LMFDB - Embedded newform 1155.2.c.a.694.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

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, 1, 0, 0]))

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

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

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.a.694.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} -1.00000 q^{11} -1.00000i q^{12} -4.00000i q^{13} -1.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} -1.00000 q^{16} -2.00000i q^{17} +1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} -1.00000 q^{21} +1.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -4.00000 q^{26} +1.00000i q^{27} -1.00000i q^{28} -4.00000 q^{29} +(2.00000 + 1.00000i) q^{30} +2.00000 q^{31} -5.00000i q^{32} +1.00000i q^{33} -2.00000 q^{34} +(-1.00000 + 2.00000i) q^{35} -1.00000 q^{36} -4.00000i q^{37} -4.00000 q^{39} +(-3.00000 + 6.00000i) q^{40} -10.0000 q^{41} +1.00000i q^{42} +4.00000i q^{43} -1.00000 q^{44} +(2.00000 + 1.00000i) q^{45} +6.00000 q^{46} +1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000 q^{51} -4.00000i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(2.00000 + 1.00000i) q^{55} -3.00000 q^{56} +4.00000i q^{58} -4.00000 q^{59} +(-1.00000 + 2.00000i) q^{60} -2.00000 q^{61} -2.00000i q^{62} +1.00000i q^{63} -7.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +1.00000 q^{66} +8.00000i q^{67} -2.00000i q^{68} +6.00000 q^{69} +(2.00000 + 1.00000i) q^{70} -8.00000 q^{71} +3.00000i q^{72} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +1.00000i q^{77} +4.00000i q^{78} +14.0000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} +10.0000i q^{82} -14.0000i q^{83} -1.00000 q^{84} +(-2.00000 + 4.00000i) q^{85} +4.00000 q^{86} +4.00000i q^{87} +3.00000i q^{88} +12.0000 q^{89} +(1.00000 - 2.00000i) q^{90} -4.00000 q^{91} +6.00000i q^{92} -2.00000i q^{93} -5.00000 q^{96} -14.0000i q^{97} +1.00000i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9	$ 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{14} - 2 q^{15} - 2 q^{16} - 4 q^{20} - 2 q^{21} - 6 q^{24} + 6 q^{25} - 8 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} - 4 q^{34} - 2 q^{35} - 2 q^{36} - 8 q^{39} - 6 q^{40} - 20 q^{41} - 2 q^{44} + 4 q^{45} + 12 q^{46} - 2 q^{49} + 8 q^{50} - 4 q^{51} + 2 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{59} - 2 q^{60} - 4 q^{61} - 14 q^{64} - 8 q^{65} + 2 q^{66} + 12 q^{69} + 4 q^{70} - 16 q^{71} - 8 q^{74} + 8 q^{75} + 28 q^{79} + 4 q^{80} + 2 q^{81} - 2 q^{84} - 4 q^{85} + 8 q^{86} + 24 q^{89} + 2 q^{90} - 8 q^{91} - 10 q^{96} + 2 q^{99}+O(q^{100}) $ 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9 - 2 * q^10 - 2 * q^11 - 2 * q^14 - 2 * q^15 - 2 * q^16 - 4 * q^20 - 2 * q^21 - 6 * q^24 + 6 * q^25 - 8 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 - 4 * q^34 - 2 * q^35 - 2 * q^36 - 8 * q^39 - 6 * q^40 - 20 * q^41 - 2 * q^44 + 4 * q^45 + 12 * q^46 - 2 * q^49 + 8 * q^50 - 4 * q^51 + 2 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^59 - 2 * q^60 - 4 * q^61 - 14 * q^64 - 8 * q^65 + 2 * q^66 + 12 * q^69 + 4 * q^70 - 16 * q^71 - 8 * q^74 + 8 * q^75 + 28 * q^79 + 4 * q^80 + 2 * q^81 - 2 * q^84 - 4 * q^85 + 8 * q^86 + 24 * q^89 + 2 * q^90 - 8 * q^91 - 10 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i	−0.935414	−	0.353553i	$-0.884973\pi$
$2$		−	1.00000i		−	0.707107i	0.935414	−	0.353553i	$-0.115027\pi$
$3$		−	1.00000i		−	0.577350i
$3$		−	1.00000i		−	0.577350i
$4$	1.00000			0.500000
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$5$	−2.00000	−	1.00000i	−0.894427	−	0.447214i
$6$	−1.00000			−0.408248
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		−	3.00000i		−	1.06066i
$9$	−1.00000			−0.333333
$10$	−1.00000	+	2.00000i	−0.316228	+	0.632456i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$		−	1.00000i		−	0.288675i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	−1.00000			−0.267261
$15$	−1.00000	+	2.00000i	−0.258199	+	0.516398i
$16$	−1.00000			−0.250000
$17$		−	2.00000i		−	0.485071i	−0.970143	−	0.242536i	$-0.922021\pi$
$17$		−	2.00000i		−	0.485071i	0.970143	−	0.242536i	$-0.0779791\pi$
$18$			1.00000i			0.235702i
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	−2.00000	−	1.00000i	−0.447214	−	0.223607i
$21$	−1.00000			−0.218218
$22$			1.00000i			0.213201i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−3.00000			−0.612372
$25$	3.00000	+	4.00000i	0.600000	+	0.800000i
$26$	−4.00000			−0.784465
$27$			1.00000i			0.192450i
$28$		−	1.00000i		−	0.188982i
$29$	−4.00000			−0.742781			−0.371391	−	0.928477i	$-0.621119\pi$
$29$	−4.00000			−0.742781			−0.371391	+	0.928477i	$0.621119\pi$
$30$	2.00000	+	1.00000i	0.365148	+	0.182574i
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$		−	5.00000i		−	0.883883i
$33$			1.00000i			0.174078i
$34$	−2.00000			−0.342997
$35$	−1.00000	+	2.00000i	−0.169031	+	0.338062i
$36$	−1.00000			−0.166667
$37$		−	4.00000i		−	0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$		−	4.00000i		−	0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$		0			0
$39$	−4.00000			−0.640513
$40$	−3.00000	+	6.00000i	−0.474342	+	0.948683i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$			1.00000i			0.154303i
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	−1.00000			−0.150756
$45$	2.00000	+	1.00000i	0.298142	+	0.149071i
$46$	6.00000			0.884652
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$			1.00000i			0.144338i
$49$	−1.00000			−0.142857
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	−2.00000			−0.280056
$52$		−	4.00000i		−	0.554700i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	1.00000			0.136083
$55$	2.00000	+	1.00000i	0.269680	+	0.134840i
$56$	−3.00000			−0.400892
$57$		0			0
$58$			4.00000i			0.525226i
$59$	−4.00000			−0.520756			−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000			−0.520756			−0.260378	+	0.965507i	$0.583847\pi$
$60$	−1.00000	+	2.00000i	−0.129099	+	0.258199i
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$		−	2.00000i		−	0.254000i
$63$			1.00000i			0.125988i
$64$	−7.00000			−0.875000
$65$	−4.00000	+	8.00000i	−0.496139	+	0.992278i
$66$	1.00000			0.123091
