LMFDB - Embedded newform 403.2.l.c.25.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(25,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("403.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			25.20
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.216546i q^{2} +(1.35890 + 2.35368i) q^{3} +1.95311 q^{4} +(-0.933057 - 0.538701i) q^{5} +(-0.509681 + 0.294264i) q^{6} +(2.50436 - 1.44590i) q^{7} +0.856030i q^{8} +(-2.19321 + 3.79876i) q^{9} +O(q^{10})$	\(q+0.216546i q^{2} +(1.35890 + 2.35368i) q^{3} +1.95311 q^{4} +(-0.933057 - 0.538701i) q^{5} +(-0.509681 + 0.294264i) q^{6} +(2.50436 - 1.44590i) q^{7} +0.856030i q^{8} +(-2.19321 + 3.79876i) q^{9} +(0.116654 - 0.202050i) q^{10} +(-1.69734 - 0.979961i) q^{11} +(2.65408 + 4.59700i) q^{12} +(3.03278 + 1.94993i) q^{13} +(0.313103 + 0.542310i) q^{14} -2.92816i q^{15} +3.72085 q^{16} +(-2.22424 - 3.85250i) q^{17} +(-0.822606 - 0.474932i) q^{18} +(-3.53832 + 2.04285i) q^{19} +(-1.82236 - 1.05214i) q^{20} +(6.80636 + 3.92965i) q^{21} +(0.212207 - 0.367553i) q^{22} -0.663330 q^{23} +(-2.01482 + 1.16326i) q^{24} +(-1.91960 - 3.32485i) q^{25} +(-0.422249 + 0.656737i) q^{26} -3.76803 q^{27} +(4.89129 - 2.82399i) q^{28} -4.34035 q^{29} +0.634082 q^{30} +(-5.33130 + 1.60538i) q^{31} +2.51779i q^{32} -5.32668i q^{33} +(0.834243 - 0.481650i) q^{34} -3.11562 q^{35} +(-4.28358 + 7.41939i) q^{36} +(-0.514023 + 0.296771i) q^{37} +(-0.442371 - 0.766209i) q^{38} +(-0.468267 + 9.78797i) q^{39} +(0.461144 - 0.798725i) q^{40} +(-6.64980 - 3.83926i) q^{41} +(-0.850950 + 1.47389i) q^{42} +(2.15673 + 3.73557i) q^{43} +(-3.31509 - 1.91397i) q^{44} +(4.09279 - 2.36297i) q^{45} -0.143642i q^{46} -0.255427i q^{47} +(5.05625 + 8.75769i) q^{48} +(0.681225 - 1.17992i) q^{49} +(0.719983 - 0.415682i) q^{50} +(6.04504 - 10.4703i) q^{51} +(5.92335 + 3.80842i) q^{52} +(1.64889 - 2.85596i) q^{53} -0.815953i q^{54} +(1.05581 + 1.82872i) q^{55} +(1.23773 + 2.14381i) q^{56} +(-9.61644 - 5.55206i) q^{57} -0.939885i q^{58} +(9.81008 - 5.66385i) q^{59} -5.71901i q^{60} +5.31550 q^{61} +(-0.347640 - 1.15447i) q^{62} +12.6846i q^{63} +6.89647 q^{64} +(-1.77933 - 3.45316i) q^{65} +1.15347 q^{66} +(-8.18899 - 4.72791i) q^{67} +(-4.34418 - 7.52434i) q^{68} +(-0.901399 - 1.56127i) q^{69} -0.674675i q^{70} +(6.83812 + 3.94799i) q^{71} +(-3.25185 - 1.87746i) q^{72} +(0.249101 + 0.143819i) q^{73} +(-0.0642646 - 0.111310i) q^{74} +(5.21709 - 9.03627i) q^{75} +(-6.91072 + 3.98991i) q^{76} -5.66768 q^{77} +(-2.11955 - 0.101401i) q^{78} +(-2.03383 - 3.52270i) q^{79} +(-3.47176 - 2.00442i) q^{80} +(1.45926 + 2.52752i) q^{81} +(0.831377 - 1.43999i) q^{82} +(12.3268 + 7.11691i) q^{83} +(13.2935 + 7.67503i) q^{84} +4.79280i q^{85} +(-0.808923 + 0.467032i) q^{86} +(-5.89810 - 10.2158i) q^{87} +(0.838876 - 1.45298i) q^{88} +5.37232i q^{89} +(0.511692 + 0.886277i) q^{90} +(10.4146 + 0.498246i) q^{91} -1.29556 q^{92} +(-11.0233 - 10.3666i) q^{93} +0.0553117 q^{94} +4.40194 q^{95} +(-5.92609 + 3.42143i) q^{96} -1.70597i q^{97} +(0.255506 + 0.147517i) q^{98} +(7.44527 - 4.29853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	$ 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) $ 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.216546i			0.153121i	0.997065	+	0.0765606i	$0.0243939\pi$
$2$			0.216546i			0.153121i	−0.997065	+	0.0765606i	$0.975606\pi$
$3$	1.35890	+	2.35368i	0.784561	+	1.35890i	0.929261	+	0.369424i	$0.120445\pi$
$3$	1.35890	+	2.35368i	0.784561	+	1.35890i	−0.144700	+	0.989476i	$0.546222\pi$
$4$	1.95311			0.976554
$5$	−0.933057	−	0.538701i	−0.417276	−	0.240914i	0.276635	−	0.960975i	$-0.410781\pi$
$5$	−0.933057	−	0.538701i	−0.417276	−	0.240914i	−0.693911	+	0.720061i	$0.744114\pi$
$6$	−0.509681	+	0.294264i	−0.208076	+	0.120133i
$7$	2.50436	−	1.44590i	0.946560	−	0.546497i	0.0545497	−	0.998511i	$-0.482628\pi$
$7$	2.50436	−	1.44590i	0.946560	−	0.546497i	0.892011	+	0.452014i	$0.149294\pi$
$8$			0.856030i			0.302652i
$9$	−2.19321	+	3.79876i	−0.731071	+	1.26625i
$10$	0.116654	−	0.202050i	0.0368891	−	0.0638938i
$11$	−1.69734	−	0.979961i	−0.511768	−	0.295469i	0.221792	−	0.975094i	$-0.428809\pi$
$11$	−1.69734	−	0.979961i	−0.511768	−	0.295469i	−0.733560	+	0.679625i	$0.762143\pi$
$12$	2.65408	+	4.59700i	0.766166	+	1.32704i
$13$	3.03278	+	1.94993i	0.841143	+	0.540813i
$13$	3.03278	+	1.94993i	0.841143	+	0.540813i
$14$	0.313103	+	0.542310i	0.0836803	+	0.144938i
$15$		−	2.92816i		−	0.756048i
$16$	3.72085			0.930211
$17$	−2.22424	−	3.85250i	−0.539457	−	0.934368i	−0.998933	−	0.0461774i	$-0.985296\pi$
$17$	−2.22424	−	3.85250i	−0.539457	−	0.934368i	0.459476	−	0.888190i	$-0.348037\pi$
$18$	−0.822606	−	0.474932i	−0.193890	−	0.111943i
$19$	−3.53832	+	2.04285i	−0.811746	+	0.468662i	−0.847562	−	0.530696i	$-0.821930\pi$
$19$	−3.53832	+	2.04285i	−0.811746	+	0.468662i	0.0358156	+	0.999358i	$0.488597\pi$
$20$	−1.82236	−	1.05214i	−0.407492	−	0.235266i
$21$	6.80636	+	3.92965i	1.48527	+	0.857520i
$22$	0.212207	−	0.367553i	0.0452426	−	0.0783625i
$23$	−0.663330			−0.138314			−0.0691570	−	0.997606i	$-0.522031\pi$
$23$	−0.663330			−0.138314			−0.0691570	+	0.997606i	$0.522031\pi$
$24$	−2.01482	+	1.16326i	−0.411274	+	0.237449i
$25$	−1.91960	−	3.32485i	−0.383921	−	0.664970i
$26$	−0.422249	+	0.656737i	−0.0828099	+	0.128797i
$27$	−3.76803			−0.725159
$28$	4.89129	−	2.82399i	0.924367	−	0.533684i
$29$	−4.34035			−0.805982			−0.402991	−	0.915204i	$-0.632029\pi$
$29$	−4.34035			−0.805982			−0.402991	+	0.915204i	$0.632029\pi$
$30$	0.634082			0.115767
$31$	−5.33130	+	1.60538i	−0.957529	+	0.288336i
$31$	−5.33130	+	1.60538i	−0.957529	+	0.288336i
$32$			2.51779i			0.445087i
$33$		−	5.32668i		−	0.927255i
$34$	0.834243	−	0.481650i	0.143071	−	0.0826024i
$35$	−3.11562			−0.526636
$36$	−4.28358	+	7.41939i	−0.713931	+	1.23656i
$37$	−0.514023	+	0.296771i	−0.0845048	+	0.0487889i	−0.541657	−	0.840600i	$-0.682203\pi$
$37$	−0.514023	+	0.296771i	−0.0845048	+	0.0487889i	0.457152	+	0.889389i	$0.348869\pi$
$38$	−0.442371	−	0.766209i	−0.0717621	−	0.124296i
$39$	−0.468267	+	9.78797i	−0.0749828	+	1.56733i
$40$	0.461144	−	0.798725i	0.0729133	−	0.126289i
$41$	−6.64980	−	3.83926i	−1.03852	−	0.599592i	−0.119109	−	0.992881i	$-0.538004\pi$
$41$	−6.64980	−	3.83926i	−1.03852	−	0.599592i	−0.919415	+	0.393289i	$0.871337\pi$
$42$	−0.850950	+	1.47389i	−0.131305	+	0.227426i
$43$	2.15673	+	3.73557i	0.328899	+	0.569669i	0.982294	−	0.187348i	$-0.0599892\pi$
$43$	2.15673	+	3.73557i	0.328899	+	0.569669i	−0.653395	+	0.757017i	$0.726656\pi$
$44$	−3.31509	−	1.91397i	−0.499769	−	0.288542i
$45$	4.09279	−	2.36297i	0.610117	−	0.352251i
$46$		−	0.143642i		−	0.0211788i
$47$		−	0.255427i		−	0.0372579i	−0.999826	−	0.0186289i	$-0.994070\pi$
$47$		−	0.255427i		−	0.0372579i	0.999826	−	0.0186289i	$-0.00593012\pi$
$48$	5.05625	+	8.75769i	0.729807	+	1.26406i
$49$	0.681225	−	1.17992i	0.0973178	−	0.168559i
$50$	0.719983	−	0.415682i	0.101821	−	0.0587864i
$51$	6.04504	−	10.4703i	0.846474	−	1.46614i
$52$	5.92335	+	3.80842i	0.821421	+	0.528133i
$53$	1.64889	−	2.85596i	0.226492	−	0.392296i	−0.730274	−	0.683155i	$-0.760608\pi$
$53$	1.64889	−	2.85596i	0.226492	−	0.392296i	0.956766	+	0.290858i	$0.0939409\pi$
$54$		−	0.815953i		−	0.111037i
$55$	1.05581	+	1.82872i	0.142366	+	0.246585i
$56$	1.23773	+	2.14381i	0.165399	+	0.286479i
$57$	−9.61644	−	5.55206i	−1.27373	−	0.735388i
$58$		−	0.939885i		−	0.123413i
$59$	9.81008	−	5.66385i	1.27716	−	0.737371i	0.300838	−	0.953675i	$-0.402734\pi$
$59$	9.81008	−	5.66385i	1.27716	−	0.737371i	0.976326	+	0.216304i	$0.0694004\pi$
$60$		−	5.71901i		−	0.738321i
$61$	5.31550			0.680580			0.340290	−	0.940321i	$-0.389475\pi$
$61$	5.31550			0.680580			0.340290	+	0.940321i	$0.389475\pi$
$62$	−0.347640	−	1.15447i	−0.0441503	−	0.146618i
$63$			12.6846i			1.59811i
$64$	6.89647			0.862059
$65$	−1.77933	−	3.45316i	−0.220699	−	0.428312i
$66$	1.15347			0.141982
$67$	−8.18899	−	4.72791i	−1.00044	−	0.577607i	−0.0920644	−	0.995753i	$-0.529347\pi$
$67$	−8.18899	−	4.72791i	−1.00044	−	0.577607i	−0.908380	+	0.418146i	$0.862680\pi$
$68$	−4.34418	−	7.52434i	−0.526809	−	0.912460i
$69$	−0.901399	−	1.56127i	−0.108516	−	0.187955i
$70$		−	0.674675i		−	0.0806391i
$71$	6.83812	+	3.94799i	0.811535	+	0.468540i	0.847489	−	0.530813i	$-0.178113\pi$
$71$	6.83812	+	3.94799i	0.811535	+	0.468540i	−0.0359533	+	0.999353i	$0.511447\pi$
$72$	−3.25185	−	1.87746i	−0.383234	−	0.221260i
$73$	0.249101	+	0.143819i	0.0291551	+	0.0168327i	0.514507	−	0.857486i	$-0.327975\pi$
$73$	0.249101	+	0.143819i	0.0291551	+	0.0168327i	−0.485352	+	0.874319i	$0.661308\pi$
$74$	−0.0642646	−	0.111310i	−0.00747061	−	0.0129395i
$75$	5.21709	−	9.03627i	0.602418	−	1.04342i
$76$	−6.91072	+	3.98991i	−0.792714	+	0.457674i
$77$	−5.66768			−0.645893
