LMFDB - Embedded newform 273.2.bz.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(31,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("273.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bz (of order $12$, degree $4$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	273.31
Dual form			273.2.bz.b.229.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.263033 - 0.0704795i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.66783 - 0.962923i) q^{4} +(-0.650540 + 2.42785i) q^{5} +(-0.192554 - 0.192554i) q^{6} +(-2.34911 + 1.21724i) q^{7} +(0.755936 + 0.755936i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.263033 - 0.0704795i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.66783 - 0.962923i) q^{4} +(-0.650540 + 2.42785i) q^{5} +(-0.192554 - 0.192554i) q^{6} +(-2.34911 + 1.21724i) q^{7} +(0.755936 + 0.755936i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.342227 - 0.592755i) q^{10} +(-1.62478 + 0.435358i) q^{11} +(-0.962923 - 1.66783i) q^{12} +(-3.50774 - 0.834105i) q^{13} +(0.703685 - 0.154611i) q^{14} +(-1.77731 + 1.77731i) q^{15} +(1.78029 + 3.08355i) q^{16} +(-1.60806 + 2.78524i) q^{17} +(-0.0704795 - 0.263033i) q^{18} +(-1.01925 + 3.80388i) q^{19} +(3.42282 - 3.42282i) q^{20} +(-2.64301 - 0.120393i) q^{21} +0.458054 q^{22} +(4.67914 - 2.70150i) q^{23} +(0.276692 + 1.03263i) q^{24} +(-1.14111 - 0.658821i) q^{25} +(0.863866 + 0.466621i) q^{26} +1.00000i q^{27} +(5.09003 + 0.231859i) q^{28} +6.19984 q^{29} +(0.592755 - 0.342227i) q^{30} +(-8.71743 + 2.33583i) q^{31} +(-0.804331 - 3.00181i) q^{32} +(-1.62478 - 0.435358i) q^{33} +(0.619276 - 0.619276i) q^{34} +(-1.42709 - 6.49515i) q^{35} -1.92585i q^{36} +(0.882434 - 3.29329i) q^{37} +(0.536191 - 0.928711i) q^{38} +(-2.62074 - 2.47623i) q^{39} +(-2.32706 + 1.34353i) q^{40} +(0.762243 + 0.762243i) q^{41} +(0.686714 + 0.217946i) q^{42} +5.62140i q^{43} +(3.12907 + 0.838432i) q^{44} +(-2.42785 + 0.650540i) q^{45} +(-1.42117 + 0.380801i) q^{46} +(6.27707 + 1.68194i) q^{47} +3.56058i q^{48} +(4.03664 - 5.71887i) q^{49} +(0.253717 + 0.253717i) q^{50} +(-2.78524 + 1.60806i) q^{51} +(5.04715 + 4.76883i) q^{52} +(0.358264 - 0.620531i) q^{53} +(0.0704795 - 0.263033i) q^{54} -4.22793i q^{55} +(-2.69593 - 0.855621i) q^{56} +(-2.78463 + 2.78463i) q^{57} +(-1.63076 - 0.436962i) q^{58} +(-2.53194 - 9.44933i) q^{59} +(4.67566 - 1.25284i) q^{60} +(0.943810 - 0.544909i) q^{61} +2.45760 q^{62} +(-2.22872 - 1.42577i) q^{63} -6.27489i q^{64} +(4.30700 - 7.97365i) q^{65} +(0.396686 + 0.229027i) q^{66} +(0.569411 + 2.12507i) q^{67} +(5.36395 - 3.09688i) q^{68} +5.40300 q^{69} +(-0.0824036 + 1.80902i) q^{70} +(-6.04224 + 6.04224i) q^{71} +(-0.276692 + 1.03263i) q^{72} +(1.06732 + 3.98330i) q^{73} +(-0.464219 + 0.804051i) q^{74} +(-0.658821 - 1.14111i) q^{75} +(5.36278 - 5.36278i) q^{76} +(3.28684 - 3.00045i) q^{77} +(0.514819 + 0.836039i) q^{78} +(-3.96221 - 6.86275i) q^{79} +(-8.64453 + 2.31630i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.146773 - 0.254218i) q^{82} +(10.0477 + 10.0477i) q^{83} +(4.29217 + 2.74581i) q^{84} +(-5.71604 - 5.71604i) q^{85} +(0.396194 - 1.47862i) q^{86} +(5.36922 + 3.09992i) q^{87} +(-1.55733 - 0.899125i) q^{88} +(12.1468 + 3.25472i) q^{89} +0.684454 q^{90} +(9.25539 - 2.31037i) q^{91} -10.4053 q^{92} +(-8.71743 - 2.33583i) q^{93} +(-1.53254 - 0.884810i) q^{94} +(-8.57218 - 4.94915i) q^{95} +(0.804331 - 3.00181i) q^{96} +(4.84712 + 4.84712i) q^{97} +(-1.46484 + 1.21975i) q^{98} +(-1.18942 - 1.18942i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 + 18 * q^9	$ 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.263033	−	0.0704795i	−0.185993	−	0.0498366i	0.164620	−	0.986357i	$-0.447360\pi$
$2$	−0.263033	−	0.0704795i	−0.185993	−	0.0498366i	−0.350613	+	0.936520i	$0.614027\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.66783	−	0.962923i	−0.833916	−	0.481462i
$5$	−0.650540	+	2.42785i	−0.290930	+	1.08577i	0.653466	+	0.756956i	$0.273314\pi$
$5$	−0.650540	+	2.42785i	−0.290930	+	1.08577i	−0.944396	+	0.328810i	$0.893352\pi$
$6$	−0.192554	−	0.192554i	−0.0786097	−	0.0786097i
$7$	−2.34911	+	1.21724i	−0.887880	+	0.460074i
$7$	−2.34911	+	1.21724i	−0.887880	+	0.460074i
$8$	0.755936	+	0.755936i	0.267264	+	0.267264i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.342227	−	0.592755i	0.108222	−	0.187445i
$11$	−1.62478	+	0.435358i	−0.489889	+	0.131265i	−0.495303	−	0.868720i	$-0.664943\pi$
$11$	−1.62478	+	0.435358i	−0.489889	+	0.131265i	0.00541479	+	0.999985i	$0.498276\pi$
$12$	−0.962923	−	1.66783i	−0.277972	−	0.481462i
$13$	−3.50774	−	0.834105i	−0.972873	−	0.231339i
$13$	−3.50774	−	0.834105i	−0.972873	−	0.231339i
$14$	0.703685	−	0.154611i	0.188068	−	0.0413215i
$15$	−1.77731	+	1.77731i	−0.458899	+	0.458899i
$16$	1.78029	+	3.08355i	0.445072	+	0.770887i
$17$	−1.60806	+	2.78524i	−0.390012	+	0.675521i	−0.992451	−	0.122644i	$-0.960863\pi$
$17$	−1.60806	+	2.78524i	−0.390012	+	0.675521i	0.602438	+	0.798165i	$0.294196\pi$
$18$	−0.0704795	−	0.263033i	−0.0166122	−	0.0619975i
$19$	−1.01925	+	3.80388i	−0.233831	+	0.872670i	0.744841	+	0.667242i	$0.232525\pi$
$19$	−1.01925	+	3.80388i	−0.233831	+	0.872670i	−0.978672	+	0.205428i	$0.934141\pi$
$20$	3.42282	−	3.42282i	0.765366	−	0.765366i
$21$	−2.64301	−	0.120393i	−0.576752	−	0.0262719i
$22$	0.458054			0.0976574
$23$	4.67914	−	2.70150i	0.975667	−	0.563302i	0.0747079	−	0.997205i	$-0.476198\pi$
$23$	4.67914	−	2.70150i	0.975667	−	0.563302i	0.900959	+	0.433904i	$0.142864\pi$
$24$	0.276692	+	1.03263i	0.0564795	+	0.210784i
$25$	−1.14111	−	0.658821i	−0.228222	−	0.131764i
$26$	0.863866	+	0.466621i	0.169418	+	0.0915120i
$27$			1.00000i			0.192450i
$28$	5.09003	+	0.231859i	0.961926	+	0.0438172i
$29$	6.19984			1.15128			0.575641	−	0.817703i	$-0.304753\pi$
$29$	6.19984			1.15128			0.575641	+	0.817703i	$0.304753\pi$
$30$	0.592755	−	0.342227i	0.108222	−	0.0624818i
$31$	−8.71743	+	2.33583i	−1.56570	+	0.419527i	−0.934461	−	0.356065i	$-0.884118\pi$
$31$	−8.71743	+	2.33583i	−1.56570	+	0.419527i	−0.631235	+	0.775592i	$0.717452\pi$
$32$	−0.804331	−	3.00181i	−0.142187	−	0.530649i
$33$	−1.62478	−	0.435358i	−0.282837	−	0.0757860i
$34$	0.619276	−	0.619276i	0.106205	−	0.106205i
$35$	−1.42709	−	6.49515i	−0.241222	−	1.09788i
$36$		−	1.92585i		−	0.320974i
$37$	0.882434	−	3.29329i	0.145071	−	0.541414i	−0.854681	−	0.519154i	$-0.826247\pi$
$37$	0.882434	−	3.29329i	0.145071	−	0.541414i	0.999752	−	0.0222598i	$-0.00708611\pi$
$38$	0.536191	−	0.928711i	0.0869817	−	0.150657i
$39$	−2.62074	−	2.47623i	−0.419655	−	0.396514i
$40$	−2.32706	+	1.34353i	−0.367941	+	0.212431i
$41$	0.762243	+	0.762243i	0.119042	+	0.119042i	0.764118	−	0.645076i	$-0.223174\pi$
$41$	0.762243	+	0.762243i	0.119042	+	0.119042i	−0.645076	+	0.764118i	$0.723174\pi$
$42$	0.686714	+	0.217946i	0.105962	+	0.0336297i
$43$			5.62140i			0.857256i	0.903481	+	0.428628i	$0.141003\pi$
$43$			5.62140i			0.857256i	−0.903481	+	0.428628i	$0.858997\pi$
$44$	3.12907	+	0.838432i	0.471725	+	0.126398i
$45$	−2.42785	+	0.650540i	−0.361922	+	0.0969767i
$46$	−1.42117	+	0.380801i	−0.209540	+	0.0561460i
$47$	6.27707	+	1.68194i	0.915604	+	0.245335i	0.685706	−	0.727879i	$-0.259494\pi$
$47$	6.27707	+	1.68194i	0.915604	+	0.245335i	0.229899	+	0.973215i	$0.426160\pi$
$48$			3.56058i			0.513925i
$49$	4.03664	−	5.71887i	0.576664	−	0.816982i
$50$	0.253717	+	0.253717i	0.0358810	+	0.0358810i
$51$	−2.78524	+	1.60806i	−0.390012	+	0.225174i
$52$	5.04715	+	4.76883i	0.699914	+	0.661318i
$53$	0.358264	−	0.620531i	0.0492113	−	0.0852365i	−0.840370	−	0.542012i	$-0.817663\pi$
$53$	0.358264	−	0.620531i	0.0492113	−	0.0852365i	0.889582	+	0.456776i	$0.150996\pi$
$54$	0.0704795	−	0.263033i	0.00959105	−	0.0357943i
$55$		−	4.22793i		−	0.570093i
$56$	−2.69593	−	0.855621i	−0.360259	−	0.114337i
$57$	−2.78463	+	2.78463i	−0.368834	+	0.368834i
$58$	−1.63076	−	0.436962i	−0.214130	−	0.0573759i
$59$	−2.53194	−	9.44933i	−0.329631	−	1.23020i	−0.909574	−	0.415541i	$-0.863592\pi$
$59$	−2.53194	−	9.44933i	−0.329631	−	1.23020i	0.579944	−	0.814657i	$-0.303075\pi$
$60$	4.67566	−	1.25284i	0.603625	−	0.161741i
$61$	0.943810	−	0.544909i	0.120842	−	0.0697684i	−0.438360	−	0.898799i	$-0.644441\pi$
$61$	0.943810	−	0.544909i	0.120842	−	0.0697684i	0.559203	+	0.829031i	$0.311107\pi$
$62$	2.45760			0.312116
$63$	−2.22872	−	1.42577i	−0.280792	−	0.179630i
$64$		−	6.27489i		−	0.784361i
$65$	4.30700	−	7.97365i	0.534218	−	0.989009i
$66$	0.396686	+	0.229027i	0.0488287	+	0.0281913i
$67$	0.569411	+	2.12507i	0.0695646	+	0.259619i	0.991946	−	0.126662i	$-0.0404263\pi$
$67$	0.569411	+	2.12507i	0.0695646	+	0.259619i	−0.922381	+	0.386281i	$0.873760\pi$
$68$	5.36395	−	3.09688i	0.650475	−	0.375552i
$69$	5.40300			0.650445
$70$	−0.0824036	+	1.80902i	−0.00984911	+	0.216219i
$71$	−6.04224	+	6.04224i	−0.717082	+	0.717082i	−0.968007	−	0.250925i	$-0.919265\pi$
$71$	−6.04224	+	6.04224i	−0.717082	+	0.717082i	0.250925	+	0.968007i	$0.419265\pi$
$72$	−0.276692	+	1.03263i	−0.0326084	+	0.121696i
$73$	1.06732	+	3.98330i	0.124921	+	0.466210i	0.999837	−	0.0180641i	$-0.00575030\pi$
$73$	1.06732	+	3.98330i	0.124921	+	0.466210i	−0.874916	+	0.484274i	$0.839084\pi$
$74$	−0.464219	+	0.804051i	−0.0539644	+	0.0934690i
$75$	−0.658821	−	1.14111i	−0.0760741	−	0.131764i
$76$	5.36278	−	5.36278i	0.615153	−	0.615153i
$77$	3.28684	−	3.00045i	0.374571	−	0.341933i
$78$	0.514819	+	0.836039i	0.0582918	+	0.0946628i
