LMFDB - Embedded newform 555.2.bb.a.454.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [555,2,Mod(454,555)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(555, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("555.454");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 555 = 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	555.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.43169731218$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			454.3
Character	$\chi$	$=$	555.454
Dual form			555.2.bb.a.544.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.16333 - 1.24900i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.11999 + 3.67194i) q^{4} +(-2.13789 - 0.655312i) q^{5} +2.49800 q^{6} +(-0.174209 + 0.100580i) q^{7} -5.59548i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-2.16333 - 1.24900i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.11999 + 3.67194i) q^{4} +(-2.13789 - 0.655312i) q^{5} +2.49800 q^{6} +(-0.174209 + 0.100580i) q^{7} -5.59548i q^{8} +(0.500000 - 0.866025i) q^{9} +(3.80647 + 4.08787i) q^{10} +0.483348 q^{11} +(-3.67194 - 2.11999i) q^{12} +(3.16991 - 1.83015i) q^{13} +0.502496 q^{14} +(2.17912 - 0.501428i) q^{15} +(-2.74876 + 4.76099i) q^{16} +(-0.348928 - 0.201454i) q^{17} +(-2.16333 + 1.24900i) q^{18} +(0.878784 + 1.52210i) q^{19} +(-2.12605 - 9.23945i) q^{20} +(0.100580 - 0.174209i) q^{21} +(-1.04564 - 0.603701i) q^{22} -2.07034i q^{23} +(2.79774 + 4.84583i) q^{24} +(4.14113 + 2.80197i) q^{25} -9.14341 q^{26} +1.00000i q^{27} +(-0.738645 - 0.426457i) q^{28} -1.88335 q^{29} +(-5.34044 - 1.63697i) q^{30} -10.4661 q^{31} +(2.20129 - 1.27091i) q^{32} +(-0.418592 + 0.241674i) q^{33} +(0.503231 + 0.871622i) q^{34} +(0.438351 - 0.100867i) q^{35} +4.23999 q^{36} +(-5.93123 - 1.34928i) q^{37} -4.39040i q^{38} +(-1.83015 + 3.16991i) q^{39} +(-3.66678 + 11.9625i) q^{40} +(-2.25740 - 3.90993i) q^{41} +(-0.435174 + 0.251248i) q^{42} -1.65401i q^{43} +(1.02470 + 1.77482i) q^{44} +(-1.63646 + 1.52381i) q^{45} +(-2.58585 + 4.47883i) q^{46} +6.68453i q^{47} -5.49752i q^{48} +(-3.47977 + 6.02713i) q^{49} +(-5.45898 - 11.2338i) q^{50} +0.402908 q^{51} +(13.4404 + 7.75981i) q^{52} +(1.64399 + 0.949159i) q^{53} +(1.24900 - 2.16333i) q^{54} +(-1.03334 - 0.316744i) q^{55} +(0.562792 + 0.974784i) q^{56} +(-1.52210 - 0.878784i) q^{57} +(4.07430 + 2.35230i) q^{58} +(-5.13181 + 8.88856i) q^{59} +(6.46094 + 6.93857i) q^{60} +(-2.63330 - 4.56101i) q^{61} +(22.6417 + 13.0722i) q^{62} +0.201159i q^{63} +4.64557 q^{64} +(-7.97623 + 1.83537i) q^{65} +1.20740 q^{66} +(-6.50049 + 3.75306i) q^{67} -1.70832i q^{68} +(1.03517 + 1.79297i) q^{69} +(-1.07428 - 0.329291i) q^{70} +(5.48804 + 9.50556i) q^{71} +(-4.84583 - 2.79774i) q^{72} +7.61348i q^{73} +(11.1459 + 10.3270i) q^{74} +(-4.98731 - 0.356007i) q^{75} +(-3.72603 + 6.45368i) q^{76} +(-0.0842037 + 0.0486150i) q^{77} +(7.91843 - 4.57171i) q^{78} +(-7.56053 - 13.0952i) q^{79} +(8.99648 - 8.37718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +11.2780i q^{82} +(-9.61284 - 5.54997i) q^{83} +0.852914 q^{84} +(0.613955 + 0.659343i) q^{85} +(-2.06585 + 3.57816i) q^{86} +(1.63103 - 0.941674i) q^{87} -2.70457i q^{88} +(-0.221897 + 0.384336i) q^{89} +(5.44344 - 1.25256i) q^{90} +(-0.368152 + 0.637657i) q^{91} +(7.60216 - 4.38911i) q^{92} +(9.06394 - 5.23307i) q^{93} +(8.34897 - 14.4608i) q^{94} +(-0.881293 - 3.82995i) q^{95} +(-1.27091 + 2.20129i) q^{96} +3.69091i q^{97} +(15.0558 - 8.69245i) q^{98} +(0.241674 - 0.418592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	$ 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/555\mathbb{Z}\right)^\times$.

$n$	$76$	$112$	$371$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−2.16333	−	1.24900i	−1.52970	−	0.883175i	−0.999374	−	0.0353843i	$-0.988734\pi$
$2$	−2.16333	−	1.24900i	−1.52970	−	0.883175i	−0.530331	−	0.847791i	$-0.677932\pi$
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	2.11999	+	3.67194i	1.06000	+	1.83597i
$5$	−2.13789	−	0.655312i	−0.956093	−	0.293064i
$5$	−2.13789	−	0.655312i	−0.956093	−	0.293064i
$6$	2.49800			1.01980
$7$	−0.174209	+	0.100580i	−0.0658449	+	0.0380156i	−0.532561	−	0.846392i	$-0.678770\pi$
$7$	−0.174209	+	0.100580i	−0.0658449	+	0.0380156i	0.466716	+	0.884407i	$0.345437\pi$
$8$		−	5.59548i		−	1.97830i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	3.80647	+	4.08787i	1.20371	+	1.29270i
$11$	0.483348			0.145735			0.0728675	−	0.997342i	$-0.476785\pi$
$11$	0.483348			0.145735			0.0728675	+	0.997342i	$0.476785\pi$
$12$	−3.67194	−	2.11999i	−1.06000	−	0.611990i
$13$	3.16991	−	1.83015i	0.879175	−	0.507592i	0.00878869	−	0.999961i	$-0.497202\pi$
$13$	3.16991	−	1.83015i	0.879175	−	0.507592i	0.870386	+	0.492369i	$0.163869\pi$
$14$	0.502496			0.134298
$15$	2.17912	−	0.501428i	0.562647	−	0.129468i
$16$	−2.74876	+	4.76099i	−0.687190	+	1.19025i
$17$	−0.348928	−	0.201454i	−0.0846275	−	0.0488597i	0.457089	−	0.889421i	$-0.348892\pi$
$17$	−0.348928	−	0.201454i	−0.0846275	−	0.0488597i	−0.541717	+	0.840561i	$0.682225\pi$
$18$	−2.16333	+	1.24900i	−0.509901	+	0.294392i
$19$	0.878784	+	1.52210i	0.201607	+	0.349193i	0.949046	−	0.315137i	$-0.102050\pi$
$19$	0.878784	+	1.52210i	0.201607	+	0.349193i	−0.747439	+	0.664330i	$0.768717\pi$
$20$	−2.12605	−	9.23945i	−0.475399	−	2.06600i
$21$	0.100580	−	0.174209i	0.0219483	−	0.0380156i
$22$	−1.04564	−	0.603701i	−0.222931	−	0.128710i
$23$		−	2.07034i		−	0.431696i	−0.976427	−	0.215848i	$-0.930748\pi$
$23$		−	2.07034i		−	0.431696i	0.976427	−	0.215848i	$-0.0692515\pi$
$24$	2.79774	+	4.84583i	0.571087	+	0.989151i
$25$	4.14113	+	2.80197i	0.828227	+	0.560393i
$26$	−9.14341			−1.79317
$27$			1.00000i			0.192450i
$28$	−0.738645	−	0.426457i	−0.139591	−	0.0805928i
$29$	−1.88335			−0.349729			−0.174864	−	0.984593i	$-0.555949\pi$
$29$	−1.88335			−0.349729			−0.174864	+	0.984593i	$0.555949\pi$
$30$	−5.34044	−	1.63697i	−0.975026	−	0.298868i
$31$	−10.4661			−1.87977			−0.939886	−	0.341487i	$-0.889069\pi$
$31$	−10.4661			−1.87977			−0.939886	+	0.341487i	$0.889069\pi$
$32$	2.20129	−	1.27091i	0.389136	−	0.224668i
$33$	−0.418592	+	0.241674i	−0.0728675	+	0.0420701i
$34$	0.503231	+	0.871622i	0.0863034	+	0.149482i
$35$	0.438351	−	0.100867i	0.0740948	−	0.0170496i
$36$	4.23999			0.706665
$37$	−5.93123	−	1.34928i	−0.975088	−	0.221820i
$37$	−5.93123	−	1.34928i	−0.975088	−	0.221820i
$38$		−	4.39040i		−	0.712217i
$39$	−1.83015	+	3.16991i	−0.293058	+	0.507592i
$40$	−3.66678	+	11.9625i	−0.579770	+	1.89144i
$41$	−2.25740	−	3.90993i	−0.352547	−	0.610629i	0.634148	−	0.773212i	$-0.281351\pi$
$41$	−2.25740	−	3.90993i	−0.352547	−	0.610629i	−0.986695	+	0.162583i	$0.948018\pi$
$42$	−0.435174	+	0.251248i	−0.0671488	+	0.0387684i
$43$		−	1.65401i		−	0.252234i	−0.992015	−	0.126117i	$-0.959749\pi$
$43$		−	1.65401i		−	0.252234i	0.992015	−	0.126117i	$-0.0402514\pi$
$44$	1.02470	+	1.77482i	0.154479	+	0.267565i
$45$	−1.63646	+	1.52381i	−0.243949	+	0.227156i
$46$	−2.58585	+	4.47883i	−0.381263	+	0.660367i
$47$			6.68453i			0.975039i	0.873112	+	0.487519i	$0.162098\pi$
$47$			6.68453i			0.975039i	−0.873112	+	0.487519i	$0.837902\pi$
$48$		−	5.49752i		−	0.793499i
$49$	−3.47977	+	6.02713i	−0.497110	+	0.861019i
$50$	−5.45898	−	11.2338i	−0.772017	−	1.58871i
$51$	0.402908			0.0564184
$52$	13.4404	+	7.75981i	1.86385	+	1.07609i
$53$	1.64399	+	0.949159i	0.225820	+	0.130377i	0.608642	−	0.793445i	$-0.291715\pi$
$53$	1.64399	+	0.949159i	0.225820	+	0.130377i	−0.382822	+	0.923822i	$0.625048\pi$
$54$	1.24900	−	2.16333i	0.169967	−	0.294392i
$55$	−1.03334	−	0.316744i	−0.139336	−	0.0427097i
$56$	0.562792	+	0.974784i	0.0752062	+	0.130261i
$57$	−1.52210	−	0.878784i	−0.201607	−	0.116398i
$58$	4.07430	+	2.35230i	0.534982	+	0.308872i
$59$	−5.13181	+	8.88856i	−0.668105	+	1.15719i	0.310328	+	0.950629i	$0.399561\pi$
$59$	−5.13181	+	8.88856i	−0.668105	+	1.15719i	−0.978433	+	0.206563i	$0.933772\pi$
$60$	6.46094	+	6.93857i	0.834103	+	0.895766i
$61$	−2.63330	−	4.56101i	−0.337159	−	0.583977i	0.646738	−	0.762712i	$-0.276133\pi$
$61$	−2.63330	−	4.56101i	−0.337159	−	0.583977i	−0.983897	+	0.178735i	$0.942799\pi$
$62$	22.6417	+	13.0722i	2.87550	+	1.66017i
$63$			0.201159i			0.0253437i
$64$	4.64557			0.580696
$65$	−7.97623	+	1.83537i	−0.989330	+	0.227650i
$66$	1.20740			0.148621
$67$	−6.50049	+	3.75306i	−0.794162	+	0.458510i	−0.841426	−	0.540373i	$-0.818283\pi$
$67$	−6.50049	+	3.75306i	−0.794162	+	0.458510i	0.0472638	+	0.998882i	$0.484950\pi$
$68$		−	1.70832i		−	0.207165i
$69$	1.03517	+	1.79297i	0.124620	+	0.215848i
$70$	−1.07428	−	0.329291i	−0.128401	−	0.0393578i
$71$	5.48804	+	9.50556i	0.651310	+	1.12810i	0.982805	+	0.184645i	$0.0591137\pi$
$71$	5.48804	+	9.50556i	0.651310	+	1.12810i	−0.331495	+	0.943457i	$0.607553\pi$
$72$	−4.84583	−	2.79774i	−0.571087	−	0.329717i
$73$			7.61348i			0.891091i	0.895259	+	0.445545i	$0.146990\pi$
