LMFDB - Embedded newform 1365.2.f.c.274.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1365,2,Mod(274,1365)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1365, 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("1365.274");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1365 = 3 \cdot 5 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1365.f (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:	$10.8995798759$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{20})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			274.7
Root			$-0.587785 + 0.809017i$ of defining polynomial
Character	$\chi$	$=$	1365.274
Dual form			1365.2.f.c.274.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +(-1.90211 + 1.17557i) q^{5} -1.61803 q^{6} -1.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} +(-1.90211 - 3.07768i) q^{10} -4.80423 q^{11} -0.618034i q^{12} +1.00000i q^{13} +1.61803 q^{14} +(-1.17557 - 1.90211i) q^{15} -4.85410 q^{16} -3.24669i q^{17} -1.61803i q^{18} +0.891491 q^{19} +(1.17557 - 0.726543i) q^{20} +1.00000 q^{21} -7.77340i q^{22} +1.41164i q^{23} -2.23607 q^{24} +(2.23607 - 4.47214i) q^{25} -1.61803 q^{26} -1.00000i q^{27} +0.618034i q^{28} -0.459650 q^{29} +(3.07768 - 1.90211i) q^{30} +0.340519 q^{31} -3.38197i q^{32} -4.80423i q^{33} +5.25325 q^{34} +(1.17557 + 1.90211i) q^{35} +0.618034 q^{36} +1.71592i q^{37} +1.44246i q^{38} -1.00000 q^{39} +(-2.62866 - 4.25325i) q^{40} -3.07768 q^{41} +1.61803i q^{42} -11.8885i q^{43} +2.96917 q^{44} +(1.90211 - 1.17557i) q^{45} -2.28408 q^{46} +4.50953i q^{47} -4.85410i q^{48} -1.00000 q^{49} +(7.23607 + 3.61803i) q^{50} +3.24669 q^{51} -0.618034i q^{52} -0.405074i q^{53} +1.61803 q^{54} +(9.13818 - 5.64771i) q^{55} +2.23607 q^{56} +0.891491i q^{57} -0.743729i q^{58} -8.94241 q^{59} +(0.726543 + 1.17557i) q^{60} -10.3138 q^{61} +0.550972i q^{62} +1.00000i q^{63} -4.23607 q^{64} +(-1.17557 - 1.90211i) q^{65} +7.77340 q^{66} -8.24367i q^{67} +2.00656i q^{68} -1.41164 q^{69} +(-3.07768 + 1.90211i) q^{70} +7.57763 q^{71} -2.23607i q^{72} +2.48276i q^{73} -2.77642 q^{74} +(4.47214 + 2.23607i) q^{75} -0.550972 q^{76} +4.80423i q^{77} -1.61803i q^{78} +9.07112 q^{79} +(9.23305 - 5.70634i) q^{80} +1.00000 q^{81} -4.97980i q^{82} -3.83035i q^{83} -0.618034 q^{84} +(3.81671 + 6.17557i) q^{85} +19.2360 q^{86} -0.459650i q^{87} -10.7426i q^{88} -15.2935 q^{89} +(1.90211 + 3.07768i) q^{90} +1.00000 q^{91} -0.872441i q^{92} +0.340519i q^{93} -7.29657 q^{94} +(-1.69572 + 1.04801i) q^{95} +3.38197 q^{96} +10.4893i q^{97} -1.61803i q^{98} +4.80423 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{6} - 8 q^{9} - 8 q^{11} + 4 q^{14} - 12 q^{16} + 4 q^{19} + 8 q^{21} - 4 q^{26} + 12 q^{29} - 4 q^{31} + 8 q^{34} - 4 q^{36} - 8 q^{39} - 4 q^{44} - 12 q^{46} - 8 q^{49} + 40 q^{50}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^6 - 8 * q^9 - 8 * q^11 + 4 * q^14 - 12 * q^16 + 4 * q^19 + 8 * q^21 - 4 * q^26 + 12 * q^29 - 4 * q^31 + 8 * q^34 - 4 * q^36 - 8 * q^39 - 4 * q^44 - 12 * q^46 - 8 * q^49 + 40 * q^50 - 4 * q^51 + 4 * q^54 + 40 * q^55 - 8 * q^59 - 40 * q^61 - 16 * q^64 + 4 * q^66 + 16 * q^69 - 28 * q^71 - 20 * q^74 - 8 * q^76 + 52 * q^79 + 8 * q^81 + 4 * q^84 - 20 * q^85 + 8 * q^86 - 40 * q^89 + 8 * q^91 - 32 * q^94 + 20 * q^95 + 36 * q^96 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1365\mathbb{Z}\right)^\times$.

$n$	$106$	$547$	$911$	$976$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$			1.61803i			1.14412i	0.820211	+	0.572061i	$0.193856\pi$
$2$			1.61803i			1.14412i	−0.820211	+	0.572061i	$0.806144\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	−0.618034			−0.309017
$5$	−1.90211	+	1.17557i	−0.850651	+	0.525731i
$5$	−1.90211	+	1.17557i	−0.850651	+	0.525731i
$6$	−1.61803			−0.660560
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$			2.23607i			0.790569i
$9$	−1.00000			−0.333333
$10$	−1.90211	−	3.07768i	−0.601501	−	0.973249i
$11$	−4.80423			−1.44853			−0.724264	−	0.689522i	$-0.757820\pi$
$11$	−4.80423			−1.44853			−0.724264	+	0.689522i	$0.757820\pi$
$12$		−	0.618034i		−	0.178411i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.61803			0.432438
$15$	−1.17557	−	1.90211i	−0.303531	−	0.491123i
$16$	−4.85410			−1.21353
$17$		−	3.24669i		−	0.787438i	−0.919231	−	0.393719i	$-0.871188\pi$
$17$		−	3.24669i		−	0.787438i	0.919231	−	0.393719i	$-0.128812\pi$
$18$		−	1.61803i		−	0.381374i
$19$	0.891491			0.204522			0.102261	−	0.994758i	$-0.467392\pi$
$19$	0.891491			0.204522			0.102261	+	0.994758i	$0.467392\pi$
$20$	1.17557	−	0.726543i	0.262866	−	0.162460i
$21$	1.00000			0.218218
$22$		−	7.77340i		−	1.65729i
$23$			1.41164i			0.294347i	0.989111	+	0.147173i	$0.0470176\pi$
$23$			1.41164i			0.294347i	−0.989111	+	0.147173i	$0.952982\pi$
$24$	−2.23607			−0.456435
$25$	2.23607	−	4.47214i	0.447214	−	0.894427i
$26$	−1.61803			−0.317323
$27$		−	1.00000i		−	0.192450i
$28$			0.618034i			0.116797i
$29$	−0.459650			−0.0853548			−0.0426774	−	0.999089i	$-0.513589\pi$
$29$	−0.459650			−0.0853548			−0.0426774	+	0.999089i	$0.513589\pi$
$30$	3.07768	−	1.90211i	0.561906	−	0.347277i
$31$	0.340519			0.0611591			0.0305795	−	0.999532i	$-0.490265\pi$
$31$	0.340519			0.0611591			0.0305795	+	0.999532i	$0.490265\pi$
$32$		−	3.38197i		−	0.597853i
$33$		−	4.80423i		−	0.836308i
$34$	5.25325			0.900926
$35$	1.17557	+	1.90211i	0.198708	+	0.321516i
$36$	0.618034			0.103006
$37$			1.71592i			0.282096i	0.990003	+	0.141048i	$0.0450471\pi$
$37$			1.71592i			0.282096i	−0.990003	+	0.141048i	$0.954953\pi$
$38$			1.44246i			0.233998i
$39$	−1.00000			−0.160128
$40$	−2.62866	−	4.25325i	−0.415627	−	0.672499i
$41$	−3.07768			−0.480653			−0.240327	−	0.970692i	$-0.577255\pi$
$41$	−3.07768			−0.480653			−0.240327	+	0.970692i	$0.577255\pi$
$42$			1.61803i			0.249668i
$43$		−	11.8885i		−	1.81298i	−0.422232	−	0.906488i	$-0.638753\pi$
$43$		−	11.8885i		−	1.81298i	0.422232	−	0.906488i	$-0.361247\pi$
$44$	2.96917			0.447620
$45$	1.90211	−	1.17557i	0.283550	−	0.175244i
$46$	−2.28408			−0.336769
$47$			4.50953i			0.657782i	0.944368	+	0.328891i	$0.106675\pi$
$47$			4.50953i			0.657782i	−0.944368	+	0.328891i	$0.893325\pi$
$48$		−	4.85410i		−	0.700629i
$49$	−1.00000			−0.142857
$50$	7.23607	+	3.61803i	1.02333	+	0.511667i
$51$	3.24669			0.454627
$52$		−	0.618034i		−	0.0857059i
$53$		−	0.405074i		−	0.0556412i	−0.999613	−	0.0278206i	$-0.991143\pi$
$53$		−	0.405074i		−	0.0556412i	0.999613	−	0.0278206i	$-0.00885671\pi$
$54$	1.61803			0.220187
$55$	9.13818	−	5.64771i	1.23219	−	0.761537i
$56$	2.23607			0.298807
$57$			0.891491i			0.118081i
$58$		−	0.743729i		−	0.0976563i
$59$	−8.94241			−1.16420			−0.582101	−	0.813116i	$-0.697769\pi$
$59$	−8.94241			−1.16420			−0.582101	+	0.813116i	$0.697769\pi$
$60$	0.726543	+	1.17557i	0.0937962	+	0.151765i
$61$	−10.3138			−1.32054			−0.660270	−	0.751028i	$-0.729558\pi$
$61$	−10.3138			−1.32054			−0.660270	+	0.751028i	$0.729558\pi$
$62$			0.550972i			0.0699735i
$63$			1.00000i			0.125988i
$64$	−4.23607			−0.529508
$65$	−1.17557	−	1.90211i	−0.145812	−	0.235928i
