LMFDB - Embedded newform 930.2.n.f.841.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10 x^{10} - 15 x^{9} + 61 x^{8} - 25 x^{7} + 316 x^{6} + 50 x^{5} + 1336 x^{4} + \cdots + 121 $ x^12 - 3x^11 + 10x^10 - 15x^9 + 61x^8 - 25x^7 + 316x^6 + 50x^5 + 1336x^4 - 1720x^3 + 1235x^2 - 462*x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			841.1
Root			$0.784484 - 2.41439i$ of defining polynomial
Character	$\chi$	$=$	930.841
Dual form			930.2.n.f.721.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-4.03161 + 2.92914i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-4.03161 + 2.92914i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(3.07834 - 2.23654i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-0.484838 + 1.49218i) q^{13} +(4.03161 + 2.92914i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.20814 - 3.05739i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.24608 + 3.83505i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(-1.53994 - 4.73944i) q^{21} +(-3.07834 - 2.23654i) q^{22} +(-2.76439 - 2.00845i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +1.56897 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.53994 - 4.73944i) q^{28} +(-1.32840 - 4.08841i) q^{29} +1.00000 q^{30} +(-5.47277 + 1.02410i) q^{31} -1.00000 q^{32} +(1.17582 + 3.61880i) q^{33} +(-1.60737 + 4.94697i) q^{34} +(-4.03161 + 2.92914i) q^{35} +1.00000 q^{36} -10.7227 q^{37} +(3.26229 - 2.37019i) q^{38} +(-1.26932 - 0.922216i) q^{39} +(0.809017 + 0.587785i) q^{40} +(1.39947 + 4.30712i) q^{41} +(-4.03161 + 2.92914i) q^{42} +(-2.13967 - 6.58522i) q^{43} +(-1.17582 + 3.61880i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(-1.05590 + 3.24973i) q^{46} +(-0.665153 + 2.04713i) q^{47} +(0.809017 + 0.587785i) q^{48} +(5.51093 - 16.9609i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(4.20814 - 3.05739i) q^{51} +(-0.484838 - 1.49218i) q^{52} +(-8.26558 - 6.00530i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(3.07834 - 2.23654i) q^{55} -4.98335 q^{56} -4.03241 q^{57} +(-3.47781 + 2.52677i) q^{58} +(-1.59270 + 4.90182i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.45886 q^{61} +(2.66515 + 4.88845i) q^{62} +4.98335 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.484838 + 1.49218i) q^{65} +(3.07834 - 2.23654i) q^{66} -1.93515 q^{67} +5.20155 q^{68} +(2.76439 - 2.00845i) q^{69} +(4.03161 + 2.92914i) q^{70} +(6.60268 + 4.79713i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(11.7344 - 8.52556i) q^{73} +(3.31348 + 10.1979i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-3.26229 - 2.37019i) q^{76} +(-5.85952 + 18.0337i) q^{77} +(-0.484838 + 1.49218i) q^{78} +(-7.75630 - 5.63528i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.66386 - 2.66195i) q^{82} +(4.46803 + 13.7512i) q^{83} +(4.03161 + 2.92914i) q^{84} +(-4.20814 - 3.05739i) q^{85} +(-5.60172 + 4.06989i) q^{86} +4.29881 q^{87} +3.80504 q^{88} +(-5.21612 + 3.78973i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-2.41611 - 7.43603i) q^{91} +3.41697 q^{92} +(0.717206 - 5.52138i) q^{93} +2.15248 q^{94} +(1.24608 + 3.83505i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-2.87578 + 2.08938i) q^{97} -17.8337 q^{98} -3.80504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.00000			0.447214
$5$	1.00000			0.447214
$6$	1.00000			0.408248
$7$	−4.03161	+	2.92914i	−1.52381	+	1.10711i	−0.564246	+	0.825607i	$0.690833\pi$
$7$	−4.03161	+	2.92914i	−1.52381	+	1.10711i	−0.959560	+	0.281503i	$0.909167\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−0.309017	−	0.951057i	−0.0977198	−	0.300750i
$11$	3.07834	−	2.23654i	0.928154	−	0.674343i	−0.0173863	−	0.999849i	$-0.505534\pi$
$11$	3.07834	−	2.23654i	0.928154	−	0.674343i	0.945540	+	0.325506i	$0.105534\pi$
$12$	−0.309017	−	0.951057i	−0.0892055	−	0.274546i
$13$	−0.484838	+	1.49218i	−0.134470	+	0.413855i	−0.995507	−	0.0946863i	$-0.969815\pi$
$13$	−0.484838	+	1.49218i	−0.134470	+	0.413855i	0.861037	+	0.508542i	$0.169815\pi$
$14$	4.03161	+	2.92914i	1.07749	+	0.782845i
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−4.20814	−	3.05739i	−1.02062	−	0.741527i	−0.0542133	−	0.998529i	$-0.517265\pi$
$17$	−4.20814	−	3.05739i	−1.02062	−	0.741527i	−0.966411	+	0.257003i	$0.917265\pi$
$18$	−0.309017	+	0.951057i	−0.0728360	+	0.224166i
$19$	1.24608	+	3.83505i	0.285871	+	0.879821i	0.986136	+	0.165938i	$0.0530652\pi$
$19$	1.24608	+	3.83505i	0.285871	+	0.879821i	−0.700265	+	0.713883i	$0.746935\pi$
$20$	−0.809017	+	0.587785i	−0.180902	+	0.131433i
$21$	−1.53994	−	4.73944i	−0.336042	−	1.03423i
$22$	−3.07834	−	2.23654i	−0.656304	−	0.476833i
$23$	−2.76439	−	2.00845i	−0.576415	−	0.418790i	0.261015	−	0.965335i	$-0.415943\pi$
$23$	−2.76439	−	2.00845i	−0.576415	−	0.418790i	−0.837430	+	0.546545i	$0.815943\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	1.56897			0.307700
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	1.53994	−	4.73944i	0.291021	−	0.895671i
$29$	−1.32840	−	4.08841i	−0.246678	−	0.759198i	−0.995356	−	0.0962637i	$-0.969311\pi$
$29$	−1.32840	−	4.08841i	−0.246678	−	0.759198i	0.748677	−	0.662934i	$-0.230689\pi$
$30$	1.00000			0.182574
$31$	−5.47277	+	1.02410i	−0.982939	+	0.183933i
$31$	−5.47277	+	1.02410i	−0.982939	+	0.183933i
$32$	−1.00000			−0.176777
$33$	1.17582	+	3.61880i	0.204684	+	0.629953i
$34$	−1.60737	+	4.94697i	−0.275661	+	0.848398i
$35$	−4.03161	+	2.92914i	−0.681467	+	0.495115i
$36$	1.00000			0.166667
$37$	−10.7227			−1.76279			−0.881397	−	0.472376i	$-0.843397\pi$
$37$	−10.7227			−1.76279			−0.881397	+	0.472376i	$0.843397\pi$
$38$	3.26229	−	2.37019i	0.529213	−	0.384496i
$39$	−1.26932	−	0.922216i	−0.203254	−	0.147673i
$40$	0.809017	+	0.587785i	0.127917	+	0.0929370i
$41$	1.39947	+	4.30712i	0.218560	+	0.672660i	0.998882	+	0.0472807i	$0.0150555\pi$
$41$	1.39947	+	4.30712i	0.218560	+	0.672660i	−0.780321	+	0.625379i	$0.784944\pi$
$42$	−4.03161	+	2.92914i	−0.622091	+	0.451976i
$43$	−2.13967	−	6.58522i	−0.326296	−	1.00424i	−0.970852	−	0.239680i	$-0.922958\pi$
$43$	−2.13967	−	6.58522i	−0.326296	−	1.00424i	0.644556	−	0.764557i	$-0.277042\pi$
$44$	−1.17582	+	3.61880i	−0.177262	+	0.545555i
$45$	−0.809017	−	0.587785i	−0.120601	−	0.0876219i
$46$	−1.05590	+	3.24973i	−0.155684	+	0.479147i
$47$	−0.665153	+	2.04713i	−0.0970226	+	0.298605i	−0.987776	−	0.155883i	$-0.950178\pi$
$47$	−0.665153	+	2.04713i	−0.0970226	+	0.298605i	0.890753	+	0.454488i	$0.150178\pi$
$48$	0.809017	+	0.587785i	0.116772	+	0.0848395i
$49$	5.51093	−	16.9609i	0.787275	−	2.42298i
$50$	−0.309017	−	0.951057i	−0.0437016	−	0.134500i
$51$	4.20814	−	3.05739i	0.589258	−	0.428121i
$52$	−0.484838	−	1.49218i	−0.0672349	−	0.206928i
$53$	−8.26558	−	6.00530i	−1.13536	−	0.824891i	−0.148898	−	0.988853i	$-0.547573\pi$
$53$	−8.26558	−	6.00530i	−1.13536	−	0.824891i	−0.986467	+	0.163962i	$0.947573\pi$
$54$	−0.809017	−	0.587785i	−0.110093	−	0.0799874i
$55$	3.07834	−	2.23654i	0.415083	−	0.301575i
$56$	−4.98335			−0.665928
$57$	−4.03241			−0.534106
$58$	−3.47781	+	2.52677i	−0.456658	+	0.331782i
$59$	−1.59270	+	4.90182i	−0.207352	+	0.638163i	0.792257	+	0.610188i	$0.208906\pi$
$59$	−1.59270	+	4.90182i	−0.207352	+	0.638163i	−0.999609	+	0.0279754i	$0.991094\pi$
$60$	−0.309017	−	0.951057i	−0.0398939	−	0.122781i
$61$	−8.45886			−1.08305			−0.541523	−	0.840686i	$-0.682152\pi$
$61$	−8.45886			−1.08305			−0.541523	+	0.840686i	$0.682152\pi$
$62$	2.66515	+	4.88845i	0.338475	+	0.620834i
$63$	4.98335			0.627843
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.484838	+	1.49218i	−0.0601367	+	0.185082i
$66$	3.07834	−	2.23654i	0.378917	−	0.275299i
$67$	−1.93515			−0.236417			−0.118208	−	0.992989i	$-0.537715\pi$
$67$	−1.93515			−0.236417			−0.118208	+	0.992989i	$0.537715\pi$
$68$	5.20155			0.630780
$69$	2.76439	−	2.00845i	0.332793	−	0.241788i
$70$	4.03161	+	2.92914i	0.481870	+	0.350099i
$71$	6.60268	+	4.79713i	0.783594	+	0.569314i	0.906055	−	0.423159i	$-0.139079\pi$
$71$	6.60268	+	4.79713i	0.783594	+	0.569314i	−0.122462	+	0.992473i	$0.539079\pi$
$72$	−0.309017	−	0.951057i	−0.0364180	−	0.112083i
$73$	11.7344	−	8.52556i	1.37341	−	0.997841i	0.375949	−	0.926640i	$-0.377317\pi$
$73$	11.7344	−	8.52556i	1.37341	−	0.997841i	0.997462	−	0.0712009i	$-0.0226831\pi$
$74$	3.31348	+	10.1979i	0.385185	+	1.18548i
$75$	−0.309017	+	0.951057i	−0.0356822	+	0.109819i
$76$	−3.26229	−	2.37019i	−0.374210	−	0.271880i
$77$	−5.85952	+	18.0337i	−0.667754	+	2.05514i
$78$	−0.484838	+	1.49218i	−0.0548970	+	0.168956i
$79$	−7.75630	−	5.63528i	−0.872652	−	0.634019i	0.0586450	−	0.998279i	$-0.481322\pi$
$79$	−7.75630	−	5.63528i	−0.872652	−	0.634019i	−0.931297	+	0.364260i	$0.881322\pi$
$80$	0.309017	−	0.951057i	0.0345492	−	0.106331i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	3.66386	−	2.66195i	0.404605	−	0.293963i
$83$	4.46803	+	13.7512i	0.490430	+	1.50939i	0.823959	+	0.566650i	$0.191761\pi$
$83$	4.46803	+	13.7512i	0.490430	+	1.50939i	−0.333529	+	0.942740i	$0.608239\pi$
$84$	4.03161	+	2.92914i	0.439885	+	0.319595i