$78$	−2.11955	−	0.101401i	−0.239991	−	0.0114815i
$79$	−2.03383	−	3.52270i	−0.228824	−	0.396334i	0.728636	−	0.684901i	$-0.240155\pi$
$79$	−2.03383	−	3.52270i	−0.228824	−	0.396334i	−0.957460	+	0.288567i	$0.906821\pi$
$80$	−3.47176	−	2.00442i	−0.388155	−	0.224101i
$81$	1.45926	+	2.52752i	0.162140	+	0.280835i
$82$	0.831377	−	1.43999i	0.0918103	−	0.159020i
$83$	12.3268	+	7.11691i	1.35305	+	0.781182i	0.988675	−	0.150071i	$-0.0479503\pi$
$83$	12.3268	+	7.11691i	1.35305	+	0.781182i	0.364372	+	0.931253i	$0.381284\pi$
$84$	13.2935	+	7.67503i	1.45044	+	0.837415i
$85$			4.79280i			0.519852i
$86$	−0.808923	+	0.467032i	−0.0872284	+	0.0503613i
$87$	−5.89810	−	10.2158i	−0.632342	−	1.09525i
$88$	0.838876	−	1.45298i	0.0894245	−	0.154888i
$89$			5.37232i			0.569464i	0.958607	+	0.284732i	$0.0919047\pi$
$89$			5.37232i			0.569464i	−0.958607	+	0.284732i	$0.908095\pi$
$90$	0.511692	+	0.886277i	0.0539371	+	0.0934218i
$91$	10.4146	+	0.498246i	1.09175	+	0.0522303i
$92$	−1.29556			−0.135071
$93$	−11.0233	−	10.3666i	−1.14306	−	1.07497i
$94$	0.0553117			0.00570497
$95$	4.40194			0.451630
$96$	−5.92609	+	3.42143i	−0.604829	+	0.349198i
$97$		−	1.70597i		−	0.173216i	−0.996242	−	0.0866078i	$-0.972397\pi$
$97$		−	1.70597i		−	0.173216i	0.996242	−	0.0866078i	$-0.0276027\pi$
$98$	0.255506	+	0.147517i	0.0258100	+	0.0149014i
$99$	7.44527	−	4.29853i	0.748278	−	0.432019i
$100$	−3.74919	−	6.49379i	−0.374919	−	0.649379i
$101$	−8.31840			−0.827711			−0.413856	−	0.910342i	$-0.635818\pi$
$101$	−8.31840			−0.827711			−0.413856	+	0.910342i	$0.635818\pi$
$102$	2.26730	+	1.30903i	0.224497	+	0.129613i
$103$	−1.71285	+	2.96674i	−0.168772	+	0.292322i	−0.937988	−	0.346667i	$-0.887314\pi$
$103$	−1.71285	+	2.96674i	−0.168772	+	0.292322i	0.769216	+	0.638989i	$0.220647\pi$
$104$	−1.66920	+	2.59615i	−0.163678	+	0.254574i
$105$	−4.23381	−	7.33318i	−0.413178	−	0.715645i
$106$	0.618447	+	0.357060i	0.0600688	+	0.0346808i
$107$	−7.21523	−	12.4972i	−0.697523	−	1.20815i	−0.969323	−	0.245792i	$-0.920952\pi$
$107$	−7.21523	−	12.4972i	−0.697523	−	1.20815i	0.271800	−	0.962354i	$-0.412381\pi$
$108$	−7.35938			−0.708156
$109$		−	14.1796i		−	1.35816i	−0.734064	−	0.679080i	$-0.762379\pi$
$109$		−	14.1796i		−	1.35816i	0.734064	−	0.679080i	$-0.237621\pi$
$110$	−0.396002	+	0.228632i	−0.0377573	+	0.0217992i
$111$	−1.39701	−	0.806565i	−0.132598	−	0.0765557i
$112$	9.31835	−	5.37995i	0.880501	−	0.508358i
$113$	−2.72624	+	4.72198i	−0.256463	+	0.444207i	−0.965292	−	0.261174i	$-0.915890\pi$
$113$	−2.72624	+	4.72198i	−0.256463	+	0.444207i	0.708829	+	0.705380i	$0.249224\pi$
$114$	1.20228	−	2.08240i	0.112603	−	0.195035i
$115$	0.618925	+	0.357337i	0.0577151	+	0.0333218i
$116$	−8.47717			−0.787085
$117$	−14.0589	+	7.24420i	−1.29974	+	0.669727i
$118$	1.22648	+	2.12433i	0.112907	+	0.195561i
$119$	−11.1406	−	6.43204i	−1.02126	−	0.589624i
$120$	2.50659			0.228820
$121$	−3.57935	−	6.19962i	−0.325396	−	0.563602i
$122$			1.15105i			0.104211i
$123$		−	20.8687i		−	1.88167i
$124$	−10.4126	+	3.13549i	−0.935079	+	0.281575i
$125$			9.52337i			0.851797i
$126$	−2.74681			−0.244705
$127$	−9.01988	−	15.6229i	−0.800385	−	1.38631i	−0.919363	−	0.393411i	$-0.871295\pi$
$127$	−9.01988	−	15.6229i	−0.800385	−	1.38631i	0.118978	−	0.992897i	$-0.462038\pi$
$128$			6.52899i			0.577087i
$129$	−5.86156	+	10.1525i	−0.516082	+	0.893880i
$130$	0.747768	−	0.385307i	0.0655836	−	0.0337937i
$131$	2.44773	+	4.23960i	0.213859	+	0.370415i	0.952919	−	0.303225i	$-0.0980632\pi$
$131$	2.44773	+	4.23960i	0.213859	+	0.370415i	−0.739060	+	0.673640i	$0.764730\pi$
$132$		−	10.4036i		−	0.905515i
$133$	−5.90749	+	10.2321i	−0.512245	+	0.887234i
$134$	1.02381	−	1.77329i	0.0884438	−	0.153189i
$135$	3.51579	+	2.02984i	0.302591	+	0.174701i
$136$	3.29785	−	1.90402i	0.282788	−	0.163268i
$137$	12.5462	+	7.24358i	1.07190	+	0.618860i	0.928699	−	0.370834i	$-0.120928\pi$
$137$	12.5462	+	7.24358i	1.07190	+	0.618860i	0.143198	+	0.989694i	$0.454261\pi$
$138$	0.338087	−	0.195194i	0.0287798	−	0.0166160i
$139$	21.1636			1.79508			0.897538	−	0.440936i	$-0.145354\pi$
$139$	21.1636			1.79508			0.897538	+	0.440936i	$0.145354\pi$
$140$	−6.08514			−0.514288
$141$	0.601194	−	0.347100i	0.0506297	−	0.0292311i
$142$	−0.854922	+	1.48077i	−0.0717434	+	0.124263i
$143$	−3.23682	−	6.28171i	−0.270676	−	0.525303i
$144$	−8.16061	+	14.1346i	−0.680051	+	1.17788i
$145$	4.04979	+	2.33815i	0.336317	+	0.194173i
$146$	−0.0311434	+	0.0539419i	−0.00257745	+	0.00446427i
$147$	3.70286			0.305407
$148$	−1.00394	+	0.579626i	−0.0825235	+	0.0476450i
$149$	11.3091	−	6.52932i	0.926478	−	0.534902i	0.0407821	−	0.999168i	$-0.487015\pi$
$149$	11.3091	−	6.52932i	0.926478	−	0.534902i	0.885696	+	0.464266i	$0.153682\pi$
$150$	1.95677	+	1.12974i	0.159770	+	0.0922430i
$151$			21.4537i			1.74587i	0.487833	+	0.872937i	$0.337788\pi$
$151$			21.4537i			1.74587i	−0.487833	+	0.872937i	$0.662212\pi$
$152$	−1.74874	−	3.02891i	−0.141842	−	0.245677i
$153$	19.5129			1.57753
$154$		−	1.22731i		−	0.0988998i
$155$	5.83923	+	1.37406i	0.469018	+	0.110367i
$156$	−0.914577	+	19.1170i	−0.0732248	+	1.53058i
$157$	−0.204180			−0.0162954			−0.00814768	−	0.999967i	$-0.502594\pi$
$157$	−0.204180			−0.0162954			−0.00814768	+	0.999967i	$0.502594\pi$
$158$	0.762826	−	0.440418i	0.0606872	−	0.0350377i
$159$	8.96269			0.710788
$160$	1.35634	−	2.34925i	0.107228	−	0.185724i
$161$	−1.66122	+	0.959106i	−0.130922	+	0.0755881i
$162$	−0.547324	+	0.315998i	−0.0430019	+	0.0248271i
$163$		−	8.34506i		−	0.653636i	−0.945087	−	0.326818i	$-0.894024\pi$
$163$		−	8.34506i		−	0.653636i	0.945087	−	0.326818i	$-0.105976\pi$
$164$	−12.9878	−	7.49849i	−1.01417	−	0.585534i
$165$	−2.86948	+	4.97009i	−0.223389	+	0.386921i
$166$	−1.54114	+	2.66933i	−0.119616	+	0.207180i
$167$	−7.36470	+	4.25201i	−0.569898	+	0.329031i	−0.757108	−	0.653289i	$-0.773389\pi$
$167$	−7.36470	+	4.25201i	−0.569898	+	0.329031i	0.187211	+	0.982320i	$0.440055\pi$
$168$	−3.36390	+	5.82644i	−0.259530	+	0.449520i
$169$	5.39555	+	11.8274i	0.415042	+	0.909802i
$170$	−1.03786			−0.0796004
$171$		−	17.9216i		−	1.37050i
$172$	4.21233	+	7.29597i	0.321187	+	0.556312i
$173$	−12.3780	+	21.4393i	−0.941079	+	1.63000i	−0.177661	+	0.984092i	$0.556853\pi$
$173$	−12.3780	+	21.4393i	−0.941079	+	1.63000i	−0.763418	+	0.645905i	$0.776480\pi$
$174$	2.21219	−	1.27721i	0.167706	−	0.0968250i
$175$	−9.61477	−	5.55109i	−0.726808	−	0.419623i
$176$	−6.31555	−	3.64629i	−0.476053	−	0.274849i
$177$	26.6618	+	15.3932i	2.00403	+	1.15702i
$178$	−1.16335			−0.0871971
$179$	7.81732	+	13.5400i	0.584294	+	1.01203i	0.994963	+	0.100242i	$0.0319618\pi$
$179$	7.81732	+	13.5400i	0.584294	+	1.01203i	−0.410669	+	0.911784i	$0.634705\pi$
$180$	7.99366	−	4.61514i	0.595812	−	0.343992i
$181$	0.0959588	−	0.166206i	0.00713256	−	0.0123540i	−0.862437	−	0.506164i	$-0.831063\pi$
$181$	0.0959588	−	0.166206i	0.00713256	−	0.0123540i	0.869570	+	0.493810i	$0.164396\pi$
$182$	−0.107893	+	2.25524i	−0.00799757	+	0.167169i
$183$	7.22323	+	12.5110i	0.533957	+	0.924840i
$184$		−	0.567830i		−	0.0418610i
$185$	0.639484			0.0470158
$186$	2.24485	−	2.38704i	0.164601	−	0.175027i
$187$			8.71868i			0.637573i
$188$		−	0.498876i		−	0.0363843i
$189$	−9.43653	+	5.44818i	−0.686406	+	0.396297i
$190$			0.953223i			0.0691540i
$191$	10.8919	−	18.8654i	0.788112	−	1.36505i	−0.139010	−	0.990291i	$-0.544392\pi$
$191$	10.8919	−	18.8654i	0.788112	−	1.36505i	0.927122	−	0.374759i	$-0.122275\pi$
$192$	9.37161	+	16.2321i	0.676338	+	1.17145i
$193$	−20.9910	+	12.1192i	−1.51097	+	0.872357i	−0.511048	+	0.859552i	$0.670743\pi$
$193$	−20.9910	+	12.1192i	−1.51097	+	0.872357i	−0.999918	+	0.0128045i	$0.995924\pi$
$194$	0.369422			0.0265230
$195$	5.70971	−	8.88048i	0.408881	−	0.635944i
$196$	1.33051	−	2.30450i	0.0950361	−	0.164607i
$197$	4.91380	+	2.83698i	0.350093	+	0.202127i	0.664726	−	0.747087i	$-0.268548\pi$
$197$	4.91380	+	2.83698i	0.350093	+	0.202127i	−0.314633	+	0.949213i	$0.601881\pi$
$198$	0.930830	+	1.61224i	0.0661512	+	0.114577i
$199$	−8.04415	+	13.9329i	−0.570235	+	0.987676i	0.426307	+	0.904579i	$0.359814\pi$
$199$	−8.04415	+	13.9329i	−0.570235	+	0.987676i	−0.996541	+	0.0830970i	$0.973519\pi$
$200$	2.84617	−	1.64324i	0.201255	−	0.116194i
$201$		−	25.6990i		−	1.81267i
$202$		−	1.80132i		−	0.126740i
$203$	−10.8698	+	6.27569i	−0.762911	+	0.440467i
$204$	11.8066	−	20.4496i	0.826628	−	1.43176i
$205$	4.13643	+	7.16450i	0.288901	+	0.500391i
$206$	−0.642437	−	0.370911i	−0.0447607	−	0.0258426i
$207$	1.45483	−	2.51983i	0.101117	−	0.175140i
$208$	11.2845	+	7.25539i	0.782441	+	0.503071i
$209$	8.00766			0.553901
$210$	1.58797	−	0.916815i	0.109580	−	0.0632663i
$211$	−3.65726	−	6.33456i	−0.251776	−	0.436089i	0.712239	−	0.701937i	$-0.247681\pi$
$211$	−3.65726	−	6.33456i	−0.251776	−	0.436089i	−0.964015	+	0.265848i	$0.914348\pi$
