LMFDB - Embedded newform 370.2.h.e.253.10

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			253.10
Root			$2.41612 + 2.41612i$ of defining polynomial
Character	$\chi$	$=$	370.253
Dual form			370.2.h.e.117.10

$q$-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} +(-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} + 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}+ \cdots - 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

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
$3$	2.41612	−	2.41612i	1.39495	−	1.39495i	0.581158	−	0.813791i	$-0.302600\pi$
$3$	2.41612	−	2.41612i	1.39495	−	1.39495i	0.813791	−	0.581158i	$-0.197400\pi$
$4$	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	−0.852947	−	0.521998i	$-0.825187\pi$
$7$	−0.875609	+	0.875609i	−0.330949	+	0.330949i	0.521998	+	0.852947i	$0.325187\pi$
$8$	−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	$-0.906278\pi$
$11$		−	1.92497i		−	0.580400i	0.956966	−	0.290200i	$-0.0937218\pi$
$12$	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	$-0.854683\pi$
$17$		−	3.63520i		−	0.881667i	0.897589	−	0.440833i	$-0.145317\pi$
$18$			8.67529i			2.04479i
$19$	3.22623	+	3.22623i	0.740148	+	0.740148i	0.972606	−	0.232459i	$-0.0746770\pi$
$19$	3.22623	+	3.22623i	0.740148	+	0.740148i	−0.232459	+	0.972606i	$0.574677\pi$
$20$	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	−0.100089	−	0.994979i	$-0.531913\pi$
$29$	4.81913	−	4.81913i	0.894890	−	0.894890i	0.994979	+	0.100089i	$0.0319127\pi$
$30$	−6.76914	−	3.54333i	−1.23587	−	0.646920i
$31$	0.936472	+	0.936472i	0.168195	+	0.168195i	0.786186	−	0.617990i	$-0.212053\pi$
$31$	0.936472	+	0.936472i	0.168195	+	0.168195i	−0.617990	+	0.786186i	$0.712053\pi$
$32$	−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	$0.474445\pi$
$41$			12.7650i			1.99356i	−0.0801960	+	0.996779i	$0.525555\pi$
$42$		−	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	−0.990702	−	0.136048i	$-0.956560\pi$
$47$	−5.85922	+	5.85922i	−0.854654	+	0.854654i	0.136048	+	0.990702i	$0.456560\pi$
$48$	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	0.387062	−	0.922054i	$-0.373490\pi$
$53$	−3.89480	−	3.89480i	−0.534991	−	0.534991i	−0.922054	+	0.387062i	$0.873490\pi$
$54$	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	0.463124	−	0.886294i	$-0.346729\pi$
$59$	−3.25043	−	3.25043i	−0.423170	−	0.423170i	−0.886294	+	0.463124i	$0.846729\pi$
$60$	6.76914	+	3.54333i	0.873892	+	0.457442i
$61$	3.16695	+	3.16695i	0.405486	+	0.405486i	0.880161	−	0.474675i	$-0.157434\pi$
$61$	3.16695	+	3.16695i	0.405486	+	0.405486i	−0.474675	+	0.880161i	$0.657434\pi$
$62$	−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	0.442613	−	0.896713i	$-0.354052\pi$
$67$	−3.71697	−	3.71697i	−0.454100	−	0.454100i	−0.896713	+	0.442613i	$0.854052\pi$
$68$		−	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	0.00396036	−	0.999992i	$-0.498739\pi$
$73$	8.57777	−	8.57777i	1.00395	−	1.00395i	0.999992	−	0.00396036i	$-0.00126063\pi$
$74$	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	0.902422	−	0.430854i	$-0.141788\pi$
$79$	4.19139	+	4.19139i	0.471568	+	0.471568i	−0.430854	+	0.902422i	$0.641788\pi$
$80$	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	0.135212	−	0.990817i	$-0.456828\pi$
