LMFDB - Embedded newform 84.2.e.a.71.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [84,2,Mod(71,84)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(84, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("84.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 84 = 2^{2} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	84.e (of order $2$, degree $1$, 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:	$0.670743376979$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.2593100598870016.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{10} + x^{8} + 4x^{6} + 4x^{4} - 32x^{2} + 64 $ x^12 - 2x^10 + x^8 + 4x^6 + 4x^4 - 32x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			71.11
Root			$-0.430469 - 1.34711i$ of defining polynomial
Character	$\chi$	$=$	84.71
Dual form			84.2.e.a.71.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.34711 - 0.430469i) q^{2} +(-0.916638 + 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(-0.602184 + 2.37432i) q^{6} +1.00000i q^{7} +(1.69572 - 2.26374i) q^{8} +(-1.31955 - 2.69421i) q^{9} +O(q^{10})$	\(q+(1.34711 - 0.430469i) q^{2} +(-0.916638 + 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(-0.602184 + 2.37432i) q^{6} +1.00000i q^{7} +(1.69572 - 2.26374i) q^{8} +(-1.31955 - 2.69421i) q^{9} +(-0.150067 - 0.469617i) q^{10} -3.90376 q^{11} +(0.210863 + 3.45768i) q^{12} -2.93923 q^{13} +(0.430469 + 1.34711i) q^{14} +(0.512326 + 0.319551i) q^{15} +(1.30984 - 3.77946i) q^{16} +3.90376i q^{17} +(-2.93735 - 3.06137i) q^{18} -5.57834i q^{19} +(-0.404312 - 0.568026i) q^{20} +(-1.46962 - 0.916638i) q^{21} +(-5.25879 + 1.68045i) q^{22} +2.18189 q^{23} +(1.77248 + 4.56709i) q^{24} +4.87847 q^{25} +(-3.95946 + 1.26525i) q^{26} +(5.16901 + 0.530383i) q^{27} +(1.15978 + 1.62939i) q^{28} +9.75220i q^{29} +(0.827715 + 0.209928i) q^{30} +2.63910i q^{31} +(0.137557 - 5.65518i) q^{32} +(3.57834 - 5.73704i) q^{33} +(1.68045 + 5.25879i) q^{34} +0.348612 q^{35} +(-5.27475 - 2.85955i) q^{36} +0.639102 q^{37} +(-2.40130 - 7.51461i) q^{38} +(2.69421 - 4.31955i) q^{39} +(-0.789168 - 0.591148i) q^{40} -7.57031i q^{41} +(-2.37432 - 0.602184i) q^{42} +2.51757i q^{43} +(-6.36076 + 4.52749i) q^{44} +(-0.939235 + 0.460011i) q^{45} +(2.93923 - 0.939235i) q^{46} +4.36377 q^{47} +(4.35371 + 5.38936i) q^{48} -1.00000 q^{49} +(6.57182 - 2.10003i) q^{50} +(-5.73704 - 3.57834i) q^{51} +(-4.78917 + 3.40885i) q^{52} -1.72188i q^{53} +(7.19153 - 1.51062i) q^{54} +1.36090i q^{55} +(2.26374 + 1.69572i) q^{56} +(8.19802 + 5.11331i) q^{57} +(4.19802 + 13.1373i) q^{58} +8.24635 q^{59} +(1.20539 - 0.0735095i) q^{60} -14.0959 q^{61} +(1.13605 + 3.55515i) q^{62} +(2.69421 - 1.31955i) q^{63} +(-2.24908 - 7.67735i) q^{64} +1.02465i q^{65} +(2.35078 - 9.26877i) q^{66} +0.639102i q^{67} +(4.52749 + 6.36076i) q^{68} +(-2.00000 + 3.20654i) q^{69} +(0.469617 - 0.150067i) q^{70} -11.9341 q^{71} +(-8.33660 - 1.58150i) q^{72} +7.87847 q^{73} +(0.860938 - 0.275113i) q^{74} +(-4.47179 + 7.16948i) q^{75} +(-6.46962 - 9.08930i) q^{76} -3.90376i q^{77} +(1.76996 - 6.97867i) q^{78} +4.00000i q^{79} +(-1.31756 - 0.456627i) q^{80} +(-5.51757 + 7.11030i) q^{81} +(-3.25879 - 10.1980i) q^{82} -8.94358 q^{83} +(-3.45768 + 0.210863i) q^{84} +1.36090 q^{85} +(1.08374 + 3.39144i) q^{86} +(-14.3320 - 8.93923i) q^{87} +(-6.61968 + 8.83712i) q^{88} -10.5396i q^{89} +(-1.06723 + 1.02400i) q^{90} -2.93923i q^{91} +(3.55515 - 2.53050i) q^{92} +(-3.87847 - 2.41910i) q^{93} +(5.87847 - 1.87847i) q^{94} -1.94467 q^{95} +(8.18486 + 5.38591i) q^{96} -2.00000 q^{97} +(-1.34711 + 0.430469i) q^{98} +(5.15121 + 10.5176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) $ 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9	$ 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42} + 24 q^{45} + 46 q^{48} - 12 q^{49} - 28 q^{52} + 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} - 16 q^{61} + 20 q^{64} - 12 q^{66} - 24 q^{69} - 12 q^{70} - 32 q^{72} + 24 q^{73} - 60 q^{76} + 20 q^{78} + 28 q^{81} + 8 q^{82} - 14 q^{84} + 40 q^{85} - 56 q^{88} - 80 q^{90} + 24 q^{93} - 34 q^{96} - 24 q^{97}+O(q^{100}) $ 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 + 2 * q^24 - 12 * q^25 + 8 * q^28 + 20 * q^30 - 16 * q^33 + 32 * q^34 - 20 * q^36 - 16 * q^37 + 20 * q^40 + 10 * q^42 + 24 * q^45 + 46 * q^48 - 12 * q^49 - 28 * q^52 + 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 - 16 * q^61 + 20 * q^64 - 12 * q^66 - 24 * q^69 - 12 * q^70 - 32 * q^72 + 24 * q^73 - 60 * q^76 + 20 * q^78 + 28 * q^81 + 8 * q^82 - 14 * q^84 + 40 * q^85 - 56 * q^88 - 80 * q^90 + 24 * q^93 - 34 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/84\mathbb{Z}\right)^\times$.

$n$	$29$	$43$	$73$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	1.34711	−	0.430469i	0.952548	−	0.304388i
$2$	1.34711	−	0.430469i	0.952548	−	0.304388i
$3$	−0.916638	+	1.46962i	−0.529221	+	0.848484i
$3$	−0.916638	+	1.46962i	−0.529221	+	0.848484i
$4$	1.62939	−	1.15978i	0.814696	−	0.579888i
$5$		−	0.348612i		−	0.155904i	−0.996957	−	0.0779520i	$-0.975162\pi$
$5$		−	0.348612i		−	0.155904i	0.996957	−	0.0779520i	$-0.0248381\pi$
$6$	−0.602184	+	2.37432i	−0.245841	+	0.969310i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.69572	−	2.26374i	0.599527	−	0.800354i
$9$	−1.31955	−	2.69421i	−0.439850	−	0.898071i
$10$	−0.150067	−	0.469617i	−0.0474552	−	0.148506i
$11$	−3.90376			−1.17703			−0.588514	−	0.808487i	$-0.700287\pi$
$11$	−3.90376			−1.17703			−0.588514	+	0.808487i	$0.700287\pi$
$12$	0.210863	+	3.45768i	0.0608710	+	0.998146i
$13$	−2.93923			−0.815197			−0.407599	−	0.913161i	$-0.633634\pi$
$13$	−2.93923			−0.815197			−0.407599	+	0.913161i	$0.633634\pi$
$14$	0.430469	+	1.34711i	0.115048	+	0.360029i
$15$	0.512326	+	0.319551i	0.132282	+	0.0825077i
$16$	1.30984	−	3.77946i	0.327461	−	0.944865i
$17$			3.90376i			0.946802i	0.880847	+	0.473401i	$0.156974\pi$
$17$			3.90376i			0.946802i	−0.880847	+	0.473401i	$0.843026\pi$
$18$	−2.93735	−	3.06137i	−0.692340	−	0.721571i
$19$		−	5.57834i		−	1.27976i	−0.768476	−	0.639879i	$-0.778984\pi$
$19$		−	5.57834i		−	1.27976i	0.768476	−	0.639879i	$-0.221016\pi$
$20$	−0.404312	−	0.568026i	−0.0904068	−	0.127014i
$21$	−1.46962	−	0.916638i	−0.320697	−	0.200027i
$22$	−5.25879	+	1.68045i	−1.12118	+	0.358273i
$23$	2.18189			0.454955			0.227477	−	0.973783i	$-0.426952\pi$
$23$	2.18189			0.454955			0.227477	+	0.973783i	$0.426952\pi$
$24$	1.77248	+	4.56709i	0.361806	+	0.932254i
$25$	4.87847			0.975694
$26$	−3.95946	+	1.26525i	−0.776515	+	0.248136i
$27$	5.16901	+	0.530383i	0.994777	+	0.102072i
$28$	1.15978	+	1.62939i	0.219177	+	0.307926i
$29$			9.75220i			1.81094i	0.424412	+	0.905469i	$0.360481\pi$
$29$			9.75220i			1.81094i	−0.424412	+	0.905469i	$0.639519\pi$
$30$	0.827715	+	0.209928i	0.151119	+	0.0383275i
$31$			2.63910i			0.473997i	0.971510	+	0.236998i	$0.0761636\pi$
$31$			2.63910i			0.473997i	−0.971510	+	0.236998i	$0.923836\pi$
$32$	0.137557	−	5.65518i	0.0243168	−	0.999704i
$33$	3.57834	−	5.73704i	0.622908	−	0.998690i
$34$	1.68045	+	5.25879i	0.288195	+	0.901874i
$35$	0.348612			0.0589262
$36$	−5.27475	−	2.85955i	−0.879125	−	0.476592i
$37$	0.639102			0.105068			0.0525338	−	0.998619i	$-0.483270\pi$
$37$	0.639102			0.105068			0.0525338	+	0.998619i	$0.483270\pi$
$38$	−2.40130	−	7.51461i	−0.389542	−	1.21903i
$39$	2.69421	−	4.31955i	0.431419	−	0.691682i
$40$	−0.789168	−	0.591148i	−0.124778	−	0.0934687i
$41$		−	7.57031i		−	1.18228i	−0.806567	−	0.591142i	$-0.798677\pi$
$41$		−	7.57031i		−	1.18228i	0.806567	−	0.591142i	$-0.201323\pi$
$42$	−2.37432	−	0.602184i	−0.366365	−	0.0929190i
$43$			2.51757i			0.383926i	0.981402	+	0.191963i	$0.0614854\pi$
$43$			2.51757i			0.383926i	−0.981402	+	0.191963i	$0.938515\pi$
$44$	−6.36076	+	4.52749i	−0.958921	+	0.682545i
$45$	−0.939235	+	0.460011i	−0.140013	+	0.0685744i
$46$	2.93923	−	0.939235i	0.433367	−	0.138483i
$47$	4.36377			0.636522			0.318261	−	0.948003i	$-0.396901\pi$
$47$	4.36377			0.636522			0.318261	+	0.948003i	$0.396901\pi$
$48$	4.35371	+	5.38936i	0.628404	+	0.777887i
$49$	−1.00000			−0.142857
$50$	6.57182	−	2.10003i	0.929396	−	0.296989i
$51$	−5.73704	−	3.57834i	−0.803346	−	0.501067i
$52$	−4.78917	+	3.40885i	−0.664138	+	0.472723i
$53$		−	1.72188i		−	0.236518i	−0.992983	−	0.118259i	$-0.962269\pi$
$53$		−	1.72188i		−	0.236518i	0.992983	−	0.118259i	$-0.0377313\pi$
$54$	7.19153	−	1.51062i	0.978643	−	0.205569i
$55$			1.36090i			0.183504i
$56$	2.26374	+	1.69572i	0.302506	+	0.226600i
$57$	8.19802	+	5.11331i	1.08585	+	0.677275i
$58$	4.19802	+	13.1373i	0.551227	+	1.72501i
$59$	8.24635			1.07358			0.536792	−	0.843715i	$-0.319636\pi$
$59$	8.24635			1.07358			0.536792	+	0.843715i	$0.319636\pi$
