LMFDB - Embedded newform 930.2.o.e.491.20

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			491.20
Character	$\chi$	$=$	930.491
Dual form			930.2.o.e.161.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(1.64686 + 0.536508i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.536508 + 1.64686i) q^{6} +(0.615418 - 1.06593i) q^{7} -1.00000i q^{8} +(2.42432 + 1.76711i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.64686 + 0.536508i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.536508 + 1.64686i) q^{6} +(0.615418 - 1.06593i) q^{7} -1.00000i q^{8} +(2.42432 + 1.76711i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.427947 - 0.741226i) q^{11} +(-1.64686 - 0.536508i) 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} +(-1.76711 + 2.42432i) q^{18} +(-0.242571 + 0.420145i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.58539 - 1.42527i) q^{21} +(0.741226 - 0.427947i) q^{22} -7.95781 q^{23} +(0.536508 - 1.64686i) 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} +(-2.42432 - 1.76711i) 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} +(1.42527 + 1.58539i) q^{42} +(-4.37834 - 2.52784i) q^{43} +(0.427947 + 0.741226i) q^{44} +(2.98308 + 0.318204i) q^{45} -7.95781i q^{46} +2.88870i q^{47} +(1.64686 + 0.536508i) q^{48} +(2.74252 + 4.75019i) q^{49} +(0.866025 + 0.500000i) q^{50} +(8.82254 - 7.93149i) 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} +(-0.624892 + 0.561780i) 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} +(-13.1054 - 4.26943i) q^{69} +1.23084 q^{70} +(-3.36751 + 1.94423i) q^{71} +(1.76711 - 2.42432i) q^{72} +(-4.44599 + 2.56690i) q^{73} +(-4.36761 + 7.56493i) q^{74} +(1.28806 - 1.15797i) 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} +(2.75464 + 8.56808i) q^{81} +(-3.59111 - 6.21998i) q^{82} +(1.20254 + 2.08287i) q^{83} +(-1.58539 + 1.42527i) q^{84} -6.84947i q^{85} +(2.52784 - 4.37834i) q^{86} +(1.93654 + 0.630876i) q^{87} +(-0.741226 + 0.427947i) q^{88} +5.45985 q^{89} +(-0.318204 + 2.98308i) q^{90} -6.94272i q^{91} +7.95781 q^{92} +(-5.96347 + 7.57872i) q^{93} -2.88870 q^{94} +0.485142i q^{95} +(-0.536508 + 1.64686i) q^{96} -5.55358 q^{97} +(-4.75019 + 2.74252i) q^{98} +(0.272349 - 2.55320i) 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
$3$	1.64686	+	0.536508i	0.950817	+	0.309753i
$3$	1.64686	+	0.536508i	0.950817	+	0.309753i
$4$	−1.00000			−0.500000
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$5$	0.866025	−	0.500000i	0.387298	−	0.223607i
$6$	−0.536508	+	1.64686i	−0.219028	+	0.672329i
$7$	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
$9$	2.42432	+	1.76711i	0.808106	+	0.589037i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−0.427947	−	0.741226i	−0.129031	−	0.223488i	0.794270	−	0.607564i	$-0.207853\pi$
$11$	−0.427947	−	0.741226i	−0.129031	−	0.223488i	−0.923301	+	0.384076i	$0.874520\pi$
$12$	−1.64686	−	0.536508i	−0.475409	−	0.154877i
$13$	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	$-0.521319\pi$
$17$	3.42474	−	5.93182i	0.830620	−	1.43868i	0.897547	−	0.440919i	$-0.145347\pi$
$18$	−1.76711	+	2.42432i	−0.416512	+	0.571417i
$19$	−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
$21$	1.58539	−	1.42527i	0.345961	−	0.311020i
$22$	0.741226	−	0.427947i	0.158030	−	0.0912386i
$23$	−7.95781			−1.65932			−0.829660	−	0.558270i	$-0.811465\pi$
$23$	−7.95781			−1.65932			−0.829660	+	0.558270i	$0.811465\pi$
$24$	0.536508	−	1.64686i	0.109514	−	0.336165i
$25$	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	$-0.465178\pi$
$29$	1.17589			0.218358			0.109179	+	0.994022i	$0.465178\pi$
$30$	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
$36$	−2.42432	−	1.76711i	−0.404053	−	0.294518i
$37$	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	−0.899662	−	0.436587i	$-0.856187\pi$
$41$	−6.21998	+	3.59111i	−0.971398	+	0.560837i	−0.0717356	+	0.997424i	$0.522854\pi$
$42$	1.42527	+	1.58539i	0.219924	+	0.244631i
$43$	−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
$45$	2.98308	+	0.318204i	0.444691	+	0.0474350i
$46$		−	7.95781i		−	1.17332i
$47$			2.88870i			0.421360i	0.977555	+	0.210680i	$0.0675679\pi$
$47$			2.88870i			0.421360i	−0.977555	+	0.210680i	$0.932432\pi$
$48$	1.64686	+	0.536508i	0.237704	+	0.0774383i
$49$	2.74252	+	4.75019i	0.391789	+	0.678598i
$50$	0.866025	+	0.500000i	0.122474	+	0.0707107i
$51$	8.82254	−	7.93149i	1.23540	−	1.11063i
$52$	−4.88495	+	2.82033i	−0.677421	+	0.391109i
$53$	−0.346231	−	0.599690i	−0.0475585	−	0.0823738i	0.841266	−	0.540621i	$-0.181811\pi$
$53$	−0.346231	−	0.599690i	−0.0475585	−	0.0823738i	−0.888825	+	0.458247i	$0.848477\pi$
$54$	−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
$57$	−0.624892	+	0.561780i	−0.0827690	+	0.0744096i
$58$			1.17589i			0.154402i
$59$	−0.639178	−	0.369029i	−0.0832138	−	0.0480435i	0.457816	−	0.889047i	$-0.348632\pi$
$59$	−0.639178	−	0.369029i	−0.0832138	−	0.0480435i	−0.541030	+	0.841004i	$0.681965\pi$
$60$	−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
$69$	−13.1054	−	4.26943i	−1.57771	−	0.513979i
$70$	1.23084			0.147113
$71$	−3.36751	+	1.94423i	−0.399650	+	0.230738i	−0.686333	−	0.727287i	$-0.740781\pi$
$71$	−3.36751	+	1.94423i	−0.399650	+	0.230738i	0.286683	+	0.958026i	$0.407447\pi$
$72$	1.76711	−	2.42432i	0.208256	−	0.285709i
$73$	−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
$75$	1.28806	−	1.15797i	0.148733	−	0.133711i
$76$	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
