LMFDB - Embedded newform 1690.2.b.a.339.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1690,2,Mod(339,1690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1690, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1690.339");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.b (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:	$13.4947179416$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.3534400.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 3x^{4} + 16x^{3} + x^{2} - 12x + 40 $ x^6 - 2x^5 - 3x^4 + 16x^3 + x^2 - 12x + 40
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			339.2
Root			$-1.81837 - 0.301352i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.a.339.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -0.602705i q^{3} -1.00000 q^{4} +(0.301352 - 2.21567i) q^{5} -0.602705 q^{6} -3.63675i q^{7} +1.00000i q^{8} +2.63675 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -0.602705i q^{3} -1.00000 q^{4} +(0.301352 - 2.21567i) q^{5} -0.602705 q^{6} -3.63675i q^{7} +1.00000i q^{8} +2.63675 q^{9} +(-2.21567 - 0.301352i) q^{10} -2.00000 q^{11} +0.602705i q^{12} -3.63675 q^{14} +(-1.33539 - 0.181627i) q^{15} +1.00000 q^{16} -6.67079i q^{17} -2.63675i q^{18} +8.06808 q^{19} +(-0.301352 + 2.21567i) q^{20} -2.19189 q^{21} +2.00000i q^{22} -0.794590i q^{23} +0.602705 q^{24} +(-4.81837 - 1.33539i) q^{25} -3.39730i q^{27} +3.63675i q^{28} +8.06808 q^{29} +(-0.181627 + 1.33539i) q^{30} -5.20541 q^{31} -1.00000i q^{32} +1.20541i q^{33} -6.67079 q^{34} +(-8.05783 - 1.09594i) q^{35} -2.63675 q^{36} -0.431337i q^{37} -8.06808i q^{38} +(2.21567 + 0.301352i) q^{40} -6.86267 q^{41} +2.19189i q^{42} +5.80811i q^{43} +2.00000 q^{44} +(0.794590 - 5.84216i) q^{45} -0.794590 q^{46} +7.63675i q^{47} -0.602705i q^{48} -6.22593 q^{49} +(-1.33539 + 4.81837i) q^{50} -4.02052 q^{51} -0.794590i q^{53} -3.39730 q^{54} +(-0.602705 + 4.43134i) q^{55} +3.63675 q^{56} -4.86267i q^{57} -8.06808i q^{58} +8.06808 q^{59} +(1.33539 + 0.181627i) q^{60} -2.86267 q^{61} +5.20541i q^{62} -9.58918i q^{63} -1.00000 q^{64} +1.20541 q^{66} +5.20541i q^{67} +6.67079i q^{68} -0.478903 q^{69} +(-1.09594 + 8.05783i) q^{70} +9.46538 q^{71} +2.63675i q^{72} -6.00000i q^{73} -0.431337 q^{74} +(-0.804849 + 2.90406i) q^{75} -8.06808 q^{76} +7.27349i q^{77} -1.93192 q^{79} +(0.301352 - 2.21567i) q^{80} +5.86267 q^{81} +6.86267i q^{82} +2.06808i q^{83} +2.19189 q^{84} +(-14.7803 - 2.01026i) q^{85} +5.80811 q^{86} -4.86267i q^{87} -2.00000i q^{88} -8.06808 q^{89} +(-5.84216 - 0.794590i) q^{90} +0.794590i q^{92} +3.13733i q^{93} +7.63675 q^{94} +(2.43134 - 17.8762i) q^{95} -0.602705 q^{96} +13.6573i q^{97} +6.22593i q^{98} -5.27349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 10 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 10 * q^9	$ 6 q - 6 q^{4} - 10 q^{9} - 4 q^{10} - 12 q^{11} + 4 q^{14} + 16 q^{15} + 6 q^{16} + 4 q^{19} - 24 q^{21} - 16 q^{25} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 8 q^{34} - 6 q^{35} + 10 q^{36} + 4 q^{40} - 4 q^{41} + 12 q^{44} + 12 q^{45} - 12 q^{46} - 26 q^{49} + 16 q^{50} - 20 q^{51} - 24 q^{54} - 4 q^{56} + 4 q^{59} - 16 q^{60} + 20 q^{61} - 6 q^{64} + 56 q^{69} - 12 q^{70} + 16 q^{71} + 16 q^{74} - 10 q^{75} - 4 q^{76} - 56 q^{79} - 2 q^{81} + 24 q^{84} - 28 q^{85} + 24 q^{86} - 4 q^{89} - 2 q^{90} + 20 q^{94} - 4 q^{95} + 20 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 10 * q^9 - 4 * q^10 - 12 * q^11 + 4 * q^14 + 16 * q^15 + 6 * q^16 + 4 * q^19 - 24 * q^21 - 16 * q^25 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 8 * q^34 - 6 * q^35 + 10 * q^36 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^45 - 12 * q^46 - 26 * q^49 + 16 * q^50 - 20 * q^51 - 24 * q^54 - 4 * q^56 + 4 * q^59 - 16 * q^60 + 20 * q^61 - 6 * q^64 + 56 * q^69 - 12 * q^70 + 16 * q^71 + 16 * q^74 - 10 * q^75 - 4 * q^76 - 56 * q^79 - 2 * q^81 + 24 * q^84 - 28 * q^85 + 24 * q^86 - 4 * q^89 - 2 * q^90 + 20 * q^94 - 4 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1690\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	0.602705i		−	0.347972i	−0.984748	−	0.173986i	$-0.944335\pi$
$3$		−	0.602705i		−	0.347972i	0.984748	−	0.173986i	$-0.0556647\pi$
$4$	−1.00000			−0.500000
$5$	0.301352	−	2.21567i	0.134769	−	0.990877i
$5$	0.301352	−	2.21567i	0.134769	−	0.990877i
$6$	−0.602705			−0.246053
$7$		−	3.63675i		−	1.37456i	−0.726392	−	0.687281i	$-0.758804\pi$
$7$		−	3.63675i		−	1.37456i	0.726392	−	0.687281i	$-0.241196\pi$
$8$			1.00000i			0.353553i
$9$	2.63675			0.878916
$10$	−2.21567	−	0.301352i	−0.700656	−	0.0952960i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$			0.602705i			0.173986i
$13$		0			0
$13$		0			0
$14$	−3.63675			−0.971961
$15$	−1.33539	−	0.181627i	−0.344797	−	0.0468958i
$16$	1.00000			0.250000
$17$		−	6.67079i		−	1.61790i	−0.587875	−	0.808952i	$-0.700035\pi$
$17$		−	6.67079i		−	1.61790i	0.587875	−	0.808952i	$-0.299965\pi$
$18$		−	2.63675i		−	0.621487i
$19$	8.06808			1.85095			0.925473	−	0.378814i	$-0.123668\pi$
$19$	8.06808			1.85095			0.925473	+	0.378814i	$0.123668\pi$
$20$	−0.301352	+	2.21567i	−0.0673845	+	0.495439i
$21$	−2.19189			−0.478309
$22$			2.00000i			0.426401i
$23$		−	0.794590i		−	0.165683i	−0.996563	−	0.0828417i	$-0.973600\pi$
$23$		−	0.794590i		−	0.165683i	0.996563	−	0.0828417i	$-0.0263996\pi$
$24$	0.602705			0.123027
$25$	−4.81837	−	1.33539i	−0.963675	−	0.267079i
$26$		0			0
$27$		−	3.39730i		−	0.653810i
$28$			3.63675i			0.687281i
$29$	8.06808			1.49821			0.749103	−	0.662454i	$-0.230485\pi$
$29$	8.06808			1.49821			0.749103	+	0.662454i	$0.230485\pi$
$30$	−0.181627	+	1.33539i	−0.0331603	+	0.243809i
$31$	−5.20541			−0.934919			−0.467460	−	0.884014i	$-0.654831\pi$
$31$	−5.20541			−0.934919			−0.467460	+	0.884014i	$0.654831\pi$
$32$		−	1.00000i		−	0.176777i
$33$			1.20541i			0.209835i
$34$	−6.67079			−1.14403
$35$	−8.05783	−	1.09594i	−1.36202	−	0.185248i
$36$	−2.63675			−0.439458
$37$		−	0.431337i		−	0.0709114i	−0.999371	−	0.0354557i	$-0.988712\pi$
$37$		−	0.431337i		−	0.0709114i	0.999371	−	0.0354557i	$-0.0112883\pi$
$38$		−	8.06808i		−	1.30882i
$39$		0			0
$40$	2.21567	+	0.301352i	0.350328	+	0.0476480i
$41$	−6.86267			−1.07177			−0.535885	−	0.844291i	$-0.680022\pi$
$41$	−6.86267			−1.07177			−0.535885	+	0.844291i	$0.680022\pi$
$42$			2.19189i			0.338215i
$43$			5.80811i			0.885729i	0.896589	+	0.442865i	$0.146038\pi$
$43$			5.80811i			0.885729i	−0.896589	+	0.442865i	$0.853962\pi$
$44$	2.00000			0.301511
$45$	0.794590	−	5.84216i	0.118451	−	0.870897i
$46$	−0.794590			−0.117156
$47$			7.63675i			1.11393i	0.830535	+	0.556967i	$0.188035\pi$
$47$			7.63675i			1.11393i	−0.830535	+	0.556967i	$0.811965\pi$
$48$		−	0.602705i		−	0.0869930i
$49$	−6.22593			−0.889418
$50$	−1.33539	+	4.81837i	−0.188853	+	0.681421i
$51$	−4.02052			−0.562985
$52$		0			0
$53$		−	0.794590i		−	0.109145i	−0.998510	−	0.0545727i	$-0.982620\pi$
$53$		−	0.794590i		−	0.109145i	0.998510	−	0.0545727i	$-0.0173797\pi$
$54$	−3.39730			−0.462313
$55$	−0.602705	+	4.43134i	−0.0812687	+	0.597521i
$56$	3.63675			0.485981
$57$		−	4.86267i		−	0.644077i
