LMFDB - Embedded newform 336.2.bs.a.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(19,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 0, 10]))

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

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

chi := DirichletCharacter("336.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, 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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	336.19
Dual form			336.2.bs.a.283.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29731 + 0.563017i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.36602 - 1.46081i) q^{4} +(3.94718 - 1.05764i) q^{5} +(0.208064 + 1.39882i) q^{6} +(2.38481 - 1.14572i) q^{7} +(-0.949691 + 2.66422i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-1.29731 + 0.563017i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.36602 - 1.46081i) q^{4} +(3.94718 - 1.05764i) q^{5} +(0.208064 + 1.39882i) q^{6} +(2.38481 - 1.14572i) q^{7} +(-0.949691 + 2.66422i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-4.52524 + 3.59442i) q^{10} +(-0.377505 + 1.40887i) q^{11} +(-1.05749 - 1.69756i) q^{12} +(1.55074 - 1.55074i) q^{13} +(-2.44878 + 2.82904i) q^{14} -4.08642i q^{15} +(-0.267960 - 3.99101i) q^{16} +(-3.65086 + 2.10783i) q^{17} +(1.40501 + 0.161068i) q^{18} +(-6.63952 + 1.77905i) q^{19} +(3.84692 - 7.21087i) q^{20} +(-0.489441 - 2.60009i) q^{21} +(-0.303476 - 2.04028i) q^{22} +(-1.53768 + 2.66335i) q^{23} +(2.32764 + 1.60688i) q^{24} +(10.1315 - 5.84943i) q^{25} +(-1.13870 + 2.88488i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.58403 - 5.04885i) q^{28} +(5.67032 + 5.67032i) q^{29} +(2.30073 + 5.30136i) q^{30} +(-3.19445 - 5.53294i) q^{31} +(2.59464 + 5.02671i) q^{32} +(1.26316 + 0.729284i) q^{33} +(3.54956 - 4.79000i) q^{34} +(8.20153 - 7.04463i) q^{35} +(-1.91342 + 0.582091i) q^{36} +(0.144622 + 0.539737i) q^{37} +(7.61187 - 6.04614i) q^{38} +(-1.09654 - 1.89926i) q^{39} +(-0.930803 + 11.5206i) q^{40} +3.14705 q^{41} +(2.09885 + 3.09755i) q^{42} +(2.23394 + 2.23394i) q^{43} +(1.54241 + 2.47601i) q^{44} +(-3.94718 - 1.05764i) q^{45} +(0.495342 - 4.32093i) q^{46} +(-2.38164 + 4.12513i) q^{47} +(-3.92438 - 0.774121i) q^{48} +(4.37467 - 5.46464i) q^{49} +(-9.85037 + 13.2927i) q^{50} +(1.09109 + 4.07201i) q^{51} +(-0.146997 - 4.38369i) q^{52} +(-11.9937 - 3.21370i) q^{53} +(0.519223 - 1.31545i) q^{54} +5.96032i q^{55} +(0.787607 + 7.44175i) q^{56} +6.87373i q^{57} +(-10.5486 - 4.16367i) q^{58} +(-6.58514 - 1.76448i) q^{59} +(-5.96951 - 5.58215i) q^{60} +(-0.553206 - 2.06459i) q^{61} +(7.25933 + 5.37941i) q^{62} +(-2.63817 - 0.200188i) q^{63} +(-6.19617 - 5.06038i) q^{64} +(4.48092 - 7.76117i) q^{65} +(-2.04930 - 0.234928i) q^{66} +(-0.776828 - 0.208151i) q^{67} +(-1.90802 + 8.21258i) q^{68} +(2.17461 + 2.17461i) q^{69} +(-6.67368 + 13.7567i) q^{70} +8.12189 q^{71} +(2.15457 - 1.83244i) q^{72} +(2.72822 + 4.72542i) q^{73} +(-0.491501 - 0.618782i) q^{74} +(-3.02789 - 11.3002i) q^{75} +(-6.47087 + 12.1293i) q^{76} +(0.713883 + 3.79240i) q^{77} +(2.49186 + 1.84656i) q^{78} +(-0.227003 - 0.131061i) q^{79} +(-5.27876 - 15.4699i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.08270 + 1.77184i) q^{82} +(-7.65911 - 7.65911i) q^{83} +(-4.46683 - 2.83679i) q^{84} +(-12.1813 + 12.1813i) q^{85} +(-4.15586 - 1.64036i) q^{86} +(6.94469 - 4.00952i) q^{87} +(-3.39503 - 2.34375i) q^{88} +(4.98938 - 8.64185i) q^{89} +(5.71619 - 0.850239i) q^{90} +(1.92152 - 5.47493i) q^{91} +(1.79014 + 5.88446i) q^{92} +(-6.17120 + 1.65357i) q^{93} +(0.767211 - 6.69247i) q^{94} +(-24.3258 + 14.0445i) q^{95} +(5.52697 - 1.20522i) q^{96} +16.9468i q^{97} +(-2.59862 + 9.55234i) q^{98} +(1.03136 - 1.03136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) $ 128 * q + 4 * q^4 - 24 * q^8	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.29731	+	0.563017i	−0.917336	+	0.398113i
$2$	−1.29731	+	0.563017i	−0.917336	+	0.398113i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$3$	0.258819	−	0.965926i	0.149429	−	0.557678i
$4$	1.36602	−	1.46081i	0.683012	−	0.730407i
$5$	3.94718	−	1.05764i	1.76523	−	0.472993i	0.777466	−	0.628925i	$-0.216505\pi$
$5$	3.94718	−	1.05764i	1.76523	−	0.472993i	0.987768	+	0.155933i	$0.0498383\pi$
$6$	0.208064	+	1.39882i	0.0849419	+	0.571068i
$7$	2.38481	−	1.14572i	0.901375	−	0.433040i
$7$	2.38481	−	1.14572i	0.901375	−	0.433040i
$8$	−0.949691	+	2.66422i	−0.335767	+	0.941945i
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	−4.52524	+	3.59442i	−1.43101	+	1.13666i
$11$	−0.377505	+	1.40887i	−0.113822	+	0.424790i	−0.999196	−	0.0400897i	$-0.987236\pi$
$11$	−0.377505	+	1.40887i	−0.113822	+	0.424790i	0.885374	+	0.464879i	$0.153902\pi$
$12$	−1.05749	−	1.69756i	−0.305270	−	0.490045i
$13$	1.55074	−	1.55074i	0.430097	−	0.430097i	−0.458564	−	0.888661i	$-0.651636\pi$
$13$	1.55074	−	1.55074i	0.430097	−	0.430097i	0.888661	+	0.458564i	$0.151636\pi$
$14$	−2.44878	+	2.82904i	−0.654465	+	0.756092i
$15$		−	4.08642i		−	1.05511i
$16$	−0.267960	−	3.99101i	−0.0669901	−	0.997754i
$17$	−3.65086	+	2.10783i	−0.885465	+	0.511223i	−0.872456	−	0.488692i	$-0.837474\pi$
$17$	−3.65086	+	2.10783i	−0.885465	+	0.511223i	−0.0130083	+	0.999915i	$0.504141\pi$
$18$	1.40501	+	0.161068i	0.331164	+	0.0379640i
$19$	−6.63952	+	1.77905i	−1.52321	+	0.408143i	−0.920797	−	0.390042i	$-0.872460\pi$
$19$	−6.63952	+	1.77905i	−1.52321	+	0.408143i	−0.602413	+	0.798185i	$0.705794\pi$
$20$	3.84692	−	7.21087i	0.860197	−	1.61240i
$21$	−0.489441	−	2.60009i	−0.106805	−	0.567385i
$22$	−0.303476	−	2.04028i	−0.0647013	−	0.434989i
$23$	−1.53768	+	2.66335i	−0.320629	+	0.555346i	−0.980618	−	0.195929i	$-0.937228\pi$
$23$	−1.53768	+	2.66335i	−0.320629	+	0.555346i	0.659989	+	0.751275i	$0.270561\pi$
$24$	2.32764	+	1.60688i	0.475128	+	0.328004i
$25$	10.1315	−	5.84943i	2.02630	−	1.16989i
$26$	−1.13870	+	2.88488i	−0.223316	+	0.565771i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.58403	−	5.04885i	0.299354	−	0.954142i
$29$	5.67032	+	5.67032i	1.05295	+	1.05295i	0.998517	+	0.0544345i	$0.0173356\pi$
$29$	5.67032	+	5.67032i	1.05295	+	1.05295i	0.0544345	+	0.998517i	$0.482664\pi$
$30$	2.30073	+	5.30136i	0.420053	+	0.967891i
$31$	−3.19445	−	5.53294i	−0.573740	−	0.993746i	−0.996177	−	0.0873541i	$-0.972159\pi$
$31$	−3.19445	−	5.53294i	−0.573740	−	0.993746i	0.422438	−	0.906392i	$-0.361175\pi$
$32$	2.59464	+	5.02671i	0.458671	+	0.888606i
$33$	1.26316	+	0.729284i	0.219887	+	0.126952i
$34$	3.54956	−	4.79000i	0.608744	−	0.821479i
$35$	8.20153	−	7.04463i	1.38631	−	1.19076i
$36$	−1.91342	+	0.582091i	−0.318903	+	0.0970152i
$37$	0.144622	+	0.539737i	0.0237757	+	0.0887323i	0.976794	−	0.214180i	$-0.0687078\pi$
$37$	0.144622	+	0.539737i	0.0237757	+	0.0887323i	−0.953019	+	0.302912i	$0.902041\pi$
$38$	7.61187	−	6.04614i	1.23481	−	0.980814i
$39$	−1.09654	−	1.89926i	−0.175587	−	0.304125i
$40$	−0.930803	+	11.5206i	−0.147173	+	1.82157i
$41$	3.14705			0.491487			0.245744	−	0.969335i	$-0.420968\pi$
$41$	3.14705			0.491487			0.245744	+	0.969335i	$0.420968\pi$
$42$	2.09885	+	3.09755i	0.323860	+	0.477963i
$43$	2.23394	+	2.23394i	0.340673	+	0.340673i	0.856620	−	0.515948i	$-0.172560\pi$
$43$	2.23394	+	2.23394i	0.340673	+	0.340673i	−0.515948	+	0.856620i	$0.672560\pi$
$44$	1.54241	+	2.47601i	0.232528	+	0.373273i
$45$	−3.94718	−	1.05764i	−0.588411	−	0.157664i
$46$	0.495342	−	4.32093i	0.0730341	−	0.637086i
$47$	−2.38164	+	4.12513i	−0.347398	+	0.601712i	−0.985786	−	0.168003i	$-0.946268\pi$
$47$	−2.38164	+	4.12513i	−0.347398	+	0.601712i	0.638388	+	0.769715i	$0.279601\pi$
$48$	−3.92438	−	0.774121i	−0.566435	−	0.111735i
$49$	4.37467	−	5.46464i	0.624953	−	0.780662i
$50$	−9.85037	+	13.2927i	−1.39305	+	1.87988i
$51$	1.09109	+	4.07201i	0.152783	+	0.570195i
$52$	−0.146997	−	4.38369i	−0.0203848	−	0.607908i
$53$	−11.9937	−	3.21370i	−1.64746	−	0.441436i	−0.688562	−	0.725178i	$-0.741758\pi$
$53$	−11.9937	−	3.21370i	−1.64746	−	0.441436i	−0.958901	+	0.283741i	$0.908424\pi$
$54$	0.519223	−	1.31545i	0.0706573	−	0.179010i
$55$			5.96032i			0.803690i
$56$	0.787607	+	7.44175i	0.105248	+	0.994446i
$57$			6.87373i			0.910448i
$58$	−10.5486	−	4.16367i	−1.38510	−	0.546717i
$59$	−6.58514	−	1.76448i	−0.857313	−	0.229716i	−0.196719	−	0.980460i	$-0.563029\pi$
$59$	−6.58514	−	1.76448i	−0.857313	−	0.229716i	−0.660594	+	0.750744i	$0.729695\pi$
$60$	−5.96951	−	5.58215i	−0.770660	−	0.720652i
$61$	−0.553206	−	2.06459i	−0.0708307	−	0.264344i	0.921425	−	0.388556i	$-0.127026\pi$
$61$	−0.553206	−	2.06459i	−0.0708307	−	0.264344i	−0.992256	+	0.124213i	$0.960360\pi$
$62$	7.25933	+	5.37941i	0.921936	+	0.683186i
$63$	−2.63817	−	0.200188i	−0.332378	−	0.0252213i
$64$	−6.19617	−	5.06038i	−0.774522	−	0.632547i
$65$	4.48092	−	7.76117i	0.555789	−	0.962655i
$66$	−2.04930	−	0.234928i	−0.252252	−	0.0289176i
$67$	−0.776828	−	0.208151i	−0.0949047	−	0.0254296i	0.211054	−	0.977474i	$-0.432310\pi$
$67$	−0.776828	−	0.208151i	−0.0949047	−	0.0254296i	−0.305959	+	0.952045i	$0.598977\pi$
$68$	−1.90802	+	8.21258i	−0.231381	+	0.995921i
$69$	2.17461	+	2.17461i	0.261793	+	0.261793i
$70$	−6.67368	+	13.7567i	−0.797657	+	1.64424i
$71$	8.12189			0.963891			0.481945	−	0.876201i	$-0.339930\pi$
$71$	8.12189			0.963891			0.481945	+	0.876201i	$0.339930\pi$
$72$	2.15457	−	1.83244i	0.253918	−	0.215955i
