LMFDB - Embedded newform 61.2.f.b.48.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(14,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("61.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.542936601.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 2x^{6} - 4x^{5} + x^{4} - 8x^{3} + 8x^{2} - 8x + 16 $ x^8 - x^7 + 2x^6 - 4x^5 + x^4 - 8x^3 + 8x^2 - 8*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			48.4
Root			$1.41379 + 0.0347146i$ of defining polynomial
Character	$\chi$	$=$	61.48
Dual form			61.2.f.b.14.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.15074 + 1.24173i) q^{2} -2.82757 q^{3} +(2.08380 + 3.60925i) q^{4} +(1.17683 - 2.03833i) q^{5} +(-6.08139 - 3.51109i) q^{6} +(-2.32076 - 1.33989i) q^{7} +5.38317i q^{8} +4.99518 q^{9} +O(q^{10})$	\(q+(2.15074 + 1.24173i) q^{2} -2.82757 q^{3} +(2.08380 + 3.60925i) q^{4} +(1.17683 - 2.03833i) q^{5} +(-6.08139 - 3.51109i) q^{6} +(-2.32076 - 1.33989i) q^{7} +5.38317i q^{8} +4.99518 q^{9} +(5.06212 - 2.92262i) q^{10} -0.681986i q^{11} +(-5.89211 - 10.2054i) q^{12} +(-2.09062 + 3.62106i) q^{13} +(-3.32757 - 5.76353i) q^{14} +(-3.32757 + 5.76353i) q^{15} +(-2.51686 + 4.35933i) q^{16} +(-0.990775 + 0.572024i) q^{17} +(10.7434 + 6.20268i) q^{18} +(-1.14393 - 1.98134i) q^{19} +9.80912 q^{20} +(6.56212 + 3.78864i) q^{21} +(0.846845 - 1.46678i) q^{22} +6.21331i q^{23} -15.2213i q^{24} +(-0.269858 - 0.467407i) q^{25} +(-8.99277 + 5.19198i) q^{26} -5.64152 q^{27} -11.1683i q^{28} +(-2.79112 + 1.61146i) q^{29} +(-14.3135 + 8.26392i) q^{30} +(7.38288 - 4.26251i) q^{31} +(-1.50232 + 0.867363i) q^{32} +1.92837i q^{33} -2.84120 q^{34} +(-5.46228 + 3.15365i) q^{35} +(10.4090 + 18.0289i) q^{36} -9.43622i q^{37} -5.68182i q^{38} +(5.91138 - 10.2388i) q^{39} +(10.9727 + 6.33508i) q^{40} -0.405830 q^{41} +(9.40897 + 16.2968i) q^{42} +(-1.28023 - 0.739138i) q^{43} +(2.46146 - 1.42112i) q^{44} +(5.87848 - 10.1818i) q^{45} +(-7.71528 + 13.3633i) q^{46} +(4.73455 + 8.20048i) q^{47} +(7.11661 - 12.3263i) q^{48} +(0.0906174 + 0.156954i) q^{49} -1.34036i q^{50} +(2.80149 - 1.61744i) q^{51} -17.4257 q^{52} -5.68277i q^{53} +(-12.1335 - 7.00526i) q^{54} +(-1.39011 - 0.802582i) q^{55} +(7.21287 - 12.4931i) q^{56} +(3.23455 + 5.60240i) q^{57} -8.00399 q^{58} +(1.80117 + 1.03990i) q^{59} -27.7360 q^{60} +(-7.68238 - 1.40751i) q^{61} +21.1716 q^{62} +(-11.5926 - 6.69300i) q^{63} +5.75930 q^{64} +(4.92060 + 8.52273i) q^{65} +(-2.39452 + 4.14743i) q^{66} +(-7.07217 - 4.08312i) q^{67} +(-4.12916 - 2.38397i) q^{68} -17.5686i q^{69} -15.6640 q^{70} +(-2.40133 + 1.38641i) q^{71} +26.8899i q^{72} +(2.94187 + 5.09546i) q^{73} +(11.7173 - 20.2949i) q^{74} +(0.763043 + 1.32163i) q^{75} +(4.76745 - 8.25746i) q^{76} +(-0.913787 + 1.58273i) q^{77} +(25.4277 - 14.6807i) q^{78} +(8.50114 + 4.90814i) q^{79} +(5.92383 + 10.2604i) q^{80} +0.966280 q^{81} +(-0.872837 - 0.503933i) q^{82} +(-5.67683 + 9.83256i) q^{83} +31.5791i q^{84} +2.69270i q^{85} +(-1.83563 - 3.17940i) q^{86} +(7.89211 - 4.55651i) q^{87} +3.67125 q^{88} +5.38412i q^{89} +(25.2862 - 14.5990i) q^{90} +(9.70364 - 5.60240i) q^{91} +(-22.4254 + 12.9473i) q^{92} +(-20.8757 + 12.0526i) q^{93} +23.5162i q^{94} -5.38484 q^{95} +(4.24791 - 2.45253i) q^{96} +(-3.93505 - 6.81571i) q^{97} +0.450091i q^{98} -3.40664i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 8 q^{4} + 6 q^{5} - 21 q^{6} - 3 q^{7} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^3 + 8 * q^4 + 6 * q^5 - 21 * q^6 - 3 * q^7 + 2 * q^9	$ 8 q - 2 q^{3} + 8 q^{4} + 6 q^{5} - 21 q^{6} - 3 q^{7} + 2 q^{9} - 6 q^{10} + q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 20 q^{16} + 6 q^{17} + 12 q^{18} + 3 q^{19} + 30 q^{20} + 6 q^{21} + 5 q^{22} - 4 q^{25} - 15 q^{26} - 14 q^{27} - 42 q^{30} - 3 q^{31} + 48 q^{32} + 8 q^{34} + 3 q^{35} + 35 q^{36} + 18 q^{39} + 21 q^{40} - 24 q^{41} + 27 q^{42} - 18 q^{44} + 9 q^{45} - 17 q^{46} + 12 q^{47} - 22 q^{48} - 13 q^{49} - 12 q^{51} - 12 q^{52} - 18 q^{54} - 6 q^{55} - 6 q^{56} + 22 q^{58} - 3 q^{59} - 12 q^{60} - 8 q^{61} + 66 q^{62} - 36 q^{63} - 98 q^{64} + 24 q^{65} + 10 q^{66} - 15 q^{67} - 57 q^{68} - 36 q^{70} + 15 q^{71} - 16 q^{73} + 6 q^{74} + 13 q^{75} + 21 q^{76} + 3 q^{77} + 33 q^{78} + 42 q^{79} + 42 q^{80} + 8 q^{81} + 60 q^{82} - 42 q^{83} - 42 q^{86} + 15 q^{87} + 84 q^{88} + 63 q^{90} - 69 q^{92} - 48 q^{93} + 54 q^{95} + 102 q^{96} + 3 q^{97}+O(q^{100}) $ 8 * q - 2 * q^3 + 8 * q^4 + 6 * q^5 - 21 * q^6 - 3 * q^7 + 2 * q^9 - 6 * q^10 + q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 20 * q^16 + 6 * q^17 + 12 * q^18 + 3 * q^19 + 30 * q^20 + 6 * q^21 + 5 * q^22 - 4 * q^25 - 15 * q^26 - 14 * q^27 - 42 * q^30 - 3 * q^31 + 48 * q^32 + 8 * q^34 + 3 * q^35 + 35 * q^36 + 18 * q^39 + 21 * q^40 - 24 * q^41 + 27 * q^42 - 18 * q^44 + 9 * q^45 - 17 * q^46 + 12 * q^47 - 22 * q^48 - 13 * q^49 - 12 * q^51 - 12 * q^52 - 18 * q^54 - 6 * q^55 - 6 * q^56 + 22 * q^58 - 3 * q^59 - 12 * q^60 - 8 * q^61 + 66 * q^62 - 36 * q^63 - 98 * q^64 + 24 * q^65 + 10 * q^66 - 15 * q^67 - 57 * q^68 - 36 * q^70 + 15 * q^71 - 16 * q^73 + 6 * q^74 + 13 * q^75 + 21 * q^76 + 3 * q^77 + 33 * q^78 + 42 * q^79 + 42 * q^80 + 8 * q^81 + 60 * q^82 - 42 * q^83 - 42 * q^86 + 15 * q^87 + 84 * q^88 + 63 * q^90 - 69 * q^92 - 48 * q^93 + 54 * q^95 + 102 * q^96 + 3 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	2.15074	+	1.24173i	1.52081	+	0.878038i	0.999699	+	0.0245469i	$0.00781432\pi$
$2$	2.15074	+	1.24173i	1.52081	+	0.878038i	0.521108	+	0.853491i	$0.325519\pi$
$3$	−2.82757			−1.63250			−0.816251	−	0.577698i	$-0.803951\pi$
$3$	−2.82757			−1.63250			−0.816251	+	0.577698i	$0.803951\pi$
$4$	2.08380	+	3.60925i	1.04190	+	1.80463i
$5$	1.17683	−	2.03833i	0.526294	−	0.911569i	−0.473236	−	0.880936i	$-0.656914\pi$
$5$	1.17683	−	2.03833i	0.526294	−	0.911569i	0.999531	−	0.0306331i	$-0.00975233\pi$
$6$	−6.08139	−	3.51109i	−2.48272	−	1.43340i
$7$	−2.32076	−	1.33989i	−0.877165	−	0.506431i	−0.00744223	−	0.999972i	$-0.502369\pi$
$7$	−2.32076	−	1.33989i	−0.877165	−	0.506431i	−0.869723	+	0.493541i	$0.835702\pi$
$8$			5.38317i			1.90324i
$9$	4.99518			1.66506
$10$	5.06212	−	2.92262i	1.60078	−	0.924213i
$11$		−	0.681986i		−	0.205627i	−0.994701	−	0.102813i	$-0.967216\pi$
$11$		−	0.681986i		−	0.205627i	0.994701	−	0.102813i	$-0.0327844\pi$
$12$	−5.89211	−	10.2054i	−1.70090	−	2.94605i
$13$	−2.09062	+	3.62106i	−0.579833	+	1.00430i	0.415665	+	0.909518i	$0.363549\pi$
$13$	−2.09062	+	3.62106i	−0.579833	+	1.00430i	−0.995498	+	0.0947824i	$0.969784\pi$
$14$	−3.32757	−	5.76353i	−0.889332	−	1.54037i
$15$	−3.32757	+	5.76353i	−0.859176	+	1.48814i
$16$	−2.51686	+	4.35933i	−0.629215	+	1.08983i
$17$	−0.990775	+	0.572024i	−0.240298	+	0.138736i	−0.615314	−	0.788282i	$-0.710971\pi$
$17$	−0.990775	+	0.572024i	−0.240298	+	0.138736i	0.375016	+	0.927019i	$0.377637\pi$
$18$	10.7434	+	6.20268i	2.53223	+	1.46199i
$19$	−1.14393	−	1.98134i	−0.262436	−	0.454552i	0.704453	−	0.709751i	$-0.251192\pi$
$19$	−1.14393	−	1.98134i	−0.262436	−	0.454552i	−0.966889	+	0.255199i	$0.917859\pi$
$20$	9.80912			2.19339
$21$	6.56212	+	3.78864i	1.43197	+	0.826750i
$22$	0.846845	−	1.46678i	0.180548	−	0.312718i
$23$			6.21331i			1.29557i	0.761825	+	0.647783i	$0.224304\pi$
$23$			6.21331i			1.29557i	−0.761825	+	0.647783i	$0.775696\pi$
$24$		−	15.2213i		−	3.10704i
$25$	−0.269858	−	0.467407i	−0.0539715	−	0.0934814i
$26$	−8.99277	+	5.19198i	−1.76363	+	1.01823i
$27$	−5.64152			−1.08571
$28$		−	11.1683i		−	2.11061i
$29$	−2.79112	+	1.61146i	−0.518298	+	0.299240i	−0.736238	−	0.676722i	$-0.763400\pi$
$29$	−2.79112	+	1.61146i	−0.518298	+	0.299240i	0.217940	+	0.975962i	$0.430066\pi$
$30$	−14.3135	+	8.26392i	−2.61328	+	1.50878i
$31$	7.38288	−	4.26251i	1.32600	−	0.765569i	0.341326	−	0.939945i	$-0.389124\pi$
$31$	7.38288	−	4.26251i	1.32600	−	0.765569i	0.984679	+	0.174376i	$0.0557908\pi$
$32$	−1.50232	+	0.867363i	−0.265575	+	0.153330i
$33$			1.92837i			0.335686i
$34$	−2.84120			−0.487263
$35$	−5.46228	+	3.15365i	−0.923294	+	0.533064i
$36$	10.4090	+	18.0289i	1.73483	+	3.00481i
$37$		−	9.43622i		−	1.55131i	−0.631160	−	0.775653i	$-0.717421\pi$
$37$		−	9.43622i		−	1.55131i	0.631160	−	0.775653i	$-0.282579\pi$
$38$		−	5.68182i		−	0.921713i
$39$	5.91138	−	10.2388i	0.946578	−	1.63952i
$40$	10.9727	+	6.33508i	1.73493	+	1.00166i
$41$	−0.405830			−0.0633800			−0.0316900	−	0.999498i	$-0.510089\pi$
$41$	−0.405830			−0.0633800			−0.0316900	+	0.999498i	$0.510089\pi$
$42$	9.40897	+	16.2968i	1.45184	+	2.51465i
$43$	−1.28023	−	0.739138i	−0.195232	−	0.112718i	0.399197	−	0.916865i	$-0.369289\pi$
$43$	−1.28023	−	0.739138i	−0.195232	−	0.112718i	−0.594430	+	0.804148i	$0.702622\pi$
$44$	2.46146	−	1.42112i	0.371079	−	0.214243i
$45$	5.87848	−	10.1818i	0.876312	−	1.51782i
$46$	−7.71528	+	13.3633i	−1.13756	+	1.97030i
$47$	4.73455	+	8.20048i	0.690605	+	1.19616i	0.971640	+	0.236465i	$0.0759889\pi$
