LMFDB - Embedded newform 560.2.bb.d.29.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(29,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 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("560.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.bb (of order $4$, 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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$70$
Relative dimension:	$35$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.17
Character	$\chi$	$=$	560.29
Dual form			560.2.bb.d.309.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.171434 - 1.40378i) q^{2} +(0.104638 - 0.104638i) q^{3} +(-1.94122 + 0.481312i) q^{4} +(2.23517 + 0.0634380i) q^{5} +(-0.164828 - 0.128951i) q^{6} +1.00000 q^{7} +(1.00845 + 2.64254i) q^{8} +2.97810i q^{9} +O(q^{10})$	\(q+(-0.171434 - 1.40378i) q^{2} +(0.104638 - 0.104638i) q^{3} +(-1.94122 + 0.481312i) q^{4} +(2.23517 + 0.0634380i) q^{5} +(-0.164828 - 0.128951i) q^{6} +1.00000 q^{7} +(1.00845 + 2.64254i) q^{8} +2.97810i q^{9} +(-0.294130 - 3.14857i) q^{10} +(-1.73389 + 1.73389i) q^{11} +(-0.152762 + 0.253489i) q^{12} +(4.26620 - 4.26620i) q^{13} +(-0.171434 - 1.40378i) q^{14} +(0.240522 - 0.227246i) q^{15} +(3.53668 - 1.86867i) q^{16} +8.02204i q^{17} +(4.18061 - 0.510547i) q^{18} +(-1.67411 - 1.67411i) q^{19} +(-4.36949 + 0.952666i) q^{20} +(0.104638 - 0.104638i) q^{21} +(2.73126 + 2.13676i) q^{22} +8.05693 q^{23} +(0.382033 + 0.170989i) q^{24} +(4.99195 + 0.283589i) q^{25} +(-6.72020 - 5.25745i) q^{26} +(0.625538 + 0.625538i) q^{27} +(-1.94122 + 0.481312i) q^{28} +(1.66576 + 1.66576i) q^{29} +(-0.360238 - 0.298683i) q^{30} -6.54775 q^{31} +(-3.22951 - 4.64438i) q^{32} +0.362862i q^{33} +(11.2612 - 1.37525i) q^{34} +(2.23517 + 0.0634380i) q^{35} +(-1.43340 - 5.78115i) q^{36} +(-2.80565 - 2.80565i) q^{37} +(-2.06310 + 2.63710i) q^{38} -0.892815i q^{39} +(2.08642 + 5.97050i) q^{40} -9.47223i q^{41} +(-0.164828 - 0.128951i) q^{42} +(-1.58514 - 1.58514i) q^{43} +(2.53132 - 4.20041i) q^{44} +(-0.188925 + 6.65656i) q^{45} +(-1.38123 - 11.3102i) q^{46} -9.07783i q^{47} +(0.174538 - 0.565605i) q^{48} +1.00000 q^{49} +(-0.457691 - 7.05624i) q^{50} +(0.839412 + 0.839412i) q^{51} +(-6.22826 + 10.3350i) q^{52} +(0.823193 + 0.823193i) q^{53} +(0.770882 - 0.985358i) q^{54} +(-3.98553 + 3.76554i) q^{55} +(1.00845 + 2.64254i) q^{56} -0.350353 q^{57} +(2.05280 - 2.62394i) q^{58} +(2.62463 - 2.62463i) q^{59} +(-0.357530 + 0.556901i) q^{60} +(6.84958 + 6.84958i) q^{61} +(1.12251 + 9.19163i) q^{62} +2.97810i q^{63} +(-5.96606 + 5.32974i) q^{64} +(9.80631 - 9.26504i) q^{65} +(0.509381 - 0.0622069i) q^{66} +(-1.33966 + 1.33966i) q^{67} +(-3.86111 - 15.5726i) q^{68} +(0.843062 - 0.843062i) q^{69} +(-0.294130 - 3.14857i) q^{70} +8.36474i q^{71} +(-7.86976 + 3.00326i) q^{72} -0.578219 q^{73} +(-3.45754 + 4.41951i) q^{74} +(0.552023 - 0.492675i) q^{75} +(4.05560 + 2.44405i) q^{76} +(-1.73389 + 1.73389i) q^{77} +(-1.25332 + 0.153059i) q^{78} -12.1067 q^{79} +(8.02361 - 3.95242i) q^{80} -8.80339 q^{81} +(-13.2970 + 1.62386i) q^{82} +(4.88463 - 4.88463i) q^{83} +(-0.152762 + 0.253489i) q^{84} +(-0.508902 + 17.9306i) q^{85} +(-1.95345 + 2.49694i) q^{86} +0.348605 q^{87} +(-6.33042 - 2.83334i) q^{88} -0.882403i q^{89} +(9.37676 - 0.875949i) q^{90} +(4.26620 - 4.26620i) q^{91} +(-15.6403 + 3.87790i) q^{92} +(-0.685145 + 0.685145i) q^{93} +(-12.7433 + 1.55625i) q^{94} +(-3.63572 - 3.84813i) q^{95} +(-0.823910 - 0.148049i) q^{96} +9.29488i q^{97} +(-0.171434 - 1.40378i) q^{98} +(-5.16370 - 5.16370i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	$ 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) $ 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.171434	−	1.40378i	−0.121222	−	0.992625i
$2$	−0.171434	−	1.40378i	−0.121222	−	0.992625i
$3$	0.104638	−	0.104638i	0.0604129	−	0.0604129i	−0.676255	−	0.736668i	$-0.736398\pi$
$3$	0.104638	−	0.104638i	0.0604129	−	0.0604129i	0.736668	+	0.676255i	$0.236398\pi$
$4$	−1.94122	+	0.481312i	−0.970610	+	0.240656i
$5$	2.23517	+	0.0634380i	0.999597	+	0.0283703i
$5$	2.23517	+	0.0634380i	0.999597	+	0.0283703i
$6$	−0.164828	−	0.128951i	−0.0672907	−	0.0526440i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	1.00845	+	2.64254i	0.356541	+	0.934280i
$9$			2.97810i			0.992701i
$10$	−0.294130	−	3.14857i	−0.0930121	−	0.995665i
$11$	−1.73389	+	1.73389i	−0.522788	+	0.522788i	−0.918412	−	0.395625i	$-0.870528\pi$
$11$	−1.73389	+	1.73389i	−0.522788	+	0.522788i	0.395625	+	0.918412i	$0.370528\pi$
$12$	−0.152762	+	0.253489i	−0.0440987	+	0.0731761i
$13$	4.26620	−	4.26620i	1.18323	−	1.18323i	0.204329	−	0.978902i	$-0.434499\pi$
$13$	4.26620	−	4.26620i	1.18323	−	1.18323i	0.978902	−	0.204329i	$-0.0655012\pi$
$14$	−0.171434	−	1.40378i	−0.0458176	−	0.375177i
$15$	0.240522	−	0.227246i	0.0621025	−	0.0586746i
$16$	3.53668	−	1.86867i	0.884169	−	0.467167i
$17$			8.02204i			1.94563i	0.231582	+	0.972815i	$0.425610\pi$
$17$			8.02204i			1.94563i	−0.231582	+	0.972815i	$0.574390\pi$
$18$	4.18061	−	0.510547i	0.985380	−	0.120337i
$19$	−1.67411	−	1.67411i	−0.384068	−	0.384068i	0.488497	−	0.872565i	$-0.337545\pi$
$19$	−1.67411	−	1.67411i	−0.384068	−	0.384068i	−0.872565	+	0.488497i	$0.837545\pi$
$20$	−4.36949	+	0.952666i	−0.977047	+	0.213023i
$21$	0.104638	−	0.104638i	0.0228339	−	0.0228339i
$22$	2.73126	+	2.13676i	0.582306	+	0.455559i
$23$	8.05693			1.67999			0.839993	−	0.542598i	$-0.182559\pi$
$23$	8.05693			1.67999			0.839993	+	0.542598i	$0.182559\pi$
$24$	0.382033	+	0.170989i	0.0779822	+	0.0349029i
$25$	4.99195	+	0.283589i	0.998390	+	0.0567178i
$26$	−6.72020	−	5.25745i	−1.31794	−	1.03107i
$27$	0.625538	+	0.625538i	0.120385	+	0.120385i
$28$	−1.94122	+	0.481312i	−0.366856	+	0.0909594i
$29$	1.66576	+	1.66576i	0.309324	+	0.309324i	0.844647	−	0.535323i	$-0.179810\pi$
$29$	1.66576	+	1.66576i	0.309324	+	0.309324i	−0.535323	+	0.844647i	$0.679810\pi$
$30$	−0.360238	−	0.298683i	−0.0657701	−	0.0545319i
$31$	−6.54775			−1.17601			−0.588005	−	0.808857i	$-0.700087\pi$
$31$	−6.54775			−1.17601			−0.588005	+	0.808857i	$0.700087\pi$
$32$	−3.22951	−	4.64438i	−0.570902	−	0.821018i
$33$			0.362862i			0.0631662i
$34$	11.2612	−	1.37525i	1.93128	−	0.235853i
$35$	2.23517	+	0.0634380i	0.377812	+	0.0107230i
$36$	−1.43340	−	5.78115i	−0.238899	−	0.963526i
$37$	−2.80565	−	2.80565i	−0.461246	−	0.461246i	0.437818	−	0.899064i	$-0.355752\pi$
$37$	−2.80565	−	2.80565i	−0.461246	−	0.461246i	−0.899064	+	0.437818i	$0.855752\pi$
$38$	−2.06310	+	2.63710i	−0.334678	+	0.427793i
$39$		−	0.892815i		−	0.142965i
$40$	2.08642	+	5.97050i	0.329891	+	0.944019i
$41$		−	9.47223i		−	1.47931i	−0.672984	−	0.739657i	$-0.734988\pi$
$41$		−	9.47223i		−	1.47931i	0.672984	−	0.739657i	$-0.265012\pi$
$42$	−0.164828	−	0.128951i	−0.0254335	−	0.0198976i
$43$	−1.58514	−	1.58514i	−0.241732	−	0.241732i	0.575834	−	0.817566i	$-0.304677\pi$
$43$	−1.58514	−	1.58514i	−0.241732	−	0.241732i	−0.817566	+	0.575834i	$0.804677\pi$
$44$	2.53132	−	4.20041i	0.381611	−	0.633235i
$45$	−0.188925	+	6.65656i	−0.0281632	+	0.992301i
$46$	−1.38123	−	11.3102i	−0.203651	−	1.66760i
$47$		−	9.07783i		−	1.32414i	−0.749443	−	0.662069i	$-0.769679\pi$
$47$		−	9.07783i		−	1.32414i	0.749443	−	0.662069i	$-0.230321\pi$
$48$	0.174538	−	0.565605i	0.0251923	−	0.0816381i
$49$	1.00000			0.142857
$50$	−0.457691	−	7.05624i	−0.0647273	−	0.997903i
$51$	0.839412	+	0.839412i	0.117541	+	0.117541i
$52$	−6.22826	+	10.3350i	−0.863705	+	1.43321i
$53$	0.823193	+	0.823193i	0.113074	+	0.113074i	0.761380	−	0.648306i	$-0.224522\pi$
$53$	0.823193	+	0.823193i	0.113074	+	0.113074i	−0.648306	+	0.761380i	$0.724522\pi$
$54$	0.770882	−	0.985358i	0.104904	−	0.134090i
$55$	−3.98553	+	3.76554i	−0.537409	+	0.507746i
$56$	1.00845	+	2.64254i	0.134760	+	0.353125i
$57$	−0.350353			−0.0464053
$58$	2.05280	−	2.62394i	0.269546	−	0.344540i
$59$	2.62463	−	2.62463i	0.341697	−	0.341697i	−0.515308	−	0.857005i	$-0.672322\pi$
$59$	2.62463	−	2.62463i	0.341697	−	0.341697i	0.857005	+	0.515308i	$0.172322\pi$
$60$	−0.357530	+	0.556901i	−0.0461569	+	0.0718956i
$61$	6.84958	+	6.84958i	0.876999	+	0.876999i	0.993223	−	0.116224i	$-0.0370791\pi$
$61$	6.84958	+	6.84958i	0.876999	+	0.876999i	−0.116224	+	0.993223i	$0.537079\pi$
$62$	1.12251	+	9.19163i	0.142558	+	1.16734i
$63$			2.97810i			0.375206i
$64$	−5.96606	+	5.32974i	−0.745758	+	0.666217i
$65$	9.80631	−	9.26504i	1.21632	−	1.14919i
$66$	0.509381	−	0.0622069i	0.0627004	−	0.00765714i
$67$	−1.33966	+	1.33966i	−0.163666	+	0.163666i	−0.784188	−	0.620523i	$-0.786920\pi$
$67$	−1.33966	+	1.33966i	−0.163666	+	0.163666i	0.620523	+	0.784188i	$0.286920\pi$
$68$	−3.86111	−	15.5726i	−0.468228	−	1.88845i
$69$	0.843062	−	0.843062i	0.101493	−	0.101493i
$70$	−0.294130	−	3.14857i	−0.0351553	−	0.376326i
$71$			8.36474i			0.992712i	0.868119	+	0.496356i	$0.165329\pi$
$71$			8.36474i			0.992712i	−0.868119	+	0.496356i	$0.834671\pi$
$72$	−7.86976	+	3.00326i	−0.927460	+	0.353938i
$73$	−0.578219			−0.0676754			−0.0338377	−	0.999427i	$-0.510773\pi$
$73$	−0.578219			−0.0676754			−0.0338377	+	0.999427i	$0.510773\pi$
$74$	−3.45754	+	4.41951i	−0.401931	+	0.513758i
