LMFDB - Embedded newform 1155.2.i.b.76.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (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:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.b.76.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +1.00000i q^{5} -1.93185 q^{6} +(0.189469 - 2.63896i) q^{7} -0.517638i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +1.00000i q^{5} -1.93185 q^{6} +(0.189469 - 2.63896i) q^{7} -0.517638i q^{8} -1.00000 q^{9} +1.93185 q^{10} +(-3.00000 + 1.41421i) q^{11} +1.73205i q^{12} +4.24264 q^{13} +(-5.09808 - 0.366025i) q^{14} +1.00000 q^{15} -4.46410 q^{16} -2.44949 q^{17} +1.93185i q^{18} -3.86370 q^{19} -1.73205i q^{20} +(-2.63896 - 0.189469i) q^{21} +(2.73205 + 5.79555i) q^{22} -4.00000 q^{23} -0.517638 q^{24} -1.00000 q^{25} -8.19615i q^{26} +1.00000i q^{27} +(-0.328169 + 4.57081i) q^{28} -3.86370i q^{29} -1.93185i q^{30} -10.9282i q^{31} +7.58871i q^{32} +(1.41421 + 3.00000i) q^{33} +4.73205i q^{34} +(2.63896 + 0.189469i) q^{35} +1.73205 q^{36} -7.46410 q^{37} +7.46410i q^{38} -4.24264i q^{39} +0.517638 q^{40} +1.79315 q^{41} +(-0.366025 + 5.09808i) q^{42} -2.44949i q^{43} +(5.19615 - 2.44949i) q^{44} -1.00000i q^{45} +7.72741i q^{46} +10.9282i q^{47} +4.46410i q^{48} +(-6.92820 - 1.00000i) q^{49} +1.93185i q^{50} +2.44949i q^{51} -7.34847 q^{52} +3.46410 q^{53} +1.93185 q^{54} +(-1.41421 - 3.00000i) q^{55} +(-1.36603 - 0.0980762i) q^{56} +3.86370i q^{57} -7.46410 q^{58} +0.928203i q^{59} -1.73205 q^{60} +4.89898 q^{61} -21.1117 q^{62} +(-0.189469 + 2.63896i) q^{63} +5.73205 q^{64} +4.24264i q^{65} +(5.79555 - 2.73205i) q^{66} +1.46410 q^{67} +4.24264 q^{68} +4.00000i q^{69} +(0.366025 - 5.09808i) q^{70} -6.92820 q^{71} +0.517638i q^{72} +9.14162 q^{73} +14.4195i q^{74} +1.00000i q^{75} +6.69213 q^{76} +(3.16364 + 8.18482i) q^{77} -8.19615 q^{78} +1.03528i q^{79} -4.46410i q^{80} +1.00000 q^{81} -3.46410i q^{82} +1.41421 q^{83} +(4.57081 + 0.328169i) q^{84} -2.44949i q^{85} -4.73205 q^{86} -3.86370 q^{87} +(0.732051 + 1.55291i) q^{88} +8.92820i q^{89} -1.93185 q^{90} +(0.803848 - 11.1962i) q^{91} +6.92820 q^{92} -10.9282 q^{93} +21.1117 q^{94} -3.86370i q^{95} +7.58871 q^{96} -8.92820i q^{97} +(-1.93185 + 13.3843i) q^{98} +(3.00000 - 1.41421i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^9	$ 8 q - 8 q^{9} - 24 q^{11} - 20 q^{14} + 8 q^{15} - 8 q^{16} + 8 q^{22} - 32 q^{23} - 8 q^{25} - 32 q^{37} + 4 q^{42} - 4 q^{56} - 32 q^{58} + 32 q^{64} - 16 q^{67} - 4 q^{70} + 16 q^{77} - 24 q^{78} + 8 q^{81} - 24 q^{86} - 8 q^{88} + 48 q^{91} - 32 q^{93} + 24 q^{99}+O(q^{100}) $ 8 * q - 8 * q^9 - 24 * q^11 - 20 * q^14 + 8 * q^15 - 8 * q^16 + 8 * q^22 - 32 * q^23 - 8 * q^25 - 32 * q^37 + 4 * q^42 - 4 * q^56 - 32 * q^58 + 32 * q^64 - 16 * q^67 - 4 * q^70 + 16 * q^77 - 24 * q^78 + 8 * q^81 - 24 * q^86 - 8 * q^88 + 48 * q^91 - 32 * q^93 + 24 * 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 $

$2$		−	1.93185i		−	1.36603i	−0.730406	−	0.683013i	$-0.760669\pi$
$2$		−	1.93185i		−	1.36603i	0.730406	−	0.683013i	$-0.239331\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	−1.73205			−0.866025
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.93185			−0.788675
$7$	0.189469	−	2.63896i	0.0716124	−	0.997433i
$7$	0.189469	−	2.63896i	0.0716124	−	0.997433i
$8$		−	0.517638i		−	0.183013i
$9$	−1.00000			−0.333333
$10$	1.93185			0.610905
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$11$	−3.00000	+	1.41421i	−0.904534	+	0.426401i
$12$			1.73205i			0.500000i
$13$	4.24264			1.17670			0.588348	−	0.808608i	$-0.299778\pi$
$13$	4.24264			1.17670			0.588348	+	0.808608i	$0.299778\pi$
$14$	−5.09808	−	0.366025i	−1.36252	−	0.0978244i
$15$	1.00000			0.258199
$16$	−4.46410			−1.11603
$17$	−2.44949			−0.594089			−0.297044	−	0.954864i	$-0.596001\pi$
$17$	−2.44949			−0.594089			−0.297044	+	0.954864i	$0.596001\pi$
$18$			1.93185i			0.455342i
$19$	−3.86370			−0.886394			−0.443197	−	0.896424i	$-0.646156\pi$
$19$	−3.86370			−0.886394			−0.443197	+	0.896424i	$0.646156\pi$
$20$		−	1.73205i		−	0.387298i
$21$	−2.63896	−	0.189469i	−0.575868	−	0.0413455i
$22$	2.73205	+	5.79555i	0.582475	+	1.23562i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−0.517638			−0.105662
$25$	−1.00000			−0.200000
$26$		−	8.19615i		−	1.60740i
$27$			1.00000i			0.192450i
$28$	−0.328169	+	4.57081i	−0.0620182	+	0.863802i
$29$		−	3.86370i		−	0.717472i	−0.933439	−	0.358736i	$-0.883208\pi$
$29$		−	3.86370i		−	0.717472i	0.933439	−	0.358736i	$-0.116792\pi$
$30$		−	1.93185i		−	0.352706i
$31$		−	10.9282i		−	1.96276i	−0.192068	−	0.981382i	$-0.561519\pi$
$31$		−	10.9282i		−	1.96276i	0.192068	−	0.981382i	$-0.438481\pi$
$32$			7.58871i			1.34151i
$33$	1.41421	+	3.00000i	0.246183	+	0.522233i
$34$			4.73205i			0.811540i
$35$	2.63896	+	0.189469i	0.446065	+	0.0320261i
$36$	1.73205			0.288675
$37$	−7.46410			−1.22709			−0.613545	−	0.789659i	$-0.710257\pi$
$37$	−7.46410			−1.22709			−0.613545	+	0.789659i	$0.710257\pi$
$38$			7.46410i			1.21084i
$39$		−	4.24264i		−	0.679366i
$40$	0.517638			0.0818458
$41$	1.79315			0.280043			0.140022	−	0.990148i	$-0.455283\pi$
$41$	1.79315			0.280043			0.140022	+	0.990148i	$0.455283\pi$
$42$	−0.366025	+	5.09808i	−0.0564789	+	0.786650i
$43$		−	2.44949i		−	0.373544i	−0.982403	−	0.186772i	$-0.940197\pi$
$43$		−	2.44949i		−	0.373544i	0.982403	−	0.186772i	$-0.0598025\pi$
$44$	5.19615	−	2.44949i	0.783349	−	0.369274i
$45$		−	1.00000i		−	0.149071i
$46$			7.72741i			1.13934i
$47$			10.9282i			1.59404i	0.603951	+	0.797021i	$0.293592\pi$
$47$			10.9282i			1.59404i	−0.603951	+	0.797021i	$0.706408\pi$
$48$			4.46410i			0.644338i
$49$	−6.92820	−	1.00000i	−0.989743	−	0.142857i
$50$			1.93185i			0.273205i
$51$			2.44949i			0.342997i
$52$	−7.34847			−1.01905
$53$	3.46410			0.475831			0.237915	−	0.971286i	$-0.423536\pi$
$53$	3.46410			0.475831			0.237915	+	0.971286i	$0.423536\pi$
$54$	1.93185			0.262892
$55$	−1.41421	−	3.00000i	−0.190693	−	0.404520i
$56$	−1.36603	−	0.0980762i	−0.182543	−	0.0131060i
$57$			3.86370i			0.511760i
$58$	−7.46410			−0.980085
$59$			0.928203i			0.120842i	0.998173	+	0.0604209i	$0.0192443\pi$
$59$			0.928203i			0.120842i	−0.998173	+	0.0604209i	$0.980756\pi$
$60$	−1.73205			−0.223607
$61$	4.89898			0.627250			0.313625	−	0.949547i	$-0.398457\pi$
$61$	4.89898			0.627250			0.313625	+	0.949547i	$0.398457\pi$
$62$	−21.1117			−2.68118
$63$	−0.189469	+	2.63896i	−0.0238708	+	0.332478i
$64$	5.73205			0.716506
$65$			4.24264i			0.526235i
$66$	5.79555	−	2.73205i	0.713384	−	0.336292i
$67$	1.46410			0.178868			0.0894342	−	0.995993i	$-0.471494\pi$
$67$	1.46410			0.178868			0.0894342	+	0.995993i	$0.471494\pi$
$68$	4.24264			0.514496
$69$			4.00000i			0.481543i
$70$	0.366025	−	5.09808i	0.0437484	−	0.609337i
$71$	−6.92820			−0.822226			−0.411113	−	0.911584i	$-0.634860\pi$
$71$	−6.92820			−0.822226			−0.411113	+	0.911584i	$0.634860\pi$
$72$			0.517638i			0.0610042i
$73$	9.14162			1.06995			0.534973	−	0.844869i	$-0.320322\pi$