$83$	−7.79493	−	7.79493i	−0.855604	−	0.855604i	−0.990817	+	0.135212i	$0.956828\pi$
$84$			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	−0.986987	−	0.160799i	$-0.948593\pi$
$89$	−7.79425	+	7.79425i	−0.826188	+	0.826188i	0.160799	+	0.986987i	$0.448593\pi$
$90$	−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	$0.272901\pi$
$97$			14.8936i			1.51221i	−0.654449	+	0.756106i	$0.727099\pi$
$98$		−	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	$0.0154856\pi$
$101$			0.977455i			0.0972604i	−0.998817	+	0.0486302i	$0.984514\pi$
$102$	8.78310	+	8.78310i	0.869656	+	0.869656i
$103$			11.3553i			1.11887i	0.828873	+	0.559437i	$0.188982\pi$
$103$			11.3553i			1.11887i	−0.828873	+	0.559437i	$0.811018\pi$
$104$	−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	−0.889634	−	0.456674i	$-0.849041\pi$
$107$	−4.47857	+	4.47857i	−0.432960	+	0.432960i	0.456674	+	0.889634i	$0.349041\pi$
$108$	−13.7122	−	13.7122i	−1.31946	−	1.31946i
$109$	7.18760	+	7.18760i	0.688447	+	0.688447i	0.961889	−	0.273442i	$-0.0881621\pi$
$109$	7.18760	+	7.18760i	0.688447	+	0.688447i	−0.273442	+	0.961889i	$0.588162\pi$
$110$	−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	$-0.947733\pi$
$113$		−	3.47531i		−	0.326930i	0.986549	−	0.163465i	$-0.0522671\pi$
$114$	−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	−0.404093	−	0.914718i	$-0.632413\pi$
$127$	5.75444	−	5.75444i	0.510624	−	0.510624i	0.914718	+	0.404093i	$0.132413\pi$
$128$	−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	0.787876	−	0.615833i	$-0.211181\pi$
$131$	1.96912	+	1.96912i	0.172043	+	0.172043i	−0.615833	+	0.787876i	$0.711181\pi$
$132$	−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	−0.288309	−	0.957537i	$-0.593093\pi$
$137$	7.83311	−	7.83311i	0.669228	−	0.669228i	0.957537	+	0.288309i	$0.0930932\pi$
$138$	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	$-0.932709\pi$
$149$		−	5.12261i		−	0.419660i	0.977738	−	0.209830i	$-0.0672911\pi$
$150$	3.04299	−	16.8114i	0.248459	−	1.37264i
$151$		−	20.3046i		−	1.65236i	−0.563405	−	0.826181i	$-0.690509\pi$
$151$		−	20.3046i		−	1.65236i	0.563405	−	0.826181i	$-0.309491\pi$
$152$	−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	−0.974059	−	0.226292i	$-0.927340\pi$
$157$	−9.36950	+	9.36950i	−0.747767	+	0.747767i	0.226292	+	0.974059i	$0.427340\pi$
$158$	−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	$-0.678140\pi$
$163$		−	21.6389i		−	1.69489i	0.530884	−	0.847445i	$-0.321860\pi$
$164$			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	$0.197186\pi$
$167$			15.0063i			1.16122i	−0.814181	+	0.580611i	$0.802814\pi$
$168$		−	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	−0.820655	−	0.571424i	$-0.806391\pi$
$173$	−3.27813	+	3.27813i	−0.249231	+	0.249231i	0.571424	+	0.820655i	$0.306391\pi$
$174$			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	0.164623	−	0.986357i	$-0.447359\pi$
$179$	15.3991	−	15.3991i	1.15098	−	1.15098i	0.986357	−	0.164623i	$-0.0526406\pi$
$180$	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	−0.600997	−	0.799251i	$-0.705230\pi$
$191$	2.73993	−	2.73993i	0.198255	−	0.198255i	0.799251	+	0.600997i	$0.205230\pi$
$192$	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	−0.603454	−	0.797398i	$-0.706209\pi$