$85$	−4.20814	−	3.05739i	−0.456437	−	0.331621i
$86$	−5.60172	+	4.06989i	−0.604049	+	0.438868i
$87$	4.29881			0.460880
$88$	3.80504			0.405618
$89$	−5.21612	+	3.78973i	−0.552908	+	0.401711i	−0.828856	−	0.559461i	$-0.811008\pi$
$89$	−5.21612	+	3.78973i	−0.552908	+	0.401711i	0.275949	+	0.961172i	$0.411008\pi$
$90$	−0.309017	+	0.951057i	−0.0325733	+	0.100250i
$91$	−2.41611	−	7.43603i	−0.253277	−	0.779508i
$92$	3.41697			0.356244
$93$	0.717206	−	5.52138i	0.0743708	−	0.572540i
$94$	2.15248			0.222011
$95$	1.24608	+	3.83505i	0.127846	+	0.393468i
$96$	0.309017	−	0.951057i	0.0315389	−	0.0970668i
$97$	−2.87578	+	2.08938i	−0.291992	+	0.212144i	−0.724131	−	0.689663i	$-0.757759\pi$
$97$	−2.87578	+	2.08938i	−0.291992	+	0.212144i	0.432139	+	0.901807i	$0.357759\pi$
$98$	−17.8337			−1.80148
$99$	−3.80504			−0.382420
$100$	−0.809017	+	0.587785i	−0.0809017	+	0.0587785i
$101$	−15.4559	−	11.2294i	−1.53792	−	1.11736i	−0.951625	−	0.307263i	$-0.900587\pi$
$101$	−15.4559	−	11.2294i	−1.53792	−	1.11736i	−0.586292	−	0.810100i	$-0.699413\pi$
$102$	−4.20814	−	3.05739i	−0.416668	−	0.302727i
$103$	4.98486	+	15.3418i	0.491172	+	1.51167i	0.822838	+	0.568276i	$0.192389\pi$
$103$	4.98486	+	15.3418i	0.491172	+	1.51167i	−0.331665	+	0.943397i	$0.607611\pi$
$104$	−1.26932	+	0.922216i	−0.124467	+	0.0904307i
$105$	−1.53994	−	4.73944i	−0.150283	−	0.462522i
$106$	−3.15717	+	9.71677i	−0.306652	+	0.943777i
$107$	−2.91729	−	2.11953i	−0.282025	−	0.204903i	0.437775	−	0.899084i	$-0.355767\pi$
$107$	−2.91729	−	2.11953i	−0.282025	−	0.204903i	−0.719800	+	0.694181i	$0.755767\pi$
$108$	−0.309017	+	0.951057i	−0.0297352	+	0.0915155i
$109$	−0.565181	+	1.73945i	−0.0541345	+	0.166609i	−0.974468	−	0.224525i	$-0.927917\pi$
$109$	−0.565181	+	1.73945i	−0.0541345	+	0.166609i	0.920334	+	0.391134i	$0.127917\pi$
$110$	−3.07834	−	2.23654i	−0.293508	−	0.213246i
$111$	3.31348	−	10.1979i	0.314502	−	0.967938i
$112$	1.53994	+	4.73944i	0.145511	+	0.447835i
$113$	−5.70475	+	4.14474i	−0.536657	+	0.389904i	−0.822842	−	0.568270i	$-0.807613\pi$
$113$	−5.70475	+	4.14474i	−0.536657	+	0.389904i	0.286185	+	0.958174i	$0.407613\pi$
$114$	1.24608	+	3.83505i	0.116706	+	0.359186i
$115$	−2.76439	−	2.00845i	−0.257781	−	0.187289i
$116$	3.47781	+	2.52677i	0.322906	+	0.234605i
$117$	1.26932	−	0.922216i	0.117349	−	0.0852589i
$118$	5.15408			0.474472
$119$	25.9211			2.37618
$120$	−0.809017	+	0.587785i	−0.0738528	+	0.0536572i
$121$	1.07485	−	3.30805i	0.0977138	−	0.300732i
$122$	2.61393	+	8.04485i	0.236654	+	0.728347i
$123$	−4.52878			−0.408346
$124$	3.82562	−	4.04533i	0.343550	−	0.363281i
$125$	1.00000			0.0894427
$126$	−1.53994	−	4.73944i	−0.137189	−	0.422223i
$127$	−0.389015	+	1.19727i	−0.0345195	+	0.106240i	−0.966832	−	0.255415i	$-0.917788\pi$
$127$	−0.389015	+	1.19727i	−0.0345195	+	0.106240i	0.932312	+	0.361655i	$0.117788\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	6.92411			0.609634
$130$	1.56897			0.137608
$131$	14.1673	−	10.2932i	1.23781	−	0.899319i	0.240356	−	0.970685i	$-0.422736\pi$
$131$	14.1673	−	10.2932i	1.23781	−	0.899319i	0.997450	+	0.0713662i	$0.0227359\pi$
$132$	−3.07834	−	2.23654i	−0.267935	−	0.194666i
$133$	−16.2571	−	11.8115i	−1.40967	−	1.02419i
$134$	0.597996	+	1.84044i	0.0516590	+	0.158990i
$135$	0.809017	−	0.587785i	0.0696291	−	0.0505885i
$136$	−1.60737	−	4.94697i	−0.137831	−	0.424199i
$137$	−2.11477	+	6.50860i	−0.180677	+	0.556067i	−0.999847	−	0.0174837i	$-0.994434\pi$
$137$	−2.11477	+	6.50860i	−0.180677	+	0.556067i	0.819170	+	0.573551i	$0.194434\pi$
$138$	−2.76439	−	2.00845i	−0.235320	−	0.170970i
$139$	−4.20521	+	12.9423i	−0.356681	+	1.09775i	0.598347	+	0.801237i	$0.295825\pi$
$139$	−4.20521	+	12.9423i	−0.356681	+	1.09775i	−0.955028	+	0.296515i	$0.904175\pi$
$140$	1.53994	−	4.73944i	0.130149	−	0.400556i
$141$	−1.74139	−	1.26520i	−0.146652	−	0.106549i
$142$	2.52200	−	7.76191i	0.211641	−	0.651365i
$143$	1.84482	+	5.67778i	0.154272	+	0.474800i
$144$	−0.809017	+	0.587785i	−0.0674181	+	0.0489821i
$145$	−1.32840	−	4.08841i	−0.110318	−	0.339524i
$146$	−11.7344	−	8.52556i	−0.971148	−	0.705580i
$147$	14.4278	+	10.4824i	1.18998	+	0.864574i
$148$	8.67481	−	6.30262i	0.713065	−	0.518072i
$149$	7.64716			0.626480			0.313240	−	0.949674i	$-0.398586\pi$
$149$	7.64716			0.626480			0.313240	+	0.949674i	$0.398586\pi$
$150$	1.00000			0.0816497
$151$	−8.09620	+	5.88224i	−0.658860	+	0.478690i	−0.866278	−	0.499563i	$-0.833494\pi$
$151$	−8.09620	+	5.88224i	−0.658860	+	0.478690i	0.207418	+	0.978252i	$0.433494\pi$
$152$	−1.24608	+	3.83505i	−0.101071	+	0.311064i
$153$	1.60737	+	4.94697i	0.129948	+	0.399938i
$154$	18.9618			1.52799
$155$	−5.47277	+	1.02410i	−0.439584	+	0.0822574i
$156$	1.56897			0.125618
$157$	−2.48662	−	7.65303i	−0.198454	−	0.610778i	−0.999919	−	0.0127365i	$-0.995946\pi$
$157$	−2.48662	−	7.65303i	−0.198454	−	0.610778i	0.801465	−	0.598042i	$-0.204054\pi$
$158$	−2.96264	+	9.11808i	−0.235695	+	0.725396i
$159$	8.26558	−	6.00530i	0.655503	−	0.476251i
$160$	−1.00000			−0.0790569
$161$	17.0280			1.34199
$162$	0.809017	−	0.587785i	0.0635624	−	0.0461808i
$163$	12.9789	+	9.42976i	1.01659	+	0.738595i	0.965581	−	0.260103i	$-0.0837564\pi$
$163$	12.9789	+	9.42976i	1.01659	+	0.738595i	0.0510085	+	0.998698i	$0.483756\pi$
$164$	−3.66386	−	2.66195i	−0.286099	−	0.207863i
$165$	1.17582	+	3.61880i	0.0915375	+	0.281723i
$166$	11.6975	−	8.49870i	0.907899	−	0.659627i
$167$	1.97769	+	6.08669i	0.153038	+	0.471002i	0.997957	−	0.0638921i	$-0.0203514\pi$
$167$	1.97769	+	6.08669i	0.153038	+	0.471002i	−0.844919	+	0.534894i	$0.820351\pi$
$168$	1.53994	−	4.73944i	0.118809	−	0.365656i
$169$	8.52570	+	6.19428i	0.655823	+	0.476483i
$170$	−1.60737	+	4.94697i	−0.123279	+	0.379415i
$171$	1.24608	−	3.83505i	0.0952904	−	0.293274i
$172$	5.60172	+	4.06989i	0.427127	+	0.310326i
$173$	0.240656	−	0.740662i	0.0182967	−	0.0563115i	−0.941491	−	0.337037i	$-0.890575\pi$
$173$	0.240656	−	0.740662i	0.0182967	−	0.0563115i	0.959788	+	0.280726i	$0.0905752\pi$
$174$	−1.32840	−	4.08841i	−0.100706	−	0.309941i
$175$	−4.03161	+	2.92914i	−0.304761	+	0.221422i
$176$	−1.17582	−	3.61880i	−0.0886308	−	0.272778i
$177$	−4.16974	−	3.02949i	−0.313417	−	0.227711i
$178$	5.21612	+	3.78973i	0.390965	+	0.284053i
$179$	−2.43821	+	1.77147i	−0.182241	+	0.132406i	−0.675165	−	0.737666i	$-0.735928\pi$
$179$	−2.43821	+	1.77147i	−0.182241	+	0.132406i	0.492925	+	0.870072i	$0.335928\pi$
$180$	1.00000			0.0745356
$181$	18.2338			1.35530			0.677652	−	0.735383i	$-0.262998\pi$
$181$	18.2338			1.35530			0.677652	+	0.735383i	$0.262998\pi$
$182$	−6.32547	+	4.59572i	−0.468875	+	0.340657i
$183$	2.61393	−	8.04485i	0.193227	−	0.594693i
$184$	−1.05590	−	3.24973i	−0.0778422	−	0.239574i
$185$	−10.7227			−0.788346
$186$	−5.47277	+	1.02410i	−0.401283	+	0.0750904i
$187$	−19.7921			−1.44734
$188$	−0.665153	−	2.04713i	−0.0485113	−	0.149302i
$189$	−1.53994	+	4.73944i	−0.112014	+	0.344744i
$190$	3.26229	−	2.37019i	0.236671	−	0.171952i
$191$	14.1453			1.02352			0.511759	−	0.859129i	$-0.328994\pi$
$191$	14.1453			1.02352			0.511759	+	0.859129i	$0.328994\pi$
$192$	−1.00000			−0.0721688
$193$	12.7511	−	9.26418i	0.917841	−	0.666851i	−0.0251447	−	0.999684i	$-0.508005\pi$
$193$	12.7511	−	9.26418i	0.917841	−	0.666851i	0.942986	+	0.332833i	$0.108005\pi$
$194$	2.87578	+	2.08938i	0.206469	+	0.150009i
$195$	−1.26932	−	0.922216i	−0.0908980	−	0.0660412i
$196$	5.51093	+	16.9609i	0.393638	+	1.21149i
$197$	5.36662	−	3.89908i	0.382356	−	0.277798i	−0.379960	−	0.925003i	$-0.624062\pi$
$197$	5.36662	−	3.89908i	0.382356	−	0.277798i	0.762316	+	0.647205i	$0.224062\pi$
$198$	1.17582	+	3.61880i	0.0835619	+	0.257177i
$199$	7.06054	−	21.7301i	0.500508	−	1.54041i	−0.307685	−	0.951488i	$-0.599554\pi$
$199$	7.06054	−	21.7301i	0.500508	−	1.54041i	0.808193	−	0.588918i	$-0.200446\pi$
$200$	0.809017	+	0.587785i	0.0572061	+	0.0415627i
$201$	0.597996	−	1.84044i	0.0421794	−	0.129815i
$202$	−5.90362	+	18.1695i	−0.415377	+	1.27840i
$203$	17.3311	+	12.5918i	1.21641	+	0.883771i
$204$	−1.60737	+	4.94697i	−0.112538	+	0.346357i
$205$	1.39947	+	4.30712i	0.0977432	+	0.300822i
$206$	13.0505	−	9.48176i	0.909273	−	0.660625i
$207$	1.05590	+	3.24973i	0.0733903	+	0.225872i
$208$	1.26932	+	0.922216i	0.0880116	+	0.0639442i
$209$	12.4131	+	9.01867i	0.858634	+	0.623834i
$210$	−4.03161	+	2.92914i	−0.278208	+	0.202130i
$211$	−20.9742			−1.44392			−0.721962	−	0.691933i	$-0.756759\pi$
$211$	−20.9742			−1.44392			−0.721962	+	0.691933i	$0.756759\pi$
$212$	10.2168			0.701694
$213$	−6.60268	+	4.79713i	−0.452408	+	0.328694i
$214$	−1.11430	+	3.42948i	−0.0761723	+	0.234434i
$215$	−2.13967	−	6.58522i	−0.145924	−	0.449108i
$216$	1.00000			0.0680414
$217$	19.0644	−	20.1593i	1.29417	−	1.36850i
$218$	1.82896			0.123873
$219$	4.48215	+	13.7946i	0.302876	+	0.932156i
$220$	−1.17582	+	3.61880i	−0.0792738	+	0.243980i
$221$	6.60243	−	4.79695i	0.444128	−	0.322678i
$222$	−10.7227			−0.719658
$223$	2.85280			0.191038			0.0955188	−	0.995428i	$-0.469549\pi$
$223$	2.85280			0.191038			0.0955188	+	0.995428i	$0.469549\pi$
