LMFDB - Embedded newform 798.2.bj.a.601.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,Mod(559,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

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

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

chi := DirichletCharacter("798.559");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			601.11
Character	$\chi$	$=$	798.601
Dual form			798.2.bj.a.559.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30671 - 1.33178i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54299 + 2.14923i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30671 - 1.33178i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54299 + 2.14923i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.33178 - 2.30671i) q^{10} -2.78470 q^{11} -1.00000 q^{12} +(2.77941 - 4.81407i) q^{13} +(-0.261654 + 2.63278i) q^{14} +(-2.30671 - 1.33178i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52001 - 2.60963i) q^{17} +1.00000i q^{18} +(0.386221 - 4.34175i) q^{19} -2.66356i q^{20} +(2.63278 + 0.261654i) q^{21} +(-2.41162 + 1.39235i) q^{22} +(2.46907 - 4.27656i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.04728 - 1.81393i) q^{25} -5.55881i q^{26} +1.00000 q^{27} +(1.08979 + 2.41088i) q^{28} +(-3.06925 - 1.77203i) q^{29} -2.66356 q^{30} -7.60822 q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.39235 + 2.41162i) q^{33} +(2.60963 - 4.52001i) q^{34} +(-0.696930 + 7.01257i) q^{35} +(0.500000 + 0.866025i) q^{36} +7.64895i q^{37} +(-1.83640 - 3.95318i) q^{38} -5.55881 q^{39} +(-1.33178 - 2.30671i) q^{40} +(4.95839 + 8.58818i) q^{41} +(2.41088 - 1.08979i) q^{42} +(-2.35331 - 4.07605i) q^{43} +(-1.39235 + 2.41162i) q^{44} +2.66356i q^{45} -4.93815i q^{46} +(5.75686 + 3.32372i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.23837 - 6.63247i) q^{49} -2.09455i q^{50} +(-4.52001 - 2.60963i) q^{51} +(-2.77941 - 4.81407i) q^{52} +(4.54490 + 2.62400i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-6.42351 + 3.70861i) q^{55} +(2.14923 + 1.54299i) q^{56} +(-3.95318 + 1.83640i) q^{57} -3.54407 q^{58} +(-2.50337 - 4.33596i) q^{59} +(-2.30671 + 1.33178i) q^{60} +(7.15424 + 4.13050i) q^{61} +(-6.58891 + 3.80411i) q^{62} +(-1.08979 - 2.41088i) q^{63} -1.00000 q^{64} -14.8062i q^{65} +(2.41162 + 1.39235i) q^{66} +(4.96644 + 2.86737i) q^{67} -5.21926i q^{68} -4.93815 q^{69} +(2.90273 + 6.42153i) q^{70} +(-13.3355 + 7.69926i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-2.78746 + 1.60934i) q^{73} +(3.82447 + 6.62418i) q^{74} -2.09455 q^{75} +(-3.56696 - 2.50535i) q^{76} +(4.29677 - 5.98497i) q^{77} +(-4.81407 + 2.77941i) q^{78} +(14.2278 - 8.21444i) q^{79} +(-2.30671 - 1.33178i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.58818 + 4.95839i) q^{82} +1.77535i q^{83} +(1.54299 - 2.14923i) q^{84} +(6.95090 - 12.0393i) q^{85} +(-4.07605 - 2.35331i) q^{86} +3.54407i q^{87} +2.78470i q^{88} +(-2.85315 + 4.94180i) q^{89} +(1.33178 + 2.30671i) q^{90} +(6.05795 + 13.4016i) q^{91} +(-2.46907 - 4.27656i) q^{92} +(3.80411 + 6.58891i) q^{93} +6.64745 q^{94} +(-4.89136 - 10.5295i) q^{95} +1.00000i q^{96} +(-3.49688 - 6.05678i) q^{97} +(-5.25472 - 4.62471i) q^{98} +(1.39235 - 2.41162i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) $ 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9	$ 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9} + 2 q^{10} - 24 q^{12} + 10 q^{13} + 4 q^{14} - 12 q^{16} - 10 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{25} + 24 q^{27} + 12 q^{28} - 4 q^{30} - 36 q^{31} + 2 q^{34} - 16 q^{35} + 12 q^{36} + 12 q^{38} - 20 q^{39} - 2 q^{40} - 20 q^{41} - 8 q^{42} - 6 q^{43} - 12 q^{48} + 2 q^{49} - 10 q^{52} + 12 q^{53} - 30 q^{55} - 4 q^{56} + 2 q^{57} - 8 q^{58} + 8 q^{59} - 42 q^{61} - 12 q^{62} - 12 q^{63} - 24 q^{64} - 6 q^{66} + 6 q^{67} + 6 q^{70} - 24 q^{71} + 66 q^{73} - 12 q^{75} - 8 q^{76} + 16 q^{77} - 24 q^{78} + 30 q^{79} - 12 q^{81} - 6 q^{82} - 6 q^{84} - 2 q^{85} + 12 q^{86} - 8 q^{89} + 2 q^{90} - 66 q^{91} + 18 q^{93} + 20 q^{95} + 36 q^{97} - 32 q^{98}+O(q^{100}) $ 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9 + 2 * q^10 - 24 * q^12 + 10 * q^13 + 4 * q^14 - 12 * q^16 - 10 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^25 + 24 * q^27 + 12 * q^28 - 4 * q^30 - 36 * q^31 + 2 * q^34 - 16 * q^35 + 12 * q^36 + 12 * q^38 - 20 * q^39 - 2 * q^40 - 20 * q^41 - 8 * q^42 - 6 * q^43 - 12 * q^48 + 2 * q^49 - 10 * q^52 + 12 * q^53 - 30 * q^55 - 4 * q^56 + 2 * q^57 - 8 * q^58 + 8 * q^59 - 42 * q^61 - 12 * q^62 - 12 * q^63 - 24 * q^64 - 6 * q^66 + 6 * q^67 + 6 * q^70 - 24 * q^71 + 66 * q^73 - 12 * q^75 - 8 * q^76 + 16 * q^77 - 24 * q^78 + 30 * q^79 - 12 * q^81 - 6 * q^82 - 6 * q^84 - 2 * q^85 + 12 * q^86 - 8 * q^89 + 2 * q^90 - 66 * q^91 + 18 * q^93 + 20 * q^95 + 36 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.30671	−	1.33178i	1.03159	−	0.595590i	0.114152	−	0.993463i	$-0.463585\pi$
$5$	2.30671	−	1.33178i	1.03159	−	0.595590i	0.917440	+	0.397873i	$0.130252\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.54299	+	2.14923i	−0.583195	+	0.812332i
$7$	−1.54299	+	2.14923i	−0.583195	+	0.812332i
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.33178	−	2.30671i	0.421146	−	0.729446i
$11$	−2.78470			−0.839620			−0.419810	−	0.907612i	$-0.637903\pi$
$11$	−2.78470			−0.839620			−0.419810	+	0.907612i	$0.637903\pi$
$12$	−1.00000			−0.288675
$13$	2.77941	−	4.81407i	0.770868	−	1.33518i	−0.166219	−	0.986089i	$-0.553156\pi$
$13$	2.77941	−	4.81407i	0.770868	−	1.33518i	0.937088	−	0.349094i	$-0.113511\pi$
$14$	−0.261654	+	2.63278i	−0.0699299	+	0.703640i
$15$	−2.30671	−	1.33178i	−0.595590	−	0.343864i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	4.52001	−	2.60963i	1.09626	−	0.632928i	0.161026	−	0.986950i	$-0.448520\pi$
$17$	4.52001	−	2.60963i	1.09626	−	0.632928i	0.935237	+	0.354022i	$0.115186\pi$
$18$			1.00000i			0.235702i
$19$	0.386221	−	4.34175i	0.0886053	−	0.996067i
$19$	0.386221	−	4.34175i	0.0886053	−	0.996067i
$20$		−	2.66356i		−	0.595590i
$21$	2.63278	+	0.261654i	0.574520	+	0.0570975i
$22$	−2.41162	+	1.39235i	−0.514160	+	0.296850i
$23$	2.46907	−	4.27656i	0.514837	−	0.891724i	−0.485014	−	0.874506i	$-0.661186\pi$
$23$	2.46907	−	4.27656i	0.514837	−	0.891724i	0.999852	−	0.0172182i	$-0.00548101\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.04728	−	1.81393i	0.209455	−	0.362787i
$26$		−	5.55881i		−	1.09017i
$27$	1.00000			0.192450
$28$	1.08979	+	2.41088i	0.205951	+	0.455614i
$29$	−3.06925	−	1.77203i	−0.569946	−	0.329058i	0.187182	−	0.982325i	$-0.440065\pi$
$29$	−3.06925	−	1.77203i	−0.569946	−	0.329058i	−0.757128	+	0.653267i	$0.773398\pi$
$30$	−2.66356			−0.486297
$31$	−7.60822			−1.36648			−0.683238	−	0.730196i	$-0.739429\pi$
$31$	−7.60822			−1.36648			−0.683238	+	0.730196i	$0.739429\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.39235	+	2.41162i	0.242377	+	0.419810i
$34$	2.60963	−	4.52001i	0.447548	−	0.775175i
$35$	−0.696930	+	7.01257i	−0.117803	+	1.18534i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			7.64895i			1.25748i	0.777616	+	0.628740i	$0.216429\pi$
$37$			7.64895i			1.25748i	−0.777616	+	0.628740i	$0.783571\pi$
$38$	−1.83640	−	3.95318i	−0.297903	−	0.641291i
$39$	−5.55881			−0.890122
$40$	−1.33178	−	2.30671i	−0.210573	−	0.364723i
$41$	4.95839	+	8.58818i	0.774370	+	1.34125i	0.935148	+	0.354257i	$0.115266\pi$
$41$	4.95839	+	8.58818i	0.774370	+	1.34125i	−0.160778	+	0.986991i	$0.551400\pi$
$42$	2.41088	−	1.08979i	0.372007	−	0.168159i
$43$	−2.35331	−	4.07605i	−0.358876	−	0.621592i	0.628897	−	0.777489i	$-0.283507\pi$
$43$	−2.35331	−	4.07605i	−0.358876	−	0.621592i	−0.987773	+	0.155897i	$0.950173\pi$
$44$	−1.39235	+	2.41162i	−0.209905	+	0.363566i
$45$			2.66356i			0.397060i
$46$		−	4.93815i		−	0.728090i
$47$	5.75686	+	3.32372i	0.839724	+	0.484815i	0.857170	−	0.515033i	$-0.172220\pi$
$47$	5.75686	+	3.32372i	0.839724	+	0.484815i	−0.0174462	+	0.999848i	$0.505554\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−2.23837	−	6.63247i	−0.319767	−	0.947496i
$50$		−	2.09455i		−	0.296214i
$51$	−4.52001	−	2.60963i	−0.632928	−	0.365421i
$52$	−2.77941	−	4.81407i	−0.385434	−	0.667592i
$53$	4.54490	+	2.62400i	0.624290	+	0.360434i	0.778538	−	0.627598i	$-0.215962\pi$
$53$	4.54490	+	2.62400i	0.624290	+	0.360434i	−0.154247	+	0.988032i	$0.549295\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−6.42351	+	3.70861i	−0.866145	+	0.500069i
$56$	2.14923	+	1.54299i	0.287203	+	0.206191i
$57$	−3.95318	+	1.83640i	−0.523612	+	0.243237i
$58$	−3.54407			−0.465359
$59$	−2.50337	−	4.33596i	−0.325911	−	0.564494i	0.655786	−	0.754947i	$-0.272337\pi$
$59$	−2.50337	−	4.33596i	−0.325911	−	0.564494i	−0.981696	+	0.190454i	$0.939004\pi$
$60$	−2.30671	+	1.33178i	−0.297795	+	0.171932i
$61$	7.15424	+	4.13050i	0.916007	+	0.528857i	0.882359	−	0.470577i	$-0.155954\pi$