$75$	0.552023	−	0.492675i	0.0637421	−	0.0568892i
$76$	4.05560	+	2.44405i	0.465209	+	0.280352i
$77$	−1.73389	+	1.73389i	−0.197595	+	0.197595i
$78$	−1.25332	+	0.153059i	−0.141911	+	0.0173305i
$79$	−12.1067			−1.36211			−0.681056	−	0.732232i	$-0.738479\pi$
$79$	−12.1067			−1.36211			−0.681056	+	0.732232i	$0.738479\pi$
$80$	8.02361	−	3.95242i	0.897067	−	0.441894i
$81$	−8.80339			−0.978155
$82$	−13.2970	+	1.62386i	−1.46840	+	0.179325i
$83$	4.88463	−	4.88463i	0.536158	−	0.536158i	−0.386240	−	0.922398i	$-0.626226\pi$
$83$	4.88463	−	4.88463i	0.536158	−	0.536158i	0.922398	+	0.386240i	$0.126226\pi$
$84$	−0.152762	+	0.253489i	−0.0166677	+	0.0276580i
$85$	−0.508902	+	17.9306i	−0.0551982	+	1.94485i
$86$	−1.95345	+	2.49694i	−0.210646	+	0.269252i
$87$	0.348605			0.0373744
$88$	−6.33042	−	2.83334i	−0.674825	−	0.302035i
$89$		−	0.882403i		−	0.0935345i	−0.998906	−	0.0467673i	$-0.985108\pi$
$89$		−	0.882403i		−	0.0935345i	0.998906	−	0.0467673i	$-0.0148919\pi$
$90$	9.37676	−	0.875949i	0.988397	−	0.0923332i
$91$	4.26620	−	4.26620i	0.447219	−	0.447219i
$92$	−15.6403	+	3.87790i	−1.63061	+	0.404299i
$93$	−0.685145	+	0.685145i	−0.0710462	+	0.0710462i
$94$	−12.7433	+	1.55625i	−1.31437	+	0.160515i
$95$	−3.63572	−	3.84813i	−0.373017	−	0.394810i
$96$	−0.823910	−	0.148049i	−0.0840899	−	0.0151102i
$97$			9.29488i			0.943752i	0.881665	+	0.471876i	$0.156423\pi$
$97$			9.29488i			0.943752i	−0.881665	+	0.471876i	$0.843577\pi$
$98$	−0.171434	−	1.40378i	−0.0173174	−	0.141804i
$99$	−5.16370	−	5.16370i	−0.518972	−	0.518972i
$100$	−9.82698	+	1.85218i	−0.982698	+	0.185218i
$101$	3.85960	−	3.85960i	0.384045	−	0.384045i	−0.488512	−	0.872557i	$-0.662460\pi$
$101$	3.85960	−	3.85960i	0.384045	−	0.384045i	0.872557	+	0.488512i	$0.162460\pi$
$102$	1.03445	−	1.32226i	0.102426	−	0.130923i
$103$	−5.43135			−0.535167			−0.267583	−	0.963535i	$-0.586225\pi$
$103$	−5.43135			−0.535167			−0.267583	+	0.963535i	$0.586225\pi$
$104$	15.5759	+	6.97137i	1.52734	+	0.683599i
$105$	0.240522	−	0.227246i	0.0234725	−	0.0221769i
$106$	1.01446	−	1.29671i	0.0985333	−	0.125947i
$107$	−11.5864	−	11.5864i	−1.12010	−	1.12010i	−0.991726	−	0.128373i	$-0.959024\pi$
$107$	−11.5864	−	11.5864i	−1.12010	−	1.12010i	−0.128373	−	0.991726i	$-0.540976\pi$
$108$	−1.51539	−	0.913228i	−0.145818	−	0.0878754i
$109$	−4.25084	−	4.25084i	−0.407156	−	0.407156i	0.473589	−	0.880746i	$-0.342958\pi$
$109$	−4.25084	−	4.25084i	−0.407156	−	0.407156i	−0.880746	+	0.473589i	$0.842958\pi$
$110$	5.96926	+	4.94929i	0.569147	+	0.471896i
$111$	−0.587156			−0.0557304
$112$	3.53668	−	1.86867i	0.334185	−	0.176572i
$113$			8.00824i			0.753352i	0.926345	+	0.376676i	$0.122933\pi$
$113$			8.00824i			0.753352i	−0.926345	+	0.376676i	$0.877067\pi$
$114$	0.0600623	+	0.491820i	0.00562535	+	0.0460631i
$115$	18.0086	+	0.511115i	1.67931	+	0.0476617i
$116$	−4.03537	−	2.43186i	−0.374674	−	0.225793i
$117$	12.7052	+	12.7052i	1.17459	+	1.17459i
$118$	−4.13436	−	3.23446i	−0.380599	−	0.297756i
$119$			8.02204i			0.735379i
$120$	0.843061	+	0.406424i	0.0769606	+	0.0371012i
$121$			4.98725i			0.453386i
$122$	8.44108	−	10.7896i	0.764220	−	0.976843i
$123$	−0.991157	−	0.991157i	−0.0893696	−	0.0893696i
$124$	12.7106	−	3.15151i	1.14145	−	0.283014i
$125$	11.1399	+	0.950548i	0.996379	+	0.0850196i
$126$	4.18061	−	0.510547i	0.372439	−	0.0454832i
$127$			13.9749i			1.24007i	0.784574	+	0.620035i	$0.212882\pi$
$127$			13.9749i			1.24007i	−0.784574	+	0.620035i	$0.787118\pi$
$128$	8.50459	+	7.46136i	0.751707	+	0.659498i
$129$	−0.331733			−0.0292074
$130$	−14.6872	−	12.1776i	−1.28816	−	1.06805i
$131$	9.30572	+	9.30572i	0.813045	+	0.813045i	0.985089	−	0.172045i	$-0.0550373\pi$
$131$	9.30572	+	9.30572i	0.813045	+	0.813045i	−0.172045	+	0.985089i	$0.555037\pi$
$132$	−0.174650	−	0.704396i	−0.0152013	−	0.0613098i
$133$	−1.67411	−	1.67411i	−0.145164	−	0.145164i
$134$	2.11026	+	1.65093i	0.182299	+	0.142619i
$135$	1.35850	+	1.43786i	0.116921	+	0.123752i
$136$	−21.1986	+	8.08982i	−1.81776	+	0.693696i
$137$	−7.28917			−0.622756			−0.311378	−	0.950286i	$-0.600791\pi$
$137$	−7.28917			−0.622756			−0.311378	+	0.950286i	$0.600791\pi$
$138$	−1.32801	−	1.03895i	−0.113047	−	0.0884411i
$139$	−12.7409	+	12.7409i	−1.08067	+	1.08067i	−0.0842245	+	0.996447i	$0.526841\pi$
$139$	−12.7409	+	12.7409i	−1.08067	+	1.08067i	−0.996447	+	0.0842245i	$0.973159\pi$
$140$	−4.36949	+	0.952666i	−0.369289	+	0.0805150i
$141$	−0.949887	−	0.949887i	−0.0799949	−	0.0799949i
$142$	11.7423	−	1.43400i	0.985391	−	0.120338i
$143$			14.7943i			1.23716i
$144$	5.56508	+	10.5326i	0.463757	+	0.877715i
$145$	3.61759	+	3.82893i	0.300424	+	0.317975i
$146$	0.0991262	+	0.811695i	0.00820375	+	0.0671763i
$147$	0.104638	−	0.104638i	0.00863041	−	0.00863041i
$148$	6.79678	+	4.09599i	0.558692	+	0.336689i
$149$	3.52750	−	3.52750i	0.288984	−	0.288984i	−0.547694	−	0.836679i	$-0.684494\pi$
$149$	3.52750	−	3.52750i	0.288984	−	0.288984i	0.836679	+	0.547694i	$0.184494\pi$
$150$	−0.786244	−	0.690460i	−0.0641966	−	0.0563758i
$151$		−	12.3242i		−	1.00293i	−0.865179	−	0.501463i	$-0.832795\pi$
$151$		−	12.3242i		−	1.00293i	0.865179	−	0.501463i	$-0.167205\pi$
$152$	2.73566	−	6.11218i	0.221891	−	0.495763i
$153$	−23.8905			−1.93143
$154$	2.73126	+	2.13676i	0.220091	+	0.172185i
$155$	−14.6353	−	0.415376i	−1.17554	−	0.0333638i
$156$	0.429723	+	1.73315i	0.0344054	+	0.138763i
$157$	−2.04609	+	2.04609i	−0.163296	+	0.163296i	−0.784025	−	0.620729i	$-0.786837\pi$
$157$	−2.04609	+	2.04609i	−0.163296	+	0.163296i	0.620729	+	0.784025i	$0.286837\pi$
$158$	2.07550	+	16.9952i	0.165118	+	1.35207i
$159$	0.172275			0.0136623
$160$	−6.92387	−	10.5858i	−0.547380	−	0.836884i
$161$	8.05693			0.634975
$162$	1.50920	+	12.3581i	0.118574	+	0.970941i
$163$	9.20392	−	9.20392i	0.720907	−	0.720907i	−0.247883	−	0.968790i	$-0.579735\pi$
$163$	9.20392	−	9.20392i	0.720907	−	0.720907i	0.968790	+	0.247883i	$0.0797350\pi$
$164$	4.55910	+	18.3877i	0.356006	+	1.43584i
$165$	−0.0230193	+	0.811058i	−0.00179205	+	0.0631408i
$166$	−7.69436	−	6.01958i	−0.597198	−	0.467210i
$167$	1.38860			0.107453			0.0537266	−	0.998556i	$-0.482890\pi$
$167$	1.38860			0.107453			0.0537266	+	0.998556i	$0.482890\pi$
$168$	0.382033	+	0.170989i	0.0294745	+	0.0131921i
$169$		−	23.4009i		−	1.80007i
$170$	25.2579	−	2.35952i	1.93720	−	0.180967i
$171$	4.98568	−	4.98568i	0.381265	−	0.381265i
$172$	3.84006	+	2.31416i	0.292802	+	0.176453i
$173$	8.96114	−	8.96114i	0.681303	−	0.681303i	−0.278991	−	0.960294i	$-0.590000\pi$
$173$	8.96114	−	8.96114i	0.681303	−	0.681303i	0.960294	+	0.278991i	$0.0900000\pi$
$174$	−0.0597626	−	0.489366i	−0.00453059	−	0.0370987i
$175$	4.99195	+	0.283589i	0.377356	+	0.0214373i
$176$	−2.89215	+	9.37228i	−0.218004	+	0.706462i
$177$		−	0.549272i		−	0.0412858i
$178$	−1.23870	+	0.151274i	−0.0928448	+	0.0113384i
$179$	−8.30769	−	8.30769i	−0.620946	−	0.620946i	0.324828	−	0.945773i	$-0.394694\pi$
$179$	−8.30769	−	8.30769i	−0.620946	−	0.620946i	−0.945773	+	0.324828i	$0.894694\pi$
$180$	−2.83714	−	13.0128i	−0.211468	−	0.969915i
$181$	−3.15079	+	3.15079i	−0.234196	+	0.234196i	−0.814442	−	0.580245i	$-0.802957\pi$
$181$	−3.15079	+	3.15079i	−0.234196	+	0.234196i	0.580245	+	0.814442i	$0.302957\pi$
$182$	−6.72020	−	5.25745i	−0.498134	−	0.389708i
$183$	1.43346			0.105964
$184$	8.12500	+	21.2908i	0.598983	+	1.56958i
$185$	−6.09311	−	6.44908i	−0.447975	−	0.474146i
$186$	1.07925	+	0.844339i	0.0791346	+	0.0619099i
$187$	−13.9093	−	13.9093i	−1.01715	−	1.01715i
$188$	4.36927	+	17.6221i	0.318662	+	1.28522i
$189$	0.625538	+	0.625538i	0.0455012	+	0.0455012i
$190$	−4.77866	+	5.76347i	−0.346680	+	0.418126i
$191$	−15.7658			−1.14077			−0.570387	−	0.821376i	$-0.693207\pi$
$191$	−15.7658			−1.14077			−0.570387	+	0.821376i	$0.693207\pi$
$192$	−0.0665834	+	1.18197i	−0.00480524	+	0.0853015i
$193$		−	11.9840i		−	0.862626i	−0.902202	−	0.431313i	$-0.858051\pi$
$193$		−	11.9840i		−	0.862626i	0.902202	−	0.431313i	$-0.141949\pi$
$194$	13.0480	−	1.59346i	0.936793	−	0.114404i
$195$	0.0566384	−	1.99559i	0.00405596	−	0.142907i
$196$	−1.94122	+	0.481312i	−0.138659	+	0.0343794i
$197$	−8.67114	−	8.67114i	−0.617793	−	0.617793i	0.327172	−	0.944965i	$-0.393904\pi$
$197$	−8.67114	−	8.67114i	−0.617793	−	0.617793i	−0.944965	+	0.327172i	$0.893904\pi$
$198$	−6.36349	+	8.13396i	−0.452234	+	0.578055i
$199$		−	4.17895i		−	0.296238i	−0.988970	−	0.148119i	$-0.952678\pi$
$199$		−	4.17895i		−	0.296238i	0.988970	−	0.148119i	$-0.0473219\pi$
$200$	4.28473	+	13.4774i	0.302976	+	0.952998i
$201$			0.280360i			0.0197750i
$202$	−6.07972	−	4.75638i	−0.427767	−	0.334658i
$203$	1.66576	+	1.66576i	0.116914	+	0.116914i
$204$	−2.03350	−	1.22546i	−0.142374	−	0.0857997i
$205$	0.600899	−	21.1720i	0.0419686	−	1.47872i
$206$	0.931116	+	7.62444i	0.0648740	+	0.531220i
$207$			23.9943i			1.66772i
$208$	7.11607	−	23.0603i	0.493411	−	1.59894i
$209$	5.80546			0.401572
$210$	−0.360238	−	0.298683i	−0.0248588	−	0.0206111i
$211$	−10.0227	−	10.0227i	−0.689990	−	0.689990i	0.272240	−	0.962229i	$-0.412236\pi$
$211$	−10.0227	−	10.0227i	−0.689990	−	0.689990i	−0.962229	+	0.272240i	$0.912236\pi$
$212$	−1.99421	−	1.20179i	−0.136963	−	0.0825391i
