LMFDB - Embedded newform 231.2.y.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(4,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 20, 6]))

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

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

chi := DirichletCharacter("231.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.y (of order $15$, degree $8$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			4.4
Character	$\chi$	$=$	231.4
Dual form			231.2.y.a.58.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00677966 + 0.0645042i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.95218 + 0.414949i) q^{4} +(-1.02829 - 0.457823i) q^{5} +(0.0524724 - 0.0381234i) q^{6} +(2.43175 + 1.04239i) q^{7} +(-0.0800864 + 0.246481i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.00677966 + 0.0645042i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.95218 + 0.414949i) q^{4} +(-1.02829 - 0.457823i) q^{5} +(0.0524724 - 0.0381234i) q^{6} +(2.43175 + 1.04239i) q^{7} +(-0.0800864 + 0.246481i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0365029 - 0.0632249i) q^{10} +(2.04214 - 2.61336i) q^{11} +(-0.997897 - 1.72841i) q^{12} +(-0.0840203 - 0.0610443i) q^{13} +(-0.0837250 + 0.149791i) q^{14} +(0.347830 + 1.07051i) q^{15} +(3.63114 + 1.61669i) q^{16} +(-0.274895 - 2.61545i) q^{17} +(-0.0634421 - 0.0134850i) q^{18} +(1.82152 - 0.387177i) q^{19} +(-1.81743 - 1.32044i) q^{20} +(-0.852513 - 2.50464i) q^{21} +(0.154728 + 0.149445i) q^{22} +(1.05360 + 1.82490i) q^{23} +(0.236759 - 0.105412i) q^{24} +(-2.49788 - 2.77418i) q^{25} +(0.00450724 - 0.00500580i) q^{26} +(0.809017 - 0.587785i) q^{27} +(4.31468 + 3.04399i) q^{28} +(1.94866 + 5.99736i) q^{29} +(-0.0714105 + 0.0151788i) q^{30} +(-7.56642 + 3.36879i) q^{31} +(-0.388066 + 0.672150i) q^{32} +(-3.30857 + 0.231070i) q^{33} +0.170571 q^{34} +(-2.02331 - 2.18519i) q^{35} +(-0.616734 + 1.89811i) q^{36} +(1.40175 - 1.55680i) q^{37} +(0.0126252 + 0.120121i) q^{38} +(0.0108558 + 0.103286i) q^{39} +(0.195196 - 0.216787i) q^{40} +(0.521765 - 1.60583i) q^{41} +(0.167339 - 0.0380100i) q^{42} -6.80371 q^{43} +(5.07104 - 4.25436i) q^{44} +(0.562800 - 0.974798i) q^{45} +(-0.124856 + 0.0555897i) q^{46} +(-11.4134 + 2.42600i) q^{47} +(-1.22827 - 3.78024i) q^{48} +(4.82684 + 5.06967i) q^{49} +(0.195881 - 0.142316i) q^{50} +(-1.75972 + 1.95437i) q^{51} +(-0.138692 - 0.154034i) q^{52} +(-8.66379 + 3.85737i) q^{53} +(0.0324297 + 0.0561700i) q^{54} +(-3.29637 + 1.75234i) q^{55} +(-0.451679 + 0.515899i) q^{56} +(-1.50657 - 1.09458i) q^{57} +(-0.400066 + 0.0850366i) q^{58} +(-4.48076 - 0.952415i) q^{59} +(0.234820 + 2.23416i) q^{60} +(4.40337 + 1.96051i) q^{61} +(-0.166003 - 0.510905i) q^{62} +(-1.29087 + 2.30947i) q^{63} +(6.39060 + 4.64304i) q^{64} +(0.0584495 + 0.101237i) q^{65} +(0.00752600 - 0.214983i) q^{66} +(0.951855 - 1.64866i) q^{67} +(0.548634 - 5.21990i) q^{68} +(0.651163 - 2.00407i) q^{69} +(0.154671 - 0.115697i) q^{70} +(-8.07772 + 5.86881i) q^{71} +(-0.236759 - 0.105412i) q^{72} +(-10.1378 - 2.15485i) q^{73} +(0.0909167 + 0.100973i) q^{74} +(-0.390207 + 3.71257i) q^{75} +3.71660 q^{76} +(7.69013 - 4.22633i) q^{77} -0.00673597 q^{78} +(1.24026 - 11.8003i) q^{79} +(-2.99370 - 3.32484i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.100045 + 0.0445430i) q^{82} +(8.21556 - 5.96895i) q^{83} +(-0.624962 - 5.24326i) q^{84} +(-0.914742 + 2.81529i) q^{85} +(0.0461269 - 0.438868i) q^{86} +(3.15300 - 5.46115i) q^{87} +(0.480594 + 0.712644i) q^{88} +(6.55860 + 11.3598i) q^{89} +(0.0590630 + 0.0429117i) q^{90} +(-0.140685 - 0.236027i) q^{91} +(1.29959 + 3.99972i) q^{92} +(7.56642 + 3.36879i) q^{93} +(-0.0791079 - 0.752661i) q^{94} +(-2.05031 - 0.435806i) q^{95} +(0.759172 - 0.161367i) q^{96} +(6.71739 + 4.88047i) q^{97} +(-0.359739 + 0.276981i) q^{98} +(2.38558 + 2.30413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.00677966	+	0.0645042i	−0.00479394	+	0.0456113i	−0.996657	−	0.0816953i	$-0.973967\pi$
$2$	−0.00677966	+	0.0645042i	−0.00479394	+	0.0456113i	0.991863	+	0.127307i	$0.0406332\pi$
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$3$	−0.669131	−	0.743145i	−0.386323	−	0.429055i
$4$	1.95218	+	0.414949i	0.976090	+	0.207474i
$5$	−1.02829	−	0.457823i	−0.459864	−	0.204745i	0.163711	−	0.986508i	$-0.447654\pi$
$5$	−1.02829	−	0.457823i	−0.459864	−	0.204745i	−0.623575	+	0.781764i	$0.714320\pi$
$6$	0.0524724	−	0.0381234i	0.0214218	−	0.0155638i
$7$	2.43175	+	1.04239i	0.919116	+	0.393987i
$7$	2.43175	+	1.04239i	0.919116	+	0.393987i
$8$	−0.0800864	+	0.246481i	−0.0283148	+	0.0871441i
$9$	−0.104528	+	0.994522i	−0.0348428	+	0.331507i
$10$	0.0365029	−	0.0632249i	0.0115432	−	0.0199935i
$11$	2.04214	−	2.61336i	0.615730	−	0.787957i
$11$	2.04214	−	2.61336i	0.615730	−	0.787957i
$12$	−0.997897	−	1.72841i	−0.288068	−	0.498948i
$13$	−0.0840203	−	0.0610443i	−0.0233030	−	0.0169306i	0.576073	−	0.817398i	$-0.304584\pi$
$13$	−0.0840203	−	0.0610443i	−0.0233030	−	0.0169306i	−0.599376	+	0.800468i	$0.704584\pi$
$14$	−0.0837250	+	0.149791i	−0.0223764	+	0.0400334i
$15$	0.347830	+	1.07051i	0.0898092	+	0.276404i
$16$	3.63114	+	1.61669i	0.907785	+	0.404172i
$17$	−0.274895	−	2.61545i	−0.0666718	−	0.634340i	−0.975926	−	0.218100i	$-0.930014\pi$
$17$	−0.274895	−	2.61545i	−0.0666718	−	0.634340i	0.909255	−	0.416240i	$-0.136653\pi$
$18$	−0.0634421	−	0.0134850i	−0.0149535	−	0.00317846i
$19$	1.82152	−	0.387177i	0.417886	−	0.0888245i	0.00583032	−	0.999983i	$-0.498144\pi$
$19$	1.82152	−	0.387177i	0.417886	−	0.0888245i	0.412056	+	0.911159i	$0.364811\pi$
$20$	−1.81743	−	1.32044i	−0.406389	−	0.295259i
$21$	−0.852513	−	2.50464i	−0.186034	−	0.546557i
$22$	0.154728	+	0.149445i	0.0329880	+	0.0318617i
$23$	1.05360	+	1.82490i	0.219692	+	0.380517i	0.954714	−	0.297526i	$-0.0961615\pi$
$23$	1.05360	+	1.82490i	0.219692	+	0.380517i	−0.735022	+	0.678043i	$0.762828\pi$
$24$	0.236759	−	0.105412i	0.0483282	−	0.0215171i
$25$	−2.49788	−	2.77418i	−0.499576	−	0.554836i
$26$	0.00450724	−	0.00500580i	0.000883943	−	0.000981718i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	4.31468	+	3.04399i	0.815398	+	0.575260i
$29$	1.94866	+	5.99736i	0.361857	+	1.11368i	0.951926	+	0.306328i	$0.0991005\pi$
$29$	1.94866	+	5.99736i	0.361857	+	1.11368i	−0.590069	+	0.807353i	$0.700899\pi$
$30$	−0.0714105	+	0.0151788i	−0.0130377	+	0.00277125i
$31$	−7.56642	+	3.36879i	−1.35897	+	0.605052i	−0.951353	−	0.308102i	$-0.900306\pi$
$31$	−7.56642	+	3.36879i	−1.35897	+	0.605052i	−0.407615	+	0.913154i	$0.633639\pi$
$32$	−0.388066	+	0.672150i	−0.0686010	+	0.118820i
$33$	−3.30857	+	0.231070i	−0.575947	+	0.0402241i
$34$	0.170571			0.0292527
$35$	−2.02331	−	2.18519i	−0.342002	−	0.369364i
$36$	−0.616734	+	1.89811i	−0.102789	+	0.316352i
$37$	1.40175	−	1.55680i	0.230446	−	0.255936i	−0.616821	−	0.787104i	$-0.711580\pi$
$37$	1.40175	−	1.55680i	0.230446	−	0.255936i	0.847267	+	0.531167i	$0.178246\pi$
$38$	0.0126252	+	0.120121i	0.00204808	+	0.0194862i
$39$	0.0108558	+	0.103286i	0.00173832	+	0.0165390i
$40$	0.195196	−	0.216787i	0.0308632	−	0.0342771i
$41$	0.521765	−	1.60583i	0.0814860	−	0.250788i	−0.902011	−	0.431713i	$-0.857909\pi$
$41$	0.521765	−	1.60583i	0.0814860	−	0.250788i	0.983497	+	0.180925i	$0.0579092\pi$
$42$	0.167339	−	0.0380100i	0.0258210	−	0.00586507i
$43$	−6.80371			−1.03756			−0.518778	−	0.854909i	$-0.673613\pi$
$43$	−6.80371			−1.03756			−0.518778	+	0.854909i	$0.673613\pi$
$44$	5.07104	−	4.25436i	0.764489	−	0.641369i
$45$	0.562800	−	0.974798i	0.0838973	−	0.145314i
$46$	−0.124856	+	0.0555897i	−0.0184091	+	0.00819625i
$47$	−11.4134	+	2.42600i	−1.66482	+	0.353868i	−0.941596	−	0.336746i	$-0.890674\pi$
$47$	−11.4134	+	2.42600i	−1.66482	+	0.353868i	−0.723224	+	0.690614i	$0.757340\pi$
$48$	−1.22827	−	3.78024i	−0.177286	−	0.545630i
$49$	4.82684	+	5.06967i	0.689549	+	0.724239i
$50$	0.195881	−	0.142316i	0.0277017	−	0.0201265i
$51$	−1.75972	+	1.95437i	−0.246410	+	0.273666i
$52$	−0.138692	−	0.154034i	−0.0192332	−	0.0213606i
$53$	−8.66379	+	3.85737i	−1.19006	+	0.529850i	−0.903657	−	0.428258i	$-0.859127\pi$
$53$	−8.66379	+	3.85737i	−1.19006	+	0.529850i	−0.286407	+	0.958108i	$0.592461\pi$
$54$	0.0324297	+	0.0561700i	0.00441313	+	0.00764376i
$55$	−3.29637	+	1.75234i	−0.444482	+	0.236286i
$56$	−0.451679	+	0.515899i	−0.0603582	+	0.0689399i
$57$	−1.50657	−	1.09458i	−0.199550	−	0.144981i
$58$	−0.400066	+	0.0850366i	−0.0525312	+	0.0111659i
$59$	−4.48076	−	0.952415i	−0.583345	−	0.123994i	−0.0932194	−	0.995646i	$-0.529716\pi$
$59$	−4.48076	−	0.952415i	−0.583345	−	0.123994i	−0.490126	+	0.871652i	$0.663049\pi$
$60$	0.234820	+	2.23416i	0.0303151	+	0.288429i
$61$	4.40337	+	1.96051i	0.563794	+	0.251017i	0.668785	−	0.743456i	$-0.266815\pi$
$61$	4.40337	+	1.96051i	0.563794	+	0.251017i	−0.104991	+	0.994473i	$0.533481\pi$
$62$	−0.166003	−	0.510905i	−0.0210824	−	0.0648849i
$63$	−1.29087	+	2.30947i	−0.162634	+	0.290966i
$64$	6.39060	+	4.64304i	0.798825	+	0.580380i
$65$	0.0584495	+	0.101237i	0.00724976	+	0.0125570i
$66$	0.00752600	−	0.214983i	0.000926386	−	0.0264626i
$67$	0.951855	−	1.64866i	0.116288	−	0.201416i	−0.802006	−	0.597316i	$-0.796234\pi$
$67$	0.951855	−	1.64866i	0.116288	−	0.201416i	0.918294	+	0.395900i	$0.129567\pi$
$68$	0.548634	−	5.21990i	0.0665316	−	0.633006i
$69$	0.651163	−	2.00407i	0.0783908	−	0.241262i
$70$	0.154671	−	0.115697i	0.0184867	−	0.0138284i
$71$	−8.07772	+	5.86881i	−0.958649	+	0.696499i	−0.952837	−	0.303484i	$-0.901850\pi$
$71$	−8.07772	+	5.86881i	−0.958649	+	0.696499i	−0.00581253	+	0.999983i	$0.501850\pi$
$72$	−0.236759	−	0.105412i	−0.0279023	−	0.0124229i
$73$	−10.1378	−	2.15485i	−1.18654	−	0.252206i	−0.427965	−	0.903795i	$-0.640769\pi$
$73$	−10.1378	−	2.15485i	−1.18654	−	0.252206i	−0.758572	+	0.651589i	$0.774103\pi$
$74$	0.0909167	+	0.100973i	0.0105689	+	0.0117379i
$75$	−0.390207	+	3.71257i	−0.0450573	+	0.428691i
$76$	3.71660			0.426324
$77$	7.69013	−	4.22633i	0.876372	−	0.481635i
