LMFDB - Embedded newform 740.2.be.a.251.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(51,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.be (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$304$
Relative dimension:	$76$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			251.5
Character	$\chi$	$=$	740.251
Dual form			740.2.be.a.171.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38579 + 0.282123i) q^{2} +(1.12336 - 1.94572i) q^{3} +(1.84081 - 0.781925i) q^{4} +(0.258819 + 0.965926i) q^{5} +(-1.00781 + 3.01328i) q^{6} +(1.60753 + 0.928106i) q^{7} +(-2.33038 + 1.60292i) q^{8} +(-1.02388 - 1.77341i) q^{9} +(-0.631178 - 1.26555i) q^{10} +3.47350 q^{11} +(0.546491 - 4.46009i) q^{12} +(-0.295069 - 1.10121i) q^{13} +(-2.48953 - 0.832637i) q^{14} +(2.17017 + 0.581494i) q^{15} +(2.77719 - 2.87876i) q^{16} +(1.17349 + 0.314435i) q^{17} +(1.91919 + 2.16871i) q^{18} +(-2.20442 + 0.590671i) q^{19} +(1.23172 + 1.57571i) q^{20} +(3.61166 - 2.08519i) q^{21} +(-4.81353 + 0.979954i) q^{22} +(1.16462 + 1.16462i) q^{23} +(0.500974 + 6.33491i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(0.719581 + 1.44280i) q^{26} +2.13943 q^{27} +(3.68486 + 0.451503i) q^{28} +(6.89629 + 6.89629i) q^{29} +(-3.17144 - 0.193573i) q^{30} +(2.87982 - 2.87982i) q^{31} +(-3.03642 + 4.77285i) q^{32} +(3.90199 - 6.75844i) q^{33} +(-1.71491 - 0.104672i) q^{34} +(-0.480423 + 1.79296i) q^{35} +(-3.27144 - 2.46391i) q^{36} +(-5.58182 + 2.41728i) q^{37} +(2.88821 - 1.44046i) q^{38} +(-2.47412 - 0.662939i) q^{39} +(-2.15145 - 1.83610i) q^{40} +(4.56676 + 2.63662i) q^{41} +(-4.41671 + 3.90857i) q^{42} +(-5.16942 - 5.16942i) q^{43} +(6.39406 - 2.71602i) q^{44} +(1.44798 - 1.44798i) q^{45} +(-1.94249 - 1.28535i) q^{46} +1.59507i q^{47} +(-2.48147 - 8.63750i) q^{48} +(-1.77724 - 3.07827i) q^{49} +(1.05907 - 0.937220i) q^{50} +(1.93005 - 1.93005i) q^{51} +(-1.40423 - 1.79641i) q^{52} +(-4.76374 - 8.25104i) q^{53} +(-2.96480 + 0.603583i) q^{54} +(0.899007 + 3.35514i) q^{55} +(-5.23382 + 0.413898i) q^{56} +(-1.32707 + 4.95271i) q^{57} +(-11.5024 - 7.61119i) q^{58} +(1.75649 - 6.55532i) q^{59} +(4.44955 - 0.626486i) q^{60} +(1.99446 - 0.534414i) q^{61} +(-3.17836 + 4.80329i) q^{62} -3.80106i q^{63} +(2.86131 - 7.47081i) q^{64} +(0.987321 - 0.570030i) q^{65} +(-3.50061 + 10.4666i) q^{66} +(4.50545 - 7.80368i) q^{67} +(2.40604 - 0.338764i) q^{68} +(3.57432 - 0.957736i) q^{69} +(0.159928 - 2.62020i) q^{70} +(0.643678 + 0.371628i) q^{71} +(5.22864 + 2.49151i) q^{72} -6.35564i q^{73} +(7.05325 - 4.92460i) q^{74} +2.24672i q^{75} +(-3.59606 + 2.81100i) q^{76} +(5.58374 + 3.22377i) q^{77} +(3.61563 + 0.220685i) q^{78} +(-0.269260 + 0.0721481i) q^{79} +(3.49945 + 1.93748i) q^{80} +(5.47498 - 9.48295i) q^{81} +(-7.07242 - 2.36541i) q^{82} +(-2.11102 + 1.21880i) q^{83} +(5.01793 - 6.66250i) q^{84} +1.21488i q^{85} +(8.62213 + 5.70530i) q^{86} +(21.1652 - 5.67121i) q^{87} +(-8.09456 + 5.56773i) q^{88} +(-2.64417 + 9.86817i) q^{89} +(-1.59808 + 2.41510i) q^{90} +(0.547711 - 2.04409i) q^{91} +(3.05450 + 1.23321i) q^{92} +(-2.36824 - 8.83841i) q^{93} +(-0.450008 - 2.21043i) q^{94} +(-1.14109 - 1.97642i) q^{95} +(5.87562 + 11.2697i) q^{96} +(-12.4567 + 12.4567i) q^{97} +(3.33133 + 3.76443i) q^{98} +(-3.55643 - 6.15992i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) $ 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$1$	$-1$

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 $

$2$	−1.38579	+	0.282123i	−0.979900	+	0.199491i
$2$	−1.38579	+	0.282123i	−0.979900	+	0.199491i
$3$	1.12336	−	1.94572i	0.648572	−	1.12336i	−0.334892	−	0.942257i	$-0.608700\pi$
$3$	1.12336	−	1.94572i	0.648572	−	1.12336i	0.983464	−	0.181104i	$-0.0579670\pi$
$4$	1.84081	−	0.781925i	0.920407	−	0.390963i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$5$	0.258819	+	0.965926i	0.115747	+	0.431975i
$6$	−1.00781	+	3.01328i	−0.411435	+	1.23016i
$7$	1.60753	+	0.928106i	0.607588	+	0.350791i	0.772021	−	0.635597i	$-0.219246\pi$
$7$	1.60753	+	0.928106i	0.607588	+	0.350791i	−0.164433	+	0.986388i	$0.552579\pi$
$8$	−2.33038	+	1.60292i	−0.823912	+	0.566717i
$9$	−1.02388	−	1.77341i	−0.341292	−	0.591136i
$10$	−0.631178	−	1.26555i	−0.199596	−	0.400202i
$11$	3.47350			1.04730			0.523650	−	0.851934i	$-0.324570\pi$
$11$	3.47350			1.04730			0.523650	+	0.851934i	$0.324570\pi$
$12$	0.546491	−	4.46009i	0.157758	−	1.28752i
$13$	−0.295069	−	1.10121i	−0.0818375	−	0.305422i	0.912859	−	0.408275i	$-0.133870\pi$
$13$	−0.295069	−	1.10121i	−0.0818375	−	0.305422i	−0.994697	+	0.102853i	$0.967203\pi$
$14$	−2.48953	−	0.832637i	−0.665355	−	0.222531i
$15$	2.17017	+	0.581494i	0.560334	+	0.150141i
$16$	2.77719	−	2.87876i	0.694296	−	0.719689i
$17$	1.17349	+	0.314435i	0.284613	+	0.0762618i	0.398301	−	0.917255i	$-0.369600\pi$
$17$	1.17349	+	0.314435i	0.284613	+	0.0762618i	−0.113688	+	0.993516i	$0.536267\pi$
$18$	1.91919	+	2.16871i	0.452359	+	0.511169i
$19$	−2.20442	+	0.590671i	−0.505728	+	0.135509i	−0.502657	−	0.864486i	$-0.667644\pi$
$19$	−2.20442	+	0.590671i	−0.505728	+	0.135509i	−0.00307064	+	0.999995i	$0.500977\pi$
$20$	1.23172	+	1.57571i	0.275421	+	0.352340i
$21$	3.61166	−	2.08519i	0.788129	−	0.455027i
$22$	−4.81353	+	0.979954i	−1.02625	+	0.208927i
$23$	1.16462	+	1.16462i	0.242841	+	0.242841i	0.818024	−	0.575184i	$-0.195069\pi$
$23$	1.16462	+	1.16462i	0.242841	+	0.242841i	−0.575184	+	0.818024i	$0.695069\pi$
$24$	0.500974	+	6.33491i	0.102261	+	1.29311i
$25$	−0.866025	+	0.500000i	−0.173205	+	0.100000i
$26$	0.719581	+	1.44280i	0.141122	+	0.282957i
$27$	2.13943			0.411734
$28$	3.68486	+	0.451503i	0.696374	+	0.0853261i
$29$	6.89629	+	6.89629i	1.28061	+	1.28061i	0.940321	+	0.340287i	$0.110524\pi$
$29$	6.89629	+	6.89629i	1.28061	+	1.28061i	0.340287	+	0.940321i	$0.389476\pi$
$30$	−3.17144	−	0.193573i	−0.579023	−	0.0353415i
$31$	2.87982	−	2.87982i	0.517232	−	0.517232i	−0.399501	−	0.916733i	$-0.630817\pi$
$31$	2.87982	−	2.87982i	0.517232	−	0.517232i	0.916733	+	0.399501i	$0.130817\pi$
$32$	−3.03642	+	4.77285i	−0.536769	+	0.843729i
$33$	3.90199	−	6.75844i	0.679249	−	1.17649i
$34$	−1.71491	−	0.104672i	−0.294105	−	0.0179511i
$35$	−0.480423	+	1.79296i	−0.0812063	+	0.303066i
$36$	−3.27144	−	2.46391i	−0.545240	−	0.410652i
$37$	−5.58182	+	2.41728i	−0.917646	+	0.397399i
$37$	−5.58182	+	2.41728i	−0.917646	+	0.397399i
$38$	2.88821	−	1.44046i	0.468529	−	0.233674i
$39$	−2.47412	−	0.662939i	−0.396176	−	0.106155i
$40$	−2.15145	−	1.83610i	−0.340173	−	0.290314i
$41$	4.56676	+	2.63662i	0.713209	+	0.411771i	0.812248	−	0.583312i	$-0.198244\pi$
$41$	4.56676	+	2.63662i	0.713209	+	0.411771i	−0.0990392	+	0.995084i	$0.531577\pi$
$42$	−4.41671	+	3.90857i	−0.681514	+	0.603105i
$43$	−5.16942	−	5.16942i	−0.788329	−	0.788329i	0.192891	−	0.981220i	$-0.438214\pi$
$43$	−5.16942	−	5.16942i	−0.788329	−	0.788329i	−0.981220	+	0.192891i	$0.938214\pi$
$44$	6.39406	−	2.71602i	0.963941	−	0.409455i
$45$	1.44798	−	1.44798i	0.215852	−	0.215852i
$46$	−1.94249	−	1.28535i	−0.286404	−	0.189515i
$47$			1.59507i			0.232666i	0.993210	+	0.116333i	$0.0371139\pi$
$47$			1.59507i			0.232666i	−0.993210	+	0.116333i	$0.962886\pi$
$48$	−2.48147	−	8.63750i	−0.358169	−	1.24672i
$49$	−1.77724	−	3.07827i	−0.253891	−	0.439753i
$50$	1.05907	−	0.937220i	0.149774	−	0.132543i
$51$	1.93005	−	1.93005i	0.270261	−	0.270261i
$52$	−1.40423	−	1.79641i	−0.194732	−	0.249117i
$53$	−4.76374	−	8.25104i	−0.654350	−	1.13337i	−0.982056	−	0.188588i	$-0.939609\pi$
$53$	−4.76374	−	8.25104i	−0.654350	−	1.13337i	0.327707	−	0.944780i	$-0.393724\pi$
$54$	−2.96480	+	0.603583i	−0.403458	+	0.0821373i
$55$	0.899007	+	3.35514i	0.121222	+	0.452407i
$56$	−5.23382	+	0.413898i	−0.699398	+	0.0553095i
$57$	−1.32707	+	4.95271i	−0.175775	+	0.656002i
$58$	−11.5024	−	7.61119i	−1.51034	−	0.999398i
$59$	1.75649	−	6.55532i	0.228676	−	0.853430i	−0.752223	−	0.658909i	$-0.771018\pi$
$59$	1.75649	−	6.55532i	0.228676	−	0.853430i	0.980898	−	0.194521i	$-0.0623151\pi$
$60$	4.44955	−	0.626486i	0.574435	−	0.0808790i
$61$	1.99446	−	0.534414i	0.255364	−	0.0684247i	−0.128866	−	0.991662i	$-0.541134\pi$
$61$	1.99446	−	0.534414i	0.255364	−	0.0684247i	0.384230	+	0.923237i	$0.374467\pi$
$62$	−3.17836	+	4.80329i	−0.403652	+	0.610018i
$63$		−	3.80106i		−	0.478889i
$64$	2.86131	−	7.47081i	0.357663	−	0.933851i
$65$	0.987321	−	0.570030i	0.122462	−	0.0707036i
$66$	−3.50061	+	10.4666i	−0.430896	+	1.28835i
$67$	4.50545	−	7.80368i	0.550429	−	0.953371i	−0.447815	−	0.894126i	$-0.647798\pi$
$67$	4.50545	−	7.80368i	0.550429	−	0.953371i	0.998244	−	0.0592443i	$-0.0188691\pi$
$68$	2.40604	−	0.338764i	0.291775	−	0.0410812i
$69$	3.57432	−	0.957736i	0.430298	−	0.115298i
$70$	0.159928	−	2.62020i	0.0191150	−	0.313174i
$71$	0.643678	+	0.371628i	0.0763905	+	0.0441041i	0.537709	−	0.843131i	$-0.319290\pi$
$71$	0.643678	+	0.371628i	0.0763905	+	0.0441041i	−0.461318	+	0.887235i	$0.652623\pi$
$72$	5.22864	+	2.49151i	0.616202	+	0.293628i
$73$		−	6.35564i		−	0.743871i	−0.928259	−	0.371936i	$-0.878694\pi$
$73$		−	6.35564i		−	0.743871i	0.928259	−	0.371936i	$-0.121306\pi$
$74$	7.05325	−	4.92460i	0.819923	−	0.572474i
$75$			2.24672i			0.259429i
$76$	−3.59606	+	2.81100i	−0.412496	+	0.322444i
$77$	5.58374	+	3.22377i	0.636326	+	0.367383i
$78$	3.61563	+	0.220685i	0.409390	+	0.0249877i