$224$	4.03161	−	2.92914i	0.269373	−	0.195711i
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$	5.70475	+	4.14474i	0.379474	+	0.275704i
$227$	1.05735	+	3.25419i	0.0701787	+	0.215988i	0.979995	−	0.199024i	$-0.0637773\pi$
$227$	1.05735	+	3.25419i	0.0701787	+	0.215988i	−0.909816	+	0.415012i	$0.863777\pi$
$228$	3.26229	−	2.37019i	0.216050	−	0.156970i
$229$	2.71639	+	8.36020i	0.179504	+	0.552457i	0.999810	−	0.0194672i	$-0.00619699\pi$
$229$	2.71639	+	8.36020i	0.179504	+	0.552457i	−0.820306	+	0.571925i	$0.806197\pi$
$230$	−1.05590	+	3.24973i	−0.0696241	+	0.214281i
$231$	−15.3404	−	11.1455i	−1.00933	−	0.733318i
$232$	1.32840	−	4.08841i	0.0872140	−	0.268417i
$233$	4.73125	−	14.5613i	0.309954	−	0.953941i	−0.667828	−	0.744316i	$-0.732776\pi$
$233$	4.73125	−	14.5613i	0.309954	−	0.953941i	0.977782	−	0.209625i	$-0.0672243\pi$
$234$	−1.26932	−	0.922216i	−0.0829781	−	0.0602871i
$235$	−0.665153	+	2.04713i	−0.0433898	+	0.133540i
$236$	−1.59270	−	4.90182i	−0.103676	−	0.319082i
$237$	7.75630	−	5.63528i	0.503826	−	0.366051i
$238$	−8.01006	−	24.6524i	−0.519215	−	1.59798i
$239$	−23.9532	−	17.4030i	−1.54940	−	1.12571i	−0.944075	−	0.329730i	$-0.893042\pi$
$239$	−23.9532	−	17.4030i	−1.54940	−	1.12571i	−0.605327	−	0.795977i	$-0.706958\pi$
$240$	0.809017	+	0.587785i	0.0522218	+	0.0379414i
$241$	−18.0030	+	13.0800i	−1.15968	+	0.842554i	−0.989737	−	0.142901i	$-0.954357\pi$
$241$	−18.0030	+	13.0800i	−1.15968	+	0.842554i	−0.169939	+	0.985455i	$0.554357\pi$
$242$	−3.47829			−0.223593
$243$	−1.00000			−0.0641500
$244$	6.84336	−	4.97199i	0.438101	−	0.318299i
$245$	5.51093	−	16.9609i	0.352080	−	1.08359i
$246$	1.39947	+	4.30712i	0.0892269	+	0.274612i
$247$	−6.32672			−0.402560
$248$	−5.02951	−	2.38830i	−0.319374	−	0.151657i
$249$	−14.4589			−0.916293
$250$	−0.309017	−	0.951057i	−0.0195440	−	0.0601501i
$251$	−0.442864	+	1.36300i	−0.0279533	+	0.0860316i	−0.964060	−	0.265685i	$-0.914402\pi$
$251$	−0.442864	+	1.36300i	−0.0279533	+	0.0860316i	0.936107	+	0.351717i	$0.114402\pi$
$252$	−4.03161	+	2.92914i	−0.253968	+	0.184518i
$253$	−13.0017			−0.817410
$254$	1.25888			0.0789891
$255$	4.20814	−	3.05739i	0.263524	−	0.191461i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−5.93986	−	4.31556i	−0.370518	−	0.269197i	0.386907	−	0.922119i	$-0.373543\pi$
$257$	−5.93986	−	4.31556i	−0.370518	−	0.269197i	−0.757426	+	0.652921i	$0.773543\pi$
$258$	−2.13967	−	6.58522i	−0.133210	−	0.409978i
$259$	43.2296	−	31.4081i	2.68616	−	1.95161i
$260$	−0.484838	−	1.49218i	−0.0300683	−	0.0925409i
$261$	−1.32840	+	4.08841i	−0.0822261	+	0.253066i
$262$	−14.1673	−	10.2932i	−0.875261	−	0.635914i
$263$	0.760163	−	2.33954i	0.0468737	−	0.144262i	−0.924880	−	0.380258i	$-0.875835\pi$
$263$	0.760163	−	2.33954i	0.0468737	−	0.144262i	0.971754	+	0.235996i	$0.0758352\pi$
$264$	−1.17582	+	3.61880i	−0.0723667	+	0.222722i
$265$	−8.26558	−	6.00530i	−0.507751	−	0.368902i
$266$	−6.20967	+	19.1114i	−0.380739	+	1.17179i
$267$	−1.99238	−	6.13192i	−0.121932	−	0.375267i
$268$	1.56557	−	1.13746i	0.0956326	−	0.0694811i
$269$	−6.02334	−	18.5379i	−0.367250	−	1.13028i	−0.948560	−	0.316596i	$-0.897460\pi$
$269$	−6.02334	−	18.5379i	−0.367250	−	1.13028i	0.581311	−	0.813682i	$-0.302540\pi$
$270$	−0.809017	−	0.587785i	−0.0492352	−	0.0357715i
$271$	−5.53896	−	4.02429i	−0.336468	−	0.244458i	0.406702	−	0.913561i	$-0.366679\pi$
$271$	−5.53896	−	4.02429i	−0.336468	−	0.244458i	−0.743170	+	0.669103i	$0.766679\pi$
$272$	−4.20814	+	3.05739i	−0.255156	+	0.185382i
$273$	7.81871			0.473210
$274$	6.84355			0.413434
$275$	3.07834	−	2.23654i	0.185631	−	0.134869i
$276$	−1.05590	+	3.24973i	−0.0635579	+	0.195611i
$277$	−1.86603	−	5.74304i	−0.112119	−	0.345066i	0.879217	−	0.476422i	$-0.158067\pi$
$277$	−1.86603	−	5.74304i	−0.112119	−	0.345066i	−0.991335	+	0.131357i	$0.958067\pi$
$278$	13.6084			0.816175
$279$	5.02951	+	2.38830i	0.301109	+	0.142984i
$280$	−4.98335			−0.297812
$281$	9.75237	+	30.0147i	0.581777	+	1.79053i	0.611843	+	0.790979i	$0.290428\pi$
$281$	9.75237	+	30.0147i	0.581777	+	1.79053i	−0.0300659	+	0.999548i	$0.509572\pi$
$282$	−0.665153	+	2.04713i	−0.0396093	+	0.121905i
$283$	−3.06059	+	2.22365i	−0.181933	+	0.132182i	−0.675024	−	0.737795i	$-0.735867\pi$
$283$	−3.06059	+	2.22365i	−0.181933	+	0.132182i	0.493091	+	0.869978i	$0.335867\pi$
$284$	−8.16136			−0.484287
$285$	−4.03241			−0.238860
$286$	4.82981	−	3.50906i	0.285593	−	0.207495i
$287$	−18.2583	−	13.2654i	−1.07775	−	0.783032i
$288$	0.809017	+	0.587785i	0.0476718	+	0.0346356i
$289$	3.10750	+	9.56392i	0.182794	+	0.562583i
$290$	−3.47781	+	2.52677i	−0.204224	+	0.148377i
$291$	−1.09845	−	3.38069i	−0.0643924	−	0.198179i
$292$	−4.48215	+	13.7946i	−0.262298	+	0.807271i
$293$	−2.73649	−	1.98817i	−0.159867	−	0.116150i	0.504976	−	0.863134i	$-0.331501\pi$
$293$	−2.73649	−	1.98817i	−0.159867	−	0.116150i	−0.664843	+	0.746983i	$0.731501\pi$
$294$	5.51093	−	16.9609i	0.321404	−	0.989179i
$295$	−1.59270	+	4.90182i	−0.0927305	+	0.285395i
$296$	−8.67481	−	6.30262i	−0.504213	−	0.366332i
$297$	1.17582	−	3.61880i	0.0682280	−	0.209984i
$298$	−2.36310	−	7.27289i	−0.136891	−	0.421307i
$299$	4.33723	−	3.15119i	0.250829	−	0.182238i
$300$	−0.309017	−	0.951057i	−0.0178411	−	0.0549093i
$301$	27.9153	+	20.2817i	1.60901	+	1.16902i
$302$	8.09620	+	5.88224i	0.465884	+	0.338485i
$303$	15.4559	−	11.2294i	0.887917	−	0.645109i
$304$	4.03241			0.231275
$305$	−8.45886			−0.484353
$306$	4.20814	−	3.05739i	0.240563	−	0.174780i
$307$	1.61899	−	4.98273i	0.0924004	−	0.284379i	−0.894167	−	0.447733i	$-0.852231\pi$
$307$	1.61899	−	4.98273i	0.0924004	−	0.284379i	0.986567	+	0.163354i	$0.0522314\pi$
$308$	−5.85952	−	18.0337i	−0.333877	−	1.02757i
$309$	−16.1313			−0.917679
$310$	2.66515	+	4.88845i	0.151371	+	0.277645i
$311$	14.8676			0.843066			0.421533	−	0.906813i	$-0.361492\pi$
$311$	14.8676			0.843066			0.421533	+	0.906813i	$0.361492\pi$
$312$	−0.484838	−	1.49218i	−0.0274485	−	0.0844779i
$313$	−7.15490	+	22.0205i	−0.404419	+	1.24467i	0.516960	+	0.856009i	$0.327063\pi$
$313$	−7.15490	+	22.0205i	−0.404419	+	1.24467i	−0.921379	+	0.388664i	$0.872937\pi$
$314$	−6.51005	+	4.72983i	−0.367384	+	0.266920i
$315$	4.98335			0.280780
$316$	9.58732			0.539329
$317$	−19.2994	+	14.0218i	−1.08396	+	0.787543i	−0.978369	−	0.206867i	$-0.933673\pi$
$317$	−19.2994	+	14.0218i	−1.08396	+	0.787543i	−0.105591	+	0.994410i	$0.533673\pi$
$318$	−8.26558	−	6.00530i	−0.463511	−	0.336760i
$319$	−13.2332	−	9.61447i	−0.740916	−	0.538307i
$320$	0.309017	+	0.951057i	0.0172746	+	0.0531657i
$321$	2.91729	−	2.11953i	0.162827	−	0.118301i
$322$	−5.26193	−	16.1945i	−0.293236	−	0.902487i
$323$	6.48157	−	19.9482i	0.360644	−	1.10995i
$324$	−0.809017	−	0.587785i	−0.0449454	−	0.0326547i
$325$	−0.484838	+	1.49218i	−0.0268939	+	0.0827711i
$326$	4.95752	−	15.2577i	0.274571	−	0.845044i
$327$	−1.47966	−	1.07504i	−0.0818255	−	0.0594497i
$328$	−1.39947	+	4.30712i	−0.0772727	+	0.237821i
$329$	−3.31469	−	10.2016i	−0.182745	−	0.562430i
$330$	3.07834	−	2.23654i	0.169457	−	0.123118i
$331$	7.59627	+	23.3789i	0.417529	+	1.28502i	0.909969	+	0.414675i	$0.136105\pi$
$331$	7.59627	+	23.3789i	0.417529	+	1.28502i	−0.492441	+	0.870346i	$0.663895\pi$
$332$	−11.6975	−	8.49870i	−0.641982	−	0.466427i
$333$	8.67481	+	6.30262i	0.475377	+	0.345382i
$334$	5.17765	−	3.76178i	0.283308	−	0.205836i
$335$	−1.93515			−0.105729
$336$	−4.98335			−0.271864
$337$	−3.91658	+	2.84556i	−0.213350	+	0.155008i	−0.689328	−	0.724449i	$-0.742094\pi$
$337$	−3.91658	+	2.84556i	−0.213350	+	0.155008i	0.475978	+	0.879457i	$0.342094\pi$
$338$	3.25653	−	10.0226i	0.177132	−	0.545155i
$339$	−2.17902	−	6.70633i	−0.118348	−	0.364238i
$340$	5.20155			0.282094
$341$	−14.5566	+	15.3926i	−0.788284	+	0.833556i
$342$	−4.03241			−0.218048
$343$	16.6833	+	51.3459i	0.900813	+	2.77242i
$344$	2.13967	−	6.58522i	0.115363	−	0.355051i
$345$	2.76439	−	2.00845i	0.148830	−	0.108131i
$346$	−0.778778			−0.0418674
$347$	−15.3813			−0.825709			−0.412855	−	0.910797i	$-0.635468\pi$
$347$	−15.3813			−0.825709			−0.412855	+	0.910797i	$0.635468\pi$
$348$	−3.47781	+	2.52677i	−0.186430	+	0.135449i
$349$	−18.1404	−	13.1798i	−0.971035	−	0.705498i	−0.0153478	−	0.999882i	$-0.504886\pi$
$349$	−18.1404	−	13.1798i	−0.971035	−	0.705498i	−0.955687	+	0.294384i	$0.904886\pi$
$350$	4.03161	+	2.92914i	0.215499	+	0.156569i
$351$	0.484838	+	1.49218i	0.0258787	+	0.0796465i
$352$	−3.07834	+	2.23654i	−0.164076	+	0.119208i
$353$	10.3408	+	31.8257i	0.550385	+	1.69391i	0.707830	+	0.706383i	$0.249674\pi$
$353$	10.3408	+	31.8257i	0.550385	+	1.69391i	−0.157444	+	0.987528i	$0.550326\pi$
$354$	−1.59270	+	4.90182i	−0.0846510	+	0.260529i
$355$	6.60268	+	4.79713i	0.350434	+	0.254605i
$356$	1.99238	−	6.13192i	0.105596	−	0.324991i
$357$	−8.01006	+	24.6524i	−0.423938	+	1.30475i
$358$	2.43821	+	1.77147i	0.128864	+	0.0936249i
$359$	−7.59403	+	23.3720i	−0.400798	+	1.23353i	0.523556	+	0.851991i	$0.324605\pi$
$359$	−7.59403	+	23.3720i	−0.400798	+	1.23353i	−0.924354	+	0.381537i	$0.875395\pi$
