LMFDB - Embedded newform 150.2.l.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, degree $8$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			83.3
Character	$\chi$	$=$	150.83
Dual form			150.2.l.a.47.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 + 0.891007i) q^{2} +(1.00736 - 1.40898i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.998457 - 2.00077i) q^{5} +(0.798080 + 1.53723i) q^{6} +(0.712495 - 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.970457 - 2.83870i) q^{9} +O(q^{10})$	\(q+(-0.453990 + 0.891007i) q^{2} +(1.00736 - 1.40898i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.998457 - 2.00077i) q^{5} +(0.798080 + 1.53723i) q^{6} +(0.712495 - 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.970457 - 2.83870i) q^{9} +(2.23599 + 0.0186987i) q^{10} +(-0.348148 + 0.113120i) q^{11} +(-1.73200 + 0.0132082i) q^{12} +(2.33563 - 1.19006i) q^{13} +(0.311372 + 0.958303i) q^{14} +(-3.82485 - 0.608686i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.919013 + 5.80242i) q^{17} +(2.96988 + 0.424059i) q^{18} +(0.341785 - 0.470426i) q^{19} +(-1.03178 + 1.98379i) q^{20} +(-0.286154 - 1.72163i) q^{21} +(0.0572652 - 0.361558i) q^{22} +(6.05243 + 3.08387i) q^{23} +(0.774543 - 1.54922i) q^{24} +(-3.00617 + 3.99537i) q^{25} +2.62134i q^{26} +(-4.97727 - 1.49223i) q^{27} +(-0.995214 - 0.157626i) q^{28} +(0.368253 - 0.267552i) q^{29} +(2.27879 - 3.13163i) q^{30} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.191326 + 0.604487i) q^{33} +(-5.58722 - 1.81540i) q^{34} +(-2.13693 - 0.714143i) q^{35} +(-1.72614 + 2.45366i) q^{36} +(4.35053 + 8.53839i) q^{37} +(0.263986 + 0.518102i) q^{38} +(0.676040 - 4.48967i) q^{39} +(-1.29915 - 1.81994i) q^{40} +(-10.0917 - 3.27898i) q^{41} +(1.66389 + 0.526638i) q^{42} +(-7.18512 - 7.18512i) q^{43} +(0.296153 + 0.215168i) q^{44} +(-4.71063 + 4.77598i) q^{45} +(-5.49549 + 3.99271i) q^{46} +(8.16222 + 1.29277i) q^{47} +(1.02873 + 1.39345i) q^{48} +5.98470i q^{49} +(-2.19513 - 4.49237i) q^{50} +(9.10128 + 4.55025i) q^{51} +(-2.33563 - 1.19006i) q^{52} +(-1.38217 + 8.72670i) q^{53} +(3.58922 - 3.75732i) q^{54} +(0.573939 + 0.583619i) q^{55} +(0.592264 - 0.815182i) q^{56} +(-0.318522 - 0.955457i) q^{57} +(0.0712068 + 0.449582i) q^{58} +(2.91096 - 8.95903i) q^{59} +(1.75576 + 3.45215i) q^{60} +(-0.335312 - 1.03198i) q^{61} +(2.60811 - 1.32890i) q^{62} +(-2.71400 - 1.33111i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-4.71307 - 3.48483i) q^{65} +(-0.451742 - 0.444904i) q^{66} +(13.0896 - 2.07319i) q^{67} +(4.15407 - 4.15407i) q^{68} +(10.4421 - 5.42120i) q^{69} +(1.60645 - 1.57981i) q^{70} +(0.755873 + 1.04037i) q^{71} +(-1.40258 - 2.65194i) q^{72} +(4.33350 - 8.50497i) q^{73} -9.58285 q^{74} +(2.60111 + 8.26040i) q^{75} -0.581479 q^{76} +(-0.167456 + 0.328652i) q^{77} +(3.69341 + 2.64063i) q^{78} +(7.17322 + 9.87309i) q^{79} +(2.21139 - 0.331317i) q^{80} +(-7.11643 + 5.50967i) q^{81} +(7.50310 - 7.50310i) q^{82} +(-0.937190 + 0.148436i) q^{83} +(-1.22463 + 1.24345i) q^{84} +(10.6917 - 7.63220i) q^{85} +(9.66396 - 3.14001i) q^{86} +(-0.00601220 - 0.788383i) q^{87} +(-0.326166 + 0.166190i) q^{88} +(0.626378 + 1.92779i) q^{89} +(-2.11685 - 6.36545i) q^{90} +(0.816210 - 2.51204i) q^{91} +(-1.06263 - 6.70917i) q^{92} +(-4.80974 + 1.60343i) q^{93} +(-4.85743 + 6.68568i) q^{94} +(-1.28247 - 0.214132i) q^{95} +(-1.70861 + 0.283990i) q^{96} +(-2.81727 + 17.7876i) q^{97} +(-5.33241 - 2.71700i) q^{98} +(0.658978 + 0.878510i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$2$	−0.453990	+	0.891007i	−0.321020	+	0.630037i
$3$	1.00736	−	1.40898i	0.581599	−	0.813476i
$3$	1.00736	−	1.40898i	0.581599	−	0.813476i
$4$	−0.587785	−	0.809017i	−0.293893	−	0.404508i
$5$	−0.998457	−	2.00077i	−0.446524	−	0.894772i
$5$	−0.998457	−	2.00077i	−0.446524	−	0.894772i
$6$	0.798080	+	1.53723i	0.325815	+	0.627570i
$7$	0.712495	−	0.712495i	0.269298	−	0.269298i	−0.559519	−	0.828817i	$-0.689014\pi$
$7$	0.712495	−	0.712495i	0.269298	−	0.269298i	0.828817	+	0.559519i	$0.189014\pi$
$8$	0.987688	−	0.156434i	0.349201	−	0.0553079i
$9$	−0.970457	−	2.83870i	−0.323486	−	0.946233i
$10$	2.23599	+	0.0186987i	0.707082	+	0.00591305i
$11$	−0.348148	+	0.113120i	−0.104971	+	0.0341070i	−0.361031	−	0.932554i	$-0.617575\pi$
$11$	−0.348148	+	0.113120i	−0.104971	+	0.0341070i	0.256061	+	0.966661i	$0.417575\pi$
$12$	−1.73200	+	0.0132082i	−0.499985	+	0.00381289i
$13$	2.33563	−	1.19006i	0.647787	−	0.330064i	−0.0990392	−	0.995084i	$-0.531577\pi$
$13$	2.33563	−	1.19006i	0.647787	−	0.330064i	0.746826	+	0.665020i	$0.231577\pi$
$14$	0.311372	+	0.958303i	0.0832176	+	0.256117i
$15$	−3.82485	−	0.608686i	−0.987573	−	0.157162i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	0.919013	+	5.80242i	0.222893	+	1.40729i	0.804562	+	0.593868i	$0.202400\pi$
$17$	0.919013	+	5.80242i	0.222893	+	1.40729i	−0.581669	+	0.813426i	$0.697600\pi$
$18$	2.96988	+	0.424059i	0.700007	+	0.0999516i
$19$	0.341785	−	0.470426i	0.0784108	−	0.107923i	−0.768010	−	0.640438i	$-0.778753\pi$
$19$	0.341785	−	0.470426i	0.0784108	−	0.107923i	0.846421	+	0.532515i	$0.178753\pi$
$20$	−1.03178	+	1.98379i	−0.230713	+	0.443589i
$21$	−0.286154	−	1.72163i	−0.0624439	−	0.375690i
$22$	0.0572652	−	0.361558i	0.0122090	−	0.0770844i
$23$	6.05243	+	3.08387i	1.26202	+	0.643031i	0.951533	−	0.307548i	$-0.0995083\pi$
$23$	6.05243	+	3.08387i	1.26202	+	0.643031i	0.310486	+	0.950578i	$0.399508\pi$
$24$	0.774543	−	1.54922i	0.158103	−	0.316233i
$25$	−3.00617	+	3.99537i	−0.601233	+	0.799074i
$26$			2.62134i			0.514086i
$27$	−4.97727	−	1.49223i	−0.957877	−	0.287180i
$28$	−0.995214	−	0.157626i	−0.188078	−	0.0297886i
$29$	0.368253	−	0.267552i	0.0683830	−	0.0496831i	−0.553069	−	0.833136i	$-0.686543\pi$
$29$	0.368253	−	0.267552i	0.0683830	−	0.0496831i	0.621452	+	0.783453i	$0.286543\pi$
$30$	2.27879	−	3.13163i	0.416048	−	0.571755i
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	0.354451	−	0.935074i	$-0.384668\pi$
$31$	−2.36811	−	1.72054i	−0.425326	−	0.309017i	−0.779777	+	0.626057i	$0.784668\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.191326	+	0.604487i	−0.0333056	+	0.105228i
$34$	−5.58722	−	1.81540i	−0.958200	−	0.311338i
$35$	−2.13693	−	0.714143i	−0.361208	−	0.120712i
$36$	−1.72614	+	2.45366i	−0.287689	+	0.408944i
$37$	4.35053	+	8.53839i	0.715222	+	1.40370i	0.906517	+	0.422169i	$0.138731\pi$
$37$	4.35053	+	8.53839i	0.715222	+	1.40370i	−0.191295	+	0.981533i	$0.561269\pi$
$38$	0.263986	+	0.518102i	0.0428242	+	0.0840472i
$39$	0.676040	−	4.48967i	0.108253	−	0.718923i
$40$	−1.29915	−	1.81994i	−0.205414	−	0.287759i
$41$	−10.0917	−	3.27898i	−1.57605	−	0.512090i	−0.615016	−	0.788515i	$-0.710850\pi$
$41$	−10.0917	−	3.27898i	−1.57605	−	0.512090i	−0.961036	+	0.276425i	$0.910850\pi$
$42$	1.66389	+	0.526638i	0.256745	+	0.0812621i
$43$	−7.18512	−	7.18512i	−1.09572	−	1.09572i	−0.994905	−	0.100815i	$-0.967855\pi$
$43$	−7.18512	−	7.18512i	−1.09572	−	1.09572i	−0.100815	−	0.994905i	$-0.532145\pi$
$44$	0.296153	+	0.215168i	0.0446467	+	0.0324377i
$45$	−4.71063	+	4.77598i	−0.702219	+	0.711961i
$46$	−5.49549	+	3.99271i	−0.810266	+	0.588693i
$47$	8.16222	+	1.29277i	1.19058	+	0.188570i	0.720119	−	0.693850i	$-0.244087\pi$
$47$	8.16222	+	1.29277i	1.19058	+	0.188570i	0.470463	+	0.882420i	$0.344087\pi$
$48$	1.02873	+	1.39345i	0.148484	+	0.201128i
$49$			5.98470i			0.854957i
$50$	−2.19513	−	4.49237i	−0.310438	−	0.635317i
$51$	9.10128	+	4.55025i	1.27443	+	0.637162i
$52$	−2.33563	−	1.19006i	−0.323893	−	0.165032i
$53$	−1.38217	+	8.72670i	−0.189856	+	1.19870i	0.690123	+	0.723692i	$0.257556\pi$
$53$	−1.38217	+	8.72670i	−0.189856	+	1.19870i	−0.879979	+	0.475012i	$0.842444\pi$
$54$	3.58922	−	3.75732i	0.488431	−	0.511307i
$55$	0.573939	+	0.583619i	0.0773899	+	0.0786952i
$56$	0.592264	−	0.815182i	0.0791446	−	0.108933i
$57$	−0.318522	−	0.955457i	−0.0421893	−	0.126553i
$58$	0.0712068	+	0.449582i	0.00934992	+	0.0590330i
$59$	2.91096	−	8.95903i	0.378975	−	1.16637i	−0.561782	−	0.827285i	$-0.689884\pi$
$59$	2.91096	−	8.95903i	0.378975	−	1.16637i	0.940757	−	0.339081i	$-0.110116\pi$
$60$	1.75576	+	3.45215i	0.226667	+	0.445670i
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	0.927293	−	0.374337i	$-0.122130\pi$
$61$	−0.335312	−	1.03198i	−0.0429323	−	0.132132i	−0.970225	+	0.242205i	$0.922130\pi$
$62$	2.60811	−	1.32890i	0.331230	−	0.168770i
$63$	−2.71400	−	1.33111i	−0.341932	−	0.167704i
$64$	0.951057	−	0.309017i	0.118882	−	0.0386271i
$65$	−4.71307	−	3.48483i	−0.584584	−	0.432240i
$66$	−0.451742	−	0.444904i	−0.0556056	−	0.0547639i
$67$	13.0896	−	2.07319i	1.59915	−	0.253280i	0.707737	−	0.706476i	$-0.249716\pi$
$67$	13.0896	−	2.07319i	1.59915	−	0.253280i	0.891411	+	0.453196i	$0.149716\pi$
$68$	4.15407	−	4.15407i	0.503756	−	0.503756i
$69$	10.4421	−	5.42120i	1.25708	−	0.652636i
$70$	1.60645	−	1.57981i	0.192008	−	0.188823i
$71$	0.755873	+	1.04037i	0.0897056	+	0.123469i	0.851511	−	0.524337i	$-0.175687\pi$
$71$	0.755873	+	1.04037i	0.0897056	+	0.123469i	−0.761805	+	0.647806i	$0.775687\pi$
$72$	−1.40258	−	2.65194i	−0.165296	−	0.312534i
$73$	4.33350	−	8.50497i	0.507198	−	0.995432i	−0.485435	−	0.874273i	$-0.661339\pi$
$73$	4.33350	−	8.50497i	0.507198	−	0.995432i	0.992633	−	0.121159i	$-0.0386612\pi$
$74$	−9.58285			−1.11398
$75$	2.60111	+	8.26040i	0.300351	+	0.953829i
$76$	−0.581479			−0.0667002
$77$	−0.167456	+	0.328652i	−0.0190834	+	0.0374533i
$78$	3.69341	+	2.64063i	0.418197	+	0.298992i
$79$	7.17322	+	9.87309i	0.807050	+	1.11081i	0.991772	+	0.128018i	$0.0408616\pi$
