LMFDB - Embedded newform 273.2.l.b.16.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(16,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("273.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.l (of order $3$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + \cdots + 1 $ x^16 + 11x^14 - 4x^13 + 87x^12 - 35x^11 + 326x^10 - 205x^9 + 895x^8 - 481x^7 + 1005x^6 - 544x^5 + 811x^4 - 312x^3 + 195x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.4
Root			$0.379240 + 0.656863i$ of defining polynomial
Character	$\chi$	$=$	273.16
Dual form			273.2.l.b.256.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.758480 q^{2} +(0.500000 - 0.866025i) q^{3} -1.42471 q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 + 0.656863i) q^{6} +(-1.32400 + 2.29064i) q^{7} +2.59757 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q-0.758480 q^{2} +(0.500000 - 0.866025i) q^{3} -1.42471 q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 + 0.656863i) q^{6} +(-1.32400 + 2.29064i) q^{7} +2.59757 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.271437 - 0.470142i) q^{10} +(-2.24386 + 3.88648i) q^{11} +(-0.712354 + 1.23383i) q^{12} +(3.26504 + 1.52954i) q^{13} +(1.00422 - 1.73741i) q^{14} +(0.357869 + 0.619848i) q^{15} +0.879208 q^{16} -3.77454 q^{17} +(0.379240 + 0.656863i) q^{18} +(2.96005 + 5.12696i) q^{19} +(0.509859 - 0.883102i) q^{20} +(1.32176 + 2.29193i) q^{21} +(1.70192 - 2.94782i) q^{22} -0.931345 q^{23} +(1.29879 - 2.24956i) q^{24} +(2.24386 + 3.88648i) q^{25} +(-2.47647 - 1.16012i) q^{26} -1.00000 q^{27} +(1.88631 - 3.26349i) q^{28} +(-1.12150 - 1.94250i) q^{29} +(-0.271437 - 0.470142i) q^{30} +(0.191136 + 0.331058i) q^{31} -5.86201 q^{32} +(2.24386 + 3.88648i) q^{33} +2.86291 q^{34} +(-0.946032 - 1.64043i) q^{35} +(0.712354 + 1.23383i) q^{36} -0.657446 q^{37} +(-2.24514 - 3.88870i) q^{38} +(2.95714 - 2.06284i) q^{39} +(-0.929592 + 1.61010i) q^{40} +(-2.29549 - 3.97591i) q^{41} +(-1.00253 - 1.73839i) q^{42} +(-2.50110 + 4.33202i) q^{43} +(3.19684 - 5.53710i) q^{44} +0.715739 q^{45} +0.706407 q^{46} +(-4.18536 + 7.24926i) q^{47} +(0.439604 - 0.761417i) q^{48} +(-3.49407 - 6.06560i) q^{49} +(-1.70192 - 2.94782i) q^{50} +(-1.88727 + 3.26885i) q^{51} +(-4.65173 - 2.17914i) q^{52} +(-1.21338 - 2.10164i) q^{53} +0.758480 q^{54} +(-1.60602 - 2.78170i) q^{55} +(-3.43917 + 5.95011i) q^{56} +5.92010 q^{57} +(0.850636 + 1.47335i) q^{58} +5.61400 q^{59} +(-0.509859 - 0.883102i) q^{60} +(-0.996890 - 1.72666i) q^{61} +(-0.144973 - 0.251101i) q^{62} +(2.64575 + 0.00129331i) q^{63} +2.68780 q^{64} +(-2.11654 + 1.47646i) q^{65} +(-1.70192 - 2.94782i) q^{66} +(7.23273 - 12.5274i) q^{67} +5.37762 q^{68} +(-0.465673 + 0.806569i) q^{69} +(0.717546 + 1.24423i) q^{70} +(2.14741 - 3.71943i) q^{71} +(-1.29879 - 2.24956i) q^{72} +(-1.34127 - 2.32315i) q^{73} +0.498660 q^{74} +4.48772 q^{75} +(-4.21721 - 7.30442i) q^{76} +(-5.93167 - 10.2856i) q^{77} +(-2.24293 + 1.56463i) q^{78} +(2.75173 - 4.76614i) q^{79} +(-0.314642 + 0.544975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.74108 + 3.01565i) q^{82} +11.5302 q^{83} +(-1.88312 - 3.26534i) q^{84} +(1.35079 - 2.33964i) q^{85} +(1.89703 - 3.28575i) q^{86} -2.24300 q^{87} +(-5.82859 + 10.0954i) q^{88} -12.1018 q^{89} -0.542874 q^{90} +(-7.82652 + 5.45395i) q^{91} +1.32689 q^{92} +0.382273 q^{93} +(3.17451 - 5.49842i) q^{94} -4.23725 q^{95} +(-2.93100 + 5.07665i) q^{96} +(-1.79870 + 3.11544i) q^{97} +(2.65018 + 4.60063i) q^{98} +4.48772 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.758480			−0.536326			−0.268163	−	0.963373i	$-0.586417\pi$
$2$	−0.758480			−0.536326			−0.268163	+	0.963373i	$0.586417\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−1.42471			−0.712354
$5$	−0.357869	+	0.619848i	−0.160044	+	0.277204i	−0.934884	−	0.354953i	$-0.884497\pi$
$5$	−0.357869	+	0.619848i	−0.160044	+	0.277204i	0.774840	+	0.632157i	$0.217830\pi$
$6$	−0.379240	+	0.656863i	−0.154824	+	0.268163i
$7$	−1.32400	+	2.29064i	−0.500423	+	0.865781i
$7$	−1.32400	+	2.29064i	−0.500423	+	0.865781i
$8$	2.59757			0.918381
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.271437	−	0.470142i	0.0858359	−	0.148672i
$11$	−2.24386	+	3.88648i	−0.676549	+	1.17182i	0.299465	+	0.954107i	$0.403192\pi$
$11$	−2.24386	+	3.88648i	−0.676549	+	1.17182i	−0.976014	+	0.217710i	$0.930141\pi$
$12$	−0.712354	+	1.23383i	−0.205639	+	0.356177i
$13$	3.26504	+	1.52954i	0.905560	+	0.424217i
$13$	3.26504	+	1.52954i	0.905560	+	0.424217i
$14$	1.00422	−	1.73741i	0.268390	−	0.464341i
$15$	0.357869	+	0.619848i	0.0924015	+	0.160044i
$16$	0.879208			0.219802
$17$	−3.77454			−0.915461			−0.457730	−	0.889091i	$-0.651338\pi$
$17$	−3.77454			−0.915461			−0.457730	+	0.889091i	$0.651338\pi$
$18$	0.379240	+	0.656863i	0.0893877	+	0.154824i
$19$	2.96005	+	5.12696i	0.679082	+	1.17621i	0.975258	+	0.221072i	$0.0709554\pi$
$19$	2.96005	+	5.12696i	0.679082	+	1.17621i	−0.296175	+	0.955134i	$0.595711\pi$
$20$	0.509859	−	0.883102i	0.114008	−	0.197468i
$21$	1.32176	+	2.29193i	0.288431	+	0.500141i
$22$	1.70192	−	2.94782i	0.362851	−	0.628477i
$23$	−0.931345			−0.194199			−0.0970995	−	0.995275i	$-0.530956\pi$
$23$	−0.931345			−0.194199			−0.0970995	+	0.995275i	$0.530956\pi$
$24$	1.29879	−	2.24956i	0.265114	−	0.459190i
$25$	2.24386	+	3.88648i	0.448772	+	0.777296i
$26$	−2.47647	−	1.16012i	−0.485676	−	0.227519i
$27$	−1.00000			−0.192450
$28$	1.88631	−	3.26349i	0.356478	−	0.616742i
$29$	−1.12150	−	1.94250i	−0.208257	−	0.360713i	0.742908	−	0.669393i	$-0.233446\pi$
$29$	−1.12150	−	1.94250i	−0.208257	−	0.360713i	−0.951166	+	0.308681i	$0.900113\pi$
$30$	−0.271437	−	0.470142i	−0.0495574	−	0.0858359i
$31$	0.191136	+	0.331058i	0.0343291	+	0.0594597i	0.882679	−	0.469975i	$-0.155737\pi$
$31$	0.191136	+	0.331058i	0.0343291	+	0.0594597i	−0.848350	+	0.529435i	$0.822404\pi$
$32$	−5.86201			−1.03627
$33$	2.24386	+	3.88648i	0.390606	+	0.676549i
$34$	2.86291			0.490986
$35$	−0.946032	−	1.64043i	−0.159909	−	0.277283i
$36$	0.712354	+	1.23383i	0.118726	+	0.205639i
$37$	−0.657446			−0.108083			−0.0540417	−	0.998539i	$-0.517210\pi$
$37$	−0.657446			−0.108083			−0.0540417	+	0.998539i	$0.517210\pi$
$38$	−2.24514	−	3.88870i	−0.364210	−	0.630830i
$39$	2.95714	−	2.06284i	0.473521	−	0.330319i
$40$	−0.929592	+	1.61010i	−0.146981	+	0.254579i
$41$	−2.29549	−	3.97591i	−0.358495	−	0.620932i	0.629214	−	0.777232i	$-0.283377\pi$
$41$	−2.29549	−	3.97591i	−0.358495	−	0.620932i	−0.987710	+	0.156300i	$0.950043\pi$
$42$	−1.00253	−	1.73839i	−0.154693	−	0.268239i
$43$	−2.50110	+	4.33202i	−0.381413	+	0.660627i	−0.991265	−	0.131889i	$-0.957896\pi$
$43$	−2.50110	+	4.33202i	−0.381413	+	0.660627i	0.609851	+	0.792516i	$0.291229\pi$
$44$	3.19684	−	5.53710i	0.481942	−	0.834749i
$45$	0.715739			0.106696
$46$	0.706407			0.104154
$47$	−4.18536	+	7.24926i	−0.610498	+	1.05741i	0.380659	+	0.924716i	$0.375697\pi$
$47$	−4.18536	+	7.24926i	−0.610498	+	1.05741i	−0.991157	+	0.132698i	$0.957636\pi$
$48$	0.439604	−	0.761417i	0.0634514	−	0.109901i
$49$	−3.49407	−	6.06560i	−0.499153	−	0.866514i
$50$	−1.70192	−	2.94782i	−0.240688	−	0.416884i
$51$	−1.88727	+	3.26885i	−0.264271	+	0.457730i
$52$	−4.65173	−	2.17914i	−0.645080	−	0.302193i
$53$	−1.21338	−	2.10164i	−0.166671	−	0.288682i	0.770577	−	0.637347i	$-0.219968\pi$
$53$	−1.21338	−	2.10164i	−0.166671	−	0.288682i	−0.937247	+	0.348665i	$0.886635\pi$
$54$	0.758480			0.103216
$55$	−1.60602	−	2.78170i	−0.216555	−	0.375085i
$56$	−3.43917	+	5.95011i	−0.459579	+	0.795116i
$57$	5.92010			0.784137
$58$	0.850636	+	1.47335i	0.111694	+	0.193460i
$59$	5.61400			0.730881			0.365441	−	0.930835i	$-0.380918\pi$
$59$	5.61400			0.730881			0.365441	+	0.930835i	$0.380918\pi$
$60$	−0.509859	−	0.883102i	−0.0658225	−	0.114008i
$61$	−0.996890	−	1.72666i	−0.127639	−	0.221077i	0.795123	−	0.606449i	$-0.207406\pi$
$61$	−0.996890	−	1.72666i	−0.127639	−	0.221077i	−0.922761	+	0.385372i	$0.874073\pi$
$62$	−0.144973	−	0.251101i	−0.0184116	−	0.0318898i
$63$	2.64575	+	0.00129331i	0.333333	+	0.000162942i
$64$	2.68780			0.335975
$65$	−2.11654	+	1.47646i	−0.262524	+	0.183132i
$66$	−1.70192	−	2.94782i	−0.209492	−	0.362851i
$67$	7.23273	−	12.5274i	0.883618	−	1.53047i	0.0363288	−	0.999340i	$-0.488434\pi$
$67$	7.23273	−	12.5274i	0.883618	−	1.53047i	0.847289	−	0.531132i	$-0.178233\pi$
$68$	5.37762			0.652132
$69$	−0.465673	+	0.806569i	−0.0560604	+	0.0970995i
$70$	0.717546	+	1.24423i	0.0857632	+	0.148714i
$71$	2.14741	−	3.71943i	0.254851	−	0.441415i	−0.710004	−	0.704198i	$-0.751307\pi$
$71$	2.14741	−	3.71943i	0.254851	−	0.441415i	0.964855	+	0.262783i	$0.0846402\pi$
$72$	−1.29879	−	2.24956i	−0.153063	−	0.265114i
$73$	−1.34127	−	2.32315i	−0.156984	−	0.271905i	0.776796	−	0.629753i	$-0.216844\pi$
$73$	−1.34127	−	2.32315i	−0.156984	−	0.271905i	−0.933780	+	0.357848i	$0.883511\pi$
$74$	0.498660			0.0579680
$75$	4.48772			0.518197
$76$	−4.21721	−	7.30442i	−0.483747	−	0.837874i
