i
$256$	−14.6086	−	10.6138i	−0.913040	−	0.663363i
$257$	−2.16800	+	1.57514i	−0.135236	+	0.0982548i	−0.653347	−	0.757059i	$-0.726636\pi$
$257$	−2.16800	+	1.57514i	−0.135236	+	0.0982548i	0.518111	+	0.855314i	$0.326636\pi$
$258$	9.69264	−	29.8309i	0.603438	−	1.85719i
$259$	−0.0789907	+	0.243108i	−0.00490825	+	0.0151060i
$260$	9.86042	−	7.16401i	0.611517	−	0.444293i
$261$	−0.444576	−	0.323004i	−0.0275186	−	0.0199934i
$262$	6.62149	+	20.3788i	0.409077	+	1.25901i
$263$	9.97733			0.615229			0.307614	−	0.951511i	$-0.400469\pi$
$263$	9.97733			0.615229			0.307614	+	0.951511i	$0.400469\pi$
$264$		0			0
$265$	−20.3556			−1.25044
$266$	1.14041	+	3.50982i	0.0699231	+	0.215201i
$267$	−30.8316	−	22.4005i	−1.88686	−	1.37089i
$268$	2.22445	−	1.61616i	0.135880	−	0.0987227i
$269$	−6.66778	+	20.5213i	−0.406542	+	1.25121i	0.513059	+	0.858353i	$0.328512\pi$
$269$	−6.66778	+	20.5213i	−0.406542	+	1.25121i	−0.919601	+	0.392854i	$0.871488\pi$
$270$	−3.68085	+	11.3285i	−0.224009	+	0.689429i
$271$	−12.1241	+	8.80869i	−0.736488	+	0.535090i	−0.891609	−	0.452806i	$-0.850423\pi$
$271$	−12.1241	+	8.80869i	−0.736488	+	0.535090i	0.155121	+	0.987895i	$0.450423\pi$
$272$	5.33525	+	3.87628i	0.323497	+	0.235034i
$273$	2.32119	+	7.14389i	0.140485	+	0.432368i
$274$	−10.8032			−0.652647
$275$		0			0
$276$	−3.91021			−0.235367
$277$	−1.60887	−	4.95158i	−0.0966674	−	0.297512i	0.891017	−	0.453969i	$-0.149992\pi$
$277$	−1.60887	−	4.95158i	−0.0966674	−	0.297512i	−0.987685	+	0.156458i	$0.949992\pi$
$278$	19.9474	+	14.4927i	1.19637	+	0.869212i
$279$	12.5119	−	9.09046i	0.749070	−	0.544231i
$280$	2.32882	−	7.16738i	0.139174	−	0.428333i
$281$	−4.68472	+	14.4181i	−0.279467	+	0.860110i	0.708536	+	0.705675i	$0.249356\pi$
$281$	−4.68472	+	14.4181i	−0.279467	+	0.860110i	−0.988003	+	0.154436i	$0.950644\pi$
$282$	12.8738	−	9.35339i	0.766626	−	0.556986i
$283$	−4.58356	−	3.33015i	−0.272464	−	0.197957i	0.443160	−	0.896443i	$-0.353857\pi$
$283$	−4.58356	−	3.33015i	−0.272464	−	0.197957i	−0.715624	+	0.698486i	$0.753857\pi$
$284$	1.82999	+	5.63214i	0.108590	+	0.334206i
$285$	−20.1438			−1.19322
$286$		0			0
$287$	−5.73233			−0.338369
$288$	−3.35079	−	10.3127i	−0.197447	−	0.607680i
$289$	12.3418	+	8.96682i	0.725987	+	0.527460i
$290$	−1.37091	+	0.996025i	−0.0805027	+	0.0584886i
$291$	−1.83093	+	5.63503i	−0.107331	+	0.330331i
$292$	2.72719	−	8.39343i	0.159597	−	0.491188i
$293$	−21.7952	+	15.8351i	−1.27329	+	0.925098i	−0.999328	−	0.0366430i	$-0.988334\pi$
$293$	−21.7952	+	15.8351i	−1.27329	+	0.925098i	−0.273960	+	0.961741i	$0.588334\pi$
$294$	−3.16491	−	2.29944i	−0.184581	−	0.134106i
$295$	−1.23596	−	3.80389i	−0.0719604	−	0.221471i
$296$	−0.473741			−0.0275356
$297$		0			0
$298$	−41.0729			−2.37929
$299$	1.89025	+	5.81759i	0.109316	+	0.336440i
$300$	−19.5547	−	14.2073i	−1.12899	−	0.820260i
$301$	6.48655	−	4.71275i	0.373878	−	0.271638i
$302$	0.698560	−	2.14995i	0.0401976	−	0.123716i
$303$	−7.48393	+	23.0332i	−0.429941	+	1.32322i
$304$	−8.73163	+	6.34390i	−0.500794	+	0.363848i
$305$	6.07524	+	4.41392i	0.347867	+	0.252740i
$306$	1.56869	+	4.82794i	0.0896762	+	0.275995i
$307$	−24.6157			−1.40489			−0.702447	−	0.711736i	$-0.747909\pi$
$307$	−24.6157			−1.40489			−0.702447	+	0.711736i	$0.747909\pi$
$308$		0			0
$309$	31.7355			1.80537
$310$	−14.7371	−	45.3562i	−0.837012	−	2.57606i
$311$	8.26257	+	6.00311i	0.468527	+	0.340405i	0.796867	−	0.604155i	$-0.206489\pi$
$311$	8.26257	+	6.00311i	0.468527	+	0.340405i	−0.328340	+	0.944560i	$0.606489\pi$
$312$	−11.2625	+	8.18266i	−0.637612	+	0.463252i
$313$	6.92206	−	21.3039i	0.391258	−	1.20417i	−0.540580	−	0.841293i	$-0.681795\pi$
$313$	6.92206	−	21.3039i	0.391258	−	1.20417i	0.931838	−	0.362875i	$-0.118205\pi$
$314$	7.70952	−	23.7275i	0.435074	−	1.33902i
$315$	7.40598	−	5.38076i	0.417280	−	0.303171i
$316$	−4.09419	−	2.97460i	−0.230316	−	0.167335i
$317$	7.21848	+	22.2162i	0.405430	+	1.24779i	0.920536	+	0.390659i	$0.127753\pi$
$317$	7.21848	+	22.2162i	0.405430	+	1.24779i	−0.515105	+	0.857127i	$0.672247\pi$
$318$	−19.5831			−1.09817
$319$		0			0
$320$	7.16707			0.400651
$321$	−8.80109	−	27.0870i	−0.491229	−	1.51185i
$322$	−2.57733	−	1.87254i	−0.143629	−	0.104352i
$323$	2.31008	−	1.67837i	0.128536	−	0.0933869i
$324$	−3.01937	+	9.29266i	−0.167743	+	0.516259i
$325$	−11.6846	+	35.9614i	−0.648143	+	1.99478i
$326$	28.8951	−	20.9935i	1.60035	−	1.16272i
$327$	−13.6586	−	9.92356i	−0.755323	−	0.548774i
$328$	−3.28292	−	10.1038i	−0.181269	−	0.557889i
$329$	4.06768			0.224258
$330$		0			0
$331$	15.6444			0.859892			0.429946	−	0.902855i	$-0.358533\pi$
$331$	15.6444			0.859892			0.429946	+	0.902855i	$0.358533\pi$
$332$	−0.584968	−	1.80035i	−0.0321043	−	0.0988069i
$333$	−0.465553	−	0.338244i	−0.0255122	−	0.0185357i
$334$	6.78593	−	4.93026i	0.371309	−	0.269772i
$335$	−3.77853	+	11.6291i	−0.206443	+	0.635367i
$336$	3.53546	−	10.8810i	0.192875	−	0.593608i
$337$	26.3666	−	19.1565i	1.43628	−	1.04352i	0.447480	−	0.894294i	$-0.352322\pi$
$337$	26.3666	−	19.1565i	1.43628	−	1.04352i	0.988803	−	0.149227i	$-0.0476784\pi$
$338$	3.11474	+	2.26299i	0.169420	+	0.123091i
$339$	8.07853	+	24.8632i	0.438766	+	1.35038i
$340$	4.91137			0.266356
$341$		0			0
$342$	−8.30801			−0.449245
$343$	−0.309017	−	0.951057i	−0.0166853	−	0.0513522i
$344$	12.0216	+	8.73417i	0.648159	+	0.470915i
$345$	14.0680	−	10.2210i	0.757396	−	0.550281i
$346$	−10.3703	+	31.9165i	−0.557512	+	1.71584i
$347$	−1.77773	+	5.47127i	−0.0954333	+	0.293713i	−0.987366	−	0.158454i	$-0.949349\pi$
$347$	−1.77773	+	5.47127i	−0.0954333	+	0.293713i	0.891933	+	0.452167i	$0.149349\pi$
$348$	−0.413800	+	0.300643i	−0.0221820	+	0.0161162i
$349$	−0.148810	−	0.108117i	−0.00796563	−	0.00578737i	0.583795	−	0.811901i	$-0.301567\pi$
$349$	−0.148810	−	0.108117i	−0.00796563	−	0.00578737i	−0.591761	+	0.806114i	$0.701567\pi$
$350$	−6.08538	−	18.7289i	−0.325277	−	1.00110i
$351$	5.62449			0.300213
$352$		0			0
$353$	19.0211			1.01239			0.506195	−	0.862419i	$-0.331052\pi$
$353$	19.0211			1.01239			0.506195	+	0.862419i	$0.331052\pi$
$354$	−1.18905	−	3.65953i	−0.0631975	−	0.194502i
$355$	−21.3059	−	15.4796i	−1.13080	−	0.821573i
$356$	−12.3026	+	8.93839i	−0.652039	+	0.473734i
$357$	−0.935354	+	2.87873i	−0.0495042	+	0.152358i
$358$	−13.3778	+	41.1727i	−0.707040	+	2.17605i
$359$	−0.581625	+	0.422575i	−0.0306970	+	0.0223027i	−0.603028	−	0.797720i	$-0.706039\pi$
