LMFDB - Embedded newform 760.2.w.c.267.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [760,2,Mod(267,760)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(760, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 1, 0]))

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

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

chi := DirichletCharacter("760.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.10
Character	$\chi$	$=$	760.267
Dual form			760.2.w.c.723.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18702 + 0.768758i) q^{2} +(-0.696739 + 0.696739i) q^{3} +(0.818024 - 1.82506i) q^{4} +(2.11169 - 0.735369i) q^{5} +(0.291418 - 1.36267i) q^{6} +(-3.48083 + 3.48083i) q^{7} +(0.432019 + 2.79524i) q^{8} +2.02911i q^{9} +O(q^{10})$	\(q+(-1.18702 + 0.768758i) q^{2} +(-0.696739 + 0.696739i) q^{3} +(0.818024 - 1.82506i) q^{4} +(2.11169 - 0.735369i) q^{5} +(0.291418 - 1.36267i) q^{6} +(-3.48083 + 3.48083i) q^{7} +(0.432019 + 2.79524i) q^{8} +2.02911i q^{9} +(-1.94129 + 2.49627i) q^{10} +4.34436 q^{11} +(0.701640 + 1.84154i) q^{12} +(1.70353 + 1.70353i) q^{13} +(1.45589 - 6.80773i) q^{14} +(-0.958937 + 1.98366i) q^{15} +(-2.66167 - 2.98588i) q^{16} +(-4.29935 - 4.29935i) q^{17} +(-1.55989 - 2.40859i) q^{18} -1.00000i q^{19} +(0.385322 - 4.45551i) q^{20} -4.85047i q^{21} +(-5.15683 + 3.33976i) q^{22} +(3.20581 + 3.20581i) q^{23} +(-2.24856 - 1.64655i) q^{24} +(3.91847 - 3.10574i) q^{25} +(-3.33171 - 0.712517i) q^{26} +(-3.50398 - 3.50398i) q^{27} +(3.50532 + 9.20013i) q^{28} -0.975159 q^{29} +(-0.386676 - 3.09183i) q^{30} +7.93436i q^{31} +(5.45487 + 1.49811i) q^{32} +(-3.02689 + 3.02689i) q^{33} +(8.40857 + 1.79825i) q^{34} +(-4.79074 + 9.91013i) q^{35} +(3.70324 + 1.65986i) q^{36} +(-2.95616 + 2.95616i) q^{37} +(0.768758 + 1.18702i) q^{38} -2.37383 q^{39} +(2.96782 + 5.58498i) q^{40} -3.68629 q^{41} +(3.72883 + 5.75759i) q^{42} +(-7.28201 + 7.28201i) q^{43} +(3.55379 - 7.92871i) q^{44} +(1.49214 + 4.28485i) q^{45} +(-6.26985 - 1.34086i) q^{46} +(-2.94050 + 2.94050i) q^{47} +(3.93487 + 0.225887i) q^{48} -17.2324i q^{49} +(-2.26373 + 6.69892i) q^{50} +5.99105 q^{51} +(4.50256 - 1.71551i) q^{52} +(0.396814 + 0.396814i) q^{53} +(6.85299 + 1.46558i) q^{54} +(9.17394 - 3.19470i) q^{55} +(-11.2335 - 8.22598i) q^{56} +(0.696739 + 0.696739i) q^{57} +(1.15753 - 0.749661i) q^{58} +12.7921i q^{59} +(2.83586 + 3.37279i) q^{60} +2.90021i q^{61} +(-6.09960 - 9.41823i) q^{62} +(-7.06299 - 7.06299i) q^{63} +(-7.62672 + 2.41519i) q^{64} +(4.85004 + 2.34460i) q^{65} +(1.26603 - 5.91991i) q^{66} +(-1.67091 - 1.67091i) q^{67} +(-11.3635 + 4.32960i) q^{68} -4.46723 q^{69} +(-1.93179 - 15.4464i) q^{70} +3.39780i q^{71} +(-5.67184 + 0.876613i) q^{72} +(10.6643 - 10.6643i) q^{73} +(1.23645 - 5.78160i) q^{74} +(-0.566258 + 4.89404i) q^{75} +(-1.82506 - 0.818024i) q^{76} +(-15.1220 + 15.1220i) q^{77} +(2.81777 - 1.82490i) q^{78} -12.4394 q^{79} +(-7.81635 - 4.34794i) q^{80} -1.20461 q^{81} +(4.37569 - 2.83386i) q^{82} +(3.39352 - 3.39352i) q^{83} +(-8.85238 - 3.96780i) q^{84} +(-12.2405 - 5.91729i) q^{85} +(3.04578 - 14.2420i) q^{86} +(0.679431 - 0.679431i) q^{87} +(1.87684 + 12.1435i) q^{88} +10.5856i q^{89} +(-5.06521 - 3.93910i) q^{90} -11.8594 q^{91} +(8.47322 - 3.22836i) q^{92} +(-5.52818 - 5.52818i) q^{93} +(1.22990 - 5.75096i) q^{94} +(-0.735369 - 2.11169i) q^{95} +(-4.84442 + 2.75683i) q^{96} +(10.2334 + 10.2334i) q^{97} +(13.2475 + 20.4552i) q^{98} +8.81518i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 8 q^{3} - 8 q^{6}+O(q^{10}) $ 104 * q - 8 * q^3 - 8 * q^6	$ 104 q - 8 q^{3} - 8 q^{6} + 4 q^{10} + 16 q^{11} - 18 q^{12} - 16 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{26} + 16 q^{27} + 16 q^{28} - 44 q^{30} + 50 q^{32} + 32 q^{33} - 36 q^{35} + 136 q^{36} + 4 q^{40} + 8 q^{41} + 20 q^{42} - 44 q^{43} - 56 q^{46} + 38 q^{48} + 24 q^{50} - 16 q^{51} - 94 q^{52} - 28 q^{56} + 8 q^{57} + 8 q^{58} - 2 q^{60} - 20 q^{62} + 44 q^{65} + 52 q^{66} - 40 q^{67} - 56 q^{68} - 32 q^{70} + 88 q^{72} - 48 q^{73} + 56 q^{75} + 8 q^{76} + 52 q^{78} - 80 q^{80} - 152 q^{81} - 100 q^{82} - 44 q^{83} - 104 q^{86} + 20 q^{88} + 72 q^{90} - 64 q^{91} - 64 q^{92} - 52 q^{96} + 20 q^{97} - 100 q^{98}+O(q^{100}) $ 104 * q - 8 * q^3 - 8 * q^6 + 4 * q^10 + 16 * q^11 - 18 * q^12 - 16 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^26 + 16 * q^27 + 16 * q^28 - 44 * q^30 + 50 * q^32 + 32 * q^33 - 36 * q^35 + 136 * q^36 + 4 * q^40 + 8 * q^41 + 20 * q^42 - 44 * q^43 - 56 * q^46 + 38 * q^48 + 24 * q^50 - 16 * q^51 - 94 * q^52 - 28 * q^56 + 8 * q^57 + 8 * q^58 - 2 * q^60 - 20 * q^62 + 44 * q^65 + 52 * q^66 - 40 * q^67 - 56 * q^68 - 32 * q^70 + 88 * q^72 - 48 * q^73 + 56 * q^75 + 8 * q^76 + 52 * q^78 - 80 * q^80 - 152 * q^81 - 100 * q^82 - 44 * q^83 - 104 * q^86 + 20 * q^88 + 72 * q^90 - 64 * q^91 - 64 * q^92 - 52 * q^96 + 20 * q^97 - 100 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$-1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.18702	+	0.768758i	−0.839348	+	0.543594i
$2$	−1.18702	+	0.768758i	−0.839348	+	0.543594i
$3$	−0.696739	+	0.696739i	−0.402263	+	0.402263i	−0.879030	−	0.476767i	$-0.841809\pi$
$3$	−0.696739	+	0.696739i	−0.402263	+	0.402263i	0.476767	+	0.879030i	$0.341809\pi$
$4$	0.818024	−	1.82506i	0.409012	−	0.912529i
$5$	2.11169	−	0.735369i	0.944376	−	0.328867i
$5$	2.11169	−	0.735369i	0.944376	−	0.328867i
$6$	0.291418	−	1.36267i	0.118971	−	0.556306i
$7$	−3.48083	+	3.48083i	−1.31563	+	1.31563i	−0.398435	+	0.917197i	$0.630446\pi$
$7$	−3.48083	+	3.48083i	−1.31563	+	1.31563i	−0.917197	+	0.398435i	$0.869554\pi$
$8$	0.432019	+	2.79524i	0.152742	+	0.988266i
$9$			2.02911i			0.676370i
$10$	−1.94129	+	2.49627i	−0.613891	+	0.789391i
$11$	4.34436			1.30987			0.654937	−	0.755684i	$-0.272695\pi$
$11$	4.34436			1.30987			0.654937	+	0.755684i	$0.272695\pi$
$12$	0.701640	+	1.84154i	0.202546	+	0.531606i
$13$	1.70353	+	1.70353i	0.472473	+	0.472473i	0.902714	−	0.430241i	$-0.141571\pi$
$13$	1.70353	+	1.70353i	0.472473	+	0.472473i	−0.430241	+	0.902714i	$0.641571\pi$
$14$	1.45589	−	6.80773i	0.389104	−	1.81944i
$15$	−0.958937	+	1.98366i	−0.247596	+	0.512178i
$16$	−2.66167	−	2.98588i	−0.665419	−	0.746470i
$17$	−4.29935	−	4.29935i	−1.04275	−	1.04275i	−0.999045	−	0.0437012i	$-0.986085\pi$
$17$	−4.29935	−	4.29935i	−1.04275	−	1.04275i	−0.0437012	−	0.999045i	$-0.513915\pi$
$18$	−1.55989	−	2.40859i	−0.367670	−	0.567710i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	0.385322	−	4.45551i	0.0861605	−	0.996281i
$21$		−	4.85047i		−	1.05846i
$22$	−5.15683	+	3.33976i	−1.09944	+	0.712039i
$23$	3.20581	+	3.20581i	0.668458	+	0.668458i	0.957359	−	0.288901i	$-0.0932898\pi$
$23$	3.20581	+	3.20581i	0.668458	+	0.668458i	−0.288901	+	0.957359i	$0.593290\pi$
$24$	−2.24856	−	1.64655i	−0.458985	−	0.336100i
$25$	3.91847	−	3.10574i	0.783693	−	0.621148i
$26$	−3.33171	−	0.712517i	−0.653403	−	0.139736i
$27$	−3.50398	−	3.50398i	−0.674341	−	0.674341i
$28$	3.50532	+	9.20013i	0.662443	+	1.73866i
$29$	−0.975159			−0.181082			−0.0905412	−	0.995893i	$-0.528860\pi$
$29$	−0.975159			−0.181082			−0.0905412	+	0.995893i	$0.528860\pi$
$30$	−0.386676	−	3.09183i	−0.0705971	−	0.564488i
$31$			7.93436i			1.42505i	0.701645	+	0.712526i	$0.252449\pi$
$31$			7.93436i			1.42505i	−0.701645	+	0.712526i	$0.747551\pi$
$32$	5.45487	+	1.49811i	0.964295	+	0.264831i
$33$	−3.02689	+	3.02689i	−0.526913	+	0.526913i
$34$	8.40857	+	1.79825i	1.44206	+	0.308397i
$35$	−4.79074	+	9.91013i	−0.809784	+	1.67512i
$36$	3.70324	+	1.65986i	0.617207	+	0.276643i
$37$	−2.95616	+	2.95616i	−0.485991	+	0.485991i	−0.907038	−	0.421048i	$-0.861662\pi$
$37$	−2.95616	+	2.95616i	−0.485991	+	0.485991i	0.421048	+	0.907038i	$0.361662\pi$
$38$	0.768758	+	1.18702i	0.124709	+	0.192560i
$39$	−2.37383			−0.380116
$40$	2.96782	+	5.58498i	0.469254	+	0.883064i
$41$	−3.68629			−0.575702			−0.287851	−	0.957675i	$-0.592941\pi$
$41$	−3.68629			−0.575702			−0.287851	+	0.957675i	$0.592941\pi$
$42$	3.72883	+	5.75759i	0.575371	+	0.888416i
$43$	−7.28201	+	7.28201i	−1.11050	+	1.11050i	−0.117413	+	0.993083i	$0.537460\pi$
$43$	−7.28201	+	7.28201i	−1.11050	+	1.11050i	−0.993083	+	0.117413i	$0.962540\pi$
$44$	3.55379	−	7.92871i	0.535754	−	1.19530i
$45$	1.49214	+	4.28485i	0.222436	+	0.638747i
$46$	−6.26985	−	1.34086i	−0.924439	−	0.197700i
$47$	−2.94050	+	2.94050i	−0.428916	+	0.428916i	−0.888259	−	0.459343i	$-0.848085\pi$
$47$	−2.94050	+	2.94050i	−0.428916	+	0.428916i	0.459343	+	0.888259i	$0.348085\pi$
$48$	3.93487	+	0.225887i	0.567950	+	0.0326040i
$49$		−	17.2324i		−	2.46177i
$50$	−2.26373	+	6.69892i	−0.320140	+	0.947370i
$51$	5.99105			0.838915
$52$	4.50256	−	1.71551i	0.624392	−	0.237898i
$53$	0.396814	+	0.396814i	0.0545067	+	0.0545067i	0.733835	−	0.679328i	$-0.237729\pi$
$53$	0.396814	+	0.396814i	0.0545067	+	0.0545067i	−0.679328	+	0.733835i	$0.737729\pi$
$54$	6.85299	+	1.46558i	0.932574	+	0.199440i
$55$	9.17394	−	3.19470i	1.23701	−	0.430774i
$56$	−11.2335	−	8.22598i	−1.50115	−	1.09924i
$57$	0.696739	+	0.696739i	0.0922854	+	0.0922854i