$73$	9.14162			1.06995			0.534973	+	0.844869i	$0.320322\pi$
$74$			14.4195i			1.67624i
$75$			1.00000i			0.115470i
$76$	6.69213			0.767640
$77$	3.16364	+	8.18482i	0.360531	+	0.932747i
$78$	−8.19615			−0.928032
$79$			1.03528i			0.116478i	0.998303	+	0.0582388i	$0.0185485\pi$
$79$			1.03528i			0.116478i	−0.998303	+	0.0582388i	$0.981452\pi$
$80$		−	4.46410i		−	0.499102i
$81$	1.00000			0.111111
$82$		−	3.46410i		−	0.382546i
$83$	1.41421			0.155230			0.0776151	−	0.996983i	$-0.475269\pi$
$83$	1.41421			0.155230			0.0776151	+	0.996983i	$0.475269\pi$
$84$	4.57081	+	0.328169i	0.498716	+	0.0358062i
$85$		−	2.44949i		−	0.265684i
$86$	−4.73205			−0.510270
$87$	−3.86370			−0.414232
$88$	0.732051	+	1.55291i	0.0780369	+	0.165541i
$89$			8.92820i			0.946388i	0.880958	+	0.473194i	$0.156899\pi$
$89$			8.92820i			0.946388i	−0.880958	+	0.473194i	$0.843101\pi$
$90$	−1.93185			−0.203635
$91$	0.803848	−	11.1962i	0.0842661	−	1.17368i
$92$	6.92820			0.722315
$93$	−10.9282			−1.13320
$94$	21.1117			2.17750
$95$		−	3.86370i		−	0.396408i
$96$	7.58871			0.774519
$97$		−	8.92820i		−	0.906522i	−0.891378	−	0.453261i	$-0.850261\pi$
$97$		−	8.92820i		−	0.906522i	0.891378	−	0.453261i	$-0.149739\pi$
$98$	−1.93185	+	13.3843i	−0.195146	+	1.35201i
$99$	3.00000	−	1.41421i	0.301511	−	0.142134i
$100$	1.73205			0.173205
$101$	−3.10583			−0.309041			−0.154521	−	0.987990i	$-0.549383\pi$
$101$	−3.10583			−0.309041			−0.154521	+	0.987990i	$0.549383\pi$
$102$	4.73205			0.468543
$103$		−	8.39230i		−	0.826918i	−0.910523	−	0.413459i	$-0.864320\pi$
$103$		−	8.39230i		−	0.826918i	0.910523	−	0.413459i	$-0.135680\pi$
$104$		−	2.19615i		−	0.215350i
$105$	0.189469	−	2.63896i	0.0184903	−	0.257536i
$106$		−	6.69213i		−	0.649997i
$107$		−	18.9396i		−	1.83096i	−0.402365	−	0.915479i	$-0.631812\pi$
$107$		−	18.9396i		−	1.83096i	0.402365	−	0.915479i	$-0.368188\pi$
$108$		−	1.73205i		−	0.166667i
$109$			11.8685i			1.13680i	0.822753	+	0.568399i	$0.192437\pi$
$109$			11.8685i			1.13680i	−0.822753	+	0.568399i	$0.807563\pi$
$110$	−5.79555	+	2.73205i	−0.552584	+	0.260491i
$111$			7.46410i			0.708461i
$112$	−0.845807	+	11.7806i	−0.0799213	+	1.11316i
$113$	15.4641			1.45474			0.727370	−	0.686245i	$-0.240742\pi$
$113$	15.4641			1.45474			0.727370	+	0.686245i	$0.240742\pi$
$114$	7.46410			0.699077
$115$		−	4.00000i		−	0.373002i
$116$			6.69213i			0.621349i
$117$	−4.24264			−0.392232
$118$	1.79315			0.165073
$119$	−0.464102	+	6.46410i	−0.0425441	+	0.592563i
$120$		−	0.517638i		−	0.0472537i
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$		−	9.46410i		−	0.856840i
$123$		−	1.79315i		−	0.161683i
$124$			18.9282i			1.69980i
$125$		−	1.00000i		−	0.0894427i
$126$	5.09808	+	0.366025i	0.454173	+	0.0326081i
$127$		−	12.2474i		−	1.08679i	−0.839479	−	0.543393i	$-0.817139\pi$
$127$		−	12.2474i		−	1.08679i	0.839479	−	0.543393i	$-0.182861\pi$
$128$			4.10394i			0.362740i
$129$	−2.44949			−0.215666
$130$	8.19615			0.718850
$131$	−4.89898			−0.428026			−0.214013	−	0.976831i	$-0.568653\pi$
$131$	−4.89898			−0.428026			−0.214013	+	0.976831i	$0.568653\pi$
$132$	−2.44949	−	5.19615i	−0.213201	−	0.452267i
$133$	−0.732051	+	10.1962i	−0.0634769	+	0.884119i
$134$		−	2.82843i		−	0.244339i
$135$	−1.00000			−0.0860663
$136$			1.26795i			0.108726i
$137$	−7.07180			−0.604184			−0.302092	−	0.953279i	$-0.597685\pi$
$137$	−7.07180			−0.604184			−0.302092	+	0.953279i	$0.597685\pi$
$138$	7.72741			0.657801
$139$	12.9038			1.09448			0.547242	−	0.836974i	$-0.315678\pi$
$139$	12.9038			1.09448			0.547242	+	0.836974i	$0.315678\pi$
$140$	−4.57081	−	0.328169i	−0.386304	−	0.0277354i
$141$	10.9282			0.920321
$142$			13.3843i			1.12318i
$143$	−12.7279	+	6.00000i	−1.06436	+	0.501745i
$144$	4.46410			0.372008
$145$	3.86370			0.320863
$146$		−	17.6603i		−	1.46157i
$147$	−1.00000	+	6.92820i	−0.0824786	+	0.571429i
$148$	12.9282			1.06269
$149$		−	23.6627i		−	1.93852i	−0.246032	−	0.969262i	$-0.579127\pi$
$149$		−	23.6627i		−	1.93852i	0.246032	−	0.969262i	$-0.420873\pi$
$150$	1.93185			0.157735
$151$		−	8.76268i		−	0.713097i	−0.934277	−	0.356549i	$-0.883953\pi$
$151$		−	8.76268i		−	0.713097i	0.934277	−	0.356549i	$-0.116047\pi$
$152$			2.00000i			0.162221i
$153$	2.44949			0.198030
$154$	15.8119	−	6.11169i	1.27416	−	0.492494i
$155$	10.9282			0.877774
$156$			7.34847i			0.588348i
$157$			14.3923i			1.14863i	0.818634	+	0.574315i	$0.194732\pi$
$157$			14.3923i			1.14863i	−0.818634	+	0.574315i	$0.805268\pi$
$158$	2.00000			0.159111
$159$		−	3.46410i		−	0.274721i
$160$	−7.58871			−0.599940
$161$	−0.757875	+	10.5558i	−0.0597289	+	0.831916i
$162$		−	1.93185i		−	0.151781i
$163$	12.3923			0.970640			0.485320	−	0.874337i	$-0.338703\pi$
$163$	12.3923			0.970640			0.485320	+	0.874337i	$0.338703\pi$
$164$	−3.10583			−0.242524
$165$	−3.00000	+	1.41421i	−0.233550	+	0.110096i
$166$		−	2.73205i		−	0.212048i
$167$	−7.07107			−0.547176			−0.273588	−	0.961847i	$-0.588210\pi$
$167$	−7.07107			−0.547176			−0.273588	+	0.961847i	$0.588210\pi$
$168$	−0.0980762	+	1.36603i	−0.00756674	+	0.105391i
$169$	5.00000			0.384615
$170$	−4.73205			−0.362932
$171$	3.86370			0.295465
$172$			4.24264i			0.323498i
$173$	−2.44949			−0.186231			−0.0931156	−	0.995655i	$-0.529683\pi$
$173$	−2.44949			−0.186231			−0.0931156	+	0.995655i	$0.529683\pi$
$174$			7.46410i			0.565852i
$175$	−0.189469	+	2.63896i	−0.0143225	+	0.199487i
$176$	13.3923	−	6.31319i	1.00948	−	0.475875i
$177$	0.928203			0.0697680
$178$	17.2480			1.29279
$179$	8.92820			0.667325			0.333663	−	0.942693i	$-0.391715\pi$
$179$	8.92820			0.667325			0.333663	+	0.942693i	$0.391715\pi$
$180$			1.73205i			0.129099i
$181$		−	3.07180i		−	0.228325i	−0.993462	−	0.114162i	$-0.963582\pi$
$181$		−	3.07180i		−	0.228325i	0.993462	−	0.114162i	$-0.0364184\pi$
$182$	−21.6293	−	1.55291i	−1.60327	−	0.115110i
$183$		−	4.89898i		−	0.362143i
$184$			2.07055i			0.152643i
$185$		−	7.46410i		−	0.548772i
$186$			21.1117i			1.54798i
$187$	7.34847	−	3.46410i	0.537373	−	0.253320i
$188$		−	18.9282i		−	1.38048i
$189$	2.63896	+	0.189469i	0.191956	+	0.0137818i
$190$	−7.46410			−0.541503
$191$	−24.9282			−1.80374			−0.901871	−	0.432006i	$-0.857806\pi$
$191$	−24.9282			−1.80374			−0.901871	+	0.432006i	$0.857806\pi$
$192$		−	5.73205i		−	0.413675i
$193$		−	21.2132i		−	1.52696i	−0.645832	−	0.763480i	$-0.723489\pi$
$193$		−	21.2132i		−	1.52696i	0.645832	−	0.763480i	$-0.276511\pi$
$194$	−17.2480			−1.23833
$195$	4.24264			0.303822
$196$	12.0000	+	1.73205i	0.857143	+	0.123718i
$197$		−	6.59059i		−	0.469560i	−0.972048	−	0.234780i	$-0.924563\pi$
$197$		−	6.59059i		−	0.469560i	0.972048	−	0.234780i	$-0.0754370\pi$
$198$	−2.73205	−	5.79555i	−0.194158	−	0.411872i
$199$		−	12.5359i		−	0.888646i	−0.895867	−	0.444323i	$-0.853444\pi$
$199$		−	12.5359i		−	0.888646i	0.895867	−	0.444323i	$-0.146556\pi$
$200$			0.517638i			0.0366025i
$201$		−	1.46410i		−	0.103270i
$202$			6.00000i			0.422159i
$203$	−10.1962	−	0.732051i	−0.715630	−	0.0513799i
$204$		−	4.24264i		−	0.297044i
$205$			1.79315i			0.125239i
