LMFDB - Embedded newform 1155.2.l.f.1121.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.13
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.892777 q^{2} +(0.497839 - 1.65896i) q^{3} -1.20295 q^{4} -1.00000i q^{5} +(-0.444460 + 1.48108i) q^{6} -1.00000i q^{7} +2.85952 q^{8} +(-2.50431 - 1.65179i) q^{9} +O(q^{10})$	\(q-0.892777 q^{2} +(0.497839 - 1.65896i) q^{3} -1.20295 q^{4} -1.00000i q^{5} +(-0.444460 + 1.48108i) q^{6} -1.00000i q^{7} +2.85952 q^{8} +(-2.50431 - 1.65179i) q^{9} +0.892777i q^{10} +(0.586925 + 3.26428i) q^{11} +(-0.598875 + 1.99565i) q^{12} +5.84640i q^{13} +0.892777i q^{14} +(-1.65896 - 0.497839i) q^{15} -0.147016 q^{16} +4.41856 q^{17} +(2.23579 + 1.47468i) q^{18} +1.11335i q^{19} +1.20295i q^{20} +(-1.65896 - 0.497839i) q^{21} +(-0.523993 - 2.91427i) q^{22} +7.41992i q^{23} +(1.42358 - 4.74384i) q^{24} -1.00000 q^{25} -5.21953i q^{26} +(-3.98701 + 3.33223i) q^{27} +1.20295i q^{28} +9.75592 q^{29} +(1.48108 + 0.444460i) q^{30} -0.0544980 q^{31} -5.58779 q^{32} +(5.70751 + 0.651400i) q^{33} -3.94479 q^{34} -1.00000 q^{35} +(3.01256 + 1.98702i) q^{36} -4.09802 q^{37} -0.993970i q^{38} +(9.69896 + 2.91057i) q^{39} -2.85952i q^{40} +0.969641 q^{41} +(1.48108 + 0.444460i) q^{42} -0.978013i q^{43} +(-0.706041 - 3.92676i) q^{44} +(-1.65179 + 2.50431i) q^{45} -6.62433i q^{46} -11.0023i q^{47} +(-0.0731905 + 0.243895i) q^{48} -1.00000 q^{49} +0.892777 q^{50} +(2.19973 - 7.33023i) q^{51} -7.03292i q^{52} +0.255651i q^{53} +(3.55951 - 2.97494i) q^{54} +(3.26428 - 0.586925i) q^{55} -2.85952i q^{56} +(1.84700 + 0.554267i) q^{57} -8.70987 q^{58} +1.86448i q^{59} +(1.99565 + 0.598875i) q^{60} +5.07381i q^{61} +0.0486546 q^{62} +(-1.65179 + 2.50431i) q^{63} +5.28268 q^{64} +5.84640 q^{65} +(-5.09554 - 0.581555i) q^{66} +5.79382 q^{67} -5.31530 q^{68} +(12.3094 + 3.69393i) q^{69} +0.892777 q^{70} +14.9085i q^{71} +(-7.16113 - 4.72334i) q^{72} +7.44139i q^{73} +3.65862 q^{74} +(-0.497839 + 1.65896i) q^{75} -1.33930i q^{76} +(3.26428 - 0.586925i) q^{77} +(-8.65901 - 2.59849i) q^{78} -7.49918i q^{79} +0.147016i q^{80} +(3.54316 + 8.27321i) q^{81} -0.865673 q^{82} +5.81466 q^{83} +(1.99565 + 0.598875i) q^{84} -4.41856i q^{85} +0.873148i q^{86} +(4.85688 - 16.1847i) q^{87} +(1.67832 + 9.33427i) q^{88} -13.8992i q^{89} +(1.47468 - 2.23579i) q^{90} +5.84640 q^{91} -8.92578i q^{92} +(-0.0271312 + 0.0904101i) q^{93} +9.82263i q^{94} +1.11335 q^{95} +(-2.78182 + 9.26993i) q^{96} +1.50371 q^{97} +0.892777 q^{98} +(3.92207 - 9.14425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.892777			−0.631289			−0.315644	−	0.948878i	$-0.602221\pi$
$2$	−0.892777			−0.631289			−0.315644	+	0.948878i	$0.602221\pi$
$3$	0.497839	−	1.65896i	0.287428	−	0.957802i
$3$	0.497839	−	1.65896i	0.287428	−	0.957802i
$4$	−1.20295			−0.601474
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.444460	+	1.48108i	−0.181450	+	0.604650i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	2.85952			1.01099
$9$	−2.50431	−	1.65179i	−0.834771	−	0.550598i
$10$			0.892777i			0.282321i
$11$	0.586925	+	3.26428i	0.176965	+	0.984217i
$11$	0.586925	+	3.26428i	0.176965	+	0.984217i
$12$	−0.598875	+	1.99565i	−0.172880	+	0.576094i
$13$			5.84640i			1.62150i	0.585393	+	0.810750i	$0.300940\pi$
$13$			5.84640i			1.62150i	−0.585393	+	0.810750i	$0.699060\pi$
$14$			0.892777i			0.238605i
$15$	−1.65896	−	0.497839i	−0.428342	−	0.128542i
$16$	−0.147016			−0.0367541
$17$	4.41856			1.07166			0.535829	−	0.844326i	$-0.319999\pi$
$17$	4.41856			1.07166			0.535829	+	0.844326i	$0.319999\pi$
$18$	2.23579	+	1.47468i	0.526981	+	0.347586i
$19$			1.11335i			0.255419i	0.991812	+	0.127710i	$0.0407625\pi$
$19$			1.11335i			0.255419i	−0.991812	+	0.127710i	$0.959237\pi$
$20$			1.20295i			0.268988i
$21$	−1.65896	−	0.497839i	−0.362015	−	0.108637i
$22$	−0.523993	−	2.91427i	−0.111716	−	0.621325i
$23$			7.41992i			1.54716i	0.633699	+	0.773580i	$0.281536\pi$
$23$			7.41992i			1.54716i	−0.633699	+	0.773580i	$0.718464\pi$
$24$	1.42358	−	4.74384i	0.290587	−	0.968331i
$25$	−1.00000			−0.200000
$26$		−	5.21953i		−	1.02363i
$27$	−3.98701	+	3.33223i	−0.767300	+	0.641288i
$28$			1.20295i			0.227336i
$29$	9.75592			1.81163			0.905815	−	0.423674i	$-0.139260\pi$
$29$	9.75592			1.81163			0.905815	+	0.423674i	$0.139260\pi$
$30$	1.48108	+	0.444460i	0.270408	+	0.0811469i
$31$	−0.0544980			−0.00978813			−0.00489406	−	0.999988i	$-0.501558\pi$
$31$	−0.0544980			−0.00978813			−0.00489406	+	0.999988i	$0.501558\pi$
$32$	−5.58779			−0.987790
$33$	5.70751	+	0.651400i	0.993550	+	0.113394i
$34$	−3.94479			−0.676526
$35$	−1.00000			−0.169031
$36$	3.01256	+	1.98702i	0.502093	+	0.331170i
$37$	−4.09802			−0.673711			−0.336855	−	0.941556i	$-0.609363\pi$
$37$	−4.09802			−0.673711			−0.336855	+	0.941556i	$0.609363\pi$
$38$		−	0.993970i		−	0.161243i
$39$	9.69896	+	2.91057i	1.55308	+	0.466064i
$40$		−	2.85952i		−	0.452130i
$41$	0.969641			0.151432			0.0757162	−	0.997129i	$-0.475876\pi$
$41$	0.969641			0.151432			0.0757162	+	0.997129i	$0.475876\pi$
$42$	1.48108	+	0.444460i	0.228536	+	0.0685816i
$43$		−	0.978013i		−	0.149146i	−0.997216	−	0.0745728i	$-0.976241\pi$
$43$		−	0.978013i		−	0.149146i	0.997216	−	0.0745728i	$-0.0237593\pi$
$44$	−0.706041	−	3.92676i	−0.106440	−	0.591981i
$45$	−1.65179	+	2.50431i	−0.246235	+	0.373321i
$46$		−	6.62433i		−	0.976705i
$47$		−	11.0023i		−	1.60485i	−0.596750	−	0.802427i	$-0.703541\pi$
$47$		−	11.0023i		−	1.60485i	0.596750	−	0.802427i	$-0.296459\pi$
$48$	−0.0731905	+	0.243895i	−0.0105641	+	0.0352032i
$49$	−1.00000			−0.142857
$50$	0.892777			0.126258
$51$	2.19973	−	7.33023i	0.308024	−	1.02644i
$52$		−	7.03292i		−	0.975291i
$53$			0.255651i			0.0351163i	0.999846	+	0.0175582i	$0.00558923\pi$
$53$			0.255651i			0.0351163i	−0.999846	+	0.0175582i	$0.994411\pi$
$54$	3.55951	−	2.97494i	0.484388	−	0.404838i
$55$	3.26428	−	0.586925i	0.440155	−	0.0791409i
$56$		−	2.85952i		−	0.382119i
$57$	1.84700	+	0.554267i	0.244641	+	0.0734145i
$58$	−8.70987			−1.14366
$59$			1.86448i			0.242735i	0.992608	+	0.121367i	$0.0387279\pi$
$59$			1.86448i			0.242735i	−0.992608	+	0.121367i	$0.961272\pi$
$60$	1.99565	+	0.598875i	0.257637	+	0.0773145i
$61$			5.07381i			0.649635i	0.945777	+	0.324818i	$0.105303\pi$
$61$			5.07381i			0.649635i	−0.945777	+	0.324818i	$0.894697\pi$
$62$	0.0486546			0.00617914
$63$	−1.65179	+	2.50431i	−0.208106	+	0.315514i
$64$	5.28268			0.660335
$65$	5.84640			0.725157
$66$	−5.09554	−	0.581555i	−0.627217	−	0.0715845i
$67$	5.79382			0.707828			0.353914	−	0.935278i	$-0.384851\pi$
$67$	5.79382			0.707828			0.353914	+	0.935278i	$0.384851\pi$
$68$	−5.31530			−0.644575
$69$	12.3094	+	3.69393i	1.48187	+	0.444697i
$70$	0.892777			0.106707
$71$			14.9085i			1.76931i	0.466244	+	0.884656i	$0.345607\pi$
$71$			14.9085i			1.76931i	−0.466244	+	0.884656i	$0.654393\pi$
$72$	−7.16113	−	4.72334i	−0.843947	−	0.556650i
$73$			7.44139i			0.870948i	0.900201	+	0.435474i	$0.143419\pi$
$73$			7.44139i			0.870948i	−0.900201	+	0.435474i	$0.856581\pi$
$74$	3.65862			0.425306
$75$	−0.497839	+	1.65896i	−0.0574855	+	0.191560i
$76$		−	1.33930i		−	0.153628i
$77$	3.26428	−	0.586925i	0.371999	−	0.0668863i
$78$	−8.65901	−	2.59849i	−0.980440	−	0.294221i
$79$		−	7.49918i		−	0.843724i	−0.906660	−	0.421862i	$-0.861377\pi$
$79$		−	7.49918i		−	0.843724i	0.906660	−	0.421862i	$-0.138623\pi$
$80$			0.147016i			0.0164369i
$81$	3.54316	+	8.27321i	0.393684	+	0.919246i