$213$	0.875271	+	0.875271i	0.0599726	+	0.0599726i
$214$	−14.2785	+	18.2511i	−0.976058	+	1.24762i
$215$	−3.44250	−	3.64362i	−0.234777	−	0.248493i
$216$	−1.02219	+	2.28383i	−0.0695510	+	0.155395i
$217$	−6.54775			−0.444490
$218$	−5.23852	+	6.69600i	−0.354798	+	0.453510i
$219$	−0.0605038	+	0.0605038i	−0.00408847	+	0.00408847i
$220$	5.92440	−	9.22803i	0.399423	−	0.622154i
$221$	34.2236	+	34.2236i	2.30213	+	2.30213i
$222$	0.100658	+	0.824241i	0.00675575	+	0.0553194i
$223$		−	18.6669i		−	1.25003i	−0.780613	−	0.625015i	$-0.785093\pi$
$223$		−	18.6669i		−	1.25003i	0.780613	−	0.625015i	$-0.214907\pi$
$224$	−3.22951	−	4.64438i	−0.215781	−	0.310316i
$225$	−0.844557	+	14.8665i	−0.0563038	+	0.991103i
$226$	11.2418	−	1.37288i	0.747796	−	0.0913228i
$227$	−8.78488	+	8.78488i	−0.583073	+	0.583073i	−0.935746	−	0.352674i	$-0.885273\pi$
$227$	−8.78488	+	8.78488i	−0.583073	+	0.583073i	0.352674	+	0.935746i	$0.385273\pi$
$228$	0.680112	−	0.168629i	0.0450415	−	0.0111677i
$229$	2.58269	−	2.58269i	0.170669	−	0.170669i	−0.616604	−	0.787273i	$-0.711492\pi$
$229$	2.58269	−	2.58269i	0.170669	−	0.170669i	0.787273	+	0.616604i	$0.211492\pi$
$230$	−2.36978	−	25.3678i	−0.156259	−	1.67270i
$231$			0.362862i			0.0238746i
$232$	−2.72201	+	6.08169i	−0.178709	+	0.399282i
$233$	−13.0423			−0.854431			−0.427215	−	0.904150i	$-0.640505\pi$
$233$	−13.0423			−0.854431			−0.427215	+	0.904150i	$0.640505\pi$
$234$	15.6572	−	20.0134i	1.02355	−	1.30832i
$235$	0.575879	−	20.2905i	0.0375662	−	1.32360i
$236$	−3.83172	+	6.35824i	−0.249423	+	0.413886i
$237$	−1.26682	+	1.26682i	−0.0822891	+	0.0822891i
$238$	11.2612	−	1.37525i	0.729956	−	0.0891441i
$239$	−4.72733			−0.305786			−0.152893	−	0.988243i	$-0.548859\pi$
$239$	−4.72733			−0.305786			−0.152893	+	0.988243i	$0.548859\pi$
$240$	0.426002	−	1.25315i	0.0274983	−	0.0808905i
$241$	−7.57134			−0.487713			−0.243857	−	0.969811i	$-0.578413\pi$
$241$	−7.57134			−0.487713			−0.243857	+	0.969811i	$0.578413\pi$
$242$	7.00102	−	0.854982i	0.450042	−	0.0549603i
$243$	−2.79778	+	2.79778i	−0.179478	+	0.179478i
$244$	−16.5933	−	9.99976i	−1.06228	−	0.640169i
$245$	2.23517	+	0.0634380i	0.142800	+	0.00405290i
$246$	−1.22145	+	1.56129i	−0.0778770	+	0.0995441i
$247$	−14.2842			−0.908883
$248$	−6.60308	−	17.3027i	−0.419296	−	1.09872i
$249$		−	1.02224i		−	0.0647817i
$250$	−0.575383	−	15.8009i	−0.0363904	−	0.999338i
$251$	19.5099	−	19.5099i	1.23145	−	1.23145i	0.268048	−	0.963405i	$-0.413621\pi$
$251$	19.5099	−	19.5099i	1.23145	−	1.23145i	0.963405	−	0.268048i	$-0.0863787\pi$
$252$	−1.43340	−	5.78115i	−0.0902955	−	0.364178i
$253$	−13.9698	+	13.9698i	−0.878276	+	0.878276i
$254$	19.6177	−	2.39577i	1.23093	−	0.150324i
$255$	1.82298	+	1.92948i	0.114159	+	0.120829i
$256$	9.01617	−	13.2177i	0.563511	−	0.826109i
$257$		−	2.30117i		−	0.143543i	−0.997421	−	0.0717714i	$-0.977135\pi$
$257$		−	2.30117i		−	0.143543i	0.997421	−	0.0717714i	$-0.0228652\pi$
$258$	0.0568702	+	0.465681i	0.00354058	+	0.0289920i
$259$	−2.80565	−	2.80565i	−0.174335	−	0.174335i
$260$	−14.5768	+	22.7054i	−0.904018	+	1.40813i
$261$	−4.96081	+	4.96081i	−0.307066	+	0.307066i
$262$	11.4679	−	14.6585i	0.708490	−	0.905608i
$263$	2.18476			0.134718			0.0673589	−	0.997729i	$-0.478543\pi$
$263$	2.18476			0.134718			0.0673589	+	0.997729i	$0.478543\pi$
$264$	−0.958879	+	0.365928i	−0.0590149	+	0.0225213i
$265$	1.78775	+	1.89220i	0.109821	+	0.116237i
$266$	−2.06310	+	2.63710i	−0.126497	+	0.161691i
$267$	−0.0923331	−	0.0923331i	−0.00565069	−	0.00565069i
$268$	1.95578	−	3.24537i	0.119468	−	0.198243i
$269$	−6.25331	−	6.25331i	−0.381271	−	0.381271i	0.490289	−	0.871560i	$-0.336891\pi$
$269$	−6.25331	−	6.25331i	−0.381271	−	0.381271i	−0.871560	+	0.490289i	$0.836891\pi$
$270$	1.78556	−	2.15354i	0.108666	−	0.131060i
$271$	−15.5753			−0.946133			−0.473067	−	0.881027i	$-0.656853\pi$
$271$	−15.5753			−0.946133			−0.473067	+	0.881027i	$0.656853\pi$
$272$	14.9905	+	28.3714i	0.908934	+	1.72027i
$273$		−	0.892815i		−	0.0540356i
$274$	1.24961	+	10.2324i	0.0754917	+	0.618163i
$275$	−9.14721	+	8.16379i	−0.551598	+	0.492295i
$276$	−1.23079	+	2.04235i	−0.0740851	+	0.122935i
$277$	17.6950	+	17.6950i	1.06319	+	1.06319i	0.997864	+	0.0653231i	$0.0208078\pi$
$277$	17.6950	+	17.6950i	1.06319	+	1.06319i	0.0653231	+	0.997864i	$0.479192\pi$
$278$	20.0697	+	15.7013i	1.20370	+	0.941701i
$279$		−	19.4999i		−	1.16743i
$280$	2.08642	+	5.97050i	0.124687	+	0.356806i
$281$		−	12.8079i		−	0.764055i	−0.924151	−	0.382028i	$-0.875226\pi$
$281$		−	12.8079i		−	0.764055i	0.924151	−	0.382028i	$-0.124774\pi$
$282$	−1.17059	+	1.49628i	−0.0697079	+	0.0891022i
$283$	17.6194	+	17.6194i	1.04736	+	1.04736i	0.998821	+	0.0485418i	$0.0154574\pi$
$283$	17.6194	+	17.6194i	1.04736	+	1.04736i	0.0485418	+	0.998821i	$0.484543\pi$
$284$	−4.02605	−	16.2378i	−0.238902	−	0.963536i
$285$	−0.783097	−	0.0222257i	−0.0463867	−	0.00131653i
$286$	20.7679	−	2.53623i	1.22803	−	0.149971i
$287$		−	9.47223i		−	0.559128i
$288$	13.8314	−	9.61781i	0.815025	−	0.566735i
$289$	−47.3531			−2.78548
$290$	4.75482	−	5.73472i	0.279213	−	0.336754i
$291$	0.972600	+	0.972600i	0.0570148	+	0.0570148i
$292$	1.12245	−	0.278304i	0.0656865	−	0.0162865i
$293$	−8.39594	−	8.39594i	−0.490496	−	0.490496i	0.417966	−	0.908462i	$-0.362743\pi$
$293$	−8.39594	−	8.39594i	−0.490496	−	0.490496i	−0.908462	+	0.417966i	$0.862743\pi$
$294$	−0.164828	−	0.128951i	−0.00961296	−	0.00752057i
$295$	6.03298	−	5.69998i	0.351254	−	0.331866i
$296$	4.58469	−	10.2434i	0.266480	−	0.595386i
$297$	−2.16923			−0.125871
$298$	−5.55659	−	4.34712i	−0.321884	−	0.251822i
$299$	34.3725	−	34.3725i	1.98781	−	1.98781i
$300$	−0.834468	+	1.22209i	−0.0481781	+	0.0705571i
$301$	−1.58514	−	1.58514i	−0.0913660	−	0.0913660i
$302$	−17.3005	+	2.11278i	−0.995530	+	0.121577i
$303$		−	0.807724i		−	0.0464025i
$304$	−9.04916	−	2.79244i	−0.519005	−	0.160157i
$305$	14.8754	+	15.7445i	0.851765	+	0.901527i
$306$	4.09563	+	33.5370i	0.234132	+	1.91719i
$307$	11.0261	−	11.0261i	0.629292	−	0.629292i	−0.318598	−	0.947890i	$-0.603212\pi$
$307$	11.0261	−	11.0261i	0.629292	−	0.629292i	0.947890	+	0.318598i	$0.103212\pi$
$308$	2.53132	−	4.20041i	0.144235	−	0.239340i
$309$	−0.568326	+	0.568326i	−0.0323310	+	0.0323310i
$310$	1.92589	+	20.6160i	0.109383	+	1.17091i
$311$			20.0037i			1.13431i	0.823612	+	0.567154i	$0.191955\pi$
$311$			20.0037i			1.13431i	−0.823612	+	0.567154i	$0.808045\pi$
$312$	2.35930	−	0.900359i	0.133569	−	0.0509728i
$313$	−0.775159			−0.0438146			−0.0219073	−	0.999760i	$-0.506974\pi$
$313$	−0.775159			−0.0438146			−0.0219073	+	0.999760i	$0.506974\pi$
$314$	3.22304	+	2.52150i	0.181887	+	0.142297i
$315$	−0.188925	+	6.65656i	−0.0106447	+	0.375055i
$316$	23.5018	−	5.82711i	1.32208	−	0.327800i
$317$	13.6756	−	13.6756i	0.768097	−	0.768097i	−0.209674	−	0.977771i	$-0.567240\pi$
$317$	13.6756	−	13.6756i	0.768097	−	0.768097i	0.977771	+	0.209674i	$0.0672404\pi$
$318$	−0.0295337	−	0.241837i	−0.00165617	−	0.0135615i
$319$	−5.77650			−0.323422
$320$	−13.6733	+	11.5344i	−0.764358	+	0.644792i
$321$	−2.42476			−0.135337
$322$	−1.38123	−	11.3102i	−0.0769729	−	0.630292i
$323$	13.4298	−	13.4298i	0.747255	−	0.747255i
$324$	17.0893	−	4.23718i	0.949407	−	0.235399i
$325$	22.5065	−	20.0868i	1.24844	−	1.11422i
$326$	−14.4982	−	11.3425i	−0.802980	−	0.628200i
$327$	−0.889600			−0.0491950
$328$	25.0308	−	9.55226i	1.38209	−	0.527436i
$329$		−	9.07783i		−	0.500477i
$330$	1.14250	−	0.106729i	0.0628924	−	0.00587522i
$331$	5.24436	−	5.24436i	0.288256	−	0.288256i	−0.548134	−	0.836390i	$-0.684662\pi$
$331$	5.24436	−	5.24436i	0.288256	−	0.288256i	0.836390	+	0.548134i	$0.184662\pi$
$332$	−7.13111	+	11.8332i	−0.391371	+	0.649430i
$333$	8.35551	−	8.35551i	0.457879	−	0.457879i
$334$	−0.238053	−	1.94930i	−0.0130257	−	0.106661i
$335$	−3.07935	+	2.90938i	−0.168243	+	0.158957i
$336$	0.174538	−	0.565605i	0.00952181	−	0.0308563i
$337$		−	28.6194i		−	1.55900i	−0.626402	−	0.779500i	$-0.715473\pi$
$337$		−	28.6194i		−	1.55900i	0.626402	−	0.779500i	$-0.284527\pi$
$338$	−32.8499	+	4.01171i	−1.78680	+	0.218208i
$339$	0.837968	+	0.837968i	0.0455122	+	0.0455122i
$340$	−7.64233	−	35.0522i	−0.414463	−	1.90097i
$341$	11.3531	−	11.3531i	0.614804	−	0.614804i
$342$	−7.85354	−	6.14411i	−0.424671	−	0.332235i
$343$	1.00000			0.0539949
$344$	2.59027	−	5.78734i	0.139658	−	0.312032i
$345$	1.93787	−	1.83090i	0.104331	−	0.0985725i
$346$	−14.1157	−	11.0433i	−0.758867	−	0.593689i
$347$	4.92205	+	4.92205i	0.264230	+	0.264230i	0.826770	−	0.562540i	$-0.190176\pi$
$347$	4.92205	+	4.92205i	0.264230	+	0.264230i	−0.562540	+	0.826770i	$0.690176\pi$
$348$	−0.676719	+	0.167788i	−0.0362759	+	0.00899437i
$349$	−18.6160	−	18.6160i	−0.996490	−	0.996490i	0.00350407	−	0.999994i	$-0.498885\pi$
$349$	−18.6160	−	18.6160i	−0.996490	−	0.996490i	−0.999994	+	0.00350407i	$0.998885\pi$
$350$	−0.457691	−	7.05624i	−0.0244646	−	0.377172i
$351$	5.33734			0.284886
$352$	13.6525	+	2.45323i	0.727679	+	0.130758i
$353$		−	2.69176i		−	0.143268i	−0.997431	−	0.0716339i	$-0.977179\pi$
$353$		−	2.69176i		−	0.143268i	0.997431	−	0.0716339i	$-0.0228213\pi$
$354$	−0.771060	+	0.0941638i	−0.0409814	+	0.00500475i
