LMFDB - Embedded newform 312.2.bt.d.115.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [312,2,Mod(19,312)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("312.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(312, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 6, 0, 5])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$312 = 2^{3} \cdot 3 \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	312.bt (of order $12$ , degree $4$ , minimal)

Newform invariants

comment:select newform

sage:traces = [56,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.d.19.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41411 + 0.0173234i) q^{2} +(0.500000 + 0.866025i) q^{3} +(1.99940 - 0.0489943i) q^{4} +(0.403590 - 0.403590i) q^{5} +(-0.722056 - 1.21599i) q^{6} +(-4.65174 + 1.24643i) q^{7} +(-2.82652 + 0.103920i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.563728 + 0.577711i) q^{10} +(-5.72510 - 1.53404i) q^{11} +(1.04213 + 1.70703i) q^{12} +(0.849788 + 3.50398i) q^{13} +(6.55647 - 1.84317i) q^{14} +(0.551314 + 0.147724i) q^{15} +(3.99520 - 0.195919i) q^{16} +(-0.917794 - 0.529889i) q^{17} +(0.692051 - 1.23331i) q^{18} +(0.617530 - 0.165467i) q^{19} +(0.787164 - 0.826711i) q^{20} +(-3.40531 - 3.40531i) q^{21} +(8.12248 + 2.07011i) q^{22} +(-1.02761 - 1.77988i) q^{23} +(-1.50326 - 2.39588i) q^{24} +4.67423i q^{25} +(-1.26239 - 4.94028i) q^{26} -1.00000 q^{27} +(-9.23963 + 2.72002i) q^{28} +(-4.86733 + 2.81016i) q^{29} +(-0.782176 - 0.199347i) q^{30} +(2.54931 - 2.54931i) q^{31} +(-5.64625 + 0.346260i) q^{32} +(-1.53404 - 5.72510i) q^{33} +(1.30704 + 0.733420i) q^{34} +(-1.37435 + 2.38044i) q^{35} +(-0.957270 + 1.75603i) q^{36} +(-1.83349 + 6.84268i) q^{37} +(-0.870387 + 0.244685i) q^{38} +(-2.60964 + 2.48793i) q^{39} +(-1.09881 + 1.18269i) q^{40} +(1.37457 - 5.12996i) q^{41} +(4.87447 + 4.75649i) q^{42} +(-8.58213 - 4.95490i) q^{43} +(-11.5219 - 2.78665i) q^{44} +(0.147724 + 0.551314i) q^{45} +(1.48399 + 2.49914i) q^{46} +(5.92269 + 5.92269i) q^{47} +(2.16727 + 3.36198i) q^{48} +(14.0230 - 8.09616i) q^{49} +(-0.0809736 - 6.60986i) q^{50} -1.05978i q^{51} +(1.87074 + 6.96422i) q^{52} +1.19577i q^{53} +(1.41411 - 0.0173234i) q^{54} +(-2.92971 + 1.69147i) q^{55} +(13.0187 - 4.00647i) q^{56} +(0.452063 + 0.452063i) q^{57} +(6.83425 - 4.05818i) q^{58} +(2.11560 + 7.89551i) q^{59} +(1.10953 + 0.268348i) q^{60} +(-5.30143 - 3.06078i) q^{61} +(-3.56083 + 3.64916i) q^{62} +(1.24643 - 4.65174i) q^{63} +(7.97840 - 0.587462i) q^{64} +(1.75714 + 1.07120i) q^{65} +(2.26847 + 8.06933i) q^{66} +(-2.06834 + 7.71916i) q^{67} +(-1.86100 - 1.01449i) q^{68} +(1.02761 - 1.77988i) q^{69} +(1.90224 - 3.39001i) q^{70} +(-0.113135 - 0.422224i) q^{71} +(1.32326 - 2.49980i) q^{72} +(7.34514 - 7.34514i) q^{73} +(2.47421 - 9.70805i) q^{74} +(-4.04800 + 2.33712i) q^{75} +(1.22658 - 0.361089i) q^{76} +28.5438 q^{77} +(3.64721 - 3.56340i) q^{78} -7.20853i q^{79} +(1.53335 - 1.69149i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.85492 + 7.27813i) q^{82} +(7.79731 + 7.79731i) q^{83} +(-6.97542 - 6.64174i) q^{84} +(-0.584270 + 0.156555i) q^{85} +(12.2219 + 6.85808i) q^{86} +(-4.86733 - 2.81016i) q^{87} +(16.3415 + 3.74103i) q^{88} +(-0.708365 - 0.189806i) q^{89} +(-0.218448 - 0.777058i) q^{90} +(-8.32047 - 15.2404i) q^{91} +(-2.14181 - 3.50834i) q^{92} +(3.48242 + 0.933112i) q^{93} +(-8.47791 - 8.27271i) q^{94} +(0.182448 - 0.316009i) q^{95} +(-3.12299 - 4.71666i) q^{96} +(-4.48735 + 1.20238i) q^{97} +(-19.6897 + 11.6918i) q^{98} +(4.19106 - 4.19106i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$56 q + 28 q^{3} - 12 q^{8} - 28 q^{9} - 28 q^{14} + 12 q^{16} - 8 q^{19} - 4 q^{20} + 10 q^{22} - 6 q^{24} + 34 q^{26} - 56 q^{27} - 14 q^{28} - 30 q^{32} + 56 q^{34} - 28 q^{40} + 40 q^{41} - 14 q^{42}+ \cdots + 4 q^{98}+O(q^{100})$ 56 * q + 28 * q^3 - 12 * q^8 - 28 * q^9 - 28 * q^14 + 12 * q^16 - 8 * q^19 - 4 * q^20 + 10 * q^22 - 6 * q^24 + 34 * q^26 - 56 * q^27 - 14 * q^28 - 30 * q^32 + 56 * q^34 - 28 * q^40 + 40 * q^41 - 14 * q^42 - 44 * q^44 - 18 * q^46 - 12 * q^48 + 24 * q^49 - 72 * q^50 + 32 * q^52 - 54 * q^56 - 16 * q^57 - 16 * q^58 + 32 * q^59 - 20 * q^60 + 48 * q^65 + 20 * q^66 - 24 * q^67 - 26 * q^68 + 64 * q^70 + 6 * q^72 + 44 * q^73 - 6 * q^74 - 12 * q^75 + 6 * q^76 + 32 * q^78 - 4 * q^80 - 28 * q^81 - 30 * q^82 + 40 * q^83 + 2 * q^84 - 28 * q^86 + 126 * q^88 - 68 * q^89 - 72 * q^91 + 52 * q^92 + 34 * q^94 - 4 * q^97 + 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/312\mathbb{Z}\right)^\times$ .

$n$	$79$	$145$	$157$	$209$
$\chi(n)$	$-1$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.41411	+	0.0173234i	−0.999925	+	0.0122495i
$2$	−1.41411	+	0.0173234i	−0.999925	+	0.0122495i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.99940	−	0.0489943i	0.999700	−	0.0244972i
$5$	0.403590	−	0.403590i	0.180491	−	0.180491i	−0.611079	−	0.791570i	$-0.709264\pi$
$5$	0.403590	−	0.403590i	0.180491	−	0.180491i	0.791570	+	0.611079i	$0.209264\pi$
$6$	−0.722056	−	1.21599i	−0.294778	−	0.496426i
$7$	−4.65174	+	1.24643i	−1.75819	+	0.471107i	−0.986344	−	0.164698i	$-0.947335\pi$
$7$	−4.65174	+	1.24643i	−1.75819	+	0.471107i	−0.771850	+	0.635805i	$0.780668\pi$
$8$	−2.82652	+	0.103920i	−0.999325	+	0.0367412i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.563728	+	0.577711i	−0.178266	+	0.182688i
$11$	−5.72510	−	1.53404i	−1.72618	−	0.462529i	−0.746885	−	0.664953i	$-0.768451\pi$
$11$	−5.72510	−	1.53404i	−1.72618	−	0.462529i	−0.979298	+	0.202424i	$0.935118\pi$
$12$	1.04213	+	1.70703i	0.300837	+	0.492778i
$13$	0.849788	+	3.50398i	0.235689	+	0.971829i
$13$	0.849788	+	3.50398i	0.235689	+	0.971829i
$14$	6.55647	−	1.84317i	1.75229	−	0.492608i
$15$	0.551314	+	0.147724i	0.142349	+	0.0381422i
$16$	3.99520	−	0.195919i	0.998800	−	0.0489796i
$17$	−0.917794	−	0.529889i	−0.222598	−	0.128517i	0.384555	−	0.923102i	$-0.374355\pi$
$17$	−0.917794	−	0.529889i	−0.222598	−	0.128517i	−0.607153	+	0.794585i	$0.707688\pi$
$18$	0.692051	−	1.23331i	0.163118	−	0.290695i
$19$	0.617530	−	0.165467i	0.141671	−	0.0379606i	−0.187287	−	0.982305i	$-0.559969\pi$
$19$	0.617530	−	0.165467i	0.141671	−	0.0379606i	0.328958	+	0.944345i	$0.393303\pi$
$20$	0.787164	−	0.826711i	0.176015	−	0.184858i
$21$	−3.40531	−	3.40531i	−0.743100	−	0.743100i
$22$	8.12248	+	2.07011i	1.73172	+	0.441350i
$23$	−1.02761	−	1.77988i	−0.214272	−	0.371130i	0.738775	−	0.673952i	$-0.235405\pi$
$23$	−1.02761	−	1.77988i	−0.214272	−	0.371130i	−0.953047	+	0.302822i	$0.902071\pi$
$24$	−1.50326	−	2.39588i	−0.306851	−	0.489056i
$25$			4.67423i			0.934846i
$26$	−1.26239	−	4.94028i	−0.247576	−	0.968869i
$27$	−1.00000			−0.192450
$28$	−9.23963	+	2.72002i	−1.74613	+	0.514036i
$29$	−4.86733	+	2.81016i	−0.903841	+	0.521833i	−0.878444	−	0.477845i	$-0.841418\pi$
$29$	−4.86733	+	2.81016i	−0.903841	+	0.521833i	−0.0253965	+	0.999677i	$0.508085\pi$
$30$	−0.782176	−	0.199347i	−0.142805	−	0.0363956i
$31$	2.54931	−	2.54931i	0.457869	−	0.457869i	−0.440086	−	0.897956i	$-0.645052\pi$
$31$	2.54931	−	2.54931i	0.457869	−	0.457869i	0.897956	+	0.440086i	$0.145052\pi$
$32$	−5.64625	+	0.346260i	−0.998125	+	0.0612108i
$33$	−1.53404	−	5.72510i	−0.267041	−	0.996612i
$34$	1.30704	+	0.733420i	0.224155	+	0.125781i
$35$	−1.37435	+	2.38044i	−0.232308	+	0.402368i
$36$	−0.957270	+	1.75603i	−0.159545	+	0.292671i
$37$	−1.83349	+	6.84268i	−0.301424	+	1.12493i	0.634556	+	0.772877i	$0.281183\pi$
$37$	−1.83349	+	6.84268i	−0.301424	+	1.12493i	−0.935980	+	0.352053i	$0.885484\pi$
$38$	−0.870387	+	0.244685i	−0.141195	+	0.0396932i
$39$	−2.60964	+	2.48793i	−0.417877	+	0.398387i
$40$	−1.09881	+	1.18269i	−0.173738	+	0.187000i
$41$	1.37457	−	5.12996i	0.214672	−	0.801166i	−0.771610	−	0.636096i	$-0.780548\pi$
$41$	1.37457	−	5.12996i	0.214672	−	0.801166i	0.986282	−	0.165070i	$-0.0527850\pi$
$42$	4.87447	+	4.75649i	0.752147	+	0.733942i
$43$	−8.58213	−	4.95490i	−1.30876	−	0.755615i	−0.326873	−	0.945068i	$-0.605995\pi$
$43$	−8.58213	−	4.95490i	−1.30876	−	0.755615i	−0.981890	+	0.189454i	$0.939328\pi$
$44$	−11.5219	−	2.78665i	−1.73700	−	0.420104i
$45$	0.147724	+	0.551314i	0.0220214	+	0.0821850i
$46$	1.48399	+	2.49914i	0.218802	+	0.368477i
$47$	5.92269	+	5.92269i	0.863912	+	0.863912i	0.991790	−	0.127878i	$-0.0408164\pi$
$47$	5.92269	+	5.92269i	0.863912	+	0.863912i	−0.127878	+	0.991790i	$0.540816\pi$
$48$	2.16727	+	3.36198i	0.312818	+	0.485261i
$49$	14.0230	−	8.09616i	2.00328	−	1.15659i
$50$	−0.0809736	−	6.60986i	−0.0114514	−	0.934776i
$51$		−	1.05978i		−	0.148399i
$52$	1.87074	+	6.96422i	0.259425	+	0.965763i
$53$			1.19577i			0.164251i	0.996622	+	0.0821255i	$0.0261708\pi$
$53$			1.19577i			0.164251i	−0.996622	+	0.0821255i	$0.973829\pi$
$54$	1.41411	−	0.0173234i	0.192436	−	0.00235742i
$55$	−2.92971	+	1.69147i	−0.395043	+	0.228078i
$56$	13.0187	−	4.00647i	1.73970	−	0.535387i
$57$	0.452063	+	0.452063i	0.0598772	+	0.0598772i
$58$	6.83425	−	4.05818i	0.897381	−	0.532865i
$59$	2.11560	+	7.89551i	0.275427	+	1.02791i	0.955555	+	0.294814i	$0.0952578\pi$
