LMFDB - Embedded newform 370.2.g.e.327.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(43,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 3]))

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

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

chi := DirichletCharacter("370.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.g (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} + 4 x^{17} + 103 x^{16} - 394 x^{15} + 760 x^{14} + 278 x^{13} + 2009 x^{12} + \cdots + 256 $ x^20 - 4x^19 + 8x^18 + 4x^17 + 103x^16 - 394x^15 + 760x^14 + 278x^13 + 2009x^12 - 7362x^11 + 13826x^10 + 4848x^9 + 13544x^8 - 44248x^7 + 76384x^6 + 24512x^5 + 28432x^4 - 61952x^3 + 61952x^2 - 5632*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			327.9
Root			$-1.28900 - 1.28900i$ of defining polynomial
Character	$\chi$	$=$	370.327
Dual form			370.2.g.e.43.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.28900 + 1.28900i) q^{3} -1.00000 q^{4} +(-1.52231 - 1.63786i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 - 3.01566i) q^{7} +1.00000i q^{8} +0.323040i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.28900 + 1.28900i) q^{3} -1.00000 q^{4} +(-1.52231 - 1.63786i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 - 3.01566i) q^{7} +1.00000i q^{8} +0.323040i q^{9} +(-1.63786 + 1.52231i) q^{10} -2.38854i q^{11} +(-1.28900 - 1.28900i) q^{12} -1.44800i q^{13} +(-3.01566 + 3.01566i) q^{14} +(0.148945 - 4.07345i) q^{15} +1.00000 q^{16} -2.09597 q^{17} +0.323040 q^{18} +(2.46518 + 2.46518i) q^{19} +(1.52231 + 1.63786i) q^{20} -7.77437i q^{21} -2.38854 q^{22} +0.168727i q^{23} +(-1.28900 + 1.28900i) q^{24} +(-0.365159 + 4.98665i) q^{25} -1.44800 q^{26} +(3.45060 - 3.45060i) q^{27} +(3.01566 + 3.01566i) q^{28} +(4.74797 - 4.74797i) q^{29} +(-4.07345 - 0.148945i) q^{30} +(-3.34342 - 3.34342i) q^{31} -1.00000i q^{32} +(3.07882 - 3.07882i) q^{33} +2.09597i q^{34} +(-0.348461 + 9.52998i) q^{35} -0.323040i q^{36} +(5.78058 - 1.89339i) q^{37} +(2.46518 - 2.46518i) q^{38} +(1.86647 - 1.86647i) q^{39} +(1.63786 - 1.52231i) q^{40} +6.22969i q^{41} -7.77437 q^{42} +3.07893i q^{43} +2.38854i q^{44} +(0.529094 - 0.491767i) q^{45} +0.168727 q^{46} +(-4.67540 - 4.67540i) q^{47} +(1.28900 + 1.28900i) q^{48} +11.1884i q^{49} +(4.98665 + 0.365159i) q^{50} +(-2.70170 - 2.70170i) q^{51} +1.44800i q^{52} +(-2.87955 + 2.87955i) q^{53} +(-3.45060 - 3.45060i) q^{54} +(-3.91208 + 3.63609i) q^{55} +(3.01566 - 3.01566i) q^{56} +6.35524i q^{57} +(-4.74797 - 4.74797i) q^{58} +(-6.78438 - 6.78438i) q^{59} +(-0.148945 + 4.07345i) q^{60} +(6.94487 + 6.94487i) q^{61} +(-3.34342 + 3.34342i) q^{62} +(0.974180 - 0.974180i) q^{63} -1.00000 q^{64} +(-2.37161 + 2.20430i) q^{65} +(-3.07882 - 3.07882i) q^{66} +(-7.89993 + 7.89993i) q^{67} +2.09597 q^{68} +(-0.217489 + 0.217489i) q^{69} +(9.52998 + 0.348461i) q^{70} +12.6621 q^{71} -0.323040 q^{72} +(-4.83010 - 4.83010i) q^{73} +(-1.89339 - 5.78058i) q^{74} +(-6.89848 + 5.95710i) q^{75} +(-2.46518 - 2.46518i) q^{76} +(-7.20301 + 7.20301i) q^{77} +(-1.86647 - 1.86647i) q^{78} +(5.31500 + 5.31500i) q^{79} +(-1.52231 - 1.63786i) q^{80} +9.86477 q^{81} +6.22969 q^{82} +(8.43313 - 8.43313i) q^{83} +7.77437i q^{84} +(3.19071 + 3.43290i) q^{85} +3.07893 q^{86} +12.2403 q^{87} +2.38854 q^{88} +(11.6295 - 11.6295i) q^{89} +(-0.491767 - 0.529094i) q^{90} +(-4.36667 + 4.36667i) q^{91} -0.168727i q^{92} -8.61934i q^{93} +(-4.67540 + 4.67540i) q^{94} +(0.284853 - 7.79038i) q^{95} +(1.28900 - 1.28900i) q^{96} +5.04296 q^{97} +11.1884 q^{98} +0.771593 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	$ 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.28900	+	1.28900i	0.744204	+	0.744204i	0.973384	−	0.229180i	$-0.0736044\pi$
$3$	1.28900	+	1.28900i	0.744204	+	0.744204i	−0.229180	+	0.973384i	$0.573604\pi$
$4$	−1.00000			−0.500000
$5$	−1.52231	−	1.63786i	−0.680797	−	0.732472i
$5$	−1.52231	−	1.63786i	−0.680797	−	0.732472i
$6$	1.28900	−	1.28900i	0.526232	−	0.526232i
$7$	−3.01566	−	3.01566i	−1.13981	−	1.13981i	−0.988484	−	0.151328i	$-0.951645\pi$
$7$	−3.01566	−	3.01566i	−1.13981	−	1.13981i	−0.151328	−	0.988484i	$-0.548355\pi$
$8$			1.00000i			0.353553i
$9$			0.323040i			0.107680i
$10$	−1.63786	+	1.52231i	−0.517936	+	0.481396i
$11$		−	2.38854i		−	0.720171i	−0.932919	−	0.360085i	$-0.882748\pi$
$11$		−	2.38854i		−	0.720171i	0.932919	−	0.360085i	$-0.117252\pi$
$12$	−1.28900	−	1.28900i	−0.372102	−	0.372102i
$13$		−	1.44800i		−	0.401602i	−0.979632	−	0.200801i	$-0.935646\pi$
$13$		−	1.44800i		−	0.401602i	0.979632	−	0.200801i	$-0.0643545\pi$
$14$	−3.01566	+	3.01566i	−0.805969	+	0.805969i
$15$	0.148945	−	4.07345i	0.0384573	−	1.05176i
$16$	1.00000			0.250000
$17$	−2.09597			−0.508347			−0.254173	−	0.967159i	$-0.581803\pi$
$17$	−2.09597			−0.508347			−0.254173	+	0.967159i	$0.581803\pi$
$18$	0.323040			0.0761413
$19$	2.46518	+	2.46518i	0.565551	+	0.565551i	0.930879	−	0.365328i	$-0.119043\pi$
$19$	2.46518	+	2.46518i	0.565551	+	0.565551i	−0.365328	+	0.930879i	$0.619043\pi$
$20$	1.52231	+	1.63786i	0.340398	+	0.366236i
$21$		−	7.77437i		−	1.69651i
$22$	−2.38854			−0.509238
$23$			0.168727i			0.0351820i	0.999845	+	0.0175910i	$0.00559967\pi$
$23$			0.168727i			0.0351820i	−0.999845	+	0.0175910i	$0.994400\pi$
$24$	−1.28900	+	1.28900i	−0.263116	+	0.263116i
$25$	−0.365159	+	4.98665i	−0.0730318	+	0.997330i
$26$	−1.44800			−0.283976
$27$	3.45060	−	3.45060i	0.664068	−	0.664068i
$28$	3.01566	+	3.01566i	0.569906	+	0.569906i
$29$	4.74797	−	4.74797i	0.881676	−	0.881676i	−0.112029	−	0.993705i	$-0.535735\pi$
$29$	4.74797	−	4.74797i	0.881676	−	0.881676i	0.993705	+	0.112029i	$0.0357349\pi$
$30$	−4.07345	−	0.148945i	−0.743707	−	0.0271934i
$31$	−3.34342	−	3.34342i	−0.600496	−	0.600496i	0.339948	−	0.940444i	$-0.389590\pi$
$31$	−3.34342	−	3.34342i	−0.600496	−	0.600496i	−0.940444	+	0.339948i	$0.889590\pi$
$32$		−	1.00000i		−	0.176777i
$33$	3.07882	−	3.07882i	0.535954	−	0.535954i
$34$			2.09597i			0.359456i
$35$	−0.348461	+	9.52998i	−0.0589007	+	1.61086i
$36$		−	0.323040i		−	0.0538401i
$37$	5.78058	−	1.89339i	0.950321	−	0.311271i
$37$	5.78058	−	1.89339i	0.950321	−	0.311271i
$38$	2.46518	−	2.46518i	0.399905	−	0.399905i
$39$	1.86647	−	1.86647i	0.298874	−	0.298874i
$40$	1.63786	−	1.52231i	0.258968	−	0.240698i
$41$			6.22969i			0.972913i	0.873705	+	0.486457i	$0.161711\pi$
$41$			6.22969i			0.972913i	−0.873705	+	0.486457i	$0.838289\pi$
$42$	−7.77437			−1.19961
$43$			3.07893i			0.469532i	0.972052	+	0.234766i	$0.0754323\pi$
$43$			3.07893i			0.469532i	−0.972052	+	0.234766i	$0.924568\pi$
$44$			2.38854i			0.360085i
$45$	0.529094	−	0.491767i	0.0788727	−	0.0733083i
$46$	0.168727			0.0248774
$47$	−4.67540	−	4.67540i	−0.681978	−	0.681978i	0.278468	−	0.960446i	$-0.410173\pi$
$47$	−4.67540	−	4.67540i	−0.681978	−	0.681978i	−0.960446	+	0.278468i	$0.910173\pi$
$48$	1.28900	+	1.28900i	0.186051	+	0.186051i
$49$			11.1884i			1.59834i
$50$	4.98665	+	0.365159i	0.705219	+	0.0516413i
$51$	−2.70170	−	2.70170i	−0.378314	−	0.378314i
$52$			1.44800i			0.200801i
$53$	−2.87955	+	2.87955i	−0.395537	+	0.395537i	−0.876656	−	0.481119i	$-0.840231\pi$
$53$	−2.87955	+	2.87955i	−0.395537	+	0.395537i	0.481119	+	0.876656i	$0.340231\pi$
$54$	−3.45060	−	3.45060i	−0.469567	−	0.469567i
$55$	−3.91208	+	3.63609i	−0.527505	+	0.490290i
$56$	3.01566	−	3.01566i	0.402984	−	0.402984i
$57$			6.35524i			0.841772i
$58$	−4.74797	−	4.74797i	−0.623439	−	0.623439i
$59$	−6.78438	−	6.78438i	−0.883251	−	0.883251i	0.110612	−	0.993864i	$-0.464719\pi$
$59$	−6.78438	−	6.78438i	−0.883251	−	0.883251i	−0.993864	+	0.110612i	$0.964719\pi$
$60$	−0.148945	+	4.07345i	−0.0192287	+	0.525880i
$61$	6.94487	+	6.94487i	0.889199	+	0.889199i	0.994446	−	0.105247i	$-0.0335634\pi$
$61$	6.94487	+	6.94487i	0.889199	+	0.889199i	−0.105247	+	0.994446i	$0.533563\pi$
$62$	−3.34342	+	3.34342i	−0.424615	+	0.424615i
$63$	0.974180	−	0.974180i	0.122735	−	0.122735i
$64$	−1.00000			−0.125000
$65$	−2.37161	+	2.20430i	−0.294162	+	0.273409i
$66$	−3.07882	−	3.07882i	−0.378977	−	0.378977i
$67$	−7.89993	+	7.89993i	−0.965130	+	0.965130i	−0.999412	−	0.0342818i	$-0.989086\pi$
$67$	−7.89993	+	7.89993i	−0.965130	+	0.965130i	0.0342818	+	0.999412i	$0.489086\pi$
$68$	2.09597			0.254173
$69$	−0.217489	+	0.217489i	−0.0261826	+	0.0261826i
$70$	9.52998	+	0.348461i	1.13905	+	0.0416491i
$71$	12.6621			1.50272			0.751358	−	0.659895i	$-0.229399\pi$
$71$	12.6621			1.50272			0.751358	+	0.659895i	$0.229399\pi$
$72$	−0.323040			−0.0380707