$77$	−5.93167	−	10.2856i	−0.675976	−	1.17215i
$78$	−2.24293	+	1.56463i	−0.253962	+	0.177159i
$79$	2.75173	−	4.76614i	0.309594	−	0.536233i	−0.668679	−	0.743551i	$-0.733140\pi$
$79$	2.75173	−	4.76614i	0.309594	−	0.536233i	0.978274	+	0.207318i	$0.0664735\pi$
$80$	−0.314642	+	0.544975i	−0.0351780	+	0.0609301i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.74108	+	3.01565i	0.192271	+	0.333022i
$83$	11.5302			1.26560			0.632800	−	0.774316i	$-0.281906\pi$
$83$	11.5302			1.26560			0.632800	+	0.774316i	$0.281906\pi$
$84$	−1.88312	−	3.26534i	−0.205465	−	0.356277i
$85$	1.35079	−	2.33964i	0.146514	−	0.253770i
$86$	1.89703	−	3.28575i	0.204562	−	0.354312i
$87$	−2.24300			−0.240475
$88$	−5.82859	+	10.0954i	−0.621330	+	1.07617i
$89$	−12.1018			−1.28278			−0.641392	−	0.767213i	$-0.721643\pi$
$89$	−12.1018			−1.28278			−0.641392	+	0.767213i	$0.721643\pi$
$90$	−0.542874			−0.0572239
$91$	−7.82652	+	5.45395i	−0.820443	+	0.571729i
$92$	1.32689			0.138338
$93$	0.382273			0.0396398
$94$	3.17451	−	5.49842i	0.327426	−	0.567119i
$95$	−4.23725			−0.434732
$96$	−2.93100	+	5.07665i	−0.299144	+	0.518133i
$97$	−1.79870	+	3.11544i	−0.182630	+	0.316325i	−0.942775	−	0.333429i	$-0.891794\pi$
$97$	−1.79870	+	3.11544i	−0.182630	+	0.316325i	0.760145	+	0.649753i	$0.225128\pi$
$98$	2.65018	+	4.60063i	0.267709	+	0.464734i
$99$	4.48772			0.451033
$100$	−3.19684	−	5.53710i	−0.319684	−	0.553710i
$101$	−5.98958	+	10.3743i	−0.595986	+	1.03228i	0.397421	+	0.917636i	$0.369905\pi$
$101$	−5.98958	+	10.3743i	−0.595986	+	1.03228i	−0.993407	+	0.114642i	$0.963428\pi$
$102$	1.43146	−	2.47936i	0.141735	−	0.245493i
$103$	−1.54966	+	2.68409i	−0.152692	+	0.264471i	−0.932216	−	0.361901i	$-0.882128\pi$
$103$	−1.54966	+	2.68409i	−0.152692	+	0.264471i	0.779524	+	0.626372i	$0.215461\pi$
$104$	8.48119	+	3.97308i	0.831649	+	0.389593i
$105$	−1.89367		0.000925671i	−0.184803		9.03363e-5i
$106$	0.920325	+	1.59405i	0.0893898	+	0.154828i
$107$	11.1863			1.08142			0.540708	−	0.841210i	$-0.318156\pi$
$107$	11.1863			1.08142			0.540708	+	0.841210i	$0.318156\pi$
$108$	1.42471			0.137093
$109$	10.1906	+	17.6506i	0.976082	+	1.69062i	0.676316	+	0.736611i	$0.263575\pi$
$109$	10.1906	+	17.6506i	0.976082	+	1.69062i	0.299766	+	0.954013i	$0.403091\pi$
$110$	1.21813	+	2.10987i	0.116144	+	0.201168i
$111$	−0.328723	+	0.569365i	−0.0312010	+	0.0540417i
$112$	−1.16407	+	2.01395i	−0.109994	+	0.190300i
$113$	8.55107	−	14.8109i	0.804417	−	1.39329i	−0.112266	−	0.993678i	$-0.535811\pi$
$113$	8.55107	−	14.8109i	0.804417	−	1.39329i	0.916684	−	0.399613i	$-0.130856\pi$
$114$	−4.49028			−0.420553
$115$	0.333300	−	0.577292i	0.0310804	−	0.0538328i
$116$	1.59781	+	2.76749i	0.148353	+	0.256955i
$117$	−0.307905	−	3.59238i	−0.0284658	−	0.332116i
$118$	−4.25811			−0.391991
$119$	4.99748	−	8.64612i	0.458118	−	0.792588i
$120$	0.929592	+	1.61010i	0.0848597	+	0.146981i
$121$	−4.56981	−	7.91514i	−0.415437	−	0.719558i
$122$	0.756122	+	1.30964i	0.0684560	+	0.118569i
$123$	−4.59098			−0.413955
$124$	−0.272313	−	0.471661i	−0.0244545	−	0.0423564i
$125$	−6.79073			−0.607381
$126$	−2.00675		0.000980949i	−0.178775		8.73899e-5i
$127$	9.01920	+	15.6217i	0.800325	+	1.38620i	0.919402	+	0.393318i	$0.128673\pi$
$127$	9.01920	+	15.6217i	0.800325	+	1.38620i	−0.119077	+	0.992885i	$0.537994\pi$
$128$	9.68537			0.856074
$129$	2.50110	+	4.33202i	0.220209	+	0.381413i
$130$	1.60535	−	1.11986i	0.140799	−	0.0982185i
$131$	−9.83728	+	17.0387i	−0.859487	+	1.48868i	0.0129316	+	0.999916i	$0.495884\pi$
$131$	−9.83728	+	17.0387i	−0.859487	+	1.48868i	−0.872419	+	0.488759i	$0.837450\pi$
$132$	−3.19684	−	5.53710i	−0.278250	−	0.481942i
$133$	−15.6631	−	0.00765652i	−1.35816	−	0.000663905i
$134$	−5.48588	+	9.50182i	−0.473908	+	0.820832i
$135$	0.357869	−	0.619848i	0.0308005	−	0.0533480i
$136$	−9.80465			−0.840742
$137$	19.2827			1.64744			0.823718	−	0.567000i	$-0.191896\pi$
$137$	19.2827			1.64744			0.823718	+	0.567000i	$0.191896\pi$
$138$	0.353203	−	0.611766i	0.0300667	−	0.0520770i
$139$	−1.31388	+	2.27571i	−0.111442	+	0.193023i	−0.916352	−	0.400374i	$-0.868880\pi$
$139$	−1.31388	+	2.27571i	−0.111442	+	0.193023i	0.804910	+	0.593397i	$0.202214\pi$
$140$	1.34782	+	2.33713i	0.113911	+	0.197523i
$141$	4.18536	+	7.24926i	0.352471	+	0.610498i
$142$	−1.62877	+	2.82111i	−0.136683	+	0.236743i
$143$	−13.2708	+	9.25746i	−1.10976	+	0.774148i
$144$	−0.439604	−	0.761417i	−0.0366337	−	0.0634514i
$145$	1.60540			0.133321
$146$	1.01733	+	1.76207i	0.0841948	+	0.145830i
$147$	−7.00000	−	0.00684355i	−0.577350	−	0.000564446i
$148$	0.936669			0.0769937
$149$	7.79478	+	13.5010i	0.638573	+	1.10604i	0.985746	+	0.168240i	$0.0538084\pi$
$149$	7.79478	+	13.5010i	0.638573	+	1.10604i	−0.347173	+	0.937801i	$0.612858\pi$
$150$	−3.40385			−0.277923
$151$	4.61134	+	7.98707i	0.375265	+	0.649978i	0.990367	−	0.138470i	$-0.0442183\pi$
$151$	4.61134	+	7.98707i	0.375265	+	0.649978i	−0.615102	+	0.788448i	$0.710885\pi$
$152$	7.68895	+	13.3177i	0.623656	+	1.08020i
$153$	1.88727	+	3.26885i	0.152577	+	0.264271i
$154$	4.49905	+	7.80139i	0.362544	+	0.628654i
$155$	−0.273607			−0.0219767
$156$	−4.21306	+	2.93895i	−0.337315	+	0.235304i
$157$	−9.20539	−	15.9442i	−0.734670	−	1.27249i	−0.954868	−	0.297031i	$-0.904003\pi$
$157$	−9.20539	−	15.9442i	−0.734670	−	1.27249i	0.220197	−	0.975455i	$-0.429330\pi$
$158$	−2.08714	+	3.61502i	−0.166044	+	0.287596i
$159$	−2.42676			−0.192455
$160$	2.09783	−	3.63355i	0.165848	−	0.287258i
$161$	1.23310	−	2.13338i	0.0971817	−	0.168134i
$162$	0.379240	−	0.656863i	0.0297959	−	0.0516080i
$163$	−5.58430	−	9.67230i	−0.437396	−	0.757593i	0.560091	−	0.828431i	$-0.310766\pi$
$163$	−5.58430	−	9.67230i	−0.437396	−	0.757593i	−0.997488	+	0.0708379i	$0.977433\pi$
$164$	3.27040	+	5.66451i	0.255376	+	0.442324i
$165$	−3.21203			−0.250056
$166$	−8.74540			−0.678774
$167$	7.09719	+	12.2927i	0.549197	+	0.951237i	0.998330	+	0.0577721i	$0.0183997\pi$
$167$	7.09719	+	12.2927i	0.549197	+	0.951237i	−0.449133	+	0.893465i	$0.648267\pi$
$168$	3.43336	+	5.95347i	0.264889	+	0.459320i
$169$	8.32104	+	9.98801i	0.640080	+	0.768309i
$170$	−1.02455	+	1.77457i	−0.0785794	+	0.136103i
$171$	2.96005	−	5.12696i	0.226361	−	0.392068i
$172$	3.56333	−	6.17187i	0.271701	−	0.470601i
$173$	−9.63624	−	16.6905i	−0.732630	−	1.26895i	−0.955755	−	0.294163i	$-0.904959\pi$
$173$	−9.63624	−	16.6905i	−0.732630	−	1.26895i	0.223125	−	0.974790i	$-0.428374\pi$
$174$	1.70127			0.128973
$175$	−11.8734	−	0.00580401i	−0.897544	−	0.000438742i
$176$	−1.97282	+	3.41702i	−0.148707	+	0.257568i
$177$	2.80700	−	4.86187i	0.210987	−	0.365441i
$178$	9.17895			0.687992
$179$	5.61622	−	9.72758i	0.419776	−	0.727074i	−0.576140	−	0.817351i	$-0.695442\pi$
$179$	5.61622	−	9.72758i	0.419776	−	0.727074i	0.995917	+	0.0902769i	$0.0287752\pi$
$180$	−1.01972			−0.0760053
$181$	2.43304			0.180846			0.0904232	−	0.995903i	$-0.471178\pi$
$181$	2.43304			0.180846			0.0904232	+	0.995903i	$0.471178\pi$
$182$	5.93626	−	4.13671i	0.440025	−	0.306633i
$183$	−1.99378			−0.147385
$184$	−2.41924			−0.178349
$185$	0.235280	−	0.407517i	0.0172981	−	0.0299612i
$186$	−0.289946			−0.0212599
$187$	8.46954	−	14.6697i	0.619354	−	1.07275i
$188$	5.96292	−	10.3281i	0.434890	−	0.753252i
$189$	1.32400	−	2.29064i	0.0963065	−	0.166620i
$190$	3.21387			0.233158
$191$	6.86953	+	11.8984i	0.497062	+	0.860936i	0.999994	−	0.00338944i	$-0.00107890\pi$
$191$	6.86953	+	11.8984i	0.497062	+	0.860936i	−0.502932	+	0.864326i	$0.667746\pi$
$192$	1.34390	−	2.32770i	0.0969876	−	0.167988i
$193$	6.93363	−	12.0094i	0.499094	−	0.864456i	−0.500906	−	0.865502i	$-0.667000\pi$
$193$	6.93363	−	12.0094i	0.499094	−	0.864456i	0.999999	+	0.00104614i	$0.000332996\pi$
$194$	1.36428	−	2.36300i	0.0979493	−	0.169653i
$195$	0.220379	+	2.57121i	0.0157817	+	0.184128i
$196$	4.97803	+	8.64170i	0.355574	+	0.617265i
$197$	−9.15733	−	15.8610i	−0.652433	−	1.13005i	−0.982531	−	0.186100i	$-0.940415\pi$
$197$	−9.15733	−	15.8610i	−0.652433	−	1.13005i	0.330098	−	0.943947i	$-0.392918\pi$
$198$	−3.40385			−0.241901
$199$	−7.11723			−0.504527			−0.252264	−	0.967659i	$-0.581175\pi$
$199$	−7.11723			−0.504527			−0.252264	+	0.967659i	$0.581175\pi$
$200$	5.82859	+	10.0954i	0.412143	+	0.713853i
$201$	−7.23273	−	12.5274i	−0.510157	−	0.883618i
$202$	4.54298	−	7.86867i	0.319643	−	0.553638i
$203$	5.93442	+	0.00290089i	0.416515	+	0.000203603i
$204$	2.68881	−	4.65715i	0.188254	−	0.326066i
$205$	3.28594			0.229500
$206$	1.17538	−	2.03583i	0.0818929	−	0.141843i
$207$	0.465673	+	0.806569i	0.0323665	+	0.0560604i
$208$	2.87065	+	1.34478i	0.199044	+	0.0932438i
$209$	−26.5678			−1.83773
$210$	1.43631		0.000702103i	0.0991147		4.84497e-5i
$211$	−5.95003	−	10.3058i	−0.409617	−	0.709478i	0.585230	−	0.810868i	$-0.301004\pi$
$211$	−5.95003	−	10.3058i	−0.409617	−	0.709478i	−0.994847	+	0.101390i	$0.967671\pi$
$212$	1.72871	+	2.99422i	0.118728	+	0.205644i
$213$	−2.14741	−	3.71943i	−0.147138	−	0.254851i
$214$	−8.48455			−0.579992
$215$	−1.79013	−	3.10060i	−0.122086	−	0.211459i
