LMFDB - Embedded newform 273.2.cg.a.115.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(19,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 5]))

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

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

chi := DirichletCharacter("273.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.7
Character	$\chi$	$=$	273.115
Dual form			273.2.cg.a.19.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.64664 - 0.441217i) q^{2} +1.00000i q^{3} +(0.784712 - 0.453054i) q^{4} +(1.35835 + 0.363968i) q^{5} +(0.441217 + 1.64664i) q^{6} +(0.501823 + 2.59772i) q^{7} +(-1.31861 + 1.31861i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.64664 - 0.441217i) q^{2} +1.00000i q^{3} +(0.784712 - 0.453054i) q^{4} +(1.35835 + 0.363968i) q^{5} +(0.441217 + 1.64664i) q^{6} +(0.501823 + 2.59772i) q^{7} +(-1.31861 + 1.31861i) q^{8} -1.00000 q^{9} +2.39731 q^{10} +(1.07237 - 1.07237i) q^{11} +(0.453054 + 0.784712i) q^{12} +(1.37191 - 3.33435i) q^{13} +(1.97248 + 4.05611i) q^{14} +(-0.363968 + 1.35835i) q^{15} +(-2.49559 + 4.32249i) q^{16} +(-2.58513 - 4.47758i) q^{17} +(-1.64664 + 0.441217i) q^{18} +(3.42980 - 3.42980i) q^{19} +(1.23081 - 0.329795i) q^{20} +(-2.59772 + 0.501823i) q^{21} +(1.29267 - 2.23896i) q^{22} +(1.86178 + 1.07490i) q^{23} +(-1.31861 - 1.31861i) q^{24} +(-2.61749 - 1.51121i) q^{25} +(0.787879 - 6.09579i) q^{26} -1.00000i q^{27} +(1.57070 + 1.81111i) q^{28} +(-0.744307 - 1.28918i) q^{29} +2.39731i q^{30} +(0.506544 + 1.89045i) q^{31} +(-1.23691 + 4.61620i) q^{32} +(1.07237 + 1.07237i) q^{33} +(-6.23237 - 6.23237i) q^{34} +(-0.263839 + 3.71126i) q^{35} +(-0.784712 + 0.453054i) q^{36} +(2.45563 + 9.16453i) q^{37} +(4.13437 - 7.16094i) q^{38} +(3.33435 + 1.37191i) q^{39} +(-2.27106 + 1.31120i) q^{40} +(-6.34762 - 1.70084i) q^{41} +(-4.05611 + 1.97248i) q^{42} +(-7.27334 - 4.19927i) q^{43} +(0.355661 - 1.32735i) q^{44} +(-1.35835 - 0.363968i) q^{45} +(3.53996 + 0.948528i) q^{46} +(1.66212 - 6.20311i) q^{47} +(-4.32249 - 2.49559i) q^{48} +(-6.49635 + 2.60720i) q^{49} +(-4.97684 - 1.33354i) q^{50} +(4.47758 - 2.58513i) q^{51} +(-0.434083 - 3.23805i) q^{52} +(1.87579 - 3.24897i) q^{53} +(-0.441217 - 1.64664i) q^{54} +(1.84696 - 1.06635i) q^{55} +(-4.08709 - 2.76367i) q^{56} +(3.42980 + 3.42980i) q^{57} +(-1.79442 - 1.79442i) q^{58} +(2.19104 - 8.17707i) q^{59} +(0.329795 + 1.23081i) q^{60} +3.23280i q^{61} +(1.66819 + 2.88940i) q^{62} +(-0.501823 - 2.59772i) q^{63} -1.83539i q^{64} +(3.07713 - 4.02987i) q^{65} +(2.23896 + 1.29267i) q^{66} +(9.21001 + 9.21001i) q^{67} +(-4.05717 - 2.34241i) q^{68} +(-1.07490 + 1.86178i) q^{69} +(1.20302 + 6.22754i) q^{70} +(-2.71213 + 0.726713i) q^{71} +(1.31861 - 1.31861i) q^{72} +(-14.2879 + 3.82844i) q^{73} +(8.08709 + 14.0072i) q^{74} +(1.51121 - 2.61749i) q^{75} +(1.13752 - 4.24529i) q^{76} +(3.32387 + 2.24759i) q^{77} +(6.09579 + 0.787879i) q^{78} +(3.67744 + 6.36951i) q^{79} +(-4.96314 + 4.96314i) q^{80} +1.00000 q^{81} -11.2027 q^{82} +(-0.0684765 + 0.0684765i) q^{83} +(-1.81111 + 1.57070i) q^{84} +(-1.88181 - 7.02301i) q^{85} +(-13.8294 - 3.70557i) q^{86} +(1.28918 - 0.744307i) q^{87} +2.82807i q^{88} +(10.7801 - 2.88852i) q^{89} -2.39731 q^{90} +(9.35017 + 1.89059i) q^{91} +1.94795 q^{92} +(-1.89045 + 0.506544i) q^{93} -10.9477i q^{94} +(5.90720 - 3.41052i) q^{95} +(-4.61620 - 1.23691i) q^{96} +(3.39415 + 12.6671i) q^{97} +(-9.54683 + 7.15942i) q^{98} +(-1.07237 + 1.07237i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^7 - 36 * q^9	$ 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) $ 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.64664	−	0.441217i	1.16435	−	0.311987i	0.375650	−	0.926762i	$-0.377420\pi$
$2$	1.64664	−	0.441217i	1.16435	−	0.311987i	0.788703	+	0.614774i	$0.210753\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.784712	−	0.453054i	0.392356	−	0.226527i
$5$	1.35835	+	0.363968i	0.607472	+	0.162772i	0.549426	−	0.835542i	$-0.314846\pi$
$5$	1.35835	+	0.363968i	0.607472	+	0.162772i	0.0580459	+	0.998314i	$0.481513\pi$
$6$	0.441217	+	1.64664i	0.180126	+	0.672239i
$7$	0.501823	+	2.59772i	0.189671	+	0.981848i
$7$	0.501823	+	2.59772i	0.189671	+	0.981848i
$8$	−1.31861	+	1.31861i	−0.466198	+	0.466198i
$9$	−1.00000			−0.333333
$10$	2.39731			0.758095
$11$	1.07237	−	1.07237i	0.323332	−	0.323332i	−0.526712	−	0.850044i	$-0.676575\pi$
$11$	1.07237	−	1.07237i	0.323332	−	0.323332i	0.850044	+	0.526712i	$0.176575\pi$
$12$	0.453054	+	0.784712i	0.130785	+	0.226527i
$13$	1.37191	−	3.33435i	0.380500	−	0.924781i
$13$	1.37191	−	3.33435i	0.380500	−	0.924781i
$14$	1.97248	+	4.05611i	0.527169	+	1.08404i
$15$	−0.363968	+	1.35835i	−0.0939762	+	0.350724i
$16$	−2.49559	+	4.32249i	−0.623898	+	1.08062i
$17$	−2.58513	−	4.47758i	−0.626986	−	1.08597i	−0.988153	−	0.153471i	$-0.950955\pi$
$17$	−2.58513	−	4.47758i	−0.626986	−	1.08597i	0.361167	−	0.932501i	$-0.382378\pi$
$18$	−1.64664	+	0.441217i	−0.388118	+	0.103996i
$19$	3.42980	−	3.42980i	0.786850	−	0.786850i	−0.194127	−	0.980976i	$-0.562187\pi$
$19$	3.42980	−	3.42980i	0.786850	−	0.786850i	0.980976	+	0.194127i	$0.0621872\pi$
$20$	1.23081	−	0.329795i	0.275218	−	0.0737443i
$21$	−2.59772	+	0.501823i	−0.566870	+	0.109507i
$22$	1.29267	−	2.23896i	0.275597	−	0.477348i
$23$	1.86178	+	1.07490i	0.388208	+	0.224132i	0.681384	−	0.731927i	$-0.261379\pi$
$23$	1.86178	+	1.07490i	0.388208	+	0.224132i	−0.293175	+	0.956059i	$0.594712\pi$
$24$	−1.31861	−	1.31861i	−0.269160	−	0.269160i
$25$	−2.61749	−	1.51121i	−0.523498	−	0.302242i
$26$	0.787879	−	6.09579i	0.154516	−	1.19548i
$27$		−	1.00000i		−	0.192450i
$28$	1.57070	+	1.81111i	0.296834	+	0.342268i
$29$	−0.744307	−	1.28918i	−0.138214	−	0.239394i	0.788606	−	0.614898i	$-0.210803\pi$
$29$	−0.744307	−	1.28918i	−0.138214	−	0.239394i	−0.926821	+	0.375504i	$0.877470\pi$
$30$			2.39731i			0.437686i
$31$	0.506544	+	1.89045i	0.0909779	+	0.339534i	0.996379	−	0.0850231i	$-0.0270964\pi$
$31$	0.506544	+	1.89045i	0.0909779	+	0.339534i	−0.905401	+	0.424557i	$0.860430\pi$
$32$	−1.23691	+	4.61620i	−0.218656	+	0.816037i
$33$	1.07237	+	1.07237i	0.186676	+	0.186676i
$34$	−6.23237	−	6.23237i	−1.06884	−	1.06884i
$35$	−0.263839	+	3.71126i	−0.0445969	+	0.627318i
$36$	−0.784712	+	0.453054i	−0.130785	+	0.0755090i
$37$	2.45563	+	9.16453i	0.403703	+	1.50664i	0.806436	+	0.591322i	$0.201394\pi$
$37$	2.45563	+	9.16453i	0.403703	+	1.50664i	−0.402733	+	0.915318i	$0.631940\pi$
$38$	4.13437	−	7.16094i	0.670684	−	1.16166i
$39$	3.33435	+	1.37191i	0.533923	+	0.219682i
$40$	−2.27106	+	1.31120i	−0.359086	+	0.207318i
$41$	−6.34762	−	1.70084i	−0.991331	−	0.265626i	−0.273522	−	0.961866i	$-0.588188\pi$
$41$	−6.34762	−	1.70084i	−0.991331	−	0.265626i	−0.717810	+	0.696239i	$0.754855\pi$
$42$	−4.05611	+	1.97248i	−0.625872	+	0.304361i
$43$	−7.27334	−	4.19927i	−1.10917	−	0.640382i	−0.170559	−	0.985347i	$-0.554557\pi$
$43$	−7.27334	−	4.19927i	−1.10917	−	0.640382i	−0.938615	+	0.344965i	$0.887891\pi$
$44$	0.355661	−	1.32735i	0.0536179	−	0.200105i
$45$	−1.35835	−	0.363968i	−0.202491	−	0.0542572i
$46$	3.53996	+	0.948528i	0.521938	+	0.139853i
$47$	1.66212	−	6.20311i	0.242445	−	0.904817i	−0.732206	−	0.681084i	$-0.761509\pi$
$47$	1.66212	−	6.20311i	0.242445	−	0.904817i	0.974650	−	0.223733i	$-0.0718243\pi$
$48$	−4.32249	−	2.49559i	−0.623898	−	0.360208i
$49$	−6.49635	+	2.60720i	−0.928050	+	0.372457i
$50$	−4.97684	−	1.33354i	−0.703832	−	0.188591i
$51$	4.47758	−	2.58513i	0.626986	−	0.361991i
$52$	−0.434083	−	3.23805i	−0.0601965	−	0.449037i
$53$	1.87579	−	3.24897i	0.257660	−	0.446280i	−0.707955	−	0.706258i	$-0.750382\pi$
$53$	1.87579	−	3.24897i	0.257660	−	0.446280i	0.965615	+	0.259978i	$0.0837152\pi$
$54$	−0.441217	−	1.64664i	−0.0600420	−	0.224080i
$55$	1.84696	−	1.06635i	0.249045	−	0.143786i
$56$	−4.08709	−	2.76367i	−0.546160	−	0.369311i
$57$	3.42980	+	3.42980i	0.454288	+	0.454288i
$58$	−1.79442	−	1.79442i	−0.235618	−	0.235618i
$59$	2.19104	−	8.17707i	0.285249	−	1.06456i	−0.663408	−	0.748258i	$-0.730891\pi$
$59$	2.19104	−	8.17707i	0.285249	−	1.06456i	0.948657	−	0.316306i	$-0.102443\pi$
$60$	0.329795	+	1.23081i	0.0425763	+	0.158897i
$61$			3.23280i			0.413918i	0.978350	+	0.206959i	$0.0663567\pi$
$61$			3.23280i			0.413918i	−0.978350	+	0.206959i	$0.933643\pi$
$62$	1.66819	+	2.88940i	0.211861	+	0.366954i
$63$	−0.501823	−	2.59772i	−0.0632238	−	0.327283i
$64$		−	1.83539i		−	0.229423i
$65$	3.07713	−	4.02987i	0.381671	−	0.499844i
$66$	2.23896	+	1.29267i	0.275597	+	0.159116i
$67$	9.21001	+	9.21001i	1.12518	+	1.12518i	0.990950	+	0.134232i	$0.0428566\pi$
$67$	9.21001	+	9.21001i	1.12518	+	1.12518i	0.134232	+	0.990950i	$0.457143\pi$
$68$	−4.05717	−	2.34241i	−0.492004	−	0.284058i
$69$	−1.07490	+	1.86178i	−0.129403	+	0.224132i
$70$	1.20302	+	6.22754i	0.143789	+	0.744333i
$71$	−2.71213	+	0.726713i	−0.321870	+	0.0862449i	−0.416137	−	0.909302i	$-0.636616\pi$
$71$	−2.71213	+	0.726713i	−0.321870	+	0.0862449i	0.0942662	+	0.995547i	$0.469950\pi$
$72$	1.31861	−	1.31861i	0.155399	−	0.155399i
$73$	−14.2879	+	3.82844i	−1.67228	+	0.448085i	−0.965723	−	0.259574i	$-0.916418\pi$
$73$	−14.2879	+	3.82844i	−1.67228	+	0.448085i	−0.706554	+	0.707660i	$0.749751\pi$
$74$	8.08709	+	14.0072i	0.940105	+	1.62831i
$75$	1.51121	−	2.61749i	0.174499	−	0.302242i
$76$	1.13752	−	4.24529i	0.130483	−	0.486968i
$77$	3.32387	+	2.24759i	0.378790	+	0.256136i