$79$	−0.269260	+	0.0721481i	−0.0302942	+	0.00811730i	−0.273934	−	0.961748i	$-0.588325\pi$
$79$	−0.269260	+	0.0721481i	−0.0302942	+	0.00811730i	0.243640	+	0.969866i	$0.421658\pi$
$80$	3.49945	+	1.93748i	0.391251	+	0.216617i
$81$	5.47498	−	9.48295i	0.608331	−	1.05366i
$82$	−7.07242	−	2.36541i	−0.781018	−	0.261216i
$83$	−2.11102	+	1.21880i	−0.231715	+	0.133781i	−0.611363	−	0.791350i	$-0.709378\pi$
$83$	−2.11102	+	1.21880i	−0.231715	+	0.133781i	0.379648	+	0.925131i	$0.376045\pi$
$84$	5.01793	−	6.66250i	0.547501	−	0.726939i
$85$			1.21488i			0.131773i
$86$	8.62213	+	5.70530i	0.929748	+	0.615219i
$87$	21.1652	−	5.67121i	2.26915	−	0.608018i
$88$	−8.09456	+	5.56773i	−0.862883	+	0.593522i
$89$	−2.64417	+	9.86817i	−0.280281	+	1.04602i	0.671938	+	0.740608i	$0.265462\pi$
$89$	−2.64417	+	9.86817i	−0.280281	+	1.04602i	−0.952219	+	0.305416i	$0.901204\pi$
$90$	−1.59808	+	2.41510i	−0.168453	+	0.254574i
$91$	0.547711	−	2.04409i	0.0574157	−	0.214278i
$92$	3.05450	+	1.23321i	0.318454	+	0.128571i
$93$	−2.36824	−	8.83841i	−0.245575	−	0.916500i
$94$	−0.450008	−	2.21043i	−0.0464147	−	0.227989i
$95$	−1.14109	−	1.97642i	−0.117073	−	0.202777i
$96$	5.87562	+	11.2697i	0.599678	+	1.15020i
$97$	−12.4567	+	12.4567i	−1.26478	+	1.26478i	−0.316037	+	0.948747i	$0.602353\pi$
$97$	−12.4567	+	12.4567i	−1.26478	+	1.26478i	−0.948747	+	0.316037i	$0.897647\pi$
$98$	3.33133	+	3.76443i	0.336515	+	0.380265i
$99$	−3.55643	−	6.15992i	−0.357435	−	0.619096i
$100$	−1.20323	+	1.59757i	−0.120323	+	0.159757i
$101$			14.5472i			1.44750i	0.690060	+	0.723752i	$0.257584\pi$
$101$			14.5472i			1.44750i	−0.690060	+	0.723752i	$0.742416\pi$
$102$	−2.13013	+	3.21915i	−0.210914	+	0.318744i
$103$	3.40672	−	3.40672i	0.335674	−	0.335674i	−0.519063	−	0.854736i	$-0.673719\pi$
$103$	3.40672	−	3.40672i	0.335674	−	0.335674i	0.854736	+	0.519063i	$0.173719\pi$
$104$	2.45278	+	2.09327i	0.240515	+	0.205262i
$105$	2.94891	+	2.94891i	0.287784	+	0.287784i
$106$	8.92934	+	10.0902i	0.867294	+	0.980049i
$107$	−10.2736	−	5.93147i	−0.993188	−	0.573417i	−0.0869622	−	0.996212i	$-0.527716\pi$
$107$	−10.2736	−	5.93147i	−0.993188	−	0.573417i	−0.906226	+	0.422794i	$0.861049\pi$
$108$	3.93829	−	1.67288i	0.378962	−	0.160973i
$109$	7.31076	+	1.95891i	0.700244	+	0.187630i	0.591340	−	0.806423i	$-0.298599\pi$
$109$	7.31076	+	1.95891i	0.700244	+	0.187630i	0.108904	+	0.994052i	$0.465266\pi$
$110$	−2.19240	−	4.39588i	−0.209037	−	0.419131i
$111$	−1.56704	+	13.5761i	−0.148737	+	1.28859i
$112$	7.13619	−	2.05016i	0.674306	−	0.193722i
$113$	−0.329527	+	1.22981i	−0.0309993	+	0.115691i	−0.979692	−	0.200509i	$-0.935740\pi$
$113$	−0.329527	+	1.22981i	−0.0309993	+	0.115691i	0.948693	+	0.316200i	$0.102407\pi$
$114$	0.441768	−	7.23779i	0.0413754	−	0.677882i
$115$	−0.823513	+	1.42637i	−0.0767930	+	0.133009i
$116$	18.0872	+	7.30240i	1.67935	+	0.678010i
$117$	−1.65079	+	1.65079i	−0.152615	+	0.152615i
$118$	−0.584717	+	9.57982i	−0.0538276	+	0.881894i
$119$	1.59458	+	1.59458i	0.146175	+	0.146175i
$120$	−5.98939	+	2.12350i	−0.546754	+	0.193848i
$121$	1.06519			0.0968352
$122$	−2.61313	+	1.30327i	−0.236581	+	0.117992i
$123$	10.2602	−	5.92376i	0.925135	−	0.534127i
$124$	3.04941	−	7.55303i	0.273845	−	0.678282i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	1.07237	+	5.26747i	0.0955341	+	0.469263i
$127$	13.2922	−	7.67425i	1.17949	−	0.680980i	0.223594	−	0.974682i	$-0.428221\pi$
$127$	13.2922	−	7.67425i	1.17949	−	0.680980i	0.955897	+	0.293703i	$0.0948876\pi$
$128$	−1.85747	+	11.1602i	−0.164179	+	0.986431i
$129$	−15.8654	+	4.25111i	−1.39687	+	0.374289i
$130$	−1.20740	+	1.06849i	−0.105896	+	0.0937125i
$131$	−6.30274	−	1.68881i	−0.550673	−	0.147552i	−0.0272551	−	0.999629i	$-0.508677\pi$
$131$	−6.30274	−	1.68881i	−0.550673	−	0.147552i	−0.523418	+	0.852076i	$0.675343\pi$
$132$	1.89823	−	15.4921i	0.165220	−	1.34841i
$133$	−4.09186	−	1.09641i	−0.354809	−	0.0950709i
$134$	−4.04200	+	12.0853i	−0.349176	+	1.04401i
$135$	0.553726	+	2.06653i	0.0476571	+	0.177859i
$136$	−3.23868	+	1.14825i	−0.277715	+	0.0984620i
$137$	−6.04973			−0.516864			−0.258432	−	0.966030i	$-0.583206\pi$
$137$	−6.04973			−0.516864			−0.258432	+	0.966030i	$0.583206\pi$
$138$	−4.68305	+	2.33562i	−0.398648	+	0.198821i
$139$	−10.8908	−	18.8634i	−0.923745	−	1.59997i	−0.793568	−	0.608482i	$-0.791779\pi$
$139$	−10.8908	−	18.8634i	−0.923745	−	1.59997i	−0.130177	−	0.991491i	$-0.541554\pi$
$140$	0.517594	+	3.67616i	0.0437447	+	0.310692i
$141$	3.10356	+	1.79184i	0.261367	+	0.150900i
$142$	−0.996845	−	0.333400i	−0.0836534	−	0.0279783i
$143$	−1.02492	−	3.82506i	−0.0857084	−	0.319868i
$144$	−7.94870	−	1.97759i	−0.662392	−	0.164799i
$145$	−4.87641	+	8.44620i	−0.404964	+	0.701418i
$146$	1.79307	+	8.80756i	0.148396	+	0.728919i
$147$	−7.98592			−0.658668
$148$	−8.38495	+	8.81434i	−0.689239	+	0.724534i
$149$	11.3579			0.930476			0.465238	−	0.885186i	$-0.345969\pi$
$149$	11.3579			0.930476			0.465238	+	0.885186i	$0.345969\pi$
$150$	−0.633852	−	3.11348i	−0.0517538	−	0.254214i
$151$	−7.04348	+	12.1997i	−0.573190	+	0.992795i	0.423045	+	0.906109i	$0.360961\pi$
$151$	−7.04348	+	12.1997i	−0.573190	+	0.992795i	−0.996236	+	0.0866864i	$0.972372\pi$
$152$	4.19032	−	4.90998i	0.339880	−	0.398252i
$153$	−0.643886	−	2.40302i	−0.0520551	−	0.194272i
$154$	−8.64737	−	2.89216i	−0.696825	−	0.233057i
$155$	3.52705	+	2.03634i	0.283300	+	0.163563i
$156$	−5.07276	+	0.714232i	−0.406146	+	0.0571843i
$157$	−0.742775	−	1.28652i	−0.0592799	−	0.102676i	0.834862	−	0.550459i	$-0.185547\pi$
$157$	−0.742775	−	1.28652i	−0.0592799	−	0.102676i	−0.894142	+	0.447783i	$0.852214\pi$
$158$	0.352783	−	0.175947i	0.0280659	−	0.0139976i
$159$	−21.4056			−1.69757
$160$	−5.39611	−	1.69765i	−0.426600	−	0.134211i
$161$	0.791269	+	2.95306i	0.0623608	+	0.232734i
$162$	−4.91180	+	14.6860i	−0.385908	+	1.15384i
$163$	−15.1419	−	4.05726i	−1.18600	−	0.317789i	−0.388699	−	0.921365i	$-0.627075\pi$
$163$	−15.1419	−	4.05726i	−1.18600	−	0.317789i	−0.797306	+	0.603576i	$0.793742\pi$
$164$	10.4682	+	1.28266i	0.817429	+	0.100159i
$165$	7.53807	+	2.01982i	0.586838	+	0.157243i
$166$	2.58157	−	2.28456i	0.200369	−	0.177316i
$167$	−5.73266	+	1.53606i	−0.443607	+	0.118864i	−0.473706	−	0.880683i	$-0.657084\pi$
$167$	−5.73266	+	1.53606i	−0.443607	+	0.118864i	0.0300998	+	0.999547i	$0.490418\pi$
$168$	−5.07413	+	10.6485i	−0.391478	+	0.821549i
$169$	10.1327	−	5.85013i	0.779440	−	0.450010i
$170$	−0.342747	−	1.68357i	−0.0262875	−	0.129124i
$171$	3.30455	+	3.30455i	0.252705	+	0.252705i
$172$	−13.5580	−	5.47384i	−1.03379	−	0.417376i
$173$	−2.67589	+	1.54492i	−0.203444	+	0.117458i	−0.598261	−	0.801301i	$-0.704141\pi$
$173$	−2.67589	+	1.54492i	−0.203444	+	0.117458i	0.394817	+	0.918760i	$0.370808\pi$
$174$	−27.7306	+	13.8303i	−2.10225	+	1.04847i
$175$	−1.85621			−0.140316
$176$	9.64655	−	9.99936i	0.727136	−	0.753730i
$177$	−10.7816	−	10.7816i	−0.810396	−	0.810396i
$178$	0.880215	−	14.4212i	0.0659749	−	1.08091i
$179$	−6.23866	+	6.23866i	−0.466300	+	0.466300i	−0.900713	−	0.434414i	$-0.856956\pi$
$179$	−6.23866	+	6.23866i	−0.466300	+	0.466300i	0.434414	+	0.900713i	$0.356956\pi$
$180$	1.53325	−	3.79767i	0.114282	−	0.283062i
$181$	−2.44667	+	4.23775i	−0.181859	+	0.314990i	−0.942514	−	0.334167i	$-0.891545\pi$
$181$	−2.44667	+	4.23775i	−0.181859	+	0.314990i	0.760654	+	0.649157i	$0.224878\pi$
$182$	−0.182327	+	2.98719i	−0.0135150	+	0.221425i
$183$	1.20068	−	4.48099i	0.0887567	−	0.331244i
$184$	−4.58081	−	0.847215i	−0.337702	−	0.0624575i
$185$	−3.77960	−	4.76599i	−0.277882	−	0.350402i
$186$	5.77540	+	11.5800i	0.423473	+	0.849088i
$187$	4.07611	+	1.09219i	0.298075	+	0.0798689i
$188$	1.24723	+	2.93623i	0.0909636	+	0.214147i
$189$	3.43919	+	1.98562i	0.250164	+	0.144432i
$190$	2.13890	+	2.41698i	0.155172	+	0.175346i
$191$	−5.62607	−	5.62607i	−0.407088	−	0.407088i	0.473634	−	0.880722i	$-0.342942\pi$
$191$	−5.62607	−	5.62607i	−0.407088	−	0.407088i	−0.880722	+	0.473634i	$0.842942\pi$
$192$	−11.3218	−	13.9597i	−0.817080	−	1.00745i
$193$	−10.0957	+	10.0957i	−0.726708	+	0.726708i	−0.969962	−	0.243255i	$-0.921785\pi$
$193$	−10.0957	+	10.0957i	−0.726708	+	0.726708i	0.243255	+	0.969962i	$0.421785\pi$
$194$	13.7480	−	20.7766i	0.987048	−	1.49167i
$195$		−	2.56140i		−	0.183426i
$196$	−5.67854	−	4.27685i	−0.405610	−	0.305489i
$197$	2.09490	+	3.62848i	0.149256	+	0.258519i	0.930953	−	0.365140i	$-0.118979\pi$
$197$	2.09490	+	3.62848i	0.149256	+	0.258519i	−0.781697	+	0.623659i	$0.785646\pi$
$198$	6.66632	+	7.53299i	0.473755	+	0.535347i
$199$	−3.44652	+	3.44652i	−0.244317	+	0.244317i	−0.818634	−	0.574316i	$-0.805268\pi$
$199$	−3.44652	+	3.44652i	−0.244317	+	0.244317i	0.574316	+	0.818634i	$0.305268\pi$
$200$	1.21671	−	2.55336i	0.0860341	−	0.180550i
$201$	−10.1225	−	17.5327i	−0.713986	−	1.23666i
$202$	−4.10411	−	20.1594i	−0.288764	−	1.41841i
$203$	4.68548	+	17.4865i	0.328856	+	1.22731i
$204$	2.04371	−	5.06202i	0.143088	−	0.354413i
$205$	−1.36482	+	5.09356i	−0.0953229	+	0.355750i
$206$	−3.75987	+	5.68210i	−0.261963	+	0.395890i
$207$	0.872920	−	3.25778i	0.0606722	−	0.226432i
$208$	−3.98959	−	2.20884i	−0.276628	−	0.153156i
$209$	−7.65703	+	2.05170i	−0.529648	+	0.141919i
$210$	−4.91852	−	3.25461i	−0.339410	−	0.224589i
$211$			25.4948i			1.75513i	0.479456	+	0.877566i	$0.340834\pi$
