LMFDB - Embedded newform 403.2.l.c.25.15

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			25.15
Character	$\chi$	$=$	403.25
Dual form			403.2.l.c.129.20

$q$-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} +(-3.20508 - 1.65150i) 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} +(-0.357626 + 0.694047i) 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} +(-6.25987 - 3.22556i) 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} +(-2.10086 - 3.26753i) 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	$-0.975606\pi$
$2$		−	0.216546i		−	0.153121i	0.997065	−	0.0765606i	$-0.0243939\pi$
$3$	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	0.693911	−	0.720061i	$-0.255886\pi$
$5$	0.933057	+	0.538701i	0.417276	+	0.240914i	−0.276635	+	0.960975i	$0.589219\pi$
$6$	0.509681	−	0.294264i	0.208076	−	0.120133i
$7$	−2.50436	+	1.44590i	−0.946560	+	0.546497i	−0.892011	−	0.452014i	$-0.850706\pi$
$7$	−2.50436	+	1.44590i	−0.946560	+	0.546497i	−0.0545497	+	0.998511i	$0.517372\pi$
$8$		−	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	0.733560	−	0.679625i	$-0.237857\pi$
$11$	1.69734	+	0.979961i	0.511768	+	0.295469i	−0.221792	+	0.975094i	$0.571191\pi$
$12$	2.65408	+	4.59700i	0.766166	+	1.32704i
$13$	−3.20508	−	1.65150i	−0.888929	−	0.458044i
$13$	−3.20508	−	1.65150i	−0.888929	−	0.458044i
$14$	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	−0.0358156	−	0.999358i	$-0.511403\pi$
$19$	3.53832	−	2.04285i	0.811746	−	0.468662i	0.847562	+	0.530696i	$0.178070\pi$
$20$	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
$26$	−0.357626	+	0.694047i	−0.0701363	+	0.136114i
$27$	−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	−0.457152	−	0.889389i	$-0.651131\pi$
$37$	0.514023	−	0.296771i	0.0845048	−	0.0487889i	0.541657	+	0.840600i	$0.317797\pi$
$38$	−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	0.919415	−	0.393289i	$-0.128663\pi$
$41$	6.64980	+	3.83926i	1.03852	+	0.599592i	0.119109	+	0.992881i	$0.461996\pi$
$42$	−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	$0.00593012\pi$
$47$			0.255427i			0.0372579i	−0.999826	+	0.0186289i	$0.994070\pi$
$48$	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
$52$	−6.25987	−	3.22556i	−0.868087	−	0.447305i
$53$	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	−0.976326	−	0.216304i	$-0.930600\pi$
$59$	−9.81008	+	5.66385i	−1.27716	+	0.737371i	−0.300838	+	0.953675i	$0.597266\pi$
$60$			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
$65$	−2.10086	−	3.26753i	−0.260579	−	0.405287i
$66$	1.15347			0.141982
$67$	8.18899	+	4.72791i	1.00044	+	0.577607i	0.908380	−	0.418146i	$-0.137320\pi$
$67$	8.18899	+	4.72791i	1.00044	+	0.577607i	0.0920644	+	0.995753i	$0.470653\pi$
$68$	−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	0.0359533	−	0.999353i	$-0.488553\pi$
$71$	−6.83812	−	3.94799i	−0.811535	−	0.468540i	−0.847489	+	0.530813i	$0.821887\pi$
$72$	3.25185	+	1.87746i	0.383234	+	0.221260i
$73$	−0.249101	−	0.143819i	−0.0291551	−	0.0168327i	0.485352	−	0.874319i	$-0.338692\pi$
$73$	−0.249101	−	0.143819i	−0.0291551	−	0.0168327i	−0.514507	+	0.857486i	$0.672025\pi$
$74$	−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	−0.364372	−	0.931253i	$-0.618716\pi$
$83$	−12.3268	−	7.11691i	−1.35305	−	0.781182i	−0.988675	+	0.150071i	$0.952050\pi$
$84$	−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	$-0.908095\pi$
$89$		−	5.37232i		−	0.569464i	0.958607	−	0.284732i	$-0.0919047\pi$
$90$	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	$0.0276027\pi$
$97$			1.70597i			0.173216i	−0.996242	+	0.0866078i	$0.972397\pi$
$98$	−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	$0.220647\pi$