$206$	−16.2127			−1.12959
$207$	4.00000			0.278019
$208$	−18.9396			−1.31322
$209$	11.5911	−	5.46410i	0.801774	−	0.377960i
$210$	−5.09808	−	0.366025i	−0.351801	−	0.0252582i
$211$		−	16.4901i		−	1.13522i	−0.823296	−	0.567612i	$-0.807867\pi$
$211$		−	16.4901i		−	1.13522i	0.823296	−	0.567612i	$-0.192133\pi$
$212$	−6.00000			−0.412082
$213$			6.92820i			0.474713i
$214$	−36.5885			−2.50114
$215$	2.44949			0.167054
$216$	0.517638			0.0352208
$217$	−28.8391	−	2.07055i	−1.95772	−	0.140558i
$218$	22.9282			1.55289
$219$		−	9.14162i		−	0.617733i
$220$	2.44949	+	5.19615i	0.165145	+	0.350325i
$221$	−10.3923			−0.699062
$222$	14.4195			0.967776
$223$			17.8564i			1.19575i	0.801588	+	0.597877i	$0.203989\pi$
$223$			17.8564i			1.19575i	−0.801588	+	0.597877i	$0.796011\pi$
$224$	20.0263	+	1.43782i	1.33806	+	0.0960685i
$225$	1.00000			0.0666667
$226$		−	29.8744i		−	1.98721i
$227$	−18.3848			−1.22024			−0.610120	−	0.792309i	$-0.708879\pi$
$227$	−18.3848			−1.22024			−0.610120	+	0.792309i	$0.708879\pi$
$228$		−	6.69213i		−	0.443197i
$229$		−	9.85641i		−	0.651330i	−0.945485	−	0.325665i	$-0.894412\pi$
$229$		−	9.85641i		−	0.651330i	0.945485	−	0.325665i	$-0.105588\pi$
$230$	−7.72741			−0.509530
$231$	8.18482	−	3.16364i	0.538522	−	0.208153i
$232$	−2.00000			−0.131306
$233$			17.1464i			1.12330i	0.827375	+	0.561650i	$0.189833\pi$
$233$			17.1464i			1.12330i	−0.827375	+	0.561650i	$0.810167\pi$
$234$			8.19615i			0.535799i
$235$	−10.9282			−0.712877
$236$		−	1.60770i		−	0.104652i
$237$	1.03528			0.0672484
$238$	12.4877	+	0.896575i	0.809456	+	0.0581164i
$239$		−	17.5254i		−	1.13362i	−0.823848	−	0.566811i	$-0.808177\pi$
$239$		−	17.5254i		−	1.13362i	0.823848	−	0.566811i	$-0.191823\pi$
$240$	−4.46410			−0.288157
$241$	28.0812			1.80887			0.904435	−	0.426612i	$-0.140293\pi$
$241$	28.0812			1.80887			0.904435	+	0.426612i	$0.140293\pi$
$242$	−16.3923	−	13.5230i	−1.05374	−	0.869289i
$243$		−	1.00000i		−	0.0641500i
$244$	−8.48528			−0.543214
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$	−3.46410			−0.220863
$247$	−16.3923			−1.04302
$248$	−5.65685			−0.359211
$249$		−	1.41421i		−	0.0896221i
$250$	−1.93185			−0.122181
$251$			7.85641i			0.495892i	0.968774	+	0.247946i	$0.0797556\pi$
$251$			7.85641i			0.495892i	−0.968774	+	0.247946i	$0.920244\pi$
$252$	0.328169	−	4.57081i	0.0206727	−	0.287934i
$253$	12.0000	−	5.65685i	0.754434	−	0.355643i
$254$	−23.6603			−1.48458
$255$	−2.44949			−0.153393
$256$	19.3923			1.21202
$257$		−	14.0000i		−	0.873296i	−0.899632	−	0.436648i	$-0.856166\pi$
$257$		−	14.0000i		−	0.873296i	0.899632	−	0.436648i	$-0.143834\pi$
$258$			4.73205i			0.294605i
$259$	−1.41421	+	19.6975i	−0.0878750	+	1.22394i
$260$		−	7.34847i		−	0.455733i
$261$			3.86370i			0.239157i
$262$			9.46410i			0.584694i
$263$			3.48477i			0.214880i	0.994212	+	0.107440i	$0.0342653\pi$
$263$			3.48477i			0.214880i	−0.994212	+	0.107440i	$0.965735\pi$
$264$	1.55291	−	0.732051i	0.0955753	−	0.0450546i
$265$			3.46410i			0.212798i
$266$	19.6975	+	1.41421i	1.20773	+	0.0867110i
$267$	8.92820			0.546397
$268$	−2.53590			−0.154905
$269$			9.46410i			0.577036i	0.957474	+	0.288518i	$0.0931626\pi$
$269$			9.46410i			0.577036i	−0.957474	+	0.288518i	$0.906837\pi$
$270$			1.93185i			0.117569i
$271$	−26.4911			−1.60922			−0.804610	−	0.593803i	$-0.797626\pi$
$271$	−26.4911			−1.60922			−0.804610	+	0.593803i	$0.797626\pi$
$272$	10.9348			0.663018
$273$	−11.1962	−	0.803848i	−0.677622	−	0.0486511i
$274$			13.6617i			0.825331i
$275$	3.00000	−	1.41421i	0.180907	−	0.0852803i
$276$		−	6.92820i		−	0.417029i
$277$		−	2.72689i		−	0.163843i	−0.996639	−	0.0819215i	$-0.973894\pi$
$277$		−	2.72689i		−	0.163843i	0.996639	−	0.0819215i	$-0.0261057\pi$
$278$		−	24.9282i		−	1.49509i
$279$			10.9282i			0.654254i
$280$	0.0980762	−	1.36603i	0.00586117	−	0.0816356i
$281$			7.45001i			0.444430i	0.974998	+	0.222215i	$0.0713287\pi$
$281$			7.45001i			0.444430i	−0.974998	+	0.222215i	$0.928671\pi$
$282$		−	21.1117i		−	1.25718i
$283$	−14.5211			−0.863188			−0.431594	−	0.902068i	$-0.642049\pi$
$283$	−14.5211			−0.863188			−0.431594	+	0.902068i	$0.642049\pi$
$284$	12.0000			0.712069
$285$	−3.86370			−0.228866
$286$	11.5911	+	24.5885i	0.685397	+	1.45395i
$287$	0.339746	−	4.73205i	0.0200546	−	0.279324i
$288$		−	7.58871i		−	0.447169i
$289$	−11.0000			−0.647059
$290$		−	7.46410i		−	0.438307i
$291$	−8.92820			−0.523381
$292$	−15.8338			−0.926600
$293$	27.7023			1.61838			0.809192	−	0.587545i	$-0.199905\pi$
$293$	27.7023			1.61838			0.809192	+	0.587545i	$0.199905\pi$
$294$	13.3843	+	1.93185i	0.780586	+	0.112668i
$295$	−0.928203			−0.0540421
$296$			3.86370i			0.224573i
$297$	−1.41421	−	3.00000i	−0.0820610	−	0.174078i
$298$	−45.7128			−2.64807
$299$	−16.9706			−0.981433
$300$		−	1.73205i		−	0.100000i
$301$	−6.46410	−	0.464102i	−0.372585	−	0.0267504i
$302$	−16.9282			−0.974109
$303$			3.10583i			0.178425i
$304$	17.2480			0.989239
$305$			4.89898i			0.280515i
$306$		−	4.73205i		−	0.270513i
$307$	−9.41902			−0.537572			−0.268786	−	0.963200i	$-0.586622\pi$
$307$	−9.41902			−0.537572			−0.268786	+	0.963200i	$0.586622\pi$
$308$	−5.47959	−	14.1765i	−0.312229	−	0.807783i
$309$	−8.39230			−0.477422
$310$		−	21.1117i		−	1.19906i
$311$		−	22.7846i		−	1.29200i	−0.763339	−	0.645998i	$-0.776441\pi$
$311$		−	22.7846i		−	1.29200i	0.763339	−	0.645998i	$-0.223559\pi$
$312$	−2.19615			−0.124333
$313$		−	4.14359i		−	0.234210i	−0.993120	−	0.117105i	$-0.962639\pi$
$313$		−	4.14359i		−	0.234210i	0.993120	−	0.117105i	$-0.0373614\pi$
$314$	27.8038			1.56906
$315$	−2.63896	−	0.189469i	−0.148688	−	0.0106754i
$316$		−	1.79315i		−	0.100873i
$317$	20.2487			1.13728			0.568640	−	0.822586i	$-0.307470\pi$
$317$	20.2487			1.13728			0.568640	+	0.822586i	$0.307470\pi$
$318$	−6.69213			−0.375276
$319$	5.46410	+	11.5911i	0.305931	+	0.648978i
$320$			5.73205i			0.320431i
$321$	−18.9396			−1.05710
$322$	20.3923	+	1.46410i	1.13642	+	0.0815912i
$323$	9.46410			0.526597
$324$	−1.73205			−0.0962250
$325$	−4.24264			−0.235339
$326$		−	23.9401i		−	1.32592i
$327$	11.8685			0.656330
$328$		−	0.928203i		−	0.0512514i
$329$	28.8391	+	2.07055i	1.58995	+	0.114153i
$330$	2.73205	+	5.79555i	0.150394	+	0.319035i
$331$	16.2487			0.893110			0.446555	−	0.894756i	$-0.352651\pi$
$331$	16.2487			0.893110			0.446555	+	0.894756i	$0.352651\pi$
$332$	−2.44949			−0.134433
$333$	7.46410			0.409030
$334$			13.6603i			0.747456i
$335$			1.46410i			0.0799924i
$336$	11.7806	+	0.845807i	0.642683	+	0.0461426i
$337$		−	3.48477i		−	0.189827i	−0.995486	−	0.0949136i	$-0.969743\pi$
$337$		−	3.48477i		−	0.189827i	0.995486	−	0.0949136i	$-0.0302575\pi$
$338$		−	9.65926i		−	0.525394i
$339$		−	15.4641i		−	0.839895i
$340$			4.24264i			0.230089i
$341$	15.4548	+	32.7846i	0.836925	+	1.77539i
$342$		−	7.46410i		−	0.403612i
$343$	−3.95164	+	18.0938i	−0.213368	+	0.976972i
$344$	−1.26795			−0.0683632
$345$	−4.00000			−0.215353
$346$			4.73205i			0.254397i
$347$		−	0.656339i		−	0.0352341i	−0.999845	−	0.0176171i	$-0.994392\pi$
