LMFDB - Embedded newform 370.2.h.e.253.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(117,370)]

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([1, 3]))

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

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

chi := DirichletCharacter("370.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.h (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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			253.2
Root			$-1.28900 - 1.28900i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	−1.28900	+	1.28900i	−0.744204	+	0.744204i	−0.973384	−	0.229180i	$-0.926396\pi$
$3$	−1.28900	+	1.28900i	−0.744204	+	0.744204i	0.229180	+	0.973384i	$0.426396\pi$
$4$	1.00000			0.500000
$5$	1.63786	+	1.52231i	0.732472	+	0.680797i
$5$	1.63786	+	1.52231i	0.732472	+	0.680797i
$6$	1.28900	−	1.28900i	0.526232	−	0.526232i
$7$	−3.01566	+	3.01566i	−1.13981	+	1.13981i	−0.151328	+	0.988484i	$0.548355\pi$
$7$	−3.01566	+	3.01566i	−1.13981	+	1.13981i	−0.988484	+	0.151328i	$0.951645\pi$
$8$	−1.00000			−0.353553
$9$		−	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
$13$	1.44800			0.401602			0.200801	−	0.979632i	$-0.435646\pi$
$13$	1.44800			0.401602			0.200801	+	0.979632i	$0.435646\pi$
$14$	3.01566	−	3.01566i	0.805969	−	0.805969i
$15$	−4.07345	+	0.148945i	−1.05176	+	0.0384573i
$16$	1.00000			0.250000
$17$			2.09597i			0.508347i	0.967159	+	0.254173i	$0.0818034\pi$
$17$			2.09597i			0.508347i	−0.967159	+	0.254173i	$0.918197\pi$
$18$			0.323040i			0.0761413i
$19$	−2.46518	−	2.46518i	−0.565551	−	0.565551i	0.365328	−	0.930879i	$-0.380957\pi$
$19$	−2.46518	−	2.46518i	−0.565551	−	0.565551i	−0.930879	+	0.365328i	$0.880957\pi$
$20$	1.63786	+	1.52231i	0.366236	+	0.340398i
$21$		−	7.77437i		−	1.69651i
$22$			2.38854i			0.509238i
$23$	−0.168727			−0.0351820			−0.0175910	−	0.999845i	$-0.505600\pi$
$23$	−0.168727			−0.0351820			−0.0175910	+	0.999845i	$0.505600\pi$
$24$	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	−0.993705	−	0.112029i	$-0.964265\pi$
$29$	−4.74797	+	4.74797i	−0.881676	+	0.881676i	0.112029	+	0.993705i	$0.464265\pi$
$30$	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	$0.889590\pi$
$32$	−1.00000			−0.176777
$33$	3.07882	+	3.07882i	0.535954	+	0.535954i
$34$		−	2.09597i		−	0.359456i
$35$	−9.52998	+	0.348461i	−1.61086	+	0.0589007i
$36$		−	0.323040i		−	0.0538401i
$37$	−1.89339	−	5.78058i	−0.311271	−	0.950321i
$37$	−1.89339	−	5.78058i	−0.311271	−	0.950321i
$38$	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	$0.838289\pi$
$42$			7.77437i			1.19961i
$43$	−3.07893			−0.469532			−0.234766	−	0.972052i	$-0.575432\pi$
$43$	−3.07893			−0.469532			−0.234766	+	0.972052i	$0.575432\pi$
$44$		−	2.38854i		−	0.360085i
$45$	0.491767	−	0.529094i	0.0733083	−	0.0788727i
$46$	0.168727			0.0248774
$47$	−4.67540	+	4.67540i	−0.681978	+	0.681978i	−0.960446	−	0.278468i	$-0.910173\pi$
$47$	−4.67540	+	4.67540i	−0.681978	+	0.681978i	0.278468	+	0.960446i	$0.410173\pi$
$48$	−1.28900	+	1.28900i	−0.186051	+	0.186051i
$49$		−	11.1884i		−	1.59834i
$50$	−0.365159	−	4.98665i	−0.0516413	−	0.705219i
$51$	−2.70170	−	2.70170i	−0.378314	−	0.378314i
$52$	1.44800			0.200801
$53$	−2.87955	−	2.87955i	−0.395537	−	0.395537i	0.481119	−	0.876656i	$-0.340231\pi$
$53$	−2.87955	−	2.87955i	−0.395537	−	0.395537i	−0.876656	+	0.481119i	$0.840231\pi$
$54$	3.45060	+	3.45060i	0.469567	+	0.469567i
$55$	3.63609	−	3.91208i	0.490290	−	0.527505i
$56$	3.01566	−	3.01566i	0.402984	−	0.402984i
$57$	6.35524			0.841772
$58$	4.74797	−	4.74797i	0.623439	−	0.623439i
$59$	6.78438	+	6.78438i	0.883251	+	0.883251i	0.993864	−	0.110612i	$-0.0352812\pi$
$59$	6.78438	+	6.78438i	0.883251	+	0.883251i	−0.110612	+	0.993864i	$0.535281\pi$
$60$	−4.07345	+	0.148945i	−0.525880	+	0.0192287i
$61$	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	$-0.0109144\pi$
$67$	7.89993	+	7.89993i	0.965130	+	0.965130i	−0.0342818	+	0.999412i	$0.510914\pi$
$68$			2.09597i			0.254173i
$69$	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	$0.229399\pi$
$72$			0.323040i			0.0380707i
$73$	4.83010	−	4.83010i	0.565321	−	0.565321i	−0.365493	−	0.930814i	$-0.619100\pi$
$73$	4.83010	−	4.83010i	0.565321	−	0.565321i	0.930814	+	0.365493i	$0.119100\pi$
$74$	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	0.341792	−	0.939776i	$-0.388966\pi$
$79$	−5.31500	−	5.31500i	−0.597984	−	0.597984i	−0.939776	+	0.341792i	$0.888966\pi$
$80$	1.63786	+	1.52231i	0.183118	+	0.170199i
$81$	9.86477			1.09609
$82$		−	6.22969i		−	0.687954i
$83$	8.43313	+	8.43313i	0.925657	+	0.925657i	0.997422	−	0.0717648i	$-0.0228631\pi$
$83$	8.43313	+	8.43313i	0.925657	+	0.925657i	−0.0717648	+	0.997422i	$0.522863\pi$
$84$		−	7.77437i		−	0.848253i
$85$	−3.19071	+	3.43290i	−0.346081	+	0.372350i
$86$	3.07893			0.332009
$87$		−	12.2403i		−	1.31229i
$88$			2.38854i			0.254619i
$89$	−11.6295	+	11.6295i	−1.23273	+	1.23273i	−0.269814	+	0.962912i	$0.586962\pi$
$89$	−11.6295	+	11.6295i	−1.23273	+	1.23273i	−0.962912	+	0.269814i	$0.913038\pi$
$90$	−0.491767	+	0.529094i	−0.0518368	+	0.0557714i
$91$	−4.36667	+	4.36667i	−0.457751	+	0.457751i
$92$	−0.168727			−0.0175910
$93$	8.61934			0.893784
$94$	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
$97$		−	5.04296i		−	0.512035i	−0.966672	−	0.256018i	$-0.917589\pi$
$97$		−	5.04296i		−	0.512035i	0.966672	−	0.256018i	$-0.0824105\pi$
$98$			11.1884i			1.13020i
$99$	−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
$103$		−	6.35592i		−	0.626267i	−0.949709	−	0.313134i	$-0.898621\pi$
$103$		−	6.35592i		−	0.626267i	0.949709	−	0.313134i	$-0.101379\pi$
$104$	−1.44800			−0.141988
$105$	11.8350	−	12.7333i	1.15498	−	1.24264i