$355$	−0.530642	+	18.6966i	−0.0281636	+	0.992312i
$356$	0.424711	+	1.71294i	0.0225097	+	0.0907856i
$357$	0.839412	+	0.839412i	0.0444264	+	0.0444264i
$358$	−10.2380	+	13.0864i	−0.541094	+	0.691639i
$359$		−	23.6938i		−	1.25051i	−0.780421	−	0.625254i	$-0.784995\pi$
$359$		−	23.6938i		−	1.25051i	0.780421	−	0.625254i	$-0.215005\pi$
$360$	−17.7808	+	6.21356i	−0.937128	+	0.327483i
$361$		−	13.3947i		−	0.704983i
$362$	4.96318	+	3.88288i	0.260859	+	0.204080i
$363$	0.521856	+	0.521856i	0.0273904	+	0.0273904i
$364$	−6.22826	+	10.3350i	−0.326450	+	0.541702i
$365$	−1.29242	−	0.0366810i	−0.0676482	−	0.00191997i
$366$	−0.245743	−	2.01226i	−0.0128452	−	0.105183i
$367$			12.9993i			0.678557i	0.940686	+	0.339278i	$0.110183\pi$
$367$			12.9993i			0.678557i	−0.940686	+	0.339278i	$0.889817\pi$
$368$	28.4948	−	15.0557i	1.48539	−	0.784833i
$369$	28.2093			1.46852
$370$	−8.00856	+	9.65901i	−0.416345	+	0.502148i
$371$	0.823193	+	0.823193i	0.0427381	+	0.0427381i
$372$	1.00025	−	1.65979i	0.0518605	−	0.0860559i
$373$	−5.60903	−	5.60903i	−0.290424	−	0.290424i	0.546823	−	0.837248i	$-0.315837\pi$
$373$	−5.60903	−	5.60903i	−0.290424	−	0.290424i	−0.837248	+	0.546823i	$0.815837\pi$
$374$	−17.1412	+	21.9102i	−0.886350	+	1.13295i
$375$	1.26512	−	1.06619i	0.0653304	−	0.0550579i
$376$	23.9885	−	9.15453i	1.23711	−	0.472109i
$377$	14.2130			0.732004
$378$	0.770882	−	0.985358i	0.0396499	−	0.0506814i
$379$	−18.0027	+	18.0027i	−0.924734	+	0.924734i	−0.997359	−	0.0726250i	$-0.976862\pi$
$379$	−18.0027	+	18.0027i	−0.924734	+	0.924734i	0.0726250	+	0.997359i	$0.476862\pi$
$380$	8.90990	+	5.72015i	0.457068	+	0.293438i
$381$	1.46231	+	1.46231i	0.0749162	+	0.0749162i
$382$	2.70279	+	22.1318i	0.138287	+	1.13236i
$383$			38.9814i			1.99186i	0.0901510	+	0.995928i	$0.471265\pi$
$383$			38.9814i			1.99186i	−0.0901510	+	0.995928i	$0.528735\pi$
$384$	1.67065	−	0.109161i	0.0852549	−	0.00557061i
$385$	−3.98553	+	3.76554i	−0.203121	+	0.191910i
$386$	−16.8229	+	2.05446i	−0.856264	+	0.104569i
$387$	4.72071	−	4.72071i	0.239967	−	0.239967i
$388$	−4.47374	−	18.0434i	−0.227120	−	0.916016i
$389$	−25.1887	+	25.1887i	−1.27712	+	1.27712i	−0.334848	+	0.942272i	$0.608685\pi$
$389$	−25.1887	+	25.1887i	−1.27712	+	1.27712i	−0.942272	+	0.334848i	$0.891315\pi$
$390$	−2.81109	+	0.262604i	−0.142345	+	0.0132975i
$391$			64.6330i			3.26863i
$392$	1.00845	+	2.64254i	0.0509344	+	0.133469i
$393$	1.94747			0.0982367
$394$	−10.6859	+	13.6589i	−0.538347	+	0.688127i
$395$	−27.0605	−	0.768025i	−1.36156	−	0.0386435i
$396$	12.5092	+	7.53854i	0.628613	+	0.378826i
$397$	2.83242	−	2.83242i	0.142155	−	0.142155i	−0.632448	−	0.774603i	$-0.717950\pi$
$397$	2.83242	−	2.83242i	0.142155	−	0.142155i	0.774603	+	0.632448i	$0.217950\pi$
$398$	−5.86635	+	0.716414i	−0.294053	+	0.0359106i
$399$	−0.350353			−0.0175396
$400$	18.1849	−	8.32533i	0.909243	−	0.416266i
$401$	−6.64448			−0.331809			−0.165905	−	0.986142i	$-0.553054\pi$
$401$	−6.64448			−0.331809			−0.165905	+	0.986142i	$0.553054\pi$
$402$	0.393564	−	0.0480631i	0.0196292	−	0.00239717i
$403$	−27.9340	+	27.9340i	−1.39149	+	1.39149i
$404$	−5.63467	+	9.35002i	−0.280335	+	0.465181i
$405$	−19.6771	−	0.558470i	−0.977761	−	0.0277506i
$406$	2.05280	−	2.62394i	0.101879	−	0.130224i
$407$	9.72938			0.482267
$408$	−1.37168	+	3.06469i	−0.0679081	+	0.151725i
$409$			0.631265i			0.0312140i	0.999878	+	0.0156070i	$0.00496807\pi$
$409$			0.631265i			0.0312140i	−0.999878	+	0.0156070i	$0.995032\pi$
$410$	−29.8240	+	2.78607i	−1.47290	+	0.137594i
$411$	−0.762726	+	0.762726i	−0.0376225	+	0.0376225i
$412$	10.5434	−	2.61417i	0.519438	−	0.128791i
$413$	2.62463	−	2.62463i	0.129149	−	0.129149i
$414$	33.6829	−	4.11344i	1.65542	−	0.202165i
$415$	11.2278	−	10.6081i	0.551153	−	0.520731i
$416$	−33.5916	−	6.03612i	−1.64696	−	0.295945i
$417$			2.66638i			0.130573i
$418$	−0.995253	−	8.14962i	−0.0486794	−	0.398611i
$419$	12.1713	+	12.1713i	0.594606	+	0.594606i	0.938872	−	0.344266i	$-0.111872\pi$
$419$	12.1713	+	12.1713i	0.594606	+	0.594606i	−0.344266	+	0.938872i	$0.611872\pi$
$420$	−0.357530	+	0.556901i	−0.0174457	+	0.0271740i
$421$	−16.3957	+	16.3957i	−0.799076	+	0.799076i	−0.982950	−	0.183874i	$-0.941136\pi$
$421$	−16.3957	+	16.3957i	−0.799076	+	0.799076i	0.183874	+	0.982950i	$0.441136\pi$
$422$	−12.3515	+	15.7879i	−0.601259	+	0.768543i
$423$	27.0347			1.31447
$424$	−1.34517	+	3.00547i	−0.0653274	+	0.145959i
$425$	−2.27496	+	40.0456i	−0.110352	+	1.94250i
$426$	1.07864	−	1.37874i	0.0522603	−	0.0668003i
$427$	6.84958	+	6.84958i	0.331474	+	0.331474i
$428$	28.0684	+	16.9151i	1.35674	+	0.817621i
$429$	1.54804	+	1.54804i	0.0747403	+	0.0747403i
$430$	−4.52469	+	5.45717i	−0.218200	+	0.263168i
$431$	39.4780			1.90159			0.950794	−	0.309824i	$-0.100270\pi$
$431$	39.4780			1.90159			0.950794	+	0.309824i	$0.100270\pi$
$432$	3.38125	+	1.04340i	0.162680	+	0.0502008i
$433$		−	28.2211i		−	1.35622i	−0.734961	−	0.678109i	$-0.762800\pi$
$433$		−	28.2211i		−	1.35622i	0.734961	−	0.678109i	$-0.237200\pi$
$434$	1.12251	+	9.19163i	0.0538820	+	0.441212i
$435$	0.779190	+	0.0221148i	0.0373593	+	0.00106032i
$436$	10.2978	+	6.20584i	0.493175	+	0.297206i
$437$	−13.4882	−	13.4882i	−0.645229	−	0.645229i
$438$	0.0953066	+	0.0745619i	0.00455393	+	0.00356270i
$439$		−	8.28411i		−	0.395379i	−0.980265	−	0.197690i	$-0.936656\pi$
$439$		−	8.28411i		−	0.395379i	0.980265	−	0.197690i	$-0.0633438\pi$
$440$	−13.9698	−	6.73458i	−0.665985	−	0.321058i
$441$			2.97810i			0.141814i
$442$	42.1755	−	53.9097i	2.00608	−	2.56422i
$443$	6.29636	+	6.29636i	0.299149	+	0.299149i	0.840681	−	0.541531i	$-0.182155\pi$
$443$	6.29636	+	6.29636i	0.299149	+	0.299149i	−0.541531	+	0.840681i	$0.682155\pi$
$444$	1.13980	−	0.282605i	0.0540925	−	0.0134119i
$445$	0.0559779	−	1.97232i	0.00265361	−	0.0934969i
$446$	−26.2043	+	3.20014i	−1.24081	+	0.151531i
$447$		−	0.738223i		−	0.0349168i
$448$	−5.96606	+	5.32974i	−0.281870	+	0.251807i
$449$	−25.7571			−1.21555			−0.607777	−	0.794108i	$-0.707938\pi$
$449$	−25.7571			−1.21555			−0.607777	+	0.794108i	$0.707938\pi$
$450$	21.0142	−	1.36305i	0.990619	−	0.0642548i
$451$	16.4238	+	16.4238i	0.773367	+	0.773367i
$452$	−3.85446	−	15.5458i	−0.181299	−	0.731211i
$453$	−1.28958	−	1.28958i	−0.0605896	−	0.0605896i
$454$	13.8381	+	10.8260i	0.649454	+	0.508092i
$455$	9.80631	−	9.26504i	0.459727	−	0.434352i
$456$	−0.353313	−	0.925822i	−0.0165454	−	0.0433556i
$457$	−5.61169			−0.262504			−0.131252	−	0.991349i	$-0.541900\pi$
$457$	−5.61169			−0.262504			−0.131252	+	0.991349i	$0.541900\pi$
$458$	−4.06830	−	3.18278i	−0.190099	−	0.148722i
$459$	−5.01809	+	5.01809i	−0.234224	+	0.234224i
$460$	−35.2046	+	7.67556i	−1.64143	+	0.357875i
$461$	−20.4880	−	20.4880i	−0.954221	−	0.954221i	0.0447760	−	0.998997i	$-0.485743\pi$
$461$	−20.4880	−	20.4880i	−0.954221	−	0.954221i	−0.998997	+	0.0447760i	$0.985743\pi$
$462$	0.509381	−	0.0622069i	0.0236985	−	0.00289413i
$463$			16.7711i			0.779421i	0.920937	+	0.389711i	$0.127425\pi$
$463$			16.7711i			0.779421i	−0.920937	+	0.389711i	$0.872575\pi$
$464$	9.00402	+	2.77851i	0.418001	+	0.128989i
$465$	−1.57488	+	1.48795i	−0.0730332	+	0.0690020i
$466$	2.23589	+	18.3086i	0.103576	+	0.848130i
$467$	−2.05043	+	2.05043i	−0.0948826	+	0.0948826i	−0.752955	−	0.658072i	$-0.771372\pi$
$467$	−2.05043	+	2.05043i	−0.0948826	+	0.0948826i	0.658072	+	0.752955i	$0.271372\pi$
$468$	−30.7787	−	18.5484i	−1.42275	−	0.857400i
$469$	−1.33966	+	1.33966i	−0.0618598	+	0.0618598i
$470$	−28.5822	+	2.67006i	−1.31840	+	0.123161i
$471$			0.428198i			0.0197303i
$472$	9.58249	+	4.28888i	0.441070	+	0.197412i
$473$	5.49693			0.252749
$474$	1.99552	+	1.56117i	0.0916575	+	0.0717070i
$475$	−7.88234	−	8.83186i	−0.361666	−	0.405233i
$476$	−3.86111	−	15.5726i	−0.176973	−	0.713767i
$477$	−2.45155	+	2.45155i	−0.112249	+	0.112249i
$478$	0.810424	+	6.63615i	0.0370679	+	0.303531i
$479$	14.3929			0.657631			0.328815	−	0.944394i	$-0.393351\pi$
$479$	14.3929			0.657631			0.328815	+	0.944394i	$0.393351\pi$
$480$	−1.83218	−	0.383182i	−0.0836274	−	0.0174898i
$481$	−23.9389			−1.09152
$482$	1.29798	+	10.6285i	0.0591216	+	0.484117i
$483$	0.843062	−	0.843062i	0.0383607	−	0.0383607i
$484$	−2.40042	−	9.68135i	−0.109110	−	0.440061i
$485$	−0.589649	+	20.7756i	−0.0267746	+	0.943372i
$486$	4.40712	+	3.44785i	0.199911	+	0.156398i
$487$	−36.9085			−1.67248			−0.836242	−	0.548361i	$-0.815252\pi$
$487$	−36.9085			−1.67248			−0.836242	+	0.548361i	$0.815252\pi$
$488$	−11.1929	+	25.0078i	−0.506677	+	1.13205i
$489$		−	1.92616i		−	0.0871041i
$490$	−0.294130	−	3.14857i	−0.0132874	−	0.142238i
$491$	5.47885	−	5.47885i	0.247257	−	0.247257i	−0.572587	−	0.819844i	$-0.694060\pi$
$491$	5.47885	−	5.47885i	0.247257	−	0.247257i	0.819844	+	0.572587i	$0.194060\pi$
$492$	2.40111	+	1.44700i	0.108250	+	0.0652357i
$493$	−13.3628	+	13.3628i	−0.601831	+	0.601831i
$494$	2.44880	+	20.0520i	0.110177	+	0.902180i
$495$	−11.2142	−	11.8693i	−0.504039	−	0.533486i
$496$	−23.1573	+	12.2356i	−1.03979	+	0.549393i
$497$			8.36474i			0.375210i
$498$	−1.43500	+	0.175246i	−0.0643039	+	0.00785296i
$499$	20.1372	+	20.1372i	0.901465	+	0.901465i	0.995563	−	0.0940982i	$-0.0299968\pi$