$78$	−0.00673597			−0.000762698
$79$	1.24026	−	11.8003i	0.139540	−	1.32764i	−0.670783	−	0.741654i	$-0.734042\pi$
$79$	1.24026	−	11.8003i	0.139540	−	1.32764i	0.810323	−	0.585983i	$-0.199292\pi$
$80$	−2.99370	−	3.32484i	−0.334705	−	0.371728i
$81$	−0.978148	−	0.207912i	−0.108683	−	0.0231013i
$82$	0.100045	+	0.0445430i	0.0110481	+	0.00491895i
$83$	8.21556	−	5.96895i	0.901775	−	0.655178i	−0.0371465	−	0.999310i	$-0.511827\pi$
$83$	8.21556	−	5.96895i	0.901775	−	0.655178i	0.938921	+	0.344132i	$0.111827\pi$
$84$	−0.624962	−	5.24326i	−0.0681889	−	0.572086i
$85$	−0.914742	+	2.81529i	−0.0992177	+	0.305361i
$86$	0.0461269	−	0.438868i	0.00497399	−	0.0473243i
$87$	3.15300	−	5.46115i	0.338037	−	0.585497i
$88$	0.480594	+	0.712644i	0.0512315	+	0.0759681i
$89$	6.55860	+	11.3598i	0.695210	+	1.20414i	0.970110	+	0.242667i	$0.0780221\pi$
$89$	6.55860	+	11.3598i	0.695210	+	1.20414i	−0.274899	+	0.961473i	$0.588645\pi$
$90$	0.0590630	+	0.0429117i	0.00622578	+	0.00452330i
$91$	−0.140685	−	0.236027i	−0.0147477	−	0.0247423i
$92$	1.29959	+	3.99972i	0.135491	+	0.416999i
$93$	7.56642	+	3.36879i	0.784601	+	0.349327i
$94$	−0.0791079	−	0.752661i	−0.00815935	−	0.0776310i
$95$	−2.05031	−	0.435806i	−0.210357	−	0.0447128i
$96$	0.759172	−	0.161367i	0.0774826	−	0.0164694i
$97$	6.71739	+	4.88047i	0.682048	+	0.495537i	0.874036	−	0.485861i	$-0.161494\pi$
$97$	6.71739	+	4.88047i	0.682048	+	0.495537i	−0.191989	+	0.981397i	$0.561494\pi$
$98$	−0.359739	+	0.276981i	−0.0363392	+	0.0279793i
$99$	2.38558	+	2.30413i	0.239760	+	0.231574i
$100$	−3.72517	−	6.45219i	−0.372517	−	0.645219i
$101$	14.9109	−	6.63875i	1.48369	−	0.660580i	0.504476	−	0.863426i	$-0.331686\pi$
$101$	14.9109	−	6.63875i	1.48369	−	0.660580i	0.979211	+	0.202846i	$0.0650189\pi$
$102$	−0.114134	−	0.126759i	−0.0113010	−	0.0125510i
$103$	−0.731806	+	0.812752i	−0.0721069	+	0.0800829i	−0.778119	−	0.628117i	$-0.783826\pi$
$103$	−0.731806	+	0.812752i	−0.0721069	+	0.0800829i	0.706012	+	0.708200i	$0.250493\pi$
$104$	0.0217751	−	0.0158206i	0.00213523	−	0.00155133i
$105$	−0.270053	+	2.96579i	−0.0263545	+	0.289431i
$106$	−0.190079	−	0.585002i	−0.0184621	−	0.0568204i
$107$	−0.611411	+	0.129959i	−0.0591074	+	0.0125637i	−0.237370	−	0.971419i	$-0.576286\pi$
$107$	−0.611411	+	0.129959i	−0.0591074	+	0.0125637i	0.178263	+	0.983983i	$0.442952\pi$
$108$	1.82325	−	0.811762i	0.175442	−	0.0781119i
$109$	6.61241	−	11.4530i	0.633354	−	1.09700i	−0.353507	−	0.935432i	$-0.615011\pi$
$109$	6.61241	−	11.4530i	0.633354	−	1.09700i	0.986861	−	0.161570i	$-0.0516557\pi$
$110$	−0.0906852	−	0.224510i	−0.00864649	−	0.0214061i
$111$	−2.09488			−0.198837
$112$	7.14481	+	7.71645i	0.675121	+	0.729136i
$113$	−0.499871	+	1.53844i	−0.0470239	+	0.144725i	−0.971812	−	0.235759i	$-0.924242\pi$
$113$	−0.499871	+	1.53844i	−0.0470239	+	0.144725i	0.924788	+	0.380484i	$0.124242\pi$
$114$	0.0808193	−	0.0897589i	0.00756942	−	0.00840669i
$115$	−0.247928	−	2.35888i	−0.0231194	−	0.219967i
$116$	1.31554	+	12.5165i	0.122145	+	1.16213i
$117$	0.0694924	−	0.0771791i	0.00642458	−	0.00713521i
$118$	0.0918127	−	0.282571i	0.00845205	−	0.0260127i
$119$	2.05785	−	6.64668i	0.188642	−	0.609300i
$120$	−0.291716			−0.0266299
$121$	−2.65929	−	10.6737i	−0.241754	−	0.970338i
$122$	−0.156314	+	0.270744i	−0.0141520	+	0.0245120i
$123$	−1.54249	+	0.686761i	−0.139082	+	0.0619232i
$124$	−16.1689	+	3.43680i	−1.45201	+	0.308634i
$125$	3.03760	+	9.34878i	0.271692	+	0.836181i
$126$	−0.140219	−	0.0989238i	−0.0124917	−	0.00881283i
$127$	−14.5662	+	10.5830i	−1.29254	+	0.939086i	−0.999853	−	0.0171217i	$-0.994550\pi$
$127$	−14.5662	+	10.5830i	−1.29254	+	0.939086i	−0.292688	+	0.956208i	$0.594550\pi$
$128$	−1.38149	+	1.53430i	−0.122108	+	0.135614i
$129$	4.55257	+	5.05614i	0.400832	+	0.445169i
$130$	−0.00692650	+	0.00308388i	−0.000607495	+	0.000270474i
$131$	−0.871442	−	1.50938i	−0.0761382	−	0.131875i	0.825442	−	0.564486i	$-0.190926\pi$
$131$	−0.871442	−	1.50938i	−0.0761382	−	0.131875i	−0.901581	+	0.432611i	$0.857592\pi$
$132$	−6.55480	−	0.921796i	−0.570522	−	0.0802320i
$133$	4.83309	+	0.957221i	0.419082	+	0.0830016i
$134$	0.0998922	+	0.0725760i	0.00862937	+	0.00626961i
$135$	−1.10100	+	0.234025i	−0.0947592	+	0.0201417i
$136$	0.666674	+	0.141706i	0.0571668	+	0.0121512i
$137$	−1.34205	−	12.7688i	−0.114659	−	1.09091i	−0.888926	−	0.458050i	$-0.848548\pi$
$137$	−1.34205	−	12.7688i	−0.114659	−	1.09091i	0.774267	−	0.632859i	$-0.218119\pi$
$138$	0.124856	+	0.0555897i	0.0106285	+	0.00473211i
$139$	0.876307	+	2.69700i	0.0743274	+	0.228756i	0.981317	−	0.192396i	$-0.0616258\pi$
$139$	0.876307	+	2.69700i	0.0743274	+	0.228756i	−0.906990	+	0.421152i	$0.861626\pi$
$140$	−3.04312	−	5.10545i	−0.257191	−	0.431489i
$141$	9.43994	+	6.85852i	0.794986	+	0.577591i
$142$	−0.323798	−	0.560835i	−0.0271726	−	0.0470642i
$143$	−0.331112	+	0.0949139i	−0.0276890	+	0.00793710i
$144$	−1.98739	+	3.44226i	−0.165616	+	0.286855i
$145$	0.741946	−	7.05914i	0.0616152	−	0.586230i
$146$	0.207728	−	0.639320i	0.0171917	−	0.0529105i
$147$	0.537713	−	6.97932i	0.0443498	−	0.575644i
$148$	3.38246	−	2.45750i	0.278036	−	0.202005i
$149$	20.9631	+	9.33339i	1.71737	+	0.764621i	0.997512	+	0.0704973i	$0.0224586\pi$
$149$	20.9631	+	9.33339i	1.71737	+	0.764621i	0.719855	+	0.694124i	$0.244208\pi$
$150$	−0.236831	−	0.0503400i	−0.0193372	−	0.00411024i
$151$	1.06095	+	1.17831i	0.0863392	+	0.0958894i	0.784766	−	0.619792i	$-0.212783\pi$
$151$	1.06095	+	1.17831i	0.0863392	+	0.0958894i	−0.698427	+	0.715681i	$0.746116\pi$
$152$	−0.0504477	+	0.479978i	−0.00409185	+	0.0389314i
$153$	2.62986			0.212611
$154$	0.220480	+	0.524699i	0.0177667	+	0.0422814i
$155$	9.32275			0.748821
$156$	−0.0216659	+	0.206137i	−0.00173466	+	0.0165042i
$157$	−10.5956	−	11.7676i	−0.845617	−	0.939153i	0.153179	−	0.988198i	$-0.451049\pi$
$157$	−10.5956	−	11.7676i	−0.845617	−	0.939153i	−0.998797	+	0.0490451i	$0.984382\pi$
$158$	0.752760	+	0.160004i	0.0598863	+	0.0127292i
$159$	8.66379	+	3.85737i	0.687083	+	0.305909i
$160$	0.706769	−	0.513498i	0.0558750	−	0.0405955i
$161$	0.659850	+	5.53596i	0.0520035	+	0.436295i
$162$	0.0200427	−	0.0616850i	0.00157470	−	0.00484643i
$163$	0.156665	−	1.49057i	0.0122710	−	0.116751i	−0.986672	−	0.162724i	$-0.947972\pi$
$163$	0.156665	−	1.49057i	0.0122710	−	0.116751i	0.998943	+	0.0459730i	$0.0146388\pi$
$164$	1.68491	−	2.91836i	0.131570	−	0.227885i
$165$	3.50794	+	1.27713i	0.273093	+	0.0994245i
$166$	0.329324	+	0.570405i	0.0255605	+	0.0442720i
$167$	−10.1815	−	7.39726i	−0.787865	−	0.572417i	0.119464	−	0.992839i	$-0.461882\pi$
$167$	−10.1815	−	7.39726i	−0.787865	−	0.572417i	−0.907329	+	0.420421i	$0.861882\pi$
$168$	0.685620	−	0.00954030i	0.0528967	−	0.000736050i
$169$	−4.01389	−	12.3535i	−0.308761	−	0.950267i
$170$	−0.175396	−	0.0780914i	−0.0134523	−	0.00598934i
$171$	0.194655	+	1.85202i	0.0148856	+	0.141627i
$172$	−13.2821	−	2.82319i	−1.01275	−	0.215266i
$173$	14.3706	−	3.05456i	1.09258	−	0.232234i	0.373823	−	0.927500i	$-0.378047\pi$
$173$	14.3706	−	3.05456i	1.09258	−	0.232234i	0.718753	+	0.695266i	$0.244713\pi$
$174$	0.330891	+	0.240406i	0.0250848	+	0.0182251i
$175$	−3.18245	−	9.34988i	−0.240571	−	0.706785i
$176$	11.6403	−	6.18796i	0.877420	−	0.466435i
$177$	2.29043	+	3.96714i	0.172159	+	0.298189i
$178$	−0.777221	+	0.346041i	−0.0582552	+	0.0259369i
$179$	7.80642	+	8.66991i	0.583480	+	0.648020i	0.960531	−	0.278173i	$-0.0897287\pi$
$179$	7.80642	+	8.66991i	0.583480	+	0.648020i	−0.377052	+	0.926192i	$0.623062\pi$
$180$	1.50318	−	1.66945i	0.112040	−	0.124433i
$181$	5.59895	−	4.06787i	0.416166	−	0.302363i	−0.359927	−	0.932980i	$-0.617198\pi$
$181$	5.59895	−	4.06787i	0.416166	−	0.302363i	0.776093	+	0.630618i	$0.217198\pi$
$182$	0.0161785	−	0.00747456i	0.00119923	−	0.000554051i
$183$	−1.48949	−	4.58418i	−0.110106	−	0.338872i
$184$	−0.534181	+	0.113544i	−0.0393803	+	0.00837055i
$185$	−2.15414	+	0.959084i	−0.158375	+	0.0705133i
$186$	−0.268598	+	0.465226i	−0.0196946	+	0.0341120i
$187$	−7.39649	−	4.62273i	−0.540885	−	0.338048i
$188$	−23.2877			−1.69843
$189$	2.58003	−	0.586037i	0.187670	−	0.0426279i
$190$	0.0420117	−	0.129299i	0.00304785	−	0.00938032i
$191$	−7.28540	+	8.09126i	−0.527153	+	0.585463i	−0.946638	−	0.322300i	$-0.895544\pi$
$191$	−7.28540	+	8.09126i	−0.527153	+	0.585463i	0.419485	+	0.907762i	$0.362211\pi$
$192$	−0.825693	−	7.85594i	−0.0595892	−	0.566954i
$193$	0.118538	+	1.12782i	0.00853256	+	0.0811819i	0.997959	−	0.0638504i	$-0.0203381\pi$
$193$	0.118538	+	1.12782i	0.00853256	+	0.0811819i	−0.989427	+	0.145032i	$0.953671\pi$
$194$	−0.360352	+	0.400212i	−0.0258718	+	0.0287335i
$195$	0.0361238	−	0.111177i	0.00258688	−	0.00796159i
$196$	7.31921	+	11.8998i	0.522801	+	0.849986i
$197$	−17.3790			−1.23820			−0.619101	−	0.785311i	$-0.712503\pi$
$197$	−17.3790			−1.23820			−0.619101	+	0.785311i	$0.712503\pi$
$198$	−0.164799	+	0.138259i	−0.0117118	+	0.00982562i
$199$	−11.3313	+	19.6263i	−0.803252	+	1.39127i	0.114213	+	0.993456i	$0.463565\pi$
$199$	−11.3313	+	19.6263i	−0.803252	+	1.39127i	−0.917465	+	0.397817i	$0.869768\pi$
$200$	0.883827	−	0.393505i	0.0624960	−	0.0278250i
$201$	−1.86211	+	0.395803i	−0.131343	+	0.0279178i
$202$	0.327136	+	1.00682i	0.0230172	+	0.0708397i
$203$	−1.51293	+	16.6154i	−0.106187	+	1.16617i
$204$	−4.24625	+	3.08508i	−0.297297	+	0.215999i
$205$	−1.27171	+	1.41237i	−0.0888199	+	0.0986445i
$206$	−0.0474645	−	0.0527147i	−0.00330701	−	0.00367281i
$207$	−1.92503	+	0.857079i	−0.133799	+	0.0595711i
$208$	−0.206400	−	0.357495i	−0.0143113	−	0.0247878i
$209$	2.70798	−	5.55097i	0.187315	−	0.383969i
$210$	−0.189475	−	0.0375266i	−0.0130750	−	0.00258958i
$211$	−13.4333	−	9.75983i	−0.924783	−	0.671894i	0.0199268	−	0.999801i	$-0.493657\pi$
$211$	−13.4333	−	9.75983i	−0.924783	−	0.671894i	−0.944710	+	0.327907i	$0.893657\pi$
$212$	−18.5139	+	3.93525i	−1.27154	+	0.270274i
$213$	9.76642	+	2.07592i	0.669184	+	0.142240i
$214$	−0.00423777	−	0.0403197i	−0.000289688	−	0.00275620i
