LMFDB - Embedded newform 1110.2.h.d.961.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(961,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1110.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.h (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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 37x^{2} + 324 $ x^4 + 37*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			961.4
Root			$4.77200i$ of defining polynomial
Character	$\chi$	$=$	1110.961
Dual form			1110.2.h.d.961.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.77200i q^{13} -1.00000i q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} -0.772002i q^{19} +1.00000i q^{20} +1.00000 q^{21} -1.00000i q^{22} -0.772002i q^{23} +1.00000i q^{24} -1.00000 q^{25} -4.77200 q^{26} -1.00000 q^{27} +1.00000 q^{28} -7.77200i q^{29} -1.00000 q^{30} -7.77200i q^{31} +1.00000i q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000i q^{35} -1.00000 q^{36} +(-3.77200 - 4.77200i) q^{37} +0.772002 q^{38} -4.77200i q^{39} -1.00000 q^{40} +7.77200 q^{41} +1.00000i q^{42} -9.77200i q^{43} +1.00000 q^{44} -1.00000i q^{45} +0.772002 q^{46} -1.00000 q^{48} -6.00000 q^{49} -1.00000i q^{50} +1.00000i q^{51} -4.77200i q^{52} +6.54400 q^{53} -1.00000i q^{54} +1.00000i q^{55} +1.00000i q^{56} +0.772002i q^{57} +7.77200 q^{58} -9.54400i q^{59} -1.00000i q^{60} +4.22800i q^{61} +7.77200 q^{62} -1.00000 q^{63} -1.00000 q^{64} +4.77200 q^{65} +1.00000i q^{66} -7.54400 q^{67} +1.00000i q^{68} +0.772002i q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000i q^{72} +8.77200 q^{73} +(4.77200 - 3.77200i) q^{74} +1.00000 q^{75} +0.772002i q^{76} +1.00000 q^{77} +4.77200 q^{78} -5.54400i q^{79} -1.00000i q^{80} +1.00000 q^{81} +7.77200i q^{82} +6.77200 q^{83} -1.00000 q^{84} -1.00000 q^{85} +9.77200 q^{86} +7.77200i q^{87} +1.00000i q^{88} -8.31601i q^{89} +1.00000 q^{90} -4.77200i q^{91} +0.772002i q^{92} +7.77200i q^{93} -0.772002 q^{95} -1.00000i q^{96} +2.22800i q^{97} -6.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9	$ 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{16} + 4 q^{21} - 4 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{30} + 4 q^{33} + 4 q^{34} - 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{40} + 14 q^{41} + 4 q^{44} - 14 q^{46} - 4 q^{48} - 24 q^{49} - 8 q^{53} + 14 q^{58} + 14 q^{62} - 4 q^{63} - 4 q^{64} + 2 q^{65} + 4 q^{67} - 4 q^{70} - 24 q^{71} + 18 q^{73} + 2 q^{74} + 4 q^{75} + 4 q^{77} + 2 q^{78} + 4 q^{81} + 10 q^{83} - 4 q^{84} - 4 q^{85} + 22 q^{86} + 4 q^{90} + 14 q^{95} - 4 q^{99}+O(q^{100}) $ 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^16 + 4 * q^21 - 4 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^30 + 4 * q^33 + 4 * q^34 - 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^40 + 14 * q^41 + 4 * q^44 - 14 * q^46 - 4 * q^48 - 24 * q^49 - 8 * q^53 + 14 * q^58 + 14 * q^62 - 4 * q^63 - 4 * q^64 + 2 * q^65 + 4 * q^67 - 4 * q^70 - 24 * q^71 + 18 * q^73 + 2 * q^74 + 4 * q^75 + 4 * q^77 + 2 * q^78 + 4 * q^81 + 10 * q^83 - 4 * q^84 - 4 * q^85 + 22 * q^86 + 4 * q^90 + 14 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.00000			−0.500000
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		−	1.00000i		−	0.408248i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	1.00000			0.316228
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$	1.00000			0.288675
$13$			4.77200i			1.32352i	0.749718	+	0.661758i	$0.230189\pi$
$13$			4.77200i			1.32352i	−0.749718	+	0.661758i	$0.769811\pi$
$14$		−	1.00000i		−	0.267261i
$15$			1.00000i			0.258199i
$16$	1.00000			0.250000
$17$		−	1.00000i		−	0.242536i	−0.992620	−	0.121268i	$-0.961304\pi$
$17$		−	1.00000i		−	0.242536i	0.992620	−	0.121268i	$-0.0386960\pi$
$18$			1.00000i			0.235702i
$19$		−	0.772002i		−	0.177109i	−0.996071	−	0.0885547i	$-0.971775\pi$
$19$		−	0.772002i		−	0.177109i	0.996071	−	0.0885547i	$-0.0282248\pi$
$20$			1.00000i			0.223607i
$21$	1.00000			0.218218
$22$		−	1.00000i		−	0.213201i
$23$		−	0.772002i		−	0.160974i	−0.996756	−	0.0804868i	$-0.974353\pi$
$23$		−	0.772002i		−	0.160974i	0.996756	−	0.0804868i	$-0.0256475\pi$
$24$			1.00000i			0.204124i
$25$	−1.00000			−0.200000
$26$	−4.77200			−0.935867
$27$	−1.00000			−0.192450
$28$	1.00000			0.188982
$29$		−	7.77200i		−	1.44322i	−0.692297	−	0.721612i	$-0.743401\pi$
$29$		−	7.77200i		−	1.44322i	0.692297	−	0.721612i	$-0.256599\pi$
$30$	−1.00000			−0.182574
$31$		−	7.77200i		−	1.39589i	−0.716150	−	0.697946i	$-0.754097\pi$
$31$		−	7.77200i		−	1.39589i	0.716150	−	0.697946i	$-0.245903\pi$
$32$			1.00000i			0.176777i
$33$	1.00000			0.174078
$34$	1.00000			0.171499
$35$			1.00000i			0.169031i
$36$	−1.00000			−0.166667
$37$	−3.77200	−	4.77200i	−0.620113	−	0.784512i
$37$	−3.77200	−	4.77200i	−0.620113	−	0.784512i
$38$	0.772002			0.125235
$39$		−	4.77200i		−	0.764132i
$40$	−1.00000			−0.158114
$41$	7.77200			1.21378			0.606891	−	0.794785i	$-0.292416\pi$
$41$	7.77200			1.21378			0.606891	+	0.794785i	$0.292416\pi$
$42$			1.00000i			0.154303i
$43$		−	9.77200i		−	1.49022i	−0.666944	−	0.745108i	$-0.732398\pi$
$43$		−	9.77200i		−	1.49022i	0.666944	−	0.745108i	$-0.267602\pi$
$44$	1.00000			0.150756
$45$		−	1.00000i		−	0.149071i
$46$	0.772002			0.113825
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$	−1.00000			−0.144338
$49$	−6.00000			−0.857143
$50$		−	1.00000i		−	0.141421i
$51$			1.00000i			0.140028i
$52$		−	4.77200i		−	0.661758i
$53$	6.54400			0.898888			0.449444	−	0.893308i	$-0.351622\pi$
$53$	6.54400			0.898888			0.449444	+	0.893308i	$0.351622\pi$
$54$		−	1.00000i		−	0.136083i
$55$			1.00000i			0.134840i
$56$			1.00000i			0.133631i
$57$			0.772002i			0.102254i
$58$	7.77200			1.02051
$59$		−	9.54400i		−	1.24252i	−0.783603	−	0.621262i	$-0.786620\pi$
$59$		−	9.54400i		−	1.24252i	0.783603	−	0.621262i	$-0.213380\pi$
$60$		−	1.00000i		−	0.129099i
$61$			4.22800i			0.541340i	0.962672	+	0.270670i	$0.0872452\pi$
$61$			4.22800i			0.541340i	−0.962672	+	0.270670i	$0.912755\pi$
$62$	7.77200			0.987045
$63$	−1.00000			−0.125988
$64$	−1.00000			−0.125000
$65$	4.77200			0.591894
$66$			1.00000i			0.123091i
$67$	−7.54400			−0.921647			−0.460823	−	0.887492i	$-0.652446\pi$
$67$	−7.54400			−0.921647			−0.460823	+	0.887492i	$0.652446\pi$
$68$			1.00000i			0.121268i
$69$			0.772002i			0.0929381i
$70$	−1.00000			−0.119523
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		−	1.00000i		−	0.117851i
