LMFDB - Embedded newform 930.2.o.e.491.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(161,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("930.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.7
Character	$\chi$	$=$	930.491
Dual form			930.2.o.e.161.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.28806 + 1.15797i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.15797 - 1.28806i) q^{6} +(0.615418 - 1.06593i) q^{7} +1.00000i q^{8} +(0.318204 + 2.98308i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.28806 + 1.15797i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.15797 - 1.28806i) q^{6} +(0.615418 - 1.06593i) q^{7} +1.00000i q^{8} +(0.318204 + 2.98308i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.427947 + 0.741226i) q^{11} +(-1.28806 - 1.15797i) q^{12} +(4.88495 - 2.82033i) q^{13} +(-1.06593 - 0.615418i) q^{14} +(-1.69448 - 0.358802i) q^{15} +1.00000 q^{16} +(-3.42474 + 5.93182i) q^{17} +(2.98308 - 0.318204i) q^{18} +(-0.242571 + 0.420145i) q^{19} +(0.866025 - 0.500000i) q^{20} +(2.02702 - 0.660353i) q^{21} +(0.741226 - 0.427947i) q^{22} +7.95781 q^{23} +(-1.15797 + 1.28806i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.82033 - 4.88495i) q^{26} +(-3.04445 + 4.21086i) q^{27} +(-0.615418 + 1.06593i) q^{28} -1.17589 q^{29} +(-0.358802 + 1.69448i) q^{30} +(-1.91832 + 5.22686i) q^{31} -1.00000i q^{32} +(-0.307097 + 1.45030i) q^{33} +(5.93182 + 3.42474i) q^{34} +1.23084i q^{35} +(-0.318204 - 2.98308i) q^{36} +(7.56493 + 4.36761i) q^{37} +(0.420145 + 0.242571i) q^{38} +(9.55797 + 2.02388i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(6.21998 - 3.59111i) q^{41} +(-0.660353 - 2.02702i) q^{42} +(-4.37834 - 2.52784i) q^{43} +(-0.427947 - 0.741226i) q^{44} +(-1.76711 - 2.42432i) q^{45} -7.95781i q^{46} -2.88870i q^{47} +(1.28806 + 1.15797i) q^{48} +(2.74252 + 4.75019i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-11.2801 + 3.67480i) q^{51} +(-4.88495 + 2.82033i) q^{52} +(0.346231 + 0.599690i) q^{53} +(4.21086 + 3.04445i) q^{54} +(-0.741226 - 0.427947i) q^{55} +(1.06593 + 0.615418i) q^{56} +(-0.798962 + 0.260282i) q^{57} +1.17589i q^{58} +(0.639178 + 0.369029i) q^{59} +(1.69448 + 0.358802i) q^{60} -6.48651i q^{61} +(5.22686 + 1.91832i) q^{62} +(3.37559 + 1.49665i) q^{63} -1.00000 q^{64} +(-2.82033 + 4.88495i) q^{65} +(1.45030 + 0.307097i) q^{66} +(4.07315 + 7.05491i) q^{67} +(3.42474 - 5.93182i) q^{68} +(10.2502 + 9.21492i) q^{69} +1.23084 q^{70} +(3.36751 - 1.94423i) q^{71} +(-2.98308 + 0.318204i) q^{72} +(-4.44599 + 2.56690i) q^{73} +(4.36761 - 7.56493i) q^{74} +(1.64686 - 0.536508i) q^{75} +(0.242571 - 0.420145i) q^{76} +1.05346 q^{77} +(2.02388 - 9.55797i) q^{78} +(2.99903 + 1.73149i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-8.79749 + 1.89845i) q^{81} +(-3.59111 - 6.21998i) q^{82} +(-1.20254 - 2.08287i) q^{83} +(-2.02702 + 0.660353i) q^{84} -6.84947i q^{85} +(-2.52784 + 4.37834i) q^{86} +(-1.51462 - 1.36165i) q^{87} +(-0.741226 + 0.427947i) q^{88} -5.45985 q^{89} +(-2.42432 + 1.76711i) q^{90} -6.94272i q^{91} -7.95781 q^{92} +(-8.52347 + 4.51115i) q^{93} -2.88870 q^{94} -0.485142i q^{95} +(1.15797 - 1.28806i) q^{96} -5.55358 q^{97} +(4.75019 - 2.74252i) q^{98} +(-2.07496 + 1.51246i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	$ 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) $ 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.28806	+	1.15797i	0.743663	+	0.668555i
$3$	1.28806	+	1.15797i	0.743663	+	0.668555i
$4$	−1.00000			−0.500000
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$	1.15797	−	1.28806i	0.472740	−	0.525849i
$7$	0.615418	−	1.06593i	0.232606	−	0.402885i	−0.725968	−	0.687728i	$-0.758608\pi$
$7$	0.615418	−	1.06593i	0.232606	−	0.402885i	0.958574	+	0.284843i	$0.0919414\pi$
$8$			1.00000i			0.353553i
$9$	0.318204	+	2.98308i	0.106068	+	0.994359i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.427947	+	0.741226i	0.129031	+	0.223488i	0.923301	−	0.384076i	$-0.125480\pi$
$11$	0.427947	+	0.741226i	0.129031	+	0.223488i	−0.794270	+	0.607564i	$0.792147\pi$
$12$	−1.28806	−	1.15797i	−0.371831	−	0.334278i
$13$	4.88495	−	2.82033i	1.35484	−	0.782218i	0.365918	−	0.930647i	$-0.380755\pi$
$13$	4.88495	−	2.82033i	1.35484	−	0.782218i	0.988923	+	0.148429i	$0.0474217\pi$
$14$	−1.06593	−	0.615418i	−0.284883	−	0.164477i
$15$	−1.69448	−	0.358802i	−0.437513	−	0.0926423i
$16$	1.00000			0.250000
$17$	−3.42474	+	5.93182i	−0.830620	+	1.43868i	0.0669268	+	0.997758i	$0.478681\pi$
$17$	−3.42474	+	5.93182i	−0.830620	+	1.43868i	−0.897547	+	0.440919i	$0.854653\pi$
$18$	2.98308	−	0.318204i	0.703118	−	0.0750014i
$19$	−0.242571	+	0.420145i	−0.0556496	+	0.0963879i	−0.892508	−	0.451031i	$-0.851056\pi$
$19$	−0.242571	+	0.420145i	−0.0556496	+	0.0963879i	0.836859	+	0.547419i	$0.184390\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	2.02702	−	0.660353i	0.442332	−	0.144101i
$22$	0.741226	−	0.427947i	0.158030	−	0.0912386i
$23$	7.95781			1.65932			0.829660	−	0.558270i	$-0.188535\pi$
$23$	7.95781			1.65932			0.829660	+	0.558270i	$0.188535\pi$
$24$	−1.15797	+	1.28806i	−0.236370	+	0.262924i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−2.82033	−	4.88495i	−0.553112	−	0.958017i
$27$	−3.04445	+	4.21086i	−0.585905	+	0.810380i
$28$	−0.615418	+	1.06593i	−0.116303	+	0.201443i
$29$	−1.17589			−0.218358			−0.109179	−	0.994022i	$-0.534822\pi$
$29$	−1.17589			−0.218358			−0.109179	+	0.994022i	$0.534822\pi$
$30$	−0.358802	+	1.69448i	−0.0655080	+	0.309368i
$31$	−1.91832	+	5.22686i	−0.344541	+	0.938771i
$31$	−1.91832	+	5.22686i	−0.344541	+	0.938771i
$32$		−	1.00000i		−	0.176777i
$33$	−0.307097	+	1.45030i	−0.0534587	+	0.252464i
$34$	5.93182	+	3.42474i	1.01730	+	0.587337i
$35$			1.23084i			0.208049i
$36$	−0.318204	−	2.98308i	−0.0530340	−	0.497179i
$37$	7.56493	+	4.36761i	1.24367	+	0.718031i	0.969839	−	0.243747i	$-0.0783768\pi$
$37$	7.56493	+	4.36761i	1.24367	+	0.718031i	0.273828	+	0.961779i	$0.411710\pi$
$38$	0.420145	+	0.242571i	0.0681565	+	0.0393502i
$39$	9.55797	+	2.02388i	1.53050	+	0.324080i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	6.21998	−	3.59111i	0.971398	−	0.560837i	0.0717356	−	0.997424i	$-0.477146\pi$
$41$	6.21998	−	3.59111i	0.971398	−	0.560837i	0.899662	+	0.436587i	$0.143813\pi$
$42$	−0.660353	−	2.02702i	−0.101895	−	0.312776i
$43$	−4.37834	−	2.52784i	−0.667691	−	0.385492i	0.127510	−	0.991837i	$-0.459301\pi$
$43$	−4.37834	−	2.52784i	−0.667691	−	0.385492i	−0.795201	+	0.606346i	$0.792635\pi$
$44$	−0.427947	−	0.741226i	−0.0645155	−	0.111744i
$45$	−1.76711	−	2.42432i	−0.263425	−	0.361396i
$46$		−	7.95781i		−	1.17332i
$47$		−	2.88870i		−	0.421360i	−0.977555	−	0.210680i	$-0.932432\pi$
$47$		−	2.88870i		−	0.421360i	0.977555	−	0.210680i	$-0.0675679\pi$
$48$	1.28806	+	1.15797i	0.185916	+	0.167139i
$49$	2.74252	+	4.75019i	0.391789	+	0.678598i
$50$	−0.866025	−	0.500000i	−0.122474	−	0.0707107i
$51$	−11.2801	+	3.67480i	−1.57954	+	0.514574i
$52$	−4.88495	+	2.82033i	−0.677421	+	0.391109i
$53$	0.346231	+	0.599690i	0.0475585	+	0.0823738i	0.888825	−	0.458247i	$-0.151523\pi$
$53$	0.346231	+	0.599690i	0.0475585	+	0.0823738i	−0.841266	+	0.540621i	$0.818189\pi$
$54$	4.21086	+	3.04445i	0.573025	+	0.414297i
$55$	−0.741226	−	0.427947i	−0.0999469	−	0.0577044i
$56$	1.06593	+	0.615418i	0.142442	+	0.0822386i
$57$	−0.798962	+	0.260282i	−0.105825	+	0.0344753i
$58$			1.17589i			0.154402i
$59$	0.639178	+	0.369029i	0.0832138	+	0.0480435i	0.541030	−	0.841004i	$-0.318035\pi$
$59$	0.639178	+	0.369029i	0.0832138	+	0.0480435i	−0.457816	+	0.889047i	$0.651368\pi$
$60$	1.69448	+	0.358802i	0.218756	+	0.0463212i
$61$		−	6.48651i		−	0.830512i	−0.909705	−	0.415256i	$-0.863692\pi$
$61$		−	6.48651i		−	0.830512i	0.909705	−	0.415256i	$-0.136308\pi$
$62$	5.22686	+	1.91832i	0.663811	+	0.243627i
$63$	3.37559	+	1.49665i	0.425285	+	0.188561i
$64$	−1.00000			−0.125000
$65$	−2.82033	+	4.88495i	−0.349818	+	0.605903i
$66$	1.45030	+	0.307097i	0.178519	+	0.0378010i
$67$	4.07315	+	7.05491i	0.497615	+	0.861894i	0.999996	−	0.00275216i	$-0.000876040\pi$
$67$	4.07315	+	7.05491i	0.497615	+	0.861894i	−0.502382	+	0.864646i	$0.667543\pi$
$68$	3.42474	−	5.93182i	0.415310	−	0.719338i
$69$	10.2502	+	9.21492i	1.23397	+	1.10935i
$70$	1.23084			0.147113
$71$	3.36751	−	1.94423i	0.399650	−	0.230738i	−0.286683	−	0.958026i	$-0.592553\pi$
$71$	3.36751	−	1.94423i	0.399650	−	0.230738i	0.686333	+	0.727287i	$0.259219\pi$
$72$	−2.98308	+	0.318204i	−0.351559	+	0.0375007i
$73$	−4.44599	+	2.56690i	−0.520364	+	0.300432i	−0.737084	−	0.675801i	$-0.763798\pi$
$73$	−4.44599	+	2.56690i	−0.520364	+	0.300432i	0.216719	+	0.976234i	$0.430464\pi$
$74$	4.36761	−	7.56493i	0.507725	−	0.879405i
$75$	1.64686	−	0.536508i	0.190163	−	0.0619506i
$76$	0.242571	−	0.420145i	0.0278248	−	0.0481939i
$77$	1.05346			0.120053
$78$	2.02388	−	9.55797i	0.229159	−	1.08223i
$79$	2.99903	+	1.73149i	0.337417	+	0.194808i	0.659129	−	0.752030i	$-0.270925\pi$