$82$	−0.865673			−0.0955976
$83$	5.81466			0.638242			0.319121	−	0.947714i	$-0.396612\pi$
$83$	5.81466			0.638242			0.319121	+	0.947714i	$0.396612\pi$
$84$	1.99565	+	0.598875i	0.217743	+	0.0653426i
$85$		−	4.41856i		−	0.479260i
$86$			0.873148i			0.0941539i
$87$	4.85688	−	16.1847i	0.520712	−	1.73518i
$88$	1.67832	+	9.33427i	0.178910	+	0.995037i
$89$		−	13.8992i		−	1.47331i	−0.676266	−	0.736657i	$-0.736403\pi$
$89$		−	13.8992i		−	1.47331i	0.676266	−	0.736657i	$-0.263597\pi$
$90$	1.47468	−	2.23579i	0.155445	−	0.235673i
$91$	5.84640			0.612869
$92$		−	8.92578i		−	0.930577i
$93$	−0.0271312	+	0.0904101i	−0.00281338	+	0.00937509i
$94$			9.82263i			1.01313i
$95$	1.11335			0.114227
$96$	−2.78182	+	9.26993i	−0.283918	+	0.946108i
$97$	1.50371			0.152679			0.0763393	−	0.997082i	$-0.475677\pi$
$97$	1.50371			0.152679			0.0763393	+	0.997082i	$0.475677\pi$
$98$	0.892777			0.0901841
$99$	3.92207	−	9.14425i	0.394183	−	0.919032i
$100$	1.20295			0.120295
$101$	6.01334			0.598350			0.299175	−	0.954198i	$-0.403289\pi$
$101$	6.01334			0.598350			0.299175	+	0.954198i	$0.403289\pi$
$102$	−1.96387	+	6.54426i	−0.194452	+	0.647978i
$103$	−3.40537			−0.335541			−0.167771	−	0.985826i	$-0.553657\pi$
$103$	−3.40537			−0.335541			−0.167771	+	0.985826i	$0.553657\pi$
$104$			16.7179i			1.63932i
$105$	−0.497839	+	1.65896i	−0.0485841	+	0.161898i
$106$		−	0.228239i		−	0.0221686i
$107$	−0.635719			−0.0614573			−0.0307287	−	0.999528i	$-0.509783\pi$
$107$	−0.635719			−0.0614573			−0.0307287	+	0.999528i	$0.509783\pi$
$108$	4.79617	−	4.00850i	0.461511	−	0.385718i
$109$			6.12063i			0.586250i	0.956074	+	0.293125i	$0.0946951\pi$
$109$			6.12063i			0.586250i	−0.956074	+	0.293125i	$0.905305\pi$
$110$	−2.91427	+	0.523993i	−0.277865	+	0.0499608i
$111$	−2.04016	+	6.79846i	−0.193643	+	0.645282i
$112$			0.147016i			0.0138917i
$113$		−	20.8631i		−	1.96264i	−0.192394	−	0.981318i	$-0.561625\pi$
$113$		−	20.8631i		−	1.96264i	0.192394	−	0.981318i	$-0.438375\pi$
$114$	−1.64896	−	0.494837i	−0.154439	−	0.0463458i
$115$	7.41992			0.691911
$116$	−11.7359			−1.08965
$117$	9.65705	−	14.6412i	0.892794	−	1.35358i
$118$		−	1.66457i		−	0.153236i
$119$		−	4.41856i		−	0.405049i
$120$	−4.74384	−	1.42358i	−0.433051	−	0.129955i
$121$	−10.3110	+	3.83177i	−0.937367	+	0.348343i
$122$		−	4.52978i		−	0.410107i
$123$	0.482725	−	1.60860i	0.0435259	−	0.145042i
$124$	0.0655583			0.00588731
$125$			1.00000i			0.0894427i
$126$	1.47468	−	2.23579i	0.131375	−	0.199180i
$127$			15.3812i			1.36486i	0.730950	+	0.682431i	$0.239077\pi$
$127$			15.3812i			1.36486i	−0.730950	+	0.682431i	$0.760923\pi$
$128$	6.45932			0.570928
$129$	−1.62249	−	0.486893i	−0.142852	−	0.0428686i
$130$	−5.21953			−0.457783
$131$	15.8634			1.38599			0.692997	−	0.720941i	$-0.256290\pi$
$131$	15.8634			1.38599			0.692997	+	0.720941i	$0.256290\pi$
$132$	−6.86584	−	0.783601i	−0.597595	−	0.0682037i
$133$	1.11335			0.0965393
$134$	−5.17259			−0.446844
$135$	3.33223	+	3.98701i	0.286793	+	0.343147i
$136$	12.6350			1.08344
$137$		−	0.713406i		−	0.0609504i	−0.999536	−	0.0304752i	$-0.990298\pi$
$137$		−	0.713406i		−	0.0609504i	0.999536	−	0.0304752i	$-0.00970205\pi$
$138$	−10.9895	−	3.29785i	−0.935490	−	0.280732i
$139$			12.9766i			1.10066i	0.834947	+	0.550330i	$0.185498\pi$
$139$			12.9766i			1.10066i	−0.834947	+	0.550330i	$0.814502\pi$
$140$	1.20295			0.101668
$141$	−18.2525	−	5.47739i	−1.53713	−	0.461280i
$142$		−	13.3100i		−	1.11695i
$143$	−19.0843	+	3.43140i	−1.59591	+	0.286948i
$144$	0.368175	+	0.242841i	0.0306812	+	0.0202367i
$145$		−	9.75592i		−	0.810185i
$146$		−	6.64350i		−	0.549820i
$147$	−0.497839	+	1.65896i	−0.0410611	+	0.136829i
$148$	4.92971			0.405220
$149$	−2.96967			−0.243285			−0.121642	−	0.992574i	$-0.538816\pi$
$149$	−2.96967			−0.243285			−0.121642	+	0.992574i	$0.538816\pi$
$150$	0.444460	−	1.48108i	0.0362900	−	0.120930i
$151$			5.66908i			0.461343i	0.973032	+	0.230671i	$0.0740923\pi$
$151$			5.66908i			0.461343i	−0.973032	+	0.230671i	$0.925908\pi$
$152$			3.18363i			0.258227i
$153$	−11.0655	−	7.29855i	−0.894589	−	0.590053i
$154$	−2.91427	+	0.523993i	−0.234839	+	0.0422246i
$155$			0.0544980i			0.00437738i
$156$	−11.6674	−	3.50126i	−0.934136	−	0.280326i
$157$	19.1129			1.52537			0.762687	−	0.646768i	$-0.223880\pi$
$157$	19.1129			1.52537			0.762687	+	0.646768i	$0.223880\pi$
$158$			6.69510i			0.532633i
$159$	0.424115	+	0.127273i	0.0336345	+	0.0100934i
$160$			5.58779i			0.441753i
$161$	7.41992			0.584771
$162$	−3.16325	−	7.38614i	−0.248528	−	0.580310i
$163$	−1.32587			−0.103850			−0.0519251	−	0.998651i	$-0.516536\pi$
$163$	−1.32587			−0.103850			−0.0519251	+	0.998651i	$0.516536\pi$
$164$	−1.16643			−0.0910827
$165$	0.651400	−	5.70751i	0.0507114	−	0.444329i
$166$	−5.19119			−0.402915
$167$	2.11565			0.163714			0.0818571	−	0.996644i	$-0.473915\pi$
$167$	2.11565			0.163714			0.0818571	+	0.996644i	$0.473915\pi$
$168$	−4.74384	−	1.42358i	−0.365995	−	0.109832i
$169$	−21.1804			−1.62926
$170$			3.94479i			0.302552i
$171$	1.83902	−	2.78817i	0.140633	−	0.213216i
$172$			1.17650i			0.0897072i
$173$	5.68542			0.432255			0.216127	−	0.976365i	$-0.430657\pi$
$173$	5.68542			0.432255			0.216127	+	0.976365i	$0.430657\pi$
$174$	−4.33611	+	14.4493i	−0.328720	+	1.09540i
$175$			1.00000i			0.0755929i
$176$	−0.0862876	−	0.479903i	−0.00650417	−	0.0361740i
$177$	3.09310	+	0.928212i	0.232492	+	0.0697687i
$178$			12.4089i			0.930087i
$179$			4.67674i			0.349556i	0.984608	+	0.174778i	$0.0559208\pi$
$179$			4.67674i			0.349556i	−0.984608	+	0.174778i	$0.944079\pi$
$180$	1.98702	−	3.01256i	0.148104	−	0.224543i
$181$	16.4226			1.22068			0.610340	−	0.792140i	$-0.291033\pi$
$181$	16.4226			1.22068			0.610340	+	0.792140i	$0.291033\pi$
$182$	−5.21953			−0.386898
$183$	8.41726	+	2.52594i	0.622222	+	0.186723i
$184$			21.2174i			1.56417i
$185$			4.09802i			0.301293i
$186$	0.0242222	−	0.0807161i	0.00177605	−	0.00591839i
$187$	2.59336	+	14.4234i	0.189646	+	1.05475i
$188$			13.2352i			0.965279i
$189$	3.33223	+	3.98701i	0.242384	+	0.290012i
$190$	−0.993970			−0.0721101
$191$		−	14.6938i		−	1.06321i	−0.846994	−	0.531603i	$-0.821590\pi$
$191$		−	14.6938i		−	1.06321i	0.846994	−	0.531603i	$-0.178410\pi$
$192$	2.62993	−	8.76377i	0.189799	−	0.632471i
$193$			8.62104i			0.620556i	0.950646	+	0.310278i	$0.100422\pi$
$193$			8.62104i			0.620556i	−0.950646	+	0.310278i	$0.899578\pi$
$194$	−1.34248			−0.0963843
$195$	2.91057	−	9.69896i	0.208430	−	0.694557i
$196$	1.20295			0.0859249
$197$	−25.2639			−1.79998			−0.899989	−	0.435912i	$-0.856426\pi$
$197$	−25.2639			−1.79998			−0.899989	+	0.435912i	$0.856426\pi$
$198$	−3.50154	+	8.16378i	−0.248843	+	0.580175i
$199$	13.8673			0.983027			0.491513	−	0.870870i	$-0.336444\pi$
$199$	13.8673			0.983027			0.491513	+	0.870870i	$0.336444\pi$
$200$	−2.85952			−0.202199
$201$	2.88439	−	9.61173i	0.203449	−	0.677959i
$202$	−5.36857			−0.377731
$203$		−	9.75592i		−	0.684732i
$204$	−2.64617	+	8.81789i	−0.185269	+	0.617376i
$205$		−	0.969641i		−	0.0677227i
$206$	3.04024			0.211823
$207$	12.2562	−	18.5818i	0.851863	−	1.29152i
$208$		−	0.859517i		−	0.0595968i
$209$	−3.63427	+	0.653450i	−0.251388	+	0.0452001i
$210$	0.444460	−	1.48108i	0.0306706	−	0.102204i
$211$			26.7930i			1.84451i	0.386586	+	0.922254i	$0.373654\pi$
$211$			26.7930i			1.84451i	−0.386586	+	0.922254i	$0.626346\pi$
$212$		−	0.307535i		−	0.0211216i
