LMFDB - Embedded newform 483.2.i.g.277.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} + \cdots + 6400 $ x^16 - x^15 + 16x^14 - 7x^13 + 161x^12 - 50x^11 + 929x^10 - 47x^9 + 3741x^8 - 158x^7 + 8993x^6 + 265x^5 + 15176x^4 + 383x^3 + 12649x^2 + 2960x + 6400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.7
Root			$-0.939958 + 1.62805i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.g.415.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.939958 + 1.62805i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.767041 + 1.32855i) q^{4} +(1.32777 + 2.29977i) q^{5} -1.87992 q^{6} +(-1.98456 - 1.74973i) q^{7} +0.875886 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.939958 + 1.62805i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.767041 + 1.32855i) q^{4} +(1.32777 + 2.29977i) q^{5} -1.87992 q^{6} +(-1.98456 - 1.74973i) q^{7} +0.875886 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.49610 + 4.32337i) q^{10} +(-3.02543 + 5.24020i) q^{11} +(-0.767041 - 1.32855i) q^{12} +2.90301 q^{13} +(0.983251 - 4.87563i) q^{14} -2.65555 q^{15} +(2.35738 + 4.08310i) q^{16} +(-2.80993 + 4.86694i) q^{17} +(0.939958 - 1.62805i) q^{18} +(-3.61844 - 6.26733i) q^{19} -4.07383 q^{20} +(2.50758 - 0.843812i) q^{21} -11.3751 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.437943 + 0.758539i) q^{24} +(-1.02596 + 1.77701i) q^{25} +(2.72870 + 4.72625i) q^{26} +1.00000 q^{27} +(3.84684 - 1.29448i) q^{28} +8.39241 q^{29} +(-2.49610 - 4.32337i) q^{30} +(3.04925 - 5.28145i) q^{31} +(-3.55579 + 6.15880i) q^{32} +(-3.02543 - 5.24020i) q^{33} -10.5649 q^{34} +(1.38893 - 6.88726i) q^{35} +1.53408 q^{36} +(-0.390745 - 0.676791i) q^{37} +(6.80237 - 11.7820i) q^{38} +(-1.45150 + 2.51408i) q^{39} +(1.16298 + 2.01434i) q^{40} -3.31700 q^{41} +(3.73080 + 3.28934i) q^{42} +7.59896 q^{43} +(-4.64126 - 8.03889i) q^{44} +(1.32777 - 2.29977i) q^{45} +(-0.939958 + 1.62805i) q^{46} +(-2.52667 - 4.37633i) q^{47} -4.71476 q^{48} +(0.876920 + 6.94486i) q^{49} -3.85744 q^{50} +(-2.80993 - 4.86694i) q^{51} +(-2.22672 + 3.85680i) q^{52} +(0.924749 - 1.60171i) q^{53} +(0.939958 + 1.62805i) q^{54} -16.0683 q^{55} +(-1.73824 - 1.53256i) q^{56} +7.23689 q^{57} +(7.88851 + 13.6633i) q^{58} +(-0.982589 + 1.70189i) q^{59} +(2.03691 - 3.52804i) q^{60} +(6.92843 + 12.0004i) q^{61} +11.4647 q^{62} +(-0.523029 + 2.59354i) q^{63} -3.93964 q^{64} +(3.85453 + 6.67624i) q^{65} +(5.68755 - 9.85112i) q^{66} +(3.88990 - 6.73750i) q^{67} +(-4.31066 - 7.46629i) q^{68} -1.00000 q^{69} +(12.5184 - 4.21248i) q^{70} +9.12822 q^{71} +(-0.437943 - 0.758539i) q^{72} +(-0.441528 + 0.764749i) q^{73} +(0.734568 - 1.27231i) q^{74} +(-1.02596 - 1.77701i) q^{75} +11.1020 q^{76} +(15.1730 - 5.10579i) q^{77} -5.45740 q^{78} +(2.95597 + 5.11988i) q^{79} +(-6.26012 + 10.8429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.11784 - 5.40026i) q^{82} -8.51343 q^{83} +(-0.802370 + 3.97870i) q^{84} -14.9238 q^{85} +(7.14270 + 12.3715i) q^{86} +(-4.19620 + 7.26804i) q^{87} +(-2.64993 + 4.58981i) q^{88} +(-4.26583 - 7.38863i) q^{89} +4.99220 q^{90} +(-5.76117 - 5.07946i) q^{91} -1.53408 q^{92} +(3.04925 + 5.28145i) q^{93} +(4.74994 - 8.22713i) q^{94} +(9.60894 - 16.6432i) q^{95} +(-3.55579 - 6.15880i) q^{96} -0.669718 q^{97} +(-10.4823 + 7.95554i) q^{98} +6.05086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.939958	+	1.62805i	0.664651	+	1.15121i	0.979380	+	0.202027i	$0.0647529\pi$
$2$	0.939958	+	1.62805i	0.664651	+	1.15121i	−0.314729	+	0.949181i	$0.601914\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.767041	+	1.32855i	−0.383521	+	0.664277i
$5$	1.32777	+	2.29977i	0.593798	+	1.02849i	0.993715	+	0.111937i	$0.0357055\pi$
$5$	1.32777	+	2.29977i	0.593798	+	1.02849i	−0.399917	+	0.916551i	$0.630961\pi$
$6$	−1.87992			−0.767472
$7$	−1.98456	−	1.74973i	−0.750091	−	0.661334i
$7$	−1.98456	−	1.74973i	−0.750091	−	0.661334i
$8$	0.875886			0.309672
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−2.49610	+	4.32337i	−0.789336	+	1.36717i
$11$	−3.02543	+	5.24020i	−0.912201	+	1.57998i	−0.101252	+	0.994861i	$0.532285\pi$
$11$	−3.02543	+	5.24020i	−0.912201	+	1.57998i	−0.810948	+	0.585118i	$0.801048\pi$
$12$	−0.767041	−	1.32855i	−0.221426	−	0.383521i
$13$	2.90301			0.805149			0.402574	−	0.915387i	$-0.368115\pi$
$13$	2.90301			0.805149			0.402574	+	0.915387i	$0.368115\pi$
$14$	0.983251	−	4.87563i	0.262785	−	1.30307i
$15$	−2.65555			−0.685659
$16$	2.35738	+	4.08310i	0.589344	+	1.02077i
$17$	−2.80993	+	4.86694i	−0.681508	+	1.18041i	0.293013	+	0.956109i	$0.405342\pi$
$17$	−2.80993	+	4.86694i	−0.681508	+	1.18041i	−0.974521	+	0.224298i	$0.927991\pi$
$18$	0.939958	−	1.62805i	0.221550	−	0.383736i
$19$	−3.61844	−	6.26733i	−0.830128	−	1.43782i	−0.897936	−	0.440125i	$-0.854934\pi$
$19$	−3.61844	−	6.26733i	−0.830128	−	1.43782i	0.0678083	−	0.997698i	$-0.478399\pi$
$20$	−4.07383			−0.910935
$21$	2.50758	−	0.843812i	0.547200	−	0.184135i
$22$	−11.3751			−2.42518
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−0.437943	+	0.758539i	−0.0893947	+	0.154836i
$25$	−1.02596	+	1.77701i	−0.205192	+	0.355403i
$26$	2.72870	+	4.72625i	0.535143	+	0.926894i
$27$	1.00000			0.192450
$28$	3.84684	−	1.29448i	0.726985	−	0.244633i
$29$	8.39241			1.55843			0.779215	−	0.626756i	$-0.215618\pi$
$29$	8.39241			1.55843			0.779215	+	0.626756i	$0.215618\pi$
$30$	−2.49610	−	4.32337i	−0.455723	−	0.789336i
$31$	3.04925	−	5.28145i	0.547661	−	0.948577i	−0.450773	−	0.892638i	$-0.648852\pi$
$31$	3.04925	−	5.28145i	0.547661	−	0.948577i	0.998434	−	0.0559381i	$-0.0178149\pi$
$32$	−3.55579	+	6.15880i	−0.628580	+	1.08873i
$33$	−3.02543	−	5.24020i	−0.526659	−	0.912201i
$34$	−10.5649			−1.81186
$35$	1.38893	−	6.88726i	0.234772	−	1.16416i
$36$	1.53408			0.255680
$37$	−0.390745	−	0.676791i	−0.0642381	−	0.111264i	0.832118	−	0.554599i	$-0.187128\pi$
$37$	−0.390745	−	0.676791i	−0.0642381	−	0.111264i	−0.896356	+	0.443335i	$0.853795\pi$
$38$	6.80237	−	11.7820i	1.10349	−	1.91130i
$39$	−1.45150	+	2.51408i	−0.232426	+	0.402574i
$40$	1.16298	+	2.01434i	0.183883	+	0.318494i
$41$	−3.31700			−0.518029			−0.259014	−	0.965873i	$-0.583398\pi$
$41$	−3.31700			−0.518029			−0.259014	+	0.965873i	$0.583398\pi$
$42$	3.73080	+	3.28934i	0.575674	+	0.507556i
$43$	7.59896			1.15883			0.579415	−	0.815033i	$-0.303281\pi$
$43$	7.59896			1.15883			0.579415	+	0.815033i	$0.303281\pi$
$44$	−4.64126	−	8.03889i	−0.699696	−	1.21191i
$45$	1.32777	−	2.29977i	0.197933	−	0.342829i
$46$	−0.939958	+	1.62805i	−0.138589	+	0.240044i
$47$	−2.52667	−	4.37633i	−0.368553	−	0.638353i	0.620786	−	0.783980i	$-0.286814\pi$
$47$	−2.52667	−	4.37633i	−0.368553	−	0.638353i	−0.989340	+	0.145627i	$0.953480\pi$
$48$	−4.71476			−0.680516
$49$	0.876920	+	6.94486i	0.125274	+	0.992122i
$50$	−3.85744			−0.545524
$51$	−2.80993	−	4.86694i	−0.393469	−	0.681508i
$52$	−2.22672	+	3.85680i	−0.308791	+	0.534842i
$53$	0.924749	−	1.60171i	0.127024	−	0.220012i	−0.795498	−	0.605956i	$-0.792791\pi$
$53$	0.924749	−	1.60171i	0.127024	−	0.220012i	0.922522	+	0.385944i	$0.126124\pi$
$54$	0.939958	+	1.62805i	0.127912	+	0.221550i
$55$	−16.0683			−2.16665
$56$	−1.73824	−	1.53256i	−0.232283	−	0.204797i
$57$	7.23689			0.958549
$58$	7.88851	+	13.6633i	1.03581	+	1.79408i
$59$	−0.982589	+	1.70189i	−0.127922	+	0.221568i	−0.922871	−	0.385108i	$-0.874164\pi$
$59$	−0.982589	+	1.70189i	−0.127922	+	0.221568i	0.794949	+	0.606676i	$0.207497\pi$
$60$	2.03691	−	3.52804i	0.262964	−	0.455467i
$61$	6.92843	+	12.0004i	0.887095	+	1.53649i	0.843293	+	0.537453i	$0.180614\pi$
$61$	6.92843	+	12.0004i	0.887095	+	1.53649i	0.0438015	+	0.999040i	$0.486053\pi$
$62$	11.4647			1.45601
$63$	−0.523029	+	2.59354i	−0.0658955	+	0.326755i
$64$	−3.93964			−0.492455
$65$	3.85453	+	6.67624i	0.478096	+	0.828086i
$66$	5.68755	−	9.85112i	0.700089	−	1.21259i
$67$	3.88990	−	6.73750i	0.475227	−	0.823117i	−0.524371	−	0.851490i	$-0.675699\pi$
$67$	3.88990	−	6.73750i	0.475227	−	0.823117i	0.999597	+	0.0283732i	$0.00903268\pi$
$68$	−4.31066	−	7.46629i	−0.522745	−	0.905420i
$69$	−1.00000			−0.120386
$70$	12.5184	−	4.21248i	1.49623	−	0.503488i
$71$	9.12822			1.08332			0.541660	−	0.840597i	$-0.317796\pi$
$71$	9.12822			1.08332			0.541660	+	0.840597i	$0.317796\pi$
$72$	−0.437943	−	0.758539i	−0.0516121	−	0.0893947i
$73$	−0.441528	+	0.764749i	−0.0516769	+	0.0895071i	−0.890707	−	0.454578i	$-0.849790\pi$
$73$	−0.441528	+	0.764749i	−0.0516769	+	0.0895071i	0.839030	+	0.544085i	$0.183123\pi$
$74$	0.734568	−	1.27231i	0.0853918	−	0.147903i
$75$	−1.02596	−	1.77701i	−0.118468	−	0.205192i
$76$	11.1020			1.27348
$77$	15.1730	−	5.10579i	1.72913	−	0.581859i
$78$	−5.45740			−0.617929
$79$	2.95597	+	5.11988i	0.332572	+	0.576032i	0.983015	−	0.183523i	$-0.0587502\pi$