$66$	7.77340			0.956840
$67$		−	8.24367i		−	1.00712i	−0.863959	−	0.503562i	$-0.832022\pi$
$67$		−	8.24367i		−	1.00712i	0.863959	−	0.503562i	$-0.167978\pi$
$68$			2.00656i			0.243332i
$69$	−1.41164			−0.169941
$70$	−3.07768	+	1.90211i	−0.367854	+	0.227346i
$71$	7.57763			0.899299			0.449649	−	0.893205i	$-0.351549\pi$
$71$	7.57763			0.899299			0.449649	+	0.893205i	$0.351549\pi$
$72$		−	2.23607i		−	0.263523i
$73$			2.48276i			0.290585i	0.989389	+	0.145292i	$0.0464123\pi$
$73$			2.48276i			0.290585i	−0.989389	+	0.145292i	$0.953588\pi$
$74$	−2.77642			−0.322752
$75$	4.47214	+	2.23607i	0.516398	+	0.258199i
$76$	−0.550972			−0.0632008
$77$			4.80423i			0.547492i
$78$		−	1.61803i		−	0.183206i
$79$	9.07112			1.02058			0.510290	−	0.860002i	$-0.329538\pi$
$79$	9.07112			1.02058			0.510290	+	0.860002i	$0.329538\pi$
$80$	9.23305	−	5.70634i	1.03229	−	0.637988i
$81$	1.00000			0.111111
$82$		−	4.97980i		−	0.549927i
$83$		−	3.83035i		−	0.420436i	−0.977655	−	0.210218i	$-0.932583\pi$
$83$		−	3.83035i		−	0.420436i	0.977655	−	0.210218i	$-0.0674173\pi$
$84$	−0.618034			−0.0674330
$85$	3.81671	+	6.17557i	0.413981	+	0.669835i
$86$	19.2360			2.07427
$87$		−	0.459650i		−	0.0492796i
$88$		−	10.7426i		−	1.14516i
$89$	−15.2935			−1.62111			−0.810556	−	0.585661i	$-0.800835\pi$
$89$	−15.2935			−1.62111			−0.810556	+	0.585661i	$0.800835\pi$
$90$	1.90211	+	3.07768i	0.200500	+	0.324416i
$91$	1.00000			0.104828
$92$		−	0.872441i		−	0.0909582i
$93$			0.340519i			0.0353102i
$94$	−7.29657			−0.752583
$95$	−1.69572	+	1.04801i	−0.173977	+	0.107524i
$96$	3.38197			0.345170
$97$			10.4893i			1.06503i	0.846421	+	0.532515i	$0.178753\pi$
$97$			10.4893i			1.06503i	−0.846421	+	0.532515i	$0.821247\pi$
$98$		−	1.61803i		−	0.163446i
$99$	4.80423			0.482843
$100$	−1.38197	+	2.76393i	−0.138197	+	0.276393i
$101$	2.46151			0.244930			0.122465	−	0.992473i	$-0.460920\pi$
$101$	2.46151			0.244930			0.122465	+	0.992473i	$0.460920\pi$
$102$			5.25325i			0.520150i
$103$		−	4.66906i		−	0.460056i	−0.973184	−	0.230028i	$-0.926118\pi$
$103$		−	4.66906i		−	0.460056i	0.973184	−	0.230028i	$-0.0738818\pi$
$104$	−2.23607			−0.219265
$105$	−1.90211	+	1.17557i	−0.185627	+	0.114724i
$106$	0.655423			0.0636604
$107$			6.28949i			0.608028i	0.952668	+	0.304014i	$0.0983270\pi$
$107$			6.28949i			0.608028i	−0.952668	+	0.304014i	$0.901673\pi$
$108$			0.618034i			0.0594703i
$109$	3.92045			0.375511			0.187756	−	0.982216i	$-0.439879\pi$
$109$	3.92045			0.375511			0.187756	+	0.982216i	$0.439879\pi$
$110$	9.13818	+	14.7859i	0.871291	+	1.40978i
$111$	−1.71592			−0.162868
$112$			4.85410i			0.458670i
$113$		−	2.43841i		−	0.229386i	−0.993401	−	0.114693i	$-0.963412\pi$
$113$		−	2.43841i		−	0.229386i	0.993401	−	0.114693i	$-0.0365884\pi$
$114$	−1.44246			−0.135099
$115$	−1.65948	−	2.68510i	−0.154747	−	0.250386i
$116$	0.284079			0.0263761
$117$		−	1.00000i		−	0.0924500i
$118$		−	14.4691i		−	1.33199i
$119$	−3.24669			−0.297624
$120$	4.25325	−	2.62866i	0.388267	−	0.239962i
$121$	12.0806			1.09824
$122$		−	16.6880i		−	1.51086i
$123$		−	3.07768i		−	0.277505i
$124$	−0.210453			−0.0188992
$125$	1.00406	+	11.1352i	0.0898056	+	0.995959i
$126$	−1.61803			−0.144146
$127$			13.3974i			1.18882i	0.804161	+	0.594412i	$0.202615\pi$
$127$			13.3974i			1.18882i	−0.804161	+	0.594412i	$0.797385\pi$
$128$		−	13.6180i		−	1.20368i
$129$	11.8885			1.04672
$130$	3.07768	−	1.90211i	0.269931	−	0.166826i
$131$	−20.5593			−1.79627			−0.898137	−	0.439716i	$-0.855079\pi$
$131$	−20.5593			−1.79627			−0.898137	+	0.439716i	$0.855079\pi$
$132$			2.96917i			0.258434i
$133$		−	0.891491i		−	0.0773021i
$134$	13.3385			1.15227
$135$	1.17557	+	1.90211i	0.101177	+	0.163708i
$136$	7.25982			0.622524
$137$			4.74258i			0.405186i	0.979263	+	0.202593i	$0.0649368\pi$
$137$			4.74258i			0.405186i	−0.979263	+	0.202593i	$0.935063\pi$
$138$		−	2.28408i		−	0.194434i
$139$	−14.9069			−1.26439			−0.632193	−	0.774811i	$-0.717845\pi$
$139$	−14.9069			−1.26439			−0.632193	+	0.774811i	$0.717845\pi$
$140$	−0.726543	−	1.17557i	−0.0614041	−	0.0993538i
$141$	−4.50953			−0.379771
$142$			12.2609i			1.02891i
$143$		−	4.80423i		−	0.401750i
$144$	4.85410			0.404508
$145$	0.874305	−	0.540350i	0.0726071	−	0.0448737i
$146$	−4.01719			−0.332465
$147$		−	1.00000i		−	0.0824786i
$148$		−	1.06050i		−	0.0871724i
$149$	9.09372			0.744986			0.372493	−	0.928035i	$-0.378503\pi$
$149$	9.09372			0.744986			0.372493	+	0.928035i	$0.378503\pi$
$150$	−3.61803	+	7.23607i	−0.295411	+	0.590822i
$151$	−12.9864			−1.05682			−0.528408	−	0.848991i	$-0.677211\pi$
$151$	−12.9864			−1.05682			−0.528408	+	0.848991i	$0.677211\pi$
$152$			1.99344i			0.161689i
$153$			3.24669i			0.262479i
$154$	−7.77340			−0.626399
$155$	−0.647706	+	0.400305i	−0.0520250	+	0.0321532i
$156$	0.618034			0.0494823
$157$		−	2.55703i		−	0.204073i	−0.994781	−	0.102036i	$-0.967464\pi$
$157$		−	2.55703i		−	0.204073i	0.994781	−	0.102036i	$-0.0325358\pi$
$158$			14.6774i			1.16767i
$159$	0.405074			0.0321245
$160$	3.97574	+	6.43288i	0.314310	+	0.508564i
$161$	1.41164			0.111253
$162$			1.61803i			0.127125i
$163$			25.2136i			1.97488i	0.157999	+	0.987439i	$0.449496\pi$
$163$			25.2136i			1.97488i	−0.157999	+	0.987439i	$0.550504\pi$
$164$	1.90211			0.148530
$165$	5.64771	+	9.13818i	0.439673	+	0.711406i
$166$	6.19764			0.481030
$167$			14.4068i			1.11483i	0.830235	+	0.557414i	$0.188206\pi$
$167$			14.4068i			1.11483i	−0.830235	+	0.557414i	$0.811794\pi$
$168$			2.23607i			0.172516i
$169$	−1.00000			−0.0769231
$170$	−9.99228	+	6.17557i	−0.766373	+	0.473645i
$171$	−0.891491			−0.0681741
$172$			7.34748i			0.560240i
$173$		−	10.0659i		−	0.765297i	−0.923894	−	0.382648i	$-0.875012\pi$
$173$		−	10.0659i		−	0.765297i	0.923894	−	0.382648i	$-0.124988\pi$
$174$	0.743729			0.0563819
$175$	−4.47214	−	2.23607i	−0.338062	−	0.169031i
$176$	23.3202			1.75783
$177$		−	8.94241i		−	0.672152i
$178$		−	24.7455i		−	1.85475i
$179$	−8.15910			−0.609840			−0.304920	−	0.952378i	$-0.598630\pi$
$179$	−8.15910			−0.609840			−0.304920	+	0.952378i	$0.598630\pi$
$180$	−1.17557	+	0.726543i	−0.0876219	+	0.0541533i
$181$	−20.5509			−1.52753			−0.763767	−	0.645492i	$-0.776652\pi$
$181$	−20.5509			−1.52753			−0.763767	+	0.645492i	$0.776652\pi$
$182$			1.61803i			0.119937i
$183$		−	10.3138i		−	0.762414i
$184$	−3.15652			−0.232702
$185$	−2.01719	−	3.26388i	−0.148306	−	0.239965i
$186$	−0.550972			−0.0403992
$187$			15.5978i			1.14063i
$188$		−	2.78704i		−	0.203266i
$189$	−1.00000			−0.0727393
$190$	−1.69572	−	2.74373i	−0.123020	−	0.199051i
$191$	14.8310			1.07313			0.536567	−	0.843858i	$-0.319721\pi$
$191$	14.8310			1.07313			0.536567	+	0.843858i	$0.319721\pi$
$192$		−	4.23607i		−	0.305712i
$193$		−	4.38447i		−	0.315601i	−0.987471	−	0.157801i	$-0.949560\pi$
$193$		−	4.38447i		−	0.315601i	0.987471	−	0.157801i	$-0.0504403\pi$
$194$	−16.9721			−1.21852
$195$	1.90211	−	1.17557i	0.136213	−	0.0841844i
$196$	0.618034			0.0441453
$197$			5.40321i			0.384963i	0.981301	+	0.192481i	$0.0616535\pi$
$197$			5.40321i			0.384963i	−0.981301	+	0.192481i	$0.938347\pi$
