LMFDB - Embedded newform 315.2.bl.j.41.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(41,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("315.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bl (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:	$2.51528766367$
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			41.9
Character	$\chi$	$=$	315.41
Dual form			315.2.bl.j.146.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58089 - 0.912729i) q^{2} +(-0.791176 + 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.155560 + 3.15796i) q^{6} +(0.317742 + 2.62660i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} +O(q^{10})$	\(q+(1.58089 - 0.912729i) q^{2} +(-0.791176 + 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.155560 + 3.15796i) q^{6} +(0.317742 + 2.62660i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} +1.82546i q^{10} +(-0.549675 + 0.317355i) q^{11} +(1.25073 + 1.93925i) q^{12} +(2.73324 + 1.57804i) q^{13} +(2.89969 + 3.86236i) q^{14} +(-0.938777 - 1.45557i) q^{15} +(2.44479 + 4.23450i) q^{16} +2.83015 q^{17} +(-4.98883 - 2.25881i) q^{18} -4.89715i q^{19} +(0.666147 + 1.15380i) q^{20} +(-4.29844 - 1.58853i) q^{21} +(-0.579318 + 1.00341i) q^{22} +(-3.83011 - 2.21132i) q^{23} +(-1.87802 - 0.964339i) q^{24} +(-0.500000 - 0.866025i) q^{25} +5.76127 q^{26} +(5.13961 - 0.764479i) q^{27} +(3.24224 + 1.38309i) q^{28} +(0.0996181 - 0.0575146i) q^{29} +(-2.81265 - 1.44426i) q^{30} +(-0.272686 - 0.157435i) q^{31} +(5.61876 + 3.24399i) q^{32} +(-0.0540882 - 1.09802i) q^{33} +(4.47417 - 2.58316i) q^{34} +(-2.43358 - 1.03813i) q^{35} +(-3.97753 + 0.392818i) q^{36} +10.7800 q^{37} +(-4.46977 - 7.74186i) q^{38} +(-4.59390 + 2.96285i) q^{39} +(-1.05557 - 0.609434i) q^{40} +(1.11318 - 1.92808i) q^{41} +(-8.24527 + 1.41201i) q^{42} +(-0.870817 - 1.50830i) q^{43} +0.845620i q^{44} +(2.98548 - 0.294843i) q^{45} -8.07333 q^{46} +(-3.95084 - 6.84306i) q^{47} +(-8.45874 + 0.416676i) q^{48} +(-6.79808 + 1.66916i) q^{49} +(-1.58089 - 0.912729i) q^{50} +(-2.23915 + 4.36068i) q^{51} +(3.64148 - 2.10241i) q^{52} -8.63571i q^{53} +(7.42741 - 5.89963i) q^{54} -0.634710i q^{55} +(-3.20148 + 0.387285i) q^{56} +(7.54548 + 3.87451i) q^{57} +(0.104990 - 0.181849i) q^{58} +(-7.65048 + 13.2510i) q^{59} +(-2.30481 + 0.113534i) q^{60} +(8.94576 - 5.16484i) q^{61} -0.574783 q^{62} +(5.84842 - 5.36619i) q^{63} +2.06438 q^{64} +(-2.73324 + 1.57804i) q^{65} +(-1.08770 - 1.68648i) q^{66} +(-2.40584 + 4.16704i) q^{67} +(1.88530 - 3.26543i) q^{68} +(6.43747 - 4.15186i) q^{69} +(-4.79475 + 0.580024i) q^{70} -12.9744i q^{71} +(2.97169 - 2.13068i) q^{72} +6.45973i q^{73} +(17.0421 - 9.83926i) q^{74} +(1.72995 - 0.0852172i) q^{75} +(-5.65033 - 3.26222i) q^{76} +(-1.00822 - 1.34294i) q^{77} +(-4.55818 + 8.87692i) q^{78} +(6.51973 + 11.2925i) q^{79} -4.88958 q^{80} +(-2.88843 + 8.52391i) q^{81} -4.06412i q^{82} +(-2.25090 - 3.89867i) q^{83} +(-4.69624 + 3.90135i) q^{84} +(-1.41508 + 2.45099i) q^{85} +(-2.75334 - 1.58964i) q^{86} +(0.00980246 + 0.198995i) q^{87} +(-0.386814 - 0.669981i) q^{88} +11.1029 q^{89} +(4.45060 - 3.19105i) q^{90} +(-3.27641 + 7.68054i) q^{91} +(-5.10284 + 2.94612i) q^{92} +(0.458318 - 0.295593i) q^{93} +(-12.4917 - 7.21210i) q^{94} +(4.24105 + 2.44857i) q^{95} +(-9.44375 + 6.09077i) q^{96} +(-0.266943 + 0.154120i) q^{97} +(-9.22354 + 8.84357i) q^{98} +(1.73461 + 0.785387i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	$ 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) $ 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.58089	−	0.912729i	1.11786	−	0.645397i	0.177006	−	0.984210i	$-0.443359\pi$
$2$	1.58089	−	0.912729i	1.11786	−	0.645397i	0.940854	+	0.338813i	$0.110025\pi$
$3$	−0.791176	+	1.54079i	−0.456786	+	0.889577i
$3$	−0.791176	+	1.54079i	−0.456786	+	0.889577i
$4$	0.666147	−	1.15380i	0.333074	−	0.576901i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	0.155560	+	3.15796i	0.0635072	+	1.28923i
$7$	0.317742	+	2.62660i	0.120095	+	0.992762i
$7$	0.317742	+	2.62660i	0.120095	+	0.992762i
$8$			1.21887i			0.430935i
$9$	−1.74808	−	2.43808i	−0.582693	−	0.812692i
$10$			1.82546i			0.577260i
$11$	−0.549675	+	0.317355i	−0.165733	+	0.0956861i	−0.580572	−	0.814209i	$-0.697171\pi$
$11$	−0.549675	+	0.317355i	−0.165733	+	0.0956861i	0.414839	+	0.909895i	$0.363838\pi$
$12$	1.25073	+	1.93925i	0.361054	+	0.559815i
$13$	2.73324	+	1.57804i	0.758064	+	0.437668i	0.828600	−	0.559841i	$-0.189138\pi$
$13$	2.73324	+	1.57804i	0.758064	+	0.437668i	−0.0705364	+	0.997509i	$0.522471\pi$
$14$	2.89969	+	3.86236i	0.774975	+	1.03226i
$15$	−0.938777	−	1.45557i	−0.242391	−	0.375828i
$16$	2.44479	+	4.23450i	0.611198	+	1.05863i
$17$	2.83015			0.686413			0.343207	−	0.939260i	$-0.388487\pi$
$17$	2.83015			0.686413			0.343207	+	0.939260i	$0.388487\pi$
$18$	−4.98883	−	2.25881i	−1.17588	−	0.532408i
$19$		−	4.89715i		−	1.12348i	−0.827313	−	0.561741i	$-0.810132\pi$
$19$		−	4.89715i		−	1.12348i	0.827313	−	0.561741i	$-0.189868\pi$
$20$	0.666147	+	1.15380i	0.148955	+	0.257998i
$21$	−4.29844	−	1.58853i	−0.937996	−	0.346646i
$22$	−0.579318	+	1.00341i	−0.123511	+	0.213927i
$23$	−3.83011	−	2.21132i	−0.798633	−	0.461091i	0.0443596	−	0.999016i	$-0.485875\pi$
$23$	−3.83011	−	2.21132i	−0.798633	−	0.461091i	−0.842993	+	0.537924i	$0.819209\pi$
$24$	−1.87802	−	0.964339i	−0.383350	−	0.196845i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	5.76127			1.12988
$27$	5.13961	−	0.764479i	0.989118	−	0.147124i
$28$	3.24224	+	1.38309i	0.612726	+	0.261380i
$29$	0.0996181	−	0.0575146i	0.0184986	−	0.0106802i	−0.490722	−	0.871316i	$-0.663267\pi$
$29$	0.0996181	−	0.0575146i	0.0184986	−	0.0106802i	0.509221	+	0.860636i	$0.329934\pi$
$30$	−2.81265	−	1.44426i	−0.513517	−	0.263684i
$31$	−0.272686	−	0.157435i	−0.0489759	−	0.0282762i	0.475312	−	0.879817i	$-0.342335\pi$
$31$	−0.272686	−	0.157435i	−0.0489759	−	0.0282762i	−0.524288	+	0.851541i	$0.675668\pi$
$32$	5.61876	+	3.24399i	0.993266	+	0.573462i
$33$	−0.0540882	−	1.09802i	−0.00941554	−	0.191140i
$34$	4.47417	−	2.58316i	0.767314	−	0.443009i
$35$	−2.43358	−	1.03813i	−0.411349	−	0.175476i
$36$	−3.97753	+	0.392818i	−0.662922	+	0.0654697i
$37$	10.7800			1.77223			0.886115	−	0.463466i	$-0.153395\pi$
$37$	10.7800			1.77223			0.886115	+	0.463466i	$0.153395\pi$
$38$	−4.46977	−	7.74186i	−0.725092	−	1.25590i
$39$	−4.59390	+	2.96285i	−0.735612	+	0.474435i
$40$	−1.05557	−	0.609434i	−0.166900	−	0.0963599i
$41$	1.11318	−	1.92808i	0.173849	−	0.301115i	−0.765913	−	0.642944i	$-0.777713\pi$
$41$	1.11318	−	1.92808i	0.173849	−	0.301115i	0.939762	+	0.341828i	$0.111046\pi$
$42$	−8.24527	+	1.41201i	−1.27227	+	0.217878i
$43$	−0.870817	−	1.50830i	−0.132798	−	0.230013i	0.791956	−	0.610578i	$-0.209063\pi$
$43$	−0.870817	−	1.50830i	−0.132798	−	0.230013i	−0.924754	+	0.380565i	$0.875730\pi$
$44$			0.845620i			0.127482i
$45$	2.98548	−	0.294843i	0.445048	−	0.0439527i
$46$	−8.07333			−1.19035
$47$	−3.95084	−	6.84306i	−0.576290	−	0.998163i	−0.995900	−	0.0904591i	$-0.971167\pi$
$47$	−3.95084	−	6.84306i	−0.576290	−	0.998163i	0.419610	−	0.907704i	$-0.362167\pi$
$48$	−8.45874	+	0.416676i	−1.22091	+	0.0601420i
$49$	−6.79808	+	1.66916i	−0.971154	+	0.238452i
$50$	−1.58089	−	0.912729i	−0.223572	−	0.129079i
$51$	−2.23915	+	4.36068i	−0.313544	+	0.610617i
$52$	3.64148	−	2.10241i	0.504982	−	0.291552i
$53$		−	8.63571i		−	1.18621i	−0.805127	−	0.593103i	$-0.797903\pi$
$53$		−	8.63571i		−	1.18621i	0.805127	−	0.593103i	$-0.202097\pi$
$54$	7.42741	−	5.89963i	1.01074	−	0.802838i
$55$		−	0.634710i		−	0.0855842i
$56$	−3.20148	+	0.387285i	−0.427816	+	0.0517531i
$57$	7.54548	+	3.87451i	0.999424	+	0.513191i
$58$	0.104990	−	0.181849i	0.0137859	−	0.0238779i
$59$	−7.65048	+	13.2510i	−0.996008	+	1.72514i	−0.420699	+	0.907200i	$0.638215\pi$
$59$	−7.65048	+	13.2510i	−0.996008	+	1.72514i	−0.575309	+	0.817936i	$0.695118\pi$
$60$	−2.30481	+	0.113534i	−0.297549	+	0.0146572i
$61$	8.94576	−	5.16484i	1.14539	−	0.661290i	0.197628	−	0.980277i	$-0.436676\pi$
$61$	8.94576	−	5.16484i	1.14539	−	0.661290i	0.947759	+	0.318987i	$0.103343\pi$
$62$	−0.574783			−0.0729975
$63$	5.84842	−	5.36619i	0.736832	−	0.676076i
$64$	2.06438			0.258048
$65$	−2.73324	+	1.57804i	−0.339016	+	0.195731i
$66$	−1.08770	−	1.68648i	−0.133887	−	0.207591i
$67$	−2.40584	+	4.16704i	−0.293920	+	0.509084i	−0.974733	−	0.223373i	$-0.928293\pi$
$67$	−2.40584	+	4.16704i	−0.293920	+	0.509084i	0.680813	+	0.732457i	$0.261627\pi$
$68$	1.88530	−	3.26543i	0.228626	−	0.395992i
$69$	6.43747	−	4.15186i	0.774981	−	0.499826i
$70$	−4.79475	+	0.580024i	−0.573082	+	0.0693261i
$71$		−	12.9744i		−	1.53978i	−0.638175	−	0.769892i	$-0.720310\pi$
$71$		−	12.9744i		−	1.53978i	0.638175	−	0.769892i	$-0.279690\pi$
$72$	2.97169	−	2.13068i	0.350217	−	0.251103i
$73$			6.45973i			0.756054i	0.925794	+	0.378027i	$0.123397\pi$
$73$			6.45973i			0.756054i	−0.925794	+	0.378027i	$0.876603\pi$
$74$	17.0421	−	9.83926i	1.98110	−	1.14379i
$75$	1.72995	−	0.0852172i	0.199758	−	0.00984003i
$76$	−5.65033	−	3.26222i	−0.648138	−	0.374202i
$77$	−1.00822	−	1.34294i	−0.114897	−	0.153042i
$78$	−4.55818	+	8.87692i	−0.516113	+	1.00511i