$59$	2.11560	+	7.89551i	0.275427	+	1.02791i	−0.680127	+	0.733094i	$0.738076\pi$
$60$	1.10953	+	0.268348i	0.143240	+	0.0346436i
$61$	−5.30143	−	3.06078i	−0.678778	−	0.391893i	0.120616	−	0.992699i	$-0.461513\pi$
$61$	−5.30143	−	3.06078i	−0.678778	−	0.391893i	−0.799395	+	0.600806i	$0.794846\pi$
$62$	−3.56083	+	3.64916i	−0.452226	+	0.463444i
$63$	1.24643	−	4.65174i	0.157036	−	0.586065i
$64$	7.97840	−	0.587462i	0.997300	−	0.0734327i
$65$	1.75714	+	1.07120i	0.217946	+	0.132866i
$66$	2.26847	+	8.06933i	0.279229	+	0.993266i
$67$	−2.06834	+	7.71916i	−0.252688	+	0.943045i	0.716674	+	0.697409i	$0.245664\pi$
$67$	−2.06834	+	7.71916i	−0.252688	+	0.943045i	−0.969362	+	0.245637i	$0.921003\pi$
$68$	−1.86100	−	1.01449i	−0.225679	−	0.123025i
$69$	1.02761	−	1.77988i	0.123710	−	0.214272i
$70$	1.90224	−	3.39001i	0.227361	−	0.405184i
$71$	−0.113135	−	0.422224i	−0.0134266	−	0.0501087i	0.958888	−	0.283786i	$-0.0915906\pi$
$71$	−0.113135	−	0.422224i	−0.0134266	−	0.0501087i	−0.972314	+	0.233678i	$0.924924\pi$
$72$	1.32326	−	2.49980i	0.155948	−	0.294604i
$73$	7.34514	−	7.34514i	0.859684	−	0.859684i	−0.131617	−	0.991301i	$-0.542017\pi$
$73$	7.34514	−	7.34514i	0.859684	−	0.859684i	0.991301	+	0.131617i	$0.0420169\pi$
$74$	2.47421	−	9.70805i	0.287621	−	1.12854i
$75$	−4.04800	+	2.33712i	−0.467423	+	0.269867i
$76$	1.22658	−	0.361089i	0.140699	−	0.0414198i
$77$	28.5438			3.25287
$78$	3.64721	−	3.56340i	0.412965	−	0.403476i
$79$		−	7.20853i		−	0.811023i	−0.914090	−	0.405511i	$-0.867093\pi$
$79$		−	7.20853i		−	0.811023i	0.914090	−	0.405511i	$-0.132907\pi$
$80$	1.53335	−	1.69149i	0.171434	−	0.189115i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.85492	+	7.27813i	−0.204842	+	0.803735i
$83$	7.79731	+	7.79731i	0.855866	+	0.855866i	0.990848	−	0.134982i	$-0.0430977\pi$
$83$	7.79731	+	7.79731i	0.855866	+	0.855866i	−0.134982	+	0.990848i	$0.543098\pi$
$84$	−6.97542	−	6.64174i	−0.761081	−	0.724673i
$85$	−0.584270	+	0.156555i	−0.0633730	+	0.0169807i
$86$	12.2219	+	6.85808i	1.31792	+	0.739526i
$87$	−4.86733	−	2.81016i	−0.521833	−	0.301280i
$88$	16.3415	+	3.74103i	1.74201	+	0.398795i
$89$	−0.708365	−	0.189806i	−0.0750865	−	0.0201194i	0.221080	−	0.975256i	$-0.429042\pi$
$89$	−0.708365	−	0.189806i	−0.0750865	−	0.0201194i	−0.296167	+	0.955136i	$0.595708\pi$
$90$	−0.218448	−	0.777058i	−0.0230265	−	0.0819091i
$91$	−8.32047	−	15.2404i	−0.872222	−	1.59763i
$92$	−2.14181	−	3.50834i	−0.223299	−	0.365770i
$93$	3.48242	+	0.933112i	0.361110	+	0.0967592i
$94$	−8.47791	−	8.27271i	−0.874430	−	0.853265i
$95$	0.182448	−	0.316009i	0.0187188	−	0.0324219i
$96$	−3.12299	−	4.71666i	−0.318739	−	0.481392i
$97$	−4.48735	+	1.20238i	−0.455621	+	0.122083i	−0.479329	−	0.877636i	$-0.659120\pi$
$97$	−4.48735	+	1.20238i	−0.455621	+	0.122083i	0.0237071	+	0.999719i	$0.492453\pi$
$98$	−19.6897	+	11.6918i	−1.98896	+	1.18105i
$99$	4.19106	−	4.19106i	0.421218	−	0.421218i
$100$	0.229011	+	9.34566i	0.0229011	+	0.934566i
$101$	−2.03641	−	3.52717i	−0.202631	−	0.350966i	0.746745	−	0.665111i	$-0.231616\pi$
$101$	−2.03641	−	3.52717i	−0.202631	−	0.350966i	−0.949375	+	0.314144i	$0.898282\pi$
$102$	0.0183590	+	1.49864i	0.00181781	+	0.148387i
$103$	0.447521			0.0440955			0.0220478	−	0.999757i	$-0.492981\pi$
$103$	0.447521			0.0440955			0.0220478	+	0.999757i	$0.492981\pi$
$104$	−2.76607	−	9.81574i	−0.271236	−	0.962513i
$105$	−2.74870			−0.268246
$106$	−0.0207147	−	1.69094i	−0.00201199	−	0.164239i
$107$	3.67665	+	6.36815i	0.355436	+	0.615632i	0.987192	−	0.159534i	$-0.0509992\pi$
$107$	3.67665	+	6.36815i	0.355436	+	0.615632i	−0.631757	+	0.775167i	$0.717666\pi$
$108$	−1.99940	+	0.0489943i	−0.192392	+	0.00471448i
$109$	1.83648	−	1.83648i	0.175903	−	0.175903i	−0.613664	−	0.789567i	$-0.710305\pi$
$109$	1.83648	−	1.83648i	0.175903	−	0.175903i	0.789567	+	0.613664i	$0.210305\pi$
$110$	4.11363	−	2.44267i	0.392219	−	0.232900i
$111$	−6.84268	+	1.83349i	−0.649478	+	0.174027i
$112$	−18.3404	+	5.89110i	−1.73301	+	0.556657i
$113$	−9.71582	+	16.8283i	−0.913987	+	1.58307i	−0.105609	+	0.994408i	$0.533679\pi$
$113$	−9.71582	+	16.8283i	−0.913987	+	1.58307i	−0.808378	+	0.588664i	$0.799654\pi$
$114$	−0.647097	−	0.631435i	−0.0606062	−	0.0591393i
$115$	−1.13307	−	0.303606i	−0.105660	−	0.0283114i
$116$	−9.59406	+	5.85710i	−0.890786	+	0.543818i
$117$	−3.45943	−	1.01605i	−0.319824	−	0.0939339i
$118$	−3.12846	−	11.1285i	−0.287998	−	1.02446i
$119$	4.92981	+	1.32094i	0.451915	+	0.121090i
$120$	−1.57365	−	0.360253i	−0.143654	−	0.0328864i
$121$	20.8972	+	12.0650i	1.89975	+	1.09682i
$122$	7.54981	+	4.23644i	0.683528	+	0.383549i
$123$	5.12996	−	1.37457i	0.462553	−	0.123941i
$124$	4.97219	−	5.22199i	0.446516	−	0.468949i
$125$	3.90442	+	3.90442i	0.349222	+	0.349222i
$126$	−1.68200	+	6.59966i	−0.149845	+	0.587944i
$127$	6.86367	+	11.8882i	0.609053	+	1.05491i	0.991397	+	0.130890i	$0.0417835\pi$
$127$	6.86367	+	11.8882i	0.609053	+	1.05491i	−0.382344	+	0.924020i	$0.624883\pi$
$128$	−11.2721	+	0.968947i	−0.996326	+	0.0856436i
$129$		−	9.90979i		−	0.872509i
$130$	−2.50334	−	1.48436i	−0.219557	−	0.130187i
$131$	−5.90363			−0.515802			−0.257901	−	0.966171i	$-0.583031\pi$
$131$	−5.90363			−0.515802			−0.257901	+	0.966171i	$0.583031\pi$
$132$	−3.34765	−	11.3716i	−0.291375	−	0.989771i
$133$	−2.66635	+	1.53942i	−0.231202	+	0.133484i
$134$	2.79114	−	10.9516i	0.241117	−	0.946070i
$135$	−0.403590	+	0.403590i	−0.0347355	+	0.0347355i
$136$	2.64923	+	1.40236i	0.227169	+	0.120252i
$137$	−4.50130	−	16.7991i	−0.384572	−	1.43524i	−0.838840	−	0.544378i	$-0.816766\pi$
$137$	−4.50130	−	16.7991i	−0.384572	−	1.43524i	0.454268	−	0.890865i	$-0.349901\pi$
$138$	−1.42232	+	2.53474i	−0.121076	+	0.215771i
$139$	−7.04702	+	12.2058i	−0.597721	+	1.03528i	0.395436	+	0.918494i	$0.370594\pi$
$139$	−7.04702	+	12.2058i	−0.597721	+	1.03528i	−0.993157	+	0.116789i	$0.962740\pi$
$140$	−2.63125	+	4.82679i	−0.222381	+	0.407939i
$141$	−2.16785	+	8.09054i	−0.182566	+	0.681346i
$142$	0.167299	+	0.595110i	0.0140394	+	0.0499405i
$143$	0.510104	−	21.3642i	0.0426570	−	1.78657i
$144$	−1.82793	+	3.55790i	−0.152327	+	0.296492i
$145$	−0.830256	+	3.09856i	−0.0689490	+	0.257321i
$146$	−10.2596	+	10.5141i	−0.849089	+	0.870150i
$147$	14.0230	+	8.09616i	1.15659	+	0.667760i
$148$	−3.33063	+	13.7711i	−0.273776	+	1.13198i
$149$	−2.88789	−	10.7777i	−0.236585	−	0.882947i	−0.977428	−	0.211269i	$-0.932240\pi$
$149$	−2.88789	−	10.7777i	−0.236585	−	0.882947i	0.740843	−	0.671678i	$-0.234426\pi$
$150$	5.68382	−	3.37506i	0.464082	−	0.275572i
$151$	8.18475	+	8.18475i	0.666066	+	0.666066i	0.956803	−	0.290737i	$-0.0939006\pi$
$151$	8.18475	+	8.18475i	0.666066	+	0.666066i	−0.290737	+	0.956803i	$0.593901\pi$
$152$	−1.72826	+	0.531868i	−0.140181	+	0.0431402i
$153$	0.917794	−	0.529889i	0.0741993	−	0.0428390i
$154$	−40.3640	+	0.494476i	−3.25262	+	0.0398460i
$155$		−	2.05775i		−	0.165283i
$156$	−5.09582	+	5.10222i	−0.407992	+	0.408504i
$157$		−	19.5674i		−	1.56165i	−0.624750	−	0.780825i	$-0.714799\pi$
$157$		−	19.5674i		−	1.56165i	0.624750	−	0.780825i	$-0.285201\pi$
$158$	0.124876	+	10.1936i	0.00993463	+	0.810962i
$159$	−1.03556	+	0.597883i	−0.0821255	+	0.0474152i
$160$	−2.13902	+	2.41852i	−0.169104	+	0.191200i
$161$	6.99869	+	6.99869i	0.551574	+	0.551574i
$162$	0.722056	+	1.21599i	0.0567301	+	0.0955373i
$163$	−1.63834	−	6.11436i	−0.128325	−	0.478914i	0.871612	−	0.490197i	$-0.163075\pi$
$163$	−1.63834	−	6.11436i	−0.128325	−	0.478914i	−0.999936	+	0.0112829i	$0.996408\pi$
$164$	2.49697	−	10.3242i	0.194981	−	0.806184i
$165$	−2.92971	−	1.69147i	−0.228078	−	0.131681i
$166$	−11.1613	−	10.8912i	−0.866286	−	0.845318i
$167$	−1.29517	+	4.83364i	−0.100223	+	0.374039i	−0.997760	−	0.0669022i	$-0.978688\pi$
$167$	−1.29517	+	4.83364i	−0.100223	+	0.374039i	0.897536	+	0.440941i	$0.145355\pi$
$168$	9.97906	+	9.27130i	0.769901	+	0.715296i
$169$	−11.5557	+	5.95528i	−0.888901	+	0.458098i
$170$	0.823509	−	0.231507i	0.0631602	−	0.0177558i
$171$	−0.165467	+	0.617530i	−0.0126535	+	0.0472237i
$172$	−17.4019	−	9.48634i	−1.32688	−	0.723327i
$173$	−6.02967	+	10.4437i	−0.458427	+	0.794019i	−0.998878	−	0.0473563i	$-0.984920\pi$
$173$	−6.02967	+	10.4437i	−0.458427	+	0.794019i	0.540451	+	0.841376i	$0.318254\pi$
$174$	6.93161	+	3.88954i	0.525484	+	0.294865i
$175$	−5.82611	−	21.7433i	−0.440412	−	1.64364i
$176$	−23.1735	−	5.00713i	−1.74677	−	0.377426i
$177$	−5.77992	+	5.77992i	−0.434445	+	0.434445i
$178$	1.00499	+	0.256134i	0.0753273	+	0.0191981i
$179$	−15.2086	+	8.78071i	−1.13675	+	0.656301i	−0.945623	−	0.325265i	$-0.894546\pi$
$179$	−15.2086	+	8.78071i	−1.13675	+	0.656301i	−0.191123	+	0.981566i	$0.561213\pi$
$180$	0.322371	+	1.09506i	0.0240281	+	0.0816209i
$181$	−7.03736			−0.523083			−0.261541	−	0.965192i	$-0.584231\pi$
$181$	−7.03736			−0.523083			−0.261541	+	0.965192i	$0.584231\pi$
$182$	12.0300	+	21.4074i	0.891727	+	1.58682i
$183$		−	6.12156i		−	0.452519i
$184$	3.08953	+	4.92406i	0.227763	+	0.363007i
$185$	2.02166	+	3.50161i	0.148635	+	0.257444i
$186$	−4.94068	−	1.25919i	−0.362268	−	0.0923285i
$187$	4.44160	+	4.44160i	0.324802	+	0.324802i