$347$		−	0.656339i		−	0.0352341i	0.999845	−	0.0176171i	$-0.00560797\pi$
$348$	6.69213			0.358736
$349$	8.48528			0.454207			0.227103	−	0.973871i	$-0.427074\pi$
$349$	8.48528			0.454207			0.227103	+	0.973871i	$0.427074\pi$
$350$	5.09808	+	0.366025i	0.272504	+	0.0195649i
$351$			4.24264i			0.226455i
$352$	−10.7321	−	22.7661i	−0.572020	−	1.21344i
$353$			12.5359i			0.667219i	0.942711	+	0.333609i	$0.108267\pi$
$353$			12.5359i			0.667219i	−0.942711	+	0.333609i	$0.891733\pi$
$354$		−	1.79315i		−	0.0953049i
$355$		−	6.92820i		−	0.367711i
$356$		−	15.4641i		−	0.819596i
$357$	6.46410	+	0.464102i	0.342117	+	0.0245629i
$358$		−	17.2480i		−	0.911583i
$359$		−	24.6980i		−	1.30351i	−0.758430	−	0.651754i	$-0.774033\pi$
$359$		−	24.6980i		−	1.30351i	0.758430	−	0.651754i	$-0.225967\pi$
$360$	−0.517638			−0.0272819
$361$	−4.07180			−0.214305
$362$	−5.93426			−0.311898
$363$	−8.48528	−	7.00000i	−0.445362	−	0.367405i
$364$	−1.39230	+	19.3923i	−0.0729766	+	1.01643i
$365$			9.14162i			0.478494i
$366$	−9.46410			−0.494697
$367$			24.7846i			1.29375i	0.762598	+	0.646873i	$0.223924\pi$
$367$			24.7846i			1.29375i	−0.762598	+	0.646873i	$0.776076\pi$
$368$	17.8564			0.930830
$369$	−1.79315			−0.0933477
$370$	−14.4195			−0.749636
$371$	0.656339	−	9.14162i	0.0340754	−	0.474609i
$372$	18.9282			0.981382
$373$		−	6.51626i		−	0.337399i	−0.985667	−	0.168700i	$-0.946043\pi$
$373$		−	6.51626i		−	0.337399i	0.985667	−	0.168700i	$-0.0539568\pi$
$374$	−6.69213	−	14.1962i	−0.346042	−	0.734066i
$375$	−1.00000			−0.0516398
$376$	5.65685			0.291730
$377$		−	16.3923i		−	0.844247i
$378$	0.366025	−	5.09808i	0.0188263	−	0.262217i
$379$	33.8564			1.73909			0.869543	−	0.493857i	$-0.164413\pi$
$379$	33.8564			1.73909			0.869543	+	0.493857i	$0.164413\pi$
$380$			6.69213i			0.343299i
$381$	−12.2474			−0.627456
$382$			48.1576i			2.46396i
$383$			24.3923i			1.24639i	0.782067	+	0.623194i	$0.214165\pi$
$383$			24.3923i			1.24639i	−0.782067	+	0.623194i	$0.785835\pi$
$384$	4.10394			0.209428
$385$	−8.18482	+	3.16364i	−0.417137	+	0.161234i
$386$	−40.9808			−2.08587
$387$			2.44949i			0.124515i
$388$			15.4641i			0.785071i
$389$	−10.7846			−0.546801			−0.273401	−	0.961900i	$-0.588148\pi$
$389$	−10.7846			−0.546801			−0.273401	+	0.961900i	$0.588148\pi$
$390$		−	8.19615i		−	0.415028i
$391$	9.79796			0.495504
$392$	−0.517638	+	3.58630i	−0.0261447	+	0.181136i
$393$			4.89898i			0.247121i
$394$	−12.7321			−0.641431
$395$	−1.03528			−0.0520904
$396$	−5.19615	+	2.44949i	−0.261116	+	0.123091i
$397$		−	8.92820i		−	0.448094i	−0.974578	−	0.224047i	$-0.928073\pi$
$397$		−	8.92820i		−	0.448094i	0.974578	−	0.224047i	$-0.0719269\pi$
$398$	−24.2175			−1.21391
$399$	10.1962	+	0.732051i	0.510446	+	0.0366484i
$400$	4.46410			0.223205
$401$	−10.5359			−0.526138			−0.263069	−	0.964777i	$-0.584735\pi$
$401$	−10.5359			−0.526138			−0.263069	+	0.964777i	$0.584735\pi$
$402$	−2.82843			−0.141069
$403$		−	46.3644i		−	2.30958i
$404$	5.37945			0.267638
$405$			1.00000i			0.0496904i
$406$	−1.41421	+	19.6975i	−0.0701862	+	0.977568i
$407$	22.3923	−	10.5558i	1.10995	−	0.523233i
$408$	1.26795			0.0627728
$409$	20.5569			1.01647			0.508236	−	0.861218i	$-0.330298\pi$
$409$	20.5569			1.01647			0.508236	+	0.861218i	$0.330298\pi$
$410$	3.46410			0.171080
$411$			7.07180i			0.348826i
$412$			14.5359i			0.716132i
$413$	2.44949	+	0.175865i	0.120532	+	0.00865377i
$414$		−	7.72741i		−	0.379781i
$415$			1.41421i			0.0694210i
$416$			32.1962i			1.57855i
$417$		−	12.9038i		−	0.631901i
$418$	−10.5558	−	22.3923i	−0.516303	−	1.09524i
$419$		−	30.9282i		−	1.51094i	−0.655182	−	0.755471i	$-0.727408\pi$
$419$		−	30.9282i		−	1.51094i	0.655182	−	0.755471i	$-0.272592\pi$
$420$	−0.328169	+	4.57081i	−0.0160130	+	0.223033i
$421$	25.8564			1.26016			0.630082	−	0.776529i	$-0.283021\pi$
$421$	25.8564			1.26016			0.630082	+	0.776529i	$0.283021\pi$
$422$	−31.8564			−1.55075
$423$		−	10.9282i		−	0.531347i
$424$		−	1.79315i		−	0.0870831i
$425$	2.44949			0.118818
$426$	13.3843			0.648470
$427$	0.928203	−	12.9282i	0.0449189	−	0.625640i
$428$			32.8043i			1.58566i
$429$	6.00000	+	12.7279i	0.289683	+	0.614510i
$430$		−	4.73205i		−	0.228200i
$431$		−	24.4949i		−	1.17988i	−0.807448	−	0.589939i	$-0.799152\pi$
$431$		−	24.4949i		−	1.17988i	0.807448	−	0.589939i	$-0.200848\pi$
$432$		−	4.46410i		−	0.214779i
$433$			3.07180i			0.147621i	0.997272	+	0.0738106i	$0.0235160\pi$
$433$			3.07180i			0.147621i	−0.997272	+	0.0738106i	$0.976484\pi$
$434$	−4.00000	+	55.7128i	−0.192006	+	2.67430i
$435$		−	3.86370i		−	0.185250i
$436$		−	20.5569i		−	0.984495i
$437$	15.4548			0.739304
$438$	−17.6603			−0.843840
$439$	4.06678			0.194097			0.0970483	−	0.995280i	$-0.469060\pi$
$439$	4.06678			0.194097			0.0970483	+	0.995280i	$0.469060\pi$
$440$	−1.55291	+	0.732051i	−0.0740323	+	0.0348992i
$441$	6.92820	+	1.00000i	0.329914	+	0.0476190i
$442$			20.0764i			0.954937i
$443$	36.7846			1.74769			0.873845	−	0.486205i	$-0.161619\pi$
$443$	36.7846			1.74769			0.873845	+	0.486205i	$0.161619\pi$
$444$		−	12.9282i		−	0.613545i
$445$	−8.92820			−0.423237
$446$	34.4959			1.63343
$447$	−23.6627			−1.11921
$448$	1.08604	−	15.1266i	0.0513108	−	0.714667i
$449$	−11.3205			−0.534248			−0.267124	−	0.963662i	$-0.586073\pi$
$449$	−11.3205			−0.534248			−0.267124	+	0.963662i	$0.586073\pi$
$450$		−	1.93185i		−	0.0910684i
$451$	−5.37945	+	2.53590i	−0.253309	+	0.119411i
$452$	−26.7846			−1.25984
$453$	−8.76268			−0.411707
$454$			35.5167i			1.66688i
$455$	11.1962	+	0.803848i	0.524884	+	0.0376850i
$456$	2.00000			0.0936586
$457$			30.4564i			1.42469i	0.701830	+	0.712344i	$0.252366\pi$
$457$			30.4564i			1.42469i	−0.701830	+	0.712344i	$0.747634\pi$
$458$	−19.0411			−0.889733
$459$		−	2.44949i		−	0.114332i
$460$			6.92820i			0.323029i
$461$	−17.0449			−0.793860			−0.396930	−	0.917849i	$-0.629924\pi$
$461$	−17.0449			−0.793860			−0.396930	+	0.917849i	$0.629924\pi$
$462$	−6.11169	−	15.8119i	−0.284342	−	0.735635i
$463$	−23.7128			−1.10203			−0.551014	−	0.834496i	$-0.685759\pi$
$463$	−23.7128			−1.10203			−0.551014	+	0.834496i	$0.685759\pi$
$464$			17.2480i			0.800717i
$465$		−	10.9282i		−	0.506783i
$466$	33.1244			1.53446
$467$			22.2487i			1.02955i	0.857326	+	0.514774i	$0.172124\pi$
$467$			22.2487i			1.02955i	−0.857326	+	0.514774i	$0.827876\pi$
$468$	7.34847			0.339683
$469$	0.277401	−	3.86370i	0.0128092	−	0.178409i
$470$			21.1117i			0.973809i
$471$	14.3923			0.663162
$472$	0.480473			0.0221156
$473$	3.46410	+	7.34847i	0.159280	+	0.337883i
$474$		−	2.00000i		−	0.0918630i
$475$	3.86370			0.177279
$476$	0.803848	−	11.1962i	0.0368443	−	0.513175i
$477$	−3.46410			−0.158610
$478$	−33.8564			−1.54856
$479$	2.82843			0.129234			0.0646171	−	0.997910i	$-0.479417\pi$
$479$	2.82843			0.129234			0.0646171	+	0.997910i	$0.479417\pi$
$480$			7.58871i			0.346375i
$481$	−31.6675			−1.44391
$482$		−	54.2487i		−	2.47096i
$483$	10.5558	+	0.757875i	0.480307	+	0.0344845i
$484$	−12.1244	+	14.6969i	−0.551107	+	0.668043i
$485$	8.92820			0.405409
