LMFDB - Embedded newform 336.2.w.b.253.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(85,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("336.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.w (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.6
Character	$\chi$	$=$	336.253
Dual form			336.2.w.b.85.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.394485 - 1.35808i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68876 + 1.07148i) q^{4} +(-0.646579 + 0.646579i) q^{5} +(0.681365 - 1.23925i) q^{6} +1.00000i q^{7} +(2.12135 + 1.87079i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.394485 - 1.35808i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68876 + 1.07148i) q^{4} +(-0.646579 + 0.646579i) q^{5} +(0.681365 - 1.23925i) q^{6} +1.00000i q^{7} +(2.12135 + 1.87079i) q^{8} +1.00000i q^{9} +(1.13317 + 0.623041i) q^{10} +(-3.50482 + 3.50482i) q^{11} +(-1.95179 - 0.436482i) q^{12} +(1.85997 + 1.85997i) q^{13} +(1.35808 - 0.394485i) q^{14} -0.914401 q^{15} +(1.70384 - 3.61897i) q^{16} -1.11616 q^{17} +(1.35808 - 0.394485i) q^{18} +(3.49842 + 3.49842i) q^{19} +(0.399120 - 1.78472i) q^{20} +(-0.707107 + 0.707107i) q^{21} +(6.14243 + 3.37723i) q^{22} -1.28106i q^{23} +(0.177175 + 2.82287i) q^{24} +4.16387i q^{25} +(1.79226 - 3.25973i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.07148 - 1.68876i) q^{28} +(1.28814 + 1.28814i) q^{29} +(0.360718 + 1.24183i) q^{30} +1.67865 q^{31} +(-5.58699 - 0.886325i) q^{32} -4.95657 q^{33} +(0.440308 + 1.51583i) q^{34} +(-0.646579 - 0.646579i) q^{35} +(-1.07148 - 1.68876i) q^{36} +(4.01360 - 4.01360i) q^{37} +(3.37106 - 6.13120i) q^{38} +2.63040i q^{39} +(-2.58124 + 0.162009i) q^{40} -8.34155i q^{41} +(1.23925 + 0.681365i) q^{42} +(-2.79353 + 2.79353i) q^{43} +(2.16345 - 9.67418i) q^{44} +(-0.646579 - 0.646579i) q^{45} +(-1.73978 + 0.505358i) q^{46} -2.27269 q^{47} +(3.76379 - 1.35420i) q^{48} -1.00000 q^{49} +(5.65487 - 1.64258i) q^{50} +(-0.789243 - 0.789243i) q^{51} +(-5.13399 - 1.14812i) q^{52} +(9.00612 - 9.00612i) q^{53} +(1.23925 + 0.681365i) q^{54} -4.53229i q^{55} +(-1.87079 + 2.12135i) q^{56} +4.94751i q^{57} +(1.24125 - 2.25756i) q^{58} +(-10.4403 + 10.4403i) q^{59} +(1.54421 - 0.979767i) q^{60} +(-6.58105 - 6.58105i) q^{61} +(-0.662204 - 2.27975i) q^{62} -1.00000 q^{63} +(1.00028 + 7.93722i) q^{64} -2.40524 q^{65} +(1.95529 + 6.73142i) q^{66} +(11.0941 + 11.0941i) q^{67} +(1.88493 - 1.19595i) q^{68} +(0.905845 - 0.905845i) q^{69} +(-0.623041 + 1.13317i) q^{70} -0.0956898i q^{71} +(-1.87079 + 2.12135i) q^{72} -7.55336i q^{73} +(-7.03410 - 3.86749i) q^{74} +(-2.94430 + 2.94430i) q^{75} +(-9.65649 - 2.15950i) q^{76} +(-3.50482 - 3.50482i) q^{77} +(3.57229 - 1.03765i) q^{78} +2.61962 q^{79} +(1.23828 + 3.44162i) q^{80} -1.00000 q^{81} +(-11.3285 + 3.29062i) q^{82} +(-2.75229 - 2.75229i) q^{83} +(0.436482 - 1.95179i) q^{84} +(0.721685 - 0.721685i) q^{85} +(4.89583 + 2.69183i) q^{86} +1.82171i q^{87} +(-13.9918 + 0.878178i) q^{88} -1.24439i q^{89} +(-0.623041 + 1.13317i) q^{90} +(-1.85997 + 1.85997i) q^{91} +(1.37263 + 2.16340i) q^{92} +(1.18699 + 1.18699i) q^{93} +(0.896542 + 3.08649i) q^{94} -4.52401 q^{95} +(-3.32387 - 4.57732i) q^{96} -8.68699 q^{97} +(0.394485 + 1.35808i) q^{98} +(-3.50482 - 3.50482i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q+O(q^{10}) $ 28 * q	$ 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) $ 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.394485	−	1.35808i	−0.278943	−	0.960308i
$2$	−0.394485	−	1.35808i	−0.278943	−	0.960308i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$	−1.68876	+	1.07148i	−0.844382	+	0.535742i
$5$	−0.646579	+	0.646579i	−0.289159	+	0.289159i	−0.836748	−	0.547589i	$-0.815546\pi$
$5$	−0.646579	+	0.646579i	−0.289159	+	0.289159i	0.547589	+	0.836748i	$0.315546\pi$
$6$	0.681365	−	1.23925i	0.278166	−	0.505922i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.12135	+	1.87079i	0.750012	+	0.661424i
$9$			1.00000i			0.333333i
$10$	1.13317	+	0.623041i	0.358341	+	0.197023i
$11$	−3.50482	+	3.50482i	−1.05674	+	1.05674i	−0.0584537	+	0.998290i	$0.518617\pi$
$11$	−3.50482	+	3.50482i	−1.05674	+	1.05674i	−0.998290	+	0.0584537i	$0.981383\pi$
$12$	−1.95179	−	0.436482i	−0.563433	−	0.126001i
$13$	1.85997	+	1.85997i	0.515864	+	0.515864i	0.916317	−	0.400453i	$-0.131147\pi$
$13$	1.85997	+	1.85997i	0.515864	+	0.515864i	−0.400453	+	0.916317i	$0.631147\pi$
$14$	1.35808	−	0.394485i	0.362962	−	0.105431i
$15$	−0.914401			−0.236097
$16$	1.70384	−	3.61897i	0.425960	−	0.904742i
$17$	−1.11616			−0.270708			−0.135354	−	0.990797i	$-0.543217\pi$
$17$	−1.11616			−0.270708			−0.135354	+	0.990797i	$0.543217\pi$
$18$	1.35808	−	0.394485i	0.320103	−	0.0929810i
$19$	3.49842	+	3.49842i	0.802592	+	0.802592i	0.983500	−	0.180908i	$-0.0579037\pi$
$19$	3.49842	+	3.49842i	0.802592	+	0.802592i	−0.180908	+	0.983500i	$0.557904\pi$
$20$	0.399120	−	1.78472i	0.0892458	−	0.399075i
$21$	−0.707107	+	0.707107i	−0.154303	+	0.154303i
$22$	6.14243	+	3.37723i	1.30957	+	0.720028i
$23$		−	1.28106i		−	0.267119i	−0.991041	−	0.133559i	$-0.957359\pi$
$23$		−	1.28106i		−	0.267119i	0.991041	−	0.133559i	$-0.0426407\pi$
$24$	0.177175	+	2.82287i	0.0361656	+	0.576216i
$25$			4.16387i			0.832774i
$26$	1.79226	−	3.25973i	0.351491	−	0.639285i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.07148	−	1.68876i	−0.202492	−	0.319146i
$29$	1.28814	+	1.28814i	0.239202	+	0.239202i	0.816520	−	0.577317i	$-0.195900\pi$
$29$	1.28814	+	1.28814i	0.239202	+	0.239202i	−0.577317	+	0.816520i	$0.695900\pi$
$30$	0.360718	+	1.24183i	0.0658577	+	0.226726i
$31$	1.67865			0.301495			0.150748	−	0.988572i	$-0.451832\pi$
$31$	1.67865			0.301495			0.150748	+	0.988572i	$0.451832\pi$
$32$	−5.58699	−	0.886325i	−0.987649	−	0.156682i
$33$	−4.95657			−0.862828
$34$	0.440308	+	1.51583i	0.0755122	+	0.259963i
$35$	−0.646579	−	0.646579i	−0.109292	−	0.109292i
$36$	−1.07148	−	1.68876i	−0.178581	−	0.281461i
$37$	4.01360	−	4.01360i	0.659832	−	0.659832i	−0.295508	−	0.955340i	$-0.595489\pi$
$37$	4.01360	−	4.01360i	0.659832	−	0.659832i	0.955340	+	0.295508i	$0.0954889\pi$
$38$	3.37106	−	6.13120i	0.546858	−	0.994612i
$39$			2.63040i			0.421201i
$40$	−2.58124	+	0.162009i	−0.408130	+	0.0256158i
$41$		−	8.34155i		−	1.30273i	−0.758764	−	0.651365i	$-0.774197\pi$
$41$		−	8.34155i		−	1.30273i	0.758764	−	0.651365i	$-0.225803\pi$
$42$	1.23925	+	0.681365i	0.191221	+	0.105137i
$43$	−2.79353	+	2.79353i	−0.426009	+	0.426009i	−0.887266	−	0.461258i	$-0.847398\pi$
$43$	−2.79353	+	2.79353i	−0.426009	+	0.426009i	0.461258	+	0.887266i	$0.347398\pi$
$44$	2.16345	−	9.67418i	0.326153	−	1.45844i
$45$	−0.646579	−	0.646579i	−0.0963864	−	0.0963864i
$46$	−1.73978	+	0.505358i	−0.256516	+	0.0745110i
$47$	−2.27269			−0.331506			−0.165753	−	0.986167i	$-0.553005\pi$
$47$	−2.27269			−0.331506			−0.165753	+	0.986167i	$0.553005\pi$
$48$	3.76379	−	1.35420i	0.543257	−	0.195462i
$49$	−1.00000			−0.142857
$50$	5.65487	−	1.64258i	0.799719	−	0.232297i
$51$	−0.789243	−	0.789243i	−0.110516	−	0.110516i
$52$	−5.13399	−	1.14812i	−0.711956	−	0.159216i
$53$	9.00612	−	9.00612i	1.23709	−	1.23709i	0.275900	−	0.961186i	$-0.411024\pi$
$53$	9.00612	−	9.00612i	1.23709	−	1.23709i	0.961186	−	0.275900i	$-0.0889757\pi$
$54$	1.23925	+	0.681365i	0.168641	+	0.0927220i
$55$		−	4.53229i		−	0.611134i
$56$	−1.87079	+	2.12135i	−0.249995	+	0.283478i
$57$			4.94751i			0.655313i
$58$	1.24125	−	2.25756i	0.162984	−	0.296432i
$59$	−10.4403	+	10.4403i	−1.35921	+	1.35921i	−0.484313	+	0.874895i	$0.660930\pi$
$59$	−10.4403	+	10.4403i	−1.35921	+	1.35921i	−0.874895	+	0.484313i	$0.839070\pi$
$60$	1.54421	−	0.979767i	0.199356	−	0.126487i
$61$	−6.58105	−	6.58105i	−0.842617	−	0.842617i	0.146582	−	0.989199i	$-0.453173\pi$
$61$	−6.58105	−	6.58105i	−0.842617	−	0.842617i	−0.989199	+	0.146582i	$0.953173\pi$
$62$	−0.662204	−	2.27975i	−0.0841000	−	0.289528i
$63$	−1.00000			−0.125988
$64$	1.00028	+	7.93722i	0.125035	+	0.992152i
$65$	−2.40524			−0.298334
$66$	1.95529	+	6.73142i	0.240680	+	0.828580i
$67$	11.0941	+	11.0941i	1.35536	+	1.35536i	0.879551	+	0.475805i	$0.157843\pi$
$67$	11.0941	+	11.0941i	1.35536	+	1.35536i	0.475805	+	0.879551i	$0.342157\pi$
$68$	1.88493	−	1.19595i	0.228581	−	0.145030i
$69$	0.905845	−	0.905845i	0.109051	−	0.109051i
$70$	−0.623041	+	1.13317i	−0.0744676	+	0.135440i
$71$		−	0.0956898i		−	0.0113563i	−0.999984	−	0.00567814i	$-0.998193\pi$
$71$		−	0.0956898i		−	0.0113563i	0.999984	−	0.00567814i	$-0.00180742\pi$
$72$	−1.87079	+	2.12135i	−0.220475	+	0.250004i
$73$		−	7.55336i		−	0.884054i	−0.897002	−	0.442027i	$-0.854260\pi$
$73$		−	7.55336i		−	0.884054i	0.897002	−	0.442027i	$-0.145740\pi$
$74$	−7.03410	−	3.86749i	−0.817698	−	0.449586i
$75$	−2.94430	+	2.94430i	−0.339979	+	0.339979i
$76$	−9.65649	−	2.15950i	−1.10768	−	0.247711i
$77$	−3.50482	−	3.50482i	−0.399412	−	0.399412i
