LMFDB - Embedded newform 78.3.l.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [78,3,Mod(7,78)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(78, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("78.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 78 = 2 \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	78.l (of order $12$, degree $4$, 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:	$2.12534606201$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	78.7
Dual form			78.3.l.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(6.73205 + 1.80385i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(6.73205 + 1.80385i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(4.09808 + 2.36603i) q^{10} +(-0.339746 - 1.26795i) q^{11} +3.46410i q^{12} +(-11.2583 - 6.50000i) q^{13} +9.85641 q^{14} +(-5.59808 + 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-21.1865 + 12.2321i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(5.80385 - 21.6603i) q^{19} +(6.46410 + 1.73205i) q^{20} +(-8.53590 + 8.53590i) q^{21} +(-0.928203 - 1.60770i) q^{22} +(-12.5885 - 7.26795i) q^{23} +(1.26795 + 4.73205i) q^{24} -13.8038i q^{25} +(-17.7583 - 4.75833i) q^{26} +5.19615 q^{27} +(13.4641 - 3.60770i) q^{28} +(-10.6699 + 18.4808i) q^{29} +(-7.09808 + 4.09808i) q^{30} +(18.5359 + 18.5359i) q^{31} +(1.46410 - 5.46410i) q^{32} +(2.19615 + 0.588457i) q^{33} +(-24.4641 + 24.4641i) q^{34} +(11.6603 + 20.1962i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(-3.96410 - 14.7942i) q^{37} -31.7128i q^{38} +(19.5000 - 11.2583i) q^{39} +9.46410 q^{40} +(-31.9186 + 8.55256i) q^{41} +(-8.53590 + 14.7846i) q^{42} +(57.3731 - 33.1244i) q^{43} +(-1.85641 - 1.85641i) q^{44} +(2.59808 - 9.69615i) q^{45} +(-19.8564 - 5.32051i) q^{46} +(-30.0000 + 30.0000i) q^{47} +(3.46410 + 6.00000i) q^{48} +(-0.368603 - 0.212813i) q^{49} +(-5.05256 - 18.8564i) q^{50} -42.3731i q^{51} -26.0000 q^{52} +53.1051 q^{53} +(7.09808 - 1.90192i) q^{54} +(2.19615 - 3.80385i) q^{55} +(17.0718 - 9.85641i) q^{56} +(27.4641 + 27.4641i) q^{57} +(-7.81089 + 29.1506i) q^{58} +(102.497 + 27.4641i) q^{59} +(-8.19615 + 8.19615i) q^{60} +(41.8923 + 72.5596i) q^{61} +(32.1051 + 18.5359i) q^{62} +(-5.41154 - 20.1962i) q^{63} -8.00000i q^{64} +(-11.2583 - 42.0167i) q^{65} +3.21539 q^{66} +(-53.5167 + 14.3397i) q^{67} +(-24.4641 + 42.3731i) q^{68} +(21.8038 - 12.5885i) q^{69} +(23.3205 + 23.3205i) q^{70} +(8.87564 - 33.1244i) q^{71} +(-8.19615 - 2.19615i) q^{72} +(-73.0788 + 73.0788i) q^{73} +(-10.8301 - 18.7583i) q^{74} +(20.7058 + 11.9545i) q^{75} +(-11.6077 - 43.3205i) q^{76} -9.14875i q^{77} +(22.5167 - 22.5167i) q^{78} -6.43078 q^{79} +(12.9282 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-40.4711 + 23.3660i) q^{82} +(-13.4256 - 13.4256i) q^{83} +(-6.24871 + 23.3205i) q^{84} +(-79.0692 - 21.1865i) q^{85} +(66.2487 - 66.2487i) q^{86} +(-18.4808 - 32.0096i) q^{87} +(-3.21539 - 1.85641i) q^{88} +(-28.2224 - 105.328i) q^{89} -14.1962i q^{90} +(-64.0666 - 64.0666i) q^{91} -29.0718 q^{92} +(-43.8564 + 11.7513i) q^{93} +(-30.0000 + 51.9615i) q^{94} +(64.9808 - 37.5167i) q^{95} +(6.92820 + 6.92820i) q^{96} +(-47.6340 + 177.772i) q^{97} +(-0.581416 - 0.155790i) q^{98} +(-2.78461 + 2.78461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9} + 6 q^{10} - 36 q^{11} - 16 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} - 12 q^{18} + 44 q^{19} + 12 q^{20} - 48 q^{21} + 24 q^{22} + 12 q^{23} + 12 q^{24} - 26 q^{26} + 40 q^{28} - 60 q^{29} - 18 q^{30} + 88 q^{31} - 8 q^{32} - 12 q^{33} - 84 q^{34} + 12 q^{35} - 2 q^{37} + 78 q^{39} + 24 q^{40} - 48 q^{41} - 48 q^{42} + 84 q^{43} + 48 q^{44} - 24 q^{46} - 120 q^{47} - 192 q^{49} + 56 q^{50} - 104 q^{52} + 60 q^{53} + 18 q^{54} - 12 q^{55} + 96 q^{56} + 96 q^{57} + 90 q^{58} + 216 q^{59} - 12 q^{60} + 126 q^{61} - 24 q^{62} - 84 q^{63} + 96 q^{66} - 124 q^{67} - 84 q^{68} + 108 q^{69} + 24 q^{70} + 84 q^{71} - 12 q^{72} - 178 q^{73} - 26 q^{74} + 114 q^{75} - 88 q^{76} - 192 q^{79} + 24 q^{80} - 18 q^{81} - 6 q^{82} + 168 q^{83} + 72 q^{84} - 150 q^{85} + 168 q^{86} + 30 q^{87} - 96 q^{88} - 54 q^{89} + 104 q^{91} - 144 q^{92} - 120 q^{93} - 120 q^{94} + 156 q^{95} - 194 q^{97} - 82 q^{98} + 72 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 + 6 * q^10 - 36 * q^11 - 16 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 - 12 * q^18 + 44 * q^19 + 12 * q^20 - 48 * q^21 + 24 * q^22 + 12 * q^23 + 12 * q^24 - 26 * q^26 + 40 * q^28 - 60 * q^29 - 18 * q^30 + 88 * q^31 - 8 * q^32 - 12 * q^33 - 84 * q^34 + 12 * q^35 - 2 * q^37 + 78 * q^39 + 24 * q^40 - 48 * q^41 - 48 * q^42 + 84 * q^43 + 48 * q^44 - 24 * q^46 - 120 * q^47 - 192 * q^49 + 56 * q^50 - 104 * q^52 + 60 * q^53 + 18 * q^54 - 12 * q^55 + 96 * q^56 + 96 * q^57 + 90 * q^58 + 216 * q^59 - 12 * q^60 + 126 * q^61 - 24 * q^62 - 84 * q^63 + 96 * q^66 - 124 * q^67 - 84 * q^68 + 108 * q^69 + 24 * q^70 + 84 * q^71 - 12 * q^72 - 178 * q^73 - 26 * q^74 + 114 * q^75 - 88 * q^76 - 192 * q^79 + 24 * q^80 - 18 * q^81 - 6 * q^82 + 168 * q^83 + 72 * q^84 - 150 * q^85 + 168 * q^86 + 30 * q^87 - 96 * q^88 - 54 * q^89 + 104 * q^91 - 144 * q^92 - 120 * q^93 - 120 * q^94 + 156 * q^95 - 194 * q^97 - 82 * q^98 + 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/78\mathbb{Z}\right)^\times$.

$n$	$53$	$67$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$2$	1.36603	−	0.366025i	0.683013	−	0.183013i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$3$	−0.866025	+	1.50000i	−0.288675	+	0.500000i
$4$	1.73205	−	1.00000i	0.433013	−	0.250000i
$5$	2.36603	+	2.36603i	0.473205	+	0.473205i	0.902950	−	0.429745i	$-0.141397\pi$
$5$	2.36603	+	2.36603i	0.473205	+	0.473205i	−0.429745	+	0.902950i	$0.641397\pi$
$6$	−0.633975	+	2.36603i	−0.105662	+	0.394338i
$7$	6.73205	+	1.80385i	0.961722	+	0.257693i	0.705329	−	0.708880i	$-0.250799\pi$
$7$	6.73205	+	1.80385i	0.961722	+	0.257693i	0.256393	+	0.966573i	$0.417466\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$	4.09808	+	2.36603i	0.409808	+	0.236603i
$11$	−0.339746	−	1.26795i	−0.0308860	−	0.115268i	0.948762	−	0.315992i	$-0.102337\pi$
$11$	−0.339746	−	1.26795i	−0.0308860	−	0.115268i	−0.979648	+	0.200724i	$0.935671\pi$
$12$			3.46410i			0.288675i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$13$	−11.2583	−	6.50000i	−0.866025	−	0.500000i
$14$	9.85641			0.704029
$15$	−5.59808	+	1.50000i	−0.373205	+	0.100000i
$16$	2.00000	−	3.46410i	0.125000	−	0.216506i
$17$	−21.1865	+	12.2321i	−1.24627	+	0.719532i	−0.970363	−	0.241653i	$-0.922310\pi$
$17$	−21.1865	+	12.2321i	−1.24627	+	0.719532i	−0.275904	+	0.961185i	$0.588977\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	5.80385	−	21.6603i	0.305466	−	1.14001i	−0.627078	−	0.778956i	$-0.715749\pi$
$19$	5.80385	−	21.6603i	0.305466	−	1.14001i	0.932544	−	0.361057i	$-0.117584\pi$
$20$	6.46410	+	1.73205i	0.323205	+	0.0866025i
$21$	−8.53590	+	8.53590i	−0.406471	+	0.406471i
$22$	−0.928203	−	1.60770i	−0.0421911	−	0.0730771i
$23$	−12.5885	−	7.26795i	−0.547324	−	0.315998i	0.200718	−	0.979649i	$-0.435673\pi$
$23$	−12.5885	−	7.26795i	−0.547324	−	0.315998i	−0.748042	+	0.663651i	$0.769006\pi$
$24$	1.26795	+	4.73205i	0.0528312	+	0.197169i
$25$		−	13.8038i		−	0.552154i
$26$	−17.7583	−	4.75833i	−0.683013	−	0.183013i
$27$	5.19615			0.192450
$28$	13.4641	−	3.60770i	0.480861	−	0.128846i
$29$	−10.6699	+	18.4808i	−0.367927	+	0.637268i	−0.989241	−	0.146294i	$-0.953266\pi$
$29$	−10.6699	+	18.4808i	−0.367927	+	0.637268i	0.621315	+	0.783561i	$0.286599\pi$
$30$	−7.09808	+	4.09808i	−0.236603	+	0.136603i
$31$	18.5359	+	18.5359i	0.597932	+	0.597932i	0.939762	−	0.341830i	$-0.111047\pi$
$31$	18.5359	+	18.5359i	0.597932	+	0.597932i	−0.341830	+	0.939762i	$0.611047\pi$
$32$	1.46410	−	5.46410i	0.0457532	−	0.170753i
$33$	2.19615	+	0.588457i	0.0665501	+	0.0178320i
$34$	−24.4641	+	24.4641i	−0.719532	+	0.719532i
$35$	11.6603	+	20.1962i	0.333150	+	0.577033i
$36$	−5.19615	−	3.00000i	−0.144338	−	0.0833333i
$37$	−3.96410	−	14.7942i	−0.107138	−	0.399844i	0.891441	−	0.453137i	$-0.149695\pi$
$37$	−3.96410	−	14.7942i	−0.107138	−	0.399844i	−0.998579	+	0.0532927i	$0.983028\pi$
$38$		−	31.7128i		−	0.834548i
$39$	19.5000	−	11.2583i	0.500000	−	0.288675i
$40$	9.46410			0.236603
$41$	−31.9186	+	8.55256i	−0.778502	+	0.208599i	−0.626124	−	0.779723i	$-0.715360\pi$
$41$	−31.9186	+	8.55256i	−0.778502	+	0.208599i	−0.152378	+	0.988322i	$0.548693\pi$
$42$	−8.53590	+	14.7846i	−0.203236	+	0.352015i
$43$	57.3731	−	33.1244i	1.33426	−	0.770334i	0.348308	−	0.937380i	$-0.386756\pi$
$43$	57.3731	−	33.1244i	1.33426	−	0.770334i	0.985949	+	0.167046i	$0.0534229\pi$
$44$	−1.85641	−	1.85641i	−0.0421911	−	0.0421911i
$45$	2.59808	−	9.69615i	0.0577350	−	0.215470i
$46$	−19.8564	−	5.32051i	−0.431661	−	0.115663i
$47$	−30.0000	+	30.0000i	−0.638298	+	0.638298i	−0.950135	−	0.311838i	$-0.899056\pi$
$47$	−30.0000	+	30.0000i	−0.638298	+	0.638298i	0.311838	+	0.950135i	$0.399056\pi$
$48$	3.46410	+	6.00000i	0.0721688	+	0.125000i
$49$	−0.368603	−	0.212813i	−0.00752251	−	0.00434312i
$50$	−5.05256	−	18.8564i	−0.101051	−	0.377128i
$51$		−	42.3731i		−	0.830844i
$52$	−26.0000			−0.500000
$53$	53.1051			1.00198			0.500992	−	0.865452i	$-0.332969\pi$
$53$	53.1051			1.00198			0.500992	+	0.865452i	$0.332969\pi$
$54$	7.09808	−	1.90192i	0.131446	−	0.0352208i
$55$	2.19615	−	3.80385i	0.0399300	−	0.0691609i
$56$	17.0718	−	9.85641i	0.304854	−	0.176007i
$57$	27.4641	+	27.4641i	0.481826	+	0.481826i
