LMFDB - Embedded newform 430.2.p.a.59.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(59,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([7, 8]))

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

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

chi := DirichletCharacter("430.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.p (of order $14$, degree $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			59.4
Character	$\chi$	$=$	430.59
Dual form			430.2.p.a.379.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.974928 + 0.222521i) q^{2} +(-1.09644 - 0.250255i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.67031 - 1.48663i) q^{5} +1.12463 q^{6} -4.66029i q^{7} +(-0.781831 + 0.623490i) q^{8} +(-1.56336 - 0.752874i) q^{9} +O(q^{10})$	\(q+(-0.974928 + 0.222521i) q^{2} +(-1.09644 - 0.250255i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.67031 - 1.48663i) q^{5} +1.12463 q^{6} -4.66029i q^{7} +(-0.781831 + 0.623490i) q^{8} +(-1.56336 - 0.752874i) q^{9} +(-1.29763 + 1.82103i) q^{10} +(3.30664 + 1.59239i) q^{11} +(-1.09644 + 0.250255i) q^{12} +(-3.70458 + 2.95430i) q^{13} +(1.03701 + 4.54344i) q^{14} +(-2.20343 + 1.21199i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-3.27785 - 2.61400i) q^{17} +(1.69169 + 0.386118i) q^{18} +(-3.34316 + 1.60998i) q^{19} +(0.859875 - 2.06413i) q^{20} +(-1.16626 + 5.10971i) q^{21} +(-3.57808 - 0.816673i) q^{22} +(0.205426 - 0.426571i) q^{23} +(1.01326 - 0.487961i) q^{24} +(0.579878 - 4.96626i) q^{25} +(2.95430 - 3.70458i) q^{26} +(4.16354 + 3.32031i) q^{27} +(-2.02202 - 4.19877i) q^{28} +(-0.965991 - 4.23228i) q^{29} +(1.87849 - 1.67191i) q^{30} +(-0.621012 - 2.72083i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(-3.22702 - 2.57346i) q^{33} +(3.77733 + 1.81907i) q^{34} +(-6.92811 - 7.78413i) q^{35} -1.73520 q^{36} +10.0336i q^{37} +(2.90109 - 2.31354i) q^{38} +(4.80116 - 2.31212i) q^{39} +(-0.379005 + 2.20371i) q^{40} +(-1.50842 - 6.60882i) q^{41} -5.24112i q^{42} +(4.60568 - 4.66773i) q^{43} +3.67009 q^{44} +(-3.73054 + 1.06660i) q^{45} +(-0.105354 + 0.461587i) q^{46} +(-3.20149 - 6.64796i) q^{47} +(-0.879275 + 0.701198i) q^{48} -14.7183 q^{49} +(0.539758 + 4.97078i) q^{50} +(2.93979 + 3.68638i) q^{51} +(-2.05589 + 4.26909i) q^{52} +(-10.4387 - 8.32456i) q^{53} +(-4.79799 - 2.31059i) q^{54} +(7.89041 - 2.25595i) q^{55} +(2.90564 + 3.64356i) q^{56} +(4.06848 - 0.928603i) q^{57} +(1.88354 + 3.91122i) q^{58} +(-1.38983 + 1.74279i) q^{59} +(-1.45936 + 2.04800i) q^{60} +(0.518436 - 2.27141i) q^{61} +(1.21088 + 2.51442i) q^{62} +(-3.50861 + 7.28570i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-1.79585 + 10.4419i) q^{65} +(3.71876 + 1.79086i) q^{66} +(6.09321 + 12.6527i) q^{67} +(-4.08741 - 0.932924i) q^{68} +(-0.331988 + 0.416300i) q^{69} +(8.48654 + 6.04732i) q^{70} +(6.88074 - 3.31359i) q^{71} +(1.69169 - 0.386118i) q^{72} +(7.18714 - 5.73156i) q^{73} +(-2.23269 - 9.78204i) q^{74} +(-1.87863 + 5.30008i) q^{75} +(-2.31354 + 2.90109i) q^{76} +(7.42101 - 15.4099i) q^{77} +(-4.16629 + 3.32251i) q^{78} +14.4713 q^{79} +(-0.120870 - 2.23280i) q^{80} +(-0.488503 - 0.612564i) q^{81} +(2.94120 + 6.10747i) q^{82} +(10.1800 + 2.32351i) q^{83} +(1.16626 + 5.10971i) q^{84} +(-9.36106 + 0.506751i) q^{85} +(-3.45154 + 5.57556i) q^{86} +4.88218i q^{87} +(-3.57808 + 0.816673i) q^{88} +(-0.917942 + 4.02177i) q^{89} +(3.39967 - 1.86998i) q^{90} +(13.7679 + 17.2644i) q^{91} -0.473458i q^{92} +3.13863i q^{93} +(4.60053 + 5.76888i) q^{94} +(-3.19068 + 7.65921i) q^{95} +(0.701198 - 0.879275i) q^{96} +(-6.53900 + 13.5784i) q^{97} +(14.3493 - 3.27513i) q^{98} +(-3.97059 - 4.97897i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	$ 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) $ 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$-1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$2$	−0.974928	+	0.222521i	−0.689378	+	0.157346i
$3$	−1.09644	−	0.250255i	−0.633029	−	0.144485i	−0.106047	−	0.994361i	$-0.533819\pi$
$3$	−1.09644	−	0.250255i	−0.633029	−	0.144485i	−0.526982	+	0.849877i	$0.676676\pi$
$4$	0.900969	−	0.433884i	0.450484	−	0.216942i
$5$	1.67031	−	1.48663i	0.746986	−	0.664840i
$5$	1.67031	−	1.48663i	0.746986	−	0.664840i
$6$	1.12463			0.459130
$7$		−	4.66029i		−	1.76142i	−0.473653	−	0.880712i	$-0.657065\pi$
$7$		−	4.66029i		−	1.76142i	0.473653	−	0.880712i	$-0.342935\pi$
$8$	−0.781831	+	0.623490i	−0.276419	+	0.220437i
$9$	−1.56336	−	0.752874i	−0.521120	−	0.250958i
$10$	−1.29763	+	1.82103i	−0.410346	+	0.575861i
$11$	3.30664	+	1.59239i	0.996989	+	0.480125i	0.859916	−	0.510436i	$-0.170516\pi$
$11$	3.30664	+	1.59239i	0.996989	+	0.480125i	0.137074	+	0.990561i	$0.456230\pi$
$12$	−1.09644	+	0.250255i	−0.316514	+	0.0722423i
$13$	−3.70458	+	2.95430i	−1.02746	+	0.819376i	−0.983727	−	0.179667i	$-0.942498\pi$
$13$	−3.70458	+	2.95430i	−1.02746	+	0.819376i	−0.0437373	+	0.999043i	$0.513926\pi$
$14$	1.03701	+	4.54344i	0.277153	+	1.21429i
$15$	−2.20343	+	1.21199i	−0.568922	+	0.312935i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	−3.27785	−	2.61400i	−0.794995	−	0.633987i	0.139396	−	0.990237i	$-0.455484\pi$
$17$	−3.27785	−	2.61400i	−0.794995	−	0.633987i	−0.934391	+	0.356250i	$0.884055\pi$
$18$	1.69169	+	0.386118i	0.398736	+	0.0910088i
$19$	−3.34316	+	1.60998i	−0.766974	+	0.369355i	−0.776106	−	0.630603i	$-0.782808\pi$
$19$	−3.34316	+	1.60998i	−0.766974	+	0.369355i	0.00913131	+	0.999958i	$0.497093\pi$
$20$	0.859875	−	2.06413i	0.192274	−	0.461553i
$21$	−1.16626	+	5.10971i	−0.254499	+	1.11503i
$22$	−3.57808	−	0.816673i	−0.762848	−	0.174115i
$23$	0.205426	−	0.426571i	0.0428342	−	0.0889462i	−0.878453	−	0.477828i	$-0.841424\pi$
$23$	0.205426	−	0.426571i	0.0428342	−	0.0889462i	0.921288	+	0.388882i	$0.127139\pi$
$24$	1.01326	−	0.487961i	0.206831	−	0.0996045i
$25$	0.579878	−	4.96626i	0.115976	−	0.993252i
$26$	2.95430	−	3.70458i	0.579386	−	0.726527i
$27$	4.16354	+	3.32031i	0.801273	+	0.638994i
$28$	−2.02202	−	4.19877i	−0.382126	−	0.793494i
$29$	−0.965991	−	4.23228i	−0.179380	−	0.785916i	−0.981917	−	0.189313i	$-0.939374\pi$
$29$	−0.965991	−	4.23228i	−0.179380	−	0.785916i	0.802537	−	0.596603i	$-0.203483\pi$
$30$	1.87849	−	1.67191i	0.342964	−	0.305248i
$31$	−0.621012	−	2.72083i	−0.111537	−	0.488675i	−0.999582	−	0.0289185i	$-0.990794\pi$
$31$	−0.621012	−	2.72083i	−0.111537	−	0.488675i	0.888045	−	0.459757i	$-0.152063\pi$
$32$	−0.433884	+	0.900969i	−0.0767005	+	0.159270i
$33$	−3.22702	−	2.57346i	−0.561752	−	0.447982i
$34$	3.77733	+	1.81907i	0.647807	+	0.311968i
$35$	−6.92811	−	7.78413i	−1.17106	−	1.31576i
$36$	−1.73520			−0.289200
$37$			10.0336i			1.64951i	0.565487	+	0.824757i	$0.308688\pi$
$37$			10.0336i			1.64951i	−0.565487	+	0.824757i	$0.691312\pi$
$38$	2.90109	−	2.31354i	0.470619	−	0.375306i
$39$	4.80116	−	2.31212i	0.768802	−	0.370235i
$40$	−0.379005	+	2.20371i	−0.0599259	+	0.348438i
$41$	−1.50842	−	6.60882i	−0.235576	−	1.03212i	−0.944930	−	0.327272i	$-0.893871\pi$
$41$	−1.50842	−	6.60882i	−0.235576	−	1.03212i	0.709354	−	0.704852i	$-0.248987\pi$
$42$		−	5.24112i		−	0.808722i
$43$	4.60568	−	4.66773i	0.702360	−	0.711822i
$43$	4.60568	−	4.66773i	0.702360	−	0.711822i
$44$	3.67009			0.553287
$45$	−3.73054	+	1.06660i	−0.556116	+	0.158999i
$46$	−0.105354	+	0.461587i	−0.0155336	+	0.0680574i
$47$	−3.20149	−	6.64796i	−0.466985	−	0.969705i	−0.992876	−	0.119153i	$-0.961982\pi$
$47$	−3.20149	−	6.64796i	−0.466985	−	0.969705i	0.525891	−	0.850552i	$-0.323732\pi$
$48$	−0.879275	+	0.701198i	−0.126912	+	0.101209i
$49$	−14.7183			−2.10261
$50$	0.539758	+	4.97078i	0.0763333	+	0.702975i
$51$	2.93979	+	3.68638i	0.411653	+	0.516197i
$52$	−2.05589	+	4.26909i	−0.285100	+	0.592016i
$53$	−10.4387	−	8.32456i	−1.43386	−	1.14347i	−0.965649	−	0.259851i	$-0.916327\pi$
$53$	−10.4387	−	8.32456i	−1.43386	−	1.14347i	−0.468213	−	0.883616i	$-0.655102\pi$
$54$	−4.79799	−	2.31059i	−0.652924	−	0.314431i
$55$	7.89041	−	2.25595i	1.06394	−	0.304192i
$56$	2.90564	+	3.64356i	0.388283	+	0.486891i
$57$	4.06848	−	0.928603i	0.538883	−	0.122996i
$58$	1.88354	+	3.91122i	0.247321	+	0.513568i
$59$	−1.38983	+	1.74279i	−0.180940	+	0.226891i	−0.864027	−	0.503445i	$-0.832065\pi$
$59$	−1.38983	+	1.74279i	−0.180940	+	0.226891i	0.683087	+	0.730337i	$0.260637\pi$
$60$	−1.45936	+	2.04800i	−0.188402	+	0.264395i
$61$	0.518436	−	2.27141i	0.0663789	−	0.290825i	−0.930833	−	0.365444i	$-0.880917\pi$
$61$	0.518436	−	2.27141i	0.0663789	−	0.290825i	0.997212	+	0.0746194i	$0.0237742\pi$
$62$	1.21088	+	2.51442i	0.153782	+	0.319332i
$63$	−3.50861	+	7.28570i	−0.442043	+	0.917912i
$64$	0.222521	−	0.974928i	0.0278151	−	0.121866i
$65$	−1.79585	+	10.4419i	−0.222748	+	1.29516i
$66$	3.71876	+	1.79086i	0.457748	+	0.220440i
$67$	6.09321	+	12.6527i	0.744404	+	1.54577i	0.835228	+	0.549903i	$0.185336\pi$
$67$	6.09321	+	12.6527i	0.744404	+	1.54577i	−0.0908244	+	0.995867i	$0.528950\pi$
$68$	−4.08741	−	0.932924i	−0.495671	−	0.113134i
$69$	−0.331988	+	0.416300i	−0.0399666	+	0.0501166i
$70$	8.48654	+	6.04732i	1.01434	+	0.722792i
$71$	6.88074	−	3.31359i	0.816594	−	0.393251i	0.0215236	−	0.999768i	$-0.493148\pi$
$71$	6.88074	−	3.31359i	0.816594	−	0.393251i	0.795070	+	0.606518i	$0.207434\pi$
$72$	1.69169	−	0.386118i	0.199368	−	0.0455044i
$73$	7.18714	−	5.73156i	0.841192	−	0.670828i	−0.104987	−	0.994474i	$-0.533480\pi$
