LMFDB - Embedded newform 930.2.y.a.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.1
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.68775 + 0.389232i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.12975 + 1.92968i) q^{5} +(1.59420 + 0.677139i) q^{6} +(1.54573 - 0.502238i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.69700 - 1.31385i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.68775 + 0.389232i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.12975 + 1.92968i) q^{5} +(1.59420 + 0.677139i) q^{6} +(1.54573 - 0.502238i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.69700 - 1.31385i) q^{9} +(2.04823 - 0.897090i) q^{10} +(-0.268212 - 0.825472i) q^{11} +(-0.891724 - 1.48487i) q^{12} +(1.83314 - 1.33186i) q^{13} +(-1.54573 - 0.502238i) q^{14} +(1.15565 - 3.69655i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.72382 - 1.53486i) q^{17} +(-2.95418 - 0.522328i) q^{18} +(1.15222 + 0.837138i) q^{19} +(-2.18435 - 0.478156i) q^{20} +(-2.41332 + 1.44930i) q^{21} +(-0.268212 + 0.825472i) q^{22} +(-0.576367 - 0.187273i) q^{23} +(-0.151362 + 1.72542i) q^{24} +(-2.44732 - 4.36012i) q^{25} -2.26589 q^{26} +(-4.04046 + 3.26721i) q^{27} +(0.955313 + 1.31488i) q^{28} +(0.697495 + 0.506760i) q^{29} +(-3.10772 + 2.31130i) q^{30} +(5.48684 + 0.945827i) q^{31} +1.00000 q^{32} +(0.773975 + 1.28879i) q^{33} +(2.91948 + 4.01832i) q^{34} +(-0.777135 + 3.55016i) q^{35} +(2.08296 + 2.15899i) q^{36} +6.29256 q^{37} +(-0.440109 - 1.35452i) q^{38} +(-2.57548 + 2.96135i) q^{39} +(1.48612 + 1.67076i) q^{40} +(3.88485 - 5.34704i) q^{41} +(2.80429 + 0.246005i) q^{42} +(4.86707 + 3.53613i) q^{43} +(0.702189 - 0.510170i) q^{44} +(-0.511632 + 6.68866i) q^{45} +(0.356214 + 0.490287i) q^{46} +(-0.815384 + 0.592411i) q^{47} +(1.13663 - 1.30693i) q^{48} +(-3.52608 + 2.56185i) q^{49} +(-0.582894 + 4.96591i) q^{50} +(8.57005 + 0.751804i) q^{51} +(1.83314 + 1.33186i) q^{52} +(13.0449 + 4.23855i) q^{53} +(5.18922 - 0.268301i) q^{54} +(1.89591 + 0.415017i) q^{55} -1.62528i q^{56} +(-2.27050 - 0.964398i) q^{57} +(-0.266419 - 0.819955i) q^{58} +(-1.40322 - 1.93136i) q^{59} +(3.87274 - 0.0432092i) q^{60} -7.03995i q^{61} +(-3.88300 - 3.99027i) q^{62} +(3.50896 - 3.38539i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.499055 + 5.04204i) q^{65} +(0.131375 - 1.49759i) q^{66} +13.0864i q^{67} -4.96692i q^{68} +(1.04566 + 0.0917297i) q^{69} +(2.71545 - 2.41535i) q^{70} +(10.6039 + 3.44541i) q^{71} +(-0.416128 - 2.97100i) q^{72} +(-0.262191 - 0.806942i) q^{73} +(-5.09079 - 3.69867i) q^{74} +(5.82755 + 6.40622i) q^{75} +(-0.440109 + 1.35452i) q^{76} +(-0.829167 - 1.14125i) q^{77} +(3.82425 - 0.881955i) q^{78} +(3.70706 + 1.20450i) q^{79} +(-0.220247 - 2.22519i) q^{80} +(5.54759 - 7.08690i) q^{81} +(-6.28582 + 2.04239i) q^{82} +(-2.16626 + 2.98161i) q^{83} +(-2.12412 - 1.84734i) q^{84} +(8.29855 - 7.38144i) q^{85} +(-1.85905 - 5.72158i) q^{86} +(-1.37444 - 0.583797i) q^{87} -0.867953 q^{88} +(-0.0107535 - 0.0330958i) q^{89} +(4.34542 - 5.11051i) q^{90} +(2.16463 - 2.97936i) q^{91} -0.606028i q^{92} +(-9.62856 + 0.539332i) q^{93} +1.00787 q^{94} +(-2.91713 + 1.27766i) q^{95} +(-1.68775 + 0.389232i) q^{96} +(9.24214 - 3.00295i) q^{97} +4.35848 q^{98} +(-1.80792 - 1.87391i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.68775	+	0.389232i	−0.974423	+	0.224723i
$3$	−1.68775	+	0.389232i	−0.974423	+	0.224723i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−1.12975	+	1.92968i	−0.505241	+	0.862978i
$5$	−1.12975	+	1.92968i	−0.505241	+	0.862978i
$6$	1.59420	+	0.677139i	0.650831	+	0.276441i
$7$	1.54573	−	0.502238i	0.584231	−	0.189828i	−0.00196430	−	0.999998i	$-0.500625\pi$
$7$	1.54573	−	0.502238i	0.584231	−	0.189828i	0.586195	+	0.810170i	$0.300625\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.69700	−	1.31385i	0.898999	−	0.437950i
$10$	2.04823	−	0.897090i	0.647706	−	0.283685i
$11$	−0.268212	−	0.825472i	−0.0808690	−	0.248889i	0.902445	−	0.430805i	$-0.141770\pi$
$11$	−0.268212	−	0.825472i	−0.0808690	−	0.248889i	−0.983314	+	0.181916i	$0.941770\pi$
$12$	−0.891724	−	1.48487i	−0.257419	−	0.428644i
$13$	1.83314	−	1.33186i	0.508422	−	0.369390i	−0.303803	−	0.952735i	$-0.598256\pi$
$13$	1.83314	−	1.33186i	0.508422	−	0.369390i	0.812225	+	0.583345i	$0.198256\pi$
$14$	−1.54573	−	0.502238i	−0.413113	−	0.134229i
$15$	1.15565	−	3.69655i	0.298387	−	0.954445i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−4.72382	−	1.53486i	−1.14570	−	0.372259i	−0.326175	−	0.945309i	$-0.605760\pi$
$17$	−4.72382	−	1.53486i	−1.14570	−	0.372259i	−0.819520	+	0.573050i	$0.805760\pi$
$18$	−2.95418	−	0.522328i	−0.696307	−	0.123114i
$19$	1.15222	+	0.837138i	0.264338	+	0.192053i	0.712057	−	0.702122i	$-0.247764\pi$
$19$	1.15222	+	0.837138i	0.264338	+	0.192053i	−0.447719	+	0.894174i	$0.647764\pi$
$20$	−2.18435	−	0.478156i	−0.488435	−	0.106919i
$21$	−2.41332	+	1.44930i	−0.526629	+	0.316263i
$22$	−0.268212	+	0.825472i	−0.0571830	+	0.175991i
$23$	−0.576367	−	0.187273i	−0.120181	−	0.0390491i	0.248309	−	0.968681i	$-0.420125\pi$
$23$	−0.576367	−	0.187273i	−0.120181	−	0.0390491i	−0.368490	+	0.929632i	$0.620125\pi$
$24$	−0.151362	+	1.72542i	−0.0308967	+	0.352201i
$25$	−2.44732	−	4.36012i	−0.489463	−	0.872024i
$26$	−2.26589			−0.444377
$27$	−4.04046	+	3.26721i	−0.777588	+	0.628774i
$28$	0.955313	+	1.31488i	0.180537	+	0.248488i
$29$	0.697495	+	0.506760i	0.129522	+	0.0941029i	0.650660	−	0.759369i	$-0.274492\pi$
$29$	0.697495	+	0.506760i	0.129522	+	0.0941029i	−0.521138	+	0.853472i	$0.674492\pi$
$30$	−3.10772	+	2.31130i	−0.567389	+	0.421983i
$31$	5.48684	+	0.945827i	0.985466	+	0.169876i
$31$	5.48684	+	0.945827i	0.985466	+	0.169876i
$32$	1.00000			0.176777
$33$	0.773975	+	1.28879i	0.134732	+	0.224350i
$34$	2.91948	+	4.01832i	0.500687	+	0.689137i
$35$	−0.777135	+	3.55016i	−0.131360	+	0.600087i
$36$	2.08296	+	2.15899i	0.347161	+	0.359832i
$37$	6.29256			1.03449			0.517245	−	0.855837i	$-0.326958\pi$
$37$	6.29256			1.03449			0.517245	+	0.855837i	$0.326958\pi$
$38$	−0.440109	−	1.35452i	−0.0713952	−	0.219732i
$39$	−2.57548	+	2.96135i	−0.412407	+	0.474196i
$40$	1.48612	+	1.67076i	0.234976	+	0.264171i
$41$	3.88485	−	5.34704i	0.606712	−	0.835068i	−0.389590	−	0.920988i	$-0.627383\pi$
$41$	3.88485	−	5.34704i	0.606712	−	0.835068i	0.996302	+	0.0859209i	$0.0273832\pi$
$42$	2.80429	+	0.246005i	0.432711	+	0.0379594i
$43$	4.86707	+	3.53613i	0.742221	+	0.539255i	0.893406	−	0.449250i	$-0.148309\pi$
$43$	4.86707	+	3.53613i	0.742221	+	0.539255i	−0.151185	+	0.988505i	$0.548309\pi$
$44$	0.702189	−	0.510170i	0.105859	−	0.0769110i
$45$	−0.511632	+	6.68866i	−0.0762697	+	0.997087i
$46$	0.356214	+	0.490287i	0.0525210	+	0.0722889i
$47$	−0.815384	+	0.592411i	−0.118936	+	0.0864120i	−0.645663	−	0.763622i	$-0.723419\pi$
$47$	−0.815384	+	0.592411i	−0.118936	+	0.0864120i	0.526727	+	0.850034i	$0.323419\pi$
$48$	1.13663	−	1.30693i	0.164059	−	0.188639i
$49$	−3.52608	+	2.56185i	−0.503726	+	0.365979i
$50$	−0.582894	+	4.96591i	−0.0824337	+	0.702285i
$51$	8.57005	+	0.751804i	1.20005	+	0.105274i
$52$	1.83314	+	1.33186i	0.254211	+	0.184695i
$53$	13.0449	+	4.23855i	1.79186	+	0.582209i	0.999608	−	0.0279898i	$-0.00891058\pi$
$53$	13.0449	+	4.23855i	1.79186	+	0.582209i	0.792248	+	0.610199i	$0.208911\pi$
$54$	5.18922	−	0.268301i	0.706164	−	0.0365111i
$55$	1.89591	+	0.415017i	0.255644	+	0.0559608i
$56$		−	1.62528i		−	0.217187i
$57$	−2.27050	−	0.964398i	−0.300735	−	0.127738i
$58$	−0.266419	−	0.819955i	−0.0349826	−	0.107665i
$59$	−1.40322	−	1.93136i	−0.182683	−	0.251442i	0.707847	−	0.706366i	$-0.249667\pi$
$59$	−1.40322	−	1.93136i	−0.182683	−	0.251442i	−0.890531	+	0.454924i	$0.849667\pi$
$60$	3.87274	−	0.0432092i	0.499969	−	0.00557828i
$61$		−	7.03995i		−	0.901373i	−0.892682	−	0.450687i	$-0.851179\pi$
$61$		−	7.03995i		−	0.901373i	0.892682	−	0.450687i	$-0.148821\pi$
$62$	−3.88300	−	3.99027i	−0.493142	−	0.506765i
$63$	3.50896	−	3.38539i	0.442088	−	0.426519i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.499055	+	5.04204i	0.0619001	+	0.625388i
$66$	0.131375	−	1.49759i	0.0161712	−	0.184340i
$67$			13.0864i			1.59876i	0.600825	+	0.799381i	$0.294839\pi$
$67$			13.0864i			1.59876i	−0.600825	+	0.799381i	$0.705161\pi$
$68$		−	4.96692i		−	0.602328i
$69$	1.04566	+	0.0917297i	0.125882	+	0.0110430i
$70$	2.71545	−	2.41535i	0.324558	−	0.288690i
$71$	10.6039	+	3.44541i	1.25845	+	0.408895i	0.860942	−	0.508704i	$-0.169875\pi$
$71$	10.6039	+	3.44541i	1.25845	+	0.408895i	0.397508	+	0.917599i	$0.369875\pi$
$72$	−0.416128	−	2.97100i	−0.0490412	−	0.350136i
$73$	−0.262191	−	0.806942i	−0.0306872	−	0.0944454i	0.934540	−	0.355859i	$-0.115812\pi$
$73$	−0.262191	−	0.806942i	−0.0306872	−	0.0944454i	−0.965227	+	0.261413i	$0.915812\pi$
$74$	−5.09079	−	3.69867i	−0.591792	−	0.429962i
$75$	5.82755	+	6.40622i	0.672908	+	0.739726i
$76$	−0.440109	+	1.35452i	−0.0504840	+	0.155374i
$77$	−0.829167	−	1.14125i	−0.0944923	−	0.130058i
$78$	3.82425	−	0.881955i	0.433011	−	0.0998617i
$79$	3.70706	+	1.20450i	0.417077	+	0.135516i	0.510035	−	0.860154i	$-0.329632\pi$
$79$	3.70706	+	1.20450i	0.417077	+	0.135516i	−0.0929586	+	0.995670i	$0.529632\pi$
$80$	−0.220247	−	2.22519i	−0.0246244	−	0.248784i