$198$			7.77340i			0.552432i
$199$	11.5692			0.820119			0.410059	−	0.912059i	$-0.365508\pi$
$199$	11.5692			0.820119			0.410059	+	0.912059i	$0.365508\pi$
$200$	10.0000	+	5.00000i	0.707107	+	0.353553i
$201$	8.24367			0.581464
$202$			3.98281i			0.280230i
$203$			0.459650i			0.0322611i
$204$	−2.00656			−0.140488
$205$	5.85410	−	3.61803i	0.408868	−	0.252694i
$206$	7.55470			0.526361
$207$		−	1.41164i		−	0.0981157i
$208$		−	4.85410i		−	0.336571i
$209$	−4.28293			−0.296256
$210$	−1.90211	−	3.07768i	−0.131258	−	0.212380i
$211$	−10.7653			−0.741113			−0.370556	−	0.928810i	$-0.620833\pi$
$211$	−10.7653			−0.741113			−0.370556	+	0.928810i	$0.620833\pi$
$212$			0.250349i			0.0171941i
$213$			7.57763i			0.519210i
$214$	−10.1766			−0.695659
$215$	13.9757	+	22.6132i	0.953138	+	1.54221i
$216$	2.23607			0.152145
$217$		−	0.340519i		−	0.0231160i
$218$			6.34342i			0.429631i
$219$	−2.48276			−0.167769
$220$	−5.64771	+	3.49047i	−0.380768	+	0.235328i
$221$	3.24669			0.218396
$222$		−	2.77642i		−	0.186341i
$223$		−	9.65948i		−	0.646847i	−0.946254	−	0.323423i	$-0.895166\pi$
$223$		−	9.65948i		−	0.646847i	0.946254	−	0.323423i	$-0.104834\pi$
$224$	−3.38197			−0.225967
$225$	−2.23607	+	4.47214i	−0.149071	+	0.298142i
$226$	3.94542			0.262446
$227$		−	27.8250i		−	1.84681i	−0.383825	−	0.923406i	$-0.625393\pi$
$227$		−	27.8250i		−	1.84681i	0.383825	−	0.923406i	$-0.374607\pi$
$228$		−	0.550972i		−	0.0364890i
$229$	−8.53026			−0.563695			−0.281848	−	0.959459i	$-0.590947\pi$
$229$	−8.53026			−0.563695			−0.281848	+	0.959459i	$0.590947\pi$
$230$	4.34458	−	2.68510i	0.286473	−	0.177050i
$231$	−4.80423			−0.316095
$232$		−	1.02781i		−	0.0674789i
$233$			21.1471i			1.38540i	0.721228	+	0.692698i	$0.243578\pi$
$233$			21.1471i			1.38540i	−0.721228	+	0.692698i	$0.756422\pi$
$234$	1.61803			0.105774
$235$	−5.30127	−	8.57763i	−0.345816	−	0.559543i
$236$	5.52671			0.359758
$237$			9.07112i			0.589233i
$238$		−	5.25325i		−	0.340518i
$239$	−18.1840			−1.17623			−0.588113	−	0.808779i	$-0.700129\pi$
$239$	−18.1840			−1.17623			−0.588113	+	0.808779i	$0.700129\pi$
$240$	5.70634	+	9.23305i	0.368343	+	0.595991i
$241$	−11.7022			−0.753803			−0.376901	−	0.926253i	$-0.623010\pi$
$241$	−11.7022			−0.753803			−0.376901	+	0.926253i	$0.623010\pi$
$242$			19.5468i			1.25652i
$243$			1.00000i			0.0641500i
$244$	6.37425			0.408069
$245$	1.90211	−	1.17557i	0.121522	−	0.0751044i
$246$	4.97980			0.317500
$247$			0.891491i			0.0567242i
$248$			0.761425i			0.0483505i
$249$	3.83035			0.242739
$250$	−18.0171	+	1.62460i	−1.13950	+	0.102749i
$251$	6.64185			0.419230			0.209615	−	0.977784i	$-0.432779\pi$
$251$	6.64185			0.419230			0.209615	+	0.977784i	$0.432779\pi$
$252$		−	0.618034i		−	0.0389325i
$253$		−	6.78183i		−	0.426370i
$254$	−21.6774			−1.36016
$255$	−6.17557	+	3.81671i	−0.386729	+	0.239012i
$256$	13.5623			0.847644
$257$			16.4358i			1.02524i	0.858617	+	0.512618i	$0.171324\pi$
$257$			16.4358i			1.02524i	−0.858617	+	0.512618i	$0.828676\pi$
$258$			19.2360i			1.19758i
$259$	1.71592			0.106622
$260$	0.726543	+	1.17557i	0.0450583	+	0.0729058i
$261$	0.459650			0.0284516
$262$		−	33.2656i		−	2.05516i
$263$		−	27.9057i		−	1.72074i	−0.509673	−	0.860368i	$-0.670234\pi$
$263$		−	27.9057i		−	1.72074i	0.509673	−	0.860368i	$-0.329766\pi$
$264$	10.7426			0.661160
$265$	0.476193	+	0.770497i	0.0292523	+	0.0473312i
$266$	1.44246			0.0884431
$267$		−	15.2935i		−	0.935950i
$268$			5.09487i			0.311219i
$269$	−27.3788			−1.66932			−0.834659	−	0.550768i	$-0.814335\pi$
$269$	−27.3788			−1.66932			−0.834659	+	0.550768i	$0.814335\pi$
$270$	−3.07768	+	1.90211i	−0.187302	+	0.115759i
$271$	−3.10600			−0.188676			−0.0943381	−	0.995540i	$-0.530073\pi$
$271$	−3.10600			−0.188676			−0.0943381	+	0.995540i	$0.530073\pi$
$272$			15.7598i			0.955576i
$273$			1.00000i			0.0605228i
$274$	−7.67365			−0.463582
$275$	−10.7426	+	21.4852i	−0.647802	+	1.29560i
$276$	0.872441			0.0525148
$277$		−	30.2146i		−	1.81542i	−0.419599	−	0.907710i	$-0.637829\pi$
$277$		−	30.2146i		−	1.81542i	0.419599	−	0.907710i	$-0.362171\pi$
$278$		−	24.1198i		−	1.44661i
$279$	−0.340519			−0.0203864
$280$	−4.25325	+	2.62866i	−0.254181	+	0.157092i
$281$	−0.922959			−0.0550591			−0.0275296	−	0.999621i	$-0.508764\pi$
$281$	−0.922959			−0.0550591			−0.0275296	+	0.999621i	$0.508764\pi$
$282$		−	7.29657i		−	0.434504i
$283$		−	16.7953i		−	0.998376i	−0.866494	−	0.499188i	$-0.833632\pi$
$283$		−	16.7953i		−	0.998376i	0.866494	−	0.499188i	$-0.166368\pi$
$284$	−4.68323			−0.277899
$285$	−1.04801	−	1.69572i	−0.0620788	−	0.100446i
$286$	7.77340			0.459651
$287$			3.07768i			0.181670i
$288$			3.38197i			0.199284i
$289$	6.45901			0.379942
$290$	0.874305	+	1.41466i	0.0513410	+	0.0830715i
$291$	−10.4893			−0.614895
$292$		−	1.53443i		−	0.0897956i
$293$			5.53066i			0.323104i	0.986864	+	0.161552i	$0.0516500\pi$
$293$			5.53066i			0.323104i	−0.986864	+	0.161552i	$0.948350\pi$
$294$	1.61803			0.0943657
$295$	17.0095	−	10.5124i	0.990330	−	0.612057i
$296$	−3.83692			−0.223016
$297$			4.80423i			0.278769i
$298$			14.7139i			0.852356i
$299$	−1.41164			−0.0816372
$300$	−2.76393	−	1.38197i	−0.159576	−	0.0797878i
$301$	−11.8885			−0.685240
$302$		−	21.0124i		−	1.20913i
$303$			2.46151i			0.141410i
$304$	−4.32739			−0.248193
$305$	19.6179	−	12.1245i	1.12332	−	0.694249i
$306$	−5.25325			−0.300309
$307$			31.3957i			1.79185i	0.444208	+	0.895923i	$0.353485\pi$
$307$			31.3957i			1.79185i	−0.444208	+	0.895923i	$0.646515\pi$
$308$		−	2.96917i		−	0.169184i
$309$	4.66906			0.265614
$310$	−0.647706	−	1.04801i	−0.0367873	−	0.0595230i
$311$	2.73362			0.155009			0.0775046	−	0.996992i	$-0.475305\pi$
$311$	2.73362			0.155009			0.0775046	+	0.996992i	$0.475305\pi$
$312$		−	2.23607i		−	0.126592i
$313$		−	2.92489i		−	0.165325i	−0.996578	−	0.0826624i	$-0.973658\pi$
$313$		−	2.92489i		−	0.165325i	0.996578	−	0.0826624i	$-0.0263423\pi$
$314$	4.13736			0.233485
$315$	−1.17557	−	1.90211i	−0.0662359	−	0.107172i
$316$	−5.60626			−0.315377
$317$		−	0.810148i		−	0.0455024i	−0.999741	−	0.0227512i	$-0.992757\pi$
$317$		−	0.810148i		−	0.0455024i	0.999741	−	0.0227512i	$-0.00724256\pi$
$318$			0.655423i			0.0367543i
$319$	2.20826			0.123639
$320$	8.05748	−	4.97980i	0.450427	−	0.278379i
$321$	−6.28949			−0.351045
$322$			2.28408i			0.127287i
$323$		−	2.89440i		−	0.161049i
$324$	−0.618034			−0.0343352
$325$	4.47214	+	2.23607i	0.248069	+	0.124035i
$326$	−40.7964			−2.25950
$327$			3.92045i			0.216801i
$328$		−	6.88191i		−	0.379990i
$329$	4.50953			0.248618
$330$	−14.7859	+	9.13818i	−0.813936	+	0.503040i
$331$	−5.02278			−0.276077			−0.138038	−	0.990427i	$-0.544080\pi$
$331$	−5.02278			−0.276077			−0.138038	+	0.990427i	$0.544080\pi$
$332$			2.36729i			0.129922i
$333$		−	1.71592i		−	0.0940319i
$334$	−23.3106			−1.27550
$335$	9.69102	+	15.6804i	0.529477	+	0.856712i
$336$	−4.85410			−0.264813
$337$			14.9881i			0.816455i	0.912880	+	0.408227i	$0.133853\pi$
$337$			14.9881i			0.816455i	−0.912880	+	0.408227i	$0.866147\pi$
$338$		−	1.61803i		−	0.0880094i
