LMFDB - Embedded newform 930.2.k.a.247.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(247,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("930.247");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.k (of order $4$, 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:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			247.16
Character	$\chi$	$=$	930.247
Dual form			930.2.k.a.433.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.23399 - 0.0964676i) q^{5} -1.00000i q^{6} +(-1.13560 - 1.13560i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.23399 - 0.0964676i) q^{5} -1.00000i q^{6} +(-1.13560 - 1.13560i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.64788 + 1.51145i) q^{10} -5.98186i q^{11} +(0.707107 - 0.707107i) q^{12} +(0.515345 + 0.515345i) q^{13} -1.60598i q^{14} +(-1.64788 - 1.51145i) q^{15} -1.00000 q^{16} +(2.59395 - 2.59395i) q^{17} +(-0.707107 + 0.707107i) q^{18} -0.796628i q^{19} +(0.0964676 + 2.23399i) q^{20} +1.60598i q^{21} +(4.22981 - 4.22981i) q^{22} +(-0.904567 - 0.904567i) q^{23} +1.00000 q^{24} +(4.98139 - 0.431015i) q^{25} +0.728809i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.13560 - 1.13560i) q^{28} -3.11608 q^{29} +(-0.0964676 - 2.23399i) q^{30} +(5.10027 - 2.23320i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.22981 + 4.22981i) q^{33} +3.66840 q^{34} +(-2.64646 - 2.42736i) q^{35} -1.00000 q^{36} +(-2.27666 + 2.27666i) q^{37} +(0.563301 - 0.563301i) q^{38} -0.728809i q^{39} +(-1.51145 + 1.64788i) q^{40} +3.72145 q^{41} +(-1.13560 + 1.13560i) q^{42} +(-2.06543 - 2.06543i) q^{43} +5.98186 q^{44} +(0.0964676 + 2.23399i) q^{45} -1.27925i q^{46} +(5.48791 + 5.48791i) q^{47} +(0.707107 + 0.707107i) q^{48} -4.42083i q^{49} +(3.82715 + 3.21760i) q^{50} -3.66840 q^{51} +(-0.515345 + 0.515345i) q^{52} +(5.23051 + 5.23051i) q^{53} +1.00000 q^{54} +(-0.577056 - 13.3634i) q^{55} +1.60598 q^{56} +(-0.563301 + 0.563301i) q^{57} +(-2.20340 - 2.20340i) q^{58} -9.53350i q^{59} +(1.51145 - 1.64788i) q^{60} +1.27761i q^{61} +(5.18555 + 2.02733i) q^{62} +(1.13560 - 1.13560i) q^{63} -1.00000i q^{64} +(1.20099 + 1.10156i) q^{65} -5.98186 q^{66} +(-4.19895 - 4.19895i) q^{67} +(2.59395 + 2.59395i) q^{68} +1.27925i q^{69} +(-0.154925 - 3.58774i) q^{70} -6.20904 q^{71} +(-0.707107 - 0.707107i) q^{72} +(10.1965 + 10.1965i) q^{73} -3.21968 q^{74} +(-3.82715 - 3.21760i) q^{75} +0.796628 q^{76} +(-6.79299 + 6.79299i) q^{77} +(0.515345 - 0.515345i) q^{78} +1.08942 q^{79} +(-2.23399 + 0.0964676i) q^{80} -1.00000 q^{81} +(2.63146 + 2.63146i) q^{82} +(5.43134 + 5.43134i) q^{83} -1.60598 q^{84} +(5.54461 - 6.04508i) q^{85} -2.92097i q^{86} +(2.20340 + 2.20340i) q^{87} +(4.22981 + 4.22981i) q^{88} -0.818030 q^{89} +(-1.51145 + 1.64788i) q^{90} -1.17045i q^{91} +(0.904567 - 0.904567i) q^{92} +(-5.18555 - 2.02733i) q^{93} +7.76108i q^{94} +(-0.0768488 - 1.77966i) q^{95} +1.00000i q^{96} +(-13.3240 - 13.3240i) q^{97} +(3.12600 - 3.12600i) q^{98} +5.98186 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7}+O(q^{10}) $ 32 * q - 4 * q^7	$ 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	2.23399	−	0.0964676i	0.999069	−	0.0431416i
$5$	2.23399	−	0.0964676i	0.999069	−	0.0431416i
$6$		−	1.00000i		−	0.408248i
$7$	−1.13560	−	1.13560i	−0.429216	−	0.429216i	0.459145	−	0.888361i	$-0.348156\pi$
$7$	−1.13560	−	1.13560i	−0.429216	−	0.429216i	−0.888361	+	0.459145i	$0.848156\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	1.64788	+	1.51145i	0.521105	+	0.477964i
$11$		−	5.98186i		−	1.80360i	−0.432156	−	0.901799i	$-0.642247\pi$
$11$		−	5.98186i		−	1.80360i	0.432156	−	0.901799i	$-0.357753\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	0.515345	+	0.515345i	0.142931	+	0.142931i	0.774952	−	0.632021i	$-0.217774\pi$
$13$	0.515345	+	0.515345i	0.142931	+	0.142931i	−0.632021	+	0.774952i	$0.717774\pi$
$14$		−	1.60598i		−	0.429216i
$15$	−1.64788	−	1.51145i	−0.425481	−	0.390256i
$16$	−1.00000			−0.250000
$17$	2.59395	−	2.59395i	0.629125	−	0.629125i	−0.318723	−	0.947848i	$-0.603254\pi$
$17$	2.59395	−	2.59395i	0.629125	−	0.629125i	0.947848	+	0.318723i	$0.103254\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$		−	0.796628i		−	0.182759i	−0.995816	−	0.0913795i	$-0.970872\pi$
$19$		−	0.796628i		−	0.182759i	0.995816	−	0.0913795i	$-0.0291276\pi$
$20$	0.0964676	+	2.23399i	0.0215708	+	0.499534i
$21$			1.60598i			0.350453i
$22$	4.22981	−	4.22981i	0.901799	−	0.901799i
$23$	−0.904567	−	0.904567i	−0.188615	−	0.188615i	0.606482	−	0.795097i	$-0.292580\pi$
$23$	−0.904567	−	0.904567i	−0.188615	−	0.188615i	−0.795097	+	0.606482i	$0.792580\pi$
$24$	1.00000			0.204124
$25$	4.98139	−	0.431015i	0.996278	−	0.0862029i
$26$			0.728809i			0.142931i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	1.13560	−	1.13560i	0.214608	−	0.214608i
$29$	−3.11608			−0.578641			−0.289321	−	0.957232i	$-0.593429\pi$
$29$	−3.11608			−0.578641			−0.289321	+	0.957232i	$0.593429\pi$
$30$	−0.0964676	−	2.23399i	−0.0176125	−	0.407868i
$31$	5.10027	−	2.23320i	0.916036	−	0.401095i
$31$	5.10027	−	2.23320i	0.916036	−	0.401095i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−4.22981	+	4.22981i	−0.736316	+	0.736316i
$34$	3.66840			0.629125
$35$	−2.64646	−	2.42736i	−0.447333	−	0.410299i
$36$	−1.00000			−0.166667
$37$	−2.27666	+	2.27666i	−0.374280	+	0.374280i	−0.869034	−	0.494753i	$-0.835258\pi$
$37$	−2.27666	+	2.27666i	−0.374280	+	0.374280i	0.494753	+	0.869034i	$0.335258\pi$
$38$	0.563301	−	0.563301i	0.0913795	−	0.0913795i
$39$		−	0.728809i		−	0.116703i
$40$	−1.51145	+	1.64788i	−0.238982	+	0.260553i
$41$	3.72145			0.581193			0.290597	−	0.956846i	$-0.406146\pi$
$41$	3.72145			0.581193			0.290597	+	0.956846i	$0.406146\pi$
$42$	−1.13560	+	1.13560i	−0.175227	+	0.175227i
$43$	−2.06543	−	2.06543i	−0.314976	−	0.314976i	0.531858	−	0.846834i	$-0.321494\pi$
$43$	−2.06543	−	2.06543i	−0.314976	−	0.314976i	−0.846834	+	0.531858i	$0.821494\pi$
$44$	5.98186			0.901799
$45$	0.0964676	+	2.23399i	0.0143805	+	0.333023i
$46$		−	1.27925i		−	0.188615i
$47$	5.48791	+	5.48791i	0.800494	+	0.800494i	0.983173	−	0.182678i	$-0.0584767\pi$
$47$	5.48791	+	5.48791i	0.800494	+	0.800494i	−0.182678	+	0.983173i	$0.558477\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$		−	4.42083i		−	0.631547i
$50$	3.82715	+	3.21760i	0.541240	+	0.455037i
$51$	−3.66840			−0.513679
$52$	−0.515345	+	0.515345i	−0.0714656	+	0.0714656i
$53$	5.23051	+	5.23051i	0.718466	+	0.718466i	0.968291	−	0.249825i	$-0.0803732\pi$
$53$	5.23051	+	5.23051i	0.718466	+	0.718466i	−0.249825	+	0.968291i	$0.580373\pi$
$54$	1.00000			0.136083
$55$	−0.577056	−	13.3634i	−0.0778102	−	1.80192i
$56$	1.60598			0.214608
$57$	−0.563301	+	0.563301i	−0.0746110	+	0.0746110i
$58$	−2.20340	−	2.20340i	−0.289321	−	0.289321i
$59$		−	9.53350i		−	1.24116i	−0.784145	−	0.620578i	$-0.786898\pi$
$59$		−	9.53350i		−	1.24116i	0.784145	−	0.620578i	$-0.213102\pi$
$60$	1.51145	−	1.64788i	0.195128	−	0.212740i
$61$			1.27761i			0.163582i	0.996650	+	0.0817909i	$0.0260640\pi$
$61$			1.27761i			0.163582i	−0.996650	+	0.0817909i	$0.973936\pi$
$62$	5.18555	+	2.02733i	0.658566	+	0.257471i
$63$	1.13560	−	1.13560i	0.143072	−	0.143072i
$64$		−	1.00000i		−	0.125000i
$65$	1.20099	+	1.10156i	0.148964	+	0.136632i
$66$	−5.98186			−0.736316
$67$	−4.19895	−	4.19895i	−0.512983	−	0.512983i	0.402456	−	0.915439i	$-0.368157\pi$
$67$	−4.19895	−	4.19895i	−0.512983	−	0.512983i	−0.915439	+	0.402456i	$0.868157\pi$
$68$	2.59395	+	2.59395i	0.314563	+	0.314563i
$69$			1.27925i			0.154004i
$70$	−0.154925	−	3.58774i	−0.0185171	−	0.428816i
$71$	−6.20904			−0.736877			−0.368439	−	0.929652i	$-0.620107\pi$
$71$	−6.20904			−0.736877			−0.368439	+	0.929652i	$0.620107\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	10.1965	+	10.1965i	1.19341	+	1.19341i	0.976103	+	0.217308i	$0.0697276\pi$
$73$	10.1965	+	10.1965i	1.19341	+	1.19341i	0.217308	+	0.976103i	$0.430272\pi$
$74$	−3.21968			−0.374280
$75$	−3.82715	−	3.21760i	−0.441921	−	0.371536i
$76$	0.796628			0.0913795
$77$	−6.79299	+	6.79299i	−0.774133	+	0.774133i
$78$	0.515345	−	0.515345i	0.0583514	−	0.0583514i
$79$	1.08942			0.122569			0.0612845	−	0.998120i	$-0.480480\pi$
$79$	1.08942			0.122569			0.0612845	+	0.998120i	$0.480480\pi$
$80$	−2.23399	+	0.0964676i	−0.249767	+	0.0107854i
$81$	−1.00000			−0.111111
$82$	2.63146	+	2.63146i	0.290597	+	0.290597i