$73$	2.72822	+	4.72542i	0.319314	+	0.553069i	0.980345	−	0.197290i	$-0.0632140\pi$
$73$	2.72822	+	4.72542i	0.319314	+	0.553069i	−0.661031	+	0.750359i	$0.729881\pi$
$74$	−0.491501	−	0.618782i	−0.0571359	−	0.0719319i
$75$	−3.02789	−	11.3002i	−0.349630	−	1.30484i
$76$	−6.47087	+	12.1293i	−0.742259	+	1.39133i
$77$	0.713883	+	3.79240i	0.0813546	+	0.432184i
$78$	2.49186	+	1.84656i	0.282148	+	0.209081i
$79$	−0.227003	−	0.131061i	−0.0255399	−	0.0147455i	0.487176	−	0.873304i	$-0.338027\pi$
$79$	−0.227003	−	0.131061i	−0.0255399	−	0.0147455i	−0.512716	+	0.858559i	$0.671360\pi$
$80$	−5.27876	−	15.4699i	−0.590183	−	1.72958i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	−4.08270	+	1.77184i	−0.450859	+	0.195668i
$83$	−7.65911	−	7.65911i	−0.840697	−	0.840697i	0.148253	−	0.988950i	$-0.452635\pi$
$83$	−7.65911	−	7.65911i	−0.840697	−	0.840697i	−0.988950	+	0.148253i	$0.952635\pi$
$84$	−4.46683	−	2.83679i	−0.487371	−	0.309520i
$85$	−12.1813	+	12.1813i	−1.32125	+	1.32125i
$86$	−4.15586	−	1.64036i	−0.448138	−	0.176885i
$87$	6.94469	−	4.00952i	0.744549	−	0.429866i
$88$	−3.39503	−	2.34375i	−0.361911	−	0.249844i
$89$	4.98938	−	8.64185i	0.528873	−	0.916035i	−0.470560	−	0.882368i	$-0.655948\pi$
$89$	4.98938	−	8.64185i	0.528873	−	0.916035i	0.999433	−	0.0336668i	$-0.0107185\pi$
$90$	5.71619	−	0.850239i	0.602539	−	0.0896231i
$91$	1.92152	−	5.47493i	0.201430	−	0.573928i
$92$	1.79014	+	5.88446i	0.186635	+	0.613498i
$93$	−6.17120	+	1.65357i	−0.639923	+	0.171467i
$94$	0.767211	−	6.69247i	0.0791317	−	0.690276i
$95$	−24.3258	+	14.0445i	−2.49577	+	1.44093i
$96$	5.52697	−	1.20522i	0.564095	−	0.123007i
$97$			16.9468i			1.72069i	0.509713	+	0.860345i	$0.329752\pi$
$97$			16.9468i			1.72069i	−0.509713	+	0.860345i	$0.670248\pi$
$98$	−2.59862	+	9.55234i	−0.262500	+	0.964932i
$99$	1.03136	−	1.03136i	0.103656	−	0.103656i
$100$	5.29494	−	22.7907i	0.529494	−	2.27907i
$101$	0.505693	−	1.88727i	0.0503184	−	0.187791i	−0.936192	−	0.351489i	$-0.885676\pi$
$101$	0.505693	−	1.88727i	0.0503184	−	0.187791i	0.986511	+	0.163698i	$0.0523423\pi$
$102$	−3.70809	−	4.66835i	−0.367156	−	0.462236i
$103$	6.21435	+	3.58786i	0.612318	+	0.353522i	0.773872	−	0.633342i	$-0.218317\pi$
$103$	6.21435	+	3.58786i	0.612318	+	0.353522i	−0.161554	+	0.986864i	$0.551651\pi$
$104$	2.65879	+	5.60424i	0.260716	+	0.549540i
$105$	−4.68188	−	9.74536i	−0.456905	−	0.951049i
$106$	17.3689	−	2.58349i	1.68702	−	0.250931i
$107$	−7.24922	+	1.94242i	−0.700809	+	0.187781i	−0.591593	−	0.806237i	$-0.701501\pi$
$107$	−7.24922	+	1.94242i	−0.700809	+	0.187781i	−0.109216	+	0.994018i	$0.534834\pi$
$108$	0.0670277	+	1.99888i	0.00644975	+	0.192342i
$109$	−2.70748	+	10.1044i	−0.259329	+	0.967830i	0.706301	+	0.707911i	$0.250362\pi$
$109$	−2.70748	+	10.1044i	−0.259329	+	0.967830i	−0.965631	+	0.259919i	$0.916304\pi$
$110$	−3.35576	−	7.73238i	−0.319960	−	0.737254i
$111$	0.558777			0.0530368
$112$	−5.21160	−	9.21082i	−0.492450	−	0.870341i
$113$	−11.8391			−1.11373			−0.556864	−	0.830604i	$-0.687995\pi$
$113$	−11.8391			−1.11373			−0.556864	+	0.830604i	$0.687995\pi$
$114$	−3.87003	−	8.91736i	−0.362461	−	0.835187i
$115$	−3.25264	+	12.1390i	−0.303311	+	1.13197i
$116$	16.0291	−	0.537498i	1.48826	−	0.0499055i
$117$	−2.11835	+	0.567610i	−0.195841	+	0.0524755i
$118$	9.53640	−	1.41847i	0.877897	−	0.130581i
$119$	−6.29166	+	9.20963i	−0.576755	+	0.844245i
$120$	10.8871	+	3.88084i	0.993856	+	0.354271i
$121$	7.68388	+	4.43629i	0.698535	+	0.403299i
$122$	1.88008	+	2.36695i	0.170214	+	0.214294i
$123$	0.814517	−	3.03982i	0.0734425	−	0.274091i
$124$	−12.4463	−	2.89164i	−1.11771	−	0.259677i
$125$	19.3566	−	19.3566i	1.73131	−	1.73131i
$126$	3.53523	−	1.22563i	0.314943	−	0.109188i
$127$			16.6830i			1.48038i	0.672397	+	0.740190i	$0.265265\pi$
$127$			16.6830i			1.48038i	−0.672397	+	0.740190i	$0.734735\pi$
$128$	10.8874	+	3.07632i	0.962322	+	0.271911i
$129$	2.73601	−	1.57963i	0.240892	−	0.139079i
$130$	−1.44346	+	12.5915i	−0.126600	+	1.10435i
$131$	8.94017	−	2.39551i	0.781106	−	0.209297i	0.153834	−	0.988097i	$-0.450838\pi$
$131$	8.94017	−	2.39551i	0.781106	−	0.209297i	0.627272	+	0.778800i	$0.284171\pi$
$132$	2.79085	−	0.849019i	0.242912	−	0.0738976i
$133$	−13.7957	+	11.8497i	−1.19624	+	1.02750i
$134$	1.12498	−	0.167332i	0.0971834	−	0.0144553i
$135$	−2.04321	+	3.53895i	−0.175852	+	0.304584i
$136$	−2.14853	−	11.7285i	−0.184235	−	1.00571i
$137$	14.0505	−	8.11204i	1.20041	−	0.693059i	0.239766	−	0.970831i	$-0.422929\pi$
$137$	14.0505	−	8.11204i	1.20041	−	0.693059i	0.960647	+	0.277772i	$0.0895961\pi$
$138$	−4.04549	−	1.59680i	−0.344375	−	0.135929i
$139$	12.0215	−	12.0215i	1.01965	−	1.01965i	0.0198462	−	0.999803i	$-0.493682\pi$
$139$	12.0215	−	12.0215i	1.01965	−	1.01965i	0.999803	−	0.0198462i	$-0.00631765\pi$
$140$	0.912580	−	21.6041i	0.0771271	−	1.82588i
$141$	3.36815	+	3.36815i	0.283650	+	0.283650i
$142$	−10.5366	+	4.57276i	−0.884212	+	0.383738i
$143$	1.59937	+	2.77020i	0.133746	+	0.231656i
$144$	−1.76345	+	3.59030i	−0.146954	+	0.299192i
$145$	28.3790	+	16.3846i	2.35674	+	1.36067i
$146$	−6.19985	−	4.59430i	−0.513103	−	0.380227i
$147$	−4.14619	−	5.63996i	−0.341972	−	0.465176i
$148$	0.986014	+	0.526028i	0.0810498	+	0.0432392i
$149$	2.27466	+	8.48914i	0.186347	+	0.695458i	0.994338	+	0.106263i	$0.0338884\pi$
$149$	2.27466	+	8.48914i	0.186347	+	0.695458i	−0.807991	+	0.589195i	$0.799445\pi$
$150$	10.2903	+	12.9551i	0.840202	+	1.05778i
$151$	−6.01510	−	10.4185i	−0.489502	−	0.847842i	0.510425	−	0.859922i	$-0.329488\pi$
$151$	−6.01510	−	10.4185i	−0.489502	−	0.847842i	−0.999927	+	0.0120804i	$0.996155\pi$
$152$	1.56569	−	19.3787i	0.126995	−	1.57182i
$153$	4.21565			0.340815
$154$	−3.06131	−	4.51799i	−0.246688	−	0.364070i
$155$	−18.4609	−	18.4609i	−1.48282	−	1.48282i
$156$	−4.27236	−	0.992593i	−0.342063	−	0.0794711i
$157$	−14.5324	−	3.89395i	−1.15981	−	0.310771i	−0.372923	−	0.927862i	$-0.621644\pi$
$157$	−14.5324	−	3.89395i	−1.15981	−	0.310771i	−0.786892	+	0.617091i	$0.788311\pi$
$158$	0.368283	+	0.0422192i	0.0292990	+	0.00335878i
$159$	−6.20840	+	10.7533i	−0.492358	+	0.852789i
$160$	15.5580	+	17.0972i	1.22997	+	1.35165i
$161$	−0.615651	+	8.11333i	−0.0485201	+	0.639420i
$162$	−1.13624	−	0.841994i	−0.0892716	−	0.0661533i
$163$	−0.647583	−	2.41681i	−0.0507226	−	0.189299i	0.935916	−	0.352223i	$-0.114574\pi$
$163$	−0.647583	−	2.41681i	−0.0507226	−	0.189299i	−0.986639	+	0.162924i	$0.947908\pi$
$164$	4.29895	−	4.59726i	0.335691	−	0.358986i
$165$	5.75723	+	1.54265i	0.448200	+	0.120095i
$166$	14.2485	+	5.62403i	1.10589	+	0.436509i
$167$			19.4769i			1.50717i	0.657352	+	0.753583i	$0.271676\pi$
$167$			19.4769i			1.50717i	−0.657352	+	0.753583i	$0.728324\pi$
$168$	7.39203	+	1.16530i	0.570307	+	0.0899046i
$169$			8.19042i			0.630032i
$170$	8.94463	−	22.6612i	0.686022	−	1.73803i
$171$	6.63952	+	1.77905i	0.507737	+	0.136048i
$172$	6.31499	−	0.211759i	0.481513	−	0.0161464i
$173$	−2.46823	−	9.21157i	−0.187656	−	0.700342i	−0.994046	−	0.108958i	$-0.965248\pi$
$173$	−2.46823	−	9.21157i	−0.187656	−	0.700342i	0.806390	−	0.591384i	$-0.201418\pi$
$174$	−6.75199	+	9.11157i	−0.511867	+	0.690746i
$175$	17.4600	−	25.5576i	1.31985	−	1.93197i
$176$	5.72397	+	1.12911i	0.431460	+	0.0851097i
$177$	−3.40872	+	5.90408i	−0.256215	+	0.443778i
$178$	−1.60725	+	14.0203i	−0.120469	+	1.05086i
$179$	−8.40870	−	2.25310i	−0.628495	−	0.168405i	−0.0695086	−	0.997581i	$-0.522143\pi$
$179$	−8.40870	−	2.25310i	−0.628495	−	0.168405i	−0.558987	+	0.829177i	$0.688810\pi$
$180$	−6.93696	+	4.32134i	−0.517051	+	0.322093i
$181$	−12.1985	−	12.1985i	−0.906704	−	0.906704i	0.0893003	−	0.996005i	$-0.471537\pi$
$181$	−12.1985	−	12.1985i	−0.906704	−	0.906704i	−0.996005	+	0.0893003i	$0.971537\pi$
$182$	0.589677	+	8.18452i	0.0437098	+	0.606677i
$183$	−2.13742			−0.158003
$184$	−5.63542	−	6.62609i	−0.415449	−	0.488482i
$185$	1.14170	+	1.97748i	0.0839395	+	0.145387i
$186$	7.07497	−	5.61968i	0.518762	−	0.412055i
$187$	−1.59143	−	5.93930i	−0.116377	−	0.434325i
$188$	2.77267	+	9.11416i	0.202217	+	0.664718i
$189$	−0.876174	+	2.49646i	−0.0637323	+	0.181591i
$190$	23.6508	−	31.9159i	1.71581	−	2.31542i
$191$	7.44241	+	4.29688i	0.538514	+	0.310911i	0.744476	−	0.667649i	$-0.232699\pi$
$191$	7.44241	+	4.29688i	0.538514	+	0.310911i	−0.205963	+	0.978560i	$0.566033\pi$
$192$	−6.49164	+	4.67532i	−0.468494	+	0.337412i
$193$	−4.77318	−	8.26739i	−0.343581	−	0.595100i	0.641514	−	0.767111i	$-0.278307\pi$
$193$	−4.77318	−	8.26739i	−0.343581	−	0.595100i	−0.985095	+	0.172012i	$0.944973\pi$
$194$	−9.54135	−	21.9853i	−0.685029	−	1.57845i
$195$	−6.33697	−	6.33697i	−0.453800	−	0.453800i
$196$	−2.00692	−	13.8554i	−0.143352	−	0.989672i
$197$	−4.05951	+	4.05951i	−0.289228	+	0.289228i	−0.836775	−	0.547547i	$-0.815562\pi$
$197$	−4.05951	+	4.05951i	−0.289228	+	0.289228i	0.547547	+	0.836775i	$0.315562\pi$
$198$	−0.757322	+	1.91867i	−0.0538205	+	0.136354i
$199$	8.72335	−	5.03643i	0.618382	−	0.357023i	−0.157857	−	0.987462i	$-0.550458\pi$
$199$	8.72335	−	5.03643i	0.618382	−	0.357023i	0.776239	+	0.630439i	$0.217125\pi$
$200$	5.96238	+	32.5477i	0.421604	+	2.30147i
$201$	−0.402116	+	0.696485i	−0.0283631	+	0.0491263i
$202$	0.406526	+	2.73309i	0.0286031	+	0.192300i
$203$	20.0192	+	7.02608i	1.40507	+	0.493134i
$204$	7.43891	+	3.96858i	0.520828	+	0.277856i
$205$	12.4220	−	3.32846i	0.867589	−	0.232470i