$339$	2.43841			0.132436
$340$	−2.35886	−	3.81671i	−0.127927	−	0.206990i
$341$	−1.63593			−0.0885907
$342$		−	1.44246i		−	0.0779995i
$343$			1.00000i			0.0539949i
$344$	26.5834			1.43328
$345$	2.68510	−	1.65948i	0.144561	−	0.0893434i
$346$	16.2870			0.875594
$347$			3.88544i			0.208581i	0.994547	+	0.104291i	$0.0332572\pi$
$347$			3.88544i			0.208581i	−0.994547	+	0.104291i	$0.966743\pi$
$348$			0.284079i			0.0152282i
$349$	−33.1267			−1.77323			−0.886616	−	0.462507i	$-0.846950\pi$
$349$	−33.1267			−1.77323			−0.886616	+	0.462507i	$0.846950\pi$
$350$	3.61803	−	7.23607i	0.193392	−	0.386784i
$351$	1.00000			0.0533761
$352$			16.2477i			0.866007i
$353$			6.16721i			0.328248i	0.986440	+	0.164124i	$0.0524796\pi$
$353$			6.16721i			0.328248i	−0.986440	+	0.164124i	$0.947520\pi$
$354$	14.4691			0.769025
$355$	−14.4135	+	8.90803i	−0.764989	+	0.472789i
$356$	9.45193			0.500951
$357$		−	3.24669i		−	0.171833i
$358$		−	13.2017i		−	0.697731i
$359$	4.35926			0.230073			0.115036	−	0.993361i	$-0.463302\pi$
$359$	4.35926			0.230073			0.115036	+	0.993361i	$0.463302\pi$
$360$	2.62866	+	4.25325i	0.138542	+	0.224166i
$361$	−18.2052			−0.958171
$362$		−	33.2520i		−	1.74769i
$363$			12.0806i			0.634066i
$364$	−0.618034			−0.0323938
$365$	−2.91866	−	4.72249i	−0.152769	−	0.247186i
$366$	16.6880			0.872296
$367$			35.6921i			1.86311i	0.363600	+	0.931555i	$0.381547\pi$
$367$			35.6921i			1.86311i	−0.363600	+	0.931555i	$0.618453\pi$
$368$		−	6.85224i		−	0.357198i
$369$	3.07768			0.160218
$370$	5.28106	−	3.26388i	0.274549	−	0.169681i
$371$	−0.405074			−0.0210304
$372$		−	0.210453i		−	0.0109115i
$373$			11.6759i			0.604556i	0.953220	+	0.302278i	$0.0977471\pi$
$373$			11.6759i			0.604556i	−0.953220	+	0.302278i	$0.902253\pi$
$374$	−25.2378			−1.30502
$375$	−11.1352	+	1.00406i	−0.575017	+	0.0518493i
$376$	−10.0836			−0.520022
$377$		−	0.459650i		−	0.0236732i
$378$		−	1.61803i		−	0.0832227i
$379$	−20.0941			−1.03217			−0.516083	−	0.856539i	$-0.672610\pi$
$379$	−20.0941			−1.03217			−0.516083	+	0.856539i	$0.672610\pi$
$380$	1.04801	−	0.647706i	0.0537618	−	0.0332266i
$381$	−13.3974			−0.686367
$382$			23.9971i			1.22780i
$383$		−	0.874948i		−	0.0447078i	−0.999750	−	0.0223539i	$-0.992884\pi$
$383$		−	0.874948i		−	0.0447078i	0.999750	−	0.0223539i	$-0.00711605\pi$
$384$	13.6180			0.694942
$385$	−5.64771	−	9.13818i	−0.287834	−	0.465725i
$386$	7.09423			0.361087
$387$			11.8885i			0.604325i
$388$		−	6.48276i		−	0.329112i
$389$	−32.7010			−1.65801			−0.829004	−	0.559243i	$-0.811092\pi$
$389$	−32.7010			−1.65801			−0.829004	+	0.559243i	$0.811092\pi$
$390$	1.90211	+	3.07768i	0.0963172	+	0.155845i
$391$	4.58315			0.231780
$392$		−	2.23607i		−	0.112938i
$393$		−	20.5593i		−	1.03708i
$394$	−8.74258			−0.440445
$395$	−17.2543	+	10.6637i	−0.868158	+	0.536551i
$396$	−2.96917			−0.149207
$397$			37.1937i			1.86670i	0.358971	+	0.933349i	$0.383128\pi$
$397$			37.1937i			1.86670i	−0.358971	+	0.933349i	$0.616872\pi$
$398$			18.7194i			0.938316i
$399$	0.891491			0.0446304
$400$	−10.8541	+	21.7082i	−0.542705	+	1.08541i
$401$	−3.69636			−0.184587			−0.0922937	−	0.995732i	$-0.529420\pi$
$401$	−3.69636			−0.184587			−0.0922937	+	0.995732i	$0.529420\pi$
$402$			13.3385i			0.665266i
$403$			0.340519i			0.0169625i
$404$	−1.52130			−0.0756875
$405$	−1.90211	+	1.17557i	−0.0945168	+	0.0584146i
$406$	−0.743729			−0.0369106
$407$		−	8.24367i		−	0.408624i
$408$			7.25982i			0.359415i
$409$	5.50837			0.272372			0.136186	−	0.990683i	$-0.456516\pi$
$409$	5.50837			0.272372			0.136186	+	0.990683i	$0.456516\pi$
$410$	5.85410	+	9.47214i	0.289113	+	0.467795i
$411$	−4.74258			−0.233934
$412$			2.88564i			0.142165i
$413$			8.94241i			0.440027i
$414$	2.28408			0.112256
$415$	4.50285	+	7.28576i	0.221036	+	0.357644i
$416$	3.38197			0.165815
$417$		−	14.9069i		−	0.729993i
$418$		−	6.92992i		−	0.338953i
$419$	24.5229			1.19802			0.599012	−	0.800740i	$-0.295560\pi$
$419$	24.5229			1.19802			0.599012	+	0.800740i	$0.295560\pi$
$420$	1.17557	−	0.726543i	0.0573620	−	0.0354516i
$421$	−6.91531			−0.337032			−0.168516	−	0.985699i	$-0.553897\pi$
$421$	−6.91531			−0.337032			−0.168516	+	0.985699i	$0.553897\pi$
$422$		−	17.4186i		−	0.847924i
$423$		−	4.50953i		−	0.219261i
$424$	0.905773			0.0439882
$425$	−14.5196	−	7.25982i	−0.704306	−	0.352153i
$426$	−12.2609			−0.594041
$427$			10.3138i			0.499117i
$428$		−	3.88712i		−	0.187891i
$429$	4.80423			0.231950
$430$	−36.5890	+	22.6132i	−1.76448	+	1.09051i
$431$	6.75428			0.325342			0.162671	−	0.986680i	$-0.447989\pi$
$431$	6.75428			0.325342			0.162671	+	0.986680i	$0.447989\pi$
$432$			4.85410i			0.233543i
$433$			26.2842i			1.26314i	0.775320	+	0.631568i	$0.217588\pi$
$433$			26.2842i			1.26314i	−0.775320	+	0.631568i	$0.782412\pi$
$434$	0.550972			0.0264475
$435$	0.540350	+	0.874305i	0.0259078	+	0.0419197i
$436$	−2.42297			−0.116039
$437$			1.25846i			0.0602005i
$438$		−	4.01719i		−	0.191949i
$439$	21.6867			1.03505			0.517526	−	0.855668i	$-0.326853\pi$
$439$	21.6867			1.03505			0.517526	+	0.855668i	$0.326853\pi$
$440$	12.6287	+	20.4336i	0.602048	+	0.974133i
$441$	1.00000			0.0476190
$442$			5.25325i			0.249872i
$443$		−	30.0870i		−	1.42948i	−0.699391	−	0.714739i	$-0.746545\pi$
$443$		−	30.0870i		−	1.42948i	0.699391	−	0.714739i	$-0.253455\pi$
$444$	1.06050			0.0503290
$445$	29.0901	−	17.9786i	1.37900	−	0.852269i
$446$	15.6294			0.740072
$447$			9.09372i			0.430118i
$448$			4.23607i			0.200135i
$449$	37.4141			1.76568			0.882840	−	0.469673i	$-0.155628\pi$
$449$	37.4141			1.76568			0.882840	+	0.469673i	$0.155628\pi$
$450$	−7.23607	−	3.61803i	−0.341112	−	0.170556i
$451$	14.7859			0.696240
$452$			1.50702i			0.0708842i
$453$		−	12.9864i		−	0.610152i
$454$	45.0218			2.11298
$455$	−1.90211	+	1.17557i	−0.0891724	+	0.0551116i
$456$	−1.99344			−0.0933512
$457$			8.26452i			0.386598i	0.981140	+	0.193299i	$0.0619187\pi$
$457$			8.26452i			0.386598i	−0.981140	+	0.193299i	$0.938081\pi$
$458$		−	13.8022i		−	0.644937i
$459$	−3.24669			−0.151542
$460$	1.02562	+	1.65948i	0.0478196	+	0.0773737i
$461$	0.874815			0.0407442			0.0203721	−	0.999792i	$-0.493515\pi$
$461$	0.874815			0.0407442			0.0203721	+	0.999792i	$0.493515\pi$
$462$		−	7.77340i		−	0.361651i
$463$		−	20.4850i		−	0.952020i	−0.879440	−	0.476010i	$-0.842083\pi$
$463$		−	20.4850i		−	0.952020i	0.879440	−	0.476010i	$-0.157917\pi$
$464$	2.23119			0.103580
$465$	−0.400305	−	0.647706i	−0.0185637	−	0.0300367i
$466$	−34.2168			−1.58506
$467$			12.7298i			0.589063i	0.955642	+	0.294532i	$0.0951636\pi$
$467$			12.7298i			0.589063i	−0.955642	+	0.294532i	$0.904836\pi$
$468$			0.618034i			0.0285686i
$469$	−8.24367			−0.380657
$470$	13.8789	−	8.57763i	0.640186	−	0.395656i
$471$	2.55703			0.117822
$472$		−	19.9958i		−	0.920383i
$473$			57.1149i			2.62615i
$474$	−14.6774			−0.674154
$475$	1.99344	−	3.98687i	0.0914651	−	0.182930i
$476$	2.00656			0.0919707
$477$			0.405074i			0.0185471i
$478$		−	29.4223i		−	1.34575i
$479$	−24.9962			−1.14210			−0.571052	−	0.820914i	$-0.693464\pi$
$479$	−24.9962			−1.14210			−0.571052	+	0.820914i	$0.693464\pi$
