LMFDB - Embedded newform 1690.2.c.d.1689.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1690,2,Mod(1689,1690)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1690, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1690.1689"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1690 = 2 \cdot 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1690.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,6,0,6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1689.5
Root			$0.627553 + 1.14620i$ of defining polynomial
Character	$\chi$	$=$	1690.1689
Dual form			1690.2.c.d.1689.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +2.29240i q^{3} +1.00000 q^{4} +(-1.91995 - 1.14620i) q^{5} +2.29240i q^{6} +1.25511 q^{7} +1.00000 q^{8} -2.25511 q^{9} +(-1.91995 - 1.14620i) q^{10} -2.00000i q^{11} +2.29240i q^{12} +1.25511 q^{14} +(2.62755 - 4.40131i) q^{15} +1.00000 q^{16} +4.80261i q^{17} -2.25511 q^{18} +5.09501i q^{19} +(-1.91995 - 1.14620i) q^{20} +2.87720i q^{21} -2.00000i q^{22} +2.58480i q^{23} +2.29240i q^{24} +(2.37245 + 4.40131i) q^{25} +1.70760i q^{27} +1.25511 q^{28} -5.09501 q^{29} +(2.62755 - 4.40131i) q^{30} +8.58480i q^{31} +1.00000 q^{32} +4.58480 q^{33} +4.80261i q^{34} +(-2.40974 - 1.43860i) q^{35} -2.25511 q^{36} +7.83991 q^{37} +5.09501i q^{38} +(-1.91995 - 1.14620i) q^{40} -9.67982i q^{41} +2.87720i q^{42} +10.8772i q^{43} -2.00000i q^{44} +(4.32970 + 2.58480i) q^{45} +2.58480i q^{46} +2.74489 q^{47} +2.29240i q^{48} -5.42471 q^{49} +(2.37245 + 4.40131i) q^{50} -11.0095 q^{51} -2.58480i q^{53} +1.70760i q^{54} +(-2.29240 + 3.83991i) q^{55} +1.25511 q^{56} -11.6798 q^{57} -5.09501 q^{58} -5.09501i q^{59} +(2.62755 - 4.40131i) q^{60} +13.6798 q^{61} +8.58480i q^{62} -2.83039 q^{63} +1.00000 q^{64} +4.58480 q^{66} -8.58480 q^{67} +4.80261i q^{68} -5.92541 q^{69} +(-2.40974 - 1.43860i) q^{70} +5.38741i q^{71} -2.25511 q^{72} -6.00000 q^{73} +7.83991 q^{74} +(-10.0896 + 5.43860i) q^{75} +5.09501i q^{76} -2.51021i q^{77} -15.0950 q^{79} +(-1.91995 - 1.14620i) q^{80} -10.6798 q^{81} -9.67982i q^{82} +11.0950 q^{83} +2.87720i q^{84} +(5.50476 - 9.22079i) q^{85} +10.8772i q^{86} -11.6798i q^{87} -2.00000i q^{88} +5.09501i q^{89} +(4.32970 + 2.58480i) q^{90} +2.58480i q^{92} -19.6798 q^{93} +2.74489 q^{94} +(5.83991 - 9.78219i) q^{95} +2.29240i q^{96} +6.26462 q^{97} -5.42471 q^{98} +4.51021i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 10 q^{9} + 4 q^{10} + 4 q^{14} + 14 q^{15} + 6 q^{16} - 10 q^{18} + 4 q^{20} + 16 q^{25} + 4 q^{28} + 4 q^{29} + 14 q^{30} + 6 q^{32} - 6 q^{35} - 10 q^{36}+ \cdots + 26 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 10 * q^9 + 4 * q^10 + 4 * q^14 + 14 * q^15 + 6 * q^16 - 10 * q^18 + 4 * q^20 + 16 * q^25 + 4 * q^28 + 4 * q^29 + 14 * q^30 + 6 * q^32 - 6 * q^35 - 10 * q^36 + 16 * q^37 + 4 * q^40 + 2 * q^45 + 20 * q^47 + 26 * q^49 + 16 * q^50 + 20 * q^51 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 14 * q^60 + 20 * q^61 - 72 * q^63 + 6 * q^64 - 24 * q^67 - 56 * q^69 - 6 * q^70 - 10 * q^72 - 36 * q^73 + 16 * q^74 + 10 * q^75 - 56 * q^79 + 4 * q^80 - 2 * q^81 + 32 * q^83 - 10 * q^85 + 2 * q^90 - 56 * q^93 + 20 * q^94 + 4 * q^95 - 52 * q^97 + 26 * q^98

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$			2.29240i			1.32352i	0.749716	+	0.661759i	$0.230190\pi$
$3$			2.29240i			1.32352i	−0.749716	+	0.661759i	$0.769810\pi$
$4$	1.00000			0.500000
$5$	−1.91995	−	1.14620i	−0.858630	−	0.512597i
$5$	−1.91995	−	1.14620i	−0.858630	−	0.512597i
$6$			2.29240i			0.935869i
$7$	1.25511			0.474385			0.237193	−	0.971463i	$-0.423773\pi$
$7$	1.25511			0.474385			0.237193	+	0.971463i	$0.423773\pi$
$8$	1.00000			0.353553
$9$	−2.25511			−0.751702
$10$	−1.91995	−	1.14620i	−0.607143	−	0.362461i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$			2.29240i			0.661759i
$13$		0			0
$13$		0			0
$14$	1.25511			0.335441
$15$	2.62755	−	4.40131i	0.678431	−	1.13641i
$16$	1.00000			0.250000
$17$			4.80261i			1.16480i	0.812901	+	0.582402i	$0.197887\pi$
$17$			4.80261i			1.16480i	−0.812901	+	0.582402i	$0.802113\pi$
$18$	−2.25511			−0.531533
$19$			5.09501i			1.16888i	0.811438	+	0.584438i	$0.198685\pi$
$19$			5.09501i			1.16888i	−0.811438	+	0.584438i	$0.801315\pi$
$20$	−1.91995	−	1.14620i	−0.429315	−	0.256298i
$21$			2.87720i			0.627858i
$22$		−	2.00000i		−	0.426401i
$23$			2.58480i			0.538969i	0.963005	+	0.269484i	$0.0868533\pi$
$23$			2.58480i			0.538969i	−0.963005	+	0.269484i	$0.913147\pi$
$24$			2.29240i			0.467935i
$25$	2.37245	+	4.40131i	0.474489	+	0.880261i
$26$		0			0
$27$			1.70760i			0.328627i
$28$	1.25511			0.237193
$29$	−5.09501			−0.946120			−0.473060	−	0.881030i	$-0.656851\pi$
$29$	−5.09501			−0.946120			−0.473060	+	0.881030i	$0.656851\pi$
$30$	2.62755	−	4.40131i	0.479723	−	0.803565i
$31$			8.58480i			1.54188i	0.636910	+	0.770938i	$0.280212\pi$
$31$			8.58480i			1.54188i	−0.636910	+	0.770938i	$0.719788\pi$
$32$	1.00000			0.176777
$33$	4.58480			0.798112
$34$			4.80261i			0.823641i
$35$	−2.40974	−	1.43860i	−0.407321	−	0.243168i
$36$	−2.25511			−0.375851
$37$	7.83991			1.28887			0.644436	−	0.764658i	$-0.277092\pi$
$37$	7.83991			1.28887			0.644436	+	0.764658i	$0.277092\pi$
$38$			5.09501i			0.826520i
$39$		0			0
$40$	−1.91995	−	1.14620i	−0.303571	−	0.181230i
$41$		−	9.67982i		−	1.51173i	−0.654726	−	0.755867i	$-0.727216\pi$
$41$		−	9.67982i		−	1.51173i	0.654726	−	0.755867i	$-0.272784\pi$
$42$			2.87720i			0.443962i
$43$			10.8772i			1.65876i	0.558686	+	0.829379i	$0.311306\pi$
$43$			10.8772i			1.65876i	−0.558686	+	0.829379i	$0.688694\pi$
$44$		−	2.00000i		−	0.301511i
$45$	4.32970	+	2.58480i	0.645433	+	0.385320i
$46$			2.58480i			0.381108i
$47$	2.74489			0.400384			0.200192	−	0.979757i	$-0.435843\pi$
$47$	2.74489			0.400384			0.200192	+	0.979757i	$0.435843\pi$
$48$			2.29240i			0.330880i
$49$	−5.42471			−0.774959
$50$	2.37245	+	4.40131i	0.335515	+	0.622439i
$51$	−11.0095			−1.54164
$52$		0			0
$53$		−	2.58480i		−	0.355050i	−0.984116	−	0.177525i	$-0.943191\pi$
$53$		−	2.58480i		−	0.355050i	0.984116	−	0.177525i	$-0.0568091\pi$
$54$			1.70760i			0.232375i
$55$	−2.29240	+	3.83991i	−0.309107	+	0.517773i
$56$	1.25511			0.167720
$57$	−11.6798			−1.54703
$58$	−5.09501			−0.669008
$59$		−	5.09501i		−	0.663314i	−0.943400	−	0.331657i	$-0.892392\pi$
$59$		−	5.09501i		−	0.663314i	0.943400	−	0.331657i	$-0.107608\pi$
$60$	2.62755	−	4.40131i	0.339216	−	0.568206i
$61$	13.6798			1.75152			0.875761	−	0.482746i	$-0.160361\pi$
$61$	13.6798			1.75152			0.875761	+	0.482746i	$0.160361\pi$
$62$			8.58480i			1.09027i
$63$	−2.83039			−0.356596
$64$	1.00000			0.125000