$212$	3.22046	−	5.57800i	0.221182	−	0.383098i
$213$			21.4597i			1.47039i
$214$	2.70621	−	1.56243i	0.184993	−	0.106806i
$215$		−	4.64733i		−	0.316946i
$216$		−	3.22555i		−	0.219471i
$217$	−11.0303	+	11.7290i	−0.748785	+	0.796214i
$218$	3.07054			0.207963
$219$			0.781741i			0.0528252i
$220$	2.06211	+	3.57169i	0.139028	+	0.240803i
$221$	0.766458	−	16.0209i	0.0515575	−	1.07768i
$222$	0.174658	−	0.302517i	0.0117223	−	0.0203036i
$223$	24.4234	−	14.1009i	1.63551	−	0.944263i	0.653159	−	0.757220i	$-0.273443\pi$
$223$	24.4234	−	14.1009i	1.63551	−	0.944263i	0.982352	−	0.187042i	$-0.0598902\pi$
$224$	3.64047	+	6.30547i	0.243239	+	0.421302i
$225$	16.8404			1.12269
$226$	−1.02253	−	0.590356i	−0.0680175	−	0.0392699i
$227$	−19.4653	−	11.2383i	−1.29196	−	0.745913i	−0.312957	−	0.949767i	$-0.601320\pi$
$227$	−19.4653	−	11.2383i	−1.29196	−	0.745913i	−0.979001	+	0.203855i	$0.934653\pi$
$228$	−18.7819	−	10.8438i	−1.24386	−	0.718146i
$229$	−7.09051	+	4.09371i	−0.468554	+	0.270520i	−0.715634	−	0.698475i	$-0.753862\pi$
$229$	−7.09051	+	4.09371i	−0.468554	+	0.270520i	0.247080	+	0.968995i	$0.420529\pi$
$230$	−0.0773798	+	0.134026i	−0.00510227	+	0.00883740i
$231$	−7.70181	−	13.3399i	−0.506742	−	0.877703i
$232$		−	3.71547i		−	0.243932i
$233$	2.12578			0.139265			0.0696323	−	0.997573i	$-0.477817\pi$
$233$	2.12578			0.139265			0.0696323	+	0.997573i	$0.477817\pi$
$234$	−1.56870	−	3.04439i	−0.102549	−	0.199018i
$235$	−0.137599	+	0.238328i	−0.00897595	+	0.0155468i
$236$	19.1601	−	11.0621i	1.24722	−	0.720082i
$237$	5.52754	−	9.57398i	0.359052	−	0.621897i
$238$	1.39283	−	2.41246i	0.0902839	−	0.156376i
$239$	7.07031	+	4.08204i	0.457340	+	0.264045i	0.710925	−	0.703268i	$-0.248276\pi$
$239$	7.07031	+	4.08204i	0.457340	+	0.264045i	−0.253585	+	0.967313i	$0.581610\pi$
$240$		−	10.8952i		−	0.703284i
$241$	19.6980	−	11.3727i	1.26886	−	0.732577i	0.294088	−	0.955778i	$-0.404984\pi$
$241$	19.6980	−	11.3727i	1.26886	−	0.732577i	0.974772	+	0.223201i	$0.0716506\pi$
$242$	1.34250	−	0.775094i	0.0862994	−	0.0498250i
$243$	−9.61804	+	16.6589i	−0.616997	+	1.06867i
$244$	10.3817			0.664623
$245$	−1.27124	+	0.733953i	−0.0812168	+	0.0468905i
$246$	4.51903			0.288123
$247$	−14.7144	−	0.703952i	−0.936253	−	0.0447914i
$248$	−1.37426	−	4.56375i	−0.0872654	−	0.289798i
$249$			38.6846i			2.45154i
$250$	−2.06225			−0.130428
$251$	8.40806	+	14.5632i	0.530712	+	0.919221i	0.999358	+	0.0358343i	$0.0114088\pi$
$251$	8.40806	+	14.5632i	0.530712	+	0.919221i	−0.468646	+	0.883386i	$0.655258\pi$
$252$			24.7745i			1.56064i
$253$	1.12590	+	0.650038i	0.0707847	+	0.0408675i
$254$	3.38308	−	1.95322i	0.212273	−	0.122556i
$255$	−11.2807	+	6.51293i	−0.706427	+	0.407856i
$256$	12.3791			0.773695
$257$	−11.6255	+	20.1359i	−0.725177	+	1.25604i	0.233725	+	0.972303i	$0.424909\pi$
$257$	−11.6255	+	20.1359i	−0.725177	+	1.25604i	−0.958901	+	0.283740i	$0.908425\pi$
$258$	−2.19849	−	1.26930i	−0.136872	−	0.0790231i
$259$	−0.858200	+	1.48645i	−0.0533260	+	0.0923633i
$260$	−3.47523	−	6.74439i	−0.215524	−	0.418269i
$261$	9.51931	−	16.4879i	0.589231	−	1.02058i
$262$	−0.918068	+	0.530047i	−0.0567184	+	0.0327464i
$263$	−21.7782			−1.34290			−0.671451	−	0.741049i	$-0.734328\pi$
$263$	−21.7782			−1.34290			−0.671451	+	0.741049i	$0.734328\pi$
$264$	4.55979			0.280636
$265$	−3.07701	+	1.77652i	−0.189020	+	0.109130i
$266$	−2.21572	−	1.27924i	−0.135854	−	0.0784355i
$267$	−12.6447	+	7.30044i	−0.773845	+	0.446779i
$268$	−15.9940	−	9.23413i	−0.976988	−	0.564064i
$269$	−13.7118	+	23.7495i	−0.836020	+	1.44803i	0.0571764	+	0.998364i	$0.481790\pi$
$269$	−13.7118	+	23.7495i	−0.836020	+	1.44803i	−0.893197	+	0.449666i	$0.851543\pi$
$270$	−0.439555	+	0.761331i	−0.0267504	+	0.0463331i
$271$			10.2933i			0.625271i	0.949873	+	0.312635i	$0.101212\pi$
$271$			10.2933i			0.625271i	−0.949873	+	0.312635i	$0.898788\pi$
$272$	−8.27605	−	14.3345i	−0.501810	−	0.869160i
$273$	12.9797	+	25.1897i	0.785565	+	1.52455i
$274$	−1.56857	+	2.71684i	−0.0947606	+	0.164130i
$275$			7.52455i			0.453747i
$276$	−1.76053	−	3.04933i	−0.105971	−	0.183548i
$277$	−25.6564			−1.54154			−0.770772	−	0.637111i	$-0.780129\pi$
$277$	−25.6564			−1.54154			−0.770772	+	0.637111i	$0.780129\pi$
$278$			4.58290i			0.274864i
$279$	5.59421	−	23.7733i	0.334917	−	1.42327i
$280$		−	2.66706i		−	0.159388i
$281$		−	10.7924i		−	0.643819i	−0.946771	−	0.321909i	$-0.895675\pi$
$281$		−	10.7924i		−	0.643819i	0.946771	−	0.321909i	$-0.104325\pi$
$282$	0.0751630	+	0.130186i	0.00447589	+	0.00775248i
$283$	−1.13064			−0.0672096			−0.0336048	−	0.999435i	$-0.510699\pi$
$283$	−1.13064			−0.0672096			−0.0336048	+	0.999435i	$0.510699\pi$
$284$	13.3556	+	7.71085i	0.792508	+	0.457555i
$285$	5.98179	+	10.3608i	0.354331	+	0.613719i
$286$	1.36028	−	0.700920i	0.0804350	−	0.0414463i
$287$	−22.2047			−1.31070
$288$	−9.56449	−	5.52206i	−0.563593	−	0.325391i
$289$	−1.39449	+	2.41532i	−0.0820287	+	0.142078i
$290$	−0.506317	+	0.876967i	−0.0297320	+	0.0514973i
$291$	4.01532	−	2.31825i	0.235382	−	0.135898i
$292$	0.486522	+	0.280894i	0.0284715	+	0.0164381i
$293$	8.91703	−	5.14825i	0.520938	−	0.300764i	−0.216380	−	0.976309i	$-0.569425\pi$
$293$	8.91703	−	5.14825i	0.520938	−	0.300764i	0.737318	+	0.675545i	$0.236092\pi$
$294$			0.801840i			0.0467643i
$295$	−12.2045			−0.710573
$296$	−0.254045	−	0.440019i	−0.0147661	−	0.0255756i
$297$	6.39565	+	3.69253i	0.371113	+	0.214262i
$298$	1.41390	+	2.44894i	0.0819049	+	0.141863i
$299$	−2.01174	−	1.29345i	−0.116342	−	0.0748020i
$300$	10.1895	−	17.6488i	0.588294	−	1.01895i
$301$	10.8025	+	6.23682i	0.622645	+	0.359484i
$302$	−4.64571			−0.267330
$303$	−11.3039	−	19.5789i	−0.649390	−	1.12478i
$304$	−13.1655	+	7.60113i	−0.755096	+	0.435955i
$305$	−4.95967	−	2.86346i	−0.283990	−	0.163962i
$306$			4.22545i			0.241553i
$307$	−2.74732	+	1.58616i	−0.156798	+	0.0905272i	−0.576346	−	0.817206i	$-0.695522\pi$
$307$	−2.74732	+	1.58616i	−0.156798	+	0.0905272i	0.419548	+	0.907733i	$0.362189\pi$
$308$	−11.0696			−0.630749
$309$	−9.31036			−0.529648
$310$	−0.297547	+	1.26446i	−0.0168995	+	0.0718166i
$311$	−12.7270			−0.721682			−0.360841	−	0.932627i	$-0.617510\pi$
$311$	−12.7270			−0.721682			−0.360841	+	0.932627i	$0.617510\pi$
$312$	−8.37879	−	0.400851i	−0.474356	−	0.0226937i
$313$	5.03964	+	8.72891i	0.284857	+	0.493387i	0.972575	−	0.232592i	$-0.0747205\pi$
$313$	5.03964	+	8.72891i	0.284857	+	0.493387i	−0.687717	+	0.725978i	$0.741387\pi$
$314$		−	0.0442144i		−	0.00249517i
$315$	6.83322	−	11.8355i	0.385008	−	0.666854i
$316$	−3.97229	−	6.88020i	−0.223459	−	0.387042i
$317$	−28.7576	+	16.6032i	−1.61519	+	0.932530i	−0.627049	+	0.778980i	$0.715737\pi$
$317$	−28.7576	+	16.6032i	−1.61519	+	0.932530i	−0.988141	+	0.153550i	$0.950929\pi$
$318$			1.94084i			0.108837i
$319$	7.36706	+	4.25337i	0.412476	+	0.238143i
$320$	−6.43480	−	3.71514i	−0.359716	−	0.207682i
$321$	19.6096	−	33.9647i	1.09450	−	1.89573i
$322$	−0.207691	−	0.359731i	−0.0115741	−	0.0200470i
$323$	15.7401	+	9.08758i	0.875805	+	0.505646i
$324$	2.85010	+	4.93652i	0.158339	+	0.274251i
$325$	0.661482	−	13.8266i	0.0366924	−	0.766964i
$326$	1.80709			0.100085
$327$	33.3743	−	19.2687i	1.84560	−	1.06556i
$328$	3.28652	−	5.69243i	0.181468	−	0.314312i
$329$	−0.369321	−	0.639682i	−0.0203613	−	0.0352668i
$330$	−1.07625	−	0.621375i	−0.0592458	−	0.0342056i
$331$	−4.91037	−	2.83500i	−0.269898	−	0.155826i	0.358943	−	0.933359i	$-0.383137\pi$
$331$	−4.91037	−	2.83500i	−0.269898	−	0.155826i	−0.628841	+	0.777534i	$0.716471\pi$
$332$	24.0757	+	13.9001i	1.32132	+	0.762867i
$333$		−	2.60353i		−	0.142673i
$334$	−0.920756	−	1.59480i	−0.0503815	−	0.0872634i
$335$	5.09386	+	8.82283i	0.278307	+	0.482043i
$336$	25.3254	+	14.6216i	1.38161	+	0.797675i
$337$	21.0424			1.14625			0.573127	−	0.819467i	$-0.305730\pi$
$337$	21.0424			1.14625			0.573127	+	0.819467i	$0.305730\pi$
$338$	−2.56118	+	1.16839i	−0.139310	+	0.0635518i
$339$	−14.8187			−0.804843
$340$			9.36085i			0.507664i
$341$	10.6223	+	2.49958i	0.575227	+	0.135360i
$342$	3.88086			0.209853
$343$			16.3026i			0.880258i
$344$	−3.19776	+	1.84623i	−0.172412	+	0.0995419i
$345$			1.94234i			0.104572i
$346$	−4.64259	−	2.68040i	−0.249587	−	0.144099i
$347$	−3.45932	−	5.99172i	−0.185706	−	0.321653i	0.758108	−	0.652129i	$-0.226124\pi$
$347$	−3.45932	−	5.99172i	−0.185706	−	0.321653i	−0.943814	+	0.330476i	$0.892791\pi$
$348$	−11.5196	−	19.9526i	−0.617516	−	1.06957i
$349$		−	20.4459i		−	1.09444i	−0.836988	−	0.547221i	$-0.815686\pi$
$349$		−	20.4459i		−	1.09444i	0.836988	−	0.547221i	$-0.184314\pi$
$350$	1.20207	−	2.08204i	0.0642531	−	0.111290i
$351$	−11.4276	−	7.34740i	−0.609962	−	0.392175i
$352$	2.46734	−	4.27356i	0.131510	−	0.227782i
$353$	10.3755	−	5.99032i	0.552234	−	0.318832i	−0.197789	−	0.980245i	$-0.563376\pi$