$359$	−0.581625	+	0.422575i	−0.0306970	+	0.0223027i	0.572331	+	0.820023i	$0.306039\pi$
$360$	13.7255	+	9.97220i	0.723400	+	0.525581i
$361$	−4.42724	−	13.6256i	−0.233013	−	0.717139i
$362$	−3.37281			−0.177271
$363$		0			0
$364$	2.99730			0.157101
$365$	12.1280	+	37.3263i	0.634810	+	1.95375i
$366$	5.84467	+	4.24640i	0.305506	+	0.221963i
$367$	6.38553	−	4.63936i	0.333322	−	0.242173i	−0.408517	−	0.912751i	$-0.633954\pi$
$367$	6.38553	−	4.63936i	0.333322	−	0.242173i	0.741839	+	0.670578i	$0.233954\pi$
$368$	2.87908	−	8.86089i	0.150082	−	0.461906i
$369$	3.98778	−	12.2731i	0.207596	−	0.638914i
$370$	−1.43560	+	1.04302i	−0.0746331	+	0.0542241i
$371$	−4.04982	−	2.94237i	−0.210256	−	0.152760i
$372$	−4.44830	−	13.6904i	−0.230633	−	0.709817i
$373$	−15.6686			−0.811292			−0.405646	−	0.914030i	$-0.632953\pi$
$373$	−15.6686			−0.811292			−0.405646	+	0.914030i	$0.632953\pi$
$374$		0			0
$375$	60.8985			3.14479
$376$	2.32957	+	7.16968i	0.120138	+	0.369748i
$377$	0.647332	+	0.470314i	0.0333393	+	0.0242224i
$378$	−2.36982	+	1.72178i	−0.121891	+	0.0885587i
$379$	−4.11437	+	12.6627i	−0.211341	+	0.650441i	0.788052	+	0.615609i	$0.211090\pi$
$379$	−4.11437	+	12.6627i	−0.211341	+	0.650441i	−0.999393	+	0.0348325i	$0.988910\pi$
$380$	−2.48386	+	7.64452i	−0.127419	+	0.392156i
$381$	−16.2188	+	11.7837i	−0.830915	+	0.603695i
$382$	−1.34382	−	0.976345i	−0.0687560	−	0.0499542i
$383$	3.66136	+	11.2685i	0.187087	+	0.575794i	0.999978	−	0.00662124i	$-0.00210762\pi$
$383$	3.66136	+	11.2685i	0.187087	+	0.575794i	−0.812891	+	0.582416i	$0.802108\pi$
$384$	28.9704			1.47839
$385$		0			0
$386$	39.4911			2.01004
$387$	5.57771	+	17.1664i	0.283531	+	0.872619i
$388$	1.91271	+	1.38967i	0.0971032	+	0.0705496i
$389$	4.89432	−	3.55594i	0.248152	−	0.180293i	−0.456755	−	0.889592i	$-0.650989\pi$
$389$	4.89432	−	3.55594i	0.248152	−	0.180293i	0.704907	+	0.709299i	$0.250989\pi$
$390$	−16.1136	+	49.5925i	−0.815943	+	2.51121i
$391$	−0.761701	+	2.34427i	−0.0385209	+	0.118555i
$392$	1.49936	−	1.08935i	0.0757289	−	0.0550203i
$393$	−23.2695	−	16.9063i	−1.17379	−	0.852809i
$394$	5.22918	+	16.0938i	0.263442	+	0.810793i
$395$	22.5053			1.13237
$396$		0			0
$397$	−11.5763			−0.580996			−0.290498	−	0.956876i	$-0.593821\pi$
$397$	−11.5763			−0.580996			−0.290498	+	0.956876i	$0.593821\pi$
$398$	5.47837	+	16.8607i	0.274606	+	0.845150i
$399$	−4.00768	−	2.91175i	−0.200635	−	0.145770i
$400$	46.5931	−	33.8519i	2.32966	−	1.69259i
$401$	10.4424	−	32.1385i	0.521469	−	1.60492i	−0.249724	−	0.968317i	$-0.580340\pi$
$401$	10.4424	−	32.1385i	0.521469	−	1.60492i	0.771193	−	0.636601i	$-0.219660\pi$
$402$	−3.63513	+	11.1878i	−0.181304	+	0.557996i
$403$	−18.2182	+	13.2363i	−0.907513	+	0.659347i
$404$	7.81821	+	5.68026i	0.388970	+	0.282604i
$405$	−13.4274	−	41.3252i	−0.667211	−	2.05347i
$406$	−0.416720			−0.0206815
$407$		0			0
$408$	−5.60972			−0.277722
$409$	−5.57837	−	17.1684i	−0.275832	−	0.848925i	−0.988998	−	0.147929i	$-0.952739\pi$
$409$	−5.57837	−	17.1684i	−0.275832	−	0.848925i	0.713165	−	0.700996i	$-0.247261\pi$
$410$	−32.1936	−	23.3900i	−1.58993	−	1.15515i
$411$	11.7319	−	8.52370i	0.578690	−	0.420443i
$412$	3.91317	−	12.0435i	0.192788	−	0.593341i
$413$	0.303947	−	0.935452i	0.0149562	−	0.0460306i
$414$	5.80213	−	4.21550i	0.285159	−	0.207180i
$415$	6.81056	+	4.94816i	0.334317	+	0.242896i
$416$	4.87897	+	15.0159i	0.239211	+	0.736216i
$417$	−33.0968			−1.62076
$418$		0			0
$419$	2.58559			0.126314			0.0631571	−	0.998004i	$-0.479883\pi$
$419$	2.58559			0.126314			0.0631571	+	0.998004i	$0.479883\pi$
$420$	−2.63300	−	8.10355i	−0.128477	−	0.395413i
$421$	−11.3220	−	8.22592i	−0.551801	−	0.400907i	0.276648	−	0.960971i	$-0.410776\pi$
$421$	−11.3220	−	8.22592i	−0.551801	−	0.400907i	−0.828449	+	0.560064i	$0.810776\pi$
$422$	−17.9430	+	13.0363i	−0.873449	+	0.634598i
$423$	−2.82974	+	8.70905i	−0.137587	+	0.423448i
$424$	2.86687	−	8.82331i	0.139227	−	0.428498i
$425$	−12.3269	+	8.95599i	−0.597941	+	0.434430i
$426$	−20.4973	−	14.8922i	−0.993097	−	0.721527i
$427$	0.570665	+	1.75633i	0.0276164	+	0.0849945i
$428$	−11.3646			−0.549331
$429$		0			0
$430$	55.6592			2.68412
$431$	10.4040	+	32.0203i	0.501145	+	1.54237i	0.807156	+	0.590338i	$0.201005\pi$
$431$	10.4040	+	32.0203i	0.501145	+	1.54237i	−0.306011	+	0.952028i	$0.598995\pi$
$432$	−6.93067	−	5.03542i	−0.333452	−	0.242267i
$433$	−6.08617	+	4.42186i	−0.292483	+	0.212501i	−0.724344	−	0.689439i	$-0.757857\pi$
$433$	−6.08617	+	4.42186i	−0.292483	+	0.212501i	0.431861	+	0.901940i	$0.357857\pi$
$434$	3.62414	−	11.1540i	0.173964	−	0.535408i
$435$	0.702895	−	2.16329i	0.0337012	−	0.103722i
$436$	−5.45015	+	3.95977i	−0.261015	+	0.189638i
$437$	−3.26363	−	2.37116i	−0.156121	−	0.113428i
$438$	11.6678	+	35.9097i	0.557507	+	1.71583i
$439$	22.0123			1.05059			0.525294	−	0.850921i	$-0.323955\pi$
$439$	22.0123			1.05059			0.525294	+	0.850921i	$0.323955\pi$
$440$		0			0
$441$	2.25122			0.107201
$442$	−2.28412	−	7.02979i	−0.108644	−	0.334373i
$443$	−19.1650	−	13.9242i	−0.910558	−	0.661559i	0.0305977	−	0.999532i	$-0.490259\pi$
$443$	−19.1650	−	13.9242i	−0.910558	−	0.661559i	−0.941156	+	0.337972i	$0.890259\pi$
$444$	−0.433325	+	0.314829i	−0.0205647	+	0.0149411i
$445$	20.8977	−	64.3164i	0.990645	−	3.04889i
$446$	−7.57163	+	23.3031i	−0.358527	+	1.10343i
$447$	44.6035	−	32.4064i	2.10967	−	1.53277i
$448$	1.42591	+	1.03598i	0.0673679	+	0.0489457i
$449$	0.703055	+	2.16378i	0.0331792	+	0.102115i	0.966275	−	0.257514i	$-0.0829033\pi$
$449$	0.703055	+	2.16378i	0.0331792	+	0.102115i	−0.933095	+	0.359629i	$0.882903\pi$
$450$	44.3326			2.08986
$451$		0			0
$452$	10.4316			0.490663
$453$	0.937692	+	2.88592i	0.0440566	+	0.135592i
$454$	8.80436	+	6.39674i	0.413209	+	0.300214i
$455$	−10.7836	+	7.83473i	−0.505542	+	0.367298i
$456$	2.83703	−	8.73149i	0.132856	−	0.408890i
$457$	8.44030	−	25.9766i	0.394821	−	1.21513i	−0.534281	−	0.845307i	$-0.679417\pi$
$457$	8.44030	−	25.9766i	0.394821	−	1.21513i	0.929101	−	0.369826i	$-0.120583\pi$
$458$	11.0522	−	8.02992i	0.516437	−	0.375214i
$459$	1.83360	+	1.33219i	0.0855853	+	0.0621814i
$460$	−2.14417	−	6.59908i	−0.0999725	−	0.307684i
$461$	8.21908			0.382801			0.191400	−	0.981512i	$-0.438697\pi$
$461$	8.21908			0.382801			0.191400	+	0.981512i	$0.438697\pi$
$462$		0			0
$463$	−27.9839			−1.30052			−0.650261	−	0.759711i	$-0.725340\pi$
