LMFDB - Embedded newform 342.2.h.g.277.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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([2, 2]))

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.2
Root			$-1.24302 - 1.20619i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.g.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-1.66610 + 0.473389i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.94363 q^{5} +(-1.24302 - 1.20619i) q^{6} +(1.02646 - 1.77787i) q^{7} -1.00000 q^{8} +(2.55181 - 1.57743i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.66610 + 0.473389i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.94363 q^{5} +(-1.24302 - 1.20619i) q^{6} +(1.02646 - 1.77787i) q^{7} -1.00000 q^{8} +(2.55181 - 1.57743i) q^{9} +(1.97181 + 3.41528i) q^{10} +(2.58114 - 4.47067i) q^{11} +(0.423085 - 1.67958i) q^{12} +(-1.94128 + 3.36239i) q^{13} +2.05291 q^{14} +(-6.57049 + 1.86687i) q^{15} +(-0.500000 - 0.866025i) 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} +(-0.868557 + 3.44803i) q^{21} +5.16229 q^{22} +(-2.60260 + 4.50783i) q^{23} +(1.66610 - 0.473389i) q^{24} +10.5522 q^{25} -3.88255 q^{26} +(-3.50484 + 3.83616i) q^{27} +(1.02646 + 1.77787i) q^{28} -1.20243 q^{29} +(-4.90200 - 4.75678i) q^{30} +(-4.20987 - 7.29170i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.18409 + 8.67049i) q^{33} -4.10938 q^{34} +(4.04796 - 7.01126i) q^{35} +(0.0901911 + 2.99864i) q^{36} +0.435335 q^{37} +(1.23667 + 4.17979i) q^{38} +(1.64265 - 6.52107i) q^{39} -3.94363 q^{40} +2.76709 q^{41} +(-3.42036 + 0.971825i) q^{42} +(0.838250 + 1.45189i) q^{43} +(2.58114 + 4.47067i) q^{44} +(10.0634 - 6.22079i) q^{45} -5.20520 q^{46} -7.13833 q^{47} +(1.24302 + 1.20619i) q^{48} +(1.39278 + 2.41236i) q^{49} +(5.27609 + 9.13846i) q^{50} +(1.73862 - 6.90204i) q^{51} +(-1.94128 - 3.36239i) q^{52} +(-0.708689 - 1.22749i) q^{53} +(-5.07463 - 1.11720i) q^{54} +(10.1791 - 17.6307i) q^{55} +(-1.02646 + 1.77787i) q^{56} +(-7.54352 + 0.308678i) q^{57} +(-0.601213 - 1.04133i) q^{58} -14.4637 q^{59} +(1.66849 - 6.62365i) q^{60} -6.59332 q^{61} +(4.20987 - 7.29170i) q^{62} +(-0.185154 - 6.15595i) q^{63} +1.00000 q^{64} +(-7.65567 + 13.2600i) q^{65} +(-8.60091 + 2.44377i) q^{66} +(7.35934 - 12.7467i) q^{67} +(-2.05469 - 3.55883i) q^{68} +(2.20224 - 8.74256i) q^{69} +8.09591 q^{70} +(-2.20789 + 3.82418i) q^{71} +(-2.55181 + 1.57743i) q^{72} +(5.08361 - 8.80507i) q^{73} +(0.217668 + 0.377012i) q^{74} +(-17.5810 + 4.99528i) q^{75} +(-3.00147 + 3.16088i) q^{76} +(-5.29886 - 9.17789i) q^{77} +(6.46874 - 1.83796i) q^{78} +(0.998660 + 1.72973i) q^{79} +(-1.97181 - 3.41528i) q^{80} +(4.02343 - 8.05059i) q^{81} +(1.38355 + 2.39637i) q^{82} +(-2.63550 + 4.56482i) q^{83} +(-2.55181 - 2.47621i) q^{84} +(-8.10293 + 14.0347i) q^{85} +(-0.838250 + 1.45189i) q^{86} +(2.00337 - 0.569215i) q^{87} +(-2.58114 + 4.47067i) q^{88} +(-0.817559 - 1.41605i) q^{89} +(10.4190 + 5.60474i) q^{90} +(3.98527 + 6.90269i) q^{91} +(-2.60260 - 4.50783i) q^{92} +(10.4659 + 10.1558i) q^{93} +(-3.56916 - 6.18197i) q^{94} +(16.7136 + 4.01820i) q^{95} +(-0.423085 + 1.67958i) q^{96} +(2.23760 + 3.87564i) q^{97} +(-1.39278 + 2.41236i) q^{98} +(-0.465593 - 15.4799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	$ 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) $ 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.66610	+	0.473389i	−0.961926	+	0.273311i
$3$	−1.66610	+	0.473389i	−0.961926	+	0.273311i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	3.94363			1.76364			0.881821	−	0.471583i	$-0.156317\pi$
$5$	3.94363			1.76364			0.881821	+	0.471583i	$0.156317\pi$
$6$	−1.24302	−	1.20619i	−0.507460	−	0.492427i
$7$	1.02646	−	1.77787i	0.387964	−	0.671973i	−0.604212	−	0.796824i	$-0.706512\pi$
$7$	1.02646	−	1.77787i	0.387964	−	0.671973i	0.992176	+	0.124851i	$0.0398453\pi$
$8$	−1.00000			−0.353553
$9$	2.55181	−	1.57743i	0.850602	−	0.525810i
$10$	1.97181	+	3.41528i	0.623542	+	1.08001i
$11$	2.58114	−	4.47067i	0.778244	−	1.34796i	−0.154708	−	0.987960i	$-0.549444\pi$
$11$	2.58114	−	4.47067i	0.778244	−	1.34796i	0.932953	−	0.359999i	$-0.117223\pi$
$12$	0.423085	−	1.67958i	0.122134	−	0.484854i
$13$	−1.94128	+	3.36239i	−0.538413	+	0.932559i	0.460576	+	0.887620i	$0.347643\pi$
$13$	−1.94128	+	3.36239i	−0.538413	+	0.932559i	−0.998990	+	0.0449392i	$0.985691\pi$
$14$	2.05291			0.548663
$15$	−6.57049	+	1.86687i	−1.69649	+	0.482023i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−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
$21$	−0.868557	+	3.44803i	−0.189535	+	0.752423i
$22$	5.16229			1.10060
$23$	−2.60260	+	4.50783i	−0.542679	+	0.939948i	0.456070	+	0.889944i	$0.349257\pi$
$23$	−2.60260	+	4.50783i	−0.542679	+	0.939948i	−0.998749	+	0.0500039i	$0.984077\pi$
$24$	1.66610	−	0.473389i	0.340092	−	0.0966301i
$25$	10.5522			2.11044
$26$	−3.88255			−0.761431
$27$	−3.50484	+	3.83616i	−0.674506	+	0.738269i
$28$	1.02646	+	1.77787i	0.193982	+	0.335986i
$29$	−1.20243			−0.223285			−0.111642	−	0.993748i	$-0.535611\pi$
$29$	−1.20243			−0.223285			−0.111642	+	0.993748i	$0.535611\pi$
$30$	−4.90200	−	4.75678i	−0.894979	−	0.868465i
$31$	−4.20987	−	7.29170i	−0.756114	−	1.30963i	−0.944818	−	0.327594i	$-0.893762\pi$
$31$	−4.20987	−	7.29170i	−0.756114	−	1.30963i	0.188704	−	0.982034i	$-0.439571\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.18409	+	8.67049i	−0.380201	+	1.50934i
$34$	−4.10938			−0.704753
$35$	4.04796	−	7.01126i	0.684229	−	1.18512i
$36$	0.0901911	+	2.99864i	0.0150319	+	0.499774i
$37$	0.435335			0.0715687			0.0357844	−	0.999360i	$-0.488607\pi$
$37$	0.435335			0.0715687			0.0357844	+	0.999360i	$0.488607\pi$
$38$	1.23667	+	4.17979i	0.200614	+	0.678052i
$39$	1.64265	−	6.52107i	0.263035	−	1.04421i
$40$	−3.94363			−0.623542
$41$	2.76709			0.432147			0.216073	−	0.976377i	$-0.430675\pi$
$41$	2.76709			0.432147			0.216073	+	0.976377i	$0.430675\pi$
$42$	−3.42036	+	0.971825i	−0.527773	+	0.149956i
$43$	0.838250	+	1.45189i	0.127832	+	0.221411i	0.922836	−	0.385192i	$-0.125865\pi$
$43$	0.838250	+	1.45189i	0.127832	+	0.221411i	−0.795004	+	0.606604i	$0.792532\pi$
$44$	2.58114	+	4.47067i	0.389122	+	0.673980i
$45$	10.0634	−	6.22079i	1.50016	−	0.927341i
$46$	−5.20520			−0.767464
$47$	−7.13833			−1.04123			−0.520616	−	0.853791i	$-0.674298\pi$
$47$	−7.13833			−1.04123			−0.520616	+	0.853791i	$0.674298\pi$
$48$	1.24302	+	1.20619i	0.179414	+	0.174099i
$49$	1.39278	+	2.41236i	0.198968	+	0.344623i
$50$	5.27609	+	9.13846i	0.746152	+	1.29237i
$51$	1.73862	−	6.90204i	0.243455	−	0.966479i
$52$	−1.94128	−	3.36239i	−0.269207	−	0.466280i
$53$	−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	$0.864369\pi$
$54$	−5.07463	−	1.11720i	−0.690570	−	0.152032i
$55$	10.1791	−	17.6307i	1.37255	−	2.37732i
$56$	−1.02646	+	1.77787i	−0.137166	+	0.237578i
$57$	−7.54352	+	0.308678i	−0.999164	+	0.0408854i
$58$	−0.601213	−	1.04133i	−0.0789431	−	0.136733i
$59$	−14.4637			−1.88301			−0.941506	−	0.336997i	$-0.890589\pi$
$59$	−14.4637			−1.88301			−0.941506	+	0.336997i	$0.890589\pi$
$60$	1.66849	−	6.62365i	0.215401	−	0.855109i
$61$	−6.59332			−0.844189			−0.422094	−	0.906552i	$-0.638705\pi$
$61$	−6.59332			−0.844189			−0.422094	+	0.906552i	$0.638705\pi$
$62$	4.20987	−	7.29170i	0.534653	−	0.926047i
$63$	−0.185154	−	6.15595i	−0.0233272	−	0.775577i
$64$	1.00000			0.125000
$65$	−7.65567	+	13.2600i	−0.949569	+	1.64470i
$66$	−8.60091	+	2.44377i	−1.05870	+	0.300807i
$67$	7.35934	−	12.7467i	0.899086	−	1.55726i	0.0704222	−	0.997517i	$-0.477565\pi$
$67$	7.35934	−	12.7467i	0.899086	−	1.55726i	0.828664	−	0.559746i	$-0.189101\pi$
$68$	−2.05469	−	3.55883i	−0.249168	−	0.431571i
$69$	2.20224	−	8.74256i	0.265119	−	1.05248i
$70$	8.09591			0.967646
$71$	−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	$0.251058\pi$
$72$	−2.55181	+	1.57743i	−0.300733	+	0.185902i