$79$	7.17322	+	9.87309i	0.807050	+	1.11081i	−0.184722	+	0.982791i	$0.559138\pi$
$80$	2.21139	−	0.331317i	0.247240	−	0.0370424i
$81$	−7.11643	+	5.50967i	−0.790714	+	0.612186i
$82$	7.50310	−	7.50310i	0.828579	−	0.828579i
$83$	−0.937190	+	0.148436i	−0.102870	+	0.0162930i	−0.207657	−	0.978202i	$-0.566584\pi$
$83$	−0.937190	+	0.148436i	−0.102870	+	0.0162930i	0.104787	+	0.994495i	$0.466584\pi$
$84$	−1.22463	+	1.24345i	−0.133618	+	0.135672i
$85$	10.6917	−	7.63220i	1.15968	−	0.827829i
$86$	9.66396	−	3.14001i	1.04209	−	0.338596i
$87$	−0.00601220	−	0.788383i	−0.000644576	−	0.0845235i
$88$	−0.326166	+	0.166190i	−0.0347694	+	0.0177159i
$89$	0.626378	+	1.92779i	0.0663960	+	0.204346i	0.978750	−	0.205056i	$-0.0657375\pi$
$89$	0.626378	+	1.92779i	0.0663960	+	0.204346i	−0.912354	+	0.409401i	$0.865738\pi$
$90$	−2.11685	−	6.36545i	−0.223136	−	0.670977i
$91$	0.816210	−	2.51204i	0.0855620	−	0.263333i
$92$	−1.06263	−	6.70917i	−0.110787	−	0.699479i
$93$	−4.80974	+	1.60343i	−0.498747	+	0.166268i
$94$	−4.85743	+	6.68568i	−0.501006	+	0.689576i
$95$	−1.28247	−	0.214132i	−0.131579	−	0.0219695i
$96$	−1.70861	+	0.283990i	−0.174384	+	0.0289846i
$97$	−2.81727	+	17.7876i	−0.286051	+	1.80605i	0.257065	+	0.966394i	$0.417245\pi$
$97$	−2.81727	+	17.7876i	−0.286051	+	1.80605i	−0.543115	+	0.839658i	$0.682755\pi$
$98$	−5.33241	−	2.71700i	−0.538655	−	0.274458i
$99$	0.658978	+	0.878510i	0.0662297	+	0.0882936i
$100$	4.99930	+	0.0836202i	0.499930	+	0.00836202i
$101$		−	0.362340i		−	0.0360542i	−0.999837	−	0.0180271i	$-0.994261\pi$
$101$		−	0.362340i		−	0.0360542i	0.999837	−	0.0180271i	$-0.00573851\pi$
$102$	−8.18619	+	6.04353i	−0.810554	+	0.598399i
$103$	−7.83651	−	1.24118i	−0.772154	−	0.122297i	−0.242089	−	0.970254i	$-0.577833\pi$
$103$	−7.83651	−	1.24118i	−0.772154	−	0.122297i	−0.530065	+	0.847957i	$0.677833\pi$
$104$	2.12071	−	1.54078i	0.207952	−	0.151086i
$105$	−3.15887	+	2.29150i	−0.308274	+	0.223628i
$106$	−7.14805	−	5.19336i	−0.694280	−	0.504424i
$107$	−9.06892	−	9.06892i	−0.876725	−	0.876725i	0.116469	−	0.993194i	$-0.462842\pi$
$107$	−9.06892	−	9.06892i	−0.876725	−	0.876725i	−0.993194	+	0.116469i	$0.962842\pi$
$108$	1.71833	+	4.90381i	0.165346	+	0.471869i
$109$	−4.33696	−	1.40916i	−0.415405	−	0.134973i	0.0938551	−	0.995586i	$-0.470081\pi$
$109$	−4.33696	−	1.40916i	−0.415405	−	0.134973i	−0.509260	+	0.860613i	$0.670081\pi$
$110$	−0.780572	+	0.246426i	−0.0744246	+	0.0234958i
$111$	16.4130	+	2.47141i	1.55785	+	0.234576i
$112$	0.457450	+	0.897796i	0.0432249	+	0.0848337i
$113$	−6.17652	−	12.1221i	−0.581038	−	1.14035i	−0.975203	−	0.221311i	$-0.928966\pi$
$113$	−6.17652	−	12.1221i	−0.581038	−	1.14035i	0.394166	−	0.919039i	$-0.371034\pi$
$114$	0.995924	+	0.149963i	0.0932768	+	0.0140453i
$115$	0.127017	−	15.1886i	0.0118444	−	1.41635i
$116$	−0.432908	−	0.140660i	−0.0401945	−	0.0130600i
$117$	−5.64485	−	5.47524i	−0.521867	−	0.506186i
$118$	6.66100	+	6.66100i	0.613195	+	0.613195i
$119$	4.78899	+	3.47940i	0.439006	+	0.318956i
$120$	−3.87298	−	0.00285272i	−0.353553	−	0.000260416i
$121$	−8.79078	+	6.38687i	−0.799161	+	0.580625i
$122$	1.07173	+	0.169746i	0.0970301	+	0.0153681i
$123$	−14.7859	+	10.9158i	−1.33320	+	0.984249i
$124$			2.92715i			0.262866i
$125$	10.9953	+	2.02544i	0.983453	+	0.181161i
$126$	2.41816	−	1.81388i	0.215427	−	0.161594i
$127$	−17.5736	−	8.95420i	−1.55941	−	0.794557i	−0.559982	−	0.828505i	$-0.689192\pi$
$127$	−17.5736	−	8.95420i	−1.55941	−	0.794557i	−0.999424	+	0.0339477i	$0.989192\pi$
$128$	−0.156434	+	0.987688i	−0.0138270	+	0.0873001i
$129$	−17.3617	+	2.88571i	−1.52861	+	0.254072i
$130$	5.24469	−	2.61729i	0.459990	−	0.229552i
$131$	6.37019	−	8.76782i	0.556566	−	0.766048i	−0.434318	−	0.900759i	$-0.643011\pi$
$131$	6.37019	−	8.76782i	0.556566	−	0.766048i	0.990885	+	0.134711i	$0.0430107\pi$
$132$	0.601499	−	0.200523i	0.0523538	−	0.0174533i
$133$	−0.0916565	−	0.578696i	−0.00794763	−	0.0501793i
$134$	−4.09532	+	12.6041i	−0.353782	+	1.08883i
$135$	1.98398	+	11.4483i	0.170754	+	0.985314i
$136$	1.81540	+	5.58722i	0.155669	+	0.479100i
$137$	−7.75294	+	3.95032i	−0.662378	+	0.337498i	−0.752652	−	0.658419i	$-0.771226\pi$
$137$	−7.75294	+	3.95032i	−0.662378	+	0.337498i	0.0902740	+	0.995917i	$0.471226\pi$
$138$	0.0897208	+	11.7651i	0.00763754	+	1.00151i
$139$	−2.91069	+	0.945741i	−0.246882	+	0.0802167i	−0.429844	−	0.902903i	$-0.641431\pi$
$139$	−2.91069	+	0.945741i	−0.246882	+	0.0802167i	0.182962	+	0.983120i	$0.441431\pi$
$140$	0.678305	+	2.14858i	0.0573272	+	0.181588i
$141$	10.0438	−	10.1981i	0.845838	−	0.858838i
$142$	−1.27013	+	0.201170i	−0.106587	+	0.0168818i
$143$	−0.678525	+	0.678525i	−0.0567411	+	0.0567411i
$144$	2.99965	−	0.0457533i	0.249971	−	0.00381278i
$145$	−0.902995	−	0.469652i	−0.0749897	−	0.0390024i
$146$	5.61062	+	7.72236i	0.464338	+	0.639107i
$147$	8.43233	+	6.02874i	0.695487	+	0.497242i
$148$	4.35053	−	8.53839i	0.357611	−	0.701851i
$149$	5.85789			0.479897			0.239948	−	0.970786i	$-0.422869\pi$
$149$	5.85789			0.479897			0.239948	+	0.970786i	$0.422869\pi$
$150$	−8.54095	−	1.43253i	−0.697366	−	0.116966i
$151$	3.64976			0.297013			0.148507	−	0.988911i	$-0.452553\pi$
$151$	3.64976			0.297013			0.148507	+	0.988911i	$0.452553\pi$
$152$	0.263986	−	0.518102i	0.0214121	−	0.0420236i
$153$	15.5795	−	8.23980i	1.25952	−	0.666149i
$154$	−0.216807	−	0.298409i	−0.0174708	−	0.0240465i
$155$	−1.07794	+	6.45593i	−0.0865819	+	0.518553i
$156$	−4.02959	+	2.09204i	−0.322625	+	0.167497i
$157$	2.27502	−	2.27502i	0.181567	−	0.181567i	−0.610472	−	0.792038i	$-0.709020\pi$
$157$	2.27502	−	2.27502i	0.181567	−	0.181567i	0.792038	+	0.610472i	$0.209020\pi$
$158$	−12.0536	+	1.90910i	−0.958930	+	0.151880i
$159$	10.9034	+	10.7384i	0.864697	+	0.851608i
$160$	−0.708742	+	2.12077i	−0.0560310	+	0.167662i
$161$	6.50956	−	2.11508i	0.513025	−	0.166692i
$162$	−1.67836	−	8.84212i	−0.131865	−	0.694703i
$163$	−3.29567	+	1.67923i	−0.258137	+	0.131527i	−0.578270	−	0.815845i	$-0.696272\pi$
$163$	−3.29567	+	1.67923i	−0.258137	+	0.131527i	0.320134	+	0.947372i	$0.396272\pi$
$164$	3.27898	+	10.0917i	0.256045	+	0.788026i
$165$	1.40047	−	0.220756i	0.109027	−	0.0171858i
$166$	0.293218	−	0.902431i	0.0227581	−	0.0700422i
$167$	−1.42932	−	9.02439i	−0.110604	−	0.698328i	−0.979214	−	0.202831i	$-0.934986\pi$
$167$	−1.42932	−	9.02439i	−0.110604	−	0.698328i	0.868610	−	0.495497i	$-0.165014\pi$
$168$	−0.551953	−	1.65567i	−0.0425841	−	0.127738i
$169$	−3.60230	+	4.95814i	−0.277100	+	0.381395i
$170$	1.94641	+	12.9913i	0.149283	+	0.996390i
$171$	−1.66709	−	0.513696i	−0.127485	−	0.0392833i
$172$	−1.58958	+	10.0362i	−0.121204	+	0.765252i
$173$	8.21156	+	4.18400i	0.624313	+	0.318104i	0.737374	−	0.675485i	$-0.236065\pi$
$173$	8.21156	+	4.18400i	0.624313	+	0.318104i	−0.113061	+	0.993588i	$0.536065\pi$
$174$	0.705184	+	0.352561i	0.0534598	+	0.0267276i
$175$	0.704802	+	4.98856i	0.0532780	+	0.377099i
$176$		−	0.366065i		−	0.0275932i
$177$	−9.69072	−	13.1264i	−0.728399	−	0.986644i
$178$	−2.00205	−	0.317093i	−0.150060	−	0.0237671i
$179$	−10.9316	+	7.94230i	−0.817069	+	0.593635i	−0.915871	−	0.401472i	$-0.868499\pi$
$179$	−10.9316	+	7.94230i	−0.817069	+	0.593635i	0.0988026	+	0.995107i	$0.468499\pi$
$180$	6.63269	+	1.00372i	0.494371	+	0.0748132i
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.0172639	−	0.999851i	$-0.505496\pi$
$181$	−13.0973	−	9.51573i	−0.973514	−	0.707299i	−0.956250	+	0.292552i	$0.905496\pi$
$182$	1.86769	+	1.86769i	0.138442	+	0.138442i
$183$	−1.79183	−	0.567130i	−0.132456	−	0.0419234i
$184$	6.46034	+	2.09909i	0.476262	+	0.154747i
$185$	12.7395	−	17.2296i	0.936629	−	1.26675i
$186$	0.754909	−	5.01346i	0.0553526	−	0.367604i
$187$	−0.976324	−	1.91614i	−0.0713959	−	0.140122i
$188$	−3.75176	−	7.36324i	−0.273625	−	0.537020i
$189$	−4.60949	+	2.48307i	−0.335291	+	0.180617i
$190$	0.773024	−	1.04548i	0.0560810	−	0.0758469i
$191$	−14.6868	−	4.77202i	−1.06270	−	0.345291i	−0.275058	−	0.961428i	$-0.588697\pi$
$191$	−14.6868	−	4.77202i	−1.06270	−	0.345291i	−0.787639	+	0.616136i	$0.788697\pi$
$192$	0.522656	−	1.65131i	0.0377194	−	0.119173i
$193$	6.05387	+	6.05387i	0.435767	+	0.435767i	0.890585	−	0.454817i	$-0.150296\pi$
$193$	6.05387	+	6.05387i	0.435767	+	0.435767i	−0.454817	+	0.890585i	$0.650296\pi$
$194$	−14.5698	−	10.5856i	−1.04605	−	0.760001i
$195$	−9.65781	+	3.13015i	−0.691610	+	0.224155i
$196$	4.84173	−	3.51772i	0.345838	−	0.251266i
$197$	6.25646	+	0.990925i	0.445754	+	0.0706005i	0.375277	−	0.926913i	$-0.377548\pi$
$197$	6.25646	+	0.990925i	0.445754	+	0.0706005i	0.0704774	+	0.997513i	$0.477548\pi$
$198$	−1.08193	+	0.188318i	−0.0768893	+	0.0133832i
$199$		−	10.3976i		−	0.737069i	−0.929614	−	0.368535i	$-0.879860\pi$
$199$		−	10.3976i		−	0.737069i	0.929614	−	0.368535i	$-0.120140\pi$
$200$	−2.34414	+	4.41645i	−0.165756	+	0.312290i
$201$	10.2648	−	20.5314i	0.724025	−	1.44817i
$202$	0.322847	+	0.164499i	0.0227155	+	0.0115741i
$203$	0.0717494	−	0.453008i	0.00503582	−	0.0317949i
$204$	−1.66837	−	10.0377i	−0.116809	−	0.702777i
$205$	3.51561	+	23.4650i	0.245541	+	1.63887i
$206$	4.66360	−	6.41889i	0.324928	−	0.447225i
$207$	2.88055	−	20.1738i	0.200212	−	1.40217i
$208$	0.410067	+	2.58906i	0.0284331	+	0.179519i
$209$	−0.0657771	+	0.202441i	−0.00454990	+	0.0140031i
$210$	−0.607645	−	3.85490i	−0.0419315	−	0.266013i
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	0.982380	−	0.186896i	$-0.0598427\pi$
$211$	1.12958	+	3.47648i	0.0777632	+	0.239331i	−0.904617	+	0.426226i	$0.859843\pi$
$212$	7.87247	−	4.01122i	0.540683	−	0.275492i