$61$	7.15424	+	4.13050i	0.916007	+	0.528857i	0.0336479	+	0.999434i	$0.489288\pi$
$62$	−6.58891	+	3.80411i	−0.836792	+	0.483122i
$63$	−1.08979	−	2.41088i	−0.137301	−	0.303743i
$64$	−1.00000			−0.125000
$65$		−	14.8062i		−	1.83649i
$66$	2.41162	+	1.39235i	0.296850	+	0.171387i
$67$	4.96644	+	2.86737i	0.606747	+	0.350305i	0.771691	−	0.635998i	$-0.219411\pi$
$67$	4.96644	+	2.86737i	0.606747	+	0.350305i	−0.164944	+	0.986303i	$0.552744\pi$
$68$		−	5.21926i		−	0.632928i
$69$	−4.93815			−0.594483
$70$	2.90273	+	6.42153i	0.346942	+	0.767520i
$71$	−13.3355	+	7.69926i	−1.58263	+	0.913734i	−0.588161	+	0.808744i	$0.700148\pi$
$71$	−13.3355	+	7.69926i	−1.58263	+	0.913734i	−0.994473	+	0.104990i	$0.966519\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	−2.78746	+	1.60934i	−0.326248	+	0.188359i	−0.654174	−	0.756344i	$-0.726984\pi$
$73$	−2.78746	+	1.60934i	−0.326248	+	0.188359i	0.327926	+	0.944703i	$0.393650\pi$
$74$	3.82447	+	6.62418i	0.444586	+	0.770046i
$75$	−2.09455			−0.241858
$76$	−3.56696	−	2.50535i	−0.409158	−	0.287384i
$77$	4.29677	−	5.98497i	0.489662	−	0.682050i
$78$	−4.81407	+	2.77941i	−0.545086	+	0.314706i
$79$	14.2278	−	8.21444i	1.60076	−	0.924197i	0.609419	−	0.792848i	$-0.291403\pi$
$79$	14.2278	−	8.21444i	1.60076	−	0.924197i	0.991336	−	0.131349i	$-0.0419308\pi$
$80$	−2.30671	−	1.33178i	−0.257898	−	0.148898i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	8.58818	+	4.95839i	0.948406	+	0.547562i
$83$			1.77535i			0.194870i	0.995242	+	0.0974350i	$0.0310638\pi$
$83$			1.77535i			0.194870i	−0.995242	+	0.0974350i	$0.968936\pi$
$84$	1.54299	−	2.14923i	0.168354	−	0.234500i
$85$	6.95090	−	12.0393i	0.753931	−	1.30585i
$86$	−4.07605	−	2.35331i	−0.439532	−	0.253764i
$87$			3.54407i			0.379964i
$88$			2.78470i			0.296850i
$89$	−2.85315	+	4.94180i	−0.302434	+	0.523830i	−0.976687	−	0.214670i	$-0.931132\pi$
$89$	−2.85315	+	4.94180i	−0.302434	+	0.523830i	0.674253	+	0.738500i	$0.264466\pi$
$90$	1.33178	+	2.30671i	0.140382	+	0.243149i
$91$	6.05795	+	13.4016i	0.635045	+	1.40487i
$92$	−2.46907	−	4.27656i	−0.257419	−	0.445862i
$93$	3.80411	+	6.58891i	0.394468	+	0.683238i
$94$	6.64745			0.685632
$95$	−4.89136	−	10.5295i	−0.501843	−	1.08031i
$96$			1.00000i			0.102062i
$97$	−3.49688	−	6.05678i	−0.355055	−	0.614973i	0.632073	−	0.774909i	$-0.282204\pi$
$97$	−3.49688	−	6.05678i	−0.355055	−	0.614973i	−0.987127	+	0.159936i	$0.948871\pi$
$98$	−5.25472	−	4.62471i	−0.530807	−	0.467166i
$99$	1.39235	−	2.41162i	0.139937	−	0.242377i
$100$	−1.04728	−	1.81393i	−0.104728	−	0.181393i
$101$	−4.13587	−	2.38784i	−0.411534	−	0.237599i	0.279915	−	0.960025i	$-0.409694\pi$
$101$	−4.13587	−	2.38784i	−0.411534	−	0.237599i	−0.691449	+	0.722426i	$0.743027\pi$
$102$	−5.21926			−0.516784
$103$	5.55175			0.547030			0.273515	−	0.961868i	$-0.411814\pi$
$103$	5.55175			0.547030			0.273515	+	0.961868i	$0.411814\pi$
$104$	−4.81407	−	2.77941i	−0.472059	−	0.272543i
$105$	6.42153	−	2.90273i	0.626677	−	0.283277i
$106$	5.24800			0.509731
$107$			19.2313i			1.85916i	0.368627	+	0.929578i	$0.379828\pi$
$107$			19.2313i			1.85916i	−0.368627	+	0.929578i	$0.620172\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	15.7374	−	9.08601i	1.50737	−	0.870282i	0.507409	−	0.861705i	$-0.330603\pi$
$109$	15.7374	−	9.08601i	1.50737	−	0.870282i	0.999963	−	0.00857671i	$-0.00273008\pi$
$110$	−3.70861	+	6.42351i	−0.353602	+	0.612457i
$111$	6.62418	−	3.82447i	0.628740	−	0.363003i
$112$	2.63278	+	0.261654i	0.248774	+	0.0247240i
$113$			15.6701i			1.47412i	0.675830	+	0.737058i	$0.263785\pi$
$113$			15.6701i			1.47412i	−0.675830	+	0.737058i	$0.736215\pi$
$114$	−2.50535	+	3.56696i	−0.234648	+	0.334076i
$115$		−	13.1530i		−	1.22653i
$116$	−3.06925	+	1.77203i	−0.284973	+	0.164529i
$117$	2.77941	+	4.81407i	0.256956	+	0.445061i
$118$	−4.33596	−	2.50337i	−0.399157	−	0.230454i
$119$	−1.36564	+	13.7412i	−0.125188	+	1.25965i
$120$	−1.33178	+	2.30671i	−0.121574	+	0.210573i
$121$	−3.24542			−0.295039
$122$	8.26101			0.747917
$123$	4.95839	−	8.58818i	0.447083	−	0.774370i
$124$	−3.80411	+	6.58891i	−0.341619	+	0.591702i
$125$			7.73884i			0.692183i
$126$	−2.14923	−	1.54299i	−0.191469	−	0.137460i
$127$	−3.68295	−	2.12635i	−0.326809	−	0.188683i	0.327614	−	0.944812i	$-0.393755\pi$
$127$	−3.68295	−	2.12635i	−0.326809	−	0.188683i	−0.654424	+	0.756128i	$0.727089\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−2.35331	+	4.07605i	−0.207197	+	0.358876i
$130$	−7.40311	−	12.8226i	−0.649296	−	1.12461i
$131$	10.8018	−	6.23643i	0.943759	−	0.544879i	0.0526220	−	0.998615i	$-0.483242\pi$
$131$	10.8018	−	6.23643i	0.943759	−	0.544879i	0.891137	+	0.453735i	$0.149909\pi$
$132$	2.78470			0.242377
$133$	8.73549	+	7.52936i	0.757463	+	0.652878i
$134$	5.73475			0.495407
$135$	2.30671	−	1.33178i	0.198530	−	0.114621i
$136$	−2.60963	−	4.52001i	−0.223774	−	0.387588i
$137$	3.29313	−	5.70387i	0.281351	−	0.487315i	−0.690366	−	0.723460i	$-0.742551\pi$
$137$	3.29313	−	5.70387i	0.281351	−	0.487315i	0.971718	+	0.236145i	$0.0758840\pi$
$138$	−4.27656	+	2.46907i	−0.364045	+	0.210181i
$139$	16.8867	+	9.74952i	1.43231	+	0.826943i	0.997297	−	0.0734821i	$-0.0234112\pi$
$139$	16.8867	+	9.74952i	1.43231	+	0.826943i	0.435011	+	0.900425i	$0.356745\pi$
$140$	5.72460	+	4.10984i	0.483817	+	0.347345i
$141$		−	6.64745i		−	0.559816i
$142$	−7.69926	+	13.3355i	−0.646108	+	1.11909i
$143$	−7.73982	+	13.4058i	−0.647236	+	1.12105i
$144$	1.00000			0.0833333
$145$	−9.43984			−0.783936
$146$	−1.60934	+	2.78746i	−0.133190	+	0.230692i
$147$	−4.62471	+	5.25472i	−0.381439	+	0.433402i
$148$	6.62418	+	3.82447i	0.544504	+	0.314370i
$149$	−0.385522	−	0.667744i	−0.0315832	−	0.0547037i	0.849802	−	0.527102i	$-0.176722\pi$
$149$	−0.385522	−	0.667744i	−0.0315832	−	0.0547037i	−0.881385	+	0.472399i	$0.843388\pi$
$150$	−1.81393	+	1.04728i	−0.148107	+	0.0855097i
$151$			16.3871i			1.33357i	0.745251	+	0.666784i	$0.232329\pi$
$151$			16.3871i			1.33357i	−0.745251	+	0.666784i	$0.767671\pi$
$152$	−4.34175	−	0.386221i	−0.352163	−	0.0313267i
$153$			5.21926i			0.421952i
$154$	0.728628	−	7.33152i	0.0587145	−	0.590790i
$155$	−17.5500	+	10.1325i	−1.40965	+	0.813860i
$156$	−2.77941	+	4.81407i	−0.222531	+	0.385434i
$157$	−2.24931	+	1.29864i	−0.179515	+	0.103643i	−0.587065	−	0.809540i	$-0.699717\pi$
$157$	−2.24931	+	1.29864i	−0.179515	+	0.103643i	0.407550	+	0.913183i	$0.366383\pi$
$158$	8.21444	−	14.2278i	0.653506	−	1.13191i
$159$		−	5.24800i		−	0.416194i
$160$	−2.66356			−0.210573
$161$	5.38155	+	11.9053i	0.424126	+	0.938268i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	−0.265071			−0.0207620			−0.0103810	−	0.999946i	$-0.503304\pi$
$163$	−0.265071			−0.0207620			−0.0103810	+	0.999946i	$0.503304\pi$
$164$	9.91677			0.774370
$165$	6.42351	+	3.70861i	0.500069	+	0.288715i
$166$	0.887675	+	1.53750i	0.0688970	+	0.119333i
$167$	−4.64289	+	8.04172i	−0.359277	+	0.622287i	−0.987840	−	0.155472i	$-0.950310\pi$
$167$	−4.64289	+	8.04172i	−0.359277	+	0.622287i	0.628563	+	0.777759i	$0.283643\pi$
$168$	0.261654	−	2.63278i	0.0201870	−	0.203123i
$169$	−8.95019	−	15.5022i	−0.688476	−	1.19248i
$170$		−	13.9018i		−	1.06622i
$171$	3.56696	+	2.50535i	0.272772	+	0.191589i
$172$	−4.70662			−0.358876
$173$	−2.20907	−	3.82622i	−0.167952	−	0.290902i	0.769747	−	0.638349i	$-0.220382\pi$
$173$	−2.20907	−	3.82622i	−0.167952	−	0.290902i	−0.937700	+	0.347446i	$0.887049\pi$
$174$	1.77203	+	3.06925i	0.134338	+	0.232679i
$175$	2.28262	+	5.04972i	0.172550	+	0.381723i
$176$	1.39235	+	2.41162i	0.104952	+	0.181783i
$177$	−2.50337	+	4.33596i	−0.188165	+	0.325911i
$178$			5.70630i			0.427706i
$179$			17.9214i			1.33951i	0.742584	+	0.669753i	$0.233600\pi$
$179$			17.9214i			1.33951i	−0.742584	+	0.669753i	$0.766400\pi$
$180$	2.30671	+	1.33178i	0.171932	+	0.0992650i
$181$	5.90218	−	10.2229i	0.438706	−	0.759861i	−0.558884	−	0.829246i	$-0.688770\pi$
$181$	5.90218	−	10.2229i	0.438706	−	0.759861i	0.997590	+	0.0693850i	$0.0221037\pi$
$182$	11.9472	+	8.57719i	0.885582	+	0.635783i
$183$		−	8.26101i		−	0.610671i
$184$	−4.27656	−	2.46907i	−0.315272	−	0.182022i
$185$	10.1867	+	17.6439i	0.748942	+	1.29721i
$186$	6.58891	+	3.80411i	0.483122	+	0.278931i
$187$	−12.5869	+	7.26704i	−0.920445	+	0.531419i
$188$	5.75686	−	3.32372i	0.419862	−	0.242408i
$189$	−1.54299	+	2.14923i	−0.112236	+	0.156333i
$190$	−9.50081	−	6.67316i	−0.689261	−	0.484122i
$191$	13.9511			1.00947			0.504734	−	0.863275i	$-0.331590\pi$
$191$	13.9511			1.00947			0.504734	+	0.863275i	$0.331590\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−8.19346	+	4.73049i	−0.589778	+	0.340508i	−0.765010	−	0.644019i	$-0.777266\pi$
$193$	−8.19346	+	4.73049i	−0.589778	+	0.340508i	0.175232	+	0.984527i	$0.443932\pi$
$194$	−6.05678	−	3.49688i	−0.434852	−	0.251062i
$195$	−12.8226	+	7.40311i	−0.918243	+	0.530148i
$196$	−6.86307	−	1.37775i	−0.490220	−	0.0984110i
$197$	−12.4822			−0.889317			−0.444659	−	0.895700i	$-0.646675\pi$
$197$	−12.4822			−0.889317			−0.444659	+	0.895700i	$0.646675\pi$