$353$	10.3755	−	5.99032i	0.552234	−	0.318832i	0.750022	+	0.661412i	$0.230043\pi$
$354$	−3.33334	+	5.77351i	−0.177165	+	0.306859i
$355$	−4.25357	−	7.36740i	−0.225756	−	0.391021i
$356$			10.4927i			0.556113i
$357$		−	34.9620i		−	1.85038i
$358$	−2.93203	+	1.69281i	−0.154963	+	0.0894678i
$359$	−26.0022	−	15.0124i	−1.37234	−	0.792322i	−0.381119	−	0.924526i	$-0.624461\pi$
$359$	−26.0022	−	15.0124i	−1.37234	−	0.792322i	−0.991223	+	0.132204i	$0.957795\pi$
$360$	2.02278	+	3.50355i	0.106610	+	0.184653i
$361$	−1.15353	+	1.99797i	−0.0607120	+	0.105156i
$362$	0.0359912	+	0.0207795i	0.00189165	+	0.00109215i
$363$	9.72796	−	16.8493i	0.510585	−	0.884360i
$364$	20.3408	+	0.973127i	1.06615	+	0.0510057i
$365$	−0.154951	−	0.268382i	−0.00811049	−	0.0140478i
$366$	−2.70921	+	1.56416i	−0.141613	+	0.0817601i
$367$	−4.65412	+	8.06117i	−0.242943	+	0.420790i	−0.961551	−	0.274626i	$-0.911446\pi$
$367$	−4.65412	+	8.06117i	−0.242943	+	0.420790i	0.718608	+	0.695415i	$0.244779\pi$
$368$	−2.46815			−0.128661
$369$	29.1689	−	16.8407i	1.51847	−	0.876689i
$370$			0.138478i			0.00719911i
$371$		−	9.53648i		−	0.495109i
$372$	−21.5296	−	20.2471i	−1.11626	−	1.04977i
$373$	22.1171			1.14518			0.572589	−	0.819843i	$-0.305939\pi$
$373$	22.1171			1.14518			0.572589	+	0.819843i	$0.305939\pi$
$374$	−1.88800			−0.0976259
$375$	−22.4150	+	12.9413i	−1.15751	+	0.668286i
$376$	0.218653			0.0112762
$377$	−13.1633	−	8.46337i	−0.677946	−	0.435886i
$378$	−1.17978	−	2.04344i	−0.0606815	−	0.105103i
$379$	−3.68888	+	2.12978i	−0.189485	+	0.109399i	−0.591742	−	0.806128i	$-0.701559\pi$
$379$	−3.68888	+	2.12978i	−0.189485	+	0.109399i	0.402256	+	0.915527i	$0.368226\pi$
$380$	8.59746			0.441041
$381$	24.5142	−	42.4599i	1.25590	−	2.17529i
$382$	4.08522	+	2.35860i	0.209018	+	0.120677i
$383$	−19.5460	−	11.2849i	−0.998751	−	0.576629i	−0.0908728	−	0.995863i	$-0.528966\pi$
$383$	−19.5460	−	11.2849i	−0.998751	−	0.576629i	−0.907879	+	0.419233i	$0.862299\pi$
$384$	−15.3672	+	8.87224i	−0.784203	+	0.452760i
$385$	5.28827	+	3.05319i	0.269515	+	0.155605i
$386$	−2.62436	−	4.54552i	−0.133576	−	0.231361i
$387$	−18.9207			−0.961793
$388$		−	3.33195i		−	0.169154i
$389$	−3.81794	−	6.61287i	−0.193577	−	0.335286i	0.752856	−	0.658185i	$-0.228676\pi$
$389$	−3.81794	−	6.61287i	−0.193577	−	0.335286i	−0.946433	+	0.322900i	$0.895342\pi$
$390$	1.92303	+	1.23641i	0.0973765	+	0.0626083i
$391$	1.47541	+	2.55548i	0.0746145	+	0.129236i
$392$	1.01004	+	0.583149i	0.0510149	+	0.0294535i
$393$	−6.65244	+	11.5224i	−0.335571	+	0.581227i
$394$	−0.614337	+	1.06406i	−0.0309499	+	0.0536067i
$395$			4.38250i			0.220508i
$396$	14.5414	−	8.39549i	0.730734	−	0.421889i
$397$	7.76424	−	4.48269i	0.389676	−	0.224980i	−0.292344	−	0.956313i	$-0.594435\pi$
$397$	7.76424	−	4.48269i	0.389676	−	0.224980i	0.682020	+	0.731334i	$0.261102\pi$
$398$	−3.01711	−	1.74193i	−0.151234	−	0.0873150i
$399$	−32.1108			−1.60755
$400$	−7.14255	−	12.3713i	−0.357127	−	0.618563i
$401$			35.4154i			1.76856i	0.466955	+	0.884281i	$0.345351\pi$
$401$			35.4154i			1.76856i	−0.466955	+	0.884281i	$0.654649\pi$
$402$	5.56502			0.277558
$403$	−19.2991	−	5.52687i	−0.961355	−	0.275313i
$404$	−16.2467			−0.808305
$405$		−	3.14443i		−	0.156248i
$406$	−1.35898	−	2.35381i	−0.0674448	−	0.116818i
$407$	1.16330			0.0576625
$408$	8.96290	+	5.17473i	0.443730	+	0.256187i
$409$	−14.9021	+	8.60372i	−0.736860	+	0.425426i	−0.820927	−	0.571034i	$-0.806543\pi$
$409$	−14.9021	+	8.60372i	−0.736860	+	0.425426i	0.0840665	+	0.996460i	$0.473209\pi$
$410$	−1.55145	+	0.895727i	−0.0766204	+	0.0442368i
$411$			39.3732i			1.94213i
$412$	−3.34538	+	5.79437i	−0.164815	+	0.285468i
$413$	16.3787	−	28.3687i	0.805942	−	1.39593i
$414$	0.545660	+	0.315037i	0.0268177	+	0.0154832i
$415$	−7.66777	−	13.2810i	−0.376396	−	0.651937i
$416$	−4.90952	+	7.63592i	−0.240709	+	0.374382i
$417$	28.7593	+	49.8125i	1.40835	+	2.43933i
$418$			1.73403i			0.0848140i
$419$	26.3377			1.28668			0.643341	−	0.765580i	$-0.277548\pi$
$419$	26.3377			1.28668			0.643341	+	0.765580i	$0.277548\pi$
$420$	−8.26909	−	14.3225i	−0.403490	−	0.698866i
$421$	10.0044	+	5.77603i	0.487583	+	0.281506i	0.723571	−	0.690250i	$-0.242499\pi$
$421$	10.0044	+	5.77603i	0.487583	+	0.281506i	−0.235988	+	0.971756i	$0.575833\pi$
$422$	1.37172	−	0.791965i	0.0667744	−	0.0385522i
$423$	0.970306	+	0.560206i	0.0471779	+	0.0272382i
$424$	2.44479	+	1.41150i	0.118729	+	0.0685484i
$425$	−8.53932	+	14.7905i	−0.414218	+	0.717446i
$426$	−4.64701			−0.225148
$427$	13.3119	−	7.68566i	0.644210	−	0.371935i
$428$	−14.0921	−	24.4083i	−0.681169	−	1.17982i
$429$	10.3866	−	16.1547i	0.501472	−	0.779954i
$430$	1.00636			0.0485311
$431$	0.0776939	−	0.0448566i	0.00374239	−	0.00216067i	−0.498128	−	0.867104i	$-0.665979\pi$
$431$	0.0776939	−	0.0448566i	0.00374239	−	0.00216067i	0.501870	+	0.864943i	$0.332646\pi$
$432$	−14.0203			−0.674551
$433$	26.7326			1.28469			0.642344	−	0.766416i	$-0.277962\pi$
$433$	26.7326			1.28469			0.642344	+	0.766416i	$0.277962\pi$
$434$	−2.53986	−	2.38857i	−0.121917	−	0.114655i
$435$			12.7092i			0.609361i
$436$		−	27.6943i		−	1.32632i
$437$	2.34707	−	1.35508i	0.112276	−	0.0648225i
$438$	−0.169283			−0.00808865
$439$	0.475013	−	0.822747i	0.0226711	−	0.0392676i	−0.854467	−	0.519505i	$-0.826116\pi$
$439$	0.475013	−	0.822747i	0.0226711	−	0.0392676i	0.877138	+	0.480238i	$0.159450\pi$
$440$	−1.56544	+	0.903807i	−0.0746294	+	0.0430873i
$441$	2.98814	+	5.17562i	0.142293	+	0.246458i
$442$	3.46926	+	0.165973i	0.165016	+	0.00789455i
$443$	14.3958	−	24.9342i	0.683964	−	1.18466i	−0.289797	−	0.957088i	$-0.593588\pi$
$443$	14.3958	−	24.9342i	0.683964	−	1.18466i	0.973761	−	0.227573i	$-0.0730790\pi$
$444$	−2.72851	−	1.57531i	−0.129489	−	0.0747608i
$445$	2.89407	−	5.01268i	0.137192	−	0.237624i
$446$	3.05348	+	5.28879i	0.144587	+	0.250431i
$447$	30.7359	+	17.7454i	1.45376	+	0.839327i
$448$	17.2713	−	9.97158i	0.815991	−	0.471113i
$449$			27.7320i			1.30875i	0.756169	+	0.654377i	$0.227069\pi$
$449$			27.7320i			1.30875i	−0.756169	+	0.654377i	$0.772931\pi$
$450$			3.64672i			0.171908i
$451$	7.52466	+	13.0331i	0.354322	+	0.613704i
$452$	−5.32464	+	9.22254i	−0.250450	+	0.433792i
$453$	−50.4951	+	29.1534i	−2.37247	+	1.36974i
$454$	2.43361	−	4.21514i	0.114215	−	0.197826i
$455$	−9.44900	−	6.07524i	−0.442976	−	0.284812i
$456$	4.75272	−	8.23196i	0.222567	−	0.385497i
$457$		−	26.0706i		−	1.21953i	−0.792582	−	0.609765i	$-0.791264\pi$
$457$		−	26.0706i		−	1.21953i	0.792582	−	0.609765i	$-0.208736\pi$
$458$	−0.886477	−	1.53542i	−0.0414223	−	0.0717456i
$459$	8.38101	+	14.5163i	0.391192	+	0.677565i
$460$	1.20883	+	0.697917i	0.0563619	+	0.0325405i
$461$		−	1.87261i		−	0.0872160i	−0.999049	−	0.0436080i	$-0.986115\pi$
$461$		−	1.87261i		−	0.0872160i	0.999049	−	0.0436080i	$-0.0138853\pi$
$462$	2.88871	−	1.66780i	0.134395	−	0.0775929i
$463$			2.06017i			0.0957441i	0.998853	+	0.0478720i	$0.0152440\pi$
$463$			2.06017i			0.0957441i	−0.998853	+	0.0478720i	$0.984756\pi$
$464$	−16.1498			−0.749734
$465$	4.70082	+	15.6109i	0.217995	+	0.723938i
$466$			0.460330i			0.0213244i
$467$	25.5423			1.18196			0.590979	−	0.806687i	$-0.298741\pi$
$467$	25.5423			1.18196			0.590979	+	0.806687i	$0.298741\pi$
$468$	−27.4585	+	14.1487i	−1.26927	+	0.654024i
$469$	−27.3443			−1.26264
$470$	−0.0516090	−	0.0297965i	−0.00238054	−	0.00137441i
$471$	−0.277461	−	0.480576i	−0.0127847	−	0.0221438i
$472$	4.84843	+	8.39772i	0.223167	+	0.386536i
$473$		−	8.45406i		−	0.388718i
$474$	2.07321	+	1.19697i	0.0952255	+	0.0549785i
$475$	13.5843	+	7.84292i	0.623292	+	0.359858i
$476$	−21.7588	−	12.5625i	−0.997314	−	0.575799i
$477$	7.23273	+	12.5275i	0.331164	+	0.573593i
$478$	−0.883950	+	1.53105i	−0.0404309	+	0.0700284i
$479$	35.3344	−	20.4004i	1.61447	−	0.932116i	0.626156	−	0.779698i	$-0.284627\pi$
$479$	35.3344	−	20.4004i	1.61447	−	0.932116i	0.988316	−	0.152418i	$-0.0487060\pi$
$480$	7.37251			0.336507
$481$	−2.13760	−	0.102265i	−0.0974663	−	0.00466290i
$482$	2.46270	+	4.26553i	0.112173	+	0.194289i
$483$	−4.51486	−	2.60666i	−0.205433	−	0.118607i
$484$	−6.99086	−	12.1085i	−0.317766	−	0.550387i
$485$	−0.919010	+	1.59177i	−0.0417301	+	0.0722786i
$486$	−3.60743	−	2.08275i	−0.163636	−	0.0944754i
$487$	−25.0470	−	14.4609i	−1.13499	−	0.655287i	−0.189805	−	0.981822i	$-0.560785\pi$
$487$	−25.0470	−	14.4609i	−1.13499	−	0.655287i	−0.945185	+	0.326535i	$0.894119\pi$
$488$			4.55023i			0.205979i
$489$	19.6416	−	11.3401i	0.888225	−	0.512817i
$490$	−0.158935	−	0.275283i	−0.00717993	−	0.0124360i
$491$	14.1441	−	24.4983i	0.638313	−	1.10559i	−0.347489	−	0.937684i	$-0.612966\pi$
$491$	14.1441	−	24.4983i	0.638313	−	1.10559i	0.985803	−	0.167907i	$-0.0537010\pi$
$492$		−	40.7588i		−	1.83755i
