LMFDB - Embedded newform 930.2.v.a.401.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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([5, 0, 3]))

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

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

chi := DirichletCharacter("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.8
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(1.35636 + 1.07717i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.679429 + 2.92205i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(1.35636 + 1.07717i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.679429 + 2.92205i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.477187 + 1.46863i) q^{11} +(0.605307 - 1.62284i) q^{12} +(-0.190055 - 0.261588i) q^{13} +(-1.79744 - 0.584024i) q^{14} +(1.07717 - 1.35636i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.19339 - 3.67287i) q^{17} +(-2.76335 - 1.16787i) q^{18} +(6.86216 + 4.98565i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-1.14399 + 3.06707i) q^{21} +(-1.46863 - 0.477187i) q^{22} +(-0.144742 + 0.445469i) q^{23} +(0.957113 + 1.44358i) q^{24} -1.00000 q^{25} +0.323341 q^{26} +(-2.22598 + 4.69521i) q^{27} +(1.52899 - 1.11088i) q^{28} +(-3.90941 - 2.84035i) q^{29} +(0.464177 + 1.66869i) q^{30} +(-5.26827 + 1.80147i) q^{31} -1.00000i q^{32} +(-0.934721 + 2.50600i) q^{33} +(2.26996 + 3.12433i) q^{34} +(1.79744 - 0.584024i) q^{35} +(2.56908 - 1.54914i) q^{36} +5.75161i q^{37} +(-8.06695 + 2.62111i) q^{38} +(0.0239907 - 0.559528i) q^{39} +(0.309017 - 0.951057i) q^{40} +(5.28220 - 7.27033i) q^{41} +(-1.80889 - 2.72829i) q^{42} +(-3.29598 + 4.53652i) q^{43} +(1.24929 - 0.907664i) q^{44} +(2.92205 - 0.679429i) q^{45} +(-0.275315 - 0.378938i) q^{46} +(6.83937 + 9.41358i) q^{47} +(-1.73046 - 0.0741964i) q^{48} +(2.77341 - 2.01500i) q^{49} +(0.587785 - 0.809017i) q^{50} +(5.57496 - 3.69626i) q^{51} +(-0.190055 + 0.261588i) q^{52} +(-3.59432 + 11.0622i) q^{53} +(-2.49011 - 4.56063i) q^{54} +(1.46863 - 0.477187i) q^{55} +1.88994i q^{56} +(3.93719 + 14.1540i) q^{57} +(4.59578 - 1.49326i) q^{58} +(0.437766 + 0.602534i) q^{59} +(-1.62284 - 0.605307i) q^{60} -0.790467i q^{61} +(1.63919 - 5.32100i) q^{62} +(-4.85541 + 2.92778i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.261588 + 0.190055i) q^{65} +(-1.47798 - 2.22920i) q^{66} +6.62011 q^{67} -3.86189 q^{68} +(-0.676165 + 0.448306i) q^{69} +(-0.584024 + 1.79744i) q^{70} +(-9.48945 - 3.08331i) q^{71} +(-0.256788 + 2.98899i) q^{72} +(4.30980 - 1.40034i) q^{73} +(-4.65315 - 3.38071i) q^{74} +(-1.35636 - 1.07717i) q^{75} +(2.62111 - 8.06695i) q^{76} +(-2.36109 + 1.71543i) q^{77} +(0.438567 + 0.348291i) q^{78} +(8.90634 + 2.89384i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-8.07675 + 3.97065i) q^{81} +(2.77702 + 8.54678i) q^{82} +(-5.70547 - 4.14527i) q^{83} +(3.27047 + 0.140227i) q^{84} +(-3.67287 - 1.19339i) q^{85} +(-1.73280 - 5.33300i) q^{86} +(-2.24304 - 8.06362i) q^{87} +1.54421i q^{88} +(0.263336 + 0.810465i) q^{89} +(-1.16787 + 2.76335i) q^{90} +(0.359192 - 0.494386i) q^{91} +0.468393 q^{92} +(-9.08616 - 3.23136i) q^{93} -11.6358 q^{94} +(4.98565 - 6.86216i) q^{95} +(1.07717 - 1.35636i) q^{96} +(-5.86265 - 18.0434i) q^{97} +3.42812i q^{98} +(-3.96720 + 2.39220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	1.35636	+	1.07717i	0.783095	+	0.621902i
$3$	1.35636	+	1.07717i	0.783095	+	0.621902i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.66869	+	0.464177i	−0.681241	+	0.189499i
$7$	0.584024	+	1.79744i	0.220740	+	0.679369i	0.998696	+	0.0510498i	$0.0162567\pi$
$7$	0.584024	+	1.79744i	0.220740	+	0.679369i	−0.777956	+	0.628319i	$0.783743\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	0.679429	+	2.92205i	0.226476	+	0.974017i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	0.477187	+	1.46863i	0.143877	+	0.442809i	0.996865	−	0.0791223i	$-0.0252117\pi$
$11$	0.477187	+	1.46863i	0.143877	+	0.442809i	−0.852988	+	0.521931i	$0.825212\pi$
$12$	0.605307	−	1.62284i	0.174737	−	0.468473i
$13$	−0.190055	−	0.261588i	−0.0527117	−	0.0725515i	0.781847	−	0.623470i	$-0.214278\pi$
$13$	−0.190055	−	0.261588i	−0.0527117	−	0.0725515i	−0.834559	+	0.550918i	$0.814278\pi$
$14$	−1.79744	−	0.584024i	−0.480386	−	0.156087i
$15$	1.07717	−	1.35636i	0.278123	−	0.350211i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.19339	−	3.67287i	0.289439	−	0.890802i	−0.695594	−	0.718435i	$-0.744859\pi$
$17$	1.19339	−	3.67287i	0.289439	−	0.890802i	0.985033	−	0.172367i	$-0.0551414\pi$
$18$	−2.76335	−	1.16787i	−0.651327	−	0.275269i
$19$	6.86216	+	4.98565i	1.57429	+	1.14379i	0.922900	+	0.385041i	$0.125813\pi$
$19$	6.86216	+	4.98565i	1.57429	+	1.14379i	0.651387	+	0.758746i	$0.274187\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	−1.14399	+	3.06707i	−0.249640	+	0.669289i
$22$	−1.46863	−	0.477187i	−0.313113	−	0.101737i
$23$	−0.144742	+	0.445469i	−0.0301807	+	0.0928866i	−0.965012	−	0.262205i	$-0.915550\pi$
$23$	−0.144742	+	0.445469i	−0.0301807	+	0.0928866i	0.934831	+	0.355092i	$0.115550\pi$
$24$	0.957113	+	1.44358i	0.195370	+	0.294670i
$25$	−1.00000			−0.200000
$26$	0.323341			0.0634123
$27$	−2.22598	+	4.69521i	−0.428390	+	0.903594i
$28$	1.52899	−	1.11088i	0.288953	−	0.209936i
$29$	−3.90941	−	2.84035i	−0.725959	−	0.527440i	0.162324	−	0.986738i	$-0.448101\pi$
$29$	−3.90941	−	2.84035i	−0.725959	−	0.527440i	−0.888282	+	0.459298i	$0.848101\pi$
$30$	0.464177	+	1.66869i	0.0847467	+	0.304660i
$31$	−5.26827	+	1.80147i	−0.946210	+	0.323554i
$31$	−5.26827	+	1.80147i	−0.946210	+	0.323554i
$32$		−	1.00000i		−	0.176777i
$33$	−0.934721	+	2.50600i	−0.162714	+	0.436239i
$34$	2.26996	+	3.12433i	0.389295	+	0.535818i
$35$	1.79744	−	0.584024i	0.303823	−	0.0987181i
$36$	2.56908	−	1.54914i	0.428180	−	0.258190i
$37$			5.75161i			0.945559i	0.881181	+	0.472779i	$0.156749\pi$
$37$			5.75161i			0.945559i	−0.881181	+	0.472779i	$0.843251\pi$
$38$	−8.06695	+	2.62111i	−1.30863	+	0.425200i
$39$	0.0239907	−	0.559528i	0.00384159	−	0.0895962i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	5.28220	−	7.27033i	0.824942	−	1.13543i	−0.163902	−	0.986477i	$-0.552408\pi$
$41$	5.28220	−	7.27033i	0.824942	−	1.13543i	0.988844	−	0.148958i	$-0.0475919\pi$
$42$	−1.80889	−	2.72829i	−0.279117	−	0.420984i
$43$	−3.29598	+	4.53652i	−0.502632	+	0.691813i	−0.982655	−	0.185443i	$-0.940628\pi$
$43$	−3.29598	+	4.53652i	−0.502632	+	0.691813i	0.480024	+	0.877256i	$0.340628\pi$
$44$	1.24929	−	0.907664i	0.188338	−	0.136836i
$45$	2.92205	−	0.679429i	0.435594	−	0.101283i
$46$	−0.275315	−	0.378938i	−0.0405929	−	0.0558714i
$47$	6.83937	+	9.41358i	0.997624	+	1.37311i	0.926772	+	0.375626i	$0.122572\pi$
$47$	6.83937	+	9.41358i	0.997624	+	1.37311i	0.0708529	+	0.997487i	$0.477428\pi$
$48$	−1.73046	−	0.0741964i	−0.249771	−	0.0107093i
$49$	2.77341	−	2.01500i	0.396201	−	0.287857i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	5.57496	−	3.69626i	0.780650	−	0.517580i
$52$	−0.190055	+	0.261588i	−0.0263559	+	0.0362757i
$53$	−3.59432	+	11.0622i	−0.493718	+	1.51951i	0.325228	+	0.945636i	$0.394559\pi$
$53$	−3.59432	+	11.0622i	−0.493718	+	1.51951i	−0.818945	+	0.573871i	$0.805441\pi$
$54$	−2.49011	−	4.56063i	−0.338861	−	0.620623i
$55$	1.46863	−	0.477187i	0.198030	−	0.0643439i
$56$			1.88994i			0.252554i
$57$	3.93719	+	14.1540i	0.521494	+	1.87475i
$58$	4.59578	−	1.49326i	0.603456	−	0.196075i
$59$	0.437766	+	0.602534i	0.0569923	+	0.0784432i	0.836562	−	0.547872i	$-0.184562\pi$
$59$	0.437766	+	0.602534i	0.0569923	+	0.0784432i	−0.779570	+	0.626316i	$0.784562\pi$
$60$	−1.62284	−	0.605307i	−0.209508	−	0.0781448i
$61$		−	0.790467i		−	0.101209i	−0.998719	−	0.0506045i	$-0.983885\pi$
$61$		−	0.790467i		−	0.101209i	0.998719	−	0.0506045i	$-0.0161148\pi$
$62$	1.63919	−	5.32100i	0.208177	−	0.675768i
$63$	−4.85541	+	2.92778i	−0.611724	+	0.368866i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−0.261588	+	0.190055i	−0.0324460	+	0.0235734i
$66$	−1.47798	−	2.22920i	−0.181927	−	0.274395i
$67$	6.62011			0.808775			0.404387	−	0.914588i	$-0.367485\pi$
$67$	6.62011			0.808775			0.404387	+	0.914588i	$0.367485\pi$
$68$	−3.86189			−0.468322
$69$	−0.676165	+	0.448306i	−0.0814007	+	0.0539696i
$70$	−0.584024	+	1.79744i	−0.0698042	+	0.214835i
$71$	−9.48945	−	3.08331i	−1.12619	−	0.365922i	−0.314064	−	0.949402i	$-0.601690\pi$
$71$	−9.48945	−	3.08331i	−1.12619	−	0.365922i	−0.812127	+	0.583480i	$0.801690\pi$
$72$	−0.256788	+	2.98899i	−0.0302628	+	0.352256i
$73$	4.30980	−	1.40034i	0.504424	−	0.163897i	−0.0457407	−	0.998953i	$-0.514565\pi$
$73$	4.30980	−	1.40034i	0.504424	−	0.163897i	0.550165	+	0.835056i	$0.314565\pi$
$74$	−4.65315	−	3.38071i	−0.540918	−	0.393000i
$75$	−1.35636	−	1.07717i	−0.156619	−	0.124380i
$76$	2.62111	−	8.06695i	0.300662	−	0.925342i
$77$	−2.36109	+	1.71543i	−0.269071	+	0.195492i
$78$	0.438567	+	0.348291i	0.0496579	+	0.0394362i
$79$	8.90634	+	2.89384i	1.00204	+	0.325583i	0.763681	−	0.645594i	$-0.223390\pi$