$198$		−	2.78470i		−	0.197900i
$199$	−3.61876	−	2.08929i	−0.256527	−	0.148106i	0.366222	−	0.930527i	$-0.380651\pi$
$199$	−3.61876	−	2.08929i	−0.256527	−	0.148106i	−0.622749	+	0.782421i	$0.713984\pi$
$200$	−1.81393	−	1.04728i	−0.128265	−	0.0740535i
$201$		−	5.73475i		−	0.404498i
$202$	−4.77569			−0.336016
$203$	8.54433	−	3.86230i	0.599695	−	0.271080i
$204$	−4.52001	+	2.60963i	−0.316464	+	0.182711i
$205$	22.8751	+	13.2070i	1.59767	+	0.922414i
$206$	4.80795	−	2.77587i	0.334986	−	0.193404i
$207$	2.46907	+	4.27656i	0.171612	+	0.297241i
$208$	−5.55881			−0.385434
$209$	−1.07551	+	12.0905i	−0.0743947	+	0.836317i
$210$	4.10984	−	5.72460i	0.283606	−	0.395035i
$211$	0.635998	−	0.367194i	0.0437839	−	0.0252787i	−0.477948	−	0.878388i	$-0.658619\pi$
$211$	0.635998	−	0.367194i	0.0437839	−	0.0252787i	0.521732	+	0.853109i	$0.325286\pi$
$212$	4.54490	−	2.62400i	0.312145	−	0.180217i
$213$	13.3355	+	7.69926i	0.913734	+	0.527545i
$214$	9.61563	+	16.6548i	0.657311	+	1.13850i
$215$	−10.8568	−	6.26818i	−0.740428	−	0.427486i
$216$		−	1.00000i		−	0.0680414i
$217$	11.7394	−	16.3518i	0.796922	−	1.11003i
$218$	9.08601	−	15.7374i	0.615382	−	1.06587i
$219$	2.78746	+	1.60934i	0.188359	+	0.108749i
$220$			7.41723i			0.500069i
$221$		−	29.0129i		−	1.95162i
$222$	3.82447	−	6.62418i	0.256682	−	0.444586i
$223$	−10.4131	−	18.0361i	−0.697315	−	1.20778i	−0.969394	−	0.245510i	$-0.921045\pi$
$223$	−10.4131	−	18.0361i	−0.697315	−	1.20778i	0.272079	−	0.962275i	$-0.412289\pi$
$224$	2.41088	−	1.08979i	0.161084	−	0.0728148i
$225$	1.04728	+	1.81393i	0.0698184	+	0.120929i
$226$	7.83503	+	13.5707i	0.521178	+	0.902708i
$227$	2.49025			0.165284			0.0826420	−	0.996579i	$-0.473664\pi$
$227$	2.49025			0.165284			0.0826420	+	0.996579i	$0.473664\pi$
$228$	−0.386221	+	4.34175i	−0.0255781	+	0.287540i
$229$		−	25.3056i		−	1.67224i	−0.548548	−	0.836119i	$-0.684819\pi$
$229$		−	25.3056i		−	1.67224i	0.548548	−	0.836119i	$-0.315181\pi$
$230$	−6.57652	−	11.3909i	−0.433643	−	0.751092i
$231$	−7.33152	−	0.728628i	−0.482378	−	0.0479402i
$232$	−1.77203	+	3.06925i	−0.116340	+	0.201506i
$233$	−4.51955	−	7.82809i	−0.296086	−	0.512835i	0.679151	−	0.733998i	$-0.262348\pi$
$233$	−4.51955	−	7.82809i	−0.296086	−	0.512835i	−0.975237	+	0.221163i	$0.929015\pi$
$234$	4.81407	+	2.77941i	0.314706	+	0.181695i
$235$	17.7059			1.15500
$236$	−5.00673			−0.325911
$237$	−14.2278	−	8.21444i	−0.924197	−	0.533585i
$238$	5.68790	+	12.5830i	0.368692	+	0.815636i
$239$	−7.09459			−0.458911			−0.229455	−	0.973319i	$-0.573695\pi$
$239$	−7.09459			−0.458911			−0.229455	+	0.973319i	$0.573695\pi$
$240$			2.66356i			0.171932i
$241$	−4.47952	+	7.75875i	−0.288551	+	0.499785i	−0.973464	−	0.228840i	$-0.926507\pi$
$241$	−4.47952	+	7.75875i	−0.288551	+	0.499785i	0.684913	+	0.728625i	$0.259840\pi$
$242$	−2.81062	+	1.62271i	−0.180673	+	0.104312i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	7.15424	−	4.13050i	0.458003	−	0.264428i
$245$	−13.9963	−	12.3182i	−0.894188	−	0.786980i
$246$		−	9.91677i		−	0.632270i
$247$	−19.8281	−	13.9268i	−1.26163	−	0.886141i
$248$			7.60822i			0.483122i
$249$	1.53750	−	0.887675i	0.0974350	−	0.0562541i
$250$	3.86942	+	6.70203i	0.244724	+	0.423874i
$251$	22.8024	+	13.1650i	1.43928	+	0.830966i	0.997799	−	0.0663071i	$-0.0211217\pi$
$251$	22.8024	+	13.1650i	1.43928	+	0.830966i	0.441476	+	0.897273i	$0.354455\pi$
$252$	−2.63278	−	0.261654i	−0.165850	−	0.0164826i
$253$	−6.87564	+	11.9090i	−0.432268	+	0.748709i
$254$	−4.25271			−0.266839
$255$	−13.9018			−0.870565
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.79853	−	10.0433i	0.361702	−	0.626486i	−0.626539	−	0.779390i	$-0.715529\pi$
$257$	5.79853	−	10.0433i	0.361702	−	0.626486i	0.988241	+	0.152904i	$0.0488624\pi$
$258$			4.70662i			0.293021i
$259$	−16.4393	−	11.8022i	−1.02149	−	0.733356i
$260$	−12.8226	−	7.40311i	−0.795222	−	0.459122i
$261$	3.06925	−	1.77203i	0.189982	−	0.109686i
$262$	6.23643	−	10.8018i	0.385288	−	0.667338i
$263$	−1.85651	−	3.21557i	−0.114477	−	0.198280i	0.803093	−	0.595853i	$-0.203186\pi$
$263$	−1.85651	−	3.21557i	−0.114477	−	0.198280i	−0.917571	+	0.397573i	$0.869853\pi$
$264$	2.41162	−	1.39235i	0.148425	−	0.0856933i
$265$	13.9784			0.858684
$266$	11.3298	+	2.15287i	0.694677	+	0.132001i
$267$	5.70630			0.349220
$268$	4.96644	−	2.86737i	0.303373	−	0.175153i
$269$	11.4915	+	19.9039i	0.700649	+	1.21356i	0.968239	+	0.250027i	$0.0804394\pi$
$269$	11.4915	+	19.9039i	0.700649	+	1.21356i	−0.267590	+	0.963533i	$0.586227\pi$
$270$	1.33178	−	2.30671i	0.0810495	−	0.140382i
$271$	−9.44262	+	5.45170i	−0.573598	+	0.331167i	−0.758585	−	0.651574i	$-0.774109\pi$
$271$	−9.44262	+	5.45170i	−0.573598	+	0.331167i	0.184987	+	0.982741i	$0.440776\pi$
$272$	−4.52001	−	2.60963i	−0.274066	−	0.158232i
$273$	8.57719	−	11.9472i	0.519115	−	0.723075i
$274$		−	6.58627i		−	0.397891i
$275$	−2.91635	+	5.05127i	−0.175863	+	0.304603i
$276$	−2.46907	+	4.27656i	−0.148621	+	0.257419i
$277$	10.5080			0.631367			0.315683	−	0.948865i	$-0.397766\pi$
$277$	10.5080			0.631367			0.315683	+	0.948865i	$0.397766\pi$
$278$	19.4990			1.16947
$279$	3.80411	−	6.58891i	0.227746	−	0.394468i
$280$	7.01257	+	0.696930i	0.419081	+	0.0416495i
$281$	−24.0195	−	13.8676i	−1.43288	−	0.827275i	−0.435542	−	0.900168i	$-0.643443\pi$
$281$	−24.0195	−	13.8676i	−1.43288	−	0.827275i	−0.997340	+	0.0728939i	$0.976777\pi$
$282$	−3.32372	−	5.75686i	−0.197925	−	0.342816i
$283$	20.4966	−	11.8337i	1.21840	−	0.703441i	0.253821	−	0.967251i	$-0.418313\pi$
$283$	20.4966	−	11.8337i	1.21840	−	0.703441i	0.964575	+	0.263811i	$0.0849794\pi$
$284$			15.3985i			0.913734i
$285$	−6.67316	+	9.50081i	−0.395284	+	0.562779i
$286$			15.4796i			0.915331i
$287$	−26.1087	−	2.59476i	−1.54115	−	0.153164i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	5.12033	−	8.86867i	0.301196	−	0.521686i
$290$	−8.17514	+	4.71992i	−0.480061	+	0.277163i
$291$	−3.49688	+	6.05678i	−0.204991	+	0.355055i
$292$			3.21869i			0.188359i
$293$	−28.4304			−1.66092			−0.830461	−	0.557076i	$-0.811923\pi$
$293$	−28.4304			−1.66092			−0.830461	+	0.557076i	$0.811923\pi$
$294$	−1.37775	+	6.86307i	−0.0803522	+	0.400263i
$295$	−11.5491	−	6.66787i	−0.672414	−	0.388218i
$296$	7.64895			0.444586
$297$	−2.78470			−0.161585
$298$	−0.667744	−	0.385522i	−0.0386814	−	0.0223327i
$299$	−13.7251	−	23.7726i	−0.793744	−	1.37480i
$300$	−1.04728	+	1.81393i	−0.0604645	+	0.104728i
$301$	12.3915	+	1.23150i	0.714234	+	0.0709827i
$302$	8.19357	+	14.1917i	0.471487	+	0.816640i
$303$			4.77569i			0.274356i
$304$	−3.95318	+	1.83640i	−0.226730	+	0.105325i
$305$	22.0037			1.25993
$306$	2.60963	+	4.52001i	0.149183	+	0.258392i
$307$	−8.96734	−	15.5319i	−0.511793	−	0.886452i	−0.999907	−	0.0136716i	$-0.995648\pi$
$307$	−8.96734	−	15.5319i	−0.511793	−	0.886452i	0.488113	−	0.872780i	$-0.337685\pi$
$308$	−3.03475	−	6.71359i	−0.172921	−	0.382542i
$309$	−2.77587	−	4.80795i	−0.157914	−	0.273515i
$310$	−10.1325	+	17.5500i	−0.575486	+	0.996770i
$311$			9.70184i			0.550141i	0.961424	+	0.275070i	$0.0887012\pi$
$311$			9.70184i			0.550141i	−0.961424	+	0.275070i	$0.911299\pi$
$312$			5.55881i			0.314706i
$313$	20.3361	+	11.7410i	1.14946	+	0.663643i	0.948756	−	0.316009i	$-0.102343\pi$
$313$	20.3361	+	11.7410i	1.14946	+	0.663643i	0.200707	+	0.979651i	$0.435676\pi$
$314$	−1.29864	+	2.24931i	−0.0732866	+	0.126936i
$315$	−5.72460	−	4.10984i	−0.322545	−	0.231564i
$316$		−	16.4289i		−	0.924197i
$317$	−6.56177	−	3.78844i	−0.368546	−	0.212780i	0.304277	−	0.952584i	$-0.401585\pi$
$317$	−6.56177	−	3.78844i	−0.368546	−	0.212780i	−0.672823	+	0.739804i	$0.734918\pi$
$318$	−2.62400	−	4.54490i	−0.147147	−	0.254866i
$319$	8.54696	+	4.93459i	0.478538	+	0.276284i
$320$	−2.30671	+	1.33178i	−0.128949	+	0.0744488i
$321$	16.6548	−	9.61563i	0.929578	−	0.536692i
$322$	10.6132	+	7.61951i	0.591451	+	0.424619i
$323$	−9.58464	−	20.6327i	−0.533304	−	1.14803i
$324$	−1.00000			−0.0555556
$325$	−5.82161	−	10.0833i	−0.322925	−	0.559322i
$326$	−0.229558	+	0.132535i	−0.0127140	+	0.00734046i
$327$	−15.7374	−	9.08601i	−0.870282	−	0.502457i
$328$	8.58818	−	4.95839i	0.474203	−	0.273781i
$329$	−16.0262	+	7.24434i	−0.883554	+	0.399393i
$330$	7.41723			0.408305
$331$		−	10.3359i		−	0.568111i	−0.958808	−	0.284056i	$-0.908320\pi$
$331$		−	10.3359i		−	0.568111i	0.958808	−	0.284056i	$-0.0916801\pi$
$332$	1.53750	+	0.887675i	0.0843812	+	0.0487175i
$333$	−6.62418	−	3.82447i	−0.363003	−	0.209580i
$334$			9.28578i			0.508095i
$335$	15.2748			0.834554
$336$	−1.08979	−	2.41088i	−0.0594530	−	0.131524i
$337$	−25.9794	+	14.9992i	−1.41519	+	0.817060i	−0.995871	−	0.0907796i	$-0.971064\pi$
$337$	−25.9794	+	14.9992i	−1.41519	+	0.817060i	−0.419318	+	0.907839i	$0.637731\pi$
$338$	−15.5022	−	8.95019i	−0.843208	−	0.486826i
$339$	13.5707	−	7.83503i	0.737058	−	0.425540i
$340$	−6.95090	−	12.0393i	−0.376966	−	0.652924i
$341$	21.1866			1.14732
$342$	4.34175	+	0.386221i	0.234775	+	0.0208845i
