LMFDB - Embedded newform 322.2.e.d.93.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,2,Mod(93,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("322.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	322.e (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:	$2.57118294509$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.6498455769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} + 3x^{5} + 25x^{4} - 3x^{3} + 6x^{2} + x + 1 $ x^8 - x^7 + 6x^6 + 3x^5 + 25x^4 - 3x^3 + 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.2
Root			$0.271028 + 0.469434i$ of defining polynomial
Character	$\chi$	$=$	322.93
Dual form			322.2.e.d.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.271028 - 0.469434i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.298300 - 0.516670i) q^{5} -0.542055 q^{6} +(-2.61586 + 0.396592i) q^{7} -1.00000 q^{8} +(1.35309 - 2.34362i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.271028 - 0.469434i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.298300 - 0.516670i) q^{5} -0.542055 q^{6} +(-2.61586 + 0.396592i) q^{7} -1.00000 q^{8} +(1.35309 - 2.34362i) q^{9} +(-0.298300 - 0.516670i) q^{10} +(-2.92689 - 5.06952i) q^{11} +(-0.271028 + 0.469434i) q^{12} +0.239279 q^{13} +(-0.964471 + 2.46370i) q^{14} -0.323390 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.20170 + 2.08141i) q^{17} +(-1.35309 - 2.34362i) q^{18} +(2.54653 - 4.41072i) q^{19} -0.596599 q^{20} +(0.895143 + 1.12048i) q^{21} -5.85378 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.271028 + 0.469434i) q^{24} +(2.32203 + 4.02188i) q^{25} +(0.119640 - 0.207222i) q^{26} -3.09306 q^{27} +(1.65139 + 2.06710i) q^{28} -5.19369 q^{29} +(-0.161695 + 0.280064i) q^{30} +(1.22072 + 2.11434i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.58654 + 2.74796i) q^{33} +2.40340 q^{34} +(-0.575403 + 1.46984i) q^{35} -2.70618 q^{36} +(-1.33005 + 2.30371i) q^{37} +(-2.54653 - 4.41072i) q^{38} +(-0.0648513 - 0.112326i) q^{39} +(-0.298300 + 0.516670i) q^{40} +11.6365 q^{41} +(1.41794 - 0.214975i) q^{42} +3.93789 q^{43} +(-2.92689 + 5.06952i) q^{44} +(-0.807252 - 1.39820i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(3.86787 - 6.69935i) q^{47} +0.542055 q^{48} +(6.68543 - 2.07486i) q^{49} +4.64407 q^{50} +(0.651388 - 1.12824i) q^{51} +(-0.119640 - 0.207222i) q^{52} +(-2.18692 - 3.78785i) q^{53} +(-1.54653 + 2.67867i) q^{54} -3.49236 q^{55} +(2.61586 - 0.396592i) q^{56} -2.76072 q^{57} +(-2.59684 + 4.49786i) q^{58} +(5.08206 + 8.80239i) q^{59} +(0.161695 + 0.280064i) q^{60} +(0.340355 - 0.589512i) q^{61} +2.44143 q^{62} +(-2.61003 + 6.66719i) q^{63} +1.00000 q^{64} +(0.0713770 - 0.123629i) q^{65} +(1.58654 + 2.74796i) q^{66} +(1.56131 + 2.70428i) q^{67} +(1.20170 - 2.08141i) q^{68} -0.542055 q^{69} +(0.985217 + 1.23323i) q^{70} -5.55947 q^{71} +(-1.35309 + 2.34362i) q^{72} +(3.30483 + 5.72413i) q^{73} +(1.33005 + 2.30371i) q^{74} +(1.25867 - 2.18008i) q^{75} -5.09306 q^{76} +(9.66687 + 12.1004i) q^{77} -0.129703 q^{78} +(2.99199 - 5.18227i) q^{79} +(0.298300 + 0.516670i) q^{80} +(-3.22096 - 5.57887i) q^{81} +(5.81825 - 10.0775i) q^{82} -0.386886 q^{83} +(0.522796 - 1.33546i) q^{84} +1.43387 q^{85} +(1.96895 - 3.41032i) q^{86} +(1.40763 + 2.43809i) q^{87} +(2.92689 + 5.06952i) q^{88} +(6.54653 - 11.3389i) q^{89} -1.61450 q^{90} +(-0.625921 + 0.0948963i) q^{91} -1.00000 q^{92} +(0.661695 - 1.14609i) q^{93} +(-3.86787 - 6.69935i) q^{94} +(-1.51926 - 2.63143i) q^{95} +(0.271028 - 0.469434i) q^{96} -0.0666948 q^{97} +(1.54584 - 6.82718i) q^{98} -15.8414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) $ 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/322\mathbb{Z}\right)^\times$.

$n$	$185$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.271028	−	0.469434i	−0.156478	−	0.271028i	0.777118	−	0.629355i	$-0.216681\pi$
$3$	−0.271028	−	0.469434i	−0.156478	−	0.271028i	−0.933596	+	0.358327i	$0.883347\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.298300	−	0.516670i	0.133404	−	0.231062i	−0.791583	−	0.611062i	$-0.790743\pi$
$5$	0.298300	−	0.516670i	0.133404	−	0.231062i	0.924987	+	0.380000i	$0.124076\pi$
$6$	−0.542055			−0.221293
$7$	−2.61586	+	0.396592i	−0.988702	+	0.149898i
$7$	−2.61586	+	0.396592i	−0.988702	+	0.149898i
$8$	−1.00000			−0.353553
$9$	1.35309	−	2.34362i	0.451029	−	0.781206i
$10$	−0.298300	−	0.516670i	−0.0943306	−	0.163385i
$11$	−2.92689	−	5.06952i	−0.882491	−	1.52852i	−0.848563	−	0.529095i	$-0.822532\pi$
$11$	−2.92689	−	5.06952i	−0.882491	−	1.52852i	−0.0339283	−	0.999424i	$-0.510802\pi$
$12$	−0.271028	+	0.469434i	−0.0782389	+	0.135514i
$13$	0.239279			0.0663642			0.0331821	−	0.999449i	$-0.489436\pi$
$13$	0.239279			0.0663642			0.0331821	+	0.999449i	$0.489436\pi$
$14$	−0.964471	+	2.46370i	−0.257766	+	0.658450i
$15$	−0.323390			−0.0834989
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.20170	+	2.08141i	0.291455	+	0.504815i	0.974154	−	0.225885i	$-0.0725273\pi$
$17$	1.20170	+	2.08141i	0.291455	+	0.504815i	−0.682699	+	0.730700i	$0.739194\pi$
$18$	−1.35309	−	2.34362i	−0.318926	−	0.552396i
$19$	2.54653	−	4.41072i	0.584214	−	1.01189i	−0.410759	−	0.911744i	$-0.634736\pi$
$19$	2.54653	−	4.41072i	0.584214	−	1.01189i	0.994973	−	0.100145i	$-0.0319306\pi$
$20$	−0.596599			−0.133404
$21$	0.895143	+	1.12048i	0.195336	+	0.244510i
$22$	−5.85378			−1.24803
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i
$24$	0.271028	+	0.469434i	0.0553233	+	0.0958227i
$25$	2.32203	+	4.02188i	0.464407	+	0.804376i
$26$	0.119640	−	0.207222i	0.0234633	−	0.0406396i
$27$	−3.09306			−0.595260
$28$	1.65139	+	2.06710i	0.312083	+	0.390646i
$29$	−5.19369			−0.964443			−0.482222	−	0.876049i	$-0.660170\pi$
$29$	−5.19369			−0.964443			−0.482222	+	0.876049i	$0.660170\pi$
$30$	−0.161695	+	0.280064i	−0.0295213	+	0.0511324i
$31$	1.22072	+	2.11434i	0.219247	+	0.379747i	0.954578	−	0.297961i	$-0.0963066\pi$
$31$	1.22072	+	2.11434i	0.219247	+	0.379747i	−0.735331	+	0.677708i	$0.762973\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.58654	+	2.74796i	−0.276181	+	0.478359i
$34$	2.40340			0.412180
$35$	−0.575403	+	1.46984i	−0.0972608	+	0.248448i
$36$	−2.70618			−0.451029
$37$	−1.33005	+	2.30371i	−0.218659	+	0.378728i	−0.954398	−	0.298537i	$-0.903501\pi$
$37$	−1.33005	+	2.30371i	−0.218659	+	0.378728i	0.735740	+	0.677265i	$0.236835\pi$
$38$	−2.54653	−	4.41072i	−0.413102	−	0.715513i
$39$	−0.0648513	−	0.112326i	−0.0103845	−	0.0179865i
$40$	−0.298300	+	0.516670i	−0.0471653	+	0.0816927i
$41$	11.6365			1.81732			0.908658	−	0.417540i	$-0.137108\pi$
$41$	11.6365			1.81732			0.908658	+	0.417540i	$0.137108\pi$
$42$	1.41794	−	0.214975i	0.218793	−	0.0331713i
$43$	3.93789			0.600523			0.300262	−	0.953857i	$-0.402926\pi$
$43$	3.93789			0.600523			0.300262	+	0.953857i	$0.402926\pi$
$44$	−2.92689	+	5.06952i	−0.441245	+	0.764260i
$45$	−0.807252	−	1.39820i	−0.120338	−	0.208431i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	3.86787	−	6.69935i	0.564187	−	0.977201i	−0.432938	−	0.901424i	$-0.642523\pi$
$47$	3.86787	−	6.69935i	0.564187	−	0.977201i	0.997125	−	0.0757767i	$-0.0241436\pi$
$48$	0.542055			0.0782389
$49$	6.68543	−	2.07486i	0.955061	−	0.296408i
$50$	4.64407			0.656771
$51$	0.651388	−	1.12824i	0.0912125	−	0.157985i
$52$	−0.119640	−	0.207222i	−0.0165910	−	0.0287365i
$53$	−2.18692	−	3.78785i	−0.300396	−	0.520301i	0.675830	−	0.737058i	$-0.263786\pi$
$53$	−2.18692	−	3.78785i	−0.300396	−	0.520301i	−0.976226	+	0.216757i	$0.930452\pi$
$54$	−1.54653	+	2.67867i	−0.210456	+	0.364521i
$55$	−3.49236			−0.470910
$56$	2.61586	−	0.396592i	0.349559	−	0.0529968i
$57$	−2.76072			−0.365666
$58$	−2.59684	+	4.49786i	−0.340982	+	0.590599i
$59$	5.08206	+	8.80239i	0.661628	+	1.14597i	0.980188	+	0.198070i	$0.0634675\pi$
$59$	5.08206	+	8.80239i	0.661628	+	1.14597i	−0.318560	+	0.947903i	$0.603199\pi$
$60$	0.161695	+	0.280064i	0.0208747	+	0.0361561i
$61$	0.340355	−	0.589512i	0.0435780	−	0.0754793i	−0.843414	−	0.537265i	$-0.819458\pi$
$61$	0.340355	−	0.589512i	0.0435780	−	0.0754793i	0.886992	+	0.461785i	$0.152791\pi$
$62$	2.44143			0.310062
$63$	−2.61003	+	6.66719i	−0.328833	+	0.839988i
$64$	1.00000			0.125000
$65$	0.0713770	−	0.123629i	0.00885323	−	0.0153342i
$66$	1.58654	+	2.74796i	0.195289	+	0.338251i
$67$	1.56131	+	2.70428i	0.190745	+	0.330380i	0.945497	−	0.325630i	$-0.105576\pi$
$67$	1.56131	+	2.70428i	0.190745	+	0.330380i	−0.754752	+	0.656010i	$0.772243\pi$
$68$	1.20170	−	2.08141i	0.145728	−	0.252408i
$69$	−0.542055			−0.0652558
$70$	0.985217	+	1.23323i	0.117756	+	0.147400i
$71$	−5.55947			−0.659788			−0.329894	−	0.944018i	$-0.607013\pi$
$71$	−5.55947			−0.659788			−0.329894	+	0.944018i	$0.607013\pi$
$72$	−1.35309	+	2.34362i	−0.159463	+	0.276198i
$73$	3.30483	+	5.72413i	0.386801	+	0.669958i	0.992017	−	0.126103i	$-0.0402469\pi$
$73$	3.30483	+	5.72413i	0.386801	+	0.669958i	−0.605217	+	0.796061i	$0.706914\pi$