$216$	−2.59757			−0.176742
$217$	−1.01140		0.000494397i	−0.0686582		3.35618e-5i
$218$	−7.72937	−	13.3877i	−0.523499	−	0.906726i
$219$	−2.68255			−0.181270
$220$	2.28810	+	3.96311i	0.154264	+	0.267193i
$221$	−12.3240	−	5.77330i	−0.829005	−	0.388354i
$222$	0.249330	−	0.431852i	0.0167339	−	0.0289840i
$223$	11.9432	+	20.6863i	0.799778	+	1.38526i	0.919760	+	0.392481i	$0.128383\pi$
$223$	11.9432	+	20.6863i	0.799778	+	1.38526i	−0.119982	+	0.992776i	$0.538284\pi$
$224$	7.76127	−	13.4278i	0.518572	−	0.897180i
$225$	2.24386	−	3.88648i	0.149591	−	0.259099i
$226$	−6.48582	+	11.2338i	−0.431430	+	0.747259i
$227$	12.5878			0.835483			0.417741	−	0.908566i	$-0.362822\pi$
$227$	12.5878			0.835483			0.417741	+	0.908566i	$0.362822\pi$
$228$	−8.43442			−0.558583
$229$	7.66365	−	13.2738i	0.506429	−	0.877160i	−0.493544	−	0.869721i	$-0.664299\pi$
$229$	7.66365	−	13.2738i	0.506429	−	0.877160i	0.999972	−	0.00743905i	$-0.00236795\pi$
$230$	−0.252801	+	0.437865i	−0.0166692	+	0.0288720i
$231$	−11.8734	−	0.00580401i	−0.781211	−	0.000381876i
$232$	−2.91318	−	5.04578i	−0.191260	−	0.331271i
$233$	13.3343	−	23.0957i	0.873559	−	1.51305i	0.0152699	−	0.999883i	$-0.495139\pi$
$233$	13.3343	−	23.0957i	0.873559	−	1.51305i	0.858289	−	0.513166i	$-0.171527\pi$
$234$	0.233540	+	2.72475i	0.0152670	+	0.178122i
$235$	−2.99563	−	5.18858i	−0.195413	−	0.338465i
$236$	−7.99832			−0.520646
$237$	−2.75173	−	4.76614i	−0.178744	−	0.309594i
$238$	−3.79049	+	6.55791i	−0.245701	+	0.425086i
$239$	−14.5891			−0.943693			−0.471846	−	0.881681i	$-0.656412\pi$
$239$	−14.5891			−0.943693			−0.471846	+	0.881681i	$0.656412\pi$
$240$	0.314642	+	0.544975i	0.0203100	+	0.0351780i
$241$	12.8923			0.830465			0.415233	−	0.909715i	$-0.363700\pi$
$241$	12.8923			0.830465			0.415233	+	0.909715i	$0.363700\pi$
$242$	3.46611	+	6.00347i	0.222810	+	0.385918i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	1.42028	+	2.45999i	0.0909240	+	0.157485i
$245$	5.01017	+	0.00489819i	0.320088	+	0.000312934i
$246$	3.48217			0.222015
$247$	1.82283	+	21.2673i	0.115984	+	1.35320i
$248$	0.496490	+	0.859947i	0.0315272	+	0.0546067i
$249$	5.76508	−	9.98541i	0.365347	−	0.632800i
$250$	5.15063			0.325755
$251$	−12.0203	+	20.8198i	−0.758717	+	1.31414i	0.184787	+	0.982779i	$0.440840\pi$
$251$	−12.0203	+	20.8198i	−0.758717	+	1.31414i	−0.943505	+	0.331359i	$0.892493\pi$
$252$	−3.76942	−	0.00184259i	−0.237451	−	0.000116072i
$253$	2.08981	−	3.61965i	0.131385	−	0.227566i
$254$	−6.84089	−	11.8488i	−0.429235	−	0.743458i
$255$	−1.35079	−	2.33964i	−0.0845899	−	0.146514i
$256$	−12.7218			−0.795110
$257$	18.7145			1.16738			0.583689	−	0.811978i	$-0.301609\pi$
$257$	18.7145			1.16738			0.583689	+	0.811978i	$0.301609\pi$
$258$	−1.89703	−	3.28575i	−0.118104	−	0.204562i
$259$	0.870456	−	1.50597i	0.0540875	−	0.0935766i
$260$	3.01545	−	2.10352i	0.187010	−	0.130455i
$261$	−1.12150	+	1.94250i	−0.0694192	+	0.120238i
$262$	7.46138	−	12.9235i	0.460966	−	0.798416i
$263$	4.68565	−	8.11578i	0.288929	−	0.500440i	−0.684625	−	0.728895i	$-0.740034\pi$
$263$	4.68565	−	8.11578i	0.288929	−	0.500440i	0.973554	+	0.228455i	$0.0733674\pi$
$264$	5.82859	+	10.0954i	0.358725	+	0.621330i
$265$	1.73693			0.106699
$266$	11.8802	+	0.00580732i	0.728420	+	0.000356070i
$267$	−6.05088	+	10.4804i	−0.370308	+	0.641392i
$268$	−10.3045	+	17.8480i	−0.629449	+	1.09024i
$269$	12.1493			0.740754			0.370377	−	0.928881i	$-0.379228\pi$
$269$	12.1493			0.740754			0.370377	+	0.928881i	$0.379228\pi$
$270$	−0.271437	+	0.470142i	−0.0165191	+	0.0286120i
$271$	−14.6585			−0.890441			−0.445221	−	0.895421i	$-0.646875\pi$
$271$	−14.6585			−0.890441			−0.445221	+	0.895421i	$0.646875\pi$
$272$	−3.31861			−0.201220
$273$	0.809993	+	9.50494i	0.0490230	+	0.575265i
$274$	−14.6256			−0.883563
$275$	−20.1396			−1.21446
$276$	0.663447	−	1.14912i	0.0399348	−	0.0691692i
$277$	−5.03215			−0.302353			−0.151176	−	0.988507i	$-0.548306\pi$
$277$	−5.03215			−0.302353			−0.151176	+	0.988507i	$0.548306\pi$
$278$	0.996555	−	1.72608i	0.0597694	−	0.103524i
$279$	0.191136	−	0.331058i	0.0114430	−	0.0198199i
$280$	−2.45739	−	4.26113i	−0.146857	−	0.254651i
$281$	0.854888			0.0509984			0.0254992	−	0.999675i	$-0.491882\pi$
$281$	0.854888			0.0509984			0.0254992	+	0.999675i	$0.491882\pi$
$282$	−3.17451	−	5.49842i	−0.189040	−	0.327426i
$283$	15.6387	−	27.0871i	0.929625	−	1.61016i	0.145677	−	0.989332i	$-0.453464\pi$
$283$	15.6387	−	27.0871i	0.929625	−	1.61016i	0.783948	−	0.620826i	$-0.213203\pi$
$284$	−3.05944	+	5.29910i	−0.181544	+	0.314444i
$285$	−2.11862	+	3.66956i	−0.125496	+	0.217366i
$286$	10.0656	−	7.02160i	0.595194	−	0.415196i
$287$	12.1466	+	0.00593756i	0.716991	+	0.000350483i
$288$	2.93100	+	5.07665i	0.172711	+	0.299144i
$289$	−2.75284			−0.161931
$290$	−1.21767			−0.0715038
$291$	1.79870	+	3.11544i	0.105442	+	0.182630i
$292$	1.91092	+	3.30982i	0.111828	+	0.193692i
$293$	0.339044	−	0.587241i	0.0198071	−	0.0343070i	−0.855952	−	0.517055i	$-0.827028\pi$
$293$	0.339044	−	0.587241i	0.0198071	−	0.0343070i	0.875759	+	0.482748i	$0.160361\pi$
$294$	5.30936	+	0.00519069i	0.309648	+	0.000302727i
$295$	−2.00908	+	3.47983i	−0.116973	+	0.202603i
$296$	−1.70776			−0.0992618
$297$	2.24386	−	3.88648i	0.130202	−	0.225516i
$298$	−5.91219	−	10.2402i	−0.342484	−	0.593199i
$299$	−3.04088	−	1.42453i	−0.175859	−	0.0823825i
$300$	−6.39369			−0.369140
$301$	−6.61167	−	11.4647i	−0.381090	−	0.660814i
$302$	−3.49761	−	6.05803i	−0.201265	−	0.348601i
$303$	5.98958	+	10.3743i	0.344093	+	0.595986i
$304$	2.60250	+	4.50766i	0.149264	+	0.258532i
$305$	1.42703			0.0817113
$306$	−1.43146	−	2.47936i	−0.0818310	−	0.141735i
$307$	−27.2103			−1.55297			−0.776487	−	0.630134i	$-0.783000\pi$
$307$	−27.2103			−1.55297			−0.776487	+	0.630134i	$0.783000\pi$
$308$	8.45089	+	14.6539i	0.481534	+	0.834984i
$309$	1.54966	+	2.68409i	0.0881569	+	0.152692i
$310$	0.207526			0.0117867
$311$	7.06426	+	12.2357i	0.400577	+	0.693821i	0.993796	−	0.111221i	$-0.0354762\pi$
$311$	7.06426	+	12.2357i	0.400577	+	0.693821i	−0.593218	+	0.805042i	$0.702143\pi$
$312$	7.68139	−	5.35839i	0.434873	−	0.303359i
$313$	9.84907	−	17.0591i	0.556703	−	0.964237i	−0.441066	−	0.897475i	$-0.645400\pi$
$313$	9.84907	−	17.0591i	0.556703	−	0.964237i	0.997769	−	0.0667627i	$-0.0212670\pi$
$314$	6.98211	+	12.0934i	0.394023	+	0.682468i
$315$	−0.947635	+	1.63950i	−0.0533932	+	0.0923754i
$316$	−3.92042	+	6.79036i	−0.220541	+	0.381988i
$317$	−7.83931	+	13.5781i	−0.440299	+	0.762621i	−0.997711	−	0.0676152i	$-0.978461\pi$
$317$	−7.83931	+	13.5781i	−0.440299	+	0.762621i	0.557412	+	0.830236i	$0.311794\pi$
$318$	1.84065			0.103218
$319$	10.0660			0.563586
$320$	−0.961881	+	1.66603i	−0.0537708	+	0.0931338i
$321$	5.59313	−	9.68758i	0.312178	−	0.540708i
$322$	−0.935280	+	1.61812i	−0.0521211	+	0.0901746i
$323$	−11.1728	−	19.3519i	−0.621673	−	1.07677i
$324$	0.712354	−	1.23383i	0.0395752	−	0.0685463i
$325$	1.38179	+	16.1216i	0.0766479	+	0.894265i
$326$	4.23558	+	7.33625i	0.234587	+	0.406317i
$327$	20.3812			1.12708
$328$	−5.96270	−	10.3277i	−0.329235	−	0.570252i
$329$	−11.0640	−	19.1851i	−0.609981	−	1.05771i
$330$	2.43626			0.134112
$331$	−7.21180	−	12.4912i	−0.396396	−	0.686579i	0.596882	−	0.802329i	$-0.296406\pi$
$331$	−7.21180	−	12.4912i	−0.396396	−	0.686579i	−0.993278	+	0.115750i	$0.963073\pi$
$332$	−16.4271			−0.901555
$333$	0.328723	+	0.569365i	0.0180139	+	0.0312010i
$334$	−5.38308	−	9.32376i	−0.294549	−	0.510174i
$335$	5.17674	+	8.96638i	0.282836	+	0.489886i
$336$	1.16210	+	2.01509i	0.0633977	+	0.109932i
$337$	14.4299			0.786049			0.393025	−	0.919528i	$-0.371429\pi$
$337$	14.4299			0.786049			0.393025	+	0.919528i	$0.371429\pi$
$338$	−6.31134	−	7.57571i	−0.343292	−	0.412064i
$339$	−8.55107	−	14.8109i	−0.464431	−	0.804417i
$340$	−1.92449	+	3.33331i	−0.104370	+	0.180774i
$341$	−1.71553			−0.0929012
$342$	−2.24514	+	3.88870i	−0.121403	+	0.210277i
$343$	18.5202	+	0.0271595i	0.999999	+	0.00146647i
$344$	−6.49678	+	11.2527i	−0.350283	+	0.606707i
$345$	−0.333300	−	0.577292i	−0.0179443	−	0.0310804i
$346$	7.30890	+	12.6594i	0.392929	+	0.680573i
$347$	−4.66868			−0.250628			−0.125314	−	0.992117i	$-0.539994\pi$
$347$	−4.66868			−0.250628			−0.125314	+	0.992117i	$0.539994\pi$
$348$	3.19562			0.171303
$349$	2.06807	+	3.58201i	0.110701	+	0.191740i	0.916053	−	0.401057i	$-0.131357\pi$
$349$	2.06807	+	3.58201i	0.110701	+	0.191740i	−0.805352	+	0.592797i	$0.798024\pi$
$350$	9.00573	+	0.00440222i	0.481376	+	0.000235309i
$351$	−3.26504	−	1.52954i	−0.174275	−	0.0816406i
$352$	13.1535	−	22.7826i	0.701085	−	1.21431i
$353$	−17.8950	+	30.9950i	−0.952453	+	1.64970i	−0.212362	+	0.977191i	$0.568116\pi$
$353$	−17.8950	+	30.9950i	−0.952453	+	1.64970i	−0.740091	+	0.672507i	$0.765218\pi$
$354$	−2.12906	+	3.68763i	−0.113158	+	0.195995i
$355$	1.53699	+	2.66214i	0.0815748	+	0.141292i
$356$	17.2415			0.913797
$357$	−4.98902	−	8.65100i	−0.264047	−	0.457860i
$358$	−4.25979	+	7.37818i	−0.225137	+	0.389949i
