LMFDB - Embedded newform 650.2.t.g.643.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(7,650)] 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("650.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([3, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,8,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.19027613138$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.1
Root			$-2.38987 + 0.640364i$ of defining polynomial
Character	$\chi$	$=$	650.643
Dual form			650.2.t.g.557.1

$q$-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} +(-2.38987 - 0.640364i) q^{6} +(-0.551051 - 0.954448i) q^{7} +1.00000i q^{8} +(2.70334 - 1.56078i) q^{9} +(-3.23142 + 0.865856i) q^{11} +(-1.74951 - 1.74951i) q^{12} +(-1.57779 - 3.24200i) q^{13} -1.10210i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.749677 + 2.79783i) q^{17} +3.12155 q^{18} +(1.15009 - 4.29219i) q^{19} +(1.92813 + 1.92813i) q^{21} +(-3.23142 - 0.865856i) q^{22} +(-1.93811 - 7.23312i) q^{23} +(-0.640364 - 2.38987i) q^{24} +(0.254593 - 3.59655i) q^{26} +(-0.212657 + 0.212657i) q^{27} +(0.551051 - 0.954448i) q^{28} +(-1.66838 - 0.963240i) q^{29} +(-3.17717 + 3.17717i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(7.16821 - 4.13857i) q^{33} +(-2.04816 + 2.04816i) q^{34} +(2.70334 + 1.56078i) q^{36} +(5.46855 - 9.47181i) q^{37} +(3.14210 - 3.14210i) q^{38} +(5.84678 + 6.73761i) q^{39} +(-0.348623 - 1.30108i) q^{41} +(0.705746 + 2.63388i) q^{42} +(-4.64760 - 1.24532i) q^{43} +(-2.36556 - 2.36556i) q^{44} +(1.93811 - 7.23312i) q^{46} -7.88729 q^{47} +(0.640364 - 2.38987i) q^{48} +(2.89269 - 5.01028i) q^{49} -7.16653i q^{51} +(2.01876 - 2.98741i) q^{52} +(8.09456 + 8.09456i) q^{53} +(-0.290495 + 0.0778379i) q^{54} +(0.954448 - 0.551051i) q^{56} +10.9943i q^{57} +(-0.963240 - 1.66838i) q^{58} +(-9.63111 - 2.58065i) q^{59} +(-3.68778 - 6.38743i) q^{61} +(-4.34009 + 1.16292i) q^{62} +(-2.97936 - 1.72013i) q^{63} -1.00000 q^{64} +8.27714 q^{66} +(-3.69332 - 2.13234i) q^{67} +(-2.79783 + 0.749677i) q^{68} +(9.26366 + 16.0451i) q^{69} +(4.81110 + 1.28913i) q^{71} +(1.56078 + 2.70334i) q^{72} +16.4413i q^{73} +(9.47181 - 5.46855i) q^{74} +(4.29219 - 1.15009i) q^{76} +(2.60709 + 2.60709i) q^{77} +(1.69466 + 8.75833i) q^{78} +0.747852i q^{79} +(-4.31028 + 7.46563i) q^{81} +(0.348623 - 1.30108i) q^{82} -10.5558 q^{83} +(-0.705746 + 2.63388i) q^{84} +(-3.40228 - 3.40228i) q^{86} +(4.60404 + 1.23365i) q^{87} +(-0.865856 - 3.23142i) q^{88} +(0.953984 + 3.56032i) q^{89} +(-2.22488 + 3.29243i) q^{91} +(5.29501 - 5.29501i) q^{92} +(5.55848 - 9.62757i) q^{93} +(-6.83060 - 3.94365i) q^{94} +(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} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 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 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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	−0.871046	−	0.491202i	$-0.836558\pi$
$3$	−2.38987	+	0.640364i	−1.37979	+	0.369714i	−0.508747	+	0.860916i	$0.669891\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−2.38987	−	0.640364i	−0.975661	−	0.261428i
$7$	−0.551051	−	0.954448i	−0.208278	−	0.360747i	0.742894	−	0.669409i	$-0.233452\pi$
$7$	−0.551051	−	0.954448i	−0.208278	−	0.360747i	−0.951172	+	0.308661i	$0.900119\pi$
$8$			1.00000i			0.353553i
$9$	2.70334	−	1.56078i	0.901115	−	0.520259i
$10$		0			0
$11$	−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
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.749677	+	2.79783i	−0.181823	+	0.678574i	0.813465	+	0.581614i	$0.197579\pi$
$17$	−0.749677	+	2.79783i	−0.181823	+	0.678574i	−0.995288	+	0.0969602i	$0.969088\pi$
$18$	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	$-0.0869164\pi$
$20$		0			0
$21$	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	$-0.798193\pi$
$23$	−1.93811	−	7.23312i	−0.404123	−	1.50821i	0.401543	−	0.915840i	$-0.368474\pi$
$24$	−0.640364	−	2.38987i	−0.130714	−	0.487830i
$25$		0			0
$26$	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			0
$31$	−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
$35$		0			0
$36$	2.70334	+	1.56078i	0.450557	+	0.260129i
$37$	5.46855	−	9.47181i	0.899025	−	1.55716i	0.0702817	−	0.997527i	$-0.477610\pi$
$37$	5.46855	−	9.47181i	0.899025	−	1.55716i	0.828743	−	0.559629i	$-0.189056\pi$
$38$	3.14210	−	3.14210i	0.509717	−	0.509717i
$39$	5.84678	+	6.73761i	0.936234	+	1.07888i
$40$		0			0
$41$	−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	−0.113605	−	0.993526i	$-0.536240\pi$
$43$	−4.64760	−	1.24532i	−0.708753	−	0.189910i	−0.595148	+	0.803616i	$0.702906\pi$
$44$	−2.36556	−	2.36556i	−0.356622	−	0.356622i
$45$		0			0
$46$	1.93811	−	7.23312i	0.285758	−	1.06646i
$47$	−7.88729			−1.15048			−0.575240	−	0.817985i	$-0.695091\pi$
$47$	−7.88729			−1.15048			−0.575240	+	0.817985i	$0.695091\pi$
