LMFDB - Embedded newform 1155.2.i.d.76.3

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:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.3
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.370647i q^{2} -1.00000i q^{3} +1.86262 q^{4} -1.00000i q^{5} -0.370647 q^{6} +(-2.39596 + 1.12222i) q^{7} -1.43167i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.370647i q^{2} -1.00000i q^{3} +1.86262 q^{4} -1.00000i q^{5} -0.370647 q^{6} +(-2.39596 + 1.12222i) q^{7} -1.43167i q^{8} -1.00000 q^{9} -0.370647 q^{10} +(2.11090 - 2.55814i) q^{11} -1.86262i q^{12} +5.18990 q^{13} +(0.415948 + 0.888056i) q^{14} -1.00000 q^{15} +3.19460 q^{16} -2.13309 q^{17} +0.370647i q^{18} -5.11883 q^{19} -1.86262i q^{20} +(1.12222 + 2.39596i) q^{21} +(-0.948170 - 0.782400i) q^{22} +7.91984 q^{23} -1.43167 q^{24} -1.00000 q^{25} -1.92362i q^{26} +1.00000i q^{27} +(-4.46276 + 2.09027i) q^{28} -7.81291i q^{29} +0.370647i q^{30} -7.84432i q^{31} -4.04741i q^{32} +(-2.55814 - 2.11090i) q^{33} +0.790625i q^{34} +(1.12222 + 2.39596i) q^{35} -1.86262 q^{36} -8.48839 q^{37} +1.89728i q^{38} -5.18990i q^{39} -1.43167 q^{40} +2.17082 q^{41} +(0.888056 - 0.415948i) q^{42} +7.76125i q^{43} +(3.93180 - 4.76485i) q^{44} +1.00000i q^{45} -2.93547i q^{46} -5.62252i q^{47} -3.19460i q^{48} +(4.48125 - 5.37759i) q^{49} +0.370647i q^{50} +2.13309i q^{51} +9.66682 q^{52} -10.7569 q^{53} +0.370647 q^{54} +(-2.55814 - 2.11090i) q^{55} +(1.60665 + 3.43022i) q^{56} +5.11883i q^{57} -2.89583 q^{58} +2.14980i q^{59} -1.86262 q^{60} +8.26503 q^{61} -2.90748 q^{62} +(2.39596 - 1.12222i) q^{63} +4.88903 q^{64} -5.18990i q^{65} +(-0.782400 + 0.948170i) q^{66} -2.80794 q^{67} -3.97314 q^{68} -7.91984i q^{69} +(0.888056 - 0.415948i) q^{70} +9.32895 q^{71} +1.43167i q^{72} -10.0221 q^{73} +3.14620i q^{74} +1.00000i q^{75} -9.53443 q^{76} +(-2.18683 + 8.49810i) q^{77} -1.92362 q^{78} +8.98914i q^{79} -3.19460i q^{80} +1.00000 q^{81} -0.804610i q^{82} +3.96061 q^{83} +(2.09027 + 4.46276i) q^{84} +2.13309i q^{85} +2.87669 q^{86} -7.81291 q^{87} +(-3.66242 - 3.02211i) q^{88} +8.45786i q^{89} +0.370647 q^{90} +(-12.4348 + 5.82421i) q^{91} +14.7517 q^{92} -7.84432 q^{93} -2.08397 q^{94} +5.11883i q^{95} -4.04741 q^{96} -8.31015i q^{97} +(-1.99319 - 1.66096i) q^{98} +(-2.11090 + 2.55814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * 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 $

$2$		−	0.370647i		−	0.262087i	−0.991377	−	0.131044i	$-0.958167\pi$
$2$		−	0.370647i		−	0.262087i	0.991377	−	0.131044i	$-0.0418328\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.86262			0.931310
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.370647			−0.151316
$7$	−2.39596	+	1.12222i	−0.905588	+	0.424159i
$7$	−2.39596	+	1.12222i	−0.905588	+	0.424159i
$8$		−	1.43167i		−	0.506172i
$9$	−1.00000			−0.333333
$10$	−0.370647			−0.117209
$11$	2.11090	−	2.55814i	0.636460	−	0.771310i
$11$	2.11090	−	2.55814i	0.636460	−	0.771310i
$12$		−	1.86262i		−	0.537692i
$13$	5.18990			1.43942			0.719710	−	0.694275i	$-0.244275\pi$
$13$	5.18990			1.43942			0.719710	+	0.694275i	$0.244275\pi$
$14$	0.415948	+	0.888056i	0.111167	+	0.237343i
$15$	−1.00000			−0.258199
$16$	3.19460			0.798649
$17$	−2.13309			−0.517351			−0.258675	−	0.965964i	$-0.583286\pi$
$17$	−2.13309			−0.517351			−0.258675	+	0.965964i	$0.583286\pi$
$18$			0.370647i			0.0873624i
$19$	−5.11883			−1.17434			−0.587170	−	0.809464i	$-0.699758\pi$
$19$	−5.11883			−1.17434			−0.587170	+	0.809464i	$0.699758\pi$
$20$		−	1.86262i		−	0.416495i
$21$	1.12222	+	2.39596i	0.244888	+	0.522841i
$22$	−0.948170	−	0.782400i	−0.202150	−	0.166808i
$23$	7.91984			1.65140			0.825700	−	0.564109i	$-0.190780\pi$
$23$	7.91984			1.65140			0.825700	+	0.564109i	$0.190780\pi$
$24$	−1.43167			−0.292239
$25$	−1.00000			−0.200000
$26$		−	1.92362i		−	0.377254i
$27$			1.00000i			0.192450i
$28$	−4.46276	+	2.09027i	−0.843383	+	0.395024i
$29$		−	7.81291i		−	1.45082i	−0.688317	−	0.725410i	$-0.741650\pi$
$29$		−	7.81291i		−	1.45082i	0.688317	−	0.725410i	$-0.258350\pi$
$30$			0.370647i			0.0676707i
$31$		−	7.84432i		−	1.40888i	−0.709763	−	0.704441i	$-0.751198\pi$
$31$		−	7.84432i		−	1.40888i	0.709763	−	0.704441i	$-0.248802\pi$
$32$		−	4.04741i		−	0.715488i
$33$	−2.55814	−	2.11090i	−0.445316	−	0.367460i
$34$			0.790625i			0.135591i
$35$	1.12222	+	2.39596i	0.189690	+	0.404991i
$36$	−1.86262			−0.310437
$37$	−8.48839			−1.39548			−0.697741	−	0.716350i	$-0.745812\pi$
$37$	−8.48839			−1.39548			−0.697741	+	0.716350i	$0.745812\pi$
$38$			1.89728i			0.307779i
$39$		−	5.18990i		−	0.831050i
$40$	−1.43167			−0.226367
$41$	2.17082			0.339026			0.169513	−	0.985528i	$-0.445781\pi$
$41$	2.17082			0.339026			0.169513	+	0.985528i	$0.445781\pi$
$42$	0.888056	−	0.415948i	0.137030	−	0.0641821i
$43$			7.76125i			1.18358i	0.806092	+	0.591790i	$0.201578\pi$
$43$			7.76125i			1.18358i	−0.806092	+	0.591790i	$0.798422\pi$
$44$	3.93180	−	4.76485i	0.592742	−	0.718329i
$45$			1.00000i			0.149071i
$46$		−	2.93547i		−	0.432811i
$47$		−	5.62252i		−	0.820129i	−0.912057	−	0.410064i	$-0.865506\pi$
$47$		−	5.62252i		−	0.820129i	0.912057	−	0.410064i	$-0.134494\pi$
$48$		−	3.19460i		−	0.461100i
$49$	4.48125	−	5.37759i	0.640178	−	0.768227i
$50$			0.370647i			0.0524175i
$51$			2.13309i			0.298693i
$52$	9.66682			1.34055
$53$	−10.7569			−1.47757			−0.738785	−	0.673941i	$-0.764600\pi$
$53$	−10.7569			−1.47757			−0.738785	+	0.673941i	$0.764600\pi$
$54$	0.370647			0.0504387
$55$	−2.55814	−	2.11090i	−0.344940	−	0.284634i
$56$	1.60665	+	3.43022i	0.214697	+	0.458383i
$57$			5.11883i			0.678005i
$58$	−2.89583			−0.380242
$59$			2.14980i			0.279881i	0.990160	+	0.139940i	$0.0446911\pi$
$59$			2.14980i			0.279881i	−0.990160	+	0.139940i	$0.955309\pi$
$60$	−1.86262			−0.240463
$61$	8.26503			1.05823			0.529114	−	0.848551i	$-0.322524\pi$
$61$	8.26503			1.05823			0.529114	+	0.848551i	$0.322524\pi$
$62$	−2.90748			−0.369250
$63$	2.39596	−	1.12222i	0.301863	−	0.141386i
$64$	4.88903			0.611129
$65$		−	5.18990i		−	0.643728i
$66$	−0.782400	+	0.948170i	−0.0963067	+	0.116712i
$67$	−2.80794			−0.343045			−0.171522	−	0.985180i	$-0.554869\pi$
$67$	−2.80794			−0.343045			−0.171522	+	0.985180i	$0.554869\pi$
$68$	−3.97314			−0.481814
$69$		−	7.91984i		−	0.953436i
$70$	0.888056	−	0.415948i	0.106143	−	0.0497153i
$71$	9.32895			1.10714			0.553571	−	0.832802i	$-0.313265\pi$
$71$	9.32895			1.10714			0.553571	+	0.832802i	$0.313265\pi$
$72$			1.43167i			0.168724i
$73$	−10.0221			−1.17300			−0.586499	−	0.809950i	$-0.699494\pi$
$73$	−10.0221			−1.17300			−0.586499	+	0.809950i	$0.699494\pi$
$74$			3.14620i			0.365738i
$75$			1.00000i			0.115470i
$76$	−9.53443			−1.09367
$77$	−2.18683	+	8.49810i	−0.249212	+	0.968449i
$78$	−1.92362			−0.217808
$79$			8.98914i			1.01136i	0.862722	+	0.505679i	$0.168758\pi$
$79$			8.98914i			1.01136i	−0.862722	+	0.505679i	$0.831242\pi$