$47$	4.73455	+	8.20048i	0.690605	+	1.19616i	−0.281035	+	0.959697i	$0.590678\pi$
$48$	7.11661	−	12.3263i	1.02719	−	1.77915i
$49$	0.0906174	+	0.156954i	0.0129453	+	0.0224220i
$50$		−	1.34036i		−	0.189556i
$51$	2.80149	−	1.61744i	0.392287	−	0.226487i
$52$	−17.4257			−2.41651
$53$		−	5.68277i		−	0.780588i	−0.920690	−	0.390294i	$-0.872373\pi$
$53$		−	5.68277i		−	0.780588i	0.920690	−	0.390294i	$-0.127627\pi$
$54$	−12.1335	−	7.00526i	−1.65116	−	0.953295i
$55$	−1.39011	−	0.802582i	−0.187443	−	0.108220i
$56$	7.21287	−	12.4931i	0.963860	−	1.66945i
$57$	3.23455	+	5.60240i	0.428426	+	0.742056i
$58$	−8.00399			−1.05098
$59$	1.80117	+	1.03990i	0.234492	+	0.135384i	0.612643	−	0.790360i	$-0.290107\pi$
$59$	1.80117	+	1.03990i	0.234492	+	0.135384i	−0.378151	+	0.925744i	$0.623440\pi$
$60$	−27.7360			−3.58071
$61$	−7.68238	−	1.40751i	−0.983628	−	0.180213i
$61$	−7.68238	−	1.40751i	−0.983628	−	0.180213i
$62$	21.1716			2.68880
$63$	−11.5926	−	6.69300i	−1.46053	−	0.843238i
$64$	5.75930			0.719913
$65$	4.92060	+	8.52273i	0.610326	+	1.05711i
$66$	−2.39452	+	4.14743i	−0.294745	+	0.510513i
$67$	−7.07217	−	4.08312i	−0.864003	−	0.498832i	0.00134794	−	0.999999i	$-0.499571\pi$
$67$	−7.07217	−	4.08312i	−0.864003	−	0.498832i	−0.865351	+	0.501167i	$0.832904\pi$
$68$	−4.12916	−	2.38397i	−0.500734	−	0.289099i
$69$		−	17.5686i		−	2.11501i
$70$	−15.6640			−1.87220
$71$	−2.40133	+	1.38641i	−0.284986	+	0.164537i	−0.635678	−	0.771954i	$-0.719280\pi$
$71$	−2.40133	+	1.38641i	−0.284986	+	0.164537i	0.350693	+	0.936491i	$0.385946\pi$
$72$			26.8899i			3.16901i
$73$	2.94187	+	5.09546i	0.344320	+	0.596379i	0.985230	−	0.171237i	$-0.0547763\pi$
$73$	2.94187	+	5.09546i	0.344320	+	0.596379i	−0.640910	+	0.767616i	$0.721443\pi$
$74$	11.7173	−	20.2949i	1.36211	−	2.35924i
$75$	0.763043	+	1.32163i	0.0881086	+	0.152609i
$76$	4.76745	−	8.25746i	0.546864	−	0.947196i
$77$	−0.913787	+	1.58273i	−0.104136	+	0.180368i
$78$	25.4277	−	14.6807i	2.87912	−	1.66226i
$79$	8.50114	+	4.90814i	0.956453	+	0.552209i	0.895080	−	0.445906i	$-0.147119\pi$
$79$	8.50114	+	4.90814i	0.956453	+	0.552209i	0.0613736	+	0.998115i	$0.480452\pi$
$80$	5.92383	+	10.2604i	0.662305	+	1.14715i
$81$	0.966280			0.107364
$82$	−0.872837	−	0.503933i	−0.0963887	−	0.0556501i
$83$	−5.67683	+	9.83256i	−0.623113	+	1.07926i	0.365789	+	0.930698i	$0.380799\pi$
$83$	−5.67683	+	9.83256i	−0.623113	+	1.07926i	−0.988903	+	0.148566i	$0.952534\pi$
$84$			31.5791i			3.44557i
$85$			2.69270i			0.292064i
$86$	−1.83563	−	3.17940i	−0.197941	−	0.342843i
$87$	7.89211	−	4.55651i	0.846123	−	0.488509i
$88$	3.67125			0.391357
$89$			5.38412i			0.570716i	0.958421	+	0.285358i	$0.0921124\pi$
$89$			5.38412i			0.570716i	−0.958421	+	0.285358i	$0.907888\pi$
$90$	25.2862	−	14.5990i	2.66540	−	1.53887i
$91$	9.70364	−	5.60240i	1.01722	−	0.587291i
$92$	−22.4254	+	12.9473i	−2.33801	+	1.34985i
$93$	−20.8757	+	12.0526i	−2.16470	+	1.24979i
$94$			23.5162i			2.42551i
$95$	−5.38484			−0.552473
$96$	4.24791	−	2.45253i	0.433551	−	0.250311i
$97$	−3.93505	−	6.81571i	−0.399544	−	0.692031i	0.594126	−	0.804372i	$-0.297498\pi$
$97$	−3.93505	−	6.81571i	−0.399544	−	0.692031i	−0.993670	+	0.112342i	$0.964165\pi$
$98$			0.450091i			0.0454660i
$99$		−	3.40664i		−	0.342381i
$100$	1.12466	−	1.94797i	0.112466	−	0.194797i
$101$	7.76177	+	4.48126i	0.772325	+	0.445902i	0.833704	−	0.552212i	$-0.186216\pi$
$101$	7.76177	+	4.48126i	0.772325	+	0.445902i	−0.0613781	+	0.998115i	$0.519550\pi$
$102$	8.03372			0.795457
$103$	−7.38855	−	12.7974i	−0.728016	−	1.26096i	−0.957721	−	0.287700i	$-0.907109\pi$
$103$	−7.38855	−	12.7974i	−0.728016	−	1.26096i	0.229705	−	0.973260i	$-0.426224\pi$
$104$	−19.4928	−	11.2542i	−1.91142	−	1.10356i
$105$	15.4450	−	8.91718i	1.50728	−	0.870227i
$106$	7.05648	−	12.2222i	0.685386	−	1.18712i
$107$	7.99036	−	13.8397i	0.772457	−	1.33794i	−0.163755	−	0.986501i	$-0.552361\pi$
$107$	7.99036	−	13.8397i	0.772457	−	1.33794i	0.936213	−	0.351434i	$-0.114306\pi$
$108$	−11.7558	−	20.3617i	−1.13120	−	1.95930i
$109$	−3.92060	+	6.79068i	−0.375526	+	0.650429i	−0.990406	−	0.138191i	$-0.955871\pi$
$109$	−3.92060	+	6.79068i	−0.375526	+	0.650429i	0.614880	+	0.788621i	$0.289204\pi$
$110$	−1.99318	−	3.45230i	−0.190043	−	0.329164i
$111$			26.6816i			2.53251i
$112$	11.6821	−	6.74464i	1.10385	−	0.637308i
$113$	−12.5982			−1.18514			−0.592568	−	0.805521i	$-0.701886\pi$
$113$	−12.5982			−1.18514			−0.592568	+	0.805521i	$0.701886\pi$
$114$			16.0658i			1.50470i
$115$	12.6648	+	7.31201i	1.18100	+	0.681849i
$116$	−11.6323	−	6.71591i	−1.08003	−	0.623556i
$117$	−10.4430	+	18.0878i	−0.965457	+	1.67222i
$118$	2.58257	+	4.47314i	0.237745	+	0.411786i
$119$	3.06580			0.281041
$120$	−31.0261	−	17.9129i	−2.83228	−	1.63522i
$121$	10.5349			0.957718
$122$	−14.7751	−	12.5667i	−1.33767	−	1.13773i
$123$	1.14752			0.103468
$124$	30.7689	+	17.7645i	2.76313	+	1.59529i
$125$	10.4980			0.938969
$126$	−16.6218	−	28.7899i	−1.48079	−	2.56480i
$127$	1.56013	−	2.70222i	0.138439	−	0.239783i	−0.788467	−	0.615077i	$-0.789125\pi$
$127$	1.56013	−	2.70222i	0.138439	−	0.239783i	0.926906	+	0.375294i	$0.122458\pi$
$128$	15.3914	+	8.88625i	1.36042	+	0.785441i
$129$	3.61993	+	2.08997i	0.318717	+	0.184011i
$130$			24.4403i			2.14356i
$131$	−10.6078			−0.926808			−0.463404	−	0.886147i	$-0.653372\pi$
$131$	−10.6078			−0.926808			−0.463404	+	0.886147i	$0.653372\pi$
$132$	−6.95996	+	4.01834i	−0.605787	+	0.349751i
$133$			6.13097i			0.531622i
$134$	−10.1403	−	17.5635i	−0.875987	−	1.51725i
$135$	−6.63911	+	11.4993i	−0.571404	+	0.989700i
$136$	−3.07930	−	5.33351i	−0.264048	−	0.457345i
$137$	−3.80390	+	6.58855i	−0.324989	+	0.562898i	−0.981510	−	0.191410i	$-0.938694\pi$
$137$	−3.80390	+	6.58855i	−0.324989	+	0.562898i	0.656521	+	0.754308i	$0.272027\pi$
$138$	21.8155	−	37.7856i	1.85706	−	3.21652i
$139$	−12.7839	+	7.38080i	−1.08432	+	0.626031i	−0.932058	−	0.362309i	$-0.881989\pi$
$139$	−12.7839	+	7.38080i	−1.08432	+	0.626031i	−0.152260	+	0.988340i	$0.548655\pi$
$140$	−22.7646	−	13.1432i	−1.92396	−	1.11080i
$141$	−13.3873	−	23.1875i	−1.12741	−	1.95274i
$142$	−6.88620			−0.577877
$143$	2.46951	+	1.42577i	0.206511	+	0.119229i
$144$	−12.5722	+	21.7756i	−1.04768	+	1.81464i
$145$			7.58564i			0.629953i
$146$			14.6121i			1.20930i
$147$	−0.256228	−	0.443799i	−0.0211333	−	0.0366039i
$148$	34.0577	−	19.6632i	2.79953	−	1.61631i
$149$	−2.93420			−0.240379			−0.120190	−	0.992751i	$-0.538350\pi$
$149$	−2.93420			−0.240379			−0.120190	+	0.992751i	$0.538350\pi$
$150$			3.78998i			0.309451i
$151$	11.2313	−	6.48440i	0.913992	−	0.527693i	0.0322783	−	0.999479i	$-0.489724\pi$
$151$	11.2313	−	6.48440i	0.913992	−	0.527693i	0.881713	+	0.471786i	$0.156390\pi$
$152$	10.6659	−	6.15797i	0.865120	−	0.499478i
$153$	−4.94910	+	2.85736i	−0.400111	+	0.231004i
$154$	−3.93065	+	2.26936i	−0.316741	+	0.182870i
$155$		−	20.0650i		−	1.61166i
$156$	49.2726			3.94496
$157$	15.9321	−	9.19843i	1.27152	−	0.734114i	0.296249	−	0.955111i	$-0.404264\pi$
$157$	15.9321	−	9.19843i	1.27152	−	0.734114i	0.975275	+	0.220996i	$0.0709309\pi$
$158$	12.1892	+	21.1123i	0.969720	+	1.67960i
$159$			16.0685i			1.27431i
$160$			4.08296i			0.322786i
$161$	8.32516	−	14.4196i	0.656115	−	1.13642i
$162$	2.07822	+	1.19986i	0.163281	+	0.0942701i
$163$	−6.08817			−0.476863			−0.238431	−	0.971159i	$-0.576633\pi$
$163$	−6.08817			−0.476863			−0.238431	+	0.971159i	$0.576633\pi$
$164$	−0.845670	−	1.46474i	−0.0660357	−	0.114377i
$165$	3.93065	+	2.26936i	0.306000	+	0.176669i
$166$	−24.4188	+	14.0982i	−1.89527	+	1.09423i
$167$	−7.15274	+	12.3889i	−0.553496	+	0.958683i	0.444523	+	0.895767i	$0.353373\pi$
$167$	−7.15274	+	12.3889i	−0.553496	+	0.958683i	−0.998019	+	0.0629152i	$0.979960\pi$
$168$	−20.3949	+	35.3250i	−1.57350	+	2.72539i
$169$	−2.24136	−	3.88215i	−0.172412	−	0.298627i
$170$	−3.34362	+	5.79131i	−0.256444	+	0.444173i
$171$	−5.71413	−	9.89717i	−0.436971	−	0.756856i
$172$		−	6.16087i		−	0.469762i
$173$	3.95027	−	2.28069i	0.300334	−	0.173398i	−0.342259	−	0.939606i	$-0.611192\pi$
$173$	3.95027	−	2.28069i	0.300334	−	0.173398i	0.642593	+	0.766208i	$0.277859\pi$
$174$	22.6319			1.71572
$175$			1.44632i			0.109331i
$176$	2.97300	+	1.71646i	0.224098	+	0.129383i
$177$	−5.09293	−	2.94041i	−0.382808	−	0.221015i
$178$	−6.68564	+	11.5799i	−0.501110	+	0.867948i
$179$	−9.86247	−	17.0823i	−0.737156	−	1.27679i	−0.953771	−	0.300534i	$-0.902835\pi$
$179$	−9.86247	−	17.0823i	−0.737156	−	1.27679i	0.216616	−	0.976257i	$-0.430498\pi$
$180$	48.9983			3.65212
$181$	−8.52159	−	4.91994i	−0.633405	−	0.365696i	0.148665	−	0.988888i	$-0.452502\pi$
$181$	−8.52159	−	4.91994i	−0.633405	−	0.365696i	−0.782069	+	0.623191i	$0.785836\pi$
$182$	27.8267			2.06266
$183$	21.7225	+	3.97984i	1.60577	+	0.294198i
$184$	−33.4473			−2.46577
$185$	−19.2341	−	11.1048i	−1.41412	−	0.816443i
$186$	−59.8643			−4.38946
$187$	0.390113	+	0.675695i	0.0285279	+	0.0494117i
$188$	−19.7317	+	34.1763i	−1.43908	+	2.49257i
$189$	13.0926	+	7.55902i	0.952347	+	0.549838i