$48$	0.640364	−	2.38987i	0.0924286	−	0.344948i
$49$	2.89269	−	5.01028i	0.413241	−	0.715754i
$50$		0			0
$51$		−	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	$0.0379612\pi$
$53$	8.09456	+	8.09456i	1.11187	+	1.11187i	0.118976	+	0.992897i	$0.462039\pi$
$54$	−0.290495	+	0.0778379i	−0.0395314	+	0.0105924i
$55$		0			0
$56$	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	$0.808166\pi$
$60$		0			0
$61$	−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
$65$		0			0
$66$	8.27714			1.01884
$67$	−3.69332	−	2.13234i	−0.451210	−	0.260506i	0.257131	−	0.966377i	$-0.417223\pi$
$67$	−3.69332	−	2.13234i	−0.451210	−	0.260506i	−0.708341	+	0.705870i	$0.750556\pi$
$68$	−2.79783	+	0.749677i	−0.339287	+	0.0909117i
$69$	9.26366	+	16.0451i	1.11521	+	1.93161i
$70$		0			0
$71$	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	$0.412150\pi$
$73$			16.4413i			1.92431i	−0.272499	+	0.962156i	$0.587850\pi$
$74$	9.47181	−	5.46855i	1.10108	−	0.635706i
$75$		0			0
$76$	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	$0.986605\pi$
$80$		0			0
$81$	−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	$-0.696685\pi$
$83$	−10.5558			−1.15865			−0.579327	+	0.815095i	$0.696685\pi$
$84$	−0.705746	+	2.63388i	−0.0770032	+	0.287380i
$85$		0			0
$86$	−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	$0.854081\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	1.74951	−	1.74951i	0.178558	−	0.178558i
$97$	−4.98325	+	2.87708i	−0.505972	+	0.292123i	−0.731176	−	0.682189i	$-0.761028\pi$
$97$	−4.98325	+	2.87708i	−0.505972	+	0.292123i	0.225204	+	0.974312i	$0.427695\pi$
$98$	5.01028	−	2.89269i	0.506115	−	0.292205i
$99$	−7.38422	+	7.38422i	−0.742143	+	0.742143i
$100$		0			0
$101$	−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	$0.539153\pi$
$103$	−11.3174	+	11.3174i	−1.11514	+	1.11514i	−0.992445	+	0.122693i	$0.960847\pi$
$104$	3.24200	−	1.57779i	0.317904	−	0.154715i
$105$		0			0
$106$	2.96281	+	11.0574i	0.287774	+	1.07399i
$107$	2.82498	+	10.5430i	0.273101	+	1.01923i	0.957103	+	0.289747i	$0.0935713\pi$
$107$	2.82498	+	10.5430i	0.273101	+	1.01923i	−0.684002	+	0.729480i	$0.739762\pi$
$108$	−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			0
$111$	−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	$-0.779670\pi$
$113$	2.29579	−	8.56802i	0.215970	−	0.806012i	0.985823	−	0.167790i	$-0.0536630\pi$
$114$	−5.49713	+	9.52131i	−0.514854	+	0.891753i
$115$		0			0
$116$		−	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
$120$		0			0
$121$	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
$125$		0			0
$126$	−1.72013	−	2.97936i	−0.153242	−	0.265422i
$127$	3.20926	−	0.859919i	0.284776	−	0.0763055i	−0.113604	−	0.993526i	$-0.536239\pi$
$127$	3.20926	−	0.859919i	0.284776	−	0.0763055i	0.398380	+	0.917221i	$0.369573\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	11.9046			1.04814
$130$		0			0
$131$	−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			0
$136$	−2.79783	−	0.749677i	−0.239912	−	0.0642843i
$137$	4.37451	+	7.57687i	0.373739	+	0.647335i	0.990137	−	0.140099i	$-0.0447421\pi$
$137$	4.37451	+	7.57687i	0.373739	+	0.647335i	−0.616398	+	0.787435i	$0.711409\pi$
$138$			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	$0.217993\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	−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	$0.121593\pi$
$150$		0			0
$151$	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
$155$		0			0
$156$	−2.91155	+	8.43226i	−0.233110	+	0.675121i
$157$	6.72089	−	6.72089i	0.536386	−	0.536386i	−0.386080	−	0.922465i	$-0.626171\pi$
$157$	6.72089	−	6.72089i	0.536386	−	0.536386i	0.922465	+	0.386080i	$0.126171\pi$
$158$	−0.373926	+	0.647659i	−0.0297480	+	0.0515250i
$159$	−24.5284	−	14.1615i	−1.94523	−	1.12308i
$160$		0			0
$161$	−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	−0.573585	−	0.819146i	$-0.694448\pi$
$163$	−1.92752	+	1.11286i	−0.150975	+	0.0871656i	0.422609	+	0.906312i	$0.361114\pi$
$164$	0.952456	−	0.952456i	0.0743743	−	0.0743743i
$165$		0			0
$166$	−9.14163	−	5.27792i	−0.709528	−	0.409646i
$167$	8.96406	−	15.5262i	0.693660	−	1.20145i	−0.276971	−	0.960878i	$-0.589330\pi$
$167$	8.96406	−	15.5262i	0.693660	−	1.20145i	0.970630	−	0.240576i	$-0.0773362\pi$
$168$	−1.92813	+	1.92813i	−0.148759	+	0.148759i
$169$	−8.02115	+	10.2304i	−0.617011	+	0.786954i
$170$		0			0
$171$	−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	−0.0708214	−	0.997489i	$-0.522562\pi$
$173$	−8.29818	−	2.22349i	−0.630899	−	0.169049i	−0.560078	+	0.828440i	$0.689229\pi$
$174$	3.37039	+	3.37039i	0.255509	+	0.255509i
$175$		0			0
$176$	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	$0.304206\pi$
$180$		0			0
$181$		−	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
$185$		0			0
$186$	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