$206$	−10.0820	−	1.15577i	−0.702443	−	0.0805266i
$207$	2.66335	−	1.53768i	0.185115	−	0.106876i
$208$	−6.60456	−	5.77348i	−0.457944	−	0.400319i
$209$		−	10.0258i		−	0.693499i
$210$	11.5606	+	10.0068i	0.797761	+	0.690532i
$211$	−4.01520	+	4.01520i	−0.276418	+	0.276418i	−0.831677	−	0.555260i	$-0.812619\pi$
$211$	−4.01520	+	4.01520i	−0.276418	+	0.276418i	0.555260	+	0.831677i	$0.312619\pi$
$212$	−21.0783	+	13.1306i	−1.44766	+	0.901813i
$213$	2.10210	−	7.84514i	0.144033	−	0.537540i
$214$	8.31087	−	6.60136i	0.568119	−	0.451260i
$215$	11.1805	+	6.45505i	0.762503	+	0.440231i
$216$	−1.21236	−	2.55542i	−0.0824905	−	0.173875i
$217$	−13.9573	−	9.53511i	−0.947486	−	0.647286i
$218$	−2.17654	−	14.6329i	−0.147414	−	0.991068i
$219$	5.27052	−	1.41223i	0.356149	−	0.0954298i
$220$	8.70693	+	8.14194i	0.587021	+	0.548930i
$221$	−2.39285	+	8.93022i	−0.160960	+	0.600712i
$222$	−0.724907	+	0.314601i	−0.0486526	+	0.0211147i
$223$	14.5782			0.976226			0.488113	−	0.872781i	$-0.337685\pi$
$223$	14.5782			0.976226			0.488113	+	0.872781i	$0.337685\pi$
$224$	11.9469	+	9.01506i	0.798237	+	0.602344i
$225$	−11.6989			−0.779924
$226$	15.3590	−	6.66561i	1.02166	−	0.443389i
$227$	−7.40755	+	27.6454i	−0.491657	+	1.83489i	0.0563465	+	0.998411i	$0.482055\pi$
$227$	−7.40755	+	27.6454i	−0.491657	+	1.83489i	−0.548003	+	0.836476i	$0.684612\pi$
$228$	10.0413	+	9.38968i	0.664998	+	0.621847i
$229$	0.841195	−	0.225397i	0.0555877	−	0.0148947i	−0.230918	−	0.972973i	$-0.574173\pi$
$229$	0.841195	−	0.225397i	0.0555877	−	0.0148947i	0.286506	+	0.958079i	$0.407506\pi$
$230$	−2.61480	−	17.5794i	−0.172415	−	1.15915i
$231$	3.84794	+	0.291987i	0.253176	+	0.0192114i
$232$	−20.4920	+	9.72195i	−1.34537	+	0.638277i
$233$	−12.2898	−	7.09551i	−0.805131	−	0.464842i	0.0401313	−	0.999194i	$-0.487222\pi$
$233$	−12.2898	−	7.09551i	−0.805131	−	0.464842i	−0.845262	+	0.534352i	$0.820556\pi$
$234$	2.42858	−	1.92903i	0.158761	−	0.126105i
$235$	−5.03786	+	18.8016i	−0.328634	+	1.22648i
$236$	−11.5730	+	7.20935i	−0.753341	+	0.469289i
$237$	−0.185348	+	0.185348i	−0.0120396	+	0.0120396i
$238$	2.97705	−	15.4900i	0.192973	−	1.00407i
$239$		−	12.8222i		−	0.829398i	−0.909959	−	0.414699i	$-0.863887\pi$
$239$		−	12.8222i		−	0.829398i	0.909959	−	0.414699i	$-0.136113\pi$
$240$	−16.3090	+	1.09500i	−1.05274	+	0.0706819i
$241$	3.39235	−	1.95858i	0.218521	−	0.126163i	−0.386744	−	0.922187i	$-0.626400\pi$
$241$	3.39235	−	1.95858i	0.218521	−	0.126163i	0.605265	+	0.796024i	$0.293067\pi$
$242$	−12.4661	−	1.42908i	−0.801350	−	0.0918650i
$243$	0.965926	−	0.258819i	0.0619642	−	0.0166032i
$244$	−3.77168	−	2.01215i	−0.241457	−	0.128815i
$245$	11.4880	−	26.1968i	0.733940	−	1.67365i
$246$	0.654790	+	4.40217i	0.0417479	+	0.280672i
$247$	−7.53731	+	13.0550i	−0.479587	+	0.830670i
$248$	17.7747	−	3.25613i	1.12870	−	0.206765i
$249$	−9.38046	+	5.41581i	−0.594463	+	0.343213i
$250$	−14.2134	+	36.0096i	−0.898934	+	2.27745i
$251$	6.33965	−	6.33965i	0.400155	−	0.400155i	−0.478133	−	0.878288i	$-0.658686\pi$
$251$	6.33965	−	6.33965i	0.400155	−	0.400155i	0.878288	+	0.478133i	$0.158686\pi$
$252$	−3.89623	+	3.58041i	−0.245440	+	0.225545i
$253$	−3.17182	−	3.17182i	−0.199411	−	0.199411i
$254$	−9.39284	−	21.6431i	−0.589359	−	1.35801i
$255$	8.61347	+	14.9190i	0.539397	+	0.934262i
$256$	−15.8564	+	2.13887i	−0.991025	+	0.133679i
$257$	−12.9501	−	7.47675i	−0.807805	−	0.466387i	0.0383878	−	0.999263i	$-0.487778\pi$
$257$	−12.9501	−	7.47675i	−0.807805	−	0.466387i	−0.846193	+	0.532876i	$0.821111\pi$
$258$	−2.66009	+	3.58969i	−0.165610	+	0.223485i
$259$	0.963283	+	1.12148i	0.0598555	+	0.0696852i
$260$	−5.21660	−	17.1477i	−0.323520	−	1.06346i
$261$	−2.07548	−	7.74580i	−0.128469	−	0.479453i
$262$	−10.2494	+	8.14118i	−0.633213	+	0.502964i
$263$	0.400579	+	0.693823i	0.0247008	+	0.0427830i	0.878112	−	0.478456i	$-0.158803\pi$
$263$	0.400579	+	0.693823i	0.0247008	+	0.0427830i	−0.853411	+	0.521239i	$0.825470\pi$
$264$	−3.14258	+	2.67274i	−0.193413	+	0.164496i
$265$	−50.7403			−3.11695
$266$	11.2257	−	23.1400i	0.688293	−	1.41880i
$267$	−7.05604	−	7.05604i	−0.431823	−	0.431823i
$268$	−1.36524	+	0.850464i	−0.0833950	+	0.0519504i
$269$	−20.4646	−	5.48348i	−1.24775	−	0.334334i	−0.426283	−	0.904590i	$-0.640177\pi$
$269$	−20.4646	−	5.48348i	−1.24775	−	0.334334i	−0.821467	+	0.570256i	$0.806844\pi$
$270$	0.658190	−	5.74147i	0.0400562	−	0.349415i
$271$	9.69075	−	16.7849i	0.588671	−	1.01961i	−0.405736	−	0.913990i	$-0.632985\pi$
$271$	9.69075	−	16.7849i	0.588671	−	1.01961i	0.994407	−	0.105618i	$-0.0336820\pi$
$272$	9.39066	+	14.0058i	0.569392	+	0.849229i
$273$	−4.79105	−	3.27306i	−0.289967	−	0.198094i
$274$	−13.6606	+	18.4345i	−0.825266	+	1.11367i
$275$	4.41638	+	16.4821i	0.266318	+	0.993911i
$276$	6.14728	−	0.206135i	0.370023	−	0.0124079i
$277$	−4.96390	−	1.33007i	−0.298252	−	0.0799164i	0.106590	−	0.994303i	$-0.466007\pi$
$277$	−4.96390	−	1.33007i	−0.298252	−	0.0799164i	−0.404842	+	0.914387i	$0.632673\pi$
$278$	−8.82728	+	22.3639i	−0.529425	+	1.34130i
$279$			6.38889i			0.382493i
$280$	10.9796	+	28.5409i	0.656154	+	1.70565i
$281$			1.99055i			0.118746i	0.998236	+	0.0593730i	$0.0189101\pi$
$281$			1.99055i			0.118746i	−0.998236	+	0.0593730i	$0.981090\pi$
$282$	−6.26586	−	2.47321i	−0.373127	−	0.147277i
$283$	27.6185	+	7.40034i	1.64175	+	0.439905i	0.957286	−	0.289144i	$-0.0933707\pi$
$283$	27.6185	+	7.40034i	1.64175	+	0.439905i	0.684462	+	0.729049i	$0.260037\pi$
$284$	11.0947	−	11.8646i	0.658349	−	0.704033i
$285$	7.26996	+	27.1319i	0.430635	+	1.60715i
$286$	−3.63455	−	2.69333i	−0.214916	−	0.159260i
$287$	7.50513	−	3.60563i	0.443014	−	0.212833i
$288$	0.266336	−	5.65058i	0.0156940	−	0.332964i
$289$	0.385872	−	0.668350i	0.0226984	−	0.0393147i
$290$	−46.0411	−	5.27805i	−2.70363	−	0.309938i
$291$	16.3694	+	4.38616i	0.959590	+	0.257121i
$292$	10.6298	+	2.46961i	0.622061	+	0.144523i
$293$	2.11855	+	2.11855i	0.123767	+	0.123767i	0.766277	−	0.642510i	$-0.222107\pi$
$293$	2.11855	+	2.11855i	0.123767	+	0.123767i	−0.642510	+	0.766277i	$0.722107\pi$
$294$	8.55428	+	4.98240i	0.498896	+	0.290579i
$295$	−27.8590			−1.62201
$296$	−1.57533	−	0.127278i	−0.0915641	−	0.00739788i
$297$	−0.729284	−	1.26316i	−0.0423173	−	0.0732958i
$298$	−7.73047	−	9.73237i	−0.447814	−	0.563781i
$299$	1.74561	+	6.51470i	0.100951	+	0.376755i
$300$	−20.6437	−	11.0132i	−1.19186	−	0.635847i
$301$	7.88699	+	2.76807i	0.454599	+	0.159549i
$302$	13.6692	+	10.1294i	0.786574	+	0.582879i
$303$	−1.69208	−	0.976924i	−0.0972076	−	0.0561228i
$304$	8.87935	+	26.0217i	0.509266	+	1.49245i
$305$	−4.36721	−	7.56422i	−0.250065	−	0.433126i
$306$	−5.46901	+	2.37349i	−0.312642	+	0.135683i
$307$	−11.3310	−	11.3310i	−0.646696	−	0.646696i	0.305497	−	0.952193i	$-0.401177\pi$
$307$	−11.3310	−	11.3310i	−0.646696	−	0.646696i	−0.952193	+	0.305497i	$0.901177\pi$
$308$	6.51518	+	4.13766i	0.371237	+	0.235765i
$309$	5.07399	−	5.07399i	0.288649	−	0.288649i
$310$	34.3434	+	13.5557i	1.95057	+	0.769914i
$311$	6.93901	−	4.00624i	0.393475	−	0.227173i	−0.290190	−	0.956969i	$-0.593718\pi$
$311$	6.93901	−	4.00624i	0.393475	−	0.227173i	0.683665	+	0.729796i	$0.260385\pi$
$312$	6.10142	−	1.11771i	0.345425	−	0.0632780i
$313$	7.85980	−	13.6136i	0.444262	−	0.769485i	−0.553738	−	0.832691i	$-0.686799\pi$
$313$	7.85980	−	13.6136i	0.444262	−	0.769485i	0.998001	+	0.0632059i	$0.0201325\pi$
$314$	21.0454	−	3.13035i	1.18766	−	0.176656i
$315$	−10.6251	+	2.00006i	−0.598654	+	0.112691i
$316$	−0.501547	+	0.152578i	−0.0282142	+	0.00858320i
$317$	−20.9792	+	5.62135i	−1.17831	+	0.315726i	−0.794255	−	0.607585i	$-0.792138\pi$
$317$	−20.9792	+	5.62135i	−1.17831	+	0.315726i	−0.384052	+	0.923311i	$0.625472\pi$
$318$	1.99994	−	17.4457i	0.112151	−	0.978309i
$319$	−10.1293	+	5.84816i	−0.567132	+	0.327434i
$320$	−29.8095	−	13.4209i	−1.66640	−	0.750250i
$321$			7.50495i			0.418885i
$322$	−3.76925	−	10.8721i	−0.210052	−	0.605880i
$323$	20.4900	−	20.4900i	1.14010	−	1.14010i
$324$	1.94811	+	0.452603i	0.108229	+	0.0251446i
$325$	6.64038	−	24.7822i	0.368342	−	1.37467i
$326$	2.20082	+	2.77075i	0.121892	+	0.153458i
$327$	9.05939	+	5.23044i	0.500986	+	0.289244i
$328$	−2.98873	+	8.38445i	−0.165025	+	0.462954i
$329$	−0.953551	+	12.5663i	−0.0525710	+	0.692805i
$330$	−8.33745	+	1.24013i	−0.458961	+	0.0682670i
$331$	−5.82988	+	1.56211i	−0.320439	+	0.0858614i	−0.415453	−	0.909615i	$-0.636377\pi$
$331$	−5.82988	+	1.56211i	−0.320439	+	0.0858614i	0.0950143	+	0.995476i	$0.469710\pi$
$332$	−21.6511	+	0.726019i	−1.18826	+	0.0398455i
$333$	0.144622	−	0.539737i	0.00792525	−	0.0295774i
$334$	−10.9658	−	25.2675i	−0.600023	−	1.38258i
$335$	−3.28643			−0.179557
$336$	−10.2458	+	2.65009i	−0.558956	+	0.144574i
$337$	−2.53830			−0.138270			−0.0691350	−	0.997607i	$-0.522024\pi$
$337$	−2.53830			−0.138270			−0.0691350	+	0.997607i	$0.522024\pi$
$338$	−4.61135	−	10.6255i	−0.250824	−	0.577952i
$339$	−3.06418	+	11.4357i	−0.166423	+	0.621101i
$340$	1.15468	+	34.4345i	0.0626215	+	1.86748i
$341$	9.00111	−	2.41184i	0.487437	−	0.130608i
$342$	−9.61514	+	1.43018i	−0.519927	+	0.0773352i
$343$	4.17185	−	18.0443i	0.225259	−	0.974299i
$344$	−8.07327	+	3.83016i	−0.435282	+	0.206509i
$345$	10.8836	+	6.28362i	0.585951	+	0.338299i
$346$	8.38833	+	10.5606i	0.450959	+	0.567741i
$347$	−2.40728	+	8.98408i	−0.129229	+	0.482291i	−0.999955	−	0.00947822i	$-0.996983\pi$