$81$	5.54759	−	7.08690i	0.616399	−	0.787434i
$82$	−6.28582	+	2.04239i	−0.694153	+	0.225544i
$83$	−2.16626	+	2.98161i	−0.237778	+	0.327274i	−0.911184	−	0.411999i	$-0.864831\pi$
$83$	−2.16626	+	2.98161i	−0.237778	+	0.327274i	0.673406	+	0.739273i	$0.264831\pi$
$84$	−2.12412	−	1.84734i	−0.231761	−	0.201562i
$85$	8.29855	−	7.38144i	0.900104	−	0.800630i
$86$	−1.85905	−	5.72158i	−0.200467	−	0.616974i
$87$	−1.37444	−	0.583797i	−0.147356	−	0.0625896i
$88$	−0.867953			−0.0925241
$89$	−0.0107535	−	0.0330958i	−0.00113987	−	0.00350815i	0.950485	−	0.310771i	$-0.100587\pi$
$89$	−0.0107535	−	0.0330958i	−0.00113987	−	0.00350815i	−0.951625	+	0.307262i	$0.900587\pi$
$90$	4.34542	−	5.11051i	0.458047	−	0.538695i
$91$	2.16463	−	2.97936i	0.226915	−	0.312322i
$92$		−	0.606028i		−	0.0631828i
$93$	−9.62856	+	0.539332i	−0.998435	+	0.0559261i
$94$	1.00787			0.103954
$95$	−2.91713	+	1.27766i	−0.299291	+	0.131085i
$96$	−1.68775	+	0.389232i	−0.172255	+	0.0397258i
$97$	9.24214	−	3.00295i	0.938397	−	0.304904i	0.200405	−	0.979713i	$-0.435774\pi$
$97$	9.24214	−	3.00295i	0.938397	−	0.304904i	0.737992	+	0.674809i	$0.235774\pi$
$98$	4.35848			0.440273
$99$	−1.80792	−	1.87391i	−0.181702	−	0.188335i
$100$	3.39046	−	3.67489i	0.339046	−	0.367489i
$101$	6.80856	+	2.21224i	0.677477	+	0.220126i	0.627491	−	0.778624i	$-0.284082\pi$
$101$	6.80856	+	2.21224i	0.677477	+	0.220126i	0.0499867	+	0.998750i	$0.484082\pi$
$102$	−6.49142	−	5.64557i	−0.642746	−	0.558995i
$103$	−5.32587	+	7.33043i	−0.524774	+	0.722289i	−0.986323	−	0.164826i	$-0.947294\pi$
$103$	−5.32587	+	7.33043i	−0.524774	+	0.722289i	0.461549	+	0.887115i	$0.347294\pi$
$104$	−0.700198	−	2.15499i	−0.0686600	−	0.211314i
$105$	−0.0702268	−	6.29427i	−0.00685343	−	0.614258i
$106$	−8.06220	−	11.0967i	−0.783070	−	1.07780i
$107$	−3.99340	+	12.2904i	−0.386057	+	1.18816i	0.549654	+	0.835392i	$0.314760\pi$
$107$	−3.99340	+	12.2904i	−0.386057	+	1.18816i	−0.935711	+	0.352768i	$0.885240\pi$
$108$	−4.35587	−	2.83309i	−0.419144	−	0.272614i
$109$	0.120757	−	0.0877352i	0.0115664	−	0.00840351i	−0.581987	−	0.813198i	$-0.697725\pi$
$109$	0.120757	−	0.0877352i	0.0115664	−	0.00840351i	0.593553	+	0.804795i	$0.297725\pi$
$110$	−1.28988	−	1.45014i	−0.122985	−	0.138266i
$111$	−10.6203	+	2.44926i	−1.00803	+	0.232474i
$112$	−0.955313	+	1.31488i	−0.0902686	+	0.124244i
$113$	1.16036	+	3.57121i	0.109157	+	0.335951i	0.990684	−	0.136183i	$-0.0434836\pi$
$113$	1.16036	+	3.57121i	0.109157	+	0.335951i	−0.881526	+	0.472135i	$0.843484\pi$
$114$	1.27001	+	2.11478i	0.118948	+	0.198067i
$115$	1.01253	−	0.900631i	0.0944188	−	0.0839843i
$116$	−0.266419	+	0.819955i	−0.0247364	+	0.0761309i
$117$	3.19412	−	6.00048i	0.295296	−	0.554745i
$118$			2.38730i			0.219769i
$119$	−8.07262			−0.740016
$120$	−3.15851	−	2.24138i	−0.288331	−	0.204609i
$121$	8.28972	−	6.02283i	0.753611	−	0.547530i
$122$	−4.13798	+	5.69544i	−0.374635	+	0.515641i
$123$	−4.47542	+	10.5366i	−0.403535	+	0.950051i
$124$	0.795992	+	5.51057i	0.0714822	+	0.494864i
$125$	11.1785	+	0.203327i	0.999835	+	0.0181861i
$126$	−4.82869	+	0.676323i	−0.430174	+	0.0602516i
$127$	8.47455	−	6.15712i	0.751995	−	0.546356i	−0.144450	−	0.989512i	$-0.546141\pi$
$127$	8.47455	−	6.15712i	0.751995	−	0.546356i	0.896445	+	0.443156i	$0.146141\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−9.59077	−	4.07369i	−0.844420	−	0.358668i
$130$	2.55989	−	4.37243i	0.224517	−	0.383488i
$131$	11.4145	−	3.70881i	0.997294	−	0.324040i	0.235510	−	0.971872i	$-0.424324\pi$
$131$	11.4145	−	3.70881i	0.997294	−	0.324040i	0.761784	+	0.647832i	$0.224324\pi$
$132$	−0.986545	+	1.13435i	−0.0858677	+	0.0987328i
$133$	2.20146	+	0.715299i	0.190891	+	0.0620243i
$134$	7.69201	−	10.5871i	0.664488	−	0.914590i
$135$	−1.73993	−	11.4879i	−0.149749	−	0.988724i
$136$	−2.91948	+	4.01832i	−0.250344	+	0.344568i
$137$	−4.01218	−	5.52230i	−0.342784	−	0.471802i	0.602468	−	0.798143i	$-0.294184\pi$
$137$	−4.01218	−	5.52230i	−0.342784	−	0.471802i	−0.945252	+	0.326341i	$0.894184\pi$
$138$	−0.792036	−	0.688832i	−0.0674226	−	0.0586373i
$139$	−4.10486	−	5.64986i	−0.348170	−	0.479215i	0.598635	−	0.801022i	$-0.295710\pi$
$139$	−4.10486	−	5.64986i	−0.348170	−	0.479215i	−0.946805	+	0.321807i	$0.895710\pi$
$140$	−3.61655	+	0.357962i	−0.305655	+	0.0302533i
$141$	1.14558	−	1.31721i	0.0964751	−	0.110929i
$142$	−6.55356	−	9.02020i	−0.549963	−	0.756958i
$143$	−1.59108	−	1.15599i	−0.133053	−	0.0966686i
$144$	−1.40965	+	2.64818i	−0.117471	+	0.220682i
$145$	−1.76588	+	0.773427i	−0.146648	+	0.0642297i
$146$	−0.262191	+	0.806942i	−0.0216991	+	0.0667830i
$147$	4.95399	−	5.69622i	0.408598	−	0.469817i
$148$	1.94451	+	5.98458i	0.159838	+	0.491929i
$149$			22.0249i			1.80435i	0.431370	+	0.902175i	$0.358031\pi$
$149$			22.0249i			1.80435i	−0.431370	+	0.902175i	$0.641969\pi$
$150$	−0.949108	−	8.60809i	−0.0774944	−	0.702848i
$151$	−10.8005	+	3.50929i	−0.878932	+	0.285582i	−0.713514	−	0.700641i	$-0.752897\pi$
$151$	−10.8005	+	3.50929i	−0.878932	+	0.285582i	−0.165418	+	0.986224i	$0.552897\pi$
$152$	1.15222	−	0.837138i	0.0934575	−	0.0679008i
$153$	−14.7567	+	2.06688i	−1.19301	+	0.167097i
$154$			1.41066i			0.113674i
$155$	−8.02392	+	9.51928i	−0.644496	+	0.764607i
$156$	−3.61228	−	1.53432i	−0.289214	−	0.122844i
$157$	−0.886102	+	1.21961i	−0.0707186	+	0.0973358i	−0.842911	−	0.538053i	$-0.819160\pi$
$157$	−0.886102	+	1.21961i	−0.0707186	+	0.0973358i	0.772193	+	0.635389i	$0.219160\pi$
$158$	−2.29109	−	3.15341i	−0.182269	−	0.250872i
$159$	−23.6663	−	2.07612i	−1.87686	−	0.164647i
$160$	−1.12975	+	1.92968i	−0.0893148	+	0.152554i
$161$	−0.984963			−0.0776260
$162$	−8.65367	+	2.47263i	−0.679897	+	0.194268i
$163$	17.2553	+	5.60660i	1.35154	+	0.439143i	0.893211	−	0.449639i	$-0.148447\pi$
$163$	17.2553	+	5.60660i	1.35154	+	0.439143i	0.458331	+	0.888781i	$0.348447\pi$
$164$	6.28582	+	2.04239i	0.490840	+	0.159484i
$165$	−3.36136	+	0.0375035i	−0.261681	+	0.00291964i
$166$	3.50509	−	1.13887i	0.272048	−	0.0883936i
$167$	−2.59809	+	3.57597i	−0.201047	+	0.276717i	−0.897621	−	0.440767i	$-0.854706\pi$
$167$	−2.59809	+	3.57597i	−0.201047	+	0.276717i	0.696575	+	0.717484i	$0.254706\pi$
$168$	0.632609	+	2.74306i	0.0488068	+	0.211632i
$169$	−2.43065	+	7.48078i	−0.186973	+	0.575444i
$170$	−11.0524	+	1.09395i	−0.847678	+	0.0839021i
$171$	4.20741	+	0.743912i	0.321749	+	0.0568883i
$172$	−1.85905	+	5.72158i	−0.141752	+	0.436267i
$173$	4.79292	−	3.48226i	0.364399	−	0.264751i	−0.390485	−	0.920609i	$-0.627693\pi$
$173$	4.79292	−	3.48226i	0.364399	−	0.264751i	0.754885	+	0.655858i	$0.227693\pi$
$174$	0.768801	+	1.28018i	0.0582827	+	0.0970501i
$175$	−5.97270	−	5.51043i	−0.451494	−	0.416549i
$176$	0.702189	+	0.510170i	0.0529295	+	0.0384555i
$177$	3.12003	+	2.71348i	0.234516	+	0.203958i
$178$	−0.0107535	+	0.0330958i	−0.000806007	+	0.00248064i
$179$	0.747192	+	2.29962i	0.0558478	+	0.171882i	0.975089	−	0.221812i	$-0.0711971\pi$
$179$	0.747192	+	2.29962i	0.0558478	+	0.171882i	−0.919242	+	0.393694i	$0.871197\pi$
$180$	−6.51940	+	1.58032i	−0.485927	+	0.117790i
$181$		−	22.9671i		−	1.70713i	−0.520987	−	0.853565i	$-0.674436\pi$
$181$		−	22.9671i		−	1.70713i	0.520987	−	0.853565i	$-0.325564\pi$
$182$	−3.50245	+	1.13801i	−0.259619	+	0.0843552i
$183$	2.74017	+	11.8817i	0.202559	+	0.878318i
$184$	−0.356214	+	0.490287i	−0.0262605	+	0.0361445i
$185$	−7.10904	+	12.1426i	−0.522667	+	0.892743i
$186$	8.10668	+	5.22320i	0.594410	+	0.382983i
$187$			4.31106i			0.315256i
$188$	−0.815384	−	0.592411i	−0.0594680	−	0.0432060i
$189$	−4.60455	+	7.07949i	−0.334932	+	0.514957i
$190$	3.11100	+	0.681001i	0.225695	+	0.0494050i
$191$			7.95630i			0.575698i	0.957676	+	0.287849i	$0.0929401\pi$
$191$			7.95630i			0.575698i	−0.957676	+	0.287849i	$0.907060\pi$
$192$	1.59420	+	0.677139i	0.115052	+	0.0488683i
$193$	−16.2153	+	5.26869i	−1.16721	+	0.379248i	−0.827599	−	0.561319i	$-0.810294\pi$
$193$	−16.2153	+	5.26869i	−1.16721	+	0.379248i	−0.339607	+	0.940567i	$0.610294\pi$
$194$	−9.24214	−	3.00295i	−0.663547	−	0.215599i
$195$	−2.80480	−	8.31545i	−0.200856	−	0.595482i
$196$	−3.52608	−	2.56185i	−0.251863	−	0.182989i
$197$	17.9663	−	5.83761i	1.28005	−	0.415913i	0.411451	−	0.911432i	$-0.365022\pi$
$197$	17.9663	−	5.83761i	1.28005	−	0.415913i	0.868597	+	0.495519i	$0.165022\pi$
$198$	0.361180	+	2.57869i	0.0256679	+	0.183259i
$199$	−8.34678	−	11.4884i	−0.591687	−	0.814388i	0.403228	−	0.915099i	$-0.367888\pi$
$199$	−8.34678	−	11.4884i	−0.591687	−	0.814388i	−0.994916	+	0.100712i	$0.967888\pi$
$200$	−4.90298	+	0.980184i	−0.346693	+	0.0693095i
$201$	−5.09365	−	22.0866i	−0.359278	−	1.55787i
$202$	−4.20792	−	5.79171i	−0.296068	−	0.407503i
$203$	1.33265	+	0.433005i	0.0935339	+	0.0303910i
$204$	1.93328	+	8.38292i	0.135357	+	0.586922i
$205$	5.92914	+	13.5374i	0.414109	+	0.945490i
$206$	8.61744	−	2.79998i	0.600405	−	0.195084i
$207$	−1.80051	+	0.252185i	−0.125144	+	0.0175281i
$208$	−0.700198	+	2.15499i	−0.0485500	+	0.149421i
$209$	0.381994	−	1.17566i	0.0264231	−	0.0813219i
$210$	−3.64287	+	5.13345i	−0.251382	+	0.354242i
$211$	−5.04561			−0.347354			−0.173677	−	0.984803i	$-0.555565\pi$
$211$	−5.04561			−0.347354			−0.173677	+	0.984803i	$0.555565\pi$
$212$			13.7162i			0.942035i