$78$	6.09579	+	0.787879i	0.690212	+	0.0892097i
$79$	3.67744	+	6.36951i	0.413744	+	0.716626i	0.995296	−	0.0968836i	$-0.0308874\pi$
$79$	3.67744	+	6.36951i	0.413744	+	0.716626i	−0.581551	+	0.813510i	$0.697554\pi$
$80$	−4.96314	+	4.96314i	−0.554895	+	0.554895i
$81$	1.00000			0.111111
$82$	−11.2027			−1.23713
$83$	−0.0684765	+	0.0684765i	−0.00751627	+	0.00751627i	−0.710855	−	0.703339i	$-0.751692\pi$
$83$	−0.0684765	+	0.0684765i	−0.00751627	+	0.00751627i	0.703339	+	0.710855i	$0.251692\pi$
$84$	−1.81111	+	1.57070i	−0.197609	+	0.171377i
$85$	−1.88181	−	7.02301i	−0.204111	−	0.761753i
$86$	−13.8294	−	3.70557i	−1.49126	−	0.399582i
$87$	1.28918	−	0.744307i	0.138214	−	0.0797981i
$88$			2.82807i			0.301474i
$89$	10.7801	−	2.88852i	1.14269	−	0.306182i	0.362656	−	0.931923i	$-0.381870\pi$
$89$	10.7801	−	2.88852i	1.14269	−	0.306182i	0.780031	+	0.625741i	$0.215203\pi$
$90$	−2.39731			−0.252698
$91$	9.35017	+	1.89059i	0.980164	+	0.198188i
$92$	1.94795			0.203088
$93$	−1.89045	+	0.506544i	−0.196030	+	0.0525261i
$94$		−	10.9477i		−	1.12917i
$95$	5.90720	−	3.41052i	0.606066	−	0.349912i
$96$	−4.61620	−	1.23691i	−0.471139	−	0.126241i
$97$	3.39415	+	12.6671i	0.344624	+	1.28615i	0.893051	+	0.449955i	$0.148560\pi$
$97$	3.39415	+	12.6671i	0.344624	+	1.28615i	−0.548428	+	0.836198i	$0.684773\pi$
$98$	−9.54683	+	7.15942i	−0.964375	+	0.723211i
$99$	−1.07237	+	1.07237i	−0.107777	+	0.107777i
$100$	−2.73863			−0.273863
$101$	17.1955			1.71102			0.855509	−	0.517788i	$-0.173244\pi$
$101$	17.1955			1.71102			0.855509	+	0.517788i	$0.173244\pi$
$102$	6.23237	−	6.23237i	0.617096	−	0.617096i
$103$	−0.176474	−	0.305661i	−0.0173885	−	0.0301177i	0.857200	−	0.514983i	$-0.172202\pi$
$103$	−0.176474	−	0.305661i	−0.0173885	−	0.0301177i	−0.874589	+	0.484866i	$0.838869\pi$
$104$	2.58768	+	6.20570i	0.253743	+	0.608519i
$105$	−3.71126	−	0.263839i	−0.362182	−	0.0257480i
$106$	1.65526	−	6.17753i	0.160773	−	0.600014i
$107$	−6.70466	+	11.6128i	−0.648164	+	1.12265i	0.335397	+	0.942077i	$0.391130\pi$
$107$	−6.70466	+	11.6128i	−0.648164	+	1.12265i	−0.983561	+	0.180577i	$0.942204\pi$
$108$	−0.453054	−	0.784712i	−0.0435951	−	0.0755090i
$109$	−9.50358	+	2.54648i	−0.910277	+	0.243908i	−0.683425	−	0.730021i	$-0.739510\pi$
$109$	−9.50358	+	2.54648i	−0.910277	+	0.243908i	−0.226853	+	0.973929i	$0.572844\pi$
$110$	2.57080	−	2.57080i	0.245116	−	0.245116i
$111$	−9.16453	+	2.45563i	−0.869859	+	0.233078i
$112$	−12.4810	−	4.31373i	−1.17934	−	0.407610i
$113$	0.325800	−	0.564301i	0.0306486	−	0.0530850i	−0.850294	−	0.526308i	$-0.823576\pi$
$113$	0.325800	−	0.564301i	0.0306486	−	0.0530850i	0.880943	+	0.473223i	$0.156909\pi$
$114$	7.16094	+	4.13437i	0.670684	+	0.387219i
$115$	2.13772	+	2.13772i	0.199343	+	0.199343i
$116$	−1.16813	−	0.674422i	−0.108458	−	0.0626185i
$117$	−1.37191	+	3.33435i	−0.126833	+	0.308260i
$118$		−	14.4315i		−	1.32852i
$119$	10.3342	−	8.96241i	0.947337	−	0.821582i
$120$	−1.31120	−	2.27106i	−0.119695	−	0.207318i
$121$			8.70004i			0.790913i
$122$	1.42637	+	5.32327i	0.129137	+	0.481947i
$123$	1.70084	−	6.34762i	0.153359	−	0.572345i
$124$	1.25397	+	1.25397i	0.112609	+	0.112609i
$125$	−7.97733	−	7.97733i	−0.713514	−	0.713514i
$126$	−1.97248	−	4.05611i	−0.175723	−	0.361347i
$127$	−1.63609	+	0.944595i	−0.145179	+	0.0838192i	−0.570830	−	0.821068i	$-0.693378\pi$
$127$	−1.63609	+	0.944595i	−0.145179	+	0.0838192i	0.425651	+	0.904887i	$0.360045\pi$
$128$	−3.28362	−	12.2546i	−0.290234	−	1.08317i
$129$	4.19927	−	7.27334i	0.369725	−	0.640382i
$130$	3.28889	−	7.99344i	0.288455	−	0.701071i
$131$	8.89476	−	5.13539i	0.777139	−	0.448681i	−0.0582763	−	0.998300i	$-0.518560\pi$
$131$	8.89476	−	5.13539i	0.777139	−	0.448681i	0.835415	+	0.549619i	$0.185227\pi$
$132$	1.32735	+	0.355661i	0.115531	+	0.0309563i
$133$	10.6308	+	7.18852i	0.921810	+	0.623324i
$134$	19.2292	+	11.1020i	1.66115	+	0.959066i
$135$	0.363968	−	1.35835i	0.0313254	−	0.116908i
$136$	9.31293	+	2.49539i	0.798577	+	0.213978i
$137$	−9.00469	−	2.41280i	−0.769323	−	0.206139i	−0.147251	−	0.989099i	$-0.547042\pi$
$137$	−9.00469	−	2.41280i	−0.769323	−	0.206139i	−0.622072	+	0.782960i	$0.713709\pi$
$138$	−0.948528	+	3.53996i	−0.0807441	+	0.301341i
$139$	−0.141825	−	0.0818824i	−0.0120294	−	0.00694518i	0.493973	−	0.869477i	$-0.335544\pi$
$139$	−0.141825	−	0.0818824i	−0.0120294	−	0.00694518i	−0.506003	+	0.862532i	$0.668877\pi$
$140$	1.47436	+	3.03181i	0.124607	+	0.256234i
$141$	6.20311	+	1.66212i	0.522396	+	0.139976i
$142$	−4.14527	+	2.39327i	−0.347863	+	0.200839i
$143$	−2.10446	−	5.04686i	−0.175984	−	0.422039i
$144$	2.49559	−	4.32249i	0.207966	−	0.360208i
$145$	−0.541809	−	2.02206i	−0.0449947	−	0.167923i
$146$	−21.8380	+	12.6082i	−1.80732	+	1.04346i
$147$	−2.60720	−	6.49635i	−0.215038	−	0.535810i
$148$	6.07899	+	6.07899i	0.499690	+	0.499690i
$149$	−14.7328	−	14.7328i	−1.20696	−	1.20696i	−0.972008	−	0.234949i	$-0.924508\pi$
$149$	−14.7328	−	14.7328i	−1.20696	−	1.20696i	−0.234949	−	0.972008i	$-0.575492\pi$
$150$	1.33354	−	4.97684i	0.108883	−	0.406357i
$151$	−0.938197	−	3.50140i	−0.0763494	−	0.284940i	0.917187	−	0.398458i	$-0.130455\pi$
$151$	−0.938197	−	3.50140i	−0.0763494	−	0.284940i	−0.993536	+	0.113518i	$0.963788\pi$
$152$			9.04512i			0.733656i
$153$	2.58513	+	4.47758i	0.208995	+	0.361991i
$154$	6.46490	+	2.23443i	0.520956	+	0.180055i
$155$			2.75225i			0.221066i
$156$	3.23805	−	0.434083i	0.259252	−	0.0347544i
$157$	12.8664	+	7.42842i	1.02685	+	0.592852i	0.916081	−	0.400994i	$-0.131335\pi$
$157$	12.8664	+	7.42842i	1.02685	+	0.592852i	0.110770	+	0.993846i	$0.464668\pi$
$158$	8.86577	+	8.86577i	0.705323	+	0.705323i
$159$	3.24897	+	1.87579i	0.257660	+	0.148760i
$160$	−3.36030	+	5.82021i	−0.265655	+	0.460128i
$161$	−1.85801	+	5.37581i	−0.146432	+	0.423673i
$162$	1.64664	−	0.441217i	0.129373	−	0.0346653i
$163$	11.3635	−	11.3635i	0.890054	−	0.890054i	−0.104473	−	0.994528i	$-0.533316\pi$
$163$	11.3635	−	11.3635i	0.890054	−	0.890054i	0.994528	+	0.104473i	$0.0333157\pi$
$164$	−5.75162	+	1.54114i	−0.449126	+	0.120343i
$165$	1.06635	+	1.84696i	0.0830149	+	0.143786i
$166$	−0.0825434	+	0.142969i	−0.00640661	+	0.0110966i
$167$	−3.41310	+	12.7379i	−0.264114	+	0.985686i	0.698677	+	0.715438i	$0.253773\pi$
$167$	−3.41310	+	12.7379i	−0.264114	+	0.985686i	−0.962791	+	0.270249i	$0.912894\pi$
$168$	2.76367	−	4.08709i	0.213222	−	0.315326i
$169$	−9.23572	−	9.14885i	−0.710440	−	0.703758i
$170$	−6.19734	−	10.7341i	−0.475315	−	0.823269i
$171$	−3.42980	+	3.42980i	−0.262283	+	0.262283i
$172$	−7.60997			−0.580255
$173$	−14.0328			−1.06689			−0.533445	−	0.845835i	$-0.679103\pi$
$173$	−14.0328			−1.06689			−0.533445	+	0.845835i	$0.679103\pi$
$174$	1.79442	−	1.79442i	0.136034	−	0.136034i
$175$	2.61219	−	7.55787i	0.197463	−	0.571322i
$176$	1.95912	+	7.31152i	0.147674	+	0.551127i
$177$	8.17707	+	2.19104i	0.614627	+	0.164689i
$178$	16.4765	−	9.51272i	1.23497	−	0.713008i
$179$			17.9959i			1.34508i	0.740061	+	0.672540i	$0.234797\pi$
$179$			17.9959i			1.34508i	−0.740061	+	0.672540i	$0.765203\pi$
$180$	−1.23081	+	0.329795i	−0.0917392	+	0.0245814i
$181$	−14.8428			−1.10325			−0.551627	−	0.834091i	$-0.685993\pi$
$181$	−14.8428			−1.10325			−0.551627	+	0.834091i	$0.685993\pi$
$182$	16.2306	−	1.01232i	1.20309	−	0.0750379i
$183$	−3.23280			−0.238976
$184$	−3.87233	+	1.03759i	−0.285472	+	0.0764920i
$185$			13.3424i			0.980953i
$186$	−2.88940	+	1.66819i	−0.211861	+	0.122318i
$187$	−7.57385	−	2.02941i	−0.553854	−	0.148405i
$188$	−1.50606	−	5.62069i	−0.109841	−	0.409931i
$189$	2.59772	−	0.501823i	0.188957	−	0.0365023i
$190$	8.22228	−	8.22228i	0.596507	−	0.596507i
$191$	14.4657			1.04670			0.523349	−	0.852118i	$-0.324682\pi$
$191$	14.4657			1.04670			0.523349	+	0.852118i	$0.324682\pi$
$192$	1.83539			0.132458
$193$	12.8329	−	12.8329i	0.923736	−	0.923736i	−0.0735554	−	0.997291i	$-0.523435\pi$
$193$	12.8329	−	12.8329i	0.923736	−	0.923736i	0.997291	+	0.0735554i	$0.0234346\pi$
$194$	11.1779	+	19.3607i	0.802527	+	1.39002i
$195$	4.02987	+	3.07713i	0.288585	+	0.220358i
$196$	−3.91656	+	4.98909i	−0.279754	+	0.356364i
$197$	−6.18216	+	23.0721i	−0.440460	+	1.64382i	0.287191	+	0.957873i	$0.407279\pi$
$197$	−6.18216	+	23.0721i	−0.440460	+	1.64382i	−0.727651	+	0.685947i	$0.759388\pi$
$198$	−1.29267	+	2.23896i	−0.0918658	+	0.159116i
$199$	1.49177	+	2.58382i	0.105749	+	0.183162i	0.914044	−	0.405616i	$-0.132943\pi$
$199$	1.49177	+	2.58382i	0.105749	+	0.183162i	−0.808295	+	0.588777i	$0.799609\pi$
$200$	5.44413	−	1.45875i	0.384958	−	0.103149i
$201$	−9.21001	+	9.21001i	−0.649624	+	0.649624i
$202$	28.3149	−	7.58695i	1.99223	−	0.533816i
$203$	2.97542	−	2.58044i	0.208833	−	0.181112i
$204$	2.34241	−	4.05717i	0.164001	−	0.284058i
$205$	−8.00323	−	4.62066i	−0.558969	−	0.322721i
$206$	−0.425452	−	0.425452i	−0.0296426	−	0.0296426i
$207$	−1.86178	−	1.07490i	−0.129403	−	0.0747107i
$208$	10.9890	+	14.2512i	0.761947	+	0.988146i
$209$		−	7.35604i		−	0.508828i
$210$	−6.22754	+	1.20302i	−0.429741	+	0.0830165i
$211$	−2.05578	−	3.56072i	−0.141526	−	0.245130i	0.786546	−	0.617532i	$-0.211867\pi$
$211$	−2.05578	−	3.56072i	−0.141526	−	0.245130i	−0.928071	+	0.372402i	$0.878534\pi$
$212$		−	3.39934i		−	0.233468i
$213$	−0.726713	−	2.71213i	−0.0497935	−	0.185832i
$214$	−5.91642	+	22.0804i	−0.404438	+	1.50938i
$215$	−8.35133	−	8.35133i	−0.569556	−	0.569556i
$216$	1.31861	+	1.31861i	0.0897199	+	0.0897199i