$79$	−3.96221	−	6.86275i	−0.445784	−	0.772120i	0.552323	−	0.833630i	$-0.313742\pi$
$79$	−3.96221	−	6.86275i	−0.445784	−	0.772120i	−0.998106	+	0.0615104i	$0.980408\pi$
$80$	−8.64453	+	2.31630i	−0.966488	+	0.258970i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.146773	−	0.254218i	−0.0162083	−	0.0280736i
$83$	10.0477	+	10.0477i	1.10288	+	1.10288i	0.994061	+	0.108822i	$0.0347080\pi$
$83$	10.0477	+	10.0477i	1.10288	+	1.10288i	0.108822	+	0.994061i	$0.465292\pi$
$84$	4.29217	+	2.74581i	0.468314	+	0.299593i
$85$	−5.71604	−	5.71604i	−0.619991	−	0.619991i
$86$	0.396194	−	1.47862i	0.0427227	−	0.159443i
$87$	5.36922	+	3.09992i	0.575641	+	0.332346i
$88$	−1.55733	−	0.899125i	−0.166012	−	0.0958470i
$89$	12.1468	+	3.25472i	1.28756	+	0.344999i	0.836731	−	0.547613i	$-0.184464\pi$
$89$	12.1468	+	3.25472i	1.28756	+	0.344999i	0.450824	+	0.892613i	$0.351130\pi$
$90$	0.684454			0.0721478
$91$	9.25539	−	2.31037i	0.970228	−	0.242192i
$92$	−10.4053			−1.08483
$93$	−8.71743	−	2.33583i	−0.903955	−	0.242214i
$94$	−1.53254	−	0.884810i	−0.158069	−	0.0912611i
$95$	−8.57218	−	4.94915i	−0.879487	−	0.507772i
$96$	0.804331	−	3.00181i	0.0820917	−	0.306370i
$97$	4.84712	+	4.84712i	0.492151	+	0.492151i	0.908983	−	0.416833i	$-0.136860\pi$
$97$	4.84712	+	4.84712i	0.492151	+	0.492151i	−0.416833	+	0.908983i	$0.636860\pi$
$98$	−1.46484	+	1.21975i	−0.147971	+	0.123214i
$99$	−1.18942	−	1.18942i	−0.119541	−	0.119541i
$100$	1.26879	+	2.19761i	0.126879	+	0.219761i
$101$	−7.44718	+	12.8989i	−0.741022	+	1.28349i	0.211009	+	0.977484i	$0.432325\pi$
$101$	−7.44718	+	12.8989i	−0.741022	+	1.28349i	−0.952031	+	0.306003i	$0.901008\pi$
$102$	0.845947	−	0.226671i	0.0837612	−	0.0224438i
$103$	−8.25935	−	14.3056i	−0.813818	−	1.40957i	−0.910174	−	0.414227i	$-0.864052\pi$
$103$	−8.25935	−	14.3056i	−0.813818	−	1.40957i	0.0963555	−	0.995347i	$-0.469281\pi$
$104$	−2.02110	−	3.28216i	−0.198185	−	0.321842i
$105$	2.01168	−	6.33850i	0.196320	−	0.618575i
$106$	−0.137970	+	0.137970i	−0.0134008	+	0.0134008i
$107$	5.10563	+	8.84320i	0.493580	+	0.854905i	0.999973	−	0.00739788i	$-0.00235484\pi$
$107$	5.10563	+	8.84320i	0.493580	+	0.854905i	−0.506393	+	0.862303i	$0.669022\pi$
$108$	0.962923	−	1.66783i	0.0926573	−	0.160487i
$109$	−0.890142	−	3.32206i	−0.0852601	−	0.318195i	0.910103	−	0.414382i	$-0.136002\pi$
$109$	−0.890142	−	3.32206i	−0.0852601	−	0.318195i	−0.995363	+	0.0961865i	$0.969335\pi$
$110$	−0.297982	+	1.11208i	−0.0284115	+	0.106033i
$111$	2.41086	−	2.41086i	0.228828	−	0.228828i
$112$	−7.93552	−	5.07656i	−0.749836	−	0.479690i
$113$	11.1655			1.05036			0.525179	−	0.850992i	$-0.323998\pi$
$113$	11.1655			1.05036			0.525179	+	0.850992i	$0.323998\pi$
$114$	0.928711	−	0.536191i	0.0869817	−	0.0502189i
$115$	3.51487	+	13.1177i	0.327763	+	1.22323i
$116$	−10.3403	−	5.96997i	−0.960072	−	0.554298i
$117$	−1.03152	−	3.45485i	−0.0953637	−	0.319401i
$118$			2.66394i			0.245235i
$119$	0.387199	−	8.50025i	0.0354945	−	0.779216i
$120$	−2.68706			−0.245294
$121$	−7.07592	+	4.08528i	−0.643265	+	0.371389i
$122$	−0.286658	+	0.0768099i	−0.0259528	+	0.00695404i
$123$	0.279000	+	1.04124i	0.0251566	+	0.0938857i
$124$	16.7884	+	4.49844i	1.50764	+	0.403972i
$125$	−6.54468	+	6.54468i	−0.585374	+	0.585374i
$126$	0.485739	+	0.532104i	0.0432731	+	0.0474036i
$127$			7.71529i			0.684621i	0.939587	+	0.342311i	$0.111210\pi$
$127$			7.71529i			0.684621i	−0.939587	+	0.342311i	$0.888790\pi$
$128$	−2.05091	+	7.65411i	−0.181277	+	0.676535i
$129$	−2.81070	+	4.86828i	−0.247468	+	0.428628i
$130$	−1.69486	+	1.79378i	−0.148649	+	0.157325i
$131$	−13.7082	+	7.91445i	−1.19769	+	0.691489i	−0.960040	−	0.279862i	$-0.909711\pi$
$131$	−13.7082	+	7.91445i	−1.19769	+	0.691489i	−0.237653	+	0.971350i	$0.576378\pi$
$132$	2.29064	+	2.29064i	0.199374	+	0.199374i
$133$	−2.23592	−	10.1764i	−0.193879	−	0.882406i
$134$		−	0.599096i		−	0.0517540i
$135$	−2.42785	−	0.650540i	−0.208956	−	0.0559895i
$136$	−3.32106	+	0.889875i	−0.284778	+	0.0763061i
$137$	−19.0928	+	5.11589i	−1.63120	+	0.437080i	−0.954266	−	0.298960i	$-0.903360\pi$
$137$	−19.0928	+	5.11589i	−1.63120	+	0.437080i	−0.676938	+	0.736040i	$0.736694\pi$
$138$	−1.42117	−	0.380801i	−0.120978	−	0.0324159i
$139$			8.90424i			0.755248i	0.925959	+	0.377624i	$0.123259\pi$
$139$			8.90424i			0.755248i	−0.925959	+	0.377624i	$0.876741\pi$
$140$	−3.87418	+	12.2070i	−0.327428	+	1.03168i
$141$	4.59513	+	4.59513i	0.386980	+	0.386980i
$142$	2.01516	−	1.16346i	0.169109	−	0.0976350i
$143$	6.06243	−	0.171889i	0.506966	−	0.0143741i
$144$	−1.78029	+	3.08355i	−0.148357	+	0.256962i
$145$	−4.03324	+	15.0523i	−0.334942	+	1.25002i
$146$		−	1.12297i		−	0.0929373i
$147$	6.35527	−	2.93437i	0.524174	−	0.242022i
$148$	−4.64294	+	4.64294i	−0.381647	+	0.381647i
$149$	9.30422	+	2.49306i	0.762232	+	0.204239i	0.618937	−	0.785441i	$-0.287564\pi$
$149$	9.30422	+	2.49306i	0.762232	+	0.204239i	0.143295	+	0.989680i	$0.454230\pi$
$150$	0.0928668	+	0.346584i	0.00758254	+	0.0282984i
$151$	4.67041	−	1.25143i	0.380072	−	0.101840i	−0.0637244	−	0.997968i	$-0.520298\pi$
$151$	4.67041	−	1.25143i	0.380072	−	0.101840i	0.443797	+	0.896127i	$0.353631\pi$
$152$	−3.64598	+	2.10501i	−0.295728	+	0.170738i
$153$	−3.21612			−0.260008
$154$	−1.07602	+	0.557562i	−0.0867081	+	0.0449297i
$155$		−	22.6841i		−	1.82203i
$156$	1.98654	+	6.65351i	0.159051	+	0.532707i
$157$	−2.83742	−	1.63818i	−0.226451	−	0.130741i	0.382483	−	0.923963i	$-0.375069\pi$
$157$	−2.83742	−	1.63818i	−0.226451	−	0.130741i	−0.608934	+	0.793221i	$0.708402\pi$
$158$	0.558510	+	2.08439i	0.0444326	+	0.165825i
$159$	0.620531	−	0.358264i	0.0492113	−	0.0284122i
$160$	7.81117			0.617527
$161$	−7.70343	+	12.0418i	−0.607115	+	0.949024i
$162$	0.192554	−	0.192554i	0.0151284	−	0.0151284i
$163$	−4.18891	+	15.6332i	−0.328101	+	1.22449i	0.583057	+	0.812432i	$0.301857\pi$
$163$	−4.18891	+	15.6332i	−0.328101	+	1.22449i	−0.911158	+	0.412058i	$0.864810\pi$
$164$	−0.537311	−	2.00527i	−0.0419570	−	0.156586i
$165$	2.11396	−	3.66149i	0.164572	−	0.285047i
$166$	−1.93473	−	3.35105i	−0.150164	−	0.260092i
$167$	−9.74251	+	9.74251i	−0.753898	+	0.753898i	−0.975204	−	0.221306i	$-0.928968\pi$
$167$	−9.74251	+	9.74251i	−0.753898	+	0.753898i	0.221306	+	0.975204i	$0.428968\pi$
$168$	−1.90694	−	2.08896i	−0.147123	−	0.161167i
$169$	11.6085	+	5.85165i	0.892965	+	0.450127i
$170$	1.10064	+	1.90637i	0.0844156	+	0.146212i
$171$	−3.80388	+	1.01925i	−0.290890	+	0.0779437i
$172$	5.41298	−	9.37555i	0.412736	−	0.714879i
$173$	9.39739	+	16.2768i	0.714470	+	1.23750i	0.963163	+	0.268917i	$0.0866656\pi$
$173$	9.39739	+	16.2768i	0.714470	+	1.23750i	−0.248693	+	0.968582i	$0.580001\pi$
$174$	−1.19380	−	1.19380i	−0.0905019	−	0.0905019i
$175$	3.48254	+	0.158635i	0.263255	+	0.0119917i
$176$	−4.23502	−	4.23502i	−0.319226	−	0.319226i
$177$	2.53194	−	9.44933i	0.190312	−	0.710255i
$178$	−2.96561	−	1.71220i	−0.222282	−	0.128335i
$179$	−16.1863	−	9.34515i	−1.20982	−	0.698489i	−0.247099	−	0.968990i	$-0.579477\pi$
$179$	−16.1863	−	9.34515i	−1.20982	−	0.698489i	−0.962720	+	0.270501i	$0.912811\pi$
$180$	4.67566	+	1.25284i	0.348503	+	0.0933811i
$181$	13.8297			1.02796			0.513978	−	0.857803i	$-0.328171\pi$
$181$	13.8297			1.02796			0.513978	+	0.857803i	$0.328171\pi$
$182$	−2.59731	−	0.0446117i	−0.192525	−	0.00330684i
$183$	1.08982			0.0805617
$184$	5.57929	+	1.49497i	0.411311	+	0.110210i
$185$	7.42155	+	4.28483i	0.545643	+	0.315027i
$186$	2.12834	+	1.22880i	0.156058	+	0.0901000i
$187$	1.40016	−	5.22548i	0.102390	−	0.382125i
$188$	−8.84952	−	8.84952i	−0.645417	−	0.645417i
$189$	−1.21724	−	2.34911i	−0.0885413	−	0.170873i
$190$	1.90595	+	1.90595i	0.138272	+	0.138272i
$191$	−12.2050	−	21.1397i	−0.883126	−	1.52962i	−0.847847	−	0.530241i	$-0.822102\pi$
$191$	−12.2050	−	21.1397i	−0.883126	−	1.52962i	−0.0352784	−	0.999378i	$-0.511232\pi$
$192$	3.13744	−	5.43421i	0.226426	−	0.392181i
$193$	14.3910	−	3.85605i	1.03588	−	0.277565i	0.299478	−	0.954103i	$-0.403188\pi$
$193$	14.3910	−	3.85605i	1.03588	−	0.277565i	0.736407	+	0.676539i	$0.236521\pi$
$194$	−0.933331	−	1.61658i	−0.0670093	−	0.116063i
$195$	7.71680	−	4.75188i	0.552611	−	0.340289i
$196$	−12.2393	+	5.65114i	−0.874234	+	0.403653i
$197$	16.8258	−	16.8258i	1.19879	−	1.19879i	0.224256	−	0.974530i	$-0.428005\pi$
$197$	16.8258	−	16.8258i	1.19879	−	1.19879i	0.974530	−	0.224256i	$-0.0719951\pi$
$198$	0.229027	+	0.396686i	0.0162762	+	0.0281913i
$199$	6.38259	−	11.0550i	0.452450	−	0.783666i	−0.546088	−	0.837728i	$-0.683883\pi$
$199$	6.38259	−	11.0550i	0.452450	−	0.783666i	0.998538	+	0.0540617i	$0.0172168\pi$
$200$	−0.364581	−	1.36063i	−0.0257798	−	0.0962113i
$201$	−0.569411	+	2.12507i	−0.0401632	+	0.149891i
$202$	2.86796	−	2.86796i	0.201789	−	0.201789i
$203$	−14.5641	+	7.54670i	−1.02220	+	0.529675i
$204$	6.19376			0.433650
$205$	−2.34648	+	1.35474i	−0.163885	+	0.0946191i
$206$	1.16423	+	4.34497i	0.0811158	+	0.302728i
$207$	4.67914	+	2.70150i	0.325222	+	0.187767i
$208$	−3.67279	−	12.3012i	−0.254662	−	0.852938i
$209$		−	6.62419i		−	0.458205i
$210$	−0.975873	+	1.52545i	−0.0673417	+	0.105266i
$211$	−21.3715			−1.47127			−0.735637	−	0.677376i	$-0.763117\pi$
$211$	−21.3715			−1.47127			−0.735637	+	0.677376i	$0.763117\pi$
$212$	−1.19505	+	0.689961i	−0.0820762	+	0.0473867i
$213$	−8.25385	+	2.21161i	−0.565545	+	0.151537i
$214$	−0.719684	−	2.68590i	−0.0491966	−	0.183604i
$215$	−13.6479	−	3.65694i	−0.930779	−	0.249402i
