LMFDB - Embedded newform 84.2.e.a.71.1

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			71.1
Root			$0.430469 - 1.34711i$ of defining polynomial
Character	$\chi$	$=$	84.71
Dual form			84.2.e.a.71.2

$q$-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} +(-1.86743 + 1.58515i) 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} +(3.19799 - 1.33149i) 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} +(0.617800 + 4.19742i) 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} +(-4.88120 + 0.417024i) 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} +(0.552601 + 0.651010i) 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} +(0.974616 - 5.92031i) 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} +(1.58515 + 1.86743i) 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} +(6.75501 + 1.53943i) 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} +(6.73490 + 2.93958i) 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} +(-0.464173 - 1.11486i) 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} +(-7.29002 + 6.18804i) 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} +(-3.86142 + 7.55575i) 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} +(5.48883 - 4.65912i) 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} +(-1.33149 - 3.19799i) 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} +(1.46327 - 0.215373i) 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} +(-8.43704 - 4.98160i) 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} + 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}+ \cdots - 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

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	$-0.0248381\pi$
$6$	−1.86743	+	1.58515i	−0.762377	+	0.647134i
$7$		−	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	$-0.299713\pi$
$11$	3.90376			1.17703			0.588514	+	0.808487i	$0.299713\pi$
$12$	3.19799	−	1.33149i	0.923180	−	0.384368i
$13$	−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	$0.843026\pi$
$18$	0.617800	+	4.19742i	0.145617	+	0.989341i
$19$			5.57834i			1.27976i	0.768476	+	0.639879i	$0.221016\pi$
$19$			5.57834i			1.27976i	−0.768476	+	0.639879i	$0.778984\pi$
$20$	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	$-0.573048\pi$
$23$	−2.18189			−0.454955			−0.227477	+	0.973783i	$0.573048\pi$
$24$	−4.88120	+	0.417024i	−0.996370	+	0.0851247i
$25$	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	$0.639519\pi$
$30$	0.552601	+	0.651010i	0.100891	+	0.118858i
$31$		−	2.63910i		−	0.473997i	−0.971510	−	0.236998i	$-0.923836\pi$
$31$		−	2.63910i		−	0.473997i	0.971510	−	0.236998i	$-0.0761636\pi$
$32$	−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
$36$	0.974616	−	5.92031i	0.162436	−	0.986719i
$37$	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	$-0.201323\pi$
$42$	1.58515	+	1.86743i	0.244594	+	0.288151i
$43$		−	2.51757i		−	0.383926i	−0.981402	−	0.191963i	$-0.938515\pi$
$43$		−	2.51757i		−	0.383926i	0.981402	−	0.191963i	$-0.0614854\pi$
$44$	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	$-0.603099\pi$
$47$	−4.36377			−0.636522			−0.318261	+	0.948003i	$0.603099\pi$
$48$	6.75501	+	1.53943i	0.975002	+	0.222197i
$49$	−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	$-0.0377313\pi$
$54$	6.73490	+	2.93958i	0.916504	+	0.400026i
$55$		−	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	$-0.680364\pi$
$59$	−8.24635			−1.07358			−0.536792	+	0.843715i	$0.680364\pi$
$60$	−0.464173	−	1.11486i	−0.0599245	−	0.143927i
$61$	−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
$66$	−7.29002	+	6.18804i	−0.897339	+	0.761695i
$67$		−	0.639102i		−	0.0780787i	−0.999238	−	0.0390393i	$-0.987570\pi$
$67$		−	0.639102i		−	0.0780787i	0.999238	−	0.0390393i	$-0.0124298\pi$
$68$	−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	$-0.249526\pi$
$71$	11.9341			1.41632			0.708158	+	0.706054i	$0.249526\pi$
$72$	−3.86142	+	7.55575i	−0.455073	+	0.890454i
$73$	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
$78$	5.48883	−	4.65912i	0.621487	−	0.527541i
$79$		−	4.00000i		−	0.450035i	−0.974355	−	0.225018i	$-0.927756\pi$
$79$		−	4.00000i		−	0.450035i	0.974355	−	0.225018i	$-0.0722440\pi$