$486$	−1.93185			−0.0876306
$487$	19.3205			0.875496			0.437748	−	0.899098i	$-0.355776\pi$
$487$	19.3205			0.875496			0.437748	+	0.899098i	$0.355776\pi$
$488$		−	2.53590i		−	0.114795i
$489$		−	12.3923i		−	0.560399i
$490$	−13.3843	−	1.93185i	−0.604639	−	0.0872722i
$491$		−	2.82843i		−	0.127645i	−0.997961	−	0.0638226i	$-0.979671\pi$
$491$		−	2.82843i		−	0.127645i	0.997961	−	0.0638226i	$-0.0203292\pi$
$492$			3.10583i			0.140022i
$493$			9.46410i			0.426242i
$494$			31.6675i			1.42479i
$495$	1.41421	+	3.00000i	0.0635642	+	0.134840i
$496$			48.7846i			2.19049i
$497$	−1.31268	+	18.2832i	−0.0588816	+	0.820115i
$498$	−2.73205			−0.122426
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$			1.73205i			0.0774597i
$501$			7.07107i			0.315912i
$502$	15.1774			0.677401
$503$	39.2934			1.75200			0.876002	−	0.482307i	$-0.160201\pi$
$503$	39.2934			1.75200			0.876002	+	0.482307i	$0.160201\pi$
$504$	1.36603	+	0.0980762i	0.0608476	+	0.00436866i
$505$		−	3.10583i		−	0.138208i
$506$	−10.9282	−	23.1822i	−0.485818	−	1.03058i
$507$		−	5.00000i		−	0.222058i
$508$			21.2132i			0.941184i
$509$		−	30.2487i		−	1.34075i	−0.742022	−	0.670375i	$-0.766133\pi$
$509$		−	30.2487i		−	1.34075i	0.742022	−	0.670375i	$-0.233867\pi$
$510$			4.73205i			0.209539i
$511$	1.73205	−	24.1244i	0.0766214	−	1.06720i
$512$		−	29.2552i		−	1.29291i
$513$		−	3.86370i		−	0.170587i
$514$	−27.0459			−1.19294
$515$	8.39230			0.369809
$516$	4.24264			0.186772
$517$	−15.4548	−	32.7846i	−0.679702	−	1.44187i
$518$	38.0526	+	2.73205i	1.67193	+	0.120039i
$519$			2.44949i			0.107521i
$520$	2.19615			0.0963077
$521$			4.14359i			0.181534i	0.995872	+	0.0907671i	$0.0289319\pi$
$521$			4.14359i			0.181534i	−0.995872	+	0.0907671i	$0.971068\pi$
$522$	7.46410			0.326695
$523$	−15.8338			−0.692362			−0.346181	−	0.938168i	$-0.612522\pi$
$523$	−15.8338			−0.692362			−0.346181	+	0.938168i	$0.612522\pi$
$524$	8.48528			0.370681
$525$	2.63896	+	0.189469i	0.115174	+	0.00826909i
$526$	6.73205			0.293531
$527$			26.7685i			1.16606i
$528$	−6.31319	−	13.3923i	−0.274746	−	0.582825i
$529$	−7.00000			−0.304348
$530$	6.69213			0.290688
$531$		−	0.928203i		−	0.0402806i
$532$	1.26795	−	17.6603i	0.0549726	−	0.765669i
$533$	7.60770			0.329526
$534$		−	17.2480i		−	0.746392i
$535$	18.9396			0.818829
$536$		−	0.757875i		−	0.0327352i
$537$		−	8.92820i		−	0.385280i
$538$	18.2832			0.788246
$539$	22.1988	−	6.79796i	0.956171	−	0.292809i
$540$	1.73205			0.0745356
$541$			33.9411i			1.45924i	0.683851	+	0.729621i	$0.260304\pi$
$541$			33.9411i			1.45924i	−0.683851	+	0.729621i	$0.739696\pi$
$542$			51.1769i			2.19824i
$543$	−3.07180			−0.131823
$544$		−	18.5885i		−	0.796974i
$545$	−11.8685			−0.508391
$546$	−1.55291	+	21.6293i	−0.0664586	+	0.925649i
$547$			20.7327i			0.886468i	0.896406	+	0.443234i	$0.146169\pi$
$547$			20.7327i			0.886468i	−0.896406	+	0.443234i	$0.853831\pi$
$548$	12.2487			0.523239
$549$	−4.89898			−0.209083
$550$	−2.73205	−	5.79555i	−0.116495	−	0.247123i
$551$			14.9282i			0.635963i
$552$	2.07055			0.0881286
$553$	2.73205	+	0.196152i	0.116179	+	0.00834125i
$554$	−5.26795			−0.223814
$555$	−7.46410			−0.316833
$556$	−22.3500			−0.947852
$557$		−	22.2485i		−	0.942698i	−0.881947	−	0.471349i	$-0.843767\pi$
$557$		−	22.2485i		−	0.942698i	0.881947	−	0.471349i	$-0.156233\pi$
$558$	21.1117			0.893728
$559$		−	10.3923i		−	0.439548i
$560$	−11.7806	−	0.845807i	−0.497820	−	0.0357419i
$561$	−3.46410	−	7.34847i	−0.146254	−	0.310253i
$562$	14.3923			0.607103
$563$	−7.62587			−0.321392			−0.160696	−	0.987004i	$-0.551374\pi$
$563$	−7.62587			−0.321392			−0.160696	+	0.987004i	$0.551374\pi$
$564$	−18.9282			−0.797021
$565$			15.4641i			0.650580i
$566$			28.0526i			1.17914i
$567$	0.189469	−	2.63896i	0.00795694	−	0.110826i
$568$			3.58630i			0.150478i
$569$			20.6312i			0.864905i	0.901657	+	0.432452i	$0.142352\pi$
$569$			20.6312i			0.864905i	−0.901657	+	0.432452i	$0.857648\pi$
$570$			7.46410i			0.312637i
$571$			0.832204i			0.0348267i	0.999848	+	0.0174133i	$0.00554312\pi$
$571$			0.832204i			0.0348267i	−0.999848	+	0.0174133i	$0.994457\pi$
$572$	22.0454	−	10.3923i	0.921765	−	0.434524i
$573$			24.9282i			1.04139i
$574$	−9.14162	−	0.656339i	−0.381564	−	0.0273951i
$575$	4.00000			0.166812
$576$	−5.73205			−0.238835
$577$		−	27.1769i		−	1.13139i	−0.824615	−	0.565695i	$-0.808608\pi$
$577$		−	27.1769i		−	1.13139i	0.824615	−	0.565695i	$-0.191392\pi$
$578$			21.2504i			0.883899i
$579$	−21.2132			−0.881591
$580$	−6.69213			−0.277876
$581$	0.267949	−	3.73205i	0.0111164	−	0.154832i
$582$			17.2480i			0.714951i
$583$	−10.3923	+	4.89898i	−0.430405	+	0.202895i
$584$		−	4.73205i		−	0.195814i
$585$		−	4.24264i		−	0.175412i
$586$		−	53.5167i		−	2.21075i
$587$		−	36.3923i		−	1.50207i	−0.660262	−	0.751036i	$-0.729555\pi$
$587$		−	36.3923i		−	1.50207i	0.660262	−	0.751036i	$-0.270445\pi$
$588$	1.73205	−	12.0000i	0.0714286	−	0.494872i
$589$			42.2233i			1.73978i
$590$			1.79315i			0.0738229i
$591$	−6.59059			−0.271101
$592$	33.3205			1.36946
$593$	34.3201			1.40936			0.704678	−	0.709527i	$-0.251091\pi$
$593$	34.3201			1.40936			0.704678	+	0.709527i	$0.251091\pi$
$594$	−5.79555	+	2.73205i	−0.237795	+	0.112097i
$595$	−6.46410	−	0.464102i	−0.265002	−	0.0190263i
$596$			40.9850i			1.67881i
$597$	−12.5359			−0.513060
$598$			32.7846i			1.34066i
$599$	−19.8564			−0.811311			−0.405655	−	0.914026i	$-0.632957\pi$
$599$	−19.8564			−0.811311			−0.405655	+	0.914026i	$0.632957\pi$
$600$	0.517638			0.0211325
$601$	−42.9812			−1.75324			−0.876620	−	0.481183i	$-0.840207\pi$
$601$	−42.9812			−1.75324			−0.876620	+	0.481183i	$0.840207\pi$
$602$	−0.896575	+	12.4877i	−0.0365417	+	0.508960i
$603$	−1.46410			−0.0596228
$604$			15.1774i			0.617560i
$605$	8.48528	+	7.00000i	0.344976	+	0.284590i
$606$	6.00000			0.243733
$607$	46.1886			1.87474			0.937368	−	0.348340i	$-0.113255\pi$
$607$	46.1886			1.87474			0.937368	+	0.348340i	$0.113255\pi$
$608$		−	29.3205i		−	1.18910i
$609$	−0.732051	+	10.1962i	−0.0296642	+	0.413169i
$610$	9.46410			0.383190
$611$			46.3644i			1.87570i
$612$	−4.24264			−0.171499
$613$			6.51626i			0.263189i	0.991304	+	0.131595i	$0.0420098\pi$
$613$			6.51626i			0.263189i	−0.991304	+	0.131595i	$0.957990\pi$
$614$			18.1962i			0.734337i
$615$	1.79315			0.0723068
$616$	4.23678	−	1.63762i	0.170705	−	0.0659817i
$617$	27.4641			1.10566			0.552832	−	0.833293i	$-0.313547\pi$
$617$	27.4641			1.10566			0.552832	+	0.833293i	$0.313547\pi$
$618$			16.2127i			0.652170i
$619$		−	17.8564i		−	0.717710i	−0.933393	−	0.358855i	$-0.883167\pi$
$619$		−	17.8564i		−	0.717710i	0.933393	−	0.358855i	$-0.116833\pi$
$620$	−18.9282			−0.760175
$621$		−	4.00000i		−	0.160514i
$622$	−44.0165			−1.76490
$623$	23.5612	+	1.69161i	0.943958	+	0.0677731i
$624$			18.9396i			0.758190i
$625$	1.00000			0.0400000
$626$	−8.00481			−0.319936
$627$	−5.46410	−	11.5911i	−0.218215	−	0.462904i
$628$		−	24.9282i		−	0.994744i
$629$	18.2832			0.729001
$630$	−0.366025	+	5.09808i	−0.0145828	+	0.203112i