$73$	−4.83010	−	4.83010i	−0.565321	−	0.565321i	0.365493	−	0.930814i	$-0.380900\pi$
$73$	−4.83010	−	4.83010i	−0.565321	−	0.565321i	−0.930814	+	0.365493i	$0.880900\pi$
$74$	−1.89339	−	5.78058i	−0.220102	−	0.671978i
$75$	−6.89848	+	5.95710i	−0.796568	+	0.687866i
$76$	−2.46518	−	2.46518i	−0.282776	−	0.282776i
$77$	−7.20301	+	7.20301i	−0.820859	+	0.820859i
$78$	−1.86647	−	1.86647i	−0.211336	−	0.211336i
$79$	5.31500	+	5.31500i	0.597984	+	0.597984i	0.939776	−	0.341792i	$-0.111034\pi$
$79$	5.31500	+	5.31500i	0.597984	+	0.597984i	−0.341792	+	0.939776i	$0.611034\pi$
$80$	−1.52231	−	1.63786i	−0.170199	−	0.183118i
$81$	9.86477			1.09609
$82$	6.22969			0.687954
$83$	8.43313	−	8.43313i	0.925657	−	0.925657i	−0.0717648	−	0.997422i	$-0.522863\pi$
$83$	8.43313	−	8.43313i	0.925657	−	0.925657i	0.997422	+	0.0717648i	$0.0228631\pi$
$84$			7.77437i			0.848253i
$85$	3.19071	+	3.43290i	0.346081	+	0.372350i
$86$	3.07893			0.332009
$87$	12.2403			1.31229
$88$	2.38854			0.254619
$89$	11.6295	−	11.6295i	1.23273	−	1.23273i	0.269814	−	0.962912i	$-0.413038\pi$
$89$	11.6295	−	11.6295i	1.23273	−	1.23273i	0.962912	−	0.269814i	$-0.0869623\pi$
$90$	−0.491767	−	0.529094i	−0.0518368	−	0.0557714i
$91$	−4.36667	+	4.36667i	−0.457751	+	0.457751i
$92$		−	0.168727i		−	0.0175910i
$93$		−	8.61934i		−	0.893784i
$94$	−4.67540	+	4.67540i	−0.482231	+	0.482231i
$95$	0.284853	−	7.79038i	0.0292253	−	0.799276i
$96$	1.28900	−	1.28900i	0.131558	−	0.131558i
$97$	5.04296			0.512035			0.256018	−	0.966672i	$-0.417589\pi$
$97$	5.04296			0.512035			0.256018	+	0.966672i	$0.417589\pi$
$98$	11.1884			1.13020
$99$	0.771593			0.0775481
$100$	0.365159	−	4.98665i	0.0365159	−	0.498665i
$101$		−	11.7791i		−	1.17207i	−0.810287	−	0.586033i	$-0.800689\pi$
$101$		−	11.7791i		−	1.17207i	0.810287	−	0.586033i	$-0.199311\pi$
$102$	−2.70170	+	2.70170i	−0.267508	+	0.267508i
$103$	−6.35592			−0.626267			−0.313134	−	0.949709i	$-0.601379\pi$
$103$	−6.35592			−0.626267			−0.313134	+	0.949709i	$0.601379\pi$
$104$	1.44800			0.141988
$105$	−12.7333	+	11.8350i	−1.24264	+	1.15498i
$106$	2.87955	+	2.87955i	0.279687	+	0.279687i
$107$	−7.29845	−	7.29845i	−0.705568	−	0.705568i	0.260032	−	0.965600i	$-0.416267\pi$
$107$	−7.29845	−	7.29845i	−0.705568	−	0.705568i	−0.965600	+	0.260032i	$0.916267\pi$
$108$	−3.45060	+	3.45060i	−0.332034	+	0.332034i
$109$	7.27809	+	7.27809i	0.697114	+	0.697114i	0.963787	−	0.266673i	$-0.0859243\pi$
$109$	7.27809	+	7.27809i	0.697114	+	0.697114i	−0.266673	+	0.963787i	$0.585924\pi$
$110$	3.63609	+	3.91208i	0.346687	+	0.373002i
$111$	9.89174	+	5.01058i	0.938883	+	0.475583i
$112$	−3.01566	−	3.01566i	−0.284953	−	0.284953i
$113$	5.37412			0.505555			0.252777	−	0.967524i	$-0.418656\pi$
$113$	5.37412			0.505555			0.252777	+	0.967524i	$0.418656\pi$
$114$	6.35524			0.595222
$115$	0.276350	−	0.256854i	0.0257698	−	0.0239518i
$116$	−4.74797	+	4.74797i	−0.440838	+	0.440838i
$117$	0.467761			0.0432446
$118$	−6.78438	+	6.78438i	−0.624553	+	0.624553i
$119$	6.32073	+	6.32073i	0.579420	+	0.579420i
$120$	4.07345	+	0.148945i	0.371854	+	0.0135967i
$121$	5.29490			0.481354
$122$	6.94487	−	6.94487i	0.628759	−	0.628759i
$123$	−8.03006	+	8.03006i	−0.724046	+	0.724046i
$124$	3.34342	+	3.34342i	0.300248	+	0.300248i
$125$	8.72331	−	6.99313i	0.780236	−	0.625485i
$126$	−0.974180	−	0.974180i	−0.0867868	−	0.0867868i
$127$	−11.7621	−	11.7621i	−1.04371	−	1.04371i	−0.999000	−	0.0447148i	$-0.985762\pi$
$127$	−11.7621	−	11.7621i	−1.04371	−	1.04371i	−0.0447148	−	0.999000i	$-0.514238\pi$
$128$			1.00000i			0.0883883i
$129$	−3.96873	+	3.96873i	−0.349428	+	0.349428i
$130$	2.20430	+	2.37161i	0.193330	+	0.208004i
$131$	15.5939	+	15.5939i	1.36245	+	1.36245i	0.870789	+	0.491657i	$0.163609\pi$
$131$	15.5939	+	15.5939i	1.36245	+	1.36245i	0.491657	+	0.870789i	$0.336391\pi$
$132$	−3.07882	+	3.07882i	−0.267977	+	0.267977i
$133$		−	14.8683i		−	1.28924i
$134$	7.89993	+	7.89993i	0.682450	+	0.682450i
$135$	−10.9045	−	0.398719i	−0.938507	−	0.0343162i
$136$		−	2.09597i		−	0.179728i
$137$	0.952787	+	0.952787i	0.0814020	+	0.0814020i	0.746635	−	0.665233i	$-0.231668\pi$
$137$	0.952787	+	0.952787i	0.0814020	+	0.0814020i	−0.665233	+	0.746635i	$0.731668\pi$
$138$	0.217489	+	0.217489i	0.0185139	+	0.0185139i
$139$	−8.19245			−0.694874			−0.347437	−	0.937703i	$-0.612948\pi$
$139$	−8.19245			−0.694874			−0.347437	+	0.937703i	$0.612948\pi$
$140$	0.348461	−	9.52998i	0.0294503	−	0.805431i
$141$		−	12.0532i		−	1.01506i
$142$		−	12.6621i		−	1.06258i
$143$	−3.45859			−0.289222
$144$			0.323040i			0.0269200i
$145$	−15.0044	−	0.548631i	−1.24605	−	0.0455613i
$146$	−4.83010	+	4.83010i	−0.399742	+	0.399742i
$147$	−14.4218	+	14.4218i	−1.18949	+	1.18949i
$148$	−5.78058	+	1.89339i	−0.475161	+	0.155636i
$149$		−	22.8722i		−	1.87377i	−0.349641	−	0.936884i	$-0.613697\pi$
$149$		−	22.8722i		−	1.87377i	0.349641	−	0.936884i	$-0.386303\pi$
$150$	5.95710	+	6.89848i	0.486395	+	0.563258i
$151$			16.6501i			1.35496i	0.735539	+	0.677482i	$0.236929\pi$
$151$			16.6501i			1.35496i	−0.735539	+	0.677482i	$0.763071\pi$
$152$	−2.46518	+	2.46518i	−0.199953	+	0.199953i
$153$		−	0.677082i		−	0.0547389i
$154$	7.20301	+	7.20301i	0.580435	+	0.580435i
$155$	−0.386334	+	10.5658i	−0.0310311	+	0.848663i
$156$	−1.86647	+	1.86647i	−0.149437	+	0.149437i
$157$	10.1100	+	10.1100i	0.806865	+	0.806865i	0.984158	−	0.177293i	$-0.0567341\pi$
$157$	10.1100	+	10.1100i	0.806865	+	0.806865i	−0.177293	+	0.984158i	$0.556734\pi$
$158$	5.31500	−	5.31500i	0.422838	−	0.422838i
$159$	−7.42348			−0.588721
$160$	−1.63786	+	1.52231i	−0.129484	+	0.120349i
$161$	0.508822	−	0.508822i	0.0401008	−	0.0401008i
$162$		−	9.86477i		−	0.775049i
$163$	1.81513			0.142172			0.0710859	−	0.997470i	$-0.477354\pi$
$163$	1.81513			0.142172			0.0710859	+	0.997470i	$0.477354\pi$
$164$		−	6.22969i		−	0.486457i
$165$	−9.72959	−	0.355759i	−0.757447	−	0.0276958i
$166$	−8.43313	−	8.43313i	−0.654538	−	0.654538i
$167$	−16.2469			−1.25722			−0.628610	−	0.777721i	$-0.716376\pi$
$167$	−16.2469			−1.25722			−0.628610	+	0.777721i	$0.716376\pi$
$168$	7.77437			0.599805
$169$	10.9033			0.838716
$170$	3.43290	−	3.19071i	0.263291	−	0.244716i
$171$	−0.796353	+	0.796353i	−0.0608986	+	0.0608986i
$172$		−	3.07893i		−	0.234766i
$173$	−12.0071	−	12.0071i	−0.912885	−	0.912885i	0.0836133	−	0.996498i	$-0.473354\pi$
$173$	−12.0071	−	12.0071i	−0.912885	−	0.912885i	−0.996498	+	0.0836133i	$0.973354\pi$
$174$		−	12.2403i		−	0.927932i
$175$	16.1392	−	13.9368i	1.22001	−	1.05353i
$176$		−	2.38854i		−	0.180043i
$177$		−	17.4901i		−	1.31464i
$178$	−11.6295	−	11.6295i	−0.871669	−	0.871669i
$179$	−8.45867	+	8.45867i	−0.632231	+	0.632231i	−0.948627	−	0.316396i	$-0.897527\pi$
$179$	−8.45867	+	8.45867i	−0.632231	+	0.632231i	0.316396	+	0.948627i	$0.397527\pi$
$180$	−0.529094	+	0.491767i	−0.0394364	+	0.0366541i
$181$	0.961200			0.0714454			0.0357227	−	0.999362i	$-0.488627\pi$
$181$	0.961200			0.0714454			0.0357227	+	0.999362i	$0.488627\pi$
$182$	4.36667	+	4.36667i	0.323679	+	0.323679i
$183$			17.9039i			1.32349i
$184$	−0.168727			−0.0124387
$185$	−11.9009	−	6.58544i	−0.874973	−	0.484171i
$186$	−8.61934			−0.632000
$187$			5.00630i			0.366097i
$188$	4.67540	+	4.67540i	0.340989	+	0.340989i
$189$	−20.8117			−1.51383
$190$	−7.79038	−	0.284853i	−0.565174	−	0.0206654i
$191$	0.355141	−	0.355141i	0.0256971	−	0.0256971i	−0.694141	−	0.719839i	$-0.744216\pi$
$191$	0.355141	−	0.355141i	0.0256971	−	0.0256971i	0.719839	+	0.694141i	$0.244216\pi$
$192$	−1.28900	−	1.28900i	−0.0930255	−	0.0930255i
$193$			7.33106i			0.527701i	0.964564	+	0.263851i	$0.0849926\pi$
$193$			7.33106i			0.527701i	−0.964564	+	0.263851i	$0.915007\pi$
$194$		−	5.04296i		−	0.362064i
$195$	−5.89835	−	0.215671i	−0.422389	−	0.0154445i
$196$		−	11.1884i		−	0.799171i
$197$	−8.20672	−	8.20672i	−0.584704	−	0.584704i	0.351488	−	0.936192i	$-0.385676\pi$
$197$	−8.20672	−	8.20672i	−0.584704	−	0.584704i	−0.936192	+	0.351488i	$0.885676\pi$
$198$		−	0.771593i		−	0.0548348i
$199$	0.480679	−	0.480679i	0.0340744	−	0.0340744i	−0.689864	−	0.723939i	$-0.742330\pi$
$199$	0.480679	−	0.480679i	0.0340744	−	0.0340744i	0.723939	+	0.689864i	$0.242330\pi$
$200$	−4.98665	−	0.365159i	−0.352609	−	0.0258206i
$201$	−20.3660			−1.43651
$202$	−11.7791			−0.828776
$203$	−28.6365			−2.00989
$204$	2.70170	+	2.70170i	0.189157	+	0.189157i
$205$	10.2033	−	9.48350i	0.712632	−	0.662356i
$206$			6.35592i			0.442838i
$207$	−0.0545055			−0.00378840
$208$		−	1.44800i		−	0.100401i
$209$	5.88817	−	5.88817i	0.407293	−	0.407293i
$210$	11.8350	+	12.7333i	0.816691	+	0.878682i