$58$	1.15753	−	0.749661i	0.151991	−	0.0984353i
$59$			12.7921i			1.66539i	0.553734	+	0.832694i	$0.313203\pi$
$59$			12.7921i			1.66539i	−0.553734	+	0.832694i	$0.686797\pi$
$60$	2.83586	+	3.37279i	0.366108	+	0.435426i
$61$			2.90021i			0.371334i	0.982613	+	0.185667i	$0.0594445\pi$
$61$			2.90021i			0.371334i	−0.982613	+	0.185667i	$0.940555\pi$
$62$	−6.09960	−	9.41823i	−0.774650	−	1.19612i
$63$	−7.06299	−	7.06299i	−0.889853	−	0.889853i
$64$	−7.62672	+	2.41519i	−0.953340	+	0.301899i
$65$	4.85004	+	2.34460i	0.601573	+	0.290812i
$66$	1.26603	−	5.91991i	0.155837	−	0.728690i
$67$	−1.67091	−	1.67091i	−0.204135	−	0.204135i	0.597634	−	0.801769i	$-0.296107\pi$
$67$	−1.67091	−	1.67091i	−0.204135	−	0.204135i	−0.801769	+	0.597634i	$0.796107\pi$
$68$	−11.3635	+	4.32960i	−1.37803	+	0.525041i
$69$	−4.46723			−0.537791
$70$	−1.93179	−	15.4464i	−0.230893	−	1.84620i
$71$			3.39780i			0.403245i	0.979463	+	0.201622i	$0.0646214\pi$
$71$			3.39780i			0.403245i	−0.979463	+	0.201622i	$0.935379\pi$
$72$	−5.67184	+	0.876613i	−0.668433	+	0.103310i
$73$	10.6643	−	10.6643i	1.24816	−	1.24816i	0.291632	−	0.956531i	$-0.405802\pi$
$73$	10.6643	−	10.6643i	1.24816	−	1.24816i	0.956531	−	0.291632i	$-0.0941982\pi$
$74$	1.23645	−	5.78160i	0.143734	−	0.672097i
$75$	−0.566258	+	4.89404i	−0.0653858	+	0.565115i
$76$	−1.82506	−	0.818024i	−0.209349	−	0.0938337i
$77$	−15.1220	+	15.1220i	−1.72331	+	1.72331i
$78$	2.81777	−	1.82490i	0.319050	−	0.206629i
$79$	−12.4394			−1.39954			−0.699772	−	0.714367i	$-0.746715\pi$
$79$	−12.4394			−1.39954			−0.699772	+	0.714367i	$0.746715\pi$
$80$	−7.81635	−	4.34794i	−0.873895	−	0.486115i
$81$	−1.20461			−0.133846
$82$	4.37569	−	2.83386i	0.483214	−	0.312948i
$83$	3.39352	−	3.39352i	0.372487	−	0.372487i	−0.495895	−	0.868382i	$-0.665160\pi$
$83$	3.39352	−	3.39352i	0.372487	−	0.372487i	0.868382	+	0.495895i	$0.165160\pi$
$84$	−8.85238	−	3.96780i	−0.965874	−	0.432922i
$85$	−12.2405	−	5.91729i	−1.32767	−	0.641820i
$86$	3.04578	−	14.2420i	0.328435	−	1.53575i
$87$	0.679431	−	0.679431i	0.0728427	−	0.0728427i
$88$	1.87684	+	12.1435i	0.200072	+	1.29450i
$89$			10.5856i			1.12207i	0.827792	+	0.561034i	$0.189596\pi$
$89$			10.5856i			1.12207i	−0.827792	+	0.561034i	$0.810404\pi$
$90$	−5.06521	−	3.93910i	−0.533920	−	0.415217i
$91$	−11.8594			−1.24320
$92$	8.47322	−	3.22836i	0.883395	−	0.336580i
$93$	−5.52818	−	5.52818i	−0.573245	−	0.573245i
$94$	1.22990	−	5.75096i	0.126854	−	0.593167i
$95$	−0.735369	−	2.11169i	−0.0754472	−	0.216655i
$96$	−4.84442	+	2.75683i	−0.494431	+	0.281368i
$97$	10.2334	+	10.2334i	1.03904	+	1.03904i	0.999206	+	0.0398365i	$0.0126837\pi$
$97$	10.2334	+	10.2334i	1.03904	+	1.03904i	0.0398365	+	0.999206i	$0.487316\pi$
$98$	13.2475	+	20.4552i	1.33820	+	2.06628i
$99$			8.81518i			0.885959i
$100$	−2.46276	−	9.69200i	−0.246276	−	0.969200i
$101$			1.66669i			0.165842i	0.996556	+	0.0829208i	$0.0264248\pi$
$101$			1.66669i			0.165842i	−0.996556	+	0.0829208i	$0.973575\pi$
$102$	−7.11149	+	4.60567i	−0.704142	+	0.456029i
$103$	−4.49697	−	4.49697i	−0.443099	−	0.443099i	0.449953	−	0.893052i	$-0.351441\pi$
$103$	−4.49697	−	4.49697i	−0.443099	−	0.443099i	−0.893052	+	0.449953i	$0.851441\pi$
$104$	−4.02581	+	5.49771i	−0.394763	+	0.539095i
$105$	−3.56688	−	10.2427i	−0.348092	−	0.999583i
$106$	−0.776080	−	0.165972i	−0.0753796	−	0.0161206i
$107$	−6.44681	−	6.44681i	−0.623236	−	0.623236i	0.323121	−	0.946358i	$-0.395268\pi$
$107$	−6.44681	−	6.44681i	−0.623236	−	0.623236i	−0.946358	+	0.323121i	$0.895268\pi$
$108$	−9.26130	+	3.52863i	−0.891169	+	0.339542i
$109$	−4.84287			−0.463863			−0.231931	−	0.972732i	$-0.574504\pi$
$109$	−4.84287			−0.463863			−0.231931	+	0.972732i	$0.574504\pi$
$110$	−8.43368	+	10.8447i	−0.804119	+	1.03400i
$111$		−	4.11935i		−	0.390992i
$112$	19.6582	+	1.12851i	1.85753	+	0.106634i
$113$	−5.09703	+	5.09703i	−0.479488	+	0.479488i	−0.904968	−	0.425480i	$-0.860105\pi$
$113$	−5.09703	+	5.09703i	−0.479488	+	0.479488i	0.425480	+	0.904968i	$0.360105\pi$
$114$	−1.36267	−	0.291418i	−0.127625	−	0.0272938i
$115$	9.12713	+	4.41223i	0.851110	+	0.411442i
$116$	−0.797703	+	1.77972i	−0.0740648	+	0.165243i
$117$	−3.45664	+	3.45664i	−0.319566	+	0.319566i
$118$	−9.83401	−	15.1844i	−0.905294	−	1.39784i
$119$	29.9306			2.74374
$120$	−5.95907	−	1.82348i	−0.543987	−	0.166460i
$121$	7.87345			0.715768
$122$	−2.22956	−	3.44260i	−0.201855	−	0.311678i
$123$	2.56838	−	2.56838i	0.231583	−	0.231583i
$124$	14.4807	+	6.49049i	1.30040	+	0.582863i
$125$	5.99072	−	9.43988i	0.535826	−	0.844328i
$126$	13.8136	+	2.95417i	1.23062	+	0.263178i
$127$	6.03941	−	6.03941i	0.535911	−	0.535911i	−0.386414	−	0.922325i	$-0.626286\pi$
$127$	6.03941	−	6.03941i	0.535911	−	0.535911i	0.922325	+	0.386414i	$0.126286\pi$
$128$	7.19636	−	8.72997i	0.636074	−	0.771628i
$129$		−	10.1473i		−	0.893422i
$130$	−7.55951	+	0.945422i	−0.663013	+	0.0829190i
$131$	11.7673			1.02812			0.514059	−	0.857755i	$-0.328141\pi$
$131$	11.7673			1.02812			0.514059	+	0.857755i	$0.328141\pi$
$132$	3.04818	+	8.00030i	0.265310	+	0.696337i
$133$	3.48083	+	3.48083i	0.301827	+	0.301827i
$134$	3.26793	+	0.698877i	0.282306	+	0.0603738i
$135$	−9.97603	−	4.82260i	−0.858600	−	0.415063i
$136$	10.1603	−	13.8751i	0.871240	−	1.18978i
$137$	12.4602	+	12.4602i	1.06455	+	1.06455i	0.997768	+	0.0667832i	$0.0212736\pi$
$137$	12.4602	+	12.4602i	1.06455	+	1.06455i	0.0667832	+	0.997768i	$0.478726\pi$
$138$	5.30268	−	3.43422i	0.451394	−	0.292340i
$139$		−	6.38042i		−	0.541180i	−0.962695	−	0.270590i	$-0.912781\pi$
$139$		−	6.38042i		−	0.541180i	0.962695	−	0.270590i	$-0.0872188\pi$
$140$	14.1676	+	16.8501i	1.19738	+	1.42409i
$141$		−	4.09753i		−	0.345074i
$142$	−2.61208	−	4.03325i	−0.219201	−	0.338463i
$143$	7.40072	+	7.40072i	0.618880	+	0.618880i
$144$	6.05868	−	5.40083i	0.504890	−	0.450069i
$145$	−2.05923	+	0.717101i	−0.171010	+	0.0595520i
$146$	−4.46046	+	20.8570i	−0.369150	+	1.72614i
$147$	12.0065	+	12.0065i	0.990278	+	0.990278i
$148$	2.97696	+	7.81339i	0.244705	+	0.642256i
$149$	−8.91875			−0.730653			−0.365326	−	0.930879i	$-0.619043\pi$
$149$	−8.91875			−0.730653			−0.365326	+	0.930879i	$0.619043\pi$
$150$	−3.09017	−	6.24463i	−0.252311	−	0.509872i
$151$		−	21.8156i		−	1.77532i	−0.460495	−	0.887662i	$-0.652328\pi$
$151$		−	21.8156i		−	1.77532i	0.460495	−	0.887662i	$-0.347672\pi$
$152$	2.79524	−	0.432019i	0.226724	−	0.0350413i
$153$	8.72385	−	8.72385i	0.705282	−	0.705282i
$154$	6.32493	−	29.5752i	0.509677	−	2.38324i
$155$	5.83468	+	16.7549i	0.468653	+	1.34579i
$156$	−1.94185	+	4.33237i	−0.155472	+	0.346867i
$157$	5.82699	−	5.82699i	0.465045	−	0.465045i	−0.435260	−	0.900305i	$-0.643344\pi$
$157$	5.82699	−	5.82699i	0.465045	−	0.465045i	0.900305	+	0.435260i	$0.143344\pi$
$158$	14.7658	−	9.56289i	1.17470	−	0.760783i
$159$	−0.552952			−0.0438520
$160$	12.6207	−	0.847795i	0.997751	−	0.0670241i
$161$	−22.3178			−1.75889
$162$	1.42989	−	0.926053i	0.112343	−	0.0727576i
$163$	9.02096	−	9.02096i	0.706576	−	0.706576i	−0.259238	−	0.965814i	$-0.583471\pi$
$163$	9.02096	−	9.02096i	0.706576	−	0.706576i	0.965814	+	0.259238i	$0.0834712\pi$
$164$	−3.01547	+	6.72769i	−0.235469	+	0.525345i
$165$	−4.16597	+	8.61772i	−0.324320	+	0.670888i
$166$	−1.41938	+	6.63697i	−0.110165	+	0.515129i
$167$	−1.22857	+	1.22857i	−0.0950695	+	0.0950695i	−0.753042	−	0.657972i	$-0.771414\pi$
$167$	−1.22857	+	1.22857i	−0.0950695	+	0.0950695i	0.657972	+	0.753042i	$0.271414\pi$
$168$	13.5582	−	2.09549i	1.04604	−	0.161671i
$169$		−	7.19600i		−	0.553539i
$170$	19.0787	−	2.38605i	1.46327	−	0.183002i
$171$	2.02911			0.155170
$172$	7.33324	+	19.2470i	0.559154	+	1.46757i
$173$	13.0049	+	13.0049i	0.988746	+	0.988746i	0.999937	−	0.0111915i	$-0.00356244\pi$
$173$	13.0049	+	13.0049i	0.988746	+	0.988746i	−0.0111915	+	0.999937i	$0.503562\pi$
$174$	−0.284179	+	1.32881i	−0.0215436	+	0.100737i
$175$	−2.82896	+	24.4501i	−0.213850	+	1.84825i
$176$	−11.5633	−	12.9717i	−0.871614	−	0.977782i
$177$	−8.91275	−	8.91275i	−0.669923	−	0.669923i
$178$	−8.13774	−	12.5653i	−0.609950	−	0.941807i
$179$			21.1659i			1.58201i	0.611807	+	0.791007i	$0.290443\pi$
$179$			21.1659i			1.58201i	−0.611807	+	0.791007i	$0.709557\pi$
$180$	9.04071	+	0.781859i	0.673854	+	0.0582764i
$181$			7.45595i			0.554196i	0.960842	+	0.277098i	$0.0893727\pi$
$181$			7.45595i			0.554196i	−0.960842	+	0.277098i	$0.910627\pi$
$182$	14.0773	−	9.11698i	1.04348	−	0.675796i
$183$	−2.02069	−	2.02069i	−0.149374	−	0.149374i
$184$	−7.57604	+	10.3460i	−0.558513	+	0.762716i
$185$	−4.06863	+	8.41637i	−0.299132	+	0.618784i
$186$	10.8119	+	2.31222i	0.792765	+	0.169540i
$187$	−18.6779	−	18.6779i	−1.36587	−	1.36587i
$188$	2.96119	+	7.77199i	0.215967	+	0.566831i
$189$	24.3935			1.77437
$190$	2.49627	+	1.94129i	0.181099	+	0.140836i
$191$		−	11.7873i		−	0.852901i	−0.904511	−	0.426450i	$-0.859764\pi$
$191$		−	11.7873i		−	0.852901i	0.904511	−	0.426450i	$-0.140236\pi$
$192$	3.63108	−	6.99659i	0.262050	−	0.504936i
$193$	4.27948	−	4.27948i	0.308044	−	0.308044i	−0.536106	−	0.844150i	$-0.680105\pi$
$193$	4.27948	−	4.27948i	0.308044	−	0.308044i	0.844150	+	0.536106i	$0.180105\pi$