$58$	−7.81089	+	29.1506i	−0.134671	+	0.502597i
$59$	102.497	+	27.4641i	1.73724	+	0.465493i	0.981831	−	0.189756i	$-0.0607696\pi$
$59$	102.497	+	27.4641i	1.73724	+	0.465493i	0.755413	+	0.655249i	$0.227436\pi$
$60$	−8.19615	+	8.19615i	−0.136603	+	0.136603i
$61$	41.8923	+	72.5596i	0.686759	+	1.18950i	0.972881	+	0.231308i	$0.0743006\pi$
$61$	41.8923	+	72.5596i	0.686759	+	1.18950i	−0.286121	+	0.958193i	$0.592366\pi$
$62$	32.1051	+	18.5359i	0.517824	+	0.298966i
$63$	−5.41154	−	20.1962i	−0.0858975	−	0.320574i
$64$		−	8.00000i		−	0.125000i
$65$	−11.2583	−	42.0167i	−0.173205	−	0.646410i
$66$	3.21539			0.0487180
$67$	−53.5167	+	14.3397i	−0.798756	+	0.214026i	−0.635038	−	0.772481i	$-0.719015\pi$
$67$	−53.5167	+	14.3397i	−0.798756	+	0.214026i	−0.163718	+	0.986507i	$0.552349\pi$
$68$	−24.4641	+	42.3731i	−0.359766	+	0.623133i
$69$	21.8038	−	12.5885i	0.315998	−	0.182441i
$70$	23.3205	+	23.3205i	0.333150	+	0.333150i
$71$	8.87564	−	33.1244i	0.125009	−	0.466540i	−0.874831	−	0.484428i	$-0.839028\pi$
$71$	8.87564	−	33.1244i	0.125009	−	0.466540i	0.999840	+	0.0178882i	$0.00569428\pi$
$72$	−8.19615	−	2.19615i	−0.113835	−	0.0305021i
$73$	−73.0788	+	73.0788i	−1.00108	+	1.00108i	−0.00108056	+	0.999999i	$0.500344\pi$
$73$	−73.0788	+	73.0788i	−1.00108	+	1.00108i	−0.999999	+	0.00108056i	$0.999656\pi$
$74$	−10.8301	−	18.7583i	−0.146353	−	0.253491i
$75$	20.7058	+	11.9545i	0.276077	+	0.159393i
$76$	−11.6077	−	43.3205i	−0.152733	−	0.570007i
$77$		−	9.14875i		−	0.118815i
$78$	22.5167	−	22.5167i	0.288675	−	0.288675i
$79$	−6.43078			−0.0814023			−0.0407011	−	0.999171i	$-0.512959\pi$
$79$	−6.43078			−0.0814023			−0.0407011	+	0.999171i	$0.512959\pi$
$80$	12.9282	−	3.46410i	0.161603	−	0.0433013i
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−40.4711	+	23.3660i	−0.493551	+	0.284952i
$83$	−13.4256	−	13.4256i	−0.161755	−	0.161755i	0.621589	−	0.783344i	$-0.286487\pi$
$83$	−13.4256	−	13.4256i	−0.161755	−	0.161755i	−0.783344	+	0.621589i	$0.786487\pi$
$84$	−6.24871	+	23.3205i	−0.0743894	+	0.277625i
$85$	−79.0692	−	21.1865i	−0.930226	−	0.249253i
$86$	66.2487	−	66.2487i	0.770334	−	0.770334i
$87$	−18.4808	−	32.0096i	−0.212423	−	0.367927i
$88$	−3.21539	−	1.85641i	−0.0365385	−	0.0210955i
$89$	−28.2224	−	105.328i	−0.317106	−	1.18346i	−0.922013	−	0.387159i	$-0.873456\pi$
$89$	−28.2224	−	105.328i	−0.317106	−	1.18346i	0.604907	−	0.796296i	$-0.293210\pi$
$90$		−	14.1962i		−	0.157735i
$91$	−64.0666	−	64.0666i	−0.704029	−	0.704029i
$92$	−29.0718			−0.315998
$93$	−43.8564	+	11.7513i	−0.471574	+	0.126358i
$94$	−30.0000	+	51.9615i	−0.319149	+	0.552782i
$95$	64.9808	−	37.5167i	0.684008	−	0.394912i
$96$	6.92820	+	6.92820i	0.0721688	+	0.0721688i
$97$	−47.6340	+	177.772i	−0.491072	+	1.83271i	0.0599318	+	0.998202i	$0.480912\pi$
$97$	−47.6340	+	177.772i	−0.491072	+	1.83271i	−0.551004	+	0.834503i	$0.685755\pi$
$98$	−0.581416	−	0.155790i	−0.00593281	−	0.00158969i
$99$	−2.78461	+	2.78461i	−0.0281274	+	0.0281274i
$100$	−13.8038	−	23.9090i	−0.138038	−	0.239090i
$101$	−105.050	−	60.6506i	−1.04010	−	0.600501i	−0.120238	−	0.992745i	$-0.538366\pi$
$101$	−105.050	−	60.6506i	−1.04010	−	0.600501i	−0.919861	+	0.392244i	$0.871699\pi$
$102$	−15.5096	−	57.8827i	−0.152055	−	0.567477i
$103$		−	79.1103i		−	0.768061i	−0.923320	−	0.384030i	$-0.874536\pi$
$103$		−	79.1103i		−	0.768061i	0.923320	−	0.384030i	$-0.125464\pi$
$104$	−35.5167	+	9.51666i	−0.341506	+	0.0915064i
$105$	−40.3923			−0.384689
$106$	72.5429	−	19.4378i	0.684367	−	0.183376i
$107$	−83.9090	+	145.335i	−0.784196	+	1.35827i	0.145282	+	0.989390i	$0.453591\pi$
$107$	−83.9090	+	145.335i	−0.784196	+	1.35827i	−0.929478	+	0.368877i	$0.879742\pi$
$108$	9.00000	−	5.19615i	0.0833333	−	0.0481125i
$109$	−30.5026	−	30.5026i	−0.279840	−	0.279840i	0.553205	−	0.833045i	$-0.313405\pi$
$109$	−30.5026	−	30.5026i	−0.279840	−	0.279840i	−0.833045	+	0.553205i	$0.813405\pi$
$110$	1.60770	−	6.00000i	0.0146154	−	0.0545455i
$111$	25.6244	+	6.86603i	0.230850	+	0.0618561i
$112$	19.7128	−	19.7128i	0.176007	−	0.176007i
$113$	69.5596	+	120.481i	0.615572	+	1.06620i	0.990284	+	0.139060i	$0.0444082\pi$
$113$	69.5596	+	120.481i	0.615572	+	1.06620i	−0.374712	+	0.927141i	$0.622258\pi$
$114$	47.5692	+	27.4641i	0.417274	+	0.240913i
$115$	−12.5885	−	46.9808i	−0.109465	−	0.408528i
$116$			42.6795i			0.367927i
$117$			39.0000i			0.333333i
$118$	150.067			1.27175
$119$	−164.694	+	44.1295i	−1.38398	+	0.370836i
$120$	−8.19615	+	14.1962i	−0.0683013	+	0.118301i
$121$	103.297	−	59.6384i	0.853693	−	0.492880i
$122$	83.7846	+	83.7846i	0.686759	+	0.686759i
$123$	14.8135	−	55.2846i	0.120435	−	0.449468i
$124$	50.6410	+	13.5692i	0.408395	+	0.109429i
$125$	91.8109	−	91.8109i	0.734487	−	0.734487i
$126$	−14.7846	−	25.6077i	−0.117338	−	0.203236i
$127$	36.6795	+	21.1769i	0.288815	+	0.166747i	0.637407	−	0.770527i	$-0.280007\pi$
$127$	36.6795	+	21.1769i	0.288815	+	0.166747i	−0.348592	+	0.937274i	$0.613340\pi$
$128$	−2.92820	−	10.9282i	−0.0228766	−	0.0853766i
$129$			114.746i			0.889505i
$130$	−30.7583	−	53.2750i	−0.236603	−	0.409808i
$131$	186.067			1.42036			0.710178	−	0.704022i	$-0.248614\pi$
$131$	186.067			1.42036			0.710178	+	0.704022i	$0.248614\pi$
$132$	4.39230	−	1.17691i	0.0332750	−	0.00891602i
$133$	78.1436	−	135.349i	0.587546	−	1.01766i
$134$	−67.8564	+	39.1769i	−0.506391	+	0.292365i
$135$	12.2942	+	12.2942i	0.0910684	+	0.0910684i
$136$	−17.9090	+	66.8372i	−0.131684	+	0.491450i
$137$	−83.5859	−	22.3968i	−0.610116	−	0.163480i	−0.0594854	−	0.998229i	$-0.518946\pi$
$137$	−83.5859	−	22.3968i	−0.610116	−	0.163480i	−0.550630	+	0.834749i	$0.685613\pi$
$138$	25.1769	−	25.1769i	0.182441	−	0.182441i
$139$	118.354	+	204.995i	0.851466	+	1.47478i	0.879885	+	0.475187i	$0.157620\pi$
$139$	118.354	+	204.995i	0.851466	+	1.47478i	−0.0284185	+	0.999596i	$0.509047\pi$
$140$	40.3923	+	23.3205i	0.288516	+	0.166575i
$141$	−19.0192	−	70.9808i	−0.134888	−	0.503410i
$142$		−	48.4974i		−	0.341531i
$143$	−4.41670	+	16.4833i	−0.0308860	+	0.115268i
$144$	−12.0000			−0.0833333
$145$	−68.9711	+	18.4808i	−0.475663	+	0.127454i
$146$	−73.0788	+	126.576i	−0.500540	+	0.866961i
$147$	0.638439	−	0.368603i	0.00434312	−	0.00250750i
$148$	−21.6603	−	21.6603i	−0.146353	−	0.146353i
$149$	53.0551	−	198.004i	0.356075	−	1.32889i	−0.523052	−	0.852301i	$-0.675207\pi$
$149$	53.0551	−	198.004i	0.356075	−	1.32889i	0.879127	−	0.476588i	$-0.158127\pi$
$150$	32.6603	+	8.75129i	0.217735	+	0.0583419i
$151$	54.6025	−	54.6025i	0.361606	−	0.361606i	−0.502798	−	0.864404i	$-0.667696\pi$
$151$	54.6025	−	54.6025i	0.361606	−	0.361606i	0.864404	+	0.502798i	$0.167696\pi$
$152$	−31.7128	−	54.9282i	−0.208637	−	0.361370i
$153$	63.5596	+	36.6962i	0.415422	+	0.239844i
$154$	−3.34867	−	12.4974i	−0.0217446	−	0.0811521i
$155$			87.7128i			0.565889i
$156$	22.5167	−	39.0000i	0.144338	−	0.250000i
$157$	264.296			1.68341			0.841707	−	0.539934i	$-0.181551\pi$
$157$	264.296			1.68341			0.841707	+	0.539934i	$0.181551\pi$
$158$	−8.78461	+	2.35383i	−0.0555988	+	0.0148977i
$159$	−45.9904	+	79.6577i	−0.289248	+	0.500992i
$160$	16.3923	−	9.46410i	0.102452	−	0.0591506i
$161$	−71.6359	−	71.6359i	−0.444943	−	0.444943i
$162$	−3.29423	+	12.2942i	−0.0203347	+	0.0758903i
$163$	−241.138	−	64.6128i	−1.47938	−	0.396398i	−0.573242	−	0.819386i	$-0.694314\pi$
$163$	−241.138	−	64.6128i	−1.47938	−	0.396398i	−0.906135	+	0.422988i	$0.860981\pi$
$164$	−46.7321	+	46.7321i	−0.284952	+	0.284952i
$165$	3.80385	+	6.58846i	0.0230536	+	0.0399300i
$166$	−23.2539	−	13.4256i	−0.140084	−	0.0808773i
$167$	70.2769	+	262.277i	0.420820	+	1.57052i	0.772886	+	0.634545i	$0.218813\pi$
$167$	70.2769	+	262.277i	0.420820	+	1.57052i	−0.352066	+	0.935975i	$0.614521\pi$
$168$			34.1436i			0.203236i
$169$	84.5000	+	146.358i	0.500000	+	0.866025i
$170$	−115.765			−0.680973
$171$	−64.9808	+	17.4115i	−0.380004	+	0.101822i
$172$	66.2487	−	114.746i	0.385167	−	0.667129i
$173$	177.100	−	102.249i	1.02370	−	0.591033i	0.108526	−	0.994094i	$-0.465387\pi$
$173$	177.100	−	102.249i	1.02370	−	0.591033i	0.915173	+	0.403061i	$0.132054\pi$
$174$	−36.9615	−	36.9615i	−0.212423	−	0.212423i
$175$	24.9000	−	92.9282i	0.142286	−	0.531018i
$176$	−5.07180	−	1.35898i	−0.0288170	−	0.00772150i
$177$	−129.962	+	129.962i	−0.734246	+	0.734246i
$178$	−77.1051	−	133.550i	−0.433175	−	0.750281i
$179$	−116.196	−	67.0859i	−0.649141	−	0.374781i	0.138986	−	0.990294i	$-0.455616\pi$
$179$	−116.196	−	67.0859i	−0.649141	−	0.374781i	−0.788127	+	0.615513i	$0.788949\pi$
$180$	−5.19615	−	19.3923i	−0.0288675	−	0.107735i
$181$		−	120.713i		−	0.666922i	−0.942764	−	0.333461i	$-0.891784\pi$
$181$		−	120.713i		−	0.666922i	0.942764	−	0.333461i	$-0.108216\pi$
$182$	−110.967	−	64.0666i	−0.609707	−	0.352015i
$183$	−145.119			−0.793001
$184$	−39.7128	+	10.6410i	−0.215831	+	0.0578316i
$185$	25.6244	−	44.3827i	0.138510	−	0.239906i
$186$	−55.6077	+	32.1051i	−0.298966	+	0.172608i
$187$	22.7077	+	22.7077i	0.121431	+	0.121431i
$188$	−21.9615	+	81.9615i	−0.116817	+	0.435966i
$189$	34.9808	+	9.37307i	0.185083	+	0.0495929i
$190$	75.0333	−	75.0333i	0.394912	−	0.394912i
$191$	−123.282	−	213.531i	−0.645456	−	1.11796i	−0.984196	−	0.177082i	$-0.943334\pi$
$191$	−123.282	−	213.531i	−0.645456	−	1.11796i	0.338740	−	0.940880i	$-0.389999\pi$
$192$	12.0000	+	6.92820i	0.0625000	+	0.0360844i
$193$	7.84679	+	29.2846i	0.0406569	+	0.151734i	0.983270	−	0.182153i	$-0.0583065\pi$
$193$	7.84679	+	29.2846i	0.0406569	+	0.151734i	−0.942613	+	0.333886i	$0.891640\pi$
$194$			260.277i			1.34163i