$80$		−	3.19460i		−	0.357167i
$81$	1.00000			0.111111
$82$		−	0.804610i		−	0.0888543i
$83$	3.96061			0.434733			0.217367	−	0.976090i	$-0.430253\pi$
$83$	3.96061			0.434733			0.217367	+	0.976090i	$0.430253\pi$
$84$	2.09027	+	4.46276i	0.228067	+	0.486927i
$85$			2.13309i			0.231366i
$86$	2.87669			0.310201
$87$	−7.81291			−0.837632
$88$	−3.66242	−	3.02211i	−0.390415	−	0.322158i
$89$			8.45786i			0.896531i	0.893900	+	0.448265i	$0.147958\pi$
$89$			8.45786i			0.896531i	−0.893900	+	0.448265i	$0.852042\pi$
$90$	0.370647			0.0390697
$91$	−12.4348	+	5.82421i	−1.30352	+	0.610543i
$92$	14.7517			1.53797
$93$	−7.84432			−0.813418
$94$	−2.08397			−0.214945
$95$			5.11883i			0.525181i
$96$	−4.04741			−0.413087
$97$		−	8.31015i		−	0.843768i	−0.906650	−	0.421884i	$-0.861369\pi$
$97$		−	8.31015i		−	0.843768i	0.906650	−	0.421884i	$-0.138631\pi$
$98$	−1.99319	−	1.66096i	−0.201342	−	0.167783i
$99$	−2.11090	+	2.55814i	−0.212153	+	0.257103i
$100$	−1.86262			−0.186262
$101$	6.92755			0.689317			0.344658	−	0.938728i	$-0.387995\pi$
$101$	6.92755			0.689317			0.344658	+	0.938728i	$0.387995\pi$
$102$	0.790625			0.0782836
$103$			18.7232i			1.84485i	0.386174	+	0.922426i	$0.373796\pi$
$103$			18.7232i			1.84485i	−0.386174	+	0.922426i	$0.626204\pi$
$104$		−	7.43023i		−	0.728594i
$105$	2.39596	−	1.12222i	0.233822	−	0.109517i
$106$			3.98701i			0.387252i
$107$			8.22730i			0.795363i	0.917524	+	0.397681i	$0.130185\pi$
$107$			8.22730i			0.795363i	−0.917524	+	0.397681i	$0.869815\pi$
$108$			1.86262i			0.179231i
$109$		−	10.6190i		−	1.01712i	−0.861027	−	0.508560i	$-0.830178\pi$
$109$		−	10.6190i		−	1.01712i	0.861027	−	0.508560i	$-0.169822\pi$
$110$	−0.782400	+	0.948170i	−0.0745989	+	0.0904044i
$111$			8.48839i			0.805682i
$112$	−7.65412	+	3.58504i	−0.723247	+	0.338754i
$113$	8.90438			0.837654			0.418827	−	0.908066i	$-0.362441\pi$
$113$	8.90438			0.837654			0.418827	+	0.908066i	$0.362441\pi$
$114$	1.89728			0.177697
$115$		−	7.91984i		−	0.738529i
$116$		−	14.5525i		−	1.35116i
$117$	−5.18990			−0.479807
$118$	0.796819			0.0733532
$119$	5.11080	−	2.39380i	0.468507	−	0.219439i
$120$			1.43167i			0.130693i
$121$	−2.08821	−	10.8000i	−0.189837	−	0.981816i
$122$		−	3.06341i		−	0.277348i
$123$		−	2.17082i		−	0.195737i
$124$		−	14.6110i		−	1.31211i
$125$			1.00000i			0.0894427i
$126$	−0.415948	−	0.888056i	−0.0370556	−	0.0791144i
$127$			0.180847i			0.0160476i	0.999968	+	0.00802380i	$0.00255408\pi$
$127$			0.180847i			0.0160476i	−0.999968	+	0.00802380i	$0.997446\pi$
$128$		−	9.90693i		−	0.875657i
$129$	7.76125			0.683340
$130$	−1.92362			−0.168713
$131$	6.73154			0.588137			0.294069	−	0.955784i	$-0.404991\pi$
$131$	6.73154			0.588137			0.294069	+	0.955784i	$0.404991\pi$
$132$	−4.76485	−	3.93180i	−0.414727	−	0.342220i
$133$	12.2645	−	5.74445i	1.06347	−	0.498107i
$134$			1.04076i			0.0899076i
$135$	1.00000			0.0860663
$136$			3.05389i			0.261869i
$137$	−13.6144			−1.16315			−0.581576	−	0.813492i	$-0.697564\pi$
$137$	−13.6144			−1.16315			−0.581576	+	0.813492i	$0.697564\pi$
$138$	−2.93547			−0.249884
$139$	−3.80775			−0.322969			−0.161485	−	0.986875i	$-0.551628\pi$
$139$	−3.80775			−0.322969			−0.161485	+	0.986875i	$0.551628\pi$
$140$	2.09027	+	4.46276i	0.176660	+	0.377172i
$141$	−5.62252			−0.473502
$142$		−	3.45775i		−	0.290168i
$143$	10.9554	−	13.2765i	0.916134	−	1.11024i
$144$	−3.19460			−0.266216
$145$	−7.81291			−0.648827
$146$			3.71466i			0.307428i
$147$	−5.37759	−	4.48125i	−0.443536	−	0.369607i
$148$	−15.8106			−1.29963
$149$		−	14.6126i		−	1.19711i	−0.801080	−	0.598557i	$-0.795741\pi$
$149$		−	14.6126i		−	1.19711i	0.801080	−	0.598557i	$-0.204259\pi$
$150$	0.370647			0.0302632
$151$		−	3.31010i		−	0.269372i	−0.990888	−	0.134686i	$-0.956997\pi$
$151$		−	3.31010i		−	0.269372i	0.990888	−	0.134686i	$-0.0430026\pi$
$152$			7.32847i			0.594418i
$153$	2.13309			0.172450
$154$	3.14980	+	0.810543i	0.253818	+	0.0653154i
$155$	−7.84432			−0.630071
$156$		−	9.66682i		−	0.773965i
$157$			7.80076i			0.622568i	0.950317	+	0.311284i	$0.100759\pi$
$157$			7.80076i			0.622568i	−0.950317	+	0.311284i	$0.899241\pi$
$158$	3.33180			0.265064
$159$			10.7569i			0.853075i
$160$	−4.04741			−0.319976
$161$	−18.9756	+	8.88780i	−1.49549	+	0.700456i
$162$		−	0.370647i		−	0.0291208i
$163$	9.49527			0.743727			0.371864	−	0.928287i	$-0.378719\pi$
$163$	9.49527			0.743727			0.371864	+	0.928287i	$0.378719\pi$
$164$	4.04342			0.315738
$165$	−2.11090	+	2.55814i	−0.164333	+	0.199151i
$166$		−	1.46799i		−	0.113938i
$167$	20.2714			1.56865			0.784325	−	0.620351i	$-0.213010\pi$
$167$	20.2714			1.56865			0.784325	+	0.620351i	$0.213010\pi$
$168$	3.43022	−	1.60665i	0.264648	−	0.123956i
$169$	13.9351			1.07193
$170$	0.790625			0.0606382
$171$	5.11883			0.391446
$172$			14.4563i			1.10228i
$173$	12.6674			0.963084			0.481542	−	0.876423i	$-0.340077\pi$
$173$	12.6674			0.963084			0.481542	+	0.876423i	$0.340077\pi$
$174$			2.89583i			0.219533i
$175$	2.39596	−	1.12222i	0.181118	−	0.0848318i
$176$	6.74347	−	8.17224i	0.508308	−	0.616006i
$177$	2.14980			0.161589
$178$	3.13488			0.234969
$179$	18.3486			1.37144			0.685719	−	0.727866i	$-0.259488\pi$
$179$	18.3486			1.37144			0.685719	+	0.727866i	$0.259488\pi$
$180$			1.86262i			0.138832i
$181$		−	1.68503i		−	0.125247i	−0.998037	−	0.0626235i	$-0.980053\pi$
$181$		−	1.68503i		−	0.125247i	0.998037	−	0.0626235i	$-0.0199467\pi$
$182$	2.15873	+	4.60893i	0.160016	+	0.341636i
$183$		−	8.26503i		−	0.610968i
$184$		−	11.3386i		−	0.835892i
$185$			8.48839i			0.624079i
$186$			2.90748i			0.213187i
$187$	−4.50274	+	5.45676i	−0.329273	+	0.399038i
$188$		−	10.4726i		−	0.763795i
$189$	−1.12222	−	2.39596i	−0.0816295	−	0.174280i
$190$	1.89728			0.137643
$191$	−18.7733			−1.35839			−0.679195	−	0.733958i	$-0.737671\pi$
$191$	−18.7733			−1.35839			−0.679195	+	0.733958i	$0.737671\pi$
$192$		−	4.88903i		−	0.352835i
$193$			25.6970i			1.84971i	0.380322	+	0.924854i	$0.375813\pi$
$193$			25.6970i			1.84971i	−0.380322	+	0.924854i	$0.624187\pi$
$194$	−3.08014			−0.221141
$195$	−5.18990			−0.371657
$196$	8.34686	−	10.0164i	0.596204	−	0.715457i
$197$			12.6841i			0.903702i	0.892093	+	0.451851i	$0.149236\pi$
$197$			12.6841i			0.903702i	−0.892093	+	0.451851i	$0.850764\pi$
$198$	0.948170	+	0.782400i	0.0673835	+	0.0556027i
$199$			16.7628i			1.18828i	0.804361	+	0.594141i	$0.202508\pi$
$199$			16.7628i			1.18828i	−0.804361	+	0.594141i	$0.797492\pi$
$200$			1.43167i			0.101234i
$201$			2.80794i			0.198057i
$202$		−	2.56768i		−	0.180661i
$203$	8.76780	+	18.7194i	0.615379	+	1.31385i
$204$			3.97314i			0.278176i
$205$		−	2.17082i		−	0.151617i
$206$	6.93971			0.483512
$207$	−7.91984			−0.550467
$208$	16.5796			1.14959
$209$	−10.8053	+	13.0947i	−0.747420	+	0.905779i
$210$	−0.415948	−	0.888056i	−0.0287031	−	0.0612817i
$211$			3.97165i			0.273420i	0.990611	+	0.136710i	$0.0436528\pi$
