LMFDB - Embedded newform 575.2.g.b.461.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [575,2,Mod(116,575)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(575, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("575.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 575 = 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	575.g (of order $5$, 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:	$4.59139811622$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$27$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			461.6
Character	$\chi$	$=$	575.461
Dual form			575.2.g.b.116.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.62357 + 1.17959i) q^{2} +(-1.06461 + 3.27654i) q^{3} +(0.626505 - 1.92818i) q^{4} +(1.50900 - 1.65013i) q^{5} +(-2.13651 - 6.57550i) q^{6} +4.84819 q^{7} +(0.0169997 + 0.0523197i) q^{8} +(-7.17528 - 5.21315i) q^{9} +O(q^{10})$	\(q+(-1.62357 + 1.17959i) q^{2} +(-1.06461 + 3.27654i) q^{3} +(0.626505 - 1.92818i) q^{4} +(1.50900 - 1.65013i) q^{5} +(-2.13651 - 6.57550i) q^{6} +4.84819 q^{7} +(0.0169997 + 0.0523197i) q^{8} +(-7.17528 - 5.21315i) q^{9} +(-0.503493 + 4.45910i) q^{10} +(2.24190 - 1.62883i) q^{11} +(5.65079 + 4.10554i) q^{12} +(0.559162 + 0.406255i) q^{13} +(-7.87136 + 5.71888i) q^{14} +(3.80020 + 6.70105i) q^{15} +(3.19111 + 2.31847i) q^{16} +(1.43564 + 4.41845i) q^{17} +17.7990 q^{18} +(0.270031 + 0.831069i) q^{19} +(-2.23635 - 3.94344i) q^{20} +(-5.16144 + 15.8853i) q^{21} +(-1.71851 + 5.28904i) q^{22} +(-0.809017 + 0.587785i) q^{23} -0.189526 q^{24} +(-0.445830 - 4.98008i) q^{25} -1.38705 q^{26} +(16.3584 - 11.8851i) q^{27} +(3.03741 - 9.34819i) q^{28} +(-0.922231 + 2.83834i) q^{29} +(-14.0744 - 6.39693i) q^{30} +(1.44216 + 4.43852i) q^{31} -8.02586 q^{32} +(2.95019 + 9.07974i) q^{33} +(-7.54282 - 5.48018i) q^{34} +(7.31592 - 8.00012i) q^{35} +(-14.5473 + 10.5692i) q^{36} +(1.63902 + 1.19082i) q^{37} +(-1.41873 - 1.03077i) q^{38} +(-1.92640 + 1.39961i) q^{39} +(0.111987 + 0.0508989i) q^{40} +(-1.02897 - 0.747589i) q^{41} +(-10.3582 - 31.8793i) q^{42} +4.35214 q^{43} +(-1.73613 - 5.34326i) q^{44} +(-19.4299 + 3.97347i) q^{45} +(0.620148 - 1.90862i) q^{46} +(-0.286775 + 0.882602i) q^{47} +(-10.9939 + 7.98752i) q^{48} +16.5049 q^{49} +(6.59830 + 7.55961i) q^{50} -16.0056 q^{51} +(1.13365 - 0.823646i) q^{52} +(-0.859681 + 2.64583i) q^{53} +(-12.5395 + 38.5925i) q^{54} +(0.695245 - 6.15732i) q^{55} +(0.0824177 + 0.253656i) q^{56} -3.01051 q^{57} +(-1.85077 - 5.69609i) q^{58} +(-6.08598 - 4.42172i) q^{59} +(15.3017 - 3.12925i) q^{60} +(0.198655 - 0.144332i) q^{61} +(-7.57709 - 5.50508i) q^{62} +(-34.7871 - 25.2743i) q^{63} +(6.64832 - 4.83029i) q^{64} +(1.51415 - 0.309648i) q^{65} +(-15.5002 - 11.2616i) q^{66} +(4.26922 + 13.1393i) q^{67} +9.41901 q^{68} +(-1.06461 - 3.27654i) q^{69} +(-2.44103 + 21.6185i) q^{70} +(3.31363 - 10.1983i) q^{71} +(0.150773 - 0.464031i) q^{72} +(-0.106729 + 0.0775429i) q^{73} -4.06574 q^{74} +(16.7921 + 3.84108i) q^{75} +1.77163 q^{76} +(10.8691 - 7.89688i) q^{77} +(1.47667 - 4.54474i) q^{78} +(0.141933 - 0.436825i) q^{79} +(8.64116 - 1.76715i) q^{80} +(13.3045 + 40.9470i) q^{81} +2.55245 q^{82} +(-2.72539 - 8.38789i) q^{83} +(27.3961 + 19.9044i) q^{84} +(9.45738 + 4.29846i) q^{85} +(-7.06600 + 5.13375i) q^{86} +(-8.31811 - 6.04346i) q^{87} +(0.123332 + 0.0896057i) q^{88} +(1.29567 - 0.941359i) q^{89} +(26.8586 - 29.3705i) q^{90} +(2.71092 + 1.96960i) q^{91} +(0.626505 + 1.92818i) q^{92} -16.0783 q^{93} +(-0.575512 - 1.77124i) q^{94} +(1.77884 + 0.808499i) q^{95} +(8.54444 - 26.2971i) q^{96} +(0.431779 - 1.32888i) q^{97} +(-26.7969 + 19.4691i) q^{98} -24.5776 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 4 q^{2} + q^{3} - 20 q^{4} + 3 q^{5} + 8 q^{6} + 24 q^{7} + 13 q^{8} - 36 q^{9}+O(q^{10}) $ 108 * q - 4 * q^2 + q^3 - 20 * q^4 + 3 * q^5 + 8 * q^6 + 24 * q^7 + 13 * q^8 - 36 * q^9	\( 108 q - 4 q^{2} + q^{3} - 20 q^{4} + 3 q^{5} + 8 q^{6} + 24 q^{7} + 13 q^{8} - 36 q^{9} - 24 q^{10} + 9 q^{11} - 20 q^{12} - 18 q^{13} - 31 q^{14} - 5 q^{15} - 20 q^{16} - 28 q^{17} + 34 q^{18} - q^{19} - 34 q^{20} - q^{21} - 35 q^{22} - 27 q^{23} + 178 q^{24} - 13 q^{25} + 14 q^{26} - 14 q^{27} - 3 q^{28} - 12 q^{29} - 35 q^{30} + 26 q^{31} + 22 q^{32} - 33 q^{33} - 15 q^{34} - 42 q^{35} - 49 q^{36} - 21 q^{37} - 11 q^{38} - 52 q^{39} + 25 q^{40} + 29 q^{41} + 6 q^{42} + 22 q^{43} - 58 q^{44} + 16 q^{45} + q^{46} - q^{47} - 83 q^{48} + 220 q^{49} - 16 q^{50} - 70 q^{51} - 76 q^{52} - 33 q^{53} - 106 q^{54} + 26 q^{55} + 124 q^{56} + 122 q^{57} + 46 q^{58} - 11 q^{59} + 20 q^{60} + 14 q^{61} - 40 q^{62} - 47 q^{63} - 87 q^{64} + 69 q^{65} + 47 q^{66} - 3 q^{67} + 154 q^{68} + q^{69} - 79 q^{70} - 51 q^{71} + 18 q^{72} - 26 q^{73} + 118 q^{74} - 55 q^{75} - 142 q^{76} - 5 q^{77} - 78 q^{78} - 7 q^{79} + 168 q^{80} + 29 q^{81} + 88 q^{82} + 7 q^{83} - 116 q^{84} + 9 q^{85} - 36 q^{86} - 130 q^{87} + 34 q^{88} + 9 q^{89} + 187 q^{90} + 58 q^{91} - 20 q^{92} + 26 q^{93} - 7 q^{94} - 86 q^{95} - 71 q^{96} - 50 q^{97} - 82 q^{98} + 124 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 + q^3 - 20 * q^4 + 3 * q^5 + 8 * q^6 + 24 * q^7 + 13 * q^8 - 36 * q^9 - 24 * q^10 + 9 * q^11 - 20 * q^12 - 18 * q^13 - 31 * q^14 - 5 * q^15 - 20 * q^16 - 28 * q^17 + 34 * q^18 - q^19 - 34 * q^20 - q^21 - 35 * q^22 - 27 * q^23 + 178 * q^24 - 13 * q^25 + 14 * q^26 - 14 * q^27 - 3 * q^28 - 12 * q^29 - 35 * q^30 + 26 * q^31 + 22 * q^32 - 33 * q^33 - 15 * q^34 - 42 * q^35 - 49 * q^36 - 21 * q^37 - 11 * q^38 - 52 * q^39 + 25 * q^40 + 29 * q^41 + 6 * q^42 + 22 * q^43 - 58 * q^44 + 16 * q^45 + q^46 - q^47 - 83 * q^48 + 220 * q^49 - 16 * q^50 - 70 * q^51 - 76 * q^52 - 33 * q^53 - 106 * q^54 + 26 * q^55 + 124 * q^56 + 122 * q^57 + 46 * q^58 - 11 * q^59 + 20 * q^60 + 14 * q^61 - 40 * q^62 - 47 * q^63 - 87 * q^64 + 69 * q^65 + 47 * q^66 - 3 * q^67 + 154 * q^68 + q^69 - 79 * q^70 - 51 * q^71 + 18 * q^72 - 26 * q^73 + 118 * q^74 - 55 * q^75 - 142 * q^76 - 5 * q^77 - 78 * q^78 - 7 * q^79 + 168 * q^80 + 29 * q^81 + 88 * q^82 + 7 * q^83 - 116 * q^84 + 9 * q^85 - 36 * q^86 - 130 * q^87 + 34 * q^88 + 9 * q^89 + 187 * q^90 + 58 * q^91 - 20 * q^92 + 26 * q^93 - 7 * q^94 - 86 * q^95 - 71 * q^96 - 50 * q^97 - 82 * q^98 + 124 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/575\mathbb{Z}\right)^\times$.

$n$	$51$	$277$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.62357	+	1.17959i	−1.14804	+	0.834097i	−0.988219	−	0.153049i	$-0.951091\pi$
$2$	−1.62357	+	1.17959i	−1.14804	+	0.834097i	−0.159818	+	0.987147i	$0.551091\pi$
$3$	−1.06461	+	3.27654i	−0.614655	+	1.89171i	−0.208010	+	0.978127i	$0.566699\pi$
$3$	−1.06461	+	3.27654i	−0.614655	+	1.89171i	−0.406645	+	0.913586i	$0.633301\pi$
$4$	0.626505	−	1.92818i	0.313252	−	0.964092i
$5$	1.50900	−	1.65013i	0.674846	−	0.737959i
$5$	1.50900	−	1.65013i	0.674846	−	0.737959i
$6$	−2.13651	−	6.57550i	−0.872227	−	2.68444i
$7$	4.84819			1.83244			0.916221	−	0.400673i	$-0.131224\pi$
$7$	4.84819			1.83244			0.916221	+	0.400673i	$0.131224\pi$
$8$	0.0169997	+	0.0523197i	0.00601030	+	0.0184978i
$9$	−7.17528	−	5.21315i	−2.39176	−	1.73772i
$10$	−0.503493	+	4.45910i	−0.159218	+	1.41009i
$11$	2.24190	−	1.62883i	0.675957	−	0.491112i	−0.196057	−	0.980593i	$-0.562814\pi$
$11$	2.24190	−	1.62883i	0.675957	−	0.491112i	0.872014	+	0.489481i	$0.162814\pi$
$12$	5.65079	+	4.10554i	1.63124	+	1.18517i
$13$	0.559162	+	0.406255i	0.155084	+	0.112675i	0.662621	−	0.748955i	$-0.269444\pi$
$13$	0.559162	+	0.406255i	0.155084	+	0.112675i	−0.507537	+	0.861630i	$0.669444\pi$
$14$	−7.87136	+	5.71888i	−2.10371	+	1.52844i
$15$	3.80020	+	6.70105i	0.981209	+	1.73020i
$16$	3.19111	+	2.31847i	0.797776	+	0.579619i
$17$	1.43564	+	4.41845i	0.348194	+	1.07163i	0.959852	+	0.280508i	$0.0905030\pi$
$17$	1.43564	+	4.41845i	0.348194	+	1.07163i	−0.611658	+	0.791123i	$0.709497\pi$
$18$	17.7990			4.19525
$19$	0.270031	+	0.831069i	0.0619493	+	0.190660i	0.977241	−	0.212131i	$-0.0680402\pi$
$19$	0.270031	+	0.831069i	0.0619493	+	0.190660i	−0.915292	+	0.402791i	$0.868040\pi$
$20$	−2.23635	−	3.94344i	−0.500063	−	0.881781i
$21$	−5.16144	+	15.8853i	−1.12632	+	3.46645i
$22$	−1.71851	+	5.28904i	−0.366388	+	1.12763i
$23$	−0.809017	+	0.587785i	−0.168692	+	0.122562i
$23$	−0.809017	+	0.587785i	−0.168692	+	0.122562i
$24$	−0.189526			−0.0386868
$25$	−0.445830	−	4.98008i	−0.0891659	−	0.996017i
$26$	−1.38705			−0.272023
$27$	16.3584	−	11.8851i	3.14818	−	2.28729i
$28$	3.03741	−	9.34819i	0.574017	−	1.76664i
$29$	−0.922231	+	2.83834i	−0.171254	+	0.527066i	−0.999443	−	0.0333837i	$-0.989372\pi$
$29$	−0.922231	+	2.83834i	−0.171254	+	0.527066i	0.828189	+	0.560450i	$0.189372\pi$
$30$	−14.0744	−	6.39693i	−2.56962	−	1.16791i
$31$	1.44216	+	4.43852i	0.259020	+	0.797182i	0.993011	+	0.118022i	$0.0376555\pi$
$31$	1.44216	+	4.43852i	0.259020	+	0.797182i	−0.733991	+	0.679159i	$0.762345\pi$
$32$	−8.02586			−1.41878
$33$	2.95019	+	9.07974i	0.513562	+	1.58058i
$34$	−7.54282	−	5.48018i	−1.29358	−	0.939844i
$35$	7.31592	−	8.00012i	1.23662	−	1.35227i
$36$	−14.5473	+	10.5692i	−2.42454	+	1.76153i
$37$	1.63902	+	1.19082i	0.269453	+	0.195769i	0.714304	−	0.699835i	$-0.246743\pi$
$37$	1.63902	+	1.19082i	0.269453	+	0.195769i	−0.444851	+	0.895605i	$0.646743\pi$
$38$	−1.41873	−	1.03077i	−0.230149	−	0.167213i
$39$	−1.92640	+	1.39961i	−0.308471	+	0.224118i
$40$	0.111987	+	0.0508989i	0.0177066	+	0.00804782i
$41$	−1.02897	−	0.747589i	−0.160698	−	0.116754i	0.504530	−	0.863394i	$-0.331666\pi$
$41$	−1.02897	−	0.747589i	−0.160698	−	0.116754i	−0.665228	+	0.746640i	$0.731666\pi$