$216$	−0.755936	+	0.755936i	−0.0514349	+	0.0514349i
$217$	17.6349	−	16.0983i	1.19714	−	1.09283i
$218$			0.936548i			0.0634310i
$219$	−1.06732	+	3.98330i	−0.0721230	+	0.269167i
$220$	−4.07117	+	7.05147i	−0.274478	+	0.475410i
$221$	7.96385	−	8.42863i	0.535707	−	0.566971i
$222$	−0.804051	+	0.464219i	−0.0539644	+	0.0311563i
$223$	−13.5431	−	13.5431i	−0.906913	−	0.906913i	0.0891091	−	0.996022i	$-0.471598\pi$
$223$	−13.5431	−	13.5431i	−0.906913	−	0.906913i	−0.996022	+	0.0891091i	$0.971598\pi$
$224$	5.54339	+	6.07251i	0.370383	+	0.405737i
$225$		−	1.31764i		−	0.0878428i
$226$	−2.93689	−	0.786937i	−0.195359	−	0.0523463i
$227$	24.6402	−	6.60231i	1.63543	−	0.438211i	0.679945	−	0.733263i	$-0.262004\pi$
$227$	24.6402	−	6.60231i	1.63543	−	0.438211i	0.955481	+	0.295052i	$0.0953371\pi$
$228$	7.32569	−	1.96291i	0.485156	−	0.129997i
$229$	−16.2437	−	4.35250i	−1.07342	−	0.287621i	−0.321520	−	0.946903i	$-0.604194\pi$
$229$	−16.2437	−	4.35250i	−1.07342	−	0.287621i	−0.751896	+	0.659282i	$0.770861\pi$
$230$		−	3.69811i		−	0.243846i
$231$	4.34672	−	0.955043i	0.285993	−	0.0628372i
$232$	4.68668	+	4.68668i	0.307696	+	0.307696i
$233$	23.3194	−	13.4634i	1.52770	−	0.882020i	0.528245	−	0.849092i	$-0.322850\pi$
$233$	23.3194	−	13.4634i	1.52770	−	0.882020i	0.999458	−	0.0329275i	$-0.0104830\pi$
$234$	0.0278270	+	0.981440i	0.00181911	+	0.0641588i
$235$	−8.16696	+	14.1456i	−0.532754	+	0.922757i
$236$	−4.87613	+	18.1980i	−0.317409	+	1.18459i
$237$		−	7.92442i		−	0.514747i
$238$	−0.700940	+	2.20856i	−0.0454352	+	0.143160i
$239$	1.13268	−	1.13268i	0.0732671	−	0.0732671i	−0.669524	−	0.742791i	$-0.733502\pi$
$239$	1.13268	−	1.13268i	0.0732671	−	0.0732671i	0.742791	+	0.669524i	$0.233502\pi$
$240$	−8.64453	−	2.31630i	−0.558002	−	0.149516i
$241$	−2.69094	−	10.0427i	−0.173339	−	0.646910i	−0.996829	−	0.0795784i	$-0.974643\pi$
$241$	−2.69094	−	10.0427i	−0.173339	−	0.646910i	0.823490	−	0.567331i	$-0.192024\pi$
$242$	2.14913	−	0.575858i	0.138151	−	0.0370175i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−2.09882			−0.134363
$245$	11.2585	+	13.5207i	0.719282	+	0.863806i
$246$		−	0.293545i		−	0.0187158i
$247$	6.74809	−	12.4929i	0.429371	−	0.794903i
$248$	−8.35555	−	4.82408i	−0.530578	−	0.306329i
$249$	3.67773	+	13.7255i	0.233067	+	0.869817i
$250$	2.18273	−	1.26020i	0.138048	−	0.0797022i
$251$	9.75662			0.615833			0.307916	−	0.951413i	$-0.400368\pi$
$251$	9.75662			0.615833			0.307916	+	0.951413i	$0.400368\pi$
$252$	2.34422	+	4.52403i	0.147672	+	0.284987i
$253$	−6.42643	+	6.42643i	−0.404026	+	0.404026i
$254$	0.543770	−	2.02938i	0.0341192	−	0.127334i
$255$	−2.09222	−	7.80825i	−0.131020	−	0.488972i
$256$	−5.19597	+	8.99969i	−0.324748	+	0.562480i
$257$	9.84031	+	17.0439i	0.613822	+	1.06317i	0.990590	+	0.136863i	$0.0437019\pi$
$257$	9.84031	+	17.0439i	0.613822	+	1.06317i	−0.376768	+	0.926307i	$0.622965\pi$
$258$	1.08242	−	1.08242i	0.0673886	−	0.0673886i
$259$	1.93579	+	8.81044i	0.120284	+	0.547454i
$260$	−14.8614	+	9.15139i	−0.921663	+	0.567545i
$261$	3.09992	+	5.36922i	0.191880	+	0.332346i
$262$	4.16353	−	1.11561i	0.257223	−	0.0689228i
$263$	2.30989	−	4.00084i	0.142434	−	0.246703i	−0.785979	−	0.618253i	$-0.787841\pi$
$263$	2.30989	−	4.00084i	0.142434	−	0.246703i	0.928413	+	0.371551i	$0.121174\pi$
$264$	−0.899125	−	1.55733i	−0.0553373	−	0.0958470i
$265$	1.27349	+	1.27349i	0.0782299	+	0.0782299i
$266$	−0.129108	+	2.83432i	−0.00791609	+	0.173783i
$267$	8.89206	+	8.89206i	0.544185	+	0.544185i
$268$	1.09660	−	4.09256i	0.0669854	−	0.249993i
$269$	−3.63092	−	2.09631i	−0.221381	−	0.127814i	0.385209	−	0.922830i	$-0.374129\pi$
$269$	−3.63092	−	2.09631i	−0.221381	−	0.127814i	−0.606590	+	0.795015i	$0.707463\pi$
$270$	0.592755	+	0.342227i	0.0360739	+	0.0208273i
$271$	5.79316	+	1.55227i	0.351909	+	0.0942938i	0.430443	−	0.902618i	$-0.358357\pi$
$271$	5.79316	+	1.55227i	0.351909	+	0.0942938i	−0.0785340	+	0.996911i	$0.525024\pi$
$272$	−11.4513			−0.694334
$273$	9.17058	+	2.62686i	0.555029	+	0.158985i
$274$	5.38259			0.325174
$275$	2.14087	+	0.573645i	0.129100	+	0.0345921i
$276$	−9.01129	−	5.20267i	−0.542416	−	0.313164i
$277$	15.0666	+	8.69873i	0.905266	+	0.522656i	0.878905	−	0.476997i	$-0.158275\pi$
$277$	15.0666	+	8.69873i	0.905266	+	0.522656i	0.0263613	+	0.999652i	$0.491608\pi$
$278$	0.627567	−	2.34211i	0.0376389	−	0.140470i
$279$	−6.38160	−	6.38160i	−0.382056	−	0.382056i
$280$	3.83113	−	5.98870i	0.228954	−	0.357893i
$281$	10.4663	+	10.4663i	0.624370	+	0.624370i	0.946646	−	0.322276i	$-0.104448\pi$
$281$	10.4663	+	10.4663i	0.624370	+	0.624370i	−0.322276	+	0.946646i	$0.604448\pi$
$282$	−0.884810	−	1.53254i	−0.0526896	−	0.0912611i
$283$	11.8653	−	20.5512i	0.705316	−	1.22164i	−0.261261	−	0.965268i	$-0.584138\pi$
$283$	11.8653	−	20.5512i	0.705316	−	1.22164i	0.966577	−	0.256375i	$-0.0825283\pi$
$284$	15.8956	−	4.25923i	0.943233	−	0.252739i
$285$	−4.94915	−	8.57218i	−0.293162	−	0.507772i
$286$	−1.60674	−	0.382065i	−0.0950083	−	0.0225920i
$287$	−2.71843	−	0.862759i	−0.160464	−	0.0509271i
$288$	2.19747	−	2.19747i	0.129487	−	0.129487i
$289$	3.32828	+	5.76474i	0.195781	+	0.339103i
$290$	2.12175	−	3.67498i	0.124594	−	0.215802i
$291$	1.77417	+	6.62129i	0.104004	+	0.388147i
$292$	2.05550	−	7.67123i	0.120289	−	0.448925i
$293$	2.84344	−	2.84344i	0.166116	−	0.166116i	−0.619154	−	0.785270i	$-0.712524\pi$
$293$	2.84344	−	2.84344i	0.166116	−	0.166116i	0.785270	+	0.619154i	$0.212524\pi$
$294$	−1.87846	+	0.323919i	−0.109554	+	0.0188913i
$295$	24.5887			1.43161
$296$	3.15658	−	1.82245i	0.183473	−	0.105928i
$297$	−0.435358	−	1.62478i	−0.0252620	−	0.0942791i
$298$	−2.27161	−	1.31151i	−0.131591	−	0.0759740i
$299$	−18.6665	+	5.57328i	−1.07951	+	0.322311i
$300$			2.53758i			0.146507i
$301$	−6.84261	−	13.2053i	−0.394401	−	0.761141i
$302$	−1.31667			−0.0757660
$303$	−12.8989	+	7.44718i	−0.741022	+	0.427829i
$304$	−13.5440	+	3.62911i	−0.776802	+	0.208143i
$305$	0.708970	+	2.64591i	0.0405955	+	0.151504i
$306$	0.845947	+	0.226671i	0.0483596	+	0.0129579i
$307$	2.25090	−	2.25090i	0.128466	−	0.128466i	−0.639951	−	0.768416i	$-0.721045\pi$
$307$	2.25090	−	2.25090i	0.128466	−	0.128466i	0.768416	+	0.639951i	$0.221045\pi$
$308$	−8.37111	+	1.83927i	−0.476988	+	0.104802i
$309$		−	16.5187i		−	0.939716i
$310$	−1.59877	+	5.96668i	−0.0908038	+	0.338885i
$311$	−8.11431	+	14.0544i	−0.460120	+	0.796951i	−0.998966	−	0.0454526i	$-0.985527\pi$
$311$	−8.11431	+	14.0544i	−0.460120	+	0.796951i	0.538846	+	0.842404i	$0.318860\pi$
$312$	−0.109244	−	3.85298i	−0.00618475	−	0.218132i
$313$	10.2909	−	5.94143i	0.581673	−	0.335829i	−0.180125	−	0.983644i	$-0.557650\pi$
$313$	10.2909	−	5.94143i	0.581673	−	0.335829i	0.761798	+	0.647814i	$0.224317\pi$
$314$	0.630877	+	0.630877i	0.0356024	+	0.0356024i
$315$	4.91142	−	4.48347i	0.276727	−	0.252615i
$316$			15.2612i			0.858511i
$317$	−8.83796	−	2.36812i	−0.496389	−	0.133007i	0.00193457	−	0.999998i	$-0.499384\pi$
$317$	−8.83796	−	2.36812i	−0.496389	−	0.133007i	−0.498324	+	0.866991i	$0.666051\pi$
$318$	−0.188471	+	0.0505005i	−0.0105689	+	0.00283193i
$319$	−10.0734	+	2.69915i	−0.563999	+	0.151123i
$320$	15.2345	+	4.08206i	0.851633	+	0.228194i
$321$			10.2113i			0.569937i
$322$	2.87496	−	2.62445i	0.160215	−	0.146255i
$323$	−8.95572	−	8.95572i	−0.498310	−	0.498310i
$324$	1.66783	−	0.962923i	0.0926573	−	0.0534957i
$325$	3.45320	+	3.26278i	0.191549	+	0.180987i
$326$	2.20365	−	3.81683i	0.122049	−	0.211395i
$327$	0.890142	−	3.32206i	0.0492250	−	0.183710i
$328$			1.15241i			0.0636314i
$329$	−16.7929	+	3.68966i	−0.925820	+	0.203417i
$330$	−0.814103	+	0.814103i	−0.0448149	+	0.0448149i
$331$	−17.4501	−	4.67575i	−0.959146	−	0.257002i	−0.254907	−	0.966966i	$-0.582045\pi$
$331$	−17.4501	−	4.67575i	−0.959146	−	0.257002i	−0.704239	+	0.709963i	$0.748712\pi$
$332$	−7.08274	−	26.4332i	−0.388716	−	1.45071i
$333$	3.29329	−	0.882434i	0.180471	−	0.0483571i
$334$	3.24925	−	1.87596i	0.177791	−	0.102648i
$335$	−5.52977			−0.302124
$336$	−4.33408	−	8.36419i	−0.236444	−	0.456304i
$337$		−	28.5273i		−	1.55398i	−0.629514	−	0.776989i	$-0.716746\pi$
$337$		−	28.5273i		−	1.55398i	0.629514	−	0.776989i	$-0.283254\pi$
$338$	−2.64101	−	2.35734i	−0.143652	−	0.128223i
$339$	9.66958	+	5.58273i	0.525179	+	0.303212i
$340$	4.02929	+	15.0375i	0.218519	+	0.815523i
$341$	13.1469	−	7.59039i	0.711947	−	0.411043i
$342$	1.07238			0.0579878
$343$	−2.52128	+	18.3478i	−0.136136	+	0.990690i
$344$	−4.24942	+	4.24942i	−0.229113	+	0.229113i
$345$	−3.51487	+	13.1177i	−0.189234	+	0.706231i
$346$	−1.32465	−	4.94365i	−0.0712135	−	0.265772i
$347$	−5.60560	+	9.70918i	−0.300924	+	0.521216i	−0.976346	−	0.216216i	$-0.930629\pi$
$347$	−5.60560	+	9.70918i	−0.300924	+	0.521216i	0.675421	+	0.737432i	$0.263962\pi$
$348$	−5.96997	−	10.3403i	−0.320024	−	0.554298i
$349$	−11.0732	+	11.0732i	−0.592736	+	0.592736i	−0.938369	−	0.345634i	$-0.887664\pi$
$349$	−11.0732	+	11.0732i	−0.592736	+	0.592736i	0.345634	+	0.938369i	$0.387664\pi$
$350$	−0.904844	−	0.287174i	−0.0483659	−	0.0153501i
$351$	0.834105	−	3.50774i	0.0445212	−	0.187230i
$352$	2.61372	+	4.52709i	0.139312	+	0.241295i
$353$	28.0796	−	7.52390i	1.49453	−	0.400457i	0.583263	−	0.812283i	$-0.301776\pi$
$353$	28.0796	−	7.52390i	1.49453	−	0.400457i	0.911262	+	0.411827i	$0.135109\pi$
$354$	−1.33197	+	2.30704i	−0.0707933	+	0.122618i
$355$	−10.7389	−	18.6003i	−0.569962	−	0.987204i
$356$	−17.1247	−	17.1247i	−0.907609	−	0.907609i