$74$	1.33005	+	2.30371i	0.154615	+	0.267801i
$75$	1.25867	−	2.18008i	0.145339	−	0.251734i
$76$	−5.09306			−0.584214
$77$	9.66687	+	12.1004i	1.10164	+	1.37897i
$78$	−0.129703			−0.0146859
$79$	2.99199	−	5.18227i	0.336625	−	0.583051i	−0.647171	−	0.762345i	$-0.724048\pi$
$79$	2.99199	−	5.18227i	0.336625	−	0.583051i	0.983796	+	0.179294i	$0.0573813\pi$
$80$	0.298300	+	0.516670i	0.0333509	+	0.0577655i
$81$	−3.22096	−	5.57887i	−0.357884	−	0.619874i
$82$	5.81825	−	10.0775i	0.642519	−	1.11287i
$83$	−0.386886			−0.0424662			−0.0212331	−	0.999775i	$-0.506759\pi$
$83$	−0.386886			−0.0424662			−0.0212331	+	0.999775i	$0.506759\pi$
$84$	0.522796	−	1.33546i	0.0570417	−	0.145711i
$85$	1.43387			0.155525
$86$	1.96895	−	3.41032i	0.212317	−	0.367744i
$87$	1.40763	+	2.43809i	0.150914	+	0.261391i
$88$	2.92689	+	5.06952i	0.312008	+	0.540413i
$89$	6.54653	−	11.3389i	0.693931	−	1.20192i	−0.276609	−	0.960983i	$-0.589211\pi$
$89$	6.54653	−	11.3389i	0.693931	−	1.20192i	0.970540	−	0.240941i	$-0.0774560\pi$
$90$	−1.61450			−0.170184
$91$	−0.625921	+	0.0948963i	−0.0656144	+	0.00994784i
$92$	−1.00000			−0.104257
$93$	0.661695	−	1.14609i	0.0686146	−	0.118844i
$94$	−3.86787	−	6.69935i	−0.398940	−	0.690985i
$95$	−1.51926	−	2.63143i	−0.155873	−	0.269979i
$96$	0.271028	−	0.469434i	0.0276616	−	0.0479114i
$97$	−0.0666948			−0.00677183			−0.00338592	−	0.999994i	$-0.501078\pi$
$97$	−0.0666948			−0.00677183			−0.00338592	+	0.999994i	$0.501078\pi$
$98$	1.54584	−	6.82718i	0.156153	−	0.689649i
$99$	−15.8414			−1.59212
$100$	2.32203	−	4.02188i	0.232203	−	0.402188i
$101$	8.17935	+	14.1671i	0.813876	+	1.40967i	0.910132	+	0.414318i	$0.135980\pi$
$101$	8.17935	+	14.1671i	0.813876	+	1.40967i	−0.0962559	+	0.995357i	$0.530687\pi$
$102$	−0.651388	−	1.12824i	−0.0644970	−	0.111712i
$103$	−9.90684	+	17.1591i	−0.976150	+	1.69074i	−0.300063	+	0.953919i	$0.597008\pi$
$103$	−9.90684	+	17.1591i	−0.976150	+	1.69074i	−0.676087	+	0.736822i	$0.736326\pi$
$104$	−0.239279			−0.0234633
$105$	0.845942	−	0.128254i	0.0825555	−	0.0125163i
$106$	−4.37383			−0.424824
$107$	7.69837	−	13.3340i	0.744229	−	1.28904i	−0.206324	−	0.978484i	$-0.566150\pi$
$107$	7.69837	−	13.3340i	0.744229	−	1.28904i	0.950554	−	0.310560i	$-0.100516\pi$
$108$	1.54653	+	2.67867i	0.148815	+	0.257755i
$109$	−8.14407	−	14.1059i	−0.780060	−	1.35110i	−0.931906	−	0.362700i	$-0.881855\pi$
$109$	−8.14407	−	14.1059i	−0.780060	−	1.35110i	0.151846	−	0.988404i	$-0.451478\pi$
$110$	−1.74618	+	3.02448i	−0.166492	+	0.288372i
$111$	1.44192			0.136861
$112$	0.964471	−	2.46370i	0.0911339	−	0.232797i
$113$	−2.86135			−0.269173			−0.134586	−	0.990902i	$-0.542971\pi$
$113$	−2.86135			−0.269173			−0.134586	+	0.990902i	$0.542971\pi$
$114$	−1.38036	+	2.39085i	−0.129283	+	0.223924i
$115$	−0.298300	−	0.516670i	−0.0278166	−	0.0481797i
$116$	2.59684	+	4.49786i	0.241111	+	0.417616i
$117$	0.323766	−	0.560780i	0.0299322	−	0.0518441i
$118$	10.1641			0.935683
$119$	−3.96895	−	4.96808i	−0.363833	−	0.455423i
$120$	0.323390			0.0295213
$121$	−11.6334	+	20.1496i	−1.05758	+	1.83178i
$122$	−0.340355	−	0.589512i	−0.0308143	−	0.0533719i
$123$	−3.15381	−	5.46257i	−0.284370	−	0.492543i
$124$	1.22072	−	2.11434i	0.109623	−	0.189873i
$125$	5.75365			0.514622
$126$	4.46895	+	5.59395i	0.398125	+	0.498348i
$127$	−1.66420			−0.147673			−0.0738367	−	0.997270i	$-0.523524\pi$
$127$	−1.66420			−0.147673			−0.0738367	+	0.997270i	$0.523524\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.06728	−	1.84858i	−0.0939685	−	0.162758i
$130$	−0.0713770	−	0.123629i	−0.00626018	−	0.0108429i
$131$	7.44820	−	12.9007i	0.650752	−	1.12714i	−0.332188	−	0.943213i	$-0.607787\pi$
$131$	7.44820	−	12.9007i	0.650752	−	1.12714i	0.982941	−	0.183923i	$-0.0588797\pi$
$132$	3.17307			0.276181
$133$	−4.91211	+	12.5478i	−0.425934	+	1.08803i
$134$	3.12263			0.269754
$135$	−0.922660	+	1.59809i	−0.0794099	+	0.137542i
$136$	−1.20170	−	2.08141i	−0.103045	−	0.178479i
$137$	−1.13442	−	1.96488i	−0.0969203	−	0.167871i	0.813488	−	0.581581i	$-0.197566\pi$
$137$	−1.13442	−	1.96488i	−0.0969203	−	0.167871i	−0.910408	+	0.413711i	$0.864233\pi$
$138$	−0.271028	+	0.469434i	−0.0230714	+	0.0399608i
$139$	−18.1536			−1.53977			−0.769883	−	0.638185i	$-0.779686\pi$
$139$	−18.1536			−1.53977			−0.769883	+	0.638185i	$0.779686\pi$
$140$	1.56062	−	0.236606i	0.131896	−	0.0199969i
$141$	−4.19320			−0.353131
$142$	−2.77974	+	4.81464i	−0.233270	+	0.404036i
$143$	−0.700345	−	1.21303i	−0.0585658	−	0.101439i
$144$	1.35309	+	2.34362i	0.112757	+	0.195301i
$145$	−1.54928	+	2.68342i	−0.128660	+	0.222846i
$146$	6.60965			0.547019
$147$	−2.78594	−	2.57602i	−0.229781	−	0.212467i
$148$	2.66010			0.218659
$149$	2.67661	−	4.63602i	0.219276	−	0.379798i	−0.735311	−	0.677730i	$-0.762964\pi$
$149$	2.67661	−	4.63602i	0.219276	−	0.379798i	0.954587	+	0.297932i	$0.0962970\pi$
$150$	−1.25867	−	2.18008i	−0.102770	−	0.178003i
$151$	3.49244	+	6.04908i	0.284211	+	0.492267i	0.972417	−	0.233247i	$-0.0749352\pi$
$151$	3.49244	+	6.04908i	0.284211	+	0.492267i	−0.688207	+	0.725514i	$0.741602\pi$
$152$	−2.54653	+	4.41072i	−0.206551	+	0.357757i
$153$	6.50403			0.525819
$154$	15.3127	−	2.32156i	1.23393	−	0.187077i
$155$	1.45656			0.116993
$156$	−0.0648513	+	0.112326i	−0.00519226	+	0.00899326i
$157$	3.96471	+	6.86709i	0.316419	+	0.548053i	0.979738	−	0.200283i	$-0.0641862\pi$
$157$	3.96471	+	6.86709i	0.316419	+	0.548053i	−0.663319	+	0.748336i	$0.730853\pi$
$158$	−2.99199	−	5.18227i	−0.238030	−	0.412280i
$159$	−1.18543	+	2.05322i	−0.0940107	+	0.162831i
$160$	0.596599			0.0471653
$161$	−0.964471	+	2.46370i	−0.0760109	+	0.194166i
$162$	−6.44192			−0.506125
$163$	−7.07232	+	12.2496i	−0.553947	+	0.959464i	0.444038	+	0.896008i	$0.353545\pi$
$163$	−7.07232	+	12.2496i	−0.553947	+	0.959464i	−0.997985	+	0.0634556i	$0.979788\pi$
$164$	−5.81825	−	10.0775i	−0.454329	−	0.786921i
$165$	0.946527	+	1.63943i	0.0736870	+	0.127630i
$166$	−0.193443	+	0.335053i	−0.0150141	+	0.0260052i
$167$	−17.8346			−1.38008			−0.690040	−	0.723771i	$-0.742407\pi$
$167$	−17.8346			−1.38008			−0.690040	+	0.723771i	$0.742407\pi$
$168$	−0.895143	−	1.12048i	−0.0690618	−	0.0864472i
$169$	−12.9427			−0.995596
$170$	0.716934	−	1.24177i	0.0549863	−	0.0952391i
$171$	−6.89136	−	11.9362i	−0.526996	−	0.912783i
$172$	−1.96895	−	3.41032i	−0.150131	−	0.260034i
$173$	3.34060	−	5.78609i	0.253981	−	0.439908i	−0.710637	−	0.703559i	$-0.751593\pi$
$173$	3.34060	−	5.78609i	0.253981	−	0.439908i	0.964618	+	0.263651i	$0.0849266\pi$
$174$	2.81526			0.213425
$175$	−7.66916	−	9.59977i	−0.579734	−	0.725675i
$176$	5.85378			0.441245
$177$	2.75476	−	4.77138i	0.207060	−	0.358639i
$178$	−6.54653	−	11.3389i	−0.490683	−	0.849888i
$179$	−6.68140	−	11.5725i	−0.499392	−	0.864972i	0.500608	−	0.865674i	$-0.333110\pi$
$179$	−6.68140	−	11.5725i	−0.499392	−	0.864972i	−1.00000		0.000702380i	$0.999776\pi$
$180$	−0.807252	+	1.39820i	−0.0601690	+	0.104216i
$181$	−23.6069			−1.75469			−0.877345	−	0.479860i	$-0.840687\pi$
$181$	−23.6069			−1.75469			−0.877345	+	0.479860i	$0.840687\pi$
$182$	−0.230778	+	0.589512i	−0.0171064	+	0.0436975i
$183$	−0.368982			−0.0272759
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	0.793506	+	1.37439i	0.0583397	+	0.101047i
$186$	−0.661695	−	1.14609i	−0.0485178	−	0.0840353i
$187$	7.03449	−	12.1841i	0.514413	−	0.890989i
$188$	−7.73574			−0.564187
$189$	8.09101	−	1.22668i	0.588535	−	0.0892281i
$190$	−3.03852			−0.220437
$191$	−3.45243	+	5.97979i	−0.249809	+	0.432682i	−0.963473	−	0.267806i	$-0.913701\pi$
$191$	−3.45243	+	5.97979i	−0.249809	+	0.432682i	0.713664	+	0.700489i	$0.247035\pi$
$192$	−0.271028	−	0.469434i	−0.0195597	−	0.0338784i
$193$	9.74650	+	16.8814i	0.701568	+	1.21515i	0.967916	+	0.251275i	$0.0808498\pi$
$193$	9.74650	+	16.8814i	0.701568	+	1.21515i	−0.266347	+	0.963877i	$0.585817\pi$
$194$	−0.0333474	+	0.0577594i	−0.00239420	+	0.00414688i
$195$	−0.0773805			−0.00554134
$196$	−5.13959	−	4.75232i	−0.367114	−	0.339452i
$197$	15.5739			1.10960			0.554798	−	0.831985i	$-0.312796\pi$
$197$	15.5739			1.10960			0.554798	+	0.831985i	$0.312796\pi$
$198$	−7.92068	+	13.7190i	−0.562898	+	0.974969i
$199$	−1.68897	−	2.92538i	−0.119728	−	0.207374i	0.799932	−	0.600091i	$-0.204869\pi$
$199$	−1.68897	−	2.92538i	−0.119728	−	0.207374i	−0.919660	+	0.392716i	$0.871535\pi$
$200$	−2.32203	−	4.02188i	−0.164193	−	0.284390i
$201$	0.846318	−	1.46587i	0.0596947	−	0.103394i
$202$	16.3587			1.15099
$203$	13.5859	−	2.05977i	0.953547	−	0.144568i
$204$	−1.30278			−0.0912125
$205$	3.47117	−	6.01224i	0.242437	−	0.419913i
$206$	9.90684	+	17.1591i	0.690242	+	1.19553i
$207$	−1.35309	−	2.34362i	−0.0940461	−	0.162893i
$208$	−0.119640	+	0.207222i	−0.00829552	+	0.0143683i
$209$	−29.8137			−2.06226
$210$	0.311900	−	0.796734i	0.0215231	−	0.0549799i
$211$	4.02818			0.277311			0.138656	−	0.990341i	$-0.455722\pi$
$211$	4.02818			0.277311			0.138656	+	0.990341i	$0.455722\pi$