$343$	17.7085	+	5.42307i	0.956168	+	0.292818i
$344$	−4.07605	+	2.35331i	−0.219766	+	0.126882i
$345$	−11.3909	+	6.57652i	−0.613264	+	0.354068i
$346$	−3.82622	−	2.20907i	−0.205699	−	0.118760i
$347$	3.61675	+	6.26439i	0.194157	+	0.336290i	0.946624	−	0.322340i	$-0.104470\pi$
$347$	3.61675	+	6.26439i	0.194157	+	0.336290i	−0.752467	+	0.658630i	$0.771136\pi$
$348$	3.06925	+	1.77203i	0.164529	+	0.0949910i
$349$			27.0864i			1.44990i	0.688800	+	0.724952i	$0.258138\pi$
$349$			27.0864i			1.44990i	−0.688800	+	0.724952i	$0.741862\pi$
$350$	4.50167	+	3.23187i	0.240624	+	0.172751i
$351$	2.77941	−	4.81407i	0.148354	−	0.256956i
$352$	2.41162	+	1.39235i	0.128540	+	0.0742126i
$353$		−	2.01739i		−	0.107375i	−0.998558	−	0.0536875i	$-0.982903\pi$
$353$		−	2.01739i		−	0.107375i	0.998558	−	0.0536875i	$-0.0170975\pi$
$354$			5.00673i			0.266105i
$355$	−20.5074	+	35.5199i	−1.08842	+	1.88520i
$356$	2.85315	+	4.94180i	0.151217	+	0.261915i
$357$	12.5830	−	5.68790i	0.665964	−	0.301036i
$358$	8.96068	+	15.5204i	0.473587	+	0.820276i
$359$	13.3185	+	23.0683i	0.702922	+	1.21750i	0.967436	+	0.253115i	$0.0814550\pi$
$359$	13.3185	+	23.0683i	0.702922	+	1.21750i	−0.264514	+	0.964382i	$0.585212\pi$
$360$	2.66356			0.140382
$361$	−18.7017	−	3.35376i	−0.984298	−	0.176514i
$362$		−	11.8044i		−	0.620424i
$363$	1.62271	+	2.81062i	0.0851703	+	0.147519i
$364$	14.6351	+	1.45448i	0.767089	+	0.0762357i
$365$	−4.28658	+	7.42458i	−0.224370	+	0.388620i
$366$	−4.13050	−	7.15424i	−0.215905	−	0.373958i
$367$	−8.11774	−	4.68678i	−0.423743	−	0.244648i	0.272935	−	0.962033i	$-0.412006\pi$
$367$	−8.11774	−	4.68678i	−0.423743	−	0.244648i	−0.696677	+	0.717385i	$0.745339\pi$
$368$	−4.93815			−0.257419
$369$	−9.91677			−0.516247
$370$	17.6439	+	10.1867i	0.917263	+	0.529582i
$371$	−12.6523	+	5.71923i	−0.656875	+	0.296928i
$372$	7.60822			0.394468
$373$			1.64964i			0.0854149i	0.999088	+	0.0427075i	$0.0135983\pi$
$373$			1.64964i			0.0854149i	−0.999088	+	0.0427075i	$0.986402\pi$
$374$	−7.26704	+	12.5869i	−0.375770	+	0.650853i
$375$	6.70203	−	3.86942i	0.346091	−	0.199816i
$376$	3.32372	−	5.75686i	0.171408	−	0.296887i
$377$	−17.0614	+	9.85040i	−0.878707	+	0.507322i
$378$	−0.261654	+	2.63278i	−0.0134580	+	0.135416i
$379$			19.7977i			1.01694i	0.861080	+	0.508470i	$0.169789\pi$
$379$			19.7977i			1.01694i	−0.861080	+	0.508470i	$0.830211\pi$
$380$	−11.5645	−	1.02872i	−0.593248	−	0.0527724i
$381$			4.25271i			0.217873i
$382$	12.0820	−	6.97557i	0.618171	−	0.356901i
$383$	−1.32544	−	2.29573i	−0.0677267	−	0.117306i	0.830174	−	0.557505i	$-0.188241\pi$
$383$	−1.32544	−	2.29573i	−0.0677267	−	0.117306i	−0.897900	+	0.440199i	$0.854908\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$	1.94074	−	19.5279i	0.0989095	−	0.995236i
$386$	−4.73049	+	8.19346i	−0.240776	+	0.417036i
$387$	4.70662			0.239251
$388$	−6.99377			−0.355055
$389$	−9.09545	+	15.7538i	−0.461158	+	0.798749i	−0.999019	−	0.0442847i	$-0.985899\pi$
$389$	−9.09545	+	15.7538i	−0.461158	+	0.798749i	0.537861	+	0.843033i	$0.319232\pi$
$390$	−7.40311	+	12.8226i	−0.374871	+	0.649296i
$391$		−	25.7735i		−	1.30342i
$392$	−6.63247	+	2.23837i	−0.334991	+	0.113055i
$393$	−10.8018	−	6.23643i	−0.544879	−	0.314586i
$394$	−10.8099	+	6.24108i	−0.544594	+	0.314421i
$395$	21.8797	−	37.8967i	1.10088	−	1.90679i
$396$	−1.39235	−	2.41162i	−0.0699683	−	0.121189i
$397$	−5.16186	+	2.98020i	−0.259066	+	0.149572i	−0.623909	−	0.781497i	$-0.714456\pi$
$397$	−5.16186	+	2.98020i	−0.259066	+	0.149572i	0.364842	+	0.931069i	$0.381123\pi$
$398$	−4.17859			−0.209454
$399$	2.15287	−	11.3298i	0.107778	−	0.567201i
$400$	−2.09455			−0.104728
$401$	2.76778	−	1.59798i	0.138216	−	0.0797993i	−0.429297	−	0.903163i	$-0.641239\pi$
$401$	2.76778	−	1.59798i	0.138216	−	0.0797993i	0.567514	+	0.823364i	$0.307905\pi$
$402$	−2.86737	−	4.96644i	−0.143012	−	0.247703i
$403$	−21.1463	+	36.6265i	−1.05337	+	1.82450i
$404$	−4.13587	+	2.38784i	−0.205767	+	0.118800i
$405$	−2.30671	−	1.33178i	−0.114621	−	0.0661767i
$406$	5.46846	−	7.61701i	0.271395	−	0.378026i
$407$		−	21.3001i		−	1.05580i
$408$	−2.60963	+	4.52001i	−0.129196	+	0.223774i
$409$	11.6779	−	20.2266i	0.577433	−	1.00014i	−0.418340	−	0.908291i	$-0.637388\pi$
$409$	11.6779	−	20.2266i	0.577433	−	1.00014i	0.995773	−	0.0918524i	$-0.0292788\pi$
$410$	26.4139			1.30449
$411$	−6.58627			−0.324877
$412$	2.77587	−	4.80795i	0.136757	−	0.236871i
$413$	13.1816	+	1.31003i	0.648626	+	0.0644624i
$414$	4.27656	+	2.46907i	0.210181	+	0.121348i
$415$	2.36438	+	4.09522i	0.116063	+	0.201026i
$416$	−4.81407	+	2.77941i	−0.236029	+	0.136272i
$417$		−	19.4990i		−	0.954872i
$418$	5.11383	+	11.0084i	0.250126	+	0.538440i
$419$		−	17.4956i		−	0.854715i	−0.904083	−	0.427357i	$-0.859445\pi$
$419$		−	17.4956i		−	0.854715i	0.904083	−	0.427357i	$-0.140555\pi$
$420$	0.696930	−	7.01257i	0.0340067	−	0.342178i
$421$	−18.7120	+	10.8034i	−0.911967	+	0.526524i	−0.881064	−	0.472998i	$-0.843172\pi$
$421$	−18.7120	+	10.8034i	−0.911967	+	0.526524i	−0.0309035	+	0.999522i	$0.509838\pi$
$422$	0.367194	−	0.635998i	0.0178747	−	0.0309599i
$423$	−5.75686	+	3.32372i	−0.279908	+	0.161605i
$424$	2.62400	−	4.54490i	0.127433	−	0.220720i
$425$		−	10.9320i		−	0.530280i
$426$	15.3985			0.746061
$427$	−19.9163	+	9.00278i	−0.963818	+	0.435675i
$428$	16.6548	+	9.61563i	0.805038	+	0.464789i
$429$	15.4796			0.747364
$430$	−12.5364			−0.604557
$431$	23.0378	+	13.3009i	1.10969	+	0.640680i	0.938749	−	0.344601i	$-0.111986\pi$
$431$	23.0378	+	13.3009i	1.10969	+	0.640680i	0.170942	+	0.985281i	$0.445319\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	9.36371	−	16.2184i	0.449991	−	0.779407i	−0.548394	−	0.836220i	$-0.684760\pi$
$433$	9.36371	−	16.2184i	0.449991	−	0.779407i	0.998385	+	0.0568128i	$0.0180938\pi$
$434$	1.99072	−	20.0308i	0.0955575	−	0.961508i
$435$	4.71992	+	8.17514i	0.226303	+	0.391968i
$436$		−	18.1720i		−	0.870282i
$437$	−17.6142	−	12.3718i	−0.842600	−	0.591824i
$438$	3.21869			0.153795
$439$	0.116386	+	0.201587i	0.00555482	+	0.00962123i	0.868789	−	0.495182i	$-0.164899\pi$
$439$	0.116386	+	0.201587i	0.00555482	+	0.00962123i	−0.863235	+	0.504803i	$0.831565\pi$
$440$	3.70861	+	6.42351i	0.176801	+	0.306229i
$441$	6.86307	+	1.37775i	0.326813	+	0.0656073i
$442$	−14.5064	−	25.1259i	−0.690001	−	1.19512i
$443$	2.27999	−	3.94906i	0.108326	−	0.187625i	−0.806767	−	0.590870i	$-0.798784\pi$
$443$	2.27999	−	3.94906i	0.108326	−	0.187625i	0.915092	+	0.403245i	$0.132118\pi$
$444$		−	7.64895i		−	0.363003i
$445$			15.1991i			0.720506i
$446$	−18.0361	−	10.4131i	−0.854033	−	0.493076i
$447$	−0.385522	+	0.667744i	−0.0182346	+	0.0315832i
$448$	1.54299	−	2.14923i	0.0728994	−	0.101542i
$449$		−	26.0980i		−	1.23164i	−0.787887	−	0.615820i	$-0.788825\pi$
$449$		−	26.0980i		−	1.23164i	0.787887	−	0.615820i	$-0.211175\pi$
$450$	1.81393	+	1.04728i	0.0855097	+	0.0493690i
$451$	−13.8076	−	23.9155i	−0.650176	−	1.12614i
$452$	13.5707	+	7.83503i	0.638311	+	0.368529i
$453$	14.1917	−	8.19357i	0.666784	−	0.384968i
$454$	2.15662	−	1.24513i	0.101215	−	0.0584367i
$455$	31.8220	+	22.8458i	1.49184	+	1.07103i
$456$	1.83640	+	3.95318i	0.0859973	+	0.185125i
$457$	−3.32554			−0.155562			−0.0777810	−	0.996970i	$-0.524784\pi$
$457$	−3.32554			−0.155562			−0.0777810	+	0.996970i	$0.524784\pi$
$458$	−12.6528	−	21.9153i	−0.591225	−	1.02403i
$459$	4.52001	−	2.60963i	0.210976	−	0.121807i
$460$	−11.3909	−	6.57652i	−0.531102	−	0.306632i
$461$	6.98839	−	4.03475i	0.325482	−	0.187917i	−0.328352	−	0.944556i	$-0.606493\pi$
$461$	6.98839	−	4.03475i	0.325482	−	0.187917i	0.653833	+	0.756639i	$0.273160\pi$
$462$	−6.71359	+	3.03475i	−0.312345	+	0.141189i
$463$	−6.46153			−0.300293			−0.150146	−	0.988664i	$-0.547975\pi$
$463$	−6.46153			−0.300293			−0.150146	+	0.988664i	$0.547975\pi$
$464$			3.54407i			0.164529i
$465$	17.5500	+	10.1325i	0.813860	+	0.469882i
$466$	−7.82809	−	4.51955i	−0.362629	−	0.209364i
$467$		−	24.6746i		−	1.14180i	−0.821018	−	0.570902i	$-0.806594\pi$
$467$		−	24.6746i		−	1.14180i	0.821018	−	0.570902i	$-0.193406\pi$
$468$	5.55881			0.256956
$469$	−13.8258	+	6.24968i	−0.638416	+	0.288583i
$470$	15.3337	−	8.85294i	0.707293	−	0.408356i
$471$	2.24931	+	1.29864i	0.103643	+	0.0598383i
$472$	−4.33596	+	2.50337i	−0.199579	+	0.115227i
$473$	6.55327	+	11.3506i	0.301320	+	0.521901i
$474$	−16.4289			−0.754603
$475$	−7.47118	−	5.24759i	−0.342801	−	0.240776i
$476$	11.2174	+	8.05326i	0.514148	+	0.369121i
$477$	−4.54490	+	2.62400i	−0.208097	+	0.120145i
$478$	−6.14410	+	3.54730i	−0.281024	+	0.162250i
$479$	−2.92565	−	1.68912i	−0.133676	−	0.0771780i	0.431671	−	0.902031i	$-0.357924\pi$
$479$	−2.92565	−	1.68912i	−0.133676	−	0.0771780i	−0.565347	+	0.824853i	$0.691258\pi$
$480$	1.33178	+	2.30671i	0.0607872	+	0.105286i
$481$	36.8226	+	21.2595i	1.67897	+	0.969351i
$482$			8.95904i			0.408073i
$483$	7.61951	−	10.6132i	0.346700	−	0.482918i
$484$	−1.62271	+	2.81062i	−0.0737596	+	0.127755i
$485$	−16.1326	−	9.31416i	−0.732544	−	0.422934i