$79$	2.95597	+	5.11988i	0.332572	+	0.576032i	−0.650443	+	0.759555i	$0.725417\pi$
$80$	−6.26012	+	10.8429i	−0.699903	+	1.21227i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.11784	−	5.40026i	−0.344308	−	0.596359i
$83$	−8.51343			−0.934471			−0.467235	−	0.884133i	$-0.654750\pi$
$83$	−8.51343			−0.934471			−0.467235	+	0.884133i	$0.654750\pi$
$84$	−0.802370	+	3.97870i	−0.0875457	+	0.434112i
$85$	−14.9238			−1.61871
$86$	7.14270	+	12.3715i	0.770217	+	1.33405i
$87$	−4.19620	+	7.26804i	−0.449880	+	0.779215i
$88$	−2.64993	+	4.58981i	−0.282483	+	0.489276i
$89$	−4.26583	−	7.38863i	−0.452177	−	0.783193i	0.546344	−	0.837561i	$-0.316019\pi$
$89$	−4.26583	−	7.38863i	−0.452177	−	0.783193i	−0.998521	+	0.0543676i	$0.982686\pi$
$90$	4.99220			0.526224
$91$	−5.76117	−	5.07946i	−0.603935	−	0.532472i
$92$	−1.53408			−0.159939
$93$	3.04925	+	5.28145i	0.316192	+	0.547661i
$94$	4.74994	−	8.22713i	0.489918	−	0.848564i
$95$	9.60894	−	16.6432i	0.985857	−	1.70755i
$96$	−3.55579	−	6.15880i	−0.362911	−	0.628580i
$97$	−0.669718			−0.0679996			−0.0339998	−	0.999422i	$-0.510825\pi$
$97$	−0.669718			−0.0679996			−0.0339998	+	0.999422i	$0.510825\pi$
$98$	−10.4823	+	7.95554i	−1.05888	+	0.803631i
$99$	6.05086			0.608134
$100$	−1.57391	−	2.72609i	−0.157391	−	0.272609i
$101$	6.45154	−	11.1744i	0.641952	−	1.11189i	−0.343044	−	0.939319i	$-0.611458\pi$
$101$	6.45154	−	11.1744i	0.641952	−	1.11189i	0.984996	−	0.172575i	$-0.0552087\pi$
$102$	5.28243	−	9.14944i	0.523038	−	0.905929i
$103$	5.06337	+	8.77002i	0.498909	+	0.864136i	0.999999	−	0.00125918i	$-0.000400810\pi$
$103$	5.06337	+	8.77002i	0.498909	+	0.864136i	−0.501090	+	0.865395i	$0.667067\pi$
$104$	2.54270			0.249332
$105$	5.27008	+	4.64648i	0.514307	+	0.453450i
$106$	3.47690			0.337706
$107$	3.78526	+	6.55626i	0.365935	+	0.633818i	0.988926	−	0.148411i	$-0.0474160\pi$
$107$	3.78526	+	6.55626i	0.365935	+	0.633818i	−0.622991	+	0.782229i	$0.714083\pi$
$108$	−0.767041	+	1.32855i	−0.0738086	+	0.127840i
$109$	3.25356	−	5.63532i	0.311634	−	0.539766i	−0.667082	−	0.744984i	$-0.732457\pi$
$109$	3.25356	−	5.63532i	0.311634	−	0.539766i	0.978716	+	0.205218i	$0.0657904\pi$
$110$	−15.1035	−	26.1601i	−1.44007	−	2.49427i
$111$	0.781491			0.0741758
$112$	2.46596	−	12.2279i	0.233011	−	1.15543i
$113$	1.47158			0.138435			0.0692174	−	0.997602i	$-0.477950\pi$
$113$	1.47158			0.138435			0.0692174	+	0.997602i	$0.477950\pi$
$114$	6.80237	+	11.7820i	0.637100	+	1.10349i
$115$	−1.32777	+	2.29977i	−0.123815	+	0.214455i
$116$	−6.43732	+	11.1498i	−0.597690	+	1.03523i
$117$	−1.45150	−	2.51408i	−0.134191	−	0.232426i
$118$	−3.69437			−0.340094
$119$	14.0923	−	4.74211i	1.29184	−	0.434708i
$120$	−2.32595			−0.212330
$121$	−12.8064	−	22.1814i	−1.16422	−	2.01649i
$122$	−13.0249	+	22.5597i	−1.17922	+	2.04246i
$123$	1.65850	−	2.87261i	0.149542	−	0.259014i
$124$	4.67780	+	8.10218i	0.420078	+	0.727597i
$125$	7.82876			0.700226
$126$	−4.71405	+	1.58630i	−0.419961	+	0.141318i
$127$	18.8588			1.67345			0.836724	−	0.547625i	$-0.184468\pi$
$127$	18.8588			1.67345			0.836724	+	0.547625i	$0.184468\pi$
$128$	3.40847	+	5.90365i	0.301269	+	0.521814i
$129$	−3.79948	+	6.58089i	−0.334525	+	0.579415i
$130$	−7.24619	+	12.5508i	−0.635533	+	1.10078i
$131$	−8.47971	−	14.6873i	−0.740876	−	1.28323i	−0.952097	−	0.305797i	$-0.901077\pi$
$131$	−8.47971	−	14.6873i	−0.740876	−	1.28323i	0.211221	−	0.977438i	$-0.432256\pi$
$132$	9.28251			0.807939
$133$	−3.78510	+	18.7691i	−0.328210	+	1.62749i
$134$	14.6254			1.26344
$135$	1.32777	+	2.29977i	0.114276	+	0.197933i
$136$	−2.46118	+	4.26288i	−0.211044	+	0.365539i
$137$	−6.28156	+	10.8800i	−0.536670	+	0.929540i	0.462410	+	0.886666i	$0.346985\pi$
$137$	−6.28156	+	10.8800i	−0.536670	+	0.929540i	−0.999080	+	0.0428738i	$0.986349\pi$
$138$	−0.939958	−	1.62805i	−0.0800145	−	0.138589i
$139$	−13.9762			−1.18545			−0.592725	−	0.805405i	$-0.701948\pi$
$139$	−13.9762			−1.18545			−0.592725	+	0.805405i	$0.701948\pi$
$140$	8.08473	+	7.12808i	0.683285	+	0.602432i
$141$	5.05335			0.425569
$142$	8.58014	+	14.8612i	0.720030	+	1.24713i
$143$	−8.78283	+	15.2123i	−0.734457	+	1.27212i
$144$	2.35738	−	4.08310i	0.196448	−	0.340258i
$145$	11.1432	+	19.3006i	0.925393	+	1.60283i
$146$	−1.66007			−0.137388
$147$	−6.45288	−	2.71299i	−0.532225	−	0.223764i
$148$	1.19887			0.0985466
$149$	−4.96708	−	8.60323i	−0.406919	−	0.704804i	0.587624	−	0.809134i	$-0.300064\pi$
$149$	−4.96708	−	8.60323i	−0.406919	−	0.704804i	−0.994543	+	0.104330i	$0.966730\pi$
$150$	1.92872	−	3.34064i	0.157479	−	0.272762i
$151$	−5.47935	+	9.49051i	−0.445903	+	0.772327i	−0.998115	−	0.0613770i	$-0.980451\pi$
$151$	−5.47935	+	9.49051i	−0.445903	+	0.772327i	0.552211	+	0.833704i	$0.313784\pi$
$152$	−3.16934	−	5.48946i	−0.257068	−	0.445254i
$153$	5.61986			0.454339
$154$	22.5745	+	19.9033i	1.81911	+	1.60385i
$155$	16.1948			1.30080
$156$	−2.22672	−	3.85680i	−0.178281	−	0.308791i
$157$	4.02477	−	6.97110i	0.321211	−	0.556354i	−0.659527	−	0.751681i	$-0.729243\pi$
$157$	4.02477	−	6.97110i	0.321211	−	0.556354i	0.980738	+	0.195327i	$0.0625767\pi$
$158$	−5.55696	+	9.62495i	−0.442088	+	0.765720i
$159$	0.924749	+	1.60171i	0.0733373	+	0.127024i
$160$	−18.8851			−1.49300
$161$	0.523029	−	2.59354i	0.0412205	−	0.204399i
$162$	−1.87992			−0.147700
$163$	−1.46887	−	2.54416i	−0.115051	−	0.199274i	0.802749	−	0.596317i	$-0.203370\pi$
$163$	−1.46887	−	2.54416i	−0.115051	−	0.199274i	−0.917800	+	0.397043i	$0.870037\pi$
$164$	2.54428	−	4.40682i	0.198675	−	0.344115i
$165$	8.03416	−	13.9156i	0.625459	−	1.08333i
$166$	−8.00227	−	13.8603i	−0.621096	−	1.07577i
$167$	−8.45552			−0.654308			−0.327154	−	0.944971i	$-0.606090\pi$
$167$	−8.45552			−0.654308			−0.327154	+	0.944971i	$0.606090\pi$
$168$	2.19636	−	0.739083i	0.169453	−	0.0570215i
$169$	−4.57256			−0.351735
$170$	−14.0277	−	24.2967i	−1.07588	−	1.86347i
$171$	−3.61844	+	6.26733i	−0.276709	+	0.479275i
$172$	−5.82871	+	10.0956i	−0.444435	+	0.769784i
$173$	−3.05919	−	5.29867i	−0.232586	−	0.402850i	0.725983	−	0.687713i	$-0.241385\pi$
$173$	−3.05919	−	5.29867i	−0.232586	−	0.402850i	−0.958568	+	0.284863i	$0.908052\pi$
$174$	−15.7770			−1.19605
$175$	5.14536	−	1.73144i	0.388953	−	0.130884i
$176$	−28.5283			−2.15040
$177$	−0.982589	−	1.70189i	−0.0738559	−	0.127922i
$178$	8.01939	−	13.8900i	0.601079	−	1.04110i
$179$	−8.36825	+	14.4942i	−0.625472	+	1.08335i	0.362977	+	0.931798i	$0.381760\pi$
$179$	−8.36825	+	14.4942i	−0.625472	+	1.08335i	−0.988449	+	0.151552i	$0.951573\pi$
$180$	2.03691	+	3.52804i	0.151822	+	0.262964i
$181$	−1.61304			−0.119897			−0.0599483	−	0.998201i	$-0.519094\pi$
$181$	−1.61304			−0.119897			−0.0599483	+	0.998201i	$0.519094\pi$
$182$	2.85438	−	14.1540i	0.211581	−	1.04916i
$183$	−13.8569			−1.02433
$184$	0.437943	+	0.758539i	0.0322856	+	0.0559203i
$185$	1.03764	−	1.79725i	0.0762889	−	0.132136i
$186$	−5.73233	+	9.92868i	−0.420315	+	0.728006i
$187$	−17.0025	−	29.4492i	−1.24334	−	2.15354i
$188$	7.75226			0.565391
$189$	−1.98456	−	1.74973i	−0.144355	−	0.127274i
$190$	36.1280			2.62100
$191$	−7.47816	−	12.9525i	−0.541100	−	0.937214i	−0.998841	−	0.0481278i	$-0.984675\pi$
$191$	−7.47816	−	12.9525i	−0.541100	−	0.937214i	0.457741	−	0.889086i	$-0.348659\pi$
$192$	1.96982	−	3.41183i	0.142160	−	0.246228i
$193$	7.88623	−	13.6593i	0.567663	−	0.983221i	−0.429133	−	0.903241i	$-0.641181\pi$
$193$	7.88623	−	13.6593i	0.567663	−	0.983221i	0.996796	−	0.0799802i	$-0.0254857\pi$
$194$	−0.629507	−	1.09034i	−0.0451959	−	0.0782817i
$195$	−7.70906			−0.552057
$196$	−9.89925	−	4.16195i	−0.707089	−	0.297282i
$197$	−7.28311			−0.518900			−0.259450	−	0.965757i	$-0.583541\pi$
$197$	−7.28311			−0.518900			−0.259450	+	0.965757i	$0.583541\pi$
$198$	5.68755	+	9.85112i	0.404197	+	0.700089i
$199$	8.95658	−	15.5133i	0.634915	−	1.09971i	−0.351618	−	0.936144i	$-0.614368\pi$
$199$	8.95658	−	15.5133i	0.634915	−	1.09971i	0.986533	−	0.163562i	$-0.0522983\pi$
$200$	−0.898623	+	1.55646i	−0.0635423	+	0.110058i
$201$	3.88990	+	6.73750i	0.274372	+	0.475227i
$202$	24.2567			1.70670
$203$	−16.6552	−	14.6844i	−1.16897	−	1.03064i
$204$	8.62133			0.603614
$205$	−4.40423	−	7.62834i	−0.307604	−	0.532787i
$206$	−9.51872	+	16.4869i	−0.663200	+	1.14870i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	6.84348	+	11.8533i	0.474510	+	0.821875i
$209$	43.7894			3.02897
$210$	−2.61107	+	12.9475i	−0.180181	+	0.893460i
$211$	−2.02819			−0.139626			−0.0698132	−	0.997560i	$-0.522240\pi$
$211$	−2.02819			−0.139626			−0.0698132	+	0.997560i	$0.522240\pi$
$212$	1.41864	+	2.45716i	0.0974326	+	0.168758i
$213$	−4.56411	+	7.90527i	−0.312728	+	0.541660i
$214$	−7.11597	+	12.3252i	−0.486438	+	0.842535i
$215$	10.0897	+	17.4758i	0.688111	+	1.19184i
$216$	0.875886			0.0595965
$217$	−15.2925	+	5.14599i	−1.03812	+	0.349332i