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$		−	2.00000i		−	0.242536i
$69$	6.00000			0.722315
$70$	2.00000	+	1.00000i	0.239046	+	0.119523i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$			3.00000i			0.353553i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	−4.00000			−0.464991
$75$	4.00000	−	3.00000i	0.461880	−	0.346410i
$76$		0			0
$77$			1.00000i			0.113961i
$78$			4.00000i			0.452911i
$79$	14.0000			1.57512			0.787562	−	0.616236i	$-0.211343\pi$
$79$	14.0000			1.57512			0.787562	+	0.616236i	$0.211343\pi$
$80$	2.00000	+	1.00000i	0.223607	+	0.111803i
$81$	1.00000			0.111111
$82$			10.0000i			1.10432i
$83$		−	14.0000i		−	1.53670i	−0.640030	−	0.768350i	$-0.721078\pi$
$83$		−	14.0000i		−	1.53670i	0.640030	−	0.768350i	$-0.278922\pi$
$84$	−1.00000			−0.109109
$85$	−2.00000	+	4.00000i	−0.216930	+	0.433861i
$86$	4.00000			0.431331
$87$			4.00000i			0.428845i
$88$			3.00000i			0.319801i
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	1.00000	−	2.00000i	0.105409	−	0.210819i
$91$	−4.00000			−0.419314
$92$			6.00000i			0.625543i
$93$		−	2.00000i		−	0.207390i
$94$		0			0
$95$		0			0
$96$	−5.00000			−0.510310
$97$		−	14.0000i		−	1.42148i	−0.703452	−	0.710742i	$-0.748359\pi$
$97$		−	14.0000i		−	1.42148i	0.703452	−	0.710742i	$-0.251641\pi$
$98$			1.00000i			0.101015i
$99$	1.00000			0.100504
$100$	3.00000	+	4.00000i	0.300000	+	0.400000i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$			2.00000i			0.198030i
$103$		−	8.00000i		−	0.788263i	−0.919054	−	0.394132i	$-0.871045\pi$
$103$		−	8.00000i		−	0.788263i	0.919054	−	0.394132i	$-0.128955\pi$
$104$	−12.0000			−1.17670
$105$	2.00000	+	1.00000i	0.195180	+	0.0975900i
$106$	−6.00000			−0.582772
$107$		−	8.00000i		−	0.773389i	−0.922208	−	0.386695i	$-0.873617\pi$
$107$		−	8.00000i		−	0.773389i	0.922208	−	0.386695i	$-0.126383\pi$
$108$			1.00000i			0.0962250i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$	1.00000	−	2.00000i	0.0953463	−	0.190693i
$111$	−4.00000			−0.379663
$112$			1.00000i			0.0944911i
$113$			6.00000i			0.564433i	0.959351	+	0.282216i	$0.0910696\pi$
$113$			6.00000i			0.564433i	−0.959351	+	0.282216i	$0.908930\pi$
$114$		0			0
$115$	6.00000	−	12.0000i	0.559503	−	1.11901i
$116$	−4.00000			−0.371391
$117$			4.00000i			0.369800i
$118$			4.00000i			0.368230i
$119$	−2.00000			−0.183340
$120$	6.00000	+	3.00000i	0.547723	+	0.273861i
$121$	1.00000			0.0909091
$122$			2.00000i			0.181071i
$123$			10.0000i			0.901670i
$124$	2.00000			0.179605
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	1.00000			0.0890871
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$		−	3.00000i		−	0.265165i
$129$	4.00000			0.352180
$130$	8.00000	+	4.00000i	0.701646	+	0.350823i
$131$	4.00000			0.349482			0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000			0.349482			0.174741	+	0.984614i	$0.444091\pi$
$132$			1.00000i			0.0870388i
$133$		0			0
$134$	8.00000			0.691095
$135$	1.00000	−	2.00000i	0.0860663	−	0.172133i
$136$	−6.00000			−0.514496
$137$			18.0000i			1.53784i	0.639343	+	0.768922i	$0.279207\pi$
$137$			18.0000i			1.53784i	−0.639343	+	0.768922i	$0.720793\pi$
$138$		−	6.00000i		−	0.510754i
$139$	16.0000			1.35710			0.678551	−	0.734553i	$-0.262608\pi$
$139$	16.0000			1.35710			0.678551	+	0.734553i	$0.262608\pi$
$140$	−1.00000	+	2.00000i	−0.0845154	+	0.169031i
$141$		0			0
$142$			8.00000i			0.671345i
$143$			4.00000i			0.334497i
$144$	1.00000			0.0833333
$145$	8.00000	+	4.00000i	0.664364	+	0.332182i
$146$		0			0
$147$			1.00000i			0.0824786i
$148$		−	4.00000i		−	0.328798i
$149$	20.0000			1.63846			0.819232	−	0.573462i	$-0.194400\pi$
$149$	20.0000			1.63846			0.819232	+	0.573462i	$0.194400\pi$
$150$	−3.00000	−	4.00000i	−0.244949	−	0.326599i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$		0			0
$153$			2.00000i			0.161690i
$154$	1.00000			0.0805823
$155$	−4.00000	−	2.00000i	−0.321288	−	0.160644i
$156$	−4.00000			−0.320256
$157$		−	6.00000i		−	0.478852i	−0.970915	−	0.239426i	$-0.923041\pi$
$157$		−	6.00000i		−	0.478852i	0.970915	−	0.239426i	$-0.0769593\pi$
$158$		−	14.0000i		−	1.11378i
$159$	−6.00000			−0.475831
$160$	−5.00000	+	10.0000i	−0.395285	+	0.790569i
$161$	6.00000			0.472866
$162$		−	1.00000i		−	0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−10.0000			−0.780869
$165$	1.00000	−	2.00000i	0.0778499	−	0.155700i
$166$	−14.0000			−1.08661
$167$		−	6.00000i		−	0.464294i	−0.972681	−	0.232147i	$-0.925425\pi$
$167$		−	6.00000i		−	0.464294i	0.972681	−	0.232147i	$-0.0745750\pi$
$168$			3.00000i			0.231455i
$169$	−3.00000			−0.230769
$170$	4.00000	+	2.00000i	0.306786	+	0.153393i
$171$		0			0
$172$			4.00000i			0.304997i
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	4.00000			0.303239
$175$	4.00000	−	3.00000i	0.302372	−	0.226779i
$176$	1.00000			0.0753778
$177$			4.00000i			0.300658i
$178$		−	12.0000i		−	0.899438i
$179$	−4.00000			−0.298974			−0.149487	−	0.988764i	$-0.547762\pi$
$179$	−4.00000			−0.298974			−0.149487	+	0.988764i	$0.547762\pi$
$180$	2.00000	+	1.00000i	0.149071	+	0.0745356i
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$			4.00000i			0.296500i
$183$			2.00000i			0.147844i
$184$	18.0000			1.32698
$185$	−4.00000	+	8.00000i	−0.294086	+	0.588172i
$186$	−2.00000			−0.146647
$187$			2.00000i			0.146254i
$188$		0			0
$189$	1.00000			0.0727393
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$			7.00000i			0.505181i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	−14.0000			−1.00514
$195$	8.00000	+	4.00000i	0.572892	+	0.286446i
$196$	−1.00000			−0.0714286
$197$		−	22.0000i		−	1.56744i	−0.621117	−	0.783718i	$-0.713321\pi$
$197$		−	22.0000i		−	1.56744i	0.621117	−	0.783718i	$-0.286679\pi$
$198$		−	1.00000i		−	0.0710669i
$199$	−2.00000			−0.141776			−0.0708881	−	0.997484i	$-0.522583\pi$
$199$	−2.00000			−0.141776			−0.0708881	+	0.997484i	$0.522583\pi$
$200$	12.0000	−	9.00000i	0.848528	−	0.636396i
$201$	8.00000			0.564276
$202$		−	6.00000i		−	0.422159i
$203$			4.00000i			0.280745i
$204$	−2.00000			−0.140028
$205$	20.0000	+	10.0000i	1.39686	+	0.698430i
$206$	−8.00000			−0.557386
$207$		−	6.00000i		−	0.417029i
$208$			4.00000i			0.277350i
$209$		0			0
$210$	1.00000	−	2.00000i	0.0690066	−	0.138013i
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$		−	6.00000i		−	0.412082i