$65$		0			0
$66$	4.58480			0.564350
$67$	−8.58480			−1.04880			−0.524400	−	0.851472i	$-0.675710\pi$
$67$	−8.58480			−1.04880			−0.524400	+	0.851472i	$0.675710\pi$
$68$			4.80261i			0.582402i
$69$	−5.92541			−0.713335
$70$	−2.40974	−	1.43860i	−0.288020	−	0.171946i
$71$			5.38741i			0.639369i	0.947524	+	0.319684i	$0.103577\pi$
$71$			5.38741i			0.639369i	−0.947524	+	0.319684i	$0.896423\pi$
$72$	−2.25511			−0.265767
$73$	−6.00000			−0.702247			−0.351123	−	0.936329i	$-0.614200\pi$
$73$	−6.00000			−0.702247			−0.351123	+	0.936329i	$0.614200\pi$
$74$	7.83991			0.911371
$75$	−10.0896	+	5.43860i	−1.16504	+	0.627996i
$76$			5.09501i			0.584438i
$77$		−	2.51021i		−	0.286065i
$78$		0			0
$79$	−15.0950			−1.69832			−0.849161	−	0.528134i	$-0.822892\pi$
$79$	−15.0950			−1.69832			−0.849161	+	0.528134i	$0.822892\pi$
$80$	−1.91995	−	1.14620i	−0.214657	−	0.128149i
$81$	−10.6798			−1.18665
$82$		−	9.67982i		−	1.06896i
$83$	11.0950			1.21784			0.608918	−	0.793233i	$-0.291604\pi$
$83$	11.0950			1.21784			0.608918	+	0.793233i	$0.291604\pi$
$84$			2.87720i			0.313929i
$85$	5.50476	−	9.22079i	0.597075	−	1.00014i
$86$			10.8772i			1.17292i
$87$		−	11.6798i		−	1.25221i
$88$		−	2.00000i		−	0.213201i
$89$			5.09501i			0.540070i	0.962850	+	0.270035i	$0.0870353\pi$
$89$			5.09501i			0.540070i	−0.962850	+	0.270035i	$0.912965\pi$
$90$	4.32970	+	2.58480i	0.456390	+	0.272462i
$91$		0			0
$92$			2.58480i			0.269484i
$93$	−19.6798			−2.04070
$94$	2.74489			0.283114
$95$	5.83991	−	9.78219i	0.599162	−	1.00363i
$96$			2.29240i			0.233967i
$97$	6.26462			0.636076			0.318038	−	0.948078i	$-0.396976\pi$
$97$	6.26462			0.636076			0.318038	+	0.948078i	$0.396976\pi$
$98$	−5.42471			−0.547979
$99$			4.51021i			0.453293i
$100$	2.37245	+	4.40131i	0.237245	+	0.440131i
$101$	12.6594			1.25966			0.629829	−	0.776734i	$-0.283125\pi$
$101$	12.6594			1.25966			0.629829	+	0.776734i	$0.283125\pi$
$102$	−11.0095			−1.09010
$103$		−	7.60522i		−	0.749365i	−0.927153	−	0.374682i	$-0.877752\pi$
$103$		−	7.60522i		−	0.749365i	0.927153	−	0.374682i	$-0.122248\pi$
$104$		0			0
$105$	3.29785	−	5.52410i	0.321838	−	0.539097i
$106$		−	2.58480i		−	0.251058i
$107$		−	4.58480i		−	0.443230i	−0.975134	−	0.221615i	$-0.928867\pi$
$107$		−	4.58480i		−	0.443230i	0.975134	−	0.221615i	$-0.0711328\pi$
$108$			1.70760i			0.164314i
$109$		−	14.8772i		−	1.42498i	−0.701683	−	0.712489i	$-0.747568\pi$
$109$		−	14.8772i		−	1.42498i	0.701683	−	0.712489i	$-0.252432\pi$
$110$	−2.29240	+	3.83991i	−0.218572	+	0.366121i
$111$			17.9722i			1.70585i
$112$	1.25511			0.118596
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$	−11.6798			−1.09392
$115$	2.96270	−	4.96270i	0.276274	−	0.462774i
$116$	−5.09501			−0.473060
$117$		0			0
$118$		−	5.09501i		−	0.469034i
$119$			6.02778i			0.552566i
$120$	2.62755	−	4.40131i	0.239862	−	0.401782i
$121$	7.00000			0.636364
$122$	13.6798			1.23851
$123$	22.1900			2.00081
$124$			8.58480i			0.770938i
$125$	0.489790	−	11.1696i	0.0438081	−	0.999040i
$126$	−2.83039			−0.252152
$127$			1.41520i			0.125578i	0.998027	+	0.0627892i	$0.0199996\pi$
$127$			1.41520i			0.125578i	−0.998027	+	0.0627892i	$0.980000\pi$
$128$	1.00000			0.0883883
$129$	−24.9349			−2.19540
$130$		0			0
$131$	11.0095			0.961906			0.480953	−	0.876746i	$-0.340291\pi$
$131$	11.0095			0.961906			0.480953	+	0.876746i	$0.340291\pi$
$132$	4.58480			0.399056
$133$			6.39478i			0.554497i
$134$	−8.58480			−0.741614
$135$	1.95725	−	3.27851i	0.168453	−	0.282169i
$136$			4.80261i			0.411821i
$137$	−14.5848			−1.24606			−0.623032	−	0.782196i	$-0.714099\pi$
$137$	−14.5848			−1.24606			−0.623032	+	0.782196i	$0.714099\pi$
$138$	−5.92541			−0.504404
$139$	−7.32970			−0.621697			−0.310848	−	0.950459i	$-0.600613\pi$
$139$	−7.32970			−0.621697			−0.310848	+	0.950459i	$0.600613\pi$
$140$	−2.40974	−	1.43860i	−0.203661	−	0.121584i
$141$			6.29240i			0.529916i
$142$			5.38741i			0.452102i
$143$		0			0
$144$	−2.25511			−0.187925
$145$	9.78219	+	5.83991i	0.812367	+	0.484978i
$146$	−6.00000			−0.496564
$147$		−	12.4356i		−	1.02567i
$148$	7.83991			0.644436
$149$		0			0		1.00000			$0$
$149$		0			0		−1.00000			$\pi$
$150$	−10.0896	+	5.43860i	−0.823809	+	0.444060i
$151$			14.5570i			1.18463i	0.805705	+	0.592317i	$0.201787\pi$
$151$			14.5570i			1.18463i	−0.805705	+	0.592317i	$0.798213\pi$
$152$			5.09501i			0.413260i
$153$		−	10.8304i		−	0.875585i
$154$		−	2.51021i		−	0.202278i
$155$	9.83991	−	16.4824i	0.790360	−	1.32390i
$156$		0			0
$157$		−	13.0950i		−	1.04510i	−0.852610	−	0.522548i	$-0.824982\pi$
$157$		−	13.0950i		−	1.04510i	0.852610	−	0.522548i	$-0.175018\pi$
$158$	−15.0950			−1.20089
$159$	5.92541			0.469915
$160$	−1.91995	−	1.14620i	−0.151786	−	0.0906151i
$161$			3.24420i			0.255679i
$162$	−10.6798			−0.839086
$163$	12.2646			0.960639			0.480320	−	0.877094i	$-0.340521\pi$
$163$	12.2646			0.960639			0.480320	+	0.877094i	$0.340521\pi$
$164$		−	9.67982i		−	0.755867i
$165$	−8.80261	−	5.25511i	−0.685282	−	0.409109i
$166$	11.0950			0.861140
$167$	18.3392			1.41913			0.709565	−	0.704640i	$-0.248891\pi$
$167$	18.3392			1.41913			0.709565	+	0.704640i	$0.248891\pi$
$168$			2.87720i			0.221981i
$169$		0			0
$170$	5.50476	−	9.22079i	0.422196	−	0.707203i
$171$		−	11.4898i		−	0.878646i
$172$			10.8772i			0.829379i
$173$			9.41520i			0.715824i	0.933755	+	0.357912i	$0.116511\pi$
$173$			9.41520i			0.715824i	−0.933755	+	0.357912i	$0.883489\pi$
$174$		−	11.6798i		−	0.885445i
$175$	2.97767	+	5.52410i	0.225091	+	0.417583i
$176$		−	2.00000i		−	0.150756i
$177$	11.6798			0.877909
$178$			5.09501i			0.381887i
$179$	−7.32970			−0.547847			−0.273924	−	0.961751i	$-0.588322\pi$
$179$	−7.32970			−0.547847			−0.273924	+	0.961751i	$0.588322\pi$
$180$	4.32970	+	2.58480i	0.322717	+	0.192660i
$181$	−11.7544			−0.873698			−0.436849	−	0.899535i	$-0.643906\pi$
$181$	−11.7544			−0.873698			−0.436849	+	0.899535i	$0.643906\pi$
$182$		0			0
$183$			31.3596i			2.31817i
$184$			2.58480i			0.190554i
$185$	−15.0523	−	8.98611i	−1.10666	−	0.660672i
$186$	−19.6798			−1.44299
$187$	9.60522			0.702403
$188$	2.74489			0.200192
$189$			2.14322i			0.155896i
$190$	5.83991	−	9.78219i	0.423671	−	0.709675i
$191$	−1.60522			−0.116150			−0.0580749	−	0.998312i	$-0.518496\pi$
$191$	−1.60522			−0.116150			−0.0580749	+	0.998312i	$0.518496\pi$
$192$			2.29240i			0.165440i
$193$	−15.7544			−1.13403			−0.567014	−	0.823708i	$-0.691901\pi$
$193$	−15.7544			−1.13403			−0.567014	+	0.823708i	$0.691901\pi$
$194$	6.26462			0.449773
$195$		0			0
$196$	−5.42471			−0.387479
$197$	−1.00951			−0.0719249			−0.0359625	−	0.999353i	$-0.511450\pi$
$197$	−1.00951			−0.0719249			−0.0359625	+	0.999353i	$0.511450\pi$