$499$	20.1372	+	20.1372i	0.901465	+	0.901465i	−0.0940982	+	0.995563i	$0.529997\pi$
$500$	−22.0824	+	3.51652i	−0.987557	+	0.157264i
$501$	0.145301	−	0.145301i	0.00649156	−	0.00649156i
$502$	−30.7323	−	24.0430i	−1.37165	−	1.07309i
$503$	33.9792			1.51506			0.757528	−	0.652802i	$-0.226407\pi$
$503$	33.9792			1.51506			0.757528	+	0.652802i	$0.226407\pi$
$504$	−7.86976	+	3.00326i	−0.350547	+	0.133776i
$505$	8.87171	−	8.38201i	0.394786	−	0.372995i
$506$	22.0055	+	17.2157i	0.978265	+	0.765333i
$507$	−2.44863	−	2.44863i	−0.108748	−	0.108748i
$508$	−6.72628	−	27.1283i	−0.298430	−	1.20363i
$509$	−6.11409	−	6.11409i	−0.271002	−	0.271002i	0.558501	−	0.829504i	$-0.311377\pi$
$509$	−6.11409	−	6.11409i	−0.271002	−	0.271002i	−0.829504	+	0.558501i	$0.811377\pi$
$510$	2.39605	−	2.88984i	0.106099	−	0.127964i
$511$	−0.578219			−0.0255789
$512$	−20.1005	−	10.3908i	−0.888326	−	0.459213i
$513$		−	2.09444i		−	0.0924719i
$514$	−3.23034	+	0.394497i	−0.142484	+	0.0174005i
$515$	−12.1400	−	0.344554i	−0.534951	−	0.0151829i
$516$	0.643966	−	0.159667i	0.0283490	−	0.00702895i
$517$	15.7400	+	15.7400i	0.692243	+	0.692243i
$518$	−3.45754	+	4.41951i	−0.151916	+	0.194182i
$519$		−	1.87535i		−	0.0823189i
$520$	34.3724	+	16.5703i	1.50733	+	0.726655i
$521$		−	3.74342i		−	0.164002i	−0.996632	−	0.0820012i	$-0.973869\pi$
$521$		−	3.74342i		−	0.164002i	0.996632	−	0.0820012i	$-0.0261311\pi$
$522$	7.81436	+	6.11346i	0.342025	+	0.267579i
$523$	28.6720	+	28.6720i	1.25374	+	1.25374i	0.954030	+	0.299710i	$0.0968900\pi$
$523$	28.6720	+	28.6720i	1.25374	+	1.25374i	0.299710	+	0.954030i	$0.403110\pi$
$524$	−22.5434	−	13.5855i	−0.984814	−	0.593485i
$525$	0.552023	−	0.492675i	0.0240923	−	0.0215021i
$526$	−0.374541	−	3.06693i	−0.0163308	−	0.133724i
$527$		−	52.5263i		−	2.28808i
$528$	0.678069	+	1.28333i	0.0295092	+	0.0558496i
$529$	41.9141			1.82235
$530$	2.34975	−	2.83401i	0.102067	−	0.123101i
$531$	7.81640	+	7.81640i	0.339203	+	0.339203i
$532$	4.05560	+	2.44405i	0.175832	+	0.105963i
$533$	−40.4104	−	40.4104i	−1.75037	−	1.75037i
$534$	−0.113787	+	0.145445i	−0.00492403	+	0.00629401i
$535$	−25.1625	−	26.6326i	−1.08787	−	1.15143i
$536$	−4.89109	−	2.18913i	−0.211263	−	0.0945561i
$537$	−1.73860			−0.0750262
$538$	−7.70628	+	9.85033i	−0.332241	+	0.424678i
$539$	−1.73389	+	1.73389i	−0.0746840	+	0.0746840i
$540$	−3.32921	−	2.13735i	−0.143266	−	0.0919769i
$541$	16.7412	+	16.7412i	0.719759	+	0.719759i	0.968556	−	0.248797i	$-0.0800352\pi$
$541$	16.7412	+	16.7412i	0.719759	+	0.719759i	−0.248797	+	0.968556i	$0.580035\pi$
$542$	2.67014	+	21.8644i	0.114692	+	0.939156i
$543$			0.659386i			0.0282970i
$544$	37.2574	−	25.9073i	1.59740	−	1.11076i
$545$	−9.23167	−	9.77100i	−0.395441	−	0.418544i
$546$	−1.25332	+	0.153059i	−0.0536371	+	0.00655031i
$547$	11.7827	−	11.7827i	0.503790	−	0.503790i	−0.408823	−	0.912614i	$-0.634061\pi$
$547$	11.7827	−	11.7827i	0.503790	−	0.503790i	0.912614	+	0.408823i	$0.134061\pi$
$548$	14.1499	−	3.50837i	0.604454	−	0.149870i
$549$	−20.3987	+	20.3987i	−0.870597	+	0.870597i
$550$	13.0283	+	11.4412i	0.555530	+	0.487853i
$551$		−	5.57735i		−	0.237603i
$552$	3.07801	+	1.37764i	0.131009	+	0.0586363i
$553$	−12.1067			−0.514830
$554$	21.8064	−	27.8734i	0.926465	−	1.18423i
$555$	−1.31239	−	0.0372480i	−0.0557080	−	0.00158109i
$556$	18.6006	−	30.8653i	0.788841	−	1.30898i
$557$	11.3931	−	11.3931i	0.482743	−	0.482743i	−0.423264	−	0.906006i	$-0.639116\pi$
$557$	11.3931	−	11.3931i	0.482743	−	0.482743i	0.906006	+	0.423264i	$0.139116\pi$
$558$	−27.3736	+	3.34294i	−1.15882	+	0.141518i
$559$	−13.5251			−0.572049
$560$	8.02361	−	3.95242i	0.339059	−	0.167020i
$561$	−2.91090			−0.122898
$562$	−17.9795	+	2.19571i	−0.758421	+	0.0926203i
$563$	7.04393	−	7.04393i	0.296866	−	0.296866i	−0.542919	−	0.839785i	$-0.682681\pi$
$563$	7.04393	−	7.04393i	0.296866	−	0.296866i	0.839785	+	0.542919i	$0.182681\pi$
$564$	2.30113	+	1.38675i	0.0968952	+	0.0583927i
$565$	−0.508027	+	17.8998i	−0.0213728	+	0.753049i
$566$	21.7132	−	27.7544i	0.912676	−	1.16660i
$567$	−8.80339			−0.369708
$568$	−22.1042	+	8.43541i	−0.927471	+	0.353942i
$569$			23.0479i			0.966218i	0.875560	+	0.483109i	$0.160492\pi$
$569$			23.0479i			0.966218i	−0.875560	+	0.483109i	$0.839508\pi$
$570$	0.103049	+	1.10311i	0.00431626	+	0.0462042i
$571$	15.2220	−	15.2220i	0.637021	−	0.637021i	−0.312798	−	0.949820i	$-0.601266\pi$
$571$	15.2220	−	15.2220i	0.637021	−	0.637021i	0.949820	+	0.312798i	$0.101266\pi$
$572$	−7.12065	−	28.7189i	−0.297729	−	1.20080i
$573$	−1.64971	+	1.64971i	−0.0689174	+	0.0689174i
$574$	−13.2970	+	1.62386i	−0.555005	+	0.0677786i
$575$	40.2198	+	2.28486i	1.67728	+	0.0952851i
$576$	−15.8725	−	17.7675i	−0.661354	−	0.740314i
$577$			4.82302i			0.200785i	0.994948	+	0.100392i	$0.0320098\pi$
$577$			4.82302i			0.200785i	−0.994948	+	0.100392i	$0.967990\pi$
$578$	8.11793	+	66.4736i	0.337661	+	2.76494i
$579$	−1.25398	−	1.25398i	−0.0521137	−	0.0521137i
$580$	−8.86545	−	5.69161i	−0.368118	−	0.236331i
$581$	4.88463	−	4.88463i	0.202649	−	0.202649i
$582$	1.19858	−	1.53206i	0.0496829	−	0.0635058i
$583$	−2.85465			−0.118228
$584$	−0.583104	−	1.52797i	−0.0241290	−	0.0632278i
$585$	27.5922	+	29.2042i	1.14080	+	1.20745i
$586$	−10.3467	+	13.2254i	−0.427420	+	0.546338i
$587$	12.9692	+	12.9692i	0.535297	+	0.535297i	0.922144	−	0.386847i	$-0.126436\pi$
$587$	12.9692	+	12.9692i	0.535297	+	0.535297i	−0.386847	+	0.922144i	$0.626436\pi$
$588$	−0.152762	+	0.253489i	−0.00629981	+	0.0104537i
$589$	10.9617	+	10.9617i	0.451668	+	0.451668i
$590$	−9.03580	−	7.49184i	−0.371998	−	0.308434i
$591$	−1.81467			−0.0746454
$592$	−15.1655	−	4.67985i	−0.623298	−	0.192341i
$593$			15.9785i			0.656158i	0.944650	+	0.328079i	$0.106401\pi$
$593$			15.9785i			0.656158i	−0.944650	+	0.328079i	$0.893599\pi$
$594$	0.371879	+	3.04513i	0.0152584	+	0.124943i
$595$	−0.508902	+	17.9306i	−0.0208629	+	0.735083i
$596$	−5.14983	+	8.54549i	−0.210945	+	0.350037i
$597$	−0.437278	−	0.437278i	−0.0178966	−	0.0178966i
$598$	−54.1441	−	42.3589i	−2.21412	−	1.73219i
$599$			15.5536i			0.635502i	0.948174	+	0.317751i	$0.102928\pi$
$599$			15.5536i			0.635502i	−0.948174	+	0.317751i	$0.897072\pi$
$600$	1.85860	+	0.961907i	0.0758770	+	0.0392697i
$601$			3.74083i			0.152592i	0.997085	+	0.0762959i	$0.0243094\pi$
$601$			3.74083i			0.152592i	−0.997085	+	0.0762959i	$0.975691\pi$
$602$	−1.95345	+	2.49694i	−0.0796167	+	0.101768i
$603$	−3.98965	−	3.98965i	−0.162471	−	0.162471i
$604$	5.93177	+	23.9239i	0.241360	+	0.973450i
$605$	−0.316381	+	11.1473i	−0.0128627	+	0.453203i
$606$	−1.13387	+	0.138471i	−0.0460603	+	0.00562501i
$607$			5.31208i			0.215611i	0.994172	+	0.107805i	$0.0343824\pi$
$607$			5.31208i			0.215611i	−0.994172	+	0.107805i	$0.965618\pi$
$608$	−2.36865	+	13.1818i	−0.0960616	+	0.534592i
$609$	0.348605			0.0141262
$610$	19.5517	−	23.5810i	0.791626	−	0.954769i
$611$	−38.7278	−	38.7278i	−1.56676	−	1.56676i
$612$	46.3766	−	11.4988i	1.87466	−	0.464810i
$613$	−11.7094	−	11.7094i	−0.472936	−	0.472936i	0.429927	−	0.902864i	$-0.358539\pi$
$613$	−11.7094	−	11.7094i	−0.472936	−	0.472936i	−0.902864	+	0.429927i	$0.858539\pi$
$614$	−17.3685	−	13.5880i	−0.700935	−	0.548367i
$615$	−2.15253	−	2.27828i	−0.0867982	−	0.0918691i
$616$	−6.33042	−	2.83334i	−0.255060	−	0.114158i
$617$	7.45706			0.300210			0.150105	−	0.988670i	$-0.452039\pi$
$617$	7.45706			0.300210			0.150105	+	0.988670i	$0.452039\pi$
$618$	0.895238	+	0.700377i	0.0360118	+	0.0281733i
$619$	−12.1549	+	12.1549i	−0.488548	+	0.488548i	−0.907848	−	0.419300i	$-0.862276\pi$
$619$	−12.1549	+	12.1549i	−0.488548	+	0.488548i	0.419300	+	0.907848i	$0.362276\pi$
$620$	28.6103	−	6.23782i	1.14902	−	0.250517i
$621$	5.03991	+	5.03991i	0.202245	+	0.202245i
$622$	28.0809	−	3.42931i	1.12594	−	0.137503i
$623$		−	0.882403i		−	0.0353527i
$624$	−1.66837	−	3.15760i	−0.0667884	−	0.126405i
$625$	24.8392	+	2.83133i	0.993566	+	0.113253i
$626$	0.132888	+	1.08816i	0.00531129	+	0.0434915i
$627$	0.607473	−	0.607473i	0.0242601	−	0.0242601i
$628$	2.98711	−	4.95672i	0.119198	−	0.197795i
$629$	22.5070	−	22.5070i	0.897414	−	0.897414i
$630$	9.37676	−	0.875949i	0.373579	−	0.0348987i
$631$			14.0984i			0.561249i	0.959818	+	0.280625i	$0.0905416\pi$
$631$			14.0984i			0.561249i	−0.959818	+	0.280625i	$0.909458\pi$
$632$	−12.2090	−	31.9925i	−0.485648	−	1.27259i
$633$	−2.09751			−0.0833685
$634$	−21.5420	−	16.8531i	−0.855543	−	0.669322i
$635$	−0.886538	+	31.2362i	−0.0351812	+	1.23957i
$636$	−0.334424	+	0.0829180i	−0.0132608	+	0.00328791i
$637$	4.26620	−	4.26620i	0.169033	−	0.169033i
$638$	0.990287	+	8.10896i	0.0392059	+	0.321037i
$639$	−24.9110			−0.985466
$640$	18.5359	+	17.2169i	0.732694	+	0.680558i
$641$	−33.8525			−1.33709			−0.668547	−	0.743670i	$-0.733084\pi$
$641$	−33.8525			−1.33709			−0.668547	+	0.743670i	$0.733084\pi$
$642$	0.415686	+	3.40384i	0.0164058	+	0.134339i
$643$	−27.5413	+	27.5413i	−1.08612	+	1.08612i	−0.0901981	+	0.995924i	$0.528750\pi$
$643$	−27.5413	+	27.5413i	−1.08612	+	1.08612i	−0.995924	+	0.0901981i	$0.971250\pi$
$644$	−15.6403	+	3.87790i	−0.616313	+	0.152811i
$645$	−0.741478	−	0.0210445i	−0.0291957	−	0.000828625i