$73$			7.61348i			0.891091i	−0.895259	+	0.445545i	$0.853010\pi$
$74$	11.1459	+	10.3270i	1.29569	+	1.20049i
$75$	−4.98731	−	0.356007i	−0.575885	−	0.0411082i
$76$	−3.72603	+	6.45368i	−0.427405	+	0.740288i
$77$	−0.0842037	+	0.0486150i	−0.00959590	+	0.00554020i
$78$	7.91843	−	4.57171i	0.896585	−	0.517644i
$79$	−7.56053	−	13.0952i	−0.850627	−	1.47333i	−0.880644	−	0.473779i	$-0.842889\pi$
$79$	−7.56053	−	13.0952i	−0.850627	−	1.47333i	0.0300170	−	0.999549i	$-0.490444\pi$
$80$	8.99648	−	8.37718i	1.00584	−	0.936597i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			11.2780i			1.24544i
$83$	−9.61284	−	5.54997i	−1.05515	−	0.609189i	−0.131060	−	0.991374i	$-0.541838\pi$
$83$	−9.61284	−	5.54997i	−1.05515	−	0.609189i	−0.924086	+	0.382186i	$0.875172\pi$
$84$	0.852914			0.0930605
$85$	0.613955	+	0.659343i	0.0665927	+	0.0715157i
$86$	−2.06585	+	3.57816i	−0.222766	+	0.385843i
$87$	1.63103	−	0.941674i	0.174864	−	0.100958i
$88$		−	2.70457i		−	0.288308i
$89$	−0.221897	+	0.384336i	−0.0235210	+	0.0407396i	−0.877546	−	0.479492i	$-0.840821\pi$
$89$	−0.221897	+	0.384336i	−0.0235210	+	0.0407396i	0.854025	+	0.520231i	$0.174154\pi$
$90$	5.44344	−	1.25256i	0.573789	−	0.132032i
$91$	−0.368152	+	0.637657i	−0.0385928	+	0.0668447i
$92$	7.60216	−	4.38911i	0.792580	−	0.457596i
$93$	9.06394	−	5.23307i	0.939886	−	0.542644i
$94$	8.34897	−	14.4608i	0.861130	−	1.49152i
$95$	−0.881293	−	3.82995i	−0.0904188	−	0.392945i
$96$	−1.27091	+	2.20129i	−0.129712	+	0.224668i
$97$			3.69091i			0.374755i	0.982288	+	0.187378i	$0.0599988\pi$
$97$			3.69091i			0.374755i	−0.982288	+	0.187378i	$0.940001\pi$
$98$	15.0558	−	8.69245i	1.52086	−	0.878070i
$99$	0.241674	−	0.418592i	0.0242892	−	0.0420701i
$100$	−1.50947	+	21.1461i	−0.150947	+	2.11461i
$101$	2.33378			0.232219			0.116110	−	0.993236i	$-0.462958\pi$
$101$	2.33378			0.232219			0.116110	+	0.993236i	$0.462958\pi$
$102$	−0.871622	−	0.503231i	−0.0863034	−	0.0498273i
$103$		−	2.64936i		−	0.261050i	−0.991445	−	0.130525i	$-0.958334\pi$
$103$		−	2.64936i		−	0.261050i	0.991445	−	0.130525i	$-0.0416662\pi$
$104$	−10.2406	−	17.7372i	−1.00417	−	1.73927i
$105$	−0.329189	+	0.306529i	−0.0321256	+	0.0299141i
$106$	−2.37100	−	4.10669i	−0.230291	−	0.398877i
$107$	−10.0895	+	5.82517i	−0.975387	+	0.563140i	−0.900874	−	0.434080i	$-0.857073\pi$
$107$	−10.0895	+	5.82517i	−0.975387	+	0.563140i	−0.0745128	+	0.997220i	$0.523740\pi$
$108$	−3.67194	+	2.11999i	−0.353332	+	0.203997i
$109$	6.11672	−	10.5945i	0.585876	−	1.01477i	−0.408890	−	0.912584i	$-0.634084\pi$
$109$	6.11672	−	10.5945i	0.585876	−	1.01477i	0.994766	−	0.102183i	$-0.0325826\pi$
$110$	1.83985	+	1.97587i	0.175423	+	0.188391i
$111$	5.81123	−	1.79710i	0.551578	−	0.170573i
$112$		−	1.10588i		−	0.104496i
$113$	−9.22668	−	5.32702i	−0.867973	−	0.501124i	−0.00129871	−	0.999999i	$-0.500413\pi$
$113$	−9.22668	−	5.32702i	−0.867973	−	0.501124i	−0.866674	+	0.498875i	$0.833747\pi$
$114$	2.19520	+	3.80220i	0.205599	+	0.356108i
$115$	−1.35672	+	4.42616i	−0.126515	+	0.412741i
$116$	−3.99269	−	6.91553i	−0.370712	−	0.642091i
$117$		−	3.66030i		−	0.338395i
$118$	22.2036	−	12.8193i	2.04401	−	1.18011i
$119$	0.0810487			0.00742972
$120$	−2.80573	−	12.1932i	−0.256127	−	1.11309i
$121$	−10.7664			−0.978761
$122$			13.1559i			1.19108i
$123$	3.90993	+	2.25740i	0.352547	+	0.203543i
$124$	−22.1881	−	38.4310i	−1.99255	−	3.45120i
$125$	−7.01712	−	8.70402i	−0.627630	−	0.778512i
$126$	0.251248	−	0.435174i	0.0223829	−	0.0387684i
$127$	−13.1947	−	7.61796i	−1.17084	−	0.675985i	−0.216962	−	0.976180i	$-0.569615\pi$
$127$	−13.1947	−	7.61796i	−1.17084	−	0.675985i	−0.953878	+	0.300195i	$0.902948\pi$
$128$	−14.4525	−	8.34413i	−1.27743	−	0.737524i
$129$	0.827003	+	1.43241i	0.0728136	+	0.126117i
$130$	19.5476	+	5.99178i	1.71444	+	0.525514i
$131$	−2.36937	+	4.10386i	−0.207012	+	0.358556i	−0.950772	−	0.309891i	$-0.899707\pi$
$131$	−2.36937	+	4.10386i	−0.207012	+	0.358556i	0.743760	+	0.668447i	$0.233041\pi$
$132$	−1.77482	−	1.02470i	−0.154479	−	0.0891883i
$133$	−0.306184	−	0.176776i	−0.0265496	−	0.0153284i
$134$	18.7503			1.61978
$135$	0.655312	−	2.13789i	0.0564002	−	0.184000i
$136$	−1.12723	+	1.95242i	−0.0966593	+	0.167419i
$137$		−	11.4994i		−	0.982460i	−0.871030	−	0.491230i	$-0.836547\pi$
$137$		−	11.4994i		−	0.982460i	0.871030	−	0.491230i	$-0.163453\pi$
$138$		−	5.17170i		−	0.440244i
$139$	4.43083	−	7.67442i	0.375818	−	0.650936i	−0.614631	−	0.788815i	$-0.710695\pi$
$139$	4.43083	−	7.67442i	0.375818	−	0.650936i	0.990449	+	0.137879i	$0.0440284\pi$
$140$	1.29968	+	1.39576i	0.109843	+	0.117963i
$141$	−3.34226	−	5.78897i	−0.281469	−	0.487519i
$142$		−	27.4182i		−	2.30088i
$143$	1.53217	−	0.884599i	0.128127	−	0.0739739i
$144$	2.74876	+	4.76099i	0.229063	+	0.396749i
$145$	4.02639	+	1.23418i	0.334373	+	0.102493i
$146$	9.50923	−	16.4705i	0.786989	−	1.36311i
$147$		−	6.95953i		−	0.574013i
$148$	−7.61969	−	24.6396i	−0.626335	−	2.02536i
$149$	−11.7471			−0.962364			−0.481182	−	0.876621i	$-0.659792\pi$
$149$	−11.7471			−0.962364			−0.481182	+	0.876621i	$0.659792\pi$
$150$	10.3445	+	6.99930i	0.844628	+	0.571491i
$151$	6.51706	+	11.2879i	0.530351	+	0.918594i	0.999373	+	0.0354078i	$0.0112730\pi$
$151$	6.51706	+	11.2879i	0.530351	+	0.918594i	−0.469022	+	0.883186i	$0.655394\pi$
$152$	8.51688	−	4.91722i	0.690810	−	0.398839i
$153$	−0.348928	+	0.201454i	−0.0282092	+	0.0162866i
$154$	0.242880			0.0195719
$155$	22.3754	+	6.85858i	1.79724	+	0.550894i
$156$	−15.5196			−1.24256
$157$	−4.58875	−	2.64932i	−0.366222	−	0.211439i	0.305584	−	0.952165i	$-0.401148\pi$
$157$	−4.58875	−	2.64932i	−0.366222	−	0.211439i	−0.671807	+	0.740726i	$0.734481\pi$
$158$			37.7724i			3.00501i
$159$	−1.89832			−0.150546
$160$	−5.53895	+	1.27454i	−0.437892	+	0.100761i
$161$	0.208234	+	0.360672i	0.0164112	+	0.0284249i
$162$			2.49800i			0.196261i
$163$	14.0049	+	8.08571i	1.09694	+	0.633321i	0.935417	−	0.353547i	$-0.115024\pi$
$163$	14.0049	+	8.08571i	1.09694	+	0.633321i	0.161528	+	0.986868i	$0.448358\pi$
$164$	9.57136	−	16.5781i	0.747397	−	1.29453i
$165$	1.05327	−	0.242364i	0.0819973	−	0.0188680i
$166$	13.8638	+	24.0128i	1.07604	+	1.86376i
$167$	−14.0899	+	8.13482i	−1.09031	+	0.629491i	−0.933659	−	0.358163i	$-0.883403\pi$
$167$	−14.0899	+	8.13482i	−1.09031	+	0.629491i	−0.156652	+	0.987654i	$0.550070\pi$
$168$	−0.974784	−	0.562792i	−0.0752062	−	0.0434203i
$169$	0.198888	−	0.344485i	0.0152991	−	0.0264988i
$170$	−0.504668	−	2.19320i	−0.0387063	−	0.168211i
$171$	1.75757			0.134405
$172$	6.07341	−	3.50648i	0.463093	−	0.267367i
$173$	15.1860	+	8.76761i	1.15457	+	0.666589i	0.949996	−	0.312262i	$-0.101087\pi$
$173$	15.1860	+	8.76761i	1.15457	+	0.666589i	0.204571	+	0.978852i	$0.434420\pi$
$174$	−4.70460			−0.356654
$175$	−1.00324	−	0.0716142i	−0.0758381	−	0.00541352i
$176$	−1.32861	+	2.30122i	−0.100148	+	0.173461i
$177$		−	10.2636i		−	0.771461i
$178$	0.960071	−	0.554297i	0.0719603	−	0.0415463i
$179$	23.3346			1.74411			0.872056	−	0.489406i	$-0.162786\pi$
$179$	23.3346			1.74411			0.872056	+	0.489406i	$0.162786\pi$
$180$	−9.06462	−	2.77851i	−0.675637	−	0.207098i
$181$	−0.880728	−	1.52547i	−0.0654640	−	0.113387i	0.831436	−	0.555621i	$-0.187519\pi$
$181$	−0.880728	−	1.52547i	−0.0654640	−	0.113387i	−0.896900	+	0.442234i	$0.854186\pi$
$182$	1.59287	−	0.919642i	0.118071	−	0.0681684i
$183$	4.56101	+	2.63330i	0.337159	+	0.194659i
$184$	−11.5846			−0.854024
$185$	11.7961	+	6.77141i	0.867267	+	0.497844i
$186$	−26.1444			−1.91700
$187$	−0.168654	−	0.0973724i	−0.0123332	−	0.00712057i
$188$	−24.5452	+	14.1712i	−1.79014	+	1.03354i
$189$	−0.100580	−	0.174209i	−0.00731610	−	0.0126719i
$190$	−2.87708	+	9.38618i	−0.208725	+	0.680945i
$191$	11.4426			0.827959			0.413980	−	0.910286i	$-0.364138\pi$
$191$	11.4426			0.827959			0.413980	+	0.910286i	$0.364138\pi$
$192$	−4.02318	+	2.32278i	−0.290348	+	0.167632i
$193$		−	9.42190i		−	0.678203i	−0.940750	−	0.339102i	$-0.889877\pi$
$193$		−	9.42190i		−	0.678203i	0.940750	−	0.339102i	$-0.110123\pi$
$194$	4.60994	−	7.98466i	0.330975	−	0.573265i
$195$	5.98993	−	5.57760i	0.428948	−	0.399420i
$196$	−29.5083			−2.10774
$197$	−12.4895	−	7.21084i	−0.889843	−	0.513751i	−0.0159517	−	0.999873i	$-0.505078\pi$
$197$	−12.4895	−	7.21084i	−0.889843	−	0.513751i	−0.873891	+	0.486122i	$0.838411\pi$
$198$	−1.04564	+	0.603701i	−0.0743105	+	0.0429032i
$199$	−12.9434			−0.917535			−0.458767	−	0.888556i	$-0.651709\pi$
$199$	−12.9434			−0.917535			−0.458767	+	0.888556i	$0.651709\pi$
$200$	15.6784	−	23.1716i	1.10863	−	1.63848i
$201$	3.75306	−	6.50049i	0.264721	−	0.458510i
$202$	−5.04872	−	2.91488i	−0.355227	−	0.205090i
$203$	0.328096	−	0.189427i	0.0230279	−	0.0132951i
$204$	0.854162	+	1.47945i	0.0598033	+	0.103582i
$205$	2.26385	+	9.83830i	0.158114	+	0.687137i
$206$	−3.30905	+	5.73144i	−0.230552	+	0.399329i
$207$	−1.79297	−	1.03517i	−0.124620	−	0.0719493i
$208$			20.1226i			1.39525i
$209$	0.424759	+	0.735704i	0.0293812	+	0.0508897i
$210$	1.09500	−	0.251965i	0.0755621	−	0.0173872i