$79$	6.51973	+	11.2925i	0.733527	+	1.27051i	0.955366	+	0.295423i	$0.0954606\pi$
$79$	6.51973	+	11.2925i	0.733527	+	1.27051i	−0.221839	+	0.975083i	$0.571206\pi$
$80$	−4.88958			−0.546672
$81$	−2.88843	+	8.52391i	−0.320937	+	0.947101i
$82$		−	4.06412i		−	0.448807i
$83$	−2.25090	−	3.89867i	−0.247068	−	0.427935i	0.715643	−	0.698466i	$-0.246134\pi$
$83$	−2.25090	−	3.89867i	−0.247068	−	0.427935i	−0.962711	+	0.270532i	$0.912801\pi$
$84$	−4.69624	+	3.90135i	−0.512402	+	0.425672i
$85$	−1.41508	+	2.45099i	−0.153487	+	0.265847i
$86$	−2.75334	−	1.58964i	−0.296900	−	0.171415i
$87$	0.00980246	+	0.198995i	0.00105093	+	0.0213345i
$88$	−0.386814	−	0.669981i	−0.0412345	−	0.0714202i
$89$	11.1029			1.17691			0.588454	−	0.808531i	$-0.299737\pi$
$89$	11.1029			1.17691			0.588454	+	0.808531i	$0.299737\pi$
$90$	4.45060	−	3.19105i	0.469135	−	0.336366i
$91$	−3.27641	+	7.68054i	−0.343461	+	0.805139i
$92$	−5.10284	+	2.94612i	−0.532008	+	0.307155i
$93$	0.458318	−	0.295593i	0.0475254	−	0.0306516i
$94$	−12.4917	−	7.21210i	−1.28842	−	0.743871i
$95$	4.24105	+	2.44857i	0.435123	+	0.251218i
$96$	−9.44375	+	6.09077i	−0.963848	+	0.621637i
$97$	−0.266943	+	0.154120i	−0.0271040	+	0.0156485i	−0.513491	−	0.858095i	$-0.671648\pi$
$97$	−0.266943	+	0.154120i	−0.0271040	+	0.0156485i	0.486387	+	0.873744i	$0.338315\pi$
$98$	−9.22354	+	8.84357i	−0.931718	+	0.893335i
$99$	1.73461	+	0.785387i	0.174335	+	0.0789344i
$100$	−1.33229			−0.133229
$101$	−0.986427	−	1.70854i	−0.0981531	−	0.170006i	0.812767	−	0.582589i	$-0.197960\pi$
$101$	−0.986427	−	1.70854i	−0.0981531	−	0.170006i	−0.910920	+	0.412583i	$0.864627\pi$
$102$	0.440260	+	8.93750i	0.0435922	+	0.884945i
$103$	13.9294	+	8.04212i	1.37250	+	0.792413i	0.991242	−	0.132056i	$-0.0421577\pi$
$103$	13.9294	+	8.04212i	1.37250	+	0.792413i	0.381258	+	0.924469i	$0.375491\pi$
$104$	−1.92342	+	3.33145i	−0.188606	+	0.326676i
$105$	3.52493	−	2.92829i	0.343998	−	0.285772i
$106$	−7.88206	−	13.6521i	−0.765573	−	1.32601i
$107$		−	10.0764i		−	0.974121i	−0.873368	−	0.487061i	$-0.838069\pi$
$107$		−	10.0764i		−	0.974121i	0.873368	−	0.487061i	$-0.161931\pi$
$108$	2.54168	−	6.43934i	0.244573	−	0.619626i
$109$	−14.2509			−1.36499			−0.682496	−	0.730889i	$-0.739106\pi$
$109$	−14.2509			−1.36499			−0.682496	+	0.730889i	$0.739106\pi$
$110$	−0.579318	−	1.00341i	−0.0552358	−	0.0956712i
$111$	−8.52892	+	16.6098i	−0.809529	+	1.57653i
$112$	−10.3455	+	7.76697i	−0.977561	+	0.733910i
$113$	0.175863	+	0.101534i	0.0165438	+	0.00955155i	0.508249	−	0.861210i	$-0.330293\pi$
$113$	0.175863	+	0.101534i	0.0165438	+	0.00955155i	−0.491705	+	0.870762i	$0.663626\pi$
$114$	15.4650	−	0.761802i	1.44843	−	0.0713493i
$115$	3.83011	−	2.21132i	0.357160	−	0.206206i
$116$		−	0.153253i		−	0.0142292i
$117$	−0.930547	−	9.42237i	−0.0860291	−	0.871099i
$118$			27.9313i			2.57128i
$119$	0.899258	+	7.43369i	0.0824348	+	0.681445i
$120$	1.77415	−	1.14424i	0.161957	−	0.104455i
$121$	−5.29857	+	9.17740i	−0.481688	+	0.834309i
$122$	9.42819	−	16.3301i	0.853588	−	1.47846i
$123$	2.09005	+	3.24063i	0.188453	+	0.292197i
$124$	−0.363298	+	0.209750i	−0.0326251	+	0.0188361i
$125$	1.00000			0.0894427
$126$	4.34785	−	13.8214i	0.387337	−	1.23131i
$127$	4.60267			0.408421			0.204211	−	0.978927i	$-0.434537\pi$
$127$	4.60267			0.408421			0.204211	+	0.978927i	$0.434537\pi$
$128$	−7.97396	+	4.60377i	−0.704805	+	0.406919i
$129$	3.01295	−	0.148417i	0.265275	−	0.0130674i
$130$	−2.88064	+	4.98941i	−0.252649	+	0.437600i
$131$	−0.755338	+	1.30828i	−0.0659942	+	0.114305i	−0.897135	−	0.441757i	$-0.854355\pi$
$131$	−0.755338	+	1.30828i	−0.0659942	+	0.114305i	0.831140	+	0.556063i	$0.187689\pi$
$132$	−1.30293	−	0.669035i	−0.113405	−	0.0582320i
$133$	12.8629	−	1.55603i	1.11535	−	0.134925i
$134$			8.78351i			0.758780i
$135$	−1.90775	+	4.83327i	−0.164193	+	0.415982i
$136$			3.44958i			0.295799i
$137$	10.9225	−	6.30611i	0.933172	−	0.538767i	0.0453589	−	0.998971i	$-0.485557\pi$
$137$	10.9225	−	6.30611i	0.933172	−	0.538767i	0.887814	+	0.460203i	$0.152224\pi$
$138$	6.38742	−	12.4393i	0.543734	−	1.05890i
$139$	−4.86731	−	2.81014i	−0.412840	−	0.238353i	0.279169	−	0.960242i	$-0.409941\pi$
$139$	−4.86731	−	2.81014i	−0.412840	−	0.238353i	−0.692009	+	0.721889i	$0.743274\pi$
$140$	−2.81891	+	2.11631i	−0.238242	+	0.178861i
$141$	13.6696	−	0.673360i	1.15118	−	0.0567071i
$142$	−11.8421	−	20.5112i	−0.993771	−	1.72126i
$143$	−2.00319			−0.167515
$144$	6.05035	−	13.3628i	0.504196	−	1.11357i
$145$			0.115029i			0.00955265i
$146$	5.89598	+	10.2121i	0.487955	+	0.845163i
$147$	2.80665	−	11.7950i	0.231488	−	0.972838i
$148$	7.18110	−	12.4380i	0.590283	−	1.02240i
$149$	−10.8483	−	6.26327i	−0.888727	−	0.513107i	−0.0152013	−	0.999884i	$-0.504839\pi$
$149$	−10.8483	−	6.26327i	−0.888727	−	0.513107i	−0.873526	+	0.486778i	$0.838172\pi$
$150$	2.65709	−	1.71370i	0.216950	−	0.139923i
$151$	−4.44709	−	7.70259i	−0.361899	−	0.626828i	0.626374	−	0.779523i	$-0.284538\pi$
$151$	−4.44709	−	7.70259i	−0.361899	−	0.626828i	−0.988273	+	0.152695i	$0.951205\pi$
$152$	5.96897			0.484148
$153$	−4.94734	−	6.90013i	−0.399968	−	0.557843i
$154$	−2.81963	−	1.20281i	−0.227212	−	0.0969254i
$155$	0.272686	−	0.157435i	0.0219027	−	0.0126455i
$156$	0.358323	+	7.27414i	0.0286888	+	0.582397i
$157$	−1.47404	−	0.851038i	−0.117641	−	0.0679202i	0.440025	−	0.897986i	$-0.354970\pi$
$157$	−1.47404	−	0.851038i	−0.117641	−	0.0679202i	−0.557666	+	0.830065i	$0.688303\pi$
$158$	20.6140	+	11.9015i	1.63996	+	0.946832i
$159$	13.3058	+	6.83237i	1.05522	+	0.541842i
$160$	−5.61876	+	3.24399i	−0.444202	+	0.256460i
$161$	4.59126	−	10.7628i	0.361842	−	0.848228i
$162$	3.21371	+	16.1117i	0.252493	+	1.26586i
$163$	18.8951			1.47998			0.739988	−	0.672620i	$-0.234831\pi$
$163$	18.8951			1.47998			0.739988	+	0.672620i	$0.234831\pi$
$164$	−1.48308	−	2.56877i	−0.115809	−	0.200587i
$165$	0.977956	+	0.502167i	0.0761337	+	0.0390937i
$166$	−7.11686	−	4.10892i	−0.552375	−	0.318914i
$167$	−6.20475	+	10.7469i	−0.480138	+	0.831624i	−0.999740	−	0.0227845i	$-0.992747\pi$
$167$	−6.20475	+	10.7469i	−0.480138	+	0.831624i	0.519602	+	0.854408i	$0.326080\pi$
$168$	1.93621	−	5.23923i	0.149382	−	0.404215i
$169$	−1.51961	−	2.63204i	−0.116893	−	0.202465i
$170$			5.16633i			0.396239i
$171$	−11.9396	+	8.56060i	−0.913045	+	0.654646i
$172$	−2.32037			−0.176927
$173$	−6.14289	−	10.6398i	−0.467035	−	0.808929i	0.532255	−	0.846584i	$-0.321345\pi$
$173$	−6.14289	−	10.6398i	−0.467035	−	0.808929i	−0.999291	+	0.0376549i	$0.988011\pi$
$174$	0.197125	+	0.305643i	0.0149440	+	0.0231707i
$175$	2.11583	−	1.58847i	0.159942	−	0.120077i
$176$	−2.68768	−	1.55173i	−0.202591	−	0.116966i
$177$	−14.3642	−	22.2717i	−1.07968	−	1.67404i
$178$	17.5525	−	10.1340i	1.31562	−	0.759572i
$179$			4.60808i			0.344424i	0.985060	+	0.172212i	$0.0550914\pi$
$179$			4.60808i			0.344424i	−0.985060	+	0.172212i	$0.944909\pi$
$180$	1.64858	−	3.64105i	0.122878	−	0.271388i
$181$		−	16.3361i		−	1.21425i	−0.794605	−	0.607127i	$-0.792322\pi$
$181$		−	16.3361i		−	1.21425i	0.794605	−	0.607127i	$-0.207678\pi$
$182$	1.83060	+	15.1326i	0.135693	+	1.12170i
$183$	0.880266	+	17.8699i	0.0650711	+	1.32098i
$184$	2.69530	−	4.66840i	0.198700	−	0.344159i
$185$	−5.39002	+	9.33580i	−0.396282	+	0.686381i
$186$	0.454755	−	0.885621i	0.0333442	−	0.0649369i
$187$	−1.55566	+	0.898163i	−0.113761	+	0.0656802i
$188$	−10.5274			−0.767788
$189$	3.64105	+	13.2568i	0.264847	+	0.964290i
$190$	8.93953			0.648542
$191$	−21.0061	+	12.1279i	−1.51995	+	0.877543i	−0.520225	+	0.854029i	$0.674152\pi$
$191$	−21.0061	+	12.1279i	−1.51995	+	0.877543i	−0.999724	+	0.0235140i	$0.992515\pi$
$192$	−1.63329	+	3.18078i	−0.117872	+	0.229553i
$193$	6.56678	−	11.3740i	0.472687	−	0.818718i	−0.526825	−	0.849974i	$-0.676618\pi$
$193$	6.56678	−	11.3740i	0.472687	−	0.818718i	0.999511	+	0.0312564i	$0.00995083\pi$
$194$	−0.281339	+	0.487293i	−0.0201990	+	0.0349856i
$195$	−0.268951	−	5.45985i	−0.0192600	−	0.390988i
$196$	−2.60264	+	8.95554i	−0.185903	+	0.639681i
$197$			3.76813i			0.268468i	0.990950	+	0.134234i	$0.0428573\pi$
$197$			3.76813i			0.268468i	−0.990950	+	0.134234i	$0.957143\pi$
$198$	3.45908	−	0.341616i	0.245826	−	0.0242776i
$199$			18.8678i			1.33750i	0.743487	+	0.668751i	$0.233171\pi$
$199$			18.8678i			1.33750i	−0.743487	+	0.668751i	$0.766829\pi$
$200$	1.05557	−	0.609434i	0.0746401	−	0.0430935i
$201$	−4.51709	−	7.00376i	−0.318611	−	0.494007i
$202$	−3.11887	−	1.80068i	−0.219443	−	0.126695i
$203$	0.182721	+	0.243382i	0.0128245	+	0.0170821i
$204$	3.53975	+	5.48839i	0.247832	+	0.384264i
$205$	1.11318	+	1.92808i	0.0777477	+	0.134663i
$206$	29.3611			2.04568
$207$	1.30398	+	13.2037i	0.0906332	+	0.917718i
$208$			15.4319i			1.07001i
$209$	1.55413	+	2.69184i	0.107502	+	0.186198i
$210$	2.89980	−	7.84661i	0.200105	−	0.541468i
$211$	12.9903	−	22.4999i	0.894292	−	1.54896i	0.0596142	−	0.998221i	$-0.481013\pi$
$211$	12.9903	−	22.4999i	0.894292	−	1.54896i	0.834678	−	0.550738i	$-0.185654\pi$
$212$	−9.96389	−	5.75265i	−0.684323	−	0.395094i
$213$	19.9909	+	10.2651i	1.36976	+	0.703351i
$214$	−9.19701	−	15.9297i	−0.628695	−	1.08893i
$215$	1.74163			0.118778
$216$	0.931799	+	6.26450i	0.0634009	+	0.426245i
$217$	0.326876	−	0.766262i	0.0221898	−	0.0520172i