$357$	4.58545	−	7.16783i	0.242688	−	0.379362i
$358$	3.59888	+	3.59888i	0.190207	+	0.190207i
$359$	1.32102	−	4.93013i	0.0697210	−	0.260202i	−0.922264	−	0.386562i	$-0.873663\pi$
$359$	1.32102	−	4.93013i	0.0697210	−	0.260202i	0.991985	+	0.126359i	$0.0403293\pi$
$360$	−2.32706	−	1.34353i	−0.122647	−	0.0708103i
$361$	3.02384	+	1.74582i	0.159150	+	0.0918850i
$362$	−3.63768	−	0.974714i	−0.191192	−	0.0512298i
$363$	−8.17057			−0.428843
$364$	−17.6611	−	5.05892i	−0.925695	−	0.265159i
$365$	−10.3652			−0.542539
$366$	−0.286658	−	0.0768099i	−0.0149839	−	0.00401492i
$367$	14.6249	+	8.44369i	0.763414	+	0.440757i	0.830520	−	0.556989i	$-0.188043\pi$
$367$	14.6249	+	8.44369i	0.763414	+	0.440757i	−0.0671064	+	0.997746i	$0.521377\pi$
$368$	16.6604	+	9.61890i	0.868484	+	0.501420i
$369$	−0.279000	+	1.04124i	−0.0145242	+	0.0542049i
$370$	−1.65012	−	1.65012i	−0.0857856	−	0.0857856i
$371$	−0.0862651	+	1.89379i	−0.00447866	+	0.0983207i
$372$	12.2900	+	12.2900i	0.637206	+	0.637206i
$373$	−3.45010	−	5.97576i	−0.178640	−	0.309413i	0.762775	−	0.646664i	$-0.223836\pi$
$373$	−3.45010	−	5.97576i	−0.178640	−	0.309413i	−0.941415	+	0.337251i	$0.890503\pi$
$374$	−0.736579	+	1.27579i	−0.0380876	+	0.0659696i
$375$	−8.94020	+	2.39552i	−0.461670	+	0.123704i
$376$	3.47363	+	6.01650i	0.179139	+	0.310277i
$377$	−21.7474	−	5.17131i	−1.12005	−	0.266336i
$378$	0.154611	+	0.703685i	0.00795232	+	0.0361936i
$379$	−23.9464	+	23.9464i	−1.23005	+	1.23005i	−0.266101	+	0.963945i	$0.585736\pi$
$379$	−23.9464	+	23.9464i	−1.23005	+	1.23005i	−0.963945	+	0.266101i	$0.914264\pi$
$380$	9.53130	+	16.5087i	0.488945	+	0.846878i
$381$	−3.85765	+	6.68164i	−0.197633	+	0.342311i
$382$	1.72041	+	6.42066i	0.0880239	+	0.328510i
$383$	1.44049	−	5.37600i	0.0736058	−	0.274701i	−0.919308	−	0.393539i	$-0.871251\pi$
$383$	1.44049	−	5.37600i	0.0736058	−	0.274701i	0.992914	+	0.118839i	$0.0379172\pi$
$384$	−5.60320	+	5.60320i	−0.285937	+	0.285937i
$385$	5.14641	+	9.93187i	0.262285	+	0.506175i
$386$	−4.05708			−0.206500
$387$	−4.86828	+	2.81070i	−0.247468	+	0.142876i
$388$	−3.41678	−	12.7516i	−0.173461	−	0.647364i
$389$	27.8629	+	16.0866i	1.41270	+	0.815625i	0.995642	−	0.0932534i	$-0.0297267\pi$
$389$	27.8629	+	16.0866i	1.41270	+	0.815625i	0.417061	+	0.908878i	$0.363060\pi$
$390$	−2.36468	+	0.706026i	−0.119740	+	0.0357510i
$391$			17.3767i			0.878778i
$392$	7.37455	−	1.27166i	0.372471	−	0.0642283i
$393$	−15.8289			−0.798462
$394$	−5.61161	+	3.23986i	−0.282709	+	0.163222i
$395$	19.2393	−	5.15515i	0.968034	−	0.259384i
$396$	0.838432	+	3.12907i	0.0421328	+	0.157242i
$397$	−9.05886	−	2.42732i	−0.454651	−	0.121823i	0.0242236	−	0.999707i	$-0.492289\pi$
$397$	−9.05886	−	2.42732i	−0.454651	−	0.121823i	−0.478875	+	0.877883i	$0.658955\pi$
$398$	−2.45798	+	2.45798i	−0.123208	+	0.123208i
$399$	3.15184	−	9.93099i	0.157789	−	0.497171i
$400$		−	4.69156i		−	0.234578i
$401$	8.16105	−	30.4574i	0.407543	−	1.52097i	−0.391773	−	0.920062i	$-0.628138\pi$
$401$	8.16105	−	30.4574i	0.407543	−	1.52097i	0.799316	−	0.600910i	$-0.205195\pi$
$402$	0.299548	−	0.518833i	0.0149401	−	0.0258770i
$403$	32.5268	−	0.922240i	1.62028	−	0.0459400i
$404$	24.8413	−	14.3421i	1.23590	−	0.713547i
$405$	−1.77731	−	1.77731i	−0.0883151	−	0.0883151i
$406$	4.36273	−	0.958562i	0.216519	−	0.0475726i
$407$			5.73503i			0.284275i
$408$	−3.32106	−	0.889875i	−0.164417	−	0.0440554i
$409$	7.22097	−	1.93485i	0.357054	−	0.0956723i	−0.0758330	−	0.997121i	$-0.524162\pi$
$409$	7.22097	−	1.93485i	0.357054	−	0.0956723i	0.432887	+	0.901448i	$0.357495\pi$
$410$	0.712683	−	0.190963i	0.0351969	−	0.00943098i
$411$	−19.0928	−	5.11589i	−0.941776	−	0.252348i
$412$			31.8125i			1.56729i
$413$	17.4499	+	19.1155i	0.858655	+	0.940614i
$414$	−1.04037	−	1.04037i	−0.0511313	−	0.0511313i
$415$	−30.9309	+	17.8579i	−1.51834	+	0.876612i
$416$	0.317569	+	11.2005i	0.0155701	+	0.549148i
$417$	−4.45212	+	7.71130i	−0.218021	+	0.377624i
$418$	−0.466870	+	1.74238i	−0.0228354	+	0.0852227i
$419$			11.9331i			0.582969i	0.956575	+	0.291485i	$0.0941493\pi$
$419$			11.9331i			0.582969i	−0.956575	+	0.291485i	$0.905851\pi$
$420$	−9.45863	+	8.63447i	−0.461534	+	0.421319i
$421$	2.09088	−	2.09088i	0.101903	−	0.101903i	−0.654317	−	0.756220i	$-0.727044\pi$
$421$	2.09088	−	2.09088i	0.101903	−	0.101903i	0.756220	+	0.654317i	$0.227044\pi$
$422$	5.62141	+	1.50625i	0.273646	+	0.0733232i
$423$	1.68194	+	6.27707i	0.0817785	+	0.305201i
$424$	0.739906	−	0.198257i	0.0359330	−	0.00962823i
$425$	3.66995	−	2.11885i	0.178019	−	0.102779i
$426$	2.32691			0.112739
$427$	−1.55383	+	2.42890i	−0.0751950	+	0.117543i
$428$		−	19.6653i		−	0.950558i
$429$	5.33617	+	2.88236i	0.257633	+	0.139161i
$430$	3.33211	+	1.92380i	0.160689	+	0.0927737i
$431$	−5.27803	−	19.6979i	−0.254234	−	0.948814i	−0.968515	−	0.248955i	$-0.919913\pi$
$431$	−5.27803	−	19.6979i	−0.254234	−	0.948814i	0.714281	−	0.699859i	$-0.246754\pi$
$432$	−3.08355	+	1.78029i	−0.148357	+	0.0856541i
$433$	−17.8044			−0.855625			−0.427813	−	0.903867i	$-0.640716\pi$
$433$	−17.8044			−0.855625			−0.427813	+	0.903867i	$0.640716\pi$
$434$	−5.77318	+	2.99149i	−0.277121	+	0.143596i
$435$	−11.0190	+	11.0190i	−0.528321	+	0.528321i
$436$	−1.71428	+	6.39777i	−0.0820990	+	0.306397i
$437$	5.50699	+	20.5524i	0.263435	+	0.983153i
$438$	0.561483	−	0.972516i	0.0268287	−	0.0464686i
$439$	−5.44240	−	9.42652i	−0.259752	−	0.449903i	0.706424	−	0.707789i	$-0.250307\pi$
$439$	−5.44240	−	9.42652i	−0.259752	−	0.449903i	−0.966175	+	0.257886i	$0.916974\pi$
$440$	3.19604	−	3.19604i	0.152365	−	0.152365i
$441$	6.97101	+	0.636401i	0.331953	+	0.0303048i
$442$	−2.68880	+	1.65572i	−0.127893	+	0.0787546i
$443$	0.504674	+	0.874120i	0.0239778	+	0.0415307i	0.877765	−	0.479091i	$-0.159034\pi$
$443$	0.504674	+	0.874120i	0.0239778	+	0.0415307i	−0.853788	+	0.520622i	$0.825700\pi$
$444$	−6.34237	+	1.69943i	−0.300996	+	0.0806515i
$445$	−15.8039	+	27.3732i	−0.749177	+	1.29761i
$446$	2.60777	+	4.51680i	0.123482	+	0.213876i
$447$	6.81116	+	6.81116i	0.322157	+	0.322157i
$448$	7.63806	+	14.7404i	0.360864	+	0.696419i
$449$	4.39731	+	4.39731i	0.207522	+	0.207522i	0.803213	−	0.595691i	$-0.203122\pi$
$449$	4.39731	+	4.39731i	0.207522	+	0.207522i	−0.595691	+	0.803213i	$0.703122\pi$
$450$	−0.0928668	+	0.346584i	−0.00437778	+	0.0163381i
$451$	−1.57032	−	0.906626i	−0.0739436	−	0.0426913i
$452$	−18.6221	−	10.7515i	−0.875911	−	0.505707i
$453$	4.67041	+	1.25143i	0.219435	+	0.0587974i
$454$	−6.94651			−0.326016
$455$	−0.411775	+	23.9736i	−0.0193043	+	1.12390i
$456$	−4.21001			−0.197152
$457$	−7.96500	−	2.13422i	−0.372587	−	0.0998344i	0.0676663	−	0.997708i	$-0.478445\pi$
$457$	−7.96500	−	2.13422i	−0.372587	−	0.0998344i	−0.440253	+	0.897874i	$0.645111\pi$
$458$	3.96588	+	2.28970i	0.185313	+	0.106991i
$459$	−2.78524	−	1.60806i	−0.130004	−	0.0750579i
$460$	6.76909	−	25.2626i	0.315610	−	1.17787i
$461$	−8.70768	−	8.70768i	−0.405557	−	0.405557i	0.474629	−	0.880186i	$-0.342582\pi$
$461$	−8.70768	−	8.70768i	−0.405557	−	0.405557i	−0.880186	+	0.474629i	$0.842582\pi$
$462$	−1.21064	−	0.0551466i	−0.0563241	−	0.00256565i
$463$	−14.5871	−	14.5871i	−0.677922	−	0.677922i	0.281608	−	0.959530i	$-0.409132\pi$
$463$	−14.5871	−	14.5871i	−0.677922	−	0.677922i	−0.959530	+	0.281608i	$0.909132\pi$
$464$	11.0375	+	19.1175i	0.512403	+	0.887508i
$465$	11.3421	−	19.6450i	0.525976	−	0.911016i
$466$	−7.08267	+	1.89779i	−0.328098	+	0.0879136i
$467$	1.12496	+	1.94848i	0.0520568	+	0.0901650i	0.890880	−	0.454240i	$-0.150089\pi$
$467$	1.12496	+	1.94848i	0.0520568	+	0.0901650i	−0.838823	+	0.544405i	$0.816756\pi$
$468$	−1.60636	+	6.75538i	−0.0742539	+	0.312267i
$469$	−3.92434	−	4.29892i	−0.181209	−	0.198506i
$470$	3.14516	−	3.14516i	0.145075	−	0.145075i
$471$	−1.63818	−	2.83742i	−0.0754836	−	0.130741i
$472$	5.22910	−	9.05707i	0.240689	−	0.416886i
$473$	−2.44732	−	9.13352i	−0.112528	−	0.419960i
$474$	−0.558510	+	2.08439i	−0.0256532	+	0.0957390i
$475$	3.66915	−	3.66915i	0.168352	−	0.168352i
$476$	−8.83087	+	13.8041i	−0.404762	+	0.632712i
$477$	0.716528			0.0328076
$478$	−0.377764	+	0.218102i	−0.0172785	+	0.00997576i
$479$	−5.98049	−	22.3195i	−0.273256	−	1.01980i	−0.957001	−	0.290084i	$-0.906317\pi$
$479$	−5.98049	−	22.3195i	−0.273256	−	1.01980i	0.683746	−	0.729721i	$-0.260350\pi$
$480$	6.76467	+	3.90559i	0.308764	+	0.178265i
$481$	−5.84230	+	10.8160i	−0.266386	+	0.493166i
$482$			2.83123i			0.128959i
$483$	−12.6922	+	6.57676i	−0.577517	+	0.299253i
$484$	15.7353			0.715239
$485$	−14.9213	+	8.61482i	−0.677542	+	0.391179i
$486$	0.263033	−	0.0704795i	0.0119314	−	0.00319702i
$487$	−8.08015	−	30.1555i	−0.366147	−	1.36648i	−0.865860	−	0.500287i	$-0.833228\pi$
$487$	−8.08015	−	30.1555i	−0.366147	−	1.36648i	0.499713	−	0.866191i	$-0.333439\pi$
$488$	1.12538	+	0.301544i	0.0509434	+	0.0136502i
$489$	−11.4443	+	11.4443i	−0.517530	+	0.517530i
$490$	−2.00844	−	4.34989i	−0.0907320	−	0.196508i
$491$			23.7061i			1.06984i	0.844902	+	0.534922i	$0.179659\pi$
$491$			23.7061i			1.06984i	−0.844902	+	0.534922i	$0.820341\pi$
$492$	0.537311	−	2.00527i	0.0242239	−	0.0904047i
$493$	−9.96972	+	17.2681i	−0.449014	+	0.777715i
$494$	−2.65546	+	2.81044i	−0.119475	+	0.126448i
$495$	3.66149	−	2.11396i	0.164572	−	0.0950156i
$496$	−22.7222	−	22.7222i	−1.02026	−	1.02026i
$497$	6.83902	−	21.5488i	0.306772	−	0.966594i
$498$		−	3.86946i		−	0.173395i
$499$	36.3108	+	9.72944i	1.62549	+	0.435550i	0.952609	−	0.304198i	$-0.0983884\pi$