$347$	−2.40728	+	8.98408i	−0.129229	+	0.482291i	0.870726	+	0.491769i	$0.163650\pi$
$348$	3.62945	−	15.6220i	0.194559	−	0.837428i
$349$	−16.0106	+	16.0106i	−0.857030	+	0.857030i	−0.990987	−	0.133957i	$-0.957231\pi$
$349$	−16.0106	+	16.0106i	−0.857030	+	0.857030i	0.133957	+	0.990987i	$0.457231\pi$
$350$	−8.26160	+	42.9864i	−0.441601	+	2.29772i
$351$			2.19307i			0.117058i
$352$	−8.06147	+	1.75789i	−0.429678	+	0.0936959i
$353$	17.8021	−	10.2781i	0.947511	−	0.547046i	0.0552041	−	0.998475i	$-0.482419\pi$
$353$	17.8021	−	10.2781i	0.947511	−	0.547046i	0.892307	+	0.451429i	$0.149086\pi$
$354$	1.09807	−	9.57859i	0.0583617	−	0.509096i
$355$	32.0586	−	8.59007i	1.70149	−	0.455914i
$356$	−5.80854	−	19.0935i	−0.307852	−	1.01196i
$357$	7.26742	+	8.46090i	0.384632	+	0.447798i
$358$	12.1772	−	1.81127i	0.643586	−	0.0957285i
$359$	15.1635	−	26.2639i	0.800297	−	1.38616i	−0.119124	−	0.992879i	$-0.538008\pi$
$359$	15.1635	−	26.2639i	0.800297	−	1.38616i	0.919421	−	0.393276i	$-0.128658\pi$
$360$	6.56640	−	9.51174i	0.346080	−	0.501313i
$361$	24.4637	−	14.1241i	1.28756	−	0.743374i
$362$	22.6931	+	8.95723i	1.19272	+	0.470782i
$363$	6.27386	−	6.27386i	0.329292	−	0.329292i
$364$	−5.37302	−	10.2859i	−0.281623	−	0.539125i
$365$	15.7666	+	15.7666i	0.825262	+	0.825262i
$366$	2.77290	−	1.20341i	0.144942	−	0.0629030i
$367$	2.37301	+	4.11018i	0.123870	+	0.214550i	0.921291	−	0.388874i	$-0.127136\pi$
$367$	2.37301	+	4.11018i	0.123870	+	0.214550i	−0.797420	+	0.603424i	$0.793803\pi$
$368$	11.0415	+	5.42325i	0.575577	+	0.282706i
$369$	−2.72543	−	1.57353i	−0.141880	−	0.0819145i
$370$	−2.59450	−	1.92261i	−0.134881	−	0.0999518i
$371$	−32.2848	+	6.07730i	−1.67614	+	0.315518i
$372$	−6.01444	+	11.2738i	−0.311834	+	0.584519i
$373$	8.60269	+	32.1057i	0.445430	+	1.66237i	0.714798	+	0.699331i	$0.246519\pi$
$373$	8.60269	+	32.1057i	0.445430	+	1.66237i	−0.269368	+	0.963037i	$0.586815\pi$
$374$	5.40851	+	6.80911i	0.279667	+	0.352091i
$375$	−13.6872	−	23.7069i	−0.706803	−	1.22422i
$376$	−8.72843	−	10.2628i	−0.450135	−	0.529265i
$377$	17.5864			0.905744
$378$	−0.268881	−	3.73198i	−0.0138298	−	0.191953i
$379$	24.3970	+	24.3970i	1.25319	+	1.25319i	0.954281	+	0.298911i	$0.0966233\pi$
$379$	24.3970	+	24.3970i	1.25319	+	1.25319i	0.298911	+	0.954281i	$0.403377\pi$
$380$	−12.7132	+	54.7206i	−0.652172	+	2.80711i
$381$	16.1146	+	4.31789i	0.825575	+	0.221212i
$382$	−12.0743	−	1.38417i	−0.617776	−	0.0708205i
$383$	7.63983	−	13.2326i	0.390377	−	0.676153i	−0.602122	−	0.798404i	$-0.705678\pi$
$383$	7.63983	−	13.2326i	0.390377	−	0.676153i	0.992499	+	0.122251i	$0.0390113\pi$
$384$	5.78938	−	9.72024i	0.295438	−	0.496034i
$385$	6.82884	+	14.2143i	0.348030	+	0.724426i
$386$	10.8470	+	8.03798i	0.552096	+	0.409122i
$387$	−0.817679	−	3.05162i	−0.0415650	−	0.155123i
$388$	24.7562	+	23.1498i	1.25680	+	1.17525i
$389$	−14.9753	−	4.01263i	−0.759280	−	0.203448i	−0.141649	−	0.989917i	$-0.545241\pi$
$389$	−14.9753	−	4.01263i	−0.759280	−	0.203448i	−0.617630	+	0.786468i	$0.711907\pi$
$390$	11.7888	+	4.65319i	0.596951	+	0.235623i
$391$		−	12.9647i		−	0.655652i
$392$	10.4044	+	16.8448i	0.525503	+	0.850792i
$393$		−	9.25554i		−	0.466880i
$394$	2.98086	−	7.55201i	0.150174	−	0.380465i
$395$	−1.03464	−	0.277231i	−0.0520584	−	0.0139490i
$396$	−0.0977645	−	2.91550i	−0.00491285	−	0.146509i
$397$	−2.60887	−	9.73643i	−0.130935	−	0.488658i	0.869046	−	0.494731i	$-0.164733\pi$
$397$	−2.60887	−	9.73643i	−0.130935	−	0.488658i	−0.999982	+	0.00607344i	$0.998067\pi$
$398$	−8.48129	+	11.4452i	−0.425129	+	0.573696i
$399$	7.87535	+	16.3926i	0.394260	+	0.820655i
$400$	−26.0600	−	38.8676i	−1.30300	−	1.94338i
$401$	0.652117	−	1.12950i	0.0325652	−	0.0564046i	−0.849283	−	0.527937i	$-0.822966\pi$
$401$	0.652117	−	1.12950i	0.0325652	−	0.0564046i	0.881849	+	0.471533i	$0.156299\pi$
$402$	0.129536	−	1.12996i	0.00646065	−	0.0563570i
$403$	−13.5339	−	3.62640i	−0.674171	−	0.180644i
$404$	−2.06617	−	3.31678i	−0.102796	−	0.165016i
$405$	2.88954	+	2.88954i	0.143582	+	0.143582i
$406$	−29.9269	+	2.15617i	−1.48525	+	0.107009i
$407$	−0.815014			−0.0403988
$408$	−11.8849	−	0.960239i	−0.588392	−	0.0475389i
$409$	−11.6055	−	20.1014i	−0.573857	−	0.993950i	−0.996165	−	0.0874971i	$-0.972113\pi$
$409$	−11.6055	−	20.1014i	−0.573857	−	0.993950i	0.422308	−	0.906453i	$-0.361220\pi$
$410$	−14.2412	+	11.3118i	−0.703322	+	0.558652i
$411$	−4.19910	−	15.6713i	−0.207126	−	0.773006i
$412$	13.7301	−	4.17692i	0.676435	−	0.205782i
$413$	−17.7259	+	3.33674i	−0.872236	+	0.164190i
$414$	−2.58944	+	3.49436i	−0.127264	+	0.171738i
$415$	−38.3325	−	22.1313i	−1.88167	−	1.08638i
$416$	11.8187	+	3.77152i	0.579460	+	0.184914i
$417$	−8.50048	−	14.7233i	−0.416270	−	0.721001i
$418$	5.64470	+	13.0066i	0.276091	+	0.636172i
$419$	3.61878	+	3.61878i	0.176789	+	0.176789i	0.789955	−	0.613165i	$-0.210104\pi$
$419$	3.61878	+	3.61878i	0.176789	+	0.176789i	−0.613165	+	0.789955i	$0.710104\pi$
$420$	−20.6317	−	6.47303i	−1.00672	−	0.315851i
$421$	19.8583	−	19.8583i	0.967836	−	0.967836i	−0.0316626	−	0.999499i	$-0.510080\pi$
$421$	19.8583	−	19.8583i	0.967836	−	0.967836i	0.999499	+	0.0316626i	$0.0100802\pi$
$422$	2.94833	−	7.46958i	0.143522	−	0.363613i
$423$	4.12513	−	2.38164i	0.200571	−	0.115799i
$424$	19.9523	−	28.9019i	0.968972	−	1.40360i
$425$	−24.6592	+	42.7109i	−1.19615	+	2.07178i
$426$	1.68988	+	11.3611i	0.0818748	+	0.550447i
$427$	−3.68473	−	4.28985i	−0.178316	−	0.207600i
$428$	−7.06509	+	13.2432i	−0.341504	+	0.640133i
$429$	3.08975	−	0.827897i	0.149175	−	0.0399712i
$430$	−18.1389	−	2.07940i	−0.874733	−	0.100278i
$431$	−13.7282	+	7.92597i	−0.661263	+	0.381781i	−0.792758	−	0.609536i	$-0.791356\pi$
$431$	−13.7282	+	7.92597i	−0.661263	+	0.381781i	0.131495	+	0.991317i	$0.458022\pi$
$432$	3.01155	+	2.63260i	0.144893	+	0.126661i
$433$		−	3.95972i		−	0.190292i	−0.995463	−	0.0951461i	$-0.969668\pi$
$433$		−	3.95972i		−	0.190292i	0.995463	−	0.0951461i	$-0.0303318\pi$
$434$	23.4754	+	4.51177i	1.12686	+	0.216572i
$435$	23.1713	−	23.1713i	1.11098	−	1.11098i
$436$	11.0622	+	17.7580i	0.529785	+	0.850455i
$437$	5.47124	−	20.4189i	0.261725	−	0.976771i
$438$	−6.04239	+	4.79950i	−0.288717	+	0.229329i
$439$	9.45732	+	5.46019i	0.451373	+	0.260600i	0.708410	−	0.705801i	$-0.249413\pi$
$439$	9.45732	+	5.46019i	0.451373	+	0.260600i	−0.257037	+	0.966402i	$0.582746\pi$
$440$	−15.8796	−	5.66047i	−0.757032	−	0.269852i
$441$	−6.52089	+	2.54518i	−0.310519	+	0.121199i
$442$	−1.92361	−	12.9325i	−0.0914967	−	0.615135i
$443$	6.40045	−	1.71500i	0.304095	−	0.0814819i	−0.103545	−	0.994625i	$-0.533019\pi$
$443$	6.40045	−	1.71500i	0.304095	−	0.0814819i	0.407640	+	0.913143i	$0.366352\pi$
$444$	0.763303	−	0.816270i	0.0362248	−	0.0387385i
$445$	10.5540	−	39.3880i	0.500306	−	1.86717i
$446$	−18.9124	+	8.20775i	−0.895527	+	0.388648i
$447$	8.78861			0.415687
$448$	−20.5745	−	4.96900i	−0.972053	−	0.234763i
$449$	15.1760			0.716200			0.358100	−	0.933683i	$-0.383425\pi$
$449$	15.1760			0.716200			0.358100	+	0.933683i	$0.383425\pi$
$450$	15.1770	−	6.58666i	0.715452	−	0.310498i
$451$	−1.18803	+	4.43378i	−0.0559421	+	0.208779i
$452$	−16.1725	+	17.2947i	−0.760689	+	0.813475i
$453$	−11.6203	+	3.11364i	−0.545968	+	0.146292i
$454$	−5.95493	−	40.0352i	−0.279479	−	1.87894i
$455$	1.79405	−	23.6428i	0.0841063	−	1.10839i
$456$	−18.3132	−	6.52792i	−0.857592	−	0.305698i
$457$	29.6650	+	17.1271i	1.38767	+	0.801172i	0.993052	−	0.117673i	$-0.0375433\pi$
$457$	29.6650	+	17.1271i	1.38767	+	0.801172i	0.394619	+	0.918845i	$0.370877\pi$
$458$	−0.964387	+	0.766017i	−0.0450629	+	0.0357936i
$459$	1.09109	−	4.07201i	0.0509278	−	0.190065i
$460$	13.2897	+	21.3337i	0.619635	+	0.994689i
$461$	18.9746	−	18.9746i	0.883735	−	0.883735i	−0.110177	−	0.993912i	$-0.535142\pi$
$461$	18.9746	−	18.9746i	0.883735	−	0.883735i	0.993912	+	0.110177i	$0.0351416\pi$
$462$	−5.15637	+	1.78766i	−0.239896	+	0.0831695i
$463$		−	17.0444i		−	0.792119i	−0.918225	−	0.396060i	$-0.870377\pi$
$463$		−	17.0444i		−	0.792119i	0.918225	−	0.396060i	$-0.129623\pi$
$464$	21.1109	−	24.1497i	0.980049	−	1.12112i
$465$	−22.6100	+	13.0539i	−1.04851	+	0.605358i
$466$	19.9386	+	2.28571i	0.923636	+	0.105884i
$467$	13.6439	−	3.65586i	0.631363	−	0.169173i	0.0710747	−	0.997471i	$-0.477357\pi$
$467$	13.6439	−	3.65586i	0.631363	−	0.169173i	0.560288	+	0.828298i	$0.310690\pi$
$468$	−2.06454	+	3.86988i	−0.0954334	+	0.178885i
$469$	−2.09107	+	0.393624i	−0.0965567	+	0.0181759i
$470$	−4.04993	−	27.2278i	−0.186809	−	1.25593i
$471$	−7.52254	+	13.0294i	−0.346620	+	0.600364i
$472$	10.9548	−	15.8686i	0.504237	−	0.730411i
$473$	−3.99065	+	2.30400i	−0.183490	+	0.105938i
$474$	0.136099	−	0.344807i	0.00625125	−	0.0158375i
$475$	−56.8619	+	56.8619i	−2.60900	+	2.60900i
$476$	4.85901	+	21.7715i	0.222712	+	0.997896i
$477$	8.78001	+	8.78001i	0.402009	+	0.402009i
$478$	7.21911	+	16.6343i	0.330194	+	0.760837i
$479$	0.0461705	+	0.0799697i	0.00210959	+	0.00365391i	0.867078	−	0.498172i	$-0.165995\pi$
$479$	0.0461705	+	0.0799697i	0.00210959	+	0.00365391i	−0.864969	+	0.501826i	$0.832662\pi$
$480$	20.5413	−	10.6028i	0.937577	−	0.483949i
$481$	1.06126	+	0.612720i	0.0483894	+	0.0279376i
$482$	−3.29822	+	4.45083i	−0.150230	+	0.202730i
$483$	7.67753	+	2.69456i	0.349340	+	0.122607i
$484$	16.9770	−	5.16465i	0.771680	−	0.234757i
$485$	17.9237	+	66.8922i	0.813874	+	3.03742i
$486$	−1.10739	+	0.879601i	−0.0502320	+	0.0398995i