$212$	−2.18692	+	3.78785i	−0.150198	+	0.260151i
$213$	1.50677	+	2.60980i	0.103242	+	0.178821i
$214$	−7.69837	−	13.3340i	−0.526250	−	0.911491i
$215$	1.17467	−	2.03459i	0.0801120	−	0.138758i
$216$	3.09306			0.210456
$217$	−4.03175	−	5.04669i	−0.273693	−	0.342592i
$218$	−16.2881			−1.10317
$219$	1.79140	−	3.10279i	0.121051	−	0.209667i
$220$	1.74618	+	3.02448i	0.117728	+	0.203910i
$221$	0.287542	+	0.498038i	0.0193422	+	0.0335016i
$222$	0.720959	−	1.24874i	0.0483876	−	0.0838098i
$223$	28.2386			1.89100			0.945498	−	0.325628i	$-0.105576\pi$
$223$	28.2386			1.89100			0.945498	+	0.325628i	$0.105576\pi$
$224$	−1.65139	−	2.06710i	−0.110338	−	0.138114i
$225$	12.5677			0.837845
$226$	−1.43067	+	2.47800i	−0.0951669	+	0.164834i
$227$	5.11176	+	8.85383i	0.339279	+	0.587649i	0.984297	−	0.176518i	$-0.0564835\pi$
$227$	5.11176	+	8.85383i	0.339279	+	0.587649i	−0.645018	+	0.764167i	$0.723150\pi$
$228$	1.38036	+	2.39085i	0.0914166	+	0.158338i
$229$	1.25041	−	2.16578i	0.0826296	−	0.143119i	−0.821749	−	0.569850i	$-0.807001\pi$
$229$	1.25041	−	2.16578i	0.0826296	−	0.143119i	0.904379	+	0.426731i	$0.140335\pi$
$230$	−0.596599			−0.0393386
$231$	3.06034	−	7.81749i	0.201355	−	0.514353i
$232$	5.19369			0.340982
$233$	−2.23300	+	3.86767i	−0.146289	+	0.253379i	−0.929853	−	0.367931i	$-0.880066\pi$
$233$	−2.23300	+	3.86767i	−0.146289	+	0.253379i	0.783564	+	0.621311i	$0.213399\pi$
$234$	−0.323766	−	0.560780i	−0.0211653	−	0.0366593i
$235$	−2.30757	−	3.99683i	−0.150529	−	0.260724i
$236$	5.08206	−	8.80239i	0.330814	−	0.572987i
$237$	−3.24364			−0.210697
$238$	−6.28696	+	0.953169i	−0.407523	+	0.0617848i
$239$	20.8462			1.34843			0.674215	−	0.738535i	$-0.264482\pi$
$239$	20.8462			1.34843			0.674215	+	0.738535i	$0.264482\pi$
$240$	0.161695	−	0.280064i	0.0104374	−	0.0180780i
$241$	−2.03244	−	3.52029i	−0.130921	−	0.226762i	0.793111	−	0.609077i	$-0.208460\pi$
$241$	−2.03244	−	3.52029i	−0.130921	−	0.226762i	−0.924032	+	0.382315i	$0.875127\pi$
$242$	11.6334	+	20.1496i	0.747822	+	1.29527i
$243$	−6.38553	+	11.0601i	−0.409632	+	0.709503i
$244$	−0.680710			−0.0435780
$245$	0.922245	−	4.07309i	0.0589201	−	0.260220i
$246$	−6.30763			−0.402160
$247$	0.609333	−	1.05540i	0.0387709	−	0.0671532i
$248$	−1.22072	−	2.11434i	−0.0775155	−	0.134261i
$249$	0.104857	+	0.181617i	0.00664503	+	0.0115095i
$250$	2.87682	−	4.98280i	0.181946	−	0.315140i
$251$	−27.8969			−1.76084			−0.880418	−	0.474198i	$-0.842738\pi$
$251$	−27.8969			−1.76084			−0.880418	+	0.474198i	$0.842738\pi$
$252$	7.07897	−	1.07325i	0.445933	−	0.0676082i
$253$	−5.85378			−0.368024
$254$	−0.832098	+	1.44124i	−0.0522104	+	0.0904311i
$255$	−0.388618	−	0.673105i	−0.0243362	−	0.0421515i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.9929	−	24.2364i	0.872852	−	1.51182i	0.0138193	−	0.999905i	$-0.495601\pi$
$257$	13.9929	−	24.2364i	0.872852	−	1.51182i	0.859033	−	0.511920i	$-0.171066\pi$
$258$	−2.13456			−0.132892
$259$	2.56558	−	6.55367i	0.159418	−	0.407225i
$260$	−0.142754			−0.00885323
$261$	−7.02752	+	12.1720i	−0.434992	+	0.753429i
$262$	−7.44820	−	12.9007i	−0.460151	−	0.797005i
$263$	14.4661	+	25.0560i	0.892018	+	1.54502i	0.837452	+	0.546511i	$0.184044\pi$
$263$	14.4661	+	25.0560i	0.892018	+	1.54502i	0.0545660	+	0.998510i	$0.482622\pi$
$264$	1.58654	−	2.74796i	0.0976446	−	0.169125i
$265$	−2.60943			−0.160296
$266$	8.41062	+	10.5279i	0.515688	+	0.645506i
$267$	−7.09716			−0.434339
$268$	1.56131	−	2.70428i	0.0953724	−	0.165190i
$269$	7.95590	+	13.7800i	0.485079	+	0.840182i	0.999853	−	0.0171439i	$-0.00545733\pi$
$269$	7.95590	+	13.7800i	0.485079	+	0.840182i	−0.514774	+	0.857326i	$0.672124\pi$
$270$	0.922660	+	1.59809i	0.0561513	+	0.0972569i
$271$	−3.08379	+	5.34128i	−0.187327	+	0.324460i	−0.944358	−	0.328919i	$-0.893316\pi$
$271$	−3.08379	+	5.34128i	−0.187327	+	0.324460i	0.757031	+	0.653379i	$0.226649\pi$
$272$	−2.40340			−0.145728
$273$	0.214189	+	0.268109i	0.0129633	+	0.0162267i
$274$	−2.26885			−0.137066
$275$	13.5927	−	23.5432i	0.819670	−	1.41971i
$276$	0.271028	+	0.469434i	0.0163139	+	0.0282566i
$277$	−2.61828	−	4.53500i	−0.157317	−	0.272482i	0.776583	−	0.630015i	$-0.216951\pi$
$277$	−2.61828	−	4.53500i	−0.157317	−	0.272482i	−0.933900	+	0.357533i	$0.883618\pi$
$278$	−9.07679	+	15.7215i	−0.544390	+	0.942911i
$279$	6.60694			0.395547
$280$	0.575403	−	1.46984i	0.0343869	−	0.0878397i
$281$	12.4295			0.741482			0.370741	−	0.928736i	$-0.379104\pi$
$281$	12.4295			0.741482			0.370741	+	0.928736i	$0.379104\pi$
$282$	−2.09660	+	3.63142i	−0.124851	+	0.216248i
$283$	1.16798	+	2.02299i	0.0694290	+	0.120255i	0.898650	−	0.438666i	$-0.144549\pi$
$283$	1.16798	+	2.02299i	0.0694290	+	0.120255i	−0.829221	+	0.558921i	$0.811216\pi$
$284$	2.77974	+	4.81464i	0.164947	+	0.285696i
$285$	−0.823522	+	1.42638i	−0.0487812	+	0.0844916i
$286$	−1.40069			−0.0828245
$287$	−30.4395	+	4.61494i	−1.79678	+	0.272412i
$288$	2.70618			0.159463
$289$	5.61183	−	9.71998i	0.330108	−	0.571764i
$290$	1.54928	+	2.68342i	0.0909766	+	0.157576i
$291$	0.0180761	+	0.0313088i	0.00105964	+	0.00183535i
$292$	3.30483	−	5.72413i	0.193400	−	0.334979i
$293$	2.87120			0.167737			0.0838686	−	0.996477i	$-0.473272\pi$
$293$	2.87120			0.167737			0.0838686	+	0.996477i	$0.473272\pi$
$294$	−3.62387	+	1.12469i	−0.211348	+	0.0655931i
$295$	6.06391			0.353054
$296$	1.33005	−	2.30371i	0.0773075	−	0.133900i
$297$	9.05306	+	15.6804i	0.525312	+	0.909866i
$298$	−2.67661	−	4.63602i	−0.155052	−	0.268558i
$299$	0.119640	−	0.207222i	0.00691895	−	0.0119840i
$300$	−2.51734			−0.145339
$301$	−10.3010	+	1.56174i	−0.593738	+	0.0900170i
$302$	6.98487			0.401934
$303$	4.43366	−	7.67933i	0.254707	−	0.441166i
$304$	2.54653	+	4.41072i	0.146054	+	0.252972i
$305$	−0.203055	−	0.351702i	−0.0116269	−	0.0201384i
$306$	3.25201	−	5.63265i	0.185905	−	0.321997i
$307$	25.5863			1.46029			0.730144	−	0.683293i	$-0.239453\pi$
$307$	25.5863			1.46029			0.730144	+	0.683293i	$0.239453\pi$
$308$	5.64580	−	14.4219i	0.321699	−	0.821766i
$309$	10.7401			0.610983
$310$	0.728278	−	1.26141i	0.0413634	−	0.0716435i
$311$	6.46093	+	11.1907i	0.366366	+	0.634564i	0.988994	−	0.147953i	$-0.0472685\pi$
$311$	6.46093	+	11.1907i	0.366366	+	0.634564i	−0.622628	+	0.782518i	$0.713935\pi$
$312$	0.0648513	+	0.112326i	0.00367148	+	0.00635920i
$313$	−12.9010	+	22.3452i	−0.729208	+	1.26303i	0.228010	+	0.973659i	$0.426778\pi$
$313$	−12.9010	+	22.3452i	−0.729208	+	1.26303i	−0.957218	+	0.289367i	$0.906555\pi$
$314$	7.92943			0.447484
$315$	2.66617	+	3.33735i	0.150222	+	0.188038i
$316$	−5.98397			−0.336625
$317$	12.5012	−	21.6527i	0.702136	−	1.21614i	−0.265579	−	0.964089i	$-0.585563\pi$
$317$	12.5012	−	21.6527i	0.702136	−	1.21614i	0.967715	−	0.252047i	$-0.0811037\pi$
$318$	1.18543	+	2.05322i	0.0664756	+	0.115139i
$319$	15.2014	+	26.3295i	0.851113	+	1.47417i
$320$	0.298300	−	0.516670i	0.0166755	−	0.0288827i
$321$	−8.34588			−0.465822
$322$	1.65139	+	2.06710i	0.0920282	+	0.115195i
$323$	12.2407			0.681089
$324$	−3.22096	+	5.57887i	−0.178942	+	0.309937i
$325$	0.555615	+	0.962354i	0.0308200	+	0.0533818i
$326$	7.07232	+	12.2496i	0.391699	+	0.678443i
$327$	−4.41453	+	7.64620i	−0.244124	+	0.422836i
$328$	−11.6365			−0.642519
$329$	−7.46090	+	19.0585i	−0.411332	+	1.05073i
$330$	1.89305			0.104209
$331$	−5.20868	+	9.02169i	−0.286295	+	0.495877i	−0.972922	−	0.231132i	$-0.925757\pi$
$331$	−5.20868	+	9.02169i	−0.286295	+	0.495877i	0.686628	+	0.727009i	$0.259090\pi$
$332$	0.193443	+	0.335053i	0.0106166	+	0.0183884i
$333$	3.59934	+	6.23425i	0.197243	+	0.341635i
$334$	−8.91728	+	15.4452i	−0.487932	+	0.845123i
$335$	1.86296			0.101784
$336$	−1.41794	+	0.214975i	−0.0773549	+	0.0117278i
$337$	22.8133			1.24272			0.621359	−	0.783526i	$-0.286581\pi$
$337$	22.8133			1.24272			0.621359	+	0.783526i	$0.286581\pi$
$338$	−6.47137	+	11.2087i	−0.351996	+	0.609675i
$339$	0.775504	+	1.34321i	0.0421196	+	0.0729532i
$340$	−0.716934	−	1.24177i	−0.0388812	−	0.0673442i
$341$	7.14580	−	12.3769i	0.386967	−	0.670246i
$342$	−13.7827			−0.745284
$343$	−16.6653	+	8.07892i	−0.899840	+	0.436221i
$344$	−3.93789			−0.212317
$345$	−0.161695	+	0.280064i	−0.00870536	+	0.0150781i
$346$	−3.34060	−	5.78609i	−0.179592	−	0.311062i
$347$	−6.26544	−	10.8521i	−0.336346	−	0.582569i	0.647396	−	0.762154i	$-0.275858\pi$
$347$	−6.26544	−	10.8521i	−0.336346	−	0.582569i	−0.983743	+	0.179585i	$0.942525\pi$
$348$	1.40763	−	2.43809i	0.0754570	−	0.130695i
$349$	13.8292			0.740261			0.370131	−	0.928980i	$-0.379313\pi$
$349$	13.8292			0.740261			0.370131	+	0.928980i	$0.379313\pi$
$350$	−12.1482	+	1.84180i	−0.649350	+	0.0984484i
$351$	−0.740106			−0.0395040
$352$	2.92689	−	5.06952i	0.156004	−	0.270207i
$353$	0.360064	+	0.623649i	0.0191643	+	0.0331935i	0.875448	−	0.483311i	$-0.160566\pi$
$353$	0.360064	+	0.623649i	0.0191643	+	0.0331935i	−0.856284	+	0.516505i	$0.827233\pi$
$354$	−2.75476	−	4.77138i	−0.146414	−	0.253596i