$188$	12.1320	+	11.5516i	0.884817	+	0.842490i
$189$	4.65174	−	1.24643i	0.338365	−	0.0906645i
$190$	−0.252527	+	0.450032i	−0.0183202	+	0.0326488i
$191$	17.8511	+	10.3063i	1.29166	+	0.745740i	0.978948	−	0.204108i	$-0.0654295\pi$
$191$	17.8511	+	10.3063i	1.29166	+	0.745740i	0.312711	+	0.949848i	$0.398763\pi$
$192$	4.49796	+	6.61577i	0.324612	+	0.477452i
$193$	−4.18310	−	1.12086i	−0.301106	−	0.0806812i	0.105103	−	0.994461i	$-0.466483\pi$
$193$	−4.18310	−	1.12086i	−0.301106	−	0.0806812i	−0.406209	+	0.913780i	$0.633150\pi$
$194$	6.32477	−	1.77803i	0.454092	−	0.127655i
$195$	−0.0491218	+	2.05733i	−0.00351769	+	0.147328i
$196$	27.6408	−	16.8745i	1.97435	−	1.20532i
$197$	−10.2512	−	2.74681i	−0.730370	−	0.195702i	−0.125576	−	0.992084i	$-0.540078\pi$
$197$	−10.2512	−	2.74681i	−0.730370	−	0.195702i	−0.604794	+	0.796382i	$0.706745\pi$
$198$	−5.85401	+	5.99922i	−0.416027	+	0.426346i
$199$	12.0604	−	20.8892i	0.854937	−	1.48079i	−0.0217665	−	0.999763i	$-0.506929\pi$
$199$	12.0604	−	20.8892i	0.854937	−	1.48079i	0.876703	−	0.481031i	$-0.159738\pi$
$200$	−0.485745	−	13.2118i	−0.0343473	−	0.934215i
$201$	−7.71916	+	2.06834i	−0.544467	+	0.145890i
$202$	2.94081	+	4.95252i	0.206915	+	0.348458i
$203$	19.1389	−	19.1389i	1.34329	−	1.34329i
$204$	−0.0519231	−	2.11892i	−0.00363534	−	0.148354i
$205$	−1.51564	−	2.62516i	−0.105857	−	0.183349i
$206$	−0.632843	+	0.00775259i	−0.0440922	+	0.000540149i
$207$	2.05523			0.142848
$208$	4.08157	+	13.8326i	0.283006	+	0.959118i
$209$	−3.78925			−0.262108
$210$	3.88696	−	0.0476169i	0.268226	−	0.00328588i
$211$	−7.25156	−	12.5601i	−0.499218	−	0.864671i	0.500782	−	0.865574i	$-0.333046\pi$
$211$	−7.25156	−	12.5601i	−0.499218	−	0.864671i	−1.00000		0.000902928i	$0.999713\pi$
$212$	0.0585857	+	2.39081i	0.00402369	+	0.164202i
$213$	0.309089	−	0.309089i	0.0211784	−	0.0211784i
$214$	−5.30950	−	8.94156i	−0.362950	−	0.611232i
$215$	−5.46341	+	1.46392i	−0.372601	+	0.0998382i
$216$	2.82652	−	0.103920i	0.192320	−	0.00707084i
$217$	−8.68120	+	15.0363i	−0.589318	+	1.02073i
$218$	−2.56517	+	2.62880i	−0.173735	+	0.178044i
$219$	10.0336	+	2.68851i	0.678011	+	0.181673i
$220$	−5.77480	+	3.52547i	−0.389337	+	0.237687i
$221$	1.07679	−	3.66622i	0.0724325	−	0.246617i
$222$	9.64452	−	2.71129i	0.647298	−	0.181970i
$223$	−23.4642	−	6.28722i	−1.57128	−	0.421024i	−0.635068	−	0.772456i	$-0.719028\pi$
$223$	−23.4642	−	6.28722i	−1.57128	−	0.421024i	−0.936213	+	0.351432i	$0.885695\pi$
$224$	25.8333	−	8.64837i	1.72606	−	0.577844i
$225$	−4.04800	−	2.33712i	−0.269867	−	0.155808i
$226$	13.4477	−	23.9653i	0.894527	−	1.59415i
$227$	19.5131	−	5.22852i	1.29513	−	0.347029i	0.455524	−	0.890224i	$-0.349452\pi$
$227$	19.5131	−	5.22852i	1.29513	−	0.347029i	0.839607	+	0.543195i	$0.182785\pi$
$228$	0.926004	+	0.881707i	0.0613261	+	0.0583924i
$229$	−0.537694	−	0.537694i	−0.0355318	−	0.0355318i	0.689118	−	0.724649i	$-0.257998\pi$
$229$	−0.537694	−	0.537694i	−0.0355318	−	0.0355318i	−0.724649	+	0.689118i	$0.757998\pi$
$230$	1.60755	+	0.409703i	0.105999	+	0.0270150i
$231$	14.2719	+	24.7196i	0.939021	+	1.62643i
$232$	13.4656	−	8.44877i	0.884058	−	0.554689i
$233$		−	5.06336i		−	0.331712i	−0.986150	−	0.165856i	$-0.946961\pi$
$233$		−	5.06336i		−	0.331712i	0.986150	−	0.165856i	$-0.0530387\pi$
$234$	4.90960	+	1.37688i	0.320951	+	0.0900092i
$235$	4.78067			0.311857
$236$	4.61676	+	15.6826i	0.300525	+	1.02085i
$237$	6.24277	−	3.60426i	0.405511	−	0.234122i
$238$	−6.99417	−	1.78255i	−0.453365	−	0.115546i
$239$	−20.1780	+	20.1780i	−1.30521	+	1.30521i	−0.380376	+	0.924832i	$0.624205\pi$
$239$	−20.1780	+	20.1780i	−1.30521	+	1.30521i	−0.924832	+	0.380376i	$0.875795\pi$
$240$	2.23155	+	0.482175i	0.144046	+	0.0311242i
$241$	3.50678	+	13.0875i	0.225891	+	0.843038i	0.982045	+	0.188645i	$0.0604094\pi$
$241$	3.50678	+	13.0875i	0.225891	+	0.843038i	−0.756154	+	0.654394i	$0.772924\pi$
$242$	−29.7599	−	16.6992i	−1.91304	−	1.07347i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−10.7496	−	5.85999i	−0.688175	−	0.375147i
$245$	2.39200	−	8.92705i	0.152819	−	0.570328i
$246$	−7.23051	+	2.03266i	−0.461000	+	0.129597i
$247$	1.10456	+	2.02320i	0.0702815	+	0.128733i
$248$	−6.94074	+	7.47059i	−0.440738	+	0.474383i
$249$	−2.85401	+	10.6513i	−0.180866	+	0.675000i
$250$	−5.58891	−	5.45363i	−0.353474	−	0.344918i
$251$	14.5185	+	8.38225i	0.916398	+	0.529083i	0.882484	−	0.470342i	$-0.155869\pi$
$251$	14.5185	+	8.38225i	0.916398	+	0.529083i	0.0339142	+	0.999425i	$0.489203\pi$
$252$	2.26421	−	9.36177i	0.142632	−	0.589736i
$253$	3.15279	+	11.7664i	0.198214	+	0.739745i
$254$	−9.91192	−	16.6923i	−0.621929	−	1.04737i
$255$	−0.427715	−	0.427715i	−0.0267846	−	0.0267846i
$256$	15.9232	−	1.56547i	0.995202	−	0.0978417i
$257$	−7.66304	+	4.42426i	−0.478007	+	0.275978i	−0.719586	−	0.694404i	$-0.755668\pi$
$257$	−7.66304	+	4.42426i	−0.478007	+	0.275978i	0.241578	+	0.970381i	$0.422335\pi$
$258$	0.171671	+	14.0135i	0.0106878	+	0.872443i
$259$		−	34.1157i		−	2.11985i
$260$	3.56570	+	2.05568i	0.221135	+	0.127488i
$261$		−	5.62031i		−	0.347889i
$262$	8.34836	−	0.102271i	0.515763	−	0.00631832i
$263$	5.49660	−	3.17346i	0.338935	−	0.195684i	−0.320866	−	0.947125i	$-0.603974\pi$
$263$	5.49660	−	3.17346i	0.338935	−	0.195684i	0.659801	+	0.751440i	$0.270641\pi$
$264$	4.93093	+	16.0227i	0.303478	+	0.986128i
$265$	0.482599	+	0.482599i	0.0296458	+	0.0296458i
$266$	3.74384	−	2.22309i	0.229549	−	0.136306i
$267$	−0.189806	−	0.708365i	−0.0116159	−	0.0433512i
$268$	−3.75725	+	15.5350i	−0.229510	+	0.948952i
$269$	5.51917	+	3.18649i	0.336509	+	0.194284i	0.658727	−	0.752382i	$-0.271095\pi$
$269$	5.51917	+	3.18649i	0.336509	+	0.194284i	−0.322218	+	0.946666i	$0.604428\pi$
$270$	0.563728	−	0.577711i	0.0343074	−	0.0351584i
$271$	−2.27246	+	8.48094i	−0.138042	+	0.515181i	0.861925	+	0.507036i	$0.169259\pi$
$271$	−2.27246	+	8.48094i	−0.138042	+	0.515181i	−0.999967	+	0.00814415i	$0.997408\pi$
$272$	−3.77058	−	1.93720i	−0.228625	−	0.117460i
$273$	9.03835	−	14.8259i	0.547026	−	0.897307i
$274$	6.65634	+	23.6777i	0.402124	+	1.43042i
$275$	7.17044	−	26.7604i	0.432394	−	1.61372i
$276$	1.96740	−	3.60903i	0.118424	−	0.217238i
$277$	−3.44140	+	5.96068i	−0.206774	+	0.358143i	−0.950696	−	0.310123i	$-0.899630\pi$
$277$	−3.44140	+	5.96068i	−0.206774	+	0.358143i	0.743923	+	0.668266i	$0.232963\pi$
$278$	9.75380	−	17.3824i	0.584994	−	1.04253i
$279$	0.933112	+	3.48242i	0.0558639	+	0.208487i
$280$	3.63725	−	6.87119i	0.217367	−	0.410632i
$281$	1.24628	−	1.24628i	0.0743466	−	0.0743466i	−0.668956	−	0.743302i	$-0.733258\pi$
$281$	1.24628	−	1.24628i	0.0743466	−	0.0743466i	0.743302	+	0.668956i	$0.233258\pi$
$282$	2.92542	−	11.4784i	0.174206	−	0.683531i
$283$	11.6080	−	6.70190i	0.690025	−	0.398386i	−0.113596	−	0.993527i	$-0.536237\pi$
$283$	11.6080	−	6.70190i	0.690025	−	0.398386i	0.803622	+	0.595141i	$0.202904\pi$
$284$	−0.246888	−	0.838651i	−0.0146501	−	0.0497648i
$285$	0.364896			0.0216146
$286$	−0.351240	+	30.2202i	−0.0207693	+	1.78696i
$287$			25.5766i			1.50974i
$288$	2.52325	−	5.06292i	0.148684	−	0.298336i
$289$	−7.93844	−	13.7498i	−0.466967	−	0.808810i
$290$	1.12039	−	4.39607i	0.0657918	−	0.258146i
$291$	−3.28497	−	3.28497i	−0.192568	−	0.192568i
$292$	14.3260	−	15.0457i	0.838366	−	0.880486i
$293$	−22.6215	+	6.06142i	−1.32156	+	0.354112i	−0.849563	−	0.527486i	$-0.823135\pi$
$293$	−22.6215	+	6.06142i	−1.32156	+	0.354112i	−0.472000	+	0.881598i	$0.656468\pi$
$294$	−19.9702	−	11.2059i	−1.16469	−	0.653542i
$295$	4.04038	+	2.33272i	0.235240	+	0.135816i
$296$	4.47130	−	19.5315i	0.259889	−	1.13524i
$297$	5.72510	+	1.53404i	0.332204	+	0.0890138i
$298$	4.27049	+	15.1909i	0.247383	+	0.879983i
$299$	5.36340	−	5.11325i	0.310173	−	0.295707i
$300$	−7.97907	+	4.87116i	−0.460672	+	0.281236i
$301$	46.0978	+	12.3519i	2.65703	+	0.711950i
$302$	−11.7159	−	11.4323i	−0.674175	−	0.657857i
$303$	2.03641	−	3.52717i	0.116989	−	0.202631i
$304$	2.43474	−	0.782058i	0.139642	−	0.0448541i
$305$	−3.37490	+	0.904303i	−0.193246	+	0.0517802i
$306$	−1.28868	+	0.765219i	−0.0736689	+	0.0437446i
$307$	−21.1986	+	21.1986i	−1.20987	+	1.20987i	−0.238798	+	0.971069i	$0.576753\pi$
$307$	−21.1986	+	21.1986i	−1.20987	+	1.20987i	−0.971069	+	0.238798i	$0.923247\pi$
$308$	57.0704	−	1.39848i	3.25189	−	0.0796860i
$309$	0.223760	+	0.387565i	0.0127293	+	0.0220478i
$310$	0.0356473	+	2.90988i	0.00202463	+	0.165270i
$311$	−23.6077			−1.33867			−0.669335	−	0.742961i	$-0.733421\pi$
$311$	−23.6077			−1.33867			−0.669335	+	0.742961i	$0.733421\pi$
$312$	7.11765	−	7.30336i	0.402957	−	0.413471i
$313$	−1.67315			−0.0945720			−0.0472860	−	0.998881i	$-0.515057\pi$
$313$	−1.67315			−0.0945720			−0.0472860	+	0.998881i	$0.515057\pi$
$314$	0.338974	+	27.6704i	0.0191294	+	1.56153i
$315$	−1.37435	−	2.38044i	−0.0774359	−	0.134123i
$316$	−0.353177	−	14.4127i	−0.0198678	−	0.810779i
$317$	1.99292	−	1.99292i	0.111933	−	0.111933i	−0.648922	−	0.760855i	$-0.724780\pi$
$317$	1.99292	−	1.99292i	0.111933	−	0.111933i	0.760855	+	0.648922i	$0.224780\pi$
$318$	1.45404	−	0.863410i	0.0815385	−	0.0484176i
$319$	32.1768	−	8.62176i	1.80156	−	0.482726i
