LMFDB - Embedded newform 360.2.bm.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.b.131.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33590 - 0.464076i) q^{2} +(-1.29784 + 1.14700i) q^{3} +(1.56927 + 1.23992i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.26609 - 0.929977i) q^{6} +(-3.14000 - 1.81288i) q^{7} +(-1.52097 - 2.38467i) q^{8} +(0.368796 - 2.97725i) q^{9} +O(q^{10})$	\(q+(-1.33590 - 0.464076i) q^{2} +(-1.29784 + 1.14700i) q^{3} +(1.56927 + 1.23992i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.26609 - 0.929977i) q^{6} +(-3.14000 - 1.81288i) q^{7} +(-1.52097 - 2.38467i) q^{8} +(0.368796 - 2.97725i) q^{9} +(-0.266049 - 1.38896i) q^{10} +(-2.02891 - 1.17139i) q^{11} +(-3.45885 + 0.190721i) q^{12} +(4.70695 - 2.71756i) q^{13} +(3.35342 + 3.87903i) q^{14} +(-1.64225 - 0.550467i) q^{15} +(0.925196 + 3.89153i) q^{16} +4.45073i q^{17} +(-1.87434 + 3.80616i) q^{18} +7.29765 q^{19} +(-0.289169 + 1.97898i) q^{20} +(6.15460 - 1.24874i) q^{21} +(2.16681 + 2.50644i) q^{22} +(-2.97353 - 5.15031i) q^{23} +(4.70919 + 1.35038i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-7.54918 + 1.44601i) q^{26} +(2.93625 + 4.28701i) q^{27} +(-2.67967 - 6.73825i) q^{28} +(1.52275 - 2.63748i) q^{29} +(1.93843 + 1.49750i) q^{30} +(6.43361 - 3.71445i) q^{31} +(0.569996 - 5.62806i) q^{32} +(3.97680 - 0.806871i) q^{33} +(2.06548 - 5.94574i) q^{34} -3.62576i q^{35} +(4.27029 - 4.21481i) q^{36} -4.85559i q^{37} +(-9.74895 - 3.38667i) q^{38} +(-2.99186 + 8.92583i) q^{39} +(1.30470 - 2.50953i) q^{40} +(0.201473 - 0.116321i) q^{41} +(-8.80145 - 1.18801i) q^{42} +(-0.490794 + 0.850080i) q^{43} +(-1.73147 - 4.35392i) q^{44} +(2.76277 - 1.16924i) q^{45} +(1.58221 + 8.26025i) q^{46} +(1.48425 - 2.57079i) q^{47} +(-5.66433 - 3.98940i) q^{48} +(3.07308 + 5.32273i) q^{49} +(1.06985 - 0.924887i) q^{50} +(-5.10497 - 5.77635i) q^{51} +(10.7560 + 1.57167i) q^{52} +11.3468 q^{53} +(-1.93304 - 7.08966i) q^{54} -2.34279i q^{55} +(0.452721 + 10.2452i) q^{56} +(-9.47121 + 8.37039i) q^{57} +(-3.25824 + 2.81675i) q^{58} +(1.02217 - 0.590148i) q^{59} +(-1.89459 - 2.90009i) q^{60} +(-10.1682 - 5.87061i) q^{61} +(-10.3185 + 1.97645i) q^{62} +(-6.55541 + 8.67997i) q^{63} +(-3.37331 + 7.25402i) q^{64} +(4.70695 + 2.71756i) q^{65} +(-5.68706 - 0.767635i) q^{66} +(-2.00541 - 3.47348i) q^{67} +(-5.51855 + 6.98438i) q^{68} +(9.76657 + 3.27366i) q^{69} +(-1.68263 + 4.84366i) q^{70} -9.10623 q^{71} +(-7.66068 + 3.64884i) q^{72} -1.90547 q^{73} +(-2.25336 + 6.48659i) q^{74} +(-0.344407 - 1.69746i) q^{75} +(11.4520 + 9.04851i) q^{76} +(4.24719 + 7.35636i) q^{77} +(8.13909 - 10.5356i) q^{78} +(-0.784069 - 0.452683i) q^{79} +(-2.90757 + 2.74701i) q^{80} +(-8.72798 - 2.19599i) q^{81} +(-0.323130 + 0.0618941i) q^{82} +(11.9999 + 6.92813i) q^{83} +(11.2065 + 5.67161i) q^{84} +(-3.85445 + 2.22537i) q^{85} +(1.05015 - 0.907857i) q^{86} +(1.04889 + 5.16963i) q^{87} +(0.292525 + 6.61994i) q^{88} -12.5342i q^{89} +(-4.23340 + 0.279849i) q^{90} -19.7065 q^{91} +(1.71971 - 11.7692i) q^{92} +(-4.08936 + 12.2001i) q^{93} +(-3.17585 + 2.74552i) q^{94} +(3.64883 + 6.31995i) q^{95} +(5.71561 + 7.95813i) q^{96} +(6.51236 - 11.2797i) q^{97} +(-1.63518 - 8.53678i) q^{98} +(-4.23578 + 5.60856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8	$ 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.33590	−	0.464076i	−0.944625	−	0.328151i
$2$	−1.33590	−	0.464076i	−0.944625	−	0.328151i
$3$	−1.29784	+	1.14700i	−0.749310	+	0.662219i
$3$	−1.29784	+	1.14700i	−0.749310	+	0.662219i
$4$	1.56927	+	1.23992i	0.784633	+	0.619960i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.26609	−	0.929977i	0.925126	−	0.379661i
$7$	−3.14000	−	1.81288i	−1.18681	−	0.685205i	−0.229230	−	0.973372i	$-0.573621\pi$
$7$	−3.14000	−	1.81288i	−1.18681	−	0.685205i	−0.957580	+	0.288168i	$0.906954\pi$
$8$	−1.52097	−	2.38467i	−0.537744	−	0.843108i
$9$	0.368796	−	2.97725i	0.122932	−	0.992415i
$10$	−0.266049	−	1.38896i	−0.0841321	−	0.439229i
$11$	−2.02891	−	1.17139i	−0.611740	−	0.353188i	0.161906	−	0.986806i	$-0.448236\pi$
$11$	−2.02891	−	1.17139i	−0.611740	−	0.353188i	−0.773646	+	0.633618i	$0.781569\pi$
$12$	−3.45885	+	0.190721i	−0.998483	+	0.0550565i
$13$	4.70695	−	2.71756i	1.30547	−	0.753716i	0.324137	−	0.946010i	$-0.394926\pi$
$13$	4.70695	−	2.71756i	1.30547	−	0.753716i	0.981337	+	0.192295i	$0.0615929\pi$
$14$	3.35342	+	3.87903i	0.896239	+	1.03671i
$15$	−1.64225	−	0.550467i	−0.424027	−	0.142130i
$16$	0.925196	+	3.89153i	0.231299	+	0.972883i
$17$			4.45073i			1.07946i	0.841838	+	0.539730i	$0.181474\pi$
$17$			4.45073i			1.07946i	−0.841838	+	0.539730i	$0.818526\pi$
$18$	−1.87434	+	3.80616i	−0.441787	+	0.897120i
$19$	7.29765			1.67420			0.837098	−	0.547053i	$-0.184250\pi$
$19$	7.29765			1.67420			0.837098	+	0.547053i	$0.184250\pi$
$20$	−0.289169	+	1.97898i	−0.0646602	+	0.442514i
$21$	6.15460	−	1.24874i	1.34304	−	0.272497i
$22$	2.16681	+	2.50644i	0.461966	+	0.534374i
$23$	−2.97353	−	5.15031i	−0.620024	−	1.07391i	−0.989481	−	0.144666i	$-0.953789\pi$
$23$	−2.97353	−	5.15031i	−0.620024	−	1.07391i	0.369456	−	0.929248i	$-0.379544\pi$
$24$	4.70919	+	1.35038i	0.961259	+	0.275646i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−7.54918	+	1.44601i	−1.48052	+	0.283586i
$27$	2.93625	+	4.28701i	0.565082	+	0.825035i
$28$	−2.67967	−	6.73825i	−0.506411	−	1.27341i
$29$	1.52275	−	2.63748i	0.282768	−	0.489768i	−0.689298	−	0.724478i	$-0.742081\pi$
$29$	1.52275	−	2.63748i	0.282768	−	0.489768i	0.972065	+	0.234710i	$0.0754140\pi$
$30$	1.93843	+	1.49750i	0.353907	+	0.273405i
$31$	6.43361	−	3.71445i	1.15551	−	0.667134i	0.205287	−	0.978702i	$-0.434187\pi$
$31$	6.43361	−	3.71445i	1.15551	−	0.667134i	0.950224	+	0.311568i	$0.100854\pi$
$32$	0.569996	−	5.62806i	0.100762	−	0.994911i
$33$	3.97680	−	0.806871i	0.692271	−	0.140458i
$34$	2.06548	−	5.94574i	0.354227	−	1.01969i
$35$		−	3.62576i		−	0.612866i
$36$	4.27029	−	4.21481i	0.711714	−	0.702469i
$37$		−	4.85559i		−	0.798254i	−0.916896	−	0.399127i	$-0.869313\pi$
$37$		−	4.85559i		−	0.798254i	0.916896	−	0.399127i	$-0.130687\pi$
$38$	−9.74895	−	3.38667i	−1.58149	−	0.549390i
$39$	−2.99186	+	8.92583i	−0.479080	+	1.42928i
$40$	1.30470	−	2.50953i	0.206291	−	0.396792i
$41$	0.201473	−	0.116321i	0.0314649	−	0.0181662i	−0.484185	−	0.874966i	$-0.660884\pi$
$41$	0.201473	−	0.116321i	0.0314649	−	0.0181662i	0.515650	+	0.856799i	$0.327551\pi$
$42$	−8.80145	−	1.18801i	−1.35809	−	0.183315i
$43$	−0.490794	+	0.850080i	−0.0748453	+	0.129636i	−0.901019	−	0.433780i	$-0.857180\pi$
$43$	−0.490794	+	0.850080i	−0.0748453	+	0.129636i	0.826174	+	0.563416i	$0.190513\pi$
$44$	−1.73147	−	4.35392i	−0.261029	−	0.656378i
$45$	2.76277	−	1.16924i	0.411849	−	0.174299i
$46$	1.58221	+	8.26025i	0.233284	+	1.21791i
$47$	1.48425	−	2.57079i	0.216500	−	0.374989i	−0.737236	−	0.675636i	$-0.763869\pi$
$47$	1.48425	−	2.57079i	0.216500	−	0.374989i	0.953735	+	0.300647i	$0.0972026\pi$
$48$	−5.66433	−	3.98940i	−0.817576	−	0.575821i
$49$	3.07308	+	5.32273i	0.439011	+	0.760390i
$50$	1.06985	−	0.924887i	0.151300	−	0.130799i
$51$	−5.10497	−	5.77635i	−0.714839	−	0.808851i
$52$	10.7560	+	1.57167i	1.49159	+	0.217951i
$53$	11.3468			1.55860			0.779299	−	0.626652i	$-0.215575\pi$
$53$	11.3468			1.55860			0.779299	+	0.626652i	$0.215575\pi$
$54$	−1.93304	−	7.08966i	−0.263054	−	0.964781i
$55$		−	2.34279i		−	0.315901i
$56$	0.452721	+	10.2452i	0.0604973	+	1.36907i
$57$	−9.47121	+	8.37039i	−1.25449	+	1.10868i
$58$	−3.25824	+	2.81675i	−0.427828	+	0.369857i
$59$	1.02217	−	0.590148i	0.133075	−	0.0768308i	−0.431985	−	0.901881i	$-0.642187\pi$
$59$	1.02217	−	0.590148i	0.133075	−	0.0768308i	0.565059	+	0.825050i	$0.308853\pi$
$60$	−1.89459	−	2.90009i	−0.244591	−	0.374400i
$61$	−10.1682	−	5.87061i	−1.30190	−	0.751655i	−0.321174	−	0.947020i	$-0.604077\pi$
$61$	−10.1682	−	5.87061i	−1.30190	−	0.751655i	−0.980731	+	0.195365i	$0.937411\pi$
$62$	−10.3185	+	1.97645i	−1.31045	+	0.251010i
$63$	−6.55541	+	8.67997i	−0.825905	+	1.09357i
$64$	−3.37331	+	7.25402i	−0.421664	+	0.906752i
$65$	4.70695	+	2.71756i	0.583826	+	0.337072i
$66$	−5.68706	−	0.767635i	−0.700028	−	0.0944894i
$67$	−2.00541	−	3.47348i	−0.245000	−	0.424353i	0.717131	−	0.696938i	$-0.245455\pi$
$67$	−2.00541	−	3.47348i	−0.245000	−	0.424353i	−0.962132	+	0.272585i	$0.912121\pi$
$68$	−5.51855	+	6.98438i	−0.669223	+	0.846981i
$69$	9.76657	+	3.27366i	1.17576	+	0.394103i
$70$	−1.68263	+	4.84366i	−0.201113	+	0.578928i
$71$	−9.10623			−1.08071			−0.540355	−	0.841437i	$-0.681710\pi$
$71$	−9.10623			−1.08071			−0.540355	+	0.841437i	$0.681710\pi$
$72$	−7.66068	+	3.64884i	−0.902819	+	0.430020i
$73$	−1.90547			−0.223019			−0.111509	−	0.993763i	$-0.535569\pi$
$73$	−1.90547			−0.223019			−0.111509	+	0.993763i	$0.535569\pi$
$74$	−2.25336	+	6.48659i	−0.261948	+	0.754050i
$75$	−0.344407	−	1.69746i	−0.0397686	−	0.196006i
$76$	11.4520	+	9.04851i	1.31363	+	1.03793i
$77$	4.24719	+	7.35636i	0.484013	+	0.838335i
$78$	8.13909	−	10.5356i	0.921570	−	1.19292i
$79$	−0.784069	−	0.452683i	−0.0882147	−	0.0509308i	0.455244	−	0.890367i	$-0.349552\pi$
$79$	−0.784069	−	0.452683i	−0.0882147	−	0.0509308i	−0.543458	+	0.839436i	$0.682885\pi$
$80$	−2.90757	+	2.74701i	−0.325076	+	0.307125i
$81$	−8.72798	−	2.19599i	−0.969775	−	0.243999i