$106$	2.87955	+	2.87955i	0.279687	+	0.279687i
$107$	−7.29845	+	7.29845i	−0.705568	+	0.705568i	−0.965600	−	0.260032i	$-0.916267\pi$
$107$	−7.29845	+	7.29845i	−0.705568	+	0.705568i	0.260032	+	0.965600i	$0.416267\pi$
$108$	−3.45060	−	3.45060i	−0.332034	−	0.332034i
$109$	−7.27809	−	7.27809i	−0.697114	−	0.697114i	0.266673	−	0.963787i	$-0.414076\pi$
$109$	−7.27809	−	7.27809i	−0.697114	−	0.697114i	−0.963787	+	0.266673i	$0.914076\pi$
$110$	−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
$113$			5.37412i			0.505555i	0.967524	+	0.252777i	$0.0813440\pi$
$113$			5.37412i			0.505555i	−0.967524	+	0.252777i	$0.918656\pi$
$114$	−6.35524			−0.595222
$115$	−0.276350	−	0.256854i	−0.0257698	−	0.0239518i
$116$	−4.74797	+	4.74797i	−0.440838	+	0.440838i
$117$		−	0.467761i		−	0.0432446i
$118$	−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
$125$	−6.99313	+	8.72331i	−0.625485	+	0.780236i
$126$	−0.974180	−	0.974180i	−0.0867868	−	0.0867868i
$127$	−11.7621	+	11.7621i	−1.04371	+	1.04371i	−0.0447148	+	0.999000i	$0.514238\pi$
$127$	−11.7621	+	11.7621i	−1.04371	+	1.04371i	−0.999000	+	0.0447148i	$0.985762\pi$
$128$	−1.00000			−0.0883883
$129$	3.96873	−	3.96873i	0.349428	−	0.349428i
$130$	−2.37161	−	2.20430i	−0.208004	−	0.193330i
$131$	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
$133$	14.8683			1.28924
$134$	−7.89993	−	7.89993i	−0.682450	−	0.682450i
$135$	−0.398719	−	10.9045i	−0.0343162	−	0.938507i
$136$		−	2.09597i		−	0.179728i
$137$	0.952787	−	0.952787i	0.0814020	−	0.0814020i	−0.665233	−	0.746635i	$-0.731668\pi$
$137$	0.952787	−	0.952787i	0.0814020	−	0.0814020i	0.746635	+	0.665233i	$0.231668\pi$
$138$	−0.217489	+	0.217489i	−0.0185139	+	0.0185139i
$139$	8.19245			0.694874			0.347437	−	0.937703i	$-0.387052\pi$
$139$	8.19245			0.694874			0.347437	+	0.937703i	$0.387052\pi$
$140$	−9.52998	+	0.348461i	−0.805431	+	0.0294503i
$141$		−	12.0532i		−	1.01506i
$142$	−12.6621			−1.06258
$143$		−	3.45859i		−	0.289222i
$144$		−	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
$148$	−1.89339	−	5.78058i	−0.155636	−	0.475161i
$149$			22.8722i			1.87377i	0.349641	+	0.936884i	$0.386303\pi$
$149$			22.8722i			1.87377i	−0.349641	+	0.936884i	$0.613697\pi$
$150$	6.89848	+	5.95710i	0.563258	+	0.486395i
$151$			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
$153$	0.677082			0.0547389
$154$	−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	−0.177293	−	0.984158i	$-0.556734\pi$
$157$	10.1100	−	10.1100i	0.806865	−	0.806865i	0.984158	+	0.177293i	$0.0567341\pi$
$158$	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
$162$	−9.86477			−0.775049
$163$			1.81513i			0.142172i	0.997470	+	0.0710859i	$0.0226465\pi$
$163$			1.81513i			0.142172i	−0.997470	+	0.0710859i	$0.977354\pi$
$164$			6.22969i			0.486457i
$165$	0.355759	+	9.72959i	0.0276958	+	0.757447i
$166$	−8.43313	−	8.43313i	−0.654538	−	0.654538i
$167$			16.2469i			1.25722i	0.777721	+	0.628610i	$0.216376\pi$
$167$			16.2469i			1.25722i	−0.777721	+	0.628610i	$0.783624\pi$
$168$			7.77437i			0.599805i
$169$	−10.9033			−0.838716
$170$	3.19071	−	3.43290i	0.244716	−	0.263291i
$171$	−0.796353	+	0.796353i	−0.0608986	+	0.0608986i
$172$	−3.07893			−0.234766
$173$	12.0071	−	12.0071i	0.912885	−	0.912885i	−0.0836133	−	0.996498i	$-0.526646\pi$
$173$	12.0071	−	12.0071i	0.912885	−	0.912885i	0.996498	+	0.0836133i	$0.0266461\pi$
$174$			12.2403i			0.927932i
$175$	−16.1392	−	13.9368i	−1.22001	−	1.05353i
$176$		−	2.38854i		−	0.180043i
$177$	−17.4901			−1.31464
$178$	11.6295	−	11.6295i	0.871669	−	0.871669i
$179$	8.45867	−	8.45867i	0.632231	−	0.632231i	−0.316396	−	0.948627i	$-0.602473\pi$
$179$	8.45867	−	8.45867i	0.632231	−	0.632231i	0.948627	+	0.316396i	$0.102473\pi$
$180$	0.491767	−	0.529094i	0.0366541	−	0.0394364i
$181$	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
$183$	−17.9039			−1.32349
$184$	0.168727			0.0124387
$185$	5.69871	−	12.3501i	0.418978	−	0.907997i
$186$	−8.61934			−0.632000
$187$	5.00630			0.366097
$188$	−4.67540	+	4.67540i	−0.340989	+	0.340989i
$189$	20.8117			1.51383
$190$	0.284853	+	7.79038i	0.0206654	+	0.565174i
$191$	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
$193$	−7.33106			−0.527701			−0.263851	−	0.964564i	$-0.584993\pi$
$193$	−7.33106			−0.527701			−0.263851	+	0.964564i	$0.584993\pi$
$194$			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	−0.936192	−	0.351488i	$-0.885676\pi$
$197$	−8.20672	+	8.20672i	−0.584704	+	0.584704i	0.351488	+	0.936192i	$0.385676\pi$
$198$	0.771593			0.0548348
$199$	−0.480679	+	0.480679i	−0.0340744	+	0.0340744i	−0.723939	−	0.689864i	$-0.757670\pi$
$199$	−0.480679	+	0.480679i	−0.0340744	+	0.0340744i	0.689864	+	0.723939i	$0.257670\pi$
$200$	−0.365159	−	4.98665i	−0.0258206	−	0.352609i
$201$	−20.3660			−1.43651
$202$			11.7791i			0.828776i
$203$		−	28.6365i		−	2.00989i
$204$	−2.70170	−	2.70170i	−0.189157	−	0.189157i
$205$	−9.48350	+	10.2033i	−0.662356	+	0.712632i
$206$			6.35592i			0.442838i
$207$			0.0545055i			0.00378840i
$208$	1.44800			0.100401
$209$	−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
$217$	20.1652			1.36891
$218$	7.27809	+	7.27809i	0.492934	+	0.492934i
$219$			12.4520i			0.841429i
$220$	3.63609	−	3.91208i	0.245145	−	0.263753i
$221$			3.03496i			0.204153i
$222$	−9.89174	−	5.01058i	−0.663890	−	0.336288i
$223$	13.8026	+	13.8026i	0.924289	+	0.924289i	0.997329	−	0.0730404i	$-0.0232702\pi$
$223$	13.8026	+	13.8026i	0.924289	+	0.924289i	−0.0730404	+	0.997329i	$0.523270\pi$
$224$	3.01566	−	3.01566i	0.201492	−	0.201492i
$225$	1.61089	−	0.117961i	0.107393	−	0.00786407i
$226$		−	5.37412i		−	0.357481i
$227$		−	10.8328i		−	0.718995i	−0.933146	−	0.359498i	$-0.882948\pi$