$499$	36.3108	+	9.72944i	1.62549	+	0.435550i	0.672885	+	0.739747i	$0.265055\pi$
$500$	17.2175	−	4.61340i	0.769988	−	0.206318i
$501$	−13.3085	+	3.56601i	−0.594580	+	0.159317i
$502$	−2.56632	−	0.687642i	−0.114540	−	0.0306910i
$503$			1.81099i			0.0807479i	0.999185	+	0.0403740i	$0.0128549\pi$
$503$			1.81099i			0.0807479i	−0.999185	+	0.0403740i	$0.987145\pi$
$504$	−0.606978	−	2.76256i	−0.0270370	−	0.123054i
$505$	−26.4718	−	26.4718i	−1.17798	−	1.17798i
$506$	2.14330	−	1.23743i	0.0952811	−	0.0550106i
$507$	7.12746	+	10.8719i	0.316542	+	0.482840i
$508$	7.42923	−	12.8678i	0.329619	−	0.570917i
$509$	2.72066	−	10.1537i	0.120591	−	0.450053i	−0.879053	−	0.476724i	$-0.841824\pi$
$509$	2.72066	−	10.1537i	0.120591	−	0.450053i	0.999644	+	0.0266713i	$0.00849073\pi$
$510$			2.20129i			0.0974747i
$511$	−7.35590	−	8.05803i	−0.325406	−	0.356466i
$512$	13.2074	−	13.2074i	0.583690	−	0.583690i
$513$	−3.80388	−	1.01925i	−0.167945	−	0.0450008i
$514$	−1.38708	−	5.17666i	−0.0611815	−	0.228332i
$515$	40.1049	−	10.7461i	1.76723	−	0.473528i
$516$	9.37555	−	5.41298i	0.412736	−	0.238293i
$517$	−10.9311			−0.480748
$518$	0.111778	−	2.45387i	0.00491123	−	0.107817i
$519$			18.7948i			0.824999i
$520$	9.28339	−	2.77175i	0.407103	−	0.121549i
$521$	−38.1189	−	22.0079i	−1.67002	−	0.964185i	−0.967624	−	0.252396i	$-0.918781\pi$
$521$	−38.1189	−	22.0079i	−1.67002	−	0.964185i	−0.702394	−	0.711789i	$-0.747885\pi$
$522$	−0.436962	−	1.63076i	−0.0191253	−	0.0713766i
$523$	−6.68744	+	3.86100i	−0.292422	+	0.168830i	−0.639033	−	0.769179i	$-0.720665\pi$
$523$	−6.68744	+	3.86100i	−0.292422	+	0.168830i	0.346612	+	0.938009i	$0.387332\pi$
$524$	30.4840			1.33170
$525$	2.93665	+	1.87865i	0.128166	+	0.0819911i
$526$	−0.889555	+	0.889555i	−0.0387864	+	0.0387864i
$527$	7.51231	−	28.0363i	0.327241	−	1.22128i
$528$	−1.55012	−	5.78514i	−0.0674605	−	0.251766i
$529$	3.09621	−	5.36279i	0.134618	−	0.233165i
$530$	−0.245215	−	0.424725i	−0.0106515	−	0.0184489i
$531$	6.91739	−	6.91739i	0.300189	−	0.300189i
$532$	−6.06996	+	19.1256i	−0.263166	+	0.829198i
$533$	−2.03796	−	3.30954i	−0.0882739	−	0.143352i
$534$	−1.71220	−	2.96561i	−0.0740941	−	0.128335i
$535$	−24.7914	+	6.64282i	−1.07182	+	0.287194i
$536$	−1.17598	+	2.03686i	−0.0507946	+	0.0879788i
$537$	−9.34515	−	16.1863i	−0.403273	−	0.698489i
$538$	0.807305	+	0.807305i	0.0348054	+	0.0348054i
$539$	−4.06889	+	11.0493i	−0.175260	+	0.475926i
$540$	3.42282	+	3.42282i	0.147295	+	0.147295i
$541$	0.0916984	−	0.342223i	0.00394242	−	0.0147133i	−0.963927	−	0.266168i	$-0.914242\pi$
$541$	0.0916984	−	0.342223i	0.00394242	−	0.0147133i	0.967869	+	0.251455i	$0.0809090\pi$
$542$	−1.41439	−	0.816598i	−0.0607532	−	0.0350759i
$543$	11.9769	+	6.91487i	0.513978	+	0.296745i
$544$	9.65418	+	2.58683i	0.413919	+	0.110909i
$545$	8.64451			0.370290
$546$	−2.22703	−	1.33729i	−0.0953080	−	0.0572307i
$547$	39.2068			1.67636			0.838180	−	0.545393i	$-0.183620\pi$
$547$	39.2068			1.67636			0.838180	+	0.545393i	$0.183620\pi$
$548$	36.7697	+	9.85241i	1.57072	+	0.420874i
$549$	0.943810	+	0.544909i	0.0402808	+	0.0232561i
$550$	−0.522691	−	0.301776i	−0.0222876	−	0.0128678i
$551$	−6.31916	+	23.5834i	−0.269205	+	1.00469i
$552$	4.08432	+	4.08432i	0.173840	+	0.173840i
$553$	17.6613	+	11.2984i	0.751035	+	0.480457i
$554$	−3.34994	−	3.34994i	−0.142325	−	0.142325i
$555$	4.28483	+	7.42155i	0.181881	+	0.315027i
$556$	8.57410	−	14.8508i	0.363623	−	0.629813i
$557$	14.9841	−	4.01498i	0.634898	−	0.170120i	0.0730065	−	0.997331i	$-0.476741\pi$
$557$	14.9841	−	4.01498i	0.634898	−	0.170120i	0.561891	+	0.827211i	$0.310074\pi$
$558$	1.22880	+	2.12834i	0.0520193	+	0.0901000i
$559$	4.68884	−	19.7184i	0.198317	−	0.834001i
$560$	17.4875	−	15.9637i	0.738981	−	0.674590i
$561$	3.82532	−	3.82532i	0.161505	−	0.161505i
$562$	−2.01533	−	3.49066i	−0.0850117	−	0.147245i
$563$	7.57791	−	13.1253i	0.319371	−	0.553167i	−0.660986	−	0.750398i	$-0.729862\pi$
$563$	7.57791	−	13.1253i	0.319371	−	0.553167i	0.980357	+	0.197231i	$0.0631950\pi$
$564$	−3.23915	−	12.0887i	−0.136393	−	0.509025i
$565$	−7.26358	+	27.1080i	−0.305581	+	1.14044i
$566$	−4.56940	+	4.56940i	−0.192066	+	0.192066i
$567$	0.120393	−	2.64301i	0.00505604	−	0.110996i
$568$	−9.13509			−0.383300
$569$	−31.1862	+	18.0054i	−1.30739	+	0.754824i	−0.981660	−	0.190638i	$-0.938944\pi$
$569$	−31.1862	+	18.0054i	−1.30739	+	0.754824i	−0.325733	+	0.945462i	$0.605611\pi$
$570$	0.697627	+	2.60358i	0.0292204	+	0.109052i
$571$	30.5823	+	17.6567i	1.27983	+	0.738910i	0.976817	−	0.214077i	$-0.0686744\pi$
$571$	30.5823	+	17.6567i	1.27983	+	0.738910i	0.303012	+	0.952987i	$0.402008\pi$
$572$	−10.2766	−	5.55098i	−0.429688	−	0.232098i
$573$		−	24.4101i		−	1.01975i
$574$	0.654229	+	0.418528i	0.0273070	+	0.0174690i
$575$	−7.11922			−0.296892
$576$	5.43421	−	3.13744i	0.226426	−	0.130727i
$577$	19.0519	−	5.10495i	0.793142	−	0.212522i	0.160571	−	0.987024i	$-0.448666\pi$
$577$	19.0519	−	5.10495i	0.793142	−	0.212522i	0.632571	+	0.774503i	$0.282000\pi$
$578$	−0.469151	−	1.75089i	−0.0195141	−	0.0728276i
$579$	14.3910	+	3.85605i	0.598068	+	0.160252i
$580$	21.2209	−	21.2209i	0.881151	−	0.881151i
$581$	−35.8338	−	11.3727i	−1.48664	−	0.471821i
$582$		−	1.86666i		−	0.0773756i
$583$	−0.311946	+	1.16420i	−0.0129195	+	0.0482161i
$584$	−2.20429	+	3.81795i	−0.0912144	+	0.157988i
$585$	9.05888	−	0.256848i	0.374539	−	0.0106194i
$586$	−0.948324	+	0.547515i	−0.0391749	+	0.0226176i
$587$	10.7666	+	10.7666i	0.444387	+	0.444387i	0.893483	−	0.449096i	$-0.148254\pi$
$587$	10.7666	+	10.7666i	0.444387	+	0.444387i	−0.449096	+	0.893483i	$0.648254\pi$
$588$	−13.4251	−	1.22561i	−0.553642	−	0.0505433i
$589$		−	35.5408i		−	1.46443i
$590$	−6.46763	−	1.73300i	−0.266268	−	0.0713463i
$591$	22.9844	−	6.15866i	0.945453	−	0.253333i
$592$	11.7260	−	3.14197i	0.481936	−	0.129134i
$593$	11.2454	+	3.01321i	0.461795	+	0.123738i	0.482213	−	0.876054i	$-0.339833\pi$
$593$	11.2454	+	3.01321i	0.461795	+	0.123738i	−0.0204181	+	0.999792i	$0.506500\pi$
$594$			0.458054i			0.0187942i
$595$	20.3854	+	6.46981i	0.835720	+	0.265236i
$596$	−13.1173	−	13.1173i	−0.537304	−	0.537304i
$597$	11.0550	−	6.38259i	0.452450	−	0.261222i
$598$	5.30272	−	0.150349i	0.216844	−	0.00614824i
$599$	−8.70889	+	15.0842i	−0.355836	+	0.616325i	−0.987261	−	0.159112i	$-0.949137\pi$
$599$	−8.70889	+	15.0842i	−0.355836	+	0.616325i	0.631425	+	0.775437i	$0.282470\pi$
$600$	0.364581	−	1.36063i	0.0148839	−	0.0555476i
$601$			8.65804i			0.353169i	0.984285	+	0.176584i	$0.0565049\pi$
$601$			8.65804i			0.353169i	−0.984285	+	0.176584i	$0.943495\pi$
$602$	0.869129	+	3.95570i	0.0354231	+	0.161222i
$603$	−1.55566	+	1.55566i	−0.0633514	+	0.0633514i
$604$	−8.99449	−	2.41007i	−0.365981	−	0.0980642i
$605$	−5.31528	−	19.8369i	−0.216097	−	0.806484i
$606$	3.91771	−	1.04975i	0.159146	−	0.0426431i
$607$	−27.6529	+	15.9654i	−1.12240	+	0.648017i	−0.942012	−	0.335579i	$-0.891068\pi$
$607$	−27.6529	+	15.9654i	−1.12240	+	0.648017i	−0.180386	+	0.983596i	$0.557735\pi$
$608$	12.2383			0.496329
$609$	−16.3862	−	0.746418i	−0.664004	−	0.0302464i
$610$		−	0.745930i		−	0.0302018i
$611$	−20.6154	−	11.1355i	−0.834011	−	0.450495i
$612$	5.36395	+	3.09688i	0.216825	+	0.125184i
$613$	8.34209	+	31.1331i	0.336934	+	1.25745i	0.901757	+	0.432243i	$0.142278\pi$
$613$	8.34209	+	31.1331i	0.336934	+	1.25745i	−0.564823	+	0.825212i	$0.691056\pi$
$614$	−0.750703	+	0.433419i	−0.0302959	+	0.0174914i
$615$	−2.70948			−0.109257
$616$	4.75279	+	0.216497i	0.191495	+	0.00872291i
$617$	−4.00949	+	4.00949i	−0.161416	+	0.161416i	−0.783194	−	0.621778i	$-0.786411\pi$
$617$	−4.00949	+	4.00949i	−0.161416	+	0.161416i	0.621778	+	0.783194i	$0.286411\pi$
$618$	−1.16423	+	4.34497i	−0.0468322	+	0.174780i
$619$	−1.91958	−	7.16396i	−0.0771544	−	0.287944i	0.916559	−	0.399900i	$-0.130955\pi$
$619$	−1.91958	−	7.16396i	−0.0771544	−	0.287944i	−0.993713	+	0.111956i	$0.964288\pi$
$620$	−21.8431	+	37.8333i	−0.877239	+	1.51942i
$621$	2.70150	+	4.67914i	0.108407	+	0.187767i
$622$	3.12488	−	3.12488i	0.125296	−	0.125296i
$623$	−32.4959	+	7.13987i	−1.30192	+	0.286053i
$624$	2.96989	−	12.4896i	0.118891	−	0.499984i
$625$	−14.9260	−	25.8526i	−0.597041	−	1.03410i
$626$	−3.12558	+	0.837498i	−0.124923	+	0.0334732i
$627$	3.31210	−	5.73672i	0.132272	−	0.229102i
$628$	3.15489	+	5.46443i	0.125894	+	0.218055i
$629$	7.75361	+	7.75361i	0.309157	+	0.309157i
$630$	−1.60786	+	0.833146i	−0.0640586	+	0.0331933i
$631$	33.6574	+	33.6574i	1.33988	+	1.33988i	0.896171	+	0.443709i	$0.146338\pi$
$631$	33.6574	+	33.6574i	1.33988	+	1.33988i	0.443709	+	0.896171i	$0.353662\pi$
$632$	2.19262	−	8.18298i	0.0872179	−	0.325502i
$633$	−18.5083	−	10.6857i	−0.735637	−	0.424720i
$634$	2.15777	+	1.24579i	0.0856961	+	0.0494766i
$635$	−18.7315	−	5.01910i	−0.743339	−	0.199177i
$636$	−1.37992			−0.0547175
$637$	−18.9297	+	16.6934i	−0.750020	+	0.661415i
$638$	2.83986			0.112431
$639$	−8.25385	−	2.21161i	−0.326517	−	0.0874900i
$640$	−17.2488	−	9.95861i	−0.681819	−	0.393649i
$641$	−36.4104	−	21.0215i	−1.43812	−	0.830301i	−0.440404	−	0.897800i	$-0.645165\pi$
$641$	−36.4104	−	21.0215i	−1.43812	−	0.830301i	−0.997719	+	0.0674993i	$0.978498\pi$
$642$	0.719684	−	2.68590i	0.0284037	−	0.106004i
$643$	−5.96442	−	5.96442i	−0.235214	−	0.235214i	0.579651	−	0.814865i	$-0.303189\pi$
$643$	−5.96442	−	5.96442i	−0.235214	−	0.235214i	−0.814865	+	0.579651i	$0.803189\pi$
$644$	24.4433	−	12.6658i	0.963202	−	0.499103i