$80$	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	$-0.336689\pi$
$83$	8.94358			0.981685			0.490843	+	0.871248i	$0.336689\pi$
$84$	−1.33149	−	3.19799i	−0.145278	−	0.348929i
$85$	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	$-0.188661\pi$
$90$	1.46327	−	0.215373i	0.154242	−	0.0227023i
$91$			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
$96$	−8.43704	−	4.98160i	−0.861102	−	0.508432i
$97$	−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	$0.950788\pi$
$102$	−6.18804	−	7.29002i	−0.612707	−	0.721819i
$103$		−	7.23937i		−	0.713316i	−0.934235	−	0.356658i	$-0.883916\pi$
$103$		−	7.23937i		−	0.713316i	0.934235	−	0.356658i	$-0.116084\pi$
$104$	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	$-0.678704\pi$
$107$	−11.0141			−1.06477			−0.532385	+	0.846502i	$0.678704\pi$
$108$	−7.80723	−	6.85910i	−0.751251	−	0.660017i
$109$	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	$-0.136369\pi$
$114$	−8.84249	−	10.4172i	−0.828175	−	0.975658i
$115$			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
$120$	0.145380	+	1.70164i	0.0132713	+	0.155338i
$121$	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
$126$	4.19742	−	0.617800i	0.373936	−	0.0550380i
$127$			12.3960i			1.09997i	0.835174	+	0.549985i	$0.185367\pi$
$127$			12.3960i			1.09997i	−0.835174	+	0.549985i	$0.814633\pi$
$128$	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	$-0.522413\pi$
$131$	−1.61048			−0.140708			−0.0703540	+	0.997522i	$0.522413\pi$
$132$	12.4842	−	5.19782i	1.08661	−	0.452412i
$133$	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	$0.940314\pi$
$138$	4.07453	−	3.45861i	0.346847	−	0.294417i
$139$			16.8177i			1.42646i	0.700931	+	0.713230i	$0.252768\pi$
$139$			16.8177i			1.42646i	−0.700931	+	0.713230i	$0.747232\pi$
$140$	−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
$144$	8.45427	−	8.51618i	0.704522	−	0.709682i
$145$	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	$-0.101598\pi$
$150$	−9.11022	+	7.73309i	−0.743846	+	0.631404i
$151$		−	12.6391i		−	1.02856i	−0.857624	−	0.514278i	$-0.828060\pi$
$151$		−	12.6391i		−	1.02856i	0.857624	−	0.514278i	$-0.171940\pi$
$152$	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
$156$	−9.39964	+	3.91356i	−0.752574	+	0.313336i
$157$	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
$162$	10.4935	−	7.20319i	0.824449	−	0.565936i
$163$			5.23937i			0.410379i	0.978722	+	0.205189i	$0.0657811\pi$
$163$			5.23937i			0.410379i	−0.978722	+	0.205189i	$0.934219\pi$
$164$	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	$-0.646422\pi$
$167$	−11.4741			−0.887891			−0.443945	+	0.896054i	$0.646422\pi$
$168$	0.417024	+	4.88120i	0.0321741	+	0.376593i
$169$	−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	$0.701576\pi$
$174$	−15.4587	−	18.2116i	−1.17192	−	1.38062i
$175$		−	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	$-0.478427\pi$
$179$	1.81209			0.135442			0.0677211	+	0.997704i	$0.478427\pi$
$180$	−2.06389	−	0.339763i	−0.153833	−	0.0253244i
$181$	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
$186$	4.18336	+	4.92835i	0.306739	+	0.361364i
$187$			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	$-0.481199\pi$
$191$	1.63166			0.118063			0.0590314	+	0.998256i	$0.481199\pi$
$192$	9.22117	+	10.3426i	0.665481	+	0.746415i
$193$	−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	$-0.272924\pi$
$198$	2.41175	+	16.3857i	0.171395	+	1.16448i
$199$			3.75694i			0.266322i	0.991094	+	0.133161i	$0.0425128\pi$
$199$			3.75694i			0.266322i	−0.991094	+	0.133161i	$0.957487\pi$
$200$	−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
$204$	5.19782	+	12.4842i	0.363920	+	0.874068i
$205$	−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
$210$	0.651010	−	0.552601i	0.0449239	−	0.0381331i
$211$		−	9.83963i		−	0.677388i	−0.940897	−	0.338694i	$-0.890015\pi$
$211$		−	9.83963i		−	0.677388i	0.940897	−	0.338694i	$-0.109985\pi$
$212$	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
$216$	7.56454	+	12.6007i	0.514702	+	0.857369i
$217$	−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
$222$	−1.19348	+	1.01307i	−0.0801011	+	0.0679928i