$213$			8.00000i			0.548151i
$214$	−8.00000			−0.546869
$215$	4.00000	−	8.00000i	0.272798	−	0.545595i
$216$	3.00000			0.204124
$217$		−	2.00000i		−	0.135769i
$218$			14.0000i			0.948200i
$219$		0			0
$220$	2.00000	+	1.00000i	0.134840	+	0.0674200i
$221$	−8.00000			−0.538138
$222$			4.00000i			0.268462i
$223$		−	24.0000i		−	1.60716i	−0.595198	−	0.803579i	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$	−5.00000			−0.334077
$225$	−3.00000	−	4.00000i	−0.200000	−	0.266667i
$226$	6.00000			0.399114
$227$		−	10.0000i		−	0.663723i	−0.943328	−	0.331862i	$-0.892323\pi$
$227$		−	10.0000i		−	0.663723i	0.943328	−	0.331862i	$-0.107677\pi$
$228$		0			0
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	−12.0000	−	6.00000i	−0.791257	−	0.395628i
$231$	1.00000			0.0657952
$232$			12.0000i			0.787839i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	4.00000			0.261488
$235$		0			0
$236$	−4.00000			−0.260378
$237$		−	14.0000i		−	0.909398i
$238$			2.00000i			0.129641i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$	1.00000	−	2.00000i	0.0645497	−	0.129099i
$241$	−2.00000			−0.128831			−0.0644157	−	0.997923i	$-0.520518\pi$
$241$	−2.00000			−0.128831			−0.0644157	+	0.997923i	$0.520518\pi$
$242$		−	1.00000i		−	0.0642824i
$243$		−	1.00000i		−	0.0641500i
$244$	−2.00000			−0.128037
$245$	2.00000	+	1.00000i	0.127775	+	0.0638877i
$246$	10.0000			0.637577
$247$		0			0
$248$		−	6.00000i		−	0.381000i
$249$	−14.0000			−0.887214
$250$	−11.0000	+	2.00000i	−0.695701	+	0.126491i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$			1.00000i			0.0629941i
$253$		−	6.00000i		−	0.377217i
$254$	8.00000			0.501965
$255$	4.00000	+	2.00000i	0.250490	+	0.125245i
$256$	−17.0000			−1.06250
$257$		−	2.00000i		−	0.124757i	−0.998053	−	0.0623783i	$-0.980131\pi$
$257$		−	2.00000i		−	0.124757i	0.998053	−	0.0623783i	$-0.0198685\pi$
$258$		−	4.00000i		−	0.249029i
$259$	−4.00000			−0.248548
$260$	−4.00000	+	8.00000i	−0.248069	+	0.496139i
$261$	4.00000			0.247594
$262$		−	4.00000i		−	0.247121i
$263$		−	12.0000i		−	0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$		−	12.0000i		−	0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$	3.00000			0.184637
$265$	−6.00000	+	12.0000i	−0.368577	+	0.737154i
$266$		0			0
$267$		−	12.0000i		−	0.734388i
$268$			8.00000i			0.488678i
$269$	32.0000			1.95107			0.975537	−	0.219834i	$-0.0705517\pi$
$269$	32.0000			1.95107			0.975537	+	0.219834i	$0.0705517\pi$
$270$	−2.00000	−	1.00000i	−0.121716	−	0.0608581i
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$			2.00000i			0.121268i
$273$			4.00000i			0.242091i
$274$	18.0000			1.08742
$275$	−3.00000	−	4.00000i	−0.180907	−	0.241209i
$276$	6.00000			0.361158
$277$		−	22.0000i		−	1.32185i	−0.750451	−	0.660926i	$-0.770164\pi$
$277$		−	22.0000i		−	1.32185i	0.750451	−	0.660926i	$-0.229836\pi$
$278$		−	16.0000i		−	0.959616i
$279$	−2.00000			−0.119737
$280$	6.00000	+	3.00000i	0.358569	+	0.179284i
$281$	4.00000			0.238620			0.119310	−	0.992857i	$-0.461932\pi$
$281$	4.00000			0.238620			0.119310	+	0.992857i	$0.461932\pi$
$282$		0			0
$283$		−	20.0000i		−	1.18888i	−0.804141	−	0.594438i	$-0.797374\pi$
$283$		−	20.0000i		−	1.18888i	0.804141	−	0.594438i	$-0.202626\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	4.00000			0.236525
$287$			10.0000i			0.590281i
$288$			5.00000i			0.294628i
$289$	13.0000			0.764706
$290$	4.00000	−	8.00000i	0.234888	−	0.469776i
$291$	−14.0000			−0.820695
$292$		0			0
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	1.00000			0.0583212
$295$	8.00000	+	4.00000i	0.465778	+	0.232889i
$296$	−12.0000			−0.697486
$297$		−	1.00000i		−	0.0580259i
$298$		−	20.0000i		−	1.15857i
$299$	24.0000			1.38796
$300$	4.00000	−	3.00000i	0.230940	−	0.173205i
$301$	4.00000			0.230556
$302$		−	2.00000i		−	0.115087i
$303$		−	6.00000i		−	0.344691i
$304$		0			0
$305$	4.00000	+	2.00000i	0.229039	+	0.114520i
$306$	2.00000			0.114332
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$			1.00000i			0.0569803i
$309$	−8.00000			−0.455104
$310$	−2.00000	+	4.00000i	−0.113592	+	0.227185i
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$			12.0000i			0.679366i
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−6.00000			−0.338600
$315$	1.00000	−	2.00000i	0.0563436	−	0.112687i
$316$	14.0000			0.787562
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$			6.00000i			0.336463i
$319$	4.00000			0.223957
$320$	14.0000	+	7.00000i	0.782624	+	0.391312i
$321$	−8.00000			−0.446516
$322$		−	6.00000i		−	0.334367i
$323$		0			0
$324$	1.00000			0.0555556
$325$	16.0000	−	12.0000i	0.887520	−	0.665640i
$326$	−4.00000			−0.221540
$327$			14.0000i			0.774202i
$328$			30.0000i			1.65647i
$329$		0			0
$330$	−2.00000	−	1.00000i	−0.110096	−	0.0550482i
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$		−	14.0000i		−	0.768350i
$333$			4.00000i			0.219199i
$334$	−6.00000			−0.328305
$335$	8.00000	−	16.0000i	0.437087	−	0.874173i
$336$	1.00000			0.0545545
$337$			30.0000i			1.63420i	0.576493	+	0.817102i	$0.304421\pi$
$337$			30.0000i			1.63420i	−0.576493	+	0.817102i	$0.695579\pi$
$338$			3.00000i			0.163178i
$339$	6.00000			0.325875
$340$	−2.00000	+	4.00000i	−0.108465	+	0.216930i
$341$	−2.00000			−0.108306
$342$		0			0
$343$			1.00000i			0.0539949i
$344$	12.0000			0.646997
$345$	−12.0000	−	6.00000i	−0.646058	−	0.323029i
$346$	6.00000			0.322562
$347$		−	24.0000i		−	1.28839i	−0.764862	−	0.644194i	$-0.777193\pi$
$347$		−	24.0000i		−	1.28839i	0.764862	−	0.644194i	$-0.222807\pi$
$348$			4.00000i			0.214423i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−3.00000	−	4.00000i	−0.160357	−	0.213809i
$351$	4.00000			0.213504
$352$			5.00000i			0.266501i
$353$			22.0000i			1.17094i	0.810693	+	0.585471i	$0.199090\pi$
$353$			22.0000i			1.17094i	−0.810693	+	0.585471i	$0.800910\pi$
$354$	4.00000			0.212598
$355$	16.0000	+	8.00000i	0.849192	+	0.424596i
$356$	12.0000			0.635999
$357$			2.00000i			0.105851i
$358$			4.00000i			0.211407i
$359$	20.0000			1.05556			0.527780	−	0.849381i	$-0.323025\pi$
$359$	20.0000			1.05556			0.527780	+	0.849381i	$0.323025\pi$
$360$	3.00000	−	6.00000i	0.158114	−	0.316228i
$361$	−19.0000			−1.00000
$362$			18.0000i			0.946059i
