LMFDB - Embedded newform 342.2.f.g.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(7,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 2]))

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

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

chi := DirichletCharacter("342.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.f (of order $3$, degree $2$, 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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 4 x^{16} - 6 x^{15} + x^{14} - 21 x^{13} - 12 x^{12} + 9 x^{10} + 135 x^{9} + 27 x^{8} + \cdots + 19683 $ x^18 + 4x^16 - 6x^15 + x^14 - 21x^13 - 12x^12 + 9x^10 + 135x^9 + 27x^8 - 324x^6 - 1701x^5 + 243x^4 - 4374x^3 + 8748x^2 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.5
Root			$-1.24302 + 1.20619i$ of defining polynomial
Character	$\chi$	$=$	342.49
Dual form			342.2.f.g.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(0.423085 + 1.67958i) q^{3} +1.00000 q^{4} +(-1.97181 - 3.41528i) q^{5} +(-0.423085 - 1.67958i) q^{6} +(1.02646 + 1.77787i) q^{7} -1.00000 q^{8} +(-2.64200 + 1.42121i) q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(0.423085 + 1.67958i) q^{3} +1.00000 q^{4} +(-1.97181 - 3.41528i) q^{5} +(-0.423085 - 1.67958i) q^{6} +(1.02646 + 1.77787i) q^{7} -1.00000 q^{8} +(-2.64200 + 1.42121i) q^{9} +(1.97181 + 3.41528i) q^{10} +(2.58114 + 4.47067i) q^{11} +(0.423085 + 1.67958i) q^{12} +3.88255 q^{13} +(-1.02646 - 1.77787i) q^{14} +(4.90200 - 4.75678i) q^{15} +1.00000 q^{16} +(-2.05469 + 3.55883i) q^{17} +(2.64200 - 1.42121i) q^{18} +(4.23814 + 1.01891i) q^{19} +(-1.97181 - 3.41528i) q^{20} +(-2.55181 + 2.47621i) q^{21} +(-2.58114 - 4.47067i) q^{22} +5.20520 q^{23} +(-0.423085 - 1.67958i) q^{24} +(-5.27609 + 9.13846i) q^{25} -3.88255 q^{26} +(-3.50484 - 3.83616i) q^{27} +(1.02646 + 1.77787i) q^{28} +(0.601213 - 1.04133i) q^{29} +(-4.90200 + 4.75678i) q^{30} +(-4.20987 + 7.29170i) q^{31} -1.00000 q^{32} +(-6.41682 + 6.22672i) q^{33} +(2.05469 - 3.55883i) q^{34} +(4.04796 - 7.01126i) q^{35} +(-2.64200 + 1.42121i) q^{36} +0.435335 q^{37} +(-4.23814 - 1.01891i) q^{38} +(1.64265 + 6.52107i) q^{39} +(1.97181 + 3.41528i) q^{40} +(-1.38355 - 2.39637i) q^{41} +(2.55181 - 2.47621i) q^{42} -1.67650 q^{43} +(2.58114 + 4.47067i) q^{44} +(10.0634 + 6.22079i) q^{45} -5.20520 q^{46} +(3.56916 - 6.18197i) q^{47} +(0.423085 + 1.67958i) q^{48} +(1.39278 - 2.41236i) q^{49} +(5.27609 - 9.13846i) q^{50} +(-6.84665 - 1.94533i) q^{51} +3.88255 q^{52} +(-0.708689 - 1.22749i) q^{53} +(3.50484 + 3.83616i) q^{54} +(10.1791 - 17.6307i) q^{55} +(-1.02646 - 1.77787i) q^{56} +(0.0817523 + 7.54939i) q^{57} +(-0.601213 + 1.04133i) q^{58} +(7.23184 + 12.5259i) q^{59} +(4.90200 - 4.75678i) q^{60} +(3.29666 - 5.70999i) q^{61} +(4.20987 - 7.29170i) q^{62} +(-5.23863 - 3.23832i) q^{63} +1.00000 q^{64} +(-7.65567 - 13.2600i) q^{65} +(6.41682 - 6.22672i) q^{66} -14.7187 q^{67} +(-2.05469 + 3.55883i) q^{68} +(2.20224 + 8.74256i) q^{69} +(-4.04796 + 7.01126i) q^{70} +(-2.20789 + 3.82418i) q^{71} +(2.64200 - 1.42121i) q^{72} +(5.08361 - 8.80507i) q^{73} -0.435335 q^{74} +(-17.5810 - 4.99528i) q^{75} +(4.23814 + 1.01891i) q^{76} +(-5.29886 + 9.17789i) q^{77} +(-1.64265 - 6.52107i) q^{78} -1.99732 q^{79} +(-1.97181 - 3.41528i) q^{80} +(4.96030 - 7.50969i) q^{81} +(1.38355 + 2.39637i) q^{82} +(-2.63550 - 4.56482i) q^{83} +(-2.55181 + 2.47621i) q^{84} +16.2059 q^{85} +1.67650 q^{86} +(2.00337 + 0.569215i) q^{87} +(-2.58114 - 4.47067i) q^{88} +(-0.817559 - 1.41605i) q^{89} +(-10.0634 - 6.22079i) q^{90} +(3.98527 + 6.90269i) q^{91} +5.20520 q^{92} +(-14.0282 - 3.98581i) q^{93} +(-3.56916 + 6.18197i) q^{94} +(-4.87696 - 16.4835i) q^{95} +(-0.423085 - 1.67958i) q^{96} -4.47521 q^{97} +(-1.39278 + 2.41236i) q^{98} +(-13.1732 - 8.14315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) $ 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.423085	+	1.67958i	0.244269	+	0.969708i
$3$	0.423085	+	1.67958i	0.244269	+	0.969708i
$4$	1.00000			0.500000
$5$	−1.97181	−	3.41528i	−0.881821	−	1.52736i	−0.849314	−	0.527888i	$-0.822984\pi$
$5$	−1.97181	−	3.41528i	−0.881821	−	1.52736i	−0.0325075	−	0.999471i	$-0.510349\pi$
$6$	−0.423085	−	1.67958i	−0.172724	−	0.685687i
$7$	1.02646	+	1.77787i	0.387964	+	0.671973i	0.992176	−	0.124851i	$-0.0398453\pi$
$7$	1.02646	+	1.77787i	0.387964	+	0.671973i	−0.604212	+	0.796824i	$0.706512\pi$
$8$	−1.00000			−0.353553
$9$	−2.64200	+	1.42121i	−0.880666	+	0.473738i
$10$	1.97181	+	3.41528i	0.623542	+	1.08001i
$11$	2.58114	+	4.47067i	0.778244	+	1.34796i	0.932953	+	0.359999i	$0.117223\pi$
$11$	2.58114	+	4.47067i	0.778244	+	1.34796i	−0.154708	+	0.987960i	$0.549444\pi$
$12$	0.423085	+	1.67958i	0.122134	+	0.484854i
$13$	3.88255			1.07683			0.538413	−	0.842681i	$-0.319024\pi$
$13$	3.88255			1.07683			0.538413	+	0.842681i	$0.319024\pi$
$14$	−1.02646	−	1.77787i	−0.274332	−	0.475156i
$15$	4.90200	−	4.75678i	1.26569	−	1.22819i
$16$	1.00000			0.250000
$17$	−2.05469	+	3.55883i	−0.498335	+	0.863142i	−0.999998	−	0.00192099i	$-0.999389\pi$
$17$	−2.05469	+	3.55883i	−0.498335	+	0.863142i	0.501663	+	0.865063i	$0.332722\pi$
$18$	2.64200	−	1.42121i	0.622725	−	0.334983i
$19$	4.23814	+	1.01891i	0.972296	+	0.233754i
$19$	4.23814	+	1.01891i	0.972296	+	0.233754i
$20$	−1.97181	−	3.41528i	−0.440911	−	0.763680i
$21$	−2.55181	+	2.47621i	−0.556850	+	0.540353i
$22$	−2.58114	−	4.47067i	−0.550302	−	0.953151i
$23$	5.20520			1.08536			0.542679	−	0.839940i	$-0.317410\pi$
$23$	5.20520			1.08536			0.542679	+	0.839940i	$0.317410\pi$
$24$	−0.423085	−	1.67958i	−0.0863620	−	0.342843i
$25$	−5.27609	+	9.13846i	−1.05522	+	1.82769i
$26$	−3.88255			−0.761431
$27$	−3.50484	−	3.83616i	−0.674506	−	0.738269i
$28$	1.02646	+	1.77787i	0.193982	+	0.335986i
$29$	0.601213	−	1.04133i	0.111642	−	0.193370i	−0.804790	−	0.593559i	$-0.797722\pi$
$29$	0.601213	−	1.04133i	0.111642	−	0.193370i	0.916433	+	0.400189i	$0.131056\pi$
$30$	−4.90200	+	4.75678i	−0.894979	+	0.868465i
$31$	−4.20987	+	7.29170i	−0.756114	+	1.30963i	0.188704	+	0.982034i	$0.439571\pi$
$31$	−4.20987	+	7.29170i	−0.756114	+	1.30963i	−0.944818	+	0.327594i	$0.893762\pi$
$32$	−1.00000			−0.176777
$33$	−6.41682	+	6.22672i	−1.11703	+	1.08393i
$34$	2.05469	−	3.55883i	0.352376	−	0.610334i
$35$	4.04796	−	7.01126i	0.684229	−	1.18512i
$36$	−2.64200	+	1.42121i	−0.440333	+	0.236869i
$37$	0.435335			0.0715687			0.0357844	−	0.999360i	$-0.488607\pi$
$37$	0.435335			0.0715687			0.0357844	+	0.999360i	$0.488607\pi$
$38$	−4.23814	−	1.01891i	−0.687517	−	0.165289i
$39$	1.64265	+	6.52107i	0.263035	+	1.04421i
$40$	1.97181	+	3.41528i	0.311771	+	0.540003i
$41$	−1.38355	−	2.39637i	−0.216073	−	0.374250i	0.737531	−	0.675314i	$-0.235992\pi$
$41$	−1.38355	−	2.39637i	−0.216073	−	0.374250i	−0.953604	+	0.301063i	$0.902658\pi$
$42$	2.55181	−	2.47621i	0.393752	−	0.382087i
$43$	−1.67650			−0.255664			−0.127832	−	0.991796i	$-0.540802\pi$
$43$	−1.67650			−0.255664			−0.127832	+	0.991796i	$0.540802\pi$
$44$	2.58114	+	4.47067i	0.389122	+	0.673980i
$45$	10.0634	+	6.22079i	1.50016	+	0.927341i
$46$	−5.20520			−0.767464
$47$	3.56916	−	6.18197i	0.520616	−	0.901733i	−0.479097	−	0.877762i	$-0.659036\pi$
$47$	3.56916	−	6.18197i	0.520616	−	0.901733i	0.999713	−	0.0239712i	$-0.00763100\pi$
$48$	0.423085	+	1.67958i	0.0610671	+	0.242427i
$49$	1.39278	−	2.41236i	0.198968	−	0.344623i
$50$	5.27609	−	9.13846i	0.746152	−	1.29237i
$51$	−6.84665	−	1.94533i	−0.958723	−	0.272401i
$52$	3.88255			0.538413
$53$	−0.708689	−	1.22749i	−0.0973460	−	0.168608i	0.813239	−	0.581929i	$-0.197702\pi$
$53$	−0.708689	−	1.22749i	−0.0973460	−	0.168608i	−0.910585	+	0.413321i	$0.864369\pi$
$54$	3.50484	+	3.83616i	0.476948	+	0.522035i
$55$	10.1791	−	17.6307i	1.37255	−	2.37732i
$56$	−1.02646	−	1.77787i	−0.137166	−	0.237578i
$57$	0.0817523	+	7.54939i	0.0108284	+	0.999941i
$58$	−0.601213	+	1.04133i	−0.0789431	+	0.136733i
$59$	7.23184	+	12.5259i	0.941506	+	1.63074i	0.762601	+	0.646869i	$0.223922\pi$
$59$	7.23184	+	12.5259i	0.941506	+	1.63074i	0.178904	+	0.983866i	$0.442745\pi$
$60$	4.90200	−	4.75678i	0.632846	−	0.614097i
$61$	3.29666	−	5.70999i	0.422094	−	0.731089i	−0.574050	−	0.818820i	$-0.694628\pi$
$61$	3.29666	−	5.70999i	0.422094	−	0.731089i	0.996144	+	0.0877315i	$0.0279618\pi$
$62$	4.20987	−	7.29170i	0.534653	−	0.926047i
$63$	−5.23863	−	3.23832i	−0.660005	−	0.407990i
$64$	1.00000			0.125000
$65$	−7.65567	−	13.2600i	−0.949569	−	1.64470i
$66$	6.41682	−	6.22672i	0.789856	−	0.766457i
$67$	−14.7187			−1.79817			−0.899086	−	0.437771i	$-0.855768\pi$
$67$	−14.7187			−1.79817			−0.899086	+	0.437771i	$0.855768\pi$
$68$	−2.05469	+	3.55883i	−0.249168	+	0.431571i
$69$	2.20224	+	8.74256i	0.265119	+	1.05248i
$70$	−4.04796	+	7.01126i	−0.483823	+	0.838006i
$71$	−2.20789	+	3.82418i	−0.262028	+	0.453847i	−0.966781	−	0.255607i	$-0.917725\pi$
$71$	−2.20789	+	3.82418i	−0.262028	+	0.453847i	0.704752	+	0.709453i	$0.251058\pi$
$72$	2.64200	−	1.42121i	0.311362	−	0.167492i
$73$	5.08361	−	8.80507i	0.594991	−	1.03056i	−0.398557	−	0.917144i	$-0.630489\pi$