$227$		−	10.8328i		−	0.718995i	0.933146	−	0.359498i	$-0.117052\pi$
$228$	6.35524			0.420886
$229$			17.5884i			1.16227i	0.813806	+	0.581136i	$0.197392\pi$
$229$			17.5884i			1.16227i	−0.813806	+	0.581136i	$0.802608\pi$
$230$	0.276350	+	0.256854i	0.0182220	+	0.0169365i
$231$	−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	$-0.771748\pi$
$233$	−1.47378	+	1.47378i	−0.0965505	+	0.0965505i	0.657182	+	0.753732i	$0.271748\pi$
$234$			0.467761i			0.0305785i
$235$	−14.7750	+	0.540245i	−0.963818	+	0.0352417i
$236$	6.78438	+	6.78438i	0.441626	+	0.441626i
$237$	13.7021			0.890044
$238$	6.32073	+	6.32073i	0.409712	+	0.409712i
$239$	−0.869275	−	0.869275i	−0.0562288	−	0.0562288i	0.678433	−	0.734662i	$-0.262659\pi$
$239$	−0.869275	−	0.869275i	−0.0562288	−	0.0562288i	−0.734662	+	0.678433i	$0.762659\pi$
$240$	−4.07345	+	0.148945i	−0.262940	+	0.00961433i
$241$	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	$0.140655\pi$
$242$	−5.29490			−0.340369
$243$	−2.36388	+	2.36388i	−0.151643	+	0.151643i
$244$	6.94487	+	6.94487i	0.444599	+	0.444599i
$245$	17.0322	−	18.3250i	1.08815	−	1.17074i
$246$	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
$253$			0.403010i			0.0253370i
$254$	11.7621	−	11.7621i	0.738018	−	0.738018i
$255$	−0.312183	−	8.53783i	−0.0195497	−	0.534660i
$256$	1.00000			0.0625000
$257$		−	23.1629i		−	1.44486i	−0.691443	−	0.722431i	$-0.743025\pi$
$257$		−	23.1629i		−	1.44486i	0.691443	−	0.722431i	$-0.256975\pi$
$258$	−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	$-0.938100\pi$
$263$	−12.7777	+	12.7777i	−0.787909	+	0.787909i	0.193242	+	0.981151i	$0.438100\pi$
$264$	−3.07882	−	3.07882i	−0.189488	−	0.189488i
$265$	−0.332734	−	9.09986i	−0.0204397	−	0.559000i
$266$	−14.8683			−0.911634
$267$		−	29.9809i		−	1.83480i
$268$	7.89993	+	7.89993i	0.482565	+	0.482565i
$269$		−	5.62728i		−	0.343101i	−0.985175	−	0.171551i	$-0.945122\pi$
$269$		−	5.62728i		−	0.343101i	0.985175	−	0.171551i	$-0.0548777\pi$
$270$	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	$0.723943\pi$
$272$			2.09597i			0.127087i
$273$		−	11.2573i		−	0.681320i
$274$	−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
$277$	24.8652			1.49401			0.747003	−	0.664821i	$-0.231492\pi$
$277$	24.8652			1.49401			0.747003	+	0.664821i	$0.231492\pi$
$278$	−8.19245			−0.491350
$279$	−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	$0.237572\pi$
$282$			12.0532i			0.717757i
$283$		−	0.300587i		−	0.0178681i	−0.999960	−	0.00893403i	$-0.997156\pi$
$283$		−	0.300587i		−	0.0178681i	0.999960	−	0.00893403i	$-0.00284383\pi$
$284$	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
$288$			0.323040i			0.0190353i
$289$	12.6069			0.741583
$290$	15.0044	−	0.548631i	0.881087	−	0.0322167i
$291$	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	−0.920865	−	0.389881i	$-0.872516\pi$
$293$	−22.4364	−	22.4364i	−1.31075	−	1.31075i	−0.389881	−	0.920865i	$-0.627484\pi$
$294$	−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
$298$		−	22.8722i		−	1.32495i
$299$	−0.244316			−0.0141291
$300$	−6.89848	−	5.95710i	−0.398284	−	0.343933i
$301$	9.28499	−	9.28499i	0.535178	−	0.535178i
$302$		−	16.6501i		−	0.958104i
$303$	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	$-0.287950\pi$
$307$	−2.94724	−	2.94724i	−0.168208	−	0.168208i	−0.786191	+	0.617983i	$0.787950\pi$
$308$	7.20301	+	7.20301i	0.410430	+	0.410430i
$309$	8.19278	+	8.19278i	0.466071	+	0.466071i
$310$	0.386334	+	10.5658i	0.0219423	+	0.600095i
$311$	−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
$313$	2.00477			0.113316			0.0566582	−	0.998394i	$-0.481955\pi$
$313$	2.00477			0.113316			0.0566582	+	0.998394i	$0.481955\pi$
$314$	−10.1100	+	10.1100i	−0.570540	+	0.570540i
$315$	0.112567	+	3.07857i	0.00634243	+	0.173458i
$316$	−5.31500	−	5.31500i	−0.298992	−	0.298992i
$317$	−7.28840	−	7.28840i	−0.409357	−	0.409357i	0.472157	−	0.881514i	$-0.343475\pi$
$317$	−7.28840	−	7.28840i	−0.409357	−	0.409357i	−0.881514	+	0.472157i	$0.843475\pi$
$318$	−7.42348			−0.416288
$319$	11.3407	+	11.3407i	0.634957	+	0.634957i
$320$	1.63786	+	1.52231i	0.0915591	+	0.0850996i
$321$		−	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
$325$	0.528749	+	7.22065i	0.0293297	+	0.400530i
$326$		−	1.81513i		−	0.100531i
$327$	18.7629			1.03759
$328$		−	6.22969i		−	0.343977i
$329$		−	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
$333$	−1.86736	+	0.611642i	−0.102331	+	0.0335178i
$334$		−	16.2469i		−	0.888988i
$335$	0.912841	+	24.9651i	0.0498739	+	1.36399i
$336$		−	7.77437i		−	0.424127i
$337$	7.69155	+	7.69155i	0.418986	+	0.418986i	0.884854	−	0.465868i	$-0.154258\pi$
$337$	7.69155	+	7.69155i	0.418986	+	0.418986i	−0.465868	+	0.884854i	$0.654258\pi$
$338$	10.9033			0.593062
$339$	−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
$347$	21.8436			1.17263			0.586313	−	0.810085i	$-0.300579\pi$
$347$	21.8436			1.17263			0.586313	+	0.810085i	$0.300579\pi$
$348$		−	12.2403i		−	0.656147i
$349$		−	4.00432i		−	0.214346i	−0.994240	−	0.107173i	$-0.965820\pi$
$349$		−	4.00432i		−	0.214346i	0.994240	−	0.107173i	$-0.0341799\pi$
$350$	16.1392	+	13.9368i	0.862678	+	0.744955i
$351$	−4.99646	−	4.99646i	−0.266691	−	0.266691i
$352$			2.38854i			0.127309i
$353$		−	11.1747i		−	0.594769i	−0.954758	−	0.297384i	$-0.903886\pi$
$353$		−	11.1747i		−	0.594769i	0.954758	−	0.297384i	$-0.0961143\pi$
$354$	17.4901			0.929590
$355$	20.7387	+	19.2756i	1.10070	+	1.02304i
$356$	−11.6295	+	11.6295i	−0.616363	+	0.616363i
$357$	16.2948			0.862414
$358$	−8.45867	+	8.45867i	−0.447055	+	0.447055i
$359$			19.4341i			1.02570i	0.858480	+	0.512848i	$0.171409\pi$
