LMFDB - Embedded newform 847.2.f.w.148.1

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			148.1
Root			$-1.38112 + 1.00344i$ of defining polynomial
Character	$\chi$	$=$	847.148
Dual form			847.2.f.w.372.1

$q$-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	$-0.893744\pi$
$2$	−0.527541	−	1.62360i	−0.373028	−	1.14806i	0.571772	−	0.820413i	$-0.306256\pi$
$3$	−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	$0.0502056\pi$
$13$	1.01293	+	3.11749i	0.280937	+	0.864636i	−0.706650	+	0.707563i	$0.749794\pi$
$14$	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	−0.988275	−	0.152686i	$-0.951208\pi$
$17$	−0.408175	+	1.25623i	−0.0989969	+	0.304681i	0.889278	+	0.457367i	$0.151208\pi$
$18$	3.10921	−	2.25897i	0.732847	−	0.532444i
$19$	−1.74889	−	1.27064i	−0.401223	−	0.291506i	0.368816	−	0.929502i	$-0.379763\pi$
$19$	−1.74889	−	1.27064i	−0.401223	−	0.291506i	−0.770039	+	0.637997i	$0.779763\pi$
$20$	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	−0.569298	−	0.822131i	$-0.692785\pi$
$29$	0.197482	−	0.143479i	0.0366716	−	0.0266435i	0.605970	+	0.795487i	$0.292785\pi$
$30$	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	0.887744	−	0.460338i	$-0.152272\pi$
$41$	4.63755	+	3.36938i	0.724264	+	0.526208i	−0.163480	+	0.986547i	$0.552272\pi$
$42$	−1.20889	−	3.72058i	−0.186536	−	0.574098i
$43$	−8.01781			−1.22270			−0.611352	−	0.791358i	$-0.709374\pi$
$43$	−8.01781			−1.22270			−0.611352	+	0.791358i	$0.709374\pi$
$44$		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	−0.907854	−	0.419287i	$-0.862280\pi$
$61$	0.570665	−	1.75633i	0.0730661	−	0.224874i	0.980920	+	0.194413i	$0.0622801\pi$
$62$	−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	−0.0281002	−	0.999605i	$-0.508946\pi$
$73$	7.80834	−	5.67309i	0.913897	−	0.663985i	0.941998	+	0.335620i	$0.108946\pi$
$74$	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	$-0.999222\pi$
$79$	−1.71025	−	5.26362i	−0.192419	−	0.592204i	0.807578	−	0.589760i	$-0.200778\pi$
$80$	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	−0.909788	−	0.415074i	$-0.863756\pi$
$83$	0.639735	−	1.96890i	0.0702201	−	0.216115i	0.980008	+	0.198958i	$0.0637559\pi$
$84$	−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	$0.0762368\pi$
$101$	3.26588	+	10.0513i	0.324967	+	1.00015i	−0.646489	+	0.762924i	$0.723763\pi$
$102$	−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	−0.0161339	−	0.999870i	$-0.505136\pi$
$107$	−10.0550	−	7.30538i	−0.972052	−	0.706237i	−0.955918	+	0.293633i	$0.905136\pi$
$108$	−0.484840	−	1.49219i	−0.0466538	−	0.143586i
$109$	−7.36748			−0.705676			−0.352838	−	0.935684i	$-0.614783\pi$
$109$	−7.36748			−0.705676			−0.352838	+	0.935684i	$0.614783\pi$
$110$		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	$0.226886\pi$
$127$	−2.70342	+	8.32027i	−0.239890	+	0.738305i	−0.996435	+	0.0843635i	$0.973114\pi$
$128$	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	$-0.684732\pi$
$131$	−12.5516			−1.09664			−0.548319	+	0.836269i	$0.684732\pi$
$132$		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	−0.960156	−	0.279465i	$-0.909843\pi$
$139$	−11.6846	+	8.48935i	−0.991073	+	0.720057i	−0.0309175	+	0.999522i	$0.509843\pi$
$140$	−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	$-0.454265\pi$
