LMFDB - Embedded newform 85.2.l.a.76.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,2,Mod(26,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("85.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$85 = 5 \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	85.l (of order $8$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.678728417181$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			76.4
Character	$\chi$	$=$	85.76
Dual form			85.2.l.a.66.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.680853 - 0.680853i) q^{2} +(-1.01372 + 2.44733i) q^{3} +1.07288i q^{4} +(-0.923880 - 0.382683i) q^{5} +(0.976080 + 2.35647i) q^{6} +(2.85906 - 1.18426i) q^{7} +(2.09218 + 2.09218i) q^{8} +(-2.84049 - 2.84049i) q^{9} +(-0.889577 + 0.368475i) q^{10} +(-2.34612 - 5.66403i) q^{11} +(-2.62569 - 1.08760i) q^{12} +1.16017i q^{13} +(1.14029 - 2.75291i) q^{14} +(1.87311 - 1.87311i) q^{15} +0.703170 q^{16} +(1.25804 + 3.92649i) q^{17} -3.86791 q^{18} +(3.83665 - 3.83665i) q^{19} +(0.410573 - 0.991211i) q^{20} +8.19759i q^{21} +(-5.45373 - 2.25901i) q^{22} +(-1.19300 - 2.88015i) q^{23} +(-7.24113 + 2.99938i) q^{24} +(0.707107 + 0.707107i) q^{25} +(0.789908 + 0.789908i) q^{26} +(2.48908 - 1.03101i) q^{27} +(1.27057 + 3.06743i) q^{28} +(-4.61660 - 1.91226i) q^{29} -2.55062i q^{30} +(-1.42666 + 3.44426i) q^{31} +(-3.70560 + 3.70560i) q^{32} +16.2401 q^{33} +(3.52990 + 1.81682i) q^{34} -3.09463 q^{35} +(3.04750 - 3.04750i) q^{36} +(-0.151817 + 0.366518i) q^{37} -5.22439i q^{38} +(-2.83933 - 1.17609i) q^{39} +(-1.13228 - 2.73356i) q^{40} +(1.57303 - 0.651568i) q^{41} +(5.58135 + 5.58135i) q^{42} +(0.0189720 + 0.0189720i) q^{43} +(6.07683 - 2.51710i) q^{44} +(1.53726 + 3.71128i) q^{45} +(-2.77321 - 1.14870i) q^{46} -5.43715i q^{47} +(-0.712817 + 1.72089i) q^{48} +(1.82202 - 1.82202i) q^{49} +0.962871 q^{50} +(-10.8847 - 0.901513i) q^{51} -1.24473 q^{52} +(-0.244014 + 0.244014i) q^{53} +(0.992732 - 2.39667i) q^{54} +6.13071i q^{55} +(8.45936 + 3.50398i) q^{56} +(5.50028 + 13.2788i) q^{57} +(-4.44519 + 1.84126i) q^{58} +(2.87128 + 2.87128i) q^{59} +(2.00962 + 2.00962i) q^{60} +(-11.4953 + 4.76149i) q^{61} +(1.37369 + 3.31638i) q^{62} +(-11.4850 - 4.75726i) q^{63} +6.45228i q^{64} +(0.443980 - 1.07186i) q^{65} +(11.0571 - 11.0571i) q^{66} -5.62508 q^{67} +(-4.21265 + 1.34973i) q^{68} +8.25804 q^{69} +(-2.10699 + 2.10699i) q^{70} +(4.12510 - 9.95888i) q^{71} -11.8856i q^{72} +(-1.52840 - 0.633083i) q^{73} +(0.146180 + 0.352909i) q^{74} +(-2.44733 + 1.01372i) q^{75} +(4.11627 + 4.11627i) q^{76} +(-13.4154 - 13.4154i) q^{77} +(-2.73391 + 1.13242i) q^{78} +(2.01785 + 4.87153i) q^{79} +(-0.649645 - 0.269092i) q^{80} -4.91441i q^{81} +(0.627376 - 1.51462i) q^{82} +(-8.78638 + 8.78638i) q^{83} -8.79502 q^{84} +(0.340325 - 4.10904i) q^{85} +0.0258342 q^{86} +(9.35987 - 9.35987i) q^{87} +(6.94167 - 16.7587i) q^{88} +3.22930i q^{89} +(3.57348 + 1.48019i) q^{90} +(1.37395 + 3.31701i) q^{91} +(3.09005 - 1.27994i) q^{92} +(-6.98302 - 6.98302i) q^{93} +(-3.70190 - 3.70190i) q^{94} +(-5.01283 + 2.07638i) q^{95} +(-5.31240 - 12.8253i) q^{96} +(11.9502 + 4.94995i) q^{97} -2.48105i q^{98} +(-9.42450 + 22.7528i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$24 q - 8 q^{6} - 24 q^{9} - 8 q^{11} + 24 q^{12} - 8 q^{15} - 24 q^{16} - 8 q^{17} + 8 q^{18} - 8 q^{19} - 32 q^{22} - 16 q^{23} - 8 q^{24} + 16 q^{26} + 24 q^{27} + 48 q^{28} - 8 q^{29} + 16 q^{34} - 32 q^{35}+ \cdots - 8 q^{99}+O(q^{100})$ 24 * q - 8 * q^6 - 24 * q^9 - 8 * q^11 + 24 * q^12 - 8 * q^15 - 24 * q^16 - 8 * q^17 + 8 * q^18 - 8 * q^19 - 32 * q^22 - 16 * q^23 - 8 * q^24 + 16 * q^26 + 24 * q^27 + 48 * q^28 - 8 * q^29 + 16 * q^34 - 32 * q^35 - 24 * q^36 + 24 * q^37 + 8 * q^39 + 16 * q^40 + 16 * q^41 - 24 * q^42 + 8 * q^43 + 16 * q^44 + 16 * q^45 + 8 * q^46 + 80 * q^48 + 8 * q^50 - 56 * q^51 - 48 * q^52 + 24 * q^53 - 32 * q^54 + 64 * q^56 + 32 * q^57 - 64 * q^58 + 32 * q^59 + 24 * q^60 + 32 * q^61 - 32 * q^62 - 56 * q^63 + 8 * q^65 + 96 * q^66 + 16 * q^67 - 40 * q^68 + 96 * q^69 - 24 * q^71 - 64 * q^74 - 8 * q^75 - 8 * q^76 + 24 * q^77 - 112 * q^78 - 32 * q^80 - 80 * q^82 - 96 * q^83 - 64 * q^84 - 16 * q^86 - 48 * q^87 - 8 * q^88 - 24 * q^91 + 80 * q^92 + 64 * q^93 + 56 * q^94 - 16 * q^95 - 168 * q^96 - 40 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$ .

$n$	$52$	$71$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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

)

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

$2$	0.680853	−	0.680853i	0.481435	−	0.481435i	−0.424154	−	0.905590i	$-0.639429\pi$
$2$	0.680853	−	0.680853i	0.481435	−	0.481435i	0.905590	+	0.424154i	$0.139429\pi$
$3$	−1.01372	+	2.44733i	−0.585271	+	1.41297i	0.302708	+	0.953083i	$0.402109\pi$
$3$	−1.01372	+	2.44733i	−0.585271	+	1.41297i	−0.887979	+	0.459885i	$0.847891\pi$
$4$			1.07288i			0.536440i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$5$	−0.923880	−	0.382683i	−0.413171	−	0.171141i
$6$	0.976080	+	2.35647i	0.398483	+	0.962023i
$7$	2.85906	−	1.18426i	1.08062	−	0.447609i	0.229896	−	0.973215i	$-0.426161\pi$
$7$	2.85906	−	1.18426i	1.08062	−	0.447609i	0.850728	+	0.525606i	$0.176161\pi$
$8$	2.09218	+	2.09218i	0.739697	+	0.739697i
$9$	−2.84049	−	2.84049i	−0.946830	−	0.946830i
$10$	−0.889577	+	0.368475i	−0.281309	+	0.116522i
$11$	−2.34612	−	5.66403i	−0.707382	−	1.70777i	−0.706442	−	0.707771i	$-0.749701\pi$
$11$	−2.34612	−	5.66403i	−0.707382	−	1.70777i	−0.000939675	−	1.00000i	$-0.500299\pi$
$12$	−2.62569	−	1.08760i	−0.757972	−	0.313962i
$13$			1.16017i			0.321775i	0.986973	+	0.160887i	$0.0514356\pi$
$13$			1.16017i			0.321775i	−0.986973	+	0.160887i	$0.948564\pi$
$14$	1.14029	−	2.75291i	0.304756	−	0.735746i
$15$	1.87311	−	1.87311i	0.483634	−	0.483634i
$16$	0.703170			0.175793
$17$	1.25804	+	3.92649i	0.305120	+	0.952314i
$17$	1.25804	+	3.92649i	0.305120	+	0.952314i
$18$	−3.86791			−0.911675
$19$	3.83665	−	3.83665i	0.880188	−	0.880188i	−0.113365	−	0.993553i	$-0.536163\pi$
$19$	3.83665	−	3.83665i	0.880188	−	0.880188i	0.993553	+	0.113365i	$0.0361629\pi$
$20$	0.410573	−	0.991211i	0.0918070	−	0.221642i
$21$			8.19759i			1.78886i
$22$	−5.45373	−	2.25901i	−1.16274	−	0.481623i
$23$	−1.19300	−	2.88015i	−0.248757	−	0.600552i	0.749342	−	0.662183i	$-0.230370\pi$
$23$	−1.19300	−	2.88015i	−0.248757	−	0.600552i	−0.998099	+	0.0616306i	$0.980370\pi$
$24$	−7.24113	+	2.99938i	−1.47809	+	0.612245i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	0.789908	+	0.789908i	0.154914	+	0.154914i
$27$	2.48908	−	1.03101i	0.479025	−	0.198418i
$28$	1.27057	+	3.06743i	0.240115	+	0.579690i
$29$	−4.61660	−	1.91226i	−0.857282	−	0.355098i	−0.0896380	−	0.995974i	$-0.528571\pi$
$29$	−4.61660	−	1.91226i	−0.857282	−	0.355098i	−0.767644	+	0.640877i	$0.778571\pi$
$30$		−	2.55062i		−	0.465677i
$31$	−1.42666	+	3.44426i	−0.256236	+	0.618608i	−0.998683	−	0.0512962i	$-0.983665\pi$
$31$	−1.42666	+	3.44426i	−0.256236	+	0.618608i	0.742448	+	0.669904i	$0.233665\pi$
$32$	−3.70560	+	3.70560i	−0.655064	+	0.655064i
$33$	16.2401			2.82703
$34$	3.52990	+	1.81682i	0.605373	+	0.311582i
$35$	−3.09463			−0.523088
$36$	3.04750	−	3.04750i	0.507917	−	0.507917i
$37$	−0.151817	+	0.366518i	−0.0249585	+	0.0602551i	−0.935867	−	0.352352i	$-0.885382\pi$
$37$	−0.151817	+	0.366518i	−0.0249585	+	0.0602551i	0.910909	+	0.412607i	$0.135382\pi$
$38$		−	5.22439i		−	0.847508i
$39$	−2.83933	−	1.17609i	−0.454657	−	0.188325i
$40$	−1.13228	−	2.73356i	−0.179029	−	0.432214i
$41$	1.57303	−	0.651568i	0.245665	−	0.101758i	−0.256453	−	0.966557i	$-0.582554\pi$
$41$	1.57303	−	0.651568i	0.245665	−	0.101758i	0.502119	+	0.864799i	$0.332554\pi$
$42$	5.58135	+	5.58135i	0.861221	+	0.861221i
$43$	0.0189720	+	0.0189720i	0.00289320	+	0.00289320i	0.708552	−	0.705659i	$-0.249349\pi$
$43$	0.0189720	+	0.0189720i	0.00289320	+	0.00289320i	−0.705659	+	0.708552i	$0.749349\pi$
$44$	6.07683	−	2.51710i	0.916116	−	0.379468i
$45$	1.53726	+	3.71128i	0.229162	+	0.553245i
$46$	−2.77321	−	1.14870i	−0.408888	−	0.169367i
$47$		−	5.43715i		−	0.793090i	−0.918015	−	0.396545i	$-0.870209\pi$
$47$		−	5.43715i		−	0.793090i	0.918015	−	0.396545i	$-0.129791\pi$
$48$	−0.712817	+	1.72089i	−0.102886	+	0.248389i
$49$	1.82202	−	1.82202i	0.260288	−	0.260288i
$50$	0.962871			0.136171
$51$	−10.8847	−	0.901513i	−1.52417	−	0.126237i
$52$	−1.24473			−0.172613
$53$	−0.244014	+	0.244014i	−0.0335179	+	0.0335179i	−0.723667	−	0.690149i	$-0.757545\pi$
$53$	−0.244014	+	0.244014i	−0.0335179	+	0.0335179i	0.690149	+	0.723667i	$0.257545\pi$
$54$	0.992732	−	2.39667i	0.135094	−	0.326145i
$55$			6.13071i			0.826664i