$194$	−20.0142	−	4.28022i	−1.43694	−	0.307302i
$195$	−5.01278	+	1.74564i	−0.358973	+	0.125008i
$196$	−31.4501	−	14.0965i	−2.24644	−	1.00689i
$197$	−2.69243	+	2.69243i	−0.191828	+	0.191828i	−0.796485	−	0.604658i	$-0.793310\pi$
$197$	−2.69243	+	2.69243i	−0.191828	+	0.191828i	0.604658	+	0.796485i	$0.293310\pi$
$198$	−6.77673	−	10.4638i	−0.481602	−	0.743628i
$199$	10.8357			0.768124			0.384062	−	0.923307i	$-0.374525\pi$
$199$	10.8357			0.768124			0.384062	+	0.923307i	$0.374525\pi$
$200$	10.3741	+	9.61131i	0.733562	+	0.679622i
$201$	2.32838			0.164231
$202$	−1.28128	−	1.97839i	−0.0901504	−	0.139199i
$203$	3.39436	−	3.39436i	0.238238	−	0.238238i
$204$	4.90082	−	10.9340i	0.343126	−	0.765535i
$205$	−7.78430	+	2.71078i	−0.543679	+	0.189329i
$206$	8.79505	+	1.88090i	0.612780	+	0.131049i
$207$	−6.50494	+	6.50494i	−0.452125	+	0.452125i
$208$	0.552294	−	9.62075i	0.0382947	−	0.667079i
$209$		−	4.34436i		−	0.300506i
$210$	12.1081	+	9.41618i	0.835537	+	0.649778i
$211$	−9.50020			−0.654021			−0.327010	−	0.945021i	$-0.606041\pi$
$211$	−9.50020			−0.654021			−0.327010	+	0.945021i	$0.606041\pi$
$212$	1.04881	−	0.399606i	0.0720328	−	0.0274450i
$213$	−2.36738	−	2.36738i	−0.162210	−	0.162210i
$214$	12.6085	+	2.69644i	0.861900	+	0.184325i
$215$	−10.0224	+	20.7323i	−0.683521	+	1.41393i
$216$	8.28067	−	11.3082i	0.563428	−	0.769428i
$217$	−27.6182	−	27.6182i	−1.87484	−	1.87484i
$218$	5.74857	−	3.72299i	0.389342	−	0.252153i
$219$			14.8605i			1.00418i
$220$	1.67398	−	19.3563i	0.112859	−	1.30500i
$221$		−	14.6481i		−	0.985338i
$222$	3.16678	+	4.88974i	0.212541	+	0.328178i
$223$	12.3211	+	12.3211i	0.825081	+	0.825081i	0.986832	−	0.161751i	$-0.0517141\pi$
$223$	12.3211	+	12.3211i	0.825081	+	0.825081i	−0.161751	+	0.986832i	$0.551714\pi$
$224$	−24.2022	+	13.7728i	−1.61708	+	0.920236i
$225$	6.30189	+	7.95099i	0.420126	+	0.530066i
$226$	2.13189	−	9.96865i	0.141811	−	0.663104i
$227$	7.16733	+	7.16733i	0.475713	+	0.475713i	0.903757	−	0.428045i	$-0.140797\pi$
$227$	7.16733	+	7.16733i	0.475713	+	0.475713i	−0.428045	+	0.903757i	$0.640797\pi$
$228$	1.84154	−	0.701640i	0.121959	−	0.0464673i
$229$	18.2039			1.20295			0.601474	−	0.798893i	$-0.294581\pi$
$229$	18.2039			1.20295			0.601474	+	0.798893i	$0.294581\pi$
$230$	−14.2260	+	1.77916i	−0.938035	+	0.117314i
$231$		−	21.0722i		−	1.38645i
$232$	−0.421287	−	2.72580i	−0.0276588	−	0.178958i
$233$	6.59274	−	6.59274i	0.431905	−	0.431905i	−0.457371	−	0.889276i	$-0.651209\pi$
$233$	6.59274	−	6.59274i	0.431905	−	0.431905i	0.889276	+	0.457371i	$0.151209\pi$
$234$	1.44578	−	6.76041i	0.0945133	−	0.441942i
$235$	−4.04708	+	8.37178i	−0.264002	+	0.546115i
$236$	23.3463	+	10.4642i	1.51971	+	0.681163i
$237$	8.66703	−	8.66703i	0.562984	−	0.562984i
$238$	−35.5282	+	23.0094i	−2.30295	+	1.49148i
$239$	−24.4162			−1.57935			−0.789676	−	0.613524i	$-0.789751\pi$
$239$	−24.4162			−1.57935			−0.789676	+	0.613524i	$0.789751\pi$
$240$	8.47534	−	2.41658i	0.547081	−	0.155989i
$241$	−0.148229			−0.00954828			−0.00477414	−	0.999989i	$-0.501520\pi$
$241$	−0.148229			−0.00954828			−0.00477414	+	0.999989i	$0.501520\pi$
$242$	−9.34593	+	6.05278i	−0.600779	+	0.389087i
$243$	11.3512	−	11.3512i	0.728182	−	0.728182i
$244$	5.29305	+	2.37244i	0.338853	+	0.151880i
$245$	−12.6722	−	36.3895i	−0.809595	−	2.32484i
$246$	−1.07425	+	5.02318i	−0.0684919	+	0.320266i
$247$	1.70353	−	1.70353i	0.108393	−	0.108393i
$248$	−22.1784	+	3.42779i	−1.40833	+	0.217665i
$249$			4.72880i			0.299675i
$250$	0.145883	+	15.8107i	0.00922646	+	0.999957i
$251$	1.36338			0.0860559			0.0430280	−	0.999074i	$-0.486300\pi$
$251$	1.36338			0.0860559			0.0430280	+	0.999074i	$0.486300\pi$
$252$	−18.6681	+	7.11267i	−1.17598	+	0.448056i
$253$	13.9272	+	13.9272i	0.875595	+	0.875595i
$254$	−2.52605	+	11.8117i	−0.158498	+	0.741134i
$255$	12.6512	−	4.40563i	0.792252	−	0.275891i
$256$	−1.83098	+	15.8949i	−0.114436	+	0.993431i
$257$	−5.39565	−	5.39565i	−0.336572	−	0.336572i	0.518504	−	0.855075i	$-0.326489\pi$
$257$	−5.39565	−	5.39565i	−0.336572	−	0.336572i	−0.855075	+	0.518504i	$0.826489\pi$
$258$	7.80083	+	12.0451i	0.485659	+	0.749893i
$259$		−	20.5798i		−	1.27877i
$260$	8.24647	−	6.93366i	0.511424	−	0.430007i
$261$		−	1.97870i		−	0.122479i
$262$	−13.9681	+	9.04624i	−0.862949	+	0.558878i
$263$	−5.53257	−	5.53257i	−0.341153	−	0.341153i	0.515648	−	0.856801i	$-0.327551\pi$
$263$	−5.53257	−	5.53257i	−0.341153	−	0.341153i	−0.856801	+	0.515648i	$0.827551\pi$
$264$	−9.76854	−	7.15320i	−0.601212	−	0.440249i
$265$	1.12975	+	0.546144i	0.0694002	+	0.0335494i
$266$	−6.80773	−	1.45589i	−0.417409	−	0.0892666i
$267$	−7.37539	−	7.37539i	−0.451366	−	0.451366i
$268$	−4.41636	+	1.68267i	−0.269772	+	0.102785i
$269$	21.1339			1.28856			0.644278	−	0.764792i	$-0.277158\pi$
$269$	21.1339			1.28856			0.644278	+	0.764792i	$0.277158\pi$
$270$	15.5491	−	1.94464i	0.946290	−	0.118347i
$271$		−	1.80171i		−	0.109446i	−0.998502	−	0.0547230i	$-0.982572\pi$
$271$		−	1.80171i		−	0.109446i	0.998502	−	0.0547230i	$-0.0174276\pi$
$272$	−1.39388	+	24.2808i	−0.0845163	+	1.47224i
$273$	8.26289	−	8.26289i	0.500093	−	0.500093i
$274$	−24.3694	−	5.21163i	−1.47221	−	0.314846i
$275$	17.0232	−	13.4925i	1.02654	−	0.813625i
$276$	−3.65430	+	8.15295i	−0.219963	+	0.490750i
$277$	−10.6798	+	10.6798i	−0.641690	+	0.641690i	−0.950971	−	0.309281i	$-0.899912\pi$
$277$	−10.6798	+	10.6798i	−0.641690	+	0.641690i	0.309281	+	0.950971i	$0.399912\pi$
$278$	4.90500	+	7.57368i	0.294182	+	0.454239i
$279$	−16.0997			−0.963862
$280$	−29.7709	−	9.10991i	−1.77915	−	0.544421i
$281$	27.2063			1.62299			0.811495	−	0.584359i	$-0.198654\pi$
$281$	27.2063			1.62299			0.811495	+	0.584359i	$0.198654\pi$
$282$	3.15000	+	4.86384i	0.187580	+	0.289637i
$283$	3.76007	−	3.76007i	0.223513	−	0.223513i	−0.586463	−	0.809976i	$-0.699480\pi$
$283$	3.76007	−	3.76007i	0.223513	−	0.223513i	0.809976	+	0.586463i	$0.199480\pi$
$284$	6.20118	+	2.77948i	0.367973	+	0.164932i
$285$	1.98366	+	0.958937i	0.117502	+	0.0568025i
$286$	−14.4742	−	3.09543i	−0.855875	−	0.183037i
$287$	12.8314	−	12.8314i	0.757411	−	0.757411i
$288$	−3.03983	+	11.0685i	−0.179124	+	0.652220i
$289$			19.9688i			1.17464i
$290$	1.89307	−	2.43426i	0.111165	−	0.142945i
$291$	−14.2600			−0.835936
$292$	−10.7393	−	28.1866i	−0.628471	−	1.64950i
$293$	−6.15520	−	6.15520i	−0.359591	−	0.359591i	0.504071	−	0.863662i	$-0.331835\pi$
$293$	−6.15520	−	6.15520i	−0.359591	−	0.359591i	−0.863662	+	0.504071i	$0.831835\pi$
$294$	−23.4820	−	5.02184i	−1.36950	−	0.292880i
$295$	9.40690	+	27.0129i	0.547691	+	1.57275i
$296$	−9.54030	−	6.98607i	−0.554519	−	0.406057i
$297$	−15.2225	−	15.2225i	−0.883301	−	0.883301i
$298$	10.5867	−	6.85636i	0.613272	−	0.397178i
$299$			10.9224i			0.631657i
$300$	8.46870	+	5.03689i	0.488940	+	0.290805i
$301$		−	50.6949i		−	2.92201i
$302$	16.7709	+	25.8955i	0.965055	+	1.49012i
$303$	−1.16125	−	1.16125i	−0.0667118	−	0.0667118i
$304$	−2.98588	+	2.66167i	−0.171252	+	0.152658i
$305$	2.13272	+	6.12434i	0.122119	+	0.350679i
$306$	−3.64884	+	17.0619i	−0.208590	+	0.975364i
$307$	8.09067	+	8.09067i	0.461759	+	0.461759i	0.899232	−	0.437473i	$-0.144126\pi$
$307$	8.09067	+	8.09067i	0.461759	+	0.461759i	−0.437473	+	0.899232i	$0.644126\pi$
$308$	15.2284	+	39.9687i	0.867717	+	2.27743i
$309$	6.26642			0.356484
$310$	−19.8063	−	15.4029i	−1.12492	−	0.874827i
$311$			0.515851i			0.0292512i	0.999893	+	0.0146256i	$0.00465565\pi$
$311$			0.515851i			0.0292512i	−0.999893	+	0.0146256i	$0.995344\pi$
$312$	−1.02554	−	6.63541i	−0.0580596	−	0.375656i
$313$	3.34624	−	3.34624i	0.189141	−	0.189141i	−0.606184	−	0.795325i	$-0.707300\pi$
$313$	3.34624	−	3.34624i	0.189141	−	0.189141i	0.795325	+	0.606184i	$0.207300\pi$
$314$	−2.43720	+	11.3963i	−0.137539	+	0.643130i
$315$	−20.1087	−	9.72094i	−1.13300	−	0.547713i
$316$	−10.1757	+	22.7027i	−0.572430	+	1.27712i
$317$	6.05652	−	6.05652i	0.340168	−	0.340168i	−0.516262	−	0.856430i	$-0.672677\pi$
$317$	6.05652	−	6.05652i	0.340168	−	0.340168i	0.856430	+	0.516262i	$0.172677\pi$
$318$	0.656364	−	0.425086i	0.0368071	−	0.0238377i
$319$	−4.23644			−0.237195
$320$	−14.3292	+	10.7086i	−0.801027	+	0.598628i
$321$	8.98349			0.501409
$322$	26.4916	−	17.1570i	1.47632	−	0.956121i
$323$	−4.29935	+	4.29935i	−0.239222	+	0.239222i
$324$	−0.985399	+	2.19848i	−0.0547444	+	0.122138i
$325$	11.9659	+	1.38450i	0.663749	+	0.0767982i
$326$	−3.77311	+	17.6430i	−0.208973	+	0.977154i
$327$	3.37422	−	3.37422i	0.186595	−	0.186595i
$328$	−1.59255	−	10.3041i	−0.0879336	−	0.568947i
$329$		−	20.4708i		−	1.12859i
$330$	−1.67986	−	13.4320i	−0.0924732	−	0.739407i
$331$	23.4562			1.28927			0.644635	−	0.764491i	$-0.277009\pi$
$331$	23.4562			1.28927			0.644635	+	0.764491i	$0.277009\pi$
$332$	−3.41739	−	8.96936i	−0.187554	−	0.492257i
$333$	−5.99838	−	5.99838i	−0.328709	−	0.328709i
$334$	0.513862	−	2.40281i	0.0281173	−	0.131476i
$335$	−4.75719	−	2.29971i	−0.259913	−	0.125647i
$336$	−14.4829	+	12.9104i	−0.790108	+	0.704318i
$337$	−3.76167	−	3.76167i	−0.204911	−	0.204911i	0.597189	−	0.802100i	$-0.296284\pi$
$337$	−3.76167	−	3.76167i	−0.204911	−	0.204911i	−0.802100	+	0.597189i	$0.796284\pi$