$81$	2.75464	+	8.56808i	0.306071	+	0.952009i
$82$	−3.59111	−	6.21998i	−0.396571	−	0.686882i
$83$	1.20254	+	2.08287i	0.131996	+	0.228624i	0.924446	−	0.381313i	$-0.124528\pi$
$83$	1.20254	+	2.08287i	0.131996	+	0.228624i	−0.792450	+	0.609937i	$0.791195\pi$
$84$	−1.58539	+	1.42527i	−0.172980	+	0.155510i
$85$		−	6.84947i		−	0.742929i
$86$	2.52784	−	4.37834i	0.272584	−	0.472129i
$87$	1.93654	+	0.630876i	0.207618	+	0.0676370i
$88$	−0.741226	+	0.427947i	−0.0790150	+	0.0456193i
$89$	5.45985			0.578742			0.289371	−	0.957217i	$-0.406554\pi$
$89$	5.45985			0.578742			0.289371	+	0.957217i	$0.406554\pi$
$90$	−0.318204	+	2.98308i	−0.0335416	+	0.314444i
$91$		−	6.94272i		−	0.727794i
$92$	7.95781			0.829660
$93$	−5.96347	+	7.57872i	−0.618383	+	0.785877i
$94$	−2.88870			−0.297947
$95$			0.485142i			0.0497745i
$96$	−0.536508	+	1.64686i	−0.0547571	+	0.168082i
$97$	−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
$99$	0.272349	−	2.55320i	0.0273721	−	0.256606i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$		−	4.31376i		−	0.429235i	−0.976698	−	0.214618i	$-0.931149\pi$
$101$		−	4.31376i		−	0.429235i	0.976698	−	0.214618i	$-0.0688506\pi$
$102$	7.93149	+	8.82254i	0.785335	+	0.873561i
$103$	−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
$105$	0.660353	−	2.02702i	0.0644439	−	0.197817i
$106$	0.599690	−	0.346231i	0.0582471	−	0.0336290i
$107$	8.01947	+	4.63004i	0.775271	+	0.447603i	0.834752	−	0.550627i	$-0.185611\pi$
$107$	8.01947	+	4.63004i	0.775271	+	0.447603i	−0.0594807	+	0.998229i	$0.518944\pi$
$108$	−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
$111$	10.1151	+	11.2515i	0.960087	+	1.06795i
$112$	0.615418	−	1.06593i	0.0581515	−	0.100721i
$113$	−16.5283	+	9.54261i	−1.55485	+	0.897693i	−0.557114	+	0.830436i	$0.688092\pi$
$113$	−16.5283	+	9.54261i	−1.55485	+	0.897693i	−0.997736	+	0.0672575i	$0.978575\pi$
$114$	−0.561780	−	0.624892i	−0.0526156	−	0.0585265i
$115$	−6.89167	+	3.97891i	−0.642652	+	0.371035i
$116$	−1.17589			−0.109179
$117$	16.8265	+	1.79488i	1.55561	+	0.165937i
$118$	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
$129$	−5.85433	−	6.51202i	−0.515445	−	0.573351i
$130$	4.88495	+	2.82033i	0.428438	+	0.247359i
$131$	−7.08508	−	4.09057i	−0.619026	−	0.357395i	0.157464	−	0.987525i	$-0.449668\pi$
$131$	−7.08508	−	4.09057i	−0.619026	−	0.357395i	−0.776490	+	0.630130i	$0.783002\pi$
$132$	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
$135$	4.74200	+	2.12448i	0.408126	+	0.182846i
$136$	−5.93182	−	3.42474i	−0.508649	−	0.293669i
$137$	11.1693	+	19.3458i	0.954258	+	1.65282i	0.736057	+	0.676919i	$0.236685\pi$
$137$	11.1693	+	19.3458i	0.954258	+	1.65282i	0.218201	+	0.975904i	$0.429981\pi$
$138$	4.26943	−	13.1054i	0.363438	−	1.11561i
$139$		−	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
$141$	−1.54981	+	4.75730i	−0.130518	+	0.400637i
$142$	−1.94423	−	3.36751i	−0.163157	−	0.282595i
$143$	−4.18100	−	2.41390i	−0.349633	−	0.201861i
$144$	2.42432	+	1.76711i	0.202027	+	0.147259i
$145$	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	0.781402	−	0.624028i	$-0.214505\pi$
$149$	7.71061	+	4.45172i	0.631678	+	0.364700i	−0.149724	+	0.988728i	$0.547838\pi$
$150$	1.15797	+	1.28806i	0.0945480	+	0.105170i
$151$		−	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
$162$	−8.56808	+	2.75464i	−0.673172	+	0.216425i
$163$	−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
$165$	−0.991101	−	1.10244i	−0.0771571	−	0.0858252i
$166$	−2.08287	+	1.20254i	−0.161662	+	0.0933355i
$167$	4.93083	−	8.54044i	0.381559	−	0.660879i	−0.609727	−	0.792612i	$-0.708721\pi$
$167$	4.93083	−	8.54044i	0.381559	−	0.660879i	0.991285	+	0.131733i	$0.0420541\pi$
$168$	−1.42527	−	1.58539i	−0.109962	−	0.122316i
$169$	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	−0.129493	−	0.991580i	$-0.541335\pi$
$173$	8.74006	−	5.04608i	0.664495	−	0.383646i	0.793987	+	0.607934i	$0.208002\pi$
$174$	−0.630876	+	1.93654i	−0.0478266	+	0.146808i
$175$	−0.615418	−	1.06593i	−0.0465212	−	0.0805771i
$176$	−0.427947	−	0.741226i	−0.0322577	−	0.0558720i
$177$	−0.854651	−	0.950665i	−0.0642395	−	0.0714563i
$178$			5.45985i			0.409233i
$179$	−12.2409	+	21.2018i	−0.914926	+	1.58470i	−0.107917	+	0.994160i	$0.534418\pi$
$179$	−12.2409	+	21.2018i	−0.914926	+	1.58470i	−0.807009	+	0.590539i	$0.798915\pi$
$180$	−2.98308	−	0.318204i	−0.222345	−	0.0237175i
$181$	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
$183$	3.48006	−	10.6824i	0.257254	−	0.789665i
$184$			7.95781i			0.586658i
$185$	8.73523			0.642227
$186$	−7.57872	−	5.96347i	−0.555699	−	0.437263i
$187$	−5.86242			−0.428703
$188$		−	2.88870i		−	0.210680i
$189$	6.36211	−	0.653751i	0.462775	−	0.0475534i
$190$	−0.485142			−0.0351959
$191$	−10.6075	+	6.12422i	−0.767529	+	0.443133i	−0.831992	−	0.554787i	$-0.812800\pi$
$191$	−10.6075	+	6.12422i	−0.767529	+	0.443133i	0.0644637	+	0.997920i	$0.479466\pi$
$192$	−1.64686	−	0.536508i	−0.118852	−	0.0387191i
$193$	−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
$195$	7.26551	−	6.53172i	0.520294	−	0.467746i
$196$	−2.74252	−	4.75019i	−0.195894	−	0.339299i
$197$	0.823054	+	1.42557i	0.0586402	+	0.101568i	0.893855	−	0.448356i	$-0.147990\pi$
$197$	0.823054	+	1.42557i	0.0586402	+	0.101568i	−0.835215	+	0.549923i	$0.814657\pi$
$198$	2.55320	+	0.272349i	0.181448	+	0.0193550i
$199$	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
$204$	−8.82254	+	7.93149i	−0.617701	+	0.555315i
