LMFDB - Embedded newform 370.2.h.e.117.10

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			117.10
Root			$2.41612 - 2.41612i$ of defining polynomial
Character	$\chi$	$=$	370.117
Dual form			370.2.h.e.253.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +(-0.667560 + 2.13410i) q^{10} +1.92497i q^{11} +(2.41612 + 2.41612i) q^{12} +3.05698 q^{13} +(0.875609 + 0.875609i) q^{14} +(6.76914 - 3.54333i) q^{15} +1.00000 q^{16} +3.63520i q^{17} -8.67529i q^{18} +(3.22623 - 3.22623i) q^{19} +(0.667560 - 2.13410i) q^{20} -4.23116i q^{21} -1.92497i q^{22} -2.01378 q^{23} +(-2.41612 - 2.41612i) q^{24} +(-4.10873 - 2.84927i) q^{25} -3.05698 q^{26} +(-13.7122 + 13.7122i) q^{27} +(-0.875609 - 0.875609i) q^{28} +(4.81913 + 4.81913i) q^{29} +(-6.76914 + 3.54333i) q^{30} +(0.936472 - 0.936472i) q^{31} -1.00000 q^{32} +(-4.65096 + 4.65096i) q^{33} -3.63520i q^{34} +(-2.45316 + 1.28411i) q^{35} +8.67529i q^{36} +(-0.586931 - 6.05438i) q^{37} +(-3.22623 + 3.22623i) q^{38} +(7.38603 + 7.38603i) q^{39} +(-0.667560 + 2.13410i) q^{40} -12.7650i q^{41} +4.23116i q^{42} -4.81157 q^{43} +1.92497i q^{44} +(18.5139 + 5.79128i) q^{45} +2.01378 q^{46} +(-5.85922 - 5.85922i) q^{47} +(2.41612 + 2.41612i) q^{48} -5.46662i q^{49} +(4.10873 + 2.84927i) q^{50} +(-8.78310 + 8.78310i) q^{51} +3.05698 q^{52} +(-3.89480 + 3.89480i) q^{53} +(13.7122 - 13.7122i) q^{54} +(4.10806 + 1.28503i) q^{55} +(0.875609 + 0.875609i) q^{56} +15.5899 q^{57} +(-4.81913 - 4.81913i) q^{58} +(-3.25043 + 3.25043i) q^{59} +(6.76914 - 3.54333i) q^{60} +(3.16695 - 3.16695i) q^{61} +(-0.936472 + 0.936472i) q^{62} +(7.59617 - 7.59617i) q^{63} +1.00000 q^{64} +(2.04072 - 6.52388i) q^{65} +(4.65096 - 4.65096i) q^{66} +(-3.71697 + 3.71697i) q^{67} +3.63520i q^{68} +(-4.86553 - 4.86553i) q^{69} +(2.45316 - 1.28411i) q^{70} -3.90508 q^{71} -8.67529i q^{72} +(8.57777 + 8.57777i) q^{73} +(0.586931 + 6.05438i) q^{74} +(-3.04299 - 16.8114i) q^{75} +(3.22623 - 3.22623i) q^{76} +(1.68552 - 1.68552i) q^{77} +(-7.38603 - 7.38603i) q^{78} +(4.19139 - 4.19139i) q^{79} +(0.667560 - 2.13410i) q^{80} -40.2348 q^{81} +12.7650i q^{82} +(-7.79493 + 7.79493i) q^{83} -4.23116i q^{84} +(7.75787 + 2.42672i) q^{85} +4.81157 q^{86} +23.2872i q^{87} -1.92497i q^{88} +(-7.79425 - 7.79425i) q^{89} +(-18.5139 - 5.79128i) q^{90} +(-2.67672 - 2.67672i) q^{91} -2.01378 q^{92} +4.52526 q^{93} +(5.85922 + 5.85922i) q^{94} +(-4.73138 - 9.03878i) q^{95} +(-2.41612 - 2.41612i) q^{96} -14.8936i q^{97} +5.46662i q^{98} -16.6997 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	2.41612	+	2.41612i	1.39495	+	1.39495i	0.813791	+	0.581158i	$0.197400\pi$
$3$	2.41612	+	2.41612i	1.39495	+	1.39495i	0.581158	+	0.813791i	$0.302600\pi$
$4$	1.00000			0.500000
$5$	0.667560	−	2.13410i	0.298542	−	0.954397i
$5$	0.667560	−	2.13410i	0.298542	−	0.954397i
$6$	−2.41612	−	2.41612i	−0.986378	−	0.986378i
$7$	−0.875609	−	0.875609i	−0.330949	−	0.330949i	0.521998	−	0.852947i	$-0.325187\pi$
$7$	−0.875609	−	0.875609i	−0.330949	−	0.330949i	−0.852947	+	0.521998i	$0.825187\pi$
$8$	−1.00000			−0.353553
$9$			8.67529i			2.89176i
$10$	−0.667560	+	2.13410i	−0.211101	+	0.674860i
$11$			1.92497i			0.580400i	0.956966	+	0.290200i	$0.0937218\pi$
$11$			1.92497i			0.580400i	−0.956966	+	0.290200i	$0.906278\pi$
$12$	2.41612	+	2.41612i	0.697474	+	0.697474i
$13$	3.05698			0.847853			0.423927	−	0.905697i	$-0.360651\pi$
$13$	3.05698			0.847853			0.423927	+	0.905697i	$0.360651\pi$
$14$	0.875609	+	0.875609i	0.234016	+	0.234016i
$15$	6.76914	−	3.54333i	1.74778	−	0.914884i
$16$	1.00000			0.250000
$17$			3.63520i			0.881667i	0.897589	+	0.440833i	$0.145317\pi$
$17$			3.63520i			0.881667i	−0.897589	+	0.440833i	$0.854683\pi$
$18$		−	8.67529i		−	2.04479i
$19$	3.22623	−	3.22623i	0.740148	−	0.740148i	−0.232459	−	0.972606i	$-0.574677\pi$
$19$	3.22623	−	3.22623i	0.740148	−	0.740148i	0.972606	+	0.232459i	$0.0746770\pi$
$20$	0.667560	−	2.13410i	0.149271	−	0.477198i
$21$		−	4.23116i		−	0.923314i
$22$		−	1.92497i		−	0.410404i
$23$	−2.01378			−0.419902			−0.209951	−	0.977712i	$-0.567330\pi$
$23$	−2.01378			−0.419902			−0.209951	+	0.977712i	$0.567330\pi$
$24$	−2.41612	−	2.41612i	−0.493189	−	0.493189i
$25$	−4.10873	−	2.84927i	−0.821745	−	0.569855i
$26$	−3.05698			−0.599523
$27$	−13.7122	+	13.7122i	−2.63891	+	2.63891i
$28$	−0.875609	−	0.875609i	−0.165475	−	0.165475i
$29$	4.81913	+	4.81913i	0.894890	+	0.894890i	0.994979	−	0.100089i	$-0.0319127\pi$
$29$	4.81913	+	4.81913i	0.894890	+	0.894890i	−0.100089	+	0.994979i	$0.531913\pi$
$30$	−6.76914	+	3.54333i	−1.23587	+	0.646920i
$31$	0.936472	−	0.936472i	0.168195	−	0.168195i	−0.617990	−	0.786186i	$-0.712053\pi$
$31$	0.936472	−	0.936472i	0.168195	−	0.168195i	0.786186	+	0.617990i	$0.212053\pi$
$32$	−1.00000			−0.176777
$33$	−4.65096	+	4.65096i	−0.809628	+	0.809628i
$34$		−	3.63520i		−	0.623432i
$35$	−2.45316	+	1.28411i	−0.414659	+	0.217055i
$36$			8.67529i			1.44588i
$37$	−0.586931	−	6.05438i	−0.0964908	−	0.995334i
$37$	−0.586931	−	6.05438i	−0.0964908	−	0.995334i
$38$	−3.22623	+	3.22623i	−0.523363	+	0.523363i
$39$	7.38603	+	7.38603i	1.18271	+	1.18271i
$40$	−0.667560	+	2.13410i	−0.105551	+	0.337430i
$41$		−	12.7650i		−	1.99356i	−0.0801960	−	0.996779i	$-0.525555\pi$
$41$		−	12.7650i		−	1.99356i	0.0801960	−	0.996779i	$-0.474445\pi$
$42$			4.23116i			0.652882i
$43$	−4.81157			−0.733757			−0.366879	−	0.930269i	$-0.619574\pi$
$43$	−4.81157			−0.733757			−0.366879	+	0.930269i	$0.619574\pi$
$44$			1.92497i			0.290200i
$45$	18.5139	+	5.79128i	2.75989	+	0.863313i
$46$	2.01378			0.296915
$47$	−5.85922	−	5.85922i	−0.854654	−	0.854654i	0.136048	−	0.990702i	$-0.456560\pi$
$47$	−5.85922	−	5.85922i	−0.854654	−	0.854654i	−0.990702	+	0.136048i	$0.956560\pi$
$48$	2.41612	+	2.41612i	0.348737	+	0.348737i
$49$		−	5.46662i		−	0.780945i
$50$	4.10873	+	2.84927i	0.581062	+	0.402948i
$51$	−8.78310	+	8.78310i	−1.22988	+	1.22988i
$52$	3.05698			0.423927
$53$	−3.89480	+	3.89480i	−0.534991	+	0.534991i	−0.922054	−	0.387062i	$-0.873490\pi$
$53$	−3.89480	+	3.89480i	−0.534991	+	0.534991i	0.387062	+	0.922054i	$0.373490\pi$
$54$	13.7122	−	13.7122i	1.86599	−	1.86599i
$55$	4.10806	+	1.28503i	0.553931	+	0.173274i
$56$	0.875609	+	0.875609i	0.117008	+	0.117008i
$57$	15.5899			2.06494
$58$	−4.81913	−	4.81913i	−0.632783	−	0.632783i
$59$	−3.25043	+	3.25043i	−0.423170	+	0.423170i	−0.886294	−	0.463124i	$-0.846729\pi$
$59$	−3.25043	+	3.25043i	−0.423170	+	0.423170i	0.463124	+	0.886294i	$0.346729\pi$
$60$	6.76914	−	3.54333i	0.873892	−	0.457442i
$61$	3.16695	−	3.16695i	0.405486	−	0.405486i	−0.474675	−	0.880161i	$-0.657434\pi$
$61$	3.16695	−	3.16695i	0.405486	−	0.405486i	0.880161	+	0.474675i	$0.157434\pi$
$62$	−0.936472	+	0.936472i	−0.118932	+	0.118932i
$63$	7.59617	−	7.59617i	0.957027	−	0.957027i
$64$	1.00000			0.125000
$65$	2.04072	−	6.52388i	0.253120	−	0.809188i
$66$	4.65096	−	4.65096i	0.572493	−	0.572493i
$67$	−3.71697	+	3.71697i	−0.454100	+	0.454100i	−0.896713	−	0.442613i	$-0.854052\pi$
$67$	−3.71697	+	3.71697i	−0.454100	+	0.454100i	0.442613	+	0.896713i	$0.354052\pi$
$68$			3.63520i			0.440833i
$69$	−4.86553	−	4.86553i	−0.585741	−	0.585741i
$70$	2.45316	−	1.28411i	0.293208	−	0.153481i
$71$	−3.90508			−0.463448			−0.231724	−	0.972782i	$-0.574437\pi$
$71$	−3.90508			−0.463448			−0.231724	+	0.972782i	$0.574437\pi$
$72$		−	8.67529i		−	1.02239i
$73$	8.57777	+	8.57777i	1.00395	+	1.00395i	0.999992	+	0.00396036i	$0.00126063\pi$
$73$	8.57777	+	8.57777i	1.00395	+	1.00395i	0.00396036	+	0.999992i	$0.498739\pi$
$74$	0.586931	+	6.05438i	0.0682293	+	0.703807i
$75$	−3.04299	−	16.8114i	−0.351375	−	1.94121i
$76$	3.22623	−	3.22623i	0.370074	−	0.370074i
$77$	1.68552	−	1.68552i	0.192083	−	0.192083i
$78$	−7.38603	−	7.38603i	−0.836303	−	0.836303i
$79$	4.19139	−	4.19139i	0.471568	−	0.471568i	−0.430854	−	0.902422i	$-0.641788\pi$
$79$	4.19139	−	4.19139i	0.471568	−	0.471568i	0.902422	+	0.430854i	$0.141788\pi$
$80$	0.667560	−	2.13410i	0.0746355	−	0.238599i
$81$	−40.2348			−4.47053
$82$			12.7650i			1.40966i