$480$	−6.43288	+	3.97574i	−0.293620	+	0.181467i
$481$	−1.71592			−0.0782393
$482$		−	18.9345i		−	0.862443i
$483$			1.41164i			0.0642318i
$484$	−7.46621			−0.339373
$485$	−12.3309	−	19.9519i	−0.559919	−	0.905968i
$486$	−1.61803			−0.0733955
$487$		−	27.6813i		−	1.25436i	−0.778874	−	0.627180i	$-0.784209\pi$
$487$		−	27.6813i		−	1.25436i	0.778874	−	0.627180i	$-0.215791\pi$
$488$		−	23.0622i		−	1.04398i
$489$	−25.2136			−1.14020
$490$	1.90211	+	3.07768i	0.0859287	+	0.139036i
$491$	5.75969			0.259931			0.129966	−	0.991518i	$-0.458513\pi$
$491$	5.75969			0.259931			0.129966	+	0.991518i	$0.458513\pi$
$492$			1.90211i			0.0857539i
$493$			1.49234i			0.0672116i
$494$	−1.44246			−0.0648995
$495$	−9.13818	+	5.64771i	−0.410731	+	0.253846i
$496$	−1.65292			−0.0742181
$497$		−	7.57763i		−	0.339903i
$498$			6.19764i			0.277723i
$499$	35.2238			1.57683			0.788416	−	0.615143i	$-0.210902\pi$
$499$	35.2238			1.57683			0.788416	+	0.615143i	$0.210902\pi$
$500$	−0.620541	−	6.88191i	−0.0277515	−	0.307768i
$501$	−14.4068			−0.643646
$502$			10.7467i			0.479651i
$503$		−	23.1576i		−	1.03254i	−0.856425	−	0.516272i	$-0.827319\pi$
$503$		−	23.1576i		−	1.03254i	0.856425	−	0.516272i	$-0.172681\pi$
$504$	−2.23607			−0.0996024
$505$	−4.68208	+	2.89368i	−0.208350	+	0.128767i
$506$	10.9732			0.487820
$507$		−	1.00000i		−	0.0444116i
$508$		−	8.28002i		−	0.367367i
$509$	−7.23722			−0.320784			−0.160392	−	0.987053i	$-0.551276\pi$
$509$	−7.23722			−0.320784			−0.160392	+	0.987053i	$0.551276\pi$
$510$	−6.17557	−	9.99228i	−0.273459	−	0.442466i
$511$	2.48276			0.109831
$512$		−	5.29180i		−	0.233867i
$513$		−	0.891491i		−	0.0393603i
$514$	−26.5937			−1.17300
$515$	5.48881	+	8.88108i	0.241866	+	0.391347i
$516$	−7.34748			−0.323455
$517$		−	21.6648i		−	0.952816i
$518$			2.77642i			0.121989i
$519$	10.0659			0.441844
$520$	4.25325	−	2.62866i	0.186518	−	0.115274i
$521$	−16.2953			−0.713910			−0.356955	−	0.934122i	$-0.616185\pi$
$521$	−16.2953			−0.713910			−0.356955	+	0.934122i	$0.616185\pi$
$522$			0.743729i			0.0325521i
$523$		−	22.1147i		−	0.967010i	−0.875342	−	0.483505i	$-0.839363\pi$
$523$		−	22.1147i		−	0.967010i	0.875342	−	0.483505i	$-0.160637\pi$
$524$	12.7063			0.555079
$525$	2.23607	−	4.47214i	0.0975900	−	0.195180i
$526$	45.1523			1.96873
$527$		−	1.10556i		−	0.0481590i
$528$			23.3202i			1.01488i
$529$	21.0073			0.913360
$530$	−1.24669	+	0.770497i	−0.0541527	+	0.0334682i
$531$	8.94241			0.388067
$532$			0.550972i			0.0238877i
$533$		−	3.07768i		−	0.133309i
$534$	24.7455			1.07084
$535$	−7.39374	−	11.9633i	−0.319659	−	0.517220i
$536$	18.4334			0.796202
$537$		−	8.15910i		−	0.352091i
$538$		−	44.2999i		−	1.90990i
$539$	4.80423			0.206933
$540$	−0.726543	−	1.17557i	−0.0312654	−	0.0505885i
$541$	−13.0517			−0.561138			−0.280569	−	0.959834i	$-0.590523\pi$
$541$	−13.0517			−0.561138			−0.280569	+	0.959834i	$0.590523\pi$
$542$		−	5.02562i		−	0.215869i
$543$		−	20.5509i		−	0.881922i
$544$	−10.9802			−0.470772
$545$	−7.45714	+	4.60877i	−0.319429	+	0.197418i
$546$	−1.61803			−0.0692455
$547$			21.3283i			0.911933i	0.889997	+	0.455966i	$0.150706\pi$
$547$			21.3283i			0.911933i	−0.889997	+	0.455966i	$0.849294\pi$
$548$		−	2.93107i		−	0.125209i
$549$	10.3138			0.440180
$550$	−34.7637	−	17.3819i	−1.48233	−	0.741165i
$551$	−0.409774			−0.0174569
$552$		−	3.15652i		−	0.134350i
$553$		−	9.07112i		−	0.385743i
$554$	48.8882			2.07706
$555$	3.26388	−	2.01719i	0.138544	−	0.0856248i
$556$	9.21296			0.390717
$557$		−	18.4676i		−	0.782496i	−0.920285	−	0.391248i	$-0.872043\pi$
$557$		−	18.4676i		−	0.782496i	0.920285	−	0.391248i	$-0.127957\pi$
$558$		−	0.550972i		−	0.0233245i
$559$	11.8885			0.502829
$560$	−5.70634	−	9.23305i	−0.241137	−	0.390168i
$561$	−15.5978			−0.658541
$562$		−	1.49338i		−	0.0629944i
$563$			3.69475i			0.155715i	0.996964	+	0.0778575i	$0.0248079\pi$
$563$			3.69475i			0.155715i	−0.996964	+	0.0778575i	$0.975192\pi$
$564$	2.78704			0.117356
$565$	2.86652	+	4.63812i	0.120595	+	0.195127i
$566$	27.1753			1.14226
$567$		−	1.00000i		−	0.0419961i
$568$			16.9441i			0.710958i
$569$	31.4370			1.31791			0.658954	−	0.752183i	$-0.270999\pi$
$569$	31.4370			1.31791			0.658954	+	0.752183i	$0.270999\pi$
$570$	2.74373	−	1.69572i	0.114922	−	0.0710258i
$571$	32.3772			1.35494			0.677471	−	0.735549i	$-0.263076\pi$
$571$	32.3772			1.35494			0.677471	+	0.735549i	$0.263076\pi$
$572$			2.96917i			0.124147i
$573$			14.8310i			0.619574i
$574$	−4.97980			−0.207853
$575$	6.31304	+	3.15652i	0.263272	+	0.131636i
$576$	4.23607			0.176503
$577$			26.6939i			1.11128i	0.831422	+	0.555642i	$0.187527\pi$
$577$			26.6939i			1.11128i	−0.831422	+	0.555642i	$0.812473\pi$
$578$			10.4509i			0.434700i
$579$	4.38447			0.182212
$580$	−0.540350	+	0.333955i	−0.0224368	+	0.0138667i
$581$	−3.83035			−0.158910
$582$		−	16.9721i		−	0.703515i
$583$			1.94607i			0.0805979i
$584$	−5.55161			−0.229727
$585$	1.17557	+	1.90211i	0.0486039	+	0.0786427i
$586$	−8.94879			−0.369671
$587$			25.0174i			1.03258i	0.856414	+	0.516289i	$0.172687\pi$
$587$			25.0174i			1.03258i	−0.856414	+	0.516289i	$0.827313\pi$
$588$			0.618034i			0.0254873i
$589$	0.303570			0.0125084
$590$	17.0095	+	27.5219i	0.700269	+	1.13306i
$591$	−5.40321			−0.222258
$592$		−	8.32926i		−	0.342330i
$593$		−	30.4293i		−	1.24958i	−0.780792	−	0.624791i	$-0.785184\pi$
$593$		−	30.4293i		−	1.24958i	0.780792	−	0.624791i	$-0.214816\pi$
$594$	−7.77340			−0.318947
$595$	6.17557	−	3.81671i	0.253174	−	0.156470i
$596$	−5.62023			−0.230213
$597$			11.5692i			0.473496i
$598$		−	2.28408i		−	0.0934029i
$599$	45.6159			1.86382			0.931908	−	0.362694i	$-0.118143\pi$
$599$	45.6159			1.86382			0.931908	+	0.362694i	$0.118143\pi$
$600$	−5.00000	+	10.0000i	−0.204124	+	0.408248i
$601$	30.8212			1.25722			0.628611	−	0.777720i	$-0.283624\pi$
$601$	30.8212			1.25722			0.628611	+	0.777720i	$0.283624\pi$
$602$		−	19.2360i		−	0.783999i
$603$			8.24367i			0.335708i
$604$	8.02601			0.326574
$605$	−22.9786	+	14.2016i	−0.934215	+	0.577376i
$606$	−3.98281			−0.161791
$607$			45.7895i			1.85854i	0.369403	+	0.929269i	$0.379562\pi$
$607$			45.7895i			1.85854i	−0.369403	+	0.929269i	$0.620438\pi$
$608$		−	3.01499i		−	0.122274i
$609$	−0.459650			−0.0186259
$610$	19.6179	+	31.7425i	0.794306	+	1.28521i
$611$	−4.50953			−0.182436
$612$		−	2.00656i		−	0.0811106i
$613$			42.3482i			1.71043i	0.518276	+	0.855214i	$0.326574\pi$
$613$			42.3482i			1.71043i	−0.518276	+	0.855214i	$0.673426\pi$
$614$	−50.7993			−2.05009
$615$	3.61803	+	5.85410i	0.145893	+	0.236060i
$616$	−10.7426			−0.432831
$617$		−	20.2302i		−	0.814438i	−0.913331	−	0.407219i	$-0.866499\pi$
$617$		−	20.2302i		−	0.814438i	0.913331	−	0.407219i	$-0.133501\pi$
$618$			7.55470i			0.303895i
$619$	42.9807			1.72754			0.863771	−	0.503885i	$-0.168097\pi$
$619$	42.9807			1.72754			0.863771	+	0.503885i	$0.168097\pi$
$620$	0.400305	−	0.247402i	0.0160766	−	0.00993590i
$621$	1.41164			0.0566471
$622$			4.42309i			0.177350i
$623$			15.2935i			0.612723i
$624$	4.85410			0.194320
$625$	−15.0000	−	20.0000i	−0.600000	−	0.800000i