$320$	2.98291	−	3.45710i	0.166750	−	0.193258i
$321$	−3.67665	+	6.36815i	−0.205211	+	0.355436i
$322$	−10.0181	−	9.77565i	−0.558289	−	0.544776i
$323$	−0.654444	−	0.175358i	−0.0364142	−	0.00975717i
$324$	−1.04213	−	1.70703i	−0.0578961	−	0.0948352i
$325$	−16.3784	+	3.97211i	−0.908510	+	0.220333i
$326$	2.42271	+	8.61799i	0.134181	+	0.477306i
$327$	2.50868	+	0.672199i	0.138730	+	0.0371727i
$328$	−3.35214	+	14.6428i	−0.185091	+	0.808512i
$329$	−34.9330	−	20.1686i	−1.92592	−	1.11193i
$330$	4.17223	+	2.34117i	0.229674	+	0.128877i
$331$	−5.44493	+	1.45897i	−0.299281	+	0.0801920i	−0.405335	−	0.914168i	$-0.632845\pi$
$331$	−5.44493	+	1.45897i	−0.299281	+	0.0801920i	0.106054	+	0.994360i	$0.466178\pi$
$332$	15.9720	+	15.2079i	0.876575	+	0.834643i
$333$	−5.00919	−	5.00919i	−0.274502	−	0.274502i
$334$	1.74778	−	6.85773i	0.0956340	−	0.375238i
$335$	2.28061	+	3.95014i	0.124603	+	0.215819i
$336$	−14.2721	−	12.9377i	−0.778605	−	0.705812i
$337$			9.98987i			0.544183i	0.962271	+	0.272091i	$0.0877153\pi$
$337$			9.98987i			0.544183i	−0.962271	+	0.272091i	$0.912285\pi$
$338$	16.2379	−	8.62159i	0.883223	−	0.468953i
$339$	−19.4316			−1.05538
$340$	−1.16052	+	0.341641i	−0.0629380	+	0.0185281i
$341$	−18.5058	+	10.6843i	−1.00214	+	0.578588i
$342$	0.223290	−	0.876120i	0.0120741	−	0.0473751i
$343$	−31.3027	+	31.3027i	−1.69019	+	1.69019i
$344$	24.7725	+	13.1132i	1.33564	+	0.707019i
$345$	−0.303606	−	1.13307i	−0.0163456	−	0.0610027i
$346$	8.34568	−	14.8730i	0.448666	−	0.799575i
$347$	−11.8582	+	20.5391i	−0.636584	+	1.10260i	0.349594	+	0.936901i	$0.386320\pi$
$347$	−11.8582	+	20.5391i	−0.636584	+	1.10260i	−0.986177	+	0.165694i	$0.947014\pi$
$348$	−9.86942	−	5.38015i	−0.529057	−	0.288406i
$349$	−5.11905	+	19.1046i	−0.274017	+	1.02264i	0.682481	+	0.730903i	$0.260901\pi$
$349$	−5.11905	+	19.1046i	−0.274017	+	1.02264i	−0.956498	+	0.291740i	$0.905766\pi$
$350$	8.61541	+	30.6465i	0.460513	+	1.63812i
$351$	−0.849788	−	3.50398i	−0.0453584	−	0.187028i
$352$	32.8565	+	6.67917i	1.75126	+	0.356001i
$353$	2.87468	−	10.7284i	0.153004	−	0.571017i	−0.846264	−	0.532763i	$-0.821154\pi$
$353$	2.87468	−	10.7284i	0.153004	−	0.571017i	0.999268	−	0.0382541i	$-0.0121796\pi$
$354$	8.07330	−	8.27355i	0.429091	−	0.439734i
$355$	−0.216065	−	0.124745i	−0.0114675	−	0.00662079i
$356$	−1.42560	−	0.344792i	−0.0755569	−	0.0182739i
$357$	1.32094	+	4.92981i	0.0699115	+	0.260913i
$358$	21.3545	−	12.6803i	1.12862	−	0.670176i
$359$	−10.0901	−	10.0901i	−0.532537	−	0.532537i	0.388790	−	0.921327i	$-0.372893\pi$
$359$	−10.0901	−	10.0901i	−0.532537	−	0.532537i	−0.921327	+	0.388790i	$0.872893\pi$
$360$	−0.474837	−	1.54295i	−0.0250261	−	0.0813205i
$361$	−16.1005	+	9.29564i	−0.847396	+	0.489244i
$362$	9.95158	−	0.121911i	0.523043	−	0.00640750i
$363$			24.1300i			1.26650i
$364$	−17.3826	−	30.0640i	−0.911097	−	1.57578i
$365$		−	5.92885i		−	0.310330i
$366$	0.106046	+	8.65655i	0.00554313	+	0.452485i
$367$	5.69564	−	3.28838i	0.297310	−	0.171652i	−0.343924	−	0.938997i	$-0.611756\pi$
$367$	5.69564	−	3.28838i	0.297310	−	0.171652i	0.641234	+	0.767346i	$0.278423\pi$
$368$	−4.45423	−	6.90964i	−0.232193	−	0.360190i
$369$	3.75539	+	3.75539i	0.195498	+	0.195498i
$370$	−2.91950	−	4.91664i	−0.151778	−	0.255604i
$371$	−1.49044	−	5.56240i	−0.0773798	−	0.288785i
$372$	7.00847	+	1.69504i	0.363372	+	0.0878840i
$373$	−7.36621	−	4.25288i	−0.381408	−	0.220206i	0.297023	−	0.954870i	$-0.404006\pi$
$373$	−7.36621	−	4.25288i	−0.381408	−	0.220206i	−0.678431	+	0.734665i	$0.737340\pi$
$374$	−6.35784	−	6.20395i	−0.328756	−	0.320799i
$375$	−1.42912	+	5.33354i	−0.0737993	+	0.275423i
$376$	−17.3561	−	16.1251i	−0.895070	−	0.831588i
$377$	−13.9829	−	14.6670i	−0.720157	−	0.755388i
$378$	−6.55647	+	1.84317i	−0.337229	+	0.0948025i
$379$	4.52705	−	16.8952i	0.232539	−	0.867847i	−0.746704	−	0.665156i	$-0.768365\pi$
$379$	4.52705	−	16.8952i	0.232539	−	0.867847i	0.979243	−	0.202690i	$-0.0649685\pi$
$380$	0.349304	−	0.640768i	0.0179189	−	0.0328707i
$381$	−6.86367	+	11.8882i	−0.351637	+	0.609053i
$382$	−25.4219	−	14.2650i	−1.30070	−	0.729862i
$383$	−2.58315	−	9.64043i	−0.131993	−	0.492603i	0.868000	−	0.496565i	$-0.165406\pi$
$383$	−2.58315	−	9.64043i	−0.131993	−	0.492603i	−0.999992	+	0.00396183i	$0.998739\pi$
$384$	−6.47520	−	9.27749i	−0.330436	−	0.473440i
$385$	11.5200	−	11.5200i	0.587113	−	0.587113i
$386$	5.93478	+	1.51255i	0.302072	+	0.0769868i
$387$	8.58213	−	4.95490i	0.436254	−	0.251872i
$388$	−8.91310	+	2.62390i	−0.452494	+	0.133208i
$389$	−0.803809			−0.0407547			−0.0203774	−	0.999792i	$-0.506487\pi$
$389$	−0.803809			−0.0407547			−0.0203774	+	0.999792i	$0.506487\pi$
$390$	0.0338236	−	2.91013i	0.00171273	−	0.147360i
$391$			2.17808i			0.110150i
$392$	−38.7948	+	24.3412i	−1.95943	+	1.22942i
$393$	−2.95181	−	5.11269i	−0.148899	−	0.257901i
$394$	14.5439	+	3.70670i	0.732713	+	0.186741i
$395$	−2.90929	−	2.90929i	−0.146382	−	0.146382i
$396$	8.17428	−	8.58495i	0.410773	−	0.431410i
$397$	−1.17900	+	0.315913i	−0.0591725	+	0.0158552i	−0.288284	−	0.957545i	$-0.593085\pi$
$397$	−1.17900	+	0.315913i	−0.0591725	+	0.0158552i	0.229111	+	0.973400i	$0.426418\pi$
$398$	−16.6928	+	29.7485i	−0.836734	+	1.49116i
$399$	−2.66635	−	1.53942i	−0.133484	−	0.0770672i
$400$	0.915768	+	18.6745i	0.0457884	+	0.933724i
$401$	−4.73196	−	1.26792i	−0.236303	−	0.0633171i	0.138724	−	0.990331i	$-0.455700\pi$
$401$	−4.73196	−	1.26792i	−0.236303	−	0.0633171i	−0.375027	+	0.927014i	$0.622367\pi$
$402$	10.8799	−	3.05858i	0.542640	−	0.152548i
$403$	11.0991	+	6.76635i	0.552885	+	0.337056i
$404$	−4.24441	−	6.95245i	−0.211167	−	0.345897i
$405$	−0.551314	−	0.147724i	−0.0273950	−	0.00734047i
$406$	−26.7329	+	27.3960i	−1.32673	+	1.35964i
$407$	20.9938	−	36.3624i	1.04063	−	1.80242i
$408$	0.110132	+	2.99548i	0.00545233	+	0.148298i
$409$	13.7141	−	3.67467i	0.678117	−	0.181701i	0.0967086	−	0.995313i	$-0.469169\pi$
$409$	13.7141	−	3.67467i	0.678117	−	0.181701i	0.581408	+	0.813612i	$0.302502\pi$
$410$	2.18875	+	3.68601i	0.108095	+	0.182039i
$411$	12.2978	−	12.2978i	0.606605	−	0.606605i
$412$	0.894773	−	0.0219260i	0.0440823	−	0.00108022i
$413$	−19.6824	−	34.0910i	−0.968509	−	1.67751i
$414$	−2.90631	+	0.0356035i	−0.142837	+	0.00174982i
$415$	6.29383			0.308952
$416$	−6.01140	−	19.4901i	−0.294733	−	0.955580i
$417$	−14.0940			−0.690189
$418$	5.35841	−	0.0656428i	0.262088	−	0.00321069i
$419$	−2.36107	−	4.08949i	−0.115346	−	0.199785i	0.802572	−	0.596555i	$-0.203464\pi$
$419$	−2.36107	−	4.08949i	−0.115346	−	0.199785i	−0.917918	+	0.396770i	$0.870131\pi$
$420$	−5.49575	+	0.134671i	−0.268165	+	0.00657126i
$421$	−4.38018	+	4.38018i	−0.213477	+	0.213477i	−0.805743	−	0.592266i	$-0.798234\pi$
$421$	−4.38018	+	4.38018i	−0.213477	+	0.213477i	0.592266	+	0.805743i	$0.298234\pi$
$422$	10.4721	+	17.6357i	0.509772	+	0.858491i
$423$	−8.09054	+	2.16785i	−0.393375	+	0.105405i
$424$	−0.124264	−	3.37985i	−0.00603477	−	0.164140i
$425$	2.47682	−	4.28998i	0.120143	−	0.208095i
$426$	−0.431731	+	0.442440i	−0.0209174	+	0.0214363i
$427$	28.4759	+	7.63011i	1.37805	+	0.369247i
$428$	7.66310	+	12.5523i	0.370410	+	0.606740i
$429$	18.7570	−	10.2404i	0.905597	−	0.494409i
$430$	7.70049	−	2.16478i	0.371350	−	0.104395i
$431$	−2.21278	−	0.592912i	−0.106586	−	0.0285596i	0.205132	−	0.978734i	$-0.434238\pi$
$431$	−2.21278	−	0.592912i	−0.106586	−	0.0285596i	−0.311718	+	0.950175i	$0.600904\pi$
$432$	−3.99520	+	0.195919i	−0.192219	+	0.00942614i
$433$	13.9535	+	8.05603i	0.670560	+	0.387148i	0.796289	−	0.604917i	$-0.206794\pi$
$433$	13.9535	+	8.05603i	0.670560	+	0.387148i	−0.125729	+	0.992065i	$0.540127\pi$
$434$	12.0157	−	21.4133i	0.576770	−	1.02787i
$435$	−3.09856	+	0.830256i	−0.148564	+	0.0398077i
$436$	3.58188	−	3.76184i	0.171541	−	0.180159i
$437$	−0.929092	−	0.929092i	−0.0444445	−	0.0444445i
$438$	−14.2352	−	3.62802i	−0.680186	−	0.173354i
$439$	10.1992	+	17.6656i	0.486783	+	0.843133i	0.999885	−	0.0151950i	$-0.00483691\pi$
$439$	10.1992	+	17.6656i	0.486783	+	0.843133i	−0.513102	+	0.858328i	$0.671504\pi$
$440$	8.10511	−	5.08543i	0.386396	−	0.242438i
$441$			16.1923i			0.771063i
$442$	−1.45918	+	5.20309i	−0.0694062	+	0.247486i
$443$	4.48358			0.213021			0.106511	−	0.994312i	$-0.466032\pi$
$443$	4.48358			0.213021			0.106511	+	0.994312i	$0.466032\pi$
$444$	−13.5914	+	4.00113i	−0.645020	+	0.189885i
$445$	−0.362493	+	0.209285i	−0.0171838	+	0.00992107i
$446$	33.2899	+	8.48433i	1.57632	+	0.401745i
$447$	7.88986	−	7.88986i	0.373177	−	0.373177i
$448$	−36.3813	+	12.6773i	−1.71885	+	0.598944i
$449$	3.28057	+	12.2433i	0.154820	+	0.577795i	0.999121	+	0.0419259i	$0.0133493\pi$
$449$	3.28057	+	12.2433i	0.154820	+	0.577795i	−0.844301	+	0.535869i	$0.819984\pi$
$450$	5.76480	+	3.23481i	0.271755	+	0.152490i
$451$	−15.7391	+	27.2609i	−0.741125	+	1.28367i
$452$	−18.6013	+	34.1225i	−0.874932	+	1.60499i
$453$	−2.99583	+	11.1806i	−0.140756	+	0.525309i
$454$	−27.5031	+	7.73172i	−1.29078	+	0.362868i
$455$	−9.50893	−	2.79282i	−0.445786	−	0.130929i
$456$	−1.32474	−	1.23079i	−0.0620368	−	0.0576369i
$457$	6.68865	−	24.9624i	0.312882	−	1.16769i	−0.613064	−	0.790033i	$-0.710063\pi$