$198$			4.51021i			0.320527i
$199$	0.435617			0.0308801			0.0154400	−	0.999881i	$-0.495085\pi$
$199$	0.435617			0.0308801			0.0154400	+	0.999881i	$0.495085\pi$
$200$	2.37245	+	4.40131i	0.167757	+	0.311219i
$201$		−	19.6798i		−	1.38811i
$202$	12.6594			0.890712
$203$	−6.39478			−0.448825
$204$	−11.0095			−0.770820
$205$	−11.0950	+	18.5848i	−0.774909	+	1.29802i
$206$		−	7.60522i		−	0.529881i
$207$		−	5.82900i		−	0.405144i
$208$		0			0
$209$	10.1900			0.704859
$210$	3.29785	−	5.52410i	0.227574	−	0.381199i
$211$	16.3501			1.12559			0.562794	−	0.826597i	$-0.309726\pi$
$211$	16.3501			1.12559			0.562794	+	0.826597i	$0.309726\pi$
$212$		−	2.58480i		−	0.177525i
$213$	−12.3501			−0.846216
$214$		−	4.58480i		−	0.313411i
$215$	12.4675	−	20.8837i	0.850274	−	1.42426i
$216$			1.70760i			0.116187i
$217$			10.7748i			0.731443i
$218$		−	14.8772i		−	1.00761i
$219$		−	13.7544i		−	0.929437i
$220$	−2.29240	+	3.83991i	−0.154554	+	0.258887i
$221$		0			0
$222$			17.9722i			1.20622i
$223$	21.7843			1.45879			0.729394	−	0.684094i	$-0.239802\pi$
$223$	21.7843			1.45879			0.729394	+	0.684094i	$0.239802\pi$
$224$	1.25511			0.0838602
$225$	−5.35012	−	9.92541i	−0.356675	−	0.661694i
$226$			4.00000i			0.266076i
$227$	−9.02042			−0.598706			−0.299353	−	0.954142i	$-0.596771\pi$
$227$	−9.02042			−0.598706			−0.299353	+	0.954142i	$0.596771\pi$
$228$	−11.6798			−0.773515
$229$			4.68718i			0.309737i	0.987935	+	0.154869i	$0.0494955\pi$
$229$			4.68718i			0.309737i	−0.987935	+	0.154869i	$0.950505\pi$
$230$	2.96270	−	4.96270i	0.195355	−	0.327231i
$231$	5.75441			0.378612
$232$	−5.09501			−0.334504
$233$		−	13.5366i		−	0.886812i	−0.896321	−	0.443406i	$-0.853770\pi$
$233$		−	13.5366i		−	0.886812i	0.896321	−	0.443406i	$-0.146230\pi$
$234$		0			0
$235$	−5.27007	−	3.14620i	−0.343782	−	0.205236i
$236$		−	5.09501i		−	0.331657i
$237$		−	34.6038i		−	2.24776i
$238$			6.02778i			0.390723i
$239$		−	3.19739i		−	0.206822i	−0.994639	−	0.103411i	$-0.967024\pi$
$239$		−	3.19739i		−	0.206822i	0.994639	−	0.103411i	$-0.0329757\pi$
$240$	2.62755	−	4.40131i	0.169608	−	0.284103i
$241$		−	14.1154i		−	0.909255i	−0.890682	−	0.454627i	$-0.849772\pi$
$241$		−	14.1154i		−	0.909255i	0.890682	−	0.454627i	$-0.150228\pi$
$242$	7.00000			0.449977
$243$		−	19.3596i		−	1.24192i
$244$	13.6798			0.875761
$245$	10.4152	+	6.21781i	0.665403	+	0.397241i
$246$	22.1900			1.41478
$247$		0			0
$248$			8.58480i			0.545136i
$249$			25.4342i			1.61183i
$250$	0.489790	−	11.1696i	0.0309770	−	0.706428i
$251$	21.1696			1.33621			0.668107	−	0.744065i	$-0.267105\pi$
$251$	21.1696			1.33621			0.668107	+	0.744065i	$0.267105\pi$
$252$	−2.83039			−0.178298
$253$	5.16961			0.325010
$254$			1.41520i			0.0887973i
$255$	21.1378	+	12.6191i	1.32370	+	0.790240i
$256$	1.00000			0.0625000
$257$			8.21781i			0.512613i	0.966596	+	0.256306i	$0.0825056\pi$
$257$			8.21781i			0.512613i	−0.966596	+	0.256306i	$0.917494\pi$
$258$	−24.9349			−1.55238
$259$	9.83991			0.611422
$260$		0			0
$261$	11.4898			0.711200
$262$	11.0095			0.680170
$263$		−	4.51021i		−	0.278111i	−0.990285	−	0.139056i	$-0.955593\pi$
$263$		−	4.51021i		−	0.278111i	0.990285	−	0.139056i	$-0.0444067\pi$
$264$	4.58480			0.282175
$265$	−2.96270	+	4.96270i	−0.181997	+	0.304856i
$266$			6.39478i			0.392089i
$267$	−11.6798			−0.714793
$268$	−8.58480			−0.524400
$269$	8.51021			0.518877			0.259438	−	0.965760i	$-0.416463\pi$
$269$	8.51021			0.518877			0.259438	+	0.965760i	$0.416463\pi$
$270$	1.95725	−	3.27851i	0.119114	−	0.199524i
$271$		−	4.95180i		−	0.300800i	−0.988625	−	0.150400i	$-0.951944\pi$
$271$		−	4.95180i		−	0.300800i	0.988625	−	0.150400i	$-0.0480562\pi$
$272$			4.80261i			0.291201i
$273$		0			0
$274$	−14.5848			−0.881100
$275$	8.80261	−	4.74489i	0.530817	−	0.286128i
$276$	−5.92541			−0.356668
$277$			19.8698i			1.19386i	0.802292	+	0.596932i	$0.203614\pi$
$277$			19.8698i			1.19386i	−0.802292	+	0.596932i	$0.796386\pi$
$278$	−7.32970			−0.439606
$279$		−	19.3596i		−	1.15903i
$280$	−2.40974	−	1.43860i	−0.144010	−	0.0859729i
$281$		−	30.2646i		−	1.80544i	−0.430233	−	0.902718i	$-0.641569\pi$
$281$		−	30.2646i		−	1.80544i	0.430233	−	0.902718i	$-0.358431\pi$
$282$			6.29240i			0.374707i
$283$		−	26.9240i		−	1.60047i	−0.599689	−	0.800233i	$-0.704709\pi$
$283$		−	26.9240i		−	1.60047i	0.599689	−	0.800233i	$-0.295291\pi$
$284$			5.38741i			0.319684i
$285$	22.4247	+	13.3874i	1.32833	+	0.793002i
$286$		0			0
$287$		−	12.1492i		−	0.717144i
$288$	−2.25511			−0.132883
$289$	−6.06508			−0.356769
$290$	9.78219	+	5.83991i	0.574430	+	0.342931i
$291$			14.3610i			0.841858i
$292$	−6.00000			−0.351123
$293$	5.18051			0.302649			0.151324	−	0.988484i	$-0.451646\pi$
$293$	5.18051			0.302649			0.151324	+	0.988484i	$0.451646\pi$
$294$		−	12.4356i		−	0.725260i
$295$	−5.83991	+	9.78219i	−0.340013	+	0.569541i
$296$	7.83991			0.455685
$297$	3.41520			0.198170
$298$		0			0
$299$		0			0
$300$	−10.0896	+	5.43860i	−0.582521	+	0.313998i
$301$			13.6520i			0.786890i
$302$			14.5570i			0.837662i
$303$			29.0204i			1.66718i
$304$			5.09501i			0.292219i
$305$	−26.2646	−	15.6798i	−1.50391	−	0.897824i
$306$		−	10.8304i		−	0.619132i
$307$	0.320184			0.0182738			0.00913692	−	0.999958i	$-0.497092\pi$
$307$	0.320184			0.0182738			0.00913692	+	0.999958i	$0.497092\pi$
$308$		−	2.51021i		−	0.143032i
$309$	17.4342			0.991798
$310$	9.83991	−	16.4824i	0.558869	−	0.936139i
$311$	9.86984			0.559667			0.279834	−	0.960048i	$-0.409721\pi$
$311$	9.86984			0.559667			0.279834	+	0.960048i	$0.409721\pi$
$312$		0			0
$313$			10.6126i			0.599859i	0.953961	+	0.299929i	$0.0969631\pi$
$313$			10.6126i			0.599859i	−0.953961	+	0.299929i	$0.903037\pi$
$314$		−	13.0950i		−	0.738994i
$315$	5.43423	+	3.24420i	0.306184	+	0.182790i
$316$	−15.0950			−0.849161
$317$	−12.1900			−0.684660			−0.342330	−	0.939580i	$-0.611216\pi$
$317$	−12.1900			−0.684660			−0.342330	+	0.939580i	$0.611216\pi$
$318$	5.92541			0.332280
$319$			10.1900i			0.570532i
$320$	−1.91995	−	1.14620i	−0.107329	−	0.0640746i
$321$	10.5102			0.586623
$322$			3.24420i			0.180792i
$323$	−24.4694			−1.36151
$324$	−10.6798			−0.593323
$325$		0			0
$326$	12.2646			0.679274
$327$	34.1045			1.88598
$328$		−	9.67982i		−	0.534478i
$329$	3.44513			0.189936
$330$	−8.80261	−	5.25511i	−0.484568	−	0.289284i
$331$		−	17.9444i		−	0.986315i	−0.869940	−	0.493158i	$-0.835843\pi$
$331$		−	17.9444i		−	0.986315i	0.869940	−	0.493158i	$-0.164157\pi$
$332$	11.0950			0.608918
$333$	−17.6798			−0.968848
$334$	18.3392			1.00348
$335$	16.4824	+	9.83991i	0.900531	+	0.537612i
$336$			2.87720i			0.156964i
$337$			20.9518i			1.14132i	0.821187	+	0.570659i	$0.193312\pi$