$205$	−3.59111	+	6.21998i	−0.250814	+	0.434422i
$206$	4.74572	−	2.73994i	0.330650	−	0.190901i
$207$	−19.2923	−	14.0623i	−1.34091	−	0.977400i
$208$	4.88495	−	2.82033i	0.338710	−	0.195554i
$209$	0.415230			0.0287221
$210$	2.02702	+	0.660353i	0.139878	+	0.0455687i
$211$	−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
$222$	−11.2515	+	10.1151i	−0.755152	+	0.678884i
$223$	−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	0.464850	−	0.885389i	$-0.346108\pi$
$227$	22.0581	−	12.7352i	1.46405	−	0.845267i	0.999195	+	0.0401223i	$0.0127748\pi$
$228$	0.624892	−	0.561780i	0.0413845	−	0.0372048i
$229$	−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
$231$	−1.73491	−	0.565192i	−0.114149	−	0.0371869i
$232$		−	1.17589i		−	0.0772012i
$233$		−	22.8670i		−	1.49806i	−0.662534	−	0.749032i	$-0.730519\pi$
$233$		−	22.8670i		−	1.49806i	0.662534	−	0.749032i	$-0.269481\pi$
$234$	−1.79488	+	16.8265i	−0.117335	+	1.09998i
$235$	1.44435	+	2.50169i	0.0942190	+	0.163192i
$236$	0.639178	+	0.369029i	0.0416069	+	0.0240218i
$237$	4.01003	+	4.46053i	0.260480	+	0.289743i
$238$	7.30109	−	4.21529i	0.473259	−	0.273236i
$239$	−5.26395	−	9.11743i	−0.340497	−	0.589758i	0.644028	−	0.765002i	$-0.277262\pi$
$239$	−5.26395	−	9.11743i	−0.340497	−	0.589758i	−0.984525	+	0.175244i	$0.943929\pi$
$240$	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
$243$	−0.0603312	+	15.5883i	−0.00387025	+	0.999993i
$244$			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	$0.499069\pi$
$251$	−13.6972	+	23.7242i	−0.864559	+	1.49746i	−0.867484	+	0.497465i	$0.834264\pi$
$252$	−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
$255$	3.67480	−	11.2801i	0.230125	−	0.706390i
$256$	1.00000			0.0625000
$257$	11.6461	−	6.72386i	0.726462	−	0.419423i	−0.0906647	−	0.995881i	$-0.528899\pi$
$257$	11.6461	−	6.72386i	0.726462	−	0.419423i	0.817126	+	0.576459i	$0.195566\pi$
$258$	6.51202	−	5.85433i	0.405421	−	0.364475i
$259$	9.31118	−	5.37581i	0.578569	−	0.334037i
$260$	−2.82033	+	4.88495i	−0.174909	+	0.302952i
$261$	2.85074	+	2.07793i	0.176456	+	0.128621i
$262$	4.09057	−	7.08508i	0.252716	−	0.437718i
$263$	9.48908			0.585122			0.292561	−	0.956247i	$-0.405493\pi$
$263$	9.48908			0.585122			0.292561	+	0.956247i	$0.405493\pi$
$264$	−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
$267$	8.99162	+	2.92925i	0.550278	+	0.179267i
$268$	−4.07315	−	7.05491i	−0.248807	−	0.430947i
$269$	−13.6081	−	23.5699i	−0.829700	−	1.43708i	−0.898273	−	0.439437i	$-0.855178\pi$
$269$	−13.6081	−	23.5699i	−0.829700	−	1.43708i	0.0685729	−	0.997646i	$-0.478155\pi$
$270$	−2.12448	+	4.74200i	−0.129292	+	0.288589i
$271$			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
$273$	3.72482	−	11.4337i	0.225437	−	0.691999i
$274$	−19.3458	+	11.1693i	−1.16872	+	0.674762i
$275$	−0.855894			−0.0516124
$276$	13.1054	+	4.26943i	0.788854	+	0.256990i
$277$			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
$279$	−13.8871	+	9.28167i	−0.831397	+	0.555679i
$280$	−1.23084			−0.0735565
$281$		−	0.335407i		−	0.0200087i	−0.999950	−	0.0100043i	$-0.996815\pi$
$281$		−	0.335407i		−	0.0200087i	0.999950	−	0.0100043i	$-0.00318453\pi$
$282$	−4.75730	−	1.54981i	−0.283293	−	0.0922899i
$283$	−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
$285$	−0.260282	+	0.798962i	−0.0154178	+	0.0473264i
$286$	2.41390	−	4.18100i	0.142737	−	0.247228i
$287$			8.84012i			0.521816i
$288$	−1.76711	+	2.42432i	−0.104128	+	0.142854i
$289$	−14.9576	−	25.9074i	−0.879860	−	1.52396i
$290$	0.587947	+	1.01835i	0.0345254	+	0.0597998i
$291$	−9.14598	−	2.97954i	−0.536147	−	0.174664i
$292$	4.44599	−	2.56690i	0.260182	−	0.150216i
$293$	−9.43540	−	5.44753i	−0.551222	−	0.318248i	0.198393	−	0.980123i	$-0.436428\pi$
$293$	−9.43540	−	5.44753i	−0.551222	−	0.318248i	−0.749615	+	0.661874i	$0.769761\pi$
$294$	−9.29430	+	1.96805i	−0.542054	+	0.114779i
$295$	−0.738059			−0.0429714
$296$	4.36761	−	7.56493i	0.253862	−	0.439703i
$297$	1.81833	−	4.05865i	0.105510	−	0.235507i
$298$	−4.45172	+	7.71061i	−0.257882	+	0.446664i
$299$	−38.8735	+	22.4436i	−2.24811	+	1.29795i
$300$	−1.28806	+	1.15797i	−0.0743663	+	0.0668555i
$301$	−5.38902	+	3.11135i	−0.310618	+	0.179335i
$302$	9.97617			0.574064
$303$	2.31437	−	7.10418i	0.132957	−	0.408124i
$304$	−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	$0.00465172\pi$
$311$			0.515416i			0.0292266i	−0.999893	+	0.0146133i	$0.995348\pi$
$312$	−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
$315$	2.17502	−	2.98394i	0.122549	−	0.168126i
$316$	−2.99903	−	1.73149i	−0.168709	−	0.0974040i
$317$	10.1149	+	5.83986i	0.568111	+	0.327999i	0.756395	−	0.654116i	$-0.226959\pi$
$317$	10.1149	+	5.83986i	0.568111	+	0.327999i	−0.188283	+	0.982115i	$0.560292\pi$
$318$	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
$321$	10.7229	+	11.9276i	0.598494	+	0.665731i
$322$	−8.48251	−	4.89738i	−0.472712	−	0.272920i
$323$	1.66148	+	2.87777i	0.0924473	+	0.160123i
$324$	−2.75464	−	8.56808i	−0.153035	−	0.476004i
$325$		−	5.64065i		−	0.312887i
$326$		−	1.12144i		−	0.0621110i
$327$	−33.4497	−	10.8971i	−1.84977	−	0.602611i
$328$	3.59111	+	6.21998i	0.198286	+	0.343441i
$329$	3.07917	+	1.77776i	0.169760	+	0.0980110i
$330$	1.10244	−	0.991101i	0.0606876	−	0.0545583i
$331$	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
$336$	1.58539	−	1.42527i	0.0864902	−	0.0777550i
$337$			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	−0.992503	−	0.122221i	$-0.960998\pi$