$355$	−1.65839	+	2.87241i	−0.0880181	+	0.152452i
$356$	−13.0931			−0.693931
$357$	−1.25649	+	3.20964i	−0.0665004	+	0.169872i
$358$	−13.3628			−0.706246
$359$	−6.49851	+	11.2558i	−0.342978	+	0.594056i	−0.984984	−	0.172644i	$-0.944769\pi$
$359$	−6.49851	+	11.2558i	−0.342978	+	0.594056i	0.642006	+	0.766700i	$0.278102\pi$
$360$	0.807252	+	1.39820i	0.0425459	+	0.0736916i
$361$	−3.46964	−	6.00959i	−0.182613	−	0.316294i
$362$	−11.8035	+	20.4442i	−0.620377	+	1.07452i
$363$	12.6119			0.661952
$364$	0.395143	+	0.494616i	0.0207111	+	0.0259249i
$365$	3.94331			0.206402
$366$	−0.184491	+	0.319548i	−0.00964350	+	0.0167030i
$367$	−2.10933	−	3.65347i	−0.110106	−	0.190710i	0.805707	−	0.592315i	$-0.201786\pi$
$367$	−2.10933	−	3.65347i	−0.110106	−	0.190710i	−0.915813	+	0.401605i	$0.868452\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	15.7452	−	27.2715i	0.819663	−	1.41970i
$370$	1.58701			0.0825048
$371$	7.22290	+	9.04117i	0.374994	+	0.469394i
$372$	−1.32339			−0.0686146
$373$	9.76371	−	16.9112i	0.505546	−	0.875631i	−0.494434	−	0.869215i	$-0.664625\pi$
$373$	9.76371	−	16.9112i	0.505546	−	0.875631i	0.999979	−	0.00641549i	$-0.00204213\pi$
$374$	−7.03449	−	12.1841i	−0.363745	−	0.630025i
$375$	−1.55940	−	2.70095i	−0.0805269	−	0.139477i
$376$	−3.86787	+	6.69935i	−0.199470	+	0.345493i
$377$	−1.24274			−0.0640045
$378$	2.98317	−	7.62036i	0.153438	−	0.391949i
$379$	21.8162			1.12063			0.560313	−	0.828281i	$-0.310681\pi$
$379$	21.8162			1.12063			0.560313	+	0.828281i	$0.310681\pi$
$380$	−1.51926	+	2.63143i	−0.0779363	+	0.134990i
$381$	0.451043	+	0.781229i	0.0231076	+	0.0400236i
$382$	3.45243	+	5.97979i	0.176642	+	0.305953i
$383$	−12.8533	+	22.2626i	−0.656775	+	1.13757i	0.324671	+	0.945827i	$0.394746\pi$
$383$	−12.8533	+	22.2626i	−0.656775	+	1.13757i	−0.981446	+	0.191740i	$0.938587\pi$
$384$	−0.542055			−0.0276616
$385$	9.13553	−	1.38504i	0.465590	−	0.0705883i
$386$	19.4930			0.992168
$387$	5.32832	−	9.22891i	0.270854	−	0.469132i
$388$	0.0333474	+	0.0577594i	0.00169296	+	0.00293229i
$389$	−10.3222	−	17.8786i	−0.523358	−	0.906483i	−0.999630	−	0.0271853i	$-0.991346\pi$
$389$	−10.3222	−	17.8786i	−0.523358	−	0.906483i	0.476272	−	0.879298i	$-0.341988\pi$
$390$	−0.0386903	+	0.0670135i	−0.00195916	+	0.00339336i
$391$	2.40340			0.121545
$392$	−6.68543	+	2.07486i	−0.337665	+	0.104796i
$393$	−8.07467			−0.407313
$394$	7.78696	−	13.4874i	0.392301	−	0.679486i
$395$	−1.78502	−	3.09174i	−0.0898140	−	0.155562i
$396$	7.92068	+	13.7190i	0.398029	+	0.689407i
$397$	−7.88241	+	13.6527i	−0.395607	+	0.685211i	−0.993178	−	0.116604i	$-0.962799\pi$
$397$	−7.88241	+	13.6527i	−0.395607	+	0.685211i	0.597572	+	0.801816i	$0.296132\pi$
$398$	−3.37793			−0.169321
$399$	7.22165	−	1.09488i	0.361535	−	0.0548125i
$400$	−4.64407			−0.232203
$401$	−5.33817	+	9.24599i	−0.266576	+	0.461723i	−0.967975	−	0.251046i	$-0.919226\pi$
$401$	−5.33817	+	9.24599i	−0.266576	+	0.461723i	0.701400	+	0.712768i	$0.252559\pi$
$402$	−0.846318	−	1.46587i	−0.0422105	−	0.0731108i
$403$	0.292092	+	0.505918i	0.0145501	+	0.0252016i
$404$	8.17935	−	14.1671i	0.406938	−	0.704837i
$405$	−3.84324			−0.190972
$406$	5.00916	−	12.7957i	0.248600	−	0.635038i
$407$	15.5716			0.771857
$408$	−0.651388	+	1.12824i	−0.0322485	+	0.0558560i
$409$	−6.03231	−	10.4483i	−0.298279	−	0.516634i	0.677464	−	0.735556i	$-0.263079\pi$
$409$	−6.03231	−	10.4483i	−0.298279	−	0.516634i	−0.975742	+	0.218923i	$0.929746\pi$
$410$	−3.47117	−	6.01224i	−0.171429	−	0.296923i
$411$	−0.614920	+	1.06507i	−0.0303318	+	0.0525361i
$412$	19.8137			0.976150
$413$	−16.7849	−	21.0103i	−0.825931	−	1.03385i
$414$	−2.70618			−0.133001
$415$	−0.115408	+	0.199892i	−0.00566515	+	0.00981233i
$416$	0.119640	+	0.207222i	0.00586582	+	0.0101599i
$417$	4.92012	+	8.52190i	0.240939	+	0.417319i
$418$	−14.9068	+	25.8194i	−0.729117	+	1.26287i
$419$	10.9183			0.533392			0.266696	−	0.963781i	$-0.414068\pi$
$419$	10.9183			0.533392			0.266696	+	0.963781i	$0.414068\pi$
$420$	−0.534042	−	0.668480i	−0.0260586	−	0.0326185i
$421$	−35.8943			−1.74938			−0.874691	−	0.484681i	$-0.838936\pi$
$421$	−35.8943			−1.74938			−0.874691	+	0.484681i	$0.838936\pi$
$422$	2.01409	−	3.48850i	0.0980443	−	0.169818i
$423$	−10.4671	−	18.1296i	−0.508930	−	0.881492i
$424$	2.18692	+	3.78785i	0.106206	+	0.183954i
$425$	−5.58078	+	9.66619i	−0.270708	+	0.468879i
$426$	3.01354			0.146006
$427$	−0.656524	+	1.67706i	−0.0317714	+	0.0811587i
$428$	−15.3967			−0.744229
$429$	−0.379626	+	0.657531i	−0.0183285	+	0.0317459i
$430$	−1.17467	−	2.03459i	−0.0566477	−	0.0981167i
$431$	12.5390	+	21.7181i	0.603981	+	1.04613i	0.992212	+	0.124563i	$0.0397530\pi$
$431$	12.5390	+	21.7181i	0.603981	+	1.04613i	−0.388231	+	0.921562i	$0.626914\pi$
$432$	1.54653	−	2.67867i	0.0744075	−	0.128878i
$433$	−4.76433			−0.228959			−0.114480	−	0.993426i	$-0.536520\pi$
$433$	−4.76433			−0.228959			−0.114480	+	0.993426i	$0.536520\pi$
$434$	−6.38644	+	0.968251i	−0.306559	+	0.0464776i
$435$	1.67959			0.0805300
$436$	−8.14407	+	14.1059i	−0.390030	+	0.675552i
$437$	−2.54653	−	4.41072i	−0.121817	−	0.210993i
$438$	−1.79140	−	3.10279i	−0.0855963	−	0.148257i
$439$	−8.68289	+	15.0392i	−0.414412	+	0.717782i	−0.995367	−	0.0961536i	$-0.969346\pi$
$439$	−8.68289	+	15.0392i	−0.414412	+	0.717782i	0.580955	+	0.813936i	$0.302679\pi$
$440$	3.49236			0.166492
$441$	4.18331	−	18.4756i	0.199205	−	0.879788i
$442$	0.575084			0.0273540
$443$	−3.10128	+	5.37158i	−0.147346	+	0.255211i	−0.930246	−	0.366937i	$-0.880407\pi$
$443$	−3.10128	+	5.37158i	−0.147346	+	0.255211i	0.782900	+	0.622148i	$0.213740\pi$
$444$	−0.720959	−	1.24874i	−0.0342152	−	0.0592625i
$445$	−3.90566	−	6.76480i	−0.185146	−	0.320682i
$446$	14.1193	−	24.4553i	0.668568	−	1.15799i
$447$	−2.90174			−0.137248
$448$	−2.61586	+	0.396592i	−0.123588	+	0.0187372i
$449$	−16.2709			−0.767870			−0.383935	−	0.923360i	$-0.625431\pi$
$449$	−16.2709			−0.767870			−0.383935	+	0.923360i	$0.625431\pi$
$450$	6.28383	−	10.8839i	0.296223	−	0.513073i
$451$	−34.0588	−	58.9916i	−1.60377	−	2.77780i
$452$	1.43067	+	2.47800i	0.0672932	+	0.116555i
$453$	1.89309	−	3.27893i	0.0889453	−	0.154058i
$454$	10.2235			0.479813
$455$	−0.137682	+	0.351702i	−0.00645463	+	0.0164881i
$456$	2.76072			0.129283
$457$	−8.18259	+	14.1727i	−0.382765	+	0.662969i	−0.991456	−	0.130438i	$-0.958362\pi$
$457$	−8.18259	+	14.1727i	−0.382765	+	0.662969i	0.608691	+	0.793407i	$0.291695\pi$
$458$	−1.25041	−	2.16578i	−0.0584280	−	0.101200i
$459$	−3.71693	−	6.43792i	−0.173492	−	0.300496i
$460$	−0.298300	+	0.516670i	−0.0139083	+	0.0240899i
$461$	18.1965			0.847494			0.423747	−	0.905781i	$-0.360715\pi$
$461$	18.1965			0.847494			0.423747	+	0.905781i	$0.360715\pi$
$462$	−5.23997	−	6.55907i	−0.243786	−	0.305156i
$463$	0.424651			0.0197352			0.00986760	−	0.999951i	$-0.496859\pi$
$463$	0.424651			0.0197352			0.00986760	+	0.999951i	$0.496859\pi$
$464$	2.59684	−	4.49786i	0.120555	−	0.208808i
$465$	−0.394767	−	0.683756i	−0.0183069	−	0.0317084i
$466$	2.23300	+	3.86767i	0.103442	+	0.179166i
$467$	−14.0860	+	24.3976i	−0.651822	+	1.12899i	0.330859	+	0.943680i	$0.392662\pi$
$467$	−14.0860	+	24.3976i	−0.651822	+	1.12899i	−0.982680	+	0.185308i	$0.940672\pi$
$468$	−0.647532			−0.0299322
$469$	−5.15667	−	6.45480i	−0.238113	−	0.298055i
$470$	−4.61514			−0.212880
$471$	2.14909	−	3.72234i	0.0990250	−	0.171516i
$472$	−5.08206	−	8.80239i	−0.233921	−	0.405163i
$473$	−11.5258	−	19.9632i	−0.529956	−	0.917911i
$474$	−1.62182	+	2.80908i	−0.0744927	+	0.129025i
$475$	23.6525			1.08525
$476$	−2.31801	+	5.92125i	−0.106246	+	0.271400i
$477$	−11.8364			−0.541950
$478$	10.4231	−	18.0534i	0.476742	−	0.825741i
$479$	−4.88310	−	8.45779i	−0.223115	−	0.386446i	0.732637	−	0.680619i	$-0.238289\pi$
$479$	−4.88310	−	8.45779i	−0.223115	−	0.386446i	−0.955752	+	0.294173i	$0.904956\pi$
$480$	−0.161695	−	0.280064i	−0.00738033	−	0.0127831i
$481$	−0.318253	+	0.551231i	−0.0145111	+	0.0251340i
$482$	−4.06489			−0.185150
$483$	1.41794	−	0.214975i	0.0645185	−	0.00978169i
$484$	23.2668			1.05758
$485$	−0.0198950	+	0.0344592i	−0.000903387	+	0.00156471i
$486$	6.38553	+	11.0601i	0.289654	+	0.501695i
$487$	−10.3765	−	17.9726i	−0.470203	−	0.814416i	0.529216	−	0.848487i	$-0.322486\pi$
$487$	−10.3765	−	17.9726i	−0.470203	−	0.814416i	−0.999419	+	0.0340712i	$0.989153\pi$
$488$	−0.340355	+	0.589512i	−0.0154071	+	0.0266859i
$489$	7.66717			0.346721
$490$	−3.06628	−	2.83523i	−0.138520	−	0.128083i
$491$	−25.9031			−1.16899			−0.584496	−	0.811397i	$-0.698708\pi$
$491$	−25.9031			−1.16899			−0.584496	+	0.811397i	$0.698708\pi$
$492$	−3.15381	+	5.46257i	−0.142185	+	0.246271i
$493$	−6.24126	−	10.8102i	−0.281092	−	0.486866i
$494$	−0.609333	−	1.05540i	−0.0274152	−	0.0474845i
$495$	−4.72548	+	8.18476i	−0.212394	+	0.367878i
$496$	−2.44143			−0.109623
$497$	14.5428	−	2.20484i	0.652333	−	0.0989006i
$498$	0.209713			0.00939749
$499$	16.8329	−	29.1555i	0.753546	−	1.30518i	−0.192548	−	0.981288i	$-0.561675\pi$