$218$	−22.5292	+	13.0072i	−1.52587	+	0.880961i
$219$	−9.95310	−	5.11079i	−0.672568	−	0.345355i
$220$	−0.732329	−	0.422810i	−0.0493736	−	0.0285059i
$221$	7.73548	+	4.46608i	0.520345	+	0.300421i
$222$	1.67695	+	34.0429i	0.112549	+	2.28481i
$223$	−20.0761	+	11.5909i	−1.34440	+	0.776187i	−0.987449	−	0.157938i	$-0.949515\pi$
$223$	−20.0761	+	11.5909i	−1.34440	+	0.776187i	−0.356946	+	0.934125i	$0.616182\pi$
$224$	−6.73536	+	15.7890i	−0.450025	+	1.05495i
$225$	−1.23740	+	2.73292i	−0.0824931	+	0.182195i
$226$	0.370693			0.0246582
$227$	9.75293	+	16.8926i	0.647325	+	1.12120i	0.983759	+	0.179493i	$0.0574456\pi$
$227$	9.75293	+	16.8926i	0.647325	+	1.12120i	−0.336434	+	0.941707i	$0.609221\pi$
$228$	9.49681	−	6.12499i	0.628942	−	0.405638i
$229$	−19.9441	−	11.5147i	−1.31794	−	0.760913i	−0.334544	−	0.942380i	$-0.608582\pi$
$229$	−19.9441	−	11.5147i	−1.31794	−	0.760913i	−0.983397	+	0.181467i	$0.941916\pi$
$230$	4.03666	−	6.99171i	0.266170	−	0.461019i
$231$	2.86687	−	0.490954i	0.188626	−	0.0323024i
$232$	0.0701026	+	0.121421i	0.00460246	+	0.00797170i
$233$			18.2501i			1.19560i	0.801644	+	0.597801i	$0.203959\pi$
$233$			18.2501i			1.19560i	−0.801644	+	0.597801i	$0.796041\pi$
$234$	−10.0712	−	14.0464i	−0.658373	−	0.918243i
$235$	7.90169			0.515449
$236$	10.1927	+	17.6543i	0.663488	+	1.14920i
$237$	−22.5577	+	1.11119i	−1.46528	+	0.0721793i
$238$	8.20657	+	10.9311i	0.531953	+	0.708557i
$239$	−16.0585	−	9.27139i	−1.03874	−	0.599716i	−0.119263	−	0.992863i	$-0.538053\pi$
$239$	−16.0585	−	9.27139i	−1.03874	−	0.599716i	−0.919476	+	0.393146i	$0.871387\pi$
$240$	3.86852	−	7.53383i	0.249712	−	0.486306i
$241$	6.19724	−	3.57798i	0.399200	−	0.230478i	−0.286939	−	0.957949i	$-0.592638\pi$
$241$	6.19724	−	3.57798i	0.399200	−	0.230478i	0.686139	+	0.727471i	$0.259304\pi$
$242$			19.3446i			1.24352i
$243$	−10.8483	−	11.1944i	−0.695919	−	0.718120i
$244$		−	13.7622i		−	0.881033i
$245$	1.95350	−	6.72189i	0.124805	−	0.429446i
$246$	6.26196	+	3.21543i	0.399248	+	0.205008i
$247$	7.72787	−	13.3851i	0.491713	−	0.851671i
$248$	0.191893	−	0.332368i	0.0121852	−	0.0211054i
$249$	7.78790	−	0.383631i	0.493538	−	0.0243116i
$250$	1.58089	−	0.912729i	0.0999844	−	0.0577260i
$251$	−29.5574			−1.86564			−0.932822	−	0.360338i	$-0.882661\pi$
$251$	−29.5574			−1.86564			−0.932822	+	0.360338i	$0.882661\pi$
$252$	−2.29561	−	10.3226i	−0.144610	−	0.650262i
$253$	2.80709			0.176480
$254$	7.27633	−	4.20099i	0.456558	−	0.263594i
$255$	−2.65688	−	4.11950i	−0.166380	−	0.257973i
$256$	−10.4684	+	18.1317i	−0.654272	+	1.13323i
$257$	−4.33852	+	7.51453i	−0.270629	+	0.468744i	−0.969023	−	0.246970i	$-0.920565\pi$
$257$	−4.33852	+	7.51453i	−0.270629	+	0.468744i	0.698394	+	0.715714i	$0.253898\pi$
$258$	4.62768	−	2.98463i	0.288107	−	0.185815i
$259$	3.42527	+	28.3149i	0.212836	+	1.75940i
$260$			4.20482i			0.260772i
$261$	−0.314365	−	0.142337i	−0.0194587	−	0.00881041i
$262$			2.75768i			0.170370i
$263$	−5.81261	+	3.35591i	−0.358421	+	0.206934i	−0.668388	−	0.743813i	$-0.733015\pi$
$263$	−5.81261	+	3.35591i	−0.358421	+	0.206934i	0.309967	+	0.950747i	$0.399682\pi$
$264$	1.33834	−	0.0659263i	0.0823691	−	0.00405749i
$265$	7.47874	+	4.31785i	0.459415	+	0.265244i
$266$	18.9146	−	14.2002i	1.15973	−	0.870671i
$267$	−8.78437	+	17.1073i	−0.537595	+	1.04695i
$268$	3.20529	+	5.55172i	0.195794	+	0.339125i
$269$	7.10403			0.433140			0.216570	−	0.976267i	$-0.430513\pi$
$269$	7.10403			0.433140			0.216570	+	0.976267i	$0.430513\pi$
$270$	1.39552	+	9.38214i	0.0849289	+	0.570979i
$271$		−	24.9418i		−	1.51511i	−0.652773	−	0.757554i	$-0.726394\pi$
$271$		−	24.9418i		−	1.51511i	0.652773	−	0.757554i	$-0.273606\pi$
$272$	6.91913	+	11.9843i	0.419534	+	0.726654i
$273$	−9.24189	−	11.1249i	−0.559345	−	0.673311i
$274$	11.5115	−	19.9386i	0.695437	−	1.20453i
$275$	0.549675	+	0.317355i	0.0331466	+	0.0191372i
$276$	−0.502121	−	10.1933i	−0.0302241	−	0.613565i
$277$	−3.69399	−	6.39818i	−0.221950	−	0.384429i	0.733450	−	0.679744i	$-0.237909\pi$
$277$	−3.69399	−	6.39818i	−0.221950	−	0.384429i	−0.955400	+	0.295314i	$0.904576\pi$
$278$	−10.2596			−0.615330
$279$	0.0928376	+	0.940039i	0.00555804	+	0.0562787i
$280$	1.26534	−	2.96621i	0.0756186	−	0.177265i
$281$	−4.56414	+	2.63511i	−0.272274	+	0.157197i	−0.629921	−	0.776660i	$-0.716913\pi$
$281$	−4.56414	+	2.63511i	−0.272274	+	0.157197i	0.357647	+	0.933857i	$0.383579\pi$
$282$	20.9955	−	13.5411i	1.25026	−	0.806361i
$283$	−19.8282	−	11.4478i	−1.17867	−	0.680503i	−0.222960	−	0.974828i	$-0.571572\pi$
$283$	−19.8282	−	11.4478i	−1.17867	−	0.680503i	−0.955706	+	0.294325i	$0.904905\pi$
$284$	−14.9699	−	8.64289i	−0.888302	−	0.512861i
$285$	−7.12816	+	4.59733i	−0.422236	+	0.272322i
$286$	−3.16683	+	1.82837i	−0.187258	+	0.108114i
$287$	5.41800	+	2.31124i	0.319815	+	0.136428i
$288$	−1.91294	−	19.3697i	−0.112721	−	1.14137i
$289$	−8.99023			−0.528837
$290$	0.104990	+	0.181849i	0.00616525	+	0.0106785i
$291$	−0.0262673	−	0.533240i	−0.00153982	−	0.0312591i
$292$	7.45325	+	4.30313i	0.436168	+	0.251822i
$293$	12.2600	−	21.2349i	0.716236	−	1.24056i	−0.246244	−	0.969208i	$-0.579197\pi$
$293$	12.2600	−	21.2349i	0.716236	−	1.24056i	0.962481	−	0.271350i	$-0.0874701\pi$
$294$	−6.32865	−	21.2084i	−0.369094	−	1.23690i
$295$	−7.65048	−	13.2510i	−0.445428	−	0.771504i
$296$			13.1395i			0.763715i
$297$	−2.58250	+	2.05129i	−0.149852	+	0.119028i
$298$	−22.8667			−1.32463
$299$	−6.97907	−	12.0881i	−0.403610	−	0.699073i
$300$	1.05408	−	2.05279i	0.0608573	−	0.118518i
$301$	3.68501	−	2.76654i	0.212400	−	0.159461i
$302$	−14.0607	−	8.11798i	−0.809105	−	0.467137i
$303$	3.41294	−	0.168121i	0.196069	−	0.00965830i
$304$	20.7370	−	11.9725i	1.18935	−	0.686670i
$305$			10.3297i			0.591475i
$306$	−14.1192	−	6.39279i	−0.807138	−	0.365452i
$307$		−	23.9095i		−	1.36459i	−0.731078	−	0.682294i	$-0.760983\pi$
$307$		−	23.9095i		−	1.36459i	0.731078	−	0.682294i	$-0.239017\pi$
$308$	−2.22111	+	0.268689i	−0.126559	+	0.0153100i
$309$	−23.4118	+	15.0995i	−1.33185	+	0.858981i
$310$	0.287392	−	0.497777i	0.0163227	−	0.0282718i
$311$	11.9796	−	20.7493i	0.679303	−	1.17659i	−0.295889	−	0.955222i	$-0.595616\pi$
$311$	11.9796	−	20.7493i	0.679303	−	1.17659i	0.975191	−	0.221364i	$-0.0710509\pi$
$312$	−3.61132	−	5.59935i	−0.204451	−	0.317001i
$313$	−20.2952	+	11.7174i	−1.14715	+	0.662307i	−0.948191	−	0.317701i	$-0.897089\pi$
$313$	−20.2952	+	11.7174i	−1.14715	+	0.662307i	−0.198959	+	0.980008i	$0.563756\pi$
$314$	−3.10707			−0.175342
$315$	1.72305	+	7.74797i	0.0970827	+	0.436549i
$316$	17.3724			0.977274
$317$	0.0621219	−	0.0358661i	0.00348911	−	0.00201444i	−0.498254	−	0.867031i	$-0.666025\pi$
$317$	0.0621219	−	0.0358661i	0.00348911	−	0.00201444i	0.501744	+	0.865016i	$0.332692\pi$
$318$	27.2712	−	1.34337i	1.52929	−	0.0753326i
$319$	−0.0365051	+	0.0632286i	−0.00204389	+	0.00354012i
$320$	−1.03219	+	1.78781i	−0.0577012	+	0.0999414i
$321$	15.5256	+	7.97220i	0.866556	+	0.444965i
$322$	−2.56523	−	21.2054i	−0.142955	−	1.18173i
$323$		−	13.8597i		−	0.771173i
$324$	7.91077	+	9.01085i	0.439487	+	0.500603i
$325$		−	3.15607i		−	0.175067i
$326$	29.8711	−	17.2461i	1.65441	−	0.955171i
$327$	11.2750	−	21.9577i	0.623509	−	1.21426i
$328$	2.35007	+	1.35682i	0.129761	+	0.0749176i
$329$	16.7187	−	12.5516i	0.921730	−	0.691993i
$330$	2.00439	−	0.0987357i	0.110338	−	0.00543522i
$331$	5.30278	+	9.18468i	0.291467	+	0.504836i	0.974157	−	0.225873i	$-0.0725233\pi$
$331$	5.30278	+	9.18468i	0.291467	+	0.504836i	−0.682690	+	0.730708i	$0.739190\pi$
$332$	−5.99772			−0.329168
$333$	−18.8444	−	26.2826i	−1.03267	−	1.44028i
$334$			22.6530i			1.23952i
$335$	−2.40584	−	4.16704i	−0.131445	−	0.227669i
$336$	−3.78214	−	22.0854i	−0.206333	−	1.20486i
$337$	−7.49923	+	12.9890i	−0.408509	+	0.707558i	−0.994723	−	0.102598i	$-0.967284\pi$
$337$	−7.49923	+	12.9890i	−0.408509	+	0.707558i	0.586214	+	0.810156i	$0.300618\pi$
$338$	−4.80468	−	2.77398i	−0.261340	−	0.150885i
$339$	−0.295582	+	0.190636i	−0.0160538	+	0.0103539i
$340$	1.88530	+	3.26543i	0.102245	+	0.177093i
$341$	0.199852			0.0108226
$342$	−11.0617	+	24.4310i	−0.598150	+	1.32108i
$343$	−6.54426	−	17.3255i	−0.353357	−	0.935489i
$344$	1.83842	−	1.06141i	0.0991208	−	0.0572274i
$345$	0.376884	+	7.65095i	0.0202908	+	0.411913i
$346$	−19.4225	−	11.2136i	−1.04416	−	0.602846i
$347$	8.94211	+	5.16273i	0.480037	+	0.277150i	0.720432	−	0.693525i	$-0.243944\pi$
$347$	8.94211	+	5.16273i	0.480037	+	0.277150i	−0.240395	+	0.970675i	$0.577277\pi$
$348$	0.236131	+	0.121250i	0.0126579	+	0.00649968i
$349$	11.0162	−	6.36020i	0.589683	−	0.340454i	−0.175289	−	0.984517i	$-0.556086\pi$
$349$	11.0162	−	6.36020i	0.589683	−	0.340454i	0.764972	+	0.644063i	$0.222753\pi$
$350$	1.89506	−	4.44239i	0.101295	−	0.237456i
$351$	15.2541	+	6.02098i	0.814206	+	0.321376i
$352$	−4.11799			−0.219489
$353$	−2.64706	−	4.58484i	−0.140889	−	0.244027i	0.786943	−	0.617026i	$-0.211663\pi$
$353$	−2.64706	−	4.58484i	−0.140889	−	0.244027i	−0.927832	+	0.372999i	$0.878329\pi$
$354$	−43.0363	−	22.0986i	−2.28735	−	1.17452i
$355$	11.2362	+	6.48722i	0.596356	+	0.344306i
$356$	7.39618	−	12.8106i	0.391997	−	0.678959i
$357$	−12.1652	−	4.49579i	−0.643853	−	0.237942i
$358$	4.20592	+	7.28488i	0.222290	+	0.385018i