$211$			25.4948i			1.75513i	−0.479456	+	0.877566i	$0.659166\pi$
$212$	−15.2208	−	11.4637i	−1.04537	−	0.787332i
$213$	1.44616	−	0.834943i	0.0990895	−	0.0572094i
$214$	15.9105	+	5.32134i	1.08762	+	0.363759i
$215$	3.65533	−	6.33122i	0.249292	−	0.431786i
$216$	−4.98568	+	3.42933i	−0.339233	+	0.233337i
$217$	7.30218	−	1.95661i	0.495704	−	0.132823i
$218$	−10.6838	−	0.652101i	−0.723599	−	0.0441658i
$219$	−12.3663	−	7.13967i	−0.835635	−	0.482454i
$220$	4.27837	+	5.47323i	0.288448	+	0.369005i
$221$		−	1.38504i		−	0.0931680i
$222$	−1.65855	−	19.2557i	−0.111315	−	1.29236i
$223$			28.4480i			1.90502i	0.304511	+	0.952509i	$0.401507\pi$
$223$			28.4480i			1.90502i	−0.304511	+	0.952509i	$0.598493\pi$
$224$	−9.31084	+	4.85436i	−0.622107	+	0.324346i
$225$	1.77341	+	1.02388i	0.118227	+	0.0682585i
$226$	0.109696	−	1.79723i	0.00729688	−	0.119550i
$227$	12.2243	−	3.27549i	0.811355	−	0.217402i	0.170792	−	0.985307i	$-0.445367\pi$
$227$	12.2243	−	3.27549i	0.811355	−	0.217402i	0.640564	+	0.767905i	$0.278701\pi$
$228$	1.42975	+	10.1547i	0.0946877	+	0.672510i
$229$	−1.13732	+	1.96990i	−0.0751563	+	0.130175i	−0.901154	−	0.433499i	$-0.857279\pi$
$229$	−1.13732	+	1.96990i	−0.0751563	+	0.130175i	0.825998	+	0.563673i	$0.190612\pi$
$230$	0.738803	−	2.20897i	0.0487152	−	0.145655i
$231$	12.5451	−	7.24292i	0.825407	−	0.476549i
$232$	−27.1251	−	5.01676i	−1.78085	−	0.329366i
$233$		−	10.1782i		−	0.666796i	−0.942786	−	0.333398i	$-0.891805\pi$
$233$		−	10.1782i		−	0.666796i	0.942786	−	0.333398i	$-0.108195\pi$
$234$	1.82191	−	2.75336i	0.119102	−	0.179993i
$235$	−1.54072	+	0.412836i	−0.100506	+	0.0269304i
$236$	−1.89240	−	13.4406i	−0.123185	−	0.874906i
$237$	−0.162097	+	0.604953i	−0.0105293	+	0.0392959i
$238$	−2.65962	−	1.75989i	−0.172398	−	0.114076i
$239$	−5.29364	+	19.7561i	−0.342417	+	1.27792i	0.553184	+	0.833059i	$0.313413\pi$
$239$	−5.29364	+	19.7561i	−0.342417	+	1.27792i	−0.895601	+	0.444858i	$0.853254\pi$
$240$	7.70093	−	4.63246i	0.497093	−	0.299024i
$241$	4.12254	+	15.3855i	0.265556	+	0.991069i	0.961909	+	0.273370i	$0.0881382\pi$
$241$	4.12254	+	15.3855i	0.265556	+	0.991069i	−0.696353	+	0.717700i	$0.745195\pi$
$242$	−1.47612	+	0.300514i	−0.0948888	+	0.0193178i
$243$	−9.09161	−	15.7471i	−0.583227	−	1.01018i
$244$	3.25355	−	2.54327i	0.208287	−	0.162816i
$245$	2.51340	−	2.51340i	0.160575	−	0.160575i
$246$	−12.5473	+	11.1037i	−0.799986	+	0.707947i
$247$	1.30091	+	2.25324i	0.0827750	+	0.143370i
$248$	−2.09495	+	11.3272i	−0.133029	+	0.719278i
$249$			5.47660i			0.347065i
$250$	1.17939	+	0.780408i	0.0745912	+	0.0493574i
$251$	−5.42561	+	5.42561i	−0.342462	+	0.342462i	−0.857292	−	0.514830i	$-0.827855\pi$
$251$	−5.42561	+	5.42561i	−0.342462	+	0.342462i	0.514830	+	0.857292i	$0.327855\pi$
$252$	−2.97215	−	6.99705i	−0.187228	−	0.440773i
$253$	4.04532	+	4.04532i	0.254327	+	0.254327i
$254$	−16.2551	+	14.3849i	−1.01993	+	0.902590i
$255$	2.36382	+	1.36475i	0.148028	+	0.0854642i
$256$	−0.574485	−	15.9897i	−0.0359053	−	0.999355i
$257$	−2.12336	−	0.568954i	−0.132452	−	0.0354904i	0.191984	−	0.981398i	$-0.438508\pi$
$257$	−2.12336	−	0.568954i	−0.132452	−	0.0354904i	−0.324436	+	0.945908i	$0.605174\pi$
$258$	20.7867	−	10.3671i	1.29412	−	0.645428i
$259$	−11.2164	−	1.29467i	−0.696954	−	0.0804470i
$260$	1.37175	−	1.82133i	0.0850725	−	0.112954i
$261$	5.16898	−	19.2909i	0.319952	−	1.19408i
$262$	9.21071	+	0.562188i	0.569040	+	0.0347321i
$263$	−8.80244	+	15.2463i	−0.542782	+	0.940125i	0.455961	+	0.890000i	$0.349296\pi$
$263$	−8.80244	+	15.2463i	−0.542782	+	0.940125i	−0.998743	+	0.0501257i	$0.984038\pi$
$264$	1.74013	+	22.0043i	0.107098	+	1.35427i
$265$	6.73694	−	6.73694i	0.413847	−	0.413847i
$266$	5.97977	+	0.364983i	0.366643	+	0.0223786i
$267$	16.2303	+	16.2303i	0.993279	+	0.993279i
$268$	2.19181	−	17.8880i	0.133886	−	1.09269i
$269$	−4.35917			−0.265784			−0.132892	−	0.991131i	$-0.542426\pi$
$269$	−4.35917			−0.265784			−0.132892	+	0.991131i	$0.542426\pi$
$270$	−1.35036	−	2.70755i	−0.0821804	−	0.164777i
$271$	4.08136	−	2.35637i	0.247925	−	0.143140i	−0.370889	−	0.928677i	$-0.620947\pi$
$271$	4.08136	−	2.35637i	0.247925	−	0.143140i	0.618814	+	0.785538i	$0.287614\pi$
$272$	4.16418	−	2.50494i	0.252490	−	0.151884i
$273$	−3.36194	−	3.36194i	−0.203474	−	0.203474i
$274$	8.38364	−	1.70677i	0.506474	−	0.103110i
$275$	−3.00814	+	1.73675i	−0.181398	+	0.104730i
$276$	5.83078	−	4.55787i	0.350972	−	0.274351i
$277$	−10.4859	+	2.80968i	−0.630035	+	0.168817i	−0.559686	−	0.828705i	$-0.689078\pi$
$277$	−10.4859	+	2.80968i	−0.630035	+	0.168817i	−0.0703495	+	0.997522i	$0.522411\pi$
$278$	20.4141	+	23.0681i	1.22436	+	1.38353i
$279$	−8.05569	−	2.15851i	−0.482281	−	0.129227i
$280$	−1.75441	−	4.94836i	−0.104846	−	0.295721i
$281$	7.33185	+	1.96456i	0.437382	+	0.117196i	0.470789	−	0.882246i	$-0.343969\pi$
$281$	7.33185	+	1.96456i	0.437382	+	0.117196i	−0.0334076	+	0.999442i	$0.510636\pi$
$282$	−4.80640	−	1.60753i	−0.286217	−	0.0957268i
$283$	−2.42379	−	9.04570i	−0.144079	−	0.537711i	−0.999795	−	0.0202643i	$-0.993549\pi$
$283$	−2.42379	−	9.04570i	−0.144079	−	0.537711i	0.855715	−	0.517447i	$-0.173117\pi$
$284$	1.47548	+	0.180789i	0.0875534	+	0.0107278i
$285$	−5.12742			−0.303722
$286$	2.49946	+	5.01157i	0.147796	+	0.296340i
$287$	4.89413	+	8.47688i	0.288891	+	0.500374i
$288$	11.5731	+	0.498000i	0.681954	+	0.0293450i
$289$	−13.4442	−	7.76203i	−0.790837	−	0.456590i
$290$	4.37480	−	13.0804i	0.256897	−	0.768106i
$291$	10.2438	+	38.2305i	0.600504	+	2.24111i
$292$	−4.96963	−	11.6995i	−0.290826	−	0.684664i
$293$	3.82014	−	6.61667i	0.223175	−	0.386550i	−0.732596	−	0.680664i	$-0.761691\pi$
$293$	3.82014	−	6.61667i	0.223175	−	0.386550i	0.955770	+	0.294114i	$0.0950246\pi$
$294$	11.0668	−	2.25301i	0.645428	−	0.131398i
$295$	6.78657			0.395129
$296$	9.13303	−	14.5804i	0.530847	−	0.847468i
$297$	7.43131			0.431208
$298$	−15.7396	+	3.20433i	−0.911773	+	0.185622i
$299$	0.938855	−	1.62615i	0.0542954	−	0.0940424i
$300$	1.75677	+	4.13579i	0.101427	+	0.238780i
$301$	−3.51221	−	13.1077i	−0.202440	−	0.755518i
$302$	6.31896	−	18.8933i	0.363615	−	1.08719i
$303$	28.3048	+	16.3418i	1.62607	+	0.938811i
$304$	−4.42167	+	7.98638i	−0.253600	+	0.458050i
$305$	1.03241	+	1.78818i	0.0591155	+	0.102391i
$306$	1.57024	+	3.14841i	0.0897644	+	0.179983i
$307$	−9.25066			−0.527963			−0.263982	−	0.964528i	$-0.585036\pi$
$307$	−9.25066			−0.527963			−0.263982	+	0.964528i	$0.585036\pi$
$308$	12.7994	+	1.56830i	0.729312	+	0.0893620i
$309$	−2.80154	−	10.4555i	−0.159374	−	0.594791i
$310$	−5.46224	−	1.82688i	−0.310234	−	0.103760i
$311$	−29.7744	−	7.97803i	−1.68835	−	0.452393i	−0.718389	−	0.695642i	$-0.755120\pi$
$311$	−29.7744	−	7.97803i	−1.68835	−	0.452393i	−0.969964	+	0.243249i	$0.921787\pi$
$312$	6.82827	−	2.42092i	0.386574	−	0.137057i
$313$	21.5767	+	5.78147i	1.21959	+	0.326788i	0.810518	−	0.585714i	$-0.199186\pi$
$313$	21.5767	+	5.78147i	1.21959	+	0.326788i	0.409072	+	0.912502i	$0.365853\pi$
$314$	1.39229	+	1.57330i	0.0785713	+	0.0887862i
$315$	3.67155	−	0.983788i	0.206868	−	0.0554302i
$316$	−0.439244	+	0.343353i	−0.0247094	+	0.0193151i
$317$	30.2188	−	17.4468i	1.69726	−	0.979911i	0.748911	−	0.662670i	$-0.230577\pi$
$317$	30.2188	−	17.4468i	1.69726	−	0.979911i	0.948345	−	0.317241i	$-0.102756\pi$
$318$	29.6636	−	6.03901i	1.66345	−	0.338651i
$319$	23.9542	+	23.9542i	1.34118	+	1.34118i
$320$	7.95680	+	0.830222i	0.444799	+	0.0464108i
$321$	−23.0819	+	13.3264i	−1.28831	+	0.743805i
$322$	−1.92966	−	3.86907i	−0.107536	−	0.215615i
$323$	−2.77258			−0.154271
$324$	2.66346	−	21.7374i	0.147970	−	1.20763i
$325$	0.806145	+	0.806145i	0.0447169	+	0.0447169i
$326$	22.1281	+	1.35062i	1.22556	+	0.0748038i
$327$	12.0241	−	12.0241i	0.664934	−	0.664934i
$328$	−14.8686	+	1.17583i	−0.820980	+	0.0649243i
$329$	−1.48040	+	2.56412i	−0.0816170	+	0.141365i
$330$	−11.0160	−	0.672376i	−0.606410	−	0.0370131i
$331$	9.23350	−	34.4599i	0.507519	−	1.89409i	0.0637033	−	0.997969i	$-0.479709\pi$
$331$	9.23350	−	34.4599i	0.507519	−	1.89409i	0.443816	−	0.896118i	$-0.353624\pi$
$332$	−2.93298	+	3.89424i	−0.160968	+	0.213724i
$333$	10.0019	+	7.42384i	0.548102	+	0.406824i
$334$	7.51089	−	3.74597i	0.410978	−	0.204970i
$335$	8.70387	+	2.33219i	0.475543	+	0.127421i
$336$	4.02749	−	16.1881i	0.219717	−	0.883131i
$337$	24.1001	+	13.9142i	1.31282	+	0.757955i	0.982562	−	0.185937i	$-0.0595320\pi$
$337$	24.1001	+	13.9142i	1.31282	+	0.757955i	0.330255	+	0.943892i	$0.392865\pi$
$338$	−12.3913	+	10.9657i	−0.674000	+	0.596456i
$339$	2.02269	+	2.02269i	0.109857	+	0.109857i
$340$	0.949949	+	2.23638i	0.0515182	+	0.121284i
$341$	10.0031	−	10.0031i	0.541696	−	0.541696i
$342$	−5.51169	−	3.64711i	−0.298038	−	0.197213i
$343$		−	19.5913i		−	1.05783i
$344$	20.3329	+	3.76053i	1.09627	+	0.202754i
$345$	1.85020	+	3.20465i	0.0996117	+	0.172532i
$346$	3.27235	−	2.89587i	0.175923	−	0.155683i
$347$	−7.36906	+	7.36906i	−0.395592	+	0.395592i	−0.876675	−	0.481083i	$-0.840244\pi$
$347$	−7.36906	+	7.36906i	−0.395592	+	0.395592i	0.481083	+	0.876675i	$0.340244\pi$
$348$	34.5268	−	26.9893i	1.85083	−	1.44678i
$349$	−9.85493	−	17.0692i	−0.527522	−	0.913696i	−0.999485	−	0.0320773i	$-0.989788\pi$
$349$	−9.85493	−	17.0692i	−0.527522	−	0.913696i	0.471963	−	0.881618i	$-0.343546\pi$
$350$	2.57231	−	0.523680i	0.137496	−	0.0279919i
$351$	−0.631281	−	2.35597i	−0.0336953	−	0.125752i