$337$			20.9518i			1.14132i	−0.821187	+	0.570659i	$0.806688\pi$
$338$		0			0
$339$	−9.16961			−0.498025
$340$	5.50476	−	9.22079i	0.298537	−	0.500068i
$341$	17.1696			0.929786
$342$		−	11.4898i		−	0.621297i
$343$	−15.5943			−0.842014
$344$			10.8772i			0.586460i
$345$	11.3765	+	6.79171i	0.612491	+	0.365653i
$346$			9.41520i			0.506164i
$347$			3.51757i			0.188833i	0.995533	+	0.0944166i	$0.0300986\pi$
$347$			3.51757i			0.188833i	−0.995533	+	0.0944166i	$0.969901\pi$
$348$		−	11.6798i		−	0.626104i
$349$			17.8568i			0.955852i	0.878400	+	0.477926i	$0.158611\pi$
$349$			17.8568i			0.955852i	−0.878400	+	0.477926i	$0.841389\pi$
$350$	2.97767	+	5.52410i	0.159163	+	0.295276i
$351$		0			0
$352$		−	2.00000i		−	0.106600i
$353$	−36.9240			−1.96527			−0.982634	−	0.185557i	$-0.940591\pi$
$353$	−36.9240			−1.96527			−0.982634	+	0.185557i	$0.940591\pi$
$354$	11.6798			0.620775
$355$	6.17506	−	10.3436i	0.327738	−	0.548981i
$356$			5.09501i			0.270035i
$357$	−13.8181			−0.731331
$358$	−7.32970			−0.387387
$359$		−	6.77483i		−	0.357562i	−0.983889	−	0.178781i	$-0.942785\pi$
$359$		−	6.77483i		−	0.357562i	0.983889	−	0.178781i	$-0.0572153\pi$
$360$	4.32970	+	2.58480i	0.228195	+	0.136231i
$361$	−6.95916			−0.366272
$362$	−11.7544			−0.617798
$363$			16.0468i			0.842239i
$364$		0			0
$365$	11.5197	+	6.87720i	0.602970	+	0.359969i
$366$			31.3596i			1.63919i
$367$		−	7.80997i		−	0.407677i	−0.979004	−	0.203839i	$-0.934658\pi$
$367$		−	7.80997i		−	0.407677i	0.979004	−	0.203839i	$-0.0653418\pi$
$368$			2.58480i			0.134742i
$369$			21.8290i			1.13637i
$370$	−15.0523	−	8.98611i	−0.782530	−	0.467166i
$371$		−	3.24420i		−	0.168430i
$372$	−19.6798			−1.02035
$373$			15.8698i			0.821709i	0.911701	+	0.410855i	$0.134770\pi$
$373$			15.8698i			0.821709i	−0.911701	+	0.410855i	$0.865230\pi$
$374$	9.60522			0.496674
$375$	25.6052	+	1.12280i	1.32225	+	0.0579809i
$376$	2.74489			0.141557
$377$		0			0
$378$			2.14322i			0.110235i
$379$			16.7748i			0.861665i	0.902432	+	0.430833i	$0.141780\pi$
$379$			16.7748i			0.861665i	−0.902432	+	0.430833i	$0.858220\pi$
$380$	5.83991	−	9.78219i	0.299581	−	0.501816i
$381$	−3.24420			−0.166205
$382$	−1.60522			−0.0821304
$383$	−16.6147			−0.848973			−0.424487	−	0.905434i	$-0.639545\pi$
$383$	−16.6147			−0.848973			−0.424487	+	0.905434i	$0.639545\pi$
$384$			2.29240i			0.116984i
$385$	−2.87720	+	4.81949i	−0.146636	+	0.245624i
$386$	−15.7544			−0.801878
$387$		−	24.5292i		−	1.24689i
$388$	6.26462			0.318038
$389$	36.7193			1.86174			0.930870	−	0.365350i	$-0.119051\pi$
$389$	36.7193			1.86174			0.930870	+	0.365350i	$0.119051\pi$
$390$		0			0
$391$	−12.4138			−0.627793
$392$	−5.42471			−0.273989
$393$			25.2382i			1.27310i
$394$	−1.00951			−0.0508586
$395$	28.9817	+	17.3019i	1.45823	+	0.870554i
$396$			4.51021i			0.226647i
$397$	29.2104			1.46603			0.733015	−	0.680212i	$-0.238112\pi$
$397$	29.2104			1.46603			0.733015	+	0.680212i	$0.238112\pi$
$398$	0.435617			0.0218355
$399$	−14.6594			−0.733888
$400$	2.37245	+	4.40131i	0.118622	+	0.220065i
$401$		−	15.6052i		−	0.779288i	−0.920966	−	0.389644i	$-0.872598\pi$
$401$		−	15.6052i		−	0.779288i	0.920966	−	0.389644i	$-0.127402\pi$
$402$		−	19.6798i		−	0.981540i
$403$		0			0
$404$	12.6594			0.629829
$405$	20.5048	+	12.2412i	1.01889	+	0.608271i
$406$	−6.39478			−0.317367
$407$		−	15.6798i		−	0.777220i
$408$	−11.0095			−0.545052
$409$		−	13.7952i		−	0.682131i	−0.940039	−	0.341066i	$-0.889212\pi$
$409$		−	13.7952i		−	0.682131i	0.940039	−	0.341066i	$-0.110788\pi$
$410$	−11.0950	+	18.5848i	−0.547944	+	0.917838i
$411$		−	33.4342i		−	1.64919i
$412$		−	7.60522i		−	0.374682i
$413$		−	6.39478i		−	0.314666i
$414$		−	5.82900i		−	0.286480i
$415$	−21.3019	−	12.7171i	−1.04567	−	0.624259i
$416$		0			0
$417$		−	16.8026i		−	0.822827i
$418$	10.1900			0.498410
$419$	30.6893			1.49927			0.749636	−	0.661850i	$-0.230229\pi$
$419$	30.6893			1.49927			0.749636	+	0.661850i	$0.230229\pi$
$420$	3.29785	−	5.52410i	0.160919	−	0.269549i
$421$		−	16.9180i		−	0.824535i	−0.911063	−	0.412268i	$-0.864737\pi$
$421$		−	16.9180i		−	0.824535i	0.911063	−	0.412268i	$-0.135263\pi$
$422$	16.3501			0.795911
$423$	−6.19003			−0.300969
$424$		−	2.58480i		−	0.125529i
$425$	−21.1378	+	11.3939i	−1.02533	+	0.552687i
$426$	−12.3501			−0.598365
$427$	17.1696			0.830895
$428$		−	4.58480i		−	0.221615i
$429$		0			0
$430$	12.4675	−	20.8837i	0.601234	−	1.00710i
$431$		−	17.9722i		−	0.865691i	−0.901468	−	0.432846i	$-0.857510\pi$
$431$		−	17.9722i		−	0.865691i	0.901468	−	0.432846i	$-0.142490\pi$
$432$			1.70760i			0.0821569i
$433$			2.61259i			0.125553i	0.998028	+	0.0627764i	$0.0199955\pi$
$433$			2.61259i			0.125553i	−0.998028	+	0.0627764i	$0.980004\pi$
$434$			10.7748i			0.517208i
$435$	−13.3874	+	22.4247i	−0.641877	+	1.07518i
$436$		−	14.8772i		−	0.712489i
$437$	−13.1696			−0.629988
$438$		−	13.7544i		−	0.657211i
$439$	14.6594			0.699655			0.349827	−	0.936814i	$-0.386240\pi$
$439$	14.6594			0.699655			0.349827	+	0.936814i	$0.386240\pi$
$440$	−2.29240	+	3.83991i	−0.109286	+	0.183060i
$441$	12.2333			0.582538
$442$		0			0
$443$		−	8.33324i		−	0.395924i	−0.980210	−	0.197962i	$-0.936568\pi$
$443$		−	8.33324i		−	0.395924i	0.980210	−	0.197962i	$-0.0634323\pi$
$444$			17.9722i			0.852924i
$445$	5.83991	−	9.78219i	0.276838	−	0.463720i
$446$	21.7843			1.03152
$447$		0			0
$448$	1.25511			0.0592981
$449$		−	4.04084i		−	0.190699i	−0.995444	−	0.0953495i	$-0.969603\pi$
$449$		−	4.04084i		−	0.190699i	0.995444	−	0.0953495i	$-0.0303969\pi$
$450$	−5.35012	−	9.92541i	−0.252207	−	0.467888i
$451$	−19.3596			−0.911610
$452$			4.00000i			0.188144i
$453$	−33.3705			−1.56788
$454$	−9.02042			−0.423349
$455$		0			0
$456$	−11.6798			−0.546958
$457$	0.979580			0.0458228			0.0229114	−	0.999737i	$-0.492706\pi$
$457$	0.979580			0.0458228			0.0229114	+	0.999737i	$0.492706\pi$
$458$			4.68718i			0.219017i
$459$	−8.20093			−0.382787
$460$	2.96270	−	4.96270i	0.138137	−	0.231387i
$461$			10.7280i			0.499654i	0.968291	+	0.249827i	$0.0803737\pi$
$461$			10.7280i			0.499654i	−0.968291	+	0.249827i	$0.919626\pi$
$462$	5.75441			0.267719
$463$	−23.2104			−1.07868			−0.539340	−	0.842088i	$-0.681326\pi$
$463$	−23.2104			−1.07868			−0.539340	+	0.842088i	$0.681326\pi$
$464$	−5.09501			−0.236530
$465$	37.7843	+	22.5570i	1.75221	+	1.04606i
$466$		−	13.5366i		−	0.627071i
$467$		−	28.5848i		−	1.32275i	−0.750057	−	0.661373i	$-0.769974\pi$
$467$		−	28.5848i		−	1.32275i	0.750057	−	0.661373i	$-0.230026\pi$
$468$		0			0
$469$	−10.7748			−0.497535
$470$	−5.27007	−	3.14620i	−0.243090	−	0.145123i
$471$	30.0190			1.38320
$472$		−	5.09501i		−	0.234517i
$473$	21.7544			1.00027