$73$	8.77200			1.02669			0.513343	−	0.858184i	$-0.328407\pi$
$73$	8.77200			1.02669			0.513343	+	0.858184i	$0.328407\pi$
$74$	4.77200	−	3.77200i	0.554734	−	0.438486i
$75$	1.00000			0.115470
$76$			0.772002i			0.0885547i
$77$	1.00000			0.113961
$78$	4.77200			0.540323
$79$		−	5.54400i		−	0.623749i	−0.950123	−	0.311875i	$-0.899043\pi$
$79$		−	5.54400i		−	0.623749i	0.950123	−	0.311875i	$-0.100957\pi$
$80$		−	1.00000i		−	0.111803i
$81$	1.00000			0.111111
$82$			7.77200i			0.858274i
$83$	6.77200			0.743324			0.371662	−	0.928368i	$-0.378788\pi$
$83$	6.77200			0.743324			0.371662	+	0.928368i	$0.378788\pi$
$84$	−1.00000			−0.109109
$85$	−1.00000			−0.108465
$86$	9.77200			1.05374
$87$			7.77200i			0.833246i
$88$			1.00000i			0.106600i
$89$		−	8.31601i		−	0.881495i	−0.897631	−	0.440747i	$-0.854713\pi$
$89$		−	8.31601i		−	0.881495i	0.897631	−	0.440747i	$-0.145287\pi$
$90$	1.00000			0.105409
$91$		−	4.77200i		−	0.500242i
$92$			0.772002i			0.0804868i
$93$			7.77200i			0.805919i
$94$		0			0
$95$	−0.772002			−0.0792057
$96$		−	1.00000i		−	0.102062i
$97$			2.22800i			0.226219i	0.993583	+	0.113109i	$0.0360811\pi$
$97$			2.22800i			0.226219i	−0.993583	+	0.113109i	$0.963919\pi$
$98$		−	6.00000i		−	0.606092i
$99$	−1.00000			−0.100504
$100$	1.00000			0.100000
$101$	5.54400			0.551649			0.275824	−	0.961208i	$-0.411049\pi$
$101$	5.54400			0.551649			0.275824	+	0.961208i	$0.411049\pi$
$102$	−1.00000			−0.0990148
$103$		−	0.455996i		−	0.0449306i	−0.999748	−	0.0224653i	$-0.992848\pi$
$103$		−	0.455996i		−	0.0449306i	0.999748	−	0.0224653i	$-0.00715154\pi$
$104$	4.77200			0.467933
$105$		−	1.00000i		−	0.0975900i
$106$			6.54400i			0.635610i
$107$	0.772002			0.0746322			0.0373161	−	0.999304i	$-0.488119\pi$
$107$	0.772002			0.0746322			0.0373161	+	0.999304i	$0.488119\pi$
$108$	1.00000			0.0962250
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$	−1.00000			−0.0953463
$111$	3.77200	+	4.77200i	0.358023	+	0.452938i
$112$	−1.00000			−0.0944911
$113$			11.3160i			1.06452i	0.846581	+	0.532260i	$0.178657\pi$
$113$			11.3160i			1.06452i	−0.846581	+	0.532260i	$0.821343\pi$
$114$	−0.772002			−0.0723046
$115$	−0.772002			−0.0719895
$116$			7.77200i			0.721612i
$117$			4.77200i			0.441172i
$118$	9.54400			0.878597
$119$			1.00000i			0.0916698i
$120$	1.00000			0.0912871
$121$	−10.0000			−0.909091
$122$	−4.22800			−0.382785
$123$	−7.77200			−0.700778
$124$			7.77200i			0.697946i
$125$			1.00000i			0.0894427i
$126$		−	1.00000i		−	0.0890871i
$127$	−12.3160			−1.09287			−0.546434	−	0.837502i	$-0.684015\pi$
$127$	−12.3160			−1.09287			−0.546434	+	0.837502i	$0.684015\pi$
$128$		−	1.00000i		−	0.0883883i
$129$			9.77200i			0.860377i
$130$			4.77200i			0.418532i
$131$		−	17.5440i		−	1.53283i	−0.642348	−	0.766413i	$-0.722039\pi$
$131$		−	17.5440i		−	1.53283i	0.642348	−	0.766413i	$-0.277961\pi$
$132$	−1.00000			−0.0870388
$133$			0.772002i			0.0669411i
$134$		−	7.54400i		−	0.651703i
$135$			1.00000i			0.0860663i
$136$	−1.00000			−0.0857493
$137$	15.0880			1.28906			0.644528	−	0.764581i	$-0.277054\pi$
$137$	15.0880			1.28906			0.644528	+	0.764581i	$0.277054\pi$
$138$	−0.772002			−0.0657172
$139$	−5.31601			−0.450898			−0.225449	−	0.974255i	$-0.572385\pi$
$139$	−5.31601			−0.450898			−0.225449	+	0.974255i	$0.572385\pi$
$140$		−	1.00000i		−	0.0845154i
$141$		0			0
$142$		−	6.00000i		−	0.503509i
$143$		−	4.77200i		−	0.399055i
$144$	1.00000			0.0833333
$145$	−7.77200			−0.645430
$146$			8.77200i			0.725976i
$147$	6.00000			0.494872
$148$	3.77200	+	4.77200i	0.310057	+	0.392256i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$			1.00000i			0.0816497i
$151$	16.7720			1.36489			0.682443	−	0.730939i	$-0.260918\pi$
$151$	16.7720			1.36489			0.682443	+	0.730939i	$0.260918\pi$
$152$	−0.772002			−0.0626176
$153$		−	1.00000i		−	0.0808452i
$154$			1.00000i			0.0805823i
$155$	−7.77200			−0.624262
$156$			4.77200i			0.382066i
$157$	−24.8600			−1.98404			−0.992022	−	0.126062i	$-0.959766\pi$
$157$	−24.8600			−1.98404			−0.992022	+	0.126062i	$0.959766\pi$
$158$	5.54400			0.441057
$159$	−6.54400			−0.518973
$160$	1.00000			0.0790569
$161$			0.772002i			0.0608423i
$162$			1.00000i			0.0785674i
$163$			20.5440i			1.60913i	0.593864	+	0.804565i	$0.297602\pi$
$163$			20.5440i			1.60913i	−0.593864	+	0.804565i	$0.702398\pi$
$164$	−7.77200			−0.606891
$165$		−	1.00000i		−	0.0778499i
$166$			6.77200i			0.525609i
$167$		−	14.3160i		−	1.10781i	−0.832581	−	0.553903i	$-0.813138\pi$
$167$		−	14.3160i		−	1.10781i	0.832581	−	0.553903i	$-0.186862\pi$
$168$		−	1.00000i		−	0.0771517i
$169$	−9.77200			−0.751692
$170$		−	1.00000i		−	0.0766965i
$171$		−	0.772002i		−	0.0590365i
$172$			9.77200i			0.745108i
$173$	15.0000			1.14043			0.570214	−	0.821496i	$-0.306860\pi$
$173$	15.0000			1.14043			0.570214	+	0.821496i	$0.306860\pi$
$174$	−7.77200			−0.589194
$175$	1.00000			0.0755929
$176$	−1.00000			−0.0753778
$177$			9.54400i			0.717371i
$178$	8.31601			0.623311
$179$		−	7.54400i		−	0.563865i	−0.959434	−	0.281933i	$-0.909025\pi$
$179$		−	7.54400i		−	0.563865i	0.959434	−	0.281933i	$-0.0909755\pi$
$180$			1.00000i			0.0745356i
$181$	6.45600			0.479870			0.239935	−	0.970789i	$-0.422874\pi$
$181$	6.45600			0.479870			0.239935	+	0.970789i	$0.422874\pi$
$182$	4.77200			0.353724
$183$		−	4.22800i		−	0.312543i
$184$	−0.772002			−0.0569127
$185$	−4.77200	+	3.77200i	−0.350845	+	0.277323i
$186$	−7.77200			−0.569871
$187$			1.00000i			0.0731272i
$188$		0			0
$189$	1.00000			0.0727393
$190$		−	0.772002i		−	0.0560069i
$191$			4.54400i			0.328793i	0.986394	+	0.164396i	$0.0525676\pi$
$191$			4.54400i			0.328793i	−0.986394	+	0.164396i	$0.947432\pi$
$192$	1.00000			0.0721688
$193$			23.5440i			1.69473i	0.531007	+	0.847367i	$0.321814\pi$
$193$			23.5440i			1.69473i	−0.531007	+	0.847367i	$0.678186\pi$
$194$	−2.22800			−0.159961
$195$	−4.77200			−0.341730
$196$	6.00000			0.428571
$197$	3.22800			0.229985			0.114993	−	0.993366i	$-0.463316\pi$
$197$	3.22800			0.229985			0.114993	+	0.993366i	$0.463316\pi$
$198$		−	1.00000i		−	0.0710669i
$199$		−	9.54400i		−	0.676556i	−0.941046	−	0.338278i	$-0.890155\pi$
$199$		−	9.54400i		−	0.676556i	0.941046	−	0.338278i	$-0.109845\pi$
$200$			1.00000i			0.0707107i
$201$	7.54400			0.532113
$202$			5.54400i			0.390075i
$203$			7.77200i			0.545488i
$204$		−	1.00000i		−	0.0700140i
$205$		−	7.77200i		−	0.542820i
$206$	0.455996			0.0317708
$207$		−	0.772002i		−	0.0536578i
$208$			4.77200i			0.330879i
$209$			0.772002i			0.0534005i