$215$	6.99617	+	3.11489i	0.477135	+	0.212434i
$216$	0.0800864	+	0.246481i	0.00544919	+	0.0167709i
$217$	−21.9112	+	0.304892i	−1.48743	+	0.0206974i
$218$	0.693938	+	0.504176i	0.0469994	+	0.0341471i
$219$	5.18213	+	8.97571i	0.350176	+	0.606522i
$220$	−7.16223	+	2.05307i	−0.482878	+	0.138418i
$221$	−0.136562	+	0.236532i	−0.00918613	+	0.0159108i
$222$	0.0142026	−	0.135129i	0.000953215	−	0.00906923i
$223$	−0.502732	+	1.54725i	−0.0336654	+	0.103612i	−0.966477	−	0.256752i	$-0.917348\pi$
$223$	−0.502732	+	1.54725i	−0.0336654	+	0.103612i	0.932812	+	0.360364i	$0.117348\pi$
$224$	−1.64432	+	1.22999i	−0.109866	+	0.0821819i
$225$	3.02008	−	2.19422i	0.201339	−	0.146281i
$226$	−0.0958471	−	0.0426739i	−0.00637566	−	0.00283862i
$227$	−0.0657351	−	0.0139724i	−0.00436299	−	0.000927383i	0.205730	−	0.978609i	$-0.434043\pi$
$227$	−0.0657351	−	0.0139724i	−0.00436299	−	0.000927383i	−0.210093	+	0.977681i	$0.567377\pi$
$228$	−2.48689	−	2.76197i	−0.164698	−	0.182916i
$229$	0.270137	−	2.57018i	0.0178511	−	0.169842i	−0.981964	−	0.189068i	$-0.939453\pi$
$229$	0.270137	−	2.57018i	0.0178511	−	0.169842i	0.999815	+	0.0192256i	$0.00612007\pi$
$230$	0.153838			0.0101438
$231$	−8.28648	−	2.88691i	−0.545210	−	0.189945i
$232$	−1.63429			−0.107297
$233$	−1.59400	+	15.1659i	−0.104426	+	0.993551i	0.809348	+	0.587329i	$0.199821\pi$
$233$	−1.59400	+	15.1659i	−0.104426	+	0.993551i	−0.913775	+	0.406222i	$0.866846\pi$
$234$	0.00450724	+	0.00500580i	0.000294648	+	0.000327239i
$235$	12.8470	+	2.73070i	0.838043	+	0.178131i
$236$	−8.35205	−	3.71857i	−0.543672	−	0.242058i
$237$	−9.59922	+	6.97424i	−0.623537	+	0.453026i
$238$	0.414787	+	0.177802i	0.0268867	+	0.0115252i
$239$	1.75895	−	5.41348i	0.113777	−	0.350169i	−0.877913	−	0.478820i	$-0.841065\pi$
$239$	1.75895	−	5.41348i	0.113777	−	0.350169i	0.991690	+	0.128651i	$0.0410647\pi$
$240$	−0.467661	+	4.44950i	−0.0301874	+	0.287214i
$241$	−10.5166	+	18.2152i	−0.677432	+	1.17335i	0.298319	+	0.954466i	$0.403574\pi$
$241$	−10.5166	+	18.2152i	−0.677432	+	1.17335i	−0.975752	+	0.218881i	$0.929759\pi$
$242$	0.706528	−	0.0991713i	0.0454173	−	0.00637497i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	7.78267	+	5.65444i	0.498234	+	0.361988i
$245$	−2.64237	−	7.42292i	−0.168815	−	0.474233i
$246$	−0.0338414	−	0.104153i	−0.00215765	−	0.00664056i
$247$	−0.176680	−	0.0786630i	−0.0112419	−	0.00500521i
$248$	−0.224373	−	2.13477i	−0.0142477	−	0.135558i
$249$	−9.93308	−	2.11134i	−0.629483	−	0.133801i
$250$	−0.623629	+	0.132557i	−0.0394418	+	0.00838361i
$251$	−20.7518	−	15.0771i	−1.30984	−	0.951657i	−1.00000		0.000869237i	$-0.999723\pi$
$251$	−20.7518	−	15.0771i	−1.30984	−	0.951657i	−0.309844	−	0.950788i	$-0.600277\pi$
$252$	−3.47832	+	3.97286i	−0.219114	+	0.250267i
$253$	6.92072	+	0.973255i	0.435102	+	0.0611880i
$254$	−0.583891	−	1.01133i	−0.0366366	−	0.0634565i
$255$	2.70425	−	1.20401i	0.169347	−	0.0753980i
$256$	10.4816	+	11.6410i	0.655101	+	0.727563i
$257$	−0.147122	+	0.163395i	−0.00917719	+	0.0101923i	−0.747716	−	0.664019i	$-0.768850\pi$
$257$	−0.147122	+	0.163395i	−0.00917719	+	0.0101923i	0.738539	+	0.674211i	$0.235516\pi$
$258$	−0.357007	+	0.259381i	−0.0222263	+	0.0161484i
$259$	5.03150	−	2.32458i	0.312642	−	0.144443i
$260$	0.0720956	+	0.221887i	0.00447118	+	0.0137609i
$261$	−6.16819	+	1.31109i	−0.381802	+	0.0811544i
$262$	0.103269	−	0.0459785i	0.00638001	−	0.00284056i
$263$	11.1164	−	19.2542i	0.685467	−	1.18726i	−0.287822	−	0.957684i	$-0.592931\pi$
$263$	11.1164	−	19.2542i	0.685467	−	1.18726i	0.973290	−	0.229581i	$-0.0737354\pi$
$264$	0.208017	−	0.834003i	0.0128026	−	0.0513293i
$265$	10.6749			0.655751
$266$	−0.0945115	+	0.305265i	−0.00579487	+	0.0187170i
$267$	4.05344	−	12.4752i	0.248066	−	0.763470i
$268$	2.54230	−	2.82351i	0.155296	−	0.172473i
$269$	1.55147	+	14.7613i	0.0945948	+	0.900009i	0.934185	+	0.356789i	$0.116129\pi$
$269$	1.55147	+	14.7613i	0.0945948	+	0.900009i	−0.839590	+	0.543220i	$0.817205\pi$
$270$	−0.00763119	−	0.0726059i	−0.000464419	−	0.00441865i
$271$	14.9567	−	16.6111i	0.908553	−	1.00905i	−0.0913597	−	0.995818i	$-0.529121\pi$
$271$	14.9567	−	16.6111i	0.908553	−	1.00905i	0.999912	−	0.0132321i	$-0.00421202\pi$
$272$	3.23019	−	9.94149i	0.195859	−	0.602791i
$273$	−0.0812656	+	0.262482i	−0.00491842	+	0.0158861i
$274$	0.832737			0.0503075
$275$	−12.3510	+	0.862589i	−0.744791	+	0.0520161i
$276$	2.10278	−	3.64211i	0.126572	−	0.219230i
$277$	3.59721	−	1.60158i	0.216135	−	0.0962296i	−0.295813	−	0.955246i	$-0.595591\pi$
$277$	3.59721	−	1.60158i	0.216135	−	0.0962296i	0.511948	+	0.859016i	$0.328924\pi$
$278$	−0.179909	+	0.0382407i	−0.0107902	+	0.00229353i
$279$	−2.55942	−	7.87710i	−0.153229	−	0.471590i
$280$	0.700646	−	0.323703i	0.0418716	−	0.0193449i
$281$	22.3417	−	16.2322i	1.33280	−	0.968333i	0.333120	−	0.942884i	$-0.391899\pi$
$281$	22.3417	−	16.2322i	1.33280	−	0.968333i	0.999676	−	0.0254487i	$-0.00810146\pi$
$282$	−0.506403	+	0.562417i	−0.0301558	+	0.0334914i
$283$	19.0554	+	21.1631i	1.13272	+	1.25802i	0.962104	+	0.272682i	$0.0879106\pi$
$283$	19.0554	+	21.1631i	1.13272	+	1.25802i	0.170621	+	0.985337i	$0.445423\pi$
$284$	−18.2044	+	8.10513i	−1.08023	+	0.480951i
$285$	1.04806	+	1.81529i	0.0620815	+	0.107528i
$286$	−0.00387751	−	0.0220016i	−0.000229282	−	0.00130098i
$287$	2.94270	−	3.36109i	0.173702	−	0.198399i
$288$	−0.627904	−	0.456199i	−0.0369996	−	0.0268818i
$289$	9.86349	−	2.09655i	0.580205	−	0.123326i
$290$	0.450314	+	0.0957172i	0.0264433	+	0.00562071i
$291$	−0.867915	−	8.25766i	−0.0508781	−	0.484073i
$292$	−18.8966	−	8.41332i	−1.10584	−	0.492352i
$293$	10.2344	+	31.4982i	0.597899	+	1.84014i	0.539733	+	0.841836i	$0.318525\pi$
$293$	10.2344	+	31.4982i	0.597899	+	1.84014i	0.0581658	+	0.998307i	$0.481475\pi$
$294$	0.446550	+	0.0820021i	0.0260433	+	0.00478246i
$295$	4.17147	+	3.03075i	0.242872	+	0.176457i
$296$	0.271460	+	0.470182i	0.0157783	+	0.0273288i
$297$	0.116035	−	3.31459i	0.00673306	−	0.192332i
$298$	−0.744166	+	1.28893i	−0.0431084	+	0.0746659i
$299$	0.0228754	−	0.217645i	0.00132292	−	0.0125867i
$300$	−2.30228	+	7.08570i	−0.132922	+	0.409093i
$301$	−16.5449	−	7.09213i	−0.953635	−	0.408783i
$302$	−0.0831987	+	0.0604474i	−0.00478755	+	0.00347836i
$303$	−14.9109	−	6.63875i	−0.856607	−	0.381386i
$304$	7.24015	+	1.53894i	0.415251	+	0.0882644i
$305$	−3.63036	−	4.03193i	−0.207874	−	0.230868i
$306$	−0.0178295	+	0.169637i	−0.00101925	+	0.00969749i
$307$	27.0171			1.54195			0.770973	−	0.636868i	$-0.219770\pi$
$307$	27.0171			1.54195			0.770973	+	0.636868i	$0.219770\pi$
$308$	16.7662	−	5.05955i	0.955345	−	0.288295i
$309$	1.09367			0.0622165
$310$	−0.0632051	+	0.601356i	−0.00358981	+	0.0341547i
$311$	14.5897	+	16.2035i	0.827307	+	0.918817i	0.997783	−	0.0665442i	$-0.0211974\pi$
$311$	14.5897	+	16.2035i	0.827307	+	0.918817i	−0.170476	+	0.985362i	$0.554531\pi$
$312$	−0.0263274	−	0.00559605i	−0.00149049	−	0.000316814i
$313$	15.3625	+	6.83983i	0.868340	+	0.386610i	0.792036	−	0.610475i	$-0.209021\pi$
$313$	15.3625	+	6.83983i	0.868340	+	0.386610i	0.0763042	+	0.997085i	$0.475688\pi$
$314$	0.830891	−	0.603678i	0.0468899	−	0.0340675i
$315$	2.38471	−	1.78381i	0.134363	−	0.100506i
$316$	7.31773	−	22.5217i	0.411654	−	1.26694i
$317$	1.98666	−	18.9018i	0.111582	−	1.06163i	−0.785226	−	0.619210i	$-0.787453\pi$
$317$	1.98666	−	18.9018i	0.111582	−	1.06163i	0.896807	−	0.442421i	$-0.145880\pi$
$318$	−0.307554	+	0.532699i	−0.0172468	+	0.0298723i
$319$	19.6527	+	7.15492i	1.10034	+	0.400599i
$320$	−4.44568	−	7.70014i	−0.248521	−	0.430451i
$321$	0.505693	+	0.367407i	0.0282250	+	0.0205067i
$322$	−0.361566	+	0.00503114i	−0.0201493	+	0.000280375i
$323$	−1.51337	−	4.65768i	−0.0842062	−	0.259160i
$324$	−1.82325	−	0.811762i	−0.101292	−	0.0450979i
$325$	0.0405249	+	0.385569i	0.00224792	+	0.0213875i
$326$	0.0950859	+	0.0202111i	0.00526632	+	0.00111939i
$327$	−12.9358	+	2.74960i	−0.715353	+	0.152053i
$328$	0.354019	+	0.257210i	0.0195474	+	0.0142020i
$329$	−30.2835	−	5.99782i	−1.66958	−	0.330670i
$330$	−0.106163	+	0.217618i	−0.00584408	+	0.0119795i
$331$	−6.04685	−	10.4734i	−0.332365	−	0.575673i	0.650610	−	0.759412i	$-0.274513\pi$
$331$	−6.04685	−	10.4734i	−0.332365	−	0.575673i	−0.982975	+	0.183739i	$0.941180\pi$
$332$	18.5151	−	8.24344i	1.01615	−	0.452417i
$333$	1.40175	+	1.55680i	0.0768154	+	0.0853121i
$334$	0.546181	−	0.606596i	0.0298857	−	0.0331914i
$335$	−1.73357	+	1.25952i	−0.0947153	+	0.0688147i
$336$	0.953627	−	10.4729i	0.0520246	−	0.571346i
$337$	0.470177	+	1.44706i	0.0256122	+	0.0788262i	0.963046	−	0.269338i	$-0.0868050\pi$
$337$	0.470177	+	1.44706i	0.0256122	+	0.0788262i	−0.937433	+	0.348165i	$0.886805\pi$
$338$	0.824064	−	0.175160i	0.0448231	−	0.00952745i
$339$	1.47777	−	0.657944i	0.0802612	−	0.0357346i
$340$	−2.95394	+	5.11638i	−0.160200	+	0.277475i
$341$	−6.64787	+	26.6533i	−0.360002	+	1.44336i
$342$	−0.120782			−0.00653117
$343$	6.45311	+	17.3596i	0.348435	+	0.937333i
$344$	0.544885	−	1.67698i	0.0293782	−	0.0904169i
$345$	−1.58709	+	1.76265i	−0.0854462	+	0.0948976i
$346$	0.0996043	+	0.947672i	0.00535476	+	0.0509471i
$347$	−1.98109	−	18.8488i	−0.106350	−	1.01186i	−0.909394	−	0.415936i	$-0.863454\pi$
$347$	−1.98109	−	18.8488i	−0.106350	−	1.01186i	0.803044	−	0.595920i	$-0.203213\pi$
$348$	8.42132	−	9.35282i	0.451430	−	0.501364i
$349$	−1.45769	+	4.48630i	−0.0780283	+	0.240146i	−0.982460	−	0.186471i	$-0.940295\pi$
$349$	−1.45769	+	4.48630i	−0.0780283	+	0.240146i	0.904432	+	0.426617i	$0.140295\pi$
$350$	0.624682	−	0.141892i	0.0333907	−	0.00758447i
$351$	−0.103855			−0.00554336
$352$	0.964083	+	2.38678i	0.0513858	+	0.127216i
$353$	15.0020	−	25.9842i	0.798475	−	1.38300i	−0.122134	−	0.992514i	$-0.538974\pi$
$353$	15.0020	−	25.9842i	0.798475	−	1.38300i	0.920609	−	0.390486i	$-0.127693\pi$
$354$	−0.271426	+	0.120846i	−0.0144261	+	0.00642292i
$355$	10.9931	−	2.33665i	0.583452	−	0.124017i
$356$	8.08982	+	24.8979i	0.428760	+	1.31959i
$357$	−6.31641	+	2.91822i	−0.334300	+	0.154449i