$83$	5.43134	+	5.43134i	0.596167	+	0.596167i	0.939290	−	0.343123i	$-0.111485\pi$
$83$	5.43134	+	5.43134i	0.596167	+	0.596167i	−0.343123	+	0.939290i	$0.611485\pi$
$84$	−1.60598			−0.175227
$85$	5.54461	−	6.04508i	0.601398	−	0.655681i
$86$		−	2.92097i		−	0.314976i
$87$	2.20340	+	2.20340i	0.236229	+	0.236229i
$88$	4.22981	+	4.22981i	0.450900	+	0.450900i
$89$	−0.818030			−0.0867111			−0.0433555	−	0.999060i	$-0.513805\pi$
$89$	−0.818030			−0.0867111			−0.0433555	+	0.999060i	$0.513805\pi$
$90$	−1.51145	+	1.64788i	−0.159321	+	0.173702i
$91$		−	1.17045i		−	0.122697i
$92$	0.904567	−	0.904567i	0.0943077	−	0.0943077i
$93$	−5.18555	−	2.02733i	−0.537717	−	0.210224i
$94$			7.76108i			0.800494i
$95$	−0.0768488	−	1.77966i	−0.00788452	−	0.182589i
$96$			1.00000i			0.102062i
$97$	−13.3240	−	13.3240i	−1.35285	−	1.35285i	−0.882458	−	0.470392i	$-0.844113\pi$
$97$	−13.3240	−	13.3240i	−1.35285	−	1.35285i	−0.470392	−	0.882458i	$-0.655887\pi$
$98$	3.12600	−	3.12600i	0.315774	−	0.315774i
$99$	5.98186			0.601199
$100$	0.431015	+	4.98139i	0.0431015	+	0.498139i
$101$	1.13242			0.112680			0.0563401	−	0.998412i	$-0.482057\pi$
$101$	1.13242			0.112680			0.0563401	+	0.998412i	$0.482057\pi$
$102$	−2.59395	−	2.59395i	−0.256839	−	0.256839i
$103$	−0.871920	+	0.871920i	−0.0859128	+	0.0859128i	−0.748757	−	0.662844i	$-0.769349\pi$
$103$	−0.871920	+	0.871920i	−0.0859128	+	0.0859128i	0.662844	+	0.748757i	$0.269349\pi$
$104$	−0.728809			−0.0714656
$105$	0.154925	+	3.58774i	0.0151191	+	0.350127i
$106$			7.39706i			0.718466i
$107$	12.3856	+	12.3856i	1.19736	+	1.19736i	0.974955	+	0.222402i	$0.0713896\pi$
$107$	12.3856	+	12.3856i	1.19736	+	1.19736i	0.222402	+	0.974955i	$0.428610\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$			15.9598i			1.52867i	0.644818	+	0.764336i	$0.276933\pi$
$109$			15.9598i			1.52867i	−0.644818	+	0.764336i	$0.723067\pi$
$110$	9.04130	−	9.85738i	0.862054	−	0.939865i
$111$	3.21968			0.305599
$112$	1.13560	+	1.13560i	0.107304	+	0.107304i
$113$	10.0816	−	10.0816i	0.948393	−	0.948393i	−0.0503392	−	0.998732i	$-0.516030\pi$
$113$	10.0816	−	10.0816i	0.948393	−	0.948393i	0.998732	+	0.0503392i	$0.0160302\pi$
$114$	−0.796628			−0.0746110
$115$	−2.10805	−	1.93353i	−0.196577	−	0.180303i
$116$		−	3.11608i		−	0.289321i
$117$	−0.515345	+	0.515345i	−0.0476437	+	0.0476437i
$118$	6.74120	−	6.74120i	0.620578	−	0.620578i
$119$	−5.89137			−0.540061
$120$	2.23399	−	0.0964676i	0.203934	−	0.00880625i
$121$	−24.7826			−2.25297
$122$	−0.903410	+	0.903410i	−0.0817909	+	0.0817909i
$123$	−2.63146	−	2.63146i	−0.237271	−	0.237271i
$124$	2.23320	+	5.10027i	0.200548	+	0.458018i
$125$	11.0868	−	1.44342i	0.991631	−	0.129104i
$126$	1.60598			0.143072
$127$	−9.56717	+	9.56717i	−0.848949	+	0.848949i	−0.990002	−	0.141053i	$-0.954951\pi$
$127$	−9.56717	+	9.56717i	−0.848949	+	0.848949i	0.141053	+	0.990002i	$0.454951\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$			2.92097i			0.257177i
$130$	0.0703064	+	1.62815i	0.00616628	+	0.142798i
$131$	4.00618			0.350022			0.175011	−	0.984567i	$-0.444004\pi$
$131$	4.00618			0.350022			0.175011	+	0.984567i	$0.444004\pi$
$132$	−4.22981	−	4.22981i	−0.368158	−	0.368158i
$133$	−0.904650	+	0.904650i	−0.0784431	+	0.0784431i
$134$		−	5.93821i		−	0.512983i
$135$	1.51145	−	1.64788i	0.130085	−	0.141827i
$136$			3.66840i			0.314563i
$137$	−15.1406	+	15.1406i	−1.29355	+	1.29355i	−0.360977	+	0.932575i	$0.617557\pi$
$137$	−15.1406	+	15.1406i	−1.29355	+	1.29355i	−0.932575	+	0.360977i	$0.882443\pi$
$138$	−0.904567	+	0.904567i	−0.0770019	+	0.0770019i
$139$	−8.35710			−0.708840			−0.354420	−	0.935086i	$-0.615322\pi$
$139$	−8.35710			−0.708840			−0.354420	+	0.935086i	$0.615322\pi$
$140$	2.42736	−	2.64646i	0.205150	−	0.223667i
$141$		−	7.76108i		−	0.653601i
$142$	−4.39045	−	4.39045i	−0.368439	−	0.368439i
$143$	3.08272	−	3.08272i	0.257790	−	0.257790i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.96128	+	0.300601i	−0.578103	+	0.0249635i
$146$			14.4200i			1.19341i
$147$	−3.12600	+	3.12600i	−0.257828	+	0.257828i
$148$	−2.27666	−	2.27666i	−0.187140	−	0.187140i
$149$			5.66808i			0.464347i	0.972674	+	0.232174i	$0.0745837\pi$
$149$			5.66808i			0.464347i	−0.972674	+	0.232174i	$0.925416\pi$
$150$	−0.431015	−	4.98139i	−0.0351922	−	0.406729i
$151$		−	16.3761i		−	1.33267i	−0.745655	−	0.666333i	$-0.767863\pi$
$151$		−	16.3761i		−	1.33267i	0.745655	−	0.666333i	$-0.232137\pi$
$152$	0.563301	+	0.563301i	0.0456897	+	0.0456897i
$153$	2.59395	+	2.59395i	0.209708	+	0.209708i
$154$	−9.60674			−0.774133
$155$	11.1785	−	5.48096i	0.897880	−	0.440241i
$156$	0.728809			0.0583514
$157$	−4.49510	−	4.49510i	−0.358748	−	0.358748i	0.504603	−	0.863351i	$-0.331639\pi$
$157$	−4.49510	−	4.49510i	−0.358748	−	0.358748i	−0.863351	+	0.504603i	$0.831639\pi$
$158$	0.770334	+	0.770334i	0.0612845	+	0.0612845i
$159$		−	7.39706i		−	0.586625i
$160$	−1.64788	−	1.51145i	−0.130276	−	0.119491i
$161$			2.05445i			0.161913i
$162$	−0.707107	−	0.707107i	−0.0555556	−	0.0555556i
$163$	−13.2697	+	13.2697i	−1.03936	+	1.03936i	−0.0401703	+	0.999193i	$0.512790\pi$
$163$	−13.2697	+	13.2697i	−1.03936	+	1.03936i	−0.999193	+	0.0401703i	$0.987210\pi$
$164$			3.72145i			0.290597i
$165$	−9.04130	+	9.85738i	−0.703864	+	0.767396i
$166$			7.68107i			0.596167i
$167$	−15.7485	+	15.7485i	−1.21866	+	1.21866i	−0.250554	+	0.968103i	$0.580613\pi$
$167$	−15.7485	+	15.7485i	−1.21866	+	1.21866i	−0.968103	+	0.250554i	$0.919387\pi$
$168$	−1.13560	−	1.13560i	−0.0876134	−	0.0876134i
$169$		−	12.4688i		−	0.959141i
$170$	8.19515	−	0.353882i	0.628539	−	0.0271415i
$171$	0.796628			0.0609197
$172$	2.06543	−	2.06543i	0.157488	−	0.157488i
$173$	−12.8308	+	12.8308i	−0.975506	+	0.975506i	−0.999707	−	0.0242009i	$-0.992296\pi$
$173$	−12.8308	+	12.8308i	−0.975506	+	0.975506i	0.0242009	+	0.999707i	$0.492296\pi$
$174$			3.11608i			0.236229i
$175$	−6.14632	−	5.16740i	−0.464618	−	0.390619i
$176$			5.98186i			0.450900i
$177$	−6.74120	+	6.74120i	−0.506700	+	0.506700i
$178$	−0.578435	−	0.578435i	−0.0433555	−	0.0433555i
$179$	5.66402			0.423349			0.211674	−	0.977340i	$-0.432108\pi$
$179$	5.66402			0.423349			0.211674	+	0.977340i	$0.432108\pi$
$180$	−2.23399	+	0.0964676i	−0.166511	+	0.00719027i
$181$			16.7872i			1.24778i	0.781511	+	0.623891i	$0.214449\pi$
$181$			16.7872i			1.24778i	−0.781511	+	0.623891i	$0.785551\pi$
$182$	0.827634	−	0.827634i	0.0613483	−	0.0613483i
$183$	0.903410	−	0.903410i	0.0667820	−	0.0667820i
$184$	1.27925			0.0943077
$185$	−4.86640	+	5.30565i	−0.357785	+	0.390079i
$186$	−2.23320	−	5.10027i	−0.163746	−	0.373970i
$187$	−15.5166	−	15.5166i	−1.13469	−	1.13469i
$188$	−5.48791	+	5.48791i	−0.400247	+	0.400247i
$189$	−1.60598			−0.116818
$190$	1.20407	−	1.31275i	0.0873522	−	0.0952367i
$191$	1.60270			0.115968			0.0579838	−	0.998318i	$-0.481533\pi$
$191$	1.60270			0.115968			0.0579838	+	0.998318i	$0.481533\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	0.103412	−	0.103412i	0.00744376	−	0.00744376i	−0.703375	−	0.710819i	$-0.748325\pi$
$193$	0.103412	−	0.103412i	0.00744376	−	0.00744376i	0.710819	+	0.703375i	$0.248325\pi$
$194$		−	18.8430i		−	1.35285i
$195$	−0.0703064	−	1.62815i	−0.00503475	−	0.116594i
$196$	4.42083			0.315774
$197$	−5.36754	+	5.36754i	−0.382422	+	0.382422i	−0.871974	−	0.489552i	$-0.837160\pi$
$197$	−5.36754	+	5.36754i	−0.382422	+	0.382422i	0.489552	+	0.871974i	$0.337160\pi$
$198$	4.22981	+	4.22981i	0.300600	+	0.300600i
$199$	−0.631667			−0.0447777			−0.0223889	−	0.999749i	$-0.507127\pi$
$199$	−0.631667			−0.0447777			−0.0223889	+	0.999749i	$0.507127\pi$
$200$	−3.21760	+	3.82715i	−0.227519	+	0.270620i
$201$			5.93821i			0.418849i
$202$	0.800744	+	0.800744i	0.0563401	+	0.0563401i
$203$	3.53862	+	3.53862i	0.248362	+	0.248362i
$204$		−	3.66840i		−	0.256839i
$205$	8.31367	−	0.359000i	0.580652	−	0.0250736i
$206$	−1.23308			−0.0859128
$207$	0.904567	−	0.904567i	0.0628718	−	0.0628718i
$208$	−0.515345	−	0.515345i	−0.0357328	−	0.0357328i
$209$	−4.76532			−0.329624
$210$	−2.42736	+	2.64646i	−0.167504	+	0.182623i
$211$	−2.94953			−0.203054			−0.101527	−	0.994833i	$-0.532373\pi$
$211$	−2.94953			−0.203054			−0.101527	+	0.994833i	$0.532373\pi$
$212$	−5.23051	+	5.23051i	−0.359233	+	0.359233i
$213$	4.39045	+	4.39045i	0.300829	+	0.300829i
$214$			17.5158i			1.19736i
$215$	−4.81340	−	4.41490i	−0.328271	−	0.301094i
$216$			1.00000i			0.0680414i
$217$	−8.32789	−	3.25584i	−0.565334	−	0.221021i