$217$	−4.65666	+	2.26453i	−0.316115	+	0.153726i
$218$	−14.5255	+	8.38628i	−0.983788	+	0.567990i
$219$	−3.82844	−	14.2879i	−0.258702	−	0.965489i
$220$	0.966224	−	1.67355i	0.0651428	−	0.112831i
$221$	−18.4764	+	2.47688i	−1.24285	+	0.166613i
$222$	−14.0072	+	8.08709i	−0.940105	+	0.542770i
$223$	16.9482	+	4.54125i	1.13493	+	0.304105i	0.776912	−	0.629609i	$-0.216785\pi$
$223$	16.9482	+	4.54125i	1.13493	+	0.304105i	0.358022	+	0.933713i	$0.383451\pi$
$224$	−12.6123	−	0.896627i	−0.842696	−	0.0599084i
$225$	2.61749	+	1.51121i	0.174499	+	0.100747i
$226$	0.287496	−	1.07295i	0.0191240	−	0.0713717i
$227$	−6.70248	−	1.79592i	−0.444859	−	0.119200i	0.0294339	−	0.999567i	$-0.490630\pi$
$227$	−6.70248	−	1.79592i	−0.444859	−	0.119200i	−0.474293	+	0.880367i	$0.657296\pi$
$228$	4.24529	+	1.13752i	0.281151	+	0.0753342i
$229$	2.31913	−	8.65510i	0.153252	−	0.571945i	−0.845996	−	0.533189i	$-0.820994\pi$
$229$	2.31913	−	8.65510i	0.153252	−	0.571945i	0.999249	−	0.0387566i	$-0.0123397\pi$
$230$	4.46326	+	2.57686i	0.294299	+	0.169913i
$231$	−2.24759	+	3.32387i	−0.147880	+	0.218694i
$232$	2.68137	+	0.718470i	0.176040	+	0.0471699i
$233$	−5.51653	+	3.18497i	−0.361400	+	0.208654i	−0.669695	−	0.742636i	$-0.733575\pi$
$233$	−5.51653	+	3.18497i	−0.361400	+	0.208654i	0.308295	+	0.951291i	$0.400242\pi$
$234$	−0.787879	+	6.09579i	−0.0515052	+	0.398494i
$235$	4.51547	−	7.82103i	0.294557	−	0.510188i
$236$	−1.98532	−	7.40931i	−0.129233	−	0.482305i
$237$	−6.36951	+	3.67744i	−0.413744	+	0.238875i
$238$	13.0624	−	19.3175i	0.846712	−	1.25217i
$239$	−11.4926	−	11.4926i	−0.743396	−	0.743396i	0.229834	−	0.973230i	$-0.426182\pi$
$239$	−11.4926	−	11.4926i	−0.743396	−	0.743396i	−0.973230	+	0.229834i	$0.926182\pi$
$240$	−4.96314	−	4.96314i	−0.320369	−	0.320369i
$241$	0.0601372	−	0.224435i	0.00387378	−	0.0144571i	−0.963962	−	0.266040i	$-0.914285\pi$
$241$	0.0601372	−	0.224435i	0.00387378	−	0.0144571i	0.967836	+	0.251583i	$0.0809512\pi$
$242$	3.83860	+	14.3259i	0.246755	+	0.920901i
$243$			1.00000i			0.0641500i
$244$	1.46463	+	2.53682i	0.0937636	+	0.162403i
$245$	−9.77324	+	1.17702i	−0.624390	+	0.0751969i
$246$		−	11.2027i		−	0.714258i
$247$	−6.73076	−	16.1415i	−0.428268	−	1.02706i
$248$	−3.16069	−	1.82482i	−0.200704	−	0.115876i
$249$	−0.0684765	−	0.0684765i	−0.00433952	−	0.00433952i
$250$	−16.6556	−	9.61609i	−1.05339	−	0.608175i
$251$	−4.39247	+	7.60798i	−0.277250	+	0.480211i	−0.970700	−	0.240293i	$-0.922756\pi$
$251$	−4.39247	+	7.60798i	−0.277250	+	0.480211i	0.693450	+	0.720504i	$0.256090\pi$
$252$	−1.57070	−	1.81111i	−0.0989445	−	0.114089i
$253$	3.14922	−	0.843830i	0.197989	−	0.0530511i
$254$	−2.27728	+	2.27728i	−0.142889	+	0.142889i
$255$	7.02301	−	1.88181i	0.439798	−	0.117844i
$256$	−8.97851	−	15.5512i	−0.561157	−	0.971952i
$257$	11.3623	−	19.6801i	0.708763	−	1.22761i	−0.256553	−	0.966530i	$-0.582587\pi$
$257$	11.3623	−	19.6801i	0.708763	−	1.22761i	0.965316	−	0.261083i	$-0.0840797\pi$
$258$	3.70557	−	13.8294i	0.230699	−	0.860980i
$259$	−22.5746	+	10.9780i	−1.40272	+	0.682141i
$260$	0.588913	−	4.55640i	0.0365228	−	0.282576i
$261$	0.744307	+	1.28918i	0.0460714	+	0.0797981i
$262$	12.3807	−	12.3807i	0.764881	−	0.764881i
$263$	−8.19543			−0.505352			−0.252676	−	0.967551i	$-0.581311\pi$
$263$	−8.19543			−0.505352			−0.252676	+	0.967551i	$0.581311\pi$
$264$	−2.82807			−0.174056
$265$	3.73050	−	3.73050i	0.229163	−	0.229163i
$266$	20.6769	+	7.14643i	1.26778	+	0.438176i
$267$	2.88852	+	10.7801i	0.176774	+	0.659731i
$268$	11.3998	+	3.05458i	0.696356	+	0.186588i
$269$	−21.2193	+	12.2510i	−1.29376	+	0.746954i	−0.979319	−	0.202322i	$-0.935151\pi$
$269$	−21.2193	+	12.2510i	−1.29376	+	0.746954i	−0.314444	+	0.949276i	$0.601818\pi$
$270$		−	2.39731i		−	0.145895i
$271$	−8.02078	+	2.14916i	−0.487228	+	0.130552i	−0.494066	−	0.869424i	$-0.664490\pi$
$271$	−8.02078	+	2.14916i	−0.487228	+	0.130552i	0.00683835	+	0.999977i	$0.497823\pi$
$272$	25.8057			1.56470
$273$	−1.89059	+	9.35017i	−0.114424	+	0.565898i
$274$	−15.8921			−0.960076
$275$	−4.42750	+	1.18634i	−0.266988	+	0.0715393i
$276$			1.94795i			0.117253i
$277$	−1.29845	+	0.749658i	−0.0780161	+	0.0450426i	−0.538501	−	0.842625i	$-0.681009\pi$
$277$	−1.29845	+	0.749658i	−0.0780161	+	0.0450426i	0.460485	+	0.887668i	$0.347676\pi$
$278$	−0.269662	−	0.0722558i	−0.0161733	−	0.00433362i
$279$	−0.506544	−	1.89045i	−0.0303260	−	0.113178i
$280$	−4.54580	−	5.24160i	−0.271663	−	0.313245i
$281$	19.5020	−	19.5020i	1.16339	−	1.16339i	0.179665	−	0.983728i	$-0.442499\pi$
$281$	19.5020	−	19.5020i	1.16339	−	1.16339i	0.983728	−	0.179665i	$-0.0575015\pi$
$282$	10.9477			0.651924
$283$	−15.6627			−0.931052			−0.465526	−	0.885034i	$-0.654135\pi$
$283$	−15.6627			−0.931052			−0.465526	+	0.885034i	$0.654135\pi$
$284$	−1.79900	+	1.79900i	−0.106751	+	0.106751i
$285$	3.41052	+	5.90720i	0.202022	+	0.349912i
$286$	−5.69205	−	7.38185i	−0.336578	−	0.436498i
$287$	1.23293	−	17.3429i	0.0727775	−	1.02372i
$288$	1.23691	−	4.61620i	0.0728855	−	0.272012i
$289$	−4.86579	+	8.42779i	−0.286223	+	0.495752i
$290$	−1.78433	−	3.09055i	−0.104780	−	0.181483i
$291$	−12.6671	+	3.39415i	−0.742561	+	0.198969i
$292$	−9.47743	+	9.47743i	−0.554625	+	0.554625i
$293$	−13.6614	+	3.66056i	−0.798107	+	0.213852i	−0.634753	−	0.772715i	$-0.718898\pi$
$293$	−13.6614	+	3.66056i	−0.798107	+	0.213852i	−0.163354	+	0.986567i	$0.552231\pi$
$294$	−7.15942	−	9.54683i	−0.417546	−	0.556782i
$295$	5.95239	−	10.3098i	0.346562	−	0.600263i
$296$	−15.3224	−	8.84640i	−0.890598	−	0.514187i
$297$	−1.07237	−	1.07237i	−0.0622253	−	0.0622253i
$298$	−30.7600	−	17.7593i	−1.78188	−	1.02877i
$299$	6.13829	−	4.73316i	0.354986	−	0.273726i
$300$		−	2.73863i		−	0.158115i
$301$	7.25860	−	21.0014i	0.418379	−	1.21050i
$302$	−3.08975	−	5.35161i	−0.177795	−	0.307950i
$303$			17.1955i			0.987857i
$304$	6.26590	+	23.3847i	0.359374	+	1.34120i
$305$	−1.17664	+	4.39127i	−0.0673741	+	0.251444i
$306$	6.23237	+	6.23237i	0.356281	+	0.356281i
$307$	−0.977336	−	0.977336i	−0.0557795	−	0.0557795i	0.678667	−	0.734446i	$-0.262558\pi$
$307$	−0.977336	−	0.977336i	−0.0557795	−	0.0557795i	−0.734446	+	0.678667i	$0.762558\pi$
$308$	3.62656	+	0.257817i	0.206642	+	0.0146905i
$309$	0.305661	−	0.176474i	0.0173885	−	0.0100392i
$310$	1.21434	+	4.53198i	0.0689699	+	0.257399i
$311$	4.20663	−	7.28609i	0.238536	−	0.413156i	−0.721759	−	0.692145i	$-0.756666\pi$
$311$	4.20663	−	7.28609i	0.238536	−	0.413156i	0.960294	+	0.278989i	$0.0899992\pi$
$312$	−6.20570	+	2.58768i	−0.351329	+	0.146499i
$313$	−14.4104	+	8.31988i	−0.814527	+	0.470267i	−0.848525	−	0.529155i	$-0.822509\pi$
$313$	−14.4104	+	8.31988i	−0.814527	+	0.470267i	0.0339987	+	0.999422i	$0.489176\pi$
$314$	24.4639	+	6.55509i	1.38058	+	0.369925i
$315$	0.263839	−	3.71126i	0.0148656	−	0.209106i
$316$	5.77146	+	3.33216i	0.324670	+	0.187448i
$317$	2.16027	−	8.06223i	0.121333	−	0.452820i	−0.878350	−	0.478019i	$-0.841355\pi$
$317$	2.16027	−	8.06223i	0.121333	−	0.452820i	0.999682	+	0.0251986i	$0.00802180\pi$
$318$	6.17753	+	1.65526i	0.346418	+	0.0928226i
$319$	−2.18065	−	0.584304i	−0.122093	−	0.0327147i
$320$	0.668023	−	2.49310i	0.0373436	−	0.139368i
$321$	−11.6128	−	6.70466i	−0.648164	−	0.374218i
$322$	−0.687583	+	9.67182i	−0.0383175	+	0.538990i
$323$	−24.2237	−	6.49071i	−1.34784	−	0.361153i
$324$	0.784712	−	0.453054i	0.0435951	−	0.0251697i
$325$	−8.62985	+	6.65437i	−0.478698	+	0.369118i
$326$	13.6978	−	23.7253i	0.758652	−	1.31402i
$327$	−2.54648	−	9.50358i	−0.140820	−	0.525549i
$328$	10.6128	−	6.12727i	0.585991	−	0.338322i
$329$	16.9481	+	1.20486i	0.934377	+	0.0664261i
$330$	2.57080	+	2.57080i	0.141518	+	0.141518i
$331$	5.23570	+	5.23570i	0.287780	+	0.287780i	0.836202	−	0.548422i	$-0.184771\pi$
$331$	5.23570	+	5.23570i	0.287780	+	0.287780i	−0.548422	+	0.836202i	$0.684771\pi$
$332$	−0.0227108	+	0.0847579i	−0.00124642	+	0.00465169i
$333$	−2.45563	−	9.16453i	−0.134568	−	0.502213i
$334$			22.4807i			1.23009i
$335$	9.15825	+	15.8626i	0.500369	+	0.866664i
$336$	4.31373	−	12.4810i	0.235333	−	0.680894i
$337$			27.7667i			1.51255i	0.654256	+	0.756273i	$0.272982\pi$
$337$			27.7667i			1.51255i	−0.654256	+	0.756273i	$0.727018\pi$
$338$	−19.2446	−	10.9899i	−1.04677	−	0.597774i
$339$	0.564301	+	0.325800i	0.0306486	+	0.0176950i
$340$	−4.65848	−	4.65848i	−0.252642	−	0.252642i
$341$	2.57046	+	1.48406i	0.139198	+	0.0803663i
$342$	−4.13437	+	7.16094i	−0.223561	+	0.387219i
$343$	−10.0328	−	15.5674i	−0.541720	−	0.840559i
$344$	15.1279	−	4.05350i	0.815640	−	0.218550i
$345$	−2.13772	+	2.13772i	−0.115091	+	0.115091i
$346$	−23.1070	+	6.19149i	−1.24224	+	0.332856i
$347$	5.41606	+	9.38090i	0.290750	+	0.503593i	0.973987	−	0.226603i	$-0.0727620\pi$
$347$	5.41606	+	9.38090i	0.290750	+	0.503593i	−0.683238	+	0.730196i	$0.739429\pi$
$348$	0.674422	−	1.16813i	0.0361528	−	0.0626185i
$349$	−0.622157	+	2.32192i	−0.0333033	+	0.124290i	−0.980576	−	0.196138i	$-0.937160\pi$
$349$	−0.622157	+	2.32192i	−0.0333033	+	0.124290i	0.947273	+	0.320428i	$0.103827\pi$
$350$	0.966677	−	13.5977i	0.0516710	−	0.726826i
$351$	−3.33435	−	1.37191i	−0.177974	−	0.0732272i
$352$	3.62386	+	6.27671i	0.193152	+	0.334550i
$353$	−8.52111	+	8.52111i	−0.453533	+	0.453533i	−0.896525	−	0.442992i	$-0.853917\pi$
$353$	−8.52111	+	8.52111i	−0.453533	+	0.453533i	0.442992	+	0.896525i	$0.353917\pi$
$354$	14.4315			0.767023
$355$	−3.94852			−0.209565