$211$			3.97165i			0.273420i	−0.990611	+	0.136710i	$0.956347\pi$
$212$	−20.0360			−1.37608
$213$		−	9.32895i		−	0.639209i
$214$	3.04943			0.208454
$215$	7.76125			0.529313
$216$	1.43167			0.0974128
$217$	8.80305	+	18.7947i	0.597590	+	1.27587i
$218$	−3.93592			−0.266574
$219$			10.0221i			0.677230i
$220$	−4.76485	−	3.93180i	−0.321246	−	0.265082i
$221$	−11.0705			−0.744686
$222$	3.14620			0.211159
$223$			28.2077i			1.88893i	0.328617	+	0.944463i	$0.393417\pi$
$223$			28.2077i			1.88893i	−0.328617	+	0.944463i	$0.606583\pi$
$224$	4.54208	+	9.69743i	0.303481	+	0.647937i
$225$	1.00000			0.0666667
$226$		−	3.30039i		−	0.219538i
$227$	−20.3828			−1.35285			−0.676426	−	0.736511i	$-0.736472\pi$
$227$	−20.3828			−1.35285			−0.676426	+	0.736511i	$0.736472\pi$
$228$			9.53443i			0.631433i
$229$			1.17784i			0.0778341i	0.999242	+	0.0389171i	$0.0123908\pi$
$229$			1.17784i			0.0778341i	−0.999242	+	0.0389171i	$0.987609\pi$
$230$	−2.93547			−0.193559
$231$	8.49810	+	2.18683i	0.559134	+	0.143883i
$232$	−11.1855			−0.734365
$233$		−	16.8343i		−	1.10285i	−0.834223	−	0.551427i	$-0.814084\pi$
$233$		−	16.8343i		−	1.10285i	0.834223	−	0.551427i	$-0.185916\pi$
$234$			1.92362i			0.125751i
$235$	−5.62252			−0.366773
$236$			4.00427i			0.260656i
$237$	8.98914			0.583908
$238$	−0.887255	−	1.89431i	−0.0575122	−	0.122790i
$239$			1.05700i			0.0683714i	0.999415	+	0.0341857i	$0.0108838\pi$
$239$			1.05700i			0.0683714i	−0.999415	+	0.0341857i	$0.989116\pi$
$240$	−3.19460			−0.206210
$241$	22.3686			1.44089			0.720443	−	0.693515i	$-0.243939\pi$
$241$	22.3686			1.44089			0.720443	+	0.693515i	$0.243939\pi$
$242$	−4.00298	+	0.773989i	−0.257321	+	0.0497539i
$243$		−	1.00000i		−	0.0641500i
$244$	15.3946			0.985539
$245$	−5.37759	−	4.48125i	−0.343561	−	0.286296i
$246$	−0.804610			−0.0513001
$247$	−26.5662			−1.69037
$248$	−11.2305			−0.713136
$249$		−	3.96061i		−	0.250993i
$250$	0.370647			0.0234418
$251$			20.2662i			1.27919i	0.768711	+	0.639596i	$0.220898\pi$
$251$			20.2662i			1.27919i	−0.768711	+	0.639596i	$0.779102\pi$
$252$	4.46276	−	2.09027i	0.281128	−	0.131675i
$253$	16.7180	−	20.2601i	1.05105	−	1.27374i
$254$	0.0670306			0.00420587
$255$	2.13309			0.133579
$256$	6.10608			0.381630
$257$		−	19.1038i		−	1.19166i	−0.803109	−	0.595832i	$-0.796822\pi$
$257$		−	19.1038i		−	1.19166i	0.803109	−	0.595832i	$-0.203178\pi$
$258$		−	2.87669i		−	0.179095i
$259$	20.3378	−	9.52584i	1.26373	−	0.591907i
$260$		−	9.66682i		−	0.599511i
$261$			7.81291i			0.483607i
$262$		−	2.49503i		−	0.154143i
$263$		−	0.181422i		−	0.0111870i	−0.999984	−	0.00559348i	$-0.998220\pi$
$263$		−	0.181422i		−	0.0111870i	0.999984	−	0.00559348i	$-0.00178047\pi$
$264$	−3.02211	+	3.66242i	−0.185998	+	0.225406i
$265$			10.7569i			0.660789i
$266$	−2.12916	−	4.54581i	−0.130547	−	0.278721i
$267$	8.45786			0.517612
$268$	−5.23013			−0.319481
$269$			20.2896i			1.23708i	0.785753	+	0.618540i	$0.212275\pi$
$269$			20.2896i			1.23708i	−0.785753	+	0.618540i	$0.787725\pi$
$270$		−	0.370647i		−	0.0225569i
$271$	−13.4475			−0.816876			−0.408438	−	0.912786i	$-0.633926\pi$
$271$	−13.4475			−0.816876			−0.408438	+	0.912786i	$0.633926\pi$
$272$	−6.81437			−0.413182
$273$	5.82421	+	12.4348i	0.352497	+	0.752588i
$274$			5.04613i			0.304848i
$275$	−2.11090	+	2.55814i	−0.127292	+	0.154262i
$276$		−	14.7517i		−	0.887945i
$277$			16.6641i			1.00125i	0.865664	+	0.500625i	$0.166896\pi$
$277$			16.6641i			1.00125i	−0.865664	+	0.500625i	$0.833104\pi$
$278$			1.41133i			0.0846461i
$279$			7.84432i			0.469627i
$280$	3.43022	−	1.60665i	0.204995	−	0.0960156i
$281$			10.6369i			0.634543i	0.948335	+	0.317272i	$0.102767\pi$
$281$			10.6369i			0.634543i	−0.948335	+	0.317272i	$0.897233\pi$
$282$			2.08397i			0.124099i
$283$	19.8717			1.18125			0.590626	−	0.806946i	$-0.298881\pi$
$283$	19.8717			1.18125			0.590626	+	0.806946i	$0.298881\pi$
$284$	17.3763			1.03109
$285$	5.11883			0.303213
$286$	−4.92091	−	4.06058i	−0.290980	−	0.240107i
$287$	−5.20121	+	2.43614i	−0.307018	+	0.143801i
$288$			4.04741i			0.238496i
$289$	−12.4499			−0.732348
$290$			2.89583i			0.170049i
$291$	−8.31015			−0.487150
$292$	−18.6674			−1.09242
$293$	13.3613			0.780576			0.390288	−	0.920693i	$-0.372376\pi$
$293$	13.3613			0.780576			0.390288	+	0.920693i	$0.372376\pi$
$294$	−1.66096	+	1.99319i	−0.0968693	+	0.116245i
$295$	2.14980			0.125166
$296$			12.1526i			0.706354i
$297$	2.55814	+	2.11090i	0.148439	+	0.122487i
$298$	−5.41614			−0.313749
$299$	41.1032			2.37706
$300$			1.86262i			0.107538i
$301$	−8.70983	−	18.5956i	−0.502026	−	1.07184i
$302$	−1.22688			−0.0705991
$303$		−	6.92755i		−	0.397977i
$304$	−16.3526			−0.937885
$305$		−	8.26503i		−	0.473254i
$306$		−	0.790625i		−	0.0451970i
$307$	28.5441			1.62910			0.814548	−	0.580097i	$-0.196985\pi$
$307$	28.5441			1.62910			0.814548	+	0.580097i	$0.196985\pi$
$308$	−4.07323	+	15.8287i	−0.232094	+	0.901926i
$309$	18.7232			1.06513
$310$			2.90748i			0.165134i
$311$			24.9752i			1.41621i	0.706106	+	0.708106i	$0.250450\pi$
$311$			24.9752i			1.41621i	−0.706106	+	0.708106i	$0.749550\pi$
$312$	−7.43023			−0.420654
$313$			13.2310i			0.747859i	0.927457	+	0.373929i	$0.121990\pi$
$313$			13.2310i			0.747859i	−0.927457	+	0.373929i	$0.878010\pi$
$314$	2.89133			0.163167
$315$	−1.12222	−	2.39596i	−0.0632299	−	0.134997i
$316$			16.7434i			0.941888i
$317$	6.66242			0.374199			0.187099	−	0.982341i	$-0.440091\pi$
$317$	6.66242			0.374199			0.187099	+	0.982341i	$0.440091\pi$
$318$	3.98701			0.223580
$319$	−19.9865	−	16.4923i	−1.11903	−	0.923389i
$320$		−	4.88903i		−	0.273305i
$321$	8.22730			0.459203
$322$	3.29424	+	7.03326i	0.183581	+	0.391948i
$323$	10.9189			0.607546
$324$	1.86262			0.103479
$325$	−5.18990			−0.287884
$326$		−	3.51940i		−	0.194921i
$327$	−10.6190			−0.587234
$328$		−	3.10790i		−	0.171605i
$329$	6.30970	+	13.4713i	0.347865	+	0.742699i
$330$	0.948170	+	0.782400i	0.0521950	+	0.0430697i
$331$	−10.1656			−0.558750			−0.279375	−	0.960182i	$-0.590127\pi$
$331$	−10.1656			−0.558750			−0.279375	+	0.960182i	$0.590127\pi$
$332$	7.37711			0.404871
$333$	8.48839			0.465161
$334$		−	7.51355i		−	0.411123i
$335$			2.80794i			0.153414i
$336$	3.58504	+	7.65412i	0.195580	+	0.417567i
$337$			34.2697i			1.86679i	0.358850	+	0.933395i	$0.383169\pi$
$337$			34.2697i			1.86679i	−0.358850	+	0.933395i	$0.616831\pi$
$338$		−	5.16501i		−	0.280940i
$339$		−	8.90438i		−	0.483620i
$340$			3.97314i			0.215474i
$341$	−20.0669	−	16.5586i	−1.08668	−	0.896697i
$342$		−	1.89728i		−	0.102593i
$343$	−4.70205	+	17.9134i	−0.253887	+	0.967234i
$344$	11.1116			0.599095
$345$	−7.91984			−0.426390
$346$		−	4.69514i		−	0.252412i
$347$		−	32.1129i		−	1.72391i	−0.506983	−	0.861956i	$-0.669239\pi$
$347$		−	32.1129i		−	1.72391i	0.506983	−	0.861956i	$-0.330761\pi$
$348$	−14.5525			−0.780095
$349$	−6.90652			−0.369697			−0.184849	−	0.982767i	$-0.559179\pi$
$349$	−6.90652			−0.369697			−0.184849	+	0.982767i	$0.559179\pi$