$78$	3.57229	−	1.03765i	0.404483	−	0.117491i
$79$	2.61962			0.294730			0.147365	−	0.989082i	$-0.452921\pi$
$79$	2.61962			0.294730			0.147365	+	0.989082i	$0.452921\pi$
$80$	1.23828	+	3.44162i	0.138444	+	0.384785i
$81$	−1.00000			−0.111111
$82$	−11.3285	+	3.29062i	−1.25102	+	0.363388i
$83$	−2.75229	−	2.75229i	−0.302103	−	0.302103i	0.539733	−	0.841836i	$-0.318525\pi$
$83$	−2.75229	−	2.75229i	−0.302103	−	0.302103i	−0.841836	+	0.539733i	$0.818525\pi$
$84$	0.436482	−	1.95179i	0.0476241	−	0.212958i
$85$	0.721685	−	0.721685i	0.0782778	−	0.0782778i
$86$	4.89583	+	2.69183i	0.527931	+	0.290267i
$87$			1.82171i			0.195308i
$88$	−13.9918	+	0.878178i	−1.49153	+	0.0936141i
$89$		−	1.24439i		−	0.131905i	−0.997823	−	0.0659525i	$-0.978991\pi$
$89$		−	1.24439i		−	0.131905i	0.997823	−	0.0659525i	$-0.0210086\pi$
$90$	−0.623041	+	1.13317i	−0.0656743	+	0.119447i
$91$	−1.85997	+	1.85997i	−0.194978	+	0.194978i
$92$	1.37263	+	2.16340i	0.143107	+	0.225550i
$93$	1.18699	+	1.18699i	0.123085	+	0.123085i
$94$	0.896542	+	3.08649i	0.0924713	+	0.318348i
$95$	−4.52401			−0.464153
$96$	−3.32387	−	4.57732i	−0.339241	−	0.467171i
$97$	−8.68699			−0.882030			−0.441015	−	0.897500i	$-0.645381\pi$
$97$	−8.68699			−0.882030			−0.441015	+	0.897500i	$0.645381\pi$
$98$	0.394485	+	1.35808i	0.0398490	+	0.137187i
$99$	−3.50482	−	3.50482i	−0.352248	−	0.352248i
$100$	−4.46152	−	7.03179i	−0.446152	−	0.703179i
$101$	−0.0732569	+	0.0732569i	−0.00728933	+	0.00728933i	−0.710742	−	0.703453i	$-0.751641\pi$
$101$	−0.0732569	+	0.0732569i	−0.00728933	+	0.00728933i	0.703453	+	0.710742i	$0.251641\pi$
$102$	−0.760511	+	1.38320i	−0.0753018	+	0.136957i
$103$		−	11.1446i		−	1.09811i	−0.835786	−	0.549055i	$-0.814988\pi$
$103$		−	11.1446i		−	1.09811i	0.835786	−	0.549055i	$-0.185012\pi$
$104$	0.466040	+	7.42529i	0.0456990	+	0.728109i
$105$		−	0.914401i		−	0.0892364i
$106$	−15.7838	−	8.67826i	−1.53306	−	0.842907i
$107$	−0.388664	+	0.388664i	−0.0375736	+	0.0375736i	−0.725644	−	0.688070i	$-0.758458\pi$
$107$	−0.388664	+	0.388664i	−0.0375736	+	0.0375736i	0.688070	+	0.725644i	$0.258458\pi$
$108$	0.436482	−	1.95179i	0.0420005	−	0.187811i
$109$	10.1314	+	10.1314i	0.970414	+	0.970414i	0.999575	−	0.0291603i	$-0.00928331\pi$
$109$	10.1314	+	10.1314i	0.970414	+	0.970414i	−0.0291603	+	0.999575i	$0.509283\pi$
$110$	−6.15522	+	1.78792i	−0.586877	+	0.170472i
$111$	5.67609			0.538751
$112$	3.61897	+	1.70384i	0.341960	+	0.160998i
$113$	5.39069			0.507113			0.253557	−	0.967321i	$-0.418400\pi$
$113$	5.39069			0.507113			0.253557	+	0.967321i	$0.418400\pi$
$114$	6.71911	−	1.95172i	0.629302	−	0.182795i
$115$	0.828305	+	0.828305i	0.0772399	+	0.0772399i
$116$	−3.55560	−	0.795144i	−0.330129	−	0.0738273i
$117$	−1.85997	+	1.85997i	−0.171955	+	0.171955i
$118$	18.2973	+	10.0602i	1.68440	+	0.926116i
$119$		−	1.11616i		−	0.102318i
$120$	−1.93977	−	1.71065i	−0.177076	−	0.156161i
$121$		−	13.5676i		−	1.23342i
$122$	−6.34146	+	11.5337i	−0.574129	+	1.04421i
$123$	5.89836	−	5.89836i	0.531838	−	0.531838i
$124$	−2.83485	+	1.79865i	−0.254577	+	0.161524i
$125$	−5.92517	−	5.92517i	−0.529963	−	0.529963i
$126$	0.394485	+	1.35808i	0.0351435	+	0.120987i
$127$	−5.31019			−0.471203			−0.235601	−	0.971850i	$-0.575706\pi$
$127$	−5.31019			−0.471203			−0.235601	+	0.971850i	$0.575706\pi$
$128$	10.3848	−	4.48958i	0.917894	−	0.396826i
$129$	−3.95064			−0.347835
$130$	0.948832	+	3.26651i	0.0832181	+	0.286492i
$131$	15.2637	+	15.2637i	1.33360	+	1.33360i	0.902129	+	0.431466i	$0.142003\pi$
$131$	15.2637	+	15.2637i	1.33360	+	1.33360i	0.431466	+	0.902129i	$0.357997\pi$
$132$	8.37047	−	5.31089i	0.728556	−	0.462253i
$133$	−3.49842	+	3.49842i	−0.303351	+	0.303351i
$134$	10.6902	−	19.4431i	0.923492	−	1.67963i
$135$		−	0.914401i		−	0.0786991i
$136$	−2.36777	−	2.08810i	−0.203034	−	0.179053i
$137$			6.68771i			0.571370i	0.958324	+	0.285685i	$0.0922211\pi$
$137$			6.68771i			0.571370i	−0.958324	+	0.285685i	$0.907779\pi$
$138$	−1.58755	−	0.872867i	−0.135141	−	0.0743034i
$139$	14.5369	−	14.5369i	1.23301	−	1.23301i	0.270202	−	0.962804i	$-0.412910\pi$
$139$	14.5369	−	14.5369i	1.23301	−	1.23301i	0.962804	−	0.270202i	$-0.0870904\pi$
$140$	1.78472	+	0.399120i	0.150836	+	0.0337318i
$141$	−1.60703	−	1.60703i	−0.135337	−	0.135337i
$142$	−0.129954	+	0.0377482i	−0.0109055	+	0.00316776i
$143$	−13.0378			−1.09027
$144$	3.61897	+	1.70384i	0.301581	+	0.141987i
$145$	−1.66578			−0.138335
$146$	−10.2581	+	2.97969i	−0.848964	+	0.246601i
$147$	−0.707107	−	0.707107i	−0.0583212	−	0.0583212i
$148$	−2.47751	+	11.0785i	−0.203650	+	0.910650i
$149$	15.6453	−	15.6453i	1.28171	−	1.28171i	0.342017	−	0.939694i	$-0.388890\pi$
$149$	15.6453	−	15.6453i	1.28171	−	1.28171i	0.939694	−	0.342017i	$-0.111110\pi$
$150$	5.16008	+	2.83711i	0.421319	+	0.231649i
$151$		−	9.07786i		−	0.738746i	−0.929281	−	0.369373i	$-0.879572\pi$
$151$		−	9.07786i		−	0.738746i	0.929281	−	0.369373i	$-0.120428\pi$
$152$	0.876573	+	13.9662i	0.0710995	+	1.13281i
$153$		−	1.11616i		−	0.0902361i
$154$	−3.37723	+	6.14243i	−0.272145	+	0.494971i
$155$	−1.08538	+	1.08538i	−0.0871801	+	0.0871801i
$156$	−2.81843	−	4.44212i	−0.225655	−	0.355655i
$157$	5.89233	+	5.89233i	0.470259	+	0.470259i	0.901998	−	0.431739i	$-0.142100\pi$
$157$	5.89233	+	5.89233i	0.470259	+	0.470259i	−0.431739	+	0.901998i	$0.642100\pi$
$158$	−1.03340	−	3.55766i	−0.0822130	−	0.283032i
$159$	12.7366			1.01008
$160$	4.18551	−	3.03935i	0.330894	−	0.240282i
$161$	1.28106			0.100961
$162$	0.394485	+	1.35808i	0.0309937	+	0.106701i
$163$	11.7047	+	11.7047i	0.916779	+	0.916779i	0.996794	−	0.0800144i	$-0.0254966\pi$
$163$	11.7047	+	11.7047i	0.916779	+	0.916779i	−0.0800144	+	0.996794i	$0.525497\pi$
$164$	8.93784	+	14.0869i	0.697928	+	1.10000i
$165$	3.20481	−	3.20481i	0.249494	−	0.249494i
$166$	−2.65209	+	4.82356i	−0.205842	+	0.374381i
$167$			12.3766i			0.957730i	0.877889	+	0.478865i	$0.158952\pi$
$167$			12.3766i			0.957730i	−0.877889	+	0.478865i	$0.841048\pi$
$168$	−2.82287	+	0.177175i	−0.217789	+	0.0136693i
$169$		−	6.08099i		−	0.467769i
$170$	−1.26480	−	0.695412i	−0.0970058	−	0.0533357i
$171$	−3.49842	+	3.49842i	−0.267531	+	0.267531i
$172$	1.72438	−	7.71082i	0.131483	−	0.587945i
$173$	16.0301	+	16.0301i	1.21874	+	1.21874i	0.968072	+	0.250671i	$0.0806513\pi$
$173$	16.0301	+	16.0301i	1.21874	+	1.21874i	0.250671	+	0.968072i	$0.419349\pi$
$174$	2.47403	−	0.718638i	0.187556	−	0.0544798i
$175$	−4.16387			−0.314759
$176$	6.71218	+	18.6555i	0.505949	+	1.40621i
$177$	−14.7648			−1.10979
$178$	−1.68998	+	0.490893i	−0.126669	+	0.0367940i
$179$	−0.759288	−	0.759288i	−0.0567519	−	0.0567519i	0.678161	−	0.734913i	$-0.262777\pi$
$179$	−0.759288	−	0.759288i	−0.0567519	−	0.0567519i	−0.734913	+	0.678161i	$0.762777\pi$
$180$	1.78472	+	0.399120i	0.133025	+	0.0297486i
$181$	3.34558	−	3.34558i	0.248675	−	0.248675i	−0.571752	−	0.820427i	$-0.693736\pi$
$181$	3.34558	−	3.34558i	0.248675	−	0.248675i	0.820427	+	0.571752i	$0.193736\pi$
$182$	3.25973	+	1.79226i	0.241627	+	0.132851i
$183$		−	9.30701i		−	0.687994i
$184$	2.39659	−	2.71758i	0.176679	−	0.200342i
$185$			5.19023i			0.381593i
$186$	1.14378	−	2.08027i	0.0838657	−	0.152533i
$187$	3.91194	−	3.91194i	0.286069	−	0.286069i
$188$	3.83803	−	2.43515i	0.279917	−	0.177602i
$189$	−0.707107	−	0.707107i	−0.0514344	−	0.0514344i
$190$	1.78465	+	6.14396i	0.129472	+	0.445730i
$191$	18.2553			1.32091			0.660454	−	0.750866i	$-0.270364\pi$
$191$	18.2553			1.32091			0.660454	+	0.750866i	$0.270364\pi$
$192$	−4.90515	+	6.31977i	−0.353999	+	0.456090i
$193$	24.1707			1.73985			0.869923	−	0.493187i	$-0.164168\pi$
$193$	24.1707			1.73985			0.869923	+	0.493187i	$0.164168\pi$
$194$	3.42689	+	11.7976i	0.246036	+	0.847020i
$195$	−1.70076	−	1.70076i	−0.121794	−	0.121794i
$196$	1.68876	−	1.07148i	0.120626	−	0.0765346i
$197$	10.7698	−	10.7698i	0.767316	−	0.767316i	−0.210317	−	0.977633i	$-0.567450\pi$
$197$	10.7698	−	10.7698i	0.767316	−	0.767316i	0.977633	+	0.210317i	$0.0674497\pi$
$198$	−3.37723	+	6.14243i	−0.240009	+	0.436524i
$199$		−	23.0260i		−	1.63227i	−0.577860	−	0.816136i	$-0.696112\pi$
$199$		−	23.0260i		−	1.63227i	0.577860	−	0.816136i	$-0.303888\pi$
$200$	−7.78973	+	8.83304i	−0.550817	+	0.624590i
$201$			15.6894i			1.10664i
$202$	0.128387	+	0.0705899i	0.00903331	+	0.00496669i
$203$	−1.28814	+	1.28814i	−0.0904100	+	0.0904100i
$204$	2.17851	+	0.487183i	0.152526	+	0.0341096i
$205$	5.39347	+	5.39347i	0.376696	+	0.376696i
$206$	−15.1353	+	4.39638i	−1.05452	+	0.306310i
$207$	1.28106			0.0890397
$208$	9.90029	−	3.56208i	0.686461	−	0.246986i
$209$	−24.5227			−1.69627
$210$	−1.24183	+	0.360718i	−0.0856944	+	0.0248919i
$211$	−15.7047	−	15.7047i	−1.08115	−	1.08115i	−0.996402	−	0.0847515i	$-0.972990\pi$
$211$	−15.7047	−	15.7047i	−1.08115	−	1.08115i	−0.0847515	−	0.996402i	$-0.527010\pi$
$212$	−5.55929	+	24.8591i	−0.381813	+	1.70733i
$213$	0.0676629	−	0.0676629i	0.00463619	−	0.00463619i