$149$	7.43471	−	22.8817i	0.609075	−	1.87454i	0.465887	−	0.884844i	$-0.345735\pi$
$150$	36.5084	−	26.5249i	2.98090	−	2.16575i
$151$	1.07129	+	0.778335i	0.0871800	+	0.0633400i	0.630521	−	0.776172i	$-0.282841\pi$
$151$	1.07129	+	0.778335i	0.0871800	+	0.0633400i	−0.543341	+	0.839512i	$0.682841\pi$
$152$	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	0.992458	−	0.122583i	$-0.0391177\pi$
$167$	1.51831	+	4.67287i	0.117490	+	0.361598i	−0.874968	+	0.484181i	$0.839118\pi$
$168$	−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	−0.213971	−	0.976840i	$-0.568640\pi$
$173$	−15.9035	−	11.5546i	−1.20912	−	0.878479i	−0.995151	+	0.0983612i	$0.968640\pi$
$174$	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	$0.413127\pi$
$193$	−7.14838	+	22.0004i	−0.514551	+	1.58363i	−0.784097	+	0.620639i	$0.786873\pi$
$194$	−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	$-0.614877\pi$
$197$	−9.91237			−0.706227			−0.353114	+	0.935580i	$0.614877\pi$
$198$		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	$-0.952425\pi$
$211$	−4.01462	−	12.3557i	−0.276378	−	0.850604i	0.712474	−	0.701699i	$-0.247575\pi$
$212$	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	−0.745633	−	0.666357i	$-0.767853\pi$
$227$	−5.15732	+	3.74701i	−0.342303	+	0.248698i	0.403330	+	0.915055i	$0.367853\pi$
$228$	−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	$-0.984877\pi$
$233$	−3.33806	−	10.2735i	−0.218684	−	0.673039i	0.780188	−	0.625545i	$-0.215123\pi$
$234$	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	$-0.997463\pi$
$239$	−20.3535	−	14.7877i	−1.31656	−	0.956534i	−0.316588	−	0.948563i	$-0.602537\pi$
$240$	−14.3765	−	44.2462i	−0.927997	−	2.85608i
$241$	−18.2462			−1.17534			−0.587669	−	0.809101i	$-0.699954\pi$
$241$	−18.2462			−1.17534			−0.587669	+	0.809101i	$0.699954\pi$
$242$		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	$-0.599531\pi$
$263$	−9.97733			−0.615229			−0.307614	+	0.951511i	$0.599531\pi$
$264$		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	−0.155121	−	0.987895i	$-0.549577\pi$
$271$	12.1241	−	8.80869i	0.736488	−	0.535090i	0.891609	+	0.452806i	$0.149577\pi$
$272$	−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	0.987685	−	0.156458i	$-0.0500075\pi$
$277$	1.60887	+	4.95158i	0.0966674	+	0.297512i	−0.891017	+	0.453969i	$0.850008\pi$
$278$	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	$-0.750644\pi$
$281$	4.68472	−	14.4181i	0.279467	−	0.860110i	0.988003	−	0.154436i	$-0.0493560\pi$
$282$	−12.8738	+	9.35339i	−0.766626	+	0.556986i
$283$	4.58356	+	3.33015i	0.272464	+	0.197957i	0.715624	−	0.698486i	$-0.246143\pi$
$283$	4.58356	+	3.33015i	0.272464	+	0.197957i	−0.443160	+	0.896443i	$0.646143\pi$
$284$	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	0.273960	−	0.961741i	$-0.411666\pi$
$293$	21.7952	−	15.8351i	1.27329	−	0.925098i	0.999328	+	0.0366430i	$0.0116664\pi$
$294$	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	$-0.252091\pi$
$307$	24.6157			1.40489			0.702447	+	0.711736i	$0.252091\pi$
$308$		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	$0.647678\pi$
$337$	−26.3666	+	19.1565i	−1.43628	+	1.04352i	−0.988803	+	0.149227i	$0.952322\pi$
$338$	−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	−0.891933	−	0.452167i	$-0.850651\pi$