$499$	16.8329	−	29.1555i	0.753546	−	1.30518i	0.946094	−	0.323892i	$-0.104991\pi$
$500$	−2.87682	−	4.98280i	−0.128655	−	0.222838i
$501$	4.83366	+	8.37214i	0.215952	+	0.374040i
$502$	−13.9484	+	24.1594i	−0.622550	+	1.07829i
$503$	7.77016			0.346454			0.173227	−	0.984882i	$-0.444581\pi$
$503$	7.77016			0.346454			0.173227	+	0.984882i	$0.444581\pi$
$504$	2.61003	−	6.66719i	0.116260	−	0.296980i
$505$	9.75960			0.434296
$506$	−2.92689	+	5.06952i	−0.130116	+	0.225368i
$507$	3.50784	+	6.07576i	0.155789	+	0.269834i
$508$	0.832098	+	1.44124i	0.0369184	+	0.0639445i
$509$	4.29785	−	7.44409i	0.190499	−	0.329954i	−0.754917	−	0.655821i	$-0.772323\pi$
$509$	4.29785	−	7.44409i	0.190499	−	0.329954i	0.945416	+	0.325867i	$0.105656\pi$
$510$	−0.777235			−0.0344166
$511$	−10.9151	−	13.6628i	−0.482855	−	0.604408i
$512$	−1.00000			−0.0441942
$513$	−7.87658	+	13.6426i	−0.347759	+	0.602337i
$514$	−13.9929	−	24.2364i	−0.617200	−	1.06902i
$515$	5.91041	+	10.2371i	0.260444	+	0.451102i
$516$	−1.06728	+	1.84858i	−0.0469843	+	0.0813791i
$517$	−45.2834			−1.99156
$518$	−4.39285	−	5.49869i	−0.193011	−	0.241599i
$519$	−3.62158			−0.158970
$520$	−0.0713770	+	0.123629i	−0.00313009	+	0.00542147i
$521$	−6.17501	−	10.6954i	−0.270532	−	0.468575i	0.698466	−	0.715643i	$-0.253866\pi$
$521$	−6.17501	−	10.6954i	−0.270532	−	0.468575i	−0.968998	+	0.247068i	$0.920533\pi$
$522$	7.02752	+	12.1720i	0.307586	+	0.532755i
$523$	12.1520	−	21.0479i	0.531369	−	0.920358i	−0.467961	−	0.883749i	$-0.655011\pi$
$523$	12.1520	−	21.0479i	0.531369	−	0.920358i	0.999330	−	0.0366090i	$-0.0116556\pi$
$524$	−14.8964			−0.650752
$525$	−2.42790	+	6.20196i	−0.105962	+	0.270676i
$526$	28.9322			1.26150
$527$	−2.93387	+	5.08161i	−0.127801	+	0.221358i
$528$	−1.58654	−	2.74796i	−0.0690451	−	0.119590i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−1.30471	+	2.25983i	−0.0566731	+	0.0981608i
$531$	27.5059			1.19365
$532$	13.3227	−	2.01987i	0.577614	−	0.0875723i
$533$	2.78438			0.120605
$534$	−3.54858	+	6.14632i	−0.153562	+	0.265977i
$535$	−4.59284	−	7.95504i	−0.198566	−	0.343926i
$536$	−1.56131	−	2.70428i	−0.0674385	−	0.116807i
$537$	−3.62169	+	6.27295i	−0.156287	+	0.270698i
$538$	15.9118			0.686006
$539$	−30.0861	−	27.8191i	−1.29590	−	1.19825i
$540$	1.84532			0.0794099
$541$	11.2091	−	19.4148i	0.481918	−	0.834706i	−0.517867	−	0.855461i	$-0.673274\pi$
$541$	11.2091	−	19.4148i	0.481918	−	0.834706i	0.999785	+	0.0207549i	$0.00660697\pi$
$542$	3.08379	+	5.34128i	0.132460	+	0.229428i
$543$	6.39813	+	11.0819i	0.274570	+	0.475569i
$544$	−1.20170	+	2.08141i	−0.0515225	+	0.0892395i
$545$	−9.71749			−0.416252
$546$	0.339284	−	0.0514390i	0.0145200	−	0.00220139i
$547$	31.1827			1.33327			0.666637	−	0.745382i	$-0.267733\pi$
$547$	31.1827			1.33327			0.666637	+	0.745382i	$0.267733\pi$
$548$	−1.13442	+	1.96488i	−0.0484601	+	0.0839354i
$549$	−0.921060	−	1.59532i	−0.0393099	−	0.0680867i
$550$	−13.5927	−	23.5432i	−0.579594	−	1.00389i
$551$	−13.2259	+	22.9079i	−0.563442	+	0.975910i
$552$	0.542055			0.0230714
$553$	−5.77137	+	14.7427i	−0.245423	+	0.626923i
$554$	−5.23657			−0.222481
$555$	0.430124	−	0.744996i	0.0182577	−	0.0316233i
$556$	9.07679	+	15.7215i	0.384942	+	0.666739i
$557$	−13.6725	−	23.6814i	−0.579320	−	1.00341i	−0.995557	−	0.0941562i	$-0.969985\pi$
$557$	−13.6725	−	23.6814i	−0.579320	−	1.00341i	0.416237	−	0.909256i	$-0.363349\pi$
$558$	3.30347	−	5.72178i	0.139847	−	0.242222i
$559$	0.942257			0.0398532
$560$	−0.985217	−	1.23323i	−0.0416330	−	0.0521136i
$561$	−7.62617			−0.321977
$562$	6.21475	−	10.7643i	0.262153	−	0.454063i
$563$	8.62780	+	14.9438i	0.363618	+	0.629805i	0.988553	−	0.150871i	$-0.0482079\pi$
$563$	8.62780	+	14.9438i	0.363618	+	0.629805i	−0.624935	+	0.780677i	$0.714875\pi$
$564$	2.09660	+	3.63142i	0.0882828	+	0.152910i
$565$	−0.853539	+	1.47837i	−0.0359086	+	0.0621956i
$566$	2.33595			0.0981874
$567$	10.6381	+	13.3161i	0.446758	+	0.559224i
$568$	5.55947			0.233270
$569$	7.75028	−	13.4239i	0.324909	−	0.562758i	−0.656585	−	0.754252i	$-0.728000\pi$
$569$	7.75028	−	13.4239i	0.324909	−	0.562758i	0.981494	+	0.191494i	$0.0613331\pi$
$570$	0.823522	+	1.42638i	0.0344935	+	0.0597446i
$571$	13.0127	+	22.5387i	0.544566	+	0.943216i	0.998634	+	0.0522489i	$0.0166389\pi$
$571$	13.0127	+	22.5387i	0.544566	+	0.943216i	−0.454068	+	0.890967i	$0.650028\pi$
$572$	−0.700345	+	1.21303i	−0.0292829	+	0.0507195i
$573$	3.74282			0.156358
$574$	−11.2231	+	28.6688i	−0.468442	+	1.19661i
$575$	4.64407			0.193671
$576$	1.35309	−	2.34362i	0.0563787	−	0.0976507i
$577$	9.17204	+	15.8864i	0.381837	+	0.661361i	0.991325	−	0.131434i	$-0.0419583\pi$
$577$	9.17204	+	15.8864i	0.381837	+	0.661361i	−0.609488	+	0.792795i	$0.708625\pi$
$578$	−5.61183	−	9.71998i	−0.233421	−	0.404298i
$579$	5.28314	−	9.15067i	0.219560	−	0.380289i
$580$	3.09855			0.128660
$581$	1.01204	−	0.153436i	0.0419864	−	0.00636559i
$582$	0.0361523			0.00149856
$583$	−12.8017	+	22.1733i	−0.530194	+	0.918323i
$584$	−3.30483	−	5.72413i	−0.136755	−	0.236866i
$585$	−0.193159	−	0.334561i	−0.00798613	−	0.0138324i
$586$	1.43560	−	2.48653i	0.0593041	−	0.102718i
$587$	−40.3997			−1.66748			−0.833738	−	0.552160i	$-0.813804\pi$
$587$	−40.3997			−1.66748			−0.833738	+	0.552160i	$0.813804\pi$
$588$	−0.837929	+	3.70071i	−0.0345556	+	0.152615i
$589$	12.4344			0.512349
$590$	3.03195	−	5.25150i	0.124824	−	0.216201i
$591$	−4.22096	−	7.31092i	−0.173627	−	0.300731i
$592$	−1.33005	−	2.30371i	−0.0546646	−	0.0946819i
$593$	−11.1406	+	19.2961i	−0.457491	+	0.792397i	−0.998828	−	0.0484085i	$-0.984585\pi$
$593$	−11.1406	+	19.2961i	−0.457491	+	0.792397i	0.541337	+	0.840806i	$0.317918\pi$
$594$	18.1061			0.742903
$595$	−3.75079	+	0.568660i	−0.153768	+	0.0233128i
$596$	−5.35322			−0.219276
$597$	−0.915513	+	1.58572i	−0.0374695	+	0.0648990i
$598$	−0.119640	−	0.207222i	−0.00489243	−	0.00847394i
$599$	4.92939	+	8.53796i	0.201409	+	0.348851i	0.948983	−	0.315328i	$-0.102114\pi$
$599$	4.92939	+	8.53796i	0.201409	+	0.348851i	−0.747573	+	0.664179i	$0.768781\pi$
$600$	−1.25867	+	2.18008i	−0.0513850	+	0.0890015i
$601$	−3.48778			−0.142269			−0.0711347	−	0.997467i	$-0.522662\pi$
$601$	−3.48778			−0.142269			−0.0711347	+	0.997467i	$0.522662\pi$
$602$	−3.79798	+	9.70177i	−0.154794	+	0.395415i
$603$	8.45038			0.344126
$604$	3.49244	−	6.04908i	0.142105	−	0.246134i
$605$	6.94047	+	12.0212i	0.282170	+	0.488733i
$606$	−4.43366	−	7.67933i	−0.180105	−	0.311951i
$607$	−19.1003	+	33.0827i	−0.775257	+	1.34278i	0.159394	+	0.987215i	$0.449046\pi$
$607$	−19.1003	+	33.0827i	−0.775257	+	1.34278i	−0.934650	+	0.355569i	$0.884287\pi$
$608$	5.09306			0.206551
$609$	−4.64909	−	5.81944i	−0.188391	−	0.235816i
$610$	−0.406111			−0.0164430
$611$	0.925502	−	1.60302i	0.0374418	−	0.0648511i
$612$	−3.25201	−	5.63265i	−0.131455	−	0.227686i
$613$	10.3547	+	17.9348i	0.418222	+	0.724381i	0.995761	−	0.0919818i	$-0.0293202\pi$
$613$	10.3547	+	17.9348i	0.418222	+	0.724381i	−0.577539	+	0.816363i	$0.695987\pi$
$614$	12.7932	−	22.1584i	0.516290	−	0.894241i
$615$	−3.76313			−0.151744
$616$	−9.66687	−	12.1004i	−0.389489	−	0.487538i
$617$	−40.1980			−1.61831			−0.809155	−	0.587595i	$-0.800075\pi$
$617$	−40.1980			−1.61831			−0.809155	+	0.587595i	$0.800075\pi$
$618$	5.37005	−	9.30120i	0.216015	−	0.374149i
$619$	10.8528	+	18.7977i	0.436213	+	0.755542i	0.997394	−	0.0721506i	$-0.0229862\pi$
$619$	10.8528	+	18.7977i	0.436213	+	0.755542i	−0.561181	+	0.827693i	$0.689653\pi$
$620$	−0.728278	−	1.26141i	−0.0292483	−	0.0506596i
$621$	−1.54653	+	2.67867i	−0.0620602	+	0.107491i
$622$	12.9219			0.518120
$623$	−12.6279	+	32.2573i	−0.505925	+	1.29236i
$624$	0.129703			0.00519226
$625$	−9.89386	+	17.1367i	−0.395754	+	0.685467i
$626$	12.9010	+	22.3452i	0.515628	+	0.893094i
$627$	8.08033	+	13.9955i	0.322697	+	0.558928i
$628$	3.96471	−	6.86709i	0.158209	−	0.274027i
$629$	−6.39328			−0.254917
$630$	4.22331	−	0.640299i	0.168261	−	0.0255101i
$631$	46.8061			1.86332			0.931661	−	0.363329i	$-0.118360\pi$
$631$	46.8061			1.86332			0.931661	+	0.363329i	$0.118360\pi$
$632$	−2.99199	+	5.18227i	−0.119015	+	0.206140i
$633$	−1.09175	−	1.89096i	−0.0433930	−	0.0751590i
$634$	−12.5012	−	21.6527i	−0.496485	−	0.859938i
$635$	−0.496429	+	0.859840i	−0.0197002	+	0.0341217i
$636$	2.37086			0.0940107
$637$	1.59969	−	0.496471i	0.0633819	−	0.0196709i
$638$	30.4027			1.20366
$639$	−7.52245	+	13.0293i	−0.297584	+	0.515430i
$640$	−0.298300	−	0.516670i	−0.0117913	−	0.0204232i
$641$	−10.8628	−	18.8150i	−0.429057	−	0.743148i	0.567733	−	0.823213i	$-0.307821\pi$
$641$	−10.8628	−	18.8150i	−0.429057	−	0.743148i	−0.996790	+	0.0800649i	$0.974487\pi$
$642$	−4.17294	+	7.22775i	−0.164693	+	0.285256i
$643$	27.3018			1.07668			0.538339	−	0.842728i	$-0.319052\pi$
$643$	27.3018			1.07668			0.538339	+	0.842728i	$0.319052\pi$
$644$	2.61586	−	0.396592i	0.103079	−	0.0156279i
$645$	−1.27347			−0.0501430
$646$	6.12033	−	10.6007i	0.240801	−	0.417080i