$56$	8.45936	+	3.50398i	1.13043	+	0.468239i
$57$	5.50028	+	13.2788i	0.728530	+	1.75883i
$58$	−4.44519	+	1.84126i	−0.583683	+	0.241769i
$59$	2.87128	+	2.87128i	0.373808	+	0.373808i	0.868862	−	0.495054i	$-0.164852\pi$
$59$	2.87128	+	2.87128i	0.373808	+	0.373808i	−0.495054	+	0.868862i	$0.664852\pi$
$60$	2.00962	+	2.00962i	0.259441	+	0.259441i
$61$	−11.4953	+	4.76149i	−1.47182	+	0.609646i	−0.967273	−	0.253740i	$-0.918339\pi$
$61$	−11.4953	+	4.76149i	−1.47182	+	0.609646i	−0.504544	+	0.863386i	$0.668339\pi$
$62$	1.37369	+	3.31638i	0.174459	+	0.421181i
$63$	−11.4850	−	4.75726i	−1.44698	−	0.599358i
$64$			6.45228i			0.806534i
$65$	0.443980	−	1.07186i	0.0550689	−	0.132948i
$66$	11.0571	−	11.0571i	1.36103	−	1.36103i
$67$	−5.62508			−0.687213			−0.343607	−	0.939114i	$-0.611649\pi$
$67$	−5.62508			−0.687213			−0.343607	+	0.939114i	$0.611649\pi$
$68$	−4.21265	+	1.34973i	−0.510859	+	0.163678i
$69$	8.25804			0.994152
$70$	−2.10699	+	2.10699i	−0.251833	+	0.251833i
$71$	4.12510	−	9.95888i	0.489560	−	1.18190i	−0.465383	−	0.885110i	$-0.654083\pi$
$71$	4.12510	−	9.95888i	0.489560	−	1.18190i	0.954942	−	0.296792i	$-0.0959167\pi$
$72$		−	11.8856i		−	1.40073i
$73$	−1.52840	−	0.633083i	−0.178886	−	0.0740968i	0.291443	−	0.956588i	$-0.405865\pi$
$73$	−1.52840	−	0.633083i	−0.178886	−	0.0740968i	−0.470329	+	0.882491i	$0.655865\pi$
$74$	0.146180	+	0.352909i	0.0169931	+	0.0410249i
$75$	−2.44733	+	1.01372i	−0.282594	+	0.117054i
$76$	4.11627	+	4.11627i	0.472168	+	0.472168i
$77$	−13.4154	−	13.4154i	−1.52883	−	1.52883i
$78$	−2.73391	+	1.13242i	−0.309554	+	0.128222i
$79$	2.01785	+	4.87153i	0.227026	+	0.548090i	0.995813	−	0.0914157i	$-0.0291392\pi$
$79$	2.01785	+	4.87153i	0.227026	+	0.548090i	−0.768787	+	0.639505i	$0.779139\pi$
$80$	−0.649645	−	0.269092i	−0.0726325	−	0.0300854i
$81$		−	4.91441i		−	0.546045i
$82$	0.627376	−	1.51462i	0.0692821	−	0.167262i
$83$	−8.78638	+	8.78638i	−0.964430	+	0.964430i	−0.999389	−	0.0349583i	$-0.988870\pi$
$83$	−8.78638	+	8.78638i	−0.964430	+	0.964430i	0.0349583	+	0.999389i	$0.488870\pi$
$84$	−8.79502			−0.959616
$85$	0.340325	−	4.10904i	0.0369135	−	0.445688i
$86$	0.0258342			0.00278577
$87$	9.35987	−	9.35987i	1.00348	−	1.00348i
$88$	6.94167	−	16.7587i	0.739984	−	1.78648i
$89$			3.22930i			0.342305i	0.985245	+	0.171152i	$0.0547490\pi$
$89$			3.22930i			0.342305i	−0.985245	+	0.171152i	$0.945251\pi$
$90$	3.57348	+	1.48019i	0.376678	+	0.156025i
$91$	1.37395	+	3.31701i	0.144029	+	0.347717i
$92$	3.09005	−	1.27994i	0.322160	−	0.133443i
$93$	−6.98302	−	6.98302i	−0.724106	−	0.724106i
$94$	−3.70190	−	3.70190i	−0.381822	−	0.381822i
$95$	−5.01283	+	2.07638i	−0.514305	+	0.213032i
$96$	−5.31240	−	12.8253i	−0.542195	−	1.30897i
$97$	11.9502	+	4.94995i	1.21336	+	0.502592i	0.895294	−	0.445476i	$-0.146965\pi$
$97$	11.9502	+	4.94995i	1.21336	+	0.502592i	0.318070	+	0.948067i	$0.396965\pi$
$98$		−	2.48105i		−	0.250624i
$99$	−9.42450	+	22.7528i	−0.947198	+	2.28674i
$100$	−0.758640	+	0.758640i	−0.0758640	+	0.0758640i
$101$	1.46947			0.146218			0.0731088	−	0.997324i	$-0.476708\pi$
$101$	1.46947			0.146218			0.0731088	+	0.997324i	$0.476708\pi$
$102$	−8.02469	+	6.79710i	−0.794563	+	0.673013i
$103$	9.80978			0.966586			0.483293	−	0.875459i	$-0.339441\pi$
$103$	9.80978			0.966586			0.483293	+	0.875459i	$0.339441\pi$
$104$	−2.42729	+	2.42729i	−0.238016	+	0.238016i
$105$	3.13708	−	7.57358i	0.306148	−	0.739106i
$106$			0.332275i			0.0322734i
$107$	−2.66763	−	1.10497i	−0.257889	−	0.106821i	0.249993	−	0.968248i	$-0.419572\pi$
$107$	−2.66763	−	1.10497i	−0.257889	−	0.106821i	−0.507882	+	0.861426i	$0.669572\pi$
$108$	1.10615	+	2.67049i	0.106440	+	0.256968i
$109$	5.32460	−	2.20552i	0.510004	−	0.211251i	−0.112816	−	0.993616i	$-0.535987\pi$
$109$	5.32460	−	2.20552i	0.510004	−	0.211251i	0.622820	+	0.782365i	$0.285987\pi$
$110$	4.17411	+	4.17411i	0.397985	+	0.397985i
$111$	−0.743091	−	0.743091i	−0.0705311	−	0.0705311i
$112$	2.01041	−	0.832738i	0.189966	−	0.0786864i
$113$	3.45197	+	8.33379i	0.324734	+	0.783977i	0.998966	+	0.0454578i	$0.0144747\pi$
$113$	3.45197	+	8.33379i	0.324734	+	0.783977i	−0.674232	+	0.738519i	$0.735525\pi$
$114$	12.7858	+	5.29606i	1.19750	+	0.496021i
$115$			3.11745i			0.290704i
$116$	2.05162	−	4.95306i	0.190489	−	0.459880i
$117$	3.29547	−	3.29547i	0.304666	−	0.304666i
$118$	3.90983			0.359929
$119$	8.24682	+	9.73624i	0.755984	+	0.892519i
$120$	7.83775			0.715485
$121$	−18.7988	+	18.7988i	−1.70898	+	1.70898i
$122$	−4.58470	+	11.0684i	−0.415079	+	1.00209i
$123$			4.51022i			0.406673i
$124$	−3.69528	−	1.53063i	−0.331846	−	0.137455i
$125$	−0.382683	−	0.923880i	−0.0342282	−	0.0826343i
$126$	−11.0586	+	4.58062i	−0.985179	+	0.408074i
$127$	−9.89892	−	9.89892i	−0.878387	−	0.878387i	0.114980	−	0.993368i	$-0.463319\pi$
$127$	−9.89892	−	9.89892i	−0.878387	−	0.878387i	−0.993368	+	0.114980i	$0.963319\pi$
$128$	−3.01815	−	3.01815i	−0.266770	−	0.266770i
$129$	−0.0656629	+	0.0271985i	−0.00578129	+	0.00239469i
$130$	−0.427495	−	1.03206i	−0.0374938	−	0.0905180i
$131$	11.7059	+	4.84875i	1.02275	+	0.423638i	0.830091	−	0.557628i	$-0.188288\pi$
$131$	11.7059	+	4.84875i	1.02275	+	0.423638i	0.192661	+	0.981265i	$0.438288\pi$
$132$			17.4236i			1.51653i
$133$	6.42563	−	15.5128i	0.557173	−	1.34513i
$134$	−3.82985	+	3.82985i	−0.330849	+	0.330849i
$135$	−2.69417			−0.231877
$136$	−5.58287	+	10.8470i	−0.478728	+	0.930119i
$137$	2.97888			0.254503			0.127251	−	0.991870i	$-0.459384\pi$
$137$	2.97888			0.254503			0.127251	+	0.991870i	$0.459384\pi$
$138$	5.62251	−	5.62251i	0.478620	−	0.478620i
$139$	7.51640	−	18.1462i	0.637533	−	1.53914i	−0.192423	−	0.981312i	$-0.561635\pi$
$139$	7.51640	−	18.1462i	0.637533	−	1.53914i	0.829956	−	0.557829i	$-0.188365\pi$
$140$		−	3.32016i		−	0.280605i
$141$	13.3065	+	5.51174i	1.12061	+	0.464172i
$142$	−3.97194	−	9.58911i	−0.333318	−	0.804700i
$143$	6.57127	−	2.72191i	0.549517	−	0.227617i
$144$	−1.99735	−	1.99735i	−0.166446	−	0.166446i
$145$	3.53340	+	3.53340i	0.293433	+	0.293433i
$146$	−1.47165	+	0.609578i	−0.121795	+	0.0504490i
$147$	2.61207	+	6.30610i	0.215440	+	0.520118i
$148$	−0.393229	−	0.162881i	−0.0323232	−	0.0133887i
$149$			2.95573i			0.242143i	0.992644	+	0.121072i	$0.0386330\pi$
$149$			2.95573i			0.242143i	−0.992644	+	0.121072i	$0.961367\pi$
$150$	−0.976080	+	2.35647i	−0.0796966	+	0.192405i
$151$	15.5848	−	15.5848i	1.26828	−	1.26828i	0.321298	−	0.946978i	$-0.395881\pi$
$151$	15.5848	−	15.5848i	1.26828	−	1.26828i	0.946978	−	0.321298i	$-0.104119\pi$
$152$	16.0539			1.30214
$153$	7.57971	−	14.7266i	0.612783	−	1.19058i
$154$	−18.2678			−1.47206
$155$	2.63612	−	2.63612i	0.211739	−	0.211739i
$156$	1.26180	−	3.04626i	0.101025	−	0.243896i
$157$		−	12.8666i		−	1.02686i	−0.858130	−	0.513432i	$-0.828374\pi$
$157$		−	12.8666i		−	1.02686i	0.858130	−	0.513432i	$-0.171626\pi$
$158$	4.69065	+	1.94293i	0.373168	+	0.154571i
$159$	−0.349821	−	0.844544i	−0.0277426	−	0.0669767i
$160$	4.84160	−	2.00546i	0.382762	−	0.158545i
$161$	−6.82171	−	6.82171i	−0.537626	−	0.537626i
$162$	−3.34599	−	3.34599i	−0.262886	−	0.262886i
$163$	−17.8239	+	7.38291i	−1.39608	+	0.578274i	−0.948730	−	0.316087i	$-0.897631\pi$
$163$	−17.8239	+	7.38291i	−1.39608	+	0.578274i	−0.447347	+	0.894361i	$0.647631\pi$
$164$	0.699055	+	1.68767i	0.0545870	+	0.131785i
$165$	−15.0039	−	6.21481i	−1.16805	−	0.483822i
$166$			11.9645i			0.928622i
$167$	−7.21707	+	17.4236i	−0.558474	+	1.34828i	0.352500	+	0.935812i	$0.385332\pi$
$167$	−7.21707	+	17.4236i	−0.558474	+	1.34828i	−0.910974	+	0.412464i	$0.864668\pi$
$168$	−17.1508	+	17.1508i	−1.32321	+	1.32321i
$169$	11.6540			0.896461
$170$	−2.56594	−	3.02936i	−0.196798	−	0.232341i
$171$	−21.7960			−1.66678
$172$	−0.0203546	+	0.0203546i	−0.00155203	+	0.00155203i
$173$	−8.63985	+	20.8584i	−0.656876	+	1.58584i	0.145728	+	0.989325i	$0.453448\pi$
$173$	−8.63985	+	20.8584i	−0.656876	+	1.58584i	−0.802603	+	0.596513i	$0.796552\pi$
$174$		−	12.7454i		−	0.966225i
$175$	2.85906	+	1.18426i	0.216125	+	0.0895219i
$176$	−1.64972	−	3.98278i	−0.124352	−	0.300213i
$177$	−9.93763	+	4.11630i	−0.746958	+	0.309400i
$178$	2.19867	+	2.19867i	0.164798	+	0.164798i
$179$	−1.38641	−	1.38641i	−0.103625	−	0.103625i	0.653393	−	0.757018i	$-0.273345\pi$
$179$	−1.38641	−	1.38641i	−0.103625	−	0.103625i	−0.757018	+	0.653393i	$0.773345\pi$
$180$	−3.98176	+	1.64930i	−0.296783	+	0.122931i
$181$	0.272363	+	0.657542i	0.0202446	+	0.0488747i	0.933679	−	0.358112i	$-0.116579\pi$
$181$	0.272363	+	0.657542i	0.0202446	+	0.0488747i	−0.913434	+	0.406987i	$0.866579\pi$
$182$	3.19386	+	1.32294i	0.236744	+	0.0980627i
$183$		−	32.9595i		−	2.43644i
$184$	3.52982	−	8.52174i	0.260222	−	0.628231i