$358$	−0.612170	+	0.444768i	−0.0323542	+	0.0235067i
$359$	−8.54388	+	9.48894i	−0.450929	+	0.500807i	−0.925152	−	0.379598i	$-0.876062\pi$
$359$	−8.54388	+	9.48894i	−0.450929	+	0.500807i	0.474223	+	0.880405i	$0.342729\pi$
$360$	0.195196	+	0.216787i	0.0102877	+	0.0114257i
$361$	−14.1893	+	6.31749i	−0.746806	+	0.332500i
$362$	0.224436	+	0.388734i	0.0117961	+	0.0204314i
$363$	−6.15270	+	9.11835i	−0.322933	+	0.478589i
$364$	−0.176703	−	0.519143i	−0.00926173	−	0.0272105i
$365$	9.43800	+	6.85711i	0.494008	+	0.358918i
$366$	0.305797	−	0.0649991i	0.0159843	−	0.00339756i
$367$	−3.74768	−	0.796594i	−0.195627	−	0.0415819i	0.109056	−	0.994036i	$-0.465217\pi$
$367$	−3.74768	−	0.796594i	−0.195627	−	0.0415819i	−0.304683	+	0.952454i	$0.598551\pi$
$368$	0.875497	+	8.32980i	0.0456385	+	0.434221i
$369$	1.54249	+	0.686761i	0.0802988	+	0.0357513i
$370$	−0.0472606	−	0.145453i	−0.00245696	−	0.00756175i
$371$	−25.0891	+	0.349111i	−1.30256	+	0.0181249i
$372$	13.3731	+	9.71615i	0.693365	+	0.503759i
$373$	0.954007	+	1.65239i	0.0493966	+	0.0855575i	0.889667	−	0.456611i	$-0.150937\pi$
$373$	0.954007	+	1.65239i	0.0493966	+	0.0855575i	−0.840270	+	0.542168i	$0.817603\pi$
$374$	0.348331	−	0.445764i	0.0180118	−	0.0230499i
$375$	4.91495	−	8.51294i	0.253807	−	0.439606i
$376$	0.316099	−	3.00748i	0.0163015	−	0.155099i
$377$	0.202378	−	0.622854i	0.0104230	−	0.0320786i
$378$	0.0203101	+	0.170396i	0.00104464	+	0.00876422i
$379$	−11.1049	+	8.06818i	−0.570421	+	0.414435i	−0.835258	−	0.549858i	$-0.814682\pi$
$379$	−11.1049	+	8.06818i	−0.570421	+	0.414435i	0.264837	+	0.964293i	$0.414682\pi$
$380$	−3.82173	−	1.70155i	−0.196051	−	0.0872874i
$381$	17.6114	+	3.74341i	0.902258	+	0.191781i
$382$	−0.472527	−	0.524795i	−0.0241766	−	0.0268508i
$383$	3.18520	−	30.3052i	0.162756	−	1.54852i	−0.542797	−	0.839864i	$-0.682635\pi$
$383$	3.18520	−	30.3052i	0.162756	−	1.54852i	0.705553	−	0.708657i	$-0.250699\pi$
$384$	2.06460			0.105359
$385$	−9.84257	+	0.825163i	−0.501624	+	0.0420542i
$386$	−0.0735524			−0.00374372
$387$	0.711182	−	6.76644i	0.0361514	−	0.343958i
$388$	11.0884	+	12.3149i	0.562929	+	0.625196i
$389$	26.2027	+	5.56955i	1.32853	+	0.282387i	0.816880	−	0.576808i	$-0.195702\pi$
$389$	26.2027	+	5.56955i	1.32853	+	0.282387i	0.511648	+	0.859195i	$0.329035\pi$
$390$	0.00692650	+	0.00308388i	0.000350737	+	0.000156158i
$391$	4.48330	−	3.25731i	0.226730	−	0.164729i
$392$	−1.63614	+	0.783711i	−0.0826376	+	0.0395834i
$393$	−0.538581	+	1.65758i	−0.0271678	+	0.0836139i
$394$	0.117824	−	1.12102i	0.00593587	−	0.0564761i
$395$	−6.67779	+	11.5663i	−0.335996	+	0.581962i
$396$	3.70099	+	5.48797i	0.185982	+	0.275781i
$397$	5.44683	+	9.43418i	0.273368	+	0.473488i	0.969722	−	0.244211i	$-0.0785288\pi$
$397$	5.44683	+	9.43418i	0.273368	+	0.473488i	−0.696354	+	0.717699i	$0.745196\pi$
$398$	−1.18916	−	0.863973i	−0.0596071	−	0.0433071i
$399$	−2.52261	−	4.23219i	−0.126289	−	0.211874i
$400$	−4.58518	−	14.1117i	−0.229259	−	0.705586i
$401$	−15.8473	−	7.05567i	−0.791376	−	0.352343i	−0.0290843	−	0.999577i	$-0.509259\pi$
$401$	−15.8473	−	7.05567i	−0.791376	−	0.352343i	−0.762292	+	0.647234i	$0.775926\pi$
$402$	−0.0129065	−	0.122797i	−0.000643718	−	0.00612457i
$403$	0.841378	+	0.178840i	0.0419120	+	0.00890867i
$404$	31.8634	−	6.77278i	1.58527	−	0.336959i
$405$	0.910629	+	0.661611i	0.0452495	+	0.0328757i
$406$	−1.06150	−	0.210237i	−0.0526815	−	0.0104339i
$407$	−1.20590	−	6.84248i	−0.0597744	−	0.339169i
$408$	−0.340784	−	0.590255i	−0.0168713	−	0.0292220i
$409$	−11.8089	+	5.25766i	−0.583913	+	0.259975i	−0.677363	−	0.735649i	$-0.736877\pi$
$409$	−11.8089	+	5.25766i	−0.583913	+	0.259975i	0.0934498	+	0.995624i	$0.470211\pi$
$410$	−0.0824823	−	0.0916059i	−0.00407351	−	0.00452409i
$411$	−8.59103	+	9.54131i	−0.423765	+	0.470638i
$412$	−1.76587	+	1.28298i	−0.0869980	+	0.0632078i
$413$	−9.90331	−	6.98674i	−0.487310	−	0.343795i
$414$	−0.0422341	−	0.129983i	−0.00207569	−	0.00638833i
$415$	−11.1807	+	2.37653i	−0.548838	+	0.116659i
$416$	0.0736364	−	0.0327850i	0.00361032	−	0.00160742i
$417$	1.41789	−	2.45587i	0.0694346	−	0.120264i
$418$	0.339701	+	0.212310i	0.0166153	+	0.0103844i
$419$	14.1189			0.689755			0.344878	−	0.938648i	$-0.387920\pi$
$419$	14.1189			0.689755			0.344878	+	0.938648i	$0.387920\pi$
$420$	−1.75784	+	5.67769i	−0.0857740	+	0.277043i
$421$	7.57171	−	23.3033i	0.369023	−	1.13573i	−0.578401	−	0.815753i	$-0.696323\pi$
$421$	7.57171	−	23.3033i	0.369023	−	1.13573i	0.947424	−	0.319982i	$-0.103677\pi$
$422$	0.720622	−	0.800332i	0.0350794	−	0.0389596i
$423$	−1.21968	−	11.6045i	−0.0593029	−	0.564229i
$424$	−0.256915	−	2.44438i	−0.0124769	−	0.118710i
$425$	−6.56907	+	7.29570i	−0.318647	+	0.353893i
$426$	−0.200118	+	0.615901i	−0.00969577	+	0.0298405i
$427$	8.66430	+	9.35751i	0.419295	+	0.452841i
$428$	−1.24751			−0.0603008
$429$	0.292092	+	0.182555i	0.0141023	+	0.00881382i
$430$	−0.248355	+	0.430164i	−0.0119768	+	0.0207444i
$431$	−28.8309	+	12.8363i	−1.38873	+	0.618305i	−0.958677	−	0.284497i	$-0.908174\pi$
$431$	−28.8309	+	12.8363i	−1.38873	+	0.618305i	−0.430058	+	0.902801i	$0.641507\pi$
$432$	3.88792	−	0.826403i	0.187058	−	0.0397603i
$433$	−0.101691	−	0.312974i	−0.00488697	−	0.0150405i	0.948583	−	0.316528i	$-0.102517\pi$
$433$	−0.101691	−	0.312974i	−0.00488697	−	0.0150405i	−0.953470	+	0.301487i	$0.902517\pi$
$434$	0.128884	−	1.41543i	0.00618663	−	0.0679430i
$435$	−5.74242	+	4.17211i	−0.275328	+	0.200038i
$436$	17.6610	−	19.6146i	0.845811	−	0.939368i
$437$	2.62572	+	2.91616i	0.125605	+	0.139499i
$438$	−0.614104	+	0.273417i	−0.0293430	+	0.0130644i
$439$	19.6642	+	34.0594i	0.938521	+	1.62557i	0.768231	+	0.640172i	$0.221137\pi$
$439$	19.6642	+	34.0594i	0.938521	+	1.62557i	0.170290	+	0.985394i	$0.445530\pi$
$440$	−0.167924	−	0.952829i	−0.00800548	−	0.0454243i
$441$	−5.54644	+	4.27048i	−0.264116	+	0.203356i
$442$	−0.0143314	−	0.0104124i	−0.000681677	−	0.000495268i
$443$	12.5319	−	2.66373i	0.595407	−	0.126558i	0.0996552	−	0.995022i	$-0.468226\pi$
$443$	12.5319	−	2.66373i	0.595407	−	0.126558i	0.495751	+	0.868464i	$0.334893\pi$
$444$	−4.08958	−	0.869268i	−0.194083	−	0.0412536i
$445$	−1.54333	−	14.6838i	−0.0731610	−	0.696081i
$446$	−0.0963958	−	0.0429182i	−0.00456447	−	0.00203223i
$447$	−7.09102	−	21.8239i	−0.335394	−	1.03224i
$448$	10.7005	+	17.9522i	0.505551	+	0.848163i
$449$	−22.9052	−	16.6416i	−1.08096	−	0.785365i	−0.103112	−	0.994670i	$-0.532880\pi$
$449$	−22.9052	−	16.6416i	−1.08096	−	0.785365i	−0.977850	+	0.209305i	$0.932880\pi$
$450$	0.121061	+	0.209684i	0.00570687	+	0.00988459i
$451$	−3.13108	−	4.64289i	−0.147437	−	0.218625i
$452$	−1.61421	+	2.79590i	−0.0759262	+	0.131508i
$453$	0.165737	−	1.57688i	0.00778701	−	0.0740885i
$454$	0.00134694	−	0.00414546i	6.32151e−5	−	0.000194556i
$455$	0.0366057	+	0.307112i	0.00171610	+	0.0143976i
$456$	0.390449	−	0.283678i	0.0182845	−	0.0132844i
$457$	−7.69746	−	3.42713i	−0.360072	−	0.160314i	0.218724	−	0.975787i	$-0.429811\pi$
$457$	−7.69746	−	3.42713i	−0.360072	−	0.160314i	−0.578796	+	0.815472i	$0.696477\pi$
$458$	0.163956	+	0.0348499i	0.00766115	+	0.00162843i
$459$	−1.75972	−	1.95437i	−0.0821366	−	0.0912220i
$460$	0.494814	−	4.70784i	0.0230708	−	0.219504i
$461$	3.62573			0.168867			0.0844336	−	0.996429i	$-0.473092\pi$
$461$	3.62573			0.168867			0.0844336	+	0.996429i	$0.473092\pi$
$462$	0.242397	−	0.514940i	0.0112774	−	0.0239572i
$463$	23.3336			1.08440			0.542201	−	0.840249i	$-0.317591\pi$
$463$	23.3336			1.08440			0.542201	+	0.840249i	$0.317591\pi$
$464$	−2.62000	+	24.9276i	−0.121630	+	1.15724i
$465$	−6.23814	−	6.92815i	−0.289287	−	0.321285i
$466$	−0.967457	−	0.205639i	−0.0448166	−	0.00952605i
$467$	−11.0626	−	4.92538i	−0.511915	−	0.227919i	0.134488	−	0.990915i	$-0.457061\pi$
$467$	−11.0626	−	4.92538i	−0.511915	−	0.227919i	−0.646403	+	0.762996i	$0.723728\pi$
$468$	0.167687	−	0.121832i	0.00775134	−	0.00563168i
$469$	4.03322	−	3.01693i	0.186237	−	0.139309i
$470$	−0.263240	+	0.810169i	−0.0121423	+	0.0373703i
$471$	−1.65519	+	15.7481i	−0.0762671	+	0.725633i
$472$	0.593600	−	1.02814i	0.0273226	−	0.0473242i
$473$	−13.8942	+	17.7805i	−0.638854	+	0.817550i
$474$	−0.384788	−	0.666473i	−0.0176739	−	0.0306121i
$475$	−5.62405	−	4.08611i	−0.258049	−	0.187484i
$476$	6.77532	−	12.1216i	0.310546	−	0.555593i
$477$	−2.93062	−	9.01953i	−0.134184	−	0.412976i
$478$	0.337267	+	0.150161i	0.0154262	+	0.00686820i
$479$	−1.67664	−	15.9522i	−0.0766077	−	0.728873i	−0.963647	−	0.267179i	$-0.913908\pi$
$479$	−1.67664	−	15.9522i	−0.0766077	−	0.728873i	0.887039	−	0.461694i	$-0.152758\pi$
$480$	−0.854524	−	0.181635i	−0.0390035	−	0.00829045i
$481$	−0.212809	+	0.0452340i	−0.00970326	+	0.00206249i
$482$	−1.10366	−	0.801856i	−0.0502704	−	0.0365236i
$483$	3.67250	−	4.19465i	0.167104	−	0.190863i
$484$	−0.762376	−	21.9405i	−0.0346534	−	0.997295i
$485$	−4.67301	−	8.09389i	−0.212191	−	0.367525i
$486$	−0.0592521	+	0.0263807i	−0.00268773	+	0.00119665i
$487$	22.8566	+	25.3848i	1.03573	+	1.15030i	0.988470	+	0.151414i	$0.0483825\pi$
$487$	22.8566	+	25.3848i	1.03573	+	1.15030i	0.0472609	+	0.998883i	$0.484951\pi$
$488$	−0.835878	+	0.928336i	−0.0378384	+	0.0420238i
$489$	−1.21254	+	0.880962i	−0.0548329	+	0.0398385i
$490$	0.496723	−	0.120119i	0.0224397	−	0.00542642i
$491$	−1.28817	−	3.96458i	−0.0581343	−	0.178919i	0.917773	−	0.397106i	$-0.129986\pi$
$491$	−1.28817	−	3.96458i	−0.0581343	−	0.178919i	−0.975907	+	0.218187i	$0.929986\pi$
$492$	−3.29619	+	0.700627i	−0.148604	+	0.0315867i
$493$	15.1501	−	6.74527i	0.682327	−	0.303792i
$494$	0.00627192	−	0.0108633i	0.000282187	−	0.000488762i
$495$	−1.39818	−	3.46148i	−0.0628435	−	0.155582i
$496$	−32.9210			−1.47820
$497$	−25.7606	+	5.85135i	−1.15552	+	0.262469i
$498$	0.203533	−	0.626411i	0.00912054	−	0.0280701i
$499$	−21.4451	+	23.8172i	−0.960014	+	1.06620i	0.0377449	+	0.999287i	$0.487983\pi$
$499$	−21.4451	+	23.8172i	−0.960014	+	1.06620i	−0.997759	+	0.0669159i	$0.978684\pi$
$500$	2.05068	+	19.5110i	0.0917094	+	0.872557i