$82$	−0.323130	+	0.0618941i	−0.0356838	+	0.00683506i
$83$	11.9999	+	6.92813i	1.31716	+	0.760461i	0.983270	−	0.182153i	$-0.0583065\pi$
$83$	11.9999	+	6.92813i	1.31716	+	0.760461i	0.333886	+	0.942613i	$0.391640\pi$
$84$	11.2065	+	5.67161i	1.22273	+	0.618824i
$85$	−3.85445	+	2.22537i	−0.418073	+	0.241375i
$86$	1.05015	−	0.907857i	0.113241	−	0.0978967i
$87$	1.04889	+	5.16963i	0.112453	+	0.554243i
$88$	0.292525	+	6.61994i	0.0311833	+	0.705688i
$89$		−	12.5342i		−	1.32862i	−0.747456	−	0.664312i	$-0.768725\pi$
$89$		−	12.5342i		−	1.32862i	0.747456	−	0.664312i	$-0.231275\pi$
$90$	−4.23340	+	0.279849i	−0.446240	+	0.0294987i
$91$	−19.7065			−2.06580
$92$	1.71971	−	11.7692i	0.179292	−	1.22702i
$93$	−4.08936	+	12.2001i	−0.424047	+	1.26509i
$94$	−3.17585	+	2.74552i	−0.327564	+	0.283179i
$95$	3.64883	+	6.31995i	0.374362	+	0.648413i
$96$	5.71561	+	7.95813i	0.583347	+	0.812223i
$97$	6.51236	−	11.2797i	0.661230	−	1.14528i	−0.319063	−	0.947734i	$-0.603368\pi$
$97$	6.51236	−	11.2797i	0.661230	−	1.14528i	0.980293	−	0.197550i	$-0.0632986\pi$
$98$	−1.63518	−	8.53678i	−0.165178	−	0.862346i
$99$	−4.23578	+	5.60856i	−0.425712	+	0.563682i
$100$	−1.85844	+	0.739065i	−0.185844	+	0.0739065i
$101$	2.70362	−	4.68280i	0.269020	−	0.465956i	−0.699589	−	0.714545i	$-0.746634\pi$
$101$	2.70362	−	4.68280i	0.269020	−	0.465956i	0.968609	+	0.248589i	$0.0799669\pi$
$102$	4.13908	+	10.0857i	0.409830	+	0.998637i
$103$	−4.85443	+	2.80271i	−0.478321	+	0.276159i	−0.719717	−	0.694268i	$-0.755728\pi$
$103$	−4.85443	+	2.80271i	−0.478321	+	0.276159i	0.241395	+	0.970427i	$0.422395\pi$
$104$	−13.6396	−	7.09121i	−1.33747	−	0.695350i
$105$	4.15874	+	4.70567i	0.405851	+	0.459227i
$106$	−15.1582	−	5.26576i	−1.47229	−	0.511456i
$107$		−	5.89584i		−	0.569972i	−0.958532	−	0.284986i	$-0.908011\pi$
$107$		−	5.89584i		−	0.569972i	0.958532	−	0.284986i	$-0.0919889\pi$
$108$	−0.707786	+	10.3682i	−0.0681067	+	0.997678i
$109$			11.1013i			1.06332i	0.846959	+	0.531658i	$0.178431\pi$
$109$			11.1013i			1.06332i	−0.846959	+	0.531658i	$0.821569\pi$
$110$	−1.08723	+	3.12973i	−0.103663	+	0.298408i
$111$	5.56934	+	6.30179i	0.528619	+	0.598140i
$112$	4.14977	−	13.8967i	0.392116	−	1.31311i
$113$	−4.25183	+	2.45479i	−0.399978	+	0.230928i	−0.686475	−	0.727154i	$-0.740843\pi$
$113$	−4.25183	+	2.45479i	−0.399978	+	0.230928i	0.286496	+	0.958081i	$0.407509\pi$
$114$	16.5371	−	6.78665i	1.54884	−	0.635628i
$115$	2.97353	−	5.15031i	0.277283	−	0.480269i
$116$	5.65987	−	2.25082i	0.525506	−	0.208984i
$117$	−6.35494	−	15.0160i	−0.587514	−	1.38823i
$118$	−1.63939	+	0.314017i	−0.150918	+	0.0289076i
$119$	8.06865	−	13.9753i	0.739652	−	1.28111i
$120$	1.18513	+	4.75347i	0.108187	+	0.433930i
$121$	−2.75568	−	4.77297i	−0.250516	−	0.433906i
$122$	10.8593	+	12.5614i	0.983155	+	1.13725i
$123$	−0.128061	+	0.382056i	−0.0115469	+	0.0344488i
$124$	14.7017	+	2.14821i	1.32025	+	0.192915i
$125$	−1.00000			−0.0894427
$126$	12.7856	−	8.55338i	1.13903	−	0.761996i
$127$			12.4207i			1.10216i	0.834453	+	0.551078i	$0.185784\pi$
$127$			12.4207i			1.10216i	−0.834453	+	0.551078i	$0.814216\pi$
$128$	7.87283	−	8.12518i	0.695866	−	0.718172i
$129$	−0.338065	−	1.66621i	−0.0297650	−	0.146702i
$130$	−5.02687	−	5.81478i	−0.440886	−	0.509990i
$131$	−7.78421	+	4.49421i	−0.680109	+	0.392661i	−0.799896	−	0.600138i	$-0.795112\pi$
$131$	−7.78421	+	4.49421i	−0.680109	+	0.392661i	0.119787	+	0.992800i	$0.461779\pi$
$132$	7.24111	+	3.66471i	0.630258	+	0.318972i
$133$	−22.9147	−	13.2298i	−1.98695	−	1.14717i
$134$	1.06708	+	5.57089i	0.0921814	+	0.481252i
$135$	−2.24453	+	4.68637i	−0.193179	+	0.403339i
$136$	10.6135	−	6.76942i	0.910103	−	0.580473i
$137$	−6.43275	−	3.71395i	−0.549587	−	0.317304i	0.199369	−	0.979925i	$-0.436111\pi$
$137$	−6.43275	−	3.71395i	−0.549587	−	0.317304i	−0.748955	+	0.662621i	$0.769444\pi$
$138$	−11.5279	−	8.90573i	−0.981324	−	0.758106i
$139$	9.12620	+	15.8071i	0.774075	+	1.34074i	0.935313	+	0.353821i	$0.115118\pi$
$139$	9.12620	+	15.8071i	0.774075	+	1.34074i	−0.161239	+	0.986915i	$0.551549\pi$
$140$	4.49566	−	5.68979i	0.379952	−	0.480875i
$141$	1.02237	+	5.03891i	0.0860990	+	0.424353i
$142$	12.1650	+	4.22598i	1.02087	+	0.354637i
$143$	−12.7333			−1.06481
$144$	11.9273	−	1.31935i	0.993938	−	0.109946i
$145$	3.04550			0.252915
$146$	2.54553	+	0.884285i	0.210669	+	0.0731840i
$147$	−10.0935	−	3.38326i	−0.832500	−	0.279046i
$148$	6.02054	−	7.61971i	0.494885	−	0.626336i
$149$	−1.11188	−	1.92582i	−0.0910884	−	0.157770i	0.816881	−	0.576806i	$-0.195701\pi$
$149$	−1.11188	−	1.92582i	−0.0910884	−	0.157770i	−0.907969	+	0.419037i	$0.862368\pi$
$150$	−0.327659	+	2.42748i	−0.0267533	+	0.198203i
$151$	−10.1328	−	5.85015i	−0.824592	−	0.476078i	0.0274053	−	0.999624i	$-0.491276\pi$
$151$	−10.1328	−	5.85015i	−0.824592	−	0.476078i	−0.851997	+	0.523546i	$0.824609\pi$
$152$	−11.0995	−	17.4025i	−0.900288	−	1.41153i
$153$	13.2509	+	1.64141i	1.07127	+	0.132700i
$154$	−2.25992	−	11.7984i	−0.182110	−	0.950741i
$155$	6.43361	+	3.71445i	0.516760	+	0.298352i
$156$	−15.7623	+	10.2973i	−1.26200	+	0.824447i
$157$	−5.56748	+	3.21439i	−0.444333	+	0.256536i	−0.705434	−	0.708776i	$-0.749248\pi$
$157$	−5.56748	+	3.21439i	−0.444333	+	0.256536i	0.261101	+	0.965312i	$0.415915\pi$
$158$	0.837361	+	0.968608i	0.0666168	+	0.0770583i
$159$	−14.7263	+	13.0147i	−1.16787	+	1.03213i
$160$	5.15904	−	2.32040i	0.407858	−	0.183444i
$161$			21.5627i			1.69937i
$162$	10.6406	+	6.98408i	0.836005	+	0.548721i
$163$	11.4706			0.898447			0.449224	−	0.893419i	$-0.351701\pi$
$163$	11.4706			0.898447			0.449224	+	0.893419i	$0.351701\pi$
$164$	0.460394	+	0.0672727i	0.0359507	+	0.00525312i
$165$	2.68717	+	3.04057i	0.209196	+	0.236708i
$166$	−12.8155	−	14.8241i	−0.994673	−	1.15058i
$167$	−3.80264	−	6.58637i	−0.294257	−	0.509669i	0.680555	−	0.732697i	$-0.261739\pi$
$167$	−3.80264	−	6.58637i	−0.294257	−	0.509669i	−0.974812	+	0.223029i	$0.928406\pi$
$168$	−12.3388	−	12.7774i	−0.951958	−	0.985799i
$169$	8.27027	−	14.3245i	0.636174	−	1.10189i
$170$	6.18190	−	1.18411i	0.474130	−	0.0908173i
$171$	2.69135	−	21.7269i	0.205813	−	1.66150i
$172$	−1.82422	+	0.725457i	−0.139095	+	0.0553155i
$173$	−7.17933	+	12.4350i	−0.545834	+	0.945413i	0.452720	+	0.891653i	$0.350454\pi$
$173$	−7.17933	+	12.4350i	−0.545834	+	0.945413i	−0.998554	+	0.0537597i	$0.982879\pi$
$174$	0.997887	−	7.39289i	0.0756496	−	0.560453i
$175$	3.14000	−	1.81288i	0.237362	−	0.137041i
$176$	2.68137	−	8.97934i	0.202116	−	0.676844i
$177$	−0.649715	+	1.93834i	−0.0488355	+	0.145695i
$178$	−5.81683	+	16.7445i	−0.435990	+	1.25505i
$179$			1.98512i			0.148374i	0.997244	+	0.0741872i	$0.0236362\pi$
$179$			1.98512i			0.148374i	−0.997244	+	0.0741872i	$0.976364\pi$
$180$	5.78528	+	1.59077i	0.431209	+	0.118569i
$181$		−	1.20120i		−	0.0892847i	−0.999003	−	0.0446424i	$-0.985785\pi$
$181$		−	1.20120i		−	0.0892847i	0.999003	−	0.0446424i	$-0.0142148\pi$
$182$	26.3259	+	9.14530i	1.95141	+	0.677895i
$183$	19.9303	−	4.04376i	1.47329	−	0.298923i
$184$	−7.75914	+	14.9244i	−0.572012	+	1.10024i
$185$	4.20506	−	2.42779i	0.309162	−	0.178495i
$186$	11.1248	−	14.4004i	0.815707	−	1.05589i
$187$	5.21356	−	9.03014i	0.381253	−	0.660350i
$188$	5.51676	−	2.19391i	0.402351	−	0.160007i
$189$	−1.44800	−	18.7843i	−0.105327	−	1.36636i
$190$	−1.94153	−	10.1362i	−0.140854	−	0.735355i
$191$	10.8619	−	18.8134i	0.785940	−	1.36129i	−0.142496	−	0.989795i	$-0.545513\pi$
$191$	10.8619	−	18.8134i	0.785940	−	1.36129i	0.928436	−	0.371493i	$-0.121154\pi$
$192$	−3.94231	−	13.2838i	−0.284512	−	0.958673i
$193$	−0.295771	−	0.512291i	−0.0212901	−	0.0368755i	0.855184	−	0.518324i	$-0.173444\pi$
$193$	−0.295771	−	0.512291i	−0.0212901	−	0.0368755i	−0.876474	+	0.481449i	$0.840111\pi$
$194$	−13.9345	+	12.0464i	−1.00044	+	0.864880i
$195$	−9.22592	+	1.87189i	−0.660682	+	0.134049i
$196$	−1.77728	+	12.1632i	−0.126948	+	0.868797i
$197$	14.5219			1.03465			0.517323	−	0.855790i	$-0.326929\pi$
$197$	14.5219			1.03465			0.517323	+	0.855790i	$0.326929\pi$
$198$	8.26139	−	5.52677i	0.587111	−	0.392770i
$199$		−	3.78516i		−	0.268323i	−0.990959	−	0.134161i	$-0.957166\pi$
$199$		−	3.78516i		−	0.268323i	0.990959	−	0.134161i	$-0.0428341\pi$
$200$	2.82567	−	0.124862i	0.199805	−	0.00882909i
$201$	6.58678	+	2.20783i	0.464596	+	0.155728i
$202$	−5.78494	+	5.00108i	−0.407027	+	0.351875i
$203$	−9.56289	+	5.52114i	−0.671183	+	0.387508i
$204$	−0.848850	−	15.3944i	−0.0594314	−	1.07782i
$205$	0.201473	+	0.116321i	0.0140715	+	0.00812419i
$206$	7.78571	−	1.49132i	0.542456	−	0.103905i
$207$	−16.4304	+	6.95352i	−1.14199	+	0.483303i
$208$	14.9303	+	15.8030i	1.03523	+	1.09574i
$209$	−14.8063	−	8.54842i	−1.02417	−	0.591307i
$210$	−3.37188	−	8.21629i	−0.232682	−	0.566978i
$211$	−4.78327	−	8.28487i	−0.329294	−	0.570354i	0.653078	−	0.757291i	$-0.273477\pi$
$211$	−4.78327	−	8.28487i	−0.329294	−	0.570354i	−0.982372	+	0.186937i	$0.940144\pi$
$212$	17.8061	+	14.0691i	1.22293	+	0.966269i
$213$	11.8185	−	10.4448i	0.809788	−	0.715667i
$214$	−2.73612	+	7.87626i	−0.187037	+	0.538410i
$215$	−0.981587			−0.0669437
$216$	5.75715	−	13.5224i	0.391725	−	0.920082i
$217$	−26.9354			−1.82849
$218$	5.15187	−	14.8303i	0.348928	−	1.00443i
$219$	2.47301	−	2.18557i	0.167110	−	0.147687i
$220$	2.90487	−	3.67646i	0.195846	−	0.247867i
$221$	12.0951	+	20.9494i	0.813607	+	1.40921i
$222$	−4.51558	−	11.0032i	−0.303066	−	0.738485i