$213$	24.7326	+	7.42203i	1.69465	+	0.508549i
$214$	0.567556			0.0387973
$215$	−0.978013			−0.0666999
$216$	−11.4009	+	9.52858i	−0.775735	+	0.648338i
$217$			0.0544980i			0.00369956i
$218$		−	5.46435i		−	0.370093i
$219$	12.3450	+	3.70461i	0.834196	+	0.250335i
$220$	−3.92676	+	0.706041i	−0.264742	+	0.0476013i
$221$			25.8327i			1.73769i
$222$	1.82141	−	6.06951i	0.122245	−	0.407359i
$223$	−20.0083			−1.33985			−0.669926	−	0.742428i	$-0.733674\pi$
$223$	−20.0083			−1.33985			−0.669926	+	0.742428i	$0.733674\pi$
$224$			5.58779i			0.373350i
$225$	2.50431	+	1.65179i	0.166954	+	0.110120i
$226$			18.6261i			1.23899i
$227$	−19.6001			−1.30090			−0.650451	−	0.759548i	$-0.725420\pi$
$227$	−19.6001			−1.30090			−0.650451	+	0.759548i	$0.725420\pi$
$228$	−2.22184	−	0.666755i	−0.147145	−	0.0441569i
$229$	−21.8184			−1.44180			−0.720900	−	0.693039i	$-0.756271\pi$
$229$	−21.8184			−1.44180			−0.720900	+	0.693039i	$0.756271\pi$
$230$	−6.62433			−0.436796
$231$	0.651400	−	5.70751i	0.0428590	−	0.375527i
$232$	27.8973			1.83154
$233$	5.61915			0.368123			0.184062	−	0.982915i	$-0.441075\pi$
$233$	5.61915			0.368123			0.184062	+	0.982915i	$0.441075\pi$
$234$	−8.62159	+	13.0713i	−0.563611	+	0.854500i
$235$	−11.0023			−0.717713
$236$		−	2.24288i		−	0.145999i
$237$	−12.4409	−	3.73339i	−0.808120	−	0.242510i
$238$			3.94479i			0.255703i
$239$	21.9024			1.41675			0.708375	−	0.705836i	$-0.249428\pi$
$239$	21.9024			1.41675			0.708375	+	0.705836i	$0.249428\pi$
$240$	0.243895	+	0.0731905i	0.0157433	+	0.00472443i
$241$		−	26.3795i		−	1.69925i	−0.527387	−	0.849625i	$-0.676828\pi$
$241$		−	26.3795i		−	1.69925i	0.527387	−	0.849625i	$-0.323172\pi$
$242$	9.20546	−	3.42092i	0.591749	−	0.219905i
$243$	15.4889	−	1.75923i	0.993611	−	0.112855i
$244$		−	6.10354i		−	0.390739i
$245$			1.00000i			0.0638877i
$246$	−0.430966	+	1.43612i	−0.0274774	+	0.0915636i
$247$	−6.50907			−0.414162
$248$	−0.155838			−0.00989573
$249$	2.89477	−	9.64630i	0.183448	−	0.611309i
$250$		−	0.892777i		−	0.0564642i
$251$			20.1458i			1.27159i	0.771858	+	0.635795i	$0.219328\pi$
$251$			20.1458i			1.27159i	−0.771858	+	0.635795i	$0.780672\pi$
$252$	1.98702	−	3.01256i	0.125171	−	0.189773i
$253$	−24.2207	+	4.35493i	−1.52274	+	0.273792i
$254$		−	13.7320i		−	0.861622i
$255$	−7.33023	−	2.19973i	−0.459037	−	0.137753i
$256$	−16.3321			−1.02076
$257$			7.60608i			0.474455i	0.971454	+	0.237227i	$0.0762386\pi$
$257$			7.60608i			0.474455i	−0.971454	+	0.237227i	$0.923761\pi$
$258$	1.44852	+	0.434687i	0.0901809	+	0.0270624i
$259$			4.09802i			0.254639i
$260$	−7.03292			−0.436163
$261$	−24.4319	−	16.1148i	−1.51230	−	0.997479i
$262$	−14.1625			−0.874962
$263$	−17.0798			−1.05319			−0.526593	−	0.850117i	$-0.676531\pi$
$263$	−17.0798			−1.05319			−0.526593	+	0.850117i	$0.676531\pi$
$264$	16.3207	+	1.86269i	1.00447	+	0.114641i
$265$	0.255651			0.0157045
$266$	−0.993970			−0.0609442
$267$	−23.0583	−	6.91958i	−1.41114	−	0.423471i
$268$	−6.96967			−0.425740
$269$			14.0311i			0.855490i	0.903899	+	0.427745i	$0.140692\pi$
$269$			14.0311i			0.855490i	−0.903899	+	0.427745i	$0.859308\pi$
$270$	−2.97494	−	3.55951i	−0.181049	−	0.216625i
$271$			22.5941i			1.37249i	0.727369	+	0.686246i	$0.240743\pi$
$271$			22.5941i			1.37249i	−0.727369	+	0.686246i	$0.759257\pi$
$272$	−0.649601			−0.0393879
$273$	2.91057	−	9.69896i	0.176156	−	0.587008i
$274$			0.636912i			0.0384773i
$275$	−0.586925	−	3.26428i	−0.0353929	−	0.196843i
$276$	−14.8075	−	4.44360i	−0.891309	−	0.267474i
$277$		−	30.3408i		−	1.82300i	−0.411298	−	0.911501i	$-0.634924\pi$
$277$		−	30.3408i		−	1.82300i	0.411298	−	0.911501i	$-0.365076\pi$
$278$		−	11.5852i		−	0.694834i
$279$	0.136480	+	0.0900194i	0.00817084	+	0.00538932i
$280$	−2.85952			−0.170889
$281$	12.6473			0.754476			0.377238	−	0.926116i	$-0.376874\pi$
$281$	12.6473			0.754476			0.377238	+	0.926116i	$0.376874\pi$
$282$	16.2954	+	4.89009i	0.970375	+	0.291201i
$283$		−	23.9740i		−	1.42511i	−0.701617	−	0.712554i	$-0.747538\pi$
$283$		−	23.9740i		−	1.42511i	0.701617	−	0.712554i	$-0.252462\pi$
$284$		−	17.9342i		−	1.06420i
$285$	0.554267	−	1.84700i	0.0328320	−	0.109407i
$286$	17.0380	−	3.06347i	1.00748	−	0.181147i
$287$		−	0.969641i		−	0.0572361i
$288$	13.9936	+	9.22987i	0.824578	+	0.543875i
$289$	2.52370			0.148453
$290$			8.70987i			0.511461i
$291$	0.748606	−	2.49460i	0.0438841	−	0.146236i
$292$		−	8.95161i		−	0.523853i
$293$	21.4022			1.25033			0.625166	−	0.780492i	$-0.285031\pi$
$293$	21.4022			1.25033			0.625166	+	0.780492i	$0.285031\pi$
$294$	0.444460	−	1.48108i	0.0259214	−	0.0863786i
$295$	1.86448			0.108554
$296$	−11.7184			−0.681117
$297$	−13.2174	−	11.0589i	−0.766952	−	0.641705i
$298$	2.65125			0.153583
$299$	−43.3798			−2.50872
$300$	0.598875	−	1.99565i	0.0345761	−	0.115219i
$301$	−0.978013			−0.0563717
$302$		−	5.06122i		−	0.291241i
$303$	2.99368	−	9.97590i	0.171982	−	0.573101i
$304$		−	0.163680i		−	0.00938770i
$305$	5.07381			0.290526
$306$	9.87899	+	6.51598i	0.564744	+	0.372494i
$307$		−	28.0466i		−	1.60070i	−0.599531	−	0.800351i	$-0.704646\pi$
$307$		−	28.0466i		−	1.60070i	0.599531	−	0.800351i	$-0.295354\pi$
$308$	−3.92676	+	0.706041i	−0.223748	+	0.0402304i
$309$	−1.69533	+	5.64938i	−0.0964438	+	0.321382i
$310$		−	0.0486546i		−	0.00276339i
$311$		−	0.167029i		−	0.00947136i	−0.999989	−	0.00473568i	$-0.998493\pi$
$311$		−	0.167029i		−	0.00947136i	0.999989	−	0.00473568i	$-0.00150742\pi$
$312$	27.7344	+	8.32283i	1.57015	+	0.471187i
$313$	−3.92631			−0.221928			−0.110964	−	0.993824i	$-0.535394\pi$
$313$	−3.92631			−0.221928			−0.110964	+	0.993824i	$0.535394\pi$
$314$	−17.0635			−0.962951
$315$	2.50431	+	1.65179i	0.141102	+	0.0930680i
$316$			9.02113i			0.507478i
$317$		−	7.45740i		−	0.418849i	−0.977825	−	0.209425i	$-0.932841\pi$
$317$		−	7.45740i		−	0.418849i	0.977825	−	0.209425i	$-0.0671591\pi$
$318$	−0.378640	−	0.113626i	−0.0212331	−	0.00637186i
$319$	5.72599	+	31.8461i	0.320594	+	1.78304i
$320$		−	5.28268i		−	0.295311i
$321$	−0.316486	+	1.05463i	−0.0176645	+	0.0588640i
$322$	−6.62433			−0.369160
$323$			4.91939i			0.273722i
$324$	−4.26224	−	9.95225i	−0.236791	−	0.552903i
$325$		−	5.84640i		−	0.324300i
$326$	1.18371			0.0655595
$327$	10.1539	+	3.04709i	0.561511	+	0.168504i
$328$	2.77271			0.153097
$329$	−11.0023			−0.606578
$330$	−0.581555	+	5.09554i	−0.0320136	+	0.280500i
$331$	−19.6177			−1.07829			−0.539143	−	0.842214i	$-0.681252\pi$
$331$	−19.6177			−1.07829			−0.539143	+	0.842214i	$0.681252\pi$
$332$	−6.99474			−0.383886
$333$	10.2627	+	6.76909i	0.562394	+	0.370944i
$334$	−1.88881			−0.103351
$335$		−	5.79382i		−	0.316550i
$336$	0.243895	+	0.0731905i	0.0133055	+	0.00399287i
$337$			0.0388756i			0.00211769i	0.999999	+	0.00105884i	$0.000337041\pi$
$337$			0.0388756i			0.00211769i	−0.999999	+	0.00105884i	$0.999663\pi$
$338$	18.9094			1.02853
$339$	−34.6111	−	10.3865i	−1.87982	−	0.564116i
$340$			5.31530i			0.288263i
$341$	−0.0319862	−	0.177897i	−0.00173215	−	0.00963364i
$342$	−1.64183	+	2.48921i	−0.0887801	+	0.134601i
$343$			1.00000i			0.0539949i
$344$		−	2.79665i		−	0.150785i
$345$	3.69393	−	12.3094i	0.198874	−	0.662714i
$346$	−5.07581			−0.272877
$347$	−30.9137			−1.65953			−0.829766	−	0.558111i	$-0.811526\pi$
$347$	−30.9137			−1.65953			−0.829766	+	0.558111i	$0.811526\pi$
$348$	−5.84258	+	19.4694i	−0.313195	+	1.04367i
$349$			25.4753i			1.36366i	0.731511	+	0.681830i	$0.238815\pi$
$349$			25.4753i			1.36366i	−0.731511	+	0.681830i	$0.761185\pi$