$359$	12.6381	−	21.8899i	0.667014	−	1.15530i	−0.311721	−	0.950174i	$-0.600905\pi$
$359$	12.6381	−	21.8899i	0.667014	−	1.15530i	0.978735	−	0.205129i	$-0.0657614\pi$
$360$	1.85918			0.0979876
$361$	−8.02381	+	13.8976i	−0.422306	+	0.731455i
$362$	−1.84541			−0.0969927
$363$	−9.13961			−0.479705
$364$	11.1505	−	7.77028i	0.584446	−	0.407273i
$365$	1.92000			0.100498
$366$	1.51224			0.0790462
$367$	−17.6999	+	30.6571i	−0.923925	+	1.60029i	−0.130645	+	0.991429i	$0.541705\pi$
$367$	−17.6999	+	30.6571i	−0.923925	+	1.60029i	−0.793280	+	0.608856i	$0.791629\pi$
$368$	−0.818846			−0.0426853
$369$	−2.29549	+	3.97591i	−0.119498	+	0.206977i
$370$	−0.178455	+	0.309093i	−0.00927744	+	0.0160690i
$371$	6.42060	+	0.00313855i	0.333341	+	0.000162945i
$372$	−0.544627			−0.0282376
$373$	16.3902	+	28.3887i	0.848652	+	1.46991i	0.882411	+	0.470479i	$0.155919\pi$
$373$	16.3902	+	28.3887i	0.848652	+	1.46991i	−0.0337586	+	0.999430i	$0.510748\pi$
$374$	−6.42398	+	11.1267i	−0.332176	+	0.575346i
$375$	−3.39536	+	5.88094i	−0.175336	+	0.303691i
$376$	−10.8718	+	18.8305i	−0.560669	+	0.971108i
$377$	−0.690631	−	8.05771i	−0.0355693	−	0.414993i
$378$	−1.00422	+	1.73741i	−0.0516517	+	0.0893625i
$379$	−6.04308	−	10.4669i	−0.310412	−	0.537650i	0.668039	−	0.744126i	$-0.267134\pi$
$379$	−6.04308	−	10.4669i	−0.310412	−	0.537650i	−0.978452	+	0.206476i	$0.933800\pi$
$380$	6.03684			0.309683
$381$	18.0384			0.924136
$382$	−5.21040	−	9.02468i	−0.266587	−	0.461743i
$383$	0.256086	+	0.443554i	0.0130854	+	0.0226646i	0.872494	−	0.488625i	$-0.162501\pi$
$383$	0.256086	+	0.443554i	0.0130854	+	0.0226646i	−0.859409	+	0.511289i	$0.829168\pi$
$384$	4.84269	−	8.38778i	0.247127	−	0.428037i
$385$	8.49824	+	0.00415415i	0.433110	+	0.000211715i
$386$	−5.25902	+	9.10889i	−0.267677	+	0.463630i
$387$	5.00219			0.254276
$388$	2.56262	−	4.43859i	0.130097	−	0.225335i
$389$	−17.7577	−	30.7573i	−0.900353	−	1.55946i	−0.827037	−	0.562148i	$-0.809975\pi$
$389$	−17.7577	−	30.7573i	−0.900353	−	1.55946i	−0.0733162	−	0.997309i	$-0.523358\pi$
$390$	−0.167153	−	1.95021i	−0.00846414	−	0.0987526i
$391$	3.51540			0.177781
$392$	−9.07611	−	15.7558i	−0.458413	−	0.795790i
$393$	9.83728	+	17.0387i	0.496225	+	0.859487i
$394$	6.94566	+	12.0302i	0.349917	+	0.606074i
$395$	1.96952	+	3.41131i	0.0990974	+	0.171642i
$396$	−6.39369			−0.321295
$397$	4.14865	+	7.18568i	0.208215	+	0.360639i	0.951152	−	0.308722i	$-0.0999013\pi$
$397$	4.14865	+	7.18568i	0.208215	+	0.360639i	−0.742937	+	0.669361i	$0.766568\pi$
$398$	5.39828			0.270591
$399$	−7.83819	+	13.5608i	−0.392400	+	0.678891i
$400$	1.97282	+	3.41702i	0.0986410	+	0.170851i
$401$	13.9204			0.695152			0.347576	−	0.937652i	$-0.387005\pi$
$401$	13.9204			0.695152			0.347576	+	0.937652i	$0.387005\pi$
$402$	5.48588	+	9.50182i	0.273611	+	0.473908i
$403$	0.117704	+	1.37327i	0.00586323	+	0.0684074i
$404$	8.53341	−	14.7803i	0.424553	−	0.735347i
$405$	−0.357869	−	0.619848i	−0.0177827	−	0.0308005i
$406$	−4.50114	−	0.00220027i	−0.223388	−	0.000109198i
$407$	1.47522	−	2.55515i	0.0731238	−	0.126654i
$408$	−4.90232	+	8.49107i	−0.242701	+	0.420371i
$409$	−4.91743			−0.243151			−0.121576	−	0.992582i	$-0.538795\pi$
$409$	−4.91743			−0.243151			−0.121576	+	0.992582i	$0.538795\pi$
$410$	−2.49232			−0.123087
$411$	9.64137	−	16.6993i	0.475574	−	0.823718i
$412$	2.20781	−	3.82404i	0.108771	−	0.188397i
$413$	−7.43292	+	12.8597i	−0.365750	+	0.632783i
$414$	−0.353203	−	0.611766i	−0.0173590	−	0.0300667i
$415$	−4.12629	+	7.14694i	−0.202552	+	0.350830i
$416$	−19.1397	−	8.96616i	−0.938402	−	0.439602i
$417$	1.31388	+	2.27571i	0.0643412	+	0.111442i
$418$	20.1511			0.985623
$419$	4.85147	+	8.40299i	0.237010	+	0.410513i	0.959855	−	0.280497i	$-0.0904993\pi$
$419$	4.85147	+	8.40299i	0.237010	+	0.410513i	−0.722845	+	0.691010i	$0.757166\pi$
$420$	2.69792	+	0.00131881i	0.131645	+	6.43514e-5i
$421$	−15.2944			−0.745405			−0.372702	−	0.927951i	$-0.621569\pi$
$421$	−15.2944			−0.745405			−0.372702	+	0.927951i	$0.621569\pi$
$422$	4.51298	+	7.81671i	0.219688	+	0.380512i
$423$	8.37072			0.406999
$424$	−3.15184	−	5.45915i	−0.153067	−	0.265120i
$425$	−8.46954	−	14.6697i	−0.410833	−	0.711584i
$426$	1.62877	+	2.82111i	0.0789142	+	0.136683i
$427$	5.27505	+	0.00257857i	0.255277	+	0.000124786i
$428$	−15.9371			−0.770351
$429$	1.38179	+	16.1216i	0.0667134	+	0.778358i
$430$	1.35778	+	2.35174i	0.0654779	+	0.113411i
$431$	−16.3290	+	28.2827i	−0.786541	+	1.36233i	0.141534	+	0.989933i	$0.454797\pi$
$431$	−16.3290	+	28.2827i	−0.786541	+	1.36233i	−0.928074	+	0.372395i	$0.878537\pi$
$432$	−0.879208			−0.0423009
$433$	9.28189	−	16.0767i	0.446059	−	0.772597i	−0.552066	−	0.833800i	$-0.686160\pi$
$433$	9.28189	−	16.0767i	0.446059	−	0.772597i	0.998125	+	0.0612034i	$0.0194938\pi$
$434$	0.767125		0.000374990i	0.0368232		1.80001e-5i
$435$	0.802702	−	1.39032i	0.0384866	−	0.0666607i
$436$	−14.5186	−	25.1470i	−0.695316	−	1.20432i
$437$	−2.75683	−	4.77497i	−0.131877	−	0.228418i
$438$	2.03466			0.0972198
$439$	9.45476			0.451251			0.225625	−	0.974214i	$-0.427557\pi$
$439$	9.45476			0.451251			0.225625	+	0.974214i	$0.427557\pi$
$440$	−4.17175	−	7.22568i	−0.198880	−	0.344471i
$441$	−3.50593	+	6.05875i	−0.166949	+	0.288512i
$442$	9.34755	+	4.37893i	0.444617	+	0.208285i
$443$	−3.71593	+	6.43618i	−0.176549	+	0.305792i	−0.940696	−	0.339250i	$-0.889827\pi$
$443$	−3.71593	+	6.43618i	−0.176549	+	0.305792i	0.764147	+	0.645042i	$0.223160\pi$
$444$	0.468334	−	0.811179i	0.0222262	−	0.0384968i
$445$	4.33085	−	7.50126i	0.205302	−	0.355594i
$446$	−9.05871	−	15.6901i	−0.428942	−	0.742950i
$447$	15.5896			0.737361
$448$	−3.55864	+	6.15679i	−0.168130	+	0.290881i
$449$	−9.42362	+	16.3222i	−0.444728	+	0.770291i	−0.998033	−	0.0626872i	$-0.980033\pi$
$449$	−9.42362	+	16.3222i	−0.444728	+	0.770291i	0.553305	+	0.832979i	$0.313366\pi$
$450$	−1.70192	+	2.94782i	−0.0802294	+	0.138961i
$451$	20.6030			0.970159
$452$	−12.1828	+	21.1012i	−0.573030	+	0.992517i
$453$	9.22267			0.433319
$454$	−9.54761			−0.448092
$455$	−0.579744	−	6.80305i	−0.0271788	−	0.318932i
$456$	15.3779			0.720136
$457$	−6.80007			−0.318094			−0.159047	−	0.987271i	$-0.550842\pi$
$457$	−6.80007			−0.318094			−0.159047	+	0.987271i	$0.550842\pi$
$458$	−5.81273	+	10.0679i	−0.271611	+	0.470444i
$459$	3.77454			0.176181
$460$	−0.474855	+	0.822473i	−0.0221402	+	0.0383480i
$461$	−4.80595	+	8.32415i	−0.223836	+	0.387694i	−0.955969	−	0.293466i	$-0.905191\pi$
$461$	−4.80595	+	8.32415i	−0.223836	+	0.387694i	0.732134	+	0.681161i	$0.238525\pi$
$462$	9.00573	+	0.00440222i	0.418984	+	0.000204810i
$463$	−23.4929			−1.09181			−0.545905	−	0.837847i	$-0.683814\pi$
$463$	−23.4929			−1.09181			−0.545905	+	0.837847i	$0.683814\pi$
$464$	−0.986033	−	1.70786i	−0.0457754	−	0.0792854i
$465$	−0.136804	+	0.236951i	−0.00634412	+	0.0109883i
$466$	−10.1138	+	17.5176i	−0.468513	+	0.811488i
$467$	7.24654	−	12.5514i	0.335330	−	0.580808i	−0.648218	−	0.761455i	$-0.724486\pi$
$467$	7.24654	−	12.5514i	0.335330	−	0.580808i	0.983548	+	0.180646i	$0.0578189\pi$
$468$	0.438674	+	5.11809i	0.0202777	+	0.236584i
$469$	19.1198	+	33.1539i	0.882870	+	1.53090i
$470$	2.27212	+	3.93543i	0.104805	+	0.181528i
$471$	−18.4108			−0.848324
$472$	14.5828			0.671227
$473$	−11.2242	−	19.4409i	−0.516090	−	0.893894i
$474$	2.08714	+	3.61502i	0.0958653	+	0.166044i
$475$	−13.2839	+	23.0083i	−0.609506	+	1.05570i
$476$	−7.11994	+	12.3182i	−0.326342	+	0.564604i
$477$	−1.21338	+	2.10164i	−0.0555569	+	0.0962273i
$478$	11.0656			0.506127
$479$	−7.25670	+	12.5690i	−0.331567	+	0.574291i	−0.982819	−	0.184570i	$-0.940911\pi$
$479$	−7.25670	+	12.5690i	−0.331567	+	0.574291i	0.651252	+	0.758861i	$0.274244\pi$
$480$	−2.09783	−	3.63355i	−0.0957525	−	0.165848i
$481$	−2.14659	−	1.00559i	−0.0978761	−	0.0458509i
$482$	−9.77855			−0.445401
$483$	−1.23101	−	2.13458i	−0.0560129	−	0.0971268i
$484$	6.51064	+	11.2768i	0.295938	+	0.512580i
$485$	−1.28740	−	2.22984i	−0.0584577	−	0.101252i
$486$	−0.379240	−	0.656863i	−0.0172027	−	0.0297959i
$487$	23.3927			1.06003			0.530013	−	0.847990i	$-0.322187\pi$
$487$	23.3927			1.06003			0.530013	+	0.847990i	$0.322187\pi$
$488$	−2.58950	−	4.48514i	−0.117221	−	0.203033i
$489$	−11.1686			−0.505062
$490$	−3.80011	−	0.00371518i	−0.171672	−	0.000167835i
$491$	0.786824	+	1.36282i	0.0355089	+	0.0615032i	0.883234	−	0.468933i	$-0.155361\pi$
$491$	0.786824	+	1.36282i	0.0355089	+	0.0615032i	−0.847725	+	0.530436i	$0.822028\pi$
$492$	6.54081			0.294882
$493$	4.23315	+	7.33203i	0.190652	+	0.330218i
$494$	−1.38258	−	16.1308i	−0.0622052	−	0.725759i
$495$	−1.60602	+	2.78170i	−0.0721851	+	0.125028i
$496$	0.168049	+	0.291069i	0.00754560	+	0.0130694i
$497$	5.67671	+	9.84346i	0.254635	+	0.441540i
$498$	−4.37270	+	7.57374i	−0.195945	+	0.339387i
$499$	−7.86689	+	13.6259i	−0.352170	+	0.609977i	−0.986629	−	0.162980i	$-0.947890\pi$
$499$	−7.86689	+	13.6259i	−0.352170	+	0.609977i	0.634459	+	0.772956i	$0.281223\pi$
$500$	9.67480			0.432670