$79$	8.90634	+	2.89384i	1.00204	+	0.325583i	0.238360	+	0.971177i	$0.423390\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	−8.07675	+	3.97065i	−0.897417	+	0.441183i
$82$	2.77702	+	8.54678i	0.306670	+	0.943834i
$83$	−5.70547	−	4.14527i	−0.626257	−	0.455002i	0.228844	−	0.973463i	$-0.426505\pi$
$83$	−5.70547	−	4.14527i	−0.626257	−	0.455002i	−0.855102	+	0.518461i	$0.826505\pi$
$84$	3.27047	+	0.140227i	0.356837	+	0.0153000i
$85$	−3.67287	−	1.19339i	−0.398379	−	0.129441i
$86$	−1.73280	−	5.33300i	−0.186852	−	0.575072i
$87$	−2.24304	−	8.06362i	−0.240479	−	0.864510i
$88$			1.54421i			0.164613i
$89$	0.263336	+	0.810465i	0.0279136	+	0.0859091i	0.964043	−	0.265747i	$-0.0856186\pi$
$89$	0.263336	+	0.810465i	0.0279136	+	0.0859091i	−0.936129	+	0.351656i	$0.885619\pi$
$90$	−1.16787	+	2.76335i	−0.123104	+	0.291282i
$91$	0.359192	−	0.494386i	0.0376536	−	0.0518257i
$92$	0.468393			0.0488334
$93$	−9.08616	−	3.23136i	−0.942191	−	0.335076i
$94$	−11.6358			−1.20014
$95$	4.98565	−	6.86216i	0.511517	−	0.704042i
$96$	1.07717	−	1.35636i	0.109938	−	0.138433i
$97$	−5.86265	−	18.0434i	−0.595262	−	1.83203i	−0.553419	−	0.832903i	$-0.686677\pi$
$97$	−5.86265	−	18.0434i	−0.595262	−	1.83203i	−0.0418429	−	0.999124i	$-0.513323\pi$
$98$			3.42812i			0.346293i
$99$	−3.96720	+	2.39220i	−0.398719	+	0.240425i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−9.86879	−	3.20656i	−0.981981	−	0.319065i	−0.226338	−	0.974049i	$-0.572675\pi$
$101$	−9.86879	−	3.20656i	−0.981981	−	0.319065i	−0.755643	+	0.654984i	$0.772675\pi$
$102$	−0.286538	+	6.68284i	−0.0283715	+	0.661700i
$103$	−9.83640	−	7.14656i	−0.969209	−	0.704172i	−0.0139379	−	0.999903i	$-0.504437\pi$
$103$	−9.83640	−	7.14656i	−0.969209	−	0.704172i	−0.955271	+	0.295731i	$0.904437\pi$
$104$	−0.0999178	−	0.307515i	−0.00979774	−	0.0301544i
$105$	3.06707	+	1.14399i	0.299315	+	0.111642i
$106$	−6.83680	−	9.41005i	−0.664049	−	0.913985i
$107$	5.82225	+	1.89176i	0.562858	+	0.182884i	0.576607	−	0.817022i	$-0.304376\pi$
$107$	5.82225	+	1.89176i	0.562858	+	0.182884i	−0.0137485	+	0.999905i	$0.504376\pi$
$108$	5.15328	+	0.666134i	0.495874	+	0.0640988i
$109$	6.83939	−	4.96910i	0.655094	−	0.475954i	−0.209908	−	0.977721i	$-0.567317\pi$
$109$	6.83939	−	4.96910i	0.655094	−	0.475954i	0.865003	+	0.501767i	$0.167317\pi$
$110$	−0.477187	+	1.46863i	−0.0454980	+	0.140028i
$111$	−6.19543	+	7.80126i	−0.588045	+	0.740462i
$112$	−1.52899	−	1.11088i	−0.144476	−	0.104968i
$113$	−9.49452	+	3.08496i	−0.893169	+	0.290208i	−0.719415	−	0.694581i	$-0.755590\pi$
$113$	−9.49452	+	3.08496i	−0.893169	+	0.290208i	−0.173754	+	0.984789i	$0.555590\pi$
$114$	−13.7651	−	5.13427i	−1.28922	−	0.480868i
$115$	0.445469	+	0.144742i	0.0415402	+	0.0134972i
$116$	−1.49326	+	4.59578i	−0.138646	+	0.426708i
$117$	0.635245	−	0.733080i	0.0587284	−	0.0677733i
$118$	−0.744773			−0.0685619
$119$	7.29874			0.669074
$120$	1.44358	−	0.957113i	0.131781	−	0.0873721i
$121$	6.97002	−	5.06401i	0.633638	−	0.460365i
$122$	0.639501	+	0.464625i	0.0578977	+	0.0420652i
$123$	14.9959	−	4.17138i	1.35214	−	0.376121i
$124$	3.34129	+	4.45374i	0.300057	+	0.399958i
$125$			1.00000i			0.0894427i
$126$	0.485314	−	5.64901i	0.0432352	−	0.503254i
$127$	8.54336	+	11.7589i	0.758101	+	1.04344i	0.997370	+	0.0724829i	$0.0230923\pi$
$127$	8.54336	+	11.7589i	0.758101	+	1.04344i	−0.239269	+	0.970953i	$0.576908\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−9.35712	+	2.60285i	−0.823848	+	0.229168i
$130$		−	0.323341i		−	0.0283589i
$131$	−1.77960	+	0.578228i	−0.155485	+	0.0505201i	−0.385725	−	0.922614i	$-0.626049\pi$
$131$	−1.77960	+	0.578228i	−0.155485	+	0.0505201i	0.230240	+	0.973134i	$0.426049\pi$
$132$	2.67220	+	0.114575i	0.232585	+	0.00997247i
$133$	−4.95374	+	15.2461i	−0.429544	+	1.32200i
$134$	−3.89120	+	5.35578i	−0.336149	+	0.462669i
$135$	4.69521	+	2.22598i	0.404099	+	0.191582i
$136$	2.26996	−	3.12433i	0.194647	−	0.267909i
$137$	5.71804	−	4.15440i	0.488525	−	0.354934i	−0.316092	−	0.948729i	$-0.602371\pi$
$137$	5.71804	−	4.15440i	0.488525	−	0.354934i	0.804617	+	0.593795i	$0.202371\pi$
$138$	0.0347531	−	0.810537i	0.00295838	−	0.0689975i
$139$	−7.39836	−	10.1830i	−0.627521	−	0.863708i	0.370353	−	0.928891i	$-0.379237\pi$
$139$	−7.39836	−	10.1830i	−0.627521	−	0.863708i	−0.997873	+	0.0651833i	$0.979237\pi$
$140$	−1.11088	−	1.52899i	−0.0938864	−	0.129224i
$141$	−0.863337	+	20.1353i	−0.0727061	+	1.69570i
$142$	8.07221	−	5.86480i	0.677405	−	0.492163i
$143$	0.293485	−	0.403947i	0.0245424	−	0.0337797i
$144$	−2.26721	−	1.96463i	−0.188934	−	0.163719i
$145$	−2.84035	+	3.90941i	−0.235878	+	0.324659i
$146$	−1.40034	+	4.30980i	−0.115893	+	0.356682i
$147$	5.93223	+	0.254355i	0.489282	+	0.0209788i
$148$	5.47010	−	1.77734i	0.449640	−	0.146097i
$149$		−	6.59311i		−	0.540129i	−0.962842	−	0.270064i	$-0.912955\pi$
$149$		−	6.59311i		−	0.540129i	0.962842	−	0.270064i	$-0.0870450\pi$
$150$	1.66869	−	0.464177i	0.136248	−	0.0378999i
$151$	3.03109	−	0.984862i	0.246667	−	0.0801469i	−0.183074	−	0.983099i	$-0.558605\pi$
$151$	3.03109	−	0.984862i	0.246667	−	0.0801469i	0.429741	+	0.902952i	$0.358605\pi$
$152$	4.98565	+	6.86216i	0.404389	+	0.556594i
$153$	11.5431	+	0.991686i	0.933207	+	0.0801731i
$154$		−	2.91847i		−	0.235177i
$155$	1.80147	+	5.26827i	0.144698	+	0.423158i
$156$	−0.539557	+	0.150087i	−0.0431991	+	0.0120166i
$157$	5.52001	+	4.01052i	0.440545	+	0.320075i	0.785851	−	0.618415i	$-0.212225\pi$
$157$	5.52001	+	4.01052i	0.440545	+	0.320075i	−0.345306	+	0.938490i	$0.612225\pi$
$158$	−7.57618	+	5.50442i	−0.602729	+	0.437908i
$159$	−16.7910	+	11.1326i	−1.33161	+	0.882875i
$160$	−1.00000			−0.0790569
$161$	−0.885236			−0.0697664
$162$	1.53507	−	8.86812i	0.120607	−	0.696745i
$163$	5.60453	−	17.2490i	0.438981	−	1.35104i	−0.449971	−	0.893043i	$-0.648566\pi$
$163$	5.60453	−	17.2490i	0.438981	−	1.35104i	0.888952	−	0.458001i	$-0.151434\pi$
$164$	−8.54678	−	2.77702i	−0.667392	−	0.216849i
$165$	2.50600	+	0.934721i	0.195092	+	0.0727679i
$166$	6.70719	−	2.17930i	0.520579	−	0.169146i
$167$	9.74357	+	7.07912i	0.753980	+	0.547799i	0.897058	−	0.441913i	$-0.145700\pi$
$167$	9.74357	+	7.07912i	0.753980	+	0.547799i	−0.143078	+	0.989711i	$0.545700\pi$
$168$	−2.03578	+	2.56344i	−0.157064	+	0.197774i
$169$	3.98491	−	12.2643i	0.306532	−	0.943408i
$170$	3.12433	−	2.26996i	0.239625	−	0.174098i
$171$	−9.90597	+	23.4390i	−0.757528	+	1.79242i
$172$	5.33300	+	1.73280i	0.406637	+	0.132125i
$173$	−2.29744	−	3.16215i	−0.174671	−	0.240414i	0.712701	−	0.701468i	$-0.247472\pi$
$173$	−2.29744	−	3.16215i	−0.174671	−	0.240414i	−0.887372	+	0.461054i	$0.847472\pi$
$174$	7.84203	+	2.92502i	0.594503	+	0.221745i
$175$	−0.584024	−	1.79744i	−0.0441481	−	0.135874i
$176$	−1.24929	−	0.907664i	−0.0941690	−	0.0684178i
$177$	−0.0552595	+	1.28880i	−0.00415356	+	0.0968722i
$178$	−0.810465	−	0.263336i	−0.0607469	−	0.0197379i
$179$	−4.77645	−	14.7004i	−0.357009	−	1.09876i	−0.954836	−	0.297135i	$-0.903969\pi$
$179$	−4.77645	−	14.7004i	−0.357009	−	1.09876i	0.597827	−	0.801625i	$-0.296031\pi$
$180$	−1.54914	−	2.56908i	−0.115466	−	0.191488i
$181$		−	20.0565i		−	1.49079i	−0.666623	−	0.745395i	$-0.732261\pi$
$181$		−	20.0565i		−	1.49079i	0.666623	−	0.745395i	$-0.267739\pi$
$182$	0.188839	+	0.581186i	0.0139977	+	0.0430803i
$183$	0.851464	−	1.07216i	0.0629420	−	0.0792563i
$184$	−0.275315	+	0.378938i	−0.0202965	+	0.0279357i
$185$	5.75161			0.422867
$186$	7.95493	−	5.45152i	0.583284	−	0.399725i
$187$	5.96356			0.436099
$188$	6.83937	−	9.41358i	0.498812	−	0.686556i
$189$	−9.73939	−	1.25895i	−0.708436	−	0.0915754i
$190$	2.62111	+	8.06695i	0.190155	+	0.585238i
$191$		−	1.75055i		−	0.126666i	−0.997992	−	0.0633328i	$-0.979827\pi$
$191$		−	1.75055i		−	0.126666i	0.997992	−	0.0633328i	$-0.0201730\pi$
$192$	0.464177	+	1.66869i	0.0334991	+	0.120428i
$193$	2.04695	+	6.29986i	0.147342	+	0.453474i	0.997305	−	0.0733700i	$-0.0233754\pi$
$193$	2.04695	+	6.29986i	0.147342	+	0.453474i	−0.849962	+	0.526843i	$0.823375\pi$
$194$	18.0434	+	5.86265i	1.29544	+	0.420914i
$195$	−0.559528	−	0.0239907i	−0.0400687	−	0.00171801i
$196$	−2.77341	−	2.01500i	−0.198101	−	0.143929i
$197$	3.87131	+	11.9147i	0.275820	+	0.848886i	0.989001	+	0.147906i	$0.0472534\pi$
$197$	3.87131	+	11.9147i	0.275820	+	0.848886i	−0.713182	+	0.700979i	$0.752747\pi$
$198$	0.396535	−	4.61563i	0.0281805	−	0.328018i
$199$	−5.14171	−	7.07696i	−0.364486	−	0.501673i	0.586905	−	0.809656i	$-0.300346\pi$
$199$	−5.14171	−	7.07696i	−0.364486	−	0.501673i	−0.951392	+	0.307983i	$0.900346\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	8.97926	+	7.13095i	0.633348	+	0.502979i
$202$	8.39489	−	6.09925i	0.590663	−	0.429141i
$203$	2.82217	−	8.68576i	0.198078	−	0.609621i
$204$	−5.23811	−	4.15989i	−0.366741	−	0.291251i
$205$	−7.27033	−	5.28220i	−0.507782	−	0.368925i
$206$	11.5634	−	3.75717i	0.805659	−	0.261774i
$207$	−1.40002	−	0.120278i	−0.0973083	−	0.00835989i
$208$	0.307515	+	0.0999178i	0.0213223	+	0.00692805i
$209$	−4.04755	+	12.4571i	−0.279975	+	0.861673i
$210$	−2.72829	+	1.80889i	−0.188270	+	0.124825i
$211$	8.00422			0.551033			0.275517	−	0.961296i	$-0.411151\pi$