$104$	−1.41374	+	2.74364i	−0.138628	+	0.269036i
$105$	−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	$0.237621\pi$
$109$			14.1796i			1.35816i	−0.734064	+	0.679080i	$0.762379\pi$
$110$	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
$117$	13.3031	−	8.55323i	1.22987	−	0.790746i
$118$	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
$130$	−0.707570	+	0.454932i	−0.0620580	+	0.0399002i
$131$	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	−0.143198	−	0.989694i	$-0.545739\pi$
$137$	−12.5462	−	7.24358i	−1.07190	−	0.618860i	−0.928699	+	0.370834i	$0.879072\pi$
$138$	−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
$143$	−3.82171	−	5.94402i	−0.319588	−	0.497064i
$144$	−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	−0.885696	−	0.464266i	$-0.846318\pi$
$149$	−11.3091	+	6.52932i	−0.926478	+	0.534902i	−0.0407821	+	0.999168i	$0.512985\pi$
$150$	−1.95677	−	1.12974i	−0.159770	−	0.0922430i
$151$		−	21.4537i		−	1.74587i	−0.487833	−	0.872937i	$-0.662212\pi$
$151$		−	21.4537i		−	1.74587i	0.487833	−	0.872937i	$-0.337788\pi$
$152$	−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	$0.105976\pi$
$163$			8.34506i			0.653636i	−0.945087	+	0.326818i	$0.894024\pi$
$164$	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	−0.187211	−	0.982320i	$-0.559945\pi$
$167$	7.36470	−	4.25201i	0.569898	−	0.329031i	0.757108	+	0.653289i	$0.226611\pi$
$168$	−3.36390	+	5.82644i	−0.259530	+	0.449520i
$169$	7.54508	+	10.5864i	0.580391	+	0.814338i
$170$	−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	$-0.329257\pi$
$193$	20.9910	−	12.1192i	1.51097	−	0.872357i	0.999918	−	0.0128045i	$-0.00407591\pi$
$194$	0.369422			0.0265230
$195$	4.83587	−	9.38499i	0.346304	−	0.672073i
$196$	1.33051	−	2.30450i	0.0950361	−	0.164607i
$197$	−4.91380	−	2.83698i	−0.350093	−	0.202127i	0.314633	−	0.949213i	$-0.398119\pi$
$197$	−4.91380	−	2.83698i	−0.350093	−	0.202127i	−0.664726	+	0.747087i	$0.731452\pi$
$198$	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
$208$	−11.9256	−	6.14499i	−0.826892	−	0.426078i
$209$	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	$0.726557\pi$
$223$	−24.4234	+	14.1009i	−1.63551	+	0.944263i	−0.982352	+	0.187042i	$0.940110\pi$
$224$	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	0.979001	−	0.203855i	$-0.0653470\pi$
$227$	19.4653	+	11.2383i	1.29196	+	0.745913i	0.312957	+	0.949767i	$0.398680\pi$
$228$	18.7819	+	10.8438i	1.24386	+	0.718146i
$229$	7.09051	−	4.09371i	0.468554	−	0.270520i	−0.247080	−	0.968995i	$-0.579471\pi$
$229$	7.09051	−	4.09371i	0.468554	−	0.270520i	0.715634	+	0.698475i	$0.246138\pi$
$230$	−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	$0.477817\pi$
$234$	−1.85217	−	2.88073i	−0.121080	−	0.188319i
$235$	−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	0.253585	−	0.967313i	$-0.418390\pi$
$239$	−7.07031	−	4.08204i	−0.457340	−	0.264045i	−0.710925	+	0.703268i	$0.751724\pi$
$240$			10.8952i			0.703284i
$241$	−19.6980	+	11.3727i	−1.26886	+	0.732577i	−0.974772	−	0.223201i	$-0.928349\pi$
$241$	−19.6980	+	11.3727i	−1.26886	+	0.732577i	−0.294088	+	0.955778i	$0.595016\pi$
$242$	−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
$260$	−4.10320	−	6.38183i	−0.254470	−	0.395784i
$261$	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	$-0.898788\pi$
$271$		−	10.2933i		−	0.625271i	0.949873	−	0.312635i	$-0.101212\pi$
$272$	−8.27605	−	14.3345i	−0.501810	−	0.869160i
$273$	15.3251	+	23.8356i	0.927516	+	1.44259i
$274$	−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	$0.104325\pi$
$281$			10.7924i			0.643819i	−0.946771	+	0.321909i	$0.895675\pi$