$185$	0.280520	−	0.280520i	0.0206243	−	0.0206243i
$186$	−9.50882			−0.697220
$187$	19.2883	−	16.3376i	1.41050	−	1.19472i
$188$	5.83341			0.425445
$189$	5.89546	−	5.89546i	0.428832	−	0.428832i
$190$	−1.99929	+	4.82671i	−0.145044	+	0.350166i
$191$			5.26341i			0.380847i	0.981702	+	0.190423i	$0.0609861\pi$
$191$			5.26341i			0.380847i	−0.981702	+	0.190423i	$0.939014\pi$
$192$	−15.7909	−	6.54079i	−1.13961	−	0.472041i
$193$	5.71352	+	13.7936i	0.411268	+	0.992888i	0.984798	+	0.173704i	$0.0555736\pi$
$193$	5.71352	+	13.7936i	0.411268	+	0.992888i	−0.573530	+	0.819184i	$0.694426\pi$
$194$	11.5065	−	4.76617i	0.826122	−	0.342191i
$195$	2.17313	+	2.17313i	0.155621	+	0.155621i
$196$	1.95481	+	1.95481i	0.139629	+	0.139629i
$197$	5.84828	−	2.42244i	0.416673	−	0.172592i	−0.164490	−	0.986379i	$-0.552598\pi$
$197$	5.84828	−	2.42244i	0.416673	−	0.172592i	0.581163	+	0.813787i	$0.302598\pi$
$198$	9.07458	+	21.9080i	0.644902	+	1.55693i
$199$	−13.7796	−	5.70769i	−0.976809	−	0.404607i	−0.163566	−	0.986532i	$-0.552300\pi$
$199$	−13.7796	−	5.70769i	−0.976809	−	0.404607i	−0.813243	+	0.581925i	$0.802300\pi$
$200$			2.95879i			0.209218i
$201$	5.70225	−	13.7664i	0.402206	−	0.971010i
$202$	1.00049	−	1.00049i	0.0703943	−	0.0703943i
$203$	−15.4638			−1.08534
$204$	0.967215	−	11.6780i	0.0677186	−	0.817624i
$205$	−1.70263			−0.118917
$206$	6.67901	−	6.67901i	0.465349	−	0.465349i
$207$	−4.79234	+	11.5697i	−0.333091	+	0.804152i
$208$			0.815800i			0.0565656i
$209$	−30.7322	−	12.7297i	−2.12579	−	0.880531i
$210$	−3.02060	−	7.29238i	−0.208441	−	0.503222i
$211$	12.3788	−	5.12746i	0.852190	−	0.352989i	0.0865417	−	0.996248i	$-0.472418\pi$
$211$	12.3788	−	5.12746i	0.852190	−	0.352989i	0.765648	+	0.643260i	$0.222418\pi$
$212$	−0.261797	−	0.261797i	−0.0179803	−	0.0179803i
$213$	20.1910	+	20.1910i	1.38346	+	1.38346i
$214$	−2.56858	+	1.06394i	−0.175585	+	0.0727295i
$215$	−0.0102675	−	0.0247881i	−0.000700241	−	0.00169053i
$216$	7.36467	+	3.05055i	0.501102	+	0.207563i
$217$			11.5369i			0.783176i
$218$	2.12363	−	5.12690i	0.143830	−	0.347238i
$219$	3.09873	−	3.09873i	0.209393	−	0.209393i
$220$	−6.57751			−0.443456
$221$	−4.55542	+	1.45955i	−0.306430	+	0.0981797i
$222$	−1.01187			−0.0679123
$223$	1.49410	−	1.49410i	0.100053	−	0.100053i	−0.655309	−	0.755361i	$-0.727461\pi$
$223$	1.49410	−	1.49410i	0.100053	−	0.100053i	0.755361	+	0.655309i	$0.227461\pi$
$224$	−6.20614	+	14.9830i	−0.414665	+	1.00109i
$225$		−	4.01706i		−	0.267804i
$226$	8.02437	+	3.32380i	0.533773	+	0.221096i
$227$	5.57168	+	13.4512i	0.369805	+	0.892789i	0.993782	+	0.111346i	$0.0355161\pi$
$227$	5.57168	+	13.4512i	0.369805	+	0.892789i	−0.623976	+	0.781443i	$0.714484\pi$
$228$	−14.2466	+	5.90114i	−0.943505	+	0.390812i
$229$	−1.87412	−	1.87412i	−0.123845	−	0.123845i	0.642468	−	0.766313i	$-0.277911\pi$
$229$	−1.87412	−	1.87412i	−0.123845	−	0.123845i	−0.766313	+	0.642468i	$0.777911\pi$
$230$	2.12252	+	2.12252i	0.139955	+	0.139955i
$231$	46.4314	−	19.2325i	3.05496	−	1.26541i
$232$	−5.65797	−	13.6595i	−0.371464	−	0.896793i
$233$	−2.90028	−	1.20133i	−0.190004	−	0.0787021i	0.285653	−	0.958333i	$-0.407790\pi$
$233$	−2.90028	−	1.20133i	−0.190004	−	0.0787021i	−0.475657	+	0.879631i	$0.657790\pi$
$234$		−	4.48745i		−	0.293354i
$235$	−2.08071	+	5.02327i	−0.135730	+	0.327682i
$236$	−3.08053	+	3.08053i	−0.200526	+	0.200526i
$237$	−13.9678			−0.907305
$238$	12.2438	+	1.01408i	0.793648	+	0.0657328i
$239$	13.7090			0.886760			0.443380	−	0.896334i	$-0.353779\pi$
$239$	13.7090			0.886760			0.443380	+	0.896334i	$0.353779\pi$
$240$	1.31711	−	1.31711i	0.0850193	−	0.0850193i
$241$	−4.77884	+	11.5371i	−0.307832	+	0.743173i	0.691943	+	0.721952i	$0.256755\pi$
$241$	−4.77884	+	11.5371i	−0.307832	+	0.743173i	−0.999775	+	0.0212201i	$0.993245\pi$
$242$			25.5985i			1.64553i
$243$	19.4944	+	8.07486i	1.25057	+	0.518003i
$244$	−5.10851	−	12.3330i	−0.327039	−	0.789541i
$245$	−2.38058	+	0.986069i	−0.152090	+	0.0629977i
$246$	3.07080	+	3.07080i	0.195787	+	0.195787i
$247$	4.45119	+	4.45119i	0.283222	+	0.283222i
$248$	−10.1908	+	4.22118i	−0.647119	+	0.268045i
$249$	−12.5963	−	30.4101i	−0.798257	−	1.92716i
$250$	−0.889577	−	0.368475i	−0.0562618	−	0.0233044i
$251$			17.4413i			1.10088i	0.834874	+	0.550441i	$0.185541\pi$
$251$			17.4413i			1.10088i	−0.834874	+	0.550441i	$0.814459\pi$
$252$	5.10396	−	12.3221i	0.321519	−	0.776217i
$253$	−13.5143	+	13.5143i	−0.849640	+	0.849640i
$254$	−13.4794			−0.845774
$255$	9.71118	+	4.99829i	0.608138	+	0.313005i
$256$	−17.0144			−1.06340
$257$	−4.86561	+	4.86561i	−0.303508	+	0.303508i	−0.842385	−	0.538876i	$-0.818849\pi$
$257$	−4.86561	+	4.86561i	−0.303508	+	0.303508i	0.538876	+	0.842385i	$0.318849\pi$
$258$	−0.0261886	+	0.0632249i	−0.00163043	+	0.00393621i
$259$			1.22769i			0.0762848i
$260$	1.14998	+	0.476337i	0.0713186	+	0.0295411i
$261$	7.68166	+	18.5452i	0.475483	+	1.14792i
$262$	11.2713	−	4.66872i	0.696343	−	0.288435i
$263$	4.41100	+	4.41100i	0.271994	+	0.271994i	0.829902	−	0.557909i	$-0.188396\pi$
$263$	4.41100	+	4.41100i	0.271994	+	0.271994i	−0.557909	+	0.829902i	$0.688396\pi$
$264$	33.9771	+	33.9771i	2.09115	+	2.09115i
$265$	0.318819	−	0.132059i	0.0195849	−	0.00811233i
$266$	−6.18705	−	14.9369i	−0.379352	−	0.915838i
$267$	−7.90316	−	3.27360i	−0.483666	−	0.200341i
$268$		−	6.03504i		−	0.368648i
$269$	0.493996	−	1.19261i	0.0301194	−	0.0727148i	−0.908104	−	0.418744i	$-0.862470\pi$
$269$	0.493996	−	1.19261i	0.0301194	−	0.0727148i	0.938224	+	0.346030i	$0.112470\pi$
$270$	−1.83433	+	1.83433i	−0.111634	+	0.111634i
$271$	−10.2849			−0.624764			−0.312382	−	0.949957i	$-0.601127\pi$
$271$	−10.2849			−0.624764			−0.312382	+	0.949957i	$0.601127\pi$
$272$	0.884617	+	2.76099i	0.0536378	+	0.167410i
$273$	−9.51063			−0.575610
$274$	2.02818	−	2.02818i	0.122527	−	0.122527i
$275$	2.34612	−	5.66403i	0.141476	−	0.341554i
$276$			8.85989i			0.533302i
$277$	23.4482	+	9.71258i	1.40887	+	0.583572i	0.952037	−	0.305982i	$-0.0989846\pi$
$277$	23.4482	+	9.71258i	1.40887	+	0.583572i	0.456831	+	0.889554i	$0.348985\pi$
$278$	−7.23733	−	17.4724i	−0.434066	−	1.04793i
$279$	13.8358	−	5.73098i	0.828328	−	0.343105i
$280$	−6.47451	−	6.47451i	−0.386926	−	0.386926i
$281$	−4.16880	−	4.16880i	−0.248690	−	0.248690i	0.571743	−	0.820433i	$-0.306267\pi$
$281$	−4.16880	−	4.16880i	−0.248690	−	0.248690i	−0.820433	+	0.571743i	$0.806267\pi$
$282$	12.8125	−	5.30710i	0.762971	−	0.316033i
$283$	−7.06675	−	17.0606i	−0.420075	−	1.01415i	−0.982325	−	0.187183i	$-0.940064\pi$
$283$	−7.06675	−	17.0606i	−0.420075	−	1.01415i	0.562250	−	0.826967i	$-0.309936\pi$
$284$	10.6847	+	4.42574i	0.634019	+	0.262619i
$285$		−	14.3729i		−	0.851378i
$286$	2.62085	−	6.32728i	0.154974	−	0.374140i
$287$	3.72575	−	3.72575i	0.219924	−	0.219924i
$288$	21.0514			1.24047
$289$	−13.8347	+	9.87937i	−0.813804	+	0.581139i
$290$	4.81144			0.282538
$291$	−24.2284	+	24.2284i	−1.42029	+	1.42029i
$292$	0.679222	−	1.63979i	0.0397485	−	0.0959613i
$293$		−	8.31894i		−	0.485998i	−0.970027	−	0.242999i	$-0.921869\pi$
$293$		−	8.31894i		−	0.485998i	0.970027	−	0.242999i	$-0.0781311\pi$
$294$	6.07196	+	2.51509i	0.354124	+	0.146683i
$295$	−1.55392	−	3.75150i	−0.0904729	−	0.218421i
$296$	−1.08445	+	0.449193i	−0.0630322	+	0.0261088i
$297$	−11.6794	−	11.6794i	−0.677706	−	0.677706i
$298$	2.01242	+	2.01242i	0.116576	+	0.116576i
$299$	3.34148	−	1.38408i	0.193243	−	0.0800437i
$300$	−1.08760	−	2.62569i	−0.0627925	−	0.151594i
$301$	0.0767098	+	0.0317742i	0.00442148	+	0.00183144i
$302$		−	21.2220i		−	1.22119i
$303$	−1.48963	+	3.59628i	−0.0855768	+	0.206601i
$304$	2.69782	−	2.69782i	0.154731	−	0.154731i
$305$	12.4424			0.712448
$306$	−4.86599	−	15.1873i	−0.278170	−	0.868201i
$307$	−12.2369			−0.698398			−0.349199	−	0.937049i	$-0.613546\pi$
$307$	−12.2369			−0.698398			−0.349199	+	0.937049i	$0.613546\pi$
$308$	14.3931	−	14.3931i	0.820124	−	0.820124i
$309$	−9.94435	+	24.0078i	−0.565715	+	1.36576i
$310$		−	3.58962i		−	0.203877i
$311$	−30.1525	−	12.4896i	−1.70979	−	0.708218i	−0.999993	−	0.00381046i	$-0.998787\pi$
$311$	−30.1525	−	12.4896i	−1.70979	−	0.708218i	−0.709796	−	0.704407i	$-0.751213\pi$
$312$	−3.47980	−	8.40098i	−0.197005	−	0.475612i
$313$	−12.4068	+	5.13906i	−0.701273	+	0.290477i	−0.704688	−	0.709517i	$-0.748913\pi$
$313$	−12.4068	+	5.13906i	−0.701273	+	0.290477i	0.00341475	+	0.999994i	$0.498913\pi$
$314$	−8.76024	−	8.76024i	−0.494369	−	0.494369i
$315$	8.79026	+	8.79026i	0.495275	+	0.495275i
$316$	−5.22656	+	2.16491i	−0.294017	+	0.121786i
$317$	−3.77845	−	9.12199i	−0.212219	−	0.512342i	0.781545	−	0.623849i	$-0.214432\pi$
$317$	−3.77845	−	9.12199i	−0.212219	−	0.512342i	−0.993764	+	0.111507i	$0.964432\pi$