$211$	8.00422			0.551033			0.275517	+	0.961296i	$0.411151\pi$
$212$	11.6315			0.798852
$213$	−9.54988	−	14.4038i	−0.654347	−	0.986931i
$214$	−4.95270	+	3.59835i	−0.338560	+	0.245978i
$215$	4.53652	+	3.29598i	0.309388	+	0.224784i
$216$	−3.56793	+	3.77754i	−0.242767	+	0.257029i
$217$	−6.31484	−	8.41730i	−0.428679	−	0.571404i
$218$			8.45395i			0.572573i
$219$	7.35405	+	2.74301i	0.496940	+	0.185355i
$220$	−0.907664	−	1.24929i	−0.0611947	−	0.0842273i
$221$	−1.18759	+	0.385871i	−0.0798859	+	0.0259565i
$222$	−2.66976	−	9.59767i	−0.179183	−	0.644154i
$223$			4.86737i			0.325943i	0.986631	+	0.162972i	$0.0521079\pi$
$223$			4.86737i			0.325943i	−0.986631	+	0.162972i	$0.947892\pi$
$224$	1.79744	−	0.584024i	0.120097	−	0.0390217i
$225$	−0.679429	−	2.92205i	−0.0452952	−	0.194803i
$226$	3.08496	−	9.49452i	0.205208	−	0.631566i
$227$	16.7907	−	23.1104i	1.11444	−	1.53389i	0.299726	−	0.954025i	$-0.403105\pi$
$227$	16.7907	−	23.1104i	1.11444	−	1.53389i	0.814711	−	0.579867i	$-0.196895\pi$
$228$	12.2446	−	8.11832i	0.810919	−	0.537649i
$229$	13.4171	−	18.4670i	0.886624	−	1.22033i	−0.0879182	−	0.996128i	$-0.528021\pi$
$229$	13.4171	−	18.4670i	0.886624	−	1.22033i	0.974542	−	0.224205i	$-0.0719786\pi$
$230$	−0.378938	+	0.275315i	−0.0249864	+	0.0181537i
$231$	−5.05029	−	0.216540i	−0.332285	−	0.0142473i
$232$	−2.84035	−	3.90941i	−0.186478	−	0.256665i
$233$	−14.2494	−	19.6126i	−0.933510	−	1.28487i	−0.958475	−	0.285177i	$-0.907948\pi$
$233$	−14.2494	−	19.6126i	−0.933510	−	1.28487i	0.0249653	−	0.999688i	$-0.492052\pi$
$234$	0.219687	+	0.944818i	0.0143614	+	0.0617647i
$235$	9.41358	−	6.83937i	0.614074	−	0.446151i
$236$	0.437766	−	0.602534i	0.0284962	−	0.0392216i
$237$	8.96306	+	13.5187i	0.582213	+	0.878134i
$238$	−4.29009	+	5.90480i	−0.278085	+	0.382751i
$239$	−3.26277	+	10.0418i	−0.211051	+	0.649549i	0.788359	+	0.615215i	$0.210931\pi$
$239$	−3.26277	+	10.0418i	−0.211051	+	0.649549i	−0.999410	+	0.0343337i	$0.989069\pi$
$240$	−0.0741964	+	1.73046i	−0.00478936	+	0.111701i
$241$	1.18466	−	0.384920i	0.0763108	−	0.0247949i	−0.270613	−	0.962688i	$-0.587226\pi$
$241$	1.18466	−	0.384920i	0.0763108	−	0.0247949i	0.346924	+	0.937893i	$0.387226\pi$
$242$			8.61541i			0.553820i
$243$	−15.2320	−	3.31437i	−0.977136	−	0.212617i
$244$	−0.751779	+	0.244268i	−0.0481277	+	0.0156376i
$245$	−2.01500	−	2.77341i	−0.128734	−	0.177187i
$246$	−5.43966	+	14.5838i	−0.346820	+	0.929831i
$247$		−	2.74261i		−	0.174508i
$248$	−5.56711	+	0.0853163i	−0.353512	+	0.00541759i
$249$	−3.27354	−	11.7682i	−0.207452	−	0.745781i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	23.9500	−	17.4007i	1.51171	−	1.09832i	0.546304	−	0.837587i	$-0.316034\pi$
$251$	23.9500	−	17.4007i	1.51171	−	1.09832i	0.965410	−	0.260737i	$-0.0839655\pi$
$252$	4.28489	+	3.71303i	0.269923	+	0.233899i
$253$	−0.723298			−0.0454734
$254$	−14.5348			−0.911997
$255$	−3.69626	−	5.57496i	−0.231469	−	0.349117i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	12.3904	+	4.02590i	0.772894	+	0.251129i	0.668803	−	0.743439i	$-0.266807\pi$
$257$	12.3904	+	4.02590i	0.772894	+	0.251129i	0.104091	+	0.994568i	$0.466807\pi$
$258$	3.39423	−	9.09998i	0.211315	−	0.566540i
$259$	−10.3382	+	3.35908i	−0.642383	+	0.208723i
$260$	0.261588	+	0.190055i	0.0162230	+	0.0117867i
$261$	5.64348	−	13.3533i	0.349323	−	0.826548i
$262$	0.578228	−	1.77960i	0.0357231	−	0.109944i
$263$	1.33593	−	0.970607i	0.0823767	−	0.0598502i	−0.545835	−	0.837893i	$-0.683787\pi$
$263$	1.33593	−	0.970607i	0.0823767	−	0.0598502i	0.628211	+	0.778043i	$0.283787\pi$
$264$	−1.66337	+	2.09451i	−0.102373	+	0.128908i
$265$	11.0622	+	3.59432i	0.679544	+	0.220797i
$266$	−9.42258	−	12.9691i	−0.577736	−	0.795185i
$267$	−0.515827	+	1.38294i	−0.0315681	+	0.0846345i
$268$	−2.04573	−	6.29610i	−0.124963	−	0.384595i
$269$	10.9119	+	7.92798i	0.665312	+	0.483377i	0.868453	−	0.495772i	$-0.165115\pi$
$269$	10.9119	+	7.92798i	0.665312	+	0.483377i	−0.203141	+	0.979150i	$0.565115\pi$
$270$	−4.56063	+	2.49011i	−0.277551	+	0.151543i
$271$	−14.6311	−	4.75394i	−0.888778	−	0.288781i	−0.171180	−	0.985240i	$-0.554758\pi$
$271$	−14.6311	−	4.75394i	−0.888778	−	0.288781i	−0.717597	+	0.696458i	$0.754758\pi$
$272$	1.19339	+	3.67287i	0.0723598	+	0.222701i
$273$	1.01973	−	0.283656i	0.0617169	−	0.0171676i
$274$			7.06788i			0.426986i
$275$	−0.477187	−	1.46863i	−0.0287755	−	0.0885618i
$276$	0.635310	+	0.504537i	0.0382412	+	0.0303696i
$277$	−9.33003	+	12.8417i	−0.560587	+	0.771582i	−0.991401	−	0.130859i	$-0.958227\pi$
$277$	−9.33003	+	12.8417i	−0.560587	+	0.771582i	0.430814	+	0.902441i	$0.358227\pi$
$278$	12.5868			0.754908
$279$	−8.84341	−	14.1702i	−0.529441	−	0.848347i
$280$	1.88994			0.112946
$281$	−17.4881	+	24.0702i	−1.04325	+	1.43591i	−0.148733	+	0.988877i	$0.547519\pi$
$281$	−17.4881	+	24.0702i	−1.04325	+	1.43591i	−0.894517	+	0.447033i	$0.852481\pi$
$282$	−15.7824	−	12.5337i	−0.939827	−	0.746372i
$283$	1.54557	+	4.75677i	0.0918744	+	0.282760i	0.986427	−	0.164203i	$-0.0525053\pi$
$283$	1.54557	+	4.75677i	0.0918744	+	0.282760i	−0.894552	+	0.446964i	$0.852505\pi$
$284$			9.97780i			0.592074i
$285$	14.1540	−	3.93719i	0.838412	−	0.233219i
$286$	0.154294	+	0.474868i	0.00912360	+	0.0280795i
$287$	16.1529	+	5.24840i	0.953477	+	0.309803i
$288$	2.92205	−	0.679429i	0.172183	−	0.0400357i
$289$	1.68748	+	1.22603i	0.0992635	+	0.0721191i
$290$	−1.49326	−	4.59578i	−0.0876873	−	0.269874i
$291$	11.4838	−	30.7884i	0.673194	−	1.80485i
$292$	−2.66360	−	3.66614i	−0.155876	−	0.214544i
$293$	6.62282	+	2.15189i	0.386909	+	0.125715i	0.496011	−	0.868316i	$-0.334797\pi$
$293$	6.62282	+	2.15189i	0.386909	+	0.125715i	−0.109102	+	0.994031i	$0.534797\pi$
$294$	−3.69266	+	4.64977i	−0.215360	+	0.271180i
$295$	0.602534	−	0.437766i	0.0350809	−	0.0254878i
$296$	−1.77734	+	5.47010i	−0.103306	+	0.317943i
$297$	−7.95774	−	1.02865i	−0.461755	−	0.0596884i
$298$	5.33394	+	3.87533i	0.308987	+	0.224492i
$299$	0.144038	−	0.0468008i	0.00832994	−	0.00270656i
$300$	−0.605307	+	1.62284i	−0.0349474	+	0.0936946i
$301$	−10.0791	−	3.27488i	−0.580947	−	0.188761i
$302$	−0.984862	+	3.03109i	−0.0566724	+	0.174420i
$303$	−9.93164	−	14.9796i	−0.570558	−	0.860554i
$304$	−8.48209			−0.486481
$305$	−0.790467			−0.0452620
$306$	−7.58718	+	8.75570i	−0.433730	+	0.500530i
$307$	−4.31014	+	3.13150i	−0.245993	+	0.178724i	−0.703949	−	0.710250i	$-0.748582\pi$
$307$	−4.31014	+	3.13150i	−0.245993	+	0.178724i	0.457956	+	0.888975i	$0.348582\pi$
$308$	2.36109	+	1.71543i	0.134536	+	0.0977458i
$309$	−5.64367	−	20.2887i	−0.321057	−	1.15419i
$310$	−5.32100	−	1.63919i	−0.302213	−	0.0930998i
$311$		−	21.5392i		−	1.22138i	−0.791871	−	0.610688i	$-0.790893\pi$
$311$		−	21.5392i		−	1.22138i	0.791871	−	0.610688i	$-0.209107\pi$
$312$	0.195720	−	0.524730i	0.0110805	−	0.0297070i
$313$	−4.80693	−	6.61618i	−0.271704	−	0.373968i	0.651260	−	0.758855i	$-0.274241\pi$
$313$	−4.80693	−	6.61618i	−0.271704	−	0.373968i	−0.922964	+	0.384886i	$0.874241\pi$
$314$	−6.48916	+	2.10846i	−0.366205	+	0.118987i
$315$	2.92778	+	4.85541i	0.164962	+	0.273571i
$316$		−	9.36468i		−	0.526804i
$317$	1.47513	−	0.479298i	0.0828514	−	0.0269201i	−0.267298	−	0.963614i	$-0.586131\pi$
$317$	1.47513	−	0.479298i	0.0828514	−	0.0269201i	0.350149	+	0.936694i	$0.386131\pi$
$318$	0.863013	−	20.1278i	0.0483954	−	1.12871i
$319$	2.30591	−	7.09686i	0.129106	−	0.397348i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	5.85933	+	8.83745i	0.327036	+	0.493258i
$322$	0.520329	−	0.716171i	0.0289968	−	0.0399106i
$323$	26.5009	−	19.2540i	1.47455	−	1.07132i
$324$	6.27217	+	6.45445i	0.348454	+	0.358581i
$325$	0.190055	+	0.261588i	0.0105423	+	0.0145103i
$326$	10.6605	+	14.6729i	0.590428	+	0.812655i
$327$	14.6292	+	0.627253i	0.808998	+	0.0346872i
$328$	7.27033	−	5.28220i	0.401437	−	0.291661i
$329$	−12.9260	+	17.7911i	−0.712634	+	0.980856i
$330$	−2.22920	+	1.47798i	−0.122713	+	0.0813603i
$331$	−15.0955	+	20.7771i	−0.829722	+	1.14201i	0.158253	+	0.987399i	$0.449414\pi$
$331$	−15.0955	+	20.7771i	−0.829722	+	1.14201i	−0.987975	+	0.154616i	$0.950586\pi$
$332$	−2.17930	+	6.70719i	−0.119604	+	0.368105i
$333$	−16.8065	+	3.90781i	−0.920990	+	0.214147i
$334$	−11.4543	+	3.72171i	−0.626749	+	0.203643i
$335$		−	6.62011i		−	0.361695i
$336$	−0.877267	−	3.15373i	−0.0478588	−	0.172050i
$337$	−27.9759	+	9.08993i	−1.52395	+	0.495160i	−0.946894	−	0.321547i	$-0.895797\pi$
$337$	−27.9759	+	9.08993i	−1.52395	+	0.495160i	−0.577052	+	0.816707i	$0.695797\pi$
$338$	7.57976	+	10.4326i	0.412284	+	0.567461i
$339$	−16.2010	−	6.04286i	−0.879918	−	0.328203i
$340$			3.86189i			0.209440i
$341$	−5.15965	−	6.87751i	−0.279411	−	0.372438i
$342$	−13.1399	−	21.7912i	−0.710526	−	1.17833i
$343$	15.9445	+	11.5844i	0.860924	+	0.625498i
$344$	−4.53652	+	3.29598i	−0.244593	+	0.177707i
$345$	0.448306	+	0.676165i	0.0241360	+	0.0364035i
$346$	3.90864			0.210130
$347$	−5.24834			−0.281746			−0.140873	−	0.990028i	$-0.544991\pi$
$347$	−5.24834			−0.281746			−0.140873	+	0.990028i	$0.544991\pi$
$348$	−6.97582	+	4.62505i	−0.373943	+	0.247929i
$349$	2.16473	−	6.66235i	0.115875	−	0.356627i	−0.876253	−	0.481851i	$-0.839965\pi$