$352$	−10.5470	+	16.5785i	−0.562158	+	0.883637i
$353$	−7.21883	+	26.9410i	−0.384220	+	1.43393i	0.455174	+	0.890403i	$0.349577\pi$
$353$	−7.21883	+	26.9410i	−0.384220	+	1.43393i	−0.839393	+	0.543524i	$0.817090\pi$
$354$	17.9828	+	11.8993i	0.955774	+	0.632440i
$355$	−0.192369	+	0.717929i	−0.0102099	+	0.0381037i
$356$	2.84875	+	20.2330i	0.150984	+	1.07235i
$357$	4.89390	−	1.31132i	0.259013	−	0.0694023i
$358$	6.88539	−	10.4055i	0.363904	−	0.549950i
$359$			12.6451i			0.667385i	0.942682	+	0.333692i	$0.108295\pi$
$359$			12.6451i			0.667385i	−0.942682	+	0.333692i	$0.891705\pi$
$360$	−1.05334	+	5.69533i	−0.0555161	+	0.300170i
$361$	−11.9439	+	6.89583i	−0.628628	+	0.362938i
$362$	2.19499	−	6.56288i	0.115366	−	0.344938i
$363$	1.19659	−	2.07255i	0.0628047	−	0.108781i
$364$	−0.590089	−	4.19105i	−0.0309291	−	0.219671i
$365$	6.13907	−	1.64496i	0.321334	−	0.0861011i
$366$	−0.399693	+	6.54844i	−0.0208923	+	0.342292i
$367$	−0.172303	−	0.0994792i	−0.00899415	−	0.00519277i	0.495496	−	0.868610i	$-0.334986\pi$
$367$	−0.172303	−	0.0994792i	−0.00899415	−	0.00519277i	−0.504490	+	0.863417i	$0.668320\pi$
$368$	6.58705	−	0.118293i	0.343373	−	0.00616646i
$369$		−	10.7983i		−	0.562138i
$370$	6.58232	+	5.53833i	0.342198	+	0.287924i
$371$		−	17.6850i		−	0.918160i
$372$	−11.2705	−	14.4181i	−0.584347	−	0.747542i
$373$	7.43685	+	4.29367i	0.385065	+	0.222318i	0.680020	−	0.733194i	$-0.261971\pi$
$373$	7.43685	+	4.29367i	0.385065	+	0.222318i	−0.294954	+	0.955511i	$0.595304\pi$
$374$	−5.95675	−	0.363578i	−0.308016	−	0.0188002i
$375$	−2.17017	+	0.581494i	−0.112067	+	0.0300282i
$376$	−2.55678	−	3.71712i	−0.131856	−	0.191696i
$377$	5.55941	−	9.62918i	0.286324	−	0.495928i
$378$	−5.32618	−	1.78137i	−0.273949	−	0.0916237i
$379$	21.2620	−	12.2756i	1.09215	−	0.630555i	0.158004	−	0.987438i	$-0.449494\pi$
$379$	21.2620	−	12.2756i	1.09215	−	0.630555i	0.934149	+	0.356883i	$0.116161\pi$
$380$	−3.64595	−	2.74598i	−0.187033	−	0.140866i
$381$		−	34.4838i		−	1.76666i
$382$	9.38378	+	6.20929i	0.480116	+	0.317695i
$383$	−20.2974	+	5.43867i	−1.03715	+	0.277903i	−0.736931	−	0.675968i	$-0.763726\pi$
$383$	−20.2974	+	5.43867i	−1.03715	+	0.277903i	−0.300217	+	0.953871i	$0.597059\pi$
$384$	19.6280	+	16.1510i	1.00164	+	0.824204i
$385$	−1.66875	+	6.22785i	−0.0850473	+	0.317401i
$386$	11.1423	−	16.8388i	0.567129	−	0.857073i
$387$	−3.87464	+	14.4603i	−0.196959	+	0.735060i
$388$	−13.1902	+	32.6706i	−0.669632	+	1.65860i
$389$	−8.44521	−	31.5179i	−0.428189	−	1.59802i	−0.756859	−	0.653578i	$-0.773267\pi$
$389$	−8.44521	−	31.5179i	−0.428189	−	1.59802i	0.328670	−	0.944445i	$-0.393400\pi$
$390$	0.722630	+	3.54955i	0.0365918	+	0.179739i
$391$	1.00047	+	1.73287i	0.0505961	+	0.0876351i
$392$	9.07585	+	4.32476i	0.458400	+	0.218433i
$393$	−10.3662	+	10.3662i	−0.522906	+	0.522906i
$394$	−3.92677	−	4.43728i	−0.197828	−	0.223547i
$395$	−0.139379	−	0.241412i	−0.00701294	−	0.0121468i
$396$	−11.3633	−	8.55840i	−0.571029	−	0.430076i
$397$			23.9445i			1.20174i	0.799346	+	0.600871i	$0.205179\pi$
$397$			23.9445i			1.20174i	−0.799346	+	0.600871i	$0.794821\pi$
$398$	3.80380	−	5.74849i	0.190667	−	0.288146i
$399$	−6.72994	+	6.72994i	−0.336918	+	0.336918i
$400$	−0.965734	+	3.88167i	−0.0482867	+	0.194083i
$401$	8.16462	+	8.16462i	0.407722	+	0.407722i	0.880943	−	0.473222i	$-0.156909\pi$
$401$	8.16462	+	8.16462i	0.407722	+	0.407722i	−0.473222	+	0.880943i	$0.656909\pi$
$402$	18.9740	+	21.4408i	0.946337	+	1.06937i
$403$	−4.02105	−	2.32156i	−0.200303	−	0.115645i
$404$	11.3749	+	26.7787i	0.565920	+	1.33229i
$405$	10.5769	+	2.83406i	0.525568	+	0.140826i
$406$	−11.4264	−	22.9106i	−0.567083	−	1.13703i
$407$	−19.3884	+	8.39643i	−0.961050	+	0.416196i
$408$	−1.40403	+	7.59147i	−0.0695099	+	0.375834i
$409$	−1.58085	+	5.89983i	−0.0781682	+	0.291728i	−0.993933	−	0.109987i	$-0.964919\pi$
$409$	−1.58085	+	5.89983i	−0.0781682	+	0.291728i	0.915765	+	0.401715i	$0.131586\pi$
$410$	0.454333	−	7.44364i	0.0224379	−	0.367615i
$411$	−6.79603	+	11.7711i	−0.335223	+	0.580624i
$412$	3.60733	−	8.93492i	0.177720	−	0.440192i
$413$	8.90763	−	8.90763i	0.438316	−	0.438316i
$414$	−0.290586	+	4.76087i	−0.0142815	+	0.233984i
$415$	−1.72364	−	1.72364i	−0.0846102	−	0.0846102i
$416$	6.15189	+	1.93543i	0.301621	+	0.0948922i
$417$	−48.9371			−2.39646
$418$	10.0322	−	5.00344i	0.490690	−	0.244726i
$419$	−11.0198	+	6.36231i	−0.538355	+	0.310819i	−0.744412	−	0.667721i	$-0.767270\pi$
$419$	−11.0198	+	6.36231i	−0.538355	+	0.310819i	0.206057	+	0.978540i	$0.433937\pi$
$420$	7.73422	+	3.12256i	0.377391	+	0.152366i
$421$	−16.8349	−	16.8349i	−0.820483	−	0.820483i	0.165694	−	0.986177i	$-0.447014\pi$
$421$	−16.8349	−	16.8349i	−0.820483	−	0.820483i	−0.986177	+	0.165694i	$0.947014\pi$
$422$	−7.19266	−	35.3303i	−0.350133	−	1.71985i
$423$	2.82872	−	1.63316i	0.137537	−	0.0794070i
$424$	24.3270	+	11.5921i	1.18143	+	0.562964i
$425$	−1.17349	+	0.314435i	−0.0569226	+	0.0152524i
$426$	−1.76852	+	1.56505i	−0.0856850	+	0.0758269i
$427$	3.70214	+	0.991985i	0.179159	+	0.0480055i
$428$	−23.5498	−	2.88553i	−1.13832	−	0.139478i
$429$	−8.59385	−	2.30272i	−0.414915	−	0.111176i
$430$	−3.27933	+	9.80498i	−0.158143	+	0.472838i
$431$	0.493530	+	1.84188i	0.0237725	+	0.0887203i	0.976793	−	0.214186i	$-0.0687098\pi$
$431$	0.493530	+	1.84188i	0.0237725	+	0.0887203i	−0.953020	+	0.302906i	$0.902043\pi$
$432$	5.94160	−	6.15890i	0.285865	−	0.296320i
$433$	−30.2129			−1.45194			−0.725971	−	0.687726i	$-0.758609\pi$
$433$	−30.2129			−1.45194			−0.725971	+	0.687726i	$0.758609\pi$
$434$	−9.56726	+	4.77156i	−0.459243	+	0.229042i
$435$	10.9559	+	18.9762i	0.525297	+	0.909841i
$436$	14.9895	−	2.11048i	0.717865	−	0.101074i
$437$	−3.25522	−	1.87940i	−0.155719	−	0.0899041i
$438$	19.1513	+	6.40525i	0.915084	+	0.306055i
$439$	−5.26478	−	19.6484i	−0.251274	−	0.937768i	−0.970125	−	0.242604i	$-0.921998\pi$
$439$	−5.26478	−	19.6484i	−0.251274	−	0.937768i	0.718851	−	0.695164i	$-0.244668\pi$
$440$	−7.47304	−	6.37771i	−0.356263	−	0.304045i
$441$	−3.63935	+	6.30354i	−0.173302	+	0.300169i
$442$	0.390753	+	1.91937i	0.0185862	+	0.0912953i
$443$	−29.1904			−1.38688			−0.693438	−	0.720516i	$-0.743905\pi$
$443$	−29.1904			−1.38688			−0.693438	+	0.720516i	$0.743905\pi$
$444$	7.73088	+	26.2164i	0.366892	+	1.24418i
$445$	−10.2163			−0.484298
$446$	−8.02584	−	39.4229i	−0.380034	−	1.86673i
$447$	12.7590	−	22.0993i	0.603481	−	1.04526i
$448$	11.5333	−	9.35392i	0.544898	−	0.441931i
$449$	−5.97524	−	22.2999i	−0.281989	−	1.05240i	−0.951012	−	0.309155i	$-0.899954\pi$
$449$	−5.97524	−	22.2999i	−0.281989	−	1.05240i	0.669023	−	0.743242i	$-0.266713\pi$
$450$	−2.74642	−	0.918556i	−0.129468	−	0.0433012i
$451$	15.8626	+	9.15830i	0.746943	+	0.431248i
$452$	0.355024	+	2.52152i	0.0166989	+	0.118602i
$453$	15.8247	+	27.4092i	0.743511	+	1.28780i
$454$	−16.0162	+	7.98789i	−0.751677	+	0.374890i
$455$	2.11619			0.0992087
$456$	−4.84620	−	13.6689i	−0.226944	−	0.640103i
$457$	−4.20542	−	15.6948i	−0.196721	−	0.734173i	−0.991815	−	0.127686i	$-0.959245\pi$
$457$	−4.20542	−	15.6948i	−0.196721	−	0.734173i	0.795093	−	0.606487i	$-0.207422\pi$
$458$	1.02033	−	3.05072i	0.0476770	−	0.142551i
$459$	2.51060	+	0.672713i	0.117185	+	0.0313995i
$460$	−0.400622	+	3.26960i	−0.0186791	+	0.152446i
$461$	33.6074	+	9.00507i	1.56525	+	0.419408i	0.934321	−	0.356432i	$-0.116007\pi$
$461$	33.6074	+	9.00507i	1.56525	+	0.419408i	0.630930	+	0.775840i	$0.282674\pi$
$462$	−15.3414	+	13.5764i	−0.713749	+	0.631632i
$463$	−9.08267	+	2.43370i	−0.422108	+	0.113103i	−0.463619	−	0.886035i	$-0.653449\pi$
$463$	−9.08267	+	2.43370i	−0.422108	+	0.113103i	0.0415114	+	0.999138i	$0.486783\pi$
$464$	39.0050	−	0.700470i	1.81076	−	0.0325185i
$465$	7.92430	−	4.57510i	0.367481	−	0.212165i
$466$	2.87151	+	14.1048i	0.133020	+	0.653393i
$467$	24.0317	+	24.0317i	1.11206	+	1.11206i	0.992872	+	0.119184i	$0.0380278\pi$
$467$	24.0317	+	24.0317i	1.11206	+	1.11206i	0.119184	+	0.992872i	$0.461972\pi$
$468$	−1.74800	+	4.32958i	−0.0808012	+	0.200135i
$469$	14.4853	−	8.36307i	0.668868	−	0.386171i
$470$	2.01865	−	1.00678i	0.0931132	−	0.0464391i
$471$	−3.33762			−0.153789
$472$	6.41435	+	18.0919i	0.295245	+	0.832746i
$473$	−17.9560	−	17.9560i	−0.825616	−	0.825616i
$474$	0.0539603	−	0.884068i	0.00247848	−	0.0406066i
$475$	1.61374	−	1.61374i	0.0740436	−	0.0740436i
$476$	4.18218	+	1.68849i	0.191690	+	0.0773916i
$477$	−9.75496	+	16.8961i	−0.446649	+	0.773619i
$478$	1.76220	−	28.8712i	0.0806009	−	1.32054i
$479$	8.00427	−	29.8724i	0.365725	−	1.36490i	−0.500711	−	0.865614i	$-0.666928\pi$
$479$	8.00427	−	29.8724i	0.365725	−	1.36490i	0.866436	−	0.499289i	$-0.166405\pi$
$480$	−9.36493	+	8.59222i	−0.427449	+	0.392179i
$481$	4.30897	+	5.43351i	0.196472	+	0.247747i
$482$	−10.0536	−	20.1580i	−0.457928	−	0.918172i
$483$	6.63469	+	1.77776i	0.301889	+	0.0808909i
$484$	1.96081	−	0.832897i	0.0891278	−	0.0378590i
$485$	−15.2563	−	8.80820i	−0.692751	−	0.399960i
$486$	17.0417	+	19.2572i	0.773026	+	0.873525i
$487$	22.7001	+	22.7001i	1.02864	+	1.02864i	0.999578	+	0.0290630i	$0.00925235\pi$
$487$	22.7001	+	22.7001i	1.02864	+	1.02864i	0.0290630	+	0.999578i	$0.490748\pi$
$488$	−3.79122	+	4.44234i	−0.171620	+	0.201095i
$489$	−24.9041	+	24.9041i	−1.12620	+	1.12620i
$490$	−2.77395	+	4.19212i	−0.125314	+	0.189381i