$474$		−	34.6038i		−	1.58941i
$475$	−22.4247	+	12.0877i	−1.02892	+	0.554619i
$476$			6.02778i			0.276283i
$477$			5.82900i			0.266892i
$478$		−	3.19739i		−	0.146245i
$479$		−	30.4078i		−	1.38937i	−0.719314	−	0.694685i	$-0.755544\pi$
$479$		−	30.4078i		−	1.38937i	0.719314	−	0.694685i	$-0.244456\pi$
$480$	2.62755	−	4.40131i	0.119931	−	0.200891i
$481$		0			0
$482$		−	14.1154i		−	0.642940i
$483$	−7.43701			−0.338396
$484$	7.00000			0.318182
$485$	−12.0278	−	7.18051i	−0.546153	−	0.326050i
$486$		−	19.3596i		−	0.878171i
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	13.6798			0.619256
$489$			28.1154i			1.27142i
$490$	10.4152	+	6.21781i	0.470511	+	0.280892i
$491$	−22.6893			−1.02396			−0.511978	−	0.858999i	$-0.671087\pi$
$491$	−22.6893			−1.02396			−0.511978	+	0.858999i	$0.671087\pi$
$492$	22.1900			1.00040
$493$		−	24.4694i		−	1.10204i
$494$		0			0
$495$	5.16961	−	8.65940i	0.232357	−	0.389211i
$496$			8.58480i			0.385469i
$497$			6.76177i			0.303307i
$498$			25.4342i			1.13973i
$499$		−	31.8698i		−	1.42669i	−0.700813	−	0.713345i	$-0.747179\pi$
$499$		−	31.8698i		−	1.42669i	0.700813	−	0.713345i	$-0.252821\pi$
$500$	0.489790	−	11.1696i	0.0219041	−	0.499520i
$501$			42.0408i			1.87825i
$502$	21.1696			0.944846
$503$		−	14.2646i		−	0.636028i	−0.948086	−	0.318014i	$-0.896984\pi$
$503$		−	14.2646i		−	0.636028i	0.948086	−	0.318014i	$-0.103016\pi$
$504$	−2.83039			−0.126076
$505$	−24.3055	−	14.5102i	−1.08158	−	0.645696i
$506$	5.16961			0.229817
$507$		0			0
$508$			1.41520i			0.0627892i
$509$		−	23.3596i		−	1.03540i	−0.855563	−	0.517699i	$-0.826789\pi$
$509$		−	23.3596i		−	1.03540i	0.855563	−	0.517699i	$-0.173211\pi$
$510$	21.1378	+	12.6191i	0.935996	+	0.558784i
$511$	−7.53063			−0.333135
$512$	1.00000			0.0441942
$513$	−8.70024			−0.384125
$514$			8.21781i			0.362472i
$515$	−8.71711	+	14.6017i	−0.384122	+	0.643427i
$516$	−24.9349			−1.09770
$517$		−	5.48979i		−	0.241441i
$518$	9.83991			0.432341
$519$	−21.5834			−0.947407
$520$		0			0
$521$	−40.4247			−1.77104			−0.885519	−	0.464602i	$-0.846197\pi$
$521$	−40.4247			−1.77104			−0.885519	+	0.464602i	$0.846197\pi$
$522$	11.4898			0.502894
$523$			37.9853i			1.66098i	0.557033	+	0.830490i	$0.311940\pi$
$523$			37.9853i			1.66098i	−0.557033	+	0.830490i	$0.688060\pi$
$524$	11.0095			0.480953
$525$	−12.6635	+	6.82602i	−0.552679	+	0.297912i
$526$		−	4.51021i		−	0.196655i
$527$	−41.2295			−1.79598
$528$	4.58480			0.199528
$529$	16.3188			0.709513
$530$	−2.96270	+	4.96270i	−0.128692	+	0.215566i
$531$			11.4898i			0.498614i
$532$			6.39478i			0.277249i
$533$		0			0
$534$	−11.6798			−0.505435
$535$	−5.25511	+	8.80261i	−0.227198	+	0.380570i
$536$	−8.58480			−0.370807
$537$		−	16.8026i		−	0.725086i
$538$	8.51021			0.366901
$539$			10.8494i			0.467318i
$540$	1.95725	−	3.27851i	0.0842267	−	0.141085i
$541$		−	26.8772i		−	1.15554i	−0.816199	−	0.577771i	$-0.803923\pi$
$541$		−	26.8772i		−	1.15554i	0.816199	−	0.577771i	$-0.196077\pi$
$542$		−	4.95180i		−	0.212698i
$543$		−	26.9458i		−	1.15636i
$544$			4.80261i			0.205910i
$545$	−17.0523	+	28.5636i	−0.730439	+	1.22353i
$546$		0			0
$547$		−	19.8976i		−	0.850761i	−0.905015	−	0.425381i	$-0.860140\pi$
$547$		−	19.8976i		−	0.850761i	0.905015	−	0.425381i	$-0.139860\pi$
$548$	−14.5848			−0.623032
$549$	−30.8494			−1.31662
$550$	8.80261	−	4.74489i	0.375345	−	0.202323i
$551$		−	25.9592i		−	1.10590i
$552$	−5.92541			−0.252202
$553$	−18.9458			−0.805659
$554$			19.8698i			0.844189i
$555$	20.5998	−	34.5058i	0.874412	−	1.46469i
$556$	−7.32970			−0.310848
$557$	1.50070			0.0635865			0.0317933	−	0.999494i	$-0.489878\pi$
$557$	1.50070			0.0635865			0.0317933	+	0.999494i	$0.489878\pi$
$558$		−	19.3596i		−	0.819559i
$559$		0			0
$560$	−2.40974	−	1.43860i	−0.101830	−	0.0607920i
$561$			22.0190i			0.929644i
$562$		−	30.2646i		−	1.27664i
$563$			20.6872i			0.871861i	0.899980	+	0.435930i	$0.143581\pi$
$563$			20.6872i			0.871861i	−0.899980	+	0.435930i	$0.856419\pi$
$564$			6.29240i			0.264958i
$565$	4.58480	−	7.67982i	0.192884	−	0.323092i
$566$		−	26.9240i		−	1.13170i
$567$	−13.4043			−0.562927
$568$			5.38741i			0.226051i
$569$	−6.08550			−0.255117			−0.127559	−	0.991831i	$-0.540714\pi$
$569$	−6.08550			−0.255117			−0.127559	+	0.991831i	$0.540714\pi$
$570$	22.4247	+	13.3874i	0.939268	+	0.560737i
$571$	9.98909			0.418031			0.209015	−	0.977912i	$-0.432974\pi$
$571$	9.98909			0.418031			0.209015	+	0.977912i	$0.432974\pi$
$572$		0			0
$573$		−	3.67982i		−	0.153727i
$574$		−	12.1492i		−	0.507097i
$575$	−11.3765	+	6.13231i	−0.474433	+	0.255735i
$576$	−2.25511			−0.0939627
$577$	−8.33921			−0.347166			−0.173583	−	0.984819i	$-0.555534\pi$
$577$	−8.33921			−0.347166			−0.173583	+	0.984819i	$0.555534\pi$
$578$	−6.06508			−0.252274
$579$		−	36.1154i		−	1.50091i
$580$	9.78219	+	5.83991i	0.406183	+	0.242489i
$581$	13.9254			0.577723
$582$			14.3610i			0.595284i
$583$	−5.16961			−0.214103
$584$	−6.00000			−0.248282
$585$		0			0
$586$	5.18051			0.214005
$587$	−23.2442			−0.959391			−0.479695	−	0.877435i	$-0.659253\pi$
$587$	−23.2442			−0.959391			−0.479695	+	0.877435i	$0.659253\pi$
$588$		−	12.4356i		−	0.512836i
$589$	−43.7397			−1.80226
$590$	−5.83991	+	9.78219i	−0.240425	+	0.402726i
$591$		−	2.31421i		−	0.0951940i
$592$	7.83991			0.322218
$593$	−34.2646			−1.40708			−0.703540	−	0.710656i	$-0.748398\pi$
$593$	−34.2646			−1.40708			−0.703540	+	0.710656i	$0.748398\pi$
$594$	3.41520			0.140127
$595$	6.90905	−	11.5731i	0.283243	−	0.474449i
$596$		0			0
$597$			0.998609i			0.0408703i
$598$		0			0
$599$	31.1886			1.27433			0.637167	−	0.770726i	$-0.280106\pi$
$599$	31.1886			1.27433			0.637167	+	0.770726i	$0.280106\pi$
$600$	−10.0896	+	5.43860i	−0.411905	+	0.222030i
$601$	−3.40429			−0.138864			−0.0694320	−	0.997587i	$-0.522119\pi$
$601$	−3.40429			−0.138864			−0.0694320	+	0.997587i	$0.522119\pi$
$602$			13.6520i			0.556415i
$603$	19.3596			0.788385
$604$			14.5570i			0.592317i
$605$	−13.4397	−	8.02341i	−0.546401	−	0.326198i
$606$			29.0204i			1.17887i
$607$			0.945827i			0.0383899i	0.999816	+	0.0191950i	$0.00611032\pi$
$607$			0.945827i			0.0383899i	−0.999816	+	0.0191950i	$0.993890\pi$
$608$			5.09501i			0.206630i
$609$		−	14.6594i		−	0.594029i
$610$	−26.2646	−	15.6798i	−1.06342	−	0.634857i
$611$		0			0
$612$		−	10.8304i		−	0.437793i
$613$	−40.7193			−1.64464			−0.822318	−	0.569028i	$-0.807319\pi$
$613$	−40.7193			−1.64464			−0.822318	+	0.569028i	$0.807319\pi$
$614$	0.320184			0.0129216
$615$	−42.6038	−	25.4342i	−1.71795	−	1.02561i
$616$		−	2.51021i		−	0.101139i
$617$	12.6594			0.509648			0.254824	−	0.966987i	$-0.417982\pi$