$213$	2.22730	−	0.0169853i	0.152612	−	0.00116382i
$214$	12.1977	−	3.96326i	0.833815	−	0.270923i
$215$	−7.20174	+	21.5498i	−0.491155	+	1.46968i
$216$	−5.14943	−	0.695243i	−0.350374	−	0.0473053i
$217$	−2.91314	+	0.461396i	−0.197757	+	0.0313216i
$218$	3.22451	−	3.22451i	0.218391	−	0.218391i
$219$	−7.61796	−	14.6734i	−0.514774	−	0.991535i
$220$	0.134805	−	0.807369i	0.00908855	−	0.0544328i
$221$	9.05171	+	12.4586i	0.608884	+	0.838057i
$222$	−9.65337	+	13.5021i	−0.647892	+	0.906199i
$223$	−0.959975	+	1.88406i	−0.0642847	+	0.126166i	−0.920913	−	0.389768i	$-0.872555\pi$
$223$	−0.959975	+	1.88406i	−0.0642847	+	0.126166i	0.856628	+	0.515934i	$0.172555\pi$
$224$	−1.00762			−0.0673244
$225$	14.2590	+	4.65627i	0.950600	+	0.310418i
$226$	13.6049			0.904987
$227$	−7.03137	+	13.7998i	−0.466689	+	0.915928i	0.530960	+	0.847397i	$0.321831\pi$
$227$	−7.03137	+	13.7998i	−0.466689	+	0.915928i	−0.997649	+	0.0685314i	$0.978169\pi$
$228$	−0.585758	+	0.819293i	−0.0387928	+	0.0542590i
$229$	−0.971347	−	1.33694i	−0.0641884	−	0.0883477i	0.775716	−	0.631082i	$-0.217389\pi$
$229$	−0.971347	−	1.33694i	−0.0641884	−	0.0883477i	−0.839904	+	0.542735i	$0.817389\pi$
$230$	13.4755	+	7.00867i	0.888548	+	0.462138i
$231$	0.294375	+	0.567013i	0.0193685	+	0.0373067i
$232$	0.321865	−	0.321865i	0.0211315	−	0.0211315i
$233$	−17.2497	+	2.73209i	−1.13007	+	0.178985i	−0.693342	−	0.720609i	$-0.743862\pi$
$233$	−17.2497	+	2.73209i	−1.13007	+	0.178985i	−0.436726	+	0.899594i	$0.643862\pi$
$234$	7.44118	−	2.54389i	0.486445	−	0.166300i
$235$	−5.56309	−	17.6215i	−0.362896	−	1.14950i
$236$	−8.95903	+	2.91096i	−0.583183	+	0.189488i
$237$	21.1370	−	0.161191i	1.37300	−	0.0104705i
$238$	−5.27432	+	2.68740i	−0.341884	+	0.174198i
$239$	−1.97435	−	6.07643i	−0.127710	−	0.393052i	0.866675	−	0.498873i	$-0.166253\pi$
$239$	−1.97435	−	6.07643i	−0.127710	−	0.393052i	−0.994385	+	0.105822i	$0.966253\pi$
$240$	1.76084	−	3.44956i	0.113662	−	0.222668i
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	−0.554993	−	0.831855i	$-0.687279\pi$
$241$	5.94510	−	18.2971i	0.382958	−	1.17862i	0.937951	−	0.346768i	$-0.112721\pi$
$242$	−1.69982	−	10.7322i	−0.109268	−	0.689893i
$243$	0.594232	+	15.5771i	0.0381200	+	0.999273i
$244$	−0.637801	+	0.877858i	−0.0408310	+	0.0561991i
$245$	11.9740	−	5.97547i	0.764992	−	0.381759i
$246$	−3.01342	−	18.1300i	−0.192128	−	1.15593i
$247$	0.238446	−	1.50549i	0.0151719	−	0.0957918i
$248$	−2.60811	−	1.32890i	−0.165615	−	0.0843851i
$249$	−0.734942	+	1.47001i	−0.0465751	+	0.0931582i
$250$	−6.79646	+	8.87739i	−0.429846	+	0.561456i
$251$			10.1849i			0.642864i	0.946933	+	0.321432i	$0.104164\pi$
$251$			10.1849i			0.642864i	−0.946933	+	0.321432i	$0.895836\pi$
$252$	0.518359	+	2.97808i	0.0326535	+	0.187602i
$253$	−2.45599	−	0.388991i	−0.154407	−	0.0244556i
$254$	15.9565	−	11.5931i	1.00120	−	0.727414i
$255$	0.0167590	−	22.7528i	0.00104949	−	1.42484i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−1.62811	−	1.62811i	−0.101558	−	0.101558i	0.654502	−	0.756060i	$-0.272878\pi$
$257$	−1.62811	−	1.62811i	−0.101558	−	0.101558i	−0.756060	+	0.654502i	$0.772878\pi$
$258$	5.31086	−	16.7795i	0.330640	−	1.04464i
$259$	9.18328	+	2.98383i	0.570621	+	0.185406i
$260$	−0.0490156	+	5.86128i	−0.00303982	+	0.363501i
$261$	−1.11687	−	0.785713i	−0.0691327	−	0.0486344i
$262$	4.92018	+	9.65639i	0.303970	+	0.596574i
$263$	7.63791	+	14.9902i	0.470973	+	0.924338i	0.997256	+	0.0740278i	$0.0235854\pi$
$263$	7.63791	+	14.9902i	0.470973	+	0.924338i	−0.526283	+	0.850310i	$0.676415\pi$
$264$	−0.0944078	+	0.626975i	−0.00581040	+	0.0385876i
$265$	18.8402	−	5.94782i	1.15734	−	0.365372i
$266$	0.557233	+	0.181056i	0.0341662	+	0.0111013i
$267$	3.34721	+	1.05943i	0.204846	+	0.0648358i
$268$	−9.37111	−	9.37111i	−0.572432	−	0.572432i
$269$	4.85348	+	3.52626i	0.295922	+	0.215000i	0.725832	−	0.687872i	$-0.241455\pi$
$269$	4.85348	+	3.52626i	0.295922	+	0.215000i	−0.429910	+	0.902872i	$0.641455\pi$
$270$	−11.1012	−	3.42968i	−0.675599	−	0.208724i
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	−0.849021	−	0.528359i	$-0.822808\pi$
$271$	−10.0235	+	7.28250i	−0.608885	+	0.442380i	0.240137	+	0.970739i	$0.422808\pi$
$272$	−5.80242	−	0.919013i	−0.351823	−	0.0557234i
$273$	−2.71720	−	3.68054i	−0.164452	−	0.222757i
$274$		−	8.70132i		−	0.525666i
$275$	0.594635	−	1.73104i	0.0358578	−	0.104386i
$276$	−10.5235	−	5.26132i	−0.633443	−	0.316694i
$277$	5.49796	+	2.80135i	0.330340	+	0.168317i	0.611292	−	0.791405i	$-0.290650\pi$
$277$	5.49796	+	2.80135i	0.330340	+	0.168317i	−0.280952	+	0.959722i	$0.590650\pi$
$278$	0.478765	−	3.02280i	0.0287144	−	0.181296i
$279$	−2.58593	+	8.39207i	−0.154816	+	0.502420i
$280$	−2.22234	−	0.371060i	−0.132810	−	0.0221751i
$281$	−5.28744	+	7.27753i	−0.315422	+	0.434141i	−0.937063	−	0.349161i	$-0.886467\pi$
$281$	−5.28744	+	7.27753i	−0.315422	+	0.434141i	0.621640	+	0.783303i	$0.286467\pi$
$282$	4.52683	+	13.5789i	0.269569	+	0.808613i
$283$	2.05054	+	12.9466i	0.121892	+	0.769594i	0.970594	+	0.240723i	$0.0773845\pi$
$283$	2.05054	+	12.9466i	0.121892	+	0.769594i	−0.848702	+	0.528871i	$0.822615\pi$
$284$	0.397386	−	1.22303i	0.0235805	−	0.0725733i
$285$	−1.59362	+	1.59127i	−0.0943978	+	0.0942589i
$286$	−0.296526	−	0.912614i	−0.0175340	−	0.0539640i
$287$	−9.52650	+	4.85400i	−0.562332	+	0.286522i
$288$	−1.32105	+	2.69348i	−0.0778434	+	0.158715i
$289$	−16.6555	+	5.41171i	−0.979737	+	0.318336i
$290$	0.828414	−	0.591357i	0.0486461	−	0.0347257i
$291$	22.2243	+	21.8879i	1.30281	+	1.28309i
$292$	−9.42784	+	1.49322i	−0.551722	+	0.0873842i
$293$	9.52977	−	9.52977i	0.556735	−	0.556735i	−0.371641	−	0.928376i	$-0.621205\pi$
$293$	9.52977	−	9.52977i	0.556735	−	0.556735i	0.928376	+	0.371641i	$0.121205\pi$
$294$	−9.19985	+	4.77627i	−0.536546	+	0.278558i
$295$	−20.8314	+	3.12104i	−1.21285	+	0.181714i
$296$	5.63266	+	7.75269i	0.327392	+	0.450616i
$297$	1.90163	−	0.0435122i	0.110344	−	0.00252484i
$298$	−2.65942	+	5.21941i	−0.154056	+	0.302353i
$299$	17.8062			1.02976
$300$	5.15391	−	6.95969i	0.297561	−	0.401818i
$301$	−10.2387			−0.590150
$302$	−1.65696	+	3.25196i	−0.0953472	+	0.187129i
$303$	−0.510530	−	0.365006i	−0.0293292	−	0.0209691i
$304$	0.341785	+	0.470426i	0.0196027	+	0.0269808i
$305$	−1.72997	+	1.70127i	−0.0990577	+	0.0974147i
$306$	0.268789	+	17.6222i	0.0153657	+	1.00739i
$307$	13.4223	−	13.4223i	0.766053	−	0.766053i	−0.211356	−	0.977409i	$-0.567788\pi$
$307$	13.4223	−	13.4223i	0.766053	−	0.766053i	0.977409	+	0.211356i	$0.0677880\pi$
$308$	0.364313	−	0.0577015i	0.0207587	−	0.00328785i
$309$	−9.64297	+	9.79118i	−0.548569	+	0.557001i
$310$	−5.26291	−	3.89138i	−0.298913	−	0.221016i
$311$	−20.3576	+	6.61457i	−1.15437	+	0.375078i	−0.822788	−	0.568348i	$-0.807583\pi$
$311$	−20.3576	+	6.61457i	−1.15437	+	0.375078i	−0.331583	+	0.943426i	$0.607583\pi$
$312$	−0.0346232	−	4.54016i	−0.00196015	−	0.257036i
$313$	11.3795	−	5.79816i	0.643210	−	0.327732i	−0.101781	−	0.994807i	$-0.532454\pi$
$313$	11.3795	−	5.79816i	0.643210	−	0.327732i	0.744990	+	0.667075i	$0.232454\pi$
$314$	0.994222	+	3.05990i	0.0561072	+	0.172680i
$315$	0.0465665	+	6.75916i	0.00262372	+	0.380835i
$316$	3.77118	−	11.6065i	0.212146	−	0.652917i
$317$	4.33787	+	27.3883i	0.243639	+	1.53828i	0.741460	+	0.670997i	$0.234134\pi$
$317$	4.33787	+	27.3883i	0.243639	+	1.53828i	−0.497821	+	0.867280i	$0.665866\pi$
$318$	−14.5180	+	4.83989i	−0.814129	+	0.271408i
$319$	−0.0979413	+	0.134805i	−0.00548366	+	0.00754761i
$320$	−1.56786	−	1.59431i	−0.0876461	−	0.0891244i
$321$	−21.9136	+	3.64228i	−1.22310	+	0.203292i
$322$	−1.07072	+	6.76029i	−0.0596692	+	0.376736i
$323$	3.04372	+	1.55085i	0.169357	+	0.0862917i
$324$	8.64035	+	2.51881i	0.480019	+	0.139934i
$325$	−2.26655	+	12.9092i	−0.125725	+	0.716074i
$326$		−	3.69881i		−	0.204858i
$327$	−6.35436	+	4.69116i	−0.351397	+	0.259422i
$328$	−10.4804	−	1.65992i	−0.578681	−	0.0916540i
$329$	6.73663	−	4.89445i	0.371402	−	0.269840i
$330$	−0.439106	+	1.34805i	−0.0241720	+	0.0742077i
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	0.918826	−	0.394664i	$-0.129139\pi$
$331$	15.0534	+	10.9369i	0.827410	+	0.601149i	−0.0914151	+	0.995813i	$0.529139\pi$
$332$	0.670954	+	0.670954i	0.0368234	+	0.0368234i
$333$	20.0159	−	20.6360i	1.09687	−	1.13084i
$334$	8.68968	+	2.82345i	0.475478	+	0.154492i
$335$	−17.2174	−	24.1193i	−0.940685	−	1.31778i
$336$	1.72579	+	0.259864i	0.0941498	+	0.0141767i
$337$	−9.42193	−	18.4916i	−0.513245	−	1.00730i	−0.991625	−	0.129148i	$-0.958776\pi$
$337$	−9.42193	−	18.4916i	−0.513245	−	1.00730i	0.478380	−	0.878153i	$-0.341224\pi$
$338$	−2.78232	−	5.46062i	−0.151339	−	0.297019i
$339$	−23.3018	−	3.50870i	−1.26558	−	0.190566i
$340$	−12.4590	−	4.16368i	−0.675685	−	0.225807i
$341$	1.01908	+	0.331120i	0.0551864	+	0.0179312i
$342$	1.21455	−	1.25217i	0.0656752	−	0.0677097i
$343$	9.25153	+	9.25153i	0.499536	+	0.499536i
$344$	−8.22066	−	5.97266i	−0.443228	−	0.322024i
$345$	−21.2725	−	15.4794i	−1.14528	−	0.833381i
$346$	−7.45594	+	5.41706i	−0.400834	+	0.291223i
$347$	−7.36133	−	1.16592i	−0.395177	−	0.0625898i	−0.0443161	−	0.999018i	$-0.514111\pi$
$347$	−7.36133	−	1.16592i	−0.395177	−	0.0625898i	−0.350861	+	0.936428i	$0.614111\pi$
$348$	−0.634281	+	0.468264i	−0.0340010	+	0.0251016i
$349$		−	16.1042i		−	0.862040i	−0.902342	−	0.431020i	$-0.858154\pi$
$349$		−	16.1042i		−	0.862040i	0.902342	−	0.431020i	$-0.141846\pi$
$350$	−4.76481	−	1.63677i	−0.254690	−	0.0874893i
$351$	−13.4009	+	2.43796i	−0.715287	+	0.130129i