$350$		−	0.892777i		−	0.0477209i
$351$	−19.4816	−	23.3096i	−1.03985	−	1.24418i
$352$	−3.27961	−	18.2401i	−0.174804	−	0.972200i
$353$			30.1900i			1.60685i	0.595406	+	0.803425i	$0.296991\pi$
$353$			30.1900i			1.60685i	−0.595406	+	0.803425i	$0.703009\pi$
$354$	−2.76145	−	0.828686i	−0.146770	−	0.0440442i
$355$	14.9085			0.791261
$356$			16.7201i			0.886161i
$357$	−7.33023	−	2.19973i	−0.387957	−	0.116422i
$358$		−	4.17529i		−	0.220671i
$359$	−5.14070			−0.271316			−0.135658	−	0.990756i	$-0.543315\pi$
$359$	−5.14070			−0.271316			−0.135658	+	0.990756i	$0.543315\pi$
$360$	−4.72334	+	7.16113i	−0.248942	+	0.377425i
$361$	17.7605			0.934761
$362$	−14.6617			−0.770601
$363$	1.22353	+	19.0132i	0.0642186	+	0.997936i
$364$	−7.03292			−0.368625
$365$	7.44139			0.389500
$366$	−7.51474	−	2.25510i	−0.392802	−	0.117876i
$367$	−12.9589			−0.676450			−0.338225	−	0.941065i	$-0.609826\pi$
$367$	−12.9589			−0.676450			−0.338225	+	0.941065i	$0.609826\pi$
$368$		−	1.09085i		−	0.0568645i
$369$	−2.42828	−	1.60165i	−0.126411	−	0.0833784i
$370$		−	3.65862i		−	0.190203i
$371$	0.255651			0.0132727
$372$	0.0326375	−	0.108759i	0.00169218	−	0.00563888i
$373$		−	13.3151i		−	0.689430i	−0.938707	−	0.344715i	$-0.887976\pi$
$373$		−	13.3151i		−	0.689430i	0.938707	−	0.344715i	$-0.112024\pi$
$374$	−2.31530	−	12.8769i	−0.119721	−	0.665849i
$375$	1.65896	+	0.497839i	0.0856684	+	0.0257083i
$376$		−	31.4614i		−	1.62250i
$377$			57.0370i			2.93756i
$378$	−2.97494	−	3.55951i	−0.153014	−	0.183081i
$379$	15.0499			0.773061			0.386531	−	0.922277i	$-0.373673\pi$
$379$	15.0499			0.773061			0.386531	+	0.922277i	$0.373673\pi$
$380$	−1.33930			−0.0687045
$381$	25.5168	+	7.65737i	1.30727	+	0.392299i
$382$			13.1183i			0.671190i
$383$		−	8.81421i		−	0.450385i	−0.974314	−	0.225192i	$-0.927699\pi$
$383$		−	8.81421i		−	0.450385i	0.974314	−	0.225192i	$-0.0723011\pi$
$384$	3.21570	−	10.7158i	0.164101	−	0.546836i
$385$	−0.586925	−	3.26428i	−0.0299125	−	0.166363i
$386$		−	7.69667i		−	0.391750i
$387$	−1.61548	+	2.44925i	−0.0821192	+	0.124502i
$388$	−1.80889			−0.0918323
$389$			9.32907i			0.473003i	0.971631	+	0.236501i	$0.0760008\pi$
$389$			9.32907i			0.473003i	−0.971631	+	0.236501i	$0.923999\pi$
$390$	−2.59849	+	8.65901i	−0.131580	+	0.438466i
$391$			32.7854i			1.65803i
$392$	−2.85952			−0.144428
$393$	7.89743	−	26.3168i	0.398373	−	1.32751i
$394$	22.5550			1.13631
$395$	−7.49918			−0.377325
$396$	−4.71805	+	11.0001i	−0.237091	+	0.552774i
$397$	9.98945			0.501356			0.250678	−	0.968071i	$-0.419346\pi$
$397$	9.98945			0.501356			0.250678	+	0.968071i	$0.419346\pi$
$398$	−12.3804			−0.620574
$399$	0.554267	−	1.84700i	0.0277481	−	0.0924656i
$400$	0.147016			0.00735082
$401$		−	6.99266i		−	0.349197i	−0.984640	−	0.174598i	$-0.944137\pi$
$401$		−	6.99266i		−	0.349197i	0.984640	−	0.174598i	$-0.0558627\pi$
$402$	−2.57512	+	8.58113i	−0.128435	+	0.427988i
$403$		−	0.318617i		−	0.0158714i
$404$	−7.23374			−0.359892
$405$	8.27321	−	3.54316i	0.411099	−	0.176061i
$406$			8.70987i			0.432263i
$407$	−2.40523	−	13.3771i	−0.119223	−	0.663078i
$408$	6.29018	−	20.9609i	0.311410	−	1.03772i
$409$			15.1903i			0.751111i	0.926800	+	0.375555i	$0.122548\pi$
$409$			15.1903i			0.751111i	−0.926800	+	0.375555i	$0.877452\pi$
$410$			0.865673i			0.0427526i
$411$	−1.18351	−	0.355161i	−0.0583784	−	0.0175188i
$412$	4.09649			0.201819
$413$	1.86448			0.0917451
$414$	−10.9420	+	16.5894i	−0.537771	+	0.815324i
$415$		−	5.81466i		−	0.285430i
$416$		−	32.6684i		−	1.60170i
$417$	21.5277	+	6.46026i	1.05421	+	0.316360i
$418$	3.24459	−	0.583386i	0.158698	−	0.0285343i
$419$		−	14.1845i		−	0.692959i	−0.938058	−	0.346479i	$-0.887377\pi$
$419$		−	14.1845i		−	0.692959i	0.938058	−	0.346479i	$-0.112623\pi$
$420$	0.598875	−	1.99565i	0.0292221	−	0.0973776i
$421$	12.4846			0.608462			0.304231	−	0.952598i	$-0.401601\pi$
$421$	12.4846			0.608462			0.304231	+	0.952598i	$0.401601\pi$
$422$		−	23.9202i		−	1.16442i
$423$	−18.1736	+	27.5533i	−0.883630	+	1.33969i
$424$			0.731039i			0.0355024i
$425$	−4.41856			−0.214332
$426$	−22.0807	−	6.62622i	−1.06981	−	0.321042i
$427$	5.07381			0.245539
$428$	0.764738			0.0369650
$429$	−3.80835	+	33.3684i	−0.183869	+	1.61104i
$430$	0.873148			0.0421069
$431$	20.1231			0.969294			0.484647	−	0.874710i	$-0.338948\pi$
$431$	20.1231			0.969294			0.484647	+	0.874710i	$0.338948\pi$
$432$	0.586156	−	0.489893i	0.0282014	−	0.0235700i
$433$	8.03765			0.386265			0.193133	−	0.981173i	$-0.438135\pi$
$433$	8.03765			0.386265			0.193133	+	0.981173i	$0.438135\pi$
$434$		−	0.0486546i		−	0.00233549i
$435$	−16.1847	−	4.85688i	−0.775997	−	0.232870i
$436$		−	7.36280i		−	0.352614i
$437$	−8.26093			−0.395174
$438$	−11.0213	−	3.30740i	−0.526619	−	0.158033i
$439$		−	9.63512i		−	0.459859i	−0.973207	−	0.229930i	$-0.926150\pi$
$439$		−	9.63512i		−	0.459859i	0.973207	−	0.229930i	$-0.0738496\pi$
$440$	9.33427	−	1.67832i	0.444994	−	0.0800109i
$441$	2.50431	+	1.65179i	0.119253	+	0.0786568i
$442$		−	23.0628i		−	1.09699i
$443$			14.4188i			0.685058i	0.939507	+	0.342529i	$0.111283\pi$
$443$			14.4188i			0.685058i	−0.939507	+	0.342529i	$0.888717\pi$
$444$	2.45420	−	8.17820i	0.116471	−	0.388120i
$445$	−13.8992			−0.658886
$446$	17.8629			0.845833
$447$	−1.47842	+	4.92657i	−0.0699268	+	0.233019i
$448$		−	5.28268i		−	0.249583i
$449$		−	27.2011i		−	1.28370i	−0.766831	−	0.641849i	$-0.778168\pi$
$449$		−	27.2011i		−	1.28370i	0.766831	−	0.641849i	$-0.221832\pi$
$450$	−2.23579	−	1.47468i	−0.105396	−	0.0695172i
$451$	0.569106	+	3.16518i	0.0267982	+	0.149042i
$452$			25.0972i			1.18048i
$453$	9.40479	+	2.82229i	0.441875	+	0.132603i
$454$	17.4985			0.821245
$455$		−	5.84640i		−	0.274083i
$456$	5.28153	+	1.58494i	0.247330	+	0.0742215i
$457$		−	24.4078i		−	1.14175i	−0.821038	−	0.570874i	$-0.806605\pi$
$457$		−	24.4078i		−	1.14175i	0.821038	−	0.570874i	$-0.193395\pi$
$458$	19.4790			0.910192
$459$	−17.6168	+	14.7237i	−0.822284	+	0.687242i
$460$	−8.92578			−0.416167
$461$	25.1867			1.17306			0.586531	−	0.809927i	$-0.300493\pi$
$461$	25.1867			1.17306			0.586531	+	0.809927i	$0.300493\pi$
$462$	−0.581555	+	5.09554i	−0.0270564	+	0.237066i
$463$	7.45335			0.346386			0.173193	−	0.984888i	$-0.444591\pi$
$463$	7.45335			0.346386			0.173193	+	0.984888i	$0.444591\pi$
$464$	−1.43428			−0.0665848
$465$	0.0904101	+	0.0271312i	0.00419267	+	0.00125818i
$466$	−5.01665			−0.232392
$467$			2.92853i			0.135516i	0.997702	+	0.0677582i	$0.0215846\pi$
$467$			2.92853i			0.135516i	−0.997702	+	0.0677582i	$0.978415\pi$
$468$	−11.6169	+	17.6126i	−0.536993	+	0.814144i
$469$		−	5.79382i		−	0.267534i
$470$	9.82263			0.453084
$471$	9.51514	−	31.7075i	0.438435	−	1.46101i
$472$			5.33152i			0.245403i
$473$	3.19251	−	0.574020i	0.146792	−	0.0263935i
$474$	11.1069	+	3.33308i	0.510157	+	0.153094i
$475$		−	1.11335i		−	0.0510838i
$476$			5.31530i			0.243627i
$477$	0.422282	−	0.640230i	0.0193350	−	0.0293141i
$478$	−19.5540			−0.894379
$479$	36.1265			1.65066			0.825330	−	0.564651i	$-0.190989\pi$
$479$	36.1265			1.65066			0.825330	+	0.564651i	$0.190989\pi$
$480$	9.26993	+	2.78182i	0.423112	+	0.126972i
$481$		−	23.9587i		−	1.09242i
$482$			23.5510i			1.07272i
$483$	3.69393	−	12.3094i	0.168079	−	0.560095i
$484$	12.4037	−	4.60943i	0.563802	−	0.209519i
$485$		−	1.50371i		−	0.0682800i
$486$	−13.8281	+	1.57060i	−0.627256	+	0.0712440i
$487$	−29.8685			−1.35347			−0.676735	−	0.736227i	$-0.736606\pi$