$486$			1.00000i			0.0453609i
$487$		−	10.8181i		−	0.490217i	−0.969496	−	0.245108i	$-0.921176\pi$
$487$		−	10.8181i		−	0.490217i	0.969496	−	0.245108i	$-0.0788236\pi$
$488$	4.13050	−	7.15424i	0.186979	−	0.323857i
$489$	0.132535	+	0.229558i	0.00599346	+	0.0103810i
$490$	−18.2802	−	3.66973i	−0.825816	−	0.165781i
$491$	4.77687	+	8.27378i	0.215577	+	0.373390i	0.953451	−	0.301548i	$-0.0975035\pi$
$491$	4.77687	+	8.27378i	0.215577	+	0.373390i	−0.737874	+	0.674939i	$0.764170\pi$
$492$	−4.95839	−	8.58818i	−0.223541	−	0.387185i
$493$	−18.4974			−0.833081
$494$	−24.1350	−	2.14693i	−1.08588	−	0.0965950i
$495$		−	7.41723i		−	0.333379i
$496$	3.80411	+	6.58891i	0.170810	+	0.295851i
$497$	4.02908	−	40.5409i	0.180729	−	1.81851i
$498$	0.887675	−	1.53750i	0.0397777	−	0.0688970i
$499$	−18.7760	−	32.5210i	−0.840530	−	1.45584i	−0.889448	−	0.457037i	$-0.848911\pi$
$499$	−18.7760	−	32.5210i	−0.840530	−	1.45584i	0.0489178	−	0.998803i	$-0.484423\pi$
$500$	6.70203	+	3.86942i	0.299724	+	0.173046i
$501$	9.28578			0.414858
$502$	26.3300			1.17516
$503$	−2.14052	−	1.23583i	−0.0954410	−	0.0551029i	0.451520	−	0.892261i	$-0.350882\pi$
$503$	−2.14052	−	1.23583i	−0.0954410	−	0.0551029i	−0.546961	+	0.837158i	$0.684215\pi$
$504$	−2.41088	+	1.08979i	−0.107389	+	0.0485432i
$505$	−12.7203			−0.566047
$506$			13.7513i			0.611319i
$507$	−8.95019	+	15.5022i	−0.397492	+	0.688476i
$508$	−3.68295	+	2.12635i	−0.163405	+	0.0943417i
$509$	−1.42612	+	2.47011i	−0.0632117	+	0.109486i	−0.895899	−	0.444257i	$-0.853468\pi$
$509$	−1.42612	+	2.47011i	−0.0632117	+	0.109486i	0.832688	+	0.553743i	$0.186801\pi$
$510$	−12.0393	+	6.95090i	−0.533110	+	0.307791i
$511$	0.842181	−	8.47410i	0.0372559	−	0.374872i
$512$			1.00000i			0.0441942i
$513$	0.386221	−	4.34175i	0.0170521	−	0.191693i
$514$		−	11.5971i		−	0.511524i
$515$	12.8063	−	7.39371i	0.564312	−	0.325806i
$516$	2.35331	+	4.07605i	0.103599	+	0.179438i
$517$	−16.0311	−	9.25559i	−0.705049	−	0.407060i
$518$	−20.1380	−	2.00138i	−0.884813	−	0.0879354i
$519$	−2.20907	+	3.82622i	−0.0969674	+	0.167952i
$520$	−14.8062			−0.649296
$521$	−31.8380			−1.39485			−0.697425	−	0.716658i	$-0.745671\pi$
$521$	−31.8380			−1.39485			−0.697425	+	0.716658i	$0.745671\pi$
$522$	1.77203	−	3.06925i	0.0775598	−	0.134338i
$523$	−13.8294	+	23.9533i	−0.604720	+	1.04740i	0.387376	+	0.921922i	$0.373381\pi$
$523$	−13.8294	+	23.9533i	−0.604720	+	1.04740i	−0.992096	+	0.125483i	$0.959952\pi$
$524$		−	12.4729i		−	0.544879i
$525$	3.23187	−	4.50167i	0.141050	−	0.196469i
$526$	−3.21557	−	1.85651i	−0.140205	−	0.0809477i
$527$	−34.3892	+	19.8546i	−1.49802	+	0.864881i
$528$	1.39235	−	2.41162i	0.0605943	−	0.104952i
$529$	−0.692643	−	1.19969i	−0.0301149	−	0.0521606i
$530$	12.1056	−	6.98918i	0.525835	−	0.303591i
$531$	5.00673			0.217274
$532$	10.8884	−	3.80047i	0.472070	−	0.164771i
$533$	55.1255			2.38775
$534$	4.94180	−	2.85315i	0.213853	−	0.123468i
$535$	25.6118	+	44.3609i	1.10729	+	1.91789i
$536$	2.86737	−	4.96644i	0.123852	−	0.214517i
$537$	15.5204	−	8.96068i	0.669753	−	0.386682i
$538$	19.9039	+	11.4915i	0.858116	+	0.495434i
$539$	6.23319	+	18.4695i	0.268483	+	0.795537i
$540$		−	2.66356i		−	0.114621i
$541$	13.3866	−	23.1863i	0.575536	−	0.996857i	−0.420447	−	0.907317i	$-0.638127\pi$
$541$	13.3866	−	23.1863i	0.575536	−	0.996857i	0.995983	−	0.0895403i	$-0.0285398\pi$
$542$	−5.45170	+	9.44262i	−0.234171	+	0.405595i
$543$	−11.8044			−0.506574
$544$	−5.21926			−0.223774
$545$	24.2011	−	41.9176i	1.03666	−	1.79555i
$546$	1.45448	−	14.6351i	0.0622461	−	0.626326i
$547$	−38.6104	−	22.2917i	−1.65086	−	0.953124i	−0.976719	−	0.214521i	$-0.931181\pi$
$547$	−38.6104	−	22.2917i	−1.65086	−	0.953124i	−0.674140	−	0.738603i	$-0.735486\pi$
$548$	−3.29313	−	5.70387i	−0.140676	−	0.243657i
$549$	−7.15424	+	4.13050i	−0.305336	+	0.176286i
$550$			5.83270i			0.248707i
$551$	−8.87915	+	12.6415i	−0.378264	+	0.538548i
$552$			4.93815i			0.210181i
$553$	−4.29868	+	43.2536i	−0.182798	+	1.83933i
$554$	9.10023	−	5.25402i	0.386632	−	0.223222i
$555$	10.1867	−	17.6439i	0.432402	−	0.748942i
$556$	16.8867	−	9.74952i	0.716154	−	0.413472i
$557$	−17.7458	+	30.7367i	−0.751916	+	1.30236i	0.194978	+	0.980808i	$0.437537\pi$
$557$	−17.7458	+	30.7367i	−0.751916	+	1.30236i	−0.946893	+	0.321548i	$0.895797\pi$
$558$		−	7.60822i		−	0.322082i
$559$	−26.1632			−1.10659
$560$	6.42153	−	2.90273i	0.271359	−	0.122663i
$561$	12.5869	+	7.26704i	0.531419	+	0.306815i
$562$	−27.7353			−1.16994
$563$	−0.216351			−0.00911809			−0.00455904	−	0.999990i	$-0.501451\pi$
$563$	−0.216351			−0.00911809			−0.00455904	+	0.999990i	$0.501451\pi$
$564$	−5.75686	−	3.32372i	−0.242408	−	0.139954i
$565$	20.8691	+	36.1463i	0.877968	+	1.52069i
$566$	11.8337	−	20.4966i	0.497408	−	0.861535i
$567$	2.63278	+	0.261654i	0.110566	+	0.0109884i
$568$	7.69926	+	13.3355i	0.323054	+	0.559546i
$569$		−	3.28925i		−	0.137892i	−0.997620	−	0.0689462i	$-0.978036\pi$
$569$		−	3.28925i		−	0.137892i	0.997620	−	0.0689462i	$-0.0219637\pi$
$570$	−1.02872	+	11.5645i	−0.0430885	+	0.484385i
$571$	24.0685			1.00724			0.503618	−	0.863926i	$-0.332002\pi$
$571$	24.0685			1.00724			0.503618	+	0.863926i	$0.332002\pi$
$572$	7.73982	+	13.4058i	0.323618	+	0.560523i
$573$	−6.97557	−	12.0820i	−0.291408	−	0.504734i
$574$	−23.9082	+	10.8072i	−0.997908	+	0.451085i
$575$	−5.17160	−	8.95747i	−0.215671	−	0.373552i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	20.0375i		−	0.834173i	−0.908867	−	0.417087i	$-0.863051\pi$
$577$		−	20.0375i		−	0.834173i	0.908867	−	0.417087i	$-0.136949\pi$
$578$		−	10.2407i		−	0.425955i
$579$	8.19346	+	4.73049i	0.340508	+	0.196593i
$580$	−4.71992	+	8.17514i	−0.195984	+	0.339454i
$581$	−3.81563	−	2.73935i	−0.158299	−	0.113647i
$582$			6.99377i			0.289901i
$583$	−12.6562	−	7.30707i	−0.524167	−	0.302628i
$584$	1.60934	+	2.78746i	0.0665951	+	0.115346i
$585$	12.8226	+	7.40311i	0.530148	+	0.306081i
$586$	−24.6215	+	14.2152i	−1.01710	+	0.587225i
$587$	−10.7979	+	6.23420i	−0.445679	+	0.257313i	−0.706004	−	0.708208i	$-0.749504\pi$
$587$	−10.7979	+	6.23420i	−0.445679	+	0.257313i	0.260325	+	0.965521i	$0.416170\pi$
$588$	2.23837	+	6.63247i	0.0923087	+	0.273519i
$589$	−2.93846	+	33.0330i	−0.121077	+	1.36110i
$590$	−13.3357			−0.549023
$591$	6.24108	+	10.8099i	0.256724	+	0.444659i
$592$	6.62418	−	3.82447i	0.272252	−	0.157185i
$593$	29.4998	+	17.0317i	1.21141	+	0.699408i	0.963066	−	0.269264i	$-0.0867804\pi$
$593$	29.4998	+	17.0317i	1.21141	+	0.699408i	0.248344	+	0.968672i	$0.420114\pi$
$594$	−2.41162	+	1.39235i	−0.0989501	+	0.0571289i
$595$	15.1501	+	33.5156i	0.621093	+	1.37401i
$596$	−0.771044			−0.0315832
$597$			4.17859i			0.171018i
$598$	−23.7726	−	13.7251i	−0.972133	−	0.561262i
$599$	−35.3814	−	20.4275i	−1.44565	−	0.834644i	−0.447428	−	0.894320i	$-0.647660\pi$
$599$	−35.3814	−	20.4275i	−1.44565	−	0.834644i	−0.998218	+	0.0596759i	$0.980993\pi$
$600$			2.09455i			0.0855097i
$601$	7.91420			0.322827			0.161414	−	0.986887i	$-0.448395\pi$
$601$	7.91420			0.322827			0.161414	+	0.986887i	$0.448395\pi$
$602$	11.3471	−	5.12924i	0.462473	−	0.209052i
$603$	−4.96644	+	2.86737i	−0.202249	+	0.116768i
$604$	14.1917	+	8.19357i	0.577452	+	0.333392i
$605$	−7.48625	+	4.32219i	−0.304359	+	0.175722i
$606$	2.38784	+	4.13587i	0.0969995	+	0.168008i
$607$	−24.6922			−1.00223			−0.501114	−	0.865381i	$-0.667076\pi$
$607$	−24.6922			−1.00223			−0.501114	+	0.865381i	$0.667076\pi$
$608$	−2.50535	+	3.56696i	−0.101606	+	0.144659i
$609$	−7.61701	−	5.46846i	−0.308657	−	0.221593i
$610$	19.0558	−	11.0018i	0.771545	−	0.445452i
$611$	32.0013	−	18.4760i	1.29463	−	0.747457i
$612$	4.52001	+	2.60963i	0.182711	+	0.105488i
$613$	−13.2054	−	22.8724i	−0.533360	−	0.923806i	−0.999241	−	0.0389587i	$-0.987596\pi$
$613$	−13.2054	−	22.8724i	−0.533360	−	0.923806i	0.465881	−	0.884847i	$-0.345737\pi$
$614$	−15.5319	−	8.96734i	−0.626816	−	0.361892i
$615$		−	26.4139i		−	1.06511i
$616$	−5.98497	−	4.29677i	−0.241141	−	0.173122i
$617$	−7.57831	+	13.1260i	−0.305091	+	0.528434i	−0.977282	−	0.211945i	$-0.932020\pi$
$617$	−7.57831	+	13.1260i	−0.305091	+	0.528434i	0.672190	+	0.740378i	$0.265354\pi$
$618$	−4.80795	−	2.77587i	−0.193404	−	0.111662i
$619$		−	44.5935i		−	1.79236i	−0.443688	−	0.896181i	$-0.646330\pi$
$619$		−	44.5935i		−	1.79236i	0.443688	−	0.896181i	$-0.353670\pi$
$620$			20.2649i			0.813860i
$621$	2.46907	−	4.27656i	0.0990805	−	0.171612i
$622$	4.85092	+	8.40204i	0.194504	+	0.336891i
$623$	−6.21868	−	13.7572i	−0.249146	−	0.551172i
$624$	2.77941	+	4.81407i	0.111265	+	0.192717i
$625$	15.5428	+	26.9209i	0.621712	+	1.07684i
$626$	23.4821			0.938533
$627$	11.0084	−	5.11383i	0.439635	−	0.204227i
$628$			2.59728i			0.103643i
$629$	19.9609	+	34.5733i	0.795894	+	1.37853i
$630$	−7.01257	−	0.696930i	−0.279387	−	0.0277664i
$631$	15.3615	−	26.6069i	0.611531	−	1.05920i	−0.379451	−	0.925212i	$-0.623887\pi$
$631$	15.3615	−	26.6069i	0.611531	−	1.05920i	0.990982	−	0.133992i	$-0.0427796\pi$