$197$	2.72212	−	2.72212i	0.193943	−	0.193943i	0.797398	+	0.603454i	$0.206209\pi$
$198$	16.6997			1.18679
$199$	−5.62070	+	5.62070i	−0.398441	+	0.398441i	−0.877683	−	0.479242i	$-0.840912\pi$
$199$	−5.62070	+	5.62070i	−0.398441	+	0.398441i	0.479242	+	0.877683i	$0.340912\pi$
$200$	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	−0.990696	−	0.136090i	$-0.956546\pi$
$223$	−16.8265	−	16.8265i	−1.12679	−	1.12679i	−0.136090	−	0.990696i	$-0.543454\pi$
$224$	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	$0.146660\pi$
$227$			13.3976i			0.889233i	−0.895721	+	0.444616i	$0.853340\pi$
$228$	15.5899			1.03247
$229$		−	12.4697i		−	0.824019i	−0.911180	−	0.412010i	$-0.864827\pi$
$229$		−	12.4697i		−	0.824019i	0.911180	−	0.412010i	$-0.135173\pi$
$230$	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	−0.231655	−	0.972798i	$-0.574414\pi$
$233$	11.3131	−	11.3131i	0.741144	−	0.741144i	0.972798	+	0.231655i	$0.0744139\pi$
$234$			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	0.948588	−	0.316514i	$-0.102512\pi$
$239$	9.77163	+	9.77163i	0.632074	+	0.632074i	−0.316514	+	0.948588i	$0.602512\pi$
$240$	6.76914	+	3.54333i	0.436946	+	0.228721i
$241$	2.61835	−	2.61835i	0.168663	−	0.168663i	−0.617729	−	0.786391i	$-0.711947\pi$
$241$	2.61835	−	2.61835i	0.168663	−	0.168663i	0.786391	+	0.617729i	$0.211947\pi$
$242$	−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	0.661477	−	0.749965i	$-0.269930\pi$
$251$	−1.40191	−	1.40191i	−0.0884879	−	0.0884879i	−0.749965	+	0.661477i	$0.769930\pi$
$252$	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	$-0.696138\pi$
$257$		−	26.1658i		−	1.63218i	0.577925	−	0.816090i	$-0.303862\pi$
$258$	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	−0.243608	−	0.969874i	$-0.578331\pi$
$263$	11.7781	−	11.7781i	0.726266	−	0.726266i	0.969874	+	0.243608i	$0.0783310\pi$
$264$	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	$-0.999701\pi$
$269$		−	0.0307805i		−	0.00187672i	1.00000		0.000938361i	$-0.000298690\pi$
$270$	−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	−0.0942188	+	0.995552i	$0.530035\pi$
$281$	−18.2679	+	18.2679i	−1.08977	+	1.08977i	−0.995552	+	0.0942188i	$0.969965\pi$
$282$		−	28.3132i		−	1.68602i
$283$		−	2.36072i		−	0.140330i	−0.997535	−	0.0701650i	$-0.977647\pi$
$283$		−	2.36072i		−	0.140330i	0.997535	−	0.0701650i	$-0.0223526\pi$
$284$	−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	0.946202	−	0.323577i	$-0.104885\pi$
$293$	10.6576	+	10.6576i	0.622625	+	0.622625i	−0.323577	+	0.946202i	$0.604885\pi$
$294$	−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	0.255323	−	0.966856i	$-0.417818\pi$
$307$	−12.4671	−	12.4671i	−0.711533	−	0.711533i	−0.966856	+	0.255323i	$0.917818\pi$
$308$	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	0.0862278	−	0.996275i	$-0.472519\pi$
$311$	−16.0489	−	16.0489i	−0.910048	−	0.910048i	−0.996275	+	0.0862278i	$0.972519\pi$
$312$	−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	0.631216	−	0.775607i	$-0.282556\pi$
$317$	−2.57082	−	2.57082i	−0.144391	−	0.144391i	−0.775607	+	0.631216i	$0.782556\pi$
$318$	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	−0.574729	−	0.818344i	$-0.694893\pi$
$331$	4.43217	−	4.43217i	0.243614	−	0.243614i	0.818344	+	0.574729i	$0.194893\pi$
