LMFDB - Embedded newform 315.2.be.c.236.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(236,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 0, 5]))

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

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

chi := DirichletCharacter("315.236");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.be (of order $6$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			236.9
Character	$\chi$	$=$	315.236
Dual form			315.2.be.c.311.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.343770 - 0.198476i) q^{2} +(-1.65197 + 0.520559i) q^{3} +(-0.921215 + 1.59559i) q^{4} -1.00000 q^{5} +(-0.464581 + 0.506829i) q^{6} +(-0.324456 - 2.62578i) q^{7} +1.52526i q^{8} +(2.45804 - 1.71990i) q^{9} +O(q^{10})$	\(q+(0.343770 - 0.198476i) q^{2} +(-1.65197 + 0.520559i) q^{3} +(-0.921215 + 1.59559i) q^{4} -1.00000 q^{5} +(-0.464581 + 0.506829i) q^{6} +(-0.324456 - 2.62578i) q^{7} +1.52526i q^{8} +(2.45804 - 1.71990i) q^{9} +(-0.343770 + 0.198476i) q^{10} -2.24205i q^{11} +(0.691225 - 3.11542i) q^{12} +(-3.23312 + 1.86664i) q^{13} +(-0.632692 - 0.838268i) q^{14} +(1.65197 - 0.520559i) q^{15} +(-1.53970 - 2.66684i) q^{16} +(-3.44490 - 5.96674i) q^{17} +(0.503641 - 1.07911i) q^{18} +(-1.97496 - 1.14024i) q^{19} +(0.921215 - 1.59559i) q^{20} +(1.90287 + 4.16882i) q^{21} +(-0.444993 - 0.770751i) q^{22} -5.41741i q^{23} +(-0.793986 - 2.51969i) q^{24} +1.00000 q^{25} +(-0.740967 + 1.28339i) q^{26} +(-3.16531 + 4.12078i) q^{27} +(4.48857 + 1.90121i) q^{28} +(1.44991 + 0.837109i) q^{29} +(0.464581 - 0.506829i) q^{30} +(2.61229 + 1.50821i) q^{31} +(-3.70043 - 2.13644i) q^{32} +(1.16712 + 3.70382i) q^{33} +(-2.36850 - 1.36746i) q^{34} +(0.324456 + 2.62578i) q^{35} +(0.479874 + 5.50642i) q^{36} +(-3.18746 + 5.52084i) q^{37} -0.905242 q^{38} +(4.36934 - 4.76668i) q^{39} -1.52526i q^{40} +(1.57421 + 2.72662i) q^{41} +(1.48156 + 1.05544i) q^{42} +(-3.90758 + 6.76813i) q^{43} +(3.57740 + 2.06541i) q^{44} +(-2.45804 + 1.71990i) q^{45} +(-1.07522 - 1.86234i) q^{46} +(-3.33040 - 5.76842i) q^{47} +(3.93180 + 3.60405i) q^{48} +(-6.78946 + 1.70390i) q^{49} +(0.343770 - 0.198476i) q^{50} +(8.79692 + 8.06363i) q^{51} -6.87832i q^{52} +(3.20390 - 1.84977i) q^{53} +(-0.270263 + 2.04484i) q^{54} +2.24205i q^{55} +(4.00499 - 0.494879i) q^{56} +(3.85615 + 0.855570i) q^{57} +0.664583 q^{58} +(-1.61897 + 2.80414i) q^{59} +(-0.691225 + 3.11542i) q^{60} +(-9.75340 + 5.63113i) q^{61} +1.19737 q^{62} +(-5.31360 - 5.89624i) q^{63} +4.46268 q^{64} +(3.23312 - 1.86664i) q^{65} +(1.13634 + 1.04162i) q^{66} +(6.08304 - 10.5361i) q^{67} +12.6940 q^{68} +(2.82008 + 8.94942i) q^{69} +(0.632692 + 0.838268i) q^{70} +3.37456i q^{71} +(2.62329 + 3.74914i) q^{72} +(-10.3660 + 5.98483i) q^{73} +2.53053i q^{74} +(-1.65197 + 0.520559i) q^{75} +(3.63872 - 2.10082i) q^{76} +(-5.88714 + 0.727448i) q^{77} +(0.555977 - 2.50585i) q^{78} +(-2.62135 - 4.54031i) q^{79} +(1.53970 + 2.66684i) q^{80} +(3.08390 - 8.45515i) q^{81} +(1.08234 + 0.624887i) q^{82} +(8.61040 - 14.9136i) q^{83} +(-8.40469 - 0.804187i) q^{84} +(3.44490 + 5.96674i) q^{85} +3.10224i q^{86} +(-2.83099 - 0.628116i) q^{87} +3.41971 q^{88} +(2.58071 - 4.46992i) q^{89} +(-0.503641 + 1.07911i) q^{90} +(5.95041 + 7.88383i) q^{91} +(8.64397 + 4.99060i) q^{92} +(-5.10055 - 1.13167i) q^{93} +(-2.28978 - 1.32201i) q^{94} +(1.97496 + 1.14024i) q^{95} +(7.22516 + 1.60306i) q^{96} +(-4.94694 - 2.85612i) q^{97} +(-1.99583 + 1.93329i) q^{98} +(-3.85611 - 5.51105i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	$ 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) $ 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.343770	−	0.198476i	0.243082	−	0.140343i	−0.373510	−	0.927626i	$-0.621846\pi$
$2$	0.343770	−	0.198476i	0.243082	−	0.140343i	0.616592	+	0.787283i	$0.288513\pi$
$3$	−1.65197	+	0.520559i	−0.953768	+	0.300545i
$3$	−1.65197	+	0.520559i	−0.953768	+	0.300545i
$4$	−0.921215	+	1.59559i	−0.460607	+	0.797795i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.464581	+	0.506829i	−0.189664	+	0.206912i
$7$	−0.324456	−	2.62578i	−0.122633	−	0.992452i
$7$	−0.324456	−	2.62578i	−0.122633	−	0.992452i
$8$			1.52526i			0.539260i
$9$	2.45804	−	1.71990i	0.819346	−	0.573300i
$10$	−0.343770	+	0.198476i	−0.108710	+	0.0627635i
$11$		−	2.24205i		−	0.676005i	−0.941145	−	0.338002i	$-0.890249\pi$
$11$		−	2.24205i		−	0.676005i	0.941145	−	0.338002i	$-0.109751\pi$
$12$	0.691225	−	3.11542i	0.199539	−	0.899345i
$13$	−3.23312	+	1.86664i	−0.896707	+	0.517714i	−0.876130	−	0.482074i	$-0.839884\pi$
$13$	−3.23312	+	1.86664i	−0.896707	+	0.517714i	−0.0205768	+	0.999788i	$0.506550\pi$
$14$	−0.632692	−	0.838268i	−0.169094	−	0.224037i
$15$	1.65197	−	0.520559i	0.426538	−	0.134408i
$16$	−1.53970	−	2.66684i	−0.384926	−	0.666711i
$17$	−3.44490	−	5.96674i	−0.835511	−	1.44715i	−0.893614	−	0.448836i	$-0.851839\pi$
$17$	−3.44490	−	5.96674i	−0.835511	−	1.44715i	0.0581034	−	0.998311i	$-0.481495\pi$
$18$	0.503641	−	1.07911i	0.118709	−	0.254349i
$19$	−1.97496	−	1.14024i	−0.453087	−	0.261590i	0.256046	−	0.966665i	$-0.417580\pi$
$19$	−1.97496	−	1.14024i	−0.453087	−	0.261590i	−0.709133	+	0.705075i	$0.750913\pi$
$20$	0.921215	−	1.59559i	0.205990	−	0.356785i
$21$	1.90287	+	4.16882i	0.415239	+	0.909712i
$22$	−0.444993	−	0.770751i	−0.0948728	−	0.164325i
$23$		−	5.41741i		−	1.12961i	−0.825225	−	0.564804i	$-0.808952\pi$
$23$		−	5.41741i		−	1.12961i	0.825225	−	0.564804i	$-0.191048\pi$
$24$	−0.793986	−	2.51969i	−0.162072	−	0.514329i
$25$	1.00000			0.200000
$26$	−0.740967	+	1.28339i	−0.145316	+	0.251694i
$27$	−3.16531	+	4.12078i	−0.609164	+	0.793045i
$28$	4.48857	+	1.90121i	0.848259	+	0.359295i
$29$	1.44991	+	0.837109i	0.269242	+	0.155447i	0.628543	−	0.777775i	$-0.283651\pi$
$29$	1.44991	+	0.837109i	0.269242	+	0.155447i	−0.359301	+	0.933222i	$0.616985\pi$
$30$	0.464581	−	0.506829i	0.0848205	−	0.0925339i
$31$	2.61229	+	1.50821i	0.469181	+	0.270882i	0.715897	−	0.698206i	$-0.246018\pi$
$31$	2.61229	+	1.50821i	0.469181	+	0.270882i	−0.246716	+	0.969088i	$0.579351\pi$
$32$	−3.70043	−	2.13644i	−0.654150	−	0.377674i
$33$	1.16712	+	3.70382i	0.203170	+	0.644752i
$34$	−2.36850	−	1.36746i	−0.406195	−	0.234517i
$35$	0.324456	+	2.62578i	0.0548431	+	0.443838i
$36$	0.479874	+	5.50642i	0.0799790	+	0.917736i
$37$	−3.18746	+	5.52084i	−0.524015	+	0.907621i	0.475594	+	0.879665i	$0.342233\pi$
$37$	−3.18746	+	5.52084i	−0.524015	+	0.907621i	−0.999609	+	0.0279559i	$0.991100\pi$
$38$	−0.905242			−0.146850
$39$	4.36934	−	4.76668i	0.699654	−	0.763280i
$40$		−	1.52526i		−	0.241164i
$41$	1.57421	+	2.72662i	0.245851	+	0.425827i	0.962371	−	0.271741i	$-0.0875993\pi$
$41$	1.57421	+	2.72662i	0.245851	+	0.425827i	−0.716519	+	0.697567i	$0.754266\pi$
$42$	1.48156	+	1.05544i	0.228609	+	0.162859i
$43$	−3.90758	+	6.76813i	−0.595900	+	1.03213i	0.397519	+	0.917594i	$0.369871\pi$
$43$	−3.90758	+	6.76813i	−0.595900	+	1.03213i	−0.993419	+	0.114536i	$0.963462\pi$
$44$	3.57740	+	2.06541i	0.539314	+	0.311373i
$45$	−2.45804	+	1.71990i	−0.366423	+	0.256387i
$46$	−1.07522	−	1.86234i	−0.158533	−	0.274587i
$47$	−3.33040	−	5.76842i	−0.485789	−	0.841411i	0.514078	−	0.857744i	$-0.328134\pi$
$47$	−3.33040	−	5.76842i	−0.485789	−	0.841411i	−0.999867	+	0.0163325i	$0.994801\pi$
$48$	3.93180	+	3.60405i	0.567506	+	0.520200i
$49$	−6.78946	+	1.70390i	−0.969922	+	0.243415i
$50$	0.343770	−	0.198476i	0.0486164	−	0.0280687i
$51$	8.79692	+	8.06363i	1.23182	+	1.12913i
$52$		−	6.87832i		−	0.953852i
$53$	3.20390	−	1.84977i	0.440090	−	0.254086i	−0.263546	−	0.964647i	$-0.584892\pi$
$53$	3.20390	−	1.84977i	0.440090	−	0.254086i	0.703636	+	0.710561i	$0.251559\pi$
$54$	−0.270263	+	2.04484i	−0.0367781	+	0.278267i
$55$			2.24205i			0.302319i
$56$	4.00499	−	0.494879i	0.535190	−	0.0661310i
$57$	3.85615	+	0.855570i	0.510759	+	0.113323i
$58$	0.664583			0.0872640
$59$	−1.61897	+	2.80414i	−0.210772	+	0.365068i	−0.951956	−	0.306234i	$-0.900931\pi$
$59$	−1.61897	+	2.80414i	−0.210772	+	0.365068i	0.741184	+	0.671302i	$0.234264\pi$
$60$	−0.691225	+	3.11542i	−0.0892367	+	0.402199i
$61$	−9.75340	+	5.63113i	−1.24879	+	0.720992i	−0.970869	−	0.239611i	$-0.922980\pi$
$61$	−9.75340	+	5.63113i	−1.24879	+	0.720992i	−0.277926	+	0.960603i	$0.589647\pi$
$62$	1.19737			0.152066
$63$	−5.31360	−	5.89624i	−0.669451	−	0.742856i
$64$	4.46268			0.557836
$65$	3.23312	−	1.86664i	0.401020	−	0.231529i
$66$	1.13634	+	1.04162i	0.139874	+	0.128214i
$67$	6.08304	−	10.5361i	0.743162	−	1.28719i	−0.207887	−	0.978153i	$-0.566659\pi$
$67$	6.08304	−	10.5361i	0.743162	−	1.28719i	0.951049	−	0.309041i	$-0.100008\pi$
$68$	12.6940			1.53937
$69$	2.82008	+	8.94942i	0.339498	+	1.07738i
$70$	0.632692	+	0.838268i	0.0756211	+	0.100192i
$71$			3.37456i			0.400486i	0.979746	+	0.200243i	$0.0641732\pi$
$71$			3.37456i			0.400486i	−0.979746	+	0.200243i	$0.935827\pi$
$72$	2.62329	+	3.74914i	0.309157	+	0.441840i
$73$	−10.3660	+	5.98483i	−1.21325	+	0.700471i	−0.963466	−	0.267830i	$-0.913694\pi$
$73$	−10.3660	+	5.98483i	−1.21325	+	0.700471i	−0.249786	+	0.968301i	$0.580360\pi$
$74$			2.53053i			0.294168i
$75$	−1.65197	+	0.520559i	−0.190754	+	0.0601089i