$645$	−9.99096	−	9.99096i	−0.393394	−	0.393394i
$646$	1.72446	+	2.98685i	0.0678479	+	0.117516i
$647$	−19.1961	+	33.2485i	−0.754675	+	1.30713i	0.190861	+	0.981617i	$0.438872\pi$
$647$	−19.1961	+	33.2485i	−0.754675	+	1.30713i	−0.945536	+	0.325518i	$0.894461\pi$
$648$	−1.03263	+	0.276692i	−0.0405655	+	0.0108695i
$649$	8.22767	+	14.2507i	0.322964	+	0.559391i
$650$	−0.678347	−	1.10160i	−0.0266070	−	0.0432083i
$651$	23.3215	−	5.12410i	0.914040	−	0.200829i
$652$	22.0400	−	22.0400i	0.863153	−	0.863153i
$653$	9.31196	+	16.1288i	0.364405	+	0.631168i	0.988681	−	0.150036i	$-0.0479390\pi$
$653$	9.31196	+	16.1288i	0.364405	+	0.631168i	−0.624275	+	0.781204i	$0.714606\pi$
$654$	−0.468274	+	0.811074i	−0.0183110	+	0.0317155i
$655$	−10.2973	−	38.4301i	−0.402350	−	1.50159i
$656$	−0.993401	+	3.70742i	−0.0387858	+	0.144751i
$657$	−2.91598	+	2.91598i	−0.113763	+	0.113763i
$658$	4.67712	+	0.213050i	0.182333	+	0.00830556i
$659$	19.0983			0.743965			0.371983	−	0.928240i	$-0.378678\pi$
$659$	19.0983			0.743965			0.371983	+	0.928240i	$0.378678\pi$
$660$	−7.05147	+	4.07117i	−0.274478	+	0.158470i
$661$	10.8568	+	40.5183i	0.422282	+	1.57598i	0.769787	+	0.638301i	$0.220363\pi$
$661$	10.8568	+	40.5183i	0.422282	+	1.57598i	−0.347504	+	0.937678i	$0.612971\pi$
$662$	4.26042	+	2.45975i	0.165586	+	0.0956010i
$663$	11.1112	−	3.31748i	0.431524	−	0.128840i
$664$			15.1909i			0.589522i
$665$	26.1613	+	1.19169i	1.01449	+	0.0462117i
$666$	−0.928438			−0.0359762
$667$	29.0099	−	16.7489i	1.12327	−	0.648519i
$668$	25.6301	−	6.86758i	0.991660	−	0.265715i
$669$	−4.95712	−	18.5002i	−0.191653	−	0.715260i
$670$	1.45451	+	0.389736i	0.0561928	+	0.0150568i
$671$	−1.29625	+	1.29625i	−0.0500412	+	0.0500412i
$672$	1.76446	+	8.03064i	0.0680655	+	0.309789i
$673$			5.07896i			0.195780i	0.995197	+	0.0978898i	$0.0312093\pi$
$673$			5.07896i			0.195780i	−0.995197	+	0.0978898i	$0.968791\pi$
$674$	−2.01059	+	7.50361i	−0.0774449	+	0.289028i
$675$	0.658821	−	1.14111i	0.0253580	−	0.0439214i
$676$	−13.7264	−	20.9377i	−0.527938	−	0.805296i
$677$	−3.95405	+	2.28287i	−0.151967	+	0.0877380i	−0.574055	−	0.818817i	$-0.694630\pi$
$677$	−3.95405	+	2.28287i	−0.151967	+	0.0877380i	0.422088	+	0.906555i	$0.361297\pi$
$678$	−2.14995	−	2.14995i	−0.0825684	−	0.0825684i
$679$	−17.2865	−	5.48631i	−0.663397	−	0.210545i
$680$		−	8.64192i		−	0.331403i
$681$	24.6402	+	6.60231i	0.944213	+	0.253001i
$682$	−3.99305	+	1.06993i	−0.152902	+	0.0409699i
$683$	−4.67716	+	1.25324i	−0.178966	+	0.0479539i	−0.347189	−	0.937795i	$-0.612864\pi$
$683$	−4.67716	+	1.25324i	−0.178966	+	0.0479539i	0.168223	+	0.985749i	$0.446197\pi$
$684$	7.32569	+	1.96291i	0.280105	+	0.0750538i
$685$		−	49.6824i		−	1.89827i
$686$	1.95633	−	4.64839i	0.0746929	−	0.177476i
$687$	−11.8912	−	11.8912i	−0.453679	−	0.453679i
$688$	−17.3339	+	10.0077i	−0.660848	+	0.381541i
$689$	−1.77429	+	1.87784i	−0.0675949	+	0.0715398i
$690$	1.84905	−	3.20265i	0.0703922	−	0.121923i
$691$	8.44042	−	31.5001i	0.321089	−	1.19832i	−0.597097	−	0.802169i	$-0.703679\pi$
$691$	8.44042	−	31.5001i	0.321089	−	1.19832i	0.918186	−	0.396151i	$-0.129654\pi$
$692$		−	36.1959i		−	1.37596i
$693$	4.24189	+	1.34627i	0.161136	+	0.0511404i
$694$	2.15876	−	2.15876i	0.0819453	−	0.0819453i
$695$	−21.6181	−	5.79256i	−0.820022	−	0.219724i
$696$	1.71544	+	6.40213i	0.0650238	+	0.242672i
$697$	−3.34877	+	0.897299i	−0.126844	+	0.0339876i
$698$	3.69306	−	2.13219i	0.139784	−	0.0807045i
$699$	26.9269			1.01847
$700$	−5.65554	−	3.61800i	−0.213759	−	0.136747i
$701$			21.7888i			0.822951i	0.911421	+	0.411475i	$0.134986\pi$
$701$			21.7888i			0.822951i	−0.911421	+	0.411475i	$0.865014\pi$
$702$	−0.466621	+	0.863866i	−0.0176115	+	0.0326045i
$703$	11.6279	+	6.71335i	0.438553	+	0.253199i
$704$	2.73182	+	10.1953i	0.102959	+	0.384249i
$705$	−14.1456	+	8.16696i	−0.532754	+	0.307586i
$706$	−7.91614			−0.297928
$707$	1.79318	−	39.3659i	0.0674394	−	1.48051i
$708$	−13.3218	+	13.3218i	−0.500665	+	0.500665i
$709$	−5.37061	+	20.0434i	−0.201698	+	0.752746i	0.788733	+	0.614736i	$0.210737\pi$
$709$	−5.37061	+	20.0434i	−0.201698	+	0.752746i	−0.990431	+	0.138010i	$0.955929\pi$
$710$	1.51375	+	5.64938i	0.0568099	+	0.212018i
$711$	3.96221	−	6.86275i	0.148595	−	0.257373i
$712$	6.72183	+	11.6425i	0.251911	+	0.436323i
$713$	−34.4798	+	34.4798i	−1.29128	+	1.29128i
$714$	−1.71131	+	1.56220i	−0.0640442	+	0.0584638i
$715$	−3.52653	+	14.8305i	−0.131885	+	0.554629i
$716$	17.9973	+	31.1723i	0.672591	+	1.16496i
$717$	1.54727	−	0.414591i	0.0577840	−	0.0154832i
$718$	−0.694947	+	1.20368i	−0.0259352	+	0.0449211i
$719$	−16.6905	−	28.9088i	−0.622452	−	1.07812i	−0.989028	−	0.147730i	$-0.952803\pi$
$719$	−16.6905	−	28.9088i	−0.622452	−	1.07812i	0.366576	−	0.930388i	$-0.380530\pi$
$720$	−6.32824	−	6.32824i	−0.235839	−	0.235839i
$721$	36.8155	+	23.5519i	1.37108	+	0.877117i
$722$	−0.672326	−	0.672326i	−0.0250214	−	0.0250214i
$723$	2.69094	−	10.0427i	0.100077	−	0.373493i
$724$	−23.0657	−	13.3170i	−0.857229	−	0.494922i
$725$	−7.07471	−	4.08458i	−0.262748	−	0.151698i
$726$	2.14913	+	0.575858i	0.0797617	+	0.0213721i
$727$	44.2909			1.64266			0.821329	−	0.570454i	$-0.193233\pi$
$727$	44.2909			1.64266			0.821329	+	0.570454i	$0.193233\pi$
$728$	8.74297	+	5.24999i	0.324036	+	0.194578i
$729$	−1.00000			−0.0370370
$730$	2.72639	+	0.730533i	0.100908	+	0.0270383i
$731$	−15.6570	−	9.03956i	−0.579094	−	0.334340i
$732$	−1.81763	−	1.04941i	−0.0671817	−	0.0387873i
$733$	−3.02925	+	11.3053i	−0.111888	+	0.417571i	−0.999035	−	0.0439152i	$-0.986017\pi$
$733$	−3.02925	+	11.3053i	−0.111888	+	0.417571i	0.887148	+	0.461486i	$0.152684\pi$
$734$	−3.25173	−	3.25173i	−0.120023	−	0.120023i
$735$	2.98983	+	17.3386i	0.110282	+	0.639542i
$736$	−11.8730	−	11.8730i	−0.437643	−	0.437643i
$737$	−1.85033	−	3.20487i	−0.0681578	−	0.118053i
$738$	0.146773	−	0.254218i	0.00540277	−	0.00935788i
$739$	−26.6035	+	7.12838i	−0.978625	+	0.262222i	−0.712465	−	0.701707i	$-0.752421\pi$
$739$	−26.6035	+	7.12838i	−0.978625	+	0.262222i	−0.266159	+	0.963929i	$0.585755\pi$
$740$	−8.25193	−	14.2928i	−0.303347	−	0.525412i
$741$	12.0905	−	7.44511i	0.444154	−	0.273503i
$742$	0.156164	−	0.492050i	0.00573296	−	0.0180637i
$743$	20.8708	−	20.8708i	0.765677	−	0.765677i	−0.211665	−	0.977342i	$-0.567889\pi$
$743$	20.8708	−	20.8708i	0.765677	−	0.765677i	0.977342	+	0.211665i	$0.0678887\pi$
$744$	−4.82408	−	8.35555i	−0.176859	−	0.306329i
$745$	−12.1055	+	20.9674i	−0.443512	+	0.768186i
$746$	0.486324	+	1.81498i	0.0178056	+	0.0664513i
$747$	−3.67773	+	13.7255i	−0.134561	+	0.502189i
$748$	−7.36697	+	7.36697i	−0.269363	+	0.269363i
$749$	−22.7580	−	14.5589i	−0.831559	−	0.531970i
$750$	2.52040			0.0920322
$751$	15.3148	−	8.84202i	0.558846	−	0.322650i	−0.193836	−	0.981034i	$-0.562093\pi$
$751$	15.3148	−	8.84202i	0.558846	−	0.322650i	0.752682	+	0.658384i	$0.228760\pi$
$752$	5.98866	+	22.3500i	0.218384	+	0.815020i
$753$	8.44948	+	4.87831i	0.307916	+	0.177776i
$754$	5.35583	+	2.89298i	0.195048	+	0.105356i
$755$			12.1531i			0.442298i
$756$	−0.231859	+	5.09003i	−0.00843262	+	0.185123i
$757$	4.84701			0.176168			0.0880838	−	0.996113i	$-0.471926\pi$
$757$	4.84701			0.176168			0.0880838	+	0.996113i	$0.471926\pi$
$758$	7.98645	−	4.61098i	0.290081	−	0.167478i
$759$	−8.77867	+	2.35224i	−0.318645	+	0.0853808i
$760$	−2.73878	−	10.2213i	−0.0993459	−	0.370764i
$761$	10.0496	+	2.69279i	0.364299	+	0.0976137i	0.436325	−	0.899789i	$-0.356280\pi$
$761$	10.0496	+	2.69279i	0.364299	+	0.0976137i	−0.0720259	+	0.997403i	$0.522946\pi$
$762$	1.48561	−	1.48561i	0.0538179	−	0.0538179i
$763$	6.13479	+	6.72036i	0.222094	+	0.243293i
$764$			47.0101i			1.70076i
$765$	2.09222	−	7.80825i	0.0756442	−	0.282308i
$766$	−0.757795	+	1.31254i	−0.0273803	+	0.0474240i
$767$	0.999670	+	35.2577i	0.0360960	+	1.27308i
$768$	−8.99969	+	5.19597i	−0.324748	+	0.187493i
$769$	−4.90786	−	4.90786i	−0.176982	−	0.176982i	0.613057	−	0.790039i	$-0.289940\pi$
$769$	−4.90786	−	4.90786i	−0.176982	−	0.176982i	−0.790039	+	0.613057i	$0.789940\pi$
$770$	−0.653683	−	2.97513i	−0.0235571	−	0.107216i
$771$			19.6806i			0.708780i
$772$	−27.7148	−	7.42616i	−0.997478	−	0.267273i
$773$	26.3864	−	7.07020i	0.949051	−	0.254298i	0.249092	−	0.968480i	$-0.419868\pi$
$773$	26.3864	−	7.07020i	0.949051	−	0.254298i	0.699960	+	0.714182i	$0.253201\pi$
$774$	1.47862	−	0.396194i	0.0531477	−	0.0142409i
$775$	11.4864	+	3.07778i	0.412605	+	0.110557i
$776$			7.32823i			0.263068i
$777$	−2.72877	+	8.59796i	−0.0978942	+	0.308450i
$778$	−6.19508	−	6.19508i	−0.222104	−	0.222104i
$779$	−3.67639	+	2.12257i	−0.131720	+	0.0760488i
$780$	−17.4460	+	0.494651i	−0.624668	+	0.0177113i
$781$	7.18675	−	12.4478i	0.257162	−	0.445418i
$782$	1.22470	−	4.57065i	0.0437953	−	0.163446i
$783$			6.19984i			0.221564i
$784$	24.8208	+	2.26595i	0.886458	+	0.0809269i
$785$	5.82311	−	5.82311i	0.207836	−	0.207836i
$786$	4.16353	+	1.11561i	0.148508	+	0.0397926i
$787$	4.69297	+	17.5144i	0.167286	+	0.624322i	0.997738	+	0.0672300i	$0.0214161\pi$
$787$	4.69297	+	17.5144i	0.167286	+	0.624322i	−0.830451	+	0.557092i	$0.811917\pi$
$788$	−44.2645	+	11.8606i	−1.57686	+	0.422517i
$789$	4.00084	−	2.30989i	0.142434	−	0.0822342i
$790$	−5.42390			−0.192974
$791$	−26.2289	+	13.5911i	−0.932593	+	0.483243i
$792$		−	1.79825i		−	0.0638980i
$793$	−3.76516	+	1.12417i	−0.133705	+	0.0399203i
$794$	2.21171	+	1.27693i	0.0784905	+	0.0453165i
$795$	0.466130	+	1.73962i	0.0165319	+	0.0616979i