$211$	−24.5328			−1.68891			−0.844453	−	0.535630i	$-0.820074\pi$
$211$	−24.5328			−1.68891			−0.844453	+	0.535630i	$0.820074\pi$
$212$	2.87955	−	2.87955i	0.197768	−	0.197768i
$213$	16.3215	+	16.3215i	1.11833	+	1.11833i
$214$	−7.29845	+	7.29845i	−0.498912	+	0.498912i
$215$	5.04284	−	4.68707i	0.343919	−	0.319656i
$216$	3.45060	+	3.45060i	0.234784	+	0.234784i
$217$			20.1652i			1.36891i
$218$	7.27809	−	7.27809i	0.492934	−	0.492934i
$219$		−	12.4520i		−	0.841429i
$220$	3.91208	−	3.63609i	0.263753	−	0.245145i
$221$			3.03496i			0.204153i
$222$	5.01058	−	9.89174i	0.336288	−	0.663890i
$223$	13.8026	−	13.8026i	0.924289	−	0.924289i	−0.0730404	−	0.997329i	$-0.523270\pi$
$223$	13.8026	−	13.8026i	0.924289	−	0.924289i	0.997329	+	0.0730404i	$0.0232702\pi$
$224$	−3.01566	+	3.01566i	−0.201492	+	0.201492i
$225$	−1.61089	−	0.117961i	−0.107393	−	0.00786407i
$226$		−	5.37412i		−	0.357481i
$227$	10.8328			0.718995			0.359498	−	0.933146i	$-0.382948\pi$
$227$	10.8328			0.718995			0.359498	+	0.933146i	$0.382948\pi$
$228$		−	6.35524i		−	0.420886i
$229$		−	17.5884i		−	1.16227i	−0.813806	−	0.581136i	$-0.802608\pi$
$229$		−	17.5884i		−	1.16227i	0.813806	−	0.581136i	$-0.197392\pi$
$230$	−0.256854	−	0.276350i	−0.0169365	−	0.0182220i
$231$	−18.5694			−1.22177
$232$	4.74797	+	4.74797i	0.311720	+	0.311720i
$233$	1.47378	+	1.47378i	0.0965505	+	0.0965505i	0.753732	−	0.657182i	$-0.228252\pi$
$233$	1.47378	+	1.47378i	0.0965505	+	0.0965505i	−0.657182	+	0.753732i	$0.728252\pi$
$234$		−	0.467761i		−	0.0305785i
$235$	−0.540245	+	14.7750i	−0.0352417	+	0.963818i
$236$	6.78438	+	6.78438i	0.441626	+	0.441626i
$237$			13.7021i			0.890044i
$238$	6.32073	−	6.32073i	0.409712	−	0.409712i
$239$	0.869275	+	0.869275i	0.0562288	+	0.0562288i	0.734662	−	0.678433i	$-0.237341\pi$
$239$	0.869275	+	0.869275i	0.0562288	+	0.0562288i	−0.678433	+	0.734662i	$0.737341\pi$
$240$	0.148945	−	4.07345i	0.00961433	−	0.262940i
$241$	7.39427	−	7.39427i	0.476307	−	0.476307i	−0.427642	−	0.903948i	$-0.640655\pi$
$241$	7.39427	−	7.39427i	0.476307	−	0.476307i	0.903948	+	0.427642i	$0.140655\pi$
$242$		−	5.29490i		−	0.340369i
$243$	2.36388	+	2.36388i	0.151643	+	0.151643i
$244$	−6.94487	−	6.94487i	−0.444599	−	0.444599i
$245$	18.3250	−	17.0322i	1.17074	−	1.08815i
$246$	8.03006	+	8.03006i	0.511978	+	0.511978i
$247$	3.56958	−	3.56958i	0.227127	−	0.227127i
$248$	3.34342	−	3.34342i	0.212307	−	0.212307i
$249$	21.7406			1.37776
$250$	−6.99313	−	8.72331i	−0.442285	−	0.551710i
$251$	15.8249	+	15.8249i	0.998857	+	0.998857i	0.999999	−	0.00114211i	$-0.000363545\pi$
$251$	15.8249	+	15.8249i	0.998857	+	0.998857i	−0.00114211	+	0.999999i	$0.500364\pi$
$252$	−0.974180	+	0.974180i	−0.0613675	+	0.0613675i
$253$	0.403010			0.0253370
$254$	−11.7621	+	11.7621i	−0.738018	+	0.738018i
$255$	−0.312183	+	8.53783i	−0.0195497	+	0.534660i
$256$	1.00000			0.0625000
$257$	23.1629			1.44486			0.722431	−	0.691443i	$-0.243025\pi$
$257$	23.1629			1.44486			0.722431	+	0.691443i	$0.243025\pi$
$258$	3.96873	+	3.96873i	0.247083	+	0.247083i
$259$	−23.1421	−	11.7224i	−1.43798	−	0.728396i
$260$	2.37161	−	2.20430i	0.147081	−	0.136705i
$261$	1.53379	+	1.53379i	0.0949390	+	0.0949390i
$262$	15.5939	−	15.5939i	0.963395	−	0.963395i
$263$	12.7777	+	12.7777i	0.787909	+	0.787909i	0.981151	−	0.193242i	$-0.0619002\pi$
$263$	12.7777	+	12.7777i	0.787909	+	0.787909i	−0.193242	+	0.981151i	$0.561900\pi$
$264$	3.07882	+	3.07882i	0.189488	+	0.189488i
$265$	9.09986	+	0.332734i	0.559000	+	0.0204397i
$266$	−14.8683			−0.911634
$267$	29.9809			1.83480
$268$	7.89993	−	7.89993i	0.482565	−	0.482565i
$269$			5.62728i			0.343101i	0.985175	+	0.171551i	$0.0548777\pi$
$269$			5.62728i			0.343101i	−0.985175	+	0.171551i	$0.945122\pi$
$270$	−0.398719	+	10.9045i	−0.0242652	+	0.663625i
$271$	−21.2992			−1.29384			−0.646919	−	0.762559i	$-0.723943\pi$
$271$	−21.2992			−1.29384			−0.646919	+	0.762559i	$0.723943\pi$
$272$	−2.09597			−0.127087
$273$	−11.2573			−0.681320
$274$	0.952787	−	0.952787i	0.0575599	−	0.0575599i
$275$	11.9108	+	0.872195i	0.718247	+	0.0525953i
$276$	0.217489	−	0.217489i	0.0130913	−	0.0130913i
$277$			24.8652i			1.49401i	0.664821	+	0.747003i	$0.268508\pi$
$277$			24.8652i			1.49401i	−0.664821	+	0.747003i	$0.731492\pi$
$278$			8.19245i			0.491350i
$279$	1.08006	−	1.08006i	0.0646615	−	0.0646615i
$280$	−9.52998	−	0.348461i	−0.569525	−	0.0208245i
$281$	0.925329	−	0.925329i	0.0552005	−	0.0552005i	−0.678968	−	0.734168i	$-0.737572\pi$
$281$	0.925329	−	0.925329i	0.0552005	−	0.0552005i	0.734168	+	0.678968i	$0.237572\pi$
$282$	−12.0532			−0.717757
$283$	−0.300587			−0.0178681			−0.00893403	−	0.999960i	$-0.502844\pi$
$283$	−0.300587			−0.0178681			−0.00893403	+	0.999960i	$0.502844\pi$
$284$	−12.6621			−0.751358
$285$	10.4090	−	9.67462i	0.616574	−	0.573075i
$286$			3.45859i			0.204511i
$287$	18.7866	−	18.7866i	1.10894	−	1.10894i
$288$	0.323040			0.0190353
$289$	−12.6069			−0.741583
$290$	−0.548631	+	15.0044i	−0.0322167	+	0.881087i
$291$	6.50038	+	6.50038i	0.381059	+	0.381059i
$292$	4.83010	+	4.83010i	0.282660	+	0.282660i
$293$	−22.4364	+	22.4364i	−1.31075	+	1.31075i	−0.389881	+	0.920865i	$0.627484\pi$
$293$	−22.4364	+	22.4364i	−1.31075	+	1.31075i	−0.920865	+	0.389881i	$0.872516\pi$
$294$	14.4218	+	14.4218i	0.841099	+	0.841099i
$295$	−0.783939	+	21.4398i	−0.0456427	+	1.24827i
$296$	1.89339	+	5.78058i	0.110051	+	0.335989i
$297$	−8.24188	−	8.24188i	−0.478242	−	0.478242i
$298$	−22.8722			−1.32495
$299$	0.244316			0.0141291
$300$	6.89848	−	5.95710i	0.398284	−	0.343933i
$301$	9.28499	−	9.28499i	0.535178	−	0.535178i
$302$	16.6501			0.958104
$303$	15.1833	−	15.1833i	0.872257	−	0.872257i
$304$	2.46518	+	2.46518i	0.141388	+	0.141388i
$305$	0.802483	−	21.9469i	0.0459500	−	1.25668i
$306$	−0.677082			−0.0387062
$307$	2.94724	−	2.94724i	0.168208	−	0.168208i	−0.617983	−	0.786191i	$-0.712050\pi$
$307$	2.94724	−	2.94724i	0.168208	−	0.168208i	0.786191	+	0.617983i	$0.212050\pi$
$308$	7.20301	−	7.20301i	0.410430	−	0.410430i
$309$	−8.19278	−	8.19278i	−0.466071	−	0.466071i
$310$	10.5658	+	0.386334i	0.600095	+	0.0219423i
$311$	−12.0863	−	12.0863i	−0.685353	−	0.685353i	0.275848	−	0.961201i	$-0.411041\pi$
$311$	−12.0863	−	12.0863i	−0.685353	−	0.685353i	−0.961201	+	0.275848i	$0.911041\pi$
$312$	1.86647	+	1.86647i	0.105668	+	0.105668i
$313$		−	2.00477i		−	0.113316i	−0.998394	−	0.0566582i	$-0.981955\pi$
$313$		−	2.00477i		−	0.113316i	0.998394	−	0.0566582i	$-0.0180445\pi$
$314$	10.1100	−	10.1100i	0.570540	−	0.570540i
$315$	−3.07857	−	0.112567i	−0.173458	−	0.00634243i
$316$	−5.31500	−	5.31500i	−0.298992	−	0.298992i
$317$	7.28840	−	7.28840i	0.409357	−	0.409357i	−0.472157	−	0.881514i	$-0.656525\pi$
$317$	7.28840	−	7.28840i	0.409357	−	0.409357i	0.881514	+	0.472157i	$0.156525\pi$
$318$			7.42348i			0.416288i
$319$	−11.3407	−	11.3407i	−0.634957	−	0.634957i
$320$	1.52231	+	1.63786i	0.0850996	+	0.0915591i
$321$		−	18.8154i		−	1.05017i
$322$	−0.508822	−	0.508822i	−0.0283556	−	0.0283556i
$323$	−5.16694	−	5.16694i	−0.287496	−	0.287496i
$324$	−9.86477			−0.548043
$325$	7.22065	+	0.528749i	0.400530	+	0.0293297i
$326$		−	1.81513i		−	0.100531i
$327$			18.7629i			1.03759i
$328$	−6.22969			−0.343977
$329$			28.1988i			1.55465i
$330$	−0.355759	+	9.72959i	−0.0195839	+	0.535596i
$331$	−0.839383	+	0.839383i	−0.0461367	+	0.0461367i	−0.729799	−	0.683662i	$-0.760386\pi$
$331$	−0.839383	+	0.839383i	−0.0461367	+	0.0461367i	0.683662	+	0.729799i	$0.260386\pi$
$332$	−8.43313	+	8.43313i	−0.462828	+	0.462828i
$333$	0.611642	+	1.86736i	0.0335178	+	0.102331i
$334$			16.2469i			0.888988i
$335$	24.9651	+	0.912841i	1.36399	+	0.0498739i
$336$		−	7.77437i		−	0.424127i
$337$	−7.69155	+	7.69155i	−0.418986	+	0.418986i	−0.884854	−	0.465868i	$-0.845742\pi$
$337$	−7.69155	+	7.69155i	−0.418986	+	0.418986i	0.465868	+	0.884854i	$0.345742\pi$
$338$		−	10.9033i		−	0.593062i
$339$	6.92724	+	6.92724i	0.376236	+	0.376236i
$340$	−3.19071	−	3.43290i	−0.173040	−	0.186175i
$341$	−7.98588	+	7.98588i	−0.432460	+	0.432460i
$342$	0.796353	+	0.796353i	0.0430618	+	0.0430618i
$343$	12.6308	−	12.6308i	0.681998	−	0.681998i
$344$	−3.07893			−0.166005
$345$	0.687300	+	0.0251309i	0.0370030	+	0.00135300i
$346$	−12.0071	+	12.0071i	−0.645507	+	0.645507i
$347$			21.8436i			1.17263i	0.810085	+	0.586313i	$0.199421\pi$
$347$			21.8436i			1.17263i	−0.810085	+	0.586313i	$0.800579\pi$
$348$	−12.2403			−0.656147
$349$			4.00432i			0.214346i	0.994240	+	0.107173i	$0.0341799\pi$
$349$			4.00432i			0.214346i	−0.994240	+	0.107173i	$0.965820\pi$