$195$	72.7750	+	19.5000i	0.373205	+	0.100000i
$196$	−0.851252			−0.00434312
$197$	−37.1314	+	9.94933i	−0.188484	+	0.0505042i	−0.351826	−	0.936065i	$-0.614439\pi$
$197$	−37.1314	+	9.94933i	−0.188484	+	0.0505042i	0.163342	+	0.986569i	$0.447773\pi$
$198$	−2.78461	+	4.82309i	−0.0140637	+	0.0243590i
$199$	−85.5833	+	49.4115i	−0.430067	+	0.248299i	−0.699375	−	0.714755i	$-0.746538\pi$
$199$	−85.5833	+	49.4115i	−0.430067	+	0.248299i	0.269308	+	0.963054i	$0.413205\pi$
$200$	−27.6077	−	27.6077i	−0.138038	−	0.138038i
$201$	24.8372	−	92.6936i	0.123568	−	0.461162i
$202$	−165.701	−	44.3993i	−0.820300	−	0.219799i
$203$	−105.167	+	105.167i	−0.518062	+	0.518062i
$204$	−42.3731	−	73.3923i	−0.207711	−	0.359766i
$205$	−95.7558	−	55.2846i	−0.467101	−	0.269681i
$206$	−28.9564	−	108.067i	−0.140565	−	0.524595i
$207$			43.6077i			0.210665i
$208$	−45.0333	+	26.0000i	−0.216506	+	0.125000i
$209$	−29.4359			−0.140842
$210$	−55.1769	+	14.7846i	−0.262747	+	0.0704029i
$211$	90.9282	−	157.492i	0.430939	−	0.746409i	−0.566015	−	0.824395i	$-0.691516\pi$
$211$	90.9282	−	157.492i	0.430939	−	0.746409i	0.996954	+	0.0779860i	$0.0248490\pi$
$212$	91.9808	−	53.1051i	0.433872	−	0.250496i
$213$	42.0000	+	42.0000i	0.197183	+	0.197183i
$214$	−61.4256	+	229.244i	−0.287036	+	1.07123i
$215$	214.119	+	57.3731i	0.995903	+	0.266851i
$216$	10.3923	−	10.3923i	0.0481125	−	0.0481125i
$217$	91.3487	+	158.221i	0.420962	+	0.729127i
$218$	−52.8320	−	30.5026i	−0.242349	−	0.139920i
$219$	−46.3301	−	172.906i	−0.211553	−	0.789527i
$220$		−	8.78461i		−	0.0399300i
$221$	318.033			1.43906
$222$	37.5167			0.168994
$223$	86.2487	−	23.1103i	0.386766	−	0.103634i	−0.0601963	−	0.998187i	$-0.519173\pi$
$223$	86.2487	−	23.1103i	0.386766	−	0.103634i	0.446962	+	0.894553i	$0.352506\pi$
$224$	19.7128	−	34.1436i	0.0880036	−	0.152427i
$225$	−35.8634	+	20.7058i	−0.159393	+	0.0920257i
$226$	139.119	+	139.119i	0.615572	+	0.615572i
$227$	7.40123	−	27.6218i	0.0326046	−	0.121682i	−0.947706	−	0.319146i	$-0.896604\pi$
$227$	7.40123	−	27.6218i	0.0326046	−	0.121682i	0.980310	+	0.197464i	$0.0632706\pi$
$228$	75.0333	+	20.1051i	0.329094	+	0.0881803i
$229$	−30.5692	+	30.5692i	−0.133490	+	0.133490i	−0.770695	−	0.637205i	$-0.780091\pi$
$229$	−30.5692	+	30.5692i	−0.133490	+	0.133490i	0.637205	+	0.770695i	$0.280091\pi$
$230$	−34.3923	−	59.5692i	−0.149532	−	0.258997i
$231$	13.7231	+	7.92305i	0.0594075	+	0.0342989i
$232$	15.6218	+	58.3013i	0.0673353	+	0.251299i
$233$			28.0770i			0.120502i	0.998183	+	0.0602510i	$0.0191901\pi$
$233$			28.0770i			0.120502i	−0.998183	+	0.0602510i	$0.980810\pi$
$234$	14.2750	+	53.2750i	0.0610042	+	0.227671i
$235$	−141.962			−0.604092
$236$	204.995	−	54.9282i	0.868622	−	0.232747i
$237$	5.56922	−	9.64617i	0.0234988	−	0.0407011i
$238$	−208.823	+	120.564i	−0.877408	+	0.506572i
$239$	−72.4308	−	72.4308i	−0.303058	−	0.303058i	0.539151	−	0.842209i	$-0.318745\pi$
$239$	−72.4308	−	72.4308i	−0.303058	−	0.303058i	−0.842209	+	0.539151i	$0.818745\pi$
$240$	−6.00000	+	22.3923i	−0.0250000	+	0.0933013i
$241$	−309.882	−	83.0326i	−1.28582	−	0.344534i	−0.449747	−	0.893156i	$-0.648486\pi$
$241$	−309.882	−	83.0326i	−1.28582	−	0.344534i	−0.836070	+	0.548622i	$0.815153\pi$
$242$	119.277	−	119.277i	0.492880	−	0.492880i
$243$	−7.79423	−	13.5000i	−0.0320750	−	0.0555556i
$244$	145.119	+	83.7846i	0.594751	+	0.343380i
$245$	−0.368603	−	1.37564i	−0.00150450	−	0.00561487i
$246$		−	80.9423i		−	0.329034i
$247$	−206.133	+	206.133i	−0.834548	+	0.834548i
$248$	74.1436			0.298966
$249$	31.7654	−	8.51151i	0.127572	−	0.0341828i
$250$	91.8109	−	159.021i	0.367244	−	0.636084i
$251$	−188.354	+	108.746i	−0.750414	+	0.433252i	−0.825843	−	0.563900i	$-0.809300\pi$
$251$	−188.354	+	108.746i	−0.750414	+	0.433252i	0.0754297	+	0.997151i	$0.475967\pi$
$252$	−29.5692	−	29.5692i	−0.117338	−	0.117338i
$253$	−4.93851	+	18.4308i	−0.0195198	+	0.0728489i
$254$	57.8564	+	15.5026i	0.227781	+	0.0610338i
$255$	100.256	−	100.256i	0.393160	−	0.393160i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	286.342	+	165.320i	1.11417	+	0.643268i	0.939907	−	0.341431i	$-0.110912\pi$
$257$	286.342	+	165.320i	1.11417	+	0.643268i	0.174266	+	0.984699i	$0.444245\pi$
$258$	42.0000	+	156.746i	0.162791	+	0.607543i
$259$		−	106.746i		−	0.412147i
$260$	−61.5167	−	61.5167i	−0.236603	−	0.236603i
$261$	64.0192			0.245284
$262$	254.172	−	68.1051i	0.970121	−	0.259943i
$263$	−64.6166	+	111.919i	−0.245691	+	0.425549i	−0.962326	−	0.271900i	$-0.912348\pi$
$263$	−64.6166	+	111.919i	−0.245691	+	0.425549i	0.716635	+	0.697448i	$0.245681\pi$
$264$	5.56922	−	3.21539i	0.0210955	−	0.0121795i
$265$	125.648	+	125.648i	0.474144	+	0.474144i
$266$	57.2051	−	213.492i	0.215057	−	0.802603i
$267$	182.433	+	48.8827i	0.683268	+	0.183081i
$268$	−78.3538	+	78.3538i	−0.292365	+	0.292365i
$269$	−223.244	−	386.669i	−0.829902	−	1.43743i	−0.898115	−	0.439761i	$-0.855063\pi$
$269$	−223.244	−	386.669i	−0.829902	−	1.43743i	0.0682131	−	0.997671i	$-0.478270\pi$
$270$	21.2942	+	12.2942i	0.0788675	+	0.0455342i
$271$	92.0282	+	343.454i	0.339587	+	1.26736i	0.898810	+	0.438339i	$0.144433\pi$
$271$	92.0282	+	343.454i	0.339587	+	1.26736i	−0.559222	+	0.829018i	$0.688900\pi$
$272$			97.8564i			0.359766i
$273$	151.583	−	40.6166i	0.555250	−	0.148779i
$274$	−122.378			−0.446636
$275$	−17.5026	+	4.68980i	−0.0636457	+	0.0170538i
$276$	25.1769	−	43.6077i	0.0912207	−	0.157999i
$277$	−88.2846	+	50.9711i	−0.318717	+	0.184011i	−0.650821	−	0.759232i	$-0.725575\pi$
$277$	−88.2846	+	50.9711i	−0.318717	+	0.184011i	0.332104	+	0.943243i	$0.392242\pi$
$278$	236.708	+	236.708i	0.851466	+	0.851466i
$279$	20.3538	−	75.9615i	0.0729528	−	0.272264i
$280$	63.7128	+	17.0718i	0.227546	+	0.0609707i
$281$	−13.1647	+	13.1647i	−0.0468495	+	0.0468495i	−0.730143	−	0.683294i	$-0.760547\pi$
$281$	−13.1647	+	13.1647i	−0.0468495	+	0.0468495i	0.683294	+	0.730143i	$0.260547\pi$
$282$	−51.9615	−	90.0000i	−0.184261	−	0.319149i
$283$	−304.914	−	176.042i	−1.07744	−	0.622057i	−0.147232	−	0.989102i	$-0.547036\pi$
$283$	−304.914	−	176.042i	−1.07744	−	0.622057i	−0.930203	+	0.367045i	$0.880370\pi$
$284$	−17.7513	−	66.2487i	−0.0625045	−	0.233270i
$285$			129.962i			0.456005i
$286$			24.1333i			0.0843821i
$287$	−230.305			−0.802457
$288$	−16.3923	+	4.39230i	−0.0569177	+	0.0152511i
$289$	154.746	−	268.028i	0.535454	−	0.927433i
$290$	−87.4519	+	50.4904i	−0.301558	+	0.174105i
$291$	−225.406	−	225.406i	−0.774592	−	0.774592i
$292$	−53.4974	+	199.655i	−0.183210	+	0.683750i
$293$	216.933	+	58.1269i	0.740385	+	0.198385i	0.609249	−	0.792979i	$-0.291471\pi$
$293$	216.933	+	58.1269i	0.740385	+	0.198385i	0.131136	+	0.991364i	$0.458138\pi$
$294$	0.737206	−	0.737206i	0.00250750	−	0.00250750i
$295$	177.531	+	307.492i	0.601799	+	1.04235i
$296$	−37.5167	−	21.6603i	−0.126745	−	0.0731765i
$297$	−1.76537	−	6.58846i	−0.00594401	−	0.0221834i
$298$		−	289.899i		−	0.972814i
$299$	94.4833	+	163.650i	0.315998	+	0.547324i
$300$	47.8179			0.159393
$301$	445.990	−	119.503i	1.48169	−	0.397019i
$302$	54.6025	−	94.5744i	0.180803	−	0.313160i
$303$	181.952	−	105.050i	0.600501	−	0.346700i
$304$	−63.4256	−	63.4256i	−0.208637	−	0.208637i
$305$	−72.5596	+	270.796i	−0.237900	+	0.887856i
$306$	100.256	+	26.8634i	0.327633	+	0.0877890i
$307$	−75.6743	+	75.6743i	−0.246496	+	0.246496i	−0.819531	−	0.573035i	$-0.805766\pi$
$307$	−75.6743	+	75.6743i	−0.246496	+	0.246496i	0.573035	+	0.819531i	$0.305766\pi$
$308$	−9.14875	−	15.8461i	−0.0297037	−	0.0514484i
$309$	118.665	+	68.5115i	0.384030	+	0.221720i
$310$	32.1051	+	119.818i	0.103565	+	0.386509i
$311$		−	241.177i		−	0.775488i	−0.921767	−	0.387744i	$-0.873254\pi$
$311$		−	241.177i		−	0.775488i	0.921767	−	0.387744i	$-0.126746\pi$
$312$	16.4833	−	61.5167i	0.0528312	−	0.197169i
$313$	−518.123			−1.65534			−0.827672	−	0.561211i	$-0.810335\pi$
$313$	−518.123			−1.65534			−0.827672	+	0.561211i	$0.810335\pi$
$314$	361.035	−	96.7391i	1.14979	−	0.308086i
$315$	34.9808	−	60.5885i	0.111050	−	0.192344i
$316$	−11.1384	+	6.43078i	−0.0352482	+	0.0203506i
$317$	−364.886	−	364.886i	−1.15106	−	1.15106i	−0.986340	−	0.164721i	$-0.947328\pi$
$317$	−364.886	−	364.886i	−1.15106	−	1.15106i	−0.164721	−	0.986340i	$-0.552672\pi$
$318$	−33.6673	+	125.648i	−0.105872	+	0.395120i
$319$	27.0577	+	7.25009i	0.0848204	+	0.0227276i
$320$	18.9282	−	18.9282i	0.0591506	−	0.0591506i
$321$	−145.335	−	251.727i	−0.452756	−	0.784196i
$322$	−124.077	−	71.6359i	−0.385332	−	0.222472i
$323$	141.986	+	529.899i	0.439585	+	1.64055i
$324$			18.0000i			0.0555556i
$325$	−89.7250	+	155.408i	−0.276077	+	0.478179i
$326$	−353.051			−1.08298
$327$	72.1699	−	19.3379i	0.220703	−	0.0591372i
$328$	−46.7321	+	80.9423i	−0.142476	+	0.246775i
$329$	−256.077	+	147.846i	−0.778349	+	0.449380i
$330$	7.60770	+	7.60770i	0.0230536	+	0.0230536i
$331$	63.6743	−	237.636i	0.192370	−	0.717933i	−0.800562	−	0.599249i	$-0.795466\pi$
$331$	63.6743	−	237.636i	0.192370	−	0.717933i	0.992932	−	0.118684i	$-0.0378675\pi$
$332$	−36.6795	−	9.82824i	−0.110480	−	0.0296031i
$333$	−32.4904	+	32.4904i	−0.0975687	+	0.0975687i
$334$	192.000	+	332.554i	0.574850	+	0.995670i
$335$	−160.550	−	92.6936i	−0.479254	−	0.276697i
$336$	12.4974	+	46.6410i	0.0371947	+	0.138813i
$337$			260.923i			0.774252i	0.922027	+	0.387126i	$0.126532\pi$
$337$			260.923i			0.774252i	−0.922027	+	0.387126i	$0.873468\pi$
$338$	169.000	+	169.000i	0.500000	+	0.500000i
$339$	−240.962			−0.710801
$340$	−158.138	+	42.3731i	−0.465113	+	0.124627i
$341$	17.2051	−	29.8001i	0.0504548	−	0.0873902i