$356$	7.15062	−	7.15062i	0.378982	−	0.378982i
$357$	8.96241	+	10.3342i	0.474341	+	0.546945i
$358$	7.94011	+	29.6329i	0.419648	+	1.56615i
$359$	26.5837	+	7.12307i	1.40303	+	0.375941i	0.879433	−	0.476023i	$-0.157922\pi$
$359$	26.5837	+	7.12307i	1.40303	+	0.375941i	0.523599	+	0.851965i	$0.324589\pi$
$360$	2.27106	−	1.31120i	0.119695	−	0.0691061i
$361$		−	4.52705i		−	0.238266i
$362$	−24.4407	+	6.54888i	−1.28458	+	0.344201i
$363$	−8.70004			−0.456634
$364$	8.19373	−	2.75256i	0.429468	−	0.144273i
$365$	−20.8014			−1.08880
$366$	−5.32327	+	1.42637i	−0.278252	+	0.0745574i
$367$			14.1137i			0.736727i	0.929682	+	0.368363i	$0.120082\pi$
$367$			14.1137i			0.736727i	−0.929682	+	0.368363i	$0.879918\pi$
$368$	−9.29250	+	5.36503i	−0.484405	+	0.279671i
$369$	6.34762	+	1.70084i	0.330444	+	0.0885421i
$370$	5.88689	+	21.9702i	0.306045	+	1.14218i
$371$	9.38124	+	3.24239i	0.487050	+	0.168336i
$372$	−1.25397	+	1.25397i	−0.0650151	+	0.0650151i
$373$	29.9891			1.55277			0.776387	−	0.630256i	$-0.217050\pi$
$373$	29.9891			1.55277			0.776387	+	0.630256i	$0.217050\pi$
$374$	−13.3668			−0.691182
$375$	7.97733	−	7.97733i	0.411948	−	0.411948i
$376$	5.98778	+	10.3711i	0.308796	+	0.534851i
$377$	−5.31969	+	0.713140i	−0.273978	+	0.0367286i
$378$	4.05611	−	1.97248i	0.208624	−	0.101454i
$379$	−6.76234	+	25.2374i	−0.347358	+	1.29636i	0.542475	+	0.840072i	$0.317487\pi$
$379$	−6.76234	+	25.2374i	−0.347358	+	1.29636i	−0.889833	+	0.456286i	$0.849179\pi$
$380$	3.09030	−	5.35256i	0.158529	−	0.274581i
$381$	−0.944595	−	1.63609i	−0.0483931	−	0.0838192i
$382$	23.8198	−	6.38250i	1.21873	−	0.326557i
$383$	22.4844	−	22.4844i	1.14890	−	1.14890i	0.162128	−	0.986770i	$-0.448164\pi$
$383$	22.4844	−	22.4844i	1.14890	−	1.14890i	0.986770	−	0.162128i	$-0.0518358\pi$
$384$	12.2546	−	3.28362i	0.625366	−	0.167566i
$385$	3.69692	+	4.26279i	0.188413	+	0.217252i
$386$	15.4692	−	26.7934i	0.787360	−	1.36375i
$387$	7.27334	+	4.19927i	0.369725	+	0.213461i
$388$	8.40233	+	8.40233i	0.426563	+	0.426563i
$389$	−12.1261	−	7.00102i	−0.614818	−	0.354966i	0.160030	−	0.987112i	$-0.448841\pi$
$389$	−12.1261	−	7.00102i	−0.614818	−	0.354966i	−0.774849	+	0.632147i	$0.782174\pi$
$390$	7.99344	+	3.28889i	0.404764	+	0.166539i
$391$		−	11.1150i		−	0.562111i
$392$	5.12826	−	12.0040i	0.259016	−	0.606293i
$393$	5.13539	+	8.89476i	0.259046	+	0.448681i
$394$			40.7192i			2.05141i
$395$	2.67694	+	9.99049i	0.134692	+	0.502676i
$396$	−0.355661	+	1.32735i	−0.0178726	+	0.0667016i
$397$	12.5848	+	12.5848i	0.631615	+	0.631615i	0.948473	−	0.316858i	$-0.102628\pi$
$397$	12.5848	+	12.5848i	0.631615	+	0.631615i	−0.316858	+	0.948473i	$0.602628\pi$
$398$	3.59643	+	3.59643i	0.180273	+	0.180273i
$399$	−7.18852	+	10.6308i	−0.359876	+	0.532207i
$400$	13.0644	−	7.54272i	0.653218	−	0.377136i
$401$	0.505865	+	1.88791i	0.0252617	+	0.0942779i	0.977406	−	0.211372i	$-0.0677931\pi$
$401$	0.505865	+	1.88791i	0.0252617	+	0.0942779i	−0.952144	+	0.305650i	$0.901126\pi$
$402$	−11.1020	+	19.2292i	−0.553717	+	0.959066i
$403$	6.99834	+	0.904532i	0.348612	+	0.0450580i
$404$	13.4935	−	7.79050i	0.671329	−	0.387592i
$405$	1.35835	+	0.363968i	0.0674969	+	0.0180857i
$406$	3.76092	−	5.56188i	0.186651	−	0.276031i
$407$	12.4611	+	7.19444i	0.617675	+	0.356615i
$408$	−2.49539	+	9.31293i	−0.123540	+	0.461059i
$409$	−15.1082	−	4.04824i	−0.747055	−	0.200173i	−0.134844	−	0.990867i	$-0.543053\pi$
$409$	−15.1082	−	4.04824i	−0.747055	−	0.200173i	−0.612211	+	0.790694i	$0.709720\pi$
$410$	−15.2172	−	4.07743i	−0.751523	−	0.201370i
$411$	2.41280	−	9.00469i	0.119015	−	0.444169i
$412$	−0.276962	−	0.159904i	−0.0136449	−	0.00787791i
$413$	22.3413	+	1.58827i	1.09934	+	0.0781538i
$414$	−3.53996	−	0.948528i	−0.173979	−	0.0466176i
$415$	−0.117938	+	0.0680917i	−0.00578936	+	0.00334249i
$416$	13.6951	+	10.4573i	0.671457	+	0.512711i
$417$	0.0818824	−	0.141825i	0.00400980	−	0.00694518i
$418$	−3.24561	−	12.1128i	−0.158748	−	0.592455i
$419$	32.1543	−	18.5643i	1.57084	−	0.906924i	0.574772	−	0.818314i	$-0.305091\pi$
$419$	32.1543	−	18.5643i	1.57084	−	0.906924i	0.996066	−	0.0886099i	$-0.0282425\pi$
$420$	−3.03181	+	1.47436i	−0.147937	+	0.0719416i
$421$	−23.1846	−	23.1846i	−1.12995	−	1.12995i	−0.990185	−	0.139764i	$-0.955366\pi$
$421$	−23.1846	−	23.1846i	−1.12995	−	1.12995i	−0.139764	−	0.990185i	$-0.544634\pi$
$422$	−4.95619	−	4.95619i	−0.241263	−	0.241263i
$423$	−1.66212	+	6.20311i	−0.0808150	+	0.301606i
$424$	1.81068	+	6.75755i	0.0879344	+	0.328176i
$425$			15.6267i			0.758005i
$426$	−2.39327	−	4.14527i	−0.115954	−	0.200839i
$427$	−8.39793	+	1.62230i	−0.406404	+	0.0785084i
$428$			12.1503i			0.587307i
$429$	5.04686	−	2.10446i	0.243665	−	0.101604i
$430$	−17.4364	−	10.0669i	−0.840859	−	0.485470i
$431$	11.7127	+	11.7127i	0.564182	+	0.564182i	0.930493	−	0.366310i	$-0.119379\pi$
$431$	11.7127	+	11.7127i	0.564182	+	0.564182i	−0.366310	+	0.930493i	$0.619379\pi$
$432$	4.32249	+	2.49559i	0.207966	+	0.120069i
$433$	−0.814551	+	1.41084i	−0.0391448	+	0.0678008i	−0.884934	−	0.465716i	$-0.845797\pi$
$433$	−0.814551	+	1.41084i	−0.0391448	+	0.0678008i	0.845789	+	0.533517i	$0.179130\pi$
$434$	−6.66872	+	5.78347i	−0.320109	+	0.277616i
$435$	2.02206	−	0.541809i	0.0969502	−	0.0259777i
$436$	−6.30388	+	6.30388i	−0.301901	+	0.301901i
$437$	10.0722	−	2.69885i	0.481820	−	0.129103i
$438$	−12.6082	−	21.8380i	−0.602441	−	1.04346i
$439$	13.9901	−	24.2316i	0.667713	−	1.15651i	−0.310829	−	0.950466i	$-0.600607\pi$
$439$	13.9901	−	24.2316i	0.667713	−	1.15651i	0.978542	−	0.206047i	$-0.0660600\pi$
$440$	−1.02933	+	3.84151i	−0.0490714	+	0.183137i
$441$	6.49635	−	2.60720i	0.309350	−	0.124152i
$442$	−29.3311	+	12.2306i	−1.39514	+	0.581751i
$443$	12.7182	+	22.0285i	0.604258	+	1.04661i	0.992168	+	0.124908i	$0.0398637\pi$
$443$	12.7182	+	22.0285i	0.604258	+	1.04661i	−0.387910	+	0.921697i	$0.626803\pi$
$444$	−6.07899	+	6.07899i	−0.288496	+	0.288496i
$445$	15.6945			0.743988
$446$	29.9113			1.41634
$447$	14.7328	−	14.7328i	0.696837	−	0.696837i
$448$	4.76783	−	0.921040i	0.225259	−	0.0435151i
$449$	−0.665392	−	2.48328i	−0.0314018	−	0.117193i	0.948446	−	0.316939i	$-0.102655\pi$
$449$	−0.665392	−	2.48328i	−0.0314018	−	0.117193i	−0.979848	+	0.199746i	$0.935988\pi$
$450$	4.97684	+	1.33354i	0.234611	+	0.0628637i
$451$	−8.63094	+	4.98307i	−0.406415	+	0.234644i
$452$		−	0.590419i		−	0.0277710i
$453$	3.50140	−	0.938197i	0.164510	−	0.0440803i
$454$	−11.8290			−0.555162
$455$	12.0127	+	5.97125i	0.563163	+	0.279937i
$456$	−9.04512			−0.423576
$457$	13.6941	−	3.66933i	0.640584	−	0.171644i	0.0761160	−	0.997099i	$-0.475748\pi$
$457$	13.6941	−	3.66933i	0.640584	−	0.171644i	0.564468	+	0.825455i	$0.309081\pi$
$458$		−	15.2751i		−	0.713759i
$459$	−4.47758	+	2.58513i	−0.208995	+	0.120664i
$460$	2.64600	+	0.708993i	0.123370	+	0.0330570i
$461$	−10.8132	−	40.3552i	−0.503619	−	1.87953i	−0.475089	−	0.879938i	$-0.657584\pi$
$461$	−10.8132	−	40.3552i	−0.503619	−	1.87953i	−0.0285297	−	0.999593i	$-0.509083\pi$
$462$	−2.23443	+	6.46490i	−0.103955	+	0.300774i
$463$	19.6177	−	19.6177i	0.911713	−	0.911713i	−0.0846939	−	0.996407i	$-0.526991\pi$
$463$	19.6177	−	19.6177i	0.911713	−	0.911713i	0.996407	+	0.0846939i	$0.0269912\pi$
$464$	7.42995			0.344927
$465$	−2.75225			−0.127633
$466$	−7.67850	+	7.67850i	−0.355700	+	0.355700i
$467$	14.6509	+	25.3761i	0.677962	+	1.17426i	0.975594	+	0.219584i	$0.0704700\pi$
$467$	14.6509	+	25.3761i	0.677962	+	1.17426i	−0.297632	+	0.954681i	$0.596197\pi$
$468$	0.434083	+	3.23805i	0.0200655	+	0.149679i
$469$	−19.3033	+	28.5469i	−0.891342	+	1.31817i
$470$	3.98461	−	14.8707i	0.183796	−	0.685937i
$471$	−7.42842	+	12.8664i	−0.342283	+	0.592852i
$472$	7.89323	+	13.6715i	0.363315	+	0.629280i
$473$	−12.3029	+	3.29655i	−0.565688	+	0.151576i
$474$	−8.86577	+	8.86577i	−0.407218	+	0.407218i
$475$	−14.1606	+	3.79432i	−0.649733	+	0.174095i
$476$	4.04894	−	11.7149i	0.185583	−	0.536950i
$477$	−1.87579	+	3.24897i	−0.0858867	+	0.148760i
$478$	−23.9950	−	13.8535i	−1.09751	−	0.633645i
$479$	−6.32550	−	6.32550i	−0.289019	−	0.289019i	0.547673	−	0.836692i	$-0.315514\pi$
$479$	−6.32550	−	6.32550i	−0.289019	−	0.289019i	−0.836692	+	0.547673i	$0.815514\pi$
$480$	−5.82021	−	3.36030i	−0.265655	−	0.153376i
$481$	33.9266	+	4.38500i	1.54692	+	0.199939i
$482$		−	0.396098i		−	0.0180418i
$483$	−5.37581	−	1.85801i	−0.244608	−	0.0845424i
$484$	3.94159	+	6.82703i	0.179163	+	0.310319i
$485$			18.4418i			0.837397i
$486$	0.441217	+	1.64664i	0.0200140	+	0.0746933i
$487$	5.30969	−	19.8160i	0.240605	−	0.897951i	−0.734936	−	0.678136i	$-0.762788\pi$
$487$	5.30969	−	19.8160i	0.240605	−	0.897951i	0.975542	−	0.219815i	$-0.0705453\pi$
$488$	−4.26280	−	4.26280i	−0.192968	−	0.192968i
$489$	11.3635	+	11.3635i	0.513873	+	0.513873i
$490$	−15.5737	+	6.25025i	−0.703549	+	0.282357i
$491$	−27.6274	+	15.9507i	−1.24681	+	0.719845i	−0.970472	−	0.241216i	$-0.922454\pi$
$491$	−27.6274	+	15.9507i	−1.24681	+	0.719845i	−0.276337	+	0.961061i	$0.589121\pi$
$492$	−1.54114	−	5.75162i	−0.0694801	−	0.259303i
$493$	−3.84826	+	6.66538i	−0.173317	+	0.300194i
$494$	−18.2051	−	23.6096i	−0.819085	−	1.06225i
$495$	−1.84696	+	1.06635i	−0.0830149	+	0.0479287i
$496$	−9.43557	−	2.52825i	−0.423669	−	0.113522i
$497$	−3.24881	−	6.68068i	−0.145729	−	0.299670i
$498$	−0.142969	−	0.0825434i	−0.00640661	−	0.00369886i
$499$	5.93111	−	22.1352i	0.265513	−	0.990907i	−0.696423	−	0.717632i	$-0.745226\pi$