$646$	−21.1549	−	16.5502i	−0.832328	−	0.651160i
$647$	41.0475			1.61374			0.806871	−	0.590728i	$-0.201159\pi$
$647$	41.0475			1.61374			0.806871	+	0.590728i	$0.201159\pi$
$648$	−8.87778	−	23.2633i	−0.348752	−	0.913870i
$649$			9.10163i			0.357270i
$650$	−32.0559	−	28.1507i	−1.25734	−	1.10416i
$651$	−0.685145	+	0.685145i	−0.0268529	+	0.0268529i
$652$	−13.4369	+	22.2968i	−0.526229	+	0.873210i
$653$	13.5992	−	13.5992i	0.532178	−	0.532178i	−0.389042	−	0.921220i	$-0.627194\pi$
$653$	13.5992	−	13.5992i	0.532178	−	0.532178i	0.921220	+	0.389042i	$0.127194\pi$
$654$	0.152507	+	1.24881i	0.00596351	+	0.0488322i
$655$	20.2095	+	21.3902i	0.789651	+	0.835784i
$656$	−17.7004	−	33.5002i	−0.691086	−	1.30796i
$657$		−	1.72199i		−	0.0671814i
$658$	−12.7433	+	1.55625i	−0.496786	+	0.0606688i
$659$	11.9617	+	11.9617i	0.465961	+	0.465961i	0.900603	−	0.434642i	$-0.143125\pi$
$659$	11.9617	+	11.9617i	0.465961	+	0.465961i	−0.434642	+	0.900603i	$0.643125\pi$
$660$	−0.345687	−	1.58552i	−0.0134558	−	0.0617164i
$661$	13.5175	−	13.5175i	0.525770	−	0.525770i	−0.393539	−	0.919308i	$-0.628749\pi$
$661$	13.5175	−	13.5175i	0.525770	−	0.525770i	0.919308	+	0.393539i	$0.128749\pi$
$662$	−8.26101	−	6.46289i	−0.321073	−	0.251187i
$663$	7.16220			0.278157
$664$	17.8337	+	7.98194i	0.692083	+	0.309759i
$665$	−3.63572	−	3.84813i	−0.140987	−	0.149224i
$666$	−13.1618	−	10.2969i	−0.510007	−	0.398997i
$667$	13.4209	+	13.4209i	0.519660	+	0.519660i
$668$	−2.69558	+	0.668351i	−0.104295	+	0.0258593i
$669$	−1.95327	−	1.95327i	−0.0755179	−	0.0755179i
$670$	4.61205	+	3.82398i	0.178179	+	0.147733i
$671$	−23.7528			−0.916969
$672$	−0.823910	−	0.148049i	−0.0317830	−	0.00571113i
$673$		−	32.5102i		−	1.25318i	−0.779350	−	0.626588i	$-0.784451\pi$
$673$		−	32.5102i		−	1.25318i	0.779350	−	0.626588i	$-0.215549\pi$
$674$	−40.1755	+	4.90634i	−1.54750	+	0.188985i
$675$	2.94526	+	3.30005i	0.113363	+	0.127019i
$676$	11.2632	+	45.4264i	0.433198	+	1.74717i
$677$	−20.0674	−	20.0674i	−0.771252	−	0.771252i	0.207074	−	0.978325i	$-0.433606\pi$
$677$	−20.0674	−	20.0674i	−0.771252	−	0.771252i	−0.978325	+	0.207074i	$0.933606\pi$
$678$	1.03267	−	1.31998i	0.0396595	−	0.0506936i
$679$			9.29488i			0.356705i
$680$	−47.8956	+	16.7373i	−1.83671	+	0.641847i
$681$			1.83847i			0.0704502i
$682$	−17.8836	−	13.9910i	−0.684798	−	0.535742i
$683$	−19.2761	−	19.2761i	−0.737581	−	0.737581i	0.234528	−	0.972109i	$-0.424646\pi$
$683$	−19.2761	−	19.2761i	−0.737581	−	0.737581i	−0.972109	+	0.234528i	$0.924646\pi$
$684$	−7.27864	+	12.0780i	−0.278306	+	0.461813i
$685$	−16.2925	−	0.462410i	−0.622505	−	0.0176678i
$686$	−0.171434	−	1.40378i	−0.00654537	−	0.0535967i
$687$		−	0.540496i		−	0.0206212i
$688$	−8.56824	−	2.64403i	−0.326661	−	0.100803i
$689$	7.02381			0.267586
$690$	−2.90241	−	2.40647i	−0.110493	−	0.0916127i
$691$	−10.6872	−	10.6872i	−0.406561	−	0.406561i	0.473976	−	0.880538i	$-0.342818\pi$
$691$	−10.6872	−	10.6872i	−0.406561	−	0.406561i	−0.880538	+	0.473976i	$0.842818\pi$
$692$	−13.0824	+	21.7087i	−0.497320	+	0.825239i
$693$	−5.16370	−	5.16370i	−0.196153	−	0.196153i
$694$	6.06569	−	7.75331i	0.230251	−	0.294311i
$695$	−29.2864	+	27.6699i	−1.11090	+	1.04958i
$696$	0.351550	+	0.921203i	0.0133255	+	0.0349181i
$697$	75.9866			2.87820
$698$	−22.9414	+	29.3242i	−0.868345	+	1.10994i
$699$	−1.36472	+	1.36472i	−0.0516186	+	0.0516186i
$700$	−9.82698	+	1.85218i	−0.371425	+	0.0700057i
$701$	32.9173	+	32.9173i	1.24327	+	1.24327i	0.958637	+	0.284631i	$0.0918712\pi$
$701$	32.9173	+	32.9173i	1.24327	+	1.24327i	0.284631	+	0.958637i	$0.408129\pi$
$702$	−0.915000	−	7.49247i	−0.0345345	−	0.282785i
$703$			9.39396i			0.354300i
$704$	1.10331	−	19.5857i	0.0415826	−	0.738163i
$705$	−2.06290	−	2.18342i	−0.0776933	−	0.0822322i
$706$	−3.77864	+	0.461458i	−0.142211	+	0.0173672i
$707$	3.85960	−	3.85960i	0.145155	−	0.145155i
$708$	0.264371	+	1.06626i	0.00993569	+	0.0400725i
$709$	−4.41718	+	4.41718i	−0.165891	+	0.165891i	−0.785170	−	0.619280i	$-0.787425\pi$
$709$	−4.41718	+	4.41718i	−0.165891	+	0.165891i	0.619280	+	0.785170i	$0.287425\pi$
$710$	26.3370	−	2.46032i	0.988408	−	0.0923342i
$711$		−	36.0550i		−	1.35217i
$712$	2.33179	−	0.889859i	0.0873874	−	0.0333489i
$713$	−52.7548			−1.97568
$714$	1.03445	−	1.32226i	0.0387133	−	0.0494842i
$715$	−0.938517	+	33.0676i	−0.0350986	+	1.23666i
$716$	20.1256	+	12.1285i	0.752131	+	0.453262i
$717$	−0.494659	+	0.494659i	−0.0184734	+	0.0184734i
$718$	−33.2609	+	4.06191i	−1.24129	+	0.151589i
$719$	19.2011			0.716079			0.358039	−	0.933707i	$-0.383445\pi$
$719$	19.2011			0.716079			0.358039	+	0.933707i	$0.383445\pi$
$720$	11.7707	+	23.8951i	0.438669	+	0.890519i
$721$	−5.43135			−0.202274
$722$	−18.8032	+	2.29630i	−0.699784	+	0.0854595i
$723$	−0.792252	+	0.792252i	−0.0294642	+	0.0294642i
$724$	4.59987	−	7.63289i	0.170953	−	0.283674i
$725$	7.84301	+	8.78780i	0.291282	+	0.326371i
$726$	0.643110	−	0.822038i	0.0238680	−	0.0305087i
$727$	23.2043			0.860600			0.430300	−	0.902686i	$-0.358408\pi$
$727$	23.2043			0.860600			0.430300	+	0.902686i	$0.358408\pi$
$728$	15.5759	+	6.97137i	0.577280	+	0.258376i
$729$		−	25.8247i		−	0.956469i
$730$	0.170072	+	1.82056i	0.00629463	+	0.0673820i
$731$	12.7161	−	12.7161i	0.470321	−	0.470321i
$732$	−2.78265	+	0.689939i	−0.102850	+	0.0255009i
$733$	2.80274	−	2.80274i	0.103521	−	0.103521i	−0.653449	−	0.756970i	$-0.726679\pi$
$733$	2.80274	−	2.80274i	0.103521	−	0.103521i	0.756970	+	0.653449i	$0.226679\pi$
$734$	18.2482	−	2.22852i	0.673553	−	0.0822560i
$735$	0.240522	−	0.227246i	0.00887179	−	0.00838209i
$736$	−26.0199	−	37.4194i	−0.959107	−	1.37930i
$737$		−	4.64565i		−	0.171125i
$738$	−4.83602	−	39.5997i	−0.178016	−	1.45769i
$739$	−20.5076	−	20.5076i	−0.754385	−	0.754385i	0.220909	−	0.975294i	$-0.429098\pi$
$739$	−20.5076	−	20.5076i	−0.754385	−	0.754385i	−0.975294	+	0.220909i	$0.929098\pi$
$740$	14.9321	+	9.58641i	0.548915	+	0.352403i
$741$	−1.49467	+	1.49467i	−0.0549082	+	0.0549082i
$742$	1.01446	−	1.29671i	0.0372421	−	0.0476037i
$743$	4.67732			0.171594			0.0857972	−	0.996313i	$-0.472656\pi$
$743$	4.67732			0.171594			0.0857972	+	0.996313i	$0.472656\pi$
$744$	−2.50146	−	1.11959i	−0.0917079	−	0.0410462i
$745$	8.10834	−	7.66078i	0.297067	−	0.280669i
$746$	−6.91229	+	8.83544i	−0.253077	+	0.323489i
$747$	14.5469	+	14.5469i	0.532244	+	0.532244i
$748$	33.6958	+	20.3064i	1.23204	+	0.742474i
$749$	−11.5864	−	11.5864i	−0.423358	−	0.423358i
$750$	−1.71359	−	1.59317i	−0.0625713	−	0.0581744i
$751$	−10.3972			−0.379400			−0.189700	−	0.981842i	$-0.560752\pi$
$751$	−10.3972			−0.379400			−0.189700	+	0.981842i	$0.560752\pi$
$752$	−16.9634	−	32.1053i	−0.618593	−	1.17076i
$753$		−	4.08296i		−	0.148791i
$754$	−2.43658	−	19.9519i	−0.0887350	−	0.726606i
$755$	0.781820	−	27.5466i	0.0284533	−	1.00252i
$756$	−1.51539	−	0.913228i	−0.0551141	−	0.0332138i
$757$	20.7914	+	20.7914i	0.755678	+	0.755678i	0.975533	−	0.219855i	$-0.0705584\pi$
$757$	20.7914	+	20.7914i	0.755678	+	0.755678i	−0.219855	+	0.975533i	$0.570558\pi$
$758$	28.3581	+	22.1856i	1.03001	+	0.805817i
$759$			2.92356i			0.106118i
$760$	6.50240	−	13.4882i	0.235867	−	0.489268i
$761$			17.3387i			0.628528i	0.949336	+	0.314264i	$0.101758\pi$
$761$			17.3387i			0.628528i	−0.949336	+	0.314264i	$0.898242\pi$
$762$	1.80207	−	2.30345i	0.0652823	−	0.0834452i
$763$	−4.25084	−	4.25084i	−0.153891	−	0.153891i
$764$	30.6049	−	7.58827i	1.10725	−	0.274534i
$765$	−53.3992	−	1.51556i	−1.93065	−	0.0547953i
$766$	54.7215	−	6.68273i	1.97717	−	0.241457i
$767$		−	22.3944i		−	0.808614i
$768$	−0.439644	−	2.32652i	−0.0158643	−	0.0839509i
$769$	−0.750953			−0.0270800			−0.0135400	−	0.999908i	$-0.504310\pi$
$769$	−0.750953			−0.0270800			−0.0135400	+	0.999908i	$0.504310\pi$
$770$	5.96926	+	4.94929i	0.215117	+	0.178360i
$771$	−0.240790	−	0.240790i	−0.00867183	−	0.00867183i
$772$	5.76803	+	23.2635i	0.207596	+	0.837273i
$773$	21.0347	+	21.0347i	0.756565	+	0.756565i	0.975695	−	0.219131i	$-0.0703221\pi$
$773$	21.0347	+	21.0347i	0.756565	+	0.756565i	−0.219131	+	0.975695i	$0.570322\pi$
$774$	−7.43615	−	5.81757i	−0.267287	−	0.209108i
$775$	−32.6861	−	1.85687i	−1.17412	−	0.0667008i
$776$	−24.5621	+	9.37342i	−0.881729	+	0.336486i
$777$	−0.587156			−0.0210641
$778$	39.6778	+	31.0414i	1.42252	+	1.11289i
$779$	−15.8576	+	15.8576i	−0.568157	+	0.568157i
$780$	0.850555	+	3.90114i	0.0304547	+	0.139683i
$781$	−14.5035	−	14.5035i	−0.518978	−	0.518978i
$782$	90.7308	−	11.0803i	3.24453	−	0.396230i
$783$			2.08399i			0.0744759i
$784$	3.53668	−	1.86867i	0.126310	−	0.0667381i
$785$	−4.70316	+	4.44356i	−0.167863	+	0.158597i
$786$	−0.333862	−	2.73382i	−0.0119085	−	0.0975123i
$787$	20.2250	−	20.2250i	0.720942	−	0.720942i	−0.247855	−	0.968797i	$-0.579726\pi$
$787$	20.2250	−	20.2250i	0.720942	−	0.720942i	0.968797	+	0.247855i	$0.0797256\pi$
$788$	21.0061	+	12.6591i	0.748312	+	0.450961i
$789$	0.228609	−	0.228609i	0.00813869	−	0.00813869i
$790$	3.56095	+	38.1188i	0.126693	+	1.35621i
$791$			8.00824i			0.284740i
$792$	8.43797	−	18.8526i	0.299830	−	0.669899i
$793$	58.4434			2.07538
$794$	−4.46168	−	3.49053i	−0.158339	−	0.123874i
$795$	0.385063	+	0.0109288i	0.0136568	+	0.000387604i