$223$		−	22.9136i		−	1.53441i	−0.641403	−	0.767204i	$-0.721647\pi$
$223$		−	22.9136i		−	1.53441i	0.641403	−	0.767204i	$-0.278353\pi$
$224$	−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	$-0.648225\pi$
$227$	−13.5302			−0.898028			−0.449014	+	0.893525i	$0.648225\pi$
$228$	7.42750	+	17.8395i	0.491898	+	1.18145i
$229$	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	$0.809618\pi$
$234$	−1.81586	−	12.3372i	−0.118706	−	0.806508i
$235$			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	$-0.344236\pi$
$239$	14.5336			0.940102			0.470051	+	0.882639i	$0.344236\pi$
$240$	0.536663	−	2.35488i	0.0346414	−	0.152007i
$241$	−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
$246$	12.0001	+	14.1371i	0.765096	+	0.901346i
$247$		−	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	$-0.274179\pi$
$251$	20.6405			1.30281			0.651407	+	0.758729i	$0.274179\pi$
$252$	−5.92031	−	0.974616i	−0.372945	−	0.0613950i
$253$	−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	$0.951928\pi$
$258$	3.99072	+	4.70140i	0.248451	+	0.292696i
$259$		−	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	$-0.352936\pi$
$263$	14.4578			0.891507			0.445754	+	0.895156i	$0.352936\pi$
$264$	−19.0550	+	1.62796i	−1.17276	+	0.100194i
$265$	−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	$-0.0458871\pi$
$270$	1.02477	−	2.34787i	0.0623657	−	0.142887i
$271$		−	15.6742i		−	0.952143i	−0.879407	−	0.476071i	$-0.842060\pi$
$271$		−	15.6742i		−	0.952143i	0.879407	−	0.476071i	$-0.157940\pi$
$272$	−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
$276$	−6.97765	+	2.90516i	−0.420005	+	0.174870i
$277$	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	$-0.0549432\pi$
$282$	8.14906	−	6.91723i	0.485269	−	0.411915i
$283$		−	5.57834i		−	0.331598i	−0.986160	−	0.165799i	$-0.946980\pi$
$283$		−	5.57834i		−	0.331598i	0.986160	−	0.165799i	$-0.0530202\pi$
$284$	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
$288$	−15.0548	+	7.83291i	−0.887110	+	0.461558i
$289$	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	$0.755686\pi$
$294$	1.86743	−	1.58515i	0.108911	−	0.0924477i
$295$			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
$300$	15.6013	−	6.49564i	0.900741	−	0.375026i
$301$	−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
$306$	−16.3857	+	2.41175i	−0.936710	+	0.137870i
$307$		−	3.69987i		−	0.211163i	−0.994411	−	0.105581i	$-0.966330\pi$
$307$		−	3.69987i		−	0.211163i	0.994411	−	0.105581i	$-0.0336703\pi$
$308$	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	$-0.568990\pi$
$311$	−7.58473			−0.430090			−0.215045	+	0.976604i	$0.568990\pi$
$312$	14.3470	−	1.22573i	0.812238	−	0.0693934i
$313$	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	$0.872420\pi$
$318$	2.72943	+	3.21549i	0.153059	+	0.180316i
$319$			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
$324$	−17.2366	+	5.18633i	−0.957591	+	0.288130i
$325$	−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
$330$	2.15722	+	2.54139i	0.118751	+	0.139899i
$331$			31.7958i			1.74765i	0.486237	+	0.873827i	$0.338369\pi$
$331$			31.7958i			1.74765i	−0.486237	+	0.873827i	$0.661631\pi$
$332$	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
$336$	1.53943	−	6.75501i	0.0839827	−	0.368516i
$337$	−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
$342$	−23.4146	+	3.44630i	−1.26612	+	0.186354i
$343$			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	$-0.572812\pi$
$347$	−8.44797			−0.453511			−0.226755	+	0.973952i	$0.572812\pi$
$348$	12.9850	+	31.1874i	0.696067	+	1.67182i
$349$	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	$0.929388\pi$
$354$	15.3995	−	13.0717i	0.818475	−	0.694752i
$355$		−	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	$-0.730784\pi$
$359$	−25.1300			−1.32631			−0.663156	+	0.748481i	$0.730784\pi$
$360$	2.63403	+	1.34614i	0.138825	+	0.0709477i
$361$	−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
$366$	26.3232	−	22.3441i	1.37593	−	1.16794i
$367$			21.7131i			1.13341i	0.823920	+	0.566707i	$0.191783\pi$
$367$			21.7131i			1.13341i	−0.823920	+	0.566707i	$0.808217\pi$
$368$	−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