$218$	12.2328			0.828511
$219$	−0.441528	−	0.764749i	−0.0298357	−	0.0516769i
$220$	12.3251	−	21.3476i	0.830956	−	1.43926i
$221$	−8.15724	+	14.1288i	−0.548715	+	0.950403i
$222$	0.734568	+	1.27231i	0.0493010	+	0.0853918i
$223$	−2.98676			−0.200008			−0.100004	−	0.994987i	$-0.531886\pi$
$223$	−2.98676			−0.200008			−0.100004	+	0.994987i	$0.531886\pi$
$224$	17.8329	−	6.00083i	1.19151	−	0.400948i
$225$	2.05192			0.136795
$226$	1.38322	+	2.39581i	0.0920107	+	0.159367i
$227$	11.3804	−	19.7114i	0.755342	−	1.30829i	−0.189863	−	0.981811i	$-0.560804\pi$
$227$	11.3804	−	19.7114i	0.755342	−	1.30829i	0.945204	−	0.326480i	$-0.105862\pi$
$228$	−5.55099	+	9.61460i	−0.367623	+	0.636742i
$229$	−11.8247	−	20.4810i	−0.781399	−	1.35342i	−0.931127	−	0.364695i	$-0.881173\pi$
$229$	−11.8247	−	20.4810i	−0.781399	−	1.35342i	0.149728	−	0.988727i	$-0.452160\pi$
$230$	−4.99220			−0.329176
$231$	−3.16477	+	15.6931i	−0.208227	+	1.03253i
$232$	7.35079			0.482603
$233$	−0.746108	−	1.29230i	−0.0488792	−	0.0846612i	0.840551	−	0.541733i	$-0.182232\pi$
$233$	−0.746108	−	1.29230i	−0.0488792	−	0.0846612i	−0.889430	+	0.457072i	$0.848898\pi$
$234$	2.72870	−	4.72625i	0.178381	−	0.308965i
$235$	6.70970	−	11.6215i	0.437693	−	0.758106i
$236$	−1.50737	−	2.61085i	−0.0981216	−	0.169952i
$237$	−5.91193			−0.384021
$238$	20.9665	+	18.4856i	1.35906	+	1.19824i
$239$	−29.9342			−1.93628			−0.968141	−	0.250407i	$-0.919436\pi$
$239$	−29.9342			−1.93628			−0.968141	+	0.250407i	$0.919436\pi$
$240$	−6.26012	−	10.8429i	−0.404089	−	0.699903i
$241$	−5.04963	+	8.74621i	−0.325275	+	0.563393i	−0.981568	−	0.191113i	$-0.938790\pi$
$241$	−5.04963	+	8.74621i	−0.325275	+	0.563393i	0.656293	+	0.754506i	$0.272124\pi$
$242$	24.0750	−	41.6991i	1.54760	−	2.68052i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−21.2576			−1.36088
$245$	−14.8072	+	11.2379i	−0.945998	+	0.717963i
$246$	6.23569			0.397573
$247$	−10.5044	−	18.1941i	−0.668377	−	1.15766i
$248$	2.67079	−	4.62595i	0.169595	−	0.293748i
$249$	4.25672	−	7.37285i	0.269758	−	0.467235i
$250$	7.35870	+	12.7456i	0.465405	+	0.806106i
$251$	2.58608			0.163232			0.0816160	−	0.996664i	$-0.473992\pi$
$251$	2.58608			0.163232			0.0816160	+	0.996664i	$0.473992\pi$
$252$	−3.04447	−	2.68422i	−0.191784	−	0.169090i
$253$	−6.05086			−0.380414
$254$	17.7265	+	30.7032i	1.11226	+	1.92649i
$255$	7.46189	−	12.9244i	0.467282	−	0.809356i
$256$	−10.3473	+	17.9220i	−0.646705	+	1.12013i
$257$	−0.656235	−	1.13663i	−0.0409348	−	0.0709011i	0.844832	−	0.535031i	$-0.179700\pi$
$257$	−0.656235	−	1.13663i	−0.0409348	−	0.0709011i	−0.885767	+	0.464130i	$0.846367\pi$
$258$	−14.2854			−0.889370
$259$	−0.408742	+	2.02683i	−0.0253980	+	0.125941i
$260$	−11.8263			−0.733438
$261$	−4.19620	−	7.26804i	−0.259738	−	0.449880i
$262$	15.9411	−	27.6109i	0.984847	−	1.70581i
$263$	−1.45740	+	2.52429i	−0.0898670	+	0.155654i	−0.907455	−	0.420150i	$-0.861978\pi$
$263$	−1.45740	+	2.52429i	−0.0898670	+	0.155654i	0.817588	+	0.575804i	$0.195311\pi$
$264$	−2.64993	−	4.58981i	−0.163092	−	0.282483i
$265$	4.91142			0.301706
$266$	−34.1150	+	11.4798i	−2.09173	+	0.703875i
$267$	8.53165			0.522129
$268$	5.96743	+	10.3359i	0.364519	+	0.631365i
$269$	1.16832	−	2.02358i	0.0712335	−	0.123380i	−0.828209	−	0.560420i	$-0.810640\pi$
$269$	1.16832	−	2.02358i	0.0712335	−	0.123380i	0.899442	+	0.437040i	$0.143973\pi$
$270$	−2.49610	+	4.32337i	−0.151908	+	0.263112i
$271$	1.05075	+	1.81996i	0.0638288	+	0.110555i	0.896174	−	0.443703i	$-0.146336\pi$
$271$	1.05075	+	1.81996i	0.0638288	+	0.110555i	−0.832345	+	0.554258i	$0.813002\pi$
$272$	−26.4963			−1.60657
$273$	7.27953	−	2.44959i	0.440577	−	0.148256i
$274$	−23.6176			−1.42679
$275$	−6.20794	−	10.7525i	−0.374353	−	0.648398i
$276$	0.767041	−	1.32855i	0.0461705	−	0.0799696i
$277$	1.63683	−	2.83508i	0.0983477	−	0.170343i	−0.812653	−	0.582748i	$-0.801978\pi$
$277$	1.63683	−	2.83508i	0.0983477	−	0.170343i	0.911001	+	0.412404i	$0.135311\pi$
$278$	−13.1371	−	22.7541i	−0.787910	−	1.36470i
$279$	−6.09849			−0.365107
$280$	1.21654	−	6.03245i	0.0727023	−	0.360508i
$281$	0.869751			0.0518850			0.0259425	−	0.999663i	$-0.491741\pi$
$281$	0.869751			0.0518850			0.0259425	+	0.999663i	$0.491741\pi$
$282$	4.74994	+	8.22713i	0.282855	+	0.489918i
$283$	−0.205939	+	0.356697i	−0.0122418	+	0.0212034i	−0.872081	−	0.489361i	$-0.837230\pi$
$283$	−0.205939	+	0.356697i	−0.0122418	+	0.0212034i	0.859840	+	0.510564i	$0.170563\pi$
$284$	−7.00172	+	12.1273i	−0.415476	+	0.719625i
$285$	9.60894	+	16.6432i	0.569185	+	0.985857i
$286$	−33.0220			−1.95263
$287$	6.58278	+	5.80385i	0.388569	+	0.342590i
$288$	7.11157			0.419053
$289$	−7.29140	−	12.6291i	−0.428906	−	0.742887i
$290$	−20.9483	+	36.2835i	−1.23013	+	2.13064i
$291$	0.334859	−	0.579993i	0.0196298	−	0.0339998i
$292$	−0.677340	−	1.17319i	−0.0396383	−	0.0686556i
$293$	−4.88076			−0.285137			−0.142569	−	0.989785i	$-0.545536\pi$
$293$	−4.88076			−0.285137			−0.142569	+	0.989785i	$0.545536\pi$
$294$	−1.64854	−	13.0557i	−0.0961445	−	0.761426i
$295$	−5.21862			−0.303840
$296$	−0.342248	−	0.592791i	−0.0198928	−	0.0344553i
$297$	−3.02543	+	5.24020i	−0.175553	+	0.304067i
$298$	9.33769	−	16.1734i	0.540918	−	0.936897i
$299$	1.45150	+	2.51408i	0.0839426	+	0.145393i
$300$	3.14781			0.181739
$301$	−15.0806	−	13.2961i	−0.869228	−	0.766374i
$302$	−20.6014			−1.18548
$303$	6.45154	+	11.1744i	0.370631	+	0.641952i
$304$	17.0601	−	29.5489i	0.978463	−	1.69475i
$305$	−18.3988	+	31.8676i	−1.05351	+	1.82473i
$306$	5.28243	+	9.14944i	0.301976	+	0.523038i
$307$	16.5174			0.942699			0.471350	−	0.881946i	$-0.343767\pi$
$307$	16.5174			0.942699			0.471350	+	0.881946i	$0.343767\pi$
$308$	−4.85503	+	24.0746i	−0.276641	+	1.37177i
$309$	−10.1267			−0.576091
$310$	15.2225	+	26.3661i	0.864577	+	1.49749i
$311$	2.74044	−	4.74658i	0.155396	−	0.269154i	−0.777807	−	0.628503i	$-0.783668\pi$
$311$	2.74044	−	4.74658i	0.155396	−	0.269154i	0.933203	+	0.359349i	$0.117001\pi$
$312$	−1.27135	+	2.20204i	−0.0719760	+	0.124666i
$313$	7.21776	+	12.5015i	0.407972	+	0.706629i	0.994662	−	0.103183i	$-0.0329027\pi$
$313$	7.21776	+	12.5015i	0.407972	+	0.706629i	−0.586690	+	0.809811i	$0.699569\pi$
$314$	15.1324			0.853973
$315$	−6.65900	+	2.24078i	−0.375192	+	0.126254i
$316$	−9.06939			−0.510193
$317$	8.54458	+	14.7997i	0.479912	+	0.831231i	0.999734	−	0.0230428i	$-0.00733540\pi$
$317$	8.54458	+	14.7997i	0.479912	+	0.831231i	−0.519823	+	0.854274i	$0.674002\pi$
$318$	−1.73845	+	3.01108i	−0.0974874	+	0.168853i
$319$	−25.3906	+	43.9779i	−1.42160	+	2.46229i
$320$	−5.23095	−	9.06027i	−0.292419	−	0.506484i
$321$	−7.57052			−0.422545
$322$	4.71405	−	1.58630i	0.262704	−	0.0884008i
$323$	40.6703			2.26296
$324$	−0.767041	−	1.32855i	−0.0426134	−	0.0738086i
$325$	−2.97837	+	5.15868i	−0.165210	+	0.286152i
$326$	2.76136	−	4.78281i	0.152938	−	0.264896i
$327$	3.25356	+	5.63532i	0.179922	+	0.311634i
$328$	−2.90532			−0.160419
$329$	−2.64305	+	13.1061i	−0.145716	+	0.722560i
$330$	30.2071			1.66285
$331$	−5.13210	−	8.88906i	−0.282086	−	0.488587i	0.689813	−	0.723988i	$-0.257693\pi$
$331$	−5.13210	−	8.88906i	−0.282086	−	0.488587i	−0.971898	+	0.235401i	$0.924360\pi$
$332$	6.53015	−	11.3106i	0.358389	−	0.620748i
$333$	−0.390745	+	0.676791i	−0.0214127	+	0.0370879i
$334$	−7.94783	−	13.7661i	−0.434886	−	0.753245i
$335$	20.6596			1.12875
$336$	9.35669	+	8.24953i	0.510450	+	0.450049i
$337$	7.36005			0.400928			0.200464	−	0.979701i	$-0.435755\pi$
$337$	7.36005			0.400928			0.200464	+	0.979701i	$0.435755\pi$
$338$	−4.29801	−	7.44438i	−0.233781	−	0.404921i
$339$	−0.735791	+	1.27443i	−0.0399627	+	0.0692174i
$340$	11.4472	−	19.8271i	0.620809	−	1.07527i
$341$	18.4506	+	31.9573i	0.999154	+	1.73058i
$342$	−13.6047			−0.735660
$343$	10.4113	−	15.3168i	0.562157	−	0.827030i
$344$	6.65582			0.358858
$345$	−1.32777	−	2.29977i	−0.0714849	−	0.123815i
$346$	5.75101	−	9.96105i	0.309176	−	0.535509i
$347$	4.36812	−	7.56581i	0.234493	−	0.406154i	−0.724632	−	0.689136i	$-0.757990\pi$
$347$	4.36812	−	7.56581i	0.234493	−	0.406154i	0.959125	+	0.282982i	$0.0913237\pi$
$348$	−6.43732	−	11.1498i	−0.345077	−	0.597690i
$349$	−19.9554			−1.06819			−0.534095	−	0.845425i	$-0.679347\pi$
$349$	−19.9554			−1.06819			−0.534095	+	0.845425i	$0.679347\pi$
$350$	7.65529	+	6.74945i	0.409193	+	0.360773i
$351$	2.90301			0.154951
$352$	−21.5155	−	37.2660i	−1.14678	−	1.98629i
$353$	−8.54746	+	14.8046i	−0.454936	+	0.787972i	−0.998685	−	0.0512764i	$-0.983671\pi$
$353$	−8.54746	+	14.8046i	−0.454936	+	0.787972i	0.543749	+	0.839248i	$0.317004\pi$
$354$	1.84719	−	3.19942i	0.0981768	−	0.170047i
$355$	12.1202	+	20.9928i	0.643274	+	1.11418i
$356$	13.0883			0.693676
$357$	−2.93935	+	14.5753i	−0.155567	+	0.771408i
$358$	−31.4632			−1.66288
$359$	−17.6756	−	30.6150i	−0.932881	−	1.61580i	−0.778370	−	0.627805i	$-0.783953\pi$