$282$	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
$286$	−1.28715	+	0.827576i	−0.0761110	+	0.0489356i
$287$	−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	−0.737318	−	0.675545i	$-0.763908\pi$
$293$	−8.91703	+	5.14825i	−0.520938	+	0.300764i	0.216380	+	0.976309i	$0.430575\pi$
$294$		−	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
$299$	2.12603	+	1.09549i	0.122951	+	0.0633539i
$300$	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	−0.419548	−	0.907733i	$-0.637811\pi$
$307$	2.74732	−	1.58616i	0.156798	−	0.0905272i	0.576346	+	0.817206i	$0.304478\pi$
$308$	−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	$-0.284263\pi$
$317$	28.7576	−	16.6032i	1.61519	−	0.932530i	0.988141	−	0.153550i	$-0.0490707\pi$
$318$		−	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	0.628841	−	0.777534i	$-0.283529\pi$
$331$	4.91037	+	2.83500i	0.269898	+	0.155826i	−0.358943	+	0.933359i	$0.616863\pi$
$332$	−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	$0.305730\pi$
$338$	2.29244	−	1.63386i	0.124692	−	0.0888701i
$339$	−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	$0.184314\pi$
$349$			20.4459i			1.09444i	−0.836988	+	0.547221i	$0.815686\pi$
$350$	1.20207	−	2.08204i	0.0642531	−	0.111290i
$351$	12.0769	+	6.22292i	0.644615	+	0.332155i
$352$	2.46734	−	4.27356i	0.131510	−	0.227782i
$353$	−10.3755	+	5.99032i	−0.552234	+	0.318832i	−0.750022	−	0.661412i	$-0.769957\pi$
$353$	−10.3755	+	5.99032i	−0.552234	+	0.318832i	0.197789	+	0.980245i	$0.436624\pi$
$354$	−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	0.991223	−	0.132204i	$-0.0422054\pi$
$359$	26.0022	+	15.0124i	1.37234	+	0.792322i	0.381119	+	0.924526i	$0.375539\pi$
$360$	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
$377$	13.9112	+	7.16810i	0.716461	+	0.369176i
$378$	−1.17978	−	2.04344i	−0.0606815	−	0.105103i
$379$	3.68888	−	2.12978i	0.189485	−	0.109399i	−0.402256	−	0.915527i	$-0.631774\pi$
$379$	3.68888	−	2.12978i	0.189485	−	0.109399i	0.591742	+	0.806128i	$0.298441\pi$
$380$	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	0.907879	−	0.419233i	$-0.137701\pi$
$383$	19.5460	+	11.2849i	0.998751	+	0.576629i	0.0908728	+	0.995863i	$0.471034\pi$
$384$	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	$0.895342\pi$
$390$	−2.03228	−	1.04719i	−0.102909	−	0.0530264i
$391$	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	−0.682020	−	0.731334i	$-0.738898\pi$
$397$	−7.76424	+	4.48269i	−0.389676	+	0.224980i	0.292344	+	0.956313i	$0.405565\pi$
$398$	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	$-0.654649\pi$
$401$		−	35.4154i		−	1.76856i	0.466955	−	0.884281i	$-0.345351\pi$
$402$	5.56502			0.277558
$403$	−19.7385	−	3.65927i	−0.983246	−	0.182281i
$404$	−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	−0.0840665	−	0.996460i	$-0.526791\pi$
$409$	14.9021	−	8.60372i	0.736860	−	0.425426i	0.820927	+	0.571034i	$0.193457\pi$
$410$	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
$416$	−4.15814	+	8.06973i	−0.203870	+	0.395651i
$417$	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	0.235988	−	0.971756i	$-0.424167\pi$
$421$	−10.0044	−	5.77603i	−0.487583	−	0.281506i	−0.723571	+	0.690250i	$0.757501\pi$
$422$	−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
$429$	8.79702	−	17.0724i	0.424724	−	0.824264i
$430$	1.00636			0.0485311
$431$	−0.0776939	+	0.0448566i	−0.00374239	+	0.00216067i	−0.501870	−	0.864943i	$-0.667354\pi$
$431$	−0.0776939	+	0.0448566i	−0.00374239	+	0.00216067i	0.498128	+	0.867104i	$0.334021\pi$
$432$	−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	$-0.772931\pi$
$449$		−	27.7320i		−	1.30875i	0.756169	−	0.654377i	$-0.227069\pi$