$350$	−0.415948	−	0.888056i	−0.0222333	−	0.0474686i
$351$			5.18990i			0.277017i
$352$	−10.3539	−	8.54367i	−0.551863	−	0.455379i
$353$			0.718357i			0.0382343i	0.999817	+	0.0191171i	$0.00608554\pi$
$353$			0.718357i			0.0382343i	−0.999817	+	0.0191171i	$0.993914\pi$
$354$		−	0.796819i		−	0.0423505i
$355$		−	9.32895i		−	0.495129i
$356$			15.7538i			0.834948i
$357$	−2.39380	−	5.11080i	−0.126693	−	0.270492i
$358$		−	6.80086i		−	0.359437i
$359$		−	0.504605i		−	0.0266320i	−0.999911	−	0.0133160i	$-0.995761\pi$
$359$		−	0.504605i		−	0.0266320i	0.999911	−	0.0133160i	$-0.00423875\pi$
$360$	1.43167			0.0754557
$361$	7.20239			0.379073
$362$	−0.624551			−0.0328257
$363$	−10.8000	+	2.08821i	−0.566852	+	0.109602i
$364$	−23.1613	+	10.8483i	−1.21398	+	0.568605i
$365$			10.0221i			0.524580i
$366$	−3.06341			−0.160127
$367$		−	1.15414i		−	0.0602454i	−0.999546	−	0.0301227i	$-0.990410\pi$
$367$		−	1.15414i		−	0.0602454i	0.999546	−	0.0301227i	$-0.00958980\pi$
$368$	25.3007			1.31889
$369$	−2.17082			−0.113009
$370$	3.14620			0.163563
$371$	25.7730	−	12.0716i	1.33807	−	0.626725i
$372$	−14.6110			−0.757545
$373$		−	27.8291i		−	1.44093i	−0.693489	−	0.720467i	$-0.743928\pi$
$373$		−	27.8291i		−	1.44093i	0.693489	−	0.720467i	$-0.256072\pi$
$374$	2.02253	+	1.66893i	0.104583	+	0.0862983i
$375$	1.00000			0.0516398
$376$	−8.04960			−0.415126
$377$		−	40.5482i		−	2.08834i
$378$	−0.888056	+	0.415948i	−0.0456767	+	0.0213940i
$379$	14.1431			0.726481			0.363241	−	0.931695i	$-0.381670\pi$
$379$	14.1431			0.726481			0.363241	+	0.931695i	$0.381670\pi$
$380$			9.53443i			0.489106i
$381$	0.180847			0.00926509
$382$			6.95829i			0.356017i
$383$		−	12.1969i		−	0.623232i	−0.950208	−	0.311616i	$-0.899130\pi$
$383$		−	12.1969i		−	0.623232i	0.950208	−	0.311616i	$-0.100870\pi$
$384$	−9.90693			−0.505561
$385$	8.49810	+	2.18683i	0.433103	+	0.111451i
$386$	9.52452			0.484785
$387$		−	7.76125i		−	0.394527i
$388$		−	15.4787i		−	0.785810i
$389$	−25.6660			−1.30132			−0.650659	−	0.759370i	$-0.725507\pi$
$389$	−25.6660			−1.30132			−0.650659	+	0.759370i	$0.725507\pi$
$390$			1.92362i			0.0974065i
$391$	−16.8937			−0.854353
$392$	−7.69893	−	6.41567i	−0.388855	−	0.324040i
$393$		−	6.73154i		−	0.339561i
$394$	4.70132			0.236849
$395$	8.98914			0.452293
$396$	−3.93180	+	4.76485i	−0.197581	+	0.239443i
$397$			9.15174i			0.459313i	0.973272	+	0.229656i	$0.0737603\pi$
$397$			9.15174i			0.459313i	−0.973272	+	0.229656i	$0.926240\pi$
$398$	6.21308			0.311433
$399$	−5.74445	−	12.2645i	−0.287582	−	0.613993i
$400$	−3.19460			−0.159730
$401$	−8.82861			−0.440880			−0.220440	−	0.975401i	$-0.570749\pi$
$401$	−8.82861			−0.440880			−0.220440	+	0.975401i	$0.570749\pi$
$402$	1.04076			0.0519082
$403$		−	40.7113i		−	2.02797i
$404$	12.9034			0.641968
$405$		−	1.00000i		−	0.0496904i
$406$	6.93830	−	3.24976i	0.344342	−	0.161283i
$407$	−17.9181	+	21.7145i	−0.888169	+	1.07635i
$408$	3.05389			0.151190
$409$	9.05371			0.447677			0.223839	−	0.974626i	$-0.428141\pi$
$409$	9.05371			0.447677			0.223839	+	0.974626i	$0.428141\pi$
$410$	−0.804610			−0.0397369
$411$			13.6144i			0.671547i
$412$			34.8742i			1.71813i
$413$	−2.41255	−	5.15084i	−0.118714	−	0.253456i
$414$			2.93547i			0.144270i
$415$		−	3.96061i		−	0.194419i
$416$		−	21.0057i		−	1.02989i
$417$			3.80775i			0.186466i
$418$	4.85352	+	4.00497i	0.237393	+	0.195889i
$419$		−	29.4127i		−	1.43690i	−0.695577	−	0.718451i	$-0.744851\pi$
$419$		−	29.4127i		−	1.43690i	0.695577	−	0.718451i	$-0.255149\pi$
$420$	4.46276	−	2.09027i	0.217761	−	0.101995i
$421$	22.1834			1.08115			0.540576	−	0.841295i	$-0.318206\pi$
$421$	22.1834			1.08115			0.540576	+	0.841295i	$0.318206\pi$
$422$	1.47208			0.0716599
$423$			5.62252i			0.273376i
$424$			15.4003i			0.747904i
$425$	2.13309			0.103470
$426$	−3.45775			−0.167529
$427$	−19.8027	+	9.27517i	−0.958318	+	0.448857i
$428$			15.3243i			0.740729i
$429$	−13.2765	−	10.9554i	−0.640997	−	0.528930i
$430$		−	2.87669i		−	0.138726i
$431$			17.5400i			0.844873i	0.906392	+	0.422437i	$0.138825\pi$
$431$			17.5400i			0.844873i	−0.906392	+	0.422437i	$0.861175\pi$
$432$			3.19460i			0.153700i
$433$		−	25.4774i		−	1.22437i	−0.790716	−	0.612184i	$-0.790291\pi$
$433$		−	25.4774i		−	1.22437i	0.790716	−	0.612184i	$-0.209709\pi$
$434$	6.96620	−	3.26283i	0.334388	−	0.156621i
$435$			7.81291i			0.374600i
$436$		−	19.7792i		−	0.947254i
$437$	−40.5403			−1.93930
$438$	3.71466			0.177493
$439$	7.12645			0.340127			0.170063	−	0.985433i	$-0.445603\pi$
$439$	7.12645			0.340127			0.170063	+	0.985433i	$0.445603\pi$
$440$	−3.02211	+	3.66242i	−0.144074	+	0.174599i
$441$	−4.48125	+	5.37759i	−0.213393	+	0.256076i
$442$			4.10327i			0.195173i
$443$	−0.289471			−0.0137532			−0.00687658	−	0.999976i	$-0.502189\pi$
$443$	−0.289471			−0.0137532			−0.00687658	+	0.999976i	$0.502189\pi$
$444$			15.8106i			0.750340i
$445$	8.45786			0.400941
$446$	10.4551			0.495064
$447$	−14.6126			−0.691155
$448$	−11.7139	+	5.48656i	−0.553431	+	0.259216i
$449$	−15.4408			−0.728696			−0.364348	−	0.931263i	$-0.618708\pi$
$449$	−15.4408			−0.728696			−0.364348	+	0.931263i	$0.618708\pi$
$450$		−	0.370647i		−	0.0174725i
$451$	4.58239	−	5.55328i	0.215776	−	0.261494i
$452$	16.5855			0.780116
$453$	−3.31010			−0.155522
$454$			7.55482i			0.354565i
$455$	5.82421	+	12.4348i	0.273043	+	0.582953i
$456$	7.32847			0.343187
$457$		−	23.0836i		−	1.07981i	−0.841727	−	0.539904i	$-0.818461\pi$
$457$		−	23.0836i		−	1.07981i	0.841727	−	0.539904i	$-0.181539\pi$
$458$	0.436565			0.0203993
$459$		−	2.13309i		−	0.0995642i
$460$		−	14.7517i		−	0.687799i
$461$	1.73308			0.0807178			0.0403589	−	0.999185i	$-0.487150\pi$
$461$	1.73308			0.0807178			0.0403589	+	0.999185i	$0.487150\pi$
$462$	0.810543	−	3.14980i	0.0377099	−	0.146542i
$463$	−5.42850			−0.252284			−0.126142	−	0.992012i	$-0.540259\pi$
$463$	−5.42850			−0.252284			−0.126142	+	0.992012i	$0.540259\pi$
$464$		−	24.9591i		−	1.15870i
$465$			7.84432i			0.363772i
$466$	−6.23960			−0.289044
$467$			0.360071i			0.0166621i	0.999965	+	0.00833105i	$0.00265189\pi$
$467$			0.360071i			0.0166621i	−0.999965	+	0.00833105i	$0.997348\pi$
$468$	−9.66682			−0.446849
$469$	6.72771	−	3.15113i	0.310657	−	0.145506i
$470$			2.08397i			0.0961265i
$471$	7.80076			0.359440
$472$	3.07781			0.141668
$473$	19.8544	+	16.3832i	0.912906	+	0.753301i
$474$		−	3.33180i		−	0.153035i
$475$	5.11883			0.234868
$476$	9.51949	−	4.45874i	0.436325	−	0.204366i
$477$	10.7569			0.492523
$478$	0.391773			0.0179193
$479$	−31.4892			−1.43878			−0.719389	−	0.694607i	$-0.755578\pi$
$479$	−31.4892			−1.43878			−0.719389	+	0.694607i	$0.755578\pi$
$480$			4.04741i			0.184738i
$481$	−44.0539			−2.00869
$482$		−	8.29085i		−	0.377638i
$483$	8.88780	+	18.9756i	0.404409	+	0.863420i
$484$	−3.88954	−	20.1162i	−0.176797	−	0.914375i
$485$	−8.31015			−0.377345
$486$	−0.370647			−0.0168129