$463$	−27.9839			−1.30052			−0.650261	+	0.759711i	$0.725340\pi$
$464$	−0.376605	−	1.15907i	−0.0174835	−	0.0538085i
$465$	51.7897	+	37.6275i	2.40169	+	1.74493i
$466$	−14.9191	+	10.8394i	−0.691115	+	0.502124i
$467$	8.24288	−	25.3690i	0.381435	−	1.17394i	−0.557598	−	0.830111i	$-0.688277\pi$
$467$	8.24288	−	25.3690i	0.381435	−	1.17394i	0.939033	−	0.343826i	$-0.111723\pi$
$468$	−2.08512	+	6.41734i	−0.0963847	+	0.296642i
$469$	−2.43271	+	1.76747i	−0.112332	+	0.0816142i
$470$	22.8447	+	16.5976i	1.05375	+	0.765591i
$471$	10.3487	+	31.8499i	0.476841	+	1.46756i
$472$	1.82290			0.0839057
$473$		0			0
$474$	21.6512			0.994474
$475$	−7.70582	−	23.7161i	−0.353567	−	1.08817i
$476$	0.977133	+	0.709928i	0.0447868	+	0.0325395i
$477$	9.11703	−	6.62391i	0.417440	−	0.303288i
$478$	−13.2720	+	40.8471i	−0.607048	+	1.86830i
$479$	7.17661	−	22.0873i	0.327908	−	1.00920i	−0.642203	−	0.766534i	$-0.721980\pi$
$479$	7.17661	−	22.0873i	0.327908	−	1.00920i	0.970111	−	0.242662i	$-0.0780205\pi$
$480$	36.3113	−	26.3817i	1.65738	−	1.20415i
$481$	0.677876	+	0.492505i	0.0309085	+	0.0224563i
$482$	9.62560	+	29.6245i	0.438434	+	1.34936i
$483$	4.27630			0.194578
$484$		0			0
$485$	−10.5140			−0.477415
$486$	−10.2022	−	31.3992i	−0.462782	−	1.42430i
$487$	15.2031	+	11.0457i	0.688917	+	0.500527i	0.876304	−	0.481759i	$-0.160002\pi$
$487$	15.2031	+	11.0457i	0.688917	+	0.500527i	−0.187387	+	0.982286i	$0.560002\pi$
$488$	−2.76888	+	2.01171i	−0.125341	+	0.0910657i
$489$	−14.8151	+	45.5962i	−0.669963	+	2.06193i
$490$	2.14518	−	6.60218i	0.0969092	−	0.298256i
$491$	5.99136	−	4.35298i	0.270386	−	0.196447i	−0.444327	−	0.895865i	$-0.646557\pi$
$491$	5.99136	−	4.35298i	0.270386	−	0.196447i	0.714713	+	0.699417i	$0.246557\pi$
$492$	−9.71742	−	7.06012i	−0.438095	−	0.318295i
$493$	0.0996362	+	0.306649i	0.00448739	+	0.0138108i
$494$	12.0970			0.544269
$495$		0			0
$496$	34.2991			1.54007
$497$	−2.00132	−	6.15944i	−0.0897716	−	0.276289i
$498$	6.55209	+	4.76037i	0.293606	+	0.213317i
$499$	−19.1497	+	13.9131i	−0.857259	+	0.622835i	−0.927138	−	0.374721i	$-0.877739\pi$
$499$	−19.1497	+	13.9131i	−0.857259	+	0.622835i	0.0698792	+	0.997555i	$0.477739\pi$
$500$	7.50916	−	23.1108i	0.335820	−	1.03355i
$501$	−3.47929	+	10.7081i	−0.155443	+	0.478404i
$502$	−21.1704	+	15.3812i	−0.944880	+	0.686495i
$503$	−6.79357	−	4.93582i	−0.302910	−	0.220077i	0.425938	−	0.904752i	$-0.359944\pi$
$503$	−6.79357	−	4.93582i	−0.302910	−	0.220077i	−0.728848	+	0.684675i	$0.759944\pi$
$504$	1.28928	+	3.96800i	0.0574291	+	0.176749i
$505$	−42.9758			−1.91240
$506$		0			0
$507$	−5.16798			−0.229518
$508$	2.47198	+	7.60798i	0.109677	+	0.337550i
$509$	−11.5742	−	8.40912i	−0.513016	−	0.372728i	0.300951	−	0.953640i	$-0.402696\pi$
$509$	−11.5742	−	8.40912i	−0.513016	−	0.372728i	−0.813966	+	0.580912i	$0.802696\pi$
$510$	−16.9994	+	12.3508i	−0.752744	+	0.546900i
$511$	−2.98252	+	9.17926i	−0.131939	+	0.406066i
$512$	1.71262	−	5.27090i	0.0756877	−	0.232943i
$513$	−3.00087	+	2.18026i	−0.132492	+	0.0962608i
$514$	−3.70112	−	2.68902i	−0.163249	−	0.118608i
$515$	17.4022	+	53.5585i	0.766832	+	2.36007i
$516$	16.8003			0.739594
$517$		0			0
$518$	−0.436383			−0.0191736
$519$	−13.9203	−	42.8422i	−0.611033	−	1.88057i
$520$	−19.9853	−	14.5202i	−0.876413	−	0.636751i
$521$	26.9956	−	19.6134i	1.18270	−	0.859280i	0.190224	−	0.981741i	$-0.439079\pi$
$521$	26.9956	−	19.6134i	1.18270	−	0.859280i	0.992473	+	0.122461i	$0.0390786\pi$
$522$	0.289898	−	0.892214i	0.0126885	−	0.0390511i
$523$	−4.13518	+	12.7268i	−0.180819	+	0.556504i	−0.999851	−	0.0172437i	$-0.994511\pi$
$523$	−4.13518	+	12.7268i	−0.180819	+	0.556504i	0.819032	+	0.573747i	$0.194511\pi$
$524$	−9.28515	+	6.74606i	−0.405624	+	0.294703i
$525$	21.3855	+	15.5375i	0.933339	+	0.678111i
$526$	5.26345	+	16.1992i	0.229497	+	0.706320i
$527$	−9.07430			−0.395283
$528$		0			0
$529$	−19.5176			−0.848592
$530$	−10.7384	−	33.0495i	−0.466448	−	1.43558i
$531$	1.79139	+	1.30152i	0.0777398	+	0.0564813i
$532$	−1.59917	+	1.16187i	−0.0693328	+	0.0503732i
$533$	−5.80647	+	17.8705i	−0.251506	+	0.774056i
$534$	20.1046	−	61.8755i	0.870010	−	2.67762i
$535$	40.8873	−	29.7064i	1.76771	−	1.28432i
$536$	−4.50857	−	3.27566i	−0.194740	−	0.141487i
$537$	−17.9573	−	55.2670i	−0.774916	−	2.38495i
$538$	−36.8360			−1.58811
$539$		0			0
$540$	−6.38004			−0.274553
$541$	10.5263	+	32.3967i	0.452563	+	1.39284i	0.873973	+	0.485974i	$0.161535\pi$
$541$	10.5263	+	32.3967i	0.452563	+	1.39284i	−0.421410	+	0.906870i	$0.638465\pi$
$542$	−20.6978	−	15.0378i	−0.889047	−	0.645930i
$543$	3.66274	−	2.66114i	0.157183	−	0.114200i
$544$	−1.96604	+	6.05086i	−0.0842934	+	0.259428i
$545$	9.25781	−	28.4926i	0.396561	−	1.22049i
$546$	−10.3743	+	7.53740i	−0.443981	+	0.322571i
$547$	−12.7512	−	9.26432i	−0.545204	−	0.396114i	0.280810	−	0.959763i	$-0.409397\pi$
$547$	−12.7512	−	9.26432i	−0.545204	−	0.396114i	−0.826014	+	0.563650i	$0.809397\pi$
$548$	−1.78811	−	5.50323i	−0.0763842	−	0.235086i
$549$	−4.15735			−0.177431
$550$		0			0
$551$	−0.527686			−0.0224802
$552$	2.44905	+	7.53741i	0.104239	+	0.320813i
$553$	4.47750	+	3.25310i	0.190403	+	0.138336i
$554$	7.19067	−	5.22433i	0.305502	−	0.221960i
$555$	0.736060	−	2.26536i	0.0312440	−	0.0961591i
$556$	−4.08103	+	12.5601i	−0.173074	+	0.532668i
$557$	13.0271	−	9.46477i	0.551978	−	0.401035i	−0.276536	−	0.961003i	$-0.589187\pi$
$557$	13.0271	−	9.46477i	0.551978	−	0.401035i	0.828514	+	0.559968i	$0.189187\pi$
$558$	21.3599	+	15.5189i	0.904236	+	0.656966i
$559$	−8.12151	−	24.9954i	−0.343503	−	1.05719i
$560$	20.3020			0.857918
$561$		0			0
$562$	−25.8806			−1.09171
$563$	5.32450	+	16.3871i	0.224401	+	0.690635i	0.998352	+	0.0573897i	$0.0182777\pi$
$563$	5.32450	+	16.3871i	0.224401	+	0.690635i	−0.773951	+	0.633246i	$0.781722\pi$
$564$	6.89551	+	5.00988i	0.290353	+	0.210954i
$565$	−37.5305	+	27.2675i	−1.57892	+	1.14715i
$566$	2.98883	−	9.19868i	0.125630	−	0.386649i
$567$	3.30205	−	10.1627i	0.138673	−	0.426792i
$568$	9.71046	−	7.05506i	0.407442	−	0.296024i
$569$	−28.8125	−	20.9335i	−1.20788	−	0.877579i	−0.212847	−	0.977085i	$-0.568274\pi$
$569$	−28.8125	−	20.9335i	−1.20788	−	0.877579i	−0.995037	+	0.0995061i	$0.968274\pi$
$570$	−10.6267	−	32.7056i	−0.445103	−	1.36989i
$571$	−26.6026			−1.11329			−0.556643	−	0.830752i	$-0.687911\pi$
$571$	−26.6026			−1.11329			−0.556643	+	0.830752i	$0.687911\pi$
$572$		0			0
$573$	2.22967			0.0931459