$73$	7.18714	−	5.73156i	0.841192	−	0.670828i	0.946178	+	0.323646i	$0.104909\pi$
$74$	−2.23269	−	9.78204i	−0.259545	−	1.13714i
$75$	−1.87863	+	5.30008i	−0.216925	+	0.612000i
$76$	−2.31354	+	2.90109i	−0.265381	+	0.332778i
$77$	7.42101	−	15.4099i	0.845703	−	1.75612i
$78$	−4.16629	+	3.32251i	−0.471740	+	0.376200i
$79$	14.4713			1.62815			0.814076	−	0.580758i	$-0.197244\pi$
$79$	14.4713			1.62815			0.814076	+	0.580758i	$0.197244\pi$
$80$	−0.120870	−	2.23280i	−0.0135137	−	0.249634i
$81$	−0.488503	−	0.612564i	−0.0542781	−	0.0680626i
$82$	2.94120	+	6.10747i	0.324801	+	0.674457i
$83$	10.1800	+	2.32351i	1.11740	+	0.255039i	0.741057	−	0.671443i	$-0.234325\pi$
$83$	10.1800	+	2.32351i	1.11740	+	0.255039i	0.376341	+	0.926481i	$0.377182\pi$
$84$	1.16626	+	5.10971i	0.127249	+	0.557516i
$85$	−9.36106	+	0.506751i	−1.01535	+	0.0549649i
$86$	−3.45154	+	5.57556i	−0.372189	+	0.601228i
$87$			4.88218i			0.523425i
$88$	−3.57808	+	0.816673i	−0.381424	+	0.0870576i
$89$	−0.917942	+	4.02177i	−0.0973016	+	0.426306i	−0.999992	−	0.00398429i	$-0.998732\pi$
$89$	−0.917942	+	4.02177i	−0.0973016	+	0.426306i	0.902690	+	0.430291i	$0.141589\pi$
$90$	3.39967	−	1.86998i	0.358356	−	0.197113i
$91$	13.7679	+	17.2644i	1.44327	+	1.80980i
$92$		−	0.473458i		−	0.0493614i
$93$			3.13863i			0.325461i
$94$	4.60053	+	5.76888i	0.474509	+	0.595015i
$95$	−3.19068	+	7.65921i	−0.327357	+	0.785818i
$96$	0.701198	−	0.879275i	0.0715657	−	0.0897406i
$97$	−6.53900	+	13.5784i	−0.663935	+	1.37868i	0.248169	+	0.968717i	$0.420171\pi$
$97$	−6.53900	+	13.5784i	−0.663935	+	1.37868i	−0.912104	+	0.409959i	$0.865543\pi$
$98$	14.3493	−	3.27513i	1.44949	−	0.330838i
$99$	−3.97059	−	4.97897i	−0.399060	−	0.500405i
$100$	−1.63233	−	4.72605i	−0.163233	−	0.472605i
$101$	8.88223	−	4.27746i	0.883815	−	0.425623i	0.0637986	−	0.997963i	$-0.479678\pi$
$101$	8.88223	−	4.27746i	0.883815	−	0.425623i	0.820017	+	0.572340i	$0.193964\pi$
$102$	−3.68638	−	2.93979i	−0.365006	−	0.291083i
$103$	−11.5948	−	9.24657i	−1.14247	−	0.911092i	−0.145540	−	0.989352i	$-0.546492\pi$
$103$	−11.5948	−	9.24657i	−1.14247	−	0.911092i	−0.996933	+	0.0782605i	$0.975063\pi$
$104$	1.05438	−	4.61953i	0.103390	−	0.452982i
$105$	5.64823	+	10.2686i	0.551210	+	1.00211i
$106$	12.0293	+	5.79303i	1.16839	+	0.562668i
$107$	−6.98889	−	1.59517i	−0.675642	−	0.154211i	−0.129086	−	0.991633i	$-0.541204\pi$
$107$	−6.98889	−	1.59517i	−0.675642	−	0.154211i	−0.546556	+	0.837423i	$0.684061\pi$
$108$	5.19185	+	1.18501i	0.499586	+	0.114027i
$109$	−10.9143	−	5.25607i	−1.04540	−	0.503441i	−0.169302	−	0.985564i	$-0.554151\pi$
$109$	−10.9143	−	5.25607i	−1.04540	−	0.503441i	−0.876103	+	0.482124i	$0.839866\pi$
$110$	−7.19059	+	3.95517i	−0.685596	+	0.377111i
$111$	2.51096	−	11.0012i	0.238330	−	1.04419i
$112$	−3.64356	−	2.90564i	−0.344284	−	0.274557i
$113$	5.83640	+	4.65437i	0.549042	+	0.437847i	0.858312	−	0.513128i	$-0.171513\pi$
$113$	5.83640	+	4.65437i	0.549042	+	0.437847i	−0.309270	+	0.950974i	$0.600085\pi$
$114$	−3.75984	+	1.81064i	−0.352141	+	0.169582i
$115$	−0.291027	−	1.01790i	−0.0271384	−	0.0949194i
$116$	−2.70665	−	3.39403i	−0.251306	−	0.315128i
$117$	8.01580	−	1.82955i	0.741061	−	0.169142i
$118$	0.967173	−	2.00836i	0.0890355	−	0.184884i
$119$	−12.1820	+	15.2757i	−1.11672	+	1.40032i
$120$	0.967045	−	2.32139i	0.0882787	−	0.211913i
$121$	1.53976	+	1.93080i	0.139978	+	0.175527i
$122$			2.32983i			0.210933i
$123$			7.62365i			0.687401i
$124$	−1.74004	−	2.18194i	−0.156260	−	0.195944i
$125$	−6.41440	−	9.15726i	−0.573722	−	0.819050i
$126$	1.79942	−	7.88377i	0.160305	−	0.702342i
$127$	10.1118	−	2.30795i	0.897277	−	0.204798i	0.251078	−	0.967967i	$-0.419215\pi$
$127$	10.1118	−	2.30795i	0.897277	−	0.204798i	0.646199	+	0.763169i	$0.276358\pi$
$128$			1.00000i			0.0883883i
$129$	−6.21797	+	3.96528i	−0.547461	+	0.349123i
$130$	−0.572723	−	10.5797i	−0.0502311	−	0.927905i
$131$	−0.366520	−	1.60583i	−0.0320230	−	0.140302i	0.956389	−	0.292095i	$-0.0943524\pi$
$131$	−0.366520	−	1.60583i	−0.0320230	−	0.140302i	−0.988412	+	0.151793i	$0.951495\pi$
$132$	−4.02403	−	0.918458i	−0.350247	−	0.0799415i
$133$	7.50298	+	15.5801i	0.650591	+	1.35097i
$134$	−8.75592	−	10.9796i	−0.756397	−	0.948491i
$135$	11.8905	−	0.643678i	1.02337	−	0.0553990i
$136$	4.19252			0.359506
$137$	7.60122	−	6.06177i	0.649416	−	0.517892i	−0.242466	−	0.970160i	$-0.577956\pi$
$137$	7.60122	−	6.06177i	0.649416	−	0.517892i	0.891882	+	0.452268i	$0.149385\pi$
$138$	0.231029	−	0.479736i	0.0196665	−	0.0408379i
$139$	2.29107	−	2.87291i	0.194326	−	0.243677i	−0.675117	−	0.737711i	$-0.735907\pi$
$139$	2.29107	−	2.87291i	0.194326	−	0.243677i	0.869443	+	0.494034i	$0.164478\pi$
$140$	−9.61942	−	4.00726i	−0.812989	−	0.338676i
$141$	1.84655	+	8.09026i	0.155508	+	0.681323i
$142$	−5.97088	+	4.76162i	−0.501065	+	0.399586i
$143$	−16.9541	+	3.86967i	−1.41777	+	0.323598i
$144$	−1.56336	+	0.752874i	−0.130280	+	0.0627395i
$145$	−7.90534	−	5.63316i	−0.656502	−	0.467809i
$146$	−5.73156	+	7.18714i	−0.474347	+	0.594812i
$147$	16.1377	+	3.68332i	1.33101	+	0.303795i
$148$	4.35342	+	9.03997i	0.357849	+	0.743081i
$149$	−4.12188	−	1.98499i	−0.337677	−	0.162617i	0.257358	−	0.966316i	$-0.417148\pi$
$149$	−4.12188	−	1.98499i	−0.337677	−	0.162617i	−0.595036	+	0.803699i	$0.702862\pi$
$150$	0.652151	−	5.58523i	0.0532479	−	0.456032i
$151$	1.53098	−	6.70768i	0.124590	−	0.545863i	−0.873650	−	0.486555i	$-0.838253\pi$
$151$	1.53098	−	6.70768i	0.124590	−	0.545863i	0.998240	−	0.0593081i	$-0.0188894\pi$
$152$	1.60998	−	3.34316i	0.130587	−	0.271166i
$153$	3.15644	+	6.55442i	0.255183	+	0.529893i
$154$	−3.80593	+	16.6749i	−0.306691	+	1.34370i
$155$	−5.08214	−	3.62142i	−0.408207	−	0.290879i
$156$	3.32251	−	4.16629i	0.266014	−	0.333571i
$157$	2.82021	+	5.85623i	0.225077	+	0.467378i	0.982673	−	0.185346i	$-0.0593405\pi$
$157$	2.82021	+	5.85623i	0.225077	+	0.467378i	−0.757596	+	0.652724i	$0.773626\pi$
$158$	−14.1085	+	3.22017i	−1.12241	+	0.256183i
$159$	9.36209	+	11.7397i	0.742462	+	0.931018i
$160$	0.614684	+	2.14992i	0.0485951	+	0.169966i
$161$	−1.98794	−	0.957343i	−0.156672	−	0.0754492i
$162$	0.612564	+	0.488503i	0.0481275	+	0.0383804i
$163$	1.33839	−	2.77919i	0.104831	−	0.217683i	−0.841955	−	0.539548i	$-0.818595\pi$
$163$	1.33839	−	2.77919i	0.104831	−	0.217683i	0.946786	+	0.321864i	$0.104310\pi$
$164$	−4.22650	−	5.29986i	−0.330034	−	0.413850i
$165$	−9.21591	+	0.498894i	−0.717457	+	0.0388388i
$166$	−10.4418			−0.810439
$167$	11.3293	−	9.03481i	0.876687	−	0.699135i	−0.0779337	−	0.996959i	$-0.524832\pi$
$167$	11.3293	−	9.03481i	0.876687	−	0.699135i	0.954621	+	0.297824i	$0.0962608\pi$
$168$	−2.27404	−	4.72209i	−0.175446	−	0.364317i
$169$	2.10322	−	9.21481i	0.161786	−	0.708832i
$170$	9.01360	−	2.57708i	0.691312	−	0.197653i
$171$	6.43868			0.492378
$172$	2.12433	−	6.20381i	0.161978	−	0.473036i
$173$		−	13.2844i		−	1.01000i	−0.863121	−	0.504998i	$-0.831493\pi$
$173$		−	13.2844i		−	1.01000i	0.863121	−	0.504998i	$-0.168507\pi$
$174$	−1.08639	−	4.75977i	−0.0823588	−	0.360837i
$175$	−23.1442	−	2.70240i	−1.74954	−	0.204282i
$176$	3.30664	−	1.59239i	0.249247	−	0.120031i
$177$	1.96000	−	1.56305i	0.147322	−	0.117486i
$178$		−	4.12519i		−	0.309196i
$179$	14.9612			1.11826			0.559128	−	0.829081i	$-0.311136\pi$
$179$	14.9612			1.11826			0.559128	+	0.829081i	$0.311136\pi$
$180$	−2.89832	+	2.57959i	−0.216028	+	0.192271i
$181$	12.5316	+	6.03492i	0.931470	+	0.448572i	0.837152	−	0.546970i	$-0.184219\pi$
$181$	12.5316	+	6.03492i	0.931470	+	0.448572i	0.0943177	+	0.995542i	$0.469933\pi$
$182$	−17.2644	−	13.7679i	−1.27972	−	1.02054i
$183$	−1.13686	+	2.36072i	−0.0840394	+	0.174510i
$184$	0.105354	+	0.461587i	0.00776682	+	0.0340287i
$185$	14.9162	+	16.7592i	1.09666	+	1.23216i
$186$	−0.698411	−	3.05994i	−0.0512100	−	0.224366i
$187$	−6.67615	−	13.8632i	−0.488208	−	1.01378i
$188$	−5.76888	−	4.60053i	−0.420739	−	0.335528i
$189$	15.4736	−	19.4033i	1.12554	−	1.41138i
$190$	1.40635	−	8.17717i	0.102027	−	0.593234i
$191$	−4.75455	+	2.28967i	−0.344027	+	0.165675i	−0.597916	−	0.801559i	$-0.704005\pi$
$191$	−4.75455	+	2.28967i	−0.344027	+	0.165675i	0.253889	+	0.967233i	$0.418290\pi$
$192$	−0.487961	+	1.01326i	−0.0352155	+	0.0731258i
$193$	15.0047	+	3.42473i	1.08006	+	0.246517i	0.725296	−	0.688437i	$-0.241703\pi$
$193$	15.0047	+	3.42473i	1.08006	+	0.246517i	0.354767	+	0.934955i	$0.384560\pi$
$194$	3.35358	−	14.6930i	0.240773	−	1.05490i
$195$	4.58218	−	10.9995i	0.328137	−	0.787691i
$196$	−13.2607	+	6.38602i	−0.947194	+	0.456144i
$197$	1.97361	+	0.450465i	0.140614	+	0.0320943i	0.292249	−	0.956342i	$-0.405597\pi$
$197$	1.97361	+	0.450465i	0.140614	+	0.0320943i	−0.151634	+	0.988437i	$0.548454\pi$
$198$	4.97897	+	3.97059i	0.353840	+	0.282178i
$199$	−11.8881	+	14.9072i	−0.842724	+	1.05674i	0.154905	+	0.987929i	$0.450493\pi$
$199$	−11.8881	+	14.9072i	−0.842724	+	1.05674i	−0.997630	+	0.0688134i	$0.978079\pi$
$200$	2.64305	+	4.24433i	0.186892	+	0.300119i
$201$	−3.51443	−	15.3977i	−0.247889	−	1.08607i
$202$	−7.70771	+	6.14670i	−0.542313	+	0.432480i
$203$	−19.7237	+	4.50180i	−1.38433	+	0.315964i
$204$	4.24812	+	2.04579i	0.297428	+	0.143234i
$205$	−12.3444	−	8.79633i	−0.862169	−	0.614362i
$206$	13.3617	+	6.43465i	0.930953	+	0.448323i
$207$	−0.642308	+	0.512224i	−0.0446435	+	0.0356020i
$208$			4.73833i			0.328544i
$209$	−13.6184			−0.942002
$210$	−7.79159	−	8.75430i	−0.537671	−	0.604104i