$213$	−19.2378	−	1.68762i	−1.31815	−	0.115634i
$214$	10.4549	−	7.59590i	0.714680	−	0.519245i
$215$	−12.3222	+	5.39692i	−0.840366	+	0.368067i
$216$	1.85873	+	4.85233i	0.126470	+	0.330159i
$217$	8.95620	−	1.29371i	0.607986	−	0.0878225i
$218$	−0.149264			−0.0101094
$219$	0.756600	+	1.25986i	0.0511263	+	0.0851336i
$220$	0.191164	+	1.93136i	0.0128883	+	0.130213i
$221$	−10.7037	+	3.47783i	−0.720006	+	0.233944i
$222$	10.0316	+	4.26094i	0.673278	+	0.285976i
$223$	−0.251251			−0.0168250			−0.00841251	−	0.999965i	$-0.502678\pi$
$223$	−0.251251			−0.0168250			−0.00841251	+	0.999965i	$0.502678\pi$
$224$	1.54573	−	0.502238i	0.103278	−	0.0335572i
$225$	−12.3290	−	8.54383i	−0.821930	−	0.569588i
$226$	1.16036	−	3.57121i	0.0771858	−	0.237554i
$227$	−8.16737	−	5.93394i	−0.542087	−	0.393850i	0.282772	−	0.959187i	$-0.408746\pi$
$227$	−8.16737	−	5.93394i	−0.542087	−	0.393850i	−0.824860	+	0.565338i	$0.808746\pi$
$228$	0.215574	−	2.45739i	0.0142767	−	0.162745i
$229$	9.01174	−	12.4036i	0.595513	−	0.819653i	−0.399776	−	0.916613i	$-0.630912\pi$
$229$	9.01174	−	12.4036i	0.595513	−	0.819653i	0.995288	+	0.0969603i	$0.0309120\pi$
$230$	−1.34853	+	0.133476i	−0.0889195	+	0.00880114i
$231$	1.84364	+	1.60341i	0.121302	+	0.105496i
$232$	0.697495	−	0.506760i	0.0457928	−	0.0332704i
$233$	9.54987	−	6.93839i	0.625633	−	0.454549i	−0.229252	−	0.973367i	$-0.573628\pi$
$233$	9.54987	−	6.93839i	0.625633	−	0.454549i	0.854885	+	0.518818i	$0.173628\pi$
$234$	−6.11109	+	2.97704i	−0.399495	+	0.194615i
$235$	−0.221980	−	2.24271i	−0.0144804	−	0.146298i
$236$	1.40322	−	1.93136i	0.0913417	−	0.125721i
$237$	−6.72541	−	0.589984i	−0.436862	−	0.0383236i
$238$	6.53088	+	4.74497i	0.423334	+	0.307570i
$239$	−5.20712	+	16.0259i	−0.336820	+	1.03663i	0.628998	+	0.777407i	$0.283465\pi$
$239$	−5.20712	+	16.0259i	−0.336820	+	1.03663i	−0.965818	+	0.259219i	$0.916535\pi$
$240$	1.23784	+	3.66984i	0.0799021	+	0.236887i
$241$	−17.2154	+	5.59363i	−1.10894	+	0.360318i	−0.805538	−	0.592544i	$-0.798124\pi$
$241$	−17.2154	+	5.59363i	−1.10894	+	0.360318i	−0.303405	+	0.952862i	$0.598124\pi$
$242$	−10.2467			−0.658680
$243$	−6.60450	+	14.1202i	−0.423679	+	0.905812i
$244$	6.69539	−	2.17546i	0.428628	−	0.139270i
$245$	−0.959941	−	9.69846i	−0.0613284	−	0.619612i
$246$	9.81394	−	5.89368i	0.625714	−	0.375767i
$247$	3.22713			0.205337
$248$	2.59506	−	4.92602i	0.164787	−	0.312802i
$249$	2.49558	−	5.87538i	0.158151	−	0.372337i
$250$	−8.92408	−	6.73505i	−0.564408	−	0.425962i
$251$	16.0494	−	11.6605i	1.01303	−	0.736007i	0.0481852	−	0.998838i	$-0.484656\pi$
$251$	16.0494	−	11.6605i	1.01303	−	0.736007i	0.964842	+	0.262831i	$0.0846562\pi$
$252$	4.30403	+	2.29108i	0.271128	+	0.144324i
$253$			0.526004i			0.0330696i
$254$	−10.4751			−0.657267
$255$	−11.1328	+	15.6881i	−0.697162	+	0.982426i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	8.04440	−	24.7581i	0.501796	−	1.54437i	−0.304295	−	0.952578i	$-0.598421\pi$
$257$	8.04440	−	24.7581i	0.501796	−	1.54437i	0.806091	−	0.591791i	$-0.201579\pi$
$258$	5.36464	+	8.93299i	0.333988	+	0.556144i
$259$	9.72659	−	3.16036i	0.604381	−	0.196375i
$260$	−4.64105	+	2.03271i	−0.287826	+	0.126063i
$261$	2.54695	+	0.450326i	0.157652	+	0.0278745i
$262$	−11.4145	−	3.70881i	−0.705193	−	0.229131i
$263$	−18.3005	−	25.1885i	−1.12846	−	1.55319i	−0.790968	−	0.611857i	$-0.790423\pi$
$263$	−18.3005	−	25.1885i	−1.12846	−	1.55319i	−0.337488	−	0.941330i	$-0.609577\pi$
$264$	1.46489	−	0.337835i	0.0901576	−	0.0207923i
$265$	−22.9166	+	20.3840i	−1.40775	+	1.25218i
$266$	−1.36058	−	1.87268i	−0.0834225	−	0.114821i
$267$	0.0310311	+	0.0516718i	0.00189907	+	0.00316226i
$268$	−12.4459	+	4.04393i	−0.760256	+	0.247022i
$269$	−0.294002	−	0.213605i	−0.0179256	−	0.0130237i	0.578786	−	0.815479i	$-0.303527\pi$
$269$	−0.294002	−	0.213605i	−0.0179256	−	0.0130237i	−0.596712	+	0.802455i	$0.703527\pi$
$270$	−5.34480	+	10.3166i	−0.325274	+	0.627851i
$271$	−5.84553	−	1.89933i	−0.355091	−	0.115376i	0.126039	−	0.992025i	$-0.459773\pi$
$271$	−5.84553	−	1.89933i	−0.355091	−	0.115376i	−0.481130	+	0.876649i	$0.659773\pi$
$272$	4.72382	−	1.53486i	0.286424	−	0.0930648i
$273$	−2.49370	+	5.87096i	−0.150925	+	0.355326i
$274$			6.82593i			0.412370i
$275$	−2.94276	+	3.18963i	−0.177455	+	0.192342i
$276$	0.235885	+	1.02282i	0.0141986	+	0.0615668i
$277$	−4.08274	−	2.96628i	−0.245308	−	0.178227i	0.458337	−	0.888779i	$-0.348445\pi$
$277$	−4.08274	−	2.96628i	−0.245308	−	0.178227i	−0.703645	+	0.710552i	$0.748445\pi$
$278$			6.98361i			0.418849i
$279$	16.0407	−	4.65800i	0.960330	−	0.278867i
$280$	3.13626	+	1.83616i	0.187427	+	0.109732i
$281$	13.2688	−	18.2630i	0.791553	−	1.08948i	−0.202360	−	0.979311i	$-0.564861\pi$
$281$	13.2688	−	18.2630i	0.791553	−	1.08948i	0.993913	−	0.110168i	$-0.0351388\pi$
$282$	−1.70103	+	0.392295i	−0.101295	+	0.0233608i
$283$	−18.2508	+	5.93006i	−1.08490	+	0.352505i	−0.796274	−	0.604937i	$-0.793198\pi$
$283$	−18.2508	+	5.93006i	−1.08490	+	0.352505i	−0.288626	+	0.957442i	$0.593198\pi$
$284$			11.1496i			0.661606i
$285$	4.42608	−	3.29180i	0.262179	−	0.194990i
$286$	0.607739	+	1.87043i	0.0359363	+	0.110601i
$287$	3.31944	−	10.2162i	0.195941	−	0.603043i
$288$	2.69700	−	1.31385i	0.158922	−	0.0774194i
$289$	6.20541	+	4.50850i	0.365024	+	0.265206i
$290$	1.88324	+	0.412243i	0.110587	+	0.0242077i
$291$	−14.4296	+	8.66556i	−0.845876	+	0.507984i
$292$	0.686426	−	0.498717i	0.0401700	−	0.0291852i
$293$	3.64767	−	11.2264i	0.213099	−	0.655851i	−0.786184	−	0.617992i	$-0.787946\pi$
$293$	3.64767	−	11.2264i	0.213099	−	0.655851i	0.999283	−	0.0378587i	$-0.0120537\pi$
$294$	−7.35602	+	1.69646i	−0.429012	+	0.0989394i
$295$	5.31220	−	0.525795i	0.309288	−	0.0306130i
$296$	1.94451	−	5.98458i	0.113022	−	0.347847i
$297$	3.78069	+	2.45899i	0.219378	+	0.142685i
$298$	12.9459	−	17.8185i	0.749937	−	1.03220i
$299$	−1.30598	+	0.424340i	−0.0755270	+	0.0245402i
$300$	−4.29186	+	7.52196i	−0.247791	+	0.434281i
$301$	9.29915	+	3.02148i	0.535994	+	0.174155i
$302$	10.8005	+	3.50929i	0.621498	+	0.201937i
$303$	−12.3522	−	1.08359i	−0.709616	−	0.0622508i
$304$	−1.42422			−0.0816848
$305$	13.5848	+	7.95340i	0.777865	+	0.455411i
$306$	13.1533	+	7.00165i	0.751925	+	0.400257i
$307$	2.77044	+	3.81318i	0.158117	+	0.217630i	0.880724	−	0.473629i	$-0.157056\pi$
$307$	2.77044	+	3.81318i	0.158117	+	0.217630i	−0.722607	+	0.691259i	$0.757056\pi$
$308$	0.829167	−	1.14125i	0.0472462	−	0.0650288i
$309$	6.13550	−	14.4449i	0.349036	−	0.821743i
$310$	12.0868	−	2.98492i	0.686483	−	0.169532i
$311$			15.7839i			0.895023i	0.894278	+	0.447511i	$0.147690\pi$
$311$			15.7839i			0.895023i	−0.894278	+	0.447511i	$0.852310\pi$
$312$	2.02055	+	3.36454i	0.114391	+	0.190480i
$313$	8.91170	−	6.47473i	0.503719	−	0.365973i	−0.306717	−	0.951801i	$-0.599230\pi$
$313$	8.91170	−	6.47473i	0.503719	−	0.365973i	0.810436	+	0.585827i	$0.199230\pi$
$314$	1.43374	−	0.465851i	0.0809108	−	0.0262895i
$315$	2.56846	+	10.5958i	0.144716	+	0.597007i
$316$			3.89783i			0.219270i
$317$	5.12217	+	15.7644i	0.287690	+	0.885418i	0.985580	+	0.169213i	$0.0541225\pi$
$317$	5.12217	+	15.7644i	0.287690	+	0.885418i	−0.697890	+	0.716205i	$0.745878\pi$
$318$	17.9261	+	15.5903i	1.00525	+	0.874262i
$319$	0.231240	−	0.711682i	0.0129469	−	0.0398465i
$320$	2.04823	−	0.897090i	0.114499	−	0.0501489i
$321$	1.95604	−	22.2975i	0.109176	−	1.24453i
$322$	0.796852	+	0.578947i	0.0444068	+	0.0322634i
$323$	−4.15800	−	5.72299i	−0.231357	−	0.318436i
$324$	8.45435	+	3.08610i	0.469686	+	0.171450i
$325$	−10.2933	−	4.73325i	−0.570971	−	0.262553i
$326$	−10.6644	−	14.6783i	−0.590646	−	0.812954i
$327$	−0.169659	+	0.195078i	−0.00938214	+	0.0107878i
$328$	−3.88485	−	5.34704i	−0.214505	−	0.295241i
$329$	−0.962831	+	1.32522i	−0.0530826	+	0.0730619i
$330$	2.74144	+	1.94542i	0.150911	+	0.107092i
$331$	5.09558	−	7.01346i	0.280078	−	0.385495i	−0.645682	−	0.763607i	$-0.723427\pi$
$331$	5.09558	−	7.01346i	0.280078	−	0.385495i	0.925760	+	0.378112i	$0.123427\pi$
$332$	−3.50509	−	1.13887i	−0.192367	−	0.0625037i
$333$	16.9710	−	8.26748i	0.930006	−	0.453055i
$334$	4.20381	−	1.36590i	0.230022	−	0.0747387i
$335$	−25.2526	−	14.7844i	−1.37970	−	0.807760i
$336$	1.10054	−	2.59102i	0.0600393	−	0.141352i
$337$	5.61203	+	17.2721i	0.305707	+	0.940869i	0.979413	+	0.201869i	$0.0647016\pi$
$337$	5.61203	+	17.2721i	0.305707	+	0.940869i	−0.673706	+	0.739000i	$0.735298\pi$
$338$	6.36353	−	4.62337i	0.346130	−	0.251478i
$339$	−3.34842	−	5.57566i	−0.181861	−	0.302829i
$340$	9.58456	+	5.61140i	0.519796	+	0.304321i
$341$	−0.690883	−	4.78292i	−0.0374134	−	0.259009i
$342$	−2.96661	−	3.07489i	−0.160416	−	0.166271i
$343$	−10.8509	+	14.9350i	−0.585894	+	0.806414i
$344$	4.86707	−	3.53613i	0.262415	−	0.190655i
$345$	−1.35834	+	1.91415i	−0.0731307	+	0.103054i
$346$	−5.92438			−0.318497
$347$			6.99613i			0.375572i	0.982210	+	0.187786i	$0.0601311\pi$
$347$			6.99613i			0.375572i	−0.982210	+	0.187786i	$0.939869\pi$
$348$	0.130497	−	1.48758i	0.00699538	−	0.0797425i
$349$	−10.2205	+	31.4553i	−0.547089	+	1.68377i	0.168883	+	0.985636i	$0.445984\pi$
$349$	−10.2205	+	31.4553i	−0.547089	+	1.68377i	−0.715972	+	0.698129i	$0.754016\pi$
$350$	1.59307	+	7.96870i	0.0851532	+	0.425945i