$76$	3.63872	−	2.10082i	0.417390	−	0.240980i
$77$	−5.88714	+	0.727448i	−0.670902	+	0.0829004i
$78$	0.555977	−	2.50585i	0.0629520	−	0.283731i
$79$	−2.62135	−	4.54031i	−0.294925	−	0.510825i	0.680043	−	0.733173i	$-0.261961\pi$
$79$	−2.62135	−	4.54031i	−0.294925	−	0.510825i	−0.974967	+	0.222348i	$0.928628\pi$
$80$	1.53970	+	2.66684i	0.172144	+	0.298162i
$81$	3.08390	−	8.45515i	0.342655	−	0.939461i
$82$	1.08234	+	0.624887i	0.119524	+	0.0690072i
$83$	8.61040	−	14.9136i	0.945114	−	1.63699i	0.189591	−	0.981863i	$-0.439284\pi$
$83$	8.61040	−	14.9136i	0.945114	−	1.63699i	0.755523	−	0.655122i	$-0.227383\pi$
$84$	−8.40469	−	0.804187i	−0.917027	−	0.0877440i
$85$	3.44490	+	5.96674i	0.373652	+	0.647184i
$86$			3.10224i			0.334523i
$87$	−2.83099	−	0.628116i	−0.303514	−	0.0673412i
$88$	3.41971			0.364542
$89$	2.58071	−	4.46992i	0.273554	−	0.473810i	−0.696215	−	0.717833i	$-0.745134\pi$
$89$	2.58071	−	4.46992i	0.273554	−	0.473810i	0.969769	+	0.244023i	$0.0784673\pi$
$90$	−0.503641	+	1.07911i	−0.0530885	+	0.113748i
$91$	5.95041	+	7.88383i	0.623772	+	0.826450i
$92$	8.64397	+	4.99060i	0.901196	+	0.520306i
$93$	−5.10055	−	1.13167i	−0.528902	−	0.117349i
$94$	−2.28978	−	1.32201i	−0.236173	−	0.136355i
$95$	1.97496	+	1.14024i	0.202627	+	0.116986i
$96$	7.22516	+	1.60306i	0.737415	+	0.163612i
$97$	−4.94694	−	2.85612i	−0.502286	−	0.289995i	0.227371	−	0.973808i	$-0.426987\pi$
$97$	−4.94694	−	2.85612i	−0.502286	−	0.289995i	−0.729657	+	0.683813i	$0.760320\pi$
$98$	−1.99583	+	1.93329i	−0.201609	+	0.195292i
$99$	−3.85611	−	5.51105i	−0.387553	−	0.553882i
$100$	−0.921215	+	1.59559i	−0.0921215	+	0.159559i
$101$	−9.22357			−0.917780			−0.458890	−	0.888493i	$-0.651753\pi$
$101$	−9.22357			−0.917780			−0.458890	+	0.888493i	$0.651753\pi$
$102$	4.62455	+	1.02606i	0.457899	+	0.101595i
$103$		−	6.67195i		−	0.657406i	−0.944433	−	0.328703i	$-0.893388\pi$
$103$		−	6.67195i		−	0.657406i	0.944433	−	0.328703i	$-0.106612\pi$
$104$	−2.84711	−	4.93135i	−0.279182	−	0.483558i
$105$	−1.90287	−	4.16882i	−0.185701	−	0.406836i
$106$	0.734270	−	1.27179i	0.0713186	−	0.123527i
$107$	−10.2395	−	5.91179i	−0.989892	−	0.571514i	−0.0846500	−	0.996411i	$-0.526977\pi$
$107$	−10.2395	−	5.91179i	−0.989892	−	0.571514i	−0.905242	+	0.424896i	$0.860311\pi$
$108$	−3.65915	−	8.84666i	−0.352102	−	0.851270i
$109$	5.34376	+	9.25567i	0.511840	+	0.886533i	0.999906	+	0.0137259i	$0.00436922\pi$
$109$	5.34376	+	9.25567i	0.511840	+	0.886533i	−0.488066	+	0.872807i	$0.662297\pi$
$110$	0.444993	+	0.770751i	0.0424284	+	0.0734882i
$111$	2.39168	−	10.7795i	0.227008	−	1.02315i
$112$	−6.50298	+	4.90820i	−0.614474	+	0.463781i
$113$	−9.43655	+	5.44820i	−0.887716	+	0.512523i	−0.873195	−	0.487371i	$-0.837956\pi$
$113$	−9.43655	+	5.44820i	−0.887716	+	0.512523i	−0.0145214	+	0.999895i	$0.504622\pi$
$114$	1.49544	−	0.471231i	0.140060	−	0.0441349i
$115$			5.41741i			0.505176i
$116$	−2.67137	+	1.54231i	−0.248030	+	0.143200i
$117$	−4.73670	+	10.1489i	−0.437908	+	0.938269i
$118$			1.28531i			0.118322i
$119$	−14.5496	+	10.9815i	−1.33376	+	1.00667i
$120$	0.793986	+	2.51969i	0.0724806	+	0.230015i
$121$	5.97319			0.543018
$122$	−2.23528	+	3.87162i	−0.202373	+	0.350520i
$123$	−4.01993	−	3.68484i	−0.362465	−	0.332250i
$124$	−4.81296	+	2.77877i	−0.432217	+	0.249540i
$125$	−1.00000			−0.0894427
$126$	−2.99692	−	0.972328i	−0.266987	−	0.0866219i
$127$	15.0598			1.33634			0.668172	−	0.744007i	$-0.267077\pi$
$127$	15.0598			1.33634			0.668172	+	0.744007i	$0.267077\pi$
$128$	8.93500	−	5.15862i	0.789750	−	0.455962i
$129$	2.93201	−	13.2149i	0.258149	−	1.16351i
$130$	0.740967	−	1.28339i	0.0649871	−	0.112561i
$131$	5.56864			0.486535			0.243267	−	0.969959i	$-0.421781\pi$
$131$	5.56864			0.486535			0.243267	+	0.969959i	$0.421781\pi$
$132$	−6.98494	−	1.54976i	−0.607961	−	0.134890i
$133$	−2.35324	+	5.55577i	−0.204052	+	0.481746i
$134$		−	4.82934i		−	0.417192i
$135$	3.16531	−	4.12078i	0.272426	−	0.354660i
$136$	9.10081	−	5.25436i	0.780388	−	0.450557i
$137$			9.25916i			0.791063i	0.918452	+	0.395532i	$0.129440\pi$
$137$			9.25916i			0.791063i	−0.918452	+	0.395532i	$0.870560\pi$
$138$	2.74570	+	2.51682i	0.233729	+	0.214246i
$139$	16.7437	−	9.66696i	1.42018	−	0.819941i	0.423865	−	0.905725i	$-0.360673\pi$
$139$	16.7437	−	9.66696i	1.42018	−	0.819941i	0.996314	+	0.0857844i	$0.0273396\pi$
$140$	−4.48857	−	1.90121i	−0.379353	−	0.160682i
$141$	8.50454	+	7.79562i	0.716211	+	0.656510i
$142$	0.669767	+	1.16007i	0.0562056	+	0.0973510i
$143$	4.18512	+	7.24884i	0.349977	+	0.606178i
$144$	−8.37135	−	3.90707i	−0.697613	−	0.325589i
$145$	−1.44991	−	0.837109i	−0.120409	−	0.0695181i
$146$	−2.37569	+	4.11481i	−0.196613	+	0.340544i
$147$	10.3290	−	6.34911i	0.851924	−	0.523666i
$148$	−5.87267	−	10.1718i	−0.482730	−	0.836114i
$149$		−	14.7553i		−	1.20880i	−0.796681	−	0.604400i	$-0.793413\pi$
$149$		−	14.7553i		−	1.20880i	0.796681	−	0.604400i	$-0.206587\pi$
$150$	−0.464581	+	0.506829i	−0.0379329	+	0.0413824i
$151$	−5.95708			−0.484781			−0.242390	−	0.970179i	$-0.577931\pi$
$151$	−5.95708			−0.484781			−0.242390	+	0.970179i	$0.577931\pi$
$152$	1.73916	−	3.01232i	0.141065	−	0.244331i
$153$	−18.7299	−	8.74159i	−1.51422	−	0.706716i
$154$	−1.87944	+	1.41853i	−0.151450	+	0.114308i
$155$	−2.61229	−	1.50821i	−0.209824	−	0.121142i
$156$	3.58057	+	11.3628i	0.286675	+	0.909753i
$157$	1.70085	+	0.981984i	0.135742	+	0.0783708i	0.566333	−	0.824176i	$-0.308362\pi$
$157$	1.70085	+	0.981984i	0.135742	+	0.0783708i	−0.430591	+	0.902547i	$0.641695\pi$
$158$	−1.80228	−	1.04055i	−0.143382	−	0.0827815i
$159$	−4.32985	+	4.72360i	−0.343379	+	0.374606i
$160$	3.70043	+	2.13644i	0.292545	+	0.168901i
$161$	−14.2249	+	1.75771i	−1.12108	+	0.138527i
$162$	−0.617990	−	3.51870i	−0.0485539	−	0.276456i
$163$	−9.54167	+	16.5267i	−0.747361	+	1.29447i	0.201722	+	0.979443i	$0.435346\pi$
$163$	−9.54167	+	16.5267i	−0.747361	+	1.29447i	−0.949083	+	0.315025i	$0.897987\pi$
$164$	−5.80076			−0.452963
$165$	−1.16712	−	3.70382i	−0.0908602	−	0.288342i
$166$		−	6.83582i		−	0.530562i
$167$	6.27847	+	10.8746i	0.485843	+	0.841504i	0.999868	−	0.0162712i	$-0.00517951\pi$
$167$	6.27847	+	10.8746i	0.485843	+	0.841504i	−0.514025	+	0.857775i	$0.671846\pi$
$168$	−6.35853	+	2.90236i	−0.490571	+	0.223922i
$169$	0.468727	−	0.811859i	0.0360559	−	0.0624507i
$170$	2.36850	+	1.36746i	0.181656	+	0.104879i
$171$	−6.81563	+	0.593969i	−0.521204	+	0.0454219i
$172$	−7.19944	−	12.4698i	−0.548952	−	0.950813i
$173$	9.92143	+	17.1844i	0.754313	+	1.30651i	0.945715	+	0.324996i	$0.105363\pi$
$173$	9.92143	+	17.1844i	0.754313	+	1.30651i	−0.191403	+	0.981512i	$0.561304\pi$
$174$	−1.09787	+	0.345954i	−0.0832296	+	0.0262267i
$175$	−0.324456	−	2.62578i	−0.0245266	−	0.198490i
$176$	−5.97921	+	3.45210i	−0.450700	+	0.260212i
$177$	1.21478	−	5.47514i	0.0913085	−	0.411537i
$178$		−	2.04883i		−	0.153566i
$179$	9.56630	−	5.52310i	0.715019	−	0.412816i	−0.0978979	−	0.995196i	$-0.531212\pi$
$179$	9.56630	−	5.52310i	0.715019	−	0.412816i	0.812916	+	0.582380i	$0.197879\pi$
$180$	−0.479874	−	5.50642i	−0.0357677	−	0.410424i
$181$		−	18.9731i		−	1.41026i	−0.709078	−	0.705130i	$-0.750889\pi$
$181$		−	18.9731i		−	1.41026i	0.709078	−	0.705130i	$-0.249111\pi$
$182$	3.61032	+	1.52921i	0.267615	+	0.113353i
$183$	13.1810	−	14.3797i	0.974370	−	1.06298i
$184$	8.26294			0.609152
$185$	3.18746	−	5.52084i	0.234347	−	0.405900i
$186$	−1.97802	+	0.623301i	−0.145036	+	0.0457026i
$187$	−13.3778	+	7.72365i	−0.978278	+	0.564809i
$188$	12.2721			0.895032
$189$	11.8473	+	6.97439i	0.861762	+	0.507312i
$190$	0.905242			0.0656732
$191$	−14.0694	+	8.12295i	−1.01802	+	0.587756i	−0.913531	−	0.406770i	$-0.866655\pi$
$191$	−14.0694	+	8.12295i	−1.01802	+	0.587756i	−0.104492	+	0.994526i	$0.533322\pi$
$192$	−7.37224	+	2.32309i	−0.532046	+	0.167654i
$193$	4.35118	−	7.53646i	0.313204	−	0.542486i	−0.665850	−	0.746086i	$-0.731931\pi$
$193$	4.35118	−	7.53646i	0.313204	−	0.542486i	0.979054	+	0.203600i	$0.0652641\pi$
$194$	−2.26748			−0.162796
$195$	−4.36934	+	4.76668i	−0.312895	+	0.341349i
$196$	3.53582	−	12.4029i	0.252558	−	0.885918i
$197$		−	1.95033i		−	0.138955i	−0.997584	−	0.0694775i	$-0.977867\pi$
$197$		−	1.95033i		−	0.138955i	0.997584	−	0.0694775i	$-0.0221332\pi$
$198$	−2.41942	−	1.12919i	−0.171941	−	0.0802481i
$199$	16.7115	−	9.64841i	1.18465	−	0.683958i	0.227564	−	0.973763i	$-0.426924\pi$
$199$	16.7115	−	9.64841i	1.18465	−	0.683958i	0.957086	+	0.289805i	$0.0935905\pi$
$200$			1.52526i			0.107852i
$201$	−4.56435	+	20.5720i	−0.321945	+	1.45104i
$202$	−3.17079	+	1.83065i	−0.223096	+	0.128804i
$203$	1.72763	−	4.07876i	0.121256	−	0.286273i
$204$	−20.9701	+	6.60795i	−1.46820	+	0.462649i
$205$	−1.57421	−	2.72662i	−0.109948	−	0.190435i
$206$	−1.32422	−	2.29361i	−0.0922627	−	0.159804i
$207$	−9.31739	−	13.3162i	−0.647604	−	0.925540i
$208$	9.95610	+	5.74816i	0.690332	+	0.398563i
$209$	−2.55649	+	4.42797i	−0.176836	+	0.306289i
$210$	−1.48156	−	1.05544i	−0.102237	−	0.0728325i
$211$	−8.03506	−	13.9171i	−0.553156	−	0.958094i	−0.998044	−	0.0625084i	$-0.980090\pi$
$211$	−8.03506	−	13.9171i	−0.553156	−	0.958094i	0.444888	−	0.895586i	$-0.353243\pi$
$212$			6.81616i			0.468136i