$352$	0.326166	+	0.166190i	0.0173847	+	0.00885796i
$353$	0.0677049	−	0.427472i	0.00360357	−	0.0227520i	−0.985821	−	0.167800i	$-0.946334\pi$
$353$	0.0677049	−	0.427472i	0.00360357	−	0.0227520i	0.989425	+	0.145048i	$0.0463337\pi$
$354$	16.0952	−	2.67521i	0.855453	−	0.142186i
$355$	1.32683	−	2.55109i	0.0704210	−	0.135398i
$356$	1.19144	−	1.63988i	0.0631463	−	0.0869135i
$357$	9.72664	−	3.24259i	0.514788	−	0.171616i
$358$	−2.11378	−	13.3459i	−0.111717	−	0.705352i
$359$	0.0683480	−	0.210354i	0.00360727	−	0.0111020i	−0.949237	−	0.314563i	$-0.898142\pi$
$359$	0.0683480	−	0.210354i	0.00360727	−	0.0111020i	0.952844	+	0.303461i	$0.0981421\pi$
$360$	−3.90550	+	5.45409i	−0.205838	+	0.287456i
$361$	5.76684	+	17.7485i	0.303518	+	0.934132i
$362$	14.4246	−	7.34971i	0.758141	−	0.386292i
$363$	0.143521	+	18.8199i	0.00753287	+	0.987789i
$364$	−2.51204	+	0.816210i	−0.131666	+	0.0427810i
$365$	−21.3433	−	0.178486i	−1.11716	−	0.00934238i
$366$	1.31879	−	1.33906i	0.0689342	−	0.0699936i
$367$	16.4940	−	2.61239i	0.860980	−	0.136366i	0.289697	−	0.957119i	$-0.406446\pi$
$367$	16.4940	−	2.61239i	0.860980	−	0.136366i	0.571284	+	0.820753i	$0.306446\pi$
$368$	−4.80323	+	4.80323i	−0.250386	+	0.250386i
$369$	0.485488	+	31.8293i	0.0252735	+	1.65697i
$370$	9.56807	+	19.1731i	0.497420	+	0.996762i
$371$	5.23293	+	7.20252i	0.271680	+	0.373936i
$372$	4.12430	+	2.94869i	0.213835	+	0.152882i
$373$	0.0479661	−	0.0941389i	0.00248359	−	0.00487433i	−0.889761	−	0.456426i	$-0.849129\pi$
$373$	0.0479661	−	0.0941389i	0.00248359	−	0.00487433i	0.892245	+	0.451552i	$0.149129\pi$
$374$	2.15054			0.111202
$375$	13.9301	−	13.4519i	0.719345	−	0.694653i
$376$	8.26396			0.426181
$377$	0.541700	−	1.06315i	0.0278990	−	0.0547548i
$378$	−0.119771	−	5.23438i	−0.00616033	−	0.269227i
$379$	−5.78536	−	7.96287i	−0.297174	−	0.409025i	0.634154	−	0.773207i	$-0.281349\pi$
$379$	−5.78536	−	7.96287i	−0.297174	−	0.409025i	−0.931328	+	0.364182i	$0.881349\pi$
$380$	0.580582	+	1.16341i	0.0297832	+	0.0596815i
$381$	−30.3192	+	15.7408i	−1.55330	+	0.806426i
$382$	10.9196	−	10.9196i	0.558693	−	0.558693i
$383$	32.8669	−	5.20561i	1.67942	−	0.265994i	0.757349	−	0.653010i	$-0.226494\pi$
$383$	32.8669	−	5.20561i	1.67942	−	0.265994i	0.922073	+	0.387016i	$0.126494\pi$
$384$	1.23405	+	1.21537i	0.0629748	+	0.0620216i
$385$	0.824754	+	0.00689710i	0.0420334	+	0.000351509i
$386$	−8.14244	+	2.64564i	−0.414439	+	0.134659i
$387$	−13.4235	+	27.3692i	−0.682357	+	1.39126i
$388$	16.0464	−	8.17604i	0.814632	−	0.415076i
$389$	−10.3312	−	31.7962i	−0.523814	−	1.61213i	−0.766650	−	0.642066i	$-0.778078\pi$
$389$	−10.3312	−	31.7962i	−0.523814	−	1.61213i	0.242836	−	0.970067i	$-0.421922\pi$
$390$	1.59557	−	10.0262i	0.0807948	−	0.507698i
$391$	−12.3316	+	37.9528i	−0.623637	+	1.91936i
$392$	0.936214	+	5.91102i	0.0472859	+	0.298552i
$393$	−5.93662	−	17.8078i	−0.299463	−	0.898286i
$394$	−3.72329	+	5.12467i	−0.187577	+	0.258177i
$395$	12.5916	−	24.2098i	0.633554	−	1.21813i
$396$	0.323392	−	1.04950i	0.0162511	−	0.0527393i
$397$	2.14742	−	13.5583i	0.107776	−	0.680471i	−0.873349	−	0.487096i	$-0.838056\pi$
$397$	2.14742	−	13.5583i	0.107776	−	0.680471i	0.981125	−	0.193376i	$-0.0619437\pi$
$398$	9.26436	+	4.72043i	0.464381	+	0.236614i
$399$	−0.907703	−	0.453812i	−0.0454420	−	0.0227190i
$400$	−2.87087	−	4.09367i	−0.143543	−	0.204683i
$401$		−	8.63025i		−	0.430974i	−0.976507	−	0.215487i	$-0.930866\pi$
$401$		−	8.63025i		−	0.430974i	0.976507	−	0.215487i	$-0.0691339\pi$
$402$	13.6335	+	18.4671i	0.679977	+	0.921055i
$403$	−7.57858	−	1.20033i	−0.377516	−	0.0597926i
$404$	−0.293139	+	0.212978i	−0.0145842	+	0.0105961i
$405$	18.1290	+	8.73716i	0.900839	+	0.434153i
$406$	0.371060	+	0.269591i	0.0184154	+	0.0133796i
$407$	−2.48049	−	2.48049i	−0.122953	−	0.122953i
$408$	9.70104	+	3.07047i	0.480273	+	0.152011i
$409$	−25.9908	−	8.44492i	−1.28516	−	0.417574i	−0.414767	−	0.909928i	$-0.636137\pi$
$409$	−25.9908	−	8.44492i	−1.28516	−	0.417574i	−0.870395	+	0.492353i	$0.836137\pi$
$410$	−22.5035	−	7.52046i	−1.11137	−	0.371409i
$411$	−2.24406	+	14.9031i	−0.110691	+	0.735117i
$412$	3.60205	+	7.06941i	0.177460	+	0.348285i
$413$	−4.30921	−	8.45731i	−0.212043	−	0.416157i
$414$	16.6672	+	11.7253i	0.819150	+	0.576267i
$415$	1.23273	+	1.72689i	0.0605124	+	0.0847699i
$416$	−2.49304	−	0.810037i	−0.122231	−	0.0397154i
$417$	−1.59958	+	5.05381i	−0.0783317	+	0.247486i
$418$	−0.150514	−	0.150514i	−0.00736189	−	0.00736189i
$419$	20.8362	+	15.1384i	1.01791	+	0.739557i	0.965854	−	0.259087i	$-0.0834215\pi$
$419$	20.8362	+	15.1384i	1.01791	+	0.739557i	0.0520594	+	0.998644i	$0.483421\pi$
$420$	3.71060	+	1.20867i	0.181059	+	0.0589771i
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.398419	−	0.917203i	$-0.369559\pi$
$421$	28.5994	−	20.7787i	1.39385	−	1.01269i	0.995431	−	0.0954876i	$-0.0304410\pi$
$422$	−3.61038	−	0.571828i	−0.175751	−	0.0278362i
$423$	−4.25130	−	24.4247i	−0.206705	−	1.18757i
$424$			8.83548i			0.429089i
$425$	−25.9455	−	13.7712i	−1.25854	−	0.668003i
$426$	−0.996037	+	1.99225i	−0.0482582	+	0.0965246i
$427$	−0.974191	−	0.496375i	−0.0471444	−	0.0240213i
$428$	−2.00633	+	12.6675i	−0.0969797	+	0.612306i
$429$	0.272511	+	1.63955i	0.0131570	+	0.0791581i
$430$	−15.9315	−	16.2002i	−0.768285	−	0.781243i
$431$	19.9752	−	27.4935i	0.962171	−	1.32432i	0.0162678	−	0.999868i	$-0.494822\pi$
$431$	19.9752	−	27.4935i	0.962171	−	1.32432i	0.945904	−	0.324448i	$-0.105178\pi$
$432$	2.95726	−	4.27254i	0.142281	−	0.205563i
$433$	2.98384	+	18.8393i	0.143394	+	0.905357i	0.949541	+	0.313641i	$0.101549\pi$
$433$	2.98384	+	18.8393i	0.143394	+	0.905357i	−0.806147	+	0.591715i	$0.798451\pi$
$434$	0.911432	−	2.80510i	0.0437501	−	0.134649i
$435$	−1.57137	+	0.799196i	−0.0753414	+	0.0383185i
$436$	1.40916	+	4.33696i	0.0674867	+	0.207703i
$437$	3.51936	−	1.79320i	0.168354	−	0.0857806i
$438$	16.5326	−	0.126077i	0.789956	−	0.00602420i
$439$	33.6517	−	10.9341i	1.60611	−	0.521856i	0.637499	−	0.770451i	$-0.279969\pi$
$439$	33.6517	−	10.9341i	1.60611	−	0.521856i	0.968607	+	0.248596i	$0.0799691\pi$
$440$	0.658171	+	0.486650i	0.0313771	+	0.0232001i
$441$	16.9888	−	5.80790i	0.808989	−	0.276567i
$442$	−15.2101	+	2.40904i	−0.723470	+	0.114586i
$443$	10.2497	−	10.2497i	0.486977	−	0.486977i	−0.420374	−	0.907351i	$-0.638101\pi$
$443$	10.2497	−	10.2497i	0.486977	−	0.486977i	0.907351	+	0.420374i	$0.138101\pi$
$444$	−7.64789	−	14.7310i	−0.362953	−	0.699104i
$445$	3.23166	−	3.17806i	0.153195	−	0.150655i
$446$	−1.24289	−	1.71069i	−0.0588524	−	0.0810034i
$447$	5.90099	−	8.25365i	0.279107	−	0.390384i
$448$	0.457450	−	0.897796i	0.0216125	−	0.0424169i
$449$	−9.47944			−0.447362			−0.223681	−	0.974662i	$-0.571807\pi$
$449$	−9.47944			−0.447362			−0.223681	+	0.974662i	$0.571807\pi$
$450$	−10.6222	+	10.5910i	−0.500736	+	0.499263i
$451$	3.88431			0.182905
$452$	−6.17652	+	12.1221i	−0.290519	+	0.570175i
$453$	3.67662	−	5.14245i	0.172743	−	0.241613i
$454$	−9.10358	−	12.5300i	−0.427252	−	0.588062i
$455$	−5.84096	+	0.875112i	−0.273828	+	0.0410259i
$456$	−0.464067	−	0.893866i	−0.0217319	−	0.0418591i
$457$	−25.4852	+	25.4852i	−1.19215	+	1.19215i	−0.215682	+	0.976464i	$0.569197\pi$
$457$	−25.4852	+	25.4852i	−1.19215	+	1.19215i	−0.976464	+	0.215682i	$0.930803\pi$
$458$	1.63221	−	0.258516i	0.0762681	−	0.0120797i
$459$	4.08438	−	30.2516i	0.190642	−	1.41202i
$460$	−12.3625	+	8.82489i	−0.576405	+	0.411463i
$461$	−21.4340	+	6.96431i	−0.998279	+	0.324360i	−0.762178	−	0.647368i	$-0.775870\pi$
$461$	−21.4340	+	6.96431i	−0.998279	+	0.324360i	−0.236101	+	0.971728i	$0.575870\pi$
$462$	−0.638856	+	0.00487191i	−0.0297223	+	0.000226662i
$463$	5.05300	−	2.57463i	0.234833	−	0.119653i	−0.332615	−	0.943063i	$-0.607931\pi$
$463$	5.05300	−	2.57463i	0.234833	−	0.119653i	0.567448	+	0.823409i	$0.307931\pi$
$464$	0.140660	+	0.432908i	0.00652999	+	0.0200972i
$465$	8.01042	+	8.02223i	0.371475	+	0.372022i
$466$	5.39691	−	16.6100i	0.250007	−	0.769442i
$467$	−1.81829	−	11.4802i	−0.0841404	−	0.531242i	−0.993371	−	0.114950i	$-0.963329\pi$
$467$	−1.81829	−	11.4802i	−0.0841404	−	0.531242i	0.909231	−	0.416292i	$-0.136671\pi$
$468$	−1.11160	+	7.78505i	−0.0513838	+	0.359864i
$469$	7.84913	−	10.8034i	0.362439	−	0.498854i
$470$	18.2265	+	3.04324i	0.840724	+	0.140374i
$471$	−0.913702	−	5.49723i	−0.0421011	−	0.253299i
$472$	1.47363	−	9.30410i	0.0678291	−	0.428256i
$473$	3.31427	+	1.68871i	0.152390	+	0.0776467i
$474$	−9.45238	+	18.9064i	−0.434162	+	0.868399i
$475$	0.852065	+	2.77974i	0.0390954	+	0.127543i
$476$		−	5.91951i		−	0.271320i
$477$	26.1138	−	4.54531i	1.19567	−	0.208116i
$478$	6.31048	+	0.999482i	0.288635	+	0.0457152i
$479$	2.20406	−	1.60135i	0.100706	−	0.0731673i	−0.536293	−	0.844032i	$-0.680176\pi$
$479$	2.20406	−	1.60135i	0.100706	−	0.0731673i	0.636999	+	0.770865i	$0.280176\pi$
$480$	2.27417	+	3.13499i	0.103801	+	0.143092i
$481$	20.3224	+	14.7651i	0.926622	+	0.673230i
$482$	13.6039	+	13.6039i	0.619639	+	0.619639i
$483$	3.57735	−	11.3025i	0.162775	−	0.514282i
$484$	10.3342	+	3.35778i	0.469735	+	0.152626i
$485$	38.4017	−	12.1234i	1.74373	−	0.550495i
$486$	−14.1491	−	6.54240i	−0.641816	−	0.296769i
$487$	−12.3082	−	24.1563i	−0.557739	−	1.09462i	−0.981964	−	0.189068i	$-0.939453\pi$
$487$	−12.3082	−	24.1563i	−0.557739	−	1.09462i	0.424225	−	0.905557i	$-0.360547\pi$
$488$	−0.492622	−	0.966824i	−0.0222999	−	0.0437661i
$489$	−0.953920	+	6.33512i	−0.0431378	+	0.286484i
$490$	−0.111906	+	13.3817i	−0.00505541	+	0.604525i
$491$	−37.5268	−	12.1932i	−1.69356	−	0.550271i	−0.706095	−	0.708117i	$-0.749545\pi$