$342$	−82.3923	+	47.5692i	−0.240913	+	0.139091i
$343$	−243.580	−	243.580i	−0.710144	−	0.710144i
$344$	48.4974	−	180.995i	0.140981	−	0.526148i
$345$	81.3731	+	21.8038i	0.235864	+	0.0631996i
$346$	204.497	−	204.497i	0.591033	−	0.591033i
$347$	112.417	+	194.711i	0.323967	+	0.561128i	0.981303	−	0.192470i	$-0.0616498\pi$
$347$	112.417	+	194.711i	0.323967	+	0.561128i	−0.657335	+	0.753598i	$0.728317\pi$
$348$	−64.0192	−	36.9615i	−0.183963	−	0.106211i
$349$	−1.15441	−	4.30831i	−0.00330776	−	0.0123447i	0.964252	−	0.264986i	$-0.0853674\pi$
$349$	−1.15441	−	4.30831i	−0.00330776	−	0.0123447i	−0.967560	+	0.252641i	$0.918701\pi$
$350$		−	136.056i		−	0.388732i
$351$	−58.5000	−	33.7750i	−0.166667	−	0.0962250i
$352$	−7.42563			−0.0210955
$353$	−429.863	+	115.181i	−1.21774	+	0.326293i	−0.809795	−	0.586713i	$-0.800422\pi$
$353$	−429.863	+	115.181i	−1.21774	+	0.326293i	−0.407947	+	0.913006i	$0.633755\pi$
$354$	−129.962	+	225.100i	−0.367123	+	0.635876i
$355$	99.3731	−	57.3731i	0.279924	−	0.161614i
$356$	−154.210	−	154.210i	−0.433175	−	0.433175i
$357$	76.4346	−	285.258i	0.214102	−	0.799041i
$358$	−183.282	−	49.1103i	−0.511961	−	0.137180i
$359$	123.415	−	123.415i	0.343775	−	0.343775i	−0.514009	−	0.857785i	$-0.671840\pi$
$359$	123.415	−	123.415i	0.343775	−	0.343775i	0.857785	+	0.514009i	$0.171840\pi$
$360$	−14.1962	−	24.5885i	−0.0394338	−	0.0683013i
$361$	−122.847	−	70.9256i	−0.340296	−	0.196470i
$362$	−44.1840	−	164.897i	−0.122055	−	0.455516i
$363$			206.594i			0.569128i
$364$	−175.033	−	46.9000i	−0.480861	−	0.128846i
$365$	−345.813			−0.947432
$366$	−198.237	+	53.1173i	−0.541630	+	0.145129i
$367$	220.158	−	381.324i	0.599885	−	1.03903i	−0.392953	−	0.919559i	$-0.628546\pi$
$367$	220.158	−	381.324i	0.599885	−	1.03903i	0.992838	−	0.119472i	$-0.0381202\pi$
$368$	−50.3538	+	29.0718i	−0.136831	+	0.0789994i
$369$	70.0981	+	70.0981i	0.189968	+	0.189968i
$370$	18.7583	−	70.0070i	0.0506982	−	0.189208i
$371$	357.506	+	95.7935i	0.963629	+	0.258204i
$372$	−64.2102	+	64.2102i	−0.172608	+	0.172608i
$373$	−93.2199	−	161.462i	−0.249919	−	0.432873i	0.713584	−	0.700570i	$-0.247071\pi$
$373$	−93.2199	−	161.462i	−0.249919	−	0.432873i	−0.963503	+	0.267697i	$0.913737\pi$
$374$	39.3308	+	22.7077i	0.105163	+	0.0607157i
$375$	58.2058	+	217.227i	0.155215	+	0.579272i
$376$			120.000i			0.319149i
$377$	240.250	−	138.708i	0.637268	−	0.367927i
$378$	51.2154			0.135490
$379$	531.951	−	142.536i	1.40357	−	0.376084i	0.523941	−	0.851754i	$-0.324461\pi$
$379$	531.951	−	142.536i	1.40357	−	0.376084i	0.879624	+	0.475670i	$0.157794\pi$
$380$	75.0333	−	129.962i	0.197456	−	0.342004i
$381$	−63.5307	+	36.6795i	−0.166747	+	0.0962716i
$382$	−246.564	−	246.564i	−0.645456	−	0.645456i
$383$	30.3820	−	113.387i	0.0793264	−	0.296050i	−0.914853	−	0.403787i	$-0.867694\pi$
$383$	30.3820	−	113.387i	0.0793264	−	0.296050i	0.994179	+	0.107737i	$0.0343604\pi$
$384$	18.9282	+	5.07180i	0.0492922	+	0.0132078i
$385$	21.6462	−	21.6462i	0.0562238	−	0.0562238i
$386$	21.4378	+	37.1314i	0.0555384	+	0.0961953i
$387$	−172.119	−	99.3731i	−0.444752	−	0.256778i
$388$	95.2679	+	355.545i	0.245536	+	0.916353i
$389$		−	113.802i		−	0.292551i	−0.989244	−	0.146276i	$-0.953271\pi$
$389$		−	113.802i		−	0.292551i	0.989244	−	0.146276i	$-0.0467287\pi$
$390$	106.550			0.273205
$391$	355.608			0.909483
$392$	−1.16283	+	0.311580i	−0.00296641	+	0.000794846i
$393$	−161.138	+	279.100i	−0.410021	+	0.710178i
$394$	−47.0807	+	27.1821i	−0.119494	+	0.0689900i
$395$	−15.2154	−	15.2154i	−0.0385200	−	0.0385200i
$396$	−2.03848	+	7.60770i	−0.00514767	+	0.0192114i
$397$	−88.3853	−	23.6828i	−0.222633	−	0.0596543i	0.145778	−	0.989317i	$-0.453431\pi$
$397$	−88.3853	−	23.6828i	−0.222633	−	0.0596543i	−0.368411	+	0.929663i	$0.620098\pi$
$398$	−98.8231	+	98.8231i	−0.248299	+	0.248299i
$399$	135.349	+	234.431i	0.339220	+	0.587546i
$400$	−47.8179	−	27.6077i	−0.119545	−	0.0690192i
$401$	26.9346	+	100.521i	0.0671685	+	0.250676i	0.991344	−	0.131293i	$-0.0419128\pi$
$401$	26.9346	+	100.521i	0.0671685	+	0.250676i	−0.924175	+	0.381969i	$0.875246\pi$
$402$		−	135.713i		−	0.337594i
$403$	−88.1999	−	329.167i	−0.218858	−	0.816791i
$404$	−242.603			−0.600501
$405$	−29.0885	+	7.79423i	−0.0718234	+	0.0192450i
$406$	−105.167	+	182.154i	−0.259031	+	0.448655i
$407$	−17.4115	+	10.0526i	−0.0427802	+	0.0246992i
$408$	−84.7461	−	84.7461i	−0.207711	−	0.207711i
$409$	−8.77637	+	32.7539i	−0.0214581	+	0.0800828i	−0.975825	−	0.218555i	$-0.929866\pi$
$409$	−8.77637	+	32.7539i	−0.0214581	+	0.0800828i	0.954366	+	0.298638i	$0.0965323\pi$
$410$	−151.040	−	40.4711i	−0.368391	−	0.0987101i
$411$	105.983	−	105.983i	0.257865	−	0.257865i
$412$	−79.1103	−	137.023i	−0.192015	−	0.332580i
$413$	640.477	+	369.779i	1.55079	+	0.895350i
$414$	15.9615	+	59.5692i	0.0385544	+	0.143887i
$415$		−	63.5307i		−	0.153086i
$416$	−52.0000	+	52.0000i	−0.125000	+	0.125000i
$417$	−409.990			−0.983189
$418$	−40.2102	+	10.7743i	−0.0961967	+	0.0257758i
$419$	144.000	−	249.415i	0.343675	−	0.595263i	−0.641437	−	0.767176i	$-0.721661\pi$
$419$	144.000	−	249.415i	0.343675	−	0.595263i	0.985112	+	0.171913i	$0.0549947\pi$
$420$	−69.9615	+	40.3923i	−0.166575	+	0.0961722i
$421$	429.107	+	429.107i	1.01926	+	1.01926i	0.999811	+	0.0194456i	$0.00619013\pi$
$421$	429.107	+	429.107i	1.01926	+	1.01926i	0.0194456	+	0.999811i	$0.493810\pi$
$422$	66.5641	−	248.420i	0.157735	−	0.588674i
$423$	122.942	+	32.9423i	0.290644	+	0.0778777i
$424$	106.210	−	106.210i	0.250496	−	0.250496i
$425$	168.849	+	292.456i	0.397293	+	0.688131i
$426$	72.7461	+	42.0000i	0.170766	+	0.0985915i
$427$	151.135	+	564.042i	0.353945	+	1.32094i
$428$			335.636i			0.784196i
$429$	−20.9000	−	20.9000i	−0.0487180	−	0.0487180i
$430$	313.492			0.729052
$431$	394.186	−	105.622i	0.914584	−	0.245062i	0.229315	−	0.973352i	$-0.426351\pi$
$431$	394.186	−	105.622i	0.914584	−	0.245062i	0.685269	+	0.728290i	$0.259685\pi$
$432$	10.3923	−	18.0000i	0.0240563	−	0.0416667i
$433$	169.218	−	97.6980i	0.390804	−	0.225631i	−0.291705	−	0.956508i	$-0.594222\pi$
$433$	169.218	−	97.6980i	0.390804	−	0.225631i	0.682508	+	0.730878i	$0.260889\pi$
$434$	182.697	+	182.697i	0.420962	+	0.420962i
$435$	32.0096	−	119.462i	0.0735853	−	0.274624i
$436$	−83.3346	−	22.3294i	−0.191134	−	0.0512143i
$437$	−230.487	+	230.487i	−0.527430	+	0.527430i
$438$	−126.576	−	219.237i	−0.288987	−	0.500540i
$439$	210.588	+	121.583i	0.479700	+	0.276955i	0.720292	−	0.693671i	$-0.244008\pi$
$439$	210.588	+	121.583i	0.479700	+	0.276955i	−0.240591	+	0.970627i	$0.577341\pi$
$440$	−3.21539	−	12.0000i	−0.00730771	−	0.0272727i
$441$			1.27688i			0.00289541i
$442$	434.442	−	116.408i	0.982900	−	0.263367i
$443$	325.359			0.734445			0.367222	−	0.930133i	$-0.380309\pi$
$443$	325.359			0.734445			0.367222	+	0.930133i	$0.380309\pi$
$444$	51.2487	−	13.7321i	0.115425	−	0.0309280i
$445$	182.433	−	315.983i	0.409961	−	0.710073i
$446$	109.359	−	63.1384i	0.245200	−	0.141566i
$447$	251.060	+	251.060i	0.561655	+	0.561655i
$448$	14.4308	−	53.8564i	0.0322116	−	0.120215i
$449$	−103.878	−	27.8339i	−0.231353	−	0.0619909i	0.141280	−	0.989970i	$-0.454878\pi$
$449$	−103.878	−	27.8339i	−0.231353	−	0.0619909i	−0.372633	+	0.927979i	$0.621545\pi$
$450$	−41.4115	+	41.4115i	−0.0920257	+	0.0920257i
$451$	21.6884	+	37.5654i	0.0480896	+	0.0832937i
$452$	240.962	+	139.119i	0.533101	+	0.307786i
$453$	34.6166	+	129.191i	0.0764164	+	0.285190i
$454$		−	40.4411i		−	0.0890773i
$455$		−	303.167i		−	0.666300i
$456$	109.856			0.240913
$457$	87.0429	−	23.3231i	0.190466	−	0.0510352i	−0.162325	−	0.986737i	$-0.551899\pi$
$457$	87.0429	−	23.3231i	0.190466	−	0.0510352i	0.352791	+	0.935702i	$0.385233\pi$
$458$	−30.5692	+	52.9474i	−0.0667450	+	0.115606i
$459$	−110.088	+	63.5596i	−0.239844	+	0.138474i
$460$	−68.7846	−	68.7846i	−0.149532	−	0.149532i
$461$	−204.796	+	764.310i	−0.444243	+	1.65794i	0.273684	+	0.961820i	$0.411758\pi$
$461$	−204.796	+	764.310i	−0.444243	+	1.65794i	−0.717927	+	0.696118i	$0.754909\pi$
$462$	21.6462	+	5.80007i	0.0468532	+	0.0125543i
$463$	524.908	−	524.908i	1.13371	−	1.13371i	0.144154	−	0.989555i	$-0.453954\pi$
$463$	524.908	−	524.908i	1.13371	−	1.13371i	0.989555	−	0.144154i	$-0.0460462\pi$
$464$	42.6795	+	73.9230i	0.0919817	+	0.159317i
$465$	−131.569	−	75.9615i	−0.282945	−	0.163358i
$466$	10.2769	+	38.3538i	0.0220534	+	0.0823044i
$467$			159.397i			0.341322i	0.985330	+	0.170661i	$0.0545903\pi$
$467$			159.397i			0.341322i	−0.985330	+	0.170661i	$0.945410\pi$
$468$	39.0000	+	67.5500i	0.0833333	+	0.144338i
$469$	−386.144			−0.823334
$470$	−193.923	+	51.9615i	−0.412602	+	0.110556i
$471$	−228.887	+	396.444i	−0.485960	+	0.841707i
$472$	259.923	−	150.067i	0.550684	−	0.317938i
$473$	−61.4923	−	61.4923i	−0.130005	−	0.130005i
$474$	4.07695	−	15.2154i	0.00860116	−	0.0321000i
$475$	−298.995	−	80.1154i	−0.629463	−	0.168664i
$476$	−241.128	+	241.128i	−0.506572	+	0.506572i
$477$	−79.6577	−	137.971i	−0.166997	−	0.289248i
$478$	−125.454	−	72.4308i	−0.262456	−	0.151529i
$479$	−184.441	−	688.344i	−0.385054	−	1.43704i	−0.838081	−	0.545546i	$-0.816322\pi$
$479$	−184.441	−	688.344i	−0.385054	−	1.43704i	0.453027	−	0.891497i	$-0.350344\pi$
$480$			32.7846i			0.0683013i
$481$	−51.5333	+	192.325i	−0.107138	+	0.399844i
$482$	−453.699			−0.941284
$483$	169.492	−	45.4153i	0.350916	−	0.0940276i
$484$	119.277	−	206.594i	0.246440	−	0.426846i
$485$	−533.317	+	307.911i	−1.09962	+	0.634868i
$486$	−15.5885	−	15.5885i	−0.0320750	−	0.0320750i
$487$	−125.822	+	469.573i	−0.258361	+	0.964216i	0.707829	+	0.706384i	$0.249675\pi$