$632$	−8.21444	−	14.2278i	−0.326753	−	0.565953i
$633$	−0.635998	−	0.367194i	−0.0252787	−	0.0145946i
$634$	−7.57688			−0.300916
$635$	−11.3273			−0.449512
$636$	−4.54490	−	2.62400i	−0.180217	−	0.104048i
$637$	−38.1505	−	7.65867i	−1.51158	−	0.303448i
$638$	9.86918			0.390725
$639$		−	15.3985i		−	0.609156i
$640$	−1.33178	+	2.30671i	−0.0526432	+	0.0911807i
$641$	27.0077	−	15.5929i	1.06674	−	0.615883i	0.139452	−	0.990229i	$-0.455466\pi$
$641$	27.0077	−	15.5929i	1.06674	−	0.615883i	0.927289	+	0.374346i	$0.122133\pi$
$642$	9.61563	−	16.6548i	0.379498	−	0.657311i
$643$	−3.31610	+	1.91455i	−0.130774	+	0.0755024i	−0.563960	−	0.825802i	$-0.690723\pi$
$643$	−3.31610	+	1.91455i	−0.130774	+	0.0755024i	0.433186	+	0.901305i	$0.357389\pi$
$644$	13.0011	+	1.29208i	0.512313	+	0.0509152i
$645$			12.5364i			0.493619i
$646$	−18.6169	−	13.0761i	−0.732471	−	0.514472i
$647$			3.67032i			0.144295i	0.997394	+	0.0721476i	$0.0229853\pi$
$647$			3.67032i			0.144295i	−0.997394	+	0.0721476i	$0.977015\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	6.97113	+	12.0744i	0.273641	+	0.473960i
$650$	−10.0833	−	5.82161i	−0.395500	−	0.228342i
$651$	−20.0308	−	1.99072i	−0.785068	−	0.0780224i
$652$	−0.132535	+	0.229558i	−0.00519049	+	0.00899019i
$653$	18.8794			0.738808			0.369404	−	0.929269i	$-0.379562\pi$
$653$	18.8794			0.738808			0.369404	+	0.929269i	$0.379562\pi$
$654$	−18.1720			−0.710582
$655$	16.6111	−	28.7713i	0.649049	−	1.12419i
$656$	4.95839	−	8.58818i	0.193592	−	0.335312i
$657$		−	3.21869i		−	0.125573i
$658$	−10.2569	+	14.2869i	−0.399857	+	0.556961i
$659$	16.3724	+	9.45263i	0.637780	+	0.368222i	0.783759	−	0.621065i	$-0.213300\pi$
$659$	16.3724	+	9.45263i	0.637780	+	0.368222i	−0.145979	+	0.989288i	$0.546633\pi$
$660$	6.42351	−	3.70861i	0.250035	−	0.144358i
$661$	−12.8096	+	22.1868i	−0.498234	+	0.862967i	−0.999998	−	0.00203779i	$-0.999351\pi$
$661$	−12.8096	+	22.1868i	−0.498234	+	0.862967i	0.501764	+	0.865005i	$0.332685\pi$
$662$	−5.16794	−	8.95114i	−0.200858	−	0.347896i
$663$	−25.1259	+	14.5064i	−0.975808	+	0.563383i
$664$	1.77535			0.0688970
$665$	30.1777	+	5.73430i	1.17024	+	0.222367i
$666$	−7.64895			−0.296391
$667$	−15.1564	+	8.75056i	−0.586859	+	0.338823i
$668$	4.64289	+	8.04172i	0.179639	+	0.311143i
$669$	−10.4131	+	18.0361i	−0.402595	+	0.697315i
$670$	13.2284	−	7.63742i	0.511058	−	0.295059i
$671$	−19.9224	−	11.5022i	−0.769098	−	0.444039i
$672$	−2.14923	−	1.54299i	−0.0829083	−	0.0595221i
$673$			3.33116i			0.128407i	0.997937	+	0.0642033i	$0.0204506\pi$
$673$			3.33116i			0.128407i	−0.997937	+	0.0642033i	$0.979549\pi$
$674$	−14.9992	+	25.9794i	−0.577749	+	1.00069i
$675$	1.04728	−	1.81393i	0.0403096	−	0.0698184i
$676$	−17.9004			−0.688476
$677$	−9.72384			−0.373717			−0.186859	−	0.982387i	$-0.559831\pi$
$677$	−9.72384			−0.373717			−0.186859	+	0.982387i	$0.559831\pi$
$678$	7.83503	−	13.5707i	0.300903	−	0.521178i
$679$	18.4131	+	1.82995i	0.706629	+	0.0702269i
$680$	−12.0393	−	6.95090i	−0.461687	−	0.266555i
$681$	−1.24513	−	2.15662i	−0.0477134	−	0.0826420i
$682$	18.3482	−	10.5933i	0.702587	−	0.405639i
$683$			28.2700i			1.08172i	0.841112	+	0.540861i	$0.181902\pi$
$683$			28.2700i			1.08172i	−0.841112	+	0.540861i	$0.818098\pi$
$684$	3.95318	−	1.83640i	0.151154	−	0.0702165i
$685$		−	17.5429i		−	0.670280i
$686$	18.0475	−	4.15772i	0.689058	−	0.158743i
$687$	−21.9153	+	12.6528i	−0.836119	+	0.482734i
$688$	−2.35331	+	4.07605i	−0.0897191	+	0.155398i
$689$	25.2643	−	14.5863i	0.962492	−	0.555695i
$690$	−6.57652	+	11.3909i	−0.250364	+	0.433643i
$691$			3.96553i			0.150856i	0.997151	+	0.0754280i	$0.0240323\pi$
$691$			3.96553i			0.150856i	−0.997151	+	0.0754280i	$0.975968\pi$
$692$	−4.41814			−0.167952
$693$	3.03475	+	6.71359i	0.115281	+	0.255028i
$694$	6.26439	+	3.61675i	0.237793	+	0.137290i
$695$	51.9368			1.97008
$696$	3.54407			0.134338
$697$	44.8239	+	25.8791i	1.69783	+	0.980241i
$698$	13.5432	+	23.4575i	0.512618	+	0.887881i
$699$	−4.51955	+	7.82809i	−0.170945	+	0.296086i
$700$	5.51449	+	0.548047i	0.208428	+	0.0207142i
$701$	−7.55706	−	13.0892i	−0.285426	−	0.494373i	0.687286	−	0.726387i	$-0.258802\pi$
$701$	−7.55706	−	13.0892i	−0.285426	−	0.494373i	−0.972712	+	0.232014i	$0.925468\pi$
$702$		−	5.55881i		−	0.209804i
$703$	33.2099	+	2.95419i	1.25253	+	0.111419i
$704$	2.78470			0.104952
$705$	−8.85294	−	15.3337i	−0.333421	−	0.577502i
$706$	−1.00870	−	1.74711i	−0.0379628	−	0.0657535i
$707$	11.5136	−	5.20451i	0.433014	−	0.195736i
$708$	2.50337	+	4.33596i	0.0940823	+	0.162955i
$709$	3.09840	−	5.36658i	0.116363	−	0.201546i	−0.801961	−	0.597377i	$-0.796210\pi$
$709$	3.09840	−	5.36658i	0.116363	−	0.201546i	0.918324	+	0.395830i	$0.129543\pi$
$710$			41.0149i			1.53926i
$711$			16.4289i			0.616131i
$712$	4.94180	+	2.85315i	0.185202	+	0.106926i
$713$	−18.7852	+	32.5370i	−0.703513	+	1.21852i
$714$	8.05326	−	11.2174i	0.301386	−	0.419800i
$715$			41.2310i			1.54195i
$716$	15.5204	+	8.96068i	0.580023	+	0.334876i
$717$	3.54730	+	6.14410i	0.132476	+	0.229455i
$718$	23.0683	+	13.3185i	0.860900	+	0.497041i
$719$	29.1944	−	16.8554i	1.08877	−	0.628600i	0.155519	−	0.987833i	$-0.450295\pi$
$719$	29.1944	−	16.8554i	1.08877	−	0.628600i	0.933248	+	0.359233i	$0.116962\pi$
$720$	2.30671	−	1.33178i	0.0859660	−	0.0496325i
$721$	−8.56629	+	11.9320i	−0.319025	+	0.444370i
$722$	−17.8730	+	6.44639i	−0.665164	+	0.239910i
$723$	8.95904			0.333190
$724$	−5.90218	−	10.2229i	−0.219353	−	0.379930i
$725$	−6.42871	+	3.71162i	−0.238756	+	0.137846i
$726$	2.81062	+	1.62271i	0.104312	+	0.0602245i
$727$	−16.3308	+	9.42859i	−0.605676	+	0.349687i	−0.771271	−	0.636507i	$-0.780379\pi$
$727$	−16.3308	+	9.42859i	−0.605676	+	0.349687i	0.165595	+	0.986194i	$0.447045\pi$
$728$	13.4016	−	6.05795i	0.496698	−	0.224522i
$729$	1.00000			0.0370370
$730$			8.57317i			0.317307i
$731$	−21.2740	−	12.2825i	−0.786846	−	0.454286i
$732$	−7.15424	−	4.13050i	−0.264428	−	0.152668i
$733$			7.39418i			0.273110i	0.990632	+	0.136555i	$0.0436031\pi$
$733$			7.39418i			0.273110i	−0.990632	+	0.136555i	$0.956397\pi$
$734$	−9.37356			−0.345985
$735$	−3.66973	+	18.2802i	−0.135360	+	0.674276i
$736$	−4.27656	+	2.46907i	−0.157636	+	0.0910112i
$737$	−13.8301	−	7.98478i	−0.509437	−	0.294123i
$738$	−8.58818	+	4.95839i	−0.316135	+	0.182521i
$739$	−18.0023	−	31.1808i	−0.662224	−	1.14701i	−0.980030	−	0.198850i	$-0.936279\pi$
$739$	−18.0023	−	31.1808i	−0.662224	−	1.14701i	0.317806	−	0.948156i	$-0.397054\pi$
$740$	20.3734			0.748942
$741$	−2.14693	+	24.1350i	−0.0788695	+	0.886621i
$742$	−8.09761	+	11.2792i	−0.297273	+	0.414071i
$743$	30.3969	−	17.5497i	1.11515	−	0.643835i	0.174995	−	0.984569i	$-0.444009\pi$
$743$	30.3969	−	17.5497i	1.11515	−	0.643835i	0.940159	+	0.340735i	$0.110676\pi$
$744$	6.58891	−	3.80411i	0.241561	−	0.139465i
$745$	−1.77858	−	1.02686i	−0.0651620	−	0.0376213i
$746$	0.824818	+	1.42863i	0.0301987	+	0.0523057i
$747$	−1.53750	−	0.887675i	−0.0562541	−	0.0324783i
$748$			14.5341i			0.531419i
$749$	−41.3324	−	29.6736i	−1.51025	−	1.08425i
$750$	3.86942	−	6.70203i	0.141291	−	0.244724i
$751$	−3.54108	−	2.04445i	−0.129216	−	0.0746029i	0.433999	−	0.900914i	$-0.357102\pi$
$751$	−3.54108	−	2.04445i	−0.129216	−	0.0746029i	−0.563215	+	0.826311i	$0.690436\pi$
$752$		−	6.64745i		−	0.242408i
$753$		−	26.3300i		−	0.959517i
$754$	−9.85040	+	17.0614i	−0.358731	+	0.621340i
$755$	21.8241	+	37.8004i	0.794259	+	1.37570i
$756$	1.08979	+	2.41088i	0.0396353	+	0.0876829i
$757$	20.5800	+	35.6456i	0.747993	+	1.29556i	0.948783	+	0.315927i	$0.102316\pi$
$757$	20.5800	+	35.6456i	0.747993	+	1.29556i	−0.200791	+	0.979634i	$0.564351\pi$
$758$	9.89885	+	17.1453i	0.359542	+	0.622745i
$759$	13.7513			0.499140
$760$	−10.5295	+	4.89136i	−0.381946	+	0.177428i
$761$		−	13.6238i		−	0.493863i	−0.969033	−	0.246931i	$-0.920578\pi$
$761$		−	13.6238i		−	0.493863i	0.969033	−	0.246931i	$-0.0794222\pi$
$762$	2.12635	+	3.68295i	0.0770297	+	0.133419i
$763$	−4.75478	+	47.8430i	−0.172134	+	1.73203i
$764$	6.97557	−	12.0820i	0.252367	−	0.437113i
$765$	6.95090	+	12.0393i	0.251310	+	0.435282i
$766$	−2.29573	−	1.32544i	−0.0829479	−	0.0478900i
$767$	−27.8315			−1.00494
$768$	1.00000			0.0360844
$769$	−38.9542	−	22.4902i	−1.40472	−	0.811017i	−0.409851	−	0.912153i	$-0.634419\pi$
$769$	−38.9542	−	22.4902i	−1.40472	−	0.811017i	−0.994873	+	0.101135i	$0.967753\pi$
$770$	−8.08323	−	17.8821i	−0.291299	−	0.644425i
$771$	−11.5971			−0.417658
$772$			9.46099i			0.340508i
$773$	−13.0065	+	22.5279i	−0.467812	+	0.810274i	−0.999323	−	0.0367772i	$-0.988291\pi$
$773$	−13.0065	+	22.5279i	−0.467812	+	0.810274i	0.531512	+	0.847051i	$0.321624\pi$
$774$	4.07605	−	2.35331i	0.146511	−	0.0845880i
$775$	−7.96790	+	13.8008i	−0.286215	+	0.495740i
$776$	−6.05678	+	3.49688i	−0.217426	+	0.125531i
$777$	−2.00138	+	20.1380i	−0.0717989	+	0.722447i
$778$			18.1909i			0.652176i
$779$	39.2028	−	18.2112i	1.40459	−	0.652483i
$780$			14.8062i			0.530148i
$781$	37.1354	−	21.4402i	1.32881	−	0.767189i