$626$	4.73258			0.189152
$627$		−	4.28293i		−	0.171044i
$628$			1.58033i			0.0630620i
$629$	5.57106			0.222133
$630$	3.07768	−	1.90211i	0.122618	−	0.0757820i
$631$	−33.9944			−1.35329			−0.676647	−	0.736307i	$-0.736568\pi$
$631$	−33.9944			−1.35329			−0.676647	+	0.736307i	$0.736568\pi$
$632$			20.2836i			0.806840i
$633$		−	10.7653i		−	0.427882i
$634$	1.31085			0.0520604
$635$	−15.7495	−	25.4833i	−0.625001	−	1.01127i
$636$	−0.250349			−0.00992700
$637$		−	1.00000i		−	0.0396214i
$638$			3.57304i			0.141458i
$639$	−7.57763			−0.299766
$640$	16.0090	+	25.9030i	0.632810	+	1.02391i
$641$	−4.61668			−0.182348			−0.0911739	−	0.995835i	$-0.529062\pi$
$641$	−4.61668			−0.182348			−0.0911739	+	0.995835i	$0.529062\pi$
$642$		−	10.1766i		−	0.401639i
$643$		−	15.0975i		−	0.595386i	−0.954662	−	0.297693i	$-0.903783\pi$
$643$		−	15.0975i		−	0.595386i	0.954662	−	0.297693i	$-0.0962171\pi$
$644$	−0.872441			−0.0343790
$645$	−22.6132	+	13.9757i	−0.890395	+	0.550294i
$646$	4.68323			0.184259
$647$		−	24.3079i		−	0.955642i	−0.878457	−	0.477821i	$-0.841427\pi$
$647$		−	24.3079i		−	0.955642i	0.878457	−	0.477821i	$-0.158573\pi$
$648$			2.23607i			0.0878410i
$649$	42.9613			1.68638
$650$	−3.61803	+	7.23607i	−0.141911	+	0.283822i
$651$	0.340519			0.0133460
$652$		−	15.5828i		−	0.610271i
$653$			36.8251i			1.44108i	0.693415	+	0.720539i	$0.256105\pi$
$653$			36.8251i			1.44108i	−0.693415	+	0.720539i	$0.743895\pi$
$654$	−6.34342			−0.248048
$655$	39.1061	−	24.1689i	1.52800	−	0.944357i
$656$	14.9394			0.583285
$657$		−	2.48276i		−	0.0968616i
$658$			7.29657i			0.284450i
$659$	−26.7208			−1.04090			−0.520448	−	0.853893i	$-0.674235\pi$
$659$	−26.7208			−1.04090			−0.520448	+	0.853893i	$0.674235\pi$
$660$	−3.49047	−	5.64771i	−0.135867	−	0.219837i
$661$	27.8739			1.08417			0.542084	−	0.840324i	$-0.317636\pi$
$661$	27.8739			1.08417			0.542084	+	0.840324i	$0.317636\pi$
$662$		−	8.12703i		−	0.315866i
$663$			3.24669i			0.126091i
$664$	8.56493			0.332384
$665$	1.04801	+	1.69572i	0.0406401	+	0.0657571i
$666$	2.77642			0.107584
$667$		−	0.648859i		−	0.0251239i
$668$		−	8.90387i		−	0.344501i
$669$	9.65948			0.373457
$670$	−25.3714	+	15.6804i	−0.980183	+	0.605787i
$671$	49.5496			1.91284
$672$		−	3.38197i		−	0.130462i
$673$		−	2.24554i		−	0.0865591i	−0.999063	−	0.0432795i	$-0.986219\pi$
$673$		−	2.24554i		−	0.0865591i	0.999063	−	0.0432795i	$-0.0137806\pi$
$674$	−24.2513			−0.934124
$675$	−4.47214	−	2.23607i	−0.172133	−	0.0860663i
$676$	0.618034			0.0237705
$677$			3.64602i			0.140128i	0.997542	+	0.0700640i	$0.0223204\pi$
$677$			3.64602i			0.140128i	−0.997542	+	0.0700640i	$0.977680\pi$
$678$			3.94542i			0.151523i
$679$	10.4893			0.402543
$680$	−13.8090	+	8.53443i	−0.529551	+	0.327280i
$681$	27.8250			1.06626
$682$		−	2.64699i		−	0.101359i
$683$		−	16.3180i		−	0.624391i	−0.950018	−	0.312196i	$-0.898936\pi$
$683$		−	16.3180i		−	0.624391i	0.950018	−	0.312196i	$-0.101064\pi$
$684$	0.550972			0.0210669
$685$	−5.57523	−	9.02092i	−0.213019	−	0.344671i
$686$	−1.61803			−0.0617768
$687$		−	8.53026i		−	0.325450i
$688$			57.7079i			2.20009i
$689$	0.405074			0.0154321
$690$	2.68510	+	4.34458i	0.102220	+	0.165395i
$691$	25.9174			0.985946			0.492973	−	0.870045i	$-0.335910\pi$
$691$	25.9174			0.985946			0.492973	+	0.870045i	$0.335910\pi$
$692$			6.22107i			0.236490i
$693$		−	4.80423i		−	0.182497i
$694$	−6.28677			−0.238642
$695$	28.3546	−	17.5241i	1.07555	−	0.664727i
$696$	1.02781			0.0389589
$697$			9.99228i			0.378485i
$698$		−	53.6001i		−	2.02879i
$699$	−21.1471			−0.799858
$700$	2.76393	+	1.38197i	0.104467	+	0.0522334i
$701$	3.27417			0.123664			0.0618318	−	0.998087i	$-0.480306\pi$
$701$	3.27417			0.123664			0.0618318	+	0.998087i	$0.480306\pi$
$702$			1.61803i			0.0610688i
$703$			1.52973i			0.0576948i
$704$	20.3510			0.767008
$705$	8.57763	−	5.30127i	0.323052	−	0.199657i
$706$	−9.97876			−0.375555
$707$		−	2.46151i		−	0.0925748i
$708$			5.52671i			0.207707i
$709$	25.4583			0.956105			0.478052	−	0.878331i	$-0.341343\pi$
$709$	25.4583			0.956105			0.478052	+	0.878331i	$0.341343\pi$
$710$	−14.4135	−	23.3215i	−0.540929	−	0.875242i
$711$	−9.07112			−0.340194
$712$		−	34.1974i		−	1.28160i
$713$			0.480690i			0.0180020i
$714$	5.25325			0.196598
$715$	5.64771	+	9.13818i	0.211212	+	0.341749i
$716$	5.04260			0.188451
$717$		−	18.1840i		−	0.679094i
$718$			7.05342i			0.263231i
$719$	31.3560			1.16938			0.584690	−	0.811257i	$-0.301216\pi$
$719$	31.3560			1.16938			0.584690	+	0.811257i	$0.301216\pi$
$720$	−9.23305	+	5.70634i	−0.344095	+	0.212663i
$721$	−4.66906			−0.173885
$722$		−	29.4567i		−	1.09626i
$723$		−	11.7022i		−	0.435208i
$724$	12.7011			0.472034
$725$	−1.02781	+	2.05562i	−0.0381718	+	0.0763436i
$726$	−19.5468			−0.725450
$727$		−	31.0101i		−	1.15010i	−0.818118	−	0.575050i	$-0.804983\pi$
$727$		−	31.0101i		−	1.15010i	0.818118	−	0.575050i	$-0.195017\pi$
$728$			2.23607i			0.0828742i
$729$	−1.00000			−0.0370370
$730$	7.64114	−	4.72249i	0.282811	−	0.174787i
$731$	−38.5982			−1.42761
$732$			6.37425i			0.235599i
$733$		−	2.45901i		−	0.0908255i	−0.998968	−	0.0454127i	$-0.985540\pi$
$733$		−	2.45901i		−	0.0908255i	0.998968	−	0.0454127i	$-0.0144603\pi$
$734$	−57.7510			−2.13163
$735$	1.17557	+	1.90211i	0.0433616	+	0.0701605i
$736$	4.77411			0.175976
$737$			39.6045i			1.45885i
$738$			4.97980i			0.183309i
$739$	8.78416			0.323130			0.161565	−	0.986862i	$-0.448346\pi$
$739$	8.78416			0.323130			0.161565	+	0.986862i	$0.448346\pi$
$740$	1.24669	+	2.01719i	0.0458292	+	0.0741532i
$741$	−0.891491			−0.0327498
$742$		−	0.655423i		−	0.0240614i
$743$		−	8.51627i		−	0.312432i	−0.987723	−	0.156216i	$-0.950070\pi$
$743$		−	8.51627i		−	0.312432i	0.987723	−	0.156216i	$-0.0499296\pi$
$744$	−0.761425			−0.0279152
$745$	−17.2973	+	10.6903i	−0.633723	+	0.391662i
$746$	−18.8920			−0.691686
$747$			3.83035i			0.140145i
$748$		−	9.63999i		−	0.352473i
$749$	6.28949			0.229813
$750$	−1.62460	−	18.0171i	−0.0593219	−	0.657890i
$751$	33.0460			1.20587			0.602933	−	0.797791i	$-0.293998\pi$
$751$	33.0460			1.20587			0.602933	+	0.797791i	$0.293998\pi$
$752$		−	21.8897i		−	0.798235i
$753$			6.64185i			0.242043i
$754$	0.743729			0.0270850
$755$	24.7015	−	15.2664i	0.898981	−	0.555601i
$756$	0.618034			0.0224777
$757$			29.7676i			1.08192i	0.841048	+	0.540961i	$0.181939\pi$
$757$			29.7676i			1.08192i	−0.841048	+	0.540961i	$0.818061\pi$
$758$		−	32.5130i		−	1.18092i
$759$	6.78183			0.246165
$760$	−2.34342	−	3.79174i	−0.0850049	−	0.137541i
$761$	14.2403			0.516209			0.258104	−	0.966117i	$-0.416902\pi$
$761$	14.2403			0.516209			0.258104	+	0.966117i	$0.416902\pi$
$762$		−	21.6774i		−	0.785289i
$763$		−	3.92045i		−	0.141930i
$764$	−9.16606			−0.331616
$765$	−3.81671	−	6.17557i	−0.137994	−	0.223278i
$766$	1.41570			0.0511512
$767$		−	8.94241i		−	0.322892i
$768$			13.5623i			0.489388i
$769$	38.0129			1.37078			0.685390	−	0.728176i	$-0.259632\pi$
$769$	38.0129			1.37078			0.685390	+	0.728176i	$0.259632\pi$
$770$	14.7859	−	9.13818i	0.532846	−	0.329317i
$771$	−16.4358			−0.591920