$214$	0.681159	+	0.374515i	0.0465631	+	0.0256013i
$215$		−	3.61247i		−	0.246369i
$216$	−2.82287	+	0.177175i	−0.192072	+	0.0120552i
$217$			1.67865i			0.113954i
$218$	9.76259	−	17.7560i	0.661206	−	1.20259i
$219$	5.34103	−	5.34103i	0.360913	−	0.360913i
$220$	4.85628	+	7.65397i	0.327410	+	0.516030i
$221$	−2.07603	−	2.07603i	−0.139649	−	0.139649i
$222$	−2.23913	−	7.70859i	−0.150281	−	0.517367i
$223$	−8.26285			−0.553322			−0.276661	−	0.960968i	$-0.589228\pi$
$223$	−8.26285			−0.553322			−0.276661	+	0.960968i	$0.589228\pi$
$224$	0.886325	−	5.58699i	0.0592201	−	0.373296i
$225$	−4.16387			−0.277591
$226$	−2.12655	−	7.32099i	−0.141456	−	0.486985i
$227$	−12.7665	−	12.7665i	−0.847344	−	0.847344i	0.142457	−	0.989801i	$-0.454500\pi$
$227$	−12.7665	−	12.7665i	−0.847344	−	0.847344i	−0.989801	+	0.142457i	$0.954500\pi$
$228$	−5.30118	−	8.35517i	−0.351079	−	0.553335i
$229$	−12.4659	+	12.4659i	−0.823769	+	0.823769i	−0.986646	−	0.162877i	$-0.947922\pi$
$229$	−12.4659	+	12.4659i	−0.823769	+	0.823769i	0.162877	+	0.986646i	$0.447922\pi$
$230$	0.798151	−	1.45166i	0.0526285	−	0.0957196i
$231$		−	4.95657i		−	0.326118i
$232$	0.322761	+	5.14246i	0.0211903	+	0.337619i
$233$			10.9929i			0.720171i	0.932919	+	0.360085i	$0.117252\pi$
$233$			10.9929i			0.720171i	−0.932919	+	0.360085i	$0.882748\pi$
$234$	3.25973	+	1.79226i	0.213095	+	0.117164i
$235$	1.46947	−	1.46947i	0.0958579	−	0.0958579i
$236$	6.44456	−	28.8177i	0.419505	−	1.87588i
$237$	1.85235	+	1.85235i	0.120323	+	0.120323i
$238$	−1.51583	+	0.440308i	−0.0982569	+	0.0285409i
$239$	−20.0823			−1.29902			−0.649509	−	0.760354i	$-0.725025\pi$
$239$	−20.0823			−1.29902			−0.649509	+	0.760354i	$0.725025\pi$
$240$	−1.55800	+	3.30919i	−0.100568	+	0.213607i
$241$	−5.34351			−0.344205			−0.172103	−	0.985079i	$-0.555056\pi$
$241$	−5.34351			−0.344205			−0.172103	+	0.985079i	$0.555056\pi$
$242$	−18.4258	+	5.35220i	−1.18446	+	0.344053i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	18.1653	+	4.06234i	1.16292	+	0.260065i
$245$	0.646579	−	0.646579i	0.0413084	−	0.0413084i
$246$	−10.3373	−	5.68363i	−0.659080	−	0.362375i
$247$			13.0139i			0.828056i
$248$	3.56102	+	3.14041i	0.226125	+	0.199416i
$249$		−	3.89232i		−	0.246666i
$250$	−5.70946	+	10.3842i	−0.361098	+	0.656757i
$251$	−1.94585	+	1.94585i	−0.122821	+	0.122821i	−0.765846	−	0.643025i	$-0.777679\pi$
$251$	−1.94585	+	1.94585i	−0.122821	+	0.122821i	0.643025	+	0.765846i	$0.277679\pi$
$252$	1.68876	−	1.07148i	0.106382	−	0.0674972i
$253$	4.48988	+	4.48988i	0.282276	+	0.282276i
$254$	2.09479	+	7.21166i	0.131439	+	0.452500i
$255$	1.02062			0.0639135
$256$	−10.1938	−	12.3323i	−0.637116	−	0.770768i
$257$	−6.10914			−0.381078			−0.190539	−	0.981680i	$-0.561023\pi$
$257$	−6.10914			−0.381078			−0.190539	+	0.981680i	$0.561023\pi$
$258$	1.55847	+	5.36529i	0.0970260	+	0.334028i
$259$	4.01360	+	4.01360i	0.249393	+	0.249393i
$260$	4.06188	−	2.57718i	0.251907	−	0.159830i
$261$	−1.28814	+	1.28814i	−0.0797342	+	0.0797342i
$262$	14.7080	−	26.7506i	0.908664	−	1.65266i
$263$			12.5436i			0.773473i	0.922190	+	0.386736i	$0.126398\pi$
$263$			12.5436i			0.773473i	−0.922190	+	0.386736i	$0.873602\pi$
$264$	−10.5146	−	9.27270i	−0.647131	−	0.570695i
$265$			11.6463i			0.715429i
$266$	6.13120	+	3.37106i	0.375928	+	0.206693i
$267$	0.879916	−	0.879916i	0.0538500	−	0.0538500i
$268$	−30.6224	−	6.84813i	−1.87056	−	0.418316i
$269$	2.97785	+	2.97785i	0.181563	+	0.181563i	0.792037	−	0.610474i	$-0.209021\pi$
$269$	2.97785	+	2.97785i	0.181563	+	0.181563i	−0.610474	+	0.792037i	$0.709021\pi$
$270$	−1.24183	+	0.360718i	−0.0755754	+	0.0219526i
$271$	17.2143			1.04569			0.522846	−	0.852427i	$-0.324870\pi$
$271$	17.2143			1.04569			0.522846	+	0.852427i	$0.324870\pi$
$272$	−1.90176	+	4.03934i	−0.115311	+	0.244921i
$273$	−2.63040			−0.159199
$274$	9.08245	−	2.63820i	0.548691	−	0.159380i
$275$	−14.5936	−	14.5936i	−0.880029	−	0.880029i
$276$	−0.559158	+	2.50036i	−0.0336574	+	0.150504i
$277$	−19.5941	+	19.5941i	−1.17730	+	1.17730i	−0.196866	+	0.980430i	$0.563076\pi$
$277$	−19.5941	+	19.5941i	−1.17730	+	1.17730i	−0.980430	+	0.196866i	$0.936924\pi$
$278$	−25.4769	−	14.0077i	−1.52800	−	0.840126i
$279$			1.67865i			0.100498i
$280$	−0.162009	−	2.58124i	−0.00968188	−	0.154259i
$281$			6.52935i			0.389508i	0.980852	+	0.194754i	$0.0623909\pi$
$281$			6.52935i			0.389508i	−0.980852	+	0.194754i	$0.937609\pi$
$282$	−1.54853	+	2.81643i	−0.0922136	+	0.167716i
$283$	−10.5524	+	10.5524i	−0.627278	+	0.627278i	−0.947382	−	0.320104i	$-0.896282\pi$
$283$	−10.5524	+	10.5524i	−0.627278	+	0.627278i	0.320104	+	0.947382i	$0.396282\pi$
$284$	0.102530	+	0.161597i	0.00608404	+	0.00958904i
$285$	−3.19896	−	3.19896i	−0.189490	−	0.189490i
$286$	5.14320	+	17.7063i	0.304124	+	1.04700i
$287$	8.34155			0.492386
$288$	0.886325	−	5.58699i	0.0522272	−	0.329216i
$289$	−15.7542			−0.926717
$290$	0.657124	+	2.26226i	0.0385876	+	0.132844i
$291$	−6.14263	−	6.14263i	−0.360087	−	0.360087i
$292$	8.09331	+	12.7558i	0.473625	+	0.746479i
$293$	−9.09118	+	9.09118i	−0.531112	+	0.531112i	−0.920903	−	0.389791i	$-0.872547\pi$
$293$	−9.09118	+	9.09118i	−0.531112	+	0.531112i	0.389791	+	0.920903i	$0.372547\pi$
$294$	−0.681365	+	1.23925i	−0.0397380	+	0.0722746i
$295$		−	13.5009i		−	0.786055i
$296$	16.0229	−	1.00566i	0.931311	−	0.0584528i
$297$		−	4.95657i		−	0.287609i
$298$	−27.4194	−	15.0757i	−1.58836	−	0.873312i
$299$	2.38273	−	2.38273i	0.137797	−	0.137797i
$300$	1.81745	−	8.12700i	0.104931	−	0.469213i
$301$	−2.79353	−	2.79353i	−0.161016	−	0.161016i
$302$	−12.3285	+	3.58108i	−0.709423	+	0.206068i
$303$	−0.103601			−0.00595171
$304$	18.6214	−	6.69991i	1.06801	−	0.384266i
$305$	8.51034			0.487301
$306$	−1.51583	+	0.440308i	−0.0866544	+	0.0251707i
$307$	14.1135	+	14.1135i	0.805497	+	0.805497i	0.983949	−	0.178452i	$-0.0571088\pi$
$307$	14.1135	+	14.1135i	0.805497	+	0.805497i	−0.178452	+	0.983949i	$0.557109\pi$
$308$	9.67418	+	2.16345i	0.551238	+	0.123274i
$309$	7.88042	−	7.88042i	0.448302	−	0.448302i
$310$	1.90221	+	1.04587i	0.108038	+	0.0594014i
$311$		−	25.7337i		−	1.45922i	−0.683863	−	0.729611i	$-0.739701\pi$
$311$		−	25.7337i		−	1.45922i	0.683863	−	0.729611i	$-0.260299\pi$
$312$	−4.92093	+	5.58001i	−0.278593	+	0.315906i
$313$		−	6.39168i		−	0.361279i	−0.983549	−	0.180640i	$-0.942183\pi$
$313$		−	6.39168i		−	0.361279i	0.983549	−	0.180640i	$-0.0578168\pi$
$314$	5.67782	−	10.3267i	0.320418	−	0.582769i
$315$	0.646579	−	0.646579i	0.0364306	−	0.0364306i
$316$	−4.42392	+	2.80688i	−0.248865	+	0.157900i
$317$	18.9925	+	18.9925i	1.06673	+	1.06673i	0.997609	+	0.0691175i	$0.0220183\pi$
$317$	18.9925	+	18.9925i	1.06673	+	1.06673i	0.0691175	+	0.997609i	$0.477982\pi$
$318$	−5.02439	−	17.2973i	−0.281754	−	0.969984i
$319$	−9.02944			−0.505552
$320$	−5.77880	−	4.48528i	−0.323045	−	0.250735i
$321$	−0.549654			−0.0306787
$322$	−0.505358	−	1.73978i	−0.0281625	−	0.0969541i
$323$	−3.90479	−	3.90479i	−0.217268	−	0.217268i
$324$	1.68876	−	1.07148i	0.0938202	−	0.0595269i
$325$	−7.74469	+	7.74469i	−0.429598	+	0.429598i
$326$	11.2785	−	20.5132i	0.624661	−	1.13612i
$327$			14.3280i			0.792340i
$328$	15.6053	−	17.6954i	0.861658	−	0.977063i
$329$		−	2.27269i		−	0.125297i
$330$	−5.61665	−	3.08814i	−0.309186	−	0.169997i
$331$	6.10969	−	6.10969i	0.335819	−	0.335819i	−0.518972	−	0.854791i	$-0.673685\pi$
$331$	6.10969	−	6.10969i	0.335819	−	0.335819i	0.854791	+	0.518972i	$0.173685\pi$
$332$	7.59700	+	1.69893i	0.416939	+	0.0932408i
$333$	4.01360	+	4.01360i	0.219944	+	0.219944i
$334$	16.8084	−	4.88238i	0.919715	−	0.267152i
$335$	−14.3464			−0.783827
$336$	1.35420	+	3.76379i	0.0738776	+	0.205332i
$337$	11.7605			0.640636			0.320318	−	0.947310i	$-0.396210\pi$
$337$	11.7605			0.640636			0.320318	+	0.947310i	$0.396210\pi$
$338$	−8.25847	+	2.39886i	−0.449202	+	0.130481i
$339$	3.81179	+	3.81179i	0.207028	+	0.207028i
$340$	−0.445481	+	1.99203i	−0.0241596	+	0.108033i
$341$	−5.88339	+	5.88339i	−0.318603	+	0.318603i
$342$	6.13120	+	3.37106i	0.331537	+	0.182286i
$343$		−	1.00000i		−	0.0539949i
$344$	−11.1522	+	0.699954i	−0.601284	+	0.0377390i
$345$			1.17140i			0.0630661i
$346$	15.4465	−	28.0937i	0.830409	−	1.51033i
$347$	−8.68280	+	8.68280i	−0.466117	+	0.466117i	−0.900654	−	0.434537i	$-0.856912\pi$
$347$	−8.68280	+	8.68280i	−0.466117	+	0.466117i	0.434537	+	0.900654i	$0.356912\pi$
$348$	−1.95194	−	3.07644i	−0.104635	−	0.164914i
$349$	−11.1221	−	11.1221i	−0.595351	−	0.595351i	0.343721	−	0.939072i	$-0.388313\pi$
$349$	−11.1221	−	11.1221i	−0.595351	−	0.595351i	−0.939072	+	0.343721i	$0.888313\pi$
$350$	1.64258	+	5.65487i	0.0877998	+	0.302265i
$351$	−2.63040			−0.140400
$352$	22.6878	−	16.4750i	1.20926	−	0.878120i
$353$	23.5049			1.25104			0.625519	−	0.780209i	$-0.284887\pi$
$353$	23.5049			1.25104			0.625519	+	0.780209i	$0.284887\pi$
$354$	5.82448	+	20.0517i	0.309568	+	1.06574i
$355$	0.0618710	+	0.0618710i	0.00328377	+	0.00328377i
