LMFDB - Embedded newform 312.2.bt.c.115.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [48,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.49133254306$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			115.5
Character	$\chi$	$=$	312.115
Dual form			312.2.bt.c.19.5

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.614612 - 1.27368i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.24450 + 1.56563i) q^{4} +(-2.47909 + 2.47909i) q^{5} +(-0.795730 + 1.16911i) q^{6} +(3.75755 - 1.00683i) q^{7} +(2.75900 + 0.622837i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(4.68125 + 1.63388i) q^{10} +(0.509830 + 0.136608i) q^{11} +(1.97813 + 0.294955i) q^{12} +(0.521969 - 3.56757i) q^{13} +(-3.59181 - 4.16709i) q^{14} +(3.38651 + 0.907411i) q^{15} +(-0.902421 - 3.89688i) q^{16} +(5.38161 + 3.10707i) q^{17} +(1.41034 + 0.104568i) q^{18} +(3.55975 - 0.953832i) q^{19} +(-0.796113 - 6.96660i) q^{20} +(-2.75071 - 2.75071i) q^{21} +(-0.139353 - 0.733319i) q^{22} +(1.37494 + 2.38147i) q^{23} +(-0.840107 - 2.70078i) q^{24} -7.29182i q^{25} +(-4.86474 + 1.52785i) q^{26} +1.00000 q^{27} +(-3.09995 + 7.13595i) q^{28} +(0.839483 - 0.484676i) q^{29} +(-0.925639 - 4.87102i) q^{30} +(-0.348039 + 0.348039i) q^{31} +(-4.40872 + 3.54446i) q^{32} +(-0.136608 - 0.509830i) q^{33} +(0.649803 - 8.76407i) q^{34} +(-6.81928 + 11.8113i) q^{35} +(-0.733627 - 1.86059i) q^{36} +(-1.50405 + 5.61319i) q^{37} +(-3.40274 - 3.94773i) q^{38} +(-3.35059 + 1.33175i) q^{39} +(-8.38389 + 5.29575i) q^{40} +(1.71600 - 6.40421i) q^{41} +(-1.81290 + 5.19414i) q^{42} +(7.50871 + 4.33516i) q^{43} +(-0.848364 + 0.628197i) q^{44} +(-0.907411 - 3.38651i) q^{45} +(2.18817 - 3.21492i) q^{46} +(1.54875 + 1.54875i) q^{47} +(-2.92358 + 2.72996i) q^{48} +(7.04327 - 4.06643i) q^{49} +(-9.28742 + 4.48164i) q^{50} -6.21414i q^{51} +(4.93592 + 5.25706i) q^{52} -14.2470i q^{53} +(-0.614612 - 1.27368i) q^{54} +(-1.60258 + 0.925250i) q^{55} +(10.9942 - 0.437508i) q^{56} +(-2.60592 - 2.60592i) q^{57} +(-1.13328 - 0.771342i) q^{58} +(3.44998 + 12.8755i) q^{59} +(-5.63519 + 4.17275i) q^{60} +(5.42370 + 3.13137i) q^{61} +(0.657198 + 0.229380i) q^{62} +(-1.00683 + 3.75755i) q^{63} +(7.22415 + 3.43681i) q^{64} +(7.55033 + 10.1383i) q^{65} +(-0.565397 + 0.487342i) q^{66} +(-1.76589 + 6.59040i) q^{67} +(-11.5620 + 4.55887i) q^{68} +(1.37494 - 2.38147i) q^{69} +(19.2350 + 1.42616i) q^{70} +(-2.98604 - 11.1440i) q^{71} +(-1.91889 + 2.07794i) q^{72} +(-5.69573 + 5.69573i) q^{73} +(8.07379 - 1.53426i) q^{74} +(-6.31490 + 3.64591i) q^{75} +(-2.93677 + 6.76031i) q^{76} +2.05325 q^{77} +(3.75553 + 3.44906i) q^{78} +4.82868i q^{79} +(11.8979 + 7.42353i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-9.21156 + 1.75047i) q^{82} +(-10.2669 - 10.2669i) q^{83} +(7.72989 - 0.883339i) q^{84} +(-21.0442 + 5.63879i) q^{85} +(0.906642 - 12.2281i) q^{86} +(-0.839483 - 0.484676i) q^{87} +(1.32153 + 0.694443i) q^{88} +(-7.12395 - 1.90886i) q^{89} +(-3.75561 + 3.23714i) q^{90} +(-1.63062 - 13.9308i) q^{91} +(-5.43964 - 0.811092i) q^{92} +(0.475430 + 0.127391i) q^{93} +(1.02073 - 2.92449i) q^{94} +(-6.46031 + 11.1896i) q^{95} +(5.27395 + 2.04583i) q^{96} +(-3.76138 + 1.00786i) q^{97} +(-9.50820 - 6.47156i) q^{98} +(-0.373221 + 0.373221i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$48 q + 2 q^{2} - 24 q^{3} + 2 q^{6} - 4 q^{8} - 24 q^{9} - 6 q^{10} + 20 q^{11} - 28 q^{14} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 20 q^{19} + 4 q^{20} + 14 q^{22} + 2 q^{24} - 12 q^{26} + 48 q^{27} - 2 q^{28}+ \cdots + 8 q^{99}+O(q^{100})$ 48 * q + 2 * q^2 - 24 * q^3 + 2 * q^6 - 4 * q^8 - 24 * q^9 - 6 * q^10 + 20 * q^11 - 28 * q^14 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 20 * q^19 + 4 * q^20 + 14 * q^22 + 2 * q^24 - 12 * q^26 + 48 * q^27 - 2 * q^28 + 6 * q^30 - 18 * q^32 - 28 * q^33 + 12 * q^35 + 52 * q^40 - 36 * q^41 + 14 * q^42 + 12 * q^43 + 12 * q^44 - 14 * q^46 + 4 * q^48 + 24 * q^49 - 32 * q^50 + 24 * q^52 + 2 * q^54 - 54 * q^56 - 40 * q^57 - 22 * q^58 + 96 * q^59 - 56 * q^60 - 108 * q^62 - 52 * q^65 - 28 * q^66 - 12 * q^67 - 6 * q^68 - 52 * q^70 + 2 * q^72 - 48 * q^73 + 114 * q^76 + 36 * q^78 - 16 * q^80 - 24 * q^81 - 60 * q^82 + 48 * q^83 + 10 * q^84 + 24 * q^86 + 102 * q^88 + 80 * q^89 - 152 * q^91 - 100 * q^92 - 10 * q^94 - 24 * q^96 - 64 * q^97 - 6 * q^98 + 8 * q^99

Character values

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

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

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−0.614612	−	1.27368i	−0.434596	−	0.900625i
$2$	−0.614612	−	1.27368i	−0.434596	−	0.900625i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.24450	+	1.56563i	−0.622252	+	0.782817i
$5$	−2.47909	+	2.47909i	−1.10868	+	1.10868i	−0.115361	+	0.993324i	$0.536802\pi$
$5$	−2.47909	+	2.47909i	−1.10868	+	1.10868i	−0.993324	+	0.115361i	$0.963198\pi$
$6$	−0.795730	+	1.16911i	−0.324855	+	0.477286i
$7$	3.75755	−	1.00683i	1.42022	−	0.380547i	0.534658	−	0.845069i	$-0.320441\pi$
$7$	3.75755	−	1.00683i	1.42022	−	0.380547i	0.885561	+	0.464522i	$0.153774\pi$
$8$	2.75900	+	0.622837i	0.975453	+	0.220206i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	4.68125	+	1.63388i	1.48034	+	0.516679i
$11$	0.509830	+	0.136608i	0.153719	+	0.0411890i	0.334858	−	0.942269i	$-0.391312\pi$
$11$	0.509830	+	0.136608i	0.153719	+	0.0411890i	−0.181139	+	0.983458i	$0.557978\pi$
$12$	1.97813	+	0.294955i	0.571037	+	0.0851461i
$13$	0.521969	−	3.56757i	0.144768	−	0.989466i
$13$	0.521969	−	3.56757i	0.144768	−	0.989466i
$14$	−3.59181	−	4.16709i	−0.959952	−	1.11370i
$15$	3.38651	+	0.907411i	0.874392	+	0.234293i
$16$	−0.902421	−	3.89688i	−0.225605	−	0.974219i
$17$	5.38161	+	3.10707i	1.30523	+	0.753576i	0.981296	−	0.192504i	$-0.0616607\pi$
$17$	5.38161	+	3.10707i	1.30523	+	0.753576i	0.323935	+	0.946079i	$0.394994\pi$
$18$	1.41034	+	0.104568i	0.332421	+	0.0246470i
$19$	3.55975	−	0.953832i	0.816662	−	0.218824i	0.173775	−	0.984785i	$-0.444403\pi$
$19$	3.55975	−	0.953832i	0.816662	−	0.218824i	0.642887	+	0.765961i	$0.277737\pi$
$20$	−0.796113	−	6.96660i	−0.178016	−	1.55778i
$21$	−2.75071	−	2.75071i	−0.600255	−	0.600255i
$22$	−0.139353	−	0.733319i	−0.0297101	−	0.156344i
$23$	1.37494	+	2.38147i	0.286696	+	0.496571i	0.973019	−	0.230725i	$-0.0741099\pi$
$23$	1.37494	+	2.38147i	0.286696	+	0.496571i	−0.686323	+	0.727296i	$0.740777\pi$
$24$	−0.840107	−	2.70078i	−0.171486	−	0.551295i
$25$		−	7.29182i		−	1.45836i
$26$	−4.86474	+	1.52785i	−0.954053	+	0.299636i
$27$	1.00000			0.192450
$28$	−3.09995	+	7.13595i	−0.585835	+	1.34857i
$29$	0.839483	−	0.484676i	0.155888	−	0.0900020i	−0.420027	−	0.907512i	$-0.637979\pi$
$29$	0.839483	−	0.484676i	0.155888	−	0.0900020i	0.575915	+	0.817510i	$0.304646\pi$
$30$	−0.925639	−	4.87102i	−0.168998	−	0.889322i
$31$	−0.348039	+	0.348039i	−0.0625097	+	0.0625097i	−0.737671	−	0.675161i	$-0.764074\pi$
$31$	−0.348039	+	0.348039i	−0.0625097	+	0.0625097i	0.675161	+	0.737671i	$0.264074\pi$
$32$	−4.40872	+	3.54446i	−0.779359	+	0.626578i
$33$	−0.136608	−	0.509830i	−0.0237805	−	0.0887499i
$34$	0.649803	−	8.76407i	0.111440	−	1.50303i
$35$	−6.81928	+	11.8113i	−1.15267	+	1.99648i
$36$	−0.733627	−	1.86059i	−0.122271	−	0.310098i
$37$	−1.50405	+	5.61319i	−0.247264	+	0.922802i	0.724968	+	0.688783i	$0.241855\pi$
$37$	−1.50405	+	5.61319i	−0.247264	+	0.922802i	−0.972232	+	0.234019i	$0.924812\pi$
$38$	−3.40274	−	3.94773i	−0.551997	−	0.640406i
$39$	−3.35059	+	1.33175i	−0.536524	+	0.213250i
$40$	−8.38389	+	5.29575i	−1.32561	+	0.837331i
$41$	1.71600	−	6.40421i	0.267994	−	1.00017i	−0.692398	−	0.721516i	$-0.743446\pi$
$41$	1.71600	−	6.40421i	0.267994	−	1.00017i	0.960392	−	0.278653i	$-0.0898878\pi$
$42$	−1.81290	+	5.19414i	−0.279736	+	0.801474i
$43$	7.50871	+	4.33516i	1.14507	+	0.661105i	0.947681	−	0.319220i	$-0.103421\pi$
$43$	7.50871	+	4.33516i	1.14507	+	0.661105i	0.197388	+	0.980326i	$0.436754\pi$
$44$	−0.848364	+	0.628197i	−0.127896	+	0.0947043i
$45$	−0.907411	−	3.38651i	−0.135269	−	0.504830i
$46$	2.18817	−	3.21492i	0.322628	−	0.474013i
$47$	1.54875	+	1.54875i	0.225908	+	0.225908i	0.810981	−	0.585073i	$-0.198934\pi$
$47$	1.54875	+	1.54875i	0.225908	+	0.225908i	−0.585073	+	0.810981i	$0.698934\pi$
$48$	−2.92358	+	2.72996i	−0.421983	+	0.394035i
$49$	7.04327	−	4.06643i	1.00618	−	0.580919i
$50$	−9.28742	+	4.48164i	−1.31344	+	0.633800i
$51$		−	6.21414i		−	0.870154i
$52$	4.93592	+	5.25706i	0.684488	+	0.729024i
$53$		−	14.2470i		−	1.95698i	−0.206300	−	0.978489i	$-0.566142\pi$
$53$		−	14.2470i		−	1.95698i	0.206300	−	0.978489i	$-0.433858\pi$
$54$	−0.614612	−	1.27368i	−0.0836381	−	0.173325i
$55$	−1.60258	+	0.925250i	−0.216092	+	0.124761i
$56$	10.9942	−	0.437508i	1.46916	−	0.0584644i
$57$	−2.60592	−	2.60592i	−0.345162	−	0.345162i
$58$	−1.13328	−	0.771342i	−0.148806	−	0.101282i
$59$	3.44998	+	12.8755i	0.449149	+	1.67625i	0.704743	+	0.709463i	$0.251062\pi$
$59$	3.44998	+	12.8755i	0.449149	+	1.67625i	−0.255594	+	0.966784i	$0.582271\pi$