$499$	5.93111	−	22.1352i	0.265513	−	0.990907i	0.961936	−	0.273276i	$-0.0881071\pi$
$500$	−9.87407	−	2.64575i	−0.441582	−	0.118322i
$501$	−12.7379	−	3.41310i	−0.569086	−	0.152486i
$502$	−3.87606	+	14.4657i	−0.172997	+	0.645634i
$503$	23.9880	+	13.8495i	1.06957	+	0.617518i	0.928065	−	0.372419i	$-0.121472\pi$
$503$	23.9880	+	13.8495i	1.06957	+	0.617518i	0.141508	+	0.989937i	$0.454805\pi$
$504$	4.08709	+	2.76367i	0.182053	+	0.123104i
$505$	23.3575	+	6.25863i	1.03940	+	0.278505i
$506$	4.81332	−	2.77897i	0.213978	−	0.123540i
$507$	9.14885	−	9.23572i	0.406315	−	0.410173i
$508$	−0.855905	+	1.48247i	−0.0379746	+	0.0657740i
$509$	−11.1553	−	41.6323i	−0.494452	−	1.84532i	−0.533080	−	0.846065i	$-0.678966\pi$
$509$	−11.1553	−	41.6323i	−0.494452	−	1.84532i	0.0386284	−	0.999254i	$-0.487701\pi$
$510$	10.7341	−	6.19734i	0.475315	−	0.274423i
$511$	−17.1153	−	35.1949i	−0.757134	−	1.55693i
$512$	−3.70385	−	3.70385i	−0.163689	−	0.163689i
$513$	−3.42980	−	3.42980i	−0.151429	−	0.151429i
$514$	10.0265	−	37.4194i	0.442250	−	1.65050i
$515$	−0.128462	−	0.479425i	−0.00566070	−	0.0211260i
$516$		−	7.60997i		−	0.335010i
$517$	−4.86963	−	8.43445i	−0.214166	−	0.370947i
$518$	−32.3287	+	28.0372i	−1.42044	+	1.23188i
$519$		−	14.0328i		−	0.615970i
$520$	1.25629	+	9.37134i	0.0550921	+	0.410961i
$521$	1.66737	+	0.962655i	0.0730487	+	0.0421747i	0.536079	−	0.844168i	$-0.319905\pi$
$521$	1.66737	+	0.962655i	0.0730487	+	0.0421747i	−0.463031	+	0.886342i	$0.653238\pi$
$522$	1.79442	+	1.79442i	0.0785394	+	0.0785394i
$523$	−1.10282	−	0.636711i	−0.0482228	−	0.0278414i	0.475695	−	0.879610i	$-0.342197\pi$
$523$	−1.10282	−	0.636711i	−0.0482228	−	0.0278414i	−0.523918	+	0.851769i	$0.675530\pi$
$524$	4.65322	−	8.05961i	0.203277	−	0.352086i
$525$	7.55787	+	2.61219i	0.329853	+	0.114005i
$526$	−13.4949	+	3.61596i	−0.588408	+	0.157663i
$527$	7.15514	−	7.15514i	0.311683	−	0.311683i
$528$	−7.31152	+	1.95912i	−0.318193	+	0.0852596i
$529$	−9.18918	−	15.9161i	−0.399530	−	0.692005i
$530$	4.49685	−	7.78877i	0.195331	−	0.338323i
$531$	−2.19104	+	8.17707i	−0.0950831	+	0.354855i
$532$	11.5989	+	0.824584i	0.502877	+	0.0357502i
$533$	−14.3795	+	18.8317i	−0.622847	+	0.815694i
$534$	9.51272	+	16.4765i	0.411655	+	0.713008i
$535$	−13.3340	+	13.3340i	−0.576478	+	0.576478i
$536$	−24.2888			−1.04911
$537$	−17.9959			−0.776582
$538$	−29.5353	+	29.5353i	−1.27336	+	1.27336i
$539$	−4.17061	+	9.76238i	−0.179641	+	0.420496i
$540$	−0.329795	−	1.23081i	−0.0141921	−	0.0529656i
$541$	22.6301	+	6.06372i	0.972944	+	0.260700i	0.710070	−	0.704131i	$-0.248663\pi$
$541$	22.6301	+	6.06372i	0.972944	+	0.260700i	0.262874	+	0.964830i	$0.415330\pi$
$542$	−12.2591	+	7.07781i	−0.526574	+	0.304018i
$543$		−	14.8428i		−	0.636964i
$544$	23.8669	−	6.39513i	1.02329	−	0.274189i
$545$	−13.8360			−0.592669
$546$	1.01232	+	16.2306i	0.0433232	+	0.694604i
$547$	39.4093			1.68502			0.842510	−	0.538680i	$-0.181077\pi$
$547$	39.4093			1.68502			0.842510	+	0.538680i	$0.181077\pi$
$548$	−8.15922	+	2.18626i	−0.348545	+	0.0933923i
$549$		−	3.23280i		−	0.137973i
$550$	−6.76708	+	3.90697i	−0.288549	+	0.166594i
$551$	−6.97444	−	1.86880i	−0.297121	−	0.0796134i
$552$	−1.03759	−	3.87233i	−0.0441627	−	0.164817i
$553$	−14.7008	+	12.7493i	−0.625142	+	0.542157i
$554$	−1.80732	+	1.80732i	−0.0767855	+	0.0767855i
$555$	−13.3424			−0.566353
$556$	−0.148389			−0.00629308
$557$	10.6318	−	10.6318i	0.450485	−	0.450485i	−0.445030	−	0.895515i	$-0.646807\pi$
$557$	10.6318	−	10.6318i	0.450485	−	0.450485i	0.895515	+	0.445030i	$0.146807\pi$
$558$	−1.66819	−	2.88940i	−0.0706203	−	0.122318i
$559$	−23.9802	+	18.4908i	−1.01425	+	0.782078i
$560$	−15.3835	−	10.4022i	−0.650070	−	0.439575i
$561$	2.02941	−	7.57385i	0.0856816	−	0.319768i
$562$	23.5083	−	40.7175i	0.991636	−	1.71756i
$563$	−8.62595	−	14.9406i	−0.363541	−	0.629671i	0.625000	−	0.780625i	$-0.285099\pi$
$563$	−8.62595	−	14.9406i	−0.363541	−	0.629671i	−0.988541	+	0.150954i	$0.951766\pi$
$564$	5.62069	−	1.50606i	0.236674	−	0.0634165i
$565$	0.647937	−	0.647937i	0.0272589	−	0.0272589i
$566$	−25.7909	+	6.91066i	−1.08407	+	0.290477i
$567$	0.501823	+	2.59772i	0.0210746	+	0.109094i
$568$	2.61798	−	4.53448i	0.109848	−	0.190263i
$569$	9.15313	+	5.28456i	0.383719	+	0.221540i	0.679435	−	0.733735i	$-0.262225\pi$
$569$	9.15313	+	5.28456i	0.383719	+	0.221540i	−0.295716	+	0.955276i	$0.595558\pi$
$570$	8.22228	+	8.22228i	0.344393	+	0.344393i
$571$	4.73797	+	2.73547i	0.198278	+	0.114476i	0.595852	−	0.803094i	$-0.296815\pi$
$571$	4.73797	+	2.73547i	0.198278	+	0.114476i	−0.397574	+	0.917570i	$0.630148\pi$
$572$	−3.93789	−	3.00690i	−0.164652	−	0.125725i
$573$			14.4657i			0.604312i
$574$	−5.62178	−	29.1015i	−0.234648	−	1.21467i
$575$	−3.24880	−	5.62708i	−0.135484	−	0.234665i
$576$			1.83539i			0.0764745i
$577$	−5.17915	−	19.3289i	−0.215611	−	0.804671i	−0.985951	−	0.167037i	$-0.946580\pi$
$577$	−5.17915	−	19.3289i	−0.215611	−	0.804671i	0.770340	−	0.637634i	$-0.220087\pi$
$578$	−4.29374	+	16.0244i	−0.178596	+	0.666529i
$579$	12.8329	+	12.8329i	0.533319	+	0.533319i
$580$	−1.34126	−	1.34126i	−0.0556930	−	0.0556930i
$581$	−0.212246	−	0.143520i	−0.00880546	−	0.00595421i
$582$	−19.3607	+	11.1779i	−0.802527	+	0.463339i
$583$	−1.47256	−	5.49565i	−0.0609870	−	0.227607i
$584$	13.7920	−	23.8884i	0.570716	−	0.988508i
$585$	−3.07713	+	4.02987i	−0.127224	+	0.166615i
$586$	−20.8803	+	12.0553i	−0.862559	+	0.497999i
$587$	1.59431	+	0.427193i	0.0658041	+	0.0176321i	0.291571	−	0.956549i	$-0.405822\pi$
$587$	1.59431	+	0.427193i	0.0658041	+	0.0176321i	−0.225767	+	0.974181i	$0.572489\pi$
$588$	−4.98909	−	3.91656i	−0.205747	−	0.161516i
$589$	8.22120	+	4.74651i	0.338748	+	0.195577i
$590$	5.25259	−	19.6029i	0.216246	−	0.807040i
$591$	−23.0721	−	6.18216i	−0.949060	−	0.254300i
$592$	−45.7419	−	12.2565i	−1.87998	−	0.503739i
$593$	−9.34258	+	34.8670i	−0.383654	+	1.43182i	0.456624	+	0.889660i	$0.349059\pi$
$593$	−9.34258	+	34.8670i	−0.383654	+	1.43182i	−0.840278	+	0.542156i	$0.817608\pi$
$594$	−2.23896	−	1.29267i	−0.0918658	−	0.0530387i
$595$	17.2995	−	8.41274i	0.709211	−	0.344889i
$596$	−18.2357	−	4.88625i	−0.746965	−	0.200149i
$597$	−2.58382	+	1.49177i	−0.105749	+	0.0610539i
$598$	8.01922	−	10.5021i	0.327930	−	0.429464i
$599$	−5.29544	+	9.17197i	−0.216366	+	0.374757i	−0.953694	−	0.300778i	$-0.902754\pi$
$599$	−5.29544	+	9.17197i	−0.216366	+	0.374757i	0.737328	+	0.675534i	$0.236087\pi$
$600$	1.45875	+	5.44413i	0.0595532	+	0.222256i
$601$	24.1270	−	13.9297i	0.984160	−	0.568205i	0.0806362	−	0.996744i	$-0.474305\pi$
$601$	24.1270	−	13.9297i	0.984160	−	0.568205i	0.903523	+	0.428539i	$0.140971\pi$
$602$	2.68615	−	37.7845i	0.109479	−	1.53998i
$603$	−9.21001	−	9.21001i	−0.375061	−	0.375061i
$604$	−2.32254	−	2.32254i	−0.0945026	−	0.0945026i
$605$	−3.16654	+	11.8177i	−0.128738	+	0.480457i
$606$	7.58695	+	28.3149i	0.308199	+	1.15021i
$607$		−	22.2828i		−	0.904433i	−0.891908	−	0.452216i	$-0.850633\pi$
$607$		−	22.2828i		−	0.904433i	0.891908	−	0.452216i	$-0.149367\pi$
$608$	11.5903	+	20.0750i	0.470049	+	0.814148i
$609$	2.58044	+	2.97542i	0.104565	+	0.120570i
$610$			7.75001i			0.313789i
$611$	−18.4030	−	14.0522i	−0.744507	−	0.568491i
$612$	4.05717	+	2.34241i	0.164001	+	0.0946861i
$613$	27.3051	+	27.3051i	1.10284	+	1.10284i	0.994066	+	0.108776i	$0.0346930\pi$
$613$	27.3051	+	27.3051i	1.10284	+	1.10284i	0.108776	+	0.994066i	$0.465307\pi$
$614$	−2.04054	−	1.17811i	−0.0823495	−	0.0475445i
$615$	4.62066	−	8.00323i	0.186323	−	0.322721i
$616$	−7.34656	+	1.41919i	−0.296001	+	0.0571809i
$617$	19.0276	−	5.09843i	0.766022	−	0.205255i	0.145409	−	0.989372i	$-0.453550\pi$
$617$	19.0276	−	5.09843i	0.766022	−	0.205255i	0.620613	+	0.784117i	$0.286884\pi$
$618$	0.425452	−	0.425452i	0.0171142	−	0.0171142i
$619$	−34.1751	+	9.15720i	−1.37361	+	0.368059i	−0.868798	−	0.495167i	$-0.835107\pi$
$619$	−34.1751	+	9.15720i	−1.37361	+	0.368059i	−0.504817	+	0.863226i	$0.668440\pi$
$620$	1.24692	+	2.15973i	0.0500774	+	0.0867367i
$621$	1.07490	−	1.86178i	0.0431343	−	0.0747107i
$622$	3.71207	−	13.8536i	0.148840	−	0.555480i
$623$	12.9133	+	26.5542i	0.517359	+	1.06387i
$624$	−14.2512	+	10.9890i	−0.570506	+	0.439910i
$625$	−0.376462	−	0.652052i	−0.0150585	−	0.0260821i
$626$	−20.0580	+	20.0580i	−0.801679	+	0.801679i
$627$	7.35604			0.293772
$628$	13.4619			0.537188
$629$	34.6868	−	34.6868i	1.38305	−	1.38305i
$630$	−1.20302	−	6.22754i	−0.0479296	−	0.248111i
$631$	1.11023	+	4.14343i	0.0441976	+	0.164948i	0.984497	−	0.175400i	$-0.0561219\pi$
$631$	1.11023	+	4.14343i	0.0441976	+	0.164948i	−0.940300	+	0.340348i	$0.889455\pi$
$632$	−13.2480	−	3.54979i	−0.526976	−	0.141203i
$633$	3.56072	−	2.05578i	0.141526	−	0.0817099i
$634$		−	14.2288i		−	0.565097i
$635$	−2.56618	+	0.687605i	−0.101836	+	0.0272868i
$636$	3.39934			0.134793
$637$	−0.219111	+	25.2379i	−0.00868150	+	0.999962i
$638$	−3.84856			−0.152366
$639$	2.71213	−	0.726713i	0.107290	−	0.0287483i
$640$		−	17.8412i		−	0.705235i
$641$	30.5821	−	17.6566i	1.20792	−	0.697393i	0.245616	−	0.969367i	$-0.421010\pi$
$641$	30.5821	−	17.6566i	1.20792	−	0.697393i	0.962305	+	0.271974i	$0.0876765\pi$
$642$	−22.0804	−	5.91642i	−0.871443	−	0.233503i
$643$	2.90713	+	10.8495i	0.114646	+	0.427864i	0.999260	−	0.0384591i	$-0.0122449\pi$
$643$	2.90713	+	10.8495i	0.114646	+	0.427864i	−0.884614	+	0.466323i	$0.845578\pi$
$644$	0.977527	+	5.06024i	0.0385200	+	0.199401i