$574$	−3.02404	−	9.30704i	−0.126221	−	0.388468i
$575$	17.4151	+	12.6528i	0.726262	+	0.527660i
$576$	−3.21004	+	2.33223i	−0.133752	+	0.0971762i
$577$	8.92210	−	27.4594i	0.371432	−	1.14315i	−0.574423	−	0.818559i	$-0.694773\pi$
$577$	8.92210	−	27.4594i	0.371432	−	1.14315i	0.945855	−	0.324591i	$-0.105227\pi$
$578$	−8.04778	+	24.7685i	−0.334744	+	1.03024i
$579$	−42.8857	+	31.1583i	−1.78227	+	1.29489i
$580$	−0.734290	−	0.533493i	−0.0304897	−	0.0221521i
$581$	0.639735	+	1.96890i	0.0265407	+	0.0816839i
$582$	−10.1150			−0.419278
$583$		0			0
$584$	−17.8874			−0.740188
$585$	−9.27269	−	28.5384i	−0.383379	−	1.17992i
$586$	−37.2078	−	27.0331i	−1.53704	−	1.11673i
$587$	−1.96926	+	1.43075i	−0.0812801	+	0.0590534i	−0.627683	−	0.778469i	$-0.715997\pi$
$587$	−1.96926	+	1.43075i	−0.0812801	+	0.0590534i	0.546403	+	0.837522i	$0.315997\pi$
$588$	0.647507	−	1.99282i	0.0267027	−	0.0821826i
$589$	4.58919	−	14.1241i	0.189094	−	0.581973i
$590$	5.52400	−	4.01342i	0.227419	−	0.165230i
$591$	−18.3766	−	13.3514i	−0.755913	−	0.549203i
$592$	−0.394375	−	1.21376i	−0.0162087	−	0.0498853i
$593$	−15.6870			−0.644187			−0.322093	−	0.946708i	$-0.604387\pi$
$593$	−15.6870			−0.644187			−0.322093	+	0.946708i	$0.604387\pi$
$594$		0			0
$595$	−5.37119			−0.220197
$596$	−6.79823	−	20.9228i	−0.278466	−	0.857031i
$597$	−19.2523	−	13.9876i	−0.787944	−	0.572475i
$598$	−8.44828	+	6.13803i	−0.345476	+	0.251003i
$599$	−4.08577	+	12.5747i	−0.166940	+	0.513789i	−0.999174	−	0.0406359i	$-0.987062\pi$
$599$	−4.08577	+	12.5747i	−0.166940	+	0.513789i	0.832234	+	0.554425i	$0.187062\pi$
$600$	−15.1388	+	46.5924i	−0.618038	+	1.90213i
$601$	−9.08550	+	6.60100i	−0.370605	+	0.269261i	−0.757462	−	0.652879i	$-0.773561\pi$
$601$	−9.08550	+	6.60100i	−0.370605	+	0.269261i	0.386857	+	0.922140i	$0.373561\pi$
$602$	11.0736	+	8.04542i	0.451325	+	0.327907i
$603$	−2.09187	−	6.43810i	−0.0851874	−	0.262180i
$604$	1.21082			0.0492676
$605$		0			0
$606$	−41.3449			−1.67952
$607$	−5.97876	−	18.4007i	−0.242670	−	0.746863i	−0.996011	−	0.0892321i	$-0.971559\pi$
$607$	−5.97876	−	18.4007i	−0.242670	−	0.746863i	0.753340	−	0.657631i	$-0.228441\pi$
$608$	−8.42383	−	6.12027i	−0.341631	−	0.248210i
$609$	0.452542	−	0.328791i	0.0183379	−	0.0133233i
$610$	−3.96152	+	12.1923i	−0.160397	+	0.493652i
$611$	4.12029	−	12.6809i	0.166689	−	0.513016i
$612$	−2.19974	+	1.59820i	−0.0889192	+	0.0646036i
$613$	17.0337	+	12.3757i	0.687986	+	0.499851i	0.875997	−	0.482316i	$-0.160204\pi$
$613$	17.0337	+	12.3757i	0.687986	+	0.499851i	−0.188011	+	0.982167i	$0.560204\pi$
$614$	−12.9858	−	39.9662i	−0.524065	−	1.61291i
$615$	53.4156			2.15392
$616$		0			0
$617$	−24.1496			−0.972228			−0.486114	−	0.873895i	$-0.661586\pi$
$617$	−24.1496			−0.972228			−0.486114	+	0.873895i	$0.661586\pi$
$618$	16.7418	+	51.5258i	0.673452	+	2.07267i
$619$	−2.12346	−	1.54279i	−0.0853492	−	0.0620099i	0.544292	−	0.838896i	$-0.316798\pi$
$619$	−2.12346	−	1.54279i	−0.0853492	−	0.0620099i	−0.629642	+	0.776886i	$0.716798\pi$
$620$	20.6655	−	15.0144i	0.829946	−	0.602991i
$621$	0.989475	−	3.04529i	0.0397063	−	0.122203i
$622$	−5.38783	+	16.5820i	−0.216032	+	0.664879i
$623$	13.4545	−	9.77524i	0.539042	−	0.391637i
$624$	−30.3403	−	22.0435i	−1.21458	−	0.882446i
$625$	15.5707	+	47.9217i	0.622828	+	1.91687i
$626$	38.2408			1.52841
$627$		0			0
$628$	13.3630			0.533241
$629$	0.104337	+	0.321117i	0.00416020	+	0.0128038i
$630$	12.6432	+	9.18581i	0.503716	+	0.365971i
$631$	20.3205	−	14.7637i	0.808948	−	0.587735i	−0.104578	−	0.994517i	$-0.533349\pi$
$631$	20.3205	−	14.7637i	0.808948	−	0.587735i	0.913525	+	0.406782i	$0.133349\pi$
$632$	−3.16963	+	9.75510i	−0.126081	+	0.388037i
$633$	9.19972	−	28.3138i	0.365656	−	1.12537i
$634$	−32.2623	+	23.4399i	−1.28130	+	0.930918i
$635$	−28.7803	−	20.9101i	−1.14211	−	0.829793i
$636$	−3.24132	−	9.97577i	−0.128527	−	0.395565i
$637$	−3.27792			−0.129876
$638$		0			0
$639$	14.5798			0.576770
$640$	15.8860	+	48.8920i	0.627948	+	1.93262i
$641$	−16.7130	−	12.1427i	−0.660124	−	0.479608i	0.206581	−	0.978430i	$-0.433766\pi$
$641$	−16.7130	−	12.1427i	−0.660124	−	0.479608i	−0.866705	+	0.498821i	$0.833766\pi$
$642$	39.3356	−	28.5790i	1.55245	−	1.12792i
$643$	5.08741	−	15.6574i	0.200628	−	0.617469i	−0.799237	−	0.601016i	$-0.794763\pi$
$643$	5.08741	−	15.6574i	0.200628	−	0.617469i	0.999865	−	0.0164529i	$-0.00523736\pi$
$644$	0.527294	−	1.62284i	0.0207783	−	0.0639490i
$645$	−60.4436	+	43.9149i	−2.37997	+	1.72915i
$646$	3.94367	+	2.86524i	0.155162	+	0.112731i
$647$	−10.8027	−	33.2474i	−0.424699	−	1.30709i	−0.903282	−	0.429047i	$-0.858850\pi$
$647$	−10.8027	−	33.2474i	−0.424699	−	1.30709i	0.478583	−	0.878042i	$-0.341150\pi$
$648$	19.8038			0.777967
$649$		0			0
$650$	−64.5511			−2.53190
$651$	4.86476	+	14.9722i	0.190665	+	0.586807i
$652$	15.4768	+	11.2446i	0.606120	+	0.440372i
$653$	−1.95498	+	1.42038i	−0.0765043	+	0.0555836i	−0.625380	−	0.780320i	$-0.715056\pi$
$653$	−1.95498	+	1.42038i	−0.0765043	+	0.0555836i	0.548876	+	0.835904i	$0.315056\pi$
$654$	8.90646	−	27.4113i	0.348270	−	1.07187i
$655$	15.7721	−	48.5414i	0.616266	−	1.89667i
$656$	23.1538	−	16.8222i	0.904003	−	0.656796i
$657$	−17.5783	−	12.7714i	−0.685795	−	0.498259i
$658$	2.14587	+	6.60430i	0.0836546	+	0.257462i
$659$	−16.9733			−0.661186			−0.330593	−	0.943773i	$-0.607249\pi$
$659$	−16.9733			−0.661186			−0.330593	+	0.943773i	$0.607249\pi$
$660$		0			0
$661$	7.96946			0.309976			0.154988	−	0.987916i	$-0.450466\pi$
$661$	7.96946			0.309976			0.154988	+	0.987916i	$0.450466\pi$
$662$	8.25305	+	25.4003i	0.320764	+	0.987209i
$663$	8.02694	+	5.83191i	0.311741	+	0.226493i
$664$	−3.10401	+	2.25519i	−0.120459	+	0.0875185i
$665$	2.71640	−	8.36023i	0.105338	−	0.324196i
$666$	0.303576	−	0.934312i	0.0117633	−	0.0362039i
$667$	0.368525	−	0.267749i	0.0142693	−	0.0103673i
$668$	3.63469	+	2.64076i	0.140630	+	0.102174i
$669$	−10.1636	−	31.2802i	−0.392946	−	1.20936i
$670$	−20.8744			−0.806449
$671$		0			0
$672$	11.0377			0.425787
$673$	−4.95199	−	15.2407i	−0.190885	−	0.587484i	0.809115	−	0.587651i	$-0.199947\pi$
$673$	−4.95199	−	15.2407i	−0.190885	−	0.587484i	−1.00000		0.000166405i	$0.999947\pi$
$674$	45.0121	+	32.7032i	1.73380	+	1.25968i
$675$	16.0130	−	11.6341i	0.616342	−	0.447798i
$676$	−0.637243	+	1.96123i	−0.0245094	+	0.0754321i
$677$	−4.70836	+	14.4908i	−0.180957	+	0.556928i	−0.999855	−	0.0170104i	$-0.994585\pi$
