LMFDB - Embedded newform 130.2.p.b.123.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [130,2,Mod(7,130)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("130.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(130, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 130 = 2 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	130.p (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.03805522628$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{13} - 48 x^{12} + 16 x^{11} + 8 x^{10} + 80 x^{9} + 2208 x^{8} + 760 x^{7} + 192 x^{6} + \cdots + 4096 $ x^16 - 4x^13 - 48x^12 + 16x^11 + 8x^10 + 80x^9 + 2208x^8 + 760x^7 + 192x^6 + 1696x^5 - 2812x^4 - 2080x^3 + 128x^2 - 1024*x + 4096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			123.4
Root			$0.640364 - 2.38987i$ of defining polynomial
Character	$\chi$	$=$	130.123
Dual form			130.2.p.b.37.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 - 0.500000i) q^{2} +(2.38987 - 0.640364i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.606329 - 2.15229i) q^{5} +(-2.38987 - 0.640364i) q^{6} +(0.551051 + 0.954448i) q^{7} -1.00000i q^{8} +(2.70334 - 1.56078i) q^{9} +(-0.551051 + 2.16710i) q^{10} +(-3.23142 + 0.865856i) q^{11} +(1.74951 + 1.74951i) q^{12} +(1.57779 + 3.24200i) q^{13} -1.10210i q^{14} +(-2.82730 - 4.75543i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.749677 - 2.79783i) q^{17} -3.12155 q^{18} +(1.15009 - 4.29219i) q^{19} +(1.56078 - 1.60124i) q^{20} +(1.92813 + 1.92813i) q^{21} +(3.23142 + 0.865856i) q^{22} +(1.93811 + 7.23312i) q^{23} +(-0.640364 - 2.38987i) q^{24} +(-4.26473 + 2.60999i) q^{25} +(0.254593 - 3.59655i) q^{26} +(0.212657 - 0.212657i) q^{27} +(-0.551051 + 0.954448i) q^{28} +(-1.66838 - 0.963240i) q^{29} +(0.0707959 + 5.53198i) q^{30} +(-3.17717 + 3.17717i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.16821 + 4.13857i) q^{33} +(-2.04816 + 2.04816i) q^{34} +(1.72013 - 1.76473i) q^{35} +(2.70334 + 1.56078i) q^{36} +(-5.46855 + 9.47181i) q^{37} +(-3.14210 + 3.14210i) q^{38} +(5.84678 + 6.73761i) q^{39} +(-2.15229 + 0.606329i) q^{40} +(-0.348623 - 1.30108i) q^{41} +(-0.705746 - 2.63388i) q^{42} +(4.64760 + 1.24532i) q^{43} +(-2.36556 - 2.36556i) q^{44} +(-4.99836 - 4.87205i) q^{45} +(1.93811 - 7.23312i) q^{46} +7.88729 q^{47} +(-0.640364 + 2.38987i) q^{48} +(2.89269 - 5.01028i) q^{49} +(4.99836 - 0.127955i) q^{50} -7.16653i q^{51} +(-2.01876 + 2.98741i) q^{52} +(-8.09456 - 8.09456i) q^{53} +(-0.290495 + 0.0778379i) q^{54} +(3.82288 + 6.42996i) q^{55} +(0.954448 - 0.551051i) q^{56} -10.9943i q^{57} +(0.963240 + 1.66838i) q^{58} +(-9.63111 - 2.58065i) q^{59} +(2.70468 - 4.82623i) q^{60} +(-3.68778 - 6.38743i) q^{61} +(4.34009 - 1.16292i) q^{62} +(2.97936 + 1.72013i) q^{63} -1.00000 q^{64} +(6.02108 - 5.36159i) q^{65} +8.27714 q^{66} +(3.69332 + 2.13234i) q^{67} +(2.79783 - 0.749677i) q^{68} +(9.26366 + 16.0451i) q^{69} +(-2.37205 + 0.668235i) q^{70} +(4.81110 + 1.28913i) q^{71} +(-1.56078 - 2.70334i) q^{72} -16.4413i q^{73} +(9.47181 - 5.46855i) q^{74} +(-8.52081 + 8.96853i) q^{75} +(4.29219 - 1.15009i) q^{76} +(-2.60709 - 2.60709i) q^{77} +(-1.69466 - 8.75833i) q^{78} +0.747852i q^{79} +(2.16710 + 0.551051i) q^{80} +(-4.31028 + 7.46563i) q^{81} +(-0.348623 + 1.30108i) q^{82} +10.5558 q^{83} +(-0.705746 + 2.63388i) q^{84} +(-6.47631 + 0.0828811i) q^{85} +(-3.40228 - 3.40228i) q^{86} +(-4.60404 - 1.23365i) q^{87} +(0.865856 + 3.23142i) q^{88} +(0.953984 + 3.56032i) q^{89} +(1.89269 + 6.71850i) q^{90} +(-2.22488 + 3.29243i) q^{91} +(-5.29501 + 5.29501i) q^{92} +(-5.55848 + 9.62757i) q^{93} +(-6.83060 - 3.94365i) q^{94} +(-9.93539 + 0.127149i) q^{95} +(1.74951 - 1.74951i) q^{96} +(4.98325 - 2.87708i) q^{97} +(-5.01028 + 2.89269i) q^{98} +(-7.38422 + 7.38422i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} - 2 q^{5} + 6 q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{16} - 16 q^{17} - 16 q^{18} + 8 q^{20} - 6 q^{22} - 6 q^{23} - 14 q^{25} - 6 q^{26} - 12 q^{27} - 6 q^{29} + 6 q^{30} - 6 q^{33} - 14 q^{34}+ \cdots - 26 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 - 2 * q^5 + 6 * q^11 + 2 * q^13 + 6 * q^15 - 8 * q^16 - 16 * q^17 - 16 * q^18 + 8 * q^20 - 6 * q^22 - 6 * q^23 - 14 * q^25 - 6 * q^26 - 12 * q^27 - 6 * q^29 + 6 * q^30 - 6 * q^33 - 14 * q^34 - 20 * q^37 + 6 * q^38 - 6 * q^39 - 44 * q^41 + 6 * q^42 + 6 * q^44 - 6 * q^46 + 52 * q^47 - 2 * q^49 + 10 * q^52 - 24 * q^53 + 6 * q^54 + 64 * q^55 + 6 * q^56 + 8 * q^58 - 46 * q^59 + 6 * q^61 + 12 * q^62 + 90 * q^63 - 16 * q^64 - 22 * q^65 + 52 * q^66 + 12 * q^67 - 2 * q^68 + 58 * q^69 - 32 * q^70 + 6 * q^71 - 8 * q^72 + 24 * q^74 + 44 * q^75 - 6 * q^76 + 58 * q^77 + 38 * q^78 + 10 * q^80 - 24 * q^81 - 44 * q^82 - 64 * q^83 + 6 * q^84 + 40 * q^85 - 44 * q^87 - 24 * q^89 - 18 * q^90 + 38 * q^91 - 26 * q^93 - 6 * q^95 - 6 * q^97 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/130\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	2.38987	−	0.640364i	1.37979	−	0.369714i	0.508747	−	0.860916i	$-0.330109\pi$
$3$	2.38987	−	0.640364i	1.37979	−	0.369714i	0.871046	+	0.491202i	$0.163442\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.606329	−	2.15229i	−0.271158	−	0.962535i
$5$	−0.606329	−	2.15229i	−0.271158	−	0.962535i
$6$	−2.38987	−	0.640364i	−0.975661	−	0.261428i
$7$	0.551051	+	0.954448i	0.208278	+	0.360747i	0.951172	−	0.308661i	$-0.0998809\pi$
$7$	0.551051	+	0.954448i	0.208278	+	0.360747i	−0.742894	+	0.669409i	$0.766548\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.70334	−	1.56078i	0.901115	−	0.520259i
$10$	−0.551051	+	2.16710i	−0.174258	+	0.685299i
$11$	−3.23142	+	0.865856i	−0.974309	+	0.261065i	−0.710646	−	0.703550i	$-0.751597\pi$
$11$	−3.23142	+	0.865856i	−0.974309	+	0.261065i	−0.263663	+	0.964615i	$0.584931\pi$
$12$	1.74951	+	1.74951i	0.505039	+	0.505039i
$13$	1.57779	+	3.24200i	0.437601	+	0.899169i
$13$	1.57779	+	3.24200i	0.437601	+	0.899169i
$14$		−	1.10210i		−	0.294549i
$15$	−2.82730	−	4.75543i	−0.730005	−	1.22785i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.749677	−	2.79783i	0.181823	−	0.678574i	−0.813465	−	0.581614i	$-0.802421\pi$
$17$	0.749677	−	2.79783i	0.181823	−	0.678574i	0.995288	−	0.0969602i	$-0.0309119\pi$
$18$	−3.12155			−0.735757
$19$	1.15009	−	4.29219i	0.263849	−	0.984697i	−0.699103	−	0.715021i	$-0.746417\pi$
$19$	1.15009	−	4.29219i	0.263849	−	0.984697i	0.962951	−	0.269675i	$-0.0869164\pi$
$20$	1.56078	−	1.60124i	0.349000	−	0.358049i
$21$	1.92813	+	1.92813i	0.420753	+	0.420753i
$22$	3.23142	+	0.865856i	0.688940	+	0.184601i
$23$	1.93811	+	7.23312i	0.404123	+	1.50821i	0.805667	+	0.592369i	$0.201807\pi$
$23$	1.93811	+	7.23312i	0.404123	+	1.50821i	−0.401543	+	0.915840i	$0.631526\pi$
$24$	−0.640364	−	2.38987i	−0.130714	−	0.487830i
$25$	−4.26473	+	2.60999i	−0.852946	+	0.521999i
$26$	0.254593	−	3.59655i	0.0499299	−	0.705342i
$27$	0.212657	−	0.212657i	0.0409259	−	0.0409259i
$28$	−0.551051	+	0.954448i	−0.104139	+	0.180374i
$29$	−1.66838	−	0.963240i	−0.309810	−	0.178869i	0.337031	−	0.941493i	$-0.390577\pi$
$29$	−1.66838	−	0.963240i	−0.309810	−	0.178869i	−0.646842	+	0.762624i	$0.723911\pi$
$30$	0.0707959	+	5.53198i	0.0129255	+	1.01000i
$31$	−3.17717	+	3.17717i	−0.570636	+	0.570636i	−0.932306	−	0.361670i	$-0.882207\pi$
$31$	−3.17717	+	3.17717i	−0.570636	+	0.570636i	0.361670	+	0.932306i	$0.382207\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−7.16821	+	4.13857i	−1.24783	+	0.720432i
$34$	−2.04816	+	2.04816i	−0.351256	+	0.351256i
$35$	1.72013	−	1.76473i	0.290756	−	0.298294i
$36$	2.70334	+	1.56078i	0.450557	+	0.260129i
$37$	−5.46855	+	9.47181i	−0.899025	+	1.55716i	−0.0702817	+	0.997527i	$0.522390\pi$
$37$	−5.46855	+	9.47181i	−0.899025	+	1.55716i	−0.828743	+	0.559629i	$0.810944\pi$
$38$	−3.14210	+	3.14210i	−0.509717	+	0.509717i
$39$	5.84678	+	6.73761i	0.936234	+	1.07888i
$40$	−2.15229	+	0.606329i	−0.340307	+	0.0958690i
$41$	−0.348623	−	1.30108i	−0.0544458	−	0.203194i	0.933345	−	0.358981i	$-0.116876\pi$
$41$	−0.348623	−	1.30108i	−0.0544458	−	0.203194i	−0.987791	+	0.155786i	$0.950209\pi$
$42$	−0.705746	−	2.63388i	−0.108899	−	0.406417i
$43$	4.64760	+	1.24532i	0.708753	+	0.189910i	0.595148	−	0.803616i	$-0.297094\pi$
$43$	4.64760	+	1.24532i	0.708753	+	0.189910i	0.113605	+	0.993526i	$0.463760\pi$
$44$	−2.36556	−	2.36556i	−0.356622	−	0.356622i
$45$	−4.99836	−	4.87205i	−0.745112	−	0.726282i
$46$	1.93811	−	7.23312i	0.285758	−	1.06646i
$47$	7.88729			1.15048			0.575240	−	0.817985i	$-0.304909\pi$
$47$	7.88729			1.15048			0.575240	+	0.817985i	$0.304909\pi$
$48$	−0.640364	+	2.38987i	−0.0924286	+	0.344948i
$49$	2.89269	−	5.01028i	0.413241	−	0.715754i
$50$	4.99836	−	0.127955i	0.706875	−	0.0180956i
$51$		−	7.16653i		−	1.00351i
$52$	−2.01876	+	2.98741i	−0.279952	+	0.414279i
$53$	−8.09456	−	8.09456i	−1.11187	−	1.11187i	−0.992897	−	0.118976i	$-0.962039\pi$
$53$	−8.09456	−	8.09456i	−1.11187	−	1.11187i	−0.118976	−	0.992897i	$-0.537961\pi$
$54$	−0.290495	+	0.0778379i	−0.0395314	+	0.0105924i
$55$	3.82288	+	6.42996i	0.515476	+	0.867016i
$56$	0.954448	−	0.551051i	0.127543	−	0.0736372i
$57$		−	10.9943i		−	1.45623i
$58$	0.963240	+	1.66838i	0.126480	+	0.219069i
$59$	−9.63111	−	2.58065i	−1.25386	−	0.335972i	−0.430036	−	0.902812i	$-0.641499\pi$
$59$	−9.63111	−	2.58065i	−1.25386	−	0.335972i	−0.823828	+	0.566840i	$0.808166\pi$
$60$	2.70468	−	4.82623i	0.349172	−	0.623063i