$347$	1.77773	−	5.47127i	0.0954333	−	0.293713i	0.987366	+	0.158454i	$0.0506510\pi$
$348$	0.413800	−	0.300643i	0.0221820	−	0.0161162i
$349$	0.148810	+	0.108117i	0.00796563	+	0.00578737i	0.591761	−	0.806114i	$-0.298433\pi$
$349$	0.148810	+	0.108117i	0.00796563	+	0.00578737i	−0.583795	+	0.811901i	$0.698433\pi$
$350$	−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	−0.572331	−	0.820023i	$-0.693961\pi$
$359$	0.581625	−	0.422575i	0.0306970	−	0.0223027i	0.603028	+	0.797720i	$0.293961\pi$
$360$	−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	$-0.367047\pi$
$373$	15.6686			0.811292			0.405646	+	0.914030i	$0.367047\pi$
$374$		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	$0.0472608\pi$
$409$	5.57837	+	17.1684i	0.275832	+	0.848925i	−0.713165	+	0.700996i	$0.752739\pi$
$410$	−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	$-0.798995\pi$
$431$	−10.4040	−	32.0203i	−0.501145	−	1.54237i	0.306011	−	0.952028i	$-0.401005\pi$
$432$	−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	$-0.676045\pi$
$439$	−22.0123			−1.05059			−0.525294	+	0.850921i	$0.676045\pi$
$440$		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	$0.320583\pi$
$457$	−8.44030	+	25.9766i	−0.394821	+	1.21513i	−0.929101	+	0.369826i	$0.879417\pi$
$458$	−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	$-0.561303\pi$
$461$	−8.21908			−0.382801			−0.191400	+	0.981512i	$0.561303\pi$
$462$		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	$0.278020\pi$
$479$	−7.17661	+	22.0873i	−0.327908	+	1.00920i	−0.970111	+	0.242662i	$0.921980\pi$
$480$	−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	−0.714713	−	0.699417i	$-0.753443\pi$
$491$	−5.99136	+	4.35298i	−0.270386	+	0.196447i	0.444327	+	0.895865i	$0.353443\pi$
$492$	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	0.728848	−	0.684675i	$-0.240056\pi$
$503$	6.79357	+	4.93582i	0.302910	+	0.220077i	−0.425938	+	0.904752i	$0.640056\pi$
$504$	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	−0.819032	−	0.573747i	$-0.805489\pi$
$523$	4.13518	−	12.7268i	0.180819	−	0.556504i	0.999851	+	0.0172437i	$0.00548912\pi$
$524$	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	$-0.838465\pi$
$541$	−10.5263	−	32.3967i	−0.452563	−	1.39284i	0.421410	−	0.906870i	$-0.361535\pi$
$542$	−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	0.826014	−	0.563650i	$-0.190603\pi$
$547$	12.7512	+	9.26432i	0.545204	+	0.396114i	−0.280810	+	0.959763i	$0.590603\pi$
$548$	−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	−0.828514	−	0.559968i	$-0.810813\pi$
$557$	−13.0271	+	9.46477i	−0.551978	+	0.401035i	0.276536	+	0.961003i	$0.410813\pi$
$558$	−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	$-0.981722\pi$
$563$	−5.32450	−	16.3871i	−0.224401	−	0.690635i	0.773951	−	0.633246i	$-0.218278\pi$
$564$	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	0.995037	−	0.0995061i	$-0.0317263\pi$
$569$	28.8125	+	20.9335i	1.20788	+	0.877579i	0.212847	+	0.977085i	$0.431726\pi$
$570$	−10.6267	−	32.7056i	−0.445103	−	1.36989i
$571$	26.6026			1.11329			0.556643	−	0.830752i	$-0.312089\pi$
$571$	26.6026			1.11329			0.556643	+	0.830752i	$0.312089\pi$
$572$		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	$-0.395613\pi$
$593$	15.6870			0.644187			0.322093	+	0.946708i	$0.395613\pi$