$211$	−2.66040			−0.183149			−0.0915747	−	0.995798i	$-0.529190\pi$
$211$	−2.66040			−0.183149			−0.0915747	+	0.995798i	$0.529190\pi$
$212$			8.04884i			0.552797i
$213$	−9.50556	−	5.48804i	−0.651310	−	0.376034i
$214$	29.1025			1.98941
$215$	−1.08389	+	3.53608i	−0.0739207	+	0.241159i
$216$	5.59548			0.380724
$217$	1.82330	−	1.05268i	0.123773	−	0.0714606i
$218$	−26.4650	+	15.2795i	−1.79243	+	1.03486i
$219$	−3.80674	−	6.59347i	−0.257236	−	0.445545i
$220$	−1.02762	−	4.46587i	−0.0692822	−	0.301089i
$221$	−1.47476			−0.0992032
$222$	−14.8162	−	3.37050i	−0.994397	−	0.226213i
$223$			26.2030i			1.75468i	0.479865	+	0.877342i	$0.340686\pi$
$223$			26.2030i			1.75468i	−0.479865	+	0.877342i	$0.659314\pi$
$224$	−0.255656	+	0.442810i	−0.0170818	+	0.0295865i
$225$	4.49714	−	2.18534i	0.299809	−	0.145690i
$226$	13.3069	+	23.0482i	0.885161	+	1.53314i
$227$	−1.28443	+	0.741566i	−0.0852506	+	0.0492195i	−0.542019	−	0.840366i	$-0.682340\pi$
$227$	−1.28443	+	0.741566i	−0.0852506	+	0.0492195i	0.456769	+	0.889586i	$0.349007\pi$
$228$		−	7.45207i		−	0.493525i
$229$	−8.21575	−	14.2301i	−0.542912	−	0.940352i	−0.998735	−	0.0502811i	$-0.983988\pi$
$229$	−8.21575	−	14.2301i	−0.542912	−	0.940352i	0.455823	−	0.890071i	$-0.349345\pi$
$230$	8.46329	−	7.88069i	0.558053	−	0.519637i
$231$	0.0486150	−	0.0842037i	0.00319863	−	0.00554020i
$232$			10.5382i			0.691869i
$233$			11.7515i			0.769870i	0.922944	+	0.384935i	$0.125776\pi$
$233$			11.7515i			0.769870i	−0.922944	+	0.384935i	$0.874224\pi$
$234$	−4.57171	+	7.91843i	−0.298862	+	0.517644i
$235$	4.38045	−	14.2908i	0.285749	−	0.932227i
$236$	−43.5177			−2.83276
$237$	13.0952	+	7.56053i	0.850627	+	0.491110i
$238$	−0.175335	−	0.101230i	−0.0113653	−	0.00656174i
$239$	−13.2084	+	22.8776i	−0.854381	+	1.47983i	0.0228371	+	0.999739i	$0.492730\pi$
$239$	−13.2084	+	22.8776i	−0.854381	+	1.47983i	−0.877218	+	0.480092i	$0.840603\pi$
$240$	−3.60259	+	11.7531i	−0.232546	+	0.758659i
$241$	10.5542	+	18.2804i	0.679855	+	1.17754i	0.975024	+	0.222099i	$0.0712907\pi$
$241$	10.5542	+	18.2804i	0.679855	+	1.17754i	−0.295169	+	0.955445i	$0.595376\pi$
$242$	23.2912	+	13.4472i	1.49722	+	0.864418i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	11.1652	−	19.3386i	0.714776	−	1.23803i
$245$	11.3890	−	10.6050i	0.727617	−	0.677529i
$246$	−5.63898	−	9.76700i	−0.359528	−	0.622721i
$247$	5.57133	+	3.21661i	0.354496	+	0.204668i
$248$			58.5631i			3.71876i
$249$	11.0999			0.703431
$250$	4.30903	+	27.5940i	0.272527	+	1.74520i
$251$	14.7200			0.929120			0.464560	−	0.885542i	$-0.346212\pi$
$251$	14.7200			0.929120			0.464560	+	0.885542i	$0.346212\pi$
$252$	−0.738645	+	0.426457i	−0.0465302	+	0.0268643i
$253$		−	1.00069i		−	0.0629132i
$254$	19.0296	+	32.9603i	1.19403	+	2.06811i
$255$	−0.861372	−	0.264030i	−0.0539412	−	0.0165342i
$256$	16.1981	+	28.0559i	1.01238	+	1.75349i
$257$	−17.6953	−	10.2164i	−1.10380	−	0.637282i	−0.166587	−	0.986027i	$-0.553275\pi$
$257$	−17.6953	−	10.2164i	−1.10380	−	0.637282i	−0.937218	+	0.348745i	$0.886608\pi$
$258$		−	4.13170i		−	0.257229i
$259$	1.16898	−	0.361504i	0.0726371	−	0.0224628i
$260$	−23.6489	−	25.3972i	−1.46665	−	1.57507i
$261$	−0.941674	+	1.63103i	−0.0582881	+	0.100958i
$262$	10.2514	−	5.91867i	0.633336	−	0.365657i
$263$	13.6161	−	7.86126i	0.839605	−	0.484746i	−0.0175252	−	0.999846i	$-0.505579\pi$
$263$	13.6161	−	7.86126i	0.839605	−	0.484746i	0.857130	+	0.515100i	$0.172245\pi$
$264$	1.35228	+	2.34222i	0.0832273	+	0.144154i
$265$	−2.89268	−	3.10652i	−0.177696	−	0.190832i
$266$	0.441585	+	0.764848i	0.0270753	+	0.0468958i
$267$		−	0.443793i		−	0.0271597i
$268$	−27.5620	−	15.9129i	−1.68362	−	0.972037i
$269$	−11.5459			−0.703966			−0.351983	−	0.936006i	$-0.614493\pi$
$269$	−11.5459			−0.703966			−0.351983	+	0.936006i	$0.614493\pi$
$270$	−4.08787	+	3.80647i	−0.248780	+	0.231655i
$271$	−0.0217635	+	0.0376955i	−0.00132204	+	0.00228984i	−0.866686	−	0.498855i	$-0.833754\pi$
$271$	−0.0217635	+	0.0376955i	−0.00132204	+	0.00228984i	0.865364	+	0.501144i	$0.167087\pi$
$272$	1.91824	−	1.10750i	0.116310	−	0.0671519i
$273$		−	0.736303i		−	0.0445631i
$274$	−14.3627	+	24.8770i	−0.867685	+	1.50287i
$275$	2.00161	+	1.35433i	0.120702	+	0.0816689i
$276$	−4.38911	+	7.60216i	−0.264193	+	0.457596i
$277$	27.7749	−	16.0359i	1.66883	−	0.963501i	0.700564	−	0.713589i	$-0.252932\pi$
$277$	27.7749	−	16.0359i	1.66883	−	0.963501i	0.968269	−	0.249912i	$-0.0804016\pi$
$278$	−19.1707	+	11.0682i	−1.14978	+	0.663827i
$279$	−5.23307	+	9.06394i	−0.313295	+	0.542644i
$280$	−0.564399	−	2.45278i	−0.0337293	−	0.146582i
$281$	−9.83234	+	17.0301i	−0.586548	+	1.01593i	0.408133	+	0.912923i	$0.366180\pi$
$281$	−9.83234	+	17.0301i	−0.586548	+	1.01593i	−0.994681	+	0.103008i	$0.967153\pi$
$282$			16.6979i			0.994347i
$283$	5.43553	−	3.13820i	0.323108	−	0.186547i	−0.329669	−	0.944097i	$-0.606937\pi$
$283$	5.43553	−	3.13820i	0.323108	−	0.186547i	0.652777	+	0.757550i	$0.273604\pi$
$284$	−23.2692	+	40.3035i	−1.38077	+	2.39157i
$285$	2.67820	+	2.87619i	0.158643	+	0.170371i
$286$	−4.41945			−0.261328
$287$	0.786520	+	0.454098i	0.0464268	+	0.0268045i
$288$		−	2.54183i		−	0.149779i
$289$	−8.41883	−	14.5818i	−0.495225	−	0.857756i
$290$	−7.16891	−	7.69889i	−0.420973	−	0.452094i
$291$	−1.84546	−	3.19642i	−0.108183	−	0.187378i
$292$	−27.9562	+	16.1405i	−1.63601	+	0.944554i
$293$	16.8085	−	9.70437i	0.981960	−	0.566935i	0.0790990	−	0.996867i	$-0.474796\pi$
$293$	16.8085	−	9.70437i	0.981960	−	0.566935i	0.902861	+	0.429932i	$0.141462\pi$
$294$	−8.69245	+	15.0558i	−0.506954	+	0.878070i
$295$	16.7960	−	15.6398i	0.977902	−	0.910585i
$296$	−7.54987	+	33.1881i	−0.438828	+	1.92902i
$297$			0.483348i			0.0280467i
$298$	25.4129	+	14.6722i	1.47213	+	0.849936i
$299$	−3.78903	−	6.56279i	−0.219125	−	0.379536i
$300$	−9.26583	−	19.0678i	−0.534963	−	1.10088i
$301$	0.166359	+	0.288143i	0.00958880	+	0.0166083i
$302$		−	32.5592i		−	1.87357i
$303$	−2.02111	+	1.16689i	−0.116110	+	0.0670359i
$304$	−9.66227			−0.554169
$305$	2.64082	+	11.4766i	0.151213	+	0.657146i
$306$	1.00646			0.0575356
$307$			26.0643i			1.48757i	0.668420	+	0.743784i	$0.266971\pi$
$307$			26.0643i			1.48757i	−0.668420	+	0.743784i	$0.733029\pi$
$308$	−0.357023	−	0.206127i	−0.0203433	−	0.0117452i
$309$	1.32468	+	2.29442i	0.0753585	+	0.130525i
$310$	−39.8390	−	42.7842i	−2.26271	−	2.42998i
$311$	4.03452	−	6.98799i	0.228776	−	0.396252i	−0.728669	−	0.684866i	$-0.759861\pi$
$311$	4.03452	−	6.98799i	0.228776	−	0.396252i	0.957446	+	0.288613i	$0.0931942\pi$
$312$	17.7372	+	10.2406i	1.00417	+	0.579758i
$313$	−22.7529	−	13.1364i	−1.28607	−	0.742513i	−0.308119	−	0.951348i	$-0.599700\pi$
$313$	−22.7529	−	13.1364i	−1.28607	−	0.742513i	−0.977951	+	0.208835i	$0.933033\pi$
$314$	6.61799	+	11.4627i	0.373475	+	0.646877i
$315$	0.131822	−	0.430056i	0.00742733	−	0.0242309i
$316$	32.0566	−	55.5236i	1.80332	−	3.12345i
$317$	−16.5999	−	9.58397i	−0.932345	−	0.538290i	−0.0447925	−	0.998996i	$-0.514263\pi$
$317$	−16.5999	−	9.58397i	−0.932345	−	0.538290i	−0.887552	+	0.460707i	$0.847596\pi$
$318$	4.10669	+	2.37100i	0.230291	+	0.132959i
$319$	−0.910313			−0.0509677
$320$	−9.93171	−	3.04429i	−0.555199	−	0.170181i
$321$	5.82517	−	10.0895i	0.325129	−	0.563140i
$322$		−	1.04034i		−	0.0579757i
$323$		−	0.708138i		−	0.0394018i
$324$	2.11999	−	3.67194i	0.117777	−	0.203997i
$325$	18.2550	+	1.30309i	1.01261	+	0.0722825i
$326$	−20.1981	−	34.9841i	−1.11867	−	1.93759i
$327$			12.2334i			0.676511i
$328$	−21.8780	+	12.6313i	−1.20801	+	0.697444i
$329$	−0.672328	−	1.16451i	−0.0370666	−	0.0642013i
$330$	−2.58129	−	0.791225i	−0.142095	−	0.0435555i
$331$	−4.10438	+	7.10900i	−0.225597	+	0.390746i	−0.956498	−	0.291737i	$-0.905767\pi$
$331$	−4.10438	+	7.10900i	−0.225597	+	0.390746i	0.730901	+	0.682483i	$0.239100\pi$
$332$		−	47.0637i		−	2.58295i
$333$	−4.13412	+	4.46195i	−0.226549	+	0.244513i
$334$	40.6415			2.22380
$335$	16.3568	−	3.76378i	0.893665	−	0.205637i
$336$	0.552939	+	0.957719i	0.0301653	+	0.0522478i
$337$	0.0144362	−	0.00833476i	0.000786392	−	0.000454024i	−0.499607	−	0.866252i	$-0.666522\pi$
$337$	0.0144362	−	0.00833476i	0.000786392	−	0.000454024i	0.500393	+	0.865798i	$0.333189\pi$
$338$	−0.860522	+	0.496823i	−0.0468062	+	0.0270236i
$339$	10.6540			0.578648
$340$	−1.11948	+	3.65221i	−0.0607126	+	0.198069i
$341$	−5.05879			−0.273949
$342$	−3.80220	−	2.19520i	−0.205599	−	0.118703i
$343$		−	2.80809i		−	0.151623i
$344$	−9.25497			−0.498994
$345$	−1.03813	−	4.51152i	−0.0558908	−	0.242892i
$346$	−21.9015	−	37.9345i	−1.17743	−	2.03937i
$347$			4.96386i			0.266474i	0.991084	+	0.133237i	$0.0425372\pi$
$347$			4.96386i			0.266474i	−0.991084	+	0.133237i	$0.957463\pi$
$348$	6.91553	+	3.99269i	0.370712	+	0.214030i
$349$	−8.07458	+	13.9856i	−0.432222	+	0.748631i	−0.997064	−	0.0765680i	$-0.975604\pi$
$349$	−8.07458	+	13.9856i	−0.432222	+	0.748631i	0.564842	+	0.825199i	$0.308937\pi$