$356$	1.33334	+	2.10148i	0.0706671	+	0.111378i
$357$	0.789243	−	0.789243i	0.0417712	−	0.0417712i
$358$	−0.731646	+	1.33070i	−0.0386687	+	0.0703298i
$359$			8.61415i			0.454637i	0.973820	+	0.227319i	$0.0729959\pi$
$359$			8.61415i			0.454637i	−0.973820	+	0.227319i	$0.927004\pi$
$360$	−0.162009	−	2.58124i	−0.00853861	−	0.136043i
$361$			5.47783i			0.288307i
$362$	−5.86334	−	3.22378i	−0.308170	−	0.169438i
$363$	9.59372	−	9.59372i	0.503540	−	0.503540i
$364$	1.14812	−	5.13399i	0.0601779	−	0.269094i
$365$	4.88385	+	4.88385i	0.255632	+	0.255632i
$366$	−12.6397	+	3.67147i	−0.660686	+	0.191911i
$367$	−24.8694			−1.29817			−0.649086	−	0.760715i	$-0.724849\pi$
$367$	−24.8694			−1.29817			−0.649086	+	0.760715i	$0.724849\pi$
$368$	−4.63611	−	2.18272i	−0.241674	−	0.113782i
$369$	8.34155			0.434244
$370$	7.04874	−	2.04747i	0.366447	−	0.106443i
$371$	9.00612	+	9.00612i	0.467575	+	0.467575i
$372$	−3.27638	−	0.732702i	−0.169872	−	0.0379888i
$373$	−20.4319	+	20.4319i	−1.05792	+	1.05792i	−0.0597073	+	0.998216i	$0.519017\pi$
$373$	−20.4319	+	20.4319i	−1.05792	+	1.05792i	−0.998216	+	0.0597073i	$0.980983\pi$
$374$	−6.85593	−	3.76952i	−0.354512	−	0.194917i
$375$		−	8.37946i		−	0.432713i
$376$	−4.82118	−	4.25173i	−0.248633	−	0.219266i
$377$			4.79183i			0.246792i
$378$	−0.681365	+	1.23925i	−0.0350456	+	0.0637402i
$379$	−4.15646	+	4.15646i	−0.213503	+	0.213503i	−0.805754	−	0.592251i	$-0.798239\pi$
$379$	−4.15646	+	4.15646i	−0.213503	+	0.213503i	0.592251	+	0.805754i	$0.298239\pi$
$380$	7.63998	−	4.84740i	0.391923	−	0.248667i
$381$	−3.75487	−	3.75487i	−0.192368	−	0.192368i
$382$	−7.20145	−	24.7922i	−0.368458	−	1.26848i
$383$	26.0047			1.32878			0.664389	−	0.747387i	$-0.268692\pi$
$383$	26.0047			1.32878			0.664389	+	0.747387i	$0.268692\pi$
$384$	10.5178	+	4.16854i	0.536732	+	0.212725i
$385$	4.53229			0.230987
$386$	−9.53499	−	32.8258i	−0.485318	−	1.67079i
$387$	−2.79353	−	2.79353i	−0.142003	−	0.142003i
$388$	14.6703	−	9.30798i	0.744770	−	0.472541i
$389$	−4.81863	+	4.81863i	−0.244314	+	0.244314i	−0.818632	−	0.574318i	$-0.805267\pi$
$389$	−4.81863	+	4.81863i	−0.244314	+	0.244314i	0.574318	+	0.818632i	$0.305267\pi$
$390$	−1.63885	+	2.98070i	−0.0829862	+	0.150933i
$391$			1.42986i			0.0723113i
$392$	−2.12135	−	1.87079i	−0.107145	−	0.0944892i
$393$			21.5861i			1.08888i
$394$	−18.8748	−	10.3777i	−0.950897	−	0.522822i
$395$	−1.69379	+	1.69379i	−0.0852240	+	0.0852240i
$396$	9.67418	+	2.16345i	0.486146	+	0.108718i
$397$	−22.7198	−	22.7198i	−1.14027	−	1.14027i	−0.988400	−	0.151874i	$-0.951469\pi$
$397$	−22.7198	−	22.7198i	−1.14027	−	1.14027i	−0.151874	−	0.988400i	$-0.548531\pi$
$398$	−31.2712	+	9.08342i	−1.56748	+	0.455311i
$399$	−4.94751			−0.247685
$400$	15.0689	+	7.09457i	0.753445	+	0.354729i
$401$	−8.29595			−0.414280			−0.207140	−	0.978311i	$-0.566416\pi$
$401$	−8.29595			−0.414280			−0.207140	+	0.978311i	$0.566416\pi$
$402$	21.3074	−	6.18923i	1.06272	−	0.308691i
$403$	3.12225	+	3.12225i	0.155531	+	0.155531i
$404$	0.0452199	−	0.202207i	0.00224977	−	0.0100602i
$405$	0.646579	−	0.646579i	0.0321288	−	0.0321288i
$406$	2.25756	+	1.24125i	0.112041	+	0.0616022i
$407$			28.1339i			1.39455i
$408$	−0.197755	−	3.15077i	−0.00979033	−	0.155987i
$409$		−	10.2495i		−	0.506804i	−0.967361	−	0.253402i	$-0.918450\pi$
$409$		−	10.2495i		−	0.506804i	0.967361	−	0.253402i	$-0.0815496\pi$
$410$	5.19712	−	9.45241i	0.256668	−	0.466821i
$411$	−4.72893	+	4.72893i	−0.233261	+	0.233261i
$412$	11.9413	+	18.8206i	0.588304	+	0.927224i
$413$	−10.4403	−	10.4403i	−0.513732	−	0.513732i
$414$	−0.505358	−	1.73978i	−0.0248370	−	0.0855055i
$415$	3.55914			0.174712
$416$	−8.74311	−	12.0402i	−0.428666	−	0.590319i
$417$	20.5583			1.00674
$418$	9.67382	+	33.3037i	0.473162	+	1.62894i
$419$	−18.6538	−	18.6538i	−0.911296	−	0.911296i	0.0850781	−	0.996374i	$-0.472886\pi$
$419$	−18.6538	−	18.6538i	−0.911296	−	0.911296i	−0.996374	+	0.0850781i	$0.972886\pi$
$420$	0.979767	+	1.54421i	0.0478077	+	0.0753496i
$421$	−12.9455	+	12.9455i	−0.630924	+	0.630924i	−0.948300	−	0.317376i	$-0.897198\pi$
$421$	−12.9455	+	12.9455i	−0.630924	+	0.630924i	0.317376	+	0.948300i	$0.397198\pi$
$422$	−15.1329	+	27.5234i	−0.736660	+	1.33982i
$423$		−	2.27269i		−	0.110502i
$424$	35.9537	−	2.25660i	1.74607	−	0.109590i
$425$		−	4.64754i		−	0.225439i
$426$	−0.118584	−	0.0651996i	−0.00574540	−	0.00315893i
$427$	6.58105	−	6.58105i	0.318479	−	0.318479i
$428$	0.239914	−	1.07281i	0.0115967	−	0.0518562i
$429$	−9.21909	−	9.21909i	−0.445102	−	0.445102i
$430$	−4.90603	+	1.42507i	−0.236590	+	0.0687228i
$431$	35.4691			1.70849			0.854243	−	0.519874i	$-0.174021\pi$
$431$	35.4691			1.70849			0.854243	+	0.519874i	$0.174021\pi$
$432$	1.35420	+	3.76379i	0.0651539	+	0.181086i
$433$	−23.2737			−1.11846			−0.559232	−	0.829012i	$-0.688904\pi$
$433$	−23.2737			−1.11846			−0.559232	+	0.829012i	$0.688904\pi$
$434$	2.27975	−	0.662204i	0.109431	−	0.0317868i
$435$	−1.17788	−	1.17788i	−0.0564751	−	0.0564751i
$436$	−27.9652	−	6.25391i	−1.33929	−	0.299508i
$437$	4.48167	−	4.48167i	0.214387	−	0.214387i
$438$	−9.36051	−	5.14659i	−0.447262	−	0.245914i
$439$		−	27.6510i		−	1.31971i	−0.751393	−	0.659855i	$-0.770618\pi$
$439$		−	27.6510i		−	1.31971i	0.751393	−	0.659855i	$-0.229382\pi$
$440$	8.47897	−	9.61460i	0.404219	−	0.458358i
$441$		−	1.00000i		−	0.0476190i
$442$	−2.00045	+	3.63837i	−0.0951516	+	0.173060i
$443$	11.8143	−	11.8143i	0.561314	−	0.561314i	−0.368367	−	0.929681i	$-0.620083\pi$
$443$	11.8143	−	11.8143i	0.561314	−	0.561314i	0.929681	+	0.368367i	$0.120083\pi$
$444$	−9.58557	+	6.08185i	−0.454911	+	0.288632i
$445$	0.804596	+	0.804596i	0.0381415	+	0.0381415i
$446$	3.25957	+	11.2216i	0.154345	+	0.531359i
$447$	22.1258			1.04651
$448$	−7.93722	+	1.00028i	−0.374998	+	0.0472589i
$449$	16.3238			0.770366			0.385183	−	0.922840i	$-0.374138\pi$
$449$	16.3238			0.770366			0.385183	+	0.922840i	$0.374138\pi$
$450$	1.64258	+	5.65487i	0.0774322	+	0.266573i
$451$	29.2356	+	29.2356i	1.37665	+	1.37665i
$452$	−9.10360	+	5.77604i	−0.428197	+	0.271682i
$453$	6.41902	−	6.41902i	0.301592	−	0.301592i
$454$	−12.3018	+	22.3742i	−0.577350	+	1.05007i
$455$		−	2.40524i		−	0.112759i
$456$	−9.25575	+	10.4954i	−0.433440	+	0.491493i
$457$			18.1301i			0.848088i	0.905641	+	0.424044i	$0.139390\pi$
$457$			18.1301i			0.848088i	−0.905641	+	0.424044i	$0.860610\pi$
$458$	21.8473	+	12.0121i	1.02086	+	0.561287i
$459$	0.789243	−	0.789243i	0.0368387	−	0.0368387i
$460$	−2.28633	−	0.511295i	−0.106601	−	0.0238393i
$461$	−5.78740	−	5.78740i	−0.269546	−	0.269546i	0.559371	−	0.828917i	$-0.311043\pi$
$461$	−5.78740	−	5.78740i	−0.269546	−	0.269546i	−0.828917	+	0.559371i	$0.811043\pi$
$462$	−6.73142	+	1.95529i	−0.313174	+	0.0909684i
$463$	−35.6119			−1.65503			−0.827513	−	0.561446i	$-0.810245\pi$
$463$	−35.6119			−1.65503			−0.827513	+	0.561446i	$0.810245\pi$
$464$	6.85655	−	2.46696i	0.318307	−	0.114526i
$465$	−1.53496			−0.0711823
$466$	14.9293	−	4.33655i	0.691585	−	0.200887i
$467$	0.126168	+	0.126168i	0.00583837	+	0.00583837i	0.710020	−	0.704182i	$-0.248686\pi$
$467$	0.126168	+	0.126168i	0.00583837	+	0.00583837i	−0.704182	+	0.710020i	$0.748686\pi$
$468$	1.14812	−	5.13399i	0.0530720	−	0.237319i
$469$	−11.0941	+	11.0941i	−0.512276	+	0.512276i
$470$	−2.57535	−	1.41598i	−0.118792	−	0.0653142i
$471$			8.33301i			0.383965i
$472$	−41.6791	+	2.61594i	−1.91844	+	0.120409i
$473$		−	19.5816i		−	0.900364i
$474$	1.78492	−	3.24637i	0.0819840	−	0.149111i
$475$	−14.5670	+	14.5670i	−0.668378	+	0.668378i
$476$	1.19595	+	1.88493i	0.0548161	+	0.0863955i
$477$	9.00612	+	9.00612i	0.412362	+	0.412362i
$478$	7.92217	+	27.2734i	0.362352	+	1.24746i
$479$	2.40687			0.109973			0.0549863	−	0.998487i	$-0.482488\pi$
$479$	2.40687			0.109973			0.0549863	+	0.998487i	$0.482488\pi$
$480$	5.10875	+	0.810457i	0.233181	+	0.0369921i
$481$	14.9304			0.680767
$482$	2.10793	+	7.25691i	0.0960137	+	0.330543i
$483$	0.905845	+	0.905845i	0.0412174	+	0.0412174i
$484$	14.5374	+	22.9124i	0.660793	+	1.04147i
$485$	5.61683	−	5.61683i	0.255047	−	0.255047i
$486$	−0.681365	+	1.23925i	−0.0309073	+	0.0562136i
$487$			32.3718i			1.46691i	0.679740	+	0.733453i	$0.262093\pi$
$487$			32.3718i			1.46691i	−0.679740	+	0.733453i	$0.737907\pi$
$488$	−1.64897	−	26.2725i	−0.0746452	−	1.18930i
$489$			16.5529i			0.748547i
$490$	−1.13317	−	0.623041i	−0.0511915	−	0.0281461i
$491$	13.2151	−	13.2151i	0.596388	−	0.596388i	−0.342962	−	0.939349i	$-0.611430\pi$
$491$	13.2151	−	13.2151i	0.596388	−	0.596388i	0.939349	+	0.342962i	$0.111430\pi$
$492$	−3.64093	+	16.2809i	−0.164146	+	0.734002i
$493$	−1.43777	−	1.43777i	−0.0647541	−	0.0647541i
$494$	17.6740	−	5.13380i	0.795189	−	0.230981i
$495$	4.53229			0.203711
$496$	2.86016	−	6.07500i	0.128425	−	0.272775i
$497$	0.0956898			0.00429227
$498$	−5.28609	+	1.53546i	−0.236875	+	0.0688057i
$499$	−23.5491	−	23.5491i	−1.05420	−	1.05420i	−0.998444	−	0.0557586i	$-0.982242\pi$