$338$	5.53198	+	8.54179i	0.300900	+	0.464612i
$339$		−	7.10260i		−	0.385760i
$340$	−20.8124	+	17.4991i	−1.12871	+	0.949025i
$341$			34.4697i			1.86664i
$342$	−2.40859	+	1.55989i	−0.130242	+	0.0843493i
$343$	35.6173	+	35.6173i	1.92315	+	1.92315i
$344$	−23.5009	−	17.2090i	−1.26709	−	0.927847i
$345$	−9.43340	+	3.28506i	−0.507877	+	0.176862i
$346$	−25.4347	−	5.43944i	−1.36738	−	0.292426i
$347$	5.61607	+	5.61607i	0.301486	+	0.301486i	0.841595	−	0.540109i	$-0.181617\pi$
$347$	5.61607	+	5.61607i	0.301486	+	0.301486i	−0.540109	+	0.841595i	$0.681617\pi$
$348$	−0.684211	−	1.79579i	−0.0366775	−	0.0962646i
$349$	19.6112			1.04976			0.524881	−	0.851175i	$-0.324110\pi$
$349$	19.6112			1.04976			0.524881	+	0.851175i	$0.324110\pi$
$350$	−15.4382	−	31.1975i	−0.825204	−	1.66758i
$351$		−	11.9382i		−	0.637215i
$352$	23.6979	+	6.50834i	1.26310	+	0.346896i
$353$	−2.71587	+	2.71587i	−0.144551	+	0.144551i	−0.775679	−	0.631128i	$-0.782592\pi$
$353$	−2.71587	+	2.71587i	−0.144551	+	0.144551i	0.631128	+	0.775679i	$0.282592\pi$
$354$	17.4313	+	3.72785i	0.926465	+	0.198133i
$355$	2.49864	+	7.17510i	0.132614	+	0.380815i
$356$	19.3193	+	8.65925i	1.02392	+	0.458939i
$357$	−20.8539	+	20.8539i	−1.10370	+	1.10370i
$358$	−16.2715	−	25.1243i	−0.859973	−	1.32786i
$359$	30.1648			1.59203			0.796017	−	0.605274i	$-0.206936\pi$
$359$	30.1648			1.59203			0.796017	+	0.605274i	$0.206936\pi$
$360$	−11.3325	+	6.02203i	−0.597277	+	0.317389i
$361$	−1.00000			−0.0526316
$362$	−5.73182	−	8.85035i	−0.301258	−	0.465164i
$363$	−5.48574	+	5.48574i	−0.287927	+	0.287927i
$364$	−9.70125	+	21.6440i	−0.508484	+	1.13446i
$365$	14.6775	−	30.3619i	0.768256	−	1.58921i
$366$	3.95201	+	0.845174i	0.206575	+	0.0441780i
$367$	17.6411	−	17.6411i	0.920859	−	0.920859i	−0.0762310	−	0.997090i	$-0.524289\pi$
$367$	17.6411	−	17.6411i	0.920859	−	0.920859i	0.997090	+	0.0762310i	$0.0242886\pi$
$368$	1.03935	−	18.1050i	0.0541796	−	0.943789i
$369$		−	7.47988i		−	0.389387i
$370$	−1.64061	−	13.1182i	−0.0852913	−	0.681982i
$371$	−2.76249			−0.143421
$372$	−14.6114	+	5.56707i	−0.757567	+	0.288639i
$373$	−12.1310	−	12.1310i	−0.628118	−	0.628118i	0.319477	−	0.947594i	$-0.396493\pi$
$373$	−12.1310	−	12.1310i	−0.628118	−	0.628118i	−0.947594	+	0.319477i	$0.896493\pi$
$374$	36.5298	+	7.81224i	1.88891	+	0.403961i
$375$	2.40316	+	10.7511i	0.124099	+	0.555185i
$376$	−9.48976	−	6.94906i	−0.489397	−	0.358370i
$377$	−1.66121	−	1.66121i	−0.0855565	−	0.0855565i
$378$	−28.9556	+	18.7527i	−1.48931	+	0.964535i
$379$		−	10.5942i		−	0.544186i	−0.962271	−	0.272093i	$-0.912284\pi$
$379$		−	10.5942i		−	0.544186i	0.962271	−	0.272093i	$-0.0877158\pi$
$380$	−4.45551	−	0.385322i	−0.228563	−	0.0197666i
$381$			8.41579i			0.431154i
$382$	9.06159	+	13.9918i	0.463631	+	0.715881i
$383$	−22.0130	−	22.0130i	−1.12481	−	1.12481i	−0.991008	−	0.133804i	$-0.957281\pi$
$383$	−22.0130	−	22.0130i	−1.12481	−	1.12481i	−0.133804	−	0.991008i	$-0.542719\pi$
$384$	1.06853	+	11.0965i	0.0545281	+	0.566266i
$385$	−20.8127	+	43.0532i	−1.06071	+	2.19419i
$386$	−1.78994	+	8.36971i	−0.0911055	+	0.426007i
$387$	−14.7760	−	14.7760i	−0.751106	−	0.751106i
$388$	27.0477	−	10.3054i	1.37314	−	0.523176i
$389$	4.15389			0.210611			0.105305	−	0.994440i	$-0.466418\pi$
$389$	4.15389			0.210611			0.105305	+	0.994440i	$0.466418\pi$
$390$	4.60829	−	5.92572i	0.233350	−	0.300060i
$391$		−	27.5658i		−	1.39406i
$392$	48.1687	−	7.44472i	2.43289	−	0.376015i
$393$	−8.19877	+	8.19877i	−0.413573	+	0.413573i
$394$	1.12614	−	5.26579i	0.0567339	−	0.265286i
$395$	−26.2682	+	9.14755i	−1.32170	+	0.460263i
$396$	16.0882	+	7.21102i	0.808463	+	0.362368i
$397$	−16.2356	+	16.2356i	−0.814839	+	0.814839i	−0.985355	−	0.170516i	$-0.945457\pi$
$397$	−16.2356	+	16.2356i	−0.814839	+	0.814839i	0.170516	+	0.985355i	$0.445457\pi$
$398$	−12.8622	+	8.33004i	−0.644724	+	0.417547i
$399$	−4.85047			−0.242827
$400$	−19.7031	−	3.43360i	−0.985153	−	0.171680i
$401$	−22.4417			−1.12069			−0.560343	−	0.828261i	$-0.689331\pi$
$401$	−22.4417			−1.12069			−0.560343	+	0.828261i	$0.689331\pi$
$402$	−2.76383	+	1.78996i	−0.137847	+	0.0892751i
$403$	−13.5164	+	13.5164i	−0.673299	+	0.673299i
$404$	3.04180	+	1.36339i	0.151335	+	0.0678312i
$405$	−2.54376	+	0.885832i	−0.126401	+	0.0440174i
$406$	−1.41973	+	6.63862i	−0.0704599	+	0.329469i
$407$	−12.8426	+	12.8426i	−0.636586	+	0.636586i
$408$	2.58825	+	16.7464i	0.128137	+	0.829072i
$409$			21.5074i			1.06347i	0.846910	+	0.531736i	$0.178460\pi$
$409$			21.5074i			1.06347i	−0.846910	+	0.531736i	$0.821540\pi$
$410$	7.15617	−	9.20199i	0.353418	−	0.454454i
$411$	−17.3631			−0.856458
$412$	−11.8858	+	4.52860i	−0.585574	+	0.223108i
$413$	−44.5271	−	44.5271i	−2.19104	−	2.19104i
$414$	2.72076	−	12.7222i	0.133718	−	0.625262i
$415$	4.67058	−	9.66155i	0.229270	−	0.474267i
$416$	6.74044	+	11.8446i	0.330477	+	0.580729i
$417$	4.44549	+	4.44549i	0.217697	+	0.217697i
$418$	3.33976	+	5.15683i	0.163353	+	0.252229i
$419$		−	19.7400i		−	0.964362i	−0.876072	−	0.482181i	$-0.839845\pi$
$419$		−	19.7400i		−	0.964362i	0.876072	−	0.482181i	$-0.160155\pi$
$420$	−21.6113	−	1.86899i	−1.05452	−	0.0911973i
$421$			34.1730i			1.66549i	0.553655	+	0.832746i	$0.313233\pi$
$421$			34.1730i			1.66549i	−0.553655	+	0.832746i	$0.686767\pi$
$422$	11.2769	−	7.30335i	0.548951	−	0.355522i
$423$	−5.96660	−	5.96660i	−0.290106	−	0.290106i
$424$	−0.937760	+	1.28062i	−0.0455417	+	0.0621925i
$425$	−30.1995	−	3.49419i	−1.46489	−	0.169493i
$426$	4.63007	+	0.990182i	0.224327	+	0.0479745i
$427$	−10.0951	−	10.0951i	−0.488538	−	0.488538i
$428$	−17.0394	+	6.49216i	−0.823632	+	0.313810i
$429$	−10.3127			−0.497904
$430$	−4.04137	−	32.3144i	−0.194892	−	1.55834i
$431$		−	7.20114i		−	0.346867i	−0.984846	−	0.173433i	$-0.944514\pi$
$431$		−	7.20114i		−	0.346867i	0.984846	−	0.173433i	$-0.0554862\pi$
$432$	−1.13601	+	19.7889i	−0.0546564	+	0.952094i
$433$	9.70653	−	9.70653i	0.466466	−	0.466466i	−0.434302	−	0.900768i	$-0.643005\pi$
$433$	9.70653	−	9.70653i	0.466466	−	0.466466i	0.900768	+	0.434302i	$0.143005\pi$
$434$	54.0150	+	11.5516i	2.59280	+	0.554494i
$435$	0.935115	−	1.93438i	0.0448354	−	0.0927464i
$436$	−3.96158	+	8.83852i	−0.189725	+	0.423288i
$437$	3.20581	−	3.20581i	0.153355	−	0.153355i
$438$	−11.4241	−	17.6397i	−0.545865	−	0.842855i
$439$	0.509924			0.0243373			0.0121687	−	0.999926i	$-0.496126\pi$
$439$	0.509924			0.0243373			0.0121687	+	0.999926i	$0.496126\pi$
$440$	12.8933	+	24.2632i	0.614663	+	1.15670i
$441$	34.9664			1.66507
$442$	11.2608	+	17.3876i	0.535624	+	0.827042i
$443$	8.00456	−	8.00456i	0.380308	−	0.380308i	−0.490905	−	0.871213i	$-0.663334\pi$
$443$	8.00456	−	8.00456i	0.380308	−	0.380308i	0.871213	+	0.490905i	$0.163334\pi$
$444$	−7.51806	−	3.36973i	−0.356791	−	0.159920i
$445$	7.78430	+	22.3535i	0.369011	+	1.05966i
$446$	−24.0973	−	5.15342i	−1.14104	−	0.244022i
$447$	6.21405	−	6.21405i	0.293914	−	0.293914i
$448$	18.1405	−	34.9542i	0.857057	−	1.65143i
$449$			14.8134i			0.699087i	0.936920	+	0.349543i	$0.113663\pi$
$449$			14.8134i			0.699087i	−0.936920	+	0.349543i	$0.886337\pi$
$450$	−13.5928	−	4.59335i	−0.640773	−	0.216533i
$451$	−16.0146			−0.754096
$452$	5.13289	+	13.4719i	0.241431	+	0.633663i
$453$	15.1997	+	15.1997i	0.714147	+	0.714147i
$454$	−14.0177	−	2.99781i	−0.657883	−	0.140694i
$455$	−25.0433	+	8.72101i	−1.17405	+	0.408847i
$456$	−1.64655	+	2.24856i	−0.0771067	+	0.105298i
$457$	13.5862	+	13.5862i	0.635538	+	0.635538i	0.949452	−	0.313914i	$-0.101640\pi$
$457$	13.5862	+	13.5862i	0.635538	+	0.635538i	−0.313914	+	0.949452i	$0.601640\pi$
$458$	−21.6084	+	13.9944i	−1.00969	+	0.653914i
$459$			30.1297i			1.40633i
$460$	15.5188	−	13.0482i	0.723567	−	0.608378i
$461$			20.2164i			0.941570i	0.882248	+	0.470785i	$0.156029\pi$
$461$			20.2164i			0.941570i	−0.882248	+	0.470785i	$0.843971\pi$
$462$	16.1994	+	25.0130i	0.753664	+	1.16371i
$463$	−11.2096	−	11.2096i	−0.520953	−	0.520953i	0.396906	−	0.917859i	$-0.370084\pi$
$463$	−11.2096	−	11.2096i	−0.520953	−	0.520953i	−0.917859	+	0.396906i	$0.870084\pi$
$464$	2.59555	+	2.91171i	0.120496	+	0.135173i
$465$	−15.7390	−	7.60855i	−0.729881	−	0.352838i
$466$	−2.75748	+	12.8939i	−0.127738	+	0.597300i
$467$	−17.6004	−	17.6004i	−0.814447	−	0.814447i	0.170850	−	0.985297i	$-0.445349\pi$
$467$	−17.6004	−	17.6004i	−0.814447	−	0.814447i	−0.985297	+	0.170850i	$0.945349\pi$
$468$	3.48095	+	9.13618i	0.160907	+	0.422320i
$469$	11.6323			0.537132
$470$	−1.63192	−	13.0487i	−0.0752748	−	0.601891i
$471$			8.11979i			0.374140i
$472$	−35.7569	+	5.52642i	−1.64585	+	0.254374i
$473$	−31.6357	+	31.6357i	−1.45461	+	1.45461i
$474$	−3.62507	+	16.9508i	−0.166505	+	0.778574i
$475$	−3.10574	−	3.91847i	−0.142501	−	0.179792i
$476$	24.4840	−	54.6252i	1.12222	−	2.50374i
$477$	−0.805180	+	0.805180i	−0.0368666	+	0.0368666i
$478$	28.9824	−	18.7701i	1.32563	−	0.858525i
$479$	−6.22015			−0.284206			−0.142103	−	0.989852i	$-0.545386\pi$
$479$	−6.22015			−0.284206			−0.142103	+	0.989852i	$0.545386\pi$
$480$	−8.20262	+	9.38401i	−0.374397	+	0.428319i
$481$	−10.0718			−0.459235
$482$	0.175951	−	0.113952i	0.00801433	−	0.00519038i