$347$	−7.27245	+	12.5962i	−0.390405	+	0.676202i	0.602098	+	0.798422i	$0.294332\pi$
$348$	−1.93654	−	0.630876i	−0.103809	−	0.0338185i
$349$	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
$351$	26.7480	+	11.9835i	1.42770	+	0.639630i
$352$	0.741226	−	0.427947i	0.0395075	−	0.0228097i
$353$	5.48052	−	9.49254i	0.291699	−	0.505237i	−0.682513	−	0.730874i	$-0.739113\pi$
$353$	5.48052	−	9.49254i	0.291699	−	0.505237i	0.974212	+	0.225637i	$0.0724463\pi$
$354$	0.950665	−	0.854651i	0.0505273	−	0.0454242i
$355$	−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	−0.708510	−	0.705700i	$-0.750633\pi$
$359$	−8.55681	+	4.94028i	−0.451611	+	0.260738i	0.256899	+	0.966438i	$0.417299\pi$
$360$	0.318204	−	2.98308i	0.0167708	−	0.157222i
$361$	9.38232	+	16.2507i	0.493806	+	0.855298i
$362$	7.50878	+	13.0056i	0.394653	+	0.683558i
$363$	13.2251	−	11.8894i	0.694138	−	0.624032i
$364$			6.94272i			0.363897i
$365$	−2.56690	+	4.44599i	−0.134357	+	0.232714i
$366$	10.6824	+	3.48006i	0.558378	+	0.181906i
$367$	−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
$369$	−21.4251	−	2.28541i	−1.11535	−	0.118974i
$370$			8.73523i			0.454123i
$371$	−0.852307			−0.0442496
$372$	5.96347	−	7.57872i	0.309191	−	0.392938i
$373$	−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
$375$	0.536508	−	1.64686i	0.0277052	−	0.0850437i
$376$	2.88870			0.148973
$377$	5.74418	−	3.31640i	0.295840	−	0.170803i
$378$	0.653751	+	6.36211i	0.0336253	+	0.327232i
$379$	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
$381$	−14.0630	−	15.6429i	−0.720469	−	0.801409i
$382$	−6.12422	−	10.6075i	−0.313342	−	0.542725i
$383$	13.4536	+	23.3023i	0.687446	+	1.19069i	0.972661	+	0.232228i	$0.0746014\pi$
$383$	13.4536	+	23.3023i	0.687446	+	1.19069i	−0.285216	+	0.958463i	$0.592065\pi$
$384$	0.536508	−	1.64686i	0.0273786	−	0.0840411i
$385$	−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	−0.897821	−	0.440360i	$-0.854851\pi$
$389$	−1.33226	+	2.30754i	−0.0675481	+	0.116997i	0.830273	+	0.557356i	$0.188184\pi$
$390$	6.53172	+	7.26551i	0.330746	+	0.367903i
$391$	−27.2534	+	47.2043i	−1.37826	+	2.38722i
$392$	4.75019	−	2.74252i	0.239921	−	0.138518i
$393$	−9.47353	−	10.5378i	−0.477877	−	0.531563i
$394$	−1.42557	+	0.823054i	−0.0718192	+	0.0414649i
$395$	3.46298			0.174242
$396$	−0.272349	+	2.55320i	−0.0136860	+	0.128303i
$397$	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	$-0.554757\pi$
$401$	−6.85565			−0.342355			−0.171177	+	0.985240i	$0.554757\pi$
$402$	−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
$408$	−7.93149	−	8.82254i	−0.392667	−	0.436781i
$409$	−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
$414$	14.0623	−	19.2923i	0.691126	−	0.948164i
$415$	2.08287	+	1.20254i	0.102244	+	0.0590305i
$416$	2.82033	+	4.88495i	0.138278	+	0.239504i
$417$	7.17139	−	22.0133i	0.351184	−	1.07799i
$418$			0.415230i			0.0203096i
$419$			37.9695i			1.85493i	0.373907	+	0.927466i	$0.378018\pi$
$419$			37.9695i			1.85493i	−0.373907	+	0.927466i	$0.621982\pi$
$420$	−0.660353	+	2.02702i	−0.0322219	+	0.0989083i
$421$	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
$423$	−5.10466	+	7.00313i	−0.248197	+	0.340504i
$424$	−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
$429$	−5.59046	−	6.21851i	−0.269910	−	0.300232i
$430$		−	5.05568i		−	0.243806i
$431$	−21.8729	−	12.6283i	−1.05358	−	0.608286i	−0.129932	−	0.991523i	$-0.541476\pi$
$431$	−21.8729	−	12.6283i	−1.05358	−	0.608286i	−0.923650	+	0.383237i	$0.874809\pi$
$432$	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
$441$	−1.74536	+	16.3623i	−0.0831125	+	0.779157i
$442$	38.6355			1.83770
$443$	−19.8597	+	11.4660i	−0.943563	+	0.544767i	−0.891076	−	0.453855i	$-0.850048\pi$
$443$	−19.8597	+	11.4660i	−0.943563	+	0.544767i	−0.0524878	+	0.998622i	$0.516715\pi$
$444$	−10.1151	−	11.2515i	−0.480044	−	0.533973i
$445$	4.72837	−	2.72992i	0.224146	−	0.129411i
$446$	6.61933	−	11.4650i	0.313435	−	0.542884i
$447$	10.3099	+	11.4682i	0.487643	+	0.542427i
$448$	−0.615418	+	1.06593i	−0.0290758	+	0.0503607i
$449$	10.9265			0.515655			0.257828	−	0.966191i	$-0.416993\pi$
$449$	10.9265			0.515655			0.257828	+	0.966191i	$0.416993\pi$
$450$	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
$453$	5.35229	−	16.4294i	0.251473	−	0.771920i
$454$	12.7352	+	22.0581i	0.597694	+	1.03524i
$455$	−3.47136	−	6.01257i	−0.162740	−	0.281874i
$456$	0.561780	+	0.624892i	0.0263078	+	0.0292633i
$457$			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
$459$	35.4045	−	3.63806i	1.65254	−	0.169810i
$460$	6.89167	−	3.97891i	0.321326	−	0.185518i
$461$	13.1893			0.614288			0.307144	−	0.951663i	$-0.400627\pi$
$461$	13.1893			0.614288			0.307144	+	0.951663i	$0.400627\pi$
$462$	0.565192	−	1.73491i	0.0262951	−	0.0807154i
$463$			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
$465$	−1.37515	+	9.54510i	−0.0637712	+	0.442643i
$466$	22.8670			1.05929
$467$			15.0537i			0.696603i	0.937383	+	0.348301i	$0.113241\pi$
$467$			15.0537i			0.696603i	−0.937383	+	0.348301i	$0.886759\pi$
$468$	−16.8265	−	1.79488i	−0.777805	−	0.0829683i
$469$	10.0268			0.462993
$470$	−2.50169	+	1.44435i	−0.115394	+	0.0666229i
$471$	−5.13345	−	1.67235i	−0.236537	−	0.0770579i
$472$	−0.369029	+	0.639178i	−0.0169860	+	0.0294205i
$473$			4.32712i			0.198961i
$474$	−4.46053	+	4.01003i	−0.204879	+	0.184187i
$475$	0.242571	+	0.420145i	0.0111299	+	0.0192776i
$476$	4.21529	+	7.30109i	0.193207	+	0.334645i