$647$	−3.56568	−	6.17594i	−0.140181	−	0.242801i	0.787384	−	0.616463i	$-0.211435\pi$
$647$	−3.56568	−	6.17594i	−0.140181	−	0.242801i	−0.927565	+	0.373662i	$0.878102\pi$
$648$	3.22096	+	5.57887i	0.126531	+	0.219159i
$649$	29.7493	−	51.5273i	1.16776	−	2.02262i
$650$	1.11123			0.0435860
$651$	−1.27637	+	3.26043i	−0.0500249	+	0.127786i
$652$	14.1446			0.553947
$653$	−8.12425	+	14.0716i	−0.317926	+	0.550665i	−0.980055	−	0.198725i	$-0.936320\pi$
$653$	−8.12425	+	14.0716i	−0.317926	+	0.550665i	0.662129	+	0.749390i	$0.269653\pi$
$654$	4.41453	+	7.64620i	0.172622	+	0.298990i
$655$	−4.44359	−	7.69653i	−0.173625	−	0.300728i
$656$	−5.81825	+	10.0775i	−0.227165	+	0.393461i
$657$	17.8869			0.697834
$658$	12.7747	+	15.9906i	0.498010	+	0.623378i
$659$	−0.0321286			−0.00125155			−0.000625776	−	1.00000i	$-0.500199\pi$
$659$	−0.0321286			−0.00125155			−0.000625776		1.00000i	$0.500199\pi$
$660$	0.946527	−	1.63943i	0.0368435	−	0.0638148i
$661$	5.33283	+	9.23673i	0.207423	+	0.359267i	0.950902	−	0.309492i	$-0.100159\pi$
$661$	5.33283	+	9.23673i	0.207423	+	0.359267i	−0.743479	+	0.668759i	$0.766826\pi$
$662$	5.20868	+	9.02169i	0.202441	+	0.350638i
$663$	0.155864	−	0.269964i	0.00605325	−	0.0104845i
$664$	0.386886			0.0150141
$665$	5.01777	+	6.28093i	0.194581	+	0.243564i
$666$	7.19869			0.278943
$667$	−2.59684	+	4.49786i	−0.100550	+	0.174158i
$668$	8.91728	+	15.4452i	0.345020	+	0.597592i
$669$	−7.65344	−	13.2561i	−0.295899	−	0.512512i
$670$	0.931479	−	1.61337i	0.0359862	−	0.0623299i
$671$	−3.98473			−0.153829
$672$	−0.522796	+	1.33546i	−0.0201673	+	0.0515164i
$673$	−25.7353			−0.992021			−0.496011	−	0.868316i	$-0.665202\pi$
$673$	−25.7353			−0.992021			−0.496011	+	0.868316i	$0.665202\pi$
$674$	11.4066	−	19.7569i	0.439367	−	0.761006i
$675$	−7.18220	−	12.4399i	−0.276443	−	0.478813i
$676$	6.47137	+	11.2087i	0.248899	+	0.431106i
$677$	−17.9812	+	31.1444i	−0.691074	+	1.19698i	0.280413	+	0.959880i	$0.409529\pi$
$677$	−17.9812	+	31.1444i	−0.691074	+	1.19698i	−0.971486	+	0.237095i	$0.923805\pi$
$678$	1.55101			0.0595661
$679$	0.174464	−	0.0264506i	0.00669532	−	0.00101508i
$680$	−1.43387			−0.0549863
$681$	2.77086	−	4.79926i	0.106179	−	0.183908i
$682$	−7.14580	−	12.3769i	−0.273627	−	0.473936i
$683$	−2.86052	−	4.95456i	−0.109455	−	0.189581i	0.806095	−	0.591786i	$-0.201577\pi$
$683$	−2.86052	−	4.95456i	−0.109455	−	0.189581i	−0.915549	+	0.402205i	$0.868244\pi$
$684$	−6.89136	+	11.9362i	−0.263498	+	0.456392i
$685$	−1.35359			−0.0517181
$686$	−1.33609	+	18.4720i	−0.0510120	+	0.705264i
$687$	−1.35559			−0.0517188
$688$	−1.96895	+	3.41032i	−0.0750654	+	0.130017i
$689$	−0.523284	−	0.906355i	−0.0199356	−	0.0345294i
$690$	0.161695	+	0.280064i	0.00615562	+	0.0106618i
$691$	−8.45465	+	14.6439i	−0.321630	+	0.557080i	−0.980825	−	0.194893i	$-0.937564\pi$
$691$	−8.45465	+	14.6439i	−0.321630	+	0.557080i	0.659194	+	0.751973i	$0.270897\pi$
$692$	−6.68120			−0.253981
$693$	41.4388	−	6.28256i	1.57413	−	0.238655i
$694$	−12.5309			−0.475666
$695$	−5.41521	+	9.37942i	−0.205411	+	0.355782i
$696$	−1.40763	−	2.43809i	−0.0533562	−	0.0924156i
$697$	13.9836	+	24.2203i	0.529666	+	0.917409i
$698$	6.91461	−	11.9765i	0.261722	−	0.453315i
$699$	2.42082			0.0915637
$700$	−4.47907	+	11.4416i	−0.169293	+	0.432451i
$701$	24.3619			0.920137			0.460068	−	0.887884i	$-0.347825\pi$
$701$	24.3619			0.920137			0.460068	+	0.887884i	$0.347825\pi$
$702$	−0.370053	+	0.640951i	−0.0139668	+	0.0241911i
$703$	6.77402	+	11.7329i	0.255487	+	0.442516i
$704$	−2.92689	−	5.06952i	−0.110311	−	0.191065i
$705$	−1.25083	+	2.16650i	−0.0471090	+	0.0815952i
$706$	0.720128			0.0271024
$707$	−27.0146	−	33.8152i	−1.01599	−	1.27175i
$708$	−5.50951			−0.207060
$709$	−6.86513	+	11.8907i	−0.257825	+	0.446566i	−0.965659	−	0.259813i	$-0.916339\pi$
$709$	−6.86513	+	11.8907i	−0.257825	+	0.446566i	0.707834	+	0.706379i	$0.249673\pi$
$710$	1.65839	+	2.87241i	0.0622382	+	0.107800i
$711$	−8.09684	−	14.0241i	−0.303655	−	0.525947i
$712$	−6.54653	+	11.3389i	−0.245342	+	0.424944i
$713$	2.44143			0.0914323
$714$	2.15139	+	2.69297i	0.0805137	+	0.100782i
$715$	−0.835651			−0.0312516
$716$	−6.68140	+	11.5725i	−0.249696	+	0.432486i
$717$	−5.64990	−	9.78591i	−0.210999	−	0.365462i
$718$	6.49851	+	11.2558i	0.242522	+	0.420061i
$719$	−24.3899	+	42.2446i	−0.909590	+	1.57546i	−0.0949556	+	0.995482i	$0.530271\pi$
$719$	−24.3899	+	42.2446i	−0.909590	+	1.57546i	−0.814634	+	0.579975i	$0.803062\pi$
$720$	1.61450			0.0601690
$721$	19.1097	−	48.8149i	0.711683	−	1.81796i
$722$	−6.93928			−0.258253
$723$	−1.10170	+	1.90819i	−0.0409725	+	0.0709665i
$724$	11.8035	+	20.4442i	0.438673	+	0.759803i
$725$	−12.0599	−	20.8884i	−0.447894	−	0.775776i
$726$	6.30594	−	10.9222i	0.234035	−	0.405361i
$727$	13.3162			0.493869			0.246935	−	0.969032i	$-0.420577\pi$
$727$	13.3162			0.493869			0.246935	+	0.969032i	$0.420577\pi$
$728$	0.625921	−	0.0948963i	0.0231982	−	0.00351709i
$729$	−12.4031			−0.459375
$730$	1.97166	−	3.41501i	0.0729743	−	0.126395i
$731$	4.73217	+	8.19635i	0.175026	+	0.303153i
$732$	0.184491	+	0.319548i	0.00681899	+	0.0118108i
$733$	−12.6501	+	21.9106i	−0.467242	+	0.809287i	−0.999300	−	0.0374209i	$-0.988086\pi$
$733$	−12.6501	+	21.9106i	−0.467242	+	0.809287i	0.532057	+	0.846708i	$0.321419\pi$
$734$	−4.21867			−0.155714
$735$	−2.16200	+	0.670987i	−0.0797466	+	0.0247497i
$736$	1.00000			0.0368605
$737$	9.13959	−	15.8302i	0.336661	−	0.583114i
$738$	−15.7452	−	27.2715i	−0.579589	−	1.00388i
$739$	16.4401	+	28.4750i	0.604758	+	1.04747i	0.992090	+	0.125531i	$0.0400635\pi$
$739$	16.4401	+	28.4750i	0.604758	+	1.04747i	−0.387332	+	0.921940i	$0.626603\pi$
$740$	0.793506	−	1.37439i	0.0291699	−	0.0505237i
$741$	−0.660584			−0.0242672
$742$	11.4413	−	1.73463i	0.420025	−	0.0636802i
$743$	11.9697			0.439127			0.219564	−	0.975598i	$-0.429537\pi$
$743$	11.9697			0.439127			0.219564	+	0.975598i	$0.429537\pi$
$744$	−0.661695	+	1.14609i	−0.0242589	+	0.0420177i
$745$	−1.59686	−	2.76585i	−0.0585046	−	0.101333i
$746$	−9.76371	−	16.9112i	−0.357475	−	0.619164i
$747$	−0.523491	+	0.906713i	−0.0191535	+	0.0331749i
$748$	−14.0690			−0.514413
$749$	−14.8497	+	37.9329i	−0.542596	+	1.38604i
$750$	−3.11879			−0.113882
$751$	−5.56933	+	9.64636i	−0.203228	+	0.352001i	−0.949567	−	0.313565i	$-0.898476\pi$
$751$	−5.56933	+	9.64636i	−0.203228	+	0.352001i	0.746339	+	0.665566i	$0.231810\pi$
$752$	3.86787	+	6.69935i	0.141047	+	0.244300i
$753$	7.56083	+	13.0957i	0.275532	+	0.477235i
$754$	−0.621371	+	1.07625i	−0.0226290	+	0.0391946i
$755$	4.16717			0.151659
$756$	−5.10785	−	6.39368i	−0.185771	−	0.232536i
$757$	−14.5258			−0.527949			−0.263975	−	0.964530i	$-0.585034\pi$
$757$	−14.5258			−0.527949			−0.263975	+	0.964530i	$0.585034\pi$
$758$	10.9081	−	18.8934i	0.396201	−	0.686240i
$759$	1.58654	+	2.74796i	0.0575876	+	0.0997447i
$760$	1.51926	+	2.63143i	0.0551093	+	0.0954521i
$761$	2.77880	−	4.81302i	0.100731	−	0.174472i	−0.811255	−	0.584693i	$-0.801215\pi$
$761$	2.77880	−	4.81302i	0.100731	−	0.174472i	0.911986	+	0.410221i	$0.134548\pi$
$762$	0.902085			0.0326791
$763$	26.8980	+	33.6693i	0.973774	+	1.21891i
$764$	6.90486			0.249809
$765$	1.94015	−	3.36044i	0.0701462	−	0.121497i
$766$	12.8533	+	22.2626i	0.464410	+	0.804381i
$767$	1.21603	+	2.10623i	0.0439084	+	0.0760516i
$768$	−0.271028	+	0.469434i	−0.00977986	+	0.0169392i
$769$	21.4784			0.774530			0.387265	−	0.921969i	$-0.373420\pi$
$769$	21.4784			0.774530			0.387265	+	0.921969i	$0.373420\pi$
$770$	3.36828	−	8.60412i	0.121384	−	0.310071i
$771$	−15.1698			−0.546328
$772$	9.74650	−	16.8814i	0.350784	−	0.607576i
$773$	−14.2853	−	24.7428i	−0.513805	−	0.889937i	−0.999872	−	0.0160149i	$-0.994902\pi$
$773$	−14.2853	−	24.7428i	−0.513805	−	0.889937i	0.486067	−	0.873922i	$-0.338431\pi$
$774$	−5.32832	−	9.22891i	−0.191522	−	0.331726i
$775$	−5.66909	+	9.81914i	−0.203640	+	0.352714i
$776$	0.0666948			0.00239420
$777$	−3.77185	+	0.571853i	−0.135315	+	0.0205151i
$778$	−20.6445			−0.740141
$779$	29.6327	−	51.3254i	1.06170	−	1.83892i
$780$	0.0386903	+	0.0670135i	0.00138533	+	0.00239947i
$781$	16.2720	+	28.1839i	0.582257	+	1.00850i
$782$	1.20170	−	2.08141i	0.0429727	−	0.0744309i
$783$	16.0644			0.574095
$784$	−1.54584	+	6.82718i	−0.0552084	+	0.243828i
$785$	4.73069			0.168846
$786$	−4.03734	+	6.99287i	−0.144007	+	0.249427i
$787$	−20.9575	−	36.2994i	−0.747053	−	1.29393i	−0.949229	−	0.314585i	$-0.898135\pi$
$787$	−20.9575	−	36.2994i	−0.747053	−	1.29393i	0.202176	−	0.979349i	$-0.435199\pi$
$788$	−7.78696	−	13.4874i	−0.277399	−	0.480469i
$789$	7.84143	−	13.5817i	0.279162	−	0.483523i
$790$	−3.57004			−0.127016
$791$	7.48487	−	1.13479i	0.266131	−	0.0403484i
$792$	15.8414			0.562898
$793$	0.0814399	−	0.141058i	0.00289202	−	0.00500912i
$794$	7.88241	+	13.6527i	0.279736	+	0.484517i
$795$	0.707227	+	1.22495i	0.0250827	+	0.0434446i
$796$	−1.68897	+	2.92538i	−0.0598638	+	0.103687i