$60$	1.20539	−	0.0735095i	0.155615	−	0.00949003i
$61$	−14.0959			−1.80480			−0.902398	−	0.430903i	$-0.858195\pi$
$61$	−14.0959			−1.80480			−0.902398	+	0.430903i	$0.858195\pi$
$62$	1.13605	+	3.55515i	0.144279	+	0.451505i
$63$	2.69421	−	1.31955i	0.339439	−	0.166248i
$64$	−2.24908	−	7.67735i	−0.281135	−	0.959668i
$65$			1.02465i			0.127092i
$66$	2.35078	−	9.26877i	0.289361	−	1.14091i
$67$			0.639102i			0.0780787i	0.999238	+	0.0390393i	$0.0124298\pi$
$67$			0.639102i			0.0780787i	−0.999238	+	0.0390393i	$0.987570\pi$
$68$	4.52749	+	6.36076i	0.549039	+	0.771356i
$69$	−2.00000	+	3.20654i	−0.240772	+	0.386022i
$70$	0.469617	−	0.150067i	0.0561300	−	0.0179364i
$71$	−11.9341			−1.41632			−0.708158	−	0.706054i	$-0.750474\pi$
$71$	−11.9341			−1.41632			−0.708158	+	0.706054i	$0.750474\pi$
$72$	−8.33660	−	1.58150i	−0.982477	−	0.186382i
$73$	7.87847			0.922105			0.461053	−	0.887373i	$-0.347472\pi$
$73$	7.87847			0.922105			0.461053	+	0.887373i	$0.347472\pi$
$74$	0.860938	−	0.275113i	0.100082	−	0.0319813i
$75$	−4.47179	+	7.16948i	−0.516358	+	0.827861i
$76$	−6.46962	−	9.08930i	−0.742116	−	1.04261i
$77$		−	3.90376i		−	0.444875i
$78$	1.76996	−	6.97867i	0.200409	−	0.790179i
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$	−1.31756	−	0.456627i	−0.147308	−	0.0510524i
$81$	−5.51757	+	7.11030i	−0.613063	+	0.790034i
$82$	−3.25879	−	10.1980i	−0.359873	−	1.12618i
$83$	−8.94358			−0.981685			−0.490843	−	0.871248i	$-0.663311\pi$
$83$	−8.94358			−0.981685			−0.490843	+	0.871248i	$0.663311\pi$
$84$	−3.45768	+	0.210863i	−0.377264	+	0.0230071i
$85$	1.36090			0.147610
$86$	1.08374	+	3.39144i	0.116862	+	0.365708i
$87$	−14.3320	−	8.93923i	−1.53655	−	0.958387i
$88$	−6.61968	+	8.83712i	−0.705661	+	0.942040i
$89$		−	10.5396i		−	1.11720i	−0.829437	−	0.558600i	$-0.811339\pi$
$89$		−	10.5396i		−	1.11720i	0.829437	−	0.558600i	$-0.188661\pi$
$90$	−1.06723	+	1.02400i	−0.112496	+	0.107939i
$91$		−	2.93923i		−	0.308116i
$92$	3.55515	−	2.53050i	0.370650	−	0.263823i
$93$	−3.87847	−	2.41910i	−0.402179	−	0.250849i
$94$	5.87847	−	1.87847i	0.606318	−	0.193749i
$95$	−1.94467			−0.199519
$96$	8.18486	+	5.38591i	0.835364	+	0.549697i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$	−1.34711	+	0.430469i	−0.136078	+	0.0434839i
$99$	5.15121	+	10.5176i	0.517716	+	1.05706i
$100$	7.94894	−	5.65793i	0.794894	−	0.565793i
$101$			3.09514i			0.307978i	0.988073	+	0.153989i	$0.0492120\pi$
$101$			3.09514i			0.307978i	−0.988073	+	0.153989i	$0.950788\pi$
$102$	−9.26877	−	2.35078i	−0.917745	−	0.232762i
$103$			7.23937i			0.713316i	0.934235	+	0.356658i	$0.116084\pi$
$103$			7.23937i			0.713316i	−0.934235	+	0.356658i	$0.883916\pi$
$104$	−4.98412	+	6.65368i	−0.488733	+	0.652447i
$105$	−0.319551	+	0.512326i	−0.0311850	+	0.0499979i
$106$	−0.741214	−	2.31955i	−0.0719931	−	0.225295i
$107$	11.0141			1.06477			0.532385	−	0.846502i	$-0.321296\pi$
$107$	11.0141			1.06477			0.532385	+	0.846502i	$0.321296\pi$
$108$	9.03748	−	5.13069i	0.869632	−	0.493701i
$109$	1.39973			0.134070			0.0670351	−	0.997751i	$-0.478646\pi$
$109$	1.39973			0.134070			0.0670351	+	0.997751i	$0.478646\pi$
$110$	0.585825	+	1.83328i	0.0558562	+	0.174796i
$111$	−0.585825	+	0.939235i	−0.0556040	+	0.0891482i
$112$	3.77946	+	1.30984i	0.357125	+	0.123768i
$113$		−	8.83218i		−	0.830862i	−0.909625	−	0.415431i	$-0.863631\pi$
$113$		−	8.83218i		−	0.830862i	0.909625	−	0.415431i	$-0.136369\pi$
$114$	13.2447	+	3.35918i	1.24048	+	0.314616i
$115$		−	0.760632i		−	0.0709293i
$116$	11.3104	+	15.8902i	1.05014	+	1.47536i
$117$	3.87847	+	7.91893i	0.358565	+	0.732105i
$118$	11.1087	−	3.54980i	1.02264	−	0.326786i
$119$	−3.90376			−0.357857
$120$	1.59214	−	0.617907i	0.145342	−	0.0564069i
$121$	4.23937			0.385397
$122$	−18.9887	+	6.06785i	−1.71916	+	0.549357i
$123$	11.1255	+	6.93923i	1.00315	+	0.625690i
$124$	3.06077	+	4.30013i	0.274865	+	0.386163i
$125$		−	3.44375i		−	0.308019i
$126$	3.06137	−	2.93735i	0.272728	−	0.261680i
$127$		−	12.3960i		−	1.09997i	−0.835174	−	0.549985i	$-0.814633\pi$
$127$		−	12.3960i		−	1.09997i	0.835174	−	0.549985i	$-0.185367\pi$
$128$	−6.33461	−	9.37405i	−0.559905	−	0.828557i
$129$	−3.69987	−	2.30770i	−0.325755	−	0.203182i
$130$	0.441081	+	1.38032i	0.0386854	+	0.121062i
$131$	1.61048			0.140708			0.0703540	−	0.997522i	$-0.477587\pi$
$131$	1.61048			0.140708			0.0703540	+	0.997522i	$0.477587\pi$
$132$	−0.823160	−	13.4980i	−0.0716469	−	1.17485i
$133$	5.57834			0.483703
$134$	0.275113	+	0.860938i	0.0237662	+	0.0743737i
$135$	0.184898	−	1.80198i	0.0159135	−	0.155090i
$136$	8.83712	+	6.61968i	0.757777	+	0.567633i
$137$			4.36377i			0.372822i	0.982472	+	0.186411i	$0.0596857\pi$
$137$			4.36377i			0.372822i	−0.982472	+	0.186411i	$0.940314\pi$
$138$	−1.31390	+	5.18049i	−0.111846	+	0.440992i
$139$		−	16.8177i		−	1.42646i	−0.700931	−	0.713230i	$-0.747232\pi$
$139$		−	16.8177i		−	1.42646i	0.700931	−	0.713230i	$-0.252768\pi$
$140$	0.568026	−	0.404312i	0.0480069	−	0.0341706i
$141$	−4.00000	+	6.41308i	−0.336861	+	0.540079i
$142$	−16.0765	+	5.13726i	−1.34911	+	0.431109i
$143$	11.4741			0.959511
$144$	−11.9111	+	1.45819i	−0.992589	+	0.121516i
$145$	3.39973			0.282332
$146$	10.6131	−	3.39144i	0.878350	−	0.280677i
$147$	0.916638	−	1.46962i	0.0756030	−	0.121212i
$148$	1.04135	−	0.741214i	0.0855982	−	0.0609274i
$149$		−	7.66053i		−	0.627575i	−0.949493	−	0.313788i	$-0.898402\pi$
$149$		−	7.66053i		−	0.627575i	0.949493	−	0.313788i	$-0.101598\pi$
$150$	−2.93774	+	11.5830i	−0.239865	+	0.945750i
$151$			12.6391i			1.02856i	0.857624	+	0.514278i	$0.171940\pi$
$151$			12.6391i			1.02856i	−0.857624	+	0.514278i	$0.828060\pi$
$152$	−12.6279	−	9.45929i	−1.02426	−	0.767250i
$153$	10.5176	−	5.15121i	0.850295	−	0.416451i
$154$	−1.68045	−	5.25879i	−0.135414	−	0.423765i
$155$	0.920022			0.0738980
$156$	−0.619777	−	10.1629i	−0.0496219	−	0.813685i
$157$	0.217438			0.0173534			0.00867672	−	0.999962i	$-0.497238\pi$
$157$	0.217438			0.0173534			0.00867672	+	0.999962i	$0.497238\pi$
$158$	1.72188	+	5.38843i	0.136985	+	0.428680i
$159$	2.53050	+	1.57834i	0.200682	+	0.125170i
$160$	−1.97146	−	0.0479539i	−0.155858	−	0.00379109i
$161$			2.18189i			0.171957i
$162$	−4.37199	+	11.9535i	−0.343496	+	0.939154i
$163$		−	5.23937i		−	0.410379i	−0.978722	−	0.205189i	$-0.934219\pi$
$163$		−	5.23937i		−	0.410379i	0.978722	−	0.205189i	$-0.0657811\pi$
$164$	−8.77986	−	12.3350i	−0.685592	−	0.963203i
$165$	−2.00000	−	1.24745i	−0.155700	−	0.0971139i
$166$	−12.0480	+	3.84993i	−0.935103	+	0.298813i
$167$	11.4741			0.887891			0.443945	−	0.896054i	$-0.353578\pi$
$167$	11.4741			0.887891			0.443945	+	0.896054i	$0.353578\pi$
$168$	−4.56709	+	1.77248i	−0.352359	+	0.136750i
$169$	−4.36090			−0.335454
$170$	1.83328	−	0.585825i	0.140606	−	0.0449307i
$171$	−15.0292	+	7.36090i	−1.14931	+	0.562902i
$172$	2.91982	+	4.10211i	0.222634	+	0.312783i
$173$			21.2051i			1.61219i	0.591784	+	0.806097i	$0.298424\pi$
$173$			21.2051i			1.61219i	−0.591784	+	0.806097i	$0.701576\pi$
$174$	−23.1548	−	5.87262i	−1.75536	−	0.445202i
$175$			4.87847i			0.368778i
$176$	−5.11331	+	14.7541i	−0.385430	+	1.11213i
$177$	−7.55892	+	12.1190i	−0.568163	+	0.910919i
$178$	−4.53699	−	14.1980i	−0.340062	−	1.06419i
$179$	−1.81209			−0.135442			−0.0677211	−	0.997704i	$-0.521573\pi$
$179$	−1.81209			−0.135442			−0.0677211	+	0.997704i	$0.521573\pi$
$180$	−0.996873	+	1.83884i	−0.0743025	+	0.137059i
$181$	7.53950			0.560407			0.280203	−	0.959941i	$-0.409598\pi$
$181$	7.53950			0.560407			0.280203	+	0.959941i	$0.409598\pi$
$182$	−1.26525	−	3.95946i	−0.0937865	−	0.293495i
$183$	12.9208	−	20.7156i	0.955136	−	1.53134i
$184$	3.69987	−	4.93923i	0.272758	−	0.364125i
$185$		−	0.222798i		−	0.0163805i
$186$	−6.26606	−	1.58922i	−0.459450	−	0.116528i
$187$		−	15.2394i		−	1.11441i
$188$	7.11030	−	5.06100i	0.518572	−	0.369111i
$189$	−0.530383	+	5.16901i	−0.0385797	+	0.375990i
$190$	−2.61968	+	0.837122i	−0.190052	+	0.0607312i
$191$	−1.63166			−0.118063			−0.0590314	−	0.998256i	$-0.518801\pi$
$191$	−1.63166			−0.118063			−0.0590314	+	0.998256i	$0.518801\pi$
$192$	13.3444	+	3.73206i	0.963046	+	0.269338i
$193$	−15.1567			−1.09100			−0.545501	−	0.838110i	$-0.683660\pi$
$193$	−15.1567			−1.09100			−0.545501	+	0.838110i	$0.683660\pi$
$194$	−2.69421	+	0.860938i	−0.193433	+	0.0618117i
$195$	−1.50585	−	0.939235i	−0.107836	−	0.0672600i
$196$	−1.62939	+	1.15978i	−0.116385	+	0.0828411i
$197$		−	21.2263i		−	1.51231i	−0.654393	−	0.756155i	$-0.727076\pi$
$197$		−	21.2263i		−	1.51231i	0.654393	−	0.756155i	$-0.272924\pi$
$198$	11.4667	+	11.9509i	0.814905	+	0.849310i
$199$		−	3.75694i		−	0.266322i	−0.991094	−	0.133161i	$-0.957487\pi$
$199$		−	3.75694i		−	0.266322i	0.991094	−	0.133161i	$-0.0425128\pi$