$491$	−37.5268	−	12.1932i	−1.69356	−	0.550271i	−0.987464	+	0.157846i	$0.949545\pi$
$492$	17.5221	+	5.54590i	0.789955	+	0.250028i
$493$	1.89088	+	1.89088i	0.0851609	+	0.0851609i
$494$	1.23315	+	0.895933i	0.0554819	+	0.0403099i
$495$	1.09974	−	2.19562i	0.0494295	−	0.0986857i
$496$	2.36811	−	1.72054i	0.106331	−	0.0772543i
$497$	1.27981	+	0.202702i	0.0574075	+	0.00909245i
$498$	−0.976133	−	1.32221i	−0.0437416	−	0.0592496i
$499$		−	11.3155i		−	0.506552i	−0.967394	−	0.253276i	$-0.918492\pi$
$499$		−	11.3155i		−	0.506552i	0.967394	−	0.253276i	$-0.0815081\pi$
$500$	−4.82428	−	10.0859i	−0.215749	−	0.451057i
$501$	−14.1550	−	7.07690i	−0.632400	−	0.316173i
$502$	−9.07480	−	4.62384i	−0.405028	−	0.206372i
$503$	−1.34669	+	8.50269i	−0.0600461	+	0.379116i	0.939305	+	0.343084i	$0.111472\pi$
$503$	−1.34669	+	8.50269i	−0.0600461	+	0.379116i	−0.999351	+	0.0360317i	$0.988528\pi$
$504$	−2.88882	−	0.890161i	−0.128678	−	0.0396509i
$505$	−0.724959	+	0.361781i	−0.0322603	+	0.0160990i
$506$	1.46159	−	2.01171i	0.0649756	−	0.0894312i
$507$	3.35712	+	10.0702i	0.149095	+	0.447233i
$508$	3.08541	+	19.4805i	0.136893	+	0.864307i
$509$	0.697725	−	2.14738i	0.0309261	−	0.0951808i	−0.934402	−	0.356220i	$-0.884065\pi$
$509$	0.697725	−	2.14738i	0.0309261	−	0.0951808i	0.965328	+	0.261039i	$0.0840653\pi$
$510$	20.2653	+	10.3445i	0.897362	+	0.458062i
$511$	−2.97215	−	9.14735i	−0.131480	−	0.404655i
$512$	0.891007	−	0.453990i	0.0393773	−	0.0200637i
$513$	−2.40314	+	1.83142i	−0.106101	+	0.0808591i
$514$	2.18980	−	0.711508i	0.0965878	−	0.0313833i
$515$	5.34110	+	16.9183i	0.235357	+	0.745510i
$516$	12.5395	+	12.3497i	0.552022	+	0.543666i
$517$	−2.98790	+	0.473237i	−0.131408	+	0.0208129i
$518$	−6.82773	+	6.82773i	−0.299993	+	0.299993i
$519$	14.1672	−	7.35515i	0.621869	−	0.322855i
$520$	−5.20019	−	2.70464i	−0.228043	−	0.118606i
$521$	13.0319	+	17.9369i	0.570938	+	0.785829i	0.992665	−	0.120894i	$-0.0385760\pi$
$521$	13.0319	+	17.9369i	0.570938	+	0.785829i	−0.421727	+	0.906723i	$0.638576\pi$
$522$	1.20713	−	0.638435i	0.0528345	−	0.0279435i
$523$	−5.09249	+	9.99457i	−0.222679	+	0.437032i	−0.975135	−	0.221610i	$-0.928869\pi$
$523$	−5.09249	+	9.99457i	−0.222679	+	0.437032i	0.752456	+	0.658642i	$0.228869\pi$
$524$	−10.8376			−0.473444
$525$	7.73877	+	4.03221i	0.337748	+	0.175980i
$526$	−16.8239			−0.733558
$527$	7.80694	−	15.3220i	0.340076	−	0.667436i
$528$	−0.515779	−	0.368759i	−0.0224464	−	0.0160482i
$529$	13.6026	+	18.7224i	0.591417	+	0.814016i
$530$	−3.25370	+	19.4870i	−0.141332	+	0.846459i
$531$	−28.2570	+	0.431000i	−1.22625	+	0.0187038i
$532$	−0.414301	+	0.414301i	−0.0179622	+	0.0179622i
$533$	−27.4725	+	4.35122i	−1.18997	+	0.188472i
$534$	−2.46356	+	2.50142i	−0.106609	+	0.108247i
$535$	−9.08989	+	27.1998i	−0.392990	+	1.17595i
$536$	12.6041	−	4.09532i	0.544415	−	0.176891i
$537$	0.178473	+	23.4032i	0.00770167	+	1.00992i
$538$	−5.34536	+	2.72359i	−0.230455	+	0.117423i
$539$	−0.676991	−	2.08356i	−0.0291601	−	0.0897455i
$540$	8.09572	−	8.33422i	0.348384	−	0.358648i
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	−0.864867	−	0.502001i	$-0.832597\pi$
$541$	3.02125	−	9.29846i	0.129894	−	0.399772i	0.994761	+	0.102229i	$0.0325974\pi$
$542$	−1.93818	−	12.2372i	−0.0832520	−	0.525632i
$543$	−26.6012	+	8.86807i	−1.14156	+	0.380565i
$544$	3.45309	−	4.75277i	0.148050	−	0.203773i
$545$	1.51086	+	10.0842i	0.0647180	+	0.431962i
$546$	4.51297	−	0.750106i	0.193137	−	0.0321016i
$547$	−1.65483	+	10.4482i	−0.0707555	+	0.446732i	0.926722	+	0.375748i	$0.122614\pi$
$547$	−1.65483	+	10.4482i	−0.0707555	+	0.446732i	−0.997477	+	0.0709846i	$0.977386\pi$
$548$	7.75294	+	3.95032i	0.331189	+	0.168749i
$549$	−2.60409	+	1.95335i	−0.111140	+	0.0833668i
$550$	1.27241	+	1.31570i	0.0542557	+	0.0561016i
$551$		−	0.264681i		−	0.0112758i
$552$	9.46545	−	6.98796i	0.402876	−	0.297427i
$553$	12.1454	+	1.92364i	0.516475	+	0.0818016i
$554$	−4.99204	+	3.62693i	−0.212092	+	0.154094i
$555$	−11.4429	−	35.3062i	−0.485725	−	1.49866i
$556$	2.47598	+	1.79891i	0.105005	+	0.0762906i
$557$	2.23937	+	2.23937i	0.0948850	+	0.0948850i	0.752956	−	0.658071i	$-0.228627\pi$
$557$	2.23937	+	2.23937i	0.0948850	+	0.0948850i	−0.658071	+	0.752956i	$0.728627\pi$
$558$	−6.30340	−	6.11400i	−0.266844	−	0.258826i
$559$	−25.3325	−	8.23103i	−1.07145	−	0.348135i
$560$	1.33954	−	1.81166i	0.0566059	−	0.0765567i
$561$	−3.68332	−	0.554622i	−0.155510	−	0.0234162i
$562$	−4.08388	−	8.01507i	−0.172268	−	0.338095i
$563$	4.61877	+	9.06485i	0.194658	+	0.382038i	0.967619	−	0.252416i	$-0.0812251\pi$
$563$	4.61877	+	9.06485i	0.194658	+	0.382038i	−0.772961	+	0.634454i	$0.781225\pi$
$564$	−14.1540	−	2.13127i	−0.595993	−	0.0897425i
$565$	−18.0865	+	24.4612i	−0.760907	+	1.02909i
$566$	−12.4664	−	4.05058i	−0.524002	−	0.170259i
$567$	−1.14480	+	8.99603i	−0.0480772	+	0.377798i
$568$	0.909316	+	0.909316i	0.0381541	+	0.0381541i
$569$	−10.0063	−	7.26997i	−0.419484	−	0.304773i	0.357946	−	0.933742i	$-0.383477\pi$
$569$	−10.0063	−	7.26997i	−0.419484	−	0.304773i	−0.777430	+	0.628969i	$0.783477\pi$
$570$	−0.694347	−	2.14235i	−0.0290830	−	0.0897331i
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.00179324	−	0.999998i	$-0.499429\pi$
$571$	22.7821	−	16.5522i	0.953402	−	0.692687i	0.951609	+	0.307311i	$0.0994292\pi$
$572$	0.947765	+	0.150111i	0.0396281	+	0.00627647i
$573$	−21.5185	+	15.8862i	−0.898949	+	0.663657i
$574$		−	10.6918i		−	0.446269i
$575$	−30.5158	+	14.9111i	−1.27260	+	0.621835i
$576$	−1.80017	−	2.39988i	−0.0750069	−	0.0999948i
$577$	−9.96640	−	5.07813i	−0.414907	−	0.211405i	0.234060	−	0.972222i	$-0.424799\pi$
$577$	−9.96640	−	5.07813i	−0.414907	−	0.211405i	−0.648967	+	0.760817i	$0.724799\pi$
$578$	2.73958	−	17.2971i	0.113952	−	0.719463i
$579$	14.6282	−	2.43137i	0.607928	−	0.101044i
$580$	0.150811	+	1.00659i	0.00626209	+	0.0417965i
$581$	−0.561983	+	0.773503i	−0.0233150	+	0.0320903i
$582$	−29.5919	+	9.86511i	−1.22662	+	0.408922i
$583$	−0.505965	−	3.19454i	−0.0209549	−	0.132304i
$584$	2.94968	−	9.07817i	0.122059	−	0.375657i
$585$	−5.31855	+	16.7609i	−0.219895	+	0.692976i
$586$	4.16466	+	12.8175i	0.172041	+	0.529487i
$587$	−0.534451	+	0.272317i	−0.0220592	+	0.0112397i	−0.464985	−	0.885318i	$-0.653940\pi$
$587$	−0.534451	+	0.272317i	−0.0220592	+	0.0112397i	0.442926	+	0.896558i	$0.353940\pi$
$588$	−0.0790473	−	10.3655i	−0.00325986	−	0.427466i
$589$	−1.61877	+	0.525971i	−0.0667003	+	0.0216722i
$590$	6.67641	−	19.9779i	0.274863	−	0.822476i
$591$	7.69869	−	7.81701i	0.316682	−	0.321549i
$592$	−9.46487	+	1.49909i	−0.389004	+	0.0616122i
$593$	1.69633	−	1.69633i	0.0696598	−	0.0696598i	−0.671419	−	0.741078i	$-0.734315\pi$
$593$	1.69633	−	1.69633i	0.0696598	−	0.0696598i	0.741078	+	0.671419i	$0.234315\pi$
$594$	−0.824553	+	1.71412i	−0.0338318	+	0.0703312i
$595$	2.17989	−	13.0557i	0.0893666	−	0.535231i
$596$	−3.44318	−	4.73913i	−0.141038	−	0.194122i
$597$	−14.6501	−	10.4742i	−0.599588	−	0.428678i
$598$	−8.08385	+	15.8654i	−0.330573	+	0.648786i
$599$	−12.0681			−0.493088			−0.246544	−	0.969132i	$-0.579295\pi$
$599$	−12.0681			−0.493088			−0.246544	+	0.969132i	$0.579295\pi$
$600$	3.86130	+	7.75180i	0.157637	+	0.316466i
$601$	8.03062			0.327576			0.163788	−	0.986496i	$-0.447629\pi$
$601$	8.03062			0.327576			0.163788	+	0.986496i	$0.447629\pi$
$602$	4.64828	−	9.12277i	0.189450	−	0.371816i
$603$	−18.5880	−	35.1455i	−0.756963	−	1.43123i
$604$	−2.14528	−	2.95272i	−0.0872900	−	0.120144i
$605$	21.5559	+	11.2113i	0.876371	+	0.455804i
$606$	0.556999	−	0.289176i	0.0226265	−	0.0117470i
$607$	−27.1756	+	27.1756i	−1.10302	+	1.10302i	−0.108980	+	0.994044i	$0.534758\pi$
$607$	−27.1756	+	27.1756i	−1.10302	+	1.10302i	−0.994044	+	0.108980i	$0.965242\pi$
$608$	−0.574320	+	0.0909634i	−0.0232918	+	0.00368905i
$609$	−0.566002	−	0.557435i	−0.0229356	−	0.0225884i
$610$	−0.730457	−	2.31378i	−0.0295753	−	0.0936820i
$611$	20.6024	−	6.69412i	0.833483	−	0.270815i
$612$	−15.8235	−	7.76082i	−0.639628	−	0.313712i
$613$	−25.9627	+	13.2287i	−1.04862	+	0.534300i	−0.891379	−	0.453259i	$-0.850261\pi$
$613$	−25.9627	+	13.2287i	−1.04862	+	0.534300i	−0.157245	+	0.987560i	$0.550261\pi$
$614$	5.86577	+	18.0530i	0.236723	+	0.728560i
$615$	36.6032	+	18.6842i	1.47598	+	0.753422i
$616$	−0.113982	+	0.350801i	−0.00459248	+	0.0141342i
$617$	3.00048	+	18.9443i	0.120795	+	0.762667i	0.971503	+	0.237029i	$0.0761736\pi$
$617$	3.00048	+	18.9443i	0.120795	+	0.762667i	−0.850708	+	0.525639i	$0.823826\pi$
$618$	−4.34618	−	13.0371i	−0.174829	−	0.524427i
$619$	11.4117	−	15.7069i	0.458676	−	0.631314i	−0.515557	−	0.856855i	$-0.672415\pi$
$619$	11.4117	−	15.7069i	0.458676	−	0.631314i	0.974234	+	0.225541i	$0.0724151\pi$
$620$	5.85656	−	2.92263i	0.235205	−	0.117376i
$621$	−25.5227	−	24.3809i	−1.02419	−	0.978371i
$622$	3.34851	−	21.1417i	0.134263	−	0.847704i
$623$	1.81984	+	0.927252i	0.0729102	+	0.0371496i
$624$	4.06103	+	2.03034i	0.162571	+	0.0812786i
$625$	−6.92594	−	24.0215i	−0.277038	−	0.960859i
$626$			12.7716i			0.510454i
$627$	0.218975	+	0.296609i	0.00874500	+	0.0118454i
$628$	−3.17776	−	0.503308i	−0.126806	−	0.0200842i
$629$	−45.5451	+	33.0905i	−1.81600	+	1.31940i
$630$	−6.04360	−	3.02710i	−0.240783	−	0.120603i
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	0.750850	−	0.660472i	$-0.229644\pi$
$631$	8.91070	+	6.47400i	0.354729	+	0.257726i	−0.396121	+	0.918198i	$0.629644\pi$
$632$	8.62939	+	8.62939i	0.343259	+	0.343259i
$633$	6.03618	+	1.91051i	0.239917	+	0.0759359i
$634$	−26.3725	−	8.56893i	−1.04738	−	0.340316i