$359$			19.4341i			1.02570i	−0.858480	+	0.512848i	$0.828591\pi$
$360$	−0.491767	+	0.529094i	−0.0259184	+	0.0278857i
$361$		−	6.84576i		−	0.360303i
$362$	−0.961200			−0.0505196
$363$	−6.82512	+	6.82512i	−0.358226	+	0.358226i
$364$	−4.36667	+	4.36667i	−0.228875	+	0.228875i
$365$	15.2639	−	0.558121i	0.798951	−	0.0292134i
$366$	17.9039			0.935850
$367$	10.2957	−	10.2957i	0.537430	−	0.537430i	−0.385343	−	0.922773i	$-0.625917\pi$
$367$	10.2957	−	10.2957i	0.537430	−	0.537430i	0.922773	+	0.385343i	$0.125917\pi$
$368$	−0.168727			−0.00879549
$369$	2.01244			0.104763
$370$	−5.69871	+	12.3501i	−0.296262	+	0.642051i
$371$	17.3675			0.901675
$372$	8.61934			0.446892
$373$	−23.2626	+	23.2626i	−1.20449	+	1.20449i	−0.231704	+	0.972786i	$0.574430\pi$
$373$	−23.2626	+	23.2626i	−1.20449	+	1.20449i	−0.972786	+	0.231704i	$0.925570\pi$
$374$	−5.00630			−0.258869
$375$	−2.23019	−	20.2585i	−0.115167	−	1.04614i
$376$	4.67540	−	4.67540i	0.241115	−	0.241115i
$377$	−6.87505	+	6.87505i	−0.354083	+	0.354083i
$378$	−20.8117			−1.07044
$379$		−	11.6263i		−	0.597203i	−0.954378	−	0.298602i	$-0.903480\pi$
$379$		−	11.6263i		−	0.597203i	0.954378	−	0.298602i	$-0.0965202\pi$
$380$	−0.284853	−	7.79038i	−0.0146127	−	0.399638i
$381$		−	30.3226i		−	1.55347i
$382$	−0.355141	+	0.355141i	−0.0181706	+	0.0181706i
$383$	8.97694			0.458700			0.229350	−	0.973344i	$-0.426340\pi$
$383$	8.97694			0.458700			0.229350	+	0.973344i	$0.426340\pi$
$384$	1.28900	−	1.28900i	0.0657790	−	0.0657790i
$385$	0.832312	+	22.7627i	0.0424185	+	1.16009i
$386$	7.33106			0.373141
$387$			0.994617i			0.0505592i
$388$		−	5.04296i		−	0.256018i
$389$	14.6826	+	14.6826i	0.744440	+	0.744440i	0.973429	−	0.228989i	$-0.0735420\pi$
$389$	14.6826	+	14.6826i	0.744440	+	0.744440i	−0.228989	+	0.973429i	$0.573542\pi$
$390$	5.89835	−	0.215671i	0.298674	−	0.0109209i
$391$		−	0.353646i		−	0.0178846i
$392$			11.1884i			0.565100i
$393$	−40.2011			−2.02788
$394$	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	$-0.246304\pi$
$397$	0.327150	+	0.327150i	0.0164192	+	0.0164192i	−0.698850	+	0.715269i	$0.746304\pi$
$398$	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	$0.513108\pi$
$402$	20.3660			1.01576
$403$	−4.84126	−	4.84126i	−0.241161	−	0.241161i
$404$		−	11.7791i		−	0.586033i
$405$	16.1571	+	15.0172i	0.802852	+	0.746211i
$406$			28.6365i			1.42121i
$407$	−13.8071	+	4.52243i	−0.684393	+	0.224169i
$408$	2.70170	+	2.70170i	0.133754	+	0.133754i
$409$	9.30031	−	9.30031i	0.459871	−	0.459871i	−0.438742	−	0.898613i	$-0.644576\pi$
$409$	9.30031	−	9.30031i	0.459871	−	0.459871i	0.898613	+	0.438742i	$0.144576\pi$
$410$	9.48350	−	10.2033i	0.468357	−	0.503907i
$411$			2.45628i			0.121160i
$412$		−	6.35592i		−	0.313134i
$413$	−40.9188			−2.01348
$414$		−	0.0545055i		−	0.00267880i
$415$	0.974453	+	26.6501i	0.0478340	+	1.30820i
$416$	−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	$0.0944093\pi$
$419$			11.9651i			0.584532i	−0.956337	+	0.292266i	$0.905591\pi$
$420$	11.8350	−	12.7333i	0.577488	−	0.621322i
$421$	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	$0.542641\pi$
$422$	24.5328			1.19424
$423$	1.51034	+	1.51034i	0.0734354	+	0.0734354i
$424$	2.87955	+	2.87955i	0.139843	+	0.139843i
$425$	−10.4519	+	0.765361i	−0.506990	+	0.0371255i
$426$	16.3215	−	16.3215i	0.790777	−	0.790777i
$427$	−41.8867			−2.02704
$428$	−7.29845	+	7.29845i	−0.352784	+	0.352784i
$429$	4.45812	+	4.45812i	0.215240	+	0.215240i
$430$	5.04284	+	4.68707i	0.243187	+	0.226031i
$431$	−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	0.928999	−	0.370083i	$-0.120671\pi$
$433$	11.6303	+	11.6303i	0.558916	+	0.558916i	−0.370083	+	0.928999i	$0.620671\pi$
$434$	−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
$438$		−	12.4520i		−	0.594980i
$439$	16.3753	−	16.3753i	0.781552	−	0.781552i	−0.198540	−	0.980093i	$-0.563620\pi$
$439$	16.3753	−	16.3753i	0.781552	−	0.781552i	0.980093	+	0.198540i	$0.0636201\pi$
$440$	−3.63609	+	3.91208i	−0.173344	+	0.186501i
$441$	−3.61430			−0.172110
$442$		−	3.03496i		−	0.144358i
$443$	18.4976	−	18.4976i	0.878850	−	0.878850i	−0.114566	−	0.993416i	$-0.536548\pi$
$443$	18.4976	−	18.4976i	0.878850	−	0.878850i	0.993416	+	0.114566i	$0.0365477\pi$
$444$	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	$-0.859990\pi$
$449$	−28.1954	−	28.1954i	−1.33062	−	1.33062i	−0.425808	−	0.904814i	$-0.640010\pi$
$450$	−1.61089	+	0.117961i	−0.0759380	+	0.00556074i
$451$	14.8798			0.700664
$452$			5.37412i			0.252777i
$453$	−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
$457$		−	30.7275i		−	1.43737i	−0.695334	−	0.718687i	$-0.744744\pi$
$457$		−	30.7275i		−	1.43737i	0.695334	−	0.718687i	$-0.255256\pi$
$458$		−	17.5884i		−	0.821851i
$459$	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	$0.348295\pi$
$462$	18.5694			0.863925
$463$	13.6064			0.632343			0.316172	−	0.948702i	$-0.397602\pi$
$463$	13.6064			0.632343			0.316172	+	0.948702i	$0.397602\pi$
$464$	−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
$467$			19.5369i			0.904059i	0.892003	+	0.452030i	$0.149300\pi$
$467$			19.5369i			0.904059i	−0.892003	+	0.452030i	$0.850700\pi$
$468$		−	0.467761i		−	0.0216223i
$469$	−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
$473$			7.35412i			0.338143i
$474$	−13.7021			−0.629356
$475$	11.3928	−	13.1932i	0.522738	−	0.605344i
$476$	−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	$-0.947990\pi$
$479$	−25.1547	−	25.1547i	−1.14935	−	1.14935i	−0.162667	−	0.986681i	$-0.552010\pi$
$480$	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
$483$			1.31174i			0.0596864i
$484$	5.29490			0.240677
$485$	7.67694	−	8.25966i	0.348592	−	0.375052i
$486$	2.36388	−	2.36388i	0.107228	−	0.107228i