$499$	−23.5491	−	23.5491i	−1.05420	−	1.05420i	−0.0557586	−	0.998444i	$-0.517758\pi$
$500$	16.3549	+	3.65748i	0.731415	+	0.163567i
$501$	−8.75157	+	8.75157i	−0.390991	+	0.390991i
$502$	3.41023	+	1.87501i	0.152206	+	0.0836859i
$503$			28.2413i			1.25922i	0.776913	+	0.629608i	$0.216784\pi$
$503$			28.2413i			1.25922i	−0.776913	+	0.629608i	$0.783216\pi$
$504$	−2.12135	−	1.87079i	−0.0944926	−	0.0833316i
$505$		−	0.0947328i		−	0.00421555i
$506$	4.32643	−	7.86881i	0.192333	−	0.349811i
$507$	4.29991	−	4.29991i	0.190966	−	0.190966i
$508$	8.96765	−	5.68978i	0.397875	−	0.252443i
$509$	−24.2565	−	24.2565i	−1.07515	−	1.07515i	−0.996937	−	0.0782115i	$-0.975079\pi$
$509$	−24.2565	−	24.2565i	−1.07515	−	1.07515i	−0.0782115	−	0.996937i	$-0.524921\pi$
$510$	−0.402618	−	1.38608i	−0.0178282	−	0.0613766i
$511$	7.55336			0.334141
$512$	−12.7269	+	18.7090i	−0.562456	+	0.826827i
$513$	−4.94751			−0.218438
$514$	2.40996	+	8.29670i	0.106299	+	0.365952i
$515$	7.20587	+	7.20587i	0.317529	+	0.317529i
$516$	6.67170	−	4.23305i	0.293705	−	0.186350i
$517$	7.96538	−	7.96538i	0.350317	−	0.350317i
$518$	3.86749	−	7.03410i	0.169928	−	0.309061i
$519$			22.6699i			0.995100i
$520$	−5.10237	−	4.49970i	−0.223754	−	0.197325i
$521$			8.89116i			0.389529i	0.980850	+	0.194765i	$0.0623943\pi$
$521$			8.89116i			0.389529i	−0.980850	+	0.194765i	$0.937606\pi$
$522$	2.25756	+	1.24125i	0.0988106	+	0.0543280i
$523$	0.334226	−	0.334226i	0.0146147	−	0.0146147i	−0.699762	−	0.714376i	$-0.746710\pi$
$523$	0.334226	−	0.334226i	0.0146147	−	0.0146147i	0.714376	+	0.699762i	$0.246710\pi$
$524$	−42.1316	−	9.42195i	−1.84053	−	0.411600i
$525$	−2.94430	−	2.94430i	−0.128500	−	0.128500i
$526$	17.0352	−	4.94827i	0.742772	−	0.215755i
$527$	−1.87364			−0.0816173
$528$	−8.44521	+	17.9377i	−0.367530	+	0.780636i
$529$	21.3589			0.928647
$530$	15.8167	−	4.59431i	0.687032	−	0.199564i
$531$	−10.4403	−	10.4403i	−0.453069	−	0.453069i
$532$	2.15950	−	9.65649i	0.0936261	−	0.418662i
$533$	15.5151	−	15.5151i	0.672032	−	0.672032i
$534$	−1.54211	−	0.847883i	−0.0667336	−	0.0366915i
$535$		−	0.502605i		−	0.0217295i
$536$	2.77976	+	44.2891i	0.120067	+	1.91300i
$537$		−	1.07380i		−	0.0463377i
$538$	2.86944	−	5.21888i	0.123710	−	0.225002i
$539$	3.50482	−	3.50482i	0.150963	−	0.150963i
$540$	0.979767	+	1.54421i	0.0421625	+	0.0664521i
$541$	4.24319	+	4.24319i	0.182429	+	0.182429i	0.792413	−	0.609984i	$-0.208824\pi$
$541$	4.24319	+	4.24319i	0.182429	+	0.182429i	−0.609984	+	0.792413i	$0.708824\pi$
$542$	−6.79077	−	23.3784i	−0.291689	−	1.00419i
$543$	4.73136			0.203042
$544$	6.23596	+	0.989279i	0.267365	+	0.0424150i
$545$	−13.1015			−0.561208
$546$	1.03765	+	3.57229i	0.0444075	+	0.152880i
$547$	−17.5093	−	17.5093i	−0.748643	−	0.748643i	0.225581	−	0.974224i	$-0.427572\pi$
$547$	−17.5093	−	17.5093i	−0.748643	−	0.748643i	−0.974224	+	0.225581i	$0.927572\pi$
$548$	−7.16578	−	11.2940i	−0.306107	−	0.482454i
$549$	6.58105	−	6.58105i	0.280872	−	0.280872i
$550$	−14.0623	+	25.5763i	−0.599620	+	1.09058i
$551$			9.01293i			0.383964i
$552$	3.61626	−	0.226971i	0.153918	−	0.00966053i
$553$			2.61962i			0.111398i
$554$	34.3400	+	18.8808i	1.45897	+	0.802168i
$555$	−3.67004	+	3.67004i	−0.155785	+	0.155785i
$556$	−8.97333	+	40.1255i	−0.380554	+	1.70170i
$557$	−24.7185	−	24.7185i	−1.04736	−	1.04736i	−0.998821	−	0.0485367i	$-0.984544\pi$
$557$	−24.7185	−	24.7185i	−1.04736	−	1.04736i	−0.0485367	−	0.998821i	$-0.515456\pi$
$558$	2.27975	−	0.662204i	0.0965094	−	0.0280333i
$559$	−10.3918			−0.439525
$560$	−3.44162	+	1.23828i	−0.145435	+	0.0523269i
$561$	5.53232			0.233575
$562$	8.86737	−	2.57573i	0.374048	−	0.108651i
$563$	−26.3032	−	26.3032i	−1.10855	−	1.10855i	−0.993342	−	0.115206i	$-0.963247\pi$
$563$	−26.3032	−	26.3032i	−1.10855	−	1.10855i	−0.115206	−	0.993342i	$-0.536753\pi$
$564$	4.43581	+	0.991988i	0.186781	+	0.0417702i
$565$	−3.48551	+	3.48551i	−0.146636	+	0.146636i
$566$	18.4939	+	10.1683i	0.777355	+	0.427405i
$567$		−	1.00000i		−	0.0419961i
$568$	0.179016	−	0.202992i	0.00751133	−	0.00851735i
$569$			10.2415i			0.429346i	0.976686	+	0.214673i	$0.0688685\pi$
$569$			10.2415i			0.429346i	−0.976686	+	0.214673i	$0.931131\pi$
$570$	−3.08250	+	5.60638i	−0.129112	+	0.234825i
$571$	6.52984	−	6.52984i	0.273265	−	0.273265i	−0.557148	−	0.830413i	$-0.688104\pi$
$571$	6.52984	−	6.52984i	0.273265	−	0.273265i	0.830413	+	0.557148i	$0.188104\pi$
$572$	22.0177	−	13.9698i	0.920606	−	0.584105i
$573$	12.9085	+	12.9085i	0.539259	+	0.539259i
$574$	−3.29062	−	11.3285i	−0.137348	−	0.472842i
$575$	5.33416			0.222450
$576$	−7.93722	+	1.00028i	−0.330717	+	0.0416785i
$577$	43.0641			1.79278			0.896391	−	0.443264i	$-0.146180\pi$
$577$	43.0641			1.79278			0.896391	+	0.443264i	$0.146180\pi$
$578$	6.21479	+	21.3955i	0.258501	+	0.889933i
$579$	17.0913	+	17.0913i	0.710289	+	0.710289i
$580$	2.81310	−	1.78485i	0.116808	−	0.0741120i
$581$	2.75229	−	2.75229i	0.114184	−	0.114184i
$582$	−5.91901	+	10.7654i	−0.245351	+	0.446238i
$583$			63.1297i			2.61457i
$584$	14.1308	−	16.0233i	0.584735	−	0.663051i
$585$		−	2.40524i		−	0.0994445i
$586$	15.9329	+	8.76021i	0.658181	+	0.361881i
$587$	14.9250	−	14.9250i	0.616021	−	0.616021i	−0.328487	−	0.944508i	$-0.606539\pi$
$587$	14.9250	−	14.9250i	0.616021	−	0.616021i	0.944508	+	0.328487i	$0.106539\pi$
$588$	1.95179	+	0.436482i	0.0804905	+	0.0180002i
$589$	5.87263	+	5.87263i	0.241978	+	0.241978i
$590$	−18.3353	+	5.32592i	−0.754854	+	0.219264i
$591$	15.2308			0.626511
$592$	−7.68655	−	21.3636i	−0.315915	−	0.878040i
$593$	40.7244			1.67235			0.836176	−	0.548461i	$-0.184786\pi$
$593$	40.7244			1.67235			0.836176	+	0.548461i	$0.184786\pi$
$594$	−6.73142	+	1.95529i	−0.276193	+	0.0802266i
$595$	0.721685	+	0.721685i	0.0295862	+	0.0295862i
$596$	−9.65749	+	43.1848i	−0.395586	+	1.76892i
$597$	16.2819	−	16.2819i	0.666372	−	0.666372i
$598$	−4.17590	−	2.29599i	−0.170765	−	0.0938900i
$599$		−	36.9029i		−	1.50781i	−0.656982	−	0.753906i	$-0.728167\pi$
$599$		−	36.9029i		−	1.50781i	0.656982	−	0.753906i	$-0.271833\pi$
$600$	−11.7541	+	0.737732i	−0.479858	+	0.0301178i
$601$		−	24.9078i		−	1.01601i	−0.861354	−	0.508006i	$-0.830383\pi$
$601$		−	24.9078i		−	1.01601i	0.861354	−	0.508006i	$-0.169617\pi$
$602$	−2.69183	+	4.89583i	−0.109711	+	0.199539i
$603$	−11.0941	+	11.0941i	−0.451785	+	0.451785i
$604$	9.72679	+	15.3304i	0.395778	+	0.623784i
$605$	8.77251	+	8.77251i	0.356653	+	0.356653i
$606$	0.0408690	+	0.140698i	0.00166019	+	0.00571548i
$607$	−18.1437			−0.736431			−0.368216	−	0.929740i	$-0.620031\pi$
$607$	−18.1437			−0.736431			−0.368216	+	0.929740i	$0.620031\pi$
$608$	−16.4449	−	22.6463i	−0.666928	−	0.918430i
$609$	−1.82171			−0.0738195
$610$	−3.35720	−	11.5577i	−0.135929	−	0.467959i
$611$	−4.22714	−	4.22714i	−0.171012	−	0.171012i
$612$	1.19595	+	1.88493i	0.0483433	+	0.0761937i
$613$	16.5472	−	16.5472i	0.668336	−	0.668336i	−0.288995	−	0.957331i	$-0.593321\pi$
$613$	16.5472	−	16.5472i	0.668336	−	0.668336i	0.957331	+	0.288995i	$0.0933210\pi$
$614$	13.5997	−	24.7347i	0.548837	−	0.998213i
$615$			7.62752i			0.307571i
$616$	−0.878178	−	13.9918i	−0.0353828	−	0.563744i
$617$		−	18.4479i		−	0.742685i	−0.928496	−	0.371343i	$-0.878898\pi$
$617$		−	18.4479i		−	0.742685i	0.928496	−	0.371343i	$-0.121102\pi$
$618$	−13.8110	−	7.59354i	−0.555558	−	0.305457i
$619$	−9.27286	+	9.27286i	−0.372708	+	0.372708i	−0.868462	−	0.495755i	$-0.834891\pi$
$619$	−9.27286	+	9.27286i	−0.372708	+	0.372708i	0.495755	+	0.868462i	$0.334891\pi$
$620$	0.669984	−	2.99593i	0.0269072	−	0.120319i
$621$	0.905845	+	0.905845i	0.0363503	+	0.0363503i
$622$	−34.9484	+	10.1515i	−1.40130	+	0.407040i
$623$	1.24439			0.0498554
$624$	9.51933	+	4.48179i	0.381078	+	0.179415i
$625$	−13.1572			−0.526287
$626$	−8.68042	+	2.52142i	−0.346939	+	0.100776i
$627$	−17.3401	−	17.3401i	−0.692498	−	0.692498i
$628$	−16.2643	−	3.63721i	−0.649016	−	0.145140i
$629$	−4.47982	+	4.47982i	−0.178622	+	0.178622i
$630$	−1.13317	−	0.623041i	−0.0451467	−	0.0248225i
$631$			4.98173i			0.198320i	0.995072	+	0.0991598i	$0.0316155\pi$
$631$			4.98173i			0.198320i	−0.995072	+	0.0991598i	$0.968384\pi$
$632$	5.55714	+	4.90076i	0.221051	+	0.194942i
$633$		−	22.2097i		−	0.882758i
$634$	18.3011	−	33.2856i	0.726829	−	1.32194i
$635$	3.43346	−	3.43346i	0.136253	−	0.136253i
$636$	−21.5091	+	13.6471i	−0.852890	+	0.541141i
$637$	−1.85997	−	1.85997i	−0.0736949	−	0.0736949i
$638$	3.56198	+	12.2627i	0.141020	+	0.485485i
$639$	0.0956898			0.00378543
$640$	−3.81172	+	9.61745i	−0.150671	+	0.380163i
$641$	−8.66410			−0.342211			−0.171106	−	0.985253i	$-0.554734\pi$
$641$	−8.66410			−0.342211			−0.171106	+	0.985253i	$0.554734\pi$
$642$	0.216830	+	0.746474i	0.00855761	+	0.0294610i
$643$	9.38927	+	9.38927i	0.370277	+	0.370277i	0.867578	−	0.497301i	$-0.165676\pi$
$643$	9.38927	+	9.38927i	0.370277	+	0.370277i	−0.497301	+	0.867578i	$0.665676\pi$