$477$	0.220344	−	2.06567i	0.0100889	−	0.0945805i
$478$	9.11743	−	5.26395i	0.417022	−	0.240768i
$479$	31.1132	+	17.9632i	1.42160	+	0.820760i	0.996436	−	0.0843575i	$-0.0268838\pi$
$479$	31.1132	+	17.9632i	1.42160	+	0.820760i	0.425162	+	0.905117i	$0.360217\pi$
$480$	0.358802	+	1.69448i	0.0163770	+	0.0773421i
$481$	49.2724			2.24663
$482$	12.8072	−	22.1828i	0.583354	−	1.01040i
$483$	−12.6163	+	11.3421i	−0.574059	+	0.516081i
$484$	−5.13372	+	8.89187i	−0.233351	+	0.404176i
$485$	−4.80954	+	2.77679i	−0.218390	+	0.126087i
$486$	−15.5883	−	0.0603312i	−0.707101	−	0.00273668i
$487$	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
$489$	−1.84687	−	0.601664i	−0.0835181	−	0.0272082i
$490$	−2.74252	+	4.75019i	−0.123895	+	0.214592i
$491$	−7.24410	−	12.5471i	−0.326922	−	0.566245i	0.654978	−	0.755648i	$-0.272678\pi$
$491$	−7.24410	−	12.5471i	−0.326922	−	0.566245i	−0.981899	+	0.189403i	$0.939345\pi$
$492$	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
$501$	12.7024	−	11.4195i	0.567502	−	0.510186i
$502$	−23.7242	−	13.6972i	−1.05886	−	0.611336i
$503$	12.2809	+	7.09036i	0.547576	+	0.316143i	0.748144	−	0.663537i	$-0.230945\pi$
$503$	12.2809	+	7.09036i	0.547576	+	0.316143i	−0.200568	+	0.979680i	$0.564279\pi$
$504$	−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
$507$	24.2374	−	21.7895i	1.07642	−	0.967706i
$508$	10.5175	+	6.07226i	0.466637	+	0.269413i
$509$	−9.88856	−	17.1275i	−0.438303	−	0.759162i	0.559256	−	0.828995i	$-0.311087\pi$
$509$	−9.88856	−	17.1275i	−0.438303	−	0.759162i	−0.997559	+	0.0698326i	$0.977753\pi$
$510$	11.2801	+	3.67480i	0.499493	+	0.162723i
$511$			6.31885i			0.279530i
$512$			1.00000i			0.0441942i
$513$	−2.50767	+	0.257680i	−0.110716	+	0.0113769i
$514$	6.72386	+	11.6461i	0.296577	+	0.513686i
$515$	−4.74572	−	2.73994i	−0.209121	−	0.120736i
$516$	5.85433	+	6.51202i	0.257722	+	0.286676i
$517$	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	−0.0220296	−	0.999757i	$-0.507013\pi$
$521$	−20.5169	−	11.8454i	−0.898860	−	0.518957i	−0.876830	+	0.480800i	$0.840346\pi$
$522$	−2.07793	+	2.85074i	−0.0909487	+	0.124774i
$523$			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
$534$	−2.92925	+	8.99162i	−0.126761	+	0.389105i
$535$	9.26008			0.400348
$536$	7.05491	−	4.07315i	0.304726	−	0.175933i
$537$	−31.5340	+	28.3492i	−1.36079	+	1.22336i
$538$	23.5699	−	13.6081i	1.01617	−	0.586687i
$539$	2.34731	−	4.06566i	0.101106	−	0.175120i
$540$	−4.74200	−	2.12448i	−0.204063	−	0.0914232i
$541$	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
$546$	11.4337	+	3.72482i	0.489317	+	0.159408i
$547$	−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
$549$	11.4624	−	15.7254i	0.489202	−	0.671142i
$550$		−	0.855894i		−	0.0364955i
$551$	−0.285238	+	0.494046i	−0.0121515	+	0.0210471i
$552$	−4.26943	+	13.1054i	−0.181719	+	0.557804i
$553$	3.69131	−	2.13118i	0.156971	−	0.0906270i
$554$	−16.7112			−0.709991
$555$	14.3857	+	4.68652i	0.610640	+	0.198932i
$556$			13.3668i			0.566878i
$557$	−2.95495			−0.125205			−0.0626025	−	0.998039i	$-0.519940\pi$
$557$	−2.95495			−0.125205			−0.0626025	+	0.998039i	$0.519940\pi$
$558$	−9.28167	−	13.8871i	−0.392925	−	0.587886i
$559$	−28.5173			−1.20615
$560$		−	1.23084i		−	0.0520123i
$561$	−9.65461	−	3.14524i	−0.407618	−	0.132792i
$562$	0.335407			0.0141483
$563$	−38.1155	+	22.0060i	−1.60638	+	0.927441i	−0.616204	+	0.787587i	$0.711330\pi$
$563$	−38.1155	+	22.0060i	−1.60638	+	0.927441i	−0.990172	+	0.139855i	$0.955336\pi$
$564$	1.54981	−	4.75730i	0.0652588	−	0.200318i
$565$	−9.54261	+	16.5283i	−0.401461	+	0.695350i
$566$		−	3.13491i		−	0.131770i
$567$	10.8283	+	2.33668i	0.454744	+	0.0981315i
$568$	1.94423	+	3.36751i	0.0815783	+	0.141298i
$569$	18.4180	+	31.9010i	0.772124	+	1.33736i	0.936397	+	0.350943i	$0.114139\pi$
$569$	18.4180	+	31.9010i	0.772124	+	1.33736i	−0.164272	+	0.986415i	$0.552528\pi$
$570$	−0.798962	−	0.260282i	−0.0334648	−	0.0109020i
$571$	−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
$576$	−2.42432	−	1.76711i	−0.101013	−	0.0736296i
$577$	−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
$579$	−32.1611	+	28.9130i	−1.33657	+	1.20158i
$580$	−1.01835	+	0.587947i	−0.0422848	+	0.0244132i
$581$	2.96027			0.122813
$582$	2.97954	−	9.14598i	0.123506	−	0.379113i
$583$	−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	$-0.647393\pi$
$587$	−21.6442			−0.893354			−0.446677	+	0.894695i	$0.647393\pi$
$588$	−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	$0.122975\pi$
$593$			18.3513i			0.753598i	−0.926295	+	0.376799i	$0.877025\pi$
$594$	4.05865	+	1.81833i	0.166528	+	0.0746071i
$595$	−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	−0.521170	−	0.853453i	$-0.674504\pi$
$599$	−1.04365	+	0.602553i	−0.0426425	+	0.0246197i	0.478527	+	0.878073i	$0.341171\pi$
$600$	−1.15797	−	1.28806i	−0.0472740	−	0.0525849i
$601$	−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
$603$	−2.59219	+	24.3010i	−0.105562	+	0.989615i
$604$			9.97617i			0.405925i
$605$		−	10.2674i		−	0.417431i
$606$	7.10418	+	2.31437i	0.288587	+	0.0940148i
$607$	−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
$609$	1.86425	−	1.67597i	0.0755433	−	0.0679137i
$610$	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
$615$	−9.25113	+	8.31680i	−0.373042	+	0.335366i
$616$			1.05346i			0.0424453i
$617$	−13.2775	−	7.66578i	−0.534533	−	0.308613i	0.208328	−	0.978059i	$-0.433198\pi$
$617$	−13.2775	−	7.66578i	−0.534533	−	0.308613i	−0.742860	+	0.669447i	$0.766531\pi$