$360$	−0.309017	−	0.951057i	−0.0162866	−	0.0501251i
$361$	2.21642	−	1.61032i	0.116654	−	0.0847539i
$362$	−5.63454	−	17.3413i	−0.296145	−	0.911440i
$363$	2.81400	+	2.04449i	0.147697	+	0.107308i
$364$	6.32547	+	4.59572i	0.331545	+	0.240881i
$365$	11.7344	−	8.52556i	0.614208	−	0.446248i
$366$	−8.45886			−0.442152
$367$	−2.19500			−0.114578			−0.0572890	−	0.998358i	$-0.518246\pi$
$367$	−2.19500			−0.114578			−0.0572890	+	0.998358i	$0.518246\pi$
$368$	−2.76439	+	2.00845i	−0.144104	+	0.104697i
$369$	1.39947	−	4.30712i	0.0728534	−	0.224220i
$370$	3.31348	+	10.1979i	0.172260	+	0.530161i
$371$	50.9140			2.64332
$372$	2.66515	+	4.88845i	0.138182	+	0.253454i
$373$	4.40476			0.228070			0.114035	−	0.993477i	$-0.463622\pi$
$373$	4.40476			0.228070			0.114035	+	0.993477i	$0.463622\pi$
$374$	6.11609	+	18.8234i	0.316255	+	0.973334i
$375$	−0.309017	+	0.951057i	−0.0159576	+	0.0491123i
$376$	−1.74139	+	1.26520i	−0.0898055	+	0.0652475i
$377$	6.74469			0.347369
$378$	4.98335			0.256316
$379$	−22.0796	+	16.0418i	−1.13415	+	0.824011i	−0.986294	−	0.164997i	$-0.947238\pi$
$379$	−22.0796	+	16.0418i	−1.13415	+	0.824011i	−0.147860	+	0.989008i	$0.547238\pi$
$380$	−3.26229	−	2.37019i	−0.167352	−	0.121588i
$381$	−1.01845	−	0.739951i	−0.0521770	−	0.0379088i
$382$	−4.37114	−	13.4530i	−0.223647	−	0.688314i
$383$	−19.9371	+	14.4852i	−1.01874	+	0.740158i	−0.966024	−	0.258451i	$-0.916788\pi$
$383$	−19.9371	+	14.4852i	−1.01874	+	0.740158i	−0.0527161	+	0.998610i	$0.516788\pi$
$384$	0.309017	+	0.951057i	0.0157695	+	0.0485334i
$385$	−5.85952	+	18.0337i	−0.298629	+	0.919085i
$386$	−12.7511	−	9.26418i	−0.649012	−	0.471535i
$387$	−2.13967	+	6.58522i	−0.108765	+	0.334746i
$388$	1.09845	−	3.38069i	0.0557654	−	0.171628i
$389$	18.1578	+	13.1924i	0.920635	+	0.668881i	0.943682	−	0.330854i	$-0.107337\pi$
$389$	18.1578	+	13.1924i	0.920635	+	0.668881i	−0.0230467	+	0.999734i	$0.507337\pi$
$390$	−0.484838	+	1.49218i	−0.0245507	+	0.0755593i
$391$	5.49233	+	16.9036i	0.277759	+	0.854854i
$392$	14.4278	−	10.4824i	0.728714	−	0.529442i
$393$	5.41144	+	16.6547i	0.272971	+	0.840119i
$394$	−5.36662	−	3.89908i	−0.270367	−	0.196433i
$395$	−7.75630	−	5.63528i	−0.390262	−	0.283542i
$396$	3.07834	−	2.23654i	0.154692	−	0.112391i
$397$	39.3286			1.97385			0.986924	−	0.161188i	$-0.0515326\pi$
$397$	39.3286			1.97385			0.986924	+	0.161188i	$0.0515326\pi$
$398$	−22.8484			−1.14529
$399$	16.2571	−	11.8115i	0.813874	−	0.591314i
$400$	0.309017	−	0.951057i	0.0154508	−	0.0475528i
$401$	5.50521	+	16.9433i	0.274917	+	0.846107i	0.989241	+	0.146292i	$0.0467340\pi$
$401$	5.50521	+	16.9433i	0.274917	+	0.846107i	−0.714325	+	0.699815i	$0.753266\pi$
$402$	−1.93515			−0.0965167
$403$	1.12527	−	8.66286i	0.0560538	−	0.431528i
$404$	19.1045			0.950485
$405$	0.309017	+	0.951057i	0.0153552	+	0.0472584i
$406$	6.61990	−	20.3739i	0.328540	−	1.01114i
$407$	−33.0080	+	23.9817i	−1.63614	+	1.18873i
$408$	5.20155			0.257515
$409$	−22.3579			−1.10553			−0.552764	−	0.833338i	$-0.686427\pi$
$409$	−22.3579			−1.10553			−0.552764	+	0.833338i	$0.686427\pi$
$410$	3.66386	−	2.66195i	0.180945	−	0.131464i
$411$	−5.53654	−	4.02253i	−0.273098	−	0.198417i
$412$	−13.0505	−	9.48176i	−0.642953	−	0.467133i
$413$	−7.93697	−	24.4275i	−0.390553	−	1.20200i
$414$	2.76439	−	2.00845i	0.135862	−	0.0987097i
$415$	4.46803	+	13.7512i	0.219327	+	0.675020i
$416$	0.484838	−	1.49218i	0.0237711	−	0.0731600i
$417$	−11.0094	−	7.99879i	−0.539132	−	0.391702i
$418$	4.74139	−	14.5925i	0.231909	−	0.713743i
$419$	−4.38617	+	13.4993i	−0.214279	+	0.659482i	0.784925	+	0.619590i	$0.212701\pi$
$419$	−4.38617	+	13.4993i	−0.214279	+	0.659482i	−0.999204	+	0.0398914i	$0.987299\pi$
$420$	4.03161	+	2.92914i	0.196723	+	0.142927i
$421$	−5.51195	+	16.9640i	−0.268636	+	0.826776i	0.722198	+	0.691687i	$0.243132\pi$
$421$	−5.51195	+	16.9640i	−0.268636	+	0.826776i	−0.990833	+	0.135089i	$0.956868\pi$
$422$	6.48139	+	19.9477i	0.315509	+	0.971037i
$423$	1.74139	−	1.26520i	0.0846694	−	0.0615160i
$424$	−3.15717	−	9.71677i	−0.153326	−	0.471888i
$425$	−4.20814	−	3.05739i	−0.204125	−	0.148305i
$426$	6.60268	+	4.79713i	0.319901	+	0.232421i
$427$	34.1028	−	24.7772i	1.65035	−	1.19905i
$428$	3.60597			0.174301
$429$	−5.96998			−0.288233
$430$	−5.60172	+	4.06989i	−0.270139	+	0.196268i
$431$	7.88331	−	24.2623i	0.379726	−	1.16868i	−0.560509	−	0.828148i	$-0.689394\pi$
$431$	7.88331	−	24.2623i	0.379726	−	1.16868i	0.940235	−	0.340527i	$-0.110606\pi$
$432$	−0.309017	−	0.951057i	−0.0148676	−	0.0457577i
$433$	−35.6182			−1.71170			−0.855852	−	0.517221i	$-0.826966\pi$
$433$	−35.6182			−1.71170			−0.855852	+	0.517221i	$0.826966\pi$
$434$	−25.0638	−	11.9017i	−1.20310	−	0.571302i
$435$	4.29881			0.206112
$436$	−0.565181	−	1.73945i	−0.0270672	−	0.0833044i
$437$	4.25783	−	13.1043i	0.203680	−	0.626862i
$438$	11.7344	−	8.52556i	0.560693	−	0.407367i
$439$	−18.1281			−0.865206			−0.432603	−	0.901584i	$-0.642405\pi$
$439$	−18.1281			−0.865206			−0.432603	+	0.901584i	$0.642405\pi$
$440$	3.80504			0.181398
$441$	−14.4278	+	10.4824i	−0.687038	+	0.499162i
$442$	−6.60243	−	4.79695i	−0.314046	−	0.228168i
$443$	8.20713	+	5.96283i	0.389933	+	0.283303i	0.765428	−	0.643522i	$-0.222527\pi$
$443$	8.20713	+	5.96283i	0.389933	+	0.283303i	−0.375495	+	0.926824i	$0.622527\pi$
$444$	3.31348	+	10.1979i	0.157251	+	0.483969i
$445$	−5.21612	+	3.78973i	−0.247268	+	0.179651i
$446$	−0.881564	−	2.71317i	−0.0417432	−	0.128472i
$447$	−2.36310	+	7.27289i	−0.111771	+	0.343996i
$448$	−4.03161	−	2.92914i	−0.190476	−	0.138389i
$449$	7.86329	−	24.2007i	0.371092	−	1.14210i	−0.574986	−	0.818163i	$-0.694992\pi$
$449$	7.86329	−	24.2007i	0.371092	−	1.14210i	0.946078	−	0.323940i	$-0.105008\pi$
$450$	−0.309017	+	0.951057i	−0.0145672	+	0.0448332i
$451$	13.9411	+	10.1288i	0.656461	+	0.476947i
$452$	2.17902	−	6.70633i	0.102492	−	0.315439i
$453$	−3.09247	−	9.51766i	−0.145297	−	0.447179i
$454$	2.76818	−	2.01120i	0.129917	−	0.0943902i
$455$	−2.41611	−	7.43603i	−0.113269	−	0.348607i
$456$	−3.26229	−	2.37019i	−0.152771	−	0.110994i
$457$	−5.21387	−	3.78810i	−0.243895	−	0.177200i	0.459122	−	0.888373i	$-0.348164\pi$
$457$	−5.21387	−	3.78810i	−0.243895	−	0.177200i	−0.703017	+	0.711173i	$0.748164\pi$
$458$	7.11161	−	5.16689i	0.332304	−	0.241433i
$459$	−5.20155			−0.242787
$460$	3.41697			0.159317
$461$	−24.9063	+	18.0955i	−1.16000	+	0.842789i	−0.989778	−	0.142616i	$-0.954448\pi$
$461$	−24.9063	+	18.0955i	−1.16000	+	0.842789i	−0.170222	+	0.985406i	$0.554448\pi$
$462$	−5.85952	+	18.0337i	−0.272610	+	0.839006i
$463$	4.25118	+	13.0838i	0.197569	+	0.608055i	0.999937	+	0.0112253i	$0.00357319\pi$
$463$	4.25118	+	13.0838i	0.197569	+	0.608055i	−0.802368	+	0.596830i	$0.796427\pi$
$464$	−4.29881			−0.199567
$465$	0.717206	−	5.52138i	0.0332596	−	0.256048i
$466$	−15.3106			−0.709251
$467$	4.11345	+	12.6599i	0.190348	+	0.585830i	0.999999	−	0.00108088i	$-0.000344054\pi$
$467$	4.11345	+	12.6599i	0.190348	+	0.585830i	−0.809652	+	0.586910i	$0.800344\pi$
$468$	−0.484838	+	1.49218i	−0.0224116	+	0.0689759i
$469$	7.80179	−	5.66833i	0.360253	−	0.261739i
$470$	2.15248			0.0992865
$471$	8.04687			0.370780
$472$	−4.16974	+	3.02949i	−0.191928	+	0.139444i
$473$	−21.3148	−	15.4861i	−0.980054	−	0.712051i
$474$	−7.75630	−	5.63528i	−0.356259	−	0.258837i
$475$	1.24608	+	3.83505i	0.0571743	+	0.175964i
$476$	−20.9706	+	15.2360i	−0.961187	+	0.698343i
$477$	3.15717	+	9.71677i	0.144557	+	0.444901i
$478$	−9.14930	+	28.1587i	−0.418479	+	1.28795i
$479$	19.0548	+	13.8441i	0.870638	+	0.632555i	0.930758	−	0.365636i	$-0.119148\pi$
$479$	19.0548	+	13.8441i	0.870638	+	0.632555i	−0.0601203	+	0.998191i	$0.519148\pi$
$480$	0.309017	−	0.951057i	0.0141046	−	0.0434096i
$481$	5.19875	−	16.0001i	0.237043	−	0.729542i
$482$	18.0030	+	13.0800i	0.820015	+	0.595776i
$483$	−5.26193	+	16.1945i	−0.239426	+	0.736877i
$484$	1.07485	+	3.30805i	0.0488569	+	0.150366i
$485$	−2.87578	+	2.08938i	−0.130583	+	0.0948738i
$486$	0.309017	+	0.951057i	0.0140173	+	0.0431408i
$487$	−25.7404	−	18.7015i	−1.16641	−	0.847446i	−0.175834	−	0.984420i	$-0.556262\pi$
$487$	−25.7404	−	18.7015i	−1.16641	−	0.847446i	−0.990575	+	0.136974i	$0.956262\pi$
$488$	−6.84336	−	4.97199i	−0.309784	−	0.225072i
$489$	−12.9789	+	9.42976i	−0.586928	+	0.426428i
$490$	−17.8337			−0.805646
$491$	−20.1959			−0.911426			−0.455713	−	0.890127i	$-0.650616\pi$
$491$	−20.1959			−0.911426			−0.455713	+	0.890127i	$0.650616\pi$
$492$	3.66386	−	2.66195i	0.165179	−	0.120010i
$493$	−6.90976	+	21.2660i	−0.311200	+	0.957774i
$494$	1.95507	+	6.01707i	0.0879625	+	0.270721i
$495$	−3.80504			−0.171024
$496$	−0.717206	+	5.52138i	−0.0322035	+	0.247917i
$497$	−40.6709			−1.82434
$498$	4.46803	+	13.7512i	0.200217	+	0.616206i
$499$	7.26325	−	22.3540i	0.325148	−	1.00070i	−0.646226	−	0.763146i	$-0.723654\pi$
$499$	7.26325	−	22.3540i	0.325148	−	1.00070i	0.971374	−	0.237556i	$-0.0763464\pi$
$500$	−0.809017	+	0.587785i	−0.0361803	+	0.0262866i
$501$	−6.39993			−0.285928
$502$	1.43314			0.0639641
$503$	−2.97500	+	2.16146i	−0.132649	+	0.0963749i	−0.652131	−	0.758106i	$-0.726125\pi$