$487$	−29.8685			−1.35347			−0.676735	+	0.736227i	$0.736606\pi$
$488$			14.5087i			0.656776i
$489$	−0.660071	+	2.19957i	−0.0298494	+	0.0994680i
$490$		−	0.892777i		−	0.0403316i
$491$	−8.52944			−0.384928			−0.192464	−	0.981304i	$-0.561648\pi$
$491$	−8.52944			−0.384928			−0.192464	+	0.981304i	$0.561648\pi$
$492$	−0.580694	+	1.93506i	−0.0261797	+	0.0872393i
$493$	43.1072			1.94145
$494$	5.81115			0.261456
$495$	−9.14425	−	3.92207i	−0.411004	−	0.176284i
$496$	0.00801210			0.000359754
$497$	14.9085			0.668737
$498$	−2.58438	+	8.61199i	−0.115809	+	0.385913i
$499$	29.2554			1.30965			0.654825	−	0.755780i	$-0.272742\pi$
$499$	29.2554			1.30965			0.654825	+	0.755780i	$0.272742\pi$
$500$		−	1.20295i		−	0.0537975i
$501$	1.05326	−	3.50979i	0.0470560	−	0.156806i
$502$		−	17.9857i		−	0.802740i
$503$	14.2300			0.634482			0.317241	−	0.948345i	$-0.397244\pi$
$503$	14.2300			0.634482			0.317241	+	0.948345i	$0.397244\pi$
$504$	−4.72334	+	7.16113i	−0.210394	+	0.318982i
$505$		−	6.01334i		−	0.267590i
$506$	21.6237	−	3.88799i	0.961290	−	0.172842i
$507$	−10.5444	+	35.1375i	−0.468295	+	1.56051i
$508$		−	18.5028i		−	0.820929i
$509$		−	1.97023i		−	0.0873287i	−0.999046	−	0.0436644i	$-0.986097\pi$
$509$		−	1.97023i		−	0.0873287i	0.999046	−	0.0436644i	$-0.0139032\pi$
$510$	6.54426	+	1.96387i	0.289785	+	0.0869617i
$511$	7.44139			0.329188
$512$	1.66229			0.0734635
$513$	−3.70993	−	4.43892i	−0.163797	−	0.195983i
$514$		−	6.79054i		−	0.299518i
$515$			3.40537i			0.150059i
$516$	1.95177	+	0.585708i	0.0859218	+	0.0257843i
$517$	35.9147	−	6.45754i	1.57953	−	0.284002i
$518$		−	3.65862i		−	0.160751i
$519$	2.83043	−	9.43190i	0.124242	−	0.414014i
$520$	16.7179			0.733128
$521$		−	8.08247i		−	0.354100i	−0.984202	−	0.177050i	$-0.943345\pi$
$521$		−	8.08247i		−	0.354100i	0.984202	−	0.177050i	$-0.0566554\pi$
$522$	21.8122	+	14.3869i	0.954695	+	0.629697i
$523$			30.0429i			1.31369i	0.754028	+	0.656843i	$0.228108\pi$
$523$			30.0429i			1.31369i	−0.754028	+	0.656843i	$0.771892\pi$
$524$	−19.0829			−0.833640
$525$	1.65896	+	0.497839i	0.0724031	+	0.0217275i
$526$	15.2485			0.664865
$527$	−0.240803			−0.0104895
$528$	−0.839098	−	0.0957665i	−0.0365170	−	0.00416770i
$529$	−32.0552			−1.39370
$530$	−0.228239			−0.00991408
$531$	3.07974	−	4.66924i	0.133649	−	0.202628i
$532$	−1.33930			−0.0580659
$533$			5.66891i			0.245548i
$534$	20.5859	+	6.17764i	0.890840	+	0.267333i
$535$			0.635719i			0.0274845i
$536$	16.5675			0.715609
$537$	7.75854	+	2.32827i	0.334806	+	0.100472i
$538$		−	12.5266i		−	0.540061i
$539$	−0.586925	−	3.26428i	−0.0252806	−	0.140602i
$540$	−4.00850	−	4.79617i	−0.172499	−	0.206394i
$541$		−	12.5226i		−	0.538387i	−0.963086	−	0.269193i	$-0.913243\pi$
$541$		−	12.5226i		−	0.538387i	0.963086	−	0.269193i	$-0.0867570\pi$
$542$		−	20.1715i		−	0.866439i
$543$	8.17580	−	27.2444i	0.350857	−	1.16917i
$544$	−24.6900			−1.05857
$545$	6.12063			0.262179
$546$	−2.59849	+	8.65901i	−0.111205	+	0.370571i
$547$		−	3.01998i		−	0.129125i	−0.997914	−	0.0645625i	$-0.979435\pi$
$547$		−	3.01998i		−	0.129125i	0.997914	−	0.0645625i	$-0.0205652\pi$
$548$			0.858191i			0.0366601i
$549$	8.38089	−	12.7064i	0.357688	−	0.542296i
$550$	0.523993	+	2.91427i	0.0223431	+	0.124265i
$551$			10.8617i			0.462725i
$552$	35.1989	+	10.5629i	1.49816	+	0.449585i
$553$	−7.49918			−0.318898
$554$			27.0876i			1.15084i
$555$	6.79846	+	2.04016i	0.288579	+	0.0865998i
$556$		−	15.6102i		−	0.662019i
$557$	−10.7167			−0.454081			−0.227041	−	0.973885i	$-0.572905\pi$
$557$	−10.7167			−0.454081			−0.227041	+	0.973885i	$0.572905\pi$
$558$	−0.121846	−	0.0803673i	−0.00515816	−	0.00340222i
$559$	5.71786			0.241840
$560$	0.147016			0.00621258
$561$	25.2190	+	2.87825i	1.06475	+	0.121520i
$562$	−11.2912			−0.476292
$563$	−34.1868			−1.44080			−0.720401	−	0.693557i	$-0.756042\pi$
$563$	−34.1868			−1.44080			−0.720401	+	0.693557i	$0.756042\pi$
$564$	21.9568	+	6.58902i	0.924547	+	0.277448i
$565$	−20.8631			−0.877717
$566$			21.4035i			0.899655i
$567$	8.27321	−	3.54316i	0.347442	−	0.148799i
$568$			42.6311i			1.78876i
$569$	7.18169			0.301072			0.150536	−	0.988605i	$-0.451900\pi$
$569$	7.18169			0.301072			0.150536	+	0.988605i	$0.451900\pi$
$570$	−0.494837	+	1.64896i	−0.0207265	+	0.0690673i
$571$		−	10.4236i		−	0.436213i	−0.975925	−	0.218107i	$-0.930012\pi$
$571$		−	10.4236i		−	0.436213i	0.975925	−	0.218107i	$-0.0699880\pi$
$572$	22.9574	−	4.12780i	0.959898	−	0.172592i
$573$	−24.3765	−	7.31515i	−1.01834	−	0.305595i
$574$			0.865673i			0.0361325i
$575$		−	7.41992i		−	0.309432i
$576$	−13.2295	−	8.72590i	−0.551228	−	0.363579i
$577$	−15.1484			−0.630635			−0.315317	−	0.948986i	$-0.602111\pi$
$577$	−15.1484			−0.630635			−0.315317	+	0.948986i	$0.602111\pi$
$578$	−2.25310			−0.0937165
$579$	14.3020	+	4.29189i	0.594370	+	0.178365i
$580$			11.7359i			0.487306i
$581$		−	5.81466i		−	0.241233i
$582$	−0.668338	+	2.22712i	−0.0277035	+	0.0923171i
$583$	−0.834516	+	0.150048i	−0.0345621	+	0.00621435i
$584$			21.2788i			0.880523i
$585$	−14.6412	−	9.65705i	−0.605340	−	0.399270i
$586$	−19.1074			−0.789321
$587$			9.41964i			0.388790i	0.980923	+	0.194395i	$0.0622744\pi$
$587$			9.41964i			0.388790i	−0.980923	+	0.194395i	$0.937726\pi$
$588$	0.598875	−	1.99565i	0.0246972	−	0.0822991i
$589$		−	0.0606751i		−	0.00250007i
$590$	−1.66457			−0.0685291
$591$	−12.5774	+	41.9119i	−0.517364	+	1.72402i
$592$	0.602476			0.0247616
$593$	25.9000			1.06359			0.531793	−	0.846874i	$-0.321518\pi$
$593$	25.9000			1.06359			0.531793	+	0.846874i	$0.321518\pi$
$594$	11.8002	+	9.87317i	0.484168	+	0.405101i
$595$	−4.41856			−0.181143
$596$	3.57236			0.146330
$597$	6.90369	−	23.0053i	0.282549	−	0.941545i
$598$	38.7285			1.58373
$599$			14.9065i			0.609062i	0.952502	+	0.304531i	$0.0984998\pi$
$599$			14.9065i			0.609062i	−0.952502	+	0.304531i	$0.901500\pi$
$600$	−1.42358	+	4.74384i	−0.0581175	+	0.193666i
$601$			14.1834i			0.578553i	0.957246	+	0.289277i	$0.0934148\pi$
$601$			14.1834i			0.578553i	−0.957246	+	0.289277i	$0.906585\pi$
$602$	0.873148			0.0355868
$603$	−14.5095	−	9.57019i	−0.590874	−	0.389728i
$604$		−	6.81961i		−	0.277486i
$605$	3.83177	+	10.3110i	0.155784	+	0.419203i
$606$	−2.67269	+	8.90626i	−0.108570	+	0.361792i
$607$			28.8272i			1.17006i	0.811011	+	0.585031i	$0.198918\pi$
$607$			28.8272i			1.17006i	−0.811011	+	0.585031i	$0.801082\pi$
$608$		−	6.22114i		−	0.252300i
$609$	−16.1847	−	4.85688i	−0.655837	−	0.196811i
$610$	−4.52978			−0.183406
$611$	64.3240			2.60227
$612$	13.3112	+	8.77979i	0.538073	+	0.354902i
$613$		−	43.1377i		−	1.74231i	−0.491005	−	0.871157i	$-0.663370\pi$
$613$		−	43.1377i		−	1.74231i	0.491005	−	0.871157i	$-0.336630\pi$
$614$			25.0393i			1.01051i
$615$	−1.60860	−	0.482725i	−0.0648649	−	0.0194654i
$616$	9.33427	−	1.67832i	0.376088	−	0.0676216i
$617$			7.90417i			0.318210i	0.987262	+	0.159105i	$0.0508609\pi$
$617$			7.90417i			0.318210i	−0.987262	+	0.159105i	$0.949139\pi$
$618$	1.51355	−	5.04364i	0.0608839	−	0.202885i
$619$	−44.0066			−1.76878			−0.884388	−	0.466753i	$-0.845424\pi$
$619$	−44.0066			−1.76878			−0.884388	+	0.466753i	$0.845424\pi$
$620$		−	0.0655583i		−	0.00263288i
$621$	−24.7249	−	29.5833i	−0.992175	−	1.18714i
$622$			0.149120i			0.00597916i
$623$	−13.8992			−0.556861
$624$	−1.42591	−	0.427901i	−0.0570819	−	0.0171298i
$625$	1.00000			0.0400000
$626$	3.50532			0.140101
$627$	−0.725234	+	6.35443i	−0.0289630	+	0.253772i