$372$	−3.51394	−	8.43982i	−0.182189	−	0.437584i
$373$	−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
$378$	2.93958	−	6.73490i	0.151196	−	0.346406i
$379$		−	18.2745i		−	0.938699i	−0.883013	−	0.469349i	$-0.844489\pi$
$379$		−	18.2745i		−	0.938699i	0.883013	−	0.469349i	$-0.155511\pi$
$380$	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	$-0.483327\pi$
$383$	2.04930			0.104715			0.0523573	+	0.998628i	$0.483327\pi$
$384$	−7.96972	−	17.9021i	−0.406703	−	0.913560i
$385$	−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	$-0.0911899\pi$
$390$	−1.62422	−	1.91347i	−0.0822458	−	0.0968923i
$391$		−	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
$396$	3.80467	−	23.1115i	0.191192	−	1.16140i
$397$	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	$-0.180170\pi$
$402$	1.01307	+	1.19348i	0.0505274	+	0.0595254i
$403$			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
$408$	−1.62796	−	19.0550i	−0.0805962	−	0.943365i
$409$	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
$414$	−1.34797	−	9.15829i	−0.0662491	−	0.450106i
$415$		−	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	$-0.756994\pi$
$419$	−29.5773			−1.44494			−0.722472	+	0.691400i	$0.756994\pi$
$420$	−1.11486	+	0.464173i	−0.0543995	+	0.0226493i
$421$	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
$426$	−22.2861	+	18.9173i	−1.07977	+	0.916546i
$427$			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	$-0.464070\pi$
$431$	4.67679			0.225273			0.112636	+	0.993636i	$0.464070\pi$
$432$	−4.76603	−	20.2308i	−0.229306	−	0.973354i
$433$	−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
$438$	−14.7125	+	12.4885i	−0.702991	+	0.596725i
$439$		−	26.4787i		−	1.26376i	−0.775066	−	0.631881i	$-0.782283\pi$
$439$		−	26.4787i		−	1.26376i	0.775066	−	0.631881i	$-0.217717\pi$
$440$	−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	$-0.534861\pi$
$443$	−4.60099			−0.218599			−0.109300	+	0.994009i	$0.534861\pi$
$444$	2.04384	−	0.850958i	0.0969963	−	0.0403847i
$445$	−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	$0.868536\pi$
$450$	3.01392	+	20.4770i	0.142078	+	0.965294i
$451$		−	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
$456$	−2.32630	−	27.2290i	−0.108939	−	1.27511i
$457$	−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	$-0.283384\pi$
$462$	6.18804	+	7.29002i	0.287894	+	0.339162i
$463$			26.4787i			1.23057i	0.788304	+	0.615286i	$0.210959\pi$
$463$			26.4787i			1.23057i	−0.788304	+	0.615286i	$0.789041\pi$
$464$	−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	$-0.358461\pi$
$467$	18.5911			0.860296			0.430148	+	0.902758i	$0.358461\pi$
$468$	−2.86462	+	17.4012i	−0.132417	+	0.804371i
$469$	−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
$474$	6.34059	+	7.46973i	0.291233	+	0.343096i
$475$			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	$-0.116405\pi$
$479$	40.8777			1.86775			0.933874	+	0.357601i	$0.116405\pi$
$480$	−1.73664	+	2.94125i	−0.0792666	+	0.134249i
$481$	−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
$486$	−0.967180	−	22.0242i	−0.0438722	−	0.999037i
$487$		−	21.4312i		−	0.971140i	−0.874198	−	0.485570i	$-0.838612\pi$
$487$		−	21.4312i		−	0.971140i	0.874198	−	0.485570i	$-0.161388\pi$
$488$	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	$-0.488278\pi$
$491$	1.63166			0.0736358			0.0368179	+	0.999322i	$0.488278\pi$
$492$	−10.0798	−	24.2098i	−0.454432	−	1.09146i
$493$	−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
$498$	−16.7015	+	14.1769i	−0.748414	+	0.635282i
$499$		−	8.88216i		−	0.397620i	−0.980038	−	0.198810i	$-0.936292\pi$
$499$		−	8.88216i		−	0.397620i	0.980038	−	0.198810i	$-0.0637077\pi$
$500$	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	$-0.216243\pi$
$503$	34.8967			1.55597			0.777983	+	0.628286i	$0.216243\pi$
$504$	7.55575	+	3.86142i	0.336560	+	0.172001i
$505$	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	$-0.176616\pi$
$510$	−2.54139	+	2.15722i	−0.112535	+	0.0955235i
$511$		−	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
$516$	−3.35212	−	8.05117i	−0.147569	−	0.354433i
$517$	−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	$-0.0400612\pi$