$213$	−1.75665	−	5.57468i	−0.120364	−	0.381971i
$214$	−4.69339			−0.320833
$215$	3.90758	−	6.76813i	0.266495	−	0.461582i
$216$	−6.28525	−	4.82791i	−0.427657	−	0.328497i
$217$	3.11265	−	7.34865i	0.211300	−	0.498859i
$218$	3.67405	+	2.12121i	0.248838	+	0.143667i
$219$	14.0090	−	15.2829i	0.946638	−	1.03272i
$220$	−3.57740	−	2.06541i	−0.241188	−	0.139250i
$221$	22.2756	+	12.8608i	1.49842	+	0.865111i
$222$	−1.31729	−	4.18037i	−0.0884107	−	0.280568i
$223$	14.8555	+	8.57681i	0.994796	+	0.574346i	0.906704	−	0.421767i	$-0.138590\pi$
$223$	14.8555	+	8.57681i	0.994796	+	0.574346i	0.0880915	+	0.996112i	$0.471923\pi$
$224$	−4.40921	+	10.4097i	−0.294603	+	0.695528i
$225$	2.45804	−	1.71990i	0.163869	−	0.114660i
$226$	−2.16267	+	3.74585i	−0.143859	+	0.249170i
$227$	−16.2999			−1.08186			−0.540931	−	0.841067i	$-0.681928\pi$
$227$	−16.2999			−1.08186			−0.540931	+	0.841067i	$0.681928\pi$
$228$	−4.91748	+	5.36467i	−0.325668	+	0.355284i
$229$		−	8.67553i		−	0.573295i	−0.958036	−	0.286648i	$-0.907459\pi$
$229$		−	8.67553i		−	0.573295i	0.958036	−	0.286648i	$-0.0925409\pi$
$230$	1.07522	+	1.86234i	0.0708981	+	0.122799i
$231$	9.34673	−	4.26633i	0.614970	−	0.280704i
$232$	−1.27681	+	2.21149i	−0.0838264	+	0.145192i
$233$	−20.6863	−	11.9432i	−1.35521	−	0.782428i	−0.366232	−	0.930524i	$-0.619352\pi$
$233$	−20.6863	−	11.9432i	−1.35521	−	0.782428i	−0.988973	+	0.148096i	$0.952686\pi$
$234$	0.385980	+	4.42902i	0.0252323	+	0.289534i
$235$	3.33040	+	5.76842i	0.217251	+	0.376291i
$236$	−2.98284	−	5.16643i	−0.194166	−	0.336306i
$237$	6.69390	+	6.13591i	0.434815	+	0.398570i
$238$	−2.82217	+	6.66286i	−0.182934	+	0.431889i
$239$	−2.56778	+	1.48251i	−0.166096	+	0.0958957i	−0.580744	−	0.814086i	$-0.697238\pi$
$239$	−2.56778	+	1.48251i	−0.166096	+	0.0958957i	0.414648	+	0.909982i	$0.363905\pi$
$240$	−3.93180	−	3.60405i	−0.253797	−	0.232641i
$241$		−	4.03938i		−	0.260199i	−0.991501	−	0.130100i	$-0.958470\pi$
$241$		−	4.03938i		−	0.260199i	0.991501	−	0.130100i	$-0.0415297\pi$
$242$	2.05340	−	1.18553i	0.131998	−	0.0762090i
$243$	−0.693118	+	15.5730i	−0.0444635	+	0.999011i
$244$		−	20.7499i		−	1.32838i
$245$	6.78946	−	1.70390i	0.433762	−	0.108858i
$246$	−2.11328	−	0.468878i	−0.134738	−	0.0298945i
$247$	8.51372			0.541715
$248$	−2.30040	+	3.98442i	−0.146076	+	0.253011i
$249$	−6.46073	+	29.1192i	−0.409432	+	1.84535i
$250$	−0.343770	+	0.198476i	−0.0217419	+	0.0125527i
$251$	−10.6458			−0.671957			−0.335978	−	0.941870i	$-0.609067\pi$
$251$	−10.6458			−0.671957			−0.335978	+	0.941870i	$0.609067\pi$
$252$	14.3030	−	3.04664i	0.901001	−	0.191920i
$253$	−12.1461			−0.763620
$254$	5.17711	−	2.98901i	0.324841	−	0.187547i
$255$	−8.79692	−	8.06363i	−0.550885	−	0.504964i
$256$	−2.41496	+	4.18284i	−0.150935	+	0.261427i
$257$	23.0725			1.43922			0.719610	−	0.694378i	$-0.244320\pi$
$257$	23.0725			1.43922			0.719610	+	0.694378i	$0.244320\pi$
$258$	−1.61490	−	5.12482i	−0.100539	−	0.319057i
$259$	15.5307	+	6.57830i	0.965032	+	0.408756i
$260$			6.87832i			0.426576i
$261$	5.00369	−	0.436062i	0.309720	−	0.0269916i
$262$	1.91433	−	1.10524i	0.118268	−	0.0682820i
$263$		−	27.4627i		−	1.69342i	−0.532051	−	0.846712i	$-0.678579\pi$
$263$		−	27.4627i		−	1.69342i	0.532051	−	0.846712i	$-0.321421\pi$
$264$	−5.64927	+	1.78016i	−0.347689	+	0.109561i
$265$	−3.20390	+	1.84977i	−0.196814	+	0.113631i
$266$	0.293711	+	2.37697i	0.0180086	+	0.145741i
$267$	−1.93641	+	8.72759i	−0.118506	+	0.534120i
$268$	11.2076	+	19.4121i	0.684612	+	1.18578i
$269$	12.3958	+	21.4702i	0.755787	+	1.30906i	0.944982	+	0.327121i	$0.106079\pi$
$269$	12.3958	+	21.4702i	0.755787	+	1.30906i	−0.189196	+	0.981939i	$0.560588\pi$
$270$	0.270263	−	2.04484i	0.0164477	−	0.124445i
$271$	−4.46704	−	2.57904i	−0.271353	−	0.156666i	0.358149	−	0.933664i	$-0.383408\pi$
$271$	−4.46704	−	2.57904i	−0.271353	−	0.156666i	−0.629502	+	0.776999i	$0.716741\pi$
$272$	−10.6082	+	18.3740i	−0.643219	+	1.11409i
$273$	−13.9339	−	9.92635i	−0.843319	−	0.600770i
$274$	1.83772	+	3.18302i	0.111021	+	0.192293i
$275$		−	2.24205i		−	0.135201i
$276$	−16.8775	−	3.74465i	−1.01591	−	0.225401i
$277$	8.65479			0.520016			0.260008	−	0.965607i	$-0.416275\pi$
$277$	8.65479			0.520016			0.260008	+	0.965607i	$0.416275\pi$
$278$	3.83731	−	6.64642i	0.230147	−	0.398626i
$279$	9.01507	−	0.785647i	0.539718	−	0.0470354i
$280$	−4.00499	+	0.494879i	−0.239344	+	0.0295747i
$281$	−19.6791	−	11.3618i	−1.17396	−	0.677786i	−0.219350	−	0.975646i	$-0.570394\pi$
$281$	−19.6791	−	11.3618i	−1.17396	−	0.677786i	−0.954609	+	0.297860i	$0.903727\pi$
$282$	4.47084	+	0.991955i	0.266235	+	0.0590701i
$283$	23.4019	+	13.5111i	1.39110	+	0.803151i	0.993437	−	0.114381i	$-0.0364883\pi$
$283$	23.4019	+	13.5111i	1.39110	+	0.803151i	0.397662	+	0.917532i	$0.369822\pi$
$284$	−5.38441	−	3.10869i	−0.319506	−	0.184467i
$285$	−3.85615	−	0.855570i	−0.228418	−	0.0506796i
$286$	2.87744	+	1.66129i	0.170146	+	0.0982340i
$287$	6.64874	−	5.01821i	0.392463	−	0.296216i
$288$	−12.7703	+	1.11290i	−0.752495	+	0.0655785i
$289$	−15.2347	+	26.3872i	−0.896156	+	1.55219i
$290$	−0.664583			−0.0390256
$291$	9.65900	+	2.14306i	0.566220	+	0.125628i
$292$		−	22.0533i		−	1.29057i
$293$	7.60468	+	13.1717i	0.444270	+	0.769498i	0.998001	−	0.0631975i	$-0.0201298\pi$
$293$	7.60468	+	13.1717i	0.444270	+	0.769498i	−0.553731	+	0.832696i	$0.686796\pi$
$294$	2.29066	−	4.23269i	0.133594	−	0.246856i
$295$	1.61897	−	2.80414i	0.0942602	−	0.163263i
$296$	−8.42070	−	4.86170i	−0.489443	−	0.282580i
$297$	9.23901	+	7.09679i	0.536102	+	0.411797i
$298$	−2.92857	−	5.07243i	−0.169647	−	0.293838i
$299$	10.1124	+	17.5152i	0.584814	+	1.01293i
$300$	0.691225	−	3.11542i	0.0399079	−	0.179869i
$301$	19.0395	+	8.06449i	1.09742	+	0.464829i
$302$	−2.04787	+	1.18234i	−0.117841	+	0.0680358i
$303$	15.2371	−	4.80141i	0.875349	−	0.275834i
$304$			7.02255i			0.402771i
$305$	9.75340	−	5.63113i	0.558478	−	0.322437i
$306$	−8.17376	+	0.712328i	−0.467263	+	0.0407211i
$307$			12.7173i			0.725817i	0.931825	+	0.362908i	$0.118216\pi$
$307$			12.7173i			0.725817i	−0.931825	+	0.362908i	$0.881784\pi$
$308$	4.26261	−	10.0636i	0.242885	−	0.573427i
$309$	3.47314	+	11.0219i	0.197580	+	0.627013i
$310$	−1.19737			−0.0680060
$311$	2.75135	−	4.76547i	0.156015	−	0.270225i	−0.777413	−	0.628990i	$-0.783469\pi$
$311$	2.75135	−	4.76547i	0.156015	−	0.270225i	0.933428	+	0.358765i	$0.116802\pi$
$312$	7.27041	+	6.66437i	0.411606	+	0.377295i
$313$	−4.10999	+	2.37290i	−0.232310	+	0.134124i	−0.611637	−	0.791138i	$-0.709489\pi$
$313$	−4.10999	+	2.37290i	−0.232310	+	0.134124i	0.379327	+	0.925263i	$0.376155\pi$
$314$	0.779599			0.0439953
$315$	5.31360	+	5.89624i	0.299388	+	0.332215i
$316$	9.65930			0.543378
$317$	1.37930	−	0.796342i	0.0774694	−	0.0447270i	−0.460765	−	0.887522i	$-0.652425\pi$
$317$	1.37930	−	0.796342i	0.0774694	−	0.0447270i	0.538234	+	0.842795i	$0.319092\pi$
$318$	−0.550952	+	2.48320i	−0.0308959	+	0.139251i
$319$	1.87684	−	3.25079i	0.105083	−	0.182009i
$320$	−4.46268			−0.249472
$321$	19.9929	+	4.43586i	1.11589	+	0.247585i
$322$	−4.54124	+	3.42755i	−0.253073	+	0.191010i
$323$			15.7121i			0.874244i
$324$	10.6500	+	12.7096i	0.591668	+	0.706092i
$325$	−3.23312	+	1.86664i	−0.179341	+	0.103543i
$326$			7.57515i			0.419549i
$327$	−13.6459	−	12.5084i	−0.754619	−	0.691716i
$328$	−4.15880	+	2.40108i	−0.229631	+	0.132578i
$329$	−14.0661	+	10.6165i	−0.775487	+	0.585307i
$330$	−1.13634	−	1.04162i	−0.0625533	−	0.0573390i
$331$	−14.8655	−	25.7479i	−0.817084	−	1.41523i	−0.907822	−	0.419356i	$-0.862256\pi$
$331$	−14.8655	−	25.7479i	−0.817084	−	1.41523i	0.0907378	−	0.995875i	$-0.471077\pi$
$332$	15.8641	+	27.4773i	0.870653	+	1.50802i
$333$	1.66039	+	19.0525i	0.0909890	+	1.04407i
$334$	4.31670	+	2.49225i	0.236199	+	0.136370i
$335$	−6.08304	+	10.5361i	−0.332352	+	0.575651i
$336$	8.18776	−	11.4934i	0.446679	−	0.627016i
$337$	17.7839	+	30.8026i	0.968751	+	1.67793i	0.699181	+	0.714945i	$0.253548\pi$
$337$	17.7839	+	30.8026i	0.968751	+	1.67793i	0.269570	+	0.962981i	$0.413118\pi$
$338$		−	0.372124i		−	0.0202409i
$339$	12.7528	−	13.9126i	0.692639	−	0.755626i
$340$	−12.6940			−0.688427
$341$	3.38148	−	5.85690i	0.183117	−	0.317169i
$342$	−2.22512	+	1.55692i	−0.120321	+	0.0841888i
$343$	6.67695	+	17.2748i	0.360522	+	0.932751i
$344$	−10.3231	−	5.96006i	−0.556586	−	0.321345i
$345$	−2.82008	−	8.94942i	−0.151828	−	0.481821i
$346$	6.82138	+	3.93833i	0.366720	+	0.211726i
$347$	−17.8725	−	10.3187i	−0.959445	−	0.553936i	−0.0634430	−	0.997985i	$-0.520208\pi$
$347$	−17.8725	−	10.3187i	−0.959445	−	0.553936i	−0.896002	+	0.444050i	$0.853541\pi$
$348$	3.61016	−	3.93847i	0.193525	−	0.211124i
$349$	3.85330	+	2.22470i	0.206262	+	0.119086i	0.599573	−	0.800320i	$-0.295337\pi$
$349$	3.85330	+	2.22470i	0.206262	+	0.119086i	−0.393311	+	0.919406i	$0.628670\pi$
$350$	−0.632692	−	0.838268i	−0.0338188	−	0.0448073i
$351$	2.54179	−	19.2315i	0.135671	−	1.02650i
$352$	−4.79002	+	8.29656i	−0.255309	+	0.442208i
$353$	23.5324			1.25250			0.626252	−	0.779621i	$-0.284588\pi$
$353$	23.5324			1.25250			0.626252	+	0.779621i	$0.284588\pi$
$354$	−0.669077	−	2.12329i	−0.0355610	−	0.112852i
$355$		−	3.37456i		−	0.179103i