$190$		0			0
$191$	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	0.0837018	−	0.996491i	$-0.473326\pi$
$193$	−10.2448	−	5.91481i	−0.737434	−	0.425758i	−0.821135	+	0.570733i	$0.806659\pi$
$194$	−5.75416			−0.413124
$195$		0			0
$196$	5.78537			0.413241
$197$	−1.62089	−	0.935821i	−0.115484	−	0.0666745i	0.441146	−	0.897436i	$-0.354572\pi$
$197$	−1.62089	−	0.935821i	−0.115484	−	0.0666745i	−0.556629	+	0.830761i	$0.687906\pi$
$198$	−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	$-0.402541\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	−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
$210$		0			0
$211$	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			0
$216$	−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
$220$		0			0
$221$	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	−0.544193	−	0.838960i	$-0.683164\pi$
$223$	6.78661	−	11.7547i	0.454465	−	0.787156i	0.998657	+	0.0518044i	$0.0164972\pi$
$224$	0.954448	+	0.551051i	0.0637717	+	0.0368186i
$225$		0			0
$226$	6.27223	−	6.27223i	0.417222	−	0.417222i
$227$	16.3644	−	9.44797i	1.08614	−	0.627084i	0.153594	−	0.988134i	$-0.450915\pi$
$227$	16.3644	−	9.44797i	1.08614	−	0.627084i	0.932546	+	0.361050i	$0.117582\pi$
$228$	−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	$0.234397\pi$
$230$		0			0
$231$	−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	$-0.474265\pi$
$233$	16.4473	−	16.4473i	1.07750	−	1.07750i	0.996733	−	0.0807620i	$-0.0257354\pi$
$234$	−4.92516	−	10.1201i	−0.321968	−	0.661570i
$235$		0			0
$236$	−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	$0.517649\pi$
$240$		0			0
$241$	−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
$245$		0			0
$246$			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
$250$		0			0
$251$	−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
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.0275	+	4.29455i	−0.999767	+	0.267887i	−0.721348	−	0.692573i	$-0.756477\pi$
$257$	−16.0275	+	4.29455i	−0.999767	+	0.267887i	−0.278419	+	0.960460i	$0.589810\pi$
$258$	10.3097	+	5.95232i	0.641855	+	0.370575i
$259$	−12.0538			−0.748987
$260$		0			0
$261$	−6.01361			−0.372233
$262$	−0.342752	−	0.197888i	−0.0211753	−	0.0122256i
$263$	4.57715	−	1.22644i	0.282239	−	0.0756257i	−0.114922	−	0.993374i	$-0.536662\pi$
$263$	4.57715	−	1.22644i	0.282239	−	0.0756257i	0.397162	+	0.917749i	$0.369995\pi$
$264$	4.13857	+	7.16821i	0.254711	+	0.441173i
$265$		0			0
$266$	−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			0
$271$	−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
$275$		0			0
$276$	−9.26366	+	16.0451i	−0.557607	+	0.965803i
$277$	1.52395	−	5.68746i	0.0915652	−	0.341726i	−0.904911	−	0.425601i	$-0.860063\pi$
$277$	1.52395	−	5.68746i	0.0915652	−	0.341726i	0.996476	+	0.0838746i	$0.0267295\pi$
$278$	8.35839			0.501303
$279$	−3.63013	+	13.5478i	−0.217330	+	0.811087i
$280$		0			0
$281$	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	0.916883	−	0.399155i	$-0.130697\pi$
$283$	−1.29094	−	4.81786i	−0.0767385	−	0.286392i	−0.993622	+	0.112763i	$0.964030\pi$
$284$	1.28913	+	4.81110i	0.0764957	+	0.285486i
$285$		0			0
$286$	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
$290$		0			0
$291$	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	−0.819043	−	0.573733i	$-0.805495\pi$
$293$	−12.5246	+	7.23110i	−0.731697	+	0.422445i	0.0873459	+	0.996178i	$0.472161\pi$
$294$	−10.1216	+	10.1216i	−0.590301	+	0.590301i
$295$		0			0
$296$	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
$300$		0			0
$301$	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
$305$		0			0
$306$	−2.34016	+	8.73358i	−0.133778	+	0.499266i
$307$	−17.0463			−0.972881			−0.486441	−	0.873714i	$-0.661705\pi$
$307$	−17.0463			−0.972881			−0.486441	+	0.873714i	$0.661705\pi$
$308$	−0.954261	+	3.56135i	−0.0543740	+	0.202927i
$309$	19.7999	−	34.2944i	1.12638	−	1.95094i
$310$		0			0
$311$			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	0.477433	−	0.878668i	$-0.341567\pi$
$313$	−7.09857	−	7.09857i	−0.401235	−	0.401235i	−0.878668	+	0.477433i	$0.841567\pi$
$314$	9.18091	−	2.46002i	0.518109	−	0.138827i
$315$		0			0
$316$	−0.647659	+	0.373926i	−0.0364337	+	0.0210350i
$317$			20.9604i			1.17725i	0.808406	+	0.588626i	$0.200331\pi$
$317$			20.9604i			1.17725i	−0.808406	+	0.588626i	$0.799669\pi$
$318$	−14.1615	−	24.5284i	−0.794137	−	1.37549i
$319$	6.22526	+	1.66805i	0.348548	+	0.0933930i
$320$		0			0
$321$	−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
$325$		0			0
$326$	−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
$330$		0			0
$331$	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
$335$		0			0
$336$	−2.63388	+	0.705746i	−0.143690	+	0.0385016i
$337$	13.3768	+	13.3768i	0.728683	+	0.728683i	0.970357	−	0.241674i	$-0.0776965\pi$