$522$	−40.9341	+	6.02491i	−1.79164	+	0.263703i
$523$			4.81770i			0.210664i	0.994437	+	0.105332i	$0.0335904\pi$
$523$			4.81770i			0.210664i	−0.994437	+	0.105332i	$0.966410\pi$
$524$	−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
$528$	26.3700	+	6.00956i	1.14761	+	0.261533i
$529$	−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
$534$	16.7069	+	19.6821i	0.722978	+	0.851727i
$535$			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
$540$	−2.39116	+	2.72169i	−0.102899	+	0.117123i
$541$	−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
$546$	−4.65912	−	5.48883i	−0.199392	−	0.234900i
$547$		−	35.3097i		−	1.50973i	−0.655879	−	0.754866i	$-0.727702\pi$
$547$		−	35.3097i		−	1.50973i	0.655879	−	0.754866i	$-0.272298\pi$
$548$	−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
$552$	10.6502	−	0.909900i	0.453304	−	0.0387279i
$553$	−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	$0.736198\pi$
$558$	11.0774	−	1.63044i	0.468944	−	0.0690219i
$559$			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	$-0.412636\pi$
$563$	12.8618			0.542058			0.271029	+	0.962571i	$0.412636\pi$
$564$	−13.9553	+	5.81032i	−0.587624	+	0.244659i
$565$	−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	$-0.106677\pi$
$570$	−3.63155	+	3.08260i	−0.152109	+	0.129116i
$571$		−	42.0315i		−	1.75896i	−0.475935	−	0.879481i	$-0.657890\pi$
$571$		−	42.0315i		−	1.75896i	0.475935	−	0.879481i	$-0.342110\pi$
$572$	−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
$576$	23.6522	−	4.07116i	0.985508	−	0.169632i
$577$	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
$582$	3.73487	−	3.17029i	0.154815	−	0.131413i
$583$		−	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	$-0.453359\pi$
$587$	7.07471			0.292004			0.146002	+	0.989284i	$0.453359\pi$
$588$	−3.19799	+	1.33149i	−0.131883	+	0.0549097i
$589$	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	$-0.123245\pi$
$594$	26.2915	+	11.4754i	1.07875	+	0.470843i
$595$		−	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	$-0.781389\pi$
$599$	−37.8516			−1.54657			−0.773287	+	0.634057i	$0.781389\pi$
$600$	−23.8128	+	2.03444i	−0.972152	+	0.0830557i
$601$	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
$606$	−4.90625	−	5.77997i	−0.199303	−	0.234795i
$607$			25.8785i			1.05037i	0.850987	+	0.525187i	$0.176005\pi$
$607$			25.8785i			1.05037i	−0.850987	+	0.525187i	$0.823995\pi$
$608$	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
$612$	23.1115	+	3.80467i	0.934227	+	0.153795i
$613$	−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	$0.821149\pi$
$618$	11.4755	+	13.5190i	0.461611	+	0.543815i
$619$			34.3390i			1.38020i	0.723714	+	0.690100i	$0.242433\pi$
$619$			34.3390i			1.38020i	−0.723714	+	0.690100i	$0.757567\pi$
$620$	−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
$624$	−19.8546	−	4.52474i	−0.794819	−	0.181135i
$625$	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
$630$	−0.215373	−	1.46327i	−0.00858065	−	0.0582981i
$631$			27.7569i			1.10499i	0.833517	+	0.552493i	$0.186323\pi$
$631$			27.7569i			1.10499i	−0.833517	+	0.552493i	$0.813677\pi$
$632$	−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
$636$	−2.29266	−	5.50654i	−0.0909099	−	0.218349i
$637$	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	$-0.0439122\pi$
$642$	20.5680	−	17.4589i	0.811756	−	0.689049i
$643$		−	9.74373i		−	0.384255i	−0.981370	−	0.192128i	$-0.938461\pi$
$643$		−	9.74373i		−	0.384255i	0.981370	−	0.192128i	$-0.0615387\pi$
$644$	−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	$-0.313054\pi$
$647$	28.1896			1.10825			0.554123	+	0.832434i	$0.313054\pi$
$648$	25.4522	+	0.433298i	0.999855	+	0.0170216i
$649$	−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	$0.931889\pi$
$654$	−2.61391	+	2.21878i	−0.102212	+	0.0867613i
$655$			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	$-0.622167\pi$
$659$	−19.2248			−0.748893			−0.374446	+	0.927249i	$0.622167\pi$
$660$	−1.81202	−	4.35214i	−0.0705329	−	0.169407i
$661$	−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
$666$	0.394837	+	2.68258i	0.0152996	+	0.103948i
$667$		−	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