$79$	2.99903	+	1.73149i	0.337417	+	0.194808i	−0.321712	+	0.946838i	$0.604258\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−8.79749	+	1.89845i	−0.977499	+	0.210939i
$82$	−3.59111	−	6.21998i	−0.396571	−	0.686882i
$83$	−1.20254	−	2.08287i	−0.131996	−	0.228624i	0.792450	−	0.609937i	$-0.208805\pi$
$83$	−1.20254	−	2.08287i	−0.131996	−	0.228624i	−0.924446	+	0.381313i	$0.875472\pi$
$84$	−2.02702	+	0.660353i	−0.221166	+	0.0720504i
$85$		−	6.84947i		−	0.742929i
$86$	−2.52784	+	4.37834i	−0.272584	+	0.472129i
$87$	−1.51462	−	1.36165i	−0.162385	−	0.145984i
$88$	−0.741226	+	0.427947i	−0.0790150	+	0.0456193i
$89$	−5.45985			−0.578742			−0.289371	−	0.957217i	$-0.593446\pi$
$89$	−5.45985			−0.578742			−0.289371	+	0.957217i	$0.593446\pi$
$90$	−2.42432	+	1.76711i	−0.255546	+	0.186270i
$91$		−	6.94272i		−	0.727794i
$92$	−7.95781			−0.829660
$93$	−8.52347	+	4.51115i	−0.883843	+	0.467784i
$94$	−2.88870			−0.297947
$95$		−	0.485142i		−	0.0497745i
$96$	1.15797	−	1.28806i	0.118185	−	0.131462i
$97$	−5.55358			−0.563880			−0.281940	−	0.959432i	$-0.590978\pi$
$97$	−5.55358			−0.563880			−0.281940	+	0.959432i	$0.590978\pi$
$98$	4.75019	−	2.74252i	0.479841	−	0.277037i
$99$	−2.07496	+	1.51246i	−0.208541	+	0.152008i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$			4.31376i			0.429235i	0.976698	+	0.214618i	$0.0688506\pi$
$101$			4.31376i			0.429235i	−0.976698	+	0.214618i	$0.931149\pi$
$102$	3.67480	+	11.2801i	0.363859	+	1.11690i
$103$	−2.73994	−	4.74572i	−0.269975	−	0.467610i	0.698880	−	0.715239i	$-0.253682\pi$
$103$	−2.73994	−	4.74572i	−0.269975	−	0.467610i	−0.968855	+	0.247629i	$0.920349\pi$
$104$	2.82033	+	4.88495i	0.276556	+	0.479009i
$105$	−1.42527	+	1.58539i	−0.139092	+	0.154718i
$106$	0.599690	−	0.346231i	0.0582471	−	0.0336290i
$107$	−8.01947	−	4.63004i	−0.775271	−	0.447603i	0.0594807	−	0.998229i	$-0.481056\pi$
$107$	−8.01947	−	4.63004i	−0.775271	−	0.447603i	−0.834752	+	0.550627i	$0.814389\pi$
$108$	3.04445	−	4.21086i	0.292953	−	0.405190i
$109$	−20.3111			−1.94545			−0.972727	−	0.231951i	$-0.925489\pi$
$109$	−20.3111			−1.94545			−0.972727	+	0.231951i	$0.925489\pi$
$110$	−0.427947	+	0.741226i	−0.0408032	+	0.0706731i
$111$	4.68652	+	14.3857i	0.444825	+	1.36543i
$112$	0.615418	−	1.06593i	0.0581515	−	0.100721i
$113$	16.5283	−	9.54261i	1.55485	−	0.897693i	0.557114	−	0.830436i	$-0.311908\pi$
$113$	16.5283	−	9.54261i	1.55485	−	0.897693i	0.997736	−	0.0672575i	$-0.0214249\pi$
$114$	0.260282	+	0.798962i	0.0243777	+	0.0748297i
$115$	−6.89167	+	3.97891i	−0.642652	+	0.371035i
$116$	1.17589			0.109179
$117$	9.96766	+	13.6747i	0.921511	+	1.26423i
$118$	0.369029	−	0.639178i	0.0339719	−	0.0588411i
$119$	4.21529	+	7.30109i	0.386415	+	0.669290i
$120$	0.358802	−	1.69448i	0.0327540	−	0.154684i
$121$	5.13372	−	8.89187i	0.466702	−	0.808352i
$122$	−6.48651			−0.587261
$123$	12.1701	+	2.57699i	1.09734	+	0.232360i
$124$	1.91832	−	5.22686i	0.172271	−	0.469386i
$125$			1.00000i			0.0894427i
$126$	1.49665	−	3.37559i	0.133333	−	0.300722i
$127$	−10.5175	−	6.07226i	−0.933273	−	0.538826i	−0.0454281	−	0.998968i	$-0.514465\pi$
$127$	−10.5175	−	6.07226i	−0.933273	−	0.538826i	−0.887845	+	0.460142i	$0.847799\pi$
$128$			1.00000i			0.0883883i
$129$	−2.71241	−	8.32601i	−0.238814	−	0.733064i
$130$	4.88495	+	2.82033i	0.428438	+	0.247359i
$131$	7.08508	+	4.09057i	0.619026	+	0.357395i	0.776490	−	0.630130i	$-0.216998\pi$
$131$	7.08508	+	4.09057i	0.619026	+	0.357395i	−0.157464	+	0.987525i	$0.550332\pi$
$132$	0.307097	−	1.45030i	0.0267293	−	0.126232i
$133$	0.298565	+	0.517129i	0.0258889	+	0.0448408i
$134$	7.05491	−	4.07315i	0.609451	−	0.351867i
$135$	0.531144	−	5.16893i	0.0457136	−	0.444871i
$136$	−5.93182	−	3.42474i	−0.508649	−	0.293669i
$137$	−11.1693	−	19.3458i	−0.954258	−	1.65282i	−0.736057	−	0.676919i	$-0.763315\pi$
$137$	−11.1693	−	19.3458i	−0.954258	−	1.65282i	−0.218201	−	0.975904i	$-0.570019\pi$
$138$	9.21492	−	10.2502i	0.784426	−	0.872551i
$139$		−	13.3668i		−	1.13376i	−0.823802	−	0.566878i	$-0.808151\pi$
$139$		−	13.3668i		−	1.13376i	0.823802	−	0.566878i	$-0.191849\pi$
$140$		−	1.23084i		−	0.104025i
$141$	3.34503	−	3.72082i	0.281703	−	0.313350i
$142$	−1.94423	−	3.36751i	−0.163157	−	0.282595i
$143$	4.18100	+	2.41390i	0.349633	+	0.201861i
$144$	0.318204	+	2.98308i	0.0265170	+	0.248590i
$145$	1.01835	−	0.587947i	0.0845697	−	0.0488263i
$146$	2.56690	+	4.44599i	0.212438	+	0.367953i
$147$	−1.96805	+	9.29430i	−0.162322	+	0.766581i
$148$	−7.56493	−	4.36761i	−0.621833	−	0.359016i
$149$	−7.71061	−	4.45172i	−0.631678	−	0.364700i	0.149724	−	0.988728i	$-0.452162\pi$
$149$	−7.71061	−	4.45172i	−0.631678	−	0.364700i	−0.781402	+	0.624028i	$0.785495\pi$
$150$	−0.536508	−	1.64686i	−0.0438057	−	0.134466i
$151$		−	9.97617i		−	0.811849i	−0.913907	−	0.405925i	$-0.866950\pi$
$151$		−	9.97617i		−	0.811849i	0.913907	−	0.405925i	$-0.133050\pi$
$152$	−0.420145	−	0.242571i	−0.0340783	−	0.0196751i
$153$	−18.7848	−	8.32872i	−1.51866	−	0.673337i
$154$		−	1.05346i		−	0.0848906i
$155$	−0.952111	−	5.48575i	−0.0764754	−	0.440626i
$156$	−9.55797	−	2.02388i	−0.765250	−	0.162040i
$157$	−3.11711			−0.248772			−0.124386	−	0.992234i	$-0.539696\pi$
$157$	−3.11711			−0.248772			−0.124386	+	0.992234i	$0.539696\pi$
$158$	1.73149	−	2.99903i	0.137750	−	0.238590i
$159$	−0.248457	+	1.17336i	−0.0197039	+	0.0930538i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	4.89738	−	8.48251i	0.385968	−	0.668516i
$162$	1.89845	+	8.79749i	0.149157	+	0.691196i
$163$	−1.12144			−0.0878383			−0.0439191	−	0.999035i	$-0.513984\pi$
$163$	−1.12144			−0.0878383			−0.0439191	+	0.999035i	$0.513984\pi$
$164$	−6.21998	+	3.59111i	−0.485699	+	0.280418i
$165$	−0.459194	−	1.40954i	−0.0357482	−	0.109733i
$166$	−2.08287	+	1.20254i	−0.161662	+	0.0933355i
$167$	−4.93083	+	8.54044i	−0.381559	+	0.660879i	−0.991285	−	0.131733i	$-0.957946\pi$
$167$	−4.93083	+	8.54044i	−0.381559	+	0.660879i	0.609727	+	0.792612i	$0.291279\pi$
$168$	0.660353	+	2.02702i	0.0509473	+	0.156388i
$169$	9.40849	−	16.2960i	0.723730	−	1.25354i
$170$	−6.84947			−0.525330
$171$	−1.33051	−	0.589916i	−0.101747	−	0.0451120i
$172$	4.37834	+	2.52784i	0.333846	+	0.192746i
$173$	−8.74006	+	5.04608i	−0.664495	+	0.383646i	−0.793987	−	0.607934i	$-0.791998\pi$
$173$	−8.74006	+	5.04608i	−0.664495	+	0.383646i	0.129493	+	0.991580i	$0.458665\pi$
$174$	−1.36165	+	1.51462i	−0.103227	+	0.114823i
$175$	−0.615418	−	1.06593i	−0.0465212	−	0.0805771i
$176$	0.427947	+	0.741226i	0.0322577	+	0.0558720i
$177$	0.395974	+	1.21548i	0.0297633	+	0.0913612i
$178$			5.45985i			0.409233i
$179$	12.2409	−	21.2018i	0.914926	−	1.58470i	0.107917	−	0.994160i	$-0.465582\pi$
$179$	12.2409	−	21.2018i	0.914926	−	1.58470i	0.807009	−	0.590539i	$-0.201085\pi$
$180$	1.76711	+	2.42432i	0.131713	+	0.180698i
$181$	13.0056	−	7.50878i	0.966697	−	0.558123i	0.0684696	−	0.997653i	$-0.478188\pi$
$181$	13.0056	−	7.50878i	0.966697	−	0.558123i	0.898228	+	0.439530i	$0.144855\pi$
$182$	−6.94272			−0.514628
$183$	7.51119	−	8.35502i	0.555243	−	0.617621i
$184$			7.95781i			0.586658i
$185$	−8.73523			−0.642227
$186$	4.51115	+	8.52347i	0.330773	+	0.624971i
$187$	−5.86242			−0.428703
$188$			2.88870i			0.210680i
$189$	2.61489	+	5.83662i	0.190205	+	0.424552i
$190$	−0.485142			−0.0351959
$191$	10.6075	−	6.12422i	0.767529	−	0.443133i	−0.0644637	−	0.997920i	$-0.520534\pi$
$191$	10.6075	−	6.12422i	0.767529	−	0.443133i	0.831992	+	0.554787i	$0.187200\pi$
$192$	−1.28806	−	1.15797i	−0.0929578	−	0.0835694i
$193$	−12.4843	+	21.6235i	−0.898641	+	1.55649i	−0.0694087	+	0.997588i	$0.522111\pi$
$193$	−12.4843	+	21.6235i	−0.898641	+	1.55649i	−0.829232	+	0.558904i	$0.811222\pi$
$194$			5.55358i			0.398724i
$195$	−9.28939	+	3.02626i	−0.665227	+	0.216715i
$196$	−2.74252	−	4.75019i	−0.195894	−	0.339299i
$197$	−0.823054	−	1.42557i	−0.0586402	−	0.101568i	0.835215	−	0.549923i	$-0.185343\pi$
$197$	−0.823054	−	1.42557i	−0.0586402	−	0.101568i	−0.893855	+	0.448356i	$0.852010\pi$
$198$	1.51246	+	2.07496i	0.107486	+	0.147461i
$199$	10.0304	−	5.79107i	0.711038	−	0.410518i	−0.100407	−	0.994946i	$-0.532015\pi$
$199$	10.0304	−	5.79107i	0.711038	−	0.410518i	0.811445	+	0.584428i	$0.198681\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	−2.92291	+	13.8037i	−0.206166	+	0.973641i
$202$	4.31376			0.303515
$203$	−0.723666	+	1.25343i	−0.0507914	+	0.0879732i
$204$	11.2801	−	3.67480i	0.789768	−	0.257287i
$205$	−3.59111	+	6.21998i	−0.250814	+	0.434422i
$206$	−4.74572	+	2.73994i	−0.330650	+	0.190901i
$207$	2.53221	+	23.7388i	0.176001	+	1.64996i
$208$	4.88495	−	2.82033i	0.338710	−	0.195554i
$209$	−0.415230			−0.0287221
$210$	1.58539	+	1.42527i	0.109402	+	0.0983531i
$211$	−6.37798	+	11.0470i	−0.439078	+	0.760505i	−0.997619	−	0.0689719i	$-0.978028\pi$
$211$	−6.37798	+	11.0470i	−0.439078	+	0.760505i	0.558541	+	0.829477i	$0.311361\pi$
$212$	−0.346231	−	0.599690i	−0.0237793	−	0.0411869i
$213$	6.58893	+	1.39519i	0.451466	+	0.0955969i
$214$	−4.63004	+	8.01947i	−0.316503	+	0.548199i