$503$	−2.97500	+	2.16146i	−0.132649	+	0.0963749i	0.519482	+	0.854481i	$0.326125\pi$
$504$	4.03161	+	2.92914i	0.179582	+	0.130474i
$505$	−15.4559	−	11.2294i	−0.687777	−	0.499700i
$506$	4.01775	+	12.3653i	0.178611	+	0.549707i
$507$	−8.52570	+	6.19428i	−0.378640	+	0.275098i
$508$	−0.389015	−	1.19727i	−0.0172598	−	0.0531201i
$509$	−0.442997	+	1.36340i	−0.0196355	+	0.0604318i	−0.960394	−	0.278645i	$-0.910115\pi$
$509$	−0.442997	+	1.36340i	−0.0196355	+	0.0604318i	0.940759	+	0.339077i	$0.110115\pi$
$510$	−4.20814	−	3.05739i	−0.186340	−	0.135384i
$511$	−22.3361	+	68.7435i	−0.988092	+	3.04103i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	3.26229	+	2.37019i	0.144034	+	0.104647i
$514$	−2.26883	+	6.98273i	−0.100074	+	0.307995i
$515$	4.98486	+	15.3418i	0.219659	+	0.676041i
$516$	−5.60172	+	4.06989i	−0.246602	+	0.179167i
$517$	2.53093	+	7.78940i	0.111310	+	0.342578i
$518$	−43.2296	−	31.4081i	−1.89940	−	1.37999i
$519$	0.630045	+	0.457754i	0.0276559	+	0.0200932i
$520$	−1.26932	+	0.922216i	−0.0556634	+	0.0404418i
$521$	2.96602			0.129944			0.0649719	−	0.997887i	$-0.479304\pi$
$521$	2.96602			0.129944			0.0649719	+	0.997887i	$0.479304\pi$
$522$	4.29881			0.188154
$523$	7.65087	−	5.55868i	0.334549	−	0.243064i	−0.407809	−	0.913067i	$-0.633707\pi$
$523$	7.65087	−	5.55868i	0.334549	−	0.243064i	0.742358	+	0.670003i	$0.233707\pi$
$524$	−5.41144	+	16.6547i	−0.236400	+	0.727564i
$525$	−1.53994	−	4.73944i	−0.0672084	−	0.206846i
$526$	−2.45994			−0.107258
$527$	26.1613	+	12.4229i	1.13960	+	0.541149i
$528$	3.80504			0.165593
$529$	−3.49940	−	10.7701i	−0.152148	−	0.468263i
$530$	−3.15717	+	9.71677i	−0.137139	+	0.422070i
$531$	4.16974	−	3.02949i	0.180951	−	0.131469i
$532$	20.0949			0.871225
$533$	−7.10550			−0.307773
$534$	−5.21612	+	3.78973i	−0.225724	+	0.163998i
$535$	−2.91729	−	2.11953i	−0.126125	−	0.0916354i
$536$	−1.56557	−	1.13746i	−0.0676224	−	0.0491306i
$537$	−0.931315	−	2.86629i	−0.0401892	−	0.123690i
$538$	−15.7693	+	11.4571i	−0.679863	+	0.493950i
$539$	−20.9693	−	64.5368i	−0.903211	−	2.77980i
$540$	−0.309017	+	0.951057i	−0.0132980	+	0.0409270i
$541$	−29.4923	−	21.4274i	−1.26797	−	0.921237i	−0.268854	−	0.963181i	$-0.586645\pi$
$541$	−29.4923	−	21.4274i	−1.26797	−	0.921237i	−0.999120	+	0.0419442i	$0.986645\pi$
$542$	−2.11569	+	6.51144i	−0.0908768	+	0.279690i
$543$	−5.63454	+	17.3413i	−0.241801	+	0.744188i
$544$	4.20814	+	3.05739i	0.180423	+	0.131085i
$545$	−0.565181	+	1.73945i	−0.0242097	+	0.0745097i
$546$	−2.41611	−	7.43603i	−0.103400	−	0.318233i
$547$	−11.1579	+	8.10670i	−0.477078	+	0.346618i	−0.800193	−	0.599742i	$-0.795270\pi$
$547$	−11.1579	+	8.10670i	−0.477078	+	0.346618i	0.323115	+	0.946360i	$0.395270\pi$
$548$	−2.11477	−	6.50860i	−0.0903386	−	0.278034i
$549$	6.84336	+	4.97199i	0.292068	+	0.212200i
$550$	−3.07834	−	2.23654i	−0.131261	−	0.0953665i
$551$	14.0240	−	10.1890i	0.597441	−	0.434066i
$552$	3.41697			0.145436
$553$	47.7769			2.03168
$554$	−4.88532	+	3.54939i	−0.207557	+	0.150799i
$555$	3.31348	−	10.1979i	0.140650	−	0.432875i
$556$	−4.20521	−	12.9423i	−0.178341	−	0.548876i
$557$	29.2992			1.24145			0.620723	−	0.784030i	$-0.286839\pi$
$557$	29.2992			1.24145			0.620723	+	0.784030i	$0.286839\pi$
$558$	0.717206	−	5.52138i	0.0303617	−	0.233739i
$559$	10.8637			0.459486
$560$	1.53994	+	4.73944i	0.0650743	+	0.200278i
$561$	6.11609	−	18.8234i	0.258221	−	0.794724i
$562$	25.5320	−	18.5501i	1.07700	−	0.782489i
$563$	41.5662			1.75181			0.875904	−	0.482485i	$-0.160266\pi$
$563$	41.5662			1.75181			0.875904	+	0.482485i	$0.160266\pi$
$564$	2.15248			0.0906358
$565$	−5.70475	+	4.14474i	−0.240000	+	0.174371i
$566$	3.06059	+	2.22365i	0.128646	+	0.0934670i
$567$	−4.03161	−	2.92914i	−0.169312	−	0.123012i
$568$	2.52200	+	7.76191i	0.105821	+	0.325683i
$569$	21.0452	−	15.2902i	0.882259	−	0.640999i	−0.0515890	−	0.998668i	$-0.516429\pi$
$569$	21.0452	−	15.2902i	0.882259	−	0.640999i	0.933848	+	0.357670i	$0.116429\pi$
$570$	1.24608	+	3.83505i	0.0521927	+	0.160633i
$571$	−2.56234	+	7.88607i	−0.107231	+	0.330022i	−0.990247	−	0.139319i	$-0.955509\pi$
$571$	−2.56234	+	7.88607i	−0.107231	+	0.330022i	0.883017	+	0.469341i	$0.155509\pi$
$572$	−4.82981	−	3.50906i	−0.201945	−	0.146721i
$573$	−4.37114	+	13.4530i	−0.182607	+	0.562006i
$574$	−6.97404	+	21.4639i	−0.291091	+	0.895885i
$575$	−2.76439	−	2.00845i	−0.115283	−	0.0837580i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−12.2400	−	37.6709i	−0.509559	−	1.56826i	−0.792969	−	0.609262i	$-0.791466\pi$
$577$	−12.2400	−	37.6709i	−0.509559	−	1.56826i	0.283410	−	0.958999i	$-0.408534\pi$
$578$	8.13555	−	5.91083i	0.338394	−	0.245858i
$579$	4.87047	+	14.9898i	0.202410	+	0.622953i
$580$	3.47781	+	2.52677i	0.144408	+	0.104919i
$581$	−58.2925	−	42.3520i	−2.41838	−	1.75706i
$582$	−2.87578	+	2.08938i	−0.119205	+	0.0866076i
$583$	−38.8754			−1.61005
$584$	14.5045			0.600203
$585$	1.26932	−	0.922216i	0.0524800	−	0.0381289i
$586$	−1.04524	+	3.21693i	−0.0431787	+	0.132890i
$587$	−12.2696	−	37.7619i	−0.506420	−	1.55860i	−0.798371	−	0.602166i	$-0.794304\pi$
$587$	−12.2696	−	37.7619i	−0.506420	−	1.55860i	0.291951	−	0.956433i	$-0.405696\pi$
$588$	−17.8337			−0.735451
$589$	−10.7470	−	19.7123i	−0.442822	−	0.812229i
$590$	5.15408			0.212190
$591$	2.04987	+	6.30885i	0.0843203	+	0.259511i
$592$	−3.31348	+	10.1979i	−0.136183	+	0.419129i
$593$	21.1257	−	15.3487i	0.867530	−	0.630297i	−0.0623930	−	0.998052i	$-0.519873\pi$
$593$	21.1257	−	15.3487i	0.867530	−	0.630297i	0.929923	+	0.367754i	$0.119873\pi$
$594$	−3.80504			−0.156122
$595$	25.9211			1.06266
$596$	−6.18669	+	4.49489i	−0.253417	+	0.184118i
$597$	18.4847	+	13.4299i	0.756530	+	0.549651i
$598$	−4.33723	−	3.15119i	−0.177363	−	0.128862i
$599$	0.0829747	+	0.255370i	0.00339026	+	0.0104341i	0.952737	−	0.303795i	$-0.0982539\pi$
$599$	0.0829747	+	0.255370i	0.00339026	+	0.0104341i	−0.949347	+	0.314229i	$0.898254\pi$
$600$	−0.809017	+	0.587785i	−0.0330280	+	0.0239962i
$601$	−5.57367	−	17.1540i	−0.227355	−	0.699726i	−0.998044	−	0.0625147i	$-0.980088\pi$
$601$	−5.57367	−	17.1540i	−0.227355	−	0.699726i	0.770689	−	0.637211i	$-0.219912\pi$
$602$	10.6627	−	32.8164i	0.434580	−	1.33750i
$603$	1.56557	+	1.13746i	0.0637551	+	0.0463208i
$604$	3.09247	−	9.51766i	0.125831	−	0.387268i
$605$	1.07485	−	3.30805i	0.0436989	−	0.134491i
$606$	−15.4559	−	11.2294i	−0.627852	−	0.456161i
$607$	−2.48114	+	7.63618i	−0.100707	+	0.309943i	−0.988699	−	0.149916i	$-0.952100\pi$
$607$	−2.48114	+	7.63618i	−0.100707	+	0.309943i	0.887992	+	0.459858i	$0.152100\pi$
$608$	−1.24608	−	3.83505i	−0.0505354	−	0.155532i
$609$	−17.3311	+	12.5918i	−0.702292	+	0.510245i
$610$	2.61393	+	8.04485i	0.105835	+	0.325727i
$611$	−2.73219	−	1.98505i	−0.110533	−	0.0803066i
$612$	−4.20814	−	3.05739i	−0.170104	−	0.123588i
$613$	−5.59613	+	4.06583i	−0.226026	+	0.164217i	−0.695035	−	0.718976i	$-0.744611\pi$
$613$	−5.59613	+	4.06583i	−0.226026	+	0.164217i	0.469009	+	0.883193i	$0.344611\pi$
$614$	−5.23915			−0.211435
$615$	−4.52878			−0.182618
$616$	−15.3404	+	11.1455i	−0.618083	+	0.449064i
$617$	1.20568	−	3.71071i	0.0485390	−	0.149388i	−0.923849	−	0.382756i	$-0.874975\pi$
$617$	1.20568	−	3.71071i	0.0485390	−	0.149388i	0.972388	+	0.233369i	$0.0749749\pi$
$618$	4.98486	+	15.3418i	0.200520	+	0.617138i
$619$	4.39207			0.176532			0.0882662	−	0.996097i	$-0.471867\pi$
$619$	4.39207			0.176532			0.0882662	+	0.996097i	$0.471867\pi$
$620$	3.82562	−	4.04533i	0.153640	−	0.162464i
$621$	−3.41697			−0.137118
$622$	−4.59435	−	14.1400i	−0.184217	−	0.566960i
$623$	9.92873	−	30.5575i	0.397786	−	1.22426i
$624$	−1.26932	+	0.922216i	−0.0508135	+	0.0369182i
$625$	1.00000			0.0400000
$626$	23.1538			0.925410
$627$	−12.4131	+	9.01867i	−0.495733	+	0.360171i
$628$	6.51005	+	4.72983i	0.259779	+	0.188741i
$629$	45.1225	+	32.7834i	1.79915	+	1.30716i
$630$	−1.53994	−	4.73944i	−0.0613526	−	0.188824i
$631$	9.73418	−	7.07230i	0.387512	−	0.281544i	−0.376923	−	0.926244i	$-0.623018\pi$
$631$	9.73418	−	7.07230i	0.387512	−	0.281544i	0.764435	+	0.644701i	$0.223018\pi$
$632$	−2.96264	−	9.11808i	−0.117848	−	0.362698i
$633$	6.48139	−	19.9477i	0.257612	−	0.792848i
$634$	19.2994	+	14.0218i	0.766475	+	0.556877i
$635$	−0.389015	+	1.19727i	−0.0154376	+	0.0475120i
$636$	−3.15717	+	9.71677i	−0.125190	+	0.385295i
$637$	22.6367	+	16.4466i	0.896900	+	0.651636i
$638$	−5.05462	+	15.5565i	−0.200114	+	0.615889i
$639$	−2.52200	−	7.76191i	−0.0997687	−	0.307056i
$640$	0.809017	−	0.587785i	0.0319792	−	0.0232343i
$641$	−8.53173	−	26.2580i	−0.336983	−	1.03713i	−0.965737	−	0.259523i	$-0.916435\pi$
$641$	−8.53173	−	26.2580i	−0.336983	−	1.03713i	0.628754	−	0.777604i	$-0.283565\pi$
$642$	−2.91729	−	2.11953i	−0.115136	−	0.0836513i
$643$	5.24286	+	3.80916i	0.206758	+	0.150219i	0.686346	−	0.727275i	$-0.259214\pi$
$643$	5.24286	+	3.80916i	0.206758	+	0.150219i	−0.479588	+	0.877494i	$0.659214\pi$
$644$	−13.7759	+	10.0088i	−0.542847	+	0.394401i
$645$	6.92411			0.272637
$646$	−20.9748			−0.825242