$617$	12.6594			0.509648			0.254824	+	0.966987i	$0.417982\pi$
$618$	17.4342			0.701307
$619$			5.03945i			0.202553i	0.994858	+	0.101276i	$0.0322926\pi$
$619$			5.03945i			0.202553i	−0.994858	+	0.101276i	$0.967707\pi$
$620$	9.83991	−	16.4824i	0.395180	−	0.661950i
$621$	−4.41381			−0.177120
$622$	9.86984			0.395745
$623$			6.39478i			0.256201i
$624$		0			0
$625$	−13.7430	+	20.8837i	−0.549719	+	0.835349i
$626$			10.6126i			0.424164i
$627$			23.3596i			0.932894i
$628$		−	13.0950i		−	0.522548i
$629$			37.6520i			1.50128i
$630$	5.43423	+	3.24420i	0.216505	+	0.129252i
$631$			1.00736i			0.0401024i	0.999799	+	0.0200512i	$0.00638293\pi$
$631$			1.00736i			0.0401024i	−0.999799	+	0.0200512i	$0.993617\pi$
$632$	−15.0950			−0.600447
$633$			37.4810i			1.48974i
$634$	−12.1900			−0.484128
$635$	1.62210	−	2.71711i	0.0643711	−	0.107825i
$636$	5.92541			0.234958
$637$		0			0
$638$			10.1900i			0.403427i
$639$		−	12.1492i		−	0.480614i
$640$	−1.91995	−	1.14620i	−0.0758928	−	0.0453076i
$641$	41.3596			1.63361			0.816804	−	0.576916i	$-0.195744\pi$
$641$	41.3596			1.63361			0.816804	+	0.576916i	$0.195744\pi$
$642$	10.5102			0.414805
$643$	3.26601			0.128799			0.0643994	−	0.997924i	$-0.479487\pi$
$643$	3.26601			0.128799			0.0643994	+	0.997924i	$0.479487\pi$
$644$			3.24420i			0.127839i
$645$	47.8739	+	28.5804i	1.88503	+	1.12535i
$646$	−24.4694			−0.962734
$647$			19.4342i			0.764038i	0.924154	+	0.382019i	$0.124771\pi$
$647$			19.4342i			0.764038i	−0.924154	+	0.382019i	$0.875229\pi$
$648$	−10.6798			−0.419543
$649$	−10.1900			−0.399994
$650$		0			0
$651$	−24.7002			−0.968079
$652$	12.2646			0.480320
$653$		−	4.51021i		−	0.176498i	−0.996098	−	0.0882491i	$-0.971873\pi$
$653$		−	4.51021i		−	0.176498i	0.996098	−	0.0882491i	$-0.0281271\pi$
$654$	34.1045			1.33359
$655$	−21.1378	−	12.6191i	−0.825921	−	0.493070i
$656$		−	9.67982i		−	0.377933i
$657$	13.5306			0.527880
$658$	3.44513			0.134305
$659$	−27.2104			−1.05997			−0.529984	−	0.848007i	$-0.677802\pi$
$659$	−27.2104			−1.05997			−0.529984	+	0.848007i	$0.677802\pi$
$660$	−8.80261	−	5.25511i	−0.342641	−	0.204555i
$661$			24.5292i			0.954077i	0.878882	+	0.477038i	$0.158290\pi$
$661$			24.5292i			0.954077i	−0.878882	+	0.477038i	$0.841710\pi$
$662$		−	17.9444i		−	0.697430i
$663$		0			0
$664$	11.0950			0.430570
$665$	7.32970	−	12.2777i	0.284234	−	0.476108i
$666$	−17.6798			−0.685079
$667$		−	13.1696i		−	0.509929i
$668$	18.3392			0.709565
$669$			49.9385i			1.93073i
$670$	16.4824	+	9.83991i	0.636772	+	0.380149i
$671$		−	27.3596i		−	1.05621i
$672$			2.87720i			0.110991i
$673$			8.95180i			0.345066i	0.985004	+	0.172533i	$0.0551952\pi$
$673$			8.95180i			0.345066i	−0.985004	+	0.172533i	$0.944805\pi$
$674$			20.9518i			0.807033i
$675$	−7.51566	+	4.05119i	−0.289278	+	0.155930i
$676$		0			0
$677$			32.6256i			1.25391i	0.779057	+	0.626953i	$0.215698\pi$
$677$			32.6256i			1.25391i	−0.779057	+	0.626953i	$0.784302\pi$
$678$	−9.16961			−0.352157
$679$	7.86276			0.301745
$680$	5.50476	−	9.22079i	0.211098	−	0.353601i
$681$		−	20.6784i		−	0.792399i
$682$	17.1696			0.657458
$683$	−11.0950			−0.424539			−0.212269	−	0.977211i	$-0.568085\pi$
$683$	−11.0950			−0.424539			−0.212269	+	0.977211i	$0.568085\pi$
$684$		−	11.4898i		−	0.439323i
$685$	28.0022	+	16.7171i	1.06991	+	0.638728i
$686$	−15.5943			−0.595394
$687$	−10.7449			−0.409943
$688$			10.8772i			0.414690i
$689$		0			0
$690$	11.3765	+	6.79171i	0.433096	+	0.258556i
$691$		−	13.5306i		−	0.514729i	−0.966314	−	0.257365i	$-0.917146\pi$
$691$		−	13.5306i		−	0.514729i	0.966314	−	0.257365i	$-0.0828542\pi$
$692$			9.41520i			0.357912i
$693$			5.66079i			0.215036i
$694$			3.51757i			0.133525i
$695$	14.0727	+	8.40131i	0.533807	+	0.318680i
$696$		−	11.6798i		−	0.442722i
$697$	46.4884			1.76087
$698$			17.8568i			0.675889i
$699$	31.0313			1.17371
$700$	2.97767	+	5.52410i	0.112545	+	0.208791i
$701$	48.1345			1.81801			0.909007	−	0.416781i	$-0.136842\pi$
$701$	48.1345			1.81801			0.909007	+	0.416781i	$0.136842\pi$
$702$		0			0
$703$			39.9444i			1.50653i
$704$		−	2.00000i		−	0.0753778i
$705$	7.21236	−	12.0811i	0.271633	−	0.455001i
$706$	−36.9240			−1.38965
$707$	15.8889			0.597563
$708$	11.6798			0.438954
$709$			16.5292i			0.620769i	0.950611	+	0.310384i	$0.100458\pi$
$709$			16.5292i			0.620769i	−0.950611	+	0.310384i	$0.899542\pi$
$710$	6.17506	−	10.3436i	0.231746	−	0.388188i
$711$	34.0408			1.27663
$712$			5.09501i			0.190944i
$713$	−22.1900			−0.831023
$714$	−13.8181			−0.517129
$715$		0			0
$716$	−7.32970			−0.273924
$717$	7.32970			0.273733
$718$		−	6.77483i		−	0.252834i
$719$	−6.39478			−0.238485			−0.119242	−	0.992865i	$-0.538047\pi$
$719$	−6.39478			−0.238485			−0.119242	+	0.992865i	$0.538047\pi$
$720$	4.32970	+	2.58480i	0.161358	+	0.0963299i
$721$		−	9.54535i		−	0.355488i
$722$	−6.95916			−0.258993
$723$	32.3582			1.20342
$724$	−11.7544			−0.436849
$725$	−12.0877	−	22.4247i	−0.448924	−	0.832833i
$726$			16.0468i			0.595553i
$727$			35.0204i			1.29884i	0.760432	+	0.649418i	$0.224987\pi$
$727$			35.0204i			1.29884i	−0.760432	+	0.649418i	$0.775013\pi$
$728$		0			0
$729$	12.3406			0.457059
$730$	11.5197	+	6.87720i	0.426364	+	0.254537i
$731$	−52.2390			−1.93213
$732$			31.3596i			1.15909i
$733$	22.6485			0.836541			0.418271	−	0.908322i	$-0.362636\pi$
$733$	22.6485			0.836541			0.418271	+	0.908322i	$0.362636\pi$
$734$		−	7.80997i		−	0.288271i
$735$	−14.2537	+	23.8758i	−0.525756	+	0.880673i
$736$			2.58480i			0.0952771i
$737$			17.1696i			0.632451i
$738$			21.8290i			0.803537i
$739$			25.0394i			0.921091i	0.887636	+	0.460546i	$0.152346\pi$
$739$			25.0394i			0.921091i	−0.887636	+	0.460546i	$0.847654\pi$
$740$	−15.0523	−	8.98611i	−0.553332	−	0.330336i
$741$		0			0
$742$		−	3.24420i		−	0.119098i
$743$	35.8252			1.31430			0.657149	−	0.753760i	$-0.271762\pi$
$743$	35.8252			1.31430			0.657149	+	0.753760i	$0.271762\pi$
$744$	−19.6798			−0.721497
$745$		0			0
$746$			15.8698i			0.581036i
$747$	−25.0204			−0.915449
$748$	9.60522			0.351202
$749$		−	5.75441i		−	0.210262i
$750$	25.6052	+	1.12280i	0.934971	+	0.0409987i
$751$	−41.6988			−1.52161			−0.760806	−	0.648979i	$-0.775196\pi$
$751$	−41.6988			−1.52161			−0.760806	+	0.648979i	$0.775196\pi$
$752$	2.74489			0.100096
$753$			48.5292i			1.76850i
$754$		0			0
$755$	16.6853	−	27.9488i	0.607239	−	1.01716i
$756$			2.14322i			0.0779480i
$757$		−	11.6052i		−	0.421799i	−0.977508	−	0.210900i	$-0.932361\pi$
$757$		−	11.6052i		−	0.421799i	0.977508	−	0.210900i	$-0.0676393\pi$
$758$			16.7748i			0.609289i
$759$			11.8508i			0.430157i
$760$	5.83991	−	9.78219i	0.211836	−	0.354837i
$761$		−	30.2646i		−	1.09709i	−0.836121	−	0.548546i	$-0.815182\pi$