$73$	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	$-0.0361778\pi$
$74$	0.217668	+	0.377012i	0.0253034	+	0.0438267i
$75$	−17.5810	+	4.99528i	−2.03008	+	0.576806i
$76$	−3.00147	+	3.16088i	−0.344292	+	0.362578i
$77$	−5.29886	−	9.17789i	−0.603861	−	1.04592i
$78$	6.46874	−	1.83796i	0.732440	−	0.208108i
$79$	0.998660	+	1.72973i	0.112358	+	0.194610i	0.916721	−	0.399529i	$-0.130826\pi$
$79$	0.998660	+	1.72973i	0.112358	+	0.194610i	−0.804363	+	0.594139i	$0.797493\pi$
$80$	−1.97181	−	3.41528i	−0.220455	−	0.381840i
$81$	4.02343	−	8.05059i	0.447048	−	0.894510i
$82$	1.38355	+	2.39637i	0.152787	+	0.264635i
$83$	−2.63550	+	4.56482i	−0.289284	+	0.501054i	−0.973639	−	0.228095i	$-0.926750\pi$
$83$	−2.63550	+	4.56482i	−0.289284	+	0.501054i	0.684355	+	0.729149i	$0.260084\pi$
$84$	−2.55181	−	2.47621i	−0.278425	−	0.270177i
$85$	−8.10293	+	14.0347i	−0.878886	+	1.52227i
$86$	−0.838250	+	1.45189i	−0.0903908	+	0.156562i
$87$	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	$0.860953\pi$
$90$	10.4190	+	5.60474i	1.09826	+	0.590791i
$91$	3.98527	+	6.90269i	0.417770	+	0.723598i
$92$	−2.60260	−	4.50783i	−0.271340	−	0.469974i
$93$	10.4659	+	10.1558i	1.08526	+	1.05311i
$94$	−3.56916	−	6.18197i	−0.368131	−	0.637622i
$95$	16.7136	+	4.01820i	1.71478	+	0.412258i
$96$	−0.423085	+	1.67958i	−0.0431810	+	0.171422i
$97$	2.23760	+	3.87564i	0.227194	+	0.393512i	0.956976	−	0.290169i	$-0.0937114\pi$
$97$	2.23760	+	3.87564i	0.227194	+	0.393512i	−0.729781	+	0.683681i	$0.760378\pi$
$98$	−1.39278	+	2.41236i	−0.140692	+	0.243686i
$99$	−0.465593	−	15.4799i	−0.0467938	−	1.55579i
$100$	−5.27609	+	9.13846i	−0.527609	+	0.913846i
$101$	4.30035			0.427901			0.213950	−	0.976845i	$-0.431367\pi$
$101$	4.30035			0.427901			0.213950	+	0.976845i	$0.431367\pi$
$102$	6.84665	−	1.94533i	0.677920	−	0.192617i
$103$	7.26626	+	12.5855i	0.715965	+	1.24009i	0.962586	+	0.270976i	$0.0873465\pi$
$103$	7.26626	+	12.5855i	0.715965	+	1.24009i	−0.246621	+	0.969112i	$0.579320\pi$
$104$	1.94128	−	3.36239i	0.190358	−	0.329709i
$105$	−3.42526	+	13.5978i	−0.334271	+	1.32700i
$106$	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	$0.532565\pi$
$108$	−1.56979	−	4.95336i	−0.151053	−	0.476637i
$109$	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	$0.0144248\pi$
$110$	20.3581			1.94107
$111$	−0.725314	+	0.206083i	−0.0688438	+	0.0195605i
$112$	−2.05291			−0.193982
$113$	−3.49351	−	6.05094i	−0.328642	−	0.569225i	0.653601	−	0.756840i	$-0.273258\pi$
$113$	−3.49351	−	6.05094i	−0.328642	−	0.569225i	−0.982243	+	0.187615i	$0.939924\pi$
$114$	−4.03908	−	6.37854i	−0.378295	−	0.597405i
$115$	−10.2637	+	17.7772i	−0.957092	+	1.65773i
$116$	0.601213	−	1.04133i	0.0558212	−	0.0966852i
$117$	0.350172	+	11.6424i	0.0323734	+	1.07634i
$118$	−7.23184	−	12.5259i	−0.665745	−	1.15310i
$119$	4.21809	+	7.30595i	0.386672	+	0.669736i
$120$	6.57049	−	1.86687i	0.599801	−	0.170421i
$121$	−7.82462	−	13.5526i	−0.711329	−	1.23206i
$122$	−3.29666	−	5.70999i	−0.298466	−	0.516958i
$123$	−4.61026	+	1.30991i	−0.415693	+	0.118111i
$124$	8.41973			0.756114
$125$	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	$0.882532\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−2.08392	−	2.02219i	−0.183479	−	0.178043i
$130$	−15.3113			−1.34289
$131$	0.360455			0.0314931			0.0157466	−	0.999876i	$-0.494988\pi$
$131$	0.360455			0.0314931			0.0157466	+	0.999876i	$0.494988\pi$
$132$	−6.41682	−	6.22672i	−0.558513	−	0.541967i
$133$	6.16175	−	6.48901i	0.534292	−	0.562668i
$134$	14.7187			1.27150
$135$	−13.8218	+	15.1284i	−1.18959	+	1.30204i
$136$	2.05469	−	3.55883i	0.176188	−	0.305167i
$137$	−17.8295			−1.52327			−0.761637	−	0.648004i	$-0.775604\pi$
$137$	−17.8295			−1.52327			−0.761637	+	0.648004i	$0.775604\pi$
$138$	8.67240	−	2.46408i	0.738244	−	0.209756i
$139$	−9.76105	+	16.9066i	−0.827922	+	1.43400i	0.0717438	+	0.997423i	$0.477144\pi$
$139$	−9.76105	+	16.9066i	−0.827922	+	1.43400i	−0.899666	+	0.436580i	$0.856190\pi$
$140$	4.04796	+	7.01126i	0.342115	+	0.592560i
$141$	11.8932	−	3.37920i	1.00159	−	0.284580i
$142$	−4.41578			−0.370564
$143$	10.0214	+	17.3576i	0.838034	+	1.45152i
$144$	−2.64200	−	1.42121i	−0.220166	−	0.118435i
$145$	−4.74192			−0.393795
$146$	10.1672			0.841445
$147$	−3.46250	−	3.35992i	−0.285582	−	0.277122i
$148$	−0.217668	+	0.377012i	−0.0178922	+	0.0309902i
$149$	−18.7583			−1.53674			−0.768371	−	0.640005i	$-0.778932\pi$
$149$	−18.7583			−1.53674			−0.768371	+	0.640005i	$0.778932\pi$
$150$	−13.1166	−	12.7280i	−1.07096	−	1.03924i
$151$	−2.80807	+	4.86372i	−0.228518	+	0.395804i	−0.957369	−	0.288868i	$-0.906721\pi$
$151$	−2.80807	+	4.86372i	−0.228518	+	0.395804i	0.728851	+	0.684672i	$0.240055\pi$
$152$	−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
$155$	−16.6021	−	28.7557i	−1.33352	−	2.30972i
$156$	4.82609	+	4.68311i	0.386396	+	0.374949i
$157$	−12.0730			−0.963529			−0.481765	−	0.876301i	$-0.660004\pi$
$157$	−12.0730			−0.963529			−0.481765	+	0.876301i	$0.660004\pi$
$158$	−0.998660	+	1.72973i	−0.0794491	+	0.137610i
$159$	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
$162$	8.98373	−	0.540902i	0.705829	−	0.0424973i
$163$	−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
$165$	−8.61323	+	34.1932i	−0.670539	+	2.66194i
$166$	−5.27100			−0.409109
$167$	9.37172	−	16.2323i	0.725206	−	1.25609i	−0.233683	−	0.972313i	$-0.575078\pi$
$167$	9.37172	−	16.2323i	0.725206	−	1.25609i	0.958889	−	0.283781i	$-0.0915887\pi$
$168$	0.868557	−	3.44803i	0.0670106	−	0.266022i
$169$	−1.03711	−	1.79633i	−0.0797779	−	0.138179i
$170$	−16.2059			−1.24293
$171$	12.4222	−	4.08531i	0.949947	−	0.312411i
$172$	−1.67650			−0.127832
$173$	0.723760	+	1.25359i	0.0550265	+	0.0953087i	0.892227	−	0.451588i	$-0.149142\pi$
$173$	0.723760	+	1.25359i	0.0550265	+	0.0953087i	−0.837200	+	0.546897i	$0.815809\pi$
$174$	1.49464	+	1.45036i	0.113308	+	0.109951i
$175$	10.8313	−	18.7604i	0.818773	−	1.41816i
$176$	−5.16229			−0.389122
$177$	24.0980	−	6.84694i	1.81132	−	0.514648i
$178$	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	$0.484360\pi$
$180$	0.355680	+	11.8255i	0.0265108	+	0.881423i
$181$	−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
$184$	2.60260	−	4.50783i	0.191866	−	0.332322i
$185$	1.71680			0.126222
$186$	−3.56227	+	14.1416i	−0.261198	+	1.03692i
$187$	10.6069	+	18.3717i	0.775654	+	1.34347i
$188$	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	−0.926179	−	0.377084i	$-0.876927\pi$
$191$	−1.88682	+	3.26807i	−0.136526	+	0.236469i	0.789654	+	0.613553i	$0.210260\pi$
$192$	−1.66610	+	0.473389i	−0.120241	+	0.0341639i
$193$	16.2305			1.16830			0.584150	−	0.811646i	$-0.301428\pi$
$193$	16.2305			1.16830			0.584150	+	0.811646i	$0.301428\pi$
$194$	−2.23760	+	3.87564i	−0.160651	+	0.278255i
$195$	6.47800	−	25.7167i	0.463900	−	1.84161i
$196$	−2.78556			−0.198968
$197$	−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	$0.759846\pi$
$200$	−10.5522			−0.746152
$201$	−6.22726	+	24.7212i	−0.439237	+	1.74370i
$202$	2.15018	+	3.72421i	0.151286	+	0.262035i
$203$	−1.23424	+	2.13776i	−0.0866264	+	0.150041i
$204$	5.10804	+	4.95671i	0.357634	+	0.347039i
$205$	10.9124			0.762153
$206$	−7.26626	+	12.5855i	−0.506264	+	0.876875i
$207$	0.469462	+	15.6085i	0.0326299	+	1.08487i
$208$	3.88255			0.269207
$209$	15.4945	−	16.3174i	1.07177	−	1.12870i
$210$	−13.4886	+	3.83251i	−0.930804	+	0.264468i
$211$	−0.405098			−0.0278881			−0.0139440	−	0.999903i	$-0.504439\pi$
$211$	−0.405098			−0.0278881			−0.0139440	+	0.999903i	$0.504439\pi$
$212$	1.41738			0.0973460
$213$	1.86825	−	7.41667i	0.128011	−	0.508182i
$214$	−1.05640	−	1.82974i	−0.0722141	−	0.125078i
$215$	3.30574	+	5.72572i	0.225450	+	0.390491i
$216$	3.50484	−	3.83616i	0.238474	−	0.261018i
$217$	−17.2850			−1.17338
$218$	9.61040			0.650898
$219$	−4.30160	+	17.0767i	−0.290675	+	1.15394i
$220$	10.1791	+	17.6307i	0.686273	+	1.18866i