$483$	15.5497	−	15.5497i	0.707535	−	0.707535i
$484$	6.44067	−	14.3695i	0.292758	−	0.653160i
$485$	29.1350	+	14.0844i	1.32295	+	0.639541i
$486$	−4.74777	+	22.2005i	−0.215363	+	1.00703i
$487$	23.1445	−	23.1445i	1.04878	−	1.04878i	0.0500301	−	0.998748i	$-0.484068\pi$
$487$	23.1445	−	23.1445i	1.04878	−	1.04878i	0.998748	−	0.0500301i	$-0.0159317\pi$
$488$	−8.10678	+	1.25294i	−0.366977	+	0.0567181i
$489$			12.5705i			0.568458i
$490$	43.0168	+	33.4531i	1.94330	+	1.51126i
$491$	21.0543			0.950169			0.475085	−	0.879940i	$-0.342417\pi$
$491$	21.0543			0.950169			0.475085	+	0.879940i	$0.342417\pi$
$492$	−2.58645	−	6.78845i	−0.116606	−	0.306047i
$493$	4.19255	+	4.19255i	0.188823	+	0.188823i
$494$	−0.712517	+	3.33171i	−0.0320577	+	0.149901i
$495$	6.48240	+	18.6149i	0.291362	+	0.836678i
$496$	23.6911	−	21.1187i	1.06376	−	0.948257i
$497$	−11.8272	−	11.8272i	−0.530521	−	0.530521i
$498$	−3.63530	−	5.61317i	−0.162902	−	0.251532i
$499$			9.70289i			0.434361i	0.976131	+	0.217181i	$0.0696860\pi$
$499$			9.70289i			0.434361i	−0.976131	+	0.217181i	$0.930314\pi$
$500$	−12.3278	−	18.6555i	−0.551315	−	0.834297i
$501$		−	1.71198i		−	0.0764858i
$502$	−1.61836	+	1.04811i	−0.0722309	+	0.0467795i
$503$	16.7895	+	16.7895i	0.748607	+	0.748607i	0.974218	−	0.225610i	$-0.0724376\pi$
$503$	16.7895	+	16.7895i	0.748607	+	0.748607i	−0.225610	+	0.974218i	$0.572438\pi$
$504$	16.6914	−	22.7941i	0.743494	−	1.01533i
$505$	1.22563	+	3.51953i	0.0545398	+	0.156617i
$506$	−27.2385	−	5.82520i	−1.21090	−	0.258962i
$507$	5.01374	+	5.01374i	0.222668	+	0.222668i
$508$	−6.08190	−	15.9627i	−0.269841	−	0.708229i
$509$	0.333173			0.0147676			0.00738382	−	0.999973i	$-0.497650\pi$
$509$	0.333173			0.0147676			0.00738382	+	0.999973i	$0.497650\pi$
$510$	−11.6304	+	14.9553i	−0.515002	+	0.662232i
$511$			74.2413i			3.28424i
$512$	−10.0459	−	20.2751i	−0.443971	−	0.896041i
$513$	−3.50398	+	3.50398i	−0.154704	+	0.154704i
$514$	10.5527	+	2.25679i	0.465459	+	0.0995427i
$515$	−12.8031	−	6.18927i	−0.564173	−	0.272732i
$516$	−18.5195	−	8.30075i	−0.815274	−	0.365420i
$517$	−12.7746	+	12.7746i	−0.561826	+	0.561826i
$518$	15.8209	+	24.4286i	0.695131	+	1.07333i
$519$	−18.1221			−0.795471
$520$	−4.45840	+	14.5699i	−0.195514	+	0.638933i
$521$	19.6803			0.862211			0.431106	−	0.902301i	$-0.358124\pi$
$521$	19.6803			0.862211			0.431106	+	0.902301i	$0.358124\pi$
$522$	1.52114	+	2.34876i	0.0665786	+	0.102802i
$523$	19.8095	−	19.8095i	0.866209	−	0.866209i	−0.125841	−	0.992050i	$-0.540163\pi$
$523$	19.8095	−	19.8095i	0.866209	−	0.866209i	0.992050	+	0.125841i	$0.0401630\pi$
$524$	9.62597	−	21.4761i	0.420512	−	0.938187i
$525$	−15.0643	−	19.0064i	−0.657459	−	0.829507i
$526$	10.8205	+	2.31405i	0.471794	+	0.100898i
$527$	34.1126	−	34.1126i	1.48597	−	1.48597i
$528$	17.0945	+	0.981336i	0.743943	+	0.0427072i
$529$		−	2.44554i		−	0.106328i
$530$	−1.76089	+	0.220224i	−0.0764882	+	0.00956592i
$531$	−25.9565			−1.12642
$532$	9.20013	−	3.50532i	0.398876	−	0.151975i
$533$	−6.27969	−	6.27969i	−0.272003	−	0.272003i
$534$	14.4246	+	3.08483i	0.624213	+	0.133494i
$535$	−18.3544	−	8.87288i	−0.793531	−	0.383608i
$536$	3.94874	−	5.39247i	0.170559	−	0.232919i
$537$	−14.7471	−	14.7471i	−0.636385	−	0.636385i
$538$	−25.0863	+	16.2468i	−1.08155	+	0.700451i
$539$		−	74.8637i		−	3.22461i
$540$	−16.9621	+	14.2618i	−0.729935	+	0.613732i
$541$			1.60100i			0.0688323i	0.999408	+	0.0344161i	$0.0109572\pi$
$541$			1.60100i			0.0688323i	−0.999408	+	0.0344161i	$0.989043\pi$
$542$	1.38508	+	2.13866i	0.0594941	+	0.0918633i
$543$	−5.19485	−	5.19485i	−0.222932	−	0.222932i
$544$	−17.0115	−	29.8933i	−0.729362	−	1.28167i
$545$	−10.2266	+	3.56129i	−0.438061	+	0.152549i
$546$	−3.45604	+	16.1604i	−0.147905	+	0.691600i
$547$	9.95474	+	9.95474i	0.425634	+	0.425634i	0.887138	−	0.461504i	$-0.152690\pi$
$547$	9.95474	+	9.95474i	0.425634	+	0.425634i	−0.461504	+	0.887138i	$0.652690\pi$
$548$	32.9334	−	12.5479i	1.40685	−	0.536020i
$549$	−5.88484			−0.251159
$550$	−9.83445	+	29.1025i	−0.419342	+	1.24094i
$551$			0.975159i			0.0415432i
$552$	−1.92993	−	12.4870i	−0.0821431	−	0.531481i
$553$	43.2995	−	43.2995i	1.84128	−	1.84128i
$554$	4.46696	−	20.8874i	0.189783	−	0.887420i
$555$	−3.02924	−	8.69879i	−0.128584	−	0.369243i
$556$	−11.6446	−	5.21934i	−0.493843	−	0.221349i
$557$	−7.00437	+	7.00437i	−0.296785	+	0.296785i	−0.839753	−	0.542968i	$-0.817300\pi$
$557$	−7.00437	+	7.00437i	−0.296785	+	0.296785i	0.542968	+	0.839753i	$0.317300\pi$
$558$	19.1106	−	12.3767i	0.809016	−	0.523950i
$559$	−24.8102			−1.04936
$560$	42.3419	−	12.0730i	1.78927	−	0.510176i
$561$	26.0273			1.09887
$562$	−32.2943	+	20.9150i	−1.36225	+	0.882247i
$563$	−28.6966	+	28.6966i	−1.20942	+	1.20942i	−0.238200	+	0.971216i	$0.576557\pi$
$563$	−28.6966	+	28.6966i	−1.20942	+	1.20942i	−0.971216	+	0.238200i	$0.923443\pi$
$564$	−7.47822	−	3.35187i	−0.314890	−	0.141139i
$565$	−7.01515	+	14.5115i	−0.295130	+	0.610505i
$566$	−1.57269	+	7.35385i	−0.0661050	+	0.309105i
$567$	4.19305	−	4.19305i	0.176091	−	0.176091i
$568$	−9.49766	+	1.46791i	−0.398513	+	0.0615922i
$569$		−	23.4660i		−	0.983744i	−0.870667	−	0.491872i	$-0.836313\pi$
$569$		−	23.4660i		−	0.983744i	0.870667	−	0.491872i	$-0.163687\pi$
$570$	−3.09183	+	0.386676i	−0.129502	+	0.0161961i
$571$	4.34032			0.181637			0.0908183	−	0.995867i	$-0.471052\pi$
$571$	4.34032			0.181637			0.0908183	+	0.995867i	$0.471052\pi$
$572$	19.5607	−	7.45278i	0.817875	−	0.311617i
$573$	8.21269	+	8.21269i	0.343090	+	0.343090i
$574$	−5.36685	+	25.0953i	−0.224008	+	1.04746i
$575$	22.5183	+	2.60545i	0.939077	+	0.108655i
$576$	−4.90068	−	15.4754i	−0.204195	−	0.644810i
$577$	16.0532	+	16.0532i	0.668302	+	0.668302i	0.957323	−	0.289021i	$-0.0933297\pi$
$577$	16.0532	+	16.0532i	0.668302	+	0.668302i	−0.289021	+	0.957323i	$0.593330\pi$
$578$	−15.3512	−	23.7034i	−0.638526	−	0.985930i
$579$			5.96337i			0.247829i
$580$	−0.375750	+	4.34482i	−0.0156022	+	0.180409i
$581$			23.6246i			0.980112i
$582$	16.9269	−	10.9625i	0.701642	−	0.454410i
$583$	1.72390	+	1.72390i	0.0713968	+	0.0713968i
$584$	34.4165	+	25.2021i	1.42416	+	1.04287i
$585$	−4.75744	+	9.84125i	−0.196696	+	0.406886i
$586$	12.0382	+	2.57448i	0.497293	+	0.106351i
$587$	25.2963	+	25.2963i	1.04409	+	1.04409i	0.998982	+	0.0451075i	$0.0143630\pi$
$587$	25.2963	+	25.2963i	1.04409	+	1.04409i	0.0451075	+	0.998982i	$0.485637\pi$
$588$	31.7341	−	12.0909i	1.30869	−	0.498622i
$589$	7.93436			0.326930
$590$	−31.9325	−	24.8332i	−1.31464	−	1.02237i
$591$		−	3.75184i		−	0.154330i
$592$	16.6951	+	0.958408i	0.686165	+	0.0393903i
$593$	3.36290	−	3.36290i	0.138098	−	0.138098i	−0.634679	−	0.772776i	$-0.718867\pi$
$593$	3.36290	−	3.36290i	0.138098	−	0.138098i	0.772776	+	0.634679i	$0.218867\pi$
$594$	29.7719	+	6.36698i	1.22155	+	0.261241i
$595$	63.2042	−	22.0101i	2.59112	−	0.902324i
$596$	−7.29575	+	16.2772i	−0.298846	+	0.666742i
$597$	−7.54967	+	7.54967i	−0.308988	+	0.308988i
$598$	−8.39665	−	12.9650i	−0.343365	−	0.530180i
$599$	−1.62422			−0.0663638			−0.0331819	−	0.999449i	$-0.510564\pi$
$599$	−1.62422			−0.0663638			−0.0331819	+	0.999449i	$0.510564\pi$
$600$	−13.9246	+	0.531490i	−0.568471	+	0.0216980i
$601$	8.42302			0.343582			0.171791	−	0.985133i	$-0.445045\pi$
$601$	8.42302			0.343582			0.171791	+	0.985133i	$0.445045\pi$
$602$	38.9721	+	60.1758i	1.58839	+	2.45258i
$603$	3.39046	−	3.39046i	0.138070	−	0.138070i
$604$	−39.8146	−	17.8456i	−1.62004	−	0.726129i
$605$	16.6263	−	5.78989i	0.675955	−	0.235392i
$606$	2.27114	+	0.485703i	0.0922586	+	0.0197304i
$607$	−6.00323	+	6.00323i	−0.243664	+	0.243664i	−0.818364	−	0.574700i	$-0.805119\pi$
$607$	−6.00323	+	6.00323i	−0.243664	+	0.243664i	0.574700	+	0.818364i	$0.305119\pi$
$608$	1.49811	−	5.45487i	0.0607565	−	0.221224i
$609$			4.72997i			0.191668i
$610$	−7.23971	−	5.63016i	−0.293127	−	0.227958i
$611$	−10.0184			−0.405303
$612$	−8.78522	−	23.0579i	−0.355121	−	0.932059i
$613$	−14.2988	−	14.2988i	−0.577523	−	0.577523i	0.356697	−	0.934220i	$-0.383903\pi$
$613$	−14.2988	−	14.2988i	−0.577523	−	0.577523i	−0.934220	+	0.356697i	$0.883903\pi$
$614$	−15.8235	−	3.38401i	−0.638586	−	0.136567i
$615$	3.53492	−	7.31234i	0.142542	−	0.294862i
$616$	−48.8025	−	35.7366i	−1.96631	−	1.43987i
$617$	8.29025	+	8.29025i	0.333753	+	0.333753i	0.854010	−	0.520257i	$-0.174164\pi$
$617$	8.29025	+	8.29025i	0.333753	+	0.333753i	−0.520257	+	0.854010i	$0.674164\pi$
$618$	−7.43836	+	4.81736i	−0.299215	+	0.193783i
$619$		−	5.23667i		−	0.210480i	−0.994447	−	0.105240i	$-0.966439\pi$
$619$		−	5.23667i		−	0.210480i	0.994447	−	0.105240i	$-0.0335610\pi$
$620$	35.3516	+	3.05728i	1.41975	+	0.122783i
$621$		−	22.4662i		−	0.901537i
$622$	−0.396565	−	0.612325i	−0.0159008	−	0.0245520i
$623$	−36.8466	−	36.8466i	−1.47623	−	1.47623i
$624$	6.31835	+	7.08796i	0.252936	+	0.283746i
$625$	5.70875	−	24.3395i	0.228350	−	0.973579i
$626$	−1.39960	+	6.54450i	−0.0559393	+	0.261571i
$627$	3.02689	+	3.02689i	0.120882	+	0.120882i
$628$	−5.86798	−	15.4012i	−0.234158	−	0.614576i
$629$	25.4192			1.01353
$630$	31.3425	−	3.91982i	1.24871	−	0.156169i
$631$			6.73065i			0.267943i	0.990985	+	0.133972i	$0.0427731\pi$