$363$		−	1.00000i		−	0.0524864i
$364$	−4.00000			−0.209657
$365$		0			0
$366$	2.00000			0.104542
$367$			24.0000i			1.25279i	0.779506	+	0.626395i	$0.215470\pi$
$367$			24.0000i			1.25279i	−0.779506	+	0.626395i	$0.784530\pi$
$368$		−	6.00000i		−	0.312772i
$369$	10.0000			0.520579
$370$	8.00000	+	4.00000i	0.415900	+	0.207950i
$371$	−6.00000			−0.311504
$372$		−	2.00000i		−	0.103695i
$373$			18.0000i			0.932005i	0.884783	+	0.466002i	$0.154306\pi$
$373$			18.0000i			0.932005i	−0.884783	+	0.466002i	$0.845694\pi$
$374$	2.00000			0.103418
$375$	−11.0000	+	2.00000i	−0.568038	+	0.103280i
$376$		0			0
$377$			16.0000i			0.824042i
$378$		−	1.00000i		−	0.0514344i
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$		0			0
$383$		−	16.0000i		−	0.817562i	−0.912633	−	0.408781i	$-0.865954\pi$
$383$		−	16.0000i		−	0.817562i	0.912633	−	0.408781i	$-0.134046\pi$
$384$	−3.00000			−0.153093
$385$	1.00000	−	2.00000i	0.0509647	−	0.101929i
$386$	−10.0000			−0.508987
$387$		−	4.00000i		−	0.203331i
$388$		−	14.0000i		−	0.710742i
$389$	34.0000			1.72387			0.861934	−	0.507020i	$-0.169253\pi$
$389$	34.0000			1.72387			0.861934	+	0.507020i	$0.169253\pi$
$390$	4.00000	−	8.00000i	0.202548	−	0.405096i
$391$	12.0000			0.606866
$392$			3.00000i			0.151523i
$393$		−	4.00000i		−	0.201773i
$394$	−22.0000			−1.10834
$395$	−28.0000	−	14.0000i	−1.40883	−	0.704416i
$396$	1.00000			0.0502519
$397$			22.0000i			1.10415i	0.833795	+	0.552074i	$0.186163\pi$
$397$			22.0000i			1.10415i	−0.833795	+	0.552074i	$0.813837\pi$
$398$			2.00000i			0.100251i
$399$		0			0
$400$	−3.00000	−	4.00000i	−0.150000	−	0.200000i
$401$	−30.0000			−1.49813			−0.749064	−	0.662497i	$-0.769497\pi$
$401$	−30.0000			−1.49813			−0.749064	+	0.662497i	$0.769497\pi$
$402$		−	8.00000i		−	0.399004i
$403$		−	8.00000i		−	0.398508i
$404$	6.00000			0.298511
$405$	−2.00000	−	1.00000i	−0.0993808	−	0.0496904i
$406$	4.00000			0.198517
$407$			4.00000i			0.198273i
$408$			6.00000i			0.297044i
$409$	10.0000			0.494468			0.247234	−	0.968956i	$-0.420478\pi$
$409$	10.0000			0.494468			0.247234	+	0.968956i	$0.420478\pi$
$410$	10.0000	−	20.0000i	0.493865	−	0.987730i
$411$	18.0000			0.887875
$412$		−	8.00000i		−	0.394132i
$413$			4.00000i			0.196827i
$414$	−6.00000			−0.294884
$415$	−14.0000	+	28.0000i	−0.687233	+	1.37447i
$416$	−20.0000			−0.980581
$417$		−	16.0000i		−	0.783523i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$	2.00000	+	1.00000i	0.0975900	+	0.0487950i
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$		−	2.00000i		−	0.0973585i
$423$		0			0
$424$	−18.0000			−0.874157
$425$	8.00000	−	6.00000i	0.388057	−	0.291043i
$426$	8.00000			0.387601
$427$			2.00000i			0.0967868i
$428$		−	8.00000i		−	0.386695i
$429$	4.00000			0.193122
$430$	−8.00000	−	4.00000i	−0.385794	−	0.192897i
$431$	16.0000			0.770693			0.385346	−	0.922772i	$-0.374082\pi$
$431$	16.0000			0.770693			0.385346	+	0.922772i	$0.374082\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	−2.00000			−0.0960031
$435$	4.00000	−	8.00000i	0.191785	−	0.383571i
$436$	−14.0000			−0.670478
$437$		0			0
$438$		0			0
$439$	−36.0000			−1.71819			−0.859093	−	0.511819i	$-0.828972\pi$
$439$	−36.0000			−1.71819			−0.859093	+	0.511819i	$0.828972\pi$
$440$	3.00000	−	6.00000i	0.143019	−	0.286039i
$441$	1.00000			0.0476190
$442$			8.00000i			0.380521i
$443$			34.0000i			1.61539i	0.589601	+	0.807694i	$0.299285\pi$
$443$			34.0000i			1.61539i	−0.589601	+	0.807694i	$0.700715\pi$
$444$	−4.00000			−0.189832
$445$	−24.0000	−	12.0000i	−1.13771	−	0.568855i
$446$	−24.0000			−1.13643
$447$		−	20.0000i		−	0.945968i
$448$			7.00000i			0.330719i
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	10.0000			0.470882
$452$			6.00000i			0.282216i
$453$		−	2.00000i		−	0.0939682i
$454$	−10.0000			−0.469323
$455$	8.00000	+	4.00000i	0.375046	+	0.187523i
$456$		0			0
$457$			22.0000i			1.02912i	0.857455	+	0.514558i	$0.172044\pi$
$457$			22.0000i			1.02912i	−0.857455	+	0.514558i	$0.827956\pi$
$458$		−	22.0000i		−	1.02799i
$459$	2.00000			0.0933520
$460$	6.00000	−	12.0000i	0.279751	−	0.559503i
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		−	1.00000i		−	0.0465242i
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	4.00000			0.185695
$465$	−2.00000	+	4.00000i	−0.0927478	+	0.185496i
$466$	−10.0000			−0.463241
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$			4.00000i			0.184900i
$469$	8.00000			0.369406
$470$		0			0
$471$	−6.00000			−0.276465
$472$			12.0000i			0.552345i
$473$		−	4.00000i		−	0.183920i
$474$	−14.0000			−0.643041
$475$		0			0
$476$	−2.00000			−0.0916698
$477$			6.00000i			0.274721i
$478$		−	24.0000i		−	1.09773i
$479$		0			0			−	1.00000i	$-0.5\pi$
$479$		0			0				1.00000i	$0.5\pi$
$480$	10.0000	+	5.00000i	0.456435	+	0.228218i
$481$	−16.0000			−0.729537
$482$			2.00000i			0.0910975i
$483$		−	6.00000i		−	0.273009i
$484$	1.00000			0.0454545
$485$	−14.0000	+	28.0000i	−0.635707	+	1.27141i
$486$	−1.00000			−0.0453609
$487$		−	24.0000i		−	1.08754i	−0.839233	−	0.543772i	$-0.816996\pi$
$487$		−	24.0000i		−	1.08754i	0.839233	−	0.543772i	$-0.183004\pi$
$488$			6.00000i			0.271607i
$489$	−4.00000			−0.180886
$490$	1.00000	−	2.00000i	0.0451754	−	0.0903508i
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$			10.0000i			0.450835i
$493$			8.00000i			0.360302i
$494$		0			0
$495$	−2.00000	−	1.00000i	−0.0898933	−	0.0449467i
$496$	−2.00000			−0.0898027
$497$			8.00000i			0.358849i
$498$			14.0000i			0.627355i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$	−2.00000	−	11.0000i	−0.0894427	−	0.491935i
$501$	−6.00000			−0.268060
$502$			24.0000i			1.07117i
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$	3.00000			0.133631
$505$	−12.0000	−	6.00000i	−0.533993	−	0.266996i
$506$	−6.00000			−0.266733
$507$			3.00000i			0.133235i
$508$			8.00000i			0.354943i
$509$	24.0000			1.06378			0.531891	−	0.846813i	$-0.321482\pi$
$509$	24.0000			1.06378			0.531891	+	0.846813i	$0.321482\pi$
$510$	2.00000	−	4.00000i	0.0885615	−	0.177123i
$511$		0			0
$512$			11.0000i			0.486136i
$513$		0			0
$514$	−2.00000			−0.0882162
$515$	−8.00000	+	16.0000i	−0.352522	+	0.705044i
$516$	4.00000			0.176090
$517$		0			0
$518$			4.00000i			0.175750i
$519$	6.00000			0.263371