$337$	13.3768	+	13.3768i	0.728683	+	0.728683i	−0.241674	+	0.970357i	$0.577697\pi$
$338$	−12.0617	+	4.84921i	−0.656071	+	0.263763i
$339$			21.9466i			1.19198i
$340$		0			0
$341$	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
$345$		0			0
$346$	−6.07469	−	6.07469i	−0.326577	−	0.326577i
$347$	4.30720	+	1.15411i	0.231222	+	0.0619559i	0.372570	−	0.928004i	$-0.378477\pi$
$347$	4.30720	+	1.15411i	0.231222	+	0.0619559i	−0.141347	+	0.989960i	$0.545143\pi$
$348$	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	$-0.204718\pi$
$350$		0			0
$351$	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	−0.852543	−	0.522657i	$-0.824941\pi$
$353$	0.495300	−	0.857885i	0.0263622	−	0.0456606i	0.878906	+	0.476996i	$0.158274\pi$
$354$	21.3646	+	12.3348i	1.13551	+	0.655589i
$355$		0			0
$356$	−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	$0.104679\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	4.72305	+	17.6267i	0.246878	+	0.921360i
$367$	−8.34106	−	31.1292i	−0.435400	−	1.62493i	−0.740108	−	0.672488i	$-0.765226\pi$
$367$	−8.34106	−	31.1292i	−0.435400	−	1.62493i	0.304708	−	0.952446i	$-0.401441\pi$
$368$	7.23312	+	1.93811i	0.377052	+	0.101031i
$369$	−2.97314	−	2.97314i	−0.154776	−	0.154776i
$370$		0			0
$371$	3.26532	−	12.1863i	0.169527	−	0.632684i
$372$	11.1170			0.576387
$373$	0.652008	−	2.43333i	0.0337597	−	0.125993i	−0.946990	−	0.321264i	$-0.895892\pi$
$373$	0.652008	−	2.43333i	0.0337597	−	0.125993i	0.980749	+	0.195272i	$0.0625588\pi$
$374$	4.84504	−	8.39185i	0.250531	−	0.433932i
$375$		0			0
$376$		−	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	$0.441607\pi$
$380$		0			0
$381$	−7.11906	+	4.11019i	−0.364721	+	0.210572i
$382$			1.77425i			0.0907783i
$383$	0.0173775	+	0.0300987i	0.000887948	+	0.00153797i	0.866469	−	0.499231i	$-0.166384\pi$
$383$	0.0173775	+	0.0300987i	0.000887948	+	0.00153797i	−0.865581	+	0.500769i	$0.833051\pi$
$384$	2.38987	+	0.640364i	0.121958	+	0.0326784i
$385$		0			0
$386$	−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	$0.319012\pi$
$390$		0			0
$391$	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
$395$		0			0
$396$	−10.0870	−	2.70281i	−0.506893	−	0.135822i
$397$	−13.1279	−	22.7382i	−0.658870	−	1.14120i	−0.980909	−	0.194469i	$-0.937702\pi$
$397$	−13.1279	−	22.7382i	−0.658870	−	1.14120i	0.322039	−	0.946726i	$-0.395632\pi$
$398$		−	19.0453i		−	0.954653i
$399$	10.4935	−	6.05840i	0.525330	−	0.303299i
$400$		0			0
$401$	−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
$405$		0			0
$406$	−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	$0.0844513\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	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	$0.528426\pi$
$420$		0			0
$421$	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
$425$		0			0
$426$	−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
$430$		0			0
$431$	−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	0.593378	−	0.804924i	$-0.297794\pi$
$433$	14.6659	+	3.92970i	0.704796	+	0.188849i	0.111418	+	0.993774i	$0.464461\pi$
$434$	3.50156	+	3.50156i	0.168080	+	0.168080i
$435$		0			0
$436$	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	$0.289916\pi$
$440$		0			0
$441$		−	18.0593i		−	0.859969i
$442$	9.87169	+	3.40856i	0.469548	+	0.162129i
$443$	5.30191	+	5.30191i	0.251901	+	0.251901i	0.821750	−	0.569848i	$-0.192998\pi$
$443$	5.30191	+	5.30191i	0.251901	+	0.251901i	−0.569848	+	0.821750i	$0.692998\pi$
$444$	−26.1383	+	7.00373i	−1.24047	+	0.332382i
$445$		0			0
$446$	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	$0.835160\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	−10.9943			−0.514854
$457$	−9.06439	−	5.23333i	−0.424014	−	0.244805i	0.272779	−	0.962077i	$-0.412057\pi$
$457$	−9.06439	−	5.23333i	−0.424014	−	0.244805i	−0.696793	+	0.717272i	$0.745391\pi$
$458$	1.43243	−	0.383818i	0.0669329	−	0.0179346i
$459$	−0.435555	−	0.754403i	−0.0203300	−	0.0352125i
$460$		0			0
$461$	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	$-0.866580\pi$
$463$		−	17.5146i		−	0.813971i	0.913435	−	0.406986i	$-0.133420\pi$
$464$	1.66838	−	0.963240i	0.0774526	−	0.0447173i
$465$		0			0
$466$	22.4674	−	6.02011i	1.04078	−	0.278876i
$467$	−7.96893	−	7.96893i	−0.368758	−	0.368758i	0.498266	−	0.867024i	$-0.333970\pi$
$467$	−7.96893	−	7.96893i	−0.368758	−	0.368758i	−0.867024	+	0.498266i	$0.833970\pi$
$468$	0.794727	−	11.2268i	0.0367363	−	0.518960i
$469$			4.70010i			0.217031i
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	$-0.196428\pi$
$480$		0			0
$481$	−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
$485$		0			0
$486$	15.7197	−	15.7197i	0.713061	−	0.713061i
$487$	28.2464	−	16.3081i	1.27997	−	0.738990i	0.303126	−	0.952950i	$-0.401970\pi$
$487$	28.2464	−	16.3081i	1.27997	−	0.738990i	0.976842	+	0.213960i	$0.0686363\pi$