$457$	6.68865	−	24.9624i	0.312882	−	1.16769i	0.925946	−	0.377657i	$-0.123270\pi$
$458$	0.769671	+	0.751042i	0.0359644	+	0.0350939i
$459$	0.917794	+	0.529889i	0.0428390	+	0.0247331i
$460$	−2.28034	−	0.551516i	−0.106322	−	0.0257146i
$461$	4.57308	+	17.0670i	0.212990	+	0.794888i	0.986865	+	0.161550i	$0.0516491\pi$
$461$	4.57308	+	17.0670i	0.212990	+	0.794888i	−0.773875	+	0.633338i	$0.781684\pi$
$462$	−20.6102	−	34.7090i	−0.958874	−	1.61481i
$463$	0.916082	+	0.916082i	0.0425740	+	0.0425740i	0.728073	−	0.685499i	$-0.240416\pi$
$463$	0.916082	+	0.916082i	0.0425740	+	0.0425740i	−0.685499	+	0.728073i	$0.740416\pi$
$464$	−18.8954	+	12.1807i	−0.877197	+	0.565476i
$465$	1.78206	−	1.02888i	0.0826413	−	0.0477130i
$466$	0.0877147	+	7.16014i	0.00406330	+	0.331687i
$467$		−	1.02377i		−	0.0473745i	−0.999719	−	0.0236872i	$-0.992459\pi$
$467$		−	1.02377i		−	0.0473745i	0.999719	−	0.0236872i	$-0.00754059\pi$
$468$	−6.96656	−	1.86200i	−0.322029	−	0.0860709i
$469$		−	38.4856i		−	1.77710i
$470$	−6.76038	+	0.0828176i	−0.311833	+	0.00382009i
$471$	16.9459	−	9.78370i	0.780825	−	0.450809i
$472$	−6.80027	−	22.0970i	−0.313008	−	1.01709i
$473$	41.5326	+	41.5326i	1.90967	+	1.90967i
$474$	−8.76551	+	5.20496i	−0.402613	+	0.239072i
$475$	0.773429	+	2.88648i	0.0354874	+	0.132441i
$476$	9.92139	+	2.39955i	0.454746	+	0.109983i
$477$	−1.03556	−	0.597883i	−0.0474152	−	0.0273752i
$478$	28.1843	−	28.8834i	1.28912	−	1.32110i
$479$	0.0511532	−	0.190906i	0.00233725	−	0.00872273i	−0.964747	−	0.263178i	$-0.915229\pi$
$479$	0.0511532	−	0.190906i	0.00233725	−	0.00872273i	0.967085	+	0.254455i	$0.0818961\pi$
$480$	−3.16401	−	0.643189i	−0.144416	−	0.0293574i
$481$	−25.5347	−	0.609680i	−1.16428	−	0.0277990i
$482$	−5.18568	−	18.4463i	−0.236201	−	0.840208i
$483$	−2.56170	+	9.56038i	−0.116561	+	0.435012i
$484$	42.3730	+	23.0990i	1.92605	+	1.04995i
$485$	−1.32578	+	2.29632i	−0.0602006	+	0.104270i
$486$	−0.692051	+	1.23331i	−0.0313921	+	0.0559443i
$487$	−2.09884	−	7.83299i	−0.0951077	−	0.354947i	0.901928	−	0.431886i	$-0.142152\pi$
$487$	−2.09884	−	7.83299i	−0.0951077	−	0.354947i	−0.997036	+	0.0769395i	$0.975485\pi$
$488$	15.3027	+	8.10043i	0.692719	+	0.366689i
$489$	4.47602	−	4.47602i	0.202413	−	0.202413i
$490$	−3.22789	+	12.6652i	−0.145821	+	0.572158i
$491$	13.2895	−	7.67272i	0.599748	−	0.346265i	−0.169194	−	0.985583i	$-0.554116\pi$
$491$	13.2895	−	7.67272i	0.599748	−	0.346265i	0.768943	+	0.639318i	$0.220783\pi$
$492$	10.1895	−	2.99965i	0.459378	−	0.135235i
$493$	5.95628			0.268257
$494$	−1.59702	−	2.84189i	−0.0718532	−	0.127863i
$495$		−	3.38294i		−	0.152052i
$496$	9.68554	−	10.6845i	0.434894	−	0.479746i
$497$	1.05255	+	1.82306i	0.0472131	+	0.0817755i
$498$	3.85136	−	15.1116i	0.172584	−	0.677165i
$499$	10.5996	+	10.5996i	0.474502	+	0.474502i	0.903368	−	0.428866i	$-0.141087\pi$
$499$	10.5996	+	10.5996i	0.474502	+	0.474502i	−0.428866	+	0.903368i	$0.641087\pi$
$500$	7.99779	+	7.61521i	0.357672	+	0.340562i
$501$	−4.83364	+	1.29517i	−0.215951	+	0.0578640i
$502$	−20.6759	−	11.6019i	−0.922811	−	0.517818i
$503$	−32.2230	−	18.6039i	−1.43675	−	0.829508i	−0.439128	−	0.898424i	$-0.644713\pi$
$503$	−32.2230	−	18.6039i	−1.43675	−	0.829508i	−0.997622	+	0.0689162i	$0.978046\pi$
$504$	−3.03965	+	13.2778i	−0.135397	+	0.591439i
$505$	−2.24541	−	0.601655i	−0.0999192	−	0.0267733i
$506$	−4.66222	−	16.5843i	−0.207261	−	0.737262i
$507$	−10.9353	−	7.02991i	−0.485653	−	0.312209i
$508$	14.3057	+	23.4330i	0.634712	+	1.03967i
$509$	39.9366	+	10.7010i	1.77016	+	0.474312i	0.988733	−	0.149687i	$-0.0478267\pi$
$509$	39.9366	+	10.7010i	1.77016	+	0.474312i	0.781425	+	0.624000i	$0.214493\pi$
$510$	0.612245	+	0.597426i	0.0271107	+	0.0264545i
$511$	−25.0125	+	43.3229i	−1.10649	+	1.91649i
$512$	−22.4900	+	2.48958i	−0.993929	+	0.110025i
$513$	−0.617530	+	0.165467i	−0.0272646	+	0.00730553i
$514$	10.7597	−	6.38912i	0.474591	−	0.281812i
$515$	0.180615	−	0.180615i	0.00795884	−	0.00795884i
$516$	−0.485524	−	19.8136i	−0.0213740	−	0.872247i
$517$	−24.8224	−	42.9936i	−1.09169	−	1.89086i
$518$	0.591001	+	48.2433i	0.0259671	+	2.11969i
$519$	−12.0593			−0.529346
$520$	−5.07789	−	2.84518i	−0.222680	−	0.124769i
$521$	35.6854			1.56341			0.781703	−	0.623650i	$-0.214351\pi$
$521$	35.6854			1.56341			0.781703	+	0.623650i	$0.214351\pi$
$522$	0.0973630	+	7.94772i	0.00426146	+	0.347862i
$523$	2.52621	+	4.37553i	0.110464	+	0.191328i	0.915957	−	0.401276i	$-0.131433\pi$
$523$	2.52621	+	4.37553i	0.110464	+	0.191328i	−0.805494	+	0.592604i	$0.798100\pi$
$524$	−11.8037	+	0.289244i	−0.515647	+	0.0126357i
$525$	15.9172	−	15.9172i	0.694684	−	0.694684i
$526$	−7.71781	+	4.58284i	−0.336512	+	0.199821i
$527$	−3.69059	+	0.988891i	−0.160765	+	0.0430768i
$528$	−7.25043	−	22.5724i	−0.315535	−	0.982336i
$529$	9.38802	−	16.2605i	0.408175	−	0.706980i
$530$	−0.690807	−	0.674086i	−0.0300067	−	0.0292804i
$531$	−7.89551	−	2.11560i	−0.342636	−	0.0918091i
$532$	−5.25567	+	3.20855i	−0.227862	+	0.139108i
$533$	19.1434	+	0.457077i	0.829191	+	0.0197982i
$534$	0.280677	+	0.998416i	0.0121461	+	0.0432057i
$535$	4.05398	+	1.08626i	0.175269	+	0.0469632i
$536$	5.04403	−	22.0333i	0.217869	−	0.951693i
$537$	−15.2086	−	8.78071i	−0.656301	−	0.378915i
$538$	−7.85989	−	4.41043i	−0.338864	−	0.190147i
$539$	−92.7027	+	24.8396i	−3.99299	+	1.06992i
$540$	−0.787164	+	0.826711i	−0.0338741	+	0.0355760i
$541$	16.2450	+	16.2450i	0.698429	+	0.698429i	0.964072	−	0.265643i	$-0.0855841\pi$
$541$	16.2450	+	16.2450i	0.698429	+	0.698429i	−0.265643	+	0.964072i	$0.585584\pi$
$542$	3.06659	−	12.0323i	0.131721	−	0.516833i
$543$	−3.51868	−	6.09453i	−0.151001	−	0.261541i
$544$	5.36557	+	2.67409i	0.230047	+	0.114651i
$545$		−	1.48237i		−	0.0634978i
$546$	−12.5244	+	21.1220i	−0.535993	+	0.903940i
$547$	−6.47392			−0.276805			−0.138402	−	0.990376i	$-0.544197\pi$
$547$	−6.47392			−0.276805			−0.138402	+	0.990376i	$0.544197\pi$
$548$	−9.82296	−	33.3675i	−0.419616	−	1.42539i
$549$	5.30143	−	3.06078i	0.226259	−	0.130631i
$550$	−9.67619	+	37.9664i	−0.412594	+	1.61889i
$551$	−2.54074	+	2.54074i	−0.108239	+	0.108239i
$552$	−2.71960	+	5.13764i	−0.115754	+	0.218673i
$553$	8.98493	+	33.5322i	0.382078	+	1.42594i
$554$	4.76325	−	8.48866i	0.202371	−	0.360649i
$555$	−2.02166	+	3.50161i	−0.0858146	+	0.148635i
$556$	−13.4918	+	24.7495i	−0.572180	+	1.04961i
$557$	−4.79101	+	17.8803i	−0.203002	+	0.757612i	0.787048	+	0.616892i	$0.211608\pi$
$557$	−4.79101	+	17.8803i	−0.203002	+	0.757612i	−0.990049	+	0.140720i	$0.955058\pi$
$558$	−1.37985	−	4.90835i	−0.0584136	−	0.207787i
$559$	10.0688	−	34.2822i	0.425867	−	1.44998i
$560$	−5.02443	+	9.77961i	−0.212321	+	0.413264i
$561$	−1.62574	+	6.06733i	−0.0686387	+	0.256163i
$562$	−1.74078	+	1.78396i	−0.0734303	+	0.0752517i
$563$	11.7692	+	6.79494i	0.496012	+	0.286373i	0.727065	−	0.686568i	$-0.240884\pi$
$563$	11.7692	+	6.79494i	0.496012	+	0.286373i	−0.231053	+	0.972941i	$0.574217\pi$
$564$	−3.93801	+	16.2824i	−0.165820	+	0.685614i
$565$	2.87052	+	10.7129i	0.120764	+	0.450696i
$566$	−16.2989	+	9.67829i	−0.685094	+	0.406809i
$567$	3.40531	+	3.40531i	0.143010	+	0.143010i
$568$	0.363654	+	1.18167i	0.0152586	+	0.0495816i
$569$	5.17128	−	2.98564i	0.216791	−	0.125164i	−0.387672	−	0.921797i	$-0.626721\pi$
$569$	5.17128	−	2.98564i	0.216791	−	0.125164i	0.604464	+	0.796633i	$0.293387\pi$
$570$	−0.516003	+	0.00632125i	−0.0216130	+	0.000264768i
$571$			7.35140i			0.307647i	0.988098	+	0.153823i	$0.0491587\pi$
$571$			7.35140i			0.307647i	−0.988098	+	0.153823i	$0.950841\pi$
$572$	−0.0268246	−	42.7406i	−0.00112159	−	1.78708i
$573$			20.6127i			0.861106i
$574$	−0.443074	−	36.1680i	−0.0184935	−	1.50962i
$575$	8.31956	−	4.80330i	0.346949	−	0.200311i
$576$	−3.48044	+	7.20323i	−0.145018	+	0.300135i
$577$	8.59954	+	8.59954i	0.358004	+	0.358004i	0.863077	−	0.505073i	$-0.168534\pi$
$577$	8.59954	+	8.59954i	0.358004	+	0.358004i	−0.505073	+	0.863077i	$0.668534\pi$
$578$	11.4640	+	19.3061i	0.476839	+	0.803029i
$579$	−1.12086	−	4.18310i	−0.0465813	−	0.173844i
$580$	−1.50820	+	6.23593i	−0.0626247	+	0.258933i
$581$	−45.9899	−	26.5523i	−1.90798	−	1.10157i
$582$	4.70221	+	4.58839i	0.194913	+	0.190195i
$583$	1.83435	−	6.84588i	0.0759709	−	0.283527i
$584$	−19.9979	+	21.5245i	−0.827518	+	0.890689i
$585$	−1.80626	+	0.986122i	−0.0746796	+	0.0407711i
$586$	31.8843	−	8.96338i	1.31713	−	0.370274i
$587$	5.77087	−	21.5372i	0.238189	−	0.888934i	−0.738496	−	0.674258i	$-0.764464\pi$
$587$	5.77087	−	21.5372i	0.238189	−	0.888934i	0.976685	−	0.214676i	$-0.0688697\pi$
$588$	28.4342	+	15.5004i	1.17261	+	0.639226i
$589$	1.15245	−	1.99610i	0.0474858	−	0.0822479i
$590$	−5.75395	−	3.22872i	−0.236886	−	0.132924i
$591$	−2.74681	−	10.2512i	−0.112989	−	0.421679i
$592$	−5.98455	+	27.6971i	−0.245964	+	1.13834i
$593$	24.9155	−	24.9155i	1.02316	−	1.02316i	0.0234302	−	0.999725i	$-0.492541\pi$
$593$	24.9155	−	24.9155i	1.02316	−	1.02316i	0.999725	−	0.0234302i	$-0.00745874\pi$
$594$	−8.12248	−	2.07011i	−0.333269	−	0.0849378i
$595$	2.52274	−	1.45650i	0.103422	−	0.0597109i
$596$	−6.30209	−	21.4075i	−0.258144	−	0.876887i