$359$	−17.6756	−	30.6150i	−0.932881	−	1.61580i	−0.154510	−	0.987991i	$-0.549380\pi$
$360$	1.16298	−	2.01434i	0.0612943	−	0.106165i
$361$	−16.6863	+	28.9015i	−0.878225	+	1.52113i
$362$	−1.51619	−	2.62612i	−0.0796893	−	0.138026i
$363$	25.6129			1.34433
$364$	11.1674	−	3.75788i	0.585331	−	0.196966i
$365$	−2.34499			−0.122743
$366$	−13.0249	−	22.5597i	−0.680821	−	1.17922i
$367$	−7.57883	+	13.1269i	−0.395612	+	0.685219i	−0.993179	−	0.116599i	$-0.962801\pi$
$367$	−7.57883	+	13.1269i	−0.395612	+	0.685219i	0.597567	+	0.801819i	$0.296134\pi$
$368$	−2.35738	+	4.08310i	−0.122887	+	0.212846i
$369$	1.65850	+	2.87261i	0.0863381	+	0.149542i
$370$	3.90136			0.202822
$371$	−4.63777	+	1.56063i	−0.240781	+	0.0810238i
$372$	−9.35559			−0.485065
$373$	−19.0682	−	33.0271i	−0.987315	−	1.71008i	−0.631162	−	0.775651i	$-0.717422\pi$
$373$	−19.0682	−	33.0271i	−0.987315	−	1.71008i	−0.356153	−	0.934428i	$-0.615912\pi$
$374$	31.9632	−	55.3619i	1.65278	−	2.86270i
$375$	−3.91438	+	6.77991i	−0.202138	+	0.350113i
$376$	−2.21308	−	3.83316i	−0.114131	−	0.197680i
$377$	24.3632			1.25477
$378$	0.983251	−	4.87563i	0.0505730	−	0.250775i
$379$	−33.5087			−1.72123			−0.860614	−	0.509258i	$-0.829920\pi$
$379$	−33.5087			−1.72123			−0.860614	+	0.509258i	$0.829920\pi$
$380$	14.7409	+	25.5320i	0.756193	+	1.30976i
$381$	−9.42940	+	16.3322i	−0.483083	+	0.836724i
$382$	14.0583	−	24.3497i	0.719285	−	1.24584i
$383$	15.7782	+	27.3286i	0.806227	+	1.39643i	0.915460	+	0.402410i	$0.131827\pi$
$383$	15.7782	+	27.3286i	0.806227	+	1.39643i	−0.109232	+	0.994016i	$0.534839\pi$
$384$	−6.81695			−0.347876
$385$	31.8885	+	28.1152i	1.62519	+	1.43288i
$386$	29.6509			1.50919
$387$	−3.79948	−	6.58089i	−0.193138	−	0.334525i
$388$	0.513701	−	0.889757i	0.0260792	−	0.0451706i
$389$	−9.23532	+	15.9961i	−0.468250	+	0.811032i	−0.999342	−	0.0362821i	$-0.988449\pi$
$389$	−9.23532	+	15.9961i	−0.468250	+	0.811032i	0.531092	+	0.847314i	$0.321782\pi$
$390$	−7.24619	−	12.5508i	−0.366925	−	0.635533i
$391$	−5.61986			−0.284208
$392$	0.768081	+	6.08290i	0.0387940	+	0.307233i
$393$	16.9594			0.855490
$394$	−6.84581	−	11.8573i	−0.344887	−	0.597362i
$395$	−7.84970	+	13.5961i	−0.394961	+	0.684093i
$396$	−4.64126	+	8.03889i	−0.233232	+	0.403970i
$397$	12.5475	+	21.7329i	0.629742	+	1.09074i	0.987603	+	0.156970i	$0.0501726\pi$
$397$	12.5475	+	21.7329i	0.629742	+	1.09074i	−0.357862	+	0.933775i	$0.616494\pi$
$398$	33.6752			1.68799
$399$	−14.3620	−	12.6626i	−0.719000	−	0.633921i
$400$	−9.67430			−0.483715
$401$	13.1623	+	22.7977i	0.657292	+	1.13846i	0.981314	+	0.192414i	$0.0616317\pi$
$401$	13.1623	+	22.7977i	0.657292	+	1.13846i	−0.324021	+	0.946050i	$0.605035\pi$
$402$	−7.31268	+	12.6659i	−0.364723	+	0.631719i
$403$	8.85198	−	15.3321i	0.440949	−	0.763745i
$404$	9.89720	+	17.1424i	0.492404	+	0.852869i
$405$	−2.65555			−0.131955
$406$	8.25184	−	40.9183i	0.409532	−	2.03074i
$407$	4.72869			0.234392
$408$	−2.46118	−	4.26288i	−0.121846	−	0.211044i
$409$	−4.45286	+	7.71257i	−0.220180	+	0.381362i	−0.954862	−	0.297049i	$-0.903998\pi$
$409$	−4.45286	+	7.71257i	−0.220180	+	0.381362i	0.734683	+	0.678411i	$0.237331\pi$
$410$	8.27957	−	14.3406i	0.408899	−	0.708234i
$411$	−6.28156	−	10.8800i	−0.309847	−	0.536670i
$412$	−15.5353			−0.765368
$413$	4.92785	−	1.65824i	0.242484	−	0.0815968i
$414$	1.87992			0.0923928
$415$	−11.3039	−	19.5789i	−0.554887	−	0.961092i
$416$	−10.3225	+	17.8790i	−0.506100	+	0.876592i
$417$	6.98812	−	12.1038i	0.342210	−	0.592725i
$418$	41.1602	+	71.2915i	2.01321	+	3.48698i
$419$	−14.4300			−0.704951			−0.352475	−	0.935821i	$-0.614660\pi$
$419$	−14.4300			−0.704951			−0.352475	+	0.935821i	$0.614660\pi$
$420$	−10.2155	+	3.43754i	−0.498463	+	0.167735i
$421$	19.5884			0.954678			0.477339	−	0.878719i	$-0.341601\pi$
$421$	19.5884			0.954678			0.477339	+	0.878719i	$0.341601\pi$
$422$	−1.90641	−	3.30201i	−0.0928028	−	0.160739i
$423$	−2.52667	+	4.37633i	−0.122851	+	0.212784i
$424$	0.809974	−	1.40292i	0.0393358	−	0.0681316i
$425$	−5.76575	−	9.98657i	−0.279680	−	0.484420i
$426$	−17.1603			−0.831419
$427$	7.24755	−	35.9383i	0.350733	−	1.73918i
$428$	−11.6138			−0.561374
$429$	−8.78283	−	15.2123i	−0.424039	−	0.734457i
$430$	−18.9678	+	32.8531i	−0.914707	+	1.58432i
$431$	−2.95042	+	5.11028i	−0.142117	+	0.246153i	−0.928294	−	0.371848i	$-0.878724\pi$
$431$	−2.95042	+	5.11028i	−0.142117	+	0.246153i	0.786177	+	0.618002i	$0.212057\pi$
$432$	2.35738	+	4.08310i	0.113419	+	0.196448i
$433$	31.6906			1.52295			0.761477	−	0.648192i	$-0.224475\pi$
$433$	31.6906			1.52295			0.761477	+	0.648192i	$0.224475\pi$
$434$	−22.7522	−	20.0600i	−1.09214	−	0.962911i
$435$	−22.2864			−1.06855
$436$	4.99122	+	8.64505i	0.239036	+	0.414023i
$437$	3.61844	−	6.26733i	0.173094	−	0.299807i
$438$	0.830035	−	1.43766i	0.0396606	−	0.0686942i
$439$	10.5372	+	18.2510i	0.502913	+	0.871071i	0.999994	+	0.00336685i	$0.00107170\pi$
$439$	10.5372	+	18.2510i	0.502913	+	0.871071i	−0.497081	+	0.867704i	$0.665595\pi$
$440$	−14.0740			−0.670952
$441$	5.57596	−	4.23186i	0.265522	−	0.201517i
$442$	−30.6698			−1.45882
$443$	14.8337	+	25.6926i	0.704768	+	1.22069i	0.966775	+	0.255628i	$0.0822823\pi$
$443$	14.8337	+	25.6926i	0.704768	+	1.22069i	−0.262007	+	0.965066i	$0.584384\pi$
$444$	−0.599435	+	1.03825i	−0.0284479	+	0.0492733i
$445$	11.3281	−	19.6208i	0.537003	−	0.930117i
$446$	−2.80743	−	4.86261i	−0.132936	−	0.230251i
$447$	9.93416			0.469870
$448$	7.81844	+	6.89329i	0.369386	+	0.325677i
$449$	9.75478			0.460357			0.230178	−	0.973148i	$-0.426069\pi$
$449$	9.75478			0.460357			0.230178	+	0.973148i	$0.426069\pi$
$450$	1.92872	+	3.34064i	0.0909206	+	0.157479i
$451$	10.0354	−	17.3817i	0.472546	−	0.818474i
$452$	−1.12876	+	1.95508i	−0.0530926	+	0.0919590i
$453$	−5.47935	−	9.49051i	−0.257442	−	0.445903i
$454$	42.7883			2.00815
$455$	4.03206	−	19.9937i	0.189026	−	0.937321i
$456$	6.33869			0.296836
$457$	−13.4811	−	23.3499i	−0.630619	−	1.09226i	−0.987425	−	0.158086i	$-0.949468\pi$
$457$	−13.4811	−	23.3499i	−0.630619	−	1.09226i	0.356806	−	0.934178i	$-0.383866\pi$
$458$	22.2295	−	38.5025i	1.03871	−	1.79911i
$459$	−2.80993	+	4.86694i	−0.131156	+	0.227169i
$460$	−2.03691	−	3.52804i	−0.0949715	−	0.164496i
$461$	18.7043			0.871148			0.435574	−	0.900153i	$-0.356545\pi$
$461$	18.7043			0.871148			0.435574	+	0.900153i	$0.356545\pi$
$462$	−28.5240	+	9.59845i	−1.32706	+	0.446560i
$463$	29.7340			1.38186			0.690929	−	0.722923i	$-0.257202\pi$
$463$	29.7340			1.38186			0.690929	+	0.722923i	$0.257202\pi$
$464$	19.7841	+	34.2670i	0.918453	+	1.59081i
$465$	−8.09741	+	14.0251i	−0.375509	+	0.650400i
$466$	1.40262	−	2.42941i	0.0649751	−	0.112540i
$467$	−7.74369	−	13.4125i	−0.358335	−	0.620655i	0.629348	−	0.777124i	$-0.283322\pi$
$467$	−7.74369	−	13.4125i	−0.358335	−	0.620655i	−0.987683	+	0.156469i	$0.949989\pi$
$468$	4.45345			0.205861
$469$	−19.5085	+	6.56469i	−0.900819	+	0.303129i
$470$	25.2273			1.16365
$471$	4.02477	+	6.97110i	0.185451	+	0.321211i
$472$	−0.860636	+	1.49067i	−0.0396140	+	0.0686134i
$473$	−22.9901	+	39.8200i	−1.05709	+	1.83093i
$474$	−5.55696	−	9.62495i	−0.255240	−	0.442088i
$475$	14.8495			0.681342
$476$	−4.50921	+	22.3597i	−0.206679	+	1.02486i
$477$	−1.84950			−0.0846827
$478$	−28.1369	−	48.7345i	−1.28695	−	2.22906i
$479$	12.5077	−	21.6640i	0.571493	−	0.989854i	−0.424920	−	0.905231i	$-0.639698\pi$
$479$	12.5077	−	21.6640i	0.571493	−	0.989854i	0.996413	−	0.0846236i	$-0.0269688\pi$
$480$	9.44255	−	16.3550i	0.430991	−	0.746499i
$481$	−1.13434	−	1.96473i	−0.0517213	−	0.0895838i
$482$	−18.9857			−0.864777
$483$	1.98456	+	1.74973i	0.0903004	+	0.0796153i
$484$	39.2922			1.78601
$485$	−0.889233	−	1.54020i	−0.0403780	−	0.0699367i
$486$	0.939958	−	1.62805i	0.0426374	−	0.0738501i
$487$	7.38204	−	12.7861i	0.334512	−	0.579392i	−0.648879	−	0.760892i	$-0.724762\pi$
$487$	7.38204	−	12.7861i	0.334512	−	0.579392i	0.983391	+	0.181500i	$0.0580952\pi$
$488$	6.06852	+	10.5110i	0.274709	+	0.475810i
$489$	2.93775			0.132850
$490$	−32.2141	−	13.5438i	−1.45528	−	0.611847i
$491$	1.18432			0.0534478			0.0267239	−	0.999643i	$-0.491492\pi$
$491$	1.18432			0.0534478			0.0267239	+	0.999643i	$0.491492\pi$
$492$	2.54428	+	4.40682i	0.114705	+	0.198675i
$493$	−23.5821	+	40.8453i	−1.06208	+	1.83958i
$494$	19.7473	−	34.2034i	0.888474	−	1.53888i
$495$	8.03416	+	13.9156i	0.361109	+	0.625459i
$496$	28.7529			1.29104
$497$	−18.1155	−	15.9719i	−0.812590	−	0.716437i
$498$	16.0045			0.717180
$499$	3.60290	+	6.24041i	0.161288	+	0.279359i	0.935331	−	0.353774i	$-0.115102\pi$
$499$	3.60290	+	6.24041i	0.161288	+	0.279359i	−0.774043	+	0.633133i	$0.781769\pi$
$500$	−6.00498	+	10.4009i	−0.268551	+	0.465144i
$501$	4.22776	−	7.32270i	0.188882	−	0.327154i