$628$	−22.9918			−0.917473
$629$	−18.1074			−0.721988
$630$	−2.23579	−	1.47468i	−0.0890761	−	0.0587528i
$631$	−23.7308			−0.944707			−0.472354	−	0.881409i	$-0.656595\pi$
$631$	−23.7308			−0.944707			−0.472354	+	0.881409i	$0.656595\pi$
$632$		−	21.4441i		−	0.852999i
$633$	44.4486	+	13.3386i	1.76667	+	0.530162i
$634$			6.65780i			0.264415i
$635$	15.3812			0.610385
$636$	−0.510189	−	0.153103i	−0.0202303	−	0.00607093i
$637$		−	5.84640i		−	0.231643i
$638$	−5.11204	−	28.4314i	−0.202387	−	1.12561i
$639$	24.6257	−	37.3355i	0.974179	−	1.47697i
$640$		−	6.45932i		−	0.255327i
$641$		−	4.21471i		−	0.166471i	−0.996530	−	0.0832354i	$-0.973475\pi$
$641$		−	4.21471i		−	0.166471i	0.996530	−	0.0832354i	$-0.0265253\pi$
$642$	0.282552	−	0.941554i	0.0111514	−	0.0371602i
$643$	11.5653			0.456091			0.228045	−	0.973651i	$-0.426767\pi$
$643$	11.5653			0.456091			0.228045	+	0.973651i	$0.426767\pi$
$644$	−8.92578			−0.351725
$645$	−0.486893	+	1.62249i	−0.0191714	+	0.0638853i
$646$		−	4.39192i		−	0.172798i
$647$			3.04184i			0.119587i	0.998211	+	0.0597936i	$0.0190443\pi$
$647$			3.04184i			0.119587i	−0.998211	+	0.0597936i	$0.980956\pi$
$648$	10.1317	+	23.6574i	0.398012	+	0.929351i
$649$	−6.08619	+	1.09431i	−0.238904	+	0.0429554i
$650$			5.21953i			0.204727i
$651$	0.0904101	+	0.0271312i	0.00354345	+	0.00106336i
$652$	1.59496			0.0624633
$653$		−	0.775978i		−	0.0303664i	−0.999885	−	0.0151832i	$-0.995167\pi$
$653$		−	0.775978i		−	0.0303664i	0.999885	−	0.0151832i	$-0.00483314\pi$
$654$	−9.06516	−	2.72037i	−0.354476	−	0.106375i
$655$		−	15.8634i		−	0.619835i
$656$	−0.142553			−0.00556576
$657$	12.2916	−	18.6356i	0.479542	−	0.727042i
$658$	9.82263			0.382926
$659$	18.3466			0.714682			0.357341	−	0.933974i	$-0.383683\pi$
$659$	18.3466			0.714682			0.357341	+	0.933974i	$0.383683\pi$
$660$	−0.783601	+	6.86584i	−0.0305016	+	0.267253i
$661$	2.24863			0.0874615			0.0437308	−	0.999043i	$-0.486076\pi$
$661$	2.24863			0.0874615			0.0437308	+	0.999043i	$0.486076\pi$
$662$	17.5142			0.680710
$663$	42.8555	+	12.8605i	1.66437	+	0.499462i
$664$	16.6271			0.645258
$665$		−	1.11335i		−	0.0431737i
$666$	−9.16233	−	6.04329i	−0.355033	−	0.234173i
$667$			72.3881i			2.80288i
$668$	−2.54502			−0.0984699
$669$	−9.96090	+	33.1929i	−0.385110	+	1.28331i
$670$			5.17259i			0.199835i
$671$	−16.5623	+	2.97795i	−0.639382	+	0.114962i
$672$	9.26993	+	2.78182i	0.357595	+	0.107311i
$673$		−	25.9590i		−	1.00065i	−0.865839	−	0.500323i	$-0.833215\pi$
$673$		−	25.9590i		−	1.00065i	0.865839	−	0.500323i	$-0.166785\pi$
$674$		−	0.0347073i		−	0.00133687i
$675$	3.98701	−	3.33223i	0.153460	−	0.128258i
$676$	25.4789			0.979959
$677$	25.4263			0.977212			0.488606	−	0.872504i	$-0.337506\pi$
$677$	25.4263			0.977212			0.488606	+	0.872504i	$0.337506\pi$
$678$	30.9000	+	9.27281i	1.18671	+	0.356120i
$679$		−	1.50371i		−	0.0577071i
$680$		−	12.6350i		−	0.484529i
$681$	−9.75768	+	32.5158i	−0.373915	+	1.24601i
$682$	0.0285566	+	0.158822i	0.00109349	+	0.00608161i
$683$		−	39.9152i		−	1.52731i	−0.645623	−	0.763656i	$-0.723402\pi$
$683$		−	39.9152i		−	1.52731i	0.645623	−	0.763656i	$-0.276598\pi$
$684$	−2.21224	+	3.35402i	−0.0845872	+	0.128244i
$685$	−0.713406			−0.0272578
$686$		−	0.892777i		−	0.0340864i
$687$	−10.8620	+	36.1959i	−0.414413	+	1.38096i
$688$			0.143784i			0.00548171i
$689$	−1.49464			−0.0569411
$690$	−3.29785	+	10.9895i	−0.125547	+	0.418364i
$691$	16.9022			0.642990			0.321495	−	0.946911i	$-0.395815\pi$
$691$	16.9022			0.642990			0.321495	+	0.946911i	$0.395815\pi$
$692$	−6.83927			−0.259990
$693$	−9.14425	−	3.92207i	−0.347361	−	0.148987i
$694$	27.5990			1.04764
$695$	12.9766			0.492230
$696$	13.8884	−	46.2805i	0.526437	−	1.75426i
$697$	4.28442			0.162284
$698$		−	22.7437i		−	0.860863i
$699$	2.79744	−	9.32196i	0.105809	−	0.352589i
$700$		−	1.20295i		−	0.0454672i
$701$	14.1171			0.533196			0.266598	−	0.963808i	$-0.414100\pi$
$701$	14.1171			0.533196			0.266598	+	0.963808i	$0.414100\pi$
$702$	17.3927	+	20.8103i	0.656445	+	0.785435i
$703$		−	4.56252i		−	0.172079i
$704$	3.10054	+	17.2441i	0.116856	+	0.649913i
$705$	−5.47739	+	18.2525i	−0.206291	+	0.687427i
$706$		−	26.9529i		−	1.01439i
$707$		−	6.01334i		−	0.226155i
$708$	−3.72085	−	1.11659i	−0.139838	−	0.0419641i
$709$	32.2985			1.21300			0.606498	−	0.795085i	$-0.292574\pi$
$709$	32.2985			1.21300			0.606498	+	0.795085i	$0.292574\pi$
$710$	−13.3100			−0.499514
$711$	−12.3871	+	18.7803i	−0.464552	+	0.704316i
$712$		−	39.7451i		−	1.48951i
$713$		−	0.404371i		−	0.0151438i
$714$	6.54426	+	1.96387i	0.244913	+	0.0734961i
$715$	3.43140	+	19.0843i	0.128327	+	0.713712i
$716$		−	5.62588i		−	0.210249i
$717$	10.9039	−	36.3353i	0.407213	−	1.35697i
$718$	4.58950			0.171279
$719$			31.7776i			1.18510i	0.805532	+	0.592552i	$0.201880\pi$
$719$			31.7776i			1.18510i	−0.805532	+	0.592552i	$0.798120\pi$
$720$	0.242841	−	0.368175i	0.00905014	−	0.0137211i
$721$			3.40537i			0.126823i
$722$	−15.8561			−0.590104
$723$	−43.7625	−	13.1327i	−1.62755	−	0.488412i
$724$	−19.7555			−0.734207
$725$	−9.75592			−0.362326
$726$	−1.09234	−	16.9746i	−0.0405405	−	0.629986i
$727$	11.9005			0.441365			0.220682	−	0.975346i	$-0.429172\pi$
$727$	11.9005			0.441365			0.220682	+	0.975346i	$0.429172\pi$
$728$	16.7179			0.619607
$729$	4.79247	−	26.5713i	0.177499	−	0.984121i
$730$	−6.64350			−0.245887
$731$		−	4.32141i		−	0.159833i
$732$	−10.1255	−	3.03858i	−0.374251	−	0.112309i
$733$			23.7923i			0.878789i	0.898294	+	0.439394i	$0.144807\pi$
$733$			23.7923i			0.878789i	−0.898294	+	0.439394i	$0.855193\pi$
$734$	11.5694			0.427035
$735$	1.65896	+	0.497839i	0.0611917	+	0.0183631i
$736$		−	41.4609i		−	1.52827i
$737$	3.40054	+	18.9126i	0.125260	+	0.696656i
$738$	2.16792	+	1.42991i	0.0798021	+	0.0526358i
$739$		−	33.4853i		−	1.23178i	−0.787833	−	0.615888i	$-0.788797\pi$
$739$		−	33.4853i		−	1.23178i	0.787833	−	0.615888i	$-0.211203\pi$
$740$		−	4.92971i		−	0.181220i
$741$	−3.24047	+	10.7983i	−0.119042	+	0.396685i
$742$	−0.228239			−0.00837893
$743$	14.4978			0.531874			0.265937	−	0.963990i	$-0.414319\pi$
$743$	14.4978			0.531874			0.265937	+	0.963990i	$0.414319\pi$
$744$	−0.0775823	+	0.258530i	−0.00284431	+	0.00947815i
$745$			2.96967i			0.108800i
$746$			11.8874i			0.435230i
$747$	−14.5617	−	9.60461i	−0.532785	−	0.351414i
$748$	−3.11968	−	17.3506i	−0.114067	−	0.634402i
$749$			0.635719i			0.0232287i
$750$	−1.48108	−	0.444460i	−0.0540815	−	0.0162294i
$751$	1.68038			0.0613180			0.0306590	−	0.999530i	$-0.490239\pi$
$751$	1.68038			0.0613180			0.0306590	+	0.999530i	$0.490239\pi$
$752$			1.61752i			0.0589850i
$753$	33.4211	+	10.0294i	1.21793	+	0.365490i
$754$		−	50.9214i		−	1.85445i
$755$	5.66908			0.206319
$756$	−4.00850	−	4.79617i	−0.145788	−	0.174435i
$757$	−3.95277			−0.143666			−0.0718329	−	0.997417i	$-0.522885\pi$
$757$	−3.95277			−0.143666			−0.0718329	+	0.997417i	$0.522885\pi$
$758$	−13.4362			−0.488025
$759$	−4.83334	+	42.3493i	−0.175439	+	1.53718i
$760$	3.18363			0.115483
$761$	−25.2785			−0.916343			−0.458172	−	0.888864i	$-0.651495\pi$
$761$	−25.2785			−0.916343			−0.458172	+	0.888864i	$0.651495\pi$
$762$	−22.7809	−	6.83633i	−0.825263	−	0.247654i
$763$	6.12063			0.221582
$764$			17.6759i			0.639491i
$765$	−7.29855	+	11.0655i	−0.263880	+	0.400073i
$766$			7.86912i			0.284323i
$767$	−10.9005			−0.393594
$768$	−8.13076	+	27.0943i	−0.293393	+	0.977682i
$769$			20.0407i			0.722687i	0.932433	+	0.361344i	$0.117682\pi$