$83$	−7.79493	+	7.79493i	−0.855604	+	0.855604i	−0.990817	−	0.135212i	$-0.956828\pi$
$83$	−7.79493	+	7.79493i	−0.855604	+	0.855604i	0.135212	+	0.990817i	$0.456828\pi$
$84$		−	4.23116i		−	0.461657i
$85$	7.75787	+	2.42672i	0.841460	+	0.263214i
$86$	4.81157			0.518845
$87$			23.2872i			2.49665i
$88$		−	1.92497i		−	0.205202i
$89$	−7.79425	−	7.79425i	−0.826188	−	0.826188i	0.160799	−	0.986987i	$-0.448593\pi$
$89$	−7.79425	−	7.79425i	−0.826188	−	0.826188i	−0.986987	+	0.160799i	$0.948593\pi$
$90$	−18.5139	−	5.79128i	−1.95154	−	0.610454i
$91$	−2.67672	−	2.67672i	−0.280596	−	0.280596i
$92$	−2.01378			−0.209951
$93$	4.52526			0.469248
$94$	5.85922	+	5.85922i	0.604332	+	0.604332i
$95$	−4.73138	−	9.03878i	−0.485429	−	0.927360i
$96$	−2.41612	−	2.41612i	−0.246594	−	0.246594i
$97$		−	14.8936i		−	1.51221i	−0.654449	−	0.756106i	$-0.727099\pi$
$97$		−	14.8936i		−	1.51221i	0.654449	−	0.756106i	$-0.272901\pi$
$98$			5.46662i			0.552212i
$99$	−16.6997			−1.67838
$100$	−4.10873	−	2.84927i	−0.410873	−	0.284927i
$101$		−	0.977455i		−	0.0972604i	−0.998817	−	0.0486302i	$-0.984514\pi$
$101$		−	0.977455i		−	0.0972604i	0.998817	−	0.0486302i	$-0.0154856\pi$
$102$	8.78310	−	8.78310i	0.869656	−	0.869656i
$103$		−	11.3553i		−	1.11887i	−0.828873	−	0.559437i	$-0.811018\pi$
$103$		−	11.3553i		−	1.11887i	0.828873	−	0.559437i	$-0.188982\pi$
$104$	−3.05698			−0.299761
$105$	−9.02969	−	2.82455i	−0.881208	−	0.275648i
$106$	3.89480	−	3.89480i	0.378296	−	0.378296i
$107$	−4.47857	−	4.47857i	−0.432960	−	0.432960i	0.456674	−	0.889634i	$-0.349041\pi$
$107$	−4.47857	−	4.47857i	−0.432960	−	0.432960i	−0.889634	+	0.456674i	$0.849041\pi$
$108$	−13.7122	+	13.7122i	−1.31946	+	1.31946i
$109$	7.18760	−	7.18760i	0.688447	−	0.688447i	−0.273442	−	0.961889i	$-0.588162\pi$
$109$	7.18760	−	7.18760i	0.688447	−	0.688447i	0.961889	+	0.273442i	$0.0881621\pi$
$110$	−4.10806	−	1.28503i	−0.391689	−	0.122523i
$111$	13.2100	−	16.0462i	1.25384	−	1.52304i
$112$	−0.875609	−	0.875609i	−0.0827373	−	0.0827373i
$113$			3.47531i			0.326930i	0.986549	+	0.163465i	$0.0522671\pi$
$113$			3.47531i			0.326930i	−0.986549	+	0.163465i	$0.947733\pi$
$114$	−15.5899			−1.46013
$115$	−1.34432	+	4.29759i	−0.125358	+	0.400753i
$116$	4.81913	+	4.81913i	0.447445	+	0.447445i
$117$			26.5202i			2.45179i
$118$	3.25043	−	3.25043i	0.299227	−	0.299227i
$119$	3.18302	−	3.18302i	0.291787	−	0.291787i
$120$	−6.76914	+	3.54333i	−0.617935	+	0.323460i
$121$	7.29450			0.663136
$122$	−3.16695	+	3.16695i	−0.286722	+	0.286722i
$123$	30.8418	−	30.8418i	2.78091	−	2.78091i
$124$	0.936472	−	0.936472i	0.0840976	−	0.0840976i
$125$	−8.82344	+	6.86635i	−0.789193	+	0.614145i
$126$	−7.59617	+	7.59617i	−0.676720	+	0.676720i
$127$	5.75444	+	5.75444i	0.510624	+	0.510624i	0.914718	−	0.404093i	$-0.132413\pi$
$127$	5.75444	+	5.75444i	0.510624	+	0.510624i	−0.404093	+	0.914718i	$0.632413\pi$
$128$	−1.00000			−0.0883883
$129$	−11.6253	−	11.6253i	−1.02355	−	1.02355i
$130$	−2.04072	+	6.52388i	−0.178983	+	0.572182i
$131$	1.96912	−	1.96912i	0.172043	−	0.172043i	−0.615833	−	0.787876i	$-0.711181\pi$
$131$	1.96912	−	1.96912i	0.172043	−	0.172043i	0.787876	+	0.615833i	$0.211181\pi$
$132$	−4.65096	+	4.65096i	−0.404814	+	0.404814i
$133$	−5.64983			−0.489903
$134$	3.71697	−	3.71697i	0.321097	−	0.321097i
$135$	20.1094	+	38.4169i	1.73074	+	3.30640i
$136$		−	3.63520i		−	0.311716i
$137$	7.83311	+	7.83311i	0.669228	+	0.669228i	0.957537	−	0.288309i	$-0.0930932\pi$
$137$	7.83311	+	7.83311i	0.669228	+	0.669228i	−0.288309	+	0.957537i	$0.593093\pi$
$138$	4.86553	+	4.86553i	0.414182	+	0.414182i
$139$	0.678086			0.0575145			0.0287572	−	0.999586i	$-0.490845\pi$
$139$	0.678086			0.0575145			0.0287572	+	0.999586i	$0.490845\pi$
$140$	−2.45316	+	1.28411i	−0.207329	+	0.108527i
$141$		−	28.3132i		−	2.38440i
$142$	3.90508			0.327707
$143$			5.88458i			0.492094i
$144$			8.67529i			0.722941i
$145$	13.5015	−	7.06742i	1.12124	−	0.586918i
$146$	−8.57777	−	8.57777i	−0.709902	−	0.709902i
$147$	13.2080	−	13.2080i	1.08938	−	1.08938i
$148$	−0.586931	−	6.05438i	−0.0482454	−	0.497667i
$149$			5.12261i			0.419660i	0.977738	+	0.209830i	$0.0672911\pi$
$149$			5.12261i			0.419660i	−0.977738	+	0.209830i	$0.932709\pi$
$150$	3.04299	+	16.8114i	0.248459	+	1.37264i
$151$			20.3046i			1.65236i	0.563405	+	0.826181i	$0.309491\pi$
$151$			20.3046i			1.65236i	−0.563405	+	0.826181i	$0.690509\pi$
$152$	−3.22623	+	3.22623i	−0.261682	+	0.261682i
$153$	−31.5365			−2.54957
$154$	−1.68552	+	1.68552i	−0.135823	+	0.135823i
$155$	−1.37337	−	2.62367i	−0.110312	−	0.210738i
$156$	7.38603	+	7.38603i	0.591356	+	0.591356i
$157$	−9.36950	−	9.36950i	−0.747767	−	0.747767i	0.226292	−	0.974059i	$-0.427340\pi$
$157$	−9.36950	−	9.36950i	−0.747767	−	0.747767i	−0.974059	+	0.226292i	$0.927340\pi$
$158$	−4.19139	+	4.19139i	−0.333449	+	0.333449i
$159$	−18.8206			−1.49257
$160$	−0.667560	+	2.13410i	−0.0527753	+	0.168715i
$161$	1.76328	+	1.76328i	0.138966	+	0.138966i
$162$	40.2348			3.16115
$163$			21.6389i			1.69489i	0.530884	+	0.847445i	$0.321860\pi$
$163$			21.6389i			1.69489i	−0.530884	+	0.847445i	$0.678140\pi$
$164$		−	12.7650i		−	0.996779i
$165$	6.82079	+	13.0304i	0.530998	+	1.01441i
$166$	7.79493	−	7.79493i	0.605004	−	0.605004i
$167$		−	15.0063i		−	1.16122i	−0.814181	−	0.580611i	$-0.802814\pi$
$167$		−	15.0063i		−	1.16122i	0.814181	−	0.580611i	$-0.197186\pi$
$168$			4.23116i			0.326441i
$169$	−3.65489			−0.281145
$170$	−7.75787	−	2.42672i	−0.595002	−	0.186121i
$171$	27.9885	+	27.9885i	2.14033	+	2.14033i
$172$	−4.81157			−0.366879
$173$	−3.27813	−	3.27813i	−0.249231	−	0.249231i	0.571424	−	0.820655i	$-0.306391\pi$
$173$	−3.27813	−	3.27813i	−0.249231	−	0.249231i	−0.820655	+	0.571424i	$0.806391\pi$
$174$		−	23.2872i		−	1.76540i
$175$	1.10279	+	6.09249i	0.0833630	+	0.460549i
$176$			1.92497i			0.145100i
$177$	−15.7069			−1.18060
$178$	7.79425	+	7.79425i	0.584203	+	0.584203i
$179$	15.3991	+	15.3991i	1.15098	+	1.15098i	0.986357	+	0.164623i	$0.0526406\pi$
$179$	15.3991	+	15.3991i	1.15098	+	1.15098i	0.164623	+	0.986357i	$0.447359\pi$
$180$	18.5139	+	5.79128i	1.37994	+	0.431656i
$181$	8.69492			0.646288			0.323144	−	0.946350i	$-0.395260\pi$
$181$	8.69492			0.646288			0.323144	+	0.946350i	$0.395260\pi$
$182$	2.67672	+	2.67672i	0.198412	+	0.198412i
$183$	15.3035			1.13126
$184$	2.01378			0.148458
$185$	−13.3124	−	2.78910i	−0.978750	−	0.205058i
$186$	−4.52526			−0.331808
$187$	−6.99765			−0.511719
$188$	−5.85922	−	5.85922i	−0.427327	−	0.427327i
$189$	24.0131			1.74669
$190$	4.73138	+	9.03878i	0.343250	+	0.655742i
$191$	2.73993	+	2.73993i	0.198255	+	0.198255i	0.799251	−	0.600997i	$-0.205230\pi$
$191$	2.73993	+	2.73993i	0.198255	+	0.198255i	−0.600997	+	0.799251i	$0.705230\pi$
$192$	2.41612	+	2.41612i	0.174369	+	0.174369i
$193$	−12.4758			−0.898030			−0.449015	−	0.893524i	$-0.648225\pi$
$193$	−12.4758			−0.898030			−0.449015	+	0.893524i	$0.648225\pi$
$194$			14.8936i			1.06930i
$195$	20.6931	−	10.8319i	1.48186	−	0.775687i
$196$		−	5.46662i		−	0.390473i
$197$	2.72212	+	2.72212i	0.193943	+	0.193943i	0.797398	−	0.603454i	$-0.206209\pi$
$197$	2.72212	+	2.72212i	0.193943	+	0.193943i	−0.603454	+	0.797398i	$0.706209\pi$
$198$	16.6997			1.18679
$199$	−5.62070	−	5.62070i	−0.398441	−	0.398441i	0.479242	−	0.877683i	$-0.340912\pi$
$199$	−5.62070	−	5.62070i	−0.398441	−	0.398441i	−0.877683	+	0.479242i	$0.840912\pi$
$200$	4.10873	+	2.84927i	0.290531	+	0.201474i
$201$	−17.9613			−1.26689
$202$			0.977455i			0.0687735i
$203$		−	8.43935i		−	0.592326i
$204$	−8.78310	+	8.78310i	−0.614940	+	0.614940i
$205$	−27.2417	−	8.52140i	−1.90265	−	0.595161i
$206$			11.3553i			0.791163i
$207$		−	17.4701i		−	1.21426i
$208$	3.05698			0.211963
$209$	6.21039	+	6.21039i	0.429581	+	0.429581i
$210$	9.02969	+	2.82455i	0.623108	+	0.194913i
$211$	25.2888			1.74095			0.870477	−	0.492210i	$-0.163811\pi$
$211$	25.2888			1.74095			0.870477	+	0.492210i	$0.163811\pi$
$212$	−3.89480	+	3.89480i	−0.267496	+	0.267496i
$213$	−9.43516	−	9.43516i	−0.646486	−	0.646486i
$214$	4.47857	+	4.47857i	0.306149	+	0.306149i
$215$	−3.21201	+	10.2683i	−0.219057	+	0.700295i