$677$	−4.70836	+	14.4908i	−0.180957	+	0.556928i	0.818898	+	0.573939i	$0.194585\pi$
$678$	−36.1062	+	26.2327i	−1.38665	+	1.00746i
$679$	−2.09179	−	1.51977i	−0.0802754	−	0.0583235i
$680$	−3.07610	−	9.46726i	−0.117963	−	0.363053i
$681$	−14.6082			−0.559787
$682$		0			0
$683$	14.3742			0.550013			0.275007	−	0.961442i	$-0.411320\pi$
$683$	14.3742			0.550013			0.275007	+	0.961442i	$0.411320\pi$
$684$	−1.37511	−	4.23215i	−0.0525786	−	0.161820i
$685$	20.8182	+	15.1253i	0.795424	+	0.577909i
$686$	1.38112	−	1.00344i	0.0527314	−	0.0383116i
$687$	−5.66671	+	17.4403i	−0.216199	+	0.665391i
$688$	−12.3700	+	38.0711i	−0.471603	+	1.45145i
$689$	−13.2750	+	9.64484i	−0.505737	+	0.367439i
$690$	24.0163	+	17.4489i	0.914286	+	0.664268i
$691$	−13.8433	−	42.6053i	−0.526624	−	1.62078i	−0.761082	−	0.648655i	$-0.775332\pi$
$691$	−13.8433	−	42.6053i	−0.526624	−	1.62078i	0.234459	−	0.972126i	$-0.424668\pi$
$692$	−17.9750			−0.683305
$693$		0			0
$694$	−9.82101			−0.372800
$695$	−18.1487	−	55.8559i	−0.688418	−	2.11873i
$696$	0.838699	+	0.609350i	0.0317908	+	0.0230974i
$697$	−6.12565	+	4.45055i	−0.232026	+	0.168577i
$698$	0.0970356	−	0.298645i	0.00367285	−	0.0113039i
$699$	7.64934	−	23.5423i	0.289325	−	0.890450i
$700$	8.53338	−	6.19986i	0.322531	−	0.234333i
$701$	−0.194431	−	0.141262i	−0.00734355	−	0.00533540i	0.584107	−	0.811676i	$-0.301445\pi$
$701$	−0.194431	−	0.141262i	−0.00734355	−	0.00533540i	−0.591451	+	0.806341i	$0.701445\pi$
$702$	2.96715	+	9.13194i	0.111988	+	0.344663i
$703$	−0.552584			−0.0208411
$704$		0			0
$705$	−37.9039			−1.42754
$706$	10.0344	+	30.8827i	0.377649	+	1.16229i
$707$	−8.55018	−	6.21207i	−0.321563	−	0.233629i
$708$	1.66738	−	1.21142i	0.0626640	−	0.0455281i
$709$	3.32298	−	10.2271i	0.124797	−	0.384086i	−0.869067	−	0.494695i	$-0.835280\pi$
$709$	3.32298	−	10.2271i	0.124797	−	0.384086i	0.993864	+	0.110608i	$0.0352799\pi$
$710$	13.8931	−	42.7585i	0.521397	−	1.60470i
$711$	−10.0798	+	7.32344i	−0.378024	+	0.274650i
$712$	24.9352	+	18.1165i	0.934487	+	0.678945i
$713$	3.96159	+	12.1925i	0.148363	+	0.456614i
$714$	−5.16735			−0.193383
$715$		0			0
$716$	−23.1879			−0.866573
$717$	−17.8153	−	54.8298i	−0.665324	−	2.04766i
$718$	−0.992926	−	0.721403i	−0.0370557	−	0.0269225i
$719$	20.8523	−	15.1501i	0.777659	−	0.565002i	−0.126616	−	0.991952i	$-0.540412\pi$
$719$	20.8523	−	15.1501i	0.777659	−	0.565002i	0.904276	+	0.426949i	$0.140412\pi$
$720$	−14.1234	+	43.4674i	−0.526349	+	1.61994i
$721$	−4.27954	+	13.1711i	−0.159378	+	0.490516i
$722$	19.7871	−	14.3762i	0.736400	−	0.535026i
$723$	−33.8267	−	24.5765i	−1.25803	−	0.914010i
$724$	−0.558255	−	1.71813i	−0.0207474	−	0.0638539i
$725$	2.81580			0.104576
$726$		0			0
$727$	−5.47160			−0.202930			−0.101465	−	0.994839i	$-0.532353\pi$
$727$	−5.47160			−0.202930			−0.101465	+	0.994839i	$0.532353\pi$
$728$	−1.87728	−	5.77766i	−0.0695765	−	0.214134i
$729$	9.91836	+	7.20611i	0.367347	+	0.266893i
$730$	−54.2050	+	39.3823i	−2.00622	+	1.45760i
$731$	3.27267	−	10.0722i	0.121044	−	0.372535i
$732$	−1.19576	+	3.68016i	−0.0441965	+	0.136023i
$733$	−16.0641	+	11.6713i	−0.593342	+	0.431088i	−0.843509	−	0.537114i	$-0.819514\pi$
$733$	−16.0641	+	11.6713i	−0.593342	+	0.431088i	0.250168	+	0.968203i	$0.419514\pi$
$734$	10.9011	+	7.92012i	0.402367	+	0.292337i
$735$	2.87952	+	8.86224i	0.106213	+	0.326889i
$736$	8.98845			0.331319
$737$		0			0
$738$	22.0304			0.810951
$739$	−0.556468	−	1.71263i	−0.0204700	−	0.0630002i	0.940300	−	0.340348i	$-0.110545\pi$
$739$	−0.556468	−	1.71263i	−0.0204700	−	0.0630002i	−0.960770	+	0.277347i	$0.910545\pi$
$740$	−0.768936	−	0.558665i	−0.0282667	−	0.0205369i
$741$	−13.1368	+	9.54448i	−0.482594	+	0.350625i
$742$	2.64079	−	8.12752i	0.0969465	−	0.298371i
$743$	−14.8507	+	45.7058i	−0.544820	+	1.67678i	0.176598	+	0.984283i	$0.443491\pi$
$743$	−14.8507	+	45.7058i	−0.544820	+	1.67678i	−0.721418	+	0.692500i	$0.756509\pi$
$744$	−23.6039	+	17.1493i	−0.865362	+	0.628722i
$745$	79.1491	+	57.5052i	2.89980	+	2.10683i
$746$	−8.26585	−	25.4397i	−0.302634	−	0.931413i
$747$	−4.66054			−0.170520
$748$		0			0
$749$	12.4286			0.454133
$750$	32.1265	+	98.8752i	1.17309	+	3.61041i
$751$	20.2631	+	14.7220i	0.739410	+	0.537213i	0.892526	−	0.450996i	$-0.148931\pi$
$751$	20.2631	+	14.7220i	0.739410	+	0.537213i	−0.153116	+	0.988208i	$0.548931\pi$
$752$	−16.4300	+	11.9371i	−0.599140	+	0.435301i
$753$	10.8545	−	33.4067i	0.395559	−	1.21741i
$754$	−0.422110	+	1.29912i	−0.0153723	+	0.0473112i
$755$	−4.35624	+	3.16500i	−0.158540	+	0.115186i
$756$	−1.26933	−	0.922221i	−0.0461650	−	0.0335409i
$757$	3.29062	+	10.1275i	0.119600	+	0.368090i	0.992879	−	0.119131i	$-0.0380108\pi$
$757$	3.29062	+	10.1275i	0.119600	+	0.368090i	−0.873279	+	0.487221i	$0.838011\pi$
$758$	−22.7298			−0.825583
$759$		0			0
$760$	16.2914			0.590952
$761$	9.21364	+	28.3567i	0.333994	+	1.02793i	0.967215	+	0.253958i	$0.0817324\pi$
$761$	9.21364	+	28.3567i	0.333994	+	1.02793i	−0.633221	+	0.773971i	$0.718268\pi$
$762$	−27.6881	−	20.1166i	−1.00303	−	0.728746i
$763$	5.96041	−	4.33049i	0.215781	−	0.156774i
$764$	0.274932	−	0.846153i	0.00994669	−	0.0306128i
$765$	3.73655	−	11.4999i	0.135095	−	0.415781i
$766$	−16.3641	+	11.8892i	−0.591259	+	0.429575i
$767$	−2.60838	−	1.89510i	−0.0941832	−	0.0684281i
$768$	12.7869	+	39.3540i	0.461407	+	1.42006i
$769$	28.3115			1.02094			0.510470	−	0.859896i	$-0.329471\pi$
$769$	28.3115			1.02094			0.510470	+	0.859896i	$0.329471\pi$
$770$		0			0
$771$	6.14090			0.221159
$772$	6.53641	+	20.1170i	0.235251	+	0.724027i
$773$	−10.7247	−	7.79192i	−0.385739	−	0.280256i	0.377968	−	0.925819i	$-0.376623\pi$
$773$	−10.7247	−	7.79192i	−0.385739	−	0.280256i	−0.763707	+	0.645563i	$0.776623\pi$
$774$	−24.9290	+	18.1120i	−0.896055	+	0.651022i
$775$	−24.4885	+	75.3680i	−0.879654	+	2.70730i
$776$	1.48078	−	4.55736i	0.0531568	−	0.163600i
$777$	0.473894	−	0.344304i	0.0170009	−	0.0123519i
$778$	8.35539	+	6.07055i	0.299555	+	0.217640i
$779$	−3.82929	−	11.7853i	−0.137199	−	0.422254i
$780$	−27.9298			−1.00005
$781$		0			0
$782$	−4.20800			−0.150478
$783$	−0.129431	−	0.398347i	−0.00462548	−	0.0142358i
$784$	4.03916	+	2.93462i	0.144256	+	0.104808i
$785$	−48.0768	+	34.9299i	−1.71594	+	1.24670i
$786$	15.1735	−	46.6992i	0.541221	−	1.66571i
$787$	−16.2781	+	50.0989i	−0.580252	+	1.78583i	0.0373024	+	0.999304i	$0.488124\pi$