$502$	2.43081	+	4.21028i	0.108492	+	0.187914i
$503$	−33.8008			−1.50710			−0.753552	−	0.657389i	$-0.771661\pi$
$503$	−33.8008			−1.50710			−0.753552	+	0.657389i	$0.771661\pi$
$504$	−0.458114	+	2.27164i	−0.0204060	+	0.101187i
$505$	34.2647			1.52476
$506$	−5.68755	−	9.85112i	−0.252842	−	0.437936i
$507$	2.28628	−	3.95995i	0.101537	−	0.175868i
$508$	−14.4655	+	25.0549i	−0.641802	+	1.11163i
$509$	−15.7397	−	27.2619i	−0.697649	−	1.20836i	−0.969280	−	0.245962i	$-0.920896\pi$
$509$	−15.7397	−	27.2619i	−0.697649	−	1.20836i	0.271631	−	0.962402i	$-0.412437\pi$
$510$	28.0555			1.24232
$511$	2.21434	−	0.745134i	0.0979565	−	0.0329628i
$512$	−25.2702			−1.11679
$513$	−3.61844	−	6.26733i	−0.159758	−	0.276709i
$514$	1.23367	−	2.13677i	0.0544147	−	0.0942490i
$515$	−13.4460	+	23.2892i	−0.592502	+	1.02624i
$516$	−5.82871	−	10.0956i	−0.256595	−	0.444435i
$517$	30.5771			1.34478
$518$	−3.68398	+	1.23968i	−0.161865	+	0.0544682i
$519$	6.11837			0.268567
$520$	3.37613	+	5.84763i	0.148053	+	0.256435i
$521$	−16.4694	+	28.5258i	−0.721536	+	1.24974i	0.238848	+	0.971057i	$0.423230\pi$
$521$	−16.4694	+	28.5258i	−0.721536	+	1.24974i	−0.960384	+	0.278680i	$0.910103\pi$
$522$	7.88851	−	13.6633i	0.345271	−	0.598026i
$523$	9.98447	+	17.2936i	0.436590	+	0.756196i	0.997424	−	0.0717320i	$-0.0228526\pi$
$523$	9.98447	+	17.2936i	0.436590	+	0.756196i	−0.560834	+	0.827928i	$0.689519\pi$
$524$	26.0172			1.13656
$525$	−1.07321	+	5.32173i	−0.0468389	+	0.232259i
$526$	−5.47957			−0.238921
$527$	17.1363	+	29.6810i	0.746470	+	1.29292i
$528$	14.2642	−	24.7062i	0.620768	−	1.07520i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	4.61653	+	7.99607i	0.200529	+	0.347327i
$531$	1.96518			0.0852815
$532$	−22.0325	−	19.4254i	−0.955230	−	0.842199i
$533$	−9.62928			−0.417090
$534$	8.01939	+	13.8900i	0.347033	+	0.601079i
$535$	−10.0519	+	17.4104i	−0.434583	+	0.752719i
$536$	3.40711	−	5.90128i	0.147165	−	0.254897i
$537$	−8.36825	−	14.4942i	−0.361117	−	0.625472i
$538$	4.39267			0.189382
$539$	−39.0455	−	16.4159i	−1.68181	−	0.707084i
$540$	−4.07383			−0.175310
$541$	0.517982	+	0.897171i	0.0222698	+	0.0385724i	0.876946	−	0.480590i	$-0.159577\pi$
$541$	0.517982	+	0.897171i	0.0222698	+	0.0385724i	−0.854676	+	0.519162i	$0.826244\pi$
$542$	−1.97533	+	3.42137i	−0.0848477	+	0.146960i
$543$	0.806522	−	1.39694i	0.0346112	−	0.0599483i
$544$	−19.9830	−	34.6116i	−0.856765	−	1.48396i
$545$	17.2799			0.740191
$546$	10.8305	+	9.54896i	0.463504	+	0.408658i
$547$	−0.720769			−0.0308179			−0.0154089	−	0.999881i	$-0.504905\pi$
$547$	−0.720769			−0.0308179			−0.0154089	+	0.999881i	$0.504905\pi$
$548$	−9.63643	−	16.6908i	−0.411648	−	0.712995i
$549$	6.92843	−	12.0004i	0.295698	−	0.512165i
$550$	11.6704	−	20.2137i	0.497627	−	0.861916i
$551$	−30.3675	−	52.5980i	−1.29370	−	2.24075i
$552$	−0.875886			−0.0372802
$553$	3.09211	−	15.3328i	0.131490	−	0.652018i
$554$	6.15421			0.261468
$555$	1.03764	+	1.79725i	0.0440454	+	0.0762889i
$556$	10.7204	−	18.5682i	0.454644	−	0.787467i
$557$	12.5738	−	21.7784i	0.532768	−	0.922781i	−0.466500	−	0.884521i	$-0.654485\pi$
$557$	12.5738	−	21.7784i	0.532768	−	0.922781i	0.999268	−	0.0382596i	$-0.0121814\pi$
$558$	−5.73233	−	9.92868i	−0.242669	−	0.420315i
$559$	22.0598			0.933031
$560$	31.3956	−	10.5647i	1.32671	−	0.446442i
$561$	34.0050			1.43569
$562$	0.817529	+	1.41600i	0.0344854	+	0.0597304i
$563$	−2.17604	+	3.76902i	−0.0917093	+	0.158845i	−0.908230	−	0.418470i	$-0.862566\pi$
$563$	−2.17604	+	3.76902i	−0.0917093	+	0.158845i	0.816521	+	0.577316i	$0.195900\pi$
$564$	−3.87613	+	6.71365i	−0.163214	+	0.282696i
$565$	1.95393	+	3.38430i	0.0822022	+	0.142378i
$566$	−0.774296			−0.0325461
$567$	2.50758	−	0.843812i	0.105309	−	0.0354368i
$568$	7.99528			0.335474
$569$	−11.6448	−	20.1695i	−0.488177	−	0.845548i	0.511730	−	0.859146i	$-0.329005\pi$
$569$	−11.6448	−	20.1695i	−0.488177	−	0.845548i	−0.999908	+	0.0135984i	$0.995671\pi$
$570$	−18.0640	+	31.2878i	−0.756618	+	1.31050i
$571$	−10.4745	+	18.1423i	−0.438343	+	0.759233i	−0.997562	−	0.0697875i	$-0.977768\pi$
$571$	−10.4745	+	18.1423i	−0.438343	+	0.759233i	0.559219	+	0.829020i	$0.311101\pi$
$572$	−13.4736	−	23.3369i	−0.563359	−	0.975767i
$573$	14.9563			0.624809
$574$	−3.26145	+	16.1725i	−0.136130	+	0.675027i
$575$	−2.05192			−0.0855710
$576$	1.96982	+	3.41183i	0.0820759	+	0.142160i
$577$	9.60322	−	16.6333i	0.399787	−	0.692452i	−0.593912	−	0.804530i	$-0.702417\pi$
$577$	9.60322	−	16.6333i	0.399787	−	0.692452i	0.993699	+	0.112078i	$0.0357507\pi$
$578$	13.7072	−	23.7416i	0.570145	−	0.987520i
$579$	7.88623	+	13.6593i	0.327740	+	0.567663i
$580$	−34.1892			−1.41963
$581$	16.8954	+	14.8962i	0.700938	+	0.617997i
$582$	1.25901			0.0521878
$583$	5.59552	+	9.69173i	0.231743	+	0.401390i
$584$	−0.386728	+	0.669833i	−0.0160029	+	0.0277179i
$585$	3.85453	−	6.67624i	0.159365	−	0.276029i
$586$	−4.58771	−	7.94615i	−0.189517	−	0.328252i
$587$	−15.2668			−0.630127			−0.315064	−	0.949071i	$-0.602026\pi$
$587$	−15.2668			−0.630127			−0.315064	+	0.949071i	$0.602026\pi$
$588$	8.55398	−	6.49203i	0.352760	−	0.267727i
$589$	−44.1341			−1.81851
$590$	−4.90528	−	8.49620i	−0.201947	−	0.349783i
$591$	3.64155	−	6.30736i	0.149794	−	0.259450i
$592$	1.84227	−	3.19090i	0.0757168	−	0.131145i
$593$	−14.5655	−	25.2282i	−0.598133	−	1.03600i	−0.993097	−	0.117300i	$-0.962576\pi$
$593$	−14.5655	−	25.2282i	−0.598133	−	1.03600i	0.394963	−	0.918697i	$-0.370757\pi$
$594$	−11.3751			−0.466726
$595$	29.6171	+	26.1125i	1.21418	+	1.07051i
$596$	15.2398			0.624247
$597$	8.95658	+	15.5133i	0.366568	+	0.634915i
$598$	−2.72870	+	4.72625i	−0.111585	+	0.193271i
$599$	−16.5170	+	28.6082i	−0.674865	+	1.16890i	0.301644	+	0.953421i	$0.402465\pi$
$599$	−16.5170	+	28.6082i	−0.674865	+	1.16890i	−0.976508	+	0.215479i	$0.930869\pi$
$600$	−0.898623	−	1.55646i	−0.0366861	−	0.0635423i
$601$	−7.74804			−0.316049			−0.158025	−	0.987435i	$-0.550513\pi$
$601$	−7.74804			−0.316049			−0.158025	+	0.987435i	$0.550513\pi$
$602$	7.47168	−	37.0497i	0.304523	−	1.51003i
$603$	−7.77980			−0.316818
$604$	−8.40578	−	14.5592i	−0.342026	−	0.592407i
$605$	34.0081	−	58.9037i	1.38262	−	2.39478i
$606$	−12.1284	+	21.0069i	−0.492681	+	0.853348i
$607$	−0.0985420	−	0.170680i	−0.00399970	−	0.00692768i	0.864019	−	0.503460i	$-0.167940\pi$
$607$	−0.0985420	−	0.170680i	−0.00399970	−	0.00692768i	−0.868018	+	0.496532i	$0.834606\pi$
$608$	51.4656			2.08721
$609$	21.0447	−	7.08162i	0.852773	−	0.286962i
$610$	−69.1763			−2.80086
$611$	−7.33495	−	12.7045i	−0.296740	−	0.513969i
$612$	−4.31066	+	7.46629i	−0.174248	+	0.301807i
$613$	5.73119	−	9.92671i	0.231481	−	0.400936i	−0.726763	−	0.686888i	$-0.758976\pi$
$613$	5.73119	−	9.92671i	0.231481	−	0.400936i	0.958244	+	0.285952i	$0.0923097\pi$
$614$	15.5257	+	26.8913i	0.626565	+	1.08524i
$615$	8.80845			0.355191
$616$	13.2898	−	4.47209i	0.535463	−	0.180186i
$617$	44.3195			1.78423			0.892117	−	0.451804i	$-0.149219\pi$
$617$	44.3195			1.78423			0.892117	+	0.451804i	$0.149219\pi$
$618$	−9.51872	−	16.4869i	−0.382899	−	0.663200i
$619$	−4.55450	+	7.88863i	−0.183061	+	0.317071i	−0.942921	−	0.333015i	$-0.891934\pi$
$619$	−4.55450	+	7.88863i	−0.183061	+	0.317071i	0.759861	+	0.650086i	$0.225267\pi$
$620$	−12.4221	+	21.5157i	−0.498883	+	0.864092i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	10.3036			0.413136
$623$	−4.46230	+	22.1272i	−0.178778	+	0.886506i
$624$	−13.6870			−0.547917
$625$	15.5246	+	26.8894i	0.620984	+	1.07558i
$626$	−13.5688	+	23.5018i	−0.542318	+	0.939322i
$627$	−21.8947	+	37.9227i	−0.874389	+	1.51449i
$628$	6.17432	+	10.6942i	0.246382	+	0.426747i
$629$	4.39187			0.175115
$630$	−9.90730	−	8.73498i	−0.394716	−	0.348010i
$631$	−16.5648			−0.659433			−0.329717	−	0.944080i	$-0.606953\pi$
$631$	−16.5648			−0.659433			−0.329717	+	0.944080i	$0.606953\pi$
$632$	2.58909	+	4.48443i	0.102988	+	0.178381i
$633$	1.01410	−	1.75647i	0.0403067	−	0.0698132i
$634$	−16.0631	+	27.8221i	−0.637947	+	1.10496i
$635$	25.0402	+	43.3709i	0.993690	+	1.72112i
$636$	−2.83728			−0.112506
$637$	2.54570	+	20.1610i	0.100864	+	0.798806i
$638$	−95.4645			−3.77947
$639$	−4.56411	−	7.90527i	−0.180553	−	0.312728i
$640$	−9.05136	+	15.6774i	−0.357786	+	0.619704i
$641$	23.9103	−	41.4139i	0.944401	−	1.63575i	0.187455	−	0.982273i	$-0.439976\pi$
$641$	23.9103	−	41.4139i	0.944401	−	1.63575i	0.756946	−	0.653478i	$-0.226691\pi$
$642$	−7.11597	−	12.3252i	−0.280845	−	0.486438i
$643$	−11.9619			−0.471733			−0.235867	−	0.971785i	$-0.575793\pi$
$643$	−11.9619			−0.471733			−0.235867	+	0.971785i	$0.575793\pi$
$644$	3.04447	+	2.68422i	0.119969	+	0.105773i
$645$	−20.1794			−0.794562
$646$	38.2283	+	66.2134i	1.50407	+	2.60513i
$647$	2.19167	−	3.79608i	0.0861633	−	0.149239i	−0.819723	−	0.572760i	$-0.805873\pi$