$487$		−	41.5088i		−	1.88094i	−0.339873	−	0.940471i	$-0.610384\pi$
$487$		−	41.5088i		−	1.88094i	0.339873	−	0.940471i	$-0.389616\pi$
$488$	−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
$495$	−1.26376	−	1.17460i	−0.0568018	−	0.0527945i
$496$	−3.34342	−	3.34342i	−0.150124	−	0.150124i
$497$	−38.1846	+	38.1846i	−1.71281	+	1.71281i
$498$	21.7406			0.974220
$499$	−16.8585	+	16.8585i	−0.754689	+	0.754689i	−0.975350	−	0.220662i	$-0.929178\pi$
$499$	−16.8585	+	16.8585i	−0.754689	+	0.754689i	0.220662	+	0.975350i	$0.429178\pi$
$500$	−6.99313	+	8.72331i	−0.312742	+	0.390118i
$501$	−20.9422	−	20.9422i	−0.935628	−	0.935628i
$502$	−15.8249	−	15.8249i	−0.706299	−	0.706299i
$503$	−14.5276			−0.647755			−0.323877	−	0.946099i	$-0.604987\pi$
$503$	−14.5276			−0.647755			−0.323877	+	0.946099i	$0.604987\pi$
$504$	−0.974180	−	0.974180i	−0.0433934	−	0.0433934i
$505$	17.9314	−	19.2925i	0.797939	−	0.858506i
$506$		−	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	$-0.170531\pi$
$509$	38.8001			1.71978			0.859892	+	0.510476i	$0.170531\pi$
$510$	0.312183	+	8.53783i	0.0138237	+	0.378061i
$511$			29.1319i			1.28872i
$512$	−1.00000			−0.0441942
$513$			17.0127i			0.751129i
$514$			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
$518$	−23.1421	−	11.7224i	−1.01680	−	0.515054i
$519$			30.9544i			1.35875i
$520$	−2.37161	−	2.20430i	−0.104002	−	0.0966648i
$521$		−	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
$523$	37.4377			1.63704			0.818519	−	0.574479i	$-0.194795\pi$
$523$	37.4377			1.63704			0.818519	+	0.574479i	$0.194795\pi$
$524$	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
$532$	14.8683			0.644622
$533$			9.02057i			0.390724i
$534$			29.9809i			1.29740i
$535$	−23.0643	+	0.843340i	−0.997157	+	0.0364608i
$536$	−7.89993	−	7.89993i	−0.341225	−	0.341225i
$537$			21.8065i			0.941018i
$538$			5.62728i			0.242609i
$539$	−26.7239			−1.15108
$540$	−0.398719	−	10.9045i	−0.0171581	−	0.469254i
$541$	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	$0.239003\pi$
$542$	21.2992			0.914881
$543$	−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
$547$	41.4457			1.77209			0.886045	−	0.463599i	$-0.153442\pi$
$547$	41.4457			1.77209			0.886045	+	0.463599i	$0.153442\pi$
$548$	0.952787	−	0.952787i	0.0407010	−	0.0407010i
$549$	2.24347	−	2.24347i	0.0957490	−	0.0957490i
$550$	−11.9108	+	0.872195i	−0.507878	+	0.0371905i
$551$	23.4092			0.997266
$552$	−0.217489	+	0.217489i	−0.00925694	+	0.00925694i
$553$	32.0564			1.36318
$554$	−24.8652			−1.05642
$555$	8.57362	+	23.2649i	0.363930	+	0.987540i
$556$	8.19245			0.347437
$557$	24.9812			1.05849			0.529244	−	0.848470i	$-0.322476\pi$
$557$	24.9812			1.05849			0.529244	+	0.848470i	$0.322476\pi$
$558$	1.08006	−	1.08006i	0.0457226	−	0.0457226i
$559$	−4.45827			−0.188565
$560$	−9.52998	+	0.348461i	−0.402715	+	0.0147252i
$561$	−6.45311	+	6.45311i	−0.272451	+	0.272451i
$562$	−0.925329	+	0.925329i	−0.0390326	+	0.0390326i
$563$	36.8702			1.55389			0.776946	−	0.629567i	$-0.216768\pi$
$563$	36.8702			1.55389			0.776946	+	0.629567i	$0.216768\pi$
$564$		−	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
$568$	−12.6621			−0.531290
$569$	−9.95317	+	9.95317i	−0.417259	+	0.417259i	−0.884258	−	0.466999i	$-0.845335\pi$
$569$	−9.95317	+	9.95317i	−0.417259	+	0.417259i	0.466999	+	0.884258i	$0.345335\pi$
$570$	−10.4090	−	9.67462i	−0.435984	−	0.405225i
$571$	13.1507			0.550340			0.275170	−	0.961396i	$-0.411266\pi$
$571$	13.1507			0.550340			0.275170	+	0.961396i	$0.411266\pi$
$572$		−	3.45859i		−	0.144611i
$573$			0.915554i			0.0382478i
$574$	18.7866	+	18.7866i	0.784138	+	0.784138i
$575$	−0.0616121	−	0.841381i	−0.00256940	−	0.0350880i
$576$		−	0.323040i		−	0.0134600i
$577$			4.76642i			0.198429i	0.995066	+	0.0992144i	$0.0316330\pi$
$577$			4.76642i			0.198429i	−0.995066	+	0.0992144i	$0.968367\pi$
$578$	−12.6069			−0.524379
$579$	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
$587$	−1.56926			−0.0647702			−0.0323851	−	0.999475i	$-0.510310\pi$
$587$	−1.56926			−0.0647702			−0.0323851	+	0.999475i	$0.510310\pi$
$588$	14.4218	+	14.4218i	0.594747	+	0.594747i
$589$			16.4843i			0.679223i
$590$	−0.783939	−	21.4398i	−0.0322743	−	0.882661i
$591$		−	21.1569i		−	0.870279i
$592$	−1.89339	−	5.78058i	−0.0778179	−	0.237580i
$593$	9.67923	+	9.67923i	0.397478	+	0.397478i	0.877343	−	0.479864i	$-0.159314\pi$
$593$	9.67923	+	9.67923i	0.397478	+	0.397478i	−0.479864	+	0.877343i	$0.659314\pi$
$594$	8.24188	−	8.24188i	0.338168	−	0.338168i
$595$	−0.730363	−	19.9745i	−0.0299420	−	0.818876i
$596$			22.8722i			0.936884i
$597$		−	1.23919i		−	0.0507167i
$598$	0.244316			0.00999082
$599$		−	43.4898i		−	1.77694i	−0.458931	−	0.888472i	$-0.651768\pi$
$599$		−	43.4898i		−	1.77694i	0.458931	−	0.888472i	$-0.348232\pi$
$600$	6.89848	+	5.95710i	0.281629	+	0.243198i
$601$	−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
$605$	8.67229	+	8.06046i	0.352579	+	0.327704i
$606$	−15.1833	−	15.1833i	−0.616779	−	0.616779i
$607$	−11.8472			−0.480862			−0.240431	−	0.970666i	$-0.577289\pi$
$607$	−11.8472			−0.480862			−0.240431	+	0.970666i	$0.577289\pi$
$608$	2.46518	+	2.46518i	0.0999763	+	0.0999763i
$609$	36.9125	+	36.9125i	1.49577	+	1.49577i
$610$	−0.802483	−	21.9469i	−0.0324916	−	0.888605i
$611$	−6.76997	+	6.76997i	−0.273884	+	0.273884i
$612$	0.677082			0.0273694
$613$	−32.8563	+	32.8563i	−1.32705	+	1.32705i	−0.419122	+	0.907930i	$0.637662\pi$
$613$	−32.8563	+	32.8563i	−1.32705	+	1.32705i	−0.907930	+	0.419122i	$0.862338\pi$
$614$	2.94724	+	2.94724i	0.118941	+	0.118941i
$615$	−0.927878	−	25.3763i	−0.0374156	−	1.02327i
$616$	−7.20301	−	7.20301i	−0.290218	−	0.290218i