$61$	−3.68778	−	6.38743i	−0.472172	−	0.817827i	0.527321	−	0.849666i	$-0.323197\pi$
$61$	−3.68778	−	6.38743i	−0.472172	−	0.817827i	−0.999493	+	0.0318398i	$0.989863\pi$
$62$	4.34009	−	1.16292i	0.551192	−	0.147692i
$63$	2.97936	+	1.72013i	0.375364	+	0.216716i
$64$	−1.00000			−0.125000
$65$	6.02108	−	5.36159i	0.746823	−	0.665023i
$66$	8.27714			1.01884
$67$	3.69332	+	2.13234i	0.451210	+	0.260506i	0.708341	−	0.705870i	$-0.249444\pi$
$67$	3.69332	+	2.13234i	0.451210	+	0.260506i	−0.257131	+	0.966377i	$0.582777\pi$
$68$	2.79783	−	0.749677i	0.339287	−	0.0909117i
$69$	9.26366	+	16.0451i	1.11521	+	1.93161i
$70$	−2.37205	+	0.668235i	−0.283514	+	0.0798694i
$71$	4.81110	+	1.28913i	0.570972	+	0.152991i	0.532742	−	0.846278i	$-0.321161\pi$
$71$	4.81110	+	1.28913i	0.570972	+	0.152991i	0.0382296	+	0.999269i	$0.487828\pi$
$72$	−1.56078	−	2.70334i	−0.183939	−	0.318592i
$73$		−	16.4413i		−	1.92431i	−0.272499	−	0.962156i	$-0.587850\pi$
$73$		−	16.4413i		−	1.92431i	0.272499	−	0.962156i	$-0.412150\pi$
$74$	9.47181	−	5.46855i	1.10108	−	0.635706i
$75$	−8.52081	+	8.96853i	−0.983899	+	1.03560i
$76$	4.29219	−	1.15009i	0.492348	−	0.131924i
$77$	−2.60709	−	2.60709i	−0.297105	−	0.297105i
$78$	−1.69466	−	8.75833i	−0.191882	−	0.991685i
$79$			0.747852i			0.0841400i	0.999115	+	0.0420700i	$0.0133952\pi$
$79$			0.747852i			0.0841400i	−0.999115	+	0.0420700i	$0.986605\pi$
$80$	2.16710	+	0.551051i	0.242290	+	0.0616093i
$81$	−4.31028	+	7.46563i	−0.478920	+	0.829514i
$82$	−0.348623	+	1.30108i	−0.0384990	+	0.143680i
$83$	10.5558			1.15865			0.579327	−	0.815095i	$-0.303315\pi$
$83$	10.5558			1.15865			0.579327	+	0.815095i	$0.303315\pi$
$84$	−0.705746	+	2.63388i	−0.0770032	+	0.287380i
$85$	−6.47631	+	0.0828811i	−0.702454	+	0.00898972i
$86$	−3.40228	−	3.40228i	−0.366877	−	0.366877i
$87$	−4.60404	−	1.23365i	−0.493605	−	0.132261i
$88$	0.865856	+	3.23142i	0.0923005	+	0.344470i
$89$	0.953984	+	3.56032i	0.101122	+	0.377393i	0.997876	−	0.0651360i	$-0.0207481\pi$
$89$	0.953984	+	3.56032i	0.101122	+	0.377393i	−0.896754	+	0.442529i	$0.854081\pi$
$90$	1.89269	+	6.71850i	0.199507	+	0.708192i
$91$	−2.22488	+	3.29243i	−0.233231	+	0.345140i
$92$	−5.29501	+	5.29501i	−0.552043	+	0.552043i
$93$	−5.55848	+	9.62757i	−0.576387	+	0.998332i
$94$	−6.83060	−	3.94365i	−0.704522	−	0.406756i
$95$	−9.93539	+	0.127149i	−1.01935	+	0.0130452i
$96$	1.74951	−	1.74951i	0.178558	−	0.178558i
$97$	4.98325	−	2.87708i	0.505972	−	0.292123i	−0.225204	−	0.974312i	$-0.572305\pi$
$97$	4.98325	−	2.87708i	0.505972	−	0.292123i	0.731176	+	0.682189i	$0.238972\pi$
$98$	−5.01028	+	2.89269i	−0.506115	+	0.292205i
$99$	−7.38422	+	7.38422i	−0.742143	+	0.742143i
$100$	−4.39269	−	2.38837i	−0.439269	−	0.238837i
$101$	−5.29048	−	3.05446i	−0.526423	−	0.303930i	0.213136	−	0.977023i	$-0.431632\pi$
$101$	−5.29048	−	3.05446i	−0.526423	−	0.303930i	−0.739559	+	0.673092i	$0.764966\pi$
$102$	−3.58326	+	6.20640i	−0.354796	+	0.614525i
$103$	11.3174	−	11.3174i	1.11514	−	1.11514i	0.122693	−	0.992445i	$-0.460847\pi$
$103$	11.3174	−	11.3174i	1.11514	−	1.11514i	0.992445	−	0.122693i	$-0.0391530\pi$
$104$	3.24200	−	1.57779i	0.317904	−	0.154715i
$105$	2.98083	−	5.31899i	0.290899	−	0.519081i
$106$	2.96281	+	11.0574i	0.287774	+	1.07399i
$107$	−2.82498	−	10.5430i	−0.273101	−	1.01923i	−0.957103	−	0.289747i	$-0.906429\pi$
$107$	−2.82498	−	10.5430i	−0.273101	−	1.01923i	0.684002	−	0.729480i	$-0.260238\pi$
$108$	0.290495	+	0.0778379i	0.0279529	+	0.00748995i
$109$	−6.08467	−	6.08467i	−0.582806	−	0.582806i	0.352868	−	0.935673i	$-0.385207\pi$
$109$	−6.08467	−	6.08467i	−0.582806	−	0.582806i	−0.935673	+	0.352868i	$0.885207\pi$
$110$	−0.0957253	−	7.47995i	−0.00912705	−	0.713185i
$111$	−7.00373	+	26.1383i	−0.664765	+	2.48094i
$112$	−1.10210			−0.104139
$113$	−2.29579	+	8.56802i	−0.215970	+	0.806012i	0.769853	+	0.638222i	$0.220330\pi$
$113$	−2.29579	+	8.56802i	−0.215970	+	0.806012i	−0.985823	+	0.167790i	$0.946337\pi$
$114$	−5.49713	+	9.52131i	−0.514854	+	0.891753i
$115$	14.3927	−	8.55702i	1.34212	−	0.797946i
$116$		−	1.92648i		−	0.178869i
$117$	9.32535	+	6.30167i	0.862129	+	0.582589i
$118$	7.05046	+	7.05046i	0.649047	+	0.649047i
$119$	3.08350	−	0.826220i	0.282664	−	0.0757395i
$120$	−4.75543	+	2.82730i	−0.434110	+	0.258096i
$121$	0.166072	−	0.0958815i	0.0150974	−	0.00871650i
$122$			7.37557i			0.667753i
$123$	−1.66633	−	2.88617i	−0.150248	−	0.260237i
$124$	−4.34009	−	1.16292i	−0.389752	−	0.104434i
$125$	8.20330	+	7.59644i	0.733725	+	0.679446i
$126$	−1.72013	−	2.97936i	−0.153242	−	0.265422i
$127$	−3.20926	+	0.859919i	−0.284776	+	0.0763055i	−0.398380	−	0.917221i	$-0.630427\pi$
$127$	−3.20926	+	0.859919i	−0.284776	+	0.0763055i	0.113604	+	0.993526i	$0.463761\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	11.9046			1.04814
$130$	−7.89520	+	1.63273i	−0.692455	+	0.143200i
$131$	−0.395776			−0.0345791			−0.0172895	−	0.999851i	$-0.505504\pi$
$131$	−0.395776			−0.0345791			−0.0172895	+	0.999851i	$0.505504\pi$
$132$	−7.16821	−	4.13857i	−0.623913	−	0.360216i
$133$	4.73043	−	1.26752i	0.410180	−	0.109908i
$134$	−2.13234	−	3.69332i	−0.184206	−	0.319054i
$135$	−0.586640	−	0.328760i	−0.0504900	−	0.0282952i
$136$	−2.79783	−	0.749677i	−0.239912	−	0.0642843i
$137$	−4.37451	−	7.57687i	−0.373739	−	0.647335i	0.616398	−	0.787435i	$-0.288591\pi$
$137$	−4.37451	−	7.57687i	−0.373739	−	0.647335i	−0.990137	+	0.140099i	$0.955258\pi$
$138$		−	18.5273i		−	1.57715i
$139$	7.23857	−	4.17919i	0.613968	−	0.354474i	−0.160549	−	0.987028i	$-0.551326\pi$
$139$	7.23857	−	4.17919i	0.613968	−	0.354474i	0.774517	+	0.632553i	$0.217993\pi$
$140$	2.38837	+	0.607314i	0.201854	+	0.0513274i
$141$	18.8496	−	5.05074i	1.58742	−	0.425349i
$142$	−3.52197	−	3.52197i	−0.295557	−	0.295557i
$143$	−7.90561	−	9.11012i	−0.661100	−	0.761827i
$144$			3.12155i			0.260129i
$145$	−1.06159	+	4.17488i	−0.0881601	+	0.346705i
$146$	−8.22067	+	14.2386i	−0.680347	+	1.17840i
$147$	3.70475	−	13.8263i	0.305562	−	1.14037i
$148$	−10.9371			−0.899025
$149$	−0.757636	+	2.82754i	−0.0620680	+	0.231641i	−0.989991	−	0.141131i	$-0.954926\pi$
$149$	−0.757636	+	2.82754i	−0.0620680	+	0.231641i	0.927923	+	0.372772i	$0.121593\pi$
$150$	11.8635	−	3.50657i	0.968651	−	0.286310i
$151$	10.2911	+	10.2911i	0.837480	+	0.837480i	0.988527	−	0.151047i	$-0.0482645\pi$
$151$	10.2911	+	10.2911i	0.837480	+	0.837480i	−0.151047	+	0.988527i	$0.548264\pi$
$152$	−4.29219	−	1.15009i	−0.348143	−	0.0932846i
$153$	−2.34016	−	8.73358i	−0.189190	−	0.706068i
$154$	0.954261	+	3.56135i	0.0768965	+	0.286982i
$155$	8.76460	+	4.91179i	0.703990	+	0.394524i
$156$	−2.91155	+	8.43226i	−0.233110	+	0.675121i
$157$	−6.72089	+	6.72089i	−0.536386	+	0.536386i	−0.922465	−	0.386080i	$-0.873829\pi$
$157$	−6.72089	+	6.72089i	−0.536386	+	0.536386i	0.386080	+	0.922465i	$0.373829\pi$
$158$	0.373926	−	0.647659i	0.0297480	−	0.0515250i
$159$	−24.5284	−	14.1615i	−1.94523	−	1.12308i
$160$	−1.60124	−	1.56078i	−0.126589	−	0.123390i
$161$	−5.83564	+	5.83564i	−0.459913	+	0.459913i
$162$	7.46563	−	4.31028i	0.586555	−	0.338648i
$163$	1.92752	−	1.11286i	0.150975	−	0.0871656i	−0.422609	−	0.906312i	$-0.638886\pi$
$163$	1.92752	−	1.11286i	0.150975	−	0.0871656i	0.573585	+	0.819146i	$0.305552\pi$
$164$	0.952456	−	0.952456i	0.0743743	−	0.0743743i
$165$	13.2537	+	12.9188i	1.03180	+	1.00572i
$166$	−9.14163	−	5.27792i	−0.709528	−	0.409646i
$167$	−8.96406	+	15.5262i	−0.693660	+	1.20145i	0.276971	+	0.960878i	$0.410670\pi$
$167$	−8.96406	+	15.5262i	−0.693660	+	1.20145i	−0.970630	+	0.240576i	$0.922664\pi$
$168$	1.92813	−	1.92813i	0.148759	−	0.148759i
$169$	−8.02115	+	10.2304i	−0.617011	+	0.786954i
$170$	5.65009	+	3.16638i	0.433342	+	0.242850i
$171$	−3.59007	−	13.3983i	−0.274539	−	1.02459i
$172$	1.24532	+	4.64760i	0.0949549	+	0.354376i
$173$	8.29818	+	2.22349i	0.630899	+	0.169049i	0.560078	−	0.828440i	$-0.310771\pi$
$173$	8.29818	+	2.22349i	0.630899	+	0.169049i	0.0708214	+	0.997489i	$0.477438\pi$
$174$	3.37039	+	3.37039i	0.255509	+	0.255509i
$175$	−4.84119	−	2.63222i	−0.365959	−	0.198977i
$176$	0.865856	−	3.23142i	0.0652663	−	0.243577i
$177$	−24.6697			−1.85429
$178$	0.953984	−	3.56032i	0.0715041	−	0.266857i
$179$	−5.60277	+	9.70428i	−0.418771	+	0.725332i	−0.995816	−	0.0913799i	$-0.970872\pi$
$179$	−5.60277	+	9.70428i	−0.418771	+	0.725332i	0.577045	+	0.816712i	$0.304206\pi$
$180$	1.72013	−	6.76473i	0.128211	−	0.504213i
$181$		−	22.8415i		−	1.69780i	−0.528555	−	0.848899i	$-0.677266\pi$
$181$		−	22.8415i		−	1.69780i	0.528555	−	0.848899i	$-0.322734\pi$
$182$	3.57301	−	1.73889i	0.264849	−	0.128895i
$183$	−12.9036	−	12.9036i	−0.953863	−	0.953863i
$184$	7.23312	−	1.93811i	0.533232	−	0.142879i
$185$	23.7019	+	6.02690i	1.74260	+	0.443107i
$186$	9.62757	−	5.55848i	0.705928	−	0.407567i
$187$			9.69008i			0.708609i
$188$	3.94365	+	6.83060i	0.287620	+	0.498172i
$189$	0.320155	+	0.0857852i	0.0232878	+	0.00623996i
$190$	8.66788	+	4.85758i	0.628834	+	0.352406i
$191$	0.887123	+	1.53654i	0.0641900	+	0.111180i	0.896334	−	0.443379i	$-0.146220\pi$
$191$	0.887123	+	1.53654i	0.0641900	+	0.111180i	−0.832144	+	0.554559i	$0.812887\pi$
$192$	−2.38987	+	0.640364i	−0.172474	+	0.0462143i
$193$	10.2448	+	5.91481i	0.737434	+	0.425758i	0.821135	−	0.570733i	$-0.193341\pi$
$193$	10.2448	+	5.91481i	0.737434	+	0.425758i	−0.0837018	+	0.996491i	$0.526674\pi$
$194$	−5.75416			−0.413124
$195$	10.9562	−	16.6692i	0.784592	−	1.19371i
$196$	5.78537			0.413241