$635$	−0.368801	+	44.1012i	−0.0146354	+	1.75010i
$636$	2.27866	−	15.1329i	0.0903547	−	0.600058i
$637$	7.12216	+	13.9780i	0.282190	+	0.553830i
$638$	−0.0756474	−	0.148466i	−0.00299491	−	0.00587784i
$639$	2.21975	−	3.15533i	0.0878121	−	0.124823i
$640$	2.13233	−	0.673175i	0.0842878	−	0.0266096i
$641$	41.8679	+	13.6037i	1.65368	+	0.537314i	0.979533	−	0.201283i	$-0.0645109\pi$
$641$	41.8679	+	13.6037i	1.65368	+	0.537314i	0.674148	+	0.738596i	$0.264511\pi$
$642$	6.70326	−	21.1787i	0.264557	−	0.835857i
$643$	21.0709	+	21.0709i	0.830957	+	0.830957i	0.987648	−	0.156691i	$-0.0500826\pi$
$643$	21.0709	+	21.0709i	0.830957	+	0.830957i	−0.156691	+	0.987648i	$0.550083\pi$
$644$	−5.53736	−	4.02313i	−0.218203	−	0.158534i
$645$	23.1085	+	31.8555i	0.909898	+	1.25431i
$646$	−2.76364	+	2.00790i	−0.108734	+	0.0789998i
$647$	32.0404	+	5.07470i	1.25964	+	0.199507i	0.750322	−	0.661073i	$-0.229899\pi$
$647$	32.0404	+	5.07470i	1.25964	+	0.199507i	0.509316	+	0.860580i	$0.329899\pi$
$648$	−6.16691	+	6.55509i	−0.242259	+	0.257508i
$649$			3.44836i			0.135360i
$650$	−10.4732	−	7.88017i	−0.410793	−	0.309086i
$651$	−2.28448	+	4.56935i	−0.0895358	+	0.179087i
$652$	3.29567	+	1.67923i	0.129068	+	0.0657636i
$653$	−4.84433	+	30.5859i	−0.189573	+	1.19692i	0.690945	+	0.722907i	$0.257195\pi$
$653$	−4.84433	+	30.5859i	−0.189573	+	1.19692i	−0.880518	+	0.474012i	$0.842805\pi$
$654$	−1.29504	−	7.79152i	−0.0506400	−	0.304672i
$655$	−23.9028	−	3.99100i	−0.933958	−	0.155941i
$656$	6.23698	−	8.58447i	0.243513	−	0.335167i
$657$	−28.3485	−	4.04779i	−1.10598	−	0.157919i
$658$	1.30262	+	8.22441i	0.0507814	+	0.320621i
$659$	−6.85074	+	21.0844i	−0.266867	+	0.821332i	0.724390	+	0.689390i	$0.242121\pi$
$659$	−6.85074	+	21.0844i	−0.266867	+	0.821332i	−0.991257	+	0.131942i	$0.957879\pi$
$660$	−1.00177	−	1.00325i	−0.0389939	−	0.0390514i
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	−0.936056	−	0.351852i	$-0.885552\pi$
$661$	−9.91334	−	30.5101i	−0.385584	−	1.18671i	0.550471	−	0.834854i	$-0.314448\pi$
$662$	−16.5790	+	8.44742i	−0.644361	+	0.328318i
$663$	26.6723	−	0.203403i	1.03587	−	0.00789950i
$664$	−0.902431	+	0.293218i	−0.0350211	+	0.0113790i
$665$	−1.06632	+	0.761187i	−0.0413503	+	0.0295176i
$666$	9.29975	+	27.2028i	0.360358	+	1.05409i
$667$	3.05392	−	0.483694i	0.118248	−	0.0187287i
$668$	−6.46075	+	6.46075i	−0.249974	+	0.249974i
$669$	1.68756	+	3.25051i	0.0652449	+	0.125672i
$670$	29.3069	−	4.39087i	1.13223	−	0.169634i
$671$	0.233477	+	0.321353i	0.00901327	+	0.0124057i
$672$	−1.01503	+	1.41972i	−0.0391558	+	0.0547668i
$673$	17.0242	−	33.4118i	0.656234	−	1.28793i	−0.287676	−	0.957728i	$-0.592883\pi$
$673$	17.0242	−	33.4118i	0.656234	−	1.28793i	0.943910	−	0.330204i	$-0.107117\pi$
$674$	20.7536			0.799398
$675$	20.9245	−	15.4001i	0.805385	−	0.592752i
$676$	6.12860			0.235715
$677$	13.6443	−	26.7784i	0.524391	−	1.02918i	−0.465192	−	0.885210i	$-0.654015\pi$
$677$	13.6443	−	26.7784i	0.524391	−	1.02918i	0.989583	−	0.143966i	$-0.0459855\pi$
$678$	13.7051	−	19.1691i	0.526340	−	0.736185i
$679$	10.6662	+	14.6808i	0.409333	+	0.563399i
$680$	9.36614	−	9.21079i	0.359175	−	0.353218i
$681$	12.3606	+	23.8085i	0.473660	+	0.912343i
$682$	−0.757684	+	0.757684i	−0.0290132	+	0.0290132i
$683$	−32.9389	+	5.21701i	−1.26037	+	0.199623i	−0.750640	−	0.660711i	$-0.770255\pi$
$683$	−32.9389	+	5.21701i	−1.26037	+	0.199623i	−0.509731	+	0.860334i	$0.670255\pi$
$684$	0.564301	+	1.65064i	0.0215766	+	0.0631140i
$685$	15.6447	+	11.5676i	0.597752	+	0.441976i
$686$	−12.4433	+	4.04307i	−0.475087	+	0.154365i
$687$	−2.86222	+	0.0218273i	−0.109201	+	0.000832763i
$688$	9.05378	−	4.61313i	0.345172	−	0.175874i
$689$	7.15707	+	22.0272i	0.272663	+	0.839169i
$690$	23.4497	−	11.9265i	0.892716	−	0.454034i
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	−0.941188	−	0.337883i	$-0.890289\pi$
$691$	0.495555	−	1.52516i	0.0188518	−	0.0580199i	0.960040	+	0.279863i	$0.0902891\pi$
$692$	−1.44171	−	9.10259i	−0.0548055	−	0.346028i
$693$	1.09545	+	0.156416i	0.0416128	+	0.00594175i
$694$	4.38081	−	6.02967i	0.166293	−	0.228883i
$695$	4.79841	+	4.87934i	0.182014	+	0.185084i
$696$	−0.129268	−	0.777736i	−0.00489991	−	0.0294800i
$697$	9.75164	−	61.5694i	0.369370	−	2.33211i
$698$	14.3490	+	7.31117i	0.543117	+	0.276732i
$699$	−13.5272	+	27.0568i	−0.511646	+	1.02338i
$700$	3.62155	−	3.50240i	0.136882	−	0.132378i
$701$		−	17.1529i		−	0.647855i	−0.946082	−	0.323928i	$-0.894997\pi$
$701$		−	17.1529i		−	0.647855i	0.946082	−	0.323928i	$-0.105003\pi$
$702$	3.91164	−	13.0471i	0.147635	−	0.492431i
$703$	5.50363	+	0.871689i	0.207573	+	0.0328764i
$704$	−0.296153	+	0.215168i	−0.0111617	+	0.00810943i
$705$	−30.4324	−	9.91287i	−1.14615	−	0.373340i
$706$	0.350143	+	0.254394i	0.0131778	+	0.00957423i
$707$	−0.258165	−	0.258165i	−0.00970931	−	0.00970931i
$708$	−4.92346	+	15.5555i	−0.185035	+	0.584611i
$709$	43.3999	+	14.1015i	1.62992	+	0.529592i	0.974252	−	0.225460i	$-0.0723886\pi$
$709$	43.3999	+	14.1015i	1.62992	+	0.529592i	0.655664	+	0.755052i	$0.272389\pi$
$710$	1.67067	+	2.34039i	0.0626991	+	0.0878332i
$711$	21.0654	−	29.9440i	0.790015	−	1.12299i
$712$	0.920240	+	1.80607i	0.0344875	+	0.0676855i
$713$	−9.02694	−	17.7164i	−0.338062	−	0.663483i
$714$	−1.52664	+	10.1386i	−0.0571329	+	0.379428i
$715$	2.03505	+	0.680094i	0.0761066	+	0.0254341i
$716$	12.8509	+	4.17551i	0.480261	+	0.156046i
$717$	−10.5505	−	3.33932i	−0.394014	−	0.124709i
$718$	0.156397	+	0.156397i	0.00583669	+	0.00583669i
$719$	18.8277	+	13.6791i	0.702155	+	0.510145i	0.880633	−	0.473798i	$-0.157117\pi$
$719$	18.8277	+	13.6791i	0.702155	+	0.510145i	−0.178478	+	0.983944i	$0.557117\pi$
$720$	−3.08657	−	5.95593i	−0.115030	−	0.221964i
$721$	−6.46780	+	4.69913i	−0.240874	+	0.175005i
$722$	−18.4321	−	2.91936i	−0.685973	−	0.108647i
$723$	−19.7915	−	26.8083i	−0.736053	−	0.997012i
$724$			16.1891i			0.601664i
$725$	−0.0380628	+	2.27561i	−0.00141362	+	0.0845142i
$726$	−16.8338	−	8.41618i	−0.624762	−	0.312354i
$727$	24.2957	+	12.3793i	0.901077	+	0.459122i	0.842213	−	0.539144i	$-0.181252\pi$
$727$	24.2957	+	12.3793i	0.901077	+	0.459122i	0.0588635	+	0.998266i	$0.481252\pi$
$728$	0.413192	−	2.60879i	0.0153139	−	0.0966882i
$729$	22.5465	+	14.8545i	0.835055	+	0.550166i
$730$	9.84870	−	18.9360i	0.364517	−	0.700853i
$731$	35.0879	−	48.2943i	1.29777	−	1.78623i
$732$	0.594391	+	1.78297i	0.0219693	+	0.0659004i
$733$	−0.915975	−	5.78324i	−0.0338323	−	0.213609i	0.964981	−	0.262322i	$-0.0844881\pi$
$733$	−0.915975	−	5.78324i	−0.0338323	−	0.213609i	−0.998813	+	0.0487128i	$0.984488\pi$
$734$	−5.16046	+	15.8823i	−0.190476	+	0.586225i
$735$	3.64280	−	22.8906i	0.134367	−	0.844333i
$736$	−2.09909	−	6.46034i	−0.0773735	−	0.238131i
$737$	−4.32260	+	2.20247i	−0.159225	+	0.0811292i
$738$	−28.5805	−	14.0176i	−1.05206	−	0.515995i
$739$	10.9906	−	3.57105i	0.404295	−	0.131363i	−0.0998086	−	0.995007i	$-0.531823\pi$
$739$	10.9906	−	3.57105i	0.404295	−	0.131363i	0.504103	+	0.863643i	$0.331823\pi$
$740$	−21.4272	−	0.179187i	−0.787678	−	0.00658705i
$741$	−1.88100	−	1.85253i	−0.0691003	−	0.0680544i
$742$	−8.79319	+	1.39270i	−0.322808	+	0.0511278i
$743$	5.09866	−	5.09866i	0.187052	−	0.187052i	−0.607369	−	0.794420i	$-0.707775\pi$
$743$	5.09866	−	5.09866i	0.187052	−	0.187052i	0.794420	+	0.607369i	$0.207775\pi$
$744$	−4.49969	+	2.33610i	−0.164967	+	0.0856456i
$745$	−5.84885	−	11.7203i	−0.214285	−	0.429398i
$746$	0.0621022	+	0.0854763i	0.00227372	+	0.00312951i
$747$	1.33087	+	2.51635i	0.0486939	+	0.0920684i
$748$	−0.976324	+	1.91614i	−0.0356980	+	0.0700612i
$749$	−12.9231			−0.472200
$750$	5.66160	+	18.5188i	0.206733	+	0.676211i
$751$	−19.8804			−0.725445			−0.362723	−	0.931897i	$-0.618153\pi$
$751$	−19.8804			−0.725445			−0.362723	+	0.931897i	$0.618153\pi$
$752$	−3.75176	+	7.36324i	−0.136813	+	0.268510i
$753$	14.3503	+	10.2598i	0.522954	+	0.373889i
$754$	0.701343	+	0.965316i	0.0255414	+	0.0351547i
$755$	−3.64413	−	7.30234i	−0.132624	−	0.265759i
$756$	4.71824	+	2.26964i	0.171601	+	0.0825460i
$757$	−16.4335	+	16.4335i	−0.597285	+	0.597285i	−0.939589	−	0.342304i	$-0.888793\pi$
$757$	−16.4335	+	16.4335i	−0.597285	+	0.597285i	0.342304	+	0.939589i	$0.388793\pi$
$758$	9.72147	−	1.53973i	0.353100	−	0.0559255i
$759$	−3.02214	+	3.06859i	−0.109697	+	0.111383i
$760$	−1.30018	−	0.0108729i	−0.0471625	−	0.000394402i
$761$	4.02479	−	1.30773i	0.145898	−	0.0474052i	−0.235157	−	0.971957i	$-0.575561\pi$
$761$	4.02479	−	1.30773i	0.145898	−	0.0474052i	0.381056	+	0.924552i	$0.375561\pi$
$762$	−0.260510	−	34.1608i	−0.00943729	−	1.23752i
$763$	−4.09408	+	2.08604i	−0.148216	+	0.0755197i
$764$	4.77202	+	14.6868i	0.172646	+	0.531349i
$765$	−32.0414	−	22.9438i	−1.15846	−	0.829536i
$766$	−10.2830	+	31.6480i	−0.371542	+	1.14349i
$767$	−3.86287	−	24.3892i	−0.139480	−	0.880642i
$768$	−1.64315	+	0.547779i	−0.0592920	+	0.0197663i
$769$	4.46592	−	6.14681i	0.161045	−	0.221660i	−0.720867	−	0.693073i	$-0.756256\pi$
$769$	4.46592	−	6.14681i	0.161045	−	0.221660i	0.881912	+	0.471414i	$0.156256\pi$
$770$	−0.380576	+	0.731730i	−0.0137150	+	0.0263697i
$771$	−3.93406	+	0.653884i	−0.141682	+	0.0235491i
$772$	1.33931	−	8.45606i	0.0482028	−	0.304340i
$773$	−12.3217	−	6.27822i	−0.443181	−	0.225812i	0.218136	−	0.975918i	$-0.430002\pi$
$773$	−12.3217	−	6.27822i	−0.443181	−	0.225812i	−0.661317	+	0.750106i	$0.730002\pi$
$774$	−18.2920	−	24.3858i	−0.657493	−	0.876531i
$775$	13.9931	−	4.28927i	0.502648	−	0.154075i
$776$			18.0093i			0.646495i
$777$	13.4550	−	9.93329i	0.482696	−	0.356355i
$778$	33.0209	+	5.23000i	1.18386	+	0.187505i