$60$	−5.63519	+	4.17275i	−0.727500	+	0.538700i
$61$	5.42370	+	3.13137i	0.694434	+	0.400931i	0.805271	−	0.592907i	$-0.202020\pi$
$61$	5.42370	+	3.13137i	0.694434	+	0.400931i	−0.110837	+	0.993839i	$0.535353\pi$
$62$	0.657198	+	0.229380i	0.0834643	+	0.0291313i
$63$	−1.00683	+	3.75755i	−0.126849	+	0.473406i
$64$	7.22415	+	3.43681i	0.903019	+	0.429602i
$65$	7.55033	+	10.1383i	0.936503	+	1.25751i
$66$	−0.565397	+	0.487342i	−0.0695955	+	0.0599877i
$67$	−1.76589	+	6.59040i	−0.215738	+	0.805146i	0.770167	+	0.637842i	$0.220173\pi$
$67$	−1.76589	+	6.59040i	−0.215738	+	0.805146i	−0.985905	+	0.167304i	$0.946494\pi$
$68$	−11.5620	+	4.55887i	−1.40209	+	0.552844i
$69$	1.37494	−	2.38147i	0.165524	−	0.286696i
$70$	19.2350	+	1.42616i	2.29903	+	0.170459i
$71$	−2.98604	−	11.1440i	−0.354377	−	1.32255i	−0.881266	−	0.472620i	$-0.843308\pi$
$71$	−2.98604	−	11.1440i	−0.354377	−	1.32255i	0.526889	−	0.849934i	$-0.323358\pi$
$72$	−1.91889	+	2.07794i	−0.226144	+	0.244888i
$73$	−5.69573	+	5.69573i	−0.666634	+	0.666634i	−0.956935	−	0.290301i	$-0.906245\pi$
$73$	−5.69573	+	5.69573i	−0.666634	+	0.666634i	0.290301	+	0.956935i	$0.406245\pi$
$74$	8.07379	−	1.53426i	0.938559	−	0.178354i
$75$	−6.31490	+	3.64591i	−0.729182	+	0.420993i
$76$	−2.93677	+	6.76031i	−0.336870	+	0.775461i
$77$	2.05325			0.233990
$78$	3.75553	+	3.44906i	0.425230	+	0.390529i
$79$			4.82868i			0.543269i	0.962400	+	0.271635i	$0.0875643\pi$
$79$			4.82868i			0.543269i	−0.962400	+	0.271635i	$0.912436\pi$
$80$	11.8979	+	7.42353i	1.33023	+	0.829976i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−9.21156	+	1.75047i	−1.01725	+	0.193307i
$83$	−10.2669	−	10.2669i	−1.12693	−	1.12693i	−0.990673	−	0.136261i	$-0.956491\pi$
$83$	−10.2669	−	10.2669i	−1.12693	−	1.12693i	−0.136261	−	0.990673i	$-0.543509\pi$
$84$	7.72989	−	0.883339i	0.843400	−	0.0963802i
$85$	−21.0442	+	5.63879i	−2.28257	+	0.611612i
$86$	0.906642	−	12.2281i	0.0977657	−	1.31859i
$87$	−0.839483	−	0.484676i	−0.0900020	−	0.0519627i
$88$	1.32153	+	0.694443i	0.140876	+	0.0740279i
$89$	−7.12395	−	1.90886i	−0.755137	−	0.202338i	−0.139342	−	0.990244i	$-0.544499\pi$
$89$	−7.12395	−	1.90886i	−0.755137	−	0.202338i	−0.615796	+	0.787906i	$0.711165\pi$
$90$	−3.75561	+	3.23714i	−0.395876	+	0.341224i
$91$	−1.63062	−	13.9308i	−0.170935	−	1.46035i
$92$	−5.43964	−	0.811092i	−0.567121	−	0.0845622i
$93$	0.475430	+	0.127391i	0.0492998	+	0.0132098i
$94$	1.02073	−	2.92449i	0.105280	−	0.301638i
$95$	−6.46031	+	11.1896i	−0.662814	+	1.14803i
$96$	5.27395	+	2.04583i	0.538270	+	0.208802i
$97$	−3.76138	+	1.00786i	−0.381911	+	0.102333i	−0.444666	−	0.895696i	$-0.646678\pi$
$97$	−3.76138	+	1.00786i	−0.381911	+	0.102333i	0.0627557	+	0.998029i	$0.480011\pi$
$98$	−9.50820	−	6.47156i	−0.960473	−	0.653727i
$99$	−0.373221	+	0.373221i	−0.0375101	+	0.0375101i
$100$	11.4163	+	9.07469i	1.14163	+	0.907469i
$101$	−2.06215	−	3.57175i	−0.205192	−	0.355402i	0.745002	−	0.667062i	$-0.232448\pi$
$101$	−2.06215	−	3.57175i	−0.205192	−	0.355402i	−0.950194	+	0.311660i	$0.899115\pi$
$102$	−7.91481	+	3.81929i	−0.783683	+	0.378166i
$103$	9.66630			0.952449			0.476224	−	0.879324i	$-0.342005\pi$
$103$	9.66630			0.952449			0.476224	+	0.879324i	$0.342005\pi$
$104$	3.66213	−	9.51782i	0.359101	−	0.933299i
$105$	13.6386			1.33099
$106$	−18.1461	+	8.75639i	−1.76250	+	0.850496i
$107$	−1.07455	−	1.86118i	−0.103881	−	0.179927i	0.809400	−	0.587258i	$-0.199793\pi$
$107$	−1.07455	−	1.86118i	−0.103881	−	0.179927i	−0.913280	+	0.407331i	$0.866459\pi$
$108$	−1.24450	+	1.56563i	−0.119752	+	0.150653i
$109$	−8.97204	+	8.97204i	−0.859365	+	0.859365i	−0.991263	−	0.131898i	$-0.957893\pi$
$109$	−8.97204	+	8.97204i	−0.859365	+	0.859365i	0.131898	+	0.991263i	$0.457893\pi$
$110$	2.16344	+	1.47250i	0.206275	+	0.140397i
$111$	5.61319	−	1.50405i	0.532780	−	0.142758i
$112$	−7.31439	−	13.7341i	−0.691145	−	1.29775i
$113$	−5.34490	+	9.25763i	−0.502806	+	0.870885i	0.497189	+	0.867642i	$0.334365\pi$
$113$	−5.34490	+	9.25763i	−0.502806	+	0.870885i	−0.999995	+	0.00324259i	$0.998968\pi$
$114$	−1.71747	+	4.92072i	−0.160855	+	0.460868i
$115$	−9.31251	−	2.49528i	−0.868396	−	0.232686i
$116$	−0.285915	+	1.91750i	−0.0265465	+	0.178036i
$117$	2.82862	+	2.23582i	0.261506	+	0.206702i
$118$	14.2788	−	12.3076i	1.31447	−	1.13301i
$119$	23.3499	+	6.25660i	2.14048	+	0.573541i
$120$	8.77820	+	4.61279i	0.801336	+	0.421088i
$121$	−9.28502	−	5.36071i	−0.844092	−	0.487337i
$122$	0.654886	−	8.83262i	0.0592906	−	0.799668i
$123$	−6.40421	+	1.71600i	−0.577448	+	0.154727i
$124$	−0.111766	−	0.978038i	−0.0100369	−	0.0878304i
$125$	5.68163	+	5.68163i	0.508180	+	0.508180i
$126$	5.40471	−	1.02706i	0.481490	−	0.0914974i
$127$	−2.10087	−	3.63881i	−0.186422	−	0.322892i	0.757633	−	0.652681i	$-0.226356\pi$
$127$	−2.10087	−	3.63881i	−0.186422	−	0.322892i	−0.944055	+	0.329789i	$0.893022\pi$
$128$	−0.0626616	−	11.3135i	−0.00553856	−	0.999985i
$129$		−	8.67032i		−	0.763379i
$130$	8.27245	−	15.8478i	0.725542	−	1.38995i
$131$	−1.54383			−0.134885			−0.0674425	−	0.997723i	$-0.521484\pi$
$131$	−1.54383			−0.134885			−0.0674425	+	0.997723i	$0.521484\pi$
$132$	0.968216	+	0.420606i	0.0842724	+	0.0366090i
$133$	12.4156	−	7.16813i	1.07657	−	0.621556i
$134$	9.47938	−	1.80137i	0.818894	−	0.155614i
$135$	−2.47909	+	2.47909i	−0.213366	+	0.213366i
$136$	12.9126	+	11.9243i	1.10725	+	1.02250i
$137$	−0.469582	−	1.75250i	−0.0401191	−	0.149726i	0.942961	−	0.332904i	$-0.108028\pi$
$137$	−0.469582	−	1.75250i	−0.0401191	−	0.149726i	−0.983080	+	0.183177i	$0.941362\pi$
$138$	−3.87828	−	0.287551i	−0.330141	−	0.0244780i
$139$	8.71429	−	15.0936i	0.739137	−	1.28022i	−0.213748	−	0.976889i	$-0.568567\pi$
$139$	8.71429	−	15.0936i	0.739137	−	1.28022i	0.952885	−	0.303333i	$-0.0980996\pi$
$140$	−10.0056	−	25.3758i	−0.845629	−	2.14464i
$141$	0.566882	−	2.11563i	0.0477401	−	0.178168i
$142$	−12.3586	+	10.6525i	−1.03711	+	0.893939i
$143$	0.753475	−	1.74755i	0.0630088	−	0.146137i
$144$	3.82600	+	1.16692i	0.318834	+	0.0972431i
$145$	−0.879600	+	3.28271i	−0.0730468	+	0.272615i
$146$	10.7552	+	3.75385i	0.890104	+	0.310671i
$147$	−7.04327	−	4.06643i	−0.580919	−	0.335394i
$148$	−6.91640	−	9.34042i	−0.568525	−	0.767778i
$149$	2.21517	+	8.26714i	0.181474	+	0.677271i	0.995358	+	0.0962430i	$0.0306826\pi$
$149$	2.21517	+	8.26714i	0.181474	+	0.677271i	−0.813884	+	0.581028i	$0.802651\pi$
$150$	8.52492	+	5.80232i	0.696057	+	0.473757i
$151$	−6.97806	−	6.97806i	−0.567867	−	0.567867i	0.363664	−	0.931530i	$-0.381526\pi$
$151$	−6.97806	−	6.97806i	−0.567867	−	0.567867i	−0.931530	+	0.363664i	$0.881526\pi$
$152$	10.4154	−	0.414477i	0.844802	−	0.0336185i
$153$	−5.38161	+	3.10707i	−0.435077	+	0.251192i
$154$	−1.26195	−	2.61518i	−0.101691	−	0.210737i
$155$		−	1.72564i		−	0.138607i
$156$	2.08479	−	6.90316i	0.166917	−	0.552695i
$157$		−	9.18347i		−	0.732921i	−0.930434	−	0.366460i	$-0.880570\pi$
$157$		−	9.18347i		−	0.732921i	0.930434	−	0.366460i	$-0.119430\pi$
$158$	6.15018	−	2.96777i	0.489282	−	0.236103i
$159$	−12.3383	+	7.12351i	−0.978489	+	0.564931i
$160$	2.14258	−	19.7167i	0.169386	−	1.55874i
$161$	7.56415	+	7.56415i	0.596139	+	0.596139i
$162$	−0.795730	+	1.16911i	−0.0625185	+	0.0918538i
$163$	1.76943	+	6.60358i	0.138592	+	0.517233i	0.999957	+	0.00924642i	$0.00294327\pi$
$163$	1.76943	+	6.60358i	0.138592	+	0.517233i	−0.861365	+	0.507986i	$0.830390\pi$
$164$	7.89107	+	10.6567i	0.616189	+	0.832147i
$165$	1.60258	+	0.925250i	0.124761	+	0.0720307i
$166$	−6.76652	+	19.3868i	−0.525184	+	1.50471i
$167$	−3.72987	+	13.9201i	−0.288626	+	1.07717i	0.657522	+	0.753435i	$0.271605\pi$
$167$	−3.72987	+	13.9201i	−0.288626	+	1.07717i	−0.946149	+	0.323733i	$0.895062\pi$
$168$	−5.87597	−	9.30247i	−0.453341	−	0.717701i
$169$	−12.4551	−	3.72432i	−0.958084	−	0.286486i
$170$	20.1160	+	23.3379i	1.54283	+	1.78993i
$171$	−0.953832	+	3.55975i	−0.0729413	+	0.272221i
$172$	−16.1319	+	6.36078i	−1.23005	+	0.485005i
$173$	5.54697	−	9.60764i	0.421728	−	0.730455i	−0.574380	−	0.818589i	$-0.694757\pi$
$173$	5.54697	−	9.60764i	0.421728	−	0.730455i	0.996109	+	0.0881335i	$0.0280902\pi$
$174$	−0.101364	+	1.36712i	−0.00768435	+	0.103641i
$175$	−7.34163	−	27.3993i	−0.554975	−	2.07120i
$176$	0.0722648	−	2.11002i	0.00544716	−	0.159049i
$177$	9.42552	−	9.42552i	0.708465	−	0.708465i
$178$	1.94720	+	10.2468i	0.145949	+	0.768031i
$179$	8.53378	−	4.92698i	0.637844	−	0.368260i	−0.145939	−	0.989294i	$-0.546620\pi$
$179$	8.53378	−	4.92698i	0.637844	−	0.368260i	0.783784	+	0.621034i	$0.213287\pi$
$180$	6.43131	+	2.79384i	0.479361	+	0.208241i
$181$	3.48599			0.259112			0.129556	−	0.991572i	$-0.458645\pi$
$181$	3.48599			0.259112			0.129556	+	0.991572i	$0.458645\pi$
$182$	−16.7412	+	10.6389i	−1.24094	+	0.788611i
$183$		−	6.26275i		−	0.462956i
$184$	2.31020	+	7.42684i	0.170310	+	0.547514i
$185$	−10.1869	−	17.6443i	−0.748959	−	1.29723i
$186$	−0.129950	−	0.683840i	−0.00952840	−	0.0501416i
$187$	2.31925	+	2.31925i	0.169600	+	0.169600i
$188$	−4.35220	+	0.497351i	−0.317417	+	0.0362731i