$647$	−15.3169	+	11.1284i	−0.602168	+	0.437501i	−0.846648	−	0.532154i	$-0.821383\pi$
$647$	−15.3169	+	11.1284i	−0.602168	+	0.437501i	0.244480	+	0.969654i	$0.421383\pi$
$648$	−0.309017	+	0.951057i	−0.0121393	+	0.0373610i
$649$	6.06028	+	18.6516i	0.237887	+	0.732140i
$650$	1.56897			0.0615400
$651$	13.2814	+	24.3608i	0.520538	+	0.954777i
$652$	−16.0429			−0.628287
$653$	7.57673	+	23.3188i	0.296500	+	0.912534i	0.982713	+	0.185134i	$0.0592718\pi$
$653$	7.57673	+	23.3188i	0.296500	+	0.912534i	−0.686213	+	0.727401i	$0.740728\pi$
$654$	−0.565181	+	1.73945i	−0.0221003	+	0.0680178i
$655$	14.1673	−	10.2932i	0.553564	−	0.402188i
$656$	4.52878			0.176819
$657$	−14.5045			−0.565876
$658$	−8.67797	+	6.30491i	−0.338302	+	0.245791i
$659$	−22.2006	−	16.1297i	−0.864811	−	0.628322i	0.0643785	−	0.997926i	$-0.479494\pi$
$659$	−22.2006	−	16.1297i	−0.864811	−	0.628322i	−0.929190	+	0.369604i	$0.879494\pi$
$660$	−3.07834	−	2.23654i	−0.119824	−	0.0870573i
$661$	8.77090	+	26.9940i	0.341148	+	1.04995i	0.963614	+	0.267299i	$0.0861312\pi$
$661$	8.77090	+	26.9940i	0.341148	+	1.04995i	−0.622465	+	0.782647i	$0.713869\pi$
$662$	19.8873	−	14.4490i	0.772942	−	0.561575i
$663$	2.52191	+	7.76163i	0.0979427	+	0.301437i
$664$	−4.46803	+	13.7512i	−0.173393	+	0.533650i
$665$	−16.2571	−	11.8115i	−0.630424	−	0.458030i
$666$	3.31348	−	10.1979i	0.128395	−	0.395159i
$667$	−4.53912	+	13.9700i	−0.175755	+	0.540920i
$668$	−5.17765	−	3.76178i	−0.200329	−	0.145548i
$669$	−0.881564	+	2.71317i	−0.0340832	+	0.104897i
$670$	0.597996	+	1.84044i	0.0231026	+	0.0711025i
$671$	−26.0392	+	18.9186i	−1.00523	+	0.730345i
$672$	1.53994	+	4.73944i	0.0594044	+	0.182828i
$673$	−10.1374	−	7.36523i	−0.390767	−	0.283909i	0.375003	−	0.927024i	$-0.377642\pi$
$673$	−10.1374	−	7.36523i	−0.390767	−	0.283909i	−0.765770	+	0.643115i	$0.777642\pi$
$674$	3.91658	+	2.84556i	0.150861	+	0.109607i
$675$	0.809017	−	0.587785i	0.0311391	−	0.0226239i
$676$	−10.5383			−0.405321
$677$	20.5948			0.791522			0.395761	−	0.918353i	$-0.370481\pi$
$677$	20.5948			0.791522			0.395761	+	0.918353i	$0.370481\pi$
$678$	−5.70475	+	4.14474i	−0.219089	+	0.159178i
$679$	5.47397	−	16.8471i	0.210072	−	0.646534i
$680$	−1.60737	−	4.94697i	−0.0616397	−	0.189707i
$681$	−3.42165			−0.131118
$682$	19.1375	+	9.08758i	0.732812	+	0.347981i
$683$	0.601320			0.0230089			0.0115044	−	0.999934i	$-0.496338\pi$
$683$	0.601320			0.0230089			0.0115044	+	0.999934i	$0.496338\pi$
$684$	1.24608	+	3.83505i	0.0476452	+	0.146637i
$685$	−2.11477	+	6.50860i	−0.0808013	+	0.248681i
$686$	43.6774	−	31.7335i	1.66761	−	1.21159i
$687$	−8.79043			−0.335376
$688$	−6.92411			−0.263979
$689$	12.9684	−	9.42211i	0.494058	−	0.358954i
$690$	−2.76439	−	2.00845i	−0.105238	−	0.0764602i
$691$	22.7457	+	16.5257i	0.865287	+	0.628668i	0.929318	−	0.369280i	$-0.120396\pi$
$691$	22.7457	+	16.5257i	0.865287	+	0.628668i	−0.0640308	+	0.997948i	$0.520396\pi$
$692$	0.240656	+	0.740662i	0.00914836	+	0.0281558i
$693$	15.3404	−	11.1455i	0.582735	−	0.423381i
$694$	4.75307	+	14.6284i	0.180424	+	0.555288i
$695$	−4.20521	+	12.9423i	−0.159513	+	0.490930i
$696$	3.47781	+	2.52677i	0.131826	+	0.0957771i
$697$	7.27940	−	22.4037i	0.275727	−	0.848601i
$698$	−6.92903	+	21.3254i	−0.262268	+	0.807177i
$699$	12.3866	+	8.99936i	0.468503	+	0.340387i
$700$	1.53994	−	4.73944i	0.0582042	−	0.179134i
$701$	−1.08461	−	3.33810i	−0.0409653	−	0.126078i	0.928482	−	0.371377i	$-0.121114\pi$
$701$	−1.08461	−	3.33810i	−0.0409653	−	0.126078i	−0.969448	+	0.245298i	$0.921114\pi$
$702$	1.26932	−	0.922216i	0.0479074	−	0.0348068i
$703$	−13.3613	−	41.1220i	−0.503932	−	1.55094i
$704$	3.07834	+	2.23654i	0.116019	+	0.0842929i
$705$	−1.74139	−	1.26520i	−0.0655847	−	0.0476501i
$706$	27.0726	−	19.6694i	1.01889	−	0.740266i
$707$	95.2044			3.58053
$708$	5.15408			0.193702
$709$	−27.9955	+	20.3399i	−1.05139	+	0.763881i	−0.972477	−	0.233000i	$-0.925146\pi$
$709$	−27.9955	+	20.3399i	−1.05139	+	0.763881i	−0.0789152	+	0.996881i	$0.525146\pi$
$710$	2.52200	−	7.76191i	0.0946489	−	0.291299i
$711$	2.96264	+	9.11808i	0.111108	+	0.341955i
$712$	−6.44748			−0.241630
$713$	17.1857	+	8.16076i	0.643610	+	0.305623i
$714$	25.9211			0.970073
$715$	1.84482	+	5.67778i	0.0689925	+	0.212337i
$716$	0.931315	−	2.86629i	0.0348049	−	0.107118i
$717$	23.9532	−	17.4030i	0.894548	−	0.649927i
$718$	24.5748			0.917123
$719$	1.86816			0.0696707			0.0348353	−	0.999393i	$-0.488909\pi$
$719$	1.86816			0.0696707			0.0348353	+	0.999393i	$0.488909\pi$
$720$	−0.809017	+	0.587785i	−0.0301503	+	0.0219055i
$721$	−65.0353	−	47.2509i	−2.42204	−	1.75971i
$722$	−2.21642	−	1.61032i	−0.0824866	−	0.0599300i
$723$	−6.87654	−	21.1638i	−0.255741	−	0.787091i
$724$	−14.7514	+	10.7175i	−0.548232	+	0.398314i
$725$	−1.32840	−	4.08841i	−0.0493357	−	0.151840i
$726$	1.07485	−	3.30805i	0.0398915	−	0.122773i
$727$	40.6115	+	29.5060i	1.50620	+	1.09432i	0.967830	+	0.251606i	$0.0809588\pi$
$727$	40.6115	+	29.5060i	1.50620	+	1.09432i	0.538368	+	0.842710i	$0.319041\pi$
$728$	2.41611	−	7.43603i	0.0895471	−	0.275598i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−11.7344	−	8.52556i	−0.434311	−	0.315545i
$731$	−11.1296	+	34.2533i	−0.411643	+	1.26691i
$732$	2.61393	+	8.04485i	0.0966137	+	0.297346i
$733$	22.8889	−	16.6298i	0.845421	−	0.614234i	−0.0784587	−	0.996917i	$-0.525000\pi$
$733$	22.8889	−	16.6298i	0.845421	−	0.614234i	0.923880	+	0.382683i	$0.125000\pi$
$734$	0.678292	+	2.08757i	0.0250362	+	0.0770536i
$735$	14.4278	+	10.4824i	0.532177	+	0.386649i
$736$	2.76439	+	2.00845i	0.101897	+	0.0740323i
$737$	−5.95706	+	4.32806i	−0.219431	+	0.159426i
$738$	−4.52878			−0.166707
$739$	−26.6202			−0.979240			−0.489620	−	0.871936i	$-0.662864\pi$
$739$	−26.6202			−0.979240			−0.489620	+	0.871936i	$0.662864\pi$
$740$	8.67481	−	6.30262i	0.318893	−	0.231689i
$741$	1.95507	−	6.01707i	0.0718211	−	0.221043i
$742$	−15.7333	−	48.4220i	−0.577587	−	1.77763i
$743$	1.62566			0.0596399			0.0298199	−	0.999555i	$-0.490507\pi$
$743$	1.62566			0.0596399			0.0298199	+	0.999555i	$0.490507\pi$
$744$	3.82562	−	4.04533i	0.140254	−	0.148309i
$745$	7.64716			0.280170
$746$	−1.36114	−	4.18917i	−0.0498351	−	0.153377i
$747$	4.46803	−	13.7512i	0.163477	−	0.503130i
$748$	16.0121	−	11.6335i	0.585461	−	0.425362i
$749$	17.9698			0.656601
$750$	1.00000			0.0365148
$751$	−31.8327	+	23.1278i	−1.16159	+	0.843946i	−0.989978	−	0.141219i	$-0.954898\pi$
$751$	−31.8327	+	23.1278i	−1.16159	+	0.843946i	−0.171613	+	0.985164i	$0.554898\pi$
$752$	1.74139	+	1.26520i	0.0635021	+	0.0461370i
$753$	−1.15943	−	0.842378i	−0.0422521	−	0.0306980i
$754$	−2.08422	−	6.41458i	−0.0759029	−	0.233605i
$755$	−8.09620	+	5.88224i	−0.294651	+	0.214076i
$756$	−1.53994	−	4.73944i	−0.0560070	−	0.172372i
$757$	5.32651	−	16.3933i	0.193595	−	0.595825i	−0.806395	−	0.591378i	$-0.798584\pi$
$757$	5.32651	−	16.3933i	0.193595	−	0.595825i	0.999990	−	0.00444753i	$-0.00141570\pi$
$758$	22.0796	+	16.0418i	0.801968	+	0.582664i
$759$	4.01775	−	12.3653i	0.145835	−	0.448834i
$760$	−1.24608	+	3.83505i	−0.0452002	+	0.139112i
$761$	−43.6264	−	31.6964i	−1.58145	−	1.14899i	−0.915004	−	0.403446i	$-0.867812\pi$
$761$	−43.6264	−	31.6964i	−1.58145	−	1.14899i	−0.666451	−	0.745549i	$-0.732188\pi$
$762$	−0.389015	+	1.19727i	−0.0140925	+	0.0433724i
$763$	−2.81649	−	8.66827i	−0.101964	−	0.313812i
$764$	−11.4438	+	8.31440i	−0.414022	+	0.300804i
$765$	1.60737	+	4.94697i	0.0581145	+	0.178858i
$766$	19.9371	+	14.4852i	0.720358	+	0.523371i
$767$	−6.54219	−	4.75318i	−0.236225	−	0.171627i
$768$	0.809017	−	0.587785i	0.0291929	−	0.0212099i
$769$	−43.1821			−1.55719			−0.778593	−	0.627530i	$-0.784066\pi$
$769$	−43.1821			−1.55719			−0.778593	+	0.627530i	$0.784066\pi$
$770$	18.9618			0.683336
$771$	5.93986	−	4.31556i	0.213919	−	0.155421i
$772$	−4.87047	+	14.9898i	−0.175292	+	0.539493i
$773$	−4.62611	−	14.2377i	−0.166390	−	0.512095i	0.832746	−	0.553655i	$-0.186767\pi$
$773$	−4.62611	−	14.2377i	−0.166390	−	0.512095i	−0.999136	+	0.0415601i	$0.986767\pi$
$774$	6.92411			0.248882
$775$	−5.47277	+	1.02410i	−0.196588	+	0.0367866i
$776$	−3.55467			−0.127605
$777$	16.5122	+	50.8194i	0.592373	+	1.82314i
$778$	6.93565	−	21.3457i	0.248655	−	0.765282i
$779$	−14.7742	+	10.7341i	−0.529340	+	0.384588i
$780$	1.56897			0.0561780
$781$	31.0542			1.11121
$782$	14.3791	−	10.4470i	0.514195	−	0.373585i
$783$	−3.47781	−	2.52677i	−0.124287	−	0.0902996i
$784$	−14.4278	−	10.4824i	−0.515278	−	0.374372i
$785$	−2.48662	−	7.65303i	−0.0887513	−	0.273148i
$786$	14.1673	−	10.2932i	0.505332	−	0.367145i
$787$	−6.64094	−	20.4387i	−0.236724	−	0.728561i	−0.996888	−	0.0788303i	$-0.974881\pi$
$787$	−6.64094	−	20.4387i	−0.236724	−	0.728561i	0.760164	−	0.649731i	$-0.225119\pi$
$788$	−2.04987	+	6.30885i	−0.0730235	+	0.224743i
$789$	1.99013	+	1.44592i	0.0708506	+	0.0514760i
$790$	−2.96264	+	9.11808i	−0.105406	+	0.324407i
$791$	10.8588	−	33.4200i	0.386095	−	1.18828i
$792$	−3.07834	−	2.23654i	−0.109384	−	0.0794721i
$793$	4.10117	−	12.6221i	0.145637	−	0.448224i
$794$	−12.1532	−	37.4038i	−0.431301	−	1.32741i
