LMFDB - Embedded newform 342.2.h.f.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.50911458676875.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} + 12x^{8} - 28x^{7} + 58x^{6} - 111x^{5} + 174x^{4} - 252x^{3} + 324x^{2} - 324x + 243 $ x^10 - 4x^9 + 12x^8 - 28x^7 + 58x^6 - 111x^5 + 174x^4 - 252x^3 + 324x^2 - 324*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$-1.01638 - 1.40249i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.f.121.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.01638 - 1.40249i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44556 q^{5} +(-1.72278 - 0.178963i) q^{6} +(-2.12597 + 3.68229i) q^{7} +1.00000 q^{8} +(-0.933957 - 2.85092i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.01638 - 1.40249i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44556 q^{5} +(-1.72278 - 0.178963i) q^{6} +(-2.12597 + 3.68229i) q^{7} +1.00000 q^{8} +(-0.933957 - 2.85092i) q^{9} +(1.72278 + 2.98394i) q^{10} +(0.876015 - 1.51730i) q^{11} +(0.706404 + 1.58145i) q^{12} +(-2.89239 + 5.00977i) q^{13} +4.25194 q^{14} +(-3.50199 + 4.83237i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.74996 + 3.03101i) q^{17} +(-2.00199 + 2.23429i) q^{18} +(-3.51836 - 2.57315i) q^{19} +(1.72278 - 2.98394i) q^{20} +(3.00359 + 6.72425i) q^{21} -1.75203 q^{22} +(1.16285 - 2.01412i) q^{23} +(1.01638 - 1.40249i) q^{24} +6.87189 q^{25} +5.78478 q^{26} +(-4.94763 - 1.58774i) q^{27} +(-2.12597 - 3.68229i) q^{28} +1.58719 q^{29} +(5.93594 + 0.616627i) q^{30} +(-2.18121 - 3.77797i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.23764 - 2.77075i) q^{33} +3.49991 q^{34} +(7.32517 - 12.6876i) q^{35} +(2.93594 + 0.616627i) q^{36} +0.00397434 q^{37} +(-0.469234 + 4.33357i) q^{38} +(4.08639 + 9.14836i) q^{39} -3.44556 q^{40} -8.53985 q^{41} +(4.32158 - 5.96331i) q^{42} +(4.62956 + 8.01864i) q^{43} +(0.876015 + 1.51730i) q^{44} +(3.21801 + 9.82301i) q^{45} -2.32570 q^{46} -7.06551 q^{47} +(-1.72278 - 0.178963i) q^{48} +(-5.53951 - 9.59472i) q^{49} +(-3.43594 - 5.95123i) q^{50} +(2.47235 + 5.53495i) q^{51} +(-2.89239 - 5.00977i) q^{52} +(-4.09880 - 7.09932i) q^{53} +(1.09880 + 5.07865i) q^{54} +(-3.01836 + 5.22796i) q^{55} +(-2.12597 + 3.68229i) q^{56} +(-7.18480 + 2.31918i) q^{57} +(-0.793596 - 1.37455i) q^{58} +5.09125 q^{59} +(-2.43396 - 5.44899i) q^{60} +4.30090 q^{61} +(-2.18121 + 3.77797i) q^{62} +(12.4835 + 2.62186i) q^{63} +1.00000 q^{64} +(9.96591 - 17.2615i) q^{65} +(-1.78072 + 2.45721i) q^{66} +(-3.54085 + 6.13294i) q^{67} +(-1.74996 - 3.03101i) q^{68} +(-1.64288 - 3.67799i) q^{69} -14.6503 q^{70} +(-7.94556 + 13.7621i) q^{71} +(-0.933957 - 2.85092i) q^{72} +(1.65522 - 2.86693i) q^{73} +(-0.00198717 - 0.00344188i) q^{74} +(6.98443 - 9.63776i) q^{75} +(3.98760 - 1.76042i) q^{76} +(3.72477 + 6.45149i) q^{77} +(5.87952 - 8.11310i) q^{78} +(1.82158 + 3.15506i) q^{79} +(1.72278 + 2.98394i) q^{80} +(-7.25545 + 5.32527i) q^{81} +(4.26992 + 7.39572i) q^{82} +(6.12796 - 10.6139i) q^{83} +(-7.32517 - 0.760940i) q^{84} +(6.02958 - 10.4435i) q^{85} +(4.62956 - 8.01864i) q^{86} +(1.61318 - 2.22602i) q^{87} +(0.876015 - 1.51730i) q^{88} +(-6.81348 - 11.8013i) q^{89} +(6.89797 - 7.69838i) q^{90} +(-12.2983 - 21.3013i) q^{91} +(1.16285 + 2.01412i) q^{92} +(-7.51551 - 0.780713i) q^{93} +(3.53275 + 6.11891i) q^{94} +(12.1227 + 8.86596i) q^{95} +(0.706404 + 1.58145i) q^{96} +(-1.62398 - 2.81282i) q^{97} +(-5.53951 + 9.59472i) q^{98} +(-5.14386 - 1.08035i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.01638	−	1.40249i	0.586805	−	0.809728i
$3$	1.01638	−	1.40249i	0.586805	−	0.809728i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.44556			−1.54090			−0.770451	−	0.637499i	$-0.779969\pi$
$5$	−3.44556			−1.54090			−0.770451	+	0.637499i	$0.779969\pi$
$6$	−1.72278	−	0.178963i	−0.703322	−	0.0730613i
$7$	−2.12597	+	3.68229i	−0.803542	+	1.39178i	0.113729	+	0.993512i	$0.463720\pi$
$7$	−2.12597	+	3.68229i	−0.803542	+	1.39178i	−0.917271	+	0.398264i	$0.869613\pi$
$8$	1.00000			0.353553
$9$	−0.933957	−	2.85092i	−0.311319	−	0.950305i
$10$	1.72278	+	2.98394i	0.544791	+	0.943606i
$11$	0.876015	−	1.51730i	0.264129	−	0.457484i	−0.703206	−	0.710986i	$-0.748249\pi$
$11$	0.876015	−	1.51730i	0.264129	−	0.457484i	0.967335	+	0.253502i	$0.0815824\pi$
$12$	0.706404	+	1.58145i	0.203921	+	0.456526i
$13$	−2.89239	+	5.00977i	−0.802205	+	1.38946i	0.115957	+	0.993254i	$0.463007\pi$
$13$	−2.89239	+	5.00977i	−0.802205	+	1.38946i	−0.918162	+	0.396206i	$0.870327\pi$
$14$	4.25194			1.13638
$15$	−3.50199	+	4.83237i	−0.904209	+	1.24771i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.74996	+	3.03101i	−0.424427	+	0.735129i	−0.996367	−	0.0851667i	$-0.972858\pi$
$17$	−1.74996	+	3.03101i	−0.424427	+	0.735129i	0.571940	+	0.820296i	$0.306191\pi$
$18$	−2.00199	+	2.23429i	−0.471873	+	0.526627i
$19$	−3.51836	−	2.57315i	−0.807168	−	0.590322i
$19$	−3.51836	−	2.57315i	−0.807168	−	0.590322i
$20$	1.72278	−	2.98394i	0.385225	−	0.667230i
$21$	3.00359	+	6.72425i	0.655437	+	1.46735i
$22$	−1.75203			−0.373534
$23$	1.16285	−	2.01412i	0.242471	−	0.419972i	−0.718946	−	0.695066i	$-0.755375\pi$
$23$	1.16285	−	2.01412i	0.242471	−	0.419972i	0.961418	+	0.275093i	$0.0887087\pi$
$24$	1.01638	−	1.40249i	0.207467	−	0.286282i
$25$	6.87189			1.37438
$26$	5.78478			1.13449
$27$	−4.94763	−	1.58774i	−0.952173	−	0.305560i
$28$	−2.12597	−	3.68229i	−0.401771	−	0.695888i
$29$	1.58719			0.294734			0.147367	−	0.989082i	$-0.452920\pi$
$29$	1.58719			0.294734			0.147367	+	0.989082i	$0.452920\pi$
$30$	5.93594	+	0.616627i	1.08375	+	0.112580i
$31$	−2.18121	−	3.77797i	−0.391758	−	0.678544i	0.600924	−	0.799306i	$-0.294800\pi$
$31$	−2.18121	−	3.77797i	−0.391758	−	0.678544i	−0.992681	+	0.120762i	$0.961466\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.23764	−	2.77075i	−0.215446	−	0.482326i
$34$	3.49991			0.600230
$35$	7.32517	−	12.6876i	1.23818	−	2.14459i
$36$	2.93594	+	0.616627i	0.489324	+	0.102771i
$37$	0.00397434			0.000653377			0.000326688	−	1.00000i	$-0.499896\pi$
$37$	0.00397434			0.000653377			0.000326688		1.00000i	$0.499896\pi$
$38$	−0.469234	+	4.33357i	−0.0761198	+	0.702998i
$39$	4.08639	+	9.14836i	0.654347	+	1.46491i
$40$	−3.44556			−0.544791
$41$	−8.53985			−1.33370			−0.666850	−	0.745192i	$-0.732358\pi$
$41$	−8.53985			−1.33370			−0.666850	+	0.745192i	$0.732358\pi$
$42$	4.32158	−	5.96331i	0.666834	−	0.920159i
$43$	4.62956	+	8.01864i	0.706002	+	1.22283i	0.966329	+	0.257310i	$0.0828362\pi$
$43$	4.62956	+	8.01864i	0.706002	+	1.22283i	−0.260327	+	0.965520i	$0.583830\pi$
$44$	0.876015	+	1.51730i	0.132064	+	0.228742i
$45$	3.21801	+	9.82301i	0.479712	+	1.46433i
$46$	−2.32570			−0.342906
$47$	−7.06551			−1.03061			−0.515305	−	0.857007i	$-0.672321\pi$
$47$	−7.06551			−1.03061			−0.515305	+	0.857007i	$0.672321\pi$
$48$	−1.72278	−	0.178963i	−0.248662	−	0.0258311i
$49$	−5.53951	−	9.59472i	−0.791359	−	1.37067i
$50$	−3.43594	−	5.95123i	−0.485916	−	0.841631i
$51$	2.47235	+	5.53495i	0.346199	+	0.775048i
$52$	−2.89239	−	5.00977i	−0.401103	−	0.694730i
$53$	−4.09880	−	7.09932i	−0.563013	−	0.975167i	−0.997232	−	0.0743594i	$-0.976309\pi$
$53$	−4.09880	−	7.09932i	−0.563013	−	0.975167i	0.434219	−	0.900808i	$-0.357025\pi$
$54$	1.09880	+	5.07865i	0.149527	+	0.691116i
$55$	−3.01836	+	5.22796i	−0.406996	+	0.704938i
$56$	−2.12597	+	3.68229i	−0.284095	+	0.492067i
$57$	−7.18480	+	2.31918i	−0.951651	+	0.307183i
$58$	−0.793596	−	1.37455i	−0.104204	−	0.180487i
$59$	5.09125			0.662825			0.331412	−	0.943486i	$-0.392475\pi$
$59$	5.09125			0.662825			0.331412	+	0.943486i	$0.392475\pi$
$60$	−2.43396	−	5.44899i	−0.314223	−	0.703462i
$61$	4.30090			0.550674			0.275337	−	0.961348i	$-0.411211\pi$
$61$	4.30090			0.550674			0.275337	+	0.961348i	$0.411211\pi$
$62$	−2.18121	+	3.77797i	−0.277015	+	0.479803i
$63$	12.4835	+	2.62186i	1.57277	+	0.330324i
$64$	1.00000			0.125000
$65$	9.96591	−	17.2615i	1.23612	−	2.14102i
$66$	−1.78072	+	2.45721i	−0.219192	+	0.302461i
$67$	−3.54085	+	6.13294i	−0.432584	+	0.749258i	−0.997095	−	0.0761680i	$-0.975731\pi$
$67$	−3.54085	+	6.13294i	−0.432584	+	0.749258i	0.564511	+	0.825426i	$0.309065\pi$
$68$	−1.74996	−	3.03101i	−0.212213	−	0.367564i
$69$	−1.64288	−	3.67799i	−0.197780	−	0.442778i
$70$	−14.6503			−1.75105
$71$	−7.94556	+	13.7621i	−0.942965	+	1.63326i	−0.183188	+	0.983078i	$0.558642\pi$
$71$	−7.94556	+	13.7621i	−0.942965	+	1.63326i	−0.759776	+	0.650185i	$0.774691\pi$
$72$	−0.933957	−	2.85092i	−0.110068	−	0.335984i
$73$	1.65522	−	2.86693i	0.193729	−	0.335549i	−0.752754	−	0.658302i	$-0.771275\pi$
$73$	1.65522	−	2.86693i	0.193729	−	0.335549i	0.946483	+	0.322753i	$0.104608\pi$
$74$	−0.00198717	−	0.00344188i	−0.000231004	−	0.000400110i
$75$	6.98443	−	9.63776i	0.806492	−	1.11287i
$76$	3.98760	−	1.76042i	0.457409	−	0.201934i
$77$	3.72477	+	6.45149i	0.424477	+	0.735215i
$78$	5.87952	−	8.11310i	0.665724	−	0.918628i
$79$	1.82158	+	3.15506i	0.204943	+	0.354972i	0.950115	−	0.311901i	$-0.100966\pi$
$79$	1.82158	+	3.15506i	0.204943	+	0.354972i	−0.745171	+	0.666873i	$0.767632\pi$