$772$			2.70975i			0.0975262i
$773$			39.9492i			1.43687i	0.695593	+	0.718436i	$0.255142\pi$
$773$			39.9492i			1.43687i	−0.695593	+	0.718436i	$0.744858\pi$
$774$	−19.2360			−0.691422
$775$	0.761425	−	1.52285i	0.0273512	−	0.0547024i
$776$	−23.4548			−0.841980
$777$			1.71592i			0.0615583i
$778$		−	52.9114i		−	1.89696i
$779$	−2.74373			−0.0983043
$780$	−1.17557	+	0.726543i	−0.0420922	+	0.0260144i
$781$	−36.4046			−1.30266
$782$			7.41570i			0.265185i
$783$			0.459650i			0.0164265i
$784$	4.85410			0.173361
$785$	3.00597	+	4.86375i	0.107287	+	0.173595i
$786$	33.2656			1.18655
$787$			40.2577i			1.43503i	0.696541	+	0.717517i	$0.254721\pi$
$787$			40.2577i			1.43503i	−0.696541	+	0.717517i	$0.745279\pi$
$788$		−	3.33937i		−	0.118960i
$789$	27.9057			0.993468
$790$	−17.2543	−	27.9180i	−0.613880	−	0.993279i
$791$	−2.43841			−0.0866998
$792$			10.7426i			0.381721i
$793$		−	10.3138i		−	0.366252i
$794$	−60.1806			−2.13573
$795$	−0.770497	+	0.476193i	−0.0273267	+	0.0168888i
$796$	−7.15016			−0.253431
$797$		−	15.9645i		−	0.565493i	−0.959195	−	0.282747i	$-0.908754\pi$
$797$		−	15.9645i		−	0.565493i	0.959195	−	0.282747i	$-0.0912455\pi$
$798$			1.44246i			0.0510627i
$799$	14.6410			0.517962
$800$	−15.1246	−	7.56231i	−0.534736	−	0.267368i
$801$	15.2935			0.540371
$802$		−	5.98084i		−	0.211191i
$803$		−	11.9277i		−	0.420920i
$804$	−5.09487			−0.179682
$805$	−2.68510	+	1.65948i	−0.0946372	+	0.0584890i
$806$	−0.550972			−0.0194072
$807$		−	27.3788i		−	0.963781i
$808$			5.50411i			0.193634i
$809$	31.1877			1.09650			0.548251	−	0.836314i	$-0.315294\pi$
$809$	31.1877			1.09650			0.548251	+	0.836314i	$0.315294\pi$
$810$	−1.90211	−	3.07768i	−0.0668334	−	0.108139i
$811$	43.7661			1.53684			0.768418	−	0.639948i	$-0.221044\pi$
$811$	43.7661			1.53684			0.768418	+	0.639948i	$0.221044\pi$
$812$		−	0.284079i		−	0.00996922i
$813$		−	3.10600i		−	0.108932i
$814$	13.3385			0.467516
$815$	−29.6403	−	47.9590i	−1.03826	−	1.67993i
$816$	−15.7598			−0.551702
$817$		−	10.5985i		−	0.370794i
$818$			8.91273i			0.311626i
$819$	−1.00000			−0.0349428
$820$	−3.61803	+	2.23607i	−0.126347	+	0.0780869i
$821$	−29.9442			−1.04506			−0.522529	−	0.852621i	$-0.675011\pi$
$821$	−29.9442			−1.04506			−0.522529	+	0.852621i	$0.675011\pi$
$822$		−	7.67365i		−	0.267649i
$823$		−	10.1764i		−	0.354728i	−0.984145	−	0.177364i	$-0.943243\pi$
$823$		−	10.1764i		−	0.354728i	0.984145	−	0.177364i	$-0.0567570\pi$
$824$	10.4403			0.363707
$825$	−21.4852	−	10.7426i	−0.748017	−	0.374008i
$826$	−14.4691			−0.503445
$827$			36.8304i			1.28072i	0.768075	+	0.640360i	$0.221215\pi$
$827$			36.8304i			1.28072i	−0.768075	+	0.640360i	$0.778785\pi$
$828$			0.872441i			0.0303194i
$829$	−18.6901			−0.649133			−0.324567	−	0.945863i	$-0.605218\pi$
$829$	−18.6901			−0.649133			−0.324567	+	0.945863i	$0.605218\pi$
$830$	−11.7886	+	7.28576i	−0.409189	+	0.252892i
$831$	30.2146			1.04813
$832$		−	4.23607i		−	0.146859i
$833$			3.24669i			0.112491i
$834$	24.1198			0.835202
$835$	−16.9362	−	27.4033i	−0.586100	−	0.948330i
$836$	2.64699			0.0915482
$837$		−	0.340519i		−	0.0117701i
$838$			39.6789i			1.37069i
$839$	−42.0400			−1.45138			−0.725692	−	0.688020i	$-0.758480\pi$
$839$	−42.0400			−1.45138			−0.725692	+	0.688020i	$0.758480\pi$
$840$	−2.62866	−	4.25325i	−0.0906972	−	0.146751i
$841$	−28.7887			−0.992715
$842$		−	11.1892i		−	0.385606i
$843$		−	0.922959i		−	0.0317884i
$844$	6.65331			0.229016
$845$	1.90211	−	1.17557i	0.0654347	−	0.0404409i
$846$	7.29657			0.250861
$847$		−	12.0806i		−	0.415094i
$848$			1.96627i			0.0675220i
$849$	16.7953			0.576413
$850$	11.7466	−	23.4933i	0.402906	−	0.805812i
$851$	−2.42226			−0.0830340
$852$		−	4.68323i		−	0.160445i
$853$		−	33.0029i		−	1.13000i	−0.825092	−	0.564998i	$-0.808877\pi$
$853$		−	33.0029i		−	1.13000i	0.825092	−	0.564998i	$-0.191123\pi$
$854$	−16.6880			−0.571052
$855$	1.69572	−	1.04801i	0.0579923	−	0.0358412i
$856$	−14.0637			−0.480688
$857$			6.77951i			0.231583i	0.993274	+	0.115792i	$0.0369405\pi$
$857$			6.77951i			0.231583i	−0.993274	+	0.115792i	$0.963059\pi$
$858$			7.77340i			0.265380i
$859$	47.5032			1.62079			0.810395	−	0.585884i	$-0.199253\pi$
$859$	47.5032			1.62079			0.810395	+	0.585884i	$0.199253\pi$
$860$	−8.63748	−	13.9757i	−0.294536	−	0.476569i
$861$	−3.07768			−0.104887
$862$			10.9287i			0.372231i
$863$		−	35.7993i		−	1.21862i	−0.792931	−	0.609311i	$-0.791446\pi$
$863$		−	35.7993i		−	1.21862i	0.792931	−	0.609311i	$-0.208554\pi$
$864$	−3.38197			−0.115057
$865$	11.8332	+	19.1465i	0.402340	+	0.651000i
$866$	−42.5287			−1.44518
$867$			6.45901i			0.219359i
$868$			0.210453i			0.00714323i
$869$	−43.5797			−1.47834
$870$	−1.41466	+	0.874305i	−0.0479613	+	0.0296417i
$871$	8.24367			0.279326
$872$			8.76640i			0.296868i
$873$		−	10.4893i		−	0.355010i
$874$	−2.03624			−0.0688767
$875$	11.1352	−	1.00406i	0.376437	−	0.0339433i
$876$	1.53443			0.0518435
$877$		−	0.361560i		−	0.0122090i	−0.999981	−	0.00610451i	$-0.998057\pi$
$877$		−	0.361560i		−	0.0122090i	0.999981	−	0.00610451i	$-0.00194314\pi$
$878$			35.0899i			1.18423i
$879$	−5.53066			−0.186544
$880$	−44.3577	+	27.4145i	−1.49530	+	0.924144i
$881$	−15.8057			−0.532506			−0.266253	−	0.963903i	$-0.585786\pi$
$881$	−15.8057			−0.532506			−0.266253	+	0.963903i	$0.585786\pi$
$882$			1.61803i			0.0544820i
$883$			16.0987i			0.541765i	0.962612	+	0.270883i	$0.0873156\pi$
$883$			16.0987i			0.541765i	−0.962612	+	0.270883i	$0.912684\pi$
$884$	−2.00656			−0.0674881
$885$	10.5124	+	17.0095i	0.353371	+	0.571767i
$886$	48.6819			1.63550
$887$		−	23.3425i		−	0.783764i	−0.920015	−	0.391882i	$-0.871824\pi$
$887$		−	23.3425i		−	0.783764i	0.920015	−	0.391882i	$-0.128176\pi$
$888$		−	3.83692i		−	0.128758i
$889$	13.3974			0.449333
$890$	29.0901	+	47.0687i	0.975101	+	1.57775i
$891$	−4.80423			−0.160948
$892$			5.96989i			0.199887i
$893$			4.02020i			0.134531i
$894$	−14.7139			−0.492108
$895$	15.5195	−	9.59159i	0.518760	−	0.320612i
$896$	−13.6180			−0.454947
$897$		−	1.41164i		−	0.0471332i
$898$			60.5373i			2.02016i
$899$	−0.156520			−0.00522022
$900$	1.38197	−	2.76393i	0.0460655	−	0.0921311i
$901$	−1.31515			−0.0438140
$902$			23.9241i			0.796584i
$903$		−	11.8885i		−	0.395624i
$904$	5.45244			0.181346
$905$	39.0901	−	24.1590i	1.29940	−	0.803072i
$906$	21.0124			0.698089
$907$		−	43.6032i		−	1.44782i	−0.689894	−	0.723910i	$-0.742343\pi$
$907$		−	43.6032i		−	1.44782i	0.689894	−	0.723910i	$-0.257657\pi$
$908$			17.1968i			0.570696i
$909$	−2.46151			−0.0816433
$910$	−1.90211	−	3.07768i	−0.0630544	−	0.102024i
$911$	−42.3998			−1.40477			−0.702385	−	0.711798i	$-0.747881\pi$
$911$	−42.3998			−1.40477			−0.702385	+	0.711798i	$0.747881\pi$
$912$		−	4.32739i		−	0.143294i
$913$			18.4019i			0.609013i
$914$	−13.3723			−0.442315
$915$	12.1245	+	19.6179i	0.400825	+	0.648548i
$916$	5.27199			0.174191
$917$			20.5593i			0.678928i
$918$		−	5.25325i		−	0.173383i
$919$	6.50432			0.214558			0.107279	−	0.994229i	$-0.465786\pi$
$919$	6.50432			0.214558			0.107279	+	0.994229i	$0.465786\pi$