$332$	−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	0.133753	−	0.991015i	$-0.457297\pi$
$337$	−15.7372	−	15.7372i	−0.857261	−	0.857261i	−0.991015	+	0.133753i	$0.957297\pi$
$338$	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	$0.0555249\pi$
$349$			6.48449i			0.347107i	−0.984824	+	0.173553i	$0.944475\pi$
$350$	−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	$-0.932715\pi$
$353$		−	7.88401i		−	0.419624i	0.977742	−	0.209812i	$-0.0672851\pi$
$354$	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	$-0.801177\pi$
$359$		−	22.1603i		−	1.16958i	0.811186	−	0.584789i	$-0.198823\pi$
$360$	−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	−0.324776	+	0.945791i	$0.605289\pi$
$367$	−24.3406	+	24.3406i	−1.27057	+	1.27057i	−0.945791	+	0.324776i	$0.894711\pi$
$368$	−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	−0.930880	−	0.365324i	$-0.880958\pi$
$373$	−10.9227	+	10.9227i	−0.565556	+	0.565556i	0.365324	+	0.930880i	$0.380958\pi$
$374$	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	$0.00404869\pi$
$379$			0.495224i			0.0254380i	−0.999919	+	0.0127190i	$0.995951\pi$
$380$	−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	0.987612	−	0.156917i	$-0.0501555\pi$
$389$	16.3839	+	16.3839i	0.830695	+	0.830695i	−0.156917	+	0.987612i	$0.550155\pi$
$390$	−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	0.986197	−	0.165576i	$-0.0529483\pi$
$397$	16.3508	+	16.3508i	0.820621	+	0.820621i	−0.165576	+	0.986197i	$0.552948\pi$
$398$	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	0.746338	−	0.665567i	$-0.231810\pi$
$401$	1.61742	+	1.61742i	0.0807703	+	0.0807703i	−0.665567	+	0.746338i	$0.731810\pi$
$402$	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	−0.573605	−	0.819132i	$-0.694456\pi$
$409$	4.96548	−	4.96548i	0.245527	−	0.245527i	0.819132	+	0.573605i	$0.194456\pi$
$410$	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	$0.0420747\pi$
$419$			5.39563i			0.263594i	−0.991277	+	0.131797i	$0.957925\pi$
$420$	−9.02969	+	2.82455i	−0.440604	+	0.137824i
$421$	1.76092	+	1.76092i	0.0858222	+	0.0858222i	0.748715	−	0.662892i	$-0.230671\pi$
$421$	1.76092	+	1.76092i	0.0858222	+	0.0858222i	−0.662892	+	0.748715i	$0.730671\pi$
$422$	−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	0.488793	−	0.872400i	$-0.337437\pi$
$431$	−7.96389	−	7.96389i	−0.383607	−	0.383607i	−0.872400	+	0.488793i	$0.837437\pi$
$432$	−13.7122	−	13.7122i	−0.659728	−	0.659728i
$433$	3.23648	+	3.23648i	0.155535	+	0.155535i	0.780585	−	0.625050i	$-0.214921\pi$
$433$	3.23648	+	3.23648i	0.155535	+	0.155535i	−0.625050	+	0.780585i	$0.714921\pi$
$434$	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	−0.671933	−	0.740612i	$-0.734536\pi$
$439$	1.43898	−	1.43898i	0.0686789	−	0.0686789i	0.740612	+	0.671933i	$0.234536\pi$
$440$	−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	−0.998441	−	0.0558147i	$-0.982224\pi$
$443$	−19.8400	+	19.8400i	−0.942626	+	0.942626i	0.0558147	+	0.998441i	$0.482224\pi$
$444$	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	0.314884	−	0.949130i	$-0.398034\pi$
$449$	−13.4394	−	13.4394i	−0.634247	−	0.634247i	−0.949130	+	0.314884i	$0.898034\pi$
$450$	−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	$0.00100282\pi$