$350$	2.08090	+	1.40798i	0.111229	+	0.0752595i
$351$	1.83015	+	3.16991i	0.0976861	+	0.169197i
$352$	1.06399	−	0.614294i	0.0567108	−	0.0327420i
$353$	1.02288	+	0.590562i	0.0544426	+	0.0314325i	0.526974	−	0.849881i	$-0.323326\pi$
$353$	1.02288	+	0.590562i	0.0544426	+	0.0314325i	−0.472532	+	0.881314i	$0.656660\pi$
$354$	−12.8193	+	22.2036i	−0.681336	+	1.18011i
$355$	−5.50371	−	23.9182i	−0.292106	−	1.26945i
$356$	−1.88168			−0.0997287
$357$	−0.0701902	+	0.0405243i	−0.00371486	+	0.00214478i
$358$	−50.4805	−	29.1449i	−2.66798	−	1.54036i
$359$	16.3114			0.860882			0.430441	−	0.902619i	$-0.358358\pi$
$359$	16.3114			0.860882			0.430441	+	0.902619i	$0.358358\pi$
$360$	8.52645	+	9.15679i	0.449383	+	0.482605i
$361$	7.95548	−	13.7793i	0.418709	−	0.725226i
$362$			4.40011i			0.231265i
$363$	9.32395	−	5.38319i	0.489381	−	0.282544i
$364$	−3.12192			−0.163633
$365$	4.98920	−	16.2768i	0.261147	−	0.851965i
$366$	−6.57797	−	11.3934i	−0.343836	−	0.595542i
$367$	−23.8352	+	13.7613i	−1.24419	+	0.718333i	−0.969944	−	0.243327i	$-0.921761\pi$
$367$	−23.8352	+	13.7613i	−1.24419	+	0.718333i	−0.274245	+	0.961660i	$0.588428\pi$
$368$	9.85687	+	5.69087i	0.513825	+	0.296657i
$369$	−4.51480			−0.235031
$370$	−17.0614	−	29.3821i	−0.886978	−	1.52750i
$371$	−0.381864			−0.0198254
$372$	38.4310	+	22.1881i	1.99255	+	1.15040i
$373$	30.9490	−	17.8684i	1.60248	−	0.925190i	0.611486	−	0.791255i	$-0.290572\pi$
$373$	30.9490	−	17.8684i	1.60248	−	0.925190i	0.990990	−	0.133935i	$-0.0427614\pi$
$374$	0.243236	+	0.421297i	0.0125774	+	0.0217847i
$375$	10.4290	+	4.02935i	0.538552	+	0.208075i
$376$	37.4032			1.92892
$377$	−5.97004	+	3.44681i	−0.307473	+	0.177520i
$378$			0.502496i			0.0258456i
$379$	13.5106	−	23.4011i	0.693995	−	1.20204i	−0.276523	−	0.961007i	$-0.589182\pi$
$379$	13.5106	−	23.4011i	0.693995	−	1.20204i	0.970518	−	0.241028i	$-0.0774845\pi$
$380$	12.1950	−	11.3555i	0.625591	−	0.582527i
$381$	15.2359			0.780560
$382$	−24.7542	−	14.2918i	−1.26653	−	0.731233i
$383$	−11.1404	+	6.43189i	−0.569246	+	0.328654i	−0.756848	−	0.653591i	$-0.773262\pi$
$383$	−11.1404	+	6.43189i	−0.569246	+	0.328654i	0.187602	+	0.982245i	$0.439928\pi$
$384$	16.6883			0.851620
$385$	0.211876	−	0.0487538i	0.0107982	−	0.00248473i
$386$	−11.7679	+	20.3827i	−0.598972	+	1.03745i
$387$	−1.43241	−	0.827003i	−0.0728136	−	0.0420389i
$388$	−13.5528	+	7.82471i	−0.688039	+	0.397240i
$389$	−6.85691	−	11.8765i	−0.347659	−	0.602163i	0.638174	−	0.769892i	$-0.279690\pi$
$389$	−6.85691	−	11.8765i	−0.347659	−	0.602163i	−0.985833	+	0.167729i	$0.946357\pi$
$390$	−19.9246	+	4.58476i	−1.00892	+	0.232158i
$391$	−0.417078	+	0.722400i	−0.0210925	+	0.0365333i
$392$	33.7247	+	19.4710i	1.70336	+	0.983433i
$393$		−	4.73873i		−	0.239037i
$394$	18.0127	+	31.1988i	0.907464	+	1.57177i
$395$	7.58212	+	32.9506i	0.381498	+	1.65793i
$396$	2.04939			0.102986
$397$		−	19.7746i		−	0.992458i	−0.868192	−	0.496229i	$-0.834718\pi$
$397$		−	19.7746i		−	0.992458i	0.868192	−	0.496229i	$-0.165282\pi$
$398$	28.0009	+	16.1663i	1.40356	+	0.810344i
$399$	0.353551			0.0176997
$400$	−24.7231	+	12.0140i	−1.23616	+	0.600699i
$401$	22.1651			1.10687			0.553436	−	0.832892i	$-0.313317\pi$
$401$	22.1651			1.10687			0.553436	+	0.832892i	$0.313317\pi$
$402$	−16.2382	+	9.37514i	−0.809889	+	0.467589i
$403$	−33.1767	+	19.1546i	−1.65265	+	0.954157i
$404$	4.94759	+	8.56948i	0.246152	+	0.426347i
$405$	0.501428	+	2.17912i	0.0249161	+	0.108281i
$406$	−0.946374			−0.0469677
$407$	−2.86685	−	0.652172i	−0.142104	−	0.0323270i
$408$		−	2.25446i		−	0.111613i
$409$	−12.2562	+	21.2284i	−0.606031	+	1.04968i	0.385856	+	0.922559i	$0.373906\pi$
$409$	−12.2562	+	21.2284i	−0.606031	+	1.04968i	−0.991888	+	0.127118i	$0.959427\pi$
$410$	7.39058	−	24.1110i	0.364995	−	1.19076i
$411$	5.74970	+	9.95877i	0.283612	+	0.491230i
$412$	9.72830	−	5.61663i	0.479279	−	0.276712i
$413$		−	2.06463i		−	0.101594i
$414$	2.58585	+	4.47883i	0.127088	+	0.220122i
$415$	16.9142	+	18.1646i	0.830286	+	0.891667i
$416$	4.65192	−	8.05737i	0.228079	−	0.395045i
$417$			8.86166i			0.433957i
$418$		−	2.12209i		−	0.103795i
$419$	−18.1197	+	31.3842i	−0.885204	+	1.53322i	−0.0397247	+	0.999211i	$0.512648\pi$
$419$	−18.1197	+	31.3842i	−0.885204	+	1.53322i	−0.845479	+	0.534008i	$0.820685\pi$
$420$	−1.82343	−	0.558924i	−0.0889745	−	0.0272727i
$421$	−28.7134			−1.39941			−0.699703	−	0.714434i	$-0.746684\pi$
$421$	−28.7134			−1.39941			−0.699703	+	0.714434i	$0.746684\pi$
$422$	5.75531	+	3.32283i	0.280164	+	0.161753i
$423$	5.78897	+	3.34226i	0.281469	+	0.162506i
$424$	5.31100	−	9.19893i	0.257925	−	0.446739i
$425$	−0.880492	−	1.81193i	−0.0427101	−	0.0878916i
$426$	13.7091	+	23.7449i	0.664208	+	1.15044i
$427$	0.917490	+	0.529713i	0.0444004	+	0.0256346i
$428$	−42.7793	−	24.6986i	−2.06781	−	1.19385i
$429$	−0.884599	+	1.53217i	−0.0427088	+	0.0739739i
$430$	6.76137	−	6.29593i	0.326062	−	0.303617i
$431$	−5.67515	−	9.82965i	−0.273363	−	0.473478i	0.696358	−	0.717694i	$-0.254803\pi$
$431$	−5.67515	−	9.82965i	−0.273363	−	0.473478i	−0.969721	+	0.244217i	$0.921469\pi$
$432$	−4.76099	−	2.74876i	−0.229063	−	0.132250i
$433$			26.7620i			1.28610i	0.765824	+	0.643050i	$0.222331\pi$
$433$			26.7620i			1.28610i	−0.765824	+	0.643050i	$0.777669\pi$
$434$	−5.25918			−0.252449
$435$	−4.10404	+	0.944363i	−0.196774	+	0.0452787i
$436$	51.8696			2.48411
$437$	3.15126	−	1.81938i	0.150745	−	0.0870328i
$438$			19.0185i			0.908737i
$439$	6.91748	+	11.9814i	0.330153	+	0.571842i	0.982542	−	0.186042i	$-0.0595662\pi$
$439$	6.91748	+	11.9814i	0.330153	+	0.571842i	−0.652388	+	0.757885i	$0.726233\pi$
$440$	−1.77233	+	5.78206i	−0.0844927	+	0.275649i
$441$	3.47977	+	6.02713i	0.165703	+	0.287006i
$442$	3.19039	+	1.84198i	0.151752	+	0.0876138i
$443$			10.6599i			0.506469i	0.967405	+	0.253234i	$0.0814944\pi$
$443$			10.6599i			0.506469i	−0.967405	+	0.253234i	$0.918506\pi$
$444$	18.9186	+	17.5286i	0.897838	+	0.831872i
$445$	0.726250	−	0.676257i	0.0344276	−	0.0320576i
$446$	32.7275	−	56.6858i	1.54969	−	2.68415i
$447$	10.1733	−	5.87357i	0.481182	−	0.277810i
$448$	−0.809300	+	0.467250i	−0.0382359	+	0.0220755i
$449$	−11.1850	−	19.3730i	−0.527854	−	0.914271i	−0.999473	−	0.0324679i	$-0.989663\pi$
$449$	−11.1850	−	19.3730i	−0.527854	−	0.914271i	0.471618	−	0.881803i	$-0.343670\pi$
$450$	−12.4583	−	0.889305i	−0.587289	−	0.0419222i
$451$	−1.09111	−	1.88986i	−0.0513784	−	0.0889900i
$452$		−	45.1730i		−	2.12476i
$453$	−11.2879	−	6.51706i	−0.530351	−	0.306198i
$454$	3.70486			0.173878
$455$	1.20493	−	1.12199i	0.0564881	−	0.0525995i
$456$	−4.91722	+	8.51688i	−0.230270	+	0.398839i
$457$	−1.11146	+	0.641704i	−0.0519921	+	0.0300177i	−0.525771	−	0.850626i	$-0.676223\pi$
$457$	−1.11146	+	0.641704i	−0.0519921	+	0.0300177i	0.473779	+	0.880644i	$0.342890\pi$
$458$			41.0458i			1.91795i
$459$	0.201454	−	0.348928i	0.00940306	−	0.0162866i
$460$	−19.1288	+	4.40164i	−0.891885	+	0.205228i
$461$	9.75044	−	16.8883i	0.454123	−	0.786565i	−0.544514	−	0.838752i	$-0.683286\pi$
$461$	9.75044	−	16.8883i	0.454123	−	0.786565i	0.998637	+	0.0521872i	$0.0166192\pi$
$462$	−0.210341	+	0.121440i	−0.00978593	+	0.00564991i
$463$	−22.7705	+	13.1466i	−1.05824	+	0.610973i	−0.924944	−	0.380104i	$-0.875888\pi$
$463$	−22.7705	+	13.1466i	−1.05824	+	0.610973i	−0.133292	+	0.991077i	$0.542555\pi$
$464$	5.17687	−	8.96661i	0.240330	−	0.416264i
$465$	−22.8070	+	5.24801i	−1.05765	+	0.243371i
$466$	14.6777	−	25.4225i	0.679930	−	1.17767i
$467$		−	18.3796i		−	0.850505i	−0.905075	−	0.425253i	$-0.860185\pi$
$467$		−	18.3796i		−	0.850505i	0.905075	−	0.425253i	$-0.139815\pi$
$468$	13.4404	−	7.75981i	0.621282	−	0.358697i
$469$	0.754964	−	1.30764i	0.0348610	−	0.0603810i
$470$	−27.3255	+	25.4445i	−1.26043	+	1.17367i
$471$	5.29864			0.244148
$472$	49.7358	+	28.7150i	2.28928	+	1.32171i
$473$		−	0.799461i		−	0.0367593i
$474$	−18.8862	−	32.7118i	−0.867472	−	1.50250i
$475$	−0.625707	+	8.76554i	−0.0287094	+	0.402190i
$476$	0.171823	+	0.297606i	0.00787548	+	0.0136407i
$477$	1.64399	−	0.949159i	0.0752732	−	0.0434590i
$478$	57.1483	−	32.9946i	2.61390	−	1.50914i
$479$	7.46581	−	12.9312i	0.341122	−	0.590840i	−0.643520	−	0.765430i	$-0.722527\pi$
$479$	7.46581	−	12.9312i	0.341122	−	0.590840i	0.984641	+	0.174590i	$0.0558599\pi$
$480$	4.15960	−	3.87326i	0.189859	−	0.176789i
$481$	−21.2708	+	6.57793i	−0.969867	+	0.299928i
$482$		−	52.7287i		−	2.40173i
$483$	−0.360672	−	0.208234i	−0.0164112	−	0.00947498i
$484$	−22.8246	−	39.5335i	−1.03748	−	1.79698i
$485$	2.41870	−	7.89076i	0.109827	−	0.358301i
$486$	−1.24900	−	2.16333i	−0.0566557	−	0.0981306i
$487$			23.8264i			1.07968i	0.841769	+	0.539838i	$0.181514\pi$
$487$			23.8264i			1.07968i	−0.841769	+	0.539838i	$0.818486\pi$
$488$	−25.5210	+	14.7346i	−1.15528	+	0.667003i
$489$	−16.1714			−0.731297
$490$	−37.8838	+	8.71727i	−1.71142	+	0.393806i
$491$	42.0949			1.89972			0.949858	−	0.312681i	$-0.101227\pi$
$491$	42.0949			1.89972			0.949858	+	0.312681i	$0.101227\pi$