$42$	−10.3582	−	31.8793i	−1.59830	−	4.91908i
$43$	4.35214			0.663696			0.331848	−	0.943333i	$-0.392328\pi$
$43$	4.35214			0.663696			0.331848	+	0.943333i	$0.392328\pi$
$44$	−1.73613	−	5.34326i	−0.261731	−	0.805526i
$45$	−19.4299	+	3.97347i	−2.89643	+	0.592330i
$46$	0.620148	−	1.90862i	0.0914358	−	0.281411i
$47$	−0.286775	+	0.882602i	−0.0418304	+	0.128741i	−0.969791	−	0.243938i	$-0.921561\pi$
$47$	−0.286775	+	0.882602i	−0.0418304	+	0.128741i	0.927960	+	0.372679i	$0.121561\pi$
$48$	−10.9939	+	7.98752i	−1.58683	+	1.15290i
$49$	16.5049			2.35784
$50$	6.59830	+	7.55961i	0.933141	+	1.06909i
$51$	−16.0056			−2.24124
$52$	1.13365	−	0.823646i	0.157209	−	0.114219i
$53$	−0.859681	+	2.64583i	−0.118086	+	0.363432i	−0.992578	−	0.121608i	$-0.961195\pi$
$53$	−0.859681	+	2.64583i	−0.118086	+	0.363432i	0.874492	+	0.485040i	$0.161195\pi$
$54$	−12.5395	+	38.5925i	−1.70641	+	5.25178i
$55$	0.695245	−	6.15732i	0.0937469	−	0.830253i
$56$	0.0824177	+	0.253656i	0.0110135	+	0.0338962i
$57$	−3.01051			−0.398752
$58$	−1.85077	−	5.69609i	−0.243018	−	0.747933i
$59$	−6.08598	−	4.42172i	−0.792327	−	0.575659i	0.116326	−	0.993211i	$-0.462888\pi$
$59$	−6.08598	−	4.42172i	−0.792327	−	0.575659i	−0.908653	+	0.417552i	$0.862888\pi$
$60$	15.3017	−	3.12925i	1.97544	−	0.403984i
$61$	0.198655	−	0.144332i	0.0254352	−	0.0184798i	−0.574995	−	0.818157i	$-0.694996\pi$
$61$	0.198655	−	0.144332i	0.0254352	−	0.0184798i	0.600430	+	0.799677i	$0.294996\pi$
$62$	−7.57709	−	5.50508i	−0.962292	−	0.699146i
$63$	−34.7871	−	25.2743i	−4.38276	−	3.18426i
$64$	6.64832	−	4.83029i	0.831040	−	0.603786i
$65$	1.51415	−	0.309648i	0.187807	−	0.0384071i
$66$	−15.5002	−	11.2616i	−1.90795	−	1.38620i
$67$	4.26922	+	13.1393i	0.521568	+	1.60522i	0.771004	+	0.636831i	$0.219755\pi$
$67$	4.26922	+	13.1393i	0.521568	+	1.60522i	−0.249435	+	0.968391i	$0.580245\pi$
$68$	9.41901			1.14222
$69$	−1.06461	−	3.27654i	−0.128164	−	0.394449i
$70$	−2.44103	+	21.6185i	−0.291759	+	2.58391i
$71$	3.31363	−	10.1983i	0.393256	−	1.21032i	−0.537056	−	0.843547i	$-0.680463\pi$
$71$	3.31363	−	10.1983i	0.393256	−	1.21032i	0.930311	−	0.366770i	$-0.119537\pi$
$72$	0.150773	−	0.464031i	0.0177687	−	0.0546865i
$73$	−0.106729	+	0.0775429i	−0.0124916	+	0.00907571i	−0.594014	−	0.804455i	$-0.702457\pi$
$73$	−0.106729	+	0.0775429i	−0.0124916	+	0.00907571i	0.581522	+	0.813531i	$0.302457\pi$
$74$	−4.06574			−0.472633
$75$	16.7921	+	3.84108i	1.93898	+	0.443530i
$76$	1.77163			0.203220
$77$	10.8691	−	7.89688i	1.23865	−	0.899933i
$78$	1.47667	−	4.54474i	0.167201	−	0.514590i
$79$	0.141933	−	0.436825i	0.0159687	−	0.0491467i	−0.942755	−	0.333487i	$-0.891775\pi$
$79$	0.141933	−	0.436825i	0.0159687	−	0.0491467i	0.958723	+	0.284340i	$0.0917746\pi$
$80$	8.64116	−	1.76715i	0.966111	−	0.197573i
$81$	13.3045	+	40.9470i	1.47827	+	4.54966i
$82$	2.55245			0.281871
$83$	−2.72539	−	8.38789i	−0.299151	−	0.920691i	−0.981796	−	0.189941i	$-0.939170\pi$
$83$	−2.72539	−	8.38789i	−0.299151	−	0.920691i	0.682645	−	0.730750i	$-0.260830\pi$
$84$	27.3961	+	19.9044i	2.98916	+	2.17175i
$85$	9.45738	+	4.29846i	1.02580	+	0.466233i
$86$	−7.06600	+	5.13375i	−0.761947	+	0.553587i
$87$	−8.31811	−	6.04346i	−0.891795	−	0.647927i
$88$	0.123332	+	0.0896057i	0.0131472	+	0.00955199i
$89$	1.29567	−	0.941359i	0.137341	−	0.0997838i	−0.516994	−	0.855989i	$-0.672949\pi$
$89$	1.29567	−	0.941359i	0.137341	−	0.0997838i	0.654334	+	0.756205i	$0.272949\pi$
$90$	26.8586	−	29.3705i	2.83115	−	3.09592i
$91$	2.71092	+	1.96960i	0.284182	+	0.206470i
$92$	0.626505	+	1.92818i	0.0653176	+	0.201027i
$93$	−16.0783			−1.66725
$94$	−0.575512	−	1.77124i	−0.0593595	−	0.182690i
$95$	1.77884	+	0.808499i	0.182506	+	0.0829503i
$96$	8.54444	−	26.2971i	0.872063	−	2.68393i
$97$	0.431779	−	1.32888i	0.0438405	−	0.134927i	−0.926740	−	0.375702i	$-0.877402\pi$
$97$	0.431779	−	1.32888i	0.0438405	−	0.134927i	0.970581	+	0.240775i	$0.0774016\pi$
$98$	−26.7969	+	19.4691i	−2.70689	+	1.96667i
$99$	−24.5776			−2.47014
$100$	−9.88183	−	2.26041i	−0.988183	−	0.226041i
$101$	−2.37095			−0.235918			−0.117959	−	0.993018i	$-0.537635\pi$
$101$	−2.37095			−0.235918			−0.117959	+	0.993018i	$0.537635\pi$
$102$	25.9862	−	18.8801i	2.57302	−	1.86941i
$103$	−3.27258	+	10.0720i	−0.322457	+	0.992419i	0.650119	+	0.759832i	$0.274719\pi$
$103$	−3.27258	+	10.0720i	−0.322457	+	0.992419i	−0.972576	+	0.232587i	$0.925281\pi$
$104$	−0.0117496	+	0.0361614i	−0.00115214	+	0.00354592i
$105$	18.4241	+	32.4880i	1.79801	+	3.17050i
$106$	−1.72524	−	5.30975i	−0.167570	−	0.515729i
$107$	10.7433			1.03860			0.519298	−	0.854593i	$-0.326193\pi$
$107$	10.7433			1.03860			0.519298	+	0.854593i	$0.326193\pi$
$108$	−12.6680	−	38.9881i	−1.21898	−	3.75163i
$109$	−0.513489	−	0.373072i	−0.0491833	−	0.0357338i	0.562922	−	0.826510i	$-0.309677\pi$
$109$	−0.513489	−	0.373072i	−0.0491833	−	0.0357338i	−0.612105	+	0.790776i	$0.709677\pi$
$110$	6.13435	+	10.8169i	0.584887	+	1.03135i
$111$	−5.64669	+	4.10256i	−0.535960	+	0.389398i
$112$	15.4711	+	11.2404i	1.46188	+	1.06212i
$113$	8.14692	+	5.91908i	0.766397	+	0.556820i	0.900866	−	0.434098i	$-0.142933\pi$
$113$	8.14692	+	5.91908i	0.766397	+	0.556820i	−0.134468	+	0.990918i	$0.542933\pi$
$114$	4.88777	−	3.55117i	0.457782	−	0.332598i
$115$	−0.250888	+	2.22195i	−0.0233954	+	0.207198i
$116$	4.89505	+	3.55646i	0.454494	+	0.330209i
$117$	−1.89428	−	5.82999i	−0.175126	−	0.538983i
$118$	15.0968			1.38978
$119$	6.96025	+	21.4215i	0.638045	+	1.96370i
$120$	−0.285995	+	0.312742i	−0.0261076	+	0.0285493i
$121$	−1.02619	+	3.15828i	−0.0932896	+	0.287116i
$122$	−0.152278	+	0.468665i	−0.0137866	+	0.0424309i
$123$	3.54496	−	2.57556i	0.319638	−	0.232231i
$124$	9.46180			0.849695
$125$	−8.89052	−	6.77928i	−0.795192	−	0.606357i
$126$	86.2926			7.68756
$127$	−4.78761	+	3.47840i	−0.424832	+	0.308658i	−0.779579	−	0.626304i	$-0.784567\pi$
$127$	−4.78761	+	3.47840i	−0.424832	+	0.308658i	0.354747	+	0.934962i	$0.384567\pi$
$128$	−0.135985	+	0.418518i	−0.0120195	+	0.0369921i
$129$	−4.63335	+	14.2600i	−0.407944	+	1.25552i
$130$	−2.09306	+	2.28881i	−0.183574	+	0.200742i
$131$	−5.37091	−	16.5299i	−0.469258	−	1.44423i	−0.853547	−	0.521016i	$-0.825553\pi$
$131$	−5.37091	−	16.5299i	−0.469258	−	1.44423i	0.384289	−	0.923213i	$-0.374447\pi$
$132$	19.3557			1.68470
$133$	1.30916	+	4.02918i	0.113518	+	0.349374i
$134$	−22.4304	−	16.2966i	−1.93769	−	1.40781i
$135$	5.07299	−	44.9281i	0.436614	−	3.86679i
$136$	−0.206766	+	0.150225i	−0.0177301	+	0.0128816i
$137$	−4.76423	−	3.46141i	−0.407035	−	0.295729i	0.365365	−	0.930864i	$-0.380944\pi$
$137$	−4.76423	−	3.46141i	−0.407035	−	0.295729i	−0.772401	+	0.635136i	$0.780944\pi$
$138$	5.59346	+	4.06388i	0.476147	+	0.345941i
$139$	−3.88596	+	2.82331i	−0.329602	+	0.239470i	−0.740262	−	0.672319i	$-0.765299\pi$
$139$	−3.88596	+	2.82331i	−0.329602	+	0.239470i	0.410659	+	0.911789i	$0.365299\pi$
$140$	−10.8422	−	19.1186i	−0.916336	−	1.61581i
$141$	−2.58658	−	1.87926i	−0.217829	−	0.158262i
$142$	6.64994	+	20.4664i	0.558050	+	1.71750i
$143$	1.91530			0.160166
$144$	−10.8105	−	33.2714i	−0.900878	−	2.77262i
$145$	3.29196	+	5.80485i	0.273383	+	0.482067i
$146$	0.0818123	−	0.251792i	0.00677084	−	0.0208385i
$147$	−17.5714	+	54.0791i	−1.44926	+	4.46037i
$148$	3.32297	−	2.41428i	0.273147	−	0.198453i
$149$	−15.2273			−1.24747			−0.623733	−	0.781638i	$-0.714385\pi$
$149$	−15.2273			−1.24747			−0.623733	+	0.781638i	$0.714385\pi$
$150$	−31.7940	+	13.5716i	−2.59597	+	1.10811i
$151$	4.74139			0.385849			0.192924	−	0.981214i	$-0.438203\pi$
$151$	4.74139			0.385849			0.192924	+	0.981214i	$0.438203\pi$
$152$	−0.0388908	+	0.0282558i	−0.00315446	+	0.00229185i
$153$	12.7329	−	39.1878i	1.02939	−	3.16815i
$154$	−8.33168	+	25.6423i	−0.671386	+	2.06631i
$155$	9.50034	+	4.31798i	0.763086	+	0.346829i
$156$	1.49181	+	4.59132i	0.119441	+	0.367600i
$157$	14.3511			1.14534			0.572671	−	0.819785i	$-0.305907\pi$
$157$	14.3511			1.14534			0.572671	+	0.819785i	$0.305907\pi$
$158$	0.284837	+	0.876639i	0.0226604	+	0.0697416i
$159$	−7.75393	−	5.63356i	−0.614927	−	0.446771i
$160$	−12.1110	+	13.2437i	−0.957461	+	1.04700i
$161$	−3.92227	+	2.84969i	−0.309118	+	0.224587i
$162$	−69.9014	−	50.7863i	−5.49197	−	3.99015i
$163$	−11.4776	−	8.33898i	−0.898996	−	0.653159i	0.0392117	−	0.999231i	$-0.487515\pi$
$163$	−11.4776	−	8.33898i	−0.898996	−	0.653159i	−0.938208	+	0.346072i	$0.887515\pi$
$164$	−2.08614	+	1.51567i	−0.162900	+	0.118354i
$165$	19.4346	+	8.83317i	1.51298	+	0.687661i
$166$	14.3191	+	10.4035i	1.11138	+	0.807466i
$167$	−4.85300	−	14.9360i	−0.375536	−	1.15578i	−0.943116	−	0.332463i	$-0.892120\pi$
$167$	−4.85300	−	14.9360i	−0.375536	−	1.15578i	0.567580	−	0.823318i	$-0.307880\pi$
$168$	−0.918857			−0.0708913
$169$	−3.86960	−	11.9094i	−0.297662	−	0.916108i
$170$	−20.4251	+	4.17700i	−1.56654	+	0.320362i
$171$	2.39494	−	7.37086i	0.183145	−	0.563664i
$172$	2.72664	−	8.39173i	0.207904	−	0.639863i
$173$	−20.9366	+	15.2113i	−1.59178	+	1.15650i	−0.690436	+	0.723394i	$0.742581\pi$
$173$	−20.9366	+	15.2113i	−1.59178	+	1.15650i	−0.901345	+	0.433102i	$0.857419\pi$
$174$	20.6338			1.56425
$175$	−2.16147	−	24.1444i	−0.163391	−	1.82514i
$176$	10.9305			0.823920
$177$	20.9672	−	15.2335i	1.57599	−	1.14502i
$178$	−0.993189	+	3.05672i	−0.0744427	+	0.229111i
$179$	−3.03614	+	9.34428i	−0.226932	+	0.698424i	0.771158	+	0.636644i	$0.219678\pi$
$179$	−3.03614	+	9.34428i	−0.226932	+	0.698424i	−0.998090	+	0.0617803i	$0.980322\pi$
$180$	−4.51132	+	39.9537i	−0.336254	+	2.97798i
$181$	−4.81062	−	14.8056i	−0.357570	−	1.10049i	−0.954504	−	0.298198i	$-0.903614\pi$
$181$	−4.81062	−	14.8056i	−0.357570	−	1.10049i	0.596934	−	0.802291i	$-0.296386\pi$