$223$	20.2019	+	11.6636i	1.35282	+	0.781050i	0.988643	−	0.150280i	$-0.0480176\pi$
$223$	20.2019	+	11.6636i	1.35282	+	0.781050i	0.364175	+	0.931330i	$0.381351\pi$
$224$	−11.9928	+	16.6388i	−0.801303	+	1.11173i
$225$	2.39397	+	1.80801i	0.159598	+	0.120534i
$226$	6.81924	−	1.30619i	0.453609	−	0.0868866i
$227$	19.1657	+	11.0653i	1.27207	+	0.734431i	0.975378	−	0.220542i	$-0.0707826\pi$
$227$	19.1657	+	11.0653i	1.27207	+	0.734431i	0.296694	+	0.954973i	$0.404116\pi$
$228$	−25.2415	+	1.39182i	−1.67166	+	0.0921754i
$229$	−19.2431	+	11.1100i	−1.27162	+	0.734170i	−0.975293	−	0.220917i	$-0.929095\pi$
$229$	−19.2431	+	11.1100i	−1.27162	+	0.734170i	−0.296326	+	0.955087i	$0.595762\pi$
$230$	−6.36248	+	5.50036i	−0.419530	+	0.362683i
$231$	−13.9499	−	4.67588i	−0.917837	−	0.307650i
$232$	−8.60559	+	0.380268i	−0.564985	+	0.0249658i
$233$			6.09171i			0.399081i	0.979890	+	0.199541i	$0.0639450\pi$
$233$			6.09171i			0.399081i	−0.979890	+	0.199541i	$0.936055\pi$
$234$	1.52101	+	23.0090i	0.0994317	+	1.50415i
$235$	2.96850			0.193643
$236$	2.33579	+	0.341305i	0.152047	+	0.0222171i
$237$	1.53683	−	0.311814i	0.0998275	−	0.0202545i
$238$	−17.2645	+	14.9252i	−1.11909	+	0.967455i
$239$	5.22528	+	9.05044i	0.337995	+	0.585424i	0.984055	−	0.177862i	$-0.0569180\pi$
$239$	5.22528	+	9.05044i	0.337995	+	0.585424i	−0.646061	+	0.763286i	$0.723585\pi$
$240$	0.622757	−	6.90016i	0.0401988	−	0.445403i
$241$	−5.25137	+	9.09564i	−0.338270	+	0.585902i	−0.984108	−	0.177574i	$-0.943175\pi$
$241$	−5.25137	+	9.09564i	−0.338270	+	0.585902i	0.645837	+	0.763475i	$0.276509\pi$
$242$	1.46629	+	7.65506i	0.0942567	+	0.492086i
$243$	13.8464	−	7.16091i	0.888244	−	0.459372i
$244$	−8.67753	−	21.8203i	−0.555522	−	1.39690i
$245$	−3.07308	+	5.32273i	−0.196332	+	0.340057i
$246$	0.348380	−	0.450958i	0.0222119	−	0.0287521i
$247$	34.3497	−	19.8318i	2.18562	−	1.26187i
$248$	−18.6431	−	9.69249i	−1.18384	−	0.615473i
$249$	−23.5205	+	4.77219i	−1.49055	+	0.302425i
$250$	1.33590	+	0.464076i	0.0844898	+	0.0293508i
$251$		−	17.3670i		−	1.09619i	−0.836415	−	0.548096i	$-0.815353\pi$
$251$		−	17.3670i		−	1.09619i	0.836415	−	0.548096i	$-0.184647\pi$
$252$	−21.0497	+	5.49300i	−1.32600	+	0.346027i
$253$			13.9327i			0.875942i
$254$	5.76414	−	16.5928i	0.361674	−	1.04113i
$255$	2.44998	−	7.30921i	0.153424	−	0.457721i
$256$	−14.2880	+	7.20086i	−0.893002	+	0.450054i
$257$	4.12089	−	2.37920i	0.257054	−	0.148410i	−0.365936	−	0.930640i	$-0.619251\pi$
$257$	4.12089	−	2.37920i	0.257054	−	0.148410i	0.622990	+	0.782230i	$0.285918\pi$
$258$	−0.321626	+	2.38278i	−0.0200236	+	0.148345i
$259$	−8.80260	+	15.2466i	−0.546967	+	0.947375i
$260$	4.01691	+	10.1008i	0.249118	+	0.626426i
$261$	−7.29085	−	5.50630i	−0.451292	−	0.340831i
$262$	12.4846	−	2.39136i	0.771301	−	0.147739i
$263$	5.52520	−	9.56992i	0.340698	−	0.590107i	−0.643864	−	0.765140i	$-0.722670\pi$
$263$	5.52520	−	9.56992i	0.340698	−	0.590107i	0.984563	+	0.175033i	$0.0560032\pi$
$264$	−7.97270	−	8.25612i	−0.490686	−	0.508129i
$265$	5.67338	+	9.82659i	0.348513	+	0.603643i
$266$	24.4721	+	28.3078i	1.50048	+	1.73566i
$267$	14.3767	+	16.2674i	0.879840	+	0.995551i
$268$	1.15981	−	7.93737i	0.0708465	−	0.484852i
$269$	11.5092			0.701729			0.350864	−	0.936426i	$-0.385888\pi$
$269$	11.5092			0.701729			0.350864	+	0.936426i	$0.385888\pi$
$270$	5.17331	−	5.21890i	0.314837	−	0.317612i
$271$			11.4347i			0.694608i	0.937753	+	0.347304i	$0.112903\pi$
$271$			11.4347i			0.694608i	−0.937753	+	0.347304i	$0.887097\pi$
$272$	−17.3202	+	4.11780i	−1.05019	+	0.249678i
$273$	25.5759	−	22.6032i	1.54792	−	1.36801i
$274$	6.86996	+	7.94675i	0.415030	+	0.480081i
$275$	2.02891	−	1.17139i	0.122348	−	0.0706377i
$276$	11.2673	+	17.2470i	0.678210	+	1.03815i
$277$	9.37584	+	5.41315i	0.563340	+	0.325244i	0.754485	−	0.656317i	$-0.227887\pi$
$277$	9.37584	+	5.41315i	0.563340	+	0.325244i	−0.191145	+	0.981562i	$0.561220\pi$
$278$	−4.85604	−	25.3519i	−0.291246	−	1.52051i
$279$	−8.68613	−	20.5243i	−0.520025	−	1.22876i
$280$	−8.64625	+	5.51467i	−0.516712	+	0.329565i
$281$	24.4780	+	14.1324i	1.46023	+	0.843066i	0.999022	−	0.0442235i	$-0.0140814\pi$
$281$	24.4780	+	14.1324i	1.46023	+	0.843066i	0.461212	+	0.887290i	$0.347415\pi$
$282$	0.972655	−	7.20595i	0.0579208	−	0.429108i
$283$	−3.42213	−	5.92730i	−0.203425	−	0.352342i	0.746205	−	0.665716i	$-0.231874\pi$
$283$	−3.42213	−	5.92730i	−0.203425	−	0.352342i	−0.949630	+	0.313374i	$0.898541\pi$
$284$	−14.2901	−	11.2910i	−0.847962	−	0.669997i
$285$	−11.9846	−	4.01712i	−0.709905	−	0.237954i
$286$	17.0105	+	5.90923i	1.00585	+	0.349420i
$287$	−0.843503			−0.0497904
$288$	−16.5459	−	3.77263i	−0.974977	−	0.222304i
$289$	−2.80901			−0.165236
$290$	−4.06849	−	1.41335i	−0.238910	−	0.0829945i
$291$	4.48580	+	22.1090i	0.262962	+	1.29605i
$292$	−2.99020	−	2.36264i	−0.174988	−	0.138263i
$293$	−1.52530	−	2.64190i	−0.0891092	−	0.154342i	0.818026	−	0.575182i	$-0.195069\pi$
$293$	−1.52530	−	2.64190i	−0.0891092	−	0.154342i	−0.907135	+	0.420840i	$0.861735\pi$
$294$	11.9139	+	9.20387i	0.694831	+	0.536780i
$295$	1.02217	+	0.590148i	0.0595129	+	0.0343598i
$296$	−11.5790	+	7.38520i	−0.673014	+	0.429256i
$297$	−0.935625	−	12.1375i	−0.0542905	−	0.704287i
$298$	0.591627	+	3.08871i	0.0342720	+	0.178924i
$299$	−27.9926	−	16.1615i	−1.61885	−	0.934644i
$300$	1.56425	−	3.09081i	0.0903123	−	0.178448i
$301$	3.08219	−	1.77950i	0.177654	−	0.102569i
$302$	10.8215	+	12.5176i	0.622705	+	0.720307i
$303$	1.86229	+	9.17858i	0.106986	+	0.527296i
$304$	6.75176	+	28.3990i	0.387240	+	1.62880i
$305$		−	11.7412i		−	0.672301i
$306$	−16.9402	−	8.34220i	−0.968406	−	0.476892i
$307$	−14.0214			−0.800245			−0.400123	−	0.916462i	$-0.631032\pi$
$307$	−14.0214			−0.800245			−0.400123	+	0.916462i	$0.631032\pi$
$308$	−2.45631	+	16.8103i	−0.139961	+	0.957854i
$309$	3.08560	−	9.20549i	0.175533	−	0.523682i
$310$	−6.87089	−	7.94782i	−0.390240	−	0.451406i
$311$	2.33350	+	4.04175i	0.132321	+	0.229186i	0.924571	−	0.381010i	$-0.124424\pi$
$311$	2.33350	+	4.04175i	0.132321	+	0.229186i	−0.792250	+	0.610197i	$0.791090\pi$
$312$	25.8357	−	6.44132i	1.46266	−	0.364668i
$313$	−8.66672	+	15.0112i	−0.489872	+	0.848483i	−0.999932	−	0.0116555i	$-0.996290\pi$
$313$	−8.66672	+	15.0112i	−0.489872	+	0.848483i	0.510060	+	0.860139i	$0.329623\pi$
$314$	8.92933	−	1.71037i	0.503911	−	0.0965217i
$315$	−10.7948	−	1.33717i	−0.608217	−	0.0753409i
$316$	−0.669124	−	1.68256i	−0.0376411	−	0.0946516i
$317$	−9.85952	+	17.0772i	−0.553766	+	0.959151i	0.444233	+	0.895911i	$0.353476\pi$
$317$	−9.85952	+	17.0772i	−0.553766	+	0.959151i	−0.997998	+	0.0632390i	$0.979857\pi$
$318$	25.7127	−	10.5522i	1.44190	−	0.591740i
$319$	−6.17906	+	3.56748i	−0.345961	+	0.199741i
$320$	−7.96882	+	0.705638i	−0.445471	+	0.0394464i
$321$	6.76250	+	7.65187i	0.377446	+	0.427086i
$322$	10.0067	−	28.8056i	0.557652	−	1.60527i
$323$			32.4799i			1.80723i
$324$	−10.9737	−	14.2681i	−0.609648	−	0.792672i
$325$			5.43512i			0.301486i
$326$	−15.3236	−	5.32323i	−0.848696	−	0.294827i
$327$	−12.7332	−	14.4078i	−0.704148	−	0.796753i
$328$	−0.583821	−	0.303528i	−0.0322361	−	0.0167595i
$329$	−9.32109	+	5.38153i	−0.513888	+	0.296693i
$330$	−2.17874	−	5.30895i	−0.119936	−	0.292248i
$331$	−10.8437	+	18.7818i	−0.596024	+	1.03234i	0.397378	+	0.917655i	$0.369920\pi$
$331$	−10.8437	+	18.7818i	−0.596024	+	1.03234i	−0.993402	+	0.114688i	$0.963413\pi$
$332$	10.2407	+	25.7510i	0.562030	+	1.41327i
$333$	−14.4563	−	1.79072i	−0.792199	−	0.0981310i
$334$	2.02338	+	10.5635i	0.110714	+	0.578007i
$335$	2.00541	−	3.47348i	0.109567	−	0.189776i
$336$	10.5537	+	22.7955i	0.575752	+	1.24360i
$337$	−15.4398	−	26.7425i	−0.841060	−	1.45676i	−0.889000	−	0.457908i	$-0.848599\pi$
$337$	−15.4398	−	26.7425i	−0.841060	−	1.45676i	0.0479400	−	0.998850i	$-0.484734\pi$
$338$	−17.6959	+	15.2981i	−0.962532	+	0.832108i
$339$	2.70257	−	8.06277i	0.146783	−	0.437910i
$340$	−8.80793	−	1.28701i	−0.477677	−	0.0697981i
$341$	−17.4043			−0.942496
$342$	−13.6783	+	27.7760i	−0.739638	+	1.50195i
$343$			3.09583i			0.167159i
$344$	2.77364	−	0.122563i	0.149545	−	0.00660816i
$345$	2.04821	+	10.0949i	0.110272	+	0.543493i
$346$	15.3616	−	13.2801i	0.825847	−	0.713944i
$347$	4.21789	−	2.43520i	0.226428	−	0.130728i	−0.382495	−	0.923958i	$-0.624935\pi$
$347$	4.21789	−	2.43520i	0.226428	−	0.130728i	0.608923	+	0.793229i	$0.291602\pi$
$348$	−4.76394	+	9.41307i	−0.255374	+	0.504594i
$349$	−22.0828	−	12.7495i	−1.18206	−	0.682464i	−0.225572	−	0.974226i	$-0.572425\pi$
$349$	−22.0828	−	12.7495i	−1.18206	−	0.682464i	−0.956491	+	0.291762i	$0.905758\pi$
$350$	−5.03605	+	0.964631i	−0.269188	+	0.0515617i
$351$	25.4710	+	12.1993i	1.35954	+	0.651150i
$352$	−7.74915	+	10.7512i	−0.413031	+	0.573039i
$353$	−10.2311	−	5.90692i	−0.544545	−	0.314393i	0.202374	−	0.979308i	$-0.435134\pi$
$353$	−10.2311	−	5.90692i	−0.544545	−	0.314393i	−0.746919	+	0.664915i	$0.768468\pi$
$354$	1.76749	−	2.28792i	0.0939412	−	0.121601i
$355$	−4.55311	−	7.88623i	−0.241654	−	0.418557i
$356$	15.5414	−	19.6695i	0.823693	−	1.04248i
$357$	5.55779	+	27.3925i	0.294150	+	1.44976i
$358$	0.921245	−	2.65192i	0.0486893	−	0.140158i
$359$	0.760028			0.0401127			0.0200564	−	0.999799i	$-0.493615\pi$
$359$	0.760028			0.0401127			0.0200564	+	0.999799i	$0.493615\pi$
$360$	−6.99033	−	4.80992i	−0.368423	−	0.253505i