$672$	−4.98160	+	8.43704i	−0.192169	+	0.325466i
$673$	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	$-0.132105\pi$
$678$	14.0003	+	16.4935i	0.537678	+	0.633429i
$679$			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	$-0.597899\pi$
$683$	−15.8234			−0.605467			−0.302734	+	0.953075i	$0.597899\pi$
$684$	33.0255	+	5.43673i	1.26276	+	0.207879i
$685$	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
$690$	−1.20571	−	1.42043i	−0.0459007	−	0.0540748i
$691$			24.4093i			0.928572i	0.885685	+	0.464286i	$0.153689\pi$
$691$			24.4093i			0.928572i	−0.885685	+	0.464286i	$0.846311\pi$
$692$	−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
$696$	−4.06690	−	47.6024i	−0.154156	−	1.80437i
$697$	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	$0.867061\pi$
$702$	−19.7954	−	8.64012i	−0.747131	−	0.326100i
$703$			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
$708$	−26.3718	+	10.9799i	−0.991111	+	0.412651i
$709$	−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
$714$	−7.29002	+	6.18804i	−0.272822	+	0.231582i
$715$			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	$-0.384349\pi$
$719$	19.0588			0.710774			0.355387	+	0.934719i	$0.384349\pi$
$720$	−2.96884	−	2.94726i	−0.110642	−	0.109838i
$721$	−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
$726$	−7.91674	+	6.72002i	−0.293818	+	0.249403i
$727$		−	3.72549i		−	0.138171i	−0.997611	−	0.0690854i	$-0.977992\pi$
$727$		−	3.72549i		−	0.138171i	0.997611	−	0.0690854i	$-0.0220081\pi$
$728$	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
$732$	−45.0786	+	18.7686i	−1.66615	+	0.693706i
$733$	−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
$738$	31.7758	−	4.67694i	1.16968	−	0.172161i
$739$			23.3097i			0.857459i	0.903433	+	0.428730i	$0.141039\pi$
$739$			23.3097i			0.857459i	−0.903433	+	0.428730i	$0.858961\pi$
$740$	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	$-0.286703\pi$
$743$	33.8576			1.24211			0.621057	+	0.783765i	$0.286703\pi$
$744$	1.10057	+	12.8820i	0.0403488	+	0.472276i
$745$	−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
$750$	5.45885	+	6.43098i	0.199329	+	0.234826i
$751$			48.1530i			1.75713i	0.477625	+	0.878564i	$0.341498\pi$
$751$			48.1530i			1.75713i	−0.477625	+	0.878564i	$0.658502\pi$
$752$	−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
$756$	−6.85910	+	7.80723i	−0.249463	+	0.283946i
$757$	−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	$0.833580\pi$
$762$	−19.6496	−	23.1488i	−0.711828	−	0.838592i
$763$		−	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
$768$	3.02979	+	27.5467i	0.109328	+	0.994006i
$769$	−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	$0.673278\pi$
$774$	10.5673	−	1.55536i	0.379834	−	0.0559061i
$775$		−	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
$780$	1.36431	+	3.27683i	0.0488503	+	0.117329i
$781$	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
$786$	3.00746	−	2.55284i	0.107272	−	0.0910569i
$787$		−	48.8177i		−	1.74016i	−0.492908	−	0.870082i	$-0.664066\pi$
$787$		−	48.8177i		−	1.74016i	0.492908	−	0.870082i	$-0.335934\pi$
$788$	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
$792$	−15.0741	+	29.4959i	−0.535634	+	1.04809i
$793$	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	$0.927616\pi$
$798$	−10.4172	+	8.84249i	−0.368764	+	0.313021i
$799$		−	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
$804$	−0.850958	−	2.04384i	−0.0300110	−	0.0720807i
$805$	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	$-0.154764\pi$
$810$	−2.51112	−	3.65817i	−0.0882317	−	0.128535i
$811$			4.13977i			0.145367i	0.997355	+	0.0726835i	$0.0231563\pi$
$811$			4.13977i			0.145367i	−0.997355	+	0.0726835i	$0.976844\pi$
$812$	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
$816$	−6.00956	+	26.3700i	−0.210377	+	0.923133i
$817$	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	$-0.172179\pi$
$822$	−6.91723	−	8.14906i	−0.241266	−	0.284231i
$823$			12.0777i			0.421001i	0.977594	+	0.210501i	$0.0675094\pi$
$823$			12.0777i			0.421001i	−0.977594	+	0.210501i	$0.932491\pi$
$824$	−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	$-0.566531\pi$
$827$	−11.9341			−0.414989			−0.207494	+	0.978236i	$0.566531\pi$