$80$	1.72278	+	2.98394i	0.192613	+	0.333615i
$81$	−7.25545	+	5.32527i	−0.806161	+	0.591697i
$82$	4.26992	+	7.39572i	0.471534	+	0.816721i
$83$	6.12796	−	10.6139i	0.672631	−	1.16503i	−0.304524	−	0.952505i	$-0.598498\pi$
$83$	6.12796	−	10.6139i	0.672631	−	1.16503i	0.977155	−	0.212526i	$-0.0681691\pi$
$84$	−7.32517	−	0.760940i	−0.799241	−	0.0830253i
$85$	6.02958	−	10.4435i	0.654000	−	1.13276i
$86$	4.62956	−	8.01864i	0.499218	−	0.864672i
$87$	1.61318	−	2.22602i	0.172952	−	0.238655i
$88$	0.876015	−	1.51730i	0.0933835	−	0.161745i
$89$	−6.81348	−	11.8013i	−0.722227	−	1.25093i	−0.960105	−	0.279639i	$-0.909785\pi$
$89$	−6.81348	−	11.8013i	−0.722227	−	1.25093i	0.237878	−	0.971295i	$-0.423548\pi$
$90$	6.89797	−	7.69838i	0.727110	−	0.811480i
$91$	−12.2983	−	21.3013i	−1.28921	−	2.23298i
$92$	1.16285	+	2.01412i	0.121236	+	0.209986i
$93$	−7.51551	−	0.780713i	−0.779322	−	0.0809561i
$94$	3.53275	+	6.11891i	0.364376	+	0.631117i
$95$	12.1227	+	8.86596i	1.24377	+	0.909628i
$96$	0.706404	+	1.58145i	0.0720970	+	0.161406i
$97$	−1.62398	−	2.81282i	−0.164891	−	0.285599i	0.771726	−	0.635955i	$-0.219394\pi$
$97$	−1.62398	−	2.81282i	−0.164891	−	0.285599i	−0.936616	+	0.350356i	$0.886060\pi$
$98$	−5.53951	+	9.59472i	−0.559575	+	0.969213i
$99$	−5.14386	−	1.08035i	−0.516978	−	0.108579i
$100$	−3.43594	+	5.95123i	−0.343594	+	0.595123i
$101$	−6.89527			−0.686105			−0.343052	−	0.939316i	$-0.611461\pi$
$101$	−6.89527			−0.686105			−0.343052	+	0.939316i	$0.611461\pi$
$102$	3.55723	−	4.90859i	0.352218	−	0.486023i
$103$	−3.77200	−	6.53329i	−0.371666	−	0.643744i	0.618156	−	0.786055i	$-0.287880\pi$
$103$	−3.77200	−	6.53329i	−0.371666	−	0.643744i	−0.989822	+	0.142311i	$0.954547\pi$
$104$	−2.89239	+	5.00977i	−0.283622	+	0.491248i
$105$	−10.3491	−	23.1688i	−1.00996	−	2.26104i
$106$	−4.09880	+	7.09932i	−0.398110	+	0.689547i
$107$	9.48769			0.917209			0.458605	−	0.888640i	$-0.348349\pi$
$107$	9.48769			0.917209			0.458605	+	0.888640i	$0.348349\pi$
$108$	3.84884	−	3.49091i	0.370355	−	0.335913i
$109$	3.59871	−	6.23315i	0.344694	−	0.597027i	−0.640604	−	0.767871i	$-0.721316\pi$
$109$	3.59871	−	6.23315i	0.344694	−	0.597027i	0.985298	+	0.170844i	$0.0546494\pi$
$110$	6.03673			0.575579
$111$	0.00403942	−	0.00557397i	0.000383405	−	0.000529058i
$112$	4.25194			0.401771
$113$	4.48148	+	7.76216i	0.421583	+	0.730203i	0.996094	−	0.0882937i	$-0.0281414\pi$
$113$	4.48148	+	7.76216i	0.421583	+	0.730203i	−0.574512	+	0.818496i	$0.694808\pi$
$114$	5.60087	+	5.06263i	0.524569	+	0.474159i
$115$	−4.00667	+	6.93976i	−0.373624	+	0.647136i
$116$	−0.793596	+	1.37455i	−0.0736836	+	0.127624i
$117$	16.9838	+	3.56706i	1.57015	+	0.329774i
$118$	−2.54563	−	4.40915i	−0.234344	−	0.405896i
$119$	−7.44072	−	12.8877i	−0.682089	−	1.18141i
$120$	−3.50199	+	4.83237i	−0.319686	+	0.441133i
$121$	3.96519	+	6.86792i	0.360472	+	0.624356i
$122$	−2.15045	−	3.72469i	−0.194692	−	0.337217i
$123$	−8.67970	+	11.9770i	−0.782622	+	1.07993i
$124$	4.36243			0.391758
$125$	−6.44971			−0.576879
$126$	−3.97113	−	12.1219i	−0.353777	−	1.07991i
$127$	6.18121	+	10.7062i	0.548494	+	0.950020i	0.998378	+	0.0569326i	$0.0181320\pi$
$127$	6.18121	+	10.7062i	0.548494	+	0.950020i	−0.449884	+	0.893087i	$0.648535\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	15.9514	+	1.65704i	1.40445	+	0.145894i
$130$	−19.9318			−1.74814
$131$	−2.50009			−0.218434			−0.109217	−	0.994018i	$-0.534834\pi$
$131$	−2.50009			−0.218434			−0.109217	+	0.994018i	$0.534834\pi$
$132$	3.01836	+	0.313548i	0.262715	+	0.0272909i
$133$	16.9550	−	7.48519i	1.47019	−	0.649048i
$134$	7.08171			0.611766
$135$	17.0474	+	5.47065i	1.46720	+	0.470838i
$136$	−1.74996	+	3.03101i	−0.150058	+	0.259907i
$137$	−9.89112			−0.845056			−0.422528	−	0.906350i	$-0.638857\pi$
$137$	−9.89112			−0.845056			−0.422528	+	0.906350i	$0.638857\pi$
$138$	−2.36379	+	3.26177i	−0.201219	+	0.277661i
$139$	−6.77126	+	11.7282i	−0.574331	+	0.994770i	0.421783	+	0.906697i	$0.361404\pi$
$139$	−6.77126	+	11.7282i	−0.574331	+	0.994770i	−0.996114	+	0.0880737i	$0.971929\pi$
$140$	7.32517	+	12.6876i	0.619089	+	1.07229i
$141$	−7.18121	+	9.90930i	−0.604767	+	0.834514i
$142$	15.8911			1.33355
$143$	5.06756	+	8.77727i	0.423771	+	0.733992i
$144$	−2.00199	+	2.23429i	−0.166832	+	0.186191i
$145$	−5.46877			−0.454156
$146$	−3.31044			−0.273974
$147$	−19.0867	−	1.98273i	−1.57425	−	0.163533i
$148$	−0.00198717	+	0.00344188i	−0.000163344	+	0.000282920i
$149$	2.26720			0.185736			0.0928682	−	0.995678i	$-0.470396\pi$
$149$	2.26720			0.185736			0.0928682	+	0.995678i	$0.470396\pi$
$150$	−11.8388	−	1.22981i	−0.966630	−	0.100414i
$151$	−4.89948	+	8.48616i	−0.398714	+	0.690594i	−0.993568	−	0.113241i	$-0.963877\pi$
$151$	−4.89948	+	8.48616i	−0.398714	+	0.690594i	0.594853	+	0.803834i	$0.297210\pi$
$152$	−3.51836	−	2.57315i	−0.285377	−	0.208710i
$153$	10.2756	+	2.15814i	0.830729	+	0.174475i
$154$	3.72477	−	6.45149i	0.300150	−	0.519876i
$155$	7.51551	+	13.0172i	0.603660	+	1.04557i
$156$	−9.96591	−	1.03526i	−0.797912	−	0.0828872i
$157$	22.8695			1.82519			0.912593	−	0.408869i	$-0.134077\pi$
$157$	22.8695			1.82519			0.912593	+	0.408869i	$0.134077\pi$
$158$	1.82158	−	3.15506i	0.144917	−	0.251003i
$159$	−14.1226	−	1.46706i	−1.12000	−	0.116346i
$160$	1.72278	−	2.98394i	0.136198	−	0.235901i
$161$	4.94438	+	8.56391i	0.389672	+	0.674931i
$162$	8.23954	+	3.62077i	0.647360	+	0.284474i
$163$	24.7772			1.94070			0.970350	−	0.241705i	$-0.0777065\pi$
$163$	24.7772			1.94070			0.970350	+	0.241705i	$0.0777065\pi$
$164$	4.26992	−	7.39572i	0.333425	−	0.577509i
$165$	4.26437	+	9.54680i	0.331981	+	0.743217i
$166$	−12.2559			−0.951244
$167$	−8.69884	+	15.0668i	−0.673137	+	1.16591i	0.303873	+	0.952713i	$0.401720\pi$
$167$	−8.69884	+	15.0668i	−0.673137	+	1.16591i	−0.977010	+	0.213195i	$0.931613\pi$
$168$	3.00359	+	6.72425i	0.231732	+	0.518787i
$169$	−10.2319	−	17.7221i	−0.787066	−	1.36324i
$170$	−12.0592			−0.924896
$171$	−4.04984	+	12.4338i	−0.309699	+	0.950835i
$172$	−9.25912			−0.706002
$173$	4.01789	+	6.95919i	0.305475	+	0.529098i	0.977367	−	0.211551i	$-0.0678515\pi$
$173$	4.01789	+	6.95919i	0.305475	+	0.529098i	−0.671892	+	0.740649i	$0.734518\pi$
$174$	−2.73438	−	0.284048i	−0.207293	−	0.0215337i
$175$	−14.6094	+	25.3043i	−1.10437	+	1.91283i
$176$	−1.75203			−0.132064
$177$	5.17463	−	7.14043i	0.388949	−	0.536708i
$178$	−6.81348	+	11.8013i	−0.510692	+	0.884544i
$179$	−9.96694			−0.744964			−0.372482	−	0.928039i	$-0.621493\pi$
$179$	−9.96694			−0.744964			−0.372482	+	0.928039i	$0.621493\pi$
$180$	−10.1160	−	2.12463i	−0.754000	−	0.158360i
$181$	−9.39797	−	16.2778i	−0.698545	−	1.20992i	−0.968971	−	0.247175i	$-0.920498\pi$
$181$	−9.39797	−	16.2778i	−0.698545	−	1.20992i	0.270425	−	0.962741i	$-0.412836\pi$
$182$	−12.2983	+	21.3013i	−0.911610	+	1.57895i
$183$	4.37133	−	6.03197i	0.323138	−	0.445896i
$184$	1.16285	−	2.01412i	0.0857265	−	0.148483i
$185$	−0.0136938			−0.00100679
$186$	3.08164	+	6.89898i	0.225957	+	0.505858i
$187$	3.06598	+	5.31043i	0.224206	+	0.388337i
$188$	3.53275	−	6.11891i	0.257652	−	0.446267i
$189$	16.3650	−	14.8431i	1.19038	−	1.07968i
$190$	1.61677	−	14.9316i	0.117293	−	1.08325i
$191$	−5.87666	+	10.1787i	−0.425220	+	0.736503i	−0.996441	−	0.0842933i	$-0.973137\pi$
$191$	−5.87666	+	10.1787i	−0.425220	+	0.736503i	0.571221	+	0.820797i	$0.306470\pi$
$192$	1.01638	−	1.40249i	0.0733507	−	0.101216i
$193$	−11.8390			−0.852187			−0.426094	−	0.904679i	$-0.640111\pi$
$193$	−11.8390			−0.852187			−0.426094	+	0.904679i	$0.640111\pi$
$194$	−1.62398	+	2.81282i	−0.116595	+	0.201949i
$195$	−14.0799	−	31.5212i	−1.00828	−	2.25728i
$196$	11.0790			0.791359
$197$	−8.79844			−0.626863			−0.313432	−	0.949611i	$-0.601479\pi$
$197$	−8.79844			−0.626863			−0.313432	+	0.949611i	$0.601479\pi$
$198$	1.63632	+	4.99489i	0.116288	+	0.354972i
$199$	−8.67709	−	15.0292i	−0.615103	−	1.06539i	−0.990367	−	0.138471i	$-0.955781\pi$
$199$	−8.67709	−	15.0292i	−0.615103	−	1.06539i	0.375264	−	0.926918i	$-0.377552\pi$
$200$	6.87189			0.485916
$201$	5.00255	+	11.1994i	0.352852	+	0.789944i
$202$	3.44763	+	5.97148i	0.242575	+	0.420152i
$203$	−3.37433	+	5.84450i	−0.236831	+	0.410204i
$204$	−6.02958	−	0.626354i	−0.422155	−	0.0438536i
$205$	29.4246			2.05510
$206$	−3.77200	+	6.53329i	−0.262807	+	0.455196i
$207$	−6.82813	−	1.43409i	−0.474588	−	0.0996762i
$208$	5.78478			0.401103
$209$	−6.98639	+	3.08430i	−0.483259	+	0.213346i
$210$	−14.8903	+	20.5469i	−1.02753	+	1.41787i
$211$	15.4415			1.06303			0.531517	−	0.847048i	$-0.321622\pi$
$211$	15.4415			1.06303			0.531517	+	0.847048i	$0.321622\pi$
$212$	8.19759			0.563013
$213$	11.2255	+	25.1311i	0.769162	+	1.72195i
$214$	−4.74384	−	8.21658i	−0.324282	−	0.561674i
$215$	−15.9514	−	27.6287i	−1.08788	−	1.88426i
$216$	−4.94763	−	1.58774i	−0.336644	−	0.108032i
$217$	18.5488			1.25917
$218$	−7.19742			−0.487471
$219$	−2.33851	−	5.23531i	−0.158022	−	0.353770i
$220$	−3.01836	−	5.22796i	−0.203498	−	0.352469i
$221$	−10.1231	−	17.5338i	−0.680955	−	1.17945i
$222$	−0.00684691		0.000711258i	−0.000459534		4.77365e-5i