$182$	−6.72469			−0.498467
$183$	0.261418	+	0.804561i	0.0193245	+	0.0594748i
$184$	−0.0445058	−	0.0323354i	−0.00328101	−	0.00238379i
$185$	4.43829	−	0.907644i	0.326309	−	0.0667313i
$186$	26.1043	−	18.9659i	1.91406	−	1.39065i
$187$	10.4155	+	7.56728i	0.761654	+	0.553374i
$188$	1.52215	+	1.10591i	0.111014	+	0.0806567i
$189$	79.3087	−	57.6211i	5.76886	−	4.19132i
$190$	−3.84177	+	0.785656i	−0.278712	+	0.0569974i
$191$	12.1965	+	8.86126i	0.882507	+	0.641179i	0.933913	−	0.357499i	$-0.116371\pi$
$191$	12.1965	+	8.86126i	0.882507	+	0.641179i	−0.0514069	+	0.998678i	$0.516371\pi$
$192$	8.74875	+	26.9259i	0.631387	+	1.94321i
$193$	9.62290			0.692671			0.346336	−	0.938111i	$-0.387426\pi$
$193$	9.62290			0.692671			0.346336	+	0.938111i	$0.387426\pi$
$194$	0.866512	+	2.66685i	0.0622119	+	0.191469i
$195$	−0.597406	+	5.29083i	−0.0427812	+	0.378884i
$196$	10.3404	−	31.8245i	0.738601	−	2.27318i
$197$	−0.775290	+	2.38610i	−0.0552371	+	0.170002i	−0.974869	−	0.222779i	$-0.928487\pi$
$197$	−0.775290	+	2.38610i	−0.0552371	+	0.170002i	0.919632	+	0.392781i	$0.128487\pi$
$198$	39.9034	−	28.9915i	2.83581	−	2.06034i
$199$	−4.76478			−0.337766			−0.168883	−	0.985636i	$-0.554016\pi$
$199$	−4.76478			−0.337766			−0.168883	+	0.985636i	$0.554016\pi$
$200$	0.252978	−	0.107986i	0.0178882	−	0.00763574i
$201$	−47.5966			−3.35720
$202$	3.84940	−	2.79675i	0.270843	−	0.196779i
$203$	−4.47115	+	13.7608i	−0.313813	+	0.965818i
$204$	−10.0276	+	30.8618i	−0.702073	+	2.16076i
$205$	−2.78633	+	0.569814i	−0.194606	+	0.0397975i
$206$	−6.56754	−	20.2128i	−0.457582	−	1.40829i
$207$	8.86914			0.616448
$208$	0.842453	+	2.59280i	0.0584136	+	0.179779i
$209$	1.95905	+	1.42333i	0.135510	+	0.0984541i
$210$	−68.2353	−	31.0135i	−4.70868	−	2.14014i
$211$	4.97557	−	3.61496i	0.342532	−	0.248864i	−0.403197	−	0.915113i	$-0.632101\pi$
$211$	4.97557	−	3.61496i	0.342532	−	0.248864i	0.745729	+	0.666249i	$0.232101\pi$
$212$	4.56304	+	3.31524i	0.313391	+	0.227692i
$213$	29.8875	+	21.7145i	2.04786	+	1.48785i
$214$	−17.4425	+	12.6727i	−1.19235	+	0.866291i
$215$	6.56739	−	7.18158i	0.447892	−	0.489780i
$216$	0.899913	+	0.653825i	0.0612313	+	0.0444871i
$217$	6.99187	+	21.5188i	0.474639	+	1.46079i
$218$	1.27376			0.0862697
$219$	−0.140448	−	0.432254i	−0.00949059	−	0.0292090i
$220$	−11.4369	−	5.19815i	−0.771074	−	0.350459i
$221$	−0.992260	+	3.05386i	−0.0667466	+	0.205425i
$222$	4.32844	−	13.3216i	0.290506	−	0.894086i
$223$	−15.1504	+	11.0074i	−1.01455	+	0.737113i	−0.965158	−	0.261667i	$-0.915728\pi$
$223$	−15.1504	+	11.0074i	−1.01455	+	0.737113i	−0.0493902	+	0.998780i	$0.515728\pi$
$224$	−38.9109			−2.59984
$225$	−22.7630	+	38.0577i	−1.51753	+	2.53718i
$226$	−20.2092			−1.34429
$227$	−15.3616	+	11.1609i	−1.01959	+	0.740773i	−0.966198	−	0.257801i	$-0.917002\pi$
$227$	−15.3616	+	11.1609i	−1.01959	+	0.740773i	−0.0533881	+	0.998574i	$0.517002\pi$
$228$	−1.88610	+	5.80482i	−0.124910	+	0.384433i
$229$	4.88447	−	15.0329i	0.322775	−	0.993400i	−0.649660	−	0.760225i	$-0.725089\pi$
$229$	4.88447	−	15.0329i	0.322775	−	0.993400i	0.972435	−	0.233175i	$-0.0749114\pi$
$230$	−2.21366	−	3.90343i	−0.145964	−	0.257385i
$231$	14.3031	+	44.0203i	0.941072	+	2.89632i
$232$	−0.164179			−0.0107789
$233$	5.50026	+	16.9281i	0.360334	+	1.10899i	0.952852	+	0.303437i	$0.0981340\pi$
$233$	5.50026	+	16.9281i	0.360334	+	1.10899i	−0.592518	+	0.805557i	$0.701866\pi$
$234$	9.95250	+	7.23091i	0.650615	+	0.472699i
$235$	1.02366	+	1.80506i	0.0667763	+	0.117749i
$236$	−12.3388	+	8.96465i	−0.803187	+	0.583549i
$237$	1.28017	+	0.930100i	0.0831561	+	0.0604165i
$238$	−36.5690	−	26.5689i	−2.37042	−	1.72221i
$239$	6.21537	−	4.51573i	0.402039	−	0.292098i	−0.368332	−	0.929694i	$-0.620071\pi$
$239$	6.21537	−	4.51573i	0.402039	−	0.292098i	0.770371	+	0.637596i	$0.220071\pi$
$240$	−3.40936	+	30.1945i	−0.220074	+	1.94904i
$241$	−13.8144	−	10.0367i	−0.889863	−	0.646523i	0.0459796	−	0.998942i	$-0.485359\pi$
$241$	−13.8144	−	10.0367i	−0.889863	−	0.646523i	−0.935842	+	0.352419i	$0.885359\pi$
$242$	−2.05939	−	6.33816i	−0.132383	−	0.407432i
$243$	−87.6682			−5.62392
$244$	−0.153839	−	0.473469i	−0.00984855	−	0.0303107i
$245$	24.9059	−	27.2352i	1.59118	−	1.73999i
$246$	−2.71737	+	8.36321i	−0.173253	+	0.533219i
$247$	−0.186635	+	0.574403i	−0.0118753	+	0.0365484i
$248$	−0.207706	+	0.150907i	−0.0131893	+	0.00958261i
$249$	30.3848			1.92556
$250$	22.4312	+	0.519439i	1.41867	+	0.0328522i
$251$	−27.2780			−1.72177			−0.860886	−	0.508798i	$-0.830090\pi$
$251$	−27.2780			−1.72177			−0.860886	+	0.508798i	$0.830090\pi$
$252$	−70.5278	+	51.2415i	−4.44283	+	3.22791i
$253$	−0.856328	+	2.63551i	−0.0538369	+	0.165693i
$254$	3.66992	−	11.2948i	0.230271	−	0.708702i
$255$	−24.1525	+	26.4113i	−1.51249	+	1.65394i
$256$	4.80596	+	14.7912i	0.300373	+	0.924452i
$257$	11.3550			0.708307			0.354153	−	0.935187i	$-0.384769\pi$
$257$	11.3550			0.708307			0.354153	+	0.935187i	$0.384769\pi$
$258$	−9.29840	−	28.6175i	−0.578893	−	1.78165i
$259$	7.94628	+	5.77331i	0.493758	+	0.358736i
$260$	0.351562	−	3.11355i	0.0218030	−	0.193094i
$261$	21.4139	−	15.5581i	1.32549	−	0.963024i
$262$	28.2186	+	20.5020i	1.74335	+	1.26662i
$263$	13.2800	+	9.64850i	0.818881	+	0.594952i	0.916392	−	0.400282i	$-0.131088\pi$
$263$	13.2800	+	9.64850i	0.818881	+	0.594952i	−0.0975105	+	0.995234i	$0.531088\pi$
$264$	−0.424897	+	0.308706i	−0.0261506	+	0.0189995i
$265$	3.06868	+	5.41114i	0.188508	+	0.332403i
$266$	−6.87829	−	4.99737i	−0.421735	−	0.306408i
$267$	1.70502	+	5.24750i	0.104345	+	0.321142i
$268$	28.0097			1.71096
$269$	5.88085	+	18.0994i	0.358562	+	1.10354i	0.953915	+	0.300076i	$0.0970119\pi$
$269$	5.88085	+	18.0994i	0.358562	+	1.10354i	−0.595354	+	0.803464i	$0.702988\pi$
$270$	44.7604	+	78.9279i	2.72403	+	4.80340i
$271$	9.98374	−	30.7268i	0.606469	−	1.86652i	0.120110	−	0.992761i	$-0.461675\pi$
$271$	9.98374	−	30.7268i	0.606469	−	1.86652i	0.486359	−	0.873759i	$-0.338325\pi$
$272$	−5.66277	+	17.4282i	−0.343356	+	1.05674i
$273$	−9.33956	+	6.78559i	−0.565256	+	0.410682i
$274$	11.8181			0.713958
$275$	−9.11123	−	10.4386i	−0.549428	−	0.629474i
$276$	−6.98476			−0.420433
$277$	−9.15721	+	6.65311i	−0.550204	+	0.399746i	−0.827861	−	0.560934i	$-0.810442\pi$
$277$	−9.15721	+	6.65311i	−0.550204	+	0.399746i	0.277657	+	0.960680i	$0.410442\pi$
$278$	2.97876	−	9.16768i	0.178654	−	0.549841i
$279$	12.7907	−	39.3658i	0.765761	−	2.35677i
$280$	0.542932	+	0.246767i	0.0324464	+	0.0147472i
$281$	3.89232	+	11.9793i	0.232196	+	0.714627i	0.997481	+	0.0709350i	$0.0225983\pi$
$281$	3.89232	+	11.9793i	0.232196	+	0.714627i	−0.765285	+	0.643692i	$0.777402\pi$
$282$	6.41625			0.382082
$283$	−2.90912	−	8.95335i	−0.172929	−	0.532221i	0.826604	−	0.562784i	$-0.190270\pi$
$283$	−2.90912	−	8.95335i	−0.172929	−	0.532221i	−0.999533	+	0.0305632i	$0.990270\pi$
$284$	−17.5882	−	12.7786i	−1.04367	−	0.758270i
$285$	−4.54286	+	4.96772i	−0.269096	+	0.294262i
$286$	−3.10963	+	2.25928i	−0.183876	+	0.133594i
$287$	−4.98863	−	3.62445i	−0.294469	−	0.213945i
$288$	57.5878	+	41.8400i	3.39339	+	2.46544i
$289$	−3.70832	+	2.69425i	−0.218136	+	0.158485i
$290$	−12.1921	−	5.54140i	−0.715944	−	0.325402i
$291$	3.89445	+	2.82948i	0.228297	+	0.165867i
$292$	0.0826509	+	0.254373i	0.00483678	+	0.0148861i
$293$	24.8293			1.45054			0.725271	−	0.688463i	$-0.241714\pi$
$293$	24.8293			1.45054			0.725271	+	0.688463i	$0.241714\pi$
$294$	−35.2629	−	108.528i	−2.05657	−	6.32949i
$295$	−16.4801	+	3.37024i	−0.959511	+	0.196223i
$296$	−0.0344404	+	0.105997i	−0.00200181	+	0.00616093i
$297$	17.3151	−	53.2903i	1.00472	−	3.09221i
$298$	24.7225	−	17.9619i	1.43214	−	1.04051i
$299$	−0.691162			−0.0399709
$300$	17.9266	−	29.9718i	1.03500	−	1.73042i
$301$	21.1000			1.21618
$302$	−7.69798	+	5.59291i	−0.442969	+	0.321836i
$303$	2.52415	−	7.76852i	0.145008	−	0.446290i
$304$	−1.06511	+	3.27809i	−0.0610885	+	0.188011i
$305$	0.0616060	−	0.545603i	0.00352755	−	0.0312411i
$306$	25.5529	+	78.6437i	1.46076	+	4.49576i
$307$	−1.91692			−0.109404			−0.0547022	−	0.998503i	$-0.517421\pi$
$307$	−1.91692			−0.109404			−0.0547022	+	0.998503i	$0.517421\pi$
$308$	−8.41708	−	25.9051i	−0.479608	−	1.47608i
$309$	−29.5172	−	21.4455i	−1.67917	−	1.21999i
$310$	−20.5179	+	4.19598i	−1.16534	+	0.238316i
$311$	23.3045	−	16.9317i	1.32148	−	0.960109i	0.321564	−	0.946888i	$-0.395792\pi$
$311$	23.3045	−	16.9317i	1.32148	−	0.960109i	0.999913	−	0.0132209i	$-0.00420845\pi$
$312$	−0.105976	−	0.0769958i	−0.00599969	−	0.00435903i
$313$	−13.2144	−	9.60081i	−0.746921	−	0.542670i	0.147950	−	0.988995i	$-0.452733\pi$
$313$	−13.2144	−	9.60081i	−0.746921	−	0.542670i	−0.894871	+	0.446325i	$0.852733\pi$
$314$	−23.3000	+	16.9284i	−1.31490	+	0.955327i
$315$	−94.1996	+	19.2641i	−5.30755	+	1.08541i
$316$	−0.753357	−	0.547346i	−0.0423797	−	0.0307906i
$317$	−4.81082	−	14.8062i	−0.270202	−	0.831597i	−0.990449	−	0.137879i	$-0.955971\pi$
$317$	−4.81082	−	14.8062i	−0.270202	−	0.831597i	0.720247	−	0.693718i	$-0.244029\pi$
$318$	19.2343			1.07861
$319$	2.55563	+	7.86542i	0.143088	+	0.440379i
$320$	2.06174	−	18.2595i	0.115255	−	1.02074i
$321$	−11.4375	+	35.2010i	−0.638378	+	1.96473i
$322$	3.00659	−	9.25334i	0.167551	−	0.515669i
$323$	−3.28437	+	2.38623i	−0.182747	+	0.132773i
$324$	87.2886			4.84936
$325$	1.77389	−	2.96579i	0.0983979	−	0.164513i
$326$	28.4713			1.57688
$327$	1.76905	−	1.28529i	0.0978288	−	0.0710768i
$328$	0.0216215	−	0.0665441i	0.00119385	−	0.00367428i
$329$	−1.39034	+	4.27902i	−0.0766518	+	0.235910i
$330$	−41.9729	+	8.58359i	−2.31053	+	0.472511i
$331$	−7.85422	−	24.1728i	−0.431707	−	1.32866i	−0.896424	−	0.443198i	$-0.853844\pi$