$501$	1.31549	+	12.5160i	0.0587717	+	0.559175i
$502$	1.11322	−	1.23636i	0.0496857	−	0.0551815i
$503$	0.570112	−	1.75462i	0.0254200	−	0.0782348i	−0.937542	−	0.347873i	$-0.886904\pi$
$503$	0.570112	−	1.75462i	0.0254200	−	0.0782348i	0.962962	+	0.269638i	$0.0869041\pi$
$504$	−0.465859	−	0.503131i	−0.0207510	−	0.0224112i
$505$	−18.3720			−0.817544
$506$	−0.109699	+	0.439817i	−0.00487672	+	0.0195522i
$507$	−6.49461	+	11.2490i	−0.288436	+	0.499585i
$508$	−32.8272	+	14.6156i	−1.45647	+	0.648464i
$509$	−16.8277	+	3.57685i	−0.745876	+	0.158541i	−0.565145	−	0.824992i	$-0.691180\pi$
$509$	−16.8277	+	3.57685i	−0.745876	+	0.158541i	−0.180731	+	0.983532i	$0.557846\pi$
$510$	0.0593297	+	0.182598i	0.00262716	+	0.00808558i
$511$	−22.4064	−	15.8076i	−0.991199	−	0.699287i
$512$	−4.16255	+	3.02427i	−0.183961	+	0.133655i
$513$	1.24607	−	1.38390i	0.0550152	−	0.0611006i
$514$	−0.00954223	−	0.0105977i	−0.000420890	−	0.000467445i
$515$	1.12460	−	0.500705i	0.0495559	−	0.0220637i
$516$	6.78940	+	11.7596i	0.298887	+	0.517687i
$517$	−16.9679	+	34.7816i	−0.746245	+	1.52969i
$518$	0.115833	+	0.340313i	0.00508943	+	0.0149525i
$519$	−11.8858	−	8.63553i	−0.521728	−	0.379058i
$520$	−0.0296341	+	0.00629892i	−0.00129954	+	0.000276226i
$521$	−8.36792	−	1.77866i	−0.366605	−	0.0779243i	0.0209258	−	0.999781i	$-0.493339\pi$
$521$	−8.36792	−	1.77866i	−0.366605	−	0.0779243i	−0.387531	+	0.921857i	$0.626672\pi$
$522$	−0.0427525	−	0.406763i	−0.00187123	−	0.0178035i
$523$	−7.39566	−	3.29276i	−0.323390	−	0.143982i	0.238620	−	0.971113i	$-0.423305\pi$
$523$	−7.39566	−	3.29276i	−0.323390	−	0.143982i	−0.562010	+	0.827131i	$0.689972\pi$
$524$	−1.07490	−	3.30819i	−0.0469570	−	0.144519i
$525$	−4.81884	+	8.62132i	−0.210311	+	0.376265i
$526$	1.16661	+	0.847592i	0.0508666	+	0.0369568i
$527$	10.8909	+	18.8635i	0.474414	+	0.821708i
$528$	−12.3874	−	4.50987i	−0.539094	−	0.196267i
$529$	9.27984	−	16.0731i	0.403471	−	0.698833i
$530$	−0.0723719	+	0.688572i	−0.00314363	+	0.0299097i
$531$	1.41556	−	4.35666i	0.0614302	−	0.189063i
$532$	9.03786	+	3.87415i	0.391841	+	0.167966i
$533$	−0.141865	+	0.103071i	−0.00614487	+	0.00446451i
$534$	0.777221	+	0.346041i	0.0336337	+	0.0149747i
$535$	0.688205	+	0.146282i	0.0297537	+	0.00632434i
$536$	0.330132	+	0.366649i	0.0142595	+	0.0158368i
$537$	1.21948	−	11.6026i	0.0526246	−	0.500689i
$538$	−0.962681			−0.0415041
$539$	23.1060	−	2.26127i	0.995245	−	0.0973999i
$540$	−2.24646			−0.0966725
$541$	1.65709	−	15.7662i	0.0712440	−	0.677841i	−0.899368	−	0.437192i	$-0.855973\pi$
$541$	1.65709	−	15.7662i	0.0712440	−	0.677841i	0.970612	−	0.240649i	$-0.0773604\pi$
$542$	0.970081	+	1.07738i	0.0416686	+	0.0462776i
$543$	−6.76944	−	1.43889i	−0.290505	−	0.0617487i
$544$	1.86465	+	0.830197i	0.0799464	+	0.0355944i
$545$	−12.0429	+	8.74969i	−0.515862	+	0.374796i
$546$	−0.0163802	−	0.00702151i	−0.000701008	−	0.000300493i
$547$	−13.3975	+	41.2332i	−0.572835	+	1.76300i	0.0706013	+	0.997505i	$0.477508\pi$
$547$	−13.3975	+	41.2332i	−0.572835	+	1.76300i	−0.643436	+	0.765500i	$0.722492\pi$
$548$	2.67846	−	25.4838i	0.114418	−	1.08861i
$549$	−2.41005	+	4.17432i	−0.102858	+	0.178156i
$550$	0.0280947	−	0.802536i	0.00119796	−	0.0342203i
$551$	5.87157	+	10.1699i	0.250137	+	0.433250i
$552$	0.441816	+	0.320998i	0.0188049	+	0.0136626i
$553$	15.3165	−	27.4026i	0.651325	−	1.16528i
$554$	0.0789207	+	0.242893i	0.00335302	+	0.0103195i
$555$	2.15414	+	0.959084i	0.0914381	+	0.0407108i
$556$	0.591595	+	5.62865i	0.0250892	+	0.238708i
$557$	2.52890	+	0.537534i	0.107153	+	0.0227761i	0.261176	−	0.965291i	$-0.415890\pi$
$557$	2.52890	+	0.537534i	0.107153	+	0.0227761i	−0.154023	+	0.988067i	$0.549223\pi$
$558$	0.525458	−	0.111690i	0.0222444	−	0.00472819i
$559$	0.571650	+	0.415328i	0.0241782	+	0.0175665i
$560$	−3.81415	−	11.2058i	−0.161177	−	0.473531i
$561$	1.51386	+	8.58987i	0.0639152	+	0.362665i
$562$	0.895577	+	1.55118i	0.0377776	+	0.0654328i
$563$	−21.7630	+	9.68953i	−0.917203	+	0.408365i	−0.810374	−	0.585912i	$-0.800736\pi$
$563$	−21.7630	+	9.68953i	−0.917203	+	0.408365i	−0.106829	+	0.994277i	$0.534070\pi$
$564$	15.5825	+	17.3062i	0.656143	+	0.728721i
$565$	1.21835	−	1.35311i	0.0512562	−	0.0569258i
$566$	−1.49430	+	1.08567i	−0.0628101	+	0.0456342i
$567$	−2.16189	−	1.52520i	−0.0907908	−	0.0640525i
$568$	−0.799632	−	2.46101i	−0.0335518	−	0.103262i
$569$	19.1985	−	4.08076i	0.804842	−	0.171074i	0.212920	−	0.977070i	$-0.431703\pi$
$569$	19.1985	−	4.08076i	0.804842	−	0.171074i	0.591922	+	0.805995i	$0.298369\pi$
$570$	−0.124199	+	0.0552970i	−0.00520212	+	0.00231614i
$571$	13.5113	−	23.4022i	0.565430	−	0.979353i	−0.431580	−	0.902075i	$-0.642044\pi$
$571$	13.5113	−	23.4022i	0.565430	−	0.979353i	0.997010	−	0.0772782i	$-0.0246230\pi$
$572$	−0.685775	+	0.0478944i	−0.0286737	+	0.00200257i
$573$	10.8879			0.454847
$574$	0.196854	+	0.212604i	0.00821652	+	0.00887390i
$575$	2.43081	−	7.48126i	0.101372	−	0.311990i
$576$	−5.28561	+	5.87026i	−0.220234	+	0.244594i
$577$	−3.13116	−	29.7910i	−0.130352	−	1.24022i	−0.842698	−	0.538387i	$-0.819034\pi$
$577$	−3.13116	−	29.7910i	−0.130352	−	1.24022i	0.712346	−	0.701829i	$-0.247633\pi$
$578$	0.0683651	+	0.650450i	0.00284361	+	0.0270552i
$579$	0.758813	−	0.842747i	0.0315352	−	0.0350234i
$580$	4.37759	−	13.4728i	0.181770	−	0.559430i
$581$	26.2002	−	5.95120i	1.08697	−	0.246897i
$582$	0.538538			0.0223231
$583$	−7.61202	+	30.5189i	−0.315258	+	1.26396i
$584$	1.34303	−	2.32619i	0.0555749	−	0.0962585i
$585$	−0.106792	+	0.0475471i	−0.00441533	+	0.00196583i
$586$	−2.10115	+	0.446613i	−0.0867977	+	0.0184494i
$587$	−7.17603	−	22.0855i	−0.296186	−	0.911568i	−0.982820	−	0.184565i	$-0.940912\pi$
$587$	−7.17603	−	22.0855i	−0.296186	−	0.911568i	0.686634	−	0.727003i	$-0.259088\pi$
$588$	3.94577	−	13.4018i	0.162721	−	0.552679i
$589$	−12.4781	+	9.06587i	−0.514151	+	0.373552i
$590$	−0.223777	+	0.248530i	−0.00921275	+	0.0102318i
$591$	11.6288	+	12.9151i	0.478346	+	0.531257i
$592$	7.60680	−	3.38677i	0.312638	−	0.139195i
$593$	11.6687	+	20.2107i	0.479174	+	0.829955i	0.999715	−	0.0238826i	$-0.00760278\pi$
$593$	11.6687	+	20.2107i	0.479174	+	0.829955i	−0.520540	+	0.853837i	$0.674269\pi$
$594$	0.213018	+	0.0299566i	0.00874025	+	0.00122913i
$595$	−5.15906	+	5.89256i	−0.211501	+	0.241572i
$596$	37.0510	+	26.9191i	1.51767	+	1.10265i
$597$	22.1673	−	4.71180i	0.907247	−	0.192841i
$598$	0.0138839	+	0.00295112i	0.000567755	+	0.000120680i
$599$	−3.12284	−	29.7119i	−0.127596	−	1.21399i	−0.851598	−	0.524196i	$-0.824366\pi$
$599$	−3.12284	−	29.7119i	−0.127596	−	1.21399i	0.724002	−	0.689798i	$-0.242301\pi$
$600$	−0.883827	−	0.393505i	−0.0360821	−	0.0160648i
$601$	−5.83639	−	17.9626i	−0.238071	−	0.732708i	−0.996699	−	0.0811840i	$-0.974130\pi$
$601$	−5.83639	−	17.9626i	−0.238071	−	0.732708i	0.758628	−	0.651524i	$-0.225870\pi$
$602$	0.569641	−	1.01914i	0.0232168	−	0.0415369i
$603$	1.54013	+	1.11897i	0.0627191	+	0.0455681i
$604$	1.58224	+	2.74051i	0.0643802	+	0.111510i
$605$	−2.15215	+	12.1931i	−0.0874975	+	0.495721i
$606$	0.529317	−	0.916805i	0.0215021	−	0.0372426i
$607$	−1.25463	+	11.9370i	−0.0509238	+	0.484508i	0.939104	+	0.343634i	$0.111658\pi$
$607$	−1.25463	+	11.9370i	−0.0509238	+	0.484508i	−0.990028	+	0.140874i	$0.955009\pi$
$608$	−0.446631	+	1.37459i	−0.0181133	+	0.0557469i
$609$	13.3600	−	9.99351i	0.541373	−	0.404958i
$610$	0.284689	−	0.206839i	0.0115267	−	0.00837465i
$611$	1.10705	+	0.492892i	0.0447866	+	0.0199403i
$612$	5.13396	+	1.09126i	0.207528	+	0.0441114i
$613$	−31.1926	−	34.6428i	−1.25986	−	1.39921i	−0.880559	−	0.473936i	$-0.842833\pi$
$613$	−31.1926	−	34.6428i	−1.25986	−	1.39921i	−0.379296	−	0.925275i	$-0.623834\pi$
$614$	−0.183167	+	1.74271i	−0.00739200	+	0.0703302i
$615$	1.90054			0.0766371
$616$	0.425834	+	2.23394i	0.0171573	+	0.0900080i
$617$	−16.5232			−0.665198			−0.332599	−	0.943068i	$-0.607926\pi$
$617$	−16.5232			−0.665198			−0.332599	+	0.943068i	$0.607926\pi$
$618$	−0.00741469	+	0.0705460i	−0.000298262	+	0.00283778i
$619$	−16.6468	−	18.4881i	−0.669090	−	0.743099i	0.309051	−	0.951046i	$-0.399989\pi$
$619$	−16.6468	−	18.4881i	−0.669090	−	0.743099i	−0.978140	+	0.207946i	$0.933322\pi$
$620$	18.1997	+	3.86846i	0.730917	+	0.155361i
$621$	1.92503	+	0.857079i	0.0772488	+	0.0343934i
$622$	−1.14411	+	0.831243i	−0.0458746	+	0.0333298i
$623$	4.10751	+	34.4609i	0.164564	+	1.38065i
$624$	−0.127562	+	0.392596i	−0.00510657	+	0.0157164i
$625$	−0.794479	+	7.55896i	−0.0317792	+	0.302358i
$626$	−0.545350	+	0.944574i	−0.0217966	+	0.0377528i
$627$	−5.93717	+	1.70190i	−0.237108	+	0.0679673i
$628$	−15.8015	−	27.3690i	−0.630549	−	1.09214i
$629$	−4.45707	−	3.23825i	−0.177715	−	0.129117i
$630$	0.0988957	+	0.165917i	0.00394010	+	0.00661031i
$631$	−2.70286	−	8.31855i	−0.107599	−	0.331156i	0.882733	−	0.469876i	$-0.155701\pi$
$631$	−2.70286	−	8.31855i	−0.107599	−	0.331156i	−0.990332	+	0.138720i	$0.955701\pi$
$632$	2.80922	+	1.25074i	0.111745	+	0.0497519i
$633$	1.73563	+	16.5135i	0.0689852	+	0.656351i
$634$	1.20578	+	0.256296i	0.0478875	+	0.0101788i
$635$	19.8234	−	4.21358i	0.786666	−	0.167211i
$636$	15.3127	+	11.1253i	0.607187	+	0.441147i
$637$	−0.0960781	−	0.720607i	−0.00380675	−	0.0285515i
$638$	−0.594761	+	1.21917i	−0.0235468	+	0.0482675i
$639$	−4.99231	−	8.64693i	−0.197493	−	0.342067i
$640$	2.12300	−	0.945222i	0.0839191	−	0.0373632i
$641$	18.8869	+	20.9760i	0.745987	+	0.828502i	0.989970	−	0.141277i	$-0.0451209\pi$
$641$	18.8869	+	20.9760i	0.745987	+	0.828502i	−0.243983	+	0.969779i	$0.578454\pi$
$642$	−0.0271277	+	0.0301284i	−0.00107065	+	0.00118907i
$643$	−6.28257	+	4.56455i	−0.247760	+	0.180008i	−0.704734	−	0.709472i	$-0.748933\pi$
$643$	−6.28257	+	4.56455i	−0.247760	+	0.180008i	0.456973	+	0.889480i	$0.348933\pi$
$644$	−1.00899	+	11.0810i	−0.0397599	+	0.436653i
$645$	−2.36653	−	7.28344i	−0.0931821	−	0.286785i
$646$	0.310700	−	0.0660412i	0.0122243	−	0.00259836i
$647$	27.0867	−	12.0598i	1.06489	−	0.474119i	0.201934	−	0.979399i	$-0.435278\pi$