$223$	9.71397	+	16.8251i	0.650495	+	1.12669i	0.983003	+	0.183590i	$0.0587720\pi$
$223$	9.71397	+	16.8251i	0.650495	+	1.12669i	−0.332507	+	0.943101i	$0.607895\pi$
$224$	−2.12597	−	3.68229i	−0.142047	−	0.246033i
$225$	−6.41805	−	19.5912i	−0.427870	−	1.30608i
$226$	4.48148	−	7.76216i	0.298104	−	0.516331i
$227$	−6.36062	+	11.0169i	−0.422169	+	0.731218i	−0.996151	−	0.0876494i	$-0.972064\pi$
$227$	−6.36062	+	11.0169i	−0.422169	+	0.731218i	0.573982	+	0.818868i	$0.305398\pi$
$228$	1.58393	−	7.38181i	0.104899	−	0.488872i
$229$	2.24799	+	3.89363i	0.148551	+	0.257299i	0.930692	−	0.365803i	$-0.119206\pi$
$229$	2.24799	+	3.89363i	0.148551	+	0.257299i	−0.782141	+	0.623102i	$0.785872\pi$
$230$	8.01335			0.528384
$231$	12.8339	+	1.33319i	0.844409	+	0.0877174i
$232$	1.58719			0.104204
$233$	−3.81807	+	6.61310i	−0.250130	+	0.433238i	−0.963561	−	0.267487i	$-0.913807\pi$
$233$	−3.81807	+	6.61310i	−0.250130	+	0.433238i	0.713431	+	0.700725i	$0.247140\pi$
$234$	−5.40274	−	16.4919i	−0.353188	−	1.07811i
$235$	24.3446			1.58807
$236$	−2.54563	+	4.40915i	−0.165706	+	0.287012i
$237$	6.27635	+	0.651989i	0.407693	+	0.0423512i
$238$	−7.44072	+	12.8877i	−0.482310	+	0.835386i
$239$	−4.12630	−	7.14697i	−0.266908	−	0.462299i	0.701153	−	0.713010i	$-0.252669\pi$
$239$	−4.12630	−	7.14697i	−0.266908	−	0.462299i	−0.968062	+	0.250711i	$0.919335\pi$
$240$	5.93594	+	0.616627i	0.383164	+	0.0398031i
$241$	−11.6580			−0.750956			−0.375478	−	0.926831i	$-0.622521\pi$
$241$	−11.6580			−0.750956			−0.375478	+	0.926831i	$0.622521\pi$
$242$	3.96519	−	6.86792i	0.254892	−	0.441487i
$243$	0.0943715	+	15.5882i	0.00605393	+	0.999982i
$244$	−2.15045	+	3.72469i	−0.137668	+	0.238449i
$245$	19.0867	+	33.0592i	1.21941	+	2.11207i
$246$	14.7123	+	1.52831i	0.938021	+	0.0974418i
$247$	23.0674	−	10.1836i	1.46774	−	0.647969i
$248$	−2.18121	−	3.77797i	−0.138507	−	0.239902i
$249$	−8.65763	−	19.3822i	−0.548655	−	1.22829i
$250$	3.22485	+	5.58561i	0.203958	+	0.353265i
$251$	13.9167	+	24.1045i	0.878415	+	1.52146i	0.853079	+	0.521781i	$0.174732\pi$
$251$	13.9167	+	24.1045i	0.878415	+	1.52146i	0.0253360	+	0.999679i	$0.491934\pi$
$252$	−8.51234	+	9.50007i	−0.536227	+	0.598448i
$253$	−2.03735	−	3.52879i	−0.128087	−	0.221853i
$254$	6.18121	−	10.7062i	0.387844	−	0.671765i
$255$	−8.51864	−	19.0710i	−0.533458	−	1.19427i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.31386	−	5.73977i	0.206713	−	0.358037i	−0.743964	−	0.668219i	$-0.767057\pi$
$257$	3.31386	−	5.73977i	0.206713	−	0.358037i	0.950677	+	0.310182i	$0.100390\pi$
$258$	−6.54068	−	14.6429i	−0.407205	−	0.911625i
$259$	−0.00844933	+	0.0146347i	−0.000525016	+	0.000909354i
$260$	9.96591	+	17.2615i	0.618060	+	1.07051i
$261$	−1.48237	−	4.52495i	−0.0917564	−	0.280088i
$262$	1.25004	+	2.16514i	0.0772279	+	0.133763i
$263$	−7.78820	−	13.4896i	−0.480241	−	0.831802i	0.519502	−	0.854469i	$-0.326117\pi$
$263$	−7.78820	−	13.4896i	−0.480241	−	0.831802i	−0.999743	+	0.0226674i	$0.992784\pi$
$264$	−1.23764	−	2.77075i	−0.0761715	−	0.170528i
$265$	14.1226	+	24.4611i	0.867547	+	1.50264i
$266$	−14.9599	−	10.9409i	−0.917249	−	0.670830i
$267$	−23.4762	−	2.43872i	−1.43672	−	0.149247i
$268$	−3.54085	−	6.13294i	−0.216292	−	0.374629i
$269$	0.444495	−	0.769888i	0.0271013	−	0.0469409i	−0.852157	−	0.523287i	$-0.824706\pi$
$269$	0.444495	−	0.769888i	0.0271013	−	0.0469409i	0.879258	+	0.476346i	$0.158039\pi$
$270$	−3.78597	−	17.4988i	−0.230407	−	1.06494i
$271$	1.17519	−	2.03549i	0.0713876	−	0.123647i	−0.828122	−	0.560548i	$-0.810591\pi$
$271$	1.17519	−	2.03549i	0.0713876	−	0.123647i	0.899510	+	0.436901i	$0.143924\pi$
$272$	3.49991			0.212213
$273$	−42.3745	−	4.40187i	−2.56462	−	0.266413i
$274$	4.94556	+	8.56596i	0.298772	+	0.517489i
$275$	6.01988	−	10.4267i	0.363012	−	0.628756i
$276$	4.00667	+	0.416214i	0.241173	+	0.0250531i
$277$	8.54859	−	14.8066i	0.513635	−	0.889642i	−0.486240	−	0.873825i	$-0.661632\pi$
$277$	8.54859	−	14.8066i	0.513635	−	0.889642i	0.999875	−	0.0158168i	$-0.00503485\pi$
$278$	13.5425			0.812227
$279$	−8.73353	+	9.74693i	−0.522863	+	0.583533i
$280$	7.32517	−	12.6876i	0.437762	−	0.758227i
$281$	25.0363			1.49354			0.746771	−	0.665081i	$-0.231603\pi$
$281$	25.0363			1.49354			0.746771	+	0.665081i	$0.231603\pi$
$282$	12.1723	+	1.26446i	0.724851	+	0.0752977i
$283$	−25.4548			−1.51313			−0.756566	−	0.653918i	$-0.773124\pi$
$283$	−25.4548			−1.51313			−0.756566	+	0.653918i	$0.773124\pi$
$284$	−7.94556	−	13.7621i	−0.471482	−	0.816631i
$285$	24.7557	−	7.99087i	1.46640	−	0.473338i
$286$	5.06756	−	8.77727i	0.299651	−	0.519011i
$287$	18.1555	−	31.4462i	1.07168	−	1.85621i
$288$	2.93594	+	0.616627i	0.173002	+	0.0363351i
$289$	2.37530	+	4.11415i	0.139724	+	0.242009i
$290$	2.73438	+	4.73609i	0.160569	+	0.278113i
$291$	−5.59554	−	0.581266i	−0.328016	−	0.0340744i
$292$	1.65522	+	2.86693i	0.0968645	+	0.167774i
$293$	−3.91307	−	6.77764i	−0.228604	−	0.395954i	0.728791	−	0.684737i	$-0.240083\pi$
$293$	−3.91307	−	6.77764i	−0.228604	−	0.395954i	−0.957395	+	0.288783i	$0.906749\pi$
$294$	7.82627	+	17.5210i	0.456437	+	1.02184i
$295$	−17.5422			−1.02135
$296$	0.00397434			0.000231004
$297$	−6.74328	+	6.11618i	−0.391285	+	0.354897i
$298$	−1.13360	−	1.96345i	−0.0656677	−	0.113740i
$299$	6.72684	+	11.6512i	0.389023	+	0.673808i
$300$	4.85433	+	10.8676i	0.280265	+	0.627439i
$301$	−39.3693			−2.26921
$302$	9.79897			0.563867
$303$	−7.00819	+	9.67055i	−0.402610	+	0.555558i
$304$	−0.469234	+	4.33357i	−0.0269124	+	0.248547i
$305$	−14.8190			−0.848534
$306$	−3.26877	−	9.97796i	−0.186863	−	0.570402i
$307$	−3.59728	+	6.23067i	−0.205308	+	0.355603i	−0.950231	−	0.311547i	$-0.899153\pi$
$307$	−3.59728	+	6.23067i	−0.205308	+	0.355603i	0.744923	+	0.667150i	$0.232486\pi$
$308$	−7.44954			−0.424477
$309$	−12.9966	−	1.35009i	−0.739353	−	0.0768042i
$310$	7.51551	−	13.0172i	0.426852	−	0.739330i
$311$	9.48021	+	16.4202i	0.537574	+	0.931105i	0.999034	+	0.0439440i	$0.0139923\pi$
$311$	9.48021	+	16.4202i	0.537574	+	0.931105i	−0.461460	+	0.887161i	$0.652674\pi$
$312$	4.08639	+	9.14836i	0.231346	+	0.517924i
$313$	−33.2051			−1.87687			−0.938433	−	0.345463i	$-0.887722\pi$
$313$	−33.2051			−1.87687			−0.938433	+	0.345463i	$0.887722\pi$
$314$	−11.4348	−	19.8056i	−0.645301	−	1.11769i
$315$	−43.0126	−	9.03379i	−2.42348	−	0.508997i
$316$	−3.64315			−0.204943
$317$	3.85676			0.216617			0.108309	−	0.994117i	$-0.465457\pi$
$317$	3.85676			0.216617			0.108309	+	0.994117i	$0.465457\pi$
$318$	5.79081	+	12.9641i	0.324733	+	0.726991i
$319$	1.39040	−	2.40825i	0.0778477	−	0.134836i
$320$	−3.44556			−0.192613
$321$	9.64306	−	13.3064i	0.538223	−	0.742690i
$322$	4.94438	−	8.56391i	0.275539	−	0.477248i
$323$	13.9562	−	6.16130i	0.776546	−	0.342824i
$324$	−0.984095	−	8.94604i	−0.0546719	−	0.497002i
$325$	−19.8762	+	34.4266i	−1.10253	+	1.90964i
$326$	−12.3886	−	21.4577i	−0.686141	−	1.18843i
$327$	−5.08428	−	11.3824i	−0.281162	−	0.629447i
$328$	−8.53985			−0.471534
$329$	15.0211	−	26.0173i	0.828138	−	1.43438i
$330$	6.13559	−	8.46645i	0.337753	−	0.466063i
$331$	1.90384	−	3.29755i	0.104644	−	0.181249i	−0.808948	−	0.587880i	$-0.799963\pi$
$331$	1.90384	−	3.29755i	0.104644	−	0.181249i	0.913593	+	0.406630i	$0.133296\pi$
$332$	6.12796	+	10.6139i	0.336315	+	0.582515i
$333$	−0.00371186	−	0.0113305i	−0.000203409	−	0.000620908i
$334$	17.3977			0.951959
$335$	12.2002	−	21.1314i	0.666570	−	1.15453i
$336$	4.32158	−	5.96331i	0.235761	−	0.325325i
$337$	−3.52044			−0.191771			−0.0958853	−	0.995392i	$-0.530568\pi$
$337$	−3.52044			−0.191771			−0.0958853	+	0.995392i	$0.530568\pi$
$338$	−10.2319	+	17.7221i	−0.556540	+	0.963955i
$339$	15.4412	+	1.60404i	0.838652	+	0.0871194i
$340$	6.02958	+	10.4435i	0.327000	+	0.566381i
$341$	−7.64311			−0.413898
$342$	12.7929	−	2.70962i	0.691760	−	0.146520i
$343$	17.3438			0.936477
$344$	4.62956	+	8.01864i	0.249609	+	0.432336i
$345$	5.66066	+	12.6727i	0.304760	+	0.682277i
$346$	4.01789	−	6.95919i	0.216003	−	0.374129i
$347$	−17.3132			−0.929420			−0.464710	−	0.885463i	$-0.653841\pi$
$347$	−17.3132			−0.929420			−0.464710	+	0.885463i	$0.653841\pi$
$348$	1.12120	+	2.51007i	0.0601026	+	0.134554i
$349$	−10.4196	+	18.0472i	−0.557747	+	0.966046i	0.439937	+	0.898028i	$0.355001\pi$
$349$	−10.4196	+	18.0472i	−0.557747	+	0.966046i	−0.997684	+	0.0680172i	$0.978333\pi$
$350$	29.2189			1.56182
$351$	22.2647	−	20.1941i	1.18840	−	1.07788i
$352$	0.876015	+	1.51730i	0.0466918	+	0.0808725i
$353$	−5.77144	+	9.99643i	−0.307183	+	0.532056i	−0.977745	−	0.209797i	$-0.932720\pi$
$353$	−5.77144	+	9.99643i	−0.307183	+	0.532056i	0.670562	+	0.741853i	$0.266053\pi$
$354$	−8.77111	−	0.911145i	−0.466179	−	0.0484268i
$355$	27.3769	−	47.4182i	1.45302	−	2.51670i
$356$	13.6270			0.722227
$357$	−25.6374	−	2.66322i	−1.35688	−	0.140953i
$358$	4.98347	+	8.63163i	0.263385	+	0.456196i
$359$	−5.13533	+	8.89464i	−0.271032	+	0.469441i	−0.969126	−	0.246564i	$-0.920698\pi$
$359$	−5.13533	+	8.89464i	−0.271032	+	0.469441i	0.698094	+	0.716006i	$0.254032\pi$
$360$	3.21801	+	9.82301i	0.169604	+	0.517718i