$318$	−0.813186	−	0.336833i	−0.0456012	−	0.0188886i
$319$			30.6350i			1.71523i
$320$	2.46918	−	5.96113i	0.138031	−	0.333237i
$321$	5.40844	−	5.40844i	0.301870	−	0.301870i
$322$	−9.28915			−0.517664
$323$	19.8912	+	10.2379i	1.10678	+	0.569653i
$324$	5.27257			0.292920
$325$	−0.820367	+	0.820367i	−0.0455058	+	0.0455058i
$326$	−7.10879	+	17.1621i	−0.393719	+	0.950523i
$327$			15.2668i			0.844258i
$328$	4.65425	+	1.92785i	0.256988	+	0.106448i
$329$	−6.43902	−	15.5452i	−0.354995	−	0.857033i
$330$	−14.4468	+	5.98406i	−0.795270	+	0.329412i
$331$	−3.99024	−	3.99024i	−0.219323	−	0.219323i	0.588890	−	0.808213i	$-0.299565\pi$
$331$	−3.99024	−	3.99024i	−0.219323	−	0.219323i	−0.808213	+	0.588890i	$0.799565\pi$
$332$	−9.42673	−	9.42673i	−0.517359	−	0.517359i
$333$	1.47232	−	0.609856i	0.0806828	−	0.0334199i
$334$	6.94911	+	16.7766i	0.380238	+	0.917977i
$335$	5.19690	+	2.15263i	0.283937	+	0.117611i
$336$			5.76430i			0.314468i
$337$	6.34969	−	15.3295i	0.345890	−	0.835051i	−0.651207	−	0.758900i	$-0.725737\pi$
$337$	6.34969	−	15.3295i	0.345890	−	0.835051i	0.997096	−	0.0761510i	$-0.0242631\pi$
$338$	7.93465	−	7.93465i	0.431588	−	0.431588i
$339$	−23.8949			−1.29779
$340$	4.40850	+	0.365128i	0.239085	+	0.0198019i
$341$	22.8555			1.23770
$342$	−14.8398	+	14.8398i	−0.802446	+	0.802446i
$343$	−5.23832	+	12.6464i	−0.282843	+	0.682843i
$344$			0.0793854i			0.00428017i
$345$	−7.62944	−	3.16022i	−0.410755	−	0.170140i
$346$	8.31906	+	20.0840i	0.447235	+	1.07972i
$347$	8.54057	−	3.53762i	0.458482	−	0.189909i	−0.141475	−	0.989942i	$-0.545184\pi$
$347$	8.54057	−	3.53762i	0.458482	−	0.189909i	0.599957	+	0.800032i	$0.295184\pi$
$348$	10.0420	+	10.0420i	0.538309	+	0.538309i
$349$	−19.0405	−	19.0405i	−1.01921	−	1.01921i	−0.999812	−	0.0194030i	$-0.993823\pi$
$349$	−19.0405	−	19.0405i	−1.01921	−	1.01921i	−0.0194030	−	0.999812i	$-0.506177\pi$
$350$	2.75291	−	1.14029i	0.147149	−	0.0609512i
$351$	1.19615	+	2.88777i	0.0638460	+	0.154138i
$352$	29.6824	+	12.2949i	1.58208	+	0.655319i
$353$		−	22.9722i		−	1.22269i	−0.791366	−	0.611343i	$-0.790630\pi$
$353$		−	22.9722i		−	1.22269i	0.791366	−	0.611343i	$-0.209370\pi$
$354$	−3.96347	+	9.56866i	−0.210656	+	0.508568i
$355$	−7.62219	+	7.62219i	−0.404544	+	0.404544i
$356$	−3.46465			−0.183626
$357$	−32.1878	+	10.3129i	−1.70356	+	0.545816i
$358$	−1.88788			−0.0997775
$359$	−24.1187	+	24.1187i	−1.27293	+	1.27293i	−0.328394	+	0.944541i	$0.606507\pi$
$359$	−24.1187	+	24.1187i	−1.27293	+	1.27293i	−0.944541	+	0.328394i	$0.893493\pi$
$360$	−4.54843	+	10.9809i	−0.239723	+	0.578743i
$361$		−	10.4398i		−	0.549463i
$362$	0.633128	+	0.262250i	0.0332765	+	0.0137836i
$363$	−26.9503	−	65.0637i	−1.41452	−	3.41496i
$364$	−3.55876	+	1.47408i	−0.186529	+	0.0772630i
$365$	1.16979	+	1.16979i	0.0612294	+	0.0612294i
$366$	−22.4406	−	22.4406i	−1.17299	−	1.17299i
$367$	8.57000	−	3.54981i	0.447351	−	0.185299i	−0.147623	−	0.989044i	$-0.547162\pi$
$367$	8.57000	−	3.54981i	0.447351	−	0.185299i	0.594974	+	0.803745i	$0.297162\pi$
$368$	−0.838880	−	2.02523i	−0.0437296	−	0.105573i
$369$	−6.31894	−	2.61739i	−0.328951	−	0.136256i
$370$		−	0.381986i		−	0.0198585i
$371$	−0.408674	+	0.986627i	−0.0212173	+	0.0512231i
$372$	7.49194	−	7.49194i	0.388439	−	0.388439i
$373$	3.06857			0.158884			0.0794422	−	0.996839i	$-0.474686\pi$
$373$	3.06857			0.158884			0.0794422	+	0.996839i	$0.474686\pi$
$374$	2.00897	−	24.2560i	0.103881	−	1.25425i
$375$	2.64897			0.136792
$376$	11.3755	−	11.3755i	0.586646	−	0.586646i
$377$	2.21856	−	5.35607i	0.114261	−	0.275851i
$378$		−	8.02788i		−	0.412910i
$379$	33.7529	+	13.9809i	1.73377	+	0.718151i	0.999215	+	0.0396029i	$0.0126093\pi$
$379$	33.7529	+	13.9809i	1.73377	+	0.718151i	0.734556	+	0.678549i	$0.237391\pi$
$380$	−2.22771	−	5.37816i	−0.114279	−	0.275894i
$381$	34.2607	−	14.1912i	1.75523	−	0.727039i
$382$	3.58361	+	3.58361i	0.183353	+	0.183353i
$383$	6.59130	+	6.59130i	0.336800	+	0.336800i	0.855161	−	0.518362i	$-0.173458\pi$
$383$	6.59130	+	6.59130i	0.336800	+	0.336800i	−0.518362	+	0.855161i	$0.673458\pi$
$384$	10.4460	−	4.32687i	0.533069	−	0.220804i
$385$	7.26037	+	17.5281i	0.370023	+	0.893314i
$386$	13.2815	+	5.50138i	0.676011	+	0.280013i
$387$		−	0.107779i		−	0.00547873i
$388$	−5.31071	+	12.8212i	−0.269610	+	0.650897i
$389$	23.4493	−	23.4493i	1.18892	−	1.18892i	0.211559	−	0.977365i	$-0.432146\pi$
$389$	23.4493	−	23.4493i	1.18892	−	1.18892i	0.977365	−	0.211559i	$-0.0678541\pi$
$390$	2.95916			0.149843
$391$	9.80804	−	8.30763i	0.496014	−	0.420135i
$392$	7.62397			0.385069
$393$	−23.7330	+	23.7330i	−1.19717	+	1.19717i
$394$	2.33250	−	5.63114i	0.117509	−	0.283693i
$395$		−	5.27290i		−	0.265309i
$396$	−24.4110	−	10.1114i	−1.22670	−	0.508115i
$397$	−3.37734	−	8.15361i	−0.169504	−	0.409218i	0.816186	−	0.577790i	$-0.196085\pi$
$397$	−3.37734	−	8.15361i	−0.169504	−	0.409218i	−0.985689	+	0.168572i	$0.946085\pi$
$398$	−13.2680	+	5.49577i	−0.665063	+	0.275478i
$399$	31.4513	+	31.4513i	1.57453	+	1.57453i
$400$	0.497216	+	0.497216i	0.0248608	+	0.0248608i
$401$	18.0332	−	7.46960i	0.900535	−	0.373014i	0.116109	−	0.993236i	$-0.462958\pi$
$401$	18.0332	−	7.46960i	0.900535	−	0.373014i	0.784426	+	0.620223i	$0.212958\pi$
$402$	−5.49053	−	13.2553i	−0.273843	−	0.661115i
$403$	−3.99595	−	1.65518i	−0.199052	−	0.0824501i
$404$			1.57656i			0.0784369i
$405$	−1.88066	+	4.54032i	−0.0934509	+	0.225610i
$406$	−10.5286	+	10.5286i	−0.522523	+	0.522523i
$407$	2.43215			0.120557
$408$	−20.8867	−	24.6589i	−1.03404	−	1.22080i
$409$	10.4152			0.514998			0.257499	−	0.966279i	$-0.417102\pi$
$409$	10.4152			0.514998			0.257499	+	0.966279i	$0.417102\pi$
$410$	−1.15924	+	1.15924i	−0.0572508	+	0.0572508i
$411$	−3.01974	+	7.29031i	−0.148953	+	0.359604i
$412$			10.5247i			0.518515i
$413$	11.6095	+	4.80881i	0.571266	+	0.236626i
$414$	4.61440	+	11.1402i	0.226786	+	0.547509i
$415$	11.4800	−	4.75515i	0.563529	−	0.233421i
$416$	−4.29914	−	4.29914i	−0.210783	−	0.210783i
$417$	36.7903	+	36.7903i	1.80163	+	1.80163i
$418$	−29.5911	+	12.2570i	−1.44735	+	0.599512i
$419$	13.5166	+	32.6320i	0.660329	+	1.59418i	0.797288	+	0.603599i	$0.206267\pi$
$419$	13.5166	+	32.6320i	0.660329	+	1.59418i	−0.136958	+	0.990577i	$0.543733\pi$
$420$	8.12554	+	3.36571i	0.396486	+	0.164230i
$421$		−	15.0205i		−	0.732052i	−0.930605	−	0.366026i	$-0.880718\pi$
$421$		−	15.0205i		−	0.732052i	0.930605	−	0.366026i	$-0.119282\pi$
$422$	4.93708	−	11.9192i	0.240333	−	0.580216i
$423$	−15.4442	+	15.4442i	−0.750922	+	0.750922i
$424$	−1.02104			−0.0495861
$425$	−1.88688	+	3.66602i	−0.0915271	+	0.177828i
$426$	27.4942			1.33210
$427$	−27.2268	+	27.2268i	−1.31760	+	1.31760i
$428$	1.18550	−	2.86204i	0.0573031	−	0.138342i
$429$			18.8413i			0.909668i
$430$	−0.0238677	−	0.00988632i	−0.00115100	−	0.000476761i
$431$	−8.93633	−	21.5742i	−0.430448	−	1.03919i	−0.979143	−	0.203171i	$-0.934875\pi$
$431$	−8.93633	−	21.5742i	−0.430448	−	1.03919i	0.548695	−	0.836022i	$-0.315125\pi$
$432$	1.75025	−	0.724977i	0.0842090	−	0.0348805i
$433$	−12.9455	−	12.9455i	−0.622120	−	0.622120i	0.323953	−	0.946073i	$-0.394988\pi$
$433$	−12.9455	−	12.9455i	−0.622120	−	0.622120i	−0.946073	+	0.323953i	$0.894988\pi$
$434$	7.85493	+	7.85493i	0.377049	+	0.377049i
$435$	−12.2293	+	5.06553i	−0.586348	+	0.242873i
$436$	2.36626	+	5.71265i	0.113323	+	0.273586i
$437$	−15.6272	−	6.47302i	−0.747552	−	0.309646i
$438$		−	4.21956i		−	0.201618i
$439$	7.75689	−	18.7268i	0.370216	−	0.893780i	−0.623497	−	0.781826i	$-0.714289\pi$
$439$	7.75689	−	18.7268i	0.370216	−	0.893780i	0.993713	−	0.111955i	$-0.0357112\pi$
$440$	−12.8265	+	12.8265i	−0.611481	+	0.611481i
$441$	−10.3509			−0.492898
$442$	−2.10783	+	4.09530i	−0.100259	+	0.194794i
$443$	29.3849			1.39612			0.698058	−	0.716041i	$-0.254048\pi$
$443$	29.3849			1.39612			0.698058	+	0.716041i	$0.254048\pi$
$444$	0.797247	−	0.797247i	0.0378357	−	0.0378357i
$445$	1.23580	−	2.98348i	0.0585825	−	0.141431i
$446$		−	2.03453i		−	0.0963376i
$447$	−7.23366	−	2.99628i	−0.342140	−	0.141719i
$448$	7.64119	+	18.4475i	0.361012	+	0.871561i
$449$	−30.1572	+	12.4915i	−1.42321	+	0.589512i	−0.955664	−	0.294459i	$-0.904861\pi$
$449$	−30.1572	+	12.4915i	−1.42321	+	0.589512i	−0.467543	+	0.883970i	$0.654861\pi$
$450$	−2.73503	−	2.73503i	−0.128930	−	0.128930i
$451$	−7.38101	−	7.38101i	−0.347558	−	0.347558i
$452$	−8.94115	+	3.70355i	−0.420557	+	0.174200i
$453$	22.3426	+	53.9399i	1.04975	+	2.53432i
$454$	12.9518	+	5.36481i	0.607858	+	0.251783i
$455$		−	3.59031i		−	0.168316i
$456$	−16.2742	+	39.2893i	−0.762107	+	1.83989i
$457$	−5.97585	+	5.97585i	−0.279538	+	0.279538i	−0.832925	−	0.553386i	$-0.813335\pi$
$457$	−5.97585	+	5.97585i	−0.279538	+	0.279538i	0.553386	+	0.832925i	$0.313335\pi$