$331$	−7.85422	−	24.1728i	−0.431707	−	1.32866i	0.464716	−	0.885460i	$-0.346156\pi$
$332$	−17.8809			−0.981340
$333$	−5.55253	−	17.0889i	−0.304277	−	0.936467i
$334$	25.4976	+	18.5251i	1.39516	+	1.01365i
$335$	28.1238	+	12.7825i	1.53657	+	0.698382i
$336$	−53.3004	+	38.7250i	−2.90777	+	2.11262i
$337$	−16.1998	−	11.7699i	−0.882462	−	0.641146i	0.0514399	−	0.998676i	$-0.483619\pi$
$337$	−16.1998	−	11.7699i	−0.882462	−	0.641146i	−0.933902	+	0.357530i	$0.883619\pi$
$338$	20.3308	+	14.7712i	1.10585	+	0.803447i
$339$	−28.0674	+	20.3922i	−1.52441	+	1.10755i
$340$	14.2133	−	15.5426i	0.770825	−	0.842913i
$341$	10.4628	+	7.60166i	0.566592	+	0.411653i
$342$	4.80626	+	14.7921i	0.259893	+	0.799868i
$343$	46.0816			2.48817
$344$	0.0739851	+	0.227703i	0.00398901	+	0.0122769i
$345$	−7.01321	−	3.18756i	−0.377579	−	0.171613i
$346$	16.0489	−	49.3933i	0.862792	−	2.65540i
$347$	7.64280	−	23.5221i	0.410287	−	1.26273i	−0.506112	−	0.862468i	$-0.668918\pi$
$347$	7.64280	−	23.5221i	0.410287	−	1.26273i	0.916399	−	0.400266i	$-0.131082\pi$
$348$	−16.8642	+	12.2526i	−0.904018	+	0.656808i
$349$	−0.575942			−0.0308295			−0.0154147	−	0.999881i	$-0.504907\pi$
$349$	−0.575942			−0.0308295			−0.0154147	+	0.999881i	$0.504907\pi$
$350$	31.9898	+	36.6504i	1.70993	+	1.95905i
$351$	13.9754			0.745951
$352$	−17.9931	+	13.0728i	−0.959037	+	0.696781i
$353$	4.77263	−	14.6887i	0.254022	−	0.781798i	−0.739999	−	0.672608i	$-0.765174\pi$
$353$	4.77263	−	14.6887i	0.254022	−	0.781798i	0.994021	−	0.109191i	$-0.0348259\pi$
$354$	−16.0723	+	49.4654i	−0.854232	+	2.62906i
$355$	−11.8282	−	20.8572i	−0.627777	−	1.10698i
$356$	−1.00337	−	3.08805i	−0.0531785	−	0.163667i
$357$	−77.5983			−4.10694
$358$	−6.09305	−	18.7525i	−0.322028	−	0.991099i
$359$	17.9757	+	13.0601i	0.948723	+	0.689288i	0.950505	−	0.310711i	$-0.100567\pi$
$359$	17.9757	+	13.0601i	0.948723	+	0.689288i	−0.00178138	+	0.999998i	$0.500567\pi$
$360$	−0.538193	−	0.949017i	−0.0283652	−	0.0500176i
$361$	14.7536	−	10.7191i	0.776503	−	0.564163i
$362$	25.2749	+	18.3633i	1.32842	+	0.965152i
$363$	−9.25574	−	6.72469i	−0.485800	−	0.352954i
$364$	5.49616	−	3.99319i	0.288077	−	0.209300i
$365$	−0.0330981	+	0.293128i	−0.00173244	+	0.0153430i
$366$	−1.37348	−	0.997893i	−0.0717931	−	0.0521607i
$367$	−5.74126	−	17.6698i	−0.299692	−	0.922356i	−0.981605	−	0.190923i	$-0.938852\pi$
$367$	−5.74126	−	17.6698i	−0.299692	−	0.922356i	0.681913	−	0.731433i	$-0.261148\pi$
$368$	−3.94442			−0.205617
$369$	3.48584	+	10.7283i	0.181466	+	0.558494i
$370$	−6.13521	+	6.70899i	−0.318954	+	0.348784i
$371$	−4.16789	+	12.8275i	−0.216386	+	0.665968i
$372$	−10.0732	+	31.0020i	−0.522269	+	1.60738i
$373$	−12.4455	+	9.04218i	−0.644403	+	0.468186i	−0.861360	−	0.507995i	$-0.830387\pi$
$373$	−12.4455	+	9.04218i	−0.644403	+	0.468186i	0.216957	+	0.976181i	$0.430387\pi$
$374$	−25.8365			−1.33597
$375$	31.6776	−	21.9129i	1.63582	−	1.13158i
$376$	−0.0510526			−0.00263284
$377$	−1.66876	+	1.21243i	−0.0859458	+	0.0624433i
$378$	−60.7937	+	187.104i	−3.12689	+	9.62358i
$379$	−0.827226	+	2.54594i	−0.0424918	+	0.130776i	−0.970052	−	0.242898i	$-0.921902\pi$
$379$	−0.827226	+	2.54594i	−0.0424918	+	0.130776i	0.927560	+	0.373674i	$0.121902\pi$
$380$	2.67339	−	2.92341i	0.137142	−	0.149968i
$381$	−6.30018	−	19.3900i	−0.322768	−	0.993378i
$382$	−30.2545			−1.54795
$383$	−4.49135	−	13.8230i	−0.229497	−	0.706320i	−0.997804	−	0.0662381i	$-0.978900\pi$
$383$	−4.49135	−	13.8230i	−0.229497	−	0.706320i	0.768306	−	0.640082i	$-0.221100\pi$
$384$	−1.22652	−	0.891120i	−0.0625907	−	0.0454748i
$385$	3.37068	−	29.8518i	0.171786	−	1.52139i
$386$	−15.6234	+	11.3511i	−0.795212	+	0.577755i
$387$	−31.2279	−	22.6884i	−1.58740	−	1.15331i
$388$	−2.29181	−	1.66510i	−0.116349	−	0.0845326i
$389$	−20.0800	+	14.5890i	−1.01810	+	0.739692i	−0.965892	−	0.258944i	$-0.916625\pi$
$389$	−20.0800	+	14.5890i	−1.01810	+	0.739692i	−0.0522063	+	0.998636i	$0.516625\pi$
$390$	−5.27108	−	9.29472i	−0.266912	−	0.470656i
$391$	−3.75856	−	2.73075i	−0.190078	−	0.138100i
$392$	0.280579	+	0.863532i	0.0141714	+	0.0436150i
$393$	59.8790			3.02050
$394$	−1.55588	−	4.78852i	−0.0783843	−	0.241242i
$395$	−0.506639	−	0.893377i	−0.0254918	−	0.0449507i
$396$	−15.3980	+	47.3901i	−0.773777	+	2.38144i
$397$	−1.46437	+	4.50688i	−0.0734948	+	0.226194i	−0.981055	−	0.193727i	$-0.937942\pi$
$397$	−1.46437	+	4.50688i	−0.0734948	+	0.226194i	0.907561	+	0.419921i	$0.137942\pi$
$398$	7.73594	−	5.62049i	0.387768	−	0.281730i
$399$	−14.5955			−0.730690
$400$	10.1235	−	16.9256i	0.506175	−	0.846281i
$401$	1.67245			0.0835182			0.0417591	−	0.999128i	$-0.486704\pi$
$401$	1.67245			0.0835182			0.0417591	+	0.999128i	$0.486704\pi$
$402$	77.2763	−	56.1445i	3.85419	−	2.80023i
$403$	−0.996768	+	3.06774i	−0.0496526	+	0.152815i
$404$	−1.48541	+	4.57163i	−0.0739020	+	0.227447i
$405$	87.6441	+	39.8350i	4.35507	+	1.97942i
$406$	−8.97289	−	27.6157i	−0.445317	−	1.37054i
$407$	5.61416			0.278283
$408$	−0.272091	−	0.837410i	−0.0134705	−	0.0414580i
$409$	7.28021	+	5.28938i	0.359983	+	0.261543i	0.753045	−	0.657969i	$-0.228584\pi$
$409$	7.28021	+	5.28938i	0.359983	+	0.261543i	−0.393062	+	0.919512i	$0.628584\pi$
$410$	3.85165	−	4.21186i	0.190219	−	0.208009i
$411$	16.4135	−	11.9251i	0.809620	−	0.588223i
$412$	17.3703	+	12.6203i	0.855773	+	0.621756i
$413$	−29.5060	−	21.4373i	−1.45189	−	1.05486i
$414$	−14.3997	+	10.4620i	−0.707704	+	0.514177i
$415$	−17.9537	−	8.16010i	−0.881312	−	0.400564i
$416$	−4.48775	−	3.26054i	−0.220030	−	0.159861i
$417$	−5.11366	−	15.7382i	−0.250417	−	0.770705i
$418$	−4.85961			−0.237691
$419$	5.27574	+	16.2371i	0.257737	+	0.793233i	0.993278	+	0.115753i	$0.0369280\pi$
$419$	5.27574	+	16.2371i	0.257737	+	0.793233i	−0.735541	+	0.677480i	$0.763072\pi$
$420$	74.1855	−	15.1712i	3.61988	−	0.740278i
$421$	8.87052	−	27.3007i	0.432323	−	1.33055i	−0.463482	−	0.886106i	$-0.653400\pi$
$421$	8.87052	−	27.3007i	0.432323	−	1.33055i	0.895805	−	0.444447i	$-0.146600\pi$
$422$	−3.81400	+	11.7383i	−0.185662	+	0.571410i
$423$	6.65883	−	4.83792i	0.323763	−	0.235228i
$424$	−0.153043			−0.00743243
$425$	21.3642	−	9.11948i	1.03632	−	0.442360i
$426$	−74.1387			−3.59203
$427$	0.963119	−	0.699747i	0.0466086	−	0.0338631i
$428$	6.73075	−	20.7151i	0.325343	−	1.00130i
$429$	−2.03906	+	6.27558i	−0.0984467	+	0.302988i
$430$	−2.19127	+	19.4066i	−0.105673	+	0.935871i
$431$	2.89017	+	8.89502i	0.139214	+	0.428458i	0.996222	−	0.0868463i	$-0.0276789\pi$
$431$	2.89017	+	8.89502i	0.139214	+	0.428458i	−0.857007	+	0.515304i	$0.827679\pi$
$432$	79.7567			3.83730
$433$	11.0603	+	34.0400i	0.531522	+	1.63586i	0.751046	+	0.660249i	$0.229549\pi$
$433$	11.0603	+	34.0400i	0.531522	+	1.63586i	−0.219524	+	0.975607i	$0.570451\pi$
$434$	−36.7352	−	26.6897i	−1.76334	−	1.28114i
$435$	−22.5245	+	4.60634i	−1.07997	+	0.220857i
$436$	−1.04105	+	0.756370i	−0.0498574	+	0.0362235i
$437$	−0.706949	−	0.513629i	−0.0338180	−	0.0245702i
$438$	0.737910	+	0.536123i	0.0352587	+	0.0256170i
$439$	−3.54406	+	2.57491i	−0.169149	+	0.122894i	−0.669139	−	0.743137i	$-0.733337\pi$
$439$	−3.54406	+	2.57491i	−0.169149	+	0.122894i	0.499990	+	0.866031i	$0.333337\pi$
$440$	0.333968	−	0.0682976i	0.0159213	−	0.00325596i
$441$	−118.427	−	86.0425i	−5.63940	−	4.09726i
$442$	−1.99131	−	6.12862i	−0.0947169	−	0.291509i
$443$	−9.67733			−0.459784			−0.229892	−	0.973216i	$-0.573837\pi$
$443$	−9.67733			−0.459784			−0.229892	+	0.973216i	$0.573837\pi$
$444$	4.37281	+	13.4581i	0.207525	+	0.638695i
$445$	0.401806	−	3.55853i	0.0190474	−	0.168690i
$446$	11.6135	−	35.7427i	0.549915	−	1.69246i
$447$	16.2111	−	49.8928i	0.766761	−	2.35985i
$448$	32.2323	−	23.4181i	1.52283	−	1.10640i
$449$	−19.4922			−0.919895			−0.459947	−	0.887946i	$-0.652132\pi$
$449$	−19.4922			−0.919895			−0.459947	+	0.887946i	$0.652132\pi$
$450$	−7.93530	−	88.6403i	−0.374074	−	4.17854i
$451$	−3.52454			−0.165964
$452$	16.5172	−	12.0004i	0.776902	−	0.564452i
$453$	−5.04775	+	15.5354i	−0.237164	+	0.729916i
$454$	11.7754	−	36.2409i	0.552646	−	1.70087i
$455$	7.34087	−	1.50123i	0.344145	−	0.0703789i
$456$	−0.0511778	−	0.157509i	−0.00239662	−	0.00737603i
$457$	−14.4144			−0.674278			−0.337139	−	0.941455i	$-0.609459\pi$
$457$	−14.4144			−0.674278			−0.337139	+	0.941455i	$0.609459\pi$
$458$	9.80237	+	30.1686i	0.458034	+	1.40969i
$459$	75.9984	+	55.2161i	3.54730	+	2.57727i
$460$	4.12714	+	1.87582i	0.192429	+	0.0874606i
$461$	−17.4665	+	12.6901i	−0.813495	+	0.591039i	−0.914842	−	0.403812i	$-0.867685\pi$
$461$	−17.4665	+	12.6901i	−0.813495	+	0.591039i	0.101347	+	0.994851i	$0.467685\pi$
$462$	−75.1480	−	54.5982i	−3.49620	−	2.54014i
$463$	0.597574	+	0.434163i	0.0277716	+	0.0201773i	0.601584	−	0.798809i	$-0.294536\pi$
$463$	0.597574	+	0.434163i	0.0277716	+	0.0201773i	−0.573813	+	0.818986i	$0.694536\pi$
$464$	−9.52355	+	6.91926i	−0.442120	+	0.321219i
$465$	−24.2623	+	26.5313i	−1.12513	+	1.23036i
$466$	−28.8982	−	20.9958i	−1.33869	−	0.972612i
$467$	4.62095	+	14.2218i	0.213832	+	0.658107i	0.999234	+	0.0391216i	$0.0124560\pi$
$467$	4.62095	+	14.2218i	0.213832	+	0.658107i	−0.785403	+	0.618985i	$0.787544\pi$
$468$	−12.4281			−0.574487
$469$	20.6980	+	63.7018i	0.955744	+	2.94148i
$470$	−3.79122	−	1.72314i	−0.174876	−	0.0794826i
$471$	−15.2784	+	47.0220i	−0.703990	+	2.16666i
$472$	0.127883	−	0.393584i	0.00588631	−	0.0181162i
$473$	9.75705	−	7.08891i	0.448630	−	0.325949i
$474$	−3.17559			−0.145860
$475$	4.01840	−	1.71529i	0.184377	−	0.0787029i
$476$	45.6651			2.09306
$477$	19.9615	−	14.5029i	0.913976	−	0.664042i
$478$	−4.76436	+	14.6632i	−0.217917	+	0.670679i
$479$	10.1775	−	31.3231i	0.465022	−	1.43119i	−0.393933	−	0.919139i	$-0.628886\pi$