$210$	1.00000			0.0690066
$211$	−19.7720			−1.36116			−0.680580	−	0.732673i	$-0.738272\pi$
$211$	−19.7720			−1.36116			−0.680580	+	0.732673i	$0.738272\pi$
$212$	−6.54400			−0.449444
$213$	6.00000			0.411113
$214$			0.772002i			0.0527730i
$215$	−9.77200			−0.666445
$216$			1.00000i			0.0680414i
$217$			7.77200i			0.527598i
$218$	7.00000			0.474100
$219$	−8.77200			−0.592757
$220$		−	1.00000i		−	0.0674200i
$221$	4.77200			0.321000
$222$	−4.77200	+	3.77200i	−0.320276	+	0.253160i
$223$	−25.7720			−1.72582			−0.862910	−	0.505357i	$-0.831361\pi$
$223$	−25.7720			−1.72582			−0.862910	+	0.505357i	$0.831361\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−1.00000			−0.0666667
$226$	−11.3160			−0.752729
$227$			1.77200i			0.117612i	0.998269	+	0.0588059i	$0.0187293\pi$
$227$			1.77200i			0.117612i	−0.998269	+	0.0588059i	$0.981271\pi$
$228$		−	0.772002i		−	0.0511271i
$229$	−3.54400			−0.234194			−0.117097	−	0.993120i	$-0.537359\pi$
$229$	−3.54400			−0.234194			−0.117097	+	0.993120i	$0.537359\pi$
$230$		−	0.772002i		−	0.0509043i
$231$	−1.00000			−0.0657952
$232$	−7.77200			−0.510257
$233$	−12.0000			−0.786146			−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000			−0.786146			−0.393073	+	0.919507i	$0.628588\pi$
$234$	−4.77200			−0.311956
$235$		0			0
$236$			9.54400i			0.621262i
$237$			5.54400i			0.360122i
$238$	−1.00000			−0.0648204
$239$			13.7720i			0.890837i	0.895323	+	0.445418i	$0.146945\pi$
$239$			13.7720i			0.890837i	−0.895323	+	0.445418i	$0.853055\pi$
$240$			1.00000i			0.0645497i
$241$		−	16.0000i		−	1.03065i	−0.856995	−	0.515325i	$-0.827671\pi$
$241$		−	16.0000i		−	1.03065i	0.856995	−	0.515325i	$-0.172329\pi$
$242$		−	10.0000i		−	0.642824i
$243$	−1.00000			−0.0641500
$244$		−	4.22800i		−	0.270670i
$245$			6.00000i			0.383326i
$246$		−	7.77200i		−	0.495525i
$247$	3.68399			0.234407
$248$	−7.77200			−0.493523
$249$	−6.77200			−0.429158
$250$	−1.00000			−0.0632456
$251$		−	7.08801i		−	0.447391i	−0.974659	−	0.223696i	$-0.928188\pi$
$251$		−	7.08801i		−	0.447391i	0.974659	−	0.223696i	$-0.0718121\pi$
$252$	1.00000			0.0629941
$253$			0.772002i			0.0485353i
$254$		−	12.3160i		−	0.772775i
$255$	1.00000			0.0626224
$256$	1.00000			0.0625000
$257$			12.7720i			0.796696i	0.917234	+	0.398348i	$0.130416\pi$
$257$			12.7720i			0.796696i	−0.917234	+	0.398348i	$0.869584\pi$
$258$	−9.77200			−0.608378
$259$	3.77200	+	4.77200i	0.234381	+	0.296518i
$260$	−4.77200			−0.295947
$261$		−	7.77200i		−	0.481075i
$262$	17.5440			1.08387
$263$	13.7720			0.849218			0.424609	−	0.905377i	$-0.360412\pi$
$263$	13.7720			0.849218			0.424609	+	0.905377i	$0.360412\pi$
$264$		−	1.00000i		−	0.0615457i
$265$		−	6.54400i		−	0.401995i
$266$	−0.772002			−0.0473345
$267$			8.31601i			0.508931i
$268$	7.54400			0.460823
$269$	−16.3160			−0.994804			−0.497402	−	0.867520i	$-0.665713\pi$
$269$	−16.3160			−0.994804			−0.497402	+	0.867520i	$0.665713\pi$
$270$	−1.00000			−0.0608581
$271$	11.0880			0.673548			0.336774	−	0.941585i	$-0.390664\pi$
$271$	11.0880			0.673548			0.336774	+	0.941585i	$0.390664\pi$
$272$		−	1.00000i		−	0.0606339i
$273$			4.77200i			0.288815i
$274$			15.0880i			0.911500i
$275$	1.00000			0.0603023
$276$		−	0.772002i		−	0.0464691i
$277$		−	14.7720i		−	0.887564i	−0.896135	−	0.443782i	$-0.853637\pi$
$277$		−	14.7720i		−	0.887564i	0.896135	−	0.443782i	$-0.146363\pi$
$278$		−	5.31601i		−	0.318833i
$279$		−	7.77200i		−	0.465298i
$280$	1.00000			0.0597614
$281$			4.77200i			0.284674i	0.989818	+	0.142337i	$0.0454616\pi$
$281$			4.77200i			0.284674i	−0.989818	+	0.142337i	$0.954538\pi$
$282$		0			0
$283$			10.7720i			0.640329i	0.947362	+	0.320165i	$0.103738\pi$
$283$			10.7720i			0.640329i	−0.947362	+	0.320165i	$0.896262\pi$
$284$	6.00000			0.356034
$285$	0.772002			0.0457294
$286$	4.77200			0.282174
$287$	−7.77200			−0.458767
$288$			1.00000i			0.0589256i
$289$	16.0000			0.941176
$290$		−	7.77200i		−	0.456388i
$291$		−	2.22800i		−	0.130608i
$292$	−8.77200			−0.513343
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$			6.00000i			0.349927i
$295$	−9.54400			−0.555673
$296$	−4.77200	+	3.77200i	−0.277367	+	0.219243i
$297$	1.00000			0.0580259
$298$		−	6.00000i		−	0.347571i
$299$	3.68399			0.213051
$300$	−1.00000			−0.0577350
$301$			9.77200i			0.563249i
$302$			16.7720i			0.965120i
$303$	−5.54400			−0.318495
$304$		−	0.772002i		−	0.0442773i
$305$	4.22800			0.242094
$306$	1.00000			0.0571662
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	−1.00000			−0.0569803
$309$			0.455996i			0.0259407i
$310$		−	7.77200i		−	0.441420i
$311$		−	1.77200i		−	0.100481i	−0.998737	−	0.0502405i	$-0.984001\pi$
$311$		−	1.77200i		−	0.100481i	0.998737	−	0.0502405i	$-0.0159988\pi$
$312$	−4.77200			−0.270161
$313$			17.0880i			0.965871i	0.875656	+	0.482936i	$0.160429\pi$
$313$			17.0880i			0.965871i	−0.875656	+	0.482936i	$0.839571\pi$
$314$		−	24.8600i		−	1.40293i
$315$			1.00000i			0.0563436i
$316$			5.54400i			0.311875i
$317$	26.4040			1.48300			0.741499	−	0.670954i	$-0.234115\pi$
$317$	26.4040			1.48300			0.741499	+	0.670954i	$0.234115\pi$
$318$		−	6.54400i		−	0.366970i
$319$			7.77200i			0.435149i
$320$			1.00000i			0.0559017i
$321$	−0.772002			−0.0430889
$322$	−0.772002			−0.0430220
$323$	−0.772002			−0.0429553
$324$	−1.00000			−0.0555556
$325$		−	4.77200i		−	0.264703i
$326$	−20.5440			−1.13783
$327$			7.00000i			0.387101i
$328$		−	7.77200i		−	0.429137i
$329$		0			0
$330$	1.00000			0.0550482
$331$			0.455996i			0.0250638i	0.999921	+	0.0125319i	$0.00398914\pi$
$331$			0.455996i			0.0250638i	−0.999921	+	0.0125319i	$0.996011\pi$
$332$	−6.77200			−0.371662
$333$	−3.77200	−	4.77200i	−0.206704	−	0.261504i
$334$	14.3160			0.783337
$335$			7.54400i			0.412173i
$336$	1.00000			0.0545545
$337$	24.3160			1.32458			0.662289	−	0.749249i	$-0.269585\pi$
$337$	24.3160			1.32458			0.662289	+	0.749249i	$0.269585\pi$
$338$		−	9.77200i		−	0.531527i
$339$		−	11.3160i		−	0.614601i
$340$	1.00000			0.0542326
$341$			7.77200i			0.420877i
$342$	0.772002			0.0417451
$343$	13.0000			0.701934
$344$	−9.77200			−0.526871
$345$	0.772002			0.0415632
$346$			15.0000i			0.806405i
$347$		−	6.45600i		−	0.346576i	−0.984871	−	0.173288i	$-0.944561\pi$
$347$		−	6.45600i		−	0.346576i	0.984871	−	0.173288i	$-0.0554391\pi$
$348$		−	7.77200i		−	0.416623i
$349$	−6.00000			−0.321173			−0.160586	−	0.987022i	$-0.551338\pi$
$349$	−6.00000			−0.321173			−0.160586	+	0.987022i	$0.551338\pi$
$350$			1.00000i			0.0534522i