$361$	34.2557			1.80293
$362$	−0.557450	+	1.60469i	−0.0292989	+	0.0843406i
$363$	9.05102	+	3.03382i	0.475055	+	0.159234i
$364$	−30.9247	−	24.4344i	−1.62089	−	1.28071i
$365$	−0.952737	−	1.65019i	−0.0498685	−	0.0863749i
$366$	−28.5015	−	3.84712i	−1.48980	−	0.201092i
$367$	5.37981	+	3.10604i	0.280824	+	0.162134i	0.633796	−	0.773500i	$-0.281496\pi$
$367$	5.37981	+	3.10604i	0.280824	+	0.162134i	−0.352972	+	0.935634i	$0.614829\pi$
$368$	17.2915	−	16.3366i	0.901381	−	0.851606i
$369$	−0.272013	−	0.642734i	−0.0141604	−	0.0334594i
$370$	−6.74423	+	1.29182i	−0.350616	+	0.0671588i
$371$	−35.6289	−	20.5703i	−1.84976	−	1.06796i
$372$	−21.5445	+	14.0747i	−1.11703	+	0.729741i
$373$	1.87562	−	1.08289i	0.0971157	−	0.0560698i	−0.450656	−	0.892698i	$-0.648810\pi$
$373$	1.87562	−	1.08289i	0.0971157	−	0.0560698i	0.547771	+	0.836628i	$0.315476\pi$
$374$	−11.1555	+	9.64390i	−0.576836	+	0.498674i
$375$	1.29784	−	1.14700i	0.0670204	−	0.0592307i
$376$	−8.38799	+	0.370653i	−0.432578	+	0.0191150i
$377$		−	16.5527i		−	0.852506i
$378$	−6.78295	+	25.7659i	−0.348878	+	1.32526i
$379$	20.7593			1.06633			0.533167	−	0.846010i	$-0.321002\pi$
$379$	20.7593			1.06633			0.533167	+	0.846010i	$0.321002\pi$
$380$	−2.11026	+	14.4419i	−0.108254	+	0.740856i
$381$	−14.2465	−	16.1201i	−0.729869	−	0.825858i
$382$	−23.2413	+	20.0921i	−1.18913	+	1.02800i
$383$	0.875949	+	1.51719i	0.0447589	+	0.0775247i	0.887537	−	0.460737i	$-0.152415\pi$
$383$	0.875949	+	1.51719i	0.0447589	+	0.0775247i	−0.842778	+	0.538261i	$0.819081\pi$
$384$	−0.898137	+	19.5753i	−0.0458328	+	0.998949i
$385$	−4.24719	+	7.35636i	−0.216457	+	0.374915i
$386$	0.157379	+	0.821630i	0.00801039	+	0.0418199i
$387$	2.34989	+	1.77472i	0.119452	+	0.0902141i
$388$	24.2056	−	9.62611i	1.22885	−	0.488692i
$389$	−4.01548	+	6.95501i	−0.203593	+	0.352633i	−0.949683	−	0.313211i	$-0.898595\pi$
$389$	−4.01548	+	6.95501i	−0.203593	+	0.352633i	0.746091	+	0.665844i	$0.231929\pi$
$390$	13.1936	+	1.78087i	0.668085	+	0.0901777i
$391$	22.9226	−	13.2344i	1.15925	−	0.669292i
$392$	8.01890	−	15.4240i	0.405016	−	0.779029i
$393$	4.94783	−	14.7612i	0.249585	−	0.744607i
$394$	−19.3999	−	6.73929i	−0.977352	−	0.339520i
$395$		−	0.905365i		−	0.0455539i
$396$	−13.6012	+	3.54930i	−0.683488	+	0.178359i
$397$		−	22.2802i		−	1.11821i	−0.829096	−	0.559106i	$-0.811144\pi$
$397$		−	22.2802i		−	1.11821i	0.829096	−	0.559106i	$-0.188856\pi$
$398$	−1.75660	+	5.05660i	−0.0880505	+	0.253465i
$399$	44.9142	−	9.11285i	2.24852	−	0.456213i
$400$	−3.83276	−	1.14452i	−0.191638	−	0.0572261i
$401$	−3.54957	+	2.04934i	−0.177257	+	0.102339i	−0.586003	−	0.810309i	$-0.699299\pi$
$401$	−3.54957	+	2.04934i	−0.177257	+	0.102339i	0.408746	+	0.912648i	$0.365966\pi$
$402$	−7.77469	−	6.00621i	−0.387766	−	0.299563i
$403$	20.1885	−	34.9675i	1.00566	−	1.74185i
$404$	10.0490	−	3.99630i	0.499956	−	0.198823i
$405$	−2.46220	−	8.65665i	−0.122348	−	0.430152i
$406$	15.3373	−	2.93779i	0.761178	−	0.145800i
$407$	−5.68780	+	9.85156i	−0.281934	+	0.488324i
$408$	−6.01019	+	20.9593i	−0.297549	+	1.03764i
$409$	19.1817	+	33.2237i	0.948476	+	1.64281i	0.748638	+	0.662979i	$0.230708\pi$
$409$	19.1817	+	33.2237i	0.948476	+	1.64281i	0.199837	+	0.979829i	$0.435959\pi$
$410$	−0.215167	−	0.248892i	−0.0106263	−	0.0122919i
$411$	12.6086	−	2.55822i	0.621936	−	0.126188i
$412$	−11.0930	−	1.62091i	−0.546514	−	0.0798566i
$413$	−4.27948			−0.210579
$414$	25.1763	−	1.66428i	1.23735	−	0.0817949i
$415$			13.8563i			0.680177i
$416$	−12.6117	−	28.0400i	−0.618337	−	1.37478i
$417$	−29.9750	−	10.0474i	−1.46788	−	0.492021i
$418$	15.8126	+	18.2911i	0.773422	+	0.894647i
$419$	27.4686	−	15.8590i	1.34193	−	0.774762i	0.354837	−	0.934928i	$-0.384536\pi$
$419$	27.4686	−	15.8590i	1.34193	−	0.774762i	0.987090	+	0.160167i	$0.0512031\pi$
$420$	0.691511	+	12.5410i	0.0337423	+	0.611936i
$421$	7.55907	+	4.36423i	0.368407	+	0.212700i	0.672762	−	0.739859i	$-0.265108\pi$
$421$	7.55907	+	4.36423i	0.368407	+	0.212700i	−0.304355	+	0.952559i	$0.598441\pi$
$422$	2.54517	+	13.2876i	0.123897	+	0.646829i
$423$	−7.10650	−	5.36707i	−0.345530	−	0.260956i
$424$	−17.2581	−	27.0583i	−0.838126	−	1.31407i
$425$	−3.85445	−	2.22537i	−0.186968	−	0.107946i
$426$	−20.6355	+	8.46858i	−0.999793	+	0.410304i
$427$	21.2855	+	36.8675i	1.03008	+	1.78414i
$428$	7.31037	−	9.25214i	0.353360	−	0.447219i
$429$	16.5259	−	14.6051i	0.797876	−	0.705140i
$430$	1.31130	+	0.455531i	0.0632367	+	0.0219677i
$431$	−17.1073			−0.824027			−0.412014	−	0.911178i	$-0.635174\pi$
$431$	−17.1073			−0.824027			−0.412014	+	0.911178i	$0.635174\pi$
$432$	−13.9664	+	15.3928i	−0.671959	+	0.740588i
$433$	−15.5412			−0.746864			−0.373432	−	0.927657i	$-0.621819\pi$
$433$	−15.5412			−0.746864			−0.373432	+	0.927657i	$0.621819\pi$
$434$	35.9831	+	12.5001i	1.72724	+	0.600023i
$435$	−3.95259	+	3.49318i	−0.189512	+	0.167485i
$436$	−13.7648	+	17.4210i	−0.659213	+	0.834313i
$437$	−21.6998	−	37.5852i	−1.03804	−	1.79794i
$438$	−4.31797	+	1.77205i	−0.206320	+	0.0846717i
$439$	14.9485	+	8.63053i	0.713454	+	0.411913i	0.812339	−	0.583186i	$-0.198194\pi$
$439$	14.9485	+	8.63053i	0.713454	+	0.411913i	−0.0988846	+	0.995099i	$0.531527\pi$
$440$	−5.58677	+	3.56330i	−0.266339	+	0.169874i
$441$	16.9804	−	7.18631i	0.808591	−	0.342205i
$442$	−6.43580	−	33.5994i	−0.306120	−	1.59816i
$443$	25.2919	+	14.6023i	1.20165	+	0.693775i	0.960923	−	0.276817i	$-0.0892796\pi$
$443$	25.2919	+	14.6023i	1.20165	+	0.693775i	0.240731	+	0.970592i	$0.422613\pi$
$444$	0.926064	+	16.7947i	0.0439491	+	0.797043i
$445$	10.8549	−	6.26710i	0.514574	−	0.297089i
$446$	−21.5750	−	24.9566i	−1.02160	−	1.18173i
$447$	3.65195	+	1.22410i	0.172732	+	0.0578980i
$448$	23.7429	−	16.6622i	1.12175	−	0.787216i
$449$		−	5.11763i		−	0.241516i	−0.992682	−	0.120758i	$-0.961467\pi$
$449$		−	5.11763i		−	0.241516i	0.992682	−	0.120758i	$-0.0385325\pi$
$450$	−2.35906	−	3.52631i	−0.111207	−	0.166232i
$451$	−0.545029			−0.0256644
$452$	−9.71600	−	1.41970i	−0.457002	−	0.0667771i
$453$	19.8608	−	4.02966i	0.933144	−	0.189330i
$454$	−20.4683	−	23.6765i	−0.960626	−	1.11119i
$455$	−9.85323	−	17.0663i	−0.461927	−	0.800080i
$456$	34.3660	+	9.85463i	1.60934	+	0.461485i
$457$	7.82613	−	13.5552i	0.366091	−	0.634088i	−0.622860	−	0.782333i	$-0.714029\pi$
$457$	7.82613	−	13.5552i	0.366091	−	0.634088i	0.988951	+	0.148246i	$0.0473626\pi$
$458$	30.8628	−	5.91161i	1.44212	−	0.276232i
$459$	−19.0803	+	13.0685i	−0.890593	+	0.609984i
$460$	11.0522	−	4.39527i	0.515313	−	0.204930i
$461$	−20.0597	+	34.7443i	−0.934271	+	1.61821i	−0.158343	+	0.987384i	$0.550615\pi$
$461$	−20.0597	+	34.7443i	−0.934271	+	1.61821i	−0.775928	+	0.630821i	$0.782718\pi$
$462$	16.4657	+	12.7203i	0.766056	+	0.591804i
$463$	19.0948	−	11.0244i	0.887409	−	0.512346i	0.0143148	−	0.999898i	$-0.495443\pi$
$463$	19.0948	−	11.0244i	0.887409	−	0.512346i	0.873094	+	0.487552i	$0.162110\pi$
$464$	11.6727	+	3.48565i	0.541891	+	0.161817i
$465$	−12.6103	+	2.55856i	−0.584788	+	0.118650i
$466$	2.82702	−	8.13793i	0.130959	−	0.376982i
$467$			2.50347i			0.115847i	0.998321	+	0.0579234i	$0.0184479\pi$
$467$			2.50347i			0.115847i	−0.998321	+	0.0579234i	$0.981552\pi$
$468$	8.64602	−	31.4437i	0.399663	−	1.45349i
$469$			14.5423i			0.671501i
$470$	−3.96562	−	1.37761i	−0.182920	−	0.0635443i
$471$	3.53883	−	10.5577i	0.163061	−	0.486471i
$472$	−2.96199	−	1.53993i	−0.136337	−	0.0708812i
$473$	1.99155	−	1.14982i	0.0915718	−	0.0528690i
$474$	−2.19775	−	0.296651i	−0.100946	−	0.0136256i
$475$	−3.64883	+	6.31995i	−0.167420	+	0.289979i
$476$	29.9901	−	11.9265i	1.37460	−	0.546651i
$477$	4.18465	−	33.7821i	0.191602	−	1.54678i
$478$	−2.78036	−	14.5154i	−0.127171	−	0.663920i
$479$	0.825331	−	1.42951i	0.0377103	−	0.0653162i	−0.846554	−	0.532302i	$-0.821327\pi$
$479$	0.825331	−	1.42951i	0.0377103	−	0.0653162i	0.884265	+	0.466986i	$0.154660\pi$
$480$	−4.03414	+	8.92893i	−0.184132	+	0.407548i
$481$	−13.1953	−	22.8550i	−0.601656	−	1.04210i
$482$	11.2364	−	9.71384i	0.511803	−	0.442453i
$483$	−24.7323	−	27.9849i	−1.12536	−	1.27336i
$484$	1.59371	−	10.9069i	0.0724415	−	0.495767i
$485$	13.0247			0.591422
$486$	−21.8206	+	3.14051i	−0.989801	+	0.142456i
$487$		−	11.5031i		−	0.521257i	−0.965439	−	0.260629i	$-0.916070\pi$
$487$		−	11.5031i		−	0.521257i	0.965439	−	0.260629i	$-0.0839298\pi$
$488$	1.46603	+	33.1768i	0.0663643	+	1.50184i
$489$	−14.8871	+	13.1567i	−0.673216	+	0.594969i
$490$	6.57548	−	5.68450i	0.297050	−	0.256800i
$491$	12.2934	−	7.09761i	0.554794	−	0.320311i	−0.196259	−	0.980552i	$-0.562879\pi$
$491$	12.2934	−	7.09761i	0.554794	−	0.320311i	0.751053	+	0.660241i	$0.229546\pi$
$492$	−0.674681	+	0.440761i	−0.0304170	+	0.0198710i
$493$	11.7387	+	6.77736i	0.528686	+	0.305237i
$494$	−55.0913	+	10.5525i	−2.47867	+	0.474778i
$495$	−6.97505	−	0.864011i	−0.313505	−	0.0388344i
$496$	20.4072	+	21.6000i	0.916312	+	0.969869i
$497$	28.5936	+	16.5085i	1.28260	+	0.740508i
$498$	33.6357	+	4.54013i	1.50725	+	0.203448i
$499$	6.80945	+	11.7943i	0.304833	+	0.527986i	0.977224	−	0.212210i	$-0.0680661\pi$
$499$	6.80945	+	11.7943i	0.304833	+	0.527986i	−0.672391	+	0.740196i	$0.734733\pi$
$500$	−1.56927	−	1.23992i	−0.0701797	−	0.0554509i
$501$	12.4898	+	4.18646i	0.558002	+	0.187037i
$502$	−8.05959	+	23.2005i	−0.359717	+	1.03549i
$503$	−15.8160			−0.705202			−0.352601	−	0.935774i	$-0.614703\pi$