$631$	11.7128			0.466280			0.233140	−	0.972443i	$-0.425100\pi$
$631$	11.7128			0.466280			0.233140	+	0.972443i	$0.425100\pi$
$632$	0.535898			0.0213169
$633$	−16.4901			−0.655422
$634$		−	39.1175i		−	1.55355i
$635$	12.2474			0.486025
$636$			6.00000i			0.237915i
$637$	−29.3939	−	4.24264i	−1.16463	−	0.168100i
$638$	22.3923	−	10.5558i	0.886520	−	0.417909i
$639$	6.92820			0.274075
$640$	−4.10394			−0.162222
$641$	−23.3205			−0.921105			−0.460552	−	0.887633i	$-0.652349\pi$
$641$	−23.3205			−0.921105			−0.460552	+	0.887633i	$0.652349\pi$
$642$			36.5885i			1.44403i
$643$			29.4641i			1.16195i	0.813921	+	0.580975i	$0.197329\pi$
$643$			29.4641i			1.16195i	−0.813921	+	0.580975i	$0.802671\pi$
$644$	1.31268	−	18.2832i	0.0517267	−	0.720461i
$645$		−	2.44949i		−	0.0964486i
$646$		−	18.2832i		−	0.719344i
$647$			40.3923i			1.58799i	0.607927	+	0.793993i	$0.292001\pi$
$647$			40.3923i			1.58799i	−0.607927	+	0.793993i	$0.707999\pi$
$648$		−	0.517638i		−	0.0203347i
$649$	−1.31268	−	2.78461i	−0.0515271	−	0.109305i
$650$			8.19615i			0.321480i
$651$	−2.07055	+	28.8391i	−0.0811513	+	1.13029i
$652$	−21.4641			−0.840599
$653$	−43.5692			−1.70500			−0.852498	−	0.522731i	$-0.824913\pi$
$653$	−43.5692			−1.70500			−0.852498	+	0.522731i	$0.824913\pi$
$654$		−	22.9282i		−	0.896564i
$655$		−	4.89898i		−	0.191419i
$656$	−8.00481			−0.312535
$657$	−9.14162			−0.356649
$658$	4.00000	−	55.7128i	0.155936	−	2.17191i
$659$			33.7381i			1.31425i	0.753783	+	0.657124i	$0.228227\pi$
$659$			33.7381i			1.31425i	−0.753783	+	0.657124i	$0.771773\pi$
$660$	5.19615	−	2.44949i	0.202260	−	0.0953463i
$661$			41.5692i			1.61686i	0.588596	+	0.808428i	$0.299681\pi$
$661$			41.5692i			1.61686i	−0.588596	+	0.808428i	$0.700319\pi$
$662$		−	31.3901i		−	1.22001i
$663$			10.3923i			0.403604i
$664$		−	0.732051i		−	0.0284091i
$665$	−10.1962	−	0.732051i	−0.395390	−	0.0283877i
$666$		−	14.4195i		−	0.558746i
$667$			15.4548i			0.598413i
$668$	12.2474			0.473868
$669$	17.8564			0.690369
$670$	2.82843			0.109272
$671$	−14.6969	+	6.92820i	−0.567369	+	0.267460i
$672$	1.43782	−	20.0263i	0.0554652	−	0.772531i
$673$			50.8102i			1.95859i	0.202445	+	0.979294i	$0.435111\pi$
$673$			50.8102i			1.95859i	−0.202445	+	0.979294i	$0.564889\pi$
$674$	−6.73205			−0.259309
$675$		−	1.00000i		−	0.0384900i
$676$	−8.66025			−0.333087
$677$	34.6718			1.33255			0.666273	−	0.745708i	$-0.267889\pi$
$677$	34.6718			1.33255			0.666273	+	0.745708i	$0.267889\pi$
$678$	−29.8744			−1.14732
$679$	−23.5612	−	1.69161i	−0.904194	−	0.0649182i
$680$	−1.26795			−0.0486236
$681$			18.3848i			0.704506i
$682$	63.3350	−	29.8564i	2.42522	−	1.14326i
$683$	32.1051			1.22847			0.614234	−	0.789124i	$-0.289465\pi$
$683$	32.1051			1.22847			0.614234	+	0.789124i	$0.289465\pi$
$684$	−6.69213			−0.255880
$685$		−	7.07180i		−	0.270199i
$686$	34.9545	+	7.63397i	1.33457	+	0.291467i
$687$	−9.85641			−0.376045
$688$			10.9348i			0.416884i
$689$	14.6969			0.559909
$690$			7.72741i			0.294177i
$691$			39.1769i			1.49036i	0.666863	+	0.745180i	$0.267636\pi$
$691$			39.1769i			1.49036i	−0.666863	+	0.745180i	$0.732364\pi$
$692$	4.24264			0.161281
$693$	−3.16364	−	8.18482i	−0.120177	−	0.310916i
$694$	−1.26795			−0.0481307
$695$			12.9038i			0.489469i
$696$			2.00000i			0.0758098i
$697$	−4.39230			−0.166370
$698$		−	16.3923i		−	0.620458i
$699$	17.1464			0.648537
$700$	0.328169	−	4.57081i	0.0124036	−	0.172760i
$701$			48.7124i			1.83984i	0.392104	+	0.919921i	$0.371747\pi$
$701$			48.7124i			1.83984i	−0.392104	+	0.919921i	$0.628253\pi$
$702$	8.19615			0.309344
$703$	28.8391			1.08769
$704$	−17.1962	+	8.10634i	−0.648104	+	0.305519i
$705$			10.9282i			0.411580i
$706$	24.2175			0.911437
$707$	−0.588457	+	8.19615i	−0.0221312	+	0.308248i
$708$	−1.60770			−0.0604209
$709$	2.92820			0.109971			0.0549855	−	0.998487i	$-0.482489\pi$
$709$	2.92820			0.109971			0.0549855	+	0.998487i	$0.482489\pi$
$710$	−13.3843			−0.502302
$711$		−	1.03528i		−	0.0388259i
$712$	4.62158			0.173201
$713$			43.7128i			1.63706i
$714$	0.896575	−	12.4877i	0.0335535	−	0.467340i
$715$	−6.00000	−	12.7279i	−0.224387	−	0.475997i
$716$	−15.4641			−0.577921
$717$	−17.5254			−0.654497
$718$	−47.7128			−1.78063
$719$		−	21.8564i		−	0.815106i	−0.913181	−	0.407553i	$-0.866382\pi$
$719$		−	21.8564i		−	0.815106i	0.913181	−	0.407553i	$-0.133618\pi$
$720$			4.46410i			0.166367i
$721$	−22.1469	−	1.59008i	−0.824795	−	0.0592176i
$722$			7.86611i			0.292746i
$723$		−	28.0812i		−	1.04435i
$724$			5.32051i			0.197735i
$725$			3.86370i			0.143494i
$726$	−13.5230	+	16.3923i	−0.501884	+	0.608375i
$727$		−	37.5692i		−	1.39337i	−0.717379	−	0.696683i	$-0.754659\pi$
$727$		−	37.5692i		−	1.39337i	0.717379	−	0.696683i	$-0.245341\pi$
$728$	−5.79555	−	0.416102i	−0.214798	−	0.0154218i
$729$	−1.00000			−0.0370370
$730$	17.6603			0.653635
$731$			6.00000i			0.221918i
$732$			8.48528i			0.313625i
$733$	19.6975			0.727542			0.363771	−	0.931488i	$-0.381489\pi$
$733$	19.6975			0.727542			0.363771	+	0.931488i	$0.381489\pi$
$734$	47.8802			1.76729
$735$	−6.92820	−	1.00000i	−0.255551	−	0.0368856i
$736$		−	30.3548i		−	1.11889i
$737$	−4.39230	+	2.07055i	−0.161793	+	0.0762698i
$738$			3.46410i			0.127515i
$739$		−	31.7418i		−	1.16764i	−0.811882	−	0.583821i	$-0.801557\pi$
$739$		−	31.7418i		−	1.16764i	0.811882	−	0.583821i	$-0.198443\pi$
$740$			12.9282i			0.475250i
$741$			16.3923i			0.602186i
$742$	−17.6603	−	1.26795i	−0.648328	−	0.0465479i
$743$			6.86800i			0.251962i	0.992033	+	0.125981i	$0.0402079\pi$
$743$			6.86800i			0.251962i	−0.992033	+	0.125981i	$0.959792\pi$
$744$			5.65685i			0.207390i
$745$	23.6627			0.866934
$746$	−12.5885			−0.460896
$747$	−1.41421			−0.0517434
$748$	−12.7279	+	6.00000i	−0.465379	+	0.219382i
$749$	−49.9808	−	3.58846i	−1.82626	−	0.131119i
$750$			1.93185i			0.0705412i
$751$	5.07180			0.185072			0.0925362	−	0.995709i	$-0.470503\pi$
$751$	5.07180			0.185072			0.0925362	+	0.995709i	$0.470503\pi$
$752$		−	48.7846i		−	1.77899i
$753$	7.85641			0.286303
$754$	−31.6675			−1.15326
$755$	8.76268			0.318907
$756$	−4.57081	−	0.328169i	−0.166239	−	0.0119354i
$757$	−48.6410			−1.76789			−0.883944	−	0.467593i	$-0.845121\pi$
$757$	−48.6410			−1.76789			−0.883944	+	0.467593i	$0.845121\pi$
$758$		−	65.4056i		−	2.37564i
$759$	−5.65685	−	12.0000i	−0.205331	−	0.435572i
$760$	−2.00000			−0.0725476
$761$	−50.0251			−1.81341			−0.906704	−	0.421768i	$-0.861410\pi$
$761$	−50.0251			−1.81341			−0.906704	+	0.421768i	$0.861410\pi$
$762$			23.6603i			0.857121i
$763$	31.3205	+	2.24871i	1.13388	+	0.0814088i
$764$	43.1769			1.56209
$765$			2.44949i			0.0885615i
$766$	47.1223			1.70260
$767$			3.93803i			0.142194i
$768$		−	19.3923i		−	0.699760i
$769$	26.9716			0.972621			0.486310	−	0.873786i	$-0.338342\pi$
$769$	26.9716			0.972621			0.486310	+	0.873786i	$0.338342\pi$
$770$	6.11169	+	15.8119i	0.220250	+	0.569820i
$771$	−14.0000			−0.504198
$772$			36.7423i			1.32239i
$773$			42.0000i			1.51064i	0.655359	+	0.755318i	$0.272517\pi$
$773$			42.0000i			1.51064i	−0.655359	+	0.755318i	$0.727483\pi$