$197$	1.62089	+	0.935821i	0.115484	+	0.0666745i	0.556629	−	0.830761i	$-0.312094\pi$
$197$	1.62089	+	0.935821i	0.115484	+	0.0666745i	−0.441146	+	0.897436i	$0.645428\pi$
$198$	10.0870	−	2.70281i	0.716855	−	0.192081i
$199$	−9.52263	−	16.4937i	−0.675042	−	1.16921i	−0.976457	−	0.215713i	$-0.930792\pi$
$199$	−9.52263	−	16.4937i	−0.675042	−	1.16921i	0.301415	−	0.953493i	$-0.402541\pi$
$200$	2.60999	+	4.26473i	0.184554	+	0.301562i
$201$	10.1920	+	2.73094i	0.718890	+	0.192626i
$202$	3.05446	+	5.29048i	0.214911	+	0.372237i
$203$		−	2.12318i		−	0.149018i
$204$	6.20640	−	3.58326i	0.434535	−	0.250879i
$205$	−2.58892	+	1.53922i	−0.180818	+	0.107504i
$206$	−15.4599	+	4.14246i	−1.07714	+	0.288619i
$207$	16.5286	+	16.5286i	1.14882	+	1.14882i
$208$	−3.59655	−	0.254593i	−0.249376	−	0.0176529i
$209$			14.8657i			1.02828i
$210$	−5.24097	+	3.11597i	−0.361661	+	0.215022i
$211$	10.2796	−	17.8049i	0.707680	−	1.22574i	−0.258036	−	0.966135i	$-0.583075\pi$
$211$	10.2796	−	17.8049i	0.707680	−	1.22574i	0.965716	−	0.259602i	$-0.0835915\pi$
$212$	2.96281	−	11.0574i	0.203487	−	0.759424i
$213$	12.3234			0.844386
$214$	−2.82498	+	10.5430i	−0.193112	+	0.720703i
$215$	−0.137677	−	10.7581i	−0.00938952	−	0.733695i
$216$	−0.212657	−	0.212657i	−0.0144695	−	0.0144695i
$217$	−4.78322	−	1.28166i	−0.324706	−	0.0870048i
$218$	2.22714	+	8.31181i	0.150841	+	0.562947i
$219$	−10.5284	−	39.2927i	−0.711446	−	2.65515i
$220$	−3.65707	+	6.52569i	−0.246560	+	0.439962i
$221$	10.2534	−	1.98394i	0.689719	−	0.133454i
$222$	19.1346	−	19.1346i	1.28423	−	1.28423i
$223$	−6.78661	+	11.7547i	−0.454465	+	0.787156i	−0.998657	−	0.0518044i	$-0.983503\pi$
$223$	−6.78661	+	11.7547i	−0.454465	+	0.787156i	0.544193	+	0.838960i	$0.316836\pi$
$224$	0.954448	+	0.551051i	0.0637717	+	0.0368186i
$225$	−7.45542	+	13.7120i	−0.497028	+	0.914133i
$226$	6.27223	−	6.27223i	0.417222	−	0.417222i
$227$	−16.3644	+	9.44797i	−1.08614	+	0.627084i	−0.932546	−	0.361050i	$-0.882418\pi$
$227$	−16.3644	+	9.44797i	−1.08614	+	0.627084i	−0.153594	+	0.988134i	$0.549085\pi$
$228$	9.52131	−	5.49713i	0.630564	−	0.364057i
$229$	1.04861	−	1.04861i	0.0692941	−	0.0692941i	−0.671610	−	0.740904i	$-0.734397\pi$
$229$	1.04861	−	1.04861i	0.0692941	−	0.0692941i	0.740904	+	0.671610i	$0.234397\pi$
$230$	−16.7429	+	0.214269i	−1.10400	+	0.0141285i
$231$	−7.90009	−	4.56112i	−0.519788	−	0.300100i
$232$	−0.963240	+	1.66838i	−0.0632398	+	0.109535i
$233$	−16.4473	+	16.4473i	−1.07750	+	1.07750i	−0.0807620	+	0.996733i	$0.525735\pi$
$233$	−16.4473	+	16.4473i	−1.07750	+	1.07750i	−0.996733	+	0.0807620i	$0.974265\pi$
$234$	−4.92516	−	10.1201i	−0.321968	−	0.661570i
$235$	−4.78229	−	16.9758i	−0.311962	−	1.10738i
$236$	−2.58065	−	9.63111i	−0.167986	−	0.626932i
$237$	0.478898	+	1.78727i	0.0311078	+	0.116096i
$238$	−3.08350	−	0.826220i	−0.199873	−	0.0535559i
$239$	14.5791	+	14.5791i	0.943047	+	0.943047i	0.998463	−	0.0554167i	$-0.0176487\pi$
$239$	14.5791	+	14.5791i	0.943047	+	0.943047i	−0.0554167	+	0.998463i	$0.517649\pi$
$240$	5.53198	−	0.0707959i	0.357087	−	0.00456986i
$241$	−0.0783697	+	0.292480i	−0.00504823	+	0.0188403i	−0.968404	−	0.249387i	$-0.919771\pi$
$241$	−0.0783697	+	0.292480i	−0.00504823	+	0.0188403i	0.963356	+	0.268227i	$0.0864377\pi$
$242$	−0.191763			−0.0123270
$243$	−5.75382	+	21.4735i	−0.369107	+	1.37753i
$244$	3.68778	−	6.38743i	0.236086	−	0.408913i
$245$	−12.5375	−	3.18803i	−0.800992	−	0.203676i
$246$			3.33266i			0.212483i
$247$	15.7299	−	3.04359i	1.00087	−	0.193659i
$248$	3.17717	+	3.17717i	0.201750	+	0.201750i
$249$	25.2271	−	6.75958i	1.59870	−	0.428371i
$250$	−3.30605	−	10.6804i	−0.209093	−	0.675485i
$251$	−9.76282	+	5.63657i	−0.616224	+	0.355777i	−0.775397	−	0.631474i	$-0.782450\pi$
$251$	−9.76282	+	5.63657i	−0.616224	+	0.355777i	0.159174	+	0.987251i	$0.449117\pi$
$252$			3.44027i			0.216716i
$253$	−12.5257	−	21.6951i	−0.787482	−	1.36396i
$254$	3.20926	+	0.859919i	0.201367	+	0.0539561i
$255$	−15.4245	+	4.34527i	−0.965918	+	0.272111i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	16.0275	−	4.29455i	0.999767	−	0.267887i	0.278419	−	0.960460i	$-0.410190\pi$
$257$	16.0275	−	4.29455i	0.999767	−	0.267887i	0.721348	+	0.692573i	$0.243523\pi$
$258$	−10.3097	−	5.95232i	−0.641855	−	0.370575i
$259$	−12.0538			−0.748987
$260$	7.65381	+	2.53361i	0.474669	+	0.157128i
$261$	−6.01361			−0.372233
$262$	0.342752	+	0.197888i	0.0211753	+	0.0122256i
$263$	−4.57715	+	1.22644i	−0.282239	+	0.0756257i	−0.397162	−	0.917749i	$-0.630005\pi$
$263$	−4.57715	+	1.22644i	−0.282239	+	0.0756257i	0.114922	+	0.993374i	$0.463338\pi$
$264$	4.13857	+	7.16821i	0.254711	+	0.441173i
$265$	−12.5139	+	22.3298i	−0.768723	+	1.37171i
$266$	−4.73043	−	1.26752i	−0.290041	−	0.0777164i
$267$	4.55980	+	7.89780i	0.279055	+	0.483338i
$268$			4.26467i			0.260506i
$269$	3.69062	−	2.13078i	0.225021	−	0.129916i	−0.383252	−	0.923644i	$-0.625196\pi$
$269$	3.69062	−	2.13078i	0.225021	−	0.129916i	0.608273	+	0.793728i	$0.291863\pi$
$270$	0.343665	+	0.578035i	0.0209148	+	0.0351781i
$271$	−9.10585	+	2.43990i	−0.553141	+	0.148214i	−0.524553	−	0.851378i	$-0.675768\pi$
$271$	−9.10585	+	2.43990i	−0.553141	+	0.148214i	−0.0285876	+	0.999591i	$0.509101\pi$
$272$	2.04816	+	2.04816i	0.124188	+	0.124188i
$273$	−3.20882	+	9.29321i	−0.194207	+	0.562451i
$274$			8.74901i			0.528547i
$275$	11.5212	−	12.1266i	0.694757	−	0.731263i
$276$	−9.26366	+	16.0451i	−0.557607	+	0.965803i
$277$	−1.52395	+	5.68746i	−0.0915652	+	0.341726i	−0.996476	−	0.0838746i	$-0.973270\pi$
$277$	−1.52395	+	5.68746i	−0.0915652	+	0.341726i	0.904911	+	0.425601i	$0.139937\pi$
$278$	−8.35839			−0.501303
$279$	−3.63013	+	13.5478i	−0.217330	+	0.811087i
$280$	−1.76473	−	1.72013i	−0.105463	−	0.102798i
$281$	3.04681	+	3.04681i	0.181757	+	0.181757i	0.792121	−	0.610364i	$-0.208977\pi$
$281$	3.04681	+	3.04681i	0.181757	+	0.181757i	−0.610364	+	0.792121i	$0.708977\pi$
$282$	−18.8496	−	5.05074i	−1.12248	−	0.300767i
$283$	1.29094	+	4.81786i	0.0767385	+	0.286392i	0.993622	−	0.112763i	$-0.0359702\pi$
$283$	1.29094	+	4.81786i	0.0767385	+	0.286392i	−0.916883	+	0.399155i	$0.869303\pi$
$284$	1.28913	+	4.81110i	0.0764957	+	0.285486i
$285$	−23.6629	+	6.66614i	−1.40167	+	0.394868i
$286$	2.29140	+	11.8424i	0.135493	+	0.700256i
$287$	1.04970	−	1.04970i	0.0619620	−	0.0619620i
$288$	1.56078	−	2.70334i	0.0919696	−	0.159296i
$289$	7.45658	+	4.30506i	0.438622	+	0.253239i
$290$	3.00680	−	3.08476i	0.176566	−	0.181143i
$291$	10.0669	−	10.0669i	0.590134	−	0.590134i
$292$	14.2386	−	8.22067i	0.833252	−	0.481078i
$293$	12.5246	−	7.23110i	0.731697	−	0.422445i	−0.0873459	−	0.996178i	$-0.527839\pi$
$293$	12.5246	−	7.23110i	0.731697	−	0.422445i	0.819043	+	0.573733i	$0.194505\pi$
$294$	−10.1216	+	10.1216i	−0.590301	+	0.590301i
$295$	0.285305	+	22.2937i	0.0166111	+	1.29799i
$296$	9.47181	+	5.46855i	0.550538	+	0.317853i
$297$	−0.503053	+	0.871314i	−0.0291901	+	0.0505588i
$298$	2.06990	−	2.06990i	0.119906	−	0.119906i
$299$	−20.3918	+	17.6957i	−1.17929	+	1.02337i
$300$	−12.0274	−	2.89498i	−0.694401	−	0.167142i
$301$	1.37247	+	5.12213i	0.0791079	+	0.295235i
$302$	−3.76681	−	14.0579i	−0.216756	−	0.808943i
$303$	−14.5995	−	3.91194i	−0.838722	−	0.224735i
$304$	3.14210	+	3.14210i	0.180212	+	0.180212i
$305$	−11.5116	+	11.8101i	−0.659153	+	0.676243i
$306$	−2.34016	+	8.73358i	−0.133778	+	0.499266i
$307$	17.0463			0.972881			0.486441	−	0.873714i	$-0.338295\pi$
$307$	17.0463			0.972881			0.486441	+	0.873714i	$0.338295\pi$
$308$	0.954261	−	3.56135i	0.0543740	−	0.202927i
$309$	19.7999	−	34.2944i	1.12638	−	1.95094i
$310$	−5.13448	−	8.63604i	−0.291619	−	0.490494i
$311$			27.4086i			1.55420i	0.629376	+	0.777101i	$0.283310\pi$
$311$			27.4086i			1.55420i	−0.629376	+	0.777101i	$0.716690\pi$
$312$	6.73761	−	5.84678i	0.381442	−	0.331009i
$313$	7.09857	+	7.09857i	0.401235	+	0.401235i	0.878668	−	0.477433i	$-0.158433\pi$
$313$	7.09857	+	7.09857i	0.401235	+	0.401235i	−0.477433	+	0.878668i	$0.658433\pi$
$314$	9.18091	−	2.46002i	0.518109	−	0.138827i
$315$	1.89576	−	7.45542i	0.106814	−	0.420065i
$316$	−0.647659	+	0.373926i	−0.0364337	+	0.0210350i
$317$		−	20.9604i		−	1.17725i	−0.808406	−	0.588626i	$-0.799669\pi$
$317$		−	20.9604i		−	1.17725i	0.808406	−	0.588626i	$-0.200331\pi$
$318$	14.1615	+	24.5284i	0.794137	+	1.37549i
$319$	6.22526	+	1.66805i	0.348548	+	0.0933930i
$320$	0.606329	+	2.15229i	0.0338948	+	0.120317i
$321$	−13.5027	−	23.3873i	−0.753646	−	1.30535i
$322$	7.97163	−	2.13599i	0.444241	−	0.119034i
$323$	−11.1466	−	6.43552i	−0.620216	−	0.358082i
$324$	−8.62057			−0.478920
$325$	−15.1905	−	9.70824i	−0.842615	−	0.538516i
$326$	−2.22571			−0.123271
$327$	−18.4380	−	10.6452i	−1.01962	−	0.588679i
$328$	−1.30108	+	0.348623i	−0.0718401	+	0.0192495i
$329$	4.34630	+	7.52801i	0.239619	+	0.415033i
$330$	−5.01866	−	17.8148i	−0.276268	−	0.980674i
$331$	16.1510	+	4.32765i	0.887741	+	0.237869i	0.673744	−	0.738965i	$-0.264685\pi$
$331$	16.1510	+	4.32765i	0.887741	+	0.237869i	0.213997	+	0.976834i	$0.431352\pi$
$332$	5.27792	+	9.14163i	0.289664	+	0.501712i
$333$			34.1408i			1.87090i
$334$	15.5262	−	8.96406i	0.849556	−	0.490492i
$335$	2.35005	−	9.24200i	0.128397	−	0.504944i
$336$	−2.63388	+	0.705746i	−0.143690	+	0.0385016i
$337$	−13.3768	−	13.3768i	−0.728683	−	0.728683i	0.241674	−	0.970357i	$-0.422303\pi$
$337$	−13.3768	−	13.3768i	−0.728683	−	0.728683i	−0.970357	+	0.241674i	$0.922303\pi$
$338$	12.0617	−	4.84921i	0.656071	−	0.263763i
$339$			21.9466i			1.19198i
$340$	−3.30993	−	5.56721i	−0.179506	−	0.301924i