$190$	−11.5814	−	6.68654i	−0.840205	−	0.485093i
$191$			12.0748i			0.873699i	0.899535	+	0.436849i	$0.143906\pi$
$191$			12.0748i			0.873699i	−0.899535	+	0.436849i	$0.856094\pi$
$192$	−16.2849			−1.17526
$193$	−4.82913	+	2.78810i	−0.347609	+	0.200692i	−0.663631	−	0.748060i	$-0.730986\pi$
$193$	−4.82913	+	2.78810i	−0.347609	+	0.200692i	0.316023	+	0.948752i	$0.397652\pi$
$194$		−	19.5451i		−	1.40326i
$195$	−13.9134	−	24.0987i	−0.996357	−	1.72574i
$196$	−0.377658	+	0.654122i	−0.0269755	+	0.0467230i
$197$	7.79908	+	13.5084i	0.555661	+	0.962434i	0.997852	+	0.0655126i	$0.0208682\pi$
$197$	7.79908	+	13.5084i	0.555661	+	0.962434i	−0.442190	+	0.896921i	$0.645798\pi$
$198$	4.23014	−	7.32682i	0.300623	−	0.520695i
$199$	6.07217	−	10.5173i	0.430444	−	0.745552i	−0.566467	−	0.824084i	$-0.691690\pi$
$199$	6.07217	−	10.5173i	0.430444	−	0.745552i	0.996912	+	0.0785327i	$0.0250235\pi$
$200$	2.51613	−	1.45269i	0.177917	−	0.102721i
$201$	19.9971	+	11.5453i	1.41049	+	0.814344i
$202$	11.1291	+	19.2761i	0.783038	+	1.35626i
$203$	8.63670			0.606177
$204$	11.6755	+	6.74085i	0.817449	+	0.471954i
$205$	−0.477593	+	0.827215i	−0.0333565	+	0.0577752i
$206$		−	36.6985i		−	2.55690i
$207$			31.0366i			2.15719i
$208$	−10.5236	−	18.2274i	−0.729679	−	1.26384i
$209$	−1.35125	+	0.780144i	−0.0934679	+	0.0539637i
$210$	44.2910			3.05637
$211$			1.79046i			0.123260i	0.998099	+	0.0616300i	$0.0196299\pi$
$211$			1.79046i			0.123260i	−0.998099	+	0.0616300i	$0.980370\pi$
$212$	20.5105	−	11.8418i	1.40867	−	0.813296i
$213$	6.78995	−	3.92018i	0.465240	−	0.268606i
$214$	34.3704	−	19.8438i	2.34952	−	1.35649i
$215$	−3.01321	+	1.73968i	−0.205500	+	0.118645i
$216$		−	30.3693i		−	2.06637i
$217$	−22.8452			−1.55083
$218$	−16.8644	+	9.73668i	−1.14220	+	0.659451i
$219$	−8.31835	−	14.4078i	−0.562102	−	0.973589i
$220$		−	6.68969i		−	0.451019i
$221$		−	4.78353i		−	0.321775i
$222$	−33.1315	+	57.3854i	−2.22364	+	3.85145i
$223$	13.4238	+	7.75022i	0.898922	+	0.518993i	0.876850	−	0.480763i	$-0.159640\pi$
$223$	13.4238	+	7.75022i	0.898922	+	0.518993i	0.0220719	+	0.999756i	$0.492974\pi$
$224$	4.64869			0.310604
$225$	−1.34799	−	2.33478i	−0.0898658	−	0.155652i
$226$	−27.0954	−	15.6436i	−1.80236	−	1.04059i
$227$	10.6755	−	6.16348i	0.708556	−	0.409085i	−0.101970	−	0.994787i	$-0.532515\pi$
$227$	10.6755	−	6.16348i	0.708556	−	0.409085i	0.810526	+	0.585703i	$0.199181\pi$
$228$	−13.4803	+	23.3486i	−0.892756	+	1.54630i
$229$	−1.98282	+	3.43434i	−0.131028	+	0.226948i	−0.924073	−	0.382216i	$-0.875161\pi$
$229$	−1.98282	+	3.43434i	−0.131028	+	0.226948i	0.793045	+	0.609163i	$0.208495\pi$
$230$	18.1591	+	31.4526i	1.19738	+	2.07392i
$231$	2.58380	−	4.47528i	0.170002	−	0.294452i
$232$	−8.67474	−	15.0251i	−0.569525	−	0.986446i
$233$		−	20.5351i		−	1.34530i	−0.739962	−	0.672649i	$-0.765157\pi$
$233$		−	20.5351i		−	1.34530i	0.739962	−	0.672649i	$-0.234843\pi$
$234$	−44.9205	+	25.9349i	−2.93654	+	1.69541i
$235$	22.2870			1.45385
$236$			8.66782i			0.564227i
$237$	−24.0376	−	13.8781i	−1.56141	−	0.901481i
$238$	6.59375	+	3.80691i	0.427410	+	0.246765i
$239$	3.64478	−	6.31295i	0.235761	−	0.408351i	−0.723732	−	0.690081i	$-0.757575\pi$
$239$	3.64478	−	6.31295i	0.235761	−	0.408351i	0.959494	+	0.281730i	$0.0909083\pi$
$240$	−16.7501	−	29.0120i	−1.08121	−	1.87272i
$241$	−21.6158			−1.39239			−0.696197	−	0.717850i	$-0.745126\pi$
$241$	−21.6158			−1.39239			−0.696197	+	0.717850i	$0.745126\pi$
$242$	22.6579	+	13.0815i	1.45650	+	0.840912i
$243$	14.1923			0.910438
$244$	−10.9285	−	30.6606i	−0.699626	−	1.96284i
$245$	0.426565			0.0272522
$246$	2.46801	+	1.42491i	0.157355	+	0.0908488i
$247$	9.56608			0.608675
$248$	22.9458	+	39.7433i	1.45706	+	2.52370i
$249$	16.0517	−	27.8023i	1.01723	−	1.76190i
$250$	22.5785	+	13.0357i	1.42799	+	0.824450i
$251$	6.74221	+	3.89262i	0.425565	+	0.245700i	0.697455	−	0.716628i	$-0.254316\pi$
$251$	6.74221	+	3.89262i	0.425565	+	0.245700i	−0.271891	+	0.962328i	$0.587649\pi$
$252$		−	55.7875i		−	3.51428i
$253$	4.23739			0.266403
$254$	6.71087	−	3.87452i	0.421078	−	0.243109i
$255$		−	7.61381i		−	0.476795i
$256$	16.3094	+	28.2487i	1.01934	+	1.76554i
$257$	7.87166	−	13.6341i	0.491021	−	0.850473i	−0.508926	−	0.860810i	$-0.669957\pi$
$257$	7.87166	−	13.6341i	0.491021	−	0.850473i	0.999947	+	0.0103375i	$0.00329057\pi$
$258$	5.19037	+	8.98998i	0.323138	+	0.559692i
$259$	−12.6435	+	21.8992i	−0.785630	+	1.36075i
$260$	−20.5071	+	35.5194i	−1.27180	+	2.20282i
$261$	−13.9422	+	8.04951i	−0.862998	+	0.498252i
$262$	−22.8147	−	13.1721i	−1.40950	−	0.813772i
$263$	1.75864	+	3.04605i	0.108442	+	0.187827i	0.915139	−	0.403138i	$-0.132080\pi$
$263$	1.75864	+	3.04605i	0.108442	+	0.187827i	−0.806697	+	0.590965i	$0.798747\pi$
$264$	−10.3807			−0.638890
$265$	−11.5834	−	6.68765i	−0.711560	−	0.410819i
$266$	−7.61302	+	13.1861i	−0.466784	+	0.808494i
$267$		−	15.2240i		−	0.931694i
$268$		−	34.0336i		−	2.07894i
$269$	8.57657	+	14.8551i	0.522923	+	0.905729i	0.999644	+	0.0266744i	$0.00849174\pi$
$269$	8.57657	+	14.8551i	0.522923	+	0.905729i	−0.476721	+	0.879054i	$0.658175\pi$
$270$	−28.5581	+	16.4880i	−1.73799	+	1.00343i
$271$	−13.8020			−0.838413			−0.419206	−	0.907891i	$-0.637692\pi$
$271$	−13.8020			−0.838413			−0.419206	+	0.907891i	$0.637692\pi$
$272$		−	5.75882i		−	0.349180i
$273$	−27.4378	+	15.8412i	−1.66061	+	0.958753i
$274$	−16.3624	+	9.44686i	−0.988491	+	0.570706i
$275$	−0.318765	+	0.184039i	−0.0192223	+	0.0110980i
$276$	63.4095	−	36.6095i	3.81681	−	2.20363i
$277$			31.8003i			1.91070i	0.295481	+	0.955349i	$0.404520\pi$
$277$			31.8003i			1.91070i	−0.295481	+	0.955349i	$0.595480\pi$
$278$	−36.6599			−2.19872
$279$	36.8788	−	21.2920i	2.20788	−	1.27472i
$280$	−16.9766	−	29.4044i	−1.01455	−	1.75725i
$281$			12.5688i			0.749790i	0.927067	+	0.374895i	$0.122321\pi$
$281$			12.5688i			0.749790i	−0.927067	+	0.374895i	$0.877679\pi$
$282$		−	66.4938i		−	3.95965i
$283$	0.478735	−	0.829194i	0.0284579	−	0.0492905i	−0.851446	−	0.524443i	$-0.824274\pi$
$283$	0.478735	−	0.829194i	0.0284579	−	0.0492905i	0.879904	+	0.475152i	$0.157607\pi$
$284$	−10.0078	−	5.77801i	−0.593854	−	0.342862i
$285$	15.2260			0.901913
$286$	3.54086	+	6.13294i	0.209375	+	0.362649i
$287$	0.941834	+	0.543768i	0.0555947	+	0.0320976i
$288$	−7.50434	+	4.33264i	−0.442198	+	0.255303i
$289$	−7.84558	+	13.5889i	−0.461505	+	0.799349i
$290$	−9.41933	+	16.3148i	−0.553122	+	0.958036i
$291$	11.1267	+	19.2719i	0.652256	+	1.12974i
$292$	−12.2605	+	21.2359i	−0.717494	+	1.24274i
$293$	−1.12551	−	1.94944i	−0.0657531	−	0.113888i	0.831275	−	0.555862i	$-0.187612\pi$
$293$	−1.12551	−	1.94944i	−0.0657531	−	0.113888i	−0.897028	+	0.441974i	$0.854278\pi$
$294$		−	1.27266i		−	0.0742233i
$295$	4.23933	−	2.44758i	0.246824	−	0.142504i
$296$	50.7968			2.95251
$297$			3.84744i			0.223251i
$298$	−6.31072	−	3.64349i	−0.365570	−	0.211062i
$299$	−22.4988	−	12.9897i	−1.30114	−	0.751212i
$300$	−3.18006	+	5.50803i	−0.183601	+	0.318006i
$301$	1.98073	+	3.43072i	0.114167	+	0.197744i
$302$	32.2076			1.85334
$303$	−21.9470	−	12.6711i	−1.26082	−	0.727936i
$304$	11.5164			0.660513
$305$	−11.9098	+	14.0028i	−0.681954	+	0.801799i
$306$	−14.1923			−0.811321
$307$	5.74189	+	3.31508i	0.327707	+	0.189202i	0.654823	−	0.755783i	$-0.272743\pi$
$307$	5.74189	+	3.31508i	0.327707	+	0.189202i	−0.327116	+	0.944984i	$0.606077\pi$
$308$	−7.61661			−0.433997
$309$	20.8917	+	36.1855i	1.18849	+	2.05852i
$310$	24.9154	−	43.1547i	1.41510	−	2.45102i
$311$	13.4637	+	7.77330i	0.763459	+	0.440783i	0.830536	−	0.556965i	$-0.188034\pi$
$311$	13.4637	+	7.77330i	0.763459	+	0.440783i	−0.0670773	+	0.997748i	$0.521367\pi$
$312$	55.1173	+	31.8220i	3.12040	+	1.80156i
$313$		−	10.4570i		−	0.591065i	−0.955333	−	0.295532i	$-0.904503\pi$
$313$		−	10.4570i		−	0.591065i	0.955333	−	0.295532i	$-0.0954971\pi$
$314$	45.6880			2.57832
$315$	−27.2851	+	15.7530i	−1.53734	+	0.887583i
$316$			40.9103i			2.30139i
$317$	14.9086	+	25.8224i	0.837348	+	1.45033i	0.892105	+	0.451829i	$0.149228\pi$
$317$	14.9086	+	25.8224i	0.837348	+	1.45033i	−0.0547569	+	0.998500i	$0.517438\pi$
$318$	−19.9527	+	34.5591i	−1.11889	+	1.93798i
$319$	1.09899	+	1.90351i	0.0615316	+	0.106576i
$320$	6.77772	−	11.7394i	0.378886	−	0.656250i
$321$	−22.5933	+	39.1328i	−1.26104	+	2.18418i
$322$	35.8106	−	20.6753i	1.99565	−	1.15219i
$323$	2.26675	+	1.30871i	0.126126	+	0.0728186i
$324$	2.01354	+	3.48755i	0.111863	+	0.193753i
$325$	2.25668			0.125178
$326$	−13.0941	−	7.55989i	−0.725216	−	0.418703i
$327$	11.0858	−	19.2012i	0.613046	−	1.06183i
$328$		−	2.18465i		−	0.120627i
$329$		−	25.3751i		−	1.39898i
$330$	5.63588	+	9.76163i	0.310245	+	0.537360i
$331$	9.62919	−	5.55942i	0.529268	−	0.305573i	−0.211450	−	0.977389i	$-0.567819\pi$
$331$	9.62919	−	5.55942i	0.529268	−	0.305573i	0.740718	+	0.671816i	$0.234485\pi$
$332$	−47.3176			−2.59689
$333$		−	47.1356i		−	2.58302i
$334$	−30.7674	+	17.7636i	−1.68352	+	0.971980i
$335$	−16.6455	+	9.61027i	−0.909440	+	0.525065i