$450$		−	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
$455$	9.98581	+	5.14545i	0.468142	+	0.241223i
$456$	4.75272	−	8.23196i	0.222567	−	0.385497i
$457$			26.0706i			1.21953i	0.792582	+	0.609765i	$0.208736\pi$
$457$			26.0706i			1.21953i	−0.792582	+	0.609765i	$0.791264\pi$
$458$	−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	$0.0138853\pi$
$461$			1.87261i			0.0872160i	−0.999049	+	0.0436080i	$0.986115\pi$
$462$	−2.88871	+	1.66780i	−0.134395	+	0.0775929i
$463$		−	2.06017i		−	0.0957441i	−0.998853	−	0.0478720i	$-0.984756\pi$
$463$		−	2.06017i		−	0.0957441i	0.998853	−	0.0478720i	$-0.0152440\pi$
$464$	−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	$0.298741\pi$
$468$	25.9824	−	16.7054i	1.20104	−	0.772206i
$469$	−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	$0.715373\pi$
$479$	−35.3344	+	20.4004i	−1.61447	+	0.932116i	−0.988316	+	0.152418i	$0.951294\pi$
$480$	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	0.945185	−	0.326535i	$-0.105881\pi$
$487$	25.0470	+	14.4609i	1.13499	+	0.655287i	0.189805	+	0.981822i	$0.439215\pi$
$488$		−	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	−0.789686	−	0.613512i	$-0.789756\pi$
$499$	−14.5917	+	8.42449i	−0.653212	+	0.377132i	0.136474	+	0.990644i	$0.456423\pi$
$500$		−	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
$507$	−14.6640	+	32.1446i	−0.651252	+	1.42759i
$508$	−17.6168	−	30.5132i	−0.781619	−	1.35380i
$509$	−20.0967	−	11.6028i	−0.890770	−	0.514286i	−0.0165755	−	0.999863i	$-0.505276\pi$
$509$	−20.0967	−	11.6028i	−0.890770	−	0.514286i	−0.874194	+	0.485577i	$0.838610\pi$
$510$	−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
$520$	−2.79710	+	1.79840i	−0.122661	+	0.0788649i
$521$	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
$533$	−14.9726	−	23.2873i	−0.648535	−	1.00869i
$534$	−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	−0.748902	−	0.662681i	$-0.769418\pi$
$541$	−12.7800	+	7.37852i	−0.549454	+	0.317227i	0.199448	+	0.979908i	$0.436085\pi$
$542$	−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
$546$	5.16150	−	3.31859i	0.220892	−	0.142022i
$547$	−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	$0.0803140\pi$
$557$			11.7837i			0.499291i	−0.968337	+	0.249645i	$0.919686\pi$
$558$	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	$-0.249040\pi$
$572$	−7.46421	−	11.6093i	−0.312094	−	0.485410i
$573$	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	0.239081	−	0.971000i	$-0.423154\pi$
$577$	28.8138	−	16.6356i	1.19953	−	0.692550i	0.960451	+	0.278449i	$0.0898204\pi$
$578$	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	$-0.954376\pi$
$587$		−	6.92154i		−	0.285683i	0.989746	−	0.142841i	$-0.0456238\pi$
$588$	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	$0.0929635\pi$
$593$			14.0226i			0.575839i	−0.957655	+	0.287919i	$0.907036\pi$
$594$	−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
$598$	0.237224	−	0.460383i	0.00970083	−	0.0188264i
$599$	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
$611$	0.421838	−	0.818664i	0.0170658	−	0.0331196i
$612$	38.1109			1.54054
$613$	11.5373	−	6.66106i	0.465987	−	0.269038i	−0.248571	−	0.968614i	$-0.579961\pi$
$613$	11.5373	−	6.66106i	0.465987	−	0.269038i	0.714558	+	0.699576i	$0.246628\pi$
$614$	−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	−0.458293	−	0.888801i	$-0.651539\pi$
$617$	2.04390	−	1.18005i	0.0822843	−	0.0475069i	0.540578	+	0.841294i	$0.318206\pi$
$618$			2.01612i			0.0811003i
$619$			9.60526i			0.386068i	0.981192	+	0.193034i	$0.0618328\pi$
$619$			9.60526i			0.386068i	−0.981192	+	0.193034i	$0.938167\pi$