$356$	4.75477	+	8.23551i	0.252002	+	0.436481i
$357$	18.3191	−	25.7151i	0.969550	−	1.36099i
$358$	2.19240	−	3.79735i	0.115872	−	0.200696i
$359$	4.44705	+	2.56751i	0.234706	+	0.135508i	0.612741	−	0.790284i	$-0.290067\pi$
$359$	4.44705	+	2.56751i	0.234706	+	0.135508i	−0.378035	+	0.925791i	$0.623400\pi$
$360$	−2.62329	−	3.74914i	−0.138259	−	0.197597i
$361$	−6.89969	−	11.9506i	−0.363142	−	0.628980i
$362$	−3.76570	−	6.52238i	−0.197921	−	0.342809i
$363$	−9.86756	+	3.10940i	−0.517913	+	0.163201i
$364$	−18.0610	+	2.23171i	−0.946652	+	0.116974i
$365$	10.3660	−	5.98483i	0.542583	−	0.313260i
$366$	1.67722	−	7.55942i	0.0876698	−	0.395137i
$367$		−	28.1644i		−	1.47017i	−0.677976	−	0.735084i	$-0.737143\pi$
$367$		−	28.1644i		−	1.47017i	0.677976	−	0.735084i	$-0.262857\pi$
$368$	−14.4474	+	8.34120i	−0.753122	+	0.434815i
$369$	8.55899	+	3.99464i	0.445563	+	0.207953i
$370$		−	2.53053i		−	0.131556i
$371$	−5.89663	−	7.81258i	−0.306138	−	0.405609i
$372$	6.50438	−	7.09588i	0.337236	−	0.367904i
$373$	−3.23711			−0.167611			−0.0838057	−	0.996482i	$-0.526707\pi$
$373$	−3.23711			−0.167611			−0.0838057	+	0.996482i	$0.526707\pi$
$374$	−3.06591	+	5.31032i	−0.158535	+	0.274590i
$375$	1.65197	−	0.520559i	0.0853076	−	0.0268815i
$376$	8.79833	−	5.07972i	0.453739	−	0.261967i
$377$	−6.25034			−0.321909
$378$	5.45698	+	0.0461907i	0.280677	+	0.00237579i
$379$	1.76688			0.0907585			0.0453793	−	0.998970i	$-0.485550\pi$
$379$	1.76688			0.0907585			0.0453793	+	0.998970i	$0.485550\pi$
$380$	−3.63872	+	2.10082i	−0.186663	+	0.107770i
$381$	−24.8784	+	7.83952i	−1.27456	+	0.401631i
$382$	−3.22441	+	5.58485i	−0.164975	+	0.285746i
$383$	−20.0384			−1.02391			−0.511957	−	0.859011i	$-0.671079\pi$
$383$	−20.0384			−1.02391			−0.511957	+	0.859011i	$0.671079\pi$
$384$	−12.0750	+	13.1731i	−0.616201	+	0.672237i
$385$	5.88714	−	0.727448i	0.300037	−	0.0370742i
$386$		−	3.45441i		−	0.175825i
$387$	2.03551	+	23.3569i	0.103471	+	1.18730i
$388$	9.11439	−	5.26220i	0.462713	−	0.267148i
$389$			9.68860i			0.491232i	0.969367	+	0.245616i	$0.0789902\pi$
$389$			9.68860i			0.491232i	−0.969367	+	0.245616i	$0.921010\pi$
$390$	−0.555977	+	2.50585i	−0.0281530	+	0.126889i
$391$	−32.3243	+	18.6624i	−1.63471	+	0.943799i
$392$	−2.59889	−	10.3557i	−0.131264	−	0.523040i
$393$	−9.19926	+	2.89880i	−0.464041	+	0.146225i
$394$	−0.387092	−	0.670464i	−0.0195014	−	0.0337775i
$395$	2.62135	+	4.54031i	0.131894	+	0.228448i
$396$	12.3457	−	1.07590i	0.620394	−	0.0540662i
$397$	−28.1420	−	16.2478i	−1.41241	−	0.815453i	−0.416792	−	0.909002i	$-0.636846\pi$
$397$	−28.1420	−	16.2478i	−1.41241	−	0.815453i	−0.995615	+	0.0935484i	$0.970179\pi$
$398$	3.82995	−	6.63367i	0.191978	−	0.332516i
$399$	0.995391	−	10.4030i	0.0498319	−	0.520801i
$400$	−1.53970	−	2.66684i	−0.0769852	−	0.133342i
$401$		−	29.8087i		−	1.48858i	−0.667858	−	0.744289i	$-0.732789\pi$
$401$		−	29.8087i		−	1.48858i	0.667858	−	0.744289i	$-0.267211\pi$
$402$	2.51396	+	7.97795i	0.125385	+	0.397904i
$403$	−11.2611			−0.560958
$404$	8.49689	−	14.7171i	0.422736	−	0.732201i
$405$	−3.08390	+	8.45515i	−0.153240	+	0.420140i
$406$	−0.215628	−	1.74505i	−0.0107014	−	0.0866053i
$407$	12.3780	+	7.14646i	0.613556	+	0.354237i
$408$	−12.2991	+	13.4176i	−0.608897	+	0.664269i
$409$	−4.38156	−	2.52970i	−0.216654	−	0.125085i	0.387746	−	0.921766i	$-0.373254\pi$
$409$	−4.38156	−	2.52970i	−0.216654	−	0.125085i	−0.604400	+	0.796681i	$0.706587\pi$
$410$	−1.08234	−	0.624887i	−0.0534527	−	0.0308609i
$411$	−4.81993	−	15.2959i	−0.237750	−	0.754491i
$412$	10.6457	+	6.14630i	0.524476	+	0.302806i
$413$	7.88835	+	3.34125i	0.388160	+	0.164412i
$414$	−5.84598	−	2.72843i	−0.287314	−	0.134095i
$415$	−8.61040	+	14.9136i	−0.422668	+	0.732082i
$416$	15.9519			0.782108
$417$	−22.6279	+	24.6856i	−1.10809	+	1.20886i
$418$			2.02960i			0.0992711i
$419$	−17.3266	−	30.0106i	−0.846462	−	1.46611i	−0.884346	−	0.466833i	$-0.845395\pi$
$419$	−17.3266	−	30.0106i	−0.846462	−	1.46611i	0.0378840	−	0.999282i	$-0.487938\pi$
$420$	8.40469	+	0.804187i	0.410107	+	0.0392403i
$421$	10.7012	−	18.5351i	0.521545	−	0.903343i	−0.478141	−	0.878283i	$-0.658689\pi$
$421$	10.7012	−	18.5351i	0.521545	−	0.903343i	0.999686	−	0.0250598i	$-0.00797763\pi$
$422$	−5.52442	−	3.18953i	−0.268925	−	0.155264i
$423$	−18.1074	−	8.45105i	−0.880410	−	0.410904i
$424$	2.82138	+	4.88677i	0.137018	+	0.237323i
$425$	−3.44490	−	5.96674i	−0.167102	−	0.289429i
$426$	−1.71032	−	1.56775i	−0.0828654	−	0.0759580i
$427$	17.9507	+	23.7832i	0.868693	+	1.15095i
$428$	18.8656	−	10.8921i	0.911903	−	0.526488i
$429$	−10.6872	−	9.79630i	−0.515981	−	0.472970i
$430$		−	3.10224i		−	0.149603i
$431$	−18.7541	+	10.8277i	−0.903353	+	0.521551i	−0.878287	−	0.478135i	$-0.841313\pi$
$431$	−18.7541	+	10.8277i	−0.903353	+	0.521551i	−0.0250666	+	0.999686i	$0.507980\pi$
$432$	15.8631	+	2.09660i	0.763214	+	0.100873i
$433$		−	12.6680i		−	0.608788i	−0.952546	−	0.304394i	$-0.901546\pi$
$433$		−	12.6680i		−	0.608788i	0.952546	−	0.304394i	$-0.0984539\pi$
$434$	−0.388494	−	3.14403i	−0.0186483	−	0.150918i
$435$	2.83099	+	0.628116i	0.135735	+	0.0301159i
$436$	−19.6910			−0.943029
$437$	−6.17716	+	10.6992i	−0.295494	+	0.511810i
$438$	1.78257	−	8.03424i	0.0851746	−	0.383891i
$439$	−3.81002	+	2.19972i	−0.181842	+	0.104987i	−0.588158	−	0.808746i	$-0.700147\pi$
$439$	−3.81002	+	2.19972i	−0.181842	+	0.104987i	0.406316	+	0.913733i	$0.366813\pi$
$440$	−3.41971			−0.163028
$441$	−13.7582	+	15.8654i	−0.655152	+	0.755497i
$442$	10.2102			0.485651
$443$	11.5243	−	6.65355i	0.547536	−	0.316120i	−0.200592	−	0.979675i	$-0.564286\pi$
$443$	11.5243	−	6.65355i	0.547536	−	0.316120i	0.748127	+	0.663555i	$0.230953\pi$
$444$	14.9965	+	13.7464i	0.711702	+	0.652376i
$445$	−2.58071	+	4.46992i	−0.122337	+	0.211894i
$446$	6.80915			0.322423
$447$	7.68099	+	24.3754i	0.363299	+	1.15292i
$448$	−1.44795	−	11.7180i	−0.0684090	−	0.553625i
$449$		−	30.4690i		−	1.43792i	−0.695052	−	0.718960i	$-0.744618\pi$
$449$		−	30.4690i		−	1.43792i	0.695052	−	0.718960i	$-0.255382\pi$
$450$	0.503641	−	1.07911i	0.0237419	−	0.0508697i
$451$	6.11323	−	3.52947i	0.287861	−	0.166196i
$452$		−	20.0758i		−	0.944288i
$453$	9.84095	−	3.10101i	0.462368	−	0.145698i
$454$	−5.60342	+	3.23513i	−0.262981	+	0.151832i
$455$	−5.95041	−	7.88383i	−0.278959	−	0.369600i
$456$	−1.30497	+	5.88161i	−0.0611106	+	0.275432i
$457$	−5.00401	−	8.66721i	−0.234078	−	0.405435i	0.724926	−	0.688826i	$-0.241874\pi$
$457$	−5.00401	−	8.66721i	−0.234078	−	0.405435i	−0.959004	+	0.283391i	$0.908540\pi$
$458$	−1.72188	−	2.98239i	−0.0804583	−	0.139358i
$459$	35.4918	+	4.69089i	1.65661	+	0.218952i
$460$	−8.64397	−	4.99060i	−0.403027	−	0.232688i
$461$	8.95629	−	15.5127i	0.417136	−	0.722501i	−0.578514	−	0.815672i	$-0.696367\pi$
$461$	8.95629	−	15.5127i	0.417136	−	0.722501i	0.995650	+	0.0931718i	$0.0297006\pi$
$462$	2.36636	−	3.32173i	0.110093	−	0.154541i
$463$	−11.0826	−	19.1957i	−0.515054	−	0.892100i	−0.999847	−	0.0174712i	$-0.994438\pi$
$463$	−11.0826	−	19.1957i	−0.515054	−	0.892100i	0.484793	−	0.874629i	$-0.338895\pi$
$464$		−	5.15560i		−	0.239343i
$465$	5.10055	+	1.13167i	0.236532	+	0.0524799i
$466$	−9.48177			−0.439235
$467$	0.733727	−	1.27085i	0.0339528	−	0.0588080i	−0.848550	−	0.529116i	$-0.822524\pi$
$467$	0.733727	−	1.27085i	0.0339528	−	0.0588080i	0.882502	+	0.470308i	$0.155857\pi$
$468$	−11.8300	−	16.9072i	−0.546843	−	0.781535i
$469$	−29.6393	−	12.5542i	−1.36861	−	0.579700i
$470$	2.28978	+	1.32201i	0.105620	+	0.0609796i
$471$	−3.32093	−	0.736822i	−0.153021	−	0.0339510i
$472$	−4.27704	−	2.46935i	−0.196867	−	0.113661i
$473$	15.1745	+	8.76100i	0.697724	+	0.402831i
$474$	3.51899	+	0.780765i	0.161632	+	0.0358617i
$475$	−1.97496	−	1.14024i	−0.0906173	−	0.0523179i
$476$	−4.11864	−	33.3316i	−0.188777	−	1.52775i
$477$	4.69389	−	10.0572i	0.214918	−	0.460488i
$478$	−0.588485	+	1.01929i	−0.0269167	+	0.0466210i
$479$	17.3466			0.792587			0.396293	−	0.918124i	$-0.370296\pi$
$479$	17.3466			0.792587			0.396293	+	0.918124i	$0.370296\pi$
$480$	−7.22516	−	1.60306i	−0.329782	−	0.0731694i
$481$		−	23.7994i		−	1.08516i
$482$	−0.801718	−	1.38862i	−0.0365172	−	0.0632497i
$483$	22.5842	−	10.3086i	1.02762	−	0.469058i
$484$	−5.50259	+	9.53077i	−0.250118	+	0.433217i
$485$	4.94694	+	2.85612i	0.224629	+	0.129690i
$486$	2.85260	+	5.49111i	0.129396	+	0.249082i
$487$	8.22626	+	14.2483i	0.372767	+	0.645652i	0.989990	−	0.141136i	$-0.0450756\pi$
$487$	8.22626	+	14.2483i	0.372767	+	0.645652i	−0.617223	+	0.786788i	$0.711742\pi$
$488$	−8.58892	−	14.8764i	−0.388802	−	0.673425i
$489$	7.15950	−	32.2686i	0.323764	−	1.45924i
$490$	1.99583	−	1.93329i	0.0901623	−	0.0873372i
$491$	−35.0741	+	20.2500i	−1.58287	+	0.913870i	−0.588432	+	0.808547i	$0.700255\pi$
$491$	−35.0741	+	20.2500i	−1.58287	+	0.913870i	−0.994438	+	0.105324i	$0.966412\pi$
$492$	9.58271	−	3.01964i	0.432022	−	0.136136i
$493$		−	11.5350i		−	0.519511i
$494$	2.92676	−	1.68977i	0.131681	−	0.0760261i
$495$	3.85611	+	5.51105i	0.173319	+	0.247703i
$496$		−	9.28877i		−	0.417078i
$497$	8.86085	−	1.09490i	0.397463	−	0.0491128i
$498$	3.55844	+	11.2926i	0.159458	+	0.506033i
$499$	−23.8328			−1.06690			−0.533452	−	0.845830i	$-0.679105\pi$