$336$	−33.0319	+	19.0710i	−1.80204	+	1.04041i
$337$	22.6659	−	13.0862i	1.23469	−	0.712849i	0.266687	−	0.963783i	$-0.414071\pi$
$337$	22.6659	−	13.0862i	1.23469	−	0.712849i	0.968004	+	0.250934i	$0.0807376\pi$
$338$		−	11.1327i		−	0.605539i
$339$	35.6222			1.93473
$340$	−9.71863	+	5.61106i	−0.527067	+	0.304302i
$341$	−2.90697	−	5.03502i	−0.157421	−	0.272662i
$342$		−	28.3817i		−	1.53471i
$343$			18.2728i			0.986639i
$344$	3.97891	−	6.89167i	0.214528	−	0.371574i
$345$	−35.8106	−	20.6753i	−1.92798	−	1.11312i
$346$	11.3280			0.608999
$347$	−8.14866	−	14.1139i	−0.437443	−	0.757673i	0.560049	−	0.828460i	$-0.310782\pi$
$347$	−8.14866	−	14.1139i	−0.437443	−	0.757673i	−0.997491	+	0.0707865i	$0.977449\pi$
$348$	32.8912	+	18.9897i	1.76315	+	1.01796i
$349$	0.111915	−	0.0646141i	0.00599067	−	0.00345871i	−0.497002	−	0.867750i	$-0.665566\pi$
$349$	0.111915	−	0.0646141i	0.00599067	−	0.00345871i	0.502992	+	0.864291i	$0.332232\pi$
$350$	−1.79594	+	3.11066i	−0.0959972	+	0.166272i
$351$	11.7943	−	20.4283i	0.629531	−	1.09038i
$352$	0.591530	+	1.02456i	0.0315286	+	0.0546092i
$353$	0.0108972	−	0.0188745i	0.000579999	−	0.00100459i	−0.865735	−	0.500502i	$-0.833149\pi$
$353$	0.0108972	−	0.0188745i	0.000579999	−	0.00100459i	0.866315	+	0.499498i	$0.166482\pi$
$354$	−7.30240	−	12.6481i	−0.388118	−	0.672241i
$355$			6.52628i			0.346379i
$356$	−19.4326	+	11.2194i	−1.02993	+	0.594629i
$357$	−8.66878			−0.458800
$358$		−	48.9862i		−	2.58900i
$359$	−7.48187	−	4.31966i	−0.394878	−	0.227983i	0.289394	−	0.957210i	$-0.406546\pi$
$359$	−7.48187	−	4.31966i	−0.394878	−	0.227983i	−0.684272	+	0.729227i	$0.739880\pi$
$360$	54.8105	+	31.6449i	2.88877	+	1.66783i
$361$	6.88285	−	11.9214i	0.362255	−	0.627444i
$362$	−12.2185	−	21.1631i	−0.642190	−	1.11231i
$363$	−29.7882			−1.56348
$364$	40.4409	+	23.3486i	2.11968	+	1.22380i
$365$	13.8483			0.724854
$366$	41.7777	+	35.5332i	2.18375	+	1.85735i
$367$	−4.38175			−0.228726			−0.114363	−	0.993439i	$-0.536483\pi$
$367$	−4.38175			−0.228726			−0.114363	+	0.993439i	$0.536483\pi$
$368$	−27.0859	−	15.6380i	−1.41195	−	0.815189i
$369$	−2.02719			−0.105532
$370$	−27.5785	−	47.7673i	−1.43374	−	2.48330i
$371$	−7.61429	+	13.1883i	−0.395314	+	0.684705i
$372$	−87.0015	−	50.2303i	−4.51082	−	2.60432i
$373$	−24.4188	−	14.0982i	−1.26436	−	0.729978i	−0.290444	−	0.956892i	$-0.593803\pi$
$373$	−24.4188	−	14.0982i	−1.26436	−	0.729978i	−0.973915	+	0.226914i	$0.927136\pi$
$374$			1.93766i			0.100194i
$375$	−29.6839			−1.53287
$376$	−44.1446	+	25.4869i	−2.27658	+	1.31439i
$377$		−	13.4757i		−	0.694036i
$378$	18.7726	+	32.5151i	0.965557	+	1.67239i
$379$	−10.2537	+	17.7600i	−0.526698	+	0.912268i	0.472818	+	0.881160i	$0.343237\pi$
$379$	−10.2537	+	17.7600i	−0.526698	+	0.912268i	−0.999516	+	0.0311081i	$0.990096\pi$
$380$	−11.2210	−	19.4353i	−0.575623	−	0.997008i
$381$	−4.41138	+	7.64073i	−0.226002	+	0.391446i
$382$	−14.9936	+	25.9697i	−0.767140	+	1.32873i
$383$	8.23103	−	4.75219i	0.420586	−	0.242825i	−0.274742	−	0.961518i	$-0.588592\pi$
$383$	8.23103	−	4.75219i	0.420586	−	0.242825i	0.695328	+	0.718693i	$0.255259\pi$
$384$	−43.5204	−	25.1265i	−2.22089	−	1.28223i
$385$	2.15074	+	3.72520i	0.109612	+	0.189854i
$386$	−13.8483			−0.704860
$387$	−6.39495	−	3.69213i	−0.325074	−	0.187681i
$388$	16.3997	−	28.4052i	0.832571	−	1.44205i
$389$			15.4097i			0.781305i	0.920538	+	0.390652i	$0.127751\pi$
$389$			15.4097i			0.781305i	−0.920538	+	0.390652i	$0.872249\pi$
$390$		−	69.1068i		−	3.49936i
$391$	−3.55416	−	6.15599i	−0.179742	−	0.311322i
$392$	−0.844910	+	0.487809i	−0.0426744	+	0.0246381i
$393$	29.9943			1.51301
$394$			38.7375i			1.95157i
$395$	20.0088	−	11.5521i	1.00675	−	0.581248i
$396$	12.2954	−	7.09877i	0.617869	−	0.356727i
$397$	1.99110	−	1.14956i	0.0999303	−	0.0576948i	−0.449202	−	0.893430i	$-0.648292\pi$
$397$	1.99110	−	1.14956i	0.0999303	−	0.0576948i	0.549132	+	0.835735i	$0.314958\pi$
$398$	26.1194	−	15.0800i	1.30925	−	0.755893i
$399$		−	17.3358i		−	0.867874i
$400$	2.71677			0.135839
$401$	−2.12114	+	1.22464i	−0.105925	+	0.0611556i	−0.552026	−	0.833827i	$-0.686145\pi$
$401$	−2.12114	+	1.22464i	−0.105925	+	0.0611556i	0.446102	+	0.894982i	$0.352812\pi$
$402$	28.6724	+	49.6621i	1.43005	+	2.47692i
$403$			35.6451i			1.77561i
$404$			37.3523i			1.85834i
$405$	1.13715	−	1.96960i	0.0565053	−	0.0978701i
$406$	18.5753	+	10.7245i	0.921878	+	0.532247i
$407$	−6.43537			−0.318990
$408$	8.70696	+	15.0809i	0.431059	+	0.746616i
$409$	−9.64433	−	5.56816i	−0.476882	−	0.275328i	0.242234	−	0.970218i	$-0.422120\pi$
$409$	−9.64433	−	5.56816i	−0.476882	−	0.275328i	−0.719116	+	0.694890i	$0.755453\pi$
$410$	−2.05436	+	1.18609i	−0.101458	+	0.0585766i
$411$	10.7558	−	18.6296i	0.530545	−	0.918931i
$412$	30.7926	−	53.3343i	1.51704	−	2.62759i
$413$	−2.78672	−	4.82674i	−0.137125	−	0.237508i
$414$	−38.5392	+	66.7518i	−1.89410	+	3.28067i
$415$	13.3613	+	23.1425i	0.655882	+	1.13602i
$416$		−	7.25330i		−	0.355622i
$417$	36.1475	−	20.8698i	1.77015	−	1.02200i
$418$	−3.87492			−0.189529
$419$			34.9761i			1.70870i	0.519701	+	0.854348i	$0.326043\pi$
$419$			34.9761i			1.70870i	−0.519701	+	0.854348i	$0.673957\pi$
$420$	64.3687	+	37.1633i	3.14087	+	1.81338i
$421$	3.80755	+	2.19829i	0.185568	+	0.107138i	0.589906	−	0.807472i	$-0.299165\pi$
$421$	3.80755	+	2.19829i	0.185568	+	0.107138i	−0.404338	+	0.914610i	$0.632498\pi$
$422$	−2.22327	+	3.85081i	−0.108227	+	0.187455i
$423$	23.6499	+	40.9629i	1.14990	+	1.99168i
$424$	30.5913			1.48565
$425$	0.534736	+	0.308730i	0.0259385	+	0.0149756i
$426$	19.4713			0.943386
$427$	15.9430	+	13.5600i	0.771538	+	0.656216i
$428$	66.6013			3.21930
$429$	−6.98272	−	4.03148i	−0.337129	−	0.194642i
$430$	−8.64087			−0.416700
$431$	−0.234547	−	0.406248i	−0.0112977	−	0.0195683i	0.860321	−	0.509752i	$-0.170263\pi$
$431$	−0.234547	−	0.406248i	−0.0112977	−	0.0195683i	−0.871619	+	0.490184i	$0.836930\pi$
$432$	14.1989	−	24.5932i	0.683146	−	1.18324i
$433$	−11.3432	−	6.54902i	−0.545121	−	0.314726i	0.202031	−	0.979379i	$-0.435246\pi$
$433$	−11.3432	−	6.54902i	−0.545121	−	0.314726i	−0.747152	+	0.664653i	$0.768579\pi$
$434$	−49.1342	−	28.3676i	−2.35852	−	1.36169i
$435$		−	21.4490i		−	1.02840i
$436$	−32.6790			−1.56504
$437$	12.3107	−	7.10759i	0.588901	−	0.340002i
$438$		−	41.3167i		−	1.97419i
$439$	−12.5822	−	21.7931i	−0.600518	−	1.04013i	−0.992743	−	0.120258i	$-0.961628\pi$
$439$	−12.5822	−	21.7931i	−0.600518	−	1.04013i	0.392225	−	0.919869i	$-0.371705\pi$
$440$	4.32044	−	7.48322i	0.205969	−	0.356748i
$441$	0.452650	+	0.784013i	0.0215548	+	0.0373340i
$442$	5.93987	−	10.2882i	0.282531	−	0.489358i
$443$	−2.28032	+	3.94963i	−0.108341	+	0.187652i	−0.915098	−	0.403231i	$-0.867887\pi$
$443$	−2.28032	+	3.94963i	−0.108341	+	0.187652i	0.806757	+	0.590883i	$0.201221\pi$
$444$	−96.3007	+	55.5992i	−4.57023	+	2.63862i
$445$	10.9746	+	6.33619i	0.520246	+	0.300364i
$446$	19.2474	+	33.3375i	0.911391	+	1.57858i
$447$	8.29667			0.392419
$448$	−13.3660	−	7.71684i	−0.631482	−	0.364587i
$449$	4.17318	−	7.22817i	0.196945	−	0.341118i	−0.750592	−	0.660766i	$-0.770231\pi$
$449$	4.17318	−	7.22817i	0.196945	−	0.341118i	0.947536	+	0.319648i	$0.103565\pi$
$450$		−	6.69536i		−	0.315622i
$451$			0.276771i			0.0130326i
$452$	−26.2521	−	45.4699i	−1.23479	−	2.13873i
$453$	−31.7574	+	18.3351i	−1.49209	+	0.861460i
$454$	30.6136			1.43677
$455$		−	26.3723i		−	1.23635i
$456$	−30.1587	+	17.4121i	−1.41231	+	0.815398i
$457$	10.6692	−	6.15986i	0.499084	−	0.288146i	−0.229251	−	0.973367i	$-0.573628\pi$
$457$	10.6692	−	6.15986i	0.499084	−	0.288146i	0.728335	+	0.685221i	$0.240294\pi$
$458$	−8.52907	+	4.92426i	−0.398537	+	0.230096i
$459$	5.58948	−	3.22708i	0.260894	−	0.150627i
$460$			60.9472i			2.84168i
$461$	34.2684			1.59604			0.798019	−	0.602632i	$-0.205881\pi$
$461$	34.2684			1.59604			0.798019	+	0.602632i	$0.205881\pi$
$462$	11.1142	−	6.41679i	0.517079	−	0.298536i
$463$	−8.14425	−	14.1063i	−0.378496	−	0.655573i	0.612348	−	0.790588i	$-0.290225\pi$
$463$	−8.14425	−	14.1063i	−0.378496	−	0.655573i	−0.990844	+	0.135015i	$0.956892\pi$
$464$		−	16.2232i		−	0.753144i
$465$			56.7353i			2.63104i
$466$	25.4991	−	44.1657i	1.18122	−	2.04594i
$467$	−31.3972	−	18.1272i	−1.45289	−	0.838826i	−0.454245	−	0.890877i	$-0.650091\pi$
$467$	−31.3972	−	18.1272i	−1.45289	−	0.838826i	−0.998644	+	0.0520507i	$0.983424\pi$
$468$	−87.0447			−4.02364
$469$	10.9419	+	18.9519i	0.505248	+	0.875116i
$470$	47.9337	+	27.6745i	2.21102	+	1.27653i
$471$	−45.0493	+	26.0092i	−2.07576	+	1.19844i
$472$	−5.59798	+	9.69599i	−0.257668	+	0.446294i
$473$	−0.504082	+	0.873096i	−0.0231777	+	0.0401450i
$474$	−34.4659	−	59.6966i	−1.58307	−	2.74196i
$475$	−0.617396	+	1.06936i	−0.0283281	+	0.0490657i
$476$	6.38852	+	11.0652i	0.292817	+	0.507175i
$477$		−	28.3864i		−	1.29973i
$478$	15.6780	−	9.05169i	0.717095	−	0.414015i
$479$	−22.7691			−1.04035			−0.520174	−	0.854061i	$-0.674133\pi$
$479$	−22.7691			−1.04035			−0.520174	+	0.854061i	$0.674133\pi$