$487$	−4.13189	−	7.15664i	−0.187234	−	0.324298i	0.757093	−	0.653307i	$-0.226619\pi$
$487$	−4.13189	−	7.15664i	−0.187234	−	0.324298i	−0.944327	+	0.329008i	$0.893286\pi$
$488$	6.02591	+	0.486861i	0.272780	+	0.0220391i
$489$	−2.50207			−0.113147
$490$	−0.154236	+	40.4532i	−0.00696766	+	1.82749i
$491$	−17.9394	−	17.9394i	−0.809592	−	0.809592i	0.174980	−	0.984572i	$-0.444014\pi$
$491$	−17.9394	−	17.9394i	−0.809592	−	0.809592i	−0.984572	+	0.174980i	$0.944014\pi$
$492$	−3.32796	−	5.34232i	−0.150036	−	0.240851i
$493$	−32.6536	−	8.74951i	−1.47064	−	0.394058i
$494$	2.42803	−	21.1800i	0.109242	−	0.952933i
$495$	2.98016	−	5.16179i	0.133948	−	0.232005i
$496$	−21.2261	+	14.2317i	−0.953079	+	0.639022i
$497$	19.3692	−	9.30538i	0.868827	−	0.417403i
$498$	9.12017	−	12.3073i	0.408684	−	0.551505i
$499$	−2.85358	−	10.6497i	−0.127744	−	0.476746i	0.872179	−	0.489187i	$-0.162707\pi$
$499$	−2.85358	−	10.6497i	−0.127744	−	0.476746i	−0.999923	+	0.0124408i	$0.996040\pi$
$500$	−1.83484	−	54.7180i	−0.0820566	−	2.44706i
$501$	18.8132	+	5.04099i	0.840513	+	0.225215i
$502$	−4.65516	+	11.7938i	−0.207770	+	0.526384i
$503$			20.3638i			0.907975i	0.891008	+	0.453988i	$0.149999\pi$
$503$			20.3638i			0.907975i	−0.891008	+	0.453988i	$0.850001\pi$
$504$	3.03879	−	6.83855i	0.135358	−	0.304613i
$505$		−	7.98425i		−	0.355295i
$506$	5.90062	+	2.32904i	0.262315	+	0.103539i
$507$	7.91134	+	2.11984i	0.351355	+	0.0941453i
$508$	24.3708	+	22.7894i	1.08128	+	1.01112i
$509$	−2.44192	−	9.11338i	−0.108236	−	0.403944i	0.890456	−	0.455070i	$-0.150386\pi$
$509$	−2.44192	−	9.11338i	−0.108236	−	0.403944i	−0.998692	+	0.0511260i	$0.983719\pi$
$510$	−19.5740	−	14.5050i	−0.866750	−	0.642292i
$511$	11.9203	+	8.14348i	0.527323	+	0.360246i
$512$	19.3664	−	11.7022i	0.855883	−	0.517169i
$513$	3.43687	−	5.95283i	0.151741	−	0.262824i
$514$	21.0098	+	2.40852i	0.926704	+	0.106235i
$515$	28.3238	+	7.58935i	1.24810	+	0.334427i
$516$	1.42990	−	6.15462i	0.0629477	−	0.270942i
$517$	−4.91268	−	4.91268i	−0.216059	−	0.216059i
$518$	−1.88109	−	0.912558i	−0.0826502	−	0.0400955i
$519$	−9.53652			−0.418607
$520$	16.4220	+	19.3089i	0.720153	+	0.846750i
$521$	−12.0060	−	20.7950i	−0.525993	−	0.911047i	−0.999541	−	0.0302790i	$-0.990360\pi$
$521$	−12.0060	−	20.7950i	−0.525993	−	0.911047i	0.473548	−	0.880768i	$-0.342973\pi$
$522$	7.05356	+	8.88017i	0.308726	+	0.388674i
$523$	−7.43023	−	27.7300i	−0.324901	−	1.21255i	−0.914411	−	0.404787i	$-0.867346\pi$
$523$	−7.43023	−	27.7300i	−0.324901	−	1.21255i	0.589509	−	0.807761i	$-0.299321\pi$
$524$	8.71308	−	16.3323i	0.380633	−	0.713478i
$525$	−20.1678	−	23.4798i	−0.880195	−	1.02474i
$526$	−0.910309	−	0.674571i	−0.0396914	−	0.0294127i
$527$	23.3250	+	13.4667i	1.01605	+	0.586618i
$528$	2.57211	−	5.23670i	0.111937	−	0.227898i
$529$	6.77106	+	11.7278i	0.294394	+	0.509905i
$530$	65.8259	−	28.5677i	2.85929	−	1.24090i
$531$	4.82066	+	4.82066i	0.209199	+	0.209199i
$532$	−1.53504	+	36.3400i	−0.0665525	+	1.57554i
$533$	4.88025	−	4.88025i	0.211387	−	0.211387i
$534$	13.1265	+	5.18120i	0.568041	+	0.224212i
$535$	−26.5596	+	15.3342i	−1.14827	+	0.662955i
$536$	1.29231	−	1.87197i	0.0558191	−	0.0808566i
$537$	−4.35266	+	7.53903i	−0.187831	+	0.325333i
$538$	29.6363	−	4.40817i	1.27771	−	0.190050i
$539$	6.04749	+	8.22626i	0.260484	+	0.354330i
$540$	2.37867	+	7.81904i	0.102362	+	0.336478i
$541$	−33.3913	+	8.94717i	−1.43560	+	0.384669i	−0.890992	−	0.454020i	$-0.849990\pi$
$541$	−33.3913	+	8.94717i	−1.43560	+	0.384669i	−0.544612	+	0.838688i	$0.683323\pi$
$542$	−3.12173	+	27.2312i	−0.134090	+	1.16968i
$543$	−14.9400	+	8.62561i	−0.641137	+	0.370161i
$544$	−20.0681	−	12.8828i	−0.860413	−	0.552346i
$545$			42.7476i			1.83111i
$546$	8.05826	+	1.54873i	0.344862	+	0.0662793i
$547$	4.16325	−	4.16325i	0.178008	−	0.178008i	−0.612479	−	0.790487i	$-0.709828\pi$
$547$	4.16325	−	4.16325i	0.178008	−	0.178008i	0.790487	+	0.612479i	$0.209828\pi$
$548$	7.34308	−	31.6064i	0.313681	−	1.35016i
$549$	−0.553206	+	2.06459i	−0.0236102	+	0.0881146i
$550$	−15.0091	−	18.8959i	−0.639992	−	0.805726i
$551$	−47.7360	−	27.5604i	−2.03362	−	1.17411i
$552$	−7.85886	+	3.72844i	−0.334495	+	0.158693i
$553$	−0.691519	−	0.0524734i	−0.0294064	−	0.00223140i
$554$	7.18857	−	1.06924i	0.305413	−	0.0454279i
$555$	2.20560	−	0.590988i	0.0936223	−	0.0250860i
$556$	−1.13954	−	33.9828i	−0.0483271	−	1.44119i
$557$	−0.00350994	+	0.0130993i	−0.000148721	+	0.000555034i	−0.966000	−	0.258542i	$-0.916758\pi$
$557$	−0.00350994	+	0.0130993i	−0.000148721	+	0.000555034i	0.965851	+	0.259097i	$0.0834248\pi$
$558$	−3.59706	−	8.28837i	−0.152276	−	0.350875i
$559$	6.92851			0.293045
$560$	−30.3129	−	30.8448i	−1.28095	−	1.30343i
$561$	−6.14882			−0.259603
$562$	−1.12071	−	2.58235i	−0.0472744	−	0.108930i
$563$	−0.823168	+	3.07210i	−0.0346924	+	0.129474i	−0.981100	−	0.193500i	$-0.938016\pi$
$563$	−0.823168	+	3.07210i	−0.0346924	+	0.129474i	0.946408	+	0.322974i	$0.104683\pi$
$564$	9.52122	−	0.319272i	0.400916	−	0.0134438i
$565$	−46.7310	+	12.5215i	−1.96599	+	0.526785i
$566$	−39.9962	+	5.94913i	−1.68117	+	0.250061i
$567$	2.18463	+	1.49245i	0.0917457	+	0.0626771i
$568$	−7.71329	+	21.6385i	−0.323642	+	0.907933i
$569$	23.9388	+	13.8211i	1.00357	+	0.579410i	0.909302	−	0.416137i	$-0.136616\pi$
$569$	23.9388	+	13.8211i	1.00357	+	0.579410i	0.0942660	+	0.995547i	$0.469950\pi$
$570$	−24.7071	−	31.1053i	−1.03487	−	1.30286i
$571$	2.27990	−	8.50868i	0.0954106	−	0.356077i	−0.901671	−	0.432423i	$-0.857659\pi$
$571$	2.27990	−	8.50868i	0.0954106	−	0.356077i	0.997081	+	0.0763459i	$0.0243253\pi$
$572$	6.23153	+	1.44776i	0.260553	+	0.0605341i
$573$	6.07670	−	6.07670i	0.253858	−	0.253858i
$574$	−7.70645	+	8.90313i	−0.321661	+	0.371610i
$575$			35.9783i			1.50040i
$576$	2.83585	+	7.48050i	0.118161	+	0.311688i
$577$	2.53730	−	1.46491i	0.105629	−	0.0609849i	−0.446255	−	0.894906i	$-0.647243\pi$
$577$	2.53730	−	1.46491i	0.105629	−	0.0609849i	0.551884	+	0.833921i	$0.313909\pi$
$578$	−0.124303	+	1.08431i	−0.00517032	+	0.0451013i
$579$	−9.22107	+	2.47078i	−0.383215	+	0.102682i
$580$	62.7012	−	19.0747i	2.60353	−	0.792032i
$581$	−27.0407	−	9.49039i	−1.12184	−	0.393728i
$582$	−23.7056	+	3.52603i	−0.982630	+	0.146159i
$583$	9.05537	−	15.6844i	0.375035	−	0.649580i
$584$	−15.1806	+	2.78091i	−0.628176	+	0.115075i
$585$	−7.76117	+	4.48092i	−0.320885	+	0.185263i
$586$	−3.94119	−	1.55563i	−0.162809	−	0.0642625i
$587$	−3.39718	+	3.39718i	−0.140217	+	0.140217i	−0.773731	−	0.633514i	$-0.781612\pi$
$587$	−3.39718	+	3.39718i	−0.140217	+	0.140217i	0.633514	+	0.773731i	$0.281612\pi$
$588$	−13.9027	−	1.64751i	−0.573339	−	0.0679420i
$589$	31.0530	+	31.0530i	1.27952	+	1.27952i
$590$	36.1417	−	15.6851i	1.48793	−	0.645744i
$591$	2.87050	+	4.97186i	0.118077	+	0.204515i
$592$	2.11535	−	0.721818i	0.0869402	−	0.0296665i
$593$	−40.4281	−	23.3412i	−1.66018	−	0.958507i	−0.972626	−	0.232376i	$-0.925350\pi$
$593$	−40.4281	−	23.3412i	−1.66018	−	0.958507i	−0.687556	−	0.726131i	$-0.741316\pi$
$594$	1.65729	+	1.22811i	0.0679992	+	0.0503898i
$595$	−15.0938	+	43.0064i	−0.618786	+	1.76309i
$596$	15.5083	+	8.27351i	0.635245	+	0.338896i
$597$	−2.60705	−	9.72963i	−0.106699	−	0.398207i
$598$	−5.93248	−	7.46877i	−0.242597	−	0.305421i
$599$	19.8174	+	34.3248i	0.809717	+	1.40247i	0.913060	+	0.407826i	$0.133713\pi$
$599$	19.8174	+	34.3248i	0.809717	+	1.40247i	−0.103342	+	0.994646i	$0.532954\pi$
$600$	32.9819	+	2.66476i	1.34648	+	0.108788i
$601$	−24.1918			−0.986805			−0.493402	−	0.869801i	$-0.664247\pi$
$601$	−24.1918			−0.986805			−0.493402	+	0.869801i	$0.664247\pi$
$602$	−11.7903	+	0.849468i	−0.480538	+	0.0346217i
$603$	0.568678	+	0.568678i	0.0231584	+	0.0231584i
$604$	−23.4362	−	5.44491i	−0.953605	−	0.221550i
$605$	35.0217	+	9.38403i	1.42383	+	0.381515i
$606$	2.74518	+	0.314702i	0.111515	+	0.0127839i
$607$	4.51754	−	7.82460i	0.183361	−	0.317591i	−0.759662	−	0.650318i	$-0.774636\pi$
$607$	4.51754	−	7.82460i	0.183361	−	0.317591i	0.943023	+	0.332727i	$0.107969\pi$
$608$	−26.1699	−	28.7590i	−1.06133	−	1.16633i
$609$	11.9680	−	17.5186i	0.484969	−	0.709890i
$610$	9.92440	+	7.35433i	0.401827	+	0.297768i
$611$	2.70369	+	10.0903i	0.109379	+	0.408210i
$612$	5.75868	−	6.15829i	0.232781	−	0.248934i
$613$	29.1002	+	7.79737i	1.17535	+	0.314933i	0.793079	−	0.609119i	$-0.208477\pi$
$613$	29.1002	+	7.79737i	1.17535	+	0.314933i	0.382267	+	0.924052i	$0.375144\pi$
$614$	21.0794	+	8.32029i	0.850696	+	0.335780i
$615$		−	12.8602i		−	0.518573i
$616$	−10.7818	−	1.69966i	−0.434410	−	0.0684814i
$617$		−	4.73029i		−	0.190434i	−0.995457	−	0.0952172i	$-0.969645\pi$
$617$		−	4.73029i		−	0.190434i	0.995457	−	0.0952172i	$-0.0303546\pi$
$618$	−3.72579	+	9.43929i	−0.149873	+	0.379704i
$619$	15.5783	+	4.17418i	0.626143	+	0.167774i	0.557919	−	0.829896i	$-0.311600\pi$
$619$	15.5783	+	4.17418i	0.626143	+	0.167774i	0.0682240	+	0.997670i	$0.478267\pi$
$620$	−52.1861	+	1.74994i	−2.09584	+	0.0702794i
$621$	−0.795963	−	2.97058i	−0.0319409	−	0.119205i
$622$	−6.74646	+	9.10411i	−0.270508	+	0.365042i
$623$	1.99762	−	26.3256i	0.0800331	−	1.05471i
$624$	−7.28614	+	4.88522i	−0.291679	+	0.195565i
$625$	26.6845	−	46.2188i	1.06738	−	1.84875i
$626$	−2.53192	+	22.0862i	−0.101196	+	0.882743i
$627$	−9.68418	−	2.59487i	−0.386749	−	0.103629i
$628$	−25.5400	+	15.9100i	−1.01916	+	0.634877i
$629$	−1.66567	−	1.66567i	−0.0664146	−	0.0664146i