$796$	2.01138	+	8.11227i	0.0712915	+	0.287532i
$797$	−19.0991	+	19.0991i	−0.676526	+	0.676526i	−0.959212	−	0.282687i	$-0.908774\pi$
$797$	−19.0991	+	19.0991i	−0.676526	+	0.676526i	0.282687	+	0.959212i	$0.408774\pi$
$798$	0.0600623	+	0.491820i	0.00212618	+	0.0174102i
$799$	72.8227			2.57628
$800$	−14.8045	−	24.1004i	−0.523417	−	0.852077i
$801$	2.62789			0.0928518
$802$	1.13909	+	9.32742i	0.0402226	+	0.329362i
$803$	1.00257	−	1.00257i	0.0353799	−	0.0353799i
$804$	−0.134940	−	0.544240i	−0.00475898	−	0.0191939i
$805$	18.0086	+	0.511115i	0.634719	+	0.0180144i
$806$	44.0022	+	34.4245i	1.54991	+	1.21255i
$807$	−1.30867			−0.0460674
$808$	14.0914	+	6.30695i	0.495733	+	0.221878i
$809$			51.6485i			1.81586i	0.419117	+	0.907932i	$0.362340\pi$
$809$			51.6485i			1.81586i	−0.419117	+	0.907932i	$0.637660\pi$
$810$	2.58934	+	27.7181i	0.0909802	+	0.973915i
$811$	6.22678	−	6.22678i	0.218652	−	0.218652i	−0.589278	−	0.807930i	$-0.700588\pi$
$811$	6.22678	−	6.22678i	0.218652	−	0.218652i	0.807930	+	0.589278i	$0.200588\pi$
$812$	−4.03537	−	2.43186i	−0.141614	−	0.0853416i
$813$	−1.62977	+	1.62977i	−0.0571586	+	0.0571586i
$814$	−1.66794	−	13.6580i	−0.0584614	−	0.478711i
$815$	21.1562	−	19.9884i	0.741069	−	0.700164i
$816$	4.53731	+	1.40015i	0.158838	+	0.0490150i
$817$			5.30742i			0.185683i
$818$	0.886159	−	0.108220i	0.0309838	−	0.00378383i
$819$	12.7052	+	12.7052i	0.443955	+	0.443955i
$820$	9.02387	+	41.3888i	0.315127	+	1.44536i
$821$	19.4275	−	19.4275i	0.678026	−	0.678026i	−0.281527	−	0.959553i	$-0.590841\pi$
$821$	19.4275	−	19.4275i	0.678026	−	0.678026i	0.959553	+	0.281527i	$0.0908410\pi$
$822$	1.20146	+	0.939946i	0.0419057	+	0.0327844i
$823$	−22.7060			−0.791483			−0.395741	−	0.918362i	$-0.629512\pi$
$823$	−22.7060			−0.791483			−0.395741	+	0.918362i	$0.629512\pi$
$824$	−5.47724	−	14.3526i	−0.190809	−	0.499995i
$825$	−0.102904	+	1.81139i	−0.00358265	+	0.0630646i
$826$	−4.13436	−	3.23446i	−0.143853	−	0.112541i
$827$	−34.6360	−	34.6360i	−1.20441	−	1.20441i	−0.972811	−	0.231602i	$-0.925603\pi$
$827$	−34.6360	−	34.6360i	−1.20441	−	1.20441i	−0.231602	−	0.972811i	$-0.574397\pi$
$828$	−11.5488	−	46.5783i	−0.401348	−	1.61871i
$829$	0.416625	+	0.416625i	0.0144700	+	0.0144700i	0.714305	−	0.699835i	$-0.246743\pi$
$829$	0.416625	+	0.416625i	0.0144700	+	0.0144700i	−0.699835	+	0.714305i	$0.746743\pi$
$830$	−16.8163	−	13.9429i	−0.583703	−	0.483964i
$831$	3.70314			0.128460
$832$	−2.71467	+	48.1901i	−0.0941143	+	1.67069i
$833$			8.02204i			0.277947i
$834$	3.74302	−	0.457107i	0.129610	−	0.0158283i
$835$	3.10376	+	0.0880901i	0.107410	+	0.00304848i
$836$	−11.2697	+	2.79424i	−0.389770	+	0.0966408i
$837$	−4.09587	−	4.09587i	−0.141574	−	0.141574i
$838$	14.9993	−	19.1724i	0.518141	−	0.662300i
$839$		−	13.0417i		−	0.450249i	−0.974330	−	0.225125i	$-0.927721\pi$
$839$		−	13.0417i		−	0.450249i	0.974330	−	0.225125i	$-0.0722789\pi$
$840$	0.843061	+	0.406424i	0.0290884	+	0.0140229i
$841$		−	23.4505i		−	0.808637i
$842$	25.8268	+	20.2052i	0.890049	+	0.696318i
$843$	−1.34020	−	1.34020i	−0.0461588	−	0.0461588i
$844$	24.2803	+	14.6322i	0.835761	+	0.503661i
$845$	1.48451	−	52.3050i	0.0510686	−	1.79935i
$846$	−4.63466	−	37.9509i	−0.159343	−	1.30478i
$847$			4.98725i			0.171364i
$848$	4.44964	+	1.37310i	0.152801	+	0.0471523i
$849$	3.68732			0.126548
$850$	56.6054	−	3.67162i	1.94155	−	0.125935i
$851$	−22.6049	−	22.6049i	−0.774886	−	0.774886i
$852$	−2.12037	−	1.27782i	−0.0726428	−	0.0437773i
$853$	13.0659	+	13.0659i	0.447370	+	0.447370i	0.894479	−	0.447110i	$-0.147547\pi$
$853$	13.0659	+	13.0659i	0.447370	+	0.447370i	−0.447110	+	0.894479i	$0.647547\pi$
$854$	8.44108	−	10.7896i	0.288848	−	0.369212i
$855$	11.4601	−	10.8276i	0.391928	−	0.370295i
$856$	18.9333	−	42.3018i	0.647125	−	1.44585i
$857$	15.9738			0.545656			0.272828	−	0.962063i	$-0.412041\pi$
$857$	15.9738			0.545656			0.272828	+	0.962063i	$0.412041\pi$
$858$	1.90773	−	2.43851i	0.0651289	−	0.0832492i
$859$	−0.378235	+	0.378235i	−0.0129052	+	0.0129052i	−0.713530	−	0.700625i	$-0.752905\pi$
$859$	−0.378235	+	0.378235i	−0.0129052	+	0.0129052i	0.700625	+	0.713530i	$0.252905\pi$
$860$	8.43637	+	5.41615i	0.287678	+	0.184689i
$861$	−0.991157	−	0.991157i	−0.0337785	−	0.0337785i
$862$	−6.76786	−	55.4186i	−0.230514	−	1.88756i
$863$			48.3271i			1.64507i	0.568712	+	0.822537i	$0.307442\pi$
$863$			48.3271i			1.64507i	−0.568712	+	0.822537i	$0.692558\pi$
$864$	0.885054	−	4.92542i	0.0301102	−	0.167566i
$865$	20.5981	−	19.4612i	0.700357	−	0.661700i
$866$	−39.6163	+	4.83805i	−1.34622	+	0.164404i
$867$	−4.95495	+	4.95495i	−0.168279	+	0.168279i
$868$	12.7106	−	3.15151i	0.431427	−	0.106969i
$869$	20.9917	−	20.9917i	0.712095	−	0.712095i
$870$	−0.102535	−	1.09761i	−0.00347627	−	0.0372123i
$871$			11.4305i			0.387309i
$872$	6.94627	−	15.5198i	0.235230	−	0.525566i
$873$	−27.6811			−0.936863
$874$	−16.6222	+	21.2469i	−0.562255	+	0.718687i
$875$	11.1399	+	0.950548i	0.376596	+	0.0321344i
$876$	0.0883300	−	0.146572i	0.00298439	−	0.00495222i
$877$	10.7327	−	10.7327i	0.362417	−	0.362417i	−0.502285	−	0.864702i	$-0.667507\pi$
$877$	10.7327	−	10.7327i	0.362417	−	0.362417i	0.864702	+	0.502285i	$0.167507\pi$
$878$	−11.6291	+	1.42018i	−0.392463	+	0.0479286i
$879$	−1.75707			−0.0592646
$880$	−7.05900	+	20.7651i	−0.237959	+	0.699993i
$881$	−43.9599			−1.48105			−0.740523	−	0.672031i	$-0.765422\pi$
$881$	−43.9599			−1.48105			−0.740523	+	0.672031i	$0.765422\pi$
$882$	4.18061	−	0.510547i	0.140769	−	0.0171910i
$883$	11.3220	−	11.3220i	0.381017	−	0.381017i	−0.490451	−	0.871469i	$-0.663168\pi$
$883$	11.3220	−	11.3220i	0.381017	−	0.381017i	0.871469	+	0.490451i	$0.163168\pi$
$884$	−82.9079	−	49.9634i	−2.78849	−	1.68045i
$885$	0.0348447	−	1.22772i	0.00117129	−	0.0412692i
$886$	7.75933	−	9.91815i	0.260680	−	0.333207i
$887$	−2.04183			−0.0685581			−0.0342790	−	0.999412i	$-0.510913\pi$
$887$	−2.04183			−0.0685581			−0.0342790	+	0.999412i	$0.510913\pi$
$888$	−0.592117	−	1.55159i	−0.0198702	−	0.0520678i
$889$			13.9749i			0.468702i
$890$	−2.77831	+	0.259541i	−0.0931291	+	0.00869984i
$891$	15.2641	−	15.2641i	0.511367	−	0.511367i
$892$	8.98462	+	36.2366i	0.300827	+	1.21329i
$893$	−15.1973	+	15.1973i	−0.508559	+	0.508559i
$894$	−1.03631	+	0.126556i	−0.0346593	+	0.00423268i
$895$	−18.0420	−	19.0961i	−0.603079	−	0.638312i
$896$	8.50459	+	7.46136i	0.284118	+	0.249267i
$897$		−	7.19335i		−	0.240179i
$898$	4.41564	+	36.1574i	0.147352	+	1.20659i
$899$	−10.9070	−	10.9070i	−0.363769	−	0.363769i
$900$	−5.51597	−	29.2657i	−0.183866	−	0.975524i
$901$	−6.60369	+	6.60369i	−0.220001	+	0.220001i
$902$	20.2399	−	25.8711i	0.673915	−	0.861413i
$903$	−0.331733			−0.0110394
$904$	−21.1621	+	8.07591i	−0.703842	+	0.268601i
$905$	−7.24242	+	6.84267i	−0.240746	+	0.227458i
$906$	−1.58921	+	2.03137i	−0.0527980	+	0.0674876i
$907$	−11.9908	−	11.9908i	−0.398148	−	0.398148i	0.479431	−	0.877580i	$-0.340843\pi$
$907$	−11.9908	−	11.9908i	−0.398148	−	0.398148i	−0.877580	+	0.479431i	$0.840843\pi$
$908$	12.8251	−	21.2817i	0.425616	−	0.706256i
$909$	11.4943	+	11.4943i	0.381242	+	0.381242i
$910$	−14.6872	−	12.1776i	−0.486877	−	0.403684i
$911$	−6.07682			−0.201334			−0.100667	−	0.994920i	$-0.532098\pi$
$911$	−6.07682			−0.201334			−0.100667	+	0.994920i	$0.532098\pi$
$912$	−1.23908	+	0.654692i	−0.0410302	+	0.0216790i
$913$			16.9388i			0.560593i
$914$	0.962033	+	7.87760i	0.0318212	+	0.260568i
$915$	3.20401	+	0.0909355i	0.105921	+	0.00300624i
$916$	−3.77049	+	6.25665i	−0.124581	+	0.206726i
$917$	9.30572	+	9.30572i	0.307302	+	0.307302i
$918$	7.90458	+	6.18404i	0.260890	+	0.204104i
$919$			8.58186i			0.283090i	0.989932	+	0.141545i	$0.0452069\pi$
$919$			8.58186i			0.283090i	−0.989932	+	0.141545i	$0.954793\pi$
$920$	16.8101	+	48.1039i	0.554213	+	1.58594i
$921$		−	2.30750i		−	0.0760347i
$922$	−25.2484	+	32.2731i	−0.831512	+	1.06286i
$923$	35.6856	+	35.6856i	1.17461	+	1.17461i
$924$	−0.174650	−	0.704396i	−0.00574557	−	0.0231729i
$925$	−13.2100	−	14.8013i	−0.434343	−	0.486664i
$926$	23.5431	−	2.87514i	0.773673	−	0.0944830i
$927$		−	16.1751i		−	0.531260i
$928$	2.35684	−	13.1160i	0.0773669	−	0.430555i
$929$	39.4214			1.29338			0.646688	−	0.762755i	$-0.276154\pi$
$929$	39.4214			1.29338			0.646688	+	0.762755i	$0.276154\pi$
$930$	2.35875	+	1.95570i	0.0773464	+	0.0641301i
$931$	−1.67411	−	1.67411i	−0.0548669	−	0.0548669i
$932$	25.3180	−	6.27743i	0.829319	−	0.205624i
$933$	2.09315	+	2.09315i	0.0685268	+	0.0685268i
$934$	3.22988	+	2.52685i	0.105685	+	0.0826811i
$935$	−30.2073	−	31.9721i	−0.987885	−	1.04560i
$936$	−20.7614	+	46.3865i	−0.678609	+	1.51619i
$937$	−38.8280			−1.26846			−0.634228	−	0.773146i	$-0.718682\pi$
$937$	−38.8280			−1.26846			−0.634228	+	0.773146i	$0.718682\pi$
$938$	2.11026	+	1.65093i	0.0689024	+	0.0539049i
$939$	−0.0811112	+	0.0811112i	−0.00264696	+	0.00264696i
$940$	8.64814	+	39.6655i	0.282071	+	1.29374i
$941$	8.99486	+	8.99486i	0.293224	+	0.293224i	0.838353	−	0.545128i	$-0.183519\pi$
$941$	8.99486	+	8.99486i	0.293224	+	0.293224i	−0.545128	+	0.838353i	$0.683519\pi$
$942$	0.601098	−	0.0734077i	0.0195848	−	0.00239175i
$943$		−	76.3171i		−	2.48523i
$944$	4.37791	−	14.1870i	0.142489	−	0.461748i