$493$	9.65398	+	16.7212i	0.434793	+	0.753084i
$494$	0.152438	−	3.18634i	0.00685851	−	0.143360i
$495$	−9.26249			−0.416318
$496$	−19.8369	+	5.97339i	−0.890705	+	0.268213i
$497$	22.8335			1.02422
$498$	−8.37701			−0.375383
$499$	14.5917	−	8.42449i	0.653212	−	0.377132i	−0.136474	−	0.990644i	$-0.543577\pi$
$499$	14.5917	−	8.42449i	0.653212	−	0.377132i	0.789686	+	0.613512i	$0.210244\pi$
$500$			18.6002i			0.831825i
$501$	−20.0158	−	11.5561i	−0.894239	−	0.516289i
$502$	−3.15360	+	1.82073i	−0.140752	+	0.0812633i
$503$	6.38581	+	11.0605i	0.284729	+	0.493165i	0.972543	−	0.232721i	$-0.0747630\pi$
$503$	6.38581	+	11.0605i	0.284729	+	0.493165i	−0.687814	+	0.725887i	$0.741430\pi$
$504$	−10.8584			−0.483673
$505$	7.76154	+	4.48113i	0.345384	+	0.199408i
$506$	−0.140763	+	0.243809i	−0.00625769	+	0.0108386i
$507$	−20.5060	+	28.7717i	−0.910703	+	1.27780i
$508$	−17.6168	−	30.5132i	−0.781619	−	1.35380i
$509$	20.0967	+	11.6028i	0.890770	+	0.514286i	0.874194	−	0.485577i	$-0.161390\pi$
$509$	20.0967	+	11.6028i	0.890770	+	0.514286i	0.0165755	+	0.999863i	$0.494724\pi$
$510$	−1.41035	−	2.44280i	−0.0624513	−	0.108169i
$511$	0.831787			0.0367961
$512$			15.7386i			0.695556i
$513$	13.3325	−	7.69753i	0.588645	−	0.339854i
$514$	−4.36035	−	2.51745i	−0.192327	−	0.111040i
$515$	3.19637	−	1.84543i	0.140849	−	0.0813193i
$516$	−11.4483	+	19.8290i	−0.503982	+	0.872922i
$517$	−0.250309	+	0.433547i	−0.0110086	+	0.0190674i
$518$	−0.321884	−	0.185840i	−0.0141428	−	0.00816533i
$519$	−67.2816			−2.95333
$520$	2.95601	−	1.52316i	0.129629	−	0.0667950i
$521$	8.40806	+	14.5632i	0.368364	+	0.638025i	0.989310	−	0.145828i	$-0.0465847\pi$
$521$	8.40806	+	14.5632i	0.368364	+	0.638025i	−0.620946	+	0.783853i	$0.713251\pi$
$522$	3.57040	+	2.06137i	0.156272	+	0.0902237i
$523$	−9.01605			−0.394244			−0.197122	−	0.980379i	$-0.563160\pi$
$523$	−9.01605			−0.394244			−0.197122	+	0.980379i	$0.563160\pi$
$524$	4.78069	+	8.28039i	0.208845	+	0.361731i
$525$		−	30.1735i		−	1.31688i
$526$		−	4.71598i		−	0.205627i
$527$	18.0428	+	16.9680i	0.785958	+	0.739140i
$528$		−	19.8197i		−	0.862543i
$529$	−22.5600			−0.980869
$530$	−0.384697	−	0.666315i	−0.0167102	−	0.0289429i
$531$			49.6882i			2.15628i
$532$	−11.5380	+	19.9844i	−0.500235	+	0.866432i
$533$	−12.6811	−	24.6103i	−0.549280	−	1.06599i
$534$	−1.58088	−	2.73817i	−0.0684114	−	0.118492i
$535$			15.5474i			0.672173i
$536$	4.04724	−	7.01002i	0.174814	−	0.302787i
$537$	−21.2459	+	36.7990i	−0.916828	+	1.58799i
$538$	−5.14285	−	2.96923i	−0.221724	−	0.128012i
$539$	−2.31254	+	1.33515i	−0.0996083	+	0.0575089i
$540$	6.86672	+	3.96450i	0.295497	+	0.170605i
$541$	12.7800	−	7.37852i	0.549454	−	0.317227i	−0.199448	−	0.979908i	$-0.563915\pi$
$541$	12.7800	−	7.37852i	0.549454	−	0.317227i	0.748902	+	0.662681i	$0.230582\pi$
$542$	−2.22896			−0.0957422
$543$	0.521593			0.0223837
$544$	9.69979	−	5.60018i	0.415875	−	0.240106i
$545$	−7.63857	+	13.2304i	−0.327200	+	0.566728i
$546$	−5.45473	+	2.81069i	−0.233441	+	0.120287i
$547$	−7.94526	+	13.7616i	−0.339715	+	0.588403i	−0.984379	−	0.176063i	$-0.943664\pi$
$547$	−7.94526	+	13.7616i	−0.339715	+	0.588403i	0.644664	+	0.764466i	$0.276997\pi$
$548$	24.5042	+	14.1475i	1.04677	+	0.604351i
$549$	−11.6580	+	20.1923i	−0.497553	+	0.861787i
$550$	−1.62941			−0.0694783
$551$	15.3575	−	8.86668i	0.654253	−	0.377733i
$552$	1.33649	−	0.771624i	0.0568849	−	0.0328425i
$553$	−10.1869	−	5.88141i	−0.433191	−	0.250103i
$554$		−	5.55579i		−	0.236043i
$555$	0.868994	+	1.50514i	0.0368867	+	0.0638897i
$556$	41.3349			1.75299
$557$		−	11.7837i		−	0.499291i	−0.968337	−	0.249645i	$-0.919686\pi$
$557$		−	11.7837i		−	0.499291i	0.968337	−	0.249645i	$-0.0803140\pi$
$558$	5.14801	+	1.21140i	0.217933	+	0.0512828i
$559$	−0.743195	+	15.5346i	−0.0314338	+	0.657046i
$560$	−11.5927			−0.489883
$561$	−20.5210	+	11.8478i	−0.866397	+	0.500215i
$562$	2.33704			0.0985823
$563$	−4.86382	+	8.42438i	−0.204985	+	0.355045i	−0.950128	−	0.311860i	$-0.899048\pi$
$563$	−4.86382	+	8.42438i	−0.204985	+	0.355045i	0.745143	+	0.666905i	$0.232381\pi$
$564$	1.17420	−	0.677923i	0.0494426	−	0.0285457i
$565$	5.08747	−	2.93725i	0.214032	−	0.123571i
$566$		−	0.244836i		−	0.0102912i
$567$	7.30905	+	4.21988i	0.306951	+	0.177219i
$568$	−3.37960	+	5.85363i	−0.141805	+	0.245613i
$569$	−18.4922	+	32.0295i	−0.775234	+	1.34275i	0.159429	+	0.987209i	$0.449035\pi$
$569$	−18.4922	+	32.0295i	−0.775234	+	1.34275i	−0.934663	+	0.355536i	$0.884298\pi$
$570$	−2.24358	+	1.29533i	−0.0939734	+	0.0542556i
$571$	23.0626	−	39.9456i	0.965141	−	1.67167i	0.255905	−	0.966702i	$-0.417627\pi$
$571$	23.0626	−	39.9456i	0.965141	−	1.67167i	0.709236	−	0.704971i	$-0.249040\pi$
$572$	−6.32185	−	12.2689i	−0.264330	−	0.512987i
$573$	59.2041			2.47329
$574$		−	4.80834i		−	0.200696i
$575$	1.27333	+	2.20547i	0.0531016	+	0.0919746i
$576$	−15.1254	+	26.1980i	−0.630227	+	1.09158i
$577$	−28.8138	+	16.6356i	−1.19953	+	0.692550i	−0.960451	−	0.278449i	$-0.910180\pi$
$577$	−28.8138	+	16.6356i	−1.19953	+	0.692550i	−0.239081	+	0.971000i	$0.576846\pi$
$578$	−0.523029	−	0.301971i	−0.0217551	−	0.0125603i
$579$	−57.0493	−	32.9375i	−2.37089	−	1.36883i
$580$	7.90968	+	4.56666i	0.328432	+	0.189620i
$581$	41.1612			1.70765
$582$	0.502007	+	0.869502i	0.0208089	+	0.0360420i
$583$	−5.59746	+	3.23169i	−0.231823	+	0.133843i
$584$	−0.123113	+	0.213238i	−0.00509446	+	0.00882386i
$585$	17.0202	+	0.814264i	0.703698	+	0.0336657i
$586$	1.11483	+	1.93095i	0.0460533	+	0.0797667i
$587$			6.92154i			0.285683i	0.989746	+	0.142841i	$0.0456238\pi$
$587$			6.92154i			0.285683i	−0.989746	+	0.142841i	$0.954376\pi$
$588$	7.23209			0.298246
$589$	15.5843	−	16.5714i	0.642139	−	0.682813i
$590$		−	2.64283i		−	0.108804i
$591$			15.4207i			0.634322i
$592$	−1.91260	+	1.10424i	−0.0786074	+	0.0453840i
$593$		−	14.0226i		−	0.575839i	−0.957655	−	0.287919i	$-0.907036\pi$
$593$		−	14.0226i		−	0.575839i	0.957655	−	0.287919i	$-0.0929635\pi$
$594$	−0.799602	+	1.38495i	−0.0328081	+	0.0568253i
$595$	6.92989	+	12.0029i	0.284098	+	0.492071i
$596$	22.0879	−	12.7525i	0.904756	−	0.522361i
$597$	−43.7248			−1.78954
$598$	0.280091	−	0.435634i	0.0114538	−	0.0178144i
$599$	5.52124	−	9.56307i	0.225592	−	0.390736i	−0.730905	−	0.682479i	$-0.760902\pi$
$599$	5.52124	−	9.56307i	0.225592	−	0.390736i	0.956497	+	0.291743i	$0.0942351\pi$
$600$	7.73532	+	4.46599i	0.315793	+	0.182323i
$601$	2.59974	+	4.50288i	0.106046	+	0.183676i	0.914165	−	0.405343i	$-0.132848\pi$
$601$	2.59974	+	4.50288i	0.106046	+	0.183676i	−0.808119	+	0.589019i	$0.799514\pi$
$602$	−1.35056	+	2.33923i	−0.0550446	+	0.0953401i
$603$	35.9204	−	20.7387i	1.46279	−	0.844544i
$604$			41.9013i			1.70494i
$605$			7.71280i			0.313570i
$606$	4.23973	−	2.44781i	0.172227	−	0.0994354i
$607$	19.7074	−	34.1341i	0.799897	−	1.38546i	−0.119786	−	0.992800i	$-0.538221\pi$
$607$	19.7074	−	34.1341i	0.799897	−	1.38546i	0.919683	−	0.392662i	$-0.128446\pi$
$608$	−5.14348	−	8.90876i	−0.208595	−	0.361298i
$609$	−29.5420	−	17.0561i	−1.19710	−	0.691146i
$610$	0.620072	−	1.07400i	0.0251060	−	0.0434848i
$611$	0.498065	−	0.774655i	0.0201495	−	0.0313392i
$612$	38.1109			1.54054
$613$	−11.5373	+	6.66106i	−0.465987	+	0.269038i	−0.714558	−	0.699576i	$-0.753372\pi$
$613$	−11.5373	+	6.66106i	−0.465987	+	0.269038i	0.248571	+	0.968614i	$0.420039\pi$
$614$	−0.343478	−	0.594921i	−0.0138616	−	0.0240091i
$615$	−11.2420	+	19.4717i	−0.453320	+	0.785174i
$616$		−	4.85171i		−	0.195481i
$617$	−2.04390	+	1.18005i	−0.0822843	+	0.0475069i	−0.540578	−	0.841294i	$-0.681794\pi$
$617$	−2.04390	+	1.18005i	−0.0822843	+	0.0475069i	0.458293	+	0.888801i	$0.348461\pi$
$618$		−	2.01612i		−	0.0811003i
$619$		−	9.60526i		−	0.386068i	−0.981192	−	0.193034i	$-0.938167\pi$
$619$		−	9.60526i		−	0.386068i	0.981192	−	0.193034i	$-0.0618328\pi$
$620$	11.4046	+	2.68369i	0.458021	+	0.107779i
$621$	2.49945			0.100300
$622$		−	2.75598i		−	0.110505i
$623$	7.76780	+	13.4542i	0.311211	+	0.539032i
$624$	−1.74235	+	36.4195i	−0.0697499	+	1.45795i
$625$	−4.46776	+	7.73839i	−0.178711	+	0.309536i
$626$	−1.89021	+	1.09131i	−0.0755480	+	0.0436177i
$627$	10.8816	+	18.8475i	0.434569	+	0.752696i
$628$	−0.398786			−0.0159133
$629$	2.28662	+	1.32018i	0.0911735	+	0.0526391i
$630$	2.56293	+	1.47971i	0.102109	+	0.0589529i
$631$	−17.6572	−	10.1944i	−0.702922	−	0.405832i	0.105513	−	0.994418i	$-0.466352\pi$
$631$	−17.6572	−	10.1944i	−0.702922	−	0.405832i	−0.808435	+	0.588586i	$0.799685\pi$
$632$	3.01553	−	1.74102i	0.119951	−	0.0692540i
$633$	9.93969	−	17.2160i	0.395067	−	0.684277i
$634$	−3.59536	−	6.22735i	−0.142790	−	0.247320i
$635$			19.4361i			0.771297i
$636$	17.5051			0.694123
$637$	4.36676	−	2.25009i	0.173017	−	0.0891518i
$638$	−0.921051	+	1.59531i	−0.0364648	+	0.0631588i
$639$	−29.9949	+	17.3176i	−1.18658	+	0.685073i