$221$	−7.97744	−	13.8173i	−0.536621	−	0.929455i
$222$	−0.541130	−	0.525099i	−0.0363183	−	0.0352423i
$223$	4.20440	+	7.28224i	0.281547	+	0.487655i	0.971766	−	0.235946i	$-0.0758190\pi$
$223$	4.20440	+	7.28224i	0.281547	+	0.487655i	−0.690219	+	0.723601i	$0.742486\pi$
$224$	−1.02646	−	1.77787i	−0.0685829	−	0.118789i
$225$	26.9271	−	16.6453i	1.79514	−	1.10969i
$226$	3.49351	−	6.05094i	0.232385	−	0.402503i
$227$	0.146997	−	0.254607i	0.00975656	−	0.0168989i	−0.861106	−	0.508426i	$-0.830228\pi$
$227$	0.146997	−	0.254607i	0.00975656	−	0.0168989i	0.870862	+	0.491527i	$0.163561\pi$
$228$	3.50444	−	6.68722i	0.232087	−	0.442872i
$229$	−3.61171	−	6.25566i	−0.238668	−	0.413386i	0.721664	−	0.692243i	$-0.243378\pi$
$229$	−3.61171	−	6.25566i	−0.238668	−	0.413386i	−0.960332	+	0.278858i	$0.910044\pi$
$230$	−20.5273			−1.35353
$231$	13.1732	+	12.7829i	0.866731	+	0.841054i
$232$	1.20243			0.0789431
$233$	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	$-0.0444373\pi$
$234$	−9.90753	+	6.12446i	−0.647675	+	0.400368i
$235$	−28.1509			−1.83636
$236$	7.23184	−	12.5259i	0.470753	−	0.815368i
$237$	−2.48271	−	2.40915i	−0.161269	−	0.156491i
$238$	−4.21809	+	7.30595i	−0.273418	+	0.473575i
$239$	−1.67306	−	2.89782i	−0.108221	−	0.187444i	0.806829	−	0.590786i	$-0.201182\pi$
$239$	−1.67306	−	2.89782i	−0.108221	−	0.187444i	−0.915050	+	0.403341i	$0.867849\pi$
$240$	4.90200	+	4.75678i	0.316423	+	0.307049i
$241$	−1.24755			−0.0803619			−0.0401810	−	0.999192i	$-0.512793\pi$
$241$	−1.24755			−0.0803619			−0.0401810	+	0.999192i	$0.512793\pi$
$242$	7.82462	−	13.5526i	0.502986	−	0.871197i
$243$	−2.89240	+	15.3178i	−0.185547	+	0.982635i
$244$	3.29666	−	5.70999i	0.211047	−	0.365544i
$245$	5.49260	+	9.51346i	0.350909	+	0.607793i
$246$	−3.43954	−	3.33765i	−0.219297	−	0.212801i
$247$	−11.6534	+	12.2723i	−0.741486	+	0.780867i
$248$	4.20987	+	7.29170i	0.267327	+	0.463024i
$249$	2.23008	−	8.85308i	0.141326	−	0.561041i
$250$	10.9479	+	18.9623i	0.692404	+	1.19928i
$251$	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	$0.781550\pi$
$252$	5.42378	+	2.91763i	0.341666	+	0.183793i
$253$	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
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.13299	+	12.3547i	−0.444943	+	0.770665i	−0.998048	−	0.0624470i	$-0.980110\pi$
$257$	−7.13299	+	12.3547i	−0.444943	+	0.770665i	0.553105	+	0.833112i	$0.313443\pi$
$258$	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
$261$	−3.06836	+	1.89674i	−0.189927	+	0.117405i
$262$	0.180228	+	0.312163i	0.0111345	+	0.0192855i
$263$	−0.251728	−	0.436005i	−0.0155222	−	0.0268852i	0.858160	−	0.513382i	$-0.171608\pi$
$263$	−0.251728	−	0.436005i	−0.0155222	−	0.0268852i	−0.873682	+	0.486497i	$0.838274\pi$
$264$	2.18409	−	8.67049i	0.134421	−	0.533632i
$265$	−2.79481	−	4.84074i	−0.171684	−	0.297365i
$266$	8.70052	+	2.09173i	0.533463	+	0.128252i
$267$	2.03248	+	1.97227i	0.124386	+	0.120701i
$268$	7.35934	+	12.7467i	0.449543	+	0.778632i
$269$	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	$0.109935\pi$
$270$	−20.0124	−	4.40582i	−1.21792	−	0.268129i
$271$	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	$-0.278125\pi$
$272$	4.10938			0.249168
$273$	−9.90753	−	9.61401i	−0.599631	−	0.581867i
$274$	−8.91473	−	15.4408i	−0.538558	−	0.932811i
$275$	27.2367	−	47.1754i	1.64244	−	2.84478i
$276$	6.47016	+	6.27848i	0.389458	+	0.377920i
$277$	9.88182	−	17.1158i	0.593741	−	1.02839i	−0.399982	−	0.916523i	$-0.630984\pi$
$277$	9.88182	−	17.1158i	0.593741	−	1.02839i	0.993723	−	0.111866i	$-0.0356829\pi$
$278$	−19.5221			−1.17086
$279$	−22.2449	−	11.9662i	−1.33177	−	0.716400i
$280$	−4.04796	+	7.01126i	−0.241912	+	0.419003i
$281$	24.5308			1.46338			0.731692	−	0.681635i	$-0.238731\pi$
$281$	24.5308			1.46338			0.731692	+	0.681635i	$0.238731\pi$
$282$	8.87307	+	8.61021i	0.528384	+	0.512730i
$283$	−2.74263			−0.163033			−0.0815163	−	0.996672i	$-0.525976\pi$
$283$	−2.74263			−0.163033			−0.0815163	+	0.996672i	$0.525976\pi$
$284$	−2.20789	−	3.82418i	−0.131014	−	0.226923i
$285$	−29.7488	+	1.21731i	−1.76217	+	0.0721072i
$286$	−10.0214	+	17.3576i	−0.592580	+	1.02638i
$287$	2.84029	−	4.91953i	0.167657	−	0.290391i
$288$	−0.0901911	−	2.99864i	−0.00531456	−	0.176697i
$289$	0.0565005	+	0.0978617i	0.00332356	+	0.00575657i
$290$	−2.37096	−	4.10662i	−0.139227	−	0.241149i
$291$	−5.56277	−	5.39797i	−0.326095	−	0.316435i
$292$	5.08361	+	8.80507i	0.297496	+	0.515278i
$293$	15.1403	+	26.2237i	0.884504	+	1.53201i	0.846281	+	0.532737i	$0.178837\pi$
$293$	15.1403	+	26.2237i	0.884504	+	1.53201i	0.0382235	+	0.999269i	$0.487830\pi$
$294$	1.17853	−	4.67858i	0.0687332	−	0.272860i
$295$	−57.0393			−3.32096
$296$	−0.435335			−0.0253034
$297$	8.10372	+	25.5707i	0.470226	+	1.48376i
$298$	−9.37916	−	16.2452i	−0.543320	−	0.941058i
$299$	−10.1047	−	17.5019i	−0.584371	−	1.01216i
$300$	4.46447	−	17.7233i	0.257757	−	1.02325i
$301$	3.44171			0.198377
$302$	−5.61615			−0.323173
$303$	−7.16483	+	2.03574i	−0.411609	+	0.116950i
$304$	−1.23667	−	4.17979i	−0.0709278	−	0.239727i
$305$	−26.0016			−1.48885
$306$	−10.4863	+	6.48226i	−0.599464	+	0.370566i
$307$	−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	$0.320717\pi$
$308$	10.5977			0.603861
$309$	−18.0642	−	17.5290i	−1.02764	−	0.997192i
$310$	16.6021	−	28.7557i	0.942938	−	1.63322i
$311$	13.3270	+	23.0831i	0.755706	+	1.30892i	0.945022	+	0.327006i	$0.106040\pi$
$311$	13.3270	+	23.0831i	0.755706	+	1.30892i	−0.189316	+	0.981916i	$0.560627\pi$
$312$	−1.64265	+	6.52107i	−0.0929969	+	0.369183i
$313$	17.9803			1.01630			0.508152	−	0.861267i	$-0.330329\pi$
$313$	17.9803			1.01630			0.508152	+	0.861267i	$0.330329\pi$
$314$	−6.03649	−	10.4555i	−0.340659	−	0.590039i
$315$	−0.730179	−	24.2768i	−0.0411409	−	1.36784i
$316$	−1.99732			−0.112358
$317$	16.6493			0.935115			0.467558	−	0.883963i	$-0.345134\pi$
$317$	16.6493			0.935115			0.467558	+	0.883963i	$0.345134\pi$
$318$	−0.599672	+	2.38060i	−0.0336279	+	0.133498i
$319$	−3.10364	+	5.37565i	−0.173770	+	0.300979i
$320$	3.94363			0.220455
$321$	3.52015	−	1.00018i	0.196475	−	0.0558244i
$322$	−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
$326$	−5.76022	−	9.97699i	−0.319029	−	0.552575i
$327$	−4.06602	+	16.1415i	−0.224851	+	0.892625i
$328$	−2.76709			−0.152787
$329$	−7.32717	+	12.6910i	−0.403960	+	0.699679i
$330$	−33.9188	+	9.63731i	−1.86717	+	0.530517i
$331$	0.156160	−	0.270477i	0.00858333	−	0.0148668i	−0.861702	−	0.507415i	$-0.830601\pi$
$331$	0.156160	−	0.270477i	0.00858333	−	0.0148668i	0.870285	+	0.492548i	$0.163934\pi$
$332$	−2.63550	−	4.56482i	−0.144642	−	0.250527i
$333$	1.11089	−	0.686711i	0.0608765	−	0.0376315i
$334$	18.7434			1.02560
$335$	29.0225	−	50.2684i	1.58567	−	2.74646i
$336$	3.42036	−	0.971825i	0.186596	−	0.0530174i
$337$	18.4676			1.00599			0.502997	−	0.864288i	$-0.332231\pi$
$337$	18.4676			1.00599			0.502997	+	0.864288i	$0.332231\pi$
$338$	1.03711	−	1.79633i	0.0564115	−	0.0977075i
$339$	8.68500	+	8.42771i	0.471705	+	0.457730i
$340$	−8.10293	−	14.0347i	−0.439443	−	0.761137i
$341$	−43.4651			−2.35377
$342$	9.74906	+	8.71526i	0.527169	+	0.471267i
$343$	20.0889			1.08470
$344$	−0.838250	−	1.45189i	−0.0451954	−	0.0782808i
$345$	8.68482	−	34.4774i	0.467575	−	1.85620i
$346$	−0.723760	+	1.25359i	−0.0389096	+	0.0673934i
$347$	7.13618			0.383090			0.191545	−	0.981484i	$-0.438650\pi$
$347$	7.13618			0.383090			0.191545	+	0.981484i	$0.438650\pi$
$348$	−0.508729	+	2.01957i	−0.0272707	+	0.108261i
$349$	6.45792	−	11.1854i	0.345685	−	0.598743i	−0.639793	−	0.768547i	$-0.720980\pi$
$349$	6.45792	−	11.1854i	0.345685	−	0.598743i	0.985478	+	0.169804i	$0.0543134\pi$
$350$	21.6627			1.15792
$351$	−6.09480	−	19.2317i	−0.325316	−	1.02651i
$352$	−2.58114	−	4.47067i	−0.137575	−	0.238288i
$353$	−13.1427	+	22.7639i	−0.699518	+	1.21160i	0.269116	+	0.963108i	$0.413268\pi$