$479$	10.1775	−	31.3231i	0.465022	−	1.43119i	0.858955	−	0.512051i	$-0.171114\pi$
$480$	−30.4999	−	53.7817i	−1.39212	−	2.45479i
$481$	0.432702	+	1.33172i	0.0197295	+	0.0607212i
$482$	34.2679			1.56086
$483$	−5.16144	−	15.8853i	−0.234854	−	0.722806i
$484$	5.44683	+	3.95735i	0.247583	+	0.179880i
$485$	−1.54126	−	2.71777i	−0.0699851	−	0.123408i
$486$	142.335	−	103.413i	6.45646	−	4.69090i
$487$	−7.85463	−	5.70672i	−0.355927	−	0.258596i	0.395424	−	0.918499i	$-0.370598\pi$
$487$	−7.85463	−	5.70672i	−0.355927	−	0.258596i	−0.751351	+	0.659902i	$0.770598\pi$
$488$	0.0109285	+	0.00794000i	0.000494709	+	0.000359427i
$489$	39.5422	−	28.7291i	1.78816	−	1.29918i
$490$	−8.31011	+	73.5970i	−0.375412	+	3.32477i
$491$	16.3796	+	11.9005i	0.739200	+	0.537060i	0.892460	−	0.451126i	$-0.148977\pi$
$491$	16.3796	+	11.9005i	0.739200	+	0.537060i	−0.153261	+	0.988186i	$0.548977\pi$
$492$	−2.74523	−	8.44894i	−0.123764	−	0.380908i
$493$	−13.8650			−0.624450
$494$	−0.374547	−	1.15274i	−0.0168516	−	0.0518640i
$495$	−37.0876	+	40.5561i	−1.66696	+	1.82286i
$496$	−5.68850	+	17.5074i	−0.255421	+	0.786106i
$497$	16.0651	−	49.4433i	0.720619	−	2.21784i
$498$	−49.3318	+	35.8416i	−2.21061	+	1.60610i
$499$	11.6054			0.519528			0.259764	−	0.965672i	$-0.416355\pi$
$499$	11.6054			0.519528			0.259764	+	0.965672i	$0.416355\pi$
$500$	−18.6416	+	12.8953i	−0.833680	+	0.576696i
$501$	54.1050			2.41723
$502$	44.2877	−	32.1769i	1.97666	−	1.43613i
$503$	4.57462	−	14.0792i	0.203972	−	0.627762i	−0.795782	−	0.605584i	$-0.792940\pi$
$503$	4.57462	−	14.0792i	0.203972	−	0.627762i	0.999754	−	0.0221787i	$-0.00706029\pi$
$504$	0.730974	−	2.24971i	0.0325602	−	0.100210i
$505$	−3.57777	+	3.91237i	−0.159209	+	0.174098i
$506$	−1.71851	−	5.28904i	−0.0763973	−	0.235127i
$507$	43.1413			1.91597
$508$	3.70754	+	11.4106i	0.164495	+	0.506265i
$509$	−24.2321	−	17.6057i	−1.07407	−	0.780357i	−0.0974303	−	0.995242i	$-0.531062\pi$
$509$	−24.2321	−	17.6057i	−1.07407	−	0.780357i	−0.976639	+	0.214885i	$0.931062\pi$
$510$	8.05872	−	71.3707i	0.356846	−	3.16035i
$511$	−0.517440	+	0.375942i	−0.0228902	+	0.0166307i
$512$	−25.9625	−	18.8628i	−1.14739	−	0.833627i
$513$	14.2946	+	10.3856i	0.631122	+	0.458537i
$514$	−18.4357	+	13.3943i	−0.813162	+	0.590797i
$515$	11.6817	+	20.5988i	0.514756	+	0.907690i
$516$	24.5931	+	17.8679i	1.08265	+	0.786590i
$517$	0.794692	+	2.44581i	0.0349505	+	0.107567i
$518$	−19.7115			−0.866073
$519$	−27.5512	−	84.7939i	−1.20936	−	3.72204i
$520$	0.0419408	+	0.0739558i	0.00183922	+	0.00324318i
$521$	1.84943	−	5.69197i	0.0810252	−	0.249370i	−0.902335	−	0.431035i	$-0.858149\pi$
$521$	1.84943	−	5.69197i	0.0810252	−	0.249370i	0.983360	+	0.181665i	$0.0581486\pi$
$522$	−16.4148	+	50.5194i	−0.718454	+	2.21117i
$523$	17.8791	−	12.9899i	0.781798	−	0.568010i	−0.123720	−	0.992317i	$-0.539482\pi$
$523$	17.8791	−	12.9899i	0.781798	−	0.568010i	0.905518	+	0.424308i	$0.139482\pi$
$524$	−35.2377			−1.53937
$525$	81.4112	+	18.6223i	3.55308	+	0.812743i
$526$	−32.9423			−1.43635
$527$	−17.5409	+	12.7442i	−0.764095	+	0.555148i
$528$	−11.6368	+	35.8144i	−0.506426	+	1.55862i
$529$	0.309017	−	0.951057i	0.0134355	−	0.0413503i
$530$	−11.3652	−	5.16556i	−0.493671	−	0.224377i
$531$	20.6175	+	63.4542i	0.894724	+	2.75368i
$532$	8.58918			0.372388
$533$	−0.271648	−	0.836047i	−0.0117664	−	0.0362132i
$534$	−8.95812	−	6.50845i	−0.387656	−	0.281648i
$535$	16.2117	−	17.7278i	0.700893	−	0.766441i
$536$	−0.614869	+	0.446729i	−0.0265583	+	0.0192957i
$537$	−27.3846	−	19.8961i	−1.18173	−	0.858579i
$538$	−30.8979	−	22.4486i	−1.33210	−	0.967828i
$539$	37.0023	−	26.8837i	1.59380	−	1.15796i
$540$	−83.4513	−	37.9293i	−3.59117	−	1.63222i
$541$	22.5703	+	16.3983i	0.970373	+	0.705018i	0.955537	−	0.294872i	$-0.0952771\pi$
$541$	22.5703	+	16.3983i	0.970373	+	0.705018i	0.0148368	+	0.999890i	$0.495277\pi$
$542$	20.0358	+	61.6638i	0.860611	+	2.64869i
$543$	53.6325			2.30159
$544$	−11.5222	−	35.4618i	−0.494012	−	1.52041i
$545$	−1.39047	+	0.284356i	−0.0595612	+	0.0121805i
$546$	7.15920	−	22.0337i	0.306385	−	0.942957i
$547$	6.12001	−	18.8354i	0.261673	−	0.805345i	−0.730769	−	0.682625i	$-0.760838\pi$
$547$	6.12001	−	18.8354i	0.261673	−	0.805345i	0.992441	−	0.122720i	$-0.0391618\pi$
$548$	−9.65905	+	7.01771i	−0.412614	+	0.299782i
$549$	−2.17783			−0.0929476
$550$	27.1060	+	6.20033i	1.15581	+	0.264383i
$551$	−2.60788			−0.111100
$552$	0.153330	−	0.111401i	0.00652614	−	0.00474152i
$553$	0.688118	−	2.11781i	0.0292618	−	0.0900584i
$554$	7.01942	−	21.6035i	0.298227	−	0.917847i
$555$	−1.75112	+	15.5085i	−0.0743310	+	0.658300i
$556$	3.00929	+	9.26165i	0.127622	+	0.392782i
$557$	−41.1026			−1.74157			−0.870787	−	0.491661i	$-0.836390\pi$
$557$	−41.1026			−1.74157			−0.870787	+	0.491661i	$0.836390\pi$
$558$	25.6690	+	79.0010i	1.08665	+	3.34438i
$559$	2.43355	+	1.76808i	0.102928	+	0.0747818i
$560$	41.8939	−	8.56745i	1.77034	−	0.362041i
$561$	−35.8830	+	26.0705i	−1.51498	+	1.10070i
$562$	−20.4502	−	14.8579i	−0.862639	−	0.626744i
$563$	15.5531	+	11.3000i	0.655485	+	0.476238i	0.865135	−	0.501539i	$-0.167232\pi$
$563$	15.5531	+	11.3000i	0.655485	+	0.476238i	−0.209650	+	0.977776i	$0.567232\pi$
$564$	−5.24406	+	3.81004i	−0.220815	+	0.160431i
$565$	22.0609	−	4.51153i	0.928111	−	0.189802i
$566$	15.2844	+	11.1048i	0.642453	+	0.466770i
$567$	64.5026	+	198.518i	2.70885	+	8.33699i
$568$	0.589904			0.0247518
$569$	−3.92276	−	12.0730i	−0.164451	−	0.506127i	0.834545	−	0.550940i	$-0.185731\pi$
$569$	−3.92276	−	12.0730i	−0.164451	−	0.506127i	−0.998995	+	0.0448134i	$0.985731\pi$
$570$	1.51577	−	13.4242i	0.0634886	−	0.562276i
$571$	−9.78726	+	30.1221i	−0.409584	+	1.26057i	0.507422	+	0.861698i	$0.330598\pi$
$571$	−9.78726	+	30.1221i	−0.409584	+	1.26057i	−0.917006	+	0.398873i	$0.869402\pi$
$572$	1.19995	−	3.69306i	0.0501723	−	0.154415i
$573$	−42.0189	+	30.5285i	−1.75536	+	1.27535i
$574$	12.3748			0.516512
$575$	3.28790	+	3.76692i	0.137115	+	0.157091i
$576$	−72.8846			−3.03686
$577$	−22.1272	+	16.0764i	−0.921168	+	0.669268i	−0.943814	−	0.330476i	$-0.892791\pi$
$577$	−22.1272	+	16.0764i	−0.921168	+	0.669268i	0.0226465	+	0.999744i	$0.492791\pi$
$578$	2.84259	−	8.74860i	0.118236	−	0.363894i
$579$	−10.2447	+	31.5298i	−0.425754	+	1.31034i
$580$	13.2553	−	2.71074i	0.550394	−	0.112557i
$581$	−13.2132	−	40.6661i	−0.548176	−	1.68711i
$582$	−9.66055			−0.400443
$583$	2.38229	+	7.33194i	0.0986645	+	0.303658i
$584$	−0.00587138	−	0.00426581i	−0.000242959	−	0.000176520i
$585$	−12.4787	−	5.67166i	−0.515930	−	0.234494i
$586$	−40.3120	+	29.2884i	−1.66528	+	1.20989i
$587$	−33.7075	−	24.4899i	−1.39126	−	1.01081i	−0.995726	−	0.0923547i	$-0.970561\pi$
$587$	−33.7075	−	24.4899i	−1.39126	−	1.01081i	−0.395531	−	0.918453i	$-0.629439\pi$
$588$	93.2658	+	67.7616i	3.84622	+	2.79444i
$589$	−3.29929	+	2.39707i	−0.135945	+	0.0987696i
$590$	22.7811	−	24.9117i	0.937885	−	1.02560i
$591$	−6.99276	−	5.08054i	−0.287644	−	0.208985i
$592$	2.46941	+	7.60006i	0.101492	+	0.312360i
$593$	11.4913			0.471891			0.235945	−	0.971766i	$-0.424181\pi$
$593$	11.4913			0.471891			0.235945	+	0.971766i	$0.424181\pi$
$594$	34.7486	+	106.945i	1.42575	+	4.38801i
$595$	45.8511	+	20.8397i	1.87971	+	0.854345i
$596$	−9.53995	+	29.3609i	−0.390772	+	1.20267i
$597$	5.07265	−	15.6120i	0.207610	−	0.638957i
$598$	1.12215	−	0.815289i	0.0458881	−	0.0333397i
$599$	40.2220			1.64342			0.821712	−	0.569902i	$-0.193019\pi$
$599$	40.2220			1.64342			0.821712	+	0.569902i	$0.193019\pi$
$600$	0.0844963	+	0.943855i	0.00344954	+	0.0385327i
$601$	27.1779			1.10861			0.554305	−	0.832314i	$-0.312984\pi$
$601$	27.1779			1.10861			0.554305	+	0.832314i	$0.312984\pi$
$602$	−34.2573	+	24.8894i	−1.39622	+	1.01442i
$603$	37.8643	−	116.534i	1.54195	−	4.74564i
$604$	2.97050	−	9.14227i	0.120868	−	0.371994i
$605$	3.66304	+	6.45918i	0.148924	+	0.262603i
$606$	5.06556	+	15.5902i	0.205774	+	0.633308i
$607$	−3.52061			−0.142897			−0.0714487	−	0.997444i	$-0.522762\pi$
$607$	−3.52061			−0.142897			−0.0714487	+	0.997444i	$0.522762\pi$
$608$	−2.16723	−	6.67004i	−0.0878926	−	0.270506i
$609$	−40.3278	−	29.2998i	−1.63416	−	1.18729i
$610$	0.543567	+	0.958494i	0.0220084	+	0.0388083i
$611$	−0.518915	+	0.377014i	−0.0209931	+	0.0152524i
$612$	−67.5841	−	49.1027i	−2.73192	−	1.98486i
$613$	−35.2766	−	25.6299i	−1.42481	−	1.03518i	−0.990954	−	0.134198i	$-0.957154\pi$
$613$	−35.2766	−	25.6299i	−1.42481	−	1.03518i	−0.433852	−	0.900984i	$-0.642846\pi$
$614$	3.11225	−	2.26118i	0.125600	−	0.0912539i
$615$	1.09935	−	9.73616i	0.0443299	−	0.392600i
$616$	0.597935	+	0.434425i	0.0240915	+	0.0175035i
$617$	12.9074	+	39.7250i	0.519634	+	1.59927i	0.774690	+	0.632341i	$0.217906\pi$
$617$	12.9074	+	39.7250i	0.519634	+	1.59927i	−0.255056	+	0.966926i	$0.582094\pi$
$618$	73.2201			2.94534
$619$	−8.41937	−	25.9122i	−0.338403	−	1.04150i	−0.965021	−	0.262172i	$-0.915561\pi$
$619$	−8.41937	−	25.9122i	−0.338403	−	1.04150i	0.626618	−	0.779327i	$-0.284439\pi$
$620$	14.2779	−	15.6132i	0.573413	−	0.627040i
$621$	−6.24836	+	19.2305i	−0.250738	+	0.771693i
$622$	−17.8639	+	54.9796i	−0.716279	+	2.20448i
$623$	6.28164	−	4.56388i	0.251669	−	0.182848i
$624$	−9.39232			−0.375994
$625$	−24.6025	+	4.44054i	−0.984099	+	0.177622i
$626$	32.7795			1.31013
$627$	−6.74925	+	4.90362i	−0.269539	+	0.195832i
$628$	8.99104	−	27.6716i	0.358781	−	1.10422i
$629$	−2.90852	+	8.95151i	−0.115970	+	0.356920i
$630$	130.216	−	142.394i	5.18792	−	5.67310i
$631$	−3.57551	−	11.0043i	−0.142339	−	0.438073i	0.854320	−	0.519747i	$-0.173974\pi$
$631$	−3.57551	−	11.0043i	−0.142339	−	0.438073i	−0.996659	+	0.0816731i	$0.973974\pi$
$632$	0.0252674			0.00100508
$633$	6.54752	+	20.1512i	0.260241	+	0.800938i