$491$			0.228186i			0.0102979i	0.999987	+	0.00514894i	$0.00163896\pi$
$491$			0.228186i			0.0102979i	−0.999987	+	0.00514894i	$0.998361\pi$
$492$	14.2553	−	18.9273i	0.642677	−	0.853307i
$493$	5.92428	+	10.2612i	0.266816	+	0.462139i
$494$	−2.43848	−	2.75550i	−0.109712	−	0.123976i
$495$	5.02956	−	5.02956i	0.226062	−	0.226062i
$496$	−0.292509	−	16.2881i	−0.0131341	−	0.731358i
$497$	0.689819	+	1.19480i	0.0309426	+	0.0535942i
$498$	−1.54508	−	7.58940i	−0.0692365	−	0.340089i
$499$	−4.03178	−	15.0468i	−0.180487	−	0.673588i	−0.995552	−	0.0942176i	$-0.969965\pi$
$499$	−4.03178	−	15.0468i	−0.180487	−	0.673588i	0.815064	−	0.579371i	$-0.196702\pi$
$500$	−1.85456	−	0.748747i	−0.0829383	−	0.0334850i
$501$	−3.45110	+	12.8797i	−0.154184	+	0.575422i
$502$	5.98806	−	9.04944i	0.267260	−	0.403896i
$503$	0.286276	−	1.06840i	0.0127644	−	0.0476374i	−0.959250	−	0.282559i	$-0.908817\pi$
$503$	0.286276	−	1.06840i	0.0127644	−	0.0476374i	0.972014	+	0.234922i	$0.0754834\pi$
$504$	6.09279	+	8.85791i	0.271395	+	0.394563i
$505$	−14.0516	+	3.76510i	−0.625286	+	0.167545i
$506$	−6.74723	−	4.46467i	−0.299951	−	0.198479i
$507$		−	26.2872i		−	1.16746i
$508$	18.4677	−	24.5204i	0.819374	−	1.08792i
$509$	25.9532	−	14.9841i	1.15036	−	0.664158i	0.201382	−	0.979513i	$-0.435457\pi$
$509$	25.9532	−	14.9841i	1.15036	−	0.664158i	0.948974	+	0.315354i	$0.102123\pi$
$510$	−3.66078	−	1.22437i	−0.162102	−	0.0542160i
$511$	5.89870	−	10.2169i	0.260943	−	0.451967i
$512$	5.30717	+	21.9962i	0.234546	+	0.972105i
$513$	−4.71619	+	1.26370i	−0.208225	+	0.0557937i
$514$	3.10305	+	0.189399i	0.136870	+	0.00835401i
$515$	4.17236	+	2.40891i	0.183856	+	0.106149i
$516$	−25.8811	+	20.2310i	−1.13935	+	0.890621i
$517$			5.54049i			0.243670i
$518$	15.9088	−	1.37027i	0.698994	−	0.0602063i
$519$			6.94203i			0.304721i
$520$	−1.38712	+	2.91098i	−0.0608292	+	0.127655i
$521$	−23.5148	−	13.5762i	−1.03020	−	0.594786i	−0.113158	−	0.993577i	$-0.536097\pi$
$521$	−23.5148	−	13.5762i	−1.03020	−	0.594786i	−0.917042	+	0.398791i	$0.869430\pi$
$522$	−1.72070	+	28.1913i	−0.0753128	+	1.23390i
$523$	−30.5465	+	8.18492i	−1.33571	+	0.357902i	−0.854840	−	0.518892i	$-0.826345\pi$
$523$	−30.5465	+	8.18492i	−1.33571	+	0.357902i	−0.480867	+	0.876794i	$0.659678\pi$
$524$	−12.9227	+	1.81948i	−0.564531	+	0.0794844i
$525$	−2.08519	+	3.61166i	−0.0910053	+	0.157626i
$526$	7.89698	−	23.6115i	0.344325	−	1.02951i
$527$	4.28496	−	2.47392i	0.186656	−	0.107766i
$528$	−8.61937	−	30.0023i	−0.375110	−	1.30568i
$529$		−	20.2873i		−	0.882057i
$530$	−7.43532	+	11.2366i	−0.322970	+	0.488088i
$531$	−13.4237	+	3.59686i	−0.582538	+	0.156091i
$532$	−8.38966	+	1.18124i	−0.363738	+	0.0512134i
$533$	1.55597	−	5.80697i	0.0673967	−	0.251528i
$534$	−27.0707	−	17.9128i	−1.17146	−	0.775163i
$535$	3.07036	−	11.4587i	0.132743	−	0.495404i
$536$	2.00925	+	25.4074i	0.0867865	+	1.09743i
$537$	5.13041	+	19.1469i	0.221393	+	0.826252i
$538$	6.04089	−	1.22982i	0.260441	−	0.0530215i
$539$	−6.17324	−	10.6924i	−0.265900	−	0.460553i
$540$	2.63518	+	3.37113i	0.113400	+	0.145070i
$541$	1.84193	−	1.84193i	0.0791909	−	0.0791909i	−0.666402	−	0.745593i	$-0.732166\pi$
$541$	1.84193	−	1.84193i	0.0791909	−	0.0791909i	0.745593	+	0.666402i	$0.232166\pi$
$542$	−4.99111	+	4.41688i	−0.214387	+	0.189721i
$543$	5.49698	+	9.52105i	0.235898	+	0.408587i
$544$	−5.06396	+	4.64613i	−0.217116	+	0.199201i
$545$			7.56865i			0.324205i
$546$	5.60741	+	3.71045i	0.239975	+	0.158793i
$547$	4.40176	−	4.40176i	0.188206	−	0.188206i	−0.606714	−	0.794920i	$-0.707513\pi$
$547$	4.40176	−	4.40176i	0.188206	−	0.188206i	0.794920	+	0.606714i	$0.207513\pi$
$548$	−11.1364	+	4.73044i	−0.475725	+	0.202074i
$549$	−2.98981	−	2.98981i	−0.127602	−	0.127602i
$550$	3.67866	−	3.25543i	0.156859	−	0.138812i
$551$	−19.2757	−	11.1288i	−0.821174	−	0.474105i
$552$	−6.79434	+	7.96123i	−0.289186	+	0.338853i
$553$	−0.499804	−	0.133922i	−0.0212538	−	0.00569495i
$554$	13.7385	−	6.85193i	0.583694	−	0.291111i
$555$	−13.5191	+	2.00011i	−0.573854	+	0.0849000i
$556$	−34.7977	−	26.2082i	−1.47575	−	1.11148i
$557$	−0.816749	+	3.04815i	−0.0346067	+	0.129154i	−0.981068	−	0.193663i	$-0.937963\pi$
$557$	−0.816749	+	3.04815i	−0.0346067	+	0.129154i	0.946461	+	0.322817i	$0.104630\pi$
$558$	11.7724	+	0.718546i	0.498367	+	0.0304185i
$559$	−4.16730	+	7.21798i	−0.176258	+	0.305288i
$560$	3.82728	+	6.36241i	0.161732	+	0.268861i
$561$	6.70403	−	6.70403i	0.283045	−	0.283045i
$562$	−10.7146	−	0.653982i	−0.451970	−	0.0275866i
$563$	−2.18228	−	2.18228i	−0.0919723	−	0.0919723i	0.659624	−	0.751596i	$-0.270716\pi$
$563$	−2.18228	−	2.18228i	−0.0919723	−	0.0919723i	−0.751596	+	0.659624i	$0.770716\pi$
$564$	7.11417	+	0.871693i	0.299561	+	0.0367049i
$565$	−1.27320			−0.0535638
$566$	5.91086	+	11.8516i	0.248452	+	0.498160i
$567$	17.6024	−	10.1627i	0.739229	−	0.426794i
$568$	−2.09570	+	0.165731i	−0.0879336	+	0.00695392i
$569$	−28.7193	−	28.7193i	−1.20398	−	1.20398i	−0.972947	−	0.231029i	$-0.925791\pi$
$569$	−28.7193	−	28.7193i	−1.20398	−	1.20398i	−0.231029	−	0.972947i	$-0.574209\pi$
$570$	7.10551	−	1.44656i	0.297617	−	0.0605899i
$571$	−5.69748	+	3.28944i	−0.238432	+	0.137659i	−0.614456	−	0.788951i	$-0.710624\pi$
$571$	−5.69748	+	3.28944i	−0.238432	+	0.137659i	0.376024	+	0.926610i	$0.377291\pi$
$572$	−4.87761	−	6.23982i	−0.203943	−	0.260900i
$573$	−17.2668	+	4.62664i	−0.721333	+	0.193280i
$574$	−9.17375	−	10.3664i	−0.382905	−	0.432685i
$575$	−1.59091	−	0.426282i	−0.0663454	−	0.0177772i
$576$	−16.1784	+	2.57493i	−0.674100	+	0.107289i
$577$	−40.2496	−	10.7849i	−1.67561	−	0.448979i	−0.708998	−	0.705210i	$-0.750853\pi$
$577$	−40.2496	−	10.7849i	−1.67561	−	0.448979i	−0.966616	+	0.256231i	$0.917519\pi$
$578$	20.8207	+	6.96359i	0.866026	+	0.289647i
$579$	8.30231	+	30.9846i	0.345032	+	1.28768i
$580$	−2.37227	+	19.3609i	−0.0985031	+	0.803916i
$581$	−4.52469			−0.187716
$582$	−24.9815	−	50.0893i	−1.03552	−	2.07627i
$583$	−16.5468	−	28.6600i	−0.685300	−	1.18697i
$584$	10.1876	+	14.8110i	0.421565	+	0.612885i
$585$	−2.02179	−	1.16728i	−0.0835908	−	0.0482612i
$586$	−3.42718	+	10.2470i	−0.141576	+	0.423302i
$587$	3.51629	+	13.1230i	0.145133	+	0.541643i	0.999749	+	0.0223835i	$0.00712547\pi$
$587$	3.51629	+	13.1230i	0.145133	+	0.541643i	−0.854617	+	0.519259i	$0.826208\pi$
$588$	−14.7006	+	6.24440i	−0.606242	+	0.257515i
$589$	−4.64730	+	8.04936i	−0.191489	+	0.331668i
$590$	−9.40474	+	1.91465i	−0.387187	+	0.0788248i
$591$	9.41333			0.387213
$592$	−8.54298	+	22.7820i	−0.351114	+	0.936333i
$593$	−1.67506			−0.0687864			−0.0343932	−	0.999408i	$-0.510950\pi$
$593$	−1.67506			−0.0687864			−0.0343932	+	0.999408i	$0.510950\pi$
$594$	−10.2982	+	2.09654i	−0.422541	+	0.0860223i
$595$	−1.12754	+	1.95296i	−0.0462247	+	0.0800635i
$596$	20.9078	−	8.88104i	0.856416	−	0.363782i
$597$	2.83427	+	10.5776i	0.115999	+	0.432914i
$598$	−0.842281	+	2.51836i	−0.0344434	+	0.102984i
$599$	−9.19501	−	5.30874i	−0.375698	−	0.216909i	0.300247	−	0.953862i	$-0.402931\pi$
$599$	−9.19501	−	5.30874i	−0.375698	−	0.216909i	−0.675945	+	0.736952i	$0.736264\pi$
$600$	−3.60131	−	5.23570i	−0.147023	−	0.213747i
$601$	15.0048	+	25.9890i	0.612057	+	1.06011i	0.990893	+	0.134651i	$0.0429912\pi$
$601$	15.0048	+	25.9890i	0.612057	+	1.06011i	−0.378836	+	0.925464i	$0.623675\pi$
$602$	8.56518	+	17.1737i	0.349090	+	0.699947i
$603$	−18.4521			−0.751428
$604$	−3.42650	+	27.9648i	−0.139422	+	1.13787i
$605$	0.275691	+	1.02889i	0.0112084	+	0.0418304i
$606$	−43.8348	−	14.6608i	−1.78067	−	0.595554i
$607$	24.6822	+	6.61358i	1.00182	+	0.268437i	0.722208	−	0.691676i	$-0.243127\pi$
$607$	24.6822	+	6.61358i	1.00182	+	0.268437i	0.279612	+	0.960113i	$0.409794\pi$
$608$	3.87435	−	12.3149i	0.157126	−	0.499434i
$609$	39.2872	+	10.5270i	1.59200	+	0.426574i
$610$	−1.93519	−	2.18677i	−0.0783534	−	0.0885399i
$611$	1.75652	−	0.470658i	0.0710611	−	0.0190408i
$612$	−3.06425	−	3.92003i	−0.123865	−	0.158458i
$613$	8.56436	−	4.94463i	0.345911	−	0.199712i	−0.316972	−	0.948435i	$-0.602666\pi$
$613$	8.56436	−	4.94463i	0.345911	−	0.199712i	0.662883	+	0.748723i	$0.269333\pi$
$614$	12.8194	−	2.60983i	0.517351	−	0.105324i
$615$	8.37746	+	8.37746i	0.337812	+	0.337812i
$616$	−18.1797	+	1.43767i	−0.732479	+	0.0579255i
$617$	−7.49988	+	4.33006i	−0.301934	+	0.174322i	−0.643311	−	0.765605i	$-0.722440\pi$
$617$	−7.49988	+	4.33006i	−0.301934	+	0.174322i	0.341377	+	0.939926i	$0.389107\pi$
$618$	6.83206	+	13.6987i	0.274826	+	0.551042i
$619$	13.2081			0.530879			0.265439	−	0.964128i	$-0.414483\pi$
$619$	13.2081			0.530879			0.265439	+	0.964128i	$0.414483\pi$
$620$	8.08491	+	0.990637i	0.324698	+	0.0397849i
$621$	2.49163	+	2.49163i	0.0999858	+	0.0999858i
$622$	43.5118	+	2.65580i	1.74466	+	0.106488i
$623$	−13.4093	+	13.4093i	−0.537231	+	0.537231i
$624$	−8.77953	+	5.28129i	−0.351462	+	0.211421i
$625$	0.500000	−	0.866025i	0.0200000	−	0.0346410i
$626$	−31.5319	−	1.92459i	−1.26027	−	0.0769220i
$627$	−4.60959	+	17.2032i	−0.184089	+	0.687030i
$628$	−2.37328	−	1.78746i	−0.0947041	−	0.0713273i
$629$	−7.31028	+	1.08153i	−0.291480	+	0.0431236i
$630$	−4.81043	+	2.39915i	−0.191652	+	0.0955844i
$631$	−27.5967	−	7.39452i	−1.09861	−	0.294371i	−0.336411	−	0.941715i	$-0.609213\pi$
$631$	−27.5967	−	7.39452i	−1.09861	−	0.294371i	−0.762198	+	0.647344i	$0.775880\pi$
$632$	0.511831	−	0.599735i	0.0203595	−	0.0238562i