$359$			28.3441i			1.49594i	0.663730	+	0.747972i	$0.268972\pi$
$359$			28.3441i			1.49594i	−0.663730	+	0.747972i	$0.731028\pi$
$360$	0.359375	+	3.63890i	0.0189407	+	0.191787i
$361$	−4.98204			−0.262212
$362$	−14.9104	−	25.8256i	−0.783675	−	1.35736i
$363$	−9.94835	−	15.4249i	−0.522153	−	0.809599i
$364$	6.67924	+	8.89669i	0.350087	+	0.466313i
$365$	−5.59429	−	3.22987i	−0.292819	−	0.169059i
$366$	17.7019	+	27.4469i	0.925295	+	1.43467i
$367$	−16.6696	+	9.62420i	−0.870146	+	0.502379i	−0.867397	−	0.497617i	$-0.834208\pi$
$367$	−16.6696	+	9.62420i	−0.870146	+	0.502379i	−0.00274922	+	0.999996i	$0.500875\pi$
$368$		−	21.6248i		−	1.12727i
$369$	−6.64673	+	0.656426i	−0.346015	+	0.0341722i
$370$			19.6785i			1.02304i
$371$	22.6826	−	2.74392i	1.17762	−	0.142457i
$372$	−0.0357487	−	0.725716i	−0.00185348	−	0.0376266i
$373$	−0.291671	+	0.505190i	−0.0151022	+	0.0261577i	−0.873478	−	0.486864i	$-0.838141\pi$
$373$	−0.291671	+	0.505190i	−0.0151022	+	0.0261577i	0.858376	+	0.513022i	$0.171474\pi$
$374$	−1.63956	+	2.83980i	−0.0847796	+	0.146843i
$375$	−0.791176	+	1.54079i	−0.0408562	+	0.0795662i
$376$	8.34079	−	4.81556i	0.430143	−	0.248343i
$377$	0.363040			0.0186975
$378$	17.8560	+	17.6343i	0.918412	+	0.907010i
$379$	−13.7533			−0.706458			−0.353229	−	0.935537i	$-0.614916\pi$
$379$	−13.7533			−0.706458			−0.353229	+	0.935537i	$0.614916\pi$
$380$	5.65033	−	3.26222i	0.289856	−	0.167348i
$381$	−3.64153	+	7.09176i	−0.186561	+	0.363322i
$382$	−22.1389	+	38.3458i	−1.13273	+	1.96194i
$383$	−17.9867	+	31.1539i	−0.919078	+	1.59189i	−0.118260	+	0.992983i	$0.537732\pi$
$383$	−17.9867	+	31.1539i	−0.919078	+	1.59189i	−0.800818	+	0.598907i	$0.795602\pi$
$384$	−0.784640	−	15.9286i	−0.0400410	−	0.812853i
$385$	1.66713	−	0.201674i	0.0849648	−	0.0102782i
$386$		−	23.9747i		−	1.22028i
$387$	−2.15509	+	4.75975i	−0.109549	+	0.241952i
$388$			0.410666i			0.0208484i
$389$	1.51792	−	0.876372i	0.0769616	−	0.0444338i	−0.461025	−	0.887387i	$-0.652518\pi$
$389$	1.51792	−	0.876372i	0.0769616	−	0.0444338i	0.537987	+	0.842953i	$0.319185\pi$
$390$	−5.40855	−	8.38596i	−0.273873	−	0.424640i
$391$	−10.8398	−	6.25836i	−0.548193	−	0.316499i
$392$	−2.03449	−	8.28596i	−0.102757	−	0.418504i
$393$	−1.41819	−	2.19890i	−0.0715381	−	0.110920i
$394$	3.43928	+	5.95700i	0.173268	+	0.300109i
$395$	−13.0395			−0.656087
$396$	2.06169	−	1.47821i	0.103604	−	0.0742830i
$397$		−	5.19511i		−	0.260735i	−0.991466	−	0.130367i	$-0.958384\pi$
$397$		−	5.19511i		−	0.260735i	0.991466	−	0.130367i	$-0.0416157\pi$
$398$	17.2212	+	29.8279i	0.863219	+	1.49514i
$399$	−7.77927	+	21.0501i	−0.389451	+	1.05382i
$400$	2.44479	−	4.23450i	0.122240	−	0.211725i
$401$	24.3757	+	14.0733i	1.21726	+	0.702788i	0.964332	−	0.264696i	$-0.0852717\pi$
$401$	24.3757	+	14.0733i	1.21726	+	0.702788i	0.252932	+	0.967484i	$0.418605\pi$
$402$	−13.5336	−	6.94931i	−0.674993	−	0.346600i
$403$	−0.496877	−	0.860617i	−0.0247512	−	0.0428704i
$404$	−2.62842			−0.130769
$405$	−5.93770	−	6.76341i	−0.295047	−	0.336076i
$406$	0.511004	+	0.217987i	0.0253607	+	0.0108185i
$407$	−5.92552	+	3.42110i	−0.293717	+	0.169578i
$408$	−5.31509	−	2.72923i	−0.263136	−	0.135117i
$409$	30.3765	+	17.5379i	1.50202	+	0.867193i	0.999997	+	0.00234081i	$0.000745104\pi$
$409$	30.3765	+	17.5379i	1.50202	+	0.867193i	0.502026	+	0.864853i	$0.332588\pi$
$410$	3.51963	+	2.03206i	0.173822	+	0.100356i
$411$	1.07478	+	21.8186i	0.0530149	+	1.07623i
$412$	18.5580	−	10.7145i	0.914287	−	0.527864i
$413$	−37.2360	−	15.8844i	−1.83227	−	0.781619i
$414$	14.1128	+	19.6834i	0.693607	+	0.967386i
$415$	4.50180			0.220985
$416$	10.2383	+	17.7332i	0.501972	+	0.869442i
$417$	8.18075	−	5.27620i	0.400613	−	0.258376i
$418$	4.91383	+	2.83700i	0.240344	+	0.138762i
$419$	5.42356	−	9.39389i	0.264958	−	0.458921i	−0.702594	−	0.711591i	$-0.747975\pi$
$419$	5.42356	−	9.39389i	0.264958	−	0.458921i	0.967553	+	0.252669i	$0.0813084\pi$
$420$	−1.03054	−	6.01774i	−0.0502854	−	0.293636i
$421$	10.3703	+	17.9619i	0.505417	+	0.875408i	0.999980	+	0.00626646i	$0.00199469\pi$
$421$	10.3703	+	17.9619i	0.505417	+	0.875408i	−0.494563	+	0.869142i	$0.664672\pi$
$422$		−	47.4266i		−	2.30869i
$423$	−9.77752	+	21.5947i	−0.475399	+	1.04997i
$424$	10.5258			0.511177
$425$	−1.41508	−	2.45099i	−0.0686413	−	0.118890i
$426$	40.9727	−	2.01831i	1.98514	−	0.0977874i
$427$	16.4084	+	21.8559i	0.794059	+	1.05768i
$428$	−11.6261	−	6.71236i	−0.561971	−	0.324454i
$429$	1.58488	−	3.08650i	0.0765185	−	0.149017i
$430$	2.75334	−	1.58964i	0.132778	−	0.0766592i
$431$			10.0323i			0.483240i	0.970371	+	0.241620i	$0.0776787\pi$
$431$			10.0323i			0.483240i	−0.970371	+	0.241620i	$0.922321\pi$
$432$	15.8025	+	19.8947i	0.760296	+	0.957183i
$433$			11.9241i			0.573034i	0.958075	+	0.286517i	$0.0924975\pi$
$433$			11.9241i			0.573034i	−0.958075	+	0.286517i	$0.907503\pi$
$434$	−0.182633	−	1.50973i	−0.00876664	−	0.0724692i
$435$	−0.177236	−	0.0910083i	−0.00849781	−	0.00436352i
$436$	−9.49322	+	16.4427i	−0.454643	+	0.787465i
$437$	−10.8291	+	18.7566i	−0.518028	+	0.897251i
$438$	−20.3995	+	1.00488i	−0.974728	+	0.0480149i
$439$	−21.8143	+	12.5945i	−1.04114	+	0.601103i	−0.920156	−	0.391552i	$-0.871938\pi$
$439$	−21.8143	+	12.5945i	−1.04114	+	0.601103i	−0.120985	+	0.992654i	$0.538605\pi$
$440$	0.773627			0.0368812
$441$	15.9531	+	13.6564i	0.759673	+	0.650305i
$442$	16.3053			0.775564
$443$	19.2098	−	11.0908i	0.912687	−	0.526940i	0.0313921	−	0.999507i	$-0.490006\pi$
$443$	19.2098	−	11.0908i	0.912687	−	0.526940i	0.881295	+	0.472567i	$0.156673\pi$
$444$	13.4829	+	20.9053i	0.639870	+	0.992120i
$445$	−5.55146	+	9.61541i	−0.263165	+	0.455814i
$446$	−21.1588	+	36.6481i	−1.00190	+	1.73534i
$447$	18.2333	−	11.7596i	0.862406	−	0.556211i
$448$	0.655940	+	5.42231i	0.0309902	+	0.256180i
$449$		−	24.3237i		−	1.14791i	−0.818888	−	0.573954i	$-0.805409\pi$
$449$		−	24.3237i		−	1.14791i	0.818888	−	0.573954i	$-0.194591\pi$
$450$	0.538224	+	5.44986i	0.0253721	+	0.256909i
$451$			1.41309i			0.0665398i
$452$	0.234301	−	0.135274i	0.0110206	−	0.00636274i
$453$	15.3865	−	0.757937i	0.722922	−	0.0356110i
$454$	30.8367	+	17.8036i	1.44724	+	0.835563i
$455$	−5.01333	−	6.67772i	−0.235029	−	0.313056i
$456$	−4.72251	+	9.19694i	−0.221152	+	0.430686i
$457$	−6.84087	−	11.8487i	−0.320002	−	0.554261i	0.660486	−	0.750839i	$-0.270350\pi$
$457$	−6.84087	−	11.8487i	−0.320002	−	0.554261i	−0.980488	+	0.196578i	$0.937017\pi$
$458$	−42.0392			−1.96436
$459$	14.5459	−	2.16359i	0.678944	−	0.100988i
$460$		−	5.89225i		−	0.274728i
$461$	−13.9624	−	24.1836i	−0.650293	−	1.12634i	−0.983052	−	0.183329i	$-0.941313\pi$
$461$	−13.9624	−	24.1836i	−0.650293	−	1.12634i	0.332759	−	0.943012i	$-0.392021\pi$
$462$	4.08411	−	3.39282i	0.190010	−	0.157848i
$463$	5.19491	−	8.99785i	0.241428	−	0.418165i	−0.719693	−	0.694292i	$-0.755718\pi$
$463$	5.19491	−	8.99785i	0.241428	−	0.418165i	0.961121	+	0.276127i	$0.0890509\pi$
$464$	0.487091	+	0.281222i	0.0226126	+	0.0130554i
$465$	0.0268324	+	0.544712i	0.00124432	+	0.0252604i
$466$	16.6574	+	28.8514i	0.771638	+	1.33652i
$467$	13.3976			0.619968			0.309984	−	0.950742i	$-0.399676\pi$
$467$	13.3976			0.619968			0.309984	+	0.950742i	$0.399676\pi$
$468$	−11.4914	−	5.20302i	−0.531191	−	0.240510i
$469$	−11.7096	−	4.99514i	−0.540698	−	0.230654i
$470$	12.4917	−	7.21210i	0.576200	−	0.332669i
$471$	2.47750	−	1.59787i	0.114157	−	0.0736259i
$472$	−16.1512	−	9.32493i	−0.743421	−	0.429214i
$473$	0.957332	+	0.552716i	0.0440182	+	0.0254139i
$474$	−34.6470	+	22.3457i	−1.59139	+	1.02637i
$475$	−4.24105	+	2.44857i	−0.194593	+	0.112348i
$476$	9.17604	+	3.91437i	0.420583	+	0.179415i
$477$	−21.0545	+	15.0959i	−0.964020	+	0.691194i
$478$	−33.8491			−1.54822
$479$	−3.08962	−	5.35139i	−0.141169	−	0.244511i	0.786768	−	0.617248i	$-0.211753\pi$
$479$	−3.08962	−	5.35139i	−0.141169	−	0.244511i	−0.927937	+	0.372737i	$0.878419\pi$
$480$	−0.552888	−	11.2239i	−0.0252358	−	0.512299i
$481$	29.4644	+	17.0113i	1.34346	+	0.775648i
$482$	6.53145	−	11.3128i	0.297499	−	0.515284i
$483$	12.9508	+	15.5895i	0.589280	+	0.709345i
$484$	7.05926	+	12.2270i	0.320875	+	0.555773i
$485$		−	0.308239i		−	0.0139964i
$486$	−27.3674	−	7.79556i	−1.24141	−	0.353614i
$487$	11.0928			0.502665			0.251332	−	0.967901i	$-0.419131\pi$
$487$	11.0928			0.502665			0.251332	+	0.967901i	$0.419131\pi$
$488$	6.29525	+	10.9037i	0.284973	+	0.493587i
$489$	−14.9493	+	29.1134i	−0.676032	+	1.31655i
$490$	−3.04698	−	12.4096i	−0.137649	−	0.560609i
$491$	−0.777992	−	0.449174i	−0.0351103	−	0.0202709i	0.482342	−	0.875983i	$-0.339786\pi$
$491$	−0.777992	−	0.449174i	−0.0351103	−	0.0202709i	−0.517452	+	0.855712i	$0.673120\pi$
$492$	5.13132	−	0.252768i	0.231338	−	0.0113957i
$493$	0.281935	−	0.162775i	0.0126977	−	0.00733102i
$494$		−	28.2138i		−	1.26940i
$495$	−1.54747	+	1.10952i	−0.0695536	+	0.0498694i
$496$		−	1.53959i		−	0.0691294i
$497$	34.0787	−	4.12252i	1.52864	−	0.184920i
$498$	11.9617	−	7.71472i	0.536016	−	0.345705i
$499$	17.0653	−	29.5579i	0.763946	−	1.32319i	−0.176857	−	0.984237i	$-0.556593\pi$
$499$	17.0653	−	29.5579i	0.763946	−	1.32319i	0.940802	−	0.338956i	$-0.110074\pi$
$500$	0.666147	−	1.15380i	0.0297910	−	0.0515996i
$501$	−11.6498	−	18.0630i	−0.520473	−	0.806994i