$488$	6.38743	−	3.68778i	0.289145	−	0.166938i
$489$	3.89390	−	3.89390i	0.176088	−	0.176088i
$490$		0			0
$491$	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
$495$		0			0
$496$	−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	$0.848845\pi$
$500$		0			0
$501$	−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	$0.282758\pi$
$503$	−6.80685	+	25.4035i	−0.303502	+	1.13269i	−0.934227	+	0.356680i	$0.883909\pi$
$504$	1.72013	−	2.97936i	0.0766208	−	0.132711i
$505$		0			0
$506$			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	$0.632394\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$	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	0.190897	−	0.981610i	$-0.438860\pi$
$523$	19.3707	−	5.19038i	0.847024	−	0.226959i	0.656127	+	0.754651i	$0.272194\pi$
$524$	−0.197888	−	0.342752i	−0.00864477	−	0.0149732i
$525$		0			0
$526$	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
$530$		0			0
$531$	−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
$535$		0			0
$536$	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			0
$541$	−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
$545$		0			0
$546$	7.42553	−	6.44374i	0.317783	−	0.275767i
$547$	−9.57195	+	9.57195i	−0.409267	+	0.409267i	−0.881483	−	0.472216i	$-0.843454\pi$
$547$	−9.57195	+	9.57195i	−0.409267	+	0.409267i	0.472216	+	0.881483i	$0.343454\pi$
$548$	−4.37451	+	7.57687i	−0.186870	+	0.323668i
$549$	−19.9387	−	11.5116i	−0.850963	−	0.491304i
$550$		0			0
$551$	−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
$555$		0			0
$556$	7.23857	+	4.17919i	0.306984	+	0.177237i
$557$	0.204041	−	0.353409i	0.00864550	−	0.0149744i	−0.861670	−	0.507469i	$-0.830581\pi$
$557$	0.204041	−	0.353409i	0.00864550	−	0.0149744i	0.870316	+	0.492494i	$0.163915\pi$
$558$	−9.91770	+	9.91770i	−0.419850	+	0.419850i
$559$	3.29561	+	17.0324i	0.139390	+	0.720393i
$560$		0			0
$561$	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	−0.0210061	−	0.999779i	$-0.506687\pi$
$563$	−12.7913	−	3.42741i	−0.539088	−	0.144448i	−0.518081	+	0.855331i	$0.673354\pi$
$564$	13.7989	+	13.7989i	0.581038	+	0.581038i
$565$		0			0
$566$	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	$0.0149966\pi$
$570$		0			0
$571$		−	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
$575$		0			0
$576$	−2.70334	+	1.56078i	−0.112639	+	0.0650323i
$577$			16.5356i			0.688388i	0.938899	+	0.344194i	$0.111848\pi$
$577$			16.5356i			0.688388i	−0.938899	+	0.344194i	$0.888152\pi$
$578$	4.30506	+	7.45658i	0.179067	+	0.310153i
$579$	28.2713	+	7.57527i	1.17491	+	0.314817i
$580$		0			0
$581$	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
$585$		0			0
$586$	−14.4622			−0.597428
$587$	29.5013	+	17.0326i	1.21765	+	0.703010i	0.964414	−	0.264395i	$-0.0851724\pi$
$587$	29.5013	+	17.0326i	1.21765	+	0.703010i	0.253234	+	0.967405i	$0.418506\pi$
$588$	−13.8263	+	3.70475i	−0.570187	+	0.152781i
$589$	9.98299	+	17.2910i	0.411342	+	0.712465i
$590$		0			0
$591$	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	$0.00886164\pi$
$593$			1.35571i			0.0556721i	−0.999613	+	0.0278361i	$0.991138\pi$
$594$	0.871314	−	0.503053i	0.0357504	−	0.0206405i
$595$		0			0
$596$	−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	$-0.0756861\pi$
$600$		0			0
$601$	−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			0
$606$	10.6876	+	10.6876i	0.434154	+	0.434154i
$607$	40.9211	+	10.9648i	1.66094	+	0.445046i	0.962645	−	0.270768i	$-0.0872776\pi$
$607$	40.9211	+	10.9648i	1.66094	+	0.445046i	0.698291	+	0.715814i	$0.253944\pi$
$608$	1.15009	+	4.29219i	0.0466423	+	0.174071i
$609$	−1.35961	−	5.07412i	−0.0550940	−	0.205614i
$610$		0			0
$611$	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	$0.504719\pi$
$613$	−21.6229	+	37.4520i	−0.873342	+	1.51267i	−0.858518	+	0.512783i	$0.828614\pi$
$614$	−14.7625	−	8.52313i	−0.595766	−	0.343965i
$615$		0			0
$616$	−2.60709	+	2.60709i	−0.105043	+	0.105043i
$617$	−35.5212	+	20.5082i	−1.43003	+	0.825628i	−0.997122	−	0.0758097i	$-0.975846\pi$
$617$	−35.5212	+	20.5082i	−1.43003	+	0.825628i	−0.432908	+	0.901438i	$0.642513\pi$
$618$	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			0
$621$	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
$625$		0			0
$626$	−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
$630$		0			0
$631$	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
$635$		0			0
$636$		−	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			0
$641$	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	0.934978	−	0.354705i	$-0.115419\pi$
$643$	4.06494	+	7.04068i	0.160305	+	0.277657i	−0.774673	+	0.632362i	$0.782085\pi$
$644$	−7.97163	−	2.13599i	−0.314126	−	0.0841698i
$645$		0			0
$646$	6.43552	+	11.1466i	0.253202	+	0.438559i
$647$	2.72310	−	0.729652i	0.107056	−	0.0286856i	−0.204893	−	0.978784i	$-0.565685\pi$