$945$	1.35850	+	1.43786i	0.0441920	+	0.0467737i
$946$	−0.942359	−	7.71650i	−0.0306387	−	0.250885i
$947$	−34.0304	+	34.0304i	−1.10584	+	1.10584i	−0.112147	+	0.993692i	$0.535773\pi$
$947$	−34.0304	+	34.0304i	−1.10584	+	1.10584i	−0.993692	+	0.112147i	$0.964227\pi$
$948$	1.84945	−	3.06892i	0.0600673	−	0.0996740i
$949$	−2.46680	+	2.46680i	−0.0800756	+	0.0800756i
$950$	−11.0467	+	12.5792i	−0.358403	+	0.408123i
$951$		−	2.86198i		−	0.0928059i
$952$	−21.1986	+	8.08982i	−0.687050	+	0.262193i
$953$	20.2620			0.656350			0.328175	−	0.944617i	$-0.393566\pi$
$953$	20.2620			0.656350			0.328175	+	0.944617i	$0.393566\pi$
$954$	3.86173	+	3.02117i	0.125028	+	0.0978141i
$955$	−35.2392	−	1.00015i	−1.14031	−	0.0323641i
$956$	9.17679	−	2.27532i	0.296799	−	0.0735892i
$957$	−0.604443	+	0.604443i	−0.0195389	+	0.0195389i
$958$	−2.46744	−	20.2046i	−0.0797193	−	0.652781i
$959$	−7.28917			−0.235380
$960$	−0.223807	+	2.63768i	−0.00722334	+	0.0851308i
$961$	11.8731			0.383002
$962$	4.10394	+	33.6051i	0.132316	+	1.08347i
$963$	34.5055	−	34.5055i	1.11192	−	1.11192i
$964$	14.6977	−	3.64418i	0.473380	−	0.117371i
$965$	0.760239	−	26.7862i	0.0244730	−	0.862278i
$966$	−1.32801	−	1.03895i	−0.0427279	−	0.0334276i
$967$	8.43942			0.271394			0.135697	−	0.990750i	$-0.456673\pi$
$967$	8.43942			0.271394			0.135697	+	0.990750i	$0.456673\pi$
$968$	−13.1790	+	5.02938i	−0.423589	+	0.161651i
$969$		−	2.81054i		−	0.0902876i
$970$	29.2656	−	2.73390i	0.939661	−	0.0877804i
$971$	11.8593	−	11.8593i	0.380582	−	0.380582i	−0.490730	−	0.871312i	$-0.663270\pi$
$971$	11.8593	−	11.8593i	0.380582	−	0.380582i	0.871312	+	0.490730i	$0.163270\pi$
$972$	4.08451	−	6.77773i	0.131011	−	0.217396i
$973$	−12.7409	+	12.7409i	−0.408455	+	0.408455i
$974$	6.32736	+	51.8116i	0.202742	+	1.66015i
$975$	0.253193	−	4.45689i	0.00810865	−	0.142735i
$976$	37.0243	+	11.4252i	1.18512	+	0.365711i
$977$			27.4913i			0.879526i	0.898114	+	0.439763i	$0.144938\pi$
$977$			27.4913i			0.879526i	−0.898114	+	0.439763i	$0.855062\pi$
$978$	−2.70392	+	0.330209i	−0.0864617	+	0.0105589i
$979$	1.52999	+	1.52999i	0.0488987	+	0.0488987i
$980$	−4.36949	+	0.952666i	−0.139578	+	0.0304318i
$981$	12.6594	−	12.6594i	0.404184	−	0.404184i
$982$	−8.63038	−	6.75186i	−0.275407	−	0.215461i
$983$	28.1654			0.898338			0.449169	−	0.893447i	$-0.351720\pi$
$983$	28.1654			0.898338			0.449169	+	0.893447i	$0.351720\pi$
$984$	1.61964	−	3.61871i	0.0516323	−	0.115360i
$985$	−18.8314	−	19.9315i	−0.600018	−	0.635072i
$986$	21.0493	+	16.4677i	0.670348	+	0.524438i
$987$	−0.949887	−	0.949887i	−0.0302352	−	0.0302352i
$988$	27.7288	−	6.87517i	0.882171	−	0.218728i
$989$	−12.7714	−	12.7714i	−0.406106	−	0.406106i
$990$	−14.7395	+	17.7771i	−0.468451	+	0.564993i
$991$	−44.0881			−1.40050			−0.700252	−	0.713896i	$-0.746929\pi$
$991$	−44.0881			−1.40050			−0.700252	+	0.713896i	$0.746929\pi$
$992$	21.1460	+	30.4102i	0.671387	+	0.965526i
$993$		−	1.09752i		−	0.0348288i
$994$	11.7423	−	1.43400i	0.372443	−	0.0454837i
$995$	0.265104	−	9.34066i	0.00840437	−	0.296119i
$996$	0.492015	+	1.98439i	0.0155901	+	0.0628778i
$997$	−40.3957	−	40.3957i	−1.27935	−	1.27935i	−0.941034	−	0.338311i	$-0.890144\pi$
$997$	−40.3957	−	40.3957i	−1.27935	−	1.27935i	−0.338311	−	0.941034i	$-0.609856\pi$
$998$	24.8161	−	31.7205i	0.785539	−	1.00409i
$999$		−	3.51008i		−	0.111054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.bb.d.29.17	yes	70
5.4	even	2		560.2.bb.c.29.19	✓	70
16.5	even	4		560.2.bb.c.309.19	yes	70
80.69	even	4	inner	560.2.bb.d.309.17	yes	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bb.c.29.19	✓	70	5.4	even	2
560.2.bb.c.309.19	yes	70	16.5	even	4
560.2.bb.d.29.17	yes	70	1.1	even	1	trivial
560.2.bb.d.309.17	yes	70	80.69	even	4	inner

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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.bb (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.171434 - 1.40378i) q^{2} +(0.104638 - 0.104638i) q^{3} +(-1.94122 + 0.481312i) q^{4} +(2.23517 + 0.0634380i) q^{5} +(-0.164828 - 0.128951i) q^{6} +1.00000 q^{7} +(1.00845 + 2.64254i) q^{8} +2.97810i q^{9} +O(q^{10})\)	\(q+(-0.171434 - 1.40378i) q^{2} +(0.104638 - 0.104638i) q^{3} +(-1.94122 + 0.481312i) q^{4} +(2.23517 + 0.0634380i) q^{5} +(-0.164828 - 0.128951i) q^{6} +1.00000 q^{7} +(1.00845 + 2.64254i) q^{8} +2.97810i q^{9} +(-0.294130 - 3.14857i) q^{10} +(-1.73389 + 1.73389i) q^{11} +(-0.152762 + 0.253489i) q^{12} +(4.26620 - 4.26620i) q^{13} +(-0.171434 - 1.40378i) q^{14} +(0.240522 - 0.227246i) q^{15} +(3.53668 - 1.86867i) q^{16} +8.02204i q^{17} +(4.18061 - 0.510547i) q^{18} +(-1.67411 - 1.67411i) q^{19} +(-4.36949 + 0.952666i) q^{20} +(0.104638 - 0.104638i) q^{21} +(2.73126 + 2.13676i) q^{22} +8.05693 q^{23} +(0.382033 + 0.170989i) q^{24} +(4.99195 + 0.283589i) q^{25} +(-6.72020 - 5.25745i) q^{26} +(0.625538 + 0.625538i) q^{27} +(-1.94122 + 0.481312i) q^{28} +(1.66576 + 1.66576i) q^{29} +(-0.360238 - 0.298683i) q^{30} -6.54775 q^{31} +(-3.22951 - 4.64438i) q^{32} +0.362862i q^{33} +(11.2612 - 1.37525i) q^{34} +(2.23517 + 0.0634380i) q^{35} +(-1.43340 - 5.78115i) q^{36} +(-2.80565 - 2.80565i) q^{37} +(-2.06310 + 2.63710i) q^{38} -0.892815i q^{39} +(2.08642 + 5.97050i) q^{40} -9.47223i q^{41} +(-0.164828 - 0.128951i) q^{42} +(-1.58514 - 1.58514i) q^{43} +(2.53132 - 4.20041i) q^{44} +(-0.188925 + 6.65656i) q^{45} +(-1.38123 - 11.3102i) q^{46} -9.07783i q^{47} +(0.174538 - 0.565605i) q^{48} +1.00000 q^{49} +(-0.457691 - 7.05624i) q^{50} +(0.839412 + 0.839412i) q^{51} +(-6.22826 + 10.3350i) q^{52} +(0.823193 + 0.823193i) q^{53} +(0.770882 - 0.985358i) q^{54} +(-3.98553 + 3.76554i) q^{55} +(1.00845 + 2.64254i) q^{56} -0.350353 q^{57} +(2.05280 - 2.62394i) q^{58} +(2.62463 - 2.62463i) q^{59} +(-0.357530 + 0.556901i) q^{60} +(6.84958 + 6.84958i) q^{61} +(1.12251 + 9.19163i) q^{62} +2.97810i q^{63} +(-5.96606 + 5.32974i) q^{64} +(9.80631 - 9.26504i) q^{65} +(0.509381 - 0.0622069i) q^{66} +(-1.33966 + 1.33966i) q^{67} +(-3.86111 - 15.5726i) q^{68} +(0.843062 - 0.843062i) q^{69} +(-0.294130 - 3.14857i) q^{70} +8.36474i q^{71} +(-7.86976 + 3.00326i) q^{72} -0.578219 q^{73} +(-3.45754 + 4.41951i) q^{74} +(0.552023 - 0.492675i) q^{75} +(4.05560 + 2.44405i) q^{76} +(-1.73389 + 1.73389i) q^{77} +(-1.25332 + 0.153059i) q^{78} -12.1067 q^{79} +(8.02361 - 3.95242i) q^{80} -8.80339 q^{81} +(-13.2970 + 1.62386i) q^{82} +(4.88463 - 4.88463i) q^{83} +(-0.152762 + 0.253489i) q^{84} +(-0.508902 + 17.9306i) q^{85} +(-1.95345 + 2.49694i) q^{86} +0.348605 q^{87} +(-6.33042 - 2.83334i) q^{88} -0.882403i q^{89} +(9.37676 - 0.875949i) q^{90} +(4.26620 - 4.26620i) q^{91} +(-15.6403 + 3.87790i) q^{92} +(-0.685145 + 0.685145i) q^{93} +(-12.7433 + 1.55625i) q^{94} +(-3.63572 - 3.84813i) q^{95} +(-0.823910 - 0.148049i) q^{96} +9.29488i q^{97} +(-0.171434 - 1.40378i) q^{98} +(-5.16370 - 5.16370i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8}+O(q^{10}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8	\( 70 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 70 q^{7} + 8 q^{8} - 18 q^{10} - 2 q^{11} - 4 q^{12} + 6 q^{13} + 2 q^{14} - 6 q^{15} + 4 q^{16} - 18 q^{18} + 14 q^{19} + 12 q^{20} + 2 q^{21} - 12 q^{22} + 20 q^{24} + 6 q^{25} - 36 q^{26} + 8 q^{27} + 2 q^{29} + 8 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{34} + 2 q^{35} - 40 q^{36} + 10 q^{37} - 12 q^{38} - 24 q^{40} + 2 q^{43} - 24 q^{44} - 24 q^{45} - 16 q^{46} - 44 q^{48} + 70 q^{49} - 10 q^{50} + 8 q^{51} + 28 q^{52} - 30 q^{53} - 32 q^{54} + 6 q^{55} + 8 q^{56} - 76 q^{57} + 56 q^{58} + 2 q^{59} - 8 q^{60} + 30 q^{61} + 48 q^{62} + 12 q^{64} - 10 q^{65} + 80 q^{66} + 6 q^{67} - 36 q^{68} - 16 q^{69} - 18 q^{70} + 4 q^{72} - 36 q^{73} - 32 q^{74} - 2 q^{75} + 44 q^{76} - 2 q^{77} - 84 q^{78} - 40 q^{79} + 12 q^{80} - 82 q^{81} + 24 q^{82} + 10 q^{83} - 4 q^{84} + 32 q^{85} + 32 q^{86} - 4 q^{87} + 32 q^{88} + 18 q^{90} + 6 q^{91} - 92 q^{92} - 56 q^{93} - 20 q^{94} + 6 q^{95} + 16 q^{96} + 2 q^{98} - 34 q^{99}+O(q^{100}) \) 70 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 70 * q^7 + 8 * q^8 - 18 * q^10 - 2 * q^11 - 4 * q^12 + 6 * q^13 + 2 * q^14 - 6 * q^15 + 4 * q^16 - 18 * q^18 + 14 * q^19 + 12 * q^20 + 2 * q^21 - 12 * q^22 + 20 * q^24 + 6 * q^25 - 36 * q^26 + 8 * q^27 + 2 * q^29 + 8 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^34 + 2 * q^35 - 40 * q^36 + 10 * q^37 - 12 * q^38 - 24 * q^40 + 2 * q^43 - 24 * q^44 - 24 * q^45 - 16 * q^46 - 44 * q^48 + 70 * q^49 - 10 * q^50 + 8 * q^51 + 28 * q^52 - 30 * q^53 - 32 * q^54 + 6 * q^55 + 8 * q^56 - 76 * q^57 + 56 * q^58 + 2 * q^59 - 8 * q^60 + 30 * q^61 + 48 * q^62 + 12 * q^64 - 10 * q^65 + 80 * q^66 + 6 * q^67 - 36 * q^68 - 16 * q^69 - 18 * q^70 + 4 * q^72 - 36 * q^73 - 32 * q^74 - 2 * q^75 + 44 * q^76 - 2 * q^77 - 84 * q^78 - 40 * q^79 + 12 * q^80 - 82 * q^81 + 24 * q^82 + 10 * q^83 - 4 * q^84 + 32 * q^85 + 32 * q^86 - 4 * q^87 + 32 * q^88 + 18 * q^90 + 6 * q^91 - 92 * q^92 - 56 * q^93 - 20 * q^94 + 6 * q^95 + 16 * q^96 + 2 * q^98 - 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more