$501$	14.1944			0.634158
$502$	9.11719	−	15.7914i	0.406920	−	0.704807i
$503$	17.7055	−	30.6668i	0.789447	−	1.36736i	−0.136858	−	0.990591i	$-0.543701\pi$
$503$	17.7055	−	30.6668i	0.789447	−	1.36736i	0.926306	−	0.376773i	$-0.122966\pi$
$504$	6.87253	+	0.00335946i	0.306127	+	0.000149642i
$505$	−4.28698	−	7.42526i	−0.190768	−	0.330420i
$506$	−1.58508	+	2.74543i	−0.0704653	+	0.122049i
$507$	12.8104	−	2.21222i	0.568929	−	0.0982482i
$508$	−12.8497	−	22.2564i	−0.570115	−	0.987467i
$509$	−10.4095			−0.461395			−0.230697	−	0.973026i	$-0.574101\pi$
$509$	−10.4095			−0.461395			−0.230697	+	0.973026i	$0.574101\pi$
$510$	1.02455	+	1.77457i	0.0453678	+	0.0785794i
$511$	7.09735	+	0.00346936i	0.313968	+	0.000153476i
$512$	−9.72154			−0.429635
$513$	−2.96005	−	5.12696i	−0.130689	−	0.226361i
$514$	−14.1946			−0.626095
$515$	−1.10915	−	1.92110i	−0.0488750	−	0.0846540i
$516$	−3.56333	−	6.17187i	−0.156867	−	0.271701i
$517$	−18.7827	−	32.5326i	−0.826063	−	1.43078i
$518$	−0.660223	+	1.14225i	−0.0290086	+	0.0501876i
$519$	−19.2725			−0.845968
$520$	−5.49787	+	3.83520i	−0.241097	+	0.168185i
$521$	−0.513222	−	0.888926i	−0.0224847	−	0.0389446i	0.854564	−	0.519346i	$-0.173824\pi$
$521$	−0.513222	−	0.888926i	−0.0224847	−	0.0389446i	−0.877049	+	0.480401i	$0.840491\pi$
$522$	0.850636	−	1.47335i	0.0372313	−	0.0644866i
$523$	−18.0428			−0.788954			−0.394477	−	0.918906i	$-0.629074\pi$
$523$	−18.0428			−0.788954			−0.394477	+	0.918906i	$0.629074\pi$
$524$	14.0153	−	24.2751i	0.612259	−	1.06046i
$525$	−5.94172	+	10.2798i	−0.259318	+	0.448645i
$526$	−3.55397	+	6.15566i	−0.154960	+	0.268399i
$527$	−0.721452	−	1.24959i	−0.0314269	−	0.0544330i
$528$	1.97282	+	3.41702i	0.0858559	+	0.148707i
$529$	−22.1326			−0.962287
$530$	−1.31742			−0.0572252
$531$	−2.80700	−	4.86187i	−0.121814	−	0.210987i
$532$	22.3154	+	0.0109083i	0.967494	+	0.000472935i
$533$	−1.41359	−	16.4926i	−0.0612292	−	0.714372i
$534$	4.58948	−	7.94921i	0.198606	−	0.343996i
$535$	−4.00322	+	6.93378i	−0.173074	+	0.299773i
$536$	18.7875	−	32.5410i	0.811498	−	1.40556i
$537$	−5.61622	−	9.72758i	−0.242358	−	0.419776i
$538$	−9.21499			−0.397286
$539$	31.4140	+	0.0307119i	1.35310	+	0.00132286i
$540$	−0.509859	+	0.883102i	−0.0219408	+	0.0380027i
$541$	16.7318	−	28.9803i	0.719355	−	1.24596i	−0.241900	−	0.970301i	$-0.577771\pi$
$541$	16.7318	−	28.9803i	0.719355	−	1.24596i	0.961256	−	0.275659i	$-0.0888960\pi$
$542$	11.1182			0.477567
$543$	1.21652	−	2.10707i	0.0522059	−	0.0904232i
$544$	22.1264			0.948661
$545$	−14.5876			−0.624865
$546$	−0.614364	−	7.20931i	−0.0262923	−	0.308530i
$547$	30.7718			1.31571			0.657853	−	0.753146i	$-0.271465\pi$
$547$	30.7718			1.31571			0.657853	+	0.753146i	$0.271465\pi$
$548$	−27.4723			−1.17356
$549$	−0.996890	+	1.72666i	−0.0425462	+	0.0736923i
$550$	15.2755			0.651349
$551$	6.63940	−	11.4998i	0.282848	−	0.489907i
$552$	−1.20962	+	2.09512i	−0.0514848	+	0.0891743i
$553$	7.27424	+	12.6136i	0.309332	+	0.536384i
$554$	3.81679			0.162160
$555$	−0.235280	−	0.407517i	−0.00998707	−	0.0172981i
$556$	1.87190	−	3.24223i	0.0793863	−	0.137501i
$557$	−7.81714	+	13.5397i	−0.331223	+	0.573695i	−0.982752	−	0.184929i	$-0.940795\pi$
$557$	−7.81714	+	13.5397i	−0.331223	+	0.573695i	0.651529	+	0.758624i	$0.274128\pi$
$558$	−0.144973	+	0.251101i	−0.00613720	+	0.0106299i
$559$	−14.7922	+	10.3187i	−0.625642	+	0.436436i
$560$	−0.831759	−	1.44228i	−0.0351482	−	0.0609473i
$561$	−8.46954	−	14.6697i	−0.357584	−	0.619354i
$562$	−0.648416			−0.0273518
$563$	33.5242			1.41288			0.706438	−	0.707775i	$-0.250301\pi$
$563$	33.5242			1.41288			0.706438	+	0.707775i	$0.250301\pi$
$564$	−5.96292	−	10.3281i	−0.251084	−	0.434890i
$565$	6.12033	+	10.6007i	0.257484	+	0.445976i
$566$	−11.8617	+	20.5450i	−0.498583	+	0.863570i
$567$	−1.32176	−	2.29193i	−0.0555085	−	0.0962522i
$568$	5.57806	−	9.66149i	0.234050	−	0.405387i
$569$	21.2061			0.889008			0.444504	−	0.895777i	$-0.353380\pi$
$569$	21.2061			0.889008			0.444504	+	0.895777i	$0.353380\pi$
$570$	1.60693	−	2.78329i	0.0673070	−	0.116579i
$571$	−0.869647	−	1.50627i	−0.0363936	−	0.0630356i	0.847255	−	0.531187i	$-0.178254\pi$
$571$	−0.869647	−	1.50627i	−0.0363936	−	0.0630356i	−0.883648	+	0.468151i	$0.844920\pi$
$572$	18.9070	−	13.1892i	0.790543	−	0.551467i
$573$	13.7391			0.573958
$574$	−9.21295	−	0.00450352i	−0.384541	−	0.000187973i
$575$	−2.08981	−	3.61965i	−0.0871510	−	0.150950i
$576$	−1.34390	−	2.32770i	−0.0559958	−	0.0969876i
$577$	−2.83193	−	4.90504i	−0.117895	−	0.204199i	0.801039	−	0.598613i	$-0.204281\pi$
$577$	−2.83193	−	4.90504i	−0.117895	−	0.204199i	−0.918933	+	0.394413i	$0.870948\pi$
$578$	2.08797			0.0868481
$579$	−6.93363	−	12.0094i	−0.288152	−	0.499094i
$580$	−2.28723			−0.0949721
$581$	−15.2659	+	26.4115i	−0.633335	+	1.09573i
$582$	−1.36428	−	2.36300i	−0.0565511	−	0.0979493i
$583$	10.8906			0.451043
$584$	−3.48406	−	6.03456i	−0.144171	−	0.249712i
$585$	2.33692	+	1.09475i	0.0966197	+	0.0452623i
$586$	−0.257158	+	0.445411i	−0.0106231	+	0.0183997i
$587$	8.06910	+	13.9761i	0.333047	+	0.576855i	0.983108	−	0.183028i	$-0.0585898\pi$
$587$	8.06910	+	13.9761i	0.333047	+	0.576855i	−0.650060	+	0.759882i	$0.725256\pi$
$588$	9.97295	+	0.00975006i	0.411278	+	0.000402086i
$589$	−1.13155	+	1.95990i	−0.0466246	+	0.0807561i
$590$	1.52385	−	2.63938i	0.0627358	−	0.108662i
$591$	−18.3147			−0.753365
$592$	−0.578032			−0.0237570
$593$	−21.1595	+	36.6493i	−0.868917	+	1.50501i	−0.00581233	+	0.999983i	$0.501850\pi$
$593$	−21.1595	+	36.6493i	−0.868917	+	1.50501i	−0.863105	+	0.505025i	$0.831483\pi$
$594$	−1.70192	+	2.94782i	−0.0698307	+	0.120950i
$595$	3.57084	+	6.19186i	0.146390	+	0.253841i
$596$	−11.1053	−	19.2349i	−0.454890	−	0.787893i
$597$	−3.55862	+	6.16371i	−0.145644	+	0.252264i
$598$	2.30645	+	1.08048i	0.0943178	+	0.0441839i
$599$	22.9026	+	39.6685i	0.935776	+	1.62081i	0.773244	+	0.634108i	$0.218633\pi$
$599$	22.9026	+	39.6685i	0.935776	+	1.62081i	0.162532	+	0.986703i	$0.448034\pi$
$600$	11.6572			0.475902
$601$	6.27579	+	10.8700i	0.255995	+	0.443396i	0.965165	−	0.261641i	$-0.0842637\pi$
$601$	6.27579	+	10.8700i	0.255995	+	0.443396i	−0.709170	+	0.705037i	$0.750930\pi$
$602$	5.01482	+	8.69574i	0.204389	+	0.354412i
$603$	−14.4655			−0.589079
$604$	−6.56981	−	11.3792i	−0.267322	−	0.463015i
$605$	6.54158			0.265953
$606$	−4.54298	−	7.86867i	−0.184546	−	0.319643i
$607$	−17.2462	−	29.8712i	−0.700000	−	1.21244i	−0.968466	−	0.249146i	$-0.919850\pi$
$607$	−17.2462	−	29.8712i	−0.700000	−	1.21244i	0.268466	−	0.963289i	$-0.413483\pi$
$608$	−17.3518	−	30.0543i	−0.703710	−	1.21886i
$609$	2.96972	−	5.13791i	0.120339	−	0.208199i
$610$	−1.08237			−0.0438239
$611$	−24.7534	+	17.2675i	−1.00142	+	0.698568i
$612$	−2.68881	−	4.65715i	−0.108689	−	0.188254i
$613$	17.0837	−	29.5898i	0.690003	−	1.19512i	−0.281833	−	0.959463i	$-0.590942\pi$
$613$	17.0837	−	29.5898i	0.690003	−	1.19512i	0.971836	−	0.235657i	$-0.0757242\pi$
$614$	20.6385			0.832901
$615$	1.64297	−	2.84571i	0.0662510	−	0.114750i
$616$	−15.4079	−	26.7175i	−0.620803	−	1.07648i
$617$	−18.4048	+	31.8781i	−0.740950	+	1.28336i	0.211113	+	0.977462i	$0.432291\pi$
$617$	−18.4048	+	31.8781i	−0.740950	+	1.28336i	−0.952063	+	0.305902i	$0.901042\pi$
$618$	−1.17538	−	2.03583i	−0.0472809	−	0.0818929i
$619$	−17.9351	−	31.0644i	−0.720871	−	1.24858i	−0.960651	−	0.277758i	$-0.910409\pi$
$619$	−17.9351	−	31.0644i	−0.720871	−	1.24858i	0.239780	−	0.970827i	$-0.422925\pi$
$620$	0.389810			0.0156552
$621$	0.931345			0.0373736
$622$	−5.35810	−	9.28050i	−0.214840	−	0.372114i
$623$	16.0227	−	27.7208i	0.641935	−	1.11061i
$624$	2.59994	−	1.81367i	0.104081	−	0.0726049i
$625$	−8.78910	+	15.2232i	−0.351564	+	0.608927i
$626$	−7.47033	+	12.9390i	−0.298574	+	0.517146i
$627$	−13.2839	+	23.0083i	−0.530507	+	0.918865i
$628$	13.1150	+	22.7158i	0.523345	+	0.906461i
$629$	2.48156			0.0989462
$630$	0.718762	−	1.24353i	0.0286362	−	0.0495434i
$631$	−9.93368	+	17.2056i	−0.395453	+	0.684945i	−0.993159	−	0.116770i	$-0.962746\pi$
$631$	−9.93368	+	17.2056i	−0.395453	+	0.684945i	0.597706	+	0.801716i	$0.296079\pi$
$632$	7.14783	−	12.3804i	0.284325	−	0.492466i
$633$	−11.9001			−0.472985
$634$	5.94596	−	10.2987i	0.236144	−	0.409014i
$635$	−12.9108			−0.512349
$636$	3.45742			0.137096
$637$	−2.13075	−	25.1488i	−0.0844233	−	0.996430i
$638$	−7.63483			−0.302266
$639$	−4.29483			−0.169901
$640$	−3.46610	+	6.00346i	−0.137010	+	0.237308i
$641$	−2.55009			−0.100723			−0.0503613	−	0.998731i	$-0.516037\pi$
$641$	−2.55009			−0.100723			−0.0503613	+	0.998731i	$0.516037\pi$
$642$	−4.24228	+	7.34784i	−0.167429	+	0.289996i
$643$	7.23729	−	12.5354i	0.285411	−	0.494346i	−0.687298	−	0.726376i	$-0.741203\pi$
$643$	7.23729	−	12.5354i	0.285411	−	0.494346i	0.972709	+	0.232029i	$0.0745366\pi$
$644$	−1.75680	+	3.03944i	−0.0692277	+	0.119771i
$645$	−3.58026			−0.140973
$646$	8.47438	+	14.6780i	0.333420	+	0.577500i
$647$	15.8310	−	27.4200i	0.622379	−	1.07799i	−0.366663	−	0.930354i	$-0.619500\pi$