$349$	2.16473	−	6.66235i	0.115875	−	0.356627i	0.992129	+	0.125223i	$0.0399648\pi$
$350$	1.79744	+	0.584024i	0.0960772	+	0.0312174i
$351$	1.65127	−	0.310058i	0.0881383	−	0.0165496i
$352$	1.46863	−	0.477187i	0.0782783	−	0.0254342i
$353$	10.1329	+	7.36199i	0.539321	+	0.391839i	0.823833	−	0.566833i	$-0.191832\pi$
$353$	10.1329	+	7.36199i	0.539321	+	0.391839i	−0.284512	+	0.958672i	$0.591832\pi$
$354$	−1.01018	−	0.802244i	−0.0536905	−	0.0426388i
$355$	−3.08331	+	9.48945i	−0.163645	+	0.503648i
$356$	0.689423	−	0.500895i	0.0365393	−	0.0265474i
$357$	9.89972	+	7.86195i	0.523949	+	0.416098i
$358$	14.7004	+	4.77645i	0.776941	+	0.252443i
$359$	−17.2240	−	23.7068i	−0.909048	−	1.25120i	−0.967491	−	0.252907i	$-0.918613\pi$
$359$	−17.2240	−	23.7068i	−0.909048	−	1.25120i	0.0584427	−	0.998291i	$-0.481387\pi$
$360$	2.98899	+	0.256788i	0.157534	+	0.0135339i
$361$	16.3612	+	50.3545i	0.861115	+	2.65024i
$362$	16.2261	+	11.7889i	0.852823	+	0.619612i
$363$	14.9086	+	0.639233i	0.782501	+	0.0335510i
$364$	−0.581186	−	0.188839i	−0.0304624	−	0.00989784i
$365$	−1.40034	−	4.30980i	−0.0732971	−	0.225585i
$366$	0.366917	+	1.31905i	0.0191790	+	0.0689477i
$367$		−	11.6753i		−	0.609445i	−0.952441	−	0.304722i	$-0.901436\pi$
$367$		−	11.6753i		−	0.609445i	0.952441	−	0.304722i	$-0.0985637\pi$
$368$	−0.144742	−	0.445469i	−0.00754517	−	0.0232217i
$369$	24.8331	+	10.4952i	1.29276	+	0.546358i
$370$	−3.38071	+	4.65315i	−0.175755	+	0.241906i
$371$	−21.9828			−1.14129
$372$	−0.265423	+	9.64000i	−0.0137616	+	0.499811i
$373$	0.348666			0.0180532			0.00902661	−	0.999959i	$-0.497127\pi$
$373$	0.348666			0.0180532			0.00902661	+	0.999959i	$0.497127\pi$
$374$	−3.50529	+	4.82462i	−0.181254	+	0.249475i
$375$	−1.07717	+	1.35636i	−0.0556246	+	0.0700422i
$376$	3.59567	+	11.0663i	0.185432	+	0.570702i
$377$			1.56248i			0.0804716i
$378$	6.74318	−	7.13934i	0.346832	−	0.367208i
$379$	−1.37904	−	4.24425i	−0.0708366	−	0.218013i	0.909371	−	0.415987i	$-0.136564\pi$
$379$	−1.37904	−	4.24425i	−0.0708366	−	0.218013i	−0.980207	+	0.197974i	$0.936564\pi$
$380$	−8.06695	−	2.62111i	−0.413826	−	0.134460i
$381$	−1.07843	+	25.1520i	−0.0552498	+	1.28857i
$382$	1.41623	+	1.02895i	0.0724605	+	0.0526456i
$383$	−4.11982	−	12.6795i	−0.210513	−	0.647892i	−0.999442	−	0.0334076i	$-0.989364\pi$
$383$	−4.11982	−	12.6795i	−0.210513	−	0.647892i	0.788929	−	0.614484i	$-0.210636\pi$
$384$	−1.62284	−	0.605307i	−0.0828151	−	0.0308894i
$385$	1.71543	+	2.36109i	0.0874265	+	0.120332i
$386$	−6.29986	−	2.04695i	−0.320654	−	0.104187i
$387$	−15.4953	−	6.54876i	−0.787672	−	0.332892i
$388$	−15.3486	+	11.1514i	−0.779208	+	0.566128i
$389$	−11.6643	+	35.8989i	−0.591402	+	1.82015i	−0.0195251	+	0.999809i	$0.506215\pi$
$389$	−11.6643	+	35.8989i	−0.591402	+	1.82015i	−0.571877	+	0.820339i	$0.693785\pi$
$390$	0.348291	−	0.438567i	0.0176364	−	0.0222077i
$391$	1.46342	+	1.06323i	0.0740081	+	0.0537701i
$392$	3.26034	−	1.05935i	0.164672	−	0.0535052i
$393$	−3.03663	−	1.13264i	−0.153178	−	0.0571342i
$394$	−11.9147	−	3.87131i	−0.600253	−	0.195034i
$395$	2.89384	−	8.90634i	0.145605	−	0.448127i
$396$	3.50104	+	3.03380i	0.175934	+	0.152454i
$397$	−5.34692			−0.268354			−0.134177	−	0.990957i	$-0.542839\pi$
$397$	−5.34692			−0.268354			−0.134177	+	0.990957i	$0.542839\pi$
$398$	8.74761			0.438478
$399$	−23.1416	+	15.3431i	−1.15853	+	0.768118i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	−22.6135	−	16.4297i	−1.12926	−	0.820458i	−0.143676	−	0.989625i	$-0.545892\pi$
$401$	−22.6135	−	16.4297i	−1.12926	−	0.820458i	−0.985587	+	0.169167i	$0.945892\pi$
$402$	−11.0469	+	3.07290i	−0.550971	+	0.153262i
$403$	1.47250	+	1.03574i	0.0733507	+	0.0515938i
$404$			10.3767i			0.516258i
$405$	3.97065	+	8.07675i	0.197303	+	0.401337i
$406$	5.36809	+	7.38855i	0.266414	+	0.366687i
$407$	−8.44699	+	2.74459i	−0.418702	+	0.136044i
$408$	6.44431	−	1.79260i	0.319041	−	0.0887468i
$409$		−	13.6060i		−	0.672775i	−0.941724	−	0.336388i	$-0.890795\pi$
$409$		−	13.6060i		−	0.672775i	0.941724	−	0.336388i	$-0.109205\pi$
$410$	8.54678	−	2.77702i	0.422096	−	0.137147i
$411$	12.2307	+	0.524412i	0.603296	+	0.0258673i
$412$	−3.75717	+	11.5634i	−0.185102	+	0.569687i
$413$	−0.827353	+	1.13875i	−0.0407114	+	0.0560344i
$414$	0.920220	−	1.06195i	0.0452263	−	0.0521918i
$415$	−4.14527	+	5.70547i	−0.203483	+	0.280071i
$416$	−0.261588	+	0.190055i	−0.0128254	+	0.00931821i
$417$	0.933899	−	21.7810i	0.0457332	−	1.06662i
$418$	−7.69889	−	10.5966i	−0.376565	−	0.518297i
$419$	−9.03557	−	12.4364i	−0.441417	−	0.607558i	0.529110	−	0.848554i	$-0.322526\pi$
$419$	−9.03557	−	12.4364i	−0.441417	−	0.607558i	−0.970526	+	0.240996i	$0.922526\pi$
$420$	0.140227	−	3.27047i	0.00684237	−	0.159583i
$421$	23.6986	−	17.2181i	1.15500	−	0.839156i	0.165862	−	0.986149i	$-0.446959\pi$
$421$	23.6986	−	17.2181i	1.15500	−	0.839156i	0.989138	+	0.146993i	$0.0469593\pi$
$422$	−4.70476	+	6.47555i	−0.229024	+	0.315225i
$423$	−22.8601	+	26.3808i	−1.11150	+	1.28268i
$424$	−6.83680	+	9.41005i	−0.332024	+	0.456992i
$425$	−1.19339	+	3.67287i	−0.0578878	+	0.178160i
$426$	17.2662	+	0.740317i	0.836550	+	0.0358685i
$427$	1.42082	−	0.461652i	0.0687582	−	0.0223409i
$428$		−	6.12188i		−	0.295912i
$429$	0.833189	−	0.231766i	0.0402267	−	0.0111898i
$430$	−5.33300	+	1.73280i	−0.257180	+	0.0835629i
$431$	−20.2390	−	27.8566i	−0.974878	−	1.34180i	−0.939544	−	0.342429i	$-0.888750\pi$
$431$	−20.2390	−	27.8566i	−0.974878	−	1.34180i	−0.0353343	−	0.999376i	$-0.511250\pi$
$432$	−0.958919	−	5.10690i	−0.0461360	−	0.245706i
$433$			33.0810i			1.58977i	0.606760	+	0.794885i	$0.292469\pi$
$433$			33.0810i			1.58977i	−0.606760	+	0.794885i	$0.707531\pi$
$434$	10.5215	−	0.161243i	0.505049	−	0.00773990i
$435$	−8.06362	+	2.24304i	−0.386621	+	0.107545i
$436$	−6.83939	−	4.96910i	−0.327547	−	0.237977i
$437$	−3.21419	+	2.33525i	−0.153756	+	0.111710i
$438$	−6.54174	+	4.33725i	−0.312576	+	0.207242i
$439$	21.6381			1.03273			0.516366	−	0.856368i	$-0.327284\pi$
$439$	21.6381			1.03273			0.516366	+	0.856368i	$0.327284\pi$
$440$	1.54421			0.0736173
$441$	7.77227	+	6.73499i	0.370108	+	0.320714i
$442$	0.385871	−	1.18759i	0.0183540	−	0.0564878i
$443$	20.6943	+	6.72398i	0.983215	+	0.319466i	0.756139	−	0.654411i	$-0.227083\pi$
$443$	20.6943	+	6.72398i	0.983215	+	0.319466i	0.227076	+	0.973877i	$0.427083\pi$
$444$	9.33393	+	3.48149i	0.442969	+	0.165224i
$445$	0.810465	−	0.263336i	0.0384197	−	0.0124833i
$446$	−3.93778	−	2.86097i	−0.186459	−	0.135471i
$447$	7.10187	−	8.94264i	0.335907	−	0.422972i
$448$	−0.584024	+	1.79744i	−0.0275925	+	0.0849211i
$449$	12.7587	−	9.26977i	0.602122	−	0.437467i	−0.244509	−	0.969647i	$-0.578627\pi$
$449$	12.7587	−	9.26977i	0.602122	−	0.437467i	0.846632	+	0.532180i	$0.178627\pi$
$450$	2.76335	+	1.16787i	0.130265	+	0.0550539i
$451$	13.1980	+	4.28830i	0.621471	+	0.201928i
$452$	5.86794	+	8.07652i	0.276004	+	0.379888i
$453$	5.17211	+	1.92916i	0.243007	+	0.0906399i
$454$	8.82739	+	27.1679i	0.414290	+	1.27505i
$455$	−0.494386	−	0.359192i	−0.0231772	−	0.0168392i
$456$	−0.629341	+	14.6779i	−0.0294716	+	0.687357i
$457$	−22.5526	−	7.32777i	−1.05496	−	0.342779i	−0.270349	−	0.962762i	$-0.587139\pi$
$457$	−22.5526	−	7.32777i	−1.05496	−	0.342779i	−0.784615	+	0.619984i	$0.787139\pi$
$458$	7.05376	+	21.7092i	0.329601	+	1.01441i
$459$	14.5884	+	13.7790i	0.680930	+	0.643146i
$460$		−	0.468393i		−	0.0218390i
$461$	6.13552	+	18.8832i	0.285760	+	0.879478i	0.986170	+	0.165737i	$0.0530003\pi$
$461$	6.13552	+	18.8832i	0.285760	+	0.879478i	−0.700410	+	0.713740i	$0.747000\pi$
$462$	3.14367	−	3.95849i	0.146257	−	0.184166i
$463$	−8.76453	+	12.0633i	−0.407322	+	0.560631i	−0.962563	−	0.271059i	$-0.912626\pi$
$463$	−8.76453	+	12.0633i	−0.407322	+	0.560631i	0.555241	+	0.831690i	$0.312626\pi$
$464$	4.83229			0.224334
$465$	−3.23136	+	9.08616i	−0.149851	+	0.421361i
$466$	24.2425			1.12301
$467$	1.84095	−	2.53385i	0.0851888	−	0.117252i	−0.764296	−	0.644866i	$-0.776913\pi$
$467$	1.84095	−	2.53385i	0.0851888	−	0.117252i	0.849484	+	0.527614i	$0.176913\pi$
$468$	−0.893502	−	0.377619i	−0.0413022	−	0.0174555i
$469$	3.86630	+	11.8993i	0.178529	+	0.549456i
$470$			11.6358i			0.536721i
$471$	3.16713	+	11.3857i	0.145934	+	0.524625i
$472$	0.230147	+	0.708321i	0.0105934	+	0.0326031i
$473$	−8.23527	−	2.67580i	−0.378658	−	0.123034i
$474$	−16.2052	−	0.694826i	−0.744330	−	0.0319144i
$475$	−6.86216	−	4.98565i	−0.314857	−	0.228757i
$476$	−2.25543	−	6.94151i	−0.103378	−	0.318164i
$477$	−34.7663	−	2.98682i	−1.59184	−	0.136757i
$478$	−6.20616	−	8.54205i	−0.283863	−	0.390704i
$479$	−5.98967	−	1.94616i	−0.273675	−	0.0889225i	0.168964	−	0.985622i	$-0.445958\pi$
$479$	−5.98967	−	1.94616i	−0.273675	−	0.0889225i	−0.442639	+	0.896700i	$0.645958\pi$
$480$	−1.35636	−	1.07717i	−0.0619091	−	0.0491657i
$481$	1.50455	−	1.09312i	0.0686017	−	0.0498420i
$482$	−0.384920	+	1.18466i	−0.0175326	+	0.0539599i
$483$	−1.20070	−	0.953546i	−0.0546337	−	0.0433878i
$484$	−6.97002	−	5.06401i	−0.316819	−	0.230182i
$485$	−18.0434	+	5.86265i	−0.819308	+	0.266209i