$618$	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
$627$	0.683827	+	0.222774i	0.0273094	+	0.00889675i
$628$	3.11711			0.124386
$629$	51.8158	−	29.9158i	2.06603	−	1.19282i
$630$	2.98394	+	2.17502i	0.118883	+	0.0866550i
$631$	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
$633$	−16.4304	+	14.7710i	−0.653052	+	0.587096i
$634$	−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
$639$	−11.5996	−	1.23733i	−0.458873	−	0.0489479i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−5.80324	−	10.0515i	−0.229214	−	0.397011i	0.728361	−	0.685193i	$-0.240282\pi$
$641$	−5.80324	−	10.0515i	−0.229214	−	0.397011i	−0.957575	+	0.288183i	$0.906949\pi$
$642$	−11.9276	+	10.7229i	−0.470743	+	0.423200i
$643$			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
$645$	−8.32601	−	2.71241i	−0.327836	−	0.106801i
$646$	−2.87777	+	1.66148i	−0.113224	+	0.0653701i
$647$	6.80419			0.267500			0.133750	−	0.991015i	$-0.457298\pi$
$647$	6.80419			0.267500			0.133750	+	0.991015i	$0.457298\pi$
$648$	8.56808	−	2.75464i	0.336586	−	0.108212i
$649$			0.631700i			0.0247964i
$650$	5.64065			0.221245
$651$	4.40840	+	11.0207i	0.172779	+	0.431937i
$652$	1.12144			0.0439191
$653$		−	12.8192i		−	0.501655i	−0.968032	−	0.250828i	$-0.919297\pi$
$653$		−	12.8192i		−	0.501655i	0.968032	−	0.250828i	$-0.0807027\pi$
$654$	10.8971	−	33.4497i	0.426110	−	1.30799i
$655$	−8.18115			−0.319664
$656$	−6.21998	+	3.59111i	−0.242849	+	0.140209i
$657$	−15.3145	−	1.63359i	−0.597475	−	0.0637325i
$658$	−1.77776	+	3.07917i	−0.0693042	+	0.120038i
$659$		−	14.6238i		−	0.569664i	−0.958577	−	0.284832i	$-0.908062\pi$
$659$		−	14.6238i		−	0.569664i	0.958577	−	0.284832i	$-0.0919378\pi$
$660$	0.991101	+	1.10244i	0.0385786	+	0.0429126i
$661$	−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
$663$	20.7283	−	63.6274i	0.805019	−	2.47108i
$664$	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
$669$	−15.3300	−	17.0522i	−0.592692	−	0.659277i
$670$	−4.07315	+	7.05491i	−0.157360	+	0.272555i
$671$	−4.80797	+	2.77588i	−0.185610	+	0.107162i
$672$	1.42527	+	1.58539i	0.0549811	+	0.0611578i
$673$	−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
$675$	5.16893	−	0.531144i	0.198952	−	0.0204437i
$676$	−9.40849	+	16.2960i	−0.361865	+	0.626768i
$677$	−8.94985	−	15.5016i	−0.343971	−	0.595774i	0.641196	−	0.767377i	$-0.278439\pi$
$677$	−8.94985	−	15.5016i	−0.343971	−	0.595774i	−0.985166	+	0.171603i	$0.945105\pi$
$678$	−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	$-0.999739\pi$
$683$		−	0.0428554i		−	0.00163982i	1.00000		0.000819909i	$-0.000260985\pi$
$684$	1.33051	−	0.589916i	0.0508734	−	0.0225560i
$685$	19.3458	+	11.1693i	0.739165	+	0.426757i
$686$			15.3670i			0.586716i
$687$	−20.0410	−	22.2924i	−0.764611	−	0.850509i
$688$	−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
$693$	−2.55393	−	1.86159i	−0.0970159	−	0.0707159i
$694$	−12.5962	−	7.27245i	−0.478147	−	0.276058i
$695$	−6.68339	−	11.5760i	−0.253516	−	0.439102i
$696$	0.630876	−	1.93654i	0.0239133	−	0.0734042i
$697$			49.1944i			1.86337i
$698$			12.3867i			0.468844i
$699$	12.2683	−	37.6588i	0.464030	−	1.42438i
$700$	0.615418	+	1.06593i	0.0232606	+	0.0402885i
$701$	−7.28410	−	4.20548i	−0.275117	−	0.158839i	0.356094	−	0.934450i	$-0.384108\pi$
$701$	−7.28410	−	4.20548i	−0.275117	−	0.158839i	−0.631211	+	0.775611i	$0.717442\pi$
$702$	−11.9835	+	26.7480i	−0.452287	+	1.00954i
$703$	−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
$708$	0.854651	+	0.950665i	0.0321197	+	0.0357282i
$709$		−	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	$-0.579237\pi$
$719$	19.2029	−	33.2604i	0.716148	−	1.24040i	0.962515	−	0.271228i	$-0.0874296\pi$
$720$	2.98308	+	0.318204i	0.111173	+	0.0118588i
$721$	−6.74484			−0.251191
$722$	−16.2507	+	9.38232i	−0.604787	+	0.349174i
$723$	−29.6608	−	32.9930i	−1.10310	−	1.22702i
$724$	−13.0056	+	7.50878i	−0.483349	+	0.279062i
$725$	0.587947	−	1.01835i	0.0218358	−	0.0378207i
$726$	11.8894	+	13.2251i	0.441257	+	0.490829i
$727$	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
$732$	−3.48006	+	10.6824i	−0.128627	+	0.394833i
$733$	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
$735$	6.35153	+	7.06507i	0.234280	+	0.260599i
$736$		−	7.95781i		−	0.293329i
$737$	3.48619	−	6.03825i	0.128415	−	0.222422i
$738$	2.28541	−	21.4251i	0.0841270	−	0.788669i
$739$	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
$741$	−1.46816	+	4.50667i	−0.0539343	+	0.165557i
$742$		−	0.852307i		−	0.0312892i
$743$	−5.85981			−0.214976			−0.107488	−	0.994206i	$-0.534281\pi$
$743$	−5.85981			−0.214976			−0.107488	+	0.994206i	$0.534281\pi$
$744$	7.57872	+	5.96347i	0.277849	+	0.218631i
$745$	8.90345			0.326197
$746$		−	7.24267i		−	0.265173i
$747$	−0.765308	+	7.17456i	−0.0280012	+	0.262503i
$748$	5.86242			0.214351
$749$	9.87064	−	5.69882i	0.360665	−	0.208230i
$750$	1.64686	+	0.536508i	0.0601349	+	0.0195905i
$751$	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
$753$	−35.2857	+	31.7219i	−1.28588	+	1.15601i
$754$	3.31640	+	5.74418i	0.120776	+	0.209191i
$755$	−4.98808	−	8.63961i	−0.181535	−	0.314428i
$756$	−6.36211	+	0.653751i	−0.231388	+	0.0237767i
$757$	−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	−0.536635	−	0.843814i	$-0.680305\pi$
$761$	12.7572	−	22.0961i	0.462447	−	0.800982i	0.999082	+	0.0428324i	$0.0136382\pi$
$762$	15.6429	−	14.0630i	0.566682	−	0.509449i
$763$	−12.4998	+	21.6504i	−0.452525	+	0.783795i