$211$	2.14010	−	1.03062i	0.147331	−	0.0709507i	−0.358766	−	0.933428i	$-0.616802\pi$
$211$	2.14010	−	1.03062i	0.147331	−	0.0709507i	0.506096	+	0.862477i	$0.331088\pi$
$212$	−13.0168	−	2.97100i	−0.893998	−	0.204049i
$213$	−8.37354	+	1.91121i	−0.573746	+	0.130954i
$214$	7.16862			0.490037
$215$	0.753753	−	14.6435i	0.0514055	−	0.998678i
$216$	−5.32537			−0.362345
$217$	−12.6798	+	2.89409i	−0.860764	+	0.196464i
$218$	11.8103	+	2.69562i	0.799894	+	0.182571i
$219$	−9.31460	+	4.48568i	−0.629423	+	0.303114i
$220$	6.13020	−	5.45606i	0.413298	−	0.367848i
$221$	19.8656			1.33630
$222$			11.2841i			0.757342i
$223$	−4.33508	+	3.45711i	−0.290299	+	0.231505i	−0.757800	−	0.652487i	$-0.773726\pi$
$223$	−4.33508	+	3.45711i	−0.290299	+	0.231505i	0.467501	+	0.883992i	$0.345154\pi$
$224$	4.19877	+	2.02202i	0.280542	+	0.135102i
$225$	−4.64552	+	7.32747i	−0.309702	+	0.488498i
$226$	−6.72576	−	3.23896i	−0.447391	−	0.215452i
$227$	8.86651	−	2.02372i	0.588491	−	0.134319i	0.0821013	−	0.996624i	$-0.473837\pi$
$227$	8.86651	−	2.02372i	0.588491	−	0.134319i	0.506390	+	0.862305i	$0.330980\pi$
$228$	3.26266	−	2.60189i	0.216075	−	0.172314i
$229$	−1.71315	−	7.50578i	−0.113208	−	0.495996i	−0.999462	−	0.0327967i	$-0.989559\pi$
$229$	−1.71315	−	7.50578i	−0.113208	−	0.495996i	0.886254	−	0.463199i	$-0.153299\pi$
$230$	0.510234	+	0.927617i	0.0336438	+	0.0611653i
$231$	−11.9931	+	15.0388i	−0.789086	+	0.989483i
$232$	3.39403	+	2.70665i	0.222829	+	0.177700i
$233$	17.4369	+	3.97985i	1.14233	+	0.260729i	0.751498	−	0.659735i	$-0.229331\pi$
$233$	17.4369	+	3.97985i	1.14233	+	0.260729i	0.390829	+	0.920463i	$0.372189\pi$
$234$	−7.40771	+	3.56737i	−0.484257	+	0.233206i
$235$	−15.2305	−	6.34474i	−0.993530	−	0.413885i
$236$	−0.496023	+	2.17322i	−0.0322884	+	0.141465i
$237$	−15.8669	−	3.62152i	−1.03067	−	0.235243i
$238$	8.47738	−	17.6035i	0.549507	−	1.14106i
$239$	14.9296	−	7.18971i	0.965714	−	0.465063i	0.116546	−	0.993185i	$-0.462818\pi$
$239$	14.9296	−	7.18971i	0.965714	−	0.465063i	0.849169	+	0.528122i	$0.177104\pi$
$240$	−0.426242	+	2.47837i	−0.0275138	+	0.159978i
$241$	−15.1171	+	18.9562i	−0.973775	+	1.22108i	0.00148088	+	0.999999i	$0.499529\pi$
$241$	−15.1171	+	18.9562i	−0.973775	+	1.22108i	−0.975256	+	0.221077i	$0.929043\pi$
$242$	−1.93080	−	1.53976i	−0.124117	−	0.0989796i
$243$	−6.54945	−	13.6001i	−0.420148	−	0.872445i
$244$	−0.518436	−	2.27141i	−0.0331894	−	0.145412i
$245$	−24.5841	+	21.8806i	−1.57062	+	1.39790i
$246$	−1.69642	−	7.43251i	−0.108160	−	0.473879i
$247$	7.62863	−	15.8410i	0.485398	−	1.00794i
$248$	2.18194	+	1.74004i	0.138553	+	0.110492i
$249$	−10.5802	−	5.09517i	−0.670495	−	0.322893i
$250$	8.29126	+	7.50033i	0.524385	+	0.474363i
$251$	6.37579			0.402436			0.201218	−	0.979546i	$-0.435510\pi$
$251$	6.37579			0.402436			0.201218	+	0.979546i	$0.435510\pi$
$252$			8.08652i			0.509403i
$253$	1.35854	−	1.08340i	0.0854105	−	0.0681126i
$254$	−9.34470	+	4.50017i	−0.586339	+	0.282366i
$255$	10.3906	+	1.78703i	0.650687	+	0.111908i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$		−	13.2133i		−	0.824221i	−0.911134	−	0.412110i	$-0.864792\pi$
$257$		−	13.2133i		−	0.824221i	0.911134	−	0.412110i	$-0.135208\pi$
$258$	5.17971	−	5.24949i	0.322475	−	0.326819i
$259$	46.7595			2.90549
$260$	2.91258	+	10.1870i	0.180630	+	0.631774i
$261$	−1.67619	+	7.34385i	−0.103753	+	0.454573i
$262$	0.714662	+	1.48401i	0.0441520	+	0.0916825i
$263$	9.76302	−	7.78575i	0.602013	−	0.480090i	−0.274422	−	0.961609i	$-0.588486\pi$
$263$	9.76302	−	7.78575i	0.602013	−	0.480090i	0.876435	+	0.481520i	$0.159915\pi$
$264$	4.12751			0.254031
$265$	−29.8113	+	1.61381i	−1.83130	+	0.0991353i
$266$	−10.7818	−	13.5199i	−0.661072	−	0.828959i
$267$	2.01293	−	4.17990i	0.123189	−	0.255805i
$268$	10.9796	+	8.75592i	0.670685	+	0.534853i
$269$	17.6388	+	8.49438i	1.07545	+	0.517911i	0.885861	−	0.463952i	$-0.153569\pi$
$269$	17.6388	+	8.49438i	1.07545	+	0.517911i	0.189593	+	0.981863i	$0.439283\pi$
$270$	−11.4491	+	3.27342i	−0.696771	+	0.199214i
$271$	−4.23104	−	5.30555i	−0.257017	−	0.322289i	0.636536	−	0.771247i	$-0.280367\pi$
$271$	−4.23104	−	5.30555i	−0.257017	−	0.322289i	−0.893553	+	0.448958i	$0.851795\pi$
$272$	−4.08741	+	0.932924i	−0.247836	+	0.0565669i
$273$	−10.7751	−	22.3748i	−0.652141	−	1.35419i
$274$	−6.06177	+	7.60122i	−0.366205	+	0.459207i
$275$	9.82569	−	15.4982i	0.592511	−	0.934579i
$276$	−0.118485	+	0.519117i	−0.00713196	+	0.0312472i
$277$	4.45094	+	9.24246i	0.267431	+	0.555326i	0.990832	−	0.135102i	$-0.0431364\pi$
$277$	4.45094	+	9.24246i	0.267431	+	0.555326i	−0.723401	+	0.690428i	$0.757422\pi$
$278$	−1.59435	+	3.31069i	−0.0956225	+	0.198562i
$279$	−1.07758	+	4.72118i	−0.0645129	+	0.282649i
$280$	10.2699	+	1.76627i	0.613746	+	0.105555i
$281$	−2.00400	−	0.965074i	−0.119548	−	0.0575715i	0.373154	−	0.927770i	$-0.378276\pi$
$281$	−2.00400	−	0.965074i	−0.119548	−	0.0575715i	−0.492702	+	0.870198i	$0.663991\pi$
$282$	−3.60051	−	7.47653i	−0.214407	−	0.445221i
$283$	−11.9915	−	2.73698i	−0.712821	−	0.162697i	−0.149292	−	0.988793i	$-0.547700\pi$
$283$	−11.9915	−	2.73698i	−0.712821	−	0.162697i	−0.563529	+	0.826096i	$0.690557\pi$
$284$	4.76162	−	5.97088i	0.282550	−	0.354307i
$285$	5.41513	−	7.59936i	0.320765	−	0.450147i
$286$	15.6680	−	7.54529i	0.926466	−	0.446162i
$287$	−30.7990	+	7.02967i	−1.81801	+	0.414948i
$288$	1.35663	−	1.08188i	0.0799403	−	0.0637503i
$289$	0.128453	+	0.562788i	0.00755604	+	0.0331052i
$290$	8.96063	+	3.73282i	0.526186	+	0.219199i
$291$	10.5677	−	13.2514i	0.619487	−	0.776812i
$292$	3.98856	−	8.28234i	0.233413	−	0.484687i
$293$	10.6521	−	8.49478i	0.622304	−	0.496271i	−0.260835	−	0.965384i	$-0.583998\pi$
$293$	10.6521	−	8.49478i	0.622304	−	0.496271i	0.883138	+	0.469113i	$0.155426\pi$
$294$	−16.5527			−0.965372
$295$	0.269433	+	4.97715i	0.0156870	+	0.289781i
$296$	−6.25585	−	7.84459i	−0.363614	−	0.455958i
$297$	8.48008	+	17.6091i	0.492064	+	1.02178i
$298$	4.46024	+	1.01802i	0.258375	+	0.0589723i
$299$	0.499204	+	2.18715i	0.0288697	+	0.126486i
$300$	0.607030	+	5.59031i	0.0350469	+	0.322757i
$301$	−21.7530	−	21.4638i	−1.25382	−	1.23715i
$302$			6.88018i			0.395910i
$303$	−10.8093	+	2.46714i	−0.620976	+	0.141734i
$304$	−0.825693	+	3.61760i	−0.0473568	+	0.207483i
$305$	−2.51080	−	4.56469i	−0.143768	−	0.261373i
$306$	−4.53580	−	5.68771i	−0.259294	−	0.325145i
$307$			13.4156i			0.765670i	0.923817	+	0.382835i	$0.125052\pi$
$307$			13.4156i			0.765670i	−0.923817	+	0.382835i	$0.874948\pi$
$308$		−	17.1037i		−	0.974573i
$309$	10.3990	+	13.0400i	0.591579	+	0.741817i
$310$	5.76056	+	2.39974i	0.327178	+	0.136296i
$311$	−8.40617	+	10.5410i	−0.476670	+	0.597725i	−0.960790	−	0.277276i	$-0.910568\pi$
$311$	−8.40617	+	10.5410i	−0.476670	+	0.597725i	0.484120	+	0.875001i	$0.339140\pi$
$312$	−2.31212	+	4.80116i	−0.130898	+	0.271812i
$313$	−4.69941	+	1.07261i	−0.265626	+	0.0606274i	−0.353260	−	0.935525i	$-0.614927\pi$
$313$	−4.69941	+	1.07261i	−0.265626	+	0.0606274i	0.0876334	+	0.996153i	$0.472070\pi$
$314$	−4.05264	−	5.08184i	−0.228703	−	0.286785i
$315$	4.97066	+	17.3854i	0.280065	+	0.979555i
$316$	13.0382	−	6.27888i	0.733457	−	0.353214i
$317$	−20.1951	−	16.1050i	−1.13427	−	0.904549i	−0.137964	−	0.990437i	$-0.544056\pi$
$317$	−20.1951	−	16.1050i	−1.13427	−	0.904549i	−0.996305	+	0.0858877i	$0.972627\pi$
$318$	−11.7397	−	9.36209i	−0.658329	−	0.525000i
$319$	3.54528	−	15.5329i	0.198497	−	0.869674i
$320$	−1.07768	−	1.95924i	−0.0602439	−	0.109525i
$321$	7.26368	+	3.49801i	0.405419	+	0.195240i
$322$	2.15113	+	0.490981i	0.119878	+	0.0273613i
$323$	15.1669	+	3.46174i	0.843907	+	0.192616i
$324$	−0.705908	−	0.339947i	−0.0392171	−	0.0188860i
$325$	12.5236	+	20.1110i	0.694686	+	1.11556i
$326$	−0.686404	+	3.00733i	−0.0380164	+	0.166561i
$327$	10.6515	+	8.49432i	0.589032	+	0.469737i
$328$	5.29986	+	4.22650i	0.292636	+	0.233369i
$329$	−30.9814	+	14.9199i	−1.70806	+	0.822559i
$330$	8.87383	−	2.53712i	0.488488	−	0.139664i
$331$	−1.42677	−	1.78911i	−0.0784223	−	0.0983385i	0.741073	−	0.671425i	$-0.234317\pi$
$331$	−1.42677	−	1.78911i	−0.0784223	−	0.0983385i	−0.819495	+	0.573086i	$0.805746\pi$
$332$	10.1800	−	2.32351i	0.558699	−	0.127519i
$333$	7.55404	−	15.6861i	0.413959	−	0.859594i
$334$	−9.03481	+	11.3293i	−0.494363	+	0.619911i
$335$	28.9874	+	12.0756i	1.58375	+	0.659759i
$336$	3.26778	+	4.09767i	0.178272	+	0.223546i
$337$			15.7243i			0.856556i	0.903647	+	0.428278i	$0.140880\pi$
$337$			15.7243i			0.856556i	−0.903647	+	0.428278i	$0.859120\pi$
$338$			9.45179i			0.514109i
$339$	−5.23447	−	6.56382i	−0.284297	−	0.356497i
$340$	−8.21416	+	4.51818i	−0.445475	+	0.245033i
$341$	2.27917	−	9.98570i	0.123424	−	0.540756i
$342$	−6.27725	+	1.43274i	−0.339435	+	0.0774737i
$343$			35.9694i			1.94216i
$344$	−0.690588	+	6.52097i	−0.0372340	+	0.351587i
$345$	0.0643594	+	1.18889i	0.00346500	+	0.0640078i
$346$	2.95606	+	12.9513i	0.158919	+	0.696269i
$347$	6.83888	+	1.56093i	0.367130	+	0.0837951i	0.402106	−	0.915593i	$-0.368278\pi$
$347$	6.83888	+	1.56093i	0.367130	+	0.0837951i	−0.0349759	+	0.999388i	$0.511135\pi$
$348$	2.11830	+	4.39869i	0.113553	+	0.235795i
$349$	17.8632	+	22.3998i	0.956196	+	1.19903i	0.979936	+	0.199314i	$0.0638714\pi$
$349$	17.8632	+	22.3998i	0.956196	+	1.19903i	−0.0237394	+	0.999718i	$0.507557\pi$
$350$	23.1653	−	2.51543i	1.23824	−	0.134455i
$351$	−25.2334			−1.34686
$352$	−2.86939	+	2.28827i	−0.152939	+	0.121965i