$499$	−23.8328			−1.06690			−0.533452	+	0.845830i	$0.679105\pi$
$500$	0.921215	−	1.59559i	0.0411980	−	0.0713570i
$501$	−16.0328	−	14.6963i	−0.716290	−	0.656582i
$502$	−3.65970	+	2.11293i	−0.163341	+	0.0943047i
$503$	−4.18434			−0.186571			−0.0932853	−	0.995639i	$-0.529737\pi$
$503$	−4.18434			−0.186571			−0.0932853	+	0.995639i	$0.529737\pi$
$504$	8.99328	−	8.10461i	0.400593	−	0.361008i
$505$	9.22357			0.410444
$506$	−4.17547	+	2.41071i	−0.185622	+	0.107169i
$507$	−0.351705	+	1.58517i	−0.0156198	+	0.0703999i
$508$	−13.8733	+	24.0293i	−0.615530	+	1.06613i
$509$	29.7851			1.32020			0.660100	−	0.751177i	$-0.270514\pi$
$509$	29.7851			1.32020			0.660100	+	0.751177i	$0.270514\pi$
$510$	−4.62455	−	1.02606i	−0.204779	−	0.0454346i
$511$	19.0782	+	25.2771i	0.843969	+	1.11819i
$512$			22.5517i			0.996655i
$513$	10.9500	−	4.52915i	0.483456	−	0.199967i
$514$	7.93162	−	4.57932i	0.349849	−	0.201985i
$515$			6.67195i			0.294001i
$516$	18.3845	+	16.8521i	0.809335	+	0.741870i
$517$	−12.9331	+	7.46694i	−0.568798	+	0.328396i
$518$	6.64462	−	0.821046i	0.291948	−	0.0360747i
$519$	−25.3355	−	23.2235i	−1.11210	−	1.01940i
$520$	2.84711	+	4.93135i	0.124854	+	0.216254i
$521$	−3.08839	−	5.34924i	−0.135305	−	0.234355i	0.790409	−	0.612579i	$-0.209868\pi$
$521$	−3.08839	−	5.34924i	−0.135305	−	0.234355i	−0.925714	+	0.378225i	$0.876535\pi$
$522$	1.63357	−	1.14301i	0.0714994	−	0.0500284i
$523$	−11.1533	−	6.43933i	−0.487698	−	0.281572i	0.235921	−	0.971772i	$-0.424189\pi$
$523$	−11.1533	−	6.43933i	−0.487698	−	0.281572i	−0.723619	+	0.690200i	$0.757523\pi$
$524$	−5.12992	+	8.88528i	−0.224101	+	0.388155i
$525$	1.90287	+	4.16882i	0.0830479	+	0.181942i
$526$	−5.45068	−	9.44086i	−0.237661	−	0.411641i
$527$		−	20.7825i		−	0.905299i
$528$	8.08048	−	8.81531i	0.351658	−	0.383637i
$529$	−6.34832			−0.276014
$530$	−0.734270	+	1.27179i	−0.0318946	+	0.0552432i
$531$	0.843346	+	9.67715i	0.0365981	+	0.419953i
$532$	−6.69690	−	8.87287i	−0.290347	−	0.384688i
$533$	−10.1793	−	5.87700i	−0.440913	−	0.254561i
$534$	1.06654	+	3.38461i	0.0461535	+	0.146467i
$535$	10.2395	+	5.91179i	0.442693	+	0.255589i
$536$	16.0703	+	9.27820i	0.694132	+	0.400757i
$537$	−12.9282	+	14.1038i	−0.557892	+	0.608626i
$538$	8.52262	+	4.92054i	0.367436	+	0.212139i
$539$	3.82024	+	15.2223i	0.164549	+	0.655672i
$540$	3.65915	+	8.84666i	0.157465	+	0.380700i
$541$	−8.43402	+	14.6082i	−0.362607	+	0.628054i	−0.988389	−	0.151944i	$-0.951447\pi$
$541$	−8.43402	+	14.6082i	−0.362607	+	0.628054i	0.625782	+	0.779998i	$0.284780\pi$
$542$	−2.04751			−0.0879481
$543$	9.87661	+	31.3431i	0.423846	+	1.34506i
$544$			29.4393i			1.26220i
$545$	−5.34376	−	9.25567i	−0.228902	−	0.396469i
$546$	−6.76020	−	0.646838i	−0.289310	−	0.0276821i
$547$	−11.8525	+	20.5291i	−0.506775	+	0.877760i	0.493194	+	0.869919i	$0.335829\pi$
$547$	−11.8525	+	20.5291i	−0.506775	+	0.877760i	−0.999969	+	0.00784098i	$0.997504\pi$
$548$	−14.7738	−	8.52967i	−0.631107	−	0.364370i
$549$	−14.2893	+	30.6164i	−0.609850	+	1.30668i
$550$	−0.444993	−	0.770751i	−0.0189746	−	0.0328649i
$551$	−1.90902	−	3.30651i	−0.0813268	−	0.140862i
$552$	−13.6502	+	4.30135i	−0.580990	+	0.183077i
$553$	−11.0713	+	8.35622i	−0.470802	+	0.355343i
$554$	2.97525	−	1.71776i	0.126406	−	0.0729808i
$555$	−2.39168	+	10.7795i	−0.101521	+	0.457566i
$556$			35.6214i			1.51068i
$557$	10.1844	−	5.87999i	0.431529	−	0.249143i	−0.268469	−	0.963288i	$-0.586518\pi$
$557$	10.1844	−	5.87999i	0.431529	−	0.249143i	0.699998	+	0.714145i	$0.253184\pi$
$558$	2.94318	−	2.05935i	0.124595	−	0.0871794i
$559$		−	29.1763i		−	1.23402i
$560$	6.50298	−	4.90820i	0.274801	−	0.207409i
$561$	18.0791	−	19.7232i	0.763300	−	0.832713i
$562$	−9.02013			−0.380491
$563$	−2.86267	+	4.95829i	−0.120647	+	0.208967i	−0.920023	−	0.391864i	$-0.871830\pi$
$563$	−2.86267	+	4.95829i	−0.120647	+	0.208967i	0.799376	+	0.600831i	$0.205164\pi$
$564$	−20.2731	+	6.38833i	−0.853653	+	0.268997i
$565$	9.43655	−	5.44820i	0.396999	−	0.229207i
$566$	10.7265			0.450868
$567$	−23.2020	−	5.35431i	−0.974391	−	0.224860i
$568$	−5.14707			−0.215966
$569$	−5.73222	+	3.30950i	−0.240307	+	0.138741i	−0.615318	−	0.788279i	$-0.710972\pi$
$569$	−5.73222	+	3.30950i	−0.240307	+	0.138741i	0.375011	+	0.927020i	$0.377639\pi$
$570$	−1.49544	+	0.471231i	−0.0626369	+	0.0197377i
$571$	−18.0295	+	31.2279i	−0.754509	+	1.30685i	0.191109	+	0.981569i	$0.438792\pi$
$571$	−18.0295	+	31.2279i	−0.754509	+	1.30685i	−0.945618	+	0.325279i	$0.894542\pi$
$572$	−15.4216			−0.644808
$573$	19.0137	−	20.7428i	0.794311	−	0.866544i
$574$	1.28965	−	3.04472i	0.0538288	−	0.127084i
$575$		−	5.41741i		−	0.225922i
$576$	10.9694	−	7.67537i	0.457060	−	0.319807i
$577$	−3.71766	+	2.14639i	−0.154768	+	0.0893555i	−0.575384	−	0.817883i	$-0.695147\pi$
$577$	−3.71766	+	2.14639i	−0.154768	+	0.0893555i	0.420616	+	0.907239i	$0.361814\pi$
$578$			12.0948i			0.503079i
$579$	−3.26486	+	14.7151i	−0.135683	+	0.611538i
$580$	2.67137	−	1.54231i	0.110922	−	0.0640411i
$581$	−41.9537	−	17.7702i	−1.74053	−	0.737232i
$582$	3.74582	−	1.18036i	0.155269	−	0.0489273i
$583$	−4.14729	−	7.18332i	−0.171763	−	0.297503i
$584$	−9.12841	−	15.8109i	−0.377736	−	0.654258i
$585$	4.73670	−	10.1489i	0.195838	−	0.419607i
$586$	5.22852	+	3.01869i	0.215988	+	0.124701i
$587$	4.89956	−	8.48629i	0.202227	−	0.350267i	−0.747019	−	0.664803i	$-0.768516\pi$
$587$	4.89956	−	8.48629i	0.202227	−	0.350267i	0.949246	+	0.314536i	$0.101849\pi$
$588$	0.615332	+	22.3298i	0.0253759	+	0.920865i
$589$	−3.43945	−	5.95729i	−0.141720	−	0.245466i
$590$		−	1.28531i		−	0.0529152i
$591$	1.01526	+	3.22189i	0.0417622	+	0.132531i
$592$	19.6310			0.806828
$593$	−9.98851	+	17.3006i	−0.410179	+	0.710451i	−0.994909	−	0.100777i	$-0.967867\pi$
$593$	−9.98851	+	17.3006i	−0.410179	+	0.710451i	0.584730	+	0.811228i	$0.301200\pi$
$594$	4.58463	+	0.605943i	0.188110	+	0.0248621i
$595$	14.5496	−	10.9815i	0.596477	−	0.450197i
$596$	23.5434	+	13.5928i	0.964376	+	0.556783i
$597$	−22.5845	+	24.6383i	−0.924321	+	1.00838i
$598$	6.95266	+	4.01412i	0.284316	+	0.164150i
$599$	−1.97286	−	1.13903i	−0.0806090	−	0.0465396i	0.459154	−	0.888357i	$-0.348153\pi$
$599$	−1.97286	−	1.13903i	−0.0806090	−	0.0465396i	−0.539763	+	0.841817i	$0.681486\pi$
$600$	−0.793986	−	2.51969i	−0.0324143	−	0.102866i
$601$	−6.01771	−	3.47433i	−0.245467	−	0.141721i	0.372220	−	0.928145i	$-0.378597\pi$
$601$	−6.01771	−	3.47433i	−0.245467	−	0.141721i	−0.617687	+	0.786424i	$0.711930\pi$
$602$	8.14580	−	1.00654i	0.331998	−	0.0410235i
$603$	−3.16874	−	36.3604i	−0.129041	−	1.48071i
$604$	5.48775	−	9.50507i	0.223294	−	0.386756i
$605$	−5.97319			−0.242845
$606$	4.28510	−	4.67477i	0.174070	−	0.189900i
$607$			1.35767i			0.0551063i	0.999620	+	0.0275531i	$0.00877154\pi$
$607$			1.35767i			0.0551063i	−0.999620	+	0.0275531i	$0.991228\pi$
$608$	4.87213	+	8.43878i	0.197591	+	0.342238i
$609$	−0.730766	+	7.63735i	−0.0296121	+	0.309481i
$610$	2.23528	−	3.87162i	0.0905040	−	0.156757i
$611$	21.5352	+	12.4334i	0.871221	+	0.503000i
$612$	31.2022	−	21.8323i	1.26128	−	0.882520i
$613$	6.66732	+	11.5481i	0.269290	+	0.466425i	0.968679	−	0.248317i	$-0.0798775\pi$
$613$	6.66732	+	11.5481i	0.269290	+	0.466425i	−0.699388	+	0.714742i	$0.746544\pi$
$614$	2.52408	+	4.37184i	0.101864	+	0.176433i
$615$	4.01993	+	3.68484i	0.162099	+	0.148587i
$616$	−1.10955	−	8.97941i	−0.0447049	−	0.361791i
$617$	33.3579	−	19.2592i	1.34294	−	0.775346i	0.355700	−	0.934600i	$-0.384242\pi$
$617$	33.3579	−	19.2592i	1.34294	−	0.775346i	0.987238	+	0.159255i	$0.0509090\pi$
$618$	3.38153	+	3.09966i	0.136025	+	0.124687i
$619$		−	39.7858i		−	1.59913i	−0.600582	−	0.799563i	$-0.705064\pi$
$619$		−	39.7858i		−	1.59913i	0.600582	−	0.799563i	$-0.294936\pi$
$620$	4.81296	−	2.77877i	0.193293	−	0.111598i
$621$	22.3240	+	17.1478i	0.895829	+	0.688116i
$622$		−	2.18430i		−	0.0875825i
$623$	−12.5743	−	5.32608i	−0.503781	−	0.213385i
$624$	−19.4395	−	4.31308i	−0.778202	−	0.172661i
$625$	1.00000			0.0400000
$626$	−0.941926	+	1.63146i	−0.0376469	+	0.0652064i
$627$	1.91824	−	8.64569i	0.0766069	−	0.345275i
$628$	−3.13369	+	1.80924i	−0.125048	+	0.0721964i
$629$	43.9219			1.75128
$630$	2.99692	+	0.972328i	0.119400	+	0.0387385i
$631$	3.24832			0.129313			0.0646567	−	0.997908i	$-0.479405\pi$
$631$	3.24832			0.129313			0.0646567	+	0.997908i	$0.479405\pi$
$632$	6.92514	−	3.99823i	0.275467	−	0.159041i
$633$	20.5184	+	18.8080i	0.815533	+	0.747552i
$634$	0.316109	−	0.547516i	0.0125543	−	0.0217447i
$635$	−15.0598			−0.597631
$636$	−3.54821	−	11.2601i	−0.140696	−	0.446493i
$637$	18.7706	−	18.1824i	0.743717	−	0.720414i
$638$		−	1.49003i		−	0.0589909i
$639$	5.80390	+	8.29479i	0.229599	+	0.328137i
$640$	−8.93500	+	5.15862i	−0.353187	+	0.203912i
$641$			13.4699i			0.532027i	0.963969	+	0.266014i	$0.0857066\pi$
$641$			13.4699i			0.532027i	−0.963969	+	0.266014i	$0.914293\pi$
$642$	7.75335	−	2.44318i	0.306000	−	0.0964247i
$643$	−27.0229	+	15.6017i	−1.06568	+	0.615271i	−0.926998	−	0.375066i	$-0.877620\pi$
$643$	−27.0229	+	15.6017i	−1.06568	+	0.615271i	−0.138683	+	0.990337i	$0.544287\pi$
$644$	10.2996	−	24.3164i	0.405862	−	0.958201i
$645$	−2.93201	+	13.2149i	−0.115448	+	0.520336i
$646$	3.11847	+	5.40134i	0.122694	+	0.212513i