$361$	5.75777	+	18.1066i	0.303040	+	0.952978i
$362$	−9.39797	+	16.2778i	−0.493946	+	0.855540i
$363$	13.6623	+	1.41924i	0.717086	+	0.0744910i
$364$	24.5966			1.28921
$365$	−5.70317	+	9.87818i	−0.298517	+	0.517047i
$366$	−7.40950	−	0.769701i	−0.387301	−	0.0402329i
$367$	11.9980			0.626292			0.313146	−	0.949705i	$-0.398617\pi$
$367$	11.9980			0.626292			0.313146	+	0.949705i	$0.398617\pi$
$368$	−2.32570			−0.121236
$369$	7.97585	+	24.3464i	0.415206	+	1.26742i
$370$	0.00684691	+	0.0118592i	0.000355954	+	0.000616530i
$371$	34.8557			1.80962
$372$	4.43387	−	6.11826i	0.229885	−	0.317217i
$373$	−17.7023	−	30.6614i	−0.916593	−	1.58759i	−0.804552	−	0.593882i	$-0.797595\pi$
$373$	−17.7023	−	30.6614i	−0.916593	−	1.58759i	−0.112040	−	0.993704i	$-0.535739\pi$
$374$	3.06598	−	5.31043i	0.158538	−	0.274596i
$375$	−6.55533	+	9.04565i	−0.338516	+	0.467115i
$376$	−7.06551			−0.364376
$377$	−4.59078	+	7.95147i	−0.236437	+	0.409521i
$378$	−21.0371	−	6.75097i	−1.08203	−	0.347233i
$379$	−9.15132			−0.470072			−0.235036	−	0.971987i	$-0.575521\pi$
$379$	−9.15132			−0.470072			−0.235036	+	0.971987i	$0.575521\pi$
$380$	−13.7395	+	6.06562i	−0.704822	+	0.311160i
$381$	21.2978	+	2.21242i	1.09112	+	0.113345i
$382$	11.7533			0.601352
$383$	−14.2558			−0.728437			−0.364218	−	0.931314i	$-0.618664\pi$
$383$	−14.2558			−0.728437			−0.364218	+	0.931314i	$0.618664\pi$
$384$	−1.72278	−	0.178963i	−0.0879153	−	0.00913266i
$385$	−12.8339	−	22.2290i	−0.654077	−	1.13289i
$386$	5.91948	+	10.2528i	0.301294	+	0.521856i
$387$	18.5366	−	20.6876i	0.942271	−	1.05161i
$388$	3.24797			0.164891
$389$	−12.6922			−0.643522			−0.321761	−	0.946821i	$-0.604275\pi$
$389$	−12.6922			−0.643522			−0.321761	+	0.946821i	$0.604275\pi$
$390$	−20.2582	+	27.9542i	−1.02582	+	1.41552i
$391$	4.06988	+	7.04924i	0.205823	+	0.356495i
$392$	−5.53951	−	9.59472i	−0.279788	−	0.484606i
$393$	−2.54103	+	3.50635i	−0.128178	+	0.176872i
$394$	4.39922	+	7.61968i	0.221630	+	0.383874i
$395$	−6.27635	−	10.8710i	−0.315797	−	0.546977i
$396$	3.50754	−	3.91454i	0.176261	−	0.196713i
$397$	−2.49777	+	4.32627i	−0.125360	+	0.217129i	−0.921873	−	0.387491i	$-0.873342\pi$
$397$	−2.49777	+	4.32627i	−0.125360	+	0.217129i	0.796514	+	0.604620i	$0.206675\pi$
$398$	−8.67709	+	15.0292i	−0.434943	+	0.753344i
$399$	6.73480	−	31.3871i	0.337162	−	1.57132i
$400$	−3.43594	−	5.95123i	−0.171797	−	0.297562i
$401$	−28.0876			−1.40263			−0.701315	−	0.712852i	$-0.747403\pi$
$401$	−28.0876			−1.40263			−0.701315	+	0.712852i	$0.747403\pi$
$402$	7.19768	−	9.93202i	0.358988	−	0.495364i
$403$	25.2357			1.25708
$404$	3.44763	−	5.97148i	0.171526	−	0.297092i
$405$	24.9991	−	18.3485i	1.24221	−	0.911746i
$406$	6.74865			0.334930
$407$	0.00348158	−	0.00603027i	0.000172575	−	0.000298909i
$408$	2.47235	+	5.53495i	0.122400	+	0.274021i
$409$	12.3654	−	21.4176i	0.611432	−	1.05903i	−0.379567	−	0.925164i	$-0.623927\pi$
$409$	12.3654	−	21.4176i	0.611432	−	1.05903i	0.990999	−	0.133867i	$-0.0427396\pi$
$410$	−14.7123	−	25.4824i	−0.726588	−	1.25849i
$411$	−10.0531	+	13.8722i	−0.495883	+	0.684265i
$412$	7.54399			0.371666
$413$	−10.8239	+	18.7475i	−0.532607	+	0.922503i
$414$	2.17211	+	6.63038i	0.106753	+	0.325865i
$415$	−21.1143	+	36.5710i	−1.03646	+	1.79520i
$416$	−2.89239	−	5.00977i	−0.141811	−	0.245624i
$417$	9.56649	+	21.4169i	0.468473	+	1.04879i
$418$	6.16428	+	4.50824i	0.301505	+	0.220505i
$419$	−7.29743	−	12.6395i	−0.356503	−	0.617481i	0.630871	−	0.775888i	$-0.282698\pi$
$419$	−7.29743	−	12.6395i	−0.356503	−	0.617481i	−0.987374	+	0.158407i	$0.949364\pi$
$420$	25.2393	+	2.62186i	1.23155	+	0.127934i
$421$	−18.4368	−	31.9334i	−0.898553	−	1.55634i	−0.829345	−	0.558738i	$-0.811286\pi$
$421$	−18.4368	−	31.9334i	−0.898553	−	1.55634i	−0.0692086	−	0.997602i	$-0.522047\pi$
$422$	−7.72073	−	13.3727i	−0.375839	−	0.650973i
$423$	6.59888	+	20.1432i	0.320849	+	0.979394i
$424$	−4.09880	−	7.09932i	−0.199055	−	0.344774i
$425$	−12.0255	+	20.8288i	−0.583323	+	1.01034i
$426$	16.1514	−	22.2871i	0.782536	−	1.07982i
$427$	−9.14359	+	15.8372i	−0.442489	+	0.766414i
$428$	−4.74384	+	8.21658i	−0.229302	+	0.397163i
$429$	17.4606	+	1.81381i	0.843005	+	0.0875715i
$430$	−15.9514	+	27.6287i	−0.769247	+	1.33237i
$431$	−3.37892	−	5.85247i	−0.162757	−	0.281903i	0.773099	−	0.634285i	$-0.218705\pi$
$431$	−3.37892	−	5.85247i	−0.162757	−	0.281903i	−0.935856	+	0.352381i	$0.885372\pi$
$432$	1.09880	+	5.07865i	0.0528658	+	0.244346i
$433$	−15.4170	−	26.7030i	−0.740892	−	1.28326i	−0.952090	−	0.305819i	$-0.901070\pi$
$433$	−15.4170	−	26.7030i	−0.740892	−	1.28326i	0.211198	−	0.977443i	$-0.432264\pi$
$434$	−9.27440	−	16.0637i	−0.445186	−	0.771084i
$435$	−5.55833	+	7.66989i	−0.266501	+	0.367743i
$436$	3.59871	+	6.23315i	0.172347	+	0.298514i
$437$	−9.27396	+	4.09420i	−0.443634	+	0.195852i
$438$	−3.36466	+	4.64287i	−0.160770	+	0.221845i
$439$	−2.37901	−	4.12057i	−0.113544	−	0.196664i	0.803653	−	0.595098i	$-0.202887\pi$
$439$	−2.37901	−	4.12057i	−0.113544	−	0.196664i	−0.917197	+	0.398435i	$0.869554\pi$
$440$	−3.01836	+	5.22796i	−0.143895	+	0.249233i
$441$	−22.1801	+	24.7537i	−1.05619	+	1.17875i
$442$	−10.1231	+	17.5338i	−0.481508	+	0.833996i
$443$	5.91543			0.281051			0.140525	−	0.990077i	$-0.455121\pi$
$443$	5.91543			0.281051			0.140525	+	0.990077i	$0.455121\pi$
$444$	0.00280749	+	0.00628523i	0.000133237	+	0.000298284i
$445$	23.4762	+	40.6620i	1.11288	+	1.92757i
$446$	9.71397	−	16.8251i	0.459970	−	0.796691i
$447$	2.30433	−	3.17973i	0.108991	−	0.150396i
$448$	−2.12597	+	3.68229i	−0.100443	+	0.173972i
$449$	39.6815			1.87269			0.936343	−	0.351088i	$-0.114188\pi$
$449$	39.6815			1.87269			0.936343	+	0.351088i	$0.114188\pi$
$450$	−13.7574	+	15.3538i	−0.648532	+	0.723784i
$451$	−7.48103	+	12.9575i	−0.352268	+	0.610146i
$452$	−8.96297			−0.421583
$453$	6.92203	+	15.4966i	0.325225	+	0.728094i
$454$	12.7212			0.597037
$455$	42.3745	+	73.3948i	1.98655	+	3.44080i
$456$	−7.18480	+	2.31918i	−0.336459	+	0.108605i
$457$	−9.59672	+	16.6220i	−0.448916	+	0.777545i	−0.998316	−	0.0580146i	$-0.981523\pi$
$457$	−9.59672	+	16.6220i	−0.448916	+	0.777545i	0.549400	+	0.835559i	$0.314856\pi$
$458$	2.24799	−	3.89363i	0.105042	−	0.181938i
$459$	13.4706	−	12.2179i	0.628754	−	0.570282i
$460$	−4.00667	−	6.93976i	−0.186812	−	0.323568i
$461$	5.85908	+	10.1482i	0.272885	+	0.472650i	0.969599	−	0.244698i	$-0.0786889\pi$
$461$	5.85908	+	10.1482i	0.272885	+	0.472650i	−0.696715	+	0.717348i	$0.745356\pi$
$462$	−5.26238	−	11.7811i	−0.244828	−	0.548106i
$463$	−14.6614	−	25.3942i	−0.681371	−	1.18017i	−0.974563	−	0.224116i	$-0.928051\pi$
$463$	−14.6614	−	25.3942i	−0.681371	−	1.18017i	0.293192	−	0.956054i	$-0.405283\pi$
$464$	−0.793596	−	1.37455i	−0.0368418	−	0.0638118i
$465$	25.8951	+	2.68999i	1.20086	+	0.124745i
$466$	7.63615			0.353738
$467$	10.6983			0.495060			0.247530	−	0.968880i	$-0.420381\pi$
$467$	10.6983			0.495060			0.247530	+	0.968880i	$0.420381\pi$
$468$	−11.5811	+	12.9249i	−0.535335	+	0.597453i
$469$	−15.0555	−	26.0769i	−0.695199	−	1.20412i
$470$	−12.1723	−	21.0831i	−0.561467	−	0.972489i
$471$	23.2440	−	32.0743i	1.07103	−	1.47790i
$472$	5.09125			0.234344
$473$	16.2223			0.745901
$474$	−2.57354	−	5.76147i	−0.118206	−	0.264633i
$475$	−24.1778	−	17.6824i	−1.10935	−	0.811325i
$476$	14.8814			0.682089
$477$	−16.4115	+	18.3158i	−0.751430	+	0.838622i
$478$	−4.12630	+	7.14697i	−0.188733	+	0.326895i
$479$	−20.5697			−0.939856			−0.469928	−	0.882705i	$-0.655720\pi$
$479$	−20.5697			−0.939856			−0.469928	+	0.882705i	$0.655720\pi$
$480$	−2.43396	−	5.44899i	−0.111094	−	0.248711i
$481$	−0.0114953	+	0.0199105i	−0.000524142	+	0.000907841i
$482$	5.82898	+	10.0961i	0.265503	+	0.459865i
$483$	17.0362	+	1.76972i	0.775172	+	0.0805250i
$484$	−7.93039			−0.360472
$485$	5.59554	+	9.69176i	0.254080	+	0.440080i
$486$	13.4526	−	7.87581i	0.610221	−	0.357254i
$487$	−23.9788			−1.08658			−0.543291	−	0.839545i	$-0.682822\pi$
$487$	−23.9788			−1.08658			−0.543291	+	0.839545i	$0.682822\pi$
$488$	4.30090			0.194692
$489$	25.1830	−	34.7498i	1.13881	−	1.57144i
$490$	19.0867	−	33.0592i	0.862251	−	1.49346i
$491$	−17.5108			−0.790251			−0.395126	−	0.918627i	$-0.629299\pi$
$491$	−17.5108			−0.790251			−0.395126	+	0.918627i	$0.629299\pi$
$492$	−6.03258	−	13.5054i	−0.271970	−	0.608869i
$493$	−2.77752	+	4.81080i	−0.125093	+	0.216668i
$494$	−20.3530	−	14.8851i	−0.915724	−	0.669714i
$495$	17.7235	+	3.72241i	0.796612	+	0.167310i
$496$	−2.18121	+	3.77797i	−0.0979394	+	0.169636i
$497$	−33.7841	−	58.5157i	−1.51542	−	2.62479i
$498$	−12.4566	+	17.1888i	−0.558195	+	0.770249i
$499$	−10.0675			−0.450681			−0.225341	−	0.974280i	$-0.572350\pi$
$499$	−10.0675			−0.450681			−0.225341	+	0.974280i	$0.572350\pi$
$500$	3.22485	−	5.58561i	0.144220	−	0.249796i
$501$	12.2898	+	27.5136i	0.549068	+	1.22922i
$502$	13.9167	−	24.1045i	0.621133	−	1.07583i
$503$	2.44636	+	4.23722i	0.109078	+	0.188928i	0.915397	−	0.402552i	$-0.131877\pi$
$503$	2.44636	+	4.23722i	0.109078	+	0.188928i	−0.806319	+	0.591481i	$0.798544\pi$
$504$	12.4835	+	2.62186i	0.556058	+	0.116787i
$505$	23.7581			1.05722