$761$		−	30.2646i		−	1.09709i	0.836121	−	0.548546i	$-0.184818\pi$
$762$	−3.24420			−0.117525
$763$		−	18.6725i		−	0.675988i
$764$	−1.60522			−0.0580749
$765$	−12.4138	+	20.7939i	−0.448822	+	0.751804i
$766$	−16.6147			−0.600315
$767$		0			0
$768$			2.29240i			0.0827199i
$769$		−	24.6594i		−	0.889241i	−0.895719	−	0.444620i	$-0.853339\pi$
$769$		−	24.6594i		−	0.889241i	0.895719	−	0.444620i	$-0.146661\pi$
$770$	−2.87720	+	4.81949i	−0.103687	+	0.173682i
$771$	−18.8385			−0.678453
$772$	−15.7544			−0.567014
$773$	30.3501			1.09162			0.545809	−	0.837910i	$-0.316222\pi$
$773$	30.3501			1.09162			0.545809	+	0.837910i	$0.316222\pi$
$774$		−	24.5292i		−	0.881685i
$775$	−37.7843	+	20.3670i	−1.35725	+	0.731604i
$776$	6.26462			0.224887
$777$			22.5570i			0.809229i
$778$	36.7193			1.31645
$779$	49.3188			1.76703
$780$		0			0
$781$	10.7748			0.385554
$782$	−12.4138			−0.443917
$783$		−	8.70024i		−	0.310921i
$784$	−5.42471			−0.193740
$785$	−15.0095	+	25.1418i	−0.535713	+	0.897350i
$786$			25.2382i			0.900218i
$787$	11.1288			0.396698			0.198349	−	0.980131i	$-0.436442\pi$
$787$	11.1288			0.396698			0.198349	+	0.980131i	$0.436442\pi$
$788$	−1.00951			−0.0359625
$789$	10.3392			0.368086
$790$	28.9817	+	17.3019i	1.03112	+	0.615575i
$791$			5.02042i			0.178506i
$792$			4.51021i			0.160263i
$793$		0			0
$794$	29.2104			1.03664
$795$	−11.3765	−	6.79171i	−0.403483	−	0.240877i
$796$	0.435617			0.0154400
$797$		−	46.7939i		−	1.65752i	−0.559602	−	0.828762i	$-0.689046\pi$
$797$		−	46.7939i		−	1.65752i	0.559602	−	0.828762i	$-0.310954\pi$
$798$	−14.6594			−0.518937
$799$			13.1827i			0.466369i
$800$	2.37245	+	4.40131i	0.0838787	+	0.155610i
$801$		−	11.4898i		−	0.405972i
$802$		−	15.6052i		−	0.551040i
$803$			12.0000i			0.423471i
$804$		−	19.6798i		−	0.694054i
$805$	3.71850	−	6.22871i	0.131060	−	0.219533i
$806$		0			0
$807$			19.5088i			0.686743i
$808$	12.6594			0.445356
$809$	−50.4437			−1.77351			−0.886754	−	0.462242i	$-0.847045\pi$
$809$	−50.4437			−1.77351			−0.886754	+	0.462242i	$0.847045\pi$
$810$	20.5048	+	12.2412i	0.720464	+	0.430112i
$811$		−	36.3991i		−	1.27814i	−0.769147	−	0.639072i	$-0.779318\pi$
$811$		−	36.3991i		−	1.27814i	0.769147	−	0.639072i	$-0.220682\pi$
$812$	−6.39478			−0.224413
$813$	11.3515			0.398115
$814$		−	15.6798i		−	0.549577i
$815$	−23.5475	−	14.0577i	−0.824833	−	0.492420i
$816$	−11.0095			−0.385410
$817$	−55.4195			−1.93888
$818$		−	13.7952i		−	0.482340i
$819$		0			0
$820$	−11.0950	+	18.5848i	−0.387455	+	0.649009i
$821$		−	6.23684i		−	0.217667i	−0.994060	−	0.108834i	$-0.965288\pi$
$821$		−	6.23684i		−	0.217667i	0.994060	−	0.108834i	$-0.0347116\pi$
$822$		−	33.4342i		−	1.16615i
$823$			33.7734i			1.17727i	0.808400	+	0.588634i	$0.200334\pi$
$823$			33.7734i			1.17727i	−0.808400	+	0.588634i	$0.799666\pi$
$824$		−	7.60522i		−	0.264941i
$825$	10.8772	+	20.1791i	0.378696	+	0.702547i
$826$		−	6.39478i		−	0.222503i
$827$	37.2295			1.29460			0.647298	−	0.762237i	$-0.275899\pi$
$827$	37.2295			1.29460			0.647298	+	0.762237i	$0.275899\pi$
$828$		−	5.82900i		−	0.202572i
$829$	−38.2646			−1.32899			−0.664493	−	0.747295i	$-0.731352\pi$
$829$	−38.2646			−1.32899			−0.664493	+	0.747295i	$0.731352\pi$
$830$	−21.3019	−	12.7171i	−0.739400	−	0.441417i
$831$	−45.5497			−1.58010
$832$		0			0
$833$		−	26.0528i		−	0.902675i
$834$		−	16.8026i		−	0.581827i
$835$	−35.2104	−	21.0204i	−1.21851	−	0.727442i
$836$	10.1900			0.352429
$837$	−14.6594			−0.506703
$838$	30.6893			1.06015
$839$			50.1345i			1.73083i	0.501052	+	0.865417i	$0.332946\pi$
$839$			50.1345i			1.73083i	−0.501052	+	0.865417i	$0.667054\pi$
$840$	3.29785	−	5.52410i	0.113787	−	0.190600i
$841$	−3.04084			−0.104857
$842$		−	16.9180i		−	0.583034i
$843$	69.3787			2.38953
$844$	16.3501			0.562794
$845$		0			0
$846$	−6.19003			−0.212817
$847$	8.78574			0.301881
$848$		−	2.58480i		−	0.0887625i
$849$	61.7207			2.11825
$850$	−21.1378	+	11.3939i	−0.725019	+	0.390809i
$851$			20.2646i			0.694662i
$852$	−12.3501			−0.423108
$853$	12.3910			0.424258			0.212129	−	0.977242i	$-0.431960\pi$
$853$	12.3910			0.424258			0.212129	+	0.977242i	$0.431960\pi$
$854$	17.1696			0.587532
$855$	−13.1696	+	22.0599i	−0.450391	+	0.754432i
$856$		−	4.58480i		−	0.156705i
$857$			25.4005i			0.867664i	0.900994	+	0.433832i	$0.142839\pi$
$857$			25.4005i			0.867664i	−0.900994	+	0.433832i	$0.857161\pi$
$858$		0			0
$859$	50.1900			1.71246			0.856231	−	0.516593i	$-0.172800\pi$
$859$	50.1900			1.71246			0.856231	+	0.516593i	$0.172800\pi$
$860$	12.4675	−	20.8837i	0.425137	−	0.712129i
$861$	27.8508			0.949153
$862$		−	17.9722i		−	0.612136i
$863$	−43.4451			−1.47889			−0.739445	−	0.673217i	$-0.764912\pi$
$863$	−43.4451			−1.47889			−0.739445	+	0.673217i	$0.764912\pi$
$864$			1.70760i			0.0580937i
$865$	10.7917	−	18.0767i	0.366929	−	0.614628i
$866$			2.61259i			0.0887793i
$867$		−	13.9036i		−	0.472191i
$868$			10.7748i			0.365722i
$869$			30.1900i			1.02413i
$870$	−13.3874	+	22.4247i	−0.453876	+	0.760269i
$871$		0			0
$872$		−	14.8772i		−	0.503806i
$873$	−14.1274			−0.478139
$874$	−13.1696			−0.445469
$875$	0.614738	−	14.0190i	0.0207819	−	0.473930i
$876$		−	13.7544i		−	0.464718i
$877$	11.6689			0.394031			0.197016	−	0.980400i	$-0.436875\pi$
$877$	11.6689			0.394031			0.197016	+	0.980400i	$0.436875\pi$
$878$	14.6594			0.494731
$879$			11.8758i			0.400561i
$880$	−2.29240	+	3.83991i	−0.0772768	+	0.129443i
$881$	0.0446585			0.00150458			0.000752291	−	1.00000i	$-0.499761\pi$
$881$	0.0446585			0.00150458			0.000752291		1.00000i	$0.499761\pi$
$882$	12.2333			0.411916
$883$			24.4269i			0.822029i	0.911629	+	0.411015i	$0.134826\pi$
$883$			24.4269i			0.822029i	−0.911629	+	0.411015i	$0.865174\pi$
$884$		0			0
$885$	−22.4247	−	13.3874i	−0.753798	−	0.450013i
$886$		−	8.33324i		−	0.279961i
$887$			47.2295i			1.58581i	0.609345	+	0.792905i	$0.291433\pi$
$887$			47.2295i			1.58581i	−0.609345	+	0.792905i	$0.708567\pi$
$888$			17.9722i			0.603108i
$889$			1.77622i			0.0595725i
$890$	5.83991	−	9.78219i	0.195754	−	0.327900i
$891$			21.3596i			0.715575i
$892$	21.7843			0.729394
$893$			13.9853i			0.467999i
$894$		0			0
$895$	14.0727	+	8.40131i	0.470398	+	0.280825i
$896$	1.25511			0.0419301
$897$		0			0
$898$		−	4.04084i		−	0.134845i
$899$		−	43.7397i		−	1.45880i
$900$	−5.35012	−	9.92541i	−0.178337	−	0.330847i
$901$	12.4138			0.413564
$902$	−19.3596			−0.644605
$903$	−31.2959			−1.04146
$904$			4.00000i			0.133038i
$905$	22.5679	+	13.4729i	0.750183	+	0.447855i
$906$	−33.3705			−1.10866
$907$		−	44.7133i		−	1.48468i	−0.670023	−	0.742340i	$-0.733716\pi$
$907$		−	44.7133i		−	1.48468i	0.670023	−	0.742340i	$-0.266284\pi$