$218$	−11.2853	+	11.2853i	−0.764336	+	0.764336i
$219$		−	14.4200i		−	0.974416i
$220$	13.3634	−	0.577056i	0.900959	−	0.0389051i
$221$	2.67356			0.179843
$222$	2.27666	+	2.27666i	0.152799	+	0.152799i
$223$	11.6805	+	11.6805i	0.782186	+	0.782186i	0.980199	−	0.198013i	$-0.0634489\pi$
$223$	11.6805	+	11.6805i	0.782186	+	0.782186i	−0.198013	+	0.980199i	$0.563449\pi$
$224$			1.60598i			0.107304i
$225$	0.431015	+	4.98139i	0.0287343	+	0.332093i
$226$	14.2575			0.948393
$227$	6.56117	+	6.56117i	0.435480	+	0.435480i	0.890488	−	0.455007i	$-0.150363\pi$
$227$	6.56117	+	6.56117i	0.435480	+	0.435480i	−0.455007	+	0.890488i	$0.650363\pi$
$228$	−0.563301	−	0.563301i	−0.0373055	−	0.0373055i
$229$	−26.6498			−1.76107			−0.880534	−	0.473983i	$-0.842816\pi$
$229$	−26.6498			−1.76107			−0.880534	+	0.473983i	$0.842816\pi$
$230$	−0.123406	−	2.85783i	−0.00813718	−	0.188440i
$231$	9.60674			0.632077
$232$	2.20340	−	2.20340i	0.144660	−	0.144660i
$233$	2.56633	−	2.56633i	0.168126	−	0.168126i	−0.618029	−	0.786155i	$-0.712069\pi$
$233$	2.56633	−	2.56633i	0.168126	−	0.168126i	0.786155	+	0.618029i	$0.212069\pi$
$234$	−0.728809			−0.0476437
$235$	12.7893	+	11.7305i	0.834284	+	0.765214i
$236$	9.53350			0.620578
$237$	−0.770334	−	0.770334i	−0.0500386	−	0.0500386i
$238$	−4.16583	−	4.16583i	−0.270031	−	0.270031i
$239$	16.0605			1.03887			0.519433	−	0.854511i	$-0.326143\pi$
$239$	16.0605			1.03887			0.519433	+	0.854511i	$0.326143\pi$
$240$	1.64788	+	1.51145i	0.106370	+	0.0975639i
$241$		−	21.5579i		−	1.38867i	−0.719653	−	0.694334i	$-0.755699\pi$
$241$		−	21.5579i		−	1.38867i	0.719653	−	0.694334i	$-0.244301\pi$
$242$	−17.5240	−	17.5240i	−1.12648	−	1.12648i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−1.27761			−0.0817909
$245$	−0.426467	−	9.87607i	−0.0272460	−	0.630959i
$246$		−	3.72145i		−	0.237271i
$247$	0.410539	−	0.410539i	0.0261219	−	0.0261219i
$248$	−2.02733	+	5.18555i	−0.128735	+	0.329283i
$249$		−	7.68107i		−	0.486768i
$250$	8.86019	+	6.81888i	0.560367	+	0.431264i
$251$			11.5559i			0.729402i	0.931125	+	0.364701i	$0.118829\pi$
$251$			11.5559i			0.729402i	−0.931125	+	0.364701i	$0.881171\pi$
$252$	1.13560	+	1.13560i	0.0715360	+	0.0715360i
$253$	−5.41099	+	5.41099i	−0.340186	+	0.340186i
$254$	−13.5300			−0.848949
$255$	−8.19515	+	0.353882i	−0.513200	+	0.0221609i
$256$	1.00000			0.0625000
$257$	9.16506	+	9.16506i	0.571701	+	0.571701i	0.932604	−	0.360903i	$-0.117531\pi$
$257$	9.16506	+	9.16506i	0.571701	+	0.571701i	−0.360903	+	0.932604i	$0.617531\pi$
$258$	−2.06543	+	2.06543i	−0.128588	+	0.128588i
$259$	5.17074			0.321294
$260$	−1.10156	+	1.20099i	−0.0683159	+	0.0744822i
$261$		−	3.11608i		−	0.192880i
$262$	2.83280	+	2.83280i	0.175011	+	0.175011i
$263$	0.848583	+	0.848583i	0.0523259	+	0.0523259i	0.732786	−	0.680460i	$-0.238220\pi$
$263$	0.848583	+	0.848583i	0.0523259	+	0.0523259i	−0.680460	+	0.732786i	$0.738220\pi$
$264$		−	5.98186i		−	0.368158i
$265$	12.1895	+	11.1803i	0.748793	+	0.686801i
$266$	−1.27937			−0.0784431
$267$	0.578435	+	0.578435i	0.0353996	+	0.0353996i
$268$	4.19895	−	4.19895i	0.256492	−	0.256492i
$269$	17.1553			1.04598			0.522989	−	0.852340i	$-0.324817\pi$
$269$	17.1553			1.04598			0.522989	+	0.852340i	$0.324817\pi$
$270$	2.23399	−	0.0964676i	0.135956	−	0.00587083i
$271$		−	29.9891i		−	1.82171i	−0.412728	−	0.910854i	$-0.635424\pi$
$271$		−	29.9891i		−	1.82171i	0.412728	−	0.910854i	$-0.364576\pi$
$272$	−2.59395	+	2.59395i	−0.157281	+	0.157281i
$273$	−0.827634	+	0.827634i	−0.0500907	+	0.0500907i
$274$	−21.4121			−1.29355
$275$	−2.57827	−	29.7980i	−0.155475	−	1.79688i
$276$	−1.27925			−0.0770019
$277$	8.68526	−	8.68526i	0.521847	−	0.521847i	−0.396282	−	0.918129i	$-0.629700\pi$
$277$	8.68526	−	8.68526i	0.521847	−	0.521847i	0.918129	+	0.396282i	$0.129700\pi$
$278$	−5.90936	−	5.90936i	−0.354420	−	0.354420i
$279$	2.23320	+	5.10027i	0.133698	+	0.305345i
$280$	3.58774	−	0.154925i	0.214408	−	0.00925854i
$281$	26.9023			1.60485			0.802427	−	0.596751i	$-0.203542\pi$
$281$	26.9023			1.60485			0.802427	+	0.596751i	$0.203542\pi$
$282$	5.48791	−	5.48791i	0.326800	−	0.326800i
$283$	9.45857	−	9.45857i	0.562254	−	0.562254i	−0.367693	−	0.929947i	$-0.619852\pi$
$283$	9.45857	−	9.45857i	0.562254	−	0.562254i	0.929947	+	0.367693i	$0.119852\pi$
$284$		−	6.20904i		−	0.368439i
$285$	−1.20407	+	1.31275i	−0.0713227	+	0.0777604i
$286$	4.35963			0.257790
$287$	−4.22608	−	4.22608i	−0.249457	−	0.249457i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			3.54285i			0.208403i
$290$	−5.13492	−	4.70981i	−0.301533	−	0.276570i
$291$			18.8430i			1.10460i
$292$	−10.1965	+	10.1965i	−0.596705	+	0.596705i
$293$	−2.97475	+	2.97475i	−0.173787	+	0.173787i	−0.788641	−	0.614854i	$-0.789215\pi$
$293$	−2.97475	+	2.97475i	−0.173787	+	0.173787i	0.614854	+	0.788641i	$0.289215\pi$
$294$	−4.42083			−0.257828
$295$	−0.919674	−	21.2977i	−0.0535455	−	1.24000i
$296$		−	3.21968i		−	0.187140i
$297$	−4.22981	−	4.22981i	−0.245439	−	0.245439i
$298$	−4.00794	+	4.00794i	−0.232174	+	0.232174i
$299$		−	0.932329i		−	0.0539180i
$300$	3.21760	−	3.82715i	0.185768	−	0.220960i
$301$			4.69101i			0.270385i
$302$	11.5796	−	11.5796i	0.666333	−	0.666333i
$303$	−0.800744	−	0.800744i	−0.0460015	−	0.0460015i
$304$			0.796628i			0.0456897i
$305$	0.123248	+	2.85417i	0.00705718	+	0.163429i
$306$			3.66840i			0.209708i
$307$	−1.31632	−	1.31632i	−0.0751266	−	0.0751266i	0.668545	−	0.743672i	$-0.266917\pi$
$307$	−1.31632	−	1.31632i	−0.0751266	−	0.0751266i	−0.743672	+	0.668545i	$0.766917\pi$
$308$	−6.79299	−	6.79299i	−0.387067	−	0.387067i
$309$	1.23308			0.0701475
$310$	11.7800	+	4.02878i	0.669060	+	0.228819i
$311$	−10.1916			−0.577912			−0.288956	−	0.957342i	$-0.593308\pi$
$311$	−10.1916			−0.577912			−0.288956	+	0.957342i	$0.593308\pi$
$312$	0.515345	+	0.515345i	0.0291757	+	0.0291757i
$313$	5.68411	+	5.68411i	0.321285	+	0.321285i	0.849260	−	0.527975i	$-0.177048\pi$
$313$	5.68411	+	5.68411i	0.321285	+	0.321285i	−0.527975	+	0.849260i	$0.677048\pi$
$314$		−	6.35703i		−	0.358748i
$315$	2.42736	−	2.64646i	0.136766	−	0.149111i
$316$			1.08942i			0.0612845i
$317$	−2.70997	−	2.70997i	−0.152207	−	0.152207i	0.626896	−	0.779103i	$-0.284325\pi$
$317$	−2.70997	−	2.70997i	−0.152207	−	0.152207i	−0.779103	+	0.626896i	$0.784325\pi$
$318$	5.23051	−	5.23051i	0.293312	−	0.293312i
$319$			18.6399i			1.04364i
$320$	−0.0964676	−	2.23399i	−0.00539270	−	0.124884i
$321$		−	17.5158i		−	0.977638i
$322$	−1.45272	+	1.45272i	−0.0809567	+	0.0809567i
$323$	−2.06641	−	2.06641i	−0.114978	−	0.114978i
$324$		−	1.00000i		−	0.0555556i
$325$	2.78926	+	2.34501i	0.154720	+	0.130078i
$326$	−18.7662			−1.03936
$327$	11.2853	−	11.2853i	0.624078	−	0.624078i
$328$	−2.63146	+	2.63146i	−0.145298	+	0.145298i
$329$		−	12.4641i		−	0.687170i
$330$	−13.3634	+	0.577056i	−0.735630	+	0.0317659i
$331$		−	0.433045i		−	0.0238023i	−0.999929	−	0.0119012i	$-0.996212\pi$
$331$		−	0.433045i		−	0.0238023i	0.999929	−	0.0119012i	$-0.00378835\pi$
$332$	−5.43134	+	5.43134i	−0.298083	+	0.298083i
$333$	−2.27666	−	2.27666i	−0.124760	−	0.124760i
$334$	−22.2718			−1.21866
$335$	−9.78545	−	8.97533i	−0.534636	−	0.490375i
$336$		−	1.60598i		−	0.0876134i
$337$	13.2399	−	13.2399i	0.721223	−	0.721223i	−0.247631	−	0.968854i	$-0.579652\pi$
$337$	13.2399	−	13.2399i	0.721223	−	0.721223i	0.968854	+	0.247631i	$0.0796521\pi$
$338$	8.81680	−	8.81680i	0.479571	−	0.479571i
$339$	−14.2575			−0.774360
$340$	6.04508	+	5.54461i	0.327840	+	0.300699i
$341$	−13.3587	−	30.5091i	−0.723415	−	1.65216i
$342$	0.563301	+	0.563301i	0.0304598	+	0.0304598i
$343$	−12.9695	+	12.9695i	−0.700286	+	0.700286i
$344$	2.92097			0.157488
$345$	0.123406	+	2.85783i	0.00664398	+	0.153860i
$346$	−18.1455			−0.975506
$347$	7.10746	−	7.10746i	0.381548	−	0.381548i	−0.490111	−	0.871660i	$-0.663044\pi$
$347$	7.10746	−	7.10746i	0.381548	−	0.381548i	0.871660	+	0.490111i	$0.163044\pi$
$348$	−2.20340	+	2.20340i	−0.118115	+	0.118115i
$349$		−	9.88683i		−	0.529230i	−0.964354	−	0.264615i	$-0.914755\pi$
$349$		−	9.88683i		−	0.529230i	0.964354	−	0.264615i	$-0.0852448\pi$
$350$	−0.692201	−	8.00001i	−0.0369997	−	0.427618i
$351$	0.728809			0.0389009
$352$	−4.22981	+	4.22981i	−0.225450	+	0.225450i
$353$	24.8623	+	24.8623i	1.32329	+	1.32329i	0.911099	+	0.412189i	$0.135236\pi$
$353$	24.8623	+	24.8623i	1.32329	+	1.32329i	0.412189	+	0.911099i	$0.364764\pi$
$354$	−9.53350			−0.506700