$506$	−2.03735	+	3.52879i	−0.0905713	+	0.156874i
$507$	−35.2545	−	3.66224i	−1.56571	−	0.162646i
$508$	−12.3624			−0.548494
$509$	6.99590	−	12.1172i	0.310088	−	0.537088i	−0.668293	−	0.743898i	$-0.732975\pi$
$509$	6.99590	−	12.1172i	0.310088	−	0.537088i	0.978381	+	0.206810i	$0.0663083\pi$
$510$	−12.2567	+	16.9129i	−0.542734	+	0.748914i
$511$	7.03791	+	12.1900i	0.311339	+	0.539255i
$512$	1.00000			0.0441942
$513$	13.3221	+	18.3173i	0.588184	+	0.808727i
$514$	−6.62772			−0.292336
$515$	12.9966	+	22.5108i	0.572701	+	0.991946i
$516$	−9.41076	+	12.9858i	−0.414285	+	0.571669i
$517$	−6.18949	+	10.7205i	−0.272214	+	0.471488i
$518$	0.0168987			0.000742484
$519$	13.8439	+	1.43811i	0.607679	+	0.0631259i
$520$	9.96591	−	17.2615i	0.437034	−	0.756965i
$521$	−31.8258			−1.39432			−0.697158	−	0.716918i	$-0.745552\pi$
$521$	−31.8258			−1.39432			−0.697158	+	0.716918i	$0.745552\pi$
$522$	−3.17754	+	3.54625i	−0.139077	+	0.155215i
$523$	−2.58242	−	4.47288i	−0.112921	−	0.195585i	0.804026	−	0.594595i	$-0.202687\pi$
$523$	−2.58242	−	4.47288i	−0.112921	−	0.195585i	−0.916947	+	0.399009i	$0.869354\pi$
$524$	1.25004	−	2.16514i	0.0546084	−	0.0945845i
$525$	20.6403	+	46.2083i	0.900818	+	2.01670i
$526$	−7.78820	+	13.4896i	−0.339582	+	0.588173i
$527$	15.2681			0.665090
$528$	−1.78072	+	2.45721i	−0.0774960	+	0.106936i
$529$	8.79556	+	15.2343i	0.382415	+	0.662363i
$530$	14.1226	−	24.4611i	0.613449	−	1.06252i
$531$	−4.75501	−	14.5147i	−0.206350	−	0.629886i
$532$	−1.99516	+	18.4261i	−0.0865010	+	0.798872i
$533$	24.7006	−	42.7827i	1.06990	−	1.85312i
$534$	9.62613	+	21.5504i	0.416563	+	0.932576i
$535$	−32.6904			−1.41333
$536$	−3.54085	+	6.13294i	−0.152942	+	0.264903i
$537$	−10.1302	+	13.9785i	−0.437149	+	0.603219i
$538$	−0.888990			−0.0383271
$539$	−19.4108			−0.836082
$540$	−13.2614	+	12.0281i	−0.570680	+	0.517609i
$541$	0.340233	+	0.589301i	0.0146278	+	0.0253360i	0.873247	−	0.487278i	$-0.162010\pi$
$541$	0.340233	+	0.589301i	0.0146278	+	0.0253360i	−0.858619	+	0.512615i	$0.828677\pi$
$542$	−2.35038			−0.100957
$543$	−32.3813	−	3.36377i	−1.38961	−	0.144353i
$544$	−1.74996	−	3.03101i	−0.0750288	−	0.129954i
$545$	−12.3996	+	21.4767i	−0.531139	+	0.919960i
$546$	17.3751	+	38.8983i	0.743586	+	1.66469i
$547$	−18.0485			−0.771699			−0.385849	−	0.922562i	$-0.626092\pi$
$547$	−18.0485			−0.771699			−0.385849	+	0.922562i	$0.626092\pi$
$548$	4.94556	−	8.56596i	0.211264	−	0.365920i
$549$	−4.01686	−	12.2615i	−0.171435	−	0.523308i
$550$	−12.0398			−0.513377
$551$	−5.58432	−	4.08409i	−0.237900	−	0.173988i
$552$	−1.64288	−	3.67799i	−0.0699258	−	0.156546i
$553$	−15.4905			−0.658722
$554$	−17.0972			−0.726390
$555$	−0.0139181	+	0.0192054i	−0.000590789	+	0.000815226i
$556$	−6.77126	−	11.7282i	−0.287166	−	0.497385i
$557$	0.771491	+	1.33626i	0.0326891	+	0.0566192i	0.881907	−	0.471423i	$-0.156260\pi$
$557$	0.771491	+	1.33626i	0.0326891	+	0.0566192i	−0.849218	+	0.528042i	$0.822926\pi$
$558$	12.8079	+	2.68999i	0.542200	+	0.113876i
$559$	−53.5620			−2.26543
$560$	−14.6503			−0.619089
$561$	10.5640	+	1.09739i	0.446013	+	0.0463319i
$562$	−12.5182	−	21.6821i	−0.528047	−	0.914604i
$563$	2.80884	+	4.86506i	0.118379	+	0.205038i	0.919125	−	0.393965i	$-0.128897\pi$
$563$	2.80884	+	4.86506i	0.118379	+	0.205038i	−0.800747	+	0.599003i	$0.795564\pi$
$564$	−4.99110	−	11.1738i	−0.210163	−	0.470500i
$565$	−15.4412	−	26.7450i	−0.649617	−	1.12517i
$566$	12.7274	+	22.0445i	0.534973	+	0.926600i
$567$	−4.18432	−	38.0380i	−0.175725	−	1.59745i
$568$	−7.94556	+	13.7621i	−0.333388	+	0.577446i
$569$	15.3236	−	26.5412i	0.642397	−	1.11266i	−0.342499	−	0.939518i	$-0.611273\pi$
$569$	15.3236	−	26.5412i	0.642397	−	1.11266i	0.984896	−	0.173146i	$-0.0553934\pi$
$570$	−19.2981	−	17.4436i	−0.808310	−	0.730633i
$571$	14.2954	+	24.7603i	0.598243	+	1.03619i	0.993080	+	0.117436i	$0.0374676\pi$
$571$	14.2954	+	24.7603i	0.598243	+	1.03619i	−0.394837	+	0.918751i	$0.629199\pi$
$572$	−10.1351			−0.423771
$573$	8.30259	+	18.5873i	0.346846	+	0.776497i
$574$	−36.3109			−1.51559
$575$	7.99098	−	13.8408i	0.333247	−	0.577201i
$576$	−0.933957	−	2.85092i	−0.0389149	−	0.118788i
$577$	25.8441			1.07590			0.537952	−	0.842975i	$-0.319198\pi$
$577$	25.8441			1.07590			0.537952	+	0.842975i	$0.319198\pi$
$578$	2.37530	−	4.11415i	0.0987996	−	0.171126i
$579$	−12.0328	+	16.6040i	−0.500068	+	0.690040i
$580$	2.73438	−	4.73609i	0.113539	−	0.196655i
$581$	26.0557	+	45.1299i	1.08097	+	1.87230i
$582$	2.29438	+	5.13651i	0.0951050	+	0.212915i
$583$	−14.3624			−0.594831
$584$	1.65522	−	2.86693i	0.0684936	−	0.118634i
$585$	−58.5187	−	12.2905i	−2.41945	−	0.508150i
$586$	−3.91307	+	6.77764i	−0.161647	+	0.279982i
$587$	12.3590	+	21.4064i	0.510110	+	0.883537i	0.999931	+	0.0117142i	$0.00372883\pi$
$587$	12.3590	+	21.4064i	0.510110	+	0.883537i	−0.489821	+	0.871823i	$0.662938\pi$
$588$	11.2605	−	15.5382i	0.464374	−	0.640786i
$589$	−2.04700	+	18.9049i	−0.0843452	+	0.778962i
$590$	8.77111	+	15.1920i	0.361101	+	0.625445i
$591$	−8.94253	+	12.3397i	−0.367847	+	0.507589i
$592$	−0.00198717	−	0.00344188i	−8.16721e−5	−	0.000141460i
$593$	10.1971	+	17.6618i	0.418743	+	0.725284i	0.995813	−	0.0914105i	$-0.0291375\pi$
$593$	10.1971	+	17.6618i	0.418743	+	0.725284i	−0.577070	+	0.816694i	$0.695804\pi$
$594$	8.66841	+	2.78177i	0.355669	+	0.114137i
$595$	25.6374	+	44.4054i	1.05103	+	1.82044i
$596$	−1.13360	+	1.96345i	−0.0464341	+	0.0804262i
$597$	−29.8974	−	3.10575i	−1.22362	−	0.127110i
$598$	6.72684	−	11.6512i	0.275081	−	0.476454i
$599$	−1.32544	+	2.29573i	−0.0541560	+	0.0938009i	−0.891832	−	0.452366i	$-0.850580\pi$
$599$	−1.32544	+	2.29573i	−0.0541560	+	0.0938009i	0.837677	+	0.546167i	$0.183913\pi$
$600$	6.98443	−	9.63776i	0.285138	−	0.393460i
$601$	2.75361	−	4.76939i	0.112322	−	0.194548i	−0.804384	−	0.594110i	$-0.797504\pi$
$601$	2.75361	−	4.76939i	0.112322	−	0.194548i	0.916706	+	0.399562i	$0.130838\pi$
$602$	19.6846	+	34.0948i	0.802286	+	1.38960i
$603$	20.7915	+	4.36677i	0.846695	+	0.177829i
$604$	−4.89948	−	8.48616i	−0.199357	−	0.345297i
$605$	−13.6623	−	23.6638i	−0.555452	−	0.962072i
$606$	11.8790	+	1.23400i	0.482553	+	0.0501277i
$607$	−3.95941	−	6.85791i	−0.160708	−	0.278354i	0.774415	−	0.632678i	$-0.218044\pi$
$607$	−3.95941	−	6.85791i	−0.160708	−	0.278354i	−0.935123	+	0.354324i	$0.884711\pi$
$608$	3.98760	−	1.76042i	0.161718	−	0.0713943i
$609$	4.76727	+	10.6727i	0.193180	+	0.432479i
$610$	7.40950	+	12.8336i	0.300002	+	0.519619i
$611$	20.4362	−	35.3966i	0.826761	−	1.43199i
$612$	−7.00678	+	7.81982i	−0.283232	+	0.316097i
$613$	−7.09258	+	12.2847i	−0.286466	+	0.496174i	−0.972964	−	0.230958i	$-0.925814\pi$
$613$	−7.09258	+	12.2847i	−0.286466	+	0.496174i	0.686497	+	0.727132i	$0.259147\pi$
$614$	7.19456			0.290349
$615$	29.9064	−	41.2677i	1.20594	−	1.66407i
$616$	3.72477	+	6.45149i	0.150075	+	0.259938i
$617$	3.10419	−	5.37662i	0.124970	−	0.216454i	−0.796751	−	0.604307i	$-0.793450\pi$
$617$	3.10419	−	5.37662i	0.124970	−	0.216454i	0.921721	+	0.387853i	$0.126783\pi$
$618$	5.32911	+	11.9305i	0.214368	+	0.479914i
$619$	−15.9788	+	27.6762i	−0.642244	+	1.11240i	0.342687	+	0.939450i	$0.388663\pi$
$619$	−15.9788	+	27.6762i	−0.642244	+	1.11240i	−0.984931	+	0.172949i	$0.944670\pi$
$620$	−15.0310			−0.603660
$621$	−8.95125	+	8.11881i	−0.359201	+	0.325797i
$622$	9.48021	−	16.4202i	0.380122	−	0.658391i
$623$	57.9410			2.32136
$624$	5.87952	−	8.11310i	0.235369	−	0.324784i
$625$	−12.1366			−0.485463
$626$	16.6026	+	28.7565i	0.663572	+	1.14934i
$627$	−2.77510	+	12.9332i	−0.110827	+	0.516501i
$628$	−11.4348	+	19.8056i	−0.456297	+	0.790329i
$629$	−0.00695492	+	0.0120463i	−0.000277311	+	0.000480316i
$630$	13.6828	+	41.7669i	0.545135	+	1.66403i
$631$	−6.41560	−	11.1121i	−0.255401	−	0.442367i	0.709603	−	0.704601i	$-0.248874\pi$
$631$	−6.41560	−	11.1121i	−0.255401	−	0.442367i	−0.965004	+	0.262234i	$0.915541\pi$
$632$	1.82158	+	3.15506i	0.0724584	+	0.125502i
$633$	15.6943	−	21.6565i	0.623794	−	0.860768i
$634$	−1.92838	−	3.34005i	−0.0765858	−	0.132650i
$635$	−21.2978	−	36.8888i	−0.845175	−	1.46389i
$636$	8.33184	−	11.4970i	0.330379	−	0.455887i
$637$	64.0898			2.53933
$638$	−2.78081			−0.110093
$639$	46.6555	+	9.79890i	1.84566	+	0.387638i
$640$	1.72278	+	2.98394i	0.0680989	+	0.117951i
$641$	−5.44439	−	9.42997i	−0.215041	−	0.372461i	0.738245	−	0.674533i	$-0.235655\pi$
$641$	−5.44439	−	9.42997i	−0.215041	−	0.372461i	−0.953285	+	0.302072i	$0.902322\pi$
$642$	−16.3452	−	1.69794i	−0.645094	−	0.0670125i
$643$	43.5550			1.71764			0.858821	−	0.512276i	$-0.171197\pi$
$643$	43.5550			1.71764			0.858821	+	0.512276i	$0.171197\pi$
$644$	−9.88875			−0.389672
$645$	−54.9616	−	5.70943i	−2.16411	−	0.224808i
$646$	−12.3140	−	9.00581i	−0.484487	−	0.354329i
$647$	32.0459			1.25986			0.629928	−	0.776654i	$-0.283084\pi$
$647$	32.0459			1.25986			0.629928	+	0.776654i	$0.283084\pi$
$648$	−7.25545	+	5.32527i	−0.285021	+	0.209196i
$649$	4.46002	−	7.72497i	0.175071	−	0.303232i
$650$	39.7524			1.55922
$651$	18.8526	−	26.0145i	0.738890	−	1.01959i
$652$	−12.3886	+	21.4577i	−0.485175	+	0.840348i