$647$	27.0867	−	12.0598i	1.06489	−	0.474119i	0.862955	+	0.505280i	$0.168611\pi$
$648$	0.129583	−	0.224444i	0.00509048	−	0.00881697i
$649$	−11.6394	+	9.76486i	−0.456885	+	0.383304i
$650$	−0.0251455			−0.000986289
$651$	14.8881	+	16.0792i	0.583509	+	0.630194i
$652$	0.924350	−	2.84486i	0.0362003	−	0.111413i
$653$	18.3858	−	20.4195i	0.719491	−	0.799076i	−0.266860	−	0.963735i	$-0.585986\pi$
$653$	18.3858	−	20.4195i	0.719491	−	0.799076i	0.986350	+	0.164660i	$0.0526526\pi$
$654$	−0.0896598	−	0.853056i	−0.00350598	−	0.0333571i
$655$	0.205063	+	1.95104i	0.00801247	+	0.0762336i
$656$	4.49072	−	4.98745i	0.175333	−	0.194727i
$657$	3.20273	−	9.85700i	0.124951	−	0.384558i
$658$	0.592196	−	1.91275i	0.0230862	−	0.0745666i
$659$	−20.2452			−0.788639			−0.394320	−	0.918973i	$-0.629020\pi$
$659$	−20.2452			−0.788639			−0.394320	+	0.918973i	$0.629020\pi$
$660$	6.31819	+	3.94881i	0.245935	+	0.153707i
$661$	4.33424	−	7.50713i	0.168583	−	0.291993i	−0.769339	−	0.638841i	$-0.779414\pi$
$661$	4.33424	−	7.50713i	0.168583	−	0.291993i	0.937922	+	0.346847i	$0.112748\pi$
$662$	0.716577	−	0.319040i	0.0278505	−	0.0123999i
$663$	0.267155	−	0.0567855i	0.0103754	−	0.00220537i
$664$	0.813277	+	2.50301i	0.0315613	+	0.0971355i
$665$	−4.53156	−	3.19699i	−0.175726	−	0.123974i
$666$	−0.109923	+	0.0798641i	−0.00425945	+	0.00309467i
$667$	−8.89144	+	9.87494i	−0.344278	+	0.382359i
$668$	−16.8066	−	18.6656i	−0.650265	−	0.722193i
$669$	1.48623	−	0.661710i	0.0574608	−	0.0255832i
$670$	−0.0694909	−	0.120362i	−0.00268467	−	0.00464998i
$671$	14.1158	−	7.50396i	0.544936	−	0.289687i
$672$	2.01433	+	0.398949i	0.0777043	+	0.0153898i
$673$	31.5240	+	22.9035i	1.21516	+	0.882867i	0.995689	−	0.0927522i	$-0.0295664\pi$
$673$	31.5240	+	22.9035i	1.21516	+	0.882867i	0.219472	+	0.975619i	$0.429566\pi$
$674$	−0.0965289	+	0.0205178i	−0.00371815	+	0.000790318i
$675$	−3.65145	−	0.776139i	−0.140544	−	0.0298736i
$676$	−2.70977	−	25.7818i	−0.104222	−	0.991607i
$677$	−23.3343	−	10.3891i	−0.896811	−	0.399286i	−0.0940364	−	0.995569i	$-0.529977\pi$
$677$	−23.3343	−	10.3891i	−0.896811	−	0.399286i	−0.802774	+	0.596283i	$0.796644\pi$
$678$	0.0324214	+	0.0997827i	0.00124513	+	0.00383213i
$679$	11.2477	+	18.8702i	0.431646	+	0.724173i
$680$	−0.620655	−	0.450933i	−0.0238010	−	0.0172925i
$681$	0.0336018	+	0.0582001i	0.00128762	+	0.00223023i
$682$	−1.67418	−	0.609516i	−0.0641076	−	0.0233396i
$683$	−8.29394	+	14.3655i	−0.317359	+	0.549682i	−0.979936	−	0.199312i	$-0.936129\pi$
$683$	−8.29394	+	14.3655i	−0.317359	+	0.549682i	0.662577	+	0.748994i	$0.269463\pi$
$684$	−0.388491	+	3.69624i	−0.0148543	+	0.141329i
$685$	−4.46582	+	13.7444i	−0.170630	+	0.525146i
$686$	−1.16352	+	0.298560i	−0.0444234	+	0.0113991i
$687$	−2.09077	+	1.51903i	−0.0797679	+	0.0579548i
$688$	−24.7052	−	10.9995i	−0.941878	−	0.419351i
$689$	0.963405	+	0.204778i	0.0367028	+	0.00780142i
$690$	−0.102938	−	0.114324i	−0.00391878	−	0.00435225i
$691$	5.14374	−	48.9394i	0.195677	−	1.86174i	−0.252237	−	0.967665i	$-0.581166\pi$
$691$	5.14374	−	48.9394i	0.195677	−	1.86174i	0.447914	−	0.894077i	$-0.352167\pi$
$692$	29.3215			1.11463
$693$	3.39934	+	8.08978i	0.129130	+	0.307305i
$694$	1.22926			0.0466619
$695$	0.333651	−	3.17448i	0.0126561	−	0.120415i
$696$	1.09356	+	1.21452i	0.0414511	+	0.0460361i
$697$	−4.34339	−	0.923217i	−0.164518	−	0.0349693i
$698$	−0.279503	−	0.124443i	−0.0105793	−	0.00471022i
$699$	12.3370	−	8.96339i	0.466630	−	0.339027i
$700$	−2.33300	−	19.5732i	−0.0881790	−	0.739798i
$701$	−14.6308	+	45.0291i	−0.552599	+	1.70073i	0.149601	+	0.988746i	$0.452201\pi$
$701$	−14.6308	+	45.0291i	−0.552599	+	1.70073i	−0.702200	+	0.711979i	$0.747799\pi$
$702$	0.000704100	−	0.00669907i	2.65746e−5	−	0.000252840i
$703$	1.95056	−	3.37847i	0.0735669	−	0.127422i
$704$	25.1845	−	7.21917i	0.949175	−	0.272083i
$705$	−6.56698	−	11.3743i	−0.247327	−	0.428383i
$706$	1.57438	+	1.14385i	0.0592526	+	0.0430495i
$707$	43.1797	−	0.600840i	1.62394	−	0.0225969i
$708$	2.82517	+	8.69499i	0.106177	+	0.326778i
$709$	−6.14483	−	2.73585i	−0.230774	−	0.102747i	0.288092	−	0.957603i	$-0.406979\pi$
$709$	−6.14483	−	2.73585i	−0.230774	−	0.102747i	−0.518866	+	0.854856i	$0.673646\pi$
$710$	0.0761944	+	0.724942i	0.00285953	+	0.0272066i
$711$	11.6060	+	2.46693i	0.435259	+	0.0925172i
$712$	−3.32523	+	0.706800i	−0.124618	+	0.0264884i
$713$	−14.1197	−	10.2586i	−0.528787	−	0.384186i
$714$	−0.145414	−	0.427220i	−0.00544199	−	0.0159883i
$715$	0.383932	+	0.0539920i	0.0143582	+	0.00201919i
$716$	11.6420	+	20.1645i	0.435081	+	0.753583i
$717$	−5.19996	+	2.31517i	−0.194196	+	0.0864617i
$718$	−0.554151	−	0.615448i	−0.0206807	−	0.0229683i
$719$	−21.2134	+	23.5599i	−0.791127	+	0.878636i	−0.994950	−	0.100372i	$-0.967997\pi$
$719$	−21.2134	+	23.5599i	−0.791127	+	0.878636i	0.203823	+	0.979008i	$0.434663\pi$
$720$	3.61955	−	2.62976i	0.134893	−	0.0980052i
$721$	−2.62678	+	1.21359i	−0.0978262	+	0.0451963i
$722$	−0.311306	−	0.958101i	−0.0115856	−	0.0356568i
$723$	20.5735	−	4.37304i	0.765138	−	0.162635i
$724$	12.6181	−	5.61794i	0.468948	−	0.208789i
$725$	11.7702	−	20.3866i	0.437135	−	0.757140i
$726$	−0.546458	−	0.458694i	−0.0202810	−	0.0170237i
$727$	8.98538			0.333249			0.166625	−	0.986020i	$-0.446713\pi$
$727$	8.98538			0.333249			0.166625	+	0.986020i	$0.446713\pi$
$728$	0.0694429	−	0.0157735i	0.00257373	−	0.000584604i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−0.506299	+	0.562302i	−0.0187390	+	0.0208117i
$731$	1.87031	+	17.7948i	0.0691758	+	0.658164i
$732$	−1.00555	−	9.56721i	−0.0371663	−	0.353614i
$733$	−4.92798	+	5.47308i	−0.182019	+	0.202153i	−0.827249	−	0.561836i	$-0.810095\pi$
$733$	−4.92798	+	5.47308i	−0.182019	+	0.202153i	0.645229	+	0.763989i	$0.276762\pi$
$734$	0.0767916	−	0.236340i	0.00283443	−	0.00872348i
$735$	−3.74821	+	6.93056i	−0.138255	+	0.255638i
$736$	−1.63547			−0.0602843
$737$	−2.36472	−	5.85434i	−0.0871055	−	0.215647i
$738$	−0.0547565	+	0.0948411i	−0.00201561	+	0.00349115i
$739$	9.00239	−	4.00812i	0.331158	−	0.147441i	−0.234421	−	0.972135i	$-0.575319\pi$
$739$	9.00239	−	4.00812i	0.331158	−	0.147441i	0.565579	+	0.824694i	$0.308653\pi$
$740$	−4.60324	+	0.978448i	−0.169218	+	0.0359685i
$741$	0.0597640	+	0.183935i	0.00219548	+	0.00675701i
$742$	0.147576	−	1.62072i	0.00541770	−	0.0594984i
$743$	39.7414	−	28.8738i	1.45797	−	1.05928i	0.474086	−	0.880478i	$-0.342778\pi$
$743$	39.7414	−	28.8738i	1.45797	−	1.05928i	0.983885	−	0.178800i	$-0.0572216\pi$
$744$	−1.43631	+	1.59518i	−0.0526576	+	0.0584822i
$745$	−17.2831	−	19.1948i	−0.633203	−	0.703243i
$746$	−0.113054	+	0.0503348i	−0.00413920	+	0.00184289i
$747$	5.07749	+	8.79448i	0.185776	+	0.321773i
$748$	−12.5211	−	12.0936i	−0.457816	−	0.442185i
$749$	−1.62227	−	0.321300i	−0.0592764	−	0.0117401i
$750$	0.515798	+	0.374749i	0.0188343	+	0.0136839i
$751$	10.7192	−	2.27845i	0.391151	−	0.0831416i	−0.00813803	−	0.999967i	$-0.502590\pi$
$751$	10.7192	−	2.27845i	0.391151	−	0.0831416i	0.399289	+	0.916825i	$0.369257\pi$
$752$	−45.3658	−	9.64280i	−1.65432	−	0.351637i
$753$	2.68122	+	25.5101i	0.0977092	+	0.929641i
$754$	0.0388046	+	0.0172769i	0.00141318	+	0.000629189i
$755$	−0.551508	−	1.69737i	−0.0200714	−	0.0617735i
$756$	5.27986	−	0.0734685i	0.192027	−	0.00267202i
$757$	31.0768	+	22.5786i	1.12950	+	0.820633i	0.985623	−	0.168961i	$-0.0540413\pi$
$757$	31.0768	+	22.5786i	1.12950	+	0.820633i	0.143882	+	0.989595i	$0.454041\pi$
$758$	−0.445144	−	0.771012i	−0.0161684	−	0.0280044i
$759$	−3.90760	−	5.79433i	−0.141837	−	0.210321i
$760$	0.271620	−	0.470459i	0.00985268	−	0.0170653i
$761$	5.28252	−	50.2598i	0.191491	−	1.82192i	−0.303289	−	0.952899i	$-0.598085\pi$
$761$	5.28252	−	50.2598i	0.191491	−	1.82192i	0.494780	−	0.869018i	$-0.335249\pi$
$762$	−0.360865	+	1.11063i	−0.0130728	+	0.0402338i
$763$	28.0183	−	20.9582i	1.01433	−	0.758739i
$764$	−17.5799	+	12.7725i	−0.636017	+	0.462094i
$765$	−2.70425	−	1.20401i	−0.0977723	−	0.0435310i
$766$	1.93321	+	0.410917i	0.0698499	+	0.0148470i
$767$	0.318335	+	0.353547i	0.0114944	+	0.0127658i
$768$	1.63739	−	15.5787i	0.0590842	−	0.562148i
$769$	−15.2003			−0.548137			−0.274068	−	0.961710i	$-0.588369\pi$
$769$	−15.2003			−0.548137			−0.274068	+	0.961710i	$0.588369\pi$
$770$	0.0135028	−	0.640481i	0.000486608	−	0.0230813i
$771$	0.219870			0.00791842
$772$	−0.236578	+	2.25089i	−0.00851462	+	0.0810112i
$773$	9.05687	+	10.0587i	0.325753	+	0.361785i	0.883669	−	0.468112i	$-0.155066\pi$
$773$	9.05687	+	10.0587i	0.325753	+	0.361785i	−0.557916	+	0.829897i	$0.688399\pi$
$774$	0.431642	+	0.0917484i	0.0155151	+	0.00329783i
$775$	28.2456	+	12.5758i	1.01461	+	0.451735i
$776$	−1.74091	+	1.26485i	−0.0624951	+	0.0454054i
$777$	−5.09423	−	2.18368i	−0.182755	−	0.0783392i
$778$	−0.536904	+	1.65242i	−0.0192490	+	0.0592422i
$779$	0.328668	−	3.12707i	0.0117758	−	0.112039i
$780$	0.116653	−	0.202049i	0.00417685	−	0.00723452i
$781$	−1.15857	+	33.0949i	−0.0414569	+	1.18423i
$782$	0.179715	+	0.311275i	0.00642658	+	0.0111312i
$783$	5.10166	+	3.70657i	0.182318	+	0.132462i
$784$	9.33087	+	26.2122i	0.333245	+	0.936150i
$785$	5.50781	+	16.9513i	0.196582	+	0.605018i
$786$	−0.103269	−	0.0459785i	−0.00368350	−	0.00164000i
$787$	−2.65957	−	25.3041i	−0.0948033	−	0.901993i	−0.933785	−	0.357834i	$-0.883515\pi$
$787$	−2.65957	−	25.3041i	−0.0948033	−	0.901993i	0.838982	−	0.544159i	$-0.183151\pi$
$788$	−33.9269	−	7.21139i	−1.20860	−	0.256895i
$789$	−21.7470	+	4.62246i	−0.774213	+	0.164564i
$790$	−0.700799	−	0.509160i	−0.0249333	−	0.0181151i
$791$	−2.81922	+	3.22006i	−0.100240	+	0.114492i
$792$	−0.758975	+	0.403470i	−0.0269690	+	0.0143367i
$793$	−0.250295	−	0.433523i	−0.00888823	−	0.0153949i
$794$	−0.645472	+	0.287383i	−0.0229069	+	0.0101988i
$795$	−7.14287	−	7.93296i	−0.253331	−	0.281353i
$796$	−30.2646	+	33.6122i	−1.07270	+	1.19135i
$797$	23.8327	−	17.3154i	0.844196	−	0.613344i	−0.0793436	−	0.996847i	$-0.525282\pi$
$797$	23.8327	−	17.3154i	0.844196	−	0.613344i	0.923540	+	0.383503i	$0.125282\pi$