$189$	3.75755	−	1.00683i	0.273321	−	0.0732362i
$190$	18.2225	+	1.35109i	1.32200	+	0.0980183i
$191$	4.19758	+	2.42347i	0.303726	+	0.175356i	0.644116	−	0.764928i	$-0.277226\pi$
$191$	4.19758	+	2.42347i	0.303726	+	0.175356i	−0.340390	+	0.940285i	$0.610559\pi$
$192$	−0.635707	−	7.97470i	−0.0458782	−	0.575525i
$193$	−25.8461	−	6.92544i	−1.86044	−	0.498504i	−0.860503	−	0.509445i	$-0.829851\pi$
$193$	−25.8461	−	6.92544i	−1.86044	−	0.498504i	−0.999940	+	0.0109406i	$0.996517\pi$
$194$	3.59548	+	4.17134i	0.258140	+	0.299485i
$195$	5.00490	−	11.6080i	0.358409	−	0.831263i
$196$	−2.39883	+	16.0879i	−0.171345	+	1.14913i
$197$	−25.6972	−	6.88555i	−1.83085	−	0.490575i	−0.832835	−	0.553522i	$-0.813284\pi$
$197$	−25.6972	−	6.88555i	−1.83085	−	0.490575i	−0.998017	+	0.0629464i	$0.979950\pi$
$198$	0.704749	+	0.245977i	0.0500844	+	0.0174808i
$199$	10.0881	−	17.4731i	0.715127	−	1.23864i	−0.247783	−	0.968816i	$-0.579702\pi$
$199$	10.0881	−	17.4731i	0.715127	−	1.23864i	0.962910	−	0.269821i	$-0.0869646\pi$
$200$	4.54161	−	20.1181i	0.321141	−	1.42257i
$201$	6.59040	−	1.76589i	0.464851	−	0.124557i
$202$	−3.28183	+	4.82175i	−0.230909	+	0.339257i
$203$	2.66641	−	2.66641i	0.187145	−	0.187145i
$204$	9.72908	+	7.73352i	0.681172	+	0.541455i
$205$	11.6225	+	20.1308i	0.811751	+	1.40599i
$206$	−5.94103	−	12.3117i	−0.413931	−	0.857799i
$207$	−2.74989			−0.191130
$208$	−14.3734	+	1.18540i	−0.996616	+	0.0821929i
$209$	1.94517			0.134550
$210$	−8.38243	−	17.3711i	−0.578442	−	1.19872i
$211$	7.10800	+	12.3114i	0.489335	+	0.847553i	0.999925	−	0.0122714i	$-0.00390622\pi$
$211$	7.10800	+	12.3114i	0.489335	+	0.847553i	−0.510590	+	0.859824i	$0.670573\pi$
$212$	22.3056	+	17.7305i	1.53196	+	1.21773i
$213$	−8.15801	+	8.15801i	−0.558977	+	0.558977i
$214$	−1.71011	+	2.51253i	−0.116900	+	0.171753i
$215$	−29.3621	+	7.86755i	−2.00248	+	0.536562i
$216$	2.75900	+	0.622837i	0.187726	+	0.0423787i
$217$	−0.957356	+	1.65819i	−0.0649896	+	0.112565i
$218$	16.9418	+	5.91315i	1.14744	+	0.400489i
$219$	7.78051	+	2.08478i	0.525758	+	0.140876i
$220$	0.545814	−	3.66053i	0.0367988	−	0.246793i
$221$	13.8937	−	17.5775i	0.934593	−	1.18239i
$222$	−5.36560	−	6.22498i	−0.360116	−	0.417793i
$223$	12.9267	+	3.46369i	0.865634	+	0.231946i	0.664199	−	0.747556i	$-0.268773\pi$
$223$	12.9267	+	3.46369i	0.865634	+	0.231946i	0.201435	+	0.979502i	$0.435440\pi$
$224$	−12.9973	+	17.7573i	−0.868418	+	1.18646i
$225$	6.31490	+	3.64591i	0.420993	+	0.243061i
$226$	15.0763	+	1.11781i	1.00286	+	0.0743559i
$227$	15.1048	−	4.04732i	1.00254	−	0.268630i	0.280031	−	0.959991i	$-0.409655\pi$
$227$	15.1048	−	4.04732i	1.00254	−	0.268630i	0.722509	+	0.691361i	$0.242989\pi$
$228$	7.32298	−	0.836840i	0.484976	−	0.0554211i
$229$	10.5268	+	10.5268i	0.695632	+	0.695632i	0.963465	−	0.267833i	$-0.0863076\pi$
$229$	10.5268	+	10.5268i	0.695632	+	0.695632i	−0.267833	+	0.963465i	$0.586308\pi$
$230$	2.54540	+	13.3948i	0.167839	+	0.883224i
$231$	−1.02662	−	1.77817i	−0.0675470	−	0.116995i
$232$	2.61801	−	0.814358i	0.171881	−	0.0534653i
$233$			23.2702i			1.52448i	0.647293	+	0.762241i	$0.275901\pi$
$233$			23.2702i			1.52448i	−0.647293	+	0.762241i	$0.724099\pi$
$234$	1.10921	−	4.97691i	0.0725113	−	0.325351i
$235$	−7.67899			−0.500922
$236$	−24.4518	−	10.6222i	−1.59168	−	0.691446i
$237$	4.18176	−	2.41434i	0.271635	−	0.156828i
$238$	−6.38228	−	33.5856i	−0.413701	−	2.17703i
$239$	−5.96683	+	5.96683i	−0.385962	+	0.385962i	−0.873244	−	0.487282i	$-0.837988\pi$
$239$	−5.96683	+	5.96683i	−0.385962	+	0.385962i	0.487282	+	0.873244i	$0.337988\pi$
$240$	0.480014	−	14.0157i	0.0309847	−	0.904707i
$241$	−8.00014	−	29.8569i	−0.515334	−	1.92325i	−0.348694	−	0.937237i	$-0.613375\pi$
$241$	−8.00014	−	29.8569i	−0.515334	−	1.92325i	−0.166641	−	0.986018i	$-0.553292\pi$
$242$	−1.12112	+	15.1209i	−0.0720684	+	0.972006i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−11.6524	+	4.59452i	−0.745969	+	0.294134i
$245$	−7.37985	+	27.5420i	−0.471482	+	1.75959i
$246$	6.12173	+	7.10221i	0.390307	+	0.452820i
$247$	−1.54478	−	13.1975i	−0.0982922	−	0.839738i
$248$	−1.17701	+	0.743468i	−0.0747403	+	0.0472102i
$249$	−3.75793	+	14.0248i	−0.238149	+	0.888785i
$250$	3.74456	−	10.7286i	0.236827	−	0.678534i
$251$	−11.3156	−	6.53307i	−0.714235	−	0.412364i	0.0983923	−	0.995148i	$-0.468630\pi$
$251$	−11.3156	−	6.53307i	−0.714235	−	0.412364i	−0.812627	+	0.582784i	$0.801963\pi$
$252$	−4.62994	−	6.25261i	−0.291659	−	0.393877i
$253$	0.375658	+	1.40197i	0.0236174	+	0.0881413i
$254$	−3.34344	+	4.91228i	−0.209786	+	0.308224i
$255$	15.4054	+	15.4054i	0.964727	+	0.964727i
$256$	−14.3713	+	7.03325i	−0.898204	+	0.439578i
$257$	13.8556	−	7.99953i	0.864288	−	0.498997i	−0.00115787	−	0.999999i	$-0.500369\pi$
$257$	13.8556	−	7.99953i	0.864288	−	0.498997i	0.865446	+	0.501002i	$0.167035\pi$
$258$	−11.0432	+	5.32888i	−0.687518	+	0.331762i
$259$			22.6061i			1.40468i
$260$	−25.2694	−	0.796158i	−1.56714	−	0.0493756i
$261$			0.969351i			0.0600013i
$262$	0.948856	+	1.96634i	0.0586205	+	0.121481i
$263$	5.61079	−	3.23939i	0.345976	−	0.199749i	−0.316935	−	0.948447i	$-0.602654\pi$
$263$	5.61079	−	3.23939i	0.345976	−	0.199749i	0.662912	+	0.748698i	$0.269320\pi$
$264$	−0.0593617	−	1.49170i	−0.00365346	−	0.0918080i
$265$	35.3197	+	35.3197i	2.16967	+	2.16967i
$266$	−16.7606	−	11.4078i	−1.02766	−	0.699457i
$267$	1.90886	+	7.12395i	0.116820	+	0.435979i
$268$	−8.12050	−	10.9665i	−0.496039	−	0.669887i
$269$	9.43060	+	5.44476i	0.574994	+	0.331973i	0.759141	−	0.650926i	$-0.225619\pi$
$269$	9.43060	+	5.44476i	0.574994	+	0.331973i	−0.184147	+	0.982899i	$0.558952\pi$
$270$	4.68125	+	1.63388i	0.284892	+	0.0994349i
$271$	−6.52629	+	24.3564i	−0.396444	+	1.47955i	0.422863	+	0.906193i	$0.361025\pi$
$271$	−6.52629	+	24.3564i	−0.396444	+	1.47955i	−0.819307	+	0.573355i	$0.805642\pi$
$272$	7.25139	−	23.7753i	0.439680	−	1.44159i
$273$	−11.2492	+	8.37758i	−0.680830	+	0.507034i
$274$	−1.94351	+	1.67521i	−0.117412	+	0.101203i
$275$	0.996124	−	3.71758i	0.0600685	−	0.224179i
$276$	2.01739	+	5.11641i	0.121433	+	0.307972i
$277$	−8.00895	+	13.8719i	−0.481211	+	0.833482i	−0.999768	−	0.0215614i	$-0.993136\pi$
$277$	−8.00895	+	13.8719i	−0.481211	+	0.833482i	0.518556	+	0.855043i	$0.326470\pi$
$278$	−24.5803	−	1.82248i	−1.47423	−	0.109305i
$279$	−0.127391	−	0.475430i	−0.00762671	−	0.0284633i
$280$	−26.1709	+	28.3402i	−1.56401	+	1.69365i
$281$	6.67944	−	6.67944i	0.398462	−	0.398462i	−0.479228	−	0.877690i	$-0.659083\pi$
$281$	6.67944	−	6.67944i	0.398462	−	0.398462i	0.877690	+	0.479228i	$0.159083\pi$
$282$	−3.04304	+	0.578269i	−0.181211	+	0.0344354i
$283$	−0.711449	+	0.410755i	−0.0422913	+	0.0244169i	−0.520997	−	0.853559i	$-0.674440\pi$
$283$	−0.711449	+	0.410755i	−0.0422913	+	0.0244169i	0.478705	+	0.877976i	$0.341106\pi$
$284$	21.1636	+	9.19376i	1.25583	+	0.545549i
$285$	12.9206			0.765352
$286$	−2.68890	+	0.114380i	−0.158998	+	0.00676344i
$287$		−	25.7918i		−	1.52244i
$288$	−0.865233	−	5.59029i	−0.0509843	−	0.329411i
$289$	10.8078	+	18.7196i	0.635753	+	1.10116i
$290$	4.72173	−	0.897270i	0.277269	−	0.0526895i
$291$	2.75352	+	2.75352i	0.161414	+	0.161414i
$292$	−1.82907	−	16.0058i	−0.107038	−	0.936667i
$293$	3.12030	−	0.836083i	0.182290	−	0.0488445i	−0.166519	−	0.986038i	$-0.553253\pi$
$293$	3.12030	−	0.836083i	0.182290	−	0.0488445i	0.348809	+	0.937194i	$0.386586\pi$
$294$	−0.850441	+	11.4701i	−0.0495987	+	0.668951i
$295$	−40.4724	−	23.3668i	−2.35639	−	1.36046i
$296$	−7.64577	+	14.5500i	−0.444401	+	0.845701i
$297$	0.509830	+	0.136608i	0.0295833	+	0.00792683i
$298$	9.16819	−	7.90250i	0.531099	−	0.457780i
$299$	9.21374	−	3.66215i	0.532845	−	0.211788i
$300$	2.15075	−	14.4242i	0.124174	−	0.832780i
$301$	32.5791	+	8.72955i	1.87783	+	0.503163i
$302$	−4.59899	+	13.1766i	−0.264642	+	0.758228i
$303$	−2.06215	+	3.57175i	−0.118467	+	0.205192i
$304$	−6.92936	−	13.0111i	−0.397426	−	0.746240i
$305$	−21.2088	+	5.68289i	−1.21441	+	0.325401i
$306$	7.26501	+	4.94478i	0.415313	+	0.282674i
$307$	13.6272	−	13.6272i	0.777747	−	0.777747i	−0.201700	−	0.979447i	$-0.564647\pi$
$307$	13.6272	−	13.6272i	0.777747	−	0.777747i	0.979447	+	0.201700i	$0.0646467\pi$
$308$	−2.55528	+	3.21464i	−0.145600	+	0.183171i
$309$	−4.83315	−	8.37126i	−0.274948	−	0.476224i
$310$	−2.19791	+	1.06060i	−0.124833	+	0.0602381i
$311$	4.76959			0.270458			0.135229	−	0.990814i	$-0.456823\pi$
$311$	4.76959			0.270458			0.135229	+	0.990814i	$0.456823\pi$
$312$	−10.0737	+	1.58741i	−0.570313	+	0.0898697i
$313$	−17.9440			−1.01426			−0.507128	−	0.861871i	$-0.669293\pi$
$313$	−17.9440			−1.01426			−0.507128	+	0.861871i	$0.669293\pi$
$314$	−11.6968	+	5.64427i	−0.660087	+	0.318525i
$315$	−6.81928	−	11.8113i	−0.384223	−	0.665494i
$316$	−7.55995	−	6.00932i	−0.425281	−	0.338050i
$317$	−4.79191	+	4.79191i	−0.269141	+	0.269141i	−0.828754	−	0.559613i	$-0.810950\pi$
$317$	−4.79191	+	4.79191i	−0.269141	+	0.269141i	0.559613	+	0.828754i	$0.310950\pi$
$318$	16.6563	+	11.3368i	0.934039	+	0.635735i
$319$	0.494204	−	0.132422i	0.0276701	−	0.00741418i