$353$	6.63055	−	13.7685i	0.352909	−	0.732822i	−0.646642	−	0.762793i	$-0.723827\pi$
$353$	6.63055	−	13.7685i	0.352909	−	0.732822i	0.999551	+	0.0299713i	$0.00954158\pi$
$354$	−1.56305	+	1.96000i	−0.0830750	+	0.104173i
$355$	6.56690	−	15.7638i	0.348535	−	0.836657i
$356$	0.917942	+	4.02177i	0.0486508	+	0.213153i
$357$	17.1796	−	13.7003i	0.909240	−	0.725095i
$358$	−14.5861	+	3.32919i	−0.770901	+	0.175953i
$359$	5.00537	−	2.41046i	0.264173	−	0.127219i	−0.297109	−	0.954844i	$-0.596022\pi$
$359$	5.00537	−	2.41046i	0.264173	−	0.127219i	0.561282	+	0.827624i	$0.310308\pi$
$360$	2.25164	−	3.15985i	0.118672	−	0.166539i
$361$	−3.26161	+	4.08993i	−0.171664	+	0.215259i
$362$	−13.5603	−	3.09506i	−0.712716	−	0.162673i
$363$	−1.20506	−	2.50233i	−0.0632493	−	0.131339i
$364$	19.8952	+	9.58102i	1.04279	+	0.502182i
$365$	3.48408	−	20.2581i	0.182365	−	1.06036i
$366$	0.583051	−	2.55451i	0.0304765	−	0.133526i
$367$	8.50256	−	17.6557i	0.443830	−	0.921622i	−0.552293	−	0.833650i	$-0.686247\pi$
$367$	8.50256	−	17.6557i	0.443830	−	0.921622i	0.996123	−	0.0879720i	$-0.0280386\pi$
$368$	−0.205426	−	0.426571i	−0.0107086	−	0.0222365i
$369$	−2.61741	+	11.4676i	−0.136257	+	0.596980i
$370$	−18.2715	−	13.0199i	−0.949892	−	0.676871i
$371$	−38.7949	+	48.6472i	−2.01413	+	2.52564i
$372$	1.36180	+	2.82781i	0.0706061	+	0.146615i
$373$	21.4453	−	4.89474i	1.11039	−	0.253440i	0.372283	−	0.928119i	$-0.378575\pi$
$373$	21.4453	−	4.89474i	1.11039	−	0.253440i	0.738111	+	0.674679i	$0.235718\pi$
$374$	9.59361	+	12.0300i	0.496074	+	0.622057i
$375$	4.74134	+	11.6456i	0.244842	+	0.601376i
$376$	6.64796	+	3.20149i	0.342842	+	0.165104i
$377$	16.0820	+	12.8250i	0.828267	+	0.660521i
$378$	−10.7680	+	22.3600i	−0.553847	+	1.15007i
$379$	−16.1905	−	20.3022i	−0.831648	−	1.04285i	−0.998383	−	0.0568519i	$-0.981894\pi$
$379$	−16.1905	−	20.3022i	−0.831648	−	1.04285i	0.166735	−	0.986002i	$-0.446678\pi$
$380$	0.448505	+	8.28509i	0.0230078	+	0.425016i
$381$	−11.6645			−0.597592
$382$	4.12585	−	3.29025i	0.211097	−	0.168344i
$383$	9.88835	+	20.5334i	0.505271	+	1.04921i	0.985122	+	0.171856i	$0.0549764\pi$
$383$	9.88835	+	20.5334i	0.505271	+	1.04921i	−0.479851	+	0.877350i	$0.659309\pi$
$384$	0.250255	−	1.09644i	0.0127708	−	0.0559523i
$385$	−10.5134	−	36.7716i	−0.535811	−	1.87405i
$386$	−15.3906			−0.783360
$387$	−10.7145	+	3.82983i	−0.544651	+	0.194681i
$388$			15.0709i			0.765107i
$389$	0.356971	+	1.56399i	0.0180991	+	0.0792975i	0.983171	−	0.182688i	$-0.0584799\pi$
$389$	0.356971	+	1.56399i	0.0180991	+	0.0792975i	−0.965072	+	0.261986i	$0.915623\pi$
$390$	−2.01967	+	11.7434i	−0.102270	+	0.594648i
$391$	−1.78841	+	0.861252i	−0.0904437	+	0.0435554i
$392$	11.5072	−	9.17670i	0.581202	−	0.463493i
$393$			1.85242i			0.0934421i
$394$	−2.02437			−0.101986
$395$	24.1716	−	21.5135i	1.21621	−	1.08246i
$396$	−5.73767	−	2.76312i	−0.288329	−	0.138852i
$397$	9.24258	+	7.37071i	0.463872	+	0.369926i	0.827359	−	0.561674i	$-0.189842\pi$
$397$	9.24258	+	7.37071i	0.463872	+	0.369926i	−0.363487	+	0.931599i	$0.618414\pi$
$398$	8.27287	−	17.1788i	0.414681	−	0.861095i
$399$	−4.32756	−	18.9603i	−0.216649	−	0.949201i
$400$	−3.52123	−	3.54978i	−0.176062	−	0.177489i
$401$	−3.09444	−	13.5576i	−0.154529	−	0.677035i	−0.991535	−	0.129841i	$-0.958553\pi$
$401$	−3.09444	−	13.5576i	−0.154529	−	0.677035i	0.837006	−	0.547194i	$-0.184304\pi$
$402$	6.85263	+	14.2296i	0.341778	+	0.709710i
$403$	10.3387	+	8.24487i	0.515009	+	0.410706i
$404$	6.14670	−	7.70771i	0.305810	−	0.383473i
$405$	−1.72661	−	0.296950i	−0.0857958	−	0.0147555i
$406$	18.2274	−	8.77786i	0.904611	−	0.435638i
$407$	−15.9775	+	33.1775i	−0.791973	+	1.64455i
$408$	−4.59684	−	1.04920i	−0.227578	−	0.0519431i
$409$	1.27746	−	5.59694i	0.0631666	−	0.276751i	−0.933475	−	0.358644i	$-0.883239\pi$
$409$	1.27746	−	5.59694i	0.0631666	−	0.276751i	0.996641	+	0.0818928i	$0.0260965\pi$
$410$	13.9923	+	5.82890i	0.691028	+	0.287869i
$411$	−9.85125	+	4.74411i	−0.485927	+	0.234010i
$412$	−14.4585	−	3.30006i	−0.712320	−	0.162582i
$413$	8.12189	+	6.47699i	0.399652	+	0.318712i
$414$	0.512224	−	0.642308i	0.0251744	−	0.0315677i
$415$	20.4579	−	11.2528i	1.00424	−	0.552380i
$416$	−1.05438	−	4.61953i	−0.0516951	−	0.226491i
$417$	−3.23098	+	2.57662i	−0.158222	+	0.126177i
$418$	13.2769	−	3.03037i	0.649396	−	0.148220i
$419$	4.34882	+	2.09428i	0.212454	+	0.102312i	0.537084	−	0.843529i	$-0.319526\pi$
$419$	4.34882	+	2.09428i	0.212454	+	0.102312i	−0.324631	+	0.945841i	$0.605240\pi$
$420$	9.54426	+	6.80102i	0.465712	+	0.331856i
$421$	−11.2565	−	5.42084i	−0.548608	−	0.264196i	0.138982	−	0.990295i	$-0.455617\pi$
$421$	−11.2565	−	5.42084i	−0.548608	−	0.264196i	−0.687590	+	0.726099i	$0.741331\pi$
$422$	−1.85711	+	1.48100i	−0.0904027	+	0.0720938i
$423$			12.8035i			0.622526i
$424$	13.3516			0.648409
$425$	−14.8825	+	14.7628i	−0.721909	+	0.716103i
$426$	7.73832	−	3.72658i	0.374923	−	0.180553i
$427$	−10.5854	−	2.41606i	−0.512266	−	0.116921i
$428$	−6.98889	+	1.59517i	−0.337821	+	0.0771054i
$429$	19.5575			0.944246
$430$	2.52363	+	14.4441i	0.121700	+	0.696555i
$431$	−19.9059			−0.958833			−0.479416	−	0.877588i	$-0.659152\pi$
$431$	−19.9059			−0.958833			−0.479416	+	0.877588i	$0.659152\pi$
$432$	5.19185	−	1.18501i	0.249793	−	0.0570136i
$433$	−24.9802	−	5.70157i	−1.20047	−	0.274000i	−0.424889	−	0.905245i	$-0.639687\pi$
$433$	−24.9802	−	5.70157i	−1.20047	−	0.274000i	−0.775583	+	0.631245i	$0.782544\pi$
$434$	11.7179	−	5.64306i	0.562479	−	0.270876i
$435$	7.25798	+	8.15476i	0.347994	+	0.390991i
$436$	−12.1140			−0.580156
$437$			1.75683i			0.0840405i
$438$	8.08291	−	6.44591i	0.386216	−	0.307997i
$439$	−26.1441	−	12.5903i	−1.24779	−	0.600904i	−0.310872	−	0.950452i	$-0.600621\pi$
$439$	−26.1441	−	12.5903i	−1.24779	−	0.600904i	−0.936918	+	0.349548i	$0.886335\pi$
$440$	−4.76241	+	6.68336i	−0.227039	+	0.318617i
$441$	23.0099	+	11.0810i	1.09571	+	0.527667i
$442$	−19.3675	+	4.42051i	−0.921218	+	0.210262i
$443$	−18.4057	+	14.6781i	−0.874483	+	0.697377i	−0.954113	−	0.299448i	$-0.903198\pi$
$443$	−18.4057	+	14.6781i	−0.874483	+	0.697377i	0.0796297	+	0.996825i	$0.474626\pi$
$444$	−2.51096	−	11.0012i	−0.119165	−	0.522095i
$445$	4.44562	+	8.08224i	0.210743	+	0.383135i
$446$	3.45711	−	4.33508i	0.163699	−	0.205272i
$447$	4.02263	+	3.20794i	0.190264	+	0.151730i
$448$	−4.54344	−	1.03701i	−0.214658	−	0.0489942i
$449$	−7.96344	+	3.83499i	−0.375818	+	0.180984i	−0.612251	−	0.790663i	$-0.709736\pi$
$449$	−7.96344	+	3.83499i	−0.375818	+	0.180984i	0.236433	+	0.971648i	$0.424022\pi$
$450$	2.89854	−	8.17748i	0.136638	−	0.385490i
$451$	5.53604	−	24.2550i	0.260682	−	1.14212i
$452$	7.27787	+	1.66113i	0.342322	+	0.0781328i
$453$	−3.35725	+	6.97141i	−0.157738	+	0.327545i
$454$	−8.19389	+	3.94597i	−0.384558	+	0.185193i
$455$	48.6624	+	8.36918i	2.28133	+	0.392353i
$456$	−2.60189	+	3.26266i	−0.121845	+	0.152788i
$457$	−2.60804	−	2.07984i	−0.121999	−	0.0972907i	0.560590	−	0.828094i	$-0.310574\pi$
$457$	−2.60804	−	2.07984i	−0.121999	−	0.0972907i	−0.682589	+	0.730803i	$0.739146\pi$
$458$	3.34039	+	6.93638i	0.156086	+	0.324116i
$459$	−4.96816	−	21.7669i	−0.231894	−	1.01599i
$460$	−0.703856	−	0.790822i	−0.0328174	−	0.0368723i
$461$	1.81036	+	7.93173i	0.0843171	+	0.369417i	0.999429	−	0.0337821i	$-0.0107552\pi$
$461$	1.81036	+	7.93173i	0.0843171	+	0.369417i	−0.915112	+	0.403199i	$0.867898\pi$
$462$	8.34593	−	17.3305i	0.388288	−	0.806288i
$463$	16.3105	+	13.0072i	0.758014	+	0.604496i	0.924338	−	0.381575i	$-0.124618\pi$
$463$	16.3105	+	13.0072i	0.758014	+	0.604496i	−0.166324	+	0.986071i	$0.553190\pi$
$464$	−3.91122	−	1.88354i	−0.181574	−	0.0874413i
$465$	4.66597	+	5.24249i	0.216379	+	0.243115i
$466$	−17.8853			−0.828520
$467$		−	22.3162i		−	1.03267i	−0.856386	−	0.516336i	$-0.827295\pi$
$467$		−	22.3162i		−	1.03267i	0.856386	−	0.516336i	$-0.172705\pi$
$468$	6.42817	−	5.12630i	0.297142	−	0.236963i
$469$	58.9651	−	28.3961i	2.72276	−	1.31121i
$470$	16.2605	+	2.79655i	0.750041	+	0.128995i
$471$	−1.62664	−	7.12676i	−0.0749514	−	0.328384i
$472$		−	2.22911i		−	0.102603i
$473$	22.6622	−	8.10043i	1.04201	−	0.372458i
$474$	16.2750			0.747534
$475$	6.05697	+	17.5366i	0.277913	+	0.804635i
$476$	−4.34770	+	19.0485i	−0.199276	+	0.873087i
$477$	10.0520	+	20.8733i	0.460251	+	0.955722i
$478$	−12.9554	+	10.3316i	−0.592566	+	0.472556i
$479$	7.06706			0.322902			0.161451	−	0.986881i	$-0.448383\pi$
$479$	7.06706			0.322902			0.161451	+	0.986881i	$0.448383\pi$
$480$	−0.135935	−	2.51108i	−0.00620455	−	0.114615i
$481$	−29.6423	−	37.1703i	−1.35157	−	1.69482i
$482$	10.5199	−	21.8448i	0.479168	−	0.995003i
$483$	1.94008	+	1.54716i	0.0882765	+	0.0703982i
$484$	2.22502	+	1.07151i	0.101137	+	0.0487052i
$485$	9.26382	+	32.4012i	0.420648	+	1.47126i
$486$	9.41155	+	11.8017i	0.426916	+	0.535336i
$487$	27.3284	−	6.23752i	1.23837	−	0.282649i	0.447303	−	0.894383i	$-0.352385\pi$
$487$	27.3284	−	6.23752i	1.23837	−	0.282649i	0.791064	+	0.611734i	$0.209528\pi$
$488$	1.01087	+	2.09910i	0.0457601	+	0.0950219i
$489$	−2.16297	+	2.71227i	−0.0978127	+	0.122653i
$490$	19.0988	−	26.8025i	0.862798	−	1.21081i
$491$	1.52393	−	6.67676i	0.0687739	−	0.301318i	−0.928830	−	0.370507i	$-0.879184\pi$
$491$	1.52393	−	6.67676i	0.0687739	−	0.301318i	0.997604	+	0.0691888i	$0.0220411\pi$
$492$	3.30778	+	6.86867i	0.149126	+	0.309664i
$493$	−7.89680	+	16.3979i	−0.355654	+	0.738523i
$494$	−3.91241	+	17.1414i	−0.176028	+	0.771227i