$341$	7.51579	−	13.0177i	0.407003	−	0.704949i
$342$	−3.59007	+	13.3983i	−0.194129	+	0.724497i
$343$	14.0908			0.760830
$344$	1.24532	−	4.64760i	0.0671432	−	0.250582i
$345$	28.9170	−	29.6667i	1.55684	−	1.59720i
$346$	−6.07469	−	6.07469i	−0.326577	−	0.326577i
$347$	−4.30720	−	1.15411i	−0.231222	−	0.0619559i	0.141347	−	0.989960i	$-0.454857\pi$
$347$	−4.30720	−	1.15411i	−0.231222	−	0.0619559i	−0.372570	+	0.928004i	$0.621523\pi$
$348$	−1.23365	−	4.60404i	−0.0661305	−	0.246802i
$349$	−3.59895	−	13.4314i	−0.192647	−	0.718969i	−0.992863	−	0.119257i	$-0.961949\pi$
$349$	−3.59895	−	13.4314i	−0.192647	−	0.718969i	0.800216	−	0.599712i	$-0.204718\pi$
$350$	2.87648	+	4.70017i	0.153754	+	0.251234i
$351$	1.02496	+	0.353906i	0.0547085	+	0.0188901i
$352$	−2.36556	+	2.36556i	−0.126085	+	0.126085i
$353$	−0.495300	+	0.857885i	−0.0263622	+	0.0456606i	−0.878906	−	0.476996i	$-0.841726\pi$
$353$	−0.495300	+	0.857885i	−0.0263622	+	0.0456606i	0.852543	+	0.522657i	$0.175059\pi$
$354$	21.3646	+	12.3348i	1.13551	+	0.655589i
$355$	−0.142521	−	11.1365i	−0.00756421	−	0.591065i
$356$	−2.60633	+	2.60633i	−0.138135	+	0.138135i
$357$	6.84008	−	3.94912i	0.362015	−	0.209010i
$358$	9.70428	−	5.60277i	0.512887	−	0.296116i
$359$	11.8127	−	11.8127i	0.623450	−	0.623450i	−0.322962	−	0.946412i	$-0.604679\pi$
$359$	11.8127	−	11.8127i	0.623450	−	0.623450i	0.946412	+	0.322962i	$0.104679\pi$
$360$	−4.87205	+	4.99836i	−0.256779	+	0.263437i
$361$	−0.645736	−	0.372816i	−0.0339861	−	0.0196219i
$362$	−11.4208	+	19.7814i	−0.600262	+	1.03969i
$363$	0.335491	−	0.335491i	0.0176087	−	0.0176087i
$364$	−3.96376	−	0.280588i	−0.207758	−	0.0147068i
$365$	−35.3866	+	9.96885i	−1.85222	+	0.521793i
$366$	4.72305	+	17.6267i	0.246878	+	0.921360i
$367$	8.34106	+	31.1292i	0.435400	+	1.62493i	0.740108	+	0.672488i	$0.234774\pi$
$367$	8.34106	+	31.1292i	0.435400	+	1.62493i	−0.304708	+	0.952446i	$0.598559\pi$
$368$	−7.23312	−	1.93811i	−0.377052	−	0.101031i
$369$	−2.97314	−	2.97314i	−0.154776	−	0.154776i
$370$	−17.5130	−	17.0704i	−0.910456	−	0.887447i
$371$	3.26532	−	12.1863i	0.169527	−	0.632684i
$372$	−11.1170			−0.576387
$373$	−0.652008	+	2.43333i	−0.0337597	+	0.125993i	−0.980749	−	0.195272i	$-0.937441\pi$
$373$	−0.652008	+	2.43333i	−0.0337597	+	0.125993i	0.946990	+	0.321264i	$0.104108\pi$
$374$	4.84504	−	8.39185i	0.250531	−	0.433932i
$375$	24.4693	+	12.9014i	1.26359	+	0.666226i
$376$		−	7.88729i		−	0.406756i
$377$	0.490469	−	6.92868i	0.0252604	−	0.356845i
$378$	−0.234370	−	0.234370i	−0.0120547	−	0.0120547i
$379$	−2.94373	+	0.788769i	−0.151209	+	0.0405163i	−0.333630	−	0.942704i	$-0.608273\pi$
$379$	−2.94373	+	0.788769i	−0.151209	+	0.0405163i	0.182420	+	0.983221i	$0.441607\pi$
$380$	−5.07781	−	8.54073i	−0.260486	−	0.438130i
$381$	−7.11906	+	4.11019i	−0.364721	+	0.210572i
$382$		−	1.77425i		−	0.0907783i
$383$	−0.0173775	−	0.0300987i	−0.000887948	−	0.00153797i	0.865581	−	0.500769i	$-0.166949\pi$
$383$	−0.0173775	−	0.0300987i	−0.000887948	−	0.00153797i	−0.866469	+	0.499231i	$0.833616\pi$
$384$	2.38987	+	0.640364i	0.121958	+	0.0326784i
$385$	−4.03047	+	7.19197i	−0.205412	+	0.366537i
$386$	−5.91481	−	10.2448i	−0.301056	−	0.521444i
$387$	14.5077	−	3.88734i	0.737470	−	0.197604i
$388$	4.98325	+	2.87708i	0.252986	+	0.146062i
$389$	21.2396			1.07689			0.538444	−	0.842661i	$-0.319012\pi$
$389$	21.2396			1.07689			0.538444	+	0.842661i	$0.319012\pi$
$390$	−17.8230	+	8.95782i	−0.902501	+	0.453597i
$391$	21.6900			1.09691
$392$	−5.01028	−	2.89269i	−0.253057	−	0.146103i
$393$	−0.945853	+	0.253441i	−0.0477120	+	0.0127844i
$394$	−0.935821	−	1.62089i	−0.0471460	−	0.0816592i
$395$	1.60960	−	0.453444i	0.0809876	−	0.0228153i
$396$	−10.0870	−	2.70281i	−0.506893	−	0.135822i
$397$	13.1279	+	22.7382i	0.658870	+	1.14120i	0.980909	+	0.194469i	$0.0622985\pi$
$397$	13.1279	+	22.7382i	0.658870	+	1.14120i	−0.322039	+	0.946726i	$0.604368\pi$
$398$			19.0453i			0.954653i
$399$	10.4935	−	6.05840i	0.525330	−	0.303299i
$400$	−0.127955	−	4.99836i	−0.00639775	−	0.249918i
$401$	−24.9456	+	6.68414i	−1.24572	+	0.333790i	−0.820682	−	0.571385i	$-0.806406\pi$
$401$	−24.9456	+	6.68414i	−1.24572	+	0.333790i	−0.425039	+	0.905175i	$0.639740\pi$
$402$	−7.46108	−	7.46108i	−0.372125	−	0.372125i
$403$	−15.3133	−	5.28748i	−0.762809	−	0.263388i
$404$		−	6.10893i		−	0.303930i
$405$	18.6817	+	4.75037i	0.928300	+	0.236048i
$406$	−1.06159	+	1.83872i	−0.0526857	+	0.0912543i
$407$	9.46996	−	35.3424i	0.469408	−	1.75186i
$408$	−7.16653			−0.354796
$409$	−0.0367688	+	0.137223i	−0.00181810	+	0.00678525i	−0.966829	−	0.255425i	$-0.917785\pi$
$409$	−0.0367688	+	0.137223i	−0.00181810	+	0.00678525i	0.965011	+	0.262210i	$0.0844513\pi$
$410$	3.01168	−	0.0385423i	0.148736	−	0.00190347i
$411$	−15.3065	−	15.3065i	−0.755012	−	0.755012i
$412$	15.4599	+	4.14246i	0.761653	+	0.204084i
$413$	−2.84413	−	10.6145i	−0.139951	−	0.522303i
$414$	−6.04990	−	22.5786i	−0.297337	−	1.10968i
$415$	−6.40031	−	22.7193i	−0.314179	−	1.11525i
$416$	2.98741	+	2.01876i	0.146470	+	0.0989779i
$417$	14.6231	−	14.6231i	0.716094	−	0.716094i
$418$	7.43284	−	12.8741i	0.363552	−	0.629691i
$419$	14.9181	+	8.61299i	0.728799	+	0.420772i	0.817982	−	0.575243i	$-0.195093\pi$
$419$	14.9181	+	8.61299i	0.728799	+	0.420772i	−0.0891839	+	0.996015i	$0.528426\pi$
$420$	6.09680	−	0.0780243i	0.297493	−	0.00380720i
$421$	10.5705	−	10.5705i	0.515175	−	0.515175i	−0.400932	−	0.916108i	$-0.631314\pi$
$421$	10.5705	−	10.5705i	0.515175	−	0.515175i	0.916108	+	0.400932i	$0.131314\pi$
$422$	−17.8049	+	10.2796i	−0.866727	+	0.500405i
$423$	21.3221	−	12.3103i	1.03671	−	0.598547i
$424$	−8.09456	+	8.09456i	−0.393107	+	0.393107i
$425$	4.10515	+	13.8887i	0.199129	+	0.673699i
$426$	−10.6724	−	6.16171i	−0.517079	−	0.298536i
$427$	4.06431	−	7.03960i	0.196686	−	0.340670i
$428$	7.71799	−	7.71799i	0.373063	−	0.373063i
$429$	−24.7272	−	16.7096i	−1.19384	−	0.806745i
$430$	−5.25981	+	9.38561i	−0.253650	+	0.452614i
$431$	−4.93983	−	18.4357i	−0.237943	−	0.888015i	−0.976800	−	0.214153i	$-0.931301\pi$
$431$	−4.93983	−	18.4357i	−0.237943	−	0.888015i	0.738857	−	0.673862i	$-0.235366\pi$
$432$	0.0778379	+	0.290495i	0.00374498	+	0.0139764i
$433$	−14.6659	−	3.92970i	−0.704796	−	0.188849i	−0.111418	−	0.993774i	$-0.535539\pi$
$433$	−14.6659	−	3.92970i	−0.704796	−	0.188849i	−0.593378	+	0.804924i	$0.702206\pi$
$434$	3.50156	+	3.50156i	0.168080	+	0.168080i
$435$	0.136387	+	10.6572i	0.00653925	+	0.510975i
$436$	2.22714	−	8.31181i	0.106661	−	0.398064i
$437$	33.2749			1.59176
$438$	−10.5284	+	39.2927i	−0.503068	+	1.87748i
$439$	−7.91150	+	13.7031i	−0.377595	+	0.654014i	−0.990712	−	0.135978i	$-0.956582\pi$
$439$	−7.91150	+	13.7031i	−0.377595	+	0.654014i	0.613117	+	0.789992i	$0.289916\pi$
$440$	6.42996	−	3.82288i	0.306537	−	0.182248i
$441$		−	18.0593i		−	0.859969i
$442$	−9.87169	−	3.40856i	−0.469548	−	0.162129i
$443$	−5.30191	−	5.30191i	−0.251901	−	0.251901i	0.569848	−	0.821750i	$-0.307002\pi$
$443$	−5.30191	−	5.30191i	−0.251901	−	0.251901i	−0.821750	+	0.569848i	$0.807002\pi$
$444$	−26.1383	+	7.00373i	−1.24047	+	0.332382i
$445$	7.08442	−	4.21197i	0.335834	−	0.199667i
$446$	11.7547	−	6.78661i	0.556603	−	0.321355i
$447$			7.24261i			0.342564i
$448$	−0.551051	−	0.954448i	−0.0260347	−	0.0450934i
$449$	−29.1112	−	7.80033i	−1.37384	−	0.368120i	−0.504962	−	0.863141i	$-0.668494\pi$
$449$	−29.1112	−	7.80033i	−1.37384	−	0.368120i	−0.868881	+	0.495021i	$0.835160\pi$
$450$	13.3126	−	8.14723i	0.627561	−	0.384064i
$451$	2.25309	+	3.90247i	0.106094	+	0.183760i
$452$	−8.56802	+	2.29579i	−0.403006	+	0.107985i
$453$	31.1845	+	18.0044i	1.46518	+	0.845920i
$454$	18.8959			0.886830
$455$	8.43527	+	2.79230i	0.395452	+	0.130905i
$456$	−10.9943			−0.514854
$457$	9.06439	+	5.23333i	0.424014	+	0.244805i	0.696793	−	0.717272i	$-0.254609\pi$
$457$	9.06439	+	5.23333i	0.424014	+	0.244805i	−0.272779	+	0.962077i	$0.587943\pi$
$458$	−1.43243	+	0.383818i	−0.0669329	+	0.0179346i
$459$	−0.435555	−	0.754403i	−0.0203300	−	0.0352125i
$460$	14.6069	+	8.18590i	0.681051	+	0.381669i
$461$	28.9862	+	7.76684i	1.35002	+	0.361738i	0.860143	−	0.510052i	$-0.170374\pi$
$461$	28.9862	+	7.76684i	1.35002	+	0.361738i	0.489880	+	0.871790i	$0.337041\pi$
$462$	4.56112	+	7.90009i	0.212203	+	0.367546i
$463$			17.5146i			0.813971i	0.913435	+	0.406986i	$0.133420\pi$
$463$			17.5146i			0.813971i	−0.913435	+	0.406986i	$0.866580\pi$
$464$	1.66838	−	0.963240i	0.0774526	−	0.0447173i
$465$	24.0916	+	6.12601i	1.11722	+	0.284087i
$466$	22.4674	−	6.02011i	1.04078	−	0.278876i
$467$	7.96893	+	7.96893i	0.368758	+	0.368758i	0.867024	−	0.498266i	$-0.166030\pi$
$467$	7.96893	+	7.96893i	0.368758	+	0.368758i	−0.498266	+	0.867024i	$0.666030\pi$
$468$	−0.794727	+	11.2268i	−0.0367363	+	0.518960i
$469$			4.70010i			0.217031i
$470$	−4.34630	+	17.0926i	−0.200480	+	0.788422i
$471$	−11.7583	+	20.3659i	−0.541792	+	0.938411i
$472$	−2.58065	+	9.63111i	−0.118784	+	0.443308i
$473$	−16.0966			−0.740123
$474$	0.478898	−	1.78727i	0.0219965	−	0.0820921i
$475$	6.29777	+	21.3068i	0.288962	+	0.977622i
$476$	2.25728	+	2.25728i	0.103462	+	0.103462i
$477$	−34.5162	−	9.24858i	−1.58039	−	0.423463i
$478$	−5.33634	−	19.9155i	−0.244078	−	0.910913i
$479$	−3.94104	−	14.7082i	−0.180071	−	0.672033i	−0.995632	−	0.0933628i	$-0.970238\pi$
$479$	−3.94104	−	14.7082i	−0.180071	−	0.672033i	0.815561	−	0.578671i	$-0.196428\pi$
$480$	−4.82623	−	2.70468i	−0.220286	−	0.123451i