$634$	25.2759	+	18.3640i	1.00384	+	0.729329i
$635$	−1.48471	+	13.1491i	−0.0589189	+	0.521805i
$636$	−15.7204	+	11.4216i	−0.623355	+	0.452894i
$637$	9.22892	+	6.70520i	0.365663	+	0.265670i
$638$	−13.4272	−	9.75544i	−0.531589	−	0.386222i
$639$	−76.9416	+	55.9013i	−3.04376	+	2.21142i
$640$	0.485407	+	0.855937i	0.0191874	+	0.0338339i
$641$	−4.90915	−	3.56670i	−0.193900	−	0.140876i	0.486600	−	0.873625i	$-0.338237\pi$
$641$	−4.90915	−	3.56670i	−0.193900	−	0.140876i	−0.680499	+	0.732749i	$0.738237\pi$
$642$	−22.9532	−	70.6428i	−0.905892	−	2.78805i
$643$	4.31438			0.170142			0.0850712	−	0.996375i	$-0.472888\pi$
$643$	4.31438			0.170142			0.0850712	+	0.996375i	$0.472888\pi$
$644$	3.03741	+	9.34819i	0.119691	+	0.368370i
$645$	16.5390	+	29.1639i	0.651224	+	1.14833i
$646$	2.51761	−	7.74842i	0.0990542	−	0.304858i
$647$	7.98099	−	24.5630i	0.313765	−	0.965669i	−0.662495	−	0.749066i	$-0.730502\pi$
$647$	7.98099	−	24.5630i	0.313765	−	0.965669i	0.976260	−	0.216603i	$-0.0694977\pi$
$648$	−1.91616	+	1.39217i	−0.0752739	+	0.0546897i
$649$	−20.8464			−0.818292
$650$	0.618389	+	6.90764i	0.0242552	+	0.270940i
$651$	−77.9508			−3.05513
$652$	−23.2699	+	16.9065i	−0.911318	+	0.662111i
$653$	−11.5662	+	35.5971i	−0.452620	+	1.39302i	0.421286	+	0.906928i	$0.361579\pi$
$653$	−11.5662	+	35.5971i	−0.452620	+	1.39302i	−0.873906	+	0.486094i	$0.838421\pi$
$654$	−1.35606	+	4.17352i	−0.0530261	+	0.163198i
$655$	−35.3812	−	16.0810i	−1.38246	−	0.628338i
$656$	−1.55028	−	4.77127i	−0.0605283	−	0.186287i
$657$	1.17005			0.0456480
$658$	−2.79019	−	8.58732i	−0.108773	−	0.334768i
$659$	9.76984	+	7.09820i	0.380579	+	0.276507i	0.761584	−	0.648066i	$-0.224422\pi$
$659$	9.76984	+	7.09820i	0.380579	+	0.276507i	−0.381005	+	0.924573i	$0.624422\pi$
$660$	29.2078	−	31.9394i	1.13691	−	1.24324i
$661$	−19.8118	+	14.3941i	−0.770590	+	0.559866i	−0.902140	−	0.431443i	$-0.858004\pi$
$661$	−19.8118	+	14.3941i	−0.770590	+	0.559866i	0.131550	+	0.991309i	$0.458004\pi$
$662$	41.2659	+	29.9814i	1.60385	+	1.16526i
$663$	−8.94974	−	6.50237i	−0.347579	−	0.252531i
$664$	0.392521	−	0.285183i	0.0152328	−	0.0110673i
$665$	8.62417	+	3.91976i	0.334431	+	0.152002i
$666$	29.1729	+	21.1953i	1.13043	+	0.821302i
$667$	−0.922231	−	2.83834i	−0.0357089	−	0.109901i
$668$	−31.8398			−1.23192
$669$	−19.9370	−	61.3597i	−0.770808	−	2.37230i
$670$	−60.7390	+	12.4213i	−2.34655	+	0.479878i
$671$	0.210273	−	0.647153i	0.00811749	−	0.0249831i
$672$	41.4250	−	127.493i	1.59800	−	4.91815i
$673$	−5.52059	+	4.01094i	−0.212803	+	0.154610i	−0.689081	−	0.724684i	$-0.741986\pi$
$673$	−5.52059	+	4.01094i	−0.212803	+	0.154610i	0.476278	+	0.879295i	$0.341986\pi$
$674$	40.1852			1.54788
$675$	−66.4818	−	76.1676i	−2.55889	−	2.93169i
$676$	−25.3879			−0.976456
$677$	−24.9798	+	18.1489i	−0.960051	+	0.697518i	−0.953163	−	0.302458i	$-0.902193\pi$
$677$	−24.9798	+	18.1489i	−0.960051	+	0.697518i	−0.00688866	+	0.999976i	$0.502193\pi$
$678$	21.5150	−	66.2162i	0.826277	−	2.54302i
$679$	2.09334	−	6.44265i	0.0803352	−	0.247246i
$680$	−0.0641213	+	0.567880i	−0.00245894	+	0.0217772i
$681$	−20.2149	−	62.2150i	−0.774636	−	2.38408i
$682$	−25.9539			−0.993826
$683$	3.54708	+	10.9168i	0.135725	+	0.417720i	0.995702	−	0.0926135i	$-0.0295221\pi$
$683$	3.54708	+	10.9168i	0.135725	+	0.417720i	−0.859977	+	0.510333i	$0.829522\pi$
$684$	−12.7119	−	9.23576i	−0.486053	−	0.353138i
$685$	−12.9010	+	2.63830i	−0.492922	+	0.100804i
$686$	−74.8166	+	54.3575i	−2.85651	+	2.07538i
$687$	44.0558	+	32.0084i	1.68083	+	1.22120i
$688$	13.8881	+	10.0903i	0.529481	+	0.384690i
$689$	−1.55558	+	1.13020i	−0.0592629	+	0.0430570i
$690$	15.1465	−	3.09750i	0.576616	−	0.117920i
$691$	−30.8222	−	22.3936i	−1.17253	−	0.851895i	−0.181222	−	0.983442i	$-0.558005\pi$
$691$	−30.8222	−	22.3936i	−1.17253	−	0.851895i	−0.991310	+	0.131548i	$0.958005\pi$
$692$	16.2134	+	49.8996i	0.616339	+	1.89690i
$693$	−119.157			−4.52639
$694$	15.3379	+	47.2052i	0.582218	+	1.79188i
$695$	−1.20509	+	10.6727i	−0.0457118	+	0.404838i
$696$	0.174787	−	0.537938i	0.00662527	−	0.0203905i
$697$	1.82595	−	5.61971i	0.0691629	−	0.212862i
$698$	0.935081	−	0.679376i	0.0353934	−	0.0257148i
$699$	−61.3212			−2.31938
$700$	−47.9090	−	10.9589i	−1.81079	−	0.414206i
$701$	35.5245			1.34174			0.670871	−	0.741574i	$-0.265920\pi$
$701$	35.5245			1.34174			0.670871	+	0.741574i	$0.265920\pi$
$702$	−22.6900	+	16.4852i	−0.856379	+	0.622196i
$703$	−0.547066	+	1.68370i	−0.0206330	+	0.0635018i
$704$	7.03711	−	21.6580i	0.265221	−	0.816267i
$705$	−7.00417	+	1.43238i	−0.263792	+	0.0539464i
$706$	9.57792	+	29.4778i	0.360470	+	1.10941i
$707$	−11.4948			−0.432307
$708$	−16.2370	−	49.9725i	−0.610225	−	1.87808i
$709$	−19.4422	−	14.1256i	−0.730166	−	0.530496i	0.159450	−	0.987206i	$-0.449028\pi$
$709$	−19.4422	−	14.1256i	−0.730166	−	0.530496i	−0.889616	+	0.456710i	$0.849028\pi$
$710$	43.8069	+	19.9106i	1.64404	+	0.747231i
$711$	−3.29564	+	2.39443i	−0.123596	+	0.0897980i
$712$	0.0712776	+	0.0517862i	0.00267124	+	0.00194077i
$713$	−3.77563	−	2.74316i	−0.141398	−	0.102732i
$714$	125.986	−	91.5343i	4.71491	−	3.42559i
$715$	2.89020	−	3.16049i	0.108087	−	0.118196i
$716$	16.1153	+	11.7085i	0.602258	+	0.437566i
$717$	8.17902	+	25.1724i	0.305451	+	0.940082i
$718$	−44.5905			−1.66410
$719$	−3.18608	−	9.80575i	−0.118821	−	0.365693i	0.873904	−	0.486099i	$-0.161580\pi$
$719$	−3.18608	−	9.80575i	−0.118821	−	0.365693i	−0.992725	+	0.120406i	$0.961580\pi$
$720$	−71.2151	−	32.3679i	−2.65403	−	1.20628i
$721$	−15.8661	+	48.8307i	−0.590883	+	1.81855i
$722$	−11.3093	+	34.8064i	−0.420888	+	1.29536i
$723$	47.5928	−	34.5782i	1.76999	−	1.28598i
$724$	−31.5617			−1.17298
$725$	14.5463	+	3.32738i	0.540236	+	0.123576i
$726$	22.9597			0.852115
$727$	−33.4907	+	24.3324i	−1.24210	+	0.902439i	−0.997737	−	0.0672440i	$-0.978579\pi$
$727$	−33.4907	+	24.3324i	−1.24210	+	0.902439i	−0.244365	+	0.969683i	$0.578579\pi$
$728$	−0.0569640	+	0.175317i	−0.00211123	+	0.00649769i
$729$	53.4193	−	164.408i	1.97849	−	6.08918i
$730$	−0.292034	−	0.514956i	−0.0108087	−	0.0190594i
$731$	6.24811	+	19.2297i	0.231095	+	0.711236i
$732$	1.71512			0.0633927
$733$	−1.58807	−	4.88757i	−0.0586566	−	0.180527i	0.917435	−	0.397885i	$-0.130256\pi$
$733$	−1.58807	−	4.88757i	−0.0586566	−	0.180527i	−0.976092	+	0.217359i	$0.930256\pi$
$734$	30.1645	+	21.9158i	1.11339	+	0.808926i
$735$	62.7220	+	110.600i	2.31354	+	4.07955i
$736$	6.49306	−	4.71748i	0.239337	−	0.173889i
$737$	30.9729	+	22.5031i	1.14090	+	0.828913i
$738$	−18.3145	−	13.3063i	−0.674168	−	0.489812i
$739$	0.274418	−	0.199376i	0.0100946	−	0.00733417i	−0.582727	−	0.812668i	$-0.698014\pi$
$739$	0.274418	−	0.199376i	0.0100946	−	0.00733417i	0.592821	+	0.805334i	$0.298014\pi$
$740$	1.03050	−	9.12647i	0.0378820	−	0.335496i
$741$	−1.68336	−	1.22303i	−0.0618399	−	0.0449293i
$742$	−8.36430	−	25.7427i	−0.307063	−	0.945043i
$743$	−21.5842			−0.791848			−0.395924	−	0.918283i	$-0.629576\pi$
$743$	−21.5842			−0.791848			−0.395924	+	0.918283i	$0.629576\pi$
$744$	−0.273327	−	0.841214i	−0.0100207	−	0.0308404i
$745$	−22.9779	+	25.1269i	−0.841847	+	0.920578i
$746$	9.54003	−	29.3612i	0.349285	−	1.07499i
$747$	−24.1719	+	74.3934i	−0.884402	+	2.72191i
$748$	21.1164	−	15.3420i	0.772094	−	0.560959i
$749$	52.0856			1.90317
$750$	−25.5825	+	72.9436i	−0.934140	+	2.66353i
$751$	9.32715			0.340352			0.170176	−	0.985414i	$-0.445566\pi$
$751$	9.32715			0.340352			0.170176	+	0.985414i	$0.445566\pi$
$752$	−2.96142	+	2.15160i	−0.107992	+	0.0784607i
$753$	29.0405	−	89.3776i	1.05830	−	3.25710i
$754$	1.27918	−	3.93692i	0.0465851	−	0.143374i
$755$	7.15477	−	7.82389i	0.260389	−	0.284741i
$756$	−61.4169	−	189.022i	−2.23371	−	6.87465i
$757$	21.6093			0.785405			0.392702	−	0.919666i	$-0.371540\pi$
$757$	21.6093			0.785405			0.392702	+	0.919666i	$0.371540\pi$
$758$	−1.66011	−	5.10930i	−0.0602980	−	0.185578i
$759$	−7.72369	−	5.61159i	−0.280352	−	0.203688i
$760$	−0.0120606	+	0.106813i	−0.000437485	+	0.00387451i
$761$	−27.2498	+	19.7981i	−0.987803	+	0.717681i	−0.959439	−	0.281917i	$-0.909030\pi$
$761$	−27.2498	+	19.7981i	−0.987803	+	0.717681i	−0.0283640	+	0.999598i	$0.509030\pi$
$762$	33.1010	+	24.0493i	1.19912	+	0.871214i
$763$	−2.48949	−	1.80872i	−0.0901256	−	0.0654801i
$764$	24.7273	−	17.9654i	0.894602	−	0.649967i
$765$	−45.4509	−	80.1453i	−1.64328	−	2.89766i
$766$	23.5975	+	17.1446i	0.852611	+	0.619458i
$767$	−1.60670	−	4.94492i	−0.0580146	−	0.178551i
$768$	−53.5806			−1.93342
$769$	−3.82427	−	11.7699i	−0.137907	−	0.424433i	0.858124	−	0.513442i	$-0.171630\pi$
$769$	−3.82427	−	11.7699i	−0.137907	−	0.424433i	−0.996031	+	0.0890090i	$0.971630\pi$
$770$	29.7405	+	52.4425i	1.07177	+	1.88990i
$771$	−12.0887	+	37.2052i	−0.435364	+	1.33991i
$772$	6.02879	−	18.5547i	0.216981	−	0.667799i
$773$	19.2544	−	13.9892i	0.692534	−	0.503155i	−0.184958	−	0.982746i	$-0.559215\pi$
$773$	19.2544	−	13.9892i	0.692534	−	0.503155i	0.877492	+	0.479591i	$0.159215\pi$
$774$	77.4636			2.78437
$775$	21.4612	−	9.16091i	0.770911	−	0.329070i
$776$	0.0768667			0.00275935
$777$	−27.3762	+	19.8900i	−0.982116	+	0.713549i
$778$	15.3923	−	47.3725i	0.551839	−	1.69839i
$779$	0.343445	−	1.05701i	0.0123052	−	0.0378715i
$780$	9.82741	+	4.46664i	0.351878	+	0.159931i
$781$	−9.18253	−	28.2609i	−0.328577	−	1.01125i
$782$	9.32344			0.333406
$783$	18.6476	+	57.3915i	0.666412	+	2.05101i
$784$	52.6689	+	38.2662i	1.88103	+	1.36665i
$785$	21.6558	−	23.6811i	0.772930	−	0.845215i
$786$	−97.2177	+	70.6328i	−3.46764	+	2.51939i
$787$	−23.4055	−	17.0051i	−0.834316	−	0.606166i	0.0864608	−	0.996255i	$-0.472444\pi$
$787$	−23.4055	−	17.0051i	−0.834316	−	0.606166i	−0.920777	+	0.390089i	$0.872444\pi$