$787$	−16.2781	+	50.0989i	−0.580252	+	1.78583i	−0.617554	+	0.786528i	$0.711876\pi$
$788$	−7.33276	+	5.32756i	−0.261219	+	0.189786i
$789$	−18.4970	−	13.4389i	−0.658512	−	0.478437i
$790$	11.8725	+	36.5397i	0.422404	+	1.30003i
$791$	−11.4083			−0.405632
$792$		0			0
$793$	6.05337			0.214961
$794$	−6.10696	−	18.7953i	−0.216728	−	0.667020i
$795$	37.7375	+	27.4179i	1.33841	+	0.972411i
$796$	−7.68218	+	5.58143i	−0.272288	+	0.197829i
$797$	−2.26658	+	6.97581i	−0.0802863	+	0.247096i	−0.983141	−	0.182851i	$-0.941468\pi$
$797$	−2.26658	+	6.97581i	−0.0802863	+	0.247096i	0.902854	+	0.429946i	$0.141468\pi$
$798$	2.61331	−	8.04295i	0.0925103	−	0.284717i
$799$	4.34678	−	3.15812i	0.153778	−	0.111726i
$800$	44.9506	+	32.6586i	1.58925	+	1.15465i
$801$	11.5693	+	35.6068i	0.408783	+	1.25810i
$802$	57.6890			2.03707
$803$		0			0
$804$	−6.30080			−0.222212
$805$	2.34492	+	7.21691i	0.0826475	+	0.254363i
$806$	−31.1014	−	22.5965i	−1.09550	−	0.795926i
$807$	40.0025	−	29.0635i	1.40815	−	1.02308i
$808$	6.05267	−	18.6282i	0.212932	−	0.655338i
$809$	−2.67859	+	8.24384i	−0.0941741	+	0.289838i	−0.987038	−	0.160489i	$-0.948693\pi$
$809$	−2.67859	+	8.24384i	−0.0941741	+	0.289838i	0.892863	+	0.450327i	$0.148693\pi$
$810$	60.0123	−	43.6015i	2.10862	−	1.53200i
$811$	16.1388	+	11.7256i	0.566711	+	0.411740i	0.833909	−	0.551902i	$-0.186098\pi$
$811$	16.1388	+	11.7256i	0.566711	+	0.411740i	−0.267198	+	0.963642i	$0.586098\pi$
$812$	−0.0689740	−	0.212280i	−0.00242051	−	0.00744957i
$813$	34.3418			1.20442
$814$		0			0
$815$	−85.0745			−2.98003
$816$	−4.66992	−	14.3725i	−0.163480	−	0.503139i
$817$	14.0223	+	10.1878i	0.490577	+	0.356425i
$818$	24.9320	−	18.1141i	0.871725	−	0.633345i
$819$	2.28034	−	7.01815i	0.0796814	−	0.245234i
$820$	6.58647	−	20.2711i	0.230009	−	0.707896i
$821$	43.3349	−	31.4846i	1.51240	−	1.09882i	0.547297	−	0.836938i	$-0.315657\pi$
$821$	43.3349	−	31.4846i	1.51240	−	1.09882i	0.965100	−	0.261883i	$-0.0843434\pi$
$822$	20.0282	+	14.5513i	0.698562	+	0.507535i
$823$	−2.61070	−	8.03492i	−0.0910034	−	0.280080i	0.895188	−	0.445689i	$-0.147041\pi$
$823$	−2.61070	−	8.03492i	−0.0910034	−	0.280080i	−0.986192	+	0.165609i	$0.947041\pi$
$824$	−25.6662			−0.894125
$825$		0			0
$826$	1.67915			0.0584250
$827$	0.983476	+	3.02683i	0.0341988	+	0.105253i	0.966699	−	0.255917i	$-0.0823774\pi$
$827$	0.983476	+	3.02683i	0.0341988	+	0.105253i	−0.932500	+	0.361170i	$0.882377\pi$
$828$	3.10775	+	2.25791i	0.108002	+	0.0784678i
$829$	−46.5257	+	33.8029i	−1.61590	+	1.17402i	−0.777809	+	0.628501i	$0.783669\pi$
$829$	−46.5257	+	33.8029i	−1.61590	+	1.17402i	−0.838096	+	0.545523i	$0.816331\pi$
$830$	−4.44100	+	13.6680i	−0.154150	+	0.474423i
$831$	−3.68680	+	11.3468i	−0.127894	+	0.393617i
$832$	4.67402	−	3.39588i	0.162043	−	0.117731i
$833$	−1.06862	−	0.776394i	−0.0370253	−	0.0269005i
$834$	−17.4599	−	53.7361i	−0.604587	−	1.86073i
$835$	−19.9795			−0.691419
$836$		0			0
$837$	11.7878			0.407447
$838$	1.36400	+	4.19797i	0.0471187	+	0.145016i
$839$	−10.1608	−	7.38225i	−0.350790	−	0.254864i	0.398411	−	0.917207i	$-0.369562\pi$
$839$	−10.1608	−	7.38225i	−0.350790	−	0.254864i	−0.749200	+	0.662344i	$0.769562\pi$
$840$	−13.9715	+	10.1509i	−0.482061	+	0.350238i
$841$	−8.94308	+	27.5240i	−0.308382	+	0.949102i
$842$	7.38282	−	22.7220i	0.254429	−	0.783051i
$843$	28.1053	−	20.4197i	0.967999	−	0.703293i
$844$	−9.61063	−	6.98253i	−0.330812	−	0.240349i
$845$	−2.83387	−	8.72176i	−0.0974881	−	0.300038i
$846$	−15.6329			−0.537469
$847$		0			0
$848$	24.9926			0.858248
$849$	4.01197	+	12.3476i	0.137690	+	0.423767i
$850$	−21.0439	−	15.2893i	−0.721801	−	0.524419i
$851$	0.385913	−	0.280382i	0.0132289	−	0.00961138i
$852$	4.19353	−	12.9063i	0.143668	−	0.442164i
$853$	−10.3000	+	31.7002i	−0.352666	+	1.08539i	0.604685	+	0.796465i	$0.293299\pi$
$853$	−10.3000	+	31.7002i	−0.352666	+	1.08539i	−0.957351	+	0.288928i	$0.906701\pi$
$854$	−2.55053	+	1.85307i	−0.0872773	+	0.0634107i
$855$	16.0099	+	11.6318i	0.547525	+	0.397801i
$856$	7.11793	+	21.9067i	0.243286	+	0.748756i
$857$	−54.0291			−1.84560			−0.922800	−	0.385279i	$-0.874105\pi$
$857$	−54.0291			−1.84560			−0.922800	+	0.385279i	$0.874105\pi$
$858$		0			0
$859$	−12.8624			−0.438860			−0.219430	−	0.975628i	$-0.570420\pi$
$859$	−12.8624			−0.438860			−0.219430	+	0.975628i	$0.570420\pi$
$860$	9.21249	+	28.3531i	0.314143	+	0.966834i
$861$	10.6272	+	7.72111i	0.362174	+	0.263135i
$862$	−46.4998	+	33.7841i	−1.58379	+	1.15069i
$863$	−10.2677	+	31.6008i	−0.349518	+	1.07570i	0.609603	+	0.792707i	$0.291329\pi$
$863$	−10.2677	+	31.6008i	−0.349518	+	1.07570i	−0.959121	+	0.282998i	$0.908671\pi$
$864$	2.55396	−	7.86027i	0.0868874	−	0.267412i
$865$	64.6696	−	46.9852i	2.19883	−	1.59755i
$866$	−10.3901	−	7.54882i	−0.353069	−	0.256519i
$867$	−10.8027	−	33.2473i	−0.366879	−	1.12914i
$868$	6.28176			0.213217
$869$		0			0
$870$	3.88313			0.131650
$871$	3.04589	+	9.37429i	0.103206	+	0.317636i
$872$	11.0465	+	8.02573i	0.374081	+	0.271786i
$873$	4.70907	−	3.42134i	0.159378	−	0.115795i
$874$	2.12814	−	6.54973i	0.0719853	−	0.221548i
$875$	−8.21219	+	25.2745i	−0.277623	+	0.854435i
$876$	−16.3614	+	11.8873i	−0.552801	+	0.401634i
$877$	22.3862	+	16.2645i	0.755928	+	0.549214i	0.897659	−	0.440691i	$-0.145267\pi$
$877$	22.3862	+	16.2645i	0.755928	+	0.549214i	−0.141731	+	0.989905i	$0.545267\pi$
$878$	11.6124	+	35.7392i	0.391898	+	1.20614i
$879$	61.7352			2.08228
$880$		0			0
$881$	48.9636			1.64963			0.824813	−	0.565406i	$-0.191280\pi$
$881$	48.9636			1.64963			0.824813	+	0.565406i	$0.191280\pi$
$882$	1.18761	+	3.65509i	0.0399889	+	0.123073i
$883$	−17.2501	−	12.5330i	−0.580514	−	0.421768i	0.258396	−	0.966039i	$-0.416806\pi$
$883$	−17.2501	−	12.5330i	−0.580514	−	0.421768i	−0.838909	+	0.544271i	$0.816806\pi$
$884$	3.20296	−	2.32709i	0.107727	−	0.0782685i
$885$	−2.83227	+	8.71683i	−0.0952057	+	0.293013i
$886$	12.4971	−	38.4620i	0.419847	−	1.29216i
$887$	−36.6067	+	26.5963i	−1.22913	+	0.893016i	−0.996825	−	0.0796262i	$-0.974627\pi$
$887$	−36.6067	+	26.5963i	−1.22913	+	0.893016i	−0.232307	+	0.972643i	$0.574627\pi$
$888$	0.878271	+	0.638102i	0.0294729	+	0.0214133i
$889$	−2.70342	−	8.32027i	−0.0906698	−	0.279053i
$890$	115.449			3.86985
$891$		0			0
$892$	−13.1240			−0.439423
$893$	2.71728	+	8.36292i	0.0909302	+	0.279854i
$894$	76.1453	+	55.3228i	2.54668	+	1.85027i
$895$	83.4246	−	60.6115i	2.78858	−	2.02602i
$896$	−3.90667	+	12.0235i	−0.130513	+	0.401677i