$351$		−	4.77200i		−	0.254711i
$352$		−	1.00000i		−	0.0533002i
$353$		−	28.2280i		−	1.50242i	−0.660061	−	0.751212i	$-0.729469\pi$
$353$		−	28.2280i		−	1.50242i	0.660061	−	0.751212i	$-0.270531\pi$
$354$	−9.54400			−0.507258
$355$			6.00000i			0.318447i
$356$			8.31601i			0.440747i
$357$		−	1.00000i		−	0.0529256i
$358$	7.54400			0.398713
$359$	−21.5440			−1.13705			−0.568525	−	0.822666i	$-0.692486\pi$
$359$	−21.5440			−1.13705			−0.568525	+	0.822666i	$0.692486\pi$
$360$	−1.00000			−0.0527046
$361$	18.4040			0.968632
$362$			6.45600i			0.339320i
$363$	10.0000			0.524864
$364$			4.77200i			0.250121i
$365$		−	8.77200i		−	0.459148i
$366$	4.22800			0.221001
$367$	18.0880			0.944186			0.472093	−	0.881549i	$-0.343499\pi$
$367$	18.0880			0.944186			0.472093	+	0.881549i	$0.343499\pi$
$368$		−	0.772002i		−	0.0402434i
$369$	7.77200			0.404594
$370$	−3.77200	−	4.77200i	−0.196097	−	0.248085i
$371$	−6.54400			−0.339748
$372$		−	7.77200i		−	0.402960i
$373$	4.45600			0.230723			0.115361	−	0.993324i	$-0.463197\pi$
$373$	4.45600			0.230723			0.115361	+	0.993324i	$0.463197\pi$
$374$	−1.00000			−0.0517088
$375$		−	1.00000i		−	0.0516398i
$376$		0			0
$377$	37.0880			1.91013
$378$			1.00000i			0.0514344i
$379$	−6.45600			−0.331622			−0.165811	−	0.986158i	$-0.553024\pi$
$379$	−6.45600			−0.331622			−0.165811	+	0.986158i	$0.553024\pi$
$380$	0.772002			0.0396029
$381$	12.3160			0.630968
$382$	−4.54400			−0.232491
$383$		−	10.3160i		−	0.527123i	−0.964643	−	0.263562i	$-0.915103\pi$
$383$		−	10.3160i		−	0.527123i	0.964643	−	0.263562i	$-0.0848972\pi$
$384$			1.00000i			0.0510310i
$385$		−	1.00000i		−	0.0509647i
$386$	−23.5440			−1.19836
$387$		−	9.77200i		−	0.496739i
$388$		−	2.22800i		−	0.113109i
$389$			1.77200i			0.0898441i	0.998990	+	0.0449220i	$0.0143039\pi$
$389$			1.77200i			0.0898441i	−0.998990	+	0.0449220i	$0.985696\pi$
$390$		−	4.77200i		−	0.241640i
$391$	−0.772002			−0.0390418
$392$			6.00000i			0.303046i
$393$			17.5440i			0.884978i
$394$			3.22800i			0.162624i
$395$	−5.54400			−0.278949
$396$	1.00000			0.0502519
$397$	−15.5440			−0.780131			−0.390066	−	0.920787i	$-0.627548\pi$
$397$	−15.5440			−0.780131			−0.390066	+	0.920787i	$0.627548\pi$
$398$	9.54400			0.478398
$399$		−	0.772002i		−	0.0386484i
$400$	−1.00000			−0.0500000
$401$			2.31601i			0.115656i	0.998327	+	0.0578279i	$0.0184175\pi$
$401$			2.31601i			0.115656i	−0.998327	+	0.0578279i	$0.981583\pi$
$402$			7.54400i			0.376261i
$403$	37.0880			1.84749
$404$	−5.54400			−0.275824
$405$		−	1.00000i		−	0.0496904i
$406$	−7.77200			−0.385718
$407$	3.77200	+	4.77200i	0.186971	+	0.236539i
$408$	1.00000			0.0495074
$409$		−	4.00000i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$		−	4.00000i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315304\pi$
$410$	7.77200			0.383832
$411$	−15.0880			−0.744237
$412$			0.455996i			0.0224653i
$413$			9.54400i			0.469630i
$414$	0.772002			0.0379418
$415$		−	6.77200i		−	0.332424i
$416$	−4.77200			−0.233967
$417$	5.31601			0.260326
$418$	−0.772002			−0.0377598
$419$	−29.8600			−1.45876			−0.729378	−	0.684110i	$-0.760191\pi$
$419$	−29.8600			−1.45876			−0.729378	+	0.684110i	$0.760191\pi$
$420$			1.00000i			0.0487950i
$421$			6.00000i			0.292422i	0.989253	+	0.146211i	$0.0467079\pi$
$421$			6.00000i			0.292422i	−0.989253	+	0.146211i	$0.953292\pi$
$422$		−	19.7720i		−	0.962486i
$423$		0			0
$424$		−	6.54400i		−	0.317805i
$425$			1.00000i			0.0485071i
$426$			6.00000i			0.290701i
$427$		−	4.22800i		−	0.204607i
$428$	−0.772002			−0.0373161
$429$			4.77200i			0.230394i
$430$		−	9.77200i		−	0.471248i
$431$			24.0880i			1.16028i	0.814517	+	0.580139i	$0.197002\pi$
$431$			24.0880i			1.16028i	−0.814517	+	0.580139i	$0.802998\pi$
$432$	−1.00000			−0.0481125
$433$	0.772002			0.0371000			0.0185500	−	0.999828i	$-0.494095\pi$
$433$	0.772002			0.0371000			0.0185500	+	0.999828i	$0.494095\pi$
$434$	−7.77200			−0.373068
$435$	7.77200			0.372639
$436$			7.00000i			0.335239i
$437$	−0.595987			−0.0285099
$438$		−	8.77200i		−	0.419142i
$439$		−	12.2280i		−	0.583611i	−0.956478	−	0.291805i	$-0.905744\pi$
$439$		−	12.2280i		−	0.583611i	0.956478	−	0.291805i	$-0.0942559\pi$
$440$	1.00000			0.0476731
$441$	−6.00000			−0.285714
$442$			4.77200i			0.226981i
$443$	−20.0000			−0.950229			−0.475114	−	0.879924i	$-0.657593\pi$
$443$	−20.0000			−0.950229			−0.475114	+	0.879924i	$0.657593\pi$
$444$	−3.77200	−	4.77200i	−0.179011	−	0.226469i
$445$	−8.31601			−0.394216
$446$		−	25.7720i		−	1.22034i
$447$	6.00000			0.283790
$448$	1.00000			0.0472456
$449$			2.00000i			0.0943858i	0.998886	+	0.0471929i	$0.0150276\pi$
$449$			2.00000i			0.0943858i	−0.998886	+	0.0471929i	$0.984972\pi$
$450$		−	1.00000i		−	0.0471405i
$451$	−7.77200			−0.365969
$452$		−	11.3160i		−	0.532260i
$453$	−16.7720			−0.788017
$454$	−1.77200			−0.0831642
$455$	−4.77200			−0.223715
$456$	0.772002			0.0361523
$457$			8.68399i			0.406220i	0.979156	+	0.203110i	$0.0651049\pi$
$457$			8.68399i			0.406220i	−0.979156	+	0.203110i	$0.934895\pi$
$458$		−	3.54400i		−	0.165600i
$459$			1.00000i			0.0466760i
$460$	0.772002			0.0359948
$461$			29.7720i			1.38662i	0.720639	+	0.693310i	$0.243848\pi$
$461$			29.7720i			1.38662i	−0.720639	+	0.693310i	$0.756152\pi$
$462$		−	1.00000i		−	0.0465242i
$463$			20.6320i			0.958851i	0.877583	+	0.479425i	$0.159155\pi$
$463$			20.6320i			0.958851i	−0.877583	+	0.479425i	$0.840845\pi$
$464$		−	7.77200i		−	0.360806i
$465$	7.77200			0.360418
$466$		−	12.0000i		−	0.555889i
$467$			21.3160i			0.986387i	0.869920	+	0.493194i	$0.164171\pi$
$467$			21.3160i			0.986387i	−0.869920	+	0.493194i	$0.835829\pi$
$468$		−	4.77200i		−	0.220586i
$469$	7.54400			0.348350
$470$		0			0
$471$	24.8600			1.14549
$472$	−9.54400			−0.439298
$473$			9.77200i			0.449317i
$474$	−5.54400			−0.254645
$475$			0.772002i			0.0354219i
$476$		−	1.00000i		−	0.0458349i
$477$	6.54400			0.299629
$478$	−13.7720			−0.629917
$479$		−	18.7720i		−	0.857715i	−0.903372	−	0.428857i	$-0.858916\pi$
$479$		−	18.7720i		−	0.857715i	0.903372	−	0.428857i	$-0.141084\pi$
$480$	−1.00000			−0.0456435
$481$	22.7720	−	18.0000i	1.03831	−	0.820729i
$482$	16.0000			0.728780
$483$		−	0.772002i		−	0.0351273i
$484$	10.0000			0.454545
$485$	2.22800			0.101168
$486$		−	1.00000i		−	0.0453609i
$487$		−	19.0880i		−	0.864960i	−0.901643	−	0.432480i	$-0.857639\pi$
$487$		−	19.0880i		−	0.864960i	0.901643	−	0.432480i	$-0.142361\pi$
$488$	4.22800			0.191392
$489$		−	20.5440i		−	0.929032i
$490$	−6.00000			−0.271052