$486$	11.6345	−	10.3748i	0.527754	−	0.470612i
$487$	37.5857	+	12.2123i	1.70317	+	0.553394i	0.989173	−	0.146754i	$-0.0468825\pi$
$487$	37.5857	+	12.2123i	1.70317	+	0.553394i	0.713998	+	0.700148i	$0.246883\pi$
$488$	0.244268	−	0.751779i	0.0110575	−	0.0340314i
$489$	26.1818	−	17.3588i	1.18398	−	0.784993i
$490$	3.42812			0.154867
$491$	17.5862			0.793653			0.396826	−	0.917894i	$-0.370112\pi$
$491$	17.5862			0.793653			0.396826	+	0.917894i	$0.370112\pi$
$492$	−8.60121	−	12.9729i	−0.387773	−	0.584865i
$493$	−15.0977	+	10.9691i	−0.679965	+	0.494024i
$494$	2.21881	+	1.61206i	0.0998292	+	0.0725301i
$495$	2.39220	+	3.96720i	0.107521	+	0.178312i
$496$	3.20324	−	4.55403i	0.143830	−	0.204482i
$497$		−	18.8575i		−	0.845872i
$498$	11.4448	+	4.26884i	0.512855	+	0.191291i
$499$	−6.78943	−	9.34484i	−0.303936	−	0.418333i	0.629542	−	0.776967i	$-0.283243\pi$
$499$	−6.78943	−	9.34484i	−0.303936	−	0.418333i	−0.933478	+	0.358634i	$0.883243\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	5.59042	+	20.0973i	0.249761	+	0.897880i
$502$			29.6039i			1.32129i
$503$	−39.1614	+	12.7243i	−1.74612	+	0.567348i	−0.995617	−	0.0935201i	$-0.970188\pi$
$503$	−39.1614	+	12.7243i	−1.74612	+	0.567348i	−0.750502	+	0.660869i	$0.770188\pi$
$504$	−5.52250	+	1.28408i	−0.245992	+	0.0571975i
$505$	−3.20656	+	9.86879i	−0.142690	+	0.439155i
$506$	0.425144	−	0.585160i	0.0189000	−	0.0260136i
$507$	18.6157	−	12.3424i	0.826751	−	0.548146i
$508$	8.54336	−	11.7589i	0.379050	−	0.521718i
$509$	−11.8004	+	8.57353i	−0.523046	+	0.380015i	−0.817750	−	0.575574i	$-0.804779\pi$
$509$	−11.8004	+	8.57353i	−0.523046	+	0.380015i	0.294704	+	0.955588i	$0.404779\pi$
$510$	6.68284	+	0.286538i	0.295921	+	0.0126881i
$511$	5.03406	+	6.92878i	0.222694	+	0.306511i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	−38.6837	+	21.1213i	−1.70793	+	0.932529i
$514$	−10.5399	+	7.65771i	−0.464897	+	0.337767i
$515$	−7.14656	+	9.83640i	−0.314915	+	0.433443i
$516$	5.36696	+	8.09482i	0.236267	+	0.356355i
$517$	−10.5614	+	14.5366i	−0.464491	+	0.639317i
$518$	3.35908	−	10.3382i	0.147589	−	0.454233i
$519$	0.290007	−	6.76374i	0.0127299	−	0.296895i
$520$	−0.307515	+	0.0999178i	−0.0134854	+	0.00438168i
$521$			9.56309i			0.418967i	0.977812	+	0.209483i	$0.0671782\pi$
$521$			9.56309i			0.418967i	−0.977812	+	0.209483i	$0.932822\pi$
$522$	7.48589	+	12.4145i	0.327648	+	0.543370i
$523$	−7.42963	+	2.41403i	−0.324875	+	0.105558i	−0.466914	−	0.884303i	$-0.654634\pi$
$523$	−7.42963	+	2.41403i	−0.324875	+	0.105558i	0.142039	+	0.989861i	$0.454634\pi$
$524$	1.09986	+	1.51382i	0.0480474	+	0.0661316i
$525$	1.14399	−	3.06707i	0.0499280	−	0.133858i
$526$			1.65130i			0.0719999i
$527$	0.329482	+	21.4995i	0.0143525	+	0.936535i
$528$	−0.716787	−	2.57681i	−0.0311941	−	0.112141i
$529$	18.4299	+	13.3901i	0.801300	+	0.582178i
$530$	−9.41005	+	6.83680i	−0.408747	+	0.296972i
$531$	−1.46320	+	1.68855i	−0.0634976	+	0.0732770i
$532$	16.0307			0.695017
$533$	−2.90574			−0.125862
$534$	−0.815627	−	1.23018i	−0.0352956	−	0.0532353i
$535$	1.89176	−	5.82225i	0.0817881	−	0.251718i
$536$	6.29610	+	2.04573i	0.271950	+	0.0883619i
$537$	9.35618	−	25.0841i	0.403749	−	1.08246i
$538$	−12.8277	+	4.16799i	−0.553043	+	0.179695i
$539$	4.28273	+	3.11158i	0.184470	+	0.134025i
$540$	0.666134	−	5.15328i	0.0286658	−	0.221762i
$541$	−7.83446	+	24.1120i	−0.336830	+	1.03666i	0.628984	+	0.777418i	$0.283471\pi$
$541$	−7.83446	+	24.1120i	−0.336830	+	1.03666i	−0.965814	+	0.259237i	$0.916529\pi$
$542$	12.4460	−	9.04253i	0.534601	−	0.388410i
$543$	21.6042	−	27.2039i	0.927125	−	1.16743i
$544$	−3.67287	−	1.19339i	−0.157473	−	0.0511661i
$545$	−4.96910	−	6.83939i	−0.212853	−	0.292967i
$546$	−0.369900	+	0.991708i	−0.0158303	+	0.0424412i
$547$	−1.74893	−	5.38265i	−0.0747788	−	0.230145i	0.906680	−	0.421819i	$-0.138608\pi$
$547$	−1.74893	−	5.38265i	−0.0747788	−	0.230145i	−0.981459	+	0.191674i	$0.938608\pi$
$548$	−5.71804	−	4.15440i	−0.244262	−	0.177467i
$549$	2.30978	−	0.537066i	0.0985792	−	0.0229214i
$550$	1.46863	+	0.477187i	0.0626226	+	0.0203473i
$551$	−12.6660	−	38.9819i	−0.539589	−	1.66068i
$552$	−0.781605	+	0.217417i	−0.0332673	+	0.00925390i
$553$			17.6987i			0.752625i
$554$	−4.90509	−	15.0963i	−0.208397	−	0.641381i
$555$	7.80126	+	6.19543i	0.331145	+	0.262982i
$556$	−7.39836	+	10.1830i	−0.313760	+	0.431854i
$557$	−21.6520			−0.917425			−0.458712	−	0.888585i	$-0.651689\pi$
$557$	−21.6520			−0.917425			−0.458712	+	0.888585i	$0.651689\pi$
$558$	16.6619	+	1.17456i	0.705356	+	0.0497230i
$559$	1.81312			0.0766866
$560$	−1.11088	+	1.52899i	−0.0469432	+	0.0646118i
$561$	8.08874	+	6.42375i	0.341507	+	0.271211i
$562$	−9.19402	−	28.2963i	−0.387826	−	1.19361i
$563$			40.9406i			1.72544i	0.505680	+	0.862721i	$0.331242\pi$
$563$			40.9406i			1.72544i	−0.505680	+	0.862721i	$0.668758\pi$
$564$	19.4166	−	5.40108i	0.817588	−	0.227427i
$565$	3.08496	+	9.49452i	0.129785	+	0.399437i
$566$	−4.75677	−	1.54557i	−0.199942	−	0.0649650i
$567$	−11.8540	−	12.1985i	−0.497822	−	0.512290i
$568$	−8.07221	−	5.86480i	−0.338702	−	0.246082i
$569$	−4.49020	−	13.8194i	−0.188239	−	0.579340i	0.811750	−	0.584005i	$-0.198515\pi$
$569$	−4.49020	−	13.8194i	−0.188239	−	0.579340i	−0.999989	+	0.00466481i	$0.998515\pi$
$570$	−5.13427	+	13.7651i	−0.215051	+	0.576555i
$571$	−20.5665	−	28.3073i	−0.860681	−	1.18463i	−0.981407	−	0.191939i	$-0.938522\pi$
$571$	−20.5665	−	28.3073i	−0.860681	−	1.18463i	0.120726	−	0.992686i	$-0.461478\pi$
$572$	−0.474868	−	0.154294i	−0.0198552	−	0.00645136i
$573$	1.88564	−	2.37438i	0.0787735	−	0.0991912i
$574$	−13.7405	+	9.98305i	−0.573517	+	0.416685i
$575$	0.144742	−	0.445469i	0.00603614	−	0.0185773i
$576$	−1.16787	+	2.76335i	−0.0486612	+	0.115139i
$577$	−11.5838	−	8.41612i	−0.482240	−	0.350368i	0.319952	−	0.947434i	$-0.396333\pi$
$577$	−11.5838	−	8.41612i	−0.482240	−	0.350368i	−0.802192	+	0.597066i	$0.796333\pi$
$578$	−1.98375	+	0.644559i	−0.0825131	+	0.0268101i
$579$	−4.00959	+	10.7498i	−0.166633	+	0.446745i
$580$	4.59578	+	1.49326i	0.190829	+	0.0620043i
$581$	4.11874	−	12.6762i	0.170874	−	0.525897i
$582$	18.1583	+	27.3876i	0.752685	+	1.13525i
$583$	−17.9614			−0.743886
$584$	4.53160			0.187519
$585$	−0.733080	−	0.635245i	−0.0303091	−	0.0262641i
$586$	−5.63371	+	4.09313i	−0.232726	+	0.169086i
$587$	0.612674	+	0.445134i	0.0252878	+	0.0183726i	0.600357	−	0.799732i	$-0.295025\pi$
$587$	0.612674	+	0.445134i	0.0252878	+	0.0183726i	−0.575070	+	0.818105i	$0.695025\pi$
$588$	−1.59126	−	5.72049i	−0.0656223	−	0.235909i
$589$	−45.1332	−	13.9038i	−1.85968	−	0.572895i
$590$			0.744773i			0.0306618i
$591$	−7.58318	+	20.3306i	−0.311930	+	0.836291i
$592$	−3.38071	−	4.65315i	−0.138946	−	0.191243i
$593$	−23.8286	+	7.74237i	−0.978521	+	0.317941i	−0.754251	−	0.656586i	$-0.772000\pi$
$593$	−23.8286	+	7.74237i	−0.978521	+	0.317941i	−0.224270	+	0.974527i	$0.572000\pi$
$594$	5.50964	−	5.83332i	0.226063	−	0.239344i
$595$		−	7.29874i		−	0.299219i
$596$	−6.27042	+	2.03738i	−0.256846	+	0.0834545i
$597$	0.649041	−	15.1374i	0.0265635	−	0.619532i
$598$	−0.0468008	+	0.144038i	−0.00191383	+	0.00589016i
$599$	−0.300012	+	0.412931i	−0.0122582	+	0.0168719i	−0.815102	−	0.579317i	$-0.803319\pi$
$599$	−0.300012	+	0.412931i	−0.0122582	+	0.0168719i	0.802844	+	0.596189i	$0.203319\pi$
$600$	−0.957113	−	1.44358i	−0.0390740	−	0.0589341i
$601$	2.18019	−	3.00078i	0.0889320	−	0.122404i	−0.762233	−	0.647303i	$-0.775897\pi$
$601$	2.18019	−	3.00078i	0.0889320	−	0.122404i	0.851165	+	0.524899i	$0.175897\pi$
$602$	8.57376	−	6.22920i	0.349440	−	0.253883i
$603$	4.49789	+	19.3443i	0.183168	+	0.787760i
$604$	−1.87332	−	2.57840i	−0.0762242	−	0.104914i
$605$	−5.06401	−	6.97002i	−0.205881	−	0.283371i
$606$	17.9564	+	0.769911i	0.729429	+	0.0312755i
$607$	−2.29244	+	1.66555i	−0.0930472	+	0.0676028i	−0.633336	−	0.773877i	$-0.718315\pi$
$607$	−2.29244	+	1.66555i	−0.0930472	+	0.0676028i	0.540289	+	0.841480i	$0.318315\pi$
$608$	4.98565	−	6.86216i	0.202195	−	0.278297i
$609$	13.1839	−	8.74107i	0.534238	−	0.354206i
$610$	0.464625	−	0.639501i	0.0188121	−	0.0258927i
$611$	1.16263	−	3.57819i	0.0470348	−	0.144758i
$612$	−2.62388	−	11.2846i	−0.106064	−	0.456154i
$613$	7.91276	−	2.57101i	0.319594	−	0.103842i	−0.144827	−	0.989457i	$-0.546263\pi$
$613$	7.91276	−	2.57101i	0.319594	−	0.103842i	0.464421	+	0.885615i	$0.346263\pi$
$614$		−	5.32763i		−	0.215006i
$615$	−4.17138	−	14.9959i	−0.168206	−	0.604694i
$616$	−2.77563	+	0.901856i	−0.111833	+	0.0363368i
$617$	10.0329	+	13.8091i	0.403908	+	0.555932i	0.961720	−	0.274036i	$-0.0883587\pi$
$617$	10.0329	+	13.8091i	0.403908	+	0.555932i	−0.557811	+	0.829968i	$0.688359\pi$
$618$	19.7312	+	7.35960i	0.793706	+	0.296046i
$619$			22.0591i			0.886630i	0.896366	+	0.443315i	$0.146198\pi$
$619$			22.0591i			0.886630i	−0.896366	+	0.443315i	$0.853802\pi$
$620$	4.45374	−	3.34129i	0.178866	−	0.134189i
$621$	−1.76938	−	1.67120i	−0.0710027	−	0.0670628i
$622$	17.4256	+	12.6604i	0.698703	+	0.507637i
$623$	−1.30297	+	0.946662i	−0.0522023	+	0.0379272i
$624$	0.309474	+	0.466769i	0.0123889	+	0.0186857i
$625$	1.00000			0.0400000