$353$	−13.1427	+	22.7639i	−0.699518	+	1.21160i	−0.968634	+	0.248492i	$0.920065\pi$
$354$	17.9786	+	17.4460i	0.955553	+	0.927245i
$355$	−8.70710	+	15.0811i	−0.462125	+	0.800423i
$356$	1.63512			0.0866610
$357$	−10.4863	−	10.1757i	−0.554996	−	0.538554i
$358$	0.657100	+	1.13813i	0.0347288	+	0.0601520i
$359$	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
$363$	19.4523	+	18.8760i	1.02098	+	0.990734i
$364$	−7.97054			−0.417770
$365$	20.0478	−	34.7239i	1.04935	−	1.81753i
$366$	8.19563	+	7.95283i	0.428392	+	0.415701i
$367$	−30.4079			−1.58728			−0.793639	−	0.608389i	$-0.791816\pi$
$367$	−30.4079			−1.58728			−0.793639	+	0.608389i	$0.791816\pi$
$368$	5.20520			0.271340
$369$	7.06108	−	4.36489i	0.367585	−	0.227227i
$370$	0.858400	+	1.48679i	0.0446261	+	0.0772947i
$371$	−2.90975			−0.151067
$372$	−14.0282	+	3.98581i	−0.727326	+	0.206654i
$373$	−5.07447	−	8.78925i	−0.262746	−	0.455090i	0.704224	−	0.709977i	$-0.251295\pi$
$373$	−5.07447	−	8.78925i	−0.262746	−	0.455090i	−0.966971	+	0.254887i	$0.917962\pi$
$374$	−10.6069	+	18.3717i	−0.548470	+	0.949978i
$375$	−36.4806	+	10.3652i	−1.88385	+	0.535256i
$376$	7.13833			0.368131
$377$	2.33424	−	4.04302i	0.120220	−	0.208226i
$378$	−7.19512	+	7.87529i	−0.370077	+	0.405061i
$379$	7.53375			0.386983			0.193491	−	0.981102i	$-0.438019\pi$
$379$	7.53375			0.386983			0.193491	+	0.981102i	$0.438019\pi$
$380$	−11.8367	+	12.4653i	−0.607209	+	0.639458i
$381$	4.31302	+	4.18525i	0.220963	+	0.214417i
$382$	−3.77365			−0.193077
$383$	−10.3678			−0.529768			−0.264884	−	0.964280i	$-0.585334\pi$
$383$	−10.3678			−0.529768			−0.264884	+	0.964280i	$0.585334\pi$
$384$	−1.24302	−	1.20619i	−0.0634325	−	0.0615533i
$385$	−20.8967	−	36.1942i	−1.06500	−	1.84463i
$386$	8.11527	+	14.0561i	0.413056	+	0.715435i
$387$	4.42931	+	2.38267i	0.225154	+	0.121118i
$388$	−4.47521			−0.227194
$389$	−38.1779			−1.93570			−0.967849	−	0.251532i	$-0.919066\pi$
$389$	−38.1779			−1.93570			−0.967849	+	0.251532i	$0.919066\pi$
$390$	25.5103	−	7.24821i	1.29176	−	0.367028i
$391$	−10.6951	−	18.5244i	−0.540873	−	0.936819i
$392$	−1.39278	−	2.41236i	−0.0703460	−	0.121843i
$393$	−0.600556	+	0.170635i	−0.0302940	+	0.00860742i
$394$	−10.3137	−	17.8639i	−0.519597	−	0.899969i
$395$	3.93834	+	6.82140i	0.198159	+	0.343222i
$396$	13.6388	+	7.33672i	0.685373	+	0.368684i
$397$	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
$399$	−7.19430	+	13.7283i	−0.360165	+	0.687273i
$400$	−5.27609	−	9.13846i	−0.263805	−	0.456923i
$401$	−2.86983			−0.143312			−0.0716562	−	0.997429i	$-0.522828\pi$
$401$	−2.86983			−0.143312			−0.0716562	+	0.997429i	$0.522828\pi$
$402$	−24.5229	+	6.96766i	−1.22309	+	0.347515i
$403$	32.6901			1.62841
$404$	−2.15018	+	3.72421i	−0.106975	+	0.185286i
$405$	15.8669	−	31.7485i	0.788433	−	1.57760i
$406$	−2.46847			−0.122508
$407$	1.12366	−	1.94624i	0.0556980	−	0.0964717i
$408$	−1.73862	+	6.90204i	−0.0860744	+	0.341702i
$409$	11.4136	−	19.7689i	0.564364	−	0.977508i	−0.432744	−	0.901517i	$-0.642455\pi$
$409$	11.4136	−	19.7689i	0.564364	−	0.977508i	0.997109	−	0.0759908i	$-0.0242120\pi$
$410$	5.45618	+	9.45039i	0.269462	+	0.466721i
$411$	29.7057	−	8.44026i	1.46528	−	0.416328i
$412$	−14.5325			−0.715965
$413$	−14.8463	+	25.7146i	−0.730540	+	1.26533i
$414$	−13.2827	+	8.21083i	−0.652807	+	0.403540i
$415$	−10.3934	+	18.0019i	−0.510193	+	0.883680i
$416$	1.94128	+	3.36239i	0.0951789	+	0.164855i
$417$	8.25952	−	32.7890i	0.404470	−	1.60568i
$418$	21.8785	+	5.25991i	1.07011	+	0.257270i
$419$	6.81387	+	11.8020i	0.332879	+	0.576564i	0.983075	−	0.183203i	$-0.0586465\pi$
$419$	6.81387	+	11.8020i	0.332879	+	0.576564i	−0.650196	+	0.759767i	$0.725313\pi$
$420$	−10.0634	−	9.76524i	−0.491042	−	0.476495i
$421$	6.22588	+	10.7835i	0.303431	+	0.525557i	0.976911	−	0.213648i	$-0.0685346\pi$
$421$	6.22588	+	10.7835i	0.303431	+	0.525557i	−0.673480	+	0.739205i	$0.735201\pi$
$422$	−0.202549	−	0.350825i	−0.00985992	−	0.0170779i
$423$	−18.2156	+	11.2602i	−0.885674	+	0.547490i
$424$	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
$427$	−6.76775	+	11.7221i	−0.327515	+	0.567272i
$428$	1.05640	−	1.82974i	0.0510630	−	0.0884438i
$429$	−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	$-0.374396\pi$
$432$	5.07463	+	1.11720i	0.244153	+	0.0537513i
$433$	−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	$0.993875\pi$
$434$	−8.64248	−	14.9692i	−0.414852	−	0.718545i
$435$	7.90053	−	2.24477i	0.378801	−	0.107628i
$436$	4.80520	+	8.32285i	0.230127	+	0.398592i
$437$	−15.6232	+	16.4530i	−0.747361	+	0.787054i
$438$	−16.9396	+	4.81304i	−0.809407	+	0.229976i
$439$	6.31870	+	10.9443i	0.301575	+	0.522343i	0.976493	−	0.215550i	$-0.0691543\pi$
$439$	6.31870	+	10.9443i	0.301575	+	0.522343i	−0.674918	+	0.737893i	$0.735821\pi$
$440$	−10.1791	+	17.6307i	−0.485268	+	0.840509i
$441$	7.35944	+	3.95887i	0.350449	+	0.188518i
$442$	7.97744	−	13.8173i	0.379448	−	0.657224i
$443$	−22.0612			−1.04816			−0.524080	−	0.851669i	$-0.675591\pi$
$443$	−22.0612			−1.04816			−0.524080	+	0.851669i	$0.675591\pi$
$444$	0.184184	−	0.731182i	0.00874099	−	0.0347004i
$445$	−3.22415	−	5.58438i	−0.152839	−	0.264725i
$446$	−4.20440	+	7.28224i	−0.199084	+	0.344824i
$447$	31.2533	−	8.87998i	1.47823	−	0.420009i
$448$	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	$0.225227\pi$
$450$	27.8788	+	14.9969i	1.31422	+	0.706961i
$451$	7.14226	−	12.3708i	0.336316	−	0.582516i
$452$	6.98702			0.328642
$453$	2.37611	−	9.43278i	0.111639	−	0.443191i
$454$	0.293995			0.0137979
$455$	15.7164	+	27.2216i	0.736796	+	1.27617i
$456$	7.54352	−	0.308678i	0.353258	−	0.0144552i
$457$	0.903329	−	1.56461i	0.0422559	−	0.0731894i	−0.844124	−	0.536148i	$-0.819879\pi$
$457$	0.903329	−	1.56461i	0.0422559	−	0.0731894i	0.886380	+	0.462959i	$0.153212\pi$
$458$	3.61171	−	6.25566i	0.168764	−	0.292308i
$459$	−6.45087	−	20.3552i	−0.301101	−	0.950101i
$460$	−10.2637	−	17.7772i	−0.478546	−	0.828866i
$461$	11.7593	+	20.3677i	0.547686	+	0.948620i	0.998433	+	0.0559681i	$0.0178245\pi$
$461$	11.7593	+	20.3677i	0.547686	+	0.948620i	−0.450746	+	0.892652i	$0.648842\pi$
$462$	−4.48374	+	17.7997i	−0.208603	+	0.828119i
$463$	10.1793	+	17.6310i	0.473071	+	0.819382i	0.999525	−	0.0308210i	$-0.00981219\pi$
$463$	10.1793	+	17.6310i	0.473071	+	0.819382i	−0.526454	+	0.850203i	$0.676479\pi$
$464$	0.601213	+	1.04133i	0.0279106	+	0.0483426i
$465$	41.2735	+	40.0508i	1.91401	+	1.85731i
$466$	18.7948			0.870652
$467$	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
$470$	−14.0754	−	24.3794i	−0.649252	−	1.12454i
$471$	20.1148	−	5.71521i	0.926843	−	0.263343i
$472$	14.4637			0.665745
$473$	8.65458			0.397938
$474$	0.845037	−	3.35466i	0.0388138	−	0.154085i
$475$	44.7216	+	10.7517i	2.05197	+	0.493323i
$476$	−8.43619			−0.386672
$477$	−3.74471	−	2.01440i	−0.171459	−	0.0922330i
$478$	1.67306	−	2.89782i	0.0765238	−	0.132543i
$479$	12.5387			0.572906			0.286453	−	0.958094i	$-0.407524\pi$
$479$	12.5387			0.572906			0.286453	+	0.958094i	$0.407524\pi$
$480$	−1.66849	+	6.62365i	−0.0761558	+	0.302327i
$481$	−0.845107	+	1.46377i	−0.0385335	+	0.0667421i
$482$	−0.623776	−	1.08041i	−0.0284122	−	0.0492114i
$483$	−13.2827	−	12.8892i	−0.604382	−	0.586477i
$484$	15.6492			0.711329
$485$	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	$0.528315\pi$
$488$	6.59332			0.298466
$489$	19.1943	−	5.45365i	0.867994	−	0.246622i
$490$	−5.49260	+	9.51346i	−0.248130	+	0.429774i
$491$	−14.7707			−0.666591			−0.333296	−	0.942822i	$-0.608161\pi$
$491$	−14.7707			−0.666591			−0.333296	+	0.942822i	$0.608161\pi$
$492$	1.17072	−	4.64756i	0.0527799	−	0.209528i
$493$	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
$497$	4.53260	+	7.85070i	0.203315	+	0.352152i
$498$	8.78203	−	2.49523i	0.393532	−	0.111814i
$499$	28.8355			1.29085			0.645427	−	0.763822i	$-0.276680\pi$
$499$	28.8355			1.29085			0.645427	+	0.763822i	$0.276680\pi$