$897$	4.33161	−	13.3313i	0.144628	−	0.445120i
$898$	−3.14223	+	2.28297i	−0.104858	+	0.0761836i
$899$	1.35668	+	0.985686i	0.0452478	+	0.0328745i
$900$	7.33776	+	22.5833i	0.244592	+	0.752777i
$901$	−6.61213			−0.220282
$902$		0			0
$903$	−18.3732			−0.611423
$904$	−6.53356	−	20.1082i	−0.217303	−	0.668789i
$905$	6.49954	+	4.72219i	0.216052	+	0.156971i
$906$	−4.19092	+	3.04488i	−0.139234	+	0.101159i
$907$	−13.9263	+	42.8608i	−0.462416	+	1.42317i	0.399787	+	0.916608i	$0.369084\pi$
$907$	−13.9263	+	42.8608i	−0.462416	+	1.42317i	−0.862203	+	0.506562i	$0.830916\pi$
$908$	−1.80128	+	5.54376i	−0.0597775	+	0.183976i
$909$	19.2483	−	13.9847i	0.638427	−	0.463844i
$910$	−18.4093	−	13.3751i	−0.610262	−	0.443381i
$911$	−2.84749	−	8.76369i	−0.0943417	−	0.290354i	0.892740	−	0.450572i	$-0.148780\pi$
$911$	−2.84749	−	8.76369i	−0.0943417	−	0.290354i	−0.987082	+	0.160219i	$0.948780\pi$
$912$	24.7325			0.818975
$913$		0			0
$914$	46.6283			1.54233
$915$	−5.31763	−	16.3660i	−0.175795	−	0.541043i
$916$	5.91982	+	4.30100i	0.195596	+	0.142109i
$917$	10.1545	−	7.37765i	0.335330	−	0.243631i
$918$	−1.19565	+	3.67984i	−0.0394624	+	0.121453i
$919$	−15.3626	+	47.2812i	−0.506765	+	1.55966i	0.291018	+	0.956718i	$0.406006\pi$
$919$	−15.3626	+	47.2812i	−0.506765	+	1.55966i	−0.797783	+	0.602945i	$0.793994\pi$
$920$	−11.3776	+	8.26630i	−0.375108	+	0.272532i
$921$	45.6353	+	33.1560i	1.50373	+	1.09253i
$922$	4.33590	+	13.3445i	0.142795	+	0.439479i
$923$	−21.2292			−0.698767
$924$		0			0
$925$	2.94866			0.0969514
$926$	−14.7626	−	45.4348i	−0.485131	−	1.49308i
$927$	−25.2226	−	18.3253i	−0.828420	−	0.601882i
$928$	0.951208	−	0.691093i	0.0312249	−	0.0226862i
$929$	15.2996	−	47.0872i	0.501963	−	1.54488i	−0.303855	−	0.952718i	$-0.598274\pi$
$929$	15.2996	−	47.0872i	0.501963	−	1.54488i	0.805818	−	0.592164i	$-0.201726\pi$
$930$	−33.7709	+	103.936i	−1.10739	+	3.40820i
$931$	1.74889	−	1.27064i	0.0573176	−	0.0416436i
$932$	−7.99101	−	5.80581i	−0.261754	−	0.190175i
$933$	−7.23219	−	22.2584i	−0.236771	−	0.728707i
$934$	45.5377			1.49004
$935$		0			0
$936$	13.6761			0.447019
$937$	−2.15938	−	6.64589i	−0.0705439	−	0.217112i	0.909569	−	0.415553i	$-0.136412\pi$
$937$	−2.15938	−	6.64589i	−0.0705439	−	0.217112i	−0.980113	+	0.198441i	$0.936412\pi$
$938$	−4.15303	−	3.01735i	−0.135601	−	0.0985201i
$939$	−41.5280	+	30.1718i	−1.35521	+	0.984621i
$940$	−4.67378	+	14.3844i	−0.152442	+	0.469167i
$941$	−14.4694	+	44.5323i	−0.471690	+	1.45171i	0.378680	+	0.925528i	$0.376378\pi$
$941$	−14.4694	+	44.5323i	−0.471690	+	1.45171i	−0.850370	+	0.526185i	$0.823622\pi$
$942$	−46.2523	+	33.6042i	−1.50698	+	1.09489i
$943$	8.65420	+	6.28764i	0.281820	+	0.204754i
$944$	1.51751	+	4.67040i	0.0493906	+	0.152009i
$945$	6.97736			0.226974
$946$		0			0
$947$	15.1286			0.491614			0.245807	−	0.969319i	$-0.420947\pi$
$947$	15.1286			0.491614			0.245807	+	0.969319i	$0.420947\pi$
$948$	3.58363	+	11.0293i	0.116391	+	0.358214i
$949$	25.5951	+	18.5960i	0.830853	+	0.603650i
$950$	34.4404	−	25.0224i	1.11739	−	0.811834i
$951$	16.5415	−	50.9096i	0.536396	−	1.65086i
$952$	0.756473	−	2.32818i	0.0245174	−	0.0754569i
$953$	−45.4888	+	33.0496i	−1.47353	+	1.07058i	−0.493956	+	0.869487i	$0.664450\pi$
$953$	−45.4888	+	33.0496i	−1.47353	+	1.07058i	−0.979572	+	0.201093i	$0.935550\pi$
$954$	15.5642	+	11.3081i	0.503910	+	0.366112i
$955$	1.22264	+	3.76291i	0.0395638	+	0.121765i
$956$	−23.0045			−0.744019
$957$		0			0
$958$	39.6470			1.28094
$959$	1.95552	+	6.01847i	0.0631470	+	0.194346i
$960$	−13.2871	−	9.65362i	−0.428838	−	0.311569i
$961$	−13.1022	+	9.51933i	−0.422653	+	0.307075i
$962$	−0.442027	+	1.36042i	−0.0142515	+	0.0438617i
$963$	−8.64618	+	26.6102i	−0.278619	+	0.857502i
$964$	−13.4977	+	9.80668i	−0.434733	+	0.315852i
$965$	−76.1009	−	55.2905i	−2.44977	−	1.77986i
$966$	2.25592	+	6.94302i	0.0725832	+	0.223388i
$967$	−46.3761			−1.49136			−0.745678	−	0.666307i	$-0.767874\pi$
$967$	−46.3761			−1.49136			−0.745678	+	0.666307i	$0.767874\pi$
$968$		0			0
$969$	−6.54333			−0.210202
$970$	−5.54655	−	17.0705i	−0.178089	−	0.548102i
$971$	−12.5721	−	9.13416i	−0.403458	−	0.293129i	0.367490	−	0.930027i	$-0.380217\pi$
$971$	−12.5721	−	9.13416i	−0.403458	−	0.293129i	−0.770948	+	0.636898i	$0.780217\pi$
$972$	14.3063	−	10.3941i	0.458875	−	0.333392i
$973$	4.46311	−	13.7361i	0.143081	−	0.440358i
$974$	−9.91357	+	30.5108i	−0.317651	+	0.977630i
$975$	70.0999	−	50.9306i	2.24500	−	1.63108i
$976$	−7.45915	−	5.41939i	−0.238762	−	0.173470i
$977$	10.1446	+	31.2219i	0.324555	+	0.998878i	0.971641	+	0.236461i	$0.0759876\pi$
$977$	10.1446	+	31.2219i	0.324555	+	0.998878i	−0.647086	+	0.762417i	$0.724012\pi$
$978$	−81.8458			−2.61714
$979$		0			0
$980$	3.71825			0.118775
$981$	5.12530	+	15.7740i	0.163638	+	0.503627i
$982$	10.2282	+	7.43123i	0.326395	+	0.237140i
$983$	−19.6740	+	14.2940i	−0.627502	+	0.455907i	−0.855534	−	0.517747i	$-0.826771\pi$
$983$	−19.6740	+	14.2940i	−0.627502	+	0.455907i	0.228032	+	0.973654i	$0.426771\pi$
$984$	−7.52300	+	23.1534i	−0.239824	+	0.738103i
$985$	12.4557	−	38.3346i	0.396870	−	1.22144i
$986$	−0.445314	+	0.323539i	−0.0141817	+	0.0103036i
$987$	−7.54109	−	5.47892i	−0.240036	−	0.174396i
$988$	2.00225	+	6.16229i	0.0637000	+	0.196048i
$989$	−14.9622			−0.475769
$990$		0			0
$991$	−47.7104			−1.51557			−0.757786	−	0.652503i	$-0.773719\pi$
$991$	−47.7104			−1.51557			−0.757786	+	0.652503i	$0.773719\pi$
$992$	10.2254	+	31.4704i	0.324655	+	0.999186i
$993$	−29.0032	−	21.0720i	−0.920388	−	0.668701i
$994$	8.94471	−	6.49871i	0.283709	−	0.206127i
$995$	13.0492	−	40.1613i	0.413688	−	1.27320i
$996$	−1.34049	+	4.12559i	−0.0424749	+	0.130724i
$997$	16.0549	−	11.6645i	0.508462	−	0.369419i	−0.303778	−	0.952743i	$-0.598248\pi$
$997$	16.0549	−	11.6645i	0.508462	−	0.369419i	0.812240	+	0.583324i	$0.198248\pi$
$998$	−32.6916	−	23.7518i	−1.03483	−	0.751851i
$999$	−0.135538	−	0.417142i	−0.00428823	−	0.0131978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.v.148.4		16
11.2	odd	10		847.2.f.w.372.1		16
11.3	even	5		847.2.a.o.1.7		8
11.4	even	5		847.2.f.x.729.1		16
11.5	even	5		847.2.f.x.323.1		16
11.6	odd	10		77.2.f.b.15.4	✓	16
11.7	odd	10		77.2.f.b.36.4	yes	16
11.8	odd	10		847.2.a.p.1.2		8
11.9	even	5	inner	847.2.f.v.372.4		16
11.10	odd	2		847.2.f.w.148.1		16
33.8	even	10		7623.2.a.ct.1.7		8
33.14	odd	10		7623.2.a.cw.1.2		8