$480$		−	11.5449i		−	0.526949i
$481$	34.1691	+	19.7275i	1.55798	+	0.899498i
$482$	−46.4900	−	26.8410i	−2.11756	−	1.22258i
$483$	−23.5400	+	40.7725i	−1.07111	+	1.85521i
$484$	21.9526	+	38.0231i	0.997847	+	1.72832i
$485$	−18.5235			−0.841111
$486$	30.5241	+	17.6231i	1.38460	+	0.799399i
$487$	−26.0425			−1.18010			−0.590050	−	0.807367i	$-0.700892\pi$
$487$	−26.0425			−1.18010			−0.590050	+	0.807367i	$0.700892\pi$
$488$	7.57687	−	41.3556i	0.342989	−	1.87208i
$489$	17.2148			0.778479
$490$	0.917433	+	0.529680i	0.0414454	+	0.0239285i
$491$	−24.0079			−1.08346			−0.541731	−	0.840552i	$-0.682231\pi$
$491$	−24.0079			−1.08346			−0.541731	+	0.840552i	$0.682231\pi$
$492$	2.39119	+	4.14167i	0.107803	+	0.186721i
$493$	1.84358	−	3.19318i	0.0830308	−	0.143814i
$494$	20.5742	+	11.8785i	0.925677	+	0.534440i
$495$	−6.94386	−	4.00904i	−0.312103	−	0.180193i
$496$			42.9125i			1.92683i
$497$	7.43055			0.333306
$498$	69.0461	−	39.8638i	3.09403	−	1.78634i
$499$		−	18.1931i		−	0.814437i	−0.913331	−	0.407218i	$-0.866499\pi$
$499$		−	18.1931i		−	0.814437i	0.913331	−	0.407218i	$-0.133501\pi$
$500$	21.8757	+	37.8899i	0.978313	+	1.69449i
$501$	20.2249	−	35.0306i	0.903582	−	1.56505i
$502$	9.66719	+	16.7441i	0.431468	+	0.747324i
$503$	−2.94942	+	5.10855i	−0.131508	+	0.227779i	−0.924258	−	0.381768i	$-0.875315\pi$
$503$	−2.94942	+	5.10855i	−0.131508	+	0.227779i	0.792750	+	0.609547i	$0.208649\pi$
$504$	36.0296	−	62.4050i	1.60488	−	2.77974i
$505$	18.2686	−	10.5474i	0.812941	−	0.469352i
$506$	9.11355	+	5.26171i	0.405147	+	0.233912i
$507$	6.33762	+	10.9771i	0.281464	+	0.487509i
$508$	13.0040			0.576959
$509$	31.3246	+	18.0853i	1.38844	+	0.801616i	0.993140	−	0.116935i	$-0.0373070\pi$
$509$	31.3246	+	18.0853i	1.38844	+	0.801616i	0.395301	+	0.918552i	$0.370640\pi$
$510$	9.45432	−	16.3754i	0.418644	−	0.725113i
$511$		−	15.7671i		−	0.697497i
$512$			45.4626i			2.00918i
$513$	6.45350	+	11.1778i	0.284929	+	0.493512i
$514$	33.8599	−	19.5490i	1.49350	−	0.862270i
$515$	−34.7803			−1.53260
$516$			17.4203i			0.766887i
$517$	5.59261	−	3.22890i	0.245963	−	0.142007i
$518$	−54.3859	+	31.3997i	−2.38958	+	1.37963i
$519$	−11.1697	+	6.44882i	−0.490295	+	0.283072i
$520$	−45.8794	+	26.4885i	−2.01194	+	1.16160i
$521$		−	38.1443i		−	1.67113i	−0.549389	−	0.835566i	$-0.685140\pi$
$521$		−	38.1443i		−	1.67113i	0.549389	−	0.835566i	$-0.314860\pi$
$522$	−39.9814			−1.74994
$523$	27.7465	−	16.0194i	1.21327	−	0.700481i	0.249798	−	0.968298i	$-0.419636\pi$
$523$	27.7465	−	16.0194i	1.21327	−	0.700481i	0.963470	+	0.267817i	$0.0863023\pi$
$524$	−22.1046	−	38.2862i	−0.965642	−	1.67254i
$525$		−	4.08958i		−	0.178484i
$526$			8.73503i			0.380866i
$527$	−4.87652	+	8.44637i	−0.212424	+	0.367930i
$528$	−8.40639	−	4.85343i	−0.365841	−	0.211218i
$529$	−15.6053			−0.678490
$530$	−16.6086	−	28.7669i	−0.721430	−	1.24955i
$531$	8.99715	+	5.19451i	0.390443	+	0.225422i
$532$	−22.1282	+	12.7757i	−0.959379	+	0.553898i
$533$	0.848436	−	1.46953i	0.0367498	−	0.0636526i
$534$	18.9041	−	32.7429i	0.818062	−	1.41693i
$535$	−18.8066	−	32.5740i	−0.813080	−	1.40830i
$536$	21.9801	−	38.0707i	0.949397	−	1.64440i
$537$	27.8869	+	48.3015i	1.20341	+	2.08436i
$538$			42.5993i			1.83658i
$539$	0.107040	−	0.0617998i	0.00461056	−	0.00266191i
$540$	−55.3384			−2.38138
$541$		−	31.8649i		−	1.36998i	−0.728554	−	0.684989i	$-0.759807\pi$
$541$		−	31.8649i		−	1.36998i	0.728554	−	0.684989i	$-0.240193\pi$
$542$	−29.6846	−	17.1384i	−1.27506	−	0.736158i
$543$	24.0954	+	13.9115i	1.03403	+	0.597000i
$544$	0.992305	−	1.71872i	0.0425447	−	0.0736897i
$545$	9.22777	+	15.9830i	0.395274	+	0.684635i
$546$	−78.6822			−3.36729
$547$	−22.4895	−	12.9843i	−0.961581	−	0.555169i	−0.0649220	−	0.997890i	$-0.520680\pi$
$547$	−22.4895	−	12.9843i	−0.961581	−	0.555169i	−0.896659	+	0.442721i	$0.854013\pi$
$548$	−31.7063			−1.35443
$549$	−38.3749	−	7.03076i	−1.63780	−	0.300066i
$550$	−0.914110			−0.0389778
$551$	6.38570	+	3.68678i	0.272040	+	0.157062i
$552$	94.5749			4.02537
$553$	−13.1527	−	22.7812i	−0.559311	−	0.968756i
$554$	−39.4875	+	68.3944i	−1.67766	+	2.90580i
$555$	54.3859	+	31.3997i	2.30855	+	1.33284i
$556$	−53.2783	−	30.7603i	−2.25951	−	1.30453i
$557$			1.06265i			0.0450258i	0.999747	+	0.0225129i	$0.00716669\pi$
$557$			1.06265i			0.0450258i	−0.999747	+	0.0225129i	$0.992833\pi$
$558$	105.756			4.47700
$559$	5.35292	−	3.09051i	0.226404	−	0.130715i
$560$		−	31.7492i		−	1.34165i
$561$	−1.10307	−	1.91058i	−0.0465718	−	0.0806646i
$562$	−15.6071	+	27.0322i	−0.658344	+	1.14029i
$563$	14.8769	+	25.7676i	0.626987	+	1.08597i	0.988153	+	0.153472i	$0.0490456\pi$
$563$	14.8769	+	25.7676i	0.626987	+	1.08597i	−0.361166	+	0.932502i	$0.617621\pi$
$564$	55.7929	−	96.6362i	2.34931	−	4.06912i
$565$	−14.8259	+	25.6792i	−0.623730	+	1.08033i
$566$	2.05928	−	1.18892i	0.0865578	−	0.0499742i
$567$	−2.24250	−	1.29471i	−0.0941763	−	0.0543727i
$568$	−7.46328	−	12.9268i	−0.313152	−	0.542396i
$569$	11.4274			0.479060			0.239530	−	0.970889i	$-0.423007\pi$
$569$	11.4274			0.479060			0.239530	+	0.970889i	$0.423007\pi$
$570$	32.7473	+	18.9067i	1.37164	+	0.791914i
$571$	0.609035	−	1.05488i	0.0254873	−	0.0441453i	−0.853000	−	0.521910i	$-0.825220\pi$
$571$	0.609035	−	1.05488i	0.0254873	−	0.0441453i	0.878488	+	0.477765i	$0.158553\pi$
$572$			11.8841i			0.496900i
$573$		−	34.1423i		−	1.42631i
$574$	1.35043	+	2.33901i	0.0563659	+	0.0976285i
$575$	2.90415	−	1.67671i	0.121111	−	0.0699236i
$576$	28.7688			1.19870
$577$			12.0167i			0.500261i	0.968212	+	0.250131i	$0.0804735\pi$
$577$			12.0167i			0.500261i	−0.968212	+	0.250131i	$0.919526\pi$
$578$	−33.7477	+	19.4842i	−1.40372	+	0.810437i
$579$	13.6547	−	7.88356i	0.567471	−	0.327630i
$580$	−27.3785	+	15.8070i	−1.13683	+	0.656348i
$581$	26.3491	−	15.2127i	1.09315	−	0.631128i
$582$			55.2653i			2.29082i
$583$	−3.87557			−0.160510
$584$	−27.4298	+	15.8366i	−1.13505	+	0.655322i
$585$	24.5793	+	42.5726i	1.01623	+	1.76016i
$586$		−	5.59034i		−	0.230935i
$587$		−	29.9327i		−	1.23546i	−0.786392	−	0.617728i	$-0.788053\pi$
$587$		−	29.9327i		−	1.23546i	0.786392	−	0.617728i	$-0.211947\pi$
$588$	1.06785	−	1.84958i	0.0440376	−	0.0762754i
$589$	−16.8910	−	9.75202i	−0.695981	−	0.401825i
$590$	12.1570			0.500495
$591$	−22.0525	−	38.1960i	−0.907118	−	1.57117i
$592$	41.1356	+	23.7497i	1.69066	+	0.976105i
$593$	38.1190	−	22.0080i	1.56536	−	0.903760i	0.568660	−	0.822573i	$-0.307462\pi$
$593$	38.1190	−	22.0080i	1.56536	−	0.903760i	0.996699	−	0.0811875i	$-0.0258713\pi$
$594$	−4.77749	+	8.27486i	−0.196023	+	0.339522i
$595$	3.60793	−	6.24911i	0.147911	−	0.256189i
$596$	−6.11429	−	10.5903i	−0.250451	−	0.433794i
$597$	−17.1695	+	29.7385i	−0.702701	+	1.21711i
$598$	−32.2594	−	55.8749i	−1.31918	−	2.28489i
$599$		−	13.9494i		−	0.569959i	−0.958534	−	0.284979i	$-0.908013\pi$
$599$		−	13.9494i		−	0.569959i	0.958534	−	0.284979i	$-0.0919868\pi$
$600$	−7.11455	+	4.10759i	−0.290450	+	0.167692i
$601$	−37.0471			−1.51118			−0.755591	−	0.655043i	$-0.772650\pi$
$601$	−37.0471			−1.51118			−0.755591	+	0.655043i	$0.772650\pi$
$602$			9.83815i			0.400973i
$603$	−35.3267	−	20.3959i	−1.43862	−	0.830585i
$604$	46.8077	+	27.0244i	1.90458	+	1.09961i
$605$	12.3978	−	21.4736i	0.504041	−	0.873025i
$606$	−31.4683	−	54.5046i	−1.27831	−	2.21410i
$607$	40.0752			1.62660			0.813302	−	0.581842i	$-0.197668\pi$
$607$	40.0752			1.62660			0.813302	+	0.581842i	$0.197668\pi$
$608$	3.43709	+	1.98441i	0.139392	+	0.0804783i
$609$	−24.4209			−0.989585
$610$	−43.0027	+	15.3277i	−1.74113	+	0.620599i
$611$	−39.5925			−1.60174
$612$	−20.6259	−	11.9084i	−0.833752	−	0.481367i
$613$	−30.0296			−1.21288			−0.606442	−	0.795128i	$-0.707404\pi$
$613$	−30.0296			−1.21288			−0.606442	+	0.795128i	$0.707404\pi$
$614$	8.23290	+	14.2598i	0.332253	+	0.575478i
$615$	1.35043	−	2.33901i	0.0544546	−	0.0943181i
$616$	−8.52009	−	4.91908i	−0.343284	−	0.198195i
$617$	23.5748	+	13.6109i	0.949085	+	0.547954i	0.892796	−	0.450460i	$-0.148740\pi$
$617$	23.5748	+	13.6109i	0.949085	+	0.547954i	0.0562882	+	0.998415i	$0.482073\pi$
$618$			103.768i			4.17415i
$619$	−17.4050			−0.699566			−0.349783	−	0.936831i	$-0.613745\pi$
$619$	−17.4050			−0.699566			−0.349783	+	0.936831i	$0.613745\pi$
$620$	72.4196	−	41.8115i	2.90844	−	1.67919i
$621$		−	35.0525i		−	1.40661i
$622$	19.3047	+	33.4368i	0.774049	+	1.34069i
$623$	7.21413	−	12.4952i	0.289028	−	0.500612i
$624$	29.7562	+	51.5393i	1.19120	+	2.06322i
$625$	13.7036	−	23.7354i	0.548146	−	0.949416i
$626$	12.9848	−	22.4904i	0.518977	−	0.898895i
$627$	3.82076	−	2.20592i	0.152586	−	0.0880958i
$628$	66.3989	+	38.3354i	2.64960	+	1.52975i
$629$	5.39775	+	9.34917i	0.215222	+	0.372776i
$630$	−78.2443			−3.11733
$631$	−10.7043	−	6.18010i	−0.426130	−	0.246026i	0.271567	−	0.962420i	$-0.412458\pi$
$631$	−10.7043	−	6.18010i	−0.426130	−	0.246026i	−0.697696	+	0.716394i	$0.745792\pi$
$632$	−26.4214	+	45.7631i	−1.05098	+	1.82036i
$633$		−	5.06265i		−	0.201222i