$633$	49.6056	+	28.6398i	1.97164	+	1.13833i
$634$	−36.9547	+	32.7030i	−1.46766	+	1.29880i
$635$	10.8530	+	10.8530i	0.430689	+	0.430689i
$636$	−39.4037	+	16.7376i	−1.56246	+	0.663688i
$637$	−2.86542	+	2.86542i	−0.113532	+	0.113532i
$638$	−39.9535	−	26.4374i	−1.58178	−	1.04667i
$639$		−	1.52200i		−	0.0602095i
$640$	−11.2607	+	1.09429i	−0.445117	+	0.0432555i
$641$	24.1713	+	41.8660i	0.954711	+	1.65361i	0.735029	+	0.678036i	$0.237169\pi$
$641$	24.1713	+	41.8660i	0.954711	+	1.65361i	0.219682	+	0.975571i	$0.429498\pi$
$642$	28.2270	−	24.9795i	1.11403	−	0.985861i
$643$	31.4056	−	31.4056i	1.23852	−	1.23852i	0.277910	−	0.960607i	$-0.410358\pi$
$643$	31.4056	−	31.4056i	1.23852	−	1.23852i	0.960607	−	0.277910i	$-0.0896417\pi$
$644$	3.76565	+	4.81731i	0.148387	+	0.189829i
$645$	−8.21251	−	14.2245i	−0.323367	−	0.560089i
$646$	3.84221	−	0.782210i	0.151170	−	0.0307756i
$647$	−8.68565	−	32.4153i	−0.341468	−	1.27438i	−0.896684	−	0.442670i	$-0.854031\pi$
$647$	−8.68565	−	32.4153i	−0.341468	−	1.27438i	0.555216	−	0.831706i	$-0.312636\pi$
$648$	2.44162	+	30.8748i	0.0959160	+	1.21288i
$649$	6.10117	−	22.7699i	0.239492	−	0.893796i
$650$	−1.34458	−	0.889713i	−0.0527387	−	0.0348974i
$651$	4.39596	−	16.4059i	0.172291	−	0.643000i
$652$	−31.0459	+	4.37118i	−1.21585	+	0.171189i
$653$	20.6263	−	5.52681i	0.807171	−	0.216281i	0.168441	−	0.985712i	$-0.446127\pi$
$653$	20.6263	−	5.52681i	0.807171	−	0.216281i	0.638730	+	0.769431i	$0.279460\pi$
$654$	−13.2706	+	20.0551i	−0.518920	+	0.784218i
$655$		−	6.52508i		−	0.254956i
$656$	20.2729	−	5.82422i	0.791526	−	0.227397i
$657$	−11.2711	+	6.50739i	−0.439729	+	0.253877i
$658$	1.32812	−	3.97099i	0.0517754	−	0.154805i
$659$	11.8689	−	20.5575i	0.462346	−	0.800807i	−0.536731	−	0.843753i	$-0.680341\pi$
$659$	11.8689	−	20.5575i	0.462346	−	0.800807i	0.999077	+	0.0429462i	$0.0136744\pi$
$660$	15.4555	−	2.17610i	0.601605	−	0.0847045i
$661$	−34.1250	+	9.14375i	−1.32731	+	0.355651i	−0.851710	−	0.524013i	$-0.824434\pi$
$661$	−34.1250	+	9.14375i	−1.32731	+	0.355651i	−0.475596	+	0.879664i	$0.657768\pi$
$662$	−3.07373	+	50.3591i	−0.119464	+	1.95726i
$663$	−2.69490	−	1.55590i	−0.104661	−	0.0604262i
$664$	2.96584	−	6.22405i	0.115097	−	0.241540i
$665$		−	4.23621i		−	0.164273i
$666$	−15.9550	−	7.46609i	−0.618243	−	0.289305i
$667$			16.0632i			0.621968i
$668$	−9.35167	+	7.31011i	−0.361827	+	0.282837i
$669$	55.3517	+	31.9573i	2.14002	+	1.23554i
$670$	−12.7197	−	0.776363i	−0.491404	−	0.0299935i
$671$	6.92775	−	1.85628i	0.267443	−	0.0716611i
$672$	−1.01421	+	23.5695i	−0.0391240	+	0.909212i
$673$	8.79896	−	15.2402i	0.339175	−	0.587468i	−0.645103	−	0.764096i	$-0.723185\pi$
$673$	8.79896	−	15.2402i	0.339175	−	0.587468i	0.984278	+	0.176628i	$0.0565188\pi$
$674$	−37.3231	−	12.4829i	−1.43763	−	0.480824i
$675$	−1.85280	+	1.06972i	−0.0713144	+	0.0411734i
$676$	14.0781	−	18.6920i	0.541465	−	0.718924i
$677$		−	14.0874i		−	0.541422i	−0.962661	−	0.270711i	$-0.912741\pi$
$677$		−	14.0874i		−	0.541422i	0.962661	−	0.270711i	$-0.0872588\pi$
$678$	−3.37367	−	2.23237i	−0.129565	−	0.0857337i
$679$	−31.5856	+	8.46332i	−1.21214	+	0.324793i
$680$	−1.94736	−	2.83114i	−0.0746779	−	0.108569i
$681$	7.35911	−	27.4646i	0.282002	−	1.05245i
$682$	−11.0400	+	16.6842i	−0.422744	+	0.638872i
$683$	1.66602	−	6.21767i	0.0637485	−	0.237913i	−0.926699	−	0.375805i	$-0.877366\pi$
$683$	1.66602	−	6.21767i	0.0637485	−	0.237913i	0.990447	+	0.137892i	$0.0440328\pi$
$684$	8.66697	+	3.49915i	0.331390	+	0.133793i
$685$	−1.56579	−	5.84359i	−0.0598256	−	0.223272i
$686$	5.52717	+	27.1494i	0.211028	+	1.03657i
$687$	2.55524	+	4.42581i	0.0974886	+	0.168855i
$688$	−29.2379	+	0.525068i	−1.11469	+	0.0200180i
$689$	−7.68052	+	7.68052i	−0.292605	+	0.292605i
$690$	−3.46810	−	3.91898i	−0.132028	−	0.149193i
$691$	−18.7018	−	32.3925i	−0.711450	−	1.23227i	−0.964313	−	0.264766i	$-0.914705\pi$
$691$	−18.7018	−	32.3925i	−0.711450	−	1.23227i	0.252862	−	0.967502i	$-0.418628\pi$
$692$	−3.71779	+	4.93626i	−0.141329	+	0.187649i
$693$		−	13.2030i		−	0.501540i
$694$	8.13297	−	12.2909i	0.308723	−	0.466557i
$695$	15.4019	−	15.4019i	0.584227	−	0.584227i
$696$	−40.2325	+	47.1422i	−1.52501	+	1.78692i
$697$	4.53000	+	4.53000i	0.171586	+	0.171586i
$698$	18.4725	+	20.8740i	0.699193	+	0.790094i
$699$	−19.8039	−	11.4338i	−0.749052	−	0.432466i
$700$	−3.41694	+	1.45142i	−0.129148	+	0.0548585i
$701$	−20.0242	−	5.36546i	−0.756302	−	0.202651i	−0.139991	−	0.990153i	$-0.544707\pi$
$701$	−20.0242	−	5.36546i	−0.756302	−	0.202651i	−0.616312	+	0.787502i	$0.711374\pi$
$702$	1.53950	+	3.08678i	0.0581045	+	0.116503i
$703$	10.8768	−	8.62572i	0.410227	−	0.325325i
$704$	9.93874	−	25.9498i	0.374580	−	0.978021i
$705$	−0.927527	+	3.46158i	−0.0349327	+	0.130371i
$706$	2.40307	−	39.3711i	0.0904408	−	1.48175i
$707$	−13.5014	+	23.3851i	−0.507771	+	0.879486i
$708$	−28.2774	−	11.4165i	−1.06273	−	0.429059i
$709$	24.4595	−	24.4595i	0.918594	−	0.918594i	−0.0783332	−	0.996927i	$-0.524960\pi$
$709$	24.4595	−	24.4595i	0.918594	−	0.918594i	0.996927	+	0.0783332i	$0.0249598\pi$
$710$	0.0640374	−	1.04917i	0.00240328	−	0.0393746i
$711$	0.403638	+	0.403638i	0.0151376	+	0.0151376i
$712$	−9.65596	−	27.2349i	−0.361873	−	1.02067i
$713$	6.70783			0.251210
$714$	−6.41195	+	3.19789i	−0.239961	+	0.119678i
$715$	3.42946	−	1.98000i	0.128254	−	0.0740478i
$716$	−6.60604	+	16.3624i	−0.246879	+	0.611491i
$717$	32.4932	+	32.4932i	1.21348	+	1.21348i
$718$	−3.56748	−	17.5235i	−0.133137	−	0.653970i
$719$	−16.8739	+	9.74214i	−0.629289	+	0.363320i	−0.780477	−	0.625185i	$-0.785024\pi$
$719$	−16.8739	+	9.74214i	−0.629289	+	0.363320i	0.151187	+	0.988505i	$0.451690\pi$
$720$	−0.147074	−	8.18969i	−0.00548113	−	0.305212i
$721$	8.63817	−	2.31459i	0.321702	−	0.0861999i
$722$	14.6063	−	12.9258i	0.543589	−	0.481049i
$723$	34.5670	+	9.26220i	1.28556	+	0.344465i
$724$	−1.19025	+	9.71402i	−0.0442353	+	0.361019i
$725$	−9.42051	−	2.52422i	−0.349869	−	0.0937471i
$726$	−1.07350	+	3.20970i	−0.0398414	+	0.119123i
$727$	−12.7233	−	47.4840i	−0.471881	−	1.76108i	−0.633003	−	0.774149i	$-0.718178\pi$
$727$	−12.7233	−	47.4840i	−0.471881	−	1.76108i	0.161122	−	0.986934i	$-0.448489\pi$
$728$	2.00013	+	5.64142i	0.0741297	+	0.209085i
$729$	−8.00272			−0.296397
$730$	−8.04337	+	4.01154i	−0.297698	+	0.148474i
$731$	−4.44081	−	7.69170i	−0.164249	−	0.284488i
$732$	−1.29358	−	9.18751i	−0.0478120	−	0.339580i
$733$	38.5349	+	22.2482i	1.42332	+	0.821755i	0.996581	−	0.0826198i	$-0.0263287\pi$
$733$	38.5349	+	22.2482i	1.42332	+	0.821755i	0.426740	+	0.904374i	$0.359662\pi$
$734$	0.266841	+	0.0892464i	0.00984927	+	0.00329414i
$735$	−2.06691	−	7.71381i	−0.0762391	−	0.284528i
$736$	−9.09487	+	2.02229i	−0.335241	+	0.0745425i
$737$	15.6497	−	27.1060i	0.576464	−	0.998464i
$738$	3.04645	+	14.9642i	0.112141	+	0.550838i
$739$	44.7874			1.64753			0.823766	−	0.566930i	$-0.191869\pi$
$739$	44.7874			1.64753			0.823766	+	0.566930i	$0.191869\pi$
$740$	−10.6842	−	5.81792i	−0.392758	−	0.213871i
$741$	5.84557			0.214742
$742$	4.98935	+	24.5077i	0.183165	+	0.899705i
$743$	−13.1432	+	22.7647i	−0.482178	+	0.835157i	−0.999791	−	0.0204581i	$-0.993488\pi$
$743$	−13.1432	+	22.7647i	−0.482178	+	0.835157i	0.517613	+	0.855615i	$0.326821\pi$
$744$	19.6861	+	16.8007i	0.721729	+	0.615944i
$745$	2.93964	+	10.9709i	0.107700	+	0.401943i
$746$	−11.5172	−	3.85200i	−0.421676	−	0.141032i
$747$	4.32285	+	2.49580i	0.158165	+	0.0913165i
$748$	8.35737	−	1.17670i	0.305576	−	0.0430243i
$749$	−11.0101	−	19.0700i	−0.402299	−	0.696803i
$750$	2.84333	−	1.41808i	0.103824	−	0.0517810i
$751$	9.65785			0.352420			0.176210	−	0.984353i	$-0.443616\pi$
$751$	9.65785			0.352420			0.176210	+	0.984353i	$0.443616\pi$
$752$	4.59183	+	4.42982i	0.167447	+	0.161539i
$753$	4.46179	+	16.6516i	0.162597	+	0.606819i
$754$	−4.98754	+	14.9124i	−0.181636	+	0.543079i
$755$	−13.6070	−	3.64597i	−0.495208	−	0.132691i
$756$	7.88351	+	0.965960i	0.286721	+	0.0351316i
$757$	34.0331	+	9.11915i	1.23695	+	0.331441i	0.817284	−	0.576235i	$-0.195479\pi$
$757$	34.0331	+	9.11915i	1.23695	+	0.331441i	0.419671	+	0.907676i	$0.362145\pi$
$758$	−26.0013	+	23.0099i	−0.944411	+	0.835756i
$759$	12.4154	−	3.32670i	0.450650	−	0.120751i
$760$	5.82721	+	2.77674i	0.211375	+	0.100723i
$761$	−16.4108	+	9.47478i	−0.594891	+	0.343461i	−0.767029	−	0.641612i	$-0.778266\pi$
$761$	−16.4108	+	9.47478i	−0.594891	+	0.343461i	0.172138	+	0.985073i	$0.444933\pi$
$762$	9.72868	+	47.7872i	0.352433	+	1.73115i
$763$	9.93416	+	9.93416i	0.359641	+	0.359641i
$764$	−14.7557	−	5.95737i	−0.533843	−	0.215530i
$765$	2.15448	−	1.24389i	0.0778956	−	0.0449730i
$766$	26.5935	−	13.2632i	0.960861	−	0.479219i
$767$	−7.73710			−0.279370
$768$	−31.7568	−	16.8444i	−1.14592	−	0.607820i
$769$	9.15322	+	9.15322i	0.330073	+	0.330073i	0.852614	−	0.522541i	$-0.175016\pi$
$769$	9.15322	+	9.15322i	0.330073	+	0.330073i	−0.522541	+	0.852614i	$0.675016\pi$
$770$	0.555508	−	9.10127i	0.0200191	−	0.327987i
$771$	−3.49233	+	3.49233i	−0.125773	+	0.125773i
$772$	−10.6903	+	26.4785i	−0.384751	+	0.952982i
$773$	−15.7756	+	27.3241i	−0.567408	+	0.982779i	0.429413	+	0.903108i	$0.358720\pi$
$773$	−15.7756	+	27.3241i	−0.567408	+	0.982779i	−0.996821	+	0.0796713i	$0.974613\pi$
$774$	1.28982	−	21.1321i	0.0463618	−	0.759577i
$775$	−1.05409	+	3.93391i	−0.0378640	+	0.141310i