$200$	8.27251	−	11.0436i	0.584955	−	0.780901i
$201$	−0.939235	−	0.585825i	−0.0662485	−	0.0413209i
$202$	1.33236	+	4.16948i	0.0937447	+	0.293364i
$203$	−9.75220			−0.684470
$204$	−13.4980	+	0.823160i	−0.945046	+	0.0576328i
$205$	−2.63910			−0.184323
$206$	3.11632	+	9.75220i	0.217125	+	0.679468i
$207$	−2.87911	−	5.87847i	−0.200112	−	0.408582i
$208$	−3.84993	+	11.1087i	−0.266945	+	0.770251i
$209$			21.7765i			1.50631i
$210$	−0.209928	+	0.827715i	−0.0144864	+	0.0571177i
$211$			9.83963i			0.677388i	0.940897	+	0.338694i	$0.109985\pi$
$211$			9.83963i			0.677388i	−0.940897	+	0.338694i	$0.890015\pi$
$212$	−1.99699	−	2.80561i	−0.137154	−	0.192690i
$213$	10.9392	−	17.5385i	0.749544	−	1.20172i
$214$	14.8371	−	4.74121i	1.01424	−	0.324103i
$215$	0.877655			0.0598556
$216$	9.96584	−	10.8019i	0.678090	−	0.734979i
$217$	−2.63910			−0.179154
$218$	1.88559	−	0.602542i	0.127708	−	0.0408093i
$219$	−7.22170	+	11.5783i	−0.487997	+	0.782391i
$220$	1.57834	+	2.21744i	0.106411	+	0.149500i
$221$		−	11.4741i		−	0.771830i
$222$	−0.384857	+	1.51743i	−0.0258299	+	0.101843i
$223$			22.9136i			1.53441i	0.641403	+	0.767204i	$0.278353\pi$
$223$			22.9136i			1.53441i	−0.641403	+	0.767204i	$0.721647\pi$
$224$	5.65518	+	0.137557i	0.377853	+	0.00919090i
$225$	−6.43739	−	13.1436i	−0.429159	−	0.876243i
$226$	−3.80198	−	11.8979i	−0.252904	−	0.791436i
$227$	13.5302			0.898028			0.449014	−	0.893525i	$-0.351775\pi$
$227$	13.5302			0.898028			0.449014	+	0.893525i	$0.351775\pi$
$228$	19.2881	−	1.17627i	1.27739	−	0.0779002i
$229$	14.6962			0.971151			0.485575	−	0.874195i	$-0.338610\pi$
$229$	14.6962			0.971151			0.485575	+	0.874195i	$0.338610\pi$
$230$	−0.327428	−	1.02465i	−0.0215900	−	0.0675636i
$231$	5.73704	+	3.57834i	0.377469	+	0.235437i
$232$	22.0765	+	16.5370i	1.44939	+	1.08571i
$233$			17.1899i			1.12615i	0.826406	+	0.563075i	$0.190382\pi$
$233$			17.1899i			1.12615i	−0.826406	+	0.563075i	$0.809618\pi$
$234$	8.63356	+	8.99808i	0.564394	+	0.588223i
$235$		−	1.52126i		−	0.0992363i
$236$	13.4366	−	9.56392i	0.874645	−	0.622558i
$237$	−5.87847	−	3.66655i	−0.381848	−	0.238168i
$238$	−5.25879	+	1.68045i	−0.340876	+	0.108927i
$239$	−14.5336			−0.940102			−0.470051	−	0.882639i	$-0.655764\pi$
$239$	−14.5336			−0.940102			−0.470051	+	0.882639i	$0.655764\pi$
$240$	1.87880	−	1.51775i	0.121276	−	0.0979707i
$241$	−18.7921			−1.21050			−0.605252	−	0.796034i	$-0.706928\pi$
$241$	−18.7921			−1.21050			−0.605252	+	0.796034i	$0.706928\pi$
$242$	5.71088	−	1.82492i	0.367109	−	0.117310i
$243$	−5.39181	−	14.6263i	−0.345885	−	0.938277i
$244$	−22.9678	+	16.3481i	−1.47036	+	1.04658i
$245$			0.348612i			0.0222720i
$246$	17.9743	+	4.55872i	1.14600	+	0.290653i
$247$			16.3960i			1.04326i
$248$	5.97425	+	4.47517i	0.379365	+	0.284174i
$249$	8.19802	−	13.1436i	0.519528	−	0.832944i
$250$	−1.48243	−	4.63910i	−0.0937570	−	0.293403i
$251$	−20.6405			−1.30281			−0.651407	−	0.758729i	$-0.725821\pi$
$251$	−20.6405			−1.30281			−0.651407	+	0.758729i	$0.725821\pi$
$252$	2.85955	−	5.27475i	0.180135	−	0.332278i
$253$	−8.51757			−0.535495
$254$	−5.33611	−	16.6988i	−0.334817	−	1.04778i
$255$	−1.24745	+	2.00000i	−0.0781184	+	0.125245i
$256$	−12.5686	−	9.90099i	−0.785539	−	0.618812i
$257$			4.82379i			0.300899i	0.988618	+	0.150450i	$0.0480722\pi$
$257$			4.82379i			0.300899i	−0.988618	+	0.150450i	$0.951928\pi$
$258$	−5.97751	−	1.51604i	−0.372143	−	0.0943846i
$259$			0.639102i			0.0397118i
$260$	1.18837	+	1.66956i	0.0736994	+	0.103542i
$261$	26.2745	−	12.8685i	1.62635	−	0.796542i
$262$	2.16948	−	0.693260i	0.134031	−	0.0428298i
$263$	−14.4578			−0.891507			−0.445754	−	0.895156i	$-0.647064\pi$
$263$	−14.4578			−0.891507			−0.445754	+	0.895156i	$0.647064\pi$
$264$	−6.91934	−	17.8288i	−0.425856	−	1.09729i
$265$	−0.600267			−0.0368741
$266$	7.51461	−	2.40130i	0.460751	−	0.147233i
$267$	15.4892	+	9.66103i	0.947926	+	0.591246i
$268$	0.741214	+	1.04135i	0.0452769	+	0.0636104i
$269$		−	4.71239i		−	0.287319i	−0.989627	−	0.143660i	$-0.954113\pi$
$269$		−	4.71239i		−	0.287319i	0.989627	−	0.143660i	$-0.0458871\pi$
$270$	−0.526619	−	2.50705i	−0.0320490	−	0.152574i
$271$			15.6742i			0.952143i	0.879407	+	0.476071i	$0.157940\pi$
$271$			15.6742i			0.952143i	−0.879407	+	0.476071i	$0.842060\pi$
$272$	14.7541	+	5.11331i	0.894600	+	0.310040i
$273$	4.31955	+	2.69421i	0.261431	+	0.163061i
$274$	1.87847	+	5.87847i	0.113483	+	0.355131i
$275$	−19.0444			−1.14842
$276$	0.460080	+	7.54426i	0.0276936	+	0.454111i
$277$	16.9963			1.02121			0.510605	−	0.859816i	$-0.329422\pi$
$277$	16.9963			1.02121			0.510605	+	0.859816i	$0.329422\pi$
$278$	−7.23950	−	22.6552i	−0.434196	−	1.35877i
$279$	7.11030	−	3.48243i	0.425683	−	0.208488i
$280$	0.591148	−	0.789168i	0.0353278	−	0.0471618i
$281$		−	5.75822i		−	0.343507i	−0.985140	−	0.171753i	$-0.945057\pi$
$281$		−	5.75822i		−	0.343507i	0.985140	−	0.171753i	$-0.0549432\pi$
$282$	−2.62779	+	10.3610i	−0.156483	+	0.616987i
$283$			5.57834i			0.331598i	0.986160	+	0.165799i	$0.0530202\pi$
$283$			5.57834i			0.331598i	−0.986160	+	0.165799i	$0.946980\pi$
$284$	−19.4453	+	13.8409i	−1.15387	+	0.821304i
$285$	1.78256	−	2.85793i	0.105590	−	0.169289i
$286$	15.4568	−	4.93923i	0.913980	−	0.292063i
$287$	7.57031			0.446862
$288$	−15.4178	+	7.09169i	−0.908501	+	0.417882i
$289$	1.76063			0.103567
$290$	4.57980	−	1.46348i	0.268935	−	0.0859385i
$291$	1.83328	−	2.93923i	0.107469	−	0.172301i
$292$	12.8371	−	9.13726i	0.751236	−	0.534717i
$293$			23.7712i			1.38873i	0.719624	+	0.694364i	$0.244314\pi$
$293$			23.7712i			1.38873i	−0.719624	+	0.694364i	$0.755686\pi$
$294$	0.602184	−	2.37432i	0.0351201	−	0.138473i
$295$		−	2.87478i		−	0.167376i
$296$	1.08374	−	1.44676i	0.0629909	−	0.0840914i
$297$	−20.1786	−	2.07049i	−1.17088	−	0.120142i
$298$	−3.29762	−	10.3196i	−0.191026	−	0.597796i
$299$	−6.41308			−0.370878
$300$	1.02869	+	16.8682i	0.0593915	+	0.973885i
$301$	−2.51757			−0.145110
$302$	5.44074	+	17.0262i	0.313080	+	0.979749i
$303$	−4.54867	−	2.83712i	−0.261314	−	0.162988i
$304$	−21.0831	−	7.30674i	−1.20920	−	0.419070i
$305$			4.91400i			0.281375i
$306$	11.9509	−	11.4667i	0.683185	−	0.655509i
$307$			3.69987i			0.211163i	0.994411	+	0.105581i	$0.0336703\pi$
$307$			3.69987i			0.211163i	−0.994411	+	0.105581i	$0.966330\pi$
$308$	−4.52749	−	6.36076i	−0.257978	−	0.362438i
$309$	−10.6391	−	6.63588i	−0.605237	−	0.377502i
$310$	1.23937	−	0.396041i	0.0703914	−	0.0224936i
$311$	7.58473			0.430090			0.215045	−	0.976604i	$-0.431010\pi$
$311$	7.58473			0.430090			0.215045	+	0.976604i	$0.431010\pi$
$312$	−5.20973	−	13.4238i	−0.294943	−	0.759970i
$313$	15.6354			0.883766			0.441883	−	0.897073i	$-0.354311\pi$
$313$	15.6354			0.883766			0.441883	+	0.897073i	$0.354311\pi$
$314$	0.292912	−	0.0936004i	0.0165300	−	0.00528217i
$315$	−0.460011	−	0.939235i	−0.0259187	−	0.0529199i
$316$	4.63910	+	6.51757i	0.260970	+	0.366642i
$317$			13.8932i			0.780319i	0.920747	+	0.390159i	$0.127580\pi$
$317$			13.8932i			0.780319i	−0.920747	+	0.390159i	$0.872420\pi$
$318$	4.08828	+	1.03689i	0.229259	+	0.0581457i
$319$		−	38.0703i		−	2.13153i
$320$	−2.67641	+	0.784055i	−0.149616	+	0.0438300i
$321$	−10.0959	+	16.1865i	−0.563499	+	0.903440i
$322$	0.939235	+	2.93923i	0.0523415	+	0.163797i
$323$	21.7765			1.21168
$324$	−0.743937	+	17.9846i	−0.0413298	+	0.999146i
$325$	−14.3390			−0.795383
$326$	−2.25539	−	7.05799i	−0.124914	−	0.390906i
$327$	−1.28305	+	2.05707i	−0.0709527	+	0.113756i
$328$	−17.1373	−	12.8371i	−0.946247	−	0.708811i
$329$			4.36377i			0.240583i
$330$	−3.23120	−	0.819511i	−0.177872	−	0.0451126i
$331$		−	31.7958i		−	1.74765i	−0.486237	−	0.873827i	$-0.661631\pi$
$331$		−	31.7958i		−	1.74765i	0.486237	−	0.873827i	$-0.338369\pi$
$332$	−14.5726	+	10.3725i	−0.799775	+	0.569267i
$333$	−0.843327	−	1.72188i	−0.0462140	−	0.0943582i
$334$	15.4568	−	4.93923i	0.845759	−	0.270263i
$335$	0.222798			0.0121728
$336$	−5.38936	+	4.35371i	−0.294014	+	0.237514i
$337$	−17.1178			−0.932468			−0.466234	−	0.884661i	$-0.654390\pi$
$337$	−17.1178			−0.932468			−0.466234	+	0.884661i	$0.654390\pi$
$338$	−5.87460	+	1.87723i	−0.319536	+	0.102108i
$339$	12.9799	+	8.09591i	0.704973	+	0.439709i
$340$	2.21744	−	1.57834i	0.120257	−	0.0855973i
$341$		−	10.3024i		−	0.557908i
$342$	−17.0773	+	16.3855i	−0.923437	+	0.886028i
$343$		−	1.00000i		−	0.0539949i
$344$	5.69914	+	4.26909i	0.307277	+	0.230174i
$345$	1.11784	+	0.697224i	0.0601824	+	0.0375373i
$346$	9.12814	+	28.5655i	0.490732	+	1.53569i
$347$	8.44797			0.453511			0.226755	−	0.973952i	$-0.427188\pi$
$347$	8.44797			0.453511			0.226755	+	0.973952i	$0.427188\pi$
$348$	−33.7200	+	2.05638i	−1.80758	+	0.110234i
$349$	17.4956			0.936520			0.468260	−	0.883591i	$-0.344881\pi$