$58$		−	8.06808i		−	1.05939i
$59$	8.06808			1.05038			0.525188	−	0.850987i	$-0.323995\pi$
$59$	8.06808			1.05038			0.525188	+	0.850987i	$0.323995\pi$
$60$	1.33539	+	0.181627i	0.172399	+	0.0234479i
$61$	−2.86267			−0.366528			−0.183264	−	0.983064i	$-0.558666\pi$
$61$	−2.86267			−0.366528			−0.183264	+	0.983064i	$0.558666\pi$
$62$			5.20541i			0.661088i
$63$		−	9.58918i		−	1.20812i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.20541			0.148376
$67$			5.20541i			0.635942i	0.948100	+	0.317971i	$0.103001\pi$
$67$			5.20541i			0.635942i	−0.948100	+	0.317971i	$0.896999\pi$
$68$			6.67079i			0.808952i
$69$	−0.478903			−0.0576532
$70$	−1.09594	+	8.05783i	−0.130990	+	0.963094i
$71$	9.46538			1.12333			0.561667	−	0.827363i	$-0.310160\pi$
$71$	9.46538			1.12333			0.561667	+	0.827363i	$0.310160\pi$
$72$			2.63675i			0.310744i
$73$		−	6.00000i		−	0.702247i	−0.936329	−	0.351123i	$-0.885800\pi$
$73$		−	6.00000i		−	0.702247i	0.936329	−	0.351123i	$-0.114200\pi$
$74$	−0.431337			−0.0501419
$75$	−0.804849	+	2.90406i	−0.0929359	+	0.335332i
$76$	−8.06808			−0.925473
$77$			7.27349i			0.828892i
$78$		0			0
$79$	−1.93192			−0.217358			−0.108679	−	0.994077i	$-0.534662\pi$
$79$	−1.93192			−0.217358			−0.108679	+	0.994077i	$0.534662\pi$
$80$	0.301352	−	2.21567i	0.0336922	−	0.247719i
$81$	5.86267			0.651408
$82$			6.86267i			0.757856i
$83$			2.06808i			0.227002i	0.993538	+	0.113501i	$0.0362065\pi$
$83$			2.06808i			0.227002i	−0.993538	+	0.113501i	$0.963794\pi$
$84$	2.19189			0.239154
$85$	−14.7803	−	2.01026i	−1.60314	−	0.218043i
$86$	5.80811			0.626305
$87$		−	4.86267i		−	0.521333i
$88$		−	2.00000i		−	0.213201i
$89$	−8.06808			−0.855215			−0.427608	−	0.903964i	$-0.640643\pi$
$89$	−8.06808			−0.855215			−0.427608	+	0.903964i	$0.640643\pi$
$90$	−5.84216	−	0.794590i	−0.615817	−	0.0837572i
$91$		0			0
$92$			0.794590i			0.0828417i
$93$			3.13733i			0.325326i
$94$	7.63675			0.787670
$95$	2.43134	−	17.8762i	0.249450	−	1.83406i
$96$	−0.602705			−0.0615133
$97$			13.6573i			1.38669i	0.720608	+	0.693343i	$0.243863\pi$
$97$			13.6573i			1.38669i	−0.720608	+	0.693343i	$0.756137\pi$
$98$			6.22593i			0.628914i
$99$	−5.27349			−0.530006
$100$	4.81837	+	1.33539i	0.481837	+	0.133539i
$101$	−15.6843			−1.56065			−0.780324	−	0.625376i	$-0.784946\pi$
$101$	−15.6843			−1.56065			−0.780324	+	0.625376i	$0.784946\pi$
$102$			4.02052i			0.398091i
$103$			15.3416i			1.51165i	0.654773	+	0.755825i	$0.272764\pi$
$103$			15.3416i			1.51165i	−0.654773	+	0.755825i	$0.727236\pi$
$104$		0			0
$105$	−0.660530	+	4.85649i	−0.0644611	+	0.473945i
$106$	−0.794590			−0.0771774
$107$			1.20541i			0.116531i	0.998301	+	0.0582657i	$0.0185571\pi$
$107$			1.20541i			0.116531i	−0.998301	+	0.0582657i	$0.981443\pi$
$108$			3.39730i			0.326905i
$109$	9.80811			0.939447			0.469724	−	0.882814i	$-0.344354\pi$
$109$	9.80811			0.939447			0.469724	+	0.882814i	$0.344354\pi$
$110$	4.43134	+	0.602705i	0.422511	+	0.0574657i
$111$	−0.259969			−0.0246752
$112$		−	3.63675i		−	0.343640i
$113$		−	4.00000i		−	0.376288i	−0.982141	−	0.188144i	$-0.939753\pi$
$113$		−	4.00000i		−	0.376288i	0.982141	−	0.188144i	$-0.0602472\pi$
$114$	−4.86267			−0.455431
$115$	−1.76055	−	0.239452i	−0.164172	−	0.0223290i
$116$	−8.06808			−0.749103
$117$		0			0
$118$		−	8.06808i		−	0.742727i
$119$	−24.2600			−2.22391
$120$	0.181627	−	1.33539i	0.0165802	−	0.121904i
$121$	−7.00000			−0.636364
$122$			2.86267i			0.259174i
$123$			4.13617i			0.372946i
$124$	5.20541			0.467460
$125$	−4.41082	+	10.2735i	−0.394516	+	0.918889i
$126$	−9.58918			−0.854272
$127$			4.79459i			0.425451i	0.977112	+	0.212726i	$0.0682340\pi$
$127$			4.79459i			0.425451i	−0.977112	+	0.212726i	$0.931766\pi$
$128$			1.00000i			0.0883883i
$129$	3.50058			0.308209
$130$		0			0
$131$	−4.02052			−0.351274			−0.175637	−	0.984455i	$-0.556199\pi$
$131$	−4.02052			−0.351274			−0.175637	+	0.984455i	$0.556199\pi$
$132$		−	1.20541i		−	0.104917i
$133$		−	29.3416i		−	2.54424i
$134$	5.20541			0.449679
$135$	−7.52728	−	1.02378i	−0.647845	−	0.0881132i
$136$	6.67079			0.572015
$137$		−	11.2054i		−	0.957343i	−0.877994	−	0.478671i	$-0.841119\pi$
$137$		−	11.2054i		−	0.957343i	0.877994	−	0.478671i	$-0.158881\pi$
$138$			0.478903i			0.0407670i
$139$	−8.84216			−0.749982			−0.374991	−	0.927028i	$-0.622354\pi$
$139$	−8.84216			−0.749982			−0.374991	+	0.927028i	$0.622354\pi$
$140$	8.05783	+	1.09594i	0.681011	+	0.0926241i
$141$	4.60270			0.387618
$142$		−	9.46538i		−	0.794317i
$143$		0			0
$144$	2.63675			0.219729
$145$	2.43134	−	17.8762i	0.201912	−	1.48454i
$146$	−6.00000			−0.496564
$147$			3.75240i			0.309492i
$148$			0.431337i			0.0354557i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	2.90406	+	0.804849i	0.237115	+	0.0657156i
$151$	−7.05456			−0.574092			−0.287046	−	0.957917i	$-0.592673\pi$
$151$	−7.05456			−0.574092			−0.287046	+	0.957917i	$0.592673\pi$
$152$			8.06808i			0.654408i
$153$		−	17.5892i		−	1.42200i
$154$	7.27349			0.586115
$155$	−1.56866	+	11.5335i	−0.125998	+	0.926390i
$156$		0			0
$157$		−	0.0680837i		−	0.00543367i	−0.999996	−	0.00271683i	$-0.999135\pi$
$157$		−	0.0680837i		−	0.00543367i	0.999996	−	0.00271683i	$-0.000864796\pi$
$158$			1.93192i			0.153695i
$159$	−0.478903			−0.0379795
$160$	−2.21567	−	0.301352i	−0.175164	−	0.0238240i
$161$	−2.88972			−0.227742
$162$		−	5.86267i		−	0.460615i
$163$		−	7.65726i		−	0.599763i	−0.953976	−	0.299882i	$-0.903053\pi$
$163$		−	7.65726i		−	0.599763i	0.953976	−	0.299882i	$-0.0969472\pi$
$164$	6.86267			0.535885
$165$	2.67079	+	0.363253i	0.207921	+	0.0282792i
$166$	2.06808			0.160514
$167$			4.82164i			0.373110i	0.982445	+	0.186555i	$0.0597322\pi$
$167$			4.82164i			0.373110i	−0.982445	+	0.186555i	$0.940268\pi$
$168$		−	2.19189i		−	0.169108i
$169$		0			0
$170$	−2.01026	+	14.7803i	−0.154180	+	1.13359i
$171$	21.2735			1.62682
$172$		−	5.80811i		−	0.442865i
$173$			12.7946i			0.972755i	0.873749	+	0.486377i	$0.161682\pi$
$173$			12.7946i			0.972755i	−0.873749	+	0.486377i	$0.838318\pi$
$174$	−4.86267			−0.368638
$175$	−4.85649	+	17.5232i	−0.367116	+	1.32463i
$176$	−2.00000			−0.150756
$177$		−	4.86267i		−	0.365501i
$178$			8.06808i			0.604728i
$179$	8.84216			0.660894			0.330447	−	0.943825i	$-0.392801\pi$
$179$	8.84216			0.660894			0.330447	+	0.943825i	$0.392801\pi$
$180$	−0.794590	+	5.84216i	−0.0592253	+	0.435449i
$181$	1.61623			0.120133			0.0600667	−	0.998194i	$-0.480869\pi$
$181$	1.61623			0.120133			0.0600667	+	0.998194i	$0.480869\pi$
$182$		0			0
$183$			1.72535i			0.127541i
$184$	0.794590			0.0585780
$185$	−0.955700	−	0.129984i	−0.0702644	−	0.00955665i
$186$	3.13733			0.230040
$187$			13.3416i			0.975633i
$188$		−	7.63675i		−	0.556967i
$189$	−12.3551			−0.898701
$190$	−17.8762	−	2.43134i	−1.29688	−	0.176388i
$191$	21.3416			1.54422			0.772111	−	0.635487i	$-0.219201\pi$
$191$	21.3416			1.54422			0.772111	+	0.635487i	$0.219201\pi$
$192$			0.602705i			0.0434965i
$193$		−	5.61623i		−	0.404265i	−0.979358	−	0.202133i	$-0.935213\pi$
$193$		−	5.61623i		−	0.404265i	0.979358	−	0.202133i	$-0.0647872\pi$
$194$	13.6573			0.980534
$195$		0			0
$196$	6.22593			0.444709