$481$	−39.3359	−	2.78452i	−1.79356	−	0.126963i
$482$	0.214110	−	0.214110i	0.00975244	−	0.00975244i
$483$	−10.2095	+	17.6834i	−0.464548	+	0.804620i
$484$	0.166072	+	0.0958815i	0.00754871	+	0.00435825i
$485$	−9.21380	−	8.98095i	−0.418377	−	0.407804i
$486$	15.7197	−	15.7197i	0.713061	−	0.713061i
$487$	−28.2464	+	16.3081i	−1.27997	+	0.738990i	−0.976842	−	0.213960i	$-0.931364\pi$
$487$	−28.2464	+	16.3081i	−1.27997	+	0.738990i	−0.303126	+	0.952950i	$0.598030\pi$
$488$	−6.38743	+	3.68778i	−0.289145	+	0.166938i
$489$	3.89390	−	3.89390i	0.176088	−	0.176088i
$490$	9.26378	+	9.02967i	0.418495	+	0.407919i
$491$	4.33762	+	2.50433i	0.195754	+	0.113019i	0.594674	−	0.803967i	$-0.297281\pi$
$491$	4.33762	+	2.50433i	0.195754	+	0.113019i	−0.398919	+	0.916986i	$0.630615\pi$
$492$	1.66633	−	2.88617i	0.0751239	−	0.130118i
$493$	−3.94573	+	3.94573i	−0.177707	+	0.177707i
$494$	−15.1443	−	5.22912i	−0.681374	−	0.235269i
$495$	20.3703	+	11.4157i	0.915576	+	0.513100i
$496$	−1.16292	−	4.34009i	−0.0522168	−	0.194876i
$497$	1.42075	+	5.30231i	0.0637294	+	0.237841i
$498$	−25.2271	−	6.75958i	−1.13045	−	0.302904i
$499$	−9.65310	−	9.65310i	−0.432132	−	0.432132i	0.457221	−	0.889353i	$-0.348845\pi$
$499$	−9.65310	−	9.65310i	−0.432132	−	0.432132i	−0.889353	+	0.457221i	$0.848845\pi$
$500$	−2.47706	+	10.9025i	−0.110777	+	0.487574i
$501$	−11.4805	+	42.8459i	−0.512912	+	1.91421i
$502$	11.2731			0.503145
$503$	6.80685	−	25.4035i	0.303502	−	1.13269i	−0.630724	−	0.776007i	$-0.717242\pi$
$503$	6.80685	−	25.4035i	0.303502	−	1.13269i	0.934227	−	0.356680i	$-0.116091\pi$
$504$	1.72013	−	2.97936i	0.0766208	−	0.132711i
$505$	−3.36633	+	13.2387i	−0.149800	+	0.589114i
$506$			25.0513i			1.11367i
$507$	−12.6183	+	29.5858i	−0.560400	+	1.31395i
$508$	−2.34934	−	2.34934i	−0.104235	−	0.104235i
$509$	−27.3286	+	7.32267i	−1.21132	+	0.324572i	−0.807279	−	0.590170i	$-0.799061\pi$
$509$	−27.3286	+	7.32267i	−1.21132	+	0.324572i	−0.404039	+	0.914742i	$0.632394\pi$
$510$	15.5306	+	3.94912i	0.687707	+	0.174870i
$511$	15.6924	−	9.06001i	0.694191	−	0.400791i
$512$			1.00000i			0.0441942i
$513$	−0.668191	−	1.15734i	−0.0295013	−	0.0510978i
$514$	−16.0275	−	4.29455i	−0.706942	−	0.189425i
$515$	−31.2205	−	17.4963i	−1.37574	−	0.770980i
$516$	5.95232	+	10.3097i	0.262036	+	0.453860i
$517$	−25.4871	+	6.82926i	−1.12092	+	0.300350i
$518$	10.4389	+	6.02690i	0.458659	+	0.264807i
$519$	21.2554			0.933010
$520$	−5.36159	−	6.02108i	−0.235121	−	0.264042i
$521$	37.1583			1.62793			0.813967	−	0.580911i	$-0.197303\pi$
$521$	37.1583			1.62793			0.813967	+	0.580911i	$0.197303\pi$
$522$	5.20794	+	3.00680i	0.227945	+	0.131604i
$523$	−19.3707	+	5.19038i	−0.847024	+	0.226959i	−0.656127	−	0.754651i	$-0.727806\pi$
$523$	−19.3707	+	5.19038i	−0.847024	+	0.226959i	−0.190897	+	0.981610i	$0.561140\pi$
$524$	−0.197888	−	0.342752i	−0.00864477	−	0.0149732i
$525$	−13.2554	−	3.19056i	−0.578513	−	0.139247i
$526$	4.57715	+	1.22644i	0.199573	+	0.0534755i
$527$	6.50734	+	11.2710i	0.283464	+	0.490974i
$528$		−	8.27714i		−	0.360216i
$529$	−28.6431	+	16.5371i	−1.24535	+	0.719005i
$530$	22.0023	−	13.0812i	0.955718	−	0.568213i
$531$	−30.0640	+	8.05563i	−1.30467	+	0.349584i
$532$	3.46292	+	3.46292i	0.150136	+	0.150136i
$533$	3.66805	−	3.18307i	0.158881	−	0.137874i
$534$		−	9.11960i		−	0.394644i
$535$	−20.9787	+	12.4727i	−0.906988	+	0.539241i
$536$	2.13234	−	3.69332i	0.0921029	−	0.159527i
$537$	−7.17563	+	26.7798i	−0.309651	+	1.15563i
$538$	−4.26156			−0.183729
$539$	−5.00930	+	18.6950i	−0.215766	+	0.805249i
$540$	−0.00860542	−	0.672426i	−0.000370319	−	0.0289366i
$541$	−26.3804	−	26.3804i	−1.13418	−	1.13418i	−0.989474	−	0.144710i	$-0.953775\pi$
$541$	−26.3804	−	26.3804i	−1.13418	−	1.13418i	−0.144710	−	0.989474i	$-0.546225\pi$
$542$	9.10585	+	2.43990i	0.391130	+	0.104803i
$543$	−14.6269	−	54.5884i	−0.627701	−	2.34261i
$544$	−0.749677	−	2.79783i	−0.0321421	−	0.119956i
$545$	−9.40668	+	16.7853i	−0.402938	+	0.719003i
$546$	7.42553	−	6.44374i	0.317783	−	0.275767i
$547$	9.57195	−	9.57195i	0.409267	−	0.409267i	−0.472216	−	0.881483i	$-0.656546\pi$
$547$	9.57195	−	9.57195i	0.409267	−	0.409267i	0.881483	+	0.472216i	$0.156546\pi$
$548$	4.37451	−	7.57687i	0.186870	−	0.323668i
$549$	−19.9387	−	11.5116i	−0.850963	−	0.491304i
$550$	−16.0410	+	4.74134i	−0.683991	+	0.202171i
$551$	−6.05320	+	6.05320i	−0.257875	+	0.257875i
$552$	16.0451	−	9.26366i	0.682926	−	0.394287i
$553$	−0.713786	+	0.412105i	−0.0303533	+	0.0175245i
$554$	4.16351	−	4.16351i	0.176890	−	0.176890i
$555$	60.5038	−	0.774303i	2.56824	−	0.0328673i
$556$	7.23857	+	4.17919i	0.306984	+	0.177237i
$557$	−0.204041	+	0.353409i	−0.00864550	+	0.0149744i	−0.870316	−	0.492494i	$-0.836085\pi$
$557$	−0.204041	+	0.353409i	−0.00864550	+	0.0149744i	0.861670	+	0.507469i	$0.169419\pi$
$558$	9.91770	−	9.91770i	0.419850	−	0.419850i
$559$	3.29561	+	17.0324i	0.139390	+	0.720393i
$560$	0.668235	+	2.37205i	0.0282381	+	0.100237i
$561$	6.20518	+	23.1580i	0.261983	+	0.977733i
$562$	−1.11521	−	4.16201i	−0.0470422	−	0.175564i
$563$	12.7913	+	3.42741i	0.539088	+	0.144448i	0.518081	−	0.855331i	$-0.326646\pi$
$563$	12.7913	+	3.42741i	0.539088	+	0.144448i	0.0210061	+	0.999779i	$0.493313\pi$
$564$	13.7989	+	13.7989i	0.581038	+	0.581038i
$565$	19.8329	−	0.253813i	0.834376	−	0.0106780i
$566$	1.29094	−	4.81786i	0.0542623	−	0.202510i
$567$	−9.50074			−0.398994
$568$	1.28913	−	4.81110i	0.0540907	−	0.201869i
$569$	10.9407	−	18.9499i	0.458659	−	0.794421i	−0.540231	−	0.841516i	$-0.681663\pi$
$569$	10.9407	−	18.9499i	0.458659	−	0.794421i	0.998890	+	0.0470959i	$0.0149966\pi$
$570$	23.8257	+	6.05840i	0.997950	+	0.253758i
$571$		−	13.4763i		−	0.563964i	−0.959420	−	0.281982i	$-0.909008\pi$
$571$		−	13.4763i		−	0.563964i	0.959420	−	0.281982i	$-0.0909919\pi$
$572$	3.93679	−	11.4015i	0.164606	−	0.476721i
$573$	3.10406	+	3.10406i	0.129674	+	0.129674i
$574$	−1.43392	+	0.384218i	−0.0598507	+	0.0160370i
$575$	−27.1439	−	25.7888i	−1.13198	−	1.07547i
$576$	−2.70334	+	1.56078i	−0.112639	+	0.0650323i
$577$		−	16.5356i		−	0.688388i	−0.938899	−	0.344194i	$-0.888152\pi$
$577$		−	16.5356i		−	0.688388i	0.938899	−	0.344194i	$-0.111848\pi$
$578$	−4.30506	−	7.45658i	−0.179067	−	0.310153i
$579$	28.2713	+	7.57527i	1.17491	+	0.314817i
$580$	−4.14635	+	1.16808i	−0.172168	+	0.0485019i
$581$	5.81680	+	10.0750i	0.241322	+	0.417981i
$582$	−13.7517	+	3.68476i	−0.570026	+	0.152738i
$583$	33.1656	+	19.1482i	1.37358	+	0.793037i
$584$	−16.4413			−0.680347
$585$	7.90881	−	23.8918i	0.326989	−	0.987803i
$586$	−14.4622			−0.597428
$587$	−29.5013	−	17.0326i	−1.21765	−	0.703010i	−0.253234	−	0.967405i	$-0.581494\pi$
$587$	−29.5013	−	17.0326i	−1.21765	−	0.703010i	−0.964414	+	0.264395i	$0.914828\pi$
$588$	13.8263	−	3.70475i	0.570187	−	0.152781i
$589$	9.98299	+	17.2910i	0.411342	+	0.712465i
$590$	10.8998	−	19.4495i	0.448736	−	0.800725i
$591$	4.47298	+	1.19853i	0.183994	+	0.0493010i
$592$	−5.46855	−	9.47181i	−0.224756	−	0.389289i
$593$		−	1.35571i		−	0.0556721i	−0.999613	−	0.0278361i	$-0.991138\pi$
$593$		−	1.35571i		−	0.0556721i	0.999613	−	0.0278361i	$-0.00886164\pi$
$594$	0.871314	−	0.503053i	0.0357504	−	0.0206405i
$595$	−3.64788	−	6.13563i	−0.149548	−	0.251536i
$596$	−2.82754	+	0.757636i	−0.115820	+	0.0310340i
$597$	−33.3198	−	33.3198i	−1.36369	−	1.36369i
$598$	26.5077	−	5.12900i	1.08398	−	0.209740i
$599$		−	11.5295i		−	0.471081i	−0.971864	−	0.235541i	$-0.924314\pi$
$599$		−	11.5295i		−	0.471081i	0.971864	−	0.235541i	$-0.0756861\pi$
$600$	8.96853	+	8.52081i	0.366139	+	0.347861i
$601$	−14.3330	+	24.8254i	−0.584654	+	1.01265i	0.410264	+	0.911967i	$0.365436\pi$
$601$	−14.3330	+	24.8254i	−0.584654	+	1.01265i	−0.994918	+	0.100684i	$0.967897\pi$
$602$	1.37247	−	5.12213i	0.0559377	−	0.208762i
$603$	13.3124			0.542123
$604$	−3.76681	+	14.0579i	−0.153269	+	0.572009i
$605$	−0.307059	−	0.299299i	−0.0124837	−	0.0121682i
$606$	10.6876	+	10.6876i	0.434154	+	0.434154i
$607$	−40.9211	−	10.9648i	−1.66094	−	0.445046i	−0.698291	−	0.715814i	$-0.746056\pi$
$607$	−40.9211	−	10.9648i	−1.66094	−	0.445046i	−0.962645	+	0.270768i	$0.912722\pi$
$608$	−1.15009	−	4.29219i	−0.0466423	−	0.174071i
$609$	−1.35961	−	5.07412i	−0.0550940	−	0.205614i
$610$	15.8744	−	4.47202i	0.642735	−	0.181067i
$611$	12.4445	+	25.5706i	0.503451	+	1.03448i
$612$	6.39343	−	6.39343i	0.258439	−	0.258439i
$613$	21.6229	−	37.4520i	0.873342	−	1.51267i	0.0148245	−	0.999890i	$-0.495281\pi$
$613$	21.6229	−	37.4520i	0.873342	−	1.51267i	0.858518	−	0.512783i	$-0.171386\pi$
$614$	−14.7625	−	8.52313i	−0.595766	−	0.343965i
$615$	−5.20153	+	5.33639i	−0.209746	+	0.215184i
$616$	−2.60709	+	2.60709i	−0.105043	+	0.105043i
$617$	35.5212	−	20.5082i	1.43003	−	0.825628i	0.432908	−	0.901438i	$-0.357487\pi$
$617$	35.5212	−	20.5082i	1.43003	−	0.825628i	0.997122	+	0.0758097i	$0.0241541\pi$
$618$	−34.2944	+	19.7999i	−1.37952	+	0.796469i
$619$	−0.641455	+	0.641455i	−0.0257823	+	0.0257823i	−0.719880	−	0.694098i	$-0.755803\pi$
$619$	−0.641455	+	0.641455i	−0.0257823	+	0.0257823i	0.694098	+	0.719880i	$0.255803\pi$
$620$	0.128568	+	10.0463i	0.00516341	+	0.403468i
$621$	1.95033	+	1.12602i	0.0782639	+	0.0451857i
$622$	13.7043	−	23.7366i	0.549493	−	0.951750i
$623$	−2.87244	+	2.87244i	−0.115082	+	0.115082i
$624$	−8.75833	+	1.69466i	−0.350614	+	0.0678406i
$625$	11.3759	−	22.2618i	0.455035	−	0.890474i
$626$	−2.59826	−	9.69683i	−0.103847	−	0.387563i
$627$	9.51945	+	35.5271i	0.380170	+	1.41881i