$503$	−15.8160			−0.705202			−0.352601	+	0.935774i	$0.614703\pi$
$504$	30.6695	+	2.43054i	1.36613	+	0.108265i
$505$	5.40723			0.240619
$506$	6.46584	−	18.6127i	0.287441	−	0.827436i
$507$	5.69667	+	28.0770i	0.252998	+	1.24694i
$508$	−15.4006	+	19.4914i	−0.683293	+	0.864789i
$509$	−3.00742	−	5.20901i	−0.133302	−	0.230885i	0.791646	−	0.610980i	$-0.209225\pi$
$509$	−3.00742	−	5.20901i	−0.133302	−	0.230885i	−0.924947	+	0.380095i	$0.875891\pi$
$510$	−6.66497	+	8.62741i	−0.295130	+	0.382028i
$511$	5.98320	+	3.45440i	0.264681	+	0.152814i
$512$	22.4291	−	2.98890i	0.991237	−	0.132092i
$513$	21.4277	+	31.2851i	0.946058	+	1.38127i
$514$	−6.60924	+	1.26597i	−0.291521	+	0.0558395i
$515$	−4.85443	−	2.80271i	−0.213912	−	0.123502i
$516$	1.53545	−	3.03390i	0.0675945	−	0.133560i
$517$	−6.02282	+	3.47728i	−0.264883	+	0.152930i
$518$	18.8350	−	16.2828i	0.827561	−	0.715426i
$519$	−4.94522	−	24.3733i	−0.217071	−	1.06987i
$520$	−0.678641	−	15.3579i	−0.0297604	−	0.673487i
$521$			30.4512i			1.33409i	0.745017	+	0.667045i	$0.232441\pi$
$521$			30.4512i			1.33409i	−0.745017	+	0.667045i	$0.767559\pi$
$522$	7.18452	+	10.7394i	0.314458	+	0.470050i
$523$	−39.9827			−1.74832			−0.874160	−	0.485638i	$-0.838587\pi$
$523$	−39.9827			−1.74832			−0.874160	+	0.485638i	$0.838587\pi$
$524$	−17.7880	−	2.59918i	−0.777071	−	0.113545i
$525$	−1.99586	+	5.95441i	−0.0871066	+	0.259872i
$526$	−11.8223	+	10.2204i	−0.515477	+	0.445629i
$527$	16.5320	+	28.6343i	0.720145	+	1.24733i
$528$	6.81928	+	14.7293i	0.296771	+	0.641011i
$529$	−6.18379	+	10.7106i	−0.268861	+	0.465680i
$530$	−3.01880	−	15.7602i	−0.131128	−	0.684581i
$531$	−1.38005	−	3.26089i	−0.0598889	−	0.141510i
$532$	−19.5553	−	49.1734i	−0.847831	−	2.13194i
$533$	0.632217	−	1.09503i	0.0273844	−	0.0474311i
$534$	−11.6565	−	28.4036i	−0.504427	−	1.22914i
$535$	5.10594	−	2.94792i	0.220749	−	0.127450i
$536$	−5.23293	+	10.0653i	−0.226028	+	0.434755i
$537$	−2.27692	−	2.57637i	−0.0982564	−	0.111179i
$538$	−15.3752	−	5.34115i	−0.662871	−	0.230273i
$539$		−	14.3991i		−	0.620215i
$540$	−9.33300	+	4.57113i	−0.401628	+	0.196710i
$541$			20.0498i			0.862006i	0.902350	+	0.431003i	$0.141840\pi$
$541$			20.0498i			0.862006i	−0.902350	+	0.431003i	$0.858160\pi$
$542$	5.30656	−	15.2756i	0.227936	−	0.656144i
$543$	1.37778	+	1.55897i	0.0591260	+	0.0669020i
$544$	25.0490	+	2.53690i	1.07397	+	0.108769i
$545$	−9.61404	+	5.55067i	−0.411820	+	0.237765i
$546$	−44.6565	+	18.3266i	−1.91112	+	0.784304i
$547$	−16.3521	+	28.3227i	−0.699166	+	1.21099i	0.269590	+	0.962975i	$0.413112\pi$
$547$	−16.3521	+	28.3227i	−0.699166	+	1.21099i	−0.968756	+	0.248016i	$0.920221\pi$
$548$	−5.48970	−	13.8043i	−0.234508	−	0.589689i
$549$	−21.2283	+	28.1082i	−0.906000	+	1.19963i
$550$	−3.25404	+	0.623296i	−0.138753	+	0.0265774i
$551$	11.1125	−	19.2474i	0.473409	−	0.819969i
$552$	−7.04804	−	28.2692i	−0.299984	−	1.20322i
$553$	1.64132	+	2.84285i	0.0697960	+	0.120890i
$554$	−10.0131	−	11.5825i	−0.425416	−	0.492095i
$555$	−2.67284	+	7.97409i	−0.113456	+	0.338481i
$556$	−5.27803	+	36.1212i	−0.223838	+	1.53188i
$557$	−7.73889			−0.327907			−0.163954	−	0.986468i	$-0.552425\pi$
$557$	−7.73889			−0.327907			−0.163954	+	0.986468i	$0.552425\pi$
$558$	2.07897	+	31.4495i	0.0880098	+	1.33136i
$559$			5.33505i			0.225648i
$560$	14.1098	−	3.35454i	0.596247	−	0.141755i
$561$	3.59117	+	17.6996i	0.151619	+	0.747280i
$562$	−26.1417	−	30.2391i	−1.10272	−	1.27556i
$563$	2.86625	−	1.65483i	0.120798	−	0.0697427i	−0.438384	−	0.898788i	$-0.644449\pi$
$563$	2.86625	−	1.65483i	0.120798	−	0.0697427i	0.559181	+	0.829045i	$0.311116\pi$
$564$	−4.64348	+	9.17506i	−0.195526	+	0.386340i
$565$	−4.25183	−	2.45479i	−0.178876	−	0.103274i
$566$	1.82091	+	9.50643i	0.0765386	+	0.399585i
$567$	23.4248	+	22.7182i	0.983749	+	0.954076i
$568$	13.8503	+	21.7154i	0.581145	+	0.911156i
$569$	−22.0919	−	12.7548i	−0.926141	−	0.534708i	−0.0405518	−	0.999177i	$-0.512912\pi$
$569$	−22.0919	−	12.7548i	−0.926141	−	0.534708i	−0.885589	+	0.464470i	$0.846245\pi$
$570$	14.1460	+	10.9282i	0.592509	+	0.457733i
$571$	−11.1589	−	19.3278i	−0.466987	−	0.808844i	0.532302	−	0.846554i	$-0.321327\pi$
$571$	−11.1589	−	19.3278i	−0.466987	−	0.808844i	−0.999289	+	0.0377100i	$0.987994\pi$
$572$	−19.9820	−	15.7883i	−0.835489	−	0.660142i
$573$	7.48183	+	36.8754i	0.312558	+	1.54049i
$574$	1.12684	+	0.391450i	0.0470333	+	0.0163388i
$575$	5.94707			0.248010
$576$	20.3529	+	12.7184i	0.848039	+	0.529934i
$577$	25.0496			1.04283			0.521414	−	0.853304i	$-0.325405\pi$
$577$	25.0496			1.04283			0.521414	+	0.853304i	$0.325405\pi$
$578$	3.75256	+	1.30359i	0.156086	+	0.0542224i
$579$	0.971460	+	0.325625i	0.0403725	+	0.0135325i
$580$	4.77921	+	3.77618i	0.198446	+	0.156797i
$581$	−25.1197	−	43.5087i	−1.04214	−	1.80504i
$582$	4.26767	−	31.6172i	0.176901	−	1.31057i
$583$	−23.0216	−	13.2915i	−0.953457	−	0.550479i
$584$	2.89817	+	4.54393i	0.119927	+	0.188029i
$585$	9.82675	−	13.0115i	0.406286	−	0.537960i
$586$	0.811612	+	4.23718i	0.0335274	+	0.175036i
$587$	7.65137	+	4.41752i	0.315806	+	0.182331i	0.649522	−	0.760343i	$-0.274969\pi$
$587$	7.65137	+	4.41752i	0.315806	+	0.182331i	−0.333716	+	0.942674i	$0.608303\pi$
$588$	−11.6445	−	17.8244i	−0.480210	−	0.735066i
$589$	46.9503	−	27.1067i	1.93455	−	1.11691i
$590$	−1.09164	−	1.26274i	−0.0449421	−	0.0519863i
$591$	−18.8472	+	16.6566i	−0.775271	+	0.685162i
$592$	18.8957	−	4.49237i	0.776607	−	0.184635i
$593$		−	37.3350i		−	1.53316i	−0.642146	−	0.766582i	$-0.721956\pi$
$593$		−	37.3350i		−	1.53316i	0.642146	−	0.766582i	$-0.278044\pi$
$594$	−4.38281	+	16.6487i	−0.179829	+	0.683103i
$595$	16.1373			0.661565
$596$	0.643040	−	4.40077i	0.0263399	−	0.180263i
$597$	4.34157	+	4.91255i	0.177689	+	0.201057i
$598$	29.8951	+	34.5809i	1.22250	+	1.41412i
$599$	−2.15941	−	3.74021i	−0.0882313	−	0.152821i	0.818532	−	0.574461i	$-0.194788\pi$
$599$	−2.15941	−	3.74021i	−0.0882313	−	0.152821i	−0.906764	+	0.421639i	$0.861455\pi$
$600$	−3.52406	+	3.40309i	−0.143869	+	0.138930i
$601$	14.8817	−	25.7759i	0.607038	−	1.05142i	−0.384687	−	0.923047i	$-0.625691\pi$
$601$	14.8817	−	25.7759i	0.607038	−	1.05142i	0.991726	−	0.128374i	$-0.0409759\pi$
$602$	−4.94332	+	0.946870i	−0.201475	+	0.0385915i
$603$	−11.0810	+	4.68960i	−0.451253	+	0.190975i
$604$	−8.64728	−	21.7443i	−0.351853	−	0.884761i
$605$	2.75568	−	4.77297i	0.112034	−	0.194049i
$606$	1.77173	−	13.1259i	0.0719716	−	0.533204i
$607$	−35.7848	+	20.6604i	−1.45246	+	0.838579i	−0.998621	−	0.0525043i	$-0.983280\pi$
$607$	−35.7848	+	20.6604i	−1.45246	+	0.838579i	−0.453840	+	0.891083i	$0.649946\pi$
$608$	4.15963	−	41.0717i	0.168695	−	1.66568i
$609$	6.07841	−	18.1342i	0.246310	−	0.734834i
$610$	−5.44882	+	15.6851i	−0.220616	+	0.635072i
$611$		−	16.1341i		−	0.652717i
$612$	18.7590	+	19.0059i	0.758288	+	0.768268i
$613$			8.75690i			0.353688i	0.984239	+	0.176844i	$0.0565888\pi$
$613$			8.75690i			0.353688i	−0.984239	+	0.176844i	$0.943411\pi$
$614$	18.7312	+	6.50701i	0.755932	+	0.262602i
$615$	−0.394901	+	0.0801233i	−0.0159239	+	0.00323088i
$616$	11.0826	−	21.3169i	0.446532	−	0.858884i
$617$	−20.2502	+	11.6915i	−0.815243	+	0.470681i	−0.848773	−	0.528757i	$-0.822658\pi$
$617$	−20.2502	+	11.6915i	−0.815243	+	0.470681i	0.0335304	+	0.999438i	$0.489325\pi$
$618$	−8.39410	+	10.8657i	−0.337660	+	0.437082i
$619$	7.24309	−	12.5454i	0.291124	−	0.504242i	−0.682952	−	0.730464i	$-0.739304\pi$
$619$	7.24309	−	12.5454i	0.291124	−	0.504242i	0.974076	+	0.226222i	$0.0726374\pi$
$620$	5.49043	+	13.8061i	0.220501	+	0.554467i
$621$	13.3484	−	27.8702i	0.535652	−	1.11839i
$622$	−1.24165	−	6.48230i	−0.0497858	−	0.259917i
$623$	−22.7230	+	39.3574i	−0.910379	+	1.57682i
$624$	−37.5032	−	3.38476i	−1.50133	−	0.135499i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	18.5442	−	16.0315i	0.741176	−	0.640746i
$627$	29.0213	−	5.88826i	1.15900	−	0.235155i
$628$	−12.7224	−	1.85900i	−0.507681	−	0.0741823i
$629$	21.6109			0.861683
$630$	13.8002	+	6.79593i	0.549814	+	0.270756i
$631$			4.12906i			0.164375i	0.996617	+	0.0821877i	$0.0261907\pi$
$631$			4.12906i			0.164375i	−0.996617	+	0.0821877i	$0.973809\pi$
$632$	0.113046	+	2.55826i	0.00449672	+	0.101762i
$633$	15.7107	+	5.26607i	0.624443	+	0.209307i
$634$	21.0965	−	18.2379i	0.837848	−	0.724319i
$635$	−10.7566	+	6.21034i	−0.426864	+	0.246450i
$636$	−39.2467	+	2.16407i	−1.55623	+	0.0858110i
$637$	28.9297	+	16.7026i	1.14624	+	0.661779i
$638$	9.91020	−	1.89825i	0.392349	−	0.0751525i
$639$	−3.35834	+	27.1115i	−0.132854	+	1.07251i
$640$	10.9730	+	2.75548i	0.433747	+	0.108920i
$641$	−6.07402	−	3.50684i	−0.239910	−	0.138512i	0.375226	−	0.926934i	$-0.377565\pi$
$641$	−6.07402	−	3.50684i	−0.239910	−	0.138512i	−0.615135	+	0.788422i	$0.710899\pi$
$642$	−5.48299	−	13.3605i	−0.216396	−	0.527296i
$643$	−10.1686	−	17.6125i	−0.401009	−	0.694567i	0.592839	−	0.805321i	$-0.298007\pi$
$643$	−10.1686	−	17.6125i	−0.401009	−	0.694567i	−0.993848	+	0.110753i	$0.964674\pi$
$644$	−26.7360	+	33.8375i	−1.05354	+	1.33339i
$645$	1.27395	−	1.12588i	0.0501616	−	0.0443314i
$646$	15.0731	−	43.3899i	0.593045	−	1.70715i
$647$	−42.3442			−1.66472			−0.832362	−	0.554232i	$-0.813012\pi$
$647$	−42.3442			−1.66472			−0.832362	+	0.554232i	$0.813012\pi$
$648$	8.03826	+	24.1534i	0.315773	+	0.948835i
$649$	−2.76518			−0.108543