$320$	−26.4295	+	9.38916i	−1.47746	+	0.524870i
$321$	−1.07455	+	1.86118i	−0.0599756	+	0.103881i
$322$	4.98526	−	14.2833i	0.277818	−	0.795978i
$323$	22.1208	+	5.92725i	1.23083	+	0.329801i
$324$	1.97813	+	0.294955i	0.109896	+	0.0163864i
$325$	−26.0141	−	3.80610i	−1.44300	−	0.211125i
$326$	7.32332	−	6.31232i	0.405601	−	0.349607i
$327$	12.2560	+	3.28399i	0.677760	+	0.181605i
$328$	8.72322	−	16.6004i	0.481659	−	0.916604i
$329$	7.37883	+	4.26017i	0.406808	+	0.234871i
$330$	0.193504	−	2.60984i	0.0106520	−	0.143667i
$331$	−15.9635	+	4.27741i	−0.877435	+	0.235108i	−0.669300	−	0.742992i	$-0.733406\pi$
$331$	−15.9635	+	4.27741i	−0.877435	+	0.235108i	−0.208135	+	0.978100i	$0.566739\pi$
$332$	28.8513	−	3.29700i	1.58342	−	0.180947i
$333$	−4.10914	−	4.10914i	−0.225179	−	0.225179i
$334$	20.0221	−	3.80480i	1.09556	−	0.208189i
$335$	−11.9604	−	20.7160i	−0.653467	−	1.13184i
$336$	−8.23689	+	13.2015i	−0.449359	+	0.720201i
$337$			22.1566i			1.20695i	0.797382	+	0.603475i	$0.206218\pi$
$337$			22.1566i			1.20695i	−0.797382	+	0.603475i	$0.793782\pi$
$338$	2.91148	+	18.1528i	0.158363	+	0.987381i
$339$	10.6898			0.580590
$340$	17.3613	−	39.9651i	0.941551	−	2.16741i
$341$	−0.224986	+	0.129896i	−0.0121837	+	0.00703424i
$342$	5.12020	−	0.972992i	0.276869	−	0.0526134i
$343$	3.11618	−	3.11618i	0.168258	−	0.168258i
$344$	18.0164	+	16.6374i	0.971381	+	0.897029i
$345$	2.49528	+	9.31251i	0.134341	+	0.501369i
$346$	−15.6463	−	1.16008i	−0.841148	−	0.0623661i
$347$	−15.3076	+	26.5135i	−0.821754	+	1.42332i	0.0826215	+	0.996581i	$0.473671\pi$
$347$	−15.3076	+	26.5135i	−0.821754	+	1.42332i	−0.904375	+	0.426738i	$0.859663\pi$
$348$	1.80356	−	0.711143i	0.0966812	−	0.0381212i
$349$	3.87693	−	14.4689i	0.207527	−	0.774502i	−0.781137	−	0.624359i	$-0.785360\pi$
$349$	3.87693	−	14.4689i	0.207527	−	0.774502i	0.988664	−	0.150143i	$-0.0479733\pi$
$350$	−30.3856	+	26.1908i	−1.62418	+	1.39996i
$351$	0.521969	−	3.56757i	0.0278606	−	0.190423i
$352$	−2.73190	+	1.20480i	−0.145611	+	0.0642162i
$353$	−0.900492	+	3.36068i	−0.0479284	+	0.178871i	−0.985741	−	0.168272i	$-0.946181\pi$
$353$	−0.900492	+	3.36068i	−0.0479284	+	0.178871i	0.937812	+	0.347143i	$0.112848\pi$
$354$	−17.7981	−	6.21202i	−0.945958	−	0.330165i
$355$	35.0298	+	20.2245i	1.85919	+	1.07340i
$356$	11.8544	−	8.77792i	0.628279	−	0.465229i
$357$	−6.25660	−	23.3499i	−0.331134	−	1.23581i
$358$	−11.5203	−	7.84109i	−0.608869	−	0.414414i
$359$	5.96490	+	5.96490i	0.314815	+	0.314815i	0.846772	−	0.531956i	$-0.178543\pi$
$359$	5.96490	+	5.96490i	0.314815	+	0.314815i	−0.531956	+	0.846772i	$0.678543\pi$
$360$	−0.394306	−	9.90853i	−0.0207817	−	0.522226i
$361$	−4.69247	+	2.70920i	−0.246972	+	0.142590i
$362$	−2.14253	−	4.44003i	−0.112609	−	0.233363i
$363$			10.7214i			0.562728i
$364$	23.8399	+	14.7840i	1.24955	+	0.774894i
$365$		−	28.2405i		−	1.47817i
$366$	−7.97672	+	3.84916i	−0.416950	+	0.201199i
$367$	−18.8420	+	10.8784i	−0.983545	+	0.567850i	−0.903339	−	0.428928i	$-0.858891\pi$
$367$	−18.8420	+	10.8784i	−0.983545	+	0.567850i	−0.0802066	+	0.996778i	$0.525558\pi$
$368$	8.03952	−	7.50707i	0.419089	−	0.391333i
$369$	4.68820	+	4.68820i	0.244058	+	0.244058i
$370$	−16.2121	+	23.8193i	−0.842827	+	1.23830i
$371$	−14.3443	−	53.5338i	−0.744721	−	2.77934i
$372$	−0.791123	+	0.585811i	−0.0410178	+	0.0303729i
$373$	−27.8295	−	16.0674i	−1.44096	−	0.831938i	−0.443045	−	0.896499i	$-0.646102\pi$
$373$	−27.8295	−	16.0674i	−1.44096	−	0.831938i	−0.997914	+	0.0645612i	$0.979435\pi$
$374$	1.52853	−	4.37941i	0.0790387	−	0.226454i
$375$	2.07962	−	7.76125i	0.107391	−	0.400789i
$376$	3.30838	+	5.23762i	0.170617	+	0.270109i
$377$	−1.29093	−	3.24790i	−0.0664863	−	0.167275i
$378$	−3.59181	−	4.16709i	−0.184743	−	0.214332i
$379$	8.60355	−	32.1089i	0.441935	−	1.64932i	−0.281971	−	0.959423i	$-0.590988\pi$
$379$	8.60355	−	32.1089i	0.441935	−	1.64932i	0.723905	−	0.689899i	$-0.242345\pi$
$380$	−9.47892	−	24.0400i	−0.486258	−	1.23322i
$381$	−2.10087	+	3.63881i	−0.107631	+	0.186422i
$382$	0.506837	−	6.83585i	0.0259321	−	0.349753i
$383$	−3.22968	−	12.0533i	−0.165029	−	0.615896i	−0.998037	−	0.0626344i	$-0.980050\pi$
$383$	−3.22968	−	12.0533i	−0.165029	−	0.615896i	0.833008	−	0.553261i	$-0.186617\pi$
$384$	−9.76648	+	5.71103i	−0.498393	+	0.291440i
$385$	−5.09020	+	5.09020i	−0.259421	+	0.259421i
$386$	7.06456	+	37.1760i	0.359577	+	1.89221i
$387$	−7.50871	+	4.33516i	−0.381689	+	0.220368i
$388$	3.10312	−	7.14324i	0.157537	−	0.362643i
$389$	12.9747			0.657845			0.328922	−	0.944357i	$-0.393315\pi$
$389$	12.9747			0.657845			0.328922	+	0.944357i	$0.393315\pi$
$390$	−17.8609	+	0.759762i	−0.904419	+	0.0384720i
$391$			17.0882i			0.864187i
$392$	21.9651	−	6.83247i	1.10940	−	0.345092i
$393$	0.771915	+	1.33700i	0.0389379	+	0.0674425i
$394$	7.02387	+	36.9619i	0.353857	+	1.86211i
$395$	−11.9708	−	11.9708i	−0.602315	−	0.602315i
$396$	−0.119853	−	1.04880i	−0.00602283	−	0.0527043i
$397$	3.20096	−	0.857695i	0.160652	−	0.0430465i	−0.177597	−	0.984103i	$-0.556832\pi$
$397$	3.20096	−	0.857695i	0.160652	−	0.0430465i	0.338248	+	0.941057i	$0.390166\pi$
$398$	−28.4554	−	2.10980i	−1.42634	−	0.105755i
$399$	−12.4156	−	7.16813i	−0.621556	−	0.358855i
$400$	−28.4153	+	6.58029i	−1.42076	+	0.329015i
$401$	12.1931	+	3.26714i	0.608896	+	0.163153i	0.550075	−	0.835115i	$-0.314599\pi$
$401$	12.1931	+	3.26714i	0.608896	+	0.163153i	0.0588209	+	0.998269i	$0.481266\pi$
$402$	−6.29972	−	7.30870i	−0.314201	−	0.364525i
$403$	1.05999	+	1.42332i	0.0528018	+	0.0709006i
$404$	8.15841	+	1.21648i	0.405896	+	0.0605222i
$405$	3.38651	+	0.907411i	0.168277	+	0.0450896i
$406$	−5.03495	−	1.75733i	−0.249880	−	0.0872151i
$407$	−1.53362	+	2.65630i	−0.0760186	+	0.131668i
$408$	3.87040	−	17.1448i	0.191613	−	0.848795i
$409$	26.0526	−	6.98078i	1.28822	−	0.345177i	0.451236	−	0.892405i	$-0.350983\pi$
$409$	26.0526	−	6.98078i	1.28822	−	0.345177i	0.836984	+	0.547228i	$0.184317\pi$
$410$	18.4967	−	27.1759i	0.913489	−	1.34212i
$411$	−1.28292	+	1.28292i	−0.0632819	+	0.0632819i
$412$	−12.0297	+	15.1339i	−0.592663	+	0.745593i
$413$	25.9269	+	44.9067i	1.27578	+	2.20972i
$414$	1.69011	+	3.50247i	0.0830646	+	0.172137i
$415$	50.9050			2.49883
$416$	10.3439	+	17.5785i	0.507151	+	0.861857i
$417$	−17.4286			−0.853481
$418$	−1.19552	−	2.47751i	−0.0584749	−	0.121179i
$419$	4.72463	+	8.18330i	0.230813	+	0.399780i	0.958048	−	0.286609i	$-0.0925280\pi$
$419$	4.72463	+	8.18330i	0.230813	+	0.399780i	−0.727234	+	0.686389i	$0.759195\pi$
$420$	−16.9732	+	21.3530i	−0.828209	+	1.04192i
$421$	−8.64486	+	8.64486i	−0.421325	+	0.421325i	−0.885660	−	0.464335i	$-0.846293\pi$
$421$	−8.64486	+	8.64486i	−0.421325	+	0.421325i	0.464335	+	0.885660i	$0.346293\pi$
$422$	11.3121	−	16.6200i	0.550664	−	0.809051i
$423$	−2.11563	+	0.566882i	−0.102866	+	0.0275627i
$424$	8.87357	−	39.3075i	0.430939	−	1.90894i
$425$	22.6562	−	39.2417i	1.09899	−	1.90350i
$426$	15.4047	+	5.37665i	0.746359	+	0.260500i
$427$	23.5326	+	6.30553i	1.13882	+	0.305146i
$428$	4.25121	+	0.633888i	0.205490	+	0.0306401i
$429$	−1.89016	+	0.221245i	−0.0912577	+	0.0106818i
$430$	28.0670	+	32.5623i	1.35351	+	1.57029i
$431$	−31.0269	−	8.31363i	−1.49451	−	0.400454i	−0.583255	−	0.812289i	$-0.698221\pi$
$431$	−31.0269	−	8.31363i	−1.49451	−	0.400454i	−0.911258	+	0.411836i	$0.864888\pi$
$432$	−0.902421	−	3.89688i	−0.0434178	−	0.187488i
$433$	−23.0742	−	13.3219i	−1.10887	−	0.640209i	−0.170337	−	0.985386i	$-0.554486\pi$
$433$	−23.0742	−	13.3219i	−1.10887	−	0.640209i	−0.938538	+	0.345177i	$0.887819\pi$
$434$	2.70040	+	0.200218i	0.129623	+	0.00961079i
$435$	3.28271	−	0.879600i	0.157394	−	0.0421736i
$436$	−2.88120	−	25.2127i	−0.137984	−	1.20747i
$437$	7.16598	+	7.16598i	0.342795	+	0.342795i
$438$	−2.12666	−	11.1912i	−0.101616	−	0.534735i
$439$	0.948699	+	1.64319i	0.0452789	+	0.0784254i	0.887777	−	0.460274i	$-0.152249\pi$
$439$	0.948699	+	1.64319i	0.0452789	+	0.0784254i	−0.842498	+	0.538700i	$0.818916\pi$
$440$	−4.99780	+	1.55462i	−0.238261	+	0.0741135i
$441$			8.13286i			0.387279i
$442$	−30.9272	−	6.89279i	−1.47106	−	0.327857i
$443$	−15.2346			−0.723819			−0.361909	−	0.932213i	$-0.617875\pi$
$443$	−15.2346			−0.723819			−0.361909	+	0.932213i	$0.617875\pi$
$444$	−4.63084	+	10.6600i	−0.219770	+	0.505901i
$445$	22.3932	−	12.9287i	1.06154	−	0.612879i
$446$	−3.53327	−	18.5932i	−0.167305	−	0.880414i
$447$	6.05197	−	6.05197i	0.286248	−	0.286248i
$448$	30.6054	+	5.64048i	1.44597	+	0.266488i
$449$	−1.46136	−	5.45387i	−0.0689658	−	0.257384i	0.922832	−	0.385204i	$-0.125869\pi$
$449$	−1.46136	−	5.45387i	−0.0689658	−	0.257384i	−0.991797	+	0.127820i	$0.959202\pi$
$450$	0.762494	−	10.2840i	0.0359443	−	0.484790i
$451$	1.74974	−	3.03063i	0.0823919	−	0.142707i
$452$	−7.84232	−	19.8893i	−0.368872	−	0.935514i
$453$	−2.55415	+	9.53221i	−0.120004	+	0.447862i
$454$	−14.4386	−	16.7511i	−0.677635	−	0.786168i
$455$	38.5783	+	30.4934i	1.80858	+	1.42955i
$456$	−5.56666	−	8.81278i	−0.260683	−	0.412696i
$457$	−0.148909	+	0.555736i	−0.00696567	+	0.0259962i	−0.969321	−	0.245797i	$-0.920950\pi$