$626$	8.17804			0.326860
$627$	−18.9083	+	12.5364i	−0.755123	+	0.500655i
$628$	2.10846	−	6.48916i	0.0841366	−	0.258946i
$629$	21.1249	+	6.86390i	0.842306	+	0.273682i
$630$	−5.64901	−	0.485314i	−0.225062	−	0.0193354i
$631$	−35.1921	+	11.4346i	−1.40097	+	0.455204i	−0.909506	−	0.415691i	$-0.863540\pi$
$631$	−35.1921	+	11.4346i	−1.40097	+	0.455204i	−0.491469	+	0.870895i	$0.663540\pi$
$632$	7.57618	+	5.50442i	0.301364	+	0.218954i
$633$	10.8566	+	8.62187i	0.431512	+	0.342689i
$634$	−0.479298	+	1.47513i	−0.0190354	+	0.0585848i
$635$	11.7589	−	8.54336i	0.466639	−	0.339033i
$636$	15.7765	+	12.5290i	0.625577	+	0.496808i
$637$	−1.05420	−	0.342530i	−0.0417689	−	0.0135715i
$638$	4.38610	+	6.03695i	0.173647	+	0.239005i
$639$	2.56218	−	29.8235i	0.101358	−	1.17980i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−13.1927	−	9.58503i	−0.521079	−	0.378586i	0.295931	−	0.955209i	$-0.404370\pi$
$641$	−13.1927	−	9.58503i	−0.521079	−	0.378586i	−0.817010	+	0.576623i	$0.804370\pi$
$642$	−10.5937	−	0.454222i	−0.418099	−	0.0179267i
$643$	−18.0584	−	5.86753i	−0.712153	−	0.231393i	−0.0695354	−	0.997579i	$-0.522152\pi$
$643$	−18.0584	−	5.86753i	−0.712153	−	0.231393i	−0.642618	+	0.766187i	$0.722152\pi$
$644$	0.273553	+	0.841909i	0.0107795	+	0.0331759i
$645$	2.60285	+	9.35712i	0.102487	+	0.368436i
$646$			32.7569i			1.28880i
$647$	−3.18609	−	9.80577i	−0.125258	−	0.385505i	0.868690	−	0.495356i	$-0.164962\pi$
$647$	−3.18609	−	9.80577i	−0.125258	−	0.385505i	−0.993948	+	0.109852i	$0.964962\pi$
$648$	−8.90845	+	1.28046i	−0.349957	+	0.0503011i
$649$	−0.676004	+	0.930439i	−0.0265355	+	0.0365229i
$650$	−0.323341			−0.0126825
$651$	0.501634	−	18.2190i	0.0196606	−	0.714060i
$652$	−18.1367			−0.710286
$653$	12.7114	−	17.4958i	0.497437	−	0.684663i	−0.484301	−	0.874901i	$-0.660926\pi$
$653$	12.7114	−	17.4958i	0.497437	−	0.684663i	0.981738	+	0.190238i	$0.0609261\pi$
$654$	−9.10630	+	11.4666i	−0.356085	+	0.448380i
$655$	0.578228	+	1.77960i	0.0225933	+	0.0695349i
$656$			8.98662i			0.350869i
$657$	7.02007	+	11.6420i	0.273879	+	0.454199i
$658$	−6.79560	−	20.9147i	−0.264920	−	0.815340i
$659$	33.2261	+	10.7958i	1.29430	+	0.420545i	0.873596	−	0.486652i	$-0.161782\pi$
$659$	33.2261	+	10.7958i	1.29430	+	0.420545i	0.420707	+	0.907196i	$0.361782\pi$
$660$	0.114575	−	2.67220i	0.00445982	−	0.104015i
$661$	−8.54700	−	6.20976i	−0.332440	−	0.241532i	0.409025	−	0.912523i	$-0.365869\pi$
$661$	−8.54700	−	6.20976i	−0.332440	−	0.241532i	−0.741465	+	0.670991i	$0.765869\pi$
$662$	−7.93616	−	24.4250i	−0.308448	−	0.949304i
$663$	−2.02645	−	0.755849i	−0.0787006	−	0.0293548i
$664$	−4.14527	−	5.70547i	−0.160868	−	0.221415i
$665$	15.2461	+	4.95374i	0.591217	+	0.192098i
$666$	6.71712	−	15.8937i	0.260283	−	0.615868i
$667$	1.83114	−	1.33040i	0.0709020	−	0.0515133i
$668$	3.72171	−	11.4543i	0.143997	−	0.443179i
$669$	−5.24296	+	6.60191i	−0.202705	+	0.255244i
$670$	5.35578	+	3.89120i	0.206912	+	0.150330i
$671$	1.16090	−	0.377201i	0.0448162	−	0.0145617i
$672$	3.06707	+	1.14399i	0.118315	+	0.0441305i
$673$	38.2256	+	12.4203i	1.47349	+	0.478766i	0.932160	−	0.362046i	$-0.117922\pi$
$673$	38.2256	+	12.4203i	1.47349	+	0.478766i	0.541329	+	0.840811i	$0.317922\pi$
$674$	9.08993	−	27.9759i	0.350131	−	1.07759i
$675$	2.22598	−	4.69521i	0.0856781	−	0.180719i
$676$	−12.8955			−0.495979
$677$	4.01787			0.154419			0.0772096	−	0.997015i	$-0.475399\pi$
$677$	4.01787			0.154419			0.0772096	+	0.997015i	$0.475399\pi$
$678$	14.4115	−	9.55498i	0.553470	−	0.366957i
$679$	29.0080	−	21.0755i	1.11322	−	0.808804i
$680$	−3.12433	−	2.26996i	−0.119813	−	0.0870490i
$681$	47.6680	−	13.2597i	1.82664	−	0.508113i
$682$	8.59679	−	0.131746i	0.329188	−	0.00504483i
$683$		−	38.2673i		−	1.46426i	−0.681165	−	0.732130i	$-0.738527\pi$
$683$		−	38.2673i		−	1.46426i	0.681165	−	0.732130i	$-0.261473\pi$
$684$	25.3529	+	2.17810i	0.969392	+	0.0832817i
$685$	−4.15440	−	5.71804i	−0.158731	−	0.218475i
$686$	−18.7439	+	6.09027i	−0.715647	+	0.232528i
$687$	38.0904	−	10.5955i	1.45324	−	0.404244i
$688$		−	5.60745i		−	0.213782i
$689$	3.57685	−	1.16219i	0.136267	−	0.0442759i
$690$	−0.810537	−	0.0347531i	−0.0308566	−	0.00132303i
$691$	−3.02771	+	9.31833i	−0.115179	+	0.354486i	−0.991984	−	0.126360i	$-0.959670\pi$
$691$	−3.02771	+	9.31833i	−0.115179	+	0.354486i	0.876805	+	0.480846i	$0.159670\pi$
$692$	−2.29744	+	3.16215i	−0.0873355	+	0.120207i
$693$	−6.61677	−	5.73371i	−0.251350	−	0.217806i
$694$	3.08490	−	4.24600i	0.117101	−	0.161176i
$695$	−10.1830	+	7.39836i	−0.386262	+	0.280636i
$696$	0.358539	−	8.36209i	0.0135904	−	0.316964i
$697$	−20.3993	−	28.0772i	−0.772677	−	1.06350i
$698$	4.11756	+	5.66733i	0.155852	+	0.214512i
$699$	1.79871	−	41.9508i	0.0680335	−	1.58672i
$700$	−1.52899	+	1.11088i	−0.0577906	+	0.0419873i
$701$	−23.8115	+	32.7738i	−0.899350	+	1.23785i	0.0713253	+	0.997453i	$0.477277\pi$
$701$	−23.8115	+	32.7738i	−0.899350	+	1.23785i	−0.970675	+	0.240396i	$0.922723\pi$
$702$	−0.719750	+	1.51815i	−0.0271652	+	0.0572990i
$703$	−28.6755	+	39.4684i	−1.08152	+	1.48858i
$704$	−0.477187	+	1.46863i	−0.0179847	+	0.0553511i
$705$	20.1353	+	0.863337i	0.758341	+	0.0325152i
$706$	−11.9120	+	3.87043i	−0.448312	+	0.145665i
$707$		−	19.6113i		−	0.737558i
$708$	1.24280	−	0.345706i	0.0467072	−	0.0129924i
$709$	16.6776	−	5.41887i	0.626339	−	0.203510i	0.0213865	−	0.999771i	$-0.493192\pi$
$709$	16.6776	−	5.41887i	0.626339	−	0.203510i	0.604953	+	0.796261i	$0.293192\pi$
$710$	−5.86480	−	8.07221i	−0.220102	−	0.302945i
$711$	−2.40474	+	27.9909i	−0.0901847	+	1.04974i
$712$			0.852174i			0.0319366i
$713$	−0.0399616	−	2.60760i	−0.00149657	−	0.0976553i
$714$	−12.1794	+	3.38790i	−0.455801	+	0.126789i
$715$	−0.403947	−	0.293485i	−0.0151068	−	0.0109757i
$716$	−12.5049	+	9.08535i	−0.467331	+	0.339536i
$717$	−15.2422	+	10.1057i	−0.569229	+	0.377406i
$718$	29.3032			1.09359
$719$	2.98024			0.111144			0.0555720	−	0.998455i	$-0.482302\pi$
$719$	2.98024			0.111144			0.0555720	+	0.998455i	$0.482302\pi$
$720$	−1.96463	+	2.26721i	−0.0732174	+	0.0844938i
$721$	7.10083	−	21.8541i	0.264449	−	0.813889i
$722$	−50.3545	−	16.3612i	−1.87400	−	0.608900i
$723$	2.02145	+	0.753987i	0.0751786	+	0.0280411i
$724$	−19.0749	+	6.19781i	−0.708912	+	0.230340i
$725$	3.90941	+	2.84035i	0.145192	+	0.105488i
$726$	−9.28023	+	11.6856i	−0.344422	+	0.433694i
$727$	10.5992	−	32.6210i	0.393103	−	1.20985i	−0.537326	−	0.843375i	$-0.680565\pi$
$727$	10.5992	−	32.6210i	0.393103	−	1.20985i	0.930429	−	0.366473i	$-0.119435\pi$
$728$	0.494386	−	0.359192i	0.0183232	−	0.0133126i
$729$	−17.0900	−	20.9029i	−0.632963	−	0.774182i
$730$	4.30980	+	1.40034i	0.159513	+	0.0518289i
$731$	12.7287	+	17.5195i	0.470787	+	0.647983i
$732$	−1.28280	−	0.478475i	−0.0474137	−	0.0176850i
$733$	−11.0678	−	34.0632i	−0.408799	−	1.25815i	−0.917681	−	0.397317i	$-0.869941\pi$
$733$	−11.0678	−	34.0632i	−0.408799	−	1.25815i	0.508883	−	0.860836i	$-0.330059\pi$
$734$	9.44551	+	6.86256i	0.348640	+	0.253302i
$735$	0.254355	−	5.93223i	0.00938201	−	0.218814i
$736$	0.445469	+	0.144742i	0.0164202	+	0.00533524i
$737$	3.15903	+	9.72250i	0.116364	+	0.358133i
$738$	−23.0873	+	13.9215i	−0.849857	+	0.512458i
$739$			52.1476i			1.91828i	0.282932	+	0.959140i	$0.408693\pi$
$739$			52.1476i			1.91828i	−0.282932	+	0.959140i	$0.591307\pi$
$740$	−1.77734	−	5.47010i	−0.0653365	−	0.201085i
$741$	2.95424	−	3.71996i	0.108527	−	0.136656i
$742$	12.9212	−	17.7844i	0.474350	−	0.652887i
$743$	18.4558			0.677076			0.338538	−	0.940953i	$-0.390068\pi$
$743$	18.4558			0.677076			0.338538	+	0.940953i	$0.390068\pi$
$744$	−7.64291	−	5.88098i	−0.280203	−	0.215607i
$745$	−6.59311			−0.241553
$746$	−0.204940	+	0.282076i	−0.00750340	+	0.0103275i
$747$	8.23622	−	19.4881i	0.301348	−	0.713032i
$748$	−1.84284	−	5.67169i	−0.0673810	−	0.207377i
$749$			11.5700i			0.422758i
$750$	−0.464177	−	1.66869i	−0.0169493	−	0.0609321i
$751$	−12.4446	−	38.3006i	−0.454110	−	1.39761i	−0.872176	−	0.489192i	$-0.837292\pi$
$751$	−12.4446	−	38.3006i	−0.454110	−	1.39761i	0.418066	−	0.908417i	$-0.362708\pi$
$752$	−11.0663	−	3.59567i	−0.403548	−	0.131121i
$753$	51.2284	+	2.19650i	1.86687	+	0.0800450i
$754$	−1.26407	−	0.918401i	−0.0460347	−	0.0334462i
$755$	−0.984862	−	3.03109i	−0.0358428	−	0.110313i
$756$	1.81230	+	9.65175i	0.0659127	+	0.351031i
$757$	−26.1746	−	36.0263i	−0.951333	−	1.30940i	−0.950933	−	0.309397i	$-0.899873\pi$
$757$	−26.1746	−	36.0263i	−0.951333	−	1.30940i	−0.000399929	−	1.00000i	$-0.500127\pi$
$758$	4.24425	+	1.37904i	0.154158	+	0.0500890i
$759$	−0.981053	−	0.779112i	−0.0356100	−	0.0282800i
$760$	6.86216	−	4.98565i	0.248917	−	0.180848i
$761$	5.36770	−	16.5201i	0.194579	−	0.598852i	−0.805402	−	0.592728i	$-0.798051\pi$
$761$	5.36770	−	16.5201i	0.194579	−	0.598852i	0.999981	−	0.00612366i	$-0.00194923\pi$
$762$	−19.7145	−	15.6564i	−0.714180	−	0.567172i
$763$	12.9260	+	9.39131i	0.467954	+	0.339988i
$764$	−1.66487	+	0.540951i	−0.0602331	+	0.0195709i
$765$	0.991686	−	11.5431i	0.0358545	−	0.417343i
$766$	12.6795	+	4.11982i	0.458129	+	0.148855i
$767$	0.0744160	−	0.229029i	0.00268701	−	0.00826976i