$631$			6.73065i			0.267943i	−0.990985	+	0.133972i	$0.957227\pi$
$632$	−5.37406	−	34.7711i	−0.213768	−	1.38312i
$633$	6.61916	−	6.61916i	0.263088	−	0.263088i
$634$	−2.53320	+	11.8452i	−0.100606	+	0.470433i
$635$	8.31217	−	17.1946i	0.329858	−	0.682345i
$636$	−0.452328	+	1.00917i	−0.0179360	+	0.0400162i
$637$	29.3558	−	29.3558i	1.16312	−	1.16312i
$638$	5.02873	−	3.25679i	0.199089	−	0.128938i
$639$	−6.89451			−0.272742
$640$	8.77673	−	23.7270i	0.346931	−	0.937891i
$641$	20.1998			0.797844			0.398922	−	0.916985i	$-0.369384\pi$
$641$	20.1998			0.797844			0.398922	+	0.916985i	$0.369384\pi$
$642$	−10.6636	+	6.90612i	−0.420857	+	0.272563i
$643$	−27.0459	+	27.0459i	−1.06659	+	1.06659i	−0.0689674	+	0.997619i	$0.521970\pi$
$643$	−27.0459	+	27.0459i	−1.06659	+	1.06659i	−0.997619	+	0.0689674i	$0.978030\pi$
$644$	−18.2565	+	40.7313i	−0.719406	+	1.60504i
$645$	−7.46203	−	21.4280i	−0.293817	−	0.843727i
$646$	1.79825	−	8.40857i	0.0707511	−	0.330831i
$647$	−12.8379	+	12.8379i	−0.504710	+	0.504710i	−0.912898	−	0.408188i	$-0.866161\pi$
$647$	−12.8379	+	12.8379i	−0.504710	+	0.504710i	0.408188	+	0.912898i	$0.366161\pi$
$648$	−0.520414	−	3.36717i	−0.0204438	−	0.132275i
$649$			55.5734i			2.18145i
$650$	−15.2681	+	7.55546i	−0.598864	+	0.296350i
$651$	38.4853			1.50836
$652$	−9.08442	−	23.8431i	−0.355773	−	0.933769i
$653$	−8.92354	−	8.92354i	−0.349205	−	0.349205i	0.510608	−	0.859813i	$-0.329420\pi$
$653$	−8.92354	−	8.92354i	−0.349205	−	0.349205i	−0.859813	+	0.510608i	$0.829420\pi$
$654$	−1.41130	+	6.59921i	−0.0551863	+	0.258050i
$655$	24.8490	−	8.65334i	0.970930	−	0.338114i
$656$	9.81170	+	11.0068i	0.383083	+	0.429744i
$657$	21.6390	+	21.6390i	0.844219	+	0.844219i
$658$	15.7371	+	24.2992i	0.613495	+	0.947282i
$659$			16.9382i			0.659820i	0.944012	+	0.329910i	$0.107018\pi$
$659$			16.9382i			0.659820i	−0.944012	+	0.329910i	$0.892982\pi$
$660$	12.3200	+	14.6526i	0.479554	+	0.570353i
$661$		−	33.9884i		−	1.32199i	−0.750388	−	0.660997i	$-0.770133\pi$
$661$		−	33.9884i		−	1.32199i	0.750388	−	0.660997i	$-0.229867\pi$
$662$	−27.8429	+	18.0321i	−1.08215	+	0.700839i
$663$	10.2059	+	10.2059i	0.396365	+	0.396365i
$664$	10.9518	+	8.01964i	0.425011	+	0.311222i
$665$	9.91013	+	4.79074i	0.384299	+	0.185777i
$666$	11.7315	+	2.50889i	0.454586	+	0.0972173i
$667$	−3.12618	−	3.12618i	−0.121046	−	0.121046i
$668$	1.23721	+	3.24721i	0.0478692	+	0.125638i
$669$	−17.1692			−0.663798
$670$	7.41479	−	0.927323i	0.286458	−	0.0358256i
$671$			12.5995i			0.486400i
$672$	7.26654	−	26.4587i	0.280313	−	1.02067i
$673$	7.02445	−	7.02445i	0.270773	−	0.270773i	−0.558639	−	0.829411i	$-0.688676\pi$
$673$	7.02445	−	7.02445i	0.270773	−	0.270773i	0.829411	+	0.558639i	$0.188676\pi$
$674$	7.35698	+	1.57336i	0.283380	+	0.0606034i
$675$	−24.6127	−	2.84777i	−0.947342	−	0.109611i
$676$	−13.1331	−	5.88650i	−0.505120	−	0.226404i
$677$	−0.362115	+	0.362115i	−0.0139172	+	0.0139172i	−0.714031	−	0.700114i	$-0.753133\pi$
$677$	−0.362115	+	0.362115i	−0.0139172	+	0.0139172i	0.700114	+	0.714031i	$0.253133\pi$
$678$	5.46018	+	8.43092i	0.209697	+	0.323787i
$679$	−71.2414			−2.73399
$680$	11.2521	−	36.7715i	0.431499	−	1.41012i
$681$	−9.98752			−0.382723
$682$	−26.4988	−	40.9162i	−1.01469	−	1.56676i
$683$	−2.55326	+	2.55326i	−0.0976976	+	0.0976976i	−0.754266	−	0.656569i	$-0.772007\pi$
$683$	−2.55326	+	2.55326i	−0.0976976	+	0.0976976i	0.656569	+	0.754266i	$0.272007\pi$
$684$	1.65986	−	3.70324i	0.0634663	−	0.141597i
$685$	35.4750	+	17.1493i	1.35543	+	0.655241i
$686$	−69.6594	−	14.8973i	−2.65961	−	0.568782i
$687$	−12.6834	+	12.6834i	−0.483901	+	0.483901i
$688$	41.1256	+	2.36088i	1.56790	+	0.0900076i
$689$			1.35197i			0.0515058i
$690$	8.67220	−	11.1514i	0.330145	−	0.424528i
$691$	14.5826			0.554750			0.277375	−	0.960762i	$-0.410536\pi$
$691$	14.5826			0.554750			0.277375	+	0.960762i	$0.410536\pi$
$692$	34.3731	−	13.0964i	1.30667	−	0.497851i
$693$	−30.6842	−	30.6842i	−1.16559	−	1.16559i
$694$	−10.9838	−	2.34898i	−0.416938	−	0.0891660i
$695$	−4.69196	−	13.4735i	−0.177976	−	0.511078i
$696$	2.19270	+	1.60565i	0.0831141	+	0.0608618i
$697$	15.8487	+	15.8487i	0.600311	+	0.600311i
$698$	−23.2788	+	15.0762i	−0.881117	+	0.570644i
$699$			9.18685i			0.347478i
$700$	42.3087	+	25.1638i	1.59912	+	0.951101i
$701$			44.2723i			1.67214i	0.548622	+	0.836071i	$0.315153\pi$
$701$			44.2723i			1.67214i	−0.548622	+	0.836071i	$0.684847\pi$
$702$	9.17760	+	14.1709i	0.346386	+	0.534846i
$703$	2.95616	+	2.95616i	0.111494	+	0.111494i
$704$	−33.1332	+	10.4925i	−1.24875	+	0.395449i
$705$	−3.01319	−	8.65270i	−0.113483	−	0.325880i
$706$	1.13594	−	5.31163i	0.0427517	−	0.199906i
$707$	−5.80146	−	5.80146i	−0.218186	−	0.218186i
$708$	−23.5571	+	8.97545i	−0.885331	+	0.337318i
$709$	−29.7312			−1.11658			−0.558290	−	0.829646i	$-0.688542\pi$
$709$	−29.7312			−1.11658			−0.558290	+	0.829646i	$0.688542\pi$
$710$	−8.48184	−	6.59613i	−0.318318	−	0.247548i
$711$		−	25.2409i		−	0.946609i
$712$	−29.5892	+	4.57316i	−1.10890	+	0.171387i
$713$	−25.4361	+	25.4361i	−0.952588	+	0.952588i
$714$	8.72234	−	40.7855i	0.326426	−	1.52636i
$715$	21.0703	+	10.1858i	0.787984	+	0.380926i
$716$	38.6290	+	17.3142i	1.44363	+	0.647063i
$717$	17.0117	−	17.0117i	0.635314	−	0.635314i
$718$	−35.8061	+	23.1894i	−1.33627	+	0.865420i
$719$	−14.6918			−0.547911			−0.273956	−	0.961742i	$-0.588332\pi$
$719$	−14.6918			−0.547911			−0.273956	+	0.961742i	$0.588332\pi$
$720$	8.82245	−	15.8602i	0.328793	−	0.591076i
$721$	31.3064			1.16591
$722$	1.18702	−	0.768758i	0.0441762	−	0.0286102i
$723$	0.103277	−	0.103277i	0.00384092	−	0.00384092i
$724$	13.6075	+	6.09914i	0.505720	+	0.226673i
$725$	−3.82113	+	3.02859i	−0.141913	+	0.112479i
$726$	2.29447	−	10.7289i	0.0851557	−	0.398186i
$727$	−19.1979	+	19.1979i	−0.712012	+	0.712012i	−0.966956	−	0.254944i	$-0.917943\pi$
$727$	−19.1979	+	19.1979i	−0.712012	+	0.712012i	0.254944	+	0.966956i	$0.417943\pi$
$728$	−5.12347	−	33.1498i	−0.189888	−	1.22861i
$729$			12.2039i			0.451995i
$730$	5.91847	+	47.3236i	0.219052	+	1.75152i
$731$	62.6159			2.31593
$732$	−5.34085	+	2.03490i	−0.197403	+	0.0752122i
$733$	−3.84339	−	3.84339i	−0.141959	−	0.141959i	0.632556	−	0.774515i	$-0.282006\pi$
$733$	−3.84339	−	3.84339i	−0.141959	−	0.141959i	−0.774515	+	0.632556i	$0.782006\pi$
$734$	−7.37859	+	34.5021i	−0.272349	+	1.27350i
$735$	34.1832	+	16.5248i	1.26087	+	0.609526i
$736$	12.6846	+	22.2900i	0.467562	+	0.821619i
$737$	−7.25905	−	7.25905i	−0.267390	−	0.267390i
$738$	5.75022	+	8.87876i	0.211668	+	0.326832i
$739$			15.1184i			0.556141i	0.960561	+	0.278070i	$0.0896948\pi$
$739$			15.1184i			0.556141i	−0.960561	+	0.278070i	$0.910305\pi$
$740$	12.0321	+	14.3103i	0.442310	+	0.526056i
$741$			2.37383i			0.0872047i
$742$	3.27913	−	2.12368i	0.120380	−	0.0779629i
$743$	−13.4589	−	13.4589i	−0.493757	−	0.493757i	0.415731	−	0.909488i	$-0.363526\pi$
$743$	−13.4589	−	13.4589i	−0.493757	−	0.493757i	−0.909488	+	0.415731i	$0.863526\pi$
$744$	13.0643	−	17.8409i	0.478961	−	0.654077i
$745$	−18.8336	+	6.55857i	−0.690011	+	0.240287i
$746$	23.7254	+	5.07390i	0.868650	+	0.185769i
$747$	6.88583	+	6.88583i	0.251939	+	0.251939i
$748$	−49.3673	+	18.8093i	−1.80505	+	0.687737i
$749$	44.8805			1.63990
$750$	−11.1176	−	10.9143i	−0.405957	−	0.398534i
$751$			2.33959i			0.0853730i	0.999089	+	0.0426865i	$0.0135917\pi$
$751$			2.33959i			0.0853730i	−0.999089	+	0.0426865i	$0.986408\pi$
$752$	16.6067	+	0.953330i	0.605582	+	0.0347644i
$753$	−0.949922	+	0.949922i	−0.0346171	+	0.0346171i
$754$	3.24895	+	0.694817i	0.118320	+	0.0253038i
$755$	−16.0425	−	46.0677i	−0.583845	−	1.67657i
$756$	19.9545	−	44.5196i	0.725737	−	1.61916i
$757$	−22.3579	+	22.3579i	−0.812610	+	0.812610i	−0.985024	−	0.172415i	$-0.944843\pi$
$757$	−22.3579	+	22.3579i	−0.812610	+	0.812610i	0.172415	+	0.985024i	$0.444843\pi$
$758$	8.14435	+	12.5755i	0.295816	+	0.456762i
$759$	−19.4072			−0.704439
$760$	5.58498	−	2.96782i	0.202589	−	0.107654i
$761$	3.41135			0.123661			0.0618306	−	0.998087i	$-0.480306\pi$
$761$	3.41135			0.123661			0.0618306	+	0.998087i	$0.480306\pi$
$762$	−6.46970	−	9.98970i	−0.234373	−	0.361888i
$763$	16.8572	−	16.8572i	0.610272	−	0.610272i
$764$	−21.5125	−	9.64231i	−0.778297	−	0.348846i
$765$	12.0068	−	24.8373i	0.434108	−	0.897995i
$766$	43.0525	+	9.20717i	1.55555	+	0.332668i
$767$	−21.7916	+	21.7916i	−0.786851	+	0.786851i
$768$	−9.79888	−	12.3503i	−0.353587	−	0.445653i
$769$			26.4395i			0.953432i	0.879057	+	0.476716i	$0.158173\pi$
$769$			26.4395i			0.953432i	−0.879057	+	0.476716i	$0.841827\pi$
$770$	−8.39239	−	67.1048i	−0.302441	−	2.41829i
$771$	7.51873			0.270780
$772$	−4.30959	−	11.3110i	−0.155105	−	0.407093i
$773$	31.2636	+	31.2636i	1.12447	+	1.12447i	0.991060	+	0.133414i	$0.0425940\pi$
$773$	31.2636	+	31.2636i	1.12447	+	1.12447i	0.133414	+	0.991060i	$0.457406\pi$
$774$	28.8985	+	6.18022i	1.03874	+	0.222143i
$775$	24.6421	+	31.0905i	0.885169	+	1.11680i
$776$	−24.1837	+	33.0258i	−0.868146	+	1.18556i
$777$	14.3388	+	14.3388i	0.514401	+	0.514401i
$778$	−4.93074	+	3.19334i	−0.176776	+	0.114487i
$779$			3.68629i			0.132075i