$647$	6.35021	+	10.9989i	0.249653	+	0.432411i	0.963429	−	0.267962i	$-0.0863503\pi$
$647$	6.35021	+	10.9989i	0.249653	+	0.432411i	−0.713777	+	0.700373i	$0.753017\pi$
$648$	12.8963	+	4.70374i	0.506614	+	0.184780i
$649$	6.28704	+	3.62982i	0.246788	+	0.142483i
$650$	−0.740967	+	1.28339i	−0.0290631	+	0.0503388i
$651$	−1.31661	+	13.7601i	−0.0516020	+	0.539301i
$652$	−17.5799	−	30.4492i	−0.688480	−	1.19248i
$653$			32.9173i			1.28815i	0.764961	+	0.644076i	$0.222758\pi$
$653$			32.9173i			1.28815i	−0.764961	+	0.644076i	$0.777242\pi$
$654$	−7.17365	−	1.59163i	−0.280512	−	0.0622378i
$655$	−5.56864			−0.217585
$656$	4.84765	−	8.39637i	0.189269	−	0.327823i
$657$	−15.1868	+	32.5395i	−0.592493	+	1.26949i
$658$	−2.72837	+	6.44140i	−0.106363	+	0.251112i
$659$	−8.02489	−	4.63317i	−0.312605	−	0.180483i	0.335486	−	0.942045i	$-0.391099\pi$
$659$	−8.02489	−	4.63317i	−0.312605	−	0.180483i	−0.648092	+	0.761562i	$0.724433\pi$
$660$	6.98494	+	1.54976i	0.271889	+	0.0603244i
$661$	19.6331	+	11.3352i	0.763639	+	0.440887i	0.830601	−	0.556869i	$-0.187997\pi$
$661$	19.6331	+	11.3352i	0.763639	+	0.440887i	−0.0669621	+	0.997756i	$0.521331\pi$
$662$	−10.2206	−	5.90089i	−0.397237	−	0.229345i
$663$	−43.4935	−	9.64998i	−1.68915	−	0.374774i
$664$	22.7471	+	13.1331i	0.882760	+	0.509662i
$665$	2.35324	−	5.55577i	0.0912548	−	0.215444i
$666$	4.35226	+	6.22014i	0.168647	+	0.241026i
$667$	4.53496	−	7.85478i	0.175594	−	0.304138i
$668$	−23.1353			−0.895131
$669$	−29.0056	−	6.43553i	−1.12142	−	0.248812i
$670$			4.82934i			0.186574i
$671$	12.6253	+	21.8676i	0.487394	+	0.844191i
$672$	1.86504	−	19.4918i	0.0719454	−	0.751913i
$673$	−7.51147	+	13.0102i	−0.289546	+	0.501508i	−0.973701	−	0.227828i	$-0.926838\pi$
$673$	−7.51147	+	13.0102i	−0.289546	+	0.501508i	0.684156	+	0.729336i	$0.260171\pi$
$674$	12.2271	+	7.05934i	0.470972	+	0.271916i
$675$	−3.16531	+	4.12078i	−0.121833	+	0.158609i
$676$	0.863597	+	1.49579i	0.0332153	+	0.0575305i
$677$	−14.1055	−	24.4315i	−0.542119	−	0.938977i	−0.998782	−	0.0493378i	$-0.984289\pi$
$677$	−14.1055	−	24.4315i	−0.542119	−	0.938977i	0.456663	−	0.889640i	$-0.349044\pi$
$678$	1.62274	−	7.31385i	0.0623208	−	0.280887i
$679$	−5.89448	+	13.9163i	−0.226209	+	0.534058i
$680$	−9.10081	+	5.25436i	−0.349000	+	0.201495i
$681$	26.9270	−	8.48506i	1.03185	−	0.325148i
$682$		−	2.68457i		−	0.102797i
$683$	−16.3693	+	9.45082i	−0.626354	+	0.361625i	−0.779339	−	0.626603i	$-0.784445\pi$
$683$	−16.3693	+	9.45082i	−0.626354	+	0.361625i	0.152985	+	0.988229i	$0.451111\pi$
$684$	5.33093	−	11.4221i	0.203833	−	0.436736i
$685$		−	9.25916i		−	0.353774i
$686$	5.72396	+	4.61334i	0.218542	+	0.176138i
$687$	4.51612	+	14.3318i	0.172301	+	0.546791i
$688$	24.0661			0.917510
$689$	−6.90574	+	11.9611i	−0.263088	+	0.455681i
$690$	−2.74570	−	2.51682i	−0.104527	−	0.0958139i
$691$	13.5520	−	7.82427i	0.515544	−	0.297649i	−0.219566	−	0.975598i	$-0.570464\pi$
$691$	13.5520	−	7.82427i	0.515544	−	0.297649i	0.735110	+	0.677948i	$0.237131\pi$
$692$	−36.5591			−1.38977
$693$	−13.2197	+	11.9134i	−0.502174	+	0.452552i
$694$	−8.19203			−0.310965
$695$	−16.7437	+	9.66696i	−0.635123	+	0.366689i
$696$	0.958039	−	4.31798i	0.0363144	−	0.163673i
$697$	10.8460	−	18.7859i	0.410822	−	0.711565i
$698$	1.76620			0.0668515
$699$	40.3904	+	8.96150i	1.52771	+	0.338955i
$700$	4.48857	+	1.90121i	0.169652	+	0.0718590i
$701$			21.4753i			0.811109i	0.914071	+	0.405555i	$0.132922\pi$
$701$			21.4753i			0.811109i	−0.914071	+	0.405555i	$0.867078\pi$
$702$	−2.94319	−	7.11569i	−0.111084	−	0.268565i
$703$	12.5902	−	7.26896i	0.474849	−	0.274154i
$704$		−	10.0056i		−	0.377100i
$705$	−8.50454	−	7.79562i	−0.320300	−	0.293600i
$706$	8.08974	−	4.67061i	0.304461	−	0.175781i
$707$	2.99265	+	24.2191i	0.112550	+	0.910853i
$708$	7.61701	+	6.98207i	0.286265	+	0.262402i
$709$	2.08806	+	3.61662i	0.0784186	+	0.135825i	0.902568	−	0.430548i	$-0.141680\pi$
$709$	2.08806	+	3.61662i	0.0784186	+	0.135825i	−0.824149	+	0.566373i	$0.808346\pi$
$710$	−0.669767	−	1.16007i	−0.0251359	−	0.0435367i
$711$	−14.2522	−	6.65180i	−0.534501	−	0.249462i
$712$	6.81777	+	3.93624i	0.255507	+	0.147517i
$713$	8.17057	−	14.1518i	0.305990	−	0.529991i
$714$	1.19374	−	12.4760i	0.0446746	−	0.466901i
$715$	−4.18512	−	7.24884i	−0.156515	−	0.271091i
$716$			20.3519i			0.760585i
$717$	3.47018	−	3.78575i	0.129596	−	0.141381i
$718$	2.03835			0.0760706
$719$	−3.86991	+	6.70289i	−0.144323	+	0.249976i	−0.929120	−	0.369778i	$-0.879434\pi$
$719$	−3.86991	+	6.70289i	−0.144323	+	0.249976i	0.784797	+	0.619753i	$0.212767\pi$
$720$	8.37135	+	3.90707i	0.311982	+	0.145608i
$721$	−17.5191	+	2.16475i	−0.652444	+	0.0806196i
$722$	−4.74381	−	2.73884i	−0.176546	−	0.101929i
$723$	2.10273	+	6.67295i	0.0782014	+	0.248170i
$724$	30.2733	+	17.4783i	1.12510	+	0.649576i
$725$	1.44991	+	0.837109i	0.0538485	+	0.0310894i
$726$	−2.77503	+	3.02739i	−0.102991	+	0.112357i
$727$	26.0953	+	15.0661i	0.967821	+	0.558772i	0.898571	−	0.438827i	$-0.144606\pi$
$727$	26.0953	+	15.0661i	0.967821	+	0.558772i	0.0692501	+	0.997599i	$0.477939\pi$
$728$	−12.0249	+	9.07590i	−0.445671	+	0.336375i
$729$	−6.96167	−	26.0871i	−0.257840	−	0.966188i
$730$	2.37569	−	4.11481i	0.0879281	−	0.152296i
$731$	53.8449			1.99152
$732$	10.8015	+	34.2783i	0.399237	+	1.26696i
$733$		−	6.93903i		−	0.256299i	−0.991755	−	0.128149i	$-0.959096\pi$
$733$		−	6.93903i		−	0.256299i	0.991755	−	0.128149i	$-0.0409037\pi$
$734$	−5.58994	−	9.68206i	−0.206328	−	0.357371i
$735$	−10.3290	+	6.34911i	−0.380992	+	0.234190i
$736$	−11.5740	+	20.0467i	−0.426623	+	0.738933i
$737$	−23.6226	−	13.6385i	−0.870149	−	0.502381i
$738$	3.73516	−	0.325512i	0.137493	−	0.0119823i
$739$	−1.84857	−	3.20182i	−0.0680007	−	0.117781i	0.830020	−	0.557733i	$-0.188329\pi$
$739$	−1.84857	−	3.20182i	−0.0680007	−	0.117781i	−0.898021	+	0.439952i	$0.854995\pi$
$740$	5.87267	+	10.1718i	0.215884	+	0.373921i
$741$	−14.0644	+	4.43189i	−0.516670	+	0.162809i
$742$	−3.57769	−	1.51539i	−0.131341	−	0.0556318i
$743$	−18.7613	+	10.8318i	−0.688286	+	0.397382i	−0.802970	−	0.596020i	$-0.796748\pi$
$743$	−18.7613	+	10.8318i	−0.688286	+	0.397382i	0.114684	+	0.993402i	$0.463415\pi$
$744$	1.72609	−	7.77965i	0.0632814	−	0.285216i
$745$			14.7553i			0.540592i
$746$	−1.11282	+	0.642488i	−0.0407433	+	0.0235232i
$747$	−4.48528	−	51.4673i	−0.164108	−	1.88309i
$748$		−	28.4606i		−	1.04062i
$749$	−12.2008	+	28.8049i	−0.445807	+	1.05251i
$750$	0.464581	−	0.506829i	0.0169641	−	0.0185068i
$751$	36.4756			1.33101			0.665506	−	0.746392i	$-0.268216\pi$
$751$	36.4756			1.33101			0.665506	+	0.746392i	$0.268216\pi$
$752$	−10.2557	+	17.7633i	−0.373985	+	0.647762i
$753$	17.5866	−	5.54176i	0.640890	−	0.201953i
$754$	−2.14868	+	1.24054i	−0.0782503	+	0.0451778i
$755$	5.95708			0.216801
$756$	−22.0422	+	12.4785i	−0.801666	+	0.453838i
$757$	12.6909			0.461259			0.230630	−	0.973042i	$-0.425921\pi$
$757$	12.6909			0.461259			0.230630	+	0.973042i	$0.425921\pi$
$758$	0.607400	−	0.350683i	0.0220618	−	0.0127374i
$759$	20.0651	−	6.32277i	0.728316	−	0.229502i
$760$	−1.73916	+	3.01232i	−0.0630861	+	0.109268i
$761$	−6.80234			−0.246585			−0.123292	−	0.992370i	$-0.539345\pi$
$761$	−6.80234			−0.246585			−0.123292	+	0.992370i	$0.539345\pi$
$762$	−6.99651	+	7.63276i	−0.253457	+	0.276506i
$763$	22.5696	−	17.0346i	0.817073	−	0.616695i
$764$		−	29.9319i		−	1.08290i
$765$	18.7299	+	8.74159i	0.677180	+	0.316053i
$766$	−6.88859	+	3.97713i	−0.248895	+	0.143700i
$767$		−	12.0882i		−	0.436479i
$768$	1.81204	−	8.16707i	0.0653865	−	0.294704i
$769$	2.04917	−	1.18309i	0.0738950	−	0.0426633i	−0.462597	−	0.886569i	$-0.653082\pi$
$769$	2.04917	−	1.18309i	0.0738950	−	0.0426633i	0.536492	+	0.843905i	$0.319749\pi$
$770$	1.87944	−	1.41853i	0.0677304	−	0.0511202i
$771$	−38.1151	+	12.0106i	−1.37268	+	0.432550i
$772$	8.01674	+	13.8854i	0.288529	+	0.499746i
$773$	−8.71589	−	15.0964i	−0.313489	−	0.542978i	0.665626	−	0.746285i	$-0.268164\pi$
$773$	−8.71589	−	15.0964i	−0.313489	−	0.542978i	−0.979115	+	0.203307i	$0.934831\pi$
$774$	5.33553	+	7.62541i	0.191782	+	0.274090i
$775$	2.61229	+	1.50821i	0.0938363	+	0.0541764i
$776$	4.35631	−	7.54536i	0.156383	−	0.270863i
$777$	−29.0807	−	2.78254i	−1.04327	−	0.0998230i
$778$	1.92295	+	3.33065i	0.0689412	+	0.119410i
$779$		−	7.17995i		−	0.257248i
$780$	−3.58057	−	11.3628i	−0.128205	−	0.406854i
$781$	7.56594			0.270731
$782$	−7.40807	+	12.8312i	−0.264912	+	0.458841i
$783$	−8.03897	+	3.32508i	−0.287289	+	0.118829i
$784$	14.9978	+	15.4829i	0.535635	+	0.552961i
$785$	−1.70085	−	0.981984i	−0.0607058	−	0.0350485i
$786$	−2.58708	+	2.82235i	−0.0922782	+	0.100670i
$787$	−31.5252	−	18.2011i	−1.12375	−	0.648799i	−0.181397	−	0.983410i	$-0.558062\pi$
$787$	−31.5252	−	18.2011i	−1.12375	−	0.648799i	−0.942356	+	0.334611i	$0.891395\pi$
$788$	3.11192	+	1.79667i	0.110858	+	0.0640037i
$789$	14.2960	+	45.3677i	0.508950	+	1.61513i
$790$	1.80228	+	1.04055i	0.0641223	+	0.0370210i
$791$	17.3675	+	23.0106i	0.617518	+	0.818164i
$792$	8.40577	−	5.88155i	0.298686	−	0.208992i
$793$	21.0226	−	36.4123i	0.746535	−	1.29304i
$794$	−12.8992			−0.457774
$795$	4.32985	−	4.72360i	0.153564	−	0.167529i
$796$			35.5530i			1.26014i