$650$	2.52231	−	7.26079i	0.0989331	−	0.284791i
$651$	34.9580	−	30.8948i	1.37011	−	1.21086i
$652$	18.0004	+	14.2226i	0.704952	+	0.557001i
$653$	−14.8100	−	25.6516i	−0.579559	−	1.00383i	−0.995530	−	0.0944475i	$-0.969892\pi$
$653$	−14.8100	−	25.6516i	−0.579559	−	1.00383i	0.415971	−	0.909378i	$-0.363442\pi$
$654$	10.3240	+	25.1566i	0.403700	+	0.983700i
$655$	−7.78421	−	4.49421i	−0.304154	−	0.175603i
$656$	0.639068	+	0.676421i	0.0249514	+	0.0264098i
$657$	−0.702732	+	5.67307i	−0.0274162	+	0.221327i
$658$	14.9495	−	2.86350i	0.582792	−	0.111631i
$659$	−10.7369	−	6.19895i	−0.418250	−	0.241477i	0.276078	−	0.961135i	$-0.410965\pi$
$659$	−10.7369	−	6.19895i	−0.418250	−	0.241477i	−0.694328	+	0.719658i	$0.744298\pi$
$660$	0.446820	+	8.10334i	0.0173924	+	0.315422i
$661$	15.6358	−	9.02736i	0.608164	−	0.351124i	−0.164083	−	0.986447i	$-0.552466\pi$
$661$	15.6358	−	9.02736i	0.608164	−	0.351124i	0.772246	+	0.635323i	$0.219133\pi$
$662$	23.2023	−	20.0584i	0.901784	−	0.779592i
$663$	−39.7265	−	13.3159i	−1.54285	−	0.517148i
$664$	−1.73012	−	39.1532i	−0.0671417	−	1.51944i
$665$		−	26.4596i		−	1.02606i
$666$	18.4811	+	9.10104i	0.716129	+	0.352658i
$667$	−18.1118			−0.701292
$668$	2.19921	−	15.0507i	0.0850901	−	0.582331i
$669$	−39.5970	+	8.03402i	−1.53091	+	0.310613i
$670$	−4.29099	+	3.70956i	−0.165776	+	0.143313i
$671$	13.7536	+	23.8219i	0.530952	+	0.919635i
$672$	−3.51987	−	35.3503i	−0.135782	−	1.36367i
$673$	−24.0901	+	41.7253i	−0.928605	+	1.60839i	−0.142947	+	0.989730i	$0.545658\pi$
$673$	−24.0901	+	41.7253i	−0.928605	+	1.60839i	−0.785658	+	0.618661i	$0.787676\pi$
$674$	8.21549	+	42.8906i	0.316449	+	1.65209i
$675$	−5.18078	+	0.399364i	−0.199408	+	0.0153715i
$676$	30.7395	−	12.2245i	1.18229	−	0.470174i
$677$	−17.2785	+	29.9273i	−0.664068	+	1.15020i	0.315469	+	0.948936i	$0.397838\pi$
$677$	−17.2785	+	29.9273i	−0.664068	+	1.15020i	−0.979537	+	0.201263i	$0.935495\pi$
$678$	−7.35210	+	9.51687i	−0.282356	+	0.365493i
$679$	−40.8977	+	23.6123i	−1.56951	+	0.906156i
$680$	11.1693	+	5.80687i	0.428321	+	0.222683i
$681$	−37.5659	+	7.62193i	−1.43953	+	0.292073i
$682$	23.2505	+	8.07693i	0.890306	+	0.309281i
$683$			31.0829i			1.18936i	0.803964	+	0.594678i	$0.202720\pi$
$683$			31.0829i			1.18936i	−0.803964	+	0.594678i	$0.797280\pi$
$684$	31.1631	−	30.7582i	1.19155	−	1.17607i
$685$		−	7.42790i		−	0.283805i
$686$	1.43670	−	4.13572i	0.0548535	−	0.157903i
$687$	12.2314	−	36.4908i	0.466656	−	1.39221i
$688$	−3.76219	−	1.12345i	−0.143432	−	0.0428311i
$689$	53.4087	−	30.8355i	2.03471	−	1.17474i
$690$	1.94861	−	14.4364i	0.0741823	−	0.549583i
$691$	−8.66100	+	15.0013i	−0.329480	+	0.570676i	−0.982409	−	0.186743i	$-0.940207\pi$
$691$	−8.66100	+	15.0013i	−0.329480	+	0.570676i	0.652929	+	0.757419i	$0.273540\pi$
$692$	−26.6846	+	10.6120i	−1.01440	+	0.403407i
$693$	23.4680	−	9.93194i	0.891477	−	0.377283i
$694$	−6.76481	+	1.29577i	−0.256789	+	0.0491866i
$695$	−9.12620	+	15.8071i	−0.346177	+	0.599596i
$696$	10.7325	−	10.3641i	0.406816	−	0.392851i
$697$	0.517712	+	0.896704i	0.0196098	+	0.0339651i
$698$	23.5837	+	27.2801i	0.892655	+	1.03257i
$699$	−6.98717	−	7.90609i	−0.264279	−	0.299036i
$700$	7.17533	+	1.04846i	0.271202	+	0.0396280i
$701$	24.5105			0.925750			0.462875	−	0.886424i	$-0.346818\pi$
$701$	24.5105			0.925750			0.462875	+	0.886424i	$0.346818\pi$
$702$	−28.3653	−	28.1175i	−1.07058	−	1.06123i
$703$		−	35.4344i		−	1.33643i
$704$	15.3415	−	10.7663i	0.578203	−	0.405770i
$705$	−3.85264	+	3.40486i	−0.145099	+	0.128234i
$706$	10.9265	+	12.6391i	0.411223	+	0.475677i
$707$	−16.9787	+	9.80267i	−0.638551	+	0.368667i
$708$	−3.42297	+	2.23618i	−0.128643	+	0.0840409i
$709$	8.65516	+	4.99706i	0.325051	+	0.187669i	0.653642	−	0.756804i	$-0.273240\pi$
$709$	8.65516	+	4.99706i	0.325051	+	0.187669i	−0.328591	+	0.944472i	$0.606574\pi$
$710$	2.42270	+	12.6482i	0.0909225	+	0.474679i
$711$	−1.63691	+	2.16742i	−0.0613889	+	0.0812846i
$712$	−29.8900	+	19.0641i	−1.12017	+	0.714459i
$713$	−38.2611	−	22.0901i	−1.43289	−	0.827279i
$714$	5.28753	−	39.1729i	0.197881	−	1.46601i
$715$	−6.36666	−	11.0274i	−0.238100	−	0.412401i
$716$	−2.46138	+	3.11518i	−0.0919863	+	0.116420i
$717$	−17.1624	−	5.75268i	−0.640942	−	0.214838i
$718$	−1.01532	−	0.352711i	−0.0378915	−	0.0131631i
$719$	−52.5970			−1.96154			−0.980769	−	0.195172i	$-0.937473\pi$
$719$	−52.5970			−1.96154			−0.980769	+	0.195172i	$0.937473\pi$
$720$	7.10622	+	9.66963i	0.264833	+	0.360366i
$721$	20.3239			0.756902
$722$	−45.7623	−	15.8973i	−1.70310	−	0.591635i
$723$	−3.61721	−	17.8280i	−0.134526	−	0.663031i
$724$	1.48940	−	1.88501i	0.0553530	−	0.0700558i
$725$	1.52275	+	2.63748i	0.0565536	+	0.0979537i
$726$	−10.6833	−	8.25324i	−0.396496	−	0.306307i
$727$	−34.4922	−	19.9141i	−1.27925	−	0.738573i	−0.302536	−	0.953138i	$-0.597833\pi$
$727$	−34.4922	−	19.9141i	−1.27925	−	0.738573i	−0.976710	+	0.214565i	$0.931167\pi$
$728$	29.9729	+	46.9934i	1.11087	+	1.74169i
$729$	−9.75686	+	25.1755i	−0.361365	+	0.932424i
$730$	0.506950	+	2.64663i	0.0187631	+	0.0979563i
$731$	−3.78348	−	2.18439i	−0.139937	−	0.0807926i
$732$	36.2899	+	18.3663i	1.34131	+	0.678837i
$733$	34.6256	−	19.9911i	1.27893	−	0.738389i	0.302276	−	0.953221i	$-0.402254\pi$
$733$	34.6256	−	19.9911i	1.27893	−	0.738389i	0.976651	+	0.214832i	$0.0689204\pi$
$734$	−5.74546	−	6.64600i	−0.212069	−	0.245308i
$735$	−2.11678	−	10.4329i	−0.0780785	−	0.384823i
$736$	−30.6812	+	13.7996i	−1.13092	+	0.508659i
$737$			9.39651i			0.346125i
$738$	0.0651045	+	0.984865i	0.00239653	+	0.0362534i
$739$	5.94363			0.218640			0.109320	−	0.994007i	$-0.465133\pi$
$739$	5.94363			0.218640			0.109320	+	0.994007i	$0.465133\pi$
$740$	9.60913	+	1.40409i	0.353239	+	0.0516152i
$741$	−21.8335	+	65.1376i	−0.802074	+	2.39289i
$742$	38.0505	+	44.0145i	1.39688	+	1.61582i
$743$	12.4009	+	21.4790i	0.454945	+	0.787987i	0.998685	−	0.0512661i	$-0.0163257\pi$
$743$	12.4009	+	21.4790i	0.454945	+	0.787987i	−0.543740	+	0.839254i	$0.682992\pi$
$744$	35.3130	−	8.80419i	1.29464	−	0.322777i
$745$	1.11188	−	1.92582i	0.0407360	−	0.0705568i
$746$	−3.00818	+	0.576202i	−0.110137	+	0.0210963i
$747$	25.0522	−	33.1715i	0.916614	−	1.21368i
$748$	19.3781	−	7.70631i	0.708534	−	0.281771i
$749$	−10.6885	+	18.5129i	−0.390547	+	0.676448i
$750$	−2.26609	+	0.929977i	−0.0827457	+	0.0339580i
$751$	−32.2535	+	18.6216i	−1.17695	+	0.679511i	−0.955306	−	0.295617i	$-0.904475\pi$
$751$	−32.2535	+	18.6216i	−1.17695	+	0.679511i	−0.221641	+	0.975128i	$0.571141\pi$
$752$	11.3775	+	3.39751i	0.414896	+	0.123894i
$753$	19.9198	+	22.5396i	0.725919	+	0.821388i
$754$	−7.68170	+	22.1128i	−0.279751	+	0.805299i
$755$		−	11.7003i		−	0.425818i
$756$	21.0187	−	31.2730i	0.764444	−	1.13739i
$757$			9.13470i			0.332006i	0.986125	+	0.166003i	$0.0530862\pi$
$757$			9.13470i			0.332006i	−0.986125	+	0.166003i	$0.946914\pi$
$758$	−27.7324	−	9.63389i	−1.00729	−	0.349919i
$759$	−15.9808	−	18.0825i	−0.580065	−	0.656352i
$760$	9.52126	−	18.3137i	0.345372	−	0.664308i
$761$	27.6195	−	15.9461i	1.00121	−	0.578046i	0.0926006	−	0.995703i	$-0.470482\pi$
$761$	27.6195	−	15.9461i	1.00121	−	0.578046i	0.908605	+	0.417657i	$0.137149\pi$
$762$	11.5509	+	28.1463i	0.418446	+	1.01963i
$763$	20.1254	−	34.8582i	0.728589	−	1.26195i
$764$	40.3723	−	16.0553i	1.46062	−	0.580861i
$765$	5.20395	+	12.2963i	0.188149	+	0.444575i
$766$	−0.466091	−	2.43332i	−0.0168406	−	0.0879195i
$767$	3.20753	−	5.55560i	0.115817	−	0.200601i
$768$	10.2843	−	25.7339i	0.371101	−	0.928592i
$769$	15.0039	+	25.9875i	0.541055	+	0.937135i	0.998844	+	0.0480738i	$0.0153083\pi$
$769$	15.0039	+	25.9875i	0.541055	+	0.937135i	−0.457789	+	0.889061i	$0.651358\pi$
$770$	9.08774	−	7.85635i	0.327500	−	0.283123i
$771$	−2.61934	+	7.81448i	−0.0943333	+	0.281432i
$772$	0.171056	−	1.17065i	0.00615643	−	0.0421327i
$773$	−11.8807			−0.427320			−0.213660	−	0.976908i	$-0.568539\pi$
$773$	−11.8807			−0.427320			−0.213660	+	0.976908i	$0.568539\pi$
$774$	−2.31562	−	3.46138i	−0.0832333	−	0.124417i
$775$			7.42889i			0.266854i
$776$	−36.8036	+	1.62629i	−1.32117	+	0.0583806i
$777$	−6.06335	−	29.8842i	−0.217521	−	1.07209i
$778$	8.59194	−	7.42772i	0.308036	−	0.266297i
$779$	1.47028	−	0.848868i	0.0526784	−	0.0304139i
$780$	−16.7989	−	8.50191i	−0.601498	−	0.304417i
$781$	18.4757	+	10.6670i	0.661114	+	0.381694i
$782$	−36.7642	+	7.04200i	−1.31468	+	0.251821i
$783$	15.7781	−	1.21627i	0.563863	−	0.0434658i
$784$	−17.8704	+	16.8835i	−0.638227	+	0.602984i
$785$	−5.56748	−	3.21439i	−0.198712	−	0.114726i
$786$	−13.4602	+	17.4234i	−0.480108	+	0.621472i
$787$	9.85466	+	17.0688i	0.351281	+	0.608436i	0.986474	−	0.163917i	$-0.0524129\pi$
$787$	9.85466	+	17.0688i	0.351281	+	0.608436i	−0.635193	+	0.772353i	$0.719080\pi$
$788$	22.7888	+	18.0060i	0.811817	+	0.641439i
$789$	3.80583	+	18.7576i	0.135491	+	0.667790i
$790$	−0.420158	+	1.20948i	−0.0149486	+	0.0430313i
$791$	17.8010			0.632931
$792$	19.8171	+	1.57049i	0.704169	+	0.0558049i
$793$	−63.8150			−2.26614
$794$	−10.3397	+	29.7642i	−0.366943	+	1.05629i
$795$	−18.6342	−	6.24602i	−0.660888	−	0.221524i
$796$	4.69330	−	5.93993i	0.166349	−	0.210535i
$797$	18.5904	+	32.1996i	0.658507	+	1.14057i	0.981002	+	0.193997i	$0.0621451\pi$
$797$	18.5904	+	32.1996i	0.658507	+	1.14057i	−0.322495	+	0.946571i	$0.604522\pi$
$798$	−64.2299	−	8.66972i	−2.27372	−	0.306905i