$355$	−13.8709	+	0.598971i	−0.736191	+	0.0317901i
$356$		−	0.818030i		−	0.0433555i
$357$	4.16583	+	4.16583i	0.220479	+	0.220479i
$358$	4.00507	+	4.00507i	0.211674	+	0.211674i
$359$		−	7.27733i		−	0.384083i	−0.981387	−	0.192041i	$-0.938489\pi$
$359$		−	7.27733i		−	0.384083i	0.981387	−	0.192041i	$-0.0615108\pi$
$360$	−1.64788	−	1.51145i	−0.0868509	−	0.0796606i
$361$	18.3654			0.966599
$362$	−11.8703	+	11.8703i	−0.623891	+	0.623891i
$363$	17.5240	+	17.5240i	0.919770	+	0.919770i
$364$	1.17045			0.0613483
$365$	23.7625	+	21.7952i	1.24379	+	1.14081i
$366$	1.27761			0.0667820
$367$	−14.7524	+	14.7524i	−0.770071	+	0.770071i	−0.978119	−	0.208048i	$-0.933289\pi$
$367$	−14.7524	+	14.7524i	−0.770071	+	0.770071i	0.208048	+	0.978119i	$0.433289\pi$
$368$	0.904567	+	0.904567i	0.0471538	+	0.0471538i
$369$			3.72145i			0.193731i
$370$	−7.19272	+	0.310595i	−0.373932	+	0.0161471i
$371$		−	11.8795i		−	0.616754i
$372$	2.02733	−	5.18555i	0.105112	−	0.268858i
$373$	2.19318	−	2.19318i	0.113558	−	0.113558i	−0.648044	−	0.761603i	$-0.724413\pi$
$373$	2.19318	−	2.19318i	0.113558	−	0.113558i	0.761603	+	0.648044i	$0.224413\pi$
$374$		−	21.9438i		−	1.13469i
$375$	−8.86019	−	6.81888i	−0.457538	−	0.352125i
$376$	−7.76108			−0.400247
$377$	−1.60586	−	1.60586i	−0.0827058	−	0.0827058i
$378$	−1.13560	−	1.13560i	−0.0584089	−	0.0584089i
$379$			27.9003i			1.43314i	0.697514	+	0.716571i	$0.254289\pi$
$379$			27.9003i			1.43314i	−0.697514	+	0.716571i	$0.745711\pi$
$380$	1.77966	−	0.0768488i	0.0912944	−	0.00394226i
$381$	13.5300			0.693164
$382$	1.13328	+	1.13328i	0.0579838	+	0.0579838i
$383$	−4.71107	−	4.71107i	−0.240724	−	0.240724i	0.576425	−	0.817150i	$-0.304447\pi$
$383$	−4.71107	−	4.71107i	−0.240724	−	0.240724i	−0.817150	+	0.576425i	$0.804447\pi$
$384$	−1.00000			−0.0510310
$385$	−14.5201	+	15.8308i	−0.740015	+	0.806810i
$386$	0.146247			0.00744376
$387$	2.06543	−	2.06543i	0.104992	−	0.104992i
$388$	13.3240	−	13.3240i	0.676425	−	0.676425i
$389$	1.03176			0.0523123			0.0261562	−	0.999658i	$-0.491673\pi$
$389$	1.03176			0.0523123			0.0261562	+	0.999658i	$0.491673\pi$
$390$	1.10156	−	1.20099i	0.0557797	−	0.0608144i
$391$	−4.69280			−0.237325
$392$	3.12600	+	3.12600i	0.157887	+	0.157887i
$393$	−2.83280	−	2.83280i	−0.142896	−	0.142896i
$394$	−7.59085			−0.382422
$395$	2.43374	−	0.105093i	0.122455	−	0.00528783i
$396$			5.98186i			0.300600i
$397$	−1.13452	−	1.13452i	−0.0569401	−	0.0569401i	0.678063	−	0.735003i	$-0.262819\pi$
$397$	−1.13452	−	1.13452i	−0.0569401	−	0.0569401i	−0.735003	+	0.678063i	$0.762819\pi$
$398$	−0.446656	−	0.446656i	−0.0223889	−	0.0223889i
$399$	1.27937			0.0640485
$400$	−4.98139	+	0.431015i	−0.249069	+	0.0215507i
$401$			5.92501i			0.295881i	0.988996	+	0.147941i	$0.0472644\pi$
$401$			5.92501i			0.295881i	−0.988996	+	0.147941i	$0.952736\pi$
$402$	−4.19895	+	4.19895i	−0.209424	+	0.209424i
$403$	3.77927	+	1.47753i	0.188259	+	0.0736011i
$404$			1.13242i			0.0563401i
$405$	−2.23399	+	0.0964676i	−0.111008	+	0.00479352i
$406$			5.00436i			0.248362i
$407$	13.6186	+	13.6186i	0.675051	+	0.675051i
$408$	2.59395	−	2.59395i	0.128420	−	0.128420i
$409$	18.1489			0.897404			0.448702	−	0.893681i	$-0.351886\pi$
$409$	18.1489			0.897404			0.448702	+	0.893681i	$0.351886\pi$
$410$	6.13251	+	5.62480i	0.302863	+	0.277789i
$411$	21.4121			1.05618
$412$	−0.871920	−	0.871920i	−0.0429564	−	0.0429564i
$413$	−10.8262	+	10.8262i	−0.532724	+	0.532724i
$414$	1.27925			0.0628718
$415$	12.6575	+	11.6096i	0.621331	+	0.569892i
$416$		−	0.728809i		−	0.0357328i
$417$	5.90936	+	5.90936i	0.289383	+	0.289383i
$418$	−3.36959	−	3.36959i	−0.164812	−	0.164812i
$419$			33.2618i			1.62495i	0.582998	+	0.812474i	$0.301880\pi$
$419$			33.2618i			1.62495i	−0.582998	+	0.812474i	$0.698120\pi$
$420$	−3.58774	+	0.154925i	−0.175064	+	0.00755957i
$421$	21.5533			1.05044			0.525222	−	0.850965i	$-0.323982\pi$
$421$	21.5533			1.05044			0.525222	+	0.850965i	$0.323982\pi$
$422$	−2.08563	−	2.08563i	−0.101527	−	0.101527i
$423$	−5.48791	+	5.48791i	−0.266831	+	0.266831i
$424$	−7.39706			−0.359233
$425$	11.8034	−	14.0395i	0.572551	−	0.681016i
$426$			6.20904i			0.300829i
$427$	1.45086	−	1.45086i	0.0702119	−	0.0702119i
$428$	−12.3856	+	12.3856i	−0.598678	+	0.598678i
$429$	−4.35963			−0.210485
$430$	−0.281779	−	6.52540i	−0.0135886	−	0.314683i
$431$	30.7616			1.48174			0.740868	−	0.671651i	$-0.234414\pi$
$431$	30.7616			1.48174			0.740868	+	0.671651i	$0.234414\pi$
$432$	−0.707107	+	0.707107i	−0.0340207	+	0.0340207i
$433$	20.3241	+	20.3241i	0.976715	+	0.976715i	0.999735	−	0.0230199i	$-0.00732811\pi$
$433$	20.3241	+	20.3241i	0.976715	+	0.976715i	−0.0230199	+	0.999735i	$0.507328\pi$
$434$	−3.58648	−	8.19094i	−0.172156	−	0.393177i
$435$	5.13492	+	4.70981i	0.246201	+	0.225818i
$436$	−15.9598			−0.764336
$437$	−0.720604	+	0.720604i	−0.0344712	+	0.0344712i
$438$	10.1965	−	10.1965i	0.487208	−	0.487208i
$439$			25.7343i			1.22823i	0.789216	+	0.614116i	$0.210487\pi$
$439$			25.7343i			1.22823i	−0.789216	+	0.614116i	$0.789513\pi$
$440$	9.85738	+	9.04130i	0.469932	+	0.431027i
$441$	4.42083			0.210516
$442$	1.89049	+	1.89049i	0.0899216	+	0.0899216i
$443$	4.35030	−	4.35030i	0.206689	−	0.206689i	−0.596170	−	0.802859i	$-0.703311\pi$
$443$	4.35030	−	4.35030i	0.206689	−	0.206689i	0.802859	+	0.596170i	$0.203311\pi$
$444$			3.21968i			0.152799i
$445$	−1.82747	+	0.0789135i	−0.0866303	+	0.00374086i
$446$			16.5188i			0.782186i
$447$	4.00794	−	4.00794i	0.189569	−	0.189569i
$448$	−1.13560	+	1.13560i	−0.0536520	+	0.0536520i
$449$	−15.9884			−0.754539			−0.377270	−	0.926103i	$-0.623137\pi$
$449$	−15.9884			−0.754539			−0.377270	+	0.926103i	$0.623137\pi$
$450$	−3.21760	+	3.82715i	−0.151679	+	0.180413i
$451$		−	22.2612i		−	1.04824i
$452$	10.0816	+	10.0816i	0.474197	+	0.474197i
$453$	−11.5796	+	11.5796i	−0.544058	+	0.544058i
$454$			9.27890i			0.435480i
$455$	−0.112911	−	2.61477i	−0.00529333	−	0.122582i
$456$		−	0.796628i		−	0.0373055i
$457$	3.68929	−	3.68929i	0.172578	−	0.172578i	−0.615533	−	0.788111i	$-0.711059\pi$
$457$	3.68929	−	3.68929i	0.172578	−	0.172578i	0.788111	+	0.615533i	$0.211059\pi$
$458$	−18.8443	−	18.8443i	−0.880534	−	0.880534i
$459$		−	3.66840i		−	0.171226i
$460$	1.93353	−	2.10805i	0.0901513	−	0.0982885i
$461$			12.5638i			0.585155i	0.956242	+	0.292578i	$0.0945130\pi$
$461$			12.5638i			0.585155i	−0.956242	+	0.292578i	$0.905487\pi$
$462$	6.79299	+	6.79299i	0.316039	+	0.316039i
$463$	3.85931	+	3.85931i	0.179357	+	0.179357i	0.791076	−	0.611718i	$-0.209521\pi$
$463$	3.85931	+	3.85931i	0.179357	+	0.179357i	−0.611718	+	0.791076i	$0.709521\pi$
$464$	3.11608			0.144660
$465$	−11.7800	−	4.02878i	−0.546285	−	0.186830i
$466$	3.62934			0.168126
$467$	−14.3049	−	14.3049i	−0.661954	−	0.661954i	0.293886	−	0.955840i	$-0.405051\pi$
$467$	−14.3049	−	14.3049i	−0.661954	−	0.661954i	−0.955840	+	0.293886i	$0.905051\pi$
$468$	−0.515345	−	0.515345i	−0.0238219	−	0.0238219i
$469$			9.53664i			0.440361i
$470$	0.748693	+	17.3381i	0.0345346	+	0.799749i
$471$			6.35703i			0.292916i
$472$	6.74120	+	6.74120i	0.310289	+	0.310289i
$473$	−12.3551	+	12.3551i	−0.568090	+	0.568090i
$474$		−	1.08942i		−	0.0500386i
$475$	−0.343358	−	3.96831i	−0.0157544	−	0.182079i
$476$		−	5.89137i		−	0.270031i
$477$	−5.23051	+	5.23051i	−0.239489	+	0.239489i
$478$	11.3565	+	11.3565i	0.519433	+	0.519433i
$479$		−	11.7765i		−	0.538083i	−0.963129	−	0.269041i	$-0.913293\pi$
$479$		−	11.7765i		−	0.538083i	0.963129	−	0.269041i	$-0.0867068\pi$
$480$	0.0964676	+	2.23399i	0.00440313	+	0.101967i
$481$	−2.34653			−0.106993
$482$	15.2438	−	15.2438i	0.694334	−	0.694334i
$483$	1.45272	−	1.45272i	0.0661009	−	0.0661009i
$484$		−	24.7826i		−	1.12648i
$485$	−31.0510	−	28.4803i	−1.40995	−	1.29323i
$486$			1.00000i			0.0453609i
$487$	25.0422	−	25.0422i	1.13477	−	1.13477i	0.145399	−	0.989373i	$-0.453553\pi$
$487$	25.0422	−	25.0422i	1.13477	−	1.13477i	0.989373	−	0.145399i	$-0.0464467\pi$
$488$	−0.903410	−	0.903410i	−0.0408954	−	0.0408954i
$489$	18.7662			0.848636
$490$	6.68188	−	7.28500i	0.301857	−	0.329103i
$491$		−	35.6259i		−	1.60777i	−0.594782	−	0.803887i	$-0.702762\pi$
$491$		−	35.6259i		−	1.60777i	0.594782	−	0.803887i	$-0.297238\pi$
$492$	2.63146	−	2.63146i	0.118636	−	0.118636i
$493$	−8.08295	+	8.08295i	−0.364038	+	0.364038i
$494$	0.580589			0.0261219
$495$	13.3634	−	0.577056i	0.600640	−	0.0259367i