$764$	10.6075	−	6.12422i	0.383764	−	0.221566i
$765$	12.1038	−	16.6053i	0.437613	−	0.600366i
$766$	−23.3023	+	13.4536i	−0.841946	+	0.486097i
$767$	−4.16313			−0.150322
$768$	1.64686	+	0.536508i	0.0594261	+	0.0193596i
$769$	−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	$-0.308585\pi$
$773$	31.4592			1.13151			0.565754	+	0.824574i	$0.308585\pi$
$774$	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
$780$	−7.26551	+	6.53172i	−0.260147	+	0.233873i
$781$	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
$786$	10.5378	−	9.47353i	0.375871	−	0.337910i
$787$	−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
$789$	15.6272	+	5.09097i	0.556344	+	0.181243i
$790$			3.46298i			0.123207i
$791$			23.4908i			0.835235i
$792$	−2.55320	−	0.272349i	−0.0907239	−	0.00967749i
$793$	−18.2941	−	31.6863i	−0.649642	−	1.12521i
$794$	16.3409	+	9.43442i	0.579917	+	0.334815i
$795$	−0.801852	−	0.891934i	−0.0284388	−	0.0316336i
$796$	−10.0304	+	5.79107i	−0.355519	+	0.205259i
$797$	1.90325	+	3.29653i	0.0674166	+	0.116769i	0.897763	−	0.440478i	$-0.145191\pi$
$797$	1.90325	+	3.29653i	0.0674166	+	0.116769i	−0.830347	+	0.557247i	$0.811858\pi$
$798$	−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
$801$	13.2364	+	9.64815i	0.467685	+	0.340901i
$802$		−	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	−0.828785	−	0.559567i	$-0.810968\pi$
$809$	1.99687	−	3.45868i	0.0702062	−	0.121601i	0.898992	+	0.437966i	$0.144301\pi$
$810$	−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
$813$	−2.26622	+	6.95639i	−0.0794799	+	0.243971i
$814$	7.47643			0.262049
$815$	−0.971199	+	0.560722i	−0.0340196	+	0.0196412i
$816$	8.82254	−	7.93149i	0.308851	−	0.277658i
$817$	2.12412	−	1.22636i	0.0743135	−	0.0429049i
$818$	5.85435	−	10.1400i	0.204693	−	0.354538i
$819$	12.2685	−	16.8314i	0.428698	−	0.588135i
$820$	3.59111	−	6.21998i	0.125407	−	0.217211i
$821$	24.6632			0.860752			0.430376	−	0.902650i	$-0.358381\pi$
$821$	24.6632			0.860752			0.430376	+	0.902650i	$0.358381\pi$
$822$	−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
$825$	−1.40954	−	0.459194i	−0.0490739	−	0.0159871i
$826$	−0.454214	−	0.786722i	−0.0158041	−	0.0273736i
$827$	27.1143	+	46.9634i	0.942858	+	1.63308i	0.759984	+	0.649942i	$0.225207\pi$
$827$	27.1143	+	46.9634i	0.942858	+	1.63308i	0.182874	+	0.983136i	$0.441460\pi$
$828$	19.2923	+	14.0623i	0.670453	+	0.488700i
$829$			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
$831$	−8.96570	+	27.5211i	−0.311017	+	0.954696i
$832$	−4.88495	+	2.82033i	−0.169355	+	0.0977772i
$833$	37.5696			1.30171
$834$	22.0133	+	7.17139i	0.762257	+	0.248325i
$835$		−	9.86165i		−	0.341276i
$836$	−0.415230			−0.0143610
$837$	−27.8498	+	7.83513i	−0.962630	+	0.270822i
$838$	−37.9695			−1.31164
$839$		−	41.9642i		−	1.44876i	−0.689399	−	0.724382i	$-0.742125\pi$
$839$		−	41.9642i		−	1.44876i	0.689399	−	0.724382i	$-0.257875\pi$
$840$	−2.02702	−	0.660353i	−0.0699388	−	0.0227843i
$841$	−27.6173			−0.952320
$842$	−28.8664	+	16.6660i	−0.994802	+	0.574349i
$843$	0.179948	−	0.552369i	0.00619775	−	0.0190246i
$844$	6.37798	−	11.0470i	0.219539	−	0.380253i
$845$		−	18.8170i		−	0.647324i
$846$	−7.00313	−	5.10466i	−0.240773	−	0.175502i
$847$	−6.31877	−	10.9444i	−0.217115	−	0.376055i
$848$	−0.346231	−	0.599690i	−0.0118896	−	0.0205934i
$849$	−5.16276	−	1.68190i	−0.177186	−	0.0577227i
$850$	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
$855$	−0.857299	+	1.17614i	−0.0293190	+	0.0402231i
$856$	4.63004	−	8.01947i	0.158252	−	0.274100i
$857$	23.4972	−	13.5661i	0.802648	−	0.463409i	−0.0417480	−	0.999128i	$-0.513293\pi$
$857$	23.4972	−	13.5661i	0.802648	−	0.463409i	0.844396	+	0.535719i	$0.179959\pi$
$858$	6.21851	−	5.59046i	0.212296	−	0.190855i
$859$	−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
$861$	−4.74280	+	14.5585i	−0.161634	+	0.496152i
$862$	12.6283	−	21.8729i	0.430123	−	0.744995i
$863$	2.49034	+	4.31339i	0.0847721	+	0.146830i	0.905294	−	0.424785i	$-0.139650\pi$
$863$	2.49034	+	4.31339i	0.0847721	+	0.146830i	−0.820522	+	0.571615i	$0.806317\pi$
$864$	−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
$873$	−13.4636	−	9.81378i	−0.455675	−	0.332146i
$874$	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
$879$	−12.6162	−	14.0335i	−0.425533	−	0.473338i
$880$	−0.741226	−	0.427947i	−0.0249867	−	0.0144261i
$881$	1.36745	+	2.36849i	0.0460704	+	0.0797963i	0.888141	−	0.459571i	$-0.151997\pi$
$881$	1.36745	+	2.36849i	0.0460704	+	0.0797963i	−0.842071	+	0.539367i	$0.818663\pi$
$882$	−16.3623	−	1.74536i	−0.550948	−	0.0587694i
$883$			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
$885$	−1.21548	−	0.395974i	−0.0408580	−	0.0133105i
$886$	−11.4660	−	19.8597i	−0.385208	−	0.667200i
$887$	−27.6973	−	15.9910i	−0.929983	−	0.536926i	−0.0431766	−	0.999067i	$-0.513748\pi$
$887$	−27.6973	−	15.9910i	−0.929983	−	0.536926i	−0.886806	+	0.462142i	$0.847081\pi$
$888$	11.2515	−	10.1151i	0.377576	−	0.339442i
$889$	−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
$894$	−11.4682	+	10.3099i	−0.383554	+	0.344816i
$895$			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
$906$	16.4294	+	5.35229i	0.545830	+	0.177818i
$907$	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
$909$	7.62290	−	10.4579i	0.252836	−	0.346868i
$910$	6.01257	−	3.47136i	0.199315	−	0.115074i
$911$	−5.35917	+	9.28235i	−0.177557	+	0.307538i	−0.941043	−	0.338286i	$-0.890153\pi$
$911$	−5.35917	+	9.28235i	−0.177557	+	0.307538i	0.763486	+	0.645824i	$0.223486\pi$