$594$		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	−0.386857	−	0.922140i	$-0.626439\pi$
$601$	9.08550	−	6.60100i	0.370605	−	0.269261i	0.757462	+	0.652879i	$0.226439\pi$
$602$	−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	$0.0284413\pi$
$607$	5.97876	+	18.4007i	0.242670	+	0.746863i	−0.753340	+	0.657631i	$0.771559\pi$
$608$	−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	0.188011	−	0.982167i	$-0.439796\pi$
$613$	−17.0337	−	12.3757i	−0.687986	−	0.499851i	−0.875997	+	0.482316i	$0.839796\pi$
$614$	−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	$-0.392751\pi$
$659$	16.9733			0.661186			0.330593	+	0.943773i	$0.392751\pi$
$660$		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	1.00000		0.000166405i	$-5.29684e-5\pi$
$673$	4.95199	+	15.2407i	0.190885	+	0.587484i	−0.809115	+	0.587651i	$0.800053\pi$
$674$	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	−0.818898	−	0.573939i	$-0.805415\pi$
$677$	4.70836	−	14.4908i	0.180957	−	0.556928i	0.999855	+	0.0170104i	$0.00541484\pi$
$678$	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	0.591451	−	0.806341i	$-0.298555\pi$
$701$	0.194431	+	0.141262i	0.00734355	+	0.00533540i	−0.584107	+	0.811676i	$0.698555\pi$
$702$	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	−0.250168	−	0.968203i	$-0.580486\pi$
$733$	16.0641	−	11.6713i	0.593342	−	0.431088i	0.843509	+	0.537114i	$0.180486\pi$
$734$	−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	0.960770	−	0.277347i	$-0.0894553\pi$
$739$	0.556468	+	1.71263i	0.0204700	+	0.0630002i	−0.940300	+	0.340348i	$0.889455\pi$
$740$	−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	$-0.556509\pi$
$743$	14.8507	−	45.7058i	0.544820	−	1.67678i	0.721418	−	0.692500i	$-0.243491\pi$
$744$	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	$-0.918268\pi$
$761$	−9.21364	−	28.3567i	−0.333994	−	1.02793i	0.633221	−	0.773971i	$-0.281732\pi$
$762$	−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	$-0.670529\pi$
$769$	−28.3115			−1.02094			−0.510470	+	0.859896i	$0.670529\pi$
$770$		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	$-0.511876\pi$
$787$	16.2781	−	50.0989i	0.580252	−	1.78583i	0.617554	−	0.786528i	$-0.288124\pi$
$788$	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	−0.892863	−	0.450327i	$-0.851307\pi$
$809$	2.67859	−	8.24384i	0.0941741	−	0.289838i	0.987038	+	0.160489i	$0.0513072\pi$
$810$	−60.0123	+	43.6015i	−2.10862	+	1.53200i
$811$	−16.1388	−	11.7256i	−0.566711	−	0.411740i	0.267198	−	0.963642i	$-0.413902\pi$
$811$	−16.1388	−	11.7256i	−0.566711	−	0.411740i	−0.833909	+	0.551902i	$0.813902\pi$
$812$	−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	$0.684343\pi$
$821$	−43.3349	+	31.4846i	−1.51240	+	1.09882i	−0.965100	+	0.261883i	$0.915657\pi$
$822$	−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	0.932500	−	0.361170i	$-0.117623\pi$
$827$	−0.983476	−	3.02683i	−0.0341988	−	0.105253i	−0.966699	+	0.255917i	$0.917623\pi$
$828$	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	$-0.706701\pi$
$853$	10.3000	−	31.7002i	0.352666	−	1.08539i	0.957351	−	0.288928i	$-0.0932989\pi$
$854$	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	$-0.125895\pi$
$857$	54.0291			1.84560			0.922800	+	0.385279i	$0.125895\pi$