$496$	−5.10027	+	2.23320i	−0.229009	+	0.100274i
$497$	7.05097	+	7.05097i	0.316279	+	0.316279i
$498$	5.43134	−	5.43134i	0.243384	−	0.243384i
$499$	8.37887			0.375090			0.187545	−	0.982256i	$-0.439947\pi$
$499$	8.37887			0.375090			0.187545	+	0.982256i	$0.439947\pi$
$500$	1.44342	+	11.0868i	0.0645519	+	0.495816i
$501$	22.2718			0.995029
$502$	−8.17126	+	8.17126i	−0.364701	+	0.364701i
$503$	−2.45681	+	2.45681i	−0.109544	+	0.109544i	−0.759754	−	0.650210i	$-0.774681\pi$
$503$	−2.45681	+	2.45681i	−0.109544	+	0.109544i	0.650210	+	0.759754i	$0.274681\pi$
$504$			1.60598i			0.0715360i
$505$	2.52982	−	0.109242i	0.112575	−	0.00486121i
$506$	−7.65230			−0.340186
$507$	−8.81680	+	8.81680i	−0.391568	+	0.391568i
$508$	−9.56717	−	9.56717i	−0.424474	−	0.424474i
$509$	−1.93050			−0.0855677			−0.0427839	−	0.999084i	$-0.513623\pi$
$509$	−1.93050			−0.0855677			−0.0427839	+	0.999084i	$0.513623\pi$
$510$	−6.04508	−	5.54461i	−0.267681	−	0.245520i
$511$		−	23.1583i		−	1.02446i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.563301	−	0.563301i	−0.0248703	−	0.0248703i
$514$			12.9614i			0.571701i
$515$	−1.86374	+	2.03197i	−0.0821264	+	0.0895392i
$516$	−2.92097			−0.128588
$517$	32.8279	−	32.8279i	1.44377	−	1.44377i
$518$	3.65627	+	3.65627i	0.160647	+	0.160647i
$519$	18.1455			0.796497
$520$	−1.62815	+	0.0703064i	−0.0713990	+	0.00308314i
$521$	−31.9891			−1.40147			−0.700734	−	0.713422i	$-0.747144\pi$
$521$	−31.9891			−1.40147			−0.700734	+	0.713422i	$0.747144\pi$
$522$	2.20340	−	2.20340i	0.0964402	−	0.0964402i
$523$	−28.0567	−	28.0567i	−1.22683	−	1.22683i	−0.965155	−	0.261678i	$-0.915724\pi$
$523$	−28.0567	−	28.0567i	−1.22683	−	1.22683i	−0.261678	−	0.965155i	$-0.584276\pi$
$524$			4.00618i			0.175011i
$525$	0.692201	+	8.00001i	0.0302101	+	0.349149i
$526$			1.20008i			0.0523259i
$527$	7.43704	−	19.0227i	0.323962	−	0.828641i
$528$	4.22981	−	4.22981i	0.184079	−	0.184079i
$529$		−	21.3635i		−	0.928849i
$530$	0.713577	+	16.5249i	0.0309958	+	0.717797i
$531$	9.53350			0.413719
$532$	−0.904650	−	0.904650i	−0.0392215	−	0.0392215i
$533$	1.91783	+	1.91783i	0.0830706	+	0.0830706i
$534$			0.818030i			0.0353996i
$535$	28.8640	+	26.4743i	1.24790	+	1.14459i
$536$	5.93821			0.256492
$537$	−4.00507	−	4.00507i	−0.172831	−	0.172831i
$538$	12.1306	+	12.1306i	0.522989	+	0.522989i
$539$	−26.4448			−1.13906
$540$	1.64788	+	1.51145i	0.0709134	+	0.0650426i
$541$	−25.7352			−1.10644			−0.553220	−	0.833035i	$-0.686601\pi$
$541$	−25.7352			−1.10644			−0.553220	+	0.833035i	$0.686601\pi$
$542$	21.2055	−	21.2055i	0.910854	−	0.910854i
$543$	11.8703	−	11.8703i	0.509405	−	0.509405i
$544$	−3.66840			−0.157281
$545$	1.53960	+	35.6540i	0.0659494	+	1.52725i
$546$	−1.17045			−0.0500907
$547$	0.183692	+	0.183692i	0.00785411	+	0.00785411i	0.711023	−	0.703169i	$-0.248232\pi$
$547$	0.183692	+	0.183692i	0.00785411	+	0.00785411i	−0.703169	+	0.711023i	$0.748232\pi$
$548$	−15.1406	−	15.1406i	−0.646776	−	0.646776i
$549$	−1.27761			−0.0545272
$550$	19.2472	−	22.8934i	0.820704	−	0.976180i
$551$			2.48236i			0.105752i
$552$	−0.904567	−	0.904567i	−0.0385009	−	0.0385009i
$553$	−1.23714	−	1.23714i	−0.0526086	−	0.0526086i
$554$	12.2828			0.521847
$555$	7.19272	−	0.310595i	0.305314	−	0.0131840i
$556$		−	8.35710i		−	0.354420i
$557$	6.17727	−	6.17727i	0.261739	−	0.261739i	−0.564021	−	0.825760i	$-0.690746\pi$
$557$	6.17727	−	6.17727i	0.261739	−	0.261739i	0.825760	+	0.564021i	$0.190746\pi$
$558$	−2.02733	+	5.18555i	−0.0858235	+	0.219522i
$559$		−	2.12882i		−	0.0900397i
$560$	2.64646	+	2.42736i	0.111833	+	0.102575i
$561$			21.9438i			0.926470i
$562$	19.0228	+	19.0228i	0.802427	+	0.802427i
$563$	−0.130515	+	0.130515i	−0.00550054	+	0.00550054i	−0.709852	−	0.704351i	$-0.751238\pi$
$563$	−0.130515	+	0.130515i	−0.00550054	+	0.00550054i	0.704351	+	0.709852i	$0.251238\pi$
$564$	7.76108			0.326800
$565$	21.5495	−	23.4946i	0.906595	−	0.988425i
$566$	13.3764			0.562254
$567$	1.13560	+	1.13560i	0.0476907	+	0.0476907i
$568$	4.39045	−	4.39045i	0.184219	−	0.184219i
$569$	25.2624			1.05905			0.529527	−	0.848293i	$-0.322370\pi$
$569$	25.2624			1.05905			0.529527	+	0.848293i	$0.322370\pi$
$570$	−1.77966	+	0.0768488i	−0.0745416	+	0.00321884i
$571$			33.9139i			1.41925i	0.704578	+	0.709627i	$0.251136\pi$
$571$			33.9139i			1.41925i	−0.704578	+	0.709627i	$0.748864\pi$
$572$	3.08272	+	3.08272i	0.128895	+	0.128895i
$573$	−1.13328	−	1.13328i	−0.0473436	−	0.0473436i
$574$		−	5.97658i		−	0.249457i
$575$	−4.89588	−	4.11612i	−0.204172	−	0.171654i
$576$	1.00000			0.0416667
$577$	−17.3456	−	17.3456i	−0.722106	−	0.722106i	0.246928	−	0.969034i	$-0.420579\pi$
$577$	−17.3456	−	17.3456i	−0.722106	−	0.722106i	−0.969034	+	0.246928i	$0.920579\pi$
$578$	−2.50518	+	2.50518i	−0.104202	+	0.104202i
$579$	−0.146247			−0.00607781
$580$	−0.300601	−	6.96128i	−0.0124818	−	0.289051i
$581$		−	12.3356i		−	0.511769i
$582$	−13.3240	+	13.3240i	−0.552298	+	0.552298i
$583$	31.2882	−	31.2882i	1.29582	−	1.29582i
$584$	−14.4200			−0.596705
$585$	−1.10156	+	1.20099i	−0.0455439	+	0.0496548i
$586$	−4.20693			−0.173787
$587$	−12.2115	+	12.2115i	−0.504022	+	0.504022i	−0.912685	−	0.408663i	$-0.865995\pi$
$587$	−12.2115	+	12.2115i	−0.504022	+	0.504022i	0.408663	+	0.912685i	$0.365995\pi$
$588$	−3.12600	−	3.12600i	−0.128914	−	0.128914i
$589$	−1.77903	−	4.06302i	−0.0733038	−	0.167414i
$590$	14.4094	−	15.7101i	0.593227	−	0.646773i
$591$	7.59085			0.312246
$592$	2.27666	−	2.27666i	0.0935701	−	0.0935701i
$593$	−20.6581	+	20.6581i	−0.848327	+	0.848327i	−0.989924	−	0.141597i	$-0.954776\pi$
$593$	−20.6581	+	20.6581i	−0.848327	+	0.848327i	0.141597	+	0.989924i	$0.454776\pi$
$594$		−	5.98186i		−	0.245439i
$595$	−13.1612	+	0.568327i	−0.539558	+	0.0232991i
$596$	−5.66808			−0.232174
$597$	0.446656	+	0.446656i	0.0182804	+	0.0182804i
$598$	0.659256	−	0.659256i	0.0269590	−	0.0269590i
$599$		−	3.16040i		−	0.129131i	−0.997913	−	0.0645653i	$-0.979434\pi$
$599$		−	3.16040i		−	0.129131i	0.997913	−	0.0645653i	$-0.0205661\pi$
$600$	4.98139	−	0.431015i	0.203364	−	0.0175961i
$601$			1.12666i			0.0459572i	0.999736	+	0.0229786i	$0.00731496\pi$
$601$			1.12666i			0.0459572i	−0.999736	+	0.0229786i	$0.992685\pi$
$602$	−3.31704	+	3.31704i	−0.135193	+	0.135193i
$603$	4.19895	−	4.19895i	0.170994	−	0.170994i
$604$	16.3761			0.666333
$605$	−55.3641	+	2.39072i	−2.25087	+	0.0971967i
$606$		−	1.13242i		−	0.0460015i
$607$	5.60346	+	5.60346i	0.227437	+	0.227437i	0.811621	−	0.584184i	$-0.198585\pi$
$607$	5.60346	+	5.60346i	0.227437	+	0.227437i	−0.584184	+	0.811621i	$0.698585\pi$
$608$	−0.563301	+	0.563301i	−0.0228449	+	0.0228449i
$609$		−	5.00436i		−	0.202787i
$610$	−1.93105	+	2.10535i	−0.0781861	+	0.0852433i
$611$			5.65634i			0.228831i
$612$	−2.59395	+	2.59395i	−0.104854	+	0.104854i
$613$	9.06076	+	9.06076i	0.365961	+	0.365961i	0.866002	−	0.500041i	$-0.166682\pi$
$613$	9.06076	+	9.06076i	0.365961	+	0.365961i	−0.500041	+	0.866002i	$0.666682\pi$
$614$		−	1.86156i		−	0.0751266i
$615$	−6.13251	−	5.62480i	−0.247287	−	0.226814i
$616$		−	9.60674i		−	0.387067i
$617$	27.3562	+	27.3562i	1.10132	+	1.10132i	0.994252	+	0.107067i	$0.0341460\pi$
$617$	27.3562	+	27.3562i	1.10132	+	1.10132i	0.107067	+	0.994252i	$0.465854\pi$
$618$	0.871920	+	0.871920i	0.0350738	+	0.0350738i
$619$	13.3473			0.536472			0.268236	−	0.963353i	$-0.413559\pi$
$619$	13.3473			0.536472			0.268236	+	0.963353i	$0.413559\pi$
$620$	5.48096	+	11.1785i	0.220121	+	0.448940i
$621$	−1.27925			−0.0513346
$622$	−7.20655	−	7.20655i	−0.288956	−	0.288956i
$623$	0.928954	+	0.928954i	0.0372178	+	0.0372178i
$624$			0.728809i			0.0291757i
$625$	24.6285	−	4.29410i	0.985138	−	0.171764i
$626$			8.03855i			0.321285i
$627$	3.36959	+	3.36959i	0.134568	+	0.134568i
$628$	4.49510	−	4.49510i	0.179374	−	0.179374i
$629$			11.8111i			0.470938i
$630$	3.58774	−	0.154925i	0.142939	−	0.00617236i
$631$			6.22075i			0.247644i	0.992304	+	0.123822i	$0.0395152\pi$
$631$			6.22075i			0.247644i	−0.992304	+	0.123822i	$0.960485\pi$
$632$	−0.770334	+	0.770334i	−0.0306422	+	0.0306422i
$633$	2.08563	+	2.08563i	0.0828963	+	0.0828963i
$634$		−	3.83248i		−	0.152207i
$635$	−20.4500	+	22.2958i	−0.811533	+	0.884784i
$636$	7.39706			0.293312
$637$	2.27825	−	2.27825i	0.0902677	−	0.0902677i
$638$	−13.1804	+	13.1804i	−0.521818	+	0.521818i
$639$		−	6.20904i		−	0.245626i
$640$	1.51145	−	1.64788i	0.0597455	−	0.0651382i
$641$		−	45.5293i		−	1.79830i	−0.437643	−	0.899149i	$-0.644187\pi$