$628$	−9.18091	−	2.46002i	−0.366358	−	0.0981654i
$629$	22.4009	+	22.4009i	0.893183	+	0.893183i
$630$	−5.36949	+	5.50870i	−0.213925	+	0.219472i
$631$	2.01738	−	7.52898i	0.0803108	−	0.299724i	−0.914074	−	0.405547i	$-0.867081\pi$
$631$	2.01738	−	7.52898i	0.0803108	−	0.299724i	0.994385	+	0.105823i	$0.0337477\pi$
$632$	0.747852			0.0297480
$633$	13.1654	−	49.1341i	0.523279	−	1.95290i
$634$	−10.4802	+	18.1522i	−0.416221	+	0.720917i
$635$	3.79667	+	6.38588i	0.150666	+	0.253416i
$636$		−	28.3230i		−	1.12308i
$637$	20.8074	+	1.47292i	0.824419	+	0.0583591i
$638$	−4.55721	−	4.55721i	−0.180422	−	0.180422i
$639$	15.0181	−	4.02408i	0.594106	−	0.159190i
$640$	0.551051	−	2.16710i	0.0217822	−	0.0856623i
$641$	27.2442	−	15.7295i	1.07608	−	0.621276i	0.146245	−	0.989248i	$-0.453281\pi$
$641$	27.2442	−	15.7295i	1.07608	−	0.621276i	0.929837	+	0.367972i	$0.119948\pi$
$642$			27.0054i			1.06582i
$643$	−4.06494	−	7.04068i	−0.160305	−	0.277657i	0.774673	−	0.632362i	$-0.217915\pi$
$643$	−4.06494	−	7.04068i	−0.160305	−	0.277657i	−0.934978	+	0.354705i	$0.884581\pi$
$644$	−7.97163	−	2.13599i	−0.314126	−	0.0841698i
$645$	−7.21812	−	25.6223i	−0.284213	−	1.00888i
$646$	6.43552	+	11.1466i	0.253202	+	0.438559i
$647$	−2.72310	+	0.729652i	−0.107056	+	0.0286856i	−0.311949	−	0.950099i	$-0.600982\pi$
$647$	−2.72310	+	0.729652i	−0.107056	+	0.0286856i	0.204893	+	0.978784i	$0.434315\pi$
$648$	7.46563	+	4.31028i	0.293278	+	0.169324i
$649$	33.3566			1.30936
$650$	8.30120	+	16.0028i	0.325600	+	0.627682i
$651$	−12.2520			−0.480194
$652$	1.92752	+	1.11286i	0.0754876	+	0.0435828i
$653$	−5.60977	+	1.50313i	−0.219527	+	0.0588222i	−0.366906	−	0.930258i	$-0.619583\pi$
$653$	−5.60977	+	1.50313i	−0.219527	+	0.0588222i	0.147379	+	0.989080i	$0.452916\pi$
$654$	10.6452	+	18.4380i	0.416259	+	0.720982i
$655$	0.239970	+	0.851825i	0.00937641	+	0.0332836i
$656$	1.30108	+	0.348623i	0.0507986	+	0.0136114i
$657$	−25.6612	−	44.4466i	−1.00114	−	1.73403i
$658$		−	8.69260i		−	0.338873i
$659$	1.91821	−	1.10748i	0.0747228	−	0.0431413i	−0.462173	−	0.886790i	$-0.652930\pi$
$659$	1.91821	−	1.10748i	0.0747228	−	0.0431413i	0.536896	+	0.843648i	$0.319597\pi$
$660$	−4.56112	+	17.9374i	−0.177541	+	0.698213i
$661$	−27.4462	+	7.35419i	−1.06753	+	0.286045i	−0.749479	−	0.662028i	$-0.769696\pi$
$661$	−27.4462	+	7.35419i	−1.06753	+	0.286045i	−0.318054	+	0.948073i	$0.603029\pi$
$662$	−11.8234	−	11.8234i	−0.459528	−	0.459528i
$663$	23.2339	−	11.3073i	0.902330	−	0.439139i
$664$		−	10.5558i		−	0.409646i
$665$	−5.59626	−	9.41275i	−0.217014	−	0.365011i
$666$	17.0704	−	29.5668i	0.661464	−	1.14569i
$667$	3.73372	−	13.9344i	0.144570	−	0.539544i
$668$	−17.9281			−0.693660
$669$	−8.69180	+	32.4382i	−0.336044	+	1.25413i
$670$	−6.65620	+	6.82878i	−0.257152	+	0.263819i
$671$	17.4474	+	17.4474i	0.673548	+	0.673548i
$672$	2.63388	+	0.705746i	0.101604	+	0.0272248i
$673$	11.6518	+	43.4850i	0.449142	+	1.67622i	0.704762	+	0.709444i	$0.251054\pi$
$673$	11.6518	+	43.4850i	0.449142	+	1.67622i	−0.255619	+	0.966778i	$0.582279\pi$
$674$	4.89627	+	18.2731i	0.188597	+	0.703854i
$675$	−0.351892	+	1.46196i	−0.0135443	+	0.0562708i
$676$	−12.8704	−	1.83132i	−0.495014	−	0.0704353i
$677$	−22.4488	+	22.4488i	−0.862778	+	0.862778i	−0.991660	−	0.128882i	$-0.958861\pi$
$677$	−22.4488	+	22.4488i	−0.862778	+	0.862778i	0.128882	+	0.991660i	$0.458861\pi$
$678$	10.9733	−	19.0063i	0.421427	−	0.729934i
$679$	5.49204	+	3.17083i	0.210765	+	0.121685i
$680$	0.0828811	+	6.47631i	0.00317835	+	0.248355i
$681$	−33.0586	+	33.0586i	−1.26681	+	1.26681i
$682$	−13.0177	+	7.51579i	−0.498474	+	0.287794i
$683$	25.5934	−	14.7764i	0.979305	−	0.565402i	0.0772447	−	0.997012i	$-0.475388\pi$
$683$	25.5934	−	14.7764i	0.979305	−	0.565402i	0.902060	+	0.431610i	$0.142054\pi$
$684$	9.80824	−	9.80824i	0.375027	−	0.375027i
$685$	−13.6553	+	14.0093i	−0.521740	+	0.535267i
$686$	−12.2030	−	7.04539i	−0.465912	−	0.268994i
$687$	1.83455	−	3.17753i	0.0699925	−	0.121231i
$688$	−3.40228	+	3.40228i	−0.129711	+	0.129711i
$689$	13.4711	−	39.0141i	0.513206	−	1.48632i
$690$	−39.8762	+	11.2336i	−1.51806	+	0.427657i
$691$	3.05516	+	11.4020i	0.116224	+	0.433753i	0.999376	−	0.0353343i	$-0.0112496\pi$
$691$	3.05516	+	11.4020i	0.116224	+	0.433753i	−0.883152	+	0.469087i	$0.844583\pi$
$692$	2.22349	+	8.29818i	0.0845244	+	0.315450i
$693$	−11.1169	−	2.97877i	−0.422298	−	0.113154i
$694$	3.15309	+	3.15309i	0.119690	+	0.119690i
$695$	−13.3838	−	13.0456i	−0.507677	−	0.494847i
$696$	−1.23365	+	4.60404i	−0.0467613	+	0.174516i
$697$	−3.90156			−0.147782
$698$	−3.59895	+	13.4314i	−0.136222	+	0.508388i
$699$	−28.7746	+	49.8391i	−1.08836	+	1.88509i
$700$	−0.141019	−	5.50870i	−0.00533003	−	0.208209i
$701$			17.5090i			0.661306i	0.943752	+	0.330653i	$0.107269\pi$
$701$			17.5090i			0.661306i	−0.943752	+	0.330653i	$0.892731\pi$
$702$	−0.710691	−	0.818973i	−0.0268233	−	0.0309101i
$703$	34.3655	+	34.3655i	1.29612	+	1.29612i
$704$	3.23142	−	0.865856i	0.121789	−	0.0326332i
$705$	−22.2997	−	37.5075i	−0.839857	−	1.41261i
$706$	0.857885	−	0.495300i	0.0322869	−	0.0186409i
$707$		−	6.73265i		−	0.253208i
$708$	−12.3348	−	21.3646i	−0.463571	−	0.802929i
$709$	−14.1418	−	3.78927i	−0.531105	−	0.142309i	−0.0167065	−	0.999860i	$-0.505318\pi$
$709$	−14.1418	−	3.78927i	−0.531105	−	0.142309i	−0.514398	+	0.857551i	$0.671985\pi$
$710$	−5.44483	+	9.71577i	−0.204341	+	0.364626i
$711$	1.16723	+	2.02170i	0.0437746	+	0.0758198i
$712$	3.56032	−	0.953984i	0.133428	−	0.0357521i
$713$	−29.1385	−	16.8231i	−1.09125	−	0.630031i
$714$	−7.89824			−0.295584
$715$	−14.8143	+	22.5389i	−0.554022	+	0.842907i
$716$	−11.2055			−0.418771
$717$	44.1783	+	25.5063i	1.64987	+	0.952551i
$718$	−16.1364	+	4.32374i	−0.602206	+	0.161361i
$719$	20.1467	+	34.8952i	0.751346	+	1.30137i	0.947170	+	0.320731i	$0.103929\pi$
$719$	20.1467	+	34.8952i	0.751346	+	1.30137i	−0.195824	+	0.980639i	$0.562738\pi$
$720$	6.71850	−	1.89269i	0.250384	−	0.0705363i
$721$	17.0383	+	4.56541i	0.634541	+	0.170025i
$722$	0.372816	+	0.645736i	0.0138748	+	0.0240318i
$723$			0.749174i			0.0278621i
$724$	19.7814	−	11.4208i	0.735168	−	0.424450i
$725$	9.62924	−	0.246502i	0.357621	−	0.00915487i
$726$	−0.458289	+	0.122798i	−0.0170087	+	0.00455747i
$727$	−9.49105	−	9.49105i	−0.352004	−	0.352004i	0.508851	−	0.860855i	$-0.330070\pi$
$727$	−9.49105	−	9.49105i	−0.352004	−	0.352004i	−0.860855	+	0.508851i	$0.830070\pi$
$728$	3.29243	+	2.22488i	0.122025	+	0.0824595i
$729$			29.1418i			1.07933i
$730$	35.6301	+	9.06001i	1.31873	+	0.335326i
$731$	6.96840	−	12.0696i	0.257736	−	0.446411i
$732$	4.72305	−	17.6267i	0.174569	−	0.651500i
$733$	4.54882			0.168015			0.0840073	−	0.996465i	$-0.473228\pi$
$733$	4.54882			0.168015			0.0840073	+	0.996465i	$0.473228\pi$
$734$	8.34106	−	31.1292i	0.307874	−	1.14900i
$735$	−32.0045	+	0.409581i	−1.18051	+	0.0151076i
$736$	5.29501	+	5.29501i	0.195177	+	0.195177i
$737$	−13.7809	−	3.69259i	−0.507628	−	0.136018i
$738$	1.08825	+	4.06139i	0.0400589	+	0.149502i
$739$	−5.30194	−	19.7871i	−0.195035	−	0.727881i	−0.992258	−	0.124196i	$-0.960365\pi$
$739$	−5.30194	−	19.7871i	−0.195035	−	0.727881i	0.797223	−	0.603685i	$-0.206302\pi$
$740$	6.63148	+	23.5399i	0.243778	+	0.865343i
$741$	35.6434	−	17.3467i	1.30939	−	0.637245i
$742$	−8.92103	+	8.92103i	−0.327501	+	0.327501i
$743$	−4.09115	+	7.08607i	−0.150090	+	0.259963i	−0.931260	−	0.364355i	$-0.881290\pi$
$743$	−4.09115	+	7.08607i	−0.150090	+	0.259963i	0.781171	+	0.624318i	$0.214623\pi$
$744$	9.62757	+	5.55848i	0.352964	+	0.203784i
$745$	6.54507	−	0.0837610i	0.239793	−	0.00306877i
$746$	1.78132	−	1.78132i	0.0652187	−	0.0652187i
$747$	28.5361	−	16.4753i	1.04408	−	0.602800i
$748$	−8.39185	+	4.84504i	−0.306837	+	0.177152i
$749$	8.50601	−	8.50601i	0.310803	−	0.310803i
$750$	−14.7403	−	23.4076i	−0.538241	−	0.854725i
$751$	21.5801	+	12.4593i	0.787469	+	0.454645i	0.839071	−	0.544022i	$-0.183099\pi$
$751$	21.5801	+	12.4593i	0.787469	+	0.454645i	−0.0516018	+	0.998668i	$0.516433\pi$
$752$	−3.94365	+	6.83060i	−0.143810	+	0.249086i
$753$	−19.7224	+	19.7224i	−0.718725	+	0.718725i
$754$	−3.88910	+	5.75518i	−0.141633	+	0.209591i
$755$	15.9097	−	28.3893i	0.579014	−	1.03319i
$756$	0.0857852	+	0.320155i	0.00311998	+	0.0116439i
$757$	3.56508	+	13.3051i	0.129575	+	0.483581i	0.999961	−	0.00878853i	$-0.00279751\pi$
$757$	3.56508	+	13.3051i	0.129575	+	0.483581i	−0.870386	+	0.492370i	$0.836131\pi$
$758$	2.94373	+	0.788769i	0.106921	+	0.0286494i
$759$	−43.8275	−	43.8275i	−1.59084	−	1.59084i
$760$	0.127149	+	9.93539i	0.00461218	+	0.360395i
$761$	8.43875	−	31.4939i	0.305905	−	1.14165i	−0.626259	−	0.779615i	$-0.715415\pi$
$761$	8.43875	−	31.4939i	0.305905	−	1.14165i	0.932164	−	0.362036i	$-0.117918\pi$
$762$	8.22039			0.297793
$763$	2.45454	−	9.16046i	0.0888602	−	0.331631i
$764$	−0.887123	+	1.53654i	−0.0320950	+	0.0555901i
$765$	−17.3783	+	10.3321i	−0.628315	+	0.373559i
$766$			0.0347550i			0.00125575i
$767$	−6.82941	−	35.2958i	−0.246596	−	1.27446i
$768$	−1.74951	−	1.74951i	−0.0631299	−	0.0631299i
$769$	−4.09555	+	1.09740i	−0.147689	+	0.0395732i	−0.331906	−	0.943312i	$-0.607692\pi$
$769$	−4.09555	+	1.09740i	−0.147689	+	0.0395732i	0.184217	+	0.982886i	$0.441025\pi$
$770$	7.08647	−	4.21320i	0.255379	−	0.151833i
$771$	35.5535	−	20.5269i	1.28043	−	0.739256i
$772$			11.8296i			0.425758i
$773$	−18.8879	−	32.7148i	−0.679350	−	1.17667i	−0.975177	−	0.221427i	$-0.928929\pi$
$773$	−18.8879	−	32.7148i	−0.679350	−	1.17667i	0.295827	−	0.955241i	$-0.404405\pi$