$828$	−2.12650	+	12.9175i	−0.0739010	+	0.448913i
$829$	−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
$834$	−26.6585	−	31.4059i	−0.923110	−	1.08750i
$835$			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	$-0.509046\pi$
$839$	−1.64607			−0.0568288			−0.0284144	+	0.999596i	$0.509046\pi$
$840$	1.70164	−	0.145380i	0.0587123	−	0.00501607i
$841$	−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
$846$	−2.69594	−	18.3166i	−0.0926884	−	0.629737i
$847$		−	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
$852$	38.1651	−	15.8901i	1.30751	−	0.544387i
$853$	−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	$-0.314868\pi$
$858$	21.4271	−	18.1881i	0.731508	−	0.620932i
$859$		−	16.0571i		−	0.547860i	−0.961750	−	0.273930i	$-0.911676\pi$
$859$		−	16.0571i		−	0.547860i	0.961750	−	0.273930i	$-0.0883237\pi$
$860$	−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	$-0.581634\pi$
$863$	−14.9034			−0.507318			−0.253659	+	0.967294i	$0.581634\pi$
$864$	−2.28838	+	29.3047i	−0.0778522	+	0.996965i
$865$	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
$870$	−6.34878	+	5.38908i	−0.215244	+	0.182707i
$871$			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
$876$	25.1953	−	10.4901i	0.851269	−	0.354428i
$877$	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	$0.789217\pi$
$882$	−0.617800	−	4.19742i	−0.0208024	−	0.141334i
$883$		−	31.1178i		−	1.04720i	−0.851965	−	0.523599i	$-0.824589\pi$
$883$		−	31.1178i		−	1.04720i	0.851965	−	0.523599i	$-0.175411\pi$
$884$	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	$-0.0951291\pi$
$887$	56.9248			1.91135			0.955674	+	0.294428i	$0.0951291\pi$
$888$	−3.11958	+	0.266521i	−0.104686	+	0.00894386i
$889$	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
$894$	12.1431	+	14.3055i	0.406125	+	0.478448i
$895$		−	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
$900$	4.75463	−	28.8821i	0.158488	−	0.962736i
$901$	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
$906$	20.0348	+	23.6027i	0.665613	+	0.784147i
$907$		−	6.70939i		−	0.222782i	−0.993777	−	0.111391i	$-0.964469\pi$
$907$		−	6.70939i		−	0.222782i	0.993777	−	0.111391i	$-0.0355305\pi$
$908$	−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	$-0.811888\pi$
$911$	−50.1275			−1.66080			−0.830399	+	0.557169i	$0.811888\pi$
$912$	−8.58745	+	37.6817i	−0.284359	+	1.24777i
$913$	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
$918$	−11.4754	+	26.2915i	−0.378746	+	0.867747i
$919$		−	17.0351i		−	0.561938i	−0.959717	−	0.280969i	$-0.909344\pi$
$919$		−	17.0351i		−	0.561938i	0.959717	−	0.280969i	$-0.0906557\pi$
$920$	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
$924$	−5.19782	−	12.4842i	−0.170996	−	0.410700i
$925$	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	$-0.125453\pi$
$930$	1.71808	−	1.45837i	0.0563381	−	0.0478219i
$931$		−	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
$936$	11.3496	−	22.2081i	0.370974	−	0.725896i
$937$	−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	$0.923455\pi$
$942$	−0.406051	+	0.344671i	−0.0132299	+	0.0112300i
$943$			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	$-0.670572\pi$
$947$	−31.4250			−1.02117			−0.510587	+	0.859826i	$0.670572\pi$
$948$	−5.32596	−	12.7920i	−0.172979	−	0.415463i
$949$	−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	$-0.0728708\pi$
$954$	7.22743	−	1.06378i	0.233997	−	0.0344410i
$955$		−	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
$960$	3.60556	−	3.21461i	0.116369	−	0.103751i
$961$	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
$966$	−3.45861	−	4.07453i	−0.111279	−	0.131096i
$967$			35.9876i			1.15728i	0.815582	+	0.578641i	$0.196417\pi$
$967$			35.9876i			1.15728i	−0.815582	+	0.578641i	$0.803583\pi$
$968$	−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	$-0.782939\pi$
$971$	−48.3844			−1.55273			−0.776365	+	0.630283i	$0.782939\pi$
$972$	−8.17783	+	30.0853i	−0.262304	+	0.964985i
$973$	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	$0.794308\pi$
$978$	−8.30517	−	9.78417i	−0.265570	−	0.312863i
$979$		−	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	$-0.527216\pi$