$351$	−3.05530	+	11.3706i	−0.163080	+	0.606916i
$352$	−0.268212	−	0.825472i	−0.0142958	−	0.0439978i
$353$	8.25578	−	11.3631i	0.439411	−	0.604797i	−0.530670	−	0.847578i	$-0.678060\pi$
$353$	8.25578	−	11.3631i	0.439411	−	0.604797i	0.970081	+	0.242781i	$0.0780598\pi$
$354$	−0.929211	−	4.02916i	−0.0493870	−	0.214147i
$355$	−18.6283	+	16.5696i	−0.988688	+	0.879424i
$356$	0.0281530	−	0.0204543i	0.00149210	−	0.00108408i
$357$	13.6246	−	3.14212i	0.721088	−	0.166298i
$358$	0.747192	−	2.29962i	0.0394903	−	0.121539i
$359$	−7.29454	−	10.0401i	−0.384991	−	0.529895i	0.571907	−	0.820318i	$-0.306204\pi$
$359$	−7.29454	−	10.0401i	−0.384991	−	0.529895i	−0.956898	+	0.290424i	$0.906204\pi$
$360$	6.20319	+	2.55350i	0.326937	+	0.134581i
$361$	−5.24451	−	16.1409i	−0.276027	−	0.849523i
$362$	−13.4997	+	18.5808i	−0.709529	+	0.976583i
$363$	−11.6467	+	13.3917i	−0.611293	+	0.702880i
$364$	3.50245	+	1.13801i	0.183578	+	0.0596482i
$365$	1.85335	+	0.405700i	0.0970087	+	0.0212353i
$366$	4.76703	−	11.2231i	0.249176	−	0.586641i
$367$	6.67953			0.348669			0.174334	−	0.984687i	$-0.444223\pi$
$367$	6.67953			0.348669			0.174334	+	0.984687i	$0.444223\pi$
$368$	0.576367	−	0.187273i	0.0300452	−	0.00976228i
$369$	3.45223	−	19.5251i	0.179716	−	1.01643i
$370$	12.8886	−	5.64499i	0.670046	−	0.293469i
$371$	22.2927			1.15738
$372$	−3.48832	−	8.99064i	−0.180861	−	0.466143i
$373$		−	36.5284i		−	1.89137i	−0.325083	−	0.945685i	$-0.605392\pi$
$373$		−	36.5284i		−	1.89137i	0.325083	−	0.945685i	$-0.394608\pi$
$374$	2.53397	−	3.48772i	0.131029	−	0.180346i
$375$	−18.9456	+	4.00786i	−0.978348	+	0.206965i
$376$	0.311449	+	0.958541i	0.0160618	+	0.0494330i
$377$	1.95354			0.100612
$378$	7.88638	−	3.02094i	0.405632	−	0.155381i
$379$	6.92677	+	21.3184i	0.355804	+	1.09505i	0.955542	+	0.294856i	$0.0952718\pi$
$379$	6.92677	+	21.3184i	0.355804	+	1.09505i	−0.599737	+	0.800197i	$0.704728\pi$
$380$	−2.11657	−	2.37954i	−0.108578	−	0.122068i
$381$	−11.9064	+	13.6902i	−0.609982	+	0.701372i
$382$	4.67660	−	6.43678i	0.239276	−	0.329335i
$383$	34.4926	−	11.2073i	1.76249	−	0.572668i	0.765036	−	0.643987i	$-0.222721\pi$
$383$	34.4926	−	11.2073i	1.76249	−	0.572668i	0.997454	+	0.0713194i	$0.0227210\pi$
$384$	−0.891724	−	1.48487i	−0.0455056	−	0.0757743i
$385$	3.13900	−	0.310694i	0.159978	−	0.0158344i
$386$	16.2153	+	5.26869i	0.825340	+	0.268169i
$387$	17.7724	+	3.14234i	0.903423	+	0.159734i
$388$	5.71196	+	7.86183i	0.289981	+	0.399124i
$389$	3.49823	−	10.7665i	0.177367	−	0.545881i	−0.822366	−	0.568959i	$-0.807346\pi$
$389$	3.49823	−	10.7665i	0.177367	−	0.545881i	0.999734	+	0.0230776i	$0.00734648\pi$
$390$	−2.61857	+	8.37596i	−0.132596	+	0.424133i
$391$	2.43522	+	1.76929i	0.123154	+	0.0894768i
$392$	1.34684	+	4.14516i	0.0680259	+	0.209362i
$393$	−17.8213	+	10.7024i	−0.898966	+	0.539867i
$394$	−17.9663	−	5.83761i	−0.905130	−	0.294095i
$395$	−6.51235	+	5.79264i	−0.327672	+	0.291460i
$396$	1.22351	−	2.29850i	0.0614839	−	0.115504i
$397$		−	28.6803i		−	1.43942i	−0.694274	−	0.719711i	$-0.744274\pi$
$397$		−	28.6803i		−	1.43942i	0.694274	−	0.719711i	$-0.255726\pi$
$398$			14.2004i			0.711801i
$399$	−3.99394	−	0.350366i	−0.199947	−	0.0175403i
$400$	4.54273	+	2.08891i	0.227137	+	0.104446i
$401$	−17.8642	−	12.9791i	−0.892096	−	0.648146i	0.0443274	−	0.999017i	$-0.485886\pi$
$401$	−17.8642	−	12.9791i	−0.892096	−	0.648146i	−0.936424	+	0.350871i	$0.885886\pi$
$402$	−8.86134	+	20.8624i	−0.441963	+	1.04052i
$403$	11.3179	−	5.57384i	0.563783	−	0.277653i
$404$			7.15895i			0.356171i
$405$	7.40804	+	18.7115i	0.368108	+	0.929783i
$406$	−0.823624	−	1.13362i	−0.0408758	−	0.0562607i
$407$	−1.68774	−	5.19433i	−0.0836582	−	0.257474i
$408$	3.36330	−	7.91828i	0.166508	−	0.392013i
$409$			31.6134i			1.56318i	0.623790	+	0.781592i	$0.285592\pi$
$409$			31.6134i			1.56318i	−0.623790	+	0.781592i	$0.714408\pi$
$410$	3.16028	−	14.4370i	0.156075	−	0.712993i
$411$	8.92101	+	7.75858i	0.440041	+	0.382703i
$412$	−8.61744	−	2.79998i	−0.424551	−	0.137945i
$413$	−3.13900	−	2.28062i	−0.154460	−	0.112222i
$414$	1.60487	+	0.854291i	0.0788752	+	0.0419861i
$415$	−3.30620	−	7.54867i	−0.162295	−	0.370550i
$416$	1.83314	−	1.33186i	0.0898772	−	0.0652996i
$417$	9.12708	+	7.93780i	0.446955	+	0.388716i
$418$	−1.00007	+	0.726596i	−0.0489152	+	0.0355390i
$419$	9.93671	+	13.6767i	0.485440	+	0.668151i	0.979539	−	0.201255i	$-0.0645019\pi$
$419$	9.93671	+	13.6767i	0.485440	+	0.668151i	−0.494099	+	0.869406i	$0.664502\pi$
$420$	5.96451	−	2.01183i	0.291038	−	0.0981671i
$421$	21.7431	−	15.7973i	1.05969	−	0.769913i	0.0856622	−	0.996324i	$-0.472699\pi$
$421$	21.7431	−	15.7973i	1.05969	−	0.769913i	0.974032	+	0.226411i	$0.0726994\pi$
$422$	4.08199	+	2.96574i	0.198708	+	0.144370i
$423$	−1.42075	+	2.66902i	−0.0690792	+	0.129772i
$424$	8.06220	−	11.0967i	0.391535	−	0.538902i
$425$	4.86850	+	24.3527i	0.236157	+	1.18128i
$426$	14.5717	+	12.6730i	0.706002	+	0.614008i
$427$	−3.53573	−	10.8819i	−0.171106	−	0.526610i
$428$	−12.9229			−0.624653
$429$	3.13529	+	1.33172i	0.151373	+	0.0642960i
$430$	13.1411	+	2.87660i	0.633719	+	0.138722i
$431$	−2.07793	−	2.86002i	−0.100090	−	0.137762i	0.756034	−	0.654532i	$-0.227134\pi$
$431$	−2.07793	−	2.86002i	−0.100090	−	0.137762i	−0.856124	+	0.516770i	$0.827134\pi$
$432$	1.34839	−	5.01815i	0.0648744	−	0.241436i
$433$	7.32514			0.352024			0.176012	−	0.984388i	$-0.443680\pi$
$433$	7.32514			0.352024			0.176012	+	0.984388i	$0.443680\pi$
$434$	−8.00614	−	4.21769i	−0.384307	−	0.202456i
$435$	2.67932	−	1.99269i	0.128464	−	0.0955421i
$436$	0.120757	+	0.0877352i	0.00578322	+	0.00420175i
$437$	−0.507329	−	0.698279i	−0.0242688	−	0.0334032i
$438$	0.128426	−	1.46397i	0.00613643	−	0.0699511i
$439$	−31.9632			−1.52552			−0.762761	−	0.646681i	$-0.776157\pi$
$439$	−31.9632			−1.52552			−0.762761	+	0.646681i	$0.776157\pi$
$440$	0.980573	−	1.67487i	0.0467470	−	0.0798463i
$441$	−6.14395	+	11.5420i	−0.292569	+	0.549621i
$442$	10.7037	+	3.47783i	0.509121	+	0.165423i
$443$	0.328477	−	1.01095i	0.0156064	−	0.0480315i	−0.942950	−	0.332934i	$-0.891961\pi$
$443$	0.328477	−	1.01095i	0.0156064	−	0.0480315i	0.958556	+	0.284903i	$0.0919613\pi$
$444$	−5.61123	−	9.34361i	−0.266297	−	0.443428i
$445$	0.0760130	+	0.0166393i	0.00360336	+	0.000788780i
$446$	0.203266	+	0.147682i	0.00962494	+	0.00699293i
$447$	−8.57279	−	37.1725i	−0.405479	−	1.75820i
$448$	−1.54573	−	0.502238i	−0.0730288	−	0.0237285i
$449$	−2.81910	+	2.04820i	−0.133042	+	0.0966605i	−0.652316	−	0.757947i	$-0.726202\pi$
$449$	−2.81910	+	2.04820i	−0.133042	+	0.0966605i	0.519274	+	0.854608i	$0.326202\pi$
$450$	4.95240	+	14.1589i	0.233458	+	0.667456i
$451$	−5.45580	−	1.77270i	−0.256904	−	0.0834730i
$452$	−3.03785	+	2.20713i	−0.142889	+	0.103815i
$453$	16.8626	−	10.1267i	0.792274	−	0.475794i
$454$	3.11966	+	9.60132i	0.146413	+	0.450612i
$455$	3.30371	+	7.54298i	0.154880	+	0.353621i
$456$	−1.61882	+	1.86136i	−0.0758082	+	0.0871661i
$457$	10.8764	−	33.4742i	0.508778	−	1.56586i	−0.285547	−	0.958365i	$-0.592175\pi$
$457$	10.8764	−	33.4742i	0.508778	−	1.56586i	0.794325	−	0.607493i	$-0.207825\pi$
$458$	−14.5813	+	4.73775i	−0.681339	+	0.221381i
$459$	24.1012	−	9.23215i	1.12495	−	0.430920i
$460$	1.16944	+	0.684662i	0.0545254	+	0.0319225i
$461$	−4.34452	−	13.3711i	−0.202344	−	0.622752i	−0.999812	−	0.0193904i	$-0.993827\pi$
$461$	−4.34452	−	13.3711i	−0.202344	−	0.622752i	0.797467	−	0.603362i	$-0.206173\pi$
$462$	−0.549075	−	2.38085i	−0.0255453	−	0.110767i
$463$	−7.80595	−	5.67136i	−0.362773	−	0.263570i	0.391434	−	0.920206i	$-0.371979\pi$
$463$	−7.80595	−	5.67136i	−0.362773	−	0.263570i	−0.754208	+	0.656636i	$0.771979\pi$
$464$	−0.862151			−0.0400244
$465$	9.83716	−	19.1893i	0.456187	−	0.889884i
$466$	−11.8043			−0.546823
$467$	11.7941	+	8.56892i	0.545766	+	0.396522i	0.826222	−	0.563345i	$-0.190486\pi$
$467$	11.7941	+	8.56892i	0.545766	+	0.396522i	−0.280456	+	0.959867i	$0.590486\pi$
$468$	6.69384	+	1.18354i	0.309423	+	0.0547090i
$469$	6.57250	+	20.2281i	0.303490	+	0.934046i
$470$	−1.13864	+	1.94486i	−0.0525217	+	0.0897099i
$471$	1.02081	−	2.40330i	0.0470362	−	0.110738i
$472$	−2.27045	+	0.737716i	−0.104506	+	0.0339561i
$473$	1.61357	−	4.96606i	0.0741921	−	0.228340i
$474$	5.09419	+	4.43041i	0.233984	+	0.203495i
$475$	0.830172	−	7.07256i	0.0380909	−	0.324511i
$476$	−2.49458	−	7.67752i	−0.114339	−	0.351898i
$477$	40.7509	−	5.70771i	1.86586	−	0.261338i
$478$	13.6324	−	9.90452i	0.623532	−	0.453022i
$479$	23.2327	+	7.54876i	1.06153	+	0.344912i	0.787183	−	0.616720i	$-0.211539\pi$
$479$	23.2327	+	7.54876i	1.06153	+	0.344912i	0.274346	+	0.961631i	$0.411539\pi$
$480$	1.15565	−	3.69655i	0.0527479	−	0.168724i
$481$	11.5352	−	8.38078i	0.525958	−	0.382131i
$482$	17.2154	+	5.59363i	0.784142	+	0.254783i
$483$	1.66237	−	0.383379i	0.0756405	−	0.0174443i
$484$	8.28972	+	6.02283i	0.376805	+	0.273765i
$485$	−4.64660	+	21.2269i	−0.210991	+	0.963866i
$486$	13.6428	−	7.54147i	0.618850	−	0.342088i
$487$	−4.71068	+	14.4980i	−0.213461	+	0.656966i	0.785798	+	0.618483i	$0.212253\pi$
$487$	−4.71068	+	14.4980i	−0.213461	+	0.656966i	−0.999259	+	0.0384830i	$0.987747\pi$
$488$	−6.69539	−	2.17546i	−0.303086	−	0.0984786i
$489$	−31.3049	−	2.74621i	−1.41566	−	0.124188i