$776$	9.06171	−	48.9958i	0.325296	−	1.75885i
$777$	−15.1191	+	20.3696i	−0.542396	+	0.730755i
$778$	20.5952	+	41.2946i	0.738374	+	1.48048i
$779$	−11.6244	−	3.11475i	−0.416488	−	0.111598i
$780$	−2.00282	−	4.71505i	−0.0717125	−	0.168826i
$781$	2.23581	+	1.29085i	0.0800037	+	0.0461902i
$782$	−1.87533	−	2.11913i	−0.0670616	−	0.0757801i
$783$	14.7541	+	14.7541i	0.527270	+	0.527270i
$784$	−13.7973	−	3.43268i	−0.492761	−	0.122596i
$785$	1.05044	−	1.05044i	0.0374919	−	0.0374919i
$786$	11.4408	−	17.2899i	0.408080	−	0.616710i
$787$			45.3531i			1.61666i	0.588728	+	0.808331i	$0.299629\pi$
$787$			45.3531i			1.61666i	−0.588728	+	0.808331i	$0.700371\pi$
$788$	6.69353	+	5.04130i	0.238447	+	0.179589i
$789$	19.7766	+	34.2541i	0.704066	+	1.21948i
$790$	0.261258	+	0.295224i	0.00929515	+	0.0105036i
$791$	−1.67112	+	1.67112i	−0.0594182	+	0.0594182i
$792$	18.1617	+	8.65427i	0.645347	+	0.307516i
$793$	−1.17701	−	2.03864i	−0.0417968	−	0.0723941i
$794$	−6.75531	−	33.1820i	−0.239737	−	1.17759i
$795$	−5.54017	−	20.6762i	−0.196490	−	0.733309i
$796$	−3.64948	+	9.03932i	−0.129352	+	0.320390i
$797$	−4.10968	+	15.3375i	−0.145572	+	0.543283i	0.854157	+	0.520015i	$0.174074\pi$
$797$	−4.10968	+	15.3375i	−0.145572	+	0.543283i	−0.999729	+	0.0232681i	$0.992593\pi$
$798$	7.42759	−	11.2249i	0.262934	−	0.397358i
$799$	−0.501548	+	1.87180i	−0.0177435	+	0.0662196i
$800$	0.243194	−	5.65162i	0.00859819	−	0.199815i
$801$	20.2076	−	5.41460i	0.714000	−	0.191316i
$802$	−13.6179	−	9.01100i	−0.480863	−	0.318189i
$803$		−	22.0763i		−	0.779055i
$804$	−32.3429	−	24.3593i	−1.14065	−	0.859088i
$805$	−2.64764	+	1.52861i	−0.0933170	+	0.0538766i
$806$	6.22729	+	2.08275i	0.219347	+	0.0733617i
$807$	−4.89692	+	8.48172i	−0.172380	+	0.298571i
$808$	−23.3180	−	33.9005i	−0.820325	−	1.19262i
$809$	34.1250	−	9.14375i	1.19977	−	0.321477i	0.397029	−	0.917806i	$-0.370041\pi$
$809$	34.1250	−	9.14375i	1.19977	−	0.321477i	0.802740	+	0.596329i	$0.203374\pi$
$810$	−15.4568	−	0.943428i	−0.543097	−	0.0331487i
$811$	23.1705	+	13.3775i	0.813625	+	0.469747i	0.848213	−	0.529655i	$-0.177679\pi$
$811$	23.1705	+	13.3775i	0.813625	+	0.469747i	−0.0345880	+	0.999402i	$0.511012\pi$
$812$	22.2982	+	28.5256i	0.782513	+	1.00105i
$813$		−	10.5882i		−	0.371346i
$814$	24.4994	−	17.1056i	0.858705	−	0.599551i
$815$		−	15.6760i		−	0.549108i
$816$	−0.196039	−	10.9163i	−0.00686275	−	0.382146i
$817$	14.4490	+	8.34212i	0.505506	+	0.291854i
$818$	0.526250	−	8.62191i	0.0183999	−	0.301458i
$819$	−4.18578	+	1.12158i	−0.146263	+	0.0391911i
$820$	1.47042	+	10.4435i	0.0513491	+	0.364702i
$821$	4.63793	−	8.03313i	0.161865	−	0.280358i	−0.773673	−	0.633586i	$-0.781582\pi$
$821$	4.63793	−	8.03313i	0.161865	−	0.280358i	0.935538	+	0.353227i	$0.114916\pi$
$822$	6.09696	−	18.2295i	0.212656	−	0.635827i
$823$	30.2919	−	17.4891i	1.05591	−	0.609630i	0.131613	−	0.991301i	$-0.457985\pi$
$823$	30.2919	−	17.4891i	1.05591	−	0.609630i	0.924298	+	0.381671i	$0.124651\pi$
$824$	−2.47824	+	13.3996i	−0.0863336	+	0.466798i
$825$			7.80398i			0.271700i
$826$	−9.83104	+	14.8571i	−0.342066	+	0.516946i
$827$	28.1411	−	7.54038i	0.978562	−	0.262205i	0.266123	−	0.963939i	$-0.414257\pi$
$827$	28.1411	−	7.54038i	0.978562	−	0.262205i	0.712439	+	0.701734i	$0.247591\pi$
$828$	−0.940461	−	6.67953i	−0.0326833	−	0.232130i
$829$	−11.1724	+	41.6961i	−0.388035	+	1.44816i	0.445293	+	0.895385i	$0.353100\pi$
$829$	−11.1724	+	41.6961i	−0.388035	+	1.44816i	−0.833327	+	0.552780i	$0.813567\pi$
$830$	2.87488	+	1.90232i	0.0997885	+	0.0660305i
$831$	−6.31257	+	23.5588i	−0.218981	+	0.817247i
$832$	−9.07124	−	0.946503i	−0.314489	−	0.0328141i
$833$	−1.11765	−	4.17114i	−0.0387244	−	0.144521i
$834$	67.8164	−	13.8063i	2.34829	−	0.478073i
$835$	−2.96744	−	5.13976i	−0.102693	−	0.177869i
$836$	−12.4909	+	9.76402i	−0.432006	+	0.337696i
$837$	6.16119	−	6.16119i	0.212962	−	0.212962i
$838$	13.4762	−	11.9258i	0.465528	−	0.411969i
$839$	−4.98803	−	8.63952i	−0.172206	−	0.298269i	0.766985	−	0.641665i	$-0.221756\pi$
$839$	−4.98803	−	8.63952i	−0.172206	−	0.298269i	−0.939191	+	0.343396i	$0.888423\pi$
$840$	−11.5989	−	2.14521i	−0.400201	−	0.0740167i
$841$			66.1176i			2.27992i
$842$	28.0791	+	18.5801i	0.967671	+	0.640312i
$843$	12.0588	−	12.0588i	0.415327	−	0.415327i
$844$	19.9350	+	46.9311i	0.686191	+	1.61543i
$845$	8.27333	+	8.27333i	0.284611	+	0.284611i
$846$	−3.45925	+	3.06126i	−0.118931	+	0.105248i
$847$	1.71232	+	0.988606i	0.0588359	+	0.0339689i
$848$	−36.9825	−	9.20101i	−1.26998	−	0.315964i
$849$	−20.3232	−	5.44558i	−0.697489	−	0.186892i
$850$	1.53750	−	0.766809i	0.0527357	−	0.0263013i
$851$	−9.31595	−	3.68550i	−0.319347	−	0.126337i
$852$	2.00925	−	2.66777i	0.0688359	−	0.0913962i
$853$	11.8870	−	44.3628i	0.407003	−	1.51895i	−0.393329	−	0.919398i	$-0.628677\pi$
$853$	11.8870	−	44.3628i	0.407003	−	1.51895i	0.800332	−	0.599557i	$-0.204657\pi$
$854$	−5.41024	−	0.330221i	−0.185134	−	0.0112999i
$855$	−2.33667	+	4.04723i	−0.0799124	+	0.138412i
$856$	33.4491	−	2.64520i	1.14327	−	0.0904111i
$857$	22.4933	−	22.4933i	0.768357	−	0.768357i	−0.209460	−	0.977817i	$-0.567171\pi$
$857$	22.4933	−	22.4933i	0.768357	−	0.768357i	0.977817	+	0.209460i	$0.0671707\pi$
$858$	12.5589	+	0.766549i	0.428754	+	0.0261696i
$859$	−21.8213	−	21.8213i	−0.744533	−	0.744533i	0.228914	−	0.973447i	$-0.426483\pi$
$859$	−21.8213	−	21.8213i	−0.744533	−	0.744533i	−0.973447	+	0.228914i	$0.926483\pi$
$860$	1.77824	−	14.5128i	0.0606375	−	0.494882i
$861$	21.9915			0.749468
$862$	−1.20357	−	2.41322i	−0.0409936	−	0.0821946i
$863$	−23.0779	+	13.3240i	−0.785582	+	0.453556i	−0.838405	−	0.545048i	$-0.816511\pi$
$863$	−23.0779	+	13.3240i	−0.785582	+	0.453556i	0.0528231	+	0.998604i	$0.483178\pi$
$864$	−6.49622	+	10.2112i	−0.221006	+	0.347392i
$865$	−2.18485	−	2.18485i	−0.0742872	−	0.0742872i
$866$	41.8687	−	8.52377i	1.42276	−	0.289650i
$867$	−30.2054	+	17.4391i	−1.02583	+	0.592263i
$868$	11.9120	−	9.31151i	0.404320	−	0.316053i
$869$	−0.935276	+	0.250606i	−0.0317271	+	0.00850124i
$870$	−20.5362	−	23.2061i	−0.696244	−	0.786761i
$871$	−9.92294	−	2.65884i	−0.336226	−	0.0900915i
$872$	−20.1768	+	7.15355i	−0.683272	+	0.242250i
$873$	34.8449	+	9.33665i	1.17932	+	0.315998i
$874$	5.04127	+	1.68608i	0.170524	+	0.0570325i
$875$	−0.480423	−	1.79296i	−0.0162413	−	0.0606132i
$876$	−28.3467	−	3.47330i	−0.957746	−	0.117352i
$877$	−14.8666			−0.502010			−0.251005	−	0.967986i	$-0.580761\pi$
$877$	−14.8666			−0.502010			−0.251005	+	0.967986i	$0.580761\pi$
$878$	12.8391	+	25.7432i	0.433300	+	0.868791i
$879$	−8.58278	−	14.8658i	−0.289490	−	0.501411i
$880$	12.1553	+	6.72982i	0.409757	+	0.226862i
$881$	−42.6070	−	24.5992i	−1.43547	−	0.828767i	−0.437937	−	0.899006i	$-0.644291\pi$
$881$	−42.6070	−	24.5992i	−1.43547	−	0.828767i	−0.997530	+	0.0702385i	$0.977624\pi$
$882$	3.26499	−	9.76211i	0.109938	−	0.328707i
$883$	−2.73636	−	10.2122i	−0.0920857	−	0.343669i	0.904476	−	0.426525i	$-0.140262\pi$
$883$	−2.73636	−	10.2122i	−0.0920857	−	0.343669i	−0.996561	+	0.0828564i	$0.973596\pi$
$884$	−1.08300	−	2.54960i	−0.0364252	−	0.0857525i
$885$	7.62376	−	13.2047i	0.256270	−	0.443872i
$886$	40.4516	−	8.23528i	1.35900	−	0.276670i
$887$	−37.1332			−1.24681			−0.623405	−	0.781899i	$-0.714251\pi$
$887$	−37.1332			−1.24681			−0.623405	+	0.781899i	$0.714251\pi$
$888$	−18.1096	−	34.1493i	−0.607719	−	1.14598i
$889$	28.4901			0.955526
$890$	14.1576	−	2.88225i	0.474564	−	0.0966132i
$891$	19.0173	−	32.9390i	0.637105	−	1.10350i
$892$	22.2442	+	52.3674i	0.744791	+	1.75339i
$893$	−0.942165	−	3.51621i	−0.0315283	−	0.117665i
$894$	−11.4466	+	34.2245i	−0.382831	+	1.14464i
$895$	−7.64077	−	4.41140i	−0.255403	−	0.147457i
$896$	−13.3438	+	16.2164i	−0.445784	+	0.541751i
$897$	−2.10935	−	3.65349i	−0.0704290	−	0.121987i
$898$	14.5717	+	29.2172i	0.486265	+	0.974989i
$899$	39.7202			1.32474
$900$	4.06511	+	0.498094i	0.135504	+	0.0166031i
$901$	−2.99578	−	11.1804i	−0.0998037	−	0.372473i
$902$	−24.5660	−	8.21624i	−0.817959	−	0.273571i
$903$	−29.4494	−	7.89095i	−0.980016	−	0.262595i
$904$	−1.20337	−	3.39413i	−0.0400234	−	0.112887i
$905$	−4.72660	−	1.26649i	−0.157117	−	0.0420995i
$906$	−29.6625	−	33.5189i	−0.985471	−	1.11359i
$907$	9.99538	−	2.67825i	0.331891	−	0.0889299i	−0.0890254	−	0.996029i	$-0.528375\pi$
$907$	9.99538	−	2.67825i	0.331891	−	0.0889299i	0.420916	+	0.907099i	$0.361709\pi$
$908$	19.9415	−	15.5881i	0.661781	−	0.517308i
$909$	25.7982	−	14.8946i	0.855671	−	0.494022i
$910$	−2.93259	+	0.597027i	−0.0972145	+	0.0197913i
$911$	−4.83808	−	4.83808i	−0.160293	−	0.160293i	0.622404	−	0.782696i	$-0.286156\pi$
$911$	−4.83808	−	4.83808i	−0.160293	−	0.160293i	−0.782696	+	0.622404i	$0.786156\pi$
$912$	10.5721	+	17.5749i	0.350077	+	0.581963i
$913$	−7.33263	+	4.23349i	−0.242675	+	0.140108i
$914$	10.2557	+	20.5633i	0.339228	+	0.680172i
$915$	4.63906			0.153363
$916$	−0.553282	+	4.51552i	−0.0182810	+	0.149197i
$917$	−8.56442	−	8.56442i	−0.282822	−	0.282822i
$918$	−3.66894	−	0.223939i	−0.121093	−	0.00739108i
$919$	−19.7133	+	19.7133i	−0.650282	+	0.650282i	−0.953061	−	0.302779i	$-0.902086\pi$
$919$	−19.7133	+	19.7133i	−0.650282	+	0.650282i	0.302779	+	0.953061i	$0.402086\pi$
$920$	−0.367254	−	4.64400i	−0.0121080	−	0.153108i
$921$	−10.3918	+	17.9992i	−0.342422	+	0.593093i
$922$	−49.1132	−	2.99769i	−1.61746	−	0.0987237i