$487$	−125.822	+	469.573i	−0.258361	+	0.964216i	−0.966190	+	0.257832i	$0.916992\pi$
$488$	228.904	+	61.3346i	0.469065	+	0.125686i
$489$	305.751	−	305.751i	0.625258	−	0.625258i
$490$	−1.00704	−	1.74425i	−0.00205519	−	0.00355969i
$491$	−428.627	−	247.468i	−0.872967	−	0.504008i	−0.00463411	−	0.999989i	$-0.501475\pi$
$491$	−428.627	−	247.468i	−0.872967	−	0.504008i	−0.868333	+	0.495981i	$0.834808\pi$
$492$	−29.6269	−	110.569i	−0.0602173	−	0.224734i
$493$		−	522.058i		−	1.05894i
$494$	−206.133	+	357.033i	−0.417274	+	0.722740i
$495$	−13.1769			−0.0266200
$496$	101.282	−	27.1384i	0.204198	−	0.0547146i
$497$	119.503	−	206.985i	0.240448	−	0.416468i
$498$	40.2769	−	23.2539i	0.0808773	−	0.0466945i
$499$	−188.315	−	188.315i	−0.377385	−	0.377385i	0.492773	−	0.870158i	$-0.335983\pi$
$499$	−188.315	−	188.315i	−0.377385	−	0.377385i	−0.870158	+	0.492773i	$0.835983\pi$
$500$	67.2102	−	250.832i	0.134420	−	0.501664i
$501$	−454.277	−	121.723i	−0.906740	−	0.242960i
$502$	−217.492	+	217.492i	−0.433252	+	0.433252i
$503$	−464.894	−	805.219i	−0.924242	−	1.60083i	−0.792776	−	0.609513i	$-0.791365\pi$
$503$	−464.894	−	805.219i	−0.924242	−	1.60083i	−0.131465	−	0.991321i	$-0.541968\pi$
$504$	−51.2154	−	29.5692i	−0.101618	−	0.0586691i
$505$	−105.050	−	392.052i	−0.208020	−	0.776340i
$506$			26.9845i			0.0533291i
$507$	−292.717			−0.577350
$508$	84.7077			0.166747
$509$	−396.253	+	106.176i	−0.778493	+	0.208597i	−0.626120	−	0.779726i	$-0.715358\pi$
$509$	−396.253	+	106.176i	−0.778493	+	0.208597i	−0.152373	+	0.988323i	$0.548692\pi$
$510$	100.256	−	173.648i	0.196580	−	0.340486i
$511$	−623.794	+	360.147i	−1.22073	+	0.704789i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	30.1577	−	112.550i	0.0587869	−	0.219396i
$514$	451.662	+	121.023i	0.878720	+	0.235452i
$515$	187.177	−	187.177i	0.363450	−	0.363450i
$516$	114.746	+	198.746i	0.222376	+	0.385167i
$517$	48.2309	+	27.8461i	0.0932899	+	0.0538609i
$518$	−39.0718	−	145.818i	−0.0754282	−	0.281502i
$519$			354.200i			0.682466i
$520$	−106.550	−	61.5167i	−0.204904	−	0.118301i
$521$	10.9474			0.0210124			0.0105062	−	0.999945i	$-0.496656\pi$
$521$	10.9474			0.0210124			0.0105062	+	0.999945i	$0.496656\pi$
$522$	87.4519	−	23.4327i	0.167532	−	0.0448902i
$523$	−207.335	+	359.114i	−0.396433	+	0.686643i	−0.993283	−	0.115711i	$-0.963086\pi$
$523$	−207.335	+	359.114i	−0.396433	+	0.686643i	0.596850	+	0.802353i	$0.296419\pi$
$524$	322.277	−	186.067i	0.615032	−	0.355089i
$525$	117.828	+	117.828i	0.224435	+	0.224435i
$526$	−47.3027	+	176.536i	−0.0899290	+	0.335620i
$527$	−619.443	−	165.979i	−1.17541	−	0.314951i
$528$	6.43078	−	6.43078i	0.0121795	−	0.0121795i
$529$	−158.854	−	275.143i	−0.300291	−	0.520119i
$530$	217.629	+	125.648i	0.410620	+	0.237072i
$531$	−82.3923	−	307.492i	−0.155164	−	0.579081i
$532$		−	312.574i		−	0.587546i
$533$	414.942	+	111.183i	0.778502	+	0.208599i
$534$	267.100			0.500187
$535$	−542.396	+	145.335i	−1.01382	+	0.271653i
$536$	−78.3538	+	135.713i	−0.146183	+	0.253196i
$537$	201.258	−	116.196i	0.374781	−	0.216380i
$538$	−446.487	−	446.487i	−0.829902	−	0.829902i
$539$	−0.144605	+	0.539672i	−0.000268283	+	0.00100125i
$540$	33.5885	+	9.00000i	0.0622008	+	0.0166667i
$541$	−630.590	+	630.590i	−1.16560	+	1.16560i	−0.182372	+	0.983230i	$0.558377\pi$
$541$	−630.590	+	630.590i	−1.16560	+	1.16560i	−0.983230	+	0.182372i	$0.941623\pi$
$542$	251.426	+	435.482i	0.463885	+	0.803472i
$543$	181.069	+	104.540i	0.333461	+	0.192524i
$544$	35.8179	+	133.674i	0.0658418	+	0.245725i
$545$		−	144.340i		−	0.264844i
$546$	192.200	−	110.967i	0.352015	−	0.203236i
$547$	907.854			1.65970			0.829848	−	0.557990i	$-0.188427\pi$
$547$	907.854			1.65970			0.829848	+	0.557990i	$0.188427\pi$
$548$	−167.172	+	44.7935i	−0.305058	+	0.0817400i
$549$	125.677	−	217.679i	0.228920	−	0.396501i
$550$	−22.1924	+	12.8128i	−0.0403498	+	0.0232960i
$551$	338.372	+	338.372i	0.614105	+	0.614105i
$552$	18.4308	−	68.7846i	0.0333891	−	0.124610i
$553$	−43.2923	−	11.6001i	−0.0782863	−	0.0209768i
$554$	−101.942	+	101.942i	−0.184011	+	0.184011i
$555$	44.3827	+	76.8731i	0.0799688	+	0.138510i
$556$	409.990	+	236.708i	0.737392	+	0.425733i
$557$	−191.583	−	714.996i	−0.343954	−	1.28366i	−0.893829	−	0.448408i	$-0.851991\pi$
$557$	−191.583	−	714.996i	−0.343954	−	1.28366i	0.549875	−	0.835247i	$-0.314676\pi$
$558$		−	111.215i		−	0.199311i
$559$	−861.233			−1.54067
$560$	93.2820			0.166575
$561$	−53.7269	+	14.3961i	−0.0957699	+	0.0256615i
$562$	−13.1647	+	22.8020i	−0.0234248	+	0.0405729i
$563$	30.0000	−	17.3205i	0.0532860	−	0.0307647i	−0.473120	−	0.880998i	$-0.656872\pi$
$563$	30.0000	−	17.3205i	0.0532860	−	0.0307647i	0.526406	+	0.850233i	$0.323539\pi$
$564$	−103.923	−	103.923i	−0.184261	−	0.184261i
$565$	−120.481	+	449.640i	−0.213240	+	0.795824i
$566$	−480.956	−	128.872i	−0.849746	−	0.227689i
$567$	−44.3538	+	44.3538i	−0.0782254	+	0.0782254i
$568$	−48.4974	−	84.0000i	−0.0853828	−	0.147887i
$569$	567.300	+	327.531i	0.997012	+	0.575625i	0.907363	−	0.420348i	$-0.138092\pi$
$569$	567.300	+	327.531i	0.997012	+	0.575625i	0.0896492	+	0.995973i	$0.471425\pi$
$570$	47.5692	+	177.531i	0.0834548	+	0.311457i
$571$			1041.18i			1.82343i	0.410826	+	0.911714i	$0.365240\pi$
$571$			1041.18i			1.82343i	−0.410826	+	0.911714i	$0.634760\pi$
$572$	8.83340	+	32.9667i	0.0154430	+	0.0576341i
$573$	427.061			0.745308
$574$	−314.603	+	84.2975i	−0.548088	+	0.146860i
$575$	−100.326	+	173.769i	−0.174479	+	0.302207i
$576$	−20.7846	+	12.0000i	−0.0360844	+	0.0208333i
$577$	107.711	+	107.711i	0.186674	+	0.186674i	0.794257	−	0.607583i	$-0.207861\pi$
$577$	107.711	+	107.711i	0.186674	+	0.186674i	−0.607583	+	0.794257i	$0.707861\pi$
$578$	113.282	−	422.774i	0.195990	−	0.731443i
$579$	−50.7224	−	13.5910i	−0.0876035	−	0.0234733i
$580$	−100.981	+	100.981i	−0.174105	+	0.174105i
$581$	−66.1642	−	114.600i	−0.113880	−	0.197246i
$582$	−390.415	−	225.406i	−0.670817	−	0.387296i
$583$	−18.0422	−	67.3346i	−0.0309473	−	0.115497i
$584$			292.315i			0.500540i
$585$	−92.2750	+	92.2750i	−0.157735	+	0.157735i
$586$	317.611			0.541999
$587$	423.100	−	113.369i	0.720784	−	0.193133i	0.120262	−	0.992742i	$-0.461626\pi$
$587$	423.100	−	113.369i	0.720784	−	0.193133i	0.600521	+	0.799609i	$0.294960\pi$
$588$	0.737206	−	1.27688i	0.00125375	−	0.00217156i
$589$	509.072	−	293.913i	0.864298	−	0.499003i
$590$	355.061	+	355.061i	0.601799	+	0.601799i
$591$	17.2327	−	64.3135i	0.0291586	−	0.108821i
$592$	−59.1769	−	15.8564i	−0.0999610	−	0.0267845i
$593$	25.8531	−	25.8531i	0.0435972	−	0.0435972i	−0.684972	−	0.728569i	$-0.740186\pi$
$593$	25.8531	−	25.8531i	0.0435972	−	0.0435972i	0.728569	+	0.684972i	$0.240186\pi$
$594$	−4.82309	−	8.35383i	−0.00811967	−	0.0140637i
$595$	−494.081	−	285.258i	−0.830388	−	0.479425i
$596$	−106.110	−	396.009i	−0.178037	−	0.664445i
$597$		−	171.167i		−	0.286711i
$598$	188.967	+	188.967i	0.315998	+	0.315998i
$599$	760.077			1.26891			0.634455	−	0.772960i	$-0.281225\pi$
$599$	760.077			1.26891			0.634455	+	0.772960i	$0.281225\pi$
$600$	65.3205	−	17.5026i	0.108868	−	0.0291710i
$601$	−297.775	+	515.761i	−0.495466	+	0.858172i	−0.999986	−	0.00522767i	$-0.998336\pi$
$601$	−297.775	+	515.761i	−0.495466	+	0.858172i	0.504520	+	0.863400i	$0.331669\pi$
$602$	565.492	−	326.487i	0.939356	−	0.542337i
$603$	117.531	+	117.531i	0.194910	+	0.194910i
$604$	39.9718	−	149.177i	0.0661785	−	0.246982i
$605$	385.509	+	103.297i	0.637205	+	0.170739i
$606$	210.100	−	210.100i	0.346700	−	0.346700i
$607$	−83.9615	−	145.426i	−0.138322	−	0.239581i	0.788539	−	0.614984i	$-0.210838\pi$
$607$	−83.9615	−	145.426i	−0.138322	−	0.239581i	−0.926862	+	0.375403i	$0.877504\pi$
$608$	−109.856	−	63.4256i	−0.180685	−	0.104318i
$609$	−66.6730	−	248.827i	−0.109479	−	0.408583i
$610$			396.473i			0.649956i
$611$	532.750	−	142.750i	0.871931	−	0.233633i
$612$	146.785			0.239844
$613$	−465.949	+	124.851i	−0.760112	+	0.203671i	−0.617999	−	0.786179i	$-0.712056\pi$
$613$	−465.949	+	124.851i	−0.760112	+	0.203671i	−0.142113	+	0.989850i	$0.545390\pi$
$614$	−75.6743	+	131.072i	−0.123248	+	0.213472i
$615$	165.854	−	95.7558i	0.269681	−	0.155700i
$616$	−18.2975	−	18.2975i	−0.0297037	−	0.0297037i
$617$	−68.3217	+	254.980i	−0.110732	+	0.413258i	−0.998932	−	0.0461989i	$-0.985289\pi$
$617$	−68.3217	+	254.980i	−0.110732	+	0.413258i	0.888200	+	0.459457i	$0.151956\pi$
$618$	187.177	+	50.1539i	0.302875	+	0.0811552i
$619$	157.520	−	157.520i	0.254476	−	0.254476i	−0.568327	−	0.822803i	$-0.692409\pi$
$619$	157.520	−	157.520i	0.254476	−	0.254476i	0.822803	+	0.568327i	$0.192409\pi$
$620$	87.7128	+	151.923i	0.141472	+	0.245037i
$621$	−65.4115	−	37.7654i	−0.105333	−	0.0608138i
$622$	−88.2769	−	329.454i	−0.141924	−	0.529668i
$623$		−	759.979i		−	1.21987i
$624$		−	90.0666i		−	0.144338i
$625$	89.3576			0.142972
$626$	−707.769	+	189.646i	−1.13062	+	0.302949i
$627$	25.4923	−	44.1539i	0.0406575	−	0.0704209i
$628$	457.774	−	264.296i	0.728940	−	0.420854i
$629$	264.949	+	264.949i	0.421223	+	0.421223i
$630$	25.6077	−	95.5692i	0.0406471	−	0.151697i
$631$	876.726	+	234.918i	1.38942	+	0.372295i	0.874535	−	0.484963i	$-0.161167\pi$
$631$	876.726	+	234.918i	1.38942	+	0.372295i	0.514888	+	0.857258i	$0.327834\pi$
$632$	−12.8616	+	12.8616i	−0.0203506	+	0.0203506i
$633$	157.492	+	272.785i	0.248803	+	0.430939i
$634$	−632.002	−	364.886i	−0.996848	−	0.575531i
$635$	36.6795	+	136.890i	0.0577630	+	0.215574i
$636$			183.962i			0.289248i
$637$	2.76657	+	4.79184i	0.00434312	+	0.00752251i