$487$	−3.46264			−0.156907			−0.0784536	−	0.996918i	$-0.524998\pi$
$487$	−3.46264			−0.156907			−0.0784536	+	0.996918i	$0.524998\pi$
$488$		−	11.8328i		−	0.535645i
$489$		−	9.49527i		−	0.429391i
$490$	−1.66096	+	1.99319i	−0.0750346	+	0.0900431i
$491$			27.8786i			1.25814i	0.777347	+	0.629072i	$0.216565\pi$
$491$			27.8786i			1.25814i	−0.777347	+	0.629072i	$0.783435\pi$
$492$		−	4.04342i		−	0.182291i
$493$			16.6657i			0.750583i
$494$			9.84670i			0.443024i
$495$	2.55814	+	2.11090i	0.114980	+	0.0948779i
$496$		−	25.0594i		−	1.12520i
$497$	−22.3518	+	10.4691i	−1.00261	+	0.469605i
$498$	−1.46799			−0.0657821
$499$	21.5530			0.964846			0.482423	−	0.875938i	$-0.339757\pi$
$499$	21.5530			0.964846			0.482423	+	0.875938i	$0.339757\pi$
$500$			1.86262i			0.0832989i
$501$		−	20.2714i		−	0.905660i
$502$	7.51162			0.335260
$503$	−15.2046			−0.677940			−0.338970	−	0.940797i	$-0.610078\pi$
$503$	−15.2046			−0.677940			−0.338970	+	0.940797i	$0.610078\pi$
$504$	−1.60665	−	3.43022i	−0.0715658	−	0.152794i
$505$		−	6.92755i		−	0.308272i
$506$	−7.50935	−	6.19648i	−0.333831	−	0.275467i
$507$		−	13.9351i		−	0.618880i
$508$			0.336850i			0.0149453i
$509$		−	1.16154i		−	0.0514845i	−0.999669	−	0.0257423i	$-0.991805\pi$
$509$		−	1.16154i		−	0.0514845i	0.999669	−	0.0257423i	$-0.00819492\pi$
$510$		−	0.790625i		−	0.0350095i
$511$	24.0125	−	11.2470i	1.06225	−	0.497537i
$512$		−	22.0771i		−	0.975677i
$513$		−	5.11883i		−	0.226002i
$514$	−7.08079			−0.312320
$515$	18.7232			0.825043
$516$	14.4563			0.636402
$517$	−14.3832	−	11.8686i	−0.632573	−	0.521979i
$518$	−3.53073	−	7.53817i	−0.155131	−	0.331208i
$519$		−	12.6674i		−	0.556037i
$520$	−7.43023			−0.325837
$521$		−	4.75670i		−	0.208395i	−0.994557	−	0.104197i	$-0.966773\pi$
$521$		−	4.75670i		−	0.208395i	0.994557	−	0.104197i	$-0.0332273\pi$
$522$	2.89583			0.126747
$523$	−12.4829			−0.545838			−0.272919	−	0.962037i	$-0.587989\pi$
$523$	−12.4829			−0.545838			−0.272919	+	0.962037i	$0.587989\pi$
$524$	12.5383			0.547738
$525$	−1.12222	−	2.39596i	−0.0489777	−	0.104568i
$526$	−0.0672436			−0.00293196
$527$			16.7327i			0.728886i
$528$	−8.17224	−	6.74347i	−0.355651	−	0.293472i
$529$	39.7238			1.72712
$530$	3.98701			0.173185
$531$		−	2.14980i		−	0.0932935i
$532$	22.8441	−	10.6997i	0.990418	−	0.463892i
$533$	11.2664			0.488001
$534$		−	3.13488i		−	0.135660i
$535$	8.22730			0.355697
$536$			4.02005i			0.173640i
$537$		−	18.3486i		−	0.791801i
$538$	7.52030			0.324223
$539$	−4.29718	−	22.8152i	−0.185093	−	0.982721i
$540$	1.86262			0.0801544
$541$			3.85008i			0.165528i	0.996569	+	0.0827638i	$0.0263747\pi$
$541$			3.85008i			0.165528i	−0.996569	+	0.0827638i	$0.973625\pi$
$542$			4.98427i			0.214093i
$543$	−1.68503			−0.0723114
$544$			8.63350i			0.370158i
$545$	−10.6190			−0.454870
$546$	4.60893	−	2.15873i	0.197244	−	0.0923851i
$547$			9.19407i			0.393110i	0.980493	+	0.196555i	$0.0629754\pi$
$547$			9.19407i			0.393110i	−0.980493	+	0.196555i	$0.937025\pi$
$548$	−25.3584			−1.08326
$549$	−8.26503			−0.352743
$550$	0.948170	+	0.782400i	0.0404301	+	0.0333616i
$551$			39.9929i			1.70376i
$552$	−11.3386			−0.482603
$553$	−10.0878	−	21.5376i	−0.428977	−	0.915873i
$554$	6.17651			0.262415
$555$	8.48839			0.360312
$556$	−7.09239			−0.300784
$557$		−	12.9459i		−	0.548535i	−0.961653	−	0.274268i	$-0.911565\pi$
$557$		−	12.9459i		−	0.548535i	0.961653	−	0.274268i	$-0.0884354\pi$
$558$	2.90748			0.123083
$559$			40.2802i			1.70367i
$560$	3.58504	+	7.65412i	0.151496	+	0.323446i
$561$	5.45676	+	4.50274i	0.230385	+	0.190106i
$562$	3.94253			0.166306
$563$	−18.8587			−0.794797			−0.397399	−	0.917646i	$-0.630087\pi$
$563$	−18.8587			−0.794797			−0.397399	+	0.917646i	$0.630087\pi$
$564$	−10.4726			−0.440977
$565$		−	8.90438i		−	0.374610i
$566$		−	7.36541i		−	0.309591i
$567$	−2.39596	+	1.12222i	−0.100621	+	0.0471288i
$568$		−	13.3560i		−	0.560404i
$569$		−	30.0659i		−	1.26043i	−0.776422	−	0.630214i	$-0.782967\pi$
$569$		−	30.0659i		−	1.26043i	0.776422	−	0.630214i	$-0.217033\pi$
$570$		−	1.89728i		−	0.0794683i
$571$			28.9251i			1.21048i	0.796045	+	0.605238i	$0.206922\pi$
$571$			28.9251i			1.21048i	−0.796045	+	0.605238i	$0.793078\pi$
$572$	20.4057	−	24.7291i	0.853205	−	1.03398i
$573$			18.7733i			0.784267i
$574$	0.902949	+	1.92781i	0.0376884	+	0.0804654i
$575$	−7.91984			−0.330280
$576$	−4.88903			−0.203710
$577$			14.0250i			0.583870i	0.956438	+	0.291935i	$0.0942991\pi$
$577$			14.0250i			0.583870i	−0.956438	+	0.291935i	$0.905701\pi$
$578$			4.61453i			0.191939i
$579$	25.6970			1.06793
$580$	−14.5525			−0.604259
$581$	−9.48945	+	4.44467i	−0.393689	+	0.184396i
$582$			3.08014i			0.127676i
$583$	−22.7067	+	27.5176i	−0.940414	+	1.13966i
$584$			14.3483i			0.593738i
$585$			5.18990i			0.214576i
$586$		−	4.95233i		−	0.204579i
$587$			17.4076i			0.718490i	0.933243	+	0.359245i	$0.116966\pi$
$587$			17.4076i			0.718490i	−0.933243	+	0.359245i	$0.883034\pi$
$588$	−10.0164	−	8.34686i	−0.413069	−	0.344219i
$589$			40.1537i			1.65450i
$590$		−	0.796819i		−	0.0328045i
$591$	12.6841			0.521753
$592$	−27.1170			−1.11450
$593$	−6.22003			−0.255426			−0.127713	−	0.991811i	$-0.540764\pi$
$593$	−6.22003			−0.255426			−0.127713	+	0.991811i	$0.540764\pi$
$594$	0.782400	−	0.948170i	0.0321022	−	0.0389039i
$595$	−2.39380	−	5.11080i	−0.0981362	−	0.209523i
$596$		−	27.2178i		−	1.11489i
$597$	16.7628			0.686055
$598$		−	15.2348i		−	0.622997i
$599$	−22.9784			−0.938872			−0.469436	−	0.882967i	$-0.655543\pi$
$599$	−22.9784			−0.938872			−0.469436	+	0.882967i	$0.655543\pi$
$600$	1.43167			0.0584477
$601$	−46.7667			−1.90765			−0.953827	−	0.300356i	$-0.902895\pi$
$601$	−46.7667			−1.90765			−0.953827	+	0.300356i	$0.902895\pi$
$602$	−6.89243	+	3.22828i	−0.280914	+	0.131575i
$603$	2.80794			0.114348
$604$		−	6.16547i		−	0.250869i
$605$	−10.8000	+	2.08821i	−0.439081	+	0.0848977i
$606$	−2.56768			−0.104305
$607$	22.0716			0.895859			0.447930	−	0.894069i	$-0.352161\pi$
$607$	22.0716			0.895859			0.447930	+	0.894069i	$0.352161\pi$
$608$			20.7180i			0.840225i
$609$	18.7194	−	8.76780i	0.758549	−	0.355289i
$610$	−3.06341			−0.124034
$611$		−	29.1803i		−	1.18051i
$612$	3.97314			0.160605
$613$		−	28.9957i		−	1.17113i	−0.810627	−	0.585563i	$-0.800874\pi$
$613$		−	28.9957i		−	1.17113i	0.810627	−	0.585563i	$-0.199126\pi$
$614$		−	10.5798i		−	0.426965i
$615$	−2.17082			−0.0875361
$616$	12.1665	+	3.13082i	0.490202	+	0.126144i
$617$	−9.01612			−0.362975			−0.181488	−	0.983393i	$-0.558091\pi$
$617$	−9.01612			−0.362975			−0.181488	+	0.983393i	$0.558091\pi$
$618$		−	6.93971i		−	0.279156i
$619$			22.2526i			0.894409i	0.894432	+	0.447204i	$0.147580\pi$
$619$			22.2526i			0.894409i	−0.894432	+	0.447204i	$0.852420\pi$
$620$	−14.6110			−0.586792
$621$			7.91984i			0.317812i
$622$	9.25699			0.371171
$623$	−9.49157	−	20.2647i	−0.380272	−	0.811887i
$624$		−	16.5796i		−	0.663717i
$625$	1.00000			0.0400000