$495$	−14.0340	−	2.41363i	−0.630781	−	0.108485i
$496$	−2.51442	−	1.21088i	−0.112901	−	0.0543702i
$497$	−15.4423	−	32.0662i	−0.692681	−	1.43837i
$498$	11.4488	+	2.61310i	0.513031	+	0.117096i
$499$	9.08651	−	11.3941i	0.406768	−	0.510071i	−0.535681	−	0.844420i	$-0.679945\pi$
$499$	9.08651	−	11.3941i	0.406768	−	0.510071i	0.942449	+	0.334349i	$0.108517\pi$
$500$	−9.75236	−	5.46730i	−0.436139	−	0.244505i
$501$	−14.6829	+	7.07090i	−0.655982	+	0.315904i
$502$	−6.21593	+	1.41875i	−0.277431	+	0.0633217i
$503$	−25.3892	+	20.2472i	−1.13205	+	0.902777i	−0.996126	−	0.0879428i	$-0.971971\pi$
$503$	−25.3892	+	20.2472i	−1.13205	+	0.902777i	−0.135921	+	0.990720i	$0.543399\pi$
$504$	−1.79942	−	7.88377i	−0.0801525	−	0.351171i
$505$	8.47710	−	20.3493i	0.377226	−	0.905530i
$506$	−1.08340	+	1.35854i	−0.0481629	+	0.0603944i
$507$	−4.61210	+	9.57712i	−0.204831	+	0.425335i
$508$	8.10903	−	6.46673i	0.359780	−	0.286915i
$509$	−39.2483			−1.73965			−0.869826	−	0.493359i	$-0.835769\pi$
$509$	−39.2483			−1.73965			−0.869826	+	0.493359i	$0.835769\pi$
$510$	−10.5278	+	0.569910i	−0.466178	+	0.0252360i
$511$	−26.7107	−	33.4942i	−1.18161	−	1.48169i
$512$	0.433884	+	0.900969i	0.0191751	+	0.0398176i
$513$	−19.2650	−	4.39712i	−0.850572	−	0.194138i
$514$	2.94023	+	12.8820i	0.129688	+	0.568200i
$515$	−33.1132	+	1.79255i	−1.45914	+	0.0789891i
$516$	−3.88172	+	6.27047i	−0.170883	+	0.276042i
$517$		−	27.0804i		−	1.19100i
$518$	−45.5871	+	10.4050i	−2.00298	+	0.457168i
$519$	−3.32449	+	14.5655i	−0.145929	+	0.639356i
$520$	−5.10638	−	9.28352i	−0.223930	−	0.407109i
$521$	8.20529	+	10.2891i	0.359480	+	0.450774i	0.928380	−	0.371633i	$-0.121202\pi$
$521$	8.20529	+	10.2891i	0.359480	+	0.450774i	−0.568900	+	0.822407i	$0.692631\pi$
$522$		−	7.53271i		−	0.329698i
$523$		−	4.87009i		−	0.212954i	−0.994315	−	0.106477i	$-0.966043\pi$
$523$		−	4.87009i		−	0.212954i	0.994315	−	0.106477i	$-0.0339571\pi$
$524$	−1.02697	−	1.28778i	−0.0448633	−	0.0562568i
$525$	24.6999	+	8.75496i	1.07799	+	0.382098i
$526$	−7.78575	+	9.76302i	−0.339475	+	0.425688i
$527$	−5.07666	+	10.5418i	−0.221143	+	0.459207i
$528$	−4.02403	+	0.918458i	−0.175123	+	0.0399708i
$529$	14.2005	+	17.8069i	0.617413	+	0.774212i
$530$	28.7048	−	8.20699i	1.24686	−	0.356489i
$531$	3.48489	−	1.67824i	0.151232	−	0.0728293i
$532$	13.5199	+	10.7818i	0.586162	+	0.467449i
$533$	25.1125	+	20.0266i	1.08774	+	0.867446i
$534$	−1.03235	+	4.52302i	−0.0446741	+	0.195730i
$535$	−14.0450	+	7.72545i	−0.607220	+	0.334000i
$536$	−12.6527	−	6.09321i	−0.546512	−	0.263186i
$537$	−16.4041	−	3.74412i	−0.707888	−	0.161571i
$538$	−19.0867	−	4.35641i	−0.822886	−	0.187818i
$539$	−48.6680	−	23.4373i	−2.09628	−	1.00952i
$540$	10.4337	−	5.73902i	0.448993	−	0.246968i
$541$	4.30453	−	18.8594i	0.185066	−	0.810828i	−0.794103	−	0.607783i	$-0.792059\pi$
$541$	4.30453	−	18.8594i	0.185066	−	0.810828i	0.979169	−	0.203045i	$-0.0650838\pi$
$542$	5.30555	+	4.23104i	0.227893	+	0.181739i
$543$	−12.2299	−	9.75302i	−0.524835	−	0.418542i
$544$	3.77733	−	1.81907i	0.161952	−	0.0779919i
$545$	−26.0442	+	7.44629i	−1.11561	+	0.318964i
$546$	15.4838	+	19.4161i	0.662648	+	0.830934i
$547$	18.4718	−	4.21607i	0.789798	−	0.180266i	0.191450	−	0.981502i	$-0.438681\pi$
$547$	18.4718	−	4.21607i	0.789798	−	0.180266i	0.598348	+	0.801236i	$0.295824\pi$
$548$	4.21836	−	8.75952i	0.180199	−	0.374188i
$549$	−2.52059	+	3.16072i	−0.107576	+	0.134896i
$550$	−6.13066	+	17.2961i	−0.261412	+	0.737508i
$551$	10.0434	+	12.5940i	0.427862	+	0.536522i
$552$		−	0.532467i		−	0.0226633i
$553$		−	67.4406i		−	2.86786i
$554$	−6.39598	−	8.02031i	−0.271739	−	0.340750i
$555$	−12.1606	−	22.1083i	−0.516190	−	0.938446i
$556$	0.817674	−	3.58246i	0.0346771	−	0.151930i
$557$	−37.1772	+	8.48545i	−1.57525	+	0.359540i	−0.918766	−	0.394803i	$-0.870813\pi$
$557$	−37.1772	+	8.48545i	−1.57525	+	0.359540i	−0.656481	+	0.754343i	$0.727956\pi$
$558$		−	4.84259i		−	0.205003i
$559$	−3.27224	+	30.8985i	−0.138401	+	1.30687i
$560$	−10.4055	+	0.563290i	−0.439712	+	0.0238033i
$561$	3.85066	+	16.8708i	0.162575	+	0.712287i
$562$	2.16850	+	0.494946i	0.0914727	+	0.0208780i
$563$	−15.1982	−	31.5594i	−0.640527	−	1.33007i	−0.928108	−	0.372312i	$-0.878565\pi$
$563$	−15.1982	−	31.5594i	−0.640527	−	1.33007i	0.287580	−	0.957757i	$-0.407149\pi$
$564$	5.17392	+	6.48789i	0.217861	+	0.273189i
$565$	16.6679	−	0.902300i	0.701225	−	0.0379601i
$566$	12.2999			0.517003
$567$	−2.85472	+	2.27657i	−0.119887	+	0.0956068i
$568$	−3.31359	+	6.88074i	−0.139035	+	0.288709i
$569$	−25.7393	+	32.2761i	−1.07905	+	1.35308i	−0.147667	+	0.989037i	$0.547176\pi$
$569$	−25.7393	+	32.2761i	−1.07905	+	1.35308i	−0.931381	+	0.364046i	$0.881395\pi$
$570$	−3.58835	+	8.61381i	−0.150299	+	0.360793i
$571$	3.86310	+	16.9254i	0.161666	+	0.708304i	0.989161	+	0.146832i	$0.0469076\pi$
$571$	3.86310	+	16.9254i	0.161666	+	0.708304i	−0.827496	+	0.561472i	$0.810235\pi$
$572$	−13.5961	+	10.8426i	−0.568483	+	0.453350i
$573$	5.78607	−	1.32063i	0.241717	−	0.0551702i
$574$	28.4626	−	13.7068i	1.18800	−	0.572113i
$575$	−1.99934	−	1.26756i	−0.0833783	−	0.0528608i
$576$	−1.08188	+	1.35663i	−0.0450782	+	0.0565263i
$577$	−18.3203	−	4.18148i	−0.762682	−	0.174077i	−0.176549	−	0.984292i	$-0.556493\pi$
$577$	−18.3203	−	4.18148i	−0.762682	−	0.174077i	−0.586133	+	0.810215i	$0.699351\pi$
$578$	−0.250464	−	0.520094i	−0.0104179	−	0.0216331i
$579$	−15.5947	−	7.51000i	−0.648093	−	0.312105i
$580$	−9.56660	−	1.64531i	−0.397231	−	0.0683177i
$581$	10.8282	−	47.4416i	0.449231	−	1.96821i
$582$	−7.35399	+	15.2707i	−0.304833	+	0.632991i
$583$	−21.2609	−	44.1488i	−0.880538	−	1.82846i
$584$	−2.04557	+	8.96222i	−0.0846462	+	0.370859i
$585$	10.6690	−	14.9724i	0.441109	−	0.619034i
$586$	−8.49478	+	10.6521i	−0.350916	+	0.440035i
$587$	1.31479	+	2.73018i	0.0542671	+	0.112687i	0.926339	−	0.376691i	$-0.122938\pi$
$587$	1.31479	+	2.73018i	0.0542671	+	0.112687i	−0.872072	+	0.489378i	$0.837224\pi$
$588$	16.1377	−	3.68332i	0.665506	−	0.151897i
$589$	6.45663	+	8.09636i	0.266041	+	0.333605i
$590$	−1.37020	−	4.79241i	−0.0564101	−	0.197300i
$591$	−2.05121	−	0.987812i	−0.0843757	−	0.0406332i
$592$	7.84459	+	6.25585i	0.322411	+	0.257114i
$593$	−4.37299	+	9.08060i	−0.179577	+	0.372896i	−0.971254	−	0.238044i	$-0.923494\pi$
$593$	−4.37299	+	9.08060i	−0.179577	+	0.372896i	0.791677	+	0.610939i	$0.209208\pi$
$594$	−12.1859	−	15.2806i	−0.499992	−	0.626970i
$595$	2.36161	+	43.6252i	0.0968164	+	1.78846i
$596$	−4.57494			−0.187397
$597$	16.7651	−	13.3698i	0.686151	−	0.547188i
$598$	−0.973375	−	2.02123i	−0.0398043	−	0.0826544i
$599$	0.0455748	−	0.199676i	0.00186214	−	0.00815855i	−0.973988	−	0.226598i	$-0.927240\pi$
$599$	0.0455748	−	0.199676i	0.00186214	−	0.00815855i	0.975850	+	0.218440i	$0.0700967\pi$
$600$	−1.83577	−	5.31507i	−0.0749451	−	0.216987i
$601$	−33.1265			−1.35126			−0.675629	−	0.737242i	$-0.736128\pi$
$601$	−33.1265			−1.35126			−0.675629	+	0.737242i	$0.736128\pi$
$602$	25.9837	+	16.0852i	1.05902	+	0.655583i
$603$		−	24.3681i		−	0.992345i
$604$	−1.53098	−	6.70768i	−0.0622948	−	0.272931i
$605$	5.44226	+	0.935985i	0.221259	+	0.0380532i
$606$	9.98926	−	4.81058i	0.405786	−	0.195416i
$607$	12.4159	−	9.90137i	0.503947	−	0.401884i	−0.338248	−	0.941057i	$-0.609834\pi$
$607$	12.4159	−	9.90137i	0.503947	−	0.401884i	0.842195	+	0.539173i	$0.181263\pi$
$608$		−	3.71063i		−	0.150486i
$609$	22.7524			0.921972
$610$	3.46359	+	3.89154i	0.140237	+	0.157564i
$611$	31.5002	+	15.1697i	1.27436	+	0.613701i
$612$	5.68771	+	4.53580i	0.229912	+	0.183349i
$613$	−9.15845	+	19.0177i	−0.369906	+	0.768118i	−0.999964	−	0.00842954i	$-0.997317\pi$
$613$	−9.15845	+	19.0177i	−0.369906	+	0.768118i	0.630058	+	0.776548i	$0.283031\pi$
$614$	−2.98526	−	13.0793i	−0.120475	−	0.527836i
$615$	11.3335	+	12.7339i	0.457012	+	0.513479i
$616$	3.80593	+	16.6749i	0.153345	+	0.671849i
$617$	10.7953	+	22.4168i	0.434604	+	0.902465i	0.997132	+	0.0756865i	$0.0241148\pi$
$617$	10.7953	+	22.4168i	0.434604	+	0.902465i	−0.562527	+	0.826779i	$0.690171\pi$
$618$	−13.0400	−	10.3990i	−0.524544	−	0.418310i
$619$	−17.6357	+	22.1145i	−0.708839	+	0.888856i	−0.997649	−	0.0685303i	$-0.978169\pi$
$619$	−17.6357	+	22.1145i	−0.708839	+	0.888856i	0.288810	+	0.957386i	$0.406740\pi$
$620$	−6.15013	−	1.05773i	−0.246995	−	0.0424793i
$621$	2.27165	−	1.09397i	0.0911580	−	0.0438994i
$622$	5.84981	−	12.1473i	0.234556	−	0.487061i
$623$	18.7426	+	4.27787i	0.750906	+	0.171389i
$624$	1.18579	−	5.19528i	0.0474696	−	0.207978i
$625$	−24.3275	−	5.75965i	−0.973099	−	0.230386i
$626$	4.34290	−	2.09143i	0.173577	−	0.0835905i
$627$	14.9317	+	3.40806i	0.596314	+	0.136105i
$628$	5.08184	+	4.05264i	0.202788	+	0.161718i
$629$	26.2278	−	32.8886i	1.04577	−	1.31136i
$630$	−8.71464	−	15.8434i	−0.347200	−	0.631217i
$631$	−3.92979	−	17.2175i	−0.156442	−	0.685419i	−0.990929	−	0.134390i	$-0.957092\pi$
$631$	−3.92979	−	17.2175i	−0.156442	−	0.685419i	0.834486	−	0.551029i	$-0.185765\pi$
$632$	−11.3141	+	9.02273i	−0.450052	+	0.358905i
$633$	−2.60440	+	0.594438i	−0.103516	+	0.0236268i
$634$	23.2725	+	11.2074i	0.924268	+	0.445104i
$635$	13.4588	−	18.8875i	0.534095	−	0.749526i
$636$	13.5286	+	6.51504i	0.536444	+	0.258338i
$637$	54.5250	−	43.4822i	2.16036	−	1.72283i
$638$			15.9323i			0.630767i
$639$	−13.2518			−0.524232
$640$	1.48663	+	1.67031i	0.0587641	+	0.0660248i