$491$	38.7720			1.74976			0.874878	−	0.484343i	$-0.160941\pi$
$491$	38.7720			1.74976			0.874878	+	0.484343i	$0.160941\pi$
$492$	7.77200			0.350389
$493$	−7.77200			−0.350033
$494$			3.68399i			0.165751i
$495$			1.00000i			0.0449467i
$496$		−	7.77200i		−	0.348973i
$497$	6.00000			0.269137
$498$		−	6.77200i		−	0.303461i
$499$			30.3160i			1.35713i	0.734540	+	0.678565i	$0.237398\pi$
$499$			30.3160i			1.35713i	−0.734540	+	0.678565i	$0.762602\pi$
$500$		−	1.00000i		−	0.0447214i
$501$			14.3160i			0.639592i
$502$	7.08801			0.316353
$503$			31.0880i			1.38615i	0.720868	+	0.693073i	$0.243744\pi$
$503$			31.0880i			1.38615i	−0.720868	+	0.693073i	$0.756256\pi$
$504$			1.00000i			0.0445435i
$505$		−	5.54400i		−	0.246705i
$506$	−0.772002			−0.0343197
$507$	9.77200			0.433990
$508$	12.3160			0.546434
$509$	−0.316006			−0.0140067			−0.00700335	−	0.999975i	$-0.502229\pi$
$509$	−0.316006			−0.0140067			−0.00700335	+	0.999975i	$0.502229\pi$
$510$			1.00000i			0.0442807i
$511$	−8.77200			−0.388051
$512$			1.00000i			0.0441942i
$513$			0.772002i			0.0340847i
$514$	−12.7720			−0.563349
$515$	−0.455996			−0.0200936
$516$		−	9.77200i		−	0.430188i
$517$		0			0
$518$	−4.77200	+	3.77200i	−0.209670	+	0.165732i
$519$	−15.0000			−0.658427
$520$		−	4.77200i		−	0.209266i
$521$	42.4040			1.85775			0.928877	−	0.370389i	$-0.120776\pi$
$521$	42.4040			1.85775			0.928877	+	0.370389i	$0.120776\pi$
$522$	7.77200			0.340171
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$			17.5440i			0.766413i
$525$	−1.00000			−0.0436436
$526$			13.7720i			0.600488i
$527$	−7.77200			−0.338554
$528$	1.00000			0.0435194
$529$	22.4040			0.974088
$530$	6.54400			0.284253
$531$		−	9.54400i		−	0.414174i
$532$		−	0.772002i		−	0.0334705i
$533$			37.0880i			1.60646i
$534$	−8.31601			−0.359869
$535$		−	0.772002i		−	0.0333766i
$536$			7.54400i			0.325851i
$537$			7.54400i			0.325548i
$538$		−	16.3160i		−	0.703433i
$539$	6.00000			0.258438
$540$		−	1.00000i		−	0.0430331i
$541$		−	3.22800i		−	0.138782i	−0.997590	−	0.0693912i	$-0.977894\pi$
$541$		−	3.22800i		−	0.138782i	0.997590	−	0.0693912i	$-0.0221057\pi$
$542$			11.0880i			0.476271i
$543$	−6.45600			−0.277053
$544$	1.00000			0.0428746
$545$	−7.00000			−0.299847
$546$	−4.77200			−0.204223
$547$		−	2.54400i		−	0.108774i	−0.998520	−	0.0543869i	$-0.982680\pi$
$547$		−	2.54400i		−	0.108774i	0.998520	−	0.0543869i	$-0.0173204\pi$
$548$	−15.0880			−0.644528
$549$			4.22800i			0.180447i
$550$			1.00000i			0.0426401i
$551$	−6.00000			−0.255609
$552$	0.772002			0.0328586
$553$			5.54400i			0.235755i
$554$	14.7720			0.627602
$555$	4.77200	−	3.77200i	0.202560	−	0.160113i
$556$	5.31601			0.225449
$557$		−	33.5440i		−	1.42131i	−0.703543	−	0.710653i	$-0.748400\pi$
$557$		−	33.5440i		−	1.42131i	0.703543	−	0.710653i	$-0.251600\pi$
$558$	7.77200			0.329015
$559$	46.6320			1.97232
$560$			1.00000i			0.0422577i
$561$		−	1.00000i		−	0.0422200i
$562$	−4.77200			−0.201295
$563$		−	33.9480i		−	1.43074i	−0.698747	−	0.715369i	$-0.746259\pi$
$563$		−	33.9480i		−	1.43074i	0.698747	−	0.715369i	$-0.253741\pi$
$564$		0			0
$565$	11.3160			0.476068
$566$	−10.7720			−0.452781
$567$	−1.00000			−0.0419961
$568$			6.00000i			0.251754i
$569$			20.3160i			0.851691i	0.904796	+	0.425846i	$0.140023\pi$
$569$			20.3160i			0.851691i	−0.904796	+	0.425846i	$0.859977\pi$
$570$			0.772002i			0.0323356i
$571$	35.9480			1.50438			0.752189	−	0.658948i	$-0.228998\pi$
$571$	35.9480			1.50438			0.752189	+	0.658948i	$0.228998\pi$
$572$			4.77200i			0.199527i
$573$		−	4.54400i		−	0.189828i
$574$		−	7.77200i		−	0.324397i
$575$			0.772002i			0.0321947i
$576$	−1.00000			−0.0416667
$577$		−	39.5440i		−	1.64624i	−0.567869	−	0.823119i	$-0.692232\pi$
$577$		−	39.5440i		−	1.64624i	0.567869	−	0.823119i	$-0.307768\pi$
$578$			16.0000i			0.665512i
$579$		−	23.5440i		−	0.978455i
$580$	7.77200			0.322715
$581$	−6.77200			−0.280950
$582$	2.22800			0.0923535
$583$	−6.54400			−0.271025
$584$		−	8.77200i		−	0.362988i
$585$	4.77200			0.197298
$586$		−	9.00000i		−	0.371787i
$587$		−	30.8600i		−	1.27373i	−0.770976	−	0.636864i	$-0.780231\pi$
$587$		−	30.8600i		−	1.27373i	0.770976	−	0.636864i	$-0.219769\pi$
$588$	−6.00000			−0.247436
$589$	−6.00000			−0.247226
$590$		−	9.54400i		−	0.392920i
$591$	−3.22800			−0.132782
$592$	−3.77200	−	4.77200i	−0.155028	−	0.196128i
$593$	5.54400			0.227665			0.113832	−	0.993500i	$-0.463687\pi$
$593$	5.54400			0.227665			0.113832	+	0.993500i	$0.463687\pi$
$594$			1.00000i			0.0410305i
$595$	1.00000			0.0409960
$596$	6.00000			0.245770
$597$			9.54400i			0.390610i
$598$			3.68399i			0.150650i
$599$	13.0880			0.534761			0.267381	−	0.963591i	$-0.413842\pi$
$599$	13.0880			0.534761			0.267381	+	0.963591i	$0.413842\pi$
$600$		−	1.00000i		−	0.0408248i
$601$	−13.4560			−0.548882			−0.274441	−	0.961604i	$-0.588493\pi$
$601$	−13.4560			−0.548882			−0.274441	+	0.961604i	$0.588493\pi$
$602$	−9.77200			−0.398277
$603$	−7.54400			−0.307216
$604$	−16.7720			−0.682443
$605$			10.0000i			0.406558i
$606$		−	5.54400i		−	0.225210i
$607$			24.0000i			0.974130i	0.873366	+	0.487065i	$0.161933\pi$
$607$			24.0000i			0.974130i	−0.873366	+	0.487065i	$0.838067\pi$
$608$	0.772002			0.0313088
$609$		−	7.77200i		−	0.314937i
$610$			4.22800i			0.171187i
$611$		0			0
$612$			1.00000i			0.0404226i
$613$	−28.8600			−1.16564			−0.582822	−	0.812600i	$-0.698052\pi$
$613$	−28.8600			−1.16564			−0.582822	+	0.812600i	$0.698052\pi$
$614$		−	28.0000i		−	1.12999i
$615$			7.77200i			0.313397i
$616$		−	1.00000i		−	0.0402911i
$617$	33.5440			1.35043			0.675215	−	0.737621i	$-0.264051\pi$
$617$	33.5440			1.35043			0.675215	+	0.737621i	$0.264051\pi$
$618$	−0.455996			−0.0183429
$619$	13.7720			0.553543			0.276772	−	0.960936i	$-0.410735\pi$
$619$	13.7720			0.553543			0.276772	+	0.960936i	$0.410735\pi$
$620$	7.77200			0.312131
$621$			0.772002i			0.0309794i
$622$	1.77200			0.0710508
$623$			8.31601i			0.333174i
$624$		−	4.77200i		−	0.191033i
$625$	1.00000			0.0400000
$626$	−17.0880			−0.682974
$627$		−	0.772002i		−	0.0308308i
$628$	24.8600			0.992022
$629$	−4.77200	+	3.77200i	−0.190272	+	0.150400i
$630$	−1.00000			−0.0398410
$631$		−	21.3160i		−	0.848577i	−0.905527	−	0.424288i	$-0.860524\pi$
$631$		−	21.3160i		−	0.848577i	0.905527	−	0.424288i	$-0.139476\pi$
$632$	−5.54400			−0.220529
$633$	19.7720			0.785867
$634$			26.4040i			1.04864i
$635$			12.3160i			0.488746i
$636$	6.54400			0.259487
$637$		−	28.6320i		−	1.13444i