$457$	−0.148909	+	0.555736i	−0.00696567	+	0.0259962i	0.962356	+	0.271794i	$0.0876168\pi$
$458$	6.93785	−	19.8777i	0.324185	−	0.928823i
$459$	5.38161	+	3.10707i	0.251192	+	0.145026i
$460$	15.4961	−	11.4746i	0.722511	−	0.535006i
$461$	0.184854	+	0.689883i	0.00860949	+	0.0321311i	0.970097	−	0.242718i	$-0.0780389\pi$
$461$	0.184854	+	0.689883i	0.00860949	+	0.0321311i	−0.961487	+	0.274849i	$0.911372\pi$
$462$	−1.63383	+	2.40047i	−0.0760128	+	0.111680i
$463$	6.31342	+	6.31342i	0.293410	+	0.293410i	0.838426	−	0.545016i	$-0.183476\pi$
$463$	6.31342	+	6.31342i	0.293410	+	0.293410i	−0.545016	+	0.838426i	$0.683476\pi$
$464$	−2.64629	−	2.83398i	−0.122851	−	0.131564i
$465$	−1.49445	+	0.862822i	−0.0693035	+	0.0400124i
$466$	29.6387	−	14.3022i	1.37299	−	0.662535i
$467$		−	6.14918i		−	0.284550i	−0.989827	−	0.142275i	$-0.954558\pi$
$467$		−	6.14918i		−	0.284550i	0.989827	−	0.142275i	$-0.0454418\pi$
$468$	−7.02071	+	1.64610i	−0.324532	+	0.0760908i
$469$			26.5417i			1.22558i
$470$	4.71960	+	9.78055i	0.217699	+	0.451143i
$471$	−7.95312	+	4.59173i	−0.366460	+	0.211576i
$472$	1.49915	+	37.6723i	0.0690040	+	1.73401i
$473$	3.23595	+	3.23595i	0.148789	+	0.148789i
$474$	−5.64525	−	3.84233i	−0.259295	−	0.176484i
$475$	−6.95516	−	25.9570i	−0.319125	−	1.19099i
$476$	−38.8546	+	28.7711i	−1.78090	+	1.31872i
$477$	12.3383	+	7.12351i	0.564931	+	0.326163i
$478$	11.2671	+	3.93252i	0.515345	+	0.179869i
$479$	−0.518005	+	1.93322i	−0.0236683	+	0.0883311i	−0.976750	−	0.214383i	$-0.931226\pi$
$479$	−0.518005	+	1.93322i	−0.0236683	+	0.0883311i	0.953081	+	0.302714i	$0.0978927\pi$
$480$	−18.1464	+	8.00281i	−0.828268	+	0.365277i
$481$	19.2404	+	8.29571i	0.877285	+	0.378252i
$482$	−33.1111	+	28.5400i	−1.50817	+	1.29996i
$483$	2.76867	−	10.3328i	0.125979	−	0.470160i
$484$	19.9481	−	7.86552i	0.906734	−	0.357524i
$485$	6.82625	−	11.8234i	0.309964	−	0.536873i
$486$	1.41034	+	0.104568i	0.0639744	+	0.00474332i
$487$	7.65344	+	28.5630i	0.346811	+	1.29432i	0.890483	+	0.455017i	$0.150367\pi$
$487$	7.65344	+	28.5630i	0.346811	+	1.29432i	−0.543672	+	0.839298i	$0.682966\pi$
$488$	13.0136	+	12.0175i	0.589100	+	0.544008i
$489$	4.83416	−	4.83416i	0.218608	−	0.218608i
$490$	39.6153	−	7.52810i	1.78964	−	0.340085i
$491$	−7.25472	+	4.18851i	−0.327401	+	0.189025i	−0.654687	−	0.755900i	$-0.727199\pi$
$491$	−7.25472	+	4.18851i	−0.327401	+	0.189025i	0.327286	+	0.944925i	$0.393866\pi$
$492$	5.28343	−	12.1622i	0.238195	−	0.548315i
$493$	6.02369			0.271293
$494$	−15.8599	+	10.0789i	−0.713572	+	0.453471i
$495$		−	1.85050i		−	0.0831738i
$496$	1.67034	+	1.04219i	0.0750006	+	0.0467956i
$497$	−22.4403	−	38.8678i	−1.00659	−	1.74346i
$498$	20.1727	−	3.83342i	0.903961	−	0.171780i
$499$	−12.4133	−	12.4133i	−0.555697	−	0.555697i	0.372383	−	0.928079i	$-0.378541\pi$
$499$	−12.4133	−	12.4133i	−0.555697	−	0.555697i	−0.928079	+	0.372383i	$0.878541\pi$
$500$	−15.9662	+	1.82455i	−0.714029	+	0.0815962i
$501$	13.9201	−	3.72987i	0.621903	−	0.166638i
$502$	−1.36631	+	18.4277i	−0.0609812	+	0.822470i
$503$	−6.14015	−	3.54502i	−0.273776	−	0.158065i	0.356826	−	0.934171i	$-0.383859\pi$
$503$	−6.14015	−	3.54502i	−0.273776	−	0.158065i	−0.630602	+	0.776106i	$0.717192\pi$
$504$	−5.11819	+	9.73997i	−0.227982	+	0.433853i
$505$	13.9670	+	3.74244i	0.621522	+	0.166536i
$506$	1.55478	−	1.34014i	0.0691183	−	0.0595763i
$507$	3.00219	+	12.6486i	0.133332	+	0.561744i
$508$	8.31158	+	1.23932i	0.368767	+	0.0549859i
$509$	−17.5776	−	4.70990i	−0.779112	−	0.208762i	−0.152719	−	0.988270i	$-0.548803\pi$
$509$	−17.5776	−	4.70990i	−0.779112	−	0.208762i	−0.626393	+	0.779507i	$0.715470\pi$
$510$	10.1532	−	29.0899i	0.449590	−	1.28812i
$511$	−15.6673	+	27.1366i	−0.693081	+	1.20045i
$512$	17.7908	+	13.9816i	0.786252	+	0.617907i
$513$	3.55975	−	0.953832i	0.157167	−	0.0421127i
$514$	−18.7046	−	12.7309i	−0.825026	−	0.561537i
$515$	−23.9637	+	23.9637i	−1.05597	+	1.05597i
$516$	13.5745	+	10.7902i	0.597586	+	0.475014i
$517$	0.578026	+	1.00117i	0.0254216	+	0.0440314i
$518$	28.7929	−	13.8940i	1.26509	−	0.610468i
$519$	−11.0939			−0.486970
$520$	14.5168	+	32.6743i	0.636604	+	1.43286i
$521$	−3.28873			−0.144082			−0.0720410	−	0.997402i	$-0.522951\pi$
$521$	−3.28873			−0.144082			−0.0720410	+	0.997402i	$0.522951\pi$
$522$	1.23464	−	0.595775i	0.0540387	−	0.0260764i
$523$	15.1538	+	26.2472i	0.662630	+	1.14771i	0.979922	+	0.199381i	$0.0638933\pi$
$523$	15.1538	+	26.2472i	0.662630	+	1.14771i	−0.317292	+	0.948328i	$0.602773\pi$
$524$	1.92130	−	2.41707i	0.0839324	−	0.105590i
$525$	−20.0577	+	20.0577i	−0.875390	+	0.875390i
$526$	−7.57440	−	5.15536i	−0.330260	−	0.224785i
$527$	−2.95439	+	0.791627i	−0.128695	+	0.0344838i
$528$	−1.86346	+	0.992427i	−0.0810969	+	0.0431898i
$529$	7.71906	−	13.3698i	0.335611	−	0.581296i
$530$	23.2779	−	66.6938i	1.01113	−	2.89699i
$531$	−12.8755	−	3.44998i	−0.558749	−	0.149716i
$532$	−4.22855	+	28.3590i	−0.183331	+	1.22952i
$533$	−21.9517	−	9.46475i	−0.950836	−	0.409964i
$534$	7.90040	−	6.80973i	0.341884	−	0.294686i
$535$	7.27795	+	1.95012i	0.314653	+	0.0843111i
$536$	−8.97684	+	17.0831i	−0.387741	+	0.737875i
$537$	−8.53378	−	4.92698i	−0.368260	−	0.212615i
$538$	1.13870	−	15.3580i	0.0490929	−	0.662128i
$539$	4.14637	−	1.11102i	0.178597	−	0.0478549i
$540$	−0.796113	−	6.96660i	−0.0342593	−	0.299795i
$541$	−6.90597	−	6.90597i	−0.296911	−	0.296911i	0.542892	−	0.839803i	$-0.317329\pi$
$541$	−6.90597	−	6.90597i	−0.296911	−	0.296911i	−0.839803	+	0.542892i	$0.817329\pi$
$542$	35.0334	−	6.65739i	1.50481	−	0.285959i
$543$	−1.74300	−	3.01896i	−0.0747991	−	0.129556i
$544$	−34.7389	+	5.37668i	−1.48942	+	0.230523i
$545$		−	44.4851i		−	1.90553i
$546$	17.5842	+	9.17882i	0.752534	+	0.392817i
$547$	−13.8102			−0.590482			−0.295241	−	0.955423i	$-0.595400\pi$
$547$	−13.8102			−0.590482			−0.295241	+	0.955423i	$0.595400\pi$
$548$	3.32818	+	1.44580i	0.142173	+	0.0617617i
$549$	−5.42370	+	3.13137i	−0.231478	+	0.133644i
$550$	−5.34723	+	1.01613i	−0.228007	+	0.0433281i
$551$	2.52605	−	2.52605i	0.107613	−	0.107613i
$552$	5.27674	−	5.71411i	0.224593	−	0.243209i
$553$	4.86167	+	18.1440i	0.206739	+	0.771562i
$554$	22.5907	+	1.67497i	0.959788	+	0.0711625i
$555$	−10.1869	+	17.6443i	−0.432412	+	0.748959i
$556$	12.7861	+	32.4274i	0.542251	+	1.37523i
$557$	2.82150	−	10.5300i	0.119551	−	0.446170i	−0.880036	−	0.474907i	$-0.842482\pi$
$557$	2.82150	−	10.5300i	0.119551	−	0.446170i	0.999587	+	0.0287368i	$0.00914846\pi$
$558$	−0.527248	+	0.454460i	−0.0223202	+	0.0192388i
$559$	19.3853	−	24.5250i	0.819911	−	1.03730i
$560$	52.1812	+	15.9151i	2.20506	+	0.672535i
$561$	0.848904	−	3.16815i	0.0358408	−	0.133760i
$562$	−12.6127	−	4.40218i	−0.532035	−	0.185695i
$563$	−1.69071	−	0.976130i	−0.0712548	−	0.0411390i	0.463949	−	0.885862i	$-0.346432\pi$
$563$	−1.69071	−	0.976130i	−0.0712548	−	0.0411390i	−0.535204	+	0.844723i	$0.679765\pi$
$564$	2.60682	+	3.52044i	0.109767	+	0.148237i
$565$	−9.70004	−	36.2010i	−0.408084	−	1.52299i
$566$	0.960435	+	0.653701i	0.0403701	+	0.0274771i
$567$	−2.75071	−	2.75071i	−0.115519	−	0.115519i
$568$	−1.29755	−	32.6062i	−0.0544440	−	1.36813i
$569$	−6.96741	+	4.02264i	−0.292089	+	0.168638i	−0.638884	−	0.769303i	$-0.720603\pi$
$569$	−6.96741	+	4.02264i	−0.292089	+	0.168638i	0.346794	+	0.937941i	$0.387270\pi$
$570$	−7.94117	−	16.4567i	−0.332619	−	0.689295i
$571$		−	30.0799i		−	1.25881i	−0.777079	−	0.629403i	$-0.783299\pi$
$571$		−	30.0799i		−	1.25881i	0.777079	−	0.629403i	$-0.216701\pi$
$572$	1.79832	+	3.35450i	0.0751914	+	0.140258i
$573$		−	4.84694i		−	0.202484i
$574$	−32.8504	+	15.8520i	−1.37115	+	0.661648i
$575$	17.3653	−	10.0258i	0.724181	−	0.418106i
$576$	−6.58844	+	4.53789i	−0.274518	+	0.189079i
$577$	−13.3448	−	13.3448i	−0.555551	−	0.555551i	0.372487	−	0.928038i	$-0.378505\pi$
$577$	−13.3448	−	13.3448i	−0.555551	−	0.555551i	−0.928038	+	0.372487i	$0.878505\pi$
$578$	17.2002	−	25.2710i	0.715433	−	1.05113i
$579$	6.92544	+	25.8461i	0.287812	+	1.07413i
$580$	−4.04486	−	5.46248i	−0.167954	−	0.226817i
$581$	−48.9152	−	28.2412i	−2.02934	−	1.17164i
$582$	1.81475	−	5.19945i	0.0752238	−	0.215524i
$583$	1.94626	−	7.26355i	0.0806059	−	0.300825i
$584$	−19.2620	+	12.1670i	−0.797068	+	0.503474i
$585$	−12.5552	+	1.46960i	−0.519095	+	0.0607606i
$586$	−2.98268	−	3.46039i	−0.123213	−	0.142947i
$587$	2.15095	−	8.02746i	0.0887793	−	0.331329i	−0.907224	−	0.420648i	$-0.861803\pi$
$587$	2.15095	−	8.02746i	0.0887793	−	0.331329i	0.996003	+	0.0893197i	$0.0284693\pi$
$588$	15.1319	−	5.96649i	0.624030	−	0.246054i
$589$	−0.906961	+	1.57090i	−0.0373707	+	0.0647279i
$590$	−4.88685	+	65.9102i	−0.201188	+	2.71348i
$591$	6.88555	+	25.6972i	0.283234	+	1.05704i
$592$	23.2312	+	0.795630i	0.954795	+	0.0327002i
$593$	−19.6649	+	19.6649i	−0.807540	+	0.807540i	−0.984261	−	0.176721i	$-0.943451\pi$
$593$	−19.6649	+	19.6649i	−0.807540	+	0.807540i	0.176721	+	0.984261i	$0.443451\pi$
$594$	−0.139353	−	0.733319i	−0.00571770	−	0.0300885i
$595$	−73.3974	+	42.3760i	−3.00900	+	1.73725i