$458$	−2.55199			−0.119247
$459$	7.17963	+	8.47631i	0.335116	+	0.395640i
$460$	−3.34465			−0.155945
$461$	27.0527	−	27.0527i	1.25997	−	1.25997i	0.308863	−	0.951106i	$-0.400051\pi$
$461$	27.0527	−	27.0527i	1.25997	−	1.25997i	0.951106	−	0.308863i	$-0.0999486\pi$
$462$	18.5184	−	44.7075i	0.861556	−	2.07998i
$463$		−	27.1761i		−	1.26298i	−0.775383	−	0.631491i	$-0.782443\pi$
$463$		−	27.1761i		−	1.26298i	0.775383	−	0.631491i	$-0.217557\pi$
$464$	−3.24626	−	1.34464i	−0.150704	−	0.0624235i
$465$	3.77919	+	9.12376i	0.175256	+	0.423104i
$466$	−2.79259	+	1.15673i	−0.129364	+	0.0535845i
$467$	2.43616	+	2.43616i	0.112732	+	0.112732i	0.761223	−	0.648491i	$-0.224599\pi$
$467$	2.43616	+	2.43616i	0.112732	+	0.112732i	−0.648491	+	0.761223i	$0.724599\pi$
$468$	3.53564	+	3.53564i	0.163435	+	0.163435i
$469$	−16.0825	+	6.66158i	−0.742619	+	0.307603i
$470$	2.00345	+	4.83676i	0.0924124	+	0.223103i
$471$	31.4888	+	13.0431i	1.45093	+	0.600994i
$472$			12.0144i			0.553009i
$473$	0.0629473	−	0.151968i	0.00289432	−	0.00698751i
$474$	−9.51000	+	9.51000i	−0.436809	+	0.436809i
$475$	5.42585			0.248955
$476$	−10.4458	+	8.84784i	−0.478783	+	0.405540i
$477$	1.38624			0.0634714
$478$	9.33380	−	9.33380i	0.426918	−	0.426918i
$479$	5.87776	−	14.1902i	0.268562	−	0.648365i	−0.730855	−	0.682533i	$-0.760878\pi$
$479$	5.87776	−	14.1902i	0.268562	−	0.648365i	0.999416	+	0.0341684i	$0.0108783\pi$
$480$			13.8820i			0.633622i
$481$	−0.425224	−	0.176134i	−0.0193886	−	0.00803101i
$482$	4.60141	+	11.1088i	0.209588	+	0.505991i
$483$	23.6103	−	9.77969i	1.07430	−	0.444992i
$484$	−20.1689	−	20.1689i	−0.916767	−	0.916767i
$485$	−9.14632	−	9.14632i	−0.415313	−	0.415313i
$486$	18.7706	−	7.77505i	0.851453	−	0.352683i
$487$	−10.0682	−	24.3068i	−0.456234	−	1.10145i	−0.969910	−	0.243463i	$-0.921717\pi$
$487$	−10.0682	−	24.3068i	−0.456234	−	1.10145i	0.513676	−	0.857984i	$-0.328283\pi$
$488$	−34.0120	−	14.0882i	−1.53965	−	0.637744i
$489$		−	51.1052i		−	2.31106i
$490$	−0.949458	+	2.29219i	−0.0428921	+	0.103551i
$491$	−20.5320	+	20.5320i	−0.926596	+	0.926596i	−0.997484	−	0.0708885i	$-0.977417\pi$
$491$	−20.5320	+	20.5320i	−0.926596	+	0.926596i	0.0708885	+	0.997484i	$0.477417\pi$
$492$	−4.83893			−0.218156
$493$	1.70060	−	20.5328i	0.0765911	−	0.924749i
$494$	6.06120			0.272706
$495$	17.4142	−	17.4142i	0.782711	−	0.782711i
$496$	−1.00319	+	2.42190i	−0.0450443	+	0.108747i
$497$		−	33.3583i		−	1.49632i
$498$	−29.2810	−	12.1286i	−1.31211	−	0.543495i
$499$	12.4718	+	30.1097i	0.558316	+	1.34789i	0.911098	+	0.412189i	$0.135236\pi$
$499$	12.4718	+	30.1097i	0.558316	+	1.34789i	−0.352782	+	0.935706i	$0.614764\pi$
$500$	0.991211	−	0.410573i	0.0443283	−	0.0183614i
$501$	−35.3252	−	35.3252i	−1.57821	−	1.57821i
$502$	11.8749	+	11.8749i	0.530004	+	0.530004i
$503$	21.7473	−	9.00803i	0.969665	−	0.401648i	0.159077	−	0.987266i	$-0.449148\pi$
$503$	21.7473	−	9.00803i	0.969665	−	0.401648i	0.810587	+	0.585618i	$0.199148\pi$
$504$	−14.0757	−	33.9818i	−0.626982	−	1.51367i
$505$	−1.35761	−	0.562341i	−0.0604129	−	0.0250239i
$506$			18.4026i			0.818093i
$507$	−11.8139	+	28.5212i	−0.524672	+	1.26667i
$508$	10.6204	−	10.6204i	0.471202	−	0.471202i
$509$	17.5818			0.779300			0.389650	−	0.920963i	$-0.372596\pi$
$509$	17.5818			0.779300			0.389650	+	0.920963i	$0.372596\pi$
$510$	10.0150	−	3.20878i	0.443471	−	0.142087i
$511$	−5.11953			−0.226474
$512$	−5.54798	+	5.54798i	−0.245189	+	0.245189i
$513$	5.59412	−	13.5054i	0.246986	−	0.596278i
$514$			6.62553i			0.292239i
$515$	−9.06306	−	3.75404i	−0.399366	−	0.165423i
$516$	−0.0291807	−	0.0704484i	−0.00128461	−	0.00310132i
$517$	−30.7962	+	12.7562i	−1.35442	+	0.561018i
$518$	0.835874	+	0.835874i	0.0367262	+	0.0367262i
$519$	−42.2892	−	42.2892i	−1.85629	−	1.85629i
$520$	3.17141	−	1.31364i	0.139076	−	0.0576070i
$521$	−7.84734	−	18.9452i	−0.343798	−	0.830002i	−0.997325	−	0.0730986i	$-0.976711\pi$
$521$	−7.84734	−	18.9452i	−0.343798	−	0.830002i	0.653527	−	0.756904i	$-0.273289\pi$
$522$	17.8566	+	7.39645i	0.781563	+	0.323734i
$523$			9.19853i			0.402224i	0.979568	+	0.201112i	$0.0644555\pi$
$523$			9.19853i			0.402224i	−0.979568	+	0.201112i	$0.935545\pi$
$524$	−5.20213	+	12.5591i	−0.227256	+	0.548645i
$525$	−5.79657	+	5.79657i	−0.252983	+	0.252983i
$526$	6.00648			0.261895
$527$	−15.3187	−	1.26875i	−0.667291	−	0.0552675i
$528$	11.4195			0.496972
$529$	9.39144	−	9.39144i	0.408324	−	0.408324i
$530$	0.127156	−	0.306982i	0.00552330	−	0.0133344i
$531$		−	16.3117i		−	0.707866i
$532$	16.6434	+	6.89393i	0.721583	+	0.298890i
$533$	0.755933	+	1.82498i	0.0327431	+	0.0790488i
$534$	−7.60972	+	3.15205i	−0.329305	+	0.136403i
$535$	2.04171	+	2.04171i	0.0882710	+	0.0882710i
$536$	−11.7687	−	11.7687i	−0.508329	−	0.508329i
$537$	4.79843	−	1.98757i	0.207068	−	0.0857702i
$538$	−0.475654	−	1.14833i	−0.0205069	−	0.0495080i
$539$	−14.5946	−	6.04530i	−0.628636	−	0.260390i
$540$		−	2.89052i		−	0.124388i
$541$	−5.46780	+	13.2004i	−0.235079	+	0.567531i	−0.996761	−	0.0804201i	$-0.974374\pi$
$541$	−5.46780	+	13.2004i	−0.235079	+	0.567531i	0.761682	+	0.647951i	$0.224374\pi$
$542$	−7.00251	+	7.00251i	−0.300784	+	0.300784i
$543$	−1.88532			−0.0809070
$544$	−19.2118	−	9.88821i	−0.823699	−	0.423954i
$545$	−5.76330			−0.246873
$546$	−6.47534	+	6.47534i	−0.277119	+	0.277119i
$547$	9.06998	−	21.8969i	0.387805	−	0.936243i	−0.602600	−	0.798043i	$-0.705869\pi$
$547$	9.06998	−	21.8969i	0.387805	−	0.936243i	0.990404	−	0.138199i	$-0.0441315\pi$
$548$			3.19598i			0.136525i
$549$	46.1771	+	19.1272i	1.97079	+	0.816329i
$550$	−2.25901	−	5.45373i	−0.0963245	−	0.232548i
$551$	−25.0490	+	10.3756i	−1.06712	+	0.442017i
$552$	17.2773	+	17.2773i	0.735371	+	0.735371i
$553$	11.5383	+	11.5383i	0.490660	+	0.490660i
$554$	22.5776	−	9.35196i	0.959231	−	0.397327i
$555$	0.402158	+	0.970895i	0.0170707	+	0.0412122i
$556$	19.4687	+	8.06419i	0.825656	+	0.341998i
$557$			0.399812i			0.0169406i	0.999964	+	0.00847028i	$0.00269621\pi$
$557$			0.399812i			0.0169406i	−0.999964	+	0.00847028i	$0.997304\pi$
$558$	5.51819	−	13.3221i	0.233604	−	0.563969i
$559$	−0.0220108	+	0.0220108i	−0.000930957	+	0.000930957i
$560$	−2.17605			−0.0919549
$561$	20.4307	+	63.7665i	0.862584	+	2.69222i
$562$	−5.67668			−0.239456
$563$	−6.55034	+	6.55034i	−0.276064	+	0.276064i	−0.831536	−	0.555472i	$-0.812538\pi$
$563$	−6.55034	+	6.55034i	−0.276064	+	0.276064i	0.555472	+	0.831536i	$0.312538\pi$
$564$	−5.91343	+	14.2763i	−0.249001	+	0.601140i
$565$		−	9.02043i		−	0.379492i
$566$	−16.4272	−	6.80437i	−0.690487	−	0.286009i
$567$	−5.81995	−	14.0506i	−0.244415	−	0.590070i
$568$	29.4662	−	12.2053i	1.23637	−	0.512123i
$569$	4.07046	+	4.07046i	0.170643	+	0.170643i	0.787262	−	0.616619i	$-0.211498\pi$
$569$	4.07046	+	4.07046i	0.170643	+	0.170643i	−0.616619	+	0.787262i	$0.711498\pi$
$570$	−9.78584	−	9.78584i	−0.409884	−	0.409884i
$571$	−12.9331	+	5.35705i	−0.541232	+	0.224186i	−0.636515	−	0.771265i	$-0.719625\pi$
$571$	−12.9331	+	5.35705i	−0.541232	+	0.224186i	0.0952826	+	0.995450i	$0.469625\pi$
$572$	2.92028	+	7.05018i	0.122103	+	0.294783i
$573$	−12.8813	−	5.33561i	−0.538125	−	0.222899i
$574$		−	5.07337i		−	0.211759i
$575$	1.19300	−	2.88015i	0.0497514	−	0.120110i
$576$	18.3276	−	18.3276i	0.763651	−	0.763651i
$577$	−18.4417			−0.767736			−0.383868	−	0.923388i	$-0.625408\pi$
$577$	−18.4417			−0.767736			−0.383868	+	0.923388i	$0.625408\pi$
$578$	−2.69298	+	16.1458i	−0.112013	+	0.671575i
$579$	−39.5495			−1.64362
$580$	−3.79091	+	3.79091i	−0.157409	+	0.157409i
$581$	−14.7154	+	35.5262i	−0.610499	+	1.47388i
$582$			32.9919i			1.36756i
$583$	1.95459	+	0.809616i	0.0809507	+	0.0335309i
$584$	−1.87316	−	4.52220i	−0.0775118	−	0.187130i
$585$	−4.30573	+	1.78349i	−0.178020	+	0.0737384i
$586$	−5.66397	−	5.66397i	−0.233977	−	0.233977i
$587$	−2.85082	−	2.85082i	−0.117666	−	0.117666i	0.645822	−	0.763488i	$-0.276515\pi$
$587$	−2.85082	−	2.85082i	−0.117666	−	0.117666i	−0.763488	+	0.645822i	$0.776515\pi$
$588$	−6.76568	+	2.80244i	−0.279012	+	0.115571i
$589$	7.74084	+	18.6880i	0.318956	+	0.770027i
$590$	−3.61221	−	1.49623i	−0.148712	−	0.0615987i
$591$			16.7684i			0.689758i
$592$	−0.106753	+	0.257724i	−0.00438752	+	0.0105924i
$593$	−4.61328	+	4.61328i	−0.189445	+	0.189445i	−0.795456	−	0.606011i	$-0.792769\pi$
$593$	−4.61328	+	4.61328i	−0.189445	+	0.189445i	0.606011	+	0.795456i	$0.292769\pi$
$594$	−15.9039			−0.652544
$595$	−3.89317	−	12.1510i	−0.159604	−	0.498144i
$596$	−3.17114			−0.129895
$597$	27.9372	−	27.9372i	1.14339	−	1.14339i
$598$	1.33269	−	3.21741i	0.0544979	−	0.131570i
$599$		−	6.81189i		−	0.278326i	−0.990269	−	0.139163i	$-0.955559\pi$