$797$	47.4495			1.68075			0.840375	−	0.542006i	$-0.182335\pi$
$797$	47.4495			1.68075			0.840375	+	0.542006i	$0.182335\pi$
$798$	2.66263	−	6.80158i	0.0942562	−	0.240773i
$799$	18.5921			0.657741
$800$	−2.32203	+	4.02188i	−0.0820963	+	0.142195i
$801$	−17.7161	−	30.6851i	−0.625966	−	1.08421i
$802$	5.33817	+	9.24599i	0.188497	+	0.326487i
$803$	19.3457	−	33.5078i	0.682696	−	1.18246i
$804$	−1.69264			−0.0596947
$805$	0.985217	+	1.23323i	0.0347243	+	0.0434657i
$806$	0.584184			0.0205770
$807$	4.31253	−	7.46953i	0.151808	−	0.262940i
$808$	−8.17935	−	14.1671i	−0.287749	−	0.498395i
$809$	−12.0705	−	20.9067i	−0.424375	−	0.735039i	0.571987	−	0.820263i	$-0.306173\pi$
$809$	−12.0705	−	20.9067i	−0.424375	−	0.735039i	−0.996362	+	0.0852235i	$0.972840\pi$
$810$	−1.92162	+	3.32835i	−0.0675189	+	0.116946i
$811$	36.4282			1.27917			0.639583	−	0.768722i	$-0.279107\pi$
$811$	36.4282			1.27917			0.639583	+	0.768722i	$0.279107\pi$
$812$	−8.57679	−	10.7359i	−0.300986	−	0.376756i
$813$	3.34317			0.117250
$814$	7.78581	−	13.4854i	0.272893	−	0.472664i
$815$	4.21934	+	7.30811i	0.147797	+	0.255992i
$816$	0.651388	+	1.12824i	0.0228031	+	0.0394962i
$817$	10.0280	−	17.3689i	0.350834	−	0.607663i
$818$	−12.0646			−0.421830
$819$	−0.624526	+	1.59532i	−0.0218227	+	0.0557451i
$820$	−6.94233			−0.242437
$821$	−18.7800	+	32.5278i	−0.655425	+	1.13523i	0.326362	+	0.945245i	$0.394177\pi$
$821$	−18.7800	+	32.5278i	−0.655425	+	1.13523i	−0.981787	+	0.189984i	$0.939156\pi$
$822$	0.614920	+	1.06507i	0.0214478	+	0.0371487i
$823$	−4.21270	−	7.29661i	−0.146846	−	0.254344i	0.783214	−	0.621752i	$-0.213579\pi$
$823$	−4.21270	−	7.29661i	−0.146846	−	0.254344i	−0.930060	+	0.367408i	$0.880245\pi$
$824$	9.90684	−	17.1591i	0.345121	−	0.597767i
$825$	−14.7360			−0.513041
$826$	−26.5879	+	4.03101i	−0.925111	+	0.140257i
$827$	36.8035			1.27978			0.639891	−	0.768466i	$-0.278980\pi$
$827$	36.8035			1.27978			0.639891	+	0.768466i	$0.278980\pi$
$828$	−1.35309	+	2.34362i	−0.0470231	+	0.0814463i
$829$	6.21592	+	10.7663i	0.215888	+	0.373929i	0.953547	−	0.301245i	$-0.0974021\pi$
$829$	6.21592	+	10.7663i	0.215888	+	0.373929i	−0.737659	+	0.675173i	$0.764069\pi$
$830$	0.115408	+	0.199892i	0.00400587	+	0.00693837i
$831$	−1.41925	+	2.45822i	−0.0492334	+	0.0852747i
$832$	0.239279			0.00829552
$833$	12.3525	+	11.4217i	0.427989	+	0.395740i
$834$	9.84024			0.340740
$835$	−5.32004	+	9.21459i	−0.184108	+	0.318884i
$836$	14.9068	+	25.8194i	0.515564	+	0.892983i
$837$	−3.77575	−	6.53979i	−0.130509	−	0.226048i
$838$	5.45913	−	9.45549i	0.188582	−	0.326634i
$839$	−21.8483			−0.754287			−0.377143	−	0.926155i	$-0.623094\pi$
$839$	−21.8483			−0.754287			−0.377143	+	0.926155i	$0.623094\pi$
$840$	−0.845942	+	0.128254i	−0.0291878	+	0.00442518i
$841$	−2.02561			−0.0698488
$842$	−17.9472	+	31.0854i	−0.618500	+	1.07127i
$843$	−3.36874	−	5.83483i	−0.116026	−	0.200962i
$844$	−2.01409	−	3.48850i	−0.0693278	−	0.120079i
$845$	−3.86082	+	6.68713i	−0.132816	+	0.230044i
$846$	−20.9343			−0.719735
$847$	22.4401	−	57.3222i	0.771051	−	1.96962i
$848$	4.37383			0.150198
$849$	0.633108	−	1.09657i	0.0217282	−	0.0376343i
$850$	5.58078	+	9.66619i	0.191419	+	0.331548i
$851$	1.33005	+	2.30371i	0.0455935	+	0.0789702i
$852$	1.50677	−	2.60980i	0.0516211	−	0.0894103i
$853$	−0.543709			−0.0186162			−0.00930812	−	0.999957i	$-0.502963\pi$
$853$	−0.543709			−0.0186162			−0.00930812	+	0.999957i	$0.502963\pi$
$854$	1.12412	+	1.40710i	0.0384664	+	0.0481499i
$855$	−8.22276			−0.281213
$856$	−7.69837	+	13.3340i	−0.263125	+	0.455746i
$857$	−14.4504	−	25.0289i	−0.493617	−	0.854970i	0.506356	−	0.862325i	$-0.330992\pi$
$857$	−14.4504	−	25.0289i	−0.493617	−	0.854970i	−0.999973	+	0.00735490i	$0.997659\pi$
$858$	0.379626	+	0.657531i	0.0129602	+	0.0224477i
$859$	−10.0895	+	17.4756i	−0.344250	+	0.596259i	−0.985217	−	0.171310i	$-0.945200\pi$
$859$	−10.0895	+	17.4756i	−0.344250	+	0.596259i	0.640967	+	0.767568i	$0.278533\pi$
$860$	−2.34934			−0.0801120
$861$	10.4163	+	13.0385i	0.354988	+	0.444352i
$862$	25.0779			0.854158
$863$	25.1190	−	43.5073i	0.855060	−	1.48101i	−0.0215294	−	0.999768i	$-0.506854\pi$
$863$	25.1190	−	43.5073i	0.855060	−	1.48101i	0.876589	−	0.481239i	$-0.159813\pi$
$864$	−1.54653	−	2.67867i	−0.0526141	−	0.0911302i
$865$	−1.99300	−	3.45198i	−0.0677640	−	0.117371i
$866$	−2.38217	+	4.12603i	−0.0809493	+	0.140208i
$867$	−6.08385			−0.206618
$868$	−2.35469	+	6.01494i	−0.0799233	+	0.204160i
$869$	−35.0289			−1.18827
$870$	0.839793	−	1.45456i	0.0284716	−	0.0493143i
$871$	0.373590	+	0.647078i	0.0126586	+	0.0219254i
$872$	8.14407	+	14.1059i	0.275793	+	0.477687i
$873$	−0.0902440	+	0.156307i	−0.00305430	+	0.00529019i
$874$	−5.09306			−0.172275
$875$	−15.0507	+	2.28185i	−0.508807	+	0.0771406i
$876$	−3.58280			−0.121051
$877$	−23.4201	+	40.5647i	−0.790839	+	1.36977i	0.134609	+	0.990899i	$0.457022\pi$
$877$	−23.4201	+	40.5647i	−0.790839	+	1.36977i	−0.925448	+	0.378875i	$0.876311\pi$
$878$	8.68289	+	15.0392i	0.293033	+	0.507549i
$879$	−0.778174	−	1.34784i	−0.0262472	−	0.0454614i
$880$	1.74618	−	3.02448i	0.0588638	−	0.101955i
$881$	−39.8060			−1.34110			−0.670549	−	0.741866i	$-0.733941\pi$
$881$	−39.8060			−1.34110			−0.670549	+	0.741866i	$0.733941\pi$
$882$	−13.9086	−	12.8606i	−0.468328	−	0.433040i
$883$	−20.8918			−0.703065			−0.351533	−	0.936176i	$-0.614339\pi$
$883$	−20.8918			−0.703065			−0.351533	+	0.936176i	$0.614339\pi$
$884$	0.287542	−	0.498038i	0.00967109	−	0.0167508i
$885$	−1.64349	−	2.84660i	−0.0552452	−	0.0956875i
$886$	3.10128	+	5.37158i	0.104190	+	0.180462i
$887$	23.4100	−	40.5473i	0.786031	−	1.36145i	−0.142351	−	0.989816i	$-0.545466\pi$
$887$	23.4100	−	40.5473i	0.786031	−	1.36145i	0.928381	−	0.371629i	$-0.121201\pi$
$888$	−1.44192			−0.0483876
$889$	4.35330	−	0.660006i	0.146005	−	0.0221359i
$890$	−7.81131			−0.261836
$891$	−18.8548	+	32.6575i	−0.631659	+	1.09407i
$892$	−14.1193	−	24.4553i	−0.472749	−	0.818825i
$893$	−19.6993	−	34.1202i	−0.659212	−	1.14179i
$894$	−1.45087	+	2.51298i	−0.0485244	+	0.0840467i
$895$	−7.97224			−0.266483
$896$	−0.964471	+	2.46370i	−0.0322207	+	0.0823063i
$897$	−0.129703			−0.00433065
$898$	−8.13544	+	14.0910i	−0.271483	+	0.470222i
$899$	−6.34001	−	10.9812i	−0.211451	−	0.366244i
$900$	−6.28383	−	10.8839i	−0.209461	−	0.362797i
$901$	5.25604	−	9.10373i	0.175104	−	0.303289i
$902$	−68.1176			−2.26807
$903$	3.52498	+	4.41235i	0.117304	+	0.146834i
$904$	2.86135			0.0951669
$905$	−7.04194	+	12.1970i	−0.234082	+	0.405442i
$906$	−1.89309	−	3.27893i	−0.0628938	−	0.108935i
$907$	7.78036	+	13.4760i	0.258342	+	0.447462i	0.965798	−	0.259296i	$-0.0834904\pi$
$907$	7.78036	+	13.4760i	0.258342	+	0.447462i	−0.707456	+	0.706758i	$0.750157\pi$
$908$	5.11176	−	8.85383i	0.169640	−	0.293825i
$909$	44.2695			1.46833
$910$	0.235742	+	0.295087i	0.00781478	+	0.00978205i
$911$	−5.19715			−0.172189			−0.0860946	−	0.996287i	$-0.527439\pi$
$911$	−5.19715			−0.172189			−0.0860946	+	0.996287i	$0.527439\pi$
$912$	1.38036	−	2.39085i	0.0457083	−	0.0791691i
$913$	1.13237	+	1.96133i	0.0374761	+	0.0649105i
$914$	8.18259	+	14.1727i	0.270656	+	0.468790i
$915$	−0.110067	+	0.190642i	−0.00363871	+	0.00630243i
$916$	−2.50083			−0.0826296
$917$	−14.3671	+	36.7002i	−0.474445	+	1.21195i
$918$	−7.43387			−0.245354
$919$	19.7906	−	34.2784i	0.652833	−	1.13074i	−0.329599	−	0.944121i	$-0.606914\pi$
$919$	19.7906	−	34.2784i	0.652833	−	1.13074i	0.982432	−	0.186619i	$-0.0597530\pi$
$920$	0.298300	+	0.516670i	0.00983465	+	0.0170341i
$921$	−6.93460	−	12.0111i	−0.228503	−	0.395779i
$922$	9.09823	−	15.7586i	0.299634	−	0.518982i
$923$	−1.33027			−0.0437863
$924$	−8.30031	+	1.25841i	−0.273060	+	0.0413988i
$925$	−12.3537			−0.406186
$926$	0.212325	−	0.367758i	0.00697745	−	0.0120853i
$927$	26.8097	+	46.4357i	0.880545	+	1.52515i
$928$	−2.59684	−	4.49786i	−0.0852456	−	0.147650i
$929$	16.0130	−	27.7353i	0.525369	−	0.909965i	−0.474195	−	0.880420i	$-0.657261\pi$
$929$	16.0130	−	27.7353i	0.525369	−	0.909965i	0.999563	−	0.0295454i	$-0.00940595\pi$
$930$	−0.789534			−0.0258898
$931$	7.87304	−	34.7713i	0.258029	−	1.13958i
$932$	4.46600			0.146289
$933$	3.50218	−	6.06596i	0.114656	−	0.198591i
$934$	14.0860	+	24.3976i	0.460908	+	0.798315i
$935$	−4.19677	−	7.26903i	−0.137249	−	0.237723i
$936$	−0.323766	+	0.560780i	−0.0105826	+	0.0183297i
$937$	−39.9634			−1.30555			−0.652773	−	0.757554i	$-0.726394\pi$
$937$	−39.9634			−1.30555			−0.652773	+	0.757554i	$0.726394\pi$
$938$	−8.16835	+	1.23841i	−0.266706	+	0.0404355i
$939$	13.9861			0.456420
$940$	−2.30757	+	3.99683i	−0.0752646	+	0.130362i
$941$	22.0476	+	38.1876i	0.718731	+	1.24488i	0.961503	+	0.274796i	$0.0886102\pi$
$941$	22.0476	+	38.1876i	0.718731	+	1.24488i	−0.242771	+	0.970084i	$0.578056\pi$
$942$	−2.14909	−	3.72234i	−0.0700213	−	0.121280i
$943$	5.81825	−	10.0775i	0.189468	−	0.328169i
$944$	−10.1641			−0.330814
$945$	1.77976	−	4.54630i	0.0578955	−	0.147891i
$946$	−23.0516			−0.749471