$858$		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	0.141731	−	0.989905i	$-0.454733\pi$
$877$	−22.3862	−	16.2645i	−0.755928	−	0.549214i	−0.897659	+	0.440691i	$0.854733\pi$
$878$	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	0.232307	−	0.972643i	$-0.425373\pi$
$887$	36.6067	−	26.5963i	1.22913	−	0.893016i	0.996825	+	0.0796262i	$0.0253727\pi$
$888$	−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	$-0.593994\pi$
$919$	15.3626	−	47.2812i	0.506765	−	1.55966i	0.797783	−	0.602945i	$-0.206006\pi$
$920$	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	0.980113	−	0.198441i	$-0.0635880\pi$
$937$	2.15938	+	6.64589i	0.0705439	+	0.217112i	−0.909569	+	0.415553i	$0.863588\pi$
$938$	−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	$-0.623622\pi$
$941$	14.4694	−	44.5323i	0.471690	−	1.45171i	0.850370	−	0.526185i	$-0.176378\pi$
$942$	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	$-0.335550\pi$
$953$	45.4888	−	33.0496i	1.47353	−	1.07058i	0.979572	−	0.201093i	$-0.0644495\pi$
$954$	−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	$-0.232126\pi$
$967$	46.3761			1.49136			0.745678	+	0.666307i	$0.232126\pi$
$968$		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	−0.812240	−	0.583324i	$-0.801752\pi$
$997$	−16.0549	+	11.6645i	−0.508462	+	0.369419i	0.303778	+	0.952743i	$0.401752\pi$
$998$	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.w.148.1		16
11.2	odd	10		847.2.f.v.372.4		16
11.3	even	5		847.2.a.p.1.2		8
11.4	even	5		77.2.f.b.36.4	yes	16
11.5	even	5		77.2.f.b.15.4	✓	16
11.6	odd	10		847.2.f.x.323.1		16
11.7	odd	10		847.2.f.x.729.1		16
11.8	odd	10		847.2.a.o.1.7		8
11.9	even	5	inner	847.2.f.w.372.1		16
11.10	odd	2		847.2.f.v.148.4		16
33.5	odd	10		693.2.m.i.631.1		16
33.8	even	10		7623.2.a.cw.1.2		8
33.14	odd	10		7623.2.a.ct.1.7		8
33.26	odd	10		693.2.m.i.190.1		16
77.4	even	15		539.2.q.g.520.4		32
77.5	odd	30		539.2.q.f.312.4		32
77.16	even	15		539.2.q.g.312.4		32
77.26	odd	30		539.2.q.f.410.1		32
77.27	odd	10		539.2.f.e.246.4		16
77.37	even	15		539.2.q.g.410.1		32
77.38	odd	30		539.2.q.f.422.1		32
77.41	even	10		5929.2.a.bs.1.7		8
77.48	odd	10		539.2.f.e.344.4		16
77.59	odd	30		539.2.q.f.520.4		32
77.60	even	15		539.2.q.g.422.1		32
77.69	odd	10		5929.2.a.bt.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.b.15.4	✓	16	11.5	even	5
77.2.f.b.36.4	yes	16	11.4	even	5
539.2.f.e.246.4		16	77.27	odd	10
539.2.f.e.344.4		16	77.48	odd	10
539.2.q.f.312.4		32	77.5	odd	30
539.2.q.f.410.1		32	77.26	odd	30
539.2.q.f.422.1		32	77.38	odd	30
539.2.q.f.520.4		32	77.59	odd	30
539.2.q.g.312.4		32	77.16	even	15
539.2.q.g.410.1		32	77.37	even	15
539.2.q.g.422.1		32	77.60	even	15
539.2.q.g.520.4		32	77.4	even	15
693.2.m.i.190.1		16	33.26	odd	10
693.2.m.i.631.1		16	33.5	odd	10
847.2.a.o.1.7		8	11.8	odd	10
847.2.a.p.1.2		8	11.3	even	5
847.2.f.v.148.4		16	11.10	odd	2
847.2.f.v.372.4		16	11.2	odd	10
847.2.f.w.148.1		16	1.1	even	1	trivial
847.2.f.w.372.1		16	11.9	even	5	inner
847.2.f.x.323.1		16	11.6	odd	10
847.2.f.x.729.1		16	11.7	odd	10
5929.2.a.bs.1.7		8	77.41	even	10
5929.2.a.bt.1.2		8	77.69	odd	10
7623.2.a.ct.1.7		8	33.14	odd	10
7623.2.a.cw.1.2		8	33.8	even	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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