$799$	11.4419	+	6.60599i	0.404786	+	0.233703i
$800$	4.58905	+	3.30766i	0.162247	+	0.116944i
$801$	−37.3174	−	4.62257i	−1.31855	−	0.163330i
$802$	5.69293	−	1.09045i	0.201024	−	0.0385052i
$803$	3.86604	+	2.23206i	0.136430	+	0.0787677i
$804$	7.59889	+	11.6318i	0.267992	+	0.410220i
$805$	−18.6738	+	10.7813i	−0.658165	+	0.379992i
$806$	−43.1974	+	37.3441i	−1.52156	+	1.31539i
$807$	−14.9372	+	13.2010i	−0.525813	+	0.464698i
$808$	−15.2791	+	0.675159i	−0.537515	+	0.0237520i
$809$			37.4249i			1.31579i	0.753110	+	0.657894i	$0.228553\pi$
$809$			37.4249i			1.31579i	−0.753110	+	0.657894i	$0.771447\pi$
$810$	−0.728084	+	12.7071i	−0.0255823	+	0.446481i
$811$	23.2973			0.818080			0.409040	−	0.912517i	$-0.365864\pi$
$811$	23.2973			0.818080			0.409040	+	0.912517i	$0.365864\pi$
$812$	−21.8525	−	3.19308i	−0.766872	−	0.112055i
$813$	−13.1155	−	14.8404i	−0.459982	−	0.520477i
$814$	12.1702	−	10.5211i	0.426566	−	0.368766i
$815$	5.73530	+	9.93384i	0.200899	+	0.347967i
$816$	17.7558	−	25.2104i	0.621576	−	0.882541i
$817$	−3.58164	+	6.20359i	−0.125306	+	0.217036i
$818$	−10.2066	−	53.2854i	−0.356864	−	1.86308i
$819$	−7.26767	+	58.6710i	−0.253953	+	2.05013i
$820$	0.171937	+	0.432349i	0.00600430	+	0.0150983i
$821$	21.7046	−	37.5934i	0.757495	−	1.31202i	−0.186630	−	0.982430i	$-0.559756\pi$
$821$	21.7046	−	37.5934i	0.757495	−	1.31202i	0.944124	−	0.329589i	$-0.106910\pi$
$822$	−18.0310	−	2.43382i	−0.628905	−	0.0848892i
$823$	2.02501	−	1.16914i	0.0705875	−	0.0407537i	−0.464291	−	0.885683i	$-0.653691\pi$
$823$	2.02501	−	1.16914i	0.0705875	−	0.0407537i	0.534878	+	0.844929i	$0.320357\pi$
$824$	14.0670	+	7.31339i	0.490046	+	0.254774i
$825$	−1.28963	+	3.84744i	−0.0448990	+	0.133951i
$826$	5.71696	+	1.98600i	0.198918	+	0.0691019i
$827$		−	16.0589i		−	0.558423i	−0.960230	−	0.279212i	$-0.909927\pi$
$827$		−	16.0589i		−	0.558423i	0.960230	−	0.279212i	$-0.0900731\pi$
$828$	−34.4054	−	9.46041i	−1.19567	−	0.328772i
$829$		−	30.1754i		−	1.04803i	−0.851708	−	0.524017i	$-0.824433\pi$
$829$		−	30.1754i		−	1.04803i	0.851708	−	0.524017i	$-0.175567\pi$
$830$	6.43036	−	18.5106i	0.223201	−	0.642512i
$831$	−18.3772	+	3.72865i	−0.637499	+	0.129345i
$832$	3.83523	+	43.3115i	0.132963	+	1.50156i
$833$	−23.6900	+	13.6774i	−0.820811	+	0.473895i
$834$	35.3809	+	27.3330i	1.22514	+	0.946463i
$835$	3.80264	−	6.58637i	0.131596	−	0.227931i
$836$	−12.6357	−	31.7734i	−0.437014	−	1.09891i
$837$	34.8146	+	16.6744i	1.20337	+	0.576351i
$838$	−44.0551	+	8.43853i	−1.52186	+	0.291504i
$839$	0.225884	−	0.391243i	0.00779839	−	0.0135072i	−0.862100	−	0.506738i	$-0.830851\pi$
$839$	0.225884	−	0.391243i	0.00779839	−	0.0135072i	0.869898	+	0.493231i	$0.164184\pi$
$840$	4.89617	−	17.0744i	0.168934	−	0.589123i
$841$	9.86245	+	17.0823i	0.340085	+	0.589044i
$842$	−8.07284	−	9.33817i	−0.278208	−	0.321815i
$843$	−47.9784	+	9.73456i	−1.65246	+	0.335276i
$844$	2.76635	−	18.9321i	0.0952217	−	0.651668i
$845$	16.5405			0.569012
$846$	7.00285	+	10.4678i	0.240763	+	0.359891i
$847$			19.9829i			0.686619i
$848$	10.4980	+	44.1563i	0.360502	+	1.51633i
$849$	11.2400	+	3.76754i	0.385755	+	0.129302i
$850$	4.11642	+	4.76163i	0.141192	+	0.163322i
$851$	−25.0078	+	14.4382i	−0.857256	+	0.494937i
$852$	31.4971	−	1.73675i	1.07907	−	0.0595002i
$853$	−7.63642	−	4.40889i	−0.261466	−	0.150958i	0.363537	−	0.931580i	$-0.381569\pi$
$853$	−7.63642	−	4.40889i	−0.261466	−	0.150958i	−0.625003	+	0.780622i	$0.714902\pi$
$854$	−11.3260	−	59.1294i	−0.387566	−	2.02337i
$855$	20.1617	−	8.53268i	0.689516	−	0.291811i
$856$	−14.0596	+	8.96738i	−0.480548	+	0.306499i
$857$	10.4454	+	6.03063i	0.356807	+	0.206003i	0.667679	−	0.744449i	$-0.267288\pi$
$857$	10.4454	+	6.03063i	0.356807	+	0.206003i	−0.310872	+	0.950452i	$0.600621\pi$
$858$	−28.8548	+	11.8417i	−0.985087	+	0.404269i
$859$	−7.11149	−	12.3175i	−0.242641	−	0.420267i	0.718825	−	0.695191i	$-0.244680\pi$
$859$	−7.11149	−	12.3175i	−0.242641	−	0.420267i	−0.961466	+	0.274925i	$0.911347\pi$
$860$	−1.54037	−	1.21709i	−0.0525263	−	0.0415024i
$861$	1.09473	−	0.967495i	0.0373085	−	0.0329721i
$862$	22.8536	+	7.93907i	0.778397	+	0.270406i
$863$	33.7597			1.14919			0.574597	−	0.818436i	$-0.305159\pi$
$863$	33.7597			1.14919			0.574597	+	0.818436i	$0.305159\pi$
$864$	25.8012	−	14.0818i	0.877775	−	0.479074i
$865$	−14.3587			−0.488209
$866$	20.7616	+	7.21232i	0.705507	+	0.245085i
$867$	3.64565	−	3.22192i	0.123813	−	0.109422i
$868$	−42.2688	−	33.3978i	−1.43470	−	1.13359i
$869$	1.06054	+	1.83691i	0.0359763	+	0.0623128i
$870$	6.90137	−	2.83225i	0.233978	−	0.0960222i
$871$	−18.8788	−	10.8997i	−0.639683	−	0.369321i
$872$	26.4730	−	16.8848i	0.896490	−	0.571791i
$873$	−31.1808	−	23.5488i	−1.05531	−	0.797007i
$874$	11.5464	+	60.2805i	0.390564	+	2.03902i
$875$	3.14000	+	1.81288i	0.106151	+	0.0612866i
$876$	6.59075	−	0.363415i	0.222681	−	0.0122786i
$877$	8.81966	−	5.09203i	0.297819	−	0.171946i	−0.343644	−	0.939100i	$-0.611661\pi$
$877$	8.81966	−	5.09203i	0.297819	−	0.171946i	0.641463	+	0.767154i	$0.278328\pi$
$878$	−15.9645	−	18.4668i	−0.538777	−	0.623224i
$879$	5.00986	+	1.67926i	0.168978	+	0.0566400i
$880$	9.11703	−	2.16754i	0.307335	−	0.0730676i
$881$			41.2117i			1.38846i	0.719755	+	0.694228i	$0.244254\pi$
$881$			41.2117i			1.38846i	−0.719755	+	0.694228i	$0.755746\pi$
$882$	−26.0192	+	1.72000i	−0.876110	+	0.0579153i
$883$	−12.8922			−0.433858			−0.216929	−	0.976187i	$-0.569604\pi$
$883$	−12.8922			−0.433858			−0.216929	+	0.976187i	$0.569604\pi$
$884$	−6.99507	+	47.8722i	−0.235270	+	1.61012i
$885$	−2.00351	+	0.406502i	−0.0673473	+	0.0136644i
$886$	−27.0109	−	31.2446i	−0.907449	−	1.04968i
$887$	−4.77796	−	8.27567i	−0.160428	−	0.277870i	0.774594	−	0.632459i	$-0.217954\pi$
$887$	−4.77796	−	8.27567i	−0.160428	−	0.277870i	−0.935022	+	0.354589i	$0.884621\pi$
$888$	6.55690	−	22.8659i	0.220035	−	0.767329i
$889$	22.5172	−	39.0010i	0.755203	−	1.30805i
$890$	−17.4095	+	3.33471i	−0.583569	+	0.111780i
$891$	15.1359	+	14.6794i	0.507073	+	0.491778i
$892$	17.2403	+	43.3520i	0.577247	+	1.45153i
$893$	10.8315	−	18.7608i	0.362463	−	0.627805i
$894$	−4.31058	−	3.33006i	−0.144167	−	0.111374i
$895$	−1.71916	+	0.992558i	−0.0574652	+	0.0331775i
$896$	−39.4507	+	11.2406i	−1.31796	+	0.375522i
$897$	54.8672	−	11.1323i	1.83196	−	0.371695i
$898$	−2.37497	+	6.83665i	−0.0792538	+	0.228142i
$899$		−	22.6247i		−	0.754577i
$900$	1.51499	+	5.80558i	0.0504998	+	0.193519i
$901$			50.5014i			1.68245i
$902$	0.728106	+	0.252935i	0.0242433	+	0.00842182i
$903$	−1.95911	+	5.84477i	−0.0651952	+	0.194502i
$904$	12.3208	+	6.40555i	0.409783	+	0.213045i
$905$	1.04027	−	0.600602i	0.0345798	−	0.0199647i
$906$	−28.4022	−	3.83371i	−0.943600	−	0.127367i
$907$	24.9555	−	43.2242i	0.828634	−	1.43524i	−0.0704754	−	0.997514i	$-0.522452\pi$
$907$	24.9555	−	43.2242i	0.828634	−	1.43524i	0.899110	−	0.437723i	$-0.144215\pi$
$908$	16.3560	+	41.1284i	0.542792	+	1.36489i
$909$	−12.9448	−	9.77633i	−0.429351	−	0.324260i
$910$	5.24289	+	27.3715i	0.173800	+	0.907358i
$911$	−26.5437	+	45.9751i	−0.879433	+	1.52322i	−0.0274697	+	0.999623i	$0.508745\pi$
$911$	−26.5437	+	45.9751i	−0.879433	+	1.52322i	−0.851964	+	0.523601i	$0.824588\pi$
$912$	−41.3363	−	29.1133i	−1.36878	−	0.964037i
$913$	−16.2311	−	28.1131i	−0.537172	−	0.930409i
$914$	−16.7456	+	14.4766i	−0.553895	+	0.478842i
$915$	13.4672	+	15.2383i	0.445210	+	0.503762i
$916$	−43.9731	−	6.42534i	−1.45291	−	0.212299i
$917$	32.5899			1.07621
$918$	31.5542	−	8.60346i	1.04144	−	0.283957i
$919$			38.5192i			1.27063i	0.772252	+	0.635316i	$0.219130\pi$
$919$			38.5192i			1.27063i	−0.772252	+	0.635316i	$0.780870\pi$
$920$	−16.8044	+	0.742563i	−0.554026	+	0.0244816i
$921$	18.1976	−	16.0825i	0.599632	−	0.529938i
$922$	42.9217	−	37.1058i	1.41355	−	1.22201i
$923$	−42.8626	+	24.7467i	−1.41084	+	0.814548i
$924$	−16.0934	−	24.6345i	−0.529434	−	0.810415i
$925$	4.20506	+	2.42779i	0.138262	+	0.0798254i
$926$	−30.6249	+	5.86605i	−1.00640	+	0.192770i
$927$	6.55405	+	15.4865i	0.215263	+	0.508642i
$928$	−13.9760	−	10.0735i	−0.458784	−	0.330679i
$929$	18.1325	+	10.4688i	0.594908	+	0.343470i	0.767036	−	0.641604i	$-0.221731\pi$
$929$	18.1325	+	10.4688i	0.594908	+	0.343470i	−0.172128	+	0.985075i	$0.555064\pi$
$930$	18.0335	+	2.43415i	0.591341	+	0.0798188i
$931$	22.4263	+	38.8434i	0.734991	+	1.27304i
$932$	−7.55324	+	9.55952i	−0.247414	+	0.313132i
$933$	−7.66440	−	2.56903i	−0.250921	−	0.0841064i
$934$	1.16180	−	3.34439i	0.0380153	−	0.109432i
$935$	10.4271			0.341003
$936$	−26.1425	+	37.9933i	−0.854494	+	1.24185i
$937$	−1.70672			−0.0557561			−0.0278781	−	0.999611i	$-0.508875\pi$
$937$	−1.70672			−0.0557561			−0.0278781	+	0.999611i	$0.508875\pi$
$938$	6.74874	−	19.4271i	0.220354	−	0.634317i
$939$	−5.96975	−	29.4229i	−0.194815	−	0.960180i
$940$	4.65836	+	3.68070i	0.151939	+	0.120051i
$941$	−23.6104	−	40.8943i	−0.769676	−	1.33312i	−0.937739	−	0.347341i	$-0.887084\pi$
$941$	−23.6104	−	40.8943i	−0.769676	−	1.33312i	0.168063	−	0.985776i	$-0.446249\pi$
$942$	−9.62708	+	12.4617i	−0.313667	+	0.406024i
$943$	−1.19818	−	0.691767i	−0.0390180	−	0.0225270i
$944$	3.24229	+	3.43179i	0.105527	+	0.111695i
$945$	15.5437	−	10.6462i	0.505636	−	0.346319i
$946$	−3.19413	+	0.611820i	−0.103850	+	0.0198920i
$947$	−14.3847	−	8.30504i	−0.467442	−	0.269877i	0.247727	−	0.968830i	$-0.420317\pi$