$500$	−10.9479	+	18.9623i	−0.489603	+	0.848018i
$501$	−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	$0.602924\pi$
$504$	0.185154	+	6.15595i	0.00824743	+	0.274208i
$505$	16.9590			0.754664
$506$	−13.4354	+	23.2707i	−0.597275	+	1.03451i
$507$	2.57830	+	2.50192i	0.114506	+	0.111114i
$508$	3.46980			0.153947
$509$	−20.5543	+	35.6011i	−0.911053	+	1.57799i	−0.0984726	+	0.995140i	$0.531396\pi$
$509$	−20.5543	+	35.6011i	−0.911053	+	1.57799i	−0.812580	+	0.582850i	$0.801938\pi$
$510$	27.0006	−	7.67167i	1.19561	−	0.339707i
$511$	−10.4362	−	18.0760i	−0.461670	−	0.799636i
$512$	−1.00000			−0.0441942
$513$	−18.7627	+	12.6871i	−0.828393	+	0.560147i
$514$	−14.2660			−0.629245
$515$	28.6554	+	49.6326i	1.26271	+	2.18707i
$516$	2.79322	−	0.793636i	0.122965	−	0.0349379i
$517$	−18.4251	+	31.9131i	−0.810333	+	1.40354i
$518$	0.893705			0.0392671
$519$	−1.79930	−	1.74599i	−0.0789803	−	0.0766405i
$520$	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	$0.322755\pi$
$522$	−3.17681	−	1.70890i	−0.139045	−	0.0747967i
$523$	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
$526$	0.251728	−	0.436005i	0.0109758	−	0.0190107i
$527$	34.5999			1.50719
$528$	8.60091	−	2.44377i	0.374307	−	0.106351i
$529$	−2.04703	−	3.54556i	−0.0890013	−	0.154155i
$530$	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
$534$	−0.691794	+	2.74631i	−0.0299369	+	0.118845i
$535$	−8.33210			−0.360228
$536$	−7.35934	+	12.7467i	−0.317875	+	0.550576i
$537$	−2.18959	+	0.622127i	−0.0944879	+	0.0268468i
$538$	5.81539			0.250719
$539$	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	$0.935280\pi$
$542$	32.4302			1.39300
$543$	13.3140	+	12.9196i	0.571360	+	0.554433i
$544$	2.05469	+	3.55883i	0.0880941	+	0.152583i
$545$	18.9499	−	32.8222i	0.811725	−	1.40595i
$546$	3.37222	−	13.3872i	0.144318	−	0.572918i
$547$	−35.7961			−1.53053			−0.765265	−	0.643716i	$-0.777392\pi$
$547$	−35.7961			−1.53053			−0.765265	+	0.643716i	$0.777392\pi$
$548$	8.91473	−	15.4408i	0.380818	−	0.659597i
$549$	−16.8249	+	10.4005i	−0.718069	+	0.443883i
$550$	54.4734			2.32275
$551$	−5.09605	−	1.22516i	−0.217099	−	0.0521937i
$552$	−2.20224	+	8.74256i	−0.0937337	+	0.372108i
$553$	4.10032			0.174363
$554$	19.7636			0.839676
$555$	−2.86037	+	0.812714i	−0.121416	+	0.0344978i
$556$	−9.76105	−	16.9066i	−0.413961	−	0.717001i
$557$	−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
$560$	−8.09591			−0.342115
$561$	−26.3692	−	25.5880i	−1.11331	−	1.08033i
$562$	12.2654	+	21.2443i	0.517385	+	0.896137i
$563$	−14.2685	−	24.7138i	−0.601346	−	1.04156i	−0.992618	−	0.121286i	$-0.961298\pi$
$563$	−14.2685	−	24.7138i	−0.601346	−	1.04156i	0.391272	−	0.920275i	$-0.372035\pi$
$564$	−3.02012	+	11.9894i	−0.127170	+	0.504845i
$565$	−13.7771	−	23.8626i	−0.579607	−	1.00391i
$566$	−1.37132	−	2.37519i	−0.0576407	−	0.0998366i
$567$	−10.1831	−	15.4167i	−0.427648	−	0.647441i
$568$	2.20789	−	3.82418i	0.0926411	−	0.160459i
$569$	−5.24159	+	9.07869i	−0.219739	+	0.380599i	−0.954728	−	0.297480i	$-0.903854\pi$
$569$	−5.24159	+	9.07869i	−0.219739	+	0.380599i	0.734989	+	0.678079i	$0.237187\pi$
$570$	−15.9286	−	25.1546i	−0.667177	−	1.05361i
$571$	−9.32650	−	16.1540i	−0.390302	−	0.676022i	0.602187	−	0.798355i	$-0.294296\pi$
$571$	−9.32650	−	16.1540i	−0.390302	−	0.676022i	−0.992489	+	0.122332i	$0.960963\pi$
$572$	−20.0429			−0.838034
$573$	1.59657	−	6.33815i	0.0666979	−	0.264780i
$574$	5.68059			0.237103
$575$	−27.4631	+	47.5675i	−1.14529	+	1.98370i
$576$	2.55181	−	1.57743i	0.106325	−	0.0657262i
$577$	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
$579$	−27.0418	+	7.68336i	−1.12382	+	0.319309i
$580$	2.37096	−	4.10662i	0.0984487	−	0.170518i
$581$	5.41045	+	9.37117i	0.224463	+	0.388782i
$582$	1.89340	−	7.51648i	0.0784838	−	0.311568i
$583$	−7.31692			−0.303036
$584$	−5.08361	+	8.80507i	−0.210361	+	0.364356i
$585$	1.38095	+	45.9133i	0.0570951	+	1.89828i
$586$	−15.1403	+	26.2237i	−0.625439	+	1.08329i
$587$	7.01522	+	12.1507i	0.289549	+	0.501514i	0.973702	−	0.227825i	$-0.0731613\pi$
$587$	7.01522	+	12.1507i	0.289549	+	0.501514i	−0.684153	+	0.729339i	$0.739828\pi$
$588$	4.64103	−	1.31865i	0.191393	−	0.0543803i
$589$	−10.4124	−	35.1927i	−0.429036	−	1.45009i
$590$	−28.5197	−	49.3975i	−1.17414	−	2.03366i
$591$	34.3674	−	9.76479i	1.41369	−	0.401670i
$592$	−0.217668	−	0.377012i	−0.00894609	−	0.0154951i
$593$	−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	$0.987666\pi$
$594$	−18.0930	+	19.8034i	−0.742364	+	0.812542i
$595$	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
$598$	10.1047	−	17.5019i	0.413213	−	0.715706i
$599$	−4.75273	+	8.23197i	−0.194191	+	0.336349i	−0.946635	−	0.322307i	$-0.895542\pi$
$599$	−4.75273	+	8.23197i	−0.194191	+	0.336349i	0.752444	+	0.658656i	$0.228875\pi$
$600$	17.5810	−	4.99528i	0.717743	−	0.203932i
$601$	9.68287	−	16.7712i	0.394973	−	0.684113i	−0.598125	−	0.801403i	$-0.704087\pi$
$601$	9.68287	−	16.7712i	0.394973	−	0.684113i	0.993098	+	0.117290i	$0.0374208\pi$
$602$	1.72085	+	2.98060i	0.0701367	+	0.121480i
$603$	−1.32749	−	44.1361i	−0.0540597	−	1.79736i
$604$	−2.80807	−	4.86372i	−0.114259	−	0.197902i
$605$	−30.8574	−	53.4465i	−1.25453	−	2.17291i
$606$	−5.34542	−	5.18706i	−0.217143	−	0.210710i
$607$	−4.51935	−	7.82774i	−0.183435	−	0.317718i	0.759613	−	0.650375i	$-0.225388\pi$
$607$	−4.51935	−	7.82774i	−0.183435	−	0.317718i	−0.943048	+	0.332657i	$0.892055\pi$
$608$	3.00147	−	3.16088i	0.121726	−	0.128191i
$609$	1.04437	−	4.14600i	0.0423202	−	0.168005i
$610$	−13.0008	−	22.5180i	−0.526387	−	0.911729i
$611$	13.8575	−	24.0018i	0.560613	−	0.971011i
$612$	−10.8570	−	5.84031i	−0.438867	−	0.236080i
$613$	−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	$0.200024\pi$
$614$	−16.3051			−0.658020
$615$	−18.1811	+	5.16579i	−0.733134	+	0.208305i
$616$	5.29886	+	9.17789i	0.213497	+	0.369788i
$617$	11.5792	−	20.0558i	0.466161	−	0.807415i	−0.533092	−	0.846057i	$-0.678970\pi$
$617$	11.5792	−	20.0558i	0.466161	−	0.807415i	0.999253	+	0.0386424i	$0.0123033\pi$
$618$	6.14849	−	24.4086i	0.247329	−	0.981856i
$619$	5.07677	−	8.79323i	0.204053	−	0.353430i	−0.745778	−	0.666195i	$-0.767922\pi$
$619$	5.07677	−	8.79323i	0.204053	−	0.353430i	0.949830	+	0.312765i	$0.101255\pi$
$620$	33.2043			1.33352
$621$	−8.17107	−	25.7832i	−0.327894	−	1.03464i
$622$	−13.3270	+	23.0831i	−0.534365	+	0.925548i
$623$	−3.35675			−0.134485
$624$	−6.46874	+	1.83796i	−0.258957	+	0.0735772i
$625$	33.5876			1.34351
$626$	8.99013	+	15.5714i	0.359318	+	0.622357i
$627$	−18.0909	+	34.5214i	−0.722482	+	1.37865i
$628$	6.03649	−	10.4555i	0.240882	−	0.417220i
$629$	−0.894479	+	1.54928i	−0.0356652	+	0.0617740i
$630$	20.6592	−	12.7707i	0.823082	−	0.508798i
$631$	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	$0.706379\pi$
$632$	−0.998660	−	1.72973i	−0.0397245	−	0.0688049i
$633$	0.674935	−	0.191769i	0.0268262	−	0.00762212i
$634$	8.32463	+	14.4187i	0.330613	+	0.572639i
$635$	−6.84179	−	11.8503i	−0.271508	−	0.470266i
$636$	−2.36150	+	0.670971i	−0.0936396	+	0.0266057i
$637$	−10.8151			−0.428509
$638$	−6.20727			−0.245748
$639$	0.398264	+	13.2414i	0.0157551	+	0.523820i
$640$	1.97181	+	3.41528i	0.0779427	+	0.135001i
$641$	15.9590	+	27.6417i	0.630341	+	1.09178i	0.987482	+	0.157732i	$0.0504181\pi$
$641$	15.9590	+	27.6417i	0.630341	+	1.09178i	−0.357141	+	0.934050i	$0.616249\pi$
$642$	2.62625	+	2.54845i	0.103650	+	0.100579i
$643$	−22.2365			−0.876922			−0.438461	−	0.898750i	$-0.644476\pi$
$643$	−22.2365			−0.876922			−0.438461	+	0.898750i	$0.644476\pi$
$644$	−10.6858			−0.421080
$645$	−8.21821	−	7.97474i	−0.323592	−	0.314005i
$646$	−17.4161	−	4.18709i	−0.685228	−	0.164739i
$647$	28.7608			1.13070			0.565352	−	0.824850i	$-0.308740\pi$
$647$	28.7608			1.13070			0.565352	+	0.824850i	$0.308740\pi$
$648$	−4.02343	+	8.05059i	−0.158055	+	0.316257i
$649$	−37.3329	+	64.6624i	−1.46544	+	2.53822i