$774$	4.73205			0.170090
$775$			10.9282i			0.392553i
$776$	−4.62158			−0.165905
$777$	19.6975	+	1.41421i	0.706642	+	0.0507346i
$778$			20.8343i			0.746945i
$779$	−6.92820			−0.248229
$780$	−7.34847			−0.263117
$781$	20.7846	−	9.79796i	0.743732	−	0.350599i
$782$		−	18.9282i		−	0.676871i
$783$	3.86370			0.138077
$784$	30.9282	+	4.46410i	1.10458	+	0.159432i
$785$	−14.3923			−0.513683
$786$	9.46410			0.337573
$787$	18.6622			0.665235			0.332617	−	0.943062i	$-0.392068\pi$
$787$	18.6622			0.665235			0.332617	+	0.943062i	$0.392068\pi$
$788$			11.4152i			0.406651i
$789$	3.48477			0.124061
$790$			2.00000i			0.0711568i
$791$	2.92996	−	40.8091i	0.104177	−	1.45101i
$792$	−0.732051	−	1.55291i	−0.0260123	−	0.0551804i
$793$	20.7846			0.738083
$794$	−17.2480			−0.612107
$795$	3.46410			0.122859
$796$			21.7128i			0.769590i
$797$		−	2.39230i		−	0.0847398i	−0.999102	−	0.0423699i	$-0.986509\pi$
$797$		−	2.39230i		−	0.0847398i	0.999102	−	0.0423699i	$-0.0134908\pi$
$798$	1.41421	−	19.6975i	0.0500626	−	0.697282i
$799$		−	26.7685i		−	0.947002i
$800$		−	7.58871i		−	0.268301i
$801$		−	8.92820i		−	0.315463i
$802$			20.3538i			0.718717i
$803$	−27.4249	+	12.9282i	−0.967802	+	0.456226i
$804$			2.53590i			0.0894342i
$805$	−10.5558	−	0.757875i	−0.372044	−	0.0267116i
$806$	−89.5692			−3.15494
$807$	9.46410			0.333152
$808$			1.60770i			0.0565585i
$809$		−	16.6932i		−	0.586900i	−0.955974	−	0.293450i	$-0.905197\pi$
$809$		−	16.6932i		−	0.586900i	0.955974	−	0.293450i	$-0.0948035\pi$
$810$	1.93185			0.0678783
$811$	−42.7038			−1.49953			−0.749767	−	0.661702i	$-0.769834\pi$
$811$	−42.7038			−1.49953			−0.749767	+	0.661702i	$0.769834\pi$
$812$	17.6603	+	1.26795i	0.619753	+	0.0444963i
$813$			26.4911i			0.929084i
$814$	−20.3923	−	43.2586i	−0.714750	−	1.51621i
$815$			12.3923i			0.434084i
$816$		−	10.9348i		−	0.382794i
$817$			9.46410i			0.331107i
$818$		−	39.7128i		−	1.38853i
$819$	−0.803848	+	11.1962i	−0.0280887	+	0.391225i
$820$		−	3.10583i		−	0.108460i
$821$		−	28.0069i		−	0.977446i	−0.872439	−	0.488723i	$-0.837463\pi$
$821$		−	28.0069i		−	0.977446i	0.872439	−	0.488723i	$-0.162537\pi$
$822$	13.6617			0.476505
$823$	−49.1769			−1.71420			−0.857100	−	0.515150i	$-0.827736\pi$
$823$	−49.1769			−1.71420			−0.857100	+	0.515150i	$0.827736\pi$
$824$	−4.34418			−0.151337
$825$	−1.41421	−	3.00000i	−0.0492366	−	0.104447i
$826$	0.339746	−	4.73205i	0.0118213	−	0.164649i
$827$		−	27.6279i		−	0.960717i	−0.877072	−	0.480359i	$-0.840506\pi$
$827$		−	27.6279i		−	0.960717i	0.877072	−	0.480359i	$-0.159494\pi$
$828$	−6.92820			−0.240772
$829$		−	39.8564i		−	1.38427i	−0.721768	−	0.692135i	$-0.756670\pi$
$829$		−	39.8564i		−	1.38427i	0.721768	−	0.692135i	$-0.243330\pi$
$830$	2.73205			0.0948309
$831$	−2.72689			−0.0945948
$832$	24.3190			0.843111
$833$	16.9706	+	2.44949i	0.587995	+	0.0848698i
$834$	−24.9282			−0.863193
$835$		−	7.07107i		−	0.244704i
$836$	−20.0764	+	9.46410i	−0.694357	+	0.327323i
$837$	10.9282			0.377734
$838$	−59.7487			−2.06398
$839$		−	5.21539i		−	0.180055i	−0.995939	−	0.0900276i	$-0.971304\pi$
$839$		−	5.21539i		−	0.180055i	0.995939	−	0.0900276i	$-0.0286955\pi$
$840$	−1.36603	−	0.0980762i	−0.0471324	−	0.00338395i
$841$	14.0718			0.485234
$842$		−	49.9507i		−	1.72142i
$843$	7.45001			0.256592
$844$			28.5617i			0.983133i
$845$			5.00000i			0.172005i
$846$	−21.1117			−0.725834
$847$	−21.0660	−	20.0804i	−0.723837	−	0.689971i
$848$	−15.4641			−0.531039
$849$			14.5211i			0.498362i
$850$		−	4.73205i		−	0.162308i
$851$	29.8564			1.02346
$852$		−	12.0000i		−	0.411113i
$853$	6.31319			0.216160			0.108080	−	0.994142i	$-0.465530\pi$
$853$	6.31319			0.216160			0.108080	+	0.994142i	$0.465530\pi$
$854$	−24.9754	−	1.79315i	−0.854640	−	0.0613604i
$855$			3.86370i			0.132136i
$856$	−9.80385			−0.335089
$857$	−24.3190			−0.830722			−0.415361	−	0.909657i	$-0.636345\pi$
$857$	−24.3190			−0.830722			−0.415361	+	0.909657i	$0.636345\pi$
$858$	24.5885	−	11.5911i	0.839436	−	0.395714i
$859$		−	42.6410i		−	1.45489i	−0.686165	−	0.727446i	$-0.740707\pi$
$859$		−	42.6410i		−	1.45489i	0.686165	−	0.727446i	$-0.259293\pi$
$860$	−4.24264			−0.144673
$861$	−4.73205	−	0.339746i	−0.161268	−	0.0115785i
$862$	−47.3205			−1.61174
$863$	−24.7846			−0.843678			−0.421839	−	0.906671i	$-0.638615\pi$
$863$	−24.7846			−0.843678			−0.421839	+	0.906671i	$0.638615\pi$
$864$	−7.58871			−0.258173
$865$		−	2.44949i		−	0.0832851i
$866$	5.93426			0.201654
$867$			11.0000i			0.373580i
$868$	49.9507	+	3.58630i	1.69544	+	0.121727i
$869$	−1.46410	−	3.10583i	−0.0496662	−	0.105358i
$870$	−7.46410			−0.253057
$871$	6.21166			0.210474
$872$	6.14359			0.208048
$873$			8.92820i			0.302174i
$874$		−	29.8564i		−	1.00991i
$875$	−2.63896	−	0.189469i	−0.0892131	−	0.00640521i
$876$			15.8338i			0.534973i
$877$		−	27.4249i		−	0.926072i	−0.886340	−	0.463036i	$-0.846760\pi$
$877$		−	27.4249i		−	0.926072i	0.886340	−	0.463036i	$-0.153240\pi$
$878$		−	7.85641i		−	0.265141i
$879$		−	27.7023i		−	0.934374i
$880$	6.31319	+	13.3923i	0.212818	+	0.451455i
$881$			42.2487i			1.42340i	0.702486	+	0.711698i	$0.252073\pi$
$881$			42.2487i			1.42340i	−0.702486	+	0.711698i	$0.747927\pi$
$882$	1.93185	−	13.3843i	0.0650488	−	0.450672i
$883$	−6.92820			−0.233153			−0.116576	−	0.993182i	$-0.537192\pi$
$883$	−6.92820			−0.233153			−0.116576	+	0.993182i	$0.537192\pi$
$884$	18.0000			0.605406
$885$			0.928203i			0.0312012i
$886$		−	71.0624i		−	2.38739i
$887$	52.6776			1.76874			0.884371	−	0.466785i	$-0.154588\pi$
$887$	52.6776			1.76874			0.884371	+	0.466785i	$0.154588\pi$
$888$	3.86370			0.129657
$889$	−32.3205	−	2.32051i	−1.08400	−	0.0778273i
$890$			17.2480i			0.578153i
$891$	−3.00000	+	1.41421i	−0.100504	+	0.0473779i
$892$		−	30.9282i		−	1.03555i
$893$		−	42.2233i		−	1.41295i
$894$			45.7128i			1.52887i
$895$			8.92820i			0.298437i
$896$	10.8301	+	0.777568i	0.361809	+	0.0259767i
$897$			16.9706i			0.566631i
$898$			21.8695i			0.729796i
$899$	−42.2233			−1.40823
$900$	−1.73205			−0.0577350
$901$	−8.48528			−0.282686
$902$	4.89898	+	10.3923i	0.163118	+	0.346026i
$903$	−0.464102	+	6.46410i	−0.0154443	+	0.215112i
$904$		−	8.00481i		−	0.266236i
$905$	3.07180			0.102110
$906$			16.9282i			0.562402i
$907$	−4.00000			−0.132818			−0.0664089	−	0.997792i	$-0.521154\pi$
$907$	−4.00000			−0.132818			−0.0664089	+	0.997792i	$0.521154\pi$
$908$	31.8434			1.05676
$909$	3.10583			0.103014
$910$	1.55291	−	21.6293i	0.0514786	−	0.717004i
$911$	7.07180			0.234299			0.117150	−	0.993114i	$-0.462624\pi$
$911$	7.07180			0.234299			0.117150	+	0.993114i	$0.462624\pi$
$912$		−	17.2480i		−	0.571137i
$913$	−4.24264	+	2.00000i	−0.140411	+	0.0661903i
$914$	58.8372			1.94616
$915$	4.89898			0.161955
$916$			17.0718i			0.564068i
$917$	−0.928203	+	12.9282i	−0.0306520	+	0.426927i
$918$	−4.73205			−0.156181
$919$		−	2.34795i		−	0.0774518i	−0.999250	−	0.0387259i	$-0.987670\pi$
$919$		−	2.34795i		−	0.0774518i	0.999250	−	0.0387259i	$-0.0123299\pi$
$920$	−2.07055			−0.0682641