$634$			74.0498i			2.94089i
$635$	−3.67201	−	6.36011i	−0.145719	−	0.252393i
$636$	−57.9951	+	33.4835i	−2.29965	+	1.32771i
$637$	−0.757785			−0.0300245
$638$			5.45861i			0.216108i
$639$	−11.9951	+	6.92537i	−0.474518	+	0.273963i
$640$	36.2262	−	20.9152i	1.43197	−	0.826746i
$641$	−5.54164	+	3.19947i	−0.218882	+	0.126371i	−0.605432	−	0.795897i	$-0.707000\pi$
$641$	−5.54164	+	3.19947i	−0.218882	+	0.126371i	0.386551	+	0.922268i	$0.373666\pi$
$642$	−97.1850	+	56.1098i	−3.83559	+	2.21448i
$643$		−	23.3663i		−	0.921477i	−0.887536	−	0.460738i	$-0.847585\pi$
$643$		−	23.3663i		−	0.921477i	0.887536	−	0.460738i	$-0.152415\pi$
$644$	69.3920			2.73443
$645$	8.52009	−	4.91908i	0.335478	−	0.193688i
$646$	3.25014	+	5.62941i	0.127875	+	0.221486i
$647$		−	18.2413i		−	0.717139i	−0.933503	−	0.358570i	$-0.883265\pi$
$647$		−	18.2413i		−	0.717139i	0.933503	−	0.358570i	$-0.116735\pi$
$648$			5.20165i			0.204340i
$649$	0.709200	−	1.22837i	0.0278386	−	0.0482178i
$650$	4.85353	+	2.80219i	0.190371	+	0.109911i
$651$	64.5965			2.53174
$652$	−12.6866	−	21.9738i	−0.496844	−	0.860559i
$653$	−34.9274	−	20.1653i	−1.36682	−	0.789131i	−0.376295	−	0.926500i	$-0.622802\pi$
$653$	−34.9274	−	20.1653i	−1.36682	−	0.789131i	−0.990520	+	0.137369i	$0.956135\pi$
$654$	47.6854	−	27.5312i	1.86465	−	1.07656i
$655$	−12.4836	+	21.6222i	−0.487774	+	0.844849i
$656$	1.02142	−	1.76915i	0.0398797	−	0.0690736i
$657$	14.6952	+	25.4528i	0.573313	+	0.993007i
$658$	31.5091	−	54.5754i	1.22835	−	2.12757i
$659$	16.5192	+	28.6121i	0.643496	+	1.11457i	0.984647	+	0.174559i	$0.0558499\pi$
$659$	16.5192	+	28.6121i	0.643496	+	1.11457i	−0.341151	+	0.940009i	$0.610817\pi$
$660$			18.9156i			0.736288i
$661$	21.5963	−	12.4686i	0.839999	−	0.484974i	−0.0172648	−	0.999851i	$-0.505496\pi$
$661$	21.5963	−	12.4686i	0.839999	−	0.484974i	0.857264	+	0.514877i	$0.172162\pi$
$662$	27.6132			1.07322
$663$			13.5258i			0.525299i
$664$	−52.9304	−	30.5594i	−2.05410	−	1.18593i
$665$	12.4969	+	7.21511i	0.484610	+	0.279790i
$666$	58.5299	−	101.377i	2.26799	−	3.92827i
$667$	−10.0125	−	17.3421i	−0.387685	−	0.671489i
$668$	−59.6196			−2.30675
$669$	−37.9567	−	21.9143i	−1.46749	−	0.847257i
$670$	−47.7336			−1.84411
$671$	−0.959902	+	5.23928i	−0.0370566	+	0.202260i
$672$	−13.1445			−0.507061
$673$	−16.0908	−	9.29005i	−0.620256	−	0.358105i	0.156713	−	0.987644i	$-0.449910\pi$
$673$	−16.0908	−	9.29005i	−0.620256	−	0.358105i	−0.776969	+	0.629539i	$0.783244\pi$
$674$	64.9982			2.50364
$675$	1.52241	+	2.63689i	0.0585975	+	0.101494i
$676$	9.34111	−	16.1793i	0.359274	−	0.622280i
$677$	10.9724	+	6.33491i	0.421703	+	0.243470i	0.695806	−	0.718230i	$-0.255047\pi$
$677$	10.9724	+	6.33491i	0.421703	+	0.243470i	−0.274103	+	0.961700i	$0.588381\pi$
$678$	76.6143	+	44.2333i	2.94236	+	1.69877i
$679$			21.0902i			0.809366i
$680$	−14.4953			−0.555868
$681$	−30.1857	+	17.4277i	−1.15672	+	0.667831i
$682$		−	14.4387i		−	0.552888i
$683$	5.91660	+	10.2479i	0.226392	+	0.392123i	0.956736	−	0.290956i	$-0.0939735\pi$
$683$	5.91660	+	10.2479i	0.226392	+	0.392123i	−0.730344	+	0.683080i	$0.760640\pi$
$684$	23.8143	−	41.2475i	0.910561	−	1.57714i
$685$	8.95309	+	15.5072i	0.342080	+	0.592500i
$686$	−22.6900	+	39.3001i	−0.866306	+	1.50049i
$687$	5.60656	−	9.71086i	0.213904	−	0.370492i
$688$	6.44429	−	3.72061i	0.245686	−	0.141847i
$689$	20.5776	+	11.8805i	0.783945	+	0.452611i
$690$	−51.3463	−	88.9344i	−1.95472	−	3.38568i
$691$	−3.65040			−0.138868			−0.0694338	−	0.997587i	$-0.522119\pi$
$691$	−3.65040			−0.138868			−0.0694338	+	0.997587i	$0.522119\pi$
$692$	16.4632	+	9.50502i	0.625836	+	0.361327i
$693$	−4.56453	+	7.90600i	−0.173392	+	0.300324i
$694$		−	40.4738i		−	1.53637i
$695$			34.7438i			1.31791i
$696$	24.5285	+	42.4846i	0.929750	+	1.61037i
$697$	0.402086	−	0.232145i	0.0152301	−	0.00879310i
$698$	0.320934			0.0121475
$699$			58.0644i			2.19620i
$700$	−5.22013	+	3.01384i	−0.197302	+	0.113913i
$701$	−17.0204	+	9.82672i	−0.642851	+	0.371150i	−0.785712	−	0.618593i	$-0.787703\pi$
$701$	−17.0204	+	9.82672i	−0.642851	+	0.371150i	0.142861	+	0.989743i	$0.454370\pi$
$702$	50.7329	−	29.2906i	1.91479	−	1.10550i
$703$	−18.6964	+	10.7944i	−0.705148	+	0.407118i
$704$		−	3.92777i		−	0.148033i
$705$	−63.0182			−2.37340
$706$	0.0468742	−	0.0270628i	0.00176413	−	0.00101852i
$707$	−12.0088	−	20.7999i	−0.451638	−	0.782260i
$708$		−	24.5089i		−	0.921101i
$709$			4.40036i			0.165259i	0.996580	+	0.0826294i	$0.0263318\pi$
$709$			4.40036i			0.165259i	−0.996580	+	0.0826294i	$0.973668\pi$
$710$	−8.10389	+	14.0364i	−0.304134	+	0.526775i
$711$	42.4647	+	24.5170i	1.59255	+	0.919460i
$712$	−28.9836			−1.08621
$713$	26.4843	+	45.8722i	0.991845	+	1.71793i
$714$	−18.6443	−	10.7643i	−0.697747	−	0.402844i
$715$	5.81239	−	3.35578i	0.217371	−	0.125499i
$716$	41.1029	−	71.1923i	1.53609	−	2.66058i
$717$	−10.3059	+	17.8503i	−0.384881	+	0.666633i
$718$	−10.7277	−	18.5810i	−0.400355	−	0.693436i
$719$	14.7694	−	25.5814i	0.550806	−	0.954024i	−0.447411	−	0.894329i	$-0.647654\pi$
$719$	14.7694	−	25.5814i	0.550806	−	0.954024i	0.998217	−	0.0596954i	$-0.0190129\pi$
$720$	29.5906	+	51.2524i	1.10278	+	1.91007i
$721$			39.5994i			1.47476i
$722$	29.6065	−	17.0933i	1.10184	−	0.636148i
$723$	61.1202			2.27309
$724$		−	41.0087i		−	1.52408i
$725$	1.50641	+	0.869727i	0.0559467	+	0.0323008i
$726$	−64.0668	−	36.9890i	−2.37774	−	1.37279i
$727$	8.79993	−	15.2419i	0.326371	−	0.565292i	−0.655418	−	0.755267i	$-0.727507\pi$
$727$	8.79993	−	15.2419i	0.326371	−	0.565292i	0.981789	+	0.189975i	$0.0608407\pi$
$728$	30.1587	+	52.2364i	1.11776	+	1.93601i
$729$	−43.0287			−1.59366
$730$	29.7842	+	17.1959i	1.10236	+	0.636449i
$731$	1.69122			0.0625520
$732$	30.9012	+	86.6951i	1.14214	+	3.20434i
$733$	20.2317			0.747276			0.373638	−	0.927575i	$-0.378110\pi$
$733$	20.2317			0.747276			0.373638	+	0.927575i	$0.378110\pi$
$734$	−9.42403	−	5.44097i	−0.347847	−	0.200830i
$735$	−1.20614			−0.0444893
$736$	−5.38920	−	9.33437i	−0.198649	−	0.344069i
$737$	−2.78463	+	4.82312i	−0.102573	+	0.177662i
$738$	−4.35998	−	2.51723i	−0.160493	−	0.0926607i
$739$	−14.6004	−	8.42953i	−0.537083	−	0.310085i	0.206813	−	0.978381i	$-0.433691\pi$
$739$	−14.6004	−	8.42953i	−0.537083	−	0.310085i	−0.743896	+	0.668295i	$0.767024\pi$
$740$		−	92.5611i		−	3.40261i
$741$	−27.0488			−0.993663
$742$	−32.7528	+	18.9098i	−1.20239	+	0.694202i
$743$			33.5417i			1.23053i	0.788322	+	0.615263i	$0.210950\pi$
$743$			33.5417i			1.23053i	−0.788322	+	0.615263i	$0.789050\pi$
$744$	−64.8810	−	112.377i	−2.37865	−	4.11995i
$745$	−3.45305	+	5.98087i	−0.126510	+	0.219122i
$746$	−35.0124	−	60.6433i	−1.28190	−	2.22031i
$747$	−28.3568	+	49.1154i	−1.03752	+	1.79704i
$748$	−1.62583	+	2.81603i	−0.0594464	+	0.102964i
$749$	−37.0874	+	21.4124i	−1.35514	+	0.782393i
$750$	−63.8424	−	36.8594i	−2.33120	−	1.34592i
$751$	18.4375	+	31.9346i	0.672792	+	1.16531i	0.977109	+	0.212739i	$0.0682385\pi$
$751$	18.4375	+	31.9346i	0.672792	+	1.16531i	−0.304317	+	0.952571i	$0.598428\pi$
$752$	−47.6648			−1.73816
$753$	−19.0641	−	11.0067i	−0.694735	−	0.401105i
$754$	16.7333	−	28.9829i	0.609390	−	1.05549i
$755$		−	30.5242i		−	1.11089i
$756$			63.0060i			2.29151i
$757$	17.6419	+	30.5566i	0.641205	+	1.11060i	0.985164	+	0.171615i	$0.0548985\pi$
$757$	17.6419	+	30.5566i	0.641205	+	1.11060i	−0.343959	+	0.938985i	$0.611768\pi$
$758$	−44.1063	+	25.4648i	−1.60201	+	0.924922i
$759$	−11.9815			−0.434903
$760$		−	28.9875i		−	1.05149i
$761$	−21.0095	+	12.1299i	−0.761596	+	0.439707i	−0.829868	−	0.557959i	$-0.811585\pi$
$761$	−21.0095	+	12.1299i	−0.761596	+	0.439707i	0.0682728	+	0.997667i	$0.478251\pi$
$762$	−18.9755	+	10.9555i	−0.687410	+	0.396876i
$763$	18.1976	−	10.5064i	0.658796	−	0.380356i
$764$	−43.5808	+	25.1614i	−1.57670	+	0.910308i
$765$			13.4505i			0.486305i
$766$	23.6038			0.852840
$767$	−7.53110	+	4.34808i	−0.271932	+	0.157000i
$768$	−46.1160	−	79.8753i	−1.66407	−	2.88225i
$769$		−	7.23081i		−	0.260750i	−0.991465	−	0.130375i	$-0.958382\pi$
$769$		−	7.23081i		−	0.260750i	0.991465	−	0.130375i	$-0.0416181\pi$
$770$			10.6826i			0.384974i
$771$	−22.2577	+	38.5515i	−0.801592	+	1.38840i
$772$	−20.1259	−	11.6197i	−0.724348	−	0.418202i
$773$	−2.94718			−0.106003			−0.0530014	−	0.998594i	$-0.516879\pi$
$773$	−2.94718			−0.106003			−0.0530014	+	0.998594i	$0.516879\pi$
$774$	−9.16928	−	15.8817i	−0.329583	−	0.570854i
$775$	−3.98465	−	2.30054i	−0.143133	−	0.0826379i
$776$	36.6901	−	21.1831i	1.31710	−	0.760428i
$777$	35.7505	−	61.9217i	1.28254	−	2.22143i
$778$	−19.1348	+	33.1424i	−0.686015	+	1.18821i
$779$	0.464241	+	0.804089i	0.0166332	+	0.0288095i
$780$	57.9854	−	100.434i	2.07621	−	3.59610i
$781$	0.945512	+	1.63768i	0.0338331	+	0.0586006i
$782$		−	17.6533i		−	0.631281i
$783$	15.7462	−	9.09106i	0.562722	−	0.324888i
$784$	−0.912285			−0.0325816
$785$		−	43.2999i		−	1.54544i
$786$	64.5102	+	37.2450i	2.30100	+	1.32848i
$787$	13.1447	+	7.58909i	0.468558	+	0.270522i	0.715636	−	0.698474i	$-0.246137\pi$