$782$	−12.8867	−	22.3205i	−0.460828	−	0.798178i
$783$	−3.06925	−	1.77203i	−0.109686	−	0.0633273i
$784$	−4.62471	+	5.25472i	−0.165168	+	0.187669i
$785$	−3.45901	+	5.99118i	−0.123457	+	0.213835i
$786$	−12.4729			−0.444892
$787$	−32.8924			−1.17249			−0.586243	−	0.810135i	$-0.699394\pi$
$787$	−32.8924			−1.17249			−0.586243	+	0.810135i	$0.699394\pi$
$788$	−6.24108	+	10.8099i	−0.222329	+	0.385086i
$789$	−1.85651	+	3.21557i	−0.0660935	+	0.114477i
$790$		−	43.7593i		−	1.55689i
$791$	−33.6785	−	24.1787i	−1.19747	−	0.859697i
$792$	−2.41162	−	1.39235i	−0.0856933	−	0.0494751i
$793$	39.7691	−	22.9607i	1.41224	−	0.815358i
$794$	−2.98020	+	5.16186i	−0.105763	+	0.183188i
$795$	−6.98918	−	12.1056i	−0.247881	−	0.429342i
$796$	−3.61876	+	2.08929i	−0.128264	+	0.0740531i
$797$	44.3267			1.57013			0.785065	−	0.619413i	$-0.212629\pi$
$797$	44.3267			1.57013			0.785065	+	0.619413i	$0.212629\pi$
$798$	−3.80047	−	10.8884i	−0.134535	−	0.385444i
$799$	34.6947			1.22741
$800$	−1.81393	+	1.04728i	−0.0641323	+	0.0370268i
$801$	−2.85315	−	4.94180i	−0.100811	−	0.174610i
$802$	1.59798	−	2.76778i	0.0564266	−	0.0977338i
$803$	7.76226	−	4.48155i	0.273924	−	0.158150i
$804$	−4.96644	−	2.86737i	−0.175153	−	0.101124i
$805$	28.2689	+	20.2950i	0.996348	+	0.715305i
$806$			42.2926i			1.48969i
$807$	11.4915	−	19.9039i	0.404520	−	0.700649i
$808$	−2.38784	+	4.13587i	−0.0840040	+	0.145499i
$809$	41.7084			1.46639			0.733194	−	0.680019i	$-0.238029\pi$
$809$	41.7084			1.46639			0.733194	+	0.680019i	$0.238029\pi$
$810$	−2.66356			−0.0935880
$811$	−15.5498	+	26.9330i	−0.546027	+	0.945746i	0.452515	+	0.891757i	$0.350527\pi$
$811$	−15.5498	+	26.9330i	−0.546027	+	0.945746i	−0.998542	+	0.0539891i	$0.982806\pi$
$812$	0.927319	−	9.33076i	0.0325425	−	0.327445i
$813$	9.44262	+	5.45170i	0.331167	+	0.191199i
$814$	−10.6500	−	18.4464i	−0.373283	−	0.646546i
$815$	−0.611442	+	0.353016i	−0.0214179	+	0.0123656i
$816$			5.21926i			0.182711i
$817$	−18.6061	+	8.64323i	−0.650946	+	0.302388i
$818$		−	23.3557i		−	0.816613i
$819$	−14.6351	−	1.45448i	−0.511393	−	0.0508238i
$820$	22.8751	−	13.2070i	0.798834	−	0.461207i
$821$	−8.50610	+	14.7330i	−0.296865	+	0.514185i	−0.975417	−	0.220367i	$-0.929274\pi$
$821$	−8.50610	+	14.7330i	−0.296865	+	0.514185i	0.678552	+	0.734552i	$0.262608\pi$
$822$	−5.70387	+	3.29313i	−0.198945	+	0.114861i
$823$	−14.3316	+	24.8230i	−0.499568	+	0.865276i	−1.00000		0.000499209i	$-0.999841\pi$
$823$	−14.3316	+	24.8230i	−0.499568	+	0.865276i	0.500432	+	0.865776i	$0.333174\pi$
$824$		−	5.55175i		−	0.193404i
$825$	5.83270			0.203069
$826$	12.0706	−	5.45630i	0.419991	−	0.189849i
$827$	32.3671	+	18.6872i	1.12552	+	0.649816i	0.942803	−	0.333350i	$-0.108179\pi$
$827$	32.3671	+	18.6872i	1.12552	+	0.649816i	0.182712	+	0.983166i	$0.441512\pi$
$828$	4.93815			0.171612
$829$	−6.39915			−0.222252			−0.111126	−	0.993806i	$-0.535446\pi$
$829$	−6.39915			−0.222252			−0.111126	+	0.993806i	$0.535446\pi$
$830$	4.09522	+	2.36438i	0.142147	+	0.0820687i
$831$	−5.25402	−	9.10023i	−0.182260	−	0.315683i
$832$	−2.77941	+	4.81407i	−0.0963586	+	0.166898i
$833$	−27.4257	−	24.1375i	−0.950246	−	0.836316i
$834$	−9.74952	−	16.8867i	−0.337598	−	0.584737i
$835$			24.7332i			0.855928i
$836$	9.93292	+	6.97667i	0.343537	+	0.241293i
$837$	−7.60822			−0.262978
$838$	−8.74779	−	15.1516i	−0.302187	−	0.523404i
$839$	12.7509	+	22.0852i	0.440210	+	0.762465i	0.997705	−	0.0677148i	$-0.0215708\pi$
$839$	12.7509	+	22.0852i	0.440210	+	0.762465i	−0.557495	+	0.830180i	$0.688237\pi$
$840$	−2.90273	−	6.42153i	−0.100154	−	0.221564i
$841$	−8.21979	−	14.2371i	−0.283441	−	0.490934i
$842$	−10.8034	+	18.7120i	−0.372309	+	0.644858i
$843$			27.7353i			0.955254i
$844$		−	0.734388i		−	0.0252787i
$845$	−41.2910	−	23.8394i	−1.42045	−	0.820099i
$846$	−3.32372	+	5.75686i	−0.114272	+	0.197925i
$847$	5.00766	−	6.97516i	0.172065	−	0.239669i
$848$		−	5.24800i		−	0.180217i
$849$	−20.4966	−	11.8337i	−0.703441	−	0.406132i
$850$	−5.46600	−	9.46739i	−0.187482	−	0.324729i
$851$	32.7112	+	18.8858i	1.12132	+	0.647397i
$852$	13.3355	−	7.69926i	0.456867	−	0.263772i
$853$	−16.0605	+	9.27252i	−0.549900	+	0.317485i	−0.749082	−	0.662478i	$-0.769505\pi$
$853$	−16.0605	+	9.27252i	−0.549900	+	0.317485i	0.199181	+	0.979963i	$0.436172\pi$
$854$	−12.7466	+	17.7548i	−0.436181	+	0.607557i
$855$	11.5645	+	1.02872i	0.395498	+	0.0351816i
$856$	19.2313			0.657311
$857$	−0.494441	−	0.856397i	−0.0168898	−	0.0292540i	0.857457	−	0.514556i	$-0.172043\pi$
$857$	−0.494441	−	0.856397i	−0.0168898	−	0.0292540i	−0.874347	+	0.485302i	$0.838710\pi$
$858$	13.4058	−	7.73982i	0.457665	−	0.264233i
$859$	10.1420	+	5.85546i	0.346039	+	0.199786i	0.662939	−	0.748673i	$-0.269309\pi$
$859$	10.1420	+	5.85546i	0.346039	+	0.199786i	−0.316900	+	0.948459i	$0.602642\pi$
$860$	−10.8568	+	6.26818i	−0.370214	+	0.213743i
$861$	10.8072	+	23.9082i	0.368309	+	0.814788i
$862$	26.6017			0.906059
$863$			26.7036i			0.909001i	0.890746	+	0.454500i	$0.150182\pi$
$863$			26.7036i			0.909001i	−0.890746	+	0.454500i	$0.849818\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$	−10.1914	−	5.88399i	−0.346517	−	0.200062i
$866$		−	18.7274i		−	0.636383i
$867$	−10.2407			−0.347791
$868$	−8.29137	−	18.3425i	−0.281428	−	0.622586i
$869$	−39.6203	+	22.8748i	−1.34403	+	0.775974i
$870$	8.17514	+	4.71992i	0.277163	+	0.160020i
$871$	27.6075	−	15.9392i	0.935444	−	0.540079i
$872$	−9.08601	−	15.7374i	−0.307691	−	0.532937i
$873$	6.99377			0.236703
$874$	−21.4402	−	1.90722i	−0.725226	−	0.0645126i
$875$	−16.6325	−	11.9409i	−0.562282	−	0.403678i
$876$	2.78746	−	1.60934i	0.0941797	−	0.0543747i
$877$	−18.3130	+	10.5730i	−0.618387	+	0.357026i	−0.776241	−	0.630437i	$-0.782876\pi$
$877$	−18.3130	+	10.5730i	−0.618387	+	0.357026i	0.157854	+	0.987462i	$0.449543\pi$
$878$	0.201587	+	0.116386i	0.00680323	+	0.00392785i
$879$	14.2152	+	24.6215i	0.479467	+	0.830461i
$880$	6.42351	+	3.70861i	0.216536	+	0.125017i
$881$		−	14.6447i		−	0.493392i	−0.969093	−	0.246696i	$-0.920655\pi$
$881$		−	14.6447i		−	0.493392i	0.969093	−	0.246696i	$-0.0793449\pi$
$882$	6.63247	−	2.23837i	0.223327	−	0.0753698i
$883$	25.9531	−	44.9522i	0.873393	−	1.51276i	0.0149282	−	0.999889i	$-0.495248\pi$
$883$	25.9531	−	44.9522i	0.873393	−	1.51276i	0.858465	−	0.512872i	$-0.171419\pi$
$884$	−25.1259	−	14.5064i	−0.845075	−	0.487904i
$885$			13.3357i			0.448276i
$886$		−	4.55998i		−	0.153195i
$887$	−15.1117	+	26.1742i	−0.507400	+	0.878843i	0.492563	+	0.870277i	$0.336060\pi$
$887$	−15.1117	+	26.1742i	−0.507400	+	0.878843i	−0.999963	+	0.00856594i	$0.997273\pi$
$888$	−3.82447	−	6.62418i	−0.128341	−	0.222293i
$889$	10.2528	−	4.63457i	0.343867	−	0.155438i
$890$	7.59954	+	13.1628i	0.254737	+	0.441218i
$891$	1.39235	+	2.41162i	0.0466455	+	0.0807925i
$892$	−20.8263			−0.697315
$893$	16.6542	−	23.7112i	0.557312	−	0.793464i
$894$			0.771044i			0.0257876i
$895$	23.8673	+	41.3394i	0.797796	+	1.38182i
$896$	0.261654	−	2.63278i	0.00874124	−	0.0879550i
$897$	−13.7251	+	23.7726i	−0.458268	+	0.793744i
$898$	−13.0490	−	22.6015i	−0.435451	−	0.754223i
$899$	23.3515	+	13.4820i	0.778818	+	0.449651i
$900$	2.09455			0.0698184
$901$	27.3907			0.912516
$902$	−23.9155	−	13.8076i	−0.796300	−	0.459744i
$903$	−5.12924	−	11.3471i	−0.170690	−	0.377608i
$904$	15.6701			0.521178
$905$		−	31.4416i		−	1.04516i
$906$	8.19357	−	14.1917i	0.272213	−	0.471487i
$907$	−35.5379	+	20.5178i	−1.18002	+	0.681283i	−0.956018	−	0.293307i	$-0.905244\pi$
$907$	−35.5379	+	20.5178i	−1.18002	+	0.681283i	−0.223998	+	0.974590i	$0.571911\pi$
$908$	1.24513	−	2.15662i	0.0413210	−	0.0715700i
$909$	4.13587	−	2.38784i	0.137178	−	0.0791998i
$910$	38.9816	+	3.87410i	1.29223	+	0.128425i
$911$		−	20.5739i		−	0.681643i	−0.940128	−	0.340821i	$-0.889295\pi$
$911$		−	20.5739i		−	0.681643i	0.940128	−	0.340821i	$-0.110705\pi$
$912$	3.56696	+	2.50535i	0.118114	+	0.0829606i
$913$		−	4.94383i		−	0.163617i
$914$	−2.88000	+	1.66277i	−0.0952619	+	0.0549995i
$915$	−11.0018	−	19.0558i	−0.363710	−	0.629964i
$916$	−21.9153	−	12.6528i	−0.724100	−	0.418059i
$917$	−3.26357	+	32.8383i	−0.107773	+	1.08442i
$918$	2.60963	−	4.52001i	0.0861306	−	0.149183i
$919$	−6.23396			−0.205639			−0.102820	−	0.994700i	$-0.532786\pi$
$919$	−6.23396			−0.205639			−0.102820	+	0.994700i	$0.532786\pi$
$920$	−13.1530			−0.433643
$921$	−8.96734	+	15.5319i	−0.295484	+	0.511793i
$922$	4.03475	−	6.98839i	0.132877	−	0.230150i
$923$			85.5975i			2.81748i
$924$	−4.29677	+	5.98497i	−0.141353	+	0.196891i
$925$	13.8747	+	8.01055i	0.456197	+	0.263385i
$926$	−5.59585	+	3.23077i	−0.183891	+	0.106170i
$927$	−2.77587	+	4.80795i	−0.0911716	+	0.157914i
$928$	1.77203	+	3.06925i	0.0581699	+	0.100753i
$929$	−12.5982	+	7.27357i	−0.413333	+	0.238638i	−0.692221	−	0.721686i	$-0.743368\pi$
$929$	−12.5982	+	7.27357i	−0.413333	+	0.238638i	0.278888	+	0.960324i	$0.410034\pi$
$930$	20.2649			0.664514
$931$	−29.6611	+	7.15684i	−0.972103	+	0.234556i