$645$	8.35133	−	8.35133i	0.328833	−	0.328833i
$646$	−42.7515			−1.68204
$647$	13.5671			0.533377			0.266689	−	0.963783i	$-0.414070\pi$
$647$	13.5671			0.533377			0.266689	+	0.963783i	$0.414070\pi$
$648$	−1.31861	+	1.31861i	−0.0517998	+	0.0517998i
$649$	−6.41925	−	11.1185i	−0.251978	−	0.436438i
$650$	−11.2743	+	14.7650i	−0.442213	+	0.579131i
$651$	−2.26453	−	4.65666i	−0.0887540	−	0.182509i
$652$	3.76878	−	14.0653i	0.147597	−	0.550839i
$653$	7.32759	−	12.6918i	0.286751	−	0.496667i	−0.686282	−	0.727336i	$-0.740758\pi$
$653$	7.32759	−	12.6918i	0.286751	−	0.496667i	0.973032	+	0.230669i	$0.0740916\pi$
$654$	−8.38628	−	14.5255i	−0.327929	−	0.567990i
$655$	13.9513	−	3.73824i	0.545123	−	0.146065i
$656$	23.1929	−	23.1929i	0.905532	−	0.905532i
$657$	14.2879	−	3.82844i	0.557426	−	0.149362i
$658$	28.4390	−	5.49379i	1.10867	−	0.214170i
$659$	−25.1178	+	43.5054i	−0.978452	+	1.69473i	−0.310415	+	0.950601i	$0.600468\pi$
$659$	−25.1178	+	43.5054i	−0.978452	+	1.69473i	−0.668037	+	0.744128i	$0.732865\pi$
$660$	1.67355	+	0.966224i	0.0651428	+	0.0376102i
$661$	−0.915779	−	0.915779i	−0.0356197	−	0.0356197i	0.689073	−	0.724692i	$-0.258018\pi$
$661$	−0.915779	−	0.915779i	−0.0356197	−	0.0356197i	−0.724692	+	0.689073i	$0.758018\pi$
$662$	10.9314	+	6.31125i	0.424861	+	0.245294i
$663$	−2.47688	−	18.4764i	−0.0961941	−	0.717562i
$664$		−	0.180587i		−	0.00700814i
$665$	11.8240	+	13.6338i	0.458514	+	0.528696i
$666$	−8.08709	−	14.0072i	−0.313368	−	0.542770i
$667$		−	3.20022i		−	0.123913i
$668$	3.09264	+	11.5419i	0.119658	+	0.446569i
$669$	−4.54125	+	16.9482i	−0.175575	+	0.655254i
$670$	22.0792	+	22.0792i	0.852994	+	0.852994i
$671$	3.46677	+	3.46677i	0.133833	+	0.133833i
$672$	0.896627	−	12.6123i	0.0345882	−	0.486531i
$673$	19.6264	−	11.3313i	0.756543	−	0.436790i	−0.0715103	−	0.997440i	$-0.522782\pi$
$673$	19.6264	−	11.3313i	0.756543	−	0.436790i	0.828053	+	0.560650i	$0.189449\pi$
$674$	12.2511	+	45.7218i	0.471895	+	1.76114i
$675$	−1.51121	+	2.61749i	−0.0581664	+	0.100747i
$676$	−11.3923	−	2.99494i	−0.438166	−	0.115190i
$677$	−23.6738	+	13.6681i	−0.909859	+	0.525307i	−0.880386	−	0.474258i	$-0.842716\pi$
$677$	−23.6738	+	13.6681i	−0.909859	+	0.525307i	−0.0294729	+	0.999566i	$0.509383\pi$
$678$	1.07295	+	0.287496i	0.0412065	+	0.0110412i
$679$	−31.2025	+	15.1737i	−1.19744	+	0.582314i
$680$	11.7420	+	6.77923i	0.450284	+	0.259972i
$681$	1.79592	−	6.70248i	0.0688199	−	0.256839i
$682$	4.88743	+	1.30958i	0.187149	+	0.0501465i
$683$	−27.4517	−	7.35567i	−1.05041	−	0.281457i	−0.307989	−	0.951390i	$-0.599656\pi$
$683$	−27.4517	−	7.35567i	−1.05041	−	0.281457i	−0.742422	+	0.669933i	$0.766323\pi$
$684$	−1.13752	+	4.24529i	−0.0434942	+	0.162323i
$685$	−11.3533	−	6.55485i	−0.433788	−	0.250448i
$686$	−23.3890	−	21.2073i	−0.892997	−	0.809697i
$687$	8.65510	+	2.31913i	0.330213	+	0.0884802i
$688$	36.3026	−	20.9593i	1.38402	−	0.799066i
$689$	−8.25977	−	10.7118i	−0.314672	−	0.408089i
$690$	−2.57686	+	4.46326i	−0.0980995	+	0.169913i
$691$	−2.58784	−	9.65796i	−0.0984462	−	0.367406i	0.899073	−	0.437798i	$-0.144242\pi$
$691$	−2.58784	−	9.65796i	−0.0984462	−	0.367406i	−0.997519	+	0.0703922i	$0.977575\pi$
$692$	−11.0117	+	6.35759i	−0.418601	+	0.241679i
$693$	−3.32387	−	2.24759i	−0.126263	−	0.0853787i
$694$	13.0573	+	13.0573i	0.495650	+	0.495650i
$695$	−0.162845	−	0.162845i	−0.00617705	−	0.00617705i
$696$	−0.718470	+	2.68137i	−0.0272335	+	0.101637i
$697$	8.79378	+	32.8188i	0.333088	+	1.24310i
$698$			4.09789i			0.155107i
$699$	−3.18497	−	5.51653i	−0.120467	−	0.208654i
$700$	−1.37431	−	7.11422i	−0.0519440	−	0.268892i
$701$		−	36.1836i		−	1.36664i	−0.730121	−	0.683318i	$-0.760536\pi$
$701$		−	36.1836i		−	1.36664i	0.730121	−	0.683318i	$-0.239464\pi$
$702$	−6.09579	−	0.787879i	−0.230071	−	0.0297366i
$703$	39.8548	+	23.0102i	1.50315	+	0.867846i
$704$	−1.96822	−	1.96822i	−0.0741800	−	0.0741800i
$705$	7.82103	+	4.51547i	0.294557	+	0.170063i
$706$	−10.2716	+	17.7909i	−0.386576	+	0.669569i
$707$	8.62911	+	44.6692i	0.324531	+	1.67996i
$708$	7.40931	−	1.98532i	0.278459	−	0.0746128i
$709$	22.6021	−	22.6021i	0.848839	−	0.848839i	−0.141150	−	0.989988i	$-0.545080\pi$
$709$	22.6021	−	22.6021i	0.848839	−	0.848839i	0.989988	+	0.141150i	$0.0450799\pi$
$710$	−6.50180	+	1.74215i	−0.244008	+	0.0653818i
$711$	−3.67744	−	6.36951i	−0.137915	−	0.238875i
$712$	−10.4059	+	18.0235i	−0.389977	+	0.675460i
$713$	−1.08897	+	4.06408i	−0.0407822	+	0.152201i
$714$	19.3175	+	13.0624i	0.722940	+	0.488849i
$715$	−1.02169	−	7.62135i	−0.0382092	−	0.285022i
$716$	8.15313	+	14.1216i	0.304697	+	0.527750i
$717$	11.4926	−	11.4926i	0.429200	−	0.429200i
$718$	46.9166			1.75091
$719$	−21.0337			−0.784423			−0.392212	−	0.919875i	$-0.628290\pi$
$719$	−21.0337			−0.784423			−0.392212	+	0.919875i	$0.628290\pi$
$720$	4.96314	−	4.96314i	0.184965	−	0.184965i
$721$	0.705465	−	0.611818i	0.0262729	−	0.0227853i
$722$	−1.99741	−	7.45444i	−0.0743359	−	0.277425i
$723$	0.224435	+	0.0601372i	0.00834683	+	0.00223653i
$724$	−11.6473	+	6.72457i	−0.432868	+	0.249917i
$725$			4.49921i			0.167096i
$726$	−14.3259	+	3.83860i	−0.531683	+	0.142464i
$727$	31.1689			1.15599			0.577995	−	0.816040i	$-0.303835\pi$
$727$	31.1689			1.15599			0.577995	+	0.816040i	$0.303835\pi$
$728$	−14.8222	+	9.83625i	−0.549345	+	0.364556i
$729$	−1.00000			−0.0370370
$730$	−34.2525	+	9.17794i	−1.26774	+	0.339691i
$731$			43.4226i			1.60604i
$732$	−2.53682	+	1.46463i	−0.0937636	+	0.0541344i
$733$	5.23797	+	1.40351i	0.193469	+	0.0518398i	0.354252	−	0.935150i	$-0.384735\pi$
$733$	5.23797	+	1.40351i	0.193469	+	0.0518398i	−0.160783	+	0.986990i	$0.551402\pi$
$734$	6.22718	+	23.2402i	0.229849	+	0.857810i
$735$	−1.17702	−	9.77324i	−0.0434150	−	0.360491i
$736$	−7.26481	+	7.26481i	−0.267784	+	0.267784i
$737$	19.7531			0.727615
$738$	11.2027			0.412377
$739$	21.6748	−	21.6748i	0.797319	−	0.797319i	−0.185353	−	0.982672i	$-0.559343\pi$
$739$	21.6748	−	21.6748i	0.797319	−	0.797319i	0.982672	+	0.185353i	$0.0593428\pi$
$740$	6.04482	+	10.4699i	0.222212	+	0.384883i
$741$	16.1415	−	6.73076i	0.592973	−	0.247261i
$742$	16.8782	+	1.19989i	0.619617	+	0.0440494i
$743$	−1.70775	+	6.37341i	−0.0626512	+	0.233818i	−0.990150	−	0.140008i	$-0.955287\pi$
$743$	−1.70775	+	6.37341i	−0.0626512	+	0.233818i	0.927499	+	0.373825i	$0.121954\pi$
$744$	1.82482	−	3.16069i	0.0669013	−	0.115876i
$745$	−14.6500	−	25.3745i	−0.536734	−	0.929651i
$746$	49.3813	−	13.2317i	1.80798	−	0.484446i
$747$	0.0684765	−	0.0684765i	0.00250542	−	0.00250542i
$748$	−6.86272	+	1.83886i	−0.250926	+	0.0672354i
$749$	−33.5315	−	11.5893i	−1.22521	−	0.423463i
$750$	9.61609	−	16.6556i	0.351130	−	0.608175i
$751$	−7.33052	−	4.23228i	−0.267494	−	0.154438i	0.360254	−	0.932854i	$-0.382690\pi$
$751$	−7.33052	−	4.23228i	−0.267494	−	0.154438i	−0.627748	+	0.778416i	$0.716023\pi$
$752$	22.6649	+	22.6649i	0.826505	+	0.826505i
$753$	−7.60798	−	4.39247i	−0.277250	−	0.160070i
$754$	−8.44498	+	3.52142i	−0.307548	+	0.128243i
$755$		−	5.09759i		−	0.185520i
$756$	1.81111	−	1.57070i	0.0658696	−	0.0571257i
$757$	13.5330	+	23.4399i	0.491866	+	0.851937i	0.999956	−	0.00936661i	$-0.00298153\pi$
$757$	13.5330	+	23.4399i	0.491866	+	0.851937i	−0.508090	+	0.861304i	$0.669648\pi$
$758$			44.5407i			1.61779i
$759$	0.843830	+	3.14922i	0.0306291	+	0.114309i
$760$	−3.29214	+	12.2864i	−0.119418	+	0.445675i
$761$	12.8334	+	12.8334i	0.465211	+	0.465211i	0.900359	−	0.435148i	$-0.143304\pi$
$761$	12.8334	+	12.8334i	0.465211	+	0.465211i	−0.435148	+	0.900359i	$0.643304\pi$
$762$	−2.27728	−	2.27728i	−0.0824971	−	0.0824971i
$763$	−11.3842	−	23.4098i	−0.412134	−	0.847491i
$764$	11.3514	−	6.55373i	0.410679	−	0.237105i
$765$	1.88181	+	7.02301i	0.0680370	+	0.253918i
$766$	27.1033	−	46.9442i	0.979281	−	1.69616i
$767$	−24.2593	−	18.5239i	−0.875952	−	0.668859i
$768$	15.5512	−	8.97851i	0.561157	−	0.323984i
$769$	−39.4162	−	10.5616i	−1.42139	−	0.380859i	−0.535411	−	0.844592i	$-0.679843\pi$
$769$	−39.4162	−	10.5616i	−1.42139	−	0.380859i	−0.885975	+	0.463732i	$0.846510\pi$
$770$	7.96833	+	5.38815i	0.287159	+	0.194175i
$771$	19.6801	+	11.3623i	0.708763	+	0.409204i
$772$	4.25616	−	15.8842i	0.153182	−	0.571684i
$773$	−10.7620	−	2.88368i	−0.387084	−	0.103719i	0.0600285	−	0.998197i	$-0.480881\pi$
$773$	−10.7620	−	2.88368i	−0.387084	−	0.103719i	−0.447112	+	0.894478i	$0.647548\pi$
$774$	13.8294	+	3.70557i	0.497087	+	0.133194i
$775$	1.53099	−	5.71372i	0.0549946	−	0.205243i
$776$	−21.1785	−	12.2274i	−0.760265	−	0.438939i
$777$	−10.9780	−	22.5746i	−0.393834	−	0.809860i
$778$	−23.0564	−	6.17793i	−0.826610	−	0.221490i
$779$	−27.6046	+	15.9375i	−0.989037	+	0.571021i
$780$	4.55640	+	0.588913i	0.163145	+	0.0210865i
$781$	−2.12910	+	3.68772i	−0.0761853	+	0.131957i
$782$	−4.90414	−	18.3025i	−0.175372	−	0.654496i
$783$	−1.28918	+	0.744307i	−0.0460714	+	0.0265994i
$784$	4.94264	−	34.5869i	0.176523	−	1.23525i
$785$	14.7733	+	14.7733i	0.527283	+	0.527283i
$786$	12.3807	+	12.3807i	0.441604	+	0.441604i
$787$	0.157112	−	0.586349i	0.00560043	−	0.0209011i	−0.963069	−	0.269254i	$-0.913223\pi$
$787$	0.157112	−	0.586349i	0.00560043	−	0.0209011i	0.968670	+	0.248353i	$0.0798894\pi$
$788$	5.60170	+	20.9058i	0.199552	+	0.744739i
$789$		−	8.19543i		−	0.291765i
$790$	8.81594	+	15.2697i	0.313657	+	0.543270i
$791$	1.62939	+	0.563158i	0.0579346	+	0.0200236i
$792$		−	2.82807i		−	0.100491i