$490$	−4.92401	+	8.41046i	−0.222444	+	0.379946i
$491$	26.6557			1.20296			0.601478	−	0.798889i	$-0.294579\pi$
$491$	26.6557			1.20296			0.601478	+	0.798889i	$0.294579\pi$
$492$	−11.4039	−	1.00040i	−0.514126	−	0.0451015i
$493$	−2.51704	−	3.46440i	−0.113362	−	0.156029i
$494$	−2.61080	−	1.89686i	−0.117466	−	0.0853437i
$495$	5.65853	−	1.37164i	0.254332	−	0.0616508i
$496$	−4.99489	+	2.45989i	−0.224277	+	0.110452i
$497$	18.1211			0.812844
$498$	−5.47243	+	3.28642i	−0.245225	+	0.147268i
$499$	18.5389	+	25.5166i	0.829913	+	1.14228i	0.987939	+	0.154843i	$0.0494871\pi$
$499$	18.5389	+	25.5166i	0.829913	+	1.14228i	−0.158026	+	0.987435i	$0.550513\pi$
$500$	3.26097	+	10.6942i	0.145835	+	0.478260i
$501$	2.99305	−	7.04660i	0.133720	−	0.314819i
$502$	−19.8381			−0.885418
$503$	−3.32636	−	10.2375i	−0.148315	−	0.456467i	0.849107	−	0.528220i	$-0.177140\pi$
$503$	−3.32636	−	10.2375i	−0.148315	−	0.456467i	−0.997422	+	0.0717536i	$0.977140\pi$
$504$	−2.13537	−	4.38336i	−0.0951169	−	0.195251i
$505$	−11.9609	+	10.6391i	−0.532253	+	0.473432i
$506$	0.309177	−	0.425546i	0.0137446	−	0.0189178i
$507$	1.19058	−	13.5718i	0.0528754	−	0.602743i
$508$	8.47455	+	6.15712i	0.375997	+	0.273178i
$509$	−8.78243	+	6.38081i	−0.389274	+	0.282824i	−0.765158	−	0.643842i	$-0.777339\pi$
$509$	−8.78243	+	6.38081i	−0.389274	+	0.282824i	0.375884	+	0.926667i	$0.377339\pi$
$510$	18.2278	−	6.14824i	0.807142	−	0.272249i
$511$	−0.810553	−	1.11563i	−0.0358568	−	0.0493526i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−7.39061	+	0.382120i	−0.326303	+	0.0168710i
$514$	−21.0605	+	15.3014i	−0.928939	+	0.674914i
$515$	−8.12845	−	18.5588i	−0.358183	−	0.817798i
$516$	0.910599	−	10.3802i	0.0400869	−	0.456963i
$517$	0.707715	+	0.514185i	0.0311253	+	0.0226138i
$518$	−9.72659	−	3.16036i	−0.427362	−	0.138858i
$519$	−6.73385	+	7.74274i	−0.295583	+	0.339869i
$520$	4.94948	+	1.08345i	0.217049	+	0.0475123i
$521$			30.4203i			1.33274i	0.745623	+	0.666368i	$0.232152\pi$
$521$			30.4203i			1.33274i	−0.745623	+	0.666368i	$0.767848\pi$
$522$	−1.79583	−	1.86138i	−0.0786014	−	0.0814704i
$523$	−12.0115	−	36.9675i	−0.525225	−	1.61647i	−0.763871	−	0.645368i	$-0.776704\pi$
$523$	−12.0115	−	36.9675i	−0.525225	−	1.61647i	0.238647	−	0.971106i	$-0.423296\pi$
$524$	7.05458	+	9.70979i	0.308181	+	0.424174i
$525$	12.2253	+	6.97546i	0.533554	+	0.304434i
$526$			31.1347i			1.35754i
$527$	−24.4671	−	12.8895i	−1.06581	−	0.561474i
$528$	−1.38369	−	0.587725i	−0.0602175	−	0.0255775i
$529$	−18.3103	−	13.3032i	−0.796098	−	0.578399i
$530$	30.5213	−	3.02096i	1.32576	−	0.131222i
$531$	−6.32200	−	3.36527i	−0.274351	−	0.146040i
$532$			2.31476i			0.100357i
$533$		−	14.9759i		−	0.648680i
$534$	0.00526725	−	0.0600430i	0.000227936	−	0.00259832i
$535$	−19.2050	−	21.5911i	−0.830305	−	0.933466i
$536$	12.4459	+	4.04393i	0.537582	+	0.174671i
$537$	−2.15616	−	3.59035i	−0.0930451	−	0.154935i
$538$	0.112299	+	0.345620i	0.00484155	+	0.0149008i
$539$	3.06047	+	2.22357i	0.131824	+	0.0957757i
$540$	10.3880	−	5.20474i	0.447029	−	0.223976i
$541$	−13.8483	+	42.6206i	−0.595384	+	1.83240i	−0.0425796	+	0.999093i	$0.513558\pi$
$541$	−13.8483	+	42.6206i	−0.595384	+	1.83240i	−0.552805	+	0.833311i	$0.686442\pi$
$542$	3.61274	+	4.97251i	0.155180	+	0.213587i
$543$	8.93951	+	38.7627i	0.383631	+	1.66347i
$544$	−4.72382	−	1.53486i	−0.202532	−	0.0658067i
$545$	0.0328749	+	0.332142i	0.00140821	+	0.0142274i
$546$	5.46830	−	3.28395i	0.234022	−	0.140540i
$547$	−7.53421	+	2.44801i	−0.322139	+	0.104669i	−0.465623	−	0.884983i	$-0.654170\pi$
$547$	−7.53421	+	2.44801i	−0.322139	+	0.104669i	0.143483	+	0.989653i	$0.454170\pi$
$548$	4.01218	−	5.52230i	0.171392	−	0.235901i
$549$	−9.24944	−	18.9867i	−0.394757	−	0.810334i
$550$	4.25556	−	0.850754i	0.181458	−	0.0362763i
$551$	0.379441	+	1.16780i	0.0161647	+	0.0497499i
$552$	0.410366	−	0.966132i	0.0174663	−	0.0411213i
$553$	6.33505			0.269394
$554$	1.55947	+	4.79955i	0.0662554	+	0.203913i
$555$	7.27199	−	23.2608i	0.308679	−	0.987364i
$556$	4.10486	−	5.64986i	0.174085	−	0.239607i
$557$			4.77277i			0.202229i	0.994875	+	0.101114i	$0.0322408\pi$
$557$			4.77277i			0.202229i	−0.994875	+	0.101114i	$0.967759\pi$
$558$	−15.7151	−	5.66007i	−0.665272	−	0.239610i
$559$	13.6316			0.576557
$560$	−1.45802	−	3.32893i	−0.0616125	−	0.140673i
$561$	−1.67800	−	7.27598i	−0.0708452	−	0.307192i
$562$	−21.4694	+	6.97584i	−0.905633	+	0.294258i
$563$	−19.2046			−0.809377			−0.404688	−	0.914455i	$-0.632620\pi$
$563$	−19.2046			−0.809377			−0.404688	+	0.914455i	$0.632620\pi$
$564$	1.60675	+	0.682469i	0.0676563	+	0.0287371i
$565$	−8.20221	−	1.79547i	−0.345069	−	0.0755361i
$566$	18.2508	+	5.93006i	0.767140	+	0.249259i
$567$	5.01576	−	13.7406i	0.210642	−	0.577053i
$568$	6.55356	−	9.02020i	0.274981	−	0.378479i
$569$	−11.1557	−	34.3337i	−0.467670	−	1.43934i	−0.855593	−	0.517649i	$-0.826807\pi$
$569$	−11.1557	−	34.3337i	−0.467670	−	1.43934i	0.387922	−	0.921692i	$-0.373193\pi$
$570$	−5.51565	+	0.0615395i	−0.231025	+	0.00257761i
$571$	14.2346	+	19.5923i	0.595701	+	0.819912i	0.995306	−	0.0967756i	$-0.0308529\pi$
$571$	14.2346	+	19.5923i	0.595701	+	0.819912i	−0.399606	+	0.916687i	$0.630853\pi$
$572$	0.607739	−	1.87043i	0.0254108	−	0.0782065i
$573$	−3.09684	−	13.4282i	−0.129372	−	0.560973i
$574$	−8.69042	+	6.31396i	−0.362731	+	0.263539i
$575$	0.594020	+	2.97135i	0.0247723	+	0.123914i
$576$	−2.95418	−	0.522328i	−0.123091	−	0.0217637i
$577$	−13.0784	+	18.0009i	−0.544463	+	0.749388i	−0.989248	−	0.146249i	$-0.953280\pi$
$577$	−13.0784	+	18.0009i	−0.544463	+	0.749388i	0.444785	+	0.895637i	$0.353280\pi$
$578$	−2.37026	−	7.29490i	−0.0985897	−	0.303428i
$579$	25.3167	−	15.2037i	1.05213	−	0.631846i
$580$	−1.28126	−	1.44045i	−0.0532014	−	0.0598114i
$581$	−1.85098	+	5.69673i	−0.0767916	+	0.236340i
$582$	16.7673	+	1.47090i	0.695025	+	0.0609708i
$583$		−	11.9050i		−	0.493057i
$584$	−0.848469			−0.0351099
$585$	7.97044	+	12.9427i	0.329537	+	0.535114i
$586$	−9.54971	+	6.93827i	−0.394495	+	0.286617i
$587$	9.29284	−	12.7905i	0.383557	−	0.527920i	−0.572966	−	0.819579i	$-0.694207\pi$
$587$	9.29284	−	12.7905i	0.383557	−	0.527920i	0.956522	+	0.291659i	$0.0942072\pi$
$588$	6.94830	+	2.95130i	0.286543	+	0.121709i
$589$	5.53026	+	5.68304i	0.227871	+	0.234166i
$590$	−4.60672	−	2.69706i	−0.189655	−	0.111036i
$591$	−28.0505	+	16.8455i	−1.15384	+	0.692931i
$592$	−5.09079	+	3.69867i	−0.209230	+	0.152015i
$593$	−5.11658	−	15.7472i	−0.210113	−	0.646661i	−0.999465	−	0.0327197i	$-0.989583\pi$
$593$	−5.11658	−	15.7472i	−0.210113	−	0.646661i	0.789352	−	0.613941i	$-0.210417\pi$
$594$	−1.61329	−	4.21160i	−0.0661940	−	0.172804i
$595$	9.12006	−	15.5776i	0.373886	−	0.638617i
$596$	−20.9469	+	6.80607i	−0.858020	+	0.278787i
$597$	18.5589	+	16.1406i	0.759565	+	0.660592i
$598$	1.30598	+	0.424340i	0.0534056	+	0.0173525i
$599$	4.85326	−	6.67993i	0.198299	−	0.272935i	−0.698275	−	0.715830i	$-0.746049\pi$
$599$	4.85326	−	6.67993i	0.198299	−	0.272935i	0.896573	+	0.442895i	$0.146049\pi$
$600$	7.89349	−	3.56270i	0.322250	−	0.145447i
$601$	−5.74028	+	7.90082i	−0.234151	+	0.322281i	−0.909882	−	0.414867i	$-0.863828\pi$
$601$	−5.74028	+	7.90082i	−0.234151	+	0.322281i	0.675731	+	0.737148i	$0.263828\pi$
$602$	−5.74719	−	7.91033i	−0.234238	−	0.322401i
$603$	17.1936	+	35.2941i	0.700178	+	1.43729i
$604$	−6.67507	−	9.18745i	−0.271605	−	0.373832i
$605$	2.25679	+	22.8008i	0.0917517	+	0.926985i
$606$	9.35623	+	8.13710i	0.380071	+	0.330547i
$607$	1.54516	+	2.12674i	0.0627163	+	0.0863215i	0.839223	−	0.543787i	$-0.183010\pi$
$607$	1.54516	+	2.12674i	0.0627163	+	0.0863215i	−0.776507	+	0.630109i	$0.783010\pi$
$608$	1.15222	+	0.837138i	0.0467287	+	0.0339504i
$609$	−2.41772	−	0.212094i	−0.0979711	−	0.00859447i
$610$	−6.31547	−	14.4194i	−0.255706	−	0.583825i
$611$	−0.705708	+	2.17195i	−0.0285499	+	0.0878676i
$612$	−6.52579	−	13.3958i	−0.263790	−	0.541492i
$613$	0.539848	+	1.66148i	0.0218043	+	0.0671066i	0.961367	−	0.275271i	$-0.0887677\pi$
$613$	0.539848	+	1.66148i	0.0218043	+	0.0671066i	−0.939562	+	0.342378i	$0.888768\pi$
$614$		−	4.71335i		−	0.190215i
$615$	−15.2761	−	20.5399i	−0.615991	−	0.828247i
$616$	−1.34162	+	0.435919i	−0.0540554	+	0.0175637i
$617$	−21.9160	+	15.9229i	−0.882304	+	0.641031i	−0.933860	−	0.357639i	$-0.883582\pi$
$617$	−21.9160	+	15.9229i	−0.882304	+	0.641031i	0.0515560	+	0.998670i	$0.483582\pi$
$618$	−13.4542	+	8.07984i	−0.541209	+	0.325019i
$619$			11.2766i			0.453246i	0.973983	+	0.226623i	$0.0727686\pi$
$619$			11.2766i			0.453246i	−0.973983	+	0.226623i	$0.927231\pi$
$620$	−11.5329	−	4.68958i	−0.463173	−	0.188338i
$621$	2.94065	−	1.12644i	0.118004	−	0.0452025i
$622$	9.27754	−	12.7694i	0.371996	−	0.512008i
$623$	−0.0332439	−	0.0457563i	−0.00133189	−	0.00183319i
$624$	0.342970	−	3.90962i	0.0137298	−	0.156510i
$625$	−13.0213	+	21.3412i	−0.520852	+	0.853647i
$626$	−11.0155			−0.440267
$627$	−0.187108	+	2.13290i	−0.00747236	+	0.0851798i
$628$	−1.43374	−	0.465851i	−0.0572126	−	0.0185895i
$629$	−29.7249	−	9.65822i	−1.18521	−	0.385098i
$630$	4.15015	−	10.0819i	0.165346	−	0.401673i
$631$	43.7678	−	14.2210i	1.74237	−	0.566130i	0.747225	−	0.664571i	$-0.231386\pi$
$631$	43.7678	−	14.2210i	1.74237	−	0.566130i	0.995143	+	0.0984413i	$0.0313857\pi$