$197$		−	14.0205i		−	0.998920i	−0.866337	−	0.499460i	$-0.833532\pi$
$197$		−	14.0205i		−	0.998920i	0.866337	−	0.499460i	$-0.166468\pi$
$198$			5.27349i			0.374771i
$199$	15.7524			1.11666			0.558329	−	0.829620i	$-0.311443\pi$
$199$	15.7524			1.11666			0.558329	+	0.829620i	$0.311443\pi$
$200$	1.33539	−	4.81837i	0.0944266	−	0.340710i
$201$	3.13733			0.221290
$202$			15.6843i			1.10354i
$203$		−	29.3416i		−	2.05937i
$204$	4.02052			0.281493
$205$	−2.06808	+	15.2054i	−0.144441	+	1.06199i
$206$	15.3416			1.06890
$207$		−	2.09513i		−	0.145622i
$208$		0			0
$209$	−16.1362			−1.11616
$210$	4.85649	+	0.660530i	0.335130	+	0.0455809i
$211$	−1.70483			−0.117365			−0.0586827	−	0.998277i	$-0.518690\pi$
$211$	−1.70483			−0.117365			−0.0586827	+	0.998277i	$0.518690\pi$
$212$			0.794590i			0.0545727i
$213$		−	5.70483i		−	0.390889i
$214$	1.20541			0.0824001
$215$	12.8689	+	1.75029i	0.877649	+	0.119369i
$216$	3.39730			0.231157
$217$			18.9308i			1.28510i
$218$		−	9.80811i		−	0.664289i
$219$	−3.61623			−0.244362
$220$	0.602705	−	4.43134i	0.0406344	−	0.298761i
$221$		0			0
$222$			0.259969i			0.0174480i
$223$			22.9513i			1.53693i	0.639891	+	0.768466i	$0.278979\pi$
$223$			22.9513i			1.53693i	−0.639891	+	0.768466i	$0.721021\pi$
$224$	−3.63675			−0.242990
$225$	−12.7048	−	3.52110i	−0.846989	−	0.234740i
$226$	−4.00000			−0.266076
$227$		−	10.5470i		−	0.700028i	−0.936744	−	0.350014i	$-0.886177\pi$
$227$		−	10.5470i		−	0.700028i	0.936744	−	0.350014i	$-0.113823\pi$
$228$			4.86267i			0.322038i
$229$	25.9443			1.71445			0.857223	−	0.514945i	$-0.172188\pi$
$229$	25.9443			1.71445			0.857223	+	0.514945i	$0.172188\pi$
$230$	−0.239452	+	1.76055i	−0.0157890	+	0.116087i
$231$	4.38377			0.288431
$232$			8.06808i			0.529696i
$233$		−	11.4924i		−	0.752894i	−0.926438	−	0.376447i	$-0.877146\pi$
$233$		−	11.4924i		−	0.752894i	0.926438	−	0.376447i	$-0.122854\pi$
$234$		0			0
$235$	16.9205	+	2.30135i	1.10377	+	0.150124i
$236$	−8.06808			−0.525188
$237$			1.16438i			0.0756343i
$238$			24.2600i			1.57254i
$239$	14.6708			0.948974			0.474487	−	0.880262i	$-0.342634\pi$
$239$	14.6708			0.948974			0.474487	+	0.880262i	$0.342634\pi$
$240$	−1.33539	−	0.181627i	−0.0861993	−	0.0117239i
$241$	18.6151			1.19910			0.599551	−	0.800337i	$-0.295346\pi$
$241$	18.6151			1.19910			0.599551	+	0.800337i	$0.295346\pi$
$242$			7.00000i			0.449977i
$243$		−	13.7253i		−	0.880481i
$244$	2.86267			0.183264
$245$	−1.87620	+	13.7946i	−0.119866	+	0.881304i
$246$	4.13617			0.263712
$247$		0			0
$248$		−	5.20541i		−	0.330544i
$249$	1.24644			0.0789902
$250$	10.2735	+	4.41082i	0.649753	+	0.278965i
$251$	−14.4108			−0.909603			−0.454801	−	0.890593i	$-0.650290\pi$
$251$	−14.4108			−0.909603			−0.454801	+	0.890593i	$0.650290\pi$
$252$			9.58918i			0.604062i
$253$			1.58918i			0.0999109i
$254$	4.79459			0.300839
$255$	−1.21159	+	8.90813i	−0.0758729	+	0.557849i
$256$	1.00000			0.0625000
$257$			0.123802i			0.00772253i	0.999993	+	0.00386126i	$0.00122908\pi$
$257$			0.123802i			0.00772253i	−0.999993	+	0.00386126i	$0.998771\pi$
$258$		−	3.50058i		−	0.217937i
$259$	−1.56866			−0.0974720
$260$		0			0
$261$	21.2735			1.31680
$262$			4.02052i			0.248388i
$263$		−	5.27349i		−	0.325178i	−0.986694	−	0.162589i	$-0.948016\pi$
$263$		−	5.27349i		−	0.325178i	0.986694	−	0.162589i	$-0.0519844\pi$
$264$	−1.20541			−0.0741878
$265$	−1.76055	−	0.239452i	−0.108150	−	0.0147094i
$266$	−29.3416			−1.79905
$267$			4.86267i			0.297591i
$268$		−	5.20541i		−	0.317971i
$269$	−1.27349			−0.0776463			−0.0388231	−	0.999246i	$-0.512361\pi$
$269$	−1.27349			−0.0776463			−0.0388231	+	0.999246i	$0.512361\pi$
$270$	−1.02378	+	7.52728i	−0.0623055	+	0.458096i
$271$	−6.28702			−0.381909			−0.190955	−	0.981599i	$-0.561158\pi$
$271$	−6.28702			−0.381909			−0.190955	+	0.981599i	$0.561158\pi$
$272$		−	6.67079i		−	0.404476i
$273$		0			0
$274$	−11.2054			−0.676944
$275$	9.63675	+	2.67079i	0.581118	+	0.161055i
$276$	0.478903			0.0288266
$277$		−	22.9988i		−	1.38187i	−0.722919	−	0.690933i	$-0.757200\pi$
$277$		−	22.9988i		−	1.38187i	0.722919	−	0.690933i	$-0.242800\pi$
$278$			8.84216i			0.530317i
$279$	−13.7253			−0.821715
$280$	1.09594	−	8.05783i	0.0654951	−	0.481547i
$281$	−10.3427			−0.616996			−0.308498	−	0.951225i	$-0.599826\pi$
$281$	−10.3427			−0.616996			−0.308498	+	0.951225i	$0.599826\pi$
$282$		−	4.60270i		−	0.274087i
$283$		−	10.0270i		−	0.596046i	−0.954559	−	0.298023i	$-0.903673\pi$
$283$		−	10.0270i		−	0.596046i	0.954559	−	0.298023i	$-0.0963272\pi$
$284$	−9.46538			−0.561667
$285$	−10.7741	−	1.46538i	−0.638201	−	0.0868015i
$286$		0			0
$287$			24.9578i			1.47321i
$288$		−	2.63675i		−	0.155372i
$289$	−27.4994			−1.61761
$290$	−17.8762	−	2.43134i	−1.04973	−	0.142773i
$291$	8.23130			0.482527
$292$			6.00000i			0.351123i
$293$		−	6.11565i		−	0.357280i	−0.983914	−	0.178640i	$-0.942830\pi$
$293$		−	6.11565i		−	0.357280i	0.983914	−	0.178640i	$-0.0571698\pi$
$294$	3.75240			0.218844
$295$	2.43134	−	17.8762i	0.141558	−	1.04079i
$296$	0.431337			0.0250709
$297$			6.79459i			0.394262i
$298$		0			0
$299$		0			0
$300$	0.804849	−	2.90406i	0.0464680	−	0.167666i
$301$	21.1226			1.21749
$302$			7.05456i			0.405944i
$303$			9.45301i			0.543061i
$304$	8.06808			0.462736
$305$	−0.862674	+	6.34274i	−0.0493966	+	0.363184i
$306$	−17.5892			−1.00551
$307$			16.8627i			0.962404i	0.876610	+	0.481202i	$0.159800\pi$
$307$			16.8627i			0.962404i	−0.876610	+	0.481202i	$0.840200\pi$
$308$		−	7.27349i		−	0.414446i
$309$	9.24644			0.526012
$310$	11.5335	+	1.56866i	0.655057	+	0.0890941i
$311$	32.9988			1.87119			0.935596	−	0.353072i	$-0.114863\pi$
$311$	32.9988			1.87119			0.935596	+	0.353072i	$0.114863\pi$
$312$		0			0
$313$		−	25.4654i		−	1.43939i	−0.694291	−	0.719694i	$-0.744282\pi$
$313$		−	25.4654i		−	1.43939i	0.694291	−	0.719694i	$-0.255718\pi$
$314$	−0.0680837			−0.00384218
$315$	−21.2464	−	2.88972i	−1.19710	−	0.162817i
$316$	1.93192			0.108679
$317$		−	14.1362i		−	0.793966i	−0.917826	−	0.396983i	$-0.870057\pi$
$317$		−	14.1362i		−	0.793966i	0.917826	−	0.396983i	$-0.129943\pi$
$318$			0.478903i			0.0268556i
$319$	−16.1362			−0.903452
$320$	−0.301352	+	2.21567i	−0.0168461	+	0.123860i
$321$	0.726506			0.0405496
$322$			2.88972i			0.161038i
$323$		−	53.8205i		−	2.99465i
$324$	−5.86267			−0.325704
$325$		0			0
$326$	−7.65726			−0.424097
$327$		−	5.91140i		−	0.326901i
$328$		−	6.86267i		−	0.378928i
$329$	27.7729			1.53117
$330$	0.363253	−	2.67079i	0.0199964	−	0.147022i
$331$	−18.5199			−1.01795			−0.508974	−	0.860782i	$-0.669975\pi$
$331$	−18.5199			−1.01795			−0.508974	+	0.860782i	$0.669975\pi$
$332$		−	2.06808i		−	0.113501i
$333$		−	1.13733i		−	0.0623251i
$334$	4.82164			0.263828
$335$	11.5335	+	1.56866i	0.630140	+	0.0857052i
$336$	−2.19189			−0.119577
$337$			22.2870i			1.21405i	0.794682	+	0.607026i	$0.207637\pi$
$337$			22.2870i			1.21405i	−0.794682	+	0.607026i	$0.792363\pi$
$338$		0			0
$339$	−2.41082			−0.130938
$340$	14.7803	+	2.01026i	0.801572	+	0.109022i
$341$	10.4108			0.563777
$342$		−	21.2735i		−	1.15034i
$343$		−	2.81511i		−	0.152002i
$344$	−5.80811			−0.313153