$647$	2.72310	−	0.729652i	0.107056	−	0.0286856i	0.311949	+	0.950099i	$0.399018\pi$
$648$	−7.46563	−	4.31028i	−0.293278	−	0.169324i
$649$	33.3566			1.30936
$650$		0			0
$651$	−12.2520			−0.480194
$652$	−1.92752	−	1.11286i	−0.0754876	−	0.0435828i
$653$	5.60977	−	1.50313i	0.219527	−	0.0588222i	−0.147379	−	0.989080i	$-0.547084\pi$
$653$	5.60977	−	1.50313i	0.219527	−	0.0588222i	0.366906	+	0.930258i	$0.380417\pi$
$654$	10.6452	+	18.4380i	0.416259	+	0.720982i
$655$		0			0
$656$	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	$0.319597\pi$
$660$		0			0
$661$	−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
$665$		0			0
$666$	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
$670$		0			0
$671$	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	$-0.748946\pi$
$673$	−11.6518	−	43.4850i	−0.449142	−	1.67622i	0.255619	−	0.966778i	$-0.417721\pi$
$674$	4.89627	+	18.2731i	0.188597	+	0.703854i
$675$		0			0
$676$	−12.8704	−	1.83132i	−0.495014	−	0.0704353i
$677$	22.4488	−	22.4488i	0.862778	−	0.862778i	−0.128882	−	0.991660i	$-0.541139\pi$
$677$	22.4488	−	22.4488i	0.862778	−	0.862778i	0.991660	+	0.128882i	$0.0411389\pi$
$678$	−10.9733	+	19.0063i	−0.421427	+	0.729934i
$679$	5.49204	+	3.17083i	0.210765	+	0.121685i
$680$		0			0
$681$	−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	−0.902060	−	0.431610i	$-0.857946\pi$
$683$	−25.5934	+	14.7764i	−0.979305	+	0.565402i	−0.0772447	+	0.997012i	$0.524612\pi$
$684$	9.80824	−	9.80824i	0.375027	−	0.375027i
$685$		0			0
$686$	−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
$690$		0			0
$691$	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
$695$		0			0
$696$	−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			0
$701$			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
$705$		0			0
$706$	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	$0.671985\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	$0.562738\pi$
$720$		0			0
$721$	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
$725$		0			0
$726$	−0.458289	+	0.122798i	−0.0170087	+	0.00455747i
$727$	9.49105	+	9.49105i	0.352004	+	0.352004i	0.860855	−	0.508851i	$-0.169930\pi$
$727$	9.49105	+	9.49105i	0.352004	+	0.352004i	−0.508851	+	0.860855i	$0.669930\pi$
$728$	−3.29243	−	2.22488i	−0.122025	−	0.0824595i
$729$			29.1418i			1.07933i
$730$		0			0
$731$	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	$-0.526772\pi$
$733$	−4.54882			−0.168015			−0.0840073	+	0.996465i	$0.526772\pi$
$734$	8.34106	−	31.1292i	0.307874	−	1.14900i
$735$		0			0
$736$	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	$-0.206302\pi$
$740$		0			0
$741$	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	−0.781171	−	0.624318i	$-0.785377\pi$
$743$	4.09115	−	7.08607i	0.150090	−	0.259963i	0.931260	+	0.364355i	$0.118710\pi$
$744$	9.62757	+	5.55848i	0.352964	+	0.203784i
$745$		0			0
$746$	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
$750$		0			0
$751$	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
$755$		0			0
$756$	0.0857852	+	0.320155i	0.00311998	+	0.0116439i
$757$	−3.56508	−	13.3051i	−0.129575	−	0.483581i	0.870386	−	0.492370i	$-0.163869\pi$
$757$	−3.56508	−	13.3051i	−0.129575	−	0.483581i	−0.999961	+	0.00878853i	$0.997202\pi$
$758$	−2.94373	−	0.788769i	−0.106921	−	0.0286494i
$759$	−43.8275	−	43.8275i	−1.59084	−	1.59084i
$760$		0			0
$761$	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
$765$		0			0
$766$			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	$0.441025\pi$
$770$		0			0
$771$	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	$0.0710714\pi$
$773$	18.8879	+	32.7148i	0.679350	+	1.17667i	−0.295827	+	0.955241i	$0.595595\pi$
$774$	−14.5077	−	3.88734i	−0.521470	−	0.139727i
$775$		0			0
$776$	−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
$780$		0			0
$781$	−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
$785$		0			0
$786$	0.945853	+	0.253441i	0.0337375	+	0.00903993i
$787$	−8.13472	−	14.0897i	−0.289971	−	0.502245i	0.683831	−	0.729640i	$-0.260312\pi$
$787$	−8.13472	−	14.0897i	−0.289971	−	0.502245i	−0.973803	+	0.227395i	$0.926979\pi$
$788$		−	1.87164i		−	0.0666745i
$789$	−10.1534	+	5.86208i	−0.361472	+	0.208696i
$790$		0			0
$791$	−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
$795$		0			0
$796$	9.52263	−	16.4937i	0.337521	−	0.584603i
$797$	8.62476	−	32.1880i	0.305505	−	1.14016i	−0.627005	−	0.779015i	$-0.715720\pi$
$797$	8.62476	−	32.1880i	0.305505	−	1.14016i	0.932510	−	0.361144i	$-0.117614\pi$
$798$	12.1168			0.428930
$799$	5.91292	−	22.0673i	0.209184	−	0.780686i
$800$		0			0
$801$	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
$805$		0			0
$806$	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	$0.661655\pi$
$810$		0			0
$811$	−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
$815$		0			0