$632$	2.29109	−	3.15341i	0.0911346	−	0.125436i
$633$	8.51573	−	1.96391i	0.338470	−	0.0780585i
$634$	5.12217	−	15.7644i	0.203427	−	0.626085i
$635$	2.30711	+	23.3092i	0.0915550	+	0.924997i
$636$	−5.33879	−	23.1496i	−0.211697	−	0.917940i
$637$	−3.05180	+	9.39246i	−0.120917	+	0.372143i
$638$	−0.605393	+	0.439844i	−0.0239677	+	0.0174136i
$639$	33.1254	−	4.63966i	1.31042	−	0.183542i
$640$	−2.18435	−	0.478156i	−0.0863439	−	0.0189008i
$641$	−25.9293	−	18.8387i	−1.02414	−	0.744084i	−0.0570160	−	0.998373i	$-0.518159\pi$
$641$	−25.9293	−	18.8387i	−1.02414	−	0.744084i	−0.967128	+	0.254289i	$0.918159\pi$
$642$	−14.6886	+	16.8893i	−0.579714	+	0.666569i
$643$	−7.13961	+	21.9735i	−0.281559	+	0.866549i	0.705850	+	0.708361i	$0.250565\pi$
$643$	−7.13961	+	21.9735i	−0.281559	+	0.866549i	−0.987409	+	0.158188i	$0.949435\pi$
$644$	−0.304370	−	0.936756i	−0.0119939	−	0.0369133i
$645$	18.6961	−	13.9048i	0.736158	−	0.547502i
$646$			7.07401i			0.278323i
$647$	−11.9576	+	3.88525i	−0.470100	+	0.152745i	−0.534481	−	0.845181i	$-0.679493\pi$
$647$	−11.9576	+	3.88525i	−0.470100	+	0.152745i	0.0643807	+	0.997925i	$0.479493\pi$
$648$	−5.02575	−	7.46605i	−0.197430	−	0.293294i
$649$	−1.21793	+	1.67633i	−0.0478078	+	0.0658018i
$650$	5.54534	+	9.87954i	0.217506	+	0.387507i
$651$	−14.6123	+	5.66949i	−0.572700	+	0.222205i
$652$			18.1433i			0.710548i
$653$	19.1917	+	13.9436i	0.751028	+	0.545654i	0.896145	−	0.443761i	$-0.146356\pi$
$653$	19.1917	+	13.9436i	0.751028	+	0.545654i	−0.145117	+	0.989414i	$0.546356\pi$
$654$	0.251920	−	0.0580983i	0.00985087	−	0.00227182i
$655$	−5.73881	+	26.2164i	−0.224234	+	1.02436i
$656$			6.60931i			0.258050i
$657$	−1.76733	−	1.83184i	−0.0689501	−	0.0714669i
$658$	1.55789	−	0.506190i	0.0607330	−	0.0197334i
$659$	−3.65270	−	1.18684i	−0.142289	−	0.0462326i	0.237007	−	0.971508i	$-0.423834\pi$
$659$	−3.65270	−	1.18684i	−0.142289	−	0.0462326i	−0.379296	+	0.925275i	$0.623834\pi$
$660$	−1.07438	−	3.18525i	−0.0418204	−	0.123986i
$661$	12.2369	+	8.89065i	0.475961	+	0.345806i	0.799760	−	0.600320i	$-0.204960\pi$
$661$	12.2369	+	8.89065i	0.475961	+	0.345806i	−0.323799	+	0.946126i	$0.604960\pi$
$662$	−8.24481	+	2.67890i	−0.320444	+	0.104119i
$663$	16.7114	−	10.0359i	0.649017	−	0.389762i
$664$	2.16626	+	2.98161i	0.0840673	+	0.115709i
$665$	−3.86741	+	3.44001i	−0.149972	+	0.133398i
$666$	−18.5893	−	3.28678i	−0.720323	−	0.127360i
$667$	−0.307111	−	0.422702i	−0.0118914	−	0.0163671i
$668$	−4.20381	−	1.36590i	−0.162650	−	0.0528482i
$669$	0.424049	−	0.0977948i	0.0163947	−	0.00378097i
$670$	11.7397	+	26.8040i	0.453544	+	1.03553i
$671$	−5.81128	+	1.88820i	−0.224342	+	0.0728932i
$672$	−2.41332	+	1.44930i	−0.0930957	+	0.0559079i
$673$	4.86805	−	14.9823i	0.187649	−	0.577526i	−0.812334	−	0.583192i	$-0.801804\pi$
$673$	4.86805	−	14.9823i	0.187649	−	0.577526i	0.999984	+	0.00566608i	$0.00180358\pi$
$674$	5.61203	−	17.2721i	0.216167	−	0.665295i
$675$	24.1337	+	9.62102i	0.928907	+	0.370313i
$676$	−7.86575			−0.302529
$677$			40.0841i			1.54056i	0.637706	+	0.770279i	$0.279883\pi$
$677$			40.0841i			1.54056i	−0.637706	+	0.770279i	$0.720117\pi$
$678$	−0.568364	+	6.47896i	−0.0218279	+	0.248823i
$679$	12.7776	−	9.28350i	0.490361	−	0.356268i
$680$	−4.45578	−	10.1734i	−0.170871	−	0.390131i
$681$	16.0942	+	6.83601i	0.616729	+	0.261956i
$682$	−2.25239	+	4.27555i	−0.0862485	+	0.163719i
$683$	15.5162			0.593711			0.296856	−	0.954922i	$-0.404062\pi$
$683$	15.5162			0.593711			0.296856	+	0.954922i	$0.404062\pi$
$684$	0.592660	+	4.23137i	0.0226609	+	0.161790i
$685$	15.1890	−	1.50339i	0.580343	−	0.0574416i
$686$	17.5571	−	5.70466i	0.670334	−	0.217805i
$687$	−10.3817	+	24.4418i	−0.396086	+	0.932513i
$688$	−6.01603			−0.229359
$689$	29.5583	−	9.60407i	1.12608	−	0.365886i
$690$	2.22403	−	0.750165i	0.0846674	−	0.0285583i
$691$	7.50349	−	23.0934i	0.285446	−	0.878513i	−0.700818	−	0.713340i	$-0.747182\pi$
$691$	7.50349	−	23.0934i	0.285446	−	0.878513i	0.986265	−	0.165173i	$-0.0528183\pi$
$692$	4.79292	+	3.48226i	0.182200	+	0.132376i
$693$	−3.73569	−	1.98855i	−0.141907	−	0.0755387i
$694$	4.11222	−	5.65999i	0.156098	−	0.214850i
$695$	15.5399	−	1.53812i	0.589462	−	0.0583441i
$696$	−0.979950	+	1.12677i	−0.0371449	+	0.0427101i
$697$	−26.5583	+	19.2958i	−1.00597	+	0.730879i
$698$	26.7575	−	19.4405i	1.01279	−	0.735832i
$699$	−13.4172	+	15.4274i	−0.507483	+	0.583517i
$700$	3.39506	−	7.38320i	0.128321	−	0.279059i
$701$	−24.6394	+	33.9133i	−0.930619	+	1.28089i	0.0289986	+	0.999579i	$0.490768\pi$
$701$	−24.6394	+	33.9133i	−0.930619	+	1.28089i	−0.959618	+	0.281308i	$0.909232\pi$
$702$	9.15524	−	7.40312i	0.345542	−	0.279413i
$703$	7.25042	+	5.26774i	0.273455	+	0.198677i
$704$	−0.268212	+	0.825472i	−0.0101086	+	0.0311112i
$705$	1.24758	+	3.69873i	0.0469866	+	0.139302i
$706$	−13.3581	+	4.34032i	−0.502740	+	0.163350i
$707$	11.6353			0.437589
$708$	−1.61653	+	3.80584i	−0.0607530	+	0.143032i
$709$	17.0562	−	5.54190i	0.640559	−	0.208130i	0.0293124	−	0.999570i	$-0.490668\pi$
$709$	17.0562	−	5.54190i	0.640559	−	0.208130i	0.611247	+	0.791440i	$0.290668\pi$
$710$	24.8100	−	2.45566i	0.931102	−	0.0921593i
$711$	11.5805	−	1.62200i	0.434301	−	0.0608296i
$712$	−0.0347990			−0.00130415
$713$	−2.98531	−	1.57268i	−0.111801	−	0.0588974i
$714$	−12.8694	−	5.46629i	−0.481625	−	0.204571i
$715$	4.02821	−	1.76429i	0.150647	−	0.0659808i
$716$	−1.95617	+	1.42124i	−0.0731057	+	0.0531144i
$717$	2.55054	−	29.0744i	0.0952517	−	1.08580i
$718$			12.4102i			0.463145i
$719$	−11.2978			−0.421335			−0.210668	−	0.977558i	$-0.567564\pi$
$719$	−11.2978			−0.421335			−0.210668	+	0.977558i	$0.567564\pi$
$720$	−3.51758	−	5.71197i	−0.131092	−	0.212873i
$721$	−4.55073	+	14.0057i	−0.169478	+	0.521600i
$722$	−5.24451	+	16.1409i	−0.195180	+	0.600704i
$723$	26.8781	−	16.1414i	0.999608	−	0.600307i
$724$	21.8430	−	7.09722i	0.811788	−	0.263766i
$725$	0.502543	−	4.28136i	0.0186640	−	0.159006i
$726$	17.2938	−	3.98832i	0.641833	−	0.148021i
$727$	24.2334	+	7.87390i	0.898766	+	0.292027i	0.721728	−	0.692177i	$-0.243348\pi$
$727$	24.2334	+	7.87390i	0.898766	+	0.292027i	0.177039	+	0.984204i	$0.443348\pi$
$728$	−2.16463	−	2.97936i	−0.0802266	−	0.110422i
$729$	5.65071	−	26.4021i	0.209286	−	0.977855i
$730$	−1.26093	−	1.41759i	−0.0466690	−	0.0524673i
$731$	−17.5637	−	24.1743i	−0.649617	−	0.894121i
$732$	−10.4534	+	6.27769i	−0.386368	+	0.232030i
$733$	−40.2170	+	13.0673i	−1.48545	+	0.482652i	−0.935736	−	0.352702i	$-0.885263\pi$
$733$	−40.2170	+	13.0673i	−1.48545	+	0.482652i	−0.549713	+	0.835354i	$0.685263\pi$
$734$	−5.40386	−	3.92613i	−0.199460	−	0.144916i
$735$	5.39509	+	15.9949i	0.199001	+	0.589982i
$736$	−0.576367	−	0.187273i	−0.0212452	−	0.00690298i
$737$	10.8025	−	3.50994i	0.397915	−	0.129290i
$738$	−14.2695	+	13.7670i	−0.525266	+	0.506768i
$739$		−	44.1333i		−	1.62347i	−0.584025	−	0.811736i	$-0.698523\pi$
$739$		−	44.1333i		−	1.62347i	0.584025	−	0.811736i	$-0.301477\pi$
$740$	−13.7451	−	3.00882i	−0.505281	−	0.110607i
$741$	−5.44659	+	1.25610i	−0.200085	+	0.0461440i
$742$	−18.0351	−	13.1033i	−0.662091	−	0.481037i
$743$		−	33.8030i		−	1.24011i	−0.784558	−	0.620055i	$-0.787110\pi$
$743$		−	33.8030i		−	1.24011i	0.784558	−	0.620055i	$-0.212890\pi$
$744$	−2.46245	+	9.32397i	−0.0902779	+	0.341833i
$745$	−42.5010	−	24.8827i	−1.55712	−	0.911632i
$746$	−21.4709	+	29.5521i	−0.786105	+	1.08198i
$747$	−1.92502	+	10.8875i	−0.0704329	+	0.398354i
$748$	−4.10006	+	1.33219i	−0.149913	+	0.0487097i
$749$			21.0033i			0.767444i
$750$	17.6831	+	7.89354i	0.645695	+	0.288231i
$751$	13.5637	+	41.7449i	0.494948	+	1.52329i	0.817038	+	0.576583i	$0.195614\pi$
$751$	13.5637	+	41.7449i	0.494948	+	1.52329i	−0.322091	+	0.946709i	$0.604386\pi$
$752$	0.311449	−	0.958541i	0.0113574	−	0.0349544i
$753$	−22.5487	+	25.9270i	−0.821719	+	0.944833i
$754$	−1.58045	−	1.14826i	−0.0575564	−	0.0418172i
$755$	5.43008	−	24.8061i	0.197621	−	0.902787i
$756$	−8.15588	−	2.19150i	−0.296627	−	0.0797042i
$757$	−6.70484	+	4.87135i	−0.243691	+	0.177052i	−0.702926	−	0.711263i	$-0.748124\pi$
$757$	−6.70484	+	4.87135i	−0.243691	+	0.177052i	0.459235	+	0.888315i	$0.348124\pi$
$758$	6.92677	−	21.3184i	0.251592	−	0.774320i
$759$	−0.204737	−	0.887763i	−0.00743150	−	0.0322238i
$760$	0.313681	+	3.16917i	0.0113784	+	0.114958i
$761$	−11.9928	+	36.9101i	−0.434740	+	1.33799i	0.458613	+	0.888636i	$0.348346\pi$
$761$	−11.9928	+	36.9101i	−0.434740	+	1.33799i	−0.893353	+	0.449356i	$0.851654\pi$
$762$	17.6794	−	4.07725i	0.640456	−	0.147703i
$763$	0.142594	−	0.196264i	0.00516225	−	0.00710522i
$764$	−7.56689	+	2.45863i	−0.273761	+	0.0889502i
$765$	12.6830	−	30.8108i	0.458557	−	1.11397i
$766$	−34.4926	−	11.2073i	−1.24627	−	0.404937i
$767$	−5.14460	−	1.67158i	−0.185761	−	0.0603573i
$768$	−0.151362	+	1.72542i	−0.00546181	+	0.0622609i
$769$	10.8008			0.389486			0.194743	−	0.980854i	$-0.437613\pi$
$769$	10.8008			0.389486			0.194743	+	0.980854i	$0.437613\pi$
$770$	−2.72213	−	1.59370i	−0.0980986	−	0.0574330i
$771$	−3.94029	+	44.9166i	−0.141906	+	1.61763i
$772$	−10.0216	−	13.7936i	−0.360687	−	0.496443i
$773$	−24.8737	+	34.2357i	−0.894644	+	1.23137i	0.0775015	+	0.996992i	$0.475306\pi$
$773$	−24.8737	+	34.2357i	−0.894644	+	1.23137i	−0.972145	+	0.234379i	$0.924694\pi$