$644$	−2.16340	+	1.37263i	−0.0852500	+	0.0540893i
$645$	2.55440	−	2.55440i	0.100580	−	0.100580i
$646$	−3.76263	+	6.84339i	−0.148039	+	0.269250i
$647$		−	26.3939i		−	1.03765i	−0.854880	−	0.518826i	$-0.826369\pi$
$647$		−	26.3939i		−	1.03765i	0.854880	−	0.518826i	$-0.173631\pi$
$648$	−2.12135	−	1.87079i	−0.0833346	−	0.0734916i
$649$		−	73.1826i		−	2.87267i
$650$	13.5731	+	7.46275i	0.532380	+	0.292713i
$651$	−1.18699	+	1.18699i	−0.0465217	+	0.0465217i
$652$	−32.3077	−	7.22503i	−1.26527	−	0.282954i
$653$	−6.49341	−	6.49341i	−0.254107	−	0.254107i	0.568545	−	0.822652i	$-0.307506\pi$
$653$	−6.49341	−	6.49341i	−0.254107	−	0.254107i	−0.822652	+	0.568545i	$0.807506\pi$
$654$	19.4586	−	5.65218i	0.760890	−	0.221018i
$655$	−19.7384			−0.771242
$656$	−30.1878	−	14.2127i	−1.17863	−	0.554912i
$657$	7.55336			0.294685
$658$	−3.08649	+	0.896542i	−0.120324	+	0.0349509i
$659$	5.09690	+	5.09690i	0.198547	+	0.198547i	0.799377	−	0.600830i	$-0.205163\pi$
$659$	5.09690	+	5.09690i	0.198547	+	0.198547i	−0.600830	+	0.799377i	$0.705163\pi$
$660$	−1.97826	+	8.84608i	−0.0770038	+	0.344333i
$661$	−16.9210	+	16.9210i	−0.658151	+	0.658151i	−0.954942	−	0.296791i	$-0.904083\pi$
$661$	−16.9210	+	16.9210i	−0.658151	+	0.658151i	0.296791	+	0.954942i	$0.404083\pi$
$662$	−10.7076	−	5.88727i	−0.416164	−	0.228815i
$663$		−	2.93594i		−	0.114023i
$664$	−0.689621	−	10.9875i	−0.0267625	−	0.426399i
$665$		−	4.52401i		−	0.175433i
$666$	3.86749	−	7.03410i	0.149862	−	0.272566i
$667$	1.65019	−	1.65019i	0.0638955	−	0.0638955i
$668$	−13.2613	−	20.9011i	−0.513096	−	0.808689i
$669$	−5.84272	−	5.84272i	−0.225893	−	0.225893i
$670$	5.65944	+	19.4835i	0.218643	+	0.752715i
$671$	46.1308			1.78086
$672$	4.57732	−	3.32387i	0.176574	−	0.128221i
$673$	33.5390			1.29284			0.646418	−	0.762984i	$-0.276266\pi$
$673$	33.5390			1.29284			0.646418	+	0.762984i	$0.276266\pi$
$674$	−4.63935	−	15.9717i	−0.178701	−	0.615208i
$675$	−2.94430	−	2.94430i	−0.113326	−	0.113326i
$676$	6.51569	+	10.2694i	0.250603	+	0.394975i
$677$	−8.06948	+	8.06948i	−0.310135	+	0.310135i	−0.844962	−	0.534827i	$-0.820377\pi$
$677$	−8.06948	+	8.06948i	−0.310135	+	0.310135i	0.534827	+	0.844962i	$0.320377\pi$
$678$	3.67302	−	6.68041i	0.141062	−	0.256560i
$679$		−	8.68699i		−	0.333376i
$680$	2.88107	−	0.180827i	0.110484	−	0.00693442i
$681$		−	18.0546i		−	0.691853i
$682$	10.3110	+	5.66920i	0.394829	+	0.217085i
$683$	6.31251	−	6.31251i	0.241541	−	0.241541i	−0.575946	−	0.817488i	$-0.695366\pi$
$683$	6.31251	−	6.31251i	0.241541	−	0.241541i	0.817488	+	0.575946i	$0.195366\pi$
$684$	2.15950	−	9.65649i	0.0825704	−	0.369225i
$685$	−4.32414	−	4.32414i	−0.165217	−	0.165217i
$686$	−1.35808	+	0.394485i	−0.0518517	+	0.0150615i
$687$	−17.6294			−0.672604
$688$	5.34995	+	14.8694i	0.203965	+	0.566891i
$689$	33.5023			1.27634
$690$	1.59086	−	0.462100i	0.0605629	−	0.0175919i
$691$	−15.4300	−	15.4300i	−0.586984	−	0.586984i	0.349829	−	0.936814i	$-0.386240\pi$
$691$	−15.4300	−	15.4300i	−0.586984	−	0.586984i	−0.936814	+	0.349829i	$0.886240\pi$
$692$	−44.2470	−	9.89502i	−1.68202	−	0.376152i
$693$	3.50482	−	3.50482i	0.133137	−	0.133137i
$694$	15.2172	+	8.36670i	0.577636	+	0.317596i
$695$			18.7985i			0.713070i
$696$	−3.40804	+	3.86450i	−0.129182	+	0.146483i
$697$			9.31049i			0.352660i
$698$	−10.7172	+	19.4922i	−0.405651	+	0.737790i
$699$	−7.77317	+	7.77317i	−0.294008	+	0.294008i
$700$	7.03179	−	4.46152i	0.265777	−	0.168630i
$701$	−0.353908	−	0.353908i	−0.0133669	−	0.0133669i	0.700392	−	0.713759i	$-0.253009\pi$
$701$	−0.353908	−	0.353908i	−0.0133669	−	0.0133669i	−0.713759	+	0.700392i	$0.753009\pi$
$702$	1.03765	+	3.57229i	0.0391637	+	0.134828i
$703$	28.0825			1.05915
$704$	−31.3244	−	24.3127i	−1.18058	−	0.916320i
$705$	2.07815			0.0782677
$706$	−9.27232	−	31.9215i	−0.348968	−	1.20138i
$707$	−0.0732569	−	0.0732569i	−0.00275511	−	0.00275511i
$708$	24.9342	−	15.8202i	0.937085	−	0.594561i
$709$	−2.75055	+	2.75055i	−0.103299	+	0.103299i	−0.756867	−	0.653568i	$-0.773271\pi$
$709$	−2.75055	+	2.75055i	−0.103299	+	0.103299i	0.653568	+	0.756867i	$0.273271\pi$
$710$	0.0596186	−	0.108433i	0.00223745	−	0.00406942i
$711$			2.61962i			0.0982435i
$712$	2.32799	−	2.63979i	0.0872452	−	0.0989303i
$713$		−	2.15045i		−	0.0805351i
$714$	−1.38320	−	0.760511i	−0.0517650	−	0.0284614i
$715$	8.42995	−	8.42995i	0.315262	−	0.315262i
$716$	2.09582	+	0.468692i	0.0783246	+	0.0175159i
$717$	−14.2003	−	14.2003i	−0.530322	−	0.530322i
$718$	11.6987	−	3.39815i	0.436592	−	0.126818i
$719$	−31.4214			−1.17182			−0.585910	−	0.810376i	$-0.699263\pi$
$719$	−31.4214			−1.17182			−0.585910	+	0.810376i	$0.699263\pi$
$720$	−3.44162	+	1.23828i	−0.128262	+	0.0461480i
$721$	11.1446			0.415047
$722$	7.43933	−	2.16092i	0.276863	−	0.0804212i
$723$	−3.77843	−	3.77843i	−0.140521	−	0.140521i
$724$	−2.06515	+	9.23462i	−0.0767508	+	0.343202i
$725$	−5.36367	+	5.36367i	−0.199202	+	0.199202i
$726$	−16.8136	−	9.24446i	−0.624012	−	0.343094i
$727$		−	16.5302i		−	0.613073i	−0.951859	−	0.306536i	$-0.900830\pi$
$727$		−	16.5302i		−	0.613073i	0.951859	−	0.306536i	$-0.0991701\pi$
$728$	−7.42529	+	0.466040i	−0.275199	+	0.0172726i
$729$		−	1.00000i		−	0.0370370i
$730$	4.70605	−	8.55926i	0.174179	−	0.316792i
$731$	3.11802	−	3.11802i	0.115324	−	0.115324i
$732$	9.97231	+	15.7173i	0.368587	+	0.580929i
$733$	0.591947	+	0.591947i	0.0218641	+	0.0218641i	0.717954	−	0.696090i	$-0.245079\pi$
$733$	0.591947	+	0.591947i	0.0218641	+	0.0218641i	−0.696090	+	0.717954i	$0.745079\pi$
$734$	9.81061	+	33.7746i	0.362116	+	1.24664i
$735$	0.914401			0.0337282
$736$	−1.13543	+	7.15725i	−0.0418526	+	0.263820i
$737$	−77.7655			−2.86453
$738$	−3.29062	−	11.3285i	−0.121129	−	0.417007i
$739$	12.1140	+	12.1140i	0.445622	+	0.445622i	0.893896	−	0.448274i	$-0.147961\pi$
$739$	12.1140	+	12.1140i	0.445622	+	0.445622i	−0.448274	+	0.893896i	$0.647961\pi$
$740$	−5.56125	−	8.76506i	−0.204436	−	0.322210i
$741$	−9.20224	+	9.20224i	−0.338053	+	0.338053i
$742$	8.67826	−	15.7838i	0.318589	−	0.579442i
$743$			21.3776i			0.784270i	0.919908	+	0.392135i	$0.128263\pi$
$743$			21.3776i			0.784270i	−0.919908	+	0.392135i	$0.871737\pi$
$744$	0.297415	+	4.73863i	0.0109038	+	0.173727i
$745$			20.2318i			0.741237i
$746$	35.8082	+	19.6881i	1.31103	+	0.720831i
$747$	2.75229	−	2.75229i	0.100701	−	0.100701i
$748$	−2.41476	+	10.7979i	−0.0882922	+	0.394811i
$749$	−0.388664	−	0.388664i	−0.0142015	−	0.0142015i
$750$	−11.3800	+	3.30557i	−0.415538	+	0.120702i
$751$	14.9106			0.544095			0.272048	−	0.962284i	$-0.412299\pi$
$751$	14.9106			0.544095			0.272048	+	0.962284i	$0.412299\pi$
$752$	−3.87230	+	8.22479i	−0.141208	+	0.299927i
$753$	−2.75185			−0.100283
$754$	6.50769	−	1.89031i	0.236996	−	0.0688409i
$755$	5.86956	+	5.86956i	0.213615	+	0.213615i
$756$	1.95179	+	0.436482i	0.0709859	+	0.0158747i
$757$	15.0344	−	15.0344i	0.546434	−	0.546434i	−0.378974	−	0.925407i	$-0.623723\pi$
$757$	15.0344	−	15.0344i	0.546434	−	0.546434i	0.925407	+	0.378974i	$0.123723\pi$
$758$	7.28446	+	4.00514i	0.264584	+	0.145473i
$759$			6.34965i			0.230478i
$760$	−9.59702	−	8.46347i	−0.348121	−	0.307002i
$761$			30.9922i			1.12346i	0.827319	+	0.561732i	$0.189865\pi$
$761$			30.9922i			1.12346i	−0.827319	+	0.561732i	$0.810135\pi$
$762$	−3.61817	+	6.58065i	−0.131073	+	0.238392i
$763$	−10.1314	+	10.1314i	−0.366782	+	0.366782i
$764$	−30.8289	+	19.5603i	−1.11535	+	0.707666i
$765$	0.721685	+	0.721685i	0.0260926	+	0.0260926i
$766$	−10.2585	−	35.3164i	−0.370653	−	1.27603i
$767$	−38.8373			−1.40233
$768$	1.51211	−	15.9284i	0.0545635	−	0.574766i
$769$	12.3879			0.446719			0.223360	−	0.974736i	$-0.428298\pi$
$769$	12.3879			0.446719			0.223360	+	0.974736i	$0.428298\pi$
$770$	−1.78792	−	6.15522i	−0.0644322	−	0.221819i
$771$	−4.31981	−	4.31981i	−0.155574	−	0.155574i
$772$	−40.8186	+	25.8986i	−1.46909	+	0.932110i
$773$	−27.1518	+	27.1518i	−0.976583	+	0.976583i	−0.999732	−	0.0231495i	$-0.992631\pi$
$773$	−27.1518	+	27.1518i	−0.976583	+	0.976583i	0.0231495	+	0.999732i	$0.492631\pi$
$774$	−2.69183	+	4.89583i	−0.0967557	+	0.175977i
$775$			6.98970i			0.251077i
$776$	−18.4282	−	16.2515i	−0.661533	−	0.583396i
$777$			5.67609i			0.203629i
$778$	8.44496	+	4.64321i	0.302767	+	0.166467i
$779$	29.1822	−	29.1822i	1.04556	−	1.04556i
$780$	4.69453	+	1.04984i	0.168091	+	0.0375905i
$781$	0.335376	+	0.335376i	0.0120007	+	0.0120007i
$782$	1.94187	−	0.564060i	0.0694411	−	0.0201707i
$783$	−1.82171			−0.0651027
$784$	−1.70384	+	3.61897i	−0.0608515	+	0.129249i
$785$	−7.61972			−0.271959
$786$	29.3157	−	8.51540i	1.04566	−	0.303734i
$787$	25.3225	+	25.3225i	0.902650	+	0.902650i	0.995665	−	0.0930144i	$-0.0296503\pi$
$787$	25.3225	+	25.3225i	0.902650	+	0.902650i	−0.0930144	+	0.995665i	$0.529650\pi$
$788$	−6.64796	+	29.7273i	−0.236824	+	1.05899i
$789$	−8.86968	+	8.86968i	−0.315769	+	0.315769i
$790$	2.96848	+	1.63213i	0.105614	+	0.0580686i
$791$			5.39069i			0.191671i