$350$	−13.9368	−	16.1392i	−0.744955	−	0.862678i
$351$	−4.99646	−	4.99646i	−0.266691	−	0.266691i
$352$	−2.38854			−0.127309
$353$	−11.1747			−0.594769			−0.297384	−	0.954758i	$-0.596114\pi$
$353$	−11.1747			−0.594769			−0.297384	+	0.954758i	$0.596114\pi$
$354$	−17.4901			−0.929590
$355$	−19.2756	−	20.7387i	−1.02304	−	1.10070i
$356$	−11.6295	+	11.6295i	−0.616363	+	0.616363i
$357$			16.2948i			0.862414i
$358$	8.45867	+	8.45867i	0.447055	+	0.447055i
$359$		−	19.4341i		−	1.02570i	−0.858480	−	0.512848i	$-0.828591\pi$
$359$		−	19.4341i		−	1.02570i	0.858480	−	0.512848i	$-0.171409\pi$
$360$	0.491767	+	0.529094i	0.0259184	+	0.0278857i
$361$		−	6.84576i		−	0.360303i
$362$		−	0.961200i		−	0.0505196i
$363$	6.82512	+	6.82512i	0.358226	+	0.358226i
$364$	4.36667	−	4.36667i	0.228875	−	0.228875i
$365$	−0.558121	+	15.2639i	−0.0292134	+	0.798951i
$366$	17.9039			0.935850
$367$	10.2957	+	10.2957i	0.537430	+	0.537430i	0.922773	−	0.385343i	$-0.125917\pi$
$367$	10.2957	+	10.2957i	0.537430	+	0.537430i	−0.385343	+	0.922773i	$0.625917\pi$
$368$			0.168727i			0.00879549i
$369$	−2.01244			−0.104763
$370$	−6.58544	+	11.9009i	−0.342361	+	0.618699i
$371$	17.3675			0.901675
$372$			8.61934i			0.446892i
$373$	23.2626	+	23.2626i	1.20449	+	1.20449i	0.972786	+	0.231704i	$0.0744302\pi$
$373$	23.2626	+	23.2626i	1.20449	+	1.20449i	0.231704	+	0.972786i	$0.425570\pi$
$374$	5.00630			0.258869
$375$	20.2585	+	2.23019i	1.04614	+	0.115167i
$376$	4.67540	−	4.67540i	0.241115	−	0.241115i
$377$	−6.87505	−	6.87505i	−0.354083	−	0.354083i
$378$			20.8117i			1.07044i
$379$			11.6263i			0.597203i	0.954378	+	0.298602i	$0.0965202\pi$
$379$			11.6263i			0.597203i	−0.954378	+	0.298602i	$0.903480\pi$
$380$	−0.284853	+	7.79038i	−0.0146127	+	0.399638i
$381$		−	30.3226i		−	1.55347i
$382$	−0.355141	−	0.355141i	−0.0181706	−	0.0181706i
$383$		−	8.97694i		−	0.458700i	−0.973344	−	0.229350i	$-0.926340\pi$
$383$		−	8.97694i		−	0.458700i	0.973344	−	0.229350i	$-0.0736601\pi$
$384$	−1.28900	+	1.28900i	−0.0657790	+	0.0657790i
$385$	22.7627	+	0.832312i	1.16009	+	0.0424185i
$386$	7.33106			0.373141
$387$	−0.994617			−0.0505592
$388$	−5.04296			−0.256018
$389$	−14.6826	−	14.6826i	−0.744440	−	0.744440i	0.228989	−	0.973429i	$-0.426458\pi$
$389$	−14.6826	−	14.6826i	−0.744440	−	0.744440i	−0.973429	+	0.228989i	$0.926458\pi$
$390$	−0.215671	+	5.89835i	−0.0109209	+	0.298674i
$391$		−	0.353646i		−	0.0178846i
$392$	−11.1884			−0.565100
$393$			40.2011i			2.02788i
$394$	−8.20672	+	8.20672i	−0.413448	+	0.413448i
$395$	0.614151	−	16.7963i	0.0309013	−	0.845112i
$396$	−0.771593			−0.0387740
$397$	−0.327150	+	0.327150i	−0.0164192	+	0.0164192i	−0.715269	−	0.698850i	$-0.753696\pi$
$397$	−0.327150	+	0.327150i	−0.0164192	+	0.0164192i	0.698850	+	0.715269i	$0.253696\pi$
$398$	−0.480679	−	0.480679i	−0.0240943	−	0.0240943i
$399$	19.1652	−	19.1652i	0.959461	−	0.959461i
$400$	−0.365159	+	4.98665i	−0.0182579	+	0.249332i
$401$	19.1836	+	19.1836i	0.957985	+	0.957985i	0.999152	−	0.0411677i	$-0.0131078\pi$
$401$	19.1836	+	19.1836i	0.957985	+	0.957985i	−0.0411677	+	0.999152i	$0.513108\pi$
$402$			20.3660i			1.01576i
$403$	−4.84126	+	4.84126i	−0.241161	+	0.241161i
$404$			11.7791i			0.586033i
$405$	−15.0172	−	16.1571i	−0.746211	−	0.802852i
$406$			28.6365i			1.42121i
$407$	−4.52243	−	13.8071i	−0.224169	−	0.684393i
$408$	2.70170	−	2.70170i	0.133754	−	0.133754i
$409$	−9.30031	+	9.30031i	−0.459871	+	0.459871i	−0.898613	−	0.438742i	$-0.855424\pi$
$409$	−9.30031	+	9.30031i	−0.459871	+	0.459871i	0.438742	+	0.898613i	$0.355424\pi$
$410$	−9.48350	−	10.2033i	−0.468357	−	0.503907i
$411$			2.45628i			0.121160i
$412$	6.35592			0.313134
$413$			40.9188i			2.01348i
$414$			0.0545055i			0.00267880i
$415$	−26.6501	−	0.974453i	−1.30820	−	0.0478340i
$416$	−1.44800			−0.0709939
$417$	−10.5601	−	10.5601i	−0.517128	−	0.517128i
$418$	−5.88817	−	5.88817i	−0.288000	−	0.288000i
$419$		−	11.9651i		−	0.584532i	−0.956337	−	0.292266i	$-0.905591\pi$
$419$		−	11.9651i		−	0.584532i	0.956337	−	0.292266i	$-0.0944093\pi$
$420$	12.7333	−	11.8350i	0.621322	−	0.577488i
$421$	17.5941	+	17.5941i	0.857482	+	0.857482i	0.991041	−	0.133559i	$-0.0426405\pi$
$421$	17.5941	+	17.5941i	0.857482	+	0.857482i	−0.133559	+	0.991041i	$0.542641\pi$
$422$			24.5328i			1.19424i
$423$	1.51034	−	1.51034i	0.0734354	−	0.0734354i
$424$	−2.87955	−	2.87955i	−0.139843	−	0.139843i
$425$	0.765361	−	10.4519i	0.0371255	−	0.506990i
$426$	16.3215	−	16.3215i	0.790777	−	0.790777i
$427$		−	41.8867i		−	2.02704i
$428$	7.29845	+	7.29845i	0.352784	+	0.352784i
$429$	−4.45812	−	4.45812i	−0.215240	−	0.215240i
$430$	−4.68707	−	5.04284i	−0.226031	−	0.243187i
$431$	−9.36769	−	9.36769i	−0.451226	−	0.451226i	0.444536	−	0.895761i	$-0.353369\pi$
$431$	−9.36769	−	9.36769i	−0.451226	−	0.451226i	−0.895761	+	0.444536i	$0.853369\pi$
$432$	3.45060	−	3.45060i	0.166017	−	0.166017i
$433$	11.6303	−	11.6303i	0.558916	−	0.558916i	−0.370083	−	0.928999i	$-0.620671\pi$
$433$	11.6303	−	11.6303i	0.558916	−	0.558916i	0.928999	+	0.370083i	$0.120671\pi$
$434$	20.1652			0.967962
$435$	−18.6335	−	20.0478i	−0.893406	−	0.961219i
$436$	−7.27809	−	7.27809i	−0.348557	−	0.348557i
$437$	−0.415942	+	0.415942i	−0.0198972	+	0.0198972i
$438$	−12.4520			−0.594980
$439$	−16.3753	+	16.3753i	−0.781552	+	0.781552i	−0.980093	−	0.198540i	$-0.936380\pi$
$439$	−16.3753	+	16.3753i	−0.781552	+	0.781552i	0.198540	+	0.980093i	$0.436380\pi$
$440$	−3.63609	−	3.91208i	−0.173344	−	0.186501i
$441$	−3.61430			−0.172110
$442$	3.03496			0.144358
$443$	−18.4976	−	18.4976i	−0.878850	−	0.878850i	0.114566	−	0.993416i	$-0.463452\pi$
$443$	−18.4976	−	18.4976i	−0.878850	−	0.878850i	−0.993416	+	0.114566i	$0.963452\pi$
$444$	−9.89174	−	5.01058i	−0.469441	−	0.237792i
$445$	−36.7512	−	1.34380i	−1.74217	−	0.0637021i
$446$	−13.8026	−	13.8026i	−0.653571	−	0.653571i
$447$	29.4823	−	29.4823i	1.39447	−	1.39447i
$448$	3.01566	+	3.01566i	0.142477	+	0.142477i
$449$	28.1954	+	28.1954i	1.33062	+	1.33062i	0.904814	+	0.425808i	$0.140010\pi$
$449$	28.1954	+	28.1954i	1.33062	+	1.33062i	0.425808	+	0.904814i	$0.359990\pi$
$450$	−0.117961	+	1.61089i	−0.00556074	+	0.0759380i
$451$	14.8798			0.700664
$452$	−5.37412			−0.252777
$453$	−21.4619	+	21.4619i	−1.00837	+	1.00837i
$454$		−	10.8328i		−	0.508406i
$455$	13.7994	+	0.504570i	0.646925	+	0.0236546i
$456$	−6.35524			−0.297611
$457$	30.7275			1.43737			0.718687	−	0.695334i	$-0.244744\pi$
$457$	30.7275			1.43737			0.718687	+	0.695334i	$0.244744\pi$
$458$	−17.5884			−0.821851
$459$	−7.23235	+	7.23235i	−0.337577	+	0.337577i
$460$	−0.276350	+	0.256854i	−0.0128849	+	0.0119759i
$461$	−9.22827	+	9.22827i	−0.429804	+	0.429804i	−0.888561	−	0.458758i	$-0.848295\pi$
$461$	−9.22827	+	9.22827i	−0.429804	+	0.429804i	0.458758	+	0.888561i	$0.348295\pi$
$462$			18.5694i			0.863925i
$463$		−	13.6064i		−	0.632343i	−0.948702	−	0.316172i	$-0.897602\pi$
$463$		−	13.6064i		−	0.632343i	0.948702	−	0.316172i	$-0.102398\pi$
$464$	4.74797	−	4.74797i	0.220419	−	0.220419i
$465$	−14.1173	+	13.1213i	−0.654672	+	0.608485i
$466$	1.47378	−	1.47378i	0.0682715	−	0.0682715i
$467$	−19.5369			−0.904059			−0.452030	−	0.892003i	$-0.649300\pi$
$467$	−19.5369			−0.904059			−0.452030	+	0.892003i	$0.649300\pi$
$468$	−0.467761			−0.0216223
$469$	47.6470			2.20013
$470$	14.7750	+	0.540245i	0.681522	+	0.0249197i
$471$			26.0635i			1.20094i
$472$	6.78438	−	6.78438i	0.312277	−	0.312277i
$473$	7.35412			0.338143
$474$	13.7021			0.629356
$475$	−13.1932	+	11.3928i	−0.605344	+	0.522738i
$476$	−6.32073	−	6.32073i	−0.289710	−	0.289710i
$477$	−0.930212	−	0.930212i	−0.0425915	−	0.0425915i
$478$	0.869275	−	0.869275i	0.0397597	−	0.0397597i
$479$	25.1547	+	25.1547i	1.14935	+	1.14935i	0.986681	+	0.162667i	$0.0520097\pi$
$479$	25.1547	+	25.1547i	1.14935	+	1.14935i	0.162667	+	0.986681i	$0.447990\pi$
$480$	−4.07345	−	0.148945i	−0.185927	−	0.00679836i
$481$	−2.74162	−	8.37026i	−0.125007	−	0.381651i
$482$	−7.39427	−	7.39427i	−0.336800	−	0.336800i
$483$	1.31174			0.0596864
$484$	−5.29490			−0.240677
$485$	−7.67694	−	8.25966i	−0.348592	−	0.375052i
$486$	2.36388	−	2.36388i	0.107228	−	0.107228i
$487$	41.5088			1.88094			0.940471	−	0.339873i	$-0.110384\pi$
$487$	41.5088			1.88094			0.940471	+	0.339873i	$0.110384\pi$
$488$	−6.94487	+	6.94487i	−0.314379	+	0.314379i
$489$	2.33970	+	2.33970i	0.105805	+	0.105805i
$490$	−17.0322	−	18.3250i	−0.769436	−	0.827840i
$491$	−24.6515			−1.11250			−0.556252	−	0.831013i	$-0.687761\pi$
$491$	−24.6515			−1.11250			−0.556252	+	0.831013i	$0.687761\pi$