$216$	13.7122	−	13.7122i	0.932997	−	0.932997i
$217$	−1.63997			−0.111328
$218$	−7.18760	+	7.18760i	−0.486805	+	0.486805i
$219$			41.4499i			2.80092i
$220$	4.10806	+	1.28503i	0.276966	+	0.0866368i
$221$			11.1127i			0.747524i
$222$	−13.2100	+	16.0462i	−0.886599	+	1.07695i
$223$	−16.8265	+	16.8265i	−1.12679	+	1.12679i	−0.136090	+	0.990696i	$0.543454\pi$
$223$	−16.8265	+	16.8265i	−1.12679	+	1.12679i	−0.990696	+	0.136090i	$0.956546\pi$
$224$	0.875609	+	0.875609i	0.0585041	+	0.0585041i
$225$	24.7183	−	35.6444i	1.64789	−	2.37629i
$226$		−	3.47531i		−	0.231174i
$227$		−	13.3976i		−	0.889233i	−0.895721	−	0.444616i	$-0.853340\pi$
$227$		−	13.3976i		−	0.889233i	0.895721	−	0.444616i	$-0.146660\pi$
$228$	15.5899			1.03247
$229$			12.4697i			0.824019i	0.911180	+	0.412010i	$0.135173\pi$
$229$			12.4697i			0.824019i	−0.911180	+	0.412010i	$0.864827\pi$
$230$	1.34432	−	4.29759i	0.0886417	−	0.283375i
$231$	8.14484			0.535891
$232$	−4.81913	−	4.81913i	−0.316391	−	0.316391i
$233$	11.3131	+	11.3131i	0.741144	+	0.741144i	0.972798	−	0.231655i	$-0.0744139\pi$
$233$	11.3131	+	11.3131i	0.741144	+	0.741144i	−0.231655	+	0.972798i	$0.574414\pi$
$234$		−	26.5202i		−	1.73368i
$235$	−16.4155	+	8.59275i	−1.07083	+	0.560529i
$236$	−3.25043	+	3.25043i	−0.211585	+	0.211585i
$237$	20.2538			1.31563
$238$	−3.18302	+	3.18302i	−0.206324	+	0.206324i
$239$	9.77163	−	9.77163i	0.632074	−	0.632074i	−0.316514	−	0.948588i	$-0.602512\pi$
$239$	9.77163	−	9.77163i	0.632074	−	0.632074i	0.948588	+	0.316514i	$0.102512\pi$
$240$	6.76914	−	3.54333i	0.436946	−	0.228721i
$241$	2.61835	+	2.61835i	0.168663	+	0.168663i	0.786391	−	0.617729i	$-0.211947\pi$
$241$	2.61835	+	2.61835i	0.168663	+	0.168663i	−0.617729	+	0.786391i	$0.711947\pi$
$242$	−7.29450			−0.468908
$243$	−56.0756	−	56.0756i	−3.59725	−	3.59725i
$244$	3.16695	−	3.16695i	0.202743	−	0.202743i
$245$	−11.6663	−	3.64929i	−0.745331	−	0.233145i
$246$	−30.8418	+	30.8418i	−1.96640	+	1.96640i
$247$	9.86251	−	9.86251i	0.627536	−	0.627536i
$248$	−0.936472	+	0.936472i	−0.0594660	+	0.0594660i
$249$	−37.6670			−2.38705
$250$	8.82344	−	6.86635i	0.558044	−	0.434266i
$251$	−1.40191	+	1.40191i	−0.0884879	+	0.0884879i	−0.749965	−	0.661477i	$-0.769930\pi$
$251$	−1.40191	+	1.40191i	−0.0884879	+	0.0884879i	0.661477	+	0.749965i	$0.269930\pi$
$252$	7.59617	−	7.59617i	0.478513	−	0.478513i
$253$		−	3.87646i		−	0.243711i
$254$	−5.75444	−	5.75444i	−0.361066	−	0.361066i
$255$	12.8807	+	24.6072i	0.806622	+	1.54096i
$256$	1.00000			0.0625000
$257$			26.1658i			1.63218i	0.577925	+	0.816090i	$0.303862\pi$
$257$			26.1658i			1.63218i	−0.577925	+	0.816090i	$0.696138\pi$
$258$	11.6253	+	11.6253i	0.723762	+	0.723762i
$259$	−4.78735	+	5.81519i	−0.297471	+	0.361338i
$260$	2.04072	−	6.52388i	0.126560	−	0.404594i
$261$	−41.8074	+	41.8074i	−2.58781	+	2.58781i
$262$	−1.96912	+	1.96912i	−0.121653	+	0.121653i
$263$	11.7781	+	11.7781i	0.726266	+	0.726266i	0.969874	−	0.243608i	$-0.0783310\pi$
$263$	11.7781	+	11.7781i	0.726266	+	0.726266i	−0.243608	+	0.969874i	$0.578331\pi$
$264$	4.65096	−	4.65096i	0.286247	−	0.286247i
$265$	5.71186	+	10.9119i	0.350877	+	0.670311i
$266$	5.64983			0.346413
$267$		−	37.6637i		−	2.30498i
$268$	−3.71697	+	3.71697i	−0.227050	+	0.227050i
$269$			0.0307805i			0.00187672i	1.00000		0.000938361i	$0.000298690\pi$
$269$			0.0307805i			0.00187672i	−1.00000		0.000938361i	$0.999701\pi$
$270$	−20.1094	−	38.4169i	−1.22382	−	2.33798i
$271$	−29.5640			−1.79588			−0.897941	−	0.440115i	$-0.854938\pi$
$271$	−29.5640			−1.79588			−0.897941	+	0.440115i	$0.854938\pi$
$272$			3.63520i			0.220417i
$273$		−	12.9346i		−	0.782835i
$274$	−7.83311	−	7.83311i	−0.473216	−	0.473216i
$275$	5.48476	−	7.90917i	0.330743	−	0.476941i
$276$	−4.86553	−	4.86553i	−0.292871	−	0.292871i
$277$	−4.25124			−0.255432			−0.127716	−	0.991811i	$-0.540765\pi$
$277$	−4.25124			−0.255432			−0.127716	+	0.991811i	$0.540765\pi$
$278$	−0.678086			−0.0406689
$279$	8.12416	+	8.12416i	0.486381	+	0.486381i
$280$	2.45316	−	1.28411i	0.146604	−	0.0767404i
$281$	−18.2679	−	18.2679i	−1.08977	−	1.08977i	−0.995552	−	0.0942188i	$-0.969965\pi$
$281$	−18.2679	−	18.2679i	−1.08977	−	1.08977i	−0.0942188	−	0.995552i	$-0.530035\pi$
$282$			28.3132i			1.68602i
$283$			2.36072i			0.140330i	0.997535	+	0.0701650i	$0.0223526\pi$
$283$			2.36072i			0.140330i	−0.997535	+	0.0701650i	$0.977647\pi$
$284$	−3.90508			−0.231724
$285$	10.4072	−	33.2704i	0.616470	−	1.97077i
$286$		−	5.88458i		−	0.347963i
$287$	−11.1772	+	11.1772i	−0.659766	+	0.659766i
$288$		−	8.67529i		−	0.511196i
$289$	3.78529			0.222664
$290$	−13.5015	+	7.06742i	−0.792838	+	0.415013i
$291$	35.9847	−	35.9847i	2.10946	−	2.10946i
$292$	8.57777	+	8.57777i	0.501976	+	0.501976i
$293$	10.6576	−	10.6576i	0.622625	−	0.622625i	−0.323577	−	0.946202i	$-0.604885\pi$
$293$	10.6576	−	10.6576i	0.622625	−	0.622625i	0.946202	+	0.323577i	$0.104885\pi$
$294$	−13.2080	+	13.2080i	−0.770307	+	0.770307i
$295$	4.76687	+	9.10659i	0.277538	+	0.530206i
$296$	0.586931	+	6.05438i	0.0341146	+	0.351904i
$297$	−26.3955	−	26.3955i	−1.53162	−	1.53162i
$298$		−	5.12261i		−	0.296745i
$299$	−6.15607			−0.356015
$300$	−3.04299	−	16.8114i	−0.175687	−	0.970605i
$301$	4.21305	+	4.21305i	0.242836	+	0.242836i
$302$		−	20.3046i		−	1.16840i
$303$	2.36165	−	2.36165i	0.135673	−	0.135673i
$304$	3.22623	−	3.22623i	0.185037	−	0.185037i
$305$	−4.64444	−	8.87270i	−0.265940	−	0.508049i
$306$	31.5365			1.80282
$307$	−12.4671	+	12.4671i	−0.711533	+	0.711533i	−0.966856	−	0.255323i	$-0.917818\pi$
$307$	−12.4671	+	12.4671i	−0.711533	+	0.711533i	0.255323	+	0.966856i	$0.417818\pi$
$308$	1.68552	−	1.68552i	0.0960414	−	0.0960414i
$309$	27.4358	−	27.4358i	1.56077	−	1.56077i
$310$	1.37337	+	2.62367i	0.0780021	+	0.149014i
$311$	−16.0489	+	16.0489i	−0.910048	+	0.910048i	−0.996275	−	0.0862278i	$-0.972519\pi$
$311$	−16.0489	+	16.0489i	−0.910048	+	0.910048i	0.0862278	+	0.996275i	$0.472519\pi$
$312$	−7.38603	−	7.38603i	−0.418152	−	0.418152i
$313$	16.5993			0.938246			0.469123	−	0.883133i	$-0.344570\pi$
$313$	16.5993			0.938246			0.469123	+	0.883133i	$0.344570\pi$
$314$	9.36950	+	9.36950i	0.528751	+	0.528751i
$315$	−11.1400	−	21.2818i	−0.627671	−	1.19910i
$316$	4.19139	−	4.19139i	0.235784	−	0.235784i
$317$	−2.57082	+	2.57082i	−0.144391	+	0.144391i	−0.775607	−	0.631216i	$-0.782556\pi$
$317$	−2.57082	+	2.57082i	−0.144391	+	0.144391i	0.631216	+	0.775607i	$0.282556\pi$
$318$	18.8206			1.05541
$319$	−9.27667	+	9.27667i	−0.519394	+	0.519394i
$320$	0.667560	−	2.13410i	0.0373177	−	0.119300i
$321$		−	21.6416i		−	1.20791i
$322$	−1.76328	−	1.76328i	−0.0982639	−	0.0982639i
$323$	11.7280	+	11.7280i	0.652564	+	0.652564i
$324$	−40.2348			−2.23527
$325$	−12.5603	−	8.71017i	−0.696719	−	0.483153i
$326$		−	21.6389i		−	1.19847i
$327$	34.7322			1.92070
$328$			12.7650i			0.704829i
$329$			10.2608i			0.565694i
$330$	−6.82079	−	13.0304i	−0.375472	−	0.717299i
$331$	4.43217	+	4.43217i	0.243614	+	0.243614i	0.818344	−	0.574729i	$-0.194893\pi$
$331$	4.43217	+	4.43217i	0.243614	+	0.243614i	−0.574729	+	0.818344i	$0.694893\pi$
$332$	−7.79493	+	7.79493i	−0.427802	+	0.427802i
$333$	52.5235	−	5.09179i	2.87827	−	0.279029i
$334$			15.0063i			0.821108i
$335$	5.45106	+	10.4137i	0.297823	+	0.568959i
$336$		−	4.23116i		−	0.230829i
$337$	−15.7372	+	15.7372i	−0.857261	+	0.857261i	−0.991015	−	0.133753i	$-0.957297\pi$
$337$	−15.7372	+	15.7372i	−0.857261	+	0.857261i	0.133753	+	0.991015i	$0.457297\pi$
$338$	3.65489			0.198800
$339$	−8.39678	+	8.39678i	−0.456050	+	0.456050i
$340$	7.75787	+	2.42672i	0.420730	+	0.131607i
$341$	1.80268	+	1.80268i	0.0976205	+	0.0976205i
$342$	−27.9885	−	27.9885i	−1.51344	−	1.51344i
$343$	−10.9159	+	10.9159i	−0.589402	+	0.589402i
$344$	4.81157			0.259422
$345$	−13.6315	+	7.13548i	−0.733898	+	0.384161i
$346$	3.27813	+	3.27813i	0.176233	+	0.176233i
$347$	−8.61447			−0.462449			−0.231225	−	0.972900i	$-0.574273\pi$
$347$	−8.61447			−0.462449			−0.231225	+	0.972900i	$0.574273\pi$
$348$			23.2872i			1.24833i
$349$		−	6.48449i		−	0.347107i	−0.984824	−	0.173553i	$-0.944475\pi$