$597$	24.1207			0.987196
$598$	−7.49584	+	7.32360i	−0.306528	+	0.299484i
$599$		−	32.0155i		−	1.30812i	−0.756444	−	0.654059i	$-0.773065\pi$
$599$		−	32.0155i		−	1.30812i	0.756444	−	0.654059i	$-0.226935\pi$
$600$	11.1989	−	7.02656i	0.457192	−	0.286858i
$601$	−6.17445	−	10.6945i	−0.251861	−	0.436236i	0.712177	−	0.702000i	$-0.247709\pi$
$601$	−6.17445	−	10.6945i	−0.251861	−	0.436236i	−0.964038	+	0.265764i	$0.914376\pi$
$602$	−65.4013	−	16.6683i	−2.66556	−	0.679349i
$603$	−5.65082	−	5.65082i	−0.230119	−	0.230119i
$604$	16.7656	+	15.9636i	0.682182	+	0.649549i
$605$	13.3032	−	3.56459i	0.540853	−	0.144921i
$606$	−2.81860	+	5.02307i	−0.114498	+	0.204048i
$607$	23.6311	+	13.6435i	0.959159	+	0.553771i	0.895914	−	0.444227i	$-0.146522\pi$
$607$	23.6311	+	13.6435i	0.959159	+	0.553771i	0.0632447	+	0.997998i	$0.479855\pi$
$608$	−3.42943	+	1.14809i	−0.139082	+	0.0465613i
$609$	26.1443	+	7.00533i	1.05942	+	0.283870i
$610$	4.75681	−	1.33725i	0.192598	−	0.0541435i
$611$	−15.7199	+	25.7860i	−0.635960	+	1.04319i
$612$	1.80908	−	1.10443i	0.0731276	−	0.0446438i
$613$	−1.68752	−	0.452170i	−0.0681583	−	0.0182630i	0.224579	−	0.974456i	$-0.427899\pi$
$613$	−1.68752	−	0.452170i	−0.0681583	−	0.0182630i	−0.292737	+	0.956193i	$0.594566\pi$
$614$	29.6098	−	30.3443i	1.19496	−	1.22460i
$615$	1.51564	−	2.62516i	0.0611165	−	0.105857i
$616$	−80.6795	+	2.96626i	−3.25067	+	0.119514i
$617$	−21.8225	+	5.84731i	−0.878539	+	0.235404i	−0.669777	−	0.742563i	$-0.733610\pi$
$617$	−21.8225	+	5.84731i	−0.878539	+	0.235404i	−0.208762	+	0.977966i	$0.566943\pi$
$618$	−0.323135	−	0.544182i	−0.0129984	−	0.0218902i
$619$	−16.8078	+	16.8078i	−0.675564	+	0.675564i	−0.958993	−	0.283429i	$-0.908528\pi$
$619$	−16.8078	+	16.8078i	−0.675564	+	0.675564i	0.283429	+	0.958993i	$0.408528\pi$
$620$	−0.100818	−	4.11427i	−0.00404895	−	0.165233i
$621$	1.02761	+	1.77988i	0.0412367	+	0.0714240i
$622$	33.3838	−	0.408966i	1.33857	−	0.0163980i
$623$	3.53171			0.141495
$624$	−9.93860	+	10.4510i	−0.397862	+	0.418376i
$625$	−20.2196			−0.808783
$626$	2.36601	−	0.0289847i	0.0945649	−	0.00115846i
$627$	−1.89463	−	3.28159i	−0.0756641	−	0.131054i
$628$	−0.958692	−	39.1231i	−0.0382560	−	1.56118i
$629$	5.30862	−	5.30862i	0.211669	−	0.211669i
$630$	1.98472	+	3.34240i	0.0790730	+	0.133164i
$631$	28.5528	−	7.65071i	1.13667	−	0.304570i	0.359059	−	0.933315i	$-0.383098\pi$
$631$	28.5528	−	7.65071i	1.13667	−	0.304570i	0.777612	+	0.628745i	$0.216431\pi$
$632$	0.749108	+	20.3750i	0.0297979	+	0.810475i
$633$	7.25156	−	12.5601i	0.288224	−	0.499218i
$634$	−2.78368	+	2.85273i	−0.110554	+	0.113296i
$635$	7.56808	+	2.02786i	0.300330	+	0.0804732i
$636$	−2.04121	+	1.24614i	−0.0809393	+	0.0494128i
$637$	40.2853	+	42.2561i	1.59616	+	1.67425i
$638$	−45.3522	+	12.7495i	−1.79551	+	0.504758i
$639$	0.422224	+	0.113135i	0.0167029	+	0.00447553i
$640$	−4.15826	+	4.94038i	−0.164370	+	0.195286i
$641$	16.7228	+	9.65492i	0.660511	+	0.381346i	0.792472	−	0.609909i	$-0.208794\pi$
$641$	16.7228	+	9.65492i	0.660511	+	0.381346i	−0.131961	+	0.991255i	$0.542127\pi$
$642$	5.08887	−	9.06894i	0.200841	−	0.357923i
$643$	20.6865	−	5.54294i	0.815797	−	0.218592i	0.173289	−	0.984871i	$-0.444561\pi$
$643$	20.6865	−	5.54294i	0.815797	−	0.218592i	0.642508	+	0.766279i	$0.277894\pi$
$644$	14.3361	+	13.6503i	0.564920	+	0.537896i
$645$	−3.99949	−	3.99949i	−0.157480	−	0.157480i
$646$	0.928492	+	0.236638i	0.0365310	+	0.00931038i
$647$	13.1707	+	22.8124i	0.517794	+	0.896846i	0.999786	+	0.0206706i	$0.00658014\pi$
$647$	13.1707	+	22.8124i	0.517794	+	0.896846i	−0.481992	+	0.876176i	$0.660087\pi$
$648$	1.50326	+	2.39588i	0.0590535	+	0.0941189i
$649$		−	48.4480i		−	1.90175i
$650$	23.0920	−	5.90072i	0.905743	−	0.231445i
$651$	−17.3624			−0.680486
$652$	−3.57526	−	12.1448i	−0.140018	−	0.475627i
$653$	−4.85800	+	2.80477i	−0.190108	+	0.109759i	−0.592033	−	0.805914i	$-0.701675\pi$
$653$	−4.85800	+	2.80477i	−0.190108	+	0.109759i	0.401925	+	0.915673i	$0.368341\pi$
$654$	−3.55919	−	0.907102i	−0.139175	−	0.0354705i
$655$	−2.38264	+	2.38264i	−0.0930976	+	0.0930976i
$656$	4.48662	−	20.7645i	0.175173	−	0.810719i
$657$	2.68851	+	10.0336i	0.104889	+	0.391450i
$658$	49.7485	+	27.9154i	1.93940	+	1.08826i
$659$	18.1430	−	31.4246i	0.706751	−	1.22413i	−0.259305	−	0.965795i	$-0.583493\pi$
$659$	18.1430	−	31.4246i	0.706751	−	1.22413i	0.966056	−	0.258333i	$-0.0831732\pi$
$660$	−5.94054	−	3.23839i	−0.231235	−	0.126054i
$661$	−3.16335	+	11.8058i	−0.123040	+	0.459192i	−0.999762	−	0.0218054i	$-0.993059\pi$
$661$	−3.16335	+	11.8058i	−0.123040	+	0.459192i	0.876722	+	0.480997i	$0.159725\pi$
$662$	7.67444	−	2.15746i	0.298276	−	0.0838520i
$663$	3.71344	−	0.900586i	0.144218	−	0.0349759i
$664$	−22.8495	−	21.2289i	−0.886734	−	0.823842i
$665$	−0.454818	+	1.69740i	−0.0176371	+	0.0658225i
$666$	7.17031	+	6.99675i	0.277844	+	0.271119i
$667$	10.0035	+	5.77550i	0.387336	+	0.223628i
$668$	−2.35274	+	9.72784i	−0.0910304	+	0.376382i
$669$	−6.28722	−	23.4642i	−0.243078	−	0.907180i
$670$	−3.29346	−	5.54641i	−0.127237	−	0.214276i
$671$	25.6559	+	25.6559i	0.990434	+	0.990434i
$672$	20.4064	+	18.0481i	0.787193	+	0.696221i
$673$	21.4840	−	12.4038i	0.828146	−	0.478130i	−0.0250717	−	0.999686i	$-0.507981\pi$
$673$	21.4840	−	12.4038i	0.828146	−	0.478130i	0.853217	+	0.521556i	$0.174648\pi$
$674$	−0.173059	−	14.1267i	−0.00666597	−	0.544142i
$675$		−	4.67423i		−	0.179911i
$676$	−22.8127	+	12.4731i	−0.877413	+	0.479737i
$677$			41.5137i			1.59550i	0.602988	+	0.797750i	$0.293977\pi$
$677$			41.5137i			1.59550i	−0.602988	+	0.797750i	$0.706023\pi$
$678$	27.4784	−	0.336622i	1.05530	−	0.0129279i
$679$	19.3753	−	11.1863i	0.743557	−	0.429293i
$680$	1.63518	−	0.503222i	0.0627063	−	0.0192977i
$681$	14.2846	+	14.2846i	0.547387	+	0.547387i
$682$	25.9841	−	15.4294i	0.994982	−	0.590821i
$683$	−9.94935	−	37.1315i	−0.380701	−	1.42080i	−0.844833	−	0.535030i	$-0.820300\pi$
$683$	−9.94935	−	37.1315i	−0.380701	−	1.42080i	0.464132	−	0.885766i	$-0.346366\pi$
$684$	−0.300578	+	1.24280i	−0.0114929	+	0.0475195i
$685$	−8.59662	−	4.96326i	−0.328460	−	0.189636i
$686$	43.7231	−	44.8077i	1.66936	−	1.71077i
$687$	0.196809	−	0.734503i	0.00750875	−	0.0280230i
$688$	−35.2581	−	18.1144i	−1.34420	−	0.690605i
$689$	−4.18994	+	1.01615i	−0.159624	+	0.0387121i
$690$	0.448961	+	1.59703i	0.0170916	+	0.0607979i
$691$	−0.476425	+	1.77804i	−0.0181241	+	0.0676399i	−0.974396	−	0.224840i	$-0.927814\pi$
$691$	−0.476425	+	1.77804i	−0.0181241	+	0.0676399i	0.956272	+	0.292480i	$0.0944806\pi$
$692$	−11.5440	+	21.1765i	−0.438838	+	0.805011i
$693$	−14.2719	+	24.7196i	−0.542144	+	0.939021i
$694$	16.4130	−	29.2499i	0.623030	−	1.11031i
$695$	2.08203	+	7.77025i	0.0789760	+	0.294742i
$696$	14.0496	+	7.43714i	0.532550	+	0.281904i
$697$	−3.97988	+	3.97988i	−0.150749	+	0.150749i
$698$	6.90793	−	27.1046i	0.261469	−	1.02592i
$699$	4.38500	−	2.53168i	0.165856	−	0.0957569i
$700$	−12.7140	−	43.1882i	−0.480545	−	1.63236i
$701$	30.7524			1.16150			0.580752	−	0.814081i	$-0.302759\pi$
$701$	30.7524			1.16150			0.580752	+	0.814081i	$0.302759\pi$
$702$	1.26239	+	4.94028i	0.0476460	+	0.186459i
$703$			4.52894i			0.170812i
$704$	−46.5783	−	8.87588i	−1.75549	−	0.334522i
$705$	2.39034	+	4.14018i	0.0900253	+	0.155928i
$706$	−3.87925	+	15.2210i	−0.145997	+	0.572849i
$707$	13.8692	+	13.8692i	0.521607	+	0.521607i
$708$	−11.2732	+	11.8395i	−0.423672	+	0.444957i
$709$	−6.75910	+	1.81110i	−0.253844	+	0.0680172i	−0.383497	−	0.923542i	$-0.625280\pi$
$709$	−6.75910	+	1.81110i	−0.253844	+	0.0680172i	0.129653	+	0.991559i	$0.458614\pi$
$710$	0.307700	+	0.172660i	0.0115478	+	0.00647982i
$711$	6.24277	+	3.60426i	0.234122	+	0.135170i
$712$	2.02193	+	0.462876i	0.0757750	+	0.0173470i
$713$	−7.15716	−	1.91775i	−0.268038	−	0.0718205i
$714$	−1.95335	−	6.94840i	−0.0731023	−	0.260037i
$715$	−8.41652	−	8.82826i	−0.314760	−	0.330158i
$716$	−29.9779	+	18.3013i	−1.12033	+	0.683951i
$717$	−27.5637	−	7.38567i	−1.02938	−	0.275823i
$718$	14.4433	+	14.0937i	0.539020	+	0.525973i
$719$	−10.9833	+	19.0236i	−0.409608	+	0.709461i	−0.994846	−	0.101400i	$-0.967668\pi$
$719$	−10.9833	+	19.0236i	−0.409608	+	0.709461i	0.585238	+	0.810862i	$0.301001\pi$
$720$	0.698200	+	2.17367i	0.0260204	+	0.0810078i
$721$	−2.08175	+	0.557804i	−0.0775285	+	0.0207737i
$722$	22.6068	−	13.4239i	0.841339	−	0.499588i
$723$	−9.58070	+	9.58070i	−0.356310	+	0.356310i
$724$	−14.0705	+	0.344791i	−0.522926	+	0.0128140i
$725$	−13.1353	−	22.7510i	−0.487833	−	0.844952i
$726$	−0.418015	−	34.1225i	−0.0155140	−	1.26640i
$727$	−32.3235			−1.19881			−0.599407	−	0.800445i	$-0.704597\pi$
$727$	−32.3235			−1.19881			−0.599407	+	0.800445i	$0.704597\pi$
$728$	25.1017	+	42.2126i	0.930332	+	1.56450i
$729$	1.00000			0.0370370
$730$	0.102708	+	8.38403i	0.00380139	+	0.310307i
$731$	5.25109	+	9.09515i	0.194218	+	0.336396i
$732$	−0.299922	−	12.2395i	−0.0110854	−	0.452383i
$733$	27.9317	−	27.9317i	1.03168	−	1.03168i	0.0321977	−	0.999482i	$-0.489749\pi$
$733$	27.9317	−	27.9317i	1.03168	−	1.03168i	0.999482	−	0.0321977i	$-0.0102506\pi$