$215$	5.05568			0.344794
$216$	−4.21086	−	3.04445i	−0.286513	−	0.207149i
$217$	4.39092	+	5.26151i	0.298075	+	0.357174i
$218$			20.3111i			1.37564i
$219$	−8.69911	−	1.84202i	−0.587831	−	0.124472i
$220$	0.741226	+	0.427947i	0.0499735	+	0.0288522i
$221$			38.6355i			2.59890i
$222$	14.3857	−	4.68652i	0.965507	−	0.314539i
$223$	−11.4650	−	6.61933i	−0.767755	−	0.443263i	0.0643184	−	0.997929i	$-0.479513\pi$
$223$	−11.4650	−	6.61933i	−0.767755	−	0.443263i	−0.832073	+	0.554666i	$0.812846\pi$
$224$	−1.06593	−	0.615418i	−0.0712208	−	0.0411193i
$225$	2.74252	+	1.21597i	0.182835	+	0.0810644i
$226$	−9.54261	−	16.5283i	−0.634765	−	1.09945i
$227$	−22.0581	+	12.7352i	−1.46405	+	0.845267i	−0.999195	−	0.0401223i	$-0.987225\pi$
$227$	−22.0581	+	12.7352i	−1.46405	+	0.845267i	−0.464850	+	0.885389i	$0.653892\pi$
$228$	0.798962	−	0.260282i	0.0529126	−	0.0172376i
$229$	−14.9883	−	8.65348i	−0.990453	−	0.571838i	−0.0850433	−	0.996377i	$-0.527103\pi$
$229$	−14.9883	−	8.65348i	−0.990453	−	0.571838i	−0.905410	+	0.424539i	$0.860436\pi$
$230$	3.97891	+	6.89167i	0.262361	+	0.454423i
$231$	1.35693	+	1.21988i	0.0892793	+	0.0802624i
$232$		−	1.17589i		−	0.0772012i
$233$			22.8670i			1.49806i	0.662534	+	0.749032i	$0.269481\pi$
$233$			22.8670i			1.49806i	−0.662534	+	0.749032i	$0.730519\pi$
$234$	13.6747	−	9.96766i	0.893946	−	0.651606i
$235$	1.44435	+	2.50169i	0.0942190	+	0.163192i
$236$	−0.639178	−	0.369029i	−0.0416069	−	0.0240218i
$237$	1.85792	+	5.70306i	0.120685	+	0.370453i
$238$	7.30109	−	4.21529i	0.473259	−	0.273236i
$239$	5.26395	+	9.11743i	0.340497	+	0.589758i	0.984525	−	0.175244i	$-0.0560714\pi$
$239$	5.26395	+	9.11743i	0.340497	+	0.589758i	−0.644028	+	0.765002i	$0.722738\pi$
$240$	−1.69448	−	0.358802i	−0.109378	−	0.0231606i
$241$	−22.1828	−	12.8072i	−1.42892	−	0.824987i	−0.431884	−	0.901929i	$-0.642151\pi$
$241$	−22.1828	−	12.8072i	−1.42892	−	0.824987i	−0.997036	+	0.0769422i	$0.975484\pi$
$242$	−8.89187	−	5.13372i	−0.571591	−	0.330008i
$243$	−13.5301	−	7.74192i	−0.867954	−	0.496645i
$244$			6.48651i			0.415256i
$245$	−4.75019	−	2.74252i	−0.303478	−	0.175213i
$246$	2.57699	−	12.1701i	0.164303	−	0.775938i
$247$			2.73652i			0.174120i
$248$	−5.22686	−	1.91832i	−0.331906	−	0.121814i
$249$	0.862950	−	4.07537i	0.0546872	−	0.258266i
$250$	1.00000			0.0632456
$251$	13.6972	−	23.7242i	0.864559	−	1.49746i	−0.00292446	−	0.999996i	$-0.500931\pi$
$251$	13.6972	−	23.7242i	0.864559	−	1.49746i	0.867484	−	0.497465i	$-0.165736\pi$
$252$	−3.37559	−	1.49665i	−0.212642	−	0.0942803i
$253$	3.40552	+	5.89854i	0.214103	+	0.370838i
$254$	−6.07226	+	10.5175i	−0.381007	+	0.659924i
$255$	7.93149	−	8.82254i	0.496689	−	0.552489i
$256$	1.00000			0.0625000
$257$	−11.6461	+	6.72386i	−0.726462	+	0.419423i	−0.817126	−	0.576459i	$-0.804434\pi$
$257$	−11.6461	+	6.72386i	−0.726462	+	0.419423i	0.0906647	+	0.995881i	$0.471101\pi$
$258$	−8.32601	+	2.71241i	−0.518355	+	0.168867i
$259$	9.31118	−	5.37581i	0.578569	−	0.334037i
$260$	2.82033	−	4.88495i	0.174909	−	0.302952i
$261$	−0.374174	−	3.50778i	−0.0231608	−	0.217126i
$262$	4.09057	−	7.08508i	0.252716	−	0.437718i
$263$	−9.48908			−0.585122			−0.292561	−	0.956247i	$-0.594507\pi$
$263$	−9.48908			−0.585122			−0.292561	+	0.956247i	$0.594507\pi$
$264$	−1.45030	−	0.307097i	−0.0892595	−	0.0189005i
$265$	−0.599690	−	0.346231i	−0.0368387	−	0.0212688i
$266$	0.517129	−	0.298565i	0.0317072	−	0.0183062i
$267$	−7.03262	−	6.32235i	−0.430389	−	0.386921i
$268$	−4.07315	−	7.05491i	−0.248807	−	0.430947i
$269$	13.6081	+	23.5699i	0.829700	+	1.43708i	0.898273	+	0.439437i	$0.144822\pi$
$269$	13.6081	+	23.5699i	0.829700	+	1.43708i	−0.0685729	+	0.997646i	$0.521845\pi$
$270$	−5.16893	−	0.531144i	−0.314571	−	0.0323244i
$271$			4.22402i			0.256591i	0.991736	+	0.128296i	$0.0409506\pi$
$271$			4.22402i			0.256591i	−0.991736	+	0.128296i	$0.959049\pi$
$272$	−3.42474	+	5.93182i	−0.207655	+	0.359669i
$273$	8.03947	−	8.94264i	0.486571	−	0.541233i
$274$	−19.3458	+	11.1693i	−1.16872	+	0.674762i
$275$	0.855894			0.0516124
$276$	−10.2502	−	9.21492i	−0.616987	−	0.554673i
$277$			16.7112i			1.00408i	0.864845	+	0.502040i	$0.167417\pi$
$277$			16.7112i			1.00408i	−0.864845	+	0.502040i	$0.832583\pi$
$278$	−13.3668			−0.801687
$279$	−16.2025	−	4.05930i	−0.970020	−	0.243024i
$280$	−1.23084			−0.0735565
$281$			0.335407i			0.0200087i	0.999950	+	0.0100043i	$0.00318453\pi$
$281$			0.335407i			0.0200087i	−0.999950	+	0.0100043i	$0.996815\pi$
$282$	−3.72082	−	3.34503i	−0.221572	−	0.199194i
$283$	−3.13491			−0.186351			−0.0931754	−	0.995650i	$-0.529702\pi$
$283$	−3.13491			−0.186351			−0.0931754	+	0.995650i	$0.529702\pi$
$284$	−3.36751	+	1.94423i	−0.199825	+	0.115369i
$285$	0.561780	−	0.624892i	0.0332770	−	0.0370154i
$286$	2.41390	−	4.18100i	0.142737	−	0.247228i
$287$		−	8.84012i		−	0.521816i
$288$	2.98308	−	0.318204i	0.175779	−	0.0187503i
$289$	−14.9576	−	25.9074i	−0.879860	−	1.52396i
$290$	−0.587947	−	1.01835i	−0.0345254	−	0.0597998i
$291$	−7.15335	−	6.43088i	−0.419337	−	0.376985i
$292$	4.44599	−	2.56690i	0.260182	−	0.150216i
$293$	9.43540	+	5.44753i	0.551222	+	0.318248i	0.749615	−	0.661874i	$-0.230239\pi$
$293$	9.43540	+	5.44753i	0.551222	+	0.318248i	−0.198393	+	0.980123i	$0.563572\pi$
$294$	9.29430	+	1.96805i	0.542054	+	0.114779i
$295$	−0.738059			−0.0429714
$296$	−4.36761	+	7.56493i	−0.253862	+	0.439703i
$297$	−4.42406	−	0.454603i	−0.256710	−	0.0263788i
$298$	−4.45172	+	7.71061i	−0.257882	+	0.446664i
$299$	38.8735	−	22.4436i	2.24811	−	1.29795i
$300$	−1.64686	+	0.536508i	−0.0950817	+	0.0309753i
$301$	−5.38902	+	3.11135i	−0.310618	+	0.179335i
$302$	−9.97617			−0.574064
$303$	−4.99521	+	5.55639i	−0.286968	+	0.319206i
$304$	−0.242571	+	0.420145i	−0.0139124	+	0.0240970i
$305$	3.24325	+	5.61748i	0.185708	+	0.321656i
$306$	−8.32872	+	18.7848i	−0.476121	+	1.07386i
$307$	15.7622	−	27.3009i	0.899595	−	1.55814i	0.0715832	−	0.997435i	$-0.477195\pi$
$307$	15.7622	−	27.3009i	0.899595	−	1.55814i	0.828012	−	0.560710i	$-0.189472\pi$
$308$	−1.05346			−0.0600267
$309$	1.96619	−	9.28555i	0.111853	−	0.528237i
$310$	−5.48575	+	0.952111i	−0.311570	+	0.0540763i
$311$		−	0.515416i		−	0.0292266i	−0.999893	−	0.0146133i	$-0.995348\pi$
$311$		−	0.515416i		−	0.0292266i	0.999893	−	0.0146133i	$-0.00465172\pi$
$312$	−2.02388	+	9.55797i	−0.114580	+	0.541114i
$313$	16.2622	+	9.38897i	0.919192	+	0.530696i	0.883377	−	0.468663i	$-0.155264\pi$
$313$	16.2622	+	9.38897i	0.919192	+	0.530696i	0.0358147	+	0.999358i	$0.488597\pi$
$314$			3.11711i			0.175908i
$315$	−3.67168	+	0.391657i	−0.206876	+	0.0220673i
$316$	−2.99903	−	1.73149i	−0.168709	−	0.0974040i
$317$	−10.1149	−	5.83986i	−0.568111	−	0.327999i	0.188283	−	0.982115i	$-0.439708\pi$
$317$	−10.1149	−	5.83986i	−0.568111	−	0.327999i	−0.756395	+	0.654116i	$0.773041\pi$
$318$	1.17336	+	0.248457i	0.0657990	+	0.0139328i
$319$	−0.503220	−	0.871603i	−0.0281749	−	0.0488004i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−4.96811	−	15.2501i	−0.277293	−	0.851177i
$322$	−8.48251	−	4.89738i	−0.472712	−	0.272920i
$323$	−1.66148	−	2.87777i	−0.0924473	−	0.160123i
$324$	8.79749	−	1.89845i	0.488750	−	0.105470i
$325$		−	5.64065i		−	0.312887i
$326$			1.12144i			0.0621110i
$327$	−26.1620	−	23.5197i	−1.44676	−	1.30064i
$328$	3.59111	+	6.21998i	0.198286	+	0.343441i
$329$	−3.07917	−	1.77776i	−0.169760	−	0.0980110i
$330$	−1.40954	+	0.459194i	−0.0775927	+	0.0252778i
$331$	15.1011	−	8.71862i	0.830031	−	0.479219i	−0.0238321	−	0.999716i	$-0.507587\pi$
$331$	15.1011	−	8.71862i	0.830031	−	0.479219i	0.853863	+	0.520497i	$0.174253\pi$
$332$	1.20254	+	2.08287i	0.0659981	+	0.114312i
$333$	−10.6217	+	23.9566i	−0.582068	+	1.31281i
$334$	8.54044	+	4.93083i	0.467312	+	0.269803i
$335$	−7.05491	−	4.07315i	−0.385451	−	0.222540i
$336$	2.02702	−	0.660353i	0.110583	−	0.0360252i
$337$			20.5120i			1.11736i	0.829384	+	0.558680i	$0.188692\pi$
$337$			20.5120i			1.11736i	−0.829384	+	0.558680i	$0.811308\pi$
$338$	−16.2960	−	9.40849i	−0.886384	−	0.511754i
$339$	32.3395	+	6.84782i	1.75644	+	0.371922i
$340$			6.84947i			0.371465i
$341$	−4.69522	+	0.814906i	−0.254261	+	0.0441297i
$342$	−0.589916	+	1.33051i	−0.0318990	+	0.0719459i
$343$	15.3670			0.829742
$344$	2.52784	−	4.37834i	0.136292	−	0.236064i
$345$	−13.4844	−	2.85528i	−0.725973	−	0.153723i
$346$	5.04608	+	8.74006i	0.271279	+	0.469869i
$347$	7.27245	−	12.5962i	0.390405	−	0.676202i	−0.602098	−	0.798422i	$-0.705668\pi$
$347$	7.27245	−	12.5962i	0.390405	−	0.676202i	0.992503	+	0.122221i	$0.0390015\pi$
$348$	1.51462	+	1.36165i	0.0811923	+	0.0729922i
$349$	12.3867			0.663045			0.331523	−	0.943447i	$-0.392438\pi$
$349$	12.3867			0.663045			0.331523	+	0.943447i	$0.392438\pi$
$350$	−1.06593	+	0.615418i	−0.0569766	+	0.0328955i
$351$	−2.99600	+	29.1562i	−0.159915	+	1.55624i
$352$	0.741226	−	0.427947i	0.0395075	−	0.0228097i
$353$	−5.48052	+	9.49254i	−0.291699	+	0.505237i	−0.974212	−	0.225637i	$-0.927554\pi$