$640$	3.51717	−	6.09192i	0.139028	−	0.240804i
$641$	16.7963	−	29.0920i	0.663413	−	1.14907i	−0.316300	−	0.948659i	$-0.602441\pi$
$641$	16.7963	−	29.0920i	0.663413	−	1.14907i	0.979713	−	0.200406i	$-0.0642261\pi$
$642$	7.35493	+	4.24637i	0.290276	+	0.167591i
$643$			0.727035i			0.0286714i	0.999897	+	0.0143357i	$0.00456336\pi$
$643$			0.727035i			0.0286714i	−0.999897	+	0.0143357i	$0.995437\pi$
$644$	−3.24454	+	1.87324i	−0.127853	+	0.0738159i
$645$	10.9383	−	6.31526i	0.430697	−	0.248663i
$646$	−1.96788	+	3.40847i	−0.0774252	+	0.134104i
$647$	32.8776			1.29255			0.646276	−	0.763104i	$-0.276325\pi$
$647$	32.8776			1.29255			0.646276	+	0.763104i	$0.276325\pi$
$648$	−2.16363	+	1.24917i	−0.0849955	+	0.0490722i
$649$	−22.2014			−0.871482
$650$	2.99410	+	0.143241i	0.117438	+	0.00561839i
$651$	−42.5953	−	10.0233i	−1.66944	−	0.392845i
$652$		−	16.2988i		−	0.638311i
$653$	8.29740			0.324702			0.162351	−	0.986733i	$-0.448092\pi$
$653$	8.29740			0.324702			0.162351	+	0.986733i	$0.448092\pi$
$654$	4.17255	+	7.22708i	0.163160	+	0.282601i
$655$		−	5.27438i		−	0.206087i
$656$	−24.7429	−	14.2853i	−0.966047	−	0.557747i
$657$	−1.09267	+	0.630851i	−0.0426290	+	0.0246118i
$658$	0.138521	−	0.0799749i	0.00540010	−	0.00311775i
$659$	27.7760			1.08200			0.541000	−	0.841023i	$-0.318046\pi$
$659$	27.7760			1.08200			0.541000	+	0.841023i	$0.318046\pi$
$660$	−5.60441	+	9.70713i	−0.218151	+	0.377849i
$661$	−5.17216	−	2.98615i	−0.201174	−	0.116148i	0.396029	−	0.918238i	$-0.370388\pi$
$661$	−5.17216	−	2.98615i	−0.201174	−	0.116148i	−0.597203	+	0.802090i	$0.703721\pi$
$662$	0.613908	−	1.06332i	0.0238602	−	0.0413271i
$663$	38.7497	−	19.9668i	1.50491	−	0.775446i
$664$	−6.09229	+	10.5521i	−0.236427	+	0.409503i
$665$	11.0241	−	6.36474i	0.427495	−	0.246814i
$666$	0.563785			0.0218462
$667$	2.87908			0.111479
$668$	−14.3841	+	8.30464i	−0.556536	+	0.321316i
$669$	66.3779	+	38.3233i	2.56632	+	1.48166i
$670$	−1.91055	+	1.10306i	−0.0738109	+	0.0426148i
$671$	−9.02223	−	5.20899i	−0.348299	−	0.201091i
$672$	−9.89405	+	17.1370i	−0.381671	+	0.661074i
$673$	−7.18552	+	12.4457i	−0.276982	+	0.479746i	−0.970633	−	0.240565i	$-0.922667\pi$
$673$	−7.18552	+	12.4457i	−0.276982	+	0.479746i	0.693652	+	0.720311i	$0.256001\pi$
$674$			4.55665i			0.175516i
$675$	7.23313	+	12.5281i	0.278403	+	0.482209i
$676$	10.5381	+	23.1002i	0.405311	+	0.888471i
$677$	6.22535	−	10.7826i	0.239260	−	0.414410i	−0.721242	−	0.692683i	$-0.756429\pi$
$677$	6.22535	−	10.7826i	0.239260	−	0.414410i	0.960502	+	0.278273i	$0.0897619\pi$
$678$		−	3.20894i		−	0.123238i
$679$	−2.46666	−	4.27238i	−0.0946617	−	0.163959i
$680$	−4.10278			−0.157334
$681$		−	61.0869i		−	2.34086i
$682$	−0.541274	+	2.30021i	−0.0207264	+	0.0880795i
$683$		−	38.4734i		−	1.47214i	−0.676903	−	0.736072i	$-0.736678\pi$
$683$		−	38.4734i		−	1.47214i	0.676903	−	0.736072i	$-0.263322\pi$
$684$		−	35.0029i		−	1.33837i
$685$	−7.80424	−	13.5173i	−0.298185	−	0.516471i
$686$	−3.53027			−0.134786
$687$	−19.2706	−	11.1259i	−0.735219	−	0.424479i
$688$	8.02487	+	13.8995i	0.305945	+	0.529913i
$689$	10.5696	−	5.44629i	0.402671	−	0.207487i
$690$	−0.420605			−0.0160122
$691$	17.3900	+	10.0401i	0.661548	+	0.381945i	0.792867	−	0.609395i	$-0.208588\pi$
$691$	17.3900	+	10.0401i	0.661548	+	0.381945i	−0.131318	+	0.991340i	$0.541921\pi$
$692$	−24.1755	+	41.8732i	−0.919014	+	1.59178i
$693$	12.4304	−	21.5302i	0.472194	−	0.817863i
$694$	1.29748	−	0.749103i	0.0492518	−	0.0284355i
$695$	−19.7469	−	11.4009i	−0.749042	−	0.432460i
$696$	8.74503	−	5.04895i	0.331480	−	0.191380i
$697$			34.1578i			1.29382i
$698$	4.42747			0.167582
$699$	2.88872	+	5.00342i	0.109262	+	0.189247i
$700$	−18.7787	−	10.8419i	−0.709767	−	0.409784i
$701$	11.6336	+	20.1499i	0.439394	+	0.761053i	0.997643	−	0.0686208i	$-0.0218599\pi$
$701$	11.6336	+	20.1499i	0.439394	+	0.761053i	−0.558249	+	0.829674i	$0.688527\pi$
$702$	1.59105	−	2.47461i	0.0600503	−	0.0933981i
$703$	1.21252	−	2.10014i	0.0457310	−	0.0792084i
$704$	−11.7057	−	6.75828i	−0.441174	−	0.254712i
$705$	−0.747931			−0.0281687
$706$	1.29718	+	2.24678i	0.0488200	+	0.0845587i
$707$	−20.8323	+	12.0275i	−0.783479	+	0.452342i
$708$	52.0734	+	30.0646i	1.95704	+	1.12990i
$709$			3.26759i			0.122717i	0.998116	+	0.0613584i	$0.0195433\pi$
$709$			3.26759i			0.122717i	−0.998116	+	0.0613584i	$0.980457\pi$
$710$	1.59538	−	0.921094i	0.0598736	−	0.0345680i
$711$	17.8425			0.669146
$712$	−4.59886			−0.172350
$713$	3.53641	−	1.06490i	0.132440	−	0.0398808i
$714$	7.57087			0.283333
$715$	−0.363826	+	7.60487i	−0.0136063	+	0.284406i
$716$	15.2681	+	26.4451i	0.570595	+	0.988299i
$717$			22.1883i			0.828639i
$718$	3.25087	−	5.63067i	0.121321	−	0.210135i
$719$	−6.07474	−	10.5218i	−0.226549	−	0.392395i	0.730234	−	0.683197i	$-0.239411\pi$
$719$	−6.07474	−	10.5218i	−0.226549	−	0.392395i	−0.956783	+	0.290802i	$0.906078\pi$
$720$	15.2286	−	8.79226i	0.567538	−	0.327668i
$721$			9.90641i			0.368934i
$722$	−0.432652	−	0.249792i	−0.0161016	−	0.00929629i
$723$	53.5352	+	30.9086i	1.99100	+	1.14950i
$724$	0.187418	−	0.324617i	0.00696533	−	0.0120643i
$725$	8.33174	+	14.4310i	0.309433	+	0.535954i
$726$	3.64865	+	2.10655i	0.135414	+	0.0781814i
$727$	15.3228	+	26.5399i	0.568293	+	0.984312i	0.996735	+	0.0807426i	$0.0257292\pi$
$727$	15.3228	+	26.5399i	0.568293	+	0.984312i	−0.428442	+	0.903569i	$0.640937\pi$
$728$	−0.426513	+	8.91520i	−0.0158076	+	0.330419i
$729$	−43.5242			−1.61201
$730$	0.0581171	−	0.0335539i	0.00215101	−	0.00124189i
$731$	9.59418	−	16.6176i	0.354854	−	0.614624i
$732$	14.1077	+	24.4353i	0.521437	+	0.903156i
$733$	−18.8745	−	10.8972i	−0.697146	−	0.402498i	0.109137	−	0.994027i	$-0.465191\pi$
$733$	−18.8745	−	10.8972i	−0.697146	−	0.402498i	−0.806284	+	0.591529i	$0.798525\pi$
$734$	−1.74561	−	1.00783i	−0.0644318	−	0.0371997i
$735$	−3.45498	−	1.99474i	−0.127439	−	0.0735769i
$736$		−	1.67013i		−	0.0615618i
$737$	9.26635	+	16.0498i	0.341330	+	0.591201i
$738$	3.64678	+	6.31640i	0.134240	+	0.232510i
$739$	17.6198	+	10.1728i	0.648156	+	0.374213i	0.787750	−	0.615996i	$-0.211246\pi$
$739$	17.6198	+	10.1728i	0.648156	+	0.374213i	−0.139593	+	0.990209i	$0.544579\pi$
$740$	1.24898			0.0459134
$741$	−18.3385	−	35.5896i	−0.673681	−	1.30742i
$742$	2.06509			0.0758117
$743$		−	41.2679i		−	1.51397i	−0.653431	−	0.756986i	$-0.726671\pi$
$743$		−	41.2679i		−	1.51397i	0.653431	−	0.756986i	$-0.273329\pi$
$744$	8.87414	−	9.43624i	0.325342	−	0.345949i
$745$	−14.0694			−0.515463
$746$			4.78936i			0.175351i
$747$	−54.0708	+	31.2178i	−1.97835	+	1.14220i
$748$			17.0285i			0.622624i
$749$	−36.1391	−	20.8649i	−1.32050	−	0.762388i
$750$	−2.80239	−	4.85388i	−0.102329	−	0.177239i
$751$	−25.0093	−	43.3173i	−0.912602	−	1.58067i	−0.810375	−	0.585911i	$-0.800737\pi$
$751$	−25.0093	−	43.3173i	−0.912602	−	1.58067i	−0.102226	−	0.994761i	$-0.532597\pi$
$752$		−	0.950404i		−	0.0346577i
$753$	−22.8514	+	39.5798i	−0.832752	+	1.44237i
$754$	1.83271	−	2.85047i	0.0667434	−	0.103808i
$755$	11.5571	−	20.0175i	0.420606	−	0.728511i
$756$	−18.4306	+	10.6409i	−0.670313	+	0.387005i
$757$	−15.6416	+	27.0921i	−0.568505	+	0.984680i	0.428209	+	0.903680i	$0.359145\pi$
$757$	−15.6416	+	27.0921i	−0.568505	+	0.984680i	−0.996714	+	0.0810000i	$0.974189\pi$
$758$	−0.461195	−	0.798813i	−0.0167514	−	0.0290142i
$759$			3.53334i			0.128252i
$760$			3.76819i			0.136687i
$761$	34.9676	−	20.1885i	1.26757	−	0.731834i	0.293045	−	0.956099i	$-0.405331\pi$
$761$	34.9676	−	20.1885i	1.26757	−	0.731834i	0.974528	+	0.224265i	$0.0719981\pi$
$762$	9.19452	+	5.30846i	0.333082	+	0.192305i
$763$	−20.5022	−	35.5109i	−0.742231	−	1.28558i
$764$	21.2731	−	36.8461i	0.769634	−	1.33305i
$765$	−18.2067	−	10.5116i	−0.658264	−	0.380049i
$766$	2.44369	−	4.23260i	0.0882942	−	0.152930i
$767$	40.7960	+	1.95173i	1.47306	+	0.0704727i
$768$	16.8220	+	29.1365i	0.607011	+	1.05137i
$769$	−9.31755	+	5.37949i	−0.336000	+	0.193989i	−0.658502	−	0.752579i	$-0.728809\pi$
$769$	−9.31755	+	5.37949i	−0.336000	+	0.193989i	0.322502	+	0.946569i	$0.395476\pi$
$770$	−0.661155	+	1.14515i	−0.0238264	+	0.0412685i
$771$	−63.1913			−2.27578
$772$	−40.9977	+	23.6700i	−1.47554	+	0.851903i
$773$			15.4275i			0.554889i	0.960742	+	0.277445i	$0.0894875\pi$
$773$			15.4275i			0.554889i	−0.960742	+	0.277445i	$0.910513\pi$
$774$		−	4.09720i		−	0.147271i
$775$	15.5716	+	14.6441i	0.559350	+	0.526030i
$776$	1.46037			0.0524241
$777$	−4.66483			−0.167350
$778$	1.43199	−	0.826761i	0.0513394	−	0.0296408i
$779$	31.3722			1.12402
$780$	11.1517	−	17.3445i	0.399294	−	0.621034i
$781$	−7.73776	−	13.4022i	−0.276879	−	0.479568i
$782$	−0.553379	+	0.319493i	−0.0197888	+	0.0114251i
$783$	16.3546			0.584465
$784$	2.53473	−	4.39029i	0.0905262	−	0.156796i
$785$	0.190512	+	0.109992i	0.00679966	+	0.00392579i