$492$			19.1427i			0.863020i
$493$	0.657153	+	0.379408i	0.0295967	+	0.0170877i
$494$	−8.03508	−	13.9172i	−0.361516	−	0.626163i
$495$	−0.790980	+	0.736531i	−0.0355519	+	0.0331046i
$496$	28.7689	−	49.8292i	1.29176	−	2.23740i
$497$	−1.91213	−	1.10397i	−0.0857709	−	0.0495198i
$498$	−24.0128	−	13.8638i	−1.07604	−	0.621253i
$499$	−14.8422	−	25.7075i	−0.664430	−	1.15083i	−0.979439	−	0.201738i	$-0.935341\pi$
$499$	−14.8422	−	25.7075i	−0.664430	−	1.15083i	0.315009	−	0.949089i	$-0.397992\pi$
$500$	17.0844	−	44.2189i	0.764037	−	1.97753i
$501$	8.13482	−	14.0899i	0.363437	−	0.629491i
$502$	−31.8443	−	18.3853i	−1.42128	−	0.820576i
$503$	35.3881	+	20.4314i	1.57788	+	0.910989i	0.995155	+	0.0983189i	$0.0313465\pi$
$503$	35.3881	+	20.4314i	1.57788	+	0.910989i	0.582724	+	0.812670i	$0.301987\pi$
$504$	1.12558			0.0501375
$505$	−4.98935	−	1.52935i	−0.222023	−	0.0680552i
$506$	−1.24987	+	2.16483i	−0.0555633	+	0.0962385i
$507$			0.397777i			0.0176659i
$508$		−	64.6001i		−	2.86617i
$509$	7.91319	−	13.7060i	0.350746	−	0.607510i	−0.635634	−	0.771990i	$-0.719261\pi$
$509$	7.91319	−	13.7060i	0.350746	−	0.607510i	0.986380	+	0.164480i	$0.0525947\pi$
$510$	1.53366	+	1.64704i	0.0679115	+	0.0729320i
$511$	−0.765762	−	1.32634i	−0.0338753	−	0.0586738i
$512$		−	47.5488i		−	2.10138i
$513$	−1.52210	+	0.878784i	−0.0672023	+	0.0387993i
$514$	25.5206	+	44.2029i	1.12566	+	1.94971i
$515$	−1.73616	+	5.66404i	−0.0765043	+	0.249588i
$516$	−3.50648	+	6.07341i	−0.154364	+	0.267367i
$517$			3.23095i			0.142097i
$518$	−2.98041	−	0.678007i	−0.130952	−	0.0297899i
$519$	−17.5352			−0.769711
$520$	10.2698	+	44.6309i	0.450361	+	1.95719i
$521$	−18.5756	−	32.1739i	−0.813814	−	1.40957i	−0.910177	−	0.414220i	$-0.864054\pi$
$521$	−18.5756	−	32.1739i	−0.813814	−	1.40957i	0.0963632	−	0.995346i	$-0.469279\pi$
$522$	4.07430	−	2.35230i	0.178327	−	0.102957i
$523$	4.57333	−	2.64041i	0.199978	−	0.115457i	−0.396667	−	0.917962i	$-0.629833\pi$
$523$	4.57333	−	2.64041i	0.199978	−	0.115457i	0.596645	+	0.802505i	$0.296500\pi$
$524$	−20.0922			−0.877730
$525$	0.904642	−	0.439602i	0.0394818	−	0.0191858i
$526$	−39.2748			−1.71246
$527$	3.65193	+	2.10844i	0.159081	+	0.0918452i
$528$		−	2.65722i		−	0.115641i
$529$	18.7137			0.813639
$530$	2.37777	+	10.3334i	0.103284	+	0.448853i
$531$	5.13181	+	8.88856i	0.222702	+	0.385731i
$532$		−	1.49905i		−	0.0649922i
$533$	−14.3115	−	8.26276i	−0.619901	−	0.357900i
$534$	−0.554297	+	0.960071i	−0.0239868	+	0.0415463i
$535$	25.3875	−	5.84180i	1.09760	−	0.252563i
$536$	21.0002	+	36.3734i	0.907070	+	1.57109i
$537$	−20.2084	+	11.6673i	−0.872056	+	0.503482i
$538$	24.9776	+	14.4208i	1.07686	+	0.621726i
$539$	−1.68194	+	2.91320i	−0.0724463	+	0.125481i
$540$	9.23945	−	2.12605i	0.397603	−	0.0914905i
$541$	−4.71512			−0.202719			−0.101359	−	0.994850i	$-0.532319\pi$
$541$	−4.71512			−0.202719			−0.101359	+	0.994850i	$0.532319\pi$
$542$	0.0941632	−	0.0543651i	0.00404466	−	0.00233518i
$543$	1.52547	+	0.880728i	0.0654640	+	0.0377957i
$544$	−1.02412			−0.0439089
$545$	−20.0195	+	18.6414i	−0.857543	+	0.798511i
$546$	−0.919642	+	1.59287i	−0.0393570	+	0.0681684i
$547$			18.4826i			0.790257i	0.918626	+	0.395129i	$0.129300\pi$
$547$			18.4826i			0.790257i	−0.918626	+	0.395129i	$0.870700\pi$
$548$	42.2251	−	24.3787i	1.80377	−	1.04140i
$549$	−5.26660			−0.224773
$550$	−2.63859	−	5.42986i	−0.112510	−	0.231530i
$551$	−1.65506	−	2.86664i	−0.0705078	−	0.122123i
$552$	10.0325	−	5.79228i	0.427012	−	0.246536i
$553$	2.63423	+	1.52087i	0.112019	+	0.0646741i
$554$	−80.1150			−3.40376
$555$	−13.6014	+	0.0338353i	−0.577348	+	0.00143623i
$556$	37.5733			1.59346
$557$	0.452751	+	0.261396i	0.0191837	+	0.0110757i	0.509561	−	0.860434i	$-0.329808\pi$
$557$	0.452751	+	0.261396i	0.0191837	+	0.0110757i	−0.490377	+	0.871510i	$0.663141\pi$
$558$	22.6417	−	13.0722i	0.958499	−	0.553390i
$559$	−3.02708	−	5.24305i	−0.128032	−	0.221758i
$560$	−0.724695	+	2.36424i	−0.0306240	+	0.0999076i
$561$	0.194745			0.00822213
$562$	42.5411	−	24.5611i	1.79449	−	1.03605i
$563$		−	18.9526i		−	0.798755i	−0.916787	−	0.399378i	$-0.869226\pi$
$563$		−	18.9526i		−	0.798755i	0.916787	−	0.399378i	$-0.130774\pi$
$564$	14.1712	−	24.5452i	0.596714	−	1.03354i
$565$	16.2347	+	17.4349i	0.683001	+	0.733493i
$566$	−15.6784			−0.659014
$567$	0.174209	+	0.100580i	0.00731610	+	0.00422395i
$568$	53.1882	−	30.7082i	2.23173	−	1.28849i
$569$	−25.7210			−1.07828			−0.539141	−	0.842216i	$-0.681251\pi$
$569$	−25.7210			−1.07828			−0.539141	+	0.842216i	$0.681251\pi$
$570$	−2.20147	−	9.56721i	−0.0922093	−	0.400727i
$571$	−15.3656	+	26.6139i	−0.643029	+	1.11376i	0.341724	+	0.939800i	$0.388989\pi$
$571$	−15.3656	+	26.6139i	−0.643029	+	1.11376i	−0.984753	+	0.173958i	$0.944344\pi$
$572$	6.49638	+	3.75069i	0.271627	+	0.156824i
$573$	−9.90961	+	5.72131i	−0.413980	+	0.239011i
$574$	−1.13433	−	1.96472i	−0.0473462	−	0.0820060i
$575$	5.80102	−	8.57355i	0.241919	−	0.357542i
$576$	2.32278	−	4.02318i	0.0967827	−	0.167632i
$577$	26.1798	+	15.1149i	1.08988	+	0.629242i	0.933544	−	0.358462i	$-0.116699\pi$
$577$	26.1798	+	15.1149i	1.08988	+	0.629242i	0.156335	+	0.987704i	$0.450032\pi$
$578$			42.0604i			1.74948i
$579$	4.71095	+	8.15961i	0.195780	+	0.339102i
$580$	4.00409	+	17.4011i	0.166261	+	0.722541i
$581$	2.23286			0.0926346
$582$			9.21989i			0.382177i
$583$	0.794620	+	0.458774i	0.0329098	+	0.0190005i
$584$	42.6011			1.76285
$585$	−2.39864	+	7.82531i	−0.0991714	+	0.323537i
$586$	−48.4830			−2.00281
$587$	7.31012	−	4.22050i	0.301721	−	0.174199i	−0.341495	−	0.939884i	$-0.610933\pi$
$587$	7.31012	−	4.22050i	0.301721	−	0.174199i	0.643216	+	0.765685i	$0.277600\pi$
$588$	25.5550	−	14.7542i	1.05387	−	0.608452i
$589$	−9.19747	−	15.9305i	−0.378975	−	0.656404i
$590$	−55.8694	+	12.8559i	−2.30011	+	0.529267i
$591$	14.4217			0.593229
$592$	22.7274	−	24.5297i	0.934092	−	1.00816i
$593$			8.19593i			0.336566i	0.985739	+	0.168283i	$0.0538223\pi$
$593$			8.19593i			0.336566i	−0.985739	+	0.168283i	$0.946178\pi$
$594$	0.603701	−	1.04564i	0.0247702	−	0.0429032i
$595$	−0.173273	−	0.0531121i	−0.00710350	−	0.00217739i
$596$	−24.9039	−	43.1348i	−1.02010	−	1.76687i
$597$	11.2093	−	6.47171i	0.458767	−	0.264869i
$598$			18.9300i			0.774104i
$599$	−19.3434	−	33.5037i	−0.790349	−	1.36892i	−0.925751	−	0.378133i	$-0.876566\pi$
$599$	−19.3434	−	33.5037i	−0.790349	−	1.36892i	0.135402	−	0.990791i	$-0.456767\pi$
$600$	−1.99203	+	27.9064i	−0.0813244	+	1.13927i
$601$	−9.89542	+	17.1394i	−0.403643	+	0.699129i	−0.994162	−	0.107894i	$-0.965589\pi$
$601$	−9.89542	+	17.1394i	−0.403643	+	0.699129i	0.590520	+	0.807023i	$0.298923\pi$
$602$		−	0.831131i		−	0.0338744i
$603$			7.50612i			0.305673i
$604$	−27.6322	+	47.8604i	−1.12434	+	1.94741i
$605$	23.0173	+	7.05533i	0.935787	+	0.286840i
$606$	5.82976			0.236818
$607$	−34.1272	−	19.7033i	−1.38518	−	0.799734i	−0.392413	−	0.919789i	$-0.628360\pi$
$607$	−34.1272	−	19.7033i	−1.38518	−	0.799734i	−0.992767	+	0.120055i	$0.961693\pi$
$608$	3.86891	+	2.23372i	0.156905	+	0.0905892i
$609$	−0.189427	+	0.328096i	−0.00767595	+	0.0132951i
$610$	8.62124	−	28.1259i	0.349064	−	1.13879i
$611$	12.2337	+	21.1894i	0.494922	+	0.857230i
$612$	−1.47945	−	0.854162i	−0.0598033	−	0.0345274i
$613$	34.5795	+	19.9645i	1.39665	+	0.806358i	0.994040	−	0.109012i	$-0.0347686\pi$
$613$	34.5795	+	19.9645i	1.39665	+	0.806358i	0.402613	+	0.915370i	$0.368102\pi$
$614$	32.5543	−	56.3857i	1.31378	−	2.27554i
$615$	−6.87970	−	7.38830i	−0.277416	−	0.297925i
$616$	0.272025	+	0.471160i	0.0109602	+	0.0189836i
$617$	5.22845	+	3.01864i	0.210489	+	0.121526i	0.601539	−	0.798844i	$-0.294555\pi$
$617$	5.22845	+	3.01864i	0.210489	+	0.121526i	−0.391049	+	0.920370i	$0.627888\pi$
$618$		−	6.61810i		−	0.266219i
$619$	16.2405			0.652761			0.326381	−	0.945238i	$-0.394171\pi$
$619$	16.2405			0.652761			0.326381	+	0.945238i	$0.394171\pi$
$620$	22.2515	+	96.7013i	0.893641	+	3.88362i
$621$	2.07034			0.0830799
$622$	−17.4560	+	10.0782i	−0.699921	+	0.404099i
$623$		−	0.0892732i		−	0.00357665i
$624$	−10.0613	−	17.4267i	−0.402774	−	0.697624i
$625$	9.29797	+	23.2066i	0.371919	+	0.928265i
$626$	32.8147	+	56.8367i	1.31154	+	2.27165i
$627$	−0.735704	−	0.424759i	−0.0293812	−	0.0169632i
$628$		−	22.4662i		−	0.896497i
$629$	1.79775	+	1.66567i	0.0716812	+	0.0664146i
$630$	−0.822314	+	0.765708i	−0.0327618	+	0.0305065i
$631$	−7.90871	+	13.6983i	−0.314841	+	0.545321i	−0.979404	−	0.201912i	$-0.935285\pi$
$631$	−7.90871	+	13.6983i	−0.314841	+	0.545321i	0.664563	+	0.747232i	$0.268618\pi$
$632$	−73.2741	+	42.3048i	−2.91469	+	1.68280i
$633$	2.30397	−	1.33020i	0.0915747	−	0.0528707i
$634$	23.9407	+	41.4666i	0.950808	+	1.64685i
$635$	23.2167	+	24.9330i	0.921325	+	0.989436i
$636$	−4.02442	−	6.97050i	−0.159579	−	0.276398i
$637$			25.4740i			1.00932i
$638$	1.96931	+	1.13698i	0.0779655	+	0.0450134i
$639$	10.9761			0.434207
$640$	25.4297	+	27.3097i	1.00520	+	1.07951i