$520$	24.0000	+	12.0000i	1.05247	+	0.526235i
$521$	−28.0000			−1.22670			−0.613351	−	0.789810i	$-0.710179\pi$
$521$	−28.0000			−1.22670			−0.613351	+	0.789810i	$0.710179\pi$
$522$		−	4.00000i		−	0.175075i
$523$		−	8.00000i		−	0.349816i	−0.984585	−	0.174908i	$-0.944037\pi$
$523$		−	8.00000i		−	0.349816i	0.984585	−	0.174908i	$-0.0559627\pi$
$524$	4.00000			0.174741
$525$	−3.00000	−	4.00000i	−0.130931	−	0.174574i
$526$	−12.0000			−0.523225
$527$		−	4.00000i		−	0.174243i
$528$		−	1.00000i		−	0.0435194i
$529$	−13.0000			−0.565217
$530$	12.0000	+	6.00000i	0.521247	+	0.260623i
$531$	4.00000			0.173585
$532$		0			0
$533$			40.0000i			1.73259i
$534$	−12.0000			−0.519291
$535$	−8.00000	+	16.0000i	−0.345870	+	0.691740i
$536$	24.0000			1.03664
$537$			4.00000i			0.172613i
$538$		−	32.0000i		−	1.37962i
$539$	1.00000			0.0430730
$540$	1.00000	−	2.00000i	0.0430331	−	0.0860663i
$541$	−18.0000			−0.773880			−0.386940	−	0.922105i	$-0.626468\pi$
$541$	−18.0000			−0.773880			−0.386940	+	0.922105i	$0.626468\pi$
$542$			8.00000i			0.343629i
$543$			18.0000i			0.772454i
$544$	−10.0000			−0.428746
$545$	28.0000	+	14.0000i	1.19939	+	0.599694i
$546$	4.00000			0.171184
$547$		−	4.00000i		−	0.171028i	−0.996337	−	0.0855138i	$-0.972747\pi$
$547$		−	4.00000i		−	0.171028i	0.996337	−	0.0855138i	$-0.0272532\pi$
$548$			18.0000i			0.768922i
$549$	2.00000			0.0853579
$550$	−4.00000	+	3.00000i	−0.170561	+	0.127920i
$551$		0			0
$552$		−	18.0000i		−	0.766131i
$553$		−	14.0000i		−	0.595341i
$554$	−22.0000			−0.934690
$555$	8.00000	+	4.00000i	0.339581	+	0.169791i
$556$	16.0000			0.678551
$557$			14.0000i			0.593199i	0.955002	+	0.296600i	$0.0958526\pi$
$557$			14.0000i			0.593199i	−0.955002	+	0.296600i	$0.904147\pi$
$558$			2.00000i			0.0846668i
$559$	16.0000			0.676728
$560$	1.00000	−	2.00000i	0.0422577	−	0.0845154i
$561$	2.00000			0.0844401
$562$		−	4.00000i		−	0.168730i
$563$			42.0000i			1.77009i	0.465506	+	0.885044i	$0.345872\pi$
$563$			42.0000i			1.77009i	−0.465506	+	0.885044i	$0.654128\pi$
$564$		0			0
$565$	6.00000	−	12.0000i	0.252422	−	0.504844i
$566$	−20.0000			−0.840663
$567$		−	1.00000i		−	0.0419961i
$568$			24.0000i			1.00702i
$569$	−24.0000			−1.00613			−0.503066	−	0.864248i	$-0.667795\pi$
$569$	−24.0000			−1.00613			−0.503066	+	0.864248i	$0.667795\pi$
$570$		0			0
$571$	42.0000			1.75765			0.878823	−	0.477149i	$-0.158330\pi$
$571$	42.0000			1.75765			0.878823	+	0.477149i	$0.158330\pi$
$572$			4.00000i			0.167248i
$573$		0			0
$574$	10.0000			0.417392
$575$	−24.0000	+	18.0000i	−1.00087	+	0.750652i
$576$	7.00000			0.291667
$577$		−	10.0000i		−	0.416305i	−0.978096	−	0.208153i	$-0.933255\pi$
$577$		−	10.0000i		−	0.416305i	0.978096	−	0.208153i	$-0.0667451\pi$
$578$		−	13.0000i		−	0.540729i
$579$	−10.0000			−0.415586
$580$	8.00000	+	4.00000i	0.332182	+	0.166091i
$581$	−14.0000			−0.580818
$582$			14.0000i			0.580319i
$583$			6.00000i			0.248495i
$584$		0			0
$585$	4.00000	−	8.00000i	0.165380	−	0.330759i
$586$	6.00000			0.247858
$587$		0			0		1.00000			$0$
$587$		0			0		−1.00000			$\pi$
$588$			1.00000i			0.0412393i
$589$		0			0
$590$	4.00000	−	8.00000i	0.164677	−	0.329355i
$591$	−22.0000			−0.904959
$592$			4.00000i			0.164399i
$593$			46.0000i			1.88899i	0.328521	+	0.944497i	$0.393450\pi$
$593$			46.0000i			1.88899i	−0.328521	+	0.944497i	$0.606550\pi$
$594$	−1.00000			−0.0410305
$595$	4.00000	+	2.00000i	0.163984	+	0.0819920i
$596$	20.0000			0.819232
$597$			2.00000i			0.0818546i
$598$		−	24.0000i		−	0.981433i
$599$	32.0000			1.30748			0.653742	−	0.756717i	$-0.273198\pi$
$599$	32.0000			1.30748			0.653742	+	0.756717i	$0.273198\pi$
$600$	−9.00000	−	12.0000i	−0.367423	−	0.489898i
$601$	−14.0000			−0.571072			−0.285536	−	0.958368i	$-0.592172\pi$
$601$	−14.0000			−0.571072			−0.285536	+	0.958368i	$0.592172\pi$
$602$		−	4.00000i		−	0.163028i
$603$		−	8.00000i		−	0.325785i
$604$	2.00000			0.0813788
$605$	−2.00000	−	1.00000i	−0.0813116	−	0.0406558i
$606$	−6.00000			−0.243733
$607$		0			0		1.00000			$0$
$607$		0			0		−1.00000			$\pi$
$608$		0			0
$609$	4.00000			0.162088
$610$	2.00000	−	4.00000i	0.0809776	−	0.161955i
$611$		0			0
$612$			2.00000i			0.0808452i
$613$		−	34.0000i		−	1.37325i	−0.727013	−	0.686624i	$-0.759092\pi$
$613$		−	34.0000i		−	1.37325i	0.727013	−	0.686624i	$-0.240908\pi$
$614$	−20.0000			−0.807134
$615$	10.0000	−	20.0000i	0.403239	−	0.806478i
$616$	3.00000			0.120873
$617$		−	2.00000i		−	0.0805170i	−0.999189	−	0.0402585i	$-0.987182\pi$
$617$		−	2.00000i		−	0.0805170i	0.999189	−	0.0402585i	$-0.0128181\pi$
$618$			8.00000i			0.321807i
$619$	38.0000			1.52735			0.763674	−	0.645601i	$-0.223393\pi$
$619$	38.0000			1.52735			0.763674	+	0.645601i	$0.223393\pi$
$620$	−4.00000	−	2.00000i	−0.160644	−	0.0803219i
$621$	−6.00000			−0.240772
$622$		−	12.0000i		−	0.481156i
$623$		−	12.0000i		−	0.480770i
$624$	4.00000			0.160128
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	6.00000			0.239808
$627$		0			0
$628$		−	6.00000i		−	0.239426i
$629$	−8.00000			−0.318981
$630$	−2.00000	−	1.00000i	−0.0796819	−	0.0398410i
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		−	42.0000i		−	1.67067i
$633$		−	2.00000i		−	0.0794929i
$634$	−18.0000			−0.714871
$635$	8.00000	−	16.0000i	0.317470	−	0.634941i
$636$	−6.00000			−0.237915
$637$			4.00000i			0.158486i
$638$		−	4.00000i		−	0.158362i
$639$	8.00000			0.316475
$640$	−3.00000	+	6.00000i	−0.118585	+	0.237171i
$641$	10.0000			0.394976			0.197488	−	0.980305i	$-0.436722\pi$
$641$	10.0000			0.394976			0.197488	+	0.980305i	$0.436722\pi$
$642$			8.00000i			0.315735i
$643$			20.0000i			0.788723i	0.918955	+	0.394362i	$0.129034\pi$
$643$			20.0000i			0.788723i	−0.918955	+	0.394362i	$0.870966\pi$
$644$	6.00000			0.236433
$645$	−8.00000	−	4.00000i	−0.315000	−	0.157500i
$646$		0			0
$647$			28.0000i			1.10079i	0.834903	+	0.550397i	$0.185524\pi$
$647$			28.0000i			1.10079i	−0.834903	+	0.550397i	$0.814476\pi$
$648$		−	3.00000i		−	0.117851i
$649$	4.00000			0.157014
$650$	−12.0000	−	16.0000i	−0.470679	−	0.627572i
$651$	−2.00000			−0.0783862
$652$		−	4.00000i		−	0.156652i
$653$			34.0000i			1.33052i	0.746611	+	0.665261i	$0.231680\pi$
$653$			34.0000i			1.33052i	−0.746611	+	0.665261i	$0.768320\pi$
$654$	14.0000			0.547443