$769$			20.0407i			0.722687i	−0.932433	+	0.361344i	$0.882318\pi$
$770$	0.523993	+	2.91427i	0.0188834	+	0.105023i
$771$	12.6182	+	3.78661i	0.454434	+	0.136371i
$772$		−	10.3707i		−	0.373249i
$773$			29.2596i			1.05239i	0.850363	+	0.526197i	$0.176383\pi$
$773$			29.2596i			1.05239i	−0.850363	+	0.526197i	$0.823617\pi$
$774$	1.44226	−	2.18663i	0.0518409	−	0.0785969i
$775$	0.0544980			0.00195763
$776$	4.29989			0.154357
$777$	6.79846	+	2.04016i	0.243894	+	0.0731902i
$778$		−	8.32879i		−	0.298601i
$779$			1.07955i			0.0386787i
$780$	−3.50126	+	11.6674i	−0.125365	+	0.417758i
$781$	−48.6655	+	8.75016i	−1.74139	+	0.313106i
$782$		−	29.2700i		−	1.04669i
$783$	−38.8969	+	32.5090i	−1.39006	+	1.16178i
$784$	0.147016			0.00525059
$785$		−	19.1129i		−	0.682168i
$786$	−7.05065	+	23.4951i	−0.251488	+	0.838041i
$787$			35.9854i			1.28274i	0.767231	+	0.641371i	$0.221634\pi$
$787$			35.9854i			1.28274i	−0.767231	+	0.641371i	$0.778366\pi$
$788$	30.3912			1.08264
$789$	−8.50301	+	28.3348i	−0.302715	+	1.00874i
$790$	6.69510			0.238201
$791$	−20.8631			−0.741807
$792$	11.2152	−	26.1482i	0.398516	−	0.929135i
$793$	−29.6635			−1.05338
$794$	−8.91835			−0.316500
$795$	0.127273	−	0.424115i	0.00451391	−	0.0150418i
$796$	−16.6816			−0.591265
$797$		−	40.4645i		−	1.43333i	−0.697419	−	0.716664i	$-0.745668\pi$
$797$		−	40.4645i		−	1.43333i	0.697419	−	0.716664i	$-0.254332\pi$
$798$	−0.494837	+	1.64896i	−0.0175170	+	0.0583725i
$799$		−	48.6145i		−	1.71986i
$800$	5.58779			0.197558
$801$	−22.9586	+	34.8080i	−0.811204	+	1.22988i
$802$			6.24289i			0.220444i
$803$	−24.2908	+	4.36753i	−0.857202	+	0.154127i
$804$	−3.46977	+	11.5624i	−0.122370	+	0.407775i
$805$		−	7.41992i		−	0.261518i
$806$			0.284454i			0.0100195i
$807$	23.2770	+	6.98523i	0.819391	+	0.245892i
$808$	17.1953			0.604927
$809$	20.3728			0.716270			0.358135	−	0.933670i	$-0.383413\pi$
$809$	20.3728			0.716270			0.358135	+	0.933670i	$0.383413\pi$
$810$	−7.38614	+	3.16325i	−0.259522	+	0.111145i
$811$		−	42.0966i		−	1.47821i	−0.673589	−	0.739107i	$-0.735248\pi$
$811$		−	42.0966i		−	1.47821i	0.673589	−	0.739107i	$-0.264752\pi$
$812$			11.7359i			0.411849i
$813$	37.4827	+	11.2482i	1.31458	+	0.394492i
$814$	2.14734	+	11.9428i	0.0752641	+	0.418593i
$815$			1.32587i			0.0464432i
$816$	−0.323397	+	1.07766i	−0.0113212	+	0.0377258i
$817$	1.08887			0.0380946
$818$		−	13.5615i		−	0.474168i
$819$	−14.6412	−	9.65705i	−0.511605	−	0.337444i
$820$			1.16643i			0.0407334i
$821$	32.5287			1.13526			0.567630	−	0.823284i	$-0.307861\pi$
$821$	32.5287			1.13526			0.567630	+	0.823284i	$0.307861\pi$
$822$	1.05661	+	0.317080i	0.0368536	+	0.0110594i
$823$	−47.7108			−1.66310			−0.831548	−	0.555454i	$-0.812545\pi$
$823$	−47.7108			−1.66310			−0.831548	+	0.555454i	$0.812545\pi$
$824$	−9.73773			−0.339230
$825$	−5.70751	−	0.651400i	−0.198710	−	0.0226788i
$826$	−1.66457			−0.0579177
$827$	−39.2286			−1.36411			−0.682057	−	0.731299i	$-0.738914\pi$
$827$	−39.2286			−1.36411			−0.682057	+	0.731299i	$0.738914\pi$
$828$	−14.7435	+	22.3529i	−0.512374	+	0.776818i
$829$	29.0589			1.00926			0.504629	−	0.863336i	$-0.331629\pi$
$829$	29.0589			1.00926			0.504629	+	0.863336i	$0.331629\pi$
$830$			5.19119i			0.180189i
$831$	−50.3343	−	15.1048i	−1.74608	−	0.523981i
$832$			30.8847i			1.07073i
$833$	−4.41856			−0.153094
$834$	−19.2194	−	5.76757i	−0.665514	−	0.199715i
$835$		−	2.11565i		−	0.0732152i
$836$	4.37184	−	0.786067i	0.151203	−	0.0271867i
$837$	0.217284	−	0.181600i	0.00751043	−	0.00627701i
$838$			12.6636i			0.437457i
$839$		−	12.7384i		−	0.439777i	−0.975525	−	0.219889i	$-0.929431\pi$
$839$		−	12.7384i		−	0.439777i	0.975525	−	0.219889i	$-0.0705694\pi$
$840$	−1.42358	+	4.74384i	−0.0491182	+	0.163678i
$841$	66.1780			2.28200
$842$	−11.1460			−0.384115
$843$	6.29633	−	20.9814i	0.216857	−	0.722639i
$844$		−	32.2306i		−	1.10942i
$845$			21.1804i			0.728628i
$846$	16.2250	−	24.5989i	0.557825	−	0.845729i
$847$	3.83177	+	10.3110i	0.131661	+	0.354291i
$848$		−	0.0375849i		−	0.00129067i
$849$	−39.7720	−	11.9352i	−1.36497	−	0.409615i
$850$	3.94479			0.135305
$851$		−	30.4070i		−	1.04234i
$852$	−29.7521	−	8.92833i	−1.01929	−	0.305879i
$853$		−	27.1415i		−	0.929307i	−0.885493	−	0.464653i	$-0.846179\pi$
$853$		−	27.1415i		−	0.929307i	0.885493	−	0.464653i	$-0.153821\pi$
$854$	−4.52978			−0.155006
$855$	−2.78817	−	1.83902i	−0.0953532	−	0.0628931i
$856$	−1.81785			−0.0621329
$857$	−46.5696			−1.59079			−0.795393	−	0.606094i	$-0.792736\pi$
$857$	−46.5696			−1.59079			−0.795393	+	0.606094i	$0.792736\pi$
$858$	3.40001	−	29.7905i	0.116074	−	1.01703i
$859$	−29.8891			−1.01980			−0.509902	−	0.860232i	$-0.670318\pi$
$859$	−29.8891			−1.01980			−0.509902	+	0.860232i	$0.670318\pi$
$860$	1.17650			0.0401183
$861$	−1.60860	−	0.482725i	−0.0548209	−	0.0164512i
$862$	−17.9654			−0.611905
$863$			38.4994i			1.31054i	0.755397	+	0.655268i	$0.227444\pi$
$863$			38.4994i			1.31054i	−0.755397	+	0.655268i	$0.772556\pi$
$864$	22.2786	−	18.6198i	0.757932	−	0.633458i
$865$		−	5.68542i		−	0.193310i
$866$	−7.17583			−0.243845
$867$	1.25639	−	4.18672i	0.0426694	−	0.142188i
$868$		−	0.0655583i		−	0.00222519i
$869$	24.4794	−	4.40146i	0.830407	−	0.149309i
$870$	14.4493	+	4.33611i	0.489878	+	0.147008i
$871$			33.8730i			1.14774i
$872$			17.5020i			0.592694i
$873$	−3.76576	−	2.48382i	−0.127452	−	0.0840645i
$874$	7.37517			0.249469
$875$	1.00000			0.0338062
$876$	−14.8504	−	4.45646i	−0.501748	−	0.150570i
$877$		−	0.233923i		−	0.00789900i	−0.999992	−	0.00394950i	$-0.998743\pi$
$877$		−	0.233923i		−	0.00789900i	0.999992	−	0.00394950i	$-0.00125717\pi$
$878$			8.60202i			0.290304i
$879$	10.6549	−	35.5055i	0.359380	−	1.19757i
$880$	−0.479903	+	0.0862876i	−0.0161775	+	0.00290875i
$881$		−	29.7264i		−	1.00151i	−0.865589	−	0.500755i	$-0.833056\pi$
$881$		−	29.7264i		−	1.00151i	0.865589	−	0.500755i	$-0.166944\pi$
$882$	−2.23579	−	1.47468i	−0.0752831	−	0.0496552i
$883$	−53.0285			−1.78455			−0.892276	−	0.451491i	$-0.850892\pi$
$883$	−53.0285			−1.78455			−0.892276	+	0.451491i	$0.850892\pi$
$884$		−	31.0754i		−	1.04518i
$885$	0.928212	−	3.09310i	0.0312015	−	0.103974i
$886$		−	12.8728i		−	0.432469i
$887$	−41.3446			−1.38821			−0.694107	−	0.719871i	$-0.744201\pi$
$887$	−41.3446			−1.38821			−0.694107	+	0.719871i	$0.744201\pi$
$888$	−5.83387	+	19.4403i	−0.195772	+	0.652375i
$889$	15.3812			0.515869
$890$	12.4089			0.415948
$891$	−24.9265	+	16.4216i	−0.835069	+	0.550145i
$892$	24.0689			0.805887
$893$	12.2494			0.409910
$894$	1.31990	−	4.39833i	0.0441440	−	0.147102i
$895$	4.67674			0.156326
$896$		−	6.45932i		−	0.215791i
$897$	−21.5962	+	71.9655i	−0.721075	+	2.40286i
$898$			24.2845i			0.810384i
$899$	−0.531678			−0.0177325
$900$	−3.01256	−	1.98702i	−0.100419	−	0.0662341i
$901$			1.12961i			0.0376327i
$902$	−0.508085	−	2.82580i	−0.0169174	−	0.0940888i
$903$	−0.486893	+	1.62249i	−0.0162028	+	0.0539930i
$904$		−	59.6585i		−	1.98421i
$905$		−	16.4226i		−	0.545904i
$906$	−8.39638	−	2.51968i	−0.278951	−	0.0837106i
$907$	21.4372			0.711810			0.355905	−	0.934522i	$-0.384173\pi$
$907$	21.4372			0.711810			0.355905	+	0.934522i	$0.384173\pi$
$908$	23.5779			0.782459
$909$	−15.0593	−	9.93279i	−0.499485	−	0.329450i
$910$			5.21953i			0.173026i
$911$		−	21.4511i		−	0.710705i	−0.934732	−	0.355353i	$-0.884361\pi$
$911$		−	21.4511i		−	0.710705i	0.934732	−	0.355353i	$-0.115639\pi$