$641$	1.36604	−	2.36605i	0.0539552	−	0.0934532i	−0.837786	−	0.545998i	$-0.816151\pi$
$641$	1.36604	−	2.36605i	0.0539552	−	0.0934532i	0.891742	+	0.452545i	$0.149484\pi$
$642$	−25.2035	+	14.5512i	−0.994703	+	0.574292i
$643$		−	30.4017i		−	1.19893i	−0.800403	−	0.599463i	$-0.795381\pi$
$643$		−	30.4017i		−	1.19893i	0.800403	−	0.599463i	$-0.204619\pi$
$644$	−0.882910	+	1.52925i	−0.0347915	+	0.0602607i
$645$	−0.829365	−	3.60428i	−0.0326562	−	0.141918i
$646$	−0.884463	+	1.53193i	−0.0347987	+	0.0602732i
$647$	−11.8424	+	6.83721i	−0.465573	+	0.268798i	−0.714384	−	0.699753i	$-0.753293\pi$
$647$	−11.8424	+	6.83721i	−0.465573	+	0.268798i	0.248812	+	0.968552i	$0.419960\pi$
$648$	−4.84583	+	2.79774i	−0.190362	+	0.109906i
$649$	−2.48045	+	4.29627i	−0.0973663	+	0.168643i
$650$	−37.8641	−	25.6195i	−1.48515	−	1.00488i
$651$	−1.05268	+	1.82330i	−0.0412578	+	0.0714606i
$652$			68.5666i			2.68528i
$653$	24.3262	−	14.0448i	0.951959	−	0.549614i	0.0582700	−	0.998301i	$-0.481442\pi$
$653$	24.3262	−	14.0448i	0.951959	−	0.549614i	0.893689	+	0.448687i	$0.148108\pi$
$654$	15.2795	−	26.4650i	0.597478	−	1.03486i
$655$	7.75475	−	7.22093i	0.303003	−	0.282145i
$656$	24.8202			0.969067
$657$	6.59347	+	3.80674i	0.257236	+	0.148515i
$658$			3.35895i			0.130945i
$659$	−8.61127	−	14.9152i	−0.335447	−	0.581012i	0.648123	−	0.761535i	$-0.275554\pi$
$659$	−8.61127	−	14.9152i	−0.335447	−	0.581012i	−0.983571	+	0.180524i	$0.942221\pi$
$660$	3.12288	+	3.35375i	0.121558	+	0.130544i
$661$	−23.7248	−	41.0926i	−0.922788	−	1.59832i	−0.795080	−	0.606504i	$-0.792571\pi$
$661$	−23.7248	−	41.0926i	−0.922788	−	1.59832i	−0.127708	−	0.991812i	$-0.540762\pi$
$662$	17.7582	−	10.2527i	0.690194	−	0.398484i
$663$	1.27718	−	0.737381i	0.0496016	−	0.0286375i
$664$	−31.0548	+	53.7885i	−1.20516	+	2.08740i
$665$	0.538745	+	0.578573i	0.0208916	+	0.0224361i
$666$	14.5164	−	4.48916i	0.562501	−	0.173951i
$667$			3.89917i			0.150976i
$668$	−59.7411	−	34.4915i	−2.31145	−	1.33452i
$669$	−13.1015	−	22.6925i	−0.506534	−	0.877342i
$670$	−40.0860	−	12.2873i	−1.54866	−	0.474699i
$671$	−1.27280	−	2.20455i	−0.0491359	−	0.0851059i
$672$		−	0.511313i		−	0.0197243i
$673$	−21.7532	+	12.5592i	−0.838525	+	0.484123i	−0.856763	−	0.515711i	$-0.827528\pi$
$673$	−21.7532	+	12.5592i	−0.838525	+	0.484123i	0.0182374	+	0.999834i	$0.494195\pi$
$674$	−0.0416404			−0.00160393
$675$	−2.80197	+	4.14113i	−0.107848	+	0.159392i
$676$	1.68657			0.0648680
$677$			19.4087i			0.745938i	0.927844	+	0.372969i	$0.121660\pi$
$677$			19.4087i			0.745938i	−0.927844	+	0.372969i	$0.878340\pi$
$678$	−23.0482	−	13.3069i	−0.885161	−	0.511048i
$679$	−0.371231	−	0.642991i	−0.0142465	−	0.0246757i
$680$	3.68934	−	3.43537i	0.141480	−	0.131741i
$681$	0.741566	−	1.28443i	0.0284169	−	0.0492195i
$682$	10.9438	+	6.31842i	0.419060	+	0.241945i
$683$	−19.7183	−	11.3844i	−0.754499	−	0.435610i	0.0728183	−	0.997345i	$-0.476801\pi$
$683$	−19.7183	−	11.3844i	−0.754499	−	0.435610i	−0.827317	+	0.561735i	$0.810134\pi$
$684$	3.72603	+	6.45368i	0.142468	+	0.246763i
$685$	−7.53569	+	24.5844i	−0.287924	+	0.939323i
$686$	−3.50730	+	6.07483i	−0.133909	+	0.231938i
$687$	14.2301	+	8.21575i	0.542912	+	0.313451i
$688$	7.87472	+	4.54647i	0.300221	+	0.173333i
$689$	6.94841			0.264713
$690$	−3.38908	+	11.0565i	−0.129020	+	0.420915i
$691$	−5.74953	+	9.95849i	−0.218723	+	0.378839i	−0.954418	−	0.298474i	$-0.903522\pi$
$691$	−5.74953	+	9.95849i	−0.218723	+	0.378839i	0.735695	+	0.677313i	$0.236856\pi$
$692$			74.3492i			2.82633i
$693$			0.0972300i			0.00369346i
$694$	6.19986	−	10.7385i	0.235343	−	0.407627i
$695$	−14.5018	+	13.5035i	−0.550083	+	0.512216i
$696$	−5.26912	−	9.12638i	−0.199725	−	0.345935i
$697$			1.81905i			0.0689014i
$698$	34.9359	−	20.1703i	1.32234	−	0.763456i
$699$	−5.87577	−	10.1771i	−0.222242	−	0.384935i
$700$	−1.86391	−	3.83567i	−0.0704491	−	0.144975i
$701$	13.6594	−	23.6588i	0.515910	−	0.893582i	−0.483920	−	0.875112i	$-0.660787\pi$
$701$	13.6594	−	23.6588i	0.515910	−	0.893582i	0.999829	−	0.0184694i	$-0.00587932\pi$
$702$		−	9.14341i		−	0.345096i
$703$	−3.15853	−	10.2136i	−0.119126	−	0.385215i
$704$	2.24543			0.0846277
$705$	3.35181	+	14.5664i	0.126236	+	0.548602i
$706$	−1.47522	−	2.55516i	−0.0555207	−	0.0961647i
$707$	−0.406565	+	0.234730i	−0.0152905	+	0.00882795i
$708$	37.6874	−	21.7588i	1.41638	−	0.817747i
$709$	1.71306			0.0643354			0.0321677	−	0.999482i	$-0.489759\pi$
$709$	1.71306			0.0643354			0.0321677	+	0.999482i	$0.489759\pi$
$710$	−17.9675	+	58.6171i	−0.674307	+	2.19986i
$711$	−15.1211			−0.567084
$712$	2.15055	+	1.24162i	0.0805951	+	0.0465316i
$713$			21.6684i			0.811490i
$714$	0.202459			0.00757685
$715$	−3.85530	+	0.887125i	−0.144180	+	0.0331766i
$716$	49.4693	+	85.6833i	1.84875	+	3.20213i
$717$		−	26.4168i		−	0.986554i
$718$	−35.2869	−	20.3729i	−1.31689	−	0.760309i
$719$	21.1507	−	36.6341i	0.788788	−	1.36622i	−0.137922	−	0.990443i	$-0.544042\pi$
$719$	21.1507	−	36.6341i	0.788788	−	1.36622i	0.926710	−	0.375778i	$-0.122624\pi$
$720$	−2.75661	−	11.9798i	−0.102733	−	0.446460i
$721$	0.266472	+	0.461543i	0.00992394	+	0.0171888i
$722$	−34.4206	+	19.8728i	−1.28100	+	0.739587i
$723$	−18.2804	−	10.5542i	−0.679855	−	0.392515i
$724$	3.73428	−	6.46796i	0.138783	−	0.240380i
$725$	−7.79919	−	5.27708i	−0.289655	−	0.195986i
$726$	−26.8944			−0.998144
$727$	−10.9683	+	6.33257i	−0.406793	+	0.234862i	−0.689411	−	0.724370i	$-0.742131\pi$
$727$	−10.9683	+	6.33257i	−0.406793	+	0.234862i	0.282618	+	0.959233i	$0.408797\pi$
$728$	3.56800	+	2.05999i	0.132239	+	0.0763482i
$729$	−1.00000			−0.0370370
$730$	−31.1230	+	28.9805i	−1.15191	+	1.07262i
$731$	−0.333206	+	0.577130i	−0.0123241	+	0.0213459i
$732$			22.3303i			0.825352i
$733$	27.7778	−	16.0375i	1.02599	−	0.592358i	0.110160	−	0.993914i	$-0.464864\pi$
$733$	27.7778	−	16.0375i	1.02599	−	0.592358i	0.915835	+	0.401555i	$0.131530\pi$
$734$	68.7513			2.53766
$735$	−4.56066	+	14.8787i	−0.168223	+	0.548809i
$736$	−2.63122	−	4.55741i	−0.0969882	−	0.167988i
$737$	−3.14200	+	1.81404i	−0.115737	+	0.0668209i
$738$	9.76700	+	5.63898i	0.359528	+	0.207574i
$739$	−21.1098			−0.776538			−0.388269	−	0.921546i	$-0.626927\pi$
$739$	−21.1098			−0.776538			−0.388269	+	0.921546i	$0.626927\pi$
$740$	0.143461	+	57.6699i	0.00527374	+	2.11999i
$741$	−6.43322			−0.236330
$742$	0.826098	+	0.476948i	0.0303270	+	0.0175093i
$743$	10.7651	−	6.21523i	0.394933	−	0.228015i	−0.289362	−	0.957220i	$-0.593443\pi$
$743$	10.7651	−	6.21523i	0.394933	−	0.228015i	0.684295	+	0.729205i	$0.260110\pi$
$744$	−29.2815	−	50.7171i	−1.07351	−	1.85938i
$745$	25.1141	+	7.69804i	0.920109	+	0.282034i
$746$	−89.2704			−3.26842
$747$	−9.61284	+	5.54997i	−0.351715	+	0.203063i
$748$		−	0.825715i		−	0.0301911i
$749$	1.17179	−	2.02959i	0.0428162	−	0.0741598i
$750$	−17.5287	−	21.7426i	−0.640059	−	0.793928i
$751$	37.9606			1.38520			0.692601	−	0.721321i	$-0.256465\pi$
$751$	37.9606			1.38520			0.692601	+	0.721321i	$0.256465\pi$
$752$	−31.8250	−	18.3742i	−1.16054	−	0.670037i
$753$	−12.7479	+	7.36002i	−0.464560	+	0.268214i
$754$	17.2202			0.627123
$755$	−6.53567	−	28.4029i	−0.237857	−	1.03369i
$756$	0.426457	−	0.738645i	0.0155101	−	0.0268643i
$757$	6.68687	+	3.86067i	0.243038	+	0.140318i	0.616572	−	0.787298i	$-0.288521\pi$
$757$	6.68687	+	3.86067i	0.243038	+	0.140318i	−0.373534	+	0.927616i	$0.621854\pi$
$758$	−58.4559	+	33.7495i	−2.12322	+	1.22584i
$759$	0.500347	+	0.866627i	0.0181615	+	0.0314566i
$760$	−21.4304	+	4.93126i	−0.777364	+	0.178876i
$761$	4.09272	−	7.08880i	0.148361	−	0.256969i	−0.782261	−	0.622951i	$-0.785934\pi$
$761$	4.09272	−	7.08880i	0.148361	−	0.256969i	0.930622	+	0.365982i	$0.119267\pi$
$762$	−32.9603	−	19.0296i	−1.19403	−	0.689371i
$763$			2.46087i			0.0890895i
$764$	24.2583	+	42.0166i	0.877635	+	1.52011i
$765$	0.877985	−	0.202029i	0.0317436	−	0.00730438i
$766$	32.1337			1.16104
$767$			37.5679i			1.35650i
$768$	−28.0559	−	16.1981i	−1.01238	−	0.584497i
$769$	−31.8848			−1.14980			−0.574898	−	0.818225i	$-0.694958\pi$
$769$	−31.8848			−1.14980			−0.574898	+	0.818225i	$0.694958\pi$
$770$	−0.519251	−	0.159162i	−0.0187125	−	0.00573581i
$771$	20.4328			0.735870
$772$	34.5966	−	19.9744i	1.24516	−	0.718894i
$773$	37.8893	−	21.8754i	1.36278	−	0.786804i	0.372791	−	0.927915i	$-0.378401\pi$
$773$	37.8893	−	21.8754i	1.36278	−	0.786804i	0.989994	+	0.141111i	$0.0450675\pi$
$774$	2.06585	+	3.57816i	0.0742555	+	0.128614i
$775$	−43.3416	−	29.3257i	−1.55688	−	1.05341i
$776$	20.6524			0.741379
$777$	−0.831618	+	0.897564i	−0.0298341	+	0.0321999i
$778$			34.2571i			1.22818i
$779$	3.96754	−	6.87198i	0.142152	−	0.246214i
$780$	33.1792	+	10.1702i	1.18801	+	0.364151i
$781$	2.65263	+	4.59450i	0.0949187	+	0.164404i
$782$	1.80455	−	1.04186i	0.0645307	−	0.0372568i
$783$		−	1.88335i		−	0.0673053i
$784$	−19.1301	−	33.1343i	−0.683218	−	1.18337i
$785$	8.07411	+	8.67101i	0.288177	+	0.309482i
$786$	−5.91867	+	10.2514i	−0.211112	+	0.365657i