$353$	−5.48052	+	9.49254i	−0.291699	+	0.505237i	0.682513	+	0.730874i	$0.260887\pi$
$354$	1.21548	−	0.395974i	0.0646021	−	0.0210458i
$355$	−1.94423	+	3.36751i	−0.103189	+	0.178729i
$356$	5.45985			0.289371
$357$	−3.02491	+	14.2854i	−0.160095	+	0.756065i
$358$	−21.2018	−	12.2409i	−1.12055	−	0.646951i
$359$	8.55681	−	4.94028i	0.451611	−	0.260738i	−0.256899	−	0.966438i	$-0.582701\pi$
$359$	8.55681	−	4.94028i	0.451611	−	0.260738i	0.708510	+	0.705700i	$0.249367\pi$
$360$	2.42432	−	1.76711i	0.127773	−	0.0931349i
$361$	9.38232	+	16.2507i	0.493806	+	0.855298i
$362$	−7.50878	−	13.0056i	−0.394653	−	0.683558i
$363$	16.9091	−	5.50857i	0.887497	−	0.289125i
$364$			6.94272i			0.363897i
$365$	2.56690	−	4.44599i	0.134357	−	0.232714i
$366$	−8.35502	−	7.51119i	−0.436724	−	0.392616i
$367$	−16.2158	+	9.36221i	−0.846459	+	0.488703i	−0.859455	−	0.511212i	$-0.829197\pi$
$367$	−16.2158	+	9.36221i	−0.846459	+	0.488703i	0.0129954	+	0.999916i	$0.495863\pi$
$368$	7.95781			0.414830
$369$	12.6918	+	17.4120i	0.660707	+	0.906431i
$370$			8.73523i			0.454123i
$371$	0.852307			0.0442496
$372$	8.52347	−	4.51115i	0.441921	−	0.233892i
$373$	−7.24267			−0.375011			−0.187506	−	0.982264i	$-0.560040\pi$
$373$	−7.24267			−0.375011			−0.187506	+	0.982264i	$0.560040\pi$
$374$			5.86242i			0.303139i
$375$	−1.15797	+	1.28806i	−0.0597974	+	0.0665152i
$376$	2.88870			0.148973
$377$	−5.74418	+	3.31640i	−0.295840	+	0.170803i
$378$	5.83662	−	2.61489i	0.300203	−	0.134495i
$379$	12.2266	−	21.1771i	0.628038	−	1.08779i	−0.359907	−	0.932988i	$-0.617192\pi$
$379$	12.2266	−	21.1771i	0.628038	−	1.08779i	0.987945	−	0.154805i	$-0.0494750\pi$
$380$			0.485142i			0.0248872i
$381$	−6.51563	−	20.0004i	−0.333806	−	1.02465i
$382$	−6.12422	−	10.6075i	−0.313342	−	0.542725i
$383$	−13.4536	−	23.3023i	−0.687446	−	1.19069i	−0.972661	−	0.232228i	$-0.925399\pi$
$383$	−13.4536	−	23.3023i	−0.687446	−	1.19069i	0.285216	−	0.958463i	$-0.407935\pi$
$384$	−1.15797	+	1.28806i	−0.0590925	+	0.0657311i
$385$	−0.912327	+	0.526732i	−0.0464965	+	0.0268448i
$386$	21.6235	+	12.4843i	1.10061	+	0.635435i
$387$	6.14753	−	13.8653i	0.312496	−	0.704813i
$388$	5.55358			0.281940
$389$	1.33226	−	2.30754i	0.0675481	−	0.116997i	−0.830273	−	0.557356i	$-0.811816\pi$
$389$	1.33226	−	2.30754i	0.0675481	−	0.116997i	0.897821	+	0.440360i	$0.145149\pi$
$390$	3.02626	+	9.28939i	0.153240	+	0.470386i
$391$	−27.2534	+	47.2043i	−1.37826	+	2.38722i
$392$	−4.75019	+	2.74252i	−0.239921	+	0.138518i
$393$	4.38925	+	13.4732i	0.221408	+	0.679635i
$394$	−1.42557	+	0.823054i	−0.0718192	+	0.0414649i
$395$	−3.46298			−0.174242
$396$	2.07496	−	1.51246i	0.104271	−	0.0760040i
$397$	9.43442	−	16.3409i	0.473500	−	0.820126i	−0.526040	−	0.850460i	$-0.676324\pi$
$397$	9.43442	−	16.3409i	0.473500	−	0.820126i	0.999540	+	0.0303340i	$0.00965710\pi$
$398$	−5.79107	−	10.0304i	−0.290280	−	0.502780i
$399$	−0.214251	+	1.01182i	−0.0107260	+	0.0506546i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	6.85565			0.342355			0.171177	−	0.985240i	$-0.445243\pi$
$401$	6.85565			0.342355			0.171177	+	0.985240i	$0.445243\pi$
$402$	13.8037	+	2.92291i	0.688468	+	0.145782i
$403$	5.37053	+	30.9432i	0.267525	+	1.54139i
$404$		−	4.31376i		−	0.214618i
$405$	6.66963	−	6.04285i	0.331416	−	0.300272i
$406$	1.25343	+	0.723666i	0.0622065	+	0.0359149i
$407$			7.47643i			0.370593i
$408$	−3.67480	−	11.2801i	−0.181930	−	0.558450i
$409$	−10.1400	−	5.85435i	−0.501393	−	0.289479i	0.227896	−	0.973686i	$-0.426815\pi$
$409$	−10.1400	−	5.85435i	−0.501393	−	0.289479i	−0.729289	+	0.684206i	$0.760149\pi$
$410$	6.21998	+	3.59111i	0.307183	+	0.177352i
$411$	8.01514	−	37.8523i	0.395358	−	1.86712i
$412$	2.73994	+	4.74572i	0.134987	+	0.233805i
$413$	0.786722	−	0.454214i	0.0387121	−	0.0223504i
$414$	23.7388	−	2.53221i	1.16670	−	0.124451i
$415$	2.08287	+	1.20254i	0.102244	+	0.0590305i
$416$	−2.82033	−	4.88495i	−0.138278	−	0.239504i
$417$	15.4784	−	17.2172i	0.757978	−	0.843132i
$418$			0.415230i			0.0203096i
$419$		−	37.9695i		−	1.85493i	−0.373907	−	0.927466i	$-0.621982\pi$
$419$		−	37.9695i		−	1.85493i	0.373907	−	0.927466i	$-0.378018\pi$
$420$	1.42527	−	1.58539i	0.0695462	−	0.0773592i
$421$	16.6660	+	28.8664i	0.812253	+	1.40686i	0.911284	+	0.411778i	$0.135092\pi$
$421$	16.6660	+	28.8664i	0.812253	+	1.40686i	−0.0990314	+	0.995084i	$0.531574\pi$
$422$	11.0470	+	6.37798i	0.537758	+	0.310475i
$423$	8.61722	−	0.919196i	0.418983	−	0.0446928i
$424$	−0.599690	+	0.346231i	−0.0291235	+	0.0168145i
$425$	3.42474	+	5.93182i	0.166124	+	0.287735i
$426$	1.39519	−	6.58893i	0.0675972	−	0.319235i
$427$	−6.91419	−	3.99191i	−0.334601	−	0.193182i
$428$	8.01947	+	4.63004i	0.387635	+	0.223801i
$429$	2.59015	+	7.95073i	0.125054	+	0.383865i
$430$		−	5.05568i		−	0.243806i
$431$	21.8729	+	12.6283i	1.05358	+	0.608286i	0.923650	−	0.383237i	$-0.125191\pi$
$431$	21.8729	+	12.6283i	1.05358	+	0.608286i	0.129932	+	0.991523i	$0.458524\pi$
$432$	−3.04445	+	4.21086i	−0.146476	+	0.202595i
$433$		−	27.2143i		−	1.30783i	−0.756566	−	0.653917i	$-0.773124\pi$
$433$		−	27.2143i		−	1.30783i	0.756566	−	0.653917i	$-0.226876\pi$
$434$	5.26151	−	4.39092i	0.252560	−	0.210771i
$435$	1.99253	+	0.421913i	0.0955344	+	0.0202292i
$436$	20.3111			0.972727
$437$	−1.93033	+	3.34344i	−0.0923404	+	0.159938i
$438$	−1.84202	+	8.69911i	−0.0880149	+	0.415659i
$439$	2.74021	+	4.74619i	0.130783	+	0.226523i	0.923979	−	0.382444i	$-0.124917\pi$
$439$	2.74021	+	4.74619i	0.130783	+	0.226523i	−0.793195	+	0.608967i	$0.791584\pi$
$440$	0.427947	−	0.741226i	0.0204016	−	0.0353366i
$441$	−13.2975	+	9.69268i	−0.633214	+	0.461556i
$442$	38.6355			1.83770
$443$	19.8597	−	11.4660i	0.943563	−	0.544767i	0.0524878	−	0.998622i	$-0.483285\pi$
$443$	19.8597	−	11.4660i	0.943563	−	0.544767i	0.891076	+	0.453855i	$0.149952\pi$
$444$	−4.68652	−	14.3857i	−0.222412	−	0.682716i
$445$	4.72837	−	2.72992i	0.224146	−	0.129411i
$446$	−6.61933	+	11.4650i	−0.313435	+	0.542884i
$447$	−4.77677	−	14.6628i	−0.225934	−	0.693525i
$448$	−0.615418	+	1.06593i	−0.0290758	+	0.0503607i
$449$	−10.9265			−0.515655			−0.257828	−	0.966191i	$-0.583007\pi$
$449$	−10.9265			−0.515655			−0.257828	+	0.966191i	$0.583007\pi$
$450$	1.21597	−	2.74252i	0.0573212	−	0.129284i
$451$	5.32364	+	3.07361i	0.250681	+	0.144731i
$452$	−16.5283	+	9.54261i	−0.777425	+	0.448847i
$453$	11.5521	−	12.8499i	0.542766	−	0.603742i
$454$	12.7352	+	22.0581i	0.597694	+	1.03524i
$455$	3.47136	+	6.01257i	0.162740	+	0.281874i
$456$	−0.260282	−	0.798962i	−0.0121888	−	0.0374148i
$457$			37.4970i			1.75404i	0.480456	+	0.877019i	$0.340471\pi$
$457$			37.4970i			1.75404i	−0.480456	+	0.877019i	$0.659529\pi$
$458$	−8.65348	+	14.9883i	−0.404351	+	0.700356i
$459$	−14.5516	−	32.4802i	−0.679210	−	1.51605i
$460$	6.89167	−	3.97891i	0.321326	−	0.185518i
$461$	−13.1893			−0.614288			−0.307144	−	0.951663i	$-0.599373\pi$
$461$	−13.1893			−0.614288			−0.307144	+	0.951663i	$0.599373\pi$
$462$	1.21988	−	1.35693i	0.0567541	−	0.0631300i
$463$			19.5842i			0.910154i	0.890452	+	0.455077i	$0.150388\pi$
$463$			19.5842i			0.910154i	−0.890452	+	0.455077i	$0.849612\pi$
$464$	−1.17589			−0.0545895
$465$	5.12597	−	8.16850i	0.237711	−	0.378805i
$466$	22.8670			1.05929
$467$		−	15.0537i		−	0.696603i	−0.937383	−	0.348301i	$-0.886759\pi$
$467$		−	15.0537i		−	0.696603i	0.937383	−	0.348301i	$-0.113241\pi$
$468$	−9.96766	−	13.6747i	−0.460755	−	0.632115i
$469$	10.0268			0.462993
$470$	2.50169	−	1.44435i	0.115394	−	0.0666229i
$471$	−4.01502	−	3.60952i	−0.185002	−	0.166318i
$472$	−0.369029	+	0.639178i	−0.0169860	+	0.0294205i
$473$		−	4.32712i		−	0.198961i
$474$	5.70306	−	1.85792i	0.261950	−	0.0853370i
$475$	0.242571	+	0.420145i	0.0111299	+	0.0192776i
$476$	−4.21529	−	7.30109i	−0.193207	−	0.334645i
$477$	−1.67875	+	1.22366i	−0.0768647	+	0.0560275i
$478$	9.11743	−	5.26395i	0.417022	−	0.240768i
$479$	−31.1132	−	17.9632i	−1.42160	−	0.820760i	−0.425162	−	0.905117i	$-0.639783\pi$
$479$	−31.1132	−	17.9632i	−1.42160	−	0.820760i	−0.996436	+	0.0843575i	$0.973116\pi$
$480$	−0.358802	+	1.69448i	−0.0163770	+	0.0773421i
$481$	49.2724			2.24663
$482$	−12.8072	+	22.1828i	−0.583354	+	1.01040i
$483$	16.1306	−	5.25497i	0.733969	−	0.239109i
$484$	−5.13372	+	8.89187i	−0.233351	+	0.404176i
$485$	4.80954	−	2.77679i	0.218390	−	0.126087i
$486$	−7.74192	+	13.5301i	−0.351181	+	0.613736i
$487$	22.0726	−	12.7436i	1.00021	−	0.577470i	0.0918972	−	0.995769i	$-0.470707\pi$
$487$	22.0726	−	12.7436i	1.00021	−	0.577470i	0.908309	+	0.418299i	$0.137374\pi$
$488$	6.48651			0.293630
$489$	−1.44449	−	1.29860i	−0.0653220	−	0.0587247i
$490$	−2.74252	+	4.75019i	−0.123895	+	0.214592i
$491$	7.24410	+	12.5471i	0.326922	+	0.566245i	0.981899	−	0.189403i	$-0.0606554\pi$
$491$	7.24410	+	12.5471i	0.326922	+	0.566245i	−0.654978	+	0.755648i	$0.727322\pi$
$492$	−12.1701	−	2.57699i	−0.548671	−	0.116180i
$493$	4.02712	−	6.97518i	0.181373	−	0.314146i
$494$	2.73652			0.123122
$495$	1.04074	−	2.34731i	0.0467777	−	0.105504i