$787$	13.1447	+	7.58909i	0.468558	+	0.270522i	−0.247078	+	0.968996i	$0.579470\pi$
$788$	−32.5035	+	56.2977i	−1.15789	+	2.00552i
$789$	−4.97268	−	8.61293i	−0.177032	−	0.306629i
$790$	57.3784			2.04143
$791$	29.2373	+	16.8802i	1.03956	+	0.600190i
$792$	18.3386			0.651632
$793$	21.1576	−	24.8758i	0.751328	−	0.883364i
$794$	5.70979			0.202633
$795$	32.7528	+	18.9098i	1.16162	+	0.670663i
$796$	50.6128			1.79392
$797$	−15.4955	−	26.8390i	−0.548880	−	0.950687i	−0.998352	−	0.0573930i	$-0.981721\pi$
$797$	−15.4955	−	26.8390i	−0.548880	−	0.950687i	0.449472	−	0.893294i	$-0.351612\pi$
$798$	21.5264	−	37.2848i	0.762026	−	1.31987i
$799$	−9.38174	−	5.41655i	−0.331902	−	0.191624i
$800$	0.810823	+	0.468129i	0.0286669	+	0.0165509i
$801$			26.8946i			0.950276i
$802$	−6.08271			−0.214788
$803$	3.47504	−	2.00631i	0.122631	−	0.0708012i
$804$			96.2327i			3.39386i
$805$	−19.5946	−	33.9389i	−0.690619	−	1.19619i
$806$	−44.2617	+	76.6635i	−1.55905	+	2.70036i
$807$	−24.2509	−	42.0038i	−0.853672	−	1.47860i
$808$	−24.1234	+	41.7830i	−0.848659	+	1.46992i
$809$	11.1070	−	19.2379i	0.390502	−	0.676370i	−0.602013	−	0.798486i	$-0.705635\pi$
$809$	11.1070	−	19.2379i	0.390502	−	0.676370i	0.992516	+	0.122116i	$0.0389680\pi$
$810$	4.89143	−	2.82407i	0.171867	−	0.0992276i
$811$	16.8830	+	9.74740i	0.592842	+	0.342277i	0.766220	−	0.642578i	$-0.222135\pi$
$811$	16.8830	+	9.74740i	0.592842	+	0.342277i	−0.173379	+	0.984855i	$0.555468\pi$
$812$	17.9972	+	31.1720i	0.631577	+	1.09392i
$813$	39.0262			1.36871
$814$	−13.8408	−	7.99102i	−0.485122	−	0.280085i
$815$	−7.16475	+	12.4097i	−0.250970	+	0.434693i
$816$			16.2835i			0.570036i
$817$			3.38209i			0.118324i
$818$	−13.8283	−	23.9514i	−0.483496	−	0.837440i
$819$	48.4714	−	27.9850i	1.69373	−	0.977875i
$820$	−3.98084			−0.139017
$821$		−	29.0827i		−	1.01499i	−0.861653	−	0.507497i	$-0.830571\pi$
$821$		−	29.0827i		−	1.01499i	0.861653	−	0.507497i	$-0.169429\pi$
$822$	46.2660	−	26.7117i	1.61371	−	0.931677i
$823$	25.2258	−	14.5641i	0.879318	−	0.507674i	0.00888422	−	0.999961i	$-0.497172\pi$
$823$	25.2258	−	14.5641i	0.879318	−	0.507674i	0.870433	+	0.492286i	$0.163839\pi$
$824$	68.8904	−	39.7739i	2.39991	−	1.38559i
$825$	0.901332	−	0.520385i	0.0313804	−	0.0181175i
$826$		−	13.8414i		−	0.481605i
$827$	−44.1770			−1.53619			−0.768093	−	0.640338i	$-0.778794\pi$
$827$	−44.1770			−1.53619			−0.768093	+	0.640338i	$0.778794\pi$
$828$	−112.019	+	64.6742i	−3.89293	+	2.24758i
$829$	6.36561	+	11.0256i	0.221087	+	0.382933i	0.955138	−	0.296160i	$-0.0957063\pi$
$829$	6.36561	+	11.0256i	0.221087	+	0.382933i	−0.734052	+	0.679094i	$0.762373\pi$
$830$			66.3648i			2.30356i
$831$		−	89.9178i		−	3.11922i
$832$	−12.0405	+	20.8548i	−0.417429	+	0.723009i
$833$	−0.179563	−	0.103671i	−0.00622148	−	0.00359198i
$834$	103.659			3.58941
$835$	16.8351	+	29.1593i	0.582603	+	1.00910i
$836$	−5.63147	−	3.25133i	−0.194769	−	0.112450i
$837$	−41.6507	+	24.0470i	−1.43966	+	0.831187i
$838$	−43.4310	+	75.2248i	−1.50030	+	2.59860i
$839$	−16.6475	+	28.8343i	−0.574736	+	0.995471i	0.421335	+	0.906905i	$0.361562\pi$
$839$	−16.6475	+	28.8343i	−0.574736	+	0.995471i	−0.996070	+	0.0885661i	$0.971772\pi$
$840$	48.0027	+	83.1431i	1.65625	+	2.86871i
$841$	−9.30642	+	16.1192i	−0.320911	+	0.555834i
$842$	5.45937	+	9.45591i	0.188142	+	0.325872i
$843$		−	35.5391i		−	1.22403i
$844$	−6.46220	+	3.73095i	−0.222438	+	0.128425i
$845$	−10.5508			−0.362959
$846$			117.468i			4.03862i
$847$	−24.4490	−	14.1156i	−0.840076	−	0.485018i
$848$	24.7731	+	14.3027i	0.850710	+	0.491158i
$849$	−1.35366	+	2.34461i	−0.0464575	+	0.0804667i
$850$	0.766721	+	1.32800i	0.0262983	+	0.0455500i
$851$	58.6302			2.00982
$852$	28.2978	+	16.3378i	0.969467	+	0.559722i
$853$	33.4653			1.14583			0.572916	−	0.819614i	$-0.305812\pi$
$853$	33.4653			1.14583			0.572916	+	0.819614i	$0.305812\pi$
$854$	17.4515	+	48.9612i	0.597177	+	1.67542i
$855$	−26.8983			−0.919901
$856$	74.5015	+	43.0135i	2.54641	+	1.47017i
$857$	−12.0255			−0.410784			−0.205392	−	0.978680i	$-0.565847\pi$
$857$	−12.0255			−0.410784			−0.205392	+	0.978680i	$0.565847\pi$
$858$	−10.0120	−	17.3414i	−0.341805	−	0.592024i
$859$	−25.1855	+	43.6226i	−0.859320	+	1.48839i	0.0132590	+	0.999912i	$0.495779\pi$
$859$	−25.1855	+	43.6226i	−0.859320	+	1.48839i	−0.872579	+	0.488473i	$0.837554\pi$
$860$	−12.5579	−	7.25030i	−0.428220	−	0.247233i
$861$	−2.66311	−	1.53755i	−0.0907584	−	0.0523994i
$862$		−	1.16498i		−	0.0396794i
$863$	−31.6007			−1.07570			−0.537850	−	0.843041i	$-0.680763\pi$
$863$	−31.6007			−1.07570			−0.537850	+	0.843041i	$0.680763\pi$
$864$	8.47535	−	4.89325i	0.288337	−	0.166472i
$865$		−	10.7359i		−	0.365033i
$866$	−16.2643	−	28.1705i	−0.552682	−	0.957274i
$867$	22.1840	−	38.4237i	0.753407	−	1.30494i
$868$	−47.6049	−	82.4541i	−1.61581	−	2.79867i
$869$	3.34728	−	5.79766i	0.113549	−	0.196672i
$870$	26.6339	−	46.1312i	0.902973	−	1.56399i
$871$	29.5704	−	17.0725i	1.00195	−	0.578479i
$872$	−36.5554	−	21.1053i	−1.23792	−	0.714715i
$873$	−19.6563	−	34.0457i	−0.665265	−	1.15227i
$874$	35.3029			1.19414
$875$	−24.3633	−	14.0662i	−0.823631	−	0.475523i
$876$	34.6676	−	60.0460i	1.17131	−	2.02877i
$877$			33.6251i			1.13544i	0.823222	+	0.567719i	$0.192174\pi$
$877$			33.6251i			1.13544i	−0.823222	+	0.567719i	$0.807826\pi$
$878$		−	62.4952i		−	2.10911i
$879$	3.18247	+	5.51220i	0.107342	+	0.185922i
$880$	6.99744	−	4.03997i	0.235884	−	0.136187i
$881$	−33.7930			−1.13852			−0.569258	−	0.822159i	$-0.692769\pi$
$881$	−33.7930			−1.13852			−0.569258	+	0.822159i	$0.692769\pi$
$882$			2.24828i			0.0757036i
$883$	19.7753	−	11.4173i	0.665491	−	0.384221i	−0.128875	−	0.991661i	$-0.541137\pi$
$883$	19.7753	−	11.4173i	0.665491	−	0.384221i	0.794366	+	0.607439i	$0.207803\pi$
$884$	17.2650	−	9.96794i	0.580684	−	0.335258i
$885$	−11.9870	+	6.92072i	−0.402940	+	0.232637i
$886$	−9.80876	+	5.66309i	−0.329532	+	0.190255i
$887$			19.7835i			0.664265i	0.943233	+	0.332132i	$0.107768\pi$
$887$			19.7835i			0.664265i	−0.943233	+	0.332132i	$0.892232\pi$
$888$	−143.632			−4.81997
$889$	−7.24136	+	4.18080i	−0.242867	+	0.140220i
$890$	15.7357	+	27.2551i	0.527463	+	0.913592i
$891$		−	0.658990i		−	0.0220770i
$892$			64.5997i			2.16296i
$893$	10.8320	−	18.7615i	0.362478	−	0.627831i
$894$	17.8440	+	10.3022i	0.596793	+	0.344559i
$895$	−46.4258			−1.55184
$896$	−23.8132	−	41.2457i	−0.795543	−	1.37792i
$897$	63.6169	+	36.7292i	2.12411	+	1.22635i
$898$	17.9509	−	10.3640i	0.599030	−	0.345850i
$899$	−13.7377	+	23.7944i	−0.458177	+	0.793587i
$900$	5.61788	−	9.73045i	0.187263	−	0.324348i
$901$	3.25068	+	5.63034i	0.108296	+	0.187574i
$902$	−0.343675	+	0.595263i	−0.0114431	+	0.0198201i
$903$	−5.60066	−	9.70063i	−0.186378	−	0.322817i
$904$		−	67.8181i		−	2.25560i
$905$	−20.0569	+	11.5799i	−0.666715	+	0.384928i
$906$	−91.0694			−3.02558
$907$			12.2712i			0.407458i	0.979027	+	0.203729i	$0.0653061\pi$
$907$			12.2712i			0.407458i	−0.979027	+	0.203729i	$0.934694\pi$
$908$	44.4911	+	25.6870i	1.47649	+	0.852452i
$909$	38.7715	+	22.3847i	1.28597	+	0.742454i
$910$	32.7473	−	56.7201i	1.08556	−	1.88025i
$911$	9.28633	+	16.0844i	0.307670	+	0.532900i	0.977852	−	0.209297i	$-0.0671174\pi$
$911$	9.28633	+	16.0844i	0.307670	+	0.532900i	−0.670182	+	0.742197i	$0.733784\pi$
$912$	−32.5636			−1.07829
$913$	6.70567	+	3.87152i	0.221925	+	0.128129i
$914$	30.5956			1.01201
$915$	33.6759	−	39.5940i	1.11329	−	1.30894i
$916$	−16.5272			−0.546074
$917$	24.6182	+	14.2133i	0.812963	+	0.469364i
$918$	16.0287			0.529026
$919$	−2.35763	−	4.08353i	−0.0777710	−	0.134703i	0.824517	−	0.565837i	$-0.191447\pi$
$919$	−2.35763	−	4.08353i	−0.0777710	−	0.134703i	−0.902288	+	0.431134i	$0.858114\pi$
$920$	−39.3618	+	68.1767i	−1.29772	+	2.24772i
$921$	−16.2356	−	9.37365i	−0.534982	−	0.308872i
$922$	73.7026	+	42.5522i	2.42726	+	1.40138i
$923$		−	11.5938i		−	0.381615i
$924$	21.5365			0.708500
$925$	−4.41056	+	2.54644i	−0.145018	+	0.0837263i
$926$		−	40.4520i		−	1.32933i
$927$	−36.9072	−	63.9251i	−1.21219	−	2.09957i
$928$	2.79543	−	4.84183i	0.0917646	−	0.158941i
$929$	−11.0359	−	19.1148i	−0.362078	−	0.627137i	0.626225	−	0.779642i	$-0.284599\pi$
$929$	−11.0359	−	19.1148i	−0.362078	−	0.627137i	−0.988303	+	0.152506i	$0.951266\pi$
$930$	−70.4501	+	122.023i	−2.31015	+	4.00129i
$931$	0.207320	−	0.359089i	0.00679464	−	0.0117687i
$932$	74.1162	−	42.7910i	2.42776	−	1.40167i
$933$	−38.0697	−	21.9796i	−1.24635	−	0.719579i
$934$	−45.0183	−	77.9739i	−1.47304	−	2.55138i
$935$	1.83638			0.0600562
$936$	−97.3699	−	56.2165i	−3.18263	−	1.83749i
$937$	−11.7101	+	20.2825i	−0.382552	+	0.662600i	−0.991426	−	0.130667i	$-0.958288\pi$
$937$	−11.7101	+	20.2825i	−0.382552	+	0.662600i	0.608874	+	0.793267i	$0.291621\pi$
$938$			54.3475i			1.77451i
$939$			29.5680i			0.964914i
$940$	46.4418	+	80.4395i	1.51476	+	2.62365i
$941$	10.8445	−	6.26108i	0.353521	−	0.204106i	−0.312714	−	0.949847i	$-0.601238\pi$