$787$		−	10.2808i		−	0.366471i	−0.983069	−	0.183235i	$-0.941343\pi$
$787$		−	10.2808i		−	0.366471i	0.983069	−	0.183235i	$-0.0586571\pi$
$788$		−	61.1477i		−	2.17830i
$789$	−7.86126	+	13.6161i	−0.279868	+	0.484746i
$790$	24.7527	−	80.7531i	0.880661	−	2.87307i
$791$	2.14316			0.0762021
$792$	−2.34222	−	1.35228i	−0.0832273	−	0.0480513i
$793$	−16.6946	−	9.63866i	−0.592844	−	0.342279i
$794$	−24.6984	+	42.7789i	−0.876514	+	1.51817i
$795$	4.05839	+	1.24399i	0.143936	+	0.0441198i
$796$	−27.4400	−	47.5274i	−0.972584	−	1.68456i
$797$	25.9739	+	14.9960i	0.920043	+	0.531187i	0.883649	−	0.468150i	$-0.155079\pi$
$797$	25.9739	+	14.9960i	0.920043	+	0.531187i	0.0363943	+	0.999338i	$0.488413\pi$
$798$	−0.764848	−	0.441585i	−0.0270753	−	0.0156319i
$799$	1.34662	−	2.33242i	0.0476401	−	0.0825151i
$800$	12.6769	+	0.904909i	0.448195	+	0.0319934i
$801$	0.221897	+	0.384336i	0.00784033	+	0.0135799i
$802$	−47.9503	−	27.6841i	−1.69319	−	0.977561i
$803$			3.67996i			0.129863i
$804$	31.8259			1.12241
$805$	−0.208829	−	0.907535i	−0.00736025	−	0.0319864i
$806$	95.6961			3.37075
$807$	9.99905	−	5.77295i	0.351983	−	0.203218i
$808$		−	13.0586i		−	0.459400i
$809$	13.5899	+	23.5385i	0.477797	+	0.827568i	0.999676	−	0.0254509i	$-0.00810216\pi$
$809$	13.5899	+	23.5385i	0.477797	+	0.827568i	−0.521879	+	0.853019i	$0.674769\pi$
$810$	1.63697	−	5.34044i	0.0575171	−	0.187644i
$811$	2.91263	+	5.04482i	0.102276	+	0.177148i	0.912622	−	0.408804i	$-0.134054\pi$
$811$	2.91263	+	5.04482i	0.102276	+	0.177148i	−0.810346	+	0.585952i	$0.800721\pi$
$812$	1.39112	+	0.803166i	0.0488189	+	0.0281856i
$813$		−	0.0435270i		−	0.00152656i
$814$	5.38737	+	4.99155i	0.188827	+	0.174954i
$815$	−24.6422	−	26.4639i	−0.863177	−	0.926989i
$816$	−1.10750	+	1.91824i	−0.0387702	+	0.0671519i
$817$	2.51756	−	1.45351i	0.0880783	−	0.0508520i
$818$	53.0285	−	30.6160i	1.85410	−	1.07046i
$819$	0.368152	+	0.637657i	0.0128643	+	0.0222816i
$820$	−31.3263	+	29.1699i	−1.09396	+	1.01866i
$821$	−16.9812	−	29.4123i	−0.592649	−	1.02650i	−0.993874	−	0.110518i	$-0.964749\pi$
$821$	−16.9812	−	29.4123i	−0.592649	−	1.02650i	0.401225	−	0.915979i	$-0.368584\pi$
$822$		−	28.7255i		−	1.00192i
$823$	−17.5921	−	10.1568i	−0.613224	−	0.354045i	0.161002	−	0.986954i	$-0.448527\pi$
$823$	−17.5921	−	10.1568i	−0.613224	−	0.354045i	−0.774226	+	0.632909i	$0.781861\pi$
$824$	−14.8245			−0.516435
$825$	−2.41061	−	0.172075i	−0.0839266	−	0.00599090i
$826$	−2.57871	+	4.46646i	−0.0897249	+	0.155408i
$827$	32.5565	−	18.7965i	1.13210	−	0.653618i	0.187638	−	0.982238i	$-0.439917\pi$
$827$	32.5565	−	18.7965i	1.13210	−	0.653618i	0.944462	+	0.328620i	$0.106584\pi$
$828$		−	8.77822i		−	0.305064i
$829$	−18.5974	+	32.2116i	−0.645913	+	1.11875i	0.338176	+	0.941083i	$0.390190\pi$
$829$	−18.5974	+	32.2116i	−0.645913	+	1.11875i	−0.984090	+	0.177672i	$0.943143\pi$
$830$	−13.9034	−	60.4219i	−0.482594	−	2.09727i
$831$	−16.0359	+	27.7749i	−0.556278	+	0.963501i
$832$	14.7260	−	8.50208i	0.510533	−	0.294757i
$833$	2.42838	−	1.40203i	0.0841383	−	0.0485773i
$834$	11.0682	−	19.1707i	0.383260	−	0.663827i
$835$	35.4535	−	8.15805i	1.22692	−	0.282321i
$836$	−1.80097	+	3.11937i	−0.0622879	+	0.107886i
$837$		−	10.4661i		−	0.361762i
$838$	78.3976	−	45.2629i	2.70820	−	1.56358i
$839$	4.97101	−	8.61005i	0.171618	−	0.297252i	−0.767367	−	0.641208i	$-0.778434\pi$
$839$	4.97101	−	8.61005i	0.171618	−	0.297252i	0.938986	+	0.343956i	$0.111767\pi$
$840$	1.71518	+	1.84197i	0.0591792	+	0.0635541i
$841$	−25.4530			−0.877690
$842$	62.1165	+	35.8630i	2.14068	+	1.23592i
$843$		−	19.6647i		−	0.677287i
$844$	−5.64003	−	9.76881i	−0.194138	−	0.336256i
$845$	−0.650946	+	0.606136i	−0.0223932	+	0.0208517i
$846$	−8.34897	−	14.4608i	−0.287043	−	0.497174i
$847$	1.87560	−	1.08288i	0.0644464	−	0.0372082i
$848$	−9.03788	+	5.21802i	−0.310362	+	0.179188i
$849$	−3.13820	+	5.43553i	−0.107703	+	0.186547i
$850$	−0.358308	+	5.01954i	−0.0122899	+	0.172169i
$851$	−2.79347	+	12.2797i	−0.0957589	+	0.420941i
$852$		−	46.5384i		−	1.59438i
$853$	−42.9383	−	24.7905i	−1.47018	−	0.848809i	−0.470741	−	0.882272i	$-0.656013\pi$
$853$	−42.9383	−	24.7905i	−1.47018	−	0.848809i	−0.999440	+	0.0334625i	$0.989347\pi$
$854$	−1.32322	−	2.29189i	−0.0452797	−	0.0784267i
$855$	−3.75748	−	1.15175i	−0.128503	−	0.0393892i
$856$	32.5946	+	56.4555i	1.11406	+	1.92961i
$857$		−	9.86150i		−	0.336862i	−0.985713	−	0.168431i	$-0.946130\pi$
$857$		−	9.86150i		−	0.336862i	0.985713	−	0.168431i	$-0.0538701\pi$
$858$	3.82736	−	2.20973i	0.130664	−	0.0754388i
$859$	5.62741			0.192005			0.0960024	−	0.995381i	$-0.469394\pi$
$859$	5.62741			0.192005			0.0960024	+	0.995381i	$0.469394\pi$
$860$	−15.2821	+	3.51650i	−0.521116	+	0.119912i
$861$	−0.908195			−0.0309512
$862$			28.3530i			0.965708i
$863$	−37.5644	−	21.6878i	−1.27871	−	0.738261i	−0.302095	−	0.953278i	$-0.597686\pi$
$863$	−37.5644	−	21.6878i	−1.27871	−	0.738261i	−0.976610	+	0.215017i	$0.931019\pi$
$864$	1.27091	+	2.20129i	0.0432374	+	0.0748893i
$865$	−26.7204	−	28.6957i	−0.908519	−	0.975683i
$866$	33.4257	−	57.8950i	1.13585	−	1.96735i
$867$	14.5818	+	8.41883i	0.495225	+	0.285919i
$868$	7.73075	+	4.46335i	0.262399	+	0.151496i
$869$	−3.65437	−	6.32956i	−0.123966	−	0.214715i
$870$	10.0579	+	3.08298i	0.340995	+	0.104523i
$871$	−13.7373	+	23.7937i	−0.465471	+	0.806220i
$872$	−59.2812	−	34.2260i	−2.00751	−	1.15904i
$873$	3.19642	+	1.84546i	0.108183	+	0.0624592i
$874$	−9.08962			−0.307461
$875$	2.09789	+	0.810541i	0.0709218	+	0.0274013i
$876$	16.1405	−	27.9562i	0.545338	−	0.944554i
$877$		−	38.4109i		−	1.29704i	−0.761196	−	0.648522i	$-0.775387\pi$
$877$		−	38.4109i		−	1.29704i	0.761196	−	0.648522i	$-0.224613\pi$
$878$		−	34.5597i		−	1.16633i
$879$	−9.70437	+	16.8085i	−0.327320	+	0.566935i
$880$	4.34843	−	4.04909i	0.146586	−	0.136495i
$881$	15.7112	+	27.2126i	0.529323	+	0.916815i	0.999415	+	0.0341975i	$0.0108875\pi$
$881$	15.7112	+	27.2126i	0.529323	+	0.916815i	−0.470092	+	0.882618i	$0.655779\pi$
$882$		−	17.3849i		−	0.585380i
$883$	−7.13299	+	4.11823i	−0.240044	+	0.138590i	−0.615197	−	0.788373i	$-0.710924\pi$
$883$	−7.13299	+	4.11823i	−0.240044	+	0.138590i	0.375153	+	0.926963i	$0.377590\pi$
$884$	−3.12649	−	5.41523i	−0.105155	−	0.182134i
$885$	−6.72587	+	21.9425i	−0.226088	+	0.737589i
$886$	13.3142	−	23.0609i	0.447301	−	0.774748i
$887$		−	4.09704i		−	0.137565i	−0.997632	−	0.0687825i	$-0.978089\pi$
$887$		−	4.09704i		−	0.137565i	0.997632	−	0.0687825i	$-0.0219114\pi$
$888$	−10.0557	−	32.5167i	−0.337446	−	1.09119i
$889$	3.06485			0.102792
$890$	−2.41576	+	0.555880i	−0.0809765	+	0.0186331i
$891$	−0.241674	−	0.418592i	−0.00809639	−	0.0140234i
$892$	−96.2159	+	55.5503i	−3.22155	+	1.85996i
$893$	−10.1745	+	5.87426i	−0.340477	+	0.196575i
$894$	−29.3443			−0.981421
$895$	−49.8868	−	15.2915i	−1.66753	−	0.511137i
$896$	3.35700			0.112150
$897$	6.56279	+	3.78903i	0.219125	+	0.126512i
$898$			55.8804i			1.86475i
$899$	19.7114			0.657411
$900$	17.5584	+	11.8803i	0.585279	+	0.396010i
$901$	−0.382423	−	0.662377i	−0.0127404	−	0.0220670i
$902$			5.45118i			0.181505i
$903$	−0.288143	−	0.166359i	−0.00958880	−	0.00553610i
$904$	−29.8073	+	51.6277i	−0.991375	+	1.71711i
$905$	0.883243	+	3.83843i	0.0293600	+	0.127594i
$906$	16.2796	+	28.1971i	0.540853	+	0.936785i
$907$	35.7396	−	20.6343i	1.18671	−	0.685150i	0.229156	−	0.973390i	$-0.426403\pi$
$907$	35.7396	−	20.6343i	1.18671	−	0.685150i	0.957558	+	0.288240i	$0.0930701\pi$
$908$	−5.44597	−	3.14423i	−0.180731	−	0.104345i
$909$	1.16689	−	2.02111i	0.0387032	−	0.0670359i
$910$	−4.00802	+	0.922268i	−0.132865	+	0.0305729i
$911$	−51.6533			−1.71135			−0.855674	−	0.517515i	$-0.826857\pi$
$911$	−51.6533			−1.71135			−0.855674	+	0.517515i	$0.826857\pi$
$912$	8.36777	−	4.83114i	0.277085	−	0.159975i
$913$	−4.64635	−	2.68257i	−0.153772	−	0.0887801i
$914$	3.20595			0.106043
$915$	−8.02529	−	8.61858i	−0.265308	−	0.284921i
$916$	34.8347	−	60.3355i	1.15097	−	1.99354i
$917$		−	0.953241i		−	0.0314788i
$918$	−0.871622	+	0.503231i	−0.0287678	+	0.0166091i
$919$	21.8624			0.721175			0.360588	−	0.932725i	$-0.382576\pi$
$919$	21.8624			0.721175			0.360588	+	0.932725i	$0.382576\pi$
$920$	24.7665	+	7.59149i	0.816526	+	0.250284i
$921$	−13.0322	−	22.5724i	−0.429424	−	0.743784i
$922$	−42.1868	+	24.3566i	−1.38935	+	0.802141i
$923$	34.7932	+	20.0879i	1.14523	+	0.661200i
$924$	0.412254			0.0135622
$925$	−20.7814	−	22.2066i	−0.683287	−	0.730150i
$926$	65.6802			2.15839
$927$	−2.29442	−	1.32468i	−0.0753585	−	0.0435083i
$928$	−4.14579	+	2.39357i	−0.136092	+	0.0785729i
$929$	12.7410	+	22.0681i	0.418019	+	0.724030i	0.995740	−	0.0922045i	$-0.0293913\pi$
$929$	12.7410	+	22.0681i	0.418019	+	0.724030i	−0.577721	+	0.816234i	$0.696058\pi$
$930$	55.8937	+	17.1327i	1.83283	+	0.561804i
$931$	−12.2319			−0.400883
$932$	−43.1510	+	24.9132i	−1.41346	+	0.816059i
$933$			8.06903i			0.264168i
$934$	−22.9561	+	39.7611i	−0.751145	+	1.30102i
$935$	0.296754	+	0.318692i	0.00970489	+	0.0104223i