$349$	17.4956			0.936520			0.468260	+	0.883591i	$0.344881\pi$
$350$	2.10003	+	6.57182i	0.112251	+	0.351279i
$351$	−15.1929	−	1.55892i	−0.810939	−	0.0832089i
$352$	−0.536989	+	22.0765i	−0.0286216	+	1.17668i
$353$			8.26754i			0.440037i	0.975496	+	0.220018i	$0.0706117\pi$
$353$			8.26754i			0.440037i	−0.975496	+	0.220018i	$0.929388\pi$
$354$	−4.96582	+	19.5794i	−0.263930	+	1.04064i
$355$			4.16037i			0.220809i
$356$	−12.2236	−	17.1732i	−0.647850	−	0.910179i
$357$	3.57834	−	5.73704i	0.189386	−	0.303636i
$358$	−2.44108	+	0.780049i	−0.129015	+	0.0412269i
$359$	25.1300			1.32631			0.663156	−	0.748481i	$-0.269216\pi$
$359$	25.1300			1.32631			0.663156	+	0.748481i	$0.269216\pi$
$360$	−0.551330	+	2.90624i	−0.0290577	+	0.153172i
$361$	−12.1178			−0.637781
$362$	10.1565	−	3.24552i	0.533814	−	0.170581i
$363$	−3.88596	+	6.23025i	−0.203960	+	0.327003i
$364$	−3.40885	−	4.78917i	−0.178672	−	0.251021i
$365$		−	2.74653i		−	0.143760i
$366$	8.48833	−	33.4681i	0.443692	−	1.74941i
$367$		−	21.7131i		−	1.13341i	−0.823920	−	0.566707i	$-0.808217\pi$
$367$		−	21.7131i		−	1.13341i	0.823920	−	0.566707i	$-0.191783\pi$
$368$	2.85793	−	8.24635i	0.148980	−	0.429871i
$369$	−20.3960	+	9.98941i	−1.06178	+	0.520028i
$370$	−0.0959078	−	0.300133i	−0.00498601	−	0.0156032i
$371$	1.72188			0.0893954
$372$	−9.12516	+	0.556490i	−0.473118	+	0.0288526i
$373$	−0.721797			−0.0373732			−0.0186866	−	0.999825i	$-0.505948\pi$
$373$	−0.721797			−0.0373732			−0.0186866	+	0.999825i	$0.505948\pi$
$374$	−6.56008	−	20.5291i	−0.339213	−	1.06153i
$375$	5.06100	+	3.15667i	0.261349	+	0.163010i
$376$	7.39973	−	9.87847i	0.381612	−	0.509443i
$377$		−	28.6640i		−	1.47627i
$378$	1.51062	+	7.19153i	0.0776978	+	0.369892i
$379$			18.2745i			0.938699i	0.883013	+	0.469349i	$0.155511\pi$
$379$			18.2745i			0.938699i	−0.883013	+	0.469349i	$0.844489\pi$
$380$	−3.16864	+	2.25539i	−0.162548	+	0.115699i
$381$	18.2174	+	11.3627i	0.933308	+	0.582128i
$382$	−2.19802	+	0.702379i	−0.112461	+	0.0359368i
$383$	−2.04930			−0.104715			−0.0523573	−	0.998628i	$-0.516673\pi$
$383$	−2.04930			−0.104715			−0.0523573	+	0.998628i	$0.516673\pi$
$384$	19.5828	−	0.716843i	0.999331	−	0.0365813i
$385$	−1.36090			−0.0693578
$386$	−20.4177	+	6.52448i	−1.03923	+	0.332087i
$387$	6.78287	−	3.32206i	0.344793	−	0.168870i
$388$	−3.25879	+	2.31955i	−0.165440	+	0.117757i
$389$		−	11.1466i		−	0.565158i	−0.959244	−	0.282579i	$-0.908810\pi$
$389$		−	11.1466i		−	0.565158i	0.959244	−	0.282579i	$-0.0911899\pi$
$390$	−2.43285	−	0.617029i	−0.123192	−	0.0312445i
$391$			8.51757i			0.430752i
$392$	−1.69572	+	2.26374i	−0.0856467	+	0.114336i
$393$	−1.47622	+	2.36678i	−0.0744656	+	0.119389i
$394$	−9.13726	−	28.5941i	−0.460328	−	1.44055i
$395$	1.39445			0.0701623
$396$	20.5914	+	11.1630i	1.03476	+	0.560962i
$397$	7.97438			0.400223			0.200111	−	0.979773i	$-0.435870\pi$
$397$	7.97438			0.400223			0.200111	+	0.979773i	$0.435870\pi$
$398$	−1.61725	−	5.06100i	−0.0810652	−	0.253685i
$399$	−5.11331	+	8.19802i	−0.255986	+	0.410414i
$400$	6.39002	−	18.4380i	0.319501	−	0.921899i
$401$		−	21.4779i		−	1.07256i	−0.844042	−	0.536278i	$-0.819830\pi$
$401$		−	21.4779i		−	1.07256i	0.844042	−	0.536278i	$-0.180170\pi$
$402$	−1.51743	−	0.384857i	−0.0756825	−	0.0191949i
$403$		−	7.75694i		−	0.386401i
$404$	3.58967	+	5.04320i	0.178593	+	0.250909i
$405$	2.47874	+	1.92349i	0.123169	+	0.0955790i
$406$	−13.1373	+	4.19802i	−0.651991	+	0.208344i
$407$	−2.49490			−0.123668
$408$	−17.8288	+	6.91934i	−0.882659	+	0.342558i
$409$	36.9136			1.82526			0.912630	−	0.408786i	$-0.134048\pi$
$409$	36.9136			1.82526			0.912630	+	0.408786i	$0.134048\pi$
$410$	−3.55515	+	1.13605i	−0.175576	+	0.0561056i
$411$	−6.41308	−	4.00000i	−0.316334	−	0.197305i
$412$	8.39604	+	11.7958i	0.413643	+	0.581136i
$413$			8.24635i			0.405777i
$414$	−6.40897	−	6.67956i	−0.314984	−	0.328282i
$415$			3.11784i			0.153049i
$416$	−0.404312	+	16.6219i	−0.0198230	+	0.814956i
$417$	24.7156	+	15.4157i	1.21033	+	0.754912i
$418$	9.37411	+	29.3353i	0.458503	+	1.43484i
$419$	29.5773			1.44494			0.722472	−	0.691400i	$-0.243006\pi$
$419$	29.5773			1.44494			0.722472	+	0.691400i	$0.243006\pi$
$420$	0.0735095	+	1.20539i	0.00358689	+	0.0588169i
$421$	36.8309			1.79503			0.897515	−	0.440985i	$-0.145371\pi$
$421$	36.8309			1.79503			0.897515	+	0.440985i	$0.145371\pi$
$422$	4.23566	+	13.2550i	0.206189	+	0.645245i
$423$	−5.75822	−	11.7569i	−0.279974	−	0.571642i
$424$	−3.89789	−	2.91982i	−0.189298	−	0.141799i
$425$			19.0444i			0.923789i
$426$	7.18652	−	28.3353i	0.348188	−	1.37285i
$427$		−	14.0959i		−	0.682149i
$428$	17.9462	−	12.7738i	0.867464	−	0.617447i
$429$	−10.5176	+	16.8625i	−0.507793	+	0.814129i
$430$	1.18230	−	0.377803i	0.0570153	−	0.0182193i
$431$	−4.67679			−0.225273			−0.112636	−	0.993636i	$-0.535930\pi$
$431$	−4.67679			−0.225273			−0.112636	+	0.993636i	$0.535930\pi$
$432$	8.77515	−	18.8414i	0.422195	−	0.906505i
$433$	−16.5564			−0.795650			−0.397825	−	0.917461i	$-0.630235\pi$
$433$	−16.5564			−0.795650			−0.397825	+	0.917461i	$0.630235\pi$
$434$	−3.55515	+	1.13605i	−0.170653	+	0.0545322i
$435$	−3.11632	+	4.99631i	−0.149416	+	0.239555i
$436$	2.28072	−	1.62338i	0.109226	−	0.0777456i
$437$		−	12.1713i		−	0.582232i
$438$	−4.74429	+	18.7060i	−0.226691	+	0.893806i
$439$			26.4787i			1.26376i	0.775066	+	0.631881i	$0.217717\pi$
$439$			26.4787i			1.26376i	−0.775066	+	0.631881i	$0.782283\pi$
$440$	3.08073	+	2.30770i	0.146868	+	0.110015i
$441$	1.31955	+	2.69421i	0.0628358	+	0.128296i
$442$	−4.93923	−	15.4568i	−0.234935	−	0.735205i
$443$	4.60099			0.218599			0.109300	−	0.994009i	$-0.465139\pi$
$443$	4.60099			0.218599			0.109300	+	0.994009i	$0.465139\pi$
$444$	0.134763	+	2.20981i	0.00639557	+	0.104873i
$445$	−3.67424			−0.174176
$446$	9.86360	+	30.8671i	0.467055	+	1.46160i
$447$	11.2580	+	7.02193i	0.532487	+	0.332126i
$448$	7.67735	−	2.24908i	0.362721	−	0.106259i
$449$			17.0095i			0.802728i	0.915919	+	0.401364i	$0.131464\pi$
$449$			17.0095i			0.802728i	−0.915919	+	0.401364i	$0.868536\pi$
$450$	−14.3298	−	14.9348i	−0.675512	−	0.704033i
$451$			29.5527i			1.39158i
$452$	−10.2433	−	14.3911i	−0.481806	−	0.676900i
$453$	−18.5746	−	11.5855i	−0.872713	−	0.544333i
$454$	18.2266	−	5.82431i	0.855415	−	0.273348i
$455$	−1.02465			−0.0480364
$456$	25.4768	−	9.88748i	1.19306	−	0.463024i
$457$	−15.4312			−0.721840			−0.360920	−	0.932597i	$-0.617537\pi$
$457$	−15.4312			−0.721840			−0.360920	+	0.932597i	$0.617537\pi$
$458$	19.7973	−	6.32625i	0.925068	−	0.295606i
$459$	−2.07049	+	20.1786i	−0.0966421	+	0.941857i
$460$	−0.882162	−	1.23937i	−0.0411310	−	0.0577858i
$461$		−	33.3764i		−	1.55449i	−0.629196	−	0.777247i	$-0.716616\pi$
$461$		−	33.3764i		−	1.55449i	0.629196	−	0.777247i	$-0.283384\pi$
$462$	9.26877	+	2.35078i	0.431222	+	0.109368i
$463$		−	26.4787i		−	1.23057i	−0.788304	−	0.615286i	$-0.789041\pi$
$463$		−	26.4787i		−	1.23057i	0.788304	−	0.615286i	$-0.210959\pi$
$464$	36.8580	+	12.7738i	1.71109	+	0.593011i
$465$	−0.843327	+	1.35208i	−0.0391084	+	0.0627012i
$466$	7.39973	+	23.1567i	0.342786	+	1.07271i
$467$	−18.5911			−0.860296			−0.430148	−	0.902758i	$-0.641539\pi$
$467$	−18.5911			−0.860296			−0.430148	+	0.902758i	$0.641539\pi$
$468$	15.5037	+	8.40489i	0.716660	+	0.388516i
$469$	−0.639102			−0.0295110
$470$	−0.654857	−	2.04930i	−0.0302063	−	0.0945274i
$471$	−0.199312	+	0.319551i	−0.00918381	+	0.0147241i
$472$	13.9835	−	18.6676i	0.643643	−	0.859248i
$473$		−	9.82800i		−	0.451892i
$474$	−9.49726	−	2.40874i	−0.436224	−	0.110637i
$475$		−	27.2137i		−	1.24865i
$476$	−6.36076	+	4.52749i	−0.291545	+	0.207517i
$477$	−4.63910	+	2.27210i	−0.212410	+	0.104032i
$478$	−19.5783	+	6.25627i	−0.895492	+	0.286155i
$479$	−40.8777			−1.86775			−0.933874	−	0.357601i	$-0.883595\pi$
$479$	−40.8777			−1.86775			−0.933874	+	0.357601i	$0.883595\pi$
$480$	1.87759	−	2.85334i	0.0856999	−	0.130237i
$481$	−1.87847			−0.0856508
$482$	−25.3149	+	8.08941i	−1.15306	+	0.368462i
$483$	−3.20654	−	2.00000i	−0.145903	−	0.0910032i
$484$	6.90760	−	4.91671i	0.313982	−	0.223487i
$485$			0.697224i			0.0316593i
$486$	−13.5595	−	17.3822i	−0.615072	−	0.788471i
$487$			21.4312i			0.971140i	0.874198	+	0.485570i	$0.161388\pi$
$487$			21.4312i			0.971140i	−0.874198	+	0.485570i	$0.838612\pi$
$488$	−23.9027	+	31.9095i	−1.08202	+	1.44448i
$489$	7.69987	+	4.80260i	0.348200	+	0.217181i
$490$	0.150067	+	0.469617i	0.00677932	+	0.0212152i
$491$	−1.63166			−0.0736358			−0.0368179	−	0.999322i	$-0.511722\pi$
$491$	−1.63166			−0.0736358			−0.0368179	+	0.999322i	$0.511722\pi$
$492$	26.1757	−	1.59630i	1.18009	−	0.0719668i
$493$	−38.0703			−1.71460
$494$	7.05799	+	22.0872i	0.317554	+	0.993751i
$495$	3.66655	−	1.79577i	0.164799	−	0.0807141i
$496$	9.97438	+	3.45681i	0.447863	+	0.155215i