$655$	−8.00000	−	4.00000i	−0.312586	−	0.156293i
$656$	10.0000			0.390434
$657$		0			0
$658$		0			0
$659$	−24.0000			−0.934907			−0.467454	−	0.884018i	$-0.654829\pi$
$659$	−24.0000			−0.934907			−0.467454	+	0.884018i	$0.654829\pi$
$660$	1.00000	−	2.00000i	0.0389249	−	0.0778499i
$661$	−42.0000			−1.63361			−0.816805	−	0.576913i	$-0.804257\pi$
$661$	−42.0000			−1.63361			−0.816805	+	0.576913i	$0.804257\pi$
$662$		0			0
$663$			8.00000i			0.310694i
$664$	−42.0000			−1.62992
$665$		0			0
$666$	4.00000			0.154997
$667$		−	24.0000i		−	0.929284i
$668$		−	6.00000i		−	0.232147i
$669$	−24.0000			−0.927894
$670$	−16.0000	−	8.00000i	−0.618134	−	0.309067i
$671$	2.00000			0.0772091
$672$			5.00000i			0.192879i
$673$		−	6.00000i		−	0.231283i	−0.993291	−	0.115642i	$-0.963108\pi$
$673$		−	6.00000i		−	0.231283i	0.993291	−	0.115642i	$-0.0368924\pi$
$674$	30.0000			1.15556
$675$	−4.00000	+	3.00000i	−0.153960	+	0.115470i
$676$	−3.00000			−0.115385
$677$			14.0000i			0.538064i	0.963131	+	0.269032i	$0.0867037\pi$
$677$			14.0000i			0.538064i	−0.963131	+	0.269032i	$0.913296\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−14.0000			−0.537271
$680$	12.0000	+	6.00000i	0.460179	+	0.230089i
$681$	−10.0000			−0.383201
$682$			2.00000i			0.0765840i
$683$			26.0000i			0.994862i	0.867503	+	0.497431i	$0.165723\pi$
$683$			26.0000i			0.994862i	−0.867503	+	0.497431i	$0.834277\pi$
$684$		0			0
$685$	18.0000	−	36.0000i	0.687745	−	1.37549i
$686$	1.00000			0.0381802
$687$		−	22.0000i		−	0.839352i
$688$		−	4.00000i		−	0.152499i
$689$	−24.0000			−0.914327
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	−14.0000			−0.532585			−0.266293	−	0.963892i	$-0.585799\pi$
$691$	−14.0000			−0.532585			−0.266293	+	0.963892i	$0.585799\pi$
$692$			6.00000i			0.228086i
$693$		−	1.00000i		−	0.0379869i
$694$	−24.0000			−0.911028
$695$	−32.0000	−	16.0000i	−1.21383	−	0.606915i
$696$	12.0000			0.454859
$697$			20.0000i			0.757554i
$698$			10.0000i			0.378506i
$699$	−10.0000			−0.378235
$700$	4.00000	−	3.00000i	0.151186	−	0.113389i
$701$	8.00000			0.302156			0.151078	−	0.988522i	$-0.451726\pi$
$701$	8.00000			0.302156			0.151078	+	0.988522i	$0.451726\pi$
$702$		−	4.00000i		−	0.150970i
$703$		0			0
$704$	7.00000			0.263822
$705$		0			0
$706$	22.0000			0.827981
$707$		−	6.00000i		−	0.225653i
$708$			4.00000i			0.150329i
$709$	−26.0000			−0.976450			−0.488225	−	0.872718i	$-0.662356\pi$
$709$	−26.0000			−0.976450			−0.488225	+	0.872718i	$0.662356\pi$
$710$	8.00000	−	16.0000i	0.300235	−	0.600469i
$711$	−14.0000			−0.525041
$712$		−	36.0000i		−	1.34916i
$713$			12.0000i			0.449404i
$714$	2.00000			0.0748481
$715$	4.00000	−	8.00000i	0.149592	−	0.299183i
$716$	−4.00000			−0.149487
$717$		−	24.0000i		−	0.896296i
$718$		−	20.0000i		−	0.746393i
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	−8.00000			−0.297936
$722$			19.0000i			0.707107i
$723$			2.00000i			0.0743808i
$724$	−18.0000			−0.668965
$725$	−12.0000	−	16.0000i	−0.445669	−	0.594225i
$726$	−1.00000			−0.0371135
$727$		−	16.0000i		−	0.593407i	−0.954970	−	0.296704i	$-0.904113\pi$
$727$		−	16.0000i		−	0.593407i	0.954970	−	0.296704i	$-0.0958873\pi$
$728$			12.0000i			0.444750i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	8.00000			0.295891
$732$			2.00000i			0.0739221i
$733$		−	40.0000i		−	1.47743i	−0.674016	−	0.738717i	$-0.735432\pi$
$733$		−	40.0000i		−	1.47743i	0.674016	−	0.738717i	$-0.264568\pi$
$734$	24.0000			0.885856
$735$	1.00000	−	2.00000i	0.0368856	−	0.0737711i
$736$	30.0000			1.10581
$737$		−	8.00000i		−	0.294684i
$738$		−	10.0000i		−	0.368105i
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$	−4.00000	+	8.00000i	−0.147043	+	0.294086i
$741$		0			0
$742$			6.00000i			0.220267i
$743$		−	4.00000i		−	0.146746i	−0.997305	−	0.0733729i	$-0.976624\pi$
$743$		−	4.00000i		−	0.146746i	0.997305	−	0.0733729i	$-0.0233763\pi$
$744$	−6.00000			−0.219971
$745$	−40.0000	−	20.0000i	−1.46549	−	0.732743i
$746$	18.0000			0.659027
$747$			14.0000i			0.512233i
$748$			2.00000i			0.0731272i
$749$	−8.00000			−0.292314
$750$	2.00000	+	11.0000i	0.0730297	+	0.401663i
$751$	12.0000			0.437886			0.218943	−	0.975738i	$-0.429739\pi$
$751$	12.0000			0.437886			0.218943	+	0.975738i	$0.429739\pi$
$752$		0			0
$753$			24.0000i			0.874609i
$754$	16.0000			0.582686
$755$	−4.00000	−	2.00000i	−0.145575	−	0.0727875i
$756$	1.00000			0.0363696
$757$		−	4.00000i		−	0.145382i	−0.997354	−	0.0726912i	$-0.976841\pi$
$757$		−	4.00000i		−	0.145382i	0.997354	−	0.0726912i	$-0.0231588\pi$
$758$			8.00000i			0.290573i
$759$	−6.00000			−0.217786
$760$		0			0
$761$	38.0000			1.37750			0.688749	−	0.724999i	$-0.258160\pi$
$761$	38.0000			1.37750			0.688749	+	0.724999i	$0.258160\pi$
$762$		−	8.00000i		−	0.289809i
$763$			14.0000i			0.506834i
$764$		0			0
$765$	2.00000	−	4.00000i	0.0723102	−	0.144620i
$766$	−16.0000			−0.578103
$767$			16.0000i			0.577727i
$768$			17.0000i			0.613435i
$769$	18.0000			0.649097			0.324548	−	0.945869i	$-0.394788\pi$
$769$	18.0000			0.649097			0.324548	+	0.945869i	$0.394788\pi$
$770$	−2.00000	−	1.00000i	−0.0720750	−	0.0360375i
$771$	−2.00000			−0.0720282
$772$		−	10.0000i		−	0.359908i
$773$			30.0000i			1.07903i	0.841978	+	0.539513i	$0.181391\pi$
$773$			30.0000i			1.07903i	−0.841978	+	0.539513i	$0.818609\pi$
$774$	−4.00000			−0.143777
$775$	6.00000	+	8.00000i	0.215526	+	0.287368i
$776$	−42.0000			−1.50771
$777$			4.00000i			0.143499i
$778$		−	34.0000i		−	1.21896i
$779$		0			0
$780$	8.00000	+	4.00000i	0.286446	+	0.143223i
$781$	8.00000			0.286263
$782$		−	12.0000i		−	0.429119i
$783$		−	4.00000i		−	0.142948i
$784$	1.00000			0.0357143
$785$	−6.00000	+	12.0000i	−0.214149	+	0.428298i
$786$	−4.00000			−0.142675
$787$			44.0000i			1.56843i	0.620489	+	0.784215i	$0.286934\pi$
$787$			44.0000i			1.56843i	−0.620489	+	0.784215i	$0.713066\pi$
$788$		−	22.0000i		−	0.783718i
$789$	−12.0000			−0.427211
$790$	−14.0000	+	28.0000i	−0.498098	+	0.996195i
$791$	6.00000			0.213335
$792$		−	3.00000i		−	0.106600i
$793$			8.00000i			0.284088i
$794$	22.0000			0.780751
$795$	12.0000	+	6.00000i	0.425596	+	0.212798i
$796$	−2.00000			−0.0708881
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		0			0
$799$		0			0
$800$	20.0000	−	15.0000i	0.707107	−	0.530330i