$502$	−46.7270	+	26.9778i	−2.08553	+	1.20408i
$503$	39.5756			1.76459			0.882294	−	0.470698i	$-0.155998\pi$
$503$	39.5756			1.76459			0.882294	+	0.470698i	$0.155998\pi$
$504$	6.54067	+	7.12845i	0.291345	+	0.317526i
$505$	1.97285			0.0877908
$506$	4.43770	−	2.56211i	0.197280	−	0.113900i
$507$	5.25770	−	0.258994i	0.233503	−	0.0115023i
$508$	3.06606	−	5.31057i	0.136034	−	0.235618i
$509$	4.36091	−	7.55332i	0.193294	−	0.334795i	−0.753046	−	0.657968i	$-0.771416\pi$
$509$	4.36091	−	7.55332i	0.193294	−	0.334795i	0.946340	+	0.323173i	$0.104750\pi$
$510$	−7.96023	−	4.08747i	−0.352485	−	0.180996i
$511$	−16.9671	+	2.05253i	−0.750582	+	0.0907984i
$512$			19.8040i			0.875222i
$513$	−3.74377	−	25.1694i	−0.165291	−	1.11126i
$514$			15.8396i			0.698653i
$515$	−13.9294	+	8.04212i	−0.613801	+	0.354378i
$516$	1.83582	−	3.57521i	0.0808175	−	0.157390i
$517$	4.34336	+	2.50764i	0.191021	+	0.110286i
$518$	31.2588	+	41.6365i	1.37343	+	1.82940i
$519$	21.2538	−	1.04696i	0.932939	−	0.0459564i
$520$	−1.92342	−	3.33145i	−0.0843474	−	0.146094i
$521$	17.4216			0.763256			0.381628	−	0.924316i	$-0.375364\pi$
$521$	17.4216			0.763256			0.381628	+	0.924316i	$0.375364\pi$
$522$	−0.626893	+	0.0619115i	−0.0274383	+	0.00270979i
$523$		−	13.2690i		−	0.580215i	−0.956994	−	0.290107i	$-0.906309\pi$
$523$		−	13.2690i		−	0.580215i	0.956994	−	0.290107i	$-0.0936910\pi$
$524$	1.00633	+	1.74302i	0.0439619	+	0.0761442i
$525$	0.773510	+	4.51682i	0.0337587	+	0.197130i
$526$	−6.12607	+	10.6107i	−0.267109	+	0.462647i
$527$	−0.771744	−	0.445566i	−0.0336177	−	0.0194092i
$528$	4.51732	−	2.91346i	0.196591	−	0.126792i
$529$	−1.72016	−	2.97941i	−0.0747897	−	0.129540i
$530$	15.7641			0.684749
$531$	45.6807	−	4.51139i	1.98237	−	0.195778i
$532$	6.77321	−	15.8777i	0.293656	−	0.688386i
$533$	6.08516	−	3.51327i	0.263577	−	0.152176i
$534$	1.72717	+	35.0625i	0.0747422	+	1.51730i
$535$	8.72641	+	5.03820i	0.377276	+	0.217820i
$536$	−5.07906	−	2.93240i	−0.219382	−	0.126660i
$537$	−7.10009	−	3.64580i	−0.306391	−	0.157328i
$538$	11.2307	−	6.48405i	0.484190	−	0.279547i
$539$	3.20702	−	3.07490i	0.138136	−	0.132445i
$540$	4.30579	+	5.42083i	0.185292	+	0.233275i
$541$	−2.60119			−0.111834			−0.0559170	−	0.998435i	$-0.517808\pi$
$541$	−2.60119			−0.111834			−0.0559170	+	0.998435i	$0.517808\pi$
$542$	−22.7651	−	39.4303i	−0.977845	−	1.69368i
$543$	25.1705	+	12.9247i	1.08017	+	0.554654i
$544$	15.9020	+	9.18100i	0.681791	+	0.393632i
$545$	7.12547	−	12.3417i	0.305221	−	0.528659i
$546$	−24.7645	−	9.15197i	−1.05982	−	0.391668i
$547$	−0.836471	−	1.44881i	−0.0357649	−	0.0619467i	0.847589	−	0.530653i	$-0.178053\pi$
$547$	−0.836471	−	1.44881i	−0.0357649	−	0.0619467i	−0.883354	+	0.468707i	$0.844720\pi$
$548$		−	16.8032i		−	0.717797i
$549$	−28.2302	−	12.7819i	−1.20483	−	0.545518i
$550$	1.15864			0.0494044
$551$	−0.281657	−	0.487845i	−0.0119990	−	0.0207829i
$552$	5.06057	+	7.84643i	0.215392	+	0.333966i
$553$	−27.5893	+	20.7128i	−1.17322	+	0.880800i
$554$	−11.6796	−	6.74322i	−0.496219	−	0.286492i
$555$	−10.1201	−	15.6912i	−0.429573	−	0.666053i
$556$	−6.48470	+	3.74394i	−0.275012	+	0.158778i
$557$			14.5888i			0.618147i	0.951038	+	0.309073i	$0.100019\pi$
$557$			14.5888i			0.618147i	−0.951038	+	0.309073i	$0.899981\pi$
$558$	1.00477	+	1.40137i	0.0425352	+	0.0593245i
$559$		−	5.49672i		−	0.232486i
$560$	−1.55362	−	12.8430i	−0.0656526	−	0.542715i
$561$	−0.153078	−	3.10756i	−0.00646295	−	0.131201i
$562$	−4.81028	+	8.33165i	−0.202909	+	0.351450i
$563$	−6.16179	+	10.6725i	−0.259688	+	0.449793i	−0.966158	−	0.257950i	$-0.916953\pi$
$563$	−6.16179	+	10.6725i	−0.259688	+	0.449793i	0.706470	+	0.707743i	$0.250287\pi$
$564$	8.32901	−	16.2205i	0.350715	−	0.683006i
$565$	−0.175863	+	0.101534i	−0.00739860	+	0.00427158i
$566$	−41.7951			−1.75678
$567$	−23.3067	−	4.87836i	−0.978789	−	0.204872i
$568$	15.8141			0.663546
$569$	21.4923	−	12.4086i	0.901004	−	0.520195i	0.0234780	−	0.999724i	$-0.492526\pi$
$569$	21.4923	−	12.4086i	0.901004	−	0.520195i	0.877526	+	0.479530i	$0.159193\pi$
$570$	−7.07275	+	13.7740i	−0.296245	+	0.576928i
$571$	14.8775	−	25.7686i	0.622605	−	1.07838i	−0.366393	−	0.930460i	$-0.619407\pi$
$571$	14.8775	−	25.7686i	0.622605	−	1.07838i	0.988999	−	0.147924i	$-0.0472592\pi$
$572$	−1.33442	+	2.31128i	−0.0557949	+	0.0966395i
$573$	−2.06701	−	41.9613i	−0.0863505	−	1.75296i
$574$	10.6748	−	1.29134i	0.445558	−	0.0538994i
$575$			4.42263i			0.184436i
$576$	−3.60870	−	5.03312i	−0.150363	−	0.209713i
$577$			37.2085i			1.54901i	0.632568	+	0.774505i	$0.282001\pi$
$577$			37.2085i			1.54901i	−0.632568	+	0.774505i	$0.717999\pi$
$578$	−14.2126	+	8.20564i	−0.591166	+	0.341310i
$579$	12.3295	+	19.1169i	0.512395	+	0.794470i
$580$	0.132721	+	0.0766264i	0.00551093	+	0.00318174i
$581$	9.52506	−	7.15099i	0.395166	−	0.296673i
$582$	−0.528229	−	0.819020i	−0.0218958	−	0.0339495i
$583$	2.74058	+	4.74683i	0.113503	+	0.196594i
$584$	−7.87356			−0.325810
$585$	8.62529	+	3.90531i	0.356612	+	0.161465i
$586$		−	44.7602i		−	1.84903i
$587$	8.94805	+	15.4985i	0.369326	+	0.639691i	0.989460	−	0.144805i	$-0.0462554\pi$
$587$	8.94805	+	15.4985i	0.369326	+	0.639691i	−0.620135	+	0.784495i	$0.712922\pi$
$588$	−11.7395	−	11.0955i	−0.484128	−	0.457572i
$589$	−0.770984	+	1.33538i	−0.0317678	+	0.0550235i
$590$	−24.1892	−	13.9656i	−0.995853	−	0.574956i
$591$	−5.80590	−	2.98125i	−0.238823	−	0.122632i
$592$	26.3550	+	45.6481i	1.08318	+	1.87613i
$593$	19.2039			0.788610			0.394305	−	0.918980i	$-0.370985\pi$
$593$	19.2039			0.788610			0.394305	+	0.918980i	$0.370985\pi$
$594$	−2.21038	+	5.60000i	−0.0906931	+	0.229771i
$595$	−6.88739	−	2.93806i	−0.282356	−	0.120449i
$596$	−14.4531	+	8.34452i	−0.592023	+	0.341805i
$597$	−29.0713	−	14.9277i	−1.18981	−	0.610952i
$598$	−22.0663	−	12.7400i	−0.902359	−	0.520977i
$599$	−11.0142	−	6.35908i	−0.450030	−	0.259825i	0.257813	−	0.966195i	$-0.416998\pi$
$599$	−11.0142	−	6.35908i	−0.450030	−	0.259825i	−0.707843	+	0.706370i	$0.750331\pi$
$600$	0.103868	+	2.10858i	0.00424041	+	0.0860826i
$601$	26.1187	−	15.0797i	1.06541	−	0.615112i	0.138483	−	0.990365i	$-0.455777\pi$
$601$	26.1187	−	15.0797i	1.06541	−	0.615112i	0.926922	+	0.375253i	$0.122444\pi$
$602$	3.30050	−	7.73701i	0.134518	−	0.315337i
$603$	14.3651	−	1.41869i	0.584994	−	0.0577736i
$604$	−11.8497			−0.482156
$605$	−5.29857	−	9.17740i	−0.215418	−	0.373114i
$606$	5.24205	−	3.38087i	0.212944	−	0.137339i
$607$	12.2648	+	7.08106i	0.497811	+	0.287411i	0.727809	−	0.685780i	$-0.240539\pi$
$607$	12.2648	+	7.08106i	0.497811	+	0.287411i	−0.229998	+	0.973191i	$0.573872\pi$
$608$	15.8863	−	27.5159i	0.644275	−	1.11592i
$609$	−0.519566	+	0.0889762i	−0.0210539	+	0.00360550i
$610$	9.42819	+	16.3301i	0.381736	+	0.661187i
$611$		−	24.9383i		−	1.00890i
$612$	−11.2570	+	1.11174i	−0.455039	+	0.0449393i
$613$	−15.2883			−0.617488			−0.308744	−	0.951145i	$-0.599909\pi$
$613$	−15.2883			−0.617488			−0.308744	+	0.951145i	$0.599909\pi$
$614$	−21.8229	−	37.7983i	−0.880700	−	1.52542i
$615$	−3.85149	+	0.189724i	−0.155307	+	0.00765040i
$616$	1.63687	−	1.22889i	0.0659512	−	0.0495132i
$617$	8.33983	+	4.81500i	0.335749	+	0.193845i	0.658391	−	0.752677i	$-0.271238\pi$
$617$	8.33983	+	4.81500i	0.335749	+	0.193845i	−0.322642	+	0.946521i	$0.604571\pi$
$618$	−23.2298	+	45.2393i	−0.934439	+	1.81979i
$619$	−0.588045	+	0.339508i	−0.0236355	+	0.0136460i	−0.511771	−	0.859122i	$-0.671010\pi$
$619$	−0.588045	+	0.339508i	−0.0236355	+	0.0136460i	0.488136	+	0.872768i	$0.337677\pi$
$620$		−	0.419501i		−	0.0168476i
$621$	−21.3758	−	8.43726i	−0.857780	−	0.338575i
$622$		−	43.7366i		−	1.75368i
$623$	3.52786	+	29.1630i	0.141341	+	1.16839i
$624$	−23.7773	−	12.2093i	−0.951853	−	0.488764i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−21.3896	+	37.0479i	−0.854902	+	1.48073i
$627$	−5.37716	+	0.264878i	−0.214743	+	0.0105782i
$628$	−1.96386	+	1.13383i	−0.0783664	+	0.0452449i
$629$	30.5092			1.21648
$630$	9.79575	+	10.6760i	0.390272	+	0.425344i
$631$	−18.5432			−0.738192			−0.369096	−	0.929391i	$-0.620333\pi$
$631$	−18.5432			−0.738192			−0.369096	+	0.929391i	$0.620333\pi$
$632$	−13.7641	+	7.94669i	−0.547505	+	0.316102i
$633$	24.3901	+	37.8168i	0.969418	+	1.50308i
$634$	0.0654720	−	0.113401i	0.00260023	−	0.00450372i
$635$	−2.30134	+	3.98603i	−0.0913258	+	0.158181i
$636$	16.7468	−	10.8009i	0.664055	−	0.428284i
$637$	−21.2148	−	6.16540i	−0.840560	−	0.244282i
$638$			0.133277i			0.00527648i
$639$	−31.6327	+	22.6804i	−1.25137	+	0.897221i
$640$		−	9.20753i		−	0.363960i
$641$	−25.0099	+	14.4395i	−0.987831	+	0.570325i	−0.904625	−	0.426208i	$-0.859849\pi$
$641$	−25.0099	+	14.4395i	−0.987831	+	0.570325i	−0.0832059	+	0.996532i	$0.526516\pi$
$642$	31.8208	−	1.56749i	1.25587	−	0.0618638i
$643$	3.83286	+	2.21290i	0.151153	+	0.0872683i	0.573669	−	0.819087i	$-0.305520\pi$
$643$	3.83286	+	2.21290i	0.151153	+	0.0872683i	−0.422516	+	0.906356i	$0.638853\pi$
$644$	−9.35968	−	12.4670i	−0.368823	−	0.491269i
$645$	−1.37794	+	2.68350i	−0.0542563	+	0.105663i
$646$	−12.6501	−	21.9107i	−0.497713	−	0.862063i
$647$	−7.06316			−0.277681			−0.138841	−	0.990315i	$-0.544338\pi$
$647$	−7.06316			−0.277681			−0.138841	+	0.990315i	$0.544338\pi$