$497$		−	11.9341i		−	0.535317i
$498$	5.38568	−	21.2349i	0.241338	−	0.951558i
$499$			8.88216i			0.397620i	0.980038	+	0.198810i	$0.0637077\pi$
$499$			8.88216i			0.397620i	−0.980038	+	0.198810i	$0.936292\pi$
$500$	−3.99398	−	5.61123i	−0.178616	−	0.250942i
$501$	−10.5176	+	16.8625i	−0.469890	+	0.753361i
$502$	−27.8049	+	8.88508i	−1.24099	+	0.396560i
$503$	−34.8967			−1.55597			−0.777983	−	0.628286i	$-0.783757\pi$
$503$	−34.8967			−1.55597			−0.777983	+	0.628286i	$0.783757\pi$
$504$	1.58150	−	8.33660i	0.0704457	−	0.371342i
$505$	1.07900			0.0480150
$506$	−11.4741	+	3.66655i	−0.510085	+	0.162998i
$507$	3.99736	−	6.40885i	0.177529	−	0.284627i
$508$	−14.3766	−	20.1980i	−0.637860	−	0.896142i
$509$		−	23.7712i		−	1.05364i	−0.849977	−	0.526820i	$-0.823384\pi$
$509$		−	23.7712i		−	1.05364i	0.849977	−	0.526820i	$-0.176616\pi$
$510$	−0.819511	+	3.23120i	−0.0362886	+	0.143080i
$511$			7.87847i			0.348523i
$512$	−21.1934	−	7.92728i	−0.936623	−	0.350340i
$513$	2.95865	−	28.8345i	0.130628	−	1.27307i
$514$	2.07649	+	6.49815i	0.0915901	+	0.286621i
$515$	2.52373			0.111209
$516$	−8.70495	+	0.530863i	−0.383214	+	0.0233700i
$517$	−17.0351			−0.749205
$518$	0.275113	+	0.860938i	0.0120878	+	0.0378274i
$519$	−31.1634	−	19.4374i	−1.36792	−	0.853207i
$520$	2.31955	+	1.73752i	0.101719	+	0.0761954i
$521$		−	5.73027i		−	0.251048i	−0.992091	−	0.125524i	$-0.959939\pi$
$521$		−	5.73027i		−	0.251048i	0.992091	−	0.125524i	$-0.0400612\pi$
$522$	29.8551	−	28.6456i	1.30672	−	1.25379i
$523$		−	4.81770i		−	0.210664i	−0.994437	−	0.105332i	$-0.966410\pi$
$523$		−	4.81770i		−	0.210664i	0.994437	−	0.105332i	$-0.0335904\pi$
$524$	2.62410	−	1.86779i	0.114634	−	0.0815948i
$525$	−7.16948	−	4.47179i	−0.312902	−	0.195165i
$526$	−19.4762	+	6.22364i	−0.849204	+	0.271364i
$527$	−10.3024			−0.448781
$528$	−16.9958	−	21.0388i	−0.739649	−	0.915596i
$529$	−18.2394			−0.793016
$530$	−0.808623	+	0.258396i	−0.0351243	+	0.0112240i
$531$	−10.8815	−	22.2174i	−0.472216	−	0.964155i
$532$	9.08930	−	6.46962i	0.394071	−	0.280493i
$533$			22.2509i			0.963795i
$534$	25.0244	+	6.34680i	1.08291	+	0.274653i
$535$		−	3.83963i		−	0.166002i
$536$	1.44676	+	1.08374i	0.0624906	+	0.0468103i
$537$	1.66103	−	2.66308i	0.0716788	−	0.114920i
$538$	−2.02854	−	6.34809i	−0.0874564	−	0.273685i
$539$	3.90376			0.168147
$540$	−1.78862	−	3.15057i	−0.0769700	−	0.135579i
$541$	−12.0388			−0.517590			−0.258795	−	0.965932i	$-0.583325\pi$
$541$	−12.0388			−0.517590			−0.258795	+	0.965932i	$0.583325\pi$
$542$	6.74728	+	21.1149i	0.289820	+	0.906962i
$543$	−6.91099	+	11.0802i	−0.296579	+	0.475496i
$544$	22.0765	+	0.536989i	0.946522	+	0.0230232i
$545$		−	0.487964i		−	0.0209021i
$546$	6.97867	+	1.76996i	0.298660	+	0.0757473i
$547$			35.3097i			1.50973i	0.655879	+	0.754866i	$0.272298\pi$
$547$			35.3097i			1.50973i	−0.655879	+	0.754866i	$0.727702\pi$
$548$	5.06100	+	7.11030i	0.216195	+	0.303737i
$549$	18.6003	+	37.9774i	0.793840	+	1.62084i
$550$	−25.6548	+	8.19802i	−1.09393	+	0.349565i
$551$	54.4011			2.31756
$552$	3.86735	+	9.96488i	0.164605	+	0.424133i
$553$	−4.00000			−0.170097
$554$	22.8958	−	7.31638i	0.972751	−	0.310843i
$555$	0.327428	+	0.204225i	0.0138986	+	0.00866889i
$556$	−19.5048	−	27.4026i	−0.827186	−	1.16213i
$557$			34.7920i			1.47419i	0.675792	+	0.737093i	$0.263802\pi$
$557$			34.7920i			1.47419i	−0.675792	+	0.737093i	$0.736198\pi$
$558$	8.07926	−	7.75197i	0.342022	−	0.328167i
$559$		−	7.39973i		−	0.312975i
$560$	0.456627	−	1.31756i	0.0192960	−	0.0556773i
$561$	22.3960	+	13.9690i	0.945562	+	0.589771i
$562$	−2.47874	−	7.75694i	−0.104559	−	0.327207i
$563$	−12.8618			−0.542058			−0.271029	−	0.962571i	$-0.587364\pi$
$563$	−12.8618			−0.542058			−0.271029	+	0.962571i	$0.587364\pi$
$564$	0.920160	+	15.0885i	0.0387457	+	0.635342i
$565$	−3.07900			−0.129535
$566$	2.40130	+	7.51461i	0.100934	+	0.315863i
$567$	−7.11030	−	5.51757i	−0.298605	−	0.231716i
$568$	−20.2369	+	27.0157i	−0.849120	+	1.13355i
$569$		−	15.6909i		−	0.657795i	−0.944366	−	0.328897i	$-0.893323\pi$
$569$		−	15.6909i		−	0.657795i	0.944366	−	0.328897i	$-0.106677\pi$
$570$	1.17105	−	4.61727i	0.0490500	−	0.193396i
$571$			42.0315i			1.75896i	0.475935	+	0.879481i	$0.342110\pi$
$571$			42.0315i			1.75896i	−0.475935	+	0.879481i	$0.657890\pi$
$572$	18.6958	−	13.3074i	0.781710	−	0.556408i
$573$	1.49564	−	2.39792i	0.0624813	−	0.100174i
$574$	10.1980	−	3.25879i	0.425657	−	0.136019i
$575$	10.6443			0.443897
$576$	−17.7166	+	16.1901i	−0.738193	+	0.674589i
$577$	38.7921			1.61494			0.807468	−	0.589912i	$-0.200837\pi$
$577$	38.7921			1.61494			0.807468	+	0.589912i	$0.200837\pi$
$578$	2.37176	−	0.757897i	0.0986522	−	0.0315244i
$579$	13.8932	−	22.2745i	0.577381	−	0.925697i
$580$	5.53950	−	3.94293i	0.230015	−	0.163721i
$581$		−	8.94358i		−	0.371042i
$582$	1.20437	−	4.74863i	0.0499227	−	0.196837i
$583$			6.72180i			0.278388i
$584$	13.3597	−	17.8348i	0.552827	−	0.738011i
$585$	2.76063	−	1.35208i	0.114138	−	0.0559017i
$586$	10.2328	+	32.0223i	0.422711	+	1.32283i
$587$	−7.07471			−0.292004			−0.146002	−	0.989284i	$-0.546641\pi$
$587$	−7.07471			−0.292004			−0.146002	+	0.989284i	$0.546641\pi$
$588$	−0.210863	−	3.45768i	−0.00869586	−	0.142592i
$589$	14.7218			0.606601
$590$	−1.23750	−	3.87263i	−0.0509472	−	0.159434i
$591$	31.1945	+	19.4568i	1.28317	+	0.800346i
$592$	0.837122	−	2.41546i	0.0344055	−	0.0992747i
$593$		−	18.3895i		−	0.755168i	−0.925975	−	0.377584i	$-0.876755\pi$
$593$		−	18.3895i		−	0.755168i	0.925975	−	0.377584i	$-0.123245\pi$
$594$	−28.0740	+	5.89710i	−1.15189	+	0.241961i
$595$			1.36090i			0.0557914i
$596$	−8.88449	−	12.4820i	−0.363923	−	0.511283i
$597$	5.52126	+	3.44375i	0.225970	+	0.140943i
$598$	−8.63910	+	2.76063i	−0.353279	+	0.112891i
$599$	37.8516			1.54657			0.773287	−	0.634057i	$-0.218611\pi$
$599$	37.8516			1.54657			0.773287	+	0.634057i	$0.218611\pi$
$600$	8.64698	+	22.2804i	0.353012	+	0.909594i
$601$	21.9488			0.895308			0.447654	−	0.894207i	$-0.352260\pi$
$601$	21.9488			0.895308			0.447654	+	0.894207i	$0.352260\pi$
$602$	−3.39144	+	1.08374i	−0.138225	+	0.0441698i
$603$	1.72188	−	0.843327i	0.0701202	−	0.0343429i
$604$	14.6585	+	20.5941i	0.596447	+	0.837960i
$605$		−	1.47789i		−	0.0600849i
$606$	−7.34884	−	1.86384i	−0.298526	−	0.0757135i
$607$		−	25.8785i		−	1.05037i	−0.850987	−	0.525187i	$-0.823995\pi$
$607$		−	25.8785i		−	1.05037i	0.850987	−	0.525187i	$-0.176005\pi$
$608$	−31.5465	−	0.767338i	−1.27938	−	0.0311197i
$609$	8.93923	−	14.3320i	0.362236	−	0.580762i
$610$	2.11533	+	6.61968i	0.0856470	+	0.268023i
$611$	−12.8262			−0.518891
$612$	11.1630	−	20.5914i	0.451238	−	0.832357i
$613$	−12.9136			−0.521576			−0.260788	−	0.965396i	$-0.583982\pi$
$613$	−12.9136			−0.521576			−0.260788	+	0.965396i	$0.583982\pi$
$614$	1.59268	+	4.98412i	0.0642753	+	0.201143i
$615$	2.41910	−	3.87847i	0.0975475	−	0.156395i
$616$	−8.83712	−	6.61968i	−0.356058	−	0.266715i
$617$			26.4677i			1.06555i	0.846257	+	0.532775i	$0.178851\pi$
$617$			26.4677i			1.06555i	−0.846257	+	0.532775i	$0.821149\pi$
$618$	−17.1885	−	4.35943i	−0.691425	−	0.175362i
$619$		−	34.3390i		−	1.38020i	−0.723714	−	0.690100i	$-0.757567\pi$
$619$		−	34.3390i		−	1.38020i	0.723714	−	0.690100i	$-0.242433\pi$
$620$	1.49908	−	1.06702i	0.0602044	−	0.0428525i
$621$	11.2782	+	1.15723i	0.452579	+	0.0464382i
$622$	10.2174	−	3.26499i	0.409682	−	0.130914i
$623$	10.5396			0.422262
$624$	−12.7966	−	15.8406i	−0.512273	−	0.634131i
$625$	23.1918			0.927673
$626$	21.0626	−	6.73056i	0.841829	−	0.269007i
$627$	−32.0031	−	19.9612i	−1.27808	−	0.797172i
$628$	0.354292	−	0.252179i	0.0141378	−	0.0100631i
$629$			2.49490i			0.0994782i
$630$	−1.02400	−	1.06723i	−0.0407970	−	0.0425194i
$631$		−	27.7569i		−	1.10499i	−0.833517	−	0.552493i	$-0.813677\pi$
$631$		−	27.7569i		−	1.10499i	0.833517	−	0.552493i	$-0.186323\pi$
$632$	9.05498	+	6.78287i	0.360188	+	0.269808i
$633$	−14.4605	−	9.01938i	−0.574753	−	0.358488i
$634$	5.98058	+	18.7156i	0.237519	+	0.743291i
$635$	−4.32141			−0.171490
$636$	5.95369	−	0.363081i	0.236079	−	0.0143971i
$637$	2.93923			0.116457
$638$	−16.3881	−	51.2847i	−0.648810	−	2.03038i
$639$	15.7476	+	32.1530i	0.622967	+	1.27195i
$640$	−3.26790	+	2.20832i	−0.129175	+	0.0872915i
$641$		−	6.96331i		−	0.275034i	−0.990499	−	0.137517i	$-0.956088\pi$
$641$		−	6.96331i		−	0.275034i	0.990499	−	0.137517i	$-0.0439122\pi$
$642$	−6.63249	+	26.1509i	−0.261764	+	1.03209i
$643$			9.74373i			0.384255i	0.981370	+	0.192128i	$0.0615387\pi$
$643$			9.74373i			0.384255i	−0.981370	+	0.192128i	$0.938461\pi$
$644$	2.53050	+	3.55515i	0.0997156	+	0.140093i
$645$	−0.804492	+	1.28982i	−0.0316768	+	0.0507865i
$646$	29.3353	−	9.37411i	1.15418	−	0.368819i