$641$		−	45.5293i		−	1.79830i	0.437643	−	0.899149i	$-0.355813\pi$
$642$	12.3856	−	12.3856i	0.488819	−	0.488819i
$643$	−24.3461	−	24.3461i	−0.960116	−	0.960116i	0.0391185	−	0.999235i	$-0.487545\pi$
$643$	−24.3461	−	24.3461i	−0.960116	−	0.960116i	−0.999235	+	0.0391185i	$0.987545\pi$
$644$	−2.05445			−0.0809567
$645$	0.281779	+	6.52540i	0.0110950	+	0.256937i
$646$		−	2.92235i		−	0.114978i
$647$	16.5503	−	16.5503i	0.650658	−	0.650658i	−0.302494	−	0.953151i	$-0.597819\pi$
$647$	16.5503	−	16.5503i	0.650658	−	0.650658i	0.953151	+	0.302494i	$0.0978191\pi$
$648$	0.707107	−	0.707107i	0.0277778	−	0.0277778i
$649$	−57.0280			−2.23855
$650$	0.314127	+	3.63048i	0.0123211	+	0.142399i
$651$	3.58648	+	8.19094i	0.140565	+	0.321028i
$652$	−13.2697	−	13.2697i	−0.519682	−	0.519682i
$653$	−24.2422	+	24.2422i	−0.948670	+	0.948670i	−0.998745	−	0.0500753i	$-0.984054\pi$
$653$	−24.2422	+	24.2422i	−0.948670	+	0.948670i	0.0500753	+	0.998745i	$0.484054\pi$
$654$	15.9598			0.624078
$655$	8.94975	−	0.386467i	0.349696	−	0.0151005i
$656$	−3.72145			−0.145298
$657$	−10.1965	+	10.1965i	−0.397804	+	0.397804i
$658$	8.81347	−	8.81347i	0.343585	−	0.343585i
$659$		−	25.3835i		−	0.988801i	−0.869234	−	0.494401i	$-0.835388\pi$
$659$		−	25.3835i		−	0.988801i	0.869234	−	0.494401i	$-0.164612\pi$
$660$	−9.85738	−	9.04130i	−0.383698	−	0.351932i
$661$	20.0242			0.778853			0.389426	−	0.921058i	$-0.372673\pi$
$661$	20.0242			0.778853			0.389426	+	0.921058i	$0.372673\pi$
$662$	0.306209	−	0.306209i	0.0119012	−	0.0119012i
$663$	−1.89049	−	1.89049i	−0.0734206	−	0.0734206i
$664$	−7.68107			−0.298083
$665$	−1.93371	+	2.10824i	−0.0749859	+	0.0817542i
$666$		−	3.21968i		−	0.124760i
$667$	2.81870	+	2.81870i	0.109141	+	0.109141i
$668$	−15.7485	−	15.7485i	−0.609328	−	0.609328i
$669$		−	16.5188i		−	0.638652i
$670$	−0.572845	−	13.2659i	−0.0221309	−	0.512505i
$671$	7.64251			0.295036
$672$	1.13560	−	1.13560i	0.0438067	−	0.0438067i
$673$	18.0714	+	18.0714i	0.696602	+	0.696602i	0.963676	−	0.267074i	$-0.0860568\pi$
$673$	18.0714	+	18.0714i	0.696602	+	0.696602i	−0.267074	+	0.963676i	$0.586057\pi$
$674$	18.7240			0.721223
$675$	3.21760	−	3.82715i	0.123845	−	0.147307i
$676$	12.4688			0.479571
$677$	16.0112	−	16.0112i	0.615360	−	0.615360i	−0.328978	−	0.944338i	$-0.606704\pi$
$677$	16.0112	−	16.0112i	0.615360	−	0.615360i	0.944338	+	0.328978i	$0.106704\pi$
$678$	−10.0816	−	10.0816i	−0.387180	−	0.387180i
$679$			30.2615i			1.16133i
$680$	0.353882	+	8.19515i	0.0135707	+	0.314270i
$681$		−	9.27890i		−	0.355568i
$682$	12.1272	−	31.0192i	0.464374	−	1.18779i
$683$	4.74763	−	4.74763i	0.181663	−	0.181663i	−0.610417	−	0.792080i	$-0.708998\pi$
$683$	4.74763	−	4.74763i	0.181663	−	0.181663i	0.792080	+	0.610417i	$0.208998\pi$
$684$			0.796628i			0.0304598i
$685$	−32.3634	+	35.2845i	−1.23654	+	1.34815i
$686$	−18.3416			−0.700286
$687$	18.8443	+	18.8443i	0.718953	+	0.718953i
$688$	2.06543	+	2.06543i	0.0787440	+	0.0787440i
$689$			5.39104i			0.205382i
$690$	−1.93353	+	2.10805i	−0.0736082	+	0.0802522i
$691$	−29.8591			−1.13589			−0.567947	−	0.823065i	$-0.692262\pi$
$691$	−29.8591			−1.13589			−0.567947	+	0.823065i	$0.692262\pi$
$692$	−12.8308	−	12.8308i	−0.487753	−	0.487753i
$693$	−6.79299	−	6.79299i	−0.258044	−	0.258044i
$694$	10.0515			0.381548
$695$	−18.6696	+	0.806189i	−0.708180	+	0.0305805i
$696$	−3.11608			−0.118115
$697$	9.65326	−	9.65326i	0.365643	−	0.365643i
$698$	6.99104	−	6.99104i	0.264615	−	0.264615i
$699$	−3.62934			−0.137274
$700$	5.16740	−	6.14632i	0.195309	−	0.232309i
$701$	−25.6357			−0.968249			−0.484124	−	0.874999i	$-0.660862\pi$
$701$	−25.6357			−0.968249			−0.484124	+	0.874999i	$0.660862\pi$
$702$	0.515345	+	0.515345i	0.0194505	+	0.0194505i
$703$	1.81365	+	1.81365i	0.0684031	+	0.0684031i
$704$	−5.98186			−0.225450
$705$	−0.748693	−	17.3381i	−0.0281974	−	0.652992i
$706$			35.1606i			1.32329i
$707$	−1.28598	−	1.28598i	−0.0483642	−	0.0483642i
$708$	−6.74120	−	6.74120i	−0.253350	−	0.253350i
$709$	37.5860			1.41157			0.705785	−	0.708426i	$-0.250594\pi$
$709$	37.5860			1.41157			0.705785	+	0.708426i	$0.250594\pi$
$710$	−10.2317	−	9.38467i	−0.383991	−	0.352200i
$711$			1.08942i			0.0408563i
$712$	0.578435	−	0.578435i	0.0216778	−	0.0216778i
$713$	−6.63363	−	2.59346i	−0.248431	−	0.0971258i
$714$			5.89137i			0.220479i
$715$	6.58938	−	7.18414i	0.246429	−	0.268672i
$716$			5.66402i			0.211674i
$717$	−11.3565	−	11.3565i	−0.424115	−	0.424115i
$718$	5.14585	−	5.14585i	0.192041	−	0.192041i
$719$	−8.09752			−0.301986			−0.150993	−	0.988535i	$-0.548247\pi$
$719$	−8.09752			−0.301986			−0.150993	+	0.988535i	$0.548247\pi$
$720$	−0.0964676	−	2.23399i	−0.00359514	−	0.0832557i
$721$	1.98030			0.0737503
$722$	12.9863	+	12.9863i	0.483300	+	0.483300i
$723$	−15.2438	+	15.2438i	−0.566921	+	0.566921i
$724$	−16.7872			−0.623891
$725$	−15.5224	+	1.34308i	−0.576487	+	0.0498806i
$726$			24.7826i			0.919770i
$727$	−25.1545	−	25.1545i	−0.932928	−	0.932928i	0.0649600	−	0.997888i	$-0.479308\pi$
$727$	−25.1545	−	25.1545i	−0.932928	−	0.932928i	−0.997888	+	0.0649600i	$0.979308\pi$
$728$	0.827634	+	0.827634i	0.0306742	+	0.0306742i
$729$		−	1.00000i		−	0.0370370i
$730$	1.39107	+	32.2142i	0.0514857	+	1.19230i
$731$	−10.7153			−0.396318
$732$	0.903410	+	0.903410i	0.0333910	+	0.0333910i
$733$	31.8309	−	31.8309i	1.17570	−	1.17570i	0.194871	−	0.980829i	$-0.437571\pi$
$733$	31.8309	−	31.8309i	1.17570	−	1.17570i	0.980829	−	0.194871i	$-0.0624289\pi$
$734$	−20.8631			−0.770071
$735$	−6.68188	+	7.28500i	−0.246465	+	0.268711i
$736$			1.27925i			0.0471538i
$737$	−25.1175	+	25.1175i	−0.925215	+	0.925215i
$738$	−2.63146	+	2.63146i	−0.0968655	+	0.0968655i
$739$	14.5234			0.534252			0.267126	−	0.963662i	$-0.413926\pi$
$739$	14.5234			0.534252			0.267126	+	0.963662i	$0.413926\pi$
$740$	−5.30565	−	4.86640i	−0.195039	−	0.178892i
$741$	−0.580589			−0.0213285
$742$	8.40009	−	8.40009i	0.308377	−	0.308377i
$743$	17.0719	+	17.0719i	0.626309	+	0.626309i	0.947137	−	0.320829i	$-0.103961\pi$
$743$	17.0719	+	17.0719i	0.626309	+	0.626309i	−0.320829	+	0.947137i	$0.603961\pi$
$744$	5.10027	−	2.23320i	0.186985	−	0.0818732i
$745$	0.546786	+	12.6624i	0.0200327	+	0.463915i
$746$	3.10162			0.113558
$747$	−5.43134	+	5.43134i	−0.198722	+	0.198722i
$748$	15.5166	−	15.5166i	0.567344	−	0.567344i
$749$		−	28.1300i		−	1.02785i
$750$	−1.44342	−	11.0868i	−0.0527064	−	0.404832i
$751$	−18.4624			−0.673703			−0.336851	−	0.941558i	$-0.609362\pi$
$751$	−18.4624			−0.673703			−0.336851	+	0.941558i	$0.609362\pi$
$752$	−5.48791	−	5.48791i	−0.200124	−	0.200124i
$753$	8.17126	−	8.17126i	0.297777	−	0.297777i
$754$		−	2.27102i		−	0.0827058i
$755$	−1.57976	−	36.5839i	−0.0574934	−	1.33142i
$756$		−	1.60598i		−	0.0584089i
$757$	−25.8617	+	25.8617i	−0.939960	+	0.939960i	−0.998297	−	0.0583371i	$-0.981420\pi$
$757$	−25.8617	+	25.8617i	−0.939960	+	0.939960i	0.0583371	+	0.998297i	$0.481420\pi$
$758$	−19.7285	+	19.7285i	−0.716571	+	0.716571i
$759$	7.65230			0.277761
$760$	1.31275	+	1.20407i	0.0476183	+	0.0436761i
$761$		−	11.1258i		−	0.403310i	−0.979457	−	0.201655i	$-0.935368\pi$
$761$		−	11.1258i		−	0.403310i	0.979457	−	0.201655i	$-0.0646320\pi$
$762$	9.56717	+	9.56717i	0.346582	+	0.346582i
$763$	18.1239	−	18.1239i	0.656130	−	0.656130i
$764$			1.60270i			0.0579838i
$765$	6.04508	+	5.54461i	0.218560	+	0.200466i
$766$		−	6.66246i		−	0.240724i
$767$	4.91305	−	4.91305i	0.177400	−	0.177400i
$768$	−0.707107	−	0.707107i	−0.0255155	−	0.0255155i
$769$		−	26.6883i		−	0.962404i	−0.876610	−	0.481202i	$-0.840200\pi$
$769$		−	26.6883i		−	0.962404i	0.876610	−	0.481202i	$-0.159800\pi$
$770$	−21.4613	+	0.926740i	−0.773412	+	0.0333974i
$771$		−	12.9614i		−	0.466792i
$772$	0.103412	+	0.103412i	0.00372188	+	0.00372188i
$773$	−20.8142	−	20.8142i	−0.748636	−	0.748636i	0.225587	−	0.974223i	$-0.427570\pi$
$773$	−20.8142	−	20.8142i	−0.748636	−	0.748636i	−0.974223	+	0.225587i	$0.927570\pi$
$774$	2.92097			0.104992
$775$	24.4439	−	13.3227i	0.878051	−	0.478567i
$776$	18.8430			0.676425
$777$	−3.65627	−	3.65627i	−0.131168	−	0.131168i
$778$	0.729565	+	0.729565i	0.0261562	+	0.0261562i
$779$		−	2.96461i		−	0.106218i
$780$	1.62815	−	0.0703064i	0.0582971	−	0.00251737i
$781$			37.1416i			1.32903i
$782$	−3.31831	−	3.31831i	−0.118663	−	0.118663i
$783$	−2.20340	+	2.20340i	−0.0787431	+	0.0787431i
$784$			4.42083i			0.157887i