$779$	−4.99169	+	3.62668i	−0.178846	+	0.129939i
$780$	8.20906	+	5.97347i	0.293931	+	0.213885i
$781$	−0.380843	−	0.276698i	−0.0136276	−	0.00990105i
$782$	−28.2178	−	28.2178i	−1.00907	−	1.00907i
$783$	−2.23215	+	0.782159i	−0.0797704	+	0.0279521i
$784$	−5.69179	−	1.84937i	−0.203278	−	0.0660491i
$785$	−6.82332	−	2.28029i	−0.243535	−	0.0813869i
$786$	18.5621	+	2.79501i	0.662087	+	0.0996947i
$787$	−5.14950	−	10.1065i	−0.183560	−	0.360257i	0.780829	−	0.624745i	$-0.214797\pi$
$787$	−5.14950	−	10.1065i	−0.183560	−	0.360257i	−0.964389	+	0.264488i	$0.914797\pi$
$788$	−2.87578	−	5.64403i	−0.102445	−	0.201060i
$789$	28.8151	+	4.33888i	1.02584	+	0.154468i
$790$	15.8546	+	22.2103i	0.564082	+	0.790205i
$791$	−13.0377	−	4.23619i	−0.463566	−	0.150622i
$792$	0.788294	+	0.764608i	0.0280108	+	0.0271691i
$793$	−2.01129	−	2.01129i	−0.0714229	−	0.0714229i
$794$	11.1056	+	8.06871i	0.394124	+	0.286348i
$795$	10.5984	−	32.5370i	0.375887	−	1.15397i
$796$	−8.41187	+	6.11158i	−0.298151	+	0.216619i
$797$	−43.6682	−	6.91637i	−1.54681	−	0.244990i	−0.676107	−	0.736804i	$-0.736334\pi$
$797$	−43.6682	−	6.91637i	−1.54681	−	0.244990i	−0.870701	+	0.491813i	$0.836334\pi$
$798$	0.816439	−	0.602743i	0.0289016	−	0.0213369i
$799$			48.5487i			1.71753i
$800$	4.95083	−	0.699472i	0.175038	−	0.0247301i
$801$	4.86456	−	3.64894i	0.171881	−	0.128929i
$802$	7.68961	+	3.91805i	0.271529	+	0.138351i
$803$	−0.546616	+	3.45120i	−0.0192897	+	0.121790i
$804$	−22.6438	+	3.76365i	−0.798585	+	0.132734i
$805$	−10.7313	−	10.9123i	−0.378229	−	0.384609i
$806$	4.51010	−	6.20762i	0.158862	−	0.218654i
$807$	9.85763	−	3.28626i	0.347005	−	0.115682i
$808$	−0.0566825	−	0.357879i	−0.00199408	−	0.0125901i
$809$	6.33598	−	19.5001i	0.222761	−	0.685589i	−0.775750	−	0.631040i	$-0.782628\pi$
$809$	6.33598	−	19.5001i	0.222761	−	0.685589i	0.998511	−	0.0545481i	$-0.0173718\pi$
$810$	−16.0153	+	12.1865i	−0.562720	+	0.428190i
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	−0.810108	−	0.586280i	$-0.800592\pi$
$811$	−14.2198	−	43.7640i	−0.499324	−	1.53676i	0.310785	−	0.950480i	$-0.399408\pi$
$812$	−0.408664	+	0.208225i	−0.0143413	+	0.00730726i
$813$	0.163646	+	21.4590i	0.00573933	+	0.752601i
$814$	3.33626	−	1.08402i	0.116936	−	0.0379947i
$815$	6.65033	+	4.91724i	0.232951	+	0.172243i
$816$	−7.13999	+	7.24973i	−0.249950	+	0.253791i
$817$	−5.83584	+	0.924305i	−0.204170	+	0.0323374i
$818$	19.3241	−	19.3241i	0.675650	−	0.675650i
$819$	−7.92301	+	0.120849i	−0.276852	+	0.00422279i
$820$	16.9172	−	16.6366i	0.590773	−	0.580974i
$821$	5.32407	+	7.32795i	0.185811	+	0.255747i	0.891753	−	0.452523i	$-0.149476\pi$
$821$	5.32407	+	7.32795i	0.185811	+	0.255747i	−0.705942	+	0.708270i	$0.749476\pi$
$822$	−12.2600	−	8.76535i	−0.427617	−	0.305727i
$823$	−21.6070	+	42.4061i	−0.753173	+	1.47819i	0.121042	+	0.992647i	$0.461376\pi$
$823$	−21.6070	+	42.4061i	−0.753173	+	1.47819i	−0.874216	+	0.485538i	$0.838624\pi$
$824$	−7.93419			−0.276401
$825$	−1.83999	−	2.58161i	−0.0640603	−	0.0898800i
$826$	9.49186			0.330264
$827$	21.7292	−	42.6460i	0.755599	−	1.48295i	−0.116276	−	0.993217i	$-0.537096\pi$
$827$	21.7292	−	42.6460i	0.755599	−	1.48295i	0.871875	−	0.489729i	$-0.162904\pi$
$828$	−18.0141	+	9.52744i	−0.626032	+	0.331101i
$829$	−8.53245	−	11.7439i	−0.296344	−	0.407883i	0.634718	−	0.772744i	$-0.281116\pi$
$829$	−8.53245	−	11.7439i	−0.296344	−	0.407883i	−0.931062	+	0.364861i	$0.881116\pi$
$830$	−2.09832	+	0.314378i	−0.0728338	+	0.0109122i
$831$	9.48547	−	4.92456i	0.329047	−	0.170831i
$832$	1.85356	−	1.85356i	0.0642608	−	0.0642608i
$833$	−34.7258	+	5.50002i	−1.20318	+	0.190564i
$834$	−3.77678	−	3.71962i	−0.130779	−	0.128800i
$835$	−16.6286	+	11.8702i	−0.575457	+	0.410786i
$836$	0.202441	−	0.0657771i	0.00700157	−	0.00227495i
$837$	9.21931	+	12.0974i	0.318666	+	0.418146i
$838$	−22.9478	+	11.6925i	−0.792719	+	0.403910i
$839$	1.29678	+	3.99108i	0.0447698	+	0.137787i	0.970943	−	0.239311i	$-0.0769217\pi$
$839$	1.29678	+	3.99108i	0.0447698	+	0.137787i	−0.926173	+	0.377099i	$0.876922\pi$
$840$	−2.76151	+	2.75745i	−0.0952812	+	0.0951410i
$841$	−8.89747	+	27.3836i	−0.306809	+	0.944262i
$842$	5.53008	+	34.9156i	0.190579	+	1.20327i
$843$	4.92756	+	14.7810i	0.169714	+	0.509084i
$844$	2.14858	−	2.95727i	0.0739572	−	0.101793i
$845$	13.5168	+	2.25688i	0.464993	+	0.0776391i
$846$	23.6926	+	7.30062i	0.814568	+	0.251001i
$847$	−1.71277	+	10.8140i	−0.0588514	+	0.371573i
$848$	−7.87247	−	4.01122i	−0.270342	−	0.137746i
$849$	20.3071	+	10.1527i	0.696938	+	0.348439i
$850$	24.0493	−	16.8656i	0.824884	−	0.578486i
$851$			65.0944i			2.23141i
$852$	−1.32291	−	1.79194i	−0.0453223	−	0.0613907i
$853$	−53.4919	−	8.47229i	−1.83153	−	0.290086i	−0.857161	−	0.515049i	$-0.827774\pi$
$853$	−53.4919	−	8.47229i	−1.83153	−	0.290086i	−0.974367	+	0.224963i	$0.927774\pi$
$854$	0.884547	−	0.642661i	0.0302686	−	0.0219914i
$855$	0.636728	+	3.84836i	0.0217756	+	0.131611i
$856$	−10.3760	−	7.53857i	−0.354643	−	0.257663i
$857$	25.7274	+	25.7274i	0.878831	+	0.878831i	0.993414	−	0.114583i	$-0.0365532\pi$
$857$	25.7274	+	25.7274i	0.878831	+	0.878831i	−0.114583	+	0.993414i	$0.536553\pi$
$858$	−1.58456	−	0.501530i	−0.0540961	−	0.0171219i
$859$	−6.06408	−	1.97034i	−0.206904	−	0.0672271i	0.203731	−	0.979027i	$-0.434693\pi$
$859$	−6.06408	−	1.97034i	−0.206904	−	0.0672271i	−0.410635	+	0.911800i	$0.634693\pi$
$860$	21.6672	−	6.84033i	0.738847	−	0.233253i
$861$	−2.75742	+	18.3124i	−0.0939725	+	0.624084i
$862$	15.4283	+	30.2798i	0.525491	+	1.03133i
$863$	−21.0090	−	41.2325i	−0.715155	−	1.40357i	−0.906567	−	0.422062i	$-0.861307\pi$
$863$	−21.0090	−	41.2325i	−0.715155	−	1.40357i	0.191412	−	0.981510i	$-0.438693\pi$
$864$	2.46430	+	4.57463i	0.0838370	+	0.155632i
$865$	0.172328	−	20.6070i	0.00585934	−	0.700659i
$866$	−18.1405	−	5.89422i	−0.616440	−	0.200294i
$867$	−9.15310	+	28.9189i	−0.310855	+	0.982137i
$868$	2.08558	+	2.08558i	0.0707892	+	0.0707892i
$869$	−3.61419	−	2.62586i	−0.122603	−	0.0890763i
$870$	0.00129852	−	1.76293i	4.40239e−5	−	0.0597689i
$871$	28.1052	−	20.4196i	0.952308	−	0.691892i
$872$	−4.50400	−	0.713364i	−0.152525	−	0.0241576i
$873$	53.2276	−	9.26467i	1.80148	−	0.313562i
$874$			3.94987i			0.133606i
$875$	9.27724	−	6.39101i	0.313628	−	0.216056i
$876$	−7.39329	+	14.7879i	−0.249796	+	0.499635i
$877$	51.8670	+	26.4275i	1.75142	+	0.892395i	0.959469	+	0.281815i	$0.0909364\pi$
$877$	51.8670	+	26.4275i	1.75142	+	0.892395i	0.791955	+	0.610580i	$0.209064\pi$
$878$	−5.53519	+	34.9478i	−0.186804	+	1.17943i
$879$	−3.82737	−	23.0272i	−0.129094	−	0.776687i
$880$	−0.732412	+	0.365500i	−0.0246896	+	0.0123210i
$881$	13.4206	−	18.4718i	0.452151	−	0.622332i	−0.520707	−	0.853735i	$-0.674332\pi$
$881$	13.4206	−	18.4718i	0.452151	−	0.622332i	0.972858	+	0.231403i	$0.0743317\pi$
$882$	−2.53787	+	17.7738i	−0.0854544	+	0.598476i
$883$	−8.64665	−	54.5928i	−0.290983	−	1.83719i	−0.508408	−	0.861116i	$-0.669766\pi$
$883$	−8.64665	−	54.5928i	−0.290983	−	1.83719i	0.217425	−	0.976077i	$-0.430234\pi$
$884$	4.75877	−	14.6460i	0.160055	−	0.492597i
$885$	−16.5872	+	32.4951i	−0.557574	+	1.09231i
$886$	4.47927	+	13.7858i	0.150484	+	0.463142i
$887$	20.4932	−	10.4418i	0.688093	−	0.350601i	−0.0747341	−	0.997203i	$-0.523811\pi$
$887$	20.4932	−	10.4418i	0.688093	−	0.350601i	0.762827	+	0.646603i	$0.223811\pi$
$888$	16.5975	−	0.126572i	0.556976	−	0.00424749i
$889$	−18.9009	+	6.14128i	−0.633917	+	0.205972i
$890$	1.36453	+	4.32224i	0.0457391	+	0.144882i
$891$	1.85432	−	2.72320i	0.0621220	−	0.0912305i
$892$	2.08849	−	0.330785i	0.0699279	−	0.0110755i
$893$	3.39787	−	3.39787i	0.113706	−	0.113706i
$894$	4.67506	+	9.00490i	0.156358	+	0.301169i
$895$	26.8055	+	13.9416i	0.896009	+	0.466018i
$896$	0.592264	+	0.815182i	0.0197862	+	0.0272333i
$897$	17.9372	−	25.0886i	0.598907	−	0.837685i
$898$	4.30358	−	8.44624i	0.143612	−	0.281855i
$899$	−1.33240			−0.0444380
$900$	−4.61423	−	14.2727i	−0.153808	−	0.475755i
$901$	−51.9062			−1.72925
$902$	−1.76344	+	3.46095i	−0.0587161	+	0.115237i
$903$	−10.3141	+	14.4262i	−0.343231	+	0.480073i
$904$	−7.99679	−	11.0066i	−0.265969	−	0.366075i
$905$	−5.96172	+	35.7057i	−0.198174	+	1.18690i
$906$	2.91280	+	5.61051i	0.0967714	+	0.186397i
$907$	−26.0875	+	26.0875i	−0.866221	+	0.866221i	−0.992052	−	0.125831i	$-0.959840\pi$
$907$	−26.0875	+	26.0875i	−0.866221	+	0.866221i	0.125831	+	0.992052i	$0.459840\pi$
$908$	15.2973	−	2.42285i	0.507657	−	0.0804050i
$909$	−1.02857	+	0.351635i	−0.0341157	+	0.0116630i
$910$	1.87201	−	5.60162i	0.0620565	−	0.185692i
$911$	−20.1733	+	6.55470i	−0.668371	+	0.217167i	−0.623497	−	0.781826i	$-0.714289\pi$
$911$	−20.1733	+	6.55470i	−0.668371	+	0.217167i	−0.0448740	+	0.998993i	$0.514289\pi$
$912$	1.00712	−	0.00768031i	0.0333491	−	0.000254320i
$913$	0.309490	−	0.157693i	0.0102426	−	0.00521888i
$914$	−11.1374	−	34.2775i	−0.368393	−	1.13380i
$915$	0.654365	+	4.15129i	0.0216326	+	0.137237i
$916$	−0.510667	+	1.57167i	−0.0168729	+	0.0519295i
$917$	−1.70830	−	10.7858i	−0.0564129	−	0.356177i
$918$	25.1001	+	17.3732i	0.828427	+	0.573399i
$919$	−20.7352	+	28.5396i	−0.683991	+	0.941433i	−0.999973	−	0.00733203i	$-0.997666\pi$
$919$	−20.7352	+	28.5396i	−0.683991	+	0.941433i	0.315982	+	0.948765i	$0.397666\pi$
$920$	−2.25057	−	15.0215i	−0.0741992	−	0.495244i
$921$	−5.39071	−	32.4329i	−0.177630	−	1.06870i
$922$	3.52556	−	22.2595i	0.116108	−	0.733079i
$923$	3.00354	+	1.53038i	0.0988627	+	0.0503731i
$924$	0.285694	−	0.571436i	0.00939863	−	0.0187989i
$925$	−47.1924	−	8.28585i	−1.55168	−	0.272437i