$596$	−15.7001	−	6.82034i	−0.643102	−	0.279372i
$597$	−20.1762			−0.825758
$598$	−10.3273	−	9.48453i	−0.422314	−	0.387851i
$599$		−	45.6842i		−	1.86661i	−0.359088	−	0.933304i	$-0.616912\pi$
$599$		−	45.6842i		−	1.86661i	0.359088	−	0.933304i	$-0.383088\pi$
$600$	−19.6936	+	6.12590i	−0.803988	+	0.250089i
$601$	−8.81170	−	15.2623i	−0.359437	−	0.622562i	0.628430	−	0.777866i	$-0.283698\pi$
$601$	−8.81170	−	15.2623i	−0.359437	−	0.622562i	−0.987867	+	0.155304i	$0.950364\pi$
$602$	−8.90490	−	46.8605i	−0.362937	−	1.90989i
$603$	−4.82451	−	4.82451i	−0.196469	−	0.196469i
$604$	19.6093	−	2.24087i	0.797892	−	0.0911797i
$605$	36.3081	−	9.72873i	1.47614	−	0.395529i
$606$	5.81668	+	0.431272i	0.236286	+	0.0175192i
$607$	24.5125	+	14.1523i	0.994932	+	0.574424i	0.906745	−	0.421680i	$-0.138559\pi$
$607$	24.5125	+	14.1523i	0.994932	+	0.574424i	0.0881869	+	0.996104i	$0.471893\pi$
$608$	−12.3131	+	16.8226i	−0.499363	+	0.682245i
$609$	−3.64238	−	0.975973i	−0.147597	−	0.0395484i
$610$	20.2734	+	23.5204i	0.820845	+	0.952314i
$611$	6.33367	−	4.71687i	0.256233	−	0.190824i
$612$	1.83289	−	12.2924i	0.0740902	−	0.496890i
$613$	7.36770	+	1.97417i	0.297579	+	0.0797360i	0.404519	−	0.914529i	$-0.367439\pi$
$613$	7.36770	+	1.97417i	0.297579	+	0.0797360i	−0.106941	+	0.994265i	$0.534106\pi$
$614$	−25.7321	−	8.98122i	−1.03846	−	0.362453i
$615$	11.6225	−	20.1308i	0.468664	−	0.811751i
$616$	5.66491	+	1.27884i	0.228246	+	0.0515259i
$617$	−2.20669	+	0.591281i	−0.0888381	+	0.0238041i	−0.302964	−	0.953002i	$-0.597976\pi$
$617$	−2.20669	+	0.591281i	−0.0888381	+	0.0238041i	0.214126	+	0.976806i	$0.431310\pi$
$618$	−7.69177	+	11.3009i	−0.309408	+	0.454591i
$619$	−16.7902	+	16.7902i	−0.674854	+	0.674854i	−0.958831	−	0.283977i	$-0.908346\pi$
$619$	−16.7902	+	16.7902i	−0.674854	+	0.674854i	0.283977	+	0.958831i	$0.408346\pi$
$620$	2.70173	+	2.14757i	0.108504	+	0.0862485i
$621$	1.37494	+	2.38147i	0.0551746	+	0.0955652i
$622$	−2.93145	−	6.07491i	−0.117540	−	0.243582i
$623$	−28.6905			−1.14946
$624$	8.21329	+	11.8550i	0.328795	+	0.474581i
$625$	8.28849			0.331540
$626$	11.0286	+	22.8549i	0.440792	+	0.913465i
$627$	−0.972583	−	1.68456i	−0.0388412	−	0.0672750i
$628$	14.3780	+	11.4289i	0.573743	+	0.456061i
$629$	−25.5348	+	25.5348i	−1.01814	+	1.01814i
$630$	−10.8526	+	15.9450i	−0.432379	+	0.635262i
$631$	−23.0380	+	6.17302i	−0.917130	+	0.245744i	−0.686358	−	0.727264i	$-0.740792\pi$
$631$	−23.0380	+	6.17302i	−0.917130	+	0.245744i	−0.230772	+	0.973008i	$0.574125\pi$
$632$	−3.00748	+	13.3223i	−0.119631	+	0.529934i
$633$	7.10800	−	12.3114i	0.282518	−	0.489335i
$634$	9.04852	+	3.15818i	0.359363	+	0.125427i
$635$	14.2292	+	3.81270i	0.564668	+	0.151302i
$636$	4.20222	−	28.1825i	0.166629	−	1.11751i
$637$	−10.8309	−	27.2499i	−0.429136	−	1.07968i
$638$	−0.472406	−	0.548068i	−0.0187027	−	0.0216982i
$639$	11.1440	+	2.98604i	0.440852	+	0.118126i
$640$	28.2027	+	27.8920i	1.11481	+	1.10253i
$641$	−2.89971	−	1.67415i	−0.114532	−	0.0661248i	0.441640	−	0.897192i	$-0.354397\pi$
$641$	−2.89971	−	1.67415i	−0.114532	−	0.0661248i	−0.556171	+	0.831068i	$0.687730\pi$
$642$	3.03097	+	0.224728i	0.119623	+	0.00886932i
$643$	−24.0364	+	6.44054i	−0.947905	+	0.253990i	−0.699473	−	0.714659i	$-0.746582\pi$
$643$	−24.0364	+	6.44054i	−0.947905	+	0.253990i	−0.248432	+	0.968649i	$0.579915\pi$
$644$	−21.2563	+	2.42908i	−0.837616	+	0.0957192i
$645$	21.4945	+	21.4945i	0.846346	+	0.846346i
$646$	−6.04631	−	31.8177i	−0.237889	−	1.25185i
$647$	11.3489	+	19.6569i	0.446172	+	0.772793i	0.998133	−	0.0610768i	$-0.0194535\pi$
$647$	11.3489	+	19.6569i	0.446172	+	0.772793i	−0.551961	+	0.833870i	$0.686120\pi$
$648$	−0.840107	−	2.70078i	−0.0330025	−	0.106097i
$649$			7.03561i			0.276172i
$650$	11.1408	+	35.4728i	0.436979	+	1.39136i
$651$	1.91471			0.0750435
$652$	−12.5409	−	5.44791i	−0.491138	−	0.213357i
$653$	−26.2663	+	15.1649i	−1.02788	+	0.593447i	−0.916377	−	0.400317i	$-0.868900\pi$
$653$	−26.2663	+	15.1649i	−1.02788	+	0.593447i	−0.111503	+	0.993764i	$0.535567\pi$
$654$	−3.34996	−	17.6286i	−0.130994	−	0.689333i
$655$	3.82730	−	3.82730i	0.149545	−	0.149545i
$656$	−26.5049	−	0.907752i	−1.03484	−	0.0354417i
$657$	−2.08478	−	7.78051i	−0.0813350	−	0.303546i
$658$	0.890958	−	12.0166i	0.0347332	−	0.468456i
$659$	−3.59371	+	6.22449i	−0.139991	+	0.242472i	−0.927493	−	0.373841i	$-0.878041\pi$
$659$	−3.59371	+	6.22449i	−0.139991	+	0.242472i	0.787502	+	0.616312i	$0.211374\pi$
$660$	−3.44302	+	1.35758i	−0.134019	+	0.0528436i
$661$	8.58726	−	32.0481i	0.334006	−	1.24653i	−0.570937	−	0.820994i	$-0.693420\pi$
$661$	8.58726	−	32.0481i	0.334006	−	1.24653i	0.904943	−	0.425533i	$-0.139913\pi$
$662$	15.2594	+	17.7034i	0.593074	+	0.688063i
$663$	−22.1694	−	3.24359i	−0.860988	−	0.125971i
$664$	−21.9317	−	34.7208i	−0.851114	−	1.34743i
$665$	−13.0089	+	48.5498i	−0.504463	+	1.88268i
$666$	−2.70819	+	7.75924i	−0.104940	+	0.300664i
$667$	2.30848	+	1.33280i	0.0893848	+	0.0516063i
$668$	−17.1519	−	23.1632i	−0.663627	−	0.896211i
$669$	−3.46369	−	12.9267i	−0.133914	−	0.499774i
$670$	−19.0345	+	27.9660i	−0.735368	+	1.08042i
$671$	2.33739	+	2.33739i	0.0902340	+	0.0902340i
$672$	21.8769	+	2.37733i	0.843921	+	0.0917075i
$673$	11.8971	−	6.86881i	0.458601	−	0.264773i	−0.252855	−	0.967504i	$-0.581370\pi$
$673$	11.8971	−	6.86881i	0.458601	−	0.264773i	0.711456	+	0.702731i	$0.248036\pi$
$674$	28.2204	−	13.6177i	1.08701	−	0.524536i
$675$		−	7.29182i		−	0.280662i
$676$	21.3313	−	14.8652i	0.820436	−	0.571738i
$677$			4.56622i			0.175494i	0.996143	+	0.0877470i	$0.0279667\pi$
$677$			4.56622i			0.175494i	−0.996143	+	0.0877470i	$0.972033\pi$
$678$	−6.57008	−	13.6153i	−0.252322	−	0.522894i
$679$	−13.1188	+	7.57416i	−0.503454	+	0.290670i
$680$	−61.5731	+	2.45027i	−2.36122	+	0.0939637i
$681$	−11.0575	−	11.0575i	−0.423723	−	0.423723i
$682$	0.303724	+	0.206724i	0.0116302	+	0.00791586i
$683$	4.87878	+	18.2078i	0.186681	+	0.696704i	0.994264	+	0.106950i	$0.0341085\pi$
$683$	4.87878	+	18.2078i	0.186681	+	0.696704i	−0.807583	+	0.589754i	$0.799225\pi$
$684$	−4.38622	−	5.92347i	−0.167711	−	0.226490i
$685$	5.50876	+	3.18048i	0.210479	+	0.121520i
$686$	−5.88425	−	2.05376i	−0.224662	−	0.0784131i
$687$	3.85308	−	14.3799i	0.147004	−	0.548628i
$688$	10.1175	−	33.1727i	0.385728	−	1.26470i
$689$	−50.8272	−	7.43650i	−1.93636	−	0.283308i
$690$	10.3275	−	8.90176i	0.393161	−	0.338884i
$691$	6.39032	−	23.8490i	0.243099	−	0.907258i	−0.731230	−	0.682131i	$-0.761053\pi$
$691$	6.39032	−	23.8490i	0.243099	−	0.907258i	0.974329	−	0.225128i	$-0.0722799\pi$
$692$	8.13882	+	20.6413i	0.309392	+	0.784663i
$693$	−1.02662	+	1.77817i	−0.0389983	+	0.0675470i
$694$	43.1778	+	3.20138i	1.63901	+	0.121523i
$695$	15.8149	+	59.0220i	0.599893	+	2.23883i
$696$	−2.01426	−	1.86008i	−0.0763503	−	0.0705062i
$697$	29.1332	−	29.1332i	1.10350	−	1.10350i
$698$	−20.8115	+	3.95481i	−0.787727	+	0.149692i
$699$	20.1526	−	11.6351i	0.762241	−	0.440080i
$700$	52.0340	+	22.6043i	1.96670	+	0.854361i
$701$	−1.74269			−0.0658204			−0.0329102	−	0.999458i	$-0.510478\pi$
$701$	−1.74269			−0.0658204			−0.0329102	+	0.999458i	$0.510478\pi$
$702$	−4.86474	+	1.52785i	−0.183608	+	0.0576651i
$703$			21.4161i			0.807725i
$704$	3.21359	+	2.73907i	0.121117	+	0.103233i
$705$	3.83950	+	6.65020i	0.144604	+	0.250461i
$706$	4.83388	−	0.918581i	0.181925	−	0.0345712i
$707$	−11.3448	−	11.3448i	−0.426664	−	0.426664i
$708$	3.02682	+	26.4870i	0.113755	+	0.995443i
$709$	−6.85982	+	1.83808i	−0.257626	+	0.0690307i	−0.385320	−	0.922783i	$-0.625909\pi$
$709$	−6.85982	+	1.83808i	−0.257626	+	0.0690307i	0.127694	+	0.991814i	$0.459242\pi$
$710$	4.22968	−	57.0468i	0.158737	−	2.14093i
$711$	−4.18176	−	2.41434i	−0.156828	−	0.0905449i
$712$	−18.4661	−	9.70359i	−0.692045	−	0.363657i
$713$	−1.30738	−	0.350311i	−0.0489617	−	0.0131193i
$714$	−25.8949	+	22.3200i	−0.969092	+	0.835306i
$715$	2.46440	+	6.20027i	0.0921632	+	0.231877i
$716$	−2.90647	+	19.4924i	−0.108620	+	0.728466i
$717$	8.15084	+	2.18401i	0.304399	+	0.0815634i
$718$	3.93125	−	11.2635i	0.146713	−	0.420348i
$719$	−4.63097	+	8.02108i	−0.172706	+	0.299136i	−0.939365	−	0.342919i	$-0.888584\pi$
$719$	−4.63097	+	8.02108i	−0.172706	+	0.299136i	0.766659	+	0.642055i	$0.221918\pi$
$720$	−12.3779	+	6.59212i	−0.461298	+	0.245674i
$721$	36.3216	−	9.73233i	1.35269	−	0.362451i
$722$	6.33470	+	4.31159i	0.235753	+	0.160461i
$723$	−21.8568	+	21.8568i	−0.812863	+	0.812863i
$724$	−4.33833	+	5.45779i	−0.161233	+	0.202837i
$725$	−3.53417	−	6.12136i	−0.131256	−	0.227341i
$726$	13.6556	−	6.58951i	0.506807	−	0.244560i
$727$	9.77196			0.362422			0.181211	−	0.983444i	$-0.441998\pi$
$727$	9.77196			0.362422			0.181211	+	0.983444i	$0.441998\pi$
$728$	4.17777	−	39.4508i	0.154838	−	1.46214i
$729$	1.00000			0.0370370
$730$	−35.9692	+	17.3569i	−1.33128	+	0.642409i
$731$	26.9393	+	46.6602i	0.996386	+	1.72579i
$732$	9.80518	+	7.79401i	0.362410	+	0.288075i
$733$	−9.27968	+	9.27968i	−0.342753	+	0.342753i	−0.857401	−	0.514648i	$-0.827922\pi$
$733$	−9.27968	+	9.27968i	−0.342753	+	0.342753i	0.514648	+	0.857401i	$0.327922\pi$