$816$	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
$820$		0			0
$821$	−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	0.603456	−	0.797396i	$-0.293790\pi$
$823$	20.8667	+	5.59121i	0.727366	+	0.194897i	0.123910	+	0.992293i	$0.460457\pi$
$824$	−11.3174	−	11.3174i	−0.394261	−	0.394261i
$825$		0			0
$826$	−2.84413	+	10.6145i	−0.0989601	+	0.369324i
$827$	−35.4430			−1.23247			−0.616237	−	0.787561i	$-0.711344\pi$
$827$	−35.4430			−1.23247			−0.616237	+	0.787561i	$0.711344\pi$
$828$	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	$0.969448\pi$
$830$		0			0
$831$			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
$835$		0			0
$836$	−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	$0.661337\pi$
$840$		0			0
$841$	−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
$845$		0			0
$846$	−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
$850$		0			0
$851$	−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	$-0.900888\pi$
$853$		−	17.8954i		−	0.612726i	0.951915	−	0.306363i	$-0.0991122\pi$
$854$	−7.03960	+	4.06431i	−0.240890	+	0.139078i
$855$		0			0
$856$	−10.5430	+	2.82498i	−0.360351	+	0.0965559i
$857$	−40.3064	−	40.3064i	−1.37684	−	1.37684i	−0.849908	−	0.526931i	$-0.823343\pi$
$857$	−40.3064	−	40.3064i	−1.37684	−	1.37684i	−0.526931	−	0.849908i	$-0.676657\pi$
$858$	−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	$-0.173466\pi$
$860$		0			0
$861$	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	$-0.309686\pi$
$863$	33.0724			1.12580			0.562898	+	0.826526i	$0.309686\pi$
$864$	0.0778379	−	0.290495i	0.00264810	−	0.00988284i
$865$		0			0
$866$	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
$870$		0			0
$871$	−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
$875$		0			0
$876$	28.7642	−	28.7642i	0.971853	−	0.971853i
$877$	−12.8063	+	7.39372i	−0.432438	+	0.249668i	−0.700385	−	0.713766i	$-0.746988\pi$
$877$	−12.8063	+	7.39372i	−0.432438	+	0.249668i	0.267947	+	0.963434i	$0.413655\pi$
$878$	−13.7031	+	7.91150i	−0.462458	+	0.267000i
$879$	25.3017	−	25.3017i	0.853406	−	0.853406i
$880$		0			0
$881$	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	$-0.395571\pi$
$883$	37.7053	−	37.7053i	1.26888	−	1.26888i	0.946665	−	0.322219i	$-0.104429\pi$
$884$	6.84485	+	7.88775i	0.230217	+	0.265294i
$885$		0			0
$886$	1.94063	+	7.24255i	0.0651969	+	0.243318i
$887$	13.1490	+	49.0728i	0.441501	+	1.64770i	0.725013	+	0.688735i	$0.241834\pi$
$887$	13.1490	+	49.0728i	0.441501	+	1.64770i	−0.283513	+	0.958968i	$0.591500\pi$
$888$	−26.1383	−	7.00373i	−0.877143	−	0.235030i
$889$	−2.58921	−	2.58921i	−0.0868395	−	0.0868395i
$890$		0			0
$891$	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
$895$		0			0
$896$			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
$900$		0			0
$901$	−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
$905$		0			0
$906$	−18.0044	−	31.1845i	−0.598156	−	1.03604i
$907$	3.18585	−	0.853646i	0.105784	−	0.0283449i	−0.205538	−	0.978649i	$-0.565895\pi$
$907$	3.18585	−	0.853646i	0.105784	−	0.0283449i	0.311323	+	0.950304i	$0.399228\pi$
$908$	16.3644	+	9.44797i	0.543070	+	0.313542i
$909$	−19.0693			−0.632490
$910$		0			0
$911$	−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
$915$		0			0
$916$	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	$-0.0953309\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	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	$0.0625467\pi$
$930$		0			0
$931$	−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
$935$		0			0
$936$	6.30167	−	9.32535i	0.205976	−	0.304809i
$937$	−17.6539	+	17.6539i	−0.576729	+	0.576729i	−0.934001	−	0.357272i	$-0.883707\pi$
$937$	−17.6539	+	17.6539i	−0.576729	+	0.576729i	0.357272	+	0.934001i	$0.383707\pi$
$938$	−2.35005	+	4.07041i	−0.0767319	+	0.132904i
$939$	21.5103	+	12.4190i	0.701963	+	0.405279i
$940$		0			0
$941$	−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			0
$946$	13.9401	+	8.04830i	0.453231	+	0.261673i
$947$	6.32607	−	10.9571i	0.205570	−	0.356057i	−0.744744	−	0.667350i	$-0.767429\pi$
$947$	6.32607	−	10.9571i	0.205570	−	0.356057i	0.950314	+	0.311293i	$0.100762\pi$
$948$	1.30837	−	1.30837i	0.0424940	−	0.0424940i
$949$	53.3028	−	25.9410i	1.73028	−	0.842080i
$950$		0			0
$951$	−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	−0.668261	−	0.743927i	$-0.732961\pi$
$953$	−49.9783	−	13.3916i	−1.61895	−	0.433798i	−0.950694	+	0.310130i	$0.899628\pi$
$954$	25.2676	+	25.2676i	0.818069	+	0.818069i
$955$		0			0
$956$	−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
$960$		0			0
$961$			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
$965$		0			0
$966$	17.6834	−	10.2095i	0.568953	−	0.328485i
$967$			22.2857i			0.716660i	0.933595	+	0.358330i	$0.116654\pi$
$967$			22.2857i			0.716660i	−0.933595	+	0.358330i	$0.883346\pi$