$345$	−0.144319	+	1.06109i	−0.00776986	+	0.0571272i
$346$	12.7946			0.687841
$347$		−	31.5335i		−	1.69280i	−0.532544	−	0.846402i	$-0.678764\pi$
$347$		−	31.5335i		−	1.69280i	0.532544	−	0.846402i	$-0.321236\pi$
$348$			4.86267i			0.260667i
$349$	32.3551			1.73193			0.865964	−	0.500106i	$-0.166705\pi$
$349$	32.3551			1.73193			0.865964	+	0.500106i	$0.166705\pi$
$350$	17.5232	+	4.85649i	0.936655	+	0.259590i
$351$		0			0
$352$			2.00000i			0.106600i
$353$			20.0270i			1.06593i	0.846137	+	0.532966i	$0.178923\pi$
$353$			20.0270i			1.06593i	−0.846137	+	0.532966i	$0.821077\pi$
$354$	−4.86267			−0.258448
$355$	2.85242	−	20.9721i	0.151390	−	1.11309i
$356$	8.06808			0.427608
$357$			14.6216i			0.773857i
$358$		−	8.84216i		−	0.467322i
$359$	22.9308			1.21024			0.605120	−	0.796135i	$-0.293125\pi$
$359$	22.9308			1.21024			0.605120	+	0.796135i	$0.293125\pi$
$360$	5.84216	+	0.794590i	0.307909	+	0.0418786i
$361$	46.0940			2.42600
$362$		−	1.61623i		−	0.0849471i
$363$			4.21893i			0.221437i
$364$		0			0
$365$	−13.2940	−	1.80811i	−0.695840	−	0.0946411i
$366$	1.72535			0.0901854
$367$			34.1362i			1.78189i	0.454108	+	0.890947i	$0.349958\pi$
$367$			34.1362i			1.78189i	−0.454108	+	0.890947i	$0.650042\pi$
$368$		−	0.794590i		−	0.0414209i
$369$	−18.0951			−0.941995
$370$	−0.129984	+	0.955700i	−0.00675757	+	0.0496845i
$371$	−2.88972			−0.150027
$372$		−	3.13733i		−	0.162663i
$373$			26.9988i			1.39795i	0.715148	+	0.698974i	$0.246359\pi$
$373$			26.9988i			1.39795i	−0.715148	+	0.698974i	$0.753641\pi$
$374$	13.3416			0.689877
$375$	6.19189	+	2.65842i	0.319748	+	0.137280i
$376$	−7.63675			−0.393835
$377$		0			0
$378$			12.3551i			0.635478i
$379$	12.9308			0.664208			0.332104	−	0.943243i	$-0.392241\pi$
$379$	12.9308			0.664208			0.332104	+	0.943243i	$0.392241\pi$
$380$	−2.43134	+	17.8762i	−0.124725	+	0.917030i
$381$	2.88972			0.148045
$382$		−	21.3416i		−	1.09193i
$383$		−	21.3621i		−	1.09155i	−0.837931	−	0.545776i	$-0.816235\pi$
$383$		−	21.3621i		−	1.09155i	0.837931	−	0.545776i	$-0.183765\pi$
$384$	0.602705			0.0307567
$385$	16.1157	+	2.19189i	0.821330	+	0.111709i
$386$	−5.61623			−0.285859
$387$			15.3145i			0.778481i
$388$		−	13.6573i		−	0.693343i
$389$	29.4507			1.49321			0.746605	−	0.665268i	$-0.231683\pi$
$389$	29.4507			1.49321			0.746605	+	0.665268i	$0.231683\pi$
$390$		0			0
$391$	−5.30054			−0.268060
$392$		−	6.22593i		−	0.314457i
$393$			2.42319i			0.122234i
$394$	−14.0205			−0.706343
$395$	−0.582188	+	4.28049i	−0.0292930	+	0.215375i
$396$	5.27349			0.265003
$397$		−	16.6832i		−	0.837304i	−0.908147	−	0.418652i	$-0.862503\pi$
$397$		−	16.6832i		−	0.837304i	0.908147	−	0.418652i	$-0.137497\pi$
$398$		−	15.7524i		−	0.789596i
$399$	−17.6843			−0.885323
$400$	−4.81837	−	1.33539i	−0.240919	−	0.0667697i
$401$	7.34158			0.366621			0.183310	−	0.983055i	$-0.441319\pi$
$401$	7.34158			0.366621			0.183310	+	0.983055i	$0.441319\pi$
$402$		−	3.13733i		−	0.156476i
$403$		0			0
$404$	15.6843			0.780324
$405$	1.76673	−	12.9897i	0.0877896	−	0.645465i
$406$	−29.3416			−1.45620
$407$			0.862674i			0.0427612i
$408$		−	4.02052i		−	0.199045i
$409$	−35.4777			−1.75426			−0.877131	−	0.480252i	$-0.840545\pi$
$409$	−35.4777			−1.75426			−0.877131	+	0.480252i	$0.840545\pi$
$410$	15.2054	+	2.06808i	0.750942	+	0.102135i
$411$	−6.75356			−0.333128
$412$		−	15.3416i		−	0.755825i
$413$		−	29.3416i		−	1.44380i
$414$	−2.09513			−0.102970
$415$	4.58219	+	0.623222i	0.224931	+	0.0305928i
$416$		0			0
$417$			5.32921i			0.260973i
$418$			16.1362i			0.789246i
$419$	−0.883191			−0.0431467			−0.0215734	−	0.999767i	$-0.506868\pi$
$419$	−0.883191			−0.0431467			−0.0215734	+	0.999767i	$0.506868\pi$
$420$	0.660530	−	4.85649i	0.0322306	−	0.236972i
$421$	−27.2859			−1.32983			−0.664916	−	0.746918i	$-0.731533\pi$
$421$	−27.2859			−1.32983			−0.664916	+	0.746918i	$0.731533\pi$
$422$			1.70483i			0.0829898i
$423$			20.1362i			0.979054i
$424$	0.794590			0.0385887
$425$	−8.90813	+	32.1424i	−0.432108	+	1.55913i
$426$	−5.70483			−0.276400
$427$			10.4108i			0.503815i
$428$		−	1.20541i		−	0.0582657i
$429$		0			0
$430$	1.75029	−	12.8689i	0.0844065	−	0.620591i
$431$	−0.259969			−0.0125223			−0.00626113	−	0.999980i	$-0.501993\pi$
$431$	−0.259969			−0.0125223			−0.00626113	+	0.999980i	$0.501993\pi$
$432$		−	3.39730i		−	0.163452i
$433$			17.4654i			0.839333i	0.907678	+	0.419666i	$0.137853\pi$
$433$			17.4654i			0.839333i	−0.907678	+	0.419666i	$0.862147\pi$
$434$	18.9308			0.908705
$435$	−10.7741	−	1.46538i	−0.516577	−	0.0702595i
$436$	−9.80811			−0.469724
$437$		−	6.41082i		−	0.306671i
$438$			3.61623i			0.172790i
$439$	−17.6843			−0.844026			−0.422013	−	0.906590i	$-0.638676\pi$
$439$	−17.6843			−0.844026			−0.422013	+	0.906590i	$0.638676\pi$
$440$	−4.43134	−	0.602705i	−0.211256	−	0.0287328i
$441$	−16.4162			−0.781723
$442$		0			0
$443$		−	32.4913i		−	1.54371i	−0.635801	−	0.771853i	$-0.719330\pi$
$443$		−	32.4913i		−	1.54371i	0.635801	−	0.771853i	$-0.280670\pi$
$444$	0.259969			0.0123376
$445$	−2.43134	+	17.8762i	−0.115256	+	0.847413i
$446$	22.9513			1.08677
$447$		0			0
$448$			3.63675i			0.171820i
$449$	35.0940			1.65619			0.828094	−	0.560590i	$-0.189426\pi$
$449$	35.0940			1.65619			0.828094	+	0.560590i	$0.189426\pi$
$450$	−3.52110	+	12.7048i	−0.165986	+	0.598911i
$451$	13.7253			0.646301
$452$			4.00000i			0.188144i
$453$			4.25182i			0.199768i
$454$	−10.5470			−0.494995
$455$		0			0
$456$	4.86267			0.227716
$457$		−	20.5470i		−	0.961148i	−0.876954	−	0.480574i	$-0.840428\pi$
$457$		−	20.5470i		−	0.961148i	0.876954	−	0.480574i	$-0.159572\pi$
$458$		−	25.9443i		−	1.21230i
$459$	−22.6626			−1.05780
$460$	1.76055	+	0.239452i	0.0820860	+	0.0111645i
$461$	7.14969			0.332994			0.166497	−	0.986042i	$-0.446754\pi$
$461$	7.14969			0.332994			0.166497	+	0.986042i	$0.446754\pi$
$462$		−	4.38377i		−	0.203951i
$463$			22.6832i			1.05418i	0.849811	+	0.527088i	$0.176716\pi$
$463$			22.6832i			1.05418i	−0.849811	+	0.527088i	$0.823284\pi$
$464$	8.06808			0.374551
$465$	6.95127	+	0.945441i	0.322358	+	0.0438438i
$466$	−11.4924			−0.532376
$467$		−	25.2054i		−	1.16637i	−0.812340	−	0.583184i	$-0.801807\pi$
$467$		−	25.2054i		−	1.16637i	0.812340	−	0.583184i	$-0.198193\pi$
$468$		0			0
$469$	18.9308			0.874141
$470$	2.30135	−	16.9205i	0.106153	−	0.780484i
$471$	−0.0410344			−0.00189076
$472$			8.06808i			0.371364i
$473$		−	11.6162i		−	0.534115i
$474$	1.16438			0.0534815
$475$	−38.8750	−	10.7741i	−1.78371	−	0.494348i
$476$	24.2600			1.11195
$477$		−	2.09513i		−	0.0959295i
$478$		−	14.6708i		−	0.671026i
$479$	4.01237			0.183330			0.0916648	−	0.995790i	$-0.470781\pi$
$479$	4.01237			0.183330			0.0916648	+	0.995790i	$0.470781\pi$
$480$	−0.181627	+	1.33539i	−0.00829008	+	0.0609521i
$481$		0			0
$482$		−	18.6151i		−	0.847893i
$483$			1.74165i			0.0792478i
$484$	7.00000			0.318182
$485$	30.2600	+	4.11565i	1.37403	+	0.186882i
$486$	−13.7253			−0.622594
$487$		−	8.00000i		−	0.362515i	−0.983436	−	0.181257i	$-0.941983\pi$
$487$		−	8.00000i		−	0.362515i	0.983436	−	0.181257i	$-0.0580167\pi$
$488$		−	2.86267i		−	0.129587i
$489$	−4.61507			−0.208701