$798$	0.290096	−	0.134026i	0.0102693	−	0.00474448i
$799$	9.48258	+	29.1844i	0.335469	+	1.03247i
$800$	2.83401	−	0.602387i	0.100197	−	0.0212976i
$801$	−11.9832	+	5.33525i	−0.423404	+	0.188512i
$802$	0.562559	−	0.974381i	0.0198647	−	0.0344066i
$803$	−26.3342	+	22.0931i	−0.929314	+	0.779650i
$804$	−3.79941			−0.133995
$805$	1.85597	−	5.99465i	0.0654145	−	0.211284i
$806$	−0.0172402	+	0.0530599i	−0.000607260	+	0.00186895i
$807$	9.93161	−	11.0302i	0.349609	−	0.388280i
$808$	0.442164	+	4.20691i	0.0155553	+	0.147999i
$809$	−1.05343	−	10.0227i	−0.0370366	−	0.352379i	−0.997309	−	0.0733146i	$-0.976642\pi$
$809$	−1.05343	−	10.0227i	−0.0370366	−	0.352379i	0.960272	−	0.279065i	$-0.0900244\pi$
$810$	−0.0488504	+	0.0542539i	−0.00171643	+	0.00190629i
$811$	7.52179	−	23.1497i	0.264126	−	0.812896i	−0.727768	−	0.685824i	$-0.759442\pi$
$811$	7.52179	−	23.1497i	0.264126	−	0.812896i	0.991893	−	0.127072i	$-0.0405580\pi$
$812$	−9.84803	+	31.8084i	−0.345598	+	1.11626i
$813$	−22.3524			−0.783932
$814$	0.449544	−	0.0313961i	0.0157565	−	0.00110043i
$815$	−0.843514	+	1.46101i	−0.0295470	+	0.0511769i
$816$	−9.54938	+	4.25166i	−0.334295	+	0.148838i
$817$	−12.3931	+	2.63424i	−0.433581	+	0.0921604i
$818$	−0.259081	−	0.797369i	−0.00905855	−	0.0278794i
$819$	0.249439	−	0.115242i	0.00871611	−	0.00402689i
$820$	−3.06867	+	2.22952i	−0.107162	+	0.0778581i
$821$	19.9309	−	22.1355i	0.695592	−	0.772533i	−0.287076	−	0.957908i	$-0.592683\pi$
$821$	19.9309	−	22.1355i	0.695592	−	0.772533i	0.982668	+	0.185374i	$0.0593498\pi$
$822$	−0.557210	−	0.618844i	−0.0194349	−	0.0215847i
$823$	−24.5445	+	10.9279i	−0.855566	+	0.380923i	−0.787170	−	0.616736i	$-0.788455\pi$
$823$	−24.5445	+	10.9279i	−0.855566	+	0.380923i	−0.0683959	+	0.997658i	$0.521788\pi$
$824$	−0.141720	−	0.245466i	−0.00493705	−	0.00855122i
$825$	8.90543	+	8.60137i	0.310047	+	0.299461i
$826$	0.517815	−	0.591437i	0.0180171	−	0.0205787i
$827$	23.3063	+	16.9330i	0.810439	+	0.588819i	0.913958	−	0.405809i	$-0.133010\pi$
$827$	23.3063	+	16.9330i	0.810439	+	0.588819i	−0.103519	+	0.994628i	$0.533010\pi$
$828$	−4.11365	+	0.874383i	−0.142959	+	0.0303869i
$829$	44.0355	+	9.36004i	1.52942	+	0.325088i	0.894349	−	0.447369i	$-0.147639\pi$
$829$	44.0355	+	9.36004i	1.52942	+	0.325088i	0.635067	+	0.772457i	$0.280972\pi$
$830$	−0.0774946	−	0.737312i	−0.00268988	−	0.0255925i
$831$	−3.59721	−	1.60158i	−0.124786	−	0.0555582i
$832$	−0.253509	−	0.780219i	−0.00878883	−	0.0270492i
$833$	11.9326	−	14.0180i	0.413440	−	0.485695i
$834$	0.148801	+	0.108110i	0.00515255	+	0.00374355i
$835$	7.08282	+	12.2678i	0.245111	+	0.424545i
$836$	7.58984	−	9.71282i	0.262500	−	0.335925i
$837$	−4.14124	+	7.17283i	−0.143142	+	0.247929i
$838$	−0.0957216	+	0.910730i	−0.00330665	+	0.0314607i
$839$	−3.80983	+	11.7255i	−0.131530	+	0.404808i	−0.995034	−	0.0995339i	$-0.968265\pi$
$839$	−3.80983	+	11.7255i	−0.131530	+	0.404808i	0.863504	+	0.504342i	$0.168265\pi$
$840$	−0.709382	−	0.304082i	−0.0244760	−	0.0104918i
$841$	−8.70952	+	6.32783i	−0.300328	+	0.218201i
$842$	1.45183	+	0.646396i	0.0500333	+	0.0222763i
$843$	−27.0124	−	5.74167i	−0.930358	−	0.197754i
$844$	−22.1743	−	24.6271i	−0.763271	−	0.847698i
$845$	−1.52827	+	14.5406i	−0.0525743	+	0.500211i
$846$	0.756807			0.0260196
$847$	4.65944	−	28.7279i	0.160100	−	0.987101i
$848$	−37.6956			−1.29447
$849$	2.97674	−	28.3218i	0.102162	−	0.972002i
$850$	−0.426067	−	0.473195i	−0.0146140	−	0.0162305i
$851$	4.31789	+	0.917795i	0.148015	+	0.0314616i
$852$	18.2044	+	8.10513i	0.623673	+	0.277677i
$853$	−16.2671	+	11.8187i	−0.556974	+	0.404665i	−0.830350	−	0.557242i	$-0.811860\pi$
$853$	−16.2671	+	11.8187i	−0.556974	+	0.404665i	0.273376	+	0.961907i	$0.411860\pi$
$854$	−0.662339	+	0.495443i	−0.0226648	+	0.0169537i
$855$	0.647734	−	1.99352i	0.0221520	−	0.0681770i
$856$	0.0169332	−	0.161109i	0.000578766	−	0.00550659i
$857$	−27.5233	+	47.6718i	−0.940179	+	1.62844i	−0.175050	+	0.984560i	$0.556009\pi$
$857$	−27.5233	+	47.6718i	−0.940179	+	1.62844i	−0.765129	+	0.643877i	$0.777325\pi$
$858$	−0.0137558	+	0.0176035i	−0.000469616	+	0.000600974i
$859$	−0.433460	−	0.750775i	−0.0147895	−	0.0256161i	0.858536	−	0.512753i	$-0.171374\pi$
$859$	−0.433460	−	0.750775i	−0.0147895	−	0.0256161i	−0.873325	+	0.487137i	$0.838041\pi$
$860$	12.3653	+	8.98389i	0.421652	+	0.306348i
$861$	−4.46683	+	0.0621553i	−0.152229	+	0.00211825i
$862$	−0.632534	−	1.94674i	−0.0215442	−	0.0663062i
$863$	−24.2601	−	10.8013i	−0.825822	−	0.367680i	−0.0500920	−	0.998745i	$-0.515951\pi$
$863$	−24.2601	−	10.8013i	−0.825822	−	0.367680i	−0.775730	+	0.631065i	$0.782618\pi$
$864$	0.0811279	+	0.771880i	0.00276003	+	0.0262599i
$865$	−16.1755	−	3.43822i	−0.549985	−	0.116903i
$866$	0.0208775	−	0.00443766i	0.000709447	−	0.000150798i
$867$	−8.15800	−	5.92714i	−0.277060	−	0.201296i
$868$	−42.9012	−	8.49684i	−1.45616	−	0.288402i
$869$	−28.3056	−	27.3391i	−0.960202	−	0.927417i
$870$	−0.230187	−	0.398696i	−0.00780407	−	0.0135171i
$871$	−0.180616	+	0.0804156i	−0.00611995	+	0.00272478i
$872$	2.29339	+	2.54706i	0.0776639	+	0.0862545i
$873$	−5.55589	+	6.17044i	−0.188038	+	0.208838i
$874$	−0.205906	+	0.149599i	−0.00696488	+	0.00506028i
$875$	−2.35838	+	25.9003i	−0.0797279	+	0.875590i
$876$	6.39199	+	19.6725i	0.215965	+	0.664673i
$877$	39.8937	−	8.47966i	1.34711	−	0.286338i	0.522792	−	0.852460i	$-0.324890\pi$
$877$	39.8937	−	8.47966i	1.34711	−	0.286338i	0.824321	+	0.566122i	$0.191557\pi$
$878$	−2.33029	+	1.03751i	−0.0786435	+	0.0350143i
$879$	16.5596	−	28.6820i	0.558541	−	0.967421i
$880$	−14.8026	+	1.03381i	−0.498994	+	0.0348497i
$881$	23.4044			0.788514			0.394257	−	0.919000i	$-0.371002\pi$
$881$	23.4044			0.788514			0.394257	+	0.919000i	$0.371002\pi$
$882$	−0.237861	−	0.386721i	−0.00800918	−	0.0130216i
$883$	−3.39146	+	10.4379i	−0.114132	+	0.351262i	−0.991765	−	0.128071i	$-0.959121\pi$
$883$	−3.39146	+	10.4379i	−0.114132	+	0.351262i	0.877633	+	0.479333i	$0.159121\pi$
$884$	−0.364742	+	0.405087i	−0.0122676	+	0.0136245i
$885$	−0.538971	−	5.12797i	−0.0181173	−	0.172375i
$886$	0.0868599	+	0.826416i	0.00291811	+	0.0277640i
$887$	28.2091	−	31.3294i	0.947170	−	1.05194i	−0.0514105	−	0.998678i	$-0.516372\pi$
$887$	28.2091	−	31.3294i	0.947170	−	1.05194i	0.998581	−	0.0532613i	$-0.0169616\pi$
$888$	0.167771	−	0.516347i	0.00563004	−	0.0173275i
$889$	−46.4530	+	10.5515i	−1.55798	+	0.353885i
$890$	0.957632			0.0320999
$891$	−2.54087	+	2.13167i	−0.0851222	+	0.0714135i
$892$	−1.62345	+	2.81190i	−0.0543573	+	0.0941495i
$893$	−19.8505	+	8.83803i	−0.664273	+	0.295753i
$894$	1.45581	−	0.309441i	0.0486895	−	0.0103493i
$895$	−4.05796	−	12.4891i	−0.135643	−	0.417465i
$896$	−4.95878	+	2.29098i	−0.165661	+	0.0765364i
$897$	−0.177048	+	0.128633i	−0.00591147	+	0.00429493i
$898$	1.22874	−	1.36466i	0.0410036	−	0.0455391i
$899$	−34.9482	−	38.8139i	−1.16559	−	1.29452i
$900$	6.80623	−	3.03033i	0.226874	−	0.101011i
$901$	12.4704	+	21.5994i	0.415449	+	0.719579i
$902$	0.320713	−	0.170491i	0.0106786	−	0.00567672i
$903$	5.80025	+	17.0409i	0.193020	+	0.567084i
$904$	−0.339164	−	0.246417i	−0.0112804	−	0.00819571i
$905$	−7.61969	+	1.61961i	−0.253287	+	0.0538378i
$906$	0.100592	+	0.0213815i	0.00334194	+	0.000710352i
$907$	4.51759	+	42.9820i	0.150004	+	1.42719i	0.767716	+	0.640790i	$0.221393\pi$
$907$	4.51759	+	42.9820i	0.150004	+	1.42719i	−0.617712	+	0.786405i	$0.711940\pi$
$908$	−0.122529	−	0.0545534i	−0.00406627	−	0.00181042i
$909$	5.04377	+	15.5231i	0.167291	+	0.514870i
$910$	−0.0200582		0.000279106i	−0.000664921		9.25229e-6i
$911$	4.44855	+	3.23206i	0.147387	+	0.107083i	0.659035	−	0.752112i	$-0.270965\pi$
$911$	4.44855	+	3.23206i	0.147387	+	0.107083i	−0.511648	+	0.859195i	$0.670965\pi$
$912$	−3.70095	−	6.41024i	−0.122551	−	0.212264i
$913$	1.17834	−	33.6597i	0.0389973	−	1.11397i
$914$	0.273250	−	0.473283i	0.00903831	−	0.0156548i
$915$	−0.567119	+	5.39577i	−0.0187484	+	0.178379i
$916$	1.59385	−	4.90536i	0.0526622	−	0.162078i
$917$	−0.545766	−	4.57883i	−0.0180228	−	0.151206i
$918$	0.137995	−	0.100259i	0.00455451	−	0.00330905i
$919$	39.7763	+	17.7096i	1.31210	+	0.584184i	0.939099	−	0.343647i	$-0.111662\pi$
$919$	39.7763	+	17.7096i	1.31210	+	0.584184i	0.373001	+	0.927831i	$0.378329\pi$
$920$	0.601274	+	0.127805i	0.0198234	+	0.00421360i
$921$	−18.0780	−	20.0776i	−0.595689	−	0.661579i
$922$	−0.0245812	+	0.233875i	−0.000809540	+	0.00770226i
$923$	1.03695			0.0341316
$924$	−14.9788	−	9.07424i	−0.492766	−	0.298521i
$925$	−7.82024			−0.257128
$926$	−0.158194	+	1.50511i	−0.00519857	+	0.0494611i
$927$	−0.731806	−	0.812752i	−0.0240356	−	0.0266943i
$928$	−4.78733	−	1.01758i	−0.157152	−	0.0334037i
$929$	−15.8353	−	7.05031i	−0.519538	−	0.231313i	0.130178	−	0.991491i	$-0.458445\pi$
$929$	−15.8353	−	7.05031i	−0.519538	−	0.231313i	−0.649715	+	0.760178i	$0.725112\pi$
$930$	0.489187	−	0.355415i	0.0160411	−	0.0116545i
$931$	10.7551	+	7.36569i	0.352483	+	0.241401i
$932$	−9.40484	+	28.9451i	−0.308066	+	0.948129i
$933$	2.27914	−	21.6845i	0.0746156	−	0.709920i
$934$	0.392708	−	0.680190i	0.0128498	−	0.0222565i
$935$	5.48932	+	8.13977i	0.179520	+	0.266199i
$936$	0.0134578	+	0.0233095i	0.000439881	+	0.000761896i
$937$	−12.0457	−	8.75171i	−0.393516	−	0.285906i	0.373379	−	0.927679i	$-0.378199\pi$
$937$	−12.0457	−	8.75171i	−0.393516	−	0.285906i	−0.766895	+	0.641773i	$0.778199\pi$
$938$	0.167261	+	0.280614i	0.00546126	+	0.00916236i
$939$	−5.19654	−	15.9933i	−0.169583	−	0.521922i
$940$	23.9465	+	10.6617i	0.781047	+	0.347745i
$941$	−0.0455393	−	0.433278i	−0.00148454	−	0.0141244i	0.993755	−	0.111588i	$-0.0355937\pi$
$941$	−0.0455393	−	0.433278i	−0.00148454	−	0.0141244i	−0.995239	+	0.0974636i	$0.968927\pi$
$942$	−1.00459	−	0.213533i	−0.0327315	−	0.00695728i
$943$	3.48020	−	0.739739i	0.113331	−	0.0240892i
$944$	−14.7305	−	10.7023i	−0.479437	−	0.348331i
$945$	−2.92131	−	0.578583i	−0.0950303	−	0.0188213i
$946$	−1.05272	−	1.01678i	−0.0342269	−	0.0330583i