$647$	−28.1896			−1.10825			−0.554123	−	0.832434i	$-0.686946\pi$
$647$	−28.1896			−1.10825			−0.554123	+	0.832434i	$0.686946\pi$
$648$	6.73966	+	24.5474i	0.264759	+	0.964315i
$649$	−32.1918			−1.26364
$650$	−19.3161	+	6.17248i	−0.757641	+	0.242105i
$651$	2.41910	−	3.87847i	0.0948120	−	0.152009i
$652$	−6.07649	−	8.53699i	−0.237974	−	0.334334i
$653$			10.8527i			0.424697i	0.977194	+	0.212349i	$0.0681112\pi$
$653$			10.8527i			0.424697i	−0.977194	+	0.212349i	$0.931889\pi$
$654$	−0.842897	+	3.32341i	−0.0329599	+	0.129956i
$655$		−	0.561431i		−	0.0219369i
$656$	−28.6117	−	9.91592i	−1.11710	−	0.387151i
$657$	−10.3960	−	21.2263i	−0.405588	−	0.828116i
$658$	1.87847	+	5.87847i	0.0732304	+	0.229167i
$659$	19.2248			0.748893			0.374446	−	0.927249i	$-0.377833\pi$
$659$	19.2248			0.748893			0.374446	+	0.927249i	$0.377833\pi$
$660$	−4.70555	+	0.286964i	−0.183163	+	0.0111700i
$661$	−2.74742			−0.106862			−0.0534311	−	0.998572i	$-0.517016\pi$
$661$	−2.74742			−0.106862			−0.0534311	+	0.998572i	$0.517016\pi$
$662$	−13.6871	−	42.8323i	−0.531964	−	1.66472i
$663$	16.8625	+	10.5176i	0.654885	+	0.408469i
$664$	−15.1658	+	20.2460i	−0.588547	+	0.785696i
$665$		−	1.94467i		−	0.0754112i
$666$	−1.87727	−	1.95652i	−0.0727426	−	0.0758138i
$667$			21.2782i			0.823895i
$668$	18.6958	−	13.3074i	0.723361	−	0.514877i
$669$	−33.6742	−	21.0035i	−1.30192	−	0.812041i
$670$	0.300133	−	0.0959078i	0.0115952	−	0.00370524i
$671$	55.0271			2.12430
$672$	−5.38591	+	8.18486i	−0.207766	+	0.315738i
$673$	31.3097			1.20690			0.603449	−	0.797401i	$-0.293793\pi$
$673$	31.3097			1.20690			0.603449	+	0.797401i	$0.293793\pi$
$674$	−23.0596	+	7.36870i	−0.888221	+	0.283832i
$675$	25.2169	+	2.58746i	0.970598	+	0.0995912i
$676$	−7.10562	+	5.05766i	−0.273293	+	0.194525i
$677$		−	20.9823i		−	0.806415i	−0.915109	−	0.403208i	$-0.867895\pi$
$677$		−	20.9823i		−	0.806415i	0.915109	−	0.403208i	$-0.132105\pi$
$678$	20.9704	+	5.31860i	0.805363	+	0.204259i
$679$		−	2.00000i		−	0.0767530i
$680$	2.30770	−	3.08073i	0.0884963	−	0.118140i
$681$	−12.4022	+	19.8841i	−0.475255	+	0.761962i
$682$	−4.43488	−	13.8785i	−0.169820	−	0.531434i
$683$	15.8234			0.605467			0.302734	−	0.953075i	$-0.402101\pi$
$683$	15.8234			0.605467			0.302734	+	0.953075i	$0.402101\pi$
$684$	−15.9515	+	29.4243i	−0.609922	+	1.12507i
$685$	1.52126			0.0581245
$686$	−0.430469	−	1.34711i	−0.0164354	−	0.0514328i
$687$	−13.4711	+	21.5978i	−0.513953	+	0.824006i
$688$	9.51506	+	3.29762i	0.362758	+	0.125721i
$689$			5.06100i			0.192809i
$690$	1.80598	+	0.458040i	0.0687525	+	0.0174373i
$691$		−	24.4093i		−	0.928572i	−0.885685	−	0.464286i	$-0.846311\pi$
$691$		−	24.4093i		−	0.928572i	0.885685	−	0.464286i	$-0.153689\pi$
$692$	24.5931	+	34.5514i	0.934891	+	1.31345i
$693$	−10.5176	+	5.15121i	−0.399529	+	0.195678i
$694$	11.3803	−	3.63659i	0.431991	−	0.138043i
$695$	−5.86285			−0.222391
$696$	−44.5392	+	17.2856i	−1.68825	+	0.655208i
$697$	29.5527			1.11939
$698$	23.5685	−	7.53133i	0.892081	−	0.285065i
$699$	−25.2626	−	15.7569i	−0.955520	−	0.595982i
$700$	5.65793	+	7.94894i	0.213850	+	0.300442i
$701$			21.4779i			0.811209i	0.914049	+	0.405605i	$0.132939\pi$
$701$			21.4779i			0.811209i	−0.914049	+	0.405605i	$0.867061\pi$
$702$	−21.1376	+	4.44006i	−0.797787	+	0.167579i
$703$		−	3.56512i		−	0.134461i
$704$	8.77986	+	29.9705i	0.330904	+	1.12956i
$705$	2.23568	+	1.39445i	0.0842004	+	0.0525179i
$706$	3.55892	+	11.1373i	0.133942	+	0.419156i
$707$	−3.09514			−0.116405
$708$	1.73885	+	28.5132i	0.0653501	+	1.07159i
$709$	−42.1918			−1.58455			−0.792273	−	0.610166i	$-0.791103\pi$
$709$	−42.1918			−1.58455			−0.792273	+	0.610166i	$0.791103\pi$
$710$	1.79091	+	5.60446i	0.0672116	+	0.210331i
$711$	10.7769	−	5.27820i	0.404164	−	0.197948i
$712$	−23.8591	−	17.8723i	−0.894156	−	0.669791i
$713$			5.75822i			0.215647i
$714$	2.35078	−	9.26877i	0.0879759	−	0.346875i
$715$		−	4.00000i		−	0.149592i
$716$	−2.95261	+	2.10162i	−0.110344	+	0.0785412i
$717$	13.3221	−	21.3589i	0.497522	−	0.797661i
$718$	33.8528	−	10.8177i	1.26338	−	0.403713i
$719$	−19.0588			−0.710774			−0.355387	−	0.934719i	$-0.615651\pi$
$719$	−19.0588			−0.710774			−0.355387	+	0.934719i	$0.615651\pi$
$720$	0.508344	+	4.15234i	0.0189449	+	0.154749i
$721$	−7.23937			−0.269608
$722$	−16.3240	+	5.21635i	−0.607517	+	0.194133i
$723$	17.2255	−	27.6172i	0.640624	−	1.02709i
$724$	12.2848	−	8.74413i	0.456561	−	0.324973i
$725$			47.5758i			1.76692i
$726$	−2.55288	+	10.0656i	−0.0947462	+	0.373569i
$727$			3.72549i			0.138171i	0.997611	+	0.0690854i	$0.0220081\pi$
$727$			3.72549i			0.138171i	−0.997611	+	0.0690854i	$0.977992\pi$
$728$	−6.65368	−	4.98412i	−0.246602	−	0.184724i
$729$	26.4374	+	5.48311i	0.979163	+	0.203078i
$730$	−1.18230	−	3.69987i	−0.0437587	−	0.136938i
$731$	−9.82800			−0.363502
$732$	−2.97231	−	48.7391i	−0.109860	−	1.80145i
$733$	−25.4180			−0.938834			−0.469417	−	0.882977i	$-0.655536\pi$
$733$	−25.4180			−0.938834			−0.469417	+	0.882977i	$0.655536\pi$
$734$	−9.34681	−	29.2498i	−0.344997	−	1.07963i
$735$	−0.512326	−	0.319551i	−0.0188974	−	0.0117868i
$736$	0.300133	−	12.3390i	0.0110631	−	0.454820i
$737$		−	2.49490i		−	0.0919009i
$738$	−23.1755	+	22.2367i	−0.853102	+	0.818543i
$739$		−	23.3097i		−	0.857459i	−0.903433	−	0.428730i	$-0.858961\pi$
$739$		−	23.3097i		−	0.857459i	0.903433	−	0.428730i	$-0.141039\pi$
$740$	−0.258396	−	0.363026i	−0.00949883	−	0.0133451i
$741$	−24.0959	−	15.0292i	−0.885185	−	0.552113i
$742$	2.31955	−	0.741214i	0.0851534	−	0.0272108i
$743$	−33.8576			−1.24211			−0.621057	−	0.783765i	$-0.713297\pi$
$743$	−33.8576			−1.24211			−0.621057	+	0.783765i	$0.713297\pi$
$744$	−12.0530	+	4.67775i	−0.441885	+	0.171495i
$745$	−2.67055			−0.0978415
$746$	−0.972337	+	0.310711i	−0.0355998	+	0.0113759i
$747$	11.8015	+	24.0959i	0.431795	+	0.881623i
$748$	−17.6742	−	24.8309i	−0.646234	−	0.907908i
$749$			11.0141i			0.402445i
$750$	8.17655	+	2.07377i	0.298566	+	0.0757235i
$751$		−	48.1530i		−	1.75713i	−0.477625	−	0.878564i	$-0.658502\pi$
$751$		−	48.1530i		−	1.75713i	0.477625	−	0.878564i	$-0.341498\pi$
$752$	5.71586	−	16.4927i	0.208436	−	0.601427i
$753$	18.9198	−	30.3336i	0.689476	−	1.10542i
$754$	−12.3390	−	38.6135i	−0.449359	−	1.40622i
$755$	4.40614			0.160356
$756$	5.13069	+	9.03748i	0.186601	+	0.328690i
$757$	−11.3923			−0.414062			−0.207031	−	0.978334i	$-0.566380\pi$
$757$	−11.3923			−0.414062			−0.207031	+	0.978334i	$0.566380\pi$
$758$	7.86661	+	24.6177i	0.285728	+	0.894156i
$759$	7.80753	−	12.5176i	0.283395	−	0.454359i
$760$	−3.29762	+	4.40225i	−0.119617	+	0.159686i
$761$			27.5491i			0.998656i	0.866413	+	0.499328i	$0.166420\pi$
$761$			27.5491i			0.998656i	−0.866413	+	0.499328i	$0.833580\pi$
$762$	29.4321	+	7.46470i	1.06621	+	0.270417i
$763$			1.39973i			0.0506738i
$764$	−2.65862	+	1.89236i	−0.0961853	+	0.0684632i
$765$	−1.79577	−	3.66655i	−0.0649264	−	0.132564i
$766$	−2.76063	+	0.882162i	−0.0997457	+	0.0318738i
$767$	−24.2380			−0.875182
$768$	26.0715	−	9.39545i	0.940776	−	0.339029i
$769$	−5.83461			−0.210401			−0.105201	−	0.994451i	$-0.533549\pi$
$769$	−5.83461			−0.210401			−0.105201	+	0.994451i	$0.533549\pi$
$770$	−1.83328	+	0.585825i	−0.0660667	+	0.0211117i
$771$	−7.08912	−	4.42166i	−0.255308	−	0.159242i
$772$	−24.6962	+	17.5783i	−0.888835	+	0.632658i
$773$			47.5682i			1.71091i	0.517879	+	0.855454i	$0.326722\pi$
$773$			47.5682i			1.71091i	−0.517879	+	0.855454i	$0.673278\pi$
$774$	7.70721	−	7.39499i	0.277030	−	0.265807i
$775$			12.8748i			0.462476i
$776$	−3.39144	+	4.52749i	−0.121745	+	0.162527i
$777$	−0.939235	−	0.585825i	−0.0336949	−	0.0210163i
$778$	−4.79829	−	15.0157i	−0.172027	−	0.538340i
$779$	−42.2298			−1.51304
$780$	−3.54292	+	0.216062i	−0.126857	+	0.00773625i
$781$	46.5879			1.66704
$782$	3.66655	+	11.4741i	0.131116	+	0.410312i
$783$	−5.17240	+	50.4093i	−0.184846	+	1.80148i
$784$	−1.30984	+	3.77946i	−0.0467801	+	0.134981i
$785$		−	0.0758015i		−	0.00270547i
$786$	−0.969803	+	3.82378i	−0.0345917	+	0.136390i
$787$			48.8177i			1.74016i	0.492908	+	0.870082i	$0.335934\pi$
$787$			48.8177i			1.74016i	−0.492908	+	0.870082i	$0.664066\pi$
$788$	−24.6177	−	34.5859i	−0.876970	−	1.23207i
$789$	13.2526	−	21.2475i	0.471804	−	0.756430i
$790$	1.87847	−	0.600267i	0.0668330	−	0.0213565i
$791$	8.83218			0.314036
$792$	32.5441	+	6.17381i	1.15640	+	0.219377i
$793$	41.4312			1.47126
$794$	10.7423	−	3.43272i	0.381231	−	0.121823i
$795$	0.550227	−	0.882162i	0.0195145	−	0.0312871i
$796$	−4.35721	−	6.12153i	−0.154437	−	0.216972i
$797$			12.7292i			0.450890i	0.974256	+	0.225445i	$0.0723837\pi$
$797$			12.7292i			0.450890i	−0.974256	+	0.225445i	$0.927616\pi$
$798$	−3.35918	+	13.2447i	−0.118914	+	0.468858i
$799$			17.0351i			0.602660i
$800$	0.671066	−	27.5886i	0.0237258	−	0.975405i