$768$	1.44358	−	0.957113i	0.0520908	−	0.0345368i
$769$	−9.76398			−0.352098			−0.176049	−	0.984381i	$-0.556332\pi$
$769$	−9.76398			−0.352098			−0.176049	+	0.984381i	$0.556332\pi$
$770$	−2.91847			−0.105174
$771$	12.4693	+	18.8071i	0.449072	+	0.677322i
$772$	5.35898	−	3.89352i	0.192874	−	0.140131i
$773$	3.55069	+	2.57973i	0.127709	+	0.0927863i	0.649806	−	0.760100i	$-0.274850\pi$
$773$	3.55069	+	2.57973i	0.127709	+	0.0927863i	−0.522097	+	0.852886i	$0.674850\pi$
$774$	14.4060	−	8.68671i	0.517812	−	0.312237i
$775$	5.26827	−	1.80147i	0.189242	−	0.0647108i
$776$		−	18.9719i		−	0.681053i
$777$	−17.6406	−	6.57981i	−0.632852	−	0.236049i
$778$	−22.1868	−	30.5375i	−0.795434	−	1.09482i
$779$	72.4946	−	23.5549i	2.59739	−	0.843943i
$780$	0.150087	+	0.539557i	0.00537399	+	0.0193192i
$781$		−	15.4078i		−	0.551335i
$782$	−1.72035	+	0.558975i	−0.0615196	+	0.0199889i
$783$	22.0383	−	12.0329i	0.787585	−	0.430022i
$784$	−1.05935	+	3.26034i	−0.0378339	+	0.116441i
$785$	4.01052	−	5.52001i	0.143142	−	0.197018i
$786$	2.70121	−	1.79094i	0.0963491	−	0.0638806i
$787$	−8.19001	+	11.2726i	−0.291942	+	0.401824i	−0.929644	−	0.368460i	$-0.879885\pi$
$787$	−8.19001	+	11.2726i	−0.291942	+	0.401824i	0.637702	+	0.770284i	$0.279885\pi$
$788$	10.1352	−	7.36368i	0.361053	−	0.262320i
$789$	2.85750	+	0.122520i	0.101730	+	0.00436184i
$790$	5.50442	+	7.57618i	0.195838	+	0.269549i
$791$	−11.0901	−	15.2641i	−0.394317	−	0.542731i
$792$	−4.51226	+	1.04918i	−0.160336	+	0.0372810i
$793$	−0.206777	+	0.150232i	−0.00734286	+	0.00533490i
$794$	3.14284	−	4.32575i	0.111535	−	0.153515i
$795$	11.1326	+	16.7910i	0.394834	+	0.595515i
$796$	−5.14171	+	7.07696i	−0.182243	+	0.250836i
$797$	−16.8773	+	51.9430i	−0.597825	+	1.83992i	−0.0576942	+	0.998334i	$0.518375\pi$
$797$	−16.8773	+	51.9430i	−0.597825	+	1.83992i	−0.540131	+	0.841581i	$0.681625\pi$
$798$	1.18942	−	27.7404i	0.0421049	−	0.982000i
$799$	42.7369	−	13.8861i	1.51192	−	0.491254i
$800$			1.00000i			0.0353553i
$801$	−2.18930	+	1.32013i	−0.0773552	+	0.0466447i
$802$	26.5837	−	8.63758i	0.938705	−	0.305004i
$803$	4.11317	+	5.66129i	0.145150	+	0.199782i
$804$	4.00720	−	10.7434i	0.141323	−	0.378889i
$805$			0.885236i			0.0312005i
$806$	−1.70345	+	0.582489i	−0.0600014	+	0.0205173i
$807$	6.26076	+	22.5072i	0.220389	+	0.792289i
$808$	−8.39489	−	6.09925i	−0.295331	−	0.214571i
$809$	19.3342	−	14.0471i	0.679753	−	0.493869i	−0.193523	−	0.981096i	$-0.561991\pi$
$809$	19.3342	−	14.0471i	0.679753	−	0.493869i	0.873276	+	0.487227i	$0.161991\pi$
$810$	−8.86812	−	1.53507i	−0.311594	−	0.0539370i
$811$	4.82580			0.169457			0.0847284	−	0.996404i	$-0.472998\pi$
$811$	4.82580			0.169457			0.0847284	+	0.996404i	$0.472998\pi$
$812$	−9.13275			−0.320497
$813$	−14.7243	−	22.2082i	−0.516404	−	0.778876i
$814$	2.74459	−	8.44699i	0.0961980	−	0.296067i
$815$	−17.2490	−	5.60453i	−0.604205	−	0.196318i
$816$	−2.33763	+	6.26722i	−0.0818333	+	0.219396i
$817$	−45.2350	+	14.6977i	−1.58257	+	0.514209i
$818$	11.0075	+	7.99743i	0.384869	+	0.279623i
$819$	1.68867	+	0.713678i	0.0590068	+	0.0249379i
$820$	−2.77702	+	8.54678i	−0.0969777	+	0.298467i
$821$	5.17893	−	3.76271i	0.180746	−	0.131320i	−0.493733	−	0.869613i	$-0.664368\pi$
$821$	5.17893	−	3.76271i	0.180746	−	0.131320i	0.674479	+	0.738294i	$0.264368\pi$
$822$	−7.61328	+	9.58660i	−0.265544	+	0.334371i
$823$	−2.28545	−	0.742588i	−0.0796658	−	0.0258850i	0.268913	−	0.963164i	$-0.413336\pi$
$823$	−2.28545	−	0.742588i	−0.0796658	−	0.0258850i	−0.348579	+	0.937279i	$0.613336\pi$
$824$	−7.14656	−	9.83640i	−0.248962	−	0.342667i
$825$	0.934721	−	2.50600i	0.0325428	−	0.0872478i
$826$	−0.434965	−	1.33868i	−0.0151344	−	0.0465788i
$827$	42.3797	+	30.7907i	1.47369	+	1.07070i	0.979524	+	0.201327i	$0.0645252\pi$
$827$	42.3797	+	30.7907i	1.47369	+	1.07070i	0.494163	+	0.869370i	$0.335475\pi$
$828$	0.318240	+	1.36867i	0.0110596	+	0.0475645i
$829$	−8.96752	−	2.91372i	−0.311455	−	0.101198i	0.149119	−	0.988819i	$-0.452356\pi$
$829$	−8.96752	−	2.91372i	−0.311455	−	0.101198i	−0.460574	+	0.887622i	$0.652356\pi$
$830$	−2.17930	−	6.70719i	−0.0756445	−	0.232810i
$831$	−26.4875	+	7.36797i	−0.918842	+	0.255592i
$832$		−	0.323341i		−	0.0112098i
$833$	−4.09108	−	12.5911i	−0.141748	−	0.436254i
$834$	17.0723	+	13.5581i	0.591165	+	0.469479i
$835$	7.07912	−	9.74357i	0.244983	−	0.337190i
$836$	13.0981			0.453008
$837$	3.26878	−	28.7457i	0.112986	−	0.993597i
$838$	15.3722			0.531025
$839$	−9.18216	+	12.6382i	−0.317003	+	0.436317i	−0.937549	−	0.347853i	$-0.886911\pi$
$839$	−9.18216	+	12.6382i	−0.317003	+	0.436317i	0.620546	+	0.784170i	$0.286911\pi$
$840$	2.56344	+	2.03578i	0.0884471	+	0.0702411i
$841$	−1.74562	−	5.37247i	−0.0601939	−	0.185258i
$842$			29.2931i			1.00951i
$843$	−49.6478	+	13.8104i	−1.70996	+	0.475656i
$844$	−2.47344	−	7.61247i	−0.0851393	−	0.262032i
$845$	−12.2643	−	3.98491i	−0.421905	−	0.137085i
$846$	−7.90572	−	34.0005i	−0.271804	−	1.16896i
$847$	13.1729	+	9.57069i	0.452627	+	0.328853i
$848$	−3.59432	−	11.0622i	−0.123429	−	0.379877i
$849$	−3.02748	+	8.11672i	−0.103903	+	0.278565i
$850$	−2.26996	−	3.12433i	−0.0778590	−	0.107164i
$851$	−2.56216	−	0.832497i	−0.0878298	−	0.0285376i
$852$	−10.7477	+	13.5335i	−0.368212	+	0.463650i
$853$	−27.4972	+	19.9779i	−0.941485	+	0.684029i	−0.948778	−	0.315944i	$-0.897679\pi$
$853$	−27.4972	+	19.9779i	−0.941485	+	0.684029i	0.00729250	+	0.999973i	$0.497679\pi$
$854$	−0.461652	+	1.42082i	−0.0157974	+	0.0486194i
$855$	23.4390	+	9.90597i	0.801595	+	0.338777i
$856$	4.95270	+	3.59835i	0.169280	+	0.122989i
$857$	−16.4181	+	5.33457i	−0.560832	+	0.182225i	−0.575696	−	0.817664i	$-0.695269\pi$
$857$	−16.4181	+	5.33457i	−0.560832	+	0.182225i	0.0148634	+	0.999890i	$0.495269\pi$
$858$	−0.302233	+	0.810293i	−0.0103181	+	0.0276629i
$859$	35.9521	+	11.6815i	1.22667	+	0.398569i	0.849507	−	0.527578i	$-0.176900\pi$
$859$	35.9521	+	11.6815i	1.22667	+	0.398569i	0.377163	+	0.926147i	$0.376900\pi$
$860$	1.73280	−	5.33300i	0.0590879	−	0.181854i
$861$	16.2558	+	24.5181i	0.553996	+	0.835574i
$862$	34.4326			1.17278
$863$	−30.4706			−1.03723			−0.518615	−	0.855008i	$-0.673552\pi$
$863$	−30.4706			−1.03723			−0.518615	+	0.855008i	$0.673552\pi$
$864$	4.69521	+	2.22598i	0.159734	+	0.0757294i
$865$	−3.16215	+	2.29744i	−0.107516	+	0.0781153i
$866$	−26.7631	−	19.4445i	−0.909446	−	0.660751i
$867$	0.968198	+	3.48063i	0.0328817	+	0.118208i
$868$	−6.05394	+	8.60686i	−0.205484	+	0.292136i
$869$			14.4610i			0.490557i
$870$	2.92502	−	7.84203i	0.0991674	−	0.265870i
$871$	−1.25818	−	1.73174i	−0.0426319	−	0.0586778i
$872$	8.04018	−	2.61241i	0.272275	−	0.0884675i
$873$	48.7404	−	29.3901i	1.64961	−	0.994705i
$874$		−	3.97296i		−	0.134387i
$875$	−1.79744	+	0.584024i	−0.0607646	+	0.0197436i
$876$	0.336228	−	7.84175i	0.0113601	−	0.264948i
$877$	−1.39984	+	4.30826i	−0.0472692	+	0.145480i	−0.971905	−	0.235372i	$-0.924369\pi$
$877$	−1.39984	+	4.30826i	−0.0472692	+	0.145480i	0.924636	+	0.380852i	$0.124369\pi$
$878$	−12.7186	+	17.5056i	−0.429231	+	0.590786i
$879$	6.66500	+	10.0526i	0.224805	+	0.339066i
$880$	−0.907664	+	1.24929i	−0.0305973	+	0.0421136i
$881$	41.6810	−	30.2830i	1.40427	−	1.02026i	0.410142	−	0.912022i	$-0.365479\pi$
$881$	41.6810	−	30.2830i	1.40427	−	1.02026i	0.994125	−	0.108238i	$-0.0345209\pi$
$882$	−10.0171	+	2.32917i	−0.337295	+	0.0784271i
$883$	−2.68768	−	3.69927i	−0.0904476	−	0.124490i	0.761395	−	0.648288i	$-0.224515\pi$
$883$	−2.68768	−	3.69927i	−0.0904476	−	0.124490i	−0.851843	+	0.523798i	$0.824515\pi$
$884$	0.733970	+	1.01022i	0.0246861	+	0.0339775i
$885$	1.28880	+	0.0552595i	0.0433225	+	0.00185753i
$886$	−17.6036	+	12.7898i	−0.591405	+	0.429681i
$887$	14.7085	−	20.2445i	0.493862	−	0.679743i	−0.487232	−	0.873273i	$-0.661993\pi$
$887$	14.7085	−	20.2445i	0.493862	−	0.679743i	0.981095	+	0.193529i	$0.0619934\pi$
$888$	−8.30293	+	5.50494i	−0.278628	+	0.184734i
$889$	−16.1464	+	22.2237i	−0.541535	+	0.745358i
$890$	−0.263336	+	0.810465i	−0.00882705	+	0.0271669i
$891$	−9.68554	−	9.96703i	−0.324478	−	0.333908i
$892$	4.62914	−	1.50410i	0.154995	−	0.0503610i
$893$			98.6962i			3.30274i
$894$	3.06037	+	11.0019i	0.102354	+	0.367958i
$895$	−14.7004	+	4.77645i	−0.491380	+	0.159659i
$896$	−1.11088	−	1.52899i	−0.0371119	−	0.0510801i
$897$	0.245780	+	0.0916741i	0.00820635	+	0.00306091i
$898$			15.7707i			0.526274i
$899$	25.7126	+	7.92105i	0.857564	+	0.264182i
$900$	−2.56908	+	1.54914i	−0.0856360	+	0.0516379i
$901$	36.3405	+	26.4030i	1.21068	+	0.879610i
$902$	−11.2269	+	8.15683i	−0.373815	+	0.271593i
$903$	−10.1432	−	15.2987i	−0.337546	−	0.509110i
$904$	−9.98313			−0.332034
$905$	−20.0565			−0.666701
$906$	−4.60082	+	3.05040i	−0.152852	+	0.101343i
$907$	−9.94088	+	30.5949i	−0.330081	+	1.01589i	0.639013	+	0.769196i	$0.279343\pi$
$907$	−9.94088	+	30.5949i	−0.330081	+	1.01589i	−0.969094	+	0.246690i	$0.920657\pi$
$908$	−27.1679	−	8.82739i	−0.901599	−	0.292947i
$909$	2.66460	−	31.0157i	0.0883793	−	1.02873i
$910$	0.581186	−	0.188839i	0.0192661	−	0.00625994i
$911$	6.05156	+	4.39672i	0.200497	+	0.145670i	0.683504	−	0.729947i	$-0.260455\pi$