$983$	−5.35499			−0.170798			−0.0853989	+	0.996347i	$0.527216\pi$
$984$	3.15700	+	36.9522i	0.100642	+	1.17799i
$985$	−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
$990$	5.71226	−	0.840763i	0.181548	−	0.0267212i
$991$			51.0278i			1.62095i	0.585773	+	0.810475i	$0.300791\pi$
$991$			51.0278i			1.62095i	−0.585773	+	0.810475i	$0.699209\pi$
$992$	−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
$996$	28.6015	−	11.9083i	0.906272	−	0.377329i
$997$	−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.71.1	✓	12
3.2	odd	2	inner	84.2.e.a.71.12	yes	12
4.3	odd	2	inner	84.2.e.a.71.11	yes	12
7.2	even	3		588.2.n.f.263.7		24
7.3	odd	6		588.2.n.g.275.10		24
7.4	even	3		588.2.n.f.275.10		24
7.5	odd	6		588.2.n.g.263.7		24
7.6	odd	2		588.2.e.c.491.1		12
8.3	odd	2		1344.2.h.h.575.9		12
8.5	even	2		1344.2.h.h.575.4		12
12.11	even	2	inner	84.2.e.a.71.2	yes	12
21.2	odd	6		588.2.n.f.263.6		24
21.5	even	6		588.2.n.g.263.6		24
21.11	odd	6		588.2.n.f.275.3		24
21.17	even	6		588.2.n.g.275.3		24
21.20	even	2		588.2.e.c.491.12		12
24.5	odd	2		1344.2.h.h.575.10		12
24.11	even	2		1344.2.h.h.575.3		12
28.3	even	6		588.2.n.g.275.6		24
28.11	odd	6		588.2.n.f.275.6		24
28.19	even	6		588.2.n.g.263.3		24
28.23	odd	6		588.2.n.f.263.3		24
28.27	even	2		588.2.e.c.491.11		12
84.11	even	6		588.2.n.f.275.7		24
84.23	even	6		588.2.n.f.263.10		24
84.47	odd	6		588.2.n.g.263.10		24
84.59	odd	6		588.2.n.g.275.7		24
84.83	odd	2		588.2.e.c.491.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.2.e.a.71.1	✓	12	1.1	even	1	trivial
84.2.e.a.71.2	yes	12	12.11	even	2	inner
84.2.e.a.71.11	yes	12	4.3	odd	2	inner
84.2.e.a.71.12	yes	12	3.2	odd	2	inner
588.2.e.c.491.1		12	7.6	odd	2
588.2.e.c.491.2		12	84.83	odd	2
588.2.e.c.491.11		12	28.27	even	2
588.2.e.c.491.12		12	21.20	even	2
588.2.n.f.263.3		24	28.23	odd	6
588.2.n.f.263.6		24	21.2	odd	6
588.2.n.f.263.7		24	7.2	even	3
588.2.n.f.263.10		24	84.23	even	6
588.2.n.f.275.3		24	21.11	odd	6
588.2.n.f.275.6		24	28.11	odd	6
588.2.n.f.275.7		24	84.11	even	6
588.2.n.f.275.10		24	7.4	even	3
588.2.n.g.263.3		24	28.19	even	6
588.2.n.g.263.6		24	21.5	even	6
588.2.n.g.263.7		24	7.5	odd	6
588.2.n.g.263.10		24	84.47	odd	6
588.2.n.g.275.3		24	21.17	even	6
588.2.n.g.275.6		24	28.3	even	6
588.2.n.g.275.7		24	84.59	odd	6
588.2.n.g.275.10		24	7.3	odd	6
1344.2.h.h.575.3		12	24.11	even	2
1344.2.h.h.575.4		12	8.5	even	2
1344.2.h.h.575.9		12	8.3	odd	2
1344.2.h.h.575.10		12	24.5	odd	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} +(-1.86743 + 1.58515i) 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} +(3.19799 - 1.33149i) 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} +(0.617800 + 4.19742i) 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} +(-4.88120 + 0.417024i) 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} +(0.552601 + 0.651010i) 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} +(0.974616 - 5.92031i) 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} +(1.58515 + 1.86743i) 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} +(6.75501 + 1.53943i) 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} +(6.73490 + 2.93958i) 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} +(-0.464173 - 1.11486i) 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} +(-7.29002 + 6.18804i) 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} +(-3.86142 + 7.55575i) 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} +(5.48883 - 4.65912i) 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} +(-1.33149 - 3.19799i) 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} +(1.46327 - 0.215373i) 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} +(-8.43704 - 4.98160i) q^{96} -2.00000 q^{97} +(1.34711 + 0.430469i) q^{98} +(-5.15121 - 10.5176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4} - 6 q^{6} - 4 q^{9} + 4 q^{10} - 6 q^{12} + 4 q^{16} - 8 q^{18} - 16 q^{22} + 2 q^{24} - 12 q^{25} + 8 q^{28} + 20 q^{30} - 16 q^{33} + 32 q^{34} - 20 q^{36} - 16 q^{37} + 20 q^{40} + 10 q^{42}+ \cdots - 24 q^{97}+O(q^{100}) \) 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

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