$638$	−7.77200			−0.307697
$639$	−6.00000			−0.237356
$640$	−1.00000			−0.0395285
$641$	8.86001			0.349949			0.174975	−	0.984573i	$-0.444016\pi$
$641$	8.86001			0.349949			0.174975	+	0.984573i	$0.444016\pi$
$642$		−	0.772002i		−	0.0304685i
$643$		−	13.0000i		−	0.512670i	−0.966588	−	0.256335i	$-0.917485\pi$
$643$		−	13.0000i		−	0.512670i	0.966588	−	0.256335i	$-0.0825150\pi$
$644$		−	0.772002i		−	0.0304211i
$645$	9.77200			0.384772
$646$		−	0.772002i		−	0.0303740i
$647$		−	2.31601i		−	0.0910516i	−0.998963	−	0.0455258i	$-0.985504\pi$
$647$		−	2.31601i		−	0.0910516i	0.998963	−	0.0455258i	$-0.0144963\pi$
$648$		−	1.00000i		−	0.0392837i
$649$			9.54400i			0.374635i
$650$	4.77200			0.187173
$651$		−	7.77200i		−	0.304609i
$652$		−	20.5440i		−	0.804565i
$653$			17.0880i			0.668705i	0.942448	+	0.334353i	$0.108518\pi$
$653$			17.0880i			0.668705i	−0.942448	+	0.334353i	$0.891482\pi$
$654$	−7.00000			−0.273722
$655$	−17.5440			−0.685501
$656$	7.77200			0.303446
$657$	8.77200			0.342228
$658$		0			0
$659$	−15.0880			−0.587745			−0.293873	−	0.955845i	$-0.594944\pi$
$659$	−15.0880			−0.587745			−0.293873	+	0.955845i	$0.594944\pi$
$660$			1.00000i			0.0389249i
$661$		−	2.08801i		−	0.0812141i	−0.999175	−	0.0406070i	$-0.987071\pi$
$661$		−	2.08801i		−	0.0812141i	0.999175	−	0.0406070i	$-0.0129292\pi$
$662$	−0.455996			−0.0177228
$663$	−4.77200			−0.185329
$664$		−	6.77200i		−	0.262805i
$665$	0.772002			0.0299369
$666$	4.77200	−	3.77200i	0.184911	−	0.146162i
$667$	−6.00000			−0.232321
$668$			14.3160i			0.553903i
$669$	25.7720			0.996403
$670$	−7.54400			−0.291450
$671$		−	4.22800i		−	0.163220i
$672$			1.00000i			0.0385758i
$673$	42.3160			1.63116			0.815581	−	0.578643i	$-0.196417\pi$
$673$	42.3160			1.63116			0.815581	+	0.578643i	$0.196417\pi$
$674$			24.3160i			0.936618i
$675$	1.00000			0.0384900
$676$	9.77200			0.375846
$677$	−19.2280			−0.738992			−0.369496	−	0.929232i	$-0.620470\pi$
$677$	−19.2280			−0.738992			−0.369496	+	0.929232i	$0.620470\pi$
$678$	11.3160			0.434589
$679$		−	2.22800i		−	0.0855027i
$680$			1.00000i			0.0383482i
$681$		−	1.77200i		−	0.0679033i
$682$	−7.77200			−0.297605
$683$		−	37.3160i		−	1.42786i	−0.700218	−	0.713929i	$-0.746914\pi$
$683$		−	37.3160i		−	1.42786i	0.700218	−	0.713929i	$-0.253086\pi$
$684$			0.772002i			0.0295182i
$685$		−	15.0880i		−	0.576483i
$686$			13.0000i			0.496342i
$687$	3.54400			0.135212
$688$		−	9.77200i		−	0.372554i
$689$			31.2280i			1.18969i
$690$			0.772002i			0.0293896i
$691$	23.7720			0.904330			0.452165	−	0.891934i	$-0.350652\pi$
$691$	23.7720			0.904330			0.452165	+	0.891934i	$0.350652\pi$
$692$	−15.0000			−0.570214
$693$	1.00000			0.0379869
$694$	6.45600			0.245066
$695$			5.31601i			0.201648i
$696$	7.77200			0.294597
$697$		−	7.77200i		−	0.294386i
$698$		−	6.00000i		−	0.227103i
$699$	12.0000			0.453882
$700$	−1.00000			−0.0377964
$701$		−	28.4560i		−	1.07477i	−0.843338	−	0.537384i	$-0.819413\pi$
$701$		−	28.4560i		−	1.07477i	0.843338	−	0.537384i	$-0.180587\pi$
$702$	4.77200			0.180108
$703$	−3.68399	+	2.91199i	−0.138944	+	0.109828i
$704$	1.00000			0.0376889
$705$		0			0
$706$	28.2280			1.06237
$707$	−5.54400			−0.208504
$708$		−	9.54400i		−	0.358686i
$709$		−	1.45600i		−	0.0546811i	−0.999626	−	0.0273405i	$-0.991296\pi$
$709$		−	1.45600i		−	0.0546811i	0.999626	−	0.0273405i	$-0.00870385\pi$
$710$	−6.00000			−0.225176
$711$		−	5.54400i		−	0.207916i
$712$	−8.31601			−0.311655
$713$	−6.00000			−0.224702
$714$	1.00000			0.0374241
$715$	−4.77200			−0.178463
$716$			7.54400i			0.281933i
$717$		−	13.7720i		−	0.514325i
$718$		−	21.5440i		−	0.804015i
$719$	−12.0000			−0.447524			−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000			−0.447524			−0.223762	+	0.974644i	$0.571834\pi$
$720$		−	1.00000i		−	0.0372678i
$721$			0.455996i			0.0169822i
$722$			18.4040i			0.684926i
$723$			16.0000i			0.595046i
$724$	−6.45600			−0.239935
$725$			7.77200i			0.288645i
$726$			10.0000i			0.371135i
$727$		−	16.1760i		−	0.599935i	−0.953949	−	0.299968i	$-0.903024\pi$
$727$		−	16.1760i		−	0.599935i	0.953949	−	0.299968i	$-0.0969759\pi$
$728$	−4.77200			−0.176862
$729$	1.00000			0.0370370
$730$	8.77200			0.324666
$731$	−9.77200			−0.361431
$732$			4.22800i			0.156271i
$733$	−39.3160			−1.45217			−0.726085	−	0.687605i	$-0.758662\pi$
$733$	−39.3160			−1.45217			−0.726085	+	0.687605i	$0.758662\pi$
$734$			18.0880i			0.667641i
$735$		−	6.00000i		−	0.221313i
$736$	0.772002			0.0284564
$737$	7.54400			0.277887
$738$			7.77200i			0.286091i
$739$	−7.13999			−0.262649			−0.131324	−	0.991339i	$-0.541923\pi$
$739$	−7.13999			−0.262649			−0.131324	+	0.991339i	$0.541923\pi$
$740$	4.77200	−	3.77200i	0.175422	−	0.138662i
$741$	−3.68399			−0.135335
$742$		−	6.54400i		−	0.240238i
$743$	−10.8600			−0.398415			−0.199208	−	0.979957i	$-0.563837\pi$
$743$	−10.8600			−0.398415			−0.199208	+	0.979957i	$0.563837\pi$
$744$	7.77200			0.284935
$745$			6.00000i			0.219823i
$746$			4.45600i			0.163146i
$747$	6.77200			0.247775
$748$		−	1.00000i		−	0.0365636i
$749$	−0.772002			−0.0282083
$750$	1.00000			0.0365148
$751$	−34.6320			−1.26374			−0.631870	−	0.775074i	$-0.717712\pi$
$751$	−34.6320			−1.26374			−0.631870	+	0.775074i	$0.717712\pi$
$752$		0			0
$753$			7.08801i			0.258301i
$754$			37.0880i			1.35067i
$755$		−	16.7720i		−	0.610396i
$756$	−1.00000			−0.0363696
$757$		−	46.4920i		−	1.68978i	−0.534939	−	0.844891i	$-0.679665\pi$
$757$		−	46.4920i		−	1.68978i	0.534939	−	0.844891i	$-0.320335\pi$
$758$		−	6.45600i		−	0.234492i
$759$		−	0.772002i		−	0.0280219i
$760$			0.772002i			0.0280035i
$761$	−53.4920			−1.93908			−0.969542	−	0.244925i	$-0.921237\pi$
$761$	−53.4920			−1.93908			−0.969542	+	0.244925i	$0.921237\pi$
$762$			12.3160i			0.446162i
$763$			7.00000i			0.253417i
$764$		−	4.54400i		−	0.164396i
$765$	−1.00000			−0.0361551
$766$	10.3160			0.372732
$767$	45.5440			1.64450
$768$	−1.00000			−0.0360844
$769$			9.54400i			0.344166i	0.985082	+	0.172083i	$0.0550497\pi$
$769$			9.54400i			0.344166i	−0.985082	+	0.172083i	$0.944950\pi$
$770$	1.00000			0.0360375
$771$		−	12.7720i		−	0.459972i
$772$		−	23.5440i		−	0.847367i
$773$	−17.6320			−0.634179			−0.317090	−	0.948396i	$-0.602706\pi$
$773$	−17.6320			−0.634179			−0.317090	+	0.948396i	$0.602706\pi$
$774$	9.77200			0.351247
$775$			7.77200i			0.279179i
$776$	2.22800			0.0799805
$777$	−3.77200	−	4.77200i	−0.135320	−	0.171195i
$778$	−1.77200			−0.0635293
$779$		−	6.00000i		−	0.214972i
$780$	4.77200			0.170865