$926$			5.67112i			0.186364i
$927$	4.08165	+	23.4500i	0.134059	+	0.770199i
$928$	−0.449582	−	0.0712068i	−0.0147583	−	0.00233748i
$929$	34.9866	−	25.4192i	1.14787	−	0.833978i	0.159676	−	0.987169i	$-0.448955\pi$
$929$	34.9866	−	25.4192i	1.14787	−	0.833978i	0.988197	+	0.153191i	$0.0489551\pi$
$930$	−10.7845	+	3.49532i	−0.353638	+	0.114616i
$931$	2.81536	+	2.04548i	0.0922698	+	0.0670379i
$932$	12.3494	+	12.3494i	0.404520	+	0.404520i
$933$	−11.1876	+	35.3467i	−0.366264	+	1.15720i
$934$	11.0544	+	3.59181i	0.361713	+	0.117528i
$935$	−2.85895	+	3.86659i	−0.0934976	+	0.126451i
$936$	−6.43187	−	4.52478i	−0.210232	−	0.147897i
$937$	−11.3158	−	22.2086i	−0.369672	−	0.725523i	0.628980	−	0.777421i	$-0.283473\pi$
$937$	−11.3158	−	22.2086i	−0.369672	−	0.725523i	−0.998652	+	0.0518988i	$0.983473\pi$
$938$	6.06247	+	11.8983i	0.197947	+	0.388492i
$939$	3.29377	−	21.8744i	0.107488	−	0.713844i
$940$	−10.9862	+	14.8583i	−0.358330	+	0.484624i
$941$	−0.769225	−	0.249936i	−0.0250760	−	0.00814769i	0.296452	−	0.955048i	$-0.404196\pi$
$941$	−0.769225	−	0.249936i	−0.0250760	−	0.00814769i	−0.321528	+	0.946900i	$0.604196\pi$
$942$	5.31288	+	1.68158i	0.173103	+	0.0547887i
$943$	−50.9671	−	50.9671i	−1.65972	−	1.65972i
$944$	7.62100	+	5.53698i	0.248043	+	0.180213i
$945$	9.57044	+	6.74329i	0.311326	+	0.219359i
$946$	−3.00929	+	2.18638i	−0.0978406	+	0.0710854i
$947$	−11.9668	−	1.89535i	−0.388868	−	0.0615907i	−0.0410609	−	0.999157i	$-0.513074\pi$
$947$	−11.9668	−	1.89535i	−0.388868	−	0.0615907i	−0.347808	+	0.937566i	$0.613074\pi$
$948$	−12.5544	−	17.0054i	−0.407749	−	0.552311i
$949$		−	25.0216i		−	0.812235i
$950$	−2.86359	−	0.502778i	−0.0929072	−	0.0163123i
$951$	42.9593	+	21.4778i	1.39305	+	0.696466i
$952$	5.27432	+	2.68740i	0.170942	+	0.0870992i
$953$	−2.11321	+	13.3423i	−0.0684536	+	0.432199i	0.929531	+	0.368744i	$0.120212\pi$
$953$	−2.11321	+	13.3423i	−0.0684536	+	0.432199i	−0.997985	+	0.0634554i	$0.979788\pi$
$954$	−7.80552	+	25.3311i	−0.252713	+	0.820125i
$955$	5.11640	+	34.1495i	0.165563	+	1.10505i
$956$	−3.75544	+	5.16892i	−0.121460	+	0.167175i
$957$	0.0912752	+	0.273794i	0.00295051	+	0.00885051i
$958$	0.426186	+	2.69083i	0.0137694	+	0.0869368i
$959$	−2.70935	+	8.33851i	−0.0874893	+	0.269264i
$960$	−3.82575	+	0.603050i	−0.123475	+	0.0194634i
$961$	−6.93181	−	21.3339i	−0.223607	−	0.688190i
$962$	−22.3820	+	11.4042i	−0.721624	+	0.367686i
$963$	−16.9429	+	34.5449i	−0.545978	+	1.11319i
$964$	−18.2971	+	5.94510i	−0.589311	+	0.191479i
$965$	6.06787	−	18.1569i	0.195332	−	0.584493i
$966$	8.44652	+	8.31867i	0.271762	+	0.267649i
$967$	−11.0440	+	1.74919i	−0.355150	+	0.0562502i	−0.331460	−	0.943469i	$-0.607541\pi$
$967$	−11.0440	+	1.74919i	−0.355150	+	0.0562502i	−0.0236894	+	0.999719i	$0.507541\pi$
$968$	−7.68342	+	7.68342i	−0.246954	+	0.246954i
$969$	5.25124	−	2.72628i	0.168694	−	0.0875806i
$970$	−6.63200	+	39.7201i	−0.212941	+	1.27534i
$971$	−15.8802	−	21.8573i	−0.509621	−	0.701434i	0.474234	−	0.880399i	$-0.342725\pi$
$971$	−15.8802	−	21.8573i	−0.509621	−	0.701434i	−0.983855	+	0.178965i	$0.942725\pi$
$972$	12.2529	−	9.63675i	0.393011	−	0.309099i
$973$	−1.40002	+	2.74769i	−0.0448825	+	0.0880868i
$974$	27.1112			0.868699
$975$	15.9056	+	16.1977i	0.509387	+	0.518743i
$976$	1.08509			0.0347330
$977$	−11.9623	+	23.4774i	−0.382709	+	0.751109i	−0.999347	−	0.0361382i	$-0.988494\pi$
$977$	−11.9623	+	23.4774i	−0.382709	+	0.751109i	0.616638	+	0.787247i	$0.288494\pi$
$978$	−5.21156	−	3.72603i	−0.166647	−	0.119145i
$979$	−0.436145	−	0.600303i	−0.0139393	−	0.0191858i
$980$	−11.8724	−	6.17489i	−0.379250	−	0.197250i
$981$	0.208642	+	13.6789i	0.00666142	+	0.436732i
$982$	27.9010	−	27.9010i	0.890357	−	0.890357i
$983$	42.8297	−	6.78356i	1.36606	−	0.216362i	0.570029	−	0.821624i	$-0.306932\pi$
$983$	42.8297	−	6.78356i	1.36606	−	0.216362i	0.796026	+	0.605263i	$0.206932\pi$
$984$	−12.8963	+	13.0945i	−0.411118	+	0.417437i
$985$	−4.26419	−	13.5071i	−0.135868	−	0.430373i
$986$	−2.54323	+	0.826344i	−0.0809928	+	0.0263162i
$987$	−0.109984	−	14.4222i	−0.00350083	−	0.459065i
$988$	−1.35812	+	0.691996i	−0.0432075	+	0.0220153i
$989$	−21.3295	−	65.6454i	−0.678238	−	2.08740i
$990$	1.45704	+	1.97666i	0.0463078	+	0.0628224i
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	0.647275	+	0.762256i	$0.275908\pi$
$991$	−10.2129	+	31.4322i	−0.324424	+	0.998476i	−0.971700	+	0.236220i	$0.924092\pi$
$992$	0.457907	+	2.89111i	0.0145386	+	0.0917929i
$993$	30.5741	−	10.1926i	0.970241	−	0.323451i
$994$	−0.761632	+	1.04830i	−0.0241575	+	0.0332500i
$995$	−20.8033	+	10.3816i	−0.659509	+	0.329119i
$996$	1.62125	−	0.269470i	0.0513713	−	0.00853849i
$997$	−5.70379	+	36.0123i	−0.180641	+	1.14052i	0.716111	+	0.697986i	$0.245920\pi$
$997$	−5.70379	+	36.0123i	−0.180641	+	1.14052i	−0.896752	+	0.442534i	$0.854080\pi$
$998$	10.0822	+	5.13714i	0.319147	+	0.162613i
$999$	−8.91250	−	48.9899i	−0.281979	−	1.54997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.83.3	yes	80
3.2	odd	2	inner	150.2.l.a.83.8	yes	80
5.2	odd	4		750.2.l.c.107.1		80
5.3	odd	4		750.2.l.a.107.10		80
5.4	even	2		750.2.l.b.143.8		80
15.2	even	4		750.2.l.c.107.10		80
15.8	even	4		750.2.l.a.107.1		80
15.14	odd	2		750.2.l.b.143.3		80
25.3	odd	20		750.2.l.b.257.3		80
25.4	even	10		750.2.l.a.743.1		80
25.21	even	5		750.2.l.c.743.10		80
25.22	odd	20	inner	150.2.l.a.47.8	yes	80
75.29	odd	10		750.2.l.a.743.10		80
75.47	even	20	inner	150.2.l.a.47.3	✓	80
75.53	even	20		750.2.l.b.257.8		80
75.71	odd	10		750.2.l.c.743.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.47.3	✓	80	75.47	even	20	inner
150.2.l.a.47.8	yes	80	25.22	odd	20	inner
150.2.l.a.83.3	yes	80	1.1	even	1	trivial
150.2.l.a.83.8	yes	80	3.2	odd	2	inner
750.2.l.a.107.1		80	15.8	even	4
750.2.l.a.107.10		80	5.3	odd	4
750.2.l.a.743.1		80	25.4	even	10
750.2.l.a.743.10		80	75.29	odd	10
750.2.l.b.143.3		80	15.14	odd	2
750.2.l.b.143.8		80	5.4	even	2
750.2.l.b.257.3		80	25.3	odd	20
750.2.l.b.257.8		80	75.53	even	20
750.2.l.c.107.1		80	5.2	odd	4
750.2.l.c.107.10		80	15.2	even	4
750.2.l.c.743.1		80	75.71	odd	10
750.2.l.c.743.10		80	25.21	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 + 0.891007i) q^{2} +(1.00736 - 1.40898i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.998457 - 2.00077i) q^{5} +(0.798080 + 1.53723i) q^{6} +(0.712495 - 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.970457 - 2.83870i) q^{9} +O(q^{10})\)	\(q+(-0.453990 + 0.891007i) q^{2} +(1.00736 - 1.40898i) q^{3} +(-0.587785 - 0.809017i) q^{4} +(-0.998457 - 2.00077i) q^{5} +(0.798080 + 1.53723i) q^{6} +(0.712495 - 0.712495i) q^{7} +(0.987688 - 0.156434i) q^{8} +(-0.970457 - 2.83870i) q^{9} +(2.23599 + 0.0186987i) q^{10} +(-0.348148 + 0.113120i) q^{11} +(-1.73200 + 0.0132082i) q^{12} +(2.33563 - 1.19006i) q^{13} +(0.311372 + 0.958303i) q^{14} +(-3.82485 - 0.608686i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(0.919013 + 5.80242i) q^{17} +(2.96988 + 0.424059i) q^{18} +(0.341785 - 0.470426i) q^{19} +(-1.03178 + 1.98379i) q^{20} +(-0.286154 - 1.72163i) q^{21} +(0.0572652 - 0.361558i) q^{22} +(6.05243 + 3.08387i) q^{23} +(0.774543 - 1.54922i) q^{24} +(-3.00617 + 3.99537i) q^{25} +2.62134i q^{26} +(-4.97727 - 1.49223i) q^{27} +(-0.995214 - 0.157626i) q^{28} +(0.368253 - 0.267552i) q^{29} +(2.27879 - 3.13163i) q^{30} +(-2.36811 - 1.72054i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.191326 + 0.604487i) q^{33} +(-5.58722 - 1.81540i) q^{34} +(-2.13693 - 0.714143i) q^{35} +(-1.72614 + 2.45366i) q^{36} +(4.35053 + 8.53839i) q^{37} +(0.263986 + 0.518102i) q^{38} +(0.676040 - 4.48967i) q^{39} +(-1.29915 - 1.81994i) q^{40} +(-10.0917 - 3.27898i) q^{41} +(1.66389 + 0.526638i) q^{42} +(-7.18512 - 7.18512i) q^{43} +(0.296153 + 0.215168i) q^{44} +(-4.71063 + 4.77598i) q^{45} +(-5.49549 + 3.99271i) q^{46} +(8.16222 + 1.29277i) q^{47} +(1.02873 + 1.39345i) q^{48} +5.98470i q^{49} +(-2.19513 - 4.49237i) q^{50} +(9.10128 + 4.55025i) q^{51} +(-2.33563 - 1.19006i) q^{52} +(-1.38217 + 8.72670i) q^{53} +(3.58922 - 3.75732i) q^{54} +(0.573939 + 0.583619i) q^{55} +(0.592264 - 0.815182i) q^{56} +(-0.318522 - 0.955457i) q^{57} +(0.0712068 + 0.449582i) q^{58} +(2.91096 - 8.95903i) q^{59} +(1.75576 + 3.45215i) q^{60} +(-0.335312 - 1.03198i) q^{61} +(2.60811 - 1.32890i) q^{62} +(-2.71400 - 1.33111i) q^{63} +(0.951057 - 0.309017i) q^{64} +(-4.71307 - 3.48483i) q^{65} +(-0.451742 - 0.444904i) q^{66} +(13.0896 - 2.07319i) q^{67} +(4.15407 - 4.15407i) q^{68} +(10.4421 - 5.42120i) q^{69} +(1.60645 - 1.57981i) q^{70} +(0.755873 + 1.04037i) q^{71} +(-1.40258 - 2.65194i) q^{72} +(4.33350 - 8.50497i) q^{73} -9.58285 q^{74} +(2.60111 + 8.26040i) q^{75} -0.581479 q^{76} +(-0.167456 + 0.328652i) q^{77} +(3.69341 + 2.64063i) q^{78} +(7.17322 + 9.87309i) q^{79} +(2.21139 - 0.331317i) q^{80} +(-7.11643 + 5.50967i) q^{81} +(7.50310 - 7.50310i) q^{82} +(-0.937190 + 0.148436i) q^{83} +(-1.22463 + 1.24345i) q^{84} +(10.6917 - 7.63220i) q^{85} +(9.66396 - 3.14001i) q^{86} +(-0.00601220 - 0.788383i) q^{87} +(-0.326166 + 0.166190i) q^{88} +(0.626378 + 1.92779i) q^{89} +(-2.11685 - 6.36545i) q^{90} +(0.816210 - 2.51204i) q^{91} +(-1.06263 - 6.70917i) q^{92} +(-4.80974 + 1.60343i) q^{93} +(-4.85743 + 6.68568i) q^{94} +(-1.28247 - 0.214132i) q^{95} +(-1.70861 + 0.283990i) q^{96} +(-2.81727 + 17.7876i) q^{97} +(-5.33241 - 2.71700i) q^{98} +(0.658978 + 0.878510i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

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