$780$	−0.914686	+	10.5766i	−0.0327510	+	0.378703i
$781$			14.7613i			0.528200i
$782$	21.1914	+	32.7211i	0.757804	+	1.17011i
$783$	3.41693	+	3.41693i	0.122111	+	0.122111i
$784$	−51.4539	+	45.8670i	−1.83764	+	1.63811i
$785$	8.01982	−	16.5898i	0.286239	−	0.592115i
$786$	3.42922	−	16.0350i	0.122316	−	0.571948i
$787$	−26.2214	−	26.2214i	−0.934693	−	0.934693i	0.0633017	−	0.997994i	$-0.479837\pi$
$787$	−26.2214	−	26.2214i	−0.934693	−	0.934693i	−0.997994	+	0.0633017i	$0.979837\pi$
$788$	2.71137	+	7.11631i	0.0965885	+	0.253508i
$789$	7.70951			0.274466
$790$	24.1486	−	31.0522i	0.859167	−	1.10479i
$791$		−	35.4838i		−	1.26166i
$792$	−24.6405	+	3.80832i	−0.875563	+	0.135323i
$793$	−4.94058	+	4.94058i	−0.175445	+	0.175445i
$794$	6.79069	−	31.7531i	0.240993	−	1.12688i
$795$	−1.16766	+	0.406624i	−0.0414128	+	0.0144215i
$796$	8.86388	−	19.7758i	0.314172	−	0.700935i
$797$	−7.43786	+	7.43786i	−0.263463	+	0.263463i	−0.826459	−	0.562997i	$-0.809648\pi$
$797$	−7.43786	+	7.43786i	−0.263463	+	0.263463i	0.562997	+	0.826459i	$0.309648\pi$
$798$	5.75759	−	3.72883i	0.203816	−	0.131999i
$799$	25.2845			0.894501
$800$	26.0275	−	11.0711i	0.920211	−	0.391423i
$801$	−21.4793			−0.758933
$802$	26.6387	−	17.2522i	0.940645	−	0.609197i
$803$	46.3296	−	46.3296i	1.63493	−	1.63493i
$804$	1.90467	−	4.24943i	0.0671726	−	0.149866i
$805$	−47.1283	+	16.4118i	−1.66105	+	0.578440i
$806$	5.65337	−	26.4350i	0.199131	−	0.931133i
$807$	−14.7248	+	14.7248i	−0.518338	+	0.518338i
$808$	−4.65879	+	0.720040i	−0.163896	+	0.0253309i
$809$		−	26.6089i		−	0.935518i	−0.883856	−	0.467759i	$-0.845061\pi$
$809$		−	26.6089i		−	0.935518i	0.883856	−	0.467759i	$-0.154939\pi$
$810$	2.33850	−	3.00704i	0.0821666	−	0.105656i
$811$	−19.6602			−0.690362			−0.345181	−	0.938536i	$-0.612182\pi$
$811$	−19.6602			−0.690362			−0.345181	+	0.938536i	$0.612182\pi$
$812$	−3.41824	−	8.97158i	−0.119957	−	0.314841i
$813$	1.25532	+	1.25532i	0.0440260	+	0.0440260i
$814$	5.37157	−	25.1173i	0.188273	−	0.880362i
$815$	12.4157	−	25.6832i	0.434904	−	0.899643i
$816$	−15.9462	−	17.8886i	−0.558230	−	0.626225i
$817$	7.28201	+	7.28201i	0.254765	+	0.254765i
$818$	−16.5340	−	25.5296i	−0.578096	−	0.892623i
$819$		−	24.0640i		−	0.840863i
$820$	−1.42041	+	16.4243i	−0.0496028	+	0.573561i
$821$			7.96723i			0.278058i	0.990288	+	0.139029i	$0.0443982\pi$
$821$			7.96723i			0.278058i	−0.990288	+	0.139029i	$0.955602\pi$
$822$	20.6103	−	13.3480i	0.718867	−	0.465565i
$823$	11.7471	+	11.7471i	0.409480	+	0.409480i	0.881557	−	0.472077i	$-0.156496\pi$
$823$	11.7471	+	11.7471i	0.409480	+	0.409480i	−0.472077	+	0.881557i	$0.656496\pi$
$824$	10.6273	−	14.5129i	0.370220	−	0.505580i
$825$	−2.46003	+	21.2615i	−0.0856472	+	0.740229i
$826$	87.0851	+	18.6239i	3.03008	+	0.648010i
$827$	7.86445	+	7.86445i	0.273474	+	0.273474i	0.830497	−	0.557023i	$-0.188057\pi$
$827$	7.86445	+	7.86445i	0.273474	+	0.273474i	−0.557023	+	0.830497i	$0.688057\pi$
$828$	6.55070	+	17.1931i	0.227653	+	0.597501i
$829$	15.4632			0.537059			0.268530	−	0.963271i	$-0.413462\pi$
$829$	15.4632			0.537059			0.268530	+	0.963271i	$0.413462\pi$
$830$	1.88334	+	15.0590i	0.0653715	+	0.522705i
$831$		−	14.8821i		−	0.516255i
$832$	−17.1066	−	8.87797i	−0.593066	−	0.307788i
$833$	−74.0881	+	74.0881i	−2.56700	+	2.56700i
$834$	−8.69438	−	1.85937i	−0.301062	−	0.0643848i
$835$	−1.69091	+	3.49781i	−0.0585162	+	0.121047i
$836$	−7.92871	−	3.55379i	−0.274220	−	0.122910i
$837$	27.8018	−	27.8018i	0.960971	−	0.960971i
$838$	15.1753	+	23.4317i	0.524221	+	0.809436i
$839$	25.3838			0.876346			0.438173	−	0.898891i	$-0.355626\pi$
$839$	25.3838			0.876346			0.438173	+	0.898891i	$0.355626\pi$
$840$	27.0898	−	14.3953i	0.934686	−	0.496685i
$841$	−28.0491			−0.967209
$842$	−26.2708	−	40.5640i	−0.905351	−	1.39793i
$843$	−18.9557	+	18.9557i	−0.652868	+	0.652868i
$844$	−7.77139	+	17.3384i	−0.267502	+	0.596813i
$845$	−5.29172	−	15.1957i	−0.182041	−	0.522749i
$846$	11.6693	+	2.49559i	0.401200	+	0.0858003i
$847$	−27.4062	+	27.4062i	−0.941687	+	0.941687i
$848$	0.128650	−	2.24103i	0.00441786	−	0.0769574i
$849$			5.23958i			0.179822i
$850$	38.5336	−	19.0684i	1.32169	−	0.654042i
$851$	−18.9538			−0.649729
$852$	−6.25718	+	2.38403i	−0.214367	+	0.0816757i
$853$	−16.8803	−	16.8803i	−0.577970	−	0.577970i	0.356374	−	0.934344i	$-0.384013\pi$
$853$	−16.8803	−	16.8803i	−0.577970	−	0.577970i	−0.934344	+	0.356374i	$0.884013\pi$
$854$	19.7438	+	4.22240i	0.675620	+	0.144488i
$855$	4.28485	−	1.49214i	0.146539	−	0.0510302i
$856$	15.2352	−	20.8055i	0.520729	−	0.711117i
$857$	−0.795551	−	0.795551i	−0.0271755	−	0.0271755i	0.693388	−	0.720564i	$-0.256117\pi$
$857$	−0.795551	−	0.795551i	−0.0271755	−	0.0271755i	−0.720564	+	0.693388i	$0.756117\pi$
$858$	12.2414	−	7.92800i	0.417915	−	0.270658i
$859$		−	36.1613i		−	1.23381i	−0.787038	−	0.616904i	$-0.788387\pi$
$859$		−	36.1613i		−	1.23381i	0.787038	−	0.616904i	$-0.211613\pi$
$860$	29.6391	+	35.2510i	1.01069	+	1.20205i
$861$			17.8802i			0.609356i
$862$	5.53593	+	8.54789i	0.188555	+	0.291142i
$863$	6.46481	+	6.46481i	0.220065	+	0.220065i	0.808526	−	0.588461i	$-0.200266\pi$
$863$	6.46481	+	6.46481i	0.220065	+	0.220065i	−0.588461	+	0.808526i	$0.700266\pi$
$864$	−13.8644	−	24.3631i	−0.471677	−	0.828850i
$865$	37.0258	+	17.8989i	1.25891	+	0.608582i
$866$	−4.05986	+	18.9838i	−0.137960	+	0.645095i
$867$	−13.9131	−	13.9131i	−0.472513	−	0.472513i
$868$	−72.9971	+	27.8125i	−2.47768	+	0.944016i
$869$	−54.0413			−1.83322
$870$	0.377070	+	3.01502i	0.0127839	+	0.102219i
$871$		−	5.69288i		−	0.192896i
$872$	−2.09221	−	13.5370i	−0.0708511	−	0.458420i
$873$	−20.7647	+	20.7647i	−0.702777	+	0.702777i
$874$	−1.34086	+	6.26985i	−0.0453554	+	0.212081i
$875$	12.0059	+	53.7113i	0.405875	+	1.81577i
$876$	27.1212	+	12.1562i	0.916342	+	0.410721i
$877$	16.6283	−	16.6283i	0.561497	−	0.561497i	−0.368235	−	0.929733i	$-0.620038\pi$
$877$	16.6283	−	16.6283i	0.561497	−	0.561497i	0.929733	+	0.368235i	$0.120038\pi$
$878$	−0.605289	+	0.392008i	−0.0204275	+	0.0132296i
$879$	8.57714			0.289300
$880$	−33.9570	−	18.8890i	−1.14469	−	0.636749i
$881$	35.9133			1.20995			0.604975	−	0.796245i	$-0.293183\pi$
$881$	35.9133			1.20995			0.604975	+	0.796245i	$0.293183\pi$
$882$	−41.5058	+	26.8807i	−1.39757	+	0.905120i
$883$	−37.5607	+	37.5607i	−1.26402	+	1.26402i	−0.314892	+	0.949127i	$0.601968\pi$
$883$	−37.5607	+	37.5607i	−1.26402	+	1.26402i	−0.949127	+	0.314892i	$0.898032\pi$
$884$	−26.7336	−	11.9825i	−0.899150	−	0.403015i
$885$	−25.3751	−	12.2668i	−0.852975	−	0.412344i
$886$	−3.34799	+	15.6551i	−0.112478	+	0.525944i
$887$	19.2889	−	19.2889i	0.647657	−	0.647657i	−0.304769	−	0.952426i	$-0.598579\pi$
$887$	19.2889	−	19.2889i	0.647657	−	0.647657i	0.952426	+	0.304769i	$0.0985794\pi$
$888$	11.5146	−	1.77964i	0.386404	−	0.0597207i
$889$			42.0444i			1.41012i
$890$	−26.4245	−	20.5497i	−0.885751	−	0.688828i
$891$	−5.23326			−0.175321
$892$	32.5656	−	12.4078i	1.09038	−	0.415442i
$893$	2.94050	+	2.94050i	0.0984002	+	0.0984002i
$894$	−2.59909	+	12.1533i	−0.0869266	+	0.406466i
$895$	15.5647	+	44.6958i	0.520272	+	1.49402i
$896$	5.33825	+	55.4369i	0.178339	+	1.85202i
$897$	−7.61004	−	7.61004i	−0.254092	−	0.254092i
$898$	−11.3879	−	17.5838i	−0.380019	−	0.586778i
$899$		−	7.73726i		−	0.258052i
$900$	19.6661	−	4.99721i	0.655537	−	0.166574i
$901$		−	3.41209i		−	0.113673i
$902$	19.0096	−	12.3113i	0.632950	−	0.409922i
$903$	35.3212	+	35.3212i	1.17541	+	1.17541i
$904$	−16.4494	−	12.0454i	−0.547100	−	0.400624i
$905$	5.48287	+	15.7447i	0.182257	+	0.523370i
$906$	−29.7273	−	6.35745i	−0.987623	−	0.211212i
$907$	−40.9075	−	40.9075i	−1.35831	−	1.35831i	−0.875999	−	0.482313i	$-0.839797\pi$
$907$	−40.9075	−	40.9075i	−1.35831	−	1.35831i	−0.482313	−	0.875999i	$-0.660203\pi$
$908$	18.9438	−	7.21775i	0.628674	−	0.239530i
$909$	−3.38189			−0.112170
$910$	23.0225	−	29.6042i	0.763189	−	0.981371i
$911$			6.24502i			0.206907i	0.994634	+	0.103453i	$0.0329892\pi$
$911$			6.24502i			0.206907i	−0.994634	+	0.103453i	$0.967011\pi$
$912$	0.225887	−	3.93487i	0.00747988	−	0.130297i
$913$	14.7427	−	14.7427i	0.487911	−	0.487911i
$914$	−26.5716	−	5.68259i	−0.878912	−	0.187963i
$915$	−5.75302	−	2.78112i	−0.190189	−	0.0919409i
$916$	14.8912	−	33.2232i	0.492020	−	1.09772i
$917$	−40.9602	+	40.9602i	−1.35262	+	1.35262i
$918$	−23.1624	−	35.7644i	−0.764473	−	1.18040i
$919$	−10.1708			−0.335504			−0.167752	−	0.985829i	$-0.553651\pi$
$919$	−10.1708			−0.335504			−0.167752	+	0.985829i	$0.553651\pi$
$920$	−8.39014	+	27.4187i	−0.276615	+	0.903967i
$921$	−11.2742			−0.371497
$922$	−15.5415	−	23.9972i	−0.511831	−	0.790305i
$923$	−5.78824	+	5.78824i	−0.190522	+	0.190522i
$924$	−38.4579	−	17.2375i	−1.26517	−	0.567073i
$925$	−2.40255	+	20.7647i	−0.0789954	+	0.682740i
$926$	21.9234	+	4.68853i	0.720449	+	0.154074i
$927$	9.12483	−	9.12483i	0.299699	−	0.299699i
$928$	−5.31937	−	1.46090i	−0.174617	−	0.0479563i
$929$		−	47.2515i		−	1.55027i	−0.631795	−	0.775135i	$-0.717682\pi$
$929$		−	47.2515i		−	1.55027i	0.631795	−	0.775135i	$-0.282318\pi$
$930$	24.5317	−	3.06803i	0.804425	−	0.100605i
$931$	−17.2324			−0.564769