$648$	−10.3895	−	3.52062i	−0.408139	−	0.138303i
$649$		−	9.71167i		−	0.381216i
$650$	−2.88064	−	4.98941i	−0.112988	−	0.195701i
$651$	0.922033	+	1.10990i	0.0361373	+	0.0435003i
$652$	12.5869	−	21.8011i	0.492941	−	0.853799i
$653$	40.1784	+	23.1970i	1.57230	+	0.907768i	0.995886	+	0.0906102i	$0.0288817\pi$
$653$	40.1784	+	23.1970i	1.57230	+	0.907768i	0.576414	+	0.817158i	$0.304452\pi$
$654$	−2.21688	−	45.0038i	−0.0866869	−	1.75979i
$655$	−0.755338	−	1.30828i	−0.0295135	−	0.0511189i
$656$	10.8859			0.425025
$657$	15.7493	−	11.2921i	0.614439	−	0.440548i
$658$	14.9742	−	35.1024i	0.583754	−	1.36843i
$659$	−17.1849	+	9.92173i	−0.669431	+	0.386496i	−0.795861	−	0.605480i	$-0.792981\pi$
$659$	−17.1849	+	9.92173i	−0.669431	+	0.386496i	0.126430	+	0.991975i	$0.459648\pi$
$660$	1.23086	−	0.793849i	0.0479113	−	0.0309005i
$661$	−3.50683	−	2.02467i	−0.136400	−	0.0787505i	0.430247	−	0.902711i	$-0.358426\pi$
$661$	−3.50683	−	2.02467i	−0.136400	−	0.0787505i	−0.566647	+	0.823961i	$0.691760\pi$
$662$	16.7662	+	9.67999i	0.651638	+	0.376224i
$663$	−13.0014	+	8.38531i	−0.504934	+	0.325658i
$664$	4.75196	−	2.74355i	0.184412	−	0.106470i
$665$	−5.08387	+	11.9176i	−0.197144	+	0.462144i
$666$	−53.7798	−	24.3501i	−2.08393	−	0.943548i
$667$	−0.508732			−0.0196982
$668$	8.26656	+	14.3181i	0.319843	+	0.553984i
$669$	−1.97550	−	40.1036i	−0.0763771	−	1.55049i
$670$	−7.60674	−	4.39176i	−0.293874	−	0.169668i
$671$	−3.27817	+	5.67796i	−0.126552	+	0.219195i
$672$	−18.9987	−	22.8697i	−0.732891	−	0.882217i
$673$	2.08333	+	3.60844i	0.0803066	+	0.139095i	0.903382	−	0.428838i	$-0.141077\pi$
$673$	2.08333	+	3.60844i	0.0803066	+	0.139095i	−0.823075	+	0.567933i	$0.807743\pi$
$674$			27.3790i			1.05460i
$675$	−3.23186	−	4.06879i	−0.124394	−	0.156608i
$676$	−4.04913			−0.155736
$677$	−10.5329	−	18.2435i	−0.404812	−	0.701155i	0.589487	−	0.807778i	$-0.299330\pi$
$677$	−10.5329	−	18.2435i	−0.404812	−	0.701155i	−0.994300	+	0.106622i	$0.965996\pi$
$678$	−0.293284	+	0.571161i	−0.0112635	+	0.0219353i
$679$	−0.489630	−	0.652183i	−0.0187903	−	0.0250285i
$680$	−2.98743	−	1.72479i	−0.114563	−	0.0661427i
$681$	−33.7442	+	1.66224i	−1.29308	+	0.0636970i
$682$	0.315944	−	0.182410i	0.0120981	−	0.00698485i
$683$			14.6226i			0.559518i	0.960070	+	0.279759i	$0.0902546\pi$
$683$			14.6226i			0.559518i	−0.960070	+	0.279759i	$0.909745\pi$
$684$	1.92369	+	19.4786i	0.0735541	+	0.744781i
$685$			12.6122i			0.481888i
$686$	−26.1592	−	21.4166i	−0.998765	−	0.817690i
$687$	33.5210	−	21.6195i	1.27891	−	0.824835i
$688$	4.25793	−	7.37495i	0.162332	−	0.281167i
$689$	13.6274	−	23.6034i	0.519164	−	0.899219i
$690$	7.57905	+	11.7513i	0.288530	+	0.447365i
$691$	−9.11482	+	5.26245i	−0.346744	+	0.200193i	−0.663250	−	0.748398i	$-0.730824\pi$
$691$	−9.11482	+	5.26245i	−0.346744	+	0.200193i	0.316506	+	0.948590i	$0.397490\pi$
$692$	−16.3683			−0.622229
$693$	−1.51174	+	4.80568i	−0.0574263	+	0.182553i
$694$	18.8487			0.715486
$695$	4.86731	−	2.81014i	0.184628	−	0.106595i
$696$	−0.242549	+	0.0119479i	−0.00919378	+	0.000452884i
$697$	3.15046	−	5.45676i	0.119332	−	0.206690i
$698$	11.6103	−	20.1096i	0.439455	−	0.761159i
$699$	−28.1196	−	14.4390i	−1.06358	−	0.546134i
$700$	−0.423326	−	3.49941i	−0.0160002	−	0.132265i
$701$			22.2426i			0.840090i	0.907503	+	0.420045i	$0.137986\pi$
$701$			22.2426i			0.840090i	−0.907503	+	0.420045i	$0.862014\pi$
$702$	29.6107	−	4.40437i	1.11758	−	0.166232i
$703$		−	52.7915i		−	1.99107i
$704$	−1.13474	+	0.655141i	−0.0427670	+	0.0246916i
$705$	−6.25163	+	12.1749i	−0.235450	+	0.458532i
$706$	−8.36944	−	4.83210i	−0.314988	−	0.181858i
$707$	4.17423	−	3.13383i	0.156988	−	0.117860i
$708$	−35.2658	+	1.73719i	−1.32537	+	0.0652874i
$709$	12.3741	+	21.4326i	0.464721	+	0.804920i	0.999189	−	0.0402687i	$-0.0128214\pi$
$709$	12.3741	+	21.4326i	0.464721	+	0.804920i	−0.534468	+	0.845189i	$0.679488\pi$
$710$	23.6843			0.888856
$711$	16.1350	−	35.6358i	0.605109	−	1.33645i
$712$			13.5330i			0.507170i
$713$	0.696279	+	1.20599i	0.0260758	+	0.0451647i
$714$	−23.3354	+	3.99620i	−0.873304	+	0.149554i
$715$	1.00159	−	1.73481i	0.0374575	−	0.0648783i
$716$	5.31680	+	3.06966i	0.198698	+	0.114719i
$717$	26.9904	−	17.4075i	1.00798	−	0.650096i
$718$	25.8705	+	44.8090i	0.965477	+	1.67226i
$719$	26.6502			0.993885			0.496942	−	0.867784i	$-0.334456\pi$
$719$	26.6502			0.993885			0.496942	+	0.867784i	$0.334456\pi$
$720$	8.54738	+	11.9212i	0.318542	+	0.444276i
$721$	−16.6975	+	39.1422i	−0.621848	+	1.45773i
$722$	−7.87606	+	4.54725i	−0.293117	+	0.169231i
$723$	0.609811	+	12.3795i	0.0226791	+	0.460398i
$724$	−18.8486	−	10.8823i	−0.700503	−	0.404436i
$725$	−0.0996181	−	0.0575146i	−0.00369973	−	0.00213604i
$726$	−29.8061	−	15.3050i	−1.10621	−	0.568022i
$727$	17.4130	−	10.0534i	0.645811	−	0.372859i	−0.141038	−	0.990004i	$-0.545044\pi$
$727$	17.4130	−	10.0534i	0.645811	−	0.372859i	0.786850	+	0.617145i	$0.211711\pi$
$728$	−9.36156	−	3.99351i	−0.346962	−	0.148009i
$729$	25.8311	−	7.85825i	0.956709	−	0.291046i
$730$	−11.7920			−0.436440
$731$	−2.46455	−	4.26872i	−0.0911545	−	0.157884i
$732$	21.2046	+	10.8883i	0.783746	+	0.402443i
$733$	−2.85584	−	1.64882i	−0.105483	−	0.0609005i	0.446331	−	0.894868i	$-0.352731\pi$
$733$	−2.85584	−	1.64882i	−0.105483	−	0.0609005i	−0.551813	+	0.833968i	$0.686064\pi$
$734$	−17.5686	+	30.4296i	−0.648467	+	1.12318i
$735$	8.81147	+	8.32814i	0.325016	+	0.307188i
$736$	−14.3470	−	24.8497i	−0.528837	−	0.915972i
$737$		−	3.05402i		−	0.112496i
$738$	−9.90862	+	7.10440i	−0.364742	+	0.261517i
$739$	44.1618			1.62452			0.812259	−	0.583296i	$-0.198237\pi$
$739$	44.1618			1.62452			0.812259	+	0.583296i	$0.198237\pi$
$740$	7.18110	+	12.4380i	0.263983	+	0.457231i
$741$	14.5095	+	22.4970i	0.533019	+	0.826447i
$742$	33.3542	−	25.0409i	1.22447	−	0.919280i
$743$	15.6185	+	9.01733i	0.572986	+	0.330814i	0.758341	−	0.651858i	$-0.226010\pi$
$743$	15.6185	+	9.01733i	0.572986	+	0.330814i	−0.185355	+	0.982672i	$0.559343\pi$
$744$	0.360289	+	0.558629i	0.0132088	+	0.0204803i
$745$	10.8483	−	6.26327i	0.397451	−	0.229468i
$746$			1.06487i			0.0389876i
$747$	−5.57051	+	12.3031i	−0.203814	+	0.450145i
$748$			2.39324i			0.0875054i
$749$	26.4667	−	3.20169i	0.967071	−	0.116987i
$750$	0.155560	+	3.15796i	0.00568026	+	0.115312i
$751$	13.9337	−	24.1338i	0.508447	−	0.880655i	−0.491505	−	0.870874i	$-0.663553\pi$
$751$	13.9337	−	24.1338i	0.508447	−	0.880655i	0.999952	−	0.00978101i	$-0.00311344\pi$
$752$	19.3180	−	33.4597i	0.704454	−	1.22015i
$753$	23.3851	−	45.5417i	0.852200	−	1.65963i
$754$	0.573927	−	0.331357i	0.0209012	−	0.0120673i
$755$	8.89418			0.323692
$756$	17.7212	+	4.62993i	0.644513	+	0.168389i
$757$	−15.4396			−0.561162			−0.280581	−	0.959830i	$-0.590527\pi$
$757$	−15.4396			−0.561162			−0.280581	+	0.959830i	$0.590527\pi$
$758$	−21.7424	+	12.5530i	−0.789721	+	0.455946i
$759$	−2.22090	+	4.32514i	−0.0806136	+	0.156993i
$760$	−2.98449	+	5.16928i	−0.108259	+	0.187510i
$761$	−25.1763	+	43.6066i	−0.912639	+	1.58074i	−0.102318	+	0.994752i	$0.532626\pi$
$761$	−25.1763	+	43.6066i	−0.912639	+	1.58074i	−0.810321	+	0.585986i	$0.800707\pi$
$762$	0.715994	+	14.5350i	0.0259377	+	0.526549i
$763$	−4.52812	−	37.4315i	−0.163929	−	1.35511i
$764$			32.3158i			1.16915i
$765$	8.44936	−	0.834453i	0.305487	−	0.0301697i
$766$			65.6680i			2.37268i
$767$	−41.8212	+	24.1455i	−1.51007	+	0.871842i
$768$	−19.6549	−	30.4750i	−0.709235	−	1.09967i
$769$	−28.8897	−	16.6795i	−1.04179	−	0.601478i	−0.121450	−	0.992598i	$-0.538755\pi$
$769$	−28.8897	−	16.6795i	−1.04179	−	0.601478i	−0.920340	+	0.391120i	$0.872088\pi$
$770$	2.45148	−	1.84046i	0.0883452	−	0.0663256i
$771$	−8.14580	−	12.6301i	−0.293364	−	0.454861i
$772$	−8.74888	−	15.1535i	−0.314879	−	0.545387i
$773$	5.27400			0.189693			0.0948463	−	0.995492i	$-0.469764\pi$
$773$	5.27400			0.189693			0.0948463	+	0.995492i	$0.469764\pi$
$774$	0.937390	+	9.49166i	0.0336938	+	0.341171i
$775$			0.314871i			0.0113105i
$776$	−0.187852	−	0.325368i	−0.00674348	−	0.0116800i
$777$	−46.3374	−	17.1245i	−1.66234	−	0.614336i
$778$	1.59978	−	2.77090i	0.0573549	−	0.0993415i
$779$	−9.44209	−	5.45139i	−0.338298	−	0.195316i
$780$	−6.47875	−	3.32675i	−0.231976	−	0.119117i
$781$	4.11750	+	7.13173i	0.147336	+	0.255193i
$782$	−22.8488			−0.817070
$783$	0.468030	−	0.371758i	0.0167260	−	0.0132856i
$784$	−23.6879	−	24.7057i	−0.845998	−	0.882347i
$785$	1.47404	−	0.851038i	0.0526108	−	0.0303748i
$786$	−4.24900	−	2.18181i	−0.151557	−	0.0778225i
$787$	9.49824	+	5.48381i	0.338576	+	0.195477i	0.659642	−	0.751580i	$-0.270708\pi$
$787$	9.49824	+	5.48381i	0.338576	+	0.195477i	−0.321066	+	0.947057i	$0.604041\pi$
$788$	4.34767	+	2.51013i	0.154879	+	0.0894196i
$789$	−0.571962	−	11.6111i	−0.0203624	−	0.413367i
$790$	−20.6140	+	11.9015i	−0.733413	+	0.423436i
$791$	−0.210812	+	0.494183i	−0.00749559	+	0.0175711i
$792$	−0.957283	+	2.11426i	−0.0340156	+	0.0751270i
$793$	32.6012			1.15770
$794$	−4.74172	−	8.21290i	−0.168277	−	0.291465i
$795$	−12.5699	+	8.10700i	−0.445809	+	0.287526i
$796$	21.7697	+	12.5687i	0.771606	+	0.445487i
$797$	−25.1385	+	43.5412i	−0.890452	+	1.54231i	−0.0511176	+	0.998693i	$0.516278\pi$
$797$	−25.1385	+	43.5412i	−0.890452	+	1.54231i	−0.839334	+	0.543615i	$0.817055\pi$