$638$	39.6152			0.0620929
$639$	−99.3731	+	26.6269i	−0.155513	+	0.0416697i
$640$	18.9282	−	32.7846i	0.0295753	−	0.0512260i
$641$	113.425	−	65.4859i	0.176950	−	0.102162i	−0.408909	−	0.912575i	$-0.634091\pi$
$641$	113.425	−	65.4859i	0.176950	−	0.102162i	0.585859	+	0.810413i	$0.300757\pi$
$642$	−290.669	−	290.669i	−0.452756	−	0.452756i
$643$	133.023	−	496.449i	0.206879	−	0.772082i	−0.781990	−	0.623291i	$-0.785795\pi$
$643$	133.023	−	496.449i	0.206879	−	0.772082i	0.988869	−	0.148791i	$-0.0475381\pi$
$644$	−195.713	−	52.4411i	−0.303902	−	0.0814303i
$645$	−271.492	+	271.492i	−0.420918	+	0.420918i
$646$	387.913	+	671.885i	0.600484	+	1.04007i
$647$	−671.138	−	387.482i	−1.03731	−	0.598890i	−0.118239	−	0.992985i	$-0.537725\pi$
$647$	−671.138	−	387.482i	−1.03731	−	0.598890i	−0.919070	+	0.394095i	$0.871058\pi$
$648$	6.58846	+	24.5885i	0.0101674	+	0.0379452i
$649$		−	139.292i		−	0.214626i
$650$	−65.6833	+	245.133i	−0.101051	+	0.377128i
$651$	−316.441			−0.486085
$652$	−482.277	+	129.226i	−0.739688	+	0.198199i
$653$	74.1718	−	128.469i	0.113586	−	0.196737i	−0.803628	−	0.595133i	$-0.797100\pi$
$653$	74.1718	−	128.469i	0.113586	−	0.196737i	0.917214	+	0.398396i	$0.130433\pi$
$654$	91.5077	−	52.8320i	0.139920	−	0.0807829i
$655$	440.238	+	440.238i	0.672120	+	0.672120i
$656$	−34.2102	+	127.674i	−0.0521497	+	0.194626i
$657$	299.483	+	80.2461i	0.455834	+	0.122140i
$658$	−295.692	+	295.692i	−0.449380	+	0.449380i
$659$	19.4078	+	33.6152i	0.0294503	+	0.0510095i	0.880375	−	0.474278i	$-0.157291\pi$
$659$	19.4078	+	33.6152i	0.0294503	+	0.0510095i	−0.850925	+	0.525288i	$0.823958\pi$
$660$	13.1769	+	7.60770i	0.0199650	+	0.0115268i
$661$	−161.738	−	603.616i	−0.244687	−	0.913186i	−0.973540	−	0.228516i	$-0.926613\pi$
$661$	−161.738	−	603.616i	−0.244687	−	0.913186i	0.728853	−	0.684670i	$-0.240054\pi$
$662$		−	347.923i		−	0.525564i
$663$	−275.425	+	477.050i	−0.415422	+	0.719532i
$664$	−53.7025			−0.0808773
$665$	505.128	−	135.349i	0.759591	−	0.203532i
$666$	−32.4904	+	56.2750i	−0.0487844	+	0.0844970i
$667$	268.634	−	155.096i	0.402750	−	0.232528i
$668$	384.000	+	384.000i	0.574850	+	0.574850i
$669$	−40.0282	+	149.387i	−0.0598328	+	0.223299i
$670$	−253.244	−	67.8564i	−0.377975	−	0.101278i
$671$	77.7691	−	77.7691i	0.115900	−	0.115900i
$672$	34.1436	+	59.1384i	0.0508089	+	0.0880036i
$673$	647.667	+	373.931i	0.962358	+	0.555618i	0.896898	−	0.442237i	$-0.145815\pi$
$673$	647.667	+	373.931i	0.962358	+	0.555618i	0.0654602	+	0.997855i	$0.479148\pi$
$674$	95.5045	+	356.428i	0.141698	+	0.528824i
$675$		−	71.7269i		−	0.106262i
$676$	292.717	+	169.000i	0.433013	+	0.250000i
$677$	1264.68			1.86806			0.934030	−	0.357194i	$-0.116267\pi$
$677$	1264.68			1.86806			0.934030	+	0.357194i	$0.116267\pi$
$678$	−329.160	+	88.1980i	−0.485486	+	0.130086i
$679$	−641.349	+	1110.85i	−0.944549	+	1.63601i
$680$	−200.512	+	115.765i	−0.294870	+	0.170243i
$681$	35.0230	+	35.0230i	0.0514288	+	0.0514288i
$682$	12.5950	−	47.0052i	0.0184677	−	0.0689225i
$683$	198.382	+	53.1563i	0.290457	+	0.0778277i	0.401105	−	0.916032i	$-0.368626\pi$
$683$	198.382	+	53.1563i	0.290457	+	0.0778277i	−0.110649	+	0.993860i	$0.535293\pi$
$684$	−95.1384	+	95.1384i	−0.139091	+	0.139091i
$685$	−144.775	−	250.758i	−0.211350	−	0.366070i
$686$	−421.892	−	243.580i	−0.615003	−	0.355072i
$687$	−19.3801	−	72.3275i	−0.0282098	−	0.105280i
$688$		−	264.995i		−	0.385167i
$689$	−597.875	−	345.183i	−0.867743	−	0.500992i
$690$	119.138			0.172664
$691$	−243.335	+	65.2013i	−0.352148	+	0.0943579i	−0.430557	−	0.902563i	$-0.641683\pi$
$691$	−243.335	+	65.2013i	−0.352148	+	0.0943579i	0.0784085	+	0.996921i	$0.475016\pi$
$692$	204.497	−	354.200i	0.295517	−	0.511850i
$693$	−23.7691	+	13.7231i	−0.0342989	+	0.0198025i
$694$	224.833	+	224.833i	0.323967	+	0.323967i
$695$	−204.995	+	765.051i	−0.294957	+	1.10079i
$696$	−100.981	−	27.0577i	−0.145087	−	0.0388760i
$697$	571.629	−	571.629i	0.820127	−	0.820127i
$698$	−3.15390	−	5.46272i	−0.00451849	−	0.00782625i
$699$	−42.1154	−	24.3154i	−0.0602510	−	0.0347859i
$700$	−49.8001	−	185.856i	−0.0711430	−	0.265509i
$701$		−	205.026i		−	0.292476i	−0.989249	−	0.146238i	$-0.953283\pi$
$701$		−	205.026i		−	0.292476i	0.989249	−	0.146238i	$-0.0467166\pi$
$702$	−92.2750	−	24.7250i	−0.131446	−	0.0352208i
$703$	−343.454			−0.488554
$704$	−10.1436	+	2.71797i	−0.0144085	+	0.00386075i
$705$	122.942	−	212.942i	0.174386	−	0.302046i
$706$	−545.044	+	314.681i	−0.772017	+	0.445724i
$707$	−597.797	−	597.797i	−0.845541	−	0.845541i
$708$	−95.1384	+	355.061i	−0.134376	+	0.501499i
$709$	−122.920	−	32.9364i	−0.173372	−	0.0464548i	0.171089	−	0.985256i	$-0.445271\pi$
$709$	−122.920	−	32.9364i	−0.173372	−	0.0464548i	−0.344460	+	0.938801i	$0.611938\pi$
$710$	114.746	−	114.746i	0.161614	−	0.161614i
$711$	9.64617	+	16.7077i	0.0135670	+	0.0234988i
$712$	−267.100	−	154.210i	−0.375140	−	0.216587i
$713$	−98.6204	−	368.056i	−0.138318	−	0.516208i
$714$		−	417.646i		−	0.584939i
$715$	−49.4500	+	28.5500i	−0.0691609	+	0.0399300i
$716$	−268.344			−0.374781
$717$	171.373	−	45.9193i	0.239014	−	0.0640436i
$718$	123.415	−	213.762i	0.171888	−	0.297718i
$719$	619.146	−	357.464i	0.861121	−	0.497168i	−0.00326653	−	0.999995i	$-0.501040\pi$
$719$	619.146	−	357.464i	0.861121	−	0.497168i	0.864388	+	0.502826i	$0.167706\pi$
$720$	−28.3923	−	28.3923i	−0.0394338	−	0.0394338i
$721$	142.703	−	532.574i	0.197924	−	0.738661i
$722$	−193.772	−	51.9212i	−0.268383	−	0.0719130i
$723$	392.915	−	392.915i	0.543450	−	0.543450i
$724$	−120.713	−	209.081i	−0.166730	−	0.288786i
$725$	255.106	+	147.285i	0.351870	+	0.203152i
$726$	75.6185	+	282.212i	0.104158	+	0.388722i
$727$			1024.72i			1.40951i	0.709450	+	0.704756i	$0.248944\pi$
$727$			1024.72i			1.40951i	−0.709450	+	0.704756i	$0.751056\pi$
$728$	−256.267			−0.352015
$729$	27.0000			0.0370370
$730$	−472.389	+	126.576i	−0.647108	+	0.173392i
$731$	−810.358	+	1403.58i	−1.10856	+	1.92008i
$732$	−251.354	+	145.119i	−0.343380	+	0.198250i
$733$	−66.3069	−	66.3069i	−0.0904597	−	0.0904597i	0.660429	−	0.750889i	$-0.270374\pi$
$733$	−66.3069	−	66.3069i	−0.0904597	−	0.0904597i	−0.750889	+	0.660429i	$0.770374\pi$
$734$	161.167	−	601.482i	0.219573	−	0.819458i
$735$	2.38269	+	0.638439i	0.00324175	+	0.000868624i
$736$	−58.1436	+	58.1436i	−0.0789994	+	0.0789994i
$737$	36.3641	+	62.9845i	0.0493408	+	0.0854607i
$738$	121.413	+	70.0981i	0.164517	+	0.0949838i
$739$	−232.595	−	868.056i	−0.314743	−	1.17464i	−0.924229	−	0.381839i	$-0.875291\pi$
$739$	−232.595	−	868.056i	−0.314743	−	1.17464i	0.609486	−	0.792797i	$-0.291376\pi$
$740$		−	102.497i		−	0.138510i
$741$	−130.683	−	487.717i	−0.176361	−	0.658187i
$742$	523.426			0.705425
$743$	−610.841	+	163.674i	−0.822128	+	0.220288i	−0.645276	−	0.763949i	$-0.723258\pi$
$743$	−610.841	+	163.674i	−0.822128	+	0.220288i	−0.176851	+	0.984238i	$0.556591\pi$
$744$	−64.2102	+	111.215i	−0.0863041	+	0.149483i
$745$	594.013	−	342.954i	0.797333	−	0.460341i
$746$	−186.440	−	186.440i	−0.249919	−	0.249919i
$747$	−14.7424	+	55.0192i	−0.0197354	+	0.0736536i
$748$	62.0385	+	16.6232i	0.0829391	+	0.0222235i
$749$	−827.041	+	827.041i	−1.10419	+	1.10419i
$750$	159.021	+	275.433i	0.212028	+	0.367244i
$751$	138.389	+	79.8987i	0.184272	+	0.106390i	0.589298	−	0.807915i	$-0.299404\pi$
$751$	138.389	+	79.8987i	0.184272	+	0.106390i	−0.405026	+	0.914305i	$0.632738\pi$
$752$	43.9230	+	163.923i	0.0584083	+	0.217983i
$753$		−	376.708i		−	0.500276i
$754$	277.417	−	277.417i	0.367927	−	0.367927i
$755$	258.382			0.342228
$756$	69.9615	−	18.7461i	0.0925417	−	0.0247965i
$757$	−76.1281	+	131.858i	−0.100566	+	0.174185i	−0.911918	−	0.410373i	$-0.865399\pi$
$757$	−76.1281	+	131.858i	−0.100566	+	0.174185i	0.811352	+	0.584558i	$0.198732\pi$
$758$	674.487	−	389.415i	0.889825	−	0.513741i
$759$	−23.3693	−	23.3693i	−0.0307896	−	0.0307896i
$760$	54.9282	−	204.995i	0.0722740	−	0.269730i
$761$	−966.015	−	258.843i	−1.26940	−	0.340135i	−0.439600	−	0.898194i	$-0.644880\pi$
$761$	−966.015	−	258.843i	−1.26940	−	0.340135i	−0.829802	+	0.558059i	$0.811546\pi$
$762$	−73.3590	+	73.3590i	−0.0962716	+	0.0962716i
$763$	−150.323	−	260.367i	−0.197016	−	0.341241i
$764$	−427.061	−	246.564i	−0.558981	−	0.322728i
$765$	63.5596	+	237.208i	0.0830844	+	0.310075i
$766$		−	166.010i		−	0.216724i
$767$	−975.433	−	975.433i	−1.27175	−	1.27175i
$768$	27.7128			0.0360844
$769$	754.494	−	202.166i	0.981137	−	0.262895i	0.267613	−	0.963526i	$-0.413765\pi$
$769$	754.494	−	202.166i	0.981137	−	0.262895i	0.713523	+	0.700632i	$0.247098\pi$
$770$	21.6462	−	37.4923i	0.0281119	−	0.0486913i
$771$	−495.959	+	286.342i	−0.643268	+	0.371391i
$772$	42.8756	+	42.8756i	0.0555384	+	0.0555384i
$773$	−357.816	+	1335.39i	−0.462893	+	1.72754i	0.200890	+	0.979614i	$0.435617\pi$
$773$	−357.816	+	1335.39i	−0.462893	+	1.72754i	−0.663783	+	0.747925i	$0.731050\pi$
$774$	−271.492	−	72.7461i	−0.350765	−	0.0939873i
$775$	255.867	−	255.867i	0.330151	−	0.330151i
$776$	260.277	+	450.813i	0.335408	+	0.580944i
$777$	160.119	+	92.4449i	0.206074	+	0.118977i
$778$	−41.6546	−	155.457i	−0.0535406	−	0.199816i
$779$			741.002i			0.951223i
$780$	145.550	−	39.0000i	0.186603	−	0.0500000i
$781$	−45.0155			−0.0576382
$782$	485.769	−	130.161i	0.621188	−	0.166447i
$783$	−55.4423	+	96.0289i	−0.0708075	+	0.122642i
$784$	−1.47441	+	0.851252i	−0.00188063	+	0.00108578i
$785$	625.331	+	625.331i	0.796600	+	0.796600i
$786$	−117.962	+	440.238i	−0.150078	+	0.560100i
$787$	188.459	+	50.4974i	0.239465	+	0.0641645i	0.376555	−	0.926394i	$-0.377108\pi$