$796$	−21.2902	+	12.2919i	−0.754610	+	0.435675i
$797$	−8.64429			−0.306196			−0.153098	−	0.988211i	$-0.548925\pi$
$797$	−8.64429			−0.306196			−0.153098	+	0.988211i	$0.548925\pi$
$798$	−1.52897	+	2.39004i	−0.0541250	+	0.0846065i
$799$	−14.7785	+	14.7785i	−0.522826	+	0.522826i
$800$	−1.05982	+	3.95530i	−0.0374703	+	0.139841i
$801$	3.25472	+	12.1468i	0.115000	+	0.429185i
$802$	−4.29325	+	7.43613i	−0.151600	+	0.262579i
$803$	−3.46832	−	6.00731i	−0.122394	−	0.211993i
$804$	2.99596	−	2.99596i	0.105659	−	0.105659i
$805$	−24.2242	−	26.5364i	−0.853790	−	0.935285i
$806$	−8.62063	−	2.04990i	−0.303649	−	0.0722045i
$807$	−2.09631	−	3.63092i	−0.0737936	−	0.127814i
$808$	−15.3803	+	4.12114i	−0.541078	+	0.144981i
$809$	−2.49511	+	4.32165i	−0.0877233	+	0.151941i	−0.906548	−	0.422102i	$-0.861292\pi$
$809$	−2.49511	+	4.32165i	−0.0877233	+	0.151941i	0.818825	+	0.574043i	$0.194626\pi$
$810$	0.342227	+	0.592755i	0.0120246	+	0.0208273i
$811$	22.1052	+	22.1052i	0.776218	+	0.776218i	0.979185	−	0.202967i	$-0.0650586\pi$
$811$	22.1052	+	22.1052i	0.776218	+	0.776218i	−0.202967	+	0.979185i	$0.565059\pi$
$812$	31.5574	+	1.43749i	1.10745	+	0.0504459i
$813$	4.24089	+	4.24089i	0.148734	+	0.148734i
$814$	0.404203	−	1.50850i	0.0141673	−	0.0528731i
$815$	−35.2300	−	20.3401i	−1.23405	−	0.712482i
$816$	−9.91707	−	5.72563i	−0.347167	−	0.200437i
$817$	−21.3831	−	5.72960i	−0.748101	−	0.200453i
$818$	−2.03572			−0.0711773
$819$	6.62853	+	6.86022i	0.231620	+	0.239715i
$820$	5.21804			0.182222
$821$	−8.60418	−	2.30548i	−0.300288	−	0.0804619i	0.105529	−	0.994416i	$-0.466346\pi$
$821$	−8.60418	−	2.30548i	−0.300288	−	0.0804619i	−0.405817	+	0.913954i	$0.633013\pi$
$822$	4.66146	+	2.69130i	0.162587	+	0.0938697i
$823$	−6.55551	−	3.78483i	−0.228511	−	0.131931i	0.381374	−	0.924421i	$-0.375451\pi$
$823$	−6.55551	−	3.78483i	−0.228511	−	0.131931i	−0.609885	+	0.792490i	$0.708784\pi$
$824$	4.57059	−	17.0577i	0.159224	−	0.594232i
$825$	1.56723	+	1.56723i	0.0545639	+	0.0545639i
$826$	−3.24266	−	6.25788i	−0.112826	−	0.217740i
$827$	10.8615	+	10.8615i	0.377691	+	0.377691i	0.870268	−	0.492578i	$-0.163945\pi$
$827$	10.8615	+	10.8615i	0.377691	+	0.377691i	−0.492578	+	0.870268i	$0.663945\pi$
$828$	−5.20267	−	9.01129i	−0.180805	−	0.313164i
$829$	17.6352	−	30.5450i	0.612495	−	1.06087i	−0.378323	−	0.925673i	$-0.623499\pi$
$829$	17.6352	−	30.5450i	0.612495	−	1.06087i	0.990818	−	0.135199i	$-0.0431674\pi$
$830$	9.39446	−	2.51724i	0.326086	−	0.0873746i
$831$	8.69873	+	15.0666i	0.301755	+	0.522656i
$832$	−5.23391	+	22.0107i	−0.181453	+	0.763084i
$833$	9.43728	+	20.4393i	0.326982	+	0.708181i
$834$	1.71454	−	1.71454i	0.0593698	−	0.0593698i
$835$	−17.3154	−	29.9912i	−0.599225	−	1.03789i
$836$	−6.37859	+	11.0480i	−0.220608	+	0.382104i
$837$	−2.33583	−	8.71743i	−0.0807380	−	0.301318i
$838$	0.841038	−	3.13880i	0.0290532	−	0.108428i
$839$	−4.53781	+	4.53781i	−0.156663	+	0.156663i	−0.781086	−	0.624423i	$-0.785334\pi$
$839$	−4.53781	+	4.53781i	−0.156663	+	0.156663i	0.624423	+	0.781086i	$0.285334\pi$
$840$	6.31221	−	3.27080i	0.217792	−	0.112853i
$841$	9.43800			0.325448
$842$	−0.697334	+	0.402606i	−0.0240317	+	0.0138747i
$843$	3.83095	+	14.2973i	0.131945	+	0.492425i
$844$	35.6441	+	20.5791i	1.22692	+	0.708362i
$845$	−21.7587	+	24.3770i	−0.748523	+	0.838595i
$846$		−	1.76962i		−	0.0608408i
$847$	11.6493	−	18.2099i	0.400276	−	0.625699i
$848$	2.55125			0.0876103
$849$	20.5512	−	11.8653i	0.705316	−	0.407215i
$850$	−1.11466	+	0.298671i	−0.0382324	+	0.0102443i
$851$	−4.76779	−	17.7936i	−0.163438	−	0.609958i
$852$	15.8956	+	4.25923i	0.544576	+	0.145919i
$853$	−14.2303	+	14.2303i	−0.487235	+	0.487235i	−0.907433	−	0.420198i	$-0.861961\pi$
$853$	−14.2303	+	14.2303i	−0.487235	+	0.487235i	0.420198	+	0.907433i	$0.361961\pi$
$854$	0.579896	−	0.529367i	0.0198436	−	0.0181146i
$855$		−	9.89830i		−	0.338515i
$856$	−2.82537	+	10.5444i	−0.0965692	+	0.360401i
$857$	−24.0631	+	41.6785i	−0.821979	+	1.42371i	0.0822268	+	0.996614i	$0.473797\pi$
$857$	−24.0631	+	41.6785i	−0.821979	+	1.42371i	−0.904206	+	0.427096i	$0.859537\pi$
$858$	−1.20044	−	1.13425i	−0.0409824	−	0.0387225i
$859$	45.8474	−	26.4700i	1.56429	−	0.903145i	0.567478	−	0.823389i	$-0.307919\pi$
$859$	45.8474	−	26.4700i	1.56429	−	0.903145i	0.996814	−	0.0797561i	$-0.0254141\pi$
$860$	19.2411	+	19.2411i	0.656114	+	0.656114i
$861$	−1.92285	−	2.10638i	−0.0655304	−	0.0717854i
$862$			5.55319i			0.189142i
$863$	−19.2581	−	5.16020i	−0.655554	−	0.175655i	−0.0843153	−	0.996439i	$-0.526870\pi$
$863$	−19.2581	−	5.16020i	−0.655554	−	0.175655i	−0.571239	+	0.820784i	$0.693537\pi$
$864$	3.00181	−	0.804331i	0.102123	−	0.0273639i
$865$	−45.6308	+	12.2267i	−1.55150	+	0.415722i
$866$	4.68315	+	1.25485i	0.159140	+	0.0426414i
$867$			6.65655i			0.226068i
$868$	−44.9136	+	9.86822i	−1.52447	+	0.334949i
$869$	9.42546	+	9.42546i	0.319737	+	0.319737i
$870$	3.67498	−	2.12175i	0.124594	−	0.0719341i
$871$	−0.224817	−	7.92916i	−0.00761763	−	0.268669i
$872$	1.83837	−	3.18415i	0.0622551	−	0.107829i
$873$	−1.77417	+	6.62129i	−0.0600465	+	0.224097i
$874$		−	5.79408i		−	0.195988i
$875$	7.40772	−	23.3406i	0.250427	−	0.789058i
$876$	5.61573	−	5.61573i	0.189738	−	0.189738i
$877$	−19.2665	−	5.16244i	−0.650583	−	0.174323i	−0.0815907	−	0.996666i	$-0.526000\pi$
$877$	−19.2665	−	5.16244i	−0.650583	−	0.174323i	−0.568993	+	0.822343i	$0.692667\pi$
$878$	0.767156	+	2.86306i	0.0258903	+	0.0966237i
$879$	3.88421	−	1.04077i	0.131011	−	0.0351044i
$880$	13.0370	−	7.52693i	0.439478	−	0.253733i
$881$	−28.5396			−0.961524			−0.480762	−	0.876851i	$-0.659640\pi$
$881$	−28.5396			−0.961524			−0.480762	+	0.876851i	$0.659640\pi$
$882$	−1.78875	−	0.658708i	−0.0602305	−	0.0221799i
$883$			6.63568i			0.223308i	0.993747	+	0.111654i	$0.0356149\pi$
$883$			6.63568i			0.223308i	−0.993747	+	0.111654i	$0.964385\pi$
$884$	−21.3985	+	6.38896i	−0.719709	+	0.214884i
$885$	21.2944	+	12.2943i	0.715803	+	0.413269i
$886$	−0.0711383	−	0.265492i	−0.00238994	−	0.00891937i
$887$	−5.34220	+	3.08432i	−0.179373	+	0.103561i	−0.586998	−	0.809588i	$-0.699690\pi$
$887$	−5.34220	+	3.08432i	−0.179373	+	0.103561i	0.407625	+	0.913150i	$0.366357\pi$
$888$	3.64491			0.122315
$889$	−9.39137	−	18.1241i	−0.314977	−	0.607862i
$890$	6.08620	−	6.08620i	0.204010	−	0.204010i
$891$	0.435358	−	1.62478i	0.0145850	−	0.0544321i
$892$	9.54665	+	35.6286i	0.319645	+	1.19293i
$893$	−12.7958	+	22.1629i	−0.428194	+	0.741653i
$894$	−1.31151	−	2.27161i	−0.0438636	−	0.0759740i
$895$	33.2184	−	33.2184i	1.11037	−	1.11037i
$896$	−4.49908	−	20.4768i	−0.150304	−	0.684083i
$897$	−18.9523	−	4.50667i	−0.632800	−	0.150473i
$898$	−0.846718	−	1.46656i	−0.0282554	−	0.0489397i
$899$	−54.0466	+	14.4818i	−1.80256	+	0.482993i
$900$	−1.26879	+	2.19761i	−0.0422929	+	0.0732535i
$901$	1.15222	+	1.99570i	0.0383860	+	0.0664866i
$902$	0.349148	+	0.349148i	0.0116254	+	0.0116254i
$903$	0.676779	−	14.8574i	0.0225218	−	0.494424i
$904$	8.44038	+	8.44038i	0.280723	+	0.280723i
$905$	−8.99679	+	33.5765i	−0.299064	+	1.11612i
$906$	−1.14027	−	0.658336i	−0.0378830	−	0.0218718i
$907$	−15.1088	−	8.72308i	−0.501680	−	0.289645i	0.227727	−	0.973725i	$-0.426871\pi$
$907$	−15.1088	−	8.72308i	−0.501680	−	0.289645i	−0.729407	+	0.684080i	$0.760204\pi$
$908$	−47.4532	−	12.7150i	−1.57479	−	0.421963i
$909$	−14.8944			−0.494014
$910$	1.79796	−	6.27684i	0.0596019	−	0.208075i
$911$	5.47776			0.181486			0.0907431	−	0.995874i	$-0.471076\pi$
$911$	5.47776			0.181486			0.0907431	+	0.995874i	$0.471076\pi$
$912$	−13.5440	−	3.62911i	−0.448487	−	0.120172i
$913$	−20.6997	−	11.9510i	−0.685060	−	0.395520i
$914$	1.94464	+	1.12274i	0.0643230	+	0.0371369i
$915$	−0.708970	+	2.64591i	−0.0234378	+	0.0874711i
$916$	22.9007	+	22.9007i	0.756661	+	0.756661i
$917$	22.5683	−	35.2781i	0.745273	−	1.16499i
$918$	0.619276	+	0.619276i	0.0204392	+	0.0204392i
$919$	26.6486	+	46.1567i	0.879056	+	1.52257i	0.852378	+	0.522925i	$0.175159\pi$
$919$	26.6486	+	46.1567i	0.879056	+	1.52257i	0.0266774	+	0.999644i	$0.491507\pi$
$920$	−7.25910	+	12.5731i	−0.239325	+	0.414524i
$921$	3.07478	−	0.823886i	0.101318	−	0.0271480i
$922$	1.67670	+	2.90412i	0.0552190	+	0.0956421i
$923$	26.2345	−	16.1548i	0.863519	−	0.531741i
$924$	−8.16922	−	2.59270i	−0.268748	−	0.0852936i
$925$	−3.17664	+	3.17664i	−0.104447	+	0.104447i
$926$	2.80881	+	4.86500i	0.0923032	+	0.159874i
$927$	8.25935	−	14.3056i	0.271273	−	0.469858i
$928$	−4.98672	−	18.6107i	−0.163697	−	0.610926i
$929$	6.01069	−	22.4322i	0.197204	−	0.735977i	−0.794481	−	0.607289i	$-0.792257\pi$
$929$	6.01069	−	22.4322i	0.197204	−	0.735977i	0.991685	−	0.128687i	$-0.0410764\pi$
$930$	−4.36791	+	4.36791i	−0.143229	+	0.143229i
$931$	17.6396	+	21.1839i	0.578114	+	0.694273i
$932$	−51.8570			−1.69863
$933$	−14.0544	+	8.11431i	−0.460120	+	0.265650i
$934$	−0.158573	−	0.591802i	−0.00518866	−	0.0193643i
$935$	11.7758	+	6.79877i	0.385110	+	0.222343i
$936$	1.83188	−	3.39140i	0.0598770	−	0.110852i
$937$			21.3348i			0.696977i	0.937313	+	0.348488i	$0.113305\pi$
$937$			21.3348i			0.696977i	−0.937313	+	0.348488i	$0.886695\pi$
$938$	0.729245	+	1.40734i	0.0238107	+	0.0459514i
$939$	11.8829			0.387782
$940$	27.2422	−	15.7283i	0.888544	−	0.513001i
$941$	35.2341	−	9.44095i	1.14860	−	0.307766i	0.366196	−	0.930538i	$-0.380660\pi$
$941$	35.2341	−	9.44095i	1.14860	−	0.307766i	0.782404	+	0.622772i	$0.213993\pi$
$942$	0.230917	+	0.861794i	0.00752368	+	0.0280788i