$947$	5.92967	+	10.2705i	0.192688	+	0.333746i	0.946140	−	0.323757i	$-0.104946\pi$
$947$	5.92967	+	10.2705i	0.192688	+	0.333746i	−0.753452	+	0.657503i	$0.771613\pi$
$948$	−21.6334	+	9.63180i	−0.702619	+	0.312826i
$949$	0.720237	+	0.799905i	0.0233799	+	0.0259660i
$950$	0.301700	−	0.335072i	0.00978845	−	0.0108712i
$951$	−15.3761	+	11.1714i	−0.498604	+	0.362257i
$952$	1.47347	+	1.03953i	0.0477555	+	0.0336913i
$953$	1.46420	+	4.50635i	0.0474301	+	0.145975i	0.971967	−	0.235118i	$-0.0755477\pi$
$953$	1.46420	+	4.50635i	0.0474301	+	0.145975i	−0.924537	+	0.381093i	$0.875548\pi$
$954$	0.601666	−	0.127888i	0.0194797	−	0.00414053i
$955$	11.1958	−	4.98471i	0.362289	−	0.161301i
$956$	5.68010	−	9.83822i	0.183707	−	0.318191i
$957$	−7.83307	−	19.3924i	−0.253207	−	0.626866i
$958$	1.04035			0.0336121
$959$	10.0465	−	32.4494i	0.324419	−	1.04785i
$960$	−2.74758	+	8.45618i	−0.0886778	+	0.272922i
$961$	25.1589	−	27.9418i	0.811577	−	0.901347i
$962$	−0.00147501	−	0.0140337i	−4.75561e−5	−	0.000452466i
$963$	−0.0653377	−	0.621646i	−0.00210548	−	0.0200323i
$964$	−28.0887	+	31.1956i	−0.904675	+	1.00474i
$965$	0.394448	−	1.21399i	0.0126977	−	0.0390796i
$966$	0.245674	+	0.265330i	0.00790443	+	0.00853684i
$967$	7.57222			0.243506			0.121753	−	0.992560i	$-0.461148\pi$
$967$	7.57222			0.243506			0.121753	+	0.992560i	$0.461148\pi$
$968$	2.84384	+	0.199355i	0.0914044	+	0.00640752i
$969$	−2.44868	+	4.24125i	−0.0786631	+	0.136248i
$970$	0.553771	−	0.246555i	0.0177805	−	0.00791640i
$971$	−6.84410	+	1.45476i	−0.219637	+	0.0466854i	−0.316416	−	0.948621i	$-0.602480\pi$
$971$	−6.84410	+	1.45476i	−0.219637	+	0.0466854i	0.0967784	+	0.995306i	$0.469146\pi$
$972$	0.616734	+	1.89811i	0.0197818	+	0.0608820i
$973$	−0.680361	+	7.47188i	−0.0218114	+	0.239538i
$974$	−1.79239	+	1.30225i	−0.0574318	+	0.0417266i
$975$	0.259417	−	0.288112i	0.00830799	−	0.00922696i
$976$	12.8197	+	14.2378i	0.410350	+	0.455739i
$977$	−47.6701	+	21.2241i	−1.52510	+	0.679018i	−0.986533	−	0.163564i	$-0.947701\pi$
$977$	−47.6701	+	21.2241i	−1.52510	+	0.679018i	−0.538567	+	0.842582i	$0.681034\pi$
$978$	−0.0486051	−	0.0841865i	−0.00155422	−	0.00269199i
$979$	43.0809	+	6.05843i	1.37687	+	0.193628i
$980$	−2.07825	−	15.5873i	−0.0663872	−	0.497919i
$981$	10.6991	+	7.77336i	0.341596	+	0.248184i
$982$	0.264465	−	0.0562139i	0.00843943	−	0.00179386i
$983$	−25.9982	−	5.52609i	−0.829214	−	0.176255i	−0.226297	−	0.974058i	$-0.572662\pi$
$983$	−25.9982	−	5.52609i	−0.829214	−	0.176255i	−0.602918	+	0.797803i	$0.705995\pi$
$984$	−0.0457408	−	0.435194i	−0.00145816	−	0.0138735i
$985$	17.8706	+	7.95650i	0.569404	+	0.253515i
$986$	0.332385	+	1.02298i	0.0105853	+	0.0325782i
$987$	15.8063	+	26.5183i	0.503122	+	0.844088i
$988$	−0.312270	−	0.226877i	−0.00993463	−	0.00721793i
$989$	−7.16842	−	12.4161i	−0.227942	−	0.394808i
$990$	0.232759	−	0.0667207i	0.00739756	−	0.00212052i
$991$	−15.5863	+	26.9963i	−0.495116	+	0.857566i	−0.999984	−	0.00563014i	$-0.998208\pi$
$991$	−15.5863	+	26.9963i	−0.495116	+	0.857566i	0.504868	+	0.863197i	$0.331541\pi$
$992$	0.671940	−	6.39308i	0.0213341	−	0.202980i
$993$	−3.73716	+	11.5018i	−0.118595	+	0.364998i
$994$	−0.202788	−	1.70134i	−0.00643205	−	0.0539631i
$995$	20.6372	−	14.9938i	0.654242	−	0.475335i
$996$	−18.5151	−	8.24344i	−0.586672	−	0.261203i
$997$	11.5805	+	2.46150i	0.366757	+	0.0779565i	0.387604	−	0.921826i	$-0.373303\pi$
$997$	11.5805	+	2.46150i	0.366757	+	0.0779565i	−0.0208470	+	0.999783i	$0.506636\pi$
$998$	−1.39092	−	1.54477i	−0.0440287	−	0.0488988i
$999$	0.218975	−	2.08340i	0.00692805	−	0.0659160i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.y.a.4.4	✓	64
3.2	odd	2		693.2.by.d.235.5		64
7.2	even	3	inner	231.2.y.a.37.5	yes	64
11.3	even	5	inner	231.2.y.a.25.5	yes	64
21.2	odd	6		693.2.by.d.37.4		64
33.14	odd	10		693.2.by.d.487.4		64
77.58	even	15	inner	231.2.y.a.58.4	yes	64
231.212	odd	30		693.2.by.d.289.5		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.y.a.4.4	✓	64	1.1	even	1	trivial
231.2.y.a.25.5	yes	64	11.3	even	5	inner
231.2.y.a.37.5	yes	64	7.2	even	3	inner
231.2.y.a.58.4	yes	64	77.58	even	15	inner
693.2.by.d.37.4		64	21.2	odd	6
693.2.by.d.235.5		64	3.2	odd	2
693.2.by.d.289.5		64	231.212	odd	30
693.2.by.d.487.4		64	33.14	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.00677966 + 0.0645042i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.95218 + 0.414949i) q^{4} +(-1.02829 - 0.457823i) q^{5} +(0.0524724 - 0.0381234i) q^{6} +(2.43175 + 1.04239i) q^{7} +(-0.0800864 + 0.246481i) q^{8} +(-0.104528 + 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.00677966 + 0.0645042i) q^{2} +(-0.669131 - 0.743145i) q^{3} +(1.95218 + 0.414949i) q^{4} +(-1.02829 - 0.457823i) q^{5} +(0.0524724 - 0.0381234i) q^{6} +(2.43175 + 1.04239i) q^{7} +(-0.0800864 + 0.246481i) q^{8} +(-0.104528 + 0.994522i) q^{9} +(0.0365029 - 0.0632249i) q^{10} +(2.04214 - 2.61336i) q^{11} +(-0.997897 - 1.72841i) q^{12} +(-0.0840203 - 0.0610443i) q^{13} +(-0.0837250 + 0.149791i) q^{14} +(0.347830 + 1.07051i) q^{15} +(3.63114 + 1.61669i) q^{16} +(-0.274895 - 2.61545i) q^{17} +(-0.0634421 - 0.0134850i) q^{18} +(1.82152 - 0.387177i) q^{19} +(-1.81743 - 1.32044i) q^{20} +(-0.852513 - 2.50464i) q^{21} +(0.154728 + 0.149445i) q^{22} +(1.05360 + 1.82490i) q^{23} +(0.236759 - 0.105412i) q^{24} +(-2.49788 - 2.77418i) q^{25} +(0.00450724 - 0.00500580i) q^{26} +(0.809017 - 0.587785i) q^{27} +(4.31468 + 3.04399i) q^{28} +(1.94866 + 5.99736i) q^{29} +(-0.0714105 + 0.0151788i) q^{30} +(-7.56642 + 3.36879i) q^{31} +(-0.388066 + 0.672150i) q^{32} +(-3.30857 + 0.231070i) q^{33} +0.170571 q^{34} +(-2.02331 - 2.18519i) q^{35} +(-0.616734 + 1.89811i) q^{36} +(1.40175 - 1.55680i) q^{37} +(0.0126252 + 0.120121i) q^{38} +(0.0108558 + 0.103286i) q^{39} +(0.195196 - 0.216787i) q^{40} +(0.521765 - 1.60583i) q^{41} +(0.167339 - 0.0380100i) q^{42} -6.80371 q^{43} +(5.07104 - 4.25436i) q^{44} +(0.562800 - 0.974798i) q^{45} +(-0.124856 + 0.0555897i) q^{46} +(-11.4134 + 2.42600i) q^{47} +(-1.22827 - 3.78024i) q^{48} +(4.82684 + 5.06967i) q^{49} +(0.195881 - 0.142316i) q^{50} +(-1.75972 + 1.95437i) q^{51} +(-0.138692 - 0.154034i) q^{52} +(-8.66379 + 3.85737i) q^{53} +(0.0324297 + 0.0561700i) q^{54} +(-3.29637 + 1.75234i) q^{55} +(-0.451679 + 0.515899i) q^{56} +(-1.50657 - 1.09458i) q^{57} +(-0.400066 + 0.0850366i) q^{58} +(-4.48076 - 0.952415i) q^{59} +(0.234820 + 2.23416i) q^{60} +(4.40337 + 1.96051i) q^{61} +(-0.166003 - 0.510905i) q^{62} +(-1.29087 + 2.30947i) q^{63} +(6.39060 + 4.64304i) q^{64} +(0.0584495 + 0.101237i) q^{65} +(0.00752600 - 0.214983i) q^{66} +(0.951855 - 1.64866i) q^{67} +(0.548634 - 5.21990i) q^{68} +(0.651163 - 2.00407i) q^{69} +(0.154671 - 0.115697i) q^{70} +(-8.07772 + 5.86881i) q^{71} +(-0.236759 - 0.105412i) q^{72} +(-10.1378 - 2.15485i) q^{73} +(0.0909167 + 0.100973i) q^{74} +(-0.390207 + 3.71257i) q^{75} +3.71660 q^{76} +(7.69013 - 4.22633i) q^{77} -0.00673597 q^{78} +(1.24026 - 11.8003i) q^{79} +(-2.99370 - 3.32484i) q^{80} +(-0.978148 - 0.207912i) q^{81} +(0.100045 + 0.0445430i) q^{82} +(8.21556 - 5.96895i) q^{83} +(-0.624962 - 5.24326i) q^{84} +(-0.914742 + 2.81529i) q^{85} +(0.0461269 - 0.438868i) q^{86} +(3.15300 - 5.46115i) q^{87} +(0.480594 + 0.712644i) q^{88} +(6.55860 + 11.3598i) q^{89} +(0.0590630 + 0.0429117i) q^{90} +(-0.140685 - 0.236027i) q^{91} +(1.29959 + 3.99972i) q^{92} +(7.56642 + 3.36879i) q^{93} +(-0.0791079 - 0.752661i) q^{94} +(-2.05031 - 0.435806i) q^{95} +(0.759172 - 0.161367i) q^{96} +(6.71739 + 4.88047i) q^{97} +(-0.359739 + 0.276981i) q^{98} +(2.38558 + 2.30413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9	\( 64 q - 8 q^{3} + 10 q^{4} - q^{7} + 8 q^{8} + 8 q^{9} - 22 q^{10} - 13 q^{11} + 30 q^{12} - 8 q^{13} - 26 q^{14} + 4 q^{17} - 5 q^{18} + 10 q^{19} + 24 q^{20} + 2 q^{21} - 38 q^{22} - 8 q^{23} + 14 q^{24} - 2 q^{25} + 4 q^{26} + 16 q^{27} - 67 q^{28} + 2 q^{29} - 3 q^{30} + 25 q^{31} + 72 q^{32} - 12 q^{33} - 56 q^{34} + 19 q^{35} - 20 q^{36} - 12 q^{37} - 37 q^{38} - 4 q^{39} - 9 q^{40} + 20 q^{41} + 9 q^{42} - 100 q^{43} - 5 q^{44} - 33 q^{46} - 18 q^{47} + 10 q^{48} + 29 q^{49} - 46 q^{50} + 6 q^{51} + 26 q^{52} - 49 q^{53} - 10 q^{54} - 24 q^{55} - 48 q^{56} + 20 q^{57} - 40 q^{58} + q^{59} + 12 q^{60} + 3 q^{61} + 4 q^{62} - 7 q^{63} - 24 q^{64} + 82 q^{65} + 11 q^{66} + 76 q^{67} - 39 q^{68} - 16 q^{69} + 59 q^{70} + 70 q^{71} - 14 q^{72} - 3 q^{73} + 32 q^{74} - 28 q^{75} + 104 q^{76} + 38 q^{77} - 12 q^{78} - 15 q^{79} - 83 q^{80} + 8 q^{81} + 42 q^{82} + 68 q^{83} + 27 q^{84} + 62 q^{85} - 47 q^{86} - 54 q^{87} - 64 q^{88} + 82 q^{89} - 16 q^{90} - 10 q^{91} + 190 q^{92} - 25 q^{93} - 6 q^{94} - 53 q^{95} + 8 q^{96} - 32 q^{97} - 152 q^{98} + 16 q^{99}+O(q^{100}) \) 64 * q - 8 * q^3 + 10 * q^4 - q^7 + 8 * q^8 + 8 * q^9 - 22 * q^10 - 13 * q^11 + 30 * q^12 - 8 * q^13 - 26 * q^14 + 4 * q^17 - 5 * q^18 + 10 * q^19 + 24 * q^20 + 2 * q^21 - 38 * q^22 - 8 * q^23 + 14 * q^24 - 2 * q^25 + 4 * q^26 + 16 * q^27 - 67 * q^28 + 2 * q^29 - 3 * q^30 + 25 * q^31 + 72 * q^32 - 12 * q^33 - 56 * q^34 + 19 * q^35 - 20 * q^36 - 12 * q^37 - 37 * q^38 - 4 * q^39 - 9 * q^40 + 20 * q^41 + 9 * q^42 - 100 * q^43 - 5 * q^44 - 33 * q^46 - 18 * q^47 + 10 * q^48 + 29 * q^49 - 46 * q^50 + 6 * q^51 + 26 * q^52 - 49 * q^53 - 10 * q^54 - 24 * q^55 - 48 * q^56 + 20 * q^57 - 40 * q^58 + q^59 + 12 * q^60 + 3 * q^61 + 4 * q^62 - 7 * q^63 - 24 * q^64 + 82 * q^65 + 11 * q^66 + 76 * q^67 - 39 * q^68 - 16 * q^69 + 59 * q^70 + 70 * q^71 - 14 * q^72 - 3 * q^73 + 32 * q^74 - 28 * q^75 + 104 * q^76 + 38 * q^77 - 12 * q^78 - 15 * q^79 - 83 * q^80 + 8 * q^81 + 42 * q^82 + 68 * q^83 + 27 * q^84 + 62 * q^85 - 47 * q^86 - 54 * q^87 - 64 * q^88 + 82 * q^89 - 16 * q^90 - 10 * q^91 + 190 * q^92 - 25 * q^93 - 6 * q^94 - 53 * q^95 + 8 * q^96 - 32 * q^97 - 152 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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