$73$	5.08361	−	8.80507i	0.594991	−	1.03056i	0.993548	−	0.113411i	$-0.0361778\pi$
$74$	−0.435335			−0.0506067
$75$	−17.5810	−	4.99528i	−2.03008	−	0.576806i
$76$	4.23814	+	1.01891i	0.486148	+	0.116877i
$77$	−5.29886	+	9.17789i	−0.603861	+	1.04592i
$78$	−1.64265	−	6.52107i	−0.185994	−	0.738366i
$79$	−1.99732			−0.224716			−0.112358	−	0.993668i	$-0.535840\pi$
$79$	−1.99732			−0.224716			−0.112358	+	0.993668i	$0.535840\pi$
$80$	−1.97181	−	3.41528i	−0.220455	−	0.381840i
$81$	4.96030	−	7.50969i	0.551144	−	0.834410i
$82$	1.38355	+	2.39637i	0.152787	+	0.264635i
$83$	−2.63550	−	4.56482i	−0.289284	−	0.501054i	0.684355	−	0.729149i	$-0.260084\pi$
$83$	−2.63550	−	4.56482i	−0.289284	−	0.501054i	−0.973639	+	0.228095i	$0.926750\pi$
$84$	−2.55181	+	2.47621i	−0.278425	+	0.270177i
$85$	16.2059			1.75777
$86$	1.67650			0.180782
$87$	2.00337	+	0.569215i	0.214783	+	0.0610262i
$88$	−2.58114	−	4.47067i	−0.275151	−	0.476575i
$89$	−0.817559	−	1.41605i	−0.0866610	−	0.150101i	0.819437	−	0.573170i	$-0.194286\pi$
$89$	−0.817559	−	1.41605i	−0.0866610	−	0.150101i	−0.906098	+	0.423068i	$0.860953\pi$
$90$	−10.0634	−	6.22079i	−1.06077	−	0.655729i
$91$	3.98527	+	6.90269i	0.417770	+	0.723598i
$92$	5.20520			0.542679
$93$	−14.0282	−	3.98581i	−1.45465	−	0.413309i
$94$	−3.56916	+	6.18197i	−0.368131	+	0.637622i
$95$	−4.87696	−	16.4835i	−0.500365	−	1.69117i
$96$	−0.423085	−	1.67958i	−0.0431810	−	0.171422i
$97$	−4.47521			−0.454389			−0.227194	−	0.973849i	$-0.572955\pi$
$97$	−4.47521			−0.454389			−0.227194	+	0.973849i	$0.572955\pi$
$98$	−1.39278	+	2.41236i	−0.140692	+	0.243686i
$99$	−13.1732	−	8.14315i	−1.32395	−	0.818417i
$100$	−5.27609	+	9.13846i	−0.527609	+	0.913846i
$101$	−2.15018	+	3.72421i	−0.213950	+	0.370573i	−0.952947	−	0.303136i	$-0.901966\pi$
$101$	−2.15018	+	3.72421i	−0.213950	+	0.370573i	0.738997	+	0.673709i	$0.235300\pi$
$102$	6.84665	+	1.94533i	0.677920	+	0.192617i
$103$	7.26626	−	12.5855i	0.715965	−	1.24009i	−0.246621	−	0.969112i	$-0.579320\pi$
$103$	7.26626	−	12.5855i	0.715965	−	1.24009i	0.962586	−	0.270976i	$-0.0873465\pi$
$104$	−3.88255			−0.380716
$105$	13.4886	+	3.83251i	1.31636	+	0.374015i
$106$	0.708689	+	1.22749i	0.0688340	+	0.119224i
$107$	−2.11280			−0.204252			−0.102126	−	0.994771i	$-0.532565\pi$
$107$	−2.11280			−0.204252			−0.102126	+	0.994771i	$0.532565\pi$
$108$	−3.50484	−	3.83616i	−0.337253	−	0.369135i
$109$	4.80520	−	8.32285i	0.460255	−	0.797184i	−0.538719	−	0.842486i	$-0.681091\pi$
$109$	4.80520	−	8.32285i	0.460255	−	0.797184i	0.998973	+	0.0453014i	$0.0144248\pi$
$110$	−10.1791	+	17.6307i	−0.970536	+	1.68102i
$111$	0.184184	+	0.731182i	0.0174820	+	0.0694007i
$112$	1.02646	+	1.77787i	0.0969909	+	0.167993i
$113$	−3.49351	+	6.05094i	−0.328642	+	0.569225i	−0.982243	−	0.187615i	$-0.939924\pi$
$113$	−3.49351	+	6.05094i	−0.328642	+	0.569225i	0.653601	+	0.756840i	$0.273258\pi$
$114$	−0.0817523	−	7.54939i	−0.00765680	−	0.707065i
$115$	−10.2637	−	17.7772i	−0.957092	−	1.65773i
$116$	0.601213	−	1.04133i	0.0558212	−	0.0966852i
$117$	−10.2577	+	5.51794i	−0.948324	+	0.510134i
$118$	−7.23184	−	12.5259i	−0.665745	−	1.15310i
$119$	−8.43619			−0.773344
$120$	−4.90200	+	4.75678i	−0.447489	+	0.434232i
$121$	−7.82462	+	13.5526i	−0.711329	+	1.23206i
$122$	−3.29666	+	5.70999i	−0.298466	+	0.516958i
$123$	3.43954	−	3.33765i	0.310133	−	0.300946i
$124$	−4.20987	+	7.29170i	−0.378057	+	0.654814i
$125$	21.8957			1.95841
$126$	5.23863	+	3.23832i	0.466694	+	0.288493i
$127$	−1.73490	−	3.00493i	−0.153947	−	0.266645i	0.778728	−	0.627362i	$-0.215865\pi$
$127$	−1.73490	−	3.00493i	−0.153947	−	0.266645i	−0.932675	+	0.360717i	$0.882532\pi$
$128$	−1.00000			−0.0883883
$129$	−0.709303	−	2.81582i	−0.0624506	−	0.247919i
$130$	7.65567	+	13.2600i	0.671447	+	1.16298i
$131$	−0.180228	−	0.312163i	−0.0157466	−	0.0272738i	0.858045	−	0.513575i	$-0.171679\pi$
$131$	−0.180228	−	0.312163i	−0.0157466	−	0.0272738i	−0.873791	+	0.486301i	$0.838346\pi$
$132$	−6.41682	+	6.22672i	−0.558513	+	0.541967i
$133$	2.53877	+	8.58074i	0.220139	+	0.744044i
$134$	14.7187			1.27150
$135$	−6.19067	+	19.5342i	−0.532808	+	1.68124i
$136$	2.05469	−	3.55883i	0.176188	−	0.305167i
$137$	8.91473	−	15.4408i	0.761637	−	1.31919i	−0.180370	−	0.983599i	$-0.557729\pi$
$137$	8.91473	−	15.4408i	0.761637	−	1.31919i	0.942007	−	0.335595i	$-0.108937\pi$
$138$	−2.20224	−	8.74256i	−0.187467	−	0.744216i
$139$	19.5221			1.65584			0.827922	−	0.560844i	$-0.189523\pi$
$139$	19.5221			1.65584			0.827922	+	0.560844i	$0.189523\pi$
$140$	4.04796	−	7.01126i	0.342115	−	0.592560i
$141$	11.8932	+	3.37920i	1.00159	+	0.284580i
$142$	2.20789	−	3.82418i	0.185282	−	0.320918i
$143$	10.0214	+	17.3576i	0.838034	+	1.45152i
$144$	−2.64200	+	1.42121i	−0.220166	+	0.118435i
$145$	−4.74192			−0.393795
$146$	−5.08361	+	8.80507i	−0.420722	+	0.728712i
$147$	4.64103	+	1.31865i	0.382786	+	0.108761i
$148$	0.435335			0.0357844
$149$	9.37916	+	16.2452i	0.768371	+	1.33086i	0.938446	+	0.345426i	$0.112266\pi$
$149$	9.37916	+	16.2452i	0.768371	+	1.33086i	−0.170075	+	0.985431i	$0.554401\pi$
$150$	17.5810	+	4.99528i	1.43549	+	0.407863i
$151$	−2.80807	−	4.86372i	−0.228518	−	0.395804i	0.728851	−	0.684672i	$-0.240055\pi$
$151$	−2.80807	−	4.86372i	−0.228518	−	0.395804i	−0.957369	+	0.288868i	$0.906721\pi$
$152$	−4.23814	−	1.01891i	−0.343758	−	0.0826445i
$153$	0.370629	−	12.3226i	0.0299636	−	0.996220i
$154$	5.29886	−	9.17789i	0.426994	−	0.739576i
$155$	33.2043			2.66703
$156$	1.64265	+	6.52107i	0.131517	+	0.522104i
$157$	6.03649	+	10.4555i	0.481765	+	0.834441i	0.999781	−	0.0209301i	$-0.00666273\pi$
$157$	6.03649	+	10.4555i	0.481765	+	0.834441i	−0.518016	+	0.855371i	$0.673329\pi$
$158$	1.99732			0.158898
$159$	1.76183	−	1.70963i	0.139722	−	0.135583i
$160$	1.97181	+	3.41528i	0.155885	+	0.270002i
$161$	5.34290	+	9.25418i	0.421080	+	0.729331i
$162$	−4.96030	+	7.50969i	−0.389718	+	0.590017i
$163$	−11.5204			−0.902351			−0.451175	−	0.892435i	$-0.648995\pi$
$163$	−11.5204			−0.902351			−0.451175	+	0.892435i	$0.648995\pi$
$164$	−1.38355	−	2.39637i	−0.108037	−	0.187125i
$165$	33.9188	+	9.63731i	2.64057	+	0.750264i
$166$	2.63550	+	4.56482i	0.204554	+	0.354299i
$167$	−18.7434			−1.45041			−0.725206	−	0.688532i	$-0.758255\pi$
$167$	−18.7434			−1.45041			−0.725206	+	0.688532i	$0.758255\pi$
$168$	2.55181	−	2.47621i	0.196876	−	0.191044i
$169$	2.07422			0.159556
$170$	−16.2059			−1.24293
$171$	−12.6452	+	3.33135i	−0.967006	+	0.254755i
$172$	−1.67650			−0.127832
$173$	−1.44752			−0.110053			−0.0550265	−	0.998485i	$-0.517524\pi$
$173$	−1.44752			−0.110053			−0.0550265	+	0.998485i	$0.517524\pi$
$174$	−2.00337	−	0.569215i	−0.151875	−	0.0431521i
$175$	−21.6627			−1.63755
$176$	2.58114	+	4.47067i	0.194561	+	0.336990i
$177$	−17.9786	+	17.4460i	−1.35136	+	1.31132i
$178$	0.817559	+	1.41605i	0.0612786	+	0.106138i
$179$	1.31420			0.0982278			0.0491139	−	0.998793i	$-0.484360\pi$
$179$	1.31420			0.0982278			0.0491139	+	0.998793i	$0.484360\pi$
$180$	10.0634	+	6.22079i	0.750079	+	0.463670i
$181$	−5.35552	−	9.27604i	−0.398073	−	0.689482i	0.595415	−	0.803418i	$-0.296988\pi$
$181$	−5.35552	−	9.27604i	−0.398073	−	0.689482i	−0.993488	+	0.113936i	$0.963654\pi$
$182$	−3.98527	−	6.90269i	−0.295408	−	0.511661i
$183$	10.9852	+	3.12121i	0.812047	+	0.230726i
$184$	−5.20520			−0.383732
$185$	−0.858400	−	1.48679i	−0.0631108	−	0.109311i
$186$	14.0282	+	3.98581i	1.02859	+	0.292253i
$187$	−21.2138			−1.55131
$188$	3.56916	−	6.18197i	0.260308	−	0.450867i
$189$	3.22264	−	10.1688i	0.234413	−	0.739671i
$190$	4.87696	+	16.4835i	0.353812	+	1.19584i
$191$	−1.88682	−	3.26807i	−0.136526	−	0.236469i	0.789654	−	0.613553i	$-0.210260\pi$
$191$	−1.88682	−	3.26807i	−0.136526	−	0.236469i	−0.926179	+	0.377084i	$0.876927\pi$
$192$	0.423085	+	1.67958i	0.0305336	+	0.121213i
$193$	−8.11527	−	14.0561i	−0.584150	−	1.01178i	−0.994981	−	0.100066i	$-0.968095\pi$
$193$	−8.11527	−	14.0561i	−0.584150	−	1.01178i	0.410831	−	0.911712i	$-0.365239\pi$
$194$	4.47521			0.321301
$195$	19.0323	−	18.4684i	1.36293	−	1.32255i
$196$	1.39278	−	2.41236i	0.0994842	−	0.172312i
$197$	−20.6274			−1.46964			−0.734821	−	0.678261i	$-0.762734\pi$
$197$	−20.6274			−1.46964			−0.734821	+	0.678261i	$0.762734\pi$
$198$	13.1732	+	8.14315i	0.936176	+	0.578708i
$199$	3.22792	+	5.59093i	0.228821	+	0.396330i	0.957459	−	0.288569i	$-0.0931795\pi$
$199$	3.22792	+	5.59093i	0.228821	+	0.396330i	−0.728638	+	0.684899i	$0.759846\pi$
$200$	5.27609	−	9.13846i	0.373076	−	0.646187i
$201$	−6.22726	−	24.7212i	−0.439237	−	1.74370i
$202$	2.15018	−	3.72421i	0.151286	−	0.262035i
$203$	2.46847			0.173253
$204$	−6.84665	−	1.94533i	−0.479362	−	0.136201i
$205$	−5.45618	+	9.45039i	−0.381076	+	0.660044i
$206$	−7.26626	+	12.5855i	−0.506264	+	0.876875i
$207$	−13.7521	+	7.39770i	−0.955838	+	0.514176i
$208$	3.88255			0.269207
$209$	6.38404	+	21.5773i	0.441593	+	1.49253i
$210$	−13.4886	−	3.83251i	−0.930804	−	0.264468i
$211$	0.202549	+	0.350825i	0.0139440	+	0.0241518i	0.872913	−	0.487876i	$-0.162228\pi$
$211$	0.202549	+	0.350825i	0.0139440	+	0.0241518i	−0.858969	+	0.512027i	$0.828895\pi$