$492$	8.03006	−	8.03006i	0.362023	−	0.362023i
$493$	−9.95160	+	9.95160i	−0.448197	+	0.448197i
$494$	−3.56958	−	3.56958i	−0.160603	−	0.160603i
$495$	−1.17460	−	1.26376i	−0.0527945	−	0.0568018i
$496$	−3.34342	−	3.34342i	−0.150124	−	0.150124i
$497$	−38.1846	−	38.1846i	−1.71281	−	1.71281i
$498$		−	21.7406i		−	0.974220i
$499$	16.8585	−	16.8585i	0.754689	−	0.754689i	−0.220662	−	0.975350i	$-0.570822\pi$
$499$	16.8585	−	16.8585i	0.754689	−	0.754689i	0.975350	+	0.220662i	$0.0708217\pi$
$500$	−8.72331	+	6.99313i	−0.390118	+	0.312742i
$501$	−20.9422	−	20.9422i	−0.935628	−	0.935628i
$502$	15.8249	−	15.8249i	0.706299	−	0.706299i
$503$			14.5276i			0.647755i	0.946099	+	0.323877i	$0.104987\pi$
$503$			14.5276i			0.647755i	−0.946099	+	0.323877i	$0.895013\pi$
$504$	0.974180	+	0.974180i	0.0433934	+	0.0433934i
$505$	−19.2925	+	17.9314i	−0.858506	+	0.797939i
$506$		−	0.403010i		−	0.0179160i
$507$	14.0544	+	14.0544i	0.624176	+	0.624176i
$508$	11.7621	+	11.7621i	0.521857	+	0.521857i
$509$	−38.8001			−1.71978			−0.859892	−	0.510476i	$-0.829469\pi$
$509$	−38.8001			−1.71978			−0.859892	+	0.510476i	$0.829469\pi$
$510$	8.53783	+	0.312183i	0.378061	+	0.0138237i
$511$			29.1319i			1.28872i
$512$		−	1.00000i		−	0.0441942i
$513$	17.0127			0.751129
$514$		−	23.1629i		−	1.02167i
$515$	9.67567	+	10.4101i	0.426361	+	0.458724i
$516$	3.96873	−	3.96873i	0.174714	−	0.174714i
$517$	−11.1674	+	11.1674i	−0.491140	+	0.491140i
$518$	−11.7224	+	23.1421i	−0.515054	+	1.01680i
$519$		−	30.9544i		−	1.35875i
$520$	−2.20430	−	2.37161i	−0.0966648	−	0.104002i
$521$		−	1.46992i		−	0.0643983i	−0.999481	−	0.0321991i	$-0.989749\pi$
$521$		−	1.46992i		−	0.0643983i	0.999481	−	0.0321991i	$-0.0102511\pi$
$522$	1.53379	−	1.53379i	0.0671320	−	0.0671320i
$523$		−	37.4377i		−	1.63704i	−0.574479	−	0.818519i	$-0.694795\pi$
$523$		−	37.4377i		−	1.63704i	0.574479	−	0.818519i	$-0.305205\pi$
$524$	−15.5939	−	15.5939i	−0.681223	−	0.681223i
$525$	38.7680	+	2.83888i	1.69198	+	0.123899i
$526$	12.7777	−	12.7777i	0.557136	−	0.557136i
$527$	7.00770	+	7.00770i	0.305260	+	0.305260i
$528$	3.07882	−	3.07882i	0.133989	−	0.133989i
$529$	22.9715			0.998762
$530$	0.332734	−	9.09986i	0.0144530	−	0.395273i
$531$	2.19163	−	2.19163i	0.0951086	−	0.0951086i
$532$			14.8683i			0.644622i
$533$	9.02057			0.390724
$534$		−	29.9809i		−	1.29740i
$535$	−0.843340	+	23.0643i	−0.0364608	+	0.997157i
$536$	−7.89993	−	7.89993i	−0.341225	−	0.341225i
$537$	−21.8065			−0.941018
$538$	5.62728			0.242609
$539$	26.7239			1.15108
$540$	10.9045	+	0.398719i	0.469254	+	0.0171581i
$541$	1.13614	−	1.13614i	0.0488465	−	0.0488465i	−0.682262	−	0.731108i	$-0.739003\pi$
$541$	1.13614	−	1.13614i	0.0488465	−	0.0488465i	0.731108	+	0.682262i	$0.239003\pi$
$542$			21.2992i			0.914881i
$543$	1.23899	+	1.23899i	0.0531700	+	0.0531700i
$544$			2.09597i			0.0898639i
$545$	0.840987	−	23.0000i	0.0360239	−	0.985210i
$546$			11.2573i			0.481766i
$547$			41.4457i			1.77209i	0.463599	+	0.886045i	$0.346558\pi$
$547$			41.4457i			1.77209i	−0.463599	+	0.886045i	$0.653442\pi$
$548$	−0.952787	−	0.952787i	−0.0407010	−	0.0407010i
$549$	−2.24347	+	2.24347i	−0.0957490	+	0.0957490i
$550$	0.872195	−	11.9108i	0.0371905	−	0.507878i
$551$	23.4092			0.997266
$552$	−0.217489	−	0.217489i	−0.00925694	−	0.00925694i
$553$		−	32.0564i		−	1.36318i
$554$	24.8652			1.05642
$555$	−6.85165	−	23.8289i	−0.290836	−	1.01148i
$556$	8.19245			0.347437
$557$			24.9812i			1.05849i	0.848470	+	0.529244i	$0.177524\pi$
$557$			24.9812i			1.05849i	−0.848470	+	0.529244i	$0.822476\pi$
$558$	−1.08006	−	1.08006i	−0.0457226	−	0.0457226i
$559$	4.45827			0.188565
$560$	−0.348461	+	9.52998i	−0.0147252	+	0.402715i
$561$	−6.45311	+	6.45311i	−0.272451	+	0.272451i
$562$	−0.925329	−	0.925329i	−0.0390326	−	0.0390326i
$563$		−	36.8702i		−	1.55389i	−0.629567	−	0.776946i	$-0.716768\pi$
$563$		−	36.8702i		−	1.55389i	0.629567	−	0.776946i	$-0.283232\pi$
$564$			12.0532i			0.507531i
$565$	−8.18106	−	8.80205i	−0.344180	−	0.370305i
$566$			0.300587i			0.0126346i
$567$	−29.7488	−	29.7488i	−1.24933	−	1.24933i
$568$			12.6621i			0.531290i
$569$	9.95317	−	9.95317i	0.417259	−	0.417259i	−0.466999	−	0.884258i	$-0.654665\pi$
$569$	9.95317	−	9.95317i	0.417259	−	0.417259i	0.884258	+	0.466999i	$0.154665\pi$
$570$	−9.67462	−	10.4090i	−0.405225	−	0.435984i
$571$	13.1507			0.550340			0.275170	−	0.961396i	$-0.411266\pi$
$571$	13.1507			0.550340			0.275170	+	0.961396i	$0.411266\pi$
$572$	3.45859			0.144611
$573$	0.915554			0.0382478
$574$	−18.7866	−	18.7866i	−0.784138	−	0.784138i
$575$	−0.841381	−	0.0616121i	−0.0350880	−	0.00256940i
$576$		−	0.323040i		−	0.0134600i
$577$	−4.76642			−0.198429			−0.0992144	−	0.995066i	$-0.531633\pi$
$577$	−4.76642			−0.198429			−0.0992144	+	0.995066i	$0.531633\pi$
$578$			12.6069i			0.524379i
$579$	−9.44973	+	9.44973i	−0.392718	+	0.392718i
$580$	15.0044	+	0.548631i	0.623023	+	0.0227806i
$581$	−50.8629			−2.11015
$582$	6.50038	−	6.50038i	0.269449	−	0.269449i
$583$	6.87791	+	6.87791i	0.284854	+	0.284854i
$584$	4.83010	−	4.83010i	0.199871	−	0.199871i
$585$	−0.712077	−	0.766127i	−0.0294408	−	0.0316755i
$586$	22.4364	+	22.4364i	0.926837	+	0.926837i
$587$		−	1.56926i		−	0.0647702i	−0.999475	−	0.0323851i	$-0.989690\pi$
$587$		−	1.56926i		−	0.0647702i	0.999475	−	0.0323851i	$-0.0103103\pi$
$588$	14.4218	−	14.4218i	0.594747	−	0.594747i
$589$		−	16.4843i		−	0.679223i
$590$	21.4398	+	0.783939i	0.882661	+	0.0322743i
$591$		−	21.1569i		−	0.870279i
$592$	5.78058	−	1.89339i	0.237580	−	0.0778179i
$593$	9.67923	−	9.67923i	0.397478	−	0.397478i	−0.479864	−	0.877343i	$-0.659314\pi$
$593$	9.67923	−	9.67923i	0.397478	−	0.397478i	0.877343	+	0.479864i	$0.159314\pi$
$594$	−8.24188	+	8.24188i	−0.338168	+	0.338168i
$595$	0.730363	−	19.9745i	0.0299420	−	0.818876i
$596$			22.8722i			0.936884i
$597$	1.23919			0.0507167
$598$		−	0.244316i		−	0.00999082i
$599$			43.4898i			1.77694i	0.458931	+	0.888472i	$0.348232\pi$
$599$			43.4898i			1.77694i	−0.458931	+	0.888472i	$0.651768\pi$
$600$	−5.95710	−	6.89848i	−0.243198	−	0.281629i
$601$	−46.6191			−1.90163			−0.950817	−	0.309754i	$-0.899753\pi$
$601$	−46.6191			−1.90163			−0.950817	+	0.309754i	$0.899753\pi$
$602$	−9.28499	−	9.28499i	−0.378428	−	0.378428i
$603$	−2.55200	−	2.55200i	−0.103925	−	0.103925i
$604$		−	16.6501i		−	0.677482i
$605$	−8.06046	−	8.67229i	−0.327704	−	0.352579i
$606$	−15.1833	−	15.1833i	−0.616779	−	0.616779i
$607$		−	11.8472i		−	0.480862i	−0.970666	−	0.240431i	$-0.922711\pi$
$607$		−	11.8472i		−	0.480862i	0.970666	−	0.240431i	$-0.0772887\pi$
$608$	2.46518	−	2.46518i	0.0999763	−	0.0999763i
$609$	−36.9125	−	36.9125i	−1.49577	−	1.49577i
$610$	−21.9469	−	0.802483i	−0.888605	−	0.0324916i
$611$	−6.76997	+	6.76997i	−0.273884	+	0.273884i
$612$			0.677082i			0.0273694i
$613$	32.8563	+	32.8563i	1.32705	+	1.32705i	0.907930	+	0.419122i	$0.137662\pi$
$613$	32.8563	+	32.8563i	1.32705	+	1.32705i	0.419122	+	0.907930i	$0.362338\pi$
$614$	−2.94724	−	2.94724i	−0.118941	−	0.118941i
$615$	25.3763	+	0.927878i	1.02327	+	0.0374156i
$616$	−7.20301	−	7.20301i	−0.290218	−	0.290218i
$617$	−7.41696	+	7.41696i	−0.298595	+	0.298595i	−0.840464	−	0.541868i	$-0.817717\pi$
$617$	−7.41696	+	7.41696i	−0.298595	+	0.298595i	0.541868	+	0.840464i	$0.317717\pi$
$618$	−8.19278	+	8.19278i	−0.329562	+	0.329562i
$619$	4.51948			0.181653			0.0908266	−	0.995867i	$-0.471049\pi$
$619$	4.51948			0.181653			0.0908266	+	0.995867i	$0.471049\pi$
$620$	0.386334	−	10.5658i	0.0155155	−	0.424331i
$621$	0.582209	+	0.582209i	0.0233632	+	0.0233632i
$622$	−12.0863	+	12.0863i	−0.484618	+	0.484618i
$623$	−70.1413			−2.81015
$624$	1.86647	−	1.86647i	0.0747185	−	0.0747185i
$625$	−24.7333	−	3.64184i	−0.989333	−	0.145673i
$626$	−2.00477			−0.0801267
$627$	15.1797			0.606219
$628$	−10.1100	−	10.1100i	−0.403432	−	0.403432i
$629$	−12.1159	+	3.96849i	−0.483093	+	0.158234i
$630$	−0.112567	+	3.07857i	−0.00448478	+	0.122653i
$631$	−5.79579	−	5.79579i	−0.230727	−	0.230727i	0.582269	−	0.812996i	$-0.302165\pi$
$631$	−5.79579	−	5.79579i	−0.230727	−	0.230727i	−0.812996	+	0.582269i	$0.802165\pi$
$632$	−5.31500	+	5.31500i	−0.211419	+	0.211419i
$633$	−31.6227	−	31.6227i	−1.25689	−	1.25689i
$634$	−7.28840	−	7.28840i	−0.289459	−	0.289459i
$635$	−1.35911	+	37.1701i	−0.0539348	+	1.47505i
$636$	7.42348			0.294360
$637$	16.2008			0.641898
$638$	−11.3407	+	11.3407i	−0.448983	+	0.448983i
$639$			4.09037i			0.161813i
$640$	1.63786	−	1.52231i	0.0647420	−	0.0601745i
$641$	34.7174			1.37125			0.685627	−	0.727953i	$-0.259528\pi$