$787$	188.459	+	50.4974i	0.239465	+	0.0641645i	−0.137090	+	0.990559i	$0.543775\pi$
$788$	−54.3641	+	54.3641i	−0.0689900	+	0.0689900i
$789$	−111.919	−	193.850i	−0.141850	−	0.245691i
$790$	−26.3538	−	15.2154i	−0.0333593	−	0.0192600i
$791$	250.950	+	936.558i	0.317256	+	1.18402i
$792$			11.1384i			0.0140637i
$793$		−	1089.20i		−	1.37352i
$794$	−129.405			−0.162979
$795$	−297.286	+	79.6577i	−0.373945	+	0.100198i
$796$	−98.8231	+	171.167i	−0.124150	+	0.215033i
$797$	−897.327	+	518.072i	−1.12588	+	0.650027i	−0.942896	−	0.333088i	$-0.891909\pi$
$797$	−897.327	+	518.072i	−1.12588	+	0.650027i	−0.182985	+	0.983116i	$0.558576\pi$
$798$	270.697	+	270.697i	0.339220	+	0.339220i
$799$	268.634	−	1002.56i	0.336213	−	1.25477i
$800$	−75.4256	−	20.2102i	−0.0942820	−	0.0252628i
$801$	−231.315	+	231.315i	−0.288783	+	0.288783i
$802$	73.5866	+	127.456i	0.0917538	+	0.158922i
$803$	117.488	+	67.8320i	0.146312	+	0.0844732i
$804$	−49.6743	−	185.387i	−0.0617840	−	0.230581i
$805$		−	338.985i		−	0.421099i
$806$	−240.967	−	417.367i	−0.298966	−	0.517824i
$807$	773.338			0.958288
$808$	−331.401	+	88.7987i	−0.410150	+	0.109899i
$809$	244.852	−	424.096i	0.302660	−	0.524223i	−0.674078	−	0.738661i	$-0.735459\pi$
$809$	244.852	−	424.096i	0.302660	−	0.524223i	0.976738	+	0.214438i	$0.0687920\pi$
$810$	−36.8827	+	21.2942i	−0.0455342	+	0.0262892i
$811$	143.580	+	143.580i	0.177040	+	0.177040i	0.790064	−	0.613024i	$-0.210047\pi$
$811$	143.580	+	143.580i	0.177040	+	0.177040i	−0.613024	+	0.790064i	$0.710047\pi$
$812$	−76.9873	+	287.321i	−0.0948119	+	0.353843i
$813$	−594.879	−	159.397i	−0.731709	−	0.196061i
$814$	−20.1051	+	20.1051i	−0.0246992	+	0.0246992i
$815$	−417.664	−	723.415i	−0.512471	−	0.887626i
$816$	−146.785	−	84.7461i	−0.179883	−	0.103856i
$817$	−384.497	−	1434.96i	−0.470621	−	1.75638i
$818$			47.9550i			0.0586247i
$819$	−70.3501	+	262.550i	−0.0858975	+	0.320574i
$820$	−221.138			−0.269681
$821$	−110.217	+	29.5326i	−0.134248	+	0.0359715i	−0.325317	−	0.945605i	$-0.605471\pi$
$821$	−110.217	+	29.5326i	−0.134248	+	0.0359715i	0.191070	+	0.981576i	$0.438804\pi$
$822$	105.983	−	183.567i	0.128933	−	0.223318i
$823$	−328.361	+	189.580i	−0.398981	+	0.230352i	−0.686044	−	0.727560i	$-0.740654\pi$
$823$	−328.361	+	189.580i	−0.398981	+	0.230352i	0.287063	+	0.957912i	$0.407321\pi$
$824$	−158.221	−	158.221i	−0.192015	−	0.192015i
$825$	8.12297	−	30.3154i	0.00984603	−	0.0367459i
$826$	1010.26	+	270.697i	1.22307	+	0.327721i
$827$	−186.249	+	186.249i	−0.225210	+	0.225210i	−0.810688	−	0.585478i	$-0.800907\pi$
$827$	−186.249	+	186.249i	−0.225210	+	0.225210i	0.585478	+	0.810688i	$0.300907\pi$
$828$	43.6077	+	75.5307i	0.0526663	+	0.0912207i
$829$	1254.03	+	724.013i	1.51270	+	0.873358i	0.999890	+	0.0148554i	$0.00472879\pi$
$829$	1254.03	+	724.013i	1.51270	+	0.873358i	0.512810	+	0.858502i	$0.328605\pi$
$830$	−23.2539	−	86.7846i	−0.0280167	−	0.104560i
$831$		−	176.569i		−	0.212478i
$832$	−52.0000	+	90.0666i	−0.0625000	+	0.108253i
$833$	10.4126			0.0125001
$834$	−560.056	+	150.067i	−0.671530	+	0.179936i
$835$	−454.277	+	786.831i	−0.544044	+	0.942312i
$836$	−50.9845	+	29.4359i	−0.0609863	+	0.0352104i
$837$	96.3154	+	96.3154i	0.115072	+	0.115072i
$838$	105.415	−	393.415i	0.125794	−	0.469469i
$839$	−252.995	−	67.7898i	−0.301543	−	0.0807983i	0.104875	−	0.994485i	$-0.466556\pi$
$839$	−252.995	−	67.7898i	−0.301543	−	0.0807983i	−0.406418	+	0.913687i	$0.633222\pi$
$840$	−80.7846	+	80.7846i	−0.0961722	+	0.0961722i
$841$	192.808	+	333.953i	0.229260	+	0.397090i
$842$	743.235	+	429.107i	0.882702	+	0.509628i
$843$	−8.34610	−	31.1481i	−0.00990047	−	0.0369491i
$844$		−	363.713i		−	0.430939i
$845$	−146.358	+	546.217i	−0.173205	+	0.646410i
$846$	180.000			0.212766
$847$	802.978	−	215.157i	0.948026	−	0.254023i
$848$	106.210	−	183.962i	0.125248	−	0.216936i
$849$	528.127	−	304.914i	0.622057	−	0.359145i
$850$	337.699	+	337.699i	0.397293	+	0.397293i
$851$	−57.6218	+	215.047i	−0.0677107	+	0.252700i
$852$	114.746	+	30.7461i	0.134679	+	0.0360870i
$853$	−405.969	+	405.969i	−0.475930	+	0.475930i	−0.903827	−	0.427897i	$-0.859255\pi$
$853$	−405.969	+	405.969i	−0.475930	+	0.475930i	0.427897	+	0.903827i	$0.359255\pi$
$854$	412.908	+	715.177i	0.483498	+	0.837444i
$855$	−194.942	−	112.550i	−0.228003	−	0.131637i
$856$	122.851	+	458.487i	0.143518	+	0.535616i
$857$		−	1063.77i		−	1.24127i	−0.784100	−	0.620635i	$-0.786875\pi$
$857$		−	1063.77i		−	1.24127i	0.784100	−	0.620635i	$-0.213125\pi$
$858$	−36.1999	−	20.9000i	−0.0421911	−	0.0243590i
$859$	−1064.54			−1.23928			−0.619640	−	0.784887i	$-0.712721\pi$
$859$	−1064.54			−1.23928			−0.619640	+	0.784887i	$0.712721\pi$
$860$	428.238	−	114.746i	0.497952	−	0.133426i
$861$	199.450	−	345.458i	0.231649	−	0.401228i
$862$	499.808	−	288.564i	0.579823	−	0.334761i
$863$	−808.677	−	808.677i	−0.937053	−	0.937053i	0.0610799	−	0.998133i	$-0.480546\pi$
$863$	−808.677	−	808.677i	−0.937053	−	0.937053i	−0.998133	+	0.0610799i	$0.980546\pi$
$864$	7.60770	−	28.3923i	0.00880520	−	0.0328615i
$865$	660.946	+	177.100i	0.764099	+	0.204740i
$866$	195.396	−	195.396i	0.225631	−	0.225631i
$867$	268.028	+	464.238i	0.309144	+	0.535454i
$868$	316.441	+	182.697i	0.364563	+	0.210481i
$869$	2.18483	+	8.15390i	0.00251419	+	0.00938309i
$870$		−	174.904i		−	0.201039i
$871$	695.717	+	186.417i	0.798756	+	0.214026i
$872$	−122.010			−0.139920
$873$	533.317	−	142.902i	0.610902	−	0.163691i
$874$	−230.487	+	399.215i	−0.263715	+	0.456768i
$875$	783.688	−	452.463i	0.895644	−	0.517100i
$876$	−253.153	−	253.153i	−0.288987	−	0.288987i
$877$	−53.7327	+	200.533i	−0.0612688	+	0.228658i	−0.989770	−	0.142671i	$-0.954431\pi$
$877$	−53.7327	+	200.533i	−0.0612688	+	0.228658i	0.928501	+	0.371329i	$0.121098\pi$
$878$	332.172	+	89.0052i	0.378328	+	0.101373i
$879$	−275.060	+	275.060i	−0.312923	+	0.312923i
$880$	−8.78461	−	15.2154i	−0.00998251	−	0.0172902i
$881$	226.758	+	130.919i	0.257387	+	0.148602i	0.623142	−	0.782109i	$-0.285856\pi$
$881$	226.758	+	130.919i	0.257387	+	0.148602i	−0.365755	+	0.930711i	$0.619189\pi$
$882$	0.467370	+	1.74425i	0.000529898	+	0.00197760i
$883$		−	910.369i		−	1.03100i	−0.856891	−	0.515498i	$-0.827607\pi$
$883$		−	910.369i		−	1.03100i	0.856891	−	0.515498i	$-0.172393\pi$
$884$	550.850	−	318.033i	0.623133	−	0.359766i
$885$	−614.985			−0.694898
$886$	444.449	−	119.090i	0.501635	−	0.134413i
$887$	−166.077	+	287.654i	−0.187234	+	0.324300i	−0.944327	−	0.329008i	$-0.893286\pi$
$887$	−166.077	+	287.654i	−0.187234	+	0.324300i	0.757093	+	0.653307i	$0.226619\pi$
$888$	64.9808	−	37.5167i	0.0731765	−	0.0422485i
$889$	208.728	+	208.728i	0.234790	+	0.234790i
$890$	133.550	−	498.415i	0.150056	−	0.560017i
$891$	11.4115	+	3.05771i	0.0128076	+	0.00343178i
$892$	126.277	−	126.277i	0.141566	−	0.141566i
$893$	475.692	+	823.923i	0.532690	+	0.922646i
$894$	434.848	+	251.060i	0.486407	+	0.280827i
$895$	−116.196	−	433.650i	−0.129828	−	0.484525i
$896$		−	78.8513i		−	0.0880036i
$897$	−327.300			−0.364883
$898$	−152.087			−0.169362
$899$	−540.333	+	144.782i	−0.601038	+	0.161048i
$900$	−41.4115	+	71.7269i	−0.0460128	+	0.0796966i
$901$	−1125.11	+	649.584i	−1.24874	+	0.720959i
$902$	43.3768	+	43.3768i	0.0480896	+	0.0480896i
$903$	−206.985	+	772.477i	−0.229219	+	0.855456i
$904$	380.081	+	101.842i	0.420443	+	0.112657i
$905$	285.610	−	285.610i	0.315591	−	0.315591i
$906$	94.5744	+	163.808i	0.104387	+	0.180803i
$907$	113.303	+	65.4153i	0.124920	+	0.0721227i	0.561158	−	0.827709i	$-0.310356\pi$
$907$	113.303	+	65.4153i	0.124920	+	0.0721227i	−0.436238	+	0.899831i	$0.643689\pi$
$908$	−14.8025	−	55.2436i	−0.0163023	−	0.0608409i
$909$			363.904i			0.400334i
$910$	−110.967	−	414.133i	−0.121941	−	0.455092i
$911$	771.482			0.846852			0.423426	−	0.905931i	$-0.360827\pi$
$911$	771.482			0.846852			0.423426	+	0.905931i	$0.360827\pi$
$912$	150.067	−	40.2102i	0.164547	−	0.0440902i
$913$	−12.4617	+	21.5843i	−0.0136492	+	0.0236411i
$914$	110.366	−	63.7199i	0.120751	−	0.0697154i
$915$	−343.356	−	343.356i	−0.375252	−	0.375252i
$916$	−22.3782	+	83.5167i	−0.0244304	+	0.0911754i
$917$	1252.61	+	335.636i	1.36599	+	0.366015i
$918$	−127.119	+	127.119i	−0.138474	+	0.138474i
$919$	136.508	+	236.438i	0.148539	+	0.257278i	0.930688	−	0.365814i	$-0.119209\pi$
$919$	136.508	+	236.438i	0.148539	+	0.257278i	−0.782148	+	0.623092i	$0.785876\pi$
$920$	−119.138	−	68.7846i	−0.129498	−	0.0747659i
$921$	−47.9756	−	179.047i	−0.0520908	−	0.194405i
$922$			1119.03i			1.21369i
$923$	−315.233	+	315.233i	−0.341531	+	0.341531i
$924$	31.6922			0.0342989
$925$	−204.217	+	54.7199i	−0.220775	+	0.0591566i
$926$	524.908	−	909.167i	0.566855	−	0.981821i
$927$	−205.535	+	118.665i	−0.221720	+	0.128010i
$928$	85.3590	+	85.3590i	0.0919817	+	0.0919817i
$929$	279.095	−	1041.60i	0.300426	−	1.12120i	−0.636386	−	0.771371i	$-0.719572\pi$
$929$	279.095	−	1041.60i	0.300426	−	1.12120i	0.936812	−	0.349833i	$-0.113762\pi$
$930$	−207.531	−	55.6077i	−0.223151	−	0.0597932i
$931$	−6.74890	+	6.74890i	−0.00724908	+	0.00724908i
$932$	28.0770	+	48.6307i	0.0301255	+	0.0521789i
$933$	361.765	+	208.865i	0.387744	+	0.223864i
$934$	58.3435	+	217.741i	0.0624663	+	0.233127i
$935$			107.454i			0.114924i
$936$	78.0000	+	78.0000i	0.0833333	+	0.0833333i
$937$	−1483.78			−1.58354			−0.791771	−	0.610818i	$-0.790841\pi$
$937$	−1483.78			−1.58354			−0.791771	+	0.610818i	$0.790841\pi$
$938$	−527.482	+	141.338i	−0.562348	+	0.150681i
$939$	448.708	−	777.184i	0.477857	−	0.827672i
$940$	−245.885	+	141.962i	−0.261579	+	0.151023i