$781$	6.00000			0.214697
$782$		−	0.772002i		−	0.0276067i
$783$			7.77200i			0.277749i
$784$	−6.00000			−0.214286
$785$			24.8600i			0.887292i
$786$	−17.5440			−0.625774
$787$	−20.1760			−0.719197			−0.359599	−	0.933107i	$-0.617086\pi$
$787$	−20.1760			−0.719197			−0.359599	+	0.933107i	$0.617086\pi$
$788$	−3.22800			−0.114993
$789$	−13.7720			−0.490296
$790$		−	5.54400i		−	0.197247i
$791$		−	11.3160i		−	0.402351i
$792$			1.00000i			0.0355335i
$793$	−20.1760			−0.716471
$794$		−	15.5440i		−	0.551636i
$795$			6.54400i			0.232092i
$796$			9.54400i			0.338278i
$797$		−	7.08801i		−	0.251070i	−0.992089	−	0.125535i	$-0.959935\pi$
$797$		−	7.08801i		−	0.251070i	0.992089	−	0.125535i	$-0.0400648\pi$
$798$	0.772002			0.0273286
$799$		0			0
$800$		−	1.00000i		−	0.0353553i
$801$		−	8.31601i		−	0.293832i
$802$	−2.31601			−0.0817810
$803$	−8.77200			−0.309557
$804$	−7.54400			−0.266056
$805$	0.772002			0.0272095
$806$			37.0880i			1.30637i
$807$	16.3160			0.574351
$808$		−	5.54400i		−	0.195037i
$809$		−	21.6840i		−	0.762369i	−0.924499	−	0.381184i	$-0.875516\pi$
$809$		−	21.6840i		−	0.762369i	0.924499	−	0.381184i	$-0.124484\pi$
$810$	1.00000			0.0351364
$811$	21.5440			0.756512			0.378256	−	0.925701i	$-0.376524\pi$
$811$	21.5440			0.756512			0.378256	+	0.925701i	$0.376524\pi$
$812$		−	7.77200i		−	0.272744i
$813$	−11.0880			−0.388873
$814$	−4.77200	+	3.77200i	−0.167259	+	0.132209i
$815$	20.5440			0.719625
$816$			1.00000i			0.0350070i
$817$	−7.54400			−0.263931
$818$	4.00000			0.139857
$819$		−	4.77200i		−	0.166747i
$820$			7.77200i			0.271410i
$821$	−36.9480			−1.28949			−0.644747	−	0.764396i	$-0.723037\pi$
$821$	−36.9480			−1.28949			−0.644747	+	0.764396i	$0.723037\pi$
$822$		−	15.0880i		−	0.526255i
$823$	5.86001			0.204267			0.102134	−	0.994771i	$-0.467433\pi$
$823$	5.86001			0.204267			0.102134	+	0.994771i	$0.467433\pi$
$824$	−0.455996			−0.0158854
$825$	−1.00000			−0.0348155
$826$	−9.54400			−0.332078
$827$			47.3160i			1.64534i	0.568520	+	0.822669i	$0.307516\pi$
$827$			47.3160i			1.64534i	−0.568520	+	0.822669i	$0.692484\pi$
$828$			0.772002i			0.0268289i
$829$			47.0000i			1.63238i	0.577785	+	0.816189i	$0.303917\pi$
$829$			47.0000i			1.63238i	−0.577785	+	0.816189i	$0.696083\pi$
$830$	6.77200			0.235060
$831$			14.7720i			0.512435i
$832$		−	4.77200i		−	0.165439i
$833$			6.00000i			0.207888i
$834$			5.31601i			0.184078i
$835$	−14.3160			−0.495426
$836$		−	0.772002i		−	0.0267002i
$837$			7.77200i			0.268640i
$838$		−	29.8600i		−	1.03150i
$839$	31.5440			1.08902			0.544510	−	0.838754i	$-0.316716\pi$
$839$	31.5440			1.08902			0.544510	+	0.838754i	$0.316716\pi$
$840$	−1.00000			−0.0345033
$841$	−31.4040			−1.08290
$842$	−6.00000			−0.206774
$843$		−	4.77200i		−	0.164356i
$844$	19.7720			0.680580
$845$			9.77200i			0.336167i
$846$		0			0
$847$	10.0000			0.343604
$848$	6.54400			0.224722
$849$		−	10.7720i		−	0.369694i
$850$	−1.00000			−0.0342997
$851$	−3.68399	+	2.91199i	−0.126286	+	0.0998218i
$852$	−6.00000			−0.205557
$853$		−	3.86001i		−	0.132164i	−0.997814	−	0.0660821i	$-0.978950\pi$
$853$		−	3.86001i		−	0.132164i	0.997814	−	0.0660821i	$-0.0210499\pi$
$854$	4.22800			0.144679
$855$	−0.772002			−0.0264019
$856$		−	0.772002i		−	0.0263865i
$857$		−	15.0000i		−	0.512390i	−0.966625	−	0.256195i	$-0.917531\pi$
$857$		−	15.0000i		−	0.512390i	0.966625	−	0.256195i	$-0.0824690\pi$
$858$	−4.77200			−0.162913
$859$			0.772002i			0.0263404i	0.999913	+	0.0131702i	$0.00419232\pi$
$859$			0.772002i			0.0263404i	−0.999913	+	0.0131702i	$0.995808\pi$
$860$	9.77200			0.333222
$861$	7.77200			0.264869
$862$	−24.0880			−0.820441
$863$	6.68399			0.227526			0.113763	−	0.993508i	$-0.463710\pi$
$863$	6.68399			0.227526			0.113763	+	0.993508i	$0.463710\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	15.0000i		−	0.510015i
$866$			0.772002i			0.0262337i
$867$	−16.0000			−0.543388
$868$		−	7.77200i		−	0.263799i
$869$			5.54400i			0.188067i
$870$			7.77200i			0.263496i
$871$		−	36.0000i		−	1.21981i
$872$	−7.00000			−0.237050
$873$			2.22800i			0.0754063i
$874$		−	0.595987i		−	0.0201596i
$875$		−	1.00000i		−	0.0338062i
$876$	8.77200			0.296378
$877$	−17.7720			−0.600118			−0.300059	−	0.953921i	$-0.597006\pi$
$877$	−17.7720			−0.600118			−0.300059	+	0.953921i	$0.597006\pi$
$878$	12.2280			0.412675
$879$	9.00000			0.303562
$880$			1.00000i			0.0337100i
$881$	−32.2280			−1.08579			−0.542894	−	0.839801i	$-0.682672\pi$
$881$	−32.2280			−1.08579			−0.542894	+	0.839801i	$0.682672\pi$
$882$		−	6.00000i		−	0.202031i
$883$			36.0880i			1.21446i	0.794527	+	0.607229i	$0.207719\pi$
$883$			36.0880i			1.21446i	−0.794527	+	0.607229i	$0.792281\pi$
$884$	−4.77200			−0.160500
$885$	9.54400			0.320818
$886$		−	20.0000i		−	0.671913i
$887$	−53.3160			−1.79018			−0.895088	−	0.445889i	$-0.852888\pi$
$887$	−53.3160			−1.79018			−0.895088	+	0.445889i	$0.852888\pi$
$888$	4.77200	−	3.77200i	0.160138	−	0.126580i
$889$	12.3160			0.413066
$890$		−	8.31601i		−	0.278753i
$891$	−1.00000			−0.0335013
$892$	25.7720			0.862910
$893$		0			0
$894$			6.00000i			0.200670i
$895$	−7.54400			−0.252168
$896$			1.00000i			0.0334077i
$897$	−3.68399			−0.123005
$898$	−2.00000			−0.0667409
$899$	−60.4040			−2.01459
$900$	1.00000			0.0333333
$901$		−	6.54400i		−	0.218012i
$902$		−	7.77200i		−	0.258779i
$903$		−	9.77200i		−	0.325192i
$904$	11.3160			0.376365
$905$		−	6.45600i		−	0.214605i
$906$		−	16.7720i		−	0.557212i
$907$		−	38.7720i		−	1.28740i	−0.765277	−	0.643702i	$-0.777398\pi$
$907$		−	38.7720i		−	1.28740i	0.765277	−	0.643702i	$-0.222602\pi$
$908$		−	1.77200i		−	0.0588059i
$909$	5.54400			0.183883
$910$		−	4.77200i		−	0.158190i
$911$			24.0000i			0.795155i	0.917568	+	0.397578i	$0.130149\pi$
$911$			24.0000i			0.795155i	−0.917568	+	0.397578i	$0.869851\pi$
$912$			0.772002i			0.0255635i
$913$	−6.77200			−0.224121
$914$	−8.68399			−0.287241
$915$	−4.22800			−0.139773
$916$	3.54400			0.117097
$917$			17.5440i			0.579354i
$918$	−1.00000			−0.0330049
$919$		−	32.0000i		−	1.05558i	−0.849374	−	0.527791i	$-0.823020\pi$
$919$		−	32.0000i		−	1.05558i	0.849374	−	0.527791i	$-0.176980\pi$
$920$			0.772002i			0.0254521i
$921$	28.0000			0.922631
$922$	−29.7720			−0.980489
$923$		−	28.6320i		−	0.942434i
$924$	1.00000			0.0328976
$925$	3.77200	+	4.77200i	0.124023	+	0.156902i
$926$	−20.6320			−0.678010
$927$		−	0.455996i		−	0.0149769i
$928$	7.77200			0.255128
$929$	37.7720			1.23926			0.619630	−	0.784894i	$-0.287283\pi$