$947$	−14.3847	−	8.30504i	−0.467442	−	0.269877i	−0.715168	+	0.698952i	$0.753650\pi$
$948$	2.79831	+	1.41622i	0.0908850	+	0.0459967i
$949$	−8.96898	+	5.17824i	−0.291145	+	0.168093i
$950$	7.80741	−	6.74950i	0.253306	−	0.218983i
$951$	−6.79137	−	33.4724i	−0.220225	−	1.08542i
$952$	−45.5987	+	2.01494i	−1.47786	+	0.0653045i
$953$			31.3390i			1.01517i	0.861602	+	0.507585i	$0.169462\pi$
$953$			31.3390i			1.01517i	−0.861602	+	0.507585i	$0.830538\pi$
$954$	−21.2677	+	43.1876i	−0.688569	+	1.39825i
$955$	21.7238			0.702966
$956$	−3.02198	+	20.6815i	−0.0977377	+	0.668887i
$957$	3.92756	−	11.7174i	0.126960	−	0.378770i
$958$	−1.76596	+	1.52667i	−0.0570557	+	0.0493246i
$959$	13.4659	+	23.3236i	0.434836	+	0.753159i
$960$	9.53292	−	10.0560i	0.307674	−	0.324557i
$961$	12.0942	−	20.9478i	0.390137	−	0.675736i
$962$	7.02122	+	36.6557i	0.226373	+	1.18183i
$963$	−17.5533	−	2.17436i	−0.565649	−	0.0700679i
$964$	−19.5187	+	7.76220i	−0.628654	+	0.250004i
$965$	0.295771	−	0.512291i	0.00952121	−	0.0164912i
$966$	20.0528	+	48.8628i	0.645187	+	1.57214i
$967$	−27.8354	+	16.0707i	−0.895125	+	0.516800i	−0.875615	−	0.483009i	$-0.839544\pi$
$967$	−27.8354	+	16.0707i	−0.895125	+	0.516800i	−0.0195093	+	0.999810i	$0.506210\pi$
$968$	−7.19067	+	13.8309i	−0.231117	+	0.444543i
$969$	−37.2543	−	42.1538i	−1.19678	−	1.35418i
$970$	−17.3997	−	6.04446i	−0.558672	−	0.194076i
$971$			9.37802i			0.300955i	0.988613	+	0.150477i	$0.0480811\pi$
$971$			9.37802i			0.300955i	−0.988613	+	0.150477i	$0.951919\pi$
$972$	30.6076	+	5.93100i	0.981738	+	0.190237i
$973$		−	66.1789i		−	2.12160i
$974$	−5.33833	+	15.3671i	−0.171051	+	0.492393i
$975$	−6.23407	−	7.05394i	−0.199650	−	0.225907i
$976$	13.4381	−	45.0013i	0.430143	−	1.44046i
$977$	−3.06313	+	1.76850i	−0.0979982	+	0.0565793i	−0.548198	−	0.836348i	$-0.684686\pi$
$977$	−3.06313	+	1.76850i	−0.0979982	+	0.0565793i	0.450200	+	0.892928i	$0.351353\pi$
$978$	25.9934	−	10.6674i	0.831176	−	0.341106i
$979$	−14.6825	+	25.4308i	−0.469254	+	0.812772i
$980$	−11.4222	+	4.54241i	−0.364870	+	0.145102i
$981$	33.0514	+	4.09413i	1.05525	+	0.130716i
$982$	−19.7166	+	3.77663i	−0.629183	+	0.120517i
$983$	27.5460	−	47.7110i	0.878580	−	1.52175i	0.0256813	−	0.999670i	$-0.491824\pi$
$983$	27.5460	−	47.7110i	0.878580	−	1.52175i	0.852899	−	0.522076i	$-0.174842\pi$
$984$	1.10585	−	0.275710i	0.0352533	−	0.00878931i
$985$	7.26097	+	12.5764i	0.231354	+	0.400717i
$986$	−12.5366	−	14.5016i	−0.399246	−	0.461823i
$987$	5.92471	−	17.6756i	0.188586	−	0.562622i
$988$	78.4937	+	11.4695i	2.49722	+	0.364893i
$989$	5.83756			0.185624
$990$	8.91701	+	4.39119i	0.283401	+	0.139561i
$991$		−	44.2326i		−	1.40510i	−0.711637	−	0.702548i	$-0.752046\pi$
$991$		−	44.2326i		−	1.40510i	0.711637	−	0.702548i	$-0.247954\pi$
$992$	−17.2380	−	38.3260i	−0.547307	−	1.21685i
$993$	−7.46928	−	36.8136i	−0.237031	−	1.16824i
$994$	−30.5370	−	35.3234i	−0.968575	−	1.12039i
$995$	3.27805	−	1.89258i	0.103921	−	0.0599988i
$996$	−42.8271	−	21.6747i	−1.35703	−	0.686789i
$997$	−21.9331	−	12.6631i	−0.694629	−	0.401044i	0.110715	−	0.993852i	$-0.464686\pi$
$997$	−21.9331	−	12.6631i	−0.694629	−	0.401044i	−0.805344	+	0.592808i	$0.798019\pi$
$998$	−3.62330	−	18.9161i	−0.114693	−	0.598780i
$999$	20.8159	−	14.2572i	0.658587	−	0.451079i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.b.11.2	yes	48
3.2	odd	2		1080.2.bm.a.251.23		48
4.3	odd	2		1440.2.cc.b.911.19		48
8.3	odd	2		360.2.bm.a.11.7	✓	48
8.5	even	2		1440.2.cc.a.911.19		48
9.4	even	3		1080.2.bm.b.611.18		48
9.5	odd	6		360.2.bm.a.131.7	yes	48
12.11	even	2		4320.2.cc.a.1871.22		48
24.5	odd	2		4320.2.cc.b.1871.3		48
24.11	even	2		1080.2.bm.b.251.18		48
36.23	even	6		1440.2.cc.a.1391.19		48
36.31	odd	6		4320.2.cc.b.3311.3		48
72.5	odd	6		1440.2.cc.b.1391.19		48
72.13	even	6		4320.2.cc.a.3311.22		48
72.59	even	6	inner	360.2.bm.b.131.2	yes	48
72.67	odd	6		1080.2.bm.a.611.23		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.7	✓	48	8.3	odd	2
360.2.bm.a.131.7	yes	48	9.5	odd	6
360.2.bm.b.11.2	yes	48	1.1	even	1	trivial
360.2.bm.b.131.2	yes	48	72.59	even	6	inner
1080.2.bm.a.251.23		48	3.2	odd	2
1080.2.bm.a.611.23		48	72.67	odd	6
1080.2.bm.b.251.18		48	24.11	even	2
1080.2.bm.b.611.18		48	9.4	even	3
1440.2.cc.a.911.19		48	8.5	even	2
1440.2.cc.a.1391.19		48	36.23	even	6
1440.2.cc.b.911.19		48	4.3	odd	2
1440.2.cc.b.1391.19		48	72.5	odd	6
4320.2.cc.a.1871.22		48	12.11	even	2
4320.2.cc.a.3311.22		48	72.13	even	6
4320.2.cc.b.1871.3		48	24.5	odd	2
4320.2.cc.b.3311.3		48	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33590 - 0.464076i) q^{2} +(-1.29784 + 1.14700i) q^{3} +(1.56927 + 1.23992i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.26609 - 0.929977i) q^{6} +(-3.14000 - 1.81288i) q^{7} +(-1.52097 - 2.38467i) q^{8} +(0.368796 - 2.97725i) q^{9} +O(q^{10})\)	\(q+(-1.33590 - 0.464076i) q^{2} +(-1.29784 + 1.14700i) q^{3} +(1.56927 + 1.23992i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.26609 - 0.929977i) q^{6} +(-3.14000 - 1.81288i) q^{7} +(-1.52097 - 2.38467i) q^{8} +(0.368796 - 2.97725i) q^{9} +(-0.266049 - 1.38896i) q^{10} +(-2.02891 - 1.17139i) q^{11} +(-3.45885 + 0.190721i) q^{12} +(4.70695 - 2.71756i) q^{13} +(3.35342 + 3.87903i) q^{14} +(-1.64225 - 0.550467i) q^{15} +(0.925196 + 3.89153i) q^{16} +4.45073i q^{17} +(-1.87434 + 3.80616i) q^{18} +7.29765 q^{19} +(-0.289169 + 1.97898i) q^{20} +(6.15460 - 1.24874i) q^{21} +(2.16681 + 2.50644i) q^{22} +(-2.97353 - 5.15031i) q^{23} +(4.70919 + 1.35038i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-7.54918 + 1.44601i) q^{26} +(2.93625 + 4.28701i) q^{27} +(-2.67967 - 6.73825i) q^{28} +(1.52275 - 2.63748i) q^{29} +(1.93843 + 1.49750i) q^{30} +(6.43361 - 3.71445i) q^{31} +(0.569996 - 5.62806i) q^{32} +(3.97680 - 0.806871i) q^{33} +(2.06548 - 5.94574i) q^{34} -3.62576i q^{35} +(4.27029 - 4.21481i) q^{36} -4.85559i q^{37} +(-9.74895 - 3.38667i) q^{38} +(-2.99186 + 8.92583i) q^{39} +(1.30470 - 2.50953i) q^{40} +(0.201473 - 0.116321i) q^{41} +(-8.80145 - 1.18801i) q^{42} +(-0.490794 + 0.850080i) q^{43} +(-1.73147 - 4.35392i) q^{44} +(2.76277 - 1.16924i) q^{45} +(1.58221 + 8.26025i) q^{46} +(1.48425 - 2.57079i) q^{47} +(-5.66433 - 3.98940i) q^{48} +(3.07308 + 5.32273i) q^{49} +(1.06985 - 0.924887i) q^{50} +(-5.10497 - 5.77635i) q^{51} +(10.7560 + 1.57167i) q^{52} +11.3468 q^{53} +(-1.93304 - 7.08966i) q^{54} -2.34279i q^{55} +(0.452721 + 10.2452i) q^{56} +(-9.47121 + 8.37039i) q^{57} +(-3.25824 + 2.81675i) q^{58} +(1.02217 - 0.590148i) q^{59} +(-1.89459 - 2.90009i) q^{60} +(-10.1682 - 5.87061i) q^{61} +(-10.3185 + 1.97645i) q^{62} +(-6.55541 + 8.67997i) q^{63} +(-3.37331 + 7.25402i) q^{64} +(4.70695 + 2.71756i) q^{65} +(-5.68706 - 0.767635i) q^{66} +(-2.00541 - 3.47348i) q^{67} +(-5.51855 + 6.98438i) q^{68} +(9.76657 + 3.27366i) q^{69} +(-1.68263 + 4.84366i) q^{70} -9.10623 q^{71} +(-7.66068 + 3.64884i) q^{72} -1.90547 q^{73} +(-2.25336 + 6.48659i) q^{74} +(-0.344407 - 1.69746i) q^{75} +(11.4520 + 9.04851i) q^{76} +(4.24719 + 7.35636i) q^{77} +(8.13909 - 10.5356i) q^{78} +(-0.784069 - 0.452683i) q^{79} +(-2.90757 + 2.74701i) q^{80} +(-8.72798 - 2.19599i) q^{81} +(-0.323130 + 0.0618941i) q^{82} +(11.9999 + 6.92813i) q^{83} +(11.2065 + 5.67161i) q^{84} +(-3.85445 + 2.22537i) q^{85} +(1.05015 - 0.907857i) q^{86} +(1.04889 + 5.16963i) q^{87} +(0.292525 + 6.61994i) q^{88} -12.5342i q^{89} +(-4.23340 + 0.279849i) q^{90} -19.7065 q^{91} +(1.71971 - 11.7692i) q^{92} +(-4.08936 + 12.2001i) q^{93} +(-3.17585 + 2.74552i) q^{94} +(3.64883 + 6.31995i) q^{95} +(5.71561 + 7.95813i) q^{96} +(6.51236 - 11.2797i) q^{97} +(-1.63518 - 8.53678i) q^{98} +(-4.23578 + 5.60856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8}+O(q^{10}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8	\( 48 q + 24 q^{5} - q^{6} + 6 q^{8} + 13 q^{12} + 15 q^{14} - 12 q^{16} + 7 q^{18} + 4 q^{21} - 21 q^{22} - 4 q^{24} - 24 q^{25} + 12 q^{27} - 2 q^{30} - 8 q^{33} - 27 q^{34} - 31 q^{36} - 27 q^{38} - 16 q^{39} + 12 q^{40} + 12 q^{41} - 9 q^{42} + 24 q^{44} - 6 q^{46} - 12 q^{47} + 7 q^{48} + 24 q^{49} - 20 q^{51} + 54 q^{52} - 32 q^{54} + 21 q^{56} + 4 q^{57} + 33 q^{58} - 36 q^{59} - q^{60} - 12 q^{61} - 42 q^{62} - 56 q^{63} - 12 q^{64} - 32 q^{66} + 51 q^{68} + 40 q^{69} + 15 q^{70} + 6 q^{72} + 54 q^{74} - 51 q^{76} - 24 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} + 41 q^{84} + 27 q^{86} - 36 q^{87} - 57 q^{88} - 22 q^{90} - 9 q^{92} - 75 q^{94} + 13 q^{96} - 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q + 24 * q^5 - q^6 + 6 * q^8 + 13 * q^12 + 15 * q^14 - 12 * q^16 + 7 * q^18 + 4 * q^21 - 21 * q^22 - 4 * q^24 - 24 * q^25 + 12 * q^27 - 2 * q^30 - 8 * q^33 - 27 * q^34 - 31 * q^36 - 27 * q^38 - 16 * q^39 + 12 * q^40 + 12 * q^41 - 9 * q^42 + 24 * q^44 - 6 * q^46 - 12 * q^47 + 7 * q^48 + 24 * q^49 - 20 * q^51 + 54 * q^52 - 32 * q^54 + 21 * q^56 + 4 * q^57 + 33 * q^58 - 36 * q^59 - q^60 - 12 * q^61 - 42 * q^62 - 56 * q^63 - 12 * q^64 - 32 * q^66 + 51 * q^68 + 40 * q^69 + 15 * q^70 + 6 * q^72 + 54 * q^74 - 51 * q^76 - 24 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 + 41 * q^84 + 27 * q^86 - 36 * q^87 - 57 * q^88 - 22 * q^90 - 9 * q^92 - 75 * q^94 + 13 * q^96 - 42 * q^98 - 16 * q^99

Introduction

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