$349$		−	6.48449i		−	0.347107i	0.984824	−	0.173553i	$-0.0555249\pi$
$350$	−1.10279	−	6.09249i	−0.0589466	−	0.325657i
$351$	−41.9179	+	41.9179i	−2.23741	+	2.23741i
$352$		−	1.92497i		−	0.102601i
$353$			7.88401i			0.419624i	0.977742	+	0.209812i	$0.0672851\pi$
$353$			7.88401i			0.419624i	−0.977742	+	0.209812i	$0.932715\pi$
$354$	15.7069			0.834811
$355$	−2.60688	+	8.33382i	−0.138359	+	0.442313i
$356$	−7.79425	−	7.79425i	−0.413094	−	0.413094i
$357$	15.3811			0.814055
$358$	−15.3991	−	15.3991i	−0.813865	−	0.813865i
$359$			22.1603i			1.16958i	0.811186	+	0.584789i	$0.198823\pi$
$359$			22.1603i			1.16958i	−0.811186	+	0.584789i	$0.801177\pi$
$360$	−18.5139	−	5.79128i	−0.975768	−	0.305227i
$361$		−	1.81711i		−	0.0956373i
$362$	−8.69492			−0.456995
$363$	17.6244	+	17.6244i	0.925041	+	0.925041i
$364$	−2.67672	−	2.67672i	−0.140298	−	0.140298i
$365$	24.0320	−	12.5796i	1.25789	−	0.658447i
$366$	−15.3035			−0.799925
$367$	−24.3406	−	24.3406i	−1.27057	−	1.27057i	−0.945791	−	0.324776i	$-0.894711\pi$
$367$	−24.3406	−	24.3406i	−1.27057	−	1.27057i	−0.324776	−	0.945791i	$-0.605289\pi$
$368$	−2.01378			−0.104975
$369$	110.740			5.76490
$370$	13.3124	+	2.78910i	0.692081	+	0.144998i
$371$	6.82064			0.354110
$372$	4.52526			0.234624
$373$	−10.9227	−	10.9227i	−0.565556	−	0.565556i	0.365324	−	0.930880i	$-0.380958\pi$
$373$	−10.9227	−	10.9227i	−0.565556	−	0.565556i	−0.930880	+	0.365324i	$0.880958\pi$
$374$	6.99765			0.361840
$375$	−37.9085	−	4.72857i	−1.95758	−	0.244182i
$376$	5.85922	+	5.85922i	0.302166	+	0.302166i
$377$	14.7320	+	14.7320i	0.758735	+	0.758735i
$378$	−24.0131			−1.23510
$379$		−	0.495224i		−	0.0254380i	−0.999919	−	0.0127190i	$-0.995951\pi$
$379$		−	0.495224i		−	0.0254380i	0.999919	−	0.0127190i	$-0.00404869\pi$
$380$	−4.73138	−	9.03878i	−0.242715	−	0.463680i
$381$			27.8069i			1.42459i
$382$	−2.73993	−	2.73993i	−0.140187	−	0.140187i
$383$	14.8669			0.759661			0.379831	−	0.925056i	$-0.375982\pi$
$383$	14.8669			0.759661			0.379831	+	0.925056i	$0.375982\pi$
$384$	−2.41612	−	2.41612i	−0.123297	−	0.123297i
$385$	−2.47187	−	4.72224i	−0.125978	−	0.240668i
$386$	12.4758			0.635003
$387$		−	41.7417i		−	2.12185i
$388$		−	14.8936i		−	0.756106i
$389$	16.3839	−	16.3839i	0.830695	−	0.830695i	−0.156917	−	0.987612i	$-0.550155\pi$
$389$	16.3839	−	16.3839i	0.830695	−	0.830695i	0.987612	+	0.156917i	$0.0501555\pi$
$390$	−20.6931	+	10.8319i	−1.04784	+	0.548493i
$391$		−	7.32049i		−	0.370213i
$392$			5.46662i			0.276106i
$393$	9.51529			0.479983
$394$	−2.72212	−	2.72212i	−0.137139	−	0.137139i
$395$	−6.14682	−	11.7428i	−0.309280	−	0.590846i
$396$	−16.6997			−0.839189
$397$	16.3508	−	16.3508i	0.820621	−	0.820621i	−0.165576	−	0.986197i	$-0.552948\pi$
$397$	16.3508	−	16.3508i	0.820621	−	0.820621i	0.986197	+	0.165576i	$0.0529483\pi$
$398$	5.62070	+	5.62070i	0.281740	+	0.281740i
$399$	−13.6507	−	13.6507i	−0.683389	−	0.683389i
$400$	−4.10873	−	2.84927i	−0.205436	−	0.142464i
$401$	1.61742	−	1.61742i	0.0807703	−	0.0807703i	−0.665567	−	0.746338i	$-0.731810\pi$
$401$	1.61742	−	1.61742i	0.0807703	−	0.0807703i	0.746338	+	0.665567i	$0.231810\pi$
$402$	17.9613			0.895828
$403$	2.86277	−	2.86277i	0.142605	−	0.142605i
$404$		−	0.977455i		−	0.0486302i
$405$	−26.8592	+	85.8649i	−1.33464	+	4.26666i
$406$			8.43935i			0.418838i
$407$	11.6545	−	1.12982i	0.577691	−	0.0560032i
$408$	8.78310	−	8.78310i	0.434828	−	0.434828i
$409$	4.96548	+	4.96548i	0.245527	+	0.245527i	0.819132	−	0.573605i	$-0.194456\pi$
$409$	4.96548	+	4.96548i	0.245527	+	0.245527i	−0.573605	+	0.819132i	$0.694456\pi$
$410$	27.2417	+	8.52140i	1.34537	+	0.420842i
$411$			37.8515i			1.86708i
$412$		−	11.3553i		−	0.559437i
$413$	5.69222			0.280096
$414$			17.4701i			0.858609i
$415$	11.4315	+	21.8387i	0.561152	+	1.07202i
$416$	−3.05698			−0.149881
$417$	1.63834	+	1.63834i	0.0802298	+	0.0802298i
$418$	−6.21039	−	6.21039i	−0.303760	−	0.303760i
$419$		−	5.39563i		−	0.263594i	−0.991277	−	0.131797i	$-0.957925\pi$
$419$		−	5.39563i		−	0.263594i	0.991277	−	0.131797i	$-0.0420747\pi$
$420$	−9.02969	−	2.82455i	−0.440604	−	0.137824i
$421$	1.76092	−	1.76092i	0.0858222	−	0.0858222i	−0.662892	−	0.748715i	$-0.730671\pi$
$421$	1.76092	−	1.76092i	0.0858222	−	0.0858222i	0.748715	+	0.662892i	$0.230671\pi$
$422$	−25.2888			−1.23104
$423$	50.8304	−	50.8304i	2.47146	−	2.47146i
$424$	3.89480	−	3.89480i	0.189148	−	0.189148i
$425$	10.3577	−	14.9361i	0.502422	−	0.724506i
$426$	9.43516	+	9.43516i	0.457135	+	0.457135i
$427$	−5.54602			−0.268391
$428$	−4.47857	−	4.47857i	−0.216480	−	0.216480i
$429$	−14.2179	+	14.2179i	−0.686445	+	0.686445i
$430$	3.21201	−	10.2683i	0.154897	−	0.495183i
$431$	−7.96389	+	7.96389i	−0.383607	+	0.383607i	−0.872400	−	0.488793i	$-0.837437\pi$
$431$	−7.96389	+	7.96389i	−0.383607	+	0.383607i	0.488793	+	0.872400i	$0.337437\pi$
$432$	−13.7122	+	13.7122i	−0.659728	+	0.659728i
$433$	3.23648	−	3.23648i	0.155535	−	0.155535i	−0.625050	−	0.780585i	$-0.714921\pi$
$433$	3.23648	−	3.23648i	0.155535	−	0.155535i	0.780585	+	0.625050i	$0.214921\pi$
$434$	1.63997			0.0787209
$435$	49.6971	+	15.5456i	2.38279	+	0.745355i
$436$	7.18760	−	7.18760i	0.344223	−	0.344223i
$437$	−6.49691	+	6.49691i	−0.310789	+	0.310789i
$438$		−	41.4499i		−	1.98055i
$439$	1.43898	+	1.43898i	0.0686789	+	0.0686789i	0.740612	−	0.671933i	$-0.234536\pi$
$439$	1.43898	+	1.43898i	0.0686789	+	0.0686789i	−0.671933	+	0.740612i	$0.734536\pi$
$440$	−4.10806	−	1.28503i	−0.195844	−	0.0612615i
$441$	47.4245			2.25831
$442$		−	11.1127i		−	0.528579i
$443$	−19.8400	−	19.8400i	−0.942626	−	0.942626i	0.0558147	−	0.998441i	$-0.482224\pi$
$443$	−19.8400	−	19.8400i	−0.942626	−	0.942626i	−0.998441	+	0.0558147i	$0.982224\pi$
$444$	13.2100	−	16.0462i	0.626920	−	0.761520i
$445$	−21.8368	+	11.4305i	−1.03516	+	0.541859i
$446$	16.8265	−	16.8265i	0.796758	−	0.796758i
$447$	−12.3768	+	12.3768i	−0.585404	+	0.585404i
$448$	−0.875609	−	0.875609i	−0.0413686	−	0.0413686i
$449$	−13.4394	+	13.4394i	−0.634247	+	0.634247i	−0.949130	−	0.314884i	$-0.898034\pi$
$449$	−13.4394	+	13.4394i	−0.634247	+	0.634247i	0.314884	+	0.949130i	$0.398034\pi$
$450$	−24.7183	+	35.6444i	−1.16523	+	1.68029i
$451$	24.5722			1.15706
$452$			3.47531i			0.163465i
$453$	−49.0583	+	49.0583i	−2.30496	+	2.30496i
$454$			13.3976i			0.628782i
$455$	−7.49924	+	3.92550i	−0.351570	+	0.184030i
$456$	−15.5899			−0.730065
$457$		−	0.134698i		−	0.00630090i	−0.999995	−	0.00315045i	$-0.998997\pi$
$457$		−	0.134698i		−	0.00630090i	0.999995	−	0.00315045i	$-0.00100282\pi$
$458$		−	12.4697i		−	0.582669i
$459$	−49.8466	−	49.8466i	−2.32664	−	2.32664i
$460$	−1.34432	+	4.29759i	−0.0626791	+	0.200376i
$461$	7.52644	+	7.52644i	0.350541	+	0.350541i	0.860311	−	0.509770i	$-0.170269\pi$
$461$	7.52644	+	7.52644i	0.350541	+	0.350541i	−0.509770	+	0.860311i	$0.670269\pi$
$462$	−8.14484			−0.378932
$463$	−19.4799			−0.905306			−0.452653	−	0.891687i	$-0.649522\pi$
$463$	−19.4799			−0.905306			−0.452653	+	0.891687i	$0.649522\pi$
$464$	4.81913	+	4.81913i	0.223722	+	0.223722i
$465$	3.02088	−	9.65734i	0.140090	−	0.447848i
$466$	−11.3131	−	11.3131i	−0.524068	−	0.524068i
$467$		−	4.43682i		−	0.205312i	−0.994717	−	0.102656i	$-0.967266\pi$
$467$		−	4.43682i		−	0.205312i	0.994717	−	0.102656i	$-0.0327340\pi$
$468$			26.5202i			1.22590i
$469$	6.50922			0.300568
$470$	16.4155	−	8.59275i	0.757191	−	0.396354i
$471$		−	45.2757i		−	2.08619i
$472$	3.25043	−	3.25043i	0.149613	−	0.149613i
$473$		−	9.26211i		−	0.425872i
$474$	−20.2538			−0.930288
$475$	−22.4481	+	4.06329i	−1.02999	+	0.186436i
$476$	3.18302	−	3.18302i	0.145893	−	0.145893i
$477$	−33.7885	−	33.7885i	−1.54707	−	1.54707i
$478$	−9.77163	+	9.77163i	−0.446944	+	0.446944i
$479$	10.5292	−	10.5292i	0.481093	−	0.481093i	−0.424387	−	0.905481i	$-0.639510\pi$
$479$	10.5292	−	10.5292i	0.481093	−	0.481093i	0.905481	+	0.424387i	$0.139510\pi$
$480$	−6.76914	+	3.54333i	−0.308968	+	0.161730i
$481$	−1.79423	−	18.5081i	−0.0818100	−	0.843897i
$482$	−2.61835	−	2.61835i	−0.119262	−	0.119262i
$483$			8.52061i			0.387701i
$484$	7.29450			0.331568