$932$	−6.63912	−	17.4252i	−0.217472	−	0.570780i
$933$	−0.359414	−	0.359414i	−0.0117667	−	0.0117667i
$934$	34.4223	+	7.36153i	1.12633	+	0.240877i
$935$	−53.1771	−	25.7068i	−1.73908	−	0.840703i
$936$	−11.1555	−	8.16880i	−0.364628	−	0.267005i
$937$	−16.8244	−	16.8244i	−0.549630	−	0.549630i	0.376704	−	0.926334i	$-0.377057\pi$
$937$	−16.8244	−	16.8244i	−0.549630	−	0.549630i	−0.926334	+	0.376704i	$0.877057\pi$
$938$	−13.8078	+	8.94245i	−0.450841	+	0.291981i
$939$			4.66291i			0.152168i
$940$	11.9684	+	14.2345i	0.390366	+	0.464277i
$941$			34.5637i			1.12675i	0.826203	+	0.563373i	$0.190496\pi$
$941$			34.5637i			1.12675i	−0.826203	+	0.563373i	$0.809504\pi$
$942$	−6.24215	−	9.63834i	−0.203380	−	0.314034i
$943$	−11.8176	−	11.8176i	−0.384832	−	0.384832i
$944$	38.1957	−	34.0484i	1.24316	−	1.10818i
$945$	51.5115	−	17.9382i	1.67567	−	0.583531i
$946$	13.2320	−	61.8723i	0.430208	−	2.01164i
$947$	−11.4678	−	11.4678i	−0.372654	−	0.372654i	0.495789	−	0.868443i	$-0.334879\pi$
$947$	−11.4678	−	11.4678i	−0.372654	−	0.372654i	−0.868443	+	0.495789i	$0.834879\pi$
$948$	−8.72800	−	22.9077i	−0.283472	−	0.744006i
$949$	36.3338			1.17945
$950$	6.69892	+	2.26373i	0.217342	+	0.0734451i
$951$			8.43963i			0.273674i
$952$	12.9306	+	83.6633i	0.419083	+	2.71154i
$953$	−23.3694	+	23.3694i	−0.757008	+	0.757008i	−0.975777	−	0.218769i	$-0.929796\pi$
$953$	−23.3694	+	23.3694i	−0.757008	+	0.757008i	0.218769	+	0.975777i	$0.429796\pi$
$954$	0.336775	−	1.57475i	0.0109035	−	0.0509844i
$955$	−8.66803	−	24.8912i	−0.280491	−	0.805459i
$956$	−19.9730	+	44.5610i	−0.645973	+	1.44120i
$957$	2.95169	−	2.95169i	0.0954147	−	0.0954147i
$958$	7.38344	−	4.78179i	0.238548	−	0.154493i
$959$	−86.7441			−2.80111
$960$	2.52263	−	17.4448i	0.0814177	−	0.563029i
$961$	−31.9540			−1.03078
$962$	11.9554	−	7.74277i	0.385458	−	0.249637i
$963$	13.0813	−	13.0813i	0.421538	−	0.421538i
$964$	−0.121255	+	0.270527i	−0.00390536	+	0.00871308i
$965$	5.88994	−	12.1839i	0.189604	−	0.392215i
$966$	−6.50382	+	30.4117i	−0.209257	+	0.978480i
$967$	17.7069	−	17.7069i	0.569415	−	0.569415i	−0.362550	−	0.931964i	$-0.618094\pi$
$967$	17.7069	−	17.7069i	0.569415	−	0.569415i	0.931964	+	0.362550i	$0.118094\pi$
$968$	3.40148	+	22.0082i	0.109328	+	0.707370i
$969$		−	5.99105i		−	0.192460i
$970$	−45.4113	+	5.67932i	−1.45807	+	0.182352i
$971$	−12.8003			−0.410781			−0.205390	−	0.978680i	$-0.565846\pi$
$971$	−12.8003			−0.410781			−0.205390	+	0.978680i	$0.565846\pi$
$972$	−11.4311	−	30.0022i	−0.366652	−	0.962322i
$973$	22.2092	+	22.2092i	0.711994	+	0.711994i
$974$	−9.68043	+	45.2655i	−0.310181	+	1.45040i
$975$	−9.30175	+	7.37249i	−0.297895	+	0.236108i
$976$	8.65968	−	7.71941i	0.277190	−	0.247092i
$977$	−33.0479	−	33.0479i	−1.05730	−	1.05730i	−0.998256	−	0.0590404i	$-0.981196\pi$
$977$	−33.0479	−	33.0479i	−1.05730	−	1.05730i	−0.0590404	−	0.998256i	$-0.518804\pi$
$978$	−9.66368	−	14.9214i	−0.309010	−	0.477135i
$979$			45.9875i			1.46977i
$980$	−76.7790	−	6.64002i	−2.45262	−	0.212108i
$981$		−	9.82671i		−	0.313743i
$982$	−24.9919	+	16.1857i	−0.797523	+	0.516506i
$983$	1.89795	+	1.89795i	0.0605351	+	0.0605351i	0.736726	−	0.676191i	$-0.236371\pi$
$983$	1.89795	+	1.89795i	0.0605351	+	0.0605351i	−0.676191	+	0.736726i	$0.736371\pi$
$984$	8.28883	+	6.06965i	0.264238	+	0.193494i
$985$	−3.70565	+	7.66550i	−0.118072	+	0.244243i
$986$	−8.19969	−	1.75358i	−0.261131	−	0.0558453i
$987$	14.2628	+	14.2628i	0.453990	+	0.453990i
$988$	−1.71551	−	4.50256i	−0.0545776	−	0.143245i
$989$	−46.6895			−1.48464
$990$	−22.0051	−	17.1128i	−0.699368	−	0.543882i
$991$		−	44.0580i		−	1.39955i	−0.714363	−	0.699775i	$-0.753284\pi$
$991$		−	44.0580i		−	1.39955i	0.714363	−	0.699775i	$-0.246716\pi$
$992$	−11.8866	+	43.2809i	−0.377399	+	1.37417i
$993$	−16.3429	+	16.3429i	−0.518625	+	0.518625i
$994$	23.1313	+	4.94684i	0.733680	+	0.156904i
$995$	22.8817	−	7.96825i	0.725398	−	0.252610i
$996$	8.63033	+	3.86827i	0.273463	+	0.122571i
$997$	−25.9072	+	25.9072i	−0.820488	+	0.820488i	−0.986178	−	0.165690i	$-0.947015\pi$
$997$	−25.9072	+	25.9072i	−0.820488	+	0.820488i	0.165690	+	0.986178i	$0.447015\pi$
$998$	−7.45917	−	11.5175i	−0.236116	−	0.364580i
$999$	20.7167			0.655446

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.w.c.267.10	✓	104
5.3	odd	4	inner	760.2.w.c.723.36	yes	104
8.3	odd	2	inner	760.2.w.c.267.36	yes	104
40.3	even	4	inner	760.2.w.c.723.10	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.w.c.267.10	✓	104	1.1	even	1	trivial
760.2.w.c.267.36	yes	104	8.3	odd	2	inner
760.2.w.c.723.10	yes	104	40.3	even	4	inner
760.2.w.c.723.36	yes	104	5.3	odd	4	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:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18702 + 0.768758i) q^{2} +(-0.696739 + 0.696739i) q^{3} +(0.818024 - 1.82506i) q^{4} +(2.11169 - 0.735369i) q^{5} +(0.291418 - 1.36267i) q^{6} +(-3.48083 + 3.48083i) q^{7} +(0.432019 + 2.79524i) q^{8} +2.02911i q^{9} +O(q^{10})\)	\(q+(-1.18702 + 0.768758i) q^{2} +(-0.696739 + 0.696739i) q^{3} +(0.818024 - 1.82506i) q^{4} +(2.11169 - 0.735369i) q^{5} +(0.291418 - 1.36267i) q^{6} +(-3.48083 + 3.48083i) q^{7} +(0.432019 + 2.79524i) q^{8} +2.02911i q^{9} +(-1.94129 + 2.49627i) q^{10} +4.34436 q^{11} +(0.701640 + 1.84154i) q^{12} +(1.70353 + 1.70353i) q^{13} +(1.45589 - 6.80773i) q^{14} +(-0.958937 + 1.98366i) q^{15} +(-2.66167 - 2.98588i) q^{16} +(-4.29935 - 4.29935i) q^{17} +(-1.55989 - 2.40859i) q^{18} -1.00000i q^{19} +(0.385322 - 4.45551i) q^{20} -4.85047i q^{21} +(-5.15683 + 3.33976i) q^{22} +(3.20581 + 3.20581i) q^{23} +(-2.24856 - 1.64655i) q^{24} +(3.91847 - 3.10574i) q^{25} +(-3.33171 - 0.712517i) q^{26} +(-3.50398 - 3.50398i) q^{27} +(3.50532 + 9.20013i) q^{28} -0.975159 q^{29} +(-0.386676 - 3.09183i) q^{30} +7.93436i q^{31} +(5.45487 + 1.49811i) q^{32} +(-3.02689 + 3.02689i) q^{33} +(8.40857 + 1.79825i) q^{34} +(-4.79074 + 9.91013i) q^{35} +(3.70324 + 1.65986i) q^{36} +(-2.95616 + 2.95616i) q^{37} +(0.768758 + 1.18702i) q^{38} -2.37383 q^{39} +(2.96782 + 5.58498i) q^{40} -3.68629 q^{41} +(3.72883 + 5.75759i) q^{42} +(-7.28201 + 7.28201i) q^{43} +(3.55379 - 7.92871i) q^{44} +(1.49214 + 4.28485i) q^{45} +(-6.26985 - 1.34086i) q^{46} +(-2.94050 + 2.94050i) q^{47} +(3.93487 + 0.225887i) q^{48} -17.2324i q^{49} +(-2.26373 + 6.69892i) q^{50} +5.99105 q^{51} +(4.50256 - 1.71551i) q^{52} +(0.396814 + 0.396814i) q^{53} +(6.85299 + 1.46558i) q^{54} +(9.17394 - 3.19470i) q^{55} +(-11.2335 - 8.22598i) q^{56} +(0.696739 + 0.696739i) q^{57} +(1.15753 - 0.749661i) q^{58} +12.7921i q^{59} +(2.83586 + 3.37279i) q^{60} +2.90021i q^{61} +(-6.09960 - 9.41823i) q^{62} +(-7.06299 - 7.06299i) q^{63} +(-7.62672 + 2.41519i) q^{64} +(4.85004 + 2.34460i) q^{65} +(1.26603 - 5.91991i) q^{66} +(-1.67091 - 1.67091i) q^{67} +(-11.3635 + 4.32960i) q^{68} -4.46723 q^{69} +(-1.93179 - 15.4464i) q^{70} +3.39780i q^{71} +(-5.67184 + 0.876613i) q^{72} +(10.6643 - 10.6643i) q^{73} +(1.23645 - 5.78160i) q^{74} +(-0.566258 + 4.89404i) q^{75} +(-1.82506 - 0.818024i) q^{76} +(-15.1220 + 15.1220i) q^{77} +(2.81777 - 1.82490i) q^{78} -12.4394 q^{79} +(-7.81635 - 4.34794i) q^{80} -1.20461 q^{81} +(4.37569 - 2.83386i) q^{82} +(3.39352 - 3.39352i) q^{83} +(-8.85238 - 3.96780i) q^{84} +(-12.2405 - 5.91729i) q^{85} +(3.04578 - 14.2420i) q^{86} +(0.679431 - 0.679431i) q^{87} +(1.87684 + 12.1435i) q^{88} +10.5856i q^{89} +(-5.06521 - 3.93910i) q^{90} -11.8594 q^{91} +(8.47322 - 3.22836i) q^{92} +(-5.52818 - 5.52818i) q^{93} +(1.22990 - 5.75096i) q^{94} +(-0.735369 - 2.11169i) q^{95} +(-4.84442 + 2.75683i) q^{96} +(10.2334 + 10.2334i) q^{97} +(13.2475 + 20.4552i) q^{98} +8.81518i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 8 q^{3} - 8 q^{6}+O(q^{10}) \) 104 * q - 8 * q^3 - 8 * q^6	\( 104 q - 8 q^{3} - 8 q^{6} + 4 q^{10} + 16 q^{11} - 18 q^{12} - 16 q^{16} + 20 q^{22} + 8 q^{25} - 24 q^{26} + 16 q^{27} + 16 q^{28} - 44 q^{30} + 50 q^{32} + 32 q^{33} - 36 q^{35} + 136 q^{36} + 4 q^{40} + 8 q^{41} + 20 q^{42} - 44 q^{43} - 56 q^{46} + 38 q^{48} + 24 q^{50} - 16 q^{51} - 94 q^{52} - 28 q^{56} + 8 q^{57} + 8 q^{58} - 2 q^{60} - 20 q^{62} + 44 q^{65} + 52 q^{66} - 40 q^{67} - 56 q^{68} - 32 q^{70} + 88 q^{72} - 48 q^{73} + 56 q^{75} + 8 q^{76} + 52 q^{78} - 80 q^{80} - 152 q^{81} - 100 q^{82} - 44 q^{83} - 104 q^{86} + 20 q^{88} + 72 q^{90} - 64 q^{91} - 64 q^{92} - 52 q^{96} + 20 q^{97} - 100 q^{98}+O(q^{100}) \) 104 * q - 8 * q^3 - 8 * q^6 + 4 * q^10 + 16 * q^11 - 18 * q^12 - 16 * q^16 + 20 * q^22 + 8 * q^25 - 24 * q^26 + 16 * q^27 + 16 * q^28 - 44 * q^30 + 50 * q^32 + 32 * q^33 - 36 * q^35 + 136 * q^36 + 4 * q^40 + 8 * q^41 + 20 * q^42 - 44 * q^43 - 56 * q^46 + 38 * q^48 + 24 * q^50 - 16 * q^51 - 94 * q^52 - 28 * q^56 + 8 * q^57 + 8 * q^58 - 2 * q^60 - 20 * q^62 + 44 * q^65 + 52 * q^66 - 40 * q^67 - 56 * q^68 - 32 * q^70 + 88 * q^72 - 48 * q^73 + 56 * q^75 + 8 * q^76 + 52 * q^78 - 80 * q^80 - 152 * q^81 - 100 * q^82 - 44 * q^83 - 104 * q^86 + 20 * q^88 + 72 * q^90 - 64 * q^91 - 64 * q^92 - 52 * q^96 + 20 * q^97 - 100 * q^98

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