$599$		−	6.81189i		−	0.278326i	0.990269	−	0.139163i	$-0.0444413\pi$
$600$	−7.24113	−	2.99938i	−0.295618	−	0.122449i
$601$	14.6029	+	35.2545i	0.595664	+	1.43806i	0.877961	+	0.478732i	$0.158904\pi$
$601$	14.6029	+	35.2545i	0.595664	+	1.43806i	−0.282297	+	0.959327i	$0.591096\pi$
$602$	0.0738616	−	0.0305945i	0.00301038	−	0.00124694i
$603$	15.9780	+	15.9780i	0.650674	+	0.650674i
$604$	16.7207	+	16.7207i	0.680354	+	0.680354i
$605$	24.5619	−	10.1739i	0.998581	−	0.413626i
$606$	1.43432	+	3.46275i	0.0582652	+	0.140665i
$607$	−25.0895	−	10.3924i	−1.01835	−	0.421816i	−0.189858	−	0.981812i	$-0.560803\pi$
$607$	−25.0895	−	10.3924i	−1.01835	−	0.421816i	−0.828495	+	0.559996i	$0.810803\pi$
$608$			28.4342i			1.15316i
$609$	15.6759	−	37.8450i	0.635220	−	1.53356i
$610$	8.47142	−	8.47142i	0.342998	−	0.342998i
$611$	6.30805			0.255196
$612$	15.7999	+	8.13212i	0.638672	+	0.328721i
$613$	2.48591			0.100405			0.0502025	−	0.998739i	$-0.484013\pi$
$613$	2.48591			0.100405			0.0502025	+	0.998739i	$0.484013\pi$
$614$	−8.33154	+	8.33154i	−0.336233	+	0.336233i
$615$	1.72599	−	4.16690i	0.0695985	−	0.168026i
$616$		−	56.1349i		−	2.26174i
$617$	39.9062	+	16.5297i	1.60656	+	0.665460i	0.992325	−	0.123661i	$-0.0394635\pi$
$617$	39.9062	+	16.5297i	1.60656	+	0.665460i	0.614238	+	0.789121i	$0.289464\pi$
$618$	9.57513	+	23.1164i	0.385168	+	0.929878i
$619$	−1.27211	+	0.526923i	−0.0511302	+	0.0211788i	−0.408102	−	0.912936i	$-0.633809\pi$
$619$	−1.27211	+	0.526923i	−0.0511302	+	0.0211788i	0.356972	+	0.934115i	$0.383809\pi$
$620$	2.82824	+	2.82824i	0.113585	+	0.113585i
$621$	−5.93894	−	5.93894i	−0.238321	−	0.238321i
$622$	−29.0329	+	12.0258i	−1.16411	+	0.482192i
$623$	3.82434	+	9.23276i	0.153219	+	0.369903i
$624$	−1.99653	−	0.826992i	−0.0799253	−	0.0331062i
$625$			1.00000i			0.0400000i
$626$	−4.94825	+	11.9461i	−0.197772	+	0.477464i
$627$	62.3075	−	62.3075i	2.48832	−	2.48832i
$628$	13.8043			0.550851
$629$	−1.63012	−	0.135012i	−0.0649971	−	0.00538330i
$630$	11.9697			0.476886
$631$	22.9351	−	22.9351i	0.913032	−	0.913032i	−0.0834781	−	0.996510i	$-0.526603\pi$
$631$	22.9351	−	22.9351i	0.913032	−	0.913032i	0.996510	+	0.0834781i	$0.0266029\pi$
$632$	−5.97040	+	14.4138i	−0.237490	+	0.573351i
$633$			35.4928i			1.41071i
$634$	−8.78330	−	3.63816i	−0.348829	−	0.144490i
$635$	5.35726	+	12.9336i	0.212596	+	0.513253i
$636$	0.906094	−	0.375316i	0.0359289	−	0.0148823i
$637$	2.11386	+	2.11386i	0.0837542	+	0.0837542i
$638$	20.8579	+	20.8579i	0.825773	+	0.825773i
$639$	−40.0054	+	16.5708i	−1.58259	+	0.655530i
$640$	1.63341	+	3.94341i	0.0645663	+	0.155877i
$641$	20.6017	+	8.53352i	0.813719	+	0.337054i	0.750437	−	0.660942i	$-0.229843\pi$
$641$	20.6017	+	8.53352i	0.813719	+	0.337054i	0.0632825	+	0.997996i	$0.479843\pi$
$642$		−	7.36471i		−	0.290662i
$643$	−4.48736	+	10.8335i	−0.176964	+	0.427230i	−0.987327	−	0.158699i	$-0.949270\pi$
$643$	−4.48736	+	10.8335i	−0.176964	+	0.427230i	0.810363	+	0.585929i	$0.199270\pi$
$644$	7.31887	−	7.31887i	0.288404	−	0.288404i
$645$	0.0710730			0.00279850
$646$	20.5135	−	6.57249i	0.807094	−	0.258591i
$647$	−37.3217			−1.46727			−0.733634	−	0.679544i	$-0.762177\pi$
$647$	−37.3217			−1.46727			−0.733634	+	0.679544i	$0.762177\pi$
$648$	10.2818	−	10.2818i	0.403908	−	0.403908i
$649$	9.52665	−	22.9994i	0.373954	−	0.902804i
$650$			1.11710i			0.0438162i
$651$	−28.2346	−	11.6952i	−1.10660	−	0.458370i
$652$	−7.92097	−	19.1229i	−0.310209	−	0.748911i
$653$	−1.62208	+	0.671889i	−0.0634771	+	0.0262931i	−0.414196	−	0.910188i	$-0.635937\pi$
$653$	−1.62208	+	0.671889i	−0.0634771	+	0.0262931i	0.350719	+	0.936481i	$0.385937\pi$
$654$	10.3945	+	10.3945i	0.406456	+	0.406456i
$655$	−8.95933	−	8.95933i	−0.350070	−	0.350070i
$656$	1.10610	−	0.458164i	0.0431861	−	0.0178883i
$657$	2.54313	+	6.13967i	0.0992171	+	0.239531i
$658$	−14.9680	−	6.19994i	−0.583513	−	0.241699i
$659$			6.02834i			0.234831i	0.993083	+	0.117415i	$0.0374609\pi$
$659$			6.02834i			0.234831i	−0.993083	+	0.117415i	$0.962539\pi$
$660$	6.66774	−	16.0974i	0.259541	−	0.626589i
$661$	22.6415	−	22.6415i	0.880652	−	0.880652i	−0.112949	−	0.993601i	$-0.536030\pi$
$661$	22.6415	−	22.6415i	0.880652	−	0.880652i	0.993601	+	0.112949i	$0.0360296\pi$
$662$	−5.43353			−0.211180
$663$	1.04591	−	12.6282i	0.0406199	−	0.490438i
$664$	−36.7653			−1.42677
$665$	−11.8730	+	11.8730i	−0.460416	+	0.460416i
$666$	0.587213	−	1.41766i	0.0227540	−	0.0549331i
$667$			15.5778i			0.603176i
$668$	−18.6934	−	7.74305i	−0.723269	−	0.299588i
$669$	2.14197	+	5.17116i	0.0828132	+	0.199929i
$670$	5.00394	−	2.07270i	0.193319	−	0.0800754i
$671$	53.9385	+	53.9385i	2.08227	+	2.08227i
$672$	−30.3770	−	30.3770i	−1.17182	−	1.17182i
$673$	−36.5765	+	15.1505i	−1.40992	+	0.584009i	−0.952307	−	0.305142i	$-0.901296\pi$
$673$	−36.5765	+	15.1505i	−1.40992	+	0.584009i	−0.457615	+	0.889150i	$0.651296\pi$
$674$	−6.11393	−	14.7603i	−0.235500	−	0.568547i
$675$	2.48908	+	1.03101i	0.0958049	+	0.0396837i
$676$			12.5033i			0.480897i
$677$	2.67674	−	6.46223i	0.102876	−	0.248364i	−0.864058	−	0.503393i	$-0.832085\pi$
$677$	2.67674	−	6.46223i	0.102876	−	0.248364i	0.966933	+	0.255029i	$0.0820850\pi$
$678$	−16.2689	+	16.2689i	−0.624803	+	0.624803i
$679$	40.0286			1.53616
$680$	9.30886	−	7.88481i	0.356978	−	0.302369i
$681$	−38.5677			−1.47792
$682$	15.5613	−	15.5613i	0.595871	−	0.595871i
$683$	14.2417	−	34.3826i	0.544945	−	1.31561i	−0.376251	−	0.926518i	$-0.622787\pi$
$683$	14.2417	−	34.3826i	0.544945	−	1.31561i	0.921197	−	0.389097i	$-0.127213\pi$
$684$		−	23.3844i		−	0.894126i
$685$	−2.75213	−	1.13997i	−0.105153	−	0.0435559i
$686$	5.04383	+	12.1769i	0.192574	+	0.464915i
$687$	6.48641	−	2.68676i	0.247472	−	0.102506i
$688$	0.0133405	+	0.0133405i	0.000508602	+	0.000508602i
$689$	−0.283098	−	0.283098i	−0.0107852	−	0.0107852i
$690$	−7.34616	+	3.04288i	−0.279664	+	0.115840i
$691$	−5.98831	−	14.4571i	−0.227806	−	0.549972i	0.768104	−	0.640325i	$-0.221200\pi$
$691$	−5.98831	−	14.4571i	−0.227806	−	0.549972i	−0.995910	+	0.0903530i	$0.971200\pi$
$692$	−22.3786	−	9.26952i	−0.850706	−	0.352374i
$693$			76.2127i			2.89508i
$694$	3.40627	−	8.22347i	0.129300	−	0.312158i
$695$	−13.8885	+	13.8885i	−0.526821	+	0.526821i
$696$	39.1650			1.48455
$697$	4.53731	+	5.35677i	0.171863	+	0.202902i
$698$	−25.9276			−0.981372
$699$	5.88013	−	5.88013i	0.222407	−	0.222407i
$700$	−1.27057	+	3.06743i	−0.0480231	+	0.115938i
$701$			6.08551i			0.229847i	0.993374	+	0.114923i	$0.0366622\pi$
$701$			6.08551i			0.229847i	−0.993374	+	0.114923i	$0.963338\pi$
$702$	2.78055	+	1.15174i	0.104945	+	0.0434697i
$703$	0.823733	+	1.98867i	0.0310677	+	0.0750040i
$704$	36.5459	−	15.1378i	1.37738	−	0.570528i
$705$	−10.1844	−	10.1844i	−0.383566	−	0.383566i
$706$	−15.6407	−	15.6407i	−0.588644	−	0.588644i
$707$	4.20130	−	1.74024i	0.158006	−	0.0654483i
$708$	−4.41630	−	10.6619i	−0.165975	−	0.400698i
$709$	18.2079	+	7.54197i	0.683813	+	0.283245i	0.697420	−	0.716663i	$-0.254331\pi$
$709$	18.2079	+	7.54197i	0.683813	+	0.283245i	−0.0136069	+	0.999907i	$0.504331\pi$
$710$			10.3792i			0.389524i
$711$	8.10584	−	19.5692i	0.303993	−	0.733903i
$712$	−6.75626	+	6.75626i	−0.253202	+	0.253202i
$713$	11.6220			0.435247
$714$	−14.8936	+	28.9367i	−0.557377	+	1.08293i
$715$	−7.11269			−0.266000
$716$	1.48745	−	1.48745i	0.0555886	−	0.0555886i
$717$	−13.8970	+	33.5504i	−0.518995	+	1.25296i
$718$			32.8425i			1.22567i
$719$	−14.7049	−	6.09095i	−0.548399	−	0.227154i	0.0912412	−	0.995829i	$-0.470917\pi$
$719$	−14.7049	−	6.09095i	−0.548399	−	0.227154i	−0.639640	+	0.768675i	$0.720917\pi$
$720$	1.08096	+	2.60966i	0.0402849	+	0.0972563i
$721$	28.0468	−	11.6174i	1.04452	−	0.432653i
$722$	−7.10797	−	7.10797i	−0.264531	−	0.264531i
$723$	−23.3908	−	23.3908i	−0.869914	−	0.869914i
$724$	−0.705464	+	0.292213i	−0.0262184	+	0.0108600i
$725$	−1.91226	−	4.61660i	−0.0710196	−	0.171456i
$726$	−62.6479	−	25.9496i	−2.32508	−	0.963081i
$727$			22.2643i			0.825736i	0.910791	+	0.412868i	$0.135473\pi$
$727$			22.2643i			0.825736i	−0.910791	+	0.412868i	$0.864527\pi$
$728$	−4.06523	+	9.81433i	−0.150667	+	0.363743i
$729$	−29.0987	+	29.0987i	−1.07773	+	1.07773i
$730$	1.59290			0.0589560
$731$	−0.0506257	+	0.0983607i	−0.00187246	+	0.00363800i
$732$	35.3616			1.30700
$733$	4.01178	−	4.01178i	0.148178	−	0.148178i	−0.629125	−	0.777304i	$-0.716587\pi$
$733$	4.01178	−	4.01178i	0.148178	−	0.148178i	0.777304	+	0.629125i	$0.216587\pi$
$734$	3.41801	−	8.25181i	0.126161	−	0.304580i
$735$		−	6.82567i		−	0.251769i
$736$	15.0934	+	6.25191i	0.556352	+	0.230449i
$737$	13.1971	+	31.8607i	0.486122	+	1.17360i
$738$	−6.08432	+	2.52021i	−0.223967	+	0.0927702i
$739$	−28.1411	−	28.1411i	−1.03519	−	1.03519i	−0.999358	−	0.0358281i	$-0.988593\pi$