$485$	−31.7843	−	9.94235i	−1.44325	−	0.451459i
$486$	56.0756	+	56.0756i	2.54364	+	2.54364i
$487$		−	9.78190i		−	0.443260i	−0.975131	−	0.221630i	$-0.928862\pi$
$487$		−	9.78190i		−	0.443260i	0.975131	−	0.221630i	$-0.0711377\pi$
$488$	−3.16695	+	3.16695i	−0.143361	+	0.143361i
$489$	−52.2822	+	52.2822i	−2.36428	+	2.36428i
$490$	11.6663	+	3.64929i	0.527029	+	0.164858i
$491$	−9.56888			−0.431837			−0.215919	−	0.976411i	$-0.569275\pi$
$491$	−9.56888			−0.431837			−0.215919	+	0.976411i	$0.569275\pi$
$492$	30.8418	−	30.8418i	1.39046	−	1.39046i
$493$	−17.5185	+	17.5185i	−0.788995	+	0.788995i
$494$	−9.86251	+	9.86251i	−0.443735	+	0.443735i
$495$	−11.1480	+	35.6387i	−0.501066	+	1.60184i
$496$	0.936472	−	0.936472i	0.0420488	−	0.0420488i
$497$	3.41933	+	3.41933i	0.153378	+	0.153378i
$498$	37.6670			1.68790
$499$	13.9261	+	13.9261i	0.623418	+	0.623418i	0.946404	−	0.322986i	$-0.104687\pi$
$499$	13.9261	+	13.9261i	0.623418	+	0.623418i	−0.322986	+	0.946404i	$0.604687\pi$
$500$	−8.82344	+	6.86635i	−0.394596	+	0.307073i
$501$	36.2570	−	36.2570i	1.61984	−	1.61984i
$502$	1.40191	−	1.40191i	0.0625704	−	0.0625704i
$503$	−0.0190379			−0.000848857			−0.000424428	−	1.00000i	$-0.500135\pi$
$503$	−0.0190379			−0.000848857			−0.000424428		1.00000i	$0.500135\pi$
$504$	−7.59617	+	7.59617i	−0.338360	+	0.338360i
$505$	−2.08598	−	0.652510i	−0.0928250	−	0.0290363i
$506$			3.87646i			0.172330i
$507$	−8.83066	−	8.83066i	−0.392183	−	0.392183i
$508$	5.75444	+	5.75444i	0.255312	+	0.255312i
$509$	−13.1961			−0.584908			−0.292454	−	0.956280i	$-0.594472\pi$
$509$	−13.1961			−0.584908			−0.292454	+	0.956280i	$0.594472\pi$
$510$	−12.8807	−	24.6072i	−0.570368	−	1.08963i
$511$		−	15.0216i		−	0.664515i
$512$	−1.00000			−0.0441942
$513$			88.4774i			3.90637i
$514$		−	26.1658i		−	1.15413i
$515$	−24.2333	−	7.58036i	−1.06785	−	0.334031i
$516$	−11.6253	−	11.6253i	−0.511777	−	0.511777i
$517$	11.2788	−	11.2788i	0.496041	−	0.496041i
$518$	4.78735	−	5.81519i	0.210344	−	0.255505i
$519$		−	15.8407i		−	0.695330i
$520$	−2.04072	+	6.52388i	−0.0894913	+	0.286091i
$521$			15.1816i			0.665117i	0.943083	+	0.332559i	$0.107912\pi$
$521$			15.1816i			0.665117i	−0.943083	+	0.332559i	$0.892088\pi$
$522$	41.8074	−	41.8074i	1.82986	−	1.82986i
$523$	−6.40480			−0.280062			−0.140031	−	0.990147i	$-0.544720\pi$
$523$	−6.40480			−0.280062			−0.140031	+	0.990147i	$0.544720\pi$
$524$	1.96912	−	1.96912i	0.0860216	−	0.0860216i
$525$	−12.0557	+	17.3847i	−0.526155	+	0.758729i
$526$	−11.7781	−	11.7781i	−0.513547	−	0.513547i
$527$	3.40427	+	3.40427i	0.148292	+	0.148292i
$528$	−4.65096	+	4.65096i	−0.202407	+	0.202407i
$529$	−18.9447			−0.823683
$530$	−5.71186	−	10.9119i	−0.248107	−	0.473982i
$531$	−28.1984	−	28.1984i	−1.22371	−	1.22371i
$532$	−5.64983			−0.244951
$533$		−	39.0223i		−	1.69024i
$534$			37.6637i			1.62987i
$535$	−12.5474	+	6.56798i	−0.542472	+	0.283959i
$536$	3.71697	−	3.71697i	0.160549	−	0.160549i
$537$			74.4120i			3.21111i
$538$		−	0.0307805i		−	0.00132704i
$539$	10.5231			0.453260
$540$	20.1094	+	38.4169i	0.865372	+	1.65320i
$541$	2.84624	+	2.84624i	0.122369	+	0.122369i	0.765639	−	0.643270i	$-0.222423\pi$
$541$	2.84624	+	2.84624i	0.122369	+	0.122369i	−0.643270	+	0.765639i	$0.722423\pi$
$542$	29.5640			1.26988
$543$	21.0080	+	21.0080i	0.901539	+	0.901539i
$544$		−	3.63520i		−	0.155858i
$545$	−10.5409	−	20.1372i	−0.451521	−	0.862582i
$546$			12.9346i			0.553548i
$547$	11.8169			0.505253			0.252627	−	0.967564i	$-0.418706\pi$
$547$	11.8169			0.505253			0.252627	+	0.967564i	$0.418706\pi$
$548$	7.83311	+	7.83311i	0.334614	+	0.334614i
$549$	27.4742	+	27.4742i	1.17257	+	1.17257i
$550$	−5.48476	+	7.90917i	−0.233871	+	0.337248i
$551$	31.0952			1.32470
$552$	4.86553	+	4.86553i	0.207091	+	0.207091i
$553$	−7.34004			−0.312130
$554$	4.25124			0.180618
$555$	−25.4257	−	38.9033i	−1.07926	−	1.65135i
$556$	0.678086			0.0287572
$557$	46.6368			1.97607			0.988033	−	0.154245i	$-0.0492944\pi$
$557$	46.6368			1.97607			0.988033	+	0.154245i	$0.0492944\pi$
$558$	−8.12416	−	8.12416i	−0.343923	−	0.343923i
$559$	−14.7089			−0.622118
$560$	−2.45316	+	1.28411i	−0.103665	+	0.0542636i
$561$	−16.9072	−	16.9072i	−0.713822	−	0.713822i
$562$	18.2679	+	18.2679i	0.770584	+	0.770584i
$563$	18.5082			0.780030			0.390015	−	0.920809i	$-0.372470\pi$
$563$	18.5082			0.780030			0.390015	+	0.920809i	$0.372470\pi$
$564$		−	28.3132i		−	1.19220i
$565$	7.41665	+	2.31998i	0.312021	+	0.0976023i
$566$		−	2.36072i		−	0.0992283i
$567$	35.2300	+	35.2300i	1.47952	+	1.47952i
$568$	3.90508			0.163854
$569$	−10.7292	−	10.7292i	−0.449790	−	0.449790i	0.445495	−	0.895285i	$-0.353028\pi$
$569$	−10.7292	−	10.7292i	−0.449790	−	0.449790i	−0.895285	+	0.445495i	$0.853028\pi$
$570$	−10.4072	+	33.2704i	−0.435910	+	1.39354i
$571$	0.731150			0.0305977			0.0152988	−	0.999883i	$-0.495130\pi$
$571$	0.731150			0.0305977			0.0152988	+	0.999883i	$0.495130\pi$
$572$			5.88458i			0.246047i
$573$			13.2400i			0.553110i
$574$	11.1772	−	11.1772i	0.466525	−	0.466525i
$575$	8.27406	+	5.73780i	0.345052	+	0.239283i
$576$			8.67529i			0.361470i
$577$		−	9.84843i		−	0.409995i	−0.978762	−	0.204998i	$-0.934281\pi$
$577$		−	9.84843i		−	0.409995i	0.978762	−	0.204998i	$-0.0657187\pi$
$578$	−3.78529			−0.157447
$579$	−30.1431	−	30.1431i	−1.25271	−	1.25271i
$580$	13.5015	−	7.06742i	0.560621	−	0.293459i
$581$	13.6506			0.566323
$582$	−35.9847	+	35.9847i	−1.49161	+	1.49161i
$583$	−7.49736	−	7.49736i	−0.310509	−	0.310509i
$584$	−8.57777	−	8.57777i	−0.354951	−	0.354951i
$585$	56.5966	+	17.7038i	2.33998	+	0.731962i
$586$	−10.6576	+	10.6576i	−0.440263	+	0.440263i
$587$	3.62231			0.149509			0.0747544	−	0.997202i	$-0.476183\pi$
$587$	3.62231			0.149509			0.0747544	+	0.997202i	$0.476183\pi$
$588$	13.2080	−	13.2080i	0.544689	−	0.544689i
$589$		−	6.04254i		−	0.248979i
$590$	−4.76687	−	9.10659i	−0.196249	−	0.374912i
$591$			13.1540i			0.541082i
$592$	−0.586931	−	6.05438i	−0.0241227	−	0.248833i
$593$	24.4083	−	24.4083i	1.00233	−	1.00233i	0.00233126	−	0.999997i	$-0.499258\pi$
$593$	24.4083	−	24.4083i	1.00233	−	1.00233i	0.999997	−	0.00233126i	$-0.000742064\pi$
$594$	26.3955	+	26.3955i	1.08302	+	1.08302i
$595$	−4.66801	−	8.91772i	−0.191370	−	0.365591i
$596$			5.12261i			0.209830i
$597$		−	27.1606i		−	1.11161i
$598$	6.15607			0.251741
$599$			10.0741i			0.411615i	0.978592	+	0.205808i	$0.0659821\pi$
$599$			10.0741i			0.411615i	−0.978592	+	0.205808i	$0.934018\pi$
$600$	3.04299	+	16.8114i	0.124230	+	0.686322i
$601$	16.4771			0.672116			0.336058	−	0.941841i	$-0.390906\pi$
$601$	16.4771			0.672116			0.336058	+	0.941841i	$0.390906\pi$
$602$	−4.21305	−	4.21305i	−0.171711	−	0.171711i
$603$	−32.2458	−	32.2458i	−1.31315	−	1.31315i
$604$			20.3046i			0.826181i
$605$	4.86952	−	15.5672i	0.197974	−	0.632895i
$606$	−2.36165	+	2.36165i	−0.0959355	+	0.0959355i
$607$	45.5231			1.84772			0.923862	−	0.382726i	$-0.125015\pi$
$607$	45.5231			1.84772			0.923862	+	0.382726i	$0.125015\pi$
$608$	−3.22623	+	3.22623i	−0.130841	+	0.130841i
$609$	20.3905	−	20.3905i	0.826265	−	0.826265i
$610$	4.64444	+	8.87270i	0.188048	+	0.359245i
$611$	−17.9115	−	17.9115i	−0.724621	−	0.724621i
$612$	−31.5365			−1.27479
$613$	17.4896	+	17.4896i	0.706398	+	0.706398i	0.965776	−	0.259378i	$-0.0835176\pi$
$613$	17.4896	+	17.4896i	0.706398	+	0.706398i	−0.259378	+	0.965776i	$0.583518\pi$
$614$	12.4671	−	12.4671i	0.503130	−	0.503130i
$615$	−45.2306	−	86.4081i	−1.82387	−	3.48431i
$616$	−1.68552	+	1.68552i	−0.0679115	+	0.0679115i
$617$	4.01386	−	4.01386i	0.161592	−	0.161592i	−0.621680	−	0.783272i	$-0.713549\pi$
$617$	4.01386	−	4.01386i	0.161592	−	0.161592i	0.783272	+	0.621680i	$0.213549\pi$
$618$	−27.4358	+	27.4358i	−1.10363	+	1.10363i
$619$	−4.28932			−0.172402			−0.0862012	−	0.996278i	$-0.527473\pi$
$619$	−4.28932			−0.172402			−0.0862012	+	0.996278i	$0.527473\pi$
$620$	−1.37337	−	2.62367i	−0.0551558	−	0.105369i
$621$	27.6133	−	27.6133i	1.10808	−	1.10808i
$622$	16.0489	−	16.0489i	0.643501	−	0.643501i
$623$			13.6494i			0.546853i
$624$	7.38603	+	7.38603i	0.295678	+	0.295678i