$490$	13.7946	+	1.87620i	0.623176	+	0.0847580i
$491$	−8.88319			−0.400893			−0.200446	−	0.979705i	$-0.564239\pi$
$491$	−8.88319			−0.400893			−0.200446	+	0.979705i	$0.564239\pi$
$492$		−	4.13617i		−	0.186473i
$493$		−	53.8205i		−	2.42395i
$494$		0			0
$495$	−1.58918	+	11.6843i	−0.0714283	+	0.525171i
$496$	−5.20541			−0.233730
$497$		−	34.4232i		−	1.54409i
$498$		−	1.24644i		−	0.0558545i
$499$	−10.9988			−0.492376			−0.246188	−	0.969222i	$-0.579178\pi$
$499$	−10.9988			−0.492376			−0.246188	+	0.969222i	$0.579178\pi$
$500$	4.41082	−	10.2735i	0.197258	−	0.459445i
$501$	2.90603			0.129832
$502$			14.4108i			0.643186i
$503$		−	5.65726i		−	0.252245i	−0.992015	−	0.126122i	$-0.959747\pi$
$503$		−	5.65726i		−	0.252245i	0.992015	−	0.126122i	$-0.0402532\pi$
$504$	9.58918			0.427136
$505$	−4.72651	+	34.7512i	−0.210327	+	1.54641i
$506$	1.58918			0.0706477
$507$		0			0
$508$		−	4.79459i		−	0.212726i
$509$	−9.72535			−0.431068			−0.215534	−	0.976496i	$-0.569149\pi$
$509$	−9.72535			−0.431068			−0.215534	+	0.976496i	$0.569149\pi$
$510$	8.90813	+	1.21159i	0.394459	+	0.0536502i
$511$	−21.8205			−0.965281
$512$		−	1.00000i		−	0.0441942i
$513$		−	27.4097i		−	1.21017i
$514$	0.123802			0.00546065
$515$	33.9918	+	4.62322i	1.49786	+	0.203724i
$516$	−3.50058			−0.154104
$517$		−	15.2735i		−	0.671727i
$518$			1.56866i			0.0689231i
$519$	7.71136			0.338491
$520$		0			0
$521$	−28.7741			−1.26062			−0.630308	−	0.776346i	$-0.717071\pi$
$521$	−28.7741			−1.26062			−0.630308	+	0.776346i	$0.717071\pi$
$522$		−	21.2735i		−	0.931116i
$523$			37.6139i			1.64474i	0.568952	+	0.822371i	$0.307349\pi$
$523$			37.6139i			1.64474i	−0.568952	+	0.822371i	$0.692651\pi$
$524$	4.02052			0.175637
$525$	10.5613	+	2.92703i	0.460934	+	0.127746i
$526$	−5.27349			−0.229935
$527$			34.7242i			1.51261i
$528$			1.20541i			0.0524587i
$529$	22.3686			0.972549
$530$	−0.239452	+	1.76055i	−0.0104011	+	0.0764733i
$531$	21.2735			0.923191
$532$			29.3416i			1.27212i
$533$		0			0
$534$	4.86267			0.210428
$535$	2.67079	+	0.363253i	0.115468	+	0.0157048i
$536$	−5.20541			−0.224839
$537$		−	5.32921i		−	0.229972i
$538$			1.27349i			0.0549042i
$539$	12.4519			0.536339
$540$	7.52728	+	1.02378i	0.323923	+	0.0440566i
$541$	−21.8081			−0.937604			−0.468802	−	0.883303i	$-0.655314\pi$
$541$	−21.8081			−0.937604			−0.468802	+	0.883303i	$0.655314\pi$
$542$			6.28702i			0.270051i
$543$		−	0.974110i		−	0.0418030i
$544$	−6.67079			−0.286008
$545$	2.95570	−	21.7315i	0.126608	−	0.930876i
$546$		0			0
$547$		−	4.73887i		−	0.202620i	−0.994855	−	0.101310i	$-0.967697\pi$
$547$		−	4.73887i		−	0.202620i	0.994855	−	0.101310i	$-0.0323033\pi$
$548$			11.2054i			0.478671i
$549$	−7.54815			−0.322147
$550$	2.67079	−	9.63675i	0.113883	−	0.410912i
$551$	65.0940			2.77310
$552$		−	0.478903i		−	0.0203835i
$553$			7.02589i			0.298771i
$554$	−22.9988			−0.977127
$555$	−0.0783423	+	0.576005i	−0.00332544	+	0.0244500i
$556$	8.84216			0.374991
$557$			6.74702i			0.285881i	0.989731	+	0.142940i	$0.0456557\pi$
$557$			6.74702i			0.285881i	−0.989731	+	0.142940i	$0.954344\pi$
$558$			13.7253i			0.581040i
$559$		0			0
$560$	−8.05783	−	1.09594i	−0.340505	−	0.0463120i
$561$	8.04103			0.339493
$562$			10.3427i			0.436282i
$563$			41.9443i			1.76774i	0.467732	+	0.883870i	$0.345071\pi$
$563$			41.9443i			1.76774i	−0.467732	+	0.883870i	$0.654929\pi$
$564$	−4.60270			−0.193809
$565$	−8.86267	−	1.20541i	−0.372855	−	0.0507120i
$566$	−10.0270			−0.421468
$567$		−	21.3211i		−	0.895400i
$568$			9.46538i			0.397158i
$569$	7.95243			0.333383			0.166692	−	0.986009i	$-0.446692\pi$
$569$	7.95243			0.333383			0.166692	+	0.986009i	$0.446692\pi$
$570$	−1.46538	+	10.7741i	−0.0613780	+	0.451276i
$571$	−14.5265			−0.607914			−0.303957	−	0.952686i	$-0.598308\pi$
$571$	−14.5265			−0.607914			−0.303957	+	0.952686i	$0.598308\pi$
$572$		0			0
$573$		−	12.8627i		−	0.537346i
$574$	24.9578			1.04172
$575$	−1.06109	+	3.82863i	−0.0442506	+	0.159665i
$576$	−2.63675			−0.109864
$577$		−	5.17836i		−	0.215578i	−0.994174	−	0.107789i	$-0.965623\pi$
$577$		−	5.17836i		−	0.215578i	0.994174	−	0.107789i	$-0.0343771\pi$
$578$			27.4994i			1.14383i
$579$	−3.38493			−0.140673
$580$	−2.43134	+	17.8762i	−0.100956	+	0.742269i
$581$	7.52110			0.312028
$582$		−	8.23130i		−	0.341198i
$583$			1.58918i			0.0658171i
$584$	6.00000			0.248282
$585$		0			0
$586$	−6.11565			−0.252635
$587$			22.8897i			0.944760i	0.881395	+	0.472380i	$0.156605\pi$
$587$			22.8897i			0.944760i	−0.881395	+	0.472380i	$0.843395\pi$
$588$		−	3.75240i		−	0.154746i
$589$	−41.9977			−1.73048
$590$	−17.8762	−	2.43134i	−0.735951	−	0.100097i
$591$	−8.45023			−0.347596
$592$		−	0.431337i		−	0.0177278i
$593$		−	14.3427i		−	0.588986i	−0.955654	−	0.294493i	$-0.904849\pi$
$593$		−	14.3427i		−	0.588986i	0.955654	−	0.294493i	$-0.0951507\pi$
$594$	6.79459			0.278785
$595$	−7.31080	+	53.7520i	−0.299714	+	2.20362i
$596$		0			0
$597$		−	9.49405i		−	0.388565i
$598$		0			0
$599$	−5.63021			−0.230044			−0.115022	−	0.993363i	$-0.536694\pi$
$599$	−5.63021			−0.230044			−0.115022	+	0.993363i	$0.536694\pi$
$600$	−2.90406	−	0.804849i	−0.118558	−	0.0328578i
$601$	−11.3211			−0.461796			−0.230898	−	0.972978i	$-0.574166\pi$
$601$	−11.3211			−0.461796			−0.230898	+	0.972978i	$0.574166\pi$
$602$		−	21.1226i		−	0.860895i
$603$			13.7253i			0.558939i
$604$	7.05456			0.287046
$605$	−2.10947	+	15.5097i	−0.0857620	+	0.630558i
$606$	9.45301			0.384002
$607$			25.0259i			1.01577i	0.861425	+	0.507885i	$0.169572\pi$
$607$			25.0259i			1.01577i	−0.861425	+	0.507885i	$0.830428\pi$
$608$		−	8.06808i		−	0.327204i
$609$	−17.6843			−0.716605
$610$	6.34274	+	0.862674i	0.256810	+	0.0349286i
$611$		0			0
$612$			17.5892i			0.711000i
$613$		−	25.4507i		−	1.02794i	−0.857807	−	0.513972i	$-0.828174\pi$
$613$		−	25.4507i		−	1.02794i	0.857807	−	0.513972i	$-0.171826\pi$
$614$	16.8627			0.680522
$615$	9.16438	+	1.24644i	0.369543	+	0.0502615i
$616$	−7.27349			−0.293057
$617$		−	15.6843i		−	0.631427i	−0.948855	−	0.315713i	$-0.897756\pi$
$617$		−	15.6843i		−	0.631427i	0.948855	−	0.315713i	$-0.102244\pi$
$618$		−	9.24644i		−	0.371947i
$619$	−44.5880			−1.79214			−0.896072	−	0.443909i	$-0.853591\pi$
$619$	−44.5880			−1.79214			−0.896072	+	0.443909i	$0.853591\pi$
$620$	1.56866	−	11.5335i	0.0629990	−	0.463195i
$621$	−2.69946			−0.108325
$622$		−	32.9988i		−	1.32313i
$623$			29.3416i			1.17555i
$624$		0			0
$625$	21.4334	+	12.8689i	0.857338	+	0.514754i
$626$	−25.4654			−1.01780
$627$			9.72535i			0.388393i
$628$			0.0680837i			0.00271683i
$629$	−2.87736			−0.114728
$630$	−2.88972	+	21.2464i	−0.115129	+	0.846479i
$631$	38.8070			1.54488			0.772440	−	0.635087i	$-0.219036\pi$
$631$	38.8070			1.54488			0.772440	+	0.635087i	$0.219036\pi$
$632$		−	1.93192i		−	0.0768475i
$633$			1.02751i			0.0408398i
$634$	−14.1362			−0.561419
$635$	10.6232	+	1.44486i	0.421570	+	0.0573376i
$636$	0.478903			0.0189898
$637$		0			0
$638$			16.1362i			0.638837i
$639$	24.9578			0.987316
$640$	2.21567	+	0.301352i	0.0875820	+	0.0119120i
$641$	−8.27465			−0.326829			−0.163415	−	0.986557i	$-0.552251\pi$
$641$	−8.27465			−0.326829			−0.163415	+	0.986557i	$0.552251\pi$