$620$	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	0.808435	−	0.588586i	$-0.200315\pi$
$631$	17.6572	+	10.1944i	0.702922	+	0.405832i	−0.105513	+	0.994418i	$0.533648\pi$
$632$	−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
$637$	−4.13201	+	2.65668i	−0.163716	+	0.105262i
$638$	−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	$-0.995437\pi$
$643$		−	0.727035i		−	0.0286714i	0.999897	−	0.0143357i	$-0.00456336\pi$
$644$	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	0.597203	−	0.802090i	$-0.296279\pi$
$661$	5.17216	+	2.98615i	0.201174	+	0.116148i	−0.396029	+	0.918238i	$0.629612\pi$
$662$	0.613908	−	1.06332i	0.0238602	−	0.0413271i
$663$	−36.6666	+	23.5748i	−1.42401	+	0.915569i
$664$	−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
$676$	14.7363	+	20.6764i	0.566783	+	0.795245i
$677$	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	$0.263322\pi$
$683$			38.4734i			1.47214i	−0.676903	+	0.736072i	$0.736678\pi$
$684$			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
$689$	−10.0014	+	6.43043i	−0.381025	+	0.244980i
$690$	−0.420605			−0.0160122
$691$	−17.3900	−	10.0401i	−0.661548	−	0.381945i	0.131318	−	0.991340i	$-0.458079\pi$
$691$	−17.3900	−	10.0401i	−0.661548	−	0.381945i	−0.792867	+	0.609395i	$0.791412\pi$
$692$	−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	$0.688527\pi$
$702$	1.34755	−	2.61519i	0.0508599	−	0.0987042i
$703$	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	$-0.980457\pi$
$709$		−	3.26759i		−	0.122717i	0.998116	−	0.0613584i	$-0.0195433\pi$
$710$	−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	0.806284	−	0.591529i	$-0.201475\pi$
$733$	18.8745	+	10.8972i	0.697146	+	0.402498i	−0.109137	+	0.994027i	$0.534809\pi$
$734$	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	0.139593	−	0.990209i	$-0.455421\pi$
$739$	−17.6198	−	10.1728i	−0.648156	−	0.374213i	−0.787750	+	0.615996i	$0.788754\pi$
$740$	1.24898			0.0459134
$741$	−21.6522	−	33.6764i	−0.795415	−	1.23713i
$742$	2.06509			0.0758117
$743$			41.2679i			1.51397i	0.653431	+	0.756986i	$0.273329\pi$
$743$			41.2679i			1.51397i	−0.653431	+	0.756986i	$0.726671\pi$
$744$	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
$754$	1.55222	−	3.01241i	0.0565286	−	0.109705i
$755$	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	−0.974528	−	0.224265i	$-0.928002\pi$
$761$	−34.9676	+	20.1885i	−1.26757	+	0.731834i	−0.293045	+	0.956099i	$0.594669\pi$
$762$	−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	−0.322502	−	0.946569i	$-0.604524\pi$
$769$	9.31755	−	5.37949i	0.336000	−	0.193989i	0.658502	+	0.752579i	$0.271191\pi$
$770$	−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	$-0.910513\pi$
$773$		−	15.4275i		−	0.554889i	0.960742	−	0.277445i	$-0.0894875\pi$
$774$			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
$780$	9.44497	−	18.3299i	0.338184	−	0.656316i
$781$	−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	−0.996331	−	0.0855783i	$-0.972726\pi$
$787$	−39.8468	+	23.0055i	−1.42038	+	0.820059i	−0.424053	+	0.905637i	$0.639393\pi$
$788$	−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
$793$	−17.0366	−	8.77857i	−0.604988	−	0.311736i
$794$	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
$806$	−0.792400	+	4.27430i	−0.0279111	+	0.150556i
$807$	−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	0.964237	−	0.265041i	$-0.0853854\pi$
$811$	34.6528	+	20.0068i	1.21682	+	0.702533i	0.252586	+	0.967574i	$0.418719\pi$
$812$	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
$819$	−20.9487	+	40.6553i	−0.732007	+	1.42061i
$820$	8.07889	+	13.9930i	0.282127	+	0.488658i
$821$		−	42.5223i		−	1.48404i	−0.670379	−	0.742019i	$-0.733868\pi$