$496$	−1.91832	+	5.22686i	−0.0861353	+	0.234693i
$497$		−	4.78606i		−	0.214684i
$498$	−4.07537	−	0.862950i	−0.182622	−	0.0386697i
$499$	16.0182	+	9.24809i	0.717071	+	0.414001i	0.813674	−	0.581322i	$-0.197464\pi$
$499$	16.0182	+	9.24809i	0.717071	+	0.414001i	−0.0966024	+	0.995323i	$0.530798\pi$
$500$		−	1.00000i		−	0.0447214i
$501$	−16.2408	+	5.29085i	−0.725585	+	0.236378i
$502$	−23.7242	−	13.6972i	−1.05886	−	0.611336i
$503$	−12.2809	−	7.09036i	−0.547576	−	0.316143i	0.200568	−	0.979680i	$-0.435721\pi$
$503$	−12.2809	−	7.09036i	−0.547576	−	0.316143i	−0.748144	+	0.663537i	$0.769055\pi$
$504$	−1.49665	+	3.37559i	−0.0666663	+	0.150361i
$505$	−2.15688	−	3.73583i	−0.0959800	−	0.166242i
$506$	5.89854	−	3.40552i	0.262222	−	0.151394i
$507$	30.9890	−	10.0955i	1.37627	−	0.448355i
$508$	10.5175	+	6.07226i	0.466637	+	0.269413i
$509$	9.88856	+	17.1275i	0.438303	+	0.759162i	0.997559	−	0.0698326i	$-0.0222465\pi$
$509$	9.88856	+	17.1275i	0.438303	+	0.759162i	−0.559256	+	0.828995i	$0.688913\pi$
$510$	−8.82254	−	7.93149i	−0.390669	−	0.351212i
$511$			6.31885i			0.279530i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.03068	−	2.30054i	−0.0455054	−	0.101571i
$514$	6.72386	+	11.6461i	0.296577	+	0.513686i
$515$	4.74572	+	2.73994i	0.209121	+	0.120736i
$516$	2.71241	+	8.32601i	0.119407	+	0.366532i
$517$	2.14118	−	1.23621i	0.0941690	−	0.0543685i
$518$	−5.37581	−	9.31118i	−0.236200	−	0.409110i
$519$	−17.1010	−	3.62109i	−0.750649	−	0.158948i
$520$	−4.88495	−	2.82033i	−0.214219	−	0.123680i
$521$	20.5169	+	11.8454i	0.898860	+	0.518957i	0.876830	−	0.480800i	$-0.159654\pi$
$521$	20.5169	+	11.8454i	0.898860	+	0.518957i	0.0220296	+	0.999757i	$0.492987\pi$
$522$	−3.50778	+	0.374174i	−0.153531	+	0.0163771i
$523$			35.6405i			1.55845i	0.626744	+	0.779225i	$0.284387\pi$
$523$			35.6405i			1.55845i	−0.626744	+	0.779225i	$0.715613\pi$
$524$	−7.08508	−	4.09057i	−0.309513	−	0.178697i
$525$	0.441626	−	2.08563i	0.0192742	−	0.0910242i
$526$			9.48908i			0.413744i
$527$	−24.4350	−	29.2797i	−1.06441	−	1.27545i
$528$	−0.307097	+	1.45030i	−0.0133647	+	0.0631160i
$529$	40.3268			1.75334
$530$	−0.346231	+	0.599690i	−0.0150393	+	0.0260489i
$531$	−0.897454	+	2.02414i	−0.0389462	+	0.0878403i
$532$	−0.298565	−	0.517129i	−0.0129444	−	0.0224204i
$533$	20.2562	−	35.0848i	0.877393	−	1.51969i
$534$	−6.32235	+	7.03262i	−0.273595	+	0.304331i
$535$	9.26008			0.400348
$536$	−7.05491	+	4.07315i	−0.304726	+	0.175933i
$537$	40.3181	−	13.1347i	1.73986	−	0.566802i
$538$	23.5699	−	13.6081i	1.01617	−	0.586687i
$539$	−2.34731	+	4.06566i	−0.101106	+	0.175120i
$540$	−0.531144	+	5.16893i	−0.0228568	+	0.222436i
$541$	15.6226	−	27.0591i	0.671668	−	1.16336i	−0.305763	−	0.952108i	$-0.598911\pi$
$541$	15.6226	−	27.0591i	0.671668	−	1.16336i	0.977431	−	0.211255i	$-0.0677552\pi$
$542$	4.22402			0.181437
$543$	25.4469	+	5.38833i	1.09203	+	0.231235i
$544$	5.93182	+	3.42474i	0.254324	+	0.146834i
$545$	17.5900	−	10.1556i	0.753471	−	0.435017i
$546$	−8.94264	−	8.03947i	−0.382710	−	0.344057i
$547$	−13.5169	−	23.4119i	−0.577940	−	1.00102i	−0.995715	−	0.0924712i	$-0.970523\pi$
$547$	−13.5169	−	23.4119i	−0.577940	−	1.00102i	0.417775	−	0.908550i	$-0.362810\pi$
$548$	11.1693	+	19.3458i	0.477129	+	0.826412i
$549$	19.3498	−	2.06403i	0.825827	−	0.0880907i
$550$		−	0.855894i		−	0.0364955i
$551$	0.285238	−	0.494046i	0.0121515	−	0.0210471i
$552$	−9.21492	+	10.2502i	−0.392213	+	0.436276i
$553$	3.69131	−	2.13118i	0.156971	−	0.0906270i
$554$	16.7112			0.709991
$555$	−11.2515	−	10.1151i	−0.477600	−	0.429364i
$556$			13.3668i			0.566878i
$557$	2.95495			0.125205			0.0626025	−	0.998039i	$-0.480060\pi$
$557$	2.95495			0.125205			0.0626025	+	0.998039i	$0.480060\pi$
$558$	−4.05930	+	16.2025i	−0.171844	+	0.685908i
$559$	−28.5173			−1.20615
$560$			1.23084i			0.0520123i
$561$	−7.55116	−	6.78852i	−0.318810	−	0.286611i
$562$	0.335407			0.0141483
$563$	38.1155	−	22.0060i	1.60638	−	0.927441i	0.616204	−	0.787587i	$-0.288670\pi$
$563$	38.1155	−	22.0060i	1.60638	−	0.927441i	0.990172	−	0.139855i	$-0.0446635\pi$
$564$	−3.34503	+	3.72082i	−0.140851	+	0.156675i
$565$	−9.54261	+	16.5283i	−0.401461	+	0.695350i
$566$			3.13491i			0.131770i
$567$	−3.39051	+	10.5459i	−0.142388	+	0.442886i
$568$	1.94423	+	3.36751i	0.0815783	+	0.141298i
$569$	−18.4180	−	31.9010i	−0.772124	−	1.33736i	−0.936397	−	0.350943i	$-0.885861\pi$
$569$	−18.4180	−	31.9010i	−0.772124	−	1.33736i	0.164272	−	0.986415i	$-0.447472\pi$
$570$	−0.624892	−	0.561780i	−0.0261739	−	0.0235304i
$571$	−33.3623	+	19.2617i	−1.39617	+	0.806078i	−0.993989	−	0.109482i	$-0.965081\pi$
$571$	−33.3623	+	19.2617i	−1.39617	+	0.806078i	−0.402180	+	0.915561i	$0.631747\pi$
$572$	−4.18100	−	2.41390i	−0.174816	−	0.100930i
$573$	20.7547	+	4.39476i	0.867041	+	0.183594i
$574$	−8.84012			−0.368980
$575$	3.97891	−	6.89167i	0.165932	−	0.287403i
$576$	−0.318204	−	2.98308i	−0.0132585	−	0.124295i
$577$	−13.6099	+	23.5731i	−0.566588	+	0.981360i	0.430312	+	0.902680i	$0.358404\pi$
$577$	−13.6099	+	23.5731i	−0.566588	+	0.981360i	−0.996900	+	0.0786795i	$0.974930\pi$
$578$	−25.9074	+	14.9576i	−1.07760	+	0.622155i
$579$	−41.1199	+	13.3959i	−1.70889	+	0.556714i
$580$	−1.01835	+	0.587947i	−0.0422848	+	0.0244132i
$581$	−2.96027			−0.122813
$582$	−6.43088	+	7.15335i	−0.266569	+	0.296516i
$583$	−0.296337	+	0.513271i	−0.0122730	+	0.0212575i
$584$	−2.56690	−	4.44599i	−0.106219	−	0.183977i
$585$	−15.4696	−	6.85884i	−0.639590	−	0.283578i
$586$	5.44753	−	9.43540i	0.225035	−	0.389773i
$587$	21.6442			0.893354			0.446677	−	0.894695i	$-0.352607\pi$
$587$	21.6442			0.893354			0.446677	+	0.894695i	$0.352607\pi$
$588$	1.96805	−	9.29430i	0.0811608	−	0.383290i
$589$	−1.73071	−	2.07386i	−0.0713126	−	0.0854518i
$590$			0.738059i			0.0303854i
$591$	0.590627	−	2.78930i	0.0242951	−	0.114736i
$592$	7.56493	+	4.36761i	0.310917	+	0.179508i
$593$		−	18.3513i		−	0.753598i	−0.926295	−	0.376799i	$-0.877025\pi$
$593$		−	18.3513i		−	0.753598i	0.926295	−	0.376799i	$-0.122975\pi$
$594$	−0.454603	+	4.42406i	−0.0186526	+	0.181521i
$595$	−7.30109	−	4.21529i	−0.299315	−	0.172810i
$596$	7.71061	+	4.45172i	0.315839	+	0.182350i
$597$	19.6257	+	4.15570i	0.803226	+	0.170081i
$598$	−22.4436	−	38.8735i	−0.917789	−	1.58966i
$599$	1.04365	−	0.602553i	0.0426425	−	0.0246197i	−0.478527	−	0.878073i	$-0.658829\pi$
$599$	1.04365	−	0.602553i	0.0426425	−	0.0246197i	0.521170	+	0.853453i	$0.325496\pi$
$600$	0.536508	+	1.64686i	0.0219028	+	0.0672329i
$601$	−17.9323	−	10.3532i	−0.731473	−	0.422316i	0.0874879	−	0.996166i	$-0.472116\pi$
$601$	−17.9323	−	10.3532i	−0.731473	−	0.422316i	−0.818961	+	0.573850i	$0.805449\pi$
$602$	3.11135	+	5.38902i	0.126809	+	0.219640i
$603$	−19.7492	+	14.3954i	−0.804251	+	0.586227i
$604$			9.97617i			0.405925i
$605$			10.2674i			0.417431i
$606$	5.55639	+	4.99521i	0.225713	+	0.202917i
$607$	−11.8171	−	20.4677i	−0.479639	−	0.830760i	0.520088	−	0.854113i	$-0.325899\pi$
$607$	−11.8171	−	20.4677i	−0.479639	−	0.830760i	−0.999727	+	0.0233530i	$0.992566\pi$
$608$	0.420145	+	0.242571i	0.0170391	+	0.00983755i
$609$	−2.38356	+	0.776505i	−0.0965866	+	0.0314656i
$610$	5.61748	−	3.24325i	0.227445	−	0.131316i
$611$	−8.14708	−	14.1112i	−0.329596	−	0.570876i
$612$	18.7848	+	8.32872i	0.759331	+	0.336669i
$613$	10.2915	+	5.94178i	0.415668	+	0.239986i	0.693222	−	0.720724i	$-0.256190\pi$
$613$	10.2915	+	5.94178i	0.415668	+	0.239986i	−0.277554	+	0.960710i	$0.589524\pi$
$614$	−27.3009	−	15.7622i	−1.10177	−	0.636110i
$615$	−11.8281	+	3.85332i	−0.476956	+	0.155381i
$616$			1.05346i			0.0424453i
$617$	13.2775	+	7.66578i	0.534533	+	0.308613i	0.742860	−	0.669447i	$-0.233469\pi$
$617$	13.2775	+	7.66578i	0.534533	+	0.308613i	−0.208328	+	0.978059i	$0.566802\pi$
$618$	−9.28555	−	1.96619i	−0.373520	−	0.0790919i
$619$		−	27.7807i		−	1.11660i	−0.829639	−	0.558300i	$-0.811454\pi$
$619$		−	27.7807i		−	1.11660i	0.829639	−	0.558300i	$-0.188546\pi$
$620$	0.952111	+	5.48575i	0.0382377	+	0.220313i
$621$	−24.2272	+	33.5092i	−0.972203	+	1.34468i
$622$	−0.515416			−0.0206663
$623$	−3.36009	+	5.81984i	−0.134619	+	0.233167i
$624$	9.55797	+	2.02388i	0.382625	+	0.0810200i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	9.38897	−	16.2622i	0.375259	−	0.649967i
$627$	−0.534842	−	0.480825i	−0.0213595	−	0.0192023i
$628$	3.11711			0.124386
$629$	−51.8158	+	29.9158i	−2.06603	+	1.19282i
$630$	0.391657	+	3.67168i	0.0156040	+	0.146283i
$631$	17.3045	−	9.99073i	0.688880	−	0.397725i	−0.114313	−	0.993445i	$-0.536467\pi$
$631$	17.3045	−	9.99073i	0.688880	−	0.397725i	0.803192	+	0.595720i	$0.203133\pi$
$632$	−1.73149	+	2.99903i	−0.0688750	+	0.119295i
$633$	−21.0073	+	6.84367i	−0.834966	+	0.272011i
$634$	−5.83986	+	10.1149i	−0.231930	+	0.401715i
$635$	12.1445			0.481940
$636$	0.248457	−	1.17336i	0.00985196	−	0.0465269i
$637$	26.7942	+	15.4696i	1.06162	+	0.612929i
$638$	−0.871603	+	0.503220i	−0.0345071	+	0.0199227i
$639$	6.87136	+	9.42689i	0.271827	+	0.372922i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	5.80324	+	10.0515i	0.229214	+	0.397011i	0.957575	−	0.288183i	$-0.0930510\pi$