$212$	−0.708689	−	1.22749i	−0.0486730	−	0.0843041i
$213$	−7.35715	−	2.09038i	−0.504104	−	0.143231i
$214$	2.11280			0.144428
$215$	3.30574	+	5.72572i	0.225450	+	0.390491i
$216$	3.50484	+	3.83616i	0.238474	+	0.261018i
$217$	−17.2850			−1.17338
$218$	−4.80520	+	8.32285i	−0.325449	+	0.563694i
$219$	16.9396	+	4.81304i	1.14467	+	0.325235i
$220$	10.1791	−	17.6307i	0.686273	−	1.18866i
$221$	−7.97744	+	13.8173i	−0.536621	+	0.929455i
$222$	−0.184184	−	0.731182i	−0.0123616	−	0.0490737i
$223$	−8.40880			−0.563095			−0.281547	−	0.959547i	$-0.590848\pi$
$223$	−8.40880			−0.563095			−0.281547	+	0.959547i	$0.590848\pi$
$224$	−1.02646	−	1.77787i	−0.0685829	−	0.118789i
$225$	0.951713	−	31.6422i	0.0634475	−	2.10948i
$226$	3.49351	−	6.05094i	0.232385	−	0.402503i
$227$	0.146997	+	0.254607i	0.00975656	+	0.0168989i	0.870862	−	0.491527i	$-0.163561\pi$
$227$	0.146997	+	0.254607i	0.00975656	+	0.0168989i	−0.861106	+	0.508426i	$0.830228\pi$
$228$	0.0817523	+	7.54939i	0.00541418	+	0.499971i
$229$	−3.61171	+	6.25566i	−0.238668	+	0.413386i	−0.960332	−	0.278858i	$-0.910044\pi$
$229$	−3.61171	+	6.25566i	−0.238668	+	0.413386i	0.721664	+	0.692243i	$0.243378\pi$
$230$	10.2637	+	17.7772i	0.676766	+	1.17219i
$231$	−17.6569	−	5.01684i	−1.16174	−	0.330084i
$232$	−0.601213	+	1.04133i	−0.0394716	+	0.0683667i
$233$	9.39739	−	16.2768i	0.615644	−	1.06633i	−0.374627	−	0.927175i	$-0.622229\pi$
$233$	9.39739	−	16.2768i	0.615644	−	1.06633i	0.990271	−	0.139151i	$-0.0444373\pi$
$234$	10.2577	−	5.51794i	0.670567	−	0.360719i
$235$	−28.1509			−1.83636
$236$	7.23184	+	12.5259i	0.470753	+	0.815368i
$237$	−0.845037	−	3.35466i	−0.0548910	−	0.217909i
$238$	8.43619			0.546837
$239$	−1.67306	+	2.89782i	−0.108221	+	0.187444i	−0.915050	−	0.403341i	$-0.867849\pi$
$239$	−1.67306	+	2.89782i	−0.108221	+	0.187444i	0.806829	+	0.590786i	$0.201182\pi$
$240$	4.90200	−	4.75678i	0.316423	−	0.307049i
$241$	0.623776	−	1.08041i	0.0401810	−	0.0695955i	−0.845236	−	0.534394i	$-0.820540\pi$
$241$	0.623776	−	1.08041i	0.0401810	−	0.0695955i	0.885416	+	0.464798i	$0.153873\pi$
$242$	7.82462	−	13.5526i	0.502986	−	0.871197i
$243$	14.7118	+	5.15400i	0.943761	+	0.330629i
$244$	3.29666	−	5.70999i	0.211047	−	0.365544i
$245$	−10.9852			−0.701819
$246$	−3.43954	+	3.33765i	−0.219297	+	0.212801i
$247$	16.4548	+	3.95597i	1.04699	+	0.251712i
$248$	4.20987	−	7.29170i	0.267327	−	0.463024i
$249$	6.55195	−	6.35785i	0.415213	−	0.402912i
$250$	−21.8957			−1.38481
$251$	2.56602	+	4.44447i	0.161966	+	0.280532i	0.935574	−	0.353132i	$-0.114883\pi$
$251$	2.56602	+	4.44447i	0.161966	+	0.280532i	−0.773608	+	0.633664i	$0.781550\pi$
$252$	−5.23863	−	3.23832i	−0.330003	−	0.203995i
$253$	13.4354	+	23.2707i	0.844674	+	1.46302i
$254$	1.73490	+	3.00493i	0.108857	+	0.188546i
$255$	6.85646	+	27.2191i	0.429368	+	1.70452i
$256$	1.00000			0.0625000
$257$	14.2660			0.889887			0.444943	−	0.895559i	$-0.353224\pi$
$257$	14.2660			0.889887			0.444943	+	0.895559i	$0.353224\pi$
$258$	0.709303	+	2.81582i	0.0441593	+	0.175305i
$259$	0.446852	+	0.773971i	0.0277661	+	0.0480922i
$260$	−7.65567	−	13.2600i	−0.474784	−	0.822351i
$261$	−0.108448	+	3.60565i	−0.00671277	+	0.223184i
$262$	0.180228	+	0.312163i	0.0111345	+	0.0192855i
$263$	0.503455			0.0310444			0.0155222	−	0.999880i	$-0.495059\pi$
$263$	0.503455			0.0310444			0.0155222	+	0.999880i	$0.495059\pi$
$264$	6.41682	−	6.22672i	0.394928	−	0.383228i
$265$	−2.79481	+	4.84074i	−0.171684	+	0.297365i
$266$	−2.53877	−	8.58074i	−0.155662	−	0.526119i
$267$	2.03248	−	1.97227i	0.124386	−	0.120701i
$268$	−14.7187			−0.899086
$269$	2.90769	−	5.03628i	0.177285	−	0.307067i	−0.763664	−	0.645613i	$-0.776602\pi$
$269$	2.90769	−	5.03628i	0.177285	−	0.307067i	0.940950	+	0.338546i	$0.109935\pi$
$270$	6.19067	−	19.5342i	0.376752	−	1.18881i
$271$	16.2151	−	28.0854i	0.984997	−	1.70606i	0.343045	−	0.939319i	$-0.388542\pi$
$271$	16.2151	−	28.0854i	0.984997	−	1.70606i	0.641952	−	0.766745i	$-0.278125\pi$
$272$	−2.05469	+	3.55883i	−0.124584	+	0.215786i
$273$	−9.90753	+	9.61401i	−0.599631	+	0.581867i
$274$	−8.91473	+	15.4408i	−0.538558	+	0.932811i
$275$	−54.4734			−3.28487
$276$	2.20224	+	8.74256i	0.132559	+	0.526240i
$277$	9.88182	+	17.1158i	0.593741	+	1.02839i	0.993723	+	0.111866i	$0.0356829\pi$
$277$	9.88182	+	17.1158i	0.593741	+	1.02839i	−0.399982	+	0.916523i	$0.630984\pi$
$278$	−19.5221			−1.17086
$279$	0.759385	−	25.2478i	0.0454632	−	1.51154i
$280$	−4.04796	+	7.01126i	−0.241912	+	0.419003i
$281$	−12.2654	+	21.2443i	−0.731692	+	1.26733i	0.224467	+	0.974482i	$0.427936\pi$
$281$	−12.2654	+	21.2443i	−0.731692	+	1.26733i	−0.956159	+	0.292847i	$0.905397\pi$
$282$	−11.8932	−	3.37920i	−0.708230	−	0.201229i
$283$	1.37132	+	2.37519i	0.0815163	+	0.141190i	0.903901	−	0.427741i	$-0.140690\pi$
$283$	1.37132	+	2.37519i	0.0815163	+	0.141190i	−0.822385	+	0.568931i	$0.807357\pi$
$284$	−2.20789	+	3.82418i	−0.131014	+	0.226923i
$285$	25.6221	−	15.1652i	1.51772	−	0.898309i
$286$	−10.0214	−	17.3576i	−0.592580	−	1.02638i
$287$	2.84029	−	4.91953i	0.167657	−	0.290391i
$288$	2.64200	−	1.42121i	0.155681	−	0.0837458i
$289$	0.0565005	+	0.0978617i	0.00332356	+	0.00575657i
$290$	4.74192			0.278455
$291$	−1.89340	−	7.51648i	−0.110993	−	0.440624i
$292$	5.08361	−	8.80507i	0.297496	−	0.515278i
$293$	15.1403	−	26.2237i	0.884504	−	1.53201i	0.0382235	−	0.999269i	$-0.487830\pi$
$293$	15.1403	−	26.2237i	0.884504	−	1.53201i	0.846281	−	0.532737i	$-0.178837\pi$
$294$	−4.64103	−	1.31865i	−0.270670	−	0.0769053i
$295$	28.5197	−	49.3975i	1.66048	−	2.87604i
$296$	−0.435335			−0.0253034
$297$	8.10372	−	25.5707i	0.470226	−	1.48376i
$298$	−9.37916	−	16.2452i	−0.543320	−	0.941058i
$299$	20.2095			1.16874
$300$	−17.5810	−	4.99528i	−1.01504	−	0.288403i
$301$	−1.72085	−	2.98060i	−0.0991883	−	0.171799i
$302$	2.80807	+	4.86372i	0.161586	+	0.279876i
$303$	−7.16483	−	2.03574i	−0.411609	−	0.116950i
$304$	4.23814	+	1.01891i	0.243074	+	0.0584385i
$305$	−26.0016			−1.48885
$306$	−0.370629	+	12.3226i	−0.0211875	+	0.704434i
$307$	−8.15255	+	14.1206i	−0.465291	+	0.805907i	−0.999215	−	0.0396256i	$-0.987383\pi$
$307$	−8.15255	+	14.1206i	−0.465291	+	0.805907i	0.533924	+	0.845532i	$0.320717\pi$
$308$	−5.29886	+	9.17789i	−0.301931	+	0.522959i
$309$	24.2127	+	6.87953i	1.37741	+	0.391363i
$310$	−33.2043			−1.88588
$311$	13.3270	−	23.0831i	0.755706	−	1.30892i	−0.189316	−	0.981916i	$-0.560627\pi$
$311$	13.3270	−	23.0831i	0.755706	−	1.30892i	0.945022	−	0.327006i	$-0.106040\pi$
$312$	−1.64265	−	6.52107i	−0.0929969	−	0.369183i
$313$	−8.99013	+	15.5714i	−0.508152	+	0.880146i	0.491803	+	0.870706i	$0.336338\pi$
$313$	−8.99013	+	15.5714i	−0.508152	+	0.880146i	−0.999955	+	0.00943931i	$0.996995\pi$
$314$	−6.03649	−	10.4555i	−0.340659	−	0.590039i
$315$	−0.730179	+	24.2768i	−0.0411409	+	1.36784i
$316$	−1.99732			−0.112358
$317$	−8.32463	+	14.4187i	−0.467558	+	0.809834i	−0.999313	−	0.0370644i	$-0.988199\pi$
$317$	−8.32463	+	14.4187i	−0.467558	+	0.809834i	0.531755	+	0.846898i	$0.321533\pi$
$318$	−1.76183	+	1.70963i	−0.0987984	+	0.0958715i
$319$	6.20727			0.347540
$320$	−1.97181	−	3.41528i	−0.110228	−	0.190920i
$321$	−0.893895	−	3.54862i	−0.0498924	−	0.198065i
$322$	−5.34290	−	9.25418i	−0.297748	−	0.515715i
$323$	−12.3342	+	12.9893i	−0.686292	+	0.722742i
$324$	4.96030	−	7.50969i	0.275572	−	0.417205i
$325$	−20.4847	+	35.4806i	−1.13629	+	1.96811i
$326$	11.5204			0.638058
$327$	16.0119	+	4.54945i	0.885461	+	0.251585i
$328$	1.38355	+	2.39637i	0.0763935	+	0.132317i
$329$	14.6543			0.807920
$330$	−33.9188	−	9.63731i	−1.86717	−	0.530517i
$331$	0.156160	+	0.270477i	0.00858333	+	0.0148668i	0.870285	−	0.492548i	$-0.163934\pi$
$331$	0.156160	+	0.270477i	0.00858333	+	0.0148668i	−0.861702	+	0.507415i	$0.830601\pi$
$332$	−2.63550	−	4.56482i	−0.144642	−	0.250527i
$333$	−1.15016	+	0.618705i	−0.0630281	+	0.0339048i
$334$	18.7434			1.02560
$335$	29.0225	+	50.2684i	1.58567	+	2.74646i
$336$	−2.55181	+	2.47621i	−0.139212	+	0.135088i
$337$	−9.23379	−	15.9934i	−0.502997	−	0.871216i	−0.999994	−	0.00346369i	$-0.998897\pi$
$337$	−9.23379	−	15.9934i	−0.502997	−	0.871216i	0.496997	−	0.867752i	$-0.334436\pi$
$338$	−2.07422			−0.112823
$339$	−11.6411	−	3.30758i	−0.632258	−	0.179643i
$340$	16.2059			0.878886
$341$	−43.4651			−2.35377
$342$	12.6452	−	3.33135i	0.683776	−	0.180139i
$343$	20.0889			1.08470
$344$	1.67650			0.0903908
$345$	25.5159	−	24.7600i	1.37373	−	1.33303i
$346$	1.44752			0.0778192
$347$	−3.56809	−	6.18011i	−0.191545	−	0.331766i	0.754217	−	0.656625i	$-0.228016\pi$
$347$	−3.56809	−	6.18011i	−0.191545	−	0.331766i	−0.945762	+	0.324859i	$0.894683\pi$
$348$	2.00337	+	0.569215i	0.107392	+	0.0305131i
$349$	6.45792	+	11.1854i	0.345685	+	0.598743i	0.985478	−	0.169804i	$-0.0543134\pi$
$349$	6.45792	+	11.1854i	0.345685	+	0.598743i	−0.639793	+	0.768547i	$0.720980\pi$
$350$	21.6627			1.15792
$351$	−13.6077	−	14.8941i	−0.726326	−	0.794988i
$352$	−2.58114	−	4.47067i	−0.137575	−	0.238288i
$353$	−13.1427	−	22.7639i	−0.699518	−	1.21160i	−0.968634	−	0.248492i	$-0.920065\pi$