$932$	−9.03910			−0.296086
$933$	8.40204	−	4.85092i	0.275070	−	0.158812i
$934$	−12.3373	−	21.3688i	−0.403688	−	0.699209i
$935$	−19.3562	+	33.5259i	−0.633016	+	1.09642i
$936$	4.81407	−	2.77941i	0.157353	−	0.0908477i
$937$	45.9679	+	26.5396i	1.50171	+	0.867011i	0.999998	+	0.00197416i	$0.000628394\pi$
$937$	45.9679	+	26.5396i	1.50171	+	0.867011i	0.501709	+	0.865037i	$0.332705\pi$
$938$	−8.84865	+	12.3253i	−0.288919	+	0.402435i
$939$		−	23.4821i		−	0.766309i
$940$	8.85294	−	15.3337i	0.288751	−	0.500131i
$941$	−9.38535	+	16.2559i	−0.305954	+	0.529927i	−0.977473	−	0.211060i	$-0.932309\pi$
$941$	−9.38535	+	16.2559i	−0.305954	+	0.529927i	0.671520	+	0.740987i	$0.265642\pi$
$942$	2.59728			0.0846241
$943$	48.9705			1.59470
$944$	−2.50337	+	4.33596i	−0.0814776	+	0.141123i
$945$	−0.696930	+	7.01257i	−0.0226711	+	0.228119i
$946$	11.3506	+	6.55327i	0.369040	+	0.213065i
$947$	11.0260	+	19.0976i	0.358296	+	0.620588i	0.987676	−	0.156510i	$-0.0500244\pi$
$947$	11.0260	+	19.0976i	0.358296	+	0.620588i	−0.629380	+	0.777098i	$0.716691\pi$
$948$	−14.2278	+	8.21444i	−0.462098	+	0.266793i
$949$			17.8921i			0.580801i
$950$	−9.09402	−	0.808960i	−0.295049	−	0.0262461i
$951$			7.57688i			0.245697i
$952$	13.7412	+	1.36564i	0.445354	+	0.0442606i
$953$	−10.5130	+	6.06969i	−0.340550	+	0.196617i	−0.660515	−	0.750813i	$-0.729662\pi$
$953$	−10.5130	+	6.06969i	−0.340550	+	0.196617i	0.319965	+	0.947429i	$0.396329\pi$
$954$	−2.62400	+	4.54490i	−0.0849552	+	0.147147i
$955$	32.1812	−	18.5798i	1.04136	−	0.601229i
$956$	−3.54730	+	6.14410i	−0.114728	+	0.198714i
$957$		−	9.86918i		−	0.319025i
$958$	−3.37824			−0.109146
$959$	7.17766	+	15.8787i	0.231779	+	0.512750i
$960$	2.30671	+	1.33178i	0.0744488	+	0.0429830i
$961$	26.8850			0.867257
$962$	42.5191			1.37087
$963$	−16.6548	−	9.61563i	−0.536692	−	0.309859i
$964$	4.47952	+	7.75875i	0.144276	+	0.249893i
$965$	−12.6000	+	21.8238i	−0.405607	+	0.702532i
$966$	1.29208	−	13.0011i	0.0415721	−	0.418302i
$967$	18.6244	+	32.2583i	0.598919	+	1.03736i	0.992981	+	0.118274i	$0.0377362\pi$
$967$	18.6244	+	32.2583i	0.598919	+	1.03736i	−0.394062	+	0.919084i	$0.628930\pi$
$968$			3.24542i			0.104312i
$969$	−13.0761	+	18.6169i	−0.420065	+	0.598060i
$970$	−18.6283			−0.598119
$971$	16.7677	+	29.0425i	0.538101	+	0.932019i	0.999006	+	0.0445693i	$0.0141916\pi$
$971$	16.7677	+	29.0425i	0.538101	+	0.932019i	−0.460905	+	0.887449i	$0.652475\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−47.0099	+	21.2499i	−1.50707	+	0.681240i
$974$	−5.40907	−	9.36879i	−0.173318	−	0.300195i
$975$	−5.82161	+	10.0833i	−0.186441	+	0.322925i
$976$		−	8.26101i		−	0.264428i
$977$		−	31.3862i		−	1.00413i	−0.864829	−	0.502066i	$-0.832573\pi$
$977$		−	31.3862i		−	1.00413i	0.864829	−	0.502066i	$-0.167427\pi$
$978$	0.229558	+	0.132535i	0.00734046	+	0.00423802i
$979$	7.94518	−	13.7615i	0.253929	−	0.439818i
$980$	−17.6660	+	5.96203i	−0.564319	+	0.190450i
$981$			18.1720i			0.580188i
$982$	8.27378	+	4.77687i	0.264027	+	0.152436i
$983$	−22.6191	−	39.1774i	−0.721436	−	1.24956i	−0.960424	−	0.278542i	$-0.910149\pi$
$983$	−22.6191	−	39.1774i	−0.721436	−	1.24956i	0.238988	−	0.971023i	$-0.423184\pi$
$984$	−8.58818	−	4.95839i	−0.273781	−	0.158068i
$985$	−28.7927	+	16.6235i	−0.917413	+	0.529669i
$986$	−16.0192	+	9.24870i	−0.510156	+	0.294539i
$987$	14.2869	+	10.2569i	0.454757	+	0.326482i
$988$	−21.9750	+	10.2082i	−0.699117	+	0.324766i
$989$	−23.2420			−0.739052
$990$	−3.70861	−	6.42351i	−0.117867	−	0.204152i
$991$	−15.4037	+	8.89335i	−0.489316	+	0.282507i	−0.724291	−	0.689495i	$-0.757833\pi$
$991$	−15.4037	+	8.89335i	−0.489316	+	0.282507i	0.234975	+	0.972001i	$0.424499\pi$
$992$	6.58891	+	3.80411i	0.209198	+	0.120781i
$993$	−8.95114	+	5.16794i	−0.284056	+	0.164000i
$994$	−16.7812	−	37.1240i	−0.532267	−	1.17750i
$995$	−11.1299			−0.352842
$996$		−	1.77535i		−	0.0562541i
$997$	1.86547	+	1.07703i	0.0590800	+	0.0341099i	0.529249	−	0.848467i	$-0.322474\pi$
$997$	1.86547	+	1.07703i	0.0590800	+	0.0341099i	−0.470169	+	0.882576i	$0.655807\pi$
$998$	−32.5210	−	18.7760i	−1.02943	−	0.594344i
$999$			7.64895i			0.242002i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bj.a.601.11	yes	24
7.6	odd	2		798.2.bj.b.601.8	yes	24
19.8	odd	6		798.2.bj.b.559.8	yes	24
133.27	even	6	inner	798.2.bj.a.559.11	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bj.a.559.11	✓	24	133.27	even	6	inner
798.2.bj.a.601.11	yes	24	1.1	even	1	trivial
798.2.bj.b.559.8	yes	24	19.8	odd	6
798.2.bj.b.601.8	yes	24	7.6	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30671 - 1.33178i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54299 + 2.14923i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.30671 - 1.33178i) q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.54299 + 2.14923i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.33178 - 2.30671i) q^{10} -2.78470 q^{11} -1.00000 q^{12} +(2.77941 - 4.81407i) q^{13} +(-0.261654 + 2.63278i) q^{14} +(-2.30671 - 1.33178i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(4.52001 - 2.60963i) q^{17} +1.00000i q^{18} +(0.386221 - 4.34175i) q^{19} -2.66356i q^{20} +(2.63278 + 0.261654i) q^{21} +(-2.41162 + 1.39235i) q^{22} +(2.46907 - 4.27656i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.04728 - 1.81393i) q^{25} -5.55881i q^{26} +1.00000 q^{27} +(1.08979 + 2.41088i) q^{28} +(-3.06925 - 1.77203i) q^{29} -2.66356 q^{30} -7.60822 q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.39235 + 2.41162i) q^{33} +(2.60963 - 4.52001i) q^{34} +(-0.696930 + 7.01257i) q^{35} +(0.500000 + 0.866025i) q^{36} +7.64895i q^{37} +(-1.83640 - 3.95318i) q^{38} -5.55881 q^{39} +(-1.33178 - 2.30671i) q^{40} +(4.95839 + 8.58818i) q^{41} +(2.41088 - 1.08979i) q^{42} +(-2.35331 - 4.07605i) q^{43} +(-1.39235 + 2.41162i) q^{44} +2.66356i q^{45} -4.93815i q^{46} +(5.75686 + 3.32372i) q^{47} +(-0.500000 + 0.866025i) q^{48} +(-2.23837 - 6.63247i) q^{49} -2.09455i q^{50} +(-4.52001 - 2.60963i) q^{51} +(-2.77941 - 4.81407i) q^{52} +(4.54490 + 2.62400i) q^{53} +(0.866025 - 0.500000i) q^{54} +(-6.42351 + 3.70861i) q^{55} +(2.14923 + 1.54299i) q^{56} +(-3.95318 + 1.83640i) q^{57} -3.54407 q^{58} +(-2.50337 - 4.33596i) q^{59} +(-2.30671 + 1.33178i) q^{60} +(7.15424 + 4.13050i) q^{61} +(-6.58891 + 3.80411i) q^{62} +(-1.08979 - 2.41088i) q^{63} -1.00000 q^{64} -14.8062i q^{65} +(2.41162 + 1.39235i) q^{66} +(4.96644 + 2.86737i) q^{67} -5.21926i q^{68} -4.93815 q^{69} +(2.90273 + 6.42153i) q^{70} +(-13.3355 + 7.69926i) q^{71} +(0.866025 + 0.500000i) q^{72} +(-2.78746 + 1.60934i) q^{73} +(3.82447 + 6.62418i) q^{74} -2.09455 q^{75} +(-3.56696 - 2.50535i) q^{76} +(4.29677 - 5.98497i) q^{77} +(-4.81407 + 2.77941i) q^{78} +(14.2278 - 8.21444i) q^{79} +(-2.30671 - 1.33178i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(8.58818 + 4.95839i) q^{82} +1.77535i q^{83} +(1.54299 - 2.14923i) q^{84} +(6.95090 - 12.0393i) q^{85} +(-4.07605 - 2.35331i) q^{86} +3.54407i q^{87} +2.78470i q^{88} +(-2.85315 + 4.94180i) q^{89} +(1.33178 + 2.30671i) q^{90} +(6.05795 + 13.4016i) q^{91} +(-2.46907 - 4.27656i) q^{92} +(3.80411 + 6.58891i) q^{93} +6.64745 q^{94} +(-4.89136 - 10.5295i) q^{95} +1.00000i q^{96} +(-3.49688 - 6.05678i) q^{97} +(-5.25472 - 4.62471i) q^{98} +(1.39235 - 2.41162i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9}+O(q^{10}) \) 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9	\( 24 q - 12 q^{3} + 12 q^{4} + 6 q^{7} - 12 q^{9} + 2 q^{10} - 24 q^{12} + 10 q^{13} + 4 q^{14} - 12 q^{16} - 10 q^{19} + 6 q^{21} + 6 q^{22} + 6 q^{25} + 24 q^{27} + 12 q^{28} - 4 q^{30} - 36 q^{31} + 2 q^{34} - 16 q^{35} + 12 q^{36} + 12 q^{38} - 20 q^{39} - 2 q^{40} - 20 q^{41} - 8 q^{42} - 6 q^{43} - 12 q^{48} + 2 q^{49} - 10 q^{52} + 12 q^{53} - 30 q^{55} - 4 q^{56} + 2 q^{57} - 8 q^{58} + 8 q^{59} - 42 q^{61} - 12 q^{62} - 12 q^{63} - 24 q^{64} - 6 q^{66} + 6 q^{67} + 6 q^{70} - 24 q^{71} + 66 q^{73} - 12 q^{75} - 8 q^{76} + 16 q^{77} - 24 q^{78} + 30 q^{79} - 12 q^{81} - 6 q^{82} - 6 q^{84} - 2 q^{85} + 12 q^{86} - 8 q^{89} + 2 q^{90} - 66 q^{91} + 18 q^{93} + 20 q^{95} + 36 q^{97} - 32 q^{98}+O(q^{100}) \) 24 * q - 12 * q^3 + 12 * q^4 + 6 * q^7 - 12 * q^9 + 2 * q^10 - 24 * q^12 + 10 * q^13 + 4 * q^14 - 12 * q^16 - 10 * q^19 + 6 * q^21 + 6 * q^22 + 6 * q^25 + 24 * q^27 + 12 * q^28 - 4 * q^30 - 36 * q^31 + 2 * q^34 - 16 * q^35 + 12 * q^36 + 12 * q^38 - 20 * q^39 - 2 * q^40 - 20 * q^41 - 8 * q^42 - 6 * q^43 - 12 * q^48 + 2 * q^49 - 10 * q^52 + 12 * q^53 - 30 * q^55 - 4 * q^56 + 2 * q^57 - 8 * q^58 + 8 * q^59 - 42 * q^61 - 12 * q^62 - 12 * q^63 - 24 * q^64 - 6 * q^66 + 6 * q^67 + 6 * q^70 - 24 * q^71 + 66 * q^73 - 12 * q^75 - 8 * q^76 + 16 * q^77 - 24 * q^78 + 30 * q^79 - 12 * q^81 - 6 * q^82 - 6 * q^84 - 2 * q^85 + 12 * q^86 - 8 * q^89 + 2 * q^90 - 66 * q^91 + 18 * q^93 + 20 * q^95 + 36 * q^97 - 32 * q^98

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