$774$	−12.5312	−	12.9886i	−0.450424	−	0.466865i
$775$	−9.30411	−	26.2380i	−0.334214	−	0.942497i
$776$		−	9.71776i		−	0.348847i
$777$	−15.1859	+	9.11980i	−0.544793	+	0.327171i
$778$	−9.15849	+	6.65404i	−0.328348	+	0.238559i
$779$	8.95242	−	2.90882i	0.320754	−	0.104219i
$780$	7.04174	−	5.23714i	0.252135	−	0.187520i
$781$		−	9.67731i		−	0.346282i
$782$	−0.930171	−	2.86277i	−0.0332628	−	0.102372i
$783$	−4.47389	+	0.231316i	−0.159884	+	0.00826656i
$784$	1.34684	−	4.14516i	0.0481016	−	0.148041i
$785$	−1.35239	−	3.08775i	−0.0482688	−	0.110207i
$786$	20.7085	+	1.81664i	0.738647	+	0.0647975i
$787$	−10.4380	−	7.58364i	−0.372074	−	0.270328i	0.385996	−	0.922500i	$-0.373858\pi$
$787$	−10.4380	−	7.58364i	−0.372074	−	0.270328i	−0.758071	+	0.652173i	$0.773858\pi$
$788$	11.1038	+	15.2831i	0.395556	+	0.544437i
$789$	40.6908	+	35.3887i	1.44863	+	1.25987i
$790$	8.67343	−	0.858485i	0.308587	−	0.0305435i
$791$	3.58720	+	4.93735i	0.127546	+	0.175552i
$792$	−2.34087	+	1.14036i	−0.0831791	+	0.0405210i
$793$	−9.37619	−	12.9052i	−0.332958	−	0.458278i
$794$	−16.8578	+	23.2028i	−0.598263	+	0.823438i
$795$	30.7433	−	43.3229i	1.09035	−	1.53650i
$796$	8.34678	−	11.4884i	0.295844	−	0.407194i
$797$	−17.3056	−	5.62293i	−0.612995	−	0.199174i	−0.0139675	−	0.999902i	$-0.504446\pi$
$797$	−17.3056	−	5.62293i	−0.612995	−	0.199174i	−0.599028	+	0.800728i	$0.704446\pi$
$798$	3.02522	+	2.63103i	0.107092	+	0.0931374i
$799$	4.76100	−	1.54694i	0.168432	−	0.0547269i
$800$	−2.44732	−	4.36012i	−0.0865257	−	0.154154i
$801$	−0.0724850	−	0.0751308i	−0.00256113	−	0.00265462i
$802$	6.82352	+	21.0006i	0.240947	+	0.741559i
$803$	−0.595785	+	0.432863i	−0.0210248	+	0.0152754i
$804$	19.4316	−	11.6695i	0.685299	−	0.411551i
$805$	1.11277	−	1.90066i	0.0392198	−	0.0669895i
$806$	−12.4326	−	2.14314i	−0.437918	−	0.0754888i
$807$	0.579344	+	0.246077i	0.0203939	+	0.00866232i
$808$	4.20792	−	5.79171i	0.148034	−	0.203752i
$809$	−13.3965	+	9.73311i	−0.470995	+	0.342198i	−0.797829	−	0.602884i	$-0.794018\pi$
$809$	−13.3965	+	9.73311i	−0.470995	+	0.342198i	0.326834	+	0.945082i	$0.394018\pi$
$810$	5.00513	−	19.4923i	0.175862	−	0.684889i
$811$	−35.4252			−1.24395			−0.621974	−	0.783038i	$-0.713669\pi$
$811$	−35.4252			−1.24395			−0.621974	+	0.783038i	$0.713669\pi$
$812$			1.40123i			0.0491737i
$813$	10.6051	+	0.930326i	0.371936	+	0.0326279i
$814$	−1.68774	+	5.19433i	−0.0591553	+	0.182061i
$815$	−30.3132	+	26.9632i	−1.06182	+	0.944479i
$816$	−7.37521	+	4.42913i	−0.258184	+	0.155050i
$817$	2.64771	+	8.14881i	0.0926316	+	0.285091i
$818$	18.5819	−	25.5758i	0.649701	−	0.894237i
$819$	1.92357	−	10.8793i	0.0672151	−	0.380155i
$820$	−11.0426	+	9.82222i	−0.385624	+	0.343007i
$821$	−21.7467	+	15.7999i	−0.758967	+	0.551421i	−0.898593	−	0.438783i	$-0.855410\pi$
$821$	−21.7467	+	15.7999i	−0.758967	+	0.551421i	0.139627	+	0.990204i	$0.455410\pi$
$822$	−2.65687	−	11.5205i	−0.0926689	−	0.401822i
$823$	−16.2516	+	50.0174i	−0.566496	+	1.74350i	0.0969673	+	0.995288i	$0.469086\pi$
$823$	−16.2516	+	50.0174i	−0.566496	+	1.74350i	−0.663464	+	0.748209i	$0.730914\pi$
$824$	5.32587	+	7.33043i	0.185535	+	0.255368i
$825$	3.72514	−	6.52871i	0.129693	−	0.227301i
$826$	1.19899	+	3.69012i	0.0417182	+	0.128396i
$827$	−17.4090	+	23.9614i	−0.605369	+	0.833219i	−0.996187	−	0.0872490i	$-0.972192\pi$
$827$	−17.4090	+	23.9614i	−0.605369	+	0.833219i	0.390817	+	0.920468i	$0.372192\pi$
$828$	−0.796231	−	1.63446i	−0.0276709	−	0.0568013i
$829$	−47.7660	−	15.5201i	−1.65898	−	0.539035i	−0.678322	−	0.734765i	$-0.737293\pi$
$829$	−47.7660	−	15.5201i	−1.65898	−	0.539035i	−0.980658	+	0.195729i	$0.937293\pi$
$830$	−1.76223	+	8.05034i	−0.0611678	+	0.279431i
$831$	8.04521	+	3.41721i	0.279085	+	0.118542i
$832$	−2.26589			−0.0785555
$833$	20.5887	−	6.68967i	0.713356	−	0.231783i
$834$	−2.71824	−	11.7866i	−0.0941250	−	0.408136i
$835$	−3.96527	−	9.05345i	−0.137224	−	0.313308i
$836$	1.23616			0.0427535
$837$	−25.2596	+	14.1051i	−0.873099	+	0.487542i
$838$		−	16.9053i		−	0.583985i
$839$	25.9144	−	35.6682i	0.894665	−	1.23140i	−0.0774731	−	0.996994i	$-0.524685\pi$
$839$	25.9144	−	35.6682i	0.894665	−	1.23140i	0.972139	−	0.234407i	$-0.0753148\pi$
$840$	−6.00791	−	1.87825i	−0.207293	−	0.0648057i
$841$	−8.73180	−	26.8737i	−0.301097	−	0.926680i
$842$	−26.8760			−0.926206
$843$	−15.2859	+	35.9880i	−0.526476	+	1.23949i
$844$	−1.55918	−	4.79866i	−0.0536692	−	0.165177i
$845$	−11.6895	−	13.1418i	−0.402130	−	0.452092i
$846$	2.71822	−	1.32419i	0.0934544	−	0.0455266i
$847$	9.78877	−	13.4731i	0.336346	−	0.462941i
$848$	−13.0449	+	4.23855i	−0.447964	+	0.145552i
$849$	28.4947	−	17.1123i	0.977935	−	0.587291i
$850$	10.3755	−	22.5634i	0.355876	−	0.773918i
$851$	−3.62682	−	1.17843i	−0.124326	−	0.0403960i
$852$	−4.33977	−	18.8177i	−0.148678	−	0.644684i
$853$	−21.3814	−	29.4290i	−0.732086	−	1.00763i	−0.999035	−	0.0439197i	$-0.986015\pi$
$853$	−21.3814	−	29.4290i	−0.732086	−	1.00763i	0.266949	−	0.963711i	$-0.413985\pi$
$854$	−3.53573	+	10.8819i	−0.120990	+	0.372369i
$855$	−6.18885	+	7.27851i	−0.211654	+	0.248920i
$856$	10.4549	+	7.59590i	0.357340	+	0.259623i
$857$	8.30335	+	25.5551i	0.283637	+	0.872945i	0.986804	+	0.161920i	$0.0517687\pi$
$857$	8.30335	+	25.5551i	0.283637	+	0.872945i	−0.703167	+	0.711025i	$0.748231\pi$
$858$	−1.75374	−	2.92026i	−0.0598717	−	0.0996961i
$859$	−54.2342	−	17.6218i	−1.85045	−	0.601247i	−0.996757	−	0.0804669i	$-0.974359\pi$
$859$	−54.2342	−	17.6218i	−1.85045	−	0.601247i	−0.853691	−	0.520780i	$-0.825641\pi$
$860$	−8.94054	−	10.0514i	−0.304870	−	0.342748i
$861$	−1.62592	+	18.5344i	−0.0554113	+	0.631651i
$862$			3.53518i			0.120409i
$863$			1.28479i			0.0437348i	0.999761	+	0.0218674i	$0.00696116\pi$
$863$			1.28479i			0.0437348i	−0.999761	+	0.0218674i	$0.993039\pi$
$864$	−4.04046	+	3.26721i	−0.137459	+	0.111153i
$865$	1.30483	+	13.1829i	0.0443654	+	0.448232i
$866$	−5.92616	−	4.30561i	−0.201379	−	0.146311i
$867$	−12.2280	−	5.19387i	−0.415286	−	0.176393i
$868$	3.99800	+	8.11807i	0.135701	+	0.275545i
$869$		−	3.38313i		−	0.114765i
$870$	−3.33889	+	0.0372528i	−0.113199	+	0.00126299i
$871$	17.4292	+	23.9893i	0.590567	+	0.812845i
$872$	−0.0461251	−	0.141959i	−0.00156199	−	0.00480732i
$873$	20.9806	−	20.2417i	0.710086	−	0.685079i
$874$			0.863120i			0.0291955i
$875$	17.3810	−	5.29997i	0.587586	−	0.179172i
$876$	−0.964398	+	1.10889i	−0.0325840	+	0.0374659i
$877$	−20.5001	−	6.66088i	−0.692239	−	0.224922i	−0.0582929	−	0.998300i	$-0.518566\pi$
$877$	−20.5001	−	6.66088i	−0.692239	−	0.224922i	−0.633946	+	0.773378i	$0.718566\pi$
$878$	25.8588	+	18.7875i	0.872692	+	0.634048i
$879$	−1.78669	+	20.3671i	−0.0602637	+	0.686964i
$880$	−1.77776	+	0.778632i	−0.0599284	+	0.0262477i
$881$	−24.3808	+	17.7137i	−0.821409	+	0.596789i	−0.917116	−	0.398621i	$-0.869489\pi$
$881$	−24.3808	+	17.7137i	−0.821409	+	0.596789i	0.0957068	+	0.995410i	$0.469489\pi$
$882$	11.7548	−	5.72639i	0.395805	−	0.192818i
$883$	−11.0920	+	8.05883i	−0.373276	+	0.271201i	−0.758568	−	0.651594i	$-0.774101\pi$
$883$	−11.0920	+	8.05883i	−0.373276	+	0.271201i	0.385292	+	0.922795i	$0.374101\pi$
$884$	−6.61522	−	9.10507i	−0.222494	−	0.306237i
$885$	−8.76101	+	2.95509i	−0.294498	+	0.0993341i
$886$	−0.859963	+	0.624800i	−0.0288910	+	0.0209906i
$887$	−42.8870	−	31.1592i	−1.44001	−	1.04622i	−0.988041	−	0.154188i	$-0.950724\pi$
$887$	−42.8870	−	31.1592i	−1.44001	−	1.04622i	−0.451964	−	0.892036i	$-0.649276\pi$
$888$	−0.952455	+	10.8573i	−0.0319623	+	0.364348i
$889$	10.0070	−	13.7735i	0.335625	−	0.461948i
$890$	−0.0517155	−	0.0581408i	−0.00173351	−	0.00194889i
$891$	−7.33798	−	2.67859i	−0.245831	−	0.0897361i
$892$	−0.0776409	−	0.238954i	−0.00259961	−	0.00800077i
$893$	−1.43543			−0.0480349
$894$	−14.9139	+	35.1122i	−0.498797	+	1.17433i
$895$	−5.28167	−	1.15616i	−0.176547	−	0.0386463i
$896$	0.955313	+	1.31488i	0.0319148	+	0.0439269i
$897$	2.03901	−	1.22451i	0.0680804	−	0.0408852i
$898$	3.48460			0.116283
$899$	3.34774	+	3.44022i	0.111653	+	0.114738i
$900$	4.31581	−	14.3657i	0.143860	−	0.478857i
$901$	−55.1163	−	40.0443i	−1.83619	−	1.33407i
$902$	3.37187	+	4.64098i	0.112271	+	0.154528i
$903$	−16.8707	−	1.47997i	−0.561421	−	0.0492504i
$904$	3.75499			0.124889
$905$	44.3191	+	25.9471i	1.47322	+	0.862512i
$906$	−19.5945	−	1.71892i	−0.650982	−	0.0571071i
$907$	38.9183	+	12.6453i	1.29226	+	0.419882i	0.872883	−	0.487930i	$-0.162248\pi$
$907$	38.9183	+	12.6453i	1.29226	+	0.419882i	0.419379	+	0.907811i	$0.362248\pi$
$908$	3.11966	−	9.60132i	0.103529	−	0.318631i
$909$	21.2692	−	2.97904i	0.705456	−	0.0988085i
$910$	1.76090	−	8.04427i	0.0583733	−	0.266665i
$911$	−34.9313	−	25.3791i	−1.15732	−	0.840846i	−0.167887	−	0.985806i	$-0.553694\pi$
$911$	−34.9313	−	25.3791i	−1.15732	−	0.840846i	−0.989437	+	0.144961i	$0.953694\pi$
$912$	2.40373	−	0.554353i	0.0795955	−	0.0183565i
$913$	3.04225	+	0.988488i	0.100684	+	0.0327142i
$914$	−28.4749	+	20.6882i	−0.941865	+	0.684305i
$915$	−26.0235	−	8.13571i	−0.860311	−	0.268958i
$916$	14.5813	+	4.73775i	0.481780	+	0.156540i
$917$	15.7811	−	11.4656i	0.521138	−	0.378629i
$918$	−24.9248	−	6.69734i	−0.822640	−	0.221045i
$919$	−6.97454	−	21.4654i	−0.230069	−	0.708079i	−0.997737	−	0.0672318i	$-0.978583\pi$