$797$	11.6006	+	20.0928i	0.410915	+	0.711725i	0.994990	−	0.0999744i	$-0.0318761\pi$
$797$	11.6006	+	20.0928i	0.410915	+	0.711725i	−0.584075	+	0.811699i	$0.698543\pi$
$798$	−1.72255	−	3.77380i	−0.0609778	−	0.133591i
$799$	−22.9458	+	39.7433i	−0.811764	+	1.40602i
$800$	−3.70043	−	2.13644i	−0.130830	−	0.0755347i
$801$	−1.34433	−	15.4258i	−0.0474995	−	0.545043i
$802$	−5.91631	−	10.2473i	−0.208912	−	0.361846i
$803$	13.4183	+	23.2412i	0.473522	+	0.820164i
$804$	−28.6198	−	26.2341i	−1.00934	−	0.925204i
$805$	14.2249	−	1.75771i	0.501363	−	0.0619512i
$806$	−3.87124	+	2.23506i	−0.136359	+	0.0787267i
$807$	−31.6541	−	29.0155i	−1.11428	−	1.02139i
$808$		−	14.0683i		−	0.494922i
$809$	−44.3607	+	25.6117i	−1.55964	+	0.900459i	−0.562350	+	0.826900i	$0.690102\pi$
$809$	−44.3607	+	25.6117i	−1.55964	+	0.900459i	−0.997291	+	0.0735592i	$0.976564\pi$
$810$	0.617990	+	3.51870i	0.0217140	+	0.123635i
$811$			31.5316i			1.10723i	0.832774	+	0.553613i	$0.186751\pi$
$811$			31.5316i			1.10723i	−0.832774	+	0.553613i	$0.813249\pi$
$812$	4.91652	+	6.51401i	0.172536	+	0.228597i
$813$	8.72197	+	1.93516i	0.305893	+	0.0678691i
$814$	5.67359			0.198859
$815$	9.54167	−	16.5267i	0.334230	−	0.578904i
$816$	7.95979	−	35.8756i	0.278648	−	1.25590i
$817$	15.4346	−	8.91118i	0.539989	−	0.311763i
$818$	−2.00833			−0.0702197
$819$	28.1857	+	9.14466i	0.984889	+	0.319540i
$820$	5.80076			0.202571
$821$	22.8012	−	13.1643i	0.795767	−	0.459436i	−0.0462219	−	0.998931i	$-0.514718\pi$
$821$	22.8012	−	13.1643i	0.795767	−	0.459436i	0.841989	+	0.539495i	$0.181385\pi$
$822$	−4.69281	−	4.30163i	−0.163681	−	0.150036i
$823$	27.1888	−	47.0924i	0.947743	−	1.64154i	0.197578	−	0.980287i	$-0.436692\pi$
$823$	27.1888	−	47.0924i	0.947743	−	1.64154i	0.750165	−	0.661251i	$-0.229974\pi$
$824$	10.1764			0.354513
$825$	1.16712	+	3.70382i	0.0406339	+	0.128950i
$826$	3.37493	−	0.417025i	0.117429	−	0.0145102i
$827$		−	33.4916i		−	1.16462i	−0.812969	−	0.582308i	$-0.802150\pi$
$827$		−	33.4916i		−	1.16462i	0.812969	−	0.582308i	$-0.197850\pi$
$828$	29.8305	−	2.59967i	1.03668	−	0.0903449i
$829$	−41.1863	+	23.7789i	−1.43046	+	0.825876i	−0.997156	−	0.0753718i	$-0.975986\pi$
$829$	−41.1863	+	23.7789i	−1.43046	+	0.825876i	−0.433304	+	0.901248i	$0.642652\pi$
$830$			6.83582i			0.237275i
$831$	−14.2975	+	4.50532i	−0.495974	+	0.156288i
$832$	−14.4284	+	8.33025i	−0.500215	+	0.288799i
$833$	33.5557	+	34.6411i	1.16264	+	1.20024i
$834$	−2.87929	+	12.9773i	−0.0997016	+	0.449366i
$835$	−6.27847	−	10.8746i	−0.217275	−	0.376332i
$836$	−4.71015	−	8.15822i	−0.162904	−	0.282158i
$837$	−14.4837	+	5.99074i	−0.500630	+	0.207070i
$838$	−11.9128	−	6.87783i	−0.411519	−	0.237591i
$839$	−9.66702	+	16.7438i	−0.333743	+	0.578059i	−0.983243	−	0.182302i	$-0.941645\pi$
$839$	−9.66702	+	16.7438i	−0.333743	+	0.578059i	0.649500	+	0.760362i	$0.274978\pi$
$840$	6.35853	−	2.90236i	0.219390	−	0.100141i
$841$	−13.0985	−	22.6873i	−0.451672	−	0.782319i
$842$		−	8.49572i		−	0.292782i
$843$	38.4239	+	8.52519i	1.32339	+	0.293623i
$844$	29.6081			1.01915
$845$	−0.468727	+	0.811859i	−0.0161247	+	0.0279288i
$846$	−7.90209	+	0.688652i	−0.271679	+	0.0236764i
$847$	−1.93804	−	15.6843i	−0.0665918	−	0.538919i
$848$	−9.86612	−	5.69621i	−0.338804	−	0.195608i
$849$	−45.6927	−	10.1379i	−1.56817	−	0.347933i
$850$	−2.36850	−	1.36746i	−0.0812390	−	0.0469034i
$851$	29.9087	+	17.2678i	1.02526	+	0.591932i
$852$	10.5132	+	2.33258i	0.360175	+	0.0799128i
$853$	−33.5065	−	19.3450i	−1.14724	−	0.662359i	−0.199026	−	0.979994i	$-0.563778\pi$
$853$	−33.5065	−	19.3450i	−1.14724	−	0.662359i	−0.948213	+	0.317635i	$0.897111\pi$
$854$	10.8913	+	4.61319i	0.372692	+	0.157860i
$855$	6.81563	−	0.593969i	0.233090	−	0.0203133i
$856$	9.01700	−	15.6179i	0.308195	−	0.533809i
$857$	−53.6592			−1.83296			−0.916482	−	0.400077i	$-0.868983\pi$
$857$	−53.6592			−1.83296			−0.916482	+	0.400077i	$0.868983\pi$
$858$	−5.61825	−	1.24653i	−0.191804	−	0.0425559i
$859$			10.0814i			0.343973i	0.985099	+	0.171986i	$0.0550185\pi$
$859$			10.0814i			0.343973i	−0.985099	+	0.171986i	$0.944982\pi$
$860$	7.19944	+	12.4698i	0.245499	+	0.425217i
$861$	−8.37128	+	11.7510i	−0.285293	+	0.400474i
$862$	−4.29806	+	7.44446i	−0.146393	+	0.253559i
$863$	−25.3989	−	14.6641i	−0.864589	−	0.499171i	0.000957011	−	1.00000i	$-0.499695\pi$
$863$	−25.3989	−	14.6641i	−0.864589	−	0.499171i	−0.865547	+	0.500829i	$0.833029\pi$
$864$	20.5168	−	8.48616i	0.697996	−	0.288705i
$865$	−9.92143	−	17.1844i	−0.337339	−	0.584288i
$866$	−2.51430	−	4.35489i	−0.0854393	−	0.147985i
$867$	11.4312	−	51.5215i	0.388223	−	1.74976i
$868$	8.85803	+	11.7362i	0.300661	+	0.398353i
$869$	−10.1796	+	5.87721i	−0.345320	+	0.199371i
$870$	1.09787	−	0.345954i	0.0372214	−	0.0117289i
$871$			45.4195i			1.53898i
$872$	−14.1173	+	8.15062i	−0.478071	+	0.276015i
$873$	−17.0720	+	1.48779i	−0.577800	+	0.0503542i
$874$			4.90407i			0.165883i
$875$	0.324456	+	2.62578i	0.0109686	+	0.0887676i
$876$	11.4800	+	36.4314i	0.387874	+	1.23090i
$877$	4.90955			0.165784			0.0828918	−	0.996559i	$-0.473584\pi$
$877$	4.90955			0.165784			0.0828918	+	0.996559i	$0.473584\pi$
$878$	−0.873181	+	1.51239i	−0.0294684	+	0.0510408i
$879$	−19.4194	−	17.8006i	−0.654999	−	0.600399i
$880$	5.97921	−	3.45210i	0.201559	−	0.116370i
$881$	31.9907			1.07779			0.538896	−	0.842372i	$-0.318841\pi$
$881$	31.9907			1.07779			0.538896	+	0.842372i	$0.318841\pi$
$882$	−1.58075	+	8.18472i	−0.0532267	+	0.275594i
$883$	39.4962			1.32915			0.664576	−	0.747220i	$-0.268612\pi$
$883$	39.4962			1.32915			0.664576	+	0.747220i	$0.268612\pi$
$884$	−41.0412	+	23.6951i	−1.38036	+	0.796953i
$885$	−1.21478	+	5.47514i	−0.0408344	+	0.184045i
$886$	2.64114	−	4.57458i	0.0887307	−	0.153686i
$887$	30.7210			1.03151			0.515755	−	0.856736i	$-0.327512\pi$
$887$	30.7210			1.03151			0.515755	+	0.856736i	$0.327512\pi$
$888$	16.4416	+	3.64793i	0.551743	+	0.122416i
$889$	−4.88625	−	39.5438i	−0.163880	−	1.32626i
$890$			2.04883i			0.0686769i
$891$	−18.9569	−	6.91426i	−0.635080	−	0.231637i
$892$	−27.3702	+	15.8022i	−0.916421	+	0.529096i
$893$			15.1899i			0.508310i
$894$	7.47841	+	6.85503i	0.250115	+	0.229266i
$895$	−9.56630	+	5.52310i	−0.319766	+	0.184617i
$896$	−16.4444	−	21.7876i	−0.549370	−	0.727873i
$897$	−25.8231	−	23.6705i	−0.862207	−	0.790335i
$898$	−6.04735	−	10.4743i	−0.201803	−	0.349532i
$899$	2.52507	+	4.37354i	0.0842157	+	0.145866i
$900$	0.479874	+	5.50642i	0.0159958	+	0.183547i
$901$	−22.0742	−	12.7446i	−0.735399	−	0.424583i
$902$	1.40103	−	2.42665i	0.0466492	−	0.0807987i
$903$	−35.6507	−	3.41118i	−1.18638	−	0.113517i
$904$	−8.30990	−	14.3932i	−0.276383	−	0.478710i
$905$			18.9731i			0.630687i
$906$	2.76755	−	3.01922i	0.0919456	−	0.100307i
$907$	−0.560066			−0.0185967			−0.00929835	−	0.999957i	$-0.502960\pi$
$907$	−0.560066			−0.0185967			−0.00929835	+	0.999957i	$0.502960\pi$
$908$	15.0157	−	26.0080i	0.498314	−	0.863105i
$909$	−22.6719	+	15.8636i	−0.751979	+	0.526163i
$910$	−3.61032	−	1.52921i	−0.119681	−	0.0506929i
$911$	0.625038	+	0.360866i	0.0207084	+	0.0119560i	0.510318	−	0.859985i	$-0.329528\pi$
$911$	0.625038	+	0.360866i	0.0207084	+	0.0119560i	−0.489610	+	0.871942i	$0.662861\pi$
$912$	−3.65565	−	11.6011i	−0.121051	−	0.384150i
$913$	−33.4372	−	19.3050i	−1.10661	−	0.638901i
$914$	−3.44046	−	1.98635i	−0.113800	−	0.0657026i
$915$	−13.1810	+	14.3797i	−0.435751	+	0.475378i
$916$	13.8426	+	7.99203i	0.457372	+	0.264064i
$917$	−1.80678	−	14.6220i	−0.0596651	−	0.482862i
$918$	13.1320	−	5.43167i	0.433422	−	0.179272i
$919$	−0.243145	+	0.421139i	−0.00802061	+	0.0138921i	−0.870008	−	0.493038i	$-0.835886\pi$
$919$	−0.243145	+	0.421139i	−0.00802061	+	0.0138921i	0.861987	+	0.506930i	$0.169220\pi$
$920$	−8.26294			−0.272421
$921$	−6.62012	−	21.0087i	−0.218140	−	0.692261i
$922$		−	7.11042i		−	0.234169i
$923$	−6.29910	−	10.9104i	−0.207337	−	0.359119i
$924$	−1.80303	+	18.8438i	−0.0593154	+	0.619914i
$925$	−3.18746	+	5.52084i	−0.104803	+	0.181524i
$926$	−7.61976	−	4.39927i	−0.250401	−	0.144569i
$927$	−11.4751	−	16.3999i	−0.376891	−	0.538643i
$928$	−3.57687	−	6.19533i	−0.117417	−	0.203372i
$929$	7.13799	+	12.3634i	0.234190	+	0.405629i	0.959037	−	0.283281i	$-0.0914229\pi$
$929$	7.13799	+	12.3634i	0.234190	+	0.405629i	−0.724847	+	0.688910i	$0.758090\pi$
$930$	1.97802	−	0.623301i	0.0648619	−	0.0204388i
$931$	15.3518	+	4.37650i	0.503134	+	0.143434i
$932$	38.1131	−	22.0046i	1.24844	−	0.720784i
$933$	−2.06445	+	9.30467i	−0.0675869	+	0.304621i
$934$		−	0.582507i		−	0.0190602i
$935$	13.3778	−	7.72365i	0.437499	−	0.252590i
$936$	−15.4797	−	7.22469i	−0.505971	−	0.236146i
$937$		−	4.24097i		−	0.138547i	−0.997598	−	0.0692733i	$-0.977932\pi$
$937$		−	4.24097i		−	0.138547i	0.997598	−	0.0692733i	$-0.0220680\pi$
$938$	−12.6808	+	1.56691i	−0.414043	+	0.0511614i
$939$	5.55436	−	6.05946i	0.181260	−	0.197743i
$940$	−12.2721			−0.400271
$941$	22.0479	−	38.1880i	0.718740	−	1.24489i	−0.242760	−	0.970086i	$-0.578053\pi$
$941$	22.0479	−	38.1880i	0.718740	−	1.24489i	0.961499	−	0.274807i	$-0.0886140\pi$
$942$	−1.28788	+	0.405827i	−0.0419613	+	0.0132226i
$943$	14.7712	−	8.52817i	0.481017	−	0.277715i
$944$	9.97095			0.324527