$653$	−24.6582	−	42.7092i	−0.964949	−	1.67134i	−0.709751	−	0.704453i	$-0.751192\pi$
$653$	−24.6582	−	42.7092i	−0.964949	−	1.67134i	−0.255199	−	0.966889i	$-0.582141\pi$
$654$	−7.31529	+	10.0943i	−0.286050	+	0.394719i
$655$	8.61420			0.336585
$656$	4.26992	+	7.39572i	0.166712	+	0.288754i
$657$	−9.71928	−	2.04131i	−0.379185	−	0.0796391i
$658$	−30.0421			−1.17116
$659$	40.2862			1.56933			0.784663	−	0.619922i	$-0.212836\pi$
$659$	40.2862			1.56933			0.784663	+	0.619922i	$0.212836\pi$
$660$	−10.4000	−	1.08035i	−0.404818	−	0.0420526i
$661$	2.73570	−	4.73838i	0.106406	−	0.184301i	−0.807905	−	0.589312i	$-0.799399\pi$
$661$	2.73570	−	4.73838i	0.106406	−	0.184301i	0.914312	+	0.405011i	$0.132732\pi$
$662$	−3.80768			−0.147990
$663$	−34.8798	−	3.62332i	−1.35462	−	0.140718i
$664$	6.12796	−	10.6139i	0.237811	−	0.411901i
$665$	−58.4196	+	25.7907i	−2.26542	+	1.00012i
$666$	−0.00795657	+	0.00887982i	−0.000308311	+	0.000344086i
$667$	1.84567	−	3.19679i	0.0714646	−	0.123780i
$668$	−8.69884	−	15.0668i	−0.336568	−	0.582954i
$669$	33.4701	+	3.47688i	1.29403	+	0.134424i
$670$	−24.4005			−0.942672
$671$	3.76765	−	6.52576i	0.145449	−	0.251924i
$672$	−7.32517	−	0.760940i	−0.282574	−	0.0293539i
$673$	−4.22574	+	7.31920i	−0.162890	+	0.282135i	−0.935904	−	0.352255i	$-0.885415\pi$
$673$	−4.22574	+	7.31920i	−0.162890	+	0.282135i	0.773014	+	0.634389i	$0.218748\pi$
$674$	1.76022	+	3.04879i	0.0678011	+	0.117435i
$675$	−33.9996	−	10.9108i	−1.30865	−	0.419955i
$676$	20.4637			0.787066
$677$	−12.3059	+	21.3145i	−0.472955	+	0.819183i	−0.999521	−	0.0309518i	$-0.990146\pi$
$677$	−12.3059	+	21.3145i	−0.472955	+	0.819183i	0.526565	+	0.850135i	$0.323480\pi$
$678$	−6.33148	−	14.1745i	−0.243159	−	0.544369i
$679$	13.8102			0.529986
$680$	6.02958	−	10.4435i	0.231224	−	0.400492i
$681$	8.98633	+	20.1180i	0.344357	+	0.770925i
$682$	3.82155	+	6.61913i	0.146335	+	0.253459i
$683$	−31.4126			−1.20197			−0.600985	−	0.799260i	$-0.705225\pi$
$683$	−31.4126			−1.20197			−0.600985	+	0.799260i	$0.705225\pi$
$684$	−8.74304	−	9.72415i	−0.334299	−	0.371812i
$685$	34.0805			1.30215
$686$	−8.67190	−	15.0202i	−0.331095	−	0.573473i
$687$	7.74559	+	0.804614i	0.295513	+	0.0306979i
$688$	4.62956	−	8.01864i	0.176500	−	0.305708i
$689$	47.4213			1.80661
$690$	8.14458	−	11.2386i	0.310059	−	0.427848i
$691$	−7.30088	+	12.6455i	−0.277738	+	0.481057i	−0.970822	−	0.239800i	$-0.922918\pi$
$691$	−7.30088	+	12.6455i	−0.277738	+	0.481057i	0.693084	+	0.720857i	$0.256252\pi$
$692$	−8.03578			−0.305475
$693$	14.9139	−	16.6444i	0.566531	−	0.632269i
$694$	8.65659	+	14.9936i	0.328600	+	0.569151i
$695$	23.3308	−	40.4101i	0.884988	−	1.53284i
$696$	1.61318	−	2.22602i	0.0611476	−	0.0843771i
$697$	14.9444	−	25.8844i	0.566058	−	0.980441i
$698$	20.8391			0.788773
$699$	5.39420	+	12.0762i	0.204027	+	0.456764i
$700$	−14.6094	−	25.3043i	−0.552185	−	0.956413i
$701$	−2.00754	+	3.47717i	−0.0758238	+	0.131331i	−0.901444	−	0.432895i	$-0.857492\pi$
$701$	−2.00754	+	3.47717i	−0.0758238	+	0.131331i	0.825620	+	0.564226i	$0.190825\pi$
$702$	−28.6210	−	9.18472i	−1.08023	−	0.346655i
$703$	−0.0139832	−	0.0102266i	−0.000527385	−	0.000385703i
$704$	0.876015	−	1.51730i	0.0330161	−	0.0571855i
$705$	24.7433	−	34.1431i	0.931887	−	1.28590i
$706$	11.5429			0.434422
$707$	14.6591	−	25.3904i	0.551314	−	0.954904i
$708$	3.59648	+	8.05158i	0.135164	+	0.302597i
$709$	−3.26417			−0.122588			−0.0612942	−	0.998120i	$-0.519523\pi$
$709$	−3.26417			−0.122588			−0.0612942	+	0.998120i	$0.519523\pi$
$710$	−54.7538			−2.05487
$711$	7.29354	−	8.13985i	0.273529	−	0.305268i
$712$	−6.81348	−	11.8013i	−0.255346	−	0.442272i
$713$	−10.1457			−0.379960
$714$	10.5123	+	23.5343i	0.393413	+	0.880749i
$715$	−17.4606	−	30.2426i	−0.652989	−	1.13101i
$716$	4.98347	−	8.63163i	0.186241	−	0.322579i
$717$	−14.2174	−	1.47691i	−0.530960	−	0.0551562i
$718$	10.2707			0.383297
$719$	12.1259	−	21.0027i	0.452220	−	0.783269i	−0.546303	−	0.837588i	$-0.683965\pi$
$719$	12.1259	−	21.0027i	0.452220	−	0.783269i	0.998524	+	0.0543187i	$0.0172987\pi$
$720$	6.89797	−	7.69838i	0.257072	−	0.286902i
$721$	32.0766			1.19460
$722$	12.8019	−	14.0397i	0.476436	−	0.522502i
$723$	−11.8489	+	16.3502i	−0.440665	+	0.608070i
$724$	18.7959			0.698545
$725$	10.9070			0.405076
$726$	−5.60206	−	12.5415i	−0.207912	−	0.465460i
$727$	−1.49094	−	2.58239i	−0.0552961	−	0.0957756i	0.837052	−	0.547123i	$-0.184277\pi$
$727$	−1.49094	−	2.58239i	−0.0552961	−	0.0957756i	−0.892348	+	0.451347i	$0.850944\pi$
$728$	−12.2983	−	21.3013i	−0.455805	−	0.789477i
$729$	21.9582	+	15.7111i	0.813266	+	0.581892i
$730$	11.4063			0.422167
$731$	−32.4061			−1.19858
$732$	3.03817	+	6.80167i	0.112294	+	0.251397i
$733$	24.4941	+	42.4250i	0.904709	+	1.56700i	0.821307	+	0.570486i	$0.193245\pi$
$733$	24.4941	+	42.4250i	0.904709	+	1.56700i	0.0834021	+	0.996516i	$0.473421\pi$
$734$	−5.99901	−	10.3906i	−0.221428	−	0.383524i
$735$	65.7645	+	6.83163i	2.42576	+	0.251988i
$736$	1.16285	+	2.01412i	0.0428633	+	0.0742413i
$737$	6.20368	+	10.7451i	0.228516	+	0.395801i
$738$	17.0967	−	19.0805i	0.629337	−	0.702362i
$739$	8.68526	−	15.0433i	0.319492	−	0.553377i	−0.660890	−	0.750483i	$-0.729821\pi$
$739$	8.68526	−	15.0433i	0.319492	−	0.553377i	0.980382	+	0.197106i	$0.0631543\pi$
$740$	0.00684691	−	0.0118592i	0.000251697	−	0.000435953i
$741$	9.16272	−	42.7022i	0.336601	−	1.56870i
$742$	−17.4278	−	30.1859i	−0.639796	−	1.10816i
$743$	−7.75180			−0.284386			−0.142193	−	0.989839i	$-0.545415\pi$
$743$	−7.75180			−0.284386			−0.142193	+	0.989839i	$0.545415\pi$
$744$	−7.51551	−	0.780713i	−0.275532	−	0.0286223i
$745$	−7.81178			−0.286202
$746$	−17.7023	+	30.6614i	−0.648129	+	1.12259i
$747$	−35.9827	−	7.55733i	−1.31654	−	0.276508i
$748$	−6.13195			−0.224206
$749$	−20.1706	+	34.9364i	−0.737016	+	1.27655i
$750$	11.1114	+	1.15426i	0.405732	+	0.0421475i
$751$	12.5347	−	21.7107i	0.457396	−	0.792233i	−0.541426	−	0.840748i	$-0.682116\pi$
$751$	12.5347	−	21.7107i	0.457396	−	0.792233i	0.998822	+	0.0485150i	$0.0154489\pi$
$752$	3.53275	+	6.11891i	0.128826	+	0.223134i
$753$	47.9509	+	4.98115i	1.74743	+	0.181523i
$754$	9.18156			0.334373
$755$	16.8815	−	29.2396i	0.614380	−	1.06414i
$756$	4.67202	+	21.5941i	0.169920	+	0.785371i
$757$	−15.1991	+	26.3256i	−0.552421	+	0.956821i	0.445678	+	0.895193i	$0.352963\pi$
$757$	−15.1991	+	26.3256i	−0.552421	+	0.956821i	−0.998099	+	0.0616279i	$0.980371\pi$
$758$	4.57566	+	7.92527i	0.166195	+	0.287859i
$759$	−7.01981	−	0.729220i	−0.254803	−	0.0264690i
$760$	12.1227	+	8.86596i	0.439738	+	0.321602i
$761$	−16.1773	−	28.0199i	−0.586427	−	1.01572i	−0.994696	−	0.102860i	$-0.967201\pi$
$761$	−16.1773	−	28.0199i	−0.586427	−	1.01572i	0.408268	−	0.912862i	$-0.366133\pi$
$762$	−8.73287	−	19.5506i	−0.316358	−	0.708244i
$763$	15.3015	+	26.5030i	0.553952	+	0.959473i
$764$	−5.87666	−	10.1787i	−0.212610	−	0.368252i
$765$	−35.4050	−	7.43601i	−1.28007	−	0.268849i
$766$	7.12789	+	12.3459i	0.257541	+	0.446075i
$767$	−14.7259	+	25.5060i	−0.531721	+	0.920968i
$768$	0.706404	+	1.58145i	0.0254902	+	0.0570658i
$769$	6.38596	−	11.0608i	0.230284	−	0.398863i	−0.727608	−	0.685993i	$-0.759368\pi$
$769$	6.38596	−	11.0608i	0.230284	−	0.398863i	0.957892	+	0.287130i	$0.0927012\pi$
$770$	−12.8339	+	22.2290i	−0.462502	+	0.801077i
$771$	−4.68185	−	10.4814i	−0.168613	−	0.377479i
$772$	5.91948	−	10.2528i	0.213047	−	0.369008i
$773$	3.54275	+	6.13623i	0.127424	+	0.220705i	0.922678	−	0.385572i	$-0.125996\pi$
$773$	3.54275	+	6.13623i	0.127424	+	0.220705i	−0.795254	+	0.606277i	$0.792662\pi$
$774$	−27.1843	−	5.70943i	−0.977119	−	0.205221i
$775$	−14.9891	−	25.9618i	−0.538423	−	0.932576i
$776$	−1.62398	−	2.81282i	−0.0582977	−	0.100975i
$777$	0.0119373	+	0.0267244i	0.000428247	+	0.000958734i
$778$	6.34612	+	10.9918i	0.227519	+	0.394075i
$779$	30.0463	+	21.9743i	1.07652	+	0.787312i
$780$	34.3382	+	3.56706i	1.22950	+	0.127721i
$781$	13.9209	+	24.1116i	0.498128	+	0.862782i
$782$	4.06988	−	7.04924i	0.145539	−	0.252080i
$783$	−7.85285	−	2.52005i	−0.280638	−	0.0900591i
$784$	−5.53951	+	9.59472i	−0.197840	+	0.342669i
$785$	−78.7983			−2.81243
$786$	4.30710	+	0.447423i	0.153629	+	0.0159590i
$787$	3.32065	+	5.75154i	0.118368	+	0.205020i	0.919121	−	0.393975i	$-0.128900\pi$
$787$	3.32065	+	5.75154i	0.118368	+	0.205020i	−0.800753	+	0.598995i	$0.795567\pi$
$788$	4.39922	−	7.61968i	0.156716	−	0.271440i
$789$	−26.8347	−	2.78760i	−0.955341	−	0.0992411i
$790$	−6.27635	+	10.8710i	−0.223303	+	0.386771i
$791$	−38.1100			−1.35504
$792$	−5.14386	−	1.08035i	−0.182779	−	0.0383886i
$793$	−12.4399	+	21.5465i	−0.441753	+	0.765139i
$794$	4.99555			0.177285
$795$	48.6604	+	5.05486i	1.72581	+	0.179277i
$796$	17.3542			0.615103
$797$	−8.49094	−	14.7067i	−0.300765	−	0.520940i	0.675545	−	0.737319i	$-0.263909\pi$
$797$	−8.49094	−	14.7067i	−0.300765	−	0.520940i	−0.976309	+	0.216379i	$0.930575\pi$
$798$	−30.5494	+	9.86102i	−1.08144	+	0.349076i
$799$	12.3643	−	21.4156i	0.437419	−	0.757631i
$800$	−3.43594	+	5.95123i	−0.121479	+	0.210408i
$801$	−27.2810	+	30.4465i	−0.963926	+	1.07578i