$647$	2.19167	−	3.79608i	0.0861633	−	0.149239i	0.905886	+	0.423521i	$0.139206\pi$
$648$	−0.437943	+	0.758539i	−0.0172040	+	0.0297982i
$649$	−5.94551	−	10.2979i	−0.233382	−	0.404229i
$650$	−11.1982			−0.439228
$651$	3.18969	−	15.8167i	0.125014	−	0.619904i
$652$	4.50675			0.176498
$653$	2.91898	+	5.05583i	0.114229	+	0.197850i	0.917471	−	0.397802i	$-0.130227\pi$
$653$	2.91898	+	5.05583i	0.114229	+	0.197850i	−0.803242	+	0.595652i	$0.796894\pi$
$654$	−6.11641	+	10.5939i	−0.239171	+	0.414255i
$655$	22.5183	−	39.0028i	0.879861	−	1.52396i
$656$	−7.81943	−	13.5437i	−0.305297	−	0.528791i
$657$	0.883056			0.0344513
$658$	−23.8217	+	8.01611i	−0.928668	+	0.312500i
$659$	−12.2904			−0.478766			−0.239383	−	0.970925i	$-0.576945\pi$
$659$	−12.2904			−0.478766			−0.239383	+	0.970925i	$0.576945\pi$
$660$	12.3251	+	21.3476i	0.479753	+	0.830956i
$661$	−1.31249	+	2.27330i	−0.0510500	+	0.0884213i	−0.890421	−	0.455137i	$-0.849590\pi$
$661$	−1.31249	+	2.27330i	−0.0510500	+	0.0884213i	0.839371	+	0.543559i	$0.182923\pi$
$662$	9.64791	−	16.7107i	0.374977	−	0.649479i
$663$	−8.15724	−	14.1288i	−0.316801	−	0.548715i
$664$	−7.45679			−0.289380
$665$	−48.1905	+	16.2163i	−1.86875	+	0.628841i
$666$	−1.46914			−0.0569279
$667$	4.19620	+	7.26804i	0.162478	+	0.281420i
$668$	6.48573	−	11.2336i	0.250941	−	0.434642i
$669$	1.49338	−	2.58661i	0.0577374	−	0.100004i
$670$	19.4192	+	33.6350i	0.750227	+	1.29943i
$671$	−83.8459			−3.23684
$672$	−3.71956	+	18.4441i	−0.143485	+	0.711498i
$673$	−10.0580			−0.387706			−0.193853	−	0.981031i	$-0.562099\pi$
$673$	−10.0580			−0.387706			−0.193853	+	0.981031i	$0.562099\pi$
$674$	6.91814	+	11.9826i	0.266477	+	0.461551i
$675$	−1.02596	+	1.77701i	−0.0394892	+	0.0683973i
$676$	3.50734	−	6.07489i	0.134898	−	0.233650i
$677$	5.59500	+	9.69082i	0.215033	+	0.372449i	0.953283	−	0.302079i	$-0.0976807\pi$
$677$	5.59500	+	9.69082i	0.215033	+	0.372449i	−0.738250	+	0.674528i	$0.764347\pi$
$678$	−2.76645			−0.106245
$679$	1.32909	+	1.17182i	0.0510059	+	0.0449704i
$680$	−13.0715			−0.501270
$681$	11.3804	+	19.7114i	0.436097	+	0.755342i
$682$	−34.6855	+	60.0770i	−1.32818	+	2.30047i
$683$	0.306271	−	0.530478i	0.0117191	−	0.0202982i	−0.860106	−	0.510115i	$-0.829603\pi$
$683$	0.306271	−	0.530478i	0.0117191	−	0.0202982i	0.871826	+	0.489817i	$0.162936\pi$
$684$	−5.55099	−	9.61460i	−0.212247	−	0.367623i
$685$	−33.3619			−1.27469
$686$	34.7228	+	2.55300i	1.32572	+	0.0974738i
$687$	23.6494			0.902282
$688$	17.9136	+	31.0273i	0.682950	+	1.18290i
$689$	2.68455	−	4.64978i	0.102273	−	0.177142i
$690$	2.49610	−	4.32337i	0.0950249	−	0.164588i
$691$	7.71218	+	13.3579i	0.293385	+	0.508158i	0.974608	−	0.223918i	$-0.0718849\pi$
$691$	7.71218	+	13.3579i	0.293385	+	0.508158i	−0.681223	+	0.732076i	$0.738552\pi$
$692$	9.38609			0.356806
$693$	−12.0083	−	10.5873i	−0.456156	−	0.402180i
$694$	16.4234			0.623424
$695$	−18.5573	−	32.1421i	−0.703918	−	1.21922i
$696$	−3.67539	+	6.36597i	−0.139315	+	0.241301i
$697$	9.32054	−	16.1437i	0.353041	−	0.611485i
$698$	−18.7573	−	32.4885i	−0.709973	−	1.22971i
$699$	1.49222			0.0564408
$700$	−1.64640	+	8.16398i	−0.0622280	+	0.308569i
$701$	13.7197			0.518186			0.259093	−	0.965852i	$-0.416576\pi$
$701$	13.7197			0.518186			0.259093	+	0.965852i	$0.416576\pi$
$702$	2.72870	+	4.72625i	0.102988	+	0.178381i
$703$	−2.82778	+	4.89786i	−0.106652	+	0.184726i
$704$	11.9191	−	20.6445i	0.449218	−	0.778069i
$705$	6.70970	+	11.6215i	0.252702	+	0.437693i
$706$	−32.1370			−1.20949
$707$	−32.3556	+	10.8878i	−1.21686	+	0.409477i
$708$	3.01475			0.113301
$709$	16.6431	+	28.8267i	0.625046	+	1.08261i	0.988532	+	0.151011i	$0.0482529\pi$
$709$	16.6431	+	28.8267i	0.625046	+	1.08261i	−0.363487	+	0.931599i	$0.618414\pi$
$710$	−22.7850	+	39.4647i	−0.855104	+	1.48108i
$711$	2.95597	−	5.11988i	0.110857	−	0.192011i
$712$	−3.73638	−	6.47159i	−0.140027	−	0.242533i
$713$	6.09849			0.228390
$714$	−26.4923	+	8.91476i	−0.991449	+	0.333626i
$715$	−46.6464			−1.74448
$716$	−12.8376	−	22.2354i	−0.479763	−	0.830974i
$717$	14.9671	−	25.9238i	0.558956	−	0.968141i
$718$	33.2286	−	57.5536i	1.24008	−	2.14788i
$719$	1.87159	+	3.24168i	0.0697984	+	0.120894i	0.898812	−	0.438333i	$-0.144431\pi$
$719$	1.87159	+	3.24168i	0.0697984	+	0.120894i	−0.829014	+	0.559228i	$0.811098\pi$
$720$	12.5202			0.466602
$721$	5.29659	−	26.2641i	0.197255	−	0.978127i
$722$	−62.7376			−2.33485
$723$	−5.04963	−	8.74621i	−0.187798	−	0.325275i
$724$	1.23727	−	2.14302i	0.0459828	−	0.0796446i
$725$	−8.61027	+	14.9134i	−0.319777	+	0.553871i
$726$	24.0750	+	41.6991i	0.893507	+	1.54760i
$727$	34.5883			1.28281			0.641404	−	0.767203i	$-0.278352\pi$
$727$	34.5883			1.28281			0.641404	+	0.767203i	$0.278352\pi$
$728$	−5.04613	−	4.44903i	−0.187022	−	0.164892i
$729$	1.00000			0.0370370
$730$	−2.20420	−	3.81778i	−0.0815810	−	0.141302i
$731$	−21.3525	+	36.9837i	−0.789752	+	1.36789i
$732$	10.6288	−	18.4096i	0.392851	−	0.680438i
$733$	10.1775	+	17.6280i	0.375915	+	0.651104i	0.990464	−	0.137775i	$-0.0439950\pi$
$733$	10.1775	+	17.6280i	0.375915	+	0.651104i	−0.614548	+	0.788879i	$0.710662\pi$
$734$	−28.4951			−1.05177
$735$	−2.32870	−	18.4424i	−0.0858954	−	0.680257i
$736$	−7.11157			−0.262136
$737$	23.5372	+	40.7677i	0.867005	+	1.50170i
$738$	−3.11784	+	5.40026i	−0.114769	+	0.198786i
$739$	−5.87856	+	10.1820i	−0.216246	+	0.374550i	−0.953657	−	0.300895i	$-0.902715\pi$
$739$	−5.87856	+	10.1820i	−0.216246	+	0.374550i	0.737411	+	0.675444i	$0.236048\pi$
$740$	1.59183	+	2.75713i	0.0585168	+	0.101354i
$741$	21.0087			0.771775
$742$	−6.90010	−	6.08362i	−0.253311	−	0.223337i
$743$	−34.9259			−1.28131			−0.640653	−	0.767831i	$-0.721336\pi$
$743$	−34.9259			−1.28131			−0.640653	+	0.767831i	$0.721336\pi$
$744$	2.67079	+	4.62595i	0.0979160	+	0.169595i
$745$	13.1903	−	22.8463i	0.483255	−	0.837023i
$746$	35.8466	−	62.0882i	1.31244	−	2.27321i
$747$	4.25672	+	7.37285i	0.155745	+	0.269758i
$748$	52.1664			1.90739
$749$	3.95960	−	19.6344i	0.144681	−	0.717426i
$750$	−14.7174			−0.537404
$751$	−13.3561	−	23.1334i	−0.487369	−	0.844149i	0.512525	−	0.858672i	$-0.328710\pi$
$751$	−13.3561	−	23.1334i	−0.487369	−	0.844149i	−0.999895	+	0.0145237i	$0.995377\pi$
$752$	11.9127	−	20.6333i	0.434410	−	0.752420i
$753$	−1.29304	+	2.23961i	−0.0471210	+	0.0816160i
$754$	22.9004	+	39.6646i	0.833983	+	1.44450i
$755$	−29.1013			−1.05911
$756$	3.84684	−	1.29448i	0.139908	−	0.0470797i
$757$	−38.4969			−1.39919			−0.699596	−	0.714539i	$-0.746637\pi$
$757$	−38.4969			−1.39919			−0.699596	+	0.714539i	$0.746637\pi$
$758$	−31.4968	−	54.5540i	−1.14401	−	1.98149i
$759$	3.02543	−	5.24020i	0.109816	−	0.190207i
$760$	8.41633	−	14.5775i	0.305293	−	0.528782i
$761$	4.12407	+	7.14310i	0.149497	+	0.258937i	0.931042	−	0.364913i	$-0.118901\pi$
$761$	4.12407	+	7.14310i	0.149497	+	0.258937i	−0.781544	+	0.623850i	$0.785568\pi$
$762$	−35.4529			−1.28432
$763$	−16.3171	+	5.49078i	−0.590720	+	0.198780i
$764$	22.9442			0.830093
$765$	7.46189	+	12.9244i	0.269785	+	0.467282i
$766$	−29.6616	+	51.3755i	−1.07172	+	1.85627i
$767$	−2.85246	+	4.94061i	−0.102996	+	0.178395i
$768$	−10.3473	−	17.9220i	−0.373376	−	0.646705i
$769$	−23.0830			−0.832394			−0.416197	−	0.909274i	$-0.636637\pi$
$769$	−23.0830			−0.832394			−0.416197	+	0.909274i	$0.636637\pi$
$770$	−15.7992	+	78.3432i	−0.569363	+	2.82329i
$771$	1.31247			0.0472674
$772$	12.0981	+	20.9546i	0.435421	+	0.754171i
$773$	6.28401	−	10.8842i	0.226020	−	0.391478i	−0.730605	−	0.682800i	$-0.760762\pi$
$773$	6.28401	−	10.8842i	0.226020	−	0.391478i	0.956625	+	0.291322i	$0.0940952\pi$
$774$	7.14270	−	12.3715i	0.256739	−	0.444685i
$775$	6.25681	+	10.8371i	0.224751	+	0.389281i
$776$	−0.586596			−0.0210576
$777$	−1.55091	−	1.36739i	−0.0556386	−	0.0490550i
$778$	−34.7233			−1.24489
$779$	12.0024	+	20.7888i	0.430030	+	0.744834i
$780$	5.91317	−	10.2419i	0.211725	−	0.366719i
$781$	−27.6168	+	47.8337i	−0.988206	+	1.71162i
$782$	−5.28243	−	9.14944i	−0.188899	−	0.327183i
$783$	8.39241			0.299920
$784$	−26.2893	+	19.9522i	−0.938903	+	0.712579i
$785$	21.3759			0.762938
$786$	15.9411	+	27.6109i	0.568602	+	0.984847i
$787$	3.19328	−	5.53093i	0.113828	−	0.197156i	−0.803483	−	0.595328i	$-0.797022\pi$
$787$	3.19328	−	5.53093i	0.113828	−	0.197156i	0.917311	+	0.398172i	$0.130355\pi$
$788$	5.58644	−	9.67601i	0.199009	−	0.344693i
$789$	−1.45740	−	2.52429i	−0.0518847	−	0.0898670i
$790$	−29.5135			−1.05004
$791$	−2.92043	−	2.57486i	−0.103839	−	0.0915516i
$792$	5.29986			0.188322
$793$	20.1133	+	34.8372i	0.714243	+	1.23711i
$794$	−23.5883	+	40.8561i	−0.837116	+	1.44993i
$795$	−2.45571	+	4.25342i	−0.0870951	+	0.150853i
$796$	13.7401	+	23.7986i	0.487006	+	0.843519i
$797$	−5.52987			−0.195878			−0.0979390	−	0.995192i	$-0.531225\pi$
$797$	−5.52987			−0.195878			−0.0979390	+	0.995192i	$0.531225\pi$