$625$	8.76328	+	23.4138i	0.350531	+	0.936551i
$626$	−16.5993			−0.663440
$627$			30.0101i			1.19849i
$628$	−9.36950	−	9.36950i	−0.373884	−	0.373884i
$629$	22.0089	−	2.13361i	0.877553	−	0.0850727i
$630$	11.1400	+	21.2818i	0.443830	+	0.847889i
$631$	7.95854	−	7.95854i	0.316825	−	0.316825i	−0.530722	−	0.847546i	$-0.678079\pi$
$631$	7.95854	−	7.95854i	0.316825	−	0.316825i	0.847546	+	0.530722i	$0.178079\pi$
$632$	−4.19139	+	4.19139i	−0.166724	+	0.166724i
$633$	61.1008	+	61.1008i	2.42854	+	2.42854i
$634$	2.57082	−	2.57082i	0.102100	−	0.102100i
$635$	16.1220	−	8.43910i	0.639781	−	0.334895i
$636$	−18.8206			−0.746285
$637$		−	16.7113i		−	0.662127i
$638$	9.27667	−	9.27667i	0.367267	−	0.367267i
$639$		−	33.8777i		−	1.34018i
$640$	−0.667560	+	2.13410i	−0.0263876	+	0.0843575i
$641$	20.2510			0.799866			0.399933	−	0.916544i	$-0.369033\pi$
$641$	20.2510			0.799866			0.399933	+	0.916544i	$0.369033\pi$
$642$			21.6416i			0.854124i
$643$			27.6440i			1.09017i	0.838379	+	0.545087i	$0.183503\pi$
$643$			27.6440i			1.09017i	−0.838379	+	0.545087i	$0.816497\pi$
$644$	1.76328	+	1.76328i	0.0694831	+	0.0694831i
$645$	−32.5702	+	17.0490i	−1.28245	+	0.671302i
$646$	−11.7280	−	11.7280i	−0.461432	−	0.461432i
$647$	21.7566			0.855342			0.427671	−	0.903934i	$-0.359334\pi$
$647$	21.7566			0.855342			0.427671	+	0.903934i	$0.359334\pi$
$648$	40.2348			1.58057
$649$	−6.25698	−	6.25698i	−0.245608	−	0.245608i
$650$	12.5603	+	8.71017i	0.492655	+	0.341641i
$651$	−3.96236	−	3.96236i	−0.155297	−	0.155297i
$652$			21.6389i			0.847445i
$653$		−	15.8716i		−	0.621105i	−0.950556	−	0.310553i	$-0.899486\pi$
$653$		−	15.8716i		−	0.621105i	0.950556	−	0.310553i	$-0.100514\pi$
$654$	−34.7322			−1.35814
$655$	−2.88779	−	5.51681i	−0.112835	−	0.215559i
$656$		−	12.7650i		−	0.498390i
$657$	−74.4147	+	74.4147i	−2.90319	+	2.90319i
$658$		−	10.2608i		−	0.400006i
$659$	−33.4745			−1.30398			−0.651990	−	0.758227i	$-0.726066\pi$
$659$	−33.4745			−1.30398			−0.651990	+	0.758227i	$0.726066\pi$
$660$	6.82079	+	13.0304i	0.265499	+	0.507207i
$661$	−33.1517	+	33.1517i	−1.28945	+	1.28945i	−0.354333	+	0.935119i	$0.615292\pi$
$661$	−33.1517	+	33.1517i	−1.28945	+	1.28945i	−0.935119	+	0.354333i	$0.884708\pi$
$662$	−4.43217	−	4.43217i	−0.172261	−	0.172261i
$663$	−26.8497	+	26.8497i	−1.04276	+	1.04276i
$664$	7.79493	−	7.79493i	0.302502	−	0.302502i
$665$	−3.77160	+	12.0573i	−0.146256	+	0.467561i
$666$	−52.5235	+	5.09179i	−2.03524	+	0.197303i
$667$	−9.70465	−	9.70465i	−0.375766	−	0.375766i
$668$		−	15.0063i		−	0.580611i
$669$	−81.3098			−3.14362
$670$	−5.45106	−	10.4137i	−0.210593	−	0.402315i
$671$	6.09627	+	6.09627i	0.235344	+	0.235344i
$672$			4.23116i			0.163220i
$673$	8.36499	−	8.36499i	0.322447	−	0.322447i	−0.527258	−	0.849705i	$-0.676780\pi$
$673$	8.36499	−	8.36499i	0.322447	−	0.322447i	0.849705	+	0.527258i	$0.176780\pi$
$674$	15.7372	−	15.7372i	0.606175	−	0.606175i
$675$	95.4095	−	17.2699i	3.67231	−	0.664718i
$676$	−3.65489			−0.140573
$677$	−27.0712	+	27.0712i	−1.04043	+	1.04043i	−0.0412815	+	0.999148i	$0.513144\pi$
$677$	−27.0712	+	27.0712i	−1.04043	+	1.04043i	−0.999148	+	0.0412815i	$0.986856\pi$
$678$	8.39678	−	8.39678i	0.322476	−	0.322476i
$679$	−13.0409	+	13.0409i	−0.500466	+	0.500466i
$680$	−7.75787	−	2.42672i	−0.297501	−	0.0930604i
$681$	32.3703	−	32.3703i	1.24043	−	1.24043i
$682$	−1.80268	−	1.80268i	−0.0690281	−	0.0690281i
$683$	12.1368			0.464403			0.232202	−	0.972668i	$-0.425407\pi$
$683$	12.1368			0.464403			0.232202	+	0.972668i	$0.425407\pi$
$684$	27.9885	+	27.9885i	1.07017	+	1.07017i
$685$	21.9457	−	11.4875i	0.838501	−	0.438916i
$686$	10.9159	−	10.9159i	0.416770	−	0.416770i
$687$	−30.1282	+	30.1282i	−1.14946	+	1.14946i
$688$	−4.81157			−0.183439
$689$	−11.9063	+	11.9063i	−0.453594	+	0.453594i
$690$	13.6315	−	7.13548i	0.518944	−	0.271643i
$691$			16.8996i			0.642892i	0.946928	+	0.321446i	$0.104169\pi$
$691$			16.8996i			0.642892i	−0.946928	+	0.321446i	$0.895831\pi$
$692$	−3.27813	−	3.27813i	−0.124616	−	0.124616i
$693$	14.6224	+	14.6224i	0.555458	+	0.555458i
$694$	8.61447			0.327001
$695$	0.452663	−	1.44710i	0.0171705	−	0.0548916i
$696$		−	23.2872i		−	0.882699i
$697$	46.4034			1.75765
$698$			6.48449i			0.245441i
$699$			54.6675i			2.06771i
$700$	1.10279	+	6.09249i	0.0416815	+	0.230274i
$701$	−29.5313	−	29.5313i	−1.11538	−	1.11538i	−0.992410	−	0.122973i	$-0.960757\pi$
$701$	−29.5313	−	29.5313i	−1.11538	−	1.11538i	−0.122973	−	0.992410i	$-0.539243\pi$
$702$	41.9179	−	41.9179i	1.58209	−	1.58209i
$703$	−21.4264	−	17.6392i	−0.808112	−	0.665277i
$704$			1.92497i			0.0725499i
$705$	−60.4230	−	18.9007i	−2.27566	−	0.711843i
$706$		−	7.88401i		−	0.296719i
$707$	−0.855869	+	0.855869i	−0.0321882	+	0.0321882i
$708$	−15.7069			−0.590301
$709$	11.8999	−	11.8999i	0.446910	−	0.446910i	−0.447416	−	0.894326i	$-0.647656\pi$
$709$	11.8999	−	11.8999i	0.446910	−	0.446910i	0.894326	+	0.447416i	$0.147656\pi$
$710$	2.60688	−	8.33382i	0.0978344	−	0.312763i
$711$	36.3615	+	36.3615i	1.36366	+	1.36366i
$712$	7.79425	+	7.79425i	0.292102	+	0.292102i
$713$	−1.88585	+	1.88585i	−0.0706255	+	0.0706255i
$714$	−15.3811			−0.575624
$715$	12.5583	+	3.92831i	0.469652	+	0.146911i
$716$	15.3991	+	15.3991i	0.575490	+	0.575490i
$717$	47.2189			1.76342
$718$		−	22.1603i		−	0.827016i
$719$		−	27.9313i		−	1.04166i	−0.853660	−	0.520831i	$-0.825622\pi$
$719$		−	27.9313i		−	1.04166i	0.853660	−	0.520831i	$-0.174378\pi$
$720$	18.5139	+	5.79128i	0.689972	+	0.215828i
$721$	−9.94282	+	9.94282i	−0.370290	+	0.370290i
$722$			1.81711i			0.0676258i
$723$			12.6525i			0.470551i
$724$	8.69492			0.323144
$725$	−6.06947	−	33.5315i	−0.225414	−	1.24533i
$726$	−17.6244	−	17.6244i	−0.654103	−	0.654103i
$727$	9.97158			0.369825			0.184913	−	0.982755i	$-0.440800\pi$
$727$	9.97158			0.369825			0.184913	+	0.982755i	$0.440800\pi$
$728$	2.67672	+	2.67672i	0.0992058	+	0.0992058i
$729$		−	150.267i		−	5.56543i
$730$	−24.0320	+	12.5796i	−0.889463	+	0.465592i
$731$		−	17.4910i		−	0.646929i
$732$	15.3035			0.565632
$733$	13.0344	+	13.0344i	0.481437	+	0.481437i	0.905590	−	0.424154i	$-0.139428\pi$
$733$	13.0344	+	13.0344i	0.481437	+	0.481437i	−0.424154	+	0.905590i	$0.639428\pi$
$734$	24.3406	+	24.3406i	0.898426	+	0.898426i
$735$	−19.3700	−	37.0043i	−0.714474	−	1.36492i
$736$	2.01378			0.0742288
$737$	−7.15504	−	7.15504i	−0.263559	−	0.263559i
$738$	−110.740			−4.07640
$739$	18.8384			0.692982			0.346491	−	0.938053i	$-0.387373\pi$
$739$	18.8384			0.692982			0.346491	+	0.938053i	$0.387373\pi$
$740$	−13.3124	−	2.78910i	−0.489375	−	0.102529i
$741$	47.6581			1.75076
$742$	−6.82064			−0.250394
$743$	12.7095	+	12.7095i	0.466266	+	0.466266i	0.900703	−	0.434436i	$-0.143052\pi$
$743$	12.7095	+	12.7095i	0.466266	+	0.466266i	−0.434436	+	0.900703i	$0.643052\pi$
$744$	−4.52526			−0.165904
$745$	10.9321	+	3.41965i	0.400522	+	0.125286i
$746$	10.9227	+	10.9227i	0.399909	+	0.399909i
$747$	−67.6233	−	67.6233i	−2.47421	−	2.47421i
$748$	−6.99765			−0.255859
$749$			7.84296i			0.286575i
$750$	37.9085	+	4.72857i	1.38422	+	0.172663i
$751$			37.9745i			1.38571i	0.721077	+	0.692855i	$0.243647\pi$
$751$			37.9745i			1.38571i	−0.721077	+	0.692855i	$0.756353\pi$
$752$	−5.85922	−	5.85922i	−0.213664	−	0.213664i
$753$	−6.77438			−0.246872
$754$	−14.7320	−	14.7320i	−0.536507	−	0.536507i
$755$	43.3319	+	13.5545i	1.57701	+	0.493299i
$756$	24.0131			0.873346
$757$		−	11.5922i		−	0.421326i	−0.977559	−	0.210663i	$-0.932438\pi$
$757$		−	11.5922i		−	0.421326i	0.977559	−	0.210663i	$-0.0675623\pi$
$758$			0.495224i			0.0179874i
$759$	9.36599	−	9.36599i	0.339964	−	0.339964i
$760$	4.73138	+	9.03878i	0.171625	+	0.327871i
$761$			12.7639i			0.462692i	0.972871	+	0.231346i	$0.0743130\pi$
$761$			12.7639i			0.462692i	−0.972871	+	0.231346i	$0.925687\pi$
$762$		−	27.8069i		−	1.00734i
$763$	−12.5871			−0.455682
$764$	2.73993	+	2.73993i	0.0991274	+	0.0991274i
$765$	−21.0525	+	67.3018i	−0.761154	+	2.43330i
$766$	−14.8669			−0.537162
$767$	−9.93650	+	9.93650i	−0.358786	+	0.358786i
$768$	2.41612	+	2.41612i	0.0871843	+	0.0871843i