$802$	14.0438	+	24.3246i	0.495905	+	0.858932i
$803$	−2.90000	−	5.02295i	−0.102339	−	0.177256i
$804$	−12.2002	−	1.26736i	−0.430269	−	0.0446964i
$805$	−17.0362	−	29.5075i	−0.600445	−	1.04000i
$806$	−12.6179	−	21.8548i	−0.444445	−	0.769801i
$807$	−0.627986	−	1.40590i	−0.0221061	−	0.0494899i
$808$	−6.89527			−0.242575
$809$	15.6381			0.549806			0.274903	−	0.961472i	$-0.411354\pi$
$809$	15.6381			0.549806			0.274903	+	0.961472i	$0.411354\pi$
$810$	−28.3898	−	12.4756i	−0.997517	−	0.438347i
$811$	−5.40132	−	9.35536i	−0.189666	−	0.328511i	0.755473	−	0.655180i	$-0.227407\pi$
$811$	−5.40132	−	9.35536i	−0.189666	−	0.328511i	−0.945139	+	0.326669i	$0.894074\pi$
$812$	−3.37433	−	5.84450i	−0.118416	−	0.205102i
$813$	−1.66031	−	3.71701i	−0.0582298	−	0.130361i
$814$	−0.00696316			−0.000244059
$815$	−85.3713			−2.99043
$816$	3.55723	−	4.90859i	0.124528	−	0.171835i
$817$	4.34470	−	40.1250i	0.152002	−	1.40380i
$818$	−24.7309			−0.864696
$819$	−49.2420	+	54.9559i	−1.72066	+	1.92031i
$820$	−14.7123	+	25.4824i	−0.513775	+	0.889885i
$821$	−24.4171			−0.852164			−0.426082	−	0.904685i	$-0.640106\pi$
$821$	−24.4171			−0.852164			−0.426082	+	0.904685i	$0.640106\pi$
$822$	17.0402	+	1.77014i	0.594346	+	0.0617408i
$823$	−15.5617	+	26.9537i	−0.542448	+	0.939548i	0.456315	+	0.889819i	$0.349169\pi$
$823$	−15.5617	+	26.9537i	−0.542448	+	0.939548i	−0.998763	+	0.0497293i	$0.984164\pi$
$824$	−3.77200	−	6.53329i	−0.131404	−	0.227598i
$825$	−8.50493	−	19.0403i	−0.296104	−	0.662899i
$826$	21.6477			0.753221
$827$	7.16897	+	12.4170i	0.249289	+	0.431782i	0.963329	−	0.268323i	$-0.0864696\pi$
$827$	7.16897	+	12.4170i	0.249289	+	0.431782i	−0.714039	+	0.700106i	$0.753136\pi$
$828$	4.65603	−	5.19629i	0.161808	−	0.180584i
$829$	20.3795			0.707810			0.353905	−	0.935281i	$-0.384854\pi$
$829$	20.3795			0.707810			0.353905	+	0.935281i	$0.384854\pi$
$830$	42.2285			1.46577
$831$	−12.0775	−	27.0384i	−0.418964	−	0.937952i
$832$	−2.89239	+	5.00977i	−0.100276	+	0.173683i
$833$	38.7756			1.34350
$834$	13.7643	−	18.9933i	0.476619	−	0.657683i
$835$	29.9724	−	51.9137i	1.03724	−	1.79655i
$836$	0.822112	−	7.59254i	0.0284334	−	0.262594i
$837$	4.79342	+	22.1552i	0.165685	+	0.765797i
$838$	−7.29743	+	12.6395i	−0.252086	+	0.436625i
$839$	5.34917	+	9.26504i	0.184674	+	0.319865i	0.943467	−	0.331468i	$-0.107544\pi$
$839$	5.34917	+	9.26504i	0.184674	+	0.319865i	−0.758793	+	0.651332i	$0.774210\pi$
$840$	−10.3491	−	23.1688i	−0.357076	−	0.799400i
$841$	−26.4808			−0.913132
$842$	−18.4368	+	31.9334i	−0.635373	+	1.10050i
$843$	25.4463	−	35.1132i	0.876418	−	1.20936i
$844$	−7.72073	+	13.3727i	−0.265758	+	0.460307i
$845$	35.2545	+	61.0626i	1.21279	+	2.10062i
$846$	14.1451	−	15.7864i	0.486317	−	0.542747i
$847$	−33.7196			−1.15862
$848$	−4.09880	+	7.09932i	−0.140753	+	0.243792i
$849$	−25.8717	+	35.7001i	−0.887913	+	1.22522i
$850$	24.0510			0.824943
$851$	0.00462156	−	0.00800478i	0.000158425	−	0.000274400i
$852$	−27.3769	−	2.84392i	−0.937918	−	0.0974311i
$853$	−1.07167	−	1.85619i	−0.0366934	−	0.0635549i	0.847095	−	0.531441i	$-0.178349\pi$
$853$	−1.07167	−	1.85619i	−0.0366934	−	0.0635549i	−0.883789	+	0.467886i	$0.845016\pi$
$854$	18.2872			0.625774
$855$	13.9540	−	42.8413i	0.477216	−	1.46514i
$856$	9.48769			0.324282
$857$	−8.62059	−	14.9313i	−0.294474	−	0.510044i	0.680389	−	0.732852i	$-0.261811\pi$
$857$	−8.62059	−	14.9313i	−0.294474	−	0.510044i	−0.974862	+	0.222808i	$0.928478\pi$
$858$	−7.15949	−	16.0282i	−0.244421	−	0.547194i
$859$	5.91986	−	10.2535i	0.201983	−	0.349845i	−0.747184	−	0.664617i	$-0.768595\pi$
$859$	5.91986	−	10.2535i	0.201983	−	0.349845i	0.949167	+	0.314772i	$0.101928\pi$
$860$	31.9029			1.08788
$861$	−25.6502	−	57.4241i	−0.874156	−	1.95701i
$862$	−3.37892	+	5.85247i	−0.115087	+	0.199336i
$863$	−14.6291			−0.497980			−0.248990	−	0.968506i	$-0.580099\pi$
$863$	−14.6291			−0.497980			−0.248990	+	0.968506i	$0.580099\pi$
$864$	3.84884	−	3.49091i	0.130940	−	0.118763i
$865$	−13.8439	−	23.9783i	−0.470706	−	0.815288i
$866$	−15.4170	+	26.7030i	−0.523890	+	0.907404i
$867$	8.18425	+	0.850182i	0.277952	+	0.0288737i
$868$	−9.27440	+	16.0637i	−0.314794	+	0.545239i
$869$	6.38291			0.216526
$870$	9.42149	+	0.978706i	0.319418	+	0.0331812i
$871$	−20.4831	−	35.4777i	−0.694042	−	1.20212i
$872$	3.59871	−	6.23315i	0.121868	−	0.211081i
$873$	−6.50239	+	7.25690i	−0.220073	+	0.245609i
$874$	8.18267	+	5.98439i	0.276783	+	0.202425i
$875$	13.7119	−	23.7497i	0.463547	−	0.802887i
$876$	5.70317	+	0.592446i	0.192692	+	0.0200169i
$877$	22.8210			0.770611			0.385306	−	0.922789i	$-0.374096\pi$
$877$	22.8210			0.770611			0.385306	+	0.922789i	$0.374096\pi$
$878$	−2.37901	+	4.12057i	−0.0802877	+	0.139062i
$879$	−13.4827	−	1.40059i	−0.454761	−	0.0472407i
$880$	6.03673			0.203498
$881$	25.2345			0.850172			0.425086	−	0.905153i	$-0.360244\pi$
$881$	25.2345			0.850172			0.425086	+	0.905153i	$0.360244\pi$
$882$	32.5274	+	6.83163i	1.09525	+	0.230033i
$883$	21.9212	+	37.9686i	0.737707	+	1.27775i	0.953525	+	0.301313i	$0.0974247\pi$
$883$	21.9212	+	37.9686i	0.737707	+	1.27775i	−0.215818	+	0.976434i	$0.569242\pi$
$884$	20.2462			0.680955
$885$	−17.8295	+	24.6028i	−0.599332	+	0.827014i
$886$	−2.95772	−	5.12292i	−0.0993665	−	0.172108i
$887$	−16.3408	+	28.3031i	−0.548671	+	0.950327i	0.449695	+	0.893182i	$0.351533\pi$
$887$	−16.3408	+	28.3031i	−0.548671	+	0.950327i	−0.998366	+	0.0571443i	$0.981800\pi$
$888$	0.00403942	−	0.00557397i	0.000135554	−	0.000187050i
$889$	−52.5644			−1.76295
$890$	23.4762	−	40.6620i	0.786926	−	1.36299i
$891$	1.72416	+	15.6737i	0.0577617	+	0.525090i
$892$	−19.4279			−0.650495
$893$	24.8590	+	18.1806i	0.831875	+	0.608392i
$894$	−3.90589	−	0.405745i	−0.130633	−	0.0135701i
$895$	34.3417			1.14792
$896$	4.25194			0.142047
$897$	23.1777	+	2.40771i	0.773882	+	0.0803911i
$898$	−19.8407	−	34.3652i	−0.662094	−	1.14678i
$899$	−3.46201	−	5.99637i	−0.115464	−	0.199990i
$900$	20.1755	+	4.23739i	0.672516	+	0.141246i
$901$	28.6909			0.955831
$902$	14.9621			0.498182
$903$	−40.0140	+	55.2150i	−1.33158	+	1.83744i
$904$	4.48148	+	7.76216i	0.149052	+	0.258166i
$905$	32.3813	+	56.0860i	1.07639	+	1.86436i
$906$	9.95944	−	13.7430i	0.330880	−	0.456579i
$907$	−9.26587	−	16.0490i	−0.307668	−	0.532897i	0.670184	−	0.742195i	$-0.266215\pi$
$907$	−9.26587	−	16.0490i	−0.307668	−	0.532897i	−0.977852	+	0.209299i	$0.932882\pi$
$908$	−6.36062	−	11.0169i	−0.211085	−	0.365609i
$909$	6.43989	+	19.6578i	0.213598	+	0.652009i
$910$	42.3745	−	73.3948i	1.40470	−	2.43301i
$911$	−21.7107	+	37.6041i	−0.719309	+	1.24588i	0.241965	+	0.970285i	$0.422208\pi$
$911$	−21.7107	+	37.6041i	−0.719309	+	1.24588i	−0.961274	+	0.275594i	$0.911125\pi$
$912$	5.60087	+	5.06263i	0.185463	+	0.167641i
$913$	−10.7364	−	18.5959i	−0.355322	−	0.615436i
$914$	19.1934			0.634863
$915$	−15.0617	+	20.7835i	−0.497924	+	0.687082i
$916$	−4.49598			−0.148551
$917$	5.31511	−	9.20605i	0.175521	−	0.304010i
$918$	−17.3163	−	5.55695i	−0.571523	−	0.183407i
$919$	5.57729			0.183978			0.0919889	−	0.995760i	$-0.470678\pi$
$919$	5.57729			0.183978			0.0919889	+	0.995760i	$0.470678\pi$
$920$	−4.00667	+	6.93976i	−0.132096	+	0.228797i
$921$	5.08226	+	11.3779i	0.167466	+	0.374913i
$922$	5.85908	−	10.1482i	0.192959	−	0.334214i
$923$	−45.9633	−	79.6109i	−1.51290	−	2.62042i
$924$	−7.57153	+	10.4479i	−0.249085	+	0.343711i
$925$	0.0273112			0.000897987
$926$	−14.6614	+	25.3942i	−0.481802	+	0.834506i
$927$	−15.1030	+	16.8555i	−0.496047	+	0.553606i
$928$	−0.793596	+	1.37455i	−0.0260511	+	0.0451218i
$929$	13.2468	+	22.9442i	0.434615	+	0.752775i	0.997264	−	0.0739207i	$-0.0235512\pi$
$929$	13.2468	+	22.9442i	0.434615	+	0.752775i	−0.562649	+	0.826696i	$0.690218\pi$
$930$	−10.6180	−	23.7708i	−0.348177	−	0.779477i
$931$	−5.19866	+	48.0117i	−0.170379	+	1.57352i
$932$	−3.81807	−	6.61310i	−0.125065	−	0.216619i
$933$	32.6647	+	3.39321i	1.06939	+	0.111089i
$934$	−5.34917	−	9.26504i	−0.175030	−	0.303161i
$935$	−10.5640	−	18.2974i	−0.345480	−	0.598389i
$936$	16.9838	+	3.56706i	0.555133	+	0.116593i
$937$	20.6141	+	35.7046i	0.673432	+	1.16642i	0.976925	+	0.213585i	$0.0685139\pi$
$937$	20.6141	+	35.7046i	0.673432	+	1.16642i	−0.303492	+	0.952834i	$0.598153\pi$
$938$	−15.0555	+	26.0769i	−0.491580	+	0.851441i
$939$	−33.7489	+	46.5699i	−1.10135	+	1.51975i
$940$	−12.1723	+	21.0831i	−0.397017	+	0.687654i
$941$	15.6635	−	27.1300i	0.510616	−	0.884413i	−0.489308	−	0.872111i	$-0.662751\pi$
$941$	15.6635	−	27.1300i	0.510616	−	0.884413i	0.999924	−	0.0123023i	$-0.00391606\pi$
$942$	−39.3992	−	4.09279i	−1.28369	−	0.133350i
$943$	−9.93057	+	17.2002i	−0.323384	+	0.560117i
$944$	−2.54563	−	4.40915i	−0.0828531	−	0.143506i
$945$	−56.3868	+	51.1430i	−1.83426	+	1.66368i
$946$	−8.11113	−	14.0489i	−0.263716	−	0.456769i
$947$	0.903451	+	1.56482i	0.0293582	+	0.0508499i	0.880331	−	0.474360i	$-0.157320\pi$
$947$	0.903451	+	1.56482i	0.0293582	+	0.0508499i	−0.850973	+	0.525209i	$0.823987\pi$
$948$	−3.70281	+	5.10949i	−0.120262	+	0.165948i
$949$	9.57510	+	16.5846i	0.310821	+	0.538358i