$630$	12.6579	−	8.57679i	0.504303	−	0.341707i
$631$	8.67470			0.345334			0.172667	−	0.984980i	$-0.444761\pi$
$631$	8.67470			0.345334			0.172667	+	0.984980i	$0.444761\pi$
$632$	0.564758	−	0.480321i	0.0224649	−	0.0191061i
$633$	2.83917	+	4.91759i	0.112847	+	0.195457i
$634$	24.0515	−	19.1043i	0.955209	−	0.758727i
$635$	17.6447	+	65.8510i	0.700210	+	2.61322i
$636$	7.22771	+	23.7585i	0.286597	+	0.942087i
$637$	−1.69025	−	15.2582i	−0.0669703	−	0.604551i
$638$	9.84823	−	13.2898i	0.389895	−	0.526150i
$639$	−7.03376	−	4.06094i	−0.278251	−	0.160648i
$640$	46.2283	+	0.627781i	1.82734	+	0.0248152i
$641$	−2.02858	−	3.51361i	−0.0801243	−	0.138779i	0.823179	−	0.567782i	$-0.192198\pi$
$641$	−2.02858	−	3.51361i	−0.0801243	−	0.138779i	−0.903303	+	0.429003i	$0.858865\pi$
$642$	−4.22541	−	9.73624i	−0.166764	−	0.384259i
$643$	−18.3714	−	18.3714i	−0.724497	−	0.724497i	0.245021	−	0.969518i	$-0.421205\pi$
$643$	−18.3714	−	18.3714i	−0.724497	−	0.724497i	−0.969518	+	0.245021i	$0.921205\pi$
$644$	11.0111	+	11.9824i	0.433897	+	0.472171i
$645$	9.12883	−	9.12883i	0.359447	−	0.359447i
$646$	−15.0457	+	38.1182i	−0.591964	+	1.49974i
$647$	−28.0998	+	16.2234i	−1.10472	+	0.637809i	−0.937456	−	0.348103i	$-0.886826\pi$
$647$	−28.0998	+	16.2234i	−1.10472	+	0.637809i	−0.167262	+	0.985913i	$0.553493\pi$
$648$	−2.78213	+	0.509655i	−0.109292	+	0.0200211i
$649$	4.97185	−	8.61150i	0.195162	−	0.338031i
$650$	5.33820	+	35.8889i	0.209381	+	1.40768i
$651$	−12.8226	+	11.0139i	−0.502559	+	0.431668i
$652$	−4.41513	−	2.35542i	−0.172910	−	0.0922455i
$653$	3.82963	−	1.02615i	0.149865	−	0.0401562i	−0.183107	−	0.983093i	$-0.558615\pi$
$653$	3.82963	−	1.02615i	0.149865	−	0.0401562i	0.332972	+	0.942937i	$0.391949\pi$
$654$	−14.6977	−	1.68491i	−0.574724	−	0.0658852i
$655$	32.7549	−	18.9110i	1.27984	−	0.738915i
$656$	−0.843285	−	12.5599i	−0.0329248	−	0.490383i
$657$		−	5.45645i		−	0.212876i
$658$	−5.83802	−	16.8393i	−0.227590	−	0.656464i
$659$	5.60438	−	5.60438i	0.218316	−	0.218316i	−0.589473	−	0.807788i	$-0.700664\pi$
$659$	5.60438	−	5.60438i	0.218316	−	0.218316i	0.807788	+	0.589473i	$0.200664\pi$
$660$	10.1180	−	6.30296i	0.393844	−	0.245342i
$661$	−7.93214	+	29.6032i	−0.308525	+	1.15143i	0.621344	+	0.783538i	$0.286587\pi$
$661$	−7.93214	+	29.6032i	−0.308525	+	1.15143i	−0.929869	+	0.367892i	$0.880080\pi$
$662$	6.68366	−	5.30886i	0.259768	−	0.206335i
$663$	8.00662	+	4.62262i	0.310951	+	0.179528i
$664$	27.6794	−	13.1318i	1.07417	−	0.509613i
$665$	−41.9214	+	61.3639i	−1.62564	+	2.37959i
$666$	0.116262	+	0.781631i	0.00450505	+	0.0302876i
$667$	−23.8212	+	6.38286i	−0.922360	+	0.247145i
$668$	28.4521	+	26.6059i	1.10085	+	1.02941i
$669$	3.77311	−	14.0814i	0.145877	−	0.544419i
$670$	4.26352	−	1.85032i	0.164714	−	0.0714840i
$671$	3.11757			0.120353
$672$	11.8000	−	9.20656i	0.455194	−	0.355151i
$673$	−34.0471			−1.31242			−0.656210	−	0.754579i	$-0.727841\pi$
$673$	−34.0471			−1.31242			−0.656210	+	0.754579i	$0.727841\pi$
$674$	3.29296	−	1.42911i	0.126840	−	0.0550472i
$675$	−3.02789	+	11.3002i	−0.116543	+	0.434946i
$676$	11.9647	+	11.1883i	0.460180	+	0.430320i
$677$	33.4313	−	8.95788i	1.28487	−	0.344279i	0.449159	−	0.893452i	$-0.351724\pi$
$677$	33.4313	−	8.95788i	1.28487	−	0.344279i	0.835709	+	0.549173i	$0.185057\pi$
$678$	−2.46329	−	16.5608i	−0.0946021	−	0.636013i
$679$	19.4162	+	40.4150i	0.745127	+	1.55099i
$680$	−20.8852	−	44.0222i	−0.800912	−	1.68817i
$681$	24.7862	+	14.3103i	0.949808	+	0.548372i
$682$	−10.3193	+	8.19668i	−0.395147	+	0.313867i
$683$	5.51090	−	20.5670i	0.210869	−	0.786973i	−0.776711	−	0.629857i	$-0.783114\pi$
$683$	5.51090	−	20.5670i	0.210869	−	0.786973i	0.987580	−	0.157117i	$-0.0502198\pi$
$684$	11.6686	−	7.26888i	0.446160	−	0.277932i
$685$	46.8801	−	46.8801i	1.79120	−	1.79120i
$686$	4.74705	+	25.7578i	0.181243	+	0.983438i
$687$		−	0.870869i		−	0.0332257i
$688$	8.31708	−	9.51430i	0.317086	−	0.362729i
$689$	−23.5827	+	13.6155i	−0.898430	+	0.518709i
$690$	−17.6571	−	2.02418i	−0.672195	−	0.0770591i
$691$	2.96400	−	0.794203i	0.112756	−	0.0302129i	−0.202000	−	0.979386i	$-0.564744\pi$
$691$	2.96400	−	0.794203i	0.112756	−	0.0302129i	0.314756	+	0.949173i	$0.398077\pi$
$692$	−16.8281	−	8.97759i	−0.639707	−	0.341277i
$693$	1.27796	−	3.64126i	0.0485457	−	0.138320i
$694$	−1.93521	−	13.0105i	−0.0734595	−	0.493871i
$695$	34.7365	−	60.1654i	1.31763	−	2.28221i
$696$	4.08695	+	22.3100i	0.154915	+	0.845659i
$697$	−11.4895	+	6.63344i	−0.435194	+	0.251260i
$698$	11.7565	−	29.7850i	0.444990	−	1.12738i
$699$	−10.0346	+	10.0346i	−0.379542	+	0.379542i
$700$	−13.4842	−	60.4181i	−0.509656	−	2.28359i
$701$	14.5262	+	14.5262i	0.548648	+	0.548648i	0.926050	−	0.377402i	$-0.123182\pi$
$701$	14.5262	+	14.5262i	0.548648	+	0.548648i	−0.377402	+	0.926050i	$0.623182\pi$
$702$	−1.23474	−	2.84510i	−0.0466022	−	0.107381i
$703$	−1.92044	−	3.32631i	−0.0724309	−	0.125454i
$704$	9.46849	−	6.81927i	0.356857	−	0.257011i
$705$	16.8570	+	9.73240i	0.634872	+	0.366543i
$706$	−17.3081	+	23.3567i	−0.651400	+	0.879042i
$707$	−0.956294	−	5.08017i	−0.0359652	−	0.191060i
$708$	3.96837	+	13.0446i	0.149141	+	0.490247i
$709$	−10.1516	−	37.8865i	−0.381253	−	1.42286i	−0.843989	−	0.536360i	$-0.819799\pi$
$709$	−10.1516	−	37.8865i	−0.381253	−	1.42286i	0.462736	−	0.886496i	$-0.346868\pi$
$710$	−36.7535	+	29.1935i	−1.37934	+	1.09561i
$711$	0.131061	+	0.227003i	0.00491515	+	0.00851329i
$712$	18.2855	+	21.4999i	0.685277	+	0.805743i
$713$	19.6482			0.735830
$714$	−14.1917	−	6.88473i	−0.531112	−	0.257654i
$715$	9.24290	+	9.24290i	0.345665	+	0.345665i
$716$	−14.7778	+	9.20576i	−0.552274	+	0.344035i
$717$	−12.3853	−	3.31863i	−0.462537	−	0.123936i
$718$	−4.88468	+	42.6097i	−0.182295	+	1.59018i
$719$	−13.6597	+	23.6594i	−0.509422	+	0.882346i	0.490518	+	0.871431i	$0.336808\pi$
$719$	−13.6597	+	23.6594i	−0.509422	+	0.882346i	−0.999940	+	0.0109145i	$0.996526\pi$
$720$	−3.16338	+	16.0367i	−0.117892	+	0.597651i
$721$	18.9307	+	1.43649i	0.705017	+	0.0534977i
$722$	−23.7848	+	32.0968i	−0.885180	+	1.19452i
$723$	−1.01383	−	3.78368i	−0.0377049	−	0.140717i
$724$	−34.4831	+	1.15631i	−1.28155	+	0.0429740i
$725$	90.6170	+	24.2807i	3.36543	+	0.901764i
$726$	−4.60685	+	11.6714i	−0.170976	+	0.433167i
$727$		−	34.3104i		−	1.27250i	−0.771482	−	0.636251i	$-0.780484\pi$
$727$		−	34.3104i		−	1.27250i	0.771482	−	0.636251i	$-0.219516\pi$
$728$	12.7616	+	10.3188i	0.472976	+	0.382442i
$729$		−	1.00000i		−	0.0370370i
$730$	−29.3310	−	11.5773i	−1.08559	−	0.428495i
$731$	−12.8646	−	3.44705i	−0.475813	−	0.127494i
$732$	−2.91977	+	3.12238i	−0.107918	+	0.115406i
$733$	4.75167	+	17.7335i	0.175507	+	0.655001i	0.996465	+	0.0840119i	$0.0267734\pi$
$733$	4.75167	+	17.7335i	0.175507	+	0.655001i	−0.820958	+	0.570989i	$0.806560\pi$
$734$	−5.39264	−	3.99613i	−0.199046	−	0.147500i
$735$	−22.3308	−	17.8768i	−0.823685	−	0.659394i
$736$	−17.3776	−	0.819079i	−0.640547	−	0.0301917i
$737$	0.586513	−	1.01587i	0.0216045	−	0.0374201i
$738$	4.42165	+	0.506888i	0.162763	+	0.0186588i
$739$	−37.3089	−	9.99689i	−1.37243	−	0.367741i	−0.504064	−	0.863666i	$-0.668163\pi$
$739$	−37.3089	−	9.99689i	−1.37243	−	0.367741i	−0.868366	+	0.495925i	$0.834829\pi$
$740$	4.44833	+	1.03348i	0.163524	+	0.0379913i
$741$	10.6594	+	10.6594i	0.391581	+	0.391581i
$742$	38.4617	−	26.0610i	1.41197	−	0.956730i
$743$	−52.7521			−1.93529			−0.967644	−	0.252321i	$-0.918806\pi$
$743$	−52.7521			−1.93529			−0.967644	+	0.252321i	$0.918806\pi$
$744$	1.45526	−	18.0118i	0.0533524	−	0.660346i
$745$	17.9570	+	31.1024i	0.657893	+	1.13950i
$746$	−29.2364	−	36.8075i	−1.07042	−	1.34762i
$747$	2.80343	+	10.4625i	0.102572	+	0.382804i
$748$	−10.8502	−	5.78844i	−0.396721	−	0.211646i
$749$	−15.0626	+	12.9379i	−0.550375	+	0.472739i
$750$	31.1039	+	23.0491i	1.13575	+	0.841632i
$751$	−34.8871	−	20.1421i	−1.27305	−	0.734995i	−0.297488	−	0.954726i	$-0.596149\pi$
$751$	−34.8871	−	20.1421i	−1.27305	−	0.734995i	−0.975561	+	0.219731i	$0.929482\pi$
$752$	17.1016	+	8.39980i	0.623632	+	0.306309i
$753$	−4.48281	−	7.76445i	−0.163363	−	0.282952i
$754$	−22.8150	+	9.90142i	−0.830872	+	0.360589i
$755$	−34.7617	−	34.7617i	−1.26511	−	1.26511i
$756$	2.44999	+	4.69015i	0.0891054	+	0.170579i
$757$	−12.4035	+	12.4035i	−0.450812	+	0.450812i	−0.895624	−	0.444812i	$-0.853270\pi$
$757$	−12.4035	+	12.4035i	−0.450812	+	0.450812i	0.444812	+	0.895624i	$0.353270\pi$
$758$	−45.3865	−	17.9146i	−1.64851	−	0.650686i
$759$	−3.88467	+	2.24281i	−0.141005	+	0.0814090i
$760$	−14.3157	−	78.1472i	−0.519285	−	2.83470i
$761$	8.27544	−	14.3335i	0.299985	−	0.519589i	−0.676147	−	0.736766i	$-0.736352\pi$
$761$	8.27544	−	14.3335i	0.299985	−	0.519589i	0.976132	+	0.217178i	$0.0696851\pi$
$762$	−23.3366	+	3.47115i	−0.845398	+	0.125746i
$763$	5.11999	+	27.1992i	0.185356	+	0.984677i
$764$	16.4434	−	5.00235i	0.594903	−	0.180979i
$765$	16.6400	−	4.45866i	0.601619	−	0.161203i
$766$	−2.46106	+	21.4681i	−0.0889216	+	0.775674i
$767$	−12.9481	+	7.47558i	−0.467528	+	0.269928i
$768$	−2.03795	+	15.8697i	−0.0735382	+	0.572648i
$769$			21.0046i			0.757445i	0.925510	+	0.378722i	$0.123636\pi$
$769$			21.0046i			0.757445i	−0.925510	+	0.378722i	$0.876364\pi$
$770$	−16.8620	−	14.5955i	−0.607664	−	0.525987i
$771$	−10.5737	+	10.5737i	−0.380803	+	0.380803i
$772$	−18.5974	−	4.32071i	−0.669335	−	0.155506i