$774$	−14.5077	−	3.88734i	−0.521470	−	0.139727i
$775$	5.25738	−	21.8422i	0.188851	−	0.784593i
$776$	−2.87708	−	4.98325i	−0.103281	−	0.178888i
$777$	−28.8070	+	7.71882i	−1.03345	+	0.276911i
$778$	−18.3940	−	10.6198i	−0.659457	−	0.380737i
$779$	−5.98543			−0.214450
$780$	19.9141	+	1.15378i	0.713038	+	0.0413121i
$781$	−16.6629			−0.596244
$782$	−18.7841	−	10.8450i	−0.671718	−	0.387817i
$783$	−0.559633	+	0.149953i	−0.0199996	+	0.00535889i
$784$	2.89269	+	5.01028i	0.103310	+	0.178939i
$785$	18.5404	+	10.3903i	0.661735	+	0.370844i
$786$	0.945853	+	0.253441i	0.0337375	+	0.00903993i
$787$	8.13472	+	14.0897i	0.289971	+	0.502245i	0.973803	−	0.227395i	$-0.0730209\pi$
$787$	8.13472	+	14.0897i	0.289971	+	0.502245i	−0.683831	+	0.729640i	$0.739688\pi$
$788$			1.87164i			0.0666745i
$789$	−10.1534	+	5.86208i	−0.361472	+	0.208696i
$790$	−1.62067	−	0.412105i	−0.0576610	−	0.0146620i
$791$	−9.44283	+	2.53020i	−0.335748	+	0.0899635i
$792$	7.38422	+	7.38422i	0.262387	+	0.262387i
$793$	14.8895	−	22.0338i	0.528742	−	0.782444i
$794$		−	26.2558i		−	0.931782i
$795$	−15.6074	+	61.3789i	−0.553537	+	2.17688i
$796$	9.52263	−	16.4937i	0.337521	−	0.584603i
$797$	−8.62476	+	32.1880i	−0.305505	+	1.14016i	0.627005	+	0.779015i	$0.284280\pi$
$797$	−8.62476	+	32.1880i	−0.305505	+	1.14016i	−0.932510	+	0.361144i	$0.882386\pi$
$798$	−12.1168			−0.428930
$799$	5.91292	−	22.0673i	0.209184	−	0.780686i
$800$	−2.38837	+	4.39269i	−0.0844416	+	0.155305i
$801$	8.13580	+	8.13580i	0.287464	+	0.287464i
$802$	24.9456	+	6.68414i	0.880858	+	0.236025i
$803$	14.2358	+	53.1288i	0.502371	+	1.87487i
$804$	2.73094	+	10.1920i	0.0963130	+	0.359445i
$805$	16.0983	+	9.02169i	0.567391	+	0.317973i
$806$	10.6180	+	12.2357i	0.374002	+	0.430985i
$807$	7.45564	−	7.45564i	0.262451	−	0.262451i
$808$	−3.05446	+	5.29048i	−0.107456	+	0.186119i
$809$	0.775625	+	0.447807i	0.0272695	+	0.0157441i	0.513573	−	0.858046i	$-0.328322\pi$
$809$	0.775625	+	0.447807i	0.0272695	+	0.0157441i	−0.486303	+	0.873790i	$0.661655\pi$
$810$	−13.8036	−	13.4548i	−0.485010	−	0.472753i
$811$	−16.2913	+	16.2913i	−0.572063	+	0.572063i	−0.932705	−	0.360641i	$-0.882558\pi$
$811$	−16.2913	+	16.2913i	−0.572063	+	0.572063i	0.360641	+	0.932705i	$0.382558\pi$
$812$	1.83872	−	1.06159i	0.0645266	−	0.0372544i
$813$	−20.1994	+	11.6621i	−0.708423	+	0.409008i
$814$	−25.8724	+	25.8724i	−0.906827	+	0.906827i
$815$	−3.56390	−	3.47384i	−0.124838	−	0.121683i
$816$	6.20640	+	3.58326i	0.217267	+	0.125439i
$817$	10.6903	−	18.5162i	0.374007	−	0.647799i
$818$	0.100454	−	0.100454i	0.00351230	−	0.00351230i
$819$	−0.875870	+	12.3731i	−0.0306054	+	0.432351i
$820$	−2.62747	−	1.47246i	−0.0917551	−	0.0514207i
$821$	−7.23200	−	26.9902i	−0.252399	−	0.941965i	−0.969519	−	0.245016i	$-0.921207\pi$
$821$	−7.23200	−	26.9902i	−0.252399	−	0.941965i	0.717120	−	0.696949i	$-0.245460\pi$
$822$	5.60255	+	20.9090i	0.195412	+	0.729286i
$823$	−20.8667	−	5.59121i	−0.727366	−	0.194897i	−0.123910	−	0.992293i	$-0.539543\pi$
$823$	−20.8667	−	5.59121i	−0.727366	−	0.194897i	−0.603456	+	0.797396i	$0.706210\pi$
$824$	−11.3174	−	11.3174i	−0.394261	−	0.394261i
$825$	19.7689	−	36.3589i	0.688263	−	1.26585i
$826$	−2.84413	+	10.6145i	−0.0989601	+	0.369324i
$827$	35.4430			1.23247			0.616237	−	0.787561i	$-0.288656\pi$
$827$	35.4430			1.23247			0.616237	+	0.787561i	$0.288656\pi$
$828$	−6.04990	+	22.5786i	−0.210249	+	0.784659i
$829$	−16.7195	+	28.9590i	−0.580693	+	1.00579i	0.414705	+	0.909956i	$0.363885\pi$
$829$	−16.7195	+	28.9590i	−0.580693	+	1.00579i	−0.995397	+	0.0958333i	$0.969448\pi$
$830$	−5.81680	+	22.8756i	−0.201904	+	0.794024i
$831$			14.5682i			0.505364i
$832$	−1.57779	−	3.24200i	−0.0547001	−	0.112396i
$833$	−11.8493	−	11.8493i	−0.410556	−	0.410556i
$834$	−19.9755	+	5.35241i	−0.691694	+	0.185339i
$835$	38.8521	+	9.87930i	1.34453	+	0.341887i
$836$	−12.8741	+	7.43284i	−0.445259	+	0.257070i
$837$			1.35129i			0.0467076i
$838$	−8.61299	−	14.9181i	−0.297531	−	0.515338i
$839$	−13.5758	−	3.63763i	−0.468690	−	0.125585i	0.0167414	−	0.999860i	$-0.494671\pi$
$839$	−13.5758	−	3.63763i	−0.468690	−	0.125585i	−0.485431	+	0.874275i	$0.661337\pi$
$840$	−5.31899	−	2.98083i	−0.183523	−	0.102848i
$841$	−12.6443	−	21.9006i	−0.436012	−	0.755194i
$842$	−14.4396	+	3.86908i	−0.497621	+	0.133337i
$843$	9.23254	+	5.33041i	0.317986	+	0.183589i
$844$	20.5593			0.707680
$845$	26.8823	+	11.0609i	0.924779	+	0.380506i
$846$	−24.6206			−0.846474
$847$	0.183028	+	0.105671i	0.00628891	+	0.00363090i
$848$	11.0574	−	2.96281i	0.379712	−	0.101743i
$849$	6.17037	+	10.6874i	0.211766	+	0.366790i
$850$	3.38916	−	14.0805i	0.116247	−	0.482958i
$851$	−79.1094	−	21.1973i	−2.71183	−	0.726634i
$852$	6.16171	+	10.6724i	0.211097	+	0.365630i
$853$			17.8954i			0.612726i	0.951915	+	0.306363i	$0.0991122\pi$
$853$			17.8954i			0.612726i	−0.951915	+	0.306363i	$0.900888\pi$
$854$	−7.03960	+	4.06431i	−0.240890	+	0.139078i
$855$	−26.6603	+	15.8506i	−0.911764	+	0.542081i
$856$	−10.5430	+	2.82498i	−0.360351	+	0.0965559i
$857$	40.3064	+	40.3064i	1.37684	+	1.37684i	0.849908	+	0.526931i	$0.176657\pi$
$857$	40.3064	+	40.3064i	1.37684	+	1.37684i	0.526931	+	0.849908i	$0.323343\pi$
$858$	13.0596	+	26.8345i	0.445847	+	0.916114i
$859$		−	30.3863i		−	1.03677i	−0.855148	−	0.518384i	$-0.826534\pi$
$859$		−	30.3863i		−	1.03677i	0.855148	−	0.518384i	$-0.173466\pi$
$860$	9.24793	−	5.49827i	0.315352	−	0.187489i
$861$	1.83646	−	3.18085i	0.0625865	−	0.108403i
$862$	−4.93983	+	18.4357i	−0.168251	+	0.627922i
$863$	−33.0724			−1.12580			−0.562898	−	0.826526i	$-0.690314\pi$
$863$	−33.0724			−1.12580			−0.562898	+	0.826526i	$0.690314\pi$
$864$	0.0778379	−	0.290495i	0.00264810	−	0.00988284i
$865$	−0.245820	−	19.2083i	−0.00835812	−	0.653101i
$866$	10.7361	+	10.7361i	0.364829	+	0.364829i
$867$	20.5771	+	5.51361i	0.698834	+	0.187252i
$868$	−1.28166	−	4.78322i	−0.0435024	−	0.162353i
$869$	−0.647532	−	2.41662i	−0.0219660	−	0.0819783i
$870$	5.21050	−	9.29763i	0.176653	−	0.315219i
$871$	−1.08576	+	15.3381i	−0.0367895	+	0.519712i
$872$	−6.08467	+	6.08467i	−0.206053	+	0.206053i
$873$	8.98095	−	15.5555i	0.303959	−	0.526473i
$874$	−28.8169	−	16.6375i	−0.974747	−	0.562771i
$875$	−2.72997	+	12.0156i	−0.0922898	+	0.406203i
$876$	28.7642	−	28.7642i	0.971853	−	0.971853i
$877$	12.8063	−	7.39372i	0.432438	−	0.249668i	−0.267947	−	0.963434i	$-0.586345\pi$
$877$	12.8063	−	7.39372i	0.432438	−	0.249668i	0.700385	+	0.713766i	$0.253012\pi$
$878$	13.7031	−	7.91150i	0.462458	−	0.267000i
$879$	25.3017	−	25.3017i	0.853406	−	0.853406i
$880$	−7.47995	+	0.0957253i	−0.252149	+	0.00322690i
$881$	32.6512	+	18.8512i	1.10005	+	0.635112i	0.936233	−	0.351379i	$-0.114287\pi$
$881$	32.6512	+	18.8512i	1.10005	+	0.635112i	0.163813	+	0.986491i	$0.447621\pi$
$882$	−9.02967	+	15.6399i	−0.304045	+	0.526621i
$883$	−37.7053	+	37.7053i	−1.26888	+	1.26888i	−0.322219	+	0.946665i	$0.604429\pi$
$883$	−37.7053	+	37.7053i	−1.26888	+	1.26888i	−0.946665	+	0.322219i	$0.895571\pi$
$884$	6.84485	+	7.88775i	0.230217	+	0.265294i
$885$	14.9579	+	53.0963i	0.502805	+	1.78481i
$886$	1.94063	+	7.24255i	0.0651969	+	0.243318i
$887$	−13.1490	−	49.0728i	−0.441501	−	1.64770i	−0.725013	−	0.688735i	$-0.758166\pi$
$887$	−13.1490	−	49.0728i	−0.441501	−	1.64770i	0.283513	−	0.958968i	$-0.408500\pi$
$888$	26.1383	+	7.00373i	0.877143	+	0.235030i
$889$	−2.58921	−	2.58921i	−0.0868395	−	0.0868395i
$890$	−8.24127	+	0.105468i	−0.276248	+	0.00353531i
$891$	7.46417	−	27.8566i	0.250059	−	0.933233i
$892$	−13.5732			−0.454465
$893$	9.07110	−	33.8538i	0.303553	−	1.13287i
$894$	3.62131	−	6.27229i	0.121115	−	0.209777i
$895$	24.2836	+	6.17482i	0.811711	+	0.206402i
$896$			1.10210i			0.0368186i
$897$	−37.4022	+	55.3486i	−1.24882	+	1.84804i
$898$	21.3109	+	21.3109i	0.711154	+	0.711154i
$899$	8.36110	−	2.24035i	0.278858	−	0.0747198i
$900$	−15.6027	+	0.399418i	−0.520088	+	0.0133139i
$901$	−28.7155	+	16.5789i	−0.956653	+	0.552324i
$902$		−	4.50619i		−	0.150040i
$903$	6.56005	+	11.3623i	0.218305	+	0.378115i
$904$	8.56802	+	2.29579i	0.284968	+	0.0763570i
$905$	−49.1617	+	13.8495i	−1.63419	+	0.460372i
$906$	−18.0044	−	31.1845i	−0.598156	−	1.03604i
$907$	−3.18585	+	0.853646i	−0.105784	+	0.0283449i	−0.311323	−	0.950304i	$-0.600772\pi$
$907$	−3.18585	+	0.853646i	−0.105784	+	0.0283449i	0.205538	+	0.978649i	$0.434105\pi$
$908$	−16.3644	−	9.44797i	−0.543070	−	0.313542i
$909$	−19.0693			−0.632490
$910$	−5.90901	−	6.63584i	−0.195882	−	0.219976i
$911$	−2.10299			−0.0696750			−0.0348375	−	0.999393i	$-0.511091\pi$
$911$	−2.10299			−0.0696750			−0.0348375	+	0.999393i	$0.511091\pi$
$912$	9.52131	+	5.49713i	0.315282	+	0.182028i
$913$	−34.1103	+	9.13984i	−1.12889	+	0.302484i
$914$	−5.23333	−	9.06439i	−0.173103	−	0.299823i
$915$	−19.9485	+	35.5962i	−0.659478	+	1.17677i
$916$	1.43243	+	0.383818i	0.0473287	+	0.0126817i
$917$	−0.218092	−	0.377747i	−0.00720205	−	0.0124743i
$918$			0.871110i			0.0287509i
$919$	51.1941	−	29.5569i	1.68874	−	0.974993i	0.733250	−	0.679959i	$-0.238002\pi$
$919$	51.1941	−	29.5569i	1.68874	−	0.974993i	0.955487	−	0.295034i	$-0.0953309\pi$
$920$	−8.55702	−	14.3927i	−0.282117	−	0.474512i
$921$	40.7384	−	10.9158i	1.34237	−	0.359688i
$922$	−21.2194	−	21.2194i	−0.698824	−	0.698824i
$923$	3.41155	+	17.6316i	0.112292	+	0.580350i
$924$		−	9.12224i		−	0.300100i
$925$	−1.39946	−	54.6676i	−0.0460139	−	1.79746i
$926$	8.75729	−	15.1681i	0.287782	−	0.498453i