$739$	−28.1411	−	28.1411i	−1.03519	−	1.03519i	−0.0358281	−	0.999358i	$-0.511407\pi$
$740$	0.300965	+	0.300965i	0.0110637	+	0.0110637i
$741$	−15.4058	+	6.38128i	−0.565946	+	0.234422i
$742$	0.393501	+	0.949994i	0.0144459	+	0.0348754i
$743$	−9.83928	−	4.07556i	−0.360968	−	0.149518i	0.194826	−	0.980838i	$-0.437586\pi$
$743$	−9.83928	−	4.07556i	−0.360968	−	0.149518i	−0.555794	+	0.831320i	$0.687586\pi$
$744$		−	29.2195i		−	1.07124i
$745$	1.13111	−	2.73074i	0.0414407	−	0.100047i
$746$	2.08924	−	2.08924i	0.0764926	−	0.0764926i
$747$	49.9153			1.82630
$748$	17.5283	+	20.6940i	0.640897	+	0.756647i
$749$	−8.93549			−0.326496
$750$	1.80356	−	1.80356i	0.0658567	−	0.0658567i
$751$	6.93403	−	16.7402i	0.253026	−	0.610860i	−0.745419	−	0.666596i	$-0.767751\pi$
$751$	6.93403	−	16.7402i	0.253026	−	0.610860i	0.998446	+	0.0557362i	$0.0177506\pi$
$752$		−	3.82324i		−	0.139419i
$753$	−42.6846	−	17.6805i	−1.55551	−	0.644314i
$754$	−2.13618	−	5.15720i	−0.0777952	−	0.187814i
$755$	−20.3626	+	8.43445i	−0.741070	+	0.306961i
$756$	6.32512	+	6.32512i	0.230042	+	0.230042i
$757$	12.0753	+	12.0753i	0.438885	+	0.438885i	0.891637	−	0.452752i	$-0.149558\pi$
$757$	12.0753	+	12.0753i	0.438885	+	0.438885i	−0.452752	+	0.891637i	$0.649558\pi$
$758$	32.4997	−	13.4618i	1.18044	−	0.488955i
$759$	−19.3744	−	46.7738i	−0.703245	−	1.69778i
$760$	−14.8319	−	6.14357i	−0.538009	−	0.222851i
$761$		−	31.9719i		−	1.15898i	−0.814979	−	0.579491i	$-0.803251\pi$
$761$		−	31.9719i		−	1.15898i	0.814979	−	0.579491i	$-0.196749\pi$
$762$	13.6643	−	32.9886i	0.495006	−	1.19505i
$763$	12.6114	−	12.6114i	0.456565	−	0.456565i
$764$	−5.64701			−0.204301
$765$	−12.6384	+	10.7050i	−0.456941	+	0.387040i
$766$	8.97540			0.324294
$767$	−3.33118	+	3.33118i	−0.120282	+	0.120282i
$768$	17.2478	−	41.6399i	0.622376	−	1.50255i
$769$			34.9147i			1.25906i	0.776977	+	0.629529i	$0.216752\pi$
$769$			34.9147i			1.25906i	−0.776977	+	0.629529i	$0.783248\pi$
$770$	16.8773	+	6.99080i	0.608215	+	0.251931i
$771$	−6.97541	−	16.8401i	−0.251213	−	0.606482i
$772$	−14.7989	+	6.12991i	−0.532625	+	0.220620i
$773$	3.17604	+	3.17604i	0.114234	+	0.114234i	0.761913	−	0.647679i	$-0.224260\pi$
$773$	3.17604	+	3.17604i	0.114234	+	0.114234i	−0.647679	+	0.761913i	$0.724260\pi$
$774$	−0.0733818	−	0.0733818i	−0.00263765	−	0.00263765i
$775$	−3.44426	+	1.42666i	−0.123722	+	0.0512472i
$776$	14.6459	+	35.3582i	0.525756	+	1.26929i
$777$	−3.00456	−	1.24453i	−0.107788	−	0.0446472i
$778$		−	31.9310i		−	1.14478i
$779$	3.53531	−	8.53499i	0.126666	−	0.305798i
$780$	−2.33151	+	2.33151i	−0.0834814	+	0.0834814i
$781$	−66.0854			−2.36472
$782$	1.02156	−	12.3341i	0.0365308	−	0.441067i
$783$	−13.4627			−0.481117
$784$	1.28119	−	1.28119i	0.0457568	−	0.0457568i
$785$	−4.92383	+	11.8872i	−0.175739	+	0.424271i
$786$			32.3174i			1.15272i
$787$	−7.99286	−	3.31075i	−0.284915	−	0.118016i	0.235649	−	0.971838i	$-0.424278\pi$
$787$	−7.99286	−	3.31075i	−0.284915	−	0.118016i	−0.520564	+	0.853823i	$0.674278\pi$
$788$	2.59899	+	6.27451i	0.0925850	+	0.223520i
$789$	−15.2667	+	6.32367i	−0.543508	+	0.225129i
$790$	−3.59007	−	3.59007i	−0.127729	−	0.127729i
$791$	19.7388	+	19.7388i	0.701831	+	0.701831i
$792$	−67.3206	+	27.8851i	−2.39213	+	0.990854i
$793$	−5.52416	−	13.3365i	−0.196169	−	0.473593i
$794$	−7.85087	−	3.25194i	−0.278617	−	0.115407i
$795$			0.914127i			0.0324208i
$796$	6.12366	−	14.7838i	0.217048	−	0.523999i
$797$	13.4447	−	13.4447i	0.476236	−	0.476236i	−0.427689	−	0.903926i	$-0.640672\pi$
$797$	13.4447	−	13.4447i	0.476236	−	0.476236i	0.903926	+	0.427689i	$0.140672\pi$
$798$	42.8274			1.51607
$799$	21.3489	−	6.84016i	0.755271	−	0.241987i
$800$	−5.24051			−0.185280
$801$	9.17279	−	9.17279i	0.324104	−	0.324104i
$802$	7.19226	−	17.3636i	0.253967	−	0.613132i
$803$			10.1422i			0.357910i
$804$	14.7697	+	6.11783i	0.520888	+	0.215759i
$805$	3.69188	+	8.91299i	0.130122	+	0.314142i
$806$	−3.84758	+	1.59372i	−0.135525	+	0.0561364i
$807$	2.41794	+	2.41794i	0.0851156	+	0.0851156i
$808$	3.07439	+	3.07439i	0.108157	+	0.108157i
$809$	−20.9455	+	8.67589i	−0.736403	+	0.305028i	−0.719180	−	0.694824i	$-0.755482\pi$
$809$	−20.9455	+	8.67589i	−0.736403	+	0.305028i	−0.0172227	+	0.999852i	$0.505482\pi$
$810$	1.81084	+	4.37174i	0.0636263	+	0.153607i
$811$	−22.2809	−	9.22904i	−0.782388	−	0.324076i	−0.0445090	−	0.999009i	$-0.514172\pi$
$811$	−22.2809	−	9.22904i	−0.782388	−	0.324076i	−0.737879	+	0.674933i	$0.764172\pi$
$812$		−	16.5908i		−	0.582222i
$813$	10.4260	−	25.1706i	0.365656	−	0.882772i
$814$	1.65593	−	1.65593i	0.0580405	−	0.0580405i
$815$	19.2925			0.675786
$816$	−7.65382	−	0.633917i	−0.267937	−	0.0221915i
$817$	0.145578			0.00509311
$818$	7.09121	−	7.09121i	0.247938	−	0.247938i
$819$	5.51925	−	13.3246i	0.192858	−	0.465601i
$820$		−	1.82672i		−	0.0637917i
$821$	−0.105957	−	0.0438888i	−0.00369792	−	0.00153173i	0.380834	−	0.924644i	$-0.375637\pi$
$821$	−0.105957	−	0.0438888i	−0.00369792	−	0.00153173i	−0.384532	+	0.923112i	$0.625637\pi$
$822$	2.90762	+	7.01962i	0.101415	+	0.244838i
$823$	−31.2835	+	12.9581i	−1.09047	+	0.451689i	−0.854172	−	0.519990i	$-0.825936\pi$
$823$	−31.2835	+	12.9581i	−1.09047	+	0.451689i	−0.236302	+	0.971680i	$0.575936\pi$
$824$	20.5238	+	20.5238i	0.714981	+	0.714981i
$825$	11.4835	+	11.4835i	0.399803	+	0.399803i
$826$	11.1785	−	4.63027i	0.388948	−	0.161108i
$827$	−7.86974	−	18.9992i	−0.273658	−	0.660668i	0.725976	−	0.687720i	$-0.241388\pi$
$827$	−7.86974	−	18.9992i	−0.273658	−	0.660668i	−0.999634	+	0.0270516i	$0.991388\pi$
$828$	−12.4129	−	5.14160i	−0.431379	−	0.178683i
$829$			26.7935i			0.930576i	0.885159	+	0.465288i	$0.154049\pi$
$829$			26.7935i			0.930576i	−0.885159	+	0.465288i	$0.845951\pi$
$830$	4.57860	−	11.0537i	0.158926	−	0.383680i
$831$	−47.5398	+	47.5398i	−1.64914	+	1.64914i
$832$	−7.48577			−0.259522
$833$	9.44631	+	4.86197i	0.327295	+	0.168457i
$834$	50.0975			1.73473
$835$	13.3354	−	13.3354i	0.461491	−	0.461491i
$836$	13.6574	−	32.9719i	0.472352	−	1.14036i
$837$			10.0440i			0.347170i
$838$	31.4204	+	13.0147i	1.08540	+	0.449587i
$839$	5.29374	+	12.7802i	0.182760	+	0.441222i	0.988533	−	0.151002i	$-0.0482500\pi$
$839$	5.29374	+	12.7802i	0.182760	+	0.441222i	−0.805773	+	0.592224i	$0.798250\pi$
$840$	22.4086	−	9.28195i	0.773171	−	0.320258i
$841$	−2.84980	−	2.84980i	−0.0982690	−	0.0982690i
$842$	−10.2267	−	10.2267i	−0.352436	−	0.352436i
$843$	14.4284	−	5.97645i	0.496942	−	0.205840i
$844$	5.50114	+	13.2809i	0.189357	+	0.457149i
$845$	−10.7669	−	4.45979i	−0.370392	−	0.153421i
$846$			21.0304i			0.723041i
$847$	−31.4843	+	76.0098i	−1.08181	+	2.61173i
$848$	−0.171583	+	0.171583i	−0.00589219	+	0.00589219i
$849$	48.9168			1.67882
$850$	1.21133	+	3.78070i	0.0415483	+	0.129677i
$851$	1.23674			0.0423950
$852$	−21.6625	+	21.6625i	−0.742145	+	0.742145i
$853$	4.89128	−	11.8086i	0.167474	−	0.404319i	−0.817753	−	0.575569i	$-0.804781\pi$
$853$	4.89128	−	11.8086i	0.167474	−	0.404319i	0.985228	+	0.171250i	$0.0547807\pi$
$854$			37.0749i			1.26868i
$855$	20.1368	+	8.34095i	0.688665	+	0.285254i
$856$	−3.26936	−	7.89294i	−0.111744	−	0.269775i
$857$	5.83483	−	2.41686i	0.199314	−	0.0825585i	−0.280794	−	0.959768i	$-0.590598\pi$
$857$	5.83483	−	2.41686i	0.199314	−	0.0825585i	0.480107	+	0.877210i	$0.340598\pi$
$858$	12.8282	+	12.8282i	0.437946	+	0.437946i
$859$	24.8431	+	24.8431i	0.847636	+	0.847636i	0.989838	−	0.142202i	$-0.0454183\pi$
$859$	24.8431	+	24.8431i	0.847636	+	0.847636i	−0.142202	+	0.989838i	$0.545418\pi$
$860$	0.0265946	−	0.0110158i	0.000906868	−	0.000375637i
$861$	5.34129	+	12.8950i	0.182031	+	0.439461i
$862$	−20.7732	−	8.60453i	−0.707537	−	0.293072i
$863$		−	44.2102i		−	1.50493i	−0.658632	−	0.752466i	$-0.728864\pi$
$863$		−	44.2102i		−	1.50493i	0.658632	−	0.752466i	$-0.271136\pi$
$864$	−5.40303	+	13.0441i	−0.183815	+	0.443768i
$865$	15.9644	−	15.9644i	0.542804	−	0.542804i
$866$	−17.6279			−0.599022
$867$	−10.1536	−	43.8729i	−0.344836	−	1.49000i
$868$	−12.3777			−0.420127
$869$	22.8584	−	22.8584i	0.775417	−	0.775417i
$870$	−4.87745	+	11.7752i	−0.165361	+	0.399217i
$871$		−	6.52608i		−	0.221128i
$872$	15.7543	+	6.52566i	0.533510	+	0.220987i
$873$	−19.8843	−	48.0049i	−0.672980	−	1.62472i
$874$	−15.0470	+	6.23268i	−0.508973	+	0.210824i
$875$	−2.18823	−	2.18823i	−0.0739758	−	0.0739758i
$876$	3.32456	+	3.32456i	0.112327	+	0.112327i
$877$	21.8103	−	9.03414i	0.736483	−	0.305061i	0.0172700	−	0.999851i	$-0.494503\pi$
$877$	21.8103	−	9.03414i	0.736483	−	0.305061i	0.719213	+	0.694790i	$0.244503\pi$
$878$	−7.46888	−	18.0315i	−0.252063	−	0.608533i
$879$	20.3592	+	8.43306i	0.686699	+	0.284440i
$880$			4.31093i			0.145321i