$641$	4.32734	−	2.08394i	0.170920	−	0.0823106i	−0.346468	−	0.938062i	$-0.612619\pi$
$641$	4.32734	−	2.08394i	0.170920	−	0.0823106i	0.517387	+	0.855751i	$0.326905\pi$
$642$	−7.85995	−	1.79398i	−0.310207	−	0.0708028i
$643$	−47.0085	+	10.7294i	−1.85383	+	0.423126i	−0.995886	−	0.0906105i	$-0.971118\pi$
$643$	−47.0085	+	10.7294i	−1.85383	+	0.423126i	−0.857948	+	0.513736i	$0.828261\pi$
$644$	−2.20645			−0.0869463
$645$	−4.49105	+	15.8670i	−0.176835	+	0.624764i
$646$	−15.5569			−0.612079
$647$	11.9551	−	2.72868i	0.470005	−	0.107276i	0.0190428	−	0.999819i	$-0.493938\pi$
$647$	11.9551	−	2.72868i	0.470005	−	0.107276i	0.450962	+	0.892543i	$0.351081\pi$
$648$	0.763854	+	0.174345i	0.0300070	+	0.00684891i
$649$	−7.37086	+	3.54962i	−0.289331	+	0.139335i
$650$	−16.6848	−	16.8200i	−0.654430	−	0.659736i
$651$	14.6269			0.573274
$652$		−	3.08467i		−	0.120805i
$653$	2.37839	−	1.89670i	0.0930735	−	0.0742237i	−0.575848	−	0.817557i	$-0.695328\pi$
$653$	2.37839	−	1.89670i	0.0930735	−	0.0742237i	0.668921	+	0.743333i	$0.266756\pi$
$654$	−12.2747	−	5.91116i	−0.479977	−	0.231145i
$655$	−2.99948	−	2.13736i	−0.117199	−	0.0835135i
$656$	−6.10747	−	2.94120i	−0.238457	−	0.114835i
$657$	−15.5512	+	3.54947i	−0.606711	+	0.138478i
$658$	26.8847	−	21.4398i	1.04807	−	0.835810i
$659$	−1.74462	−	7.64368i	−0.0679607	−	0.297755i	0.929513	−	0.368789i	$-0.120227\pi$
$659$	−1.74462	−	7.64368i	−0.0679607	−	0.297755i	−0.997474	+	0.0710334i	$0.977370\pi$
$660$	−8.08678	+	4.44812i	−0.314778	+	0.173143i
$661$	20.2698	−	25.4176i	0.788405	−	0.988629i	−0.211532	−	0.977371i	$-0.567845\pi$
$661$	20.2698	−	25.4176i	0.788405	−	0.988629i	0.999937	−	0.0112574i	$-0.00358341\pi$
$662$	1.78911	+	1.42677i	0.0695358	+	0.0554530i
$663$	−21.7814	−	4.97145i	−0.845918	−	0.193075i
$664$	−9.40771	+	4.53051i	−0.365090	+	0.175818i
$665$	35.6941	+	14.8695i	1.38416	+	0.576614i
$666$	−3.87415	+	16.9738i	−0.150120	+	0.657720i
$667$	−2.00381	−	0.457356i	−0.0775878	−	0.0177089i
$668$	6.28728	−	13.0557i	0.243262	−	0.505139i
$669$	5.61831	−	2.70563i	0.217216	−	0.104606i
$670$	−30.9477	−	5.32252i	−1.19561	−	0.205627i
$671$	5.33127	−	6.68520i	0.205811	−	0.258079i
$672$	−4.09767	−	3.26778i	−0.158071	−	0.126058i
$673$	−7.84428	−	16.2888i	−0.302375	−	0.627888i	0.693315	−	0.720635i	$-0.256150\pi$
$673$	−7.84428	−	16.2888i	−0.302375	−	0.627888i	−0.995690	+	0.0927468i	$0.970435\pi$
$674$	−3.49898	−	15.3300i	−0.134776	−	0.590491i
$675$	18.9039	−	18.7518i	0.727610	−	0.721759i
$676$	−2.10322	−	9.21481i	−0.0808931	−	0.354416i
$677$	−19.8103	+	41.1364i	−0.761370	+	1.58100i	0.0515813	+	0.998669i	$0.483574\pi$
$677$	−19.8103	+	41.1364i	−0.761370	+	1.58100i	−0.812951	+	0.582332i	$0.802140\pi$
$678$	6.56382	+	5.23447i	0.252082	+	0.201029i
$679$	63.2791	+	30.4736i	2.42843	+	1.16947i
$680$	7.00282	−	6.23272i	0.268546	−	0.239014i
$681$	−10.2280			−0.391939
$682$			10.2425i			0.392206i
$683$	−15.0230	+	11.9804i	−0.574837	+	0.458418i	−0.867249	−	0.497875i	$-0.834114\pi$
$683$	−15.0230	+	11.9804i	−0.574837	+	0.458418i	0.292411	+	0.956293i	$0.405542\pi$
$684$	5.80105	−	2.79364i	0.221809	−	0.106817i
$685$	3.68481	−	21.4252i	0.140789	−	0.818616i
$686$	−8.00394	−	35.0676i	−0.305592	−	1.33889i
$687$			8.65834i			0.330336i
$688$	−0.777779	−	6.51115i	−0.0296526	−	0.248235i
$689$	63.2641			2.41017
$690$	−0.327299	−	1.14476i	−0.0124601	−	0.0435804i
$691$	−5.07374	+	22.2295i	−0.193014	+	0.845650i	0.781959	+	0.623329i	$0.214220\pi$
$691$	−5.07374	+	22.2295i	−0.193014	+	0.845650i	−0.974974	+	0.222321i	$0.928637\pi$
$692$	−5.76389	−	11.9688i	−0.219110	−	0.454987i
$693$	−23.2034	+	18.5041i	−0.881425	+	0.702913i
$694$	−7.01475			−0.266276
$695$	−0.444149	−	8.20462i	−0.0168475	−	0.311219i
$696$	−3.04399	−	3.81704i	−0.115382	−	0.144685i
$697$	−12.3311	+	25.6057i	−0.467072	+	0.969885i
$698$	−22.3998	−	17.8632i	−0.847844	−	0.676133i
$699$	−18.1225	−	8.72732i	−0.685454	−	0.330097i
$700$	−22.0247	+	7.60712i	−0.832457	+	0.287522i
$701$	29.2278	+	36.6504i	1.10392	+	1.38427i	0.915567	+	0.402166i	$0.131743\pi$
$701$	29.2278	+	36.6504i	1.10392	+	1.38427i	0.188350	+	0.982102i	$0.439686\pi$
$702$	24.6007	−	5.61495i	0.928494	−	0.211923i
$703$	−16.1539	−	33.5440i	−0.609257	−	1.26514i
$704$	2.28827	−	2.86939i	0.0862423	−	0.108144i
$705$	15.1115	+	10.7681i	0.569133	+	0.405551i
$706$	−3.40053	+	14.8987i	−0.127981	+	0.560720i
$707$	−19.9342	−	41.3938i	−0.749702	−	1.55677i
$708$	1.08772	−	2.25867i	0.0408789	−	0.0848859i
$709$	−7.50256	+	32.8708i	−0.281764	+	1.23449i	0.613765	+	0.789489i	$0.289654\pi$
$709$	−7.50256	+	32.8708i	−0.281764	+	1.23449i	−0.895530	+	0.445002i	$0.853203\pi$
$710$	−2.89448	+	16.8299i	−0.108628	+	0.631614i
$711$	−22.6239	−	10.8951i	−0.848462	−	0.408598i
$712$	−1.78985	−	3.71667i	−0.0670776	−	0.139288i
$713$	−1.28820	−	0.294023i	−0.0482434	−	0.0110112i
$714$	−13.7003	+	17.1796i	−0.512720	+	0.642930i
$715$	−22.5659	+	31.6680i	−0.843916	+	1.18432i
$716$	13.4796	−	6.49144i	0.503757	−	0.242596i
$717$	−18.1686	+	4.14687i	−0.678519	+	0.154868i
$718$	−4.34350	+	3.46382i	−0.162098	+	0.129269i
$719$	−10.1686	−	44.5515i	−0.379224	−	1.66149i	−0.699854	−	0.714286i	$-0.746752\pi$
$719$	−10.1686	−	44.5515i	−0.379224	−	1.66149i	0.320630	−	0.947205i	$-0.396106\pi$
$720$	−1.49205	+	3.58167i	−0.0556055	+	0.133481i
$721$	−43.0917	+	54.0353i	−1.60482	+	2.01238i
$722$	2.26974	−	4.71316i	0.0844709	−	0.175406i
$723$	21.3188	−	17.0012i	0.792854	−	0.632280i
$724$	13.9091			0.516927
$725$	−21.5788	+	2.34316i	−0.801416	+	0.0870226i
$726$	1.73167	+	2.17144i	0.0642683	+	0.0805899i
$727$	−1.38406	−	2.87402i	−0.0513318	−	0.106592i	0.873725	−	0.486420i	$-0.161697\pi$
$727$	−1.38406	−	2.87402i	−0.0513318	−	0.106592i	−0.925057	+	0.379828i	$0.875983\pi$
$728$	−21.5283	−	4.91370i	−0.797894	−	0.182114i
$729$	4.30062	+	18.8422i	0.159282	+	0.697860i
$730$	1.11112	+	20.5255i	0.0411245	+	0.759681i
$731$	−27.2982	+	3.26086i	−1.00966	+	0.120607i
$732$			2.62021i			0.0968456i
$733$	43.3781	−	9.90076i	1.60221	−	0.365693i	0.674285	−	0.738471i	$-0.264452\pi$
$733$	43.3781	−	9.90076i	1.60221	−	0.365693i	0.927920	+	0.372779i	$0.121595\pi$
$734$	−4.36061	+	19.1051i	−0.160953	+	0.705181i
$735$	32.4307	−	17.8384i	1.19622	−	0.657980i
$736$	0.295196	+	0.370164i	0.0108811	+	0.0136444i
$737$			51.5406i			1.89852i
$738$		−	11.7625i		−	0.432984i
$739$	4.24007	+	5.31688i	0.155973	+	0.195585i	0.853678	−	0.520801i	$-0.174367\pi$
$739$	4.24007	+	5.31688i	0.155973	+	0.195585i	−0.697705	+	0.716385i	$0.745795\pi$
$740$	20.7106	+	8.62765i	0.761338	+	0.317159i
$741$	−12.3286	+	15.4596i	−0.452903	+	0.567922i
$742$	26.9972	−	56.0602i	0.991097	−	2.05803i
$743$	31.1828	−	7.11727i	1.14399	−	0.261107i	0.391795	−	0.920053i	$-0.371854\pi$
$743$	31.1828	−	7.11727i	1.14399	−	0.261107i	0.752191	+	0.658945i	$0.228997\pi$
$744$	−1.95690	−	2.45388i	−0.0717436	−	0.0899636i
$745$	−9.83576	+	2.81214i	−0.360354	+	0.103029i
$746$	−19.8184	+	9.54404i	−0.725603	+	0.349432i
$747$	−14.1656	−	11.2967i	−0.518294	−	0.413325i
$748$	−12.0300	−	9.59361i	−0.439861	−	0.350777i
$749$	−7.43394	+	32.5702i	−0.271630	+	1.19009i
$750$	−7.21386	−	10.2986i	−0.263413	−	0.376051i
$751$	22.9746	+	11.0640i	0.838353	+	0.403730i	0.803241	−	0.595654i	$-0.203107\pi$
$751$	22.9746	+	11.0640i	0.838353	+	0.403730i	0.0351120	+	0.999383i	$0.488821\pi$
$752$	−7.19368	−	1.64191i	−0.262327	−	0.0598743i
$753$	−6.99065	−	1.59557i	−0.254753	−	0.0581458i
$754$	−18.5327	−	8.92486i	−0.674919	−	0.325024i
$755$	−7.41460	−	13.4799i	−0.269845	−	0.490584i
$756$	5.52247	−	24.1955i	0.200850	−	0.879982i
$757$	2.01721	+	1.60867i	0.0733168	+	0.0584682i	0.659462	−	0.751737i	$-0.270784\pi$
$757$	2.01721	+	1.60867i	0.0733168	+	0.0584682i	−0.586146	+	0.810206i	$0.699355\pi$
$758$	20.3022	+	16.1905i	0.737409	+	0.588064i
$759$	−1.76068	+	0.847897i	−0.0639085	+	0.0307767i
$760$	−2.28087	−	7.97757i	−0.0827357	−	0.289377i
$761$	−16.3054	−	20.4463i	−0.591069	−	0.741177i	0.392888	−	0.919587i	$-0.371476\pi$
$761$	−16.3054	−	20.4463i	−0.591069	−	0.741177i	−0.983956	+	0.178410i	$0.942905\pi$
$762$	11.3721	−	2.59560i	0.411967	−	0.0940287i
$763$	−24.4948	+	50.8640i	−0.886772	+	1.84140i
$764$	−3.29025	+	4.12585i	−0.119037	+	0.149268i
$765$	15.0162	+	6.25547i	0.542913	+	0.226167i
$766$	−14.2095	−	17.8182i	−0.513411	−	0.643797i
$767$		−	10.5623i		−	0.381381i
$768$			1.12463i			0.0405818i
$769$	11.5618	+	14.4981i	0.416930	+	0.522814i	0.945301	−	0.326200i	$-0.105768\pi$
$769$	11.5618	+	14.4981i	0.416930	+	0.522814i	−0.528371	+	0.849014i	$0.677197\pi$
$770$	18.4322	+	33.5102i	0.664251	+	1.20762i
$771$	−3.30668	+	14.4875i	−0.119087	+	0.521755i
$772$	15.0047	−	3.42473i	0.540031	−	0.123259i
$773$			11.6835i			0.420227i	0.977677	+	0.210113i	$0.0673833\pi$
$773$			11.6835i			0.420227i	−0.977677	+	0.210113i	$0.932617\pi$
$774$	9.59369	−	6.11802i	0.344838	−	0.219908i
$775$	−13.8725	+	1.50636i	−0.498313	+	0.0541099i
$776$	−3.35358	−	14.6930i	−0.120387	−	0.527448i
$777$	−51.2689	−	11.7018i	−1.83926	−	0.419799i
$778$	−0.696041	−	1.44534i	−0.0249543	−	0.0518181i
$779$	15.6830	+	19.6658i	0.561901	+	0.704602i
$780$	−0.644104	−	11.8983i	−0.0230626	−	0.426029i
$781$	28.0287			1.00294
$782$	1.55192	−	1.23762i	0.0554967	−	0.0442571i
$783$	10.0306	−	20.8287i	0.358463	−	0.744356i
$784$	−9.17670	+	11.5072i	−0.327739	+	0.410972i
$785$	13.4167	+	5.58912i	0.478861	+	0.199484i
$786$	−0.412202	−	1.80597i	−0.0147027	−	0.0644169i