$626$	4.90403			0.196004
$627$	13.0947	+	10.8053i	0.522952	+	0.431523i
$628$			14.5299i			0.579804i
$629$	18.1065			0.721954
$630$	−0.888056	+	0.415948i	−0.0353810	+	0.0165718i
$631$	42.5674			1.69458			0.847292	−	0.531128i	$-0.178232\pi$
$631$	42.5674			1.69458			0.847292	+	0.531128i	$0.178232\pi$
$632$	12.8695			0.511921
$633$	3.97165			0.157859
$634$		−	2.46941i		−	0.0980728i
$635$	0.180847			0.00717670
$636$			20.0360i			0.794478i
$637$	23.2572	−	27.9092i	0.921485	−	1.10580i
$638$	−6.11282	+	7.40796i	−0.242009	+	0.293284i
$639$	−9.32895			−0.369047
$640$	−9.90693			−0.391606
$641$	−26.6925			−1.05429			−0.527145	−	0.849775i	$-0.676738\pi$
$641$	−26.6925			−1.05429			−0.527145	+	0.849775i	$0.676738\pi$
$642$		−	3.04943i		−	0.120351i
$643$		−	31.9237i		−	1.25895i	−0.777022	−	0.629474i	$-0.783271\pi$
$643$		−	31.9237i		−	1.25895i	0.777022	−	0.629474i	$-0.216729\pi$
$644$	−35.3444	+	16.5546i	−1.39276	+	0.652342i
$645$		−	7.76125i		−	0.305599i
$646$		−	4.04707i		−	0.159230i
$647$			11.1638i			0.438896i	0.975624	+	0.219448i	$0.0704256\pi$
$647$			11.1638i			0.438896i	−0.975624	+	0.219448i	$0.929574\pi$
$648$		−	1.43167i		−	0.0562413i
$649$	5.49951	+	4.53802i	0.215875	+	0.178133i
$650$			1.92362i			0.0754508i
$651$	18.7947	−	8.80305i	0.736621	−	0.345019i
$652$	17.6861			0.692641
$653$	−21.3149			−0.834117			−0.417058	−	0.908880i	$-0.636939\pi$
$653$	−21.3149			−0.834117			−0.417058	+	0.908880i	$0.636939\pi$
$654$			3.93592i			0.153907i
$655$		−	6.73154i		−	0.263023i
$656$	6.93490			0.270763
$657$	10.0221			0.390999
$658$	4.99312	−	2.33868i	0.194652	−	0.0911711i
$659$			23.3039i			0.907790i	0.891055	+	0.453895i	$0.149966\pi$
$659$			23.3039i			0.907790i	−0.891055	+	0.453895i	$0.850034\pi$
$660$	−3.93180	+	4.76485i	−0.153045	+	0.185472i
$661$		−	32.3485i		−	1.25821i	−0.777320	−	0.629105i	$-0.783421\pi$
$661$		−	32.3485i		−	1.25821i	0.777320	−	0.629105i	$-0.216579\pi$
$662$			3.76784i			0.146441i
$663$			11.0705i			0.429944i
$664$		−	5.67028i		−	0.220050i
$665$	−5.74445	−	12.2645i	−0.222760	−	0.475597i
$666$		−	3.14620i		−	0.121913i
$667$		−	61.8770i		−	2.39589i
$668$	37.7580			1.46090
$669$	28.2077			1.09057
$670$	1.04076			0.0402079
$671$	17.4466	−	21.1431i	0.673520	−	0.816222i
$672$	9.69743	−	4.54208i	0.374087	−	0.175215i
$673$			2.02853i			0.0781942i	0.999235	+	0.0390971i	$0.0124482\pi$
$673$			2.02853i			0.0781942i	−0.999235	+	0.0390971i	$0.987552\pi$
$674$	12.7020			0.489262
$675$		−	1.00000i		−	0.0384900i
$676$	25.9558			0.998301
$677$	−15.3289			−0.589136			−0.294568	−	0.955630i	$-0.595176\pi$
$677$	−15.3289			−0.589136			−0.294568	+	0.955630i	$0.595176\pi$
$678$	−3.30039			−0.126751
$679$	9.32582	+	19.9108i	0.357892	+	0.764106i
$680$	3.05389			0.117111
$681$			20.3828i			0.781069i
$682$	−6.13739	+	7.43775i	−0.235013	+	0.284806i
$683$	−17.7118			−0.677721			−0.338861	−	0.940837i	$-0.610042\pi$
$683$	−17.7118			−0.677721			−0.338861	+	0.940837i	$0.610042\pi$
$684$	9.53443			0.364558
$685$			13.6144i			0.520178i
$686$	6.63956	+	1.74280i	0.253500	+	0.0665406i
$687$	1.17784			0.0449375
$688$			24.7941i			0.945265i
$689$	−55.8271			−2.12684
$690$			2.93547i			0.111751i
$691$		−	23.0535i		−	0.876997i	−0.898732	−	0.438499i	$-0.855510\pi$
$691$		−	23.0535i		−	0.876997i	0.898732	−	0.438499i	$-0.144490\pi$
$692$	23.5946			0.896930
$693$	2.18683	−	8.49810i	0.0830708	−	0.322816i
$694$	−11.9026			−0.451816
$695$			3.80775i			0.144436i
$696$			11.1855i			0.423986i
$697$	−4.63057			−0.175395
$698$			2.55988i			0.0968930i
$699$	−16.8343			−0.636733
$700$	4.46276	−	2.09027i	0.168677	−	0.0790047i
$701$			37.5304i			1.41750i	0.705457	+	0.708752i	$0.250742\pi$
$701$			37.5304i			1.41750i	−0.705457	+	0.708752i	$0.749258\pi$
$702$	1.92362			0.0726025
$703$	43.4506			1.63877
$704$	10.3202	−	12.5068i	0.388959	−	0.471369i
$705$			5.62252i			0.211756i
$706$	0.266257			0.0100207
$707$	−16.5981	+	7.77423i	−0.624237	+	0.292380i
$708$	4.00427			0.150490
$709$	−33.7434			−1.26726			−0.633631	−	0.773636i	$-0.718436\pi$
$709$	−33.7434			−1.26726			−0.633631	+	0.773636i	$0.718436\pi$
$710$	−3.45775			−0.129767
$711$		−	8.98914i		−	0.337119i
$712$	12.1089			0.453799
$713$		−	62.1257i		−	2.32663i
$714$	−1.89431	+	0.887255i	−0.0708926	+	0.0332047i
$715$	−13.2765	−	10.9554i	−0.496514	−	0.409707i
$716$	34.1765			1.27723
$717$	1.05700			0.0394743
$718$	−0.187031			−0.00697992
$719$		−	24.3536i		−	0.908234i	−0.890942	−	0.454117i	$-0.849955\pi$
$719$		−	24.3536i		−	0.908234i	0.890942	−	0.454117i	$-0.150045\pi$
$720$			3.19460i			0.119056i
$721$	−21.0115	−	44.8600i	−0.782511	−	1.67068i
$722$		−	2.66955i		−	0.0993502i
$723$		−	22.3686i		−	0.831895i
$724$		−	3.13856i		−	0.116644i
$725$			7.81291i			0.290164i
$726$	0.773989	+	4.00298i	0.0287254	+	0.148565i
$727$		−	3.32234i		−	0.123219i	−0.998100	−	0.0616093i	$-0.980377\pi$
$727$		−	3.32234i		−	0.123219i	0.998100	−	0.0616093i	$-0.0196233\pi$
$728$	8.33835	+	17.8025i	0.309040	+	0.659806i
$729$	−1.00000			−0.0370370
$730$	3.71466			0.137486
$731$		−	16.5555i		−	0.612326i
$732$		−	15.3946i		−	0.569001i
$733$	−39.7281			−1.46739			−0.733695	−	0.679479i	$-0.762206\pi$
$733$	−39.7281			−1.46739			−0.733695	+	0.679479i	$0.762206\pi$
$734$	−0.427777			−0.0157896
$735$	−4.48125	+	5.37759i	−0.165293	+	0.198355i
$736$		−	32.0548i		−	1.18156i
$737$	−5.92728	+	7.18312i	−0.218334	+	0.264594i
$738$			0.804610i			0.0296181i
$739$		−	4.78100i		−	0.175872i	−0.996126	−	0.0879359i	$-0.971973\pi$
$739$		−	4.78100i		−	0.175872i	0.996126	−	0.0879359i	$-0.0280271\pi$
$740$			15.8106i			0.581211i
$741$			26.5662i			0.975935i
$742$	−4.47430	−	9.55271i	−0.164257	−	0.350691i
$743$			21.8198i			0.800491i	0.916408	+	0.400246i	$0.131075\pi$
$743$			21.8198i			0.800491i	−0.916408	+	0.400246i	$0.868925\pi$
$744$			11.2305i			0.411729i
$745$	−14.6126			−0.535366
$746$	−10.3148			−0.377650
$747$	−3.96061			−0.144911
$748$	−8.38690	+	10.1639i	−0.306656	+	0.371628i
$749$	−9.23283	−	19.7123i	−0.337360	−	0.720271i
$750$		−	0.370647i		−	0.0135341i
$751$	24.7292			0.902381			0.451190	−	0.892428i	$-0.351000\pi$
$751$	24.7292			0.902381			0.451190	+	0.892428i	$0.351000\pi$
$752$		−	17.9617i		−	0.654995i
$753$	20.2662			0.738542
$754$	−15.0291			−0.547328
$755$	−3.31010			−0.120467
$756$	−2.09027	−	4.46276i	−0.0760224	−	0.162309i
$757$	12.1753			0.442520			0.221260	−	0.975215i	$-0.428983\pi$
$757$	12.1753			0.442520			0.221260	+	0.975215i	$0.428983\pi$
$758$		−	5.24210i		−	0.190402i
$759$	−20.2601	−	16.7180i	−0.735395	−	0.606824i
$760$	7.32847			0.265832
$761$	12.2745			0.444950			0.222475	−	0.974938i	$-0.428586\pi$
$761$	12.2745			0.444950			0.222475	+	0.974938i	$0.428586\pi$
$762$		−	0.0670306i		−	0.00242826i
$763$	11.9169	+	25.4428i	0.431420	+	0.921091i
$764$	−34.9676			−1.26508
$765$		−	2.13309i		−	0.0771221i
$766$	−4.52075			−0.163341
$767$			11.1573i			0.402866i