$788$	4.11511	+	2.98980i	0.146595	+	0.106507i
$789$	−45.7518	+	33.2406i	−1.62881	+	1.18340i
$790$	1.87638	+	0.852832i	0.0667587	+	0.0303424i
$791$	39.4978	+	28.6968i	1.40438	+	1.02034i
$792$	−0.417812	−	1.28589i	−0.0148463	−	0.0456922i
$793$	0.169716			0.00602679
$794$	−2.93876	−	9.04458i	−0.104293	−	0.320980i
$795$	−20.9968	+	4.29391i	−0.744679	+	0.152289i
$796$	−2.98516	+	9.18737i	−0.105806	+	0.325638i
$797$	1.26847	−	3.90394i	0.0449314	−	0.138285i	−0.926074	−	0.377342i	$-0.876838\pi$
$797$	1.26847	−	3.90394i	0.0449314	−	0.138285i	0.971006	+	0.239057i	$0.0768383\pi$
$798$	23.6968	−	17.2167i	0.838858	−	0.609466i
$799$	−4.31144			−0.152528
$800$	3.57816	+	39.9694i	0.126507	+	1.41313i
$801$	−14.2042			−0.501882
$802$	−2.71534	+	1.97281i	−0.0958819	+	0.0696623i
$803$	−0.112970	+	0.347686i	−0.00398663	+	0.0122696i
$804$	−29.8195	+	91.7750i	−1.05165	+	3.23665i
$805$	−1.21635	+	10.7724i	−0.0428708	+	0.379678i
$806$	−2.00036	−	6.15646i	−0.0704595	−	0.216852i
$807$	−65.5643			−2.30797
$808$	−0.0403055	−	0.124047i	−0.00141794	−	0.00436397i
$809$	−4.05074	−	2.94303i	−0.142416	−	0.103471i	0.514296	−	0.857613i	$-0.328053\pi$
$809$	−4.05074	−	2.94303i	−0.142416	−	0.103471i	−0.656712	+	0.754141i	$0.728053\pi$
$810$	−189.285	+	38.7094i	−6.65080	+	1.36011i
$811$	−13.9818	+	10.1584i	−0.490967	+	0.356708i	−0.805556	−	0.592520i	$-0.798133\pi$
$811$	−13.9818	+	10.1584i	−0.490967	+	0.356708i	0.314589	+	0.949228i	$0.398133\pi$
$812$	23.7321	+	17.2424i	0.832834	+	0.605090i
$813$	90.0488	+	65.4243i	3.15815	+	2.29453i
$814$	−9.11497	+	6.62241i	−0.319480	+	0.232116i
$815$	−31.0801	+	6.35598i	−1.08869	+	0.222640i
$816$	−51.0757	−	37.1086i	−1.78801	−	1.29906i
$817$	1.17521	+	3.61693i	0.0411154	+	0.126540i
$818$	−18.0592			−0.631426
$819$	−9.18381	−	28.2649i	−0.320908	−	0.987654i
$820$	−0.646944	+	5.72955i	−0.0225923	+	0.200084i
$821$	0.468244	−	1.44111i	0.0163418	−	0.0502949i	−0.942553	−	0.334056i	$-0.891582\pi$
$821$	0.468244	−	1.44111i	0.0163418	−	0.0502949i	0.958895	+	0.283761i	$0.0915824\pi$
$822$	−12.5817	+	38.7225i	−0.438838	+	1.35060i
$823$	35.4512	−	25.7568i	1.23575	−	0.897825i	0.238443	−	0.971157i	$-0.423363\pi$
$823$	35.4512	−	25.7568i	1.23575	−	0.897825i	0.997308	+	0.0733315i	$0.0233631\pi$
$824$	−0.582595			−0.0202956
$825$	43.9026	−	18.7402i	1.52849	−	0.652450i
$826$	73.1922			2.54668
$827$	−16.3505	+	11.8793i	−0.568561	+	0.413084i	−0.834582	−	0.550883i	$-0.814291\pi$
$827$	−16.3505	+	11.8793i	−0.568561	+	0.413084i	0.266021	+	0.963967i	$0.414291\pi$
$828$	5.55656	−	17.1013i	0.193104	−	0.594312i
$829$	−13.3911	+	41.2137i	−0.465094	+	1.43141i	0.393771	+	0.919209i	$0.371170\pi$
$829$	−13.3911	+	41.2137i	−0.465094	+	1.43141i	−0.858864	+	0.512203i	$0.828830\pi$
$830$	38.7746	−	7.92954i	1.34589	−	0.275238i
$831$	−12.0503	−	37.0870i	−0.418020	−	1.28653i
$832$	5.67982			0.196912
$833$	23.6951	+	72.9261i	0.820987	+	2.52674i
$834$	26.8671	+	19.5201i	0.930331	+	0.675925i
$835$	−31.9694	−	14.5304i	−1.10635	−	0.502844i
$836$	3.97181	−	2.88569i	0.137368	−	0.0998035i
$837$	76.3437	+	55.4670i	2.63882	+	1.91722i
$838$	−27.7186	−	20.1388i	−0.957525	−	0.695683i
$839$	26.4092	−	19.1874i	0.911747	−	0.662423i	−0.0297091	−	0.999559i	$-0.509458\pi$
$839$	26.4092	−	19.1874i	0.911747	−	0.662423i	0.941456	+	0.337136i	$0.109458\pi$
$840$	−1.38656	+	1.51623i	−0.0478407	+	0.0523149i
$841$	16.2558	+	11.8106i	0.560547	+	0.407261i
$842$	17.8017	+	54.7881i	0.613488	+	1.88812i
$843$	−43.3946			−1.49459
$844$	−3.85309	−	11.8586i	−0.132629	−	0.408190i
$845$	−25.4913	−	11.5860i	−0.876926	−	0.398570i
$846$	−5.10429	+	15.7094i	−0.175489	+	0.540100i
$847$	−4.97514	+	15.3119i	−0.170948	+	0.526124i
$848$	−8.87761	+	6.44996i	−0.304858	+	0.221493i
$849$	32.4331			1.11310
$850$	−23.9290	+	40.0071i	−0.820756	+	1.37223i
$851$	−2.02594			−0.0694484
$852$	60.5942	−	44.0243i	2.07592	−	1.50825i
$853$	−3.71776	+	11.4421i	−0.127294	+	0.391770i	−0.994312	−	0.106507i	$-0.966033\pi$
$853$	−3.71776	+	11.4421i	−0.127294	+	0.391770i	0.867018	+	0.498276i	$0.166033\pi$
$854$	−0.738274	+	2.27217i	−0.0252632	+	0.0777522i
$855$	−8.54888	−	15.0746i	−0.292366	−	0.515540i
$856$	0.182633	+	0.562088i	0.00624228	+	0.0192118i
$857$	−4.78628			−0.163496			−0.0817481	−	0.996653i	$-0.526050\pi$
$857$	−4.78628			−0.163496			−0.0817481	+	0.996653i	$0.526050\pi$
$858$	−4.09207	−	12.5941i	−0.139701	−	0.429955i
$859$	24.9150	+	18.1018i	0.850088	+	0.617625i	0.925170	−	0.379552i	$-0.123922\pi$
$859$	24.9150	+	18.1018i	0.850088	+	0.617625i	−0.0750825	+	0.997177i	$0.523922\pi$
$860$	−9.73291	−	17.1624i	−0.331889	−	0.585234i
$861$	17.1866	−	12.4868i	0.585719	−	0.425550i
$862$	−15.1849	−	11.0325i	−0.517199	−	0.375767i
$863$	−32.7135	−	23.7677i	−1.11358	−	0.809062i	−0.130355	−	0.991467i	$-0.541612\pi$
$863$	−32.7135	−	23.7677i	−1.11358	−	0.809062i	−0.983224	+	0.182405i	$0.941612\pi$
$864$	−131.290	+	95.3880i	−4.46659	+	3.24517i
$865$	−6.49275	+	57.5019i	−0.220760	+	1.95512i
$866$	−58.1104	−	42.2196i	−1.97467	−	1.43468i
$867$	−4.87990	−	15.0188i	−0.165730	−	0.510065i
$868$	45.8726			1.55702
$869$	−0.393316	−	1.21050i	−0.0133423	−	0.0410635i
$870$	31.1365	−	34.0484i	1.05563	−	1.15435i
$871$	−2.95072	+	9.08139i	−0.0999814	+	0.307711i
$872$	0.0107898	−	0.0332077i	0.000365390	−	0.00112455i
$873$	−10.0258	+	7.28415i	−0.339321	+	0.246531i
$874$	1.75365			0.0593182
$875$	−43.1029	−	32.8672i	−1.45714	−	1.11111i
$876$	−0.921457			−0.0311331
$877$	−13.5549	+	9.84820i	−0.457716	+	0.332550i	−0.792635	−	0.609697i	$-0.791291\pi$
$877$	−13.5549	+	9.84820i	−0.457716	+	0.332550i	0.334919	+	0.942247i	$0.391291\pi$
$878$	2.71668	−	8.36110i	0.0916837	−	0.282173i
$879$	−26.4336	+	81.3542i	−0.891583	+	2.74401i
$880$	16.4942	−	18.0368i	0.556019	−	0.608019i
$881$	14.6416	+	45.0623i	0.493289	+	1.51819i	0.819606	+	0.572927i	$0.194192\pi$
$881$	14.6416	+	45.0623i	0.493289	+	1.51819i	−0.326317	+	0.945260i	$0.605808\pi$
$882$	293.770			9.89175
$883$	−12.4945	−	38.4541i	−0.420474	−	1.29408i	−0.907262	−	0.420565i	$-0.861832\pi$
$883$	−12.4945	−	38.4541i	−0.420474	−	1.29408i	0.486789	−	0.873520i	$-0.338168\pi$
$884$	5.26675	+	3.82652i	0.177140	+	0.128700i
$885$	6.50223	−	57.5859i	0.218570	−	1.93573i
$886$	15.7118	−	11.4153i	0.527848	−	0.383504i
$887$	6.95405	+	5.05241i	0.233494	+	0.169643i	0.698380	−	0.715727i	$-0.253905\pi$
$887$	6.95405	+	5.05241i	0.233494	+	0.169643i	−0.464886	+	0.885371i	$0.653905\pi$
$888$	−0.310637	−	0.225691i	−0.0104243	−	0.00757369i
$889$	−23.2112	+	16.8639i	−0.778479	+	0.565598i
$890$	3.54525	+	6.25148i	0.118837	+	0.209550i
$891$	96.5230	+	70.1280i	3.23364	+	2.34938i
$892$	11.7325	+	36.1090i	0.392834	+	1.20902i
$893$	−0.810941			−0.0271371
$894$	32.5332	+	100.127i	1.08807	+	3.34874i
$895$	10.8377	+	19.1105i	0.362264	+	0.638795i
$896$	−0.659280	+	2.02905i	−0.0220250	+	0.0677860i
$897$	0.735820	−	2.26462i	0.0245683	−	0.0756135i
$898$	31.6470	−	22.9929i	1.05607	−	0.767282i
$899$	−13.9280			−0.464526
$900$	59.1211	+	67.7345i	1.97070	+	2.25782i
$901$	−12.9246			−0.430582
$902$	5.72233	−	4.15751i	0.190533	−	0.138430i
$903$	−22.4633	+	69.1351i	−0.747533	+	2.30067i
$904$	−0.171189	+	0.526867i	−0.00569368	+	0.0175233i
$905$	−31.6903	−	14.4035i	−1.05342	−	0.478788i
$906$	−10.1300	−	31.1770i	−0.336548	−	1.03579i
$907$	−21.6334			−0.718326			−0.359163	−	0.933275i	$-0.616938\pi$
$907$	−21.6334			−0.718326			−0.359163	+	0.933275i	$0.616938\pi$
$908$	11.8961	+	36.6123i	0.394785	+	1.21502i
$909$	17.0122	+	12.3601i	0.564260	+	0.409959i
$910$	−10.1476	+	11.0966i	−0.336389	+	0.367848i
$911$	0.0908242	−	0.0659876i	0.00300914	−	0.00218627i	−0.586280	−	0.810109i	$-0.699408\pi$
$911$	0.0908242	−	0.0659876i	0.00300914	−	0.00218627i	0.589289	+	0.807922i	$0.299408\pi$
$912$	−9.60686	−	6.97979i	−0.318115	−	0.231124i
$913$	−19.7725	−	14.3656i	−0.654375	−	0.475431i
$914$	23.4028	−	17.0031i	0.774095	−	0.562413i
$915$	1.72211	+	0.782711i	0.0569310	+	0.0258756i
$916$	−25.9260	−	18.8363i	−0.856619	−	0.622370i
$917$	−26.0392	−	80.1403i	−0.859889	−	2.64647i
$918$	−188.521			−6.22213
$919$	−2.44380	−	7.52125i	−0.0806136	−	0.248103i	0.902625	−	0.430429i	$-0.141638\pi$
$919$	−2.44380	−	7.52125i	−0.0806136	−	0.248103i	−0.983238	+	0.182325i	$0.941638\pi$
$920$	−0.120517	+	0.0246461i	−0.00397332	+	0.000812557i
$921$	2.04078	−	6.28087i	0.0672459	−	0.206962i
$922$	13.3889	−	41.2066i	0.440938	−	1.35707i
$923$	5.99597	−	4.35633i	0.197360	−	0.143390i
$924$	93.8402			3.08711
$925$	5.19965	−	8.69336i	0.170964	−	0.285836i
$926$	−1.48234			−0.0487127
$927$	75.9883	−	55.2087i	2.49578	−	1.81329i
$928$	7.40170	−	22.7801i	0.242973	−	0.747793i
$929$	8.38987	−	25.8214i	0.275263	−	0.847171i	−0.713887	−	0.700261i	$-0.753067\pi$
$929$	8.38987	−	25.8214i	0.275263	−	0.847171i	0.989150	−	0.146911i	$-0.0469330\pi$
$930$	8.09533	−	71.6949i	0.265456	−	2.35097i
$931$	4.45683	+	13.7167i	0.146067	+	0.449547i
$932$	36.0863			1.18205
$933$	30.6672	+	94.3839i	1.00400	+	3.08999i
$934$	−24.2784	−	17.6393i	−0.794412	−	0.577174i
$935$	28.2039	−	5.76779i	0.922367	−	0.188627i
$936$	0.272821	−	0.198216i	0.00891744	−	0.00647890i
$937$	42.5302	+	30.9000i	1.38940	+	1.00946i	0.995931	+	0.0901212i	$0.0287254\pi$
$937$	42.5302	+	30.9000i	1.38940	+	1.00946i	0.393470	+	0.919338i	$0.371275\pi$
$938$	−108.747	−	79.0091i	−3.55071	−	2.57974i
$939$	45.5257	−	33.0764i	1.48567	−	1.07941i
$940$	4.12182	−	0.842926i	0.134439	−	0.0274932i
$941$	16.9772	+	12.3347i	0.553441	+	0.402098i	0.829053	−	0.559171i	$-0.188880\pi$
$941$	16.9772	+	12.3347i	0.553441	+	0.402098i	−0.275612	+	0.961269i	$0.588880\pi$
$942$	−30.6613	−	94.3657i	−0.998998	−	3.07460i