33.17	even	10		693.2.m.i.631.1		16
33.29	even	10		693.2.m.i.190.1		16
77.6	even	10		539.2.f.e.246.4		16
77.17	even	30		539.2.q.f.422.1		32
77.18	odd	30		539.2.q.g.520.4		32
77.39	odd	30		539.2.q.g.422.1		32
77.40	even	30		539.2.q.f.410.1		32
77.41	even	10		5929.2.a.bt.1.2		8
77.51	odd	30		539.2.q.g.410.1		32
77.61	even	30		539.2.q.f.312.4		32
77.62	even	10		539.2.f.e.344.4		16
77.69	odd	10		5929.2.a.bs.1.7		8
77.72	odd	30		539.2.q.g.312.4		32
77.73	even	30		539.2.q.f.520.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.4	✓	16	11.6	odd	10
77.2.f.b.36.4	yes	16	11.7	odd	10
539.2.f.e.246.4		16	77.6	even	10
539.2.f.e.344.4		16	77.62	even	10
539.2.q.f.312.4		32	77.61	even	30
539.2.q.f.410.1		32	77.40	even	30
539.2.q.f.422.1		32	77.17	even	30
539.2.q.f.520.4		32	77.73	even	30
539.2.q.g.312.4		32	77.72	odd	30
539.2.q.g.410.1		32	77.51	odd	30
539.2.q.g.422.1		32	77.39	odd	30
539.2.q.g.520.4		32	77.18	odd	30
693.2.m.i.190.1		16	33.29	even	10
693.2.m.i.631.1		16	33.17	even	10
847.2.a.o.1.7		8	11.3	even	5
847.2.a.p.1.2		8	11.8	odd	10
847.2.f.v.148.4		16	1.1	even	1	trivial
847.2.f.v.372.4		16	11.9	even	5	inner
847.2.f.w.148.1		16	11.10	odd	2
847.2.f.w.372.1		16	11.2	odd	10
847.2.f.x.323.1		16	11.5	even	5
847.2.f.x.729.1		16	11.4	even	5
5929.2.a.bs.1.7		8	77.69	odd	10
5929.2.a.bt.1.2		8	77.41	even	10
7623.2.a.ct.1.7		8	33.8	even	10
7623.2.a.cw.1.2		8	33.14	odd	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.527541 + 1.62360i) q^{2} +(-1.85391 - 1.34694i) q^{3} +(-0.739758 + 0.537466i) q^{4} +(1.25658 - 3.86735i) q^{5} +(1.20889 - 3.72058i) q^{6} +(0.809017 - 0.587785i) q^{7} +(1.49936 + 1.08935i) q^{8} +(0.695665 + 2.14104i) q^{9} +O(q^{10})\)	\(q+(0.527541 + 1.62360i) q^{2} +(-1.85391 - 1.34694i) q^{3} +(-0.739758 + 0.537466i) q^{4} +(1.25658 - 3.86735i) q^{5} +(1.20889 - 3.72058i) q^{6} +(0.809017 - 0.587785i) q^{7} +(1.49936 + 1.08935i) q^{8} +(0.695665 + 2.14104i) q^{9} +6.94194 q^{10} +2.09538 q^{12} +(-1.01293 - 3.11749i) q^{13} +(1.38112 + 1.00344i) q^{14} +(-7.53867 + 5.47716i) q^{15} +(-1.54282 + 4.74831i) q^{16} +(0.408175 - 1.25623i) q^{17} +(-3.10921 + 2.25897i) q^{18} +(1.74889 + 1.27064i) q^{19} +(1.14900 + 3.53627i) q^{20} -2.29155 q^{21} -1.86611 q^{23} +(-1.31238 - 4.03909i) q^{24} +(-9.33231 - 6.78032i) q^{25} +(4.52720 - 3.28921i) q^{26} +(-0.530233 + 1.63189i) q^{27} +(-0.282562 + 0.869638i) q^{28} +(-0.197482 + 0.143479i) q^{29} +(-12.8697 - 9.35039i) q^{30} +(-2.12291 - 6.53364i) q^{31} -4.81667 q^{32} +2.25495 q^{34} +(-1.25658 - 3.86735i) q^{35} +(-1.66536 - 1.20995i) q^{36} +(-0.206800 + 0.150249i) q^{37} +(-1.14041 + 3.50982i) q^{38} +(-2.32119 + 7.14389i) q^{39} +(6.09694 - 4.42968i) q^{40} +(-4.63755 - 3.36938i) q^{41} +(-1.20889 - 3.72058i) q^{42} +8.01781 q^{43} +9.15429 q^{45} +(-0.984452 - 3.02983i) q^{46} +(3.29082 + 2.39092i) q^{47} +(9.25594 - 6.72484i) q^{48} +(0.309017 - 0.951057i) q^{49} +(6.08538 - 18.7289i) q^{50} +(-2.44879 + 1.77915i) q^{51} +(2.42487 + 1.76177i) q^{52} +(-1.54689 - 4.76085i) q^{53} -2.92926 q^{54} +1.85331 q^{56} +(-1.53080 - 4.71131i) q^{57} +(-0.337134 - 0.244942i) q^{58} +(0.795743 - 0.578141i) q^{59} +(2.63300 - 8.10355i) q^{60} +(-0.570665 + 1.75633i) q^{61} +(9.48813 - 6.89353i) q^{62} +(1.82128 + 1.32323i) q^{63} +(0.544649 + 1.67626i) q^{64} -13.3292 q^{65} -3.00700 q^{67} +(0.373231 + 1.14869i) q^{68} +(3.45960 + 2.51355i) q^{69} +(5.61615 - 4.08037i) q^{70} +(2.00132 - 6.15944i) q^{71} +(-1.28928 + 3.96800i) q^{72} +(-7.80834 + 5.67309i) q^{73} +(-0.353041 - 0.256499i) q^{74} +(8.16853 + 25.1401i) q^{75} -1.97668 q^{76} -12.8234 q^{78} +(1.71025 + 5.26362i) q^{79} +(16.4247 + 11.9332i) q^{80} +(8.64489 - 6.28088i) q^{81} +(3.02404 - 9.30704i) q^{82} +(-0.639735 + 1.96890i) q^{83} +(1.69520 - 1.23163i) q^{84} +(-4.34539 - 3.15711i) q^{85} +(4.22973 + 13.0178i) q^{86} +0.559372 q^{87} +16.6306 q^{89} +(4.82927 + 14.8630i) q^{90} +(-2.65189 - 1.92671i) q^{91} +(1.38047 - 1.00297i) q^{92} +(-4.86476 + 14.9722i) q^{93} +(-2.14587 + 6.60430i) q^{94} +(7.11164 - 5.16691i) q^{95} +(8.92965 + 6.48777i) q^{96} +(-0.798992 - 2.45904i) q^{97} +1.70716 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9	\( 16 q - 2 q^{2} - 2 q^{3} + 4 q^{4} - 5 q^{5} + 2 q^{6} + 4 q^{7} - 5 q^{8} - 2 q^{9} - 12 q^{10} + 18 q^{12} - 13 q^{13} - 3 q^{14} + 7 q^{15} - 18 q^{16} - 10 q^{17} + 19 q^{18} + 6 q^{19} - 24 q^{20} - 8 q^{21} + 32 q^{23} - 45 q^{24} - 23 q^{25} + 33 q^{26} - 20 q^{27} + 11 q^{28} + 12 q^{29} - 38 q^{30} - 2 q^{31} - 32 q^{32} - 24 q^{34} + 5 q^{35} - 38 q^{36} - 11 q^{37} + 15 q^{38} + 24 q^{39} - 5 q^{40} - 20 q^{41} - 2 q^{42} + 8 q^{43} + 70 q^{45} - 38 q^{46} + 7 q^{47} + 39 q^{48} - 4 q^{49} + 58 q^{50} - 16 q^{51} - 8 q^{52} - 41 q^{53} - 60 q^{54} - 9 q^{57} - 5 q^{58} - 18 q^{59} + 25 q^{60} + 12 q^{61} + 61 q^{62} + 12 q^{63} - 3 q^{64} + 8 q^{65} - 38 q^{67} + 7 q^{68} - 30 q^{69} + 12 q^{70} + q^{71} - 35 q^{72} - 60 q^{73} + 4 q^{74} + 4 q^{75} - 52 q^{76} - 58 q^{78} + 15 q^{79} + 83 q^{80} + 6 q^{81} - 6 q^{82} - 20 q^{83} + 17 q^{84} + 9 q^{85} + 48 q^{86} + 72 q^{87} + 74 q^{89} - 16 q^{90} - 7 q^{91} + 20 q^{92} - 53 q^{93} - 66 q^{94} + 53 q^{95} - 48 q^{96} - 35 q^{97} - 2 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 5 * q^5 + 2 * q^6 + 4 * q^7 - 5 * q^8 - 2 * q^9 - 12 * q^10 + 18 * q^12 - 13 * q^13 - 3 * q^14 + 7 * q^15 - 18 * q^16 - 10 * q^17 + 19 * q^18 + 6 * q^19 - 24 * q^20 - 8 * q^21 + 32 * q^23 - 45 * q^24 - 23 * q^25 + 33 * q^26 - 20 * q^27 + 11 * q^28 + 12 * q^29 - 38 * q^30 - 2 * q^31 - 32 * q^32 - 24 * q^34 + 5 * q^35 - 38 * q^36 - 11 * q^37 + 15 * q^38 + 24 * q^39 - 5 * q^40 - 20 * q^41 - 2 * q^42 + 8 * q^43 + 70 * q^45 - 38 * q^46 + 7 * q^47 + 39 * q^48 - 4 * q^49 + 58 * q^50 - 16 * q^51 - 8 * q^52 - 41 * q^53 - 60 * q^54 - 9 * q^57 - 5 * q^58 - 18 * q^59 + 25 * q^60 + 12 * q^61 + 61 * q^62 + 12 * q^63 - 3 * q^64 + 8 * q^65 - 38 * q^67 + 7 * q^68 - 30 * q^69 + 12 * q^70 + q^71 - 35 * q^72 - 60 * q^73 + 4 * q^74 + 4 * q^75 - 52 * q^76 - 58 * q^78 + 15 * q^79 + 83 * q^80 + 6 * q^81 - 6 * q^82 - 20 * q^83 + 17 * q^84 + 9 * q^85 + 48 * q^86 + 72 * q^87 + 74 * q^89 - 16 * q^90 - 7 * q^91 + 20 * q^92 - 53 * q^93 - 66 * q^94 + 53 * q^95 - 48 * q^96 - 35 * q^97 - 2 * q^98

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