$798$	7.11568	−	35.2844i	0.251892	−	1.24905i
$799$	28.3991			1.00469
$800$	−7.29619	−	12.6374i	−0.257959	−	0.446798i
$801$	−4.26583	+	7.38863i	−0.150726	+	0.261064i
$802$	−24.7440	+	42.8578i	−0.873739	+	1.51336i
$803$	−2.67162	−	4.62739i	−0.0942795	−	0.163297i
$804$	−11.9349			−0.420910
$805$	6.65900	−	2.24078i	0.234699	−	0.0789772i
$806$	33.2819			1.17231
$807$	1.16832	+	2.02358i	0.0411267	+	0.0712335i
$808$	5.65081	−	9.78750i	0.198795	−	0.344323i
$809$	17.4461	−	30.2176i	0.613373	−	1.06239i	−0.377294	−	0.926093i	$-0.623146\pi$
$809$	17.4461	−	30.2176i	0.613373	−	1.06239i	0.990668	−	0.136300i	$-0.0435211\pi$
$810$	−2.49610	−	4.32337i	−0.0877040	−	0.151908i
$811$	−6.11632			−0.214773			−0.107386	−	0.994217i	$-0.534248\pi$
$811$	−6.11632			−0.214773			−0.107386	+	0.994217i	$0.534248\pi$
$812$	32.2843	−	10.8638i	1.13296	−	0.381244i
$813$	−2.10151			−0.0737031
$814$	4.44477	+	7.69856i	0.155789	+	0.269834i
$815$	3.90066	−	6.75614i	0.136634	−	0.236657i
$816$	13.2481	−	22.9464i	0.463777	−	0.803286i
$817$	−27.4964	−	47.6252i	−0.961977	−	1.66619i
$818$	−16.7420			−0.585370
$819$	−1.51836	+	7.52906i	−0.0530557	+	0.263086i
$820$	13.5129			0.471891
$821$	−2.61945	−	4.53702i	−0.0914194	−	0.158343i	0.816689	−	0.577078i	$-0.195807\pi$
$821$	−2.61945	−	4.53702i	−0.0914194	−	0.158343i	−0.908109	+	0.418735i	$0.862474\pi$
$822$	11.8088	−	20.4535i	0.411879	−	0.713396i
$823$	−17.5192	+	30.3441i	−0.610679	+	1.05773i	0.380447	+	0.924803i	$0.375770\pi$
$823$	−17.5192	+	30.3441i	−0.610679	+	1.05773i	−0.991126	+	0.132925i	$0.957563\pi$
$824$	4.43494	+	7.68154i	0.154498	+	0.267599i
$825$	12.4159			0.432265
$826$	7.33168	+	6.46413i	0.255102	+	0.224916i
$827$	37.2117			1.29398			0.646989	−	0.762499i	$-0.276028\pi$
$827$	37.2117			1.29398			0.646989	+	0.762499i	$0.276028\pi$
$828$	0.767041	+	1.32855i	0.0266565	+	0.0461705i
$829$	0.954542	−	1.65331i	0.0331526	−	0.0574220i	−0.848973	−	0.528436i	$-0.822779\pi$
$829$	0.954542	−	1.65331i	0.0331526	−	0.0574220i	0.882126	+	0.471014i	$0.156112\pi$
$830$	21.2504	−	36.8067i	0.737611	−	1.27758i
$831$	1.63683	+	2.83508i	0.0567811	+	0.0983477i
$832$	−11.4368			−0.396500
$833$	−36.2643	−	15.2466i	−1.25648	−	0.528265i
$834$	26.2742			0.909800
$835$	−11.2270	−	19.4458i	−0.388527	−	0.672948i
$836$	−33.5883	+	58.1766i	−1.16167	+	2.01208i
$837$	3.04925	−	5.28145i	0.105397	−	0.182554i
$838$	−13.5636	−	23.4928i	−0.468546	−	0.811545i
$839$	11.5455			0.398597			0.199298	−	0.979939i	$-0.436134\pi$
$839$	11.5455			0.398597			0.199298	+	0.979939i	$0.436134\pi$
$840$	4.61598	+	4.06978i	0.159267	+	0.140421i
$841$	41.4325			1.42871
$842$	18.4122	+	31.8909i	0.634527	+	1.09903i
$843$	−0.434875	+	0.753226i	−0.0149779	+	0.0259425i
$844$	1.55571	−	2.69456i	0.0535496	−	0.0927507i
$845$	−6.07132	−	10.5158i	−0.208860	−	0.361756i
$846$	−9.49987			−0.326612
$847$	−13.3963	+	66.4279i	−0.460301	+	2.28249i
$848$	8.71993			0.299444
$849$	−0.205939	−	0.356697i	−0.00706781	−	0.0122418i
$850$	10.8391	−	18.7739i	0.371779	−	0.643940i
$851$	0.390745	−	0.676791i	0.0133946	−	0.0232001i
$852$	−7.00172	−	12.1273i	−0.239875	−	0.415476i
$853$	3.27460			0.112120			0.0560601	−	0.998427i	$-0.482146\pi$
$853$	3.27460			0.112120			0.0560601	+	0.998427i	$0.482146\pi$
$854$	65.3219	−	21.9811i	2.23527	−	0.752178i
$855$	−19.2179			−0.657238
$856$	3.31545	+	5.74254i	0.113320	+	0.196276i
$857$	21.3130	−	36.9152i	0.728038	−	1.26100i	−0.229674	−	0.973268i	$-0.573766\pi$
$857$	21.3130	−	36.9152i	0.728038	−	1.26100i	0.957711	−	0.287730i	$-0.0929007\pi$
$858$	16.5110	−	28.5979i	0.563676	−	0.976315i
$859$	4.30530	+	7.45700i	0.146895	+	0.254430i	0.930078	−	0.367361i	$-0.119739\pi$
$859$	4.30530	+	7.45700i	0.146895	+	0.254430i	−0.783183	+	0.621791i	$0.786405\pi$
$860$	−30.9568			−1.05562
$861$	−8.31767	+	2.79893i	−0.283465	+	0.0953872i
$862$	−11.0931			−0.377832
$863$	15.3807	+	26.6402i	0.523565	+	0.906842i	0.999624	+	0.0274280i	$0.00873170\pi$
$863$	15.3807	+	26.6402i	0.523565	+	0.906842i	−0.476059	+	0.879414i	$0.657935\pi$
$864$	−3.55579	+	6.15880i	−0.120970	+	0.209527i
$865$	8.12381	−	14.0709i	0.276218	−	0.478423i
$866$	29.7878	+	51.5940i	1.01223	+	1.75324i
$867$	14.5828			0.495258
$868$	4.89325	−	24.2641i	0.166088	−	0.823577i
$869$	−35.7722			−1.21349
$870$	−20.9483	−	36.2835i	−0.710214	−	1.23013i
$871$	11.2924	−	19.5590i	0.382628	−	0.662732i
$872$	2.84974	−	4.93590i	0.0965044	−	0.167151i
$873$	0.334859	+	0.579993i	0.0113333	+	0.0196298i
$874$	13.6047			0.460187
$875$	−15.5366	−	13.6982i	−0.525233	−	0.463083i
$876$	1.35468			0.0457704
$877$	−6.17614	−	10.6974i	−0.208554	−	0.361225i	0.742706	−	0.669618i	$-0.233542\pi$
$877$	−6.17614	−	10.6974i	−0.208554	−	0.361225i	−0.951259	+	0.308393i	$0.900209\pi$
$878$	−19.8090	+	34.3103i	−0.668523	+	1.15792i
$879$	2.44038	−	4.22687i	0.0823120	−	0.142569i
$880$	−37.8791	−	65.6085i	−1.27690	−	2.21166i
$881$	−2.72679			−0.0918680			−0.0459340	−	0.998944i	$-0.514626\pi$
$881$	−2.72679			−0.0918680			−0.0459340	+	0.998944i	$0.514626\pi$
$882$	12.1309	+	5.10020i	0.408468	+	0.171733i
$883$	19.6643			0.661755			0.330878	−	0.943674i	$-0.392655\pi$
$883$	19.6643			0.661755			0.330878	+	0.943674i	$0.392655\pi$
$884$	−12.5139	−	21.6747i	−0.420887	−	0.728998i
$885$	2.60931	−	4.51946i	0.0877110	−	0.151920i
$886$	−27.8860	+	48.3000i	−0.936849	+	1.62267i
$887$	5.69785	+	9.86896i	0.191315	+	0.331367i	0.945686	−	0.325081i	$-0.105391\pi$
$887$	5.69785	+	9.86896i	0.191315	+	0.331367i	−0.754371	+	0.656448i	$0.772058\pi$
$888$	0.684496			0.0229702
$889$	−37.4263	−	32.9977i	−1.25524	−	1.10671i
$890$	42.5917			1.42768
$891$	−3.02543	−	5.24020i	−0.101356	−	0.175553i
$892$	2.29097	−	3.96807i	0.0767072	−	0.132861i
$893$	−18.2853	+	31.6710i	−0.611893	+	1.05983i
$894$	9.33769	+	16.1734i	0.312299	+	0.540918i
$895$	−44.4445			−1.48562
$896$	3.56546	−	17.6800i	0.119114	−	0.590648i
$897$	−2.90301			−0.0969285
$898$	9.16909	+	15.8813i	0.305976	+	0.529967i
$899$	25.5905	−	44.3241i	0.853492	−	1.47829i
$900$	−1.57391	+	2.72609i	−0.0524636	+	0.0908696i
$901$	5.19696	+	9.00139i	0.173136	+	0.299880i
$902$	37.7312			1.25631
$903$	19.0550	−	6.41209i	0.634112	−	0.213381i
$904$	1.28894			0.0428694
$905$	−2.14175	−	3.70963i	−0.0711943	−	0.123312i
$906$	10.3007	−	17.8414i	0.342218	−	0.592740i
$907$	13.7590	−	23.8314i	0.456862	−	0.791308i	−0.541931	−	0.840423i	$-0.682307\pi$
$907$	13.7590	−	23.8314i	0.456862	−	0.791308i	0.998793	+	0.0491151i	$0.0156401\pi$
$908$	17.4584	+	30.2389i	0.579378	+	1.00351i
$909$	−12.9031			−0.427968
$910$	36.3409	−	12.2289i	1.20469	−	0.405383i
$911$	−12.0557			−0.399425			−0.199712	−	0.979855i	$-0.564001\pi$
$911$	−12.0557			−0.399425			−0.199712	+	0.979855i	$0.564001\pi$
$912$	17.0601	+	29.5489i	0.564916	+	0.978463i
$913$	25.7568	−	44.6120i	0.852425	−	1.47644i
$914$	25.3433	−	43.8959i	0.838283	−	1.45195i
$915$	−18.3988	−	31.8676i	−0.608244	−	1.05351i
$916$	36.2802			1.19873
$917$	−8.87028	+	43.9849i	−0.292922	+	1.45251i
$918$	−10.5649			−0.348692
$919$	−20.6442	−	35.7567i	−0.680988	−	1.17951i	−0.974680	−	0.223606i	$-0.928217\pi$
$919$	−20.6442	−	35.7567i	−0.680988	−	1.17951i	0.293692	−	0.955900i	$-0.405116\pi$
$920$	−1.16298	+	2.01434i	−0.0383422	+	0.0664107i
$921$	−8.25871	+	14.3045i	−0.272134	+	0.471350i
$922$	17.5813	+	30.4517i	0.579009	+	1.00287i
$923$	26.4993			0.872234
$924$	−18.4217	−	16.2419i	−0.606028	−	0.534318i
$925$	1.60356			0.0527246
$926$	27.9487	+	48.4086i	0.918452	+	1.59081i
$927$	5.06337	−	8.77002i	0.166303	−	0.288045i
$928$	−29.8416	+	51.6872i	−0.979599	+	1.69671i
$929$	−7.56470	−	13.1024i	−0.248190	−	0.429877i	0.714834	−	0.699294i	$-0.246502\pi$
$929$	−7.56470	−	13.1024i	−0.248190	−	0.429877i	−0.963024	+	0.269417i	$0.913169\pi$
$930$	−30.4449			−0.998328
$931$	40.3526	−	30.6255i	1.32250	−	1.00371i
$932$	2.28918			0.0749847
$933$	2.74044	+	4.74658i	0.0897180	+	0.155396i
$934$	14.5575	−	25.2143i	0.476336	−	0.825037i
$935$	45.1508	−	78.2036i	1.47659	−	2.55753i
$936$	−1.27135	−	2.20204i	−0.0415554	−	0.0719760i
$937$	−20.4861			−0.669253			−0.334626	−	0.942351i	$-0.608610\pi$
$937$	−20.4861			−0.669253			−0.334626	+	0.942351i	$0.608610\pi$
$938$	−29.0248	−	25.5904i	−0.947695	−	0.835555i
$939$	−14.4355			−0.471086
$940$	10.2932	+	17.8284i	0.335728	+	0.581498i
$941$	−5.17570	+	8.96457i	−0.168723	+	0.292237i	−0.937971	−	0.346713i	$-0.887298\pi$
$941$	−5.17570	+	8.96457i	−0.168723	+	0.292237i	0.769248	+	0.638950i	$0.220631\pi$
$942$	−7.56622	+	13.1051i	−0.246521	+	0.426986i
$943$	−1.65850	−	2.87261i	−0.0540082	−	0.0935450i
$944$	−9.26534			−0.301561
$945$	1.38893	−	6.88726i	0.0451818	−	0.224043i
$946$	−86.4389			−2.81037
$947$	−15.3132	−	26.5232i	−0.497612	−	0.861889i	0.502385	−	0.864644i	$-0.332456\pi$