$650$	−40.9694			−1.60695
$651$	28.7985	−	8.18250i	1.12870	−	0.320698i
$652$	5.76022	−	9.97699i	0.225588	−	0.390729i
$653$	−14.1756	−	24.5528i	−0.554733	−	0.960826i	−0.997924	−	0.0643991i	$-0.979487\pi$
$653$	−14.1756	−	24.5528i	−0.554733	−	0.960826i	0.443191	−	0.896427i	$-0.353846\pi$
$654$	−16.0119	+	4.54945i	−0.626116	+	0.177898i
$655$	1.42150			0.0555426
$656$	−1.38355	−	2.39637i	−0.0540184	−	0.0935625i
$657$	−0.916992	−	30.4879i	−0.0357753	−	1.18944i
$658$	−14.6543			−0.571286
$659$	5.34029			0.208028			0.104014	−	0.994576i	$-0.466831\pi$
$659$	5.34029			0.208028			0.104014	+	0.994576i	$0.466831\pi$
$660$	−25.3055	−	24.5559i	−0.985017	−	0.955836i
$661$	−8.59702	+	14.8905i	−0.334385	+	0.579172i	−0.983367	−	0.181632i	$-0.941862\pi$
$661$	−8.59702	+	14.8905i	−0.334385	+	0.579172i	0.648981	+	0.760804i	$0.275195\pi$
$662$	0.312320			0.0121387
$663$	19.8322	+	19.2447i	0.770220	+	0.747402i
$664$	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
$668$	9.37172	+	16.2323i	0.362603	+	0.628047i
$669$	−10.4523	−	10.1426i	−0.404109	−	0.392137i
$670$	58.0450			2.24247
$671$	−17.0183	+	29.4766i	−0.656985	+	1.13793i
$672$	2.55181	+	2.47621i	0.0984381	+	0.0955218i
$673$	−16.6703	+	28.8738i	−0.642594	+	1.11300i	0.342258	+	0.939606i	$0.388808\pi$
$673$	−16.6703	+	28.8738i	−0.642594	+	1.11300i	−0.984852	+	0.173399i	$0.944525\pi$
$674$	9.23379	+	15.9934i	0.355672	+	0.616043i
$675$	−36.9837	+	40.4798i	−1.42350	+	1.55807i
$676$	2.07422			0.0797779
$677$	−5.50556	+	9.53591i	−0.211596	+	0.366495i	−0.952214	−	0.305431i	$-0.901199\pi$
$677$	−5.50556	+	9.53591i	−0.211596	+	0.366495i	0.740618	+	0.671926i	$0.234533\pi$
$678$	−2.95611	+	11.7353i	−0.113529	+	0.450691i
$679$	9.18720			0.352573
$680$	8.10293	−	14.0347i	0.310733	−	0.538205i
$681$	−0.124385	+	0.493789i	−0.00476644	+	0.0189220i
$682$	−21.7325	−	37.6419i	−0.832182	−	1.44138i
$683$	−1.26949			−0.0485758			−0.0242879	−	0.999705i	$-0.507732\pi$
$683$	−1.26949			−0.0485758			−0.0242879	+	0.999705i	$0.507732\pi$
$684$	−2.67310	+	12.8006i	−0.102209	+	0.489442i
$685$	−70.3127			−2.68651
$686$	10.0444	+	17.3975i	0.383498	+	0.664239i
$687$	8.97884	+	8.71284i	0.342564	+	0.332416i
$688$	0.838250	−	1.45189i	0.0319580	−	0.0553529i
$689$	5.50305			0.209649
$690$	34.2007	−	9.71741i	1.30200	−	0.369936i
$691$	5.66777	−	9.81687i	0.215612	−	0.373451i	−0.737850	−	0.674965i	$-0.764159\pi$
$691$	5.66777	−	9.81687i	0.215612	−	0.373451i	0.953462	+	0.301514i	$0.0974919\pi$
$692$	−1.44752			−0.0550265
$693$	−27.9991	−	15.0616i	−1.06360	−	0.572144i
$694$	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
$697$	−5.68551	+	9.84760i	−0.215354	+	0.373004i
$698$	12.9158			0.488872
$699$	−7.95180	+	31.5674i	−0.300765	+	1.19399i
$700$	10.8313	+	18.7604i	0.409386	+	0.709078i
$701$	−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
$705$	46.9023	−	13.3263i	1.76644	−	0.501898i
$706$	−26.2855			−0.989267
$707$	4.41412	−	7.64548i	0.166010	−	0.287538i
$708$	−6.11937	+	24.2930i	−0.229980	+	0.912985i
$709$	33.9784			1.27609			0.638043	−	0.770001i	$-0.279744\pi$
$709$	33.9784			1.27609			0.638043	+	0.770001i	$0.279744\pi$
$710$	−17.4142			−0.653543
$711$	5.27691	+	2.83862i	0.197900	+	0.106457i
$712$	0.817559	+	1.41605i	0.0306393	+	0.0530688i
$713$	43.8263			1.64131
$714$	3.56923	−	14.1693i	0.133575	−	0.530272i
$715$	39.5208	+	68.4520i	1.47799	+	2.55996i
$716$	−0.657100	+	1.13813i	−0.0245570	+	0.0425339i
$717$	4.15928	+	4.03606i	0.155331	+	0.150730i
$718$	15.0850			0.562966
$719$	−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	$0.324266\pi$
$720$	−10.4190	−	5.60474i	−0.388295	−	0.208876i
$721$	29.8339			1.11107
$722$	0.982344	+	18.9746i	0.0365590	+	0.706161i
$723$	2.07855	−	0.590577i	0.0773022	−	0.0219638i
$724$	10.7110			0.398073
$725$	−12.6882			−0.471228
$726$	−6.62096	+	26.2842i	−0.245727	+	0.975498i
$727$	15.0657	+	26.0946i	0.558758	+	0.967797i	0.997601	+	0.0692328i	$0.0220551\pi$
$727$	15.0657	+	26.0946i	0.558758	+	0.967797i	−0.438843	+	0.898564i	$0.644612\pi$
$728$	−3.98527	−	6.90269i	−0.147704	−	0.255831i
$729$	−2.43223	−	26.8902i	−0.0900824	−	0.995934i
$730$	40.0957			1.48401
$731$	−6.88938			−0.254813
$732$	−2.78954	+	11.0740i	−0.103104	+	0.409308i
$733$	−22.4900	−	38.9539i	−0.830688	−	1.43879i	−0.897494	−	0.441028i	$-0.854614\pi$
$733$	−22.4900	−	38.9539i	−0.830688	−	1.43879i	0.0668058	−	0.997766i	$-0.478719\pi$
$734$	−15.2039	−	26.3340i	−0.561188	−	0.972006i
$735$	−13.6548	−	13.2503i	−0.503665	−	0.488744i
$736$	2.60260	+	4.50783i	0.0959330	+	0.166161i
$737$	−37.9910	−	65.8024i	−1.39942	−	2.42386i
$738$	7.31065	+	3.93263i	0.269109	+	0.144762i
$739$	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
$741$	13.6062	−	25.9635i	0.499835	−	0.953793i
$742$	−1.45488	−	2.51992i	−0.0534102	−	0.0925091i
$743$	19.3933			0.711471			0.355735	−	0.934587i	$-0.384230\pi$
$743$	19.3933			0.711471			0.355735	+	0.934587i	$0.384230\pi$
$744$	−10.4659	−	10.1558i	−0.383698	−	0.372331i
$745$	−73.9758			−2.71026
$746$	5.07447	−	8.78925i	0.185790	−	0.321797i
$747$	0.475397	+	15.8059i	0.0173939	+	0.578306i
$748$	−21.2138			−0.775654
$749$	−2.16870	+	3.75629i	−0.0792424	+	0.137252i
$750$	−27.2168	−	26.4105i	−0.993817	−	0.964375i
$751$	14.4724	−	25.0669i	0.528104	−	0.914703i	−0.471359	−	0.881941i	$-0.656236\pi$
$751$	14.4724	−	25.0669i	0.528104	−	0.914703i	0.999463	−	0.0327619i	$-0.0104303\pi$
$752$	3.56916	+	6.18197i	0.130154	+	0.225433i
$753$	−6.37921	−	6.19023i	−0.232471	−	0.225584i
$754$	4.66848			0.170016
$755$	−11.0740	+	19.1807i	−0.403024	+	0.698057i
$756$	−10.4178	−	2.29351i	−0.378890	−	0.0834142i
$757$	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	$-0.0725405\pi$
$758$	3.76687	+	6.52442i	0.136819	+	0.236978i
$759$	−33.4008	−	32.4113i	−1.21237	−	1.17646i
$760$	−16.7136	−	4.01820i	−0.606267	−	0.145755i
$761$	5.50420	+	9.53355i	0.199527	+	0.345591i	0.948375	−	0.317151i	$-0.102726\pi$
$761$	5.50420	+	9.53355i	0.199527	+	0.345591i	−0.748848	+	0.662742i	$0.769393\pi$
$762$	−1.46802	+	5.82781i	−0.0531808	+	0.211119i
$763$	−9.86464	−	17.0861i	−0.357124	−	0.618557i
$764$	−1.88682	−	3.26807i	−0.0682629	−	0.118235i
$765$	1.46162	+	48.5956i	0.0528451	+	1.75698i
$766$	−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
$769$	22.9703	−	39.7858i	0.828331	−	1.43471i	−0.0710158	−	0.997475i	$-0.522624\pi$
$769$	22.9703	−	39.7858i	0.828331	−	1.43471i	0.899347	−	0.437236i	$-0.144043\pi$
$770$	20.8967	−	36.1942i	0.753065	−	1.30435i
$771$	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	$0.872970\pi$
$774$	0.151205	+	5.02723i	0.00543497	+	0.180700i
$775$	−44.4233	−	76.9434i	−1.59573	−	2.76389i
$776$	−2.23760	−	3.87564i	−0.0803253	−	0.139128i
$777$	−0.378113	+	1.50105i	−0.0135647	+	0.0538499i
$778$	−19.0890	−	33.0631i	−0.684373	−	1.18537i
$779$	11.7273	+	2.81941i	0.420175	+	0.101016i
$780$	19.0323	+	18.4684i	0.681465	+	0.661276i
$781$	11.3978	+	19.7415i	0.407844	+	0.706407i
$782$	10.6951	−	18.5244i	0.382455	−	0.662431i
$783$	4.21431	−	4.61270i	0.150607	−	0.164844i
$784$	1.39278	−	2.41236i	0.0497421	−	0.0861559i
$785$	−47.6113			−1.69932
$786$	−0.448053	−	0.434779i	−0.0159815	−	0.0155081i
$787$	6.00458	+	10.4002i	0.214040	+	0.370728i	0.952975	−	0.303048i	$-0.0980044\pi$
$787$	6.00458	+	10.4002i	0.214040	+	0.370728i	−0.738935	+	0.673777i	$0.764671\pi$
$788$	10.3137	−	17.8639i	0.367411	−	0.636374i
$789$	0.625804	+	0.607265i	0.0222792	+	0.0216192i
$790$	−3.93834	+	6.82140i	−0.140120	+	0.242695i
$791$	−14.3437			−0.510005
$792$	0.465593	+	15.4799i	0.0165441	+	0.550053i
$793$	12.7995	−	22.1693i	0.454522	−	0.787256i
$794$	3.97045			0.140906
$795$	6.94799	+	6.74216i	0.246420	+	0.239120i
$796$	−6.45585			−0.228821
$797$	15.3351	+	26.5611i	0.543195	+	0.940842i	0.998718	+	0.0506179i	$0.0161191\pi$
$797$	15.3351	+	26.5611i	0.543195	+	0.940842i	−0.455523	+	0.890224i	$0.650548\pi$