$787$	−12.3579	+	9.85513i	−0.440513	+	0.351297i	−0.818493	−	0.574516i	$-0.805190\pi$
$787$	−12.3579	+	9.85513i	−0.440513	+	0.351297i	0.377980	+	0.925814i	$0.376619\pi$
$788$	1.97361	−	0.450465i	0.0703071	−	0.0160471i
$789$	−12.6530	+	6.09334i	−0.450457	+	0.216929i
$790$	−18.7784	+	26.3528i	−0.668105	+	0.937590i
$791$	21.6907	−	27.1993i	0.771233	−	0.967096i
$792$	6.20867	+	1.41709i	0.220615	+	0.0503540i
$793$	4.78986	+	9.94625i	0.170093	+	0.353202i
$794$	−10.6510	−	5.12925i	−0.377990	−	0.182030i
$795$	33.0901	+	5.69099i	1.17359	+	0.201839i
$796$	−4.24281	+	18.5890i	−0.150382	+	0.658868i
$797$	9.89604	−	20.5493i	0.350536	−	0.727895i	−0.648921	−	0.760856i	$-0.724779\pi$
$797$	9.89604	−	20.5493i	0.350536	−	0.727895i	0.999457	+	0.0329610i	$0.0104937\pi$
$798$	8.43811	+	17.5219i	0.298706	+	0.620269i
$799$	−6.88375	+	30.1597i	−0.243530	+	1.06697i
$800$	4.22285	+	2.67723i	0.149300	+	0.0946544i
$801$	4.46295	−	5.59637i	0.157691	−	0.197738i
$802$	6.03371	+	12.5291i	0.213058	+	0.442419i
$803$	32.8922	−	7.50743i	1.16074	−	0.264931i
$804$	−9.84721	−	12.3480i	−0.347284	−	0.435481i
$805$	−4.74370	+	1.35627i	−0.167193	+	0.0478022i
$806$	−11.9142	−	5.73756i	−0.419659	−	0.202097i
$807$	−17.2140	−	13.7277i	−0.605963	−	0.483239i
$808$	−4.27746	+	8.88223i	−0.150480	+	0.312476i
$809$	−27.7299	−	34.7722i	−0.974931	−	1.22253i	−0.974927	−	0.222525i	$-0.928570\pi$
$809$	−27.7299	−	34.7722i	−0.974931	−	1.22253i	−4.29634e−6	−	1.00000i	$-0.500001\pi$
$810$	1.74939	−	0.0947016i	0.0614674	−	0.00332748i
$811$	−1.14472			−0.0401964			−0.0200982	−	0.999798i	$-0.506398\pi$
$811$	−1.14472			−0.0401964			−0.0200982	+	0.999798i	$0.506398\pi$
$812$	−15.8171	+	12.6138i	−0.555073	+	0.442656i
$813$	3.31133	+	6.87604i	0.116133	+	0.241153i
$814$	8.19417	−	35.9010i	0.287206	−	1.25833i
$815$	−1.89610	−	6.63181i	−0.0664175	−	0.232302i
$816$	4.71506			0.165060
$817$	−7.88259	+	23.0200i	−0.275777	+	0.805369i
$818$			5.74087i			0.200725i
$819$	−8.52625	−	37.3559i	−0.297931	−	1.30532i
$820$	−14.9385	−	2.56919i	−0.521675	−	0.0897200i
$821$	18.2468	−	8.78722i	0.636819	−	0.306676i	−0.0874752	−	0.996167i	$-0.527880\pi$
$821$	18.2468	−	8.78722i	0.636819	−	0.306676i	0.724295	+	0.689491i	$0.242166\pi$
$822$	8.54860	−	6.81728i	0.298167	−	0.237780i
$823$		−	22.2585i		−	0.775884i	−0.921684	−	0.387942i	$-0.873186\pi$
$823$		−	22.2585i		−	0.775884i	0.921684	−	0.387942i	$-0.126814\pi$
$824$	14.8304			0.516640
$825$	−14.6518	+	14.5339i	−0.510109	+	0.506006i
$826$	−9.35952	−	4.50731i	−0.325659	−	0.156829i
$827$	10.8609	+	8.66129i	0.377671	+	0.301182i	0.793866	−	0.608093i	$-0.208065\pi$
$827$	10.8609	+	8.66129i	0.377671	+	0.301182i	−0.416195	+	0.909275i	$0.636637\pi$
$828$	−0.356454	+	0.740185i	−0.0123876	+	0.0257232i
$829$	−11.0801	−	48.5453i	−0.384829	−	1.68605i	−0.682104	−	0.731255i	$-0.738935\pi$
$829$	−11.0801	−	48.5453i	−0.384829	−	1.68605i	0.297274	−	0.954792i	$-0.403922\pi$
$830$	−17.4410	+	15.5230i	−0.605386	+	0.538812i
$831$	−2.56720	−	11.2477i	−0.0890553	−	0.390177i
$832$	2.05589	+	4.26909i	0.0712750	+	0.148004i
$833$	48.2443	+	38.4735i	1.67157	+	1.33303i
$834$	2.57662	−	3.23098i	0.0892209	−	0.111880i
$835$	5.49205	−	31.9334i	0.190060	−	1.10510i
$836$	−12.2697	+	5.90879i	−0.424357	+	0.204360i
$837$	6.44840	−	13.3902i	0.222889	−	0.462834i
$838$	−4.70580	−	1.07407i	−0.162559	−	0.0371031i
$839$	5.07172	−	22.2207i	0.175095	−	0.767142i	−0.808755	−	0.588146i	$-0.799858\pi$
$839$	5.07172	−	22.2207i	0.175095	−	0.767142i	0.983850	−	0.178996i	$-0.0572850\pi$
$840$	−10.8183	−	4.50671i	−0.373268	−	0.155496i
$841$	9.14900	−	4.40593i	0.315483	−	0.151929i
$842$	12.1805	+	2.78013i	0.419769	+	0.0958095i
$843$	1.95574	+	1.55965i	0.0673593	+	0.0537173i
$844$	1.48100	−	1.85711i	0.0509780	−	0.0639244i
$845$	−10.1860	−	18.5183i	−0.350408	−	0.637049i
$846$	−2.84904	−	12.4825i	−0.0979520	−	0.429156i
$847$	8.99808	−	7.17573i	0.309178	−	0.246561i
$848$	−13.0168	+	2.97100i	−0.446999	+	0.102025i
$849$	12.4630	+	6.00186i	0.427729	+	0.205983i
$850$	11.2244	−	17.7044i	0.384992	−	0.607255i
$851$	4.28004	+	2.06116i	0.146718	+	0.0706557i
$852$	−6.71506	+	5.35508i	−0.230054	+	0.183462i
$853$		−	23.3922i		−	0.800935i	−0.916311	−	0.400468i	$-0.868848\pi$
$853$		−	23.3922i		−	0.800935i	0.916311	−	0.400468i	$-0.131152\pi$
$854$	10.8577			0.371542
$855$	10.7546	−	9.57191i	0.367799	−	0.327353i
$856$	6.45871	−	3.11035i	0.220754	−	0.106310i
$857$	40.6566	+	9.27960i	1.38880	+	0.316985i	0.850592	−	0.525826i	$-0.176244\pi$
$857$	40.6566	+	9.27960i	1.38880	+	0.316985i	0.538210	+	0.842811i	$0.319101\pi$
$858$	−19.0672	+	4.35196i	−0.650943	+	0.148573i
$859$	−1.47149			−0.0502066			−0.0251033	−	0.999685i	$-0.507991\pi$
$859$	−1.47149			−0.0502066			−0.0251033	+	0.999685i	$0.507991\pi$
$860$	−5.67446	−	13.5204i	−0.193498	−	0.461041i
$861$	35.5284			1.21080
$862$	19.4068	−	4.42948i	0.660998	−	0.150869i
$863$	14.3668	+	3.27912i	0.489051	+	0.111623i	0.459934	−	0.887953i	$-0.347873\pi$
$863$	14.3668	+	3.27912i	0.489051	+	0.111623i	0.0291173	+	0.999576i	$0.490730\pi$
$864$	−4.79799	+	2.31059i	−0.163231	+	0.0786079i
$865$	−19.7490	−	22.1891i	−0.671485	−	0.754452i
$866$	25.6226			0.870692
$867$		−	0.649208i		−	0.0220482i
$868$	−10.1684	+	8.10907i	−0.345140	+	0.275240i
$869$	47.8515	+	23.0441i	1.62325	+	0.781716i
$870$	−8.89061	−	6.33525i	−0.301420	−	0.214785i
$871$	−59.9526	−	28.8716i	−2.03142	−	0.978278i
$872$	11.8103	−	2.69562i	0.399947	−	0.0912853i
$873$	20.4456	−	16.3048i	0.691979	−	0.551835i
$874$	−0.390931	−	1.71278i	−0.0132234	−	0.0579357i
$875$	−42.6755	+	29.8930i	−1.44269	+	1.01057i
$876$	−6.44591	+	8.08291i	−0.217787	+	0.273096i
$877$	−30.3552	−	24.2074i	−1.02502	−	0.817427i	−0.0416677	−	0.999132i	$-0.513267\pi$
$877$	−30.3552	−	24.2074i	−1.02502	−	0.817427i	−0.983353	+	0.181705i	$0.941839\pi$
$878$	28.2902	+	6.45706i	0.954749	+	0.217915i
$879$	−13.8052	+	6.64826i	−0.465639	+	0.224240i
$880$	3.15582	−	7.57553i	0.106383	−	0.255371i
$881$	−1.11397	+	4.88062i	−0.0375306	+	0.164432i	−0.990220	−	0.139512i	$-0.955447\pi$
$881$	−1.11397	+	4.88062i	−0.0375306	+	0.164432i	0.952690	+	0.303944i	$0.0983037\pi$
$882$	−24.8988	−	5.68299i	−0.838386	−	0.191356i
$883$	−24.9333	+	51.7745i	−0.839072	+	1.74235i	−0.189759	+	0.981831i	$0.560771\pi$
$883$	−24.9333	+	51.7745i	−0.839072	+	1.74235i	−0.649314	+	0.760521i	$0.724944\pi$
$884$	17.8983	−	8.61935i	0.601984	−	0.289900i
$885$	0.950139	−	5.52456i	0.0319386	−	0.185706i
$886$	14.6781	−	18.4057i	0.493120	−	0.618353i
$887$	−45.6581	−	36.4111i	−1.53305	−	1.22257i	−0.889297	−	0.457331i	$-0.848806\pi$
$887$	−45.6581	−	36.4111i	−1.53305	−	1.22257i	−0.643752	−	0.765235i	$-0.722623\pi$
$888$	4.89600	+	10.1667i	0.164299	+	0.341171i
$889$	−10.7557	−	47.1239i	−0.360735	−	1.58048i
$890$	−6.13262	−	6.89035i	−0.205566	−	0.230965i
$891$	−0.639862	−	2.80342i	−0.0214362	−	0.0939180i
$892$	−2.40579	+	4.99567i	−0.0805518	+	0.167268i
$893$	21.4062	+	17.0709i	0.716331	+	0.571255i
$894$	−4.63561	−	2.23239i	−0.155038	−	0.0746623i
$895$	24.9899	−	22.2418i	0.835321	−	0.743461i
$896$	4.66029			0.155689
$897$		−	2.52301i		−	0.0842407i
$898$	6.91041	−	5.51087i	0.230603	−	0.183900i
$899$	−10.9154	+	5.25660i	−0.364050	+	0.175317i
$900$	−1.00620	+	8.61744i	−0.0335401	+	0.287248i
$901$	12.4560	+	54.5733i	0.414969	+	1.81810i
$902$			24.8787i			0.828372i
$903$	18.4793	+	28.9775i	0.614954	+	0.964311i
$904$	−7.46503			−0.248283
$905$	29.9034	−	8.54969i	0.994024	−	0.284201i
$906$	1.72180	−	7.54368i	0.0572029	−	0.250622i
$907$	18.7894	+	39.0166i	0.623892	+	1.29553i	0.938164	+	0.346192i	$0.112526\pi$
$907$	18.7894	+	39.0166i	0.623892	+	1.29553i	−0.314271	+	0.949333i	$0.601760\pi$
$908$	7.11039	−	5.67035i	0.235967	−	0.188177i
$909$	−17.1065			−0.567387
$910$	−49.3046	+	2.66905i	−1.63443	+	0.0884783i
$911$	29.1244	+	36.5208i	0.964933	+	1.20999i	0.977686	+	0.210069i	$0.0673690\pi$
$911$	29.1244	+	36.5208i	0.964933	+	1.20999i	−0.0127531	+	0.999919i	$0.504060\pi$
$912$	1.81064	−	3.75984i	0.0599563	−	0.124501i
$913$	29.9616	+	23.8935i	0.991583	+	0.790761i
$914$	3.00545	+	1.44735i	0.0994116	+	0.0478741i
$915$	1.61060	+	5.63324i	0.0532448	+	0.186229i
$916$	−4.80013	−	6.01917i	−0.158601	−	0.198879i
$917$	−7.48363	+	1.70809i	−0.247131	+	0.0564061i
$918$	9.68720	+	20.1157i	0.319725	+	0.663917i
$919$	−24.6874	+	30.9571i	−0.814363	+	1.02118i	0.184899	+	0.982758i	$0.440804\pi$
$919$	−24.6874	+	30.9571i	−0.814363	+	1.02118i	−0.999262	+	0.0384213i	$0.987767\pi$
$920$	0.862183	+	0.614372i	0.0284253	+	0.0202552i
$921$	3.35732	−	14.7094i	0.110627	−	0.484691i
$922$	−3.52995	−	7.33002i	−0.116253	−	0.241401i
$923$	−15.7009	+	32.6032i	−0.516801	+	1.07315i
$924$	−4.28028	+	18.7531i	−0.140811	+	0.616933i
$925$	49.8295	+	5.81827i	1.63838	+	0.191303i
$926$	−18.7960	−	9.05166i	−0.617674	−	0.297456i
$927$	11.1654	+	23.1852i	0.366719	+	0.761501i
$928$	4.23228	+	0.965991i	0.138932	+	0.0317102i
$929$	16.7675	−	21.0258i	0.550123	−	0.689833i	−0.426574	−	0.904453i	$-0.640280\pi$
$929$	16.7675	−	21.0258i	0.550123	−	0.689833i	0.976698	+	0.214620i	$0.0688512\pi$
$930$	−5.71555	−	4.07277i	−0.187420	−	0.133551i
$931$	49.2056	−	23.6962i	1.61265	−	0.776611i
$932$	17.4369	−	3.97985i	0.571164	−	0.130364i
$933$	11.8548	−	9.45387i	0.388108	−	0.309506i
$934$	4.96583	+	21.7567i	0.162487	+	0.711902i
$935$	−31.7606	−	13.2309i	−1.03868	−	0.432695i