$647$	15.8310	−	27.4200i	0.622379	−	1.07799i	0.989041	−	0.147638i	$-0.0471670\pi$
$648$	−1.29879	+	2.24956i	−0.0510212	+	0.0883712i
$649$	−12.5970	+	21.8187i	−0.494477	+	0.856459i
$650$	−1.04806	−	12.2279i	−0.0411083	−	0.479618i
$651$	−0.506127	+	0.875649i	−0.0198367	+	0.0343194i
$652$	7.95600	+	13.7802i	0.311581	+	0.539674i
$653$	7.05983			0.276273			0.138136	−	0.990413i	$-0.455889\pi$
$653$	7.05983			0.276273			0.138136	+	0.990413i	$0.455889\pi$
$654$	−15.4587			−0.604484
$655$	−7.04092	−	12.1952i	−0.275112	−	0.476507i
$656$	−2.01821	−	3.49565i	−0.0787980	−	0.136482i
$657$	−1.34127	+	2.32315i	−0.0523281	+	0.0906349i
$658$	8.39186	+	14.5516i	0.327149	+	0.567279i
$659$	6.73098	−	11.6584i	0.262202	−	0.454147i	−0.704625	−	0.709580i	$-0.748885\pi$
$659$	6.73098	−	11.6584i	0.262202	−	0.454147i	0.966827	+	0.255433i	$0.0822181\pi$
$660$	4.57621			0.178129
$661$	−2.06979	+	3.58498i	−0.0805054	+	0.139440i	−0.903467	−	0.428657i	$-0.858987\pi$
$661$	−2.06979	+	3.58498i	−0.0805054	+	0.139440i	0.822962	+	0.568097i	$0.192320\pi$
$662$	5.47001	+	9.47433i	0.212598	+	0.368230i
$663$	−11.1618	+	7.78629i	−0.433490	+	0.302394i
$664$	29.9504			1.16230
$665$	5.61010	−	9.70601i	0.217550	−	0.376383i
$666$	−0.249330	−	0.431852i	−0.00966134	−	0.0167339i
$667$	1.04450	+	1.80913i	0.0404434	+	0.0700500i
$668$	−10.1114	−	17.5135i	−0.391223	−	0.677617i
$669$	23.8865			0.923505
$670$	−3.92646	−	6.80082i	−0.151692	−	0.262739i
$671$	8.94753			0.345415
$672$	−7.74814	−	13.4353i	−0.298891	−	0.518279i
$673$	−3.09545	−	5.36148i	−0.119321	−	0.206670i	0.800178	−	0.599763i	$-0.204738\pi$
$673$	−3.09545	−	5.36148i	−0.119321	−	0.206670i	−0.919499	+	0.393093i	$0.871405\pi$
$674$	−10.9448			−0.421579
$675$	−2.24386	−	3.88648i	−0.0863662	−	0.149591i
$676$	−11.8550	−	14.2300i	−0.455963	−	0.547308i
$677$	8.44416	−	14.6257i	0.324535	−	0.562112i	−0.656883	−	0.753993i	$-0.728125\pi$
$677$	8.44416	−	14.6257i	0.324535	−	0.562112i	0.981418	+	0.191881i	$0.0614587\pi$
$678$	6.48582	+	11.2338i	0.249086	+	0.431430i
$679$	−4.75488	−	8.24499i	−0.182475	−	0.316414i
$680$	3.50878	−	6.07739i	0.134556	−	0.233057i
$681$	6.29391	−	10.9014i	0.241183	−	0.417741i
$682$	1.30120			0.0498254
$683$	13.3772			0.511866			0.255933	−	0.966695i	$-0.417617\pi$
$683$	13.3772			0.511866			0.255933	+	0.966695i	$0.417617\pi$
$684$	−4.21721	+	7.30442i	−0.161249	+	0.279291i
$685$	−6.90070	+	11.9524i	−0.263662	+	0.456676i
$686$	−14.0472	−	0.0205999i	−0.536326	−	0.000786509i
$687$	−7.66365	−	13.2738i	−0.292387	−	0.506429i
$688$	−2.19898	+	3.80875i	−0.0838354	+	0.145207i
$689$	−0.747211	−	8.71784i	−0.0284665	−	0.332123i
$690$	0.252801	+	0.437865i	0.00962398	+	0.0166692i
$691$	9.80379			0.372954			0.186477	−	0.982459i	$-0.440293\pi$
$691$	9.80379			0.372954			0.186477	+	0.982459i	$0.440293\pi$
$692$	13.7288	+	23.7790i	0.521892	+	0.903943i
$693$	−5.94172	+	10.2798i	−0.225707	+	0.390495i
$694$	3.54110			0.134418
$695$	−0.940397	−	1.62882i	−0.0356713	−	0.0617845i
$696$	−5.82636			−0.220848
$697$	8.66443	+	15.0072i	0.328189	+	0.568439i
$698$	−1.56859	−	2.71688i	−0.0593721	−	0.102835i
$699$	−13.3343	−	23.0957i	−0.504350	−	0.873559i
$700$	16.9161	+	0.00826901i	0.639369	+	0.000312539i
$701$	35.6715			1.34729			0.673647	−	0.739054i	$-0.264727\pi$
$701$	35.6715			1.34729			0.673647	+	0.739054i	$0.264727\pi$
$702$	2.47647	+	1.16012i	0.0934684	+	0.0437860i
$703$	−1.94607	−	3.37070i	−0.0733976	−	0.127128i
$704$	−6.03105	+	10.4461i	−0.227304	+	0.393701i
$705$	−5.99125			−0.225644
$706$	13.5730	−	23.5091i	0.510826	−	0.884777i
$707$	−15.8335	−	27.4555i	−0.595481	−	1.03257i
$708$	−3.99916	+	6.92675i	−0.150298	+	0.260323i
$709$	−15.8748	−	27.4960i	−0.596191	−	1.03263i	−0.993378	−	0.114896i	$-0.963347\pi$
$709$	−15.8748	−	27.4960i	−0.596191	−	1.03263i	0.397186	−	0.917738i	$-0.369987\pi$
$710$	−1.16577	−	2.01918i	−0.0437507	−	0.0757785i
$711$	−5.50347			−0.206396
$712$	−31.4352			−1.17809
$713$	−0.178014	−	0.308329i	−0.00666667	−	0.0115470i
$714$	3.78407	+	6.56161i	0.141615	+	0.245562i
$715$	−0.989000	−	11.5388i	−0.0369865	−	0.431528i
$716$	−8.00148	+	13.8590i	−0.299029	+	0.517934i
$717$	−7.29457	+	12.6346i	−0.272421	+	0.471846i
$718$	−9.58576	+	16.6030i	−0.357737	+	0.619619i
$719$	3.49062	+	6.04594i	0.130178	+	0.225475i	0.923745	−	0.383008i	$-0.125112\pi$
$719$	3.49062	+	6.04594i	0.130178	+	0.225475i	−0.793567	+	0.608483i	$0.791778\pi$
$720$	0.629283			0.0234520
$721$	−4.09654	−	7.10343i	−0.152563	−	0.264545i
$722$	6.08590	−	10.5411i	0.226494	−	0.392299i
$723$	6.44615	−	11.1651i	0.239735	−	0.415233i
$724$	−3.46637			−0.128827
$725$	5.03298	−	8.71738i	0.186920	−	0.323755i
$726$	6.93222			0.257279
$727$	−2.58607			−0.0959121			−0.0479561	−	0.998849i	$-0.515271\pi$
$727$	−2.58607			−0.0959121			−0.0479561	+	0.998849i	$0.515271\pi$
$728$	−20.3300	+	14.1670i	−0.753479	+	0.525065i
$729$	1.00000			0.0370370
$730$	−1.45628			−0.0538995
$731$	9.44049	−	16.3514i	0.349169	−	0.604779i
$732$	2.84056			0.104990
$733$	6.30712	−	10.9243i	0.232959	−	0.403497i	−0.725719	−	0.687992i	$-0.758493\pi$
$733$	6.30712	−	10.9243i	0.232959	−	0.403497i	0.958678	+	0.284495i	$0.0918259\pi$
$734$	13.4250	−	23.2528i	0.495526	−	0.858276i
$735$	2.50933	−	4.33648i	0.0925579	−	0.159954i
$736$	5.45955			0.201242
$737$	32.4584	+	56.2197i	1.19562	+	2.07088i
$738$	1.74108	−	3.01565i	0.0640902	−	0.111007i
$739$	−1.47038	+	2.54678i	−0.0540889	+	0.0936848i	−0.891802	−	0.452426i	$-0.850559\pi$
$739$	−1.47038	+	2.54678i	−0.0540889	+	0.0936848i	0.837713	+	0.546110i	$0.183892\pi$
$740$	−0.335205	+	0.580592i	−0.0123224	+	0.0213430i
$741$	19.3294	+	9.05501i	0.710083	+	0.332644i
$742$	−4.86990	−	0.00238053i	−0.178780	−	8.73920e-5i
$743$	20.5461	+	35.5869i	0.753763	+	1.30556i	0.945987	+	0.324205i	$0.105097\pi$
$743$	20.5461	+	35.5869i	0.753763	+	1.30556i	−0.192224	+	0.981351i	$0.561570\pi$
$744$	0.992981			0.0364044
$745$	−11.1581			−0.408799
$746$	−12.4316	−	21.5322i	−0.455155	−	0.788351i
$747$	−5.76508	−	9.98541i	−0.210933	−	0.365347i
$748$	−12.0666	+	20.9000i	−0.441199	+	0.764180i
$749$	−14.8106	+	25.6237i	−0.541166	+	0.936270i
$750$	2.57532	−	4.46058i	0.0940372	−	0.162877i
$751$	−30.4321			−1.11048			−0.555241	−	0.831690i	$-0.687374\pi$
$751$	−30.4321			−1.11048			−0.555241	+	0.831690i	$0.687374\pi$
$752$	−3.67980	+	6.37361i	−0.134189	+	0.232422i
$753$	12.0203	+	20.8198i	0.438046	+	0.758717i
$754$	0.523830	+	6.11162i	0.0190768	+	0.222572i
$755$	−6.60102			−0.240236
$756$	−1.88631	+	3.26349i	−0.0686043	+	0.118692i
$757$	15.7459	+	27.2726i	0.572293	+	0.991241i	0.996330	+	0.0855959i	$0.0272794\pi$
$757$	15.7459	+	27.2726i	0.572293	+	0.991241i	−0.424037	+	0.905645i	$0.639387\pi$
$758$	4.58356	+	7.93895i	0.166482	+	0.288356i
$759$	−2.08981	−	3.61965i	−0.0758552	−	0.131385i
$760$	−11.0066			−0.399250
$761$	22.0866	+	38.2551i	0.800638	+	1.38675i	0.919196	+	0.393799i	$0.128839\pi$
$761$	22.0866	+	38.2551i	0.800638	+	1.38675i	−0.118558	+	0.992947i	$0.537827\pi$
$762$	−13.6818			−0.495638
$763$	−53.9236	−	0.0263592i	−1.95216	−	0.000954267i
$764$	−9.78707	−	16.9517i	−0.354084	−	0.613291i
$765$	−2.70159			−0.0976760
$766$	−0.194236	−	0.336427i	−0.00701804	−	0.0121556i
$767$	18.3300	+	8.58683i	0.661857	+	0.310052i
$768$	−6.36088	+	11.0174i	−0.229529	+	0.397555i
$769$	25.4717	+	44.1182i	0.918532	+	1.59094i	0.801646	+	0.597799i	$0.203958\pi$
$769$	25.4717	+	44.1182i	0.918532	+	1.59094i	0.116887	+	0.993145i	$0.462709\pi$
$770$	−6.44575	−	0.00315084i	−0.232289	−	0.000113548i
$771$	9.35724	−	16.2072i	0.336993	−	0.583689i
$772$	−9.87840	+	17.1099i	−0.355531	+	0.615798i
$773$	−5.74207			−0.206528			−0.103264	−	0.994654i	$-0.532929\pi$
$773$	−5.74207			−0.206528			−0.103264	+	0.994654i	$0.532929\pi$
$774$	−3.79406			−0.136375
$775$	−0.857766	+	1.48569i	−0.0308119	+	0.0533677i
$776$	−4.67225	+	8.09257i	−0.167724	+	0.290506i
$777$	−0.868983	−	1.50682i	−0.0311746	−	0.0540570i
$778$	13.4689	+	23.3288i	0.482883	+	0.836378i
$779$	13.5895	−	23.5378i	0.486896	−	0.843328i
$780$	−0.313976	−	3.66322i	−0.0112422	−	0.131164i
$781$	9.63699	+	16.6918i	0.344839	+	0.597278i
$782$	−2.66636			−0.0953489
$783$	1.12150	+	1.94250i	0.0400792	+	0.0694192i
$784$	−3.07202	−	5.33292i	−0.109715	−	0.190462i
$785$	13.1773			0.470318
$786$	−7.46138	−	12.9235i	−0.266139	−	0.460966i
$787$	30.0823			1.07232			0.536160	−	0.844116i	$-0.319874\pi$
$787$	30.0823			1.07232			0.536160	+	0.844116i	$0.319874\pi$
$788$	13.0465	+	22.5972i	0.464763	+	0.804993i
$789$	−4.68565	−	8.11578i	−0.166813	−	0.288929i
$790$	−1.49384	−	2.58741i	−0.0531486	−	0.0920560i
$791$	22.6049	+	39.1970i	0.803736	+	1.39368i
$792$	11.6572			0.414220
$793$	−0.613895	−	7.16242i	−0.0218000	−	0.254345i
$794$	−3.14667	−	5.45019i	−0.111671	−	0.193420i
$795$	0.868463	−	1.50422i	0.0308012	−	0.0533493i
$796$	10.1400			0.359402
$797$	−4.03274	+	6.98491i	−0.142847	+	0.247418i	−0.928568	−	0.371163i	$-0.878959\pi$