$642$		−	0.726506i		−	0.0286729i
$643$			6.16322i			0.243054i	0.992588	+	0.121527i	$0.0387790\pi$
$643$			6.16322i			0.243054i	−0.992588	+	0.121527i	$0.961221\pi$
$644$	2.88972			0.113871
$645$	1.05491	−	7.75612i	0.0415370	−	0.305397i
$646$	−53.8205			−2.11754
$647$		−	7.24644i		−	0.284887i	−0.989803	−	0.142444i	$-0.954504\pi$
$647$		−	7.24644i		−	0.284887i	0.989803	−	0.142444i	$-0.0454959\pi$
$648$			5.86267i			0.230308i
$649$	−16.1362			−0.633400
$650$		0			0
$651$	11.4097			0.447180
$652$			7.65726i			0.299882i
$653$		−	5.27349i		−	0.206368i	−0.994662	−	0.103184i	$-0.967097\pi$
$653$		−	5.27349i		−	0.206368i	0.994662	−	0.103184i	$-0.0329030\pi$
$654$	−5.91140			−0.231154
$655$	−1.21159	+	8.90813i	−0.0473408	+	0.348070i
$656$	−6.86267			−0.267942
$657$		−	15.8205i		−	0.617216i
$658$		−	27.7729i		−	1.08270i
$659$	18.6832			0.727792			0.363896	−	0.931440i	$-0.381446\pi$
$659$	18.6832			0.727792			0.363896	+	0.931440i	$0.381446\pi$
$660$	−2.67079	−	0.363253i	−0.103960	−	0.0141396i
$661$	−15.3145			−0.595666			−0.297833	−	0.954618i	$-0.596264\pi$
$661$	−15.3145			−0.595666			−0.297833	+	0.954618i	$0.596264\pi$
$662$			18.5199i			0.719798i
$663$		0			0
$664$	−2.06808			−0.0802572
$665$	−65.0112	−	8.84216i	−2.52103	−	0.342884i
$666$	−1.13733			−0.0440705
$667$		−	6.41082i		−	0.248228i
$668$		−	4.82164i		−	0.186555i
$669$	13.8328			0.534809
$670$	1.56866	−	11.5335i	0.0606027	−	0.445577i
$671$	5.72535			0.221025
$672$			2.19189i			0.0845538i
$673$			10.2870i			0.396535i	0.980148	+	0.198268i	$0.0635315\pi$
$673$			10.2870i			0.396535i	−0.980148	+	0.198268i	$0.936468\pi$
$674$	22.2870			0.858464
$675$	−4.53673	+	16.3694i	−0.174619	+	0.630060i
$676$		0			0
$677$			9.88856i			0.380048i	0.981779	+	0.190024i	$0.0608566\pi$
$677$			9.88856i			0.380048i	−0.981779	+	0.190024i	$0.939143\pi$
$678$			2.41082i			0.0925870i
$679$	49.6680			1.90608
$680$	2.01026	−	14.7803i	0.0770899	−	0.566797i
$681$	−6.35672			−0.243590
$682$		−	10.4108i		−	0.398651i
$683$			2.06808i			0.0791330i	0.999217	+	0.0395665i	$0.0125977\pi$
$683$			2.06808i			0.0791330i	−0.999217	+	0.0395665i	$0.987402\pi$
$684$	−21.2735			−0.813412
$685$	−24.8275	−	3.37678i	−0.948609	−	0.129020i
$686$	−2.81511			−0.107481
$687$		−	15.6367i		−	0.596579i
$688$			5.80811i			0.221432i
$689$		0			0
$690$	1.06109	+	0.144319i	0.0403950	+	0.00549412i
$691$	−15.8205			−0.601839			−0.300920	−	0.953649i	$-0.597294\pi$
$691$	−15.8205			−0.601839			−0.300920	+	0.953649i	$0.597294\pi$
$692$		−	12.7946i		−	0.486377i
$693$			19.1784i			0.728526i
$694$	−31.5335			−1.19699
$695$	−2.66461	+	19.5913i	−0.101074	+	0.743140i
$696$	4.86267			0.184319
$697$			45.7794i			1.73402i
$698$		−	32.3551i		−	1.22466i
$699$	−6.92654			−0.261986
$700$	4.85649	−	17.5232i	0.183558	−	0.662315i
$701$	14.6561			0.553553			0.276777	−	0.960934i	$-0.410734\pi$
$701$	14.6561			0.553553			0.276777	+	0.960934i	$0.410734\pi$
$702$		0			0
$703$		−	3.48006i		−	0.131253i
$704$	2.00000			0.0753778
$705$	1.38704	−	10.1981i	0.0522388	−	0.384081i
$706$	20.0270			0.753728
$707$			57.0399i			2.14521i
$708$			4.86267i			0.182750i
$709$	−23.3145			−0.875595			−0.437798	−	0.899073i	$-0.644241\pi$
$709$	−23.3145			−0.875595			−0.437798	+	0.899073i	$0.644241\pi$
$710$	−20.9721	−	2.85242i	−0.787070	−	0.107049i
$711$	−5.09397			−0.191039
$712$		−	8.06808i		−	0.302364i
$713$			4.13617i			0.154901i
$714$	14.6216			0.547200
$715$		0			0
$716$	−8.84216			−0.330447
$717$		−	8.84216i		−	0.330216i
$718$		−	22.9308i		−	0.855768i
$719$	29.3416			1.09426			0.547128	−	0.837049i	$-0.315721\pi$
$719$	29.3416			1.09426			0.547128	+	0.837049i	$0.315721\pi$
$720$	0.794590	−	5.84216i	0.0296126	−	0.217724i
$721$	55.7934			2.07786
$722$		−	46.0940i		−	1.71544i
$723$		−	11.2194i		−	0.417254i
$724$	−1.61623			−0.0600667
$725$	−38.8750	−	10.7741i	−1.44378	−	0.400139i
$726$	4.21893			0.156579
$727$			15.4530i			0.573121i	0.958062	+	0.286560i	$0.0925119\pi$
$727$			15.4530i			0.573121i	−0.958062	+	0.286560i	$0.907488\pi$
$728$		0			0
$729$	9.31569			0.345025
$730$	−1.80811	+	13.2940i	−0.0669213	+	0.492033i
$731$	38.7447			1.43302
$732$		−	1.72535i		−	0.0637707i
$733$		−	30.2108i		−	1.11586i	−0.829888	−	0.557930i	$-0.811596\pi$
$733$		−	30.2108i		−	1.11586i	0.829888	−	0.557930i	$-0.188404\pi$
$734$	34.1362			1.25999
$735$	8.31407	+	1.13079i	0.306669	+	0.0417100i
$736$	−0.794590			−0.0292890
$737$		−	10.4108i		−	0.383487i
$738$			18.0951i			0.666091i
$739$	−24.5880			−0.904485			−0.452242	−	0.891895i	$-0.649376\pi$
$739$	−24.5880			−0.904485			−0.452242	+	0.891895i	$0.649376\pi$
$740$	0.955700	+	0.129984i	0.0351322	+	0.00477832i
$741$		0			0
$742$			2.88972i			0.106085i
$743$			48.0452i			1.76261i	0.472549	+	0.881305i	$0.343334\pi$
$743$			48.0452i			1.76261i	−0.472549	+	0.881305i	$0.656666\pi$
$744$	−3.13733			−0.115020
$745$		0			0
$746$	26.9988			0.988498
$747$			5.45301i			0.199515i
$748$		−	13.3416i		−	0.487816i
$749$	4.38377			0.160179
$750$	2.65842	−	6.19189i	0.0970719	−	0.226096i
$751$	−4.90371			−0.178939			−0.0894694	−	0.995990i	$-0.528517\pi$
$751$	−4.90371			−0.178939			−0.0894694	+	0.995990i	$0.528517\pi$
$752$			7.63675i			0.278484i
$753$			8.68547i			0.316516i
$754$		0			0
$755$	−2.12591	+	15.6306i	−0.0773697	+	0.568854i
$756$	12.3551			0.449351
$757$		−	11.3416i		−	0.412217i	−0.978529	−	0.206108i	$-0.933920\pi$
$757$		−	11.3416i		−	0.412217i	0.978529	−	0.206108i	$-0.0660799\pi$
$758$		−	12.9308i		−	0.469666i
$759$	0.957807			0.0347662
$760$	17.8762	+	2.43134i	0.648438	+	0.0881939i
$761$	−10.3427			−0.374924			−0.187462	−	0.982272i	$-0.560026\pi$
$761$	−10.3427			−0.374924			−0.187462	+	0.982272i	$0.560026\pi$
$762$		−	2.88972i		−	0.104684i
$763$		−	35.6696i		−	1.29133i
$764$	−21.3416			−0.772111
$765$	−38.9718	−	5.30054i	−1.40903	−	0.191642i
$766$	−21.3621			−0.771844
$767$		0			0
$768$		−	0.602705i		−	0.0217482i
$769$	27.6843			0.998322			0.499161	−	0.866509i	$-0.333642\pi$
$769$	27.6843			0.998322			0.499161	+	0.866509i	$0.333642\pi$
$770$	2.19189	−	16.1157i	0.0789901	−	0.580768i
$771$	0.0746158			0.00268722
$772$			5.61623i			0.202133i
$773$		−	12.2952i		−	0.442227i	−0.975248	−	0.221113i	$-0.929031\pi$
$773$		−	12.2952i		−	0.442227i	0.975248	−	0.221113i	$-0.0709690\pi$
$774$	15.3145			0.550469
$775$	25.0816	+	6.95127i	0.900958	+	0.249697i
$776$	−13.6573			−0.490267
$777$			0.945441i			0.0339175i
$778$		−	29.4507i		−	1.05586i
$779$	−55.3686			−1.98379
$780$		0			0
$781$	−18.9308			−0.677396
$782$			5.30054i			0.189547i
$783$		−	27.4097i		−	0.979541i
$784$	−6.22593			−0.222355
$785$	−0.150851	−	0.0205172i	−0.00538410	−	0.000732290i
$786$	2.42319			0.0864322
$787$			43.5048i			1.55078i	0.631484	+	0.775389i	$0.282446\pi$
$787$			43.5048i			1.55078i	−0.631484	+	0.775389i	$0.717554\pi$
$788$			14.0205i			0.499460i
$789$	−3.17836			−0.113153
$790$	4.28049	+	0.582188i	0.152293	+	0.0207133i
$791$	−14.5470			−0.517231
$792$		−	5.27349i		−	0.187385i
$793$		0			0
$794$	−16.6832			−0.592063
$795$	−0.144319	+	1.06109i	−0.00511846	+	0.0376330i
$796$	−15.7524			−0.558329