$821$		−	42.5223i		−	1.48404i	0.670379	−	0.742019i	$-0.266132\pi$
$822$	−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	0.637027	−	0.770842i	$-0.280164\pi$
$827$	8.28137	+	4.78125i	0.287971	+	0.166260i	−0.349055	+	0.937102i	$0.613497\pi$
$828$	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
$832$	−22.1037	−	11.3895i	−0.766310	−	0.394861i
$833$	−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	$-0.807934\pi$
$839$		−	32.8723i		−	1.13488i	0.823416	−	0.567439i	$-0.192066\pi$
$840$	−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	$-0.789985\pi$
$853$		−	35.8035i		−	1.22589i	0.790126	−	0.612945i	$-0.210015\pi$
$854$	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	$0.215093\pi$
$858$	−3.69696	−	1.90496i	−0.126212	−	0.0650343i
$859$	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	0.904074	−	0.427375i	$-0.140562\pi$
$863$	28.9654	+	16.7232i	0.985994	+	0.569264i	0.0819193	+	0.996639i	$0.473895\pi$
$864$			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
$871$	−18.4382	−	28.6775i	−0.624754	−	0.971699i
$872$	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	−0.0597853	−	0.998211i	$-0.519042\pi$
$877$	−28.2565	−	16.3139i	−0.954154	−	0.550881i	−0.894369	+	0.447330i	$0.852375\pi$
$878$	−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
$910$	1.11423	−	2.16239i	0.0369363	−	0.0716824i
$911$	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
$923$	15.3966	+	23.9468i	0.506785	+	0.788218i
$924$	−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	$-0.754763\pi$
$929$		−	42.4547i		−	1.39289i	0.717609	−	0.696446i	$-0.245237\pi$
$930$	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
$936$	−7.32182	−	11.3878i	−0.239321	−	0.372223i
$937$	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	0.796191	−	0.605045i	$-0.206845\pi$
$941$	20.5620	+	11.8715i	0.670302	+	0.386999i	−0.125889	+	0.992044i	$0.540178\pi$
$942$	−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	−0.880048	−	0.474884i	$-0.842490\pi$
$947$	−27.9672	+	16.1469i	−0.908811	+	0.524702i	−0.0287625	+	0.999586i	$0.509157\pi$
$948$	10.7959	−	18.6990i	0.350634	−	0.607316i
$949$	0.560873	+	0.872342i	0.0182067	+	0.0283174i
$950$	−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	−0.761892	−	0.647704i	$-0.775730\pi$
$967$	−18.0955	+	10.4474i	−0.581911	+	0.335966i	0.179982	+	0.983670i	$0.442396\pi$
$968$	−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
$975$	−31.6446	+	20.3459i	−1.01344	+	0.651591i
$976$	19.7782			0.633083
$977$		−	26.4825i		−	0.847250i	−0.905838	−	0.423625i	$-0.860757\pi$
$977$		−	26.4825i		−	0.847250i	0.905838	−	0.423625i	$-0.139243\pi$
$978$	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	0.846780	−	0.531943i	$-0.178538\pi$
$983$	25.3799	+	14.6531i	0.809493	+	0.467361i	−0.0372866	+	0.999305i	$0.511871\pi$
$984$	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.25.15	✓	68
13.12	even	2	inner	403.2.l.c.25.20	yes	68
31.5	even	3	inner	403.2.l.c.129.15	yes	68
403.129	even	6	inner	403.2.l.c.129.20	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.l.c.25.15	✓	68	1.1	even	1	trivial
403.2.l.c.25.20	yes	68	13.12	even	2	inner
403.2.l.c.129.15	yes	68	31.5	even	3	inner
403.2.l.c.129.20	yes	68	403.129	even	6	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} +(-3.20508 - 1.65150i) 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} +(-0.357626 + 0.694047i) 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} +(-6.25987 - 3.22556i) 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} +(-2.10086 - 3.26753i) 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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