$353$	−13.1427	−	22.7639i	−0.699518	−	1.21160i	0.269116	−	0.963108i	$-0.413268\pi$
$354$	17.9786	−	17.4460i	0.955553	−	0.927245i
$355$	17.4142			0.924249
$356$	−0.817559	−	1.41605i	−0.0433305	−	0.0750507i
$357$	−3.56923	−	14.1693i	−0.188904	−	0.749918i
$358$	−1.31420			−0.0694576
$359$	7.54249	−	13.0640i	0.398077	−	0.689490i	−0.595411	−	0.803421i	$-0.703011\pi$
$359$	7.54249	−	13.0640i	0.398077	−	0.689490i	0.993489	+	0.113931i	$0.0363442\pi$
$360$	−10.0634	−	6.22079i	−0.530386	−	0.327865i
$361$	16.9236	+	8.63656i	0.890718	+	0.454556i
$362$	5.35552	+	9.27604i	0.281480	+	0.487538i
$363$	−26.0733	−	7.40817i	−1.36849	−	0.388828i
$364$	3.98527	+	6.90269i	0.208885	+	0.361799i
$365$	−40.0957			−2.09870
$366$	−10.9852	−	3.12121i	−0.574204	−	0.163148i
$367$	15.2039	−	26.3340i	0.793639	−	1.37462i	−0.130060	−	0.991506i	$-0.541517\pi$
$367$	15.2039	−	26.3340i	0.793639	−	1.37462i	0.923700	−	0.383117i	$-0.125150\pi$
$368$	5.20520			0.271340
$369$	7.06108	+	4.36489i	0.367585	+	0.227227i
$370$	0.858400	+	1.48679i	0.0446261	+	0.0772947i
$371$	1.45488	−	2.51992i	0.0755334	−	0.130828i
$372$	−14.0282	−	3.98581i	−0.727326	−	0.206654i
$373$	−5.07447	+	8.78925i	−0.262746	+	0.455090i	−0.966971	−	0.254887i	$-0.917962\pi$
$373$	−5.07447	+	8.78925i	−0.262746	+	0.455090i	0.704224	+	0.709977i	$0.251295\pi$
$374$	21.2138			1.09694
$375$	9.26376	+	36.7757i	0.478379	+	1.89909i
$376$	−3.56916	+	6.18197i	−0.184066	+	0.318811i
$377$	2.33424	−	4.04302i	0.120220	−	0.208226i
$378$	−3.22264	+	10.1688i	−0.165755	+	0.523027i
$379$	7.53375			0.386983			0.193491	−	0.981102i	$-0.438019\pi$
$379$	7.53375			0.386983			0.193491	+	0.981102i	$0.438019\pi$
$380$	−4.87696	−	16.4835i	−0.250183	−	0.845587i
$381$	4.31302	−	4.18525i	0.220963	−	0.214417i
$382$	1.88682	+	3.26807i	0.0965383	+	0.167209i
$383$	5.18388	+	8.97875i	0.264884	+	0.458793i	0.967533	−	0.252744i	$-0.0813330\pi$
$383$	5.18388	+	8.97875i	0.264884	+	0.458793i	−0.702649	+	0.711536i	$0.748000\pi$
$384$	−0.423085	−	1.67958i	−0.0215905	−	0.0857109i
$385$	41.7934			2.12999
$386$	8.11527	+	14.0561i	0.413056	+	0.715435i
$387$	4.42931	−	2.38267i	0.225154	−	0.121118i
$388$	−4.47521			−0.227194
$389$	19.0890	−	33.0631i	0.967849	−	1.67636i	0.266092	−	0.963948i	$-0.414268\pi$
$389$	19.0890	−	33.0631i	0.967849	−	1.67636i	0.701757	−	0.712416i	$-0.252399\pi$
$390$	−19.0323	+	18.4684i	−0.963737	+	0.935186i
$391$	−10.6951	+	18.5244i	−0.540873	+	0.936819i
$392$	−1.39278	+	2.41236i	−0.0703460	+	0.121843i
$393$	0.448053	−	0.434779i	0.0226013	−	0.0219317i
$394$	20.6274			1.03919
$395$	3.93834	+	6.82140i	0.198159	+	0.343222i
$396$	−13.1732	−	8.14315i	−0.661976	−	0.409209i
$397$	1.98523	−	3.43851i	0.0996357	−	0.172574i	−0.811898	−	0.583799i	$-0.801566\pi$
$397$	1.98523	−	3.43851i	0.0996357	−	0.172574i	0.911534	+	0.411225i	$0.134899\pi$
$398$	−3.22792	−	5.59093i	−0.161801	−	0.280248i
$399$	−13.3379	+	7.89446i	−0.667732	+	0.395217i
$400$	−5.27609	+	9.13846i	−0.263805	+	0.456923i
$401$	1.43491	+	2.48535i	0.0716562	+	0.124112i	0.899627	−	0.436659i	$-0.143838\pi$
$401$	1.43491	+	2.48535i	0.0716562	+	0.124112i	−0.827971	+	0.560771i	$0.810505\pi$
$402$	6.22726	+	24.7212i	0.310587	+	1.23298i
$403$	−16.3450	+	28.3104i	−0.814204	+	1.41024i
$404$	−2.15018	+	3.72421i	−0.106975	+	0.185286i
$405$	−35.4285	−	2.13311i	−1.76045	−	0.105995i
$406$	−2.46847			−0.122508
$407$	1.12366	+	1.94624i	0.0556980	+	0.0964717i
$408$	6.84665	+	1.94533i	0.338960	+	0.0963084i
$409$	−22.8271			−1.12873			−0.564364	−	0.825526i	$-0.690879\pi$
$409$	−22.8271			−1.12873			−0.564364	+	0.825526i	$0.690879\pi$
$410$	5.45618	−	9.45039i	0.269462	−	0.466721i
$411$	29.7057	+	8.44026i	1.46528	+	0.416328i
$412$	7.26626	−	12.5855i	0.357983	−	0.620044i
$413$	−14.8463	+	25.7146i	−0.730540	+	1.26533i
$414$	13.7521	−	7.39770i	0.675879	−	0.363577i
$415$	−10.3934	+	18.0019i	−0.510193	+	0.883680i
$416$	−3.88255			−0.190358
$417$	8.25952	+	32.7890i	0.404470	+	1.60568i
$418$	−6.38404	−	21.5773i	−0.312254	−	1.05538i
$419$	6.81387	−	11.8020i	0.332879	−	0.576564i	−0.650196	−	0.759767i	$-0.725313\pi$
$419$	6.81387	−	11.8020i	0.332879	−	0.576564i	0.983075	+	0.183203i	$0.0586465\pi$
$420$	13.4886	+	3.83251i	0.658178	+	0.187007i
$421$	−12.4518			−0.606861			−0.303431	−	0.952853i	$-0.598132\pi$
$421$	−12.4518			−0.606861			−0.303431	+	0.952853i	$0.598132\pi$
$422$	−0.202549	−	0.350825i	−0.00985992	−	0.0170779i
$423$	−0.643814	+	21.4053i	−0.0313033	+	1.04076i
$424$	0.708689	+	1.22749i	0.0344170	+	0.0596120i
$425$	−21.6815	−	37.5534i	−1.05171	−	1.82161i
$426$	7.35715	+	2.09038i	0.356455	+	0.101279i
$427$	13.5355			0.655029
$428$	−2.11280			−0.102126
$429$	−24.9137	+	24.1756i	−1.20284	+	1.16721i
$430$	−3.30574	−	5.72572i	−0.159417	−	0.276119i
$431$	−12.6070	−	21.8359i	−0.607256	−	1.05180i	−0.991691	−	0.128646i	$-0.958937\pi$
$431$	−12.6070	−	21.8359i	−0.607256	−	1.05180i	0.384435	−	0.923152i	$-0.374396\pi$
$432$	−3.50484	−	3.83616i	−0.168627	−	0.184567i
$433$	−10.0557	−	17.4169i	−0.483244	−	0.837003i	0.516571	−	0.856244i	$-0.327208\pi$
$433$	−10.0557	−	17.4169i	−0.483244	−	0.837003i	−0.999815	+	0.0192414i	$0.993875\pi$
$434$	17.2850			0.829704
$435$	−2.00624	−	7.96444i	−0.0961916	−	0.381866i
$436$	4.80520	−	8.32285i	0.230127	−	0.398592i
$437$	22.0603	+	5.30362i	1.05529	+	0.253707i
$438$	−16.9396	−	4.81304i	−0.809407	−	0.229976i
$439$	−12.6374			−0.603150			−0.301575	−	0.953442i	$-0.597512\pi$
$439$	−12.6374			−0.603150			−0.301575	+	0.953442i	$0.597512\pi$
$440$	−10.1791	+	17.6307i	−0.485268	+	0.840509i
$441$	−0.251233	+	8.35290i	−0.0119635	+	0.397757i
$442$	7.97744	−	13.8173i	0.379448	−	0.657224i
$443$	11.0306	−	19.1056i	0.524080	−	0.907734i	−0.475527	−	0.879701i	$-0.657743\pi$
$443$	11.0306	−	19.1056i	0.524080	−	0.907734i	0.999607	−	0.0280323i	$-0.00892412\pi$
$444$	0.184184	+	0.731182i	0.00874099	+	0.0347004i
$445$	−3.22415	+	5.58438i	−0.152839	+	0.264725i
$446$	8.40880			0.398168
$447$	−23.3169	+	22.6262i	−1.10285	+	1.07018i
$448$	1.02646	+	1.77787i	0.0484955	+	0.0839966i
$449$	32.2058			1.51988			0.759942	−	0.649990i	$-0.225227\pi$
$449$	32.2058			1.51988			0.759942	+	0.649990i	$0.225227\pi$
$450$	−0.951713	+	31.6422i	−0.0448642	+	1.49163i
$451$	7.14226	−	12.3708i	0.336316	−	0.582516i
$452$	−3.49351	+	6.05094i	−0.164321	+	0.284612i
$453$	6.98097	−	6.77416i	0.327995	−	0.318278i
$454$	−0.146997	−	0.254607i	−0.00689893	−	0.0119493i
$455$	15.7164	−	27.2216i	0.736796	−	1.27617i
$456$	−0.0817523	−	7.54939i	−0.00382840	−	0.353533i
$457$	0.903329	+	1.56461i	0.0422559	+	0.0731894i	0.886380	−	0.462959i	$-0.153212\pi$
$457$	0.903329	+	1.56461i	0.0422559	+	0.0731894i	−0.844124	+	0.536148i	$0.819879\pi$
$458$	3.61171	−	6.25566i	0.168764	−	0.292308i
$459$	20.8536	−	4.59100i	0.973362	−	0.214289i
$460$	−10.2637	−	17.7772i	−0.478546	−	0.828866i
$461$	−23.5186			−1.09537			−0.547686	−	0.836684i	$-0.684491\pi$
$461$	−23.5186			−1.09537			−0.547686	+	0.836684i	$0.684491\pi$
$462$	17.6569	+	5.01684i	0.821474	+	0.233405i
$463$	10.1793	−	17.6310i	0.473071	−	0.819382i	−0.526454	−	0.850203i	$-0.676479\pi$
$463$	10.1793	−	17.6310i	0.473071	−	0.819382i	0.999525	+	0.0308210i	$0.00981219\pi$
$464$	0.601213	−	1.04133i	0.0279106	−	0.0483426i
$465$	14.0482	+	55.7693i	0.651472	+	2.58624i
$466$	−9.39739	+	16.2768i	−0.435326	+	0.754007i
$467$	22.2721			1.03063			0.515316	−	0.857000i	$-0.327675\pi$
$467$	22.2721			1.03063			0.515316	+	0.857000i	$0.327675\pi$
$468$	−10.2577	+	5.51794i	−0.474162	+	0.255067i
$469$	−15.1081	−	26.1679i	−0.697626	−	1.20832i
$470$	28.1509			1.29850
$471$	−15.0069	+	14.5624i	−0.691484	+	0.670998i
$472$	−7.23184	−	12.5259i	−0.332872	−	0.576552i
$473$	−4.32729	−	7.49509i	−0.198969	−	0.344624i
$474$	0.845037	+	3.35466i	0.0388138	+	0.154085i
$475$	−31.6721	+	33.3542i	−1.45321	+	1.53040i
$476$	−8.43619			−0.386672
$477$	3.61688	+	2.23582i	0.165605	+	0.102371i
$478$	1.67306	−	2.89782i	0.0765238	−	0.132543i
$479$	−6.26933	+	10.8588i	−0.286453	+	0.496151i	−0.972961	−	0.230971i	$-0.925810\pi$
$479$	−6.26933	+	10.8588i	−0.286453	+	0.496151i	0.686507	+	0.727123i	$0.259143\pi$
$480$	−4.90200	+	4.75678i	−0.223745	+	0.217116i
$481$	1.69021			0.0770671
$482$	−0.623776	+	1.08041i	−0.0284122	+	0.0492114i
$483$	−13.2827	+	12.8892i	−0.604382	+	0.586477i
$484$	−7.82462	+	13.5526i	−0.355664	+	0.616029i
$485$	8.82427	+	15.2841i	0.400690	+	0.694015i
$486$	−14.7118	−	5.15400i	−0.667340	−	0.233790i
$487$	−3.92089			−0.177672			−0.0888362	−	0.996046i	$-0.528315\pi$
$487$	−3.92089			−0.177672			−0.0888362	+	0.996046i	$0.528315\pi$
$488$	−3.29666	+	5.70999i	−0.149233	+	0.258479i
$489$	−4.87413	−	19.3495i	−0.220416	−	0.875016i
$490$	10.9852			0.496261
$491$	7.38534	+	12.7918i	0.333296	+	0.577285i	0.983156	−	0.182769i	$-0.0585060\pi$
$491$	7.38534	+	12.7918i	0.333296	+	0.577285i	−0.649860	+	0.760054i	$0.725173\pi$
$492$	3.43954	−	3.33765i	0.155067	−	0.150473i
$493$	2.47061	+	4.27922i	0.111271	+	0.192727i
$494$	−16.4548	−	3.95597i	−0.740337	−	0.177988i
$495$	−1.83612	+	61.0468i	−0.0825276	+	2.74385i
$496$	−4.20987	+	7.29170i	−0.189029	+	0.327407i