$950$	−3.22452	+	29.7798i	−0.104617	+	0.966184i
$951$	3.91992	−	5.40907i	0.127112	−	0.175401i
$952$	−7.44072	−	12.8877i	−0.241155	−	0.417693i
$953$	2.22750	−	3.85815i	0.0721558	−	0.124978i	−0.827690	−	0.561185i	$-0.810345\pi$
$953$	2.22750	−	3.85815i	0.0721558	−	0.124978i	0.899846	+	0.436208i	$0.143679\pi$
$954$	24.0677	+	5.05486i	0.779220	+	0.163657i
$955$	20.2484	−	35.0713i	0.655223	−	1.13488i
$956$	8.25261			0.266908
$957$	−1.96437	−	4.39772i	−0.0634992	−	0.142158i
$958$	10.2849	+	17.8139i	0.332289	+	0.575542i
$959$	21.0282	−	36.4220i	0.679038	−	1.17613i
$960$	−3.50199	+	4.83237i	−0.113026	+	0.155964i
$961$	5.98460	−	10.3656i	0.193052	−	0.334375i
$962$	0.0229907			0.000741249
$963$	−8.86110	−	27.0486i	−0.285545	−	0.871629i
$964$	5.82898	−	10.0961i	0.187739	−	0.325173i
$965$	40.7919			1.31314
$966$	−6.98545	−	15.6386i	−0.224753	−	0.503164i
$967$	48.8595			1.57122			0.785608	−	0.618724i	$-0.212350\pi$
$967$	48.8595			1.57122			0.785608	+	0.618724i	$0.212350\pi$
$968$	3.96519	+	6.86792i	0.127446	+	0.220743i
$969$	5.54364	−	25.8357i	0.178087	−	0.829962i
$970$	5.59554	−	9.69176i	0.179662	−	0.311184i
$971$	13.8338	−	23.9609i	0.443949	−	0.768941i	−0.554030	−	0.832497i	$-0.686911\pi$
$971$	13.8338	−	23.9609i	0.443949	−	0.768941i	0.997978	+	0.0635554i	$0.0202440\pi$
$972$	−13.5469	−	7.71236i	−0.434518	−	0.247374i
$973$	−28.7910	−	49.8675i	−0.922998	−	1.59868i
$974$	11.9894	+	20.7662i	0.384165	+	0.665393i
$975$	28.0812	+	62.8665i	0.899320	+	2.01334i
$976$	−2.15045	−	3.72469i	−0.0688342	−	0.119224i
$977$	20.2336	+	35.0456i	0.647331	+	1.12121i	0.983758	+	0.179500i	$0.0574480\pi$
$977$	20.2336	+	35.0456i	0.647331	+	1.12121i	−0.336427	+	0.941709i	$0.609219\pi$
$978$	−42.6857	−	4.43420i	−1.36494	−	0.141790i
$979$	−23.8748			−0.763043
$980$	−38.1735			−1.21941
$981$	−21.1312	−	4.43812i	−0.674668	−	0.141698i
$982$	8.75540	+	15.1648i	0.279396	+	0.483928i
$983$	15.0199	+	26.0152i	0.479061	+	0.829757i	0.999712	−	0.0240123i	$-0.00764410\pi$
$983$	15.0199	+	26.0152i	0.479061	+	0.829757i	−0.520651	+	0.853770i	$0.674311\pi$
$984$	−8.67970	+	11.9770i	−0.276699	+	0.381814i
$985$	30.3156			0.965934
$986$	5.55504			0.176908
$987$	−21.2219	−	47.5102i	−0.675500	−	1.51227i
$988$	−2.71442	+	25.0688i	−0.0863571	+	0.797543i
$989$	21.5340			0.684740
$990$	−5.63805	−	17.2102i	−0.179189	−	0.546976i
$991$	0.501566	−	0.868737i	0.0159328	−	0.0275963i	−0.857949	−	0.513735i	$-0.828262\pi$
$991$	0.501566	−	0.868737i	0.0159328	−	0.0275963i	0.873882	+	0.486138i	$0.161595\pi$
$992$	4.36243			0.138507
$993$	−2.68976	−	6.02166i	−0.0853569	−	0.191092i
$994$	−33.7841	+	58.5157i	−1.07157	+	1.85601i
$995$	29.8974	+	51.7839i	0.947812	+	1.64166i
$996$	21.1143	+	2.19335i	0.669031	+	0.0694991i
$997$	28.1098			0.890245			0.445122	−	0.895470i	$-0.353160\pi$
$997$	28.1098			0.890245			0.445122	+	0.895470i	$0.353160\pi$
$998$	5.03373	+	8.71868i	0.159340	+	0.275985i
$999$	−0.0196636	−	0.00631021i	−0.000622128	−	0.000199646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.f.277.5	yes	10
3.2	odd	2		1026.2.h.f.505.5		10
9.4	even	3		342.2.f.f.49.3	yes	10
9.5	odd	6		1026.2.f.f.847.1		10
19.7	even	3		342.2.f.f.7.3	✓	10
57.26	odd	6		1026.2.f.f.235.1		10
171.121	even	3	inner	342.2.h.f.121.5	yes	10
171.140	odd	6		1026.2.h.f.577.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.f.7.3	✓	10	19.7	even	3
342.2.f.f.49.3	yes	10	9.4	even	3
342.2.h.f.121.5	yes	10	171.121	even	3	inner
342.2.h.f.277.5	yes	10	1.1	even	1	trivial
1026.2.f.f.235.1		10	57.26	odd	6
1026.2.f.f.847.1		10	9.5	odd	6
1026.2.h.f.505.5		10	3.2	odd	2
1026.2.h.f.577.5		10	171.140	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.01638 - 1.40249i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44556 q^{5} +(-1.72278 - 0.178963i) q^{6} +(-2.12597 + 3.68229i) q^{7} +1.00000 q^{8} +(-0.933957 - 2.85092i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.01638 - 1.40249i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44556 q^{5} +(-1.72278 - 0.178963i) q^{6} +(-2.12597 + 3.68229i) q^{7} +1.00000 q^{8} +(-0.933957 - 2.85092i) q^{9} +(1.72278 + 2.98394i) q^{10} +(0.876015 - 1.51730i) q^{11} +(0.706404 + 1.58145i) q^{12} +(-2.89239 + 5.00977i) q^{13} +4.25194 q^{14} +(-3.50199 + 4.83237i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.74996 + 3.03101i) q^{17} +(-2.00199 + 2.23429i) q^{18} +(-3.51836 - 2.57315i) q^{19} +(1.72278 - 2.98394i) q^{20} +(3.00359 + 6.72425i) q^{21} -1.75203 q^{22} +(1.16285 - 2.01412i) q^{23} +(1.01638 - 1.40249i) q^{24} +6.87189 q^{25} +5.78478 q^{26} +(-4.94763 - 1.58774i) q^{27} +(-2.12597 - 3.68229i) q^{28} +1.58719 q^{29} +(5.93594 + 0.616627i) q^{30} +(-2.18121 - 3.77797i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.23764 - 2.77075i) q^{33} +3.49991 q^{34} +(7.32517 - 12.6876i) q^{35} +(2.93594 + 0.616627i) q^{36} +0.00397434 q^{37} +(-0.469234 + 4.33357i) q^{38} +(4.08639 + 9.14836i) q^{39} -3.44556 q^{40} -8.53985 q^{41} +(4.32158 - 5.96331i) q^{42} +(4.62956 + 8.01864i) q^{43} +(0.876015 + 1.51730i) q^{44} +(3.21801 + 9.82301i) q^{45} -2.32570 q^{46} -7.06551 q^{47} +(-1.72278 - 0.178963i) q^{48} +(-5.53951 - 9.59472i) q^{49} +(-3.43594 - 5.95123i) q^{50} +(2.47235 + 5.53495i) q^{51} +(-2.89239 - 5.00977i) q^{52} +(-4.09880 - 7.09932i) q^{53} +(1.09880 + 5.07865i) q^{54} +(-3.01836 + 5.22796i) q^{55} +(-2.12597 + 3.68229i) q^{56} +(-7.18480 + 2.31918i) q^{57} +(-0.793596 - 1.37455i) q^{58} +5.09125 q^{59} +(-2.43396 - 5.44899i) q^{60} +4.30090 q^{61} +(-2.18121 + 3.77797i) q^{62} +(12.4835 + 2.62186i) q^{63} +1.00000 q^{64} +(9.96591 - 17.2615i) q^{65} +(-1.78072 + 2.45721i) q^{66} +(-3.54085 + 6.13294i) q^{67} +(-1.74996 - 3.03101i) q^{68} +(-1.64288 - 3.67799i) q^{69} -14.6503 q^{70} +(-7.94556 + 13.7621i) q^{71} +(-0.933957 - 2.85092i) q^{72} +(1.65522 - 2.86693i) q^{73} +(-0.00198717 - 0.00344188i) q^{74} +(6.98443 - 9.63776i) q^{75} +(3.98760 - 1.76042i) q^{76} +(3.72477 + 6.45149i) q^{77} +(5.87952 - 8.11310i) q^{78} +(1.82158 + 3.15506i) q^{79} +(1.72278 + 2.98394i) q^{80} +(-7.25545 + 5.32527i) q^{81} +(4.26992 + 7.39572i) q^{82} +(6.12796 - 10.6139i) q^{83} +(-7.32517 - 0.760940i) q^{84} +(6.02958 - 10.4435i) q^{85} +(4.62956 - 8.01864i) q^{86} +(1.61318 - 2.22602i) q^{87} +(0.876015 - 1.51730i) q^{88} +(-6.81348 - 11.8013i) q^{89} +(6.89797 - 7.69838i) q^{90} +(-12.2983 - 21.3013i) q^{91} +(1.16285 + 2.01412i) q^{92} +(-7.51551 - 0.780713i) q^{93} +(3.53275 + 6.11891i) q^{94} +(12.1227 + 8.86596i) q^{95} +(0.706404 + 1.58145i) q^{96} +(-1.62398 - 2.81282i) q^{97} +(-5.53951 + 9.59472i) q^{98} +(-5.14386 - 1.08035i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9	\( 10 q - 5 q^{2} - 4 q^{3} - 5 q^{4} + 4 q^{5} + 2 q^{6} - 5 q^{7} + 10 q^{8} - 8 q^{9} - 2 q^{10} + q^{11} + 2 q^{12} - 7 q^{13} + 10 q^{14} - 11 q^{15} - 5 q^{16} - 9 q^{17} + 4 q^{18} + 3 q^{19} - 2 q^{20} + 15 q^{21} - 2 q^{22} + 10 q^{23} - 4 q^{24} + 18 q^{25} + 14 q^{26} - 4 q^{27} - 5 q^{28} + 26 q^{29} + 34 q^{30} + 18 q^{31} - 5 q^{32} + 13 q^{33} + 18 q^{34} + 12 q^{35} + 4 q^{36} - 48 q^{37} - 9 q^{38} - 20 q^{39} + 4 q^{40} - 10 q^{41} - 3 q^{42} + 15 q^{43} + q^{44} - 10 q^{45} - 20 q^{46} - 14 q^{47} + 2 q^{48} - 26 q^{49} - 9 q^{50} + 30 q^{51} - 7 q^{52} - 14 q^{53} - 16 q^{54} + 8 q^{55} - 5 q^{56} - 17 q^{57} - 13 q^{58} + 30 q^{59} - 23 q^{60} - 28 q^{61} + 18 q^{62} + 48 q^{63} + 10 q^{64} - q^{65} - 5 q^{66} - 2 q^{67} - 9 q^{68} - 44 q^{69} - 24 q^{70} - 41 q^{71} - 8 q^{72} + 4 q^{73} + 24 q^{74} + 22 q^{75} + 6 q^{76} - 6 q^{77} + 19 q^{78} - 28 q^{79} - 2 q^{80} - 8 q^{81} + 5 q^{82} + 21 q^{83} - 12 q^{84} + 18 q^{85} + 15 q^{86} - q^{87} + q^{88} - 27 q^{89} + 8 q^{90} - q^{91} + 10 q^{92} - 49 q^{93} + 7 q^{94} + 17 q^{95} + 2 q^{96} - 24 q^{97} - 26 q^{98} - 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 4 * q^3 - 5 * q^4 + 4 * q^5 + 2 * q^6 - 5 * q^7 + 10 * q^8 - 8 * q^9 - 2 * q^10 + q^11 + 2 * q^12 - 7 * q^13 + 10 * q^14 - 11 * q^15 - 5 * q^16 - 9 * q^17 + 4 * q^18 + 3 * q^19 - 2 * q^20 + 15 * q^21 - 2 * q^22 + 10 * q^23 - 4 * q^24 + 18 * q^25 + 14 * q^26 - 4 * q^27 - 5 * q^28 + 26 * q^29 + 34 * q^30 + 18 * q^31 - 5 * q^32 + 13 * q^33 + 18 * q^34 + 12 * q^35 + 4 * q^36 - 48 * q^37 - 9 * q^38 - 20 * q^39 + 4 * q^40 - 10 * q^41 - 3 * q^42 + 15 * q^43 + q^44 - 10 * q^45 - 20 * q^46 - 14 * q^47 + 2 * q^48 - 26 * q^49 - 9 * q^50 + 30 * q^51 - 7 * q^52 - 14 * q^53 - 16 * q^54 + 8 * q^55 - 5 * q^56 - 17 * q^57 - 13 * q^58 + 30 * q^59 - 23 * q^60 - 28 * q^61 + 18 * q^62 + 48 * q^63 + 10 * q^64 - q^65 - 5 * q^66 - 2 * q^67 - 9 * q^68 - 44 * q^69 - 24 * q^70 - 41 * q^71 - 8 * q^72 + 4 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 6 * q^77 + 19 * q^78 - 28 * q^79 - 2 * q^80 - 8 * q^81 + 5 * q^82 + 21 * q^83 - 12 * q^84 + 18 * q^85 + 15 * q^86 - q^87 + q^88 - 27 * q^89 + 8 * q^90 - q^91 + 10 * q^92 - 49 * q^93 + 7 * q^94 + 17 * q^95 + 2 * q^96 - 24 * q^97 - 26 * q^98 - 13 * q^99

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