$920$	6.00406	−	3.71071i	0.197948	−	0.122339i
$921$	−31.3957			−1.03452
$922$			1.41548i			0.0466164i
$923$			7.57763i			0.249421i
$924$	2.96917			0.0976787
$925$	7.67383	+	3.83692i	0.252314	+	0.126157i
$926$	33.1455			1.08923
$927$			4.66906i			0.153352i
$928$			1.55452i			0.0510296i
$929$	−44.7854			−1.46936			−0.734681	−	0.678412i	$-0.762668\pi$
$929$	−44.7854			−1.46936			−0.734681	+	0.678412i	$0.762668\pi$
$930$	1.04801	−	0.647706i	0.0343656	−	0.0212391i
$931$	−0.891491			−0.0292175
$932$		−	13.0697i		−	0.428111i
$933$			2.73362i			0.0894946i
$934$	−20.5972			−0.673961
$935$	−18.3363	−	29.6688i	−0.599663	−	0.970275i
$936$	2.23607			0.0730882
$937$		−	9.80796i		−	0.320412i	−0.987084	−	0.160206i	$-0.948784\pi$
$937$		−	9.80796i		−	0.320412i	0.987084	−	0.160206i	$-0.0512158\pi$
$938$		−	13.3385i		−	0.435519i
$939$	2.92489			0.0954503
$940$	3.27636	+	5.30127i	0.106863	+	0.172908i
$941$	6.56164			0.213903			0.106952	−	0.994264i	$-0.465891\pi$
$941$	6.56164			0.213903			0.106952	+	0.994264i	$0.465891\pi$
$942$			4.13736i			0.134802i
$943$		−	4.34458i		−	0.141479i
$944$	43.4074			1.41279
$945$	1.90211	−	1.17557i	0.0618757	−	0.0382413i
$946$	−92.4139			−3.00463
$947$		−	19.7936i		−	0.643206i	−0.946875	−	0.321603i	$-0.895778\pi$
$947$		−	19.7936i		−	0.643206i	0.946875	−	0.321603i	$-0.104222\pi$
$948$		−	5.60626i		−	0.182083i
$949$	−2.48276			−0.0805937
$950$	6.45089	+	3.22545i	0.209295	+	0.104647i
$951$	0.810148			0.0262708
$952$		−	7.25982i		−	0.235292i
$953$			15.0734i			0.488275i	0.969741	+	0.244138i	$0.0785049\pi$
$953$			15.0734i			0.488275i	−0.969741	+	0.244138i	$0.921495\pi$
$954$	−0.655423			−0.0212201
$955$	−28.2102	+	17.4349i	−0.912862	+	0.564179i
$956$	11.2383			0.363474
$957$			2.20826i			0.0713829i
$958$		−	40.4446i		−	1.30671i
$959$	4.74258			0.153146
$960$	4.97980	+	8.05748i	0.160722	+	0.260054i
$961$	−30.8840			−0.996260
$962$		−	2.77642i		−	0.0895153i
$963$		−	6.28949i		−	0.202676i
$964$	7.23234			0.232938
$965$	5.15426	+	8.33976i	0.165921	+	0.268467i
$966$	−2.28408			−0.0734890
$967$		−	2.83139i		−	0.0910514i	−0.998963	−	0.0455257i	$-0.985504\pi$
$967$		−	2.83139i		−	0.0910514i	0.998963	−	0.0455257i	$-0.0144963\pi$
$968$			27.0130i			0.868231i
$969$	2.89440			0.0929814
$970$	32.2828	−	19.9519i	1.03654	−	0.640616i
$971$	−2.43707			−0.0782093			−0.0391047	−	0.999235i	$-0.512451\pi$
$971$	−2.43707			−0.0782093			−0.0391047	+	0.999235i	$0.512451\pi$
$972$		−	0.618034i		−	0.0198234i
$973$			14.9069i			0.477893i
$974$	44.7893			1.43514
$975$	−2.23607	+	4.47214i	−0.0716115	+	0.143223i
$976$	50.0640			1.60251
$977$			51.3238i			1.64199i	0.570934	+	0.820996i	$0.306581\pi$
$977$			51.3238i			1.64199i	−0.570934	+	0.820996i	$0.693419\pi$
$978$		−	40.7964i		−	1.30452i
$979$	73.4737			2.34823
$980$	−1.17557	+	0.726543i	−0.0375522	+	0.0232085i
$981$	−3.92045			−0.125170
$982$			9.31938i			0.297393i
$983$			10.8569i			0.346283i	0.984897	+	0.173141i	$0.0553917\pi$
$983$			10.8569i			0.346283i	−0.984897	+	0.173141i	$0.944608\pi$
$984$	6.88191			0.219387
$985$	−6.35185	−	10.2775i	−0.202387	−	0.327469i
$986$	−2.41466			−0.0768983
$987$			4.50953i			0.143540i
$988$		−	0.550972i		−	0.0175288i
$989$	16.7822			0.533644
$990$	−9.13818	−	14.7859i	−0.290430	−	0.469926i
$991$	−5.95012			−0.189012			−0.0945060	−	0.995524i	$-0.530127\pi$
$991$	−5.95012			−0.189012			−0.0945060	+	0.995524i	$0.530127\pi$
$992$		−	1.15163i		−	0.0365641i
$993$		−	5.02278i		−	0.159393i
$994$	12.2609			0.388891
$995$	−22.0059	+	13.6004i	−0.697635	+	0.431162i
$996$	−2.36729			−0.0750104
$997$		−	3.66128i		−	0.115954i	−0.998318	−	0.0579769i	$-0.981535\pi$
$997$		−	3.66128i		−	0.115954i	0.998318	−	0.0579769i	$-0.0184650\pi$
$998$			56.9932i			1.80409i
$999$	1.71592			0.0542893

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1365.2.f.c.274.7	yes	8
5.2	odd	4		6825.2.a.be.1.1		4
5.3	odd	4		6825.2.a.bm.1.3		4
5.4	even	2	inner	1365.2.f.c.274.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1365.2.f.c.274.1	✓	8	5.4	even	2	inner
1365.2.f.c.274.7	yes	8	1.1	even	1	trivial
6825.2.a.be.1.1		4	5.2	odd	4
6825.2.a.bm.1.3		4	5.3	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:	\( N \)	\(=\)	\( 1365 = 3 \cdot 5 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1365.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.61803i q^{2} +1.00000i q^{3} -0.618034 q^{4} +(-1.90211 + 1.17557i) q^{5} -1.61803 q^{6} -1.00000i q^{7} +2.23607i q^{8} -1.00000 q^{9} +(-1.90211 - 3.07768i) q^{10} -4.80423 q^{11} -0.618034i q^{12} +1.00000i q^{13} +1.61803 q^{14} +(-1.17557 - 1.90211i) q^{15} -4.85410 q^{16} -3.24669i q^{17} -1.61803i q^{18} +0.891491 q^{19} +(1.17557 - 0.726543i) q^{20} +1.00000 q^{21} -7.77340i q^{22} +1.41164i q^{23} -2.23607 q^{24} +(2.23607 - 4.47214i) q^{25} -1.61803 q^{26} -1.00000i q^{27} +0.618034i q^{28} -0.459650 q^{29} +(3.07768 - 1.90211i) q^{30} +0.340519 q^{31} -3.38197i q^{32} -4.80423i q^{33} +5.25325 q^{34} +(1.17557 + 1.90211i) q^{35} +0.618034 q^{36} +1.71592i q^{37} +1.44246i q^{38} -1.00000 q^{39} +(-2.62866 - 4.25325i) q^{40} -3.07768 q^{41} +1.61803i q^{42} -11.8885i q^{43} +2.96917 q^{44} +(1.90211 - 1.17557i) q^{45} -2.28408 q^{46} +4.50953i q^{47} -4.85410i q^{48} -1.00000 q^{49} +(7.23607 + 3.61803i) q^{50} +3.24669 q^{51} -0.618034i q^{52} -0.405074i q^{53} +1.61803 q^{54} +(9.13818 - 5.64771i) q^{55} +2.23607 q^{56} +0.891491i q^{57} -0.743729i q^{58} -8.94241 q^{59} +(0.726543 + 1.17557i) q^{60} -10.3138 q^{61} +0.550972i q^{62} +1.00000i q^{63} -4.23607 q^{64} +(-1.17557 - 1.90211i) q^{65} +7.77340 q^{66} -8.24367i q^{67} +2.00656i q^{68} -1.41164 q^{69} +(-3.07768 + 1.90211i) q^{70} +7.57763 q^{71} -2.23607i q^{72} +2.48276i q^{73} -2.77642 q^{74} +(4.47214 + 2.23607i) q^{75} -0.550972 q^{76} +4.80423i q^{77} -1.61803i q^{78} +9.07112 q^{79} +(9.23305 - 5.70634i) q^{80} +1.00000 q^{81} -4.97980i q^{82} -3.83035i q^{83} -0.618034 q^{84} +(3.81671 + 6.17557i) q^{85} +19.2360 q^{86} -0.459650i q^{87} -10.7426i q^{88} -15.2935 q^{89} +(1.90211 + 3.07768i) q^{90} +1.00000 q^{91} -0.872441i q^{92} +0.340519i q^{93} -7.29657 q^{94} +(-1.69572 + 1.04801i) q^{95} +3.38197 q^{96} +10.4893i q^{97} -1.61803i q^{98} +4.80423 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{6} - 8 q^{9} - 8 q^{11} + 4 q^{14} - 12 q^{16} + 4 q^{19} + 8 q^{21} - 4 q^{26} + 12 q^{29} - 4 q^{31} + 8 q^{34} - 4 q^{36} - 8 q^{39} - 4 q^{44} - 12 q^{46} - 8 q^{49} + 40 q^{50}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^6 - 8 * q^9 - 8 * q^11 + 4 * q^14 - 12 * q^16 + 4 * q^19 + 8 * q^21 - 4 * q^26 + 12 * q^29 - 4 * q^31 + 8 * q^34 - 4 * q^36 - 8 * q^39 - 4 * q^44 - 12 * q^46 - 8 * q^49 + 40 * q^50 - 4 * q^51 + 4 * q^54 + 40 * q^55 - 8 * q^59 - 40 * q^61 - 16 * q^64 + 4 * q^66 + 16 * q^69 - 28 * q^71 - 20 * q^74 - 8 * q^76 + 52 * q^79 + 8 * q^81 + 4 * q^84 - 20 * q^85 + 8 * q^86 - 40 * q^89 + 8 * q^91 - 32 * q^94 + 20 * q^95 + 36 * q^96 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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