$734$	25.4361	+	17.3126i	0.938865	+	0.639020i
$735$	27.5420	−	7.37985i	1.01590	−	0.272210i
$736$	−14.5028	−	5.62581i	−0.534579	−	0.207370i
$737$	−1.80061	+	3.11875i	−0.0663263	+	0.114881i
$738$	3.08983	−	8.85268i	0.113738	−	0.325872i
$739$	−2.98398	−	0.799556i	−0.109768	−	0.0294121i	0.203517	−	0.979071i	$-0.434763\pi$
$739$	−2.98398	−	0.799556i	−0.109768	−	0.0294121i	−0.313285	+	0.949659i	$0.601429\pi$
$740$	40.3022	+	6.00937i	1.48154	+	0.220909i
$741$	−10.6570	+	7.93658i	−0.391494	+	0.291558i
$742$	−59.3685	+	51.1726i	−2.17949	+	1.87860i
$743$	30.5693	+	8.19102i	1.12148	+	0.300499i	0.771482	−	0.636251i	$-0.219516\pi$
$743$	30.5693	+	8.19102i	1.12148	+	0.300499i	0.349997	+	0.936751i	$0.386182\pi$
$744$	1.23237	+	0.647588i	0.0451808	+	0.0237417i
$745$	−25.9867	−	15.0034i	−0.952077	−	0.549682i
$746$	−3.36028	+	45.3210i	−0.123029	+	1.65932i
$747$	14.0248	−	3.75793i	0.513140	−	0.137495i
$748$	−6.51741	+	0.744782i	−0.238300	+	0.0272319i
$749$	−5.91157	−	5.91157i	−0.216004	−	0.216004i
$750$	−11.1635	+	2.12140i	−0.407633	+	0.0774624i
$751$	−17.0232	−	29.4850i	−0.621185	−	1.07592i	−0.989265	−	0.146130i	$-0.953318\pi$
$751$	−17.0232	−	29.4850i	−0.621185	−	1.07592i	0.368080	−	0.929794i	$-0.380015\pi$
$752$	4.63766	−	7.43291i	0.169118	−	0.271050i
$753$			13.0661i			0.476156i
$754$	−3.34335	+	3.64043i	−0.121758	+	0.132576i
$755$	34.5985			1.25917
$756$	−3.09995	+	7.13595i	−0.112744	+	0.259532i
$757$	−7.91251	+	4.56829i	−0.287585	+	0.166037i	−0.636852	−	0.770986i	$-0.719764\pi$
$757$	−7.91251	+	4.56829i	−0.287585	+	0.166037i	0.349267	+	0.937023i	$0.386431\pi$
$758$	−46.1842	+	8.77637i	−1.67748	+	0.318772i
$759$	1.02632	−	1.02632i	0.0372529	−	0.0372529i
$760$	−24.7933	+	26.8483i	−0.899347	+	0.973892i
$761$	10.4819	+	39.1189i	0.379968	+	1.41806i	0.845948	+	0.533265i	$0.179035\pi$
$761$	10.4819	+	39.1189i	0.379968	+	1.41806i	−0.465980	+	0.884795i	$0.654298\pi$
$762$	5.92588	+	0.439369i	0.214672	+	0.0159166i
$763$	−24.6795	+	42.7462i	−0.893458	+	1.54752i
$764$	−9.01817	+	3.55585i	−0.326266	+	0.128646i
$765$	5.63879	−	21.0442i	0.203871	−	0.760856i
$766$	−13.3670	+	11.5217i	−0.482970	+	0.416295i
$767$	47.7350	−	5.58743i	1.72361	−	0.201750i
$768$	13.2766	+	8.92926i	0.479078	+	0.322207i
$769$	−0.306215	+	1.14281i	−0.0110424	+	0.0412107i	−0.971227	−	0.238155i	$-0.923457\pi$
$769$	−0.306215	+	1.14281i	−0.0110424	+	0.0412107i	0.960185	+	0.279366i	$0.0901241\pi$
$770$	9.61177	+	3.35477i	0.346384	+	0.120897i
$771$	−13.8556	−	7.99953i	−0.498997	−	0.288096i
$772$	43.0083	−	31.8468i	1.54790	−	1.14619i
$773$	8.66967	+	32.3556i	0.311826	+	1.16375i	0.926908	+	0.375288i	$0.122456\pi$
$773$	8.66967	+	32.3556i	0.311826	+	1.16375i	−0.615082	+	0.788463i	$0.710877\pi$
$774$	10.1365	+	6.89923i	0.364350	+	0.247988i
$775$	2.53784	+	2.53784i	0.0911618	+	0.0911618i
$776$	−11.0054	+	0.437955i	−0.395070	+	0.0157217i
$777$	19.5775	−	11.3031i	0.702338	−	0.405495i
$778$	−7.97443	−	16.5256i	−0.285897	−	0.592472i
$779$		−	24.4341i		−	0.875444i
$780$	11.9452	+	22.2820i	0.427706	+	0.797823i
$781$		−	6.08948i		−	0.217899i
$782$	21.7648	−	10.5026i	0.778309	−	0.375573i
$783$	0.839483	−	0.484676i	0.0300007	−	0.0173209i
$784$	−22.2024	−	23.7771i	−0.792942	−	0.849182i
$785$	22.7667	+	22.7667i	0.812578	+	0.812578i
$786$	1.22847	−	1.80490i	0.0438181	−	0.0643788i
$787$	10.1171	+	37.7577i	0.360637	+	1.34592i	0.873240	+	0.487290i	$0.162015\pi$
$787$	10.1171	+	37.7577i	0.360637	+	1.34592i	−0.512603	+	0.858626i	$0.671319\pi$
$788$	42.7605	−	31.6634i	1.52328	−	1.12796i
$789$	−5.61079	−	3.23939i	−0.199749	−	0.115325i
$790$	−7.88950	+	22.6043i	−0.280696	+	0.804223i
$791$	−10.7628	+	40.1674i	−0.382682	+	1.42819i
$792$	−1.26217	+	0.797261i	−0.0448494	+	0.0283294i
$793$	14.0024	−	17.7149i	0.497240	−	0.629076i
$794$	−3.05978	−	3.54984i	−0.108587	−	0.125979i
$795$	12.9279	−	48.2476i	0.458505	−	1.71117i
$796$	14.8018	+	37.5397i	0.524637	+	1.33056i
$797$	−9.38012	+	16.2468i	−0.332261	+	0.575493i	−0.982955	−	0.183847i	$-0.941145\pi$
$797$	−9.38012	+	16.2468i	−0.332261	+	0.575493i	0.650694	+	0.759340i	$0.274478\pi$
$798$	−1.49912	+	20.2190i	−0.0530683	+	0.715746i
$799$	3.52268	+	13.1468i	0.124624	+	0.465102i
$800$	25.8456	+	32.1476i	0.913778	+	1.13659i
$801$	5.21509	−	5.21509i	0.184266	−	0.184266i
$802$	−3.33277	−	17.5381i	−0.117684	−	0.619293i
$803$	−3.68193	+	2.12577i	−0.129933	+	0.0750166i
$804$	−5.43704	+	12.5158i	−0.191750	+	0.441399i
$805$	−37.5045			−1.32186
$806$	1.16137	−	2.22487i	0.0409074	−	0.0783677i
$807$		−	10.8895i		−	0.383329i
$808$	−3.46485	−	11.1388i	−0.121893	−	0.391863i
$809$	−2.93058	−	5.07591i	−0.103034	−	0.178459i	0.809900	−	0.586569i	$-0.199522\pi$
$809$	−2.93058	−	5.07591i	−0.103034	−	0.178459i	−0.912933	+	0.408109i	$0.866188\pi$
$810$	−0.925639	−	4.87102i	−0.0325236	−	0.171150i
$811$	−16.1926	−	16.1926i	−0.568599	−	0.568599i	0.363137	−	0.931736i	$-0.381706\pi$
$811$	−16.1926	−	16.1926i	−0.568599	−	0.568599i	−0.931736	+	0.363137i	$0.881706\pi$
$812$	0.856266	+	7.49298i	0.0300490	+	0.262952i
$813$	24.3564	−	6.52629i	0.854218	−	0.228887i
$814$	4.32585	+	0.320736i	0.151621	+	0.0112418i
$815$	−20.7575	−	11.9843i	−0.727103	−	0.419793i
$816$	−24.2157	+	5.60778i	−0.847721	+	0.196311i
$817$	30.8641	+	8.27002i	1.07980	+	0.289331i
$818$	−24.9035	−	28.8921i	−0.870731	−	1.01019i
$819$	12.8798	+	5.55326i	0.450056	+	0.194047i
$820$	−45.9816	−	6.85622i	−1.60575	−	0.239430i
$821$	−44.8952	−	12.0296i	−1.56685	−	0.419837i	−0.632027	−	0.774946i	$-0.717777\pi$
$821$	−44.8952	−	12.0296i	−1.56685	−	0.419837i	−0.934825	+	0.355109i	$0.884444\pi$
$822$	2.42253	+	0.845528i	0.0844953	+	0.0294912i
$823$	−20.7612	+	35.9595i	−0.723691	+	1.25347i	0.235819	+	0.971797i	$0.424223\pi$
$823$	−20.7612	+	35.9595i	−0.723691	+	1.25347i	−0.959511	+	0.281673i	$0.909111\pi$
$824$	26.6693	+	6.02053i	0.929069	+	0.209735i
$825$	−3.71758	+	0.996124i	−0.129430	+	0.0346806i
$826$	41.2617	−	60.6227i	1.43568	−	2.10933i
$827$	33.7239	−	33.7239i	1.17270	−	1.17270i	0.191132	−	0.981564i	$-0.438784\pi$
$827$	33.7239	−	33.7239i	1.17270	−	1.17270i	0.981564	−	0.191132i	$-0.0612158\pi$
$828$	3.42224	−	4.30532i	0.118931	−	0.149620i
$829$	−5.05148	−	8.74942i	−0.175445	−	0.303880i	0.764870	−	0.644184i	$-0.222803\pi$
$829$	−5.05148	−	8.74942i	−0.175445	−	0.303880i	−0.940315	+	0.340305i	$0.889470\pi$
$830$	−31.2868	−	64.8365i	−1.08598	−	2.25051i
$831$	16.0179			0.555655
$832$	16.0318	−	23.9787i	0.555804	−	0.831313i
$833$	50.5388			1.75106
$834$	10.7118	+	22.1984i	0.370920	+	0.768667i
$835$	−25.2625	−	43.7559i	−0.874244	−	1.51423i
$836$	−2.42077	+	3.04542i	−0.0837240	+	0.105328i
$837$	−0.348039	+	0.348039i	−0.0120300	+	0.0120300i
$838$	7.51906	−	11.0472i	0.259742	−	0.381619i
$839$	−12.0121	+	3.21863i	−0.414704	+	0.111119i	−0.460137	−	0.887848i	$-0.652200\pi$
$839$	−12.0121	+	3.21863i	−0.414704	+	0.111119i	0.0454336	+	0.998967i	$0.485533\pi$
$840$	37.6288	+	8.49460i	1.29832	+	0.293092i
$841$	−14.0302	+	24.3010i	−0.483799	+	0.837965i
$842$	16.3240	+	5.69752i	0.562562	+	0.196349i
$843$	−9.12428	−	2.44484i	−0.314257	−	0.0842049i
$844$	−28.1211	−	4.19308i	−0.967969	−	0.144332i
$845$	40.1103	−	21.6444i	1.37984	−	0.744591i
$846$	2.02232	+	2.34622i	0.0695287	+	0.0806646i
$847$	−40.2862	−	10.7947i	−1.38425	−	0.370909i
$848$	−55.5188	+	12.8568i	−1.90652	+	0.441505i
$849$	0.711449	+	0.410755i	0.0244169	+	0.0140971i
$850$	−63.9060	−	4.73825i	−2.19196	−	0.162521i
$851$	−15.4356	+	4.13596i	−0.529127	+	0.141779i
$852$	−2.61979	−	22.9251i	−0.0897524	−	0.785402i
$853$	7.43990	+	7.43990i	0.254737	+	0.254737i	0.822910	−	0.568172i	$-0.192349\pi$
$853$	7.43990	+	7.43990i	0.254737	+	0.254737i	−0.568172	+	0.822910i	$0.692349\pi$
$854$	−6.43220	−	33.8483i	−0.220105	−	1.15827i
$855$	−6.46031	−	11.1896i	−0.220938	−	0.382676i
$856$	−1.80548	−	5.80426i	−0.0617099	−	0.198385i
$857$			4.01848i			0.137269i	0.997642	+	0.0686343i	$0.0218642\pi$
$857$			4.01848i			0.137269i	−0.997642	+	0.0686343i	$0.978136\pi$
$858$	1.44351	+	2.27147i	0.0492806	+	0.0775467i
$859$	13.7027			0.467530			0.233765	−	0.972293i	$-0.424895\pi$
$859$	13.7027			0.467530			0.233765	+	0.972293i	$0.424895\pi$
$860$	24.2235	−	55.7615i	0.826015	−	1.90145i
$861$	−22.3364	+	12.8959i	−0.761222	+	0.439491i
$862$	8.48063	+	44.6279i	0.288852	+	1.52003i
$863$	19.2109	−	19.2109i	0.653945	−	0.653945i	−0.299996	−	0.953941i	$-0.596985\pi$
$863$	19.2109	−	19.2109i	0.653945	−	0.653945i	0.953941	+	0.299996i	$0.0969852\pi$
$864$	−4.40872	+	3.54446i	−0.149988	+	0.120585i
$865$	10.0668	+	37.5697i	0.342281	+	1.27741i
$866$	−2.78610	+	37.5768i	−0.0946754	+	1.27691i
$867$	10.8078	−	18.7196i	0.367052	−	0.635753i
$868$	−1.40469	−	3.56249i	−0.0476781	−	0.120919i
$869$	−0.659639	+	2.46181i	−0.0223767	+	0.0835111i
$870$	−3.13792	−	3.64050i	−0.106386	−	0.123425i
$871$	22.5900	+	9.73993i	0.765432	+	0.330025i
$872$	−30.3420	+	19.1657i	−1.02751	+	0.649033i
$873$	1.00786	−	3.76138i	0.0341109	−	0.127304i