$941$	−50.9821	−	50.9821i	−0.0541787	−	0.0541787i	0.679498	−	0.733677i	$-0.262197\pi$
$941$	−50.9821	−	50.9821i	−0.0541787	−	0.0541787i	−0.733677	+	0.679498i	$0.762197\pi$
$942$	−167.557	+	625.331i	−0.177874	+	0.663834i
$943$	463.965	+	124.319i	0.492010	+	0.131834i
$944$	300.133	−	300.133i	0.317938	−	0.317938i
$945$	60.5885	+	104.942i	0.0641148	+	0.111050i
$946$	−106.508	−	61.4923i	−0.112587	−	0.0650024i
$947$	319.626	+	1192.86i	0.337514	+	1.25962i	0.901118	+	0.433574i	$0.142748\pi$
$947$	319.626	+	1192.86i	0.337514	+	1.25962i	−0.563604	+	0.826045i	$0.690586\pi$
$948$		−	22.2769i		−	0.0234988i
$949$	1297.76	−	347.733i	1.36750	−	0.366421i
$950$	−437.759			−0.460799
$951$	863.331	−	231.329i	0.907813	−	0.243248i
$952$	−241.128	+	417.646i	−0.253286	+	0.438704i
$953$	−1097.82	+	633.828i	−1.15197	+	0.665087i	−0.949365	−	0.314174i	$-0.898272\pi$
$953$	−1097.82	+	633.828i	−1.15197	+	0.665087i	−0.202600	+	0.979262i	$0.564939\pi$
$954$	−159.315	−	159.315i	−0.166997	−	0.166997i
$955$	213.531	−	796.908i	0.223592	−	0.834458i
$956$	−197.885	−	53.0230i	−0.206992	−	0.0554634i
$957$	−34.3078	+	34.3078i	−0.0358493	+	0.0358493i
$958$	−503.902	−	872.785i	−0.525994	−	0.911049i
$959$	−522.304	−	301.552i	−0.544634	−	0.314445i
$960$	12.0000	+	44.7846i	0.0125000	+	0.0466506i
$961$		−	273.841i		−	0.284954i
$962$			281.583i			0.292706i
$963$	503.454			0.522797
$964$	−619.764	+	166.065i	−0.642909	+	0.172267i
$965$	−50.7224	+	87.8538i	−0.0525621	+	0.0910402i
$966$	214.908	−	124.077i	0.222472	−	0.128444i
$967$	−289.397	−	289.397i	−0.299273	−	0.299273i	0.541456	−	0.840729i	$-0.317873\pi$
$967$	−289.397	−	289.397i	−0.299273	−	0.299273i	−0.840729	+	0.541456i	$0.817873\pi$
$968$	87.3167	−	325.870i	0.0902032	−	0.336643i
$969$	−917.811	−	245.927i	−0.947174	−	0.253794i
$970$	−615.822	+	615.822i	−0.634868	+	0.634868i
$971$	494.123	+	855.846i	0.508881	+	0.881407i	0.999947	+	0.0102849i	$0.00327383\pi$
$971$	494.123	+	855.846i	0.508881	+	0.881407i	−0.491067	+	0.871122i	$0.663393\pi$
$972$	−27.0000	−	15.5885i	−0.0277778	−	0.0160375i
$973$	426.985	+	1593.53i	0.438833	+	1.63775i
$974$			687.503i			0.705855i
$975$	−155.408	−	269.175i	−0.159393	−	0.276077i
$976$	335.138			0.343380
$977$	916.157	−	245.484i	0.937725	−	0.251263i	0.242579	−	0.970132i	$-0.422007\pi$
$977$	916.157	−	245.484i	0.937725	−	0.251263i	0.695146	+	0.718869i	$0.255340\pi$
$978$	305.751	−	529.577i	0.312629	−	0.541490i
$979$	−123.962	+	71.5692i	−0.126621	+	0.0731044i
$980$	−2.01408	−	2.01408i	−0.00205519	−	0.00205519i
$981$	−33.4942	+	125.002i	−0.0341429	+	0.127423i
$982$	−676.095	−	181.159i	−0.688488	−	0.184480i
$983$	1046.35	−	1046.35i	1.06445	−	1.06445i	0.0666747	−	0.997775i	$-0.478761\pi$
$983$	1046.35	−	1046.35i	1.06445	−	1.06445i	0.997775	−	0.0666747i	$-0.0212390\pi$
$984$	−80.9423	−	140.196i	−0.0822584	−	0.142476i
$985$	−111.394	−	64.3135i	−0.113091	−	0.0652929i
$986$	−191.086	−	713.144i	−0.193800	−	0.723270i
$987$		−	512.154i		−	0.518900i
$988$	−150.900	+	563.167i	−0.152733	+	0.570007i
$989$	−962.985			−0.973695
$990$	−18.0000	+	4.82309i	−0.0181818	+	0.00487180i
$991$	82.2807	−	142.514i	0.0830279	−	0.143809i	−0.821521	−	0.570178i	$-0.806874\pi$
$991$	82.2807	−	142.514i	0.0830279	−	0.143809i	0.904549	+	0.426369i	$0.140208\pi$
$992$	128.420	−	74.1436i	0.129456	−	0.0747415i
$993$	301.310	+	301.310i	0.303434	+	0.303434i
$994$	87.4820	−	326.487i	0.0880100	−	0.328458i
$995$	−319.401	−	85.5833i	−0.321006	−	0.0860134i
$996$	46.5077	−	46.5077i	0.0466945	−	0.0466945i
$997$	−418.677	−	725.170i	−0.419937	−	0.727352i	0.575996	−	0.817453i	$-0.304614\pi$
$997$	−418.677	−	725.170i	−0.419937	−	0.727352i	−0.995933	+	0.0901008i	$0.971281\pi$
$998$	−326.172	−	188.315i	−0.326825	−	0.188693i
$999$	−20.5981	−	76.8731i	−0.0206187	−	0.0769500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	78.3.l.b.7.1	✓	4
3.2	odd	2		234.3.bb.a.163.1		4
13.2	odd	12	inner	78.3.l.b.67.1	yes	4
13.4	even	6		1014.3.f.g.775.2		4
13.6	odd	12		1014.3.f.b.577.2		4
13.7	odd	12		1014.3.f.g.577.2		4
13.9	even	3		1014.3.f.b.775.2		4
39.2	even	12		234.3.bb.a.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.l.b.7.1	✓	4	1.1	even	1	trivial
78.3.l.b.67.1	yes	4	13.2	odd	12	inner
234.3.bb.a.145.1		4	39.2	even	12
234.3.bb.a.163.1		4	3.2	odd	2
1014.3.f.b.577.2		4	13.6	odd	12
1014.3.f.b.775.2		4	13.9	even	3
1014.3.f.g.577.2		4	13.7	odd	12
1014.3.f.g.775.2		4	13.4	even	6

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:	\( N \)	\(=\)	\( 78 = 2 \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	78.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(6.73205 + 1.80385i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 0.366025i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(6.73205 + 1.80385i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.50000 - 2.59808i) q^{9} +(4.09808 + 2.36603i) q^{10} +(-0.339746 - 1.26795i) q^{11} +3.46410i q^{12} +(-11.2583 - 6.50000i) q^{13} +9.85641 q^{14} +(-5.59808 + 1.50000i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-21.1865 + 12.2321i) q^{17} +(-3.00000 - 3.00000i) q^{18} +(5.80385 - 21.6603i) q^{19} +(6.46410 + 1.73205i) q^{20} +(-8.53590 + 8.53590i) q^{21} +(-0.928203 - 1.60770i) q^{22} +(-12.5885 - 7.26795i) q^{23} +(1.26795 + 4.73205i) q^{24} -13.8038i q^{25} +(-17.7583 - 4.75833i) q^{26} +5.19615 q^{27} +(13.4641 - 3.60770i) q^{28} +(-10.6699 + 18.4808i) q^{29} +(-7.09808 + 4.09808i) q^{30} +(18.5359 + 18.5359i) q^{31} +(1.46410 - 5.46410i) q^{32} +(2.19615 + 0.588457i) q^{33} +(-24.4641 + 24.4641i) q^{34} +(11.6603 + 20.1962i) q^{35} +(-5.19615 - 3.00000i) q^{36} +(-3.96410 - 14.7942i) q^{37} -31.7128i q^{38} +(19.5000 - 11.2583i) q^{39} +9.46410 q^{40} +(-31.9186 + 8.55256i) q^{41} +(-8.53590 + 14.7846i) q^{42} +(57.3731 - 33.1244i) q^{43} +(-1.85641 - 1.85641i) q^{44} +(2.59808 - 9.69615i) q^{45} +(-19.8564 - 5.32051i) q^{46} +(-30.0000 + 30.0000i) q^{47} +(3.46410 + 6.00000i) q^{48} +(-0.368603 - 0.212813i) q^{49} +(-5.05256 - 18.8564i) q^{50} -42.3731i q^{51} -26.0000 q^{52} +53.1051 q^{53} +(7.09808 - 1.90192i) q^{54} +(2.19615 - 3.80385i) q^{55} +(17.0718 - 9.85641i) q^{56} +(27.4641 + 27.4641i) q^{57} +(-7.81089 + 29.1506i) q^{58} +(102.497 + 27.4641i) q^{59} +(-8.19615 + 8.19615i) q^{60} +(41.8923 + 72.5596i) q^{61} +(32.1051 + 18.5359i) q^{62} +(-5.41154 - 20.1962i) q^{63} -8.00000i q^{64} +(-11.2583 - 42.0167i) q^{65} +3.21539 q^{66} +(-53.5167 + 14.3397i) q^{67} +(-24.4641 + 42.3731i) q^{68} +(21.8038 - 12.5885i) q^{69} +(23.3205 + 23.3205i) q^{70} +(8.87564 - 33.1244i) q^{71} +(-8.19615 - 2.19615i) q^{72} +(-73.0788 + 73.0788i) q^{73} +(-10.8301 - 18.7583i) q^{74} +(20.7058 + 11.9545i) q^{75} +(-11.6077 - 43.3205i) q^{76} -9.14875i q^{77} +(22.5167 - 22.5167i) q^{78} -6.43078 q^{79} +(12.9282 - 3.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-40.4711 + 23.3660i) q^{82} +(-13.4256 - 13.4256i) q^{83} +(-6.24871 + 23.3205i) q^{84} +(-79.0692 - 21.1865i) q^{85} +(66.2487 - 66.2487i) q^{86} +(-18.4808 - 32.0096i) q^{87} +(-3.21539 - 1.85641i) q^{88} +(-28.2224 - 105.328i) q^{89} -14.1962i q^{90} +(-64.0666 - 64.0666i) q^{91} -29.0718 q^{92} +(-43.8564 + 11.7513i) q^{93} +(-30.0000 + 51.9615i) q^{94} +(64.9808 - 37.5167i) q^{95} +(6.92820 + 6.92820i) q^{96} +(-47.6340 + 177.772i) q^{97} +(-0.581416 - 0.155790i) q^{98} +(-2.78461 + 2.78461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 20 q^{7} + 8 q^{8} - 6 q^{9} + 6 q^{10} - 36 q^{11} - 16 q^{14} - 12 q^{15} + 8 q^{16} - 12 q^{17} - 12 q^{18} + 44 q^{19} + 12 q^{20} - 48 q^{21} + 24 q^{22} + 12 q^{23} + 12 q^{24} - 26 q^{26} + 40 q^{28} - 60 q^{29} - 18 q^{30} + 88 q^{31} - 8 q^{32} - 12 q^{33} - 84 q^{34} + 12 q^{35} - 2 q^{37} + 78 q^{39} + 24 q^{40} - 48 q^{41} - 48 q^{42} + 84 q^{43} + 48 q^{44} - 24 q^{46} - 120 q^{47} - 192 q^{49} + 56 q^{50} - 104 q^{52} + 60 q^{53} + 18 q^{54} - 12 q^{55} + 96 q^{56} + 96 q^{57} + 90 q^{58} + 216 q^{59} - 12 q^{60} + 126 q^{61} - 24 q^{62} - 84 q^{63} + 96 q^{66} - 124 q^{67} - 84 q^{68} + 108 q^{69} + 24 q^{70} + 84 q^{71} - 12 q^{72} - 178 q^{73} - 26 q^{74} + 114 q^{75} - 88 q^{76} - 192 q^{79} + 24 q^{80} - 18 q^{81} - 6 q^{82} + 168 q^{83} + 72 q^{84} - 150 q^{85} + 168 q^{86} + 30 q^{87} - 96 q^{88} - 54 q^{89} + 104 q^{91} - 144 q^{92} - 120 q^{93} - 120 q^{94} + 156 q^{95} - 194 q^{97} - 82 q^{98} + 72 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 20 * q^7 + 8 * q^8 - 6 * q^9 + 6 * q^10 - 36 * q^11 - 16 * q^14 - 12 * q^15 + 8 * q^16 - 12 * q^17 - 12 * q^18 + 44 * q^19 + 12 * q^20 - 48 * q^21 + 24 * q^22 + 12 * q^23 + 12 * q^24 - 26 * q^26 + 40 * q^28 - 60 * q^29 - 18 * q^30 + 88 * q^31 - 8 * q^32 - 12 * q^33 - 84 * q^34 + 12 * q^35 - 2 * q^37 + 78 * q^39 + 24 * q^40 - 48 * q^41 - 48 * q^42 + 84 * q^43 + 48 * q^44 - 24 * q^46 - 120 * q^47 - 192 * q^49 + 56 * q^50 - 104 * q^52 + 60 * q^53 + 18 * q^54 - 12 * q^55 + 96 * q^56 + 96 * q^57 + 90 * q^58 + 216 * q^59 - 12 * q^60 + 126 * q^61 - 24 * q^62 - 84 * q^63 + 96 * q^66 - 124 * q^67 - 84 * q^68 + 108 * q^69 + 24 * q^70 + 84 * q^71 - 12 * q^72 - 178 * q^73 - 26 * q^74 + 114 * q^75 - 88 * q^76 - 192 * q^79 + 24 * q^80 - 18 * q^81 - 6 * q^82 + 168 * q^83 + 72 * q^84 - 150 * q^85 + 168 * q^86 + 30 * q^87 - 96 * q^88 - 54 * q^89 + 104 * q^91 - 144 * q^92 - 120 * q^93 - 120 * q^94 + 156 * q^95 - 194 * q^97 - 82 * q^98 + 72 * q^99

Introduction

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