$785$	−10.4756	−	9.60835i	−0.373891	−	0.342937i
$786$		−	4.00618i		−	0.142896i
$787$	−31.7488	+	31.7488i	−1.13172	+	1.13172i	−0.141833	+	0.989891i	$0.545300\pi$
$787$	−31.7488	+	31.7488i	−1.13172	+	1.13172i	−0.989891	+	0.141833i	$0.954700\pi$
$788$	−5.36754	−	5.36754i	−0.191211	−	0.191211i
$789$		−	1.20008i		−	0.0427239i
$790$	1.79523	+	1.64660i	0.0638713	+	0.0585835i
$791$	−22.8972			−0.814131
$792$	−4.22981	+	4.22981i	−0.150300	+	0.150300i
$793$	−0.658413	+	0.658413i	−0.0233809	+	0.0233809i
$794$		−	1.60446i		−	0.0569401i
$795$	−0.713577	−	16.5249i	−0.0253080	−	0.586079i
$796$		−	0.631667i		−	0.0223889i
$797$	−9.65977	+	9.65977i	−0.342167	+	0.342167i	−0.857181	−	0.515015i	$-0.827786\pi$
$797$	−9.65977	+	9.65977i	−0.342167	+	0.342167i	0.515015	+	0.857181i	$0.327786\pi$
$798$	0.904650	+	0.904650i	0.0320243	+	0.0320243i
$799$	28.4707			1.00722
$800$	−3.82715	−	3.21760i	−0.135310	−	0.113759i
$801$		−	0.818030i		−	0.0289037i
$802$	−4.18962	+	4.18962i	−0.147941	+	0.147941i
$803$	60.9941	−	60.9941i	2.15243	−	2.15243i
$804$	−5.93821			−0.209424
$805$	0.198188	+	4.58962i	0.00698521	+	0.161763i
$806$	1.62758	+	3.71712i	0.0573290	+	0.130930i
$807$	−12.1306	−	12.1306i	−0.427019	−	0.427019i
$808$	−0.800744	+	0.800744i	−0.0281701	+	0.0281701i
$809$	−31.0857			−1.09292			−0.546458	−	0.837486i	$-0.684024\pi$
$809$	−31.0857			−1.09292			−0.546458	+	0.837486i	$0.684024\pi$
$810$	−1.64788	−	1.51145i	−0.0579006	−	0.0531071i
$811$	3.53839			0.124250			0.0621248	−	0.998068i	$-0.480212\pi$
$811$	3.53839			0.124250			0.0621248	+	0.998068i	$0.480212\pi$
$812$	−3.53862	+	3.53862i	−0.124181	+	0.124181i
$813$	−21.2055	+	21.2055i	−0.743709	+	0.743709i
$814$			19.2597i			0.675051i
$815$	−28.3642	+	30.9244i	−0.993556	+	1.08324i
$816$	3.66840			0.128420
$817$	−1.64538	+	1.64538i	−0.0575647	+	0.0575647i
$818$	12.8332	+	12.8332i	0.448702	+	0.448702i
$819$	1.17045			0.0408989
$820$	0.359000	+	8.31367i	0.0125368	+	0.290326i
$821$		−	13.0715i		−	0.456199i	−0.973638	−	0.228100i	$-0.926749\pi$
$821$		−	13.0715i		−	0.456199i	0.973638	−	0.228100i	$-0.0732512\pi$
$822$	15.1406	+	15.1406i	0.528090	+	0.528090i
$823$	22.2862	+	22.2862i	0.776848	+	0.776848i	0.979294	−	0.202445i	$-0.0648888\pi$
$823$	22.2862	+	22.2862i	0.776848	+	0.776848i	−0.202445	+	0.979294i	$0.564889\pi$
$824$		−	1.23308i		−	0.0429564i
$825$	−19.2472	+	22.8934i	−0.670102	+	0.797048i
$826$	−15.3106			−0.532724
$827$	32.4739	−	32.4739i	1.12923	−	1.12923i	0.138925	−	0.990303i	$-0.455635\pi$
$827$	32.4739	−	32.4739i	1.12923	−	1.12923i	0.990303	−	0.138925i	$-0.0443646\pi$
$828$	0.904567	+	0.904567i	0.0314359	+	0.0314359i
$829$	10.2371			0.355550			0.177775	−	0.984071i	$-0.443110\pi$
$829$	10.2371			0.355550			0.177775	+	0.984071i	$0.443110\pi$
$830$	0.740975	+	17.1594i	0.0257196	+	0.595612i
$831$	−12.2828			−0.426086
$832$	0.515345	−	0.515345i	0.0178664	−	0.0178664i
$833$	−11.4674	−	11.4674i	−0.397322	−	0.397322i
$834$			8.35710i			0.289383i
$835$	−33.6627	+	36.7012i	−1.16495	+	1.27010i
$836$		−	4.76532i		−	0.164812i
$837$	2.02733	−	5.18555i	0.0700746	−	0.179239i
$838$	−23.5197	+	23.5197i	−0.812474	+	0.812474i
$839$			35.9572i			1.24138i	0.784055	+	0.620691i	$0.213148\pi$
$839$			35.9572i			1.24138i	−0.784055	+	0.620691i	$0.786852\pi$
$840$	−2.64646	−	2.42736i	−0.0913116	−	0.0837520i
$841$	−19.2901			−0.665174
$842$	15.2405	+	15.2405i	0.525222	+	0.525222i
$843$	−19.0228	−	19.0228i	−0.655179	−	0.655179i
$844$		−	2.94953i		−	0.101527i
$845$	−1.20284	−	27.8552i	−0.0413789	−	0.958248i
$846$	−7.76108			−0.266831
$847$	28.1431	+	28.1431i	0.967009	+	0.967009i
$848$	−5.23051	−	5.23051i	−0.179616	−	0.179616i
$849$	−13.3764			−0.459078
$850$	18.2737	−	1.58113i	0.626783	−	0.0542324i
$851$	4.11878			0.141190
$852$	−4.39045	+	4.39045i	−0.150414	+	0.150414i
$853$	12.0879	−	12.0879i	0.413881	−	0.413881i	−0.469207	−	0.883088i	$-0.655460\pi$
$853$	12.0879	−	12.0879i	0.413881	−	0.413881i	0.883088	+	0.469207i	$0.155460\pi$
$854$	2.05182			0.0702119
$855$	1.77966	−	0.0768488i	0.0608629	−	0.00262817i
$856$	−17.5158			−0.598678
$857$	9.31718	+	9.31718i	0.318269	+	0.318269i	0.848102	−	0.529833i	$-0.177745\pi$
$857$	9.31718	+	9.31718i	0.318269	+	0.318269i	−0.529833	+	0.848102i	$0.677745\pi$
$858$	−3.08272	−	3.08272i	−0.105242	−	0.105242i
$859$	−31.4263			−1.07225			−0.536126	−	0.844138i	$-0.680113\pi$
$859$	−31.4263			−1.07225			−0.536126	+	0.844138i	$0.680113\pi$
$860$	4.41490	−	4.81340i	0.150547	−	0.164136i
$861$			5.97658i			0.203681i
$862$	21.7518	+	21.7518i	0.740868	+	0.740868i
$863$	26.1692	+	26.1692i	0.890808	+	0.890808i	0.994599	−	0.103791i	$-0.0330973\pi$
$863$	26.1692	+	26.1692i	0.890808	+	0.890808i	−0.103791	+	0.994599i	$0.533097\pi$
$864$	−1.00000			−0.0340207
$865$	−27.4260	+	29.9015i	−0.932513	+	1.01668i
$866$			28.7427i			0.976715i
$867$	2.50518	−	2.50518i	0.0850802	−	0.0850802i
$868$	3.25584	−	8.32789i	0.110511	−	0.282667i
$869$		−	6.51674i		−	0.221065i
$870$	0.300601	+	6.96128i	0.0101913	+	0.236009i
$871$		−	4.32782i		−	0.146642i
$872$	−11.2853	−	11.2853i	−0.382168	−	0.382168i
$873$	13.3240	−	13.3240i	0.450950	−	0.450950i
$874$	−1.01909			−0.0344712
$875$	−14.2293	−	10.9510i	−0.481037	−	0.370211i
$876$	14.4200			0.487208
$877$	17.3200	+	17.3200i	0.584854	+	0.584854i	0.936233	−	0.351379i	$-0.114287\pi$
$877$	17.3200	+	17.3200i	0.584854	+	0.584854i	−0.351379	+	0.936233i	$0.614287\pi$
$878$	−18.1969	+	18.1969i	−0.614116	+	0.614116i
$879$	4.20693			0.141896
$880$	0.577056	+	13.3634i	0.0194525	+	0.450480i
$881$			46.9960i			1.58334i	0.610951	+	0.791668i	$0.290787\pi$
$881$			46.9960i			1.58334i	−0.610951	+	0.791668i	$0.709213\pi$
$882$	3.12600	+	3.12600i	0.105258	+	0.105258i
$883$	−21.5746	−	21.5746i	−0.726043	−	0.726043i	0.243786	−	0.969829i	$-0.421610\pi$
$883$	−21.5746	−	21.5746i	−0.726043	−	0.726043i	−0.969829	+	0.243786i	$0.921610\pi$
$884$			2.67356i			0.0899216i
$885$	−14.4094	+	15.7101i	−0.484368	+	0.528088i
$886$	6.15225			0.206689
$887$	9.20009	+	9.20009i	0.308909	+	0.308909i	0.844486	−	0.535577i	$-0.179906\pi$
$887$	9.20009	+	9.20009i	0.308909	+	0.308909i	−0.535577	+	0.844486i	$0.679906\pi$
$888$	−2.27666	+	2.27666i	−0.0763996	+	0.0763996i
$889$	21.7289			0.728765
$890$	−1.34802	−	1.23642i	−0.0451856	−	0.0414447i
$891$			5.98186i			0.200400i
$892$	−11.6805	+	11.6805i	−0.391093	+	0.391093i
$893$	4.37182	−	4.37182i	0.146298	−	0.146298i
$894$	5.66808			0.189569
$895$	12.6533	−	0.546395i	0.422955	−	0.0182640i
$896$	−1.60598			−0.0536520
$897$	−0.659256	+	0.659256i	−0.0220119	+	0.0220119i
$898$	−11.3055	−	11.3055i	−0.377270	−	0.377270i
$899$	−15.8929	+	6.95884i	−0.530057	+	0.232090i
$900$	−4.98139	+	0.431015i	−0.166046	+	0.0143672i
$901$	27.1354			0.904010
$902$	15.7410	−	15.7410i	0.524120	−	0.524120i
$903$	3.31704	−	3.31704i	0.110384	−	0.110384i
$904$			14.2575i			0.474197i
$905$	1.61942	+	37.5024i	0.0538314	+	1.24662i
$906$	−16.3761			−0.544058
$907$	−23.2082	−	23.2082i	−0.770615	−	0.770615i	0.207599	−	0.978214i	$-0.433435\pi$
$907$	−23.2082	−	23.2082i	−0.770615	−	0.770615i	−0.978214	+	0.207599i	$0.933435\pi$
$908$	−6.56117	+	6.56117i	−0.217740	+	0.217740i
$909$			1.13242i			0.0375601i
$910$	1.76908	−	1.92876i	0.0586445	−	0.0639379i
$911$			29.4829i			0.976813i	0.872616	+	0.488406i	$0.162422\pi$
$911$			29.4829i			0.976813i	−0.872616	+	0.488406i	$0.837578\pi$
$912$	0.563301	−	0.563301i	0.0186528	−	0.0186528i
$913$	32.4895	−	32.4895i	1.07525	−	1.07525i
$914$	5.21745			0.172578
$915$	1.93105	−	2.10535i	0.0638387	−	0.0696009i
$916$		−	26.6498i		−	0.880534i
$917$	−4.54941	−	4.54941i	−0.150235	−	0.150235i
$918$	2.59395	−	2.59395i	0.0856131	−	0.0856131i
$919$			50.4084i			1.66282i	0.555659	+	0.831410i	$0.312466\pi$
$919$			50.4084i			1.66282i	−0.555659	+	0.831410i	$0.687534\pi$
$920$	2.85783	−	0.123406i	0.0942199	−	0.00406859i
$921$			1.86156i			0.0613406i
$922$	−8.88396	+	8.88396i	−0.292578	+	0.292578i
$923$	−3.19980	−	3.19980i	−0.105323	−	0.105323i
$924$			9.60674i			0.316039i
$925$	−10.3596	+	12.3222i	−0.340623	+	0.405151i
$926$			5.45788i			0.179357i
$927$	−0.871920	−	0.871920i	−0.0286376	−	0.0286376i
$928$	2.20340	+	2.20340i	0.0723302	+	0.0723302i
$929$	24.4705			0.802850			0.401425	−	0.915892i	$-0.368515\pi$
$929$	24.4705			0.802850			0.401425	+	0.915892i	$0.368515\pi$
$930$	−5.48096	−	11.1785i	−0.179728	−	0.366558i
$931$	−3.52176			−0.115421