$947$	−15.3132	−	26.5232i	−0.497612	−	0.861889i	−0.999996	+	0.00275559i	$0.999123\pi$
$948$	4.53469	−	7.85432i	0.147280	−	0.255096i
$949$	−1.28176	+	2.22007i	−0.0416076	+	0.0720665i
$950$	13.9579	+	24.1758i	0.452855	+	0.784367i
$951$	−17.0892			−0.554154
$952$	12.3432	−	4.15354i	0.400046	−	0.134617i
$953$	−5.88206			−0.190539			−0.0952693	−	0.995452i	$-0.530371\pi$
$953$	−5.88206			−0.190539			−0.0952693	+	0.995452i	$0.530371\pi$
$954$	−1.73845	−	3.01108i	−0.0562844	−	0.0974874i
$955$	19.8586	−	34.3961i	0.642609	−	1.11303i
$956$	22.9608	−	39.7692i	0.742604	−	1.28623i
$957$	−25.3906	−	43.9779i	−0.820762	−	1.42160i
$958$	47.0269			1.51937
$959$	31.5031	−	10.6009i	1.01729	−	0.342322i
$960$	10.4619			0.337656
$961$	−3.09581	−	5.36211i	−0.0998650	−	0.172971i
$962$	2.13246	−	3.69352i	0.0687531	−	0.119084i
$963$	3.78526	−	6.55626i	0.121978	−	0.211273i
$964$	−7.74655	−	13.4174i	−0.249499	−	0.432146i
$965$	41.8845			1.34831
$966$	−0.983251	+	4.87563i	−0.0316356	+	0.156871i
$967$	−24.6570			−0.792914			−0.396457	−	0.918053i	$-0.629760\pi$
$967$	−24.6570			−0.792914			−0.396457	+	0.918053i	$0.629760\pi$
$968$	−11.2170	−	19.4284i	−0.360527	−	0.624451i
$969$	−20.3351	+	35.2215i	−0.653259	+	1.13148i
$970$	1.67168	−	2.89544i	0.0536745	−	0.0929670i
$971$	12.4246	+	21.5200i	0.398724	+	0.690611i	0.993569	−	0.113230i	$-0.0361197\pi$
$971$	12.4246	+	21.5200i	0.398724	+	0.690611i	−0.594845	+	0.803841i	$0.702786\pi$
$972$	1.53408			0.0492057
$973$	27.7366	+	24.4546i	0.889196	+	0.783978i
$974$	27.7552			0.889335
$975$	−2.97837	−	5.15868i	−0.0953841	−	0.165210i
$976$	−32.6659	+	56.5790i	−1.04561	+	1.81105i
$977$	13.4196	−	23.2434i	0.429330	−	0.743622i	−0.567484	−	0.823385i	$-0.692083\pi$
$977$	13.4196	−	23.2434i	0.429330	−	0.743622i	0.996814	+	0.0797628i	$0.0254163\pi$
$978$	2.76136	+	4.78281i	0.0882985	+	0.152938i
$979$	51.6238			1.64990
$980$	−3.57242	−	28.2921i	−0.114117	−	0.903759i
$981$	−6.50711			−0.207756
$982$	1.11322	+	1.92815i	0.0355241	+	0.0615296i
$983$	−8.91901	+	15.4482i	−0.284472	+	0.492720i	−0.972481	−	0.232982i	$-0.925152\pi$
$983$	−8.91901	+	15.4482i	−0.284472	+	0.492720i	0.688009	+	0.725702i	$0.258485\pi$
$984$	1.45266	−	2.51608i	0.0463090	−	0.0802096i
$985$	−9.67031	−	16.7495i	−0.308122	−	0.533682i
$986$	−88.6646			−2.82366
$987$	−10.0287	−	8.84198i	−0.319216	−	0.281443i
$988$	32.2291			1.02534
$989$	3.79948	+	6.58089i	0.120816	+	0.209260i
$990$	−15.1035	+	26.1601i	−0.480022	+	0.831423i
$991$	2.34694	−	4.06502i	0.0745531	−	0.129130i	−0.826339	−	0.563173i	$-0.809580\pi$
$991$	2.34694	−	4.06502i	0.0745531	−	0.129130i	0.900892	+	0.434044i	$0.142914\pi$
$992$	21.6849	+	37.5594i	0.688497	+	1.19251i
$993$	10.2642			0.325725
$994$	8.97533	−	44.5059i	0.284680	−	1.41164i
$995$	47.5692			1.50805
$996$	6.53015	+	11.3106i	0.206916	+	0.358389i
$997$	−24.7342	+	42.8409i	−0.783340	+	1.35678i	0.146646	+	0.989189i	$0.453152\pi$
$997$	−24.7342	+	42.8409i	−0.783340	+	1.35678i	−0.929986	+	0.367595i	$0.880181\pi$
$998$	−6.77315	+	11.7314i	−0.214400	+	0.371352i
$999$	−0.390745	−	0.676791i	−0.0123626	−	0.0214127i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.g.277.7	✓	16
7.2	even	3	inner	483.2.i.g.415.7	yes	16
7.3	odd	6		3381.2.a.be.1.2		8
7.4	even	3		3381.2.a.bf.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.7	✓	16	1.1	even	1	trivial
483.2.i.g.415.7	yes	16	7.2	even	3	inner
3381.2.a.be.1.2		8	7.3	odd	6
3381.2.a.bf.1.2		8	7.4	even	3

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.939958 + 1.62805i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.767041 + 1.32855i) q^{4} +(1.32777 + 2.29977i) q^{5} -1.87992 q^{6} +(-1.98456 - 1.74973i) q^{7} +0.875886 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.939958 + 1.62805i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.767041 + 1.32855i) q^{4} +(1.32777 + 2.29977i) q^{5} -1.87992 q^{6} +(-1.98456 - 1.74973i) q^{7} +0.875886 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.49610 + 4.32337i) q^{10} +(-3.02543 + 5.24020i) q^{11} +(-0.767041 - 1.32855i) q^{12} +2.90301 q^{13} +(0.983251 - 4.87563i) q^{14} -2.65555 q^{15} +(2.35738 + 4.08310i) q^{16} +(-2.80993 + 4.86694i) q^{17} +(0.939958 - 1.62805i) q^{18} +(-3.61844 - 6.26733i) q^{19} -4.07383 q^{20} +(2.50758 - 0.843812i) q^{21} -11.3751 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.437943 + 0.758539i) q^{24} +(-1.02596 + 1.77701i) q^{25} +(2.72870 + 4.72625i) q^{26} +1.00000 q^{27} +(3.84684 - 1.29448i) q^{28} +8.39241 q^{29} +(-2.49610 - 4.32337i) q^{30} +(3.04925 - 5.28145i) q^{31} +(-3.55579 + 6.15880i) q^{32} +(-3.02543 - 5.24020i) q^{33} -10.5649 q^{34} +(1.38893 - 6.88726i) q^{35} +1.53408 q^{36} +(-0.390745 - 0.676791i) q^{37} +(6.80237 - 11.7820i) q^{38} +(-1.45150 + 2.51408i) q^{39} +(1.16298 + 2.01434i) q^{40} -3.31700 q^{41} +(3.73080 + 3.28934i) q^{42} +7.59896 q^{43} +(-4.64126 - 8.03889i) q^{44} +(1.32777 - 2.29977i) q^{45} +(-0.939958 + 1.62805i) q^{46} +(-2.52667 - 4.37633i) q^{47} -4.71476 q^{48} +(0.876920 + 6.94486i) q^{49} -3.85744 q^{50} +(-2.80993 - 4.86694i) q^{51} +(-2.22672 + 3.85680i) q^{52} +(0.924749 - 1.60171i) q^{53} +(0.939958 + 1.62805i) q^{54} -16.0683 q^{55} +(-1.73824 - 1.53256i) q^{56} +7.23689 q^{57} +(7.88851 + 13.6633i) q^{58} +(-0.982589 + 1.70189i) q^{59} +(2.03691 - 3.52804i) q^{60} +(6.92843 + 12.0004i) q^{61} +11.4647 q^{62} +(-0.523029 + 2.59354i) q^{63} -3.93964 q^{64} +(3.85453 + 6.67624i) q^{65} +(5.68755 - 9.85112i) q^{66} +(3.88990 - 6.73750i) q^{67} +(-4.31066 - 7.46629i) q^{68} -1.00000 q^{69} +(12.5184 - 4.21248i) q^{70} +9.12822 q^{71} +(-0.437943 - 0.758539i) q^{72} +(-0.441528 + 0.764749i) q^{73} +(0.734568 - 1.27231i) q^{74} +(-1.02596 - 1.77701i) q^{75} +11.1020 q^{76} +(15.1730 - 5.10579i) q^{77} -5.45740 q^{78} +(2.95597 + 5.11988i) q^{79} +(-6.26012 + 10.8429i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.11784 - 5.40026i) q^{82} -8.51343 q^{83} +(-0.802370 + 3.97870i) q^{84} -14.9238 q^{85} +(7.14270 + 12.3715i) q^{86} +(-4.19620 + 7.26804i) q^{87} +(-2.64993 + 4.58981i) q^{88} +(-4.26583 - 7.38863i) q^{89} +4.99220 q^{90} +(-5.76117 - 5.07946i) q^{91} -1.53408 q^{92} +(3.04925 + 5.28145i) q^{93} +(4.74994 - 8.22713i) q^{94} +(9.60894 - 16.6432i) q^{95} +(-3.55579 - 6.15880i) q^{96} -0.669718 q^{97} +(-10.4823 + 7.95554i) q^{98} +6.05086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9	\( 16 q - q^{2} - 8 q^{3} - 15 q^{4} - 5 q^{5} + 2 q^{6} - 2 q^{7} + 18 q^{8} - 8 q^{9} + 3 q^{10} - 10 q^{11} - 15 q^{12} - 12 q^{13} - 17 q^{14} + 10 q^{15} - 13 q^{16} - 21 q^{17} - q^{18} - 5 q^{19} - 2 q^{20} + 4 q^{21} + 36 q^{22} + 8 q^{23} - 9 q^{24} - 27 q^{25} - 3 q^{26} + 16 q^{27} + 6 q^{28} + 4 q^{29} + 3 q^{30} + 13 q^{31} - 29 q^{32} - 10 q^{33} - 38 q^{34} + 27 q^{35} + 30 q^{36} - 13 q^{37} + 6 q^{38} + 6 q^{39} - 7 q^{40} + 32 q^{41} + 25 q^{42} + 30 q^{43} - 24 q^{44} - 5 q^{45} + q^{46} + q^{47} + 26 q^{48} + 16 q^{49} + 32 q^{50} - 21 q^{51} + 19 q^{52} - 3 q^{53} - q^{54} - 20 q^{55} + 33 q^{56} + 10 q^{57} + 40 q^{58} - 26 q^{59} + q^{60} + 14 q^{61} - 28 q^{62} - 2 q^{63} + 98 q^{64} + 3 q^{65} - 18 q^{66} - 38 q^{67} - 43 q^{68} - 16 q^{69} + 40 q^{70} + 18 q^{71} - 9 q^{72} + 6 q^{73} - 32 q^{74} - 27 q^{75} - 28 q^{76} + 56 q^{77} + 6 q^{78} - 23 q^{79} + 17 q^{80} - 8 q^{81} - 20 q^{82} + 60 q^{83} + 3 q^{84} - 74 q^{85} + 28 q^{86} - 2 q^{87} - 86 q^{88} - 12 q^{89} - 6 q^{90} + 26 q^{91} - 30 q^{92} + 13 q^{93} + 45 q^{94} - 16 q^{95} - 29 q^{96} + 28 q^{97} + 26 q^{98} + 20 q^{99}+O(q^{100}) \) 16 * q - q^2 - 8 * q^3 - 15 * q^4 - 5 * q^5 + 2 * q^6 - 2 * q^7 + 18 * q^8 - 8 * q^9 + 3 * q^10 - 10 * q^11 - 15 * q^12 - 12 * q^13 - 17 * q^14 + 10 * q^15 - 13 * q^16 - 21 * q^17 - q^18 - 5 * q^19 - 2 * q^20 + 4 * q^21 + 36 * q^22 + 8 * q^23 - 9 * q^24 - 27 * q^25 - 3 * q^26 + 16 * q^27 + 6 * q^28 + 4 * q^29 + 3 * q^30 + 13 * q^31 - 29 * q^32 - 10 * q^33 - 38 * q^34 + 27 * q^35 + 30 * q^36 - 13 * q^37 + 6 * q^38 + 6 * q^39 - 7 * q^40 + 32 * q^41 + 25 * q^42 + 30 * q^43 - 24 * q^44 - 5 * q^45 + q^46 + q^47 + 26 * q^48 + 16 * q^49 + 32 * q^50 - 21 * q^51 + 19 * q^52 - 3 * q^53 - q^54 - 20 * q^55 + 33 * q^56 + 10 * q^57 + 40 * q^58 - 26 * q^59 + q^60 + 14 * q^61 - 28 * q^62 - 2 * q^63 + 98 * q^64 + 3 * q^65 - 18 * q^66 - 38 * q^67 - 43 * q^68 - 16 * q^69 + 40 * q^70 + 18 * q^71 - 9 * q^72 + 6 * q^73 - 32 * q^74 - 27 * q^75 - 28 * q^76 + 56 * q^77 + 6 * q^78 - 23 * q^79 + 17 * q^80 - 8 * q^81 - 20 * q^82 + 60 * q^83 + 3 * q^84 - 74 * q^85 + 28 * q^86 - 2 * q^87 - 86 * q^88 - 12 * q^89 - 6 * q^90 + 26 * q^91 - 30 * q^92 + 13 * q^93 + 45 * q^94 - 16 * q^95 - 29 * q^96 + 28 * q^97 + 26 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more