$793$	10.7793	+	4.43512i	0.382783	+	0.157496i
$794$	26.2754	+	15.1701i	0.932478	+	0.538367i
$795$	3.73050	+	3.73050i	0.132307	+	0.132307i
$796$	2.34122	+	1.35170i	0.0829822	+	0.0479098i
$797$	25.9638	−	44.9707i	0.919687	−	1.59294i	0.119796	−	0.992799i	$-0.461776\pi$
$797$	25.9638	−	44.9707i	0.919687	−	1.59294i	0.799891	−	0.600145i	$-0.204891\pi$
$798$	−7.14643	+	20.6769i	−0.252981	+	0.731954i
$799$	−32.0717	+	8.59358i	−1.13461	+	0.304019i
$800$	10.2136	−	10.2136i	0.361106	−	0.361106i
$801$	−10.7801	+	2.88852i	−0.380896	+	0.102061i
$802$	1.66596	+	2.88552i	0.0588270	+	0.101891i
$803$	−11.2165	+	19.4275i	−0.395821	+	0.685581i
$804$	−3.05458	+	11.3998i	−0.107727	+	0.402041i
$805$	−4.48045	+	6.62596i	−0.157915	+	0.233535i
$806$	11.9229	−	1.59834i	0.419965	−	0.0562992i
$807$	−12.2510	−	21.2193i	−0.431254	−	0.746954i
$808$	−22.6741	+	22.6741i	−0.797673	+	0.797673i
$809$	7.23298			0.254298			0.127149	−	0.991884i	$-0.459417\pi$
$809$	7.23298			0.254298			0.127149	+	0.991884i	$0.459417\pi$
$810$	2.39731			0.0842327
$811$	−25.2728	+	25.2728i	−0.887448	+	0.887448i	−0.994277	−	0.106830i	$-0.965930\pi$
$811$	−25.2728	+	25.2728i	−0.887448	+	0.887448i	0.106830	+	0.994277i	$0.465930\pi$
$812$	1.16577	−	3.37293i	0.0409104	−	0.118367i
$813$	−2.14916	−	8.02078i	−0.0753744	−	0.281301i
$814$	23.6933	+	6.34861i	0.830451	+	0.222519i
$815$	19.5715	−	11.2996i	0.685559	−	0.395807i
$816$			25.8057i			0.903381i
$817$	−39.3487	+	10.5435i	−1.37664	+	0.368869i
$818$	−26.6641			−0.932287
$819$	−9.35017	−	1.89059i	−0.326721	−	0.0660627i
$820$	−8.37364			−0.292420
$821$	−35.6922	+	9.56369i	−1.24567	+	0.333775i	−0.820661	−	0.571416i	$-0.806394\pi$
$821$	−35.6922	+	9.56369i	−1.24567	+	0.333775i	−0.425005	+	0.905191i	$0.639728\pi$
$822$		−	15.8921i		−	0.554300i
$823$	−19.8429	+	11.4563i	−0.691680	+	0.399341i	−0.804241	−	0.594303i	$-0.797428\pi$
$823$	−19.8429	+	11.4563i	−0.691680	+	0.399341i	0.112561	+	0.993645i	$0.464095\pi$
$824$	0.635746	+	0.170348i	0.0221473	+	0.00593434i
$825$	−1.18634	−	4.42750i	−0.0413032	−	0.154146i
$826$	37.4889	−	7.24204i	1.30441	−	0.251983i
$827$	−1.34175	+	1.34175i	−0.0466571	+	0.0466571i	−0.730050	−	0.683393i	$-0.760503\pi$
$827$	−1.34175	+	1.34175i	−0.0466571	+	0.0466571i	0.683393	+	0.730050i	$0.260503\pi$
$828$	−1.94795			−0.0676960
$829$	7.89312			0.274139			0.137070	−	0.990561i	$-0.456232\pi$
$829$	7.89312			0.274139			0.137070	+	0.990561i	$0.456232\pi$
$830$	−0.164159	+	0.164159i	−0.00569805	+	0.00569805i
$831$	−0.749658	−	1.29845i	−0.0260054	−	0.0450426i
$832$	−6.11982	−	2.51799i	−0.212166	−	0.0872955i
$833$	28.4678	+	22.3479i	0.986351	+	0.774310i
$834$	0.0722558	−	0.269662i	0.00250201	−	0.00933764i
$835$	−9.27237	+	16.0602i	−0.320884	+	0.555787i
$836$	−3.33268	−	5.77238i	−0.115263	−	0.199642i
$837$	1.89045	−	0.506544i	0.0653434	−	0.0175087i
$838$	44.7557	−	44.7557i	1.54606	−	1.54606i
$839$	−20.2818	+	5.43449i	−0.700205	+	0.187619i	−0.591322	−	0.806435i	$-0.701394\pi$
$839$	−20.2818	+	5.43449i	−0.700205	+	0.187619i	−0.108883	+	0.994055i	$0.534727\pi$
$840$	5.24160	−	4.54580i	0.180852	−	0.156845i
$841$	13.3920	−	23.1956i	0.461794	−	0.799850i
$842$	−48.4062	−	27.9474i	−1.66819	−	0.963129i
$843$	19.5020	+	19.5020i	0.671685	+	0.671685i
$844$	−3.22639	−	1.86276i	−0.111057	−	0.0641188i
$845$	−9.21544	−	15.7888i	−0.317021	−	0.543153i
$846$			10.9477i			0.376389i
$847$	−22.6003	+	4.36588i	−0.776556	+	0.150013i
$848$	9.36243	+	16.2162i	0.321507	+	0.556867i
$849$		−	15.6627i		−	0.537543i
$850$	6.89475	+	25.7316i	0.236488	+	0.882585i
$851$	−5.27911	+	19.7019i	−0.180966	+	0.675373i
$852$	−1.79900	−	1.79900i	−0.0616327	−	0.0616327i
$853$	5.56250	+	5.56250i	0.190456	+	0.190456i	0.795893	−	0.605437i	$-0.207002\pi$
$853$	5.56250	+	5.56250i	0.190456	+	0.190456i	−0.605437	+	0.795893i	$0.707002\pi$
$854$	−13.1126	+	6.37665i	−0.448704	+	0.218205i
$855$	−5.90720	+	3.41052i	−0.202022	+	0.116637i
$856$	−6.47193	−	24.1536i	−0.221206	−	0.825552i
$857$	7.92167	−	13.7207i	0.270599	−	0.468691i	−0.698416	−	0.715692i	$-0.746112\pi$
$857$	7.92167	−	13.7207i	0.270599	−	0.468691i	0.969015	+	0.247000i	$0.0794449\pi$
$858$	7.38185	−	5.69205i	0.252012	−	0.194324i
$859$	−22.0070	+	12.7057i	−0.750867	+	0.433514i	−0.826007	−	0.563659i	$-0.809393\pi$
$859$	−22.0070	+	12.7057i	−0.750867	+	0.433514i	0.0751398	+	0.997173i	$0.476060\pi$
$860$	−10.3370	−	2.76979i	−0.352489	−	0.0944491i
$861$	17.3429	+	1.23293i	0.591044	+	0.0420181i
$862$	24.4546	+	14.1188i	0.832925	+	0.480890i
$863$	−8.45278	+	31.5462i	−0.287736	+	1.07385i	0.659081	+	0.752072i	$0.270946\pi$
$863$	−8.45278	+	31.5462i	−0.287736	+	1.07385i	−0.946817	+	0.321773i	$0.895721\pi$
$864$	4.61620	+	1.23691i	0.157046	+	0.0420804i
$865$	−19.0614	−	5.10748i	−0.648106	−	0.173660i
$866$	−0.718787	+	2.68255i	−0.0244254	+	0.0911568i
$867$	−8.42779	−	4.86579i	−0.286223	−	0.165251i
$868$	−2.62819	+	3.88672i	−0.0892065	+	0.131924i
$869$	10.7741	+	2.88690i	0.365485	+	0.0979315i
$870$	3.09055	−	1.78433i	0.104780	−	0.0604945i
$871$	43.3447	−	18.0740i	1.46868	−	0.612416i
$872$	9.17368	−	15.8893i	0.310660	−	0.538079i
$873$	−3.39415	−	12.6671i	−0.114875	−	0.428718i
$874$	15.3946	−	8.88808i	0.520730	−	0.300644i
$875$	16.7197	−	24.7261i	0.565229	−	0.835896i
$876$	−9.47743	−	9.47743i	−0.320213	−	0.320213i
$877$	−32.4898	−	32.4898i	−1.09710	−	1.09710i	−0.994748	−	0.102355i	$-0.967362\pi$
$877$	−32.4898	−	32.4898i	−1.09710	−	1.09710i	−0.102355	−	0.994748i	$-0.532638\pi$
$878$	12.3454	−	46.0736i	0.416636	−	1.55491i
$879$	−3.66056	−	13.6614i	−0.123468	−	0.460787i
$880$			10.6447i			0.358831i
$881$	−16.3535	−	28.3251i	−0.550963	−	0.954296i	−0.998205	−	0.0598832i	$-0.980927\pi$
$881$	−16.3535	−	28.3251i	−0.550963	−	0.954296i	0.447242	−	0.894413i	$-0.352406\pi$
$882$	9.54683	−	7.15942i	0.321458	−	0.241070i
$883$			57.1171i			1.92214i	0.276302	+	0.961071i	$0.410891\pi$
$883$			57.1171i			1.92214i	−0.276302	+	0.961071i	$0.589109\pi$
$884$	−13.3765	+	10.3144i	−0.449899	+	0.346912i
$885$	10.3098	+	5.95239i	0.346562	+	0.200088i
$886$	30.6616	+	30.6616i	1.03010	+	1.03010i
$887$	−22.6328	−	13.0671i	−0.759935	−	0.438749i	0.0693373	−	0.997593i	$-0.477912\pi$
$887$	−22.6328	−	13.0671i	−0.759935	−	0.438749i	−0.829272	+	0.558844i	$0.811245\pi$
$888$	8.84640	−	15.3224i	0.296866	−	0.514187i
$889$	−3.27482	−	3.77608i	−0.109834	−	0.126646i
$890$	25.8432	−	6.92466i	0.866265	−	0.232115i
$891$	1.07237	−	1.07237i	0.0359258	−	0.0359258i
$892$	15.3569	−	4.11486i	0.514186	−	0.137776i
$893$	−15.5747	−	26.9762i	−0.521187	−	0.902723i
$894$	17.7593	−	30.7600i	0.593960	−	1.02877i
$895$	−6.54995	+	24.4448i	−0.218941	+	0.817098i
$896$	30.1864	−	14.6796i	1.00846	−	0.490411i
$897$	4.73316	+	6.13829i	0.158036	+	0.204951i
$898$	−2.19133	−	3.79549i	−0.0731256	−	0.126657i
$899$	2.06010	−	2.06010i	0.0687081	−	0.0687081i
$900$	2.73863			0.0912878
$901$	−19.3967			−0.646197
$902$	−12.0135	+	12.0135i	−0.400004	+	0.400004i
$903$	21.0014	+	7.25860i	0.698884	+	0.241551i
$904$	0.314490	+	1.17369i	0.0104598	+	0.0390365i
$905$	−20.1616	−	5.40230i	−0.670196	−	0.179578i
$906$	5.35161	−	3.08975i	0.177795	−	0.102650i
$907$			10.8409i			0.359967i	0.983670	+	0.179983i	$0.0576044\pi$
$907$			10.8409i			0.359967i	−0.983670	+	0.179983i	$0.942396\pi$
$908$	−6.07317	+	1.62730i	−0.201545	+	0.0540038i
$909$	−17.1955			−0.570339
$910$	22.4152	+	4.53233i	0.743057	+	0.150245i
$911$	35.4311			1.17389			0.586943	−	0.809628i	$-0.300331\pi$
$911$	35.4311			1.17389			0.586943	+	0.809628i	$0.300331\pi$
$912$	−23.3847	+	6.26590i	−0.774344	+	0.207485i
$913$			0.146865i			0.00486051i
$914$	20.9304	−	12.0842i	0.692315	−	0.399708i
$915$	−4.39127	−	1.17664i	−0.145171	−	0.0388985i
$916$	−2.10138	−	7.84245i	−0.0694315	−	0.259122i
$917$	17.8039	+	20.5291i	0.587938	+	0.677930i
$918$	−6.23237	+	6.23237i	−0.205699	+	0.205699i
$919$	−15.5115			−0.511678			−0.255839	−	0.966719i	$-0.582352\pi$
$919$	−15.5115			−0.511678			−0.255839	+	0.966719i	$0.582352\pi$
$920$	−5.63762			−0.185867
$921$	0.977336	−	0.977336i	0.0322043	−	0.0322043i
$922$	−35.6108	−	61.6797i	−1.17278	−	2.03131i
$923$	−1.29769	+	10.0402i	−0.0427139	+	0.330476i
$924$	−0.257817	+	3.62656i	−0.00848155	+	0.119305i
$925$	7.42193	−	27.6990i	0.244032	−	0.910738i
$926$	23.6477	−	40.9591i	0.777113	−	1.34600i
$927$	0.176474	+	0.305661i	0.00579615	+	0.0100392i
$928$	6.87174	−	1.84128i	0.225576	−	0.0604429i
$929$	−39.0142	+	39.0142i	−1.28002	+	1.28002i	−0.339358	+	0.940657i	$0.610210\pi$
$929$	−39.0142	+	39.0142i	−1.28002	+	1.28002i	−0.940657	+	0.339358i	$0.889790\pi$
$930$	−4.53198	+	1.21434i	−0.148609	+	0.0398198i
$931$	−13.3390	+	31.2233i	−0.437168	+	1.02330i
$932$	−2.88593	+	4.99857i	−0.0945317	+	0.163734i
$933$	7.28609	+	4.20663i	0.238536	+	0.137719i
$934$	35.3211	+	35.3211i	1.15574	+	1.15574i
$935$	−9.54928	−	5.51328i	−0.312295	−	0.180304i
$936$	−2.58768	−	6.20570i	−0.0845810	−	0.202840i
$937$			4.36357i			0.142552i	0.997457	+	0.0712758i	$0.0227070\pi$
$937$			4.36357i			0.142552i	−0.997457	+	0.0712758i	$0.977293\pi$
$938$	−19.1902	+	55.5234i	−0.626584	+	1.81290i
$939$	−8.31988	−	14.4104i	−0.271509	−	0.470267i
$940$		−	8.18301i		−	0.266900i
$941$	−2.38605	−	8.90484i	−0.0777829	−	0.290290i	0.916067	−	0.401025i	$-0.131346\pi$
$941$	−2.38605	−	8.90484i	−0.0777829	−	0.290290i	−0.993850	+	0.110736i	$0.964679\pi$
$942$	−6.55509	+	24.4639i	−0.213576	+	0.797078i