$792$	−0.878178	−	13.9918i	−0.0312047	−	0.497176i
$793$		−	24.4812i		−	0.869351i
$794$	−21.8927	+	39.8179i	−0.776942	+	1.41308i
$795$	−8.23521	+	8.23521i	−0.292073	+	0.292073i
$796$	24.6720	+	38.8855i	0.874477	+	1.37826i
$797$	−16.4277	−	16.4277i	−0.581900	−	0.581900i	0.353525	−	0.935425i	$-0.384983\pi$
$797$	−16.4277	−	16.4277i	−0.581900	−	0.581900i	−0.935425	+	0.353525i	$0.884983\pi$
$798$	1.95172	+	6.71911i	0.0690901	+	0.237854i
$799$	2.53668			0.0897414
$800$	3.69054	−	23.2635i	0.130480	−	0.822489i
$801$	1.24439			0.0439683
$802$	3.27263	+	11.2666i	0.115561	+	0.397836i
$803$	26.4732	+	26.4732i	0.934219	+	0.934219i
$804$	−16.8109	−	26.4956i	−0.592876	−	0.934429i
$805$	−0.828305	+	0.828305i	−0.0291939	+	0.0291939i
$806$	3.00859	−	5.47195i	0.105973	−	0.192741i
$807$			4.21132i			0.148245i
$808$	−0.292452	+	0.0183554i	−0.0102884	+	0.000645742i
$809$		−	15.3925i		−	0.541172i	−0.962696	−	0.270586i	$-0.912783\pi$
$809$		−	15.3925i		−	0.541172i	0.962696	−	0.270586i	$-0.0872174\pi$
$810$	−1.13317	−	0.623041i	−0.0398156	−	0.0218914i
$811$	22.8979	−	22.8979i	0.804055	−	0.804055i	−0.179672	−	0.983727i	$-0.557504\pi$
$811$	22.8979	−	22.8979i	0.804055	−	0.804055i	0.983727	+	0.179672i	$0.0575036\pi$
$812$	0.795144	−	3.55560i	0.0279041	−	0.124777i
$813$	12.1723	+	12.1723i	0.426902	+	0.426902i
$814$	38.2081	−	11.0984i	1.33919	−	0.388999i
$815$	−15.1360			−0.530190
$816$	−4.20099	+	1.51150i	−0.147064	+	0.0529131i
$817$	−19.5458			−0.683822
$818$	−13.9196	+	4.04327i	−0.486688	+	0.141370i
$819$	−1.85997	−	1.85997i	−0.0649928	−	0.0649928i
$820$	−14.8873	−	3.32927i	−0.519888	−	0.116263i
$821$	11.3164	−	11.3164i	0.394946	−	0.394946i	−0.481500	−	0.876446i	$-0.659908\pi$
$821$	11.3164	−	11.3164i	0.394946	−	0.394946i	0.876446	+	0.481500i	$0.159908\pi$
$822$	8.28776	+	4.55677i	0.289069	+	0.158936i
$823$		−	47.4322i		−	1.65338i	−0.562656	−	0.826691i	$-0.690220\pi$
$823$		−	47.4322i		−	1.65338i	0.562656	−	0.826691i	$-0.309780\pi$
$824$	20.8492	−	23.6416i	0.726317	−	0.823596i
$825$		−	20.6385i		−	0.718541i
$826$	−10.0602	+	18.2973i	−0.350039	+	0.636643i
$827$	−28.6247	+	28.6247i	−0.995378	+	0.995378i	−0.999989	−	0.00461130i	$-0.998532\pi$
$827$	−28.6247	+	28.6247i	−0.995378	+	0.995378i	0.00461130	+	0.999989i	$0.498532\pi$
$828$	−2.16340	+	1.37263i	−0.0751834	+	0.0477023i
$829$	−28.7659	−	28.7659i	−0.999082	−	0.999082i	0.000917636	−	1.00000i	$-0.499708\pi$
$829$	−28.7659	−	28.7659i	−0.999082	−	0.999082i	−1.00000		0.000917636i	$0.999708\pi$
$830$	−1.40403	−	4.83360i	−0.0487346	−	0.167777i
$831$	−27.7103			−0.961259
$832$	−12.9025	+	16.6235i	−0.447314	+	0.576317i
$833$	1.11616			0.0386726
$834$	−8.10995	−	27.9198i	−0.280824	−	0.966785i
$835$	−8.00245	−	8.00245i	−0.276936	−	0.276936i
$836$	41.4130	−	26.2756i	1.43230	−	0.908762i
$837$	−1.18699	+	1.18699i	−0.0410283	+	0.0410283i
$838$	−17.9747	+	32.6919i	−0.620925	+	1.12932i
$839$			44.3648i			1.53164i	0.643052	+	0.765822i	$0.277668\pi$
$839$			44.3648i			1.53164i	−0.643052	+	0.765822i	$0.722332\pi$
$840$	1.71065	−	1.93977i	0.0590232	−	0.0669284i
$841$		−	25.6814i		−	0.885564i
$842$	22.6878	+	12.4742i	0.781873	+	0.429889i
$843$	−4.61694	+	4.61694i	−0.159016	+	0.159016i
$844$	43.3488	+	9.69415i	1.49213	+	0.333686i
$845$	3.93184	+	3.93184i	0.135260	+	0.135260i
$846$	−3.08649	+	0.896542i	−0.106116	+	0.0308238i
$847$	13.5676			0.466187
$848$	−17.2479	−	47.9379i	−0.592294	−	1.64619i
$849$	−14.9234			−0.512170
$850$	−6.31173	+	1.83338i	−0.216491	+	0.0628846i
$851$	−5.14166	−	5.14166i	−0.176254	−	0.176254i
$852$	−0.0417669	+	0.186766i	−0.00143091	+	0.00639851i
$853$	37.6537	−	37.6537i	1.28924	−	1.28924i	0.353986	−	0.935251i	$-0.384826\pi$
$853$	37.6537	−	37.6537i	1.28924	−	1.28924i	0.935251	−	0.353986i	$-0.115174\pi$
$854$	−11.5337	−	6.34146i	−0.394676	−	0.217000i
$855$		−	4.52401i		−	0.154718i
$856$	−1.55160	+	0.0973848i	−0.0530327	+	0.00332854i
$857$			19.4871i			0.665667i	0.942986	+	0.332833i	$0.108005\pi$
$857$			19.4871i			0.665667i	−0.942986	+	0.332833i	$0.891995\pi$
$858$	−8.88347	+	16.1571i	−0.303277	+	0.551593i
$859$	−7.16628	+	7.16628i	−0.244510	+	0.244510i	−0.818713	−	0.574203i	$-0.805312\pi$
$859$	−7.16628	+	7.16628i	−0.244510	+	0.244510i	0.574203	+	0.818713i	$0.305312\pi$
$860$	3.87071	+	6.10061i	0.131990	+	0.208029i
$861$	5.89836	+	5.89836i	0.201016	+	0.201016i
$862$	−13.9920	−	48.1699i	−0.476570	−	1.64067i
$863$	−15.9700			−0.543625			−0.271813	−	0.962350i	$-0.587623\pi$
$863$	−15.9700			−0.543625			−0.271813	+	0.962350i	$0.587623\pi$
$864$	4.57732	−	3.32387i	0.155724	−	0.113080i
$865$	−20.7294			−0.704822
$866$	9.18113	+	31.6076i	0.311988	+	1.07407i
$867$	−11.1399	−	11.1399i	−0.378331	−	0.378331i
$868$	−1.79865	−	2.83485i	−0.0610502	−	0.0962211i
$869$	−9.18131	+	9.18131i	−0.311455	+	0.311455i
$870$	−1.13500	+	2.06431i	−0.0384801	+	0.0699868i
$871$			41.2694i			1.39836i
$872$	2.53856	+	40.4461i	0.0859664	+	1.36968i
$873$		−	8.68699i		−	0.294010i
$874$	−7.85442	−	4.31852i	−0.265680	−	0.146076i
$875$	5.92517	−	5.92517i	0.200307	−	0.200307i
$876$	−3.29690	+	14.7426i	−0.111392	+	0.498105i
$877$	18.0531	+	18.0531i	0.609610	+	0.609610i	0.942844	−	0.333234i	$-0.108140\pi$
$877$	18.0531	+	18.0531i	0.609610	+	0.609610i	−0.333234	+	0.942844i	$0.608140\pi$
$878$	−37.5523	+	10.9079i	−1.26733	+	0.368124i
$879$	−12.8569			−0.433651
$880$	−16.4022	−	7.72231i	−0.552919	−	0.260319i
$881$	34.2178			1.15283			0.576413	−	0.817158i	$-0.304452\pi$
$881$	34.2178			1.15283			0.576413	+	0.817158i	$0.304452\pi$
$882$	−1.35808	+	0.394485i	−0.0457289	+	0.0132830i
$883$	−20.0504	−	20.0504i	−0.674748	−	0.674748i	0.284059	−	0.958807i	$-0.408319\pi$
$883$	−20.0504	−	20.0504i	−0.674748	−	0.674748i	−0.958807	+	0.284059i	$0.908319\pi$
$884$	5.73035	+	1.28149i	0.192732	+	0.0431011i
$885$	9.54660	−	9.54660i	0.320905	−	0.320905i
$886$	−20.7053	−	11.3842i	−0.695608	−	0.382459i
$887$		−	34.4832i		−	1.15783i	−0.815387	−	0.578916i	$-0.803476\pi$
$887$		−	34.4832i		−	1.15783i	0.815387	−	0.578916i	$-0.196524\pi$
$888$	12.0410	+	10.6188i	0.404069	+	0.356343i
$889$		−	5.31019i		−	0.178098i
$890$	0.775305	−	1.41011i	0.0259883	−	0.0472669i
$891$	3.50482	−	3.50482i	0.117416	−	0.117416i
$892$	13.9540	−	8.85352i	0.467215	−	0.296438i
$893$	−7.95082	−	7.95082i	−0.266064	−	0.266064i
$894$	−8.72828	−	30.0486i	−0.291917	−	1.00497i
$895$	0.981880			0.0328206
$896$	4.48958	+	10.3848i	0.149986	+	0.346931i
$897$	3.36969			0.112511
$898$	−6.43948	−	22.1690i	−0.214888	−	0.739789i
$899$	2.16235	+	2.16235i	0.0721184	+	0.0721184i
$900$	7.03179	−	4.46152i	0.234393	−	0.148717i
$901$	−10.0523	+	10.0523i	−0.334889	+	0.334889i
$902$	28.1713	−	51.2374i	0.938002	−	1.70602i
$903$		−	3.95064i		−	0.131469i
$904$	11.4356	+	10.0849i	0.380341	+	0.335417i
$905$			4.32636i			0.143813i
$906$	−11.2497	−	6.18533i	−0.373748	−	0.205494i
$907$	−17.9970	+	17.9970i	−0.597581	+	0.597581i	−0.939668	−	0.342087i	$-0.888866\pi$
$907$	−17.9970	+	17.9970i	−0.597581	+	0.597581i	0.342087	+	0.939668i	$0.388866\pi$
$908$	35.2388	+	7.88050i	1.16944	+	0.261524i
$909$	−0.0732569	−	0.0732569i	−0.00242978	−	0.00242978i
$910$	−3.26651	+	0.948832i	−0.108284	+	0.0314535i
$911$	43.4732			1.44033			0.720166	−	0.693802i	$-0.244066\pi$
$911$	43.4732			1.44033			0.720166	+	0.693802i	$0.244066\pi$
$912$	17.9049	+	8.42977i	0.592889	+	0.279138i
$913$	19.2926			0.638491
$914$	24.6221	−	7.15204i	0.814426	−	0.236568i
$915$	6.01772	+	6.01772i	0.198940	+	0.198940i
$916$	7.69492	−	34.4089i	0.254247	−	1.13690i
$917$	−15.2637	+	15.2637i	−0.504052	+	0.504052i
$918$	−1.38320	−	0.760511i	−0.0456524	−	0.0251006i
$919$			34.7681i			1.14689i	0.819243	+	0.573447i	$0.194394\pi$
$919$			34.7681i			1.14689i	−0.819243	+	0.573447i	$0.805606\pi$
$920$	0.207543	+	3.30672i	0.00684248	+	0.109019i
$921$			19.9594i			0.657686i
$922$	−5.57671	+	10.1428i	−0.183659	+	0.334035i
$923$	0.177981	−	0.177981i	0.00585830	−	0.00585830i
$924$	5.31089	+	8.37047i	0.174715	+	0.275368i
$925$	16.7121	+	16.7121i	0.549491	+	0.549491i
$926$	14.0484	+	48.3639i	0.461658	+	1.58933i
$927$	11.1446			0.366037
$928$	−6.05513	−	8.33856i	−0.198770	−	0.273727i
$929$	−28.4041			−0.931907			−0.465953	−	0.884809i	$-0.654289\pi$
$929$	−28.4041			−0.931907			−0.465953	+	0.884809i	$0.654289\pi$
$930$	0.605520	+	2.08460i	0.0198558	+	0.0683569i
$931$	−3.49842	−	3.49842i	−0.114656	−	0.114656i
$932$	−11.7788	−	18.5644i	−0.385826	−	0.608099i
$933$	18.1964	−	18.1964i	0.595725	−	0.595725i
$934$	0.121575	−	0.221118i	0.00397806	−	0.00723520i
$935$			5.05876i			0.165439i
$936$	−7.42529	+	0.466040i	−0.242703	+	0.0152330i
$937$			21.9023i			0.715517i	0.933814	+	0.357759i	$0.116459\pi$
$937$			21.9023i			0.715517i	−0.933814	+	0.357759i	$0.883541\pi$
$938$	19.4431	+	10.6902i	0.634839	+	0.349047i
$939$	4.51960	−	4.51960i	0.147492	−	0.147492i
$940$	−0.907075	+	4.05611i	−0.0295855	+	0.132296i