$798$	−15.4862	+	0.633688i	−0.548205	+	0.0224323i
$799$	14.6670	−	25.4041i	0.518883	−	0.898731i
$800$	5.27609	−	9.13846i	0.186538	−	0.323093i
$801$	−4.31998	−	2.32385i	−0.152639	−	0.0821093i
$802$	−1.43491	−	2.48535i	−0.0506686	−	0.0877606i
$803$	−26.2431	−	45.4543i	−0.926097	−	1.60405i
$804$	−18.2956	−	17.7536i	−0.645236	−	0.626121i
$805$	21.0704	+	36.4950i	0.742634	+	1.28628i
$806$	16.3450	+	28.3104i	0.575729	+	0.997192i
$807$	−2.46041	+	9.76743i	−0.0866104	+	0.343830i
$808$	−4.30035			−0.151286
$809$	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	$0.559312\pi$
$812$	−1.23424	−	2.13776i	−0.0433132	−	0.0750207i
$813$	−13.7207	+	54.4692i	−0.481207	+	1.91032i
$814$	2.24733			0.0787688
$815$	−45.4323			−1.59142
$816$	−6.84665	+	1.94533i	−0.239681	+	0.0681003i
$817$	2.07327	+	7.00742i	0.0725347	+	0.245159i
$818$	22.8271			0.798132
$819$	21.0581	+	11.3278i	0.735831	+	0.395827i
$820$	−5.45618	+	9.45039i	−0.190538	+	0.330022i
$821$	20.3884			0.711562			0.355781	−	0.934569i	$-0.384215\pi$
$821$	20.3884			0.711562			0.355781	+	0.934569i	$0.384215\pi$
$822$	22.1624	+	21.5058i	0.773001	+	0.750101i
$823$	−9.55183	+	16.5442i	−0.332956	+	0.576696i	−0.983090	−	0.183123i	$-0.941379\pi$
$823$	−9.55183	+	16.5442i	−0.332956	+	0.576696i	0.650134	+	0.759819i	$0.274713\pi$
$824$	−7.26626	−	12.5855i	−0.253132	−	0.438437i
$825$	−23.0469	+	91.4926i	−0.802391	+	3.18536i
$826$	−29.6926			−1.03314
$827$	−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	$0.631136\pi$
$830$	−20.7868			−0.721522
$831$	−8.36171	+	33.1947i	−0.290064	+	1.15151i
$832$	−1.94128	+	3.36239i	−0.0673017	+	0.116570i
$833$	−11.4469			−0.396612
$834$	32.5259	−	9.24155i	1.12628	−	0.320009i
$835$	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
$839$	−10.5602	−	18.2908i	−0.364579	−	0.631470i	0.624129	−	0.781321i	$-0.285454\pi$
$839$	−10.5602	−	18.2908i	−0.364579	−	0.631470i	−0.988709	+	0.149851i	$0.952120\pi$
$840$	3.42526	−	13.5978i	0.118183	−	0.469167i
$841$	−27.5542			−0.950144
$842$	−6.22588	+	10.7835i	−0.214558	+	0.371625i
$843$	−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
$846$	−18.8594	−	10.1451i	−0.648401	−	0.348795i
$847$	−32.1265			−1.10388
$848$	−0.708689	+	1.22749i	−0.0243365	+	0.0421520i
$849$	4.56951	−	1.29833i	0.156825	−	0.0445586i
$850$	−43.3629			−1.48734
$851$	−1.13300	+	1.96242i	−0.0388388	+	0.0672709i
$852$	5.48890	+	5.32629i	0.188047	+	0.182476i
$853$	−5.64078	−	9.77012i	−0.193137	−	0.334523i	0.753151	−	0.657847i	$-0.228533\pi$
$853$	−5.64078	−	9.77012i	−0.193137	−	0.334523i	−0.946288	+	0.323325i	$0.895199\pi$
$854$	−13.5355			−0.463175
$855$	48.9884	−	16.1109i	1.67537	−	0.550982i
$856$	2.11280			0.0722141
$857$	−20.6391	−	35.7479i	−0.705017	−	1.22113i	−0.966685	−	0.255968i	$-0.917606\pi$
$857$	−20.6391	−	35.7479i	−0.705017	−	1.22113i	0.261668	−	0.965158i	$-0.415727\pi$
$858$	8.47985	−	33.6637i	0.289497	−	1.14926i
$859$	13.8230	−	23.9422i	0.471636	−	0.816897i	−0.527838	−	0.849345i	$-0.676997\pi$
$859$	13.8230	−	23.9422i	0.471636	−	0.816897i	0.999473	+	0.0324485i	$0.0103305\pi$
$860$	−6.61149			−0.225450
$861$	−2.40337	+	9.54102i	−0.0819068	+	0.325157i
$862$	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	$0.506762\pi$
$864$	1.56979	+	4.95336i	0.0534054	+	0.168517i
$865$	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
$868$	8.64248	−	14.9692i	0.293345	−	0.508088i
$869$	10.3107			0.349768
$870$	5.89429	+	5.71967i	0.199835	+	0.193915i
$871$	28.5730	+	49.4899i	0.968160	+	1.67690i
$872$	−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
$876$	−12.6380	−	12.2636i	−0.427000	−	0.414350i
$877$	29.5234			0.996934			0.498467	−	0.866909i	$-0.333896\pi$
$877$	29.5234			0.996934			0.498467	+	0.866909i	$0.333896\pi$
$878$	−6.31870	+	10.9443i	−0.213246	+	0.369352i
$879$	−37.6393	−	36.5242i	−1.26954	−	1.23193i
$880$	−20.3581			−0.686273
$881$	−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	$-0.333950\pi$
$884$	15.9549			0.536621
$885$	95.0335	−	27.0018i	3.19452	−	0.907655i
$886$	−11.0306	−	19.1056i	−0.370581	−	0.641865i
$887$	18.2609	−	31.6289i	0.613142	−	1.06199i	−0.377565	−	0.925983i	$-0.623239\pi$
$887$	18.2609	−	31.6289i	0.613142	−	1.06199i	0.990707	−	0.136010i	$-0.0434280\pi$
$888$	0.725314	−	0.206083i	0.0243400	−	0.00691569i
$889$	−7.12318			−0.238904
$890$	3.22415	−	5.58438i	0.108074	−	0.187189i
$891$	−25.6065	−	38.7672i	−0.857850	−	1.29875i
$892$	−8.40880			−0.281547
$893$	−30.2532	−	7.27331i	−1.01239	−	0.243392i
$894$	23.3169	+	22.6262i	0.779835	+	0.756733i
$895$	5.18271			0.173239
$896$	2.05291			0.0685829
$897$	25.1207	+	24.3765i	0.838757	+	0.813908i
$898$	16.1029	+	27.8910i	0.537360	+	0.930736i
$899$	5.06205	+	8.76773i	0.168829	+	0.292420i
$900$	0.951713	+	31.6422i	0.0317238	+	1.05474i
$901$	5.82455			0.194044
$902$	14.2845			0.475623
$903$	−5.73424	+	1.62926i	−0.190824	+	0.0542185i
$904$	3.49351	+	6.05094i	0.116192	+	0.201251i
$905$	−21.1202	−	36.5812i	−0.702058	−	1.21600i
$906$	9.35708	−	2.65862i	0.310868	−	0.0883267i
$907$	11.7699	+	20.3860i	0.390812	+	0.676906i	0.992557	−	0.121782i	$-0.0388610\pi$
$907$	11.7699	+	20.3860i	0.390812	+	0.676906i	−0.601745	+	0.798688i	$0.705528\pi$
$908$	0.146997	+	0.254607i	0.00487828	+	0.00844943i
$909$	10.9737	−	6.78350i	0.363973	−	0.224995i
$910$	−15.7164	+	27.2216i	−0.520994	+	0.902388i
$911$	−1.39516	+	2.41648i	−0.0462236	+	0.0800617i	−0.888212	−	0.459435i	$-0.848052\pi$
$911$	−1.39516	+	2.41648i	−0.0462236	+	0.0800617i	0.841988	+	0.539496i	$0.181385\pi$
$912$	4.03908	+	6.37854i	0.133747	+	0.211215i
$913$	13.6052	+	23.5649i	0.450267	+	0.779885i
$914$	1.80666			0.0597589
$915$	43.3214	−	12.3089i	1.43216	−	0.406919i
$916$	7.22342			0.238668
$917$	0.369991	−	0.640843i	0.0122182	−	0.0211625i
$918$	14.4027	−	15.7642i	0.475360	−	0.520297i
$919$	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
$921$	6.89845	−	27.3858i	0.227312	−	0.902392i
$922$	−11.7593	+	20.3677i	−0.387273	+	0.670776i
$923$	−8.57226	−	14.8476i	−0.282159	−	0.488714i
$924$	−17.6569	+	5.01684i	−0.580870	+	0.165042i
$925$	4.59374			0.151041
$926$	−10.1793	+	17.6310i	−0.334511	+	0.579391i
$927$	38.3949	+	20.6538i	1.26105	+	0.678360i
$928$	−0.601213	+	1.04133i	−0.0197358	+	0.0341834i
$929$	22.2283	+	38.5006i	0.729288	+	1.26316i	0.957184	+	0.289479i	$0.0934821\pi$
$929$	22.2283	+	38.5006i	0.729288	+	1.26316i	−0.227896	+	0.973685i	$0.573185\pi$
$930$	−14.0482	+	55.7693i	−0.460660	+	1.82875i
$931$	3.44481	+	11.6431i	0.112899	+	0.381586i
$932$	9.39739	+	16.2768i	0.307822	+	0.533163i
$933$	−33.1315	−	32.1500i	−1.08468	−	1.05254i
$934$	11.1361	+	19.2882i	0.364383	+	0.631130i
$935$	41.8297	+	72.4511i	1.36798	+	2.36940i
$936$	−0.350172	−	11.6424i	−0.0114457	−	0.380544i
$937$	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
$940$	14.0754	−	24.3794i	0.459090	−	0.795168i
$941$	21.8085	−	37.7734i	0.710936	−	1.23138i	−0.253570	−	0.967317i	$-0.581605\pi$
$941$	21.8085	−	37.7734i	0.710936	−	1.23138i	0.964506	−	0.264060i	$-0.0850619\pi$
$942$	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
$945$	12.7089	+	40.1019i	0.413420	+	1.30452i
$946$	4.32729	+	7.49509i	0.140692	+	0.243686i
$947$	5.22901	+	9.05691i	0.169920	+	0.294310i	0.938392	−	0.345574i	$-0.112316\pi$
$947$	5.22901	+	9.05691i	0.169920	+	0.294310i	−0.768472	+	0.639884i	$0.778982\pi$
$948$	3.32774	−	0.945508i	0.108080	−	0.0307087i
$949$	19.7374	+	34.1861i	0.640702	+	1.10973i
$950$	13.0495	+	44.1059i	0.423383	+	1.43098i
$951$	−27.7394	+	7.88157i	−0.899512	+	0.255577i
$952$	−4.21809	−	7.30595i	−0.136709	−	0.236787i
$953$	−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	$0.976589\pi$
$954$	−0.127835	−	4.25021i	−0.00413881	−	0.137606i
$955$	−7.44092	+	12.8881i	−0.240783	+	0.417048i
$956$	3.34611			0.108221
$957$	2.62621	−	10.4256i	0.0848932	−	0.337013i