$786$	−2.49512	−	1.44056i	−0.0889981	−	0.0513831i
$787$	39.8468	−	23.0055i	1.42038	−	0.820059i	0.424053	−	0.905637i	$-0.360607\pi$
$787$	39.8468	−	23.0055i	1.42038	−	0.820059i	0.996331	+	0.0855783i	$0.0272738\pi$
$788$	9.59717	+	5.54093i	0.341885	+	0.197387i
$789$	−29.5944	−	51.2590i	−1.05359	−	1.82487i
$790$	−0.949013			−0.0337644
$791$			15.7674i			0.560625i
$792$	3.67967	+	6.37338i	0.130751	+	0.226468i
$793$	16.1208	+	10.3649i	0.572465	+	0.368067i
$794$	0.970708	+	1.68132i	0.0344491	+	0.0596677i
$795$	−8.36271	−	4.82821i	−0.296595	−	0.171239i
$796$	−15.7111	+	27.2124i	−0.556865	+	0.964519i
$797$	10.7954	−	18.6982i	0.382392	−	0.662323i	−0.609011	−	0.793162i	$-0.708434\pi$
$797$	10.7954	−	18.6982i	0.382392	−	0.662323i	0.991404	+	0.130839i	$0.0417669\pi$
$798$		−	6.95346i		−	0.246150i
$799$	−0.984032	+	0.568131i	−0.0348125	+	0.0200990i
$800$	8.37129	−	4.83316i	0.295970	−	0.170878i
$801$	−20.4081	−	11.7826i	−0.721086	−	0.416319i
$802$	−7.66907			−0.270804
$803$	−0.281874	−	0.488220i	−0.00994711	−	0.0172289i
$804$		−	50.1930i		−	1.77017i
$805$	2.06668			0.0728411
$806$	1.19682	−	4.17913i	0.0421563	−	0.147204i
$807$	−74.5316			−2.62364
$808$		−	7.12080i		−	0.250509i
$809$	−17.4746	−	30.2669i	−0.614374	−	1.06413i	−0.990494	−	0.137557i	$-0.956075\pi$
$809$	−17.4746	−	30.2669i	−0.614374	−	1.06413i	0.376119	−	0.926571i	$-0.377258\pi$
$810$	0.680913			0.0239248
$811$	−34.6528	−	20.0068i	−1.21682	−	0.702533i	−0.252586	−	0.967574i	$-0.581281\pi$
$811$	−34.6528	−	20.0068i	−1.21682	−	0.702533i	−0.964237	+	0.265041i	$0.914615\pi$
$812$	−21.2299	+	12.2571i	−0.745024	+	0.430140i
$813$	−24.2271	+	13.9875i	−0.849680	+	0.490563i
$814$			0.251907i			0.00882935i
$815$	−4.49549	+	7.78642i	−0.157470	+	0.272746i
$816$	22.4926	−	38.9584i	0.787400	−	1.36382i
$817$	−15.2624	−	8.81176i	−0.533964	−	0.308284i
$818$	−1.86310	−	3.22698i	−0.0651418	−	0.112829i
$819$	−24.7341	+	38.4697i	−0.864281	+	1.34424i
$820$	8.07889	+	13.9930i	0.282127	+	0.488658i
$821$			42.5223i			1.48404i	0.670379	+	0.742019i	$0.266132\pi$
$821$			42.5223i			1.48404i	−0.670379	+	0.742019i	$0.733868\pi$
$822$	−8.52610			−0.297382
$823$	−7.30664	−	12.6555i	−0.254693	−	0.441142i	0.710119	−	0.704082i	$-0.248641\pi$
$823$	−7.30664	−	12.6555i	−0.254693	−	0.441142i	−0.964812	+	0.262940i	$0.915308\pi$
$824$	−2.53962	−	1.46625i	−0.0884719	−	0.0510793i
$825$	−17.7104	+	10.2251i	−0.616597	+	0.355992i
$826$	6.14313	+	3.54674i	0.213747	+	0.123407i
$827$	−8.28137	−	4.78125i	−0.287971	−	0.166260i	0.349055	−	0.937102i	$-0.386503\pi$
$827$	−8.28137	−	4.78125i	−0.287971	−	0.166260i	−0.637027	+	0.770842i	$0.719836\pi$
$828$	2.84143	−	4.92150i	0.0987466	−	0.171034i
$829$	−38.5950			−1.34046			−0.670230	−	0.742153i	$-0.733805\pi$
$829$	−38.5950			−1.34046			−0.670230	+	0.742153i	$0.733805\pi$
$830$	2.87594	−	1.66043i	0.0998254	−	0.0576342i
$831$	−34.8645	−	60.3870i	−1.20944	−	2.09480i
$832$	20.9155	+	13.4476i	0.725115	+	0.466213i
$833$	−6.06083			−0.209995
$834$	−10.7867	+	6.22770i	−0.373513	+	0.215648i
$835$	9.16225			0.317073
$836$	15.6398			0.540914
$837$	20.0885	−	6.04914i	0.694361	−	0.209089i
$838$			5.70333i			0.197018i
$839$			32.8723i			1.13488i	0.823416	+	0.567439i	$0.192066\pi$
$839$			32.8723i			1.13488i	−0.823416	+	0.567439i	$0.807934\pi$
$840$	6.27742	−	3.62427i	0.216592	−	0.125049i
$841$	−10.1614			−0.350392
$842$	−1.25078	+	2.16641i	−0.0431046	+	0.0746594i
$843$	25.4018	−	14.6657i	0.874885	−	0.505115i
$844$	−7.14302	−	12.3721i	−0.245873	−	0.425864i
$845$	1.33709	−	13.9423i	0.0459972	−	0.479628i
$846$	−0.121310	+	0.210116i	−0.00417074	+	0.00722393i
$847$	−17.9280	−	10.3507i	−0.616013	−	0.355655i
$848$	6.13526	−	10.6266i	0.210686	−	0.364918i
$849$	−1.53643	−	2.66117i	−0.0527300	−	0.0913311i
$850$	−3.20283	−	1.84915i	−0.109856	−	0.0634255i
$851$	0.340967	−	0.196857i	0.0116882	−	0.00674818i
$852$			41.9131i			1.43592i
$853$			35.8035i			1.22589i	0.790126	+	0.612945i	$0.210015\pi$
$853$			35.8035i			1.22589i	−0.790126	+	0.612945i	$0.789985\pi$
$854$	1.66430	+	2.88265i	0.0569511	+	0.0986422i
$855$	−9.65440	+	16.7219i	−0.330173	+	0.571877i
$856$	10.6979	−	6.17646i	0.365648	−	0.211107i
$857$	−4.43656	+	7.68434i	−0.151550	+	0.262492i	−0.931797	−	0.362979i	$-0.881760\pi$
$857$	−4.43656	+	7.68434i	−0.151550	+	0.262492i	0.780248	+	0.625471i	$0.215093\pi$
$858$	3.49823	+	2.24919i	0.119427	+	0.0767859i
$859$	25.0291	−	43.3516i	0.853981	−	1.47914i	−0.0236058	−	0.999721i	$-0.507515\pi$
$859$	25.0291	−	43.3516i	0.853981	−	1.47914i	0.877587	−	0.479417i	$-0.159152\pi$
$860$		−	9.07674i		−	0.309514i
$861$	−30.1739	−	52.2628i	−1.02832	−	1.78111i
$862$	0.00971352	+	0.0168243i	0.000330844	+	0.000573039i
$863$	−28.9654	−	16.7232i	−0.985994	−	0.569264i	−0.0819193	−	0.996639i	$-0.526105\pi$
$863$	−28.9654	−	16.7232i	−0.985994	−	0.569264i	−0.904074	+	0.427375i	$0.859438\pi$
$864$		−	9.48714i		−	0.322759i
$865$	23.0987	−	13.3360i	0.785379	−	0.453439i
$866$			5.78885i			0.196713i
$867$	−7.57988			−0.257426
$868$	−21.5434	+	22.9079i	−0.731229	+	0.777546i
$869$			7.97230i			0.270442i
$870$	−2.75213			−0.0933061
$871$	−15.6163	−	30.3067i	−0.529139	−	1.02690i
$872$	12.1382			0.411050
$873$	6.48059	+	3.74157i	0.219335	+	0.126633i
$874$	0.293438	+	0.508250i	0.00992569	+	0.0171918i
$875$	13.7698	+	23.8500i	0.465504	+	0.806277i
$876$			1.52682i			0.0515866i
$877$	28.2565	+	16.3139i	0.954154	+	0.550881i	0.894369	−	0.447330i	$-0.147625\pi$
$877$	28.2565	+	16.3139i	0.954154	+	0.550881i	0.0597853	+	0.998211i	$0.480958\pi$
$878$	0.178163	+	0.102862i	0.00601270	+	0.00347143i
$879$	24.2347	+	13.9919i	0.817415	+	0.471935i
$880$	3.92851	+	6.80439i	0.132430	+	0.229376i
$881$	9.23635	−	15.9978i	0.311180	−	0.538980i	−0.667438	−	0.744666i	$-0.732609\pi$
$881$	9.23635	−	15.9978i	0.311180	−	0.538980i	0.978618	+	0.205685i	$0.0659423\pi$
$882$	−1.12076	+	0.647071i	−0.0377379	+	0.0217880i
$883$	−53.6613			−1.80584			−0.902922	−	0.429803i	$-0.858583\pi$
$883$	−53.6613			−1.80584			−0.902922	+	0.429803i	$0.858583\pi$
$884$	1.49698	−	31.2905i	0.0503487	−	1.05241i
$885$	−16.5847	−	28.7255i	−0.557488	−	0.965597i
$886$	5.39941	+	3.11735i	0.181397	+	0.104729i
$887$	−9.86117	−	17.0800i	−0.331106	−	0.573492i	0.651623	−	0.758543i	$-0.274088\pi$
$887$	−9.86117	−	17.0800i	−0.331106	−	0.573492i	−0.982729	+	0.185051i	$0.940755\pi$
$888$	0.690443	−	1.19588i	0.0231698	−	0.0401312i
$889$	−45.1781	−	26.0836i	−1.51523	−	0.874816i
$890$	1.08548	+	0.626700i	0.0363852	+	0.0210070i
$891$		−	5.72009i		−	0.191630i
$892$	47.7015	−	27.5405i	1.59716	−	0.922124i
$893$	0.521799	+	0.903783i	0.0174613	+	0.0302439i
$894$	−3.84269	+	6.65573i	−0.128519	+	0.222601i
$895$		−	16.8448i		−	0.563059i
$896$	9.44024	+	16.3510i	0.315376	+	0.546248i
$897$	0.310616	−	6.49265i	0.0103712	−	0.216783i
$898$	−6.00525			−0.200398
$899$	23.1397	−	6.96793i	0.771752	−	0.232393i
$900$	32.8911			1.09637
$901$	−14.6701			−0.488732
$902$	−2.82226	+	1.62944i	−0.0939711	+	0.0542543i
$903$			33.9008i			1.12815i
$904$	−4.04216	−	2.33374i	−0.134440	−	0.0776191i
$905$	−0.179070	+	0.103386i	−0.00595249	+	0.00343667i
$906$	−6.31305	−	10.9345i	−0.209737	−	0.363275i
$907$	23.2079			0.770607			0.385303	−	0.922790i	$-0.374097\pi$
$907$	23.2079			0.770607			0.385303	+	0.922790i	$0.374097\pi$
$908$	−38.0179	−	21.9496i	−1.26167	−	0.728424i
$909$	18.2440	−	31.5996i	0.605116	−	1.04809i
$910$	1.31557	−	2.04614i	0.0436107	−	0.0678290i
$911$	13.1869	+	22.8405i	0.436903	+	0.756738i	0.997449	−	0.0713851i	$-0.0227419\pi$
$911$	13.1869	+	22.8405i	0.436903	+	0.756738i	−0.560546	+	0.828123i	$0.689409\pi$
$912$	−35.7813	−	20.6583i	−1.18484	−	0.684066i
$913$	−13.9486	−	24.1597i	−0.461631	−	0.799568i
$914$	5.64548			0.186736
$915$		−	15.5646i		−	0.514551i
$916$	−13.8485	+	7.99546i	−0.457569	+	0.264177i
$917$	12.2600	+	7.07833i	0.404862	+	0.233747i
$918$	−3.14346	+	1.81488i	−0.103750	+	0.0598998i
$919$	−16.7700	+	29.0465i	−0.553191	+	0.958155i	0.444851	+	0.895605i	$0.353257\pi$
$919$	−16.7700	+	29.0465i	−0.553191	+	0.958155i	−0.998042	+	0.0625502i	$0.980077\pi$
$920$	−0.305891	+	0.529818i	−0.0100849	+	0.0174676i
$921$	−7.46666	−	4.31088i	−0.246035	−	0.142048i
$922$	0.405506			0.0133546
$923$	13.0402	+	25.3072i	0.429225	+	0.832998i
$924$	−15.0425	−	26.0543i	−0.494861	−	0.857124i
$925$	1.97344	+	1.13937i	0.0648863	+	0.0374621i
$926$	−0.446121			−0.0146604
$927$	−7.51330	−	13.0134i	−0.246769	−	0.427416i
$928$		−	10.9281i		−	0.358733i
$929$			42.4547i			1.39289i	0.717609	+	0.696446i	$0.245237\pi$
$929$			42.4547i			1.39289i	−0.717609	+	0.696446i	$0.754763\pi$
$930$	−3.38048	+	1.01794i	−0.110850	+	0.0333797i
$931$			5.56656i			0.182437i
$932$	4.15188			0.135999
$933$	−17.2947	−	29.9553i	−0.566204	−	0.980693i
$934$			5.53109i			0.180983i