$769$	12.7912	+	12.7912i	0.461263	+	0.461263i	0.899069	−	0.437806i	$-0.144244\pi$
$769$	12.7912	+	12.7912i	0.461263	+	0.461263i	−0.437806	+	0.899069i	$0.644244\pi$
$770$	2.47187	+	4.72224i	0.0890802	+	0.170178i
$771$	−63.2198	+	63.2198i	−2.27681	+	2.27681i
$772$	−12.4758			−0.449015
$773$	38.5353	−	38.5353i	1.38602	−	1.38602i	0.552511	−	0.833505i	$-0.313670\pi$
$773$	38.5353	−	38.5353i	1.38602	−	1.38602i	0.833505	−	0.552511i	$-0.186330\pi$
$774$			41.7417i			1.50038i
$775$	−6.51597	+	1.17944i	−0.234061	+	0.0423668i
$776$			14.8936i			0.534648i
$777$	−25.6170	+	2.48340i	−0.919006	+	0.0890913i
$778$	−16.3839	+	16.3839i	−0.587390	+	0.587390i
$779$	−41.1828	−	41.1828i	−1.47553	−	1.47553i
$780$	20.6931	−	10.8319i	0.740932	−	0.387843i
$781$		−	7.51716i		−	0.268985i
$782$			7.32049i			0.261780i
$783$	−132.162			−4.72307
$784$		−	5.46662i		−	0.195236i
$785$	−26.2501	+	13.7407i	−0.936906	+	0.490427i
$786$	−9.51529			−0.339399
$787$	−7.52971	−	7.52971i	−0.268405	−	0.268405i	0.560052	−	0.828457i	$-0.310781\pi$
$787$	−7.52971	−	7.52971i	−0.268405	−	0.268405i	−0.828457	+	0.560052i	$0.810781\pi$
$788$	2.72212	+	2.72212i	0.0969717	+	0.0969717i
$789$			56.9144i			2.02621i
$790$	6.14682	+	11.7428i	0.218694	+	0.417791i
$791$	3.04302	−	3.04302i	0.108197	−	0.108197i
$792$	16.6997			0.593396
$793$	9.68129	−	9.68129i	0.343793	−	0.343793i
$794$	−16.3508	+	16.3508i	−0.580267	+	0.580267i
$795$	−12.5639	+	40.1650i	−0.445595	+	1.42450i
$796$	−5.62070	−	5.62070i	−0.199221	−	0.199221i
$797$	−13.6505			−0.483527			−0.241763	−	0.970335i	$-0.577726\pi$
$797$	−13.6505			−0.483527			−0.241763	+	0.970335i	$0.577726\pi$
$798$	13.6507	+	13.6507i	0.483229	+	0.483229i
$799$	21.2994	−	21.2994i	0.753520	−	0.753520i
$800$	4.10873	+	2.84927i	0.145265	+	0.100737i
$801$	67.6173	−	67.6173i	2.38914	−	2.38914i
$802$	−1.61742	+	1.61742i	−0.0571132	+	0.0571132i
$803$	−16.5119	+	16.5119i	−0.582694	+	0.582694i
$804$	−17.9613			−0.633446
$805$	4.94011	−	2.58592i	0.174116	−	0.0911416i
$806$	−2.86277	+	2.86277i	−0.100837	+	0.100837i
$807$	−0.0743695	+	0.0743695i	−0.00261793	+	0.00261793i
$808$			0.977455i			0.0343867i
$809$	−20.6169	−	20.6169i	−0.724852	−	0.724852i	0.244738	−	0.969589i	$-0.421298\pi$
$809$	−20.6169	−	20.6169i	−0.724852	−	0.724852i	−0.969589	+	0.244738i	$0.921298\pi$
$810$	26.8592	−	85.8649i	0.943734	−	3.01699i
$811$	−30.6782			−1.07726			−0.538629	−	0.842543i	$-0.681057\pi$
$811$	−30.6782			−1.07726			−0.538629	+	0.842543i	$0.681057\pi$
$812$		−	8.43935i		−	0.296163i
$813$	−71.4301	−	71.4301i	−2.50516	−	2.50516i
$814$	−11.6545	+	1.12982i	−0.408489	+	0.0396003i
$815$	46.1795	+	14.4453i	1.61760	+	0.505995i
$816$	−8.78310	+	8.78310i	−0.307470	+	0.307470i
$817$	−15.5232	+	15.5232i	−0.543089	+	0.543089i
$818$	−4.96548	−	4.96548i	−0.173614	−	0.173614i
$819$	23.2213	−	23.2213i	0.811418	−	0.811418i
$820$	−27.2417	−	8.52140i	−0.951323	−	0.297580i
$821$	−35.6007			−1.24247			−0.621236	−	0.783623i	$-0.713369\pi$
$821$	−35.6007			−1.24247			−0.621236	+	0.783623i	$0.713369\pi$
$822$		−	37.8515i		−	1.32022i
$823$	−17.1598	+	17.1598i	−0.598152	+	0.598152i	−0.939820	−	0.341669i	$-0.889008\pi$
$823$	−17.1598	+	17.1598i	−0.598152	+	0.598152i	0.341669	+	0.939820i	$0.389008\pi$
$824$			11.3553i			0.395581i
$825$	32.3614	−	5.85766i	1.12668	−	0.203938i
$826$	−5.69222			−0.198058
$827$			48.2686i			1.67847i	0.543773	+	0.839233i	$0.316995\pi$
$827$			48.2686i			1.67847i	−0.543773	+	0.839233i	$0.683005\pi$
$828$		−	17.4701i		−	0.607128i
$829$	−8.64595	−	8.64595i	−0.300286	−	0.300286i	0.540840	−	0.841126i	$-0.318107\pi$
$829$	−8.64595	−	8.64595i	−0.300286	−	0.300286i	−0.841126	+	0.540840i	$0.818107\pi$
$830$	−11.4315	−	21.8387i	−0.396794	−	0.758032i
$831$	−10.2715	−	10.2715i	−0.356315	−	0.356315i
$832$	3.05698			0.105982
$833$	19.8723			0.688533
$834$	−1.63834	−	1.63834i	−0.0567310	−	0.0567310i
$835$	−32.0249	−	10.0176i	−1.10827	−	0.346673i
$836$	6.21039	+	6.21039i	0.214791	+	0.214791i
$837$			25.6822i			0.887706i
$838$			5.39563i			0.186389i
$839$	47.6915			1.64649			0.823247	−	0.567683i	$-0.192160\pi$
$839$	47.6915			1.64649			0.823247	+	0.567683i	$0.192160\pi$
$840$	9.02969	+	2.82455i	0.311554	+	0.0974563i
$841$			17.4480i			0.601656i
$842$	−1.76092	+	1.76092i	−0.0606855	+	0.0606855i
$843$		−	88.2748i		−	3.04035i
$844$	25.2888			0.870477
$845$	−2.43986	+	7.79988i	−0.0839336	+	0.268324i
$846$	−50.8304	+	50.8304i	−1.74759	+	1.74759i
$847$	−6.38713	−	6.38713i	−0.219464	−	0.219464i
$848$	−3.89480	+	3.89480i	−0.133748	+	0.133748i
$849$	−5.70378	+	5.70378i	−0.195753	+	0.195753i
$850$	−10.3577	+	14.9361i	−0.355266	+	0.512303i
$851$	1.18195	+	12.1922i	0.0405166	+	0.417942i
$852$	−9.43516	−	9.43516i	−0.323243	−	0.323243i
$853$		−	40.0385i		−	1.37089i	−0.728123	−	0.685446i	$-0.759607\pi$
$853$		−	40.0385i		−	1.37089i	0.728123	−	0.685446i	$-0.240393\pi$
$854$	5.54602			0.189781
$855$	78.4141	−	41.0461i	2.68170	−	1.40375i
$856$	4.47857	+	4.47857i	0.153074	+	0.153074i
$857$		−	41.1784i		−	1.40663i	−0.710880	−	0.703313i	$-0.751703\pi$
$857$		−	41.1784i		−	1.40663i	0.710880	−	0.703313i	$-0.248297\pi$
$858$	14.2179	−	14.2179i	0.485390	−	0.485390i
$859$	8.32021	−	8.32021i	0.283882	−	0.283882i	−0.550773	−	0.834655i	$-0.685667\pi$
$859$	8.32021	−	8.32021i	0.283882	−	0.283882i	0.834655	+	0.550773i	$0.185667\pi$
$860$	−3.21201	+	10.2683i	−0.109529	+	0.350148i
$861$	−54.0107			−1.84068
$862$	7.96389	−	7.96389i	0.271251	−	0.271251i
$863$	22.5485	−	22.5485i	0.767558	−	0.767558i	−0.210118	−	0.977676i	$-0.567385\pi$
$863$	22.5485	−	22.5485i	0.767558	−	0.767558i	0.977676	+	0.210118i	$0.0673847\pi$
$864$	13.7122	−	13.7122i	0.466498	−	0.466498i
$865$	−9.18418	+	4.80749i	−0.312271	+	0.163459i
$866$	−3.23648	+	3.23648i	−0.109980	+	0.109980i
$867$	9.14571	+	9.14571i	0.310605	+	0.310605i
$868$	−1.63997			−0.0556641
$869$	8.06829	+	8.06829i	0.273698	+	0.273698i
$870$	−49.6971	−	15.5456i	−1.68489	−	0.527046i
$871$	−11.3627	+	11.3627i	−0.385010	+	0.385010i
$872$	−7.18760	+	7.18760i	−0.243403	+	0.243403i
$873$	129.206			4.37296
$874$	6.49691	−	6.49691i	0.219761	−	0.219761i
$875$	13.7381	+	1.71365i	0.464434	+	0.0579318i
$876$			41.4499i			1.40046i
$877$	3.60601	+	3.60601i	0.121766	+	0.121766i	0.765364	−	0.643598i	$-0.222559\pi$
$877$	3.60601	+	3.60601i	0.121766	+	0.121766i	−0.643598	+	0.765364i	$0.722559\pi$
$878$	−1.43898	−	1.43898i	−0.0485633	−	0.0485633i
$879$	51.5003			1.73706
$880$	4.10806	+	1.28503i	0.138483	+	0.0433184i
$881$			20.0135i			0.674272i	0.941456	+	0.337136i	$0.109458\pi$
$881$			20.0135i			0.674272i	−0.941456	+	0.337136i	$0.890542\pi$
$882$	−47.4245			−1.59687
$883$			37.3549i			1.25709i	0.777772	+	0.628547i	$0.216350\pi$
$883$			37.3549i			1.25709i	−0.777772	+	0.628547i	$0.783650\pi$
$884$			11.1127i			0.373762i
$885$	−10.4853	+	33.5200i	−0.352459	+	1.12676i
$886$	19.8400	+	19.8400i	0.666538	+	0.666538i
$887$	−4.51173	+	4.51173i	−0.151489	+	0.151489i	−0.778783	−	0.627294i	$-0.784163\pi$
$887$	−4.51173	+	4.51173i	−0.151489	+	0.151489i	0.627294	+	0.778783i	$0.284163\pi$
$888$	−13.2100	+	16.0462i	−0.443299	+	0.538476i
$889$		−	10.0773i		−	0.337981i
$890$	21.8368	−	11.4305i	0.731971	−	0.383152i
$891$		−	77.4507i		−	2.59470i
$892$	−16.8265	+	16.8265i	−0.563393	+	0.563393i
$893$	−37.8063			−1.26514
$894$	12.3768	−	12.3768i	0.413943	−	0.413943i
$895$	43.1428	−	22.5833i	1.44211	−	0.754875i
$896$	0.875609	+	0.875609i	0.0292521	+	0.0292521i
$897$	−14.8738	−	14.8738i	−0.496623	−	0.496623i
$898$	13.4394	−	13.4394i	0.448480	−	0.448480i
$899$	9.02596			0.301032
$900$	24.7183	−	35.6444i	0.823943	−	1.18815i
$901$	−14.1584	−	14.1584i	−0.471684	−	0.471684i
$902$	−24.5722			−0.818165
$903$			20.3585i			0.677488i
$904$		−	3.47531i		−	0.115587i
$905$	5.80438	−	18.5558i	0.192944	−	0.616815i
$906$	49.0583	−	49.0583i	1.62985	−	1.62985i
$907$			0.232515i			0.00772054i	0.999993	+	0.00386027i	$0.00122876\pi$
$907$			0.232515i			0.00772054i	−0.999993	+	0.00386027i	$0.998771\pi$
$908$		−	13.3976i		−	0.444616i
$909$	8.47971			0.281254
$910$	7.49924	−	3.92550i	0.248597	−	0.130129i