$801$	−12.0000			−0.423999
$802$			30.0000i			1.05934i
$803$		0			0
$804$	8.00000			0.282138
$805$	−12.0000	−	6.00000i	−0.422944	−	0.211472i
$806$	−8.00000			−0.281788
$807$		−	32.0000i		−	1.12645i
$808$		−	18.0000i		−	0.633238i
$809$	36.0000			1.26569			0.632846	−	0.774277i	$-0.281886\pi$
$809$	36.0000			1.26569			0.632846	+	0.774277i	$0.281886\pi$
$810$	−1.00000	+	2.00000i	−0.0351364	+	0.0702728i
$811$	16.0000			0.561836			0.280918	−	0.959732i	$-0.409361\pi$
$811$	16.0000			0.561836			0.280918	+	0.959732i	$0.409361\pi$
$812$			4.00000i			0.140372i
$813$			8.00000i			0.280572i
$814$	4.00000			0.140200
$815$	−4.00000	+	8.00000i	−0.140114	+	0.280228i
$816$	2.00000			0.0700140
$817$		0			0
$818$		−	10.0000i		−	0.349642i
$819$	4.00000			0.139771
$820$	20.0000	+	10.0000i	0.698430	+	0.349215i
$821$	40.0000			1.39601			0.698005	−	0.716093i	$-0.254071\pi$
$821$	40.0000			1.39601			0.698005	+	0.716093i	$0.254071\pi$
$822$		−	18.0000i		−	0.627822i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$	−24.0000			−0.836080
$825$	−4.00000	+	3.00000i	−0.139262	+	0.104447i
$826$	4.00000			0.139178
$827$		−	48.0000i		−	1.66912i	−0.550914	−	0.834562i	$-0.685721\pi$
$827$		−	48.0000i		−	1.66912i	0.550914	−	0.834562i	$-0.314279\pi$
$828$		−	6.00000i		−	0.208514i
$829$	−54.0000			−1.87550			−0.937749	−	0.347314i	$-0.887094\pi$
$829$	−54.0000			−1.87550			−0.937749	+	0.347314i	$0.887094\pi$
$830$	28.0000	+	14.0000i	0.971894	+	0.485947i
$831$	−22.0000			−0.763172
$832$			28.0000i			0.970725i
$833$			2.00000i			0.0692959i
$834$	−16.0000			−0.554035
$835$	−6.00000	+	12.0000i	−0.207639	+	0.415277i
$836$		0			0
$837$			2.00000i			0.0691301i
$838$		0			0
$839$	−48.0000			−1.65714			−0.828572	−	0.559883i	$-0.810846\pi$
$839$	−48.0000			−1.65714			−0.828572	+	0.559883i	$0.810846\pi$
$840$	3.00000	−	6.00000i	0.103510	−	0.207020i
$841$	−13.0000			−0.448276
$842$			6.00000i			0.206774i
$843$		−	4.00000i		−	0.137767i
$844$	2.00000			0.0688428
$845$	6.00000	+	3.00000i	0.206406	+	0.103203i
$846$		0			0
$847$		−	1.00000i		−	0.0343604i
$848$			6.00000i			0.206041i
$849$	−20.0000			−0.686398
$850$	−6.00000	−	8.00000i	−0.205798	−	0.274398i
$851$	24.0000			0.822709
$852$			8.00000i			0.274075i
$853$			24.0000i			0.821744i	0.911693	+	0.410872i	$0.134776\pi$
$853$			24.0000i			0.821744i	−0.911693	+	0.410872i	$0.865224\pi$
$854$	2.00000			0.0684386
$855$		0			0
$856$	−24.0000			−0.820303
$857$			54.0000i			1.84460i	0.386469	+	0.922302i	$0.373695\pi$
$857$			54.0000i			1.84460i	−0.386469	+	0.922302i	$0.626305\pi$
$858$		−	4.00000i		−	0.136558i
$859$	38.0000			1.29654			0.648272	−	0.761409i	$-0.275492\pi$
$859$	38.0000			1.29654			0.648272	+	0.761409i	$0.275492\pi$
$860$	4.00000	−	8.00000i	0.136399	−	0.272798i
$861$	10.0000			0.340799
$862$		−	16.0000i		−	0.544962i
$863$			18.0000i			0.612727i	0.951915	+	0.306364i	$0.0991123\pi$
$863$			18.0000i			0.612727i	−0.951915	+	0.306364i	$0.900888\pi$
$864$	5.00000			0.170103
$865$	6.00000	−	12.0000i	0.204006	−	0.408012i
$866$	−14.0000			−0.475739
$867$		−	13.0000i		−	0.441503i
$868$		−	2.00000i		−	0.0678844i
$869$	−14.0000			−0.474917
$870$	−8.00000	−	4.00000i	−0.271225	−	0.135613i
$871$	32.0000			1.08428
$872$			42.0000i			1.42230i
$873$			14.0000i			0.473828i
$874$		0			0
$875$	−11.0000	+	2.00000i	−0.371868	+	0.0676123i
$876$		0			0
$877$			26.0000i			0.877958i	0.898497	+	0.438979i	$0.144660\pi$
$877$			26.0000i			0.877958i	−0.898497	+	0.438979i	$0.855340\pi$
$878$			36.0000i			1.21494i
$879$	6.00000			0.202375
$880$	−2.00000	−	1.00000i	−0.0674200	−	0.0337100i
$881$	−52.0000			−1.75192			−0.875962	−	0.482380i	$-0.839773\pi$
$881$	−52.0000			−1.75192			−0.875962	+	0.482380i	$0.839773\pi$
$882$		−	1.00000i		−	0.0336718i
$883$		−	48.0000i		−	1.61533i	−0.589643	−	0.807664i	$-0.700731\pi$
$883$		−	48.0000i		−	1.61533i	0.589643	−	0.807664i	$-0.299269\pi$
$884$	−8.00000			−0.269069
$885$	4.00000	−	8.00000i	0.134459	−	0.268917i
$886$	34.0000			1.14225
$887$		−	22.0000i		−	0.738688i	−0.929293	−	0.369344i	$-0.879582\pi$
$887$		−	22.0000i		−	0.738688i	0.929293	−	0.369344i	$-0.120418\pi$
$888$			12.0000i			0.402694i
$889$	8.00000			0.268311
$890$	−12.0000	+	24.0000i	−0.402241	+	0.804482i
$891$	−1.00000			−0.0335013
$892$		−	24.0000i		−	0.803579i
$893$		0			0
$894$	−20.0000			−0.668900
$895$	8.00000	+	4.00000i	0.267411	+	0.133705i
$896$	−3.00000			−0.100223
$897$		−	24.0000i		−	0.801337i
$898$			34.0000i			1.13459i
$899$	−8.00000			−0.266815
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$	−12.0000			−0.399778
$902$		−	10.0000i		−	0.332964i
$903$		−	4.00000i		−	0.133112i
$904$	18.0000			0.598671
$905$	36.0000	+	18.0000i	1.19668	+	0.598340i
$906$	−2.00000			−0.0664455
$907$			16.0000i			0.531271i	0.964073	+	0.265636i	$0.0855818\pi$
$907$			16.0000i			0.531271i	−0.964073	+	0.265636i	$0.914418\pi$
$908$		−	10.0000i		−	0.331862i
$909$	−6.00000			−0.199007
$910$	4.00000	−	8.00000i	0.132599	−	0.265197i
$911$	48.0000			1.59031			0.795155	−	0.606406i	$-0.207389\pi$
$911$	48.0000			1.59031			0.795155	+	0.606406i	$0.207389\pi$
$912$		0			0
$913$			14.0000i			0.463332i
$914$	22.0000			0.727695
$915$	2.00000	−	4.00000i	0.0661180	−	0.132236i
$916$	22.0000			0.726900
$917$		−	4.00000i		−	0.132092i
$918$		−	2.00000i		−	0.0660098i
$919$	50.0000			1.64935			0.824674	−	0.565608i	$-0.191359\pi$
$919$	50.0000			1.64935			0.824674	+	0.565608i	$0.191359\pi$
$920$	−36.0000	−	18.0000i	−1.18688	−	0.593442i
$921$	−20.0000			−0.659022
$922$			30.0000i			0.987997i
$923$			32.0000i			1.05329i
$924$	1.00000			0.0328976
$925$	16.0000	−	12.0000i	0.526077	−	0.394558i
$926$	24.0000			0.788689
$927$			8.00000i			0.262754i
$928$			20.0000i			0.656532i
$929$	−16.0000			−0.524943			−0.262471	−	0.964940i	$-0.584538\pi$
$929$	−16.0000			−0.524943			−0.262471	+	0.964940i	$0.584538\pi$
$930$	4.00000	+	2.00000i	0.131165	+	0.0655826i
$931$		0			0
$932$		−	10.0000i		−	0.327561i
$933$		−	12.0000i		−	0.392862i
$934$	12.0000			0.392652
$935$	2.00000	−	4.00000i	0.0654070	−	0.130814i
$936$	12.0000			0.392232
$937$		−	52.0000i		−	1.69877i	−0.527777	−	0.849383i	$-0.676974\pi$
$937$		−	52.0000i		−	1.69877i	0.527777	−	0.849383i	$-0.323026\pi$
$938$		−	8.00000i		−	0.261209i