$932$	2.56633	+	2.56633i	0.0840630	+	0.0840630i
$933$	7.20655	+	7.20655i	0.235932	+	0.235932i
$934$		−	20.2303i		−	0.661954i
$935$	−36.1608	−	33.1671i	−1.18258	−	1.08468i
$936$		−	0.728809i		−	0.0238219i
$937$	−0.266929	−	0.266929i	−0.00872020	−	0.00872020i	0.702733	−	0.711453i	$-0.251963\pi$
$937$	−0.266929	−	0.266929i	−0.00872020	−	0.00872020i	−0.711453	+	0.702733i	$0.751963\pi$
$938$	−6.74342	+	6.74342i	−0.220181	+	0.220181i
$939$		−	8.03855i		−	0.262328i
$940$	−11.7305	+	12.7893i	−0.382607	+	0.417142i
$941$			41.0271i			1.33744i	0.743512	+	0.668722i	$0.233159\pi$
$941$			41.0271i			1.33744i	−0.743512	+	0.668722i	$0.766841\pi$
$942$	−4.49510	+	4.49510i	−0.146458	+	0.146458i
$943$	−3.36630	−	3.36630i	−0.109622	−	0.109622i
$944$			9.53350i			0.310289i
$945$	−3.58774	+	0.154925i	−0.116709	+	0.00503971i
$946$	−17.4728			−0.568090
$947$	−32.6394	+	32.6394i	−1.06064	+	1.06064i	−0.0626009	+	0.998039i	$0.519940\pi$
$947$	−32.6394	+	32.6394i	−1.06064	+	1.06064i	−0.998039	+	0.0626009i	$0.980060\pi$
$948$	0.770334	−	0.770334i	0.0250193	−	0.0250193i
$949$			10.5094i			0.341151i
$950$	2.56323	−	3.04881i	0.0831622	−	0.0989165i
$951$			3.83248i			0.124277i
$952$	4.16583	−	4.16583i	0.135015	−	0.135015i
$953$	12.0984	+	12.0984i	0.391906	+	0.391906i	0.875366	−	0.483460i	$-0.160620\pi$
$953$	12.0984	+	12.0984i	0.391906	+	0.391906i	−0.483460	+	0.875366i	$0.660620\pi$
$954$	−7.39706			−0.239489
$955$	3.58042	−	0.154609i	0.115860	−	0.00500303i
$956$			16.0605i			0.519433i
$957$	13.1804	−	13.1804i	0.426063	−	0.426063i
$958$	8.32725	−	8.32725i	0.269041	−	0.269041i
$959$	34.3874			1.11043
$960$	−1.51145	+	1.64788i	−0.0487820	+	0.0531851i
$961$	21.0256	−	22.7799i	0.678245	−	0.734836i
$962$	−1.65925	−	1.65925i	−0.0534963	−	0.0534963i
$963$	−12.3856	+	12.3856i	−0.399119	+	0.399119i
$964$	21.5579			0.694334
$965$	0.221045	−	0.240997i	0.00711570	−	0.00775797i
$966$	2.05445			0.0661009
$967$	−15.0934	+	15.0934i	−0.485371	+	0.485371i	−0.906842	−	0.421471i	$-0.861514\pi$
$967$	−15.0934	+	15.0934i	−0.485371	+	0.485371i	0.421471	+	0.906842i	$0.361514\pi$
$968$	17.5240	−	17.5240i	0.563242	−	0.563242i
$969$			2.92235i			0.0938794i
$970$	−1.81774	−	42.0950i	−0.0583641	−	1.35159i
$971$	−16.9213			−0.543030			−0.271515	−	0.962434i	$-0.587525\pi$
$971$	−16.9213			−0.543030			−0.271515	+	0.962434i	$0.587525\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	9.49031	+	9.49031i	0.304245	+	0.304245i
$974$	35.4151			1.13477
$975$	−0.314127	−	3.63048i	−0.0100601	−	0.116268i
$976$		−	1.27761i		−	0.0408954i
$977$	2.59932	+	2.59932i	0.0831595	+	0.0831595i	0.747463	−	0.664303i	$-0.231272\pi$
$977$	2.59932	+	2.59932i	0.0831595	+	0.0831595i	−0.664303	+	0.747463i	$0.731272\pi$
$978$	13.2697	+	13.2697i	0.424318	+	0.424318i
$979$			4.89334i			0.156392i
$980$	9.87607	−	0.426467i	0.315480	−	0.0136230i
$981$	−15.9598			−0.509557
$982$	25.1913	−	25.1913i	0.803887	−	0.803887i
$983$	−22.8665	−	22.8665i	−0.729327	−	0.729327i	0.241158	−	0.970486i	$-0.422473\pi$
$983$	−22.8665	−	22.8665i	−0.729327	−	0.729327i	−0.970486	+	0.241158i	$0.922473\pi$
$984$	3.72145			0.118636
$985$	−11.4732	+	12.5088i	−0.365567	+	0.398564i
$986$	−11.4310			−0.364038
$987$	−8.81347	+	8.81347i	−0.280536	+	0.280536i
$988$	0.410539	+	0.410539i	0.0130610	+	0.0130610i
$989$			3.73665i			0.118819i
$990$	9.85738	+	9.04130i	0.313288	+	0.287351i
$991$		−	11.1421i		−	0.353940i	−0.984216	−	0.176970i	$-0.943370\pi$
$991$		−	11.1421i		−	0.353940i	0.984216	−	0.176970i	$-0.0566296\pi$
$992$	−5.18555	−	2.02733i	−0.164641	−	0.0643677i
$993$	−0.306209	+	0.306209i	−0.00971726	+	0.00971726i
$994$			9.97158i			0.316279i
$995$	−1.41114	+	0.0609355i	−0.0447360	+	0.00193178i
$996$	7.68107			0.243384
$997$	−19.9793	−	19.9793i	−0.632752	−	0.632752i	0.316005	−	0.948757i	$-0.397658\pi$
$997$	−19.9793	−	19.9793i	−0.632752	−	0.632752i	−0.948757	+	0.316005i	$0.897658\pi$
$998$	5.92476	+	5.92476i	0.187545	+	0.187545i
$999$			3.21968i			0.101866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.k.a.247.16	✓	32
5.3	odd	4		930.2.k.b.433.16	yes	32
31.30	odd	2		930.2.k.b.247.16	yes	32
155.123	even	4	inner	930.2.k.a.433.16	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.k.a.247.16	✓	32	1.1	even	1	trivial
930.2.k.a.433.16	yes	32	155.123	even	4	inner
930.2.k.b.247.16	yes	32	31.30	odd	2
930.2.k.b.433.16	yes	32	5.3	odd	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.23399 - 0.0964676i) q^{5} -1.00000i q^{6} +(-1.13560 - 1.13560i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(2.23399 - 0.0964676i) q^{5} -1.00000i q^{6} +(-1.13560 - 1.13560i) q^{7} +(-0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(1.64788 + 1.51145i) q^{10} -5.98186i q^{11} +(0.707107 - 0.707107i) q^{12} +(0.515345 + 0.515345i) q^{13} -1.60598i q^{14} +(-1.64788 - 1.51145i) q^{15} -1.00000 q^{16} +(2.59395 - 2.59395i) q^{17} +(-0.707107 + 0.707107i) q^{18} -0.796628i q^{19} +(0.0964676 + 2.23399i) q^{20} +1.60598i q^{21} +(4.22981 - 4.22981i) q^{22} +(-0.904567 - 0.904567i) q^{23} +1.00000 q^{24} +(4.98139 - 0.431015i) q^{25} +0.728809i q^{26} +(0.707107 - 0.707107i) q^{27} +(1.13560 - 1.13560i) q^{28} -3.11608 q^{29} +(-0.0964676 - 2.23399i) q^{30} +(5.10027 - 2.23320i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.22981 + 4.22981i) q^{33} +3.66840 q^{34} +(-2.64646 - 2.42736i) q^{35} -1.00000 q^{36} +(-2.27666 + 2.27666i) q^{37} +(0.563301 - 0.563301i) q^{38} -0.728809i q^{39} +(-1.51145 + 1.64788i) q^{40} +3.72145 q^{41} +(-1.13560 + 1.13560i) q^{42} +(-2.06543 - 2.06543i) q^{43} +5.98186 q^{44} +(0.0964676 + 2.23399i) q^{45} -1.27925i q^{46} +(5.48791 + 5.48791i) q^{47} +(0.707107 + 0.707107i) q^{48} -4.42083i q^{49} +(3.82715 + 3.21760i) q^{50} -3.66840 q^{51} +(-0.515345 + 0.515345i) q^{52} +(5.23051 + 5.23051i) q^{53} +1.00000 q^{54} +(-0.577056 - 13.3634i) q^{55} +1.60598 q^{56} +(-0.563301 + 0.563301i) q^{57} +(-2.20340 - 2.20340i) q^{58} -9.53350i q^{59} +(1.51145 - 1.64788i) q^{60} +1.27761i q^{61} +(5.18555 + 2.02733i) q^{62} +(1.13560 - 1.13560i) q^{63} -1.00000i q^{64} +(1.20099 + 1.10156i) q^{65} -5.98186 q^{66} +(-4.19895 - 4.19895i) q^{67} +(2.59395 + 2.59395i) q^{68} +1.27925i q^{69} +(-0.154925 - 3.58774i) q^{70} -6.20904 q^{71} +(-0.707107 - 0.707107i) q^{72} +(10.1965 + 10.1965i) q^{73} -3.21968 q^{74} +(-3.82715 - 3.21760i) q^{75} +0.796628 q^{76} +(-6.79299 + 6.79299i) q^{77} +(0.515345 - 0.515345i) q^{78} +1.08942 q^{79} +(-2.23399 + 0.0964676i) q^{80} -1.00000 q^{81} +(2.63146 + 2.63146i) q^{82} +(5.43134 + 5.43134i) q^{83} -1.60598 q^{84} +(5.54461 - 6.04508i) q^{85} -2.92097i q^{86} +(2.20340 + 2.20340i) q^{87} +(4.22981 + 4.22981i) q^{88} -0.818030 q^{89} +(-1.51145 + 1.64788i) q^{90} -1.17045i q^{91} +(0.904567 - 0.904567i) q^{92} +(-5.18555 - 2.02733i) q^{93} +7.76108i q^{94} +(-0.0768488 - 1.77966i) q^{95} +1.00000i q^{96} +(-13.3240 - 13.3240i) q^{97} +(3.12600 - 3.12600i) q^{98} +5.98186 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7}+O(q^{10}) \) 32 * q - 4 * q^7	\( 32 q - 4 q^{7} + 4 q^{10} - 4 q^{15} - 32 q^{16} - 8 q^{17} + 4 q^{22} + 32 q^{24} + 8 q^{25} + 4 q^{28} - 8 q^{29} - 20 q^{31} - 4 q^{33} - 24 q^{35} - 32 q^{36} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 4 q^{42} + 16 q^{43} + 8 q^{44} - 8 q^{47} - 16 q^{50} + 24 q^{53} + 32 q^{54} + 28 q^{55} - 16 q^{57} - 20 q^{58} + 16 q^{62} + 4 q^{63} - 56 q^{65} - 8 q^{66} + 32 q^{67} - 8 q^{68} - 28 q^{70} + 16 q^{71} + 20 q^{73} - 24 q^{74} + 16 q^{75} - 16 q^{76} + 40 q^{77} + 56 q^{79} - 32 q^{81} + 16 q^{82} - 72 q^{83} + 32 q^{85} + 20 q^{87} + 4 q^{88} + 64 q^{89} - 16 q^{93} + 32 q^{95} - 4 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 4 * q^10 - 4 * q^15 - 32 * q^16 - 8 * q^17 + 4 * q^22 + 32 * q^24 + 8 * q^25 + 4 * q^28 - 8 * q^29 - 20 * q^31 - 4 * q^33 - 24 * q^35 - 32 * q^36 - 4 * q^37 + 16 * q^38 - 16 * q^41 - 4 * q^42 + 16 * q^43 + 8 * q^44 - 8 * q^47 - 16 * q^50 + 24 * q^53 + 32 * q^54 + 28 * q^55 - 16 * q^57 - 20 * q^58 + 16 * q^62 + 4 * q^63 - 56 * q^65 - 8 * q^66 + 32 * q^67 - 8 * q^68 - 28 * q^70 + 16 * q^71 + 20 * q^73 - 24 * q^74 + 16 * q^75 - 16 * q^76 + 40 * q^77 + 56 * q^79 - 32 * q^81 + 16 * q^82 - 72 * q^83 + 32 * q^85 + 20 * q^87 + 4 * q^88 + 64 * q^89 - 16 * q^93 + 32 * q^95 - 4 * q^97 + 16 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more