$457$			0.134698i			0.00630090i	−0.999995	+	0.00315045i	$0.998997\pi$
$458$			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	−0.509770	−	0.860311i	$-0.670269\pi$
$461$	7.52644	−	7.52644i	0.350541	−	0.350541i	0.860311	+	0.509770i	$0.170269\pi$
$462$	−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	$0.0327340\pi$
$467$			4.43682i			0.205312i	−0.994717	+	0.102656i	$0.967266\pi$
$468$		−	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	0.905481	−	0.424387i	$-0.139510\pi$
$479$	10.5292	+	10.5292i	0.481093	+	0.481093i	−0.424387	+	0.905481i	$0.639510\pi$
$480$	−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	$0.0711377\pi$
$487$			9.78190i			0.443260i	−0.975131	+	0.221630i	$0.928862\pi$
$488$	−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	−0.322986	−	0.946404i	$-0.604687\pi$
$499$	13.9261	−	13.9261i	0.623418	−	0.623418i	0.946404	+	0.322986i	$0.104687\pi$
$500$	−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	$-0.892088\pi$
$521$		−	15.1816i		−	0.665117i	0.943083	−	0.332559i	$-0.107912\pi$
$522$	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	−0.643270	−	0.765639i	$-0.722423\pi$
$541$	2.84624	−	2.84624i	0.122369	−	0.122369i	0.765639	+	0.643270i	$0.222423\pi$
$542$	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	−0.895285	−	0.445495i	$-0.853028\pi$
$569$	−10.7292	+	10.7292i	−0.449790	+	0.449790i	0.445495	+	0.895285i	$0.353028\pi$
$570$	−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	$0.0657187\pi$
$577$			9.84843i			0.409995i	−0.978762	+	0.204998i	$0.934281\pi$
$578$	−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	0.999997	+	0.00233126i	$0.000742064\pi$
$593$	24.4083	+	24.4083i	1.00233	+	1.00233i	0.00233126	+	0.999997i	$0.499258\pi$
$594$	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	$-0.934018\pi$
$599$		−	10.0741i		−	0.411615i	0.978592	−	0.205808i	$-0.0659821\pi$
$600$	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	−0.259378	−	0.965776i	$-0.583518\pi$
$613$	17.4896	−	17.4896i	0.706398	−	0.706398i	0.965776	+	0.259378i	$0.0835176\pi$
$614$	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	0.783272	−	0.621680i	$-0.213549\pi$
$617$	4.01386	+	4.01386i	0.161592	+	0.161592i	−0.621680	+	0.783272i	$0.713549\pi$
$618$	−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	0.847546	−	0.530722i	$-0.178079\pi$
$631$	7.95854	+	7.95854i	0.316825	+	0.316825i	−0.530722	+	0.847546i	$0.678079\pi$
$632$	−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	$-0.816497\pi$
$643$		−	27.6440i		−	1.09017i	0.838379	−	0.545087i	$-0.183503\pi$
$644$	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	$0.100514\pi$
$653$			15.8716i			0.621105i	−0.950556	+	0.310553i	$0.899486\pi$
$654$	−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	−0.935119	−	0.354333i	$-0.884708\pi$
$661$	−33.1517	−	33.1517i	−1.28945	−	1.28945i	−0.354333	−	0.935119i	$-0.615292\pi$
$662$	−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	0.849705	−	0.527258i	$-0.176780\pi$
$673$	8.36499	+	8.36499i	0.322447	+	0.322447i	−0.527258	+	0.849705i	$0.676780\pi$
$674$	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	−0.999148	−	0.0412815i	$-0.986856\pi$
$677$	−27.0712	−	27.0712i	−1.04043	−	1.04043i	−0.0412815	−	0.999148i	$-0.513144\pi$