$768$		−	6.10608i		−	0.220334i
$769$	19.8750			0.716709			0.358355	−	0.933585i	$-0.383338\pi$
$769$	19.8750			0.716709			0.358355	+	0.933585i	$0.383338\pi$
$770$	0.810543	−	3.14980i	0.0292099	−	0.113511i
$771$	−19.1038			−0.688008
$772$			47.8637i			1.72265i
$773$		−	22.0744i		−	0.793962i	−0.917827	−	0.396981i	$-0.870058\pi$
$773$		−	22.0744i		−	0.793962i	0.917827	−	0.396981i	$-0.129942\pi$
$774$	−2.87669			−0.103400
$775$			7.84432i			0.281776i
$776$	−11.8974			−0.427092
$777$	−9.52584	−	20.3378i	−0.341738	−	0.729616i
$778$			9.51304i			0.341059i
$779$	−11.1121			−0.398131
$780$	−9.66682			−0.346128
$781$	19.6925	−	23.8648i	0.704652	−	0.853949i
$782$			6.26162i			0.223915i
$783$	7.81291			0.279211
$784$	14.3158	−	17.1792i	0.511278	−	0.613543i
$785$	7.80076			0.278421
$786$	−2.49503			−0.0889947
$787$	17.9948			0.641444			0.320722	−	0.947173i	$-0.396075\pi$
$787$	17.9948			0.641444			0.320722	+	0.947173i	$0.396075\pi$
$788$			23.6256i			0.841627i
$789$	−0.181422			−0.00645880
$790$		−	3.33180i		−	0.118540i
$791$	−21.3345	+	9.99267i	−0.758569	+	0.355299i
$792$	3.66242	+	3.02211i	0.130138	+	0.107386i
$793$	42.8947			1.52324
$794$	3.39207			0.120380
$795$	10.7569			0.381507
$796$			31.2227i			1.10666i
$797$		−	24.2560i		−	0.859190i	−0.903022	−	0.429595i	$-0.858656\pi$
$797$		−	24.2560i		−	0.859190i	0.903022	−	0.429595i	$-0.141344\pi$
$798$	−4.54581	+	2.12916i	−0.160920	+	0.0753716i
$799$			11.9934i			0.424294i
$800$			4.04741i			0.143098i
$801$		−	8.45786i		−	0.298844i
$802$			3.27230i			0.115549i
$803$	−21.1556	+	25.6380i	−0.746566	+	0.904744i
$804$			5.23013i			0.184452i
$805$	8.88780	+	18.9756i	0.313254	+	0.668802i
$806$	−15.0895			−0.531506
$807$	20.2896			0.714228
$808$		−	9.91797i		−	0.348913i
$809$			23.2256i			0.816567i	0.912855	+	0.408284i	$0.133873\pi$
$809$			23.2256i			0.816567i	−0.912855	+	0.408284i	$0.866127\pi$
$810$	−0.370647			−0.0130232
$811$	−13.3535			−0.468905			−0.234453	−	0.972128i	$-0.575330\pi$
$811$	−13.3535			−0.468905			−0.234453	+	0.972128i	$0.575330\pi$
$812$	16.3311	+	34.8672i	0.573109	+	1.22360i
$813$			13.4475i			0.471623i
$814$	8.04843	+	6.64131i	0.282097	+	0.232778i
$815$		−	9.49527i		−	0.332605i
$816$			6.81437i			0.238551i
$817$		−	39.7285i		−	1.38992i
$818$		−	3.35573i		−	0.117331i
$819$	12.4348	−	5.82421i	0.434507	−	0.203514i
$820$		−	4.04342i		−	0.141202i
$821$		−	5.00616i		−	0.174716i	−0.996177	−	0.0873581i	$-0.972158\pi$
$821$		−	5.00616i		−	0.174716i	0.996177	−	0.0873581i	$-0.0278424\pi$
$822$	5.04613			0.176004
$823$	23.2888			0.811798			0.405899	−	0.913918i	$-0.366958\pi$
$823$	23.2888			0.811798			0.405899	+	0.913918i	$0.366958\pi$
$824$	26.8055			0.933812
$825$	2.55814	+	2.11090i	0.0890632	+	0.0734921i
$826$	−1.90915	+	0.894206i	−0.0664277	+	0.0311134i
$827$			4.51677i			0.157064i	0.996912	+	0.0785318i	$0.0250232\pi$
$827$			4.51677i			0.157064i	−0.996912	+	0.0785318i	$0.974977\pi$
$828$	−14.7517			−0.512655
$829$			32.7485i			1.13740i	0.822544	+	0.568701i	$0.192554\pi$
$829$			32.7485i			1.13740i	−0.822544	+	0.568701i	$0.807446\pi$
$830$	−1.46799			−0.0509546
$831$	16.6641			0.578072
$832$	25.3736			0.879671
$833$	−9.55891	+	11.4709i	−0.331197	+	0.397443i
$834$	1.41133			0.0488705
$835$		−	20.2714i		−	0.701521i
$836$	−20.1262	+	24.3905i	−0.696080	+	0.843561i
$837$	7.84432			0.271139
$838$	−10.9017			−0.376594
$839$		−	29.5349i		−	1.01966i	−0.860276	−	0.509829i	$-0.829709\pi$
$839$		−	29.5349i		−	1.01966i	0.860276	−	0.509829i	$-0.170291\pi$
$840$	−1.60665	−	3.43022i	−0.0554346	−	0.118354i
$841$	−32.0415			−1.10488
$842$		−	8.22221i		−	0.283356i
$843$	10.6369			0.366354
$844$			7.39768i			0.254639i
$845$		−	13.9351i		−	0.479382i
$846$	2.08397			0.0716485
$847$	17.1232	+	23.5329i	0.588360	+	0.808599i
$848$	−34.3639			−1.18006
$849$		−	19.8717i		−	0.681996i
$850$		−	0.790625i		−	0.0271182i
$851$	−67.2267			−2.30450
$852$		−	17.3763i		−	0.595302i
$853$	−38.6918			−1.32478			−0.662392	−	0.749158i	$-0.730459\pi$
$853$	−38.6918			−1.32478			−0.662392	+	0.749158i	$0.730459\pi$
$854$	3.43782	+	7.33981i	0.117640	+	0.251163i
$855$		−	5.11883i		−	0.175060i
$856$	11.7788			0.402590
$857$	16.8408			0.575270			0.287635	−	0.957740i	$-0.407131\pi$
$857$	16.8408			0.575270			0.287635	+	0.957740i	$0.407131\pi$
$858$	−4.06058	+	4.92091i	−0.138626	+	0.167997i
$859$		−	47.3772i		−	1.61649i	−0.588847	−	0.808245i	$-0.700418\pi$
$859$		−	47.3772i		−	1.61649i	0.588847	−	0.808245i	$-0.299582\pi$
$860$	14.4563			0.492955
$861$	2.43614	+	5.20121i	0.0830235	+	0.177257i
$862$	6.50116			0.221431
$863$	−50.4277			−1.71658			−0.858289	−	0.513167i	$-0.828472\pi$
$863$	−50.4277			−1.71658			−0.858289	+	0.513167i	$0.828472\pi$
$864$	4.04741			0.137696
$865$		−	12.6674i		−	0.430704i
$866$	−9.44315			−0.320891
$867$			12.4499i			0.422821i
$868$	16.3967	+	35.0073i	0.556542	+	1.18823i
$869$	22.9955	+	18.9752i	0.780070	+	0.643689i
$870$	2.89583			0.0981780
$871$	−14.5729			−0.493785
$872$	−15.2030			−0.514837
$873$			8.31015i			0.281256i
$874$			15.0261i			0.508267i
$875$	−1.12222	−	2.39596i	−0.0379379	−	0.0809982i
$876$			18.6674i			0.630711i
$877$			18.2189i			0.615207i	0.951515	+	0.307604i	$0.0995271\pi$
$877$			18.2189i			0.615207i	−0.951515	+	0.307604i	$0.900473\pi$
$878$		−	2.64140i		−	0.0891429i
$879$		−	13.3613i		−	0.450666i
$880$	−8.17224	−	6.74347i	−0.275486	−	0.227322i
$881$		−	6.52155i		−	0.219717i	−0.993947	−	0.109858i	$-0.964960\pi$
$881$		−	6.52155i		−	0.219717i	0.993947	−	0.109858i	$-0.0350397\pi$
$882$	1.99319	+	1.66096i	0.0671142	+	0.0559275i
$883$	−3.05638			−0.102855			−0.0514276	−	0.998677i	$-0.516377\pi$
$883$	−3.05638			−0.102855			−0.0514276	+	0.998677i	$0.516377\pi$
$884$	−20.6202			−0.693533
$885$		−	2.14980i		−	0.0722649i
$886$			0.107292i			0.00360453i
$887$	−26.5124			−0.890201			−0.445100	−	0.895481i	$-0.646832\pi$
$887$	−26.5124			−0.890201			−0.445100	+	0.895481i	$0.646832\pi$
$888$	12.1526			0.407814
$889$	−0.202950	−	0.433303i	−0.00680674	−	0.0145325i
$890$		−	3.13488i		−	0.105082i
$891$	2.11090	−	2.55814i	0.0707178	−	0.0857011i
$892$			52.5402i			1.75918i
$893$			28.7807i			0.963110i
$894$			5.41614i			0.181143i
$895$		−	18.3486i		−	0.613326i
$896$	11.1177	+	23.7366i	0.371418	+	0.792984i
$897$		−	41.1032i		−	1.37240i
$898$			5.72309i			0.190982i
$899$	−61.2869			−2.04403
$900$	1.86262			0.0620873
$901$	22.9454			0.764422
$902$	−2.05831	−	1.69845i	−0.0685342	−	0.0565522i
$903$	−18.5956	+	8.70983i	−0.618824	+	0.289845i
$904$		−	12.7481i		−	0.423997i
$905$	−1.68503			−0.0560122
$906$			1.22688i			0.0407604i
$907$	1.79787			0.0596974			0.0298487	−	0.999554i	$-0.490497\pi$
$907$	1.79787			0.0596974			0.0298487	+	0.999554i	$0.490497\pi$
$908$	−37.9653			−1.25992
$909$	−6.92755			−0.229772
$910$	4.60893	−	2.15873i	0.152784	−	0.0715612i
$911$	5.43118			0.179943			0.0899715	−	0.995944i	$-0.471322\pi$