$912$	−0.624892	+	0.561780i	−0.0206923	+	0.0186024i
$913$	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
$918$	3.63806	+	35.4045i	0.120074	+	1.16852i
$919$	−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
$921$	40.6053	−	36.5043i	1.33799	−	1.20286i
$922$			13.1893i			0.434367i
$923$	−10.9668	+	18.9950i	−0.360975	+	0.625227i
$924$	1.73491	+	0.565192i	0.0570744	+	0.0185935i
$925$	7.56493	−	4.36761i	0.248733	−	0.143606i
$926$	−19.5842			−0.643576
$927$	1.74372	−	16.3469i	0.0572713	−	0.536903i
$928$			1.17589i			0.0386006i
$929$	45.4921			1.49255			0.746273	−	0.665640i	$-0.231841\pi$
$929$	45.4921			1.49255			0.746273	+	0.665640i	$0.231841\pi$
$930$	−9.54510	−	1.37515i	−0.312996	−	0.0450931i
$931$	−2.66102			−0.0872115
$932$			22.8670i			0.749032i
$933$	−0.276525	+	0.848820i	−0.00905301	+	0.0277891i
$934$	−15.0537			−0.492572
$935$	−5.07701	+	2.93121i	−0.166036	+	0.0958608i
$936$	1.79488	−	16.8265i	0.0586674	−	0.549991i
$937$	−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
$939$	21.7443	+	24.1871i	0.709599	+	0.789317i
$940$	−1.44435	−	2.50169i	−0.0471095	−	0.0815961i
$941$	17.5176	+	30.3414i	0.571059	+	0.989103i	0.996458	+	0.0840967i	$0.0268005\pi$
$941$	17.5176	+	30.3414i	0.571059	+	0.989103i	−0.425399	+	0.905006i	$0.639866\pi$
$942$	1.67235	−	5.13345i	0.0544882	−	0.167257i
$943$	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	−0.796822	−	0.604215i	$-0.793487\pi$
$947$	3.84219	−	6.65487i	0.124854	−	0.216254i	0.921676	+	0.387960i	$0.126820\pi$
$948$	−4.01003	−	4.46053i	−0.130240	−	0.144871i
$949$	−14.4790	+	25.0783i	−0.470007	+	0.814077i
$950$	−0.420145	+	0.242571i	−0.0136313	+	0.00787004i
$951$	13.5248	+	15.0442i	0.438571	+	0.487841i
$952$	−7.30109	+	4.21529i	−0.236630	+	0.136618i
$953$	27.7010			0.897325			0.448663	−	0.893701i	$-0.351901\pi$
$953$	27.7010			0.897325			0.448663	+	0.893701i	$0.351901\pi$
$954$	2.06567	+	0.220344i	0.0668785	+	0.00713391i
$955$	−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
$966$	−11.3421	−	12.6163i	−0.364925	−	0.405921i
$967$	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	−0.138913	−	0.990305i	$-0.544361\pi$
$971$	20.2315	−	11.6806i	0.649259	−	0.374850i	0.788172	+	0.615455i	$0.211028\pi$
$972$	0.0603312	−	15.5883i	0.00193513	−	0.499996i
$973$	−14.2481	−	8.22616i	−0.456774	−	0.263718i
$974$	12.7436	+	22.0726i	0.408333	+	0.707253i
$975$	3.02626	−	9.28939i	0.0969178	−	0.297498i
$976$		−	6.48651i		−	0.207628i
$977$			41.7506i			1.33572i	0.744287	+	0.667860i	$0.232789\pi$
$977$			41.7506i			1.33572i	−0.744287	+	0.667860i	$0.767211\pi$
$978$	0.601664	−	1.84687i	0.0192391	−	0.0590562i
$979$	−2.33653	−	4.04698i	−0.0746757	−	0.129342i
$980$	−4.75019	−	2.74252i	−0.151739	−	0.0876067i
$981$	−49.2407	−	35.8920i	−1.57213	−	1.14594i
$982$	12.5471	−	7.24410i	0.400396	−	0.231168i
$983$	−26.6042	−	46.0798i	−0.848541	−	1.46972i	−0.882510	−	0.470294i	$-0.844148\pi$
$983$	−26.6042	−	46.0798i	−0.848541	−	1.46972i	0.0339685	−	0.999423i	$-0.489185\pi$
$984$	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
$987$	4.11719	+	4.57972i	0.131051	+	0.145774i
$988$		−	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
$999$	4.63967	+	45.1518i	0.146793	+	1.42854i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.64686 + 0.536508i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.536508 + 1.64686i) q^{6} +(0.615418 - 1.06593i) q^{7} -1.00000i q^{8} +(2.42432 + 1.76711i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.64686 + 0.536508i) q^{3} -1.00000 q^{4} +(0.866025 - 0.500000i) q^{5} +(-0.536508 + 1.64686i) q^{6} +(0.615418 - 1.06593i) q^{7} -1.00000i q^{8} +(2.42432 + 1.76711i) q^{9} +(0.500000 + 0.866025i) q^{10} +(-0.427947 - 0.741226i) q^{11} +(-1.64686 - 0.536508i) 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} +(-1.76711 + 2.42432i) q^{18} +(-0.242571 + 0.420145i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(1.58539 - 1.42527i) q^{21} +(0.741226 - 0.427947i) q^{22} -7.95781 q^{23} +(0.536508 - 1.64686i) 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} +(-2.42432 - 1.76711i) 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} +(1.42527 + 1.58539i) q^{42} +(-4.37834 - 2.52784i) q^{43} +(0.427947 + 0.741226i) q^{44} +(2.98308 + 0.318204i) q^{45} -7.95781i q^{46} +2.88870i q^{47} +(1.64686 + 0.536508i) q^{48} +(2.74252 + 4.75019i) q^{49} +(0.866025 + 0.500000i) q^{50} +(8.82254 - 7.93149i) 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} +(-0.624892 + 0.561780i) 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} +(-13.1054 - 4.26943i) q^{69} +1.23084 q^{70} +(-3.36751 + 1.94423i) q^{71} +(1.76711 - 2.42432i) q^{72} +(-4.44599 + 2.56690i) q^{73} +(-4.36761 + 7.56493i) q^{74} +(1.28806 - 1.15797i) 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} +(2.75464 + 8.56808i) q^{81} +(-3.59111 - 6.21998i) q^{82} +(1.20254 + 2.08287i) q^{83} +(-1.58539 + 1.42527i) q^{84} -6.84947i q^{85} +(2.52784 - 4.37834i) q^{86} +(1.93654 + 0.630876i) q^{87} +(-0.741226 + 0.427947i) q^{88} +5.45985 q^{89} +(-0.318204 + 2.98308i) q^{90} -6.94272i q^{91} +7.95781 q^{92} +(-5.96347 + 7.57872i) q^{93} -2.88870 q^{94} +0.485142i q^{95} +(-0.536508 + 1.64686i) q^{96} -5.55358 q^{97} +(-4.75019 + 2.74252i) q^{98} +(0.272349 - 2.55320i) 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

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