$497$	−9.06521			−0.406630
$498$	−6.55195	+	6.35785i	−0.293600	+	0.284902i
$499$	−14.4177	−	24.9723i	−0.645427	−	1.11791i	−0.984203	−	0.177045i	$-0.943346\pi$
$499$	−14.4177	−	24.9723i	−0.645427	−	1.11791i	0.338776	−	0.940867i	$-0.389987\pi$
$500$	21.8957			0.979207
$501$	−7.93008	−	31.4812i	−0.354290	−	1.40648i
$502$	−2.56602	−	4.44447i	−0.114527	−	0.198366i
$503$	14.8533	+	25.7266i	0.662275	+	1.14709i	0.980016	+	0.198917i	$0.0637423\pi$
$503$	14.8533	+	25.7266i	0.662275	+	1.14709i	−0.317741	+	0.948177i	$0.602924\pi$
$504$	5.23863	+	3.23832i	0.233347	+	0.144246i
$505$	16.9590			0.754664
$506$	−13.4354	−	23.2707i	−0.597275	−	1.03451i
$507$	0.877574	+	3.48383i	0.0389744	+	0.154722i
$508$	−1.73490	−	3.00493i	−0.0769737	−	0.133322i
$509$	41.1086			1.82211			0.911053	−	0.412290i	$-0.135271\pi$
$509$	41.1086			1.82211			0.911053	+	0.412290i	$0.135271\pi$
$510$	−6.85646	−	27.2191i	−0.303609	−	1.20528i
$511$	20.8724			0.923340
$512$	−1.00000			−0.0441942
$513$	−10.9453	−	19.8293i	−0.483246	−	0.875484i
$514$	−14.2660			−0.629245
$515$	−57.3108			−2.52541
$516$	−0.709303	−	2.81582i	−0.0312253	−	0.123960i
$517$	36.8501			1.62067
$518$	−0.446852	−	0.773971i	−0.0196336	−	0.0340063i
$519$	−0.612425	−	2.43123i	−0.0268825	−	0.106719i
$520$	7.65567	+	13.2600i	0.335723	+	0.581490i
$521$	24.1264			1.05700			0.528499	−	0.848934i	$-0.322755\pi$
$521$	24.1264			1.05700			0.528499	+	0.848934i	$0.322755\pi$
$522$	0.108448	−	3.60565i	0.00474664	−	0.157815i
$523$	20.8795	+	36.1644i	0.912998	+	1.58136i	0.809806	+	0.586697i	$0.199572\pi$
$523$	20.8795	+	36.1644i	0.912998	+	1.58136i	0.103191	+	0.994662i	$0.467095\pi$
$524$	−0.180228	−	0.312163i	−0.00787328	−	0.0136369i
$525$	−9.16517	−	36.3843i	−0.400001	−	1.58794i
$526$	−0.503455			−0.0219517
$527$	−17.2999	−	29.9644i	−0.753597	−	1.30527i
$528$	−6.41682	+	6.22672i	−0.279256	+	0.270983i
$529$	4.09406			0.178003
$530$	2.79481	−	4.84074i	0.121399	−	0.210268i
$531$	−36.9085	−	22.8154i	−1.60169	−	0.990106i
$532$	2.53877	+	8.58074i	0.110070	+	0.372022i
$533$	−5.37169	−	9.30404i	−0.232674	−	0.403003i
$534$	−2.03248	+	1.97227i	−0.0879541	+	0.0853484i
$535$	4.16605	+	7.21581i	0.180114	+	0.311967i
$536$	14.7187			0.635750
$537$	0.556018	+	2.20731i	0.0239940	+	0.0952523i
$538$	−2.90769	+	5.03628i	−0.125360	+	0.217129i
$539$	14.3799			0.619384
$540$	−6.19067	+	19.5342i	−0.266404	+	0.840618i
$541$	−7.32270	−	12.6833i	−0.314828	−	0.545297i	0.664573	−	0.747223i	$-0.268613\pi$
$541$	−7.32270	−	12.6833i	−0.314828	−	0.545297i	−0.979401	+	0.201926i	$0.935280\pi$
$542$	−16.2151	+	28.0854i	−0.696498	+	1.20637i
$543$	13.3140	−	12.9196i	0.571360	−	0.554433i
$544$	2.05469	−	3.55883i	0.0880941	−	0.152583i
$545$	−37.8998			−1.62345
$546$	9.90753	−	9.61401i	0.424003	−	0.411442i
$547$	17.8980	−	31.0003i	0.765265	−	1.32548i	−0.174842	−	0.984597i	$-0.555941\pi$
$547$	17.8980	−	31.0003i	0.765265	−	1.32548i	0.940106	−	0.340881i	$-0.110725\pi$
$548$	8.91473	−	15.4408i	0.380818	−	0.659597i
$549$	−0.594659	+	19.7710i	−0.0253794	+	0.843807i
$550$	54.4734			2.32275
$551$	3.60905	−	3.80073i	0.153751	−	0.161916i
$552$	−2.20224	−	8.74256i	−0.0937337	−	0.372108i
$553$	−2.05016	−	3.55098i	−0.0871816	−	0.151003i
$554$	−9.88182	−	17.1158i	−0.419838	−	0.727181i
$555$	2.13401	−	2.07079i	0.0905839	−	0.0879003i
$556$	19.5221			0.827922
$557$	−4.75137	−	8.22962i	−0.201322	−	0.348700i	0.747633	−	0.664113i	$-0.231190\pi$
$557$	−4.75137	−	8.22962i	−0.201322	−	0.348700i	−0.948955	+	0.315413i	$0.897857\pi$
$558$	−0.759385	+	25.2478i	−0.0321473	+	1.06882i
$559$	−6.50910			−0.275306
$560$	4.04796	−	7.01126i	0.171057	−	0.296280i
$561$	−8.97525	−	35.6303i	−0.378936	−	1.50431i
$562$	12.2654	−	21.2443i	0.517385	−	0.896137i
$563$	−14.2685	+	24.7138i	−0.601346	+	1.04156i	0.391272	+	0.920275i	$0.372035\pi$
$563$	−14.2685	+	24.7138i	−0.601346	+	1.04156i	−0.992618	+	0.121286i	$0.961298\pi$
$564$	11.8932	+	3.37920i	0.500794	+	0.142290i
$565$	27.5542			1.15921
$566$	−1.37132	−	2.37519i	−0.0576407	−	0.0998366i
$567$	18.4428	+	1.11042i	0.774525	+	0.0466334i
$568$	2.20789	−	3.82418i	0.0926411	−	0.160459i
$569$	−5.24159	−	9.07869i	−0.219739	−	0.380599i	0.734989	−	0.678079i	$-0.237187\pi$
$569$	−5.24159	−	9.07869i	−0.219739	−	0.380599i	−0.954728	+	0.297480i	$0.903854\pi$
$570$	−25.6221	+	15.1652i	−1.07319	+	0.635200i
$571$	−9.32650	+	16.1540i	−0.390302	+	0.676022i	−0.992489	−	0.122332i	$-0.960963\pi$
$571$	−9.32650	+	16.1540i	−0.390302	+	0.676022i	0.602187	+	0.798355i	$0.294296\pi$
$572$	10.0214	+	17.3576i	0.419017	+	0.725759i
$573$	4.69071	−	4.55175i	0.195957	−	0.190152i
$574$	−2.84029	+	4.91953i	−0.118552	+	0.205337i
$575$	−27.4631	+	47.5675i	−1.14529	+	1.98370i
$576$	−2.64200	+	1.42121i	−0.110083	+	0.0592173i
$577$	34.6202			1.44126			0.720628	−	0.693322i	$-0.243853\pi$
$577$	34.6202			1.44126			0.720628	+	0.693322i	$0.243853\pi$
$578$	−0.0565005	−	0.0978617i	−0.00235011	−	0.00407051i
$579$	20.1749	−	19.5772i	0.838439	−	0.813600i
$580$	−4.74192			−0.196897
$581$	5.41045	−	9.37117i	0.224463	−	0.388782i
$582$	1.89340	+	7.51648i	0.0784838	+	0.311568i
$583$	3.65846	−	6.33664i	0.151518	−	0.262437i
$584$	−5.08361	+	8.80507i	−0.210361	+	0.364356i
$585$	39.0716	+	24.1526i	1.61541	+	0.998585i
$586$	−15.1403	+	26.2237i	−0.625439	+	1.08329i
$587$	−14.0304			−0.579098			−0.289549	−	0.957163i	$-0.593505\pi$
$587$	−14.0304			−0.579098			−0.289549	+	0.957163i	$0.593505\pi$
$588$	4.64103	+	1.31865i	0.191393	+	0.0543803i
$589$	−25.2716	+	26.6138i	−1.04130	+	1.09660i
$590$	−28.5197	+	49.3975i	−1.17414	+	2.03366i
$591$	−8.72716	−	34.6455i	−0.358987	−	1.42512i
$592$	0.435335			0.0178922
$593$	−11.3497	−	19.6582i	−0.466075	−	0.807266i	0.533174	−	0.846006i	$-0.320999\pi$
$593$	−11.3497	−	19.6582i	−0.466075	−	0.807266i	−0.999249	+	0.0387394i	$0.987666\pi$
$594$	−8.10372	+	25.5707i	−0.332500	+	1.04918i
$595$	16.6346	+	28.8119i	0.681951	+	1.18117i
$596$	9.37916	+	16.2452i	0.384185	+	0.665429i
$597$	−8.02474	+	7.78700i	−0.328431	+	0.318701i
$598$	−20.2095			−0.826426
$599$	9.50546			0.388383			0.194191	−	0.980964i	$-0.437792\pi$
$599$	9.50546			0.388383			0.194191	+	0.980964i	$0.437792\pi$
$600$	17.5810	+	4.99528i	0.717743	+	0.203932i
$601$	9.68287	+	16.7712i	0.394973	+	0.684113i	0.993098	−	0.117290i	$-0.0374208\pi$
$601$	9.68287	+	16.7712i	0.394973	+	0.684113i	−0.598125	+	0.801403i	$0.704087\pi$
$602$	1.72085	+	2.98060i	0.0701367	+	0.121480i
$603$	38.8867	−	20.9184i	1.58359	−	0.851863i
$604$	−2.80807	−	4.86372i	−0.114259	−	0.197902i
$605$	61.7147			2.50906
$606$	7.16483	+	2.03574i	0.291051	+	0.0826962i
$607$	−4.51935	+	7.82774i	−0.183435	+	0.317718i	−0.943048	−	0.332657i	$-0.892055\pi$
$607$	−4.51935	+	7.82774i	−0.183435	+	0.317718i	0.759613	+	0.650375i	$0.225388\pi$
$608$	−4.23814	−	1.01891i	−0.171879	−	0.0413222i
$609$	1.04437	+	4.14600i	0.0423202	+	0.168005i
$610$	26.0016			1.05277
$611$	13.8575	−	24.0018i	0.560613	−	0.971011i
$612$	0.370629	−	12.3226i	0.0149818	−	0.498110i
$613$	−2.58989	+	4.48582i	−0.104605	+	0.181181i	−0.913577	−	0.406667i	$-0.866691\pi$
$613$	−2.58989	+	4.48582i	−0.104605	+	0.181181i	0.808972	+	0.587847i	$0.200024\pi$
$614$	8.15255	−	14.1206i	0.329010	−	0.569862i
$615$	−18.1811	−	5.16579i	−0.733134	−	0.208305i
$616$	5.29886	−	9.17789i	0.213497	−	0.369788i
$617$	−23.1584			−0.932323			−0.466161	−	0.884700i	$-0.654363\pi$
$617$	−23.1584			−0.932323			−0.466161	+	0.884700i	$0.654363\pi$
$618$	−24.2127	−	6.87953i	−0.973977	−	0.276735i
$619$	5.07677	+	8.79323i	0.204053	+	0.353430i	0.949830	−	0.312765i	$-0.101255\pi$
$619$	5.07677	+	8.79323i	0.204053	+	0.353430i	−0.745778	+	0.666195i	$0.767922\pi$
$620$	33.2043			1.33352
$621$	−18.2434	−	19.9680i	−0.732081	−	0.801286i
$622$	−13.3270	+	23.0831i	−0.534365	+	0.925548i
$623$	1.67837	−	2.90703i	0.0672427	−	0.116468i
$624$	1.64265	+	6.52107i	0.0657587	+	0.261052i
$625$	−16.7938	−	29.0877i	−0.671753	−	1.16351i
$626$	8.99013	−	15.5714i	0.359318	−	0.622357i
$627$	−33.5399	+	19.8516i	−1.33945	+	0.792795i
$628$	6.03649	+	10.4555i	0.240882	+	0.417220i
$629$	−0.894479	+	1.54928i	−0.0356652	+	0.0617740i
$630$	0.730179	−	24.2768i	0.0290910	−	0.967209i
$631$	9.75519	+	16.8965i	0.388348	+	0.672638i	0.992227	−	0.124437i	$-0.0397126\pi$
$631$	9.75519	+	16.8965i	0.388348	+	0.672638i	−0.603880	+	0.797076i	$0.706379\pi$
$632$	1.99732			0.0794491
$633$	−0.503544	+	0.488626i	−0.0200141	+	0.0194212i
$634$	8.32463	−	14.4187i	0.330613	−	0.572639i
$635$	−6.84179	+	11.8503i	−0.271508	+	0.470266i
$636$	1.76183	−	1.70963i	0.0698610	−	0.0677914i
$637$	5.40754	−	9.36613i	0.214255	−	0.371100i
$638$	−6.20727			−0.245748
$639$	0.398264	−	13.2414i	0.0157551	−	0.523820i
$640$	1.97181	+	3.41528i	0.0779427	+	0.135001i
$641$	−31.9179			−1.26068			−0.630341	−	0.776319i	$-0.717085\pi$
$641$	−31.9179			−1.26068			−0.630341	+	0.776319i	$0.717085\pi$
$642$	0.893895	+	3.54862i	0.0352792	+	0.140053i
$643$	11.1183	+	19.2574i	0.438461	+	0.759437i	0.997571	−	0.0696566i	$-0.0221904\pi$
$643$	11.1183	+	19.2574i	0.438461	+	0.759437i	−0.559110	+	0.829094i	$0.688857\pi$