$911$	5.43118			0.179943			0.0899715	+	0.995944i	$0.471322\pi$
$912$			16.3526i			0.541488i
$913$	8.36044	−	10.1318i	0.276690	−	0.335314i
$914$	−8.55589			−0.283004
$915$	−8.26503			−0.273233
$916$			2.19388i			0.0724877i
$917$	−16.1285	+	7.55427i	−0.532610	+	0.249464i
$918$	−0.790625			−0.0260945
$919$			38.7557i			1.27843i	0.769026	+	0.639217i	$0.220741\pi$
$919$			38.7557i			1.27843i	−0.769026	+	0.639217i	$0.779259\pi$
$920$	−11.3386			−0.373822
$921$		−	28.5441i		−	0.940559i
$922$		−	0.642363i		−	0.0211551i
$923$	48.4163			1.59364
$924$	15.8287	+	4.07323i	0.520727	+	0.134000i
$925$	8.48839			0.279097
$926$			2.01206i			0.0661204i
$927$		−	18.7232i		−	0.614951i
$928$	−31.6220			−1.03804
$929$		−	43.1766i		−	1.41658i	−0.705922	−	0.708289i	$-0.749467\pi$
$929$		−	43.1766i		−	1.41658i	0.705922	−	0.708289i	$-0.250533\pi$
$930$	2.90748			0.0953399
$931$	−22.9387	+	27.5269i	−0.751786	+	0.902159i
$932$		−	31.3560i		−	1.02710i
$933$	24.9752			0.817651
$934$	0.133459			0.00436692
$935$	5.45676	+	4.50274i	0.178455	+	0.147255i
$936$			7.43023i			0.242865i
$937$	−25.3457			−0.828008			−0.414004	−	0.910275i	$-0.635870\pi$
$937$	−25.3457			−0.828008			−0.414004	+	0.910275i	$0.635870\pi$
$938$	−1.16796	−	2.49361i	−0.0381351	−	0.0814193i
$939$	13.2310			0.431777
$940$	−10.4726			−0.341579
$941$	13.2246			0.431108			0.215554	−	0.976492i	$-0.430844\pi$
$941$	13.2246			0.431108			0.215554	+	0.976492i	$0.430844\pi$
$942$		−	2.89133i		−	0.0942047i
$943$	17.1926			0.559867
$944$			6.86775i			0.223526i
$945$	−2.39596	+	1.12222i	−0.0779406	+	0.0365058i
$946$	6.07240	−	7.35898i	0.197431	−	0.239261i
$947$	15.3283			0.498102			0.249051	−	0.968490i	$-0.419881\pi$
$947$	15.3283			0.498102			0.249051	+	0.968490i	$0.419881\pi$
$948$	16.7434			0.543799
$949$	−52.0137			−1.68844
$950$		−	1.89728i		−	0.0615559i
$951$		−	6.66242i		−	0.216044i
$952$	−3.42713	−	7.31699i	−0.111074	−	0.237145i
$953$		−	59.7352i		−	1.93501i	−0.252846	−	0.967507i	$-0.581367\pi$
$953$		−	59.7352i		−	1.93501i	0.252846	−	0.967507i	$-0.418633\pi$
$954$		−	3.98701i		−	0.129084i
$955$			18.7733i			0.607491i
$956$			1.96878i			0.0636750i
$957$	−16.4923	+	19.9865i	−0.533119	+	0.646073i
$958$			11.6714i			0.377086i
$959$	32.6194	−	15.2783i	1.05334	−	0.493362i
$960$	−4.88903			−0.157793
$961$	−30.5334			−0.984947
$962$			16.3285i			0.526451i
$963$		−	8.22730i		−	0.265121i
$964$	41.6641			1.34191
$965$	25.6970			0.827215
$966$	7.03326	−	3.29424i	0.226291	−	0.105990i
$967$		−	5.02891i		−	0.161719i	−0.996726	−	0.0808594i	$-0.974234\pi$
$967$		−	5.02891i		−	0.161719i	0.996726	−	0.0808594i	$-0.0257665\pi$
$968$	−15.4620	+	2.98962i	−0.496968	+	0.0960902i
$969$		−	10.9189i		−	0.350767i
$970$			3.08014i			0.0988972i
$971$		−	28.7465i		−	0.922519i	−0.887265	−	0.461259i	$-0.847398\pi$
$971$		−	28.7465i		−	0.922519i	0.887265	−	0.461259i	$-0.152602\pi$
$972$		−	1.86262i		−	0.0597436i
$973$	9.12321	−	4.27313i	0.292477	−	0.136990i
$974$			1.28342i			0.0411234i
$975$			5.18990i			0.166210i
$976$	26.4034			0.845153
$977$	26.0158			0.832320			0.416160	−	0.909291i	$-0.363376\pi$
$977$	26.0158			0.832320			0.416160	+	0.909291i	$0.363376\pi$
$978$	−3.51940			−0.112538
$979$	21.6364	+	17.8537i	0.691503	+	0.570606i
$980$	−10.0164	−	8.34686i	−0.319962	−	0.266631i
$981$			10.6190i			0.339040i
$982$	10.3331			0.329743
$983$			34.2529i			1.09250i	0.837623	+	0.546249i	$0.183945\pi$
$983$			34.2529i			1.09250i	−0.837623	+	0.546249i	$0.816055\pi$
$984$	−3.10790			−0.0990764
$985$	12.6841			0.404148
$986$	6.17708			0.196718
$987$	13.4713	−	6.30970i	0.428797	−	0.200840i
$988$	−49.4828			−1.57426
$989$			61.4678i			1.95456i
$990$	0.782400	−	0.948170i	0.0248663	−	0.0301348i
$991$	−4.36674			−0.138714			−0.0693570	−	0.997592i	$-0.522095\pi$
$991$	−4.36674			−0.138714			−0.0693570	+	0.997592i	$0.522095\pi$
$992$	−31.7492			−1.00804
$993$			10.1656i			0.322595i
$994$	3.88036	+	8.28463i	0.123077	+	0.262773i
$995$	16.7628			0.531416
$996$		−	7.37711i		−	0.233753i
$997$	16.4708			0.521636			0.260818	−	0.965388i	$-0.416008\pi$
$997$	16.4708			0.521636			0.260818	+	0.965388i	$0.416008\pi$
$998$		−	7.98858i		−	0.252874i
$999$		−	8.48839i		−	0.268561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.3	✓	32
7.6	odd	2	inner	1155.2.i.d.76.29	yes	32
11.10	odd	2	inner	1155.2.i.d.76.30	yes	32
77.76	even	2	inner	1155.2.i.d.76.4	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.3	✓	32	1.1	even	1	trivial
1155.2.i.d.76.4	yes	32	77.76	even	2	inner
1155.2.i.d.76.29	yes	32	7.6	odd	2	inner
1155.2.i.d.76.30	yes	32	11.10	odd	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)

\(f(q)\)	\(=\)	\(q-0.370647i q^{2} -1.00000i q^{3} +1.86262 q^{4} -1.00000i q^{5} -0.370647 q^{6} +(-2.39596 + 1.12222i) q^{7} -1.43167i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.370647i q^{2} -1.00000i q^{3} +1.86262 q^{4} -1.00000i q^{5} -0.370647 q^{6} +(-2.39596 + 1.12222i) q^{7} -1.43167i q^{8} -1.00000 q^{9} -0.370647 q^{10} +(2.11090 - 2.55814i) q^{11} -1.86262i q^{12} +5.18990 q^{13} +(0.415948 + 0.888056i) q^{14} -1.00000 q^{15} +3.19460 q^{16} -2.13309 q^{17} +0.370647i q^{18} -5.11883 q^{19} -1.86262i q^{20} +(1.12222 + 2.39596i) q^{21} +(-0.948170 - 0.782400i) q^{22} +7.91984 q^{23} -1.43167 q^{24} -1.00000 q^{25} -1.92362i q^{26} +1.00000i q^{27} +(-4.46276 + 2.09027i) q^{28} -7.81291i q^{29} +0.370647i q^{30} -7.84432i q^{31} -4.04741i q^{32} +(-2.55814 - 2.11090i) q^{33} +0.790625i q^{34} +(1.12222 + 2.39596i) q^{35} -1.86262 q^{36} -8.48839 q^{37} +1.89728i q^{38} -5.18990i q^{39} -1.43167 q^{40} +2.17082 q^{41} +(0.888056 - 0.415948i) q^{42} +7.76125i q^{43} +(3.93180 - 4.76485i) q^{44} +1.00000i q^{45} -2.93547i q^{46} -5.62252i q^{47} -3.19460i q^{48} +(4.48125 - 5.37759i) q^{49} +0.370647i q^{50} +2.13309i q^{51} +9.66682 q^{52} -10.7569 q^{53} +0.370647 q^{54} +(-2.55814 - 2.11090i) q^{55} +(1.60665 + 3.43022i) q^{56} +5.11883i q^{57} -2.89583 q^{58} +2.14980i q^{59} -1.86262 q^{60} +8.26503 q^{61} -2.90748 q^{62} +(2.39596 - 1.12222i) q^{63} +4.88903 q^{64} -5.18990i q^{65} +(-0.782400 + 0.948170i) q^{66} -2.80794 q^{67} -3.97314 q^{68} -7.91984i q^{69} +(0.888056 - 0.415948i) q^{70} +9.32895 q^{71} +1.43167i q^{72} -10.0221 q^{73} +3.14620i q^{74} +1.00000i q^{75} -9.53443 q^{76} +(-2.18683 + 8.49810i) q^{77} -1.92362 q^{78} +8.98914i q^{79} -3.19460i q^{80} +1.00000 q^{81} -0.804610i q^{82} +3.96061 q^{83} +(2.09027 + 4.46276i) q^{84} +2.13309i q^{85} +2.87669 q^{86} -7.81291 q^{87} +(-3.66242 - 3.02211i) q^{88} +8.45786i q^{89} +0.370647 q^{90} +(-12.4348 + 5.82421i) q^{91} +14.7517 q^{92} -7.84432 q^{93} -2.08397 q^{94} +5.11883i q^{95} -4.04741 q^{96} -8.31015i q^{97} +(-1.99319 - 1.66096i) q^{98} +(-2.11090 + 2.55814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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