$874$	4.72284	−	13.5314i	0.159752	−	0.457707i
$875$	27.0694	+	15.6285i	0.915114	+	0.528341i
$876$	−12.9469	+	9.58691i	−0.437434	+	0.323912i
$877$	9.02153	+	33.6688i	0.304635	+	1.13691i	0.933259	+	0.359205i	$0.116952\pi$
$877$	9.02153	+	33.6688i	0.304635	+	1.13691i	−0.628623	+	0.777710i	$0.716381\pi$
$878$	1.50982	−	2.21826i	0.0509538	−	0.0748628i
$879$	−2.28422	−	2.28422i	−0.0770448	−	0.0770448i
$880$	5.05179	+	5.41009i	0.170296	+	0.182374i
$881$	35.2176	−	20.3329i	1.18651	−	0.685033i	0.229000	−	0.973426i	$-0.426454\pi$
$881$	35.2176	−	20.3329i	1.18651	−	0.685033i	0.957512	+	0.288393i	$0.0931210\pi$
$882$	10.3586	−	4.99856i	0.348793	−	0.168310i
$883$		−	42.7286i		−	1.43793i	−0.695045	−	0.718967i	$-0.744615\pi$
$883$		−	42.7286i		−	1.43793i	0.695045	−	0.718967i	$-0.255385\pi$
$884$	10.2291	+	43.6277i	0.344041	+	1.46736i
$885$			46.7335i			1.57093i
$886$	9.36339	+	19.4040i	0.314569	+	0.651890i
$887$	32.4061	−	18.7097i	1.08809	−	0.628209i	0.155022	−	0.987911i	$-0.450455\pi$
$887$	32.4061	−	18.7097i	1.08809	−	0.628209i	0.933067	+	0.359702i	$0.117122\pi$
$888$	16.4236	−	0.653568i	0.551138	−	0.0219323i
$889$	−11.5578	−	11.5578i	−0.387635	−	0.387635i
$890$	−30.2301	−	20.5755i	−1.01332	−	0.689693i
$891$	−0.136608	−	0.509830i	−0.00457655	−	0.0170799i
$892$	−21.5102	+	15.9279i	−0.720213	+	0.533304i
$893$	6.99040	+	4.03591i	0.233925	+	0.135057i
$894$	−11.4279	−	3.98864i	−0.382205	−	0.133400i
$895$	−8.94159	+	33.3705i	−0.298884	+	1.11545i
$896$	−11.6263	−	42.4480i	−0.388407	−	1.41809i
$897$	−7.77839	−	6.14826i	−0.259713	−	0.205284i
$898$	−6.04829	+	5.21331i	−0.201834	+	0.173970i
$899$	−0.123487	+	0.460859i	−0.00411851	+	0.0153705i
$900$	−13.5671	+	5.34948i	−0.452236	+	0.178316i
$901$	44.2665	−	76.6718i	1.47473	−	2.55431i
$902$	−4.93546	−	0.365935i	−0.164333	−	0.0121843i
$903$	−8.72955	−	32.5791i	−0.290501	−	1.08417i
$904$	−20.5126	+	22.2128i	−0.682238	+	0.738787i
$905$	−8.64210	+	8.64210i	−0.287273	+	0.287273i
$906$	13.7108	−	2.60545i	0.455510	−	0.0865604i
$907$	−5.92338	+	3.41986i	−0.196683	+	0.113555i	−0.595107	−	0.803646i	$-0.702890\pi$
$907$	−5.92338	+	3.41986i	−0.196683	+	0.113555i	0.398425	+	0.917201i	$0.369557\pi$
$908$	−12.4614	+	28.6855i	−0.413544	+	0.951961i
$909$	4.12430			0.136794
$910$	15.1280	−	67.8779i	0.501489	−	2.25013i
$911$		−	42.0719i		−	1.39390i	−0.717118	−	0.696952i	$-0.754539\pi$
$911$		−	42.0719i		−	1.39390i	0.717118	−	0.696952i	$-0.245461\pi$
$912$	−7.80330	+	12.5066i	−0.258393	+	0.414134i
$913$	−3.83181	−	6.63689i	−0.126814	−	0.219649i
$914$	0.799349	−	0.151900i	0.0264401	−	0.00502441i
$915$	15.5259	+	15.5259i	0.513272	+	0.513272i
$916$	−29.5818	+	3.38049i	−0.977411	+	0.111694i
$917$	−5.80101	+	1.55438i	−0.191566	+	0.0513300i
$918$	0.649803	−	8.76407i	0.0214467	−	0.289257i
$919$	−41.6791	−	24.0634i	−1.37487	−	0.793780i	−0.383331	−	0.923611i	$-0.625223\pi$
$919$	−41.6791	−	24.0634i	−1.37487	−	0.793780i	−0.991536	+	0.129831i	$0.958556\pi$
$920$	−24.1390	−	12.6846i	−0.795841	−	0.418200i
$921$	−18.6151	−	4.98791i	−0.613390	−	0.164357i
$922$	0.765075	−	0.659455i	0.0251964	−	0.0217180i
$923$	−41.3158	+	4.83605i	−1.35992	+	0.159181i
$924$	4.06160	+	0.605616i	0.133617	+	0.0199233i
$925$	40.9303	+	10.9672i	1.34578	+	0.360601i
$926$	4.16095	−	11.9216i	0.136737	−	0.391767i
$927$	−4.83315	+	8.37126i	−0.158741	+	0.274948i
$928$	−1.98313	+	5.11231i	−0.0650994	+	0.167820i
$929$	−13.2391	+	3.54740i	−0.434360	+	0.116387i	−0.469372	−	0.883000i	$-0.655520\pi$
$929$	−13.2391	+	3.54740i	−0.434360	+	0.116387i	0.0350119	+	0.999387i	$0.488853\pi$
$930$	2.01746	+	1.37315i	0.0661552	+	0.0450272i
$931$	21.1936	−	21.1936i	0.694591	−	0.694591i
$932$	−36.4326	−	28.9599i	−1.19339	−	0.948612i
$933$	−2.38479	−	4.13058i	−0.0780746	−	0.135229i
$934$	−7.83207	+	3.77936i	−0.256273	+	0.123664i
$935$	−11.4993			−0.376067
$936$	6.41161	+	7.93040i	0.209570	+	0.259213i
$937$	−39.4855			−1.28993			−0.644967	−	0.764211i	$-0.723129\pi$
$937$	−39.4855			−1.28993			−0.644967	+	0.764211i	$0.723129\pi$
$938$	33.8055	−	16.3129i	1.10379	−	0.532634i
$939$	8.97201	+	15.5400i	0.292791	+	0.507128i
$940$	9.55653	−	12.0225i	0.311700	−	0.392131i
$941$	14.7244	−	14.7244i	0.480002	−	0.480002i	−0.425130	−	0.905132i	$-0.639772\pi$
$941$	14.7244	−	14.7244i	0.480002	−	0.480002i	0.905132	+	0.425130i	$0.139772\pi$
$942$	10.7365	+	7.30756i	0.349813	+	0.238093i
$943$	17.6108	−	4.71881i	0.573488	−	0.153666i
$944$	47.0609	−	25.0633i	1.53170	−	0.815740i
$945$	−6.81928	+	11.8113i	−0.221831	+	0.384223i
$946$	2.13270	−	6.11040i	0.0693399	−	0.198666i
$947$	1.37814	+	0.369272i	0.0447836	+	0.0119997i	0.281141	−	0.959666i	$-0.409287\pi$
$947$	1.37814	+	0.369272i	0.0447836	+	0.0119997i	−0.236358	+	0.971666i	$0.575954\pi$
$948$	−1.42424	+	9.55177i	−0.0462573	+	0.310227i
$949$	17.3469	+	23.2929i	0.563104	+	0.756119i
$950$	−28.7861	+	24.8121i	−0.933945	+	0.805012i
$951$	6.54588	+	1.75396i	0.212265	+	0.0568761i
$952$	60.5256	+	31.8051i	1.96165	+	1.03081i
$953$	25.2670	+	14.5879i	0.818477	+	0.472548i	0.849891	−	0.526958i	$-0.176668\pi$
$953$	25.2670	+	14.5879i	0.818477	+	0.472548i	−0.0314138	+	0.999506i	$0.510001\pi$
$954$	1.48979	−	20.0932i	0.0482337	−	0.650540i
$955$	−16.4142	+	4.39817i	−0.531151	+	0.142322i
$956$	−1.91613	−	16.7676i	−0.0619721	−	0.542303i
$957$	−0.361782	−	0.361782i	−0.0116948	−	0.0116948i
$958$	2.78067	−	0.528410i	0.0898394	−	0.0170722i
$959$	−3.52895	−	6.11232i	−0.113956	−	0.197377i
$960$	21.3460	+	18.1941i	0.688940	+	0.587211i
$961$			30.7577i			0.992185i
$962$	−1.25932	−	29.6046i	−0.0406020	−	0.954492i
$963$	2.14910			0.0692539
$964$	56.7012	+	24.6318i	1.82622	+	0.793336i
$965$	81.2438	−	46.9061i	2.61533	−	1.50996i
$966$	−14.8623	+	2.82429i	−0.478188	+	0.0908700i
$967$	13.3289	−	13.3289i	0.428629	−	0.428629i	−0.459532	−	0.888161i	$-0.651983\pi$
$967$	13.3289	−	13.3289i	0.428629	−	0.428629i	0.888161	+	0.459532i	$0.151983\pi$
$968$	−22.2785	−	20.5732i	−0.716058	−	0.661249i
$969$	−5.92725	−	22.1208i	−0.190411	−	0.710622i
$970$	−19.2547	−	1.42762i	−0.618231	−	0.0458381i
$971$	19.8887	−	34.4483i	0.638259	−	1.10550i	−0.347555	−	0.937660i	$-0.612988\pi$
$971$	19.8887	−	34.4483i	0.638259	−	1.10550i	0.985815	−	0.167838i	$-0.0536786\pi$
$972$	−0.733627	−	1.86059i	−0.0235311	−	0.0596784i
$973$	17.5476	−	65.4887i	0.562552	−	2.09947i
$974$	31.6762	−	27.3032i	1.01497	−	0.874851i
$975$	9.71085	+	24.4319i	0.310996	+	0.782447i
$976$	7.30811	−	23.9613i	0.233927	−	0.766983i
$977$	−1.44178	+	5.38081i	−0.0461268	+	0.172147i	−0.985147	−	0.171716i	$-0.945069\pi$
$977$	−1.44178	+	5.38081i	−0.0461268	+	0.172147i	0.939020	+	0.343863i	$0.111736\pi$
$978$	−9.12829	−	3.18602i	−0.291890	−	0.101878i
$979$	−3.37123	−	1.94638i	−0.107745	−	0.0622067i
$980$	−33.9364	−	45.8303i	−1.08406	−	1.46399i
$981$	−3.28399	−	12.2560i	−0.104850	−	0.391305i
$982$	9.79365	+	6.66585i	0.312528	+	0.212716i
$983$	−18.3025	−	18.3025i	−0.583758	−	0.583758i	0.352176	−	0.935934i	$-0.385442\pi$
$983$	−18.3025	−	18.3025i	−0.583758	−	0.583758i	−0.935934	+	0.352176i	$0.885442\pi$
$984$	−18.7380	+	0.745670i	−0.597345	+	0.0237711i
$985$	80.7758	−	46.6359i	2.57373	−	1.48594i
$986$	−3.70223	−	7.67223i	−0.117903	−	0.244334i
$987$		−	8.52034i		−	0.271205i
$988$	22.5850	+	14.0058i	0.718524	+	0.445584i
$989$			23.8424i			0.758144i
$990$	−2.35694	+	1.13734i	−0.0749085	+	0.0361471i
$991$	−2.57728	+	1.48799i	−0.0818698	+	0.0472676i	−0.540376	−	0.841424i	$-0.681718\pi$
$991$	−2.57728	+	1.48799i	−0.0818698	+	0.0472676i	0.458506	+	0.888691i	$0.348385\pi$
$992$	0.300796	−	2.76802i	0.00955028	−	0.0878846i
$993$	11.6861	+	11.6861i	0.370848	+	0.370848i
$994$	−35.7129	+	52.4704i	−1.13274	+	1.66426i
$995$	18.3081	+	68.3269i	0.580407	+	2.16611i
$996$	−17.2809	−	23.3374i	−0.547567	−	0.739475i
$997$	−25.2456	−	14.5756i	−0.799537	−	0.461613i	0.0437723	−	0.999042i	$-0.486062\pi$
$997$	−25.2456	−	14.5756i	−0.799537	−	0.461613i	−0.843309	+	0.537429i	$0.819396\pi$
$998$	−8.18118	+	23.4399i	−0.258971	+	0.741978i
$999$	−1.50405	+	5.61319i	−0.0475860	+	0.177593i

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	312.2.bt.c.115.5	yes	48
3.2	odd	2		936.2.ed.c.739.8		48
8.3	odd	2	inner	312.2.bt.c.115.11	yes	48
13.6	odd	12	inner	312.2.bt.c.19.11	yes	48
24.11	even	2		936.2.ed.c.739.2		48
39.32	even	12		936.2.ed.c.19.2		48
104.19	even	12	inner	312.2.bt.c.19.5	✓	48
312.227	odd	12		936.2.ed.c.19.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bt.c.19.5	✓	48	104.19	even	12	inner
312.2.bt.c.19.11	yes	48	13.6	odd	12	inner
312.2.bt.c.115.5	yes	48	1.1	even	1	trivial
312.2.bt.c.115.11	yes	48	8.3	odd	2	inner
936.2.ed.c.19.2		48	39.32	even	12
936.2.ed.c.19.8		48	312.227	odd	12
936.2.ed.c.739.2		48	24.11	even	2
936.2.ed.c.739.8		48	3.2	odd	2

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Twists

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

Label	312.2.bt.c.115.5

Level	$312$
Weight	$2$
Character	312.115
Analytic conductor	$2.491$
Analytic rank	$0$
Dimension	$48$
Inner twists	$4$