$617$	7.41696	+	7.41696i	0.298595	+	0.298595i	0.840464	−	0.541868i	$-0.182283\pi$
$617$	7.41696	+	7.41696i	0.298595	+	0.298595i	−0.541868	+	0.840464i	$0.682283\pi$
$618$	−8.19278	−	8.19278i	−0.329562	−	0.329562i
$619$	−4.51948			−0.181653			−0.0908266	−	0.995867i	$-0.528951\pi$
$619$	−4.51948			−0.181653			−0.0908266	+	0.995867i	$0.528951\pi$
$620$	−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
$623$		−	70.1413i		−	2.81015i
$624$	−1.86647	+	1.86647i	−0.0747185	+	0.0747185i
$625$	−24.7333	+	3.64184i	−0.989333	+	0.145673i
$626$	−2.00477			−0.0801267
$627$		−	15.1797i		−	0.606219i
$628$	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
$635$	−37.1701	+	1.35911i	−1.47505	+	0.0539348i
$636$	7.42348			0.294360
$637$		−	16.2008i		−	0.641898i
$638$	−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	$0.259528\pi$
$642$			18.8154i			0.742585i
$643$		−	39.5100i		−	1.55812i	−0.626949	−	0.779060i	$-0.715697\pi$
$643$		−	39.5100i		−	1.55812i	0.626949	−	0.779060i	$-0.284303\pi$
$644$	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
$647$	−4.05796			−0.159535			−0.0797675	−	0.996813i	$-0.525418\pi$
$647$	−4.05796			−0.159535			−0.0797675	+	0.996813i	$0.525418\pi$
$648$	−9.86477			−0.387525
$649$	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
$652$			1.81513i			0.0710859i
$653$			27.8245i			1.08886i	0.838807	+	0.544429i	$0.183253\pi$
$653$			27.8245i			1.08886i	−0.838807	+	0.544429i	$0.816747\pi$
$654$	−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
$658$			28.1988i			1.09931i
$659$	34.5284			1.34503			0.672517	−	0.740082i	$-0.265213\pi$
$659$	34.5284			1.34503			0.672517	+	0.740082i	$0.265213\pi$
$660$	0.355759	+	9.72959i	0.0138479	+	0.378724i
$661$	−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
$668$			16.2469i			0.628610i
$669$	−35.5830			−1.37572
$670$	−0.912841	−	24.9651i	−0.0352661	−	0.964486i
$671$	16.5881	−	16.5881i	0.640375	−	0.640375i
$672$			7.77437i			0.299903i
$673$	7.80123	+	7.80123i	0.300715	+	0.300715i	0.841294	−	0.540578i	$-0.181795\pi$
$673$	7.80123	+	7.80123i	0.300715	+	0.300715i	−0.540578	+	0.841294i	$0.681795\pi$
$674$	−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	0.999055	+	0.0434658i	$0.0138400\pi$
$677$	27.1256	+	27.1256i	1.04252	+	1.04252i	0.0434658	+	0.999055i	$0.486160\pi$
$678$	6.92724	+	6.92724i	0.266039	+	0.266039i
$679$	15.2079	+	15.2079i	0.583624	+	0.583624i
$680$	3.19071	−	3.43290i	0.122358	−	0.131646i
$681$	13.9634	+	13.9634i	0.535079	+	0.535079i
$682$	7.98588	−	7.98588i	0.305795	−	0.305795i
$683$	−5.91525			−0.226341			−0.113170	−	0.993576i	$-0.536101\pi$
$683$	−5.91525			−0.226341			−0.113170	+	0.993576i	$0.536101\pi$
$684$	−0.796353	+	0.796353i	−0.0304493	+	0.0304493i
$685$	3.01096	−	0.110095i	0.115043	−	0.00420651i
$686$	−12.6308	−	12.6308i	−0.482246	−	0.482246i
$687$	−22.6714	−	22.6714i	−0.864968	−	0.864968i
$688$	−3.07893			−0.117383
$689$	−4.16958	−	4.16958i	−0.158848	−	0.158848i
$690$	−0.687300	+	0.0251309i	−0.0261651	+	0.000956718i
$691$		−	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
$695$	13.4181	+	12.4714i	0.508976	+	0.473068i
$696$			12.2403i			0.463966i
$697$	−13.0572			−0.494578
$698$			4.00432i			0.151566i
$699$		−	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
$703$	−9.58262	+	18.9177i	−0.361415	+	0.713495i
$704$		−	2.38854i		−	0.0900213i
$705$	18.3487	−	19.7414i	0.691050	−	0.743504i
$706$			11.1747i			0.420565i
$707$	35.5218	+	35.5218i	1.33594	+	1.33594i
$708$	−17.4901			−0.657319
$709$	−18.0591	−	18.0591i	−0.678223	−	0.678223i	0.281375	−	0.959598i	$-0.409210\pi$
$709$	−18.0591	−	18.0591i	−0.678223	−	0.678223i	−0.959598	+	0.281375i	$0.909210\pi$
$710$	−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
$717$	2.24099			0.0836914
$718$		−	19.4341i		−	0.725276i
$719$		−	18.4885i		−	0.689505i	−0.938694	−	0.344752i	$-0.887963\pi$
$719$		−	18.4885i		−	0.689505i	0.938694	−	0.344752i	$-0.112037\pi$
$720$	0.491767	−	0.529094i	0.0183271	−	0.0197182i
$721$	19.1673	+	19.1673i	0.713827	+	0.713827i
$722$			6.84576i			0.254773i
$723$			19.0624i			0.708939i
$724$	0.961200			0.0357227
$725$	−25.4102	−	21.9427i	−0.943712	−	0.814931i
$726$	6.82512	−	6.82512i	0.253304	−	0.253304i
$727$	−0.154078			−0.00571445			−0.00285722	−	0.999996i	$-0.500909\pi$
$727$	−0.154078			−0.00571445			−0.00285722	+	0.999996i	$0.500909\pi$
$728$	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
$732$	−17.9039			−0.661746
$733$	−26.0288	+	26.0288i	−0.961397	+	0.961397i	−0.999282	−	0.0378850i	$-0.987938\pi$
$733$	−26.0288	+	26.0288i	−0.961397	+	0.961397i	0.0378850	+	0.999282i	$0.487938\pi$
$734$	−10.2957	+	10.2957i	−0.380020	+	0.380020i
$735$	1.66645	+	45.5754i	0.0614680	+	1.68107i
$736$	0.168727			0.00621935
$737$	18.8693	−	18.8693i	0.695059	−	0.695059i
$738$	−2.01244			−0.0740789
$739$	36.2429			1.33322			0.666608	−	0.745408i	$-0.267745\pi$
$739$	36.2429			1.33322			0.666608	+	0.745408i	$0.267745\pi$
$740$	5.69871	−	12.3501i	0.209489	−	0.453998i
$741$	9.20236			0.338057
$742$	−17.3675			−0.637581
$743$	−7.38988	+	7.38988i	−0.271109	+	0.271109i	−0.829546	−	0.558438i	$-0.811401\pi$
$743$	−7.38988	+	7.38988i	−0.271109	+	0.271109i	0.558438	+	0.829546i	$0.311401\pi$
$744$	−8.61934			−0.316000
$745$	−34.8186	+	37.4615i	−1.27565	+	1.37248i
$746$	23.2626	−	23.2626i	0.851704	−	0.851704i
$747$	2.72424	−	2.72424i	0.0996748	−	0.0996748i
$748$	5.00630			0.183048
$749$		−	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
$753$	−40.7965			−1.48671
$754$	6.87505	−	6.87505i	0.250374	−	0.250374i
$755$	−25.3465	+	27.2705i	−0.922455	+	0.992474i
$756$	20.8117			0.756913