$929$	37.7720			1.23926			0.619630	+	0.784894i	$0.287283\pi$
$930$			7.77200i			0.254854i
$931$			4.63201i			0.151808i
$932$	12.0000			0.393073
$933$			1.77200i			0.0580127i
$934$	−21.3160			−0.697481
$935$	1.00000			0.0327035
$936$	4.77200			0.155978
$937$	−41.5440			−1.35718			−0.678592	−	0.734516i	$-0.737409\pi$
$937$	−41.5440			−1.35718			−0.678592	+	0.734516i	$0.737409\pi$
$938$			7.54400i			0.246320i
$939$		−	17.0880i		−	0.557646i
$940$		0			0
$941$	−4.63201			−0.150999			−0.0754996	−	0.997146i	$-0.524055\pi$
$941$	−4.63201			−0.150999			−0.0754996	+	0.997146i	$0.524055\pi$
$942$			24.8600i			0.809983i
$943$		−	6.00000i		−	0.195387i
$944$		−	9.54400i		−	0.310631i
$945$		−	1.00000i		−	0.0325300i
$946$	−9.77200			−0.317715
$947$			36.8600i			1.19779i	0.800828	+	0.598895i	$0.204393\pi$
$947$			36.8600i			1.19779i	−0.800828	+	0.598895i	$0.795607\pi$
$948$		−	5.54400i		−	0.180061i
$949$			41.8600i			1.35883i
$950$	−0.772002			−0.0250470
$951$	−26.4040			−0.856209
$952$	1.00000			0.0324102
$953$	8.45600			0.273917			0.136958	−	0.990577i	$-0.456267\pi$
$953$	8.45600			0.273917			0.136958	+	0.990577i	$0.456267\pi$
$954$			6.54400i			0.211870i
$955$	4.54400			0.147041
$956$		−	13.7720i		−	0.445418i
$957$		−	7.77200i		−	0.251233i
$958$	18.7720			0.606496
$959$	−15.0880			−0.487217
$960$		−	1.00000i		−	0.0322749i
$961$	−29.4040			−0.948517
$962$	18.0000	+	22.7720i	0.580343	+	0.734199i
$963$	0.772002			0.0248774
$964$			16.0000i			0.515325i
$965$	23.5440			0.757908
$966$	0.772002			0.0248388
$967$			26.6320i			0.856428i	0.903677	+	0.428214i	$0.140857\pi$
$967$			26.6320i			0.856428i	−0.903677	+	0.428214i	$0.859143\pi$
$968$			10.0000i			0.321412i
$969$	0.772002			0.0248003
$970$			2.22800i			0.0715367i
$971$	8.86001			0.284331			0.142166	−	0.989843i	$-0.454593\pi$
$971$	8.86001			0.284331			0.142166	+	0.989843i	$0.454593\pi$
$972$	1.00000			0.0320750
$973$	5.31601			0.170423
$974$	19.0880			0.611619
$975$			4.77200i			0.152826i
$976$			4.22800i			0.135335i
$977$			33.0000i			1.05576i	0.849318	+	0.527882i	$0.177014\pi$
$977$			33.0000i			1.05576i	−0.849318	+	0.527882i	$0.822986\pi$
$978$	20.5440			0.656925
$979$			8.31601i			0.265781i
$980$		−	6.00000i		−	0.191663i
$981$		−	7.00000i		−	0.223493i
$982$			38.7720i			1.23726i
$983$	32.4040			1.03353			0.516764	−	0.856128i	$-0.327137\pi$
$983$	32.4040			1.03353			0.516764	+	0.856128i	$0.327137\pi$
$984$			7.77200i			0.247762i
$985$		−	3.22800i		−	0.102853i
$986$		−	7.77200i		−	0.247511i
$987$		0			0
$988$	−3.68399			−0.117203
$989$	−7.54400			−0.239885
$990$	−1.00000			−0.0317821
$991$			50.8600i			1.61562i	0.589442	+	0.807811i	$0.299348\pi$
$991$			50.8600i			1.61562i	−0.589442	+	0.807811i	$0.700652\pi$
$992$	7.77200			0.246761
$993$		−	0.455996i		−	0.0144706i
$994$			6.00000i			0.190308i
$995$	−9.54400			−0.302565
$996$	6.77200			0.214579
$997$		−	7.40401i		−	0.234487i	−0.993103	−	0.117244i	$-0.962594\pi$
$997$		−	7.40401i		−	0.234487i	0.993103	−	0.117244i	$-0.0374059\pi$
$998$	−30.3160			−0.959636
$999$	3.77200	+	4.77200i	0.119341	+	0.150979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.h.d.961.4	yes	4
3.2	odd	2		3330.2.h.j.2071.2		4
37.36	even	2	inner	1110.2.h.d.961.1	✓	4
111.110	odd	2		3330.2.h.j.2071.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.h.d.961.1	✓	4	37.36	even	2	inner
1110.2.h.d.961.4	yes	4	1.1	even	1	trivial
3330.2.h.j.2071.2		4	3.2	odd	2
3330.2.h.j.2071.3		4	111.110	odd	2

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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.00000 q^{3} -1.00000 q^{4} -1.00000i q^{5} -1.00000i q^{6} -1.00000 q^{7} -1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +4.77200i q^{13} -1.00000i q^{14} +1.00000i q^{15} +1.00000 q^{16} -1.00000i q^{17} +1.00000i q^{18} -0.772002i q^{19} +1.00000i q^{20} +1.00000 q^{21} -1.00000i q^{22} -0.772002i q^{23} +1.00000i q^{24} -1.00000 q^{25} -4.77200 q^{26} -1.00000 q^{27} +1.00000 q^{28} -7.77200i q^{29} -1.00000 q^{30} -7.77200i q^{31} +1.00000i q^{32} +1.00000 q^{33} +1.00000 q^{34} +1.00000i q^{35} -1.00000 q^{36} +(-3.77200 - 4.77200i) q^{37} +0.772002 q^{38} -4.77200i q^{39} -1.00000 q^{40} +7.77200 q^{41} +1.00000i q^{42} -9.77200i q^{43} +1.00000 q^{44} -1.00000i q^{45} +0.772002 q^{46} -1.00000 q^{48} -6.00000 q^{49} -1.00000i q^{50} +1.00000i q^{51} -4.77200i q^{52} +6.54400 q^{53} -1.00000i q^{54} +1.00000i q^{55} +1.00000i q^{56} +0.772002i q^{57} +7.77200 q^{58} -9.54400i q^{59} -1.00000i q^{60} +4.22800i q^{61} +7.77200 q^{62} -1.00000 q^{63} -1.00000 q^{64} +4.77200 q^{65} +1.00000i q^{66} -7.54400 q^{67} +1.00000i q^{68} +0.772002i q^{69} -1.00000 q^{70} -6.00000 q^{71} -1.00000i q^{72} +8.77200 q^{73} +(4.77200 - 3.77200i) q^{74} +1.00000 q^{75} +0.772002i q^{76} +1.00000 q^{77} +4.77200 q^{78} -5.54400i q^{79} -1.00000i q^{80} +1.00000 q^{81} +7.77200i q^{82} +6.77200 q^{83} -1.00000 q^{84} -1.00000 q^{85} +9.77200 q^{86} +7.77200i q^{87} +1.00000i q^{88} -8.31601i q^{89} +1.00000 q^{90} -4.77200i q^{91} +0.772002i q^{92} +7.77200i q^{93} -0.772002 q^{95} -1.00000i q^{96} +2.22800i q^{97} -6.00000i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9	\( 4 q - 4 q^{3} - 4 q^{4} - 4 q^{7} + 4 q^{9} + 4 q^{10} - 4 q^{11} + 4 q^{12} + 4 q^{16} + 4 q^{21} - 4 q^{25} - 2 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{30} + 4 q^{33} + 4 q^{34} - 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{40} + 14 q^{41} + 4 q^{44} - 14 q^{46} - 4 q^{48} - 24 q^{49} - 8 q^{53} + 14 q^{58} + 14 q^{62} - 4 q^{63} - 4 q^{64} + 2 q^{65} + 4 q^{67} - 4 q^{70} - 24 q^{71} + 18 q^{73} + 2 q^{74} + 4 q^{75} + 4 q^{77} + 2 q^{78} + 4 q^{81} + 10 q^{83} - 4 q^{84} - 4 q^{85} + 22 q^{86} + 4 q^{90} + 14 q^{95} - 4 q^{99}+O(q^{100}) \) 4 * q - 4 * q^3 - 4 * q^4 - 4 * q^7 + 4 * q^9 + 4 * q^10 - 4 * q^11 + 4 * q^12 + 4 * q^16 + 4 * q^21 - 4 * q^25 - 2 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^30 + 4 * q^33 + 4 * q^34 - 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^40 + 14 * q^41 + 4 * q^44 - 14 * q^46 - 4 * q^48 - 24 * q^49 - 8 * q^53 + 14 * q^58 + 14 * q^62 - 4 * q^63 - 4 * q^64 + 2 * q^65 + 4 * q^67 - 4 * q^70 - 24 * q^71 + 18 * q^73 + 2 * q^74 + 4 * q^75 + 4 * q^77 + 2 * q^78 + 4 * q^81 + 10 * q^83 - 4 * q^84 - 4 * q^85 + 22 * q^86 + 4 * q^90 + 14 * q^95 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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