$923$	0.219312	−	0.818483i	0.00721874	−	0.0269407i
$924$	17.4298	−	23.1422i	0.573397	−	0.761322i
$925$	3.62536	−	4.88434i	0.119201	−	0.160596i
$926$	11.9001	−	5.93502i	0.391060	−	0.195037i
$927$	−9.52955	−	2.55343i	−0.312991	−	0.0838658i
$928$	−53.8550	+	11.9749i	−1.76788	+	0.393096i
$929$	−23.4098	−	13.5157i	−0.768052	−	0.443435i	0.0641275	−	0.997942i	$-0.479574\pi$
$929$	−23.4098	−	13.5157i	−0.768052	−	0.443435i	−0.832179	+	0.554507i	$0.812907\pi$
$930$	−9.69065	+	8.57574i	−0.317769	+	0.281210i
$931$	5.73602	+	5.73602i	0.187990	+	0.187990i
$932$	−7.95859	−	18.7362i	−0.260692	−	0.613723i
$933$	−48.9704	+	48.9704i	−1.60322	+	1.60322i
$934$	−40.0828	−	26.5230i	−1.31155	−	0.867858i
$935$			4.21990i			0.138005i
$936$	1.20088	−	6.49303i	0.0392519	−	0.212231i
$937$	0.909141	+	1.57468i	0.0297003	+	0.0514425i	0.880494	−	0.474058i	$-0.157211\pi$
$937$	0.909141	+	1.57468i	0.0297003	+	0.0514425i	−0.850793	+	0.525501i	$0.823878\pi$
$938$	−17.7141	+	15.6761i	−0.578385	+	0.511842i
$939$	35.4876	−	35.4876i	1.15809	−	1.15809i
$940$	−2.51338	+	1.96468i	−0.0819774	+	0.0640810i
$941$	−19.7106	−	34.1398i	−0.642549	−	1.11293i	−0.984862	−	0.173341i	$-0.944544\pi$
$941$	−19.7106	−	34.1398i	−0.642549	−	1.11293i	0.342313	−	0.939586i	$-0.388790\pi$
$942$	4.62523	−	0.941619i	0.150698	−	0.0306796i
$943$	2.24789	+	8.38924i	0.0732014	+	0.273191i
$944$	−13.9931	−	23.2618i	−0.455435	−	0.757109i
$945$	−1.02783	+	3.83592i	−0.0334354	+	0.124782i
$946$	29.9490	+	19.8174i	0.973724	+	0.644318i
$947$	−3.94934	+	14.7391i	−0.128336	+	0.478958i	−0.999937	−	0.0112596i	$-0.996416\pi$
$947$	−3.94934	+	14.7391i	−0.128336	+	0.478958i	0.871600	+	0.490217i	$0.163083\pi$
$948$	0.174639	+	1.24035i	0.00567200	+	0.0402848i
$949$	−6.99892	+	1.87535i	−0.227194	+	0.0608766i
$950$	−1.78103	+	2.69158i	−0.0577843	+	0.0873264i
$951$		−	78.3963i		−	2.54217i
$952$	−6.27197	−	1.15999i	−0.203276	−	0.0375956i
$953$	−40.6155	+	23.4493i	−1.31566	+	0.759599i	−0.983028	−	0.183456i	$-0.941271\pi$
$953$	−40.6155	+	23.4493i	−1.31566	+	0.759599i	−0.332636	+	0.943055i	$0.607938\pi$
$954$	8.75153	−	26.1665i	0.283341	−	0.847172i
$955$	3.97823	−	6.89050i	0.128733	−	0.222971i
$956$	5.70322	+	40.5066i	0.184455	+	1.31008i
$957$	73.5174	−	19.6989i	2.37648	−	0.636776i
$958$	−2.66454	+	43.6549i	−0.0860873	+	1.41043i
$959$	−9.72510	−	5.61479i	−0.314040	−	0.181311i
$960$	10.5537	−	14.5491i	0.340620	−	0.469569i
$961$			14.4132i			0.464943i
$962$	−7.50424	−	6.31403i	−0.241946	−	0.203573i
$963$			24.2924i			0.782812i
$964$	19.6192	+	25.0984i	0.631891	+	0.808364i
$965$	−12.3647	−	7.13877i	−0.398034	−	0.229805i
$966$	−9.69582	−	0.591798i	−0.311958	−	0.0190408i
$967$	37.0626	−	9.93090i	1.19185	−	0.319356i	0.392236	−	0.919865i	$-0.371702\pi$
$967$	37.0626	−	9.93090i	1.19185	−	0.319356i	0.799618	+	0.600508i	$0.205035\pi$
$968$	−2.48229	+	1.70741i	−0.0797837	+	0.0548782i
$969$	−3.11461	+	5.39466i	−0.100056	+	0.173302i
$970$	23.6269	+	7.90215i	0.758615	+	0.253723i
$971$	26.6548	−	15.3892i	0.855394	−	0.493862i	−0.00707309	−	0.999975i	$-0.502251\pi$
$971$	26.6548	−	15.3892i	0.855394	−	0.493862i	0.862467	+	0.506113i	$0.168918\pi$
$972$	−29.0490	−	21.8786i	−0.931748	−	0.701755i
$973$		−	40.4312i		−	1.29616i
$974$	−37.8618	−	25.0533i	−1.21317	−	0.802760i
$975$	2.47412	−	0.662939i	0.0792353	−	0.0212310i
$976$	4.00053	−	7.22573i	0.128054	−	0.231290i
$977$	6.02551	−	22.4875i	0.192773	−	0.719439i	−0.800059	−	0.599921i	$-0.795199\pi$
$977$	6.02551	−	22.4875i	0.192773	−	0.719439i	0.992832	−	0.119517i	$-0.0381347\pi$
$978$	27.4857	−	41.5378i	0.878897	−	1.32823i
$979$	−9.18451	+	34.2771i	−0.293538	+	1.09550i
$980$	2.66140	−	6.59198i	0.0850155	−	0.210573i
$981$	−4.01137	−	14.9706i	−0.128073	−	0.477975i
$982$	−0.0643764	−	0.316217i	−0.00205433	−	0.0100909i
$983$	−1.11033	−	1.92315i	−0.0354141	−	0.0613390i	0.847775	−	0.530356i	$-0.177942\pi$
$983$	−1.11033	−	1.92315i	−0.0354141	−	0.0613390i	−0.883189	+	0.469017i	$0.844608\pi$
$984$	−14.4149	+	30.2509i	−0.459531	+	0.964364i
$985$	−2.96264	+	2.96264i	−0.0943976	+	0.0943976i
$986$	−11.1047	−	12.5484i	−0.353646	−	0.399622i
$987$	3.32604	+	5.76087i	0.105869	+	0.183371i
$988$	4.15660	+	3.13059i	0.132239	+	0.0995972i
$989$		−	12.0409i		−	0.382877i
$990$	−5.55094	+	8.38885i	−0.176421	+	0.266615i
$991$	26.4306	−	26.4306i	0.839596	−	0.839596i	−0.149210	−	0.988806i	$-0.547673\pi$
$991$	26.4306	−	26.4306i	0.839596	−	0.839596i	0.988806	+	0.149210i	$0.0476730\pi$
$992$	5.00061	+	22.4894i	0.158770	+	0.714038i
$993$	−56.6767	−	56.6767i	−1.79858	−	1.79858i
$994$	−1.29302	−	1.46113i	−0.0410122	−	0.0463441i
$995$	−4.22111	−	2.43706i	−0.133818	−	0.0772599i
$996$	4.28229	+	10.0814i	0.135690	+	0.319441i
$997$	28.2088	+	7.55851i	0.893380	+	0.239381i	0.676171	−	0.736745i	$-0.263638\pi$
$997$	28.2088	+	7.55851i	0.893380	+	0.239381i	0.217209	+	0.976125i	$0.430305\pi$
$998$	9.83225	+	19.7142i	0.311234	+	0.624043i
$999$	−11.9419	+	5.17161i	−0.377826	+	0.163623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.be.a.251.5	yes	304
4.3	odd	2	inner	740.2.be.a.251.59	yes	304
37.23	odd	12	inner	740.2.be.a.171.59	yes	304
148.23	even	12	inner	740.2.be.a.171.5	✓	304

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.be.a.171.5	✓	304	148.23	even	12	inner
740.2.be.a.171.59	yes	304	37.23	odd	12	inner
740.2.be.a.251.5	yes	304	1.1	even	1	trivial
740.2.be.a.251.59	yes	304	4.3	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38579 + 0.282123i) q^{2} +(1.12336 - 1.94572i) q^{3} +(1.84081 - 0.781925i) q^{4} +(0.258819 + 0.965926i) q^{5} +(-1.00781 + 3.01328i) q^{6} +(1.60753 + 0.928106i) q^{7} +(-2.33038 + 1.60292i) q^{8} +(-1.02388 - 1.77341i) q^{9} +(-0.631178 - 1.26555i) q^{10} +3.47350 q^{11} +(0.546491 - 4.46009i) q^{12} +(-0.295069 - 1.10121i) q^{13} +(-2.48953 - 0.832637i) q^{14} +(2.17017 + 0.581494i) q^{15} +(2.77719 - 2.87876i) q^{16} +(1.17349 + 0.314435i) q^{17} +(1.91919 + 2.16871i) q^{18} +(-2.20442 + 0.590671i) q^{19} +(1.23172 + 1.57571i) q^{20} +(3.61166 - 2.08519i) q^{21} +(-4.81353 + 0.979954i) q^{22} +(1.16462 + 1.16462i) q^{23} +(0.500974 + 6.33491i) q^{24} +(-0.866025 + 0.500000i) q^{25} +(0.719581 + 1.44280i) q^{26} +2.13943 q^{27} +(3.68486 + 0.451503i) q^{28} +(6.89629 + 6.89629i) q^{29} +(-3.17144 - 0.193573i) q^{30} +(2.87982 - 2.87982i) q^{31} +(-3.03642 + 4.77285i) q^{32} +(3.90199 - 6.75844i) q^{33} +(-1.71491 - 0.104672i) q^{34} +(-0.480423 + 1.79296i) q^{35} +(-3.27144 - 2.46391i) q^{36} +(-5.58182 + 2.41728i) q^{37} +(2.88821 - 1.44046i) q^{38} +(-2.47412 - 0.662939i) q^{39} +(-2.15145 - 1.83610i) q^{40} +(4.56676 + 2.63662i) q^{41} +(-4.41671 + 3.90857i) q^{42} +(-5.16942 - 5.16942i) q^{43} +(6.39406 - 2.71602i) q^{44} +(1.44798 - 1.44798i) q^{45} +(-1.94249 - 1.28535i) q^{46} +1.59507i q^{47} +(-2.48147 - 8.63750i) q^{48} +(-1.77724 - 3.07827i) q^{49} +(1.05907 - 0.937220i) q^{50} +(1.93005 - 1.93005i) q^{51} +(-1.40423 - 1.79641i) q^{52} +(-4.76374 - 8.25104i) q^{53} +(-2.96480 + 0.603583i) q^{54} +(0.899007 + 3.35514i) q^{55} +(-5.23382 + 0.413898i) q^{56} +(-1.32707 + 4.95271i) q^{57} +(-11.5024 - 7.61119i) q^{58} +(1.75649 - 6.55532i) q^{59} +(4.44955 - 0.626486i) q^{60} +(1.99446 - 0.534414i) q^{61} +(-3.17836 + 4.80329i) q^{62} -3.80106i q^{63} +(2.86131 - 7.47081i) q^{64} +(0.987321 - 0.570030i) q^{65} +(-3.50061 + 10.4666i) q^{66} +(4.50545 - 7.80368i) q^{67} +(2.40604 - 0.338764i) q^{68} +(3.57432 - 0.957736i) q^{69} +(0.159928 - 2.62020i) q^{70} +(0.643678 + 0.371628i) q^{71} +(5.22864 + 2.49151i) q^{72} -6.35564i q^{73} +(7.05325 - 4.92460i) q^{74} +2.24672i q^{75} +(-3.59606 + 2.81100i) q^{76} +(5.58374 + 3.22377i) q^{77} +(3.61563 + 0.220685i) q^{78} +(-0.269260 + 0.0721481i) q^{79} +(3.49945 + 1.93748i) q^{80} +(5.47498 - 9.48295i) q^{81} +(-7.07242 - 2.36541i) q^{82} +(-2.11102 + 1.21880i) q^{83} +(5.01793 - 6.66250i) q^{84} +1.21488i q^{85} +(8.62213 + 5.70530i) q^{86} +(21.1652 - 5.67121i) q^{87} +(-8.09456 + 5.56773i) q^{88} +(-2.64417 + 9.86817i) q^{89} +(-1.59808 + 2.41510i) q^{90} +(0.547711 - 2.04409i) q^{91} +(3.05450 + 1.23321i) q^{92} +(-2.36824 - 8.83841i) q^{93} +(-0.450008 - 2.21043i) q^{94} +(-1.14109 - 1.97642i) q^{95} +(5.87562 + 11.2697i) q^{96} +(-12.4567 + 12.4567i) q^{97} +(3.33133 + 3.76443i) q^{98} +(-3.55643 - 6.15992i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 304 q + 4 q^{2} - 12 q^{4} - 8 q^{8} - 152 q^{9} + 16 q^{13} - 24 q^{14} + 20 q^{16} - 60 q^{18} - 16 q^{22} - 24 q^{24} - 32 q^{29} - 56 q^{32} - 32 q^{37} + 40 q^{38} + 20 q^{42} + 12 q^{44} - 8 q^{46}+ \cdots - 36 q^{98}+O(q^{100}) \) 304 * q + 4 * q^2 - 12 * q^4 - 8 * q^8 - 152 * q^9 + 16 * q^13 - 24 * q^14 + 20 * q^16 - 60 * q^18 - 16 * q^22 - 24 * q^24 - 32 * q^29 - 56 * q^32 - 32 * q^37 + 40 * q^38 + 20 * q^42 + 12 * q^44 - 8 * q^46 + 104 * q^49 + 4 * q^50 - 40 * q^52 + 40 * q^54 + 4 * q^56 - 48 * q^57 - 12 * q^58 - 28 * q^60 - 16 * q^61 - 60 * q^62 + 24 * q^65 - 52 * q^66 - 200 * q^68 - 196 * q^72 + 20 * q^74 - 40 * q^76 + 96 * q^77 - 48 * q^78 - 152 * q^81 + 32 * q^82 - 112 * q^84 + 12 * q^88 - 8 * q^89 + 140 * q^92 - 16 * q^93 - 28 * q^94 - 132 * q^96 + 48 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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