$958$	6.26933	+	10.8588i	0.202553	+	0.350832i
$959$	−18.3011	+	31.6985i	−0.590975	+	1.02360i
$960$	−6.57049	+	1.86687i	−0.212062	+	0.0602529i
$961$	−19.9459	+	34.5474i	−0.643417	+	1.11443i
$962$	−1.69021			−0.0544947
$963$	−5.39146	+	3.33280i	−0.173737	+	0.107398i
$964$	0.623776	−	1.08041i	0.0200905	−	0.0347977i
$965$	64.0072			2.06046
$966$	4.52101	−	17.9477i	0.145461	−	0.577457i
$967$	20.7731			0.668019			0.334009	−	0.942570i	$-0.391598\pi$
$967$	20.7731			0.668019			0.334009	+	0.942570i	$0.391598\pi$
$968$	7.82462	+	13.5526i	0.251493	+	0.435598i
$969$	14.4011	−	27.4803i	0.462629	−	0.882795i
$970$	−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	$-0.0588959\pi$
$972$	−11.8194	−	10.1638i	−0.379107	−	0.326003i
$973$	20.0386	+	34.7078i	0.642407	+	1.11268i
$974$	−1.96044	−	3.39559i	−0.0628167	−	0.108802i
$975$	17.3336	−	68.8115i	0.555118	−	2.20373i
$976$	3.29666	+	5.70999i	0.105524	+	0.182772i
$977$	−30.3147	−	52.5066i	−0.969852	−	1.67983i	−0.695970	−	0.718071i	$-0.745026\pi$
$977$	−30.3147	−	52.5066i	−0.969852	−	1.67983i	−0.273882	−	0.961763i	$-0.588308\pi$
$978$	14.3201	+	13.8959i	0.457907	+	0.444342i
$979$	−8.44095			−0.269774
$980$	−10.9852			−0.350909
$981$	−0.866772	−	28.8182i	−0.0276739	−	0.920093i
$982$	−7.38534	−	12.7918i	−0.235676	−	0.408202i
$983$	0.200134	+	0.346643i	0.00638329	+	0.0110562i	0.869199	−	0.494462i	$-0.164635\pi$
$983$	0.200134	+	0.346643i	0.00638329	+	0.0110562i	−0.862816	+	0.505518i	$0.831301\pi$
$984$	4.61026	−	1.30991i	0.146970	−	0.0417584i
$985$	−81.3468			−2.59192
$986$	4.94122			0.157361
$987$	6.20004	−	24.6132i	0.197349	−	0.783446i
$988$	−4.80143	−	16.2283i	−0.152754	−	0.516290i
$989$	−8.72651			−0.277487
$990$	51.9500	−	32.1135i	1.65108	−	1.02064i
$991$	−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	$0.847689\pi$
$992$	−8.41973			−0.267327
$993$	−0.132138	+	0.524568i	−0.00419328	+	0.0166466i
$994$	−4.53260	+	7.85070i	−0.143765	+	0.249009i
$995$	12.7297	+	22.0485i	0.403559	+	0.698985i
$996$	6.55195	+	6.35785i	0.207607	+	0.201456i
$997$	8.39861			0.265987			0.132993	−	0.991117i	$-0.457541\pi$
$997$	8.39861			0.265987			0.132993	+	0.991117i	$0.457541\pi$
$998$	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.h.g.277.2	yes	18
3.2	odd	2		1026.2.h.g.505.1		18
9.4	even	3		342.2.f.g.49.5	yes	18
9.5	odd	6		1026.2.f.g.847.9		18
19.7	even	3		342.2.f.g.7.5	✓	18
57.26	odd	6		1026.2.f.g.235.9		18
171.121	even	3	inner	342.2.h.g.121.2	yes	18
171.140	odd	6		1026.2.h.g.577.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.g.7.5	✓	18	19.7	even	3
342.2.f.g.49.5	yes	18	9.4	even	3
342.2.h.g.121.2	yes	18	171.121	even	3	inner
342.2.h.g.277.2	yes	18	1.1	even	1	trivial
1026.2.f.g.235.9		18	57.26	odd	6
1026.2.f.g.847.9		18	9.5	odd	6
1026.2.h.g.505.1		18	3.2	odd	2
1026.2.h.g.577.1		18	171.140	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.66610 + 0.473389i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.94363 q^{5} +(-1.24302 - 1.20619i) q^{6} +(1.02646 - 1.77787i) q^{7} -1.00000 q^{8} +(2.55181 - 1.57743i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.66610 + 0.473389i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.94363 q^{5} +(-1.24302 - 1.20619i) q^{6} +(1.02646 - 1.77787i) q^{7} -1.00000 q^{8} +(2.55181 - 1.57743i) q^{9} +(1.97181 + 3.41528i) q^{10} +(2.58114 - 4.47067i) q^{11} +(0.423085 - 1.67958i) q^{12} +(-1.94128 + 3.36239i) q^{13} +2.05291 q^{14} +(-6.57049 + 1.86687i) q^{15} +(-0.500000 - 0.866025i) 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} +(-0.868557 + 3.44803i) q^{21} +5.16229 q^{22} +(-2.60260 + 4.50783i) q^{23} +(1.66610 - 0.473389i) q^{24} +10.5522 q^{25} -3.88255 q^{26} +(-3.50484 + 3.83616i) q^{27} +(1.02646 + 1.77787i) q^{28} -1.20243 q^{29} +(-4.90200 - 4.75678i) q^{30} +(-4.20987 - 7.29170i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.18409 + 8.67049i) q^{33} -4.10938 q^{34} +(4.04796 - 7.01126i) q^{35} +(0.0901911 + 2.99864i) q^{36} +0.435335 q^{37} +(1.23667 + 4.17979i) q^{38} +(1.64265 - 6.52107i) q^{39} -3.94363 q^{40} +2.76709 q^{41} +(-3.42036 + 0.971825i) q^{42} +(0.838250 + 1.45189i) q^{43} +(2.58114 + 4.47067i) q^{44} +(10.0634 - 6.22079i) q^{45} -5.20520 q^{46} -7.13833 q^{47} +(1.24302 + 1.20619i) q^{48} +(1.39278 + 2.41236i) q^{49} +(5.27609 + 9.13846i) q^{50} +(1.73862 - 6.90204i) q^{51} +(-1.94128 - 3.36239i) q^{52} +(-0.708689 - 1.22749i) q^{53} +(-5.07463 - 1.11720i) q^{54} +(10.1791 - 17.6307i) q^{55} +(-1.02646 + 1.77787i) q^{56} +(-7.54352 + 0.308678i) q^{57} +(-0.601213 - 1.04133i) q^{58} -14.4637 q^{59} +(1.66849 - 6.62365i) q^{60} -6.59332 q^{61} +(4.20987 - 7.29170i) q^{62} +(-0.185154 - 6.15595i) q^{63} +1.00000 q^{64} +(-7.65567 + 13.2600i) q^{65} +(-8.60091 + 2.44377i) q^{66} +(7.35934 - 12.7467i) q^{67} +(-2.05469 - 3.55883i) q^{68} +(2.20224 - 8.74256i) q^{69} +8.09591 q^{70} +(-2.20789 + 3.82418i) q^{71} +(-2.55181 + 1.57743i) q^{72} +(5.08361 - 8.80507i) q^{73} +(0.217668 + 0.377012i) q^{74} +(-17.5810 + 4.99528i) q^{75} +(-3.00147 + 3.16088i) q^{76} +(-5.29886 - 9.17789i) q^{77} +(6.46874 - 1.83796i) q^{78} +(0.998660 + 1.72973i) q^{79} +(-1.97181 - 3.41528i) q^{80} +(4.02343 - 8.05059i) q^{81} +(1.38355 + 2.39637i) q^{82} +(-2.63550 + 4.56482i) q^{83} +(-2.55181 - 2.47621i) q^{84} +(-8.10293 + 14.0347i) q^{85} +(-0.838250 + 1.45189i) q^{86} +(2.00337 - 0.569215i) q^{87} +(-2.58114 + 4.47067i) q^{88} +(-0.817559 - 1.41605i) q^{89} +(10.4190 + 5.60474i) q^{90} +(3.98527 + 6.90269i) q^{91} +(-2.60260 - 4.50783i) q^{92} +(10.4659 + 10.1558i) q^{93} +(-3.56916 - 6.18197i) q^{94} +(16.7136 + 4.01820i) q^{95} +(-0.423085 + 1.67958i) q^{96} +(2.23760 + 3.87564i) q^{97} +(-1.39278 + 2.41236i) q^{98} +(-0.465593 - 15.4799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9}+O(q^{10}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9	\( 18 q + 9 q^{2} - 9 q^{4} + 5 q^{7} - 18 q^{8} + 4 q^{9} + q^{11} + q^{13} + 10 q^{14} - 3 q^{15} - 9 q^{16} - 5 q^{17} - 4 q^{18} + 9 q^{19} - 19 q^{21} + 2 q^{22} - 2 q^{23} + 18 q^{25} + 2 q^{26} - 18 q^{27} + 5 q^{28} + 18 q^{29} + 4 q^{31} + 9 q^{32} - 23 q^{33} - 10 q^{34} + 6 q^{35} - 8 q^{36} + 20 q^{37} + 3 q^{38} + 4 q^{39} - 2 q^{41} - 23 q^{42} + 7 q^{43} + q^{44} + 30 q^{45} - 4 q^{46} - 38 q^{47} + 6 q^{49} + 9 q^{50} + 4 q^{51} + q^{52} - 10 q^{53} - 18 q^{54} + 6 q^{55} - 5 q^{56} - 33 q^{57} + 9 q^{58} + 10 q^{59} + 3 q^{60} - 36 q^{61} - 4 q^{62} + 12 q^{63} + 18 q^{64} - 45 q^{65} - 7 q^{66} + 22 q^{67} - 5 q^{68} - 26 q^{69} + 12 q^{70} + 11 q^{71} - 4 q^{72} + 44 q^{73} + 10 q^{74} - 6 q^{76} - 2 q^{77} + 23 q^{78} + 2 q^{79} + 4 q^{81} - q^{82} - 7 q^{83} - 4 q^{84} - 7 q^{86} + 3 q^{87} - q^{88} + q^{89} + 60 q^{90} - 25 q^{91} - 2 q^{92} + 25 q^{93} - 19 q^{94} + 21 q^{95} - 6 q^{98} - 19 q^{99}+O(q^{100}) \) 18 * q + 9 * q^2 - 9 * q^4 + 5 * q^7 - 18 * q^8 + 4 * q^9 + q^11 + q^13 + 10 * q^14 - 3 * q^15 - 9 * q^16 - 5 * q^17 - 4 * q^18 + 9 * q^19 - 19 * q^21 + 2 * q^22 - 2 * q^23 + 18 * q^25 + 2 * q^26 - 18 * q^27 + 5 * q^28 + 18 * q^29 + 4 * q^31 + 9 * q^32 - 23 * q^33 - 10 * q^34 + 6 * q^35 - 8 * q^36 + 20 * q^37 + 3 * q^38 + 4 * q^39 - 2 * q^41 - 23 * q^42 + 7 * q^43 + q^44 + 30 * q^45 - 4 * q^46 - 38 * q^47 + 6 * q^49 + 9 * q^50 + 4 * q^51 + q^52 - 10 * q^53 - 18 * q^54 + 6 * q^55 - 5 * q^56 - 33 * q^57 + 9 * q^58 + 10 * q^59 + 3 * q^60 - 36 * q^61 - 4 * q^62 + 12 * q^63 + 18 * q^64 - 45 * q^65 - 7 * q^66 + 22 * q^67 - 5 * q^68 - 26 * q^69 + 12 * q^70 + 11 * q^71 - 4 * q^72 + 44 * q^73 + 10 * q^74 - 6 * q^76 - 2 * q^77 + 23 * q^78 + 2 * q^79 + 4 * q^81 - q^82 - 7 * q^83 - 4 * q^84 - 7 * q^86 + 3 * q^87 - q^88 + q^89 + 60 * q^90 - 25 * q^91 - 2 * q^92 + 25 * q^93 - 19 * q^94 + 21 * q^95 - 6 * q^98 - 19 * q^99

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