$936$	−5.12630	+	6.42817i	−0.167558	+	0.210111i
$937$	9.38475	−	19.4876i	0.306586	−	0.636633i	−0.689571	−	0.724218i	$-0.742201\pi$
$937$	9.38475	−	19.4876i	0.306586	−	0.636633i	0.996157	+	0.0875854i	$0.0279151\pi$
$938$	−51.1680	+	40.8051i	−1.67069	+	1.33233i
$939$	5.42103			0.176909
$940$	−16.4751	+	0.891863i	−0.537359	+	0.0290894i
$941$	−6.76268	−	8.48013i	−0.220457	−	0.276444i	0.659288	−	0.751891i	$-0.270858\pi$
$941$	−6.76268	−	8.48013i	−0.220457	−	0.276444i	−0.879745	+	0.475447i	$0.842287\pi$
$942$	3.17171	+	6.58612i	0.103340	+	0.214587i
$943$	−3.12900	−	0.714174i	−0.101894	−	0.0232567i
$944$	0.496023	+	2.17322i	0.0161442	+	0.0707323i
$945$	−2.99973	−	55.4130i	−0.0975811	−	1.80259i
$946$	−20.2915	+	12.9401i	−0.659733	+	0.420721i
$947$			9.96407i			0.323789i	0.986808	+	0.161894i	$0.0517604\pi$
$947$			9.96407i			0.323789i	−0.986808	+	0.161894i	$0.948240\pi$
$948$	−15.8669	+	3.62152i	−0.515333	+	0.117621i
$949$	−9.69258	+	42.4660i	−0.314635	+	1.37850i
$950$	−9.80737	−	15.7491i	−0.318193	−	0.510969i
$951$	18.1123	+	22.7121i	0.587331	+	0.736490i
$952$		−	19.5384i		−	0.633242i
$953$			38.9312i			1.26111i	0.776146	+	0.630553i	$0.217172\pi$
$953$			38.9312i			1.26111i	−0.776146	+	0.630553i	$0.782828\pi$
$954$	−14.4448	−	18.1132i	−0.467666	−	0.586435i
$955$	−4.53769	+	10.8927i	−0.146836	+	0.352480i
$956$	10.3316	−	12.9554i	0.334147	−	0.419008i
$957$	−7.77435	+	16.1436i	−0.251309	+	0.521849i
$958$	−6.88988	+	1.57257i	−0.222602	+	0.0508074i
$959$	−28.2496	−	35.4239i	−0.912227	−	1.14390i
$960$	0.691295	+	2.41788i	0.0223115	+	0.0780366i
$961$	20.9128	−	10.0711i	0.674606	−	0.324873i
$962$	37.1703	+	29.6423i	1.19842	+	0.955706i
$963$	9.72518	+	7.75557i	0.313390	+	0.249920i
$964$	−5.39522	+	23.6380i	−0.173768	+	0.761328i
$965$	30.1538	−	16.5861i	0.970686	−	0.533924i
$966$	−2.23571	−	1.07666i	−0.0719328	−	0.0346410i
$967$	7.19746	+	1.64277i	0.231455	+	0.0528280i	0.336675	−	0.941621i	$-0.390698\pi$
$967$	7.19746	+	1.64277i	0.231455	+	0.0528280i	−0.105220	+	0.994449i	$0.533555\pi$
$968$	−2.40767	−	0.549535i	−0.0773854	−	0.0176627i
$969$	−15.7632	−	7.59116i	−0.506387	−	0.243863i
$970$	−16.2415	−	29.5274i	−0.521483	−	0.948068i
$971$	−2.53361	+	11.1005i	−0.0813073	+	0.356231i	−0.999173	−	0.0406604i	$-0.987054\pi$
$971$	−2.53361	+	11.1005i	−0.0813073	+	0.356231i	0.917866	+	0.396891i	$0.129911\pi$
$972$	−11.8017	−	9.41155i	−0.378540	−	0.301876i
$973$	−13.3886	−	10.6770i	−0.429219	−	0.342290i
$974$	−25.2552	+	12.1623i	−0.809229	+	0.389704i
$975$	−8.69850	−	25.1846i	−0.278575	−	0.806552i
$976$	−1.45262	−	1.82153i	−0.0464974	−	0.0583059i
$977$	−24.0602	+	5.49159i	−0.769755	+	0.175692i	−0.589325	−	0.807896i	$-0.700606\pi$
$977$	−24.0602	+	5.49159i	−0.769755	+	0.175692i	−0.180430	+	0.983588i	$0.557749\pi$
$978$	1.50520	−	3.12558i	0.0481310	−	0.0999450i
$979$	−9.43954	+	11.8368i	−0.301689	+	0.378306i
$980$	−12.6559	+	30.3804i	−0.404277	+	0.970466i
$981$	13.1059	+	16.4343i	0.418439	+	0.524705i
$982$			6.84847i			0.218543i
$983$			17.3576i			0.553622i	0.960924	+	0.276811i	$0.0892777\pi$
$983$			17.3576i			0.553622i	−0.960924	+	0.276811i	$0.910722\pi$
$984$	−4.75327	−	5.96041i	−0.151529	−	0.190011i
$985$	3.96622	−	2.18161i	0.126374	−	0.0695120i
$986$	4.04994	−	17.7440i	0.128976	−	0.565083i
$987$	37.7029	−	8.60545i	1.20010	−	0.273915i
$988$		−	17.5822i		−	0.559364i
$989$	−1.04499	−	2.92352i	−0.0332288	−	0.0929626i
$990$	14.2192	−	0.769742i	0.451916	−	0.0244640i
$991$	7.87159	+	34.4877i	0.250049	+	1.09554i	0.931519	+	0.363692i	$0.118484\pi$
$991$	7.87159	+	34.4877i	0.250049	+	1.09554i	−0.681470	+	0.731846i	$0.738659\pi$
$992$	2.72083	+	0.621012i	0.0863864	+	0.0197171i
$993$	1.11663	+	2.31871i	0.0354352	+	0.0735819i
$994$	22.1905	+	27.8260i	0.703841	+	0.882588i
$995$	2.30463	+	42.5728i	0.0730618	+	1.34965i
$996$	−11.7432			−0.372097
$997$	−8.46334	+	6.74929i	−0.268037	+	0.213752i	−0.748280	−	0.663383i	$-0.769120\pi$
$997$	−8.46334	+	6.74929i	−0.268037	+	0.213752i	0.480243	+	0.877135i	$0.340548\pi$
$998$	−6.32326	+	13.1304i	−0.200159	+	0.415635i
$999$	−33.3147	+	41.7753i	−1.05403	+	1.32171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.p.a.59.4	✓	132
5.4	even	2	inner	430.2.p.a.59.19	yes	132
43.35	even	7	inner	430.2.p.a.379.19	yes	132
215.164	even	14	inner	430.2.p.a.379.4	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.p.a.59.4	✓	132	1.1	even	1	trivial
430.2.p.a.59.19	yes	132	5.4	even	2	inner
430.2.p.a.379.4	yes	132	215.164	even	14	inner
430.2.p.a.379.19	yes	132	43.35	even	7	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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.p (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.974928 + 0.222521i) q^{2} +(-1.09644 - 0.250255i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.67031 - 1.48663i) q^{5} +1.12463 q^{6} -4.66029i q^{7} +(-0.781831 + 0.623490i) q^{8} +(-1.56336 - 0.752874i) q^{9} +O(q^{10})\)	\(q+(-0.974928 + 0.222521i) q^{2} +(-1.09644 - 0.250255i) q^{3} +(0.900969 - 0.433884i) q^{4} +(1.67031 - 1.48663i) q^{5} +1.12463 q^{6} -4.66029i q^{7} +(-0.781831 + 0.623490i) q^{8} +(-1.56336 - 0.752874i) q^{9} +(-1.29763 + 1.82103i) q^{10} +(3.30664 + 1.59239i) q^{11} +(-1.09644 + 0.250255i) q^{12} +(-3.70458 + 2.95430i) q^{13} +(1.03701 + 4.54344i) q^{14} +(-2.20343 + 1.21199i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-3.27785 - 2.61400i) q^{17} +(1.69169 + 0.386118i) q^{18} +(-3.34316 + 1.60998i) q^{19} +(0.859875 - 2.06413i) q^{20} +(-1.16626 + 5.10971i) q^{21} +(-3.57808 - 0.816673i) q^{22} +(0.205426 - 0.426571i) q^{23} +(1.01326 - 0.487961i) q^{24} +(0.579878 - 4.96626i) q^{25} +(2.95430 - 3.70458i) q^{26} +(4.16354 + 3.32031i) q^{27} +(-2.02202 - 4.19877i) q^{28} +(-0.965991 - 4.23228i) q^{29} +(1.87849 - 1.67191i) q^{30} +(-0.621012 - 2.72083i) q^{31} +(-0.433884 + 0.900969i) q^{32} +(-3.22702 - 2.57346i) q^{33} +(3.77733 + 1.81907i) q^{34} +(-6.92811 - 7.78413i) q^{35} -1.73520 q^{36} +10.0336i q^{37} +(2.90109 - 2.31354i) q^{38} +(4.80116 - 2.31212i) q^{39} +(-0.379005 + 2.20371i) q^{40} +(-1.50842 - 6.60882i) q^{41} -5.24112i q^{42} +(4.60568 - 4.66773i) q^{43} +3.67009 q^{44} +(-3.73054 + 1.06660i) q^{45} +(-0.105354 + 0.461587i) q^{46} +(-3.20149 - 6.64796i) q^{47} +(-0.879275 + 0.701198i) q^{48} -14.7183 q^{49} +(0.539758 + 4.97078i) q^{50} +(2.93979 + 3.68638i) q^{51} +(-2.05589 + 4.26909i) q^{52} +(-10.4387 - 8.32456i) q^{53} +(-4.79799 - 2.31059i) q^{54} +(7.89041 - 2.25595i) q^{55} +(2.90564 + 3.64356i) q^{56} +(4.06848 - 0.928603i) q^{57} +(1.88354 + 3.91122i) q^{58} +(-1.38983 + 1.74279i) q^{59} +(-1.45936 + 2.04800i) q^{60} +(0.518436 - 2.27141i) q^{61} +(1.21088 + 2.51442i) q^{62} +(-3.50861 + 7.28570i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-1.79585 + 10.4419i) q^{65} +(3.71876 + 1.79086i) q^{66} +(6.09321 + 12.6527i) q^{67} +(-4.08741 - 0.932924i) q^{68} +(-0.331988 + 0.416300i) q^{69} +(8.48654 + 6.04732i) q^{70} +(6.88074 - 3.31359i) q^{71} +(1.69169 - 0.386118i) q^{72} +(7.18714 - 5.73156i) q^{73} +(-2.23269 - 9.78204i) q^{74} +(-1.87863 + 5.30008i) q^{75} +(-2.31354 + 2.90109i) q^{76} +(7.42101 - 15.4099i) q^{77} +(-4.16629 + 3.32251i) q^{78} +14.4713 q^{79} +(-0.120870 - 2.23280i) q^{80} +(-0.488503 - 0.612564i) q^{81} +(2.94120 + 6.10747i) q^{82} +(10.1800 + 2.32351i) q^{83} +(1.16626 + 5.10971i) q^{84} +(-9.36106 + 0.506751i) q^{85} +(-3.45154 + 5.57556i) q^{86} +4.88218i q^{87} +(-3.57808 + 0.816673i) q^{88} +(-0.917942 + 4.02177i) q^{89} +(3.39967 - 1.86998i) q^{90} +(13.7679 + 17.2644i) q^{91} -0.473458i q^{92} +3.13863i q^{93} +(4.60053 + 5.76888i) q^{94} +(-3.19068 + 7.65921i) q^{95} +(0.701198 - 0.879275i) q^{96} +(-6.53900 + 13.5784i) q^{97} +(14.3493 - 3.27513i) q^{98} +(-3.97059 - 4.97897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9}+O(q^{10}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9	\( 132 q + 22 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{9} + 8 q^{11} - 10 q^{14} - 20 q^{15} - 22 q^{16} - 4 q^{19} + 4 q^{20} - 24 q^{21} + 4 q^{24} - 16 q^{25} + 12 q^{26} + 40 q^{29} + 24 q^{31} - 4 q^{35} + 128 q^{36} - 56 q^{39} - 28 q^{41} - 8 q^{44} - 80 q^{45} - 12 q^{46} - 136 q^{49} - 56 q^{50} + 172 q^{51} + 16 q^{54} - 4 q^{56} + 16 q^{59} - 8 q^{60} - 44 q^{61} + 22 q^{64} + 42 q^{65} + 8 q^{66} - 62 q^{69} + 12 q^{70} - 8 q^{71} - 4 q^{74} - 122 q^{75} - 52 q^{76} - 64 q^{79} - 4 q^{80} - 56 q^{81} + 24 q^{84} - 72 q^{85} - 10 q^{86} + 16 q^{89} + 2 q^{90} - 24 q^{91} - 20 q^{94} + 106 q^{95} - 4 q^{96} - 104 q^{99}+O(q^{100}) \) 132 * q + 22 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^9 + 8 * q^11 - 10 * q^14 - 20 * q^15 - 22 * q^16 - 4 * q^19 + 4 * q^20 - 24 * q^21 + 4 * q^24 - 16 * q^25 + 12 * q^26 + 40 * q^29 + 24 * q^31 - 4 * q^35 + 128 * q^36 - 56 * q^39 - 28 * q^41 - 8 * q^44 - 80 * q^45 - 12 * q^46 - 136 * q^49 - 56 * q^50 + 172 * q^51 + 16 * q^54 - 4 * q^56 + 16 * q^59 - 8 * q^60 - 44 * q^61 + 22 * q^64 + 42 * q^65 + 8 * q^66 - 62 * q^69 + 12 * q^70 - 8 * q^71 - 4 * q^74 - 122 * q^75 - 52 * q^76 - 64 * q^79 - 4 * q^80 - 56 * q^81 + 24 * q^84 - 72 * q^85 - 10 * q^86 + 16 * q^89 + 2 * q^90 - 24 * q^91 - 20 * q^94 + 106 * q^95 - 4 * q^96 - 104 * q^99

Introduction

L-functions

Modular forms

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