$797$	−4.03274	+	6.98491i	−0.142847	+	0.247418i	0.785721	+	0.618581i	$0.212292\pi$
$798$	5.94511	−	10.2856i	0.210455	−	0.364107i
$799$	15.7978	−	27.3626i	0.558887	−	0.968020i
$800$	−13.1535	−	22.7826i	−0.465047	−	0.805485i
$801$	6.05088	+	10.4804i	0.213797	+	0.370308i
$802$	−10.5584			−0.372829
$803$	12.0385			0.424830
$804$	10.3045	+	17.8480i	0.363412	+	0.629449i
$805$	0.881082	+	1.52780i	0.0310541	+	0.0538480i
$806$	−0.0892758	−	1.04160i	−0.00314461	−	0.0366887i
$807$	6.07464	−	10.5216i	0.213837	−	0.370377i
$808$	−15.5584	+	26.9479i	−0.547342	+	0.948024i
$809$	9.25926	−	16.0375i	0.325538	−	0.563849i	−0.656083	−	0.754689i	$-0.727788\pi$
$809$	9.25926	−	16.0375i	0.325538	−	0.563849i	0.981621	+	0.190840i	$0.0611212\pi$
$810$	0.271437	+	0.470142i	0.00953732	+	0.0165191i
$811$	20.3264			0.713755			0.356878	−	0.934151i	$-0.383841\pi$
$811$	20.3264			0.713755			0.356878	+	0.934151i	$0.383841\pi$
$812$	−8.45482	−	0.00413293i	−0.296706	−	0.000145037i
$813$	−7.32926	+	12.6946i	−0.257048	+	0.445221i
$814$	−1.11892	+	1.93803i	−0.0392182	+	0.0679279i
$815$	7.99381			0.280011
$816$	−1.65930	+	2.87400i	−0.0580873	+	0.100610i
$817$	−29.6135			−1.03604
$818$	3.72977			0.130408
$819$	8.63652	+	4.05100i	0.301784	+	0.141553i
$820$	−4.68151			−0.163485
$821$	−2.40724			−0.0840133			−0.0420067	−	0.999117i	$-0.513375\pi$
$821$	−2.40724			−0.0840133			−0.0420067	+	0.999117i	$0.513375\pi$
$822$	−7.31279	+	12.6661i	−0.255063	+	0.441782i
$823$	−30.6420			−1.06811			−0.534057	−	0.845449i	$-0.679333\pi$
$823$	−30.6420			−1.06811			−0.534057	+	0.845449i	$0.679333\pi$
$824$	−4.02535	+	6.97211i	−0.140230	+	0.242885i
$825$	−10.0698	+	17.4414i	−0.350586	+	0.607232i
$826$	5.63772	−	9.75380i	0.196161	−	0.339378i
$827$	3.92281			0.136409			0.0682047	−	0.997671i	$-0.478273\pi$
$827$	3.92281			0.136409			0.0682047	+	0.997671i	$0.478273\pi$
$828$	−0.663447	−	1.14912i	−0.0230564	−	0.0399348i
$829$	−5.32420	+	9.22178i	−0.184917	+	0.320286i	−0.943549	−	0.331234i	$-0.892535\pi$
$829$	−5.32420	+	9.22178i	−0.184917	+	0.320286i	0.758632	+	0.651520i	$0.225868\pi$
$830$	3.12971	−	5.42082i	0.108634	−	0.188159i
$831$	−2.51608	+	4.35797i	−0.0872817	+	0.151176i
$832$	8.77579	+	4.11109i	0.304246	+	0.142526i
$833$	13.1885	+	22.8948i	0.456955	+	0.793259i
$834$	−0.996555	−	1.72608i	−0.0345079	−	0.0597694i
$835$	−10.1595			−0.351583
$836$	37.8513			1.30911
$837$	−0.191136	−	0.331058i	−0.00660664	−	0.0114430i
$838$	−3.67974	−	6.37350i	−0.127115	−	0.220169i
$839$	−13.8289	+	23.9523i	−0.477426	+	0.826925i	−0.999665	−	0.0258735i	$-0.991763\pi$
$839$	−13.8289	+	23.9523i	−0.477426	+	0.826925i	0.522240	+	0.852799i	$0.325097\pi$
$840$	−4.91894	−	0.00240450i	−0.169719	−	8.29631e-5i
$841$	11.9845	−	20.7577i	0.413258	−	0.715783i
$842$	11.6005			0.399780
$843$	0.427444	−	0.740355i	0.0147220	−	0.0254992i
$844$	8.47706	+	14.6827i	0.291792	+	0.505399i
$845$	−9.16889	+	1.58337i	−0.315419	+	0.0544697i
$846$	−6.34903			−0.218284
$847$	24.1811	+	0.0118203i	0.830874	+	0.000406152i
$848$	−1.06681	−	1.84778i	−0.0366345	−	0.0634529i
$849$	−15.6387	−	27.0871i	−0.536719	−	0.929625i
$850$	6.42398	+	11.1267i	0.220341	+	0.381641i
$851$	0.612309			0.0209897
$852$	3.05944	+	5.29910i	0.104815	+	0.181544i
$853$	−8.76490			−0.300105			−0.150052	−	0.988678i	$-0.547944\pi$
$853$	−8.76490			−0.300105			−0.150052	+	0.988678i	$0.547944\pi$
$854$	−4.00102	−	0.00195580i	−0.136912	−	6.69260e-5i
$855$	2.11862	+	3.66956i	0.0724554	+	0.125496i
$856$	29.0571			0.993152
$857$	−12.9737	−	22.4711i	−0.443173	−	0.767598i	0.554750	−	0.832017i	$-0.312814\pi$
$857$	−12.9737	−	22.4711i	−0.443173	−	0.767598i	−0.997923	+	0.0644193i	$0.979480\pi$
$858$	−1.04806	−	12.2279i	−0.0357802	−	0.417454i
$859$	−27.8958	+	48.3170i	−0.951793	+	1.64855i	−0.210251	+	0.977648i	$0.567428\pi$
$859$	−27.8958	+	48.3170i	−0.951793	+	1.64855i	−0.741542	+	0.670906i	$0.765905\pi$
$860$	2.55041	+	4.41744i	0.0869684	+	0.150634i
$861$	6.07844	−	10.5163i	0.207153	−	0.358394i
$862$	12.3852	−	21.4518i	0.421843	−	0.730653i
$863$	−5.86854	+	10.1646i	−0.199767	+	0.346007i	−0.948453	−	0.316918i	$-0.897352\pi$
$863$	−5.86854	+	10.1646i	−0.199767	+	0.346007i	0.748686	+	0.662925i	$0.230685\pi$
$864$	5.86201			0.199430
$865$	13.7941			0.469012
$866$	−7.04013	+	12.1939i	−0.239233	+	0.414364i
$867$	−1.37642	+	2.38403i	−0.0467456	+	0.0809657i
$868$	1.44095		0.000704371i	0.0489089		2.39079e-5i
$869$	12.3490	+	21.3891i	0.418911	+	0.725576i
$870$	−0.608833	+	1.05453i	−0.0206414	+	0.0357519i
$871$	42.7764	−	29.8400i	1.44942	−	1.01109i
$872$	26.4708	+	45.8488i	0.896415	+	1.55264i
$873$	3.59740			0.121753
$874$	2.09100	+	3.62172i	0.0707292	+	0.122506i
$875$	8.99089	−	15.5551i	0.303948	−	0.525859i
$876$	3.82185			0.129128
$877$	5.47779	+	9.48780i	0.184972	+	0.320380i	0.943567	−	0.331182i	$-0.107447\pi$
$877$	5.47779	+	9.48780i	0.184972	+	0.320380i	−0.758595	+	0.651562i	$0.774114\pi$
$878$	−7.17124			−0.242018
$879$	−0.339044	−	0.587241i	−0.0114357	−	0.0198071i
$880$	−1.41202	−	2.44570i	−0.0475993	−	0.0824444i
$881$	−0.925967	−	1.60382i	−0.0311966	−	0.0540341i	0.850006	−	0.526774i	$-0.176598\pi$
$881$	−0.925967	−	1.60382i	−0.0311966	−	0.0540341i	−0.881202	+	0.472740i	$0.843265\pi$
$882$	2.65917	−	4.59544i	0.0895391	−	0.154737i
$883$	−50.8664			−1.71179			−0.855896	−	0.517149i	$-0.826993\pi$
$883$	−50.8664			−1.71179			−0.855896	+	0.517149i	$0.826993\pi$
$884$	17.5582	+	8.22527i	0.590545	+	0.276646i
$885$	2.00908	+	3.47983i	0.0675345	+	0.116973i
$886$	2.81846	−	4.88172i	0.0946880	−	0.164004i
$887$	−21.0870			−0.708032			−0.354016	−	0.935239i	$-0.615184\pi$
$887$	−21.0870			−0.708032			−0.354016	+	0.935239i	$0.615184\pi$
$888$	−0.853882	+	1.47897i	−0.0286544	+	0.0496309i
$889$	−47.7251	−	0.0233292i	−1.60065	−	0.000782437i
$890$	−3.28487	+	5.68955i	−0.110109	+	0.190714i
$891$	−2.24386	−	3.88648i	−0.0751721	−	0.130202i
$892$	−17.0156	−	29.4719i	−0.569725	−	0.986793i
$893$	−49.5555			−1.65831
$894$	−11.8244			−0.395466
$895$	4.01975	+	6.96241i	0.134365	+	0.232728i
$896$	−12.8234	+	22.1857i	−0.428399	+	0.741173i
$897$	−2.75412	+	1.92122i	−0.0919573	+	0.0641476i
$898$	7.14763	−	12.3801i	0.238519	−	0.413128i
$899$	0.428719	−	0.742563i	0.0142986	−	0.0247659i
$900$	−3.19684	+	5.53710i	−0.106561	+	0.184570i
$901$	4.57995	+	7.93271i	0.152580	+	0.264277i
$902$	−15.6270			−0.520322
$903$	−13.2345	−	0.00646938i	−0.440418	−	0.000215287i
$904$	22.2120	−	38.4724i	0.738761	−	1.27957i
$905$	−0.870711	+	1.50812i	−0.0289434	+	0.0501314i
$906$	−6.99521			−0.232400
$907$	5.11282	−	8.85566i	0.169768	−	0.294047i	−0.768570	−	0.639766i	$-0.779031\pi$
$907$	5.11282	−	8.85566i	0.169768	−	0.294047i	0.938338	+	0.345718i	$0.112365\pi$
$908$	−17.9340			−0.595159
$909$	11.9792			0.397324
$910$	0.439724	+	5.15998i	0.0145767	+	0.171052i
$911$	35.4885			1.17578			0.587892	−	0.808939i	$-0.299958\pi$
$911$	35.4885			1.17578			0.587892	+	0.808939i	$0.299958\pi$
$912$	5.20500			0.172355
$913$	−25.8721	+	44.8117i	−0.856240	+	1.48305i
$914$	5.15772			0.170602
$915$	0.713513	−	1.23584i	0.0235880	−	0.0408556i
$916$	−10.9185	+	18.9113i	−0.360756	+	0.624848i
$917$	−26.0050	−	45.0928i	−0.858759	−	1.48910i
$918$	−2.86291			−0.0944903
$919$	−1.49841	−	2.59532i	−0.0494280	−	0.0856118i	0.840253	−	0.542195i	$-0.182407\pi$
$919$	−1.49841	−	2.59532i	−0.0494280	−	0.0856118i	−0.889681	+	0.456583i	$0.849073\pi$
$920$	0.865771	−	1.49956i	0.0285436	−	0.0494390i
$921$	−13.6051	+	23.5648i	−0.448305	+	0.776487i
$922$	3.64522	−	6.31371i	0.120049	−	0.207931i
$923$	12.7004	−	8.85956i	0.418039	−	0.291616i
$924$	16.9161	+	0.00826901i	0.556499	+	0.000272031i
$925$	−1.47522	−	2.55515i	−0.0485048	−	0.0840128i
$926$	17.8189			0.585566
$927$	3.09932			0.101795
$928$	6.57425	+	11.3869i	0.215810	+	0.373794i
$929$	29.9248	+	51.8312i	0.981800	+	1.70053i	0.655374	+	0.755305i	$0.272511\pi$
$929$	29.9248	+	51.8312i	0.981800	+	1.70053i	0.326426	+	0.945223i	$0.394156\pi$
$930$	0.103763	−	0.179722i	0.00340252	−	0.00589333i
$931$	20.7554	−	35.8684i	0.680232	−	1.17554i
$932$	−18.9975	+	32.9046i	−0.622283	+	1.07783i
$933$	14.1285			0.462547
$934$	−5.49636	+	9.51997i	−0.179846	+	0.311503i
$935$	6.06198	+	10.4997i	0.198248	+	0.343375i
$936$	−0.799805	−	9.33147i	−0.0261424	−	0.305009i
$937$	−60.1408			−1.96471			−0.982357	−	0.187015i	$-0.940119\pi$
$937$	−60.1408			−1.96471			−0.982357	+	0.187015i	$0.940119\pi$
$938$	−14.5020	−	25.1465i	−0.473506	−	0.821064i
$939$	−9.84907	−	17.0591i	−0.321412	−	0.556703i
$940$	4.26789	+	7.39220i	0.139203	+	0.241107i
$941$	−0.964242	−	1.67012i	−0.0314334	−	0.0544443i	0.849881	−	0.526975i	$-0.176674\pi$
$941$	−0.964242	−	1.67012i	−0.0314334	−	0.0544443i	−0.881314	+	0.472531i	$0.843341\pi$
$942$	13.9642			0.454979
$943$	2.13789	+	3.70294i	0.0696194	+	0.120584i
$944$	4.93588			0.160649
$945$	0.946032	+	1.64043i	0.0307744	+	0.0533631i
$946$	8.51334	+	14.7455i	0.276793	+	0.479419i
$947$	−0.682775			−0.0221872			−0.0110936	−	0.999938i	$-0.503531\pi$