$935$	4.69676	−	8.13502i	0.153600	−	0.266044i
$936$	−6.20125	−	12.0348i	−0.202694	−	0.393370i
$937$	9.98063	+	17.2870i	0.326053	+	0.564740i	0.981725	−	0.190306i	$-0.0609479\pi$
$937$	9.98063	+	17.2870i	0.326053	+	0.564740i	−0.655672	+	0.755046i	$0.727615\pi$
$938$		−	5.92129i		−	0.193337i
$939$	−13.6967	+	23.7234i	−0.446975	+	0.774184i
$940$	−0.268745	+	0.465480i	−0.00876550	+	0.0151823i
$941$	−20.5620	−	11.8715i	−0.670302	−	0.386999i	0.125889	−	0.992044i	$-0.459822\pi$
$941$	−20.5620	−	11.8715i	−0.670302	−	0.386999i	−0.796191	+	0.605045i	$0.793155\pi$
$942$	0.104067	−	0.0600830i	0.00339068	−	0.00195761i
$943$	4.41101	+	2.54670i	0.143642	+	0.0829319i
$944$	36.5018	−	21.0743i	1.18803	−	0.685911i
$945$	11.7398			0.381894
$946$	1.83069			0.0595209
$947$	27.9672	−	16.1469i	0.908811	−	0.524702i	0.0287625	−	0.999586i	$-0.490843\pi$
$947$	27.9672	−	16.1469i	0.908811	−	0.524702i	0.880048	+	0.474884i	$0.157510\pi$
$948$	10.7959	−	18.6990i	0.350634	−	0.607316i
$949$	0.475034	+	0.921901i	0.0154203	+	0.0299262i
$950$	−1.69835	+	2.94163i	−0.0551019	+	0.0954392i
$951$	−78.1575	−	45.1242i	−2.53443	−	1.46325i
$952$	5.50601	−	9.53670i	0.178451	−	0.309086i
$953$	−13.0405			−0.422423			−0.211211	−	0.977440i	$-0.567741\pi$
$953$	−13.0405			−0.422423			−0.211211	+	0.977440i	$0.567741\pi$
$954$	−2.71277	+	1.56622i	−0.0878292	+	0.0507082i
$955$	−20.3256	+	11.7350i	−0.657720	+	0.379735i
$956$	13.8091	+	7.97267i	0.446617	+	0.257855i
$957$			23.1196i			0.747351i
$958$	4.41762	+	7.65153i	0.142727	+	0.247210i
$959$	41.8938			1.35282
$960$		−	20.1940i		−	0.651758i
$961$	25.8455	−	17.1176i	0.833725	−	0.552180i
$962$	0.0221452	−	0.462889i	0.000713989	−	0.0149242i
$963$	63.2982			2.03976
$964$	38.4724	−	22.2120i	1.23911	−	0.715401i
$965$	26.1144			0.840653
$966$	0.564461	−	0.977675i	0.0181612	−	0.0314562i
$967$	18.0955	−	10.4474i	0.581911	−	0.335966i	−0.179982	−	0.983670i	$-0.557604\pi$
$967$	18.0955	−	10.4474i	0.581911	−	0.335966i	0.761892	+	0.647704i	$0.224270\pi$
$968$	5.30706	−	3.06403i	0.170575	−	0.0984817i
$969$			49.3964i			1.58684i
$970$	−0.344692	−	0.199008i	−0.0110674	−	0.00638976i
$971$	−5.61491	+	9.72530i	−0.180191	+	0.312100i	−0.941945	−	0.335766i	$-0.891005\pi$
$971$	−5.61491	+	9.72530i	−0.180191	+	0.312100i	0.761755	+	0.647866i	$0.224338\pi$
$972$	−18.7851	+	32.5367i	−0.602531	+	1.04361i
$973$	53.0015	−	30.6004i	1.69915	−	0.981004i
$974$	3.13145	−	5.42384i	0.100338	−	0.173791i
$975$	33.4424	−	17.2321i	1.07101	−	0.551869i
$976$	19.7782			0.633083
$977$			26.4825i			0.847250i	0.905838	+	0.423625i	$0.139243\pi$
$977$			26.4825i			0.847250i	−0.905838	+	0.423625i	$0.860757\pi$
$978$	2.45565	+	4.25332i	0.0785231	+	0.136006i
$979$	5.26466	−	9.11866i	0.168259	−	0.291434i
$980$	−2.48288	+	1.43349i	−0.0793125	+	0.0457911i
$981$	53.8649	+	31.0989i	1.71978	+	0.992913i
$982$	5.30500	+	3.06284i	0.169289	+	0.0977393i
$983$	−25.3799	−	14.6531i	−0.809493	−	0.467361i	0.0372866	−	0.999305i	$-0.488129\pi$
$983$	−25.3799	−	14.6531i	−0.809493	−	0.467361i	−0.846780	+	0.531943i	$0.821462\pi$
$984$	17.8642			0.569491
$985$	−3.05657	−	5.29413i	−0.0973904	−	0.168685i
$986$	−3.62090	+	2.09053i	−0.115313	+	0.0665761i
$987$	1.00374	−	1.73853i	0.0319494	−	0.0553379i
$988$	−28.7388	−	1.37489i	−0.914302	−	0.0437412i
$989$	−1.43063	−	2.47792i	−0.0454912	−	0.0787932i
$990$		−	2.00576i		−	0.0637471i
$991$	14.7838			0.469622			0.234811	−	0.972041i	$-0.424553\pi$
$991$	14.7838			0.469622			0.234811	+	0.972041i	$0.424553\pi$
$992$	−4.04203	−	13.4231i	−0.128334	−	0.426184i
$993$		−	15.4099i		−	0.489019i
$994$			4.94451i			0.156830i
$995$	15.0113	−	8.66678i	0.475890	−	0.274755i
$996$			75.5553i			2.39406i
$997$	11.1436	−	19.3013i	0.352921	−	0.611277i	−0.633839	−	0.773465i	$-0.718522\pi$
$997$	11.1436	−	19.3013i	0.352921	−	0.611277i	0.986760	+	0.162188i	$0.0518551\pi$
$998$	1.82429	+	3.15976i	0.0577469	+	0.100021i
$999$	1.93686	−	1.11824i	0.0612794	−	0.0353797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.l.c.25.20	yes	68
13.12	even	2	inner	403.2.l.c.25.15	✓	68
31.5	even	3	inner	403.2.l.c.129.20	yes	68
403.129	even	6	inner	403.2.l.c.129.15	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.15	✓	68	13.12	even	2	inner
403.2.l.c.25.20	yes	68	1.1	even	1	trivial
403.2.l.c.129.15	yes	68	403.129	even	6	inner
403.2.l.c.129.20	yes	68	31.5	even	3	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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.216546i q^{2} +(1.35890 + 2.35368i) q^{3} +1.95311 q^{4} +(-0.933057 - 0.538701i) q^{5} +(-0.509681 + 0.294264i) q^{6} +(2.50436 - 1.44590i) q^{7} +0.856030i q^{8} +(-2.19321 + 3.79876i) q^{9} +O(q^{10})\)	\(q+0.216546i q^{2} +(1.35890 + 2.35368i) q^{3} +1.95311 q^{4} +(-0.933057 - 0.538701i) q^{5} +(-0.509681 + 0.294264i) q^{6} +(2.50436 - 1.44590i) q^{7} +0.856030i q^{8} +(-2.19321 + 3.79876i) q^{9} +(0.116654 - 0.202050i) q^{10} +(-1.69734 - 0.979961i) q^{11} +(2.65408 + 4.59700i) q^{12} +(3.03278 + 1.94993i) q^{13} +(0.313103 + 0.542310i) q^{14} -2.92816i q^{15} +3.72085 q^{16} +(-2.22424 - 3.85250i) q^{17} +(-0.822606 - 0.474932i) q^{18} +(-3.53832 + 2.04285i) q^{19} +(-1.82236 - 1.05214i) q^{20} +(6.80636 + 3.92965i) q^{21} +(0.212207 - 0.367553i) q^{22} -0.663330 q^{23} +(-2.01482 + 1.16326i) q^{24} +(-1.91960 - 3.32485i) q^{25} +(-0.422249 + 0.656737i) q^{26} -3.76803 q^{27} +(4.89129 - 2.82399i) q^{28} -4.34035 q^{29} +0.634082 q^{30} +(-5.33130 + 1.60538i) q^{31} +2.51779i q^{32} -5.32668i q^{33} +(0.834243 - 0.481650i) q^{34} -3.11562 q^{35} +(-4.28358 + 7.41939i) q^{36} +(-0.514023 + 0.296771i) q^{37} +(-0.442371 - 0.766209i) q^{38} +(-0.468267 + 9.78797i) q^{39} +(0.461144 - 0.798725i) q^{40} +(-6.64980 - 3.83926i) q^{41} +(-0.850950 + 1.47389i) q^{42} +(2.15673 + 3.73557i) q^{43} +(-3.31509 - 1.91397i) q^{44} +(4.09279 - 2.36297i) q^{45} -0.143642i q^{46} -0.255427i q^{47} +(5.05625 + 8.75769i) q^{48} +(0.681225 - 1.17992i) q^{49} +(0.719983 - 0.415682i) q^{50} +(6.04504 - 10.4703i) q^{51} +(5.92335 + 3.80842i) q^{52} +(1.64889 - 2.85596i) q^{53} -0.815953i q^{54} +(1.05581 + 1.82872i) q^{55} +(1.23773 + 2.14381i) q^{56} +(-9.61644 - 5.55206i) q^{57} -0.939885i q^{58} +(9.81008 - 5.66385i) q^{59} -5.71901i q^{60} +5.31550 q^{61} +(-0.347640 - 1.15447i) q^{62} +12.6846i q^{63} +6.89647 q^{64} +(-1.77933 - 3.45316i) q^{65} +1.15347 q^{66} +(-8.18899 - 4.72791i) q^{67} +(-4.34418 - 7.52434i) q^{68} +(-0.901399 - 1.56127i) q^{69} -0.674675i q^{70} +(6.83812 + 3.94799i) q^{71} +(-3.25185 - 1.87746i) q^{72} +(0.249101 + 0.143819i) q^{73} +(-0.0642646 - 0.111310i) q^{74} +(5.21709 - 9.03627i) q^{75} +(-6.91072 + 3.98991i) q^{76} -5.66768 q^{77} +(-2.11955 - 0.101401i) q^{78} +(-2.03383 - 3.52270i) q^{79} +(-3.47176 - 2.00442i) q^{80} +(1.45926 + 2.52752i) q^{81} +(0.831377 - 1.43999i) q^{82} +(12.3268 + 7.11691i) q^{83} +(13.2935 + 7.67503i) q^{84} +4.79280i q^{85} +(-0.808923 + 0.467032i) q^{86} +(-5.89810 - 10.2158i) q^{87} +(0.838876 - 1.45298i) q^{88} +5.37232i q^{89} +(0.511692 + 0.886277i) q^{90} +(10.4146 + 0.498246i) q^{91} -1.29556 q^{92} +(-11.0233 - 10.3666i) q^{93} +0.0553117 q^{94} +4.40194 q^{95} +(-5.92609 + 3.42143i) q^{96} -1.70597i q^{97} +(0.255506 + 0.147517i) q^{98} +(7.44527 - 4.29853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9}+O(q^{10}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9	\( 68 q - 6 q^{3} - 76 q^{4} - 40 q^{9} + 8 q^{10} - 10 q^{12} - 3 q^{13} + 10 q^{14} + 84 q^{16} + 6 q^{17} + 4 q^{22} - 44 q^{23} + 30 q^{25} - 3 q^{26} - 12 q^{27} + 48 q^{29} - 4 q^{30} - 48 q^{35} + 40 q^{36} + 60 q^{38} - 14 q^{39} + 20 q^{40} - 10 q^{42} - 12 q^{43} + 32 q^{48} + 58 q^{49} + 20 q^{51} - 27 q^{52} + 8 q^{53} - 36 q^{55} - 50 q^{56} - 12 q^{61} - 74 q^{62} - 15 q^{65} + 164 q^{66} + 4 q^{68} - 34 q^{69} - 4 q^{74} + 20 q^{75} - 200 q^{77} - 58 q^{78} - 80 q^{79} - 82 q^{81} - 66 q^{82} + 52 q^{87} + 16 q^{88} - 14 q^{90} - 70 q^{91} + 108 q^{92} - 4 q^{94} + 76 q^{95}+O(q^{100}) \) 68 * q - 6 * q^3 - 76 * q^4 - 40 * q^9 + 8 * q^10 - 10 * q^12 - 3 * q^13 + 10 * q^14 + 84 * q^16 + 6 * q^17 + 4 * q^22 - 44 * q^23 + 30 * q^25 - 3 * q^26 - 12 * q^27 + 48 * q^29 - 4 * q^30 - 48 * q^35 + 40 * q^36 + 60 * q^38 - 14 * q^39 + 20 * q^40 - 10 * q^42 - 12 * q^43 + 32 * q^48 + 58 * q^49 + 20 * q^51 - 27 * q^52 + 8 * q^53 - 36 * q^55 - 50 * q^56 - 12 * q^61 - 74 * q^62 - 15 * q^65 + 164 * q^66 + 4 * q^68 - 34 * q^69 - 4 * q^74 + 20 * q^75 - 200 * q^77 - 58 * q^78 - 80 * q^79 - 82 * q^81 - 66 * q^82 + 52 * q^87 + 16 * q^88 - 14 * q^90 - 70 * q^91 + 108 * q^92 - 4 * q^94 + 76 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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