$644$	5.34290	+	9.25418i	0.210540	+	0.364666i
$645$	−8.21821	+	7.97474i	−0.323592	+	0.314005i
$646$	12.3342	−	12.9893i	0.485282	−	0.511056i
$647$	28.7608			1.13070			0.565352	−	0.824850i	$-0.308740\pi$
$647$	28.7608			1.13070			0.565352	+	0.824850i	$0.308740\pi$
$648$	−4.96030	+	7.50969i	−0.194859	+	0.295008i
$649$	−37.3329	+	64.6624i	−1.46544	+	2.53822i
$650$	20.4847	−	35.4806i	0.803476	−	1.39166i
$651$	−7.31301	−	29.0315i	−0.286620	−	1.13783i
$652$	−11.5204			−0.451175
$653$	−14.1756	+	24.5528i	−0.554733	+	0.960826i	0.443191	+	0.896427i	$0.353846\pi$
$653$	−14.1756	+	24.5528i	−0.554733	+	0.960826i	−0.997924	+	0.0643991i	$0.979487\pi$
$654$	−16.0119	−	4.54945i	−0.626116	−	0.177898i
$655$	−0.710750	+	1.23106i	−0.0277713	+	0.0481013i
$656$	−1.38355	−	2.39637i	−0.0540184	−	0.0935625i
$657$	−0.916992	+	30.4879i	−0.0357753	+	1.18944i
$658$	−14.6543			−0.571286
$659$	−2.67015	+	4.62483i	−0.104014	+	0.180158i	−0.913335	−	0.407209i	$-0.866502\pi$
$659$	−2.67015	+	4.62483i	−0.104014	+	0.180158i	0.809321	+	0.587367i	$0.199835\pi$
$660$	33.9188	+	9.63731i	1.32029	+	0.375132i
$661$	17.1940			0.668770			0.334385	−	0.942436i	$-0.391471\pi$
$661$	17.1940			0.668770			0.334385	+	0.942436i	$0.391471\pi$
$662$	−0.156160	−	0.270477i	−0.00606933	−	0.0105124i
$663$	−26.5825	−	7.55286i	−1.03238	−	0.293329i
$664$	2.63550	+	4.56482i	0.102277	+	0.177149i
$665$	24.2996	−	25.5902i	0.942300	−	0.992346i
$666$	1.15016	−	0.618705i	0.0445676	−	0.0239743i
$667$	3.12943	−	5.42033i	0.121172	−	0.209876i
$668$	−18.7434			−0.725206
$669$	−3.55764	−	14.1233i	−0.137546	−	0.546037i
$670$	−29.0225	−	50.2684i	−1.12124	−	1.94204i
$671$	34.0367			1.31397
$672$	2.55181	−	2.47621i	0.0984381	−	0.0955218i
$673$	−16.6703	−	28.8738i	−0.642594	−	1.11300i	−0.984852	−	0.173399i	$-0.944525\pi$
$673$	−16.6703	−	28.8738i	−0.642594	−	1.11300i	0.342258	−	0.939606i	$-0.388808\pi$
$674$	9.23379	+	15.9934i	0.355672	+	0.616043i
$675$	53.5484	−	11.7889i	2.06108	−	0.453755i
$676$	2.07422			0.0797779
$677$	−5.50556	−	9.53591i	−0.211596	−	0.366495i	0.740618	−	0.671926i	$-0.234533\pi$
$677$	−5.50556	−	9.53591i	−0.211596	−	0.366495i	−0.952214	+	0.305431i	$0.901199\pi$
$678$	11.6411	+	3.30758i	0.447074	+	0.127027i
$679$	−4.59360	−	7.95635i	−0.176286	−	0.305337i
$680$	−16.2059			−0.621466
$681$	−0.365441	+	0.354615i	−0.0140037	+	0.0135889i
$682$	43.4651			1.66436
$683$	−1.26949			−0.0485758			−0.0242879	−	0.999705i	$-0.507732\pi$
$683$	−1.26949			−0.0485758			−0.0242879	+	0.999705i	$0.507732\pi$
$684$	−12.6452	+	3.33135i	−0.483503	+	0.127377i
$685$	−70.3127			−2.68651
$686$	−20.0889			−0.766997
$687$	−12.0350	−	3.41948i	−0.459163	−	0.130461i
$688$	−1.67650			−0.0639160
$689$	−2.75152	−	4.76578i	−0.104825	−	0.181562i
$690$	−25.5159	+	24.7600i	−0.971373	+	0.942596i
$691$	5.66777	+	9.81687i	0.215612	+	0.373451i	0.953462	−	0.301514i	$-0.0974919\pi$
$691$	5.66777	+	9.81687i	0.215612	+	0.373451i	−0.737850	+	0.674965i	$0.764159\pi$
$692$	−1.44752			−0.0550265
$693$	0.955820	−	31.7788i	0.0363086	−	1.20718i
$694$	3.56809	+	6.18011i	0.135443	+	0.234594i
$695$	−38.4939	−	66.6735i	−1.46016	−	2.52907i
$696$	−2.00337	−	0.569215i	−0.0759374	−	0.0215760i
$697$	11.3710			0.430708
$698$	−6.45792	−	11.1854i	−0.244436	−	0.423375i
$699$	31.3141	+	8.89724i	1.18441	+	0.336525i
$700$	−21.6627			−0.818773
$701$	−4.81374	+	8.33765i	−0.181813	+	0.314909i	−0.942498	−	0.334212i	$-0.891530\pi$
$701$	−4.81374	+	8.33765i	−0.181813	+	0.314909i	0.760685	+	0.649121i	$0.224863\pi$
$702$	13.6077	+	14.8941i	0.513590	+	0.562141i
$703$	1.84501	+	0.443567i	0.0695860	+	0.0167295i
$704$	2.58114	+	4.47067i	0.0972806	+	0.168495i
$705$	−11.9102	−	47.2817i	−0.448565	−	1.78073i
$706$	13.1427	+	22.7639i	0.494634	+	0.856731i
$707$	−8.82823			−0.332020
$708$	−17.9786	+	17.4460i	−0.675678	+	0.655661i
$709$	−16.9892	+	29.4262i	−0.638043	+	1.10512i	0.347819	+	0.937562i	$0.386922\pi$
$709$	−16.9892	+	29.4262i	−0.638043	+	1.10512i	−0.985862	+	0.167561i	$0.946411\pi$
$710$	−17.4142			−0.653543
$711$	5.27691	−	2.83862i	0.197900	−	0.106457i
$712$	0.817559	+	1.41605i	0.0306393	+	0.0530688i
$713$	−21.9132	+	37.9547i	−0.820655	+	1.42142i
$714$	3.56923	+	14.1693i	0.133575	+	0.530272i
$715$	39.5208	−	68.4520i	1.47799	−	2.55996i
$716$	1.31420			0.0491139
$717$	−5.57497	−	1.58401i	−0.208201	−	0.0591560i
$718$	−7.54249	+	13.0640i	−0.281483	+	0.487543i
$719$	−12.7403	+	22.0668i	−0.475132	+	0.822952i	−0.999594	−	0.0284813i	$-0.990933\pi$
$719$	−12.7403	+	22.0668i	−0.475132	+	0.822952i	0.524463	+	0.851433i	$0.324266\pi$
$720$	10.0634	+	6.22079i	0.375040	+	0.231835i
$721$	29.8339			1.11107
$722$	−16.9236	−	8.63656i	−0.629833	−	0.321419i
$723$	2.07855	+	0.590577i	0.0773022	+	0.0219638i
$724$	−5.35552	−	9.27604i	−0.199036	−	0.344741i
$725$	6.34411	+	10.9883i	0.235614	+	0.408096i
$726$	26.0733	+	7.40817i	0.967669	+	0.274943i
$727$	−30.1315			−1.11752			−0.558758	−	0.829331i	$-0.688722\pi$
$727$	−30.1315			−1.11752			−0.558758	+	0.829331i	$0.688722\pi$
$728$	−3.98527	−	6.90269i	−0.147704	−	0.255831i
$729$	−2.43223	+	26.8902i	−0.0900824	+	0.995934i
$730$	40.0957			1.48401
$731$	3.44469	−	5.96638i	0.127406	−	0.220674i
$732$	10.9852	+	3.12121i	0.406023	+	0.115363i
$733$	−22.4900	+	38.9539i	−0.830688	+	1.43879i	0.0668058	+	0.997766i	$0.478719\pi$
$733$	−22.4900	+	38.9539i	−0.830688	+	1.43879i	−0.897494	+	0.441028i	$0.854614\pi$
$734$	−15.2039	+	26.3340i	−0.561188	+	0.972006i
$735$	−4.64768	−	18.4506i	−0.171432	−	0.680559i
$736$	−5.20520			−0.191866
$737$	−37.9910	−	65.8024i	−1.39942	−	2.42386i
$738$	−7.06108	−	4.36489i	−0.259922	−	0.160674i
$739$	2.68302	−	4.64713i	0.0986965	−	0.170947i	−0.812449	−	0.583032i	$-0.801866\pi$
$739$	2.68302	−	4.64713i	0.0986965	−	0.170947i	0.911145	+	0.412085i	$0.135199\pi$
$740$	−0.858400	−	1.48679i	−0.0315554	−	0.0546556i
$741$	0.317408	+	29.3109i	0.0116603	+	1.07676i
$742$	−1.45488	+	2.51992i	−0.0534102	+	0.0925091i
$743$	−9.69665	−	16.7951i	−0.355735	−	0.616152i	0.631508	−	0.775369i	$-0.282436\pi$
$743$	−9.69665	−	16.7951i	−0.355735	−	0.616152i	−0.987244	+	0.159217i	$0.949103\pi$
$744$	14.0282	+	3.98581i	0.514297	+	0.146127i
$745$	36.9879	−	64.0649i	1.35513	−	2.34716i
$746$	5.07447	−	8.78925i	0.185790	−	0.321797i
$747$	13.4506	+	8.31463i	0.492131	+	0.304216i
$748$	−21.2138			−0.775654
$749$	−2.16870	−	3.75629i	−0.0792424	−	0.137252i
$750$	−9.26376	−	36.7757i	−0.338265	−	1.34286i
$751$	−28.9447			−1.05621			−0.528104	−	0.849180i	$-0.677097\pi$
$751$	−28.9447			−1.05621			−0.528104	+	0.849180i	$0.677097\pi$
$752$	3.56916	−	6.18197i	0.130154	−	0.225433i
$753$	−6.37921	+	6.19023i	−0.232471	+	0.225584i
$754$	−2.33424	+	4.04302i	−0.0850081	+	0.147238i
$755$	−11.0740	+	19.1807i	−0.403024	+	0.698057i
$756$	3.22264	−	10.1688i	0.117206	−	0.369836i
$757$	18.7844	−	32.5355i	0.682729	−	1.18252i	−0.291415	−	0.956597i	$-0.594126\pi$
$757$	18.7844	−	32.5355i	0.682729	−	1.18252i	0.974145	−	0.225925i	$-0.0725405\pi$
$758$	−7.53375			−0.273638
$759$	−33.4008	+	32.4113i	−1.21237	+	1.17646i
$760$	4.87696	+	16.4835i	0.176906	+	0.597920i
$761$	5.50420	−	9.53355i	0.199527	−	0.345591i	−0.748848	−	0.662742i	$-0.769393\pi$
$761$	5.50420	−	9.53355i	0.199527	−	0.345591i	0.948375	+	0.317151i	$0.102726\pi$
$762$	−4.31302	+	4.18525i	−0.156244	+	0.151616i
$763$	19.7293			0.714248
$764$	−1.88682	−	3.26807i	−0.0682629	−	0.118235i
$765$	−42.8158	+	23.0320i	−1.54801	+	0.832723i
$766$	−5.18388	−	8.97875i	−0.187301	−	0.324415i
$767$	28.0780	+	48.6325i	1.01384	+	1.75602i
$768$	0.423085	+	1.67958i	0.0152668	+	0.0606067i
$769$	−45.9406			−1.65666			−0.828331	−	0.560239i	$-0.810709\pi$
$769$	−45.9406			−1.65666			−0.828331	+	0.560239i	$0.810709\pi$
$770$	−41.7934			−1.50613
$771$	6.03573	+	23.9609i	0.217371	+	0.862930i
$772$	−8.11527	−	14.0561i	−0.292075	−	0.505889i
$773$	−3.45316	−	5.98106i	−0.124202	−	0.215124i	0.797219	−	0.603690i	$-0.206304\pi$
$773$	−3.45316	−	5.98106i	−0.124202	−	0.215124i	−0.921421	+	0.388567i	$0.872970\pi$
$774$	−4.42931	+	2.38267i	−0.159208	+	0.0856432i
$775$	−44.4233	−	76.9434i	−1.59573	−	2.76389i
$776$	4.47521			0.160651
$777$	−1.11089	+	1.07798i	−0.0398530	+	0.0386724i
$778$	−19.0890	+	33.0631i	−0.684373	+	1.18537i
$779$	−3.42197	−	11.5659i	−0.122605	−	0.414390i
$780$	19.0323	−	18.4684i	0.681465	−	0.661276i
$781$	−22.7955			−0.815689
$782$	10.6951	−	18.5244i	0.382455	−	0.662431i
$783$	−6.10186	+	1.34335i	−0.218063	+	0.0480074i
$784$	1.39278	−	2.41236i	0.0497421	−	0.0861559i
$785$	23.8057	−	41.2326i	0.849661	−	1.47166i
$786$	−0.448053	+	0.434779i	−0.0159815	+	0.0155081i
$787$	6.00458	−	10.4002i	0.214040	−	0.370728i	−0.738935	−	0.673777i	$-0.764671\pi$
$787$	6.00458	−	10.4002i	0.214040	−	0.370728i	0.952975	+	0.303048i	$0.0980044\pi$
$788$	−20.6274			−0.734821
$789$	0.213004	+	0.845594i	0.00758316	+	0.0301040i
$790$	−3.93834	−	6.82140i	−0.140120	−	0.242695i
$791$	−14.3437			−0.510005
$792$	13.1732	+	8.14315i	0.468088	+	0.289354i
$793$	12.7995	−	22.1693i	0.454522	−	0.787256i