$881$	−12.6524	+	30.5457i	−0.426271	+	1.02911i	0.554189	+	0.832391i	$0.313029\pi$
$881$	−12.6524	+	30.5457i	−0.426271	+	1.02911i	−0.980460	+	0.196719i	$0.936971\pi$
$882$	−7.04741	+	7.04741i	−0.237298	+	0.237298i
$883$	−58.1141			−1.95569			−0.977847	−	0.209320i	$-0.932875\pi$
$883$	−58.1141			−1.95569			−0.977847	+	0.209320i	$0.932875\pi$
$884$	−1.56592	−	4.88741i	−0.0526675	−	0.164381i
$885$	10.7564			0.361573
$886$	20.0068	−	20.0068i	0.672140	−	0.672140i
$887$	−10.7189	+	25.8776i	−0.359904	+	0.868885i	0.635409	+	0.772176i	$0.280832\pi$
$887$	−10.7189	+	25.8776i	−0.359904	+	0.868885i	−0.995313	+	0.0967091i	$0.969168\pi$
$888$		−	3.10936i		−	0.104343i
$889$	−40.0246	−	16.5787i	−1.34238	−	0.556033i
$890$	−1.18991	−	2.87271i	−0.0398860	−	0.0962933i
$891$	−27.8354	+	11.5298i	−0.932520	+	0.386262i
$892$	1.60299	+	1.60299i	0.0536721	+	0.0536721i
$893$	−20.8605	−	20.8605i	−0.698069	−	0.698069i
$894$	−6.96508	+	2.88503i	−0.232947	+	0.0964899i
$895$	0.750319	+	1.81143i	0.0250804	+	0.0605494i
$896$	−12.2034	−	5.05480i	−0.407686	−	0.168869i
$897$			9.58077i			0.319893i
$898$	−12.0277	+	29.0375i	−0.401371	+	0.968994i
$899$	13.1727	−	13.1727i	0.439333	−	0.439333i
$900$	4.30982			0.143661
$901$	−1.26510	−	0.651138i	−0.0421465	−	0.0216926i
$902$	−10.0508			−0.334654
$903$	−0.155524	+	0.155524i	−0.00517552	+	0.00517552i
$904$	−10.2136	+	24.6579i	−0.339701	+	0.820110i
$905$		−	0.711719i		−	0.0236583i
$906$	51.9372	+	21.5131i	1.72550	+	0.714724i
$907$	19.1037	+	46.1204i	0.634328	+	1.53140i	0.834130	+	0.551568i	$0.185970\pi$
$907$	19.1037	+	46.1204i	0.634328	+	1.53140i	−0.199802	+	0.979836i	$0.564030\pi$
$908$	−14.4315	+	5.97774i	−0.478928	+	0.198378i
$909$	−4.17401	−	4.17401i	−0.138443	−	0.138443i
$910$	−2.44447	−	2.44447i	−0.0810334	−	0.0810334i
$911$	−20.2142	+	8.37302i	−0.669728	+	0.277410i	−0.691526	−	0.722352i	$-0.743061\pi$
$911$	−20.2142	+	8.37302i	−0.669728	+	0.277410i	0.0217976	+	0.999762i	$0.493061\pi$
$912$	3.86763	+	9.33729i	0.128070	+	0.309189i
$913$	70.3802	+	29.1525i	2.32925	+	0.964805i
$914$			8.13734i			0.269159i
$915$	−12.6131	+	30.4506i	−0.416975	+	1.00667i
$916$	2.01070	−	2.01070i	0.0664354	−	0.0664354i
$917$	39.2102			1.29483
$918$	10.6594	+	0.882850i	0.351812	+	0.0291384i
$919$	−11.0529			−0.364600			−0.182300	−	0.983243i	$-0.558354\pi$
$919$	−11.0529			−0.364600			−0.182300	+	0.983243i	$0.558354\pi$
$920$	−6.52226	+	6.52226i	−0.215033	+	0.215033i
$921$	12.4048	−	29.9478i	0.408752	−	0.986814i
$922$		−	36.8378i		−	1.21319i
$923$	11.5540	+	4.78584i	0.380306	+	0.157528i
$924$	20.6342	+	49.8153i	0.678815	+	1.63880i
$925$	−0.366518	+	0.151817i	−0.0120510	+	0.00499170i
$926$	−18.5029	−	18.5029i	−0.608045	−	0.608045i
$927$	−27.8646	−	27.8646i	−0.915193	−	0.915193i
$928$	24.1934	−	10.0212i	0.794186	−	0.328963i
$929$	12.6796	+	30.6112i	0.416003	+	1.00432i	0.983494	+	0.180941i	$0.0579143\pi$
$929$	12.6796	+	30.6112i	0.416003	+	1.00432i	−0.567491	+	0.823380i	$0.692086\pi$
$930$	8.78500	+	3.63887i	0.288072	+	0.119323i
$931$		−	13.9809i		−	0.458206i
$932$	1.28889	−	3.11165i	0.0422189	−	0.101925i
$933$	61.1322	−	61.1322i	2.00138	−	2.00138i
$934$	3.31733			0.108546
$935$	−24.0722	+	7.71268i	−0.787244	+	0.252231i
$936$	13.7894			0.450721
$937$	41.2820	−	41.2820i	1.34862	−	1.34862i	0.461465	−	0.887159i	$-0.347324\pi$
$937$	41.2820	−	41.2820i	1.34862	−	1.34862i	0.887159	−	0.461465i	$-0.152676\pi$
$938$	−6.41424	+	15.4853i	−0.209432	+	0.505614i
$939$		−	35.5731i		−	1.16088i
$940$	−5.38937	−	2.23235i	−0.175782	−	0.0728112i
$941$	−2.33416	−	5.63515i	−0.0760913	−	0.183701i	0.881257	−	0.472638i	$-0.156698\pi$
$941$	−2.33416	−	5.63515i	−0.0760913	−	0.183701i	−0.957348	+	0.288937i	$0.906698\pi$
$942$	30.3196	−	12.5588i	0.987867	−	0.409188i
$943$	−3.75323	−	3.75323i	−0.122222	−	0.122222i
$944$	2.01900	+	2.01900i	0.0657127	+	0.0657127i
$945$	−7.70279	+	3.19060i	−0.250572	+	0.103790i
$946$	−0.0606101	−	0.146326i	−0.00197061	−	0.00475746i
$947$	43.5595	+	18.0429i	1.41549	+	0.586317i	0.953724	−	0.300683i	$-0.0972146\pi$
$947$	43.5595	+	18.0429i	1.41549	+	0.586317i	0.461770	+	0.887000i	$0.347215\pi$
$948$		−	14.9857i		−	0.486714i
$949$	0.734487	−	1.77321i	0.0238425	−	0.0575608i
$950$	3.69420	−	3.69420i	0.119856	−	0.119856i
$951$	26.1548			0.848129
$952$	−3.11614	+	37.6237i	−0.100995	+	1.21939i
$953$	26.8459			0.869625			0.434812	−	0.900521i	$-0.356815\pi$
$953$	26.8459			0.869625			0.434812	+	0.900521i	$0.356815\pi$
$954$	0.943823	−	0.943823i	0.0305574	−	0.0305574i
$955$	2.01422	−	4.86276i	0.0651786	−	0.157355i
$956$			14.7081i			0.475694i
$957$	−74.9740	−	31.0553i	−2.42357	−	1.00387i
$958$	−5.65952	−	13.6633i	−0.182851	−	0.441441i
$959$	8.51680	−	3.52778i	0.275022	−	0.113918i
$960$	12.0858	+	12.0858i	0.390068	+	0.390068i
$961$	12.0927	+	12.0927i	0.390088	+	0.390088i
$962$	−0.409436	+	0.169594i	−0.0132008	+	0.00546793i
$963$	4.43872	+	10.7160i	0.143036	+	0.345319i
$964$	−12.3780	−	5.12712i	−0.398667	−	0.165133i
$965$		−	14.9301i		−	0.480618i
$966$	9.41658	−	22.7336i	0.302974	−	0.731443i
$967$	−24.1223	+	24.1223i	−0.775722	+	0.775722i	−0.979100	−	0.203378i	$-0.934808\pi$
$967$	−24.1223	+	24.1223i	−0.775722	+	0.775722i	0.203378	+	0.979100i	$0.434808\pi$
$968$	−78.6610			−2.52826
$969$	−45.2197	+	38.3021i	−1.45267	+	1.23044i
$970$	−12.4546			−0.399893
$971$	−16.2292	+	16.2292i	−0.520821	+	0.520821i	−0.917819	−	0.396999i	$-0.870052\pi$
$971$	−16.2292	+	16.2292i	−0.520821	+	0.520821i	0.396999	+	0.917819i	$0.370052\pi$
$972$	−8.66335	+	20.9152i	−0.277877	+	0.670855i
$973$		−	60.7825i		−	1.94860i
$974$	−23.4043	−	9.69439i	−0.749923	−	0.310628i
$975$	−1.17609	−	2.83933i	−0.0376650	−	0.0909314i
$976$	−8.08312	+	3.34814i	−0.258734	+	0.107171i
$977$	14.0530	+	14.0530i	0.449595	+	0.449595i	0.895220	−	0.445625i	$-0.147018\pi$
$977$	14.0530	+	14.0530i	0.449595	+	0.449595i	−0.445625	+	0.895220i	$0.647018\pi$
$978$	−34.7951	−	34.7951i	−1.11263	−	1.11263i
$979$	18.2908	−	7.57632i	0.584578	−	0.242140i
$980$	−1.05793	−	2.55408i	−0.0337945	−	0.0815870i
$981$	−21.3892	−	8.85971i	−0.682906	−	0.282869i
$982$			27.9585i			0.892192i
$983$	−22.6054	+	54.5743i	−0.721001	+	1.74065i	−0.0505223	+	0.998723i	$0.516089\pi$
$983$	−22.6054	+	54.5743i	−0.721001	+	1.74065i	−0.670479	+	0.741928i	$0.733911\pi$
$984$	−9.43619	+	9.43619i	−0.300815	+	0.300815i
$985$	−6.33014			−0.201695
$986$	−12.8219	−	15.1376i	−0.408333	−	0.482081i
$987$	44.5715			1.41873
$988$	−4.77559	+	4.77559i	−0.151932	+	0.151932i
$989$	0.0320086	−	0.0772755i	0.00101781	−	0.00245722i
$990$		−	23.7130i		−	0.753649i
$991$	−9.78771	−	4.05420i	−0.310917	−	0.128786i	0.221768	−	0.975099i	$-0.428817\pi$
$991$	−9.78771	−	4.05420i	−0.310917	−	0.128786i	−0.532685	+	0.846313i	$0.678817\pi$
$992$	−7.47643	−	18.0497i	−0.237377	−	0.573078i
$993$	13.8104	−	5.72046i	0.438261	−	0.181533i
$994$	−22.7121	−	22.7121i	−0.720383	−	0.720383i
$995$	10.5464	+	10.5464i	0.334345	+	0.334345i
$996$	32.6264	−	13.5143i	1.03381	−	0.428217i
$997$	15.6083	+	37.6817i	0.494319	+	1.19339i	0.952501	+	0.304534i	$0.0985008\pi$
$997$	15.6083	+	37.6817i	0.494319	+	1.19339i	−0.458182	+	0.888858i	$0.651499\pi$
$998$	28.9917	+	12.0088i	0.917718	+	0.380131i
$999$			1.06882i			0.0338159i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.2.l.a.76.4	yes	24
3.2	odd	2		765.2.be.b.586.3		24
5.2	odd	4		425.2.n.f.399.4		24
5.3	odd	4		425.2.n.c.399.3		24
5.4	even	2		425.2.m.b.76.3		24
17.6	odd	16		1445.2.d.j.866.14		24
17.7	odd	16		1445.2.a.p.1.6		12
17.10	odd	16		1445.2.a.q.1.6		12
17.11	odd	16		1445.2.d.j.866.13		24
17.15	even	8	inner	85.2.l.a.66.4	✓	24
51.32	odd	8		765.2.be.b.406.3		24
85.24	odd	16		7225.2.a.bs.1.7		12
85.32	odd	8		425.2.n.c.49.3		24
85.44	odd	16		7225.2.a.bq.1.7		12
85.49	even	8		425.2.m.b.151.3		24
85.83	odd	8		425.2.n.f.49.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.l.a.66.4	✓	24	17.15	even	8	inner
85.2.l.a.76.4	yes	24	1.1	even	1	trivial
425.2.m.b.76.3		24	5.4	even	2
425.2.m.b.151.3		24	85.49	even	8
425.2.n.c.49.3		24	85.32	odd	8
425.2.n.c.399.3		24	5.3	odd	4
425.2.n.f.49.4		24	85.83	odd	8
425.2.n.f.399.4		24	5.2	odd	4
765.2.be.b.406.3		24	51.32	odd	8
765.2.be.b.586.3		24	3.2	odd	2
1445.2.a.p.1.6		12	17.7	odd	16
1445.2.a.q.1.6		12	17.10	odd	16
1445.2.d.j.866.13		24	17.11	odd	16
1445.2.d.j.866.14		24	17.6	odd	16
7225.2.a.bq.1.7		12	85.44	odd	16
7225.2.a.bs.1.7		12	85.24	odd	16

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

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

Label	85.2.l.a.76.4

Level	$85$
Weight	$2$
Character	85.76
Analytic conductor	$0.679$
Analytic rank	$0$
Dimension	$24$
Inner twists	$2$