$912$	−0.271539	−	0.0814864i	−0.00899156	−	0.00269828i
$913$	3.41277	+	18.9807i	0.112946	+	0.628168i
$914$			21.7907i			0.720772i
$915$	2.52594	−	8.41726i	0.0835051	−	0.278266i
$916$	26.2464			0.867205
$917$		−	15.8634i		−	0.523856i
$918$	15.7279	−	13.1450i	0.519099	−	0.433848i
$919$		−	9.18706i		−	0.303053i	−0.988453	−	0.151527i	$-0.951581\pi$
$919$		−	9.18706i		−	0.303053i	0.988453	−	0.151527i	$-0.0484189\pi$
$920$	21.2174			0.699517
$921$	−46.5282	−	13.9627i	−1.53316	−	0.460086i
$922$	−22.4861			−0.740541
$923$	−87.1610			−2.86894
$924$	−0.783601	+	6.86584i	−0.0257786	+	0.225870i
$925$	4.09802			0.134742
$926$	−6.65418			−0.218670
$927$	8.52811	+	5.62497i	0.280100	+	0.184748i
$928$	−54.5140			−1.78951
$929$		−	34.9132i		−	1.14546i	−0.819743	−	0.572732i	$-0.805884\pi$
$929$		−	34.9132i		−	1.14546i	0.819743	−	0.572732i	$-0.194116\pi$
$930$	−0.0807161	−	0.0242222i	−0.00264679	−	0.000794276i
$931$		−	1.11335i		−	0.0364884i
$932$	−6.75955			−0.221417
$933$	−0.277095	−	0.0831537i	−0.00907169	−	0.00272233i
$934$		−	2.61453i		−	0.0855500i
$935$	14.4234	−	2.59336i	0.471696	−	0.0848121i
$936$	27.6145	−	41.8668i	0.902609	−	1.36846i
$937$		−	7.98064i		−	0.260716i	−0.991467	−	0.130358i	$-0.958387\pi$
$937$		−	7.98064i		−	0.260716i	0.991467	−	0.130358i	$-0.0416127\pi$
$938$			5.17259i			0.168891i
$939$	−1.95467	+	6.51360i	−0.0637883	+	0.212563i
$940$	13.2352			0.431686
$941$	22.8666			0.745428			0.372714	−	0.927946i	$-0.378427\pi$
$941$	22.8666			0.745428			0.372714	+	0.927946i	$0.378427\pi$
$942$	−8.49490	+	28.3078i	−0.276779	+	0.922317i
$943$			7.19465i			0.234290i
$944$		−	0.274109i		−	0.00892150i
$945$	3.98701	−	3.33223i	0.129697	−	0.108397i
$946$	−2.85020	+	0.512472i	−0.0926679	+	0.0166619i
$947$		−	50.0580i		−	1.62667i	−0.581799	−	0.813333i	$-0.697651\pi$
$947$		−	50.0580i		−	1.62667i	0.581799	−	0.813333i	$-0.302349\pi$
$948$	14.9657	+	4.49107i	0.486064	+	0.145863i
$949$	−43.5053			−1.41224
$950$			0.993970i			0.0322486i
$951$	−12.3715	−	3.71259i	−0.401175	−	0.120389i
$952$		−	12.6350i		−	0.409502i
$953$	−35.1209			−1.13768			−0.568838	−	0.822449i	$-0.692607\pi$
$953$	−35.1209			−1.13768			−0.568838	+	0.822449i	$0.692607\pi$
$954$	−0.377004	+	0.571582i	−0.0122060	+	0.0185057i
$955$	−14.6938			−0.475480
$956$	−26.3475			−0.852139
$957$	55.6820	+	6.35501i	1.79994	+	0.205428i
$958$	−32.2529			−1.04204
$959$	−0.713406			−0.0230371
$960$	−8.76377	−	2.62993i	−0.282849	−	0.0848805i
$961$	−30.9970			−0.999904
$962$			21.3898i			0.689634i
$963$	1.59204	+	1.05008i	0.0513028	+	0.0338383i
$964$			31.7331i			1.02206i
$965$	8.62104			0.277521
$966$	−3.29785	+	10.9895i	−0.106107	+	0.353582i
$967$			9.12238i			0.293356i	0.989184	+	0.146678i	$0.0468581\pi$
$967$			9.12238i			0.293356i	−0.989184	+	0.146678i	$0.953142\pi$
$968$	−29.4846	+	10.9570i	−0.947672	+	0.352172i
$969$	8.16108	+	2.44906i	0.262172	+	0.0786753i
$970$			1.34248i			0.0431044i
$971$			38.3670i			1.23126i	0.788037	+	0.615628i	$0.211098\pi$
$971$			38.3670i			1.23126i	−0.788037	+	0.615628i	$0.788902\pi$
$972$	−18.6323	+	2.11627i	−0.597632	+	0.0678793i
$973$	12.9766			0.416010
$974$	26.6659			0.854430
$975$	−9.69896	−	2.91057i	−0.310615	−	0.0932128i
$976$		−	0.745933i		−	0.0238767i
$977$		−	20.6324i		−	0.660088i	−0.943966	−	0.330044i	$-0.892936\pi$
$977$		−	20.6324i		−	0.660088i	0.943966	−	0.330044i	$-0.107064\pi$
$978$	0.589296	−	1.96373i	0.0188436	−	0.0627930i
$979$	45.3710	−	8.15780i	1.45006	−	0.260724i
$980$		−	1.20295i		−	0.0384268i
$981$	10.1100	−	15.3280i	0.322788	−	0.489384i
$982$	7.61489			0.243001
$983$		−	13.8284i		−	0.441056i	−0.975381	−	0.220528i	$-0.929222\pi$
$983$		−	13.8284i		−	0.441056i	0.975381	−	0.220528i	$-0.0707781\pi$
$984$	1.38036	−	4.59982i	0.0440044	−	0.146637i
$985$			25.2639i			0.804975i
$986$	−38.4851			−1.22561
$987$	−5.47739	+	18.2525i	−0.174347	+	0.580982i
$988$	7.83007			0.249108
$989$	7.25677			0.230752
$990$	8.16378	+	3.50154i	0.259462	+	0.111286i
$991$	−23.8049			−0.756189			−0.378094	−	0.925767i	$-0.623421\pi$
$991$	−23.8049			−0.756189			−0.378094	+	0.925767i	$0.623421\pi$
$992$	0.304523			0.00966862
$993$	−9.76646	+	32.5450i	−0.309929	+	1.03278i
$994$	−13.3100			−0.422166
$995$		−	13.8673i		−	0.439623i
$996$	−3.48225	+	11.6040i	−0.110339	+	0.367687i
$997$			13.9066i			0.440428i	0.975452	+	0.220214i	$0.0706755\pi$
$997$			13.9066i			0.440428i	−0.975452	+	0.220214i	$0.929324\pi$
$998$	−26.1185			−0.826768
$999$	16.3388	−	13.6556i	0.516938	−	0.432043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.13	yes	40
3.2	odd	2		1155.2.l.e.1121.28	yes	40
11.10	odd	2		1155.2.l.e.1121.27	✓	40
33.32	even	2	inner	1155.2.l.f.1121.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.27	✓	40	11.10	odd	2
1155.2.l.e.1121.28	yes	40	3.2	odd	2
1155.2.l.f.1121.13	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.14	yes	40	33.32	even	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.892777 q^{2} +(0.497839 - 1.65896i) q^{3} -1.20295 q^{4} -1.00000i q^{5} +(-0.444460 + 1.48108i) q^{6} -1.00000i q^{7} +2.85952 q^{8} +(-2.50431 - 1.65179i) q^{9} +O(q^{10})\)	\(q-0.892777 q^{2} +(0.497839 - 1.65896i) q^{3} -1.20295 q^{4} -1.00000i q^{5} +(-0.444460 + 1.48108i) q^{6} -1.00000i q^{7} +2.85952 q^{8} +(-2.50431 - 1.65179i) q^{9} +0.892777i q^{10} +(0.586925 + 3.26428i) q^{11} +(-0.598875 + 1.99565i) q^{12} +5.84640i q^{13} +0.892777i q^{14} +(-1.65896 - 0.497839i) q^{15} -0.147016 q^{16} +4.41856 q^{17} +(2.23579 + 1.47468i) q^{18} +1.11335i q^{19} +1.20295i q^{20} +(-1.65896 - 0.497839i) q^{21} +(-0.523993 - 2.91427i) q^{22} +7.41992i q^{23} +(1.42358 - 4.74384i) q^{24} -1.00000 q^{25} -5.21953i q^{26} +(-3.98701 + 3.33223i) q^{27} +1.20295i q^{28} +9.75592 q^{29} +(1.48108 + 0.444460i) q^{30} -0.0544980 q^{31} -5.58779 q^{32} +(5.70751 + 0.651400i) q^{33} -3.94479 q^{34} -1.00000 q^{35} +(3.01256 + 1.98702i) q^{36} -4.09802 q^{37} -0.993970i q^{38} +(9.69896 + 2.91057i) q^{39} -2.85952i q^{40} +0.969641 q^{41} +(1.48108 + 0.444460i) q^{42} -0.978013i q^{43} +(-0.706041 - 3.92676i) q^{44} +(-1.65179 + 2.50431i) q^{45} -6.62433i q^{46} -11.0023i q^{47} +(-0.0731905 + 0.243895i) q^{48} -1.00000 q^{49} +0.892777 q^{50} +(2.19973 - 7.33023i) q^{51} -7.03292i q^{52} +0.255651i q^{53} +(3.55951 - 2.97494i) q^{54} +(3.26428 - 0.586925i) q^{55} -2.85952i q^{56} +(1.84700 + 0.554267i) q^{57} -8.70987 q^{58} +1.86448i q^{59} +(1.99565 + 0.598875i) q^{60} +5.07381i q^{61} +0.0486546 q^{62} +(-1.65179 + 2.50431i) q^{63} +5.28268 q^{64} +5.84640 q^{65} +(-5.09554 - 0.581555i) q^{66} +5.79382 q^{67} -5.31530 q^{68} +(12.3094 + 3.69393i) q^{69} +0.892777 q^{70} +14.9085i q^{71} +(-7.16113 - 4.72334i) q^{72} +7.44139i q^{73} +3.65862 q^{74} +(-0.497839 + 1.65896i) q^{75} -1.33930i q^{76} +(3.26428 - 0.586925i) q^{77} +(-8.65901 - 2.59849i) q^{78} -7.49918i q^{79} +0.147016i q^{80} +(3.54316 + 8.27321i) q^{81} -0.865673 q^{82} +5.81466 q^{83} +(1.99565 + 0.598875i) q^{84} -4.41856i q^{85} +0.873148i q^{86} +(4.85688 - 16.1847i) q^{87} +(1.67832 + 9.33427i) q^{88} -13.8992i q^{89} +(1.47468 - 2.23579i) q^{90} +5.84640 q^{91} -8.92578i q^{92} +(-0.0271312 + 0.0904101i) q^{93} +9.82263i q^{94} +1.11335 q^{95} +(-2.78182 + 9.26993i) q^{96} +1.50371 q^{97} +0.892777 q^{98} +(3.92207 - 9.14425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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