$757$		−	7.26929i		−	0.264207i	−0.991236	−	0.132104i	$-0.957827\pi$
$757$		−	7.26929i		−	0.264207i	0.991236	−	0.132104i	$-0.0421731\pi$
$758$			11.6263i			0.422287i
$759$	−0.519480	−	0.519480i	−0.0188559	−	0.0188559i
$760$	0.284853	+	7.79038i	0.0103327	+	0.282587i
$761$			19.7277i			0.715127i	0.933889	+	0.357564i	$0.116392\pi$
$761$			19.7277i			0.715127i	−0.933889	+	0.357564i	$0.883608\pi$
$762$			30.3226i			1.09847i
$763$	43.8965			1.58916
$764$	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	−0.982963	−	0.183805i	$-0.941159\pi$
$769$	−22.1613	+	22.1613i	−0.799158	+	0.799158i	0.183805	+	0.982963i	$0.441159\pi$
$770$	−0.832312	−	22.7627i	−0.0299944	−	0.820311i
$771$	29.8570	+	29.8570i	1.07527	+	1.07527i
$772$	−7.33106			−0.263851
$773$	−30.0504	−	30.0504i	−1.08084	−	1.08084i	−0.996432	−	0.0844052i	$-0.973101\pi$
$773$	−30.0504	−	30.0504i	−1.08084	−	1.08084i	−0.0844052	−	0.996432i	$-0.526899\pi$
$774$		−	0.994617i		−	0.0357508i
$775$	15.4516	−	17.8933i	0.555037	−	0.642748i
$776$			5.04296i			0.181032i
$777$	−44.9403	+	14.7199i	−1.61223	+	0.528074i
$778$	−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
$782$			0.353646i			0.0126464i
$783$	32.7667			1.17099
$784$		−	11.1884i		−	0.399586i
$785$	31.9492	−	1.16821i	1.14032	−	0.0416954i
$786$	40.2011			1.43393
$787$	22.2914	−	22.2914i	0.794603	−	0.794603i	−0.187636	−	0.982239i	$-0.560083\pi$
$787$	22.2914	−	22.2914i	0.794603	−	0.794603i	0.982239	+	0.187636i	$0.0600825\pi$
$788$	−8.20672	+	8.20672i	−0.292352	+	0.292352i
$789$		−	32.9410i		−	1.17273i
$790$	0.614151	+	16.7963i	0.0218505	+	0.597584i
$791$	−16.2065	−	16.2065i	−0.576237	−	0.576237i
$792$	0.771593			0.0274174
$793$	10.0561	+	10.0561i	0.357104	+	0.357104i
$794$	−0.327150	−	0.327150i	−0.0116101	−	0.0116101i
$795$	12.1586	+	11.3008i	0.431222	+	0.400799i
$796$	−0.480679	+	0.480679i	−0.0170372	+	0.0170372i
$797$	17.6688			0.625862			0.312931	−	0.949776i	$-0.398689\pi$
$797$	17.6688			0.625862			0.312931	+	0.949776i	$0.398689\pi$
$798$	19.1652	−	19.1652i	0.678442	−	0.678442i
$799$	−9.79950	−	9.79950i	−0.346681	−	0.346681i
$800$	−0.365159	−	4.98665i	−0.0129103	−	0.176305i
$801$	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
$808$			11.7791i			0.414388i
$809$	16.5367	−	16.5367i	0.581399	−	0.581399i	−0.353888	−	0.935288i	$-0.615141\pi$
$809$	16.5367	−	16.5367i	0.581399	−	0.581399i	0.935288	+	0.353888i	$0.115141\pi$
$810$	−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	$0.244249\pi$
$812$		−	28.6365i		−	1.00495i
$813$	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
$820$	−9.48350	+	10.2033i	−0.331178	+	0.356316i
$821$	−15.0113			−0.523897			−0.261948	−	0.965082i	$-0.584365\pi$
$821$	−15.0113			−0.523897			−0.261948	+	0.965082i	$0.584365\pi$
$822$		−	2.45628i		−	0.0856727i
$823$	34.4033	+	34.4033i	1.19922	+	1.19922i	0.974399	+	0.224826i	$0.0721814\pi$
$823$	34.4033	+	34.4033i	1.19922	+	1.19922i	0.224826	+	0.974399i	$0.427819\pi$
$824$			6.35592i			0.221419i
$825$	−14.2287	+	16.4773i	−0.495381	+	0.573665i
$826$	40.9188			1.42375
$827$			2.14845i			0.0747090i	0.999302	+	0.0373545i	$0.0118931\pi$
$827$			2.14845i			0.0747090i	−0.999302	+	0.0373545i	$0.988107\pi$
$828$			0.0545055i			0.00189420i
$829$	18.9396	−	18.9396i	0.657800	−	0.657800i	−0.297059	−	0.954859i	$-0.596006\pi$
$829$	18.9396	−	18.9396i	0.657800	−	0.657800i	0.954859	+	0.297059i	$0.0960057\pi$
$830$	−0.974453	−	26.6501i	−0.0338238	−	0.925039i
$831$	−32.0512	+	32.0512i	−1.11185	+	1.11185i
$832$	1.44800			0.0502003
$833$	23.4505			0.812513
$834$	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
$837$			23.0736i			0.797541i
$838$		−	11.9651i		−	0.413327i
$839$	26.3122			0.908399			0.454200	−	0.890900i	$-0.349925\pi$
$839$	26.3122			0.908399			0.454200	+	0.890900i	$0.349925\pi$
$840$	−11.8350	+	12.7333i	−0.408346	+	0.439341i
$841$		−	16.0865i		−	0.554705i
$842$	−17.5941	−	17.5941i	−0.606331	−	0.606331i
$843$			2.38550i			0.0821609i
$844$	−24.5328			−0.844453
$845$	−17.8581	−	16.5982i	−0.614336	−	0.570995i
$846$	−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
$853$		−	29.3440i		−	1.00472i	−0.864658	−	0.502360i	$-0.832465\pi$
$853$		−	29.3440i		−	1.00472i	0.864658	−	0.502360i	$-0.167535\pi$
$854$	41.8867			1.43333
$855$	−2.51661	+	0.0920190i	−0.0860662	+	0.00314698i
$856$	7.29845	−	7.29845i	0.249456	−	0.249456i
$857$		−	16.7643i		−	0.572658i	−0.958131	−	0.286329i	$-0.907565\pi$
$857$		−	16.7643i		−	0.572658i	0.958131	−	0.286329i	$-0.0924350\pi$
$858$	−4.45812	−	4.45812i	−0.152198	−	0.152198i
$859$	−22.7459	−	22.7459i	−0.776081	−	0.776081i	0.203081	−	0.979162i	$-0.434905\pi$
$859$	−22.7459	−	22.7459i	−0.776081	−	0.776081i	−0.979162	+	0.203081i	$0.934905\pi$
$860$	−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	0.931192	−	0.364528i	$-0.118770\pi$
$863$	16.6468	+	16.6468i	0.566664	+	0.566664i	−0.364528	+	0.931192i	$0.618770\pi$
$864$	3.45060	+	3.45060i	0.117392	+	0.117392i
$865$	37.9445	−	1.38743i	1.29015	−	0.0471740i
$866$	−11.6303	−	11.6303i	−0.395214	−	0.395214i
$867$	−16.2503	+	16.2503i	−0.551890	+	0.551890i
$868$	20.1652			0.684453
$869$	−12.6951	+	12.6951i	−0.430650	+	0.430650i
$870$	−18.6335	+	20.0478i	−0.631733	+	0.679685i
$871$	11.4391	+	11.4391i	0.387598	+	0.387598i
$872$	7.27809	+	7.27809i	0.246467	+	0.246467i
$873$	−1.62908			−0.0551360
$874$	−0.415942	−	0.415942i	−0.0140694	−	0.0140694i
$875$	−5.21761	−	47.3954i	−0.176387	−	1.60226i
$876$			12.4520i			0.420714i
$877$	−26.6229	+	26.6229i	−0.898990	+	0.898990i	−0.995347	−	0.0963568i	$-0.969281\pi$
$877$	−26.6229	+	26.6229i	−0.898990	+	0.898990i	0.0963568	+	0.995347i	$0.469281\pi$
$878$	−16.3753	+	16.3753i	−0.552641	+	0.552641i