$921$			9.41902i			0.310367i
$922$			32.9282i			1.08443i
$923$	−29.3939			−0.967511
$924$	−14.1765	+	5.47959i	−0.466374	+	0.180265i
$925$	7.46410			0.245418
$926$			45.8096i			1.50540i
$927$			8.39230i			0.275639i
$928$	29.3205			0.962493
$929$		−	2.53590i		−	0.0832001i	−0.999134	−	0.0416001i	$-0.986754\pi$
$929$		−	2.53590i		−	0.0832001i	0.999134	−	0.0416001i	$-0.0132455\pi$
$930$	−21.1117			−0.692279
$931$	26.7685	+	3.86370i	0.877303	+	0.126628i
$932$		−	29.6985i		−	0.972806i
$933$	−22.7846			−0.745935
$934$	42.9812			1.40639
$935$	3.46410	+	7.34847i	0.113288	+	0.240321i
$936$			2.19615i			0.0717835i
$937$	4.44571			0.145235			0.0726176	−	0.997360i	$-0.476865\pi$
$937$	4.44571			0.145235			0.0726176	+	0.997360i	$0.476865\pi$
$938$	−7.46410	−	0.535898i	−0.243712	−	0.0174977i
$939$	−4.14359			−0.135221
$940$	18.9282			0.617370
$941$	37.0470			1.20770			0.603848	−	0.797099i	$-0.293633\pi$
$941$	37.0470			1.20770			0.603848	+	0.797099i	$0.293633\pi$
$942$		−	27.8038i		−	0.905897i
$943$	−7.17260			−0.233572
$944$		−	4.14359i		−	0.134862i
$945$	−0.189469	+	2.63896i	−0.00616342	+	0.0858453i
$946$	14.1962	−	6.69213i	0.461557	−	0.217580i
$947$	16.3923			0.532678			0.266339	−	0.963879i	$-0.414186\pi$
$947$	16.3923			0.532678			0.266339	+	0.963879i	$0.414186\pi$
$948$	−1.79315			−0.0582388
$949$	38.7846			1.25900
$950$		−	7.46410i		−	0.242167i
$951$		−	20.2487i		−	0.656609i
$952$	3.34607	+	0.240237i	0.108447	+	0.00778612i
$953$			9.41902i			0.305112i	0.988295	+	0.152556i	$0.0487504\pi$
$953$			9.41902i			0.305112i	−0.988295	+	0.152556i	$0.951250\pi$
$954$			6.69213i			0.216666i
$955$		−	24.9282i		−	0.806658i
$956$			30.3548i			0.981745i
$957$	11.5911	−	5.46410i	0.374687	−	0.176629i
$958$		−	5.46410i		−	0.176537i
$959$	−1.33988	+	18.6622i	−0.0432671	+	0.602633i
$960$	5.73205			0.185001
$961$	−88.4256			−2.85244
$962$			61.1769i			1.97242i
$963$			18.9396i			0.610319i
$964$	−48.6381			−1.56653
$965$	21.2132			0.682877
$966$	1.46410	−	20.3923i	0.0471067	−	0.656112i
$967$			36.7423i			1.18155i	0.806835	+	0.590777i	$0.201179\pi$
$967$			36.7423i			1.18155i	−0.806835	+	0.590777i	$0.798821\pi$
$968$	−4.39230	−	3.62347i	−0.141174	−	0.116463i
$969$		−	9.46410i		−	0.304031i
$970$		−	17.2480i		−	0.553799i
$971$		−	37.8564i		−	1.21487i	−0.794369	−	0.607435i	$-0.792199\pi$
$971$		−	37.8564i		−	1.21487i	0.794369	−	0.607435i	$-0.207801\pi$
$972$			1.73205i			0.0555556i
$973$	2.44486	−	34.0526i	0.0783787	−	1.09167i
$974$		−	37.3244i		−	1.19595i
$975$			4.24264i			0.135873i
$976$	−21.8695			−0.700027
$977$	−36.9282			−1.18144			−0.590719	−	0.806877i	$-0.701156\pi$
$977$	−36.9282			−1.18144			−0.590719	+	0.806877i	$0.701156\pi$
$978$	−23.9401			−0.765520
$979$	−12.6264	−	26.7846i	−0.403541	−	0.856040i
$980$	−1.73205	+	12.0000i	−0.0553283	+	0.383326i
$981$		−	11.8685i		−	0.378932i
$982$	−5.46410			−0.174366
$983$		−	4.39230i		−	0.140093i	−0.997544	−	0.0700464i	$-0.977685\pi$
$983$		−	4.39230i		−	0.140093i	0.997544	−	0.0700464i	$-0.0223147\pi$
$984$	−0.928203			−0.0295900
$985$	6.59059			0.209994
$986$	18.2832			0.582257
$987$	2.07055	−	28.8391i	0.0659064	−	0.917958i
$988$	28.3923			0.903280
$989$			9.79796i			0.311557i
$990$	5.79555	−	2.73205i	0.184195	−	0.0868303i
$991$	58.1051			1.84577			0.922885	−	0.385076i	$-0.125825\pi$
$991$	58.1051			1.84577			0.922885	+	0.385076i	$0.125825\pi$
$992$	82.9309			2.63306
$993$		−	16.2487i		−	0.515637i
$994$	35.3205	+	2.53590i	1.12030	+	0.0804338i
$995$	12.5359			0.397415
$996$			2.44949i			0.0776151i
$997$	−16.3142			−0.516677			−0.258338	−	0.966055i	$-0.583175\pi$
$997$	−16.3142			−0.516677			−0.258338	+	0.966055i	$0.583175\pi$
$998$			7.72741i			0.244607i
$999$		−	7.46410i		−	0.236154i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.b.76.1	✓	8
7.6	odd	2	inner	1155.2.i.b.76.2	yes	8
11.10	odd	2	inner	1155.2.i.b.76.7	yes	8
77.76	even	2	inner	1155.2.i.b.76.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.b.76.1	✓	8	1.1	even	1	trivial
1155.2.i.b.76.2	yes	8	7.6	odd	2	inner
1155.2.i.b.76.7	yes	8	11.10	odd	2	inner
1155.2.i.b.76.8	yes	8	77.76	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.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +1.00000i q^{5} -1.93185 q^{6} +(0.189469 - 2.63896i) q^{7} -0.517638i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.93185i q^{2} -1.00000i q^{3} -1.73205 q^{4} +1.00000i q^{5} -1.93185 q^{6} +(0.189469 - 2.63896i) q^{7} -0.517638i q^{8} -1.00000 q^{9} +1.93185 q^{10} +(-3.00000 + 1.41421i) q^{11} +1.73205i q^{12} +4.24264 q^{13} +(-5.09808 - 0.366025i) q^{14} +1.00000 q^{15} -4.46410 q^{16} -2.44949 q^{17} +1.93185i q^{18} -3.86370 q^{19} -1.73205i q^{20} +(-2.63896 - 0.189469i) q^{21} +(2.73205 + 5.79555i) q^{22} -4.00000 q^{23} -0.517638 q^{24} -1.00000 q^{25} -8.19615i q^{26} +1.00000i q^{27} +(-0.328169 + 4.57081i) q^{28} -3.86370i q^{29} -1.93185i q^{30} -10.9282i q^{31} +7.58871i q^{32} +(1.41421 + 3.00000i) q^{33} +4.73205i q^{34} +(2.63896 + 0.189469i) q^{35} +1.73205 q^{36} -7.46410 q^{37} +7.46410i q^{38} -4.24264i q^{39} +0.517638 q^{40} +1.79315 q^{41} +(-0.366025 + 5.09808i) q^{42} -2.44949i q^{43} +(5.19615 - 2.44949i) q^{44} -1.00000i q^{45} +7.72741i q^{46} +10.9282i q^{47} +4.46410i q^{48} +(-6.92820 - 1.00000i) q^{49} +1.93185i q^{50} +2.44949i q^{51} -7.34847 q^{52} +3.46410 q^{53} +1.93185 q^{54} +(-1.41421 - 3.00000i) q^{55} +(-1.36603 - 0.0980762i) q^{56} +3.86370i q^{57} -7.46410 q^{58} +0.928203i q^{59} -1.73205 q^{60} +4.89898 q^{61} -21.1117 q^{62} +(-0.189469 + 2.63896i) q^{63} +5.73205 q^{64} +4.24264i q^{65} +(5.79555 - 2.73205i) q^{66} +1.46410 q^{67} +4.24264 q^{68} +4.00000i q^{69} +(0.366025 - 5.09808i) q^{70} -6.92820 q^{71} +0.517638i q^{72} +9.14162 q^{73} +14.4195i q^{74} +1.00000i q^{75} +6.69213 q^{76} +(3.16364 + 8.18482i) q^{77} -8.19615 q^{78} +1.03528i q^{79} -4.46410i q^{80} +1.00000 q^{81} -3.46410i q^{82} +1.41421 q^{83} +(4.57081 + 0.328169i) q^{84} -2.44949i q^{85} -4.73205 q^{86} -3.86370 q^{87} +(0.732051 + 1.55291i) q^{88} +8.92820i q^{89} -1.93185 q^{90} +(0.803848 - 11.1962i) q^{91} +6.92820 q^{92} -10.9282 q^{93} +21.1117 q^{94} -3.86370i q^{95} +7.58871 q^{96} -8.92820i q^{97} +(-1.93185 + 13.3843i) q^{98} +(3.00000 - 1.41421i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^9	\( 8 q - 8 q^{9} - 24 q^{11} - 20 q^{14} + 8 q^{15} - 8 q^{16} + 8 q^{22} - 32 q^{23} - 8 q^{25} - 32 q^{37} + 4 q^{42} - 4 q^{56} - 32 q^{58} + 32 q^{64} - 16 q^{67} - 4 q^{70} + 16 q^{77} - 24 q^{78} + 8 q^{81} - 24 q^{86} - 8 q^{88} + 48 q^{91} - 32 q^{93} + 24 q^{99}+O(q^{100}) \) 8 * q - 8 * q^9 - 24 * q^11 - 20 * q^14 + 8 * q^15 - 8 * q^16 + 8 * q^22 - 32 * q^23 - 8 * q^25 - 32 * q^37 + 4 * q^42 - 4 * q^56 - 32 * q^58 + 32 * q^64 - 16 * q^67 - 4 * q^70 + 16 * q^77 - 24 * q^78 + 8 * q^81 - 24 * q^86 - 8 * q^88 + 48 * q^91 - 32 * q^93 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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