$795$	8.26558	−	6.00530i	0.293150	−	0.212986i
$796$	7.06054	+	21.7301i	0.250254	+	0.770203i
$797$	14.9776	+	10.8819i	0.530535	+	0.385456i	0.820558	−	0.571564i	$-0.193663\pi$
$797$	14.9776	+	10.8819i	0.530535	+	0.385456i	−0.290023	+	0.957020i	$0.593663\pi$
$798$	−16.2571	−	11.8115i	−0.575496	−	0.418122i
$799$	9.05794	−	6.58098i	0.320447	−	0.232818i
$800$	−1.00000			−0.0353553
$801$	6.44748			0.227811
$802$	14.4128	−	10.4715i	0.508934	−	0.369762i
$803$	17.0547	−	52.4891i	0.601849	−	1.85230i
$804$	0.597996	+	1.84044i	0.0210897	+	0.0649074i
$805$	17.0280			0.600156
$806$	−8.58660	+	1.60677i	−0.302450	+	0.0565962i
$807$	19.4919			0.686149
$808$	−5.90362	−	18.1695i	−0.207689	−	0.639200i
$809$	−6.97549	+	21.4683i	−0.245245	+	0.754787i	0.750351	+	0.661040i	$0.229884\pi$
$809$	−6.97549	+	21.4683i	−0.245245	+	0.754787i	−0.995596	+	0.0937470i	$0.970116\pi$
$810$	0.809017	−	0.587785i	0.0284260	−	0.0206527i
$811$	5.39634			0.189491			0.0947456	−	0.995502i	$-0.469796\pi$
$811$	5.39634			0.189491			0.0947456	+	0.995502i	$0.469796\pi$
$812$	−21.4224			−0.751780
$813$	5.53896	−	4.02429i	0.194260	−	0.141138i
$814$	33.0080	+	23.9817i	1.15693	+	0.840558i
$815$	12.9789	+	9.42976i	0.454633	+	0.330310i
$816$	−1.60737	−	4.94697i	−0.0562691	−	0.173178i
$817$	22.5885	−	16.4115i	0.790270	−	0.574165i
$818$	6.90898	+	21.2637i	0.241567	+	0.743466i
$819$	−2.41611	+	7.43603i	−0.0844258	+	0.259836i
$820$	−3.66386	−	2.66195i	−0.127947	−	0.0929593i
$821$	2.23099	−	6.86630i	0.0778623	−	0.239635i	−0.904548	−	0.426373i	$-0.859791\pi$
$821$	2.23099	−	6.86630i	0.0778623	−	0.239635i	0.982410	+	0.186737i	$0.0597913\pi$
$822$	−2.11477	+	6.50860i	−0.0737611	+	0.227013i
$823$	−8.10046	−	5.88533i	−0.282364	−	0.205150i	0.437584	−	0.899178i	$-0.355834\pi$
$823$	−8.10046	−	5.88533i	−0.282364	−	0.205150i	−0.719948	+	0.694028i	$0.755834\pi$
$824$	−4.98486	+	15.3418i	−0.173656	+	0.534457i
$825$	1.17582	+	3.61880i	0.0409368	+	0.125991i
$826$	−20.7793	+	15.0970i	−0.723003	+	0.525292i
$827$	0.492566	+	1.51596i	0.0171282	+	0.0527152i	0.959255	−	0.282541i	$-0.0911772\pi$
$827$	0.492566	+	1.51596i	0.0171282	+	0.0527152i	−0.942127	+	0.335256i	$0.891177\pi$
$828$	−2.76439	−	2.00845i	−0.0960691	−	0.0697983i
$829$	−34.4916	−	25.0596i	−1.19794	−	0.870357i	−0.203863	−	0.978999i	$-0.565350\pi$
$829$	−34.4916	−	25.0596i	−1.19794	−	0.870357i	−0.994081	+	0.108642i	$0.965350\pi$
$830$	11.6975	−	8.49870i	0.406025	−	0.294994i
$831$	6.03859			0.209476
$832$	−1.56897			−0.0543941
$833$	−75.0469	+	54.5247i	−2.60022	+	1.88917i
$834$	−4.20521	+	12.9423i	−0.145615	+	0.448156i
$835$	1.97769	+	6.08669i	0.0684406	+	0.210639i
$836$	−15.3435			−0.530665
$837$	−3.82562	+	4.04533i	−0.132233	+	0.139827i
$838$	14.1940			0.490322
$839$	−9.81630	−	30.2115i	−0.338896	−	1.04302i	−0.964771	−	0.263092i	$-0.915258\pi$
$839$	−9.81630	−	30.2115i	−0.338896	−	1.04302i	0.625875	−	0.779924i	$-0.284742\pi$
$840$	1.53994	−	4.73944i	0.0531329	−	0.163526i
$841$	8.51108	−	6.18366i	0.293485	−	0.213230i
$842$	17.8370			0.614705
$843$	−31.5593			−1.08696
$844$	16.9685	−	12.3283i	0.584080	−	0.424359i
$845$	8.52570	+	6.19428i	0.293293	+	0.213090i
$846$	−1.74139	−	1.26520i	−0.0598703	−	0.0434983i
$847$	5.35636	+	16.4852i	0.184047	+	0.566437i
$848$	−8.26558	+	6.00530i	−0.283841	+	0.206223i
$849$	−1.16904	−	3.59794i	−0.0401214	−	0.123481i
$850$	−1.60737	+	4.94697i	−0.0551322	+	0.169680i
$851$	29.6416	+	21.5359i	1.01610	+	0.738240i
$852$	2.52200	−	7.76191i	0.0864022	−	0.265919i
$853$	−9.52156	+	29.3044i	−0.326012	+	1.00336i	0.644970	+	0.764208i	$0.276870\pi$
$853$	−9.52156	+	29.3044i	−0.326012	+	1.00336i	−0.970982	+	0.239154i	$0.923130\pi$
$854$	−34.1028	−	24.7772i	−1.16698	−	0.847857i
$855$	1.24608	−	3.83505i	0.0426152	−	0.131156i
$856$	−1.11430	−	3.42948i	−0.0380861	−	0.117217i
$857$	−7.23014	+	5.25300i	−0.246977	+	0.179439i	−0.704386	−	0.709817i	$-0.748778\pi$
$857$	−7.23014	+	5.25300i	−0.246977	+	0.179439i	0.457409	+	0.889256i	$0.348778\pi$
$858$	1.84482	+	5.67778i	0.0629812	+	0.193836i
$859$	−17.5357	−	12.7404i	−0.598309	−	0.434697i	0.246969	−	0.969023i	$-0.420565\pi$
$859$	−17.5357	−	12.7404i	−0.598309	−	0.434697i	−0.845278	+	0.534326i	$0.820565\pi$
$860$	5.60172	+	4.06989i	0.191017	+	0.138782i
$861$	18.2583	−	13.2654i	0.622240	−	0.452084i
$862$	−25.5109			−0.868906
$863$	26.0672			0.887339			0.443670	−	0.896190i	$-0.353676\pi$
$863$	26.0672			0.887339			0.443670	+	0.896190i	$0.353676\pi$
$864$	−0.809017	+	0.587785i	−0.0275233	+	0.0199969i
$865$	0.240656	−	0.740662i	0.00818254	−	0.0251833i
$866$	11.0066	+	33.8750i	0.374021	+	1.15112i
$867$	−10.0561			−0.341523
$868$	−3.57408	+	27.5149i	−0.121312	+	0.933918i
$869$	−36.4801			−1.23750
$870$	−1.32840	−	4.08841i	−0.0450371	−	0.138610i
$871$	0.938235	−	2.88759i	0.0317909	−	0.0978423i
$872$	−1.47966	+	1.07504i	−0.0501077	+	0.0364054i
$873$	3.55467			0.120307
$874$	−13.7786			−0.466070
$875$	−4.03161	+	2.92914i	−0.136293	+	0.0990229i
$876$	−11.7344	−	8.52556i	−0.396470	−	0.288052i
$877$	−1.18834	−	0.863383i	−0.0401275	−	0.0291544i	0.567541	−	0.823345i	$-0.307895\pi$
$877$	−1.18834	−	0.863383i	−0.0401275	−	0.0291544i	−0.607668	+	0.794191i	$0.707895\pi$
$878$	5.60189	+	17.2408i	0.189054	+	0.581850i
$879$	2.73649	−	1.98817i	0.0922994	−	0.0670594i
$880$	−1.17582	−	3.61880i	−0.0396369	−	0.121990i
$881$	−12.1428	+	37.3716i	−0.409100	+	1.25908i	0.508322	+	0.861167i	$0.330266\pi$
$881$	−12.1428	+	37.3716i	−0.409100	+	1.25908i	−0.917423	+	0.397914i	$0.869734\pi$
$882$	14.4278	+	10.4824i	0.485809	+	0.352961i
$883$	16.2008	−	49.8610i	0.545201	−	1.67796i	−0.175310	−	0.984513i	$-0.556093\pi$
$883$	16.2008	−	49.8610i	0.545201	−	1.67796i	0.720511	−	0.693443i	$-0.243907\pi$
$884$	−2.52191	+	7.76163i	−0.0848209	+	0.261052i
$885$	−4.16974	−	3.02949i	−0.140164	−	0.101835i
$886$	3.13485	−	9.64806i	0.105317	−	0.324133i
$887$	−7.69179	−	23.6729i	−0.258265	−	0.794858i	−0.993169	−	0.116686i	$-0.962773\pi$
$887$	−7.69179	−	23.6729i	−0.258265	−	0.794858i	0.734904	−	0.678171i	$-0.237227\pi$
$888$	8.67481	−	6.30262i	0.291108	−	0.211502i
$889$	−1.93860	−	5.96639i	−0.0650185	−	0.200106i
$890$	5.21612	+	3.78973i	0.174845	+	0.127032i
$891$	3.07834	+	2.23654i	0.103128	+	0.0749270i
$892$	−2.30796	+	1.67683i	−0.0772763	+	0.0561445i
$893$	−8.67969			−0.290455
$894$	7.64716			0.255759
$895$	−2.43821	+	1.77147i	−0.0815005	+	0.0592136i
$896$	−1.53994	+	4.73944i	−0.0514457	+	0.158334i
$897$	1.65668	+	5.09872i	0.0553148	+	0.170241i
$898$	−25.4462			−0.849149
$899$	11.4570	+	21.0145i	0.382112	+	0.700873i
$900$	1.00000			0.0333333
$901$	16.4222	+	50.5423i	0.547102	+	1.68381i
$902$	5.32503	−	16.3888i	0.177304	−	0.545686i
$903$	−27.9153	+	20.2817i	−0.928964	+	0.674932i
$904$	−7.05145			−0.234528
$905$	18.2338			0.606111
$906$	−8.09620	+	5.88224i	−0.268978	+	0.195424i
$907$	−2.22906	−	1.61951i	−0.0740148	−	0.0537749i	0.550163	−	0.835058i	$-0.314566\pi$
$907$	−2.22906	−	1.61951i	−0.0740148	−	0.0537749i	−0.624177	+	0.781283i	$0.714566\pi$
$908$	−2.76818	−	2.01120i	−0.0918651	−	0.0667439i
$909$	5.90362	+	18.1695i	0.195811	+	0.602643i
$910$	−6.32547	+	4.59572i	−0.209687	+	0.152347i
$911$	−9.38427	−	28.8818i	−0.310915	−	0.956897i	−0.977403	−	0.211382i	$-0.932204\pi$
$911$	−9.38427	−	28.8818i	−0.310915	−	0.956897i	0.666489	−	0.745515i	$-0.267796\pi$
$912$	−1.24608	+	3.83505i	−0.0412620	+	0.126991i
$913$	44.5093	+	32.3379i	1.47304	+	1.07023i
$914$	−1.99152	+	6.12928i	−0.0658737	+	0.202738i
$915$	2.61393	−	8.04485i	0.0864139	−	0.265955i
$916$	−7.11161	−	5.16689i	−0.234974	−	0.170719i
$917$	−26.9671	+	82.9961i	−0.890532	+	2.74077i
$918$	1.60737	+	4.94697i	0.0530510	+	0.163274i
$919$	−16.6589	+	12.1034i	−0.549526	+	0.399254i	−0.827611	−	0.561302i	$-0.810300\pi$
$919$	−16.6589	+	12.1034i	−0.549526	+	0.399254i	0.278085	+	0.960557i	$0.410300\pi$
$920$	−1.05590	−	3.24973i	−0.0348121	−	0.107141i
$921$	4.23856	+	3.07949i	0.139665	+	0.101473i
$922$	24.9063	+	18.0955i	0.820244	+	0.595942i
$923$	−10.3594	+	7.52653i	−0.340983	+	0.247739i
$924$	18.9618			0.623798
$925$	−10.7227			−0.352559
$926$	11.1297	−	8.08622i	0.365746	−	0.265730i
$927$	4.98486	−	15.3418i	0.163724	−	0.503891i
$928$	1.32840	+	4.08841i	0.0436070	+	0.134209i
$929$	35.4821			1.16413			0.582065	−	0.813142i	$-0.302245\pi$
$929$	35.4821			1.16413			0.582065	+	0.813142i	$0.302245\pi$
$930$	−5.47277	+	1.02410i	−0.179459	+	0.0335815i
$931$	71.9130			2.35685
$932$	4.73125	+	14.5613i	0.154977	+	0.476971i
$933$	−4.59435	+	14.1400i	−0.150412	+	0.462921i
$934$	10.7691	−	7.82424i	0.352377	−	0.256017i
$935$	−19.7921			−0.647270
$936$	1.56897			0.0512833
$937$	−22.6986	+	16.4915i	−0.741530	+	0.538753i	−0.893190	−	0.449680i	$-0.851538\pi$
$937$	−22.6986	+	16.4915i	−0.741530	+	0.538753i	0.151660	+	0.988433i	$0.451538\pi$
$938$	−7.80179	−	5.66833i	−0.254738	−	0.185078i
$939$	−18.7318	−	13.6094i	−0.611288	−	0.444127i
$940$	−0.665153	−	2.04713i	−0.0216949	−	0.0667700i
$941$	40.6679	−	29.5470i	1.32574	−	0.963204i	0.325896	−	0.945406i	$-0.394334\pi$