$798$	6.91482	+	40.3783i	0.244782	+	1.42938i
$799$	−11.1815	−	19.3669i	−0.395573	−	0.685153i
$800$		−	6.48799i		−	0.229385i
$801$	−19.4088	−	27.0698i	−0.685776	−	0.956463i
$802$	51.3805			1.81431
$803$	−2.05003	−	3.55075i	−0.0723439	−	0.125303i
$804$	−11.0900	+	0.546291i	−0.391114	+	0.0192662i
$805$	7.02523	+	9.35755i	0.247607	+	0.329810i
$806$	−1.57102	−	0.907028i	−0.0553368	−	0.0319487i
$807$	−5.62054	+	10.9458i	−0.197852	+	0.385312i
$808$	2.08249	−	1.20232i	0.0732616	−	0.0422976i
$809$			35.3803i			1.24391i	0.783055	+	0.621953i	$0.213661\pi$
$809$			35.3803i			1.24391i	−0.783055	+	0.621953i	$0.786339\pi$
$810$	−15.5600	−	5.27271i	−0.546724	−	0.185264i
$811$			3.52553i			0.123798i	0.998082	+	0.0618991i	$0.0197157\pi$
$811$			3.52553i			0.123798i	−0.998082	+	0.0618991i	$0.980284\pi$
$812$	0.402534	−	0.0486948i	0.0141262	−	0.00170885i
$813$	38.4301	+	19.7334i	1.34780	+	0.692079i
$814$	−6.24507	+	10.8168i	−0.218890	+	0.379128i
$815$	−9.44753	+	16.3636i	−0.330933	+	0.573192i
$816$	−23.9396	+	1.17926i	−0.838052	+	0.0412823i
$817$	−7.38636	+	4.26452i	−0.258416	+	0.149197i
$818$	64.0294			2.23873
$819$	24.4532	−	5.43806i	0.854462	−	0.190021i
$820$	2.96616			0.103583
$821$	−6.40672	+	3.69892i	−0.223596	+	0.129093i	−0.607614	−	0.794232i	$-0.707873\pi$
$821$	−6.40672	+	3.69892i	−0.223596	+	0.129093i	0.384018	+	0.923326i	$0.374540\pi$
$822$	21.6135	+	33.5118i	0.753858	+	1.16886i
$823$	−0.413321	+	0.715893i	−0.0144075	+	0.0249545i	−0.873139	−	0.487471i	$-0.837920\pi$
$823$	−0.413321	+	0.715893i	−0.0144075	+	0.0249545i	0.858732	+	0.512425i	$0.171253\pi$
$824$	−9.80227	+	16.9780i	−0.341478	+	0.591458i
$825$	−0.923868	+	0.595851i	−0.0321649	+	0.0207449i
$826$	−73.3643	+	8.87493i	−2.55267	+	0.308798i
$827$			4.54802i			0.158150i	0.996869	+	0.0790750i	$0.0251967\pi$
$827$			4.54802i			0.158150i	−0.996869	+	0.0790750i	$0.974803\pi$
$828$	16.1030	+	7.29105i	0.559619	+	0.253381i
$829$		−	5.00576i		−	0.173857i	−0.996215	−	0.0869286i	$-0.972295\pi$
$829$		−	5.00576i		−	0.173857i	0.996215	−	0.0869286i	$-0.0277052\pi$
$830$	7.11686	−	4.10892i	0.247030	−	0.142623i
$831$	12.7809	−	0.629583i	0.443363	−	0.0218400i
$832$	5.64244	+	3.25766i	0.195616	+	0.112939i
$833$	−19.2396	+	4.72399i	−0.666613	+	0.163676i
$834$	8.11715	−	15.8079i	0.281074	−	0.547383i
$835$	−6.20475	−	10.7469i	−0.214724	−	0.371913i
$836$	4.14113			0.143224
$837$	−1.52186	−	0.600693i	−0.0526030	−	0.0207630i
$838$		−	19.8010i		−	0.684013i
$839$	−7.84346	−	13.5853i	−0.270786	−	0.469016i	0.698277	−	0.715828i	$-0.253950\pi$
$839$	−7.84346	−	13.5853i	−0.270786	−	0.469016i	−0.969063	+	0.246812i	$0.920617\pi$
$840$	3.56920	+	4.29642i	0.123149	+	0.148241i
$841$	−14.4934	+	25.1033i	−0.499772	+	0.865630i
$842$	32.7886	+	18.9305i	1.12997	+	0.652389i
$843$	−0.449113	−	9.11723i	−0.0154683	−	0.314014i
$844$	−17.3070	−	29.9765i	−0.595730	−	1.03184i
$845$	3.03922			0.104552
$846$	4.25288	+	43.0631i	0.146217	+	1.48054i
$847$	−25.7889	−	11.0012i	−0.886119	−	0.378006i
$848$	36.5679	−	21.1125i	1.25575	−	0.725006i
$849$	33.3264	−	21.4939i	1.14376	−	0.737669i
$850$	−4.47417	−	2.58316i	−0.153463	−	0.0886018i
$851$	−41.2888	−	23.8381i	−1.41536	−	0.817159i
$852$	25.1608	−	16.2275i	0.861993	−	0.555945i
$853$	−20.9096	+	12.0722i	−0.715931	+	0.413343i	−0.813253	−	0.581910i	$-0.802306\pi$
$853$	−20.9096	+	12.0722i	−0.715931	+	0.413343i	0.0973224	+	0.995253i	$0.468972\pi$
$854$	45.8884	+	19.5754i	1.57027	+	0.669855i
$855$	−1.44389	−	14.6203i	−0.0493801	−	0.500004i
$856$	12.2818			0.419783
$857$	16.3837	+	28.3774i	0.559657	+	0.969354i	0.997525	+	0.0703148i	$0.0224004\pi$
$857$	16.3837	+	28.3774i	0.559657	+	0.969354i	−0.437868	+	0.899039i	$0.644266\pi$
$858$	−0.311617	−	6.32598i	−0.0106384	−	0.215965i
$859$	17.9251	+	10.3490i	0.611595	+	0.353105i	0.773589	−	0.633687i	$-0.218459\pi$
$859$	17.9251	+	10.3490i	0.611595	+	0.353105i	−0.161994	+	0.986792i	$0.551793\pi$
$860$	1.16018	−	2.00950i	0.0395620	−	0.0685234i
$861$	−7.84774	+	6.51941i	−0.267450	+	0.222181i
$862$	9.15679	+	15.8600i	0.311881	+	0.540194i
$863$		−	21.0272i		−	0.715774i	−0.933765	−	0.357887i	$-0.883497\pi$
$863$		−	21.0272i		−	0.715774i	0.933765	−	0.357887i	$-0.116503\pi$
$864$	31.3582	+	12.3774i	1.06683	+	0.421089i
$865$	12.2858			0.417729
$866$	10.8834	+	18.8507i	0.369834	+	0.640572i
$867$	7.11286	−	13.8521i	0.241565	−	0.470441i
$868$	−0.666366	−	0.887594i	−0.0226179	−	0.0301269i
$869$	−7.16747	−	4.13814i	−0.243140	−	0.140377i
$870$	−0.363257	+	0.0178940i	−0.0123156	+	0.000606662i
$871$	−13.1515	+	7.59300i	−0.445620	+	0.257279i
$872$		−	17.3700i		−	0.588222i
$873$	0.842394	+	0.381414i	0.0285107	+	0.0129089i
$874$			39.5363i			1.33733i
$875$	0.317742	+	2.62660i	0.0107416	+	0.0887954i
$876$	−12.5271	+	8.07936i	−0.423250	+	0.272976i
$877$	−1.25552	+	2.17463i	−0.0423960	+	0.0734320i	−0.886445	−	0.462834i	$-0.846832\pi$
$877$	−1.25552	+	2.17463i	−0.0423960	+	0.0734320i	0.844049	+	0.536266i	$0.180166\pi$
$878$	−22.9907	+	39.8211i	−0.775900	+	1.34390i
$879$	23.0188	+	35.6907i	0.776405	+	1.20382i
$880$	2.68768	−	1.55173i	0.0906016	−	0.0523089i
$881$	−24.5031			−0.825531			−0.412766	−	0.910837i	$-0.635437\pi$
$881$	−24.5031			−0.825531			−0.412766	+	0.910837i	$0.635437\pi$
$882$	37.6848	+	7.02843i	1.26891	+	0.236660i
$883$	−40.4938			−1.36273			−0.681363	−	0.731945i	$-0.738613\pi$
$883$	−40.4938			−1.36273			−0.681363	+	0.731945i	$0.738613\pi$
$884$	10.3059	−	5.95014i	0.346626	−	0.200125i
$885$	26.4700	−	1.30391i	0.889778	−	0.0438303i
$886$	20.2458	−	35.0667i	0.680171	−	1.17809i
$887$	12.4282	−	21.5262i	0.417297	−	0.722779i	−0.578370	−	0.815775i	$-0.696311\pi$
$887$	12.4282	−	21.5262i	0.417297	−	0.722779i	0.995667	+	0.0929957i	$0.0296443\pi$
$888$	−20.2452	−	10.3956i	−0.679383	−	0.348854i
$889$	1.46246	+	12.0894i	0.0490494	+	0.405465i
$890$			20.2679i			0.679382i
$891$	−1.11740	−	5.60203i	−0.0374345	−	0.187675i
$892$			30.8851i			1.03411i
$893$	−33.5115	+	19.3479i	−1.12142	+	0.647452i
$894$	18.0916	−	35.2328i	0.605072	−	1.17836i
$895$	−3.99071	−	2.30404i	−0.133395	−	0.0770155i
$896$	−14.6259	−	19.4816i	−0.488618	−	0.650835i
$897$	24.1469	−	1.18947i	0.806242	−	0.0397154i
$898$	−22.2010	−	38.4532i	−0.740856	−	1.28320i
$899$	−0.0362193			−0.00120798
$900$	2.32896	+	3.24824i	0.0776319	+	0.108275i
$901$		−	24.4404i		−	0.814227i
$902$	1.28977	+	2.23394i	0.0429445	+	0.0743821i
$903$	1.34717	+	7.86665i	0.0448310	+	0.261786i
$904$	−0.123757	+	0.214353i	−0.00411610	+	0.00712929i
$905$	14.1475	+	8.16805i	0.470278	+	0.271515i
$906$	23.6326	−	15.2419i	0.785142	−	0.506379i
$907$	7.71147	+	13.3567i	0.256055	+	0.443500i	0.965182	−	0.261581i	$-0.0842438\pi$
$907$	7.71147	+	13.3567i	0.256055	+	0.443500i	−0.709127	+	0.705081i	$0.750911\pi$
$908$	25.9876			0.862428
$909$	−2.44120	+	5.39165i	−0.0809695	+	0.178830i
$910$	−14.0205	−	5.98094i	−0.464775	−	0.198266i
$911$	−22.9764	+	13.2654i	−0.761243	+	0.439504i	−0.829742	−	0.558148i	$-0.811512\pi$
$911$	−22.9764	+	13.2654i	−0.761243	+	0.439504i	0.0684992	+	0.997651i	$0.478179\pi$
$912$	2.04052	+	41.4237i	0.0675685	+	1.37168i
$913$	2.47453	+	1.42867i	0.0818948	+	0.0472820i
$914$	−21.6294	−	12.4877i	−0.715436	−	0.413057i
$915$	−15.9159	−	8.17259i	−0.526163	−	0.270178i
$916$	−26.5714	+	15.3410i	−0.877943	+	0.506881i
$917$	−3.67634	−	1.56828i	−0.121404	−	0.0517891i
$918$	21.0207	−	16.6969i	0.693787	−	0.551078i
$919$	−14.6707			−0.483943			−0.241972	−	0.970283i	$-0.577794\pi$
$919$	−14.6707			−0.483943			−0.241972	+	0.970283i	$0.577794\pi$
$920$	2.69530	+	4.66840i	0.0888615	+	0.153913i
$921$	36.8396	+	18.9166i	1.21390	+	0.623324i
$922$	−44.1461	−	25.4877i	−1.45387	−	0.839394i
$923$	20.4741	−	35.4622i	0.673914	−	1.16725i
$924$	1.34330	−	3.63485i	0.0441912	−	0.119578i
$925$	−5.39002	−	9.33580i	−0.177223	−	0.306959i
$926$		−	18.9662i		−	0.623267i
$927$	−4.74233	−	48.0191i	−0.155759	−	1.57715i
$928$	0.746307			0.0244987
$929$	−5.60554	−	9.70909i	−0.183912	−	0.318545i	0.759297	−	0.650744i	$-0.225543\pi$
$929$	−5.60554	−	9.70909i	−0.183912	−	0.318545i	−0.943209	+	0.332199i	$0.892209\pi$
$930$	0.539593	+	0.836640i	0.0176940	+	0.0274345i
$931$	8.17413	+	33.2912i	0.267896	+	1.09107i
$932$	21.0570	+	12.1572i	0.689744	+	0.398224i
$933$	22.4924	+	34.8745i	0.736368	+	1.14174i
$934$	21.1802	−	12.2284i	0.693037	−	0.400125i
$935$		−	1.79633i		−	0.0587462i
$936$	11.4846	−	1.13421i	0.375387	−	0.0370729i
$937$			9.04669i			0.295543i	0.989022	+	0.147771i	$0.0472099\pi$
$937$			9.04669i			0.295543i	−0.989022	+	0.147771i	$0.952790\pi$
$938$	−23.0708	+	2.79089i	−0.753288	+	0.0911257i
$939$	−1.99705	−	40.5411i	−0.0651713	−	1.32301i
$940$	5.26369	−	9.11698i	0.171683	−	0.297363i
$941$	25.3643	−	43.9322i	0.826851	−	1.43215i	−0.0736454	−	0.997284i	$-0.523463\pi$
$941$	25.3643	−	43.9322i	0.826851	−	1.43215i	0.900496	−	0.434863i	$-0.143203\pi$
$942$	2.45824	−	4.78734i	0.0800937	−	0.155980i
$943$	−8.52719	+	4.92317i	−0.277683	+	0.160321i
$944$	−74.8153			−2.43503
$945$	−13.3013	−	3.47516i	−0.432690	−	0.113047i
$946$	2.01792			0.0656082
$947$	−7.30505	+	4.21757i	−0.237382	+	0.137053i	−0.613973	−	0.789327i	$-0.710430\pi$