$943$	5.62584	+	1.50744i	0.183202	+	0.0490889i
$944$	24.6299	−	24.6299i	0.801635	−	0.801635i
$945$	6.49515	−	1.42709i	0.211287	−	0.0464231i
$946$			2.57491i			0.0837174i
$947$	5.60828	−	20.9304i	0.182245	−	0.680147i	−0.812959	−	0.582321i	$-0.802145\pi$
$947$	5.60828	−	20.9304i	0.182245	−	0.680147i	0.995204	−	0.0978255i	$-0.0311887\pi$
$948$	−7.63061	+	13.2166i	−0.247831	+	0.429255i
$949$	−0.421404	−	14.8627i	−0.0136794	−	0.482463i
$950$	−1.22371	+	0.706508i	−0.0397023	+	0.0229222i
$951$	−6.46983	−	6.46983i	−0.209799	−	0.209799i
$952$	6.71834	−	6.13295i	0.217743	−	0.198770i
$953$			6.31913i			0.204697i	0.994749	+	0.102348i	$0.0326357\pi$
$953$			6.31913i			0.204697i	−0.994749	+	0.102348i	$0.967364\pi$
$954$	−0.188471	−	0.0505005i	−0.00610196	−	0.00163502i
$955$	59.2639	−	15.8797i	1.91774	−	0.513856i
$956$	−2.97981	+	0.798438i	−0.0963739	+	0.0258233i
$957$	−10.0734	−	2.69915i	−0.325625	−	0.0872510i
$958$			6.29227i			0.203294i
$959$	38.6237	−	35.2583i	1.24723	−	1.13855i
$960$	11.1524	+	11.1524i	0.359942	+	0.359942i
$961$	43.6906	−	25.2248i	1.40938	−	0.813703i
$962$	2.29902	−	2.43320i	0.0741235	−	0.0784495i
$963$	−5.10563	+	8.84320i	−0.164527	+	0.284968i
$964$	−5.18234	+	19.3408i	−0.166912	+	0.622924i
$965$			37.4476i			1.20548i
$966$	3.80201	−	0.835362i	0.122328	−	0.0268773i
$967$	−26.8293	+	26.8293i	−0.862771	+	0.862771i	−0.991659	−	0.128888i	$-0.958859\pi$
$967$	−26.8293	+	26.8293i	−0.862771	+	0.862771i	0.128888	+	0.991659i	$0.458859\pi$
$968$	−8.43715	−	2.26073i	−0.271180	−	0.0726626i
$969$	−3.27802	−	12.2337i	−0.105305	−	0.393005i
$970$	4.53197	−	1.21434i	0.145513	−	0.0389900i
$971$	44.4611	−	25.6696i	1.42683	−	0.823778i	0.429957	−	0.902849i	$-0.358529\pi$
$971$	44.4611	−	25.6696i	1.42683	−	0.823778i	0.996869	+	0.0790713i	$0.0251955\pi$
$972$	1.92585			0.0617715
$973$	−10.8386	−	20.9170i	−0.347470	−	0.670570i
$974$			8.50140i			0.272402i
$975$	1.35917	+	4.55225i	0.0435283	+	0.145789i
$976$	3.36051	+	1.94019i	0.107567	+	0.0621040i
$977$	−8.77076	−	32.7329i	−0.280601	−	1.04722i	−0.951994	−	0.306117i	$-0.900970\pi$
$977$	−8.77076	−	32.7329i	−0.280601	−	1.04722i	0.671392	−	0.741102i	$-0.265697\pi$
$978$	3.81683	−	2.20365i	0.122049	−	0.0704648i
$979$	−21.1528			−0.676045
$980$	−5.75796	−	33.3914i	−0.183931	−	1.06665i
$981$	2.43191	−	2.43191i	0.0776450	−	0.0776450i
$982$	1.67080	−	6.23550i	0.0533173	−	0.198983i
$983$	2.71287	+	10.1246i	0.0865271	+	0.322923i	0.995599	−	0.0937158i	$-0.0298745\pi$
$983$	2.71287	+	10.1246i	0.0865271	+	0.322923i	−0.909072	+	0.416639i	$0.863208\pi$
$984$	−0.576207	+	0.998019i	−0.0183688	+	0.0318157i
$985$	29.9046	+	51.7962i	0.952838	+	1.65036i
$986$	3.83941	−	3.83941i	0.122272	−	0.122272i
$987$	−16.3879	−	5.20109i	−0.521631	−	0.165552i
$988$	−23.2844	+	14.3381i	−0.740774	+	0.456157i
$989$	15.1862	+	26.3033i	0.482894	+	0.836396i
$990$	−1.11208	+	0.297982i	−0.0353444	+	0.00947050i
$991$	0.445132	−	0.770992i	0.0141401	−	0.0244914i	−0.858869	−	0.512196i	$-0.828832\pi$
$991$	0.445132	−	0.770992i	0.0141401	−	0.0244914i	0.873009	+	0.487704i	$0.162166\pi$
$992$	14.0234	+	24.2892i	0.445243	+	0.771184i
$993$	−12.7744	−	12.7744i	−0.405383	−	0.405383i
$994$	−3.31764	+	5.18603i	−0.105229	+	0.164491i
$995$	22.6877	+	22.6877i	0.719247	+	0.719247i
$996$	7.08274	−	26.4332i	0.224425	−	0.837567i
$997$	−24.4661	−	14.1255i	−0.774850	−	0.447360i	0.0597519	−	0.998213i	$-0.480969\pi$
$997$	−24.4661	−	14.1255i	−0.774850	−	0.447360i	−0.834602	+	0.550853i	$0.814302\pi$
$998$	−8.86521	−	5.11833i	−0.280623	−	0.162018i
$999$	3.29329	+	0.882434i	0.104195	+	0.0279190i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bz.b.31.4	yes	36
3.2	odd	2		819.2.fn.g.577.6		36
7.5	odd	6		273.2.bz.a.187.6	yes	36
13.8	odd	4		273.2.bz.a.73.6	✓	36
21.5	even	6		819.2.fn.f.460.4		36
39.8	even	4		819.2.fn.f.73.4		36
91.47	even	12	inner	273.2.bz.b.229.4	yes	36
273.47	odd	12		819.2.fn.g.775.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bz.a.73.6	✓	36	13.8	odd	4
273.2.bz.a.187.6	yes	36	7.5	odd	6
273.2.bz.b.31.4	yes	36	1.1	even	1	trivial
273.2.bz.b.229.4	yes	36	91.47	even	12	inner
819.2.fn.f.73.4		36	39.8	even	4
819.2.fn.f.460.4		36	21.5	even	6
819.2.fn.g.577.6		36	3.2	odd	2
819.2.fn.g.775.6		36	273.47	odd	12

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.263033 - 0.0704795i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.66783 - 0.962923i) q^{4} +(-0.650540 + 2.42785i) q^{5} +(-0.192554 - 0.192554i) q^{6} +(-2.34911 + 1.21724i) q^{7} +(0.755936 + 0.755936i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.263033 - 0.0704795i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.66783 - 0.962923i) q^{4} +(-0.650540 + 2.42785i) q^{5} +(-0.192554 - 0.192554i) q^{6} +(-2.34911 + 1.21724i) q^{7} +(0.755936 + 0.755936i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.342227 - 0.592755i) q^{10} +(-1.62478 + 0.435358i) q^{11} +(-0.962923 - 1.66783i) q^{12} +(-3.50774 - 0.834105i) q^{13} +(0.703685 - 0.154611i) q^{14} +(-1.77731 + 1.77731i) q^{15} +(1.78029 + 3.08355i) q^{16} +(-1.60806 + 2.78524i) q^{17} +(-0.0704795 - 0.263033i) q^{18} +(-1.01925 + 3.80388i) q^{19} +(3.42282 - 3.42282i) q^{20} +(-2.64301 - 0.120393i) q^{21} +0.458054 q^{22} +(4.67914 - 2.70150i) q^{23} +(0.276692 + 1.03263i) q^{24} +(-1.14111 - 0.658821i) q^{25} +(0.863866 + 0.466621i) q^{26} +1.00000i q^{27} +(5.09003 + 0.231859i) q^{28} +6.19984 q^{29} +(0.592755 - 0.342227i) q^{30} +(-8.71743 + 2.33583i) q^{31} +(-0.804331 - 3.00181i) q^{32} +(-1.62478 - 0.435358i) q^{33} +(0.619276 - 0.619276i) q^{34} +(-1.42709 - 6.49515i) q^{35} -1.92585i q^{36} +(0.882434 - 3.29329i) q^{37} +(0.536191 - 0.928711i) q^{38} +(-2.62074 - 2.47623i) q^{39} +(-2.32706 + 1.34353i) q^{40} +(0.762243 + 0.762243i) q^{41} +(0.686714 + 0.217946i) q^{42} +5.62140i q^{43} +(3.12907 + 0.838432i) q^{44} +(-2.42785 + 0.650540i) q^{45} +(-1.42117 + 0.380801i) q^{46} +(6.27707 + 1.68194i) q^{47} +3.56058i q^{48} +(4.03664 - 5.71887i) q^{49} +(0.253717 + 0.253717i) q^{50} +(-2.78524 + 1.60806i) q^{51} +(5.04715 + 4.76883i) q^{52} +(0.358264 - 0.620531i) q^{53} +(0.0704795 - 0.263033i) q^{54} -4.22793i q^{55} +(-2.69593 - 0.855621i) q^{56} +(-2.78463 + 2.78463i) q^{57} +(-1.63076 - 0.436962i) q^{58} +(-2.53194 - 9.44933i) q^{59} +(4.67566 - 1.25284i) q^{60} +(0.943810 - 0.544909i) q^{61} +2.45760 q^{62} +(-2.22872 - 1.42577i) q^{63} -6.27489i q^{64} +(4.30700 - 7.97365i) q^{65} +(0.396686 + 0.229027i) q^{66} +(0.569411 + 2.12507i) q^{67} +(5.36395 - 3.09688i) q^{68} +5.40300 q^{69} +(-0.0824036 + 1.80902i) q^{70} +(-6.04224 + 6.04224i) q^{71} +(-0.276692 + 1.03263i) q^{72} +(1.06732 + 3.98330i) q^{73} +(-0.464219 + 0.804051i) q^{74} +(-0.658821 - 1.14111i) q^{75} +(5.36278 - 5.36278i) q^{76} +(3.28684 - 3.00045i) q^{77} +(0.514819 + 0.836039i) q^{78} +(-3.96221 - 6.86275i) q^{79} +(-8.64453 + 2.31630i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.146773 - 0.254218i) q^{82} +(10.0477 + 10.0477i) q^{83} +(4.29217 + 2.74581i) q^{84} +(-5.71604 - 5.71604i) q^{85} +(0.396194 - 1.47862i) q^{86} +(5.36922 + 3.09992i) q^{87} +(-1.55733 - 0.899125i) q^{88} +(12.1468 + 3.25472i) q^{89} +0.684454 q^{90} +(9.25539 - 2.31037i) q^{91} -10.4053 q^{92} +(-8.71743 - 2.33583i) q^{93} +(-1.53254 - 0.884810i) q^{94} +(-8.57218 - 4.94915i) q^{95} +(0.804331 - 3.00181i) q^{96} +(4.84712 + 4.84712i) q^{97} +(-1.46484 + 1.21975i) q^{98} +(-1.18942 - 1.18942i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} + 18 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 + 18 * q^9	\( 36 q + 4 q^{7} + 18 q^{9} + 4 q^{11} + 16 q^{12} - 36 q^{14} + 12 q^{16} - 4 q^{17} - 12 q^{19} - 44 q^{20} + 6 q^{21} - 8 q^{22} + 12 q^{23} - 18 q^{24} + 48 q^{25} - 28 q^{26} + 12 q^{28} - 16 q^{29} - 56 q^{32} + 4 q^{33} + 48 q^{34} + 8 q^{35} + 22 q^{37} - 16 q^{38} - 8 q^{39} + 60 q^{40} + 32 q^{41} + 12 q^{42} + 4 q^{44} - 44 q^{46} - 14 q^{47} - 6 q^{49} - 68 q^{50} + 12 q^{51} - 82 q^{52} - 8 q^{53} + 8 q^{56} - 6 q^{57} - 84 q^{58} + 70 q^{59} + 2 q^{60} + 36 q^{61} - 48 q^{62} + 2 q^{63} - 8 q^{65} + 38 q^{67} + 36 q^{68} + 8 q^{69} - 40 q^{70} - 36 q^{71} + 18 q^{72} - 46 q^{73} + 40 q^{74} - 10 q^{75} + 60 q^{76} - 60 q^{77} + 32 q^{78} - 38 q^{80} - 18 q^{81} - 24 q^{83} + 38 q^{84} + 44 q^{85} - 24 q^{86} + 36 q^{87} - 168 q^{88} + 38 q^{89} - 14 q^{91} - 40 q^{92} + 56 q^{96} - 36 q^{97} + 58 q^{98} + 8 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 + 18 * q^9 + 4 * q^11 + 16 * q^12 - 36 * q^14 + 12 * q^16 - 4 * q^17 - 12 * q^19 - 44 * q^20 + 6 * q^21 - 8 * q^22 + 12 * q^23 - 18 * q^24 + 48 * q^25 - 28 * q^26 + 12 * q^28 - 16 * q^29 - 56 * q^32 + 4 * q^33 + 48 * q^34 + 8 * q^35 + 22 * q^37 - 16 * q^38 - 8 * q^39 + 60 * q^40 + 32 * q^41 + 12 * q^42 + 4 * q^44 - 44 * q^46 - 14 * q^47 - 6 * q^49 - 68 * q^50 + 12 * q^51 - 82 * q^52 - 8 * q^53 + 8 * q^56 - 6 * q^57 - 84 * q^58 + 70 * q^59 + 2 * q^60 + 36 * q^61 - 48 * q^62 + 2 * q^63 - 8 * q^65 + 38 * q^67 + 36 * q^68 + 8 * q^69 - 40 * q^70 - 36 * q^71 + 18 * q^72 - 46 * q^73 + 40 * q^74 - 10 * q^75 + 60 * q^76 - 60 * q^77 + 32 * q^78 - 38 * q^80 - 18 * q^81 - 24 * q^83 + 38 * q^84 + 44 * q^85 - 24 * q^86 + 36 * q^87 - 168 * q^88 + 38 * q^89 - 14 * q^91 - 40 * q^92 + 56 * q^96 - 36 * q^97 + 58 * q^98 + 8 * q^99

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