$641$	5.80324	+	10.0515i	0.229214	+	0.397011i	−0.728361	+	0.685193i	$0.759718\pi$
$642$	−15.2501	+	4.96811i	−0.601873	+	0.196076i
$643$			20.3099i			0.800946i	0.916309	+	0.400473i	$0.131154\pi$
$643$			20.3099i			0.800946i	−0.916309	+	0.400473i	$0.868846\pi$
$644$	−4.89738	+	8.48251i	−0.192984	+	0.334258i
$645$	6.51202	+	5.85433i	0.256411	+	0.230514i
$646$	−2.87777	+	1.66148i	−0.113224	+	0.0653701i
$647$	−6.80419			−0.267500			−0.133750	−	0.991015i	$-0.542702\pi$
$647$	−6.80419			−0.267500			−0.133750	+	0.991015i	$0.542702\pi$
$648$	−1.89845	−	8.79749i	−0.0745783	−	0.345598i
$649$			0.631700i			0.0247964i
$650$	−5.64065			−0.221245
$651$	−0.436905	+	11.8617i	−0.0171237	+	0.464897i
$652$	1.12144			0.0439191
$653$			12.8192i			0.501655i	0.968032	+	0.250828i	$0.0807027\pi$
$653$			12.8192i			0.501655i	−0.968032	+	0.250828i	$0.919297\pi$
$654$	−23.5197	+	26.1620i	−0.919694	+	1.02302i
$655$	−8.18115			−0.319664
$656$	6.21998	−	3.59111i	0.242849	−	0.140209i
$657$	−9.07198	−	12.4459i	−0.353932	−	0.485563i
$658$	−1.77776	+	3.07917i	−0.0693042	+	0.120038i
$659$			14.6238i			0.569664i	0.958577	+	0.284832i	$0.0919378\pi$
$659$			14.6238i			0.569664i	−0.958577	+	0.284832i	$0.908062\pi$
$660$	0.459194	+	1.40954i	0.0178741	+	0.0548663i
$661$	−18.4963	−	32.0366i	−0.719424	−	1.24608i	−0.961228	−	0.275754i	$-0.911073\pi$
$661$	−18.4963	−	32.0366i	−0.719424	−	1.24608i	0.241804	−	0.970325i	$-0.422261\pi$
$662$	−8.71862	−	15.1011i	−0.338859	−	0.586921i
$663$	−44.7388	+	49.7649i	−1.73751	+	1.93271i
$664$	2.08287	−	1.20254i	0.0808309	−	0.0466677i
$665$	−0.517129	−	0.298565i	−0.0200534	−	0.0115778i
$666$	23.9566	+	10.6217i	0.928298	+	0.411584i
$667$	−9.35754			−0.362326
$668$	4.93083	−	8.54044i	0.190779	−	0.330440i
$669$	−7.10265	−	21.8023i	−0.274604	−	0.842925i
$670$	−4.07315	+	7.05491i	−0.157360	+	0.272555i
$671$	4.80797	−	2.77588i	0.185610	−	0.107162i
$672$	−0.660353	−	2.02702i	−0.0254737	−	0.0781939i
$673$	−10.5681	+	6.10149i	−0.407370	+	0.235195i	−0.689659	−	0.724134i	$-0.742240\pi$
$673$	−10.5681	+	6.10149i	−0.407370	+	0.235195i	0.282289	+	0.959329i	$0.408906\pi$
$674$	20.5120			0.790092
$675$	2.12448	+	4.74200i	0.0817714	+	0.182520i
$676$	−9.40849	+	16.2960i	−0.361865	+	0.626768i
$677$	8.94985	+	15.5016i	0.343971	+	0.595774i	0.985166	−	0.171603i	$-0.0548946\pi$
$677$	8.94985	+	15.5016i	0.343971	+	0.595774i	−0.641196	+	0.767377i	$0.721561\pi$
$678$	6.84782	−	32.3395i	0.262989	−	1.24199i
$679$	−3.41777	+	5.91975i	−0.131162	+	0.227179i
$680$	6.84947			0.262665
$681$	−43.1592	−	9.13885i	−1.65386	−	0.350202i
$682$	0.814906	+	4.69522i	0.0312044	+	0.179789i
$683$			0.0428554i			0.00163982i	1.00000		0.000819909i	$0.000260985\pi$
$683$			0.0428554i			0.00163982i	−1.00000		0.000819909i	$0.999739\pi$
$684$	1.33051	+	0.589916i	0.0508734	+	0.0225560i
$685$	19.3458	+	11.1693i	0.739165	+	0.426757i
$686$		−	15.3670i		−	0.586716i
$687$	−9.28533	−	28.5022i	−0.354257	−	1.08743i
$688$	−4.37834	−	2.52784i	−0.166923	−	0.0963729i
$689$	3.38264	+	1.95297i	0.128868	+	0.0744023i
$690$	−2.85528	+	13.4844i	−0.108699	+	0.513341i
$691$	−3.25896	−	5.64469i	−0.123977	−	0.214734i	0.797356	−	0.603510i	$-0.206232\pi$
$691$	−3.25896	−	5.64469i	−0.123977	−	0.214734i	−0.921333	+	0.388775i	$0.872898\pi$
$692$	8.74006	−	5.04608i	0.332247	−	0.191823i
$693$	0.335217	+	3.14257i	0.0127338	+	0.119376i
$694$	−12.5962	−	7.27245i	−0.478147	−	0.276058i
$695$	6.68339	+	11.5760i	0.253516	+	0.439102i
$696$	1.36165	−	1.51462i	0.0516133	−	0.0574116i
$697$			49.1944i			1.86337i
$698$		−	12.3867i		−	0.468844i
$699$	−26.4793	+	29.4540i	−1.00154	+	1.11405i
$700$	0.615418	+	1.06593i	0.0232606	+	0.0402885i
$701$	7.28410	+	4.20548i	0.275117	+	0.158839i	0.631211	−	0.775611i	$-0.282558\pi$
$701$	7.28410	+	4.20548i	0.275117	+	0.158839i	−0.356094	+	0.934450i	$0.615892\pi$
$702$	29.1562	+	2.99600i	1.10043	+	0.113077i
$703$	−3.67006	+	2.11891i	−0.138419	+	0.0799163i
$704$	−0.427947	−	0.741226i	−0.0161289	−	0.0279360i
$705$	−1.03647	+	4.89485i	−0.0390358	+	0.184351i
$706$	9.49254	+	5.48052i	0.357256	+	0.206262i
$707$	4.59819	+	2.65477i	0.172933	+	0.0998427i
$708$	−0.395974	−	1.21548i	−0.0148816	−	0.0456806i
$709$		−	33.2406i		−	1.24838i	−0.781274	−	0.624188i	$-0.785430\pi$
$709$		−	33.2406i		−	1.24838i	0.781274	−	0.624188i	$-0.214570\pi$
$710$	3.36751	+	1.94423i	0.126380	+	0.0729658i
$711$	−4.21087	+	9.49730i	−0.157920	+	0.356177i
$712$		−	5.45985i		−	0.204616i
$713$	−15.2657	+	41.5944i	−0.571704	+	1.55772i
$714$	14.2854	+	3.02491i	0.534619	+	0.113204i
$715$	−4.82780			−0.180550
$716$	−12.2409	+	21.2018i	−0.457463	+	0.792349i
$717$	−3.77743	+	17.8393i	−0.141071	+	0.666222i
$718$	−4.94028	−	8.55681i	−0.184370	−	0.319337i
$719$	−19.2029	+	33.2604i	−0.716148	+	1.24040i	0.246368	+	0.969176i	$0.420763\pi$
$719$	−19.2029	+	33.2604i	−0.716148	+	1.24040i	−0.962515	+	0.271228i	$0.912570\pi$
$720$	−1.76711	−	2.42432i	−0.0658563	−	0.0903490i
$721$	−6.74484			−0.251191
$722$	16.2507	−	9.38232i	0.604787	−	0.349174i
$723$	−13.7424	−	42.1836i	−0.511085	−	1.56882i
$724$	−13.0056	+	7.50878i	−0.483349	+	0.279062i
$725$	−0.587947	+	1.01835i	−0.0218358	+	0.0378207i
$726$	−5.50857	−	16.9091i	−0.204442	−	0.627555i
$727$	21.7450	−	37.6635i	0.806478	−	1.39686i	−0.108811	−	0.994062i	$-0.534704\pi$
$727$	21.7450	−	37.6635i	0.806478	−	1.39686i	0.915289	−	0.402798i	$-0.131962\pi$
$728$	6.94272			0.257314
$729$	−8.46263	−	25.6395i	−0.313431	−	0.949611i
$730$	−4.44599	−	2.56690i	−0.164554	−	0.0950051i
$731$	29.9893	−	17.3143i	1.10920	−	0.640394i
$732$	−7.51119	+	8.35502i	−0.277622	+	0.308810i
$733$	17.5447	+	30.3883i	0.648029	+	1.12242i	0.983593	+	0.180401i	$0.0577396\pi$
$733$	17.5447	+	30.3883i	0.648029	+	1.12242i	−0.335565	+	0.942017i	$0.608927\pi$
$734$	9.36221	+	16.2158i	0.345566	+	0.598537i
$735$	−2.94277	−	9.03312i	−0.108546	−	0.333192i
$736$		−	7.95781i		−	0.293329i
$737$	−3.48619	+	6.03825i	−0.128415	+	0.222422i
$738$	17.4120	−	12.6918i	0.640944	−	0.467190i
$739$	17.4495	−	10.0745i	0.641889	−	0.370595i	−0.143453	−	0.989657i	$-0.545821\pi$
$739$	17.4495	−	10.0745i	0.641889	−	0.370595i	0.785342	+	0.619062i	$0.212487\pi$
$740$	8.73523			0.321113
$741$	−3.16881	+	3.52480i	−0.116409	+	0.129487i
$742$		−	0.852307i		−	0.0312892i
$743$	5.85981			0.214976			0.107488	−	0.994206i	$-0.465719\pi$
$743$	5.85981			0.214976			0.107488	+	0.994206i	$0.465719\pi$
$744$	−4.51115	−	8.52347i	−0.165387	−	0.312486i
$745$	8.90345			0.326197
$746$			7.24267i			0.265173i
$747$	5.83070	−	4.25005i	0.213334	−	0.155501i
$748$	5.86242			0.214351
$749$	−9.87064	+	5.69882i	−0.360665	+	0.208230i
$750$	1.28806	+	1.15797i	0.0470333	+	0.0422831i
$751$	3.08572	−	5.34462i	0.112599	−	0.195028i	−0.804218	−	0.594334i	$-0.797416\pi$
$751$	3.08572	−	5.34462i	0.112599	−	0.195028i	0.916818	+	0.399306i	$0.130749\pi$
$752$		−	2.88870i		−	0.105340i
$753$	45.1148	−	14.6973i	1.64408	−	0.535600i
$754$	3.31640	+	5.74418i	0.120776	+	0.209191i
$755$	4.98808	+	8.63961i	0.181535	+	0.314428i
$756$	−2.61489	−	5.83662i	−0.0951026	−	0.212276i
$757$	−23.5697	+	13.6080i	−0.856655	+	0.494590i	−0.862891	−	0.505390i	$-0.831348\pi$
$757$	−23.5697	+	13.6080i	−0.856655	+	0.494590i	0.00623560	+	0.999981i	$0.498015\pi$
$758$	−21.1771	−	12.2266i	−0.769186	−	0.444090i
$759$	−2.44382	+	11.5412i	−0.0887050	+	0.418918i
$760$	0.485142			0.0175979
$761$	−12.7572	+	22.0961i	−0.462447	+	0.800982i	−0.999082	−	0.0428324i	$-0.986362\pi$
$761$	−12.7572	+	22.0961i	−0.462447	+	0.800982i	0.536635	+	0.843814i	$0.319695\pi$
$762$	−20.0004	+	6.51563i	−0.724536	+	0.236036i
$763$	−12.4998	+	21.6504i	−0.452525	+	0.783795i
$764$	−10.6075	+	6.12422i	−0.383764	+	0.221566i
$765$	20.4325	−	2.17953i	0.738738	−	0.0788010i
$766$	−23.3023	+	13.4536i	−0.841946	+	0.486097i
$767$	4.16313			0.150322
$768$	1.28806	+	1.15797i	0.0464789	+	0.0417847i
$769$	−13.1091	+	22.7057i	−0.472728	+	0.818788i	−0.999513	−	0.0312102i	$-0.990064\pi$
$769$	−13.1091	+	22.7057i	−0.472728	+	0.818788i	0.526785	+	0.849998i	$0.323397\pi$
$770$	0.526732	+	0.912327i	0.0189821	+	0.0328780i
$771$	−22.7869	−	4.82507i	−0.820650	−	0.173771i
$772$	12.4843	−	21.6235i	0.449321	−	0.778246i
$773$	−31.4592			−1.13151			−0.565754	−	0.824574i	$-0.691415\pi$
$773$	−31.4592			−1.13151			−0.565754	+	0.824574i	$0.691415\pi$
$774$	−13.8653	−	6.14753i	−0.498378	−	0.220968i
$775$	3.56743	+	4.27475i	0.128146	+	0.153553i
$776$		−	5.55358i		−	0.199362i
$777$	18.2184	+	3.85771i	0.653582	+	0.138394i
$778$	−2.30754	−	1.33226i	−0.0827292	−	0.0477637i
$779$			3.48439i			0.124841i
$780$	9.28939	−	3.02626i	0.332613	−	0.108357i
$781$	2.88223	+	1.66406i	0.103134	+	0.0595447i
$782$	47.2043	+	27.2534i	1.68802	+	0.974580i
$783$	3.57995	−	4.95152i	0.127937	−	0.176953i
$784$	2.74252	+	4.75019i	0.0979472	+	0.169650i
$785$	2.69949	−	1.55855i	0.0963490	−	0.0556271i