$947$	−7.30505	+	4.21757i	−0.237382	+	0.137053i	0.376591	+	0.926380i	$0.377096\pi$
$948$	−13.7446	+	26.7673i	−0.446405	+	0.869361i
$949$	−10.1937	+	17.6560i	−0.330901	+	0.573137i
$950$	−4.46977	+	7.74186i	−0.145018	+	0.251179i
$951$	0.00611281	+	0.124093i	0.000198222	+	0.00402400i
$952$	−9.06068	+	1.09608i	−0.293658	+	0.0355240i
$953$			7.58700i			0.245767i	0.992421	+	0.122884i	$0.0392142\pi$
$953$			7.58700i			0.245767i	−0.992421	+	0.122884i	$0.960786\pi$
$954$	−19.5065	+	43.0821i	−0.631545	+	1.39483i
$955$		−	24.2558i		−	0.784898i
$956$	−21.3947	+	12.3522i	−0.691953	+	0.399500i
$957$	−0.0685402	−	0.106272i	−0.00221559	−	0.00343528i
$958$	−9.76873	−	5.63998i	−0.315613	−	0.182219i
$959$	20.0342	+	26.6854i	0.646937	+	0.861715i
$960$	−1.93799	−	3.00486i	−0.0625484	−	0.0969814i
$961$	−15.4504	−	26.7609i	−0.498401	−	0.863256i
$962$	62.1068			2.00240
$963$	−24.5670	+	17.6143i	−0.791661	+	0.567614i
$964$		−	9.53385i		−	0.307065i
$965$	6.56678	+	11.3740i	0.211392	+	0.366142i
$966$	34.7027	+	12.8247i	1.11654	+	0.412629i
$967$	10.2508	−	17.7549i	0.329643	−	0.570958i	−0.652798	−	0.757532i	$-0.726405\pi$
$967$	10.2508	−	17.7549i	0.329643	−	0.570958i	0.982441	+	0.186574i	$0.0597383\pi$
$968$	−11.1860	−	6.45826i	−0.359533	−	0.207576i
$969$	21.3549	+	10.9654i	0.686018	+	0.352261i
$970$	−0.281339	−	0.487293i	−0.00903325	−	0.0156460i
$971$	−14.4194			−0.462741			−0.231370	−	0.972866i	$-0.574321\pi$
$971$	−14.4194			−0.462741			−0.231370	+	0.972866i	$0.574321\pi$
$972$	−20.1427	+	5.05968i	−0.646076	+	0.162289i
$973$	5.83458	−	13.6774i	0.187048	−	0.438477i
$974$	17.5366	−	10.1248i	0.561909	−	0.324418i
$975$	4.86285	+	2.49701i	0.155736	+	0.0799683i
$976$	43.7410	+	25.2539i	1.40012	+	0.808357i
$977$	−7.27578	−	4.20067i	−0.232773	−	0.134391i	0.379078	−	0.925365i	$-0.376241\pi$
$977$	−7.27578	−	4.20067i	−0.232773	−	0.134391i	−0.611851	+	0.790973i	$0.709575\pi$
$978$	2.93932	+	59.6698i	0.0939892	+	1.90803i
$979$	−6.10300	+	3.52357i	−0.195053	+	0.112614i
$980$	−6.45440	−	6.73172i	−0.206178	−	0.215037i
$981$	24.9118	+	34.7449i	0.795372	+	1.10932i
$982$	−1.63990			−0.0523312
$983$	1.36690	+	2.36754i	0.0435973	+	0.0755127i	0.887001	−	0.461768i	$-0.152785\pi$
$983$	1.36690	+	2.36754i	0.0435973	+	0.0755127i	−0.843403	+	0.537281i	$0.819451\pi$
$984$	−3.94989	+	2.54749i	−0.125918	+	0.0812112i
$985$	−3.26329	−	1.88406i	−0.103977	−	0.0600312i
$986$	0.297139	−	0.514660i	0.00946283	−	0.0163901i
$987$	6.11204	+	35.6905i	0.194548	+	1.13604i
$988$	−10.2958	−	17.8328i	−0.327553	−	0.567338i
$989$			7.70261i			0.244929i
$990$	−1.43369	+	3.16646i	−0.0455657	+	0.100637i
$991$	−42.1641			−1.33939			−0.669693	−	0.742638i	$-0.733574\pi$
$991$	−42.1641			−1.33939			−0.669693	+	0.742638i	$0.733574\pi$
$992$	−1.02144	−	1.76918i	−0.0324307	−	0.0561716i
$993$	−18.3471	+	0.903775i	−0.582228	+	0.0286804i
$994$	50.1120	−	37.6219i	1.58946	−	1.19329i
$995$	−16.3400	−	9.43389i	−0.518012	−	0.299075i
$996$	4.74526	−	9.24124i	0.150359	−	0.292820i
$997$	27.5027	−	15.8787i	0.871019	−	0.502883i	0.00333236	−	0.999994i	$-0.498939\pi$
$997$	27.5027	−	15.8787i	0.871019	−	0.502883i	0.867687	+	0.497111i	$0.165606\pi$
$998$		−	62.3038i		−	1.97219i
$999$	55.4052	−	8.24112i	1.75294	−	0.260738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bl.j.41.9	yes	24
3.2	odd	2		945.2.bl.j.881.4		24
7.6	odd	2		315.2.bl.i.41.9	✓	24
9.2	odd	6		315.2.bl.i.146.9	yes	24
9.7	even	3		945.2.bl.i.251.4		24
21.20	even	2		945.2.bl.i.881.4		24
63.20	even	6	inner	315.2.bl.j.146.9	yes	24
63.34	odd	6		945.2.bl.j.251.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bl.i.41.9	✓	24	7.6	odd	2
315.2.bl.i.146.9	yes	24	9.2	odd	6
315.2.bl.j.41.9	yes	24	1.1	even	1	trivial
315.2.bl.j.146.9	yes	24	63.20	even	6	inner
945.2.bl.i.251.4		24	9.7	even	3
945.2.bl.i.881.4		24	21.20	even	2
945.2.bl.j.251.4		24	63.34	odd	6
945.2.bl.j.881.4		24	3.2	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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58089 - 0.912729i) q^{2} +(-0.791176 + 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.155560 + 3.15796i) q^{6} +(0.317742 + 2.62660i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} +O(q^{10})\)	\(q+(1.58089 - 0.912729i) q^{2} +(-0.791176 + 1.54079i) q^{3} +(0.666147 - 1.15380i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.155560 + 3.15796i) q^{6} +(0.317742 + 2.62660i) q^{7} +1.21887i q^{8} +(-1.74808 - 2.43808i) q^{9} +1.82546i q^{10} +(-0.549675 + 0.317355i) q^{11} +(1.25073 + 1.93925i) q^{12} +(2.73324 + 1.57804i) q^{13} +(2.89969 + 3.86236i) q^{14} +(-0.938777 - 1.45557i) q^{15} +(2.44479 + 4.23450i) q^{16} +2.83015 q^{17} +(-4.98883 - 2.25881i) q^{18} -4.89715i q^{19} +(0.666147 + 1.15380i) q^{20} +(-4.29844 - 1.58853i) q^{21} +(-0.579318 + 1.00341i) q^{22} +(-3.83011 - 2.21132i) q^{23} +(-1.87802 - 0.964339i) q^{24} +(-0.500000 - 0.866025i) q^{25} +5.76127 q^{26} +(5.13961 - 0.764479i) q^{27} +(3.24224 + 1.38309i) q^{28} +(0.0996181 - 0.0575146i) q^{29} +(-2.81265 - 1.44426i) q^{30} +(-0.272686 - 0.157435i) q^{31} +(5.61876 + 3.24399i) q^{32} +(-0.0540882 - 1.09802i) q^{33} +(4.47417 - 2.58316i) q^{34} +(-2.43358 - 1.03813i) q^{35} +(-3.97753 + 0.392818i) q^{36} +10.7800 q^{37} +(-4.46977 - 7.74186i) q^{38} +(-4.59390 + 2.96285i) q^{39} +(-1.05557 - 0.609434i) q^{40} +(1.11318 - 1.92808i) q^{41} +(-8.24527 + 1.41201i) q^{42} +(-0.870817 - 1.50830i) q^{43} +0.845620i q^{44} +(2.98548 - 0.294843i) q^{45} -8.07333 q^{46} +(-3.95084 - 6.84306i) q^{47} +(-8.45874 + 0.416676i) q^{48} +(-6.79808 + 1.66916i) q^{49} +(-1.58089 - 0.912729i) q^{50} +(-2.23915 + 4.36068i) q^{51} +(3.64148 - 2.10241i) q^{52} -8.63571i q^{53} +(7.42741 - 5.89963i) q^{54} -0.634710i q^{55} +(-3.20148 + 0.387285i) q^{56} +(7.54548 + 3.87451i) q^{57} +(0.104990 - 0.181849i) q^{58} +(-7.65048 + 13.2510i) q^{59} +(-2.30481 + 0.113534i) q^{60} +(8.94576 - 5.16484i) q^{61} -0.574783 q^{62} +(5.84842 - 5.36619i) q^{63} +2.06438 q^{64} +(-2.73324 + 1.57804i) q^{65} +(-1.08770 - 1.68648i) q^{66} +(-2.40584 + 4.16704i) q^{67} +(1.88530 - 3.26543i) q^{68} +(6.43747 - 4.15186i) q^{69} +(-4.79475 + 0.580024i) q^{70} -12.9744i q^{71} +(2.97169 - 2.13068i) q^{72} +6.45973i q^{73} +(17.0421 - 9.83926i) q^{74} +(1.72995 - 0.0852172i) q^{75} +(-5.65033 - 3.26222i) q^{76} +(-1.00822 - 1.34294i) q^{77} +(-4.55818 + 8.87692i) q^{78} +(6.51973 + 11.2925i) q^{79} -4.88958 q^{80} +(-2.88843 + 8.52391i) q^{81} -4.06412i q^{82} +(-2.25090 - 3.89867i) q^{83} +(-4.69624 + 3.90135i) q^{84} +(-1.41508 + 2.45099i) q^{85} +(-2.75334 - 1.58964i) q^{86} +(0.00980246 + 0.198995i) q^{87} +(-0.386814 - 0.669981i) q^{88} +11.1029 q^{89} +(4.45060 - 3.19105i) q^{90} +(-3.27641 + 7.68054i) q^{91} +(-5.10284 + 2.94612i) q^{92} +(0.458318 - 0.295593i) q^{93} +(-12.4917 - 7.21210i) q^{94} +(4.24105 + 2.44857i) q^{95} +(-9.44375 + 6.09077i) q^{96} +(-0.266943 + 0.154120i) q^{97} +(-9.22354 + 8.84357i) q^{98} +(1.73461 + 0.785387i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9	\( 24 q + 6 q^{2} + 5 q^{3} + 18 q^{4} - 12 q^{5} + q^{6} + 9 q^{7} + q^{9} + 9 q^{11} - 18 q^{12} + 3 q^{13} + 18 q^{14} + 2 q^{15} - 18 q^{16} + 18 q^{17} + 2 q^{18} + 18 q^{20} + 8 q^{21} - 9 q^{22} + 9 q^{23} - 7 q^{24} - 12 q^{25} - 18 q^{26} - 4 q^{27} - 9 q^{28} + 9 q^{29} - 5 q^{30} - 42 q^{31} + 18 q^{32} + 13 q^{33} - 39 q^{34} - 9 q^{35} - 21 q^{36} - 12 q^{38} - 21 q^{39} - 6 q^{40} - 33 q^{41} - 65 q^{42} + 18 q^{43} + q^{45} - 30 q^{46} - 17 q^{48} + 9 q^{49} - 6 q^{50} - 12 q^{51} + 129 q^{52} + 52 q^{54} - 9 q^{56} + 6 q^{57} - 15 q^{58} + 12 q^{59} + 15 q^{60} - 15 q^{61} + 12 q^{62} + 46 q^{63} - 60 q^{64} - 3 q^{65} + 29 q^{66} - 15 q^{67} + 9 q^{68} + 61 q^{69} - 9 q^{70} + 61 q^{72} - 18 q^{74} - 7 q^{75} + 54 q^{76} - 45 q^{77} - 66 q^{78} + 21 q^{79} + 36 q^{80} + q^{81} - 30 q^{83} + 15 q^{84} - 9 q^{85} - 102 q^{86} + 10 q^{87} - 9 q^{88} + 102 q^{89} - 37 q^{90} + 42 q^{91} - 3 q^{92} - 6 q^{93} - 156 q^{94} - 18 q^{95} - 42 q^{96} - 45 q^{97} + 3 q^{98} + 23 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 5 * q^3 + 18 * q^4 - 12 * q^5 + q^6 + 9 * q^7 + q^9 + 9 * q^11 - 18 * q^12 + 3 * q^13 + 18 * q^14 + 2 * q^15 - 18 * q^16 + 18 * q^17 + 2 * q^18 + 18 * q^20 + 8 * q^21 - 9 * q^22 + 9 * q^23 - 7 * q^24 - 12 * q^25 - 18 * q^26 - 4 * q^27 - 9 * q^28 + 9 * q^29 - 5 * q^30 - 42 * q^31 + 18 * q^32 + 13 * q^33 - 39 * q^34 - 9 * q^35 - 21 * q^36 - 12 * q^38 - 21 * q^39 - 6 * q^40 - 33 * q^41 - 65 * q^42 + 18 * q^43 + q^45 - 30 * q^46 - 17 * q^48 + 9 * q^49 - 6 * q^50 - 12 * q^51 + 129 * q^52 + 52 * q^54 - 9 * q^56 + 6 * q^57 - 15 * q^58 + 12 * q^59 + 15 * q^60 - 15 * q^61 + 12 * q^62 + 46 * q^63 - 60 * q^64 - 3 * q^65 + 29 * q^66 - 15 * q^67 + 9 * q^68 + 61 * q^69 - 9 * q^70 + 61 * q^72 - 18 * q^74 - 7 * q^75 + 54 * q^76 - 45 * q^77 - 66 * q^78 + 21 * q^79 + 36 * q^80 + q^81 - 30 * q^83 + 15 * q^84 - 9 * q^85 - 102 * q^86 + 10 * q^87 - 9 * q^88 + 102 * q^89 - 37 * q^90 + 42 * q^91 - 3 * q^92 - 6 * q^93 - 156 * q^94 - 18 * q^95 - 42 * q^96 - 45 * q^97 + 3 * q^98 + 23 * q^99

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