$947$	14.4016	−	24.9443i	0.467989	−	0.810580i	−0.531342	−	0.847157i	$-0.678312\pi$
$947$	14.4016	−	24.9443i	0.467989	−	0.810580i	0.999331	+	0.0365770i	$0.0116454\pi$
$948$	1.62182	+	2.80908i	0.0526743	+	0.0912346i
$949$	0.790777	+	1.36967i	0.0256697	+	0.0444612i
$950$	11.8263	−	20.4837i	0.383695	−	0.664579i
$951$	−13.5527			−0.439475
$952$	3.96895	+	4.96808i	0.128634	+	0.161016i
$953$	−52.0903			−1.68737			−0.843685	−	0.536838i	$-0.819619\pi$
$953$	−52.0903			−1.68737			−0.843685	+	0.536838i	$0.819619\pi$
$954$	−5.91818	+	10.2506i	−0.191608	+	0.331875i
$955$	2.05972	+	3.56754i	0.0666509	+	0.115443i
$956$	−10.4231	−	18.0534i	−0.337107	−	0.583887i
$957$	8.23997	−	14.2721i	0.266361	−	0.461350i
$958$	−9.76621			−0.315532
$959$	3.74674	+	4.68994i	0.120989	+	0.151446i
$960$	−0.323390			−0.0104374
$961$	12.5197	−	21.6848i	0.403862	−	0.699509i
$962$	0.318253	+	0.551231i	0.0102609	+	0.0177724i
$963$	−20.8331	−	36.0841i	−0.671339	−	1.16279i
$964$	−2.03244	+	3.52029i	−0.0654606	+	0.113381i
$965$	11.6295			0.374367
$966$	0.522796	−	1.33546i	0.0168207	−	0.0429677i
$967$	−8.53400			−0.274435			−0.137218	−	0.990541i	$-0.543816\pi$
$967$	−8.53400			−0.274435			−0.137218	+	0.990541i	$0.543816\pi$
$968$	11.6334	−	20.1496i	0.373911	−	0.647633i
$969$	−3.31756	−	5.74618i	−0.106575	−	0.184594i
$970$	0.0198950	+	0.0344592i	0.000638791	+	0.00110642i
$971$	−12.2179	+	21.1621i	−0.392093	+	0.679124i	−0.992725	−	0.120401i	$-0.961582\pi$
$971$	−12.2179	+	21.1621i	−0.392093	+	0.679124i	0.600633	+	0.799525i	$0.294915\pi$
$972$	12.7711			0.409632
$973$	47.4872	−	7.19956i	1.52237	−	0.230807i
$974$	−20.7530			−0.664968
$975$	0.301174	−	0.521649i	0.00964529	−	0.0167061i
$976$	0.340355	+	0.589512i	0.0108945	+	0.0188698i
$977$	31.1750	+	53.9967i	0.997377	+	1.72751i	0.561369	+	0.827566i	$0.310275\pi$
$977$	31.1750	+	53.9967i	0.997377	+	1.72751i	0.436009	+	0.899942i	$0.356392\pi$
$978$	3.83359	−	6.63996i	0.122585	−	0.212323i
$979$	−76.6439			−2.44955
$980$	−3.98852	+	1.23786i	−0.127409	+	0.0395419i
$981$	−44.0786			−1.40732
$982$	−12.9516	+	22.4328i	−0.413301	+	0.715858i
$983$	19.9111	+	34.4870i	0.635065	+	1.09996i	0.986501	+	0.163752i	$0.0523598\pi$
$983$	19.9111	+	34.4870i	0.635065	+	1.09996i	−0.351437	+	0.936212i	$0.614307\pi$
$984$	3.15381	+	5.46257i	0.100540	+	0.174140i
$985$	4.64569	−	8.04658i	0.148024	−	0.256385i
$986$	−12.4825			−0.397524
$987$	10.9688	−	1.66299i	0.349141	−	0.0529335i
$988$	−1.21867			−0.0387709
$989$	1.96895	−	3.41032i	0.0626089	−	0.108442i
$990$	4.72548	+	8.18476i	0.150185	+	0.260129i
$991$	−3.02762	−	5.24400i	−0.0961756	−	0.166581i	0.813923	−	0.580973i	$-0.197328\pi$
$991$	−3.02762	−	5.24400i	−0.0961756	−	0.166581i	−0.910099	+	0.414392i	$0.863994\pi$
$992$	−1.22072	+	2.11434i	−0.0387577	+	0.0671304i
$993$	5.64678			0.179195
$994$	5.36195	−	13.6968i	0.170071	−	0.434438i
$995$	−2.01527			−0.0638885
$996$	0.104857	−	0.181617i	0.00332251	−	0.00575476i
$997$	−27.1119	−	46.9592i	−0.858643	−	1.48721i	−0.873224	−	0.487319i	$-0.837975\pi$
$997$	−27.1119	−	46.9592i	−0.858643	−	1.48721i	0.0145814	−	0.999894i	$-0.495358\pi$
$998$	−16.8329	−	29.1555i	−0.532837	−	0.922901i
$999$	4.11392	−	7.12552i	0.130159	−	0.225441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.2.e.d.93.2	✓	8
7.2	even	3		2254.2.a.u.1.3		4
7.4	even	3	inner	322.2.e.d.277.2	yes	8
7.5	odd	6		2254.2.a.r.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.2.e.d.93.2	✓	8	1.1	even	1	trivial
322.2.e.d.277.2	yes	8	7.4	even	3	inner
2254.2.a.r.1.2		4	7.5	odd	6
2254.2.a.u.1.3		4	7.2	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:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.271028 - 0.469434i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.298300 - 0.516670i) q^{5} -0.542055 q^{6} +(-2.61586 + 0.396592i) q^{7} -1.00000 q^{8} +(1.35309 - 2.34362i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.271028 - 0.469434i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.298300 - 0.516670i) q^{5} -0.542055 q^{6} +(-2.61586 + 0.396592i) q^{7} -1.00000 q^{8} +(1.35309 - 2.34362i) q^{9} +(-0.298300 - 0.516670i) q^{10} +(-2.92689 - 5.06952i) q^{11} +(-0.271028 + 0.469434i) q^{12} +0.239279 q^{13} +(-0.964471 + 2.46370i) q^{14} -0.323390 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.20170 + 2.08141i) q^{17} +(-1.35309 - 2.34362i) q^{18} +(2.54653 - 4.41072i) q^{19} -0.596599 q^{20} +(0.895143 + 1.12048i) q^{21} -5.85378 q^{22} +(0.500000 - 0.866025i) q^{23} +(0.271028 + 0.469434i) q^{24} +(2.32203 + 4.02188i) q^{25} +(0.119640 - 0.207222i) q^{26} -3.09306 q^{27} +(1.65139 + 2.06710i) q^{28} -5.19369 q^{29} +(-0.161695 + 0.280064i) q^{30} +(1.22072 + 2.11434i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.58654 + 2.74796i) q^{33} +2.40340 q^{34} +(-0.575403 + 1.46984i) q^{35} -2.70618 q^{36} +(-1.33005 + 2.30371i) q^{37} +(-2.54653 - 4.41072i) q^{38} +(-0.0648513 - 0.112326i) q^{39} +(-0.298300 + 0.516670i) q^{40} +11.6365 q^{41} +(1.41794 - 0.214975i) q^{42} +3.93789 q^{43} +(-2.92689 + 5.06952i) q^{44} +(-0.807252 - 1.39820i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(3.86787 - 6.69935i) q^{47} +0.542055 q^{48} +(6.68543 - 2.07486i) q^{49} +4.64407 q^{50} +(0.651388 - 1.12824i) q^{51} +(-0.119640 - 0.207222i) q^{52} +(-2.18692 - 3.78785i) q^{53} +(-1.54653 + 2.67867i) q^{54} -3.49236 q^{55} +(2.61586 - 0.396592i) q^{56} -2.76072 q^{57} +(-2.59684 + 4.49786i) q^{58} +(5.08206 + 8.80239i) q^{59} +(0.161695 + 0.280064i) q^{60} +(0.340355 - 0.589512i) q^{61} +2.44143 q^{62} +(-2.61003 + 6.66719i) q^{63} +1.00000 q^{64} +(0.0713770 - 0.123629i) q^{65} +(1.58654 + 2.74796i) q^{66} +(1.56131 + 2.70428i) q^{67} +(1.20170 - 2.08141i) q^{68} -0.542055 q^{69} +(0.985217 + 1.23323i) q^{70} -5.55947 q^{71} +(-1.35309 + 2.34362i) q^{72} +(3.30483 + 5.72413i) q^{73} +(1.33005 + 2.30371i) q^{74} +(1.25867 - 2.18008i) q^{75} -5.09306 q^{76} +(9.66687 + 12.1004i) q^{77} -0.129703 q^{78} +(2.99199 - 5.18227i) q^{79} +(0.298300 + 0.516670i) q^{80} +(-3.22096 - 5.57887i) q^{81} +(5.81825 - 10.0775i) q^{82} -0.386886 q^{83} +(0.522796 - 1.33546i) q^{84} +1.43387 q^{85} +(1.96895 - 3.41032i) q^{86} +(1.40763 + 2.43809i) q^{87} +(2.92689 + 5.06952i) q^{88} +(6.54653 - 11.3389i) q^{89} -1.61450 q^{90} +(-0.625921 + 0.0948963i) q^{91} -1.00000 q^{92} +(0.661695 - 1.14609i) q^{93} +(-3.86787 - 6.69935i) q^{94} +(-1.51926 - 2.63143i) q^{95} +(0.271028 - 0.469434i) q^{96} -0.0666948 q^{97} +(1.54584 - 6.82718i) q^{98} -15.8414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9}+O(q^{10}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9	\( 8 q + 4 q^{2} - q^{3} - 4 q^{4} + 5 q^{5} - 2 q^{6} - 3 q^{7} - 8 q^{8} + q^{9} - 5 q^{10} + 2 q^{11} - q^{12} + 14 q^{13} + 3 q^{14} - 10 q^{15} - 4 q^{16} + 7 q^{17} - q^{18} + q^{19} - 10 q^{20} - 5 q^{21} + 4 q^{22} + 4 q^{23} + q^{24} - 19 q^{25} + 7 q^{26} + 14 q^{27} + 6 q^{28} - 12 q^{29} - 5 q^{30} + 4 q^{31} + 4 q^{32} + 13 q^{33} + 14 q^{34} - 14 q^{35} - 2 q^{36} - q^{38} - 19 q^{39} - 5 q^{40} - 30 q^{41} + 20 q^{42} - 24 q^{43} + 2 q^{44} + 25 q^{45} - 4 q^{46} + 15 q^{47} + 2 q^{48} + 17 q^{49} - 38 q^{50} - 2 q^{51} - 7 q^{52} - 21 q^{53} + 7 q^{54} + 24 q^{55} + 3 q^{56} - 10 q^{57} - 6 q^{58} + 32 q^{59} + 5 q^{60} + 3 q^{61} + 8 q^{62} + 25 q^{63} + 8 q^{64} + 6 q^{65} - 13 q^{66} - 13 q^{67} + 7 q^{68} - 2 q^{69} + 14 q^{70} - 14 q^{71} - q^{72} + 16 q^{73} - 6 q^{75} - 2 q^{76} + 23 q^{77} - 38 q^{78} - 3 q^{79} + 5 q^{80} - 15 q^{82} + 16 q^{83} + 25 q^{84} - 48 q^{85} - 12 q^{86} + 9 q^{87} - 2 q^{88} + 33 q^{89} + 50 q^{90} - 18 q^{91} - 8 q^{92} + 9 q^{93} - 15 q^{94} + 11 q^{95} + q^{96} - 24 q^{97} + 34 q^{98} - 70 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - q^3 - 4 * q^4 + 5 * q^5 - 2 * q^6 - 3 * q^7 - 8 * q^8 + q^9 - 5 * q^10 + 2 * q^11 - q^12 + 14 * q^13 + 3 * q^14 - 10 * q^15 - 4 * q^16 + 7 * q^17 - q^18 + q^19 - 10 * q^20 - 5 * q^21 + 4 * q^22 + 4 * q^23 + q^24 - 19 * q^25 + 7 * q^26 + 14 * q^27 + 6 * q^28 - 12 * q^29 - 5 * q^30 + 4 * q^31 + 4 * q^32 + 13 * q^33 + 14 * q^34 - 14 * q^35 - 2 * q^36 - q^38 - 19 * q^39 - 5 * q^40 - 30 * q^41 + 20 * q^42 - 24 * q^43 + 2 * q^44 + 25 * q^45 - 4 * q^46 + 15 * q^47 + 2 * q^48 + 17 * q^49 - 38 * q^50 - 2 * q^51 - 7 * q^52 - 21 * q^53 + 7 * q^54 + 24 * q^55 + 3 * q^56 - 10 * q^57 - 6 * q^58 + 32 * q^59 + 5 * q^60 + 3 * q^61 + 8 * q^62 + 25 * q^63 + 8 * q^64 + 6 * q^65 - 13 * q^66 - 13 * q^67 + 7 * q^68 - 2 * q^69 + 14 * q^70 - 14 * q^71 - q^72 + 16 * q^73 - 6 * q^75 - 2 * q^76 + 23 * q^77 - 38 * q^78 - 3 * q^79 + 5 * q^80 - 15 * q^82 + 16 * q^83 + 25 * q^84 - 48 * q^85 - 12 * q^86 + 9 * q^87 - 2 * q^88 + 33 * q^89 + 50 * q^90 - 18 * q^91 - 8 * q^92 + 9 * q^93 - 15 * q^94 + 11 * q^95 + q^96 - 24 * q^97 + 34 * q^98 - 70 * q^99

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