$641$	34.7174			1.37125			0.685627	+	0.727953i	$0.259528\pi$
$642$	−18.8154			−0.742585
$643$	−39.5100			−1.55812			−0.779060	−	0.626949i	$-0.784303\pi$
$643$	−39.5100			−1.55812			−0.779060	+	0.626949i	$0.784303\pi$
$644$	−0.508822	+	0.508822i	−0.0200504	+	0.0200504i
$645$	12.5419	+	0.458589i	0.493835	+	0.0180569i
$646$	−5.16694	+	5.16694i	−0.203291	+	0.203291i
$647$		−	4.05796i		−	0.159535i	−0.996813	−	0.0797675i	$-0.974582\pi$
$647$		−	4.05796i		−	0.159535i	0.996813	−	0.0797675i	$-0.0254178\pi$
$648$			9.86477i			0.387525i
$649$	−16.2047	+	16.2047i	−0.636092	+	0.636092i
$650$	0.528749	−	7.22065i	0.0207392	−	0.283217i
$651$	−25.9930	+	25.9930i	−1.01875	+	1.01875i
$652$	−1.81513			−0.0710859
$653$	27.8245			1.08886			0.544429	−	0.838807i	$-0.316747\pi$
$653$	27.8245			1.08886			0.544429	+	0.838807i	$0.316747\pi$
$654$	18.7629			0.733688
$655$	1.80188	−	49.2793i	0.0704054	−	1.92550i
$656$			6.22969i			0.243228i
$657$	1.56032	−	1.56032i	0.0608738	−	0.0608738i
$658$	28.1988			1.09931
$659$	−34.5284			−1.34503			−0.672517	−	0.740082i	$-0.734787\pi$
$659$	−34.5284			−1.34503			−0.672517	+	0.740082i	$0.734787\pi$
$660$	9.72959	+	0.355759i	0.378724	+	0.0138479i
$661$	−28.4737	−	28.4737i	−1.10750	−	1.10750i	−0.993478	−	0.114022i	$-0.963627\pi$
$661$	−28.4737	−	28.4737i	−1.10750	−	1.10750i	−0.114022	−	0.993478i	$-0.536373\pi$
$662$	0.839383	+	0.839383i	0.0326236	+	0.0326236i
$663$	−3.91206	+	3.91206i	−0.151932	+	0.151932i
$664$	8.43313	+	8.43313i	0.327269	+	0.327269i
$665$	−24.3522	+	22.6341i	−0.944336	+	0.877713i
$666$	1.86736	−	0.611642i	0.0723587	−	0.0237006i
$667$	0.801110	+	0.801110i	0.0310191	+	0.0310191i
$668$	16.2469			0.628610
$669$	35.5830			1.37572
$670$	0.912841	−	24.9651i	0.0352661	−	0.964486i
$671$	16.5881	−	16.5881i	0.640375	−	0.640375i
$672$	−7.77437			−0.299903
$673$	7.80123	−	7.80123i	0.300715	−	0.300715i	−0.540578	−	0.841294i	$-0.681795\pi$
$673$	7.80123	−	7.80123i	0.300715	−	0.300715i	0.841294	+	0.540578i	$0.181795\pi$
$674$	7.69155	+	7.69155i	0.296268	+	0.296268i
$675$	15.9469	+	18.4669i	0.613797	+	0.710793i
$676$	−10.9033			−0.419358
$677$	−27.1256	+	27.1256i	−1.04252	+	1.04252i	−0.0434658	+	0.999055i	$0.513840\pi$
$677$	−27.1256	+	27.1256i	−1.04252	+	1.04252i	−0.999055	+	0.0434658i	$0.986160\pi$
$678$	6.92724	−	6.92724i	0.266039	−	0.266039i
$679$	−15.2079	−	15.2079i	−0.583624	−	0.583624i
$680$	−3.43290	+	3.19071i	−0.131646	+	0.122358i
$681$	13.9634	+	13.9634i	0.535079	+	0.535079i
$682$	7.98588	+	7.98588i	0.305795	+	0.305795i
$683$			5.91525i			0.226341i	0.993576	+	0.113170i	$0.0361006\pi$
$683$			5.91525i			0.226341i	−0.993576	+	0.113170i	$0.963899\pi$
$684$	0.796353	−	0.796353i	0.0304493	−	0.0304493i
$685$	0.110095	−	3.01096i	0.00420651	−	0.115043i
$686$	−12.6308	−	12.6308i	−0.482246	−	0.482246i
$687$	22.6714	−	22.6714i	0.864968	−	0.864968i
$688$			3.07893i			0.117383i
$689$	4.16958	+	4.16958i	0.158848	+	0.158848i
$690$	0.0251309	−	0.687300i	0.000956718	−	0.0261651i
$691$		−	8.32303i		−	0.316623i	−0.987389	−	0.158312i	$-0.949395\pi$
$691$		−	8.32303i		−	0.316623i	0.987389	−	0.158312i	$-0.0506050\pi$
$692$	12.0071	+	12.0071i	0.456442	+	0.456442i
$693$	−2.32686	−	2.32686i	−0.0883902	−	0.0883902i
$694$	21.8436			0.829171
$695$	12.4714	+	13.4181i	0.473068	+	0.508976i
$696$			12.2403i			0.463966i
$697$		−	13.0572i		−	0.494578i
$698$	4.00432			0.151566
$699$			3.79940i			0.143707i
$700$	−16.1392	+	13.9368i	−0.610005	+	0.526763i
$701$	15.3758	−	15.3758i	0.580737	−	0.580737i	−0.354369	−	0.935106i	$-0.615304\pi$
$701$	15.3758	−	15.3758i	0.580737	−	0.580737i	0.935106	+	0.354369i	$0.115304\pi$
$702$	−4.99646	+	4.99646i	−0.188579	+	0.188579i
$703$	18.9177	+	9.58262i	0.713495	+	0.361415i
$704$			2.38854i			0.0900213i
$705$	−19.7414	+	18.3487i	−0.743504	+	0.691050i
$706$			11.1747i			0.420565i
$707$	−35.5218	+	35.5218i	−1.33594	+	1.33594i
$708$			17.4901i			0.657319i
$709$	18.0591	+	18.0591i	0.678223	+	0.678223i	0.959598	−	0.281375i	$-0.0907903\pi$
$709$	18.0591	+	18.0591i	0.678223	+	0.678223i	−0.281375	+	0.959598i	$0.590790\pi$
$710$	−20.7387	+	19.2756i	−0.778311	+	0.723401i
$711$	−1.71696	+	1.71696i	−0.0643910	+	0.0643910i
$712$	11.6295	+	11.6295i	0.435835	+	0.435835i
$713$	0.564125	−	0.564125i	0.0211266	−	0.0211266i
$714$	16.2948			0.609819
$715$	5.26504	+	5.66468i	0.196901	+	0.211847i
$716$	8.45867	−	8.45867i	0.316115	−	0.316115i
$717$			2.24099i			0.0836914i
$718$	−19.4341			−0.725276
$719$			18.4885i			0.689505i	0.938694	+	0.344752i	$0.112037\pi$
$719$			18.4885i			0.689505i	−0.938694	+	0.344752i	$0.887963\pi$
$720$	0.529094	−	0.491767i	0.0197182	−	0.0183271i
$721$	19.1673	+	19.1673i	0.713827	+	0.713827i
$722$	−6.84576			−0.254773
$723$	19.0624			0.708939
$724$	−0.961200			−0.0357227
$725$	21.9427	+	25.4102i	0.814931	+	0.943712i
$726$	6.82512	−	6.82512i	0.253304	−	0.253304i
$727$		−	0.154078i		−	0.00571445i	−0.999996	−	0.00285722i	$-0.999091\pi$
$727$		−	0.154078i		−	0.00571445i	0.999996	−	0.00285722i	$-0.000909484\pi$
$728$	−4.36667	−	4.36667i	−0.161839	−	0.161839i
$729$		−	23.5002i		−	0.870378i
$730$	15.2639	+	0.558121i	0.564943	+	0.0206570i
$731$		−	6.45333i		−	0.238685i
$732$		−	17.9039i		−	0.661746i
$733$	26.0288	+	26.0288i	0.961397	+	0.961397i	0.999282	−	0.0378850i	$-0.0120621\pi$
$733$	26.0288	+	26.0288i	0.961397	+	0.961397i	−0.0378850	+	0.999282i	$0.512062\pi$
$734$	10.2957	−	10.2957i	0.380020	−	0.380020i
$735$	45.5754	+	1.66645i	1.68107	+	0.0614680i
$736$	0.168727			0.00621935
$737$	18.8693	+	18.8693i	0.695059	+	0.695059i
$738$			2.01244i			0.0740789i
$739$	−36.2429			−1.33322			−0.666608	−	0.745408i	$-0.732255\pi$
$739$	−36.2429			−1.33322			−0.666608	+	0.745408i	$0.732255\pi$
$740$	11.9009	+	6.58544i	0.437487	+	0.242086i
$741$	9.20236			0.338057
$742$		−	17.3675i		−	0.637581i
$743$	7.38988	+	7.38988i	0.271109	+	0.271109i	0.829546	−	0.558438i	$-0.188599\pi$
$743$	7.38988	+	7.38988i	0.271109	+	0.271109i	−0.558438	+	0.829546i	$0.688599\pi$
$744$	8.61934			0.316000
$745$	−37.4615	+	34.8186i	−1.37248	+	1.27565i
$746$	23.2626	−	23.2626i	0.851704	−	0.851704i
$747$	2.72424	+	2.72424i	0.0996748	+	0.0996748i
$748$		−	5.00630i		−	0.183048i
$749$			44.0193i			1.60843i
$750$	2.23019	−	20.2585i	0.0814351	−	0.739735i
$751$			18.3541i			0.669749i	0.942263	+	0.334874i	$0.108694\pi$
$751$			18.3541i			0.669749i	−0.942263	+	0.334874i	$0.891306\pi$
$752$	−4.67540	−	4.67540i	−0.170494	−	0.170494i
$753$			40.7965i			1.48671i
$754$	−6.87505	+	6.87505i	−0.250374	+	0.250374i
$755$	27.2705	−	25.3465i	0.992474	−	0.922455i
$756$	20.8117			0.756913
$757$	7.26929			0.264207			0.132104	−	0.991236i	$-0.457827\pi$
$757$	7.26929			0.264207			0.132104	+	0.991236i	$0.457827\pi$
$758$	11.6263			0.422287
$759$	0.519480	+	0.519480i	0.0188559	+	0.0188559i
$760$	7.79038	+	0.284853i	0.282587	+	0.0103327i
$761$			19.7277i			0.715127i	0.933889	+	0.357564i	$0.116392\pi$
$761$			19.7277i			0.715127i	−0.933889	+	0.357564i	$0.883608\pi$
$762$	−30.3226			−1.09847
$763$		−	43.8965i		−	1.58916i
$764$	−0.355141	+	0.355141i	−0.0128486	+	0.0128486i
$765$	−1.10896	+	1.03073i	−0.0400947	+	0.0372660i
$766$	−8.97694			−0.324350
$767$	−9.82377	+	9.82377i	−0.354716	+	0.354716i
$768$	1.28900	+	1.28900i	0.0465128	+	0.0465128i
$769$	22.1613	−	22.1613i	0.799158	−	0.799158i	−0.183805	−	0.982963i	$-0.558841\pi$
$769$	22.1613	−	22.1613i	0.799158	−	0.799158i	0.982963	+	0.183805i	$0.0588415\pi$
$770$	0.832312	−	22.7627i	0.0299944	−	0.820311i
$771$	29.8570	+	29.8570i	1.07527	+	1.07527i
$772$		−	7.33106i		−	0.263851i
$773$	−30.0504	+	30.0504i	−1.08084	+	1.08084i	−0.0844052	+	0.996432i	$0.526899\pi$
$773$	−30.0504	+	30.0504i	−1.08084	+	1.08084i	−0.996432	+	0.0844052i	$0.973101\pi$
$774$			0.994617i			0.0357508i
$775$	17.8933	−	15.4516i	0.642748	−	0.555037i
$776$			5.04296i			0.181032i
$777$	−14.7199	−	44.9403i	−0.528074	−	1.61223i
$778$	−14.6826	+	14.6826i	−0.526398	+	0.526398i
$779$	−15.3573	+	15.3573i	−0.550232	+	0.550232i
$780$	5.89835	+	0.215671i	0.211195	+	0.00772227i
$781$		−	30.2439i		−	1.08221i
$782$	−0.353646			−0.0126464
$783$		−	32.7667i		−	1.17099i
$784$			11.1884i			0.399586i
$785$	1.16821	−	31.9492i	0.0416954	−	1.14032i
$786$	40.2011			1.43393
$787$	22.2914	+	22.2914i	0.794603	+	0.794603i	0.982239	−	0.187636i	$-0.0600825\pi$
$787$	22.2914	+	22.2914i	0.794603	+	0.794603i	−0.187636	+	0.982239i	$0.560083\pi$
$788$	8.20672	+	8.20672i	0.292352	+	0.292352i
$789$			32.9410i			1.17273i
$790$	−16.7963	−	0.614151i	−0.597584	−	0.0218505i
$791$	−16.2065	−	16.2065i	−0.576237	−	0.576237i