$678$	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	$-0.895831\pi$
$691$		−	16.8996i		−	0.642892i	0.946928	−	0.321446i	$-0.104169\pi$
$692$	−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	−0.122973	+	0.992410i	$0.539243\pi$
$701$	−29.5313	+	29.5313i	−1.11538	+	1.11538i	−0.992410	+	0.122973i	$0.960757\pi$
$702$	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	0.894326	−	0.447416i	$-0.147656\pi$
$709$	11.8999	+	11.8999i	0.446910	+	0.446910i	−0.447416	+	0.894326i	$0.647656\pi$
$710$	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	$0.174378\pi$
$719$			27.9313i			1.04166i	−0.853660	+	0.520831i	$0.825622\pi$
$720$	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	−0.424154	−	0.905590i	$-0.639428\pi$
$733$	13.0344	−	13.0344i	0.481437	−	0.481437i	0.905590	+	0.424154i	$0.139428\pi$
$734$	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	−0.434436	−	0.900703i	$-0.643052\pi$
$743$	12.7095	−	12.7095i	0.466266	−	0.466266i	0.900703	+	0.434436i	$0.143052\pi$
$744$	−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	$-0.756353\pi$
$751$		−	37.9745i		−	1.38571i	0.721077	−	0.692855i	$-0.243647\pi$
$752$	−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	$0.0675623\pi$
$757$			11.5922i			0.421326i	−0.977559	+	0.210663i	$0.932438\pi$
$758$		−	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	$-0.925687\pi$
$761$		−	12.7639i		−	0.462692i	0.972871	−	0.231346i	$-0.0743130\pi$
$762$			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	−0.437806	−	0.899069i	$-0.644244\pi$
$769$	12.7912	−	12.7912i	0.461263	−	0.461263i	0.899069	+	0.437806i	$0.144244\pi$
$770$	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	0.833505	+	0.552511i	$0.186330\pi$
$773$	38.5353	+	38.5353i	1.38602	+	1.38602i	0.552511	+	0.833505i	$0.313670\pi$
$774$		−	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	−0.828457	−	0.560052i	$-0.810781\pi$
$787$	−7.52971	+	7.52971i	−0.268405	+	0.268405i	0.560052	+	0.828457i	$0.310781\pi$
$788$	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	−0.969589	−	0.244738i	$-0.921298\pi$
$809$	−20.6169	+	20.6169i	−0.724852	+	0.724852i	0.244738	+	0.969589i	$0.421298\pi$
$810$	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	0.341669	−	0.939820i	$-0.389008\pi$
$823$	−17.1598	−	17.1598i	−0.598152	−	0.598152i	−0.939820	+	0.341669i	$0.889008\pi$
$824$		−	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	$-0.683005\pi$
$827$		−	48.2686i		−	1.67847i	0.543773	−	0.839233i	$-0.316995\pi$
$828$			17.4701i			0.607128i
$829$	−8.64595	+	8.64595i	−0.300286	+	0.300286i	−0.841126	−	0.540840i	$-0.818107\pi$
$829$	−8.64595	+	8.64595i	−0.300286	+	0.300286i	0.540840	+	0.841126i	$0.318107\pi$
$830$	−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	$0.240393\pi$
$853$			40.0385i			1.37089i	−0.728123	+	0.685446i	$0.759607\pi$
$854$	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	$0.248297\pi$
$857$			41.1784i			1.40663i	−0.710880	+	0.703313i	$0.751703\pi$
$858$	14.2179	+	14.2179i	0.485390	+	0.485390i
$859$	8.32021	+	8.32021i	0.283882	+	0.283882i	0.834655	−	0.550773i	$-0.185667\pi$
$859$	8.32021	+	8.32021i	0.283882	+	0.283882i	−0.550773	+	0.834655i	$0.685667\pi$
$860$	−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	0.977676	−	0.210118i	$-0.0673847\pi$