$968$	0.0958815	+	0.166072i	0.00308175	+	0.00533775i
$969$	−30.7601	−	8.24215i	−0.988158	−	0.264776i
$970$		0			0
$971$	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
$975$		0			0
$976$	7.37557			0.236086
$977$	−34.1756	−	19.7313i	−1.09338	−	0.631260i	−0.158902	−	0.987294i	$-0.550795\pi$
$977$	−34.1756	−	19.7313i	−1.09338	−	0.631260i	−0.934473	+	0.356034i	$0.884129\pi$
$978$	5.31916	−	1.42527i	0.170088	−	0.0455750i
$979$	−6.16544	−	10.6789i	−0.197048	−	0.341298i
$980$		0			0
$981$	−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	$-0.967231\pi$
$983$		−	6.44395i		−	0.205530i	0.994706	−	0.102765i	$-0.0327690\pi$
$984$	−2.88617	+	1.66633i	−0.0920076	+	0.0531206i
$985$		0			0
$986$	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
$990$		0			0
$991$	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
$995$		0			0
$996$	18.4675	+	18.4675i	0.585166	+	0.585166i
$997$	−14.9800	−	4.01387i	−0.474421	−	0.127121i	0.0136828	−	0.999906i	$-0.495644\pi$
$997$	−14.9800	−	4.01387i	−0.474421	−	0.127121i	−0.488104	+	0.872786i	$0.662311\pi$
$998$	−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	650.2.t.g.643.1		16
5.2	odd	4		650.2.w.g.357.4		16
5.3	odd	4		130.2.s.b.97.1	yes	16
5.4	even	2		130.2.p.b.123.4	yes	16
13.11	odd	12		650.2.w.g.193.4		16
65.24	odd	12		130.2.s.b.63.1	yes	16
65.37	even	12	inner	650.2.t.g.557.1		16
65.63	even	12		130.2.p.b.37.4	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.p.b.37.4	✓	16	65.63	even	12
130.2.p.b.123.4	yes	16	5.4	even	2
130.2.s.b.63.1	yes	16	65.24	odd	12
130.2.s.b.97.1	yes	16	5.3	odd	4
650.2.t.g.557.1		16	65.37	even	12	inner
650.2.t.g.643.1		16	1.1	even	1	trivial
650.2.w.g.193.4		16	13.11	odd	12
650.2.w.g.357.4		16	5.2	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:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.t (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} +(-2.38987 - 0.640364i) q^{6} +(-0.551051 - 0.954448i) q^{7} +1.00000i q^{8} +(2.70334 - 1.56078i) q^{9} +(-3.23142 + 0.865856i) q^{11} +(-1.74951 - 1.74951i) q^{12} +(-1.57779 - 3.24200i) q^{13} -1.10210i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.749677 + 2.79783i) q^{17} +3.12155 q^{18} +(1.15009 - 4.29219i) q^{19} +(1.92813 + 1.92813i) q^{21} +(-3.23142 - 0.865856i) q^{22} +(-1.93811 - 7.23312i) q^{23} +(-0.640364 - 2.38987i) q^{24} +(0.254593 - 3.59655i) q^{26} +(-0.212657 + 0.212657i) q^{27} +(0.551051 - 0.954448i) q^{28} +(-1.66838 - 0.963240i) q^{29} +(-3.17717 + 3.17717i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(7.16821 - 4.13857i) q^{33} +(-2.04816 + 2.04816i) q^{34} +(2.70334 + 1.56078i) q^{36} +(5.46855 - 9.47181i) q^{37} +(3.14210 - 3.14210i) q^{38} +(5.84678 + 6.73761i) q^{39} +(-0.348623 - 1.30108i) q^{41} +(0.705746 + 2.63388i) q^{42} +(-4.64760 - 1.24532i) q^{43} +(-2.36556 - 2.36556i) q^{44} +(1.93811 - 7.23312i) q^{46} -7.88729 q^{47} +(0.640364 - 2.38987i) q^{48} +(2.89269 - 5.01028i) q^{49} -7.16653i q^{51} +(2.01876 - 2.98741i) q^{52} +(8.09456 + 8.09456i) q^{53} +(-0.290495 + 0.0778379i) q^{54} +(0.954448 - 0.551051i) q^{56} +10.9943i q^{57} +(-0.963240 - 1.66838i) q^{58} +(-9.63111 - 2.58065i) q^{59} +(-3.68778 - 6.38743i) q^{61} +(-4.34009 + 1.16292i) q^{62} +(-2.97936 - 1.72013i) q^{63} -1.00000 q^{64} +8.27714 q^{66} +(-3.69332 - 2.13234i) q^{67} +(-2.79783 + 0.749677i) q^{68} +(9.26366 + 16.0451i) q^{69} +(4.81110 + 1.28913i) q^{71} +(1.56078 + 2.70334i) q^{72} +16.4413i q^{73} +(9.47181 - 5.46855i) q^{74} +(4.29219 - 1.15009i) q^{76} +(2.60709 + 2.60709i) q^{77} +(1.69466 + 8.75833i) q^{78} +0.747852i q^{79} +(-4.31028 + 7.46563i) q^{81} +(0.348623 - 1.30108i) q^{82} -10.5558 q^{83} +(-0.705746 + 2.63388i) q^{84} +(-3.40228 - 3.40228i) q^{86} +(4.60404 + 1.23365i) q^{87} +(-0.865856 - 3.23142i) q^{88} +(0.953984 + 3.56032i) q^{89} +(-2.22488 + 3.29243i) q^{91} +(5.29501 - 5.29501i) q^{92} +(5.55848 - 9.62757i) q^{93} +(-6.83060 - 3.94365i) q^{94} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 6 q^{11} - 2 q^{13} - 8 q^{16} + 16 q^{17} + 16 q^{18} + 6 q^{22} + 6 q^{23} - 6 q^{26} + 12 q^{27} - 6 q^{29} + 6 q^{33} - 14 q^{34} + 20 q^{37} - 6 q^{38} - 6 q^{39} - 44 q^{41} - 6 q^{42}+ \cdots - 26 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 6 * q^11 - 2 * q^13 - 8 * q^16 + 16 * q^17 + 16 * q^18 + 6 * q^22 + 6 * q^23 - 6 * q^26 + 12 * q^27 - 6 * q^29 + 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 + 6 * q^56 - 8 * q^58 - 46 * q^59 + 6 * q^61 - 12 * q^62 - 90 * q^63 - 16 * q^64 + 52 * q^66 - 12 * q^67 + 2 * q^68 + 58 * q^69 + 6 * q^71 + 8 * q^72 + 24 * q^74 - 6 * q^76 - 58 * q^77 - 38 * q^78 - 24 * q^81 + 44 * q^82 + 64 * q^83 + 6 * q^84 + 44 * q^87 - 24 * q^89 + 38 * q^91 + 26 * q^93 + 6 * q^97 - 26 * q^99

Introduction

L-functions

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