$941$	10.8445	−	6.26108i	0.353521	−	0.204106i	0.666235	+	0.745742i	$0.267905\pi$
$942$	−129.186			−4.20911
$943$		−	2.52155i		−	0.0821130i
$944$	−9.06657	+	5.23459i	−0.295092	+	0.170371i
$945$	30.8156	−	17.7914i	1.00243	−	0.578753i
$946$	−2.16830	+	1.25187i	−0.0704977	+	0.0407018i
$947$	46.5542	−	26.8781i	1.51281	−	0.873420i	0.512921	−	0.858436i	$-0.328563\pi$
$947$	46.5542	−	26.8781i	1.51281	−	0.873420i	0.999888	−	0.0149844i	$-0.00476986\pi$
$948$		−	115.677i		−	3.75702i
$949$	−24.6013			−0.798591
$950$	−2.65572	+	1.53328i	−0.0861631	+	0.0497463i
$951$	−42.1550	−	73.0147i	−1.36697	−	2.36766i
$952$			16.5037i			0.534889i
$953$			19.4789i			0.630983i	0.948928	+	0.315491i	$0.102169\pi$
$953$			19.4789i			0.630983i	−0.948928	+	0.315491i	$0.897831\pi$
$954$	35.2484	−	61.0520i	1.14121	−	1.97663i
$955$	24.6123	+	14.2099i	0.796436	+	0.459823i
$956$	30.3800			0.982560
$957$	−3.10748	−	5.38231i	−0.100450	−	0.173985i
$958$	−48.9705	−	28.2732i	−1.58217	−	0.913464i
$959$	17.6559	−	10.1936i	0.570138	−	0.329169i
$960$	−19.1645	+	33.1939i	−0.618532	+	1.07133i
$961$	20.8380	−	36.0924i	0.672192	−	1.16427i
$962$	48.9927	+	84.8578i	1.57959	+	2.73592i
$963$	39.9133	−	69.1318i	1.28619	−	2.22774i
$964$	−45.0430	−	78.0168i	−1.45074	−	2.51275i
$965$			13.1245i			0.422492i
$966$	−101.257	+	58.4609i	−3.25790	+	1.88095i
$967$	−26.8613			−0.863801			−0.431900	−	0.901921i	$-0.642157\pi$
$967$	−26.8613			−0.863801			−0.431900	+	0.901921i	$0.642157\pi$
$968$			56.7112i			1.82277i
$969$	−6.40942	−	3.70048i	−0.205900	−	0.118876i
$970$	−39.8394	−	23.0013i	−1.27917	−	0.738527i
$971$	−25.9704	+	44.9820i	−0.833429	+	1.44354i	0.0618736	+	0.998084i	$0.480292\pi$
$971$	−25.9704	+	44.9820i	−0.833429	+	1.44354i	−0.895303	+	0.445458i	$0.853041\pi$
$972$	29.5740	+	51.2237i	0.948587	+	1.64300i
$973$	39.5579			1.26817
$974$	−56.0108	−	32.3379i	−1.79470	−	1.03617i
$975$	−6.38092			−0.204353
$976$	25.4713	−	29.9475i	0.815315	−	0.958596i
$977$	−14.0905			−0.450794			−0.225397	−	0.974267i	$-0.572368\pi$
$977$	−14.0905			−0.450794			−0.225397	+	0.974267i	$0.572368\pi$
$978$	37.0246	+	21.3761i	1.18392	+	0.683534i
$979$	3.67190			0.117354
$980$	0.888877	+	1.53958i	0.0283941	+	0.0491801i
$981$	−19.5841	+	33.9207i	−0.625273	+	1.08300i
$982$	−51.6349	−	29.8114i	−1.64774	−	0.951321i
$983$	34.6070	+	19.9804i	1.10379	+	0.637275i	0.937214	−	0.348754i	$-0.113395\pi$
$983$	34.6070	+	19.9804i	1.10379	+	0.637275i	0.166578	+	0.986028i	$0.446728\pi$
$984$			6.17727i			0.196924i
$985$	36.7128			1.16977
$986$	7.93015	−	4.57847i	0.252547	−	0.145808i
$987$			71.7500i			2.28383i
$988$	19.9338	+	34.5264i	0.634179	+	1.09843i
$989$	4.59250	−	7.95444i	0.146033	−	0.252936i
$990$	−9.95632	−	17.2448i	−0.316433	−	0.548077i
$991$	23.6792	−	41.0135i	0.752194	−	1.30284i	−0.194564	−	0.980890i	$-0.562329\pi$
$991$	23.6792	−	41.0135i	0.752194	−	1.30284i	0.946757	−	0.321948i	$-0.104338\pi$
$992$	−7.39429	+	12.8073i	−0.234769	+	0.406632i
$993$	−27.2273	+	15.7197i	−0.864031	+	0.498848i
$994$	15.9812	+	9.22677i	0.506894	+	0.292655i
$995$	−14.2918	−	24.7542i	−0.453081	−	0.784759i
$996$	133.794			4.23942
$997$	−2.74189	−	1.58303i	−0.0868366	−	0.0501351i	0.455953	−	0.890004i	$-0.349299\pi$
$997$	−2.74189	−	1.58303i	−0.0868366	−	0.0501351i	−0.542790	+	0.839869i	$0.682632\pi$
$998$	22.5910	−	39.1288i	0.715106	−	1.23860i
$999$			53.2346i			1.68427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.f.b.48.4	yes	8
3.2	odd	2		549.2.s.j.109.1		8
4.3	odd	2		976.2.ba.c.353.4		8
61.14	even	6	inner	61.2.f.b.14.4	✓	8
61.21	odd	12		3721.2.a.i.1.7		8
61.40	odd	12		3721.2.a.i.1.2		8
183.14	odd	6		549.2.s.j.136.1		8
244.75	odd	6		976.2.ba.c.929.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.f.b.14.4	✓	8	61.14	even	6	inner
61.2.f.b.48.4	yes	8	1.1	even	1	trivial
549.2.s.j.109.1		8	3.2	odd	2
549.2.s.j.136.1		8	183.14	odd	6
976.2.ba.c.353.4		8	4.3	odd	2
976.2.ba.c.929.4		8	244.75	odd	6
3721.2.a.i.1.2		8	61.40	odd	12
3721.2.a.i.1.7		8	61.21	odd	12

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:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.15074 + 1.24173i) q^{2} -2.82757 q^{3} +(2.08380 + 3.60925i) q^{4} +(1.17683 - 2.03833i) q^{5} +(-6.08139 - 3.51109i) q^{6} +(-2.32076 - 1.33989i) q^{7} +5.38317i q^{8} +4.99518 q^{9} +O(q^{10})\)	\(q+(2.15074 + 1.24173i) q^{2} -2.82757 q^{3} +(2.08380 + 3.60925i) q^{4} +(1.17683 - 2.03833i) q^{5} +(-6.08139 - 3.51109i) q^{6} +(-2.32076 - 1.33989i) q^{7} +5.38317i q^{8} +4.99518 q^{9} +(5.06212 - 2.92262i) q^{10} -0.681986i q^{11} +(-5.89211 - 10.2054i) q^{12} +(-2.09062 + 3.62106i) q^{13} +(-3.32757 - 5.76353i) q^{14} +(-3.32757 + 5.76353i) q^{15} +(-2.51686 + 4.35933i) q^{16} +(-0.990775 + 0.572024i) q^{17} +(10.7434 + 6.20268i) q^{18} +(-1.14393 - 1.98134i) q^{19} +9.80912 q^{20} +(6.56212 + 3.78864i) q^{21} +(0.846845 - 1.46678i) q^{22} +6.21331i q^{23} -15.2213i q^{24} +(-0.269858 - 0.467407i) q^{25} +(-8.99277 + 5.19198i) q^{26} -5.64152 q^{27} -11.1683i q^{28} +(-2.79112 + 1.61146i) q^{29} +(-14.3135 + 8.26392i) q^{30} +(7.38288 - 4.26251i) q^{31} +(-1.50232 + 0.867363i) q^{32} +1.92837i q^{33} -2.84120 q^{34} +(-5.46228 + 3.15365i) q^{35} +(10.4090 + 18.0289i) q^{36} -9.43622i q^{37} -5.68182i q^{38} +(5.91138 - 10.2388i) q^{39} +(10.9727 + 6.33508i) q^{40} -0.405830 q^{41} +(9.40897 + 16.2968i) q^{42} +(-1.28023 - 0.739138i) q^{43} +(2.46146 - 1.42112i) q^{44} +(5.87848 - 10.1818i) q^{45} +(-7.71528 + 13.3633i) q^{46} +(4.73455 + 8.20048i) q^{47} +(7.11661 - 12.3263i) q^{48} +(0.0906174 + 0.156954i) q^{49} -1.34036i q^{50} +(2.80149 - 1.61744i) q^{51} -17.4257 q^{52} -5.68277i q^{53} +(-12.1335 - 7.00526i) q^{54} +(-1.39011 - 0.802582i) q^{55} +(7.21287 - 12.4931i) q^{56} +(3.23455 + 5.60240i) q^{57} -8.00399 q^{58} +(1.80117 + 1.03990i) q^{59} -27.7360 q^{60} +(-7.68238 - 1.40751i) q^{61} +21.1716 q^{62} +(-11.5926 - 6.69300i) q^{63} +5.75930 q^{64} +(4.92060 + 8.52273i) q^{65} +(-2.39452 + 4.14743i) q^{66} +(-7.07217 - 4.08312i) q^{67} +(-4.12916 - 2.38397i) q^{68} -17.5686i q^{69} -15.6640 q^{70} +(-2.40133 + 1.38641i) q^{71} +26.8899i q^{72} +(2.94187 + 5.09546i) q^{73} +(11.7173 - 20.2949i) q^{74} +(0.763043 + 1.32163i) q^{75} +(4.76745 - 8.25746i) q^{76} +(-0.913787 + 1.58273i) q^{77} +(25.4277 - 14.6807i) q^{78} +(8.50114 + 4.90814i) q^{79} +(5.92383 + 10.2604i) q^{80} +0.966280 q^{81} +(-0.872837 - 0.503933i) q^{82} +(-5.67683 + 9.83256i) q^{83} +31.5791i q^{84} +2.69270i q^{85} +(-1.83563 - 3.17940i) q^{86} +(7.89211 - 4.55651i) q^{87} +3.67125 q^{88} +5.38412i q^{89} +(25.2862 - 14.5990i) q^{90} +(9.70364 - 5.60240i) q^{91} +(-22.4254 + 12.9473i) q^{92} +(-20.8757 + 12.0526i) q^{93} +23.5162i q^{94} -5.38484 q^{95} +(4.24791 - 2.45253i) q^{96} +(-3.93505 - 6.81571i) q^{97} +0.450091i q^{98} -3.40664i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 8 q^{4} + 6 q^{5} - 21 q^{6} - 3 q^{7} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^3 + 8 * q^4 + 6 * q^5 - 21 * q^6 - 3 * q^7 + 2 * q^9	\( 8 q - 2 q^{3} + 8 q^{4} + 6 q^{5} - 21 q^{6} - 3 q^{7} + 2 q^{9} - 6 q^{10} + q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 20 q^{16} + 6 q^{17} + 12 q^{18} + 3 q^{19} + 30 q^{20} + 6 q^{21} + 5 q^{22} - 4 q^{25} - 15 q^{26} - 14 q^{27} - 42 q^{30} - 3 q^{31} + 48 q^{32} + 8 q^{34} + 3 q^{35} + 35 q^{36} + 18 q^{39} + 21 q^{40} - 24 q^{41} + 27 q^{42} - 18 q^{44} + 9 q^{45} - 17 q^{46} + 12 q^{47} - 22 q^{48} - 13 q^{49} - 12 q^{51} - 12 q^{52} - 18 q^{54} - 6 q^{55} - 6 q^{56} + 22 q^{58} - 3 q^{59} - 12 q^{60} - 8 q^{61} + 66 q^{62} - 36 q^{63} - 98 q^{64} + 24 q^{65} + 10 q^{66} - 15 q^{67} - 57 q^{68} - 36 q^{70} + 15 q^{71} - 16 q^{73} + 6 q^{74} + 13 q^{75} + 21 q^{76} + 3 q^{77} + 33 q^{78} + 42 q^{79} + 42 q^{80} + 8 q^{81} + 60 q^{82} - 42 q^{83} - 42 q^{86} + 15 q^{87} + 84 q^{88} + 63 q^{90} - 69 q^{92} - 48 q^{93} + 54 q^{95} + 102 q^{96} + 3 q^{97}+O(q^{100}) \) 8 * q - 2 * q^3 + 8 * q^4 + 6 * q^5 - 21 * q^6 - 3 * q^7 + 2 * q^9 - 6 * q^10 + q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 20 * q^16 + 6 * q^17 + 12 * q^18 + 3 * q^19 + 30 * q^20 + 6 * q^21 + 5 * q^22 - 4 * q^25 - 15 * q^26 - 14 * q^27 - 42 * q^30 - 3 * q^31 + 48 * q^32 + 8 * q^34 + 3 * q^35 + 35 * q^36 + 18 * q^39 + 21 * q^40 - 24 * q^41 + 27 * q^42 - 18 * q^44 + 9 * q^45 - 17 * q^46 + 12 * q^47 - 22 * q^48 - 13 * q^49 - 12 * q^51 - 12 * q^52 - 18 * q^54 - 6 * q^55 - 6 * q^56 + 22 * q^58 - 3 * q^59 - 12 * q^60 - 8 * q^61 + 66 * q^62 - 36 * q^63 - 98 * q^64 + 24 * q^65 + 10 * q^66 - 15 * q^67 - 57 * q^68 - 36 * q^70 + 15 * q^71 - 16 * q^73 + 6 * q^74 + 13 * q^75 + 21 * q^76 + 3 * q^77 + 33 * q^78 + 42 * q^79 + 42 * q^80 + 8 * q^81 + 60 * q^82 - 42 * q^83 - 42 * q^86 + 15 * q^87 + 84 * q^88 + 63 * q^90 - 69 * q^92 - 48 * q^93 + 54 * q^95 + 102 * q^96 + 3 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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