$794$	−1.98523	+	3.43851i	−0.0704531	+	0.122028i
$795$	−9.31287	−	2.64606i	−0.330294	−	0.0938460i
$796$	3.22792	+	5.59093i	0.114411	+	0.198165i
$797$	15.3351	−	26.5611i	0.543195	−	0.940842i	−0.455523	−	0.890224i	$-0.650548\pi$
$797$	15.3351	−	26.5611i	0.543195	−	0.940842i	0.998718	−	0.0506179i	$-0.0161191\pi$
$798$	13.3379	−	7.89446i	0.472158	−	0.279461i
$799$	14.6670	+	25.4041i	0.518883	+	0.898731i
$800$	5.27609	−	9.13846i	0.186538	−	0.323093i
$801$	4.17250	+	2.57928i	0.147428	+	0.0911345i
$802$	−1.43491	−	2.48535i	−0.0506686	−	0.0877606i
$803$	52.4861			1.85219
$804$	−6.22726	−	24.7212i	−0.219618	−	0.871851i
$805$	21.0704	−	36.4950i	0.742634	−	1.28628i
$806$	16.3450	−	28.3104i	0.575729	−	0.997192i
$807$	9.68905	+	2.75294i	0.341071	+	0.0969081i
$808$	2.15018	−	3.72421i	0.0756429	−	0.131017i
$809$	25.7750			0.906200			0.453100	−	0.891460i	$-0.350318\pi$
$809$	25.7750			0.906200			0.453100	+	0.891460i	$0.350318\pi$
$810$	35.4285	+	2.13311i	1.24483	+	0.0749500i
$811$	21.5979	+	37.4087i	0.758406	+	1.31360i	0.943663	+	0.330908i	$0.107355\pi$
$811$	21.5979	+	37.4087i	0.758406	+	1.31360i	−0.185257	+	0.982690i	$0.559312\pi$
$812$	2.46847			0.0866264
$813$	54.0321	+	15.3521i	1.89499	+	0.538421i
$814$	−1.12366	−	1.94624i	−0.0393844	−	0.0682158i
$815$	22.7162	+	39.3455i	0.795712	+	1.37821i
$816$	−6.84665	−	1.94533i	−0.239681	−	0.0681003i
$817$	−7.10524	−	1.70820i	−0.248581	−	0.0597624i
$818$	22.8271			0.798132
$819$	−20.3393	−	12.5730i	−0.710711	−	0.439335i
$820$	−5.45618	+	9.45039i	−0.190538	+	0.330022i
$821$	−10.1942	+	17.6569i	−0.355781	+	0.616230i	−0.987251	−	0.159169i	$-0.949118\pi$
$821$	−10.1942	+	17.6569i	−0.355781	+	0.616230i	0.631470	+	0.775400i	$0.282452\pi$
$822$	−29.7057	−	8.44026i	−1.03611	−	0.294388i
$823$	19.1037			0.665911			0.332956	−	0.942942i	$-0.391954\pi$
$823$	19.1037			0.665911			0.332956	+	0.942942i	$0.391954\pi$
$824$	−7.26626	+	12.5855i	−0.253132	+	0.438437i
$825$	−23.0469	−	91.4926i	−0.802391	−	3.18536i
$826$	14.8463	−	25.7146i	0.516570	−	0.894725i
$827$	−26.8606	−	46.5239i	−0.934035	−	1.61780i	−0.776346	−	0.630307i	$-0.782929\pi$
$827$	−26.8606	−	46.5239i	−0.934035	−	1.61780i	−0.157689	−	0.987489i	$-0.550404\pi$
$828$	−13.7521	+	7.39770i	−0.477919	+	0.257088i
$829$	−23.0581			−0.800842			−0.400421	−	0.916331i	$-0.631136\pi$
$829$	−23.0581			−0.800842			−0.400421	+	0.916331i	$0.631136\pi$
$830$	10.3934	−	18.0019i	0.360761	−	0.624856i
$831$	−24.5666	+	23.8388i	−0.852205	+	0.826958i
$832$	3.88255			0.134603
$833$	5.72346	+	9.91332i	0.198306	+	0.343476i
$834$	−8.25952	−	32.7890i	−0.286004	−	1.13539i
$835$	36.9586	+	64.0141i	1.27900	+	2.21530i
$836$	6.38404	+	21.5773i	0.220797	+	0.746266i
$837$	42.7270	−	9.40652i	1.47686	−	0.325137i
$838$	−6.81387	+	11.8020i	−0.235381	+	0.407692i
$839$	21.1204			0.729158			0.364579	−	0.931172i	$-0.381213\pi$
$839$	21.1204			0.729158			0.364579	+	0.931172i	$0.381213\pi$
$840$	−13.4886	−	3.83251i	−0.465402	−	0.132234i
$841$	13.7771	+	23.8626i	0.475072	+	0.822849i
$842$	12.4518			0.429116
$843$	−40.8709	−	11.6126i	−1.40767	−	0.399959i
$844$	0.202549	+	0.350825i	0.00697202	+	0.0120759i
$845$	−4.08998	−	7.08406i	−0.140700	−	0.243699i
$846$	0.643814	−	21.4053i	0.0221348	−	0.735929i
$847$	−32.1265			−1.10388
$848$	−0.708689	−	1.22749i	−0.0243365	−	0.0421520i
$849$	−3.40914	+	3.30815i	−0.117001	+	0.113535i
$850$	21.6815	+	37.5534i	0.743668	+	1.28807i
$851$	2.26601			0.0776777
$852$	−7.35715	−	2.09038i	−0.252052	−	0.0716153i
$853$	11.2816			0.386274			0.193137	−	0.981172i	$-0.438134\pi$
$853$	11.2816			0.386274			0.193137	+	0.981172i	$0.438134\pi$
$854$	−13.5355			−0.463175
$855$	36.3115	+	36.6182i	1.24183	+	1.25232i
$856$	2.11280			0.0722141
$857$	41.2781			1.41003			0.705017	−	0.709190i	$-0.250939\pi$
$857$	41.2781			1.41003			0.705017	+	0.709190i	$0.250939\pi$
$858$	24.9137	−	24.1756i	0.850538	−	0.825341i
$859$	−27.6460			−0.943271			−0.471636	−	0.881794i	$-0.656336\pi$
$859$	−27.6460			−0.943271			−0.471636	+	0.881794i	$0.656336\pi$
$860$	3.30574	+	5.72572i	0.112725	+	0.195245i
$861$	9.46445	+	2.68913i	0.322548	+	0.0916452i
$862$	12.6070	+	21.8359i	0.429395	+	0.743733i
$863$	−1.24809			−0.0424856			−0.0212428	−	0.999774i	$-0.506762\pi$
$863$	−1.24809			−0.0424856			−0.0212428	+	0.999774i	$0.506762\pi$
$864$	3.50484	+	3.83616i	0.119237	+	0.130509i
$865$	2.85424	+	4.94369i	0.0970471	+	0.168090i
$866$	10.0557	+	17.4169i	0.341705	+	0.591850i
$867$	−0.140462	+	0.136301i	−0.00477035	+	0.00462903i
$868$	−17.2850			−0.586690
$869$	−5.15537	−	8.92936i	−0.174884	−	0.302908i
$870$	2.00624	+	7.96444i	0.0680178	+	0.270020i
$871$	−57.1461			−1.93632
$872$	−4.80520	+	8.32285i	−0.162725	+	0.281847i
$873$	11.8235	−	6.36023i	0.400165	−	0.215261i
$874$	−22.0603	−	5.30362i	−0.746202	−	0.179398i
$875$	22.4750	+	38.9278i	0.759793	+	1.31600i
$876$	16.9396	+	4.81304i	0.572337	+	0.162618i
$877$	−14.7617	−	25.5680i	−0.498467	−	0.863371i	0.501531	−	0.865140i	$-0.332770\pi$
$877$	−14.7617	−	25.5680i	−0.498467	−	0.863371i	−0.999998	+	0.00176898i	$0.999437\pi$
$878$	12.6374			0.426491
$879$	50.4506	+	14.3345i	1.70165	+	0.483490i
$880$	10.1791	−	17.6307i	0.343136	−	0.594330i
$881$	−23.3038			−0.785125			−0.392562	−	0.919725i	$-0.628411\pi$
$881$	−23.3038			−0.785125			−0.392562	+	0.919725i	$0.628411\pi$
$882$	0.251233	−	8.35290i	0.00845944	−	0.281257i
$883$	−14.9075	−	25.8206i	−0.501678	−	0.868931i	−0.999998	−	0.00193813i	$-0.999383\pi$
$883$	−14.9075	−	25.8206i	−0.501678	−	0.868931i	0.498321	−	0.866993i	$-0.333950\pi$
$884$	−7.97744	+	13.8173i	−0.268310	+	0.464727i
$885$	95.0335	+	27.0018i	3.19452	+	0.907655i
$886$	−11.0306	+	19.1056i	−0.370581	+	0.641865i
$887$	−36.5219			−1.22628			−0.613142	−	0.789973i	$-0.710095\pi$
$887$	−36.5219			−1.22628			−0.613142	+	0.789973i	$0.710095\pi$
$888$	−0.184184	−	0.731182i	−0.00618081	−	0.0245369i
$889$	3.56159	−	6.16886i	0.119452	−	0.206897i
$890$	3.22415	−	5.58438i	0.108074	−	0.187189i
$891$	46.3766	+	2.79229i	1.55368	+	0.0935453i
$892$	−8.40880			−0.281547
$893$	21.4255	−	22.5634i	0.716976	−	0.755056i
$894$	23.3169	−	22.6262i	0.779835	−	0.756733i
$895$	−2.59135	−	4.48836i	−0.0866194	−	0.150029i
$896$	−1.02646	−	1.77787i	−0.0342915	−	0.0593946i
$897$	8.55033	+	33.9435i	0.285487	+	1.13334i
$898$	−32.2058			−1.07472
$899$	5.06205	+	8.76773i	0.168829	+	0.292420i
$900$	0.951713	−	31.6422i	0.0317238	−	1.05474i
$901$	5.82455			0.194044
$902$	−7.14226	+	12.3708i	−0.237811	+	0.411901i
$903$	4.27810	−	4.15137i	0.142366	−	0.138149i
$904$	3.49351	−	6.05094i	0.116192	−	0.201251i
$905$	−21.1202	+	36.5812i	−0.702058	+	1.21600i
$906$	−6.98097	+	6.77416i	−0.231927	+	0.225056i
$907$	−23.5397			−0.781623			−0.390812	−	0.920471i	$-0.627806\pi$
$907$	−23.5397			−0.781623			−0.390812	+	0.920471i	$0.627806\pi$
$908$	0.146997	+	0.254607i	0.00487828	+	0.00844943i
$909$	0.387853	−	12.8952i	0.0128643	−	0.427707i
$910$	−15.7164	+	27.2216i	−0.520994	+	0.902388i
$911$	−1.39516	−	2.41648i	−0.0462236	−	0.0800617i	0.841988	−	0.539496i	$-0.181385\pi$
$911$	−1.39516	−	2.41648i	−0.0462236	−	0.0800617i	−0.888212	+	0.459435i	$0.848052\pi$
$912$	0.0817523	+	7.54939i	0.00270709	+	0.249985i
$913$	13.6052	−	23.5649i	0.450267	−	0.779885i
$914$	−0.903329	−	1.56461i	−0.0298795	−	0.0517527i
$915$	−11.0009	−	43.6718i	−0.363679	−	1.44375i
$916$	−3.61171	+	6.25566i	−0.119334	+	0.206693i
$917$	0.369991	−	0.640843i	0.0122182	−	0.0211625i
$918$	−20.8536	+	4.59100i	−0.688271	+	0.151525i
$919$	11.5145			0.379829			0.189914	−	0.981801i	$-0.439179\pi$
$919$	11.5145			0.379829			0.189914	+	0.981801i	$0.439179\pi$
$920$	10.2637	+	17.7772i	0.338383	+	0.586097i
$921$	−27.1660	−	7.71865i	−0.895150	−	0.254338i
$922$	23.5186			0.774545
$923$	−8.57226	+	14.8476i	−0.282159	+	0.488714i
$924$	−17.6569	−	5.01684i	−0.580870	−	0.165042i
$925$	−2.29687	+	3.97829i	−0.0755206	+	0.130806i
$926$	−10.1793	+	17.6310i	−0.334511	+	0.579391i
$927$	−1.31070	+	43.5778i	−0.0430491	+	1.43128i
$928$	−0.601213	+	1.04133i	−0.0197358	+	0.0341834i
$929$	−44.4567			−1.45858			−0.729288	−	0.684206i	$-0.760149\pi$
$929$	−44.4567			−1.45858			−0.729288	+	0.684206i	$0.760149\pi$
$930$	−14.0482	−	55.7693i	−0.460660	−	1.82875i
$931$	8.36077	−	8.80482i	0.274013	−	0.288566i
$932$	9.39739	−	16.2768i	0.307822	−	0.533163i
$933$	44.4084	+	12.6177i	1.45387	+	0.413086i
$934$	−22.2721			−0.728767
$935$	41.8297	+	72.4511i	1.36798	+	2.36940i
$936$	10.2577	−	5.51794i	0.335283	−	0.180360i
$937$	0.0937801	+	0.162432i	0.00306366	+	0.00530642i	0.867553	−	0.497344i	$-0.165691\pi$
$937$	0.0937801	+	0.162432i	0.00306366	+	0.00530642i	−0.864490	+	0.502651i	$0.832358\pi$
$938$	15.1081	+	26.1679i	0.493296	+	0.854413i
$939$	−29.9570	−	8.51166i	−0.977610	−	0.277767i
$940$	−28.1509			−0.918181
$941$	−43.6170			−1.42187			−0.710936	−	0.703257i	$-0.751729\pi$
$941$	−43.6170			−1.42187			−0.710936	+	0.703257i	$0.751729\pi$
$942$	15.0069	−	14.5624i	0.488953	−	0.474467i
$943$	−7.20162	−	12.4736i	−0.234517	−	0.406196i
$944$	7.23184	+	12.5259i	0.235376	+	0.407684i