$786$	13.4732	−	4.38925i	0.480574	−	0.156559i
$787$	−20.9026	−	12.0681i	−0.745097	−	0.430182i	0.0788227	−	0.996889i	$-0.474884\pi$
$787$	−20.9026	−	12.0681i	−0.745097	−	0.430182i	−0.823920	+	0.566707i	$0.808217\pi$
$788$	0.823054	+	1.42557i	0.0293201	+	0.0507839i
$789$	−12.2225	−	10.9881i	−0.435133	−	0.391186i
$790$			3.46298i			0.123207i
$791$		−	23.4908i		−	0.835235i
$792$	−1.51246	−	2.07496i	−0.0537429	−	0.0737305i
$793$	−18.2941	−	31.6863i	−0.649642	−	1.12521i
$794$	−16.3409	−	9.43442i	−0.579917	−	0.334815i
$795$	−0.371512	−	1.14039i	−0.0131762	−	0.0404455i
$796$	−10.0304	+	5.79107i	−0.355519	+	0.205259i
$797$	−1.90325	−	3.29653i	−0.0674166	−	0.116769i	0.830347	−	0.557247i	$-0.188142\pi$
$797$	−1.90325	−	3.29653i	−0.0674166	−	0.116769i	−0.897763	+	0.440478i	$0.854809\pi$
$798$	1.01182	+	0.214251i	0.0358182	+	0.00758442i
$799$	17.1352	+	9.89304i	0.606201	+	0.349990i
$800$	−0.866025	−	0.500000i	−0.0306186	−	0.0176777i
$801$	−1.73734	−	16.2871i	−0.0613860	−	0.575478i
$802$		−	6.85565i		−	0.242081i
$803$	−3.80530	−	2.19699i	−0.134286	−	0.0775302i
$804$	2.92291	−	13.8037i	0.103083	−	0.486821i
$805$			9.79476i			0.345220i
$806$	30.9432	−	5.37053i	1.08993	−	0.189169i
$807$	−9.76523	+	46.1173i	−0.343752	+	1.62341i
$808$	−4.31376			−0.151758
$809$	−1.99687	+	3.45868i	−0.0702062	+	0.121601i	−0.898992	−	0.437966i	$-0.855699\pi$
$809$	−1.99687	+	3.45868i	−0.0702062	+	0.121601i	0.828785	+	0.559567i	$0.189032\pi$
$810$	−6.04285	−	6.66963i	−0.212324	−	0.234347i
$811$	−3.08074	−	5.33600i	−0.108179	−	0.187372i	0.806853	−	0.590752i	$-0.201169\pi$
$811$	−3.08074	−	5.33600i	−0.108179	−	0.187372i	−0.915033	+	0.403380i	$0.867835\pi$
$812$	0.723666	−	1.25343i	0.0253957	−	0.0439866i
$813$	−4.89130	+	5.44080i	−0.171545	+	0.190817i
$814$	7.47643			0.262049
$815$	0.971199	−	0.560722i	0.0340196	−	0.0196412i
$816$	−11.2801	+	3.67480i	−0.394884	+	0.128644i
$817$	2.12412	−	1.22636i	0.0743135	−	0.0429049i
$818$	−5.85435	+	10.1400i	−0.204693	+	0.354538i
$819$	20.7107	−	2.20920i	0.723689	−	0.0771957i
$820$	3.59111	−	6.21998i	0.125407	−	0.217211i
$821$	−24.6632			−0.860752			−0.430376	−	0.902650i	$-0.641619\pi$
$821$	−24.6632			−0.860752			−0.430376	+	0.902650i	$0.641619\pi$
$822$	−37.8523	−	8.01514i	−1.32025	−	0.279560i
$823$	4.13730	+	2.38867i	0.144217	+	0.0832639i	0.570372	−	0.821386i	$-0.306799\pi$
$823$	4.13730	+	2.38867i	0.144217	+	0.0832639i	−0.426155	+	0.904650i	$0.640132\pi$
$824$	4.74572	−	2.73994i	0.165325	−	0.0954504i
$825$	1.10244	+	0.991101i	0.0383822	+	0.0345057i
$826$	−0.454214	−	0.786722i	−0.0158041	−	0.0273736i
$827$	−27.1143	−	46.9634i	−0.942858	−	1.63308i	−0.759984	−	0.649942i	$-0.774793\pi$
$827$	−27.1143	−	46.9634i	−0.942858	−	1.63308i	−0.182874	−	0.983136i	$-0.558540\pi$
$828$	−2.53221	−	23.7388i	−0.0880003	−	0.824979i
$829$			3.33127i			0.115700i	0.998325	+	0.0578499i	$0.0184245\pi$
$829$			3.33127i			0.115700i	−0.998325	+	0.0578499i	$0.981576\pi$
$830$	1.20254	−	2.08287i	0.0417409	−	0.0722973i
$831$	−19.3511	+	21.5251i	−0.671282	+	0.746696i
$832$	−4.88495	+	2.82033i	−0.169355	+	0.0977772i
$833$	−37.5696			−1.30171
$834$	−17.2172	−	15.4784i	−0.596184	−	0.535972i
$835$		−	9.86165i		−	0.341276i
$836$	0.415230			0.0143610
$837$	−16.1693	−	23.9907i	−0.558893	−	0.829240i
$838$	−37.9695			−1.31164
$839$			41.9642i			1.44876i	0.689399	+	0.724382i	$0.257875\pi$
$839$			41.9642i			1.44876i	−0.689399	+	0.724382i	$0.742125\pi$
$840$	−1.58539	−	1.42527i	−0.0547012	−	0.0491766i
$841$	−27.6173			−0.952320
$842$	28.8664	−	16.6660i	0.994802	−	0.574349i
$843$	−0.388391	+	0.432024i	−0.0133769	+	0.0148797i
$844$	6.37798	−	11.0470i	0.219539	−	0.380253i
$845$			18.8170i			0.647324i
$846$	−0.919196	−	8.61722i	−0.0316026	−	0.296266i
$847$	−6.31877	−	10.9444i	−0.217115	−	0.376055i
$848$	0.346231	+	0.599690i	0.0118896	+	0.0205934i
$849$	−4.03795	−	3.63013i	−0.138582	−	0.124586i
$850$	5.93182	−	3.42474i	0.203460	−	0.117467i
$851$	60.2003	+	34.7567i	2.06364	+	1.19144i
$852$	−6.58893	−	1.39519i	−0.225733	−	0.0477984i
$853$	8.08162			0.276709			0.138355	−	0.990383i	$-0.455819\pi$
$853$	8.08162			0.276709			0.138355	+	0.990383i	$0.455819\pi$
$854$	−3.99191	+	6.91419i	−0.136600	+	0.236599i
$855$	1.44722	−	0.154374i	0.0494937	−	0.00527948i
$856$	4.63004	−	8.01947i	0.158252	−	0.274100i
$857$	−23.4972	+	13.5661i	−0.802648	+	0.463409i	−0.844396	−	0.535719i	$-0.820041\pi$
$857$	−23.4972	+	13.5661i	−0.802648	+	0.463409i	0.0417480	+	0.999128i	$0.486707\pi$
$858$	7.95073	−	2.59015i	0.271433	−	0.0884264i
$859$	−33.9366	+	19.5933i	−1.15790	+	0.668515i	−0.950800	−	0.309805i	$-0.899736\pi$
$859$	−33.9366	+	19.5933i	−1.15790	+	0.668515i	−0.207101	+	0.978320i	$0.566403\pi$
$860$	−5.05568			−0.172397
$861$	10.2366	−	11.3866i	0.348863	−	0.388055i
$862$	12.6283	−	21.8729i	0.430123	−	0.744995i
$863$	−2.49034	−	4.31339i	−0.0847721	−	0.146830i	0.820522	−	0.571615i	$-0.193683\pi$
$863$	−2.49034	−	4.31339i	−0.0847721	−	0.146830i	−0.905294	+	0.424785i	$0.860350\pi$
$864$	4.21086	+	3.04445i	0.143256	+	0.103574i
$865$	5.04608	−	8.74006i	0.171572	−	0.297171i
$866$	−27.2143			−0.924779
$867$	10.7337	−	50.6908i	0.364534	−	1.72155i
$868$	−4.39092	−	5.26151i	−0.149037	−	0.178587i
$869$			2.96395i			0.100545i
$870$	0.421913	−	1.99253i	0.0143042	−	0.0675530i
$871$	39.7943	+	22.9752i	1.34838	+	0.778486i
$872$		−	20.3111i		−	0.687822i
$873$	−1.76717	−	16.5667i	−0.0598096	−	0.560699i
$874$	3.34344	+	1.93033i	0.113093	+	0.0652945i
$875$	1.06593	+	0.615418i	0.0360352	+	0.0208049i
$876$	8.69911	+	1.84202i	0.293916	+	0.0622359i
$877$	−17.3948	−	30.1286i	−0.587380	−	1.01737i	−0.994574	−	0.104030i	$-0.966826\pi$
$877$	−17.3948	−	30.1286i	−0.587380	−	1.01737i	0.407194	−	0.913342i	$-0.366507\pi$
$878$	4.74619	−	2.74021i	0.160176	−	0.0924777i
$879$	5.84529	+	17.9427i	0.197157	+	0.605192i
$880$	−0.741226	−	0.427947i	−0.0249867	−	0.0144261i
$881$	−1.36745	−	2.36849i	−0.0460704	−	0.0797963i	0.842071	−	0.539367i	$-0.181337\pi$
$881$	−1.36745	−	2.36849i	−0.0460704	−	0.0797963i	−0.888141	+	0.459571i	$0.848003\pi$
$882$	9.69268	+	13.2975i	0.326370	+	0.447750i
$883$			9.90585i			0.333358i	0.986011	+	0.166679i	$0.0533044\pi$
$883$			9.90585i			0.333358i	−0.986011	+	0.166679i	$0.946696\pi$
$884$		−	38.6355i		−	1.29945i
$885$	−0.950665	−	0.854651i	−0.0319562	−	0.0287288i
$886$	−11.4660	−	19.8597i	−0.385208	−	0.667200i
$887$	27.6973	+	15.9910i	0.929983	+	0.536926i	0.886806	−	0.462142i	$-0.152919\pi$
$887$	27.6973	+	15.9910i	0.929983	+	0.536926i	0.0431766	+	0.999067i	$0.486252\pi$
$888$	−14.3857	+	4.68652i	−0.482753	+	0.157269i
$889$	−12.9453	+	7.47395i	−0.434170	+	0.250668i
$890$	−2.72992	−	4.72837i	−0.0915072	−	0.158495i
$891$	−5.17204	−	5.70849i	−0.173270	−	0.191242i
$892$	11.4650	+	6.61933i	0.383877	+	0.221632i
$893$	1.21367	+	0.700715i	0.0406140	+	0.0234485i
$894$	−14.6628	+	4.77677i	−0.490396	+	0.159759i
$895$			24.4818i			0.818335i
$896$	1.06593	+	0.615418i	0.0356104	+	0.0205597i
$897$	76.0606	+	16.1056i	2.53959	+	0.537752i
$898$			10.9265i			0.364623i
$899$	2.25574	−	6.14623i	0.0752333	−	0.204988i
$900$	−2.74252	−	1.21597i	−0.0914174	−	0.0405322i
$901$	−4.74300			−0.158012
$902$	3.07361	−	5.32364i	0.102340	−	0.177258i
$903$	−10.5442	−	2.23272i	−0.350890	−	0.0743002i
$904$	9.54261	+	16.5283i	0.317382	+	0.549723i
$905$	−7.50878	+	13.0056i	−0.249600	+	0.432320i
$906$	−12.8499	−	11.5521i	−0.426910	−	0.383793i
$907$	6.11441			0.203026			0.101513	−	0.994834i	$-0.467632\pi$
$907$	6.11441			0.203026			0.101513	+	0.994834i	$0.467632\pi$
$908$	22.0581	−	12.7352i	0.732023	−	0.422633i
$909$	−12.8683	+	1.37266i	−0.426814	+	0.0455281i
$910$	6.01257	−	3.47136i	0.199315	−	0.115074i
$911$	5.35917	−	9.28235i	0.177557	−	0.307538i	−0.763486	−	0.645824i	$-0.776514\pi$
$911$	5.35917	−	9.28235i	0.177557	−	0.307538i	0.941043	+	0.338286i	$0.109847\pi$
$912$	−0.798962	+	0.260282i	−0.0264563	+	0.00861881i
$913$	1.02925	−	1.78271i	0.0340632	−	0.0589992i
$914$	37.4970			1.24029
$915$	−2.32737	+	10.9913i	−0.0769406	+	0.363360i
$916$	14.9883	+	8.65348i	0.495226	+	0.285919i
$917$	8.72057	−	5.03482i	0.287978	−	0.166264i
$918$	−32.4802	+	14.5516i	−1.07201	+	0.480274i
$919$	−15.4006	−	26.6746i	−0.508019	−	0.879914i	−0.999957	−	0.00928402i	$-0.997045\pi$
$919$	−15.4006	−	26.6746i	−0.508019	−	0.879914i	0.491938	−	0.870630i	$-0.336289\pi$
$920$	−3.97891	−	6.89167i	−0.131181	−	0.227212i
$921$	51.9163	−	16.9131i	1.71070	−	0.557305i
$922$			13.1893i			0.434367i
$923$	10.9668	−	18.9950i	0.360975	−	0.625227i
$924$	−1.35693	−	1.21988i	−0.0446396	−	0.0401312i
$925$	7.56493	−	4.36761i	0.248733	−	0.143606i
$926$	19.5842			0.643576
$927$	13.2850	−	9.68356i	0.436336	−	0.318050i
$928$			1.17589i			0.0386006i
$929$	−45.4921			−1.49255			−0.746273	−	0.665640i	$-0.768159\pi$
$929$	−45.4921			−1.49255			−0.746273	+	0.665640i	$0.768159\pi$
$930$	−8.16850	−	5.12597i	−0.267856	−	0.168087i
$931$	−2.66102			−0.0872115
$932$		−	22.8670i		−	0.749032i