$939$	6.00000			0.195803
$940$		0			0
$941$	−6.00000			−0.195594			−0.0977972	−	0.995206i	$-0.531180\pi$
$941$	−6.00000			−0.195594			−0.0977972	+	0.995206i	$0.531180\pi$
$942$			6.00000i			0.195491i
$943$		−	60.0000i		−	1.95387i
$944$	4.00000			0.130189
$945$	−2.00000	−	1.00000i	−0.0650600	−	0.0325300i
$946$	−4.00000			−0.130051
$947$		−	30.0000i		−	0.974869i	−0.873160	−	0.487435i	$-0.837933\pi$
$947$		−	30.0000i		−	0.974869i	0.873160	−	0.487435i	$-0.162067\pi$
$948$		−	14.0000i		−	0.454699i
$949$		0			0
$950$		0			0
$951$	−18.0000			−0.583690
$952$			6.00000i			0.194461i
$953$		−	6.00000i		−	0.194359i	−0.995267	−	0.0971795i	$-0.969018\pi$
$953$		−	6.00000i		−	0.194359i	0.995267	−	0.0971795i	$-0.0309821\pi$
$954$	6.00000			0.194257
$955$		0			0
$956$	24.0000			0.776215
$957$		−	4.00000i		−	0.129302i
$958$		0			0
$959$	18.0000			0.581250
$960$	7.00000	−	14.0000i	0.225924	−	0.451848i
$961$	−27.0000			−0.870968
$962$			16.0000i			0.515861i
$963$			8.00000i			0.257796i
$964$	−2.00000			−0.0644157
$965$	−10.0000	+	20.0000i	−0.321911	+	0.643823i
$966$	−6.00000			−0.193047
$967$		−	8.00000i		−	0.257263i	−0.991692	−	0.128631i	$-0.958942\pi$
$967$		−	8.00000i		−	0.257263i	0.991692	−	0.128631i	$-0.0410584\pi$
$968$		−	3.00000i		−	0.0964237i
$969$		0			0
$970$	28.0000	+	14.0000i	0.899026	+	0.449513i
$971$	−20.0000			−0.641831			−0.320915	−	0.947108i	$-0.603990\pi$
$971$	−20.0000			−0.641831			−0.320915	+	0.947108i	$0.603990\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	16.0000i		−	0.512936i
$974$	−24.0000			−0.769010
$975$	−12.0000	−	16.0000i	−0.384308	−	0.512410i
$976$	2.00000			0.0640184
$977$		−	42.0000i		−	1.34370i	−0.740688	−	0.671850i	$-0.765500\pi$
$977$		−	42.0000i		−	1.34370i	0.740688	−	0.671850i	$-0.234500\pi$
$978$			4.00000i			0.127906i
$979$	−12.0000			−0.383522
$980$	2.00000	+	1.00000i	0.0638877	+	0.0319438i
$981$	14.0000			0.446986
$982$		−	28.0000i		−	0.893516i
$983$		−	12.0000i		−	0.382741i	−0.981518	−	0.191370i	$-0.938707\pi$
$983$		−	12.0000i		−	0.382741i	0.981518	−	0.191370i	$-0.0612931\pi$
$984$	30.0000			0.956365
$985$	−22.0000	+	44.0000i	−0.700978	+	1.40196i
$986$	8.00000			0.254772
$987$		0			0
$988$		0			0
$989$	−24.0000			−0.763156
$990$	−1.00000	+	2.00000i	−0.0317821	+	0.0635642i
$991$	−56.0000			−1.77890			−0.889449	−	0.457034i	$-0.848912\pi$
$991$	−56.0000			−1.77890			−0.889449	+	0.457034i	$0.848912\pi$
$992$		−	10.0000i		−	0.317500i
$993$		0			0
$994$	8.00000			0.253745
$995$	4.00000	+	2.00000i	0.126809	+	0.0634043i
$996$	−14.0000			−0.443607
$997$		−	16.0000i		−	0.506725i	−0.967371	−	0.253363i	$-0.918463\pi$
$997$		−	16.0000i		−	0.506725i	0.967371	−	0.253363i	$-0.0815366\pi$
$998$			4.00000i			0.126618i
$999$	4.00000			0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.a.694.1	✓	2
5.2	odd	4		5775.2.a.s.1.1		1
5.3	odd	4		5775.2.a.h.1.1		1
5.4	even	2	inner	1155.2.c.a.694.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.a.694.1	✓	2	1.1	even	1	trivial
1155.2.c.a.694.2	yes	2	5.4	even	2	inner
5775.2.a.h.1.1		1	5.3	odd	4
5775.2.a.s.1.1		1	5.2	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} +1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} -1.00000 q^{6} -1.00000i q^{7} -3.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} -1.00000 q^{11} -1.00000i q^{12} -4.00000i q^{13} -1.00000 q^{14} +(-1.00000 + 2.00000i) q^{15} -1.00000 q^{16} -2.00000i q^{17} +1.00000i q^{18} +(-2.00000 - 1.00000i) q^{20} -1.00000 q^{21} +1.00000i q^{22} +6.00000i q^{23} -3.00000 q^{24} +(3.00000 + 4.00000i) q^{25} -4.00000 q^{26} +1.00000i q^{27} -1.00000i q^{28} -4.00000 q^{29} +(2.00000 + 1.00000i) q^{30} +2.00000 q^{31} -5.00000i q^{32} +1.00000i q^{33} -2.00000 q^{34} +(-1.00000 + 2.00000i) q^{35} -1.00000 q^{36} -4.00000i q^{37} -4.00000 q^{39} +(-3.00000 + 6.00000i) q^{40} -10.0000 q^{41} +1.00000i q^{42} +4.00000i q^{43} -1.00000 q^{44} +(2.00000 + 1.00000i) q^{45} +6.00000 q^{46} +1.00000i q^{48} -1.00000 q^{49} +(4.00000 - 3.00000i) q^{50} -2.00000 q^{51} -4.00000i q^{52} -6.00000i q^{53} +1.00000 q^{54} +(2.00000 + 1.00000i) q^{55} -3.00000 q^{56} +4.00000i q^{58} -4.00000 q^{59} +(-1.00000 + 2.00000i) q^{60} -2.00000 q^{61} -2.00000i q^{62} +1.00000i q^{63} -7.00000 q^{64} +(-4.00000 + 8.00000i) q^{65} +1.00000 q^{66} +8.00000i q^{67} -2.00000i q^{68} +6.00000 q^{69} +(2.00000 + 1.00000i) q^{70} -8.00000 q^{71} +3.00000i q^{72} -4.00000 q^{74} +(4.00000 - 3.00000i) q^{75} +1.00000i q^{77} +4.00000i q^{78} +14.0000 q^{79} +(2.00000 + 1.00000i) q^{80} +1.00000 q^{81} +10.0000i q^{82} -14.0000i q^{83} -1.00000 q^{84} +(-2.00000 + 4.00000i) q^{85} +4.00000 q^{86} +4.00000i q^{87} +3.00000i q^{88} +12.0000 q^{89} +(1.00000 - 2.00000i) q^{90} -4.00000 q^{91} +6.00000i q^{92} -2.00000i q^{93} -5.00000 q^{96} -14.0000i q^{97} +1.00000i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9	\( 2 q + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{14} - 2 q^{15} - 2 q^{16} - 4 q^{20} - 2 q^{21} - 6 q^{24} + 6 q^{25} - 8 q^{26} - 8 q^{29} + 4 q^{30} + 4 q^{31} - 4 q^{34} - 2 q^{35} - 2 q^{36} - 8 q^{39} - 6 q^{40} - 20 q^{41} - 2 q^{44} + 4 q^{45} + 12 q^{46} - 2 q^{49} + 8 q^{50} - 4 q^{51} + 2 q^{54} + 4 q^{55} - 6 q^{56} - 8 q^{59} - 2 q^{60} - 4 q^{61} - 14 q^{64} - 8 q^{65} + 2 q^{66} + 12 q^{69} + 4 q^{70} - 16 q^{71} - 8 q^{74} + 8 q^{75} + 28 q^{79} + 4 q^{80} + 2 q^{81} - 2 q^{84} - 4 q^{85} + 8 q^{86} + 24 q^{89} + 2 q^{90} - 8 q^{91} - 10 q^{96} + 2 q^{99}+O(q^{100}) \) 2 * q + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^9 - 2 * q^10 - 2 * q^11 - 2 * q^14 - 2 * q^15 - 2 * q^16 - 4 * q^20 - 2 * q^21 - 6 * q^24 + 6 * q^25 - 8 * q^26 - 8 * q^29 + 4 * q^30 + 4 * q^31 - 4 * q^34 - 2 * q^35 - 2 * q^36 - 8 * q^39 - 6 * q^40 - 20 * q^41 - 2 * q^44 + 4 * q^45 + 12 * q^46 - 2 * q^49 + 8 * q^50 - 4 * q^51 + 2 * q^54 + 4 * q^55 - 6 * q^56 - 8 * q^59 - 2 * q^60 - 4 * q^61 - 14 * q^64 - 8 * q^65 + 2 * q^66 + 12 * q^69 + 4 * q^70 - 16 * q^71 - 8 * q^74 + 8 * q^75 + 28 * q^79 + 4 * q^80 + 2 * q^81 - 2 * q^84 - 4 * q^85 + 8 * q^86 + 24 * q^89 + 2 * q^90 - 8 * q^91 - 10 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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