$911$	−6.50689	−	6.50689i	−0.215583	−	0.215583i	0.591051	−	0.806634i	$-0.298713\pi$
$911$	−6.50689	−	6.50689i	−0.215583	−	0.215583i	−0.806634	+	0.591051i	$0.798713\pi$
$912$	15.5899			0.516234
$913$	−15.0050	−	15.0050i	−0.496592	−	0.496592i
$914$			0.134698i			0.00445541i
$915$	10.2160	−	32.6591i	0.337730	−	1.07967i
$916$			12.4697i			0.412010i
$917$	−3.44837			−0.113875
$918$	49.8466	+	49.8466i	1.64518	+	1.64518i
$919$	6.29705	+	6.29705i	0.207721	+	0.207721i	0.803298	−	0.595577i	$-0.203077\pi$
$919$	6.29705	+	6.29705i	0.207721	+	0.207721i	−0.595577	+	0.803298i	$0.703077\pi$
$920$	1.34432	−	4.29759i	0.0443208	−	0.141687i
$921$	−60.2439			−1.98510
$922$	−7.52644	−	7.52644i	−0.247870	−	0.247870i
$923$	−11.9377			−0.392936
$924$	8.14484			0.267946
$925$	−14.8390	+	26.5481i	−0.487905	+	0.872897i
$926$	19.4799			0.640148
$927$	98.5107			3.23552
$928$	−4.81913	−	4.81913i	−0.158196	−	0.158196i
$929$	−11.0828			−0.363615			−0.181807	−	0.983334i	$-0.558195\pi$
$929$	−11.0828			−0.363615			−0.181807	+	0.983334i	$0.558195\pi$
$930$	−3.02088	+	9.65734i	−0.0990586	+	0.316677i
$931$	−17.6366	−	17.6366i	−0.578015	−	0.578015i
$932$	11.3131	+	11.3131i	0.370572	+	0.370572i
$933$	−77.5520			−2.53894
$934$			4.43682i			0.145177i
$935$	−4.67135	+	14.9337i	−0.152770	+	0.488383i
$936$		−	26.5202i		−	0.866839i
$937$	−14.8946	−	14.8946i	−0.486587	−	0.486587i	0.420641	−	0.907227i	$-0.361805\pi$
$937$	−14.8946	−	14.8946i	−0.486587	−	0.486587i	−0.907227	+	0.420641i	$0.861805\pi$
$938$	−6.50922			−0.212534
$939$	40.1058	+	40.1058i	1.30880	+	1.30880i
$940$	−16.4155	+	8.59275i	−0.535415	+	0.280265i
$941$	−0.771288			−0.0251433			−0.0125716	−	0.999921i	$-0.504002\pi$
$941$	−0.771288			−0.0251433			−0.0125716	+	0.999921i	$0.504002\pi$
$942$			45.2757i			1.47516i
$943$			25.7059i			0.837098i
$944$	−3.25043	+	3.25043i	−0.105793	+	0.105793i
$945$	16.0302	−	51.2462i	0.521461	−	1.66704i
$946$			9.26211i			0.301137i
$947$		−	7.47998i		−	0.243067i	−0.992587	−	0.121533i	$-0.961219\pi$
$947$		−	7.47998i		−	0.243067i	0.992587	−	0.121533i	$-0.0387812\pi$
$948$	20.2538			0.657813
$949$	26.2221	+	26.2221i	0.851204	+	0.851204i
$950$	22.4481	−	4.06329i	0.728313	−	0.131830i
$951$	−12.4228			−0.402837
$952$	−3.18302	+	3.18302i	−0.103162	+	0.103162i
$953$	31.6255	+	31.6255i	1.02445	+	1.02445i	0.999693	+	0.0247571i	$0.00788124\pi$
$953$	31.6255	+	31.6255i	1.02445	+	1.02445i	0.0247571	+	0.999693i	$0.492119\pi$
$954$	33.7885	+	33.7885i	1.09394	+	1.09394i
$955$	7.67635	−	4.01821i	0.248401	−	0.130026i
$956$	9.77163	−	9.77163i	0.316037	−	0.316037i
$957$	−44.8271			−1.44905
$958$	−10.5292	+	10.5292i	−0.340184	+	0.340184i
$959$		−	13.7175i		−	0.442961i
$960$	6.76914	−	3.54333i	0.218473	−	0.114360i
$961$			29.2460i			0.943421i
$962$	1.79423	+	18.5081i	0.0578484	+	0.596725i
$963$	38.8529	−	38.8529i	1.25202	−	1.25202i
$964$	2.61835	+	2.61835i	0.0843313	+	0.0843313i
$965$	−8.32837	+	26.6246i	−0.268100	+	0.857077i
$966$		−	8.52061i		−	0.274146i
$967$			40.0061i			1.28651i	0.765652	+	0.643255i	$0.222416\pi$
$967$			40.0061i			1.28651i	−0.765652	+	0.643255i	$0.777584\pi$
$968$	−7.29450			−0.234454
$969$			56.6726i			1.82059i
$970$	31.7843	+	9.94235i	1.02053	+	0.319230i
$971$	41.5012			1.33184			0.665918	−	0.746025i	$-0.268040\pi$
$971$	41.5012			1.33184			0.665918	+	0.746025i	$0.268040\pi$
$972$	−56.0756	−	56.0756i	−1.79863	−	1.79863i
$973$	−0.593738	−	0.593738i	−0.0190344	−	0.0190344i
$974$			9.78190i			0.313432i
$975$	−9.30236	−	51.3920i	−0.297914	−	1.64586i
$976$	3.16695	−	3.16695i	0.101372	−	0.101372i
$977$	29.2680			0.936365			0.468183	−	0.883632i	$-0.344909\pi$
$977$	29.2680			0.936365			0.468183	+	0.883632i	$0.344909\pi$
$978$	52.2822	−	52.2822i	1.67180	−	1.67180i
$979$	15.0037	−	15.0037i	0.479519	−	0.479519i
$980$	−11.6663	−	3.64929i	−0.372666	−	0.116572i
$981$	62.3545	+	62.3545i	1.99083	+	1.99083i
$982$	9.56888			0.305355
$983$	−24.4031	−	24.4031i	−0.778336	−	0.778336i	0.201211	−	0.979548i	$-0.435512\pi$
$983$	−24.4031	−	24.4031i	−0.778336	−	0.778336i	−0.979548	+	0.201211i	$0.935512\pi$
$984$	−30.8418	+	30.8418i	−0.983201	+	0.983201i
$985$	7.62646	−	3.99209i	0.242999	−	0.127199i
$986$	17.5185	−	17.5185i	0.557903	−	0.557903i
$987$	−24.7913	+	24.7913i	−0.789115	+	0.789115i
$988$	9.86251	−	9.86251i	0.313768	−	0.313768i
$989$	9.68943			0.308106
$990$	11.1480	−	35.6387i	0.354307	−	1.13267i
$991$	−32.7805	+	32.7805i	−1.04131	+	1.04131i	−0.0421980	+	0.999109i	$0.513436\pi$
$991$	−32.7805	+	32.7805i	−1.04131	+	1.04131i	−0.999109	+	0.0421980i	$0.986564\pi$
$992$	−0.936472	+	0.936472i	−0.0297330	+	0.0297330i
$993$			21.4173i			0.679659i
$994$	−3.41933	−	3.41933i	−0.108454	−	0.108454i
$995$	−15.7473	+	8.24296i	−0.499222	+	0.261319i
$996$	−37.6670			−1.19352
$997$		−	36.3297i		−	1.15057i	−0.817952	−	0.575286i	$-0.804891\pi$
$997$		−	36.3297i		−	1.15057i	0.817952	−	0.575286i	$-0.195109\pi$
$998$	−13.9261	−	13.9261i	−0.440823	−	0.440823i
$999$	91.0670	+	74.9707i	2.88123	+	2.37197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.h.e.117.10	yes	20
5.3	odd	4		370.2.g.e.43.1	✓	20
37.31	odd	4		370.2.g.e.327.1	yes	20
185.68	even	4	inner	370.2.h.e.253.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.1	✓	20	5.3	odd	4
370.2.g.e.327.1	yes	20	37.31	odd	4
370.2.h.e.117.10	yes	20	1.1	even	1	trivial
370.2.h.e.253.10	yes	20	185.68	even	4	inner

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +(2.41612 + 2.41612i) q^{3} +1.00000 q^{4} +(0.667560 - 2.13410i) q^{5} +(-2.41612 - 2.41612i) q^{6} +(-0.875609 - 0.875609i) q^{7} -1.00000 q^{8} +8.67529i q^{9} +(-0.667560 + 2.13410i) q^{10} +1.92497i q^{11} +(2.41612 + 2.41612i) q^{12} +3.05698 q^{13} +(0.875609 + 0.875609i) q^{14} +(6.76914 - 3.54333i) q^{15} +1.00000 q^{16} +3.63520i q^{17} -8.67529i q^{18} +(3.22623 - 3.22623i) q^{19} +(0.667560 - 2.13410i) q^{20} -4.23116i q^{21} -1.92497i q^{22} -2.01378 q^{23} +(-2.41612 - 2.41612i) q^{24} +(-4.10873 - 2.84927i) q^{25} -3.05698 q^{26} +(-13.7122 + 13.7122i) q^{27} +(-0.875609 - 0.875609i) q^{28} +(4.81913 + 4.81913i) q^{29} +(-6.76914 + 3.54333i) q^{30} +(0.936472 - 0.936472i) q^{31} -1.00000 q^{32} +(-4.65096 + 4.65096i) q^{33} -3.63520i q^{34} +(-2.45316 + 1.28411i) q^{35} +8.67529i q^{36} +(-0.586931 - 6.05438i) q^{37} +(-3.22623 + 3.22623i) q^{38} +(7.38603 + 7.38603i) q^{39} +(-0.667560 + 2.13410i) q^{40} -12.7650i q^{41} +4.23116i q^{42} -4.81157 q^{43} +1.92497i q^{44} +(18.5139 + 5.79128i) q^{45} +2.01378 q^{46} +(-5.85922 - 5.85922i) q^{47} +(2.41612 + 2.41612i) q^{48} -5.46662i q^{49} +(4.10873 + 2.84927i) q^{50} +(-8.78310 + 8.78310i) q^{51} +3.05698 q^{52} +(-3.89480 + 3.89480i) q^{53} +(13.7122 - 13.7122i) q^{54} +(4.10806 + 1.28503i) q^{55} +(0.875609 + 0.875609i) q^{56} +15.5899 q^{57} +(-4.81913 - 4.81913i) q^{58} +(-3.25043 + 3.25043i) q^{59} +(6.76914 - 3.54333i) q^{60} +(3.16695 - 3.16695i) q^{61} +(-0.936472 + 0.936472i) q^{62} +(7.59617 - 7.59617i) q^{63} +1.00000 q^{64} +(2.04072 - 6.52388i) q^{65} +(4.65096 - 4.65096i) q^{66} +(-3.71697 + 3.71697i) q^{67} +3.63520i q^{68} +(-4.86553 - 4.86553i) q^{69} +(2.45316 - 1.28411i) q^{70} -3.90508 q^{71} -8.67529i q^{72} +(8.57777 + 8.57777i) q^{73} +(0.586931 + 6.05438i) q^{74} +(-3.04299 - 16.8114i) q^{75} +(3.22623 - 3.22623i) q^{76} +(1.68552 - 1.68552i) q^{77} +(-7.38603 - 7.38603i) q^{78} +(4.19139 - 4.19139i) q^{79} +(0.667560 - 2.13410i) q^{80} -40.2348 q^{81} +12.7650i q^{82} +(-7.79493 + 7.79493i) q^{83} -4.23116i q^{84} +(7.75787 + 2.42672i) q^{85} +4.81157 q^{86} +23.2872i q^{87} -1.92497i q^{88} +(-7.79425 - 7.79425i) q^{89} +(-18.5139 - 5.79128i) q^{90} +(-2.67672 - 2.67672i) q^{91} -2.01378 q^{92} +4.52526 q^{93} +(5.85922 + 5.85922i) q^{94} +(-4.73138 - 9.03878i) q^{95} +(-2.41612 - 2.41612i) q^{96} -14.8936i q^{97} +5.46662i q^{98} -16.6997 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

Varieties

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Database

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