$927$	12.9309	−	48.2588i	0.424707	−	1.58503i
$928$	−1.92648			−0.0632398
$929$	1.02958	−	3.84243i	0.0337793	−	0.126066i	−0.946977	−	0.321300i	$-0.895880\pi$
$929$	1.02958	−	3.84243i	0.0337793	−	0.126066i	0.980757	+	0.195234i	$0.0625467\pi$
$930$	−17.8009	−	17.3511i	−0.583716	−	0.568964i
$931$	−18.1782	−	18.1782i	−0.595768	−	0.595768i
$932$	−22.4674	−	6.02011i	−0.735943	−	0.197195i
$933$	17.5515	+	65.5031i	0.574611	+	2.14448i
$934$	−2.91683	−	10.8858i	−0.0954416	−	0.356193i
$935$	20.8559	−	5.87537i	0.682061	−	0.192145i
$936$	6.30167	−	9.32535i	0.205976	−	0.304809i
$937$	17.6539	−	17.6539i	0.576729	−	0.576729i	−0.357272	−	0.934001i	$-0.616293\pi$
$937$	17.6539	−	17.6539i	0.576729	−	0.576729i	0.934001	+	0.357272i	$0.116293\pi$
$938$	2.35005	−	4.07041i	0.0767319	−	0.132904i
$939$	21.5103	+	12.4190i	0.701963	+	0.405279i
$940$	12.3103	−	12.6295i	0.401518	−	0.411928i
$941$	−0.784318	+	0.784318i	−0.0255680	+	0.0255680i	−0.719775	−	0.694207i	$-0.755755\pi$
$941$	−0.784318	+	0.784318i	−0.0255680	+	0.0255680i	0.694207	+	0.719775i	$0.255755\pi$
$942$	20.3659	−	11.7583i	0.663557	−	0.383105i
$943$	8.73519	−	5.04326i	0.284457	−	0.164231i
$944$	7.05046	−	7.05046i	0.229473	−	0.229473i
$945$	−0.00948405	−	0.741081i	−0.000308516	−	0.0241074i
$946$	13.9401	+	8.04830i	0.453231	+	0.261673i
$947$	−6.32607	+	10.9571i	−0.205570	+	0.356057i	−0.950314	−	0.311293i	$-0.899238\pi$
$947$	−6.32607	+	10.9571i	−0.205570	+	0.356057i	0.744744	+	0.667350i	$0.232571\pi$
$948$	−1.30837	+	1.30837i	−0.0424940	+	0.0424940i
$949$	53.3028	−	25.9410i	1.73028	−	0.842080i
$950$	5.19936	−	21.6011i	0.168689	−	0.700832i
$951$	−13.4223	−	50.0926i	−0.435247	−	1.62436i
$952$	−0.826220	−	3.08350i	−0.0267780	−	0.0999367i
$953$	49.9783	+	13.3916i	1.61895	+	0.433798i	0.950694	−	0.310130i	$-0.100372\pi$
$953$	49.9783	+	13.3916i	1.61895	+	0.433798i	0.668261	+	0.743927i	$0.267039\pi$
$954$	25.2676	+	25.2676i	0.818069	+	0.818069i
$955$	2.76920	−	2.84100i	0.0896092	−	0.0919325i
$956$	−5.33634	+	19.9155i	−0.172590	+	0.644113i
$957$	15.9457			0.515452
$958$	−3.94104	+	14.7082i	−0.127329	+	0.475199i
$959$	4.82115	−	8.35047i	0.155683	−	0.269651i
$960$	2.82730	+	4.75543i	0.0912507	+	0.153481i
$961$			10.8112i			0.348749i
$962$	32.6736	+	22.0794i	1.05344	+	0.711868i
$963$	−24.0921	−	24.0921i	−0.776358	−	0.776358i
$964$	−0.292480	+	0.0783697i	−0.00942013	+	0.00252412i
$965$	6.51872	−	25.6360i	0.209845	−	0.825253i
$966$	17.6834	−	10.2095i	0.568953	−	0.328485i
$967$		−	22.2857i		−	0.716660i	−0.933595	−	0.358330i	$-0.883346\pi$
$967$		−	22.2857i		−	0.716660i	0.933595	−	0.358330i	$-0.116654\pi$
$968$	−0.0958815	−	0.166072i	−0.00308175	−	0.00533775i
$969$	−30.7601	−	8.24215i	−0.988158	−	0.264776i
$970$	3.48891	+	12.3846i	0.112022	+	0.397647i
$971$	4.17893	+	7.23812i	0.134108	+	0.232282i	0.925256	−	0.379342i	$-0.123850\pi$
$971$	4.17893	+	7.23812i	0.134108	+	0.232282i	−0.791148	+	0.611624i	$0.790516\pi$
$972$	−21.4735	+	5.75382i	−0.688764	+	0.184554i
$973$	7.97764	+	4.60589i	0.255751	+	0.147658i
$974$	32.6162			1.04509
$975$	−42.5201	−	13.4740i	−1.36173	−	0.431514i
$976$	7.37557			0.236086
$977$	34.1756	+	19.7313i	1.09338	+	0.631260i	0.934473	−	0.356034i	$-0.115871\pi$
$977$	34.1756	+	19.7313i	1.09338	+	0.631260i	0.158902	+	0.987294i	$0.449205\pi$
$978$	−5.31916	+	1.42527i	−0.170088	+	0.0455750i
$979$	−6.16544	−	10.6789i	−0.197048	−	0.341298i
$980$	−3.50784	−	12.4518i	−0.112054	−	0.397759i
$981$	−25.9458	−	6.95215i	−0.828384	−	0.221965i
$982$	−2.50433	−	4.33762i	−0.0799163	−	0.138419i
$983$			6.44395i			0.205530i	0.994706	+	0.102765i	$0.0327690\pi$
$983$			6.44395i			0.205530i	−0.994706	+	0.102765i	$0.967231\pi$
$984$	−2.88617	+	1.66633i	−0.0920076	+	0.0531206i
$985$	1.03137	−	4.05604i	0.0328622	−	0.129236i
$986$	5.38997	−	1.44424i	0.171652	−	0.0459939i
$987$	15.2078	+	15.2078i	0.484068	+	0.484068i
$988$	10.5008	+	12.1007i	0.334074	+	0.384974i
$989$			36.0302i			1.14569i
$990$	−11.9333	−	20.0715i	−0.379265	−	0.637913i
$991$	14.7651	−	25.5740i	0.469030	−	0.812383i	−0.530343	−	0.847783i	$-0.677937\pi$
$991$	14.7651	−	25.5740i	0.469030	−	0.812383i	0.999373	+	0.0353995i	$0.0112704\pi$
$992$	−1.16292	+	4.34009i	−0.0369229	+	0.137798i
$993$	41.3701			1.31284
$994$	1.42075	−	5.30231i	0.0450635	−	0.168179i
$995$	−29.7254	+	30.4961i	−0.942359	+	0.966791i
$996$	18.4675	+	18.4675i	0.585166	+	0.585166i
$997$	14.9800	+	4.01387i	0.474421	+	0.127121i	0.488104	−	0.872786i	$-0.337689\pi$
$997$	14.9800	+	4.01387i	0.474421	+	0.127121i	−0.0136828	+	0.999906i	$0.504356\pi$
$998$	3.53328	+	13.1864i	0.111844	+	0.417408i
$999$	0.851321	+	3.17717i	0.0269346	+	0.100521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	130.2.p.b.123.4	yes	16
5.2	odd	4		130.2.s.b.97.1	yes	16
5.3	odd	4		650.2.w.g.357.4		16
5.4	even	2		650.2.t.g.643.1		16
13.11	odd	12		130.2.s.b.63.1	yes	16
65.24	odd	12		650.2.w.g.193.4		16
65.37	even	12	inner	130.2.p.b.37.4	✓	16
65.63	even	12		650.2.t.g.557.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.b.37.4	✓	16	65.37	even	12	inner
130.2.p.b.123.4	yes	16	1.1	even	1	trivial
130.2.s.b.63.1	yes	16	13.11	odd	12
130.2.s.b.97.1	yes	16	5.2	odd	4
650.2.t.g.557.1		16	65.63	even	12
650.2.t.g.643.1		16	5.4	even	2
650.2.w.g.193.4		16	65.24	odd	12
650.2.w.g.357.4		16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 130 = 2 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	130.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.38987 - 0.640364i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.606329 - 2.15229i) q^{5} +(-2.38987 - 0.640364i) q^{6} +(0.551051 + 0.954448i) q^{7} -1.00000i q^{8} +(2.70334 - 1.56078i) q^{9} +(-0.551051 + 2.16710i) q^{10} +(-3.23142 + 0.865856i) q^{11} +(1.74951 + 1.74951i) q^{12} +(1.57779 + 3.24200i) q^{13} -1.10210i q^{14} +(-2.82730 - 4.75543i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.749677 - 2.79783i) q^{17} -3.12155 q^{18} +(1.15009 - 4.29219i) q^{19} +(1.56078 - 1.60124i) q^{20} +(1.92813 + 1.92813i) q^{21} +(3.23142 + 0.865856i) q^{22} +(1.93811 + 7.23312i) q^{23} +(-0.640364 - 2.38987i) q^{24} +(-4.26473 + 2.60999i) q^{25} +(0.254593 - 3.59655i) q^{26} +(0.212657 - 0.212657i) q^{27} +(-0.551051 + 0.954448i) q^{28} +(-1.66838 - 0.963240i) q^{29} +(0.0707959 + 5.53198i) q^{30} +(-3.17717 + 3.17717i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-7.16821 + 4.13857i) q^{33} +(-2.04816 + 2.04816i) q^{34} +(1.72013 - 1.76473i) q^{35} +(2.70334 + 1.56078i) q^{36} +(-5.46855 + 9.47181i) q^{37} +(-3.14210 + 3.14210i) q^{38} +(5.84678 + 6.73761i) q^{39} +(-2.15229 + 0.606329i) q^{40} +(-0.348623 - 1.30108i) q^{41} +(-0.705746 - 2.63388i) q^{42} +(4.64760 + 1.24532i) q^{43} +(-2.36556 - 2.36556i) q^{44} +(-4.99836 - 4.87205i) q^{45} +(1.93811 - 7.23312i) q^{46} +7.88729 q^{47} +(-0.640364 + 2.38987i) q^{48} +(2.89269 - 5.01028i) q^{49} +(4.99836 - 0.127955i) q^{50} -7.16653i q^{51} +(-2.01876 + 2.98741i) q^{52} +(-8.09456 - 8.09456i) q^{53} +(-0.290495 + 0.0778379i) q^{54} +(3.82288 + 6.42996i) q^{55} +(0.954448 - 0.551051i) q^{56} -10.9943i q^{57} +(0.963240 + 1.66838i) q^{58} +(-9.63111 - 2.58065i) q^{59} +(2.70468 - 4.82623i) q^{60} +(-3.68778 - 6.38743i) q^{61} +(4.34009 - 1.16292i) q^{62} +(2.97936 + 1.72013i) q^{63} -1.00000 q^{64} +(6.02108 - 5.36159i) q^{65} +8.27714 q^{66} +(3.69332 + 2.13234i) q^{67} +(2.79783 - 0.749677i) q^{68} +(9.26366 + 16.0451i) q^{69} +(-2.37205 + 0.668235i) q^{70} +(4.81110 + 1.28913i) q^{71} +(-1.56078 - 2.70334i) q^{72} -16.4413i q^{73} +(9.47181 - 5.46855i) q^{74} +(-8.52081 + 8.96853i) q^{75} +(4.29219 - 1.15009i) q^{76} +(-2.60709 - 2.60709i) q^{77} +(-1.69466 - 8.75833i) q^{78} +0.747852i q^{79} +(2.16710 + 0.551051i) q^{80} +(-4.31028 + 7.46563i) q^{81} +(-0.348623 + 1.30108i) q^{82} +10.5558 q^{83} +(-0.705746 + 2.63388i) q^{84} +(-6.47631 + 0.0828811i) q^{85} +(-3.40228 - 3.40228i) q^{86} +(-4.60404 - 1.23365i) q^{87} +(0.865856 + 3.23142i) q^{88} +(0.953984 + 3.56032i) q^{89} +(1.89269 + 6.71850i) q^{90} +(-2.22488 + 3.29243i) q^{91} +(-5.29501 + 5.29501i) q^{92} +(-5.55848 + 9.62757i) q^{93} +(-6.83060 - 3.94365i) q^{94} +(-9.93539 + 0.127149i) q^{95} +(1.74951 - 1.74951i) q^{96} +(4.98325 - 2.87708i) q^{97} +(-5.01028 + 2.89269i) q^{98} +(-7.38422 + 7.38422i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} - 2 q^{5} + 6 q^{11} + 2 q^{13} + 6 q^{15} - 8 q^{16} - 16 q^{17} - 16 q^{18} + 8 q^{20} - 6 q^{22} - 6 q^{23} - 14 q^{25} - 6 q^{26} - 12 q^{27} - 6 q^{29} + 6 q^{30} - 6 q^{33} - 14 q^{34}+ \cdots - 26 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 - 2 * q^5 + 6 * q^11 + 2 * q^13 + 6 * q^15 - 8 * q^16 - 16 * q^17 - 16 * q^18 + 8 * q^20 - 6 * q^22 - 6 * q^23 - 14 * q^25 - 6 * q^26 - 12 * q^27 - 6 * q^29 + 6 * q^30 - 6 * q^33 - 14 * q^34 - 20 * q^37 + 6 * q^38 - 6 * q^39 - 44 * q^41 + 6 * q^42 + 6 * q^44 - 6 * q^46 + 52 * q^47 - 2 * q^49 + 10 * q^52 - 24 * q^53 + 6 * q^54 + 64 * q^55 + 6 * q^56 + 8 * q^58 - 46 * q^59 + 6 * q^61 + 12 * q^62 + 90 * q^63 - 16 * q^64 - 22 * q^65 + 52 * q^66 + 12 * q^67 - 2 * q^68 + 58 * q^69 - 32 * q^70 + 6 * q^71 - 8 * q^72 + 24 * q^74 + 44 * q^75 - 6 * q^76 + 58 * q^77 + 38 * q^78 + 10 * q^80 - 24 * q^81 - 44 * q^82 - 64 * q^83 + 6 * q^84 + 40 * q^85 - 44 * q^87 - 24 * q^89 - 18 * q^90 + 38 * q^91 - 26 * q^93 - 6 * q^95 - 6 * q^97 - 26 * q^99

Introduction

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