$801$	−28.3960	+	13.9076i	−1.00332	+	0.491401i
$802$	−9.24557	−	28.9330i	−0.326473	−	1.02166i
$803$	−30.7557			−1.08534
$804$	−2.20981	+	0.134763i	−0.0779339	+	0.00475273i
$805$	0.760632			0.0268088
$806$	−3.33912	−	10.4494i	−0.117616	−	0.368065i
$807$	6.92541	+	4.31955i	0.243786	+	0.152055i
$808$	7.00661	+	5.24849i	0.246492	+	0.184641i
$809$		−	26.5813i		−	0.934548i	−0.884113	−	0.467274i	$-0.845236\pi$
$809$		−	26.5813i		−	0.934548i	0.884113	−	0.467274i	$-0.154764\pi$
$810$	4.16713	+	1.52413i	0.146418	+	0.0535524i
$811$		−	4.13977i		−	0.145367i	−0.997355	−	0.0726835i	$-0.976844\pi$
$811$		−	4.13977i		−	0.145367i	0.997355	−	0.0726835i	$-0.0231563\pi$
$812$	−15.8902	+	11.3104i	−0.557636	+	0.396916i
$813$	−23.0351	−	14.3676i	−0.807878	−	0.503894i
$814$	−3.36090	+	1.07398i	−0.117799	+	0.0376429i
$815$	−1.82651			−0.0639797
$816$	−21.0388	+	16.9958i	−0.736505	+	0.594974i
$817$	14.0439			0.491332
$818$	49.7266	−	15.8902i	1.73865	−	0.555587i
$819$	−7.91893	+	3.87847i	−0.276710	+	0.135525i
$820$	−4.30013	+	3.06077i	−0.150167	+	0.106887i
$821$		−	29.5082i		−	1.02984i	−0.857237	−	0.514922i	$-0.827821\pi$
$821$		−	29.5082i		−	1.02984i	0.857237	−	0.514922i	$-0.172179\pi$
$822$	−10.3610	−	2.62779i	−0.361381	−	0.0916549i
$823$		−	12.0777i		−	0.421001i	−0.977594	−	0.210501i	$-0.932491\pi$
$823$		−	12.0777i		−	0.421001i	0.977594	−	0.210501i	$-0.0675094\pi$
$824$	16.3881	+	12.2759i	0.570906	+	0.427652i
$825$	17.4568	−	27.9880i	0.607768	−	0.974416i
$826$	3.54980	+	11.1087i	0.123513	+	0.386522i
$827$	11.9341			0.414989			0.207494	−	0.978236i	$-0.433469\pi$
$827$	11.9341			0.414989			0.207494	+	0.978236i	$0.433469\pi$
$828$	−11.5089	−	6.23921i	−0.399962	−	0.216828i
$829$	−2.50436			−0.0869800			−0.0434900	−	0.999054i	$-0.513848\pi$
$829$	−2.50436			−0.0869800			−0.0434900	+	0.999054i	$0.513848\pi$
$830$	1.34213	+	4.20006i	0.0465861	+	0.145786i
$831$	−15.5795	+	24.9781i	−0.540445	+	0.866480i
$832$	6.61057	+	22.5655i	0.229180	+	0.782319i
$833$		−	3.90376i		−	0.135257i
$834$	39.9305	+	10.1274i	1.38268	+	0.350682i
$835$		−	4.00000i		−	0.138426i
$836$	25.2559	+	35.4825i	0.873492	+	1.22719i
$837$	−1.39973	+	13.6416i	−0.0483819	+	0.471521i
$838$	39.8437	−	12.7321i	1.37638	−	0.439823i
$839$	1.64607			0.0568288			0.0284144	−	0.999596i	$-0.490954\pi$
$839$	1.64607			0.0568288			0.0284144	+	0.999596i	$0.490954\pi$
$840$	0.617907	+	1.59214i	0.0213198	+	0.0549341i
$841$	−66.1054			−2.27950
$842$	49.6152	−	15.8546i	1.70985	−	0.546385i
$843$	8.46238	+	5.27820i	0.291460	+	0.181791i
$844$	11.4118	+	16.0326i	0.392809	+	0.551866i
$845$			1.52026i			0.0522986i
$846$	−12.8179	−	13.3591i	−0.440690	−	0.459296i
$847$			4.23937i			0.145666i
$848$	−6.50776	−	2.25539i	−0.223477	−	0.0774503i
$849$	−8.19802	−	5.11331i	−0.281355	−	0.175488i
$850$	8.19802	+	25.6548i	0.281190	+	0.879953i
$851$	1.39445			0.0478010
$852$	−2.51646	−	41.2642i	−0.0862125	−	1.41369i
$853$	−15.1311			−0.518077			−0.259039	−	0.965867i	$-0.583406\pi$
$853$	−15.1311			−0.518077			−0.259039	+	0.965867i	$0.583406\pi$
$854$	−6.06785	−	18.9887i	−0.207638	−	0.649780i
$855$	2.56610	+	5.23937i	0.0877587	+	0.179183i
$856$	18.6768	−	24.9330i	0.638358	−	0.852193i
$857$		−	48.9224i		−	1.67116i	−0.549370	−	0.835579i	$-0.685132\pi$
$857$		−	48.9224i		−	1.67116i	0.549370	−	0.835579i	$-0.314868\pi$
$858$	−6.90950	+	27.2431i	−0.235887	+	0.930063i
$859$			16.0571i			0.547860i	0.961750	+	0.273930i	$0.0883237\pi$
$859$			16.0571i			0.547860i	−0.961750	+	0.273930i	$0.911676\pi$
$860$	1.43005	−	1.01788i	0.0487641	−	0.0347095i
$861$	−6.93923	+	11.1255i	−0.236488	+	0.379155i
$862$	−6.30013	+	2.01321i	−0.214583	+	0.0685703i
$863$	14.9034			0.507318			0.253659	−	0.967294i	$-0.418366\pi$
$863$	14.9034			0.507318			0.253659	+	0.967294i	$0.418366\pi$
$864$	3.71044	−	29.1587i	0.126232	−	0.992001i
$865$	7.39235			0.251347
$866$	−22.3032	+	7.12702i	−0.757895	+	0.242186i
$867$	−1.61386	+	2.58746i	−0.0548096	+	0.0878746i
$868$	−4.30013	+	3.06077i	−0.145956	+	0.103889i
$869$		−	15.6151i		−	0.529704i
$870$	−2.04726	+	8.07204i	−0.0694088	+	0.273668i
$871$		−	1.87847i		−	0.0636495i
$872$	2.37355	−	3.16864i	0.0803787	−	0.107304i
$873$	2.63910	+	5.38843i	0.0893201	+	0.182371i
$874$	−5.23937	−	16.3960i	−0.177224	−	0.554604i
$875$	3.44375			0.116420
$876$	1.66128	+	27.2412i	0.0561295	+	0.920395i
$877$	11.8785			0.401107			0.200554	−	0.979683i	$-0.435726\pi$
$877$	11.8785			0.401107			0.200554	+	0.979683i	$0.435726\pi$
$878$	11.3983	+	35.6697i	0.384673	+	1.20379i
$879$	−34.9346	−	21.7896i	−1.17831	−	0.734944i
$880$	5.14346	+	1.78256i	0.173386	+	0.0600901i
$881$			36.4995i			1.22970i	0.788644	+	0.614850i	$0.210783\pi$
$881$			36.4995i			1.22970i	−0.788644	+	0.614850i	$0.789217\pi$
$882$	2.93735	+	3.06137i	0.0989058	+	0.103082i
$883$			31.1178i			1.04720i	0.851965	+	0.523599i	$0.175411\pi$
$883$			31.1178i			1.04720i	−0.851965	+	0.523599i	$0.824589\pi$
$884$	−13.3074	−	18.6958i	−0.447575	−	0.628807i
$885$	4.22482	+	2.63513i	0.142016	+	0.0885789i
$886$	6.19802	−	1.98058i	0.208227	−	0.0665390i
$887$	−56.9248			−1.91135			−0.955674	−	0.294428i	$-0.904871\pi$
$887$	−56.9248			−1.91135			−0.955674	+	0.294428i	$0.904871\pi$
$888$	1.13279	+	2.91884i	0.0380141	+	0.0979497i
$889$	12.3960			0.415750
$890$	−4.94960	+	1.58165i	−0.165911	+	0.0530170i
$891$	21.5393	−	27.7569i	0.721593	−	0.929892i
$892$	26.5746	+	37.3353i	0.889785	+	1.25008i
$893$		−	24.3426i		−	0.814594i
$894$	18.1885	+	4.61305i	0.608315	+	0.154283i
$895$			0.631717i			0.0211160i
$896$	9.37405	−	6.33461i	0.313165	−	0.211624i
$897$	5.87847	−	9.42477i	0.196276	−	0.314684i
$898$	7.32206	+	22.9136i	0.244340	+	0.764637i
$899$	−25.7370			−0.858379
$900$	−25.7327	−	13.9502i	−0.857757	−	0.465008i
$901$	6.72180			0.223936
$902$	12.7215	+	39.8107i	0.423581	+	1.32555i
$903$	2.30770	−	3.69987i	0.0767955	−	0.123124i
$904$	−19.9938	−	14.9769i	−0.664984	−	0.498124i
$905$		−	2.62836i		−	0.0873696i
$906$	−30.0092	−	7.61106i	−0.996989	−	0.252861i
$907$			6.70939i			0.222782i	0.993777	+	0.111391i	$0.0355305\pi$
$907$			6.70939i			0.222782i	−0.993777	+	0.111391i	$0.964469\pi$
$908$	22.0459	−	15.6919i	0.731620	−	0.520755i
$909$	8.33897	−	4.08419i	0.276586	−	0.135464i
$910$	−1.38032	+	0.441081i	−0.0457570	+	0.0146217i
$911$	50.1275			1.66080			0.830399	−	0.557169i	$-0.188112\pi$
$911$	50.1275			1.66080			0.830399	+	0.557169i	$0.188112\pi$
$912$	30.0637	−	24.2865i	0.995508	−	0.804205i
$913$	34.9136			1.15547
$914$	−20.7875	+	6.64265i	−0.687588	+	0.219719i
$915$	−7.22170	−	4.50436i	−0.238742	−	0.148910i
$916$	23.9458	−	17.0443i	0.791193	−	0.563158i
$917$			1.61048i			0.0531826i
$918$	5.89710	+	28.0740i	0.194633	+	0.926580i
$919$			17.0351i			0.561938i	0.959717	+	0.280969i	$0.0906557\pi$
$919$			17.0351i			0.561938i	−0.959717	+	0.280969i	$0.909344\pi$
$920$	−1.72188	−	1.28982i	−0.0567686	−	0.0425240i
$921$	−5.43739	−	3.39144i	−0.179168	−	0.111752i
$922$	−14.3675	−	44.9616i	−0.473169	−	1.48073i
$923$	35.0771			1.15458
$924$	13.4980	−	0.823160i	0.444050	−	0.0270800i
$925$	3.11784			0.102514
$926$	−11.3983	−	35.6697i	−0.374571	−	1.17218i
$927$	19.5044	−	9.55271i	0.640609	−	0.313752i
$928$	55.1505	+	1.34148i	1.81040	+	0.0440363i
$929$		−	23.4082i		−	0.767997i	−0.923334	−	0.383999i	$-0.874547\pi$
$929$		−	23.4082i		−	0.767997i	0.923334	−	0.383999i	$-0.125453\pi$
$930$	−0.554023	+	2.18442i	−0.0181671	+	0.0716301i
$931$			5.57834i			0.182823i
$932$	19.9365	+	28.0092i	0.653040	+	0.917470i
$933$	−6.95245	+	11.1466i	−0.227613	+	0.364925i
$934$	−25.0443	+	8.00291i	−0.819473	+	0.261863i
$935$	−5.31263			−0.173741
$936$	24.5032	+	4.64841i	0.800913	+	0.151938i
$937$	−48.5929			−1.58746			−0.793730	−	0.608270i	$-0.791864\pi$
$937$	−48.5929			−1.58746			−0.793730	+	0.608270i	$0.791864\pi$
$938$	−0.860938	+	0.275113i	−0.0281106	+	0.00898277i
$939$	−14.3320	+	22.9781i	−0.467707	+	0.749861i
$940$	−1.76432	−	2.47874i	−0.0575459	−	0.0808475i
$941$			14.6116i			0.476324i	0.971225	+	0.238162i	$0.0765449\pi$
$941$			14.6116i			0.476324i	−0.971225	+	0.238162i	$0.923455\pi$
$942$	−0.130938	+	0.516267i	−0.00426618	+	0.0168209i
$943$		−	16.5176i		−	0.537886i
$944$	10.8014	−	31.1668i	0.351556	−	1.01439i
$945$	1.80198	+	0.184898i	0.0586184	+	0.00601472i
$946$	−4.23065	−	13.2394i	−0.137550	−	0.430449i
$947$	31.4250			1.02117			0.510587	−	0.859826i	$-0.329428\pi$
$947$	31.4250			1.02117			0.510587	+	0.859826i	$0.329428\pi$
$948$	−13.8307	+	0.843453i	−0.449201	+	0.0273941i
$949$	−23.1567			−0.751697
$950$	−11.7147	−	36.6598i	−0.380074	−	1.18940i
$951$	−20.4177	−	12.7350i	−0.662088	−	0.412961i
$952$	−6.61968	+	8.83712i	−0.214545	+	0.286413i