$936$	−20.4811			−0.669447
$937$	−16.6585	−	9.61778i	−0.544209	−	0.314199i	0.202574	−	0.979267i	$-0.435069\pi$
$937$	−16.6585	−	9.61778i	−0.544209	−	0.314199i	−0.746783	+	0.665068i	$0.768403\pi$
$938$	−3.26647	+	1.88590i	−0.106654	+	0.0615767i
$939$	26.2728			0.857380
$940$	61.7614	−	14.2116i	2.01443	−	0.463532i
$941$	−1.46315	+	2.53425i	−0.0476973	+	0.0826142i	−0.888888	−	0.458124i	$-0.848522\pi$
$941$	−1.46315	+	2.53425i	−0.0476973	+	0.0826142i	0.841191	+	0.540738i	$0.181855\pi$
$942$	−11.4627	−	6.61799i	−0.373475	−	0.215626i
$943$	−8.09489	+	4.67359i	−0.263606	+	0.152193i
$944$	−28.2123	−	48.8651i	−0.918231	−	1.59042i
$945$	0.100867	+	0.438351i	0.00328120	+	0.0142596i
$946$	−0.998526	+	1.72950i	−0.0324649	+	0.0562308i
$947$	−24.9699	−	14.4164i	−0.811414	−	0.468470i	0.0360327	−	0.999351i	$-0.488528\pi$
$947$	−24.9699	−	14.4164i	−0.811414	−	0.468470i	−0.847447	+	0.530881i	$0.821861\pi$
$948$			64.1132i			2.08230i
$949$	13.9338	+	24.1341i	0.452311	+	0.783425i
$950$	12.3018	−	18.1812i	0.399122	−	0.589877i
$951$	19.1679			0.621563
$952$		−	0.453506i		−	0.0146982i
$953$	−50.8659	−	29.3674i	−1.64771	−	0.951305i	−0.977980	−	0.208699i	$-0.933077\pi$
$953$	−50.8659	−	29.3674i	−1.64771	−	0.951305i	−0.669729	−	0.742606i	$-0.733590\pi$
$954$	−4.74199			−0.153528
$955$	−24.4631	−	7.49849i	−0.791606	−	0.242645i
$956$	−112.007			−3.62257
$957$	0.788354	−	0.455156i	0.0254839	−	0.0147131i
$958$	−32.3020	+	18.6496i	−1.04363	+	0.602540i
$959$	1.15661	+	2.00330i	0.0373488	+	0.0646900i
$960$	10.1233	−	2.32942i	0.326727	−	0.0751816i
$961$	78.5399			2.53355
$962$	54.2316	+	12.3370i	1.74850	+	0.397762i
$963$			11.6503i			0.375427i
$964$	−44.7496	+	77.5087i	−1.44129	+	2.49639i
$965$	−6.17428	+	20.1430i	−0.198757	+	0.648425i
$966$	0.520168	+	0.900958i	0.0167361	+	0.0289878i
$967$	47.2543	−	27.2823i	1.51960	−	0.877339i	0.519862	−	0.854250i	$-0.325983\pi$
$967$	47.2543	−	27.2823i	1.51960	−	0.877339i	0.999733	−	0.0230891i	$-0.00735015\pi$
$968$			60.2431i			1.93629i
$969$	0.354069	+	0.613265i	0.0113743	+	0.0197009i
$970$	−15.0880	+	14.0494i	−0.484446	+	0.451098i
$971$	1.84359	−	3.19319i	0.0591637	−	0.102474i	−0.834927	−	0.550361i	$-0.814490\pi$
$971$	1.84359	−	3.19319i	0.0591637	−	0.102474i	0.894090	+	0.447887i	$0.147823\pi$
$972$			4.23999i			0.135998i
$973$			1.78261i			0.0571477i
$974$	29.7591	−	51.5442i	0.953542	−	1.65158i
$975$	−16.4609	+	7.99901i	−0.527170	+	0.256173i
$976$	28.9532			0.926771
$977$	−6.08146	−	3.51113i	−0.194563	−	0.112331i	0.399554	−	0.916710i	$-0.369165\pi$
$977$	−6.08146	−	3.51113i	−0.194563	−	0.112331i	−0.594117	+	0.804379i	$0.702498\pi$
$978$	34.9841	+	20.1981i	1.11867	+	0.645863i
$979$	−0.107253	+	0.185768i	−0.00342783	+	0.00593718i
$980$	63.0855	+	19.3372i	2.01519	+	0.617703i
$981$	−6.11672	−	10.5945i	−0.195292	−	0.338255i
$982$	−91.0651	−	52.5765i	−2.90600	−	1.67778i
$983$	12.6371	+	7.29606i	0.403062	+	0.232708i	0.687805	−	0.725896i	$-0.258575\pi$
$983$	12.6371	+	7.29606i	0.403062	+	0.232708i	−0.284742	+	0.958604i	$0.591908\pi$
$984$	12.6313	−	21.8780i	0.402670	−	0.697444i
$985$	21.9759	+	23.6005i	0.700210	+	0.751975i
$986$	−0.947759	−	1.64157i	−0.0301828	−	0.0522781i
$987$	1.16451	+	0.672328i	0.0370666	+	0.0214004i
$988$			27.2768i			0.867790i
$989$	−3.42436			−0.108888
$990$	2.63108	−	0.605425i	0.0836211	−	0.0192417i
$991$	−3.31876			−0.105424			−0.0527119	−	0.998610i	$-0.516786\pi$
$991$	−3.31876			−0.105424			−0.0527119	+	0.998610i	$0.516786\pi$
$992$	−23.0390	+	13.3015i	−0.731488	+	0.422325i
$993$		−	8.20876i		−	0.260497i
$994$	2.75771	+	4.77650i	0.0874694	+	0.151501i
$995$	27.6716	+	8.48197i	0.877248	+	0.268897i
$996$	23.5318	+	40.7583i	0.745634	+	1.29148i
$997$	41.7317	+	24.0938i	1.32166	+	0.763059i	0.983993	−	0.178208i	$-0.0570301\pi$
$997$	41.7317	+	24.0938i	1.32166	+	0.763059i	0.337664	+	0.941267i	$0.390363\pi$
$998$			74.1518i			2.34723i
$999$	1.34928	−	5.93123i	0.0426893	−	0.187656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	555.2.bb.a.454.3	✓	72
5.4	even	2	inner	555.2.bb.a.454.34	yes	72
37.26	even	3	inner	555.2.bb.a.544.34	yes	72
185.174	even	6	inner	555.2.bb.a.544.3	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
555.2.bb.a.454.3	✓	72	1.1	even	1	trivial
555.2.bb.a.454.34	yes	72	5.4	even	2	inner
555.2.bb.a.544.3	yes	72	185.174	even	6	inner
555.2.bb.a.544.34	yes	72	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 555 = 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	555.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.16333 - 1.24900i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.11999 + 3.67194i) q^{4} +(-2.13789 - 0.655312i) q^{5} +2.49800 q^{6} +(-0.174209 + 0.100580i) q^{7} -5.59548i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-2.16333 - 1.24900i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(2.11999 + 3.67194i) q^{4} +(-2.13789 - 0.655312i) q^{5} +2.49800 q^{6} +(-0.174209 + 0.100580i) q^{7} -5.59548i q^{8} +(0.500000 - 0.866025i) q^{9} +(3.80647 + 4.08787i) q^{10} +0.483348 q^{11} +(-3.67194 - 2.11999i) q^{12} +(3.16991 - 1.83015i) q^{13} +0.502496 q^{14} +(2.17912 - 0.501428i) q^{15} +(-2.74876 + 4.76099i) q^{16} +(-0.348928 - 0.201454i) q^{17} +(-2.16333 + 1.24900i) q^{18} +(0.878784 + 1.52210i) q^{19} +(-2.12605 - 9.23945i) q^{20} +(0.100580 - 0.174209i) q^{21} +(-1.04564 - 0.603701i) q^{22} -2.07034i q^{23} +(2.79774 + 4.84583i) q^{24} +(4.14113 + 2.80197i) q^{25} -9.14341 q^{26} +1.00000i q^{27} +(-0.738645 - 0.426457i) q^{28} -1.88335 q^{29} +(-5.34044 - 1.63697i) q^{30} -10.4661 q^{31} +(2.20129 - 1.27091i) q^{32} +(-0.418592 + 0.241674i) q^{33} +(0.503231 + 0.871622i) q^{34} +(0.438351 - 0.100867i) q^{35} +4.23999 q^{36} +(-5.93123 - 1.34928i) q^{37} -4.39040i q^{38} +(-1.83015 + 3.16991i) q^{39} +(-3.66678 + 11.9625i) q^{40} +(-2.25740 - 3.90993i) q^{41} +(-0.435174 + 0.251248i) q^{42} -1.65401i q^{43} +(1.02470 + 1.77482i) q^{44} +(-1.63646 + 1.52381i) q^{45} +(-2.58585 + 4.47883i) q^{46} +6.68453i q^{47} -5.49752i q^{48} +(-3.47977 + 6.02713i) q^{49} +(-5.45898 - 11.2338i) q^{50} +0.402908 q^{51} +(13.4404 + 7.75981i) q^{52} +(1.64399 + 0.949159i) q^{53} +(1.24900 - 2.16333i) q^{54} +(-1.03334 - 0.316744i) q^{55} +(0.562792 + 0.974784i) q^{56} +(-1.52210 - 0.878784i) q^{57} +(4.07430 + 2.35230i) q^{58} +(-5.13181 + 8.88856i) q^{59} +(6.46094 + 6.93857i) q^{60} +(-2.63330 - 4.56101i) q^{61} +(22.6417 + 13.0722i) q^{62} +0.201159i q^{63} +4.64557 q^{64} +(-7.97623 + 1.83537i) q^{65} +1.20740 q^{66} +(-6.50049 + 3.75306i) q^{67} -1.70832i q^{68} +(1.03517 + 1.79297i) q^{69} +(-1.07428 - 0.329291i) q^{70} +(5.48804 + 9.50556i) q^{71} +(-4.84583 - 2.79774i) q^{72} +7.61348i q^{73} +(11.1459 + 10.3270i) q^{74} +(-4.98731 - 0.356007i) q^{75} +(-3.72603 + 6.45368i) q^{76} +(-0.0842037 + 0.0486150i) q^{77} +(7.91843 - 4.57171i) q^{78} +(-7.56053 - 13.0952i) q^{79} +(8.99648 - 8.37718i) q^{80} +(-0.500000 - 0.866025i) q^{81} +11.2780i q^{82} +(-9.61284 - 5.54997i) q^{83} +0.852914 q^{84} +(0.613955 + 0.659343i) q^{85} +(-2.06585 + 3.57816i) q^{86} +(1.63103 - 0.941674i) q^{87} -2.70457i q^{88} +(-0.221897 + 0.384336i) q^{89} +(5.44344 - 1.25256i) q^{90} +(-0.368152 + 0.637657i) q^{91} +(7.60216 - 4.38911i) q^{92} +(9.06394 - 5.23307i) q^{93} +(8.34897 - 14.4608i) q^{94} +(-0.881293 - 3.82995i) q^{95} +(-1.27091 + 2.20129i) q^{96} +3.69091i q^{97} +(15.0558 - 8.69245i) q^{98} +(0.241674 - 0.418592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9}+O(q^{10}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9	\( 72 q + 32 q^{4} - 2 q^{5} + 36 q^{9} - 8 q^{11} - 16 q^{14} - 24 q^{16} + 4 q^{19} + 4 q^{20} + 12 q^{21} + 10 q^{25} + 24 q^{26} + 16 q^{29} + 12 q^{30} + 24 q^{31} - 44 q^{34} - 2 q^{35} + 64 q^{36} - 8 q^{39} + 46 q^{40} - 48 q^{41} - 8 q^{44} - 4 q^{45} - 64 q^{46} + 32 q^{49} - 46 q^{50} - 8 q^{51} - 12 q^{55} - 72 q^{56} + 32 q^{59} - 68 q^{60} - 8 q^{61} - 136 q^{64} - 42 q^{65} - 32 q^{66} - 4 q^{69} + 4 q^{70} + 12 q^{71} - 96 q^{74} - 8 q^{75} + 8 q^{76} - 8 q^{79} - 44 q^{80} - 36 q^{81} + 136 q^{84} + 4 q^{85} + 8 q^{86} + 8 q^{91} - 28 q^{94} + 18 q^{95} - 20 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 32 * q^4 - 2 * q^5 + 36 * q^9 - 8 * q^11 - 16 * q^14 - 24 * q^16 + 4 * q^19 + 4 * q^20 + 12 * q^21 + 10 * q^25 + 24 * q^26 + 16 * q^29 + 12 * q^30 + 24 * q^31 - 44 * q^34 - 2 * q^35 + 64 * q^36 - 8 * q^39 + 46 * q^40 - 48 * q^41 - 8 * q^44 - 4 * q^45 - 64 * q^46 + 32 * q^49 - 46 * q^50 - 8 * q^51 - 12 * q^55 - 72 * q^56 + 32 * q^59 - 68 * q^60 - 8 * q^61 - 136 * q^64 - 42 * q^65 - 32 * q^66 - 4 * q^69 + 4 * q^70 + 12 * q^71 - 96 * q^74 - 8 * q^75 + 8 * q^76 - 8 * q^79 - 44 * q^80 - 36 * q^81 + 136 * q^84 + 4 * q^85 + 8 * q^86 + 8 * q^91 - 28 * q^94 + 18 * q^95 - 20 * q^96 - 4 * q^99

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