$797$			12.9718i			0.459484i	0.973252	+	0.229742i	$0.0737883\pi$
$797$			12.9718i			0.459484i	−0.973252	+	0.229742i	$0.926212\pi$
$798$			17.6843i			0.626018i
$799$	50.9431			1.80224
$800$	−1.33539	+	4.81837i	−0.0472133	+	0.170355i
$801$	−21.2735			−0.751662
$802$		−	7.34158i		−	0.259240i
$803$			12.0000i			0.423471i
$804$	−3.13733			−0.110645
$805$	−0.870825	+	6.40267i	−0.0306926	+	0.225664i
$806$		0			0
$807$			0.767541i			0.0270187i
$808$		−	15.6843i		−	0.551772i
$809$	−8.73304			−0.307037			−0.153519	−	0.988146i	$-0.549061\pi$
$809$	−8.73304			−0.307037			−0.153519	+	0.988146i	$0.549061\pi$
$810$	−12.9897	−	1.76673i	−0.456413	−	0.0620766i
$811$	−46.3134			−1.62628			−0.813141	−	0.582067i	$-0.802244\pi$
$811$	−46.3134			−1.62628			−0.813141	+	0.582067i	$0.802244\pi$
$812$			29.3416i			1.02969i
$813$			3.78922i			0.132894i
$814$	0.862674			0.0302367
$815$	−16.9660	−	2.30754i	−0.594292	−	0.0808294i
$816$	−4.02052			−0.140746
$817$			46.8604i			1.63944i
$818$			35.4777i			1.24045i
$819$		0			0
$820$	2.06808	−	15.2054i	0.0722206	−	0.530996i
$821$	−31.9172			−1.11392			−0.556960	−	0.830540i	$-0.688032\pi$
$821$	−31.9172			−1.11392			−0.556960	+	0.830540i	$0.688032\pi$
$822$			6.75356i			0.235557i
$823$		−	6.42480i		−	0.223955i	−0.993711	−	0.111977i	$-0.964282\pi$
$823$		−	6.42480i		−	0.223955i	0.993711	−	0.111977i	$-0.0357184\pi$
$824$	−15.3416			−0.534449
$825$	1.60970	−	5.80811i	0.0560425	−	0.202213i
$826$	−29.3416			−1.02092
$827$		−	38.7242i		−	1.34657i	−0.739382	−	0.673286i	$-0.764882\pi$
$827$		−	38.7242i		−	1.34657i	0.739382	−	0.673286i	$-0.235118\pi$
$828$			2.09513i			0.0728109i
$829$	18.3427			0.637070			0.318535	−	0.947911i	$-0.396809\pi$
$829$	18.3427			0.637070			0.318535	+	0.947911i	$0.396809\pi$
$830$	0.623222	−	4.58219i	0.0216324	−	0.159050i
$831$	−13.8615			−0.480851
$832$		0			0
$833$			41.5318i			1.43899i
$834$	5.32921			0.184535
$835$	10.6832	+	1.45301i	0.369706	+	0.0502836i
$836$	16.1362			0.558081
$837$			17.6843i			0.611259i
$838$			0.883191i			0.0305093i
$839$	−12.6561			−0.436937			−0.218469	−	0.975844i	$-0.570106\pi$
$839$	−12.6561			−0.436937			−0.218469	+	0.975844i	$0.570106\pi$
$840$	−4.85649	−	0.660530i	−0.167565	−	0.0227905i
$841$	36.0940			1.24462
$842$			27.2859i			0.940333i
$843$			6.23362i			0.214697i
$844$	1.70483			0.0586827
$845$		0			0
$846$	20.1362			0.692296
$847$			25.4572i			0.874721i
$848$		−	0.794590i		−	0.0272863i
$849$	−6.04335			−0.207407
$850$	32.1424	+	8.90813i	1.10247	+	0.305546i
$851$	−0.342736			−0.0117488
$852$			5.70483i			0.195444i
$853$		−	44.7988i		−	1.53388i	−0.641718	−	0.766941i	$-0.721778\pi$
$853$		−	44.7988i		−	1.53388i	0.641718	−	0.766941i	$-0.278222\pi$
$854$	10.4108			0.356251
$855$	6.41082	−	47.1350i	0.219245	−	1.61198i
$856$	−1.20541			−0.0412001
$857$		−	46.8193i		−	1.59932i	−0.600455	−	0.799659i	$-0.705014\pi$
$857$		−	46.8193i		−	1.59932i	0.600455	−	0.799659i	$-0.294986\pi$
$858$		0			0
$859$	23.8638			0.814223			0.407112	−	0.913378i	$-0.366536\pi$
$859$	23.8638			0.814223			0.407112	+	0.913378i	$0.366536\pi$
$860$	−12.8689	−	1.75029i	−0.438824	−	0.0596844i
$861$	15.0422			0.512637
$862$			0.259969i			0.00885458i
$863$			12.2271i			0.416215i	0.978106	+	0.208107i	$0.0667304\pi$
$863$			12.2271i			0.416215i	−0.978106	+	0.208107i	$0.933270\pi$
$864$	−3.39730			−0.115578
$865$	28.3486	+	3.85568i	0.963880	+	0.131097i
$866$	17.4654			0.593498
$867$			16.5740i			0.562884i
$868$		−	18.9308i		−	0.642552i
$869$	3.86383			0.131072
$870$	−1.46538	+	10.7741i	−0.0496810	+	0.365275i
$871$		0			0
$872$			9.80811i			0.332145i
$873$			36.0107i			1.21878i
$874$	−6.41082			−0.216849
$875$	37.3621	+	16.0410i	1.26307	+	0.542286i
$876$	3.61623			0.122181
$877$			0.336204i			0.0113528i	0.999984	+	0.00567640i	$0.00180686\pi$
$877$			0.336204i			0.0113528i	−0.999984	+	0.00567640i	$0.998193\pi$
$878$			17.6843i			0.596817i
$879$	−3.68593			−0.124323
$880$	−0.602705	+	4.43134i	−0.0203172	+	0.149380i
$881$	−41.0464			−1.38289			−0.691444	−	0.722430i	$-0.743025\pi$
$881$	−41.0464			−1.38289			−0.691444	+	0.722430i	$0.743025\pi$
$882$			16.4162i			0.552762i
$883$		−	40.0534i		−	1.34790i	−0.738775	−	0.673952i	$-0.764595\pi$
$883$		−	40.0534i		−	1.34790i	0.738775	−	0.673952i	$-0.235405\pi$
$884$		0			0
$885$	−10.7741	−	1.46538i	−0.362167	−	0.0492582i
$886$	−32.4913			−1.09157
$887$			28.7242i			0.964464i	0.876044	+	0.482232i	$0.160174\pi$
$887$			28.7242i			0.964464i	−0.876044	+	0.482232i	$0.839826\pi$
$888$		−	0.259969i		−	0.00872398i
$889$	17.4367			0.584808
$890$	17.8762	+	2.43134i	0.599212	+	0.0814986i
$891$	−11.7253			−0.392814
$892$		−	22.9513i		−	0.768466i
$893$			61.6139i			2.06183i
$894$		0			0
$895$	2.66461	−	19.5913i	0.0890679	−	0.654865i
$896$	3.63675			0.121495
$897$		0			0
$898$		−	35.0940i		−	1.17110i
$899$	−41.9977			−1.40070
$900$	12.7048	+	3.52110i	0.423494	+	0.117370i
$901$	−5.30054			−0.176587
$902$		−	13.7253i		−	0.457004i
$903$		−	12.7307i		−	0.423652i
$904$	4.00000			0.133038
$905$	0.487055	−	3.58103i	0.0161902	−	0.119037i
$906$	4.25182			0.141257
$907$			48.7636i			1.61917i	0.587003	+	0.809584i	$0.300308\pi$
$907$			48.7636i			1.61917i	−0.587003	+	0.809584i	$0.699692\pi$
$908$			10.5470i			0.350014i
$909$	−41.3556			−1.37168
$910$		0			0
$911$	15.4801			0.512877			0.256439	−	0.966561i	$-0.417451\pi$
$911$	15.4801			0.512877			0.256439	+	0.966561i	$0.417451\pi$
$912$		−	4.86267i		−	0.161019i
$913$		−	4.13617i		−	0.136887i
$914$	−20.5470			−0.679634
$915$	3.82280	+	0.519938i	0.126378	+	0.0171886i
$916$	−25.9443			−0.857223
$917$			14.6216i			0.482848i
$918$			22.6626i			0.747978i
$919$	−45.8615			−1.51283			−0.756416	−	0.654091i	$-0.773051\pi$
$919$	−45.8615			−1.51283			−0.756416	+	0.654091i	$0.773051\pi$
$920$	0.239452	−	1.76055i	0.00789449	−	0.0580436i
$921$	10.1632			0.334889
$922$		−	7.14969i		−	0.235463i
$923$		0			0
$924$	−4.38377			−0.144215
$925$	−0.576005	+	2.07834i	−0.0189389	+	0.0683355i
$926$	22.6832			0.745415
$927$			40.4519i			1.32861i
$928$		−	8.06808i		−	0.264848i
$929$	−26.9168			−0.883111			−0.441555	−	0.897234i	$-0.645573\pi$
$929$	−26.9168			−0.883111			−0.441555	+	0.897234i	$0.645573\pi$
$930$	0.945441	−	6.95127i	0.0310022	−	0.227941i
$931$	−50.2313			−1.64626
$932$			11.4924i			0.376447i
$933$		−	19.8886i		−	0.651122i
$934$	−25.2054			−0.824746
$935$	29.5605	+	4.02052i	0.966732	+	0.131485i
$936$		0			0
$937$			4.90371i			0.160197i	0.996787	+	0.0800986i	$0.0255235\pi$
$937$			4.90371i			0.160197i	−0.996787	+	0.0800986i	$0.974476\pi$
$938$		−	18.9308i		−	0.618111i
$939$	−15.3481			−0.500867
$940$	−16.9205	−	2.30135i	−0.551886	−	0.0750618i
$941$	46.6004			1.51913			0.759565	−	0.650432i	$-0.225412\pi$
$941$	46.6004			1.51913			0.759565	+	0.650432i	$0.225412\pi$
$942$			0.0410344i			0.00133697i
$943$			5.45301i			0.177575i
$944$	8.06808			0.262594
$945$	−3.72324	+	27.3748i	−0.121117	+	0.890503i
$946$	−11.6162			−0.377676
$947$			27.7524i			0.901832i	0.892566	+	0.450916i	$0.148903\pi$
$947$			27.7524i			0.901832i	−0.892566	+	0.450916i	$0.851097\pi$
$948$		−	1.16438i		−	0.0378172i