$945$	−11.8473	−	6.97439i	−0.385392	−	0.226877i
$946$	6.95538			0.226139
$947$	27.9018	−	16.1091i	0.906688	−	0.523476i	0.0273239	−	0.999627i	$-0.491301\pi$
$947$	27.9018	−	16.1091i	0.906688	−	0.523476i	0.879364	+	0.476150i	$0.157968\pi$
$948$	−15.9569	+	5.02823i	−0.518257	+	0.163309i
$949$	22.3431	−	38.6994i	0.725288	−	1.25624i
$950$	−0.905242			−0.0293699
$951$	−1.86403	+	2.03354i	−0.0604454	+	0.0659422i
$952$	−16.7496	−	22.1919i	−0.542858	−	0.719245i
$953$		−	32.6886i		−	1.05889i	−0.848345	−	0.529444i	$-0.822401\pi$
$953$		−	32.6886i		−	1.05889i	0.848345	−	0.529444i	$-0.177599\pi$
$954$	−0.382492	−	4.38898i	−0.0123836	−	0.142099i
$955$	14.0694	−	8.12295i	0.455274	−	0.262852i
$956$		−	5.46284i		−	0.176681i
$957$	−1.40827	+	6.34722i	−0.0455229	+	0.205177i
$958$	5.96324	−	3.44288i	0.192664	−	0.111234i
$959$	24.3125	−	3.00419i	0.785092	−	0.0970104i
$960$	7.37224	−	2.32309i	0.237938	−	0.0749774i
$961$	−10.9506	−	18.9670i	−0.353246	−	0.611840i
$962$	−4.72360	−	8.18152i	−0.152295	−	0.263783i
$963$	−35.3368	+	3.07954i	−1.13871	+	0.0992367i
$964$	6.44519	+	3.72113i	0.207586	+	0.119850i
$965$	−4.35118	+	7.53646i	−0.140069	+	0.242607i
$966$	5.71777	−	8.02621i	0.183966	−	0.258239i
$967$	24.1078	+	41.7560i	0.775256	+	1.34278i	0.934651	+	0.355568i	$0.115712\pi$
$967$	24.1078	+	41.7560i	0.775256	+	1.34278i	−0.159395	+	0.987215i	$0.550954\pi$
$968$			9.11066i			0.292828i
$969$	−8.17906	−	25.9560i	−0.262749	−	0.833826i
$970$	2.26748			0.0728044
$971$	−16.0828	+	27.8562i	−0.516122	+	0.893950i	0.483703	+	0.875232i	$0.339292\pi$
$971$	−16.0828	+	27.8562i	−0.516122	+	0.893950i	−0.999825	+	0.0187172i	$0.994042\pi$
$972$	−24.2097	−	15.4520i	−0.776526	−	0.495625i
$973$	−30.8159	−	40.8287i	−0.987913	−	1.30891i
$974$	5.65588	+	3.26542i	0.181226	+	0.104631i
$975$	4.36934	−	4.76668i	0.139931	−	0.152656i
$976$	30.0347	+	17.3405i	0.961387	+	0.555057i
$977$	−24.1793	−	13.9599i	−0.773564	−	0.446617i	0.0605808	−	0.998163i	$-0.480705\pi$
$977$	−24.1793	−	13.9599i	−0.773564	−	0.446617i	−0.834144	+	0.551546i	$0.814038\pi$
$978$	−3.94331	−	12.5140i	−0.126093	−	0.400152i
$979$	−10.0218	−	5.78609i	−0.320298	−	0.184924i
$980$	−3.53582	+	12.4029i	−0.112948	+	0.396195i
$981$	29.0540	+	13.5601i	0.927623	+	0.432939i
$982$	−8.03827	+	13.9227i	−0.256511	+	0.444291i
$983$	−15.8375			−0.505138			−0.252569	−	0.967579i	$-0.581275\pi$
$983$	−15.8375			−0.505138			−0.252569	+	0.967579i	$0.581275\pi$
$984$	5.62032	−	6.13142i	0.179169	−	0.195463i
$985$			1.95033i			0.0621426i
$986$	−2.28942	−	3.96539i	−0.0729100	−	0.126284i
$987$	17.7102	−	24.8604i	0.563723	−	0.791315i
$988$	−7.84296	+	13.5844i	−0.249518	+	0.432178i
$989$	36.6657	+	21.1690i	1.16590	+	0.673134i
$990$	2.41942	+	1.12919i	0.0768943	+	0.0358880i
$991$	18.0318	+	31.2321i	0.572800	+	0.992119i	0.996277	+	0.0862120i	$0.0274763\pi$
$991$	18.0318	+	31.2321i	0.572800	+	0.992119i	−0.423477	+	0.905907i	$0.639190\pi$
$992$	−6.44440	−	11.1620i	−0.204610	−	0.354395i
$993$	37.9608	+	34.7964i	1.20465	+	1.10423i
$994$	2.82878	−	2.13505i	0.0897236	−	0.0677198i
$995$	−16.7115	+	9.64841i	−0.529791	+	0.305875i
$996$	−40.5106	−	37.1337i	−1.28363	−	1.17663i
$997$			5.08395i			0.161010i	0.996754	+	0.0805051i	$0.0256533\pi$
$997$			5.08395i			0.161010i	−0.996754	+	0.0805051i	$0.974347\pi$
$998$	−8.19301	+	4.73024i	−0.259345	+	0.149733i
$999$	−12.6609	−	30.6100i	−0.400573	−	0.968457i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.be.c.236.9	yes	32
3.2	odd	2		945.2.be.c.656.8		32
7.3	odd	6		315.2.t.c.101.9	✓	32
9.4	even	3		945.2.t.c.341.9		32
9.5	odd	6		315.2.t.c.131.8	yes	32
21.17	even	6		945.2.t.c.521.8		32
63.31	odd	6		945.2.be.c.206.8		32
63.59	even	6	inner	315.2.be.c.311.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.t.c.101.9	✓	32	7.3	odd	6
315.2.t.c.131.8	yes	32	9.5	odd	6
315.2.be.c.236.9	yes	32	1.1	even	1	trivial
315.2.be.c.311.9	yes	32	63.59	even	6	inner
945.2.t.c.341.9		32	9.4	even	3
945.2.t.c.521.8		32	21.17	even	6
945.2.be.c.206.8		32	63.31	odd	6
945.2.be.c.656.8		32	3.2	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.343770 - 0.198476i) q^{2} +(-1.65197 + 0.520559i) q^{3} +(-0.921215 + 1.59559i) q^{4} -1.00000 q^{5} +(-0.464581 + 0.506829i) q^{6} +(-0.324456 - 2.62578i) q^{7} +1.52526i q^{8} +(2.45804 - 1.71990i) q^{9} +O(q^{10})\)	\(q+(0.343770 - 0.198476i) q^{2} +(-1.65197 + 0.520559i) q^{3} +(-0.921215 + 1.59559i) q^{4} -1.00000 q^{5} +(-0.464581 + 0.506829i) q^{6} +(-0.324456 - 2.62578i) q^{7} +1.52526i q^{8} +(2.45804 - 1.71990i) q^{9} +(-0.343770 + 0.198476i) q^{10} -2.24205i q^{11} +(0.691225 - 3.11542i) q^{12} +(-3.23312 + 1.86664i) q^{13} +(-0.632692 - 0.838268i) q^{14} +(1.65197 - 0.520559i) q^{15} +(-1.53970 - 2.66684i) q^{16} +(-3.44490 - 5.96674i) q^{17} +(0.503641 - 1.07911i) q^{18} +(-1.97496 - 1.14024i) q^{19} +(0.921215 - 1.59559i) q^{20} +(1.90287 + 4.16882i) q^{21} +(-0.444993 - 0.770751i) q^{22} -5.41741i q^{23} +(-0.793986 - 2.51969i) q^{24} +1.00000 q^{25} +(-0.740967 + 1.28339i) q^{26} +(-3.16531 + 4.12078i) q^{27} +(4.48857 + 1.90121i) q^{28} +(1.44991 + 0.837109i) q^{29} +(0.464581 - 0.506829i) q^{30} +(2.61229 + 1.50821i) q^{31} +(-3.70043 - 2.13644i) q^{32} +(1.16712 + 3.70382i) q^{33} +(-2.36850 - 1.36746i) q^{34} +(0.324456 + 2.62578i) q^{35} +(0.479874 + 5.50642i) q^{36} +(-3.18746 + 5.52084i) q^{37} -0.905242 q^{38} +(4.36934 - 4.76668i) q^{39} -1.52526i q^{40} +(1.57421 + 2.72662i) q^{41} +(1.48156 + 1.05544i) q^{42} +(-3.90758 + 6.76813i) q^{43} +(3.57740 + 2.06541i) q^{44} +(-2.45804 + 1.71990i) q^{45} +(-1.07522 - 1.86234i) q^{46} +(-3.33040 - 5.76842i) q^{47} +(3.93180 + 3.60405i) q^{48} +(-6.78946 + 1.70390i) q^{49} +(0.343770 - 0.198476i) q^{50} +(8.79692 + 8.06363i) q^{51} -6.87832i q^{52} +(3.20390 - 1.84977i) q^{53} +(-0.270263 + 2.04484i) q^{54} +2.24205i q^{55} +(4.00499 - 0.494879i) q^{56} +(3.85615 + 0.855570i) q^{57} +0.664583 q^{58} +(-1.61897 + 2.80414i) q^{59} +(-0.691225 + 3.11542i) q^{60} +(-9.75340 + 5.63113i) q^{61} +1.19737 q^{62} +(-5.31360 - 5.89624i) q^{63} +4.46268 q^{64} +(3.23312 - 1.86664i) q^{65} +(1.13634 + 1.04162i) q^{66} +(6.08304 - 10.5361i) q^{67} +12.6940 q^{68} +(2.82008 + 8.94942i) q^{69} +(0.632692 + 0.838268i) q^{70} +3.37456i q^{71} +(2.62329 + 3.74914i) q^{72} +(-10.3660 + 5.98483i) q^{73} +2.53053i q^{74} +(-1.65197 + 0.520559i) q^{75} +(3.63872 - 2.10082i) q^{76} +(-5.88714 + 0.727448i) q^{77} +(0.555977 - 2.50585i) q^{78} +(-2.62135 - 4.54031i) q^{79} +(1.53970 + 2.66684i) q^{80} +(3.08390 - 8.45515i) q^{81} +(1.08234 + 0.624887i) q^{82} +(8.61040 - 14.9136i) q^{83} +(-8.40469 - 0.804187i) q^{84} +(3.44490 + 5.96674i) q^{85} +3.10224i q^{86} +(-2.83099 - 0.628116i) q^{87} +3.41971 q^{88} +(2.58071 - 4.46992i) q^{89} +(-0.503641 + 1.07911i) q^{90} +(5.95041 + 7.88383i) q^{91} +(8.64397 + 4.99060i) q^{92} +(-5.10055 - 1.13167i) q^{93} +(-2.28978 - 1.32201i) q^{94} +(1.97496 + 1.14024i) q^{95} +(7.22516 + 1.60306i) q^{96} +(-4.94694 - 2.85612i) q^{97} +(-1.99583 + 1.93329i) q^{98} +(-3.85611 - 5.51105i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9}+O(q^{10}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9	\( 32 q + q^{3} + 16 q^{4} - 32 q^{5} + 2 q^{6} + q^{7} + 7 q^{9} + 15 q^{12} - 6 q^{13} - 6 q^{14} - q^{15} - 16 q^{16} + 3 q^{17} + 41 q^{18} - 16 q^{20} - 17 q^{21} - 21 q^{22} - 26 q^{24} + 32 q^{25} - 12 q^{26} - 23 q^{27} - 31 q^{28} + 18 q^{29} - 2 q^{30} + 24 q^{31} - 19 q^{33} + 30 q^{34} - q^{35} + 18 q^{36} - q^{37} - 60 q^{38} - 36 q^{39} - 6 q^{41} + 44 q^{42} - 19 q^{43} - 21 q^{44} - 7 q^{45} + 6 q^{46} - 15 q^{47} + 35 q^{48} + 23 q^{49} - 9 q^{51} + 24 q^{53} - 58 q^{54} + 33 q^{56} + 27 q^{57} + 15 q^{59} - 15 q^{60} - 9 q^{61} - 11 q^{63} + 76 q^{64} + 6 q^{65} + 22 q^{66} + 25 q^{67} - 6 q^{68} + 50 q^{69} + 6 q^{70} + 61 q^{72} + 12 q^{73} + q^{75} - 54 q^{76} - 27 q^{77} - 42 q^{78} - 2 q^{79} + 16 q^{80} + 43 q^{81} - 24 q^{82} + 42 q^{83} - 36 q^{84} - 3 q^{85} - 55 q^{87} - 84 q^{88} - 30 q^{89} - 41 q^{90} - 57 q^{91} + 6 q^{92} - 48 q^{93} + 24 q^{94} - 9 q^{96} + 42 q^{97} - 6 q^{98} - q^{99}+O(q^{100}) \) 32 * q + q^3 + 16 * q^4 - 32 * q^5 + 2 * q^6 + q^7 + 7 * q^9 + 15 * q^12 - 6 * q^13 - 6 * q^14 - q^15 - 16 * q^16 + 3 * q^17 + 41 * q^18 - 16 * q^20 - 17 * q^21 - 21 * q^22 - 26 * q^24 + 32 * q^25 - 12 * q^26 - 23 * q^27 - 31 * q^28 + 18 * q^29 - 2 * q^30 + 24 * q^31 - 19 * q^33 + 30 * q^34 - q^35 + 18 * q^36 - q^37 - 60 * q^38 - 36 * q^39 - 6 * q^41 + 44 * q^42 - 19 * q^43 - 21 * q^44 - 7 * q^45 + 6 * q^46 - 15 * q^47 + 35 * q^48 + 23 * q^49 - 9 * q^51 + 24 * q^53 - 58 * q^54 + 33 * q^56 + 27 * q^57 + 15 * q^59 - 15 * q^60 - 9 * q^61 - 11 * q^63 + 76 * q^64 + 6 * q^65 + 22 * q^66 + 25 * q^67 - 6 * q^68 + 50 * q^69 + 6 * q^70 + 61 * q^72 + 12 * q^73 + q^75 - 54 * q^76 - 27 * q^77 - 42 * q^78 - 2 * q^79 + 16 * q^80 + 43 * q^81 - 24 * q^82 + 42 * q^83 - 36 * q^84 - 3 * q^85 - 55 * q^87 - 84 * q^88 - 30 * q^89 - 41 * q^90 - 57 * q^91 + 6 * q^92 - 48 * q^93 + 24 * q^94 - 9 * q^96 + 42 * q^97 - 6 * q^98 - q^99

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