$792$			0.771593i			0.0274174i
$793$	10.0561	−	10.0561i	0.357104	−	0.357104i
$794$	0.327150	+	0.327150i	0.0116101	+	0.0116101i
$795$	11.3008	+	12.1586i	0.400799	+	0.431222i
$796$	−0.480679	+	0.480679i	−0.0170372	+	0.0170372i
$797$			17.6688i			0.625862i	0.949776	+	0.312931i	$0.101311\pi$
$797$			17.6688i			0.625862i	−0.949776	+	0.312931i	$0.898689\pi$
$798$	−19.1652	−	19.1652i	−0.678442	−	0.678442i
$799$	9.79950	+	9.79950i	0.346681	+	0.346681i
$800$	4.98665	+	0.365159i	0.176305	+	0.0129103i
$801$	3.75680	+	3.75680i	0.132740	+	0.132740i
$802$	19.1836	−	19.1836i	0.677397	−	0.677397i
$803$	−11.5369	+	11.5369i	−0.407128	+	0.407128i
$804$	20.3660			0.718254
$805$	−1.60796	−	0.0587947i	−0.0566733	−	0.00207224i
$806$	4.84126	+	4.84126i	0.170526	+	0.170526i
$807$	−7.25356	+	7.25356i	−0.255337	+	0.255337i
$808$	11.7791			0.414388
$809$	−16.5367	+	16.5367i	−0.581399	+	0.581399i	−0.935288	−	0.353888i	$-0.884859\pi$
$809$	−16.5367	+	16.5367i	−0.581399	+	0.581399i	0.353888	+	0.935288i	$0.384859\pi$
$810$	−16.1571	+	15.0172i	−0.567702	+	0.527651i
$811$	40.9951			1.43953			0.719767	−	0.694216i	$-0.244249\pi$
$811$	40.9951			1.43953			0.719767	+	0.694216i	$0.244249\pi$
$812$	28.6365			1.00495
$813$	−27.4547	−	27.4547i	−0.962879	−	0.962879i
$814$	−13.8071	+	4.52243i	−0.483939	+	0.158511i
$815$	−2.76318	−	2.97292i	−0.0967901	−	0.104137i
$816$	−2.70170	−	2.70170i	−0.0945785	−	0.0945785i
$817$	−7.59011	+	7.59011i	−0.265544	+	0.265544i
$818$	9.30031	+	9.30031i	0.325178	+	0.325178i
$819$	−1.41061	−	1.41061i	−0.0492907	−	0.0492907i
$820$	−10.2033	+	9.48350i	−0.356316	+	0.331178i
$821$	−15.0113			−0.523897			−0.261948	−	0.965082i	$-0.584365\pi$
$821$	−15.0113			−0.523897			−0.261948	+	0.965082i	$0.584365\pi$
$822$	2.45628			0.0856727
$823$	34.4033	−	34.4033i	1.19922	−	1.19922i	0.224826	−	0.974399i	$-0.427819\pi$
$823$	34.4033	−	34.4033i	1.19922	−	1.19922i	0.974399	−	0.224826i	$-0.0721814\pi$
$824$		−	6.35592i		−	0.221419i
$825$	14.2287	+	16.4773i	0.495381	+	0.573665i
$826$	40.9188			1.42375
$827$	−2.14845			−0.0747090			−0.0373545	−	0.999302i	$-0.511893\pi$
$827$	−2.14845			−0.0747090			−0.0373545	+	0.999302i	$0.511893\pi$
$828$	0.0545055			0.00189420
$829$	−18.9396	+	18.9396i	−0.657800	+	0.657800i	−0.954859	−	0.297059i	$-0.903994\pi$
$829$	−18.9396	+	18.9396i	−0.657800	+	0.657800i	0.297059	+	0.954859i	$0.403994\pi$
$830$	−0.974453	+	26.6501i	−0.0338238	+	0.925039i
$831$	−32.0512	+	32.0512i	−1.11185	+	1.11185i
$832$			1.44800i			0.0502003i
$833$		−	23.4505i		−	0.812513i
$834$	−10.5601	+	10.5601i	−0.365665	+	0.365665i
$835$	24.7327	+	26.6100i	0.855911	+	0.920878i
$836$	−5.88817	+	5.88817i	−0.203647	+	0.203647i
$837$	−23.0736			−0.797541
$838$	−11.9651			−0.413327
$839$	−26.3122			−0.908399			−0.454200	−	0.890900i	$-0.650075\pi$
$839$	−26.3122			−0.908399			−0.454200	+	0.890900i	$0.650075\pi$
$840$	−11.8350	−	12.7333i	−0.408346	−	0.439341i
$841$		−	16.0865i		−	0.554705i
$842$	17.5941	−	17.5941i	0.606331	−	0.606331i
$843$	2.38550			0.0821609
$844$	24.5328			0.844453
$845$	−16.5982	−	17.8581i	−0.570995	−	0.614336i
$846$	−1.51034	−	1.51034i	−0.0519267	−	0.0519267i
$847$	−15.9676	−	15.9676i	−0.548653	−	0.548653i
$848$	−2.87955	+	2.87955i	−0.0988842	+	0.0988842i
$849$	−0.387457	−	0.387457i	−0.0132975	−	0.0132975i
$850$	−10.4519	−	0.765361i	−0.358496	−	0.0262517i
$851$	0.319466	+	0.975338i	0.0109511	+	0.0334342i
$852$	−16.3215	−	16.3215i	−0.559164	−	0.559164i
$853$	−29.3440			−1.00472			−0.502360	−	0.864658i	$-0.667535\pi$
$853$	−29.3440			−1.00472			−0.502360	+	0.864658i	$0.667535\pi$
$854$	−41.8867			−1.43333
$855$	2.51661	+	0.0920190i	0.0860662	+	0.00314698i
$856$	7.29845	−	7.29845i	0.249456	−	0.249456i
$857$	16.7643			0.572658			0.286329	−	0.958131i	$-0.407565\pi$
$857$	16.7643			0.572658			0.286329	+	0.958131i	$0.407565\pi$
$858$	−4.45812	+	4.45812i	−0.152198	+	0.152198i
$859$	22.7459	+	22.7459i	0.776081	+	0.776081i	0.979162	−	0.203081i	$-0.0650955\pi$
$859$	22.7459	+	22.7459i	0.776081	+	0.776081i	−0.203081	+	0.979162i	$0.565095\pi$
$860$	−5.04284	+	4.68707i	−0.171960	+	0.159828i
$861$	48.4319			1.65055
$862$	−9.36769	+	9.36769i	−0.319065	+	0.319065i
$863$	16.6468	−	16.6468i	0.566664	−	0.566664i	−0.364528	−	0.931192i	$-0.618770\pi$
$863$	16.6468	−	16.6468i	0.566664	−	0.566664i	0.931192	+	0.364528i	$0.118770\pi$
$864$	−3.45060	−	3.45060i	−0.117392	−	0.117392i
$865$	−1.38743	+	37.9445i	−0.0471740	+	1.29015i
$866$	−11.6303	−	11.6303i	−0.395214	−	0.395214i
$867$	−16.2503	−	16.2503i	−0.551890	−	0.551890i
$868$		−	20.1652i		−	0.684453i
$869$	12.6951	−	12.6951i	0.430650	−	0.430650i
$870$	−20.0478	+	18.6335i	−0.679685	+	0.631733i
$871$	11.4391	+	11.4391i	0.387598	+	0.387598i
$872$	−7.27809	+	7.27809i	−0.246467	+	0.246467i
$873$			1.62908i			0.0551360i
$874$	0.415942	+	0.415942i	0.0140694	+	0.0140694i
$875$	−47.3954	−	5.21761i	−1.60226	−	0.176387i
$876$			12.4520i			0.420714i
$877$	−26.6229	−	26.6229i	−0.898990	−	0.898990i	0.0963568	−	0.995347i	$-0.469281\pi$
$877$	−26.6229	−	26.6229i	−0.898990	−	0.898990i	−0.995347	+	0.0963568i	$0.969281\pi$
$878$	16.3753	+	16.3753i	0.552641	+	0.552641i
$879$	−57.8409			−1.95093
$880$	−3.91208	+	3.63609i	−0.131876	+	0.122572i
$881$		−	30.3341i		−	1.02198i	−0.859587	−	0.510990i	$-0.829279\pi$
$881$		−	30.3341i		−	1.02198i	0.859587	−	0.510990i	$-0.170721\pi$
$882$			3.61430i			0.121700i
$883$	31.6440			1.06491			0.532453	−	0.846459i	$-0.321270\pi$
$883$	31.6440			1.06491			0.532453	+	0.846459i	$0.321270\pi$
$884$		−	3.03496i		−	0.102077i
$885$	−28.6464	+	26.6254i	−0.962937	+	0.895002i
$886$	−18.4976	+	18.4976i	−0.621441	+	0.621441i
$887$	6.61467	−	6.61467i	0.222099	−	0.222099i	−0.587283	−	0.809382i	$-0.699802\pi$
$887$	6.61467	−	6.61467i	0.222099	−	0.222099i	0.809382	+	0.587283i	$0.199802\pi$
$888$	−5.01058	+	9.89174i	−0.168144	+	0.331945i
$889$			70.9408i			2.37928i
$890$	−1.34380	+	36.7512i	−0.0450442	+	1.23190i
$891$		−	23.5623i		−	0.789368i
$892$	−13.8026	+	13.8026i	−0.462144	+	0.462144i
$893$		−	23.0514i		−	0.771387i
$894$	−29.4823	−	29.4823i	−0.986036	−	0.986036i
$895$	26.7308	+	0.977404i	0.893512	+	0.0326710i
$896$	3.01566	−	3.01566i	0.100746	−	0.100746i
$897$	0.314923	+	0.314923i	0.0105150	+	0.0105150i
$898$	28.1954	−	28.1954i	0.940891	−	0.940891i
$899$	−31.7489			−1.05889
$900$	1.61089	+	0.117961i	0.0536963	+	0.00393203i
$901$	6.03545	−	6.03545i	0.201070	−	0.201070i
$902$		−	14.8798i		−	0.495444i
$903$	23.9367			0.796563
$904$			5.37412i			0.178741i
$905$	−1.46324	−	1.57431i	−0.0486398	−	0.0523318i
$906$	21.4619	+	21.4619i	0.713025	+	0.713025i
$907$	41.6369			1.38253			0.691265	−	0.722602i	$-0.257054\pi$
$907$	41.6369			1.38253			0.691265	+	0.722602i	$0.257054\pi$
$908$	−10.8328			−0.359498
$909$	3.80513			0.126208
$910$	0.504570	−	13.7994i	0.0167263	−	0.457445i
$911$	5.98425	−	5.98425i	0.198267	−	0.198267i	−0.600990	−	0.799257i	$-0.705227\pi$
$911$	5.98425	−	5.98425i	0.198267	−	0.198267i	0.799257	+	0.600990i	$0.205227\pi$
$912$			6.35524i			0.210443i
$913$	−20.1428	−	20.1428i	−0.666631	−	0.666631i
$914$		−	30.7275i		−	1.01638i
$915$	29.3240	−	27.2552i	0.969421	−	0.901029i
$916$			17.5884i			0.581136i
$917$		−	94.0518i		−	3.10586i
$918$	7.23235	+	7.23235i	0.238703	+	0.238703i
$919$	12.1528	−	12.1528i	0.400885	−	0.400885i	−0.477660	−	0.878545i	$-0.658515\pi$
$919$	12.1528	−	12.1528i	0.400885	−	0.400885i	0.878545	+	0.477660i	$0.158515\pi$
$920$	0.256854	+	0.276350i	0.00846823	+	0.00911101i
$921$	7.59798			0.250362
$922$	9.22827	+	9.22827i	0.303917	+	0.303917i
$923$		−	18.3347i		−	0.603494i
$924$	18.5694			0.610887
$925$	7.33084	+	29.5171i	0.241037	+	0.970516i
$926$	−13.6064			−0.447134
$927$		−	2.05322i		−	0.0674366i
$928$	−4.74797	−	4.74797i	−0.155860	−	0.155860i
$929$	11.0600			0.362867			0.181434	−	0.983403i	$-0.441926\pi$
$929$	11.0600			0.362867			0.181434	+	0.983403i	$0.441926\pi$
$930$	13.1213	+	14.1173i	0.430264	+	0.462923i
$931$	−27.5814	+	27.5814i	−0.903945	+	0.903945i
$932$	−1.47378	−	1.47378i	−0.0482753	−	0.0482753i
$933$		−	31.1586i		−	1.02009i
$934$			19.5369i			0.639267i
$935$	8.19960	−	7.62112i	0.268156	−	0.249237i
$936$			0.467761i			0.0152893i
$937$	15.6788	+	15.6788i	0.512205	+	0.512205i	0.915202	−	0.402997i	$-0.132031\pi$
$937$	15.6788	+	15.6788i	0.512205	+	0.512205i	−0.402997	+	0.915202i	$0.632031\pi$
$938$		−	47.6470i		−	1.55573i
$939$	2.58415	−	2.58415i	0.0843305	−	0.0843305i
$940$	0.540245	−	14.7750i	0.0176209	−	0.481909i