$945$	−41.0837	+	9.04474i	−1.33645	+	0.294226i
$946$	4.32729	+	7.49509i	0.140692	+	0.243686i
$947$	−10.4580			−0.339840			−0.169920	−	0.985458i	$-0.554351\pi$
$947$	−10.4580			−0.339840			−0.169920	+	0.985458i	$0.554351\pi$
$948$	−0.845037	−	3.35466i	−0.0274455	−	0.108954i
$949$	19.7374	−	34.1861i	0.640702	−	1.10973i
$950$	31.6721	−	33.3542i	1.02758	−	1.08215i
$951$	−27.7394	−	7.88157i	−0.899512	−	0.255577i
$952$	8.43619			0.273418
$953$	−17.3582	+	30.0652i	−0.562286	+	0.973908i	0.435011	+	0.900425i	$0.356745\pi$
$953$	−17.3582	+	30.0652i	−0.562286	+	0.973908i	−0.997297	+	0.0734823i	$0.976589\pi$
$954$	−3.61688	−	2.23582i	−0.117101	−	0.0723872i
$955$	−7.44092	+	12.8881i	−0.240783	+	0.417048i
$956$	−1.67306	+	2.89782i	−0.0541105	+	0.0937222i
$957$	2.62621	+	10.4256i	0.0848932	+	0.337013i
$958$	6.26933	−	10.8588i	0.202553	−	0.350832i
$959$	36.6023			1.18195
$960$	4.90200	−	4.75678i	0.158211	−	0.153524i
$961$	−19.9459	−	34.5474i	−0.643417	−	1.11443i
$962$	−1.69021			−0.0544947
$963$	5.58201	−	3.00274i	0.179878	−	0.0967620i
$964$	0.623776	−	1.08041i	0.0200905	−	0.0347977i
$965$	−32.0036	+	55.4318i	−1.03023	+	1.78441i
$966$	13.2827	−	12.8892i	0.427362	−	0.414702i
$967$	−10.3866	−	17.9901i	−0.334009	−	0.578521i	0.649285	−	0.760545i	$-0.275068\pi$
$967$	−10.3866	−	17.9901i	−0.334009	−	0.578521i	−0.983294	+	0.182024i	$0.941735\pi$
$968$	7.82462	−	13.5526i	0.251493	−	0.435598i
$969$	−27.0350	−	15.2207i	−0.868488	−	0.488960i
$970$	−8.82427	−	15.2841i	−0.283330	−	0.490743i
$971$	20.2792	−	35.1246i	0.650791	−	1.12720i	−0.332141	−	0.943230i	$-0.607771\pi$
$971$	20.2792	−	35.1246i	0.650791	−	1.12720i	0.982931	−	0.183973i	$-0.0588959\pi$
$972$	14.7118	+	5.15400i	0.471880	+	0.165314i
$973$	20.0386	+	34.7078i	0.642407	+	1.11268i
$974$	3.92089			0.125633
$975$	−68.2593	−	19.3945i	−2.18605	−	0.621120i
$976$	3.29666	−	5.70999i	0.105524	−	0.182772i
$977$	−30.3147	+	52.5066i	−0.969852	+	1.67983i	−0.273882	+	0.961763i	$0.588308\pi$
$977$	−30.3147	+	52.5066i	−0.969852	+	1.67983i	−0.695970	+	0.718071i	$0.745026\pi$
$978$	4.87413	+	19.3495i	0.155858	+	0.618730i
$979$	4.22047	−	7.31008i	0.134887	−	0.233631i
$980$	−10.9852			−0.350909
$981$	−0.866772	+	28.8182i	−0.0276739	+	0.920093i
$982$	−7.38534	−	12.7918i	−0.235676	−	0.408202i
$983$	−0.400268			−0.0127666			−0.00638329	−	0.999980i	$-0.502032\pi$
$983$	−0.400268			−0.0127666			−0.00638329	+	0.999980i	$0.502032\pi$
$984$	−3.43954	+	3.33765i	−0.109649	+	0.106400i
$985$	40.6734	+	70.4484i	1.29596	+	2.24467i
$986$	−2.47061	−	4.27922i	−0.0786803	−	0.136278i
$987$	6.20004	+	24.6132i	0.197349	+	0.783446i
$988$	16.4548	+	3.95597i	0.523497	+	0.125856i
$989$	−8.72651			−0.277487
$990$	1.83612	−	61.0468i	0.0583558	−	1.94019i
$991$	−26.5252	+	45.9431i	−0.842602	+	1.45943i	0.0450855	+	0.998983i	$0.485644\pi$
$991$	−26.5252	+	45.9431i	−0.842602	+	1.45943i	−0.887688	+	0.460446i	$0.847689\pi$
$992$	4.20987	−	7.29170i	0.133663	−	0.231512i
$993$	−0.388220	+	0.376719i	−0.0123198	+	0.0119548i
$994$	9.06521			0.287531
$995$	12.7297	−	22.0485i	0.403559	−	0.698985i
$996$	6.55195	−	6.35785i	0.207607	−	0.201456i
$997$	−4.19931	+	7.27341i	−0.132993	+	0.230351i	−0.924829	−	0.380383i	$-0.875792\pi$
$997$	−4.19931	+	7.27341i	−0.132993	+	0.230351i	0.791836	+	0.610734i	$0.209126\pi$
$998$	14.4177	+	24.9723i	0.456386	+	0.790483i
$999$	−1.52578	−	1.67002i	−0.0482735	−	0.0528370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.f.g.49.5	yes	18
3.2	odd	2		1026.2.f.g.847.9		18
9.2	odd	6		1026.2.h.g.505.1		18
9.7	even	3		342.2.h.g.277.2	yes	18
19.7	even	3		342.2.h.g.121.2	yes	18
57.26	odd	6		1026.2.h.g.577.1		18
171.7	even	3	inner	342.2.f.g.7.5	✓	18
171.83	odd	6		1026.2.f.g.235.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.5	✓	18	171.7	even	3	inner
342.2.f.g.49.5	yes	18	1.1	even	1	trivial
342.2.h.g.121.2	yes	18	19.7	even	3
342.2.h.g.277.2	yes	18	9.7	even	3
1026.2.f.g.235.9		18	171.83	odd	6
1026.2.f.g.847.9		18	3.2	odd	2
1026.2.h.g.505.1		18	9.2	odd	6
1026.2.h.g.577.1		18	57.26	odd	6

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.423085 + 1.67958i) q^{3} +1.00000 q^{4} +(-1.97181 - 3.41528i) q^{5} +(-0.423085 - 1.67958i) q^{6} +(1.02646 + 1.77787i) q^{7} -1.00000 q^{8} +(-2.64200 + 1.42121i) q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(0.423085 + 1.67958i) q^{3} +1.00000 q^{4} +(-1.97181 - 3.41528i) q^{5} +(-0.423085 - 1.67958i) q^{6} +(1.02646 + 1.77787i) q^{7} -1.00000 q^{8} +(-2.64200 + 1.42121i) q^{9} +(1.97181 + 3.41528i) q^{10} +(2.58114 + 4.47067i) q^{11} +(0.423085 + 1.67958i) q^{12} +3.88255 q^{13} +(-1.02646 - 1.77787i) q^{14} +(4.90200 - 4.75678i) q^{15} +1.00000 q^{16} +(-2.05469 + 3.55883i) q^{17} +(2.64200 - 1.42121i) q^{18} +(4.23814 + 1.01891i) q^{19} +(-1.97181 - 3.41528i) q^{20} +(-2.55181 + 2.47621i) q^{21} +(-2.58114 - 4.47067i) q^{22} +5.20520 q^{23} +(-0.423085 - 1.67958i) q^{24} +(-5.27609 + 9.13846i) q^{25} -3.88255 q^{26} +(-3.50484 - 3.83616i) q^{27} +(1.02646 + 1.77787i) q^{28} +(0.601213 - 1.04133i) q^{29} +(-4.90200 + 4.75678i) q^{30} +(-4.20987 + 7.29170i) q^{31} -1.00000 q^{32} +(-6.41682 + 6.22672i) q^{33} +(2.05469 - 3.55883i) q^{34} +(4.04796 - 7.01126i) q^{35} +(-2.64200 + 1.42121i) q^{36} +0.435335 q^{37} +(-4.23814 - 1.01891i) q^{38} +(1.64265 + 6.52107i) q^{39} +(1.97181 + 3.41528i) q^{40} +(-1.38355 - 2.39637i) q^{41} +(2.55181 - 2.47621i) q^{42} -1.67650 q^{43} +(2.58114 + 4.47067i) q^{44} +(10.0634 + 6.22079i) q^{45} -5.20520 q^{46} +(3.56916 - 6.18197i) q^{47} +(0.423085 + 1.67958i) q^{48} +(1.39278 - 2.41236i) q^{49} +(5.27609 - 9.13846i) q^{50} +(-6.84665 - 1.94533i) q^{51} +3.88255 q^{52} +(-0.708689 - 1.22749i) q^{53} +(3.50484 + 3.83616i) q^{54} +(10.1791 - 17.6307i) q^{55} +(-1.02646 - 1.77787i) q^{56} +(0.0817523 + 7.54939i) q^{57} +(-0.601213 + 1.04133i) q^{58} +(7.23184 + 12.5259i) q^{59} +(4.90200 - 4.75678i) q^{60} +(3.29666 - 5.70999i) q^{61} +(4.20987 - 7.29170i) q^{62} +(-5.23863 - 3.23832i) q^{63} +1.00000 q^{64} +(-7.65567 - 13.2600i) q^{65} +(6.41682 - 6.22672i) q^{66} -14.7187 q^{67} +(-2.05469 + 3.55883i) q^{68} +(2.20224 + 8.74256i) q^{69} +(-4.04796 + 7.01126i) q^{70} +(-2.20789 + 3.82418i) q^{71} +(2.64200 - 1.42121i) q^{72} +(5.08361 - 8.80507i) q^{73} -0.435335 q^{74} +(-17.5810 - 4.99528i) q^{75} +(4.23814 + 1.01891i) q^{76} +(-5.29886 + 9.17789i) q^{77} +(-1.64265 - 6.52107i) q^{78} -1.99732 q^{79} +(-1.97181 - 3.41528i) q^{80} +(4.96030 - 7.50969i) q^{81} +(1.38355 + 2.39637i) q^{82} +(-2.63550 - 4.56482i) q^{83} +(-2.55181 + 2.47621i) q^{84} +16.2059 q^{85} +1.67650 q^{86} +(2.00337 + 0.569215i) q^{87} +(-2.58114 - 4.47067i) q^{88} +(-0.817559 - 1.41605i) q^{89} +(-10.0634 - 6.22079i) q^{90} +(3.98527 + 6.90269i) q^{91} +5.20520 q^{92} +(-14.0282 - 3.98581i) q^{93} +(-3.56916 + 6.18197i) q^{94} +(-4.87696 - 16.4835i) q^{95} +(-0.423085 - 1.67958i) q^{96} -4.47521 q^{97} +(-1.39278 + 2.41236i) q^{98} +(-13.1732 - 8.14315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q - 18 q^{2} + 18 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} - 2 q^{13} - 5 q^{14} + 18 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 4 q^{21} - q^{22} + 4 q^{23} - 9 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} - 9 q^{29} + 4 q^{31} - 18 q^{32} + 16 q^{33} + 5 q^{34} + 6 q^{35} + 4 q^{36} + 20 q^{37} - 9 q^{38} + 4 q^{39} + q^{41} + 4 q^{42} - 14 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} + 19 q^{47} + 6 q^{49} + 9 q^{50} + 16 q^{51} - 2 q^{52} - 10 q^{53} + 18 q^{54} + 6 q^{55} - 5 q^{56} - 36 q^{57} + 9 q^{58} - 5 q^{59} + 18 q^{61} - 4 q^{62} - 15 q^{63} + 18 q^{64} - 45 q^{65} - 16 q^{66} - 44 q^{67} - 5 q^{68} - 26 q^{69} - 6 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} - 20 q^{74} + 9 q^{76} - 2 q^{77} - 4 q^{78} - 4 q^{79} - 32 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} + 14 q^{86} + 3 q^{87} - q^{88} + q^{89} - 30 q^{90} - 25 q^{91} + 4 q^{92} + 10 q^{93} - 19 q^{94} - 24 q^{95} - 6 q^{98} + 8 q^{99}+O(q^{100}) \) 18 * q - 18 * q^2 + 18 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 - 2 * q^13 - 5 * q^14 + 18 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 4 * q^21 - q^22 + 4 * q^23 - 9 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 - 9 * q^29 + 4 * q^31 - 18 * q^32 + 16 * q^33 + 5 * q^34 + 6 * q^35 + 4 * q^36 + 20 * q^37 - 9 * q^38 + 4 * q^39 + q^41 + 4 * q^42 - 14 * q^43 + q^44 + 30 * q^45 - 4 * q^46 + 19 * q^47 + 6 * q^49 + 9 * q^50 + 16 * q^51 - 2 * q^52 - 10 * q^53 + 18 * q^54 + 6 * q^55 - 5 * q^56 - 36 * q^57 + 9 * q^58 - 5 * q^59 + 18 * q^61 - 4 * q^62 - 15 * q^63 + 18 * q^64 - 45 * q^65 - 16 * q^66 - 44 * q^67 - 5 * q^68 - 26 * q^69 - 6 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 - 20 * q^74 + 9 * q^76 - 2 * q^77 - 4 * q^78 - 4 * q^79 - 32 * q^81 - q^82 - 7 * q^83 - 4 * q^84 + 14 * q^86 + 3 * q^87 - q^88 + q^89 - 30 * q^90 - 25 * q^91 + 4 * q^92 + 10 * q^93 - 19 * q^94 - 24 * q^95 - 6 * q^98 + 8 * q^99

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