$941$	40.6679	−	29.5470i	1.32574	−	0.963204i	0.999842	−	0.0177987i	$-0.00566580\pi$
$942$	−2.48662	−	7.65303i	−0.0810184	−	0.249349i
$943$	4.78195	−	14.7173i	0.155722	−	0.479262i
$944$	4.16974	+	3.02949i	0.135714	+	0.0986016i
$945$	−1.53994	+	4.73944i	−0.0500942	+	0.154174i
$946$	−8.14151	+	25.0570i	−0.264703	+	0.814673i
$947$	−7.48246	−	5.43633i	−0.243147	−	0.176657i	0.459537	−	0.888159i	$-0.348015\pi$
$947$	−7.48246	−	5.43633i	−0.243147	−	0.176657i	−0.702684	+	0.711502i	$0.748015\pi$
$948$	−2.96264	+	9.11808i	−0.0962222	+	0.296142i
$949$	7.03235	+	21.6433i	0.228280	+	0.702573i
$950$	3.26229	−	2.37019i	0.105843	−	0.0768992i
$951$	−7.37170	−	22.6878i	−0.239044	−	0.735701i
$952$	20.9706	+	15.2360i	0.679662	+	0.493803i
$953$	2.11820	+	1.53896i	0.0686152	+	0.0498519i	0.621564	−	0.783363i	$-0.286498\pi$
$953$	2.11820	+	1.53896i	0.0686152	+	0.0498519i	−0.552949	+	0.833215i	$0.686498\pi$
$954$	8.26558	−	6.00530i	0.267608	−	0.194429i
$955$	14.1453			0.457731
$956$	29.6078			0.957583
$957$	13.2332	−	9.61447i	0.427768	−	0.310792i
$958$	7.27830	−	22.4003i	0.235151	−	0.723721i
$959$	−10.5386	−	32.4346i	−0.340310	−	1.04737i
$960$	−1.00000			−0.0322749
$961$	28.9025	−	11.2093i	0.932337	−	0.361590i
$962$	−16.8235			−0.542411
$963$	1.11430	+	3.42948i	0.0359080	+	0.110513i
$964$	6.87654	−	21.1638i	0.221478	−	0.681640i
$965$	12.7511	−	9.26418i	0.410471	−	0.298225i
$966$	17.0280			0.547865
$967$	−41.1785			−1.32421			−0.662106	−	0.749411i	$-0.730337\pi$
$967$	−41.1785			−1.32421			−0.662106	+	0.749411i	$0.730337\pi$
$968$	2.81400	−	2.04449i	0.0904453	−	0.0657124i
$969$	16.9690	+	12.3287i	0.545122	+	0.396054i
$970$	2.87578	+	2.08938i	0.0923359	+	0.0670859i
$971$	−10.7806	−	33.1792i	−0.345965	−	1.06477i	−0.961065	−	0.276322i	$-0.910884\pi$
$971$	−10.7806	−	33.1792i	−0.345965	−	1.06477i	0.615100	−	0.788449i	$-0.289116\pi$
$972$	0.809017	−	0.587785i	0.0259492	−	0.0188532i
$973$	−20.9560	−	64.4960i	−0.671819	−	2.06765i
$974$	−9.83196	+	30.2597i	−0.315036	+	0.969582i
$975$	−1.26932	−	0.922216i	−0.0406508	−	0.0295345i
$976$	−2.61393	+	8.04485i	−0.0836699	+	0.257510i
$977$	7.98866	−	24.5866i	0.255580	−	0.786594i	−0.738135	−	0.674653i	$-0.764293\pi$
$977$	7.98866	−	24.5866i	0.255580	−	0.786594i	0.993715	−	0.111941i	$-0.0357067\pi$
$978$	12.9789	+	9.42976i	0.415021	+	0.301530i
$979$	−7.58108	+	23.3322i	−0.242292	+	0.745699i
$980$	5.51093	+	16.9609i	0.176040	+	0.541796i
$981$	1.47966	−	1.07504i	0.0472420	−	0.0343233i
$982$	6.24086	+	19.2074i	0.199154	+	0.612933i
$983$	−9.58528	−	6.96411i	−0.305723	−	0.222121i	0.424336	−	0.905505i	$-0.360508\pi$
$983$	−9.58528	−	6.96411i	−0.305723	−	0.222121i	−0.730059	+	0.683384i	$0.760508\pi$
$984$	−3.66386	−	2.66195i	−0.116800	−	0.0848598i
$985$	5.36662	−	3.89908i	0.170995	−	0.124235i
$986$	22.3604			0.712102
$987$	10.7266			0.341430
$988$	5.11843	−	3.71875i	0.162839	−	0.118309i
$989$	−7.31119	+	22.5015i	−0.232482	+	0.715507i
$990$	1.17582	+	3.61880i	0.0373700	+	0.115013i
$991$	13.4917			0.428577			0.214289	−	0.976770i	$-0.431257\pi$
$991$	13.4917			0.428577			0.214289	+	0.976770i	$0.431257\pi$
$992$	5.47277	−	1.02410i	0.173761	−	0.0325151i
$993$	−24.5820			−0.780088
$994$	12.5680	+	38.6803i	0.398632	+	1.22686i
$995$	7.06054	−	21.7301i	0.223834	−	0.688890i
$996$	11.6975	−	8.49870i	0.370648	−	0.269292i
$997$	46.3656			1.46841			0.734207	−	0.678926i	$-0.237554\pi$
$997$	46.3656			1.46841			0.734207	+	0.678926i	$0.237554\pi$
$998$	−23.5044			−0.744018
$999$	−8.67481	+	6.30262i	−0.274459	+	0.199406i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.f.841.1	yes	12
31.8	even	5	inner	930.2.n.f.721.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.f.721.1	✓	12	31.8	even	5	inner
930.2.n.f.841.1	yes	12	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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-4.03161 + 2.92914i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.809017 + 0.587785i) q^{4} +1.00000 q^{5} +1.00000 q^{6} +(-4.03161 + 2.92914i) q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(-0.309017 - 0.951057i) q^{10} +(3.07834 - 2.23654i) q^{11} +(-0.309017 - 0.951057i) q^{12} +(-0.484838 + 1.49218i) q^{13} +(4.03161 + 2.92914i) q^{14} +(-0.309017 + 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-4.20814 - 3.05739i) q^{17} +(-0.309017 + 0.951057i) q^{18} +(1.24608 + 3.83505i) q^{19} +(-0.809017 + 0.587785i) q^{20} +(-1.53994 - 4.73944i) q^{21} +(-3.07834 - 2.23654i) q^{22} +(-2.76439 - 2.00845i) q^{23} +(-0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +1.56897 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.53994 - 4.73944i) q^{28} +(-1.32840 - 4.08841i) q^{29} +1.00000 q^{30} +(-5.47277 + 1.02410i) q^{31} -1.00000 q^{32} +(1.17582 + 3.61880i) q^{33} +(-1.60737 + 4.94697i) q^{34} +(-4.03161 + 2.92914i) q^{35} +1.00000 q^{36} -10.7227 q^{37} +(3.26229 - 2.37019i) q^{38} +(-1.26932 - 0.922216i) q^{39} +(0.809017 + 0.587785i) q^{40} +(1.39947 + 4.30712i) q^{41} +(-4.03161 + 2.92914i) q^{42} +(-2.13967 - 6.58522i) q^{43} +(-1.17582 + 3.61880i) q^{44} +(-0.809017 - 0.587785i) q^{45} +(-1.05590 + 3.24973i) q^{46} +(-0.665153 + 2.04713i) q^{47} +(0.809017 + 0.587785i) q^{48} +(5.51093 - 16.9609i) q^{49} +(-0.309017 - 0.951057i) q^{50} +(4.20814 - 3.05739i) q^{51} +(-0.484838 - 1.49218i) q^{52} +(-8.26558 - 6.00530i) q^{53} +(-0.809017 - 0.587785i) q^{54} +(3.07834 - 2.23654i) q^{55} -4.98335 q^{56} -4.03241 q^{57} +(-3.47781 + 2.52677i) q^{58} +(-1.59270 + 4.90182i) q^{59} +(-0.309017 - 0.951057i) q^{60} -8.45886 q^{61} +(2.66515 + 4.88845i) q^{62} +4.98335 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.484838 + 1.49218i) q^{65} +(3.07834 - 2.23654i) q^{66} -1.93515 q^{67} +5.20155 q^{68} +(2.76439 - 2.00845i) q^{69} +(4.03161 + 2.92914i) q^{70} +(6.60268 + 4.79713i) q^{71} +(-0.309017 - 0.951057i) q^{72} +(11.7344 - 8.52556i) q^{73} +(3.31348 + 10.1979i) q^{74} +(-0.309017 + 0.951057i) q^{75} +(-3.26229 - 2.37019i) q^{76} +(-5.85952 + 18.0337i) q^{77} +(-0.484838 + 1.49218i) q^{78} +(-7.75630 - 5.63528i) q^{79} +(0.309017 - 0.951057i) q^{80} +(0.309017 + 0.951057i) q^{81} +(3.66386 - 2.66195i) q^{82} +(4.46803 + 13.7512i) q^{83} +(4.03161 + 2.92914i) q^{84} +(-4.20814 - 3.05739i) q^{85} +(-5.60172 + 4.06989i) q^{86} +4.29881 q^{87} +3.80504 q^{88} +(-5.21612 + 3.78973i) q^{89} +(-0.309017 + 0.951057i) q^{90} +(-2.41611 - 7.43603i) q^{91} +3.41697 q^{92} +(0.717206 - 5.52138i) q^{93} +2.15248 q^{94} +(1.24608 + 3.83505i) q^{95} +(0.309017 - 0.951057i) q^{96} +(-2.87578 + 2.08938i) q^{97} -17.8337 q^{98} -3.80504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9	\( 12 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 12 q^{5} + 12 q^{6} - q^{7} + 3 q^{8} - 3 q^{9} + 3 q^{10} + 14 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} - 3 q^{16} - 7 q^{17} + 3 q^{18} + 12 q^{19} - 3 q^{20} + q^{21} - 14 q^{22} - 6 q^{23} - 3 q^{24} + 12 q^{25} + 6 q^{26} + 3 q^{27} - q^{28} - 23 q^{29} + 12 q^{30} + 34 q^{31} - 12 q^{32} + 11 q^{33} - 3 q^{34} - q^{35} + 12 q^{36} + 22 q^{37} + 8 q^{38} + q^{39} + 3 q^{40} + 15 q^{41} - q^{42} - 17 q^{43} - 11 q^{44} - 3 q^{45} + 6 q^{46} - 2 q^{47} + 3 q^{48} - 8 q^{49} + 3 q^{50} + 7 q^{51} + 4 q^{52} - 21 q^{53} - 3 q^{54} + 14 q^{55} - 4 q^{56} + 8 q^{57} - 17 q^{58} - 15 q^{59} + 3 q^{60} + 16 q^{61} + 26 q^{62} + 4 q^{63} - 3 q^{64} + 4 q^{65} + 14 q^{66} + 24 q^{67} + 8 q^{68} + 6 q^{69} + q^{70} + 23 q^{71} + 3 q^{72} + 56 q^{73} + 8 q^{74} + 3 q^{75} - 8 q^{76} - 8 q^{77} + 4 q^{78} - 9 q^{79} - 3 q^{80} - 3 q^{81} + 15 q^{82} - 24 q^{83} + q^{84} - 7 q^{85} - 18 q^{86} - 12 q^{87} + 6 q^{88} - 27 q^{89} + 3 q^{90} - 3 q^{91} + 24 q^{92} + 11 q^{93} - 28 q^{94} + 12 q^{95} - 3 q^{96} + 38 q^{97} - 52 q^{98} - 6 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 12 * q^5 + 12 * q^6 - q^7 + 3 * q^8 - 3 * q^9 + 3 * q^10 + 14 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 3 * q^15 - 3 * q^16 - 7 * q^17 + 3 * q^18 + 12 * q^19 - 3 * q^20 + q^21 - 14 * q^22 - 6 * q^23 - 3 * q^24 + 12 * q^25 + 6 * q^26 + 3 * q^27 - q^28 - 23 * q^29 + 12 * q^30 + 34 * q^31 - 12 * q^32 + 11 * q^33 - 3 * q^34 - q^35 + 12 * q^36 + 22 * q^37 + 8 * q^38 + q^39 + 3 * q^40 + 15 * q^41 - q^42 - 17 * q^43 - 11 * q^44 - 3 * q^45 + 6 * q^46 - 2 * q^47 + 3 * q^48 - 8 * q^49 + 3 * q^50 + 7 * q^51 + 4 * q^52 - 21 * q^53 - 3 * q^54 + 14 * q^55 - 4 * q^56 + 8 * q^57 - 17 * q^58 - 15 * q^59 + 3 * q^60 + 16 * q^61 + 26 * q^62 + 4 * q^63 - 3 * q^64 + 4 * q^65 + 14 * q^66 + 24 * q^67 + 8 * q^68 + 6 * q^69 + q^70 + 23 * q^71 + 3 * q^72 + 56 * q^73 + 8 * q^74 + 3 * q^75 - 8 * q^76 - 8 * q^77 + 4 * q^78 - 9 * q^79 - 3 * q^80 - 3 * q^81 + 15 * q^82 - 24 * q^83 + q^84 - 7 * q^85 - 18 * q^86 - 12 * q^87 + 6 * q^88 - 27 * q^89 + 3 * q^90 - 3 * q^91 + 24 * q^92 + 11 * q^93 - 28 * q^94 + 12 * q^95 - 3 * q^96 + 38 * q^97 - 52 * q^98 - 6 * q^99

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