$947$	−0.682775			−0.0221872			−0.0110936	+	0.999938i	$0.503531\pi$
$948$	3.92042	+	6.79036i	0.127329	+	0.220541i
$949$	−0.825969	−	9.63673i	−0.0268121	−	0.312822i
$950$	10.0756	−	17.4514i	0.326894	−	0.566197i
$951$	7.83931	+	13.5781i	0.254207	+	0.440299i
$952$	12.9813	−	22.4589i	0.420727	−	0.727898i
$953$	16.6889	−	28.9060i	0.540606	−	0.936358i	−0.458263	−	0.888817i	$-0.651528\pi$
$953$	16.6889	−	28.9060i	0.540606	−	0.936358i	0.998869	−	0.0475411i	$-0.0151385\pi$
$954$	0.920325	−	1.59405i	0.0297966	−	0.0516092i
$955$	−9.83358			−0.318207
$956$	20.7853			0.672243
$957$	5.03298	−	8.71738i	0.162693	−	0.281793i
$958$	5.50406	−	9.53332i	0.177828	−	0.308008i
$959$	−25.5303	+	44.1698i	−0.824415	+	1.42632i
$960$	0.961881	+	1.66603i	0.0310446	+	0.0537708i
$961$	15.4269	−	26.7202i	0.497643	−	0.861943i
$962$	1.62815	+	0.762719i	0.0524936	+	0.0245910i
$963$	−5.59313	−	9.68758i	−0.180236	−	0.312178i
$964$	−18.3677			−0.591585
$965$	4.96267	+	8.59559i	0.159754	+	0.276702i
$966$	0.933697	+	1.61904i	0.0300412	+	0.0520917i
$967$	−4.60355			−0.148040			−0.0740201	−	0.997257i	$-0.523583\pi$
$967$	−4.60355			−0.148040			−0.0740201	+	0.997257i	$0.523583\pi$
$968$	−11.8704	−	20.5601i	−0.381529	−	0.660828i
$969$	−22.3457			−0.717846
$970$	0.976465	+	1.69129i	0.0313524	+	0.0543040i
$971$	1.06649	+	1.84721i	0.0342251	+	0.0592797i	0.882631	−	0.470067i	$-0.155770\pi$
$971$	1.06649	+	1.84721i	0.0342251	+	0.0592797i	−0.848405	+	0.529347i	$0.822437\pi$
$972$	−0.712354	−	1.23383i	−0.0228488	−	0.0395752i
$973$	−3.47327	−	6.02267i	−0.111348	−	0.193078i
$974$	−17.7429			−0.568520
$975$	14.6526	+	6.86413i	0.469259	+	0.219828i
$976$	−0.876474	−	1.51810i	−0.0280553	−	0.0485931i
$977$	18.1843	−	31.4962i	0.581768	−	1.00765i	−0.413502	−	0.910503i	$-0.635695\pi$
$977$	18.1843	−	31.4962i	0.581768	−	1.00765i	0.995270	−	0.0971481i	$-0.0309720\pi$
$978$	8.47117			0.270878
$979$	27.1547	−	47.0333i	0.867867	−	1.50319i
$980$	−7.13803	−	0.00697849i	−0.228016	−	0.000222920i
$981$	10.1906	−	17.6506i	0.325361	−	0.563541i
$982$	−0.596790	−	1.03367i	−0.0190443	−	0.0329858i
$983$	−10.0001	−	17.3207i	−0.318954	−	0.552444i	0.661316	−	0.750107i	$-0.269998\pi$
$983$	−10.0001	−	17.3207i	−0.318954	−	0.552444i	−0.980270	+	0.197663i	$0.936665\pi$
$984$	−11.9254			−0.380168
$985$	13.1085			0.417672
$986$	−3.21076	−	5.56120i	−0.102251	−	0.177105i
$987$	−22.1469	−	0.0108259i	−0.704942	−	0.000344593i
$988$	−2.59700	−	30.2996i	−0.0826215	−	0.963960i
$989$	2.32938	−	4.03461i	0.0740701	−	0.128293i
$990$	1.21813	−	2.10987i	0.0387148	−	0.0670560i
$991$	−10.4003	+	18.0139i	−0.330377	+	0.572230i	−0.982586	−	0.185809i	$-0.940509\pi$
$991$	−10.4003	+	18.0139i	−0.330377	+	0.572230i	0.652209	+	0.758040i	$0.273843\pi$
$992$	−1.12044	−	1.94066i	−0.0355741	−	0.0616161i
$993$	−14.4236			−0.457719
$994$	−4.30567	−	7.46607i	−0.136568	−	0.236809i
$995$	2.54704	−	4.41160i	0.0807466	−	0.139857i
$996$	−8.21355	+	14.2263i	−0.260256	+	0.450777i
$997$	−22.1106			−0.700249			−0.350124	−	0.936703i	$-0.613861\pi$
$997$	−22.1106			−0.700249			−0.350124	+	0.936703i	$0.613861\pi$
$998$	5.96688	−	10.3349i	0.188878	−	0.327147i
$999$	0.657446			0.0208007

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.l.b.16.4	yes	16
3.2	odd	2		819.2.s.e.289.5		16
7.4	even	3		273.2.j.b.172.5	yes	16
13.9	even	3		273.2.j.b.100.5	✓	16
21.11	odd	6		819.2.n.e.172.4		16
39.35	odd	6		819.2.n.e.100.4		16
91.74	even	3	inner	273.2.l.b.256.4	yes	16
273.74	odd	6		819.2.s.e.802.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.j.b.100.5	✓	16	13.9	even	3
273.2.j.b.172.5	yes	16	7.4	even	3
273.2.l.b.16.4	yes	16	1.1	even	1	trivial
273.2.l.b.256.4	yes	16	91.74	even	3	inner
819.2.n.e.100.4		16	39.35	odd	6
819.2.n.e.172.4		16	21.11	odd	6
819.2.s.e.289.5		16	3.2	odd	2
819.2.s.e.802.5		16	273.74	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.758480 q^{2} +(0.500000 - 0.866025i) q^{3} -1.42471 q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 + 0.656863i) q^{6} +(-1.32400 + 2.29064i) q^{7} +2.59757 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q-0.758480 q^{2} +(0.500000 - 0.866025i) q^{3} -1.42471 q^{4} +(-0.357869 + 0.619848i) q^{5} +(-0.379240 + 0.656863i) q^{6} +(-1.32400 + 2.29064i) q^{7} +2.59757 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.271437 - 0.470142i) q^{10} +(-2.24386 + 3.88648i) q^{11} +(-0.712354 + 1.23383i) q^{12} +(3.26504 + 1.52954i) q^{13} +(1.00422 - 1.73741i) q^{14} +(0.357869 + 0.619848i) q^{15} +0.879208 q^{16} -3.77454 q^{17} +(0.379240 + 0.656863i) q^{18} +(2.96005 + 5.12696i) q^{19} +(0.509859 - 0.883102i) q^{20} +(1.32176 + 2.29193i) q^{21} +(1.70192 - 2.94782i) q^{22} -0.931345 q^{23} +(1.29879 - 2.24956i) q^{24} +(2.24386 + 3.88648i) q^{25} +(-2.47647 - 1.16012i) q^{26} -1.00000 q^{27} +(1.88631 - 3.26349i) q^{28} +(-1.12150 - 1.94250i) q^{29} +(-0.271437 - 0.470142i) q^{30} +(0.191136 + 0.331058i) q^{31} -5.86201 q^{32} +(2.24386 + 3.88648i) q^{33} +2.86291 q^{34} +(-0.946032 - 1.64043i) q^{35} +(0.712354 + 1.23383i) q^{36} -0.657446 q^{37} +(-2.24514 - 3.88870i) q^{38} +(2.95714 - 2.06284i) q^{39} +(-0.929592 + 1.61010i) q^{40} +(-2.29549 - 3.97591i) q^{41} +(-1.00253 - 1.73839i) q^{42} +(-2.50110 + 4.33202i) q^{43} +(3.19684 - 5.53710i) q^{44} +0.715739 q^{45} +0.706407 q^{46} +(-4.18536 + 7.24926i) q^{47} +(0.439604 - 0.761417i) q^{48} +(-3.49407 - 6.06560i) q^{49} +(-1.70192 - 2.94782i) q^{50} +(-1.88727 + 3.26885i) q^{51} +(-4.65173 - 2.17914i) q^{52} +(-1.21338 - 2.10164i) q^{53} +0.758480 q^{54} +(-1.60602 - 2.78170i) q^{55} +(-3.43917 + 5.95011i) q^{56} +5.92010 q^{57} +(0.850636 + 1.47335i) q^{58} +5.61400 q^{59} +(-0.509859 - 0.883102i) q^{60} +(-0.996890 - 1.72666i) q^{61} +(-0.144973 - 0.251101i) q^{62} +(2.64575 + 0.00129331i) q^{63} +2.68780 q^{64} +(-2.11654 + 1.47646i) q^{65} +(-1.70192 - 2.94782i) q^{66} +(7.23273 - 12.5274i) q^{67} +5.37762 q^{68} +(-0.465673 + 0.806569i) q^{69} +(0.717546 + 1.24423i) q^{70} +(2.14741 - 3.71943i) q^{71} +(-1.29879 - 2.24956i) q^{72} +(-1.34127 - 2.32315i) q^{73} +0.498660 q^{74} +4.48772 q^{75} +(-4.21721 - 7.30442i) q^{76} +(-5.93167 - 10.2856i) q^{77} +(-2.24293 + 1.56463i) q^{78} +(2.75173 - 4.76614i) q^{79} +(-0.314642 + 0.544975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.74108 + 3.01565i) q^{82} +11.5302 q^{83} +(-1.88312 - 3.26534i) q^{84} +(1.35079 - 2.33964i) q^{85} +(1.89703 - 3.28575i) q^{86} -2.24300 q^{87} +(-5.82859 + 10.0954i) q^{88} -12.1018 q^{89} -0.542874 q^{90} +(-7.82652 + 5.45395i) q^{91} +1.32689 q^{92} +0.382273 q^{93} +(3.17451 - 5.49842i) q^{94} -4.23725 q^{95} +(-2.93100 + 5.07665i) q^{96} +(-1.79870 + 3.11544i) q^{97} +(2.65018 + 4.60063i) q^{98} +4.48772 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9	\( 16 q + 8 q^{3} + 12 q^{4} + q^{7} + 12 q^{8} - 8 q^{9} - 4 q^{10} - 2 q^{11} + 6 q^{12} + 5 q^{13} - 7 q^{14} + 12 q^{16} + 4 q^{17} - 11 q^{19} - 20 q^{20} - q^{21} + 7 q^{22} - 8 q^{23} + 6 q^{24} + 2 q^{25} + 33 q^{26} - 16 q^{27} - q^{28} + 15 q^{29} + 4 q^{30} + 3 q^{31} - 6 q^{32} + 2 q^{33} - 68 q^{34} - 6 q^{36} - 8 q^{37} + 2 q^{38} + 4 q^{39} - 25 q^{40} + 19 q^{41} - 17 q^{42} + 11 q^{43} - 16 q^{44} - 4 q^{46} + 5 q^{47} + 6 q^{48} + 7 q^{49} - 7 q^{50} + 2 q^{51} - 18 q^{52} + 36 q^{53} - 15 q^{55} - 51 q^{56} - 22 q^{57} + 20 q^{58} + 34 q^{59} + 20 q^{60} - 22 q^{61} - 6 q^{62} - 2 q^{63} - 20 q^{64} - 24 q^{65} - 7 q^{66} + 26 q^{67} - 10 q^{68} - 4 q^{69} + 46 q^{70} + 9 q^{71} - 6 q^{72} - 6 q^{73} - 30 q^{74} + 4 q^{75} - 16 q^{76} - 36 q^{77} + 6 q^{78} + 16 q^{79} - 28 q^{80} - 8 q^{81} - q^{82} + 36 q^{83} - 8 q^{84} - 4 q^{85} + 16 q^{86} + 30 q^{87} + 24 q^{88} - 40 q^{89} + 8 q^{90} - 10 q^{91} - 94 q^{92} + 6 q^{93} - 20 q^{94} - 3 q^{96} + 7 q^{97} + 18 q^{98} + 4 q^{99}+O(q^{100}) \) 16 * q + 8 * q^3 + 12 * q^4 + q^7 + 12 * q^8 - 8 * q^9 - 4 * q^10 - 2 * q^11 + 6 * q^12 + 5 * q^13 - 7 * q^14 + 12 * q^16 + 4 * q^17 - 11 * q^19 - 20 * q^20 - q^21 + 7 * q^22 - 8 * q^23 + 6 * q^24 + 2 * q^25 + 33 * q^26 - 16 * q^27 - q^28 + 15 * q^29 + 4 * q^30 + 3 * q^31 - 6 * q^32 + 2 * q^33 - 68 * q^34 - 6 * q^36 - 8 * q^37 + 2 * q^38 + 4 * q^39 - 25 * q^40 + 19 * q^41 - 17 * q^42 + 11 * q^43 - 16 * q^44 - 4 * q^46 + 5 * q^47 + 6 * q^48 + 7 * q^49 - 7 * q^50 + 2 * q^51 - 18 * q^52 + 36 * q^53 - 15 * q^55 - 51 * q^56 - 22 * q^57 + 20 * q^58 + 34 * q^59 + 20 * q^60 - 22 * q^61 - 6 * q^62 - 2 * q^63 - 20 * q^64 - 24 * q^65 - 7 * q^66 + 26 * q^67 - 10 * q^68 - 4 * q^69 + 46 * q^70 + 9 * q^71 - 6 * q^72 - 6 * q^73 - 30 * q^74 + 4 * q^75 - 16 * q^76 - 36 * q^77 + 6 * q^78 + 16 * q^79 - 28 * q^80 - 8 * q^81 - q^82 + 36 * q^83 - 8 * q^84 - 4 * q^85 + 16 * q^86 + 30 * q^87 + 24 * q^88 - 40 * q^89 + 8 * q^90 - 10 * q^91 - 94 * q^92 + 6 * q^93 - 20 * q^94 - 3 * q^96 + 7 * q^97 + 18 * q^98 + 4 * q^99

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