$863$	22.5485	+	22.5485i	0.767558	+	0.767558i	−0.210118	+	0.977676i	$0.567385\pi$
$864$	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	−0.643598	−	0.765364i	$-0.722559\pi$
$877$	3.60601	−	3.60601i	0.121766	−	0.121766i	0.765364	+	0.643598i	$0.222559\pi$
$878$	−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	$-0.890542\pi$
$881$		−	20.0135i		−	0.674272i	0.941456	−	0.337136i	$-0.109458\pi$
$882$	−47.4245			−1.59687
$883$		−	37.3549i		−	1.25709i	−0.777772	−	0.628547i	$-0.783650\pi$
$883$		−	37.3549i		−	1.25709i	0.777772	−	0.628547i	$-0.216350\pi$
$884$		−	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	0.627294	−	0.778783i	$-0.284163\pi$
$887$	−4.51173	−	4.51173i	−0.151489	−	0.151489i	−0.778783	+	0.627294i	$0.784163\pi$
$888$	−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	$-0.998771\pi$
$907$		−	0.232515i		−	0.00772054i	0.999993	−	0.00386027i	$-0.00122876\pi$
$908$			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	−0.806634	−	0.591051i	$-0.798713\pi$
$911$	−6.50689	+	6.50689i	−0.215583	+	0.215583i	0.591051	+	0.806634i	$0.298713\pi$
$912$	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	−0.595577	−	0.803298i	$-0.703077\pi$
$919$	6.29705	−	6.29705i	0.207721	−	0.207721i	0.803298	+	0.595577i	$0.203077\pi$
$920$	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	−0.907227	−	0.420641i	$-0.861805\pi$
$937$	−14.8946	+	14.8946i	−0.486587	+	0.486587i	0.420641	+	0.907227i	$0.361805\pi$
$938$	−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	$0.0387812\pi$
$947$			7.47998i			0.243067i	−0.992587	+	0.121533i	$0.961219\pi$
$948$	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	0.0247571	−	0.999693i	$-0.492119\pi$
$953$	31.6255	−	31.6255i	1.02445	−	1.02445i	0.999693	−	0.0247571i	$-0.00788124\pi$
$954$	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	$-0.777584\pi$
$967$		−	40.0061i		−	1.28651i	0.765652	−	0.643255i	$-0.222416\pi$
$968$	−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	−0.979548	−	0.201211i	$-0.935512\pi$
$983$	−24.4031	+	24.4031i	−0.778336	+	0.778336i	0.201211	+	0.979548i	$0.435512\pi$
$984$	−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	−0.999109	−	0.0421980i	$-0.986564\pi$
$991$	−32.7805	−	32.7805i	−1.04131	−	1.04131i	−0.0421980	−	0.999109i	$-0.513436\pi$
$992$	−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	$0.195109\pi$
$997$			36.3297i			1.15057i	−0.817952	+	0.575286i	$0.804891\pi$
$998$	−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.253.10	yes	20
5.2	odd	4		370.2.g.e.327.1	yes	20
37.6	odd	4		370.2.g.e.43.1	✓	20
185.117	even	4	inner	370.2.h.e.117.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.g.e.43.1	✓	20	37.6	odd	4
370.2.g.e.327.1	yes	20	5.2	odd	4
370.2.h.e.117.10	yes	20	185.117	even	4	inner
370.2.h.e.253.10	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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 4 q^{3} + 20 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} - 20 q^{8} + 4 q^{10} + 4 q^{12} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 6 q^{19} - 4 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} - 20 q^{27}+ \cdots - 20 q^{99}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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