$879$	57.8409			1.95093
$880$	3.63609	−	3.91208i	0.122572	−	0.131876i
$881$		−	30.3341i		−	1.02198i	−0.859587	−	0.510990i	$-0.829279\pi$
$881$		−	30.3341i		−	1.02198i	0.859587	−	0.510990i	$-0.170721\pi$
$882$	3.61430			0.121700
$883$			31.6440i			1.06491i	0.846459	+	0.532453i	$0.178730\pi$
$883$			31.6440i			1.06491i	−0.846459	+	0.532453i	$0.821270\pi$
$884$			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	$-0.300198\pi$
$887$	−6.61467	−	6.61467i	−0.222099	−	0.222099i	−0.809382	+	0.587283i	$0.800198\pi$
$888$	−9.89174	−	5.01058i	−0.331945	−	0.168144i
$889$		−	70.9408i		−	2.37928i
$890$	36.7512	−	1.34380i	1.23190	−	0.0450442i
$891$		−	23.5623i		−	0.789368i
$892$	13.8026	+	13.8026i	0.462144	+	0.462144i
$893$	23.0514			0.771387
$894$	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
$902$	−14.8798			−0.495444
$903$			23.9367i			0.796563i
$904$		−	5.37412i		−	0.178741i
$905$	1.57431	+	1.46324i	0.0523318	+	0.0486398i
$906$	21.4619	+	21.4619i	0.713025	+	0.713025i
$907$		−	41.6369i		−	1.38253i	−0.722602	−	0.691265i	$-0.757054\pi$
$907$		−	41.6369i		−	1.38253i	0.722602	−	0.691265i	$-0.242946\pi$
$908$		−	10.8328i		−	0.359498i
$909$	−3.80513			−0.126208
$910$	13.7994	−	0.504570i	0.457445	−	0.0167263i
$911$	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	$0.205227\pi$
$912$	6.35524			0.210443
$913$	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
$917$	−94.0518			−3.10586
$918$	−7.23235	+	7.23235i	−0.238703	+	0.238703i
$919$	−12.1528	+	12.1528i	−0.400885	+	0.400885i	−0.878545	−	0.477660i	$-0.841485\pi$
$919$	−12.1528	+	12.1528i	−0.400885	+	0.400885i	0.477660	+	0.878545i	$0.341485\pi$
$920$	0.276350	+	0.256854i	0.00911101	+	0.00846823i
$921$	7.59798			0.250362
$922$	9.22827	−	9.22827i	0.303917	−	0.303917i
$923$	18.3347			0.603494
$924$	−18.5694			−0.610887
$925$	28.1343	−	11.5525i	0.925051	−	0.379844i
$926$	−13.6064			−0.447134
$927$	−2.05322			−0.0674366
$928$	4.74797	−	4.74797i	0.155860	−	0.155860i
$929$	−11.0600			−0.362867			−0.181434	−	0.983403i	$-0.558074\pi$
$929$	−11.0600			−0.362867			−0.181434	+	0.983403i	$0.558074\pi$
$930$	−14.1173	−	13.1213i	−0.462923	−	0.430264i
$931$	−27.5814	+	27.5814i	−0.903945	+	0.903945i
$932$	−1.47378	+	1.47378i	−0.0482753	+	0.0482753i
$933$	31.1586			1.02009
$934$		−	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	−0.402997	−	0.915202i	$-0.632031\pi$
$937$	15.6788	−	15.6788i	0.512205	−	0.512205i	0.915202	+	0.402997i	$0.132031\pi$
$938$	47.6470			1.55573
$939$	−2.58415	+	2.58415i	−0.0843305	+	0.0843305i
$940$	−14.7750	+	0.540245i	−0.481909	+	0.0176209i
$941$	−18.6061			−0.606540			−0.303270	−	0.952905i	$-0.598078\pi$
$941$	−18.6061			−0.606540			−0.303270	+	0.952905i	$0.598078\pi$
$942$		−	26.0635i		−	0.849196i
$943$		−	1.05111i		−	0.0342290i
$944$	6.78438	+	6.78438i	0.220813	+	0.220813i
$945$	34.0866	+	31.6818i	1.10884	+	1.03061i
$946$		−	7.35412i		−	0.239103i
$947$		−	1.38953i		−	0.0451536i	−0.999745	−	0.0225768i	$-0.992813\pi$
$947$		−	1.38953i		−	0.0451536i	0.999745	−	0.0225768i	$-0.00718702\pi$
$948$	13.7021			0.445022
$949$	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	$-0.938831\pi$
$953$	−24.4066	+	24.4066i	−0.790606	+	0.790606i	0.190987	+	0.981593i	$0.438831\pi$
$954$	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
$957$	−29.2363			−0.945076
$958$	25.1547	+	25.1547i	0.812712	+	0.812712i
$959$			5.74656i			0.185566i
$960$	−4.07345	+	0.148945i	−0.131470	+	0.00480717i
$961$		−	8.64307i		−	0.278809i
$962$	2.74162	+	8.37026i	0.0883935	+	0.269868i
$963$	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
$967$			32.8029i			1.05487i	0.849596	+	0.527434i	$0.176846\pi$
$967$			32.8029i			1.05487i	−0.849596	+	0.527434i	$0.823154\pi$
$968$	−5.29490			−0.170184
$969$			13.3204i			0.427912i
$970$	−7.67694	+	8.25966i	−0.246492	+	0.265202i
$971$	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
$975$	−9.98897	−	8.62586i	−0.319903	−	0.276249i
$976$	6.94487	+	6.94487i	0.222300	+	0.222300i
$977$	−14.6717			−0.469391			−0.234695	−	0.972069i	$-0.575409\pi$
$977$	−14.6717			−0.469391			−0.234695	+	0.972069i	$0.575409\pi$
$978$	2.33970	+	2.33970i	0.0748154	+	0.0748154i
$979$	27.7775	+	27.7775i	0.887773	+	0.887773i
$980$	17.0322	−	18.3250i	0.544073	−	0.585371i
$981$	−2.35112	+	2.35112i	−0.0750653	+	0.0750653i
$982$	24.6515			0.786659
$983$	−26.7565	+	26.7565i	−0.853400	+	0.853400i	−0.990550	−	0.137150i	$-0.956206\pi$
$983$	−26.7565	+	26.7565i	−0.853400	+	0.853400i	0.137150	+	0.990550i	$0.456206\pi$
$984$	8.03006	+	8.03006i	0.255989	+	0.255989i
$985$	−25.9346	+	0.948291i	−0.826345	+	0.0302150i
$986$	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
$993$		−	2.16393i		−	0.0686702i
$994$	38.1846	−	38.1846i	1.21114	−	1.21114i
$995$	−1.51903	+	0.0555427i	−0.0481564	+	0.00176082i
$996$	−21.7406			−0.688878
$997$			46.0799i			1.45936i	0.683787	+	0.729682i	$0.260332\pi$
$997$			46.0799i			1.45936i	−0.683787	+	0.729682i	$0.739668\pi$
$998$	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.h.e.253.2	yes	20
5.2	odd	4		370.2.g.e.327.9	yes	20
37.6	odd	4		370.2.g.e.43.9	✓	20
185.117	even	4	inner	370.2.h.e.117.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.9	✓	20	37.6	odd	4
370.2.g.e.327.9	yes	20	5.2	odd	4
370.2.h.e.117.2	yes	20	185.117	even	4	inner
370.2.h.e.253.2	yes	20	1.1	even	1	trivial

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.h (of order \(4\), degree \(2\), minimal)

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

Introduction

L-functions

Modular forms

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Database

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