$941$	28.8692	+	28.8692i	0.941109	+	0.941109i	0.998360	−	0.0572505i	$-0.0182334\pi$
$941$	28.8692	+	28.8692i	0.941109	+	0.941109i	−0.0572505	+	0.998360i	$0.518233\pi$
$942$	11.3169	−	3.28725i	0.368724	−	0.107104i
$943$	−10.6860			−0.347984
$944$	19.9944	+	55.5716i	0.650764	+	1.80870i
$945$	0.914401			0.0297455
$946$	−26.5934	+	7.72466i	−0.864626	+	0.251150i
$947$	−11.5529	−	11.5529i	−0.375419	−	0.375419i	0.494027	−	0.869446i	$-0.335524\pi$
$947$	−11.5529	−	11.5529i	−0.375419	−	0.375419i	−0.869446	+	0.494027i	$0.835524\pi$
$948$	−5.11295	−	1.14342i	−0.166061	−	0.0371365i
$949$	14.0491	−	14.0491i	0.456052	−	0.456052i
$950$	25.5295	+	14.0366i	0.828287	+	0.455409i
$951$			26.8595i			0.870978i
$952$	2.08810	−	2.36777i	0.0676757	−	0.0767398i
$953$			17.6298i			0.571086i	0.958366	+	0.285543i	$0.0921739\pi$
$953$			17.6298i			0.571086i	−0.958366	+	0.285543i	$0.907826\pi$
$954$	8.67826	−	15.7838i	0.280969	−	0.511020i
$955$	−11.8035	+	11.8035i	−0.381953	+	0.381953i
$956$	33.9143	−	21.5179i	1.09687	−	0.695938i
$957$	−6.38478	−	6.38478i	−0.206391	−	0.206391i
$958$	−0.949473	−	3.26872i	−0.0306761	−	0.105607i
$959$	−6.68771			−0.215958
$960$	−0.914660	−	7.25780i	−0.0295205	−	0.234245i
$961$	−28.1821			−0.909101
$962$	−5.88982	−	20.2767i	−0.189895	−	0.653746i
$963$	−0.388664	−	0.388664i	−0.0125245	−	0.0125245i
$964$	9.02392	−	5.72548i	0.290641	−	0.184405i
$965$	−15.6283	+	15.6283i	−0.503093	+	0.503093i
$966$	0.872867	−	1.58755i	0.0280840	−	0.0510786i
$967$			19.0991i			0.614186i	0.951680	+	0.307093i	$0.0993562\pi$
$967$			19.0991i			0.614186i	−0.951680	+	0.307093i	$0.900644\pi$
$968$	25.3821	−	28.7816i	0.815811	−	0.925076i
$969$		−	5.52220i		−	0.177399i
$970$	−9.84386	−	5.41235i	−0.316067	−	0.173780i
$971$	−38.6855	+	38.6855i	−1.24148	+	1.24148i	−0.282089	+	0.959388i	$0.591027\pi$
$971$	−38.6855	+	38.6855i	−1.24148	+	1.24148i	−0.959388	+	0.282089i	$0.908973\pi$
$972$	1.95179	+	0.436482i	0.0626037	+	0.0140002i
$973$	14.5369	+	14.5369i	0.466032	+	0.466032i
$974$	43.9635	−	12.7702i	1.40868	−	0.409183i
$975$	−10.9526			−0.350765
$976$	−35.0297	+	12.6035i	−1.12127	+	0.403429i
$977$	−28.0571			−0.897626			−0.448813	−	0.893626i	$-0.648153\pi$
$977$	−28.0571			−0.897626			−0.448813	+	0.893626i	$0.648153\pi$
$978$	22.4801	−	6.52986i	0.718836	−	0.208802i
$979$	4.36136	+	4.36136i	0.139390	+	0.139390i
$980$	−0.399120	+	1.78472i	−0.0127494	+	0.0570108i
$981$	−10.1314	+	10.1314i	−0.323471	+	0.323471i
$982$	−23.1603	−	12.7340i	−0.739074	−	0.406357i
$983$		−	10.4303i		−	0.332676i	−0.986069	−	0.166338i	$-0.946806\pi$
$983$		−	10.4303i		−	0.332676i	0.986069	−	0.166338i	$-0.0531943\pi$
$984$	23.5471	−	1.47791i	0.750655	−	0.0471141i
$985$			13.9271i			0.443753i
$986$	−1.38543	+	2.51979i	−0.0441211	+	0.0802465i
$987$	1.60703	−	1.60703i	0.0511525	−	0.0511525i
$988$	−13.9442	−	21.9774i	−0.443625	−	0.699195i
$989$	3.57867	+	3.57867i	0.113795	+	0.113795i
$990$	−1.78792	−	6.15522i	−0.0568239	−	0.195626i
$991$	−5.50750			−0.174951			−0.0874757	−	0.996167i	$-0.527880\pi$
$991$	−5.50750			−0.174951			−0.0874757	+	0.996167i	$0.527880\pi$
$992$	−9.37862	−	1.48783i	−0.297772	−	0.0472387i
$993$	8.64041			0.274195
$994$	−0.0377482	−	0.129954i	−0.00119730	−	0.00412190i
$995$	14.8882	+	14.8882i	0.471986	+	0.471986i
$996$	4.17056	+	6.57321i	0.132149	+	0.208280i
$997$	25.4153	−	25.4153i	0.804910	−	0.804910i	−0.178948	−	0.983858i	$-0.557269\pi$
$997$	25.4153	−	25.4153i	0.804910	−	0.804910i	0.983858	+	0.178948i	$0.0572695\pi$
$998$	−22.6918	+	41.2713i	−0.718297	+	1.30642i
$999$			5.67609i			0.179584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.w.b.253.6	yes	28
4.3	odd	2		1344.2.w.b.337.3		28
8.3	odd	2		2688.2.w.c.673.12		28
8.5	even	2		2688.2.w.d.673.3		28
16.3	odd	4		2688.2.w.c.2017.12		28
16.5	even	4	inner	336.2.w.b.85.6	✓	28
16.11	odd	4		1344.2.w.b.1009.3		28
16.13	even	4		2688.2.w.d.2017.3		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.w.b.85.6	✓	28	16.5	even	4	inner
336.2.w.b.253.6	yes	28	1.1	even	1	trivial
1344.2.w.b.337.3		28	4.3	odd	2
1344.2.w.b.1009.3		28	16.11	odd	4
2688.2.w.c.673.12		28	8.3	odd	2
2688.2.w.c.2017.12		28	16.3	odd	4
2688.2.w.d.673.3		28	8.5	even	2
2688.2.w.d.2017.3		28	16.13	even	4

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.394485 - 1.35808i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68876 + 1.07148i) q^{4} +(-0.646579 + 0.646579i) q^{5} +(0.681365 - 1.23925i) q^{6} +1.00000i q^{7} +(2.12135 + 1.87079i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.394485 - 1.35808i) q^{2} +(0.707107 + 0.707107i) q^{3} +(-1.68876 + 1.07148i) q^{4} +(-0.646579 + 0.646579i) q^{5} +(0.681365 - 1.23925i) q^{6} +1.00000i q^{7} +(2.12135 + 1.87079i) q^{8} +1.00000i q^{9} +(1.13317 + 0.623041i) q^{10} +(-3.50482 + 3.50482i) q^{11} +(-1.95179 - 0.436482i) q^{12} +(1.85997 + 1.85997i) q^{13} +(1.35808 - 0.394485i) q^{14} -0.914401 q^{15} +(1.70384 - 3.61897i) q^{16} -1.11616 q^{17} +(1.35808 - 0.394485i) q^{18} +(3.49842 + 3.49842i) q^{19} +(0.399120 - 1.78472i) q^{20} +(-0.707107 + 0.707107i) q^{21} +(6.14243 + 3.37723i) q^{22} -1.28106i q^{23} +(0.177175 + 2.82287i) q^{24} +4.16387i q^{25} +(1.79226 - 3.25973i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.07148 - 1.68876i) q^{28} +(1.28814 + 1.28814i) q^{29} +(0.360718 + 1.24183i) q^{30} +1.67865 q^{31} +(-5.58699 - 0.886325i) q^{32} -4.95657 q^{33} +(0.440308 + 1.51583i) q^{34} +(-0.646579 - 0.646579i) q^{35} +(-1.07148 - 1.68876i) q^{36} +(4.01360 - 4.01360i) q^{37} +(3.37106 - 6.13120i) q^{38} +2.63040i q^{39} +(-2.58124 + 0.162009i) q^{40} -8.34155i q^{41} +(1.23925 + 0.681365i) q^{42} +(-2.79353 + 2.79353i) q^{43} +(2.16345 - 9.67418i) q^{44} +(-0.646579 - 0.646579i) q^{45} +(-1.73978 + 0.505358i) q^{46} -2.27269 q^{47} +(3.76379 - 1.35420i) q^{48} -1.00000 q^{49} +(5.65487 - 1.64258i) q^{50} +(-0.789243 - 0.789243i) q^{51} +(-5.13399 - 1.14812i) q^{52} +(9.00612 - 9.00612i) q^{53} +(1.23925 + 0.681365i) q^{54} -4.53229i q^{55} +(-1.87079 + 2.12135i) q^{56} +4.94751i q^{57} +(1.24125 - 2.25756i) q^{58} +(-10.4403 + 10.4403i) q^{59} +(1.54421 - 0.979767i) q^{60} +(-6.58105 - 6.58105i) q^{61} +(-0.662204 - 2.27975i) q^{62} -1.00000 q^{63} +(1.00028 + 7.93722i) q^{64} -2.40524 q^{65} +(1.95529 + 6.73142i) q^{66} +(11.0941 + 11.0941i) q^{67} +(1.88493 - 1.19595i) q^{68} +(0.905845 - 0.905845i) q^{69} +(-0.623041 + 1.13317i) q^{70} -0.0956898i q^{71} +(-1.87079 + 2.12135i) q^{72} -7.55336i q^{73} +(-7.03410 - 3.86749i) q^{74} +(-2.94430 + 2.94430i) q^{75} +(-9.65649 - 2.15950i) q^{76} +(-3.50482 - 3.50482i) q^{77} +(3.57229 - 1.03765i) q^{78} +2.61962 q^{79} +(1.23828 + 3.44162i) q^{80} -1.00000 q^{81} +(-11.3285 + 3.29062i) q^{82} +(-2.75229 - 2.75229i) q^{83} +(0.436482 - 1.95179i) q^{84} +(0.721685 - 0.721685i) q^{85} +(4.89583 + 2.69183i) q^{86} +1.82171i q^{87} +(-13.9918 + 0.878178i) q^{88} -1.24439i q^{89} +(-0.623041 + 1.13317i) q^{90} +(-1.85997 + 1.85997i) q^{91} +(1.37263 + 2.16340i) q^{92} +(1.18699 + 1.18699i) q^{93} +(0.896542 + 3.08649i) q^{94} -4.52401 q^{95} +(-3.32387 - 4.57732i) q^{96} -8.68699 q^{97} +(0.394485 + 1.35808i) q^{98} +(-3.50482 - 3.50482i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q+O(q^{10}) \) 28 * q	\( 28 q - 4 q^{10} - 4 q^{11} - 8 q^{12} + 8 q^{15} + 4 q^{16} + 8 q^{19} - 28 q^{20} - 8 q^{22} - 16 q^{24} - 20 q^{26} + 4 q^{28} + 4 q^{29} + 8 q^{30} + 24 q^{33} + 12 q^{34} + 4 q^{36} + 4 q^{37} + 60 q^{38} - 56 q^{40} - 4 q^{42} + 20 q^{43} + 56 q^{44} - 44 q^{46} + 16 q^{48} - 28 q^{49} + 20 q^{50} - 8 q^{51} - 32 q^{52} + 20 q^{53} - 4 q^{54} - 12 q^{56} - 12 q^{58} - 12 q^{60} - 40 q^{61} - 60 q^{62} - 28 q^{63} + 60 q^{64} + 16 q^{65} + 24 q^{66} + 4 q^{67} - 108 q^{68} - 16 q^{69} - 4 q^{70} - 12 q^{72} + 28 q^{74} - 16 q^{75} - 8 q^{76} - 4 q^{77} + 12 q^{78} + 24 q^{79} - 72 q^{80} - 28 q^{81} + 36 q^{82} + 40 q^{83} + 48 q^{85} + 24 q^{86} + 4 q^{88} - 4 q^{90} + 52 q^{92} - 8 q^{94} + 40 q^{96} + 72 q^{97} - 4 q^{99}+O(q^{100}) \) 28 * q - 4 * q^10 - 4 * q^11 - 8 * q^12 + 8 * q^15 + 4 * q^16 + 8 * q^19 - 28 * q^20 - 8 * q^22 - 16 * q^24 - 20 * q^26 + 4 * q^28 + 4 * q^29 + 8 * q^30 + 24 * q^33 + 12 * q^34 + 4 * q^36 + 4 * q^37 + 60 * q^38 - 56 * q^40 - 4 * q^42 + 20 * q^43 + 56 * q^44 - 44 * q^46 + 16 * q^48 - 28 * q^49 + 20 * q^50 - 8 * q^51 - 32 * q^52 + 20 * q^53 - 4 * q^54 - 12 * q^56 - 12 * q^58 - 12 * q^60 - 40 * q^61 - 60 * q^62 - 28 * q^63 + 60 * q^64 + 16 * q^65 + 24 * q^66 + 4 * q^67 - 108 * q^68 - 16 * q^69 - 4 * q^70 - 12 * q^72 + 28 * q^74 - 16 * q^75 - 8 * q^76 - 4 * q^77 + 12 * q^78 + 24 * q^79 - 72 * q^80 - 28 * q^81 + 36 * q^82 + 40 * q^83 + 48 * q^85 + 24 * q^86 + 4 * q^88 - 4 * q^90 + 52 * q^92 - 8 * q^94 + 40 * q^96 + 72 * q^97 - 4 * q^99

Introduction

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