$734$	−7.99727	+	4.74879i	−0.295185	+	0.175281i
$735$	8.92705	−	2.39200i	0.329279	−	0.0882301i
$736$	6.41846	+	9.69380i	0.236587	+	0.357318i
$737$	23.6829	−	41.0200i	0.872372	−	1.51099i
$738$	−5.37559	−	5.24547i	−0.197878	−	0.193089i
$739$	33.0386	+	8.85267i	1.21534	+	0.325651i	0.808857	−	0.588005i	$-0.200087\pi$
$739$	33.0386	+	8.85267i	1.21534	+	0.325651i	0.406488	+	0.913656i	$0.366753\pi$
$740$	4.21366	+	6.90208i	0.154897	+	0.253725i
$741$	−1.19986	+	1.96818i	−0.0440780	+	0.0723028i
$742$	2.20400	+	7.84001i	0.0809114	+	0.287816i
$743$	48.6992	+	13.0489i	1.78660	+	0.478718i	0.991761	−	0.128102i	$-0.0408884\pi$
$743$	48.6992	+	13.0489i	1.78660	+	0.478718i	0.794839	+	0.606820i	$0.207555\pi$
$744$	−9.94009	−	2.27556i	−0.364421	−	0.0834263i
$745$	−5.51531	−	3.18427i	−0.202065	−	0.116662i
$746$	10.4903	+	5.88642i	0.384077	+	0.215517i
$747$	−10.6513	+	2.85401i	−0.389712	+	0.104423i
$748$	9.09814	+	8.66291i	0.332661	+	0.316747i
$749$	−25.0403	−	25.0403i	−0.914953	−	0.914953i
$750$	1.92853	−	7.56695i	0.0704200	−	0.276306i
$751$	−24.4568	−	42.3605i	−0.892443	−	1.54576i	−0.836938	−	0.547298i	$-0.815657\pi$
$751$	−24.4568	−	42.3605i	−0.892443	−	1.54576i	−0.0555049	−	0.998458i	$-0.517677\pi$
$752$	24.8227	+	22.5019i	0.905190	+	0.820561i
$753$			16.7645i			0.610932i
$754$	20.0274	+	20.4985i	0.729356	+	0.746510i
$755$	6.60657			0.240438
$756$	9.23963	−	2.72002i	0.336042	−	0.0989263i
$757$	−1.35085	+	0.779913i	−0.0490974	+	0.0283464i	−0.524348	−	0.851504i	$-0.675691\pi$
$757$	−1.35085	+	0.779913i	−0.0490974	+	0.0283464i	0.475250	+	0.879851i	$0.342357\pi$
$758$	−6.10905	+	23.9700i	−0.221891	+	0.870630i
$759$	−8.61358	+	8.61358i	−0.312653	+	0.312653i
$760$	−0.482853	+	0.912166i	−0.0175149	+	0.0330877i
$761$	−2.75025	−	10.2641i	−0.0996966	−	0.372073i	0.897993	−	0.440010i	$-0.145025\pi$
$761$	−2.75025	−	10.2641i	−0.0996966	−	0.372073i	−0.997690	+	0.0679370i	$0.978358\pi$
$762$	9.50003	−	16.9301i	0.344150	−	0.613314i
$763$	−6.25379	+	10.8319i	−0.226402	+	0.392141i
$764$	36.1964	+	19.7319i	1.30954	+	0.713874i
$765$	0.156555	−	0.584270i	0.00566025	−	0.0211243i
$766$	3.81985	+	13.5879i	0.138017	+	0.490949i
$767$	−25.8679	+	14.1225i	−0.934036	+	0.509935i
$768$	9.31735	+	13.0072i	0.336211	+	0.469357i
$769$	−11.1442	+	41.5908i	−0.401871	+	1.49980i	0.407885	+	0.913033i	$0.366267\pi$
$769$	−11.1442	+	41.5908i	−0.401871	+	1.49980i	−0.809755	+	0.586768i	$0.800400\pi$
$770$	−16.0909	+	16.4901i	−0.579877	+	0.594260i
$771$	−7.66304	−	4.42426i	−0.275978	−	0.159336i
$772$	−8.41861	−	2.03610i	−0.302993	−	0.0732808i
$773$	−4.01263	−	14.9753i	−0.144324	−	0.538626i	−0.999785	−	0.0207572i	$-0.993392\pi$
$773$	−4.01263	−	14.9753i	−0.144324	−	0.538626i	0.855460	−	0.517869i	$-0.173274\pi$
$774$	−12.0502	+	7.15543i	−0.433136	+	0.257197i
$775$	11.9161	+	11.9161i	0.428037	+	0.428037i
$776$	12.5586	−	3.86488i	0.450828	−	0.138741i
$777$	29.5451	−	17.0579i	1.05992	−	0.611947i
$778$	1.13667	−	0.0139247i	0.0407517	−	0.000499225i
$779$		−	3.39535i		−	0.121651i
$780$	0.00258315	+	4.11582i	9.24916e−5	+	0.147370i
$781$			2.59083i			0.0927070i
$782$	−0.0377318	−	3.08004i	−0.00134929	−	0.110142i
$783$	4.86733	−	2.81016i	0.173944	−	0.100427i
$784$	54.4383	−	35.0931i	1.94423	−	1.25333i
$785$	−7.89721	−	7.89721i	−0.281863	−	0.281863i
$786$	4.26275	+	7.17876i	0.152047	+	0.256058i
$787$	9.97812	+	37.2389i	0.355682	+	1.32742i	0.879624	+	0.475669i	$0.157794\pi$
$787$	9.97812	+	37.2389i	0.355682	+	1.32742i	−0.523943	+	0.851753i	$0.675539\pi$
$788$	−20.6309	−	4.98972i	−0.734945	−	0.177751i
$789$	5.49660	+	3.17346i	0.195684	+	0.112978i
$790$	4.16445	+	4.06365i	0.148164	+	0.144578i
$791$	24.2202	−	90.3910i	0.861171	−	3.21393i
$792$	−11.4106	+	12.2817i	−0.405457	+	0.436409i
$793$	6.21982	−	21.1771i	0.220872	−	0.752021i
$794$	1.66176	−	0.467159i	0.0589738	−	0.0165789i
$795$	−0.176643	+	0.659242i	−0.00626490	+	0.0233809i
$796$	23.0901	−	42.3567i	0.818405	−	1.50129i
$797$	−2.47797	+	4.29197i	−0.0877742	+	0.152029i	−0.906570	−	0.422055i	$-0.861309\pi$
$797$	−2.47797	+	4.29197i	−0.0877742	+	0.152029i	0.818796	+	0.574085i	$0.194642\pi$
$798$	3.79717	+	2.13071i	0.134418	+	0.0754263i
$799$	−2.29744	−	8.57417i	−0.0812776	−	0.303332i
$800$	−1.61850	−	26.3919i	−0.0572226	−	0.933093i
$801$	0.518559	−	0.518559i	0.0183224	−	0.0183224i
$802$	6.71346	+	1.71101i	0.237061	+	0.0604178i
$803$	−53.3194	+	30.7840i	−1.88160	+	1.08634i
$804$	−15.3323	+	4.51364i	−0.540730	+	0.159184i
$805$	5.64920			0.199108
$806$	−15.8125	−	9.37607i	−0.556973	−	0.330258i
$807$			6.37298i			0.224340i
$808$	6.12250	+	9.75798i	0.215389	+	0.343285i
$809$	24.9370	+	43.1921i	0.876738	+	1.51855i	0.854900	+	0.518793i	$0.173618\pi$
$809$	24.9370	+	43.1921i	0.876738	+	1.51855i	0.0218374	+	0.999762i	$0.493048\pi$
$810$	0.782176	+	0.199347i	0.0274829	+	0.00700435i
$811$	−25.0953	−	25.0953i	−0.881216	−	0.881216i	0.112442	−	0.993658i	$-0.464133\pi$
$811$	−25.0953	−	25.0953i	−0.881216	−	0.881216i	−0.993658	+	0.112442i	$0.964133\pi$
$812$	37.3287	−	39.2041i	1.30998	−	1.37579i
$813$	−8.48094	+	2.27246i	−0.297440	+	0.0796987i
$814$	−29.0576	+	51.7840i	−1.01847	+	1.81503i
$815$	−3.12891	−	1.80648i	−0.109601	−	0.0632782i
$816$	−0.207630	−	4.23402i	−0.00726851	−	0.148220i
$817$	−6.11959	−	1.63974i	−0.214097	−	0.0573672i
$818$	−19.3295	+	5.43396i	−0.675840	+	0.189994i
$819$	17.3588	+	0.414468i	0.606566	+	0.0144827i
$820$	−3.15899	−	5.17449i	−0.110317	−	0.180701i
$821$	41.6756	+	11.1669i	1.45449	+	0.389729i	0.897582	−	0.440847i	$-0.145322\pi$
$821$	41.6756	+	11.1669i	1.45449	+	0.389729i	0.556906	+	0.830576i	$0.311988\pi$
$822$	−17.1773	+	17.6034i	−0.599129	+	0.613990i
$823$	−6.03038	+	10.4449i	−0.210206	+	0.364087i	−0.951779	−	0.306785i	$-0.900747\pi$
$823$	−6.03038	+	10.4449i	−0.210206	+	0.364087i	0.741573	+	0.670872i	$0.234080\pi$
$824$	−1.26493	+	0.0465062i	−0.0440658	+	0.00162012i
$825$	26.7604	−	7.17044i	0.931679	−	0.249643i
$826$	28.4236	+	47.8673i	0.988985	+	1.66552i
$827$	−13.3380	+	13.3380i	−0.463809	+	0.463809i	−0.899902	−	0.436093i	$-0.856362\pi$
$827$	−13.3380	+	13.3380i	−0.463809	+	0.463809i	0.436093	+	0.899902i	$0.356362\pi$
$828$	4.10922	−	0.100694i	0.142805	−	0.00349937i
$829$	19.5075	+	33.7880i	0.677524	+	1.17351i	0.975724	+	0.219002i	$0.0702802\pi$
$829$	19.5075	+	33.7880i	0.677524	+	1.17351i	−0.298201	+	0.954503i	$0.596387\pi$
$830$	−8.90015	+	0.109031i	−0.308929	+	0.00378451i
$831$	−6.88280			−0.238762
$832$	8.83841	+	27.4569i	0.306417	+	0.951898i
$833$	−17.1603			−0.594567
$834$	19.9305	−	0.244157i	0.690137	−	0.00845447i
$835$	1.42809	+	2.47353i	0.0494212	+	0.0856000i
$836$	−7.57623	+	0.185652i	−0.262029	+	0.00642091i
$837$	−2.54931	+	2.54931i	−0.0881170	+	0.0881170i
$838$	3.40965	+	5.74208i	0.117784	+	0.198357i
$839$	−35.6287	+	9.54667i	−1.23004	+	0.329588i	−0.814594	−	0.580031i	$-0.803040\pi$
$839$	−35.6287	+	9.54667i	−1.23004	+	0.329588i	−0.415444	+	0.909619i	$0.636374\pi$
$840$	7.76925	−	0.285644i	0.268065	−	0.00985566i
$841$	1.29395	−	2.24118i	0.0446189	−	0.0772822i
$842$	6.11816	−	6.26992i	0.210846	−	0.216076i
$843$	1.70244	+	0.456169i	0.0586353	+	0.0157113i
$844$	−15.1141	−	24.7573i	−0.520250	−	0.852182i
$845$	−2.26028	+	7.06726i	−0.0777560	+	0.243121i
$846$	11.4033	−	3.20573i	0.392055	−	0.110215i
$847$	−112.247	−	30.0764i	−3.85685	−	1.03344i
$848$	0.234273	+	4.77732i	0.00804496	+	0.164054i
$849$	11.6080	+	6.70190i	0.398386	+	0.230008i
$850$	−3.42817	+	6.10940i	−0.117585	+	0.209551i
$851$	14.0632	−	3.76824i	0.482082	−	0.129173i
$852$	0.602849	−	0.633137i	0.0206533	−	0.0216909i
$853$	−30.9178	−	30.9178i	−1.05861	−	1.05861i	−0.998172	−	0.0604339i	$-0.980752\pi$
$853$	−30.9178	−	30.9178i	−1.05861	−	1.05861i	−0.0604339	−	0.998172i	$-0.519248\pi$
$854$	−40.4002	−	10.2965i	−1.38247	−	0.352339i
$855$	0.182448	+	0.316009i	0.00623960	+	0.0108073i
$856$	−11.0539	−	17.6176i	−0.377815	−	0.602158i
$857$		−	3.63834i		−	0.124283i	−0.998067	−	0.0621417i	$-0.980207\pi$
$857$		−	3.63834i		−	0.124283i	0.998067	−	0.0621417i	$-0.0197931\pi$
$858$	−26.3470	+	14.8059i	−0.899473	+	0.505465i
$859$	−10.4247			−0.355686			−0.177843	−	0.984059i	$-0.556912\pi$
$859$	−10.4247			−0.355686			−0.177843	+	0.984059i	$0.556912\pi$
$860$	−10.8518	+	3.19463i	−0.370044	+	0.108936i
$861$	−22.1500	+	12.7883i	−0.754869	+	0.435824i
$862$	3.13938	+	0.800109i	0.106928	+	0.0272518i
$863$	−23.3831	+	23.3831i	−0.795970	+	0.795970i	−0.982457	−	0.186488i	$-0.940290\pi$
$863$	−23.3831	+	23.3831i	−0.795970	+	0.795970i	0.186488	+	0.982457i	$0.440290\pi$
$864$	5.64625	−	0.346260i	0.192089	−	0.0117800i
$865$	1.78146	+	6.64848i	0.0605713	+	0.226055i
$866$	−19.8712	−	11.1504i	−0.675252	−	0.378905i
$867$	7.93844	−	13.7498i	0.269603	−	0.466967i
$868$	−16.6205	+	30.4889i	−0.564136	+	1.03486i
$869$	−11.0581	+	41.2695i	−0.375122	+	1.39997i
$870$	4.36731	−	1.22775i	0.148066	−	0.0416246i
$871$	−28.8054	−	0.687774i	−0.976034	−	0.0233043i
$872$	−5.00000	+	5.38169i	−0.169321	+	0.182247i
$873$	1.20238	−	4.48735i	0.0406945	−	0.151874i
$874$	1.32993	+	1.29774i	0.0449856	+	0.0438967i