$911$	6.05156	+	4.39672i	0.200497	+	0.145670i	−0.483007	+	0.875617i	$0.660455\pi$
$912$	−11.5048	−	9.13662i	−0.380961	−	0.302544i
$913$	3.36529	−	10.3573i	0.111375	−	0.342777i
$914$	19.1844	−	13.9382i	0.634562	−	0.461036i
$915$	−1.07216	−	0.851464i	−0.0354445	−	0.0281485i
$916$	−21.7092	−	7.05376i	−0.717294	−	0.233063i
$917$	−2.07866	−	2.86103i	−0.0686435	−	0.0944797i
$918$	−19.7223	+	3.70324i	−0.650932	+	0.122225i
$919$	−11.0955	−	34.1483i	−0.366006	−	1.12645i	−0.949349	−	0.314224i	$-0.898256\pi$
$919$	−11.0955	−	34.1483i	−0.366006	−	1.12645i	0.583343	−	0.812226i	$-0.301744\pi$
$920$	0.378938	+	0.275315i	0.0124932	+	0.00907686i
$921$	−9.21926	−	0.395291i	−0.303785	−	0.0130253i
$922$	−18.8832	−	6.13552i	−0.621885	−	0.202063i
$923$	0.996959	+	3.06833i	0.0328153	+	0.100995i
$924$	1.35468	+	4.87003i	0.0445658	+	0.160212i
$925$		−	5.75161i		−	0.189112i
$926$	−4.60779	−	14.1813i	−0.151421	−	0.466027i
$927$	14.1995	−	33.5980i	0.466372	−	1.10350i
$928$	−2.84035	+	3.90941i	−0.0932391	+	0.128333i
$929$	−20.5706			−0.674898			−0.337449	−	0.941344i	$-0.609564\pi$
$929$	−20.5706			−0.674898			−0.337449	+	0.941344i	$0.609564\pi$
$930$	−5.45152	−	7.95493i	−0.178762	−	0.260853i
$931$	29.0777			0.952982
$932$	−14.2494	+	19.6126i	−0.466755	+	0.642433i
$933$	23.2013	−	29.2149i	0.759576	−	0.956454i
$934$	0.967843	+	2.97871i	0.0316688	+	0.0974665i
$935$		−	5.96356i		−	0.195029i
$936$	0.830688	−	0.500899i	0.0271519	−	0.0163724i
$937$	9.52918	+	29.3278i	0.311305	+	0.958097i	0.977249	+	0.212096i	$0.0680288\pi$
$937$	9.52918	+	29.3278i	0.311305	+	0.958097i	−0.665944	+	0.746001i	$0.731971\pi$
$938$	−11.8993	−	3.86630i	−0.388524	−	0.126239i
$939$	0.606782	−	14.1518i	0.0198016	−	0.461826i
$940$	−9.41358	−	6.83937i	−0.307037	−	0.223076i
$941$	−1.16977	−	3.60018i	−0.0381334	−	0.117362i	0.930178	−	0.367109i	$-0.119653\pi$
$941$	−1.16977	−	3.60018i	−0.0381334	−	0.117362i	−0.968311	+	0.249747i	$0.919653\pi$
$942$	−11.0728	−	4.13008i	−0.360771	−	0.134565i
$943$	2.47415	+	3.40537i	0.0805694	+	0.110894i
$944$	−0.708321	−	0.230147i	−0.0230539	−	0.00749066i
$945$	−1.25895	+	9.73939i	−0.0409538	+	0.316822i
$946$	7.00534	−	5.08968i	0.227763	−	0.165480i
$947$	−8.56130	+	26.3490i	−0.278205	+	0.856226i	0.710149	+	0.704052i	$0.248628\pi$
$947$	−8.56130	+	26.3490i	−0.278205	+	0.856226i	−0.988354	+	0.152175i	$0.951372\pi$
$948$	10.0873	−	12.7019i	0.327621	−	0.412538i
$949$	−1.18541	−	0.861252i	−0.0384801	−	0.0279574i
$950$	8.06695	−	2.62111i	0.261726	−	0.0850401i
$951$	2.51709	+	0.938856i	0.0816222	+	0.0304445i
$952$	6.94151	+	2.25543i	0.224976	+	0.0730990i
$953$	−4.89676	+	15.0707i	−0.158622	+	0.488187i	−0.998510	−	0.0545721i	$-0.982621\pi$
$953$	−4.89676	+	15.0707i	−0.158622	+	0.488187i	0.839888	+	0.542760i	$0.182621\pi$
$954$	22.8515	−	26.3709i	0.739845	−	0.853791i
$955$	−1.75055			−0.0566466
$956$	10.5586			0.341488
$957$	10.7721	−	7.14205i	0.348214	−	0.230870i
$958$	5.09512	−	3.70182i	0.164616	−	0.119600i
$959$	10.8068	+	7.85156i	0.348968	+	0.253540i
$960$	1.66869	−	0.464177i	0.0538569	−	0.0149812i
$961$	24.5094	−	18.9813i	0.790626	−	0.612300i
$962$			1.85973i			0.0599601i
$963$	−1.57203	+	18.2982i	−0.0506578	+	0.589652i
$964$	−0.732162	−	1.00773i	−0.0235813	−	0.0324569i
$965$	6.29986	−	2.04695i	0.202800	−	0.0658936i
$966$	1.47719	−	0.410906i	0.0475277	−	0.0132207i
$967$		−	27.8186i		−	0.894586i	−0.894387	−	0.447293i	$-0.852388\pi$
$967$		−	27.8186i		−	0.894586i	0.894387	−	0.447293i	$-0.147612\pi$
$968$	8.19375	−	2.66231i	0.263357	−	0.0855699i
$969$	56.6845	+	2.43044i	1.82097	+	0.0780771i
$970$	5.86265	−	18.0434i	0.188238	−	0.579338i
$971$	−15.0980	+	20.7806i	−0.484519	+	0.666883i	−0.979365	−	0.202098i	$-0.935224\pi$
$971$	−15.0980	+	20.7806i	−0.484519	+	0.666883i	0.494847	+	0.868980i	$0.335224\pi$
$972$	1.55481	+	15.5107i	0.0498705	+	0.497507i
$973$	13.9825	−	19.2452i	0.448257	−	0.616973i
$974$	−31.9723	+	23.2292i	−1.02446	+	0.744313i
$975$	−0.0239907	+	0.559528i	−0.000768318	+	0.0179192i
$976$	0.464625	+	0.639501i	0.0148723	+	0.0204699i
$977$	−7.73502	−	10.6463i	−0.247465	−	0.340607i	0.667156	−	0.744918i	$-0.267511\pi$
$977$	−7.73502	−	10.6463i	−0.247465	−	0.340607i	−0.914622	+	0.404311i	$0.867511\pi$
$978$	−1.34568	+	31.3848i	−0.0430299	+	1.00357i
$979$	−1.06461	+	0.773487i	−0.0340252	+	0.0247208i
$980$	−2.01500	+	2.77341i	−0.0643668	+	0.0885933i
$981$	19.1668	+	16.6089i	0.611950	+	0.530281i
$982$	−10.3369	+	14.2275i	−0.329863	+	0.454018i
$983$	11.1777	−	34.4015i	0.356514	−	1.09724i	−0.598612	−	0.801039i	$-0.704281\pi$
$983$	11.1777	−	34.4015i	0.356514	−	1.09724i	0.955126	−	0.296199i	$-0.0957193\pi$
$984$	15.5510	+	0.666775i	0.495748	+	0.0212560i
$985$	11.9147	−	3.87131i	0.379633	−	0.123350i
$986$		−	18.6618i		−	0.594312i
$987$	−36.6963	+	10.2077i	−1.16806	+	0.324916i
$988$	−2.60837	+	0.847512i	−0.0829834	+	0.0269629i
$989$	−1.54381	−	2.12488i	−0.0490904	−	0.0675672i
$990$	−4.61563	−	0.396535i	−0.146694	−	0.0126027i
$991$		−	13.7121i		−	0.435580i	−0.975996	−	0.217790i	$-0.930115\pi$
$991$		−	13.7121i		−	0.435580i	0.975996	−	0.217790i	$-0.0698849\pi$
$992$	1.80147	+	5.26827i	0.0571968	+	0.167268i
$993$	−42.8553	+	11.9210i	−1.35997	+	0.378300i
$994$	15.2560	+	11.0841i	0.483891	+	0.351567i
$995$	−7.07696	+	5.14171i	−0.224355	+	0.163003i
$996$	−10.1807	+	6.74990i	−0.322587	+	0.213879i
$997$	18.9253			0.599370			0.299685	−	0.954038i	$-0.403118\pi$
$997$	18.9253			0.599370			0.299685	+	0.954038i	$0.403118\pi$
$998$	11.5509			0.365636
$999$	−27.0050	−	12.8030i	−0.854401	−	0.405068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.401.8	✓	80
3.2	odd	2	inner	930.2.v.a.401.18	yes	80
31.15	odd	10	inner	930.2.v.a.821.18	yes	80
93.77	even	10	inner	930.2.v.a.821.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.8	✓	80	1.1	even	1	trivial
930.2.v.a.401.18	yes	80	3.2	odd	2	inner
930.2.v.a.821.8	yes	80	93.77	even	10	inner
930.2.v.a.821.18	yes	80	31.15	odd	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(1.35636 + 1.07717i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.679429 + 2.92205i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(1.35636 + 1.07717i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(-1.66869 + 0.464177i) q^{6} +(0.584024 + 1.79744i) q^{7} +(0.951057 + 0.309017i) q^{8} +(0.679429 + 2.92205i) q^{9} +(0.809017 + 0.587785i) q^{10} +(0.477187 + 1.46863i) q^{11} +(0.605307 - 1.62284i) q^{12} +(-0.190055 - 0.261588i) q^{13} +(-1.79744 - 0.584024i) q^{14} +(1.07717 - 1.35636i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.19339 - 3.67287i) q^{17} +(-2.76335 - 1.16787i) q^{18} +(6.86216 + 4.98565i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(-1.14399 + 3.06707i) q^{21} +(-1.46863 - 0.477187i) q^{22} +(-0.144742 + 0.445469i) q^{23} +(0.957113 + 1.44358i) q^{24} -1.00000 q^{25} +0.323341 q^{26} +(-2.22598 + 4.69521i) q^{27} +(1.52899 - 1.11088i) q^{28} +(-3.90941 - 2.84035i) q^{29} +(0.464177 + 1.66869i) q^{30} +(-5.26827 + 1.80147i) q^{31} -1.00000i q^{32} +(-0.934721 + 2.50600i) q^{33} +(2.26996 + 3.12433i) q^{34} +(1.79744 - 0.584024i) q^{35} +(2.56908 - 1.54914i) q^{36} +5.75161i q^{37} +(-8.06695 + 2.62111i) q^{38} +(0.0239907 - 0.559528i) q^{39} +(0.309017 - 0.951057i) q^{40} +(5.28220 - 7.27033i) q^{41} +(-1.80889 - 2.72829i) q^{42} +(-3.29598 + 4.53652i) q^{43} +(1.24929 - 0.907664i) q^{44} +(2.92205 - 0.679429i) q^{45} +(-0.275315 - 0.378938i) q^{46} +(6.83937 + 9.41358i) q^{47} +(-1.73046 - 0.0741964i) q^{48} +(2.77341 - 2.01500i) q^{49} +(0.587785 - 0.809017i) q^{50} +(5.57496 - 3.69626i) q^{51} +(-0.190055 + 0.261588i) q^{52} +(-3.59432 + 11.0622i) q^{53} +(-2.49011 - 4.56063i) q^{54} +(1.46863 - 0.477187i) q^{55} +1.88994i q^{56} +(3.93719 + 14.1540i) q^{57} +(4.59578 - 1.49326i) q^{58} +(0.437766 + 0.602534i) q^{59} +(-1.62284 - 0.605307i) q^{60} -0.790467i q^{61} +(1.63919 - 5.32100i) q^{62} +(-4.85541 + 2.92778i) q^{63} +(0.809017 + 0.587785i) q^{64} +(-0.261588 + 0.190055i) q^{65} +(-1.47798 - 2.22920i) q^{66} +6.62011 q^{67} -3.86189 q^{68} +(-0.676165 + 0.448306i) q^{69} +(-0.584024 + 1.79744i) q^{70} +(-9.48945 - 3.08331i) q^{71} +(-0.256788 + 2.98899i) q^{72} +(4.30980 - 1.40034i) q^{73} +(-4.65315 - 3.38071i) q^{74} +(-1.35636 - 1.07717i) q^{75} +(2.62111 - 8.06695i) q^{76} +(-2.36109 + 1.71543i) q^{77} +(0.438567 + 0.348291i) q^{78} +(8.90634 + 2.89384i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-8.07675 + 3.97065i) q^{81} +(2.77702 + 8.54678i) q^{82} +(-5.70547 - 4.14527i) q^{83} +(3.27047 + 0.140227i) q^{84} +(-3.67287 - 1.19339i) q^{85} +(-1.73280 - 5.33300i) q^{86} +(-2.24304 - 8.06362i) q^{87} +1.54421i q^{88} +(0.263336 + 0.810465i) q^{89} +(-1.16787 + 2.76335i) q^{90} +(0.359192 - 0.494386i) q^{91} +0.468393 q^{92} +(-9.08616 - 3.23136i) q^{93} -11.6358 q^{94} +(4.98565 - 6.86216i) q^{95} +(1.07717 - 1.35636i) q^{96} +(-5.86265 - 18.0434i) q^{97} +3.42812i q^{98} +(-3.96720 + 2.39220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more