$943$	1.27187			0.0414179
$944$	−9.16935	−	28.2204i	−0.298437	−	0.918495i
$945$	24.5948	−	217.820i	0.800069	−	7.08567i
$946$	−7.47922	+	23.0187i	−0.243170	+	0.748402i
$947$	−8.80148	+	27.0882i	−0.286010	+	0.880247i	0.700084	+	0.714060i	$0.253146\pi$
$947$	−8.80148	+	27.0882i	−0.286010	+	0.880247i	−0.986094	+	0.166187i	$0.946854\pi$
$948$	2.59544	−	1.88570i	0.0842959	−	0.0612446i
$949$	−0.0911808			−0.00295985
$950$	−4.50081	+	7.52497i	−0.146026	+	0.244142i
$951$	53.6347			1.73922
$952$	−1.00244	+	0.728317i	−0.0324893	+	0.0236049i
$953$	−9.76407	+	30.0507i	−0.316289	+	0.973438i	0.658931	+	0.752203i	$0.271009\pi$
$953$	−9.76407	+	30.0507i	−0.316289	+	0.973438i	−0.975220	+	0.221235i	$0.928991\pi$
$954$	−15.3014	+	47.0929i	−0.495402	+	1.52469i
$955$	33.0267	−	6.75407i	1.06872	−	0.218557i
$956$	−4.81320	−	14.8135i	−0.155670	−	0.479103i
$957$	−28.4921			−0.921020
$958$	20.4246	+	62.8605i	0.659890	+	2.03093i
$959$	−23.0979	−	16.7816i	−0.745869	−	0.541905i
$960$	57.6330	+	26.1947i	1.86010	+	0.845429i
$961$	7.45890	−	5.41921i	0.240610	−	0.174813i
$962$	−2.27341	−	1.65173i	−0.0732976	−	0.0532539i
$963$	−77.0864	−	56.0065i	−2.48407	−	1.80479i
$964$	−28.0074	+	20.3486i	−0.902059	+	0.655384i
$965$	14.5210	−	15.8790i	0.467446	−	0.511163i
$966$	27.1181	+	19.7025i	0.872511	+	0.633916i
$967$	−10.9012	−	33.5506i	−0.350560	−	1.07891i	−0.958539	−	0.284960i	$-0.908020\pi$
$967$	−10.9012	−	33.5506i	−0.350560	−	1.07891i	0.607979	−	0.793953i	$-0.291980\pi$
$968$	−0.182685			−0.00587172
$969$	−4.32201	−	13.3018i	−0.138843	−	0.427315i
$970$	5.70820	+	2.59443i	0.183279	+	0.0833020i
$971$	14.6592	−	45.1164i	0.470436	−	1.44785i	−0.381580	−	0.924336i	$-0.624620\pi$
$971$	14.6592	−	45.1164i	0.470436	−	1.44785i	0.852015	−	0.523517i	$-0.175380\pi$
$972$	−54.9246	+	169.040i	−1.76171	+	5.42197i
$973$	−18.8398	+	13.6879i	−0.603977	+	0.438815i
$974$	19.4841			0.624312
$975$	7.82904	+	8.96966i	0.250730	+	0.287259i
$976$	0.968560			0.0310028
$977$	24.2773	−	17.6385i	0.776699	−	0.564305i	−0.127288	−	0.991866i	$-0.540627\pi$
$977$	24.2773	−	17.6385i	0.776699	−	0.564305i	0.903986	+	0.427561i	$0.140627\pi$
$978$	−30.3109	+	93.2874i	−0.969236	+	2.98300i
$979$	1.37144	−	4.22086i	0.0438314	−	0.134899i
$980$	−36.9107	−	65.0862i	−1.17907	−	2.07910i
$981$	1.73955	+	5.35379i	0.0555396	+	0.170933i
$982$	−40.6310			−1.29659
$983$	−7.25492	−	22.3284i	−0.231396	−	0.712164i	−0.997579	−	0.0695416i	$-0.977846\pi$
$983$	−7.25492	−	22.3284i	−0.231396	−	0.712164i	0.766183	−	0.642623i	$-0.222154\pi$
$984$	0.195016	+	0.141687i	0.00621688	+	0.00451683i
$985$	2.76745	+	4.87995i	0.0881781	+	0.155488i
$986$	22.5108	−	16.3551i	0.716891	−	0.520852i
$987$	−12.5402	−	9.11101i	−0.399160	−	0.290007i
$988$	0.990627	+	0.719733i	0.0315160	+	0.0228977i
$989$	−3.52096	+	2.55813i	−0.111960	+	0.0813436i
$990$	12.3746	−	109.594i	0.393292	−	3.48312i
$991$	19.8868	+	14.4486i	0.631725	+	0.458975i	0.856997	−	0.515321i	$-0.172327\pi$
$991$	19.8868	+	14.4486i	0.631725	+	0.458975i	−0.225273	+	0.974296i	$0.572327\pi$
$992$	−11.5746	−	35.6229i	−0.367494	−	1.13103i
$993$	87.5650			2.77879
$994$	32.2401	+	99.2249i	1.02259	+	3.14722i
$995$	−7.19006	+	7.86248i	−0.227940	+	0.249257i
$996$	19.0362	−	58.5874i	0.603185	−	1.85641i
$997$	−1.41443	+	4.35318i	−0.0447955	+	0.137866i	−0.970953	−	0.239271i	$-0.923092\pi$
$997$	−1.41443	+	4.35318i	−0.0447955	+	0.137866i	0.926157	+	0.377137i	$0.123092\pi$
$998$	−18.8421	+	13.6896i	−0.596437	+	0.433337i
$999$	40.9648			1.29607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	575.2.g.b.461.6	yes	108
25.16	even	5	inner	575.2.g.b.116.6	✓	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
575.2.g.b.116.6	✓	108	25.16	even	5	inner
575.2.g.b.461.6	yes	108	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:	\( N \)	\(=\)	\( 575 = 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	575.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.62357 + 1.17959i) q^{2} +(-1.06461 + 3.27654i) q^{3} +(0.626505 - 1.92818i) q^{4} +(1.50900 - 1.65013i) q^{5} +(-2.13651 - 6.57550i) q^{6} +4.84819 q^{7} +(0.0169997 + 0.0523197i) q^{8} +(-7.17528 - 5.21315i) q^{9} +O(q^{10})\)	\(q+(-1.62357 + 1.17959i) q^{2} +(-1.06461 + 3.27654i) q^{3} +(0.626505 - 1.92818i) q^{4} +(1.50900 - 1.65013i) q^{5} +(-2.13651 - 6.57550i) q^{6} +4.84819 q^{7} +(0.0169997 + 0.0523197i) q^{8} +(-7.17528 - 5.21315i) q^{9} +(-0.503493 + 4.45910i) q^{10} +(2.24190 - 1.62883i) q^{11} +(5.65079 + 4.10554i) q^{12} +(0.559162 + 0.406255i) q^{13} +(-7.87136 + 5.71888i) q^{14} +(3.80020 + 6.70105i) q^{15} +(3.19111 + 2.31847i) q^{16} +(1.43564 + 4.41845i) q^{17} +17.7990 q^{18} +(0.270031 + 0.831069i) q^{19} +(-2.23635 - 3.94344i) q^{20} +(-5.16144 + 15.8853i) q^{21} +(-1.71851 + 5.28904i) q^{22} +(-0.809017 + 0.587785i) q^{23} -0.189526 q^{24} +(-0.445830 - 4.98008i) q^{25} -1.38705 q^{26} +(16.3584 - 11.8851i) q^{27} +(3.03741 - 9.34819i) q^{28} +(-0.922231 + 2.83834i) q^{29} +(-14.0744 - 6.39693i) q^{30} +(1.44216 + 4.43852i) q^{31} -8.02586 q^{32} +(2.95019 + 9.07974i) q^{33} +(-7.54282 - 5.48018i) q^{34} +(7.31592 - 8.00012i) q^{35} +(-14.5473 + 10.5692i) q^{36} +(1.63902 + 1.19082i) q^{37} +(-1.41873 - 1.03077i) q^{38} +(-1.92640 + 1.39961i) q^{39} +(0.111987 + 0.0508989i) q^{40} +(-1.02897 - 0.747589i) q^{41} +(-10.3582 - 31.8793i) q^{42} +4.35214 q^{43} +(-1.73613 - 5.34326i) q^{44} +(-19.4299 + 3.97347i) q^{45} +(0.620148 - 1.90862i) q^{46} +(-0.286775 + 0.882602i) q^{47} +(-10.9939 + 7.98752i) q^{48} +16.5049 q^{49} +(6.59830 + 7.55961i) q^{50} -16.0056 q^{51} +(1.13365 - 0.823646i) q^{52} +(-0.859681 + 2.64583i) q^{53} +(-12.5395 + 38.5925i) q^{54} +(0.695245 - 6.15732i) q^{55} +(0.0824177 + 0.253656i) q^{56} -3.01051 q^{57} +(-1.85077 - 5.69609i) q^{58} +(-6.08598 - 4.42172i) q^{59} +(15.3017 - 3.12925i) q^{60} +(0.198655 - 0.144332i) q^{61} +(-7.57709 - 5.50508i) q^{62} +(-34.7871 - 25.2743i) q^{63} +(6.64832 - 4.83029i) q^{64} +(1.51415 - 0.309648i) q^{65} +(-15.5002 - 11.2616i) q^{66} +(4.26922 + 13.1393i) q^{67} +9.41901 q^{68} +(-1.06461 - 3.27654i) q^{69} +(-2.44103 + 21.6185i) q^{70} +(3.31363 - 10.1983i) q^{71} +(0.150773 - 0.464031i) q^{72} +(-0.106729 + 0.0775429i) q^{73} -4.06574 q^{74} +(16.7921 + 3.84108i) q^{75} +1.77163 q^{76} +(10.8691 - 7.89688i) q^{77} +(1.47667 - 4.54474i) q^{78} +(0.141933 - 0.436825i) q^{79} +(8.64116 - 1.76715i) q^{80} +(13.3045 + 40.9470i) q^{81} +2.55245 q^{82} +(-2.72539 - 8.38789i) q^{83} +(27.3961 + 19.9044i) q^{84} +(9.45738 + 4.29846i) q^{85} +(-7.06600 + 5.13375i) q^{86} +(-8.31811 - 6.04346i) q^{87} +(0.123332 + 0.0896057i) q^{88} +(1.29567 - 0.941359i) q^{89} +(26.8586 - 29.3705i) q^{90} +(2.71092 + 1.96960i) q^{91} +(0.626505 + 1.92818i) q^{92} -16.0783 q^{93} +(-0.575512 - 1.77124i) q^{94} +(1.77884 + 0.808499i) q^{95} +(8.54444 - 26.2971i) q^{96} +(0.431779 - 1.32888i) q^{97} +(-26.7969 + 19.4691i) q^{98} -24.5776 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 4 q^{2} + q^{3} - 20 q^{4} + 3 q^{5} + 8 q^{6} + 24 q^{7} + 13 q^{8} - 36 q^{9}+O(q^{10}) \) 108 * q - 4 * q^2 + q^3 - 20 * q^4 + 3 * q^5 + 8 * q^6 + 24 * q^7 + 13 * q^8 - 36 * q^9	\( 108 q - 4 q^{2} + q^{3} - 20 q^{4} + 3 q^{5} + 8 q^{6} + 24 q^{7} + 13 q^{8} - 36 q^{9} - 24 q^{10} + 9 q^{11} - 20 q^{12} - 18 q^{13} - 31 q^{14} - 5 q^{15} - 20 q^{16} - 28 q^{17} + 34 q^{18} - q^{19} - 34 q^{20} - q^{21} - 35 q^{22} - 27 q^{23} + 178 q^{24} - 13 q^{25} + 14 q^{26} - 14 q^{27} - 3 q^{28} - 12 q^{29} - 35 q^{30} + 26 q^{31} + 22 q^{32} - 33 q^{33} - 15 q^{34} - 42 q^{35} - 49 q^{36} - 21 q^{37} - 11 q^{38} - 52 q^{39} + 25 q^{40} + 29 q^{41} + 6 q^{42} + 22 q^{43} - 58 q^{44} + 16 q^{45} + q^{46} - q^{47} - 83 q^{48} + 220 q^{49} - 16 q^{50} - 70 q^{51} - 76 q^{52} - 33 q^{53} - 106 q^{54} + 26 q^{55} + 124 q^{56} + 122 q^{57} + 46 q^{58} - 11 q^{59} + 20 q^{60} + 14 q^{61} - 40 q^{62} - 47 q^{63} - 87 q^{64} + 69 q^{65} + 47 q^{66} - 3 q^{67} + 154 q^{68} + q^{69} - 79 q^{70} - 51 q^{71} + 18 q^{72} - 26 q^{73} + 118 q^{74} - 55 q^{75} - 142 q^{76} - 5 q^{77} - 78 q^{78} - 7 q^{79} + 168 q^{80} + 29 q^{81} + 88 q^{82} + 7 q^{83} - 116 q^{84} + 9 q^{85} - 36 q^{86} - 130 q^{87} + 34 q^{88} + 9 q^{89} + 187 q^{90} + 58 q^{91} - 20 q^{92} + 26 q^{93} - 7 q^{94} - 86 q^{95} - 71 q^{96} - 50 q^{97} - 82 q^{98} + 124 q^{99}+O(q^{100}) \) 108 * q - 4 * q^2 + q^3 - 20 * q^4 + 3 * q^5 + 8 * q^6 + 24 * q^7 + 13 * q^8 - 36 * q^9 - 24 * q^10 + 9 * q^11 - 20 * q^12 - 18 * q^13 - 31 * q^14 - 5 * q^15 - 20 * q^16 - 28 * q^17 + 34 * q^18 - q^19 - 34 * q^20 - q^21 - 35 * q^22 - 27 * q^23 + 178 * q^24 - 13 * q^25 + 14 * q^26 - 14 * q^27 - 3 * q^28 - 12 * q^29 - 35 * q^30 + 26 * q^31 + 22 * q^32 - 33 * q^33 - 15 * q^34 - 42 * q^35 - 49 * q^36 - 21 * q^37 - 11 * q^38 - 52 * q^39 + 25 * q^40 + 29 * q^41 + 6 * q^42 + 22 * q^43 - 58 * q^44 + 16 * q^45 + q^46 - q^47 - 83 * q^48 + 220 * q^49 - 16 * q^50 - 70 * q^51 - 76 * q^52 - 33 * q^53 - 106 * q^54 + 26 * q^55 + 124 * q^56 + 122 * q^57 + 46 * q^58 - 11 * q^59 + 20 * q^60 + 14 * q^61 - 40 * q^62 - 47 * q^63 - 87 * q^64 + 69 * q^65 + 47 * q^66 - 3 * q^67 + 154 * q^68 + q^69 - 79 * q^70 - 51 * q^71 + 18 * q^72 - 26 * q^73 + 118 * q^74 - 55 * q^75 - 142 * q^76 - 5 * q^77 - 78 * q^78 - 7 * q^79 + 168 * q^80 + 29 * q^81 + 88 * q^82 + 7 * q^83 - 116 * q^84 + 9 * q^85 - 36 * q^86 - 130 * q^87 + 34 * q^88 + 9 * q^89 + 187 * q^90 + 58 * q^91 - 20 * q^92 + 26 * q^93 - 7 * q^94 - 86 * q^95 - 71 * q^96 - 50 * q^97 - 82 * q^98 + 124 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more