$773$	−3.98034	+	14.8548i	−0.143163	+	0.534291i	0.856667	+	0.515869i	$0.172531\pi$
$773$	−3.98034	+	14.8548i	−0.143163	+	0.534291i	−0.999830	+	0.0184221i	$0.994136\pi$
$774$	2.77890	+	3.49853i	0.0998854	+	0.125752i
$775$	−64.7291	−	37.3714i	−2.32514	−	1.34242i
$776$	−45.1501	−	16.0942i	−1.62079	−	0.577750i
$777$	1.33258	−	0.640200i	0.0478060	−	0.0229670i
$778$	21.6868	−	3.22575i	0.777511	−	0.115649i
$779$	−20.8949	+	5.59877i	−0.748638	+	0.200597i
$780$	−17.9136	+	0.600691i	−0.641410	+	0.0215082i
$781$	−3.06605	+	11.4427i	−0.109712	+	0.409451i
$782$	7.29934	+	16.8192i	0.261024	+	0.601454i
$783$	−8.01904			−0.286577
$784$	−22.9817	−	15.9951i	−0.820774	−	0.571252i
$785$	−61.4806			−2.19434
$786$	5.21103	+	12.0073i	0.185871	+	0.428286i
$787$	13.2577	−	49.4786i	0.472588	−	1.76372i	−0.157832	−	0.987466i	$-0.550450\pi$
$787$	13.2577	−	49.4786i	0.472588	−	1.76372i	0.630419	−	0.776255i	$-0.282883\pi$
$788$	0.384807	+	11.4756i	0.0137082	+	0.408800i
$789$	0.773859	−	0.207355i	0.0275501	−	0.00738203i
$790$	1.49833	−	0.222866i	0.0533083	−	0.00792920i
$791$	−28.2340	+	13.5642i	−1.00389	+	0.482288i
$792$	1.76831	+	3.72726i	0.0628340	+	0.132442i
$793$	−4.05952	−	2.34376i	−0.144158	−	0.0832295i
$794$	8.86629	+	11.1623i	0.314653	+	0.396136i
$795$	−13.1326	+	49.0114i	−0.465764	+	1.73825i
$796$	4.55901	−	19.6231i	0.161590	−	0.695522i
$797$	−27.0310	+	27.0310i	−0.957488	+	0.957488i	−0.999132	−	0.0416449i	$-0.986740\pi$
$797$	−27.0310	+	27.0310i	−0.957488	+	0.957488i	0.0416449	+	0.999132i	$0.486740\pi$
$798$	−19.4461	−	16.8323i	−0.688383	−	0.595856i
$799$		−	20.0804i		−	0.710392i
$800$	55.6910	+	35.7510i	1.96897	+	1.26399i
$801$	−8.64185	+	4.98938i	−0.305345	+	0.176291i
$802$	−0.210070	+	1.83246i	−0.00741782	+	0.0647066i
$803$	−7.68742	+	2.05984i	−0.271283	+	0.0726901i
$804$	0.468136	+	1.53883i	0.0165099	+	0.0542704i
$805$	6.15093	+	32.6759i	0.216792	+	1.15168i
$806$	19.5994	−	2.91526i	0.690359	−	0.102686i
$807$	−10.5933	+	18.3481i	−0.372901	+	0.645883i
$808$	4.54786	+	3.13961i	0.159993	+	0.110451i
$809$	4.81933	−	2.78244i	0.169439	−	0.0978255i	−0.412882	−	0.910784i	$-0.635478\pi$
$809$	4.81933	−	2.78244i	0.169439	−	0.0978255i	0.582321	+	0.812959i	$0.302145\pi$
$810$	−5.37548	−	2.12176i	−0.188875	−	0.0745512i
$811$	4.78415	−	4.78415i	0.167994	−	0.167994i	−0.618103	−	0.786097i	$-0.712098\pi$
$811$	4.78415	−	4.78415i	0.167994	−	0.167994i	0.786097	+	0.618103i	$0.212098\pi$
$812$	37.6105	−	19.6466i	1.31987	−	0.689460i
$813$	−13.7048	−	13.7048i	−0.480648	−	0.480648i
$814$	1.05733	−	0.458867i	0.0370593	−	0.0160833i
$815$	−5.11226	−	8.85469i	−0.179075	−	0.310166i
$816$	15.9591	−	5.44570i	0.558680	−	0.190638i
$817$	−18.8066	−	10.8580i	−0.657959	−	0.379873i
$818$	26.3734	+	19.5436i	0.922124	+	0.683326i
$819$	−4.40154	+	3.78067i	−0.153802	+	0.132107i
$820$	12.1065	−	22.6930i	0.422776	−	0.792473i
$821$	−10.7533	−	40.1318i	−0.375292	−	1.40061i	−0.852918	−	0.522045i	$-0.825169\pi$
$821$	−10.7533	−	40.1318i	−0.375292	−	1.40061i	0.477626	−	0.878563i	$-0.341498\pi$
$822$	14.2707	+	17.9663i	0.497749	+	0.626647i
$823$	27.8803	+	48.2901i	0.971847	+	1.68329i	0.689970	+	0.723838i	$0.257624\pi$
$823$	27.8803	+	48.2901i	0.971847	+	1.68329i	0.281877	+	0.959451i	$0.409043\pi$
$824$	−15.4606	+	13.1491i	−0.538594	+	0.458069i
$825$	17.0636			0.594077
$826$	21.1174	−	14.3088i	0.734768	−	0.497866i
$827$	−5.32315	−	5.32315i	−0.185104	−	0.185104i	0.608472	−	0.793576i	$-0.291783\pi$
$827$	−5.32315	−	5.32315i	−0.185104	−	0.185104i	−0.793576	+	0.608472i	$0.791783\pi$
$828$	1.39192	−	5.99117i	0.0483726	−	0.208207i
$829$	−1.89399	−	0.507494i	−0.0657811	−	0.0176260i	0.225778	−	0.974179i	$-0.427507\pi$
$829$	−1.89399	−	0.507494i	−0.0657811	−	0.0176260i	−0.291560	+	0.956553i	$0.594174\pi$
$830$	62.1895	+	7.12927i	2.15863	+	0.247460i
$831$	−2.56950	+	4.45051i	−0.0891351	+	0.154387i
$832$	−17.4560	+	1.76132i	−0.605177	+	0.0610628i
$833$	−4.45282	+	29.1717i	−0.154281	+	1.01074i
$834$	19.3172	+	14.3147i	0.668900	+	0.495678i
$835$	20.5996	+	76.8788i	0.712879	+	2.66050i
$836$	−14.6458	−	13.6955i	−0.506537	−	0.473668i
$837$	6.17120	+	1.65357i	0.213308	+	0.0571556i
$838$	−6.73212	−	2.65725i	−0.232557	−	0.0917930i
$839$		−	34.6451i		−	1.19608i	−0.801466	−	0.598041i	$-0.795946\pi$
$839$		−	34.6451i		−	1.19608i	0.801466	−	0.598041i	$-0.204054\pi$
$840$	30.4101	−	3.21850i	1.04925	−	0.111049i
$841$			35.3050i			1.21742i
$842$	−14.5818	+	36.9430i	−0.502523	+	1.27314i
$843$	1.92272	+	0.515191i	0.0662220	+	0.0177441i
$844$	0.380607	+	11.3503i	0.0131010	+	0.390694i
$845$	8.66255	+	32.3291i	0.298001	+	1.11215i
$846$	−4.01066	+	5.41225i	−0.137889	+	0.186077i
$847$	23.4073	+	1.77618i	0.804286	+	0.0610303i
$848$	−9.61210	+	48.7282i	−0.330081	+	1.67333i
$849$	14.2964	−	24.7620i	0.490650	−	0.849831i
$850$	7.94358	−	69.2928i	0.272463	−	2.37672i
$851$	−1.65989	−	0.444766i	−0.0569003	−	0.0152464i
$852$	−8.58878	−	13.7874i	−0.294247	−	0.472349i
$853$	18.5750	+	18.5750i	0.635995	+	0.635995i	0.949565	−	0.313570i	$-0.101525\pi$
$853$	18.5750	+	18.5750i	0.635995	+	0.635995i	−0.313570	+	0.949565i	$0.601525\pi$
$854$	7.19549	+	3.49070i	0.246225	+	0.119449i
$855$	28.0890			0.960623
$856$	1.70947	−	21.1583i	0.0584286	−	0.723174i
$857$	−18.6170	−	32.2456i	−0.635945	−	1.10149i	−0.986314	−	0.164877i	$-0.947277\pi$
$857$	−18.6170	−	32.2456i	−0.635945	−	1.10149i	0.350369	−	0.936612i	$-0.386056\pi$
$858$	−3.54225	+	2.81362i	−0.120930	+	0.0960555i
$859$	6.95890	+	25.9710i	0.237435	+	0.886118i	0.977036	+	0.213073i	$0.0683473\pi$
$859$	6.95890	+	25.9710i	0.237435	+	0.886118i	−0.739601	+	0.673045i	$0.764986\pi$
$860$	24.7024	−	7.51486i	0.842346	−	0.256255i
$861$	−1.54030	−	8.18261i	−0.0524932	−	0.278863i
$862$	13.3472	−	18.0116i	0.454609	−	0.613479i
$863$	−7.23773	−	4.17870i	−0.246375	−	0.142245i	0.371728	−	0.928342i	$-0.378765\pi$
$863$	−7.23773	−	4.17870i	−0.246375	−	0.142245i	−0.618103	+	0.786097i	$0.712099\pi$
$864$	−5.38911	−	1.71974i	−0.183341	−	0.0585067i
$865$	−19.4851	−	33.7492i	−0.662514	−	1.14751i
$866$	2.22939	+	5.13699i	0.0757578	+	0.174562i
$867$	−0.545706	−	0.545706i	−0.0185331	−	0.0185331i
$868$	−32.9951	+	7.36391i	−1.11993	+	0.249947i
$869$	0.270342	−	0.270342i	0.00917072	−	0.00917072i
$870$	−17.0145	+	43.1062i	−0.576846	+	1.46144i
$871$	−1.52744	+	0.881870i	−0.0517555	+	0.0298810i
$872$	−24.3492	−	16.8094i	−0.824569	−	0.569239i
$873$	8.47341	−	14.6764i	0.286782	−	0.496720i
$874$	4.39833	+	29.5701i	0.148776	+	1.00022i
$875$	23.9847	−	68.3390i	0.810831	−	2.31028i
$876$	5.13665	−	9.62840i	0.173551	−	0.325314i
$877$	−13.3292	+	3.57156i	−0.450096	+	0.120603i	−0.476744	−	0.879042i	$-0.658183\pi$
$877$	−13.3292	+	3.57156i	−0.450096	+	0.120603i	0.0266482	+	0.999645i	$0.491517\pi$
$878$	−15.3432	−	1.75892i	−0.517809	−	0.0593606i
$879$	2.59468	−	1.49804i	0.0875163	−	0.0505276i
$880$	23.7877	−	1.59713i	0.801885	−	0.0538393i
$881$		−	19.6095i		−	0.660662i	−0.943865	−	0.330331i	$-0.892840\pi$
$881$		−	19.6095i		−	0.660662i	0.943865	−	0.330331i	$-0.107160\pi$
$882$	7.02664	−	6.97326i	0.236599	−	0.234802i
$883$	18.5695	−	18.5695i	0.624912	−	0.624912i	−0.321871	−	0.946783i	$-0.604312\pi$
$883$	18.5695	−	18.5695i	0.624912	−	0.624912i	0.946783	+	0.321871i	$0.104312\pi$
$884$	9.77672	+	15.6944i	0.328827	+	0.527860i
$885$	−7.21043	+	26.9097i	−0.242376	+	0.904559i
$886$	−7.33779	+	5.82844i	−0.246518	+	0.195810i
$887$	33.8793	+	19.5602i	1.13755	+	0.656767i	0.945824	−	0.324680i	$-0.105257\pi$
$887$	33.8793	+	19.5602i	1.13755	+	0.656767i	0.191731	+	0.981448i	$0.438590\pi$
$888$	−0.530666	+	1.48871i	−0.0178080	+	0.0499578i
$889$	19.1140	+	39.7860i	0.641064	+	1.33438i
$890$	8.48433	+	57.0404i	0.284395	+	1.91200i
$891$	−1.40887	+	0.377505i	−0.0471989	+	0.0126469i
$892$	19.9141	−	21.2960i	0.666774	−	0.713043i
$893$	8.47414	−	31.6259i	0.283576	−	1.05832i
$894$	−11.4015	+	4.94814i	−0.381325	+	0.165490i
$895$	−35.5736			−1.18910
$896$	29.4891	−	5.13745i	0.985161	−	0.171630i
$897$	6.74451			0.225193
$898$	−19.6880	+	8.54436i	−0.656997	+	0.285129i
$899$	13.2600	−	49.4871i	0.442247	−	1.65049i
$900$	−15.9809	+	17.0899i	−0.532697	+	0.569662i
$901$	50.5613	−	13.5479i	1.68444	−	0.451345i
$902$	−0.955055	−	6.42087i	−0.0317999	−	0.213791i
$903$	4.71505	−	6.90182i	0.156907	−	0.229678i
$904$	11.2435	−	31.5420i	0.373952	−	1.04907i
$905$	−61.0512	−	35.2479i	−2.02941	−	1.17168i
$906$	13.3221	−	10.5818i	0.442596	−	0.351556i
$907$	2.49052	−	9.29476i	0.0826965	−	0.308627i	−0.912172	−	0.409809i	$-0.865595\pi$
$907$	2.49052	−	9.29476i	0.0826965	−	0.308627i	0.994868	+	0.101181i	$0.0322622\pi$
$908$	30.2659	+	48.5853i	1.00441	+	1.61236i
$909$	−1.38158	+	1.38158i	−0.0458241	+	0.0458241i
$910$	10.9839	+	31.6821i	0.364112	+	1.05025i
$911$		−	15.0703i		−	0.499302i	−0.968336	−	0.249651i	$-0.919684\pi$
$911$		−	15.0703i		−	0.499302i	0.968336	−	0.249651i	$-0.0803159\pi$
$912$	27.4332	−	1.84189i	0.908403	−	0.0609910i
$913$	13.6820	−	7.89933i	0.452809	−	0.261430i
$914$	−48.1276	−	5.51724i	−1.59192	−	0.182494i
$915$	−8.43679	+	2.26063i	−0.278912	+	0.0747342i
$916$	0.819828	−	1.53673i	0.0270879	−	0.0507749i
$917$	18.5761	−	15.9557i	0.613435	−	0.526905i
$918$	0.877128	+	5.89696i	0.0289495	+	0.194629i
$919$	−7.99528	+	13.8482i	−0.263740	+	0.456811i	−0.967233	−	0.253891i	$-0.918289\pi$
$919$	−7.99528	+	13.8482i	−0.263740	+	0.456811i	0.703493	+	0.710702i	$0.251623\pi$