$941$	−18.6061			−0.606540			−0.303270	−	0.952905i	$-0.598078\pi$
$941$	−18.6061			−0.606540			−0.303270	+	0.952905i	$0.598078\pi$
$942$	26.0635			0.849196
$943$	−1.05111			−0.0342290
$944$	−6.78438	−	6.78438i	−0.220813	−	0.220813i
$945$	31.6818	+	34.0866i	1.03061	+	1.10884i
$946$		−	7.35412i		−	0.239103i
$947$	1.38953			0.0451536			0.0225768	−	0.999745i	$-0.492813\pi$
$947$	1.38953			0.0451536			0.0225768	+	0.999745i	$0.492813\pi$
$948$		−	13.7021i		−	0.445022i
$949$	−6.99398	+	6.99398i	−0.227034	+	0.227034i
$950$	11.3928	+	13.1932i	0.369632	+	0.428043i
$951$	18.7895			0.609291
$952$	−6.32073	+	6.32073i	−0.204856	+	0.204856i
$953$	24.4066	+	24.4066i	0.790606	+	0.790606i	0.981593	−	0.190987i	$-0.0611687\pi$
$953$	24.4066	+	24.4066i	0.790606	+	0.790606i	−0.190987	+	0.981593i	$0.561169\pi$
$954$	−0.930212	+	0.930212i	−0.0301167	+	0.0301167i
$955$	−1.12231	−	0.0410368i	−0.0363170	−	0.00132792i
$956$	−0.869275	−	0.869275i	−0.0281144	−	0.0281144i
$957$		−	29.2363i		−	0.945076i
$958$	25.1547	−	25.1547i	0.812712	−	0.812712i
$959$		−	5.74656i		−	0.185566i
$960$	−0.148945	+	4.07345i	−0.00480717	+	0.131470i
$961$		−	8.64307i		−	0.278809i
$962$	−8.37026	+	2.74162i	−0.269868	+	0.0883935i
$963$	2.35769	−	2.35769i	0.0759756	−	0.0759756i
$964$	−7.39427	+	7.39427i	−0.238153	+	0.238153i
$965$	12.0072	−	11.1601i	0.386527	−	0.359257i
$966$		−	1.31174i		−	0.0422047i
$967$	−32.8029			−1.05487			−0.527434	−	0.849596i	$-0.676846\pi$
$967$	−32.8029			−1.05487			−0.527434	+	0.849596i	$0.676846\pi$
$968$			5.29490i			0.170184i
$969$		−	13.3204i		−	0.427912i
$970$	−8.25966	+	7.67694i	−0.265202	+	0.246492i
$971$	19.3196			0.619995			0.309998	−	0.950737i	$-0.399672\pi$
$971$	19.3196			0.619995			0.309998	+	0.950737i	$0.399672\pi$
$972$	−2.36388	−	2.36388i	−0.0758215	−	0.0758215i
$973$	24.7056	+	24.7056i	0.792026	+	0.792026i
$974$		−	41.5088i		−	1.33003i
$975$	8.62586	+	9.98897i	0.276249	+	0.319903i
$976$	6.94487	+	6.94487i	0.222300	+	0.222300i
$977$		−	14.6717i		−	0.469391i	−0.972069	−	0.234695i	$-0.924591\pi$
$977$		−	14.6717i		−	0.469391i	0.972069	−	0.234695i	$-0.0754092\pi$
$978$	2.33970	−	2.33970i	0.0748154	−	0.0748154i
$979$	−27.7775	−	27.7775i	−0.887773	−	0.887773i
$980$	−18.3250	+	17.0322i	−0.585371	+	0.544073i
$981$	−2.35112	+	2.35112i	−0.0750653	+	0.0750653i
$982$			24.6515i			0.786659i
$983$	26.7565	+	26.7565i	0.853400	+	0.853400i	0.990550	−	0.137150i	$-0.0437942\pi$
$983$	26.7565	+	26.7565i	0.853400	+	0.853400i	−0.137150	+	0.990550i	$0.543794\pi$
$984$	−8.03006	−	8.03006i	−0.255989	−	0.255989i
$985$	−0.948291	+	25.9346i	−0.0302150	+	0.826345i
$986$	9.95160	+	9.95160i	0.316923	+	0.316923i
$987$	−36.3483	+	36.3483i	−1.15698	+	1.15698i
$988$	−3.56958	+	3.56958i	−0.113563	+	0.113563i
$989$	−0.519497			−0.0165190
$990$	−1.26376	+	1.17460i	−0.0401649	+	0.0373313i
$991$	−22.3239	−	22.3239i	−0.709143	−	0.709143i	0.257212	−	0.966355i	$-0.417196\pi$
$991$	−22.3239	−	22.3239i	−0.709143	−	0.709143i	−0.966355	+	0.257212i	$0.917196\pi$
$992$	−3.34342	+	3.34342i	−0.106154	+	0.106154i
$993$	−2.16393			−0.0686702
$994$	−38.1846	+	38.1846i	−1.21114	+	1.21114i
$995$	−1.51903	−	0.0555427i	−0.0481564	−	0.00176082i
$996$	−21.7406			−0.688878
$997$	−46.0799			−1.45936			−0.729682	−	0.683787i	$-0.760332\pi$
$997$	−46.0799			−1.45936			−0.729682	+	0.683787i	$0.760332\pi$
$998$	−16.8585	−	16.8585i	−0.533645	−	0.533645i
$999$	13.4131	−	26.4798i	0.424373	−	0.837784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.g.e.327.9	yes	20
5.3	odd	4		370.2.h.e.253.2	yes	20
37.6	odd	4		370.2.h.e.117.2	yes	20
185.43	even	4	inner	370.2.g.e.43.9	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.9	✓	20	185.43	even	4	inner
370.2.g.e.327.9	yes	20	1.1	even	1	trivial
370.2.h.e.117.2	yes	20	37.6	odd	4
370.2.h.e.253.2	yes	20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.28900 + 1.28900i) q^{3} -1.00000 q^{4} +(-1.52231 - 1.63786i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 - 3.01566i) q^{7} +1.00000i q^{8} +0.323040i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.28900 + 1.28900i) q^{3} -1.00000 q^{4} +(-1.52231 - 1.63786i) q^{5} +(1.28900 - 1.28900i) q^{6} +(-3.01566 - 3.01566i) q^{7} +1.00000i q^{8} +0.323040i q^{9} +(-1.63786 + 1.52231i) q^{10} -2.38854i q^{11} +(-1.28900 - 1.28900i) q^{12} -1.44800i q^{13} +(-3.01566 + 3.01566i) q^{14} +(0.148945 - 4.07345i) q^{15} +1.00000 q^{16} -2.09597 q^{17} +0.323040 q^{18} +(2.46518 + 2.46518i) q^{19} +(1.52231 + 1.63786i) q^{20} -7.77437i q^{21} -2.38854 q^{22} +0.168727i q^{23} +(-1.28900 + 1.28900i) q^{24} +(-0.365159 + 4.98665i) q^{25} -1.44800 q^{26} +(3.45060 - 3.45060i) q^{27} +(3.01566 + 3.01566i) q^{28} +(4.74797 - 4.74797i) q^{29} +(-4.07345 - 0.148945i) q^{30} +(-3.34342 - 3.34342i) q^{31} -1.00000i q^{32} +(3.07882 - 3.07882i) q^{33} +2.09597i q^{34} +(-0.348461 + 9.52998i) q^{35} -0.323040i q^{36} +(5.78058 - 1.89339i) q^{37} +(2.46518 - 2.46518i) q^{38} +(1.86647 - 1.86647i) q^{39} +(1.63786 - 1.52231i) q^{40} +6.22969i q^{41} -7.77437 q^{42} +3.07893i q^{43} +2.38854i q^{44} +(0.529094 - 0.491767i) q^{45} +0.168727 q^{46} +(-4.67540 - 4.67540i) q^{47} +(1.28900 + 1.28900i) q^{48} +11.1884i q^{49} +(4.98665 + 0.365159i) q^{50} +(-2.70170 - 2.70170i) q^{51} +1.44800i q^{52} +(-2.87955 + 2.87955i) q^{53} +(-3.45060 - 3.45060i) q^{54} +(-3.91208 + 3.63609i) q^{55} +(3.01566 - 3.01566i) q^{56} +6.35524i q^{57} +(-4.74797 - 4.74797i) q^{58} +(-6.78438 - 6.78438i) q^{59} +(-0.148945 + 4.07345i) q^{60} +(6.94487 + 6.94487i) q^{61} +(-3.34342 + 3.34342i) q^{62} +(0.974180 - 0.974180i) q^{63} -1.00000 q^{64} +(-2.37161 + 2.20430i) q^{65} +(-3.07882 - 3.07882i) q^{66} +(-7.89993 + 7.89993i) q^{67} +2.09597 q^{68} +(-0.217489 + 0.217489i) q^{69} +(9.52998 + 0.348461i) q^{70} +12.6621 q^{71} -0.323040 q^{72} +(-4.83010 - 4.83010i) q^{73} +(-1.89339 - 5.78058i) q^{74} +(-6.89848 + 5.95710i) q^{75} +(-2.46518 - 2.46518i) q^{76} +(-7.20301 + 7.20301i) q^{77} +(-1.86647 - 1.86647i) q^{78} +(5.31500 + 5.31500i) q^{79} +(-1.52231 - 1.63786i) q^{80} +9.86477 q^{81} +6.22969 q^{82} +(8.43313 - 8.43313i) q^{83} +7.77437i q^{84} +(3.19071 + 3.43290i) q^{85} +3.07893 q^{86} +12.2403 q^{87} +2.38854 q^{88} +(11.6295 - 11.6295i) q^{89} +(-0.491767 - 0.529094i) q^{90} +(-4.36667 + 4.36667i) q^{91} -0.168727i q^{92} -8.61934i q^{93} +(-4.67540 + 4.67540i) q^{94} +(0.284853 - 7.79038i) q^{95} +(1.28900 - 1.28900i) q^{96} +5.04296 q^{97} +11.1884 q^{98} +0.771593 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7}+O(q^{10}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7	\( 20 q - 4 q^{3} - 20 q^{4} + 2 q^{5} - 4 q^{6} - 2 q^{7} + 4 q^{10} + 4 q^{12} - 2 q^{14} + 20 q^{16} + 20 q^{17} + 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{22} + 4 q^{24} - 10 q^{25} + 20 q^{27} + 2 q^{28} - 18 q^{29} - 4 q^{30} + 12 q^{31} + 4 q^{33} + 12 q^{35} - 6 q^{38} - 6 q^{39} - 4 q^{40} - 12 q^{42} - 18 q^{45} + 4 q^{46} - 22 q^{47} - 4 q^{48} + 4 q^{50} + 8 q^{51} - 4 q^{53} - 20 q^{54} - 34 q^{55} + 2 q^{56} + 18 q^{58} + 10 q^{59} + 10 q^{61} + 12 q^{62} - 2 q^{63} - 20 q^{64} - 20 q^{65} - 4 q^{66} - 8 q^{67} - 20 q^{68} + 34 q^{69} + 12 q^{70} + 16 q^{71} - 24 q^{72} + 6 q^{73} - 32 q^{74} - 26 q^{75} + 6 q^{76} + 4 q^{77} + 6 q^{78} - 12 q^{79} + 2 q^{80} - 28 q^{81} + 20 q^{82} + 6 q^{83} - 10 q^{85} - 16 q^{86} + 44 q^{87} + 8 q^{88} + 44 q^{89} - 22 q^{90} - 40 q^{91} - 22 q^{94} - 50 q^{95} - 4 q^{96} - 72 q^{97} + 52 q^{98} + 20 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 20 * q^4 + 2 * q^5 - 4 * q^6 - 2 * q^7 + 4 * q^10 + 4 * q^12 - 2 * q^14 + 20 * q^16 + 20 * q^17 + 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^22 + 4 * q^24 - 10 * q^25 + 20 * q^27 + 2 * q^28 - 18 * q^29 - 4 * q^30 + 12 * q^31 + 4 * q^33 + 12 * q^35 - 6 * q^38 - 6 * q^39 - 4 * q^40 - 12 * q^42 - 18 * q^45 + 4 * q^46 - 22 * q^47 - 4 * q^48 + 4 * q^50 + 8 * q^51 - 4 * q^53 - 20 * q^54 - 34 * q^55 + 2 * q^56 + 18 * q^58 + 10 * q^59 + 10 * q^61 + 12 * q^62 - 2 * q^63 - 20 * q^64 - 20 * q^65 - 4 * q^66 - 8 * q^67 - 20 * q^68 + 34 * q^69 + 12 * q^70 + 16 * q^71 - 24 * q^72 + 6 * q^73 - 32 * q^74 - 26 * q^75 + 6 * q^76 + 4 * q^77 + 6 * q^78 - 12 * q^79 + 2 * q^80 - 28 * q^81 + 20 * q^82 + 6 * q^83 - 10 * q^85 - 16 * q^86 + 44 * q^87 + 8 * q^88 + 44 * q^89 - 22 * q^90 - 40 * q^91 - 22 * q^94 - 50 * q^95 - 4 * q^96 - 72 * q^97 + 52 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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