$875$	−23.0290	−	13.2958i	−0.778521	−	0.449479i
$876$	20.1930	+	4.88381i	0.682258	+	0.165009i
$877$	−1.72948	−	6.45450i	−0.0584004	−	0.217953i	0.930559	−	0.366143i	$-0.119322\pi$
$877$	−1.72948	−	6.45450i	−0.0584004	−	0.217953i	−0.988959	+	0.148190i	$0.952655\pi$
$878$	−14.7288	−	24.8044i	−0.497074	−	0.837107i
$879$	−16.5601	−	16.5601i	−0.558559	−	0.558559i
$880$	−11.3734	+	7.33175i	−0.383397	+	0.247153i
$881$	−5.79984	+	3.34854i	−0.195401	+	0.112815i	−0.594509	−	0.804089i	$-0.702653\pi$
$881$	−5.79984	+	3.34854i	−0.195401	+	0.112815i	0.399107	+	0.916904i	$0.369320\pi$
$882$	−0.280506	−	22.8977i	−0.00944514	−	0.771005i
$883$		−	6.47692i		−	0.217966i	−0.994044	−	0.108983i	$-0.965241\pi$
$883$		−	6.47692i		−	0.217966i	0.994044	−	0.108983i	$-0.0347594\pi$
$884$	1.97330	−	7.38300i	0.0663694	−	0.248317i
$885$			4.66543i			0.156827i
$886$	−6.34026	+	0.0776709i	−0.213005	+	0.00260941i
$887$	24.2718	−	14.0133i	0.814967	−	0.470521i	−0.0337108	−	0.999432i	$-0.510733\pi$
$887$	24.2718	−	14.0133i	0.814967	−	0.470521i	0.848678	+	0.528910i	$0.177399\pi$
$888$	19.1504	−	5.89348i	0.642646	−	0.197772i
$889$	−46.7459	−	46.7459i	−1.56781	−	1.56781i
$890$	0.508978	−	0.302231i	0.0170610	−	0.0101308i
$891$	1.53404	+	5.72510i	0.0513921	+	0.191798i
$892$	−47.2224	−	11.4211i	−1.58112	−	0.382405i
$893$	4.63744	+	2.67743i	0.155186	+	0.0895967i
$894$	−11.0204	+	11.2938i	−0.368578	+	0.377721i
$895$	−2.59424	+	9.68185i	−0.0867160	+	0.323629i
$896$	51.2274	−	18.5572i	1.71139	−	0.619954i
$897$	7.10990	+	2.08821i	0.237393	+	0.0697234i
$898$	−4.85118	−	17.2565i	−0.161886	−	0.575855i
$899$	−5.24438	+	19.5723i	−0.174910	+	0.652772i
$900$	−8.20808	−	4.47450i	−0.273603	−	0.149150i
$901$	0.633623	−	1.09747i	0.0211090	−	0.0365619i
$902$	21.7845	−	38.8225i	0.725345	−	1.29265i
$903$	12.3519	+	46.0978i	0.411045	+	1.53404i
$904$	25.7131	−	48.5751i	0.855206	−	1.61558i
$905$	−2.84021	+	2.84021i	−0.0944116	+	0.0944116i
$906$	4.04274	−	15.8624i	0.134311	−	0.526994i
$907$	12.9360	−	7.46860i	0.429533	−	0.247991i	−0.269615	−	0.962968i	$-0.586896\pi$
$907$	12.9360	−	7.46860i	0.429533	−	0.247991i	0.699148	+	0.714977i	$0.253563\pi$
$908$	38.7583	−	11.4099i	1.28624	−	0.378652i
$909$	4.07282			0.135087
$910$	13.4950	+	3.78462i	0.447356	+	0.125459i
$911$			47.5530i			1.57550i	0.615995	+	0.787750i	$0.288754\pi$
$911$			47.5530i			1.57550i	−0.615995	+	0.787750i	$0.711246\pi$
$912$	1.89465	+	1.71752i	0.0627381	+	0.0568726i
$913$	−32.6790	−	56.6017i	−1.08152	−	1.87324i
$914$	−9.02603	+	35.4153i	−0.298555	+	1.17144i
$915$	−2.47060	−	2.47060i	−0.0816756	−	0.0816756i
$916$	−1.10141	−	1.04872i	−0.0363916	−	0.0346507i
$917$	27.4622	−	7.35846i	0.906880	−	0.242998i
$918$	−1.30704	−	0.733420i	−0.0431387	−	0.0242065i
$919$	23.4113	+	13.5165i	0.772268	+	0.445869i	0.833683	−	0.552243i	$-0.186228\pi$
$919$	23.4113	+	13.5165i	0.772268	+	0.445869i	−0.0614148	+	0.998112i	$0.519561\pi$
$920$	3.23421	+	0.740400i	0.106629	+	0.0244103i
$921$	−28.9578	−	7.75922i	−0.954192	−	0.255675i
$922$	−6.76248	−	24.0553i	−0.222711	−	0.792219i
$923$	1.38332	−	0.755222i	0.0455326	−	0.0248584i
$924$	29.7463	+	48.7252i	0.978583	+	1.60294i
$925$	−31.9843	−	8.57016i	−1.05164	−	0.281785i
$926$	−1.31131	−	1.27957i	−0.0430923	−	0.0420493i
$927$	−0.223760	+	0.387565i	−0.00734926	+	0.0127293i
$928$	26.5091	−	17.5522i	0.870204	−	0.576179i
$929$	−8.36041	+	2.24016i	−0.274296	+	0.0734974i	−0.393345	−	0.919391i	$-0.628682\pi$
$929$	−8.36041	+	2.24016i	−0.274296	+	0.0734974i	0.119049	+	0.992888i	$0.462016\pi$
$930$	−2.50221	+	1.48581i	−0.0820506	+	0.0487217i
$931$	7.31995	−	7.31995i	0.239902	−	0.239902i
$932$	−0.248076	−	10.1237i	−0.00812600	−	0.331612i
$933$	−11.8038	−	20.4449i	−0.386441	−	0.669335i
$934$	0.0177352	+	1.44772i	0.000580314	+	0.0473709i
$935$	3.58517			0.117247
$936$	9.88372	+	2.51238i	0.323060	+	0.0821198i
$937$	−24.9116			−0.813826			−0.406913	−	0.913467i	$-0.633395\pi$
$937$	−24.9116			−0.813826			−0.406913	+	0.913467i	$0.633395\pi$
$938$	0.666702	+	54.4228i	0.0217686	+	1.77697i
$939$	−0.836575	−	1.44899i	−0.0273006	−	0.0472860i
$940$	9.55847	−	0.234226i	0.311763	−	0.00763961i
$941$	−1.97405	+	1.97405i	−0.0643522	+	0.0643522i	−0.738550	−	0.674198i	$-0.764489\pi$
$941$	−1.97405	+	1.97405i	−0.0643522	+	0.0643522i	0.674198	+	0.738550i	$0.264489\pi$
$942$	−23.7938	+	14.1288i	−0.775244	+	0.460340i
$943$	−10.5432	+	2.82505i	−0.343335	+	0.0919963i
$944$	9.99911	+	31.1297i	0.325443	+	1.01318i
$945$	1.37435	−	2.38044i	0.0447076	−	0.0774359i
$946$	−59.4510	−	58.0120i	−1.93292	−	1.88613i
$947$	−31.0163	−	8.31080i	−1.00790	−	0.270065i	−0.283146	−	0.959077i	$-0.591378\pi$
$947$	−31.0163	−	8.31080i	−1.00790	−	0.270065i	−0.724750	+	0.689012i	$0.758045\pi$
$948$	12.3052	−	7.51222i	0.399654	−	0.243986i
$949$	31.9790	+	19.4954i	1.03808	+	0.632847i
$950$	−1.14372	−	4.06839i	−0.0371070	−	0.131996i
$951$	2.72238	+	0.729459i	0.0882791	+	0.0236543i
$952$	−14.0715	−	3.22135i	−0.456059	−	0.104405i
$953$	12.1425	+	7.01048i	0.393334	+	0.227092i	0.683604	−	0.729853i	$-0.260412\pi$
$953$	12.1425	+	7.01048i	0.393334	+	0.227092i	−0.290269	+	0.956945i	$0.593745\pi$
$954$	1.47476	+	0.827531i	0.0477470	+	0.0267923i
$955$	11.3640	−	3.04499i	0.367732	−	0.0985335i
$956$	−39.3553	+	41.3325i	−1.27284	+	1.33679i
$957$	23.5551	+	23.5551i	0.761428	+	0.761428i
$958$	−0.0690289	+	0.270848i	−0.00223022	+	0.00875070i
$959$	41.8778	+	72.5345i	1.35230	+	2.34226i
$960$	4.48539	+	0.854727i	0.144765	+	0.0275862i
$961$			18.0020i			0.580711i
$962$	36.1193	+	0.419805i	1.16453	+	0.0135351i
$963$	−7.35331			−0.236957
$964$	7.65266	+	25.9953i	0.246476	+	0.837252i
$965$	−2.14063	+	1.23589i	−0.0689092	+	0.0397847i
$966$	3.45690	−	13.5638i	0.111224	−	0.436408i
$967$	−5.06111	+	5.06111i	−0.162754	+	0.162754i	−0.783786	−	0.621031i	$-0.786714\pi$
$967$	−5.06111	+	5.06111i	−0.162754	+	0.162754i	0.621031	+	0.783786i	$0.286714\pi$
$968$	−60.3202	−	31.9304i	−1.93876	−	1.02628i
$969$	−0.175358	−	0.654444i	−0.00563330	−	0.0210238i
$970$	1.83502	−	3.27021i	0.0589188	−	0.105000i
$971$	1.08352	−	1.87671i	0.0347718	−	0.0602264i	−0.848116	−	0.529811i	$-0.822263\pi$
$971$	1.08352	−	1.87671i	0.0347718	−	0.0602264i	0.882888	+	0.469584i	$0.155596\pi$
$972$	0.957270	−	1.75603i	0.0307044	−	0.0563246i
$973$	17.5673	−	65.5619i	0.563181	−	2.10182i
$974$	3.10368	+	11.0403i	0.0994485	+	0.353755i
$975$	−11.6291	−	12.1981i	−0.372431	−	0.390650i
$976$	−21.7799	−	11.1898i	−0.697159	−	0.358176i
$977$	4.67577	−	17.4502i	0.149591	−	0.558282i	−0.849917	−	0.526917i	$-0.823348\pi$
$977$	4.67577	−	17.4502i	0.149591	−	0.558282i	0.999508	−	0.0313649i	$-0.00998538\pi$
$978$	−6.25204	+	6.40712i	−0.199918	+	0.204877i
$979$	3.76429	+	2.17331i	0.120307	+	0.0694594i
$980$	4.34518	−	17.9659i	0.138802	−	0.573901i
$981$	0.672199	+	2.50868i	0.0214616	+	0.0800960i
$982$	−18.6599	+	11.0803i	−0.595462	+	0.353586i
$983$	−4.75595	−	4.75595i	−0.151691	−	0.151691i	0.627182	−	0.778873i	$-0.284208\pi$
$983$	−4.75595	−	4.75595i	−0.151691	−	0.151691i	−0.778873	+	0.627182i	$0.784208\pi$
$984$	−14.3571	+	4.41835i	−0.457687	+	0.140852i
$985$	−5.24588	+	3.02871i	−0.167148	+	0.0965027i
$986$	−8.42282	+	0.103183i	−0.268237	+	0.00328602i
$987$		−	40.3372i		−	1.28395i
$988$	2.30758	+	3.99107i	0.0734140	+	0.126973i
$989$			20.3669i			0.647628i
$990$	0.0586041	+	4.78384i	0.00186256	+	0.152041i
$991$	13.6470	−	7.87912i	0.433512	−	0.250288i	−0.267330	−	0.963605i	$-0.586141\pi$
$991$	13.6470	−	7.87912i	0.433512	−	0.250288i	0.700842	+	0.713317i	$0.252808\pi$
$992$	−13.5113	+	15.2768i	−0.428984	+	0.485037i
$993$	−3.98597	−	3.98597i	−0.126491	−	0.126491i
$994$	−1.51999	−	2.55977i	−0.0482113	−	0.0811911i
$995$	−3.56322	−	13.2981i	−0.112962	−	0.421578i
$996$	−5.18446	+	21.4361i	−0.164276	+	0.679228i
$997$	−43.1151	−	24.8925i	−1.36547	−	0.788354i	−0.375123	−	0.926975i	$-0.622400\pi$
$997$	−43.1151	−	24.8925i	−1.36547	−	0.788354i	−0.990345	+	0.138621i	$0.955733\pi$
$998$	−15.1726	−	14.8053i	−0.480279	−	0.468654i
$999$	1.83349	−	6.84268i	0.0580091	−	0.216493i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.d.115.1	yes	56
3.2	odd	2		936.2.ed.e.739.14		56
8.3	odd	2	inner	312.2.bt.d.115.12	yes	56
13.6	odd	12	inner	312.2.bt.d.19.12	yes	56
24.11	even	2		936.2.ed.e.739.3		56
39.32	even	12		936.2.ed.e.19.3		56
104.19	even	12	inner	312.2.bt.d.19.1	✓	56
312.227	odd	12		936.2.ed.e.19.14		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.d.19.1	✓	56	104.19	even	12	inner
312.2.bt.d.19.12	yes	56	13.6	odd	12	inner
312.2.bt.d.115.1	yes	56	1.1	even	1	trivial
312.2.bt.d.115.12	yes	56	8.3	odd	2	inner
936.2.ed.e.19.3		56	39.32	even	12
936.2.ed.e.19.14		56	312.227	odd	12
936.2.ed.e.739.3		56	24.11	even	2
936.2.ed.e.739.14		56	3.2	odd	2

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Elliptic curves over $\Q$
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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	312.2.bt.d.115.1

Level	$312$
Weight	$2$
Character	312.115
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$56$
Inner twists	$4$