$949$		0			0
$950$	−10.7741	+	38.8750i	−0.349557	+	1.26127i
$951$	−8.51994			−0.276278
$952$		−	24.2600i		−	0.786270i
$953$		−	14.9725i		−	0.485007i	−0.970151	−	0.242503i	$-0.922031\pi$
$953$		−	14.9725i		−	0.485007i	0.970151	−	0.242503i	$-0.0779685\pi$
$954$	−2.09513			−0.0678324
$955$	6.43134	−	47.2859i	0.208113	−	1.53013i
$956$	−14.6708			−0.474487
$957$			9.72535i			0.314376i
$958$		−	4.01237i		−	0.129634i
$959$	−40.7512			−1.31593
$960$	1.33539	+	0.181627i	0.0430997	+	0.00586197i
$961$	−3.90371			−0.125926
$962$		0			0
$963$			3.17836i			0.102421i
$964$	−18.6151			−0.599551
$965$	−12.4437	−	1.69246i	−0.400577	−	0.0544824i
$966$	1.74165			0.0560367
$967$		−	52.5946i		−	1.69133i	−0.533717	−	0.845663i	$-0.679205\pi$
$967$		−	52.5946i		−	1.69133i	0.533717	−	0.845663i	$-0.320795\pi$
$968$		−	7.00000i		−	0.224989i
$969$	−32.4379			−1.04205
$970$	4.11565	−	30.2600i	0.132146	−	0.971589i
$971$	−15.5253			−0.498231			−0.249115	−	0.968474i	$-0.580140\pi$
$971$	−15.5253			−0.498231			−0.249115	+	0.968474i	$0.580140\pi$
$972$			13.7253i			0.440241i
$973$			32.1567i			1.03090i
$974$	−8.00000			−0.256337
$975$		0			0
$976$	−2.86267			−0.0916320
$977$		−	47.5729i		−	1.52199i	−0.648757	−	0.760996i	$-0.724711\pi$
$977$		−	47.5729i		−	1.52199i	0.648757	−	0.760996i	$-0.275289\pi$
$978$			4.61507i			0.147574i
$979$	16.1362			0.515714
$980$	1.87620	−	13.7946i	0.0599330	−	0.440652i
$981$	25.8615			0.825695
$982$			8.88319i			0.283474i
$983$			37.3211i			1.19036i	0.803594	+	0.595178i	$0.202919\pi$
$983$			37.3211i			1.19036i	−0.803594	+	0.595178i	$0.797081\pi$
$984$	−4.13617			−0.131856
$985$	−31.0648	−	4.22512i	−0.989807	−	0.134623i
$986$	−53.8205			−1.71399
$987$		−	16.7389i		−	0.532804i
$988$		0			0
$989$	4.61507			0.146751
$990$	11.6843	+	1.58918i	0.371352	+	0.0505075i
$991$	22.5060			0.714925			0.357463	−	0.933927i	$-0.383642\pi$
$991$	22.5060			0.714925			0.357463	+	0.933927i	$0.383642\pi$
$992$			5.20541i			0.165272i
$993$			11.1621i			0.354217i
$994$	−34.4232			−1.09184
$995$	4.74702	−	34.9021i	0.150491	−	1.10647i
$996$	−1.24644			−0.0394951
$997$			24.4108i			0.773098i	0.922269	+	0.386549i	$0.126333\pi$
$997$			24.4108i			0.773098i	−0.922269	+	0.386549i	$0.873667\pi$
$998$			10.9988i			0.348162i
$999$	−1.46538			−0.0463625

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.a.339.2		6
5.2	odd	4		8450.2.a.cc.1.2		3
5.3	odd	4		8450.2.a.bs.1.2		3
5.4	even	2	inner	1690.2.b.a.339.5		6
13.5	odd	4		1690.2.c.a.1689.3		6
13.8	odd	4		1690.2.c.d.1689.3		6
13.12	even	2		130.2.b.a.79.5	yes	6
39.38	odd	2		1170.2.e.f.469.2		6
52.51	odd	2		1040.2.d.b.209.4		6
65.12	odd	4		650.2.a.n.1.2		3
65.34	odd	4		1690.2.c.a.1689.4		6
65.38	odd	4		650.2.a.o.1.2		3
65.44	odd	4		1690.2.c.d.1689.4		6
65.64	even	2		130.2.b.a.79.2	✓	6
195.38	even	4		5850.2.a.cp.1.3		3
195.77	even	4		5850.2.a.cs.1.1		3
195.194	odd	2		1170.2.e.f.469.5		6
260.103	even	4		5200.2.a.cf.1.2		3
260.207	even	4		5200.2.a.ce.1.2		3
260.259	odd	2		1040.2.d.b.209.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.b.a.79.2	✓	6	65.64	even	2
130.2.b.a.79.5	yes	6	13.12	even	2
650.2.a.n.1.2		3	65.12	odd	4
650.2.a.o.1.2		3	65.38	odd	4
1040.2.d.b.209.3		6	260.259	odd	2
1040.2.d.b.209.4		6	52.51	odd	2
1170.2.e.f.469.2		6	39.38	odd	2
1170.2.e.f.469.5		6	195.194	odd	2
1690.2.b.a.339.2		6	1.1	even	1	trivial
1690.2.b.a.339.5		6	5.4	even	2	inner
1690.2.c.a.1689.3		6	13.5	odd	4
1690.2.c.a.1689.4		6	65.34	odd	4
1690.2.c.d.1689.3		6	13.8	odd	4
1690.2.c.d.1689.4		6	65.44	odd	4
5200.2.a.ce.1.2		3	260.207	even	4
5200.2.a.cf.1.2		3	260.103	even	4
5850.2.a.cp.1.3		3	195.38	even	4
5850.2.a.cs.1.1		3	195.77	even	4
8450.2.a.bs.1.2		3	5.3	odd	4
8450.2.a.cc.1.2		3	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:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -0.602705i q^{3} -1.00000 q^{4} +(0.301352 - 2.21567i) q^{5} -0.602705 q^{6} -3.63675i q^{7} +1.00000i q^{8} +2.63675 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -0.602705i q^{3} -1.00000 q^{4} +(0.301352 - 2.21567i) q^{5} -0.602705 q^{6} -3.63675i q^{7} +1.00000i q^{8} +2.63675 q^{9} +(-2.21567 - 0.301352i) q^{10} -2.00000 q^{11} +0.602705i q^{12} -3.63675 q^{14} +(-1.33539 - 0.181627i) q^{15} +1.00000 q^{16} -6.67079i q^{17} -2.63675i q^{18} +8.06808 q^{19} +(-0.301352 + 2.21567i) q^{20} -2.19189 q^{21} +2.00000i q^{22} -0.794590i q^{23} +0.602705 q^{24} +(-4.81837 - 1.33539i) q^{25} -3.39730i q^{27} +3.63675i q^{28} +8.06808 q^{29} +(-0.181627 + 1.33539i) q^{30} -5.20541 q^{31} -1.00000i q^{32} +1.20541i q^{33} -6.67079 q^{34} +(-8.05783 - 1.09594i) q^{35} -2.63675 q^{36} -0.431337i q^{37} -8.06808i q^{38} +(2.21567 + 0.301352i) q^{40} -6.86267 q^{41} +2.19189i q^{42} +5.80811i q^{43} +2.00000 q^{44} +(0.794590 - 5.84216i) q^{45} -0.794590 q^{46} +7.63675i q^{47} -0.602705i q^{48} -6.22593 q^{49} +(-1.33539 + 4.81837i) q^{50} -4.02052 q^{51} -0.794590i q^{53} -3.39730 q^{54} +(-0.602705 + 4.43134i) q^{55} +3.63675 q^{56} -4.86267i q^{57} -8.06808i q^{58} +8.06808 q^{59} +(1.33539 + 0.181627i) q^{60} -2.86267 q^{61} +5.20541i q^{62} -9.58918i q^{63} -1.00000 q^{64} +1.20541 q^{66} +5.20541i q^{67} +6.67079i q^{68} -0.478903 q^{69} +(-1.09594 + 8.05783i) q^{70} +9.46538 q^{71} +2.63675i q^{72} -6.00000i q^{73} -0.431337 q^{74} +(-0.804849 + 2.90406i) q^{75} -8.06808 q^{76} +7.27349i q^{77} -1.93192 q^{79} +(0.301352 - 2.21567i) q^{80} +5.86267 q^{81} +6.86267i q^{82} +2.06808i q^{83} +2.19189 q^{84} +(-14.7803 - 2.01026i) q^{85} +5.80811 q^{86} -4.86267i q^{87} -2.00000i q^{88} -8.06808 q^{89} +(-5.84216 - 0.794590i) q^{90} +0.794590i q^{92} +3.13733i q^{93} +7.63675 q^{94} +(2.43134 - 17.8762i) q^{95} -0.602705 q^{96} +13.6573i q^{97} +6.22593i q^{98} -5.27349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 10 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 10 * q^9	\( 6 q - 6 q^{4} - 10 q^{9} - 4 q^{10} - 12 q^{11} + 4 q^{14} + 16 q^{15} + 6 q^{16} + 4 q^{19} - 24 q^{21} - 16 q^{25} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 8 q^{34} - 6 q^{35} + 10 q^{36} + 4 q^{40} - 4 q^{41} + 12 q^{44} + 12 q^{45} - 12 q^{46} - 26 q^{49} + 16 q^{50} - 20 q^{51} - 24 q^{54} - 4 q^{56} + 4 q^{59} - 16 q^{60} + 20 q^{61} - 6 q^{64} + 56 q^{69} - 12 q^{70} + 16 q^{71} + 16 q^{74} - 10 q^{75} - 4 q^{76} - 56 q^{79} - 2 q^{81} + 24 q^{84} - 28 q^{85} + 24 q^{86} - 4 q^{89} - 2 q^{90} + 20 q^{94} - 4 q^{95} + 20 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 10 * q^9 - 4 * q^10 - 12 * q^11 + 4 * q^14 + 16 * q^15 + 6 * q^16 + 4 * q^19 - 24 * q^21 - 16 * q^25 + 4 * q^29 - 14 * q^30 - 24 * q^31 + 8 * q^34 - 6 * q^35 + 10 * q^36 + 4 * q^40 - 4 * q^41 + 12 * q^44 + 12 * q^45 - 12 * q^46 - 26 * q^49 + 16 * q^50 - 20 * q^51 - 24 * q^54 - 4 * q^56 + 4 * q^59 - 16 * q^60 + 20 * q^61 - 6 * q^64 + 56 * q^69 - 12 * q^70 + 16 * q^71 + 16 * q^74 - 10 * q^75 - 4 * q^76 - 56 * q^79 - 2 * q^81 + 24 * q^84 - 28 * q^85 + 24 * q^86 - 4 * q^89 - 2 * q^90 + 20 * q^94 - 4 * q^95 + 20 * q^99

Introduction

L-functions

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