$953$		−	14.0113i		−	0.453872i	−0.973910	−	0.226936i	$-0.927129\pi$
$953$		−	14.0113i		−	0.453872i	0.973910	−	0.226936i	$-0.0728708\pi$
$954$	−5.27129	+	5.05775i	−0.170664	+	0.163751i
$955$			0.568816i			0.0184065i
$956$	−23.6810	+	16.8557i	−0.765898	+	0.545153i
$957$	55.9488	+	34.8967i	1.80857	+	1.12805i
$958$	−55.0666	+	17.5966i	−1.77912	+	0.568520i
$959$	−4.36377			−0.140914
$960$	1.30104	−	4.65200i	0.0419909	−	0.150143i
$961$	24.0351			0.775327
$962$	−2.53050	+	0.808623i	−0.0815866	+	0.0260711i
$963$	−14.5336	−	29.6742i	−0.468339	−	0.956239i
$964$	−30.6197	+	21.7946i	−0.986194	+	0.701957i
$965$			5.28380i			0.170091i
$966$	−5.18049	−	1.31390i	−0.166679	−	0.0422740i
$967$		−	35.9876i		−	1.15728i	−0.815582	−	0.578641i	$-0.803583\pi$
$967$		−	35.9876i		−	1.15728i	0.815582	−	0.578641i	$-0.196417\pi$
$968$	7.18878	−	9.59685i	0.231056	−	0.308454i
$969$	−19.9612	+	32.0031i	−0.641245	+	1.02809i
$970$	0.300133	+	0.939235i	0.00963670	+	0.0301570i
$971$	48.3844			1.55273			0.776365	−	0.630283i	$-0.217061\pi$
$971$	48.3844			1.55273			0.776365	+	0.630283i	$0.217061\pi$
$972$	−25.7486	−	17.5787i	−0.825886	−	0.563837i
$973$	16.8177			0.539151
$974$	9.22546	+	28.8701i	0.295603	+	0.925057i
$975$	13.1436	−	21.0728i	0.420933	−	0.674870i
$976$	−18.4634	+	53.2749i	−0.590999	+	1.70529i
$977$			37.6432i			1.20431i	0.798378	+	0.602156i	$0.205692\pi$
$977$			37.6432i			1.20431i	−0.798378	+	0.602156i	$0.794308\pi$
$978$	12.4399	+	3.15506i	0.397785	+	0.100888i
$979$			41.1443i			1.31498i
$980$	0.404312	+	0.568026i	0.0129153	+	0.0181449i
$981$	−1.84702	−	3.77118i	−0.0589708	−	0.120405i
$982$	−2.19802	+	0.702379i	−0.0701417	+	0.0224138i
$983$	5.35499			0.170798			0.0853989	−	0.996347i	$-0.472784\pi$
$983$	5.35499			0.170798			0.0853989	+	0.996347i	$0.472784\pi$
$984$	34.5743	−	13.4182i	1.10219	−	0.427757i
$985$	−7.39973			−0.235775
$986$	−51.2847	+	16.3881i	−1.63324	+	0.521903i
$987$	−6.41308	−	4.00000i	−0.204131	−	0.127321i
$988$	19.0157	+	26.7156i	0.604971	+	0.849936i
$989$			5.49306i			0.174669i
$990$	4.16621	−	3.99744i	0.132411	−	0.127047i
$991$		−	51.0278i		−	1.62095i	−0.585773	−	0.810475i	$-0.699209\pi$
$991$		−	51.0278i		−	1.62095i	0.585773	−	0.810475i	$-0.300791\pi$
$992$	14.9246	+	0.363026i	0.473856	+	0.0115261i
$993$	46.7276	+	29.1452i	1.48286	+	0.924895i
$994$	−5.13726	−	16.0765i	−0.162944	−	0.509915i
$995$	−1.30971			−0.0415207
$996$	−1.88587	−	30.9240i	−0.0597562	−	0.979865i
$997$	−53.9305			−1.70800			−0.853998	−	0.520276i	$-0.825829\pi$
$997$	−53.9305			−1.70800			−0.853998	+	0.520276i	$0.825829\pi$
$998$	3.82350	+	11.9652i	0.121031	+	0.378752i
$999$	3.30352	+	0.338968i	0.104519	+	0.0107245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	84.2.e.a.71.11	yes	12
3.2	odd	2	inner	84.2.e.a.71.2	yes	12
4.3	odd	2	inner	84.2.e.a.71.1	✓	12
7.2	even	3		588.2.n.f.263.3		24
7.3	odd	6		588.2.n.g.275.6		24
7.4	even	3		588.2.n.f.275.6		24
7.5	odd	6		588.2.n.g.263.3		24
7.6	odd	2		588.2.e.c.491.11		12
8.3	odd	2		1344.2.h.h.575.4		12
8.5	even	2		1344.2.h.h.575.9		12
12.11	even	2	inner	84.2.e.a.71.12	yes	12
21.2	odd	6		588.2.n.f.263.10		24
21.5	even	6		588.2.n.g.263.10		24
21.11	odd	6		588.2.n.f.275.7		24
21.17	even	6		588.2.n.g.275.7		24
21.20	even	2		588.2.e.c.491.2		12
24.5	odd	2		1344.2.h.h.575.3		12
24.11	even	2		1344.2.h.h.575.10		12
28.3	even	6		588.2.n.g.275.10		24
28.11	odd	6		588.2.n.f.275.10		24
28.19	even	6		588.2.n.g.263.7		24
28.23	odd	6		588.2.n.f.263.7		24
28.27	even	2		588.2.e.c.491.1		12
84.11	even	6		588.2.n.f.275.3		24
84.23	even	6		588.2.n.f.263.6		24
84.47	odd	6		588.2.n.g.263.6		24
84.59	odd	6		588.2.n.g.275.3		24
84.83	odd	2		588.2.e.c.491.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	4.3	odd	2	inner
84.2.e.a.71.2	yes	12	3.2	odd	2	inner
84.2.e.a.71.11	yes	12	1.1	even	1	trivial
84.2.e.a.71.12	yes	12	12.11	even	2	inner
588.2.e.c.491.1		12	28.27	even	2
588.2.e.c.491.2		12	21.20	even	2
588.2.e.c.491.11		12	7.6	odd	2
588.2.e.c.491.12		12	84.83	odd	2
588.2.n.f.263.3		24	7.2	even	3
588.2.n.f.263.6		24	84.23	even	6
588.2.n.f.263.7		24	28.23	odd	6
588.2.n.f.263.10		24	21.2	odd	6
588.2.n.f.275.3		24	84.11	even	6
588.2.n.f.275.6		24	7.4	even	3
588.2.n.f.275.7		24	21.11	odd	6
588.2.n.f.275.10		24	28.11	odd	6
588.2.n.g.263.3		24	7.5	odd	6
588.2.n.g.263.6		24	84.47	odd	6
588.2.n.g.263.7		24	28.19	even	6
588.2.n.g.263.10		24	21.5	even	6
588.2.n.g.275.3		24	84.59	odd	6
588.2.n.g.275.6		24	7.3	odd	6
588.2.n.g.275.7		24	21.17	even	6
588.2.n.g.275.10		24	28.3	even	6
1344.2.h.h.575.3		12	24.5	odd	2
1344.2.h.h.575.4		12	8.3	odd	2
1344.2.h.h.575.9		12	8.5	even	2
1344.2.h.h.575.10		12	24.11	even	2

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:	\( N \)	\(=\)	\( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	84.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34711 - 0.430469i) q^{2} +(-0.916638 + 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(-0.602184 + 2.37432i) q^{6} +1.00000i q^{7} +(1.69572 - 2.26374i) q^{8} +(-1.31955 - 2.69421i) q^{9} +O(q^{10})\)	\(q+(1.34711 - 0.430469i) q^{2} +(-0.916638 + 1.46962i) q^{3} +(1.62939 - 1.15978i) q^{4} -0.348612i q^{5} +(-0.602184 + 2.37432i) q^{6} +1.00000i q^{7} +(1.69572 - 2.26374i) q^{8} +(-1.31955 - 2.69421i) q^{9} +(-0.150067 - 0.469617i) q^{10} -3.90376 q^{11} +(0.210863 + 3.45768i) q^{12} -2.93923 q^{13} +(0.430469 + 1.34711i) q^{14} +(0.512326 + 0.319551i) q^{15} +(1.30984 - 3.77946i) q^{16} +3.90376i q^{17} +(-2.93735 - 3.06137i) q^{18} -5.57834i q^{19} +(-0.404312 - 0.568026i) q^{20} +(-1.46962 - 0.916638i) q^{21} +(-5.25879 + 1.68045i) q^{22} +2.18189 q^{23} +(1.77248 + 4.56709i) q^{24} +4.87847 q^{25} +(-3.95946 + 1.26525i) q^{26} +(5.16901 + 0.530383i) q^{27} +(1.15978 + 1.62939i) q^{28} +9.75220i q^{29} +(0.827715 + 0.209928i) q^{30} +2.63910i q^{31} +(0.137557 - 5.65518i) q^{32} +(3.57834 - 5.73704i) q^{33} +(1.68045 + 5.25879i) q^{34} +0.348612 q^{35} +(-5.27475 - 2.85955i) q^{36} +0.639102 q^{37} +(-2.40130 - 7.51461i) q^{38} +(2.69421 - 4.31955i) q^{39} +(-0.789168 - 0.591148i) q^{40} -7.57031i q^{41} +(-2.37432 - 0.602184i) q^{42} +2.51757i q^{43} +(-6.36076 + 4.52749i) q^{44} +(-0.939235 + 0.460011i) q^{45} +(2.93923 - 0.939235i) q^{46} +4.36377 q^{47} +(4.35371 + 5.38936i) q^{48} -1.00000 q^{49} +(6.57182 - 2.10003i) q^{50} +(-5.73704 - 3.57834i) q^{51} +(-4.78917 + 3.40885i) q^{52} -1.72188i q^{53} +(7.19153 - 1.51062i) q^{54} +1.36090i q^{55} +(2.26374 + 1.69572i) q^{56} +(8.19802 + 5.11331i) q^{57} +(4.19802 + 13.1373i) q^{58} +8.24635 q^{59} +(1.20539 - 0.0735095i) q^{60} -14.0959 q^{61} +(1.13605 + 3.55515i) q^{62} +(2.69421 - 1.31955i) q^{63} +(-2.24908 - 7.67735i) q^{64} +1.02465i q^{65} +(2.35078 - 9.26877i) q^{66} +0.639102i q^{67} +(4.52749 + 6.36076i) q^{68} +(-2.00000 + 3.20654i) q^{69} +(0.469617 - 0.150067i) q^{70} -11.9341 q^{71} +(-8.33660 - 1.58150i) q^{72} +7.87847 q^{73} +(0.860938 - 0.275113i) q^{74} +(-4.47179 + 7.16948i) q^{75} +(-6.46962 - 9.08930i) q^{76} -3.90376i q^{77} +(1.76996 - 6.97867i) q^{78} +4.00000i q^{79} +(-1.31756 - 0.456627i) q^{80} +(-5.51757 + 7.11030i) q^{81} +(-3.25879 - 10.1980i) q^{82} -8.94358 q^{83} +(-3.45768 + 0.210863i) q^{84} +1.36090 q^{85} +(1.08374 + 3.39144i) q^{86} +(-14.3320 - 8.93923i) q^{87} +(-6.61968 + 8.83712i) q^{88} -10.5396i q^{89} +(-1.06723 + 1.02400i) q^{90} -2.93923i q^{91} +(3.55515 - 2.53050i) q^{92} +(-3.87847 - 2.41910i) q^{93} +(5.87847 - 1.87847i) q^{94} -1.94467 q^{95} +(8.18486 + 5.38591i) q^{96} -2.00000 q^{97} +(-1.34711 + 0.430469i) q^{98} +(5.15121 + 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9}+O(q^{10}) \) 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9	\( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42} + 24 q^{45} + 46 q^{48} - 12 q^{49} - 28 q^{52} + 10 q^{54} + 16 q^{57} - 32 q^{58} + 28 q^{60} - 16 q^{61} + 20 q^{64} - 12 q^{66} - 24 q^{69} - 12 q^{70} - 32 q^{72} + 24 q^{73} - 60 q^{76} + 20 q^{78} + 28 q^{81} + 8 q^{82} - 14 q^{84} + 40 q^{85} - 56 q^{88} - 80 q^{90} + 24 q^{93} - 34 q^{96} - 24 q^{97}+O(q^{100}) \) 12 * q - 4 * q^4 - 6 * q^6 - 4 * q^9 + 4 * q^10 - 6 * q^12 + 4 * q^16 - 8 * q^18 - 16 * q^22 + 2 * q^24 - 12 * q^25 + 8 * q^28 + 20 * q^30 - 16 * q^33 + 32 * q^34 - 20 * q^36 - 16 * q^37 + 20 * q^40 + 10 * q^42 + 24 * q^45 + 46 * q^48 - 12 * q^49 - 28 * q^52 + 10 * q^54 + 16 * q^57 - 32 * q^58 + 28 * q^60 - 16 * q^61 + 20 * q^64 - 12 * q^66 - 24 * q^69 - 12 * q^70 - 32 * q^72 + 24 * q^73 - 60 * q^76 + 20 * q^78 + 28 * q^81 + 8 * q^82 - 14 * q^84 + 40 * q^85 - 56 * q^88 - 80 * q^90 + 24 * q^93 - 34 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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