$919$	−6.97454	−	21.4654i	−0.230069	−	0.708079i	0.767669	−	0.640847i	$-0.221417\pi$
$920$	−0.543662	−	1.24128i	−0.0179240	−	0.0409239i
$921$	−6.16001	−	5.35735i	−0.202979	−	0.176531i
$922$	−4.34452	+	13.3711i	−0.143079	+	0.440352i
$923$	24.0272	−	7.80691i	0.790865	−	0.256968i
$924$	−0.955216	+	2.24888i	−0.0314243	+	0.0739828i
$925$	−15.3999	−	27.4363i	−0.506345	−	0.902101i
$926$	2.98161	+	9.17645i	0.0979818	+	0.301557i
$927$	−4.73277	+	26.7676i	−0.155444	+	0.879162i
$928$	0.697495	+	0.506760i	0.0228964	+	0.0166352i
$929$	32.4636			1.06510			0.532548	−	0.846400i	$-0.321235\pi$
$929$	32.4636			1.06510			0.532548	+	0.846400i	$0.321235\pi$
$930$	−19.2376	+	9.74236i	−0.630827	+	0.319465i
$931$	−6.20745			−0.203441
$932$	9.54987	+	6.93839i	0.312816	+	0.227274i
$933$	−6.14359	−	26.6393i	−0.201132	−	0.872131i
$934$	−4.50495	−	13.8648i	−0.147406	−	0.453670i
$935$	−8.31895	−	4.87043i	−0.272059	−	0.159280i
$936$	−4.71976	−	4.89204i	−0.154270	−	0.159901i
$937$	24.7160	−	8.03071i	0.807436	−	0.262352i	0.123924	−	0.992292i	$-0.460452\pi$
$937$	24.7160	−	8.03071i	0.807436	−	0.262352i	0.683511	+	0.729940i	$0.260452\pi$
$938$	6.57250	−	20.2281i	0.214600	−	0.660470i
$939$	−12.5206	+	14.3964i	−0.408593	+	0.469810i
$940$	2.06435	−	0.904150i	0.0673315	−	0.0294901i
$941$	−10.8808	−	33.4875i	−0.354702	−	1.09166i	−0.956182	−	0.292773i	$-0.905422\pi$
$941$	−10.8808	−	33.4875i	−0.354702	−	1.09166i	0.601479	−	0.798888i	$-0.294578\pi$
$942$	−2.23847	+	1.34430i	−0.0729335	+	0.0437996i
$943$	−3.24046	+	2.35433i	−0.105524	+	0.0766676i
$944$	2.27045	+	0.737716i	0.0738970	+	0.0240106i
$945$	−8.45914	−	16.8834i	−0.275176	−	0.549216i
$946$	−4.22439	+	3.06920i	−0.137347	+	0.0997882i
$947$	12.6811	+	4.12035i	0.412082	+	0.133893i	0.507719	−	0.861523i	$-0.330489\pi$
$947$	12.6811	+	4.12035i	0.412082	+	0.133893i	−0.0956371	+	0.995416i	$0.530489\pi$
$948$	−1.51716	−	6.57856i	−0.0492750	−	0.213662i
$949$	−1.55536	−	1.13004i	−0.0504892	−	0.0366826i
$950$	−4.82877	+	5.23386i	−0.156666	+	0.169809i
$951$	−14.7809	−	24.6127i	−0.479305	−	0.798121i
$952$	−2.49458	+	7.67752i	−0.0808497	+	0.248830i
$953$	−29.7851	−	9.67778i	−0.964835	−	0.313494i	−0.216106	−	0.976370i	$-0.569336\pi$
$953$	−29.7851	−	9.67778i	−0.964835	−	0.313494i	−0.748729	+	0.662876i	$0.769336\pi$
$954$	−36.3231	−	19.3352i	−1.17600	−	0.625999i
$955$	−15.3531	−	8.98866i	−0.496815	−	0.290866i
$956$	−16.8506			−0.544987
$957$	−0.113265	+	1.29115i	−0.00366135	+	0.0417369i
$958$	−14.3586	−	19.7629i	−0.463905	−	0.638510i
$959$	−8.97525	−	6.52090i	−0.289826	−	0.210571i
$960$	−3.10772	+	2.31130i	−0.100301	+	0.0745968i
$961$	29.2108	+	10.3792i	0.942285	+	0.334813i
$962$	−14.2582			−0.459704
$963$	5.37759	+	38.3940i	0.173290	+	1.23723i
$964$	−10.6397	−	14.6443i	−0.342682	−	0.471662i
$965$	8.15247	−	37.2427i	0.262437	−	1.19889i
$966$	−1.57023	−	0.666957i	−0.0505213	−	0.0214590i
$967$	−16.7708			−0.539313			−0.269657	−	0.962957i	$-0.586910\pi$
$967$	−16.7708			−0.539313			−0.269657	+	0.962957i	$0.586910\pi$
$968$	−3.16639	−	9.74515i	−0.101772	−	0.313221i
$969$	9.24523	+	8.04055i	0.296999	+	0.258300i
$970$	16.2361	−	14.4418i	0.521309	−	0.463697i
$971$	−25.4939	+	35.0894i	−0.818139	+	1.12607i	0.171877	+	0.985118i	$0.445017\pi$
$971$	−25.4939	+	35.0894i	−0.818139	+	1.12607i	−0.990016	+	0.140953i	$0.954983\pi$
$972$	−15.4700	−	1.91787i	−0.496201	−	0.0615156i
$973$	−9.18258	−	6.67153i	−0.294380	−	0.213879i
$974$	12.3327	−	8.96025i	0.395166	−	0.287105i
$975$	19.2149	+	3.98205i	0.615369	+	0.127528i
$976$	4.13798	+	5.69544i	0.132453	+	0.182307i
$977$	19.0326	−	13.8280i	0.608908	−	0.442397i	−0.240122	−	0.970743i	$-0.577187\pi$
$977$	19.0326	−	13.8280i	0.608908	−	0.442397i	0.849030	+	0.528345i	$0.177187\pi$
$978$	23.7120	+	20.6223i	0.758228	+	0.659429i
$979$	−0.0244355	+	0.0177534i	−0.000780961	+	0.000567401i
$980$	8.92715	−	3.90995i	0.285167	−	0.124899i
$981$	0.210411	−	0.395279i	0.00671790	−	0.0126203i
$982$	−21.5649	−	15.6678i	−0.688165	−	0.499981i
$983$	8.44660	+	2.74447i	0.269405	+	0.0875349i	0.440604	−	0.897701i	$-0.354764\pi$
$983$	8.44660	+	2.74447i	0.269405	+	0.0875349i	−0.171199	+	0.985236i	$0.554764\pi$
$984$	8.63790	+	7.51236i	0.275366	+	0.239485i
$985$	−9.03280	+	41.2643i	−0.287809	+	1.31479i
$986$			4.28224i			0.136374i
$987$	1.10920	−	2.61141i	0.0353062	−	0.0831221i
$988$	0.997238	+	3.06918i	0.0317264	+	0.0976437i
$989$	−2.14300	−	2.94958i	−0.0681433	−	0.0937912i
$990$	−5.38408	−	2.21632i	−0.171117	−	0.0704393i
$991$			8.97599i			0.285132i	0.989785	+	0.142566i	$0.0455353\pi$
$991$			8.97599i			0.285132i	−0.989785	+	0.142566i	$0.954465\pi$
$992$	5.48684	+	0.945827i	0.174207	+	0.0300300i
$993$	−5.87020	+	13.8203i	−0.186285	+	0.438575i
$994$	−14.6603	−	10.6513i	−0.464997	−	0.337840i
$995$	31.5986	−	3.12759i	1.00174	−	0.0991513i
$996$	6.35900	+	0.557840i	0.201493	+	0.0176758i
$997$			49.0663i			1.55395i	0.629534	+	0.776973i	$0.283246\pi$
$997$			49.0663i			1.55395i	−0.629534	+	0.776973i	$0.716754\pi$
$998$		−	31.5402i		−	0.998387i
$999$	−25.4249	+	20.5591i	−0.804407	+	0.650461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.1	✓	128
3.2	odd	2		930.2.y.b.29.12	yes	128
5.4	even	2		930.2.y.b.29.32	yes	128
15.14	odd	2	inner	930.2.y.a.29.21	yes	128
31.15	odd	10	inner	930.2.y.a.449.21	yes	128
93.77	even	10		930.2.y.b.449.32	yes	128
155.139	odd	10		930.2.y.b.449.12	yes	128
465.449	even	10	inner	930.2.y.a.449.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.1	✓	128	1.1	even	1	trivial
930.2.y.a.29.21	yes	128	15.14	odd	2	inner
930.2.y.a.449.1	yes	128	465.449	even	10	inner
930.2.y.a.449.21	yes	128	31.15	odd	10	inner
930.2.y.b.29.12	yes	128	3.2	odd	2
930.2.y.b.29.32	yes	128	5.4	even	2
930.2.y.b.449.12	yes	128	155.139	odd	10
930.2.y.b.449.32	yes	128	93.77	even	10

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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.68775 + 0.389232i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.12975 + 1.92968i) q^{5} +(1.59420 + 0.677139i) q^{6} +(1.54573 - 0.502238i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.69700 - 1.31385i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.68775 + 0.389232i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-1.12975 + 1.92968i) q^{5} +(1.59420 + 0.677139i) q^{6} +(1.54573 - 0.502238i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.69700 - 1.31385i) q^{9} +(2.04823 - 0.897090i) q^{10} +(-0.268212 - 0.825472i) q^{11} +(-0.891724 - 1.48487i) q^{12} +(1.83314 - 1.33186i) q^{13} +(-1.54573 - 0.502238i) q^{14} +(1.15565 - 3.69655i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-4.72382 - 1.53486i) q^{17} +(-2.95418 - 0.522328i) q^{18} +(1.15222 + 0.837138i) q^{19} +(-2.18435 - 0.478156i) q^{20} +(-2.41332 + 1.44930i) q^{21} +(-0.268212 + 0.825472i) q^{22} +(-0.576367 - 0.187273i) q^{23} +(-0.151362 + 1.72542i) q^{24} +(-2.44732 - 4.36012i) q^{25} -2.26589 q^{26} +(-4.04046 + 3.26721i) q^{27} +(0.955313 + 1.31488i) q^{28} +(0.697495 + 0.506760i) q^{29} +(-3.10772 + 2.31130i) q^{30} +(5.48684 + 0.945827i) q^{31} +1.00000 q^{32} +(0.773975 + 1.28879i) q^{33} +(2.91948 + 4.01832i) q^{34} +(-0.777135 + 3.55016i) q^{35} +(2.08296 + 2.15899i) q^{36} +6.29256 q^{37} +(-0.440109 - 1.35452i) q^{38} +(-2.57548 + 2.96135i) q^{39} +(1.48612 + 1.67076i) q^{40} +(3.88485 - 5.34704i) q^{41} +(2.80429 + 0.246005i) q^{42} +(4.86707 + 3.53613i) q^{43} +(0.702189 - 0.510170i) q^{44} +(-0.511632 + 6.68866i) q^{45} +(0.356214 + 0.490287i) q^{46} +(-0.815384 + 0.592411i) q^{47} +(1.13663 - 1.30693i) q^{48} +(-3.52608 + 2.56185i) q^{49} +(-0.582894 + 4.96591i) q^{50} +(8.57005 + 0.751804i) q^{51} +(1.83314 + 1.33186i) q^{52} +(13.0449 + 4.23855i) q^{53} +(5.18922 - 0.268301i) q^{54} +(1.89591 + 0.415017i) q^{55} -1.62528i q^{56} +(-2.27050 - 0.964398i) q^{57} +(-0.266419 - 0.819955i) q^{58} +(-1.40322 - 1.93136i) q^{59} +(3.87274 - 0.0432092i) q^{60} -7.03995i q^{61} +(-3.88300 - 3.99027i) q^{62} +(3.50896 - 3.38539i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.499055 + 5.04204i) q^{65} +(0.131375 - 1.49759i) q^{66} +13.0864i q^{67} -4.96692i q^{68} +(1.04566 + 0.0917297i) q^{69} +(2.71545 - 2.41535i) q^{70} +(10.6039 + 3.44541i) q^{71} +(-0.416128 - 2.97100i) q^{72} +(-0.262191 - 0.806942i) q^{73} +(-5.09079 - 3.69867i) q^{74} +(5.82755 + 6.40622i) q^{75} +(-0.440109 + 1.35452i) q^{76} +(-0.829167 - 1.14125i) q^{77} +(3.82425 - 0.881955i) q^{78} +(3.70706 + 1.20450i) q^{79} +(-0.220247 - 2.22519i) q^{80} +(5.54759 - 7.08690i) q^{81} +(-6.28582 + 2.04239i) q^{82} +(-2.16626 + 2.98161i) q^{83} +(-2.12412 - 1.84734i) q^{84} +(8.29855 - 7.38144i) q^{85} +(-1.85905 - 5.72158i) q^{86} +(-1.37444 - 0.583797i) q^{87} -0.867953 q^{88} +(-0.0107535 - 0.0330958i) q^{89} +(4.34542 - 5.11051i) q^{90} +(2.16463 - 2.97936i) q^{91} -0.606028i q^{92} +(-9.62856 + 0.539332i) q^{93} +1.00787 q^{94} +(-2.91713 + 1.27766i) q^{95} +(-1.68775 + 0.389232i) q^{96} +(9.24214 - 3.00295i) q^{97} +4.35848 q^{98} +(-1.80792 - 1.87391i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

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