$920$	−29.2521	−	20.1941i	−0.964413	−	0.665780i
$921$	−13.8776	+	8.01225i	−0.457283	+	0.264013i
$922$	−13.9329	+	35.2990i	−0.458856	+	1.16251i
$923$	12.5949	−	12.5949i	0.414567	−	0.414567i
$924$	5.68292	−	5.22227i	0.186954	−	0.171800i
$925$	4.62240	+	4.62240i	0.151983	+	0.151983i
$926$	9.59628	+	22.1118i	0.315353	+	0.726640i
$927$	−3.58786	−	6.21435i	−0.117841	−	0.204106i
$928$	−13.7907	+	43.2155i	−0.452700	+	1.41862i
$929$	0.184678	+	0.106624i	0.00605910	+	0.00349822i	0.503026	−	0.864271i	$-0.332220\pi$
$929$	0.184678	+	0.106624i	0.00605910	+	0.00349822i	−0.496967	+	0.867769i	$0.665553\pi$
$930$	21.9826	−	29.6647i	0.720836	−	0.972743i
$931$	−19.3238	+	44.0653i	−0.633313	+	1.44418i
$932$	−27.1534	+	8.26047i	−0.889438	+	0.270581i
$933$	−2.07378	−	7.73946i	−0.0678925	−	0.253378i
$934$	−15.6420	+	12.4245i	−0.511822	+	0.406542i
$935$	−12.5633	−	21.7603i	−0.410865	−	0.711639i
$936$	0.499537	−	6.18281i	0.0163279	−	0.202091i
$937$	28.9302			0.945108			0.472554	−	0.881302i	$-0.343332\pi$
$937$	28.9302			0.945108			0.472554	+	0.881302i	$0.343332\pi$
$938$	2.49115	−	1.68796i	0.0813389	−	0.0551139i
$939$	−11.1154	−	11.1154i	−0.362739	−	0.362739i
$940$	20.5838	+	33.0427i	0.671368	+	1.07774i
$941$	30.0517	+	8.05233i	0.979658	+	0.262499i	0.712901	−	0.701265i	$-0.247381\pi$
$941$	30.0517	+	8.05233i	0.979658	+	0.262499i	0.266758	+	0.963764i	$0.414048\pi$
$942$	2.42327	−	21.1385i	0.0789546	−	0.688730i
$943$	−4.83917	+	8.38169i	−0.157585	+	0.272945i
$944$	−5.27752	+	26.7542i	−0.171769	+	0.870776i
$945$	−0.818052	+	10.7807i	−0.0266112	+	0.350695i
$946$	3.87992	−	5.23581i	0.126147	−	0.170231i
$947$	−6.60627	−	24.6549i	−0.214675	−	0.801178i	−0.986281	−	0.165077i	$-0.947213\pi$
$947$	−6.60627	−	24.6549i	−0.214675	−	0.801178i	0.771606	−	0.636101i	$-0.219454\pi$
$948$	0.0175694	+	0.523948i	0.000570627	+	0.0170170i
$949$	11.5587	+	3.09713i	0.375210	+	0.100537i
$950$	41.7532	−	105.782i	1.35465	−	3.43201i
$951$			21.7192i			0.704294i
$952$	−18.5614	−	25.5087i	−0.601578	−	0.826741i
$953$		−	59.9052i		−	1.94052i	−0.242062	−	0.970261i	$-0.577824\pi$
$953$		−	59.9052i		−	1.94052i	0.242062	−	0.970261i	$-0.422176\pi$
$954$	−16.3337	−	6.44709i	−0.528822	−	0.208732i
$955$	33.9211	+	9.08913i	1.09766	+	0.294117i
$956$	−18.7308	−	17.5154i	−0.605799	−	0.566489i
$957$	3.02723	+	11.2978i	0.0978564	+	0.365205i
$958$	−0.104922	−	0.0777507i	−0.00338987	−	0.00251201i
$959$	24.2137	−	35.4436i	0.781900	−	1.14453i
$960$	−20.6788	+	25.3202i	−0.667407	+	0.817206i
$961$	−4.90898	+	8.50260i	−0.158354	+	0.274277i
$962$	−1.72176	−	0.197379i	−0.0555117	−	0.00636374i
$963$	7.24922	+	1.94242i	0.233603	+	0.0625937i
$964$	1.77292	−	7.63106i	0.0571018	−	0.245780i
$965$	−27.5846	−	27.5846i	−0.887978	−	0.887978i
$966$	−11.4772	+	0.826909i	−0.369273	+	0.0266053i
$967$	−9.77824			−0.314447			−0.157223	−	0.987563i	$-0.550254\pi$
$967$	−9.77824			−0.314447			−0.157223	+	0.987563i	$0.550254\pi$
$968$	−19.1166	+	16.2585i	−0.614430	+	0.522567i
$969$	−14.4886	−	25.0951i	−0.465442	−	0.806170i
$970$	−60.9140	−	76.6885i	−1.95583	−	2.46232i
$971$	−6.44850	−	24.0661i	−0.206942	−	0.772319i	−0.988849	−	0.148923i	$-0.952419\pi$
$971$	−6.44850	−	24.0661i	−0.206942	−	0.772319i	0.781906	−	0.623396i	$-0.214247\pi$
$972$	0.941391	−	1.76459i	0.0301951	−	0.0565993i
$973$	14.8958	−	42.4422i	0.477537	−	1.36063i
$974$	9.38965	+	6.95806i	0.300864	+	0.222950i
$975$	−22.2192	−	12.8282i	−0.711582	−	0.410832i
$976$	−8.09158	+	2.76108i	−0.259005	+	0.0883800i
$977$	25.2988	+	43.8188i	0.809380	+	1.40189i	0.913294	+	0.407301i	$0.133530\pi$
$977$	25.2988	+	43.8188i	0.809380	+	1.40189i	−0.103914	+	0.994586i	$0.533137\pi$
$978$	3.24596	−	1.40871i	0.103794	−	0.0450455i
$979$	10.2917	+	10.2917i	0.328925	+	0.328925i
$980$	−22.5758	−	52.5672i	−0.721157	−	1.67920i
$981$	7.39696	−	7.39696i	0.236167	−	0.236167i
$982$	33.3731	+	13.1727i	1.06498	+	0.420359i
$983$	45.8284	−	26.4591i	1.46170	−	0.843913i	0.462610	−	0.886562i	$-0.346913\pi$
$983$	45.8284	−	26.4591i	1.46170	−	0.843913i	0.999090	+	0.0426488i	$0.0135796\pi$
$984$	7.32522	+	5.05695i	0.233519	+	0.161210i
$985$	−11.7301	+	20.3171i	−0.373752	+	0.647357i
$986$	47.2880	−	7.03372i	1.50596	−	0.223999i
$987$	11.8914	+	4.17347i	0.378506	+	0.132843i
$988$	8.77480	+	28.8440i	0.279164	+	0.917651i
$989$	−9.38485	+	2.51466i	−0.298421	+	0.0799616i
$990$	−0.960015	+	8.37432i	−0.0305113	+	0.266153i
$991$	9.82327	−	5.67147i	0.312046	−	0.180160i	−0.335795	−	0.941935i	$-0.609005\pi$
$991$	9.82327	−	5.67147i	0.312046	−	0.180160i	0.647842	+	0.761775i	$0.275672\pi$
$992$	19.5241	−	30.4136i	0.619891	−	0.965631i
$993$			6.03553i			0.191532i
$994$	−19.8887	+	22.9771i	−0.630833	+	0.728791i
$995$	29.1059	−	29.1059i	0.922719	−	0.922719i
$996$	−4.90243	+	21.1012i	−0.155339	+	0.668618i
$997$	6.10263	−	22.7753i	0.193272	−	0.721301i	−0.799435	−	0.600752i	$-0.794868\pi$
$997$	6.10263	−	22.7753i	0.193272	−	0.721301i	0.992707	−	0.120549i	$-0.0384655\pi$
$998$	9.69794	+	12.2094i	0.306983	+	0.386480i
$999$	−0.483915	−	0.279389i	−0.0153104	−	0.00883947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.19.5	✓	128
7.3	odd	6	inner	336.2.bs.a.115.16	yes	128
16.11	odd	4	inner	336.2.bs.a.187.16	yes	128
112.59	even	12	inner	336.2.bs.a.283.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.5	✓	128	1.1	even	1	trivial
336.2.bs.a.115.16	yes	128	7.3	odd	6	inner
336.2.bs.a.187.16	yes	128	16.11	odd	4	inner
336.2.bs.a.283.5	yes	128	112.59	even	12	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29731 + 0.563017i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.36602 - 1.46081i) q^{4} +(3.94718 - 1.05764i) q^{5} +(0.208064 + 1.39882i) q^{6} +(2.38481 - 1.14572i) q^{7} +(-0.949691 + 2.66422i) q^{8} +(-0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-1.29731 + 0.563017i) q^{2} +(0.258819 - 0.965926i) q^{3} +(1.36602 - 1.46081i) q^{4} +(3.94718 - 1.05764i) q^{5} +(0.208064 + 1.39882i) q^{6} +(2.38481 - 1.14572i) q^{7} +(-0.949691 + 2.66422i) q^{8} +(-0.866025 - 0.500000i) q^{9} +(-4.52524 + 3.59442i) q^{10} +(-0.377505 + 1.40887i) q^{11} +(-1.05749 - 1.69756i) q^{12} +(1.55074 - 1.55074i) q^{13} +(-2.44878 + 2.82904i) q^{14} -4.08642i q^{15} +(-0.267960 - 3.99101i) q^{16} +(-3.65086 + 2.10783i) q^{17} +(1.40501 + 0.161068i) q^{18} +(-6.63952 + 1.77905i) q^{19} +(3.84692 - 7.21087i) q^{20} +(-0.489441 - 2.60009i) q^{21} +(-0.303476 - 2.04028i) q^{22} +(-1.53768 + 2.66335i) q^{23} +(2.32764 + 1.60688i) q^{24} +(10.1315 - 5.84943i) q^{25} +(-1.13870 + 2.88488i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.58403 - 5.04885i) q^{28} +(5.67032 + 5.67032i) q^{29} +(2.30073 + 5.30136i) q^{30} +(-3.19445 - 5.53294i) q^{31} +(2.59464 + 5.02671i) q^{32} +(1.26316 + 0.729284i) q^{33} +(3.54956 - 4.79000i) q^{34} +(8.20153 - 7.04463i) q^{35} +(-1.91342 + 0.582091i) q^{36} +(0.144622 + 0.539737i) q^{37} +(7.61187 - 6.04614i) q^{38} +(-1.09654 - 1.89926i) q^{39} +(-0.930803 + 11.5206i) q^{40} +3.14705 q^{41} +(2.09885 + 3.09755i) q^{42} +(2.23394 + 2.23394i) q^{43} +(1.54241 + 2.47601i) q^{44} +(-3.94718 - 1.05764i) q^{45} +(0.495342 - 4.32093i) q^{46} +(-2.38164 + 4.12513i) q^{47} +(-3.92438 - 0.774121i) q^{48} +(4.37467 - 5.46464i) q^{49} +(-9.85037 + 13.2927i) q^{50} +(1.09109 + 4.07201i) q^{51} +(-0.146997 - 4.38369i) q^{52} +(-11.9937 - 3.21370i) q^{53} +(0.519223 - 1.31545i) q^{54} +5.96032i q^{55} +(0.787607 + 7.44175i) q^{56} +6.87373i q^{57} +(-10.5486 - 4.16367i) q^{58} +(-6.58514 - 1.76448i) q^{59} +(-5.96951 - 5.58215i) q^{60} +(-0.553206 - 2.06459i) q^{61} +(7.25933 + 5.37941i) q^{62} +(-2.63817 - 0.200188i) q^{63} +(-6.19617 - 5.06038i) q^{64} +(4.48092 - 7.76117i) q^{65} +(-2.04930 - 0.234928i) q^{66} +(-0.776828 - 0.208151i) q^{67} +(-1.90802 + 8.21258i) q^{68} +(2.17461 + 2.17461i) q^{69} +(-6.67368 + 13.7567i) q^{70} +8.12189 q^{71} +(2.15457 - 1.83244i) q^{72} +(2.72822 + 4.72542i) q^{73} +(-0.491501 - 0.618782i) q^{74} +(-3.02789 - 11.3002i) q^{75} +(-6.47087 + 12.1293i) q^{76} +(0.713883 + 3.79240i) q^{77} +(2.49186 + 1.84656i) q^{78} +(-0.227003 - 0.131061i) q^{79} +(-5.27876 - 15.4699i) q^{80} +(0.500000 + 0.866025i) q^{81} +(-4.08270 + 1.77184i) q^{82} +(-7.65911 - 7.65911i) q^{83} +(-4.46683 - 2.83679i) q^{84} +(-12.1813 + 12.1813i) q^{85} +(-4.15586 - 1.64036i) q^{86} +(6.94469 - 4.00952i) q^{87} +(-3.39503 - 2.34375i) q^{88} +(4.98938 - 8.64185i) q^{89} +(5.71619 - 0.850239i) q^{90} +(1.92152 - 5.47493i) q^{91} +(1.79014 + 5.88446i) q^{92} +(-6.17120 + 1.65357i) q^{93} +(0.767211 - 6.69247i) q^{94} +(-24.3258 + 14.0445i) q^{95} +(5.52697 - 1.20522i) q^{96} +16.9468i q^{97} +(-2.59862 + 9.55234i) q^{98} +(1.03136 - 1.03136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8}+O(q^{10}) \) 128 * q + 4 * q^4 - 24 * q^8	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44} - 20 q^{46} - 32 q^{50} - 144 q^{52} - 16 q^{53} - 56 q^{56} - 40 q^{58} - 96 q^{59} - 24 q^{60} - 32 q^{64} - 72 q^{66} + 16 q^{67} - 60 q^{68} + 28 q^{70} + 128 q^{71} - 4 q^{72} - 72 q^{74} + 72 q^{78} - 36 q^{80} + 64 q^{81} - 60 q^{82} + 24 q^{84} - 44 q^{86} - 48 q^{88} - 8 q^{91} + 56 q^{92} + 36 q^{94} + 60 q^{96} + 148 q^{98} - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

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