$933$	0.596837	−	0.663887i	0.0195396	−	0.0217347i
$934$	−15.0537			−0.492572
$935$	5.07701	−	2.93121i	0.166036	−	0.0958608i
$936$	−13.6747	+	9.96766i	−0.446973	+	0.325803i
$937$	−9.09856	+	15.7592i	−0.297237	+	0.514830i	−0.975503	−	0.219987i	$-0.929399\pi$
$937$	−9.09856	+	15.7592i	−0.297237	+	0.514830i	0.678266	+	0.734817i	$0.262732\pi$
$938$		−	10.0268i		−	0.327385i
$939$	10.0745	+	30.9247i	0.328769	+	1.00919i
$940$	−1.44435	−	2.50169i	−0.0471095	−	0.0815961i
$941$	−17.5176	−	30.3414i	−0.571059	−	0.989103i	−0.996458	−	0.0840967i	$-0.973200\pi$
$941$	−17.5176	−	30.3414i	−0.571059	−	0.989103i	0.425399	−	0.905006i	$-0.360134\pi$
$942$	−3.60952	+	4.01502i	−0.117604	+	0.130817i
$943$	49.4974	−	28.5774i	1.61186	−	0.930607i
$944$	0.639178	+	0.369029i	0.0208035	+	0.0120109i
$945$	−5.18287	−	3.74722i	−0.168599	−	0.121897i
$946$	−4.32712			−0.140687
$947$	−3.84219	+	6.65487i	−0.124854	+	0.216254i	−0.921676	−	0.387960i	$-0.873180\pi$
$947$	−3.84219	+	6.65487i	−0.124854	+	0.216254i	0.796822	+	0.604215i	$0.206513\pi$
$948$	−1.85792	−	5.70306i	−0.0603424	−	0.185227i
$949$	−14.4790	+	25.0783i	−0.470007	+	0.814077i
$950$	0.420145	−	0.242571i	0.0136313	−	0.00787004i
$951$	−6.26626	−	19.2349i	−0.203198	−	0.623734i
$952$	−7.30109	+	4.21529i	−0.236630	+	0.136618i
$953$	−27.7010			−0.897325			−0.448663	−	0.893701i	$-0.648099\pi$
$953$	−27.7010			−0.897325			−0.448663	+	0.893701i	$0.648099\pi$
$954$	1.22366	+	1.67875i	0.0396174	+	0.0543515i
$955$	−6.12422	+	10.6075i	−0.198175	+	0.343249i
$956$	−5.26395	−	9.11743i	−0.170248	−	0.294879i
$957$	0.361113	−	1.70539i	0.0116731	−	0.0551275i
$958$	−17.9632	+	31.1132i	−0.580365	+	1.00522i
$959$	−27.4951			−0.887865
$960$	1.69448	+	0.358802i	0.0546891	+	0.0115803i
$961$	−23.6401	−	20.0536i	−0.762583	−	0.646891i
$962$		−	49.2724i		−	1.58861i
$963$	11.2599	−	25.3960i	0.362847	−	0.818374i
$964$	22.1828	+	12.8072i	0.714460	+	0.412494i
$965$		−	24.9686i		−	0.803769i
$966$	−5.25497	−	16.1306i	−0.169076	−	0.518995i
$967$	35.6876	+	20.6043i	1.14764	+	0.662588i	0.948310	−	0.317345i	$-0.102791\pi$
$967$	35.6876	+	20.6043i	1.14764	+	0.662588i	0.199326	+	0.979933i	$0.436125\pi$
$968$	8.89187	+	5.13372i	0.285795	+	0.165004i
$969$	1.19229	−	5.63069i	0.0383018	−	0.180884i
$970$	−2.77679	−	4.80954i	−0.0891573	−	0.154425i
$971$	−20.2315	+	11.6806i	−0.649259	+	0.374850i	−0.788172	−	0.615455i	$-0.788972\pi$
$971$	−20.2315	+	11.6806i	−0.649259	+	0.374850i	0.138913	+	0.990305i	$0.455639\pi$
$972$	13.5301	+	7.74192i	0.433977	+	0.248322i
$973$	−14.2481	−	8.22616i	−0.456774	−	0.263718i
$974$	−12.7436	−	22.0726i	−0.408333	−	0.707253i
$975$	6.53172	−	7.26551i	0.209182	−	0.232682i
$976$		−	6.48651i		−	0.207628i
$977$		−	41.7506i		−	1.33572i	−0.744287	−	0.667860i	$-0.767211\pi$
$977$		−	41.7506i		−	1.33572i	0.744287	−	0.667860i	$-0.232789\pi$
$978$	−1.29860	+	1.44449i	−0.0415247	+	0.0461897i
$979$	−2.33653	−	4.04698i	−0.0746757	−	0.129342i
$980$	4.75019	+	2.74252i	0.151739	+	0.0876067i
$981$	−6.46308	−	60.5897i	−0.206350	−	1.93448i
$982$	12.5471	−	7.24410i	0.400396	−	0.231168i
$983$	26.6042	+	46.0798i	0.848541	+	1.46972i	0.882510	+	0.470294i	$0.155852\pi$
$983$	26.6042	+	46.0798i	0.848541	+	1.46972i	−0.0339685	+	0.999423i	$0.510815\pi$
$984$	−2.57699	+	12.1701i	−0.0821516	+	0.387969i
$985$	1.42557	+	0.823054i	0.0454225	+	0.0262247i
$986$	−6.97518	−	4.02712i	−0.222135	−	0.128250i
$987$	−1.90756	−	5.85545i	−0.0607184	−	0.186381i
$988$		−	2.73652i		−	0.0870602i
$989$	−34.8420	−	20.1161i	−1.10791	−	0.639654i
$990$	−2.34731	−	1.04074i	−0.0746024	−	0.0330768i
$991$			22.0756i			0.701256i	0.936515	+	0.350628i	$0.114032\pi$
$991$			22.0756i			0.701256i	−0.936515	+	0.350628i	$0.885968\pi$
$992$	5.22686	+	1.91832i	0.165953	+	0.0609068i
$993$	29.5471	+	6.25652i	0.937647	+	0.198545i
$994$	−4.78606			−0.151805
$995$	−5.79107	+	10.0304i	−0.183589	+	0.317986i
$996$	−0.862950	+	4.07537i	−0.0273436	+	0.129133i
$997$	14.8577	+	25.7343i	0.470548	+	0.815013i	0.999433	−	0.0336806i	$-0.0107229\pi$
$997$	14.8577	+	25.7343i	0.470548	+	0.815013i	−0.528885	+	0.848694i	$0.677390\pi$
$998$	9.24809	−	16.0182i	0.292743	−	0.507046i
$999$	−41.4225	+	18.5578i	−1.31055	+	0.587144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.o.e.491.7	yes	40
3.2	odd	2	inner	930.2.o.e.491.20	yes	40
31.6	odd	6	inner	930.2.o.e.161.10	✓	40
93.68	even	6	inner	930.2.o.e.161.17	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.o.e.161.10	✓	40	31.6	odd	6	inner
930.2.o.e.161.17	yes	40	93.68	even	6	inner
930.2.o.e.491.7	yes	40	1.1	even	1	trivial
930.2.o.e.491.20	yes	40	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.28806 + 1.15797i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.15797 - 1.28806i) q^{6} +(0.615418 - 1.06593i) q^{7} +1.00000i q^{8} +(0.318204 + 2.98308i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.28806 + 1.15797i) q^{3} -1.00000 q^{4} +(-0.866025 + 0.500000i) q^{5} +(1.15797 - 1.28806i) q^{6} +(0.615418 - 1.06593i) q^{7} +1.00000i q^{8} +(0.318204 + 2.98308i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.427947 + 0.741226i) q^{11} +(-1.28806 - 1.15797i) q^{12} +(4.88495 - 2.82033i) q^{13} +(-1.06593 - 0.615418i) q^{14} +(-1.69448 - 0.358802i) q^{15} +1.00000 q^{16} +(-3.42474 + 5.93182i) q^{17} +(2.98308 - 0.318204i) q^{18} +(-0.242571 + 0.420145i) q^{19} +(0.866025 - 0.500000i) q^{20} +(2.02702 - 0.660353i) q^{21} +(0.741226 - 0.427947i) q^{22} +7.95781 q^{23} +(-1.15797 + 1.28806i) q^{24} +(0.500000 - 0.866025i) q^{25} +(-2.82033 - 4.88495i) q^{26} +(-3.04445 + 4.21086i) q^{27} +(-0.615418 + 1.06593i) q^{28} -1.17589 q^{29} +(-0.358802 + 1.69448i) q^{30} +(-1.91832 + 5.22686i) q^{31} -1.00000i q^{32} +(-0.307097 + 1.45030i) q^{33} +(5.93182 + 3.42474i) q^{34} +1.23084i q^{35} +(-0.318204 - 2.98308i) q^{36} +(7.56493 + 4.36761i) q^{37} +(0.420145 + 0.242571i) q^{38} +(9.55797 + 2.02388i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(6.21998 - 3.59111i) q^{41} +(-0.660353 - 2.02702i) q^{42} +(-4.37834 - 2.52784i) q^{43} +(-0.427947 - 0.741226i) q^{44} +(-1.76711 - 2.42432i) q^{45} -7.95781i q^{46} -2.88870i q^{47} +(1.28806 + 1.15797i) q^{48} +(2.74252 + 4.75019i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(-11.2801 + 3.67480i) q^{51} +(-4.88495 + 2.82033i) q^{52} +(0.346231 + 0.599690i) q^{53} +(4.21086 + 3.04445i) q^{54} +(-0.741226 - 0.427947i) q^{55} +(1.06593 + 0.615418i) q^{56} +(-0.798962 + 0.260282i) q^{57} +1.17589i q^{58} +(0.639178 + 0.369029i) q^{59} +(1.69448 + 0.358802i) q^{60} -6.48651i q^{61} +(5.22686 + 1.91832i) q^{62} +(3.37559 + 1.49665i) q^{63} -1.00000 q^{64} +(-2.82033 + 4.88495i) q^{65} +(1.45030 + 0.307097i) q^{66} +(4.07315 + 7.05491i) q^{67} +(3.42474 - 5.93182i) q^{68} +(10.2502 + 9.21492i) q^{69} +1.23084 q^{70} +(3.36751 - 1.94423i) q^{71} +(-2.98308 + 0.318204i) q^{72} +(-4.44599 + 2.56690i) q^{73} +(4.36761 - 7.56493i) q^{74} +(1.64686 - 0.536508i) q^{75} +(0.242571 - 0.420145i) q^{76} +1.05346 q^{77} +(2.02388 - 9.55797i) q^{78} +(2.99903 + 1.73149i) q^{79} +(-0.866025 + 0.500000i) q^{80} +(-8.79749 + 1.89845i) q^{81} +(-3.59111 - 6.21998i) q^{82} +(-1.20254 - 2.08287i) q^{83} +(-2.02702 + 0.660353i) q^{84} -6.84947i q^{85} +(-2.52784 + 4.37834i) q^{86} +(-1.51462 - 1.36165i) q^{87} +(-0.741226 + 0.427947i) q^{88} -5.45985 q^{89} +(-2.42432 + 1.76711i) q^{90} -6.94272i q^{91} -7.95781 q^{92} +(-8.52347 + 4.51115i) q^{93} -2.88870 q^{94} -0.485142i q^{95} +(1.15797 - 1.28806i) q^{96} -5.55358 q^{97} +(4.75019 - 2.74252i) q^{98} +(-2.07496 + 1.51246i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9}+O(q^{10}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9	\( 40 q + 6 q^{3} - 40 q^{4} - 12 q^{7} - 2 q^{9} + 20 q^{10} - 6 q^{12} - 12 q^{13} + 40 q^{16} - 12 q^{18} - 12 q^{19} + 12 q^{21} - 24 q^{22} + 20 q^{25} + 12 q^{28} + 8 q^{31} + 52 q^{33} + 24 q^{34} + 2 q^{36} + 60 q^{37} - 8 q^{39} - 20 q^{40} + 12 q^{42} + 24 q^{43} - 12 q^{45} + 6 q^{48} - 4 q^{49} + 14 q^{51} + 12 q^{52} + 24 q^{55} - 12 q^{57} - 40 q^{64} + 8 q^{66} + 64 q^{67} - 26 q^{69} - 24 q^{70} + 12 q^{72} + 6 q^{75} + 12 q^{76} - 68 q^{78} - 48 q^{79} + 2 q^{81} + 4 q^{82} - 12 q^{84} + 36 q^{87} + 24 q^{88} + 2 q^{90} - 22 q^{93} - 40 q^{94} + 8 q^{97} - 90 q^{99}+O(q^{100}) \) 40 * q + 6 * q^3 - 40 * q^4 - 12 * q^7 - 2 * q^9 + 20 * q^10 - 6 * q^12 - 12 * q^13 + 40 * q^16 - 12 * q^18 - 12 * q^19 + 12 * q^21 - 24 * q^22 + 20 * q^25 + 12 * q^28 + 8 * q^31 + 52 * q^33 + 24 * q^34 + 2 * q^36 + 60 * q^37 - 8 * q^39 - 20 * q^40 + 12 * q^42 + 24 * q^43 - 12 * q^45 + 6 * q^48 - 4 * q^49 + 14 * q^51 + 12 * q^52 + 24 * q^55 - 12 * q^57 - 40 * q^64 + 8 * q^66 + 64 * q^67 - 26 * q^69 - 24 * q^70 + 12 * q^72 + 6 * q^75 + 12 * q^76 - 68 * q^78 - 48 * q^79 + 2 * q^81 + 4 * q^82 - 12 * q^84 + 36 * q^87 + 24 * q^88 + 2 * q^90 - 22 * q^93 - 40 * q^94 + 8 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more