$943$	−9.98965	−	9.98965i	−0.325308	−	0.325308i
$944$	29.8774	+	29.8774i	0.972426	+	0.972426i
$945$	3.71126	+	0.263839i	0.120727	+	0.00858268i
$946$	−18.8040	+	10.8565i	−0.611371	+	0.352975i
$947$	14.2861	+	53.3164i	0.464236	+	1.73255i	0.659411	+	0.751783i	$0.270806\pi$
$947$	14.2861	+	53.3164i	0.464236	+	1.73255i	−0.195175	+	0.980768i	$0.562528\pi$
$948$	−3.33216	+	5.77146i	−0.108223	+	0.187448i
$949$	−6.83643	+	52.8932i	−0.221920	+	1.71699i
$950$	−21.6433	+	12.4958i	−0.702203	+	0.405417i
$951$	8.06223	+	2.16027i	0.261436	+	0.0700515i
$952$	−1.80890	+	25.4447i	−0.0586267	+	0.824667i
$953$	−30.1513	−	17.4079i	−0.976697	−	0.563896i	−0.0754255	−	0.997151i	$-0.524031\pi$
$953$	−30.1513	−	17.4079i	−0.976697	−	0.563896i	−0.901271	+	0.433255i	$0.857365\pi$
$954$	−1.65526	+	6.17753i	−0.0535911	+	0.200005i
$955$	19.6494	+	5.26505i	0.635840	+	0.170373i
$956$	−14.2252	−	3.81163i	−0.460075	−	0.123277i
$957$	0.584304	−	2.18065i	0.0188879	−	0.0704904i
$958$	−13.2068	−	7.62492i	−0.426691	−	0.246350i
$959$	1.74903	−	24.6025i	0.0564790	−	0.794457i
$960$	2.49310	+	0.668023i	0.0804643	+	0.0215604i
$961$	23.5296	−	13.5848i	0.759019	−	0.438220i
$962$	57.7998	−	7.74845i	1.86354	−	0.249820i
$963$	6.70466	−	11.6128i	0.216055	−	0.374218i
$964$	−0.0544908	−	0.203362i	−0.00175503	−	0.00654986i
$965$	22.1024	−	12.7608i	0.711502	−	0.410786i
$966$	−9.67182	−	0.687583i	−0.311186	−	0.0221226i
$967$	−24.1180	−	24.1180i	−0.775583	−	0.775583i	0.203494	−	0.979076i	$-0.434770\pi$
$967$	−24.1180	−	24.1180i	−0.775583	−	0.775583i	−0.979076	+	0.203494i	$0.934770\pi$
$968$	−11.4719	−	11.4719i	−0.368722	−	0.368722i
$969$	6.49071	−	24.2237i	0.208512	−	0.778176i
$970$	8.13681	+	30.3670i	0.261257	+	0.975026i
$971$			46.2333i			1.48370i	0.670568	+	0.741848i	$0.266050\pi$
$971$			46.2333i			1.48370i	−0.670568	+	0.741848i	$0.733950\pi$
$972$	0.453054	+	0.784712i	0.0145317	+	0.0251697i
$973$	0.141537	−	0.409512i	0.00453747	−	0.0131283i
$974$		−	34.9727i		−	1.12060i
$975$	−6.65437	−	8.62985i	−0.213110	−	0.276376i
$976$	−13.9738	−	8.06776i	−0.447289	−	0.258243i
$977$	5.68674	+	5.68674i	0.181935	+	0.181935i	0.792198	−	0.610264i	$-0.208936\pi$
$977$	5.68674	+	5.68674i	0.181935	+	0.181935i	−0.610264	+	0.792198i	$0.708936\pi$
$978$	23.7253	+	13.6978i	0.758652	+	0.438008i
$979$	8.46270	−	14.6578i	0.270469	−	0.468466i
$980$	−7.13593	+	5.35143i	−0.227949	+	0.170945i
$981$	9.50358	−	2.54648i	0.303426	−	0.0813027i
$982$	−38.4548	+	38.4548i	−1.22714	+	1.22714i
$983$	8.21252	−	2.20054i	0.261939	−	0.0701863i	−0.125459	−	0.992099i	$-0.540041\pi$
$983$	8.21252	−	2.20054i	0.261939	−	0.0701863i	0.387398	+	0.921912i	$0.373374\pi$
$984$	6.12727	+	10.6128i	0.195330	+	0.338322i
$985$	−16.7951	+	29.0899i	−0.535135	+	0.926881i
$986$	−3.39583	+	12.6734i	−0.108145	+	0.403604i
$987$	−1.20486	+	16.9481i	−0.0383511	+	0.539463i
$988$	−12.5947	−	9.61705i	−0.400690	−	0.305959i
$989$	−9.02758	−	15.6362i	−0.287060	−	0.497203i
$990$	−2.57080	+	2.57080i	−0.0817055	+	0.0817055i
$991$	−10.8932			−0.346035			−0.173018	−	0.984919i	$-0.555352\pi$
$991$	−10.8932			−0.346035			−0.173018	+	0.984919i	$0.555352\pi$
$992$	−9.35323			−0.296965
$993$	−5.23570	+	5.23570i	−0.166150	+	0.166150i
$994$	−8.29726	−	9.56727i	−0.263173	−	0.303455i
$995$	1.08591	+	4.05268i	0.0344257	+	0.128479i
$996$	−0.0847579	−	0.0227108i	−0.00268566	−	0.000719620i
$997$	−0.843219	+	0.486833i	−0.0267050	+	0.0154181i	−0.513293	−	0.858213i	$-0.671575\pi$
$997$	−0.843219	+	0.486833i	−0.0267050	+	0.0154181i	0.486588	+	0.873632i	$0.338241\pi$
$998$		−	39.0657i		−	1.23660i
$999$	9.16453	−	2.45563i	0.289953	−	0.0776926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.cg.a.115.7	yes	36
3.2	odd	2		819.2.gh.c.388.3		36
7.5	odd	6		273.2.bt.a.271.3	yes	36
13.6	odd	12		273.2.bt.a.136.3	✓	36
21.5	even	6		819.2.et.c.271.7		36
39.32	even	12		819.2.et.c.136.7		36
91.19	even	12	inner	273.2.cg.a.19.7	yes	36
273.110	odd	12		819.2.gh.c.19.3		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bt.a.136.3	✓	36	13.6	odd	12
273.2.bt.a.271.3	yes	36	7.5	odd	6
273.2.cg.a.19.7	yes	36	91.19	even	12	inner
273.2.cg.a.115.7	yes	36	1.1	even	1	trivial
819.2.et.c.136.7		36	39.32	even	12
819.2.et.c.271.7		36	21.5	even	6
819.2.gh.c.19.3		36	273.110	odd	12
819.2.gh.c.388.3		36	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.64664 - 0.441217i) q^{2} +1.00000i q^{3} +(0.784712 - 0.453054i) q^{4} +(1.35835 + 0.363968i) q^{5} +(0.441217 + 1.64664i) q^{6} +(0.501823 + 2.59772i) q^{7} +(-1.31861 + 1.31861i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.64664 - 0.441217i) q^{2} +1.00000i q^{3} +(0.784712 - 0.453054i) q^{4} +(1.35835 + 0.363968i) q^{5} +(0.441217 + 1.64664i) q^{6} +(0.501823 + 2.59772i) q^{7} +(-1.31861 + 1.31861i) q^{8} -1.00000 q^{9} +2.39731 q^{10} +(1.07237 - 1.07237i) q^{11} +(0.453054 + 0.784712i) q^{12} +(1.37191 - 3.33435i) q^{13} +(1.97248 + 4.05611i) q^{14} +(-0.363968 + 1.35835i) q^{15} +(-2.49559 + 4.32249i) q^{16} +(-2.58513 - 4.47758i) q^{17} +(-1.64664 + 0.441217i) q^{18} +(3.42980 - 3.42980i) q^{19} +(1.23081 - 0.329795i) q^{20} +(-2.59772 + 0.501823i) q^{21} +(1.29267 - 2.23896i) q^{22} +(1.86178 + 1.07490i) q^{23} +(-1.31861 - 1.31861i) q^{24} +(-2.61749 - 1.51121i) q^{25} +(0.787879 - 6.09579i) q^{26} -1.00000i q^{27} +(1.57070 + 1.81111i) q^{28} +(-0.744307 - 1.28918i) q^{29} +2.39731i q^{30} +(0.506544 + 1.89045i) q^{31} +(-1.23691 + 4.61620i) q^{32} +(1.07237 + 1.07237i) q^{33} +(-6.23237 - 6.23237i) q^{34} +(-0.263839 + 3.71126i) q^{35} +(-0.784712 + 0.453054i) q^{36} +(2.45563 + 9.16453i) q^{37} +(4.13437 - 7.16094i) q^{38} +(3.33435 + 1.37191i) q^{39} +(-2.27106 + 1.31120i) q^{40} +(-6.34762 - 1.70084i) q^{41} +(-4.05611 + 1.97248i) q^{42} +(-7.27334 - 4.19927i) q^{43} +(0.355661 - 1.32735i) q^{44} +(-1.35835 - 0.363968i) q^{45} +(3.53996 + 0.948528i) q^{46} +(1.66212 - 6.20311i) q^{47} +(-4.32249 - 2.49559i) q^{48} +(-6.49635 + 2.60720i) q^{49} +(-4.97684 - 1.33354i) q^{50} +(4.47758 - 2.58513i) q^{51} +(-0.434083 - 3.23805i) q^{52} +(1.87579 - 3.24897i) q^{53} +(-0.441217 - 1.64664i) q^{54} +(1.84696 - 1.06635i) q^{55} +(-4.08709 - 2.76367i) q^{56} +(3.42980 + 3.42980i) q^{57} +(-1.79442 - 1.79442i) q^{58} +(2.19104 - 8.17707i) q^{59} +(0.329795 + 1.23081i) q^{60} +3.23280i q^{61} +(1.66819 + 2.88940i) q^{62} +(-0.501823 - 2.59772i) q^{63} -1.83539i q^{64} +(3.07713 - 4.02987i) q^{65} +(2.23896 + 1.29267i) q^{66} +(9.21001 + 9.21001i) q^{67} +(-4.05717 - 2.34241i) q^{68} +(-1.07490 + 1.86178i) q^{69} +(1.20302 + 6.22754i) q^{70} +(-2.71213 + 0.726713i) q^{71} +(1.31861 - 1.31861i) q^{72} +(-14.2879 + 3.82844i) q^{73} +(8.08709 + 14.0072i) q^{74} +(1.51121 - 2.61749i) q^{75} +(1.13752 - 4.24529i) q^{76} +(3.32387 + 2.24759i) q^{77} +(6.09579 + 0.787879i) q^{78} +(3.67744 + 6.36951i) q^{79} +(-4.96314 + 4.96314i) q^{80} +1.00000 q^{81} -11.2027 q^{82} +(-0.0684765 + 0.0684765i) q^{83} +(-1.81111 + 1.57070i) q^{84} +(-1.88181 - 7.02301i) q^{85} +(-13.8294 - 3.70557i) q^{86} +(1.28918 - 0.744307i) q^{87} +2.82807i q^{88} +(10.7801 - 2.88852i) q^{89} -2.39731 q^{90} +(9.35017 + 1.89059i) q^{91} +1.94795 q^{92} +(-1.89045 + 0.506544i) q^{93} -10.9477i q^{94} +(5.90720 - 3.41052i) q^{95} +(-4.61620 - 1.23691i) q^{96} +(3.39415 + 12.6671i) q^{97} +(-9.54683 + 7.15942i) q^{98} +(-1.07237 + 1.07237i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{7} - 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^7 - 36 * q^9	\( 36 q + 4 q^{7} - 36 q^{9} + 4 q^{11} + 16 q^{12} + 42 q^{14} + 12 q^{16} - 4 q^{17} - 24 q^{19} - 14 q^{20} + 4 q^{22} - 12 q^{23} - 24 q^{25} - 28 q^{26} - 12 q^{28} + 8 q^{29} - 6 q^{31} + 46 q^{32} + 4 q^{33} + 24 q^{34} - 10 q^{35} - 20 q^{37} + 8 q^{38} - 2 q^{39} - 30 q^{40} - 34 q^{41} + 24 q^{42} + 30 q^{43} - 32 q^{44} - 26 q^{46} + 4 q^{47} - 24 q^{48} - 20 q^{50} + 24 q^{51} + 98 q^{52} - 8 q^{53} + 30 q^{55} - 10 q^{56} - 24 q^{57} - 96 q^{58} - 14 q^{59} - 46 q^{60} + 48 q^{62} - 4 q^{63} + 28 q^{65} + 18 q^{66} + 62 q^{67} - 54 q^{68} - 4 q^{69} - 148 q^{70} + 42 q^{71} - 52 q^{73} - 20 q^{74} - 10 q^{75} - 12 q^{76} - 24 q^{77} - 16 q^{78} + 76 q^{80} + 36 q^{81} + 48 q^{82} + 60 q^{83} + 50 q^{84} + 2 q^{85} + 12 q^{86} + 18 q^{87} + 50 q^{89} + 40 q^{91} - 100 q^{92} - 6 q^{93} + 24 q^{95} - 4 q^{96} - 36 q^{97} + 16 q^{98} - 4 q^{99}+O(q^{100}) \) 36 * q + 4 * q^7 - 36 * q^9 + 4 * q^11 + 16 * q^12 + 42 * q^14 + 12 * q^16 - 4 * q^17 - 24 * q^19 - 14 * q^20 + 4 * q^22 - 12 * q^23 - 24 * q^25 - 28 * q^26 - 12 * q^28 + 8 * q^29 - 6 * q^31 + 46 * q^32 + 4 * q^33 + 24 * q^34 - 10 * q^35 - 20 * q^37 + 8 * q^38 - 2 * q^39 - 30 * q^40 - 34 * q^41 + 24 * q^42 + 30 * q^43 - 32 * q^44 - 26 * q^46 + 4 * q^47 - 24 * q^48 - 20 * q^50 + 24 * q^51 + 98 * q^52 - 8 * q^53 + 30 * q^55 - 10 * q^56 - 24 * q^57 - 96 * q^58 - 14 * q^59 - 46 * q^60 + 48 * q^62 - 4 * q^63 + 28 * q^65 + 18 * q^66 + 62 * q^67 - 54 * q^68 - 4 * q^69 - 148 * q^70 + 42 * q^71 - 52 * q^73 - 20 * q^74 - 10 * q^75 - 12 * q^76 - 24 * q^77 - 16 * q^78 + 76 * q^80 + 36 * q^81 + 48 * q^82 + 60 * q^83 + 50 * q^84 + 2 * q^85 + 12 * q^86 + 18 * q^87 + 50 * q^89 + 40 * q^91 - 100 * q^92 - 6 * q^93 + 24 * q^95 - 4 * q^96 - 36 * q^97 + 16 * q^98 - 4 * q^99

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