$908$	−9.02042			−0.299353
$909$	−28.5483			−0.946886
$910$		0			0
$911$	51.9444			1.72100			0.860498	−	0.509454i	$-0.170153\pi$
$911$	51.9444			1.72100			0.860498	+	0.509454i	$0.170153\pi$
$912$	−11.6798			−0.386757
$913$		−	22.1900i		−	0.734383i
$914$	0.979580			0.0324016
$915$	35.9444	−	60.2091i	1.18829	−	1.99045i
$916$			4.68718i			0.154869i
$917$	13.8181			0.456314
$918$	−8.20093			−0.270671
$919$	13.5497			0.446962			0.223481	−	0.974708i	$-0.428258\pi$
$919$	13.5497			0.446962			0.223481	+	0.974708i	$0.428258\pi$
$920$	2.96270	−	4.96270i	0.0976774	−	0.163615i
$921$			0.733989i			0.0241858i
$922$			10.7280i			0.353308i
$923$		0			0
$924$	5.75441			0.189306
$925$	18.5998	+	34.5058i	0.611557	+	1.13454i
$926$	−23.2104			−0.762743
$927$			17.1506i			0.563299i
$928$	−5.09501			−0.167252
$929$			44.1682i			1.44911i	0.689216	+	0.724556i	$0.257955\pi$
$929$			44.1682i			1.44911i	−0.689216	+	0.724556i	$0.742045\pi$
$930$	37.7843	+	22.5570i	1.23900	+	0.739674i
$931$		−	27.6390i		−	0.905831i
$932$		−	13.5366i		−	0.443406i
$933$			22.6256i			0.740730i
$934$		−	28.5848i		−	0.935323i
$935$	−18.4416	−	11.0095i	−0.603104	−	0.360050i
$936$		0			0
$937$			41.6988i			1.36224i	0.732171	+	0.681121i	$0.238507\pi$
$937$			41.6988i			1.36224i	−0.732171	+	0.681121i	$0.761493\pi$
$938$	−10.7748			−0.351811
$939$	−24.3283			−0.793924
$940$	−5.27007	−	3.14620i	−0.171891	−	0.102618i
$941$			37.4473i			1.22075i	0.792114	+	0.610373i	$0.208981\pi$
$941$			37.4473i			1.22075i	−0.792114	+	0.610373i	$0.791019\pi$
$942$	30.0190			0.978073
$943$	25.0204			0.814777
$944$		−	5.09501i		−	0.165829i
$945$	2.45656	−	4.11488i	0.0799117	−	0.133857i
$946$	21.7544			0.707297
$947$	11.5644			0.375792			0.187896	−	0.982189i	$-0.439833\pi$
$947$	11.5644			0.375792			0.187896	+	0.982189i	$0.439833\pi$
$948$		−	34.6038i		−	1.12388i
$949$		0			0
$950$	−22.4247	+	12.0877i	−0.727554	+	0.392175i
$951$		−	27.9444i		−	0.906160i
$952$			6.02778i			0.195362i
$953$		−	53.4810i		−	1.73242i	−0.499680	−	0.866210i	$-0.666549\pi$
$953$		−	53.4810i		−	1.73242i	0.499680	−	0.866210i	$-0.333451\pi$
$954$			5.82900i			0.188721i
$955$	3.08196	+	1.83991i	0.0997297	+	0.0595380i
$956$		−	3.19739i		−	0.103411i
$957$	−23.3596			−0.755110
$958$		−	30.4078i		−	0.982433i
$959$	−18.3055			−0.591114
$960$	2.62755	−	4.40131i	0.0848039	−	0.142052i
$961$	−42.6988			−1.37738
$962$		0			0
$963$			10.3392i			0.333176i
$964$		−	14.1154i		−	0.454627i
$965$	30.2477	+	18.0577i	0.973709	+	0.581298i
$966$	−7.43701			−0.239282
$967$	34.8941			1.12212			0.561059	−	0.827776i	$-0.310394\pi$
$967$	34.8941			1.12212			0.561059	+	0.827776i	$0.310394\pi$
$968$	7.00000			0.224989
$969$		−	56.0936i		−	1.80199i
$970$	−12.0278	−	7.18051i	−0.386189	−	0.230552i
$971$	31.8807			1.02310			0.511551	−	0.859253i	$-0.329071\pi$
$971$	31.8807			1.02310			0.511551	+	0.859253i	$0.329071\pi$
$972$		−	19.3596i		−	0.620961i
$973$	−9.19954			−0.294924
$974$	8.00000			0.256337
$975$		0			0
$976$	13.6798			0.437880
$977$	2.03375			0.0650655			0.0325328	−	0.999471i	$-0.489643\pi$
$977$	2.03375			0.0650655			0.0325328	+	0.999471i	$0.489643\pi$
$978$			28.1154i			0.899032i
$979$	10.1900			0.325675
$980$	10.4152	+	6.21781i	0.332701	+	0.198621i
$981$			33.5497i			1.07116i
$982$	−22.6893			−0.724046
$983$	29.4043			0.937851			0.468926	−	0.883238i	$-0.344641\pi$
$983$	29.4043			0.937851			0.468926	+	0.883238i	$0.344641\pi$
$984$	22.1900			0.707392
$985$	1.93822	+	1.15711i	0.0617569	+	0.0368685i
$986$		−	24.4694i		−	0.779263i
$987$			7.89762i			0.251384i
$988$		0			0
$989$	−28.1154			−0.894019
$990$	5.16961	−	8.65940i	0.164301	−	0.275214i
$991$	32.9986			1.04824			0.524118	−	0.851646i	$-0.324395\pi$
$991$	32.9986			1.04824			0.524118	+	0.851646i	$0.324395\pi$
$992$			8.58480i			0.272568i
$993$	41.1359			1.30541
$994$			6.76177i			0.214470i
$995$	−0.836365	−	0.499304i	−0.0265145	−	0.0158290i
$996$			25.4342i			0.805914i
$997$		−	31.1696i		−	0.987151i	−0.869703	−	0.493576i	$-0.835690\pi$
$997$		−	31.1696i		−	0.987151i	0.869703	−	0.493576i	$-0.164310\pi$
$998$		−	31.8698i		−	1.00882i
$999$			13.3874i			0.423559i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.c.d.1689.5		6
5.4	even	2		1690.2.c.a.1689.2		6
13.5	odd	4		130.2.b.a.79.3	✓	6
13.8	odd	4		1690.2.b.a.339.6		6
13.12	even	2		1690.2.c.a.1689.5		6
39.5	even	4		1170.2.e.f.469.6		6
52.31	even	4		1040.2.d.b.209.2		6
65.8	even	4		8450.2.a.cc.1.1		3
65.18	even	4		650.2.a.n.1.1		3
65.34	odd	4		1690.2.b.a.339.1		6
65.44	odd	4		130.2.b.a.79.4	yes	6
65.47	even	4		8450.2.a.bs.1.3		3
65.57	even	4		650.2.a.o.1.3		3
65.64	even	2	inner	1690.2.c.d.1689.2		6
195.44	even	4		1170.2.e.f.469.3		6
195.83	odd	4		5850.2.a.cs.1.2		3
195.122	odd	4		5850.2.a.cp.1.2		3
260.83	odd	4		5200.2.a.ce.1.3		3
260.187	odd	4		5200.2.a.cf.1.1		3
260.239	even	4		1040.2.d.b.209.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.b.a.79.3	✓	6	13.5	odd	4
130.2.b.a.79.4	yes	6	65.44	odd	4
650.2.a.n.1.1		3	65.18	even	4
650.2.a.o.1.3		3	65.57	even	4
1040.2.d.b.209.2		6	52.31	even	4
1040.2.d.b.209.5		6	260.239	even	4
1170.2.e.f.469.3		6	195.44	even	4
1170.2.e.f.469.6		6	39.5	even	4
1690.2.b.a.339.1		6	65.34	odd	4
1690.2.b.a.339.6		6	13.8	odd	4
1690.2.c.a.1689.2		6	5.4	even	2
1690.2.c.a.1689.5		6	13.12	even	2
1690.2.c.d.1689.2		6	65.64	even	2	inner
1690.2.c.d.1689.5		6	1.1	even	1	trivial
5200.2.a.ce.1.3		3	260.83	odd	4
5200.2.a.cf.1.1		3	260.187	odd	4
5850.2.a.cp.1.2		3	195.122	odd	4
5850.2.a.cs.1.2		3	195.83	odd	4
8450.2.a.bs.1.3		3	65.47	even	4
8450.2.a.cc.1.1		3	65.8	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.29240i q^{3} +1.00000 q^{4} +(-1.91995 - 1.14620i) q^{5} +2.29240i q^{6} +1.25511 q^{7} +1.00000 q^{8} -2.25511 q^{9} +(-1.91995 - 1.14620i) q^{10} -2.00000i q^{11} +2.29240i q^{12} +1.25511 q^{14} +(2.62755 - 4.40131i) q^{15} +1.00000 q^{16} +4.80261i q^{17} -2.25511 q^{18} +5.09501i q^{19} +(-1.91995 - 1.14620i) q^{20} +2.87720i q^{21} -2.00000i q^{22} +2.58480i q^{23} +2.29240i q^{24} +(2.37245 + 4.40131i) q^{25} +1.70760i q^{27} +1.25511 q^{28} -5.09501 q^{29} +(2.62755 - 4.40131i) q^{30} +8.58480i q^{31} +1.00000 q^{32} +4.58480 q^{33} +4.80261i q^{34} +(-2.40974 - 1.43860i) q^{35} -2.25511 q^{36} +7.83991 q^{37} +5.09501i q^{38} +(-1.91995 - 1.14620i) q^{40} -9.67982i q^{41} +2.87720i q^{42} +10.8772i q^{43} -2.00000i q^{44} +(4.32970 + 2.58480i) q^{45} +2.58480i q^{46} +2.74489 q^{47} +2.29240i q^{48} -5.42471 q^{49} +(2.37245 + 4.40131i) q^{50} -11.0095 q^{51} -2.58480i q^{53} +1.70760i q^{54} +(-2.29240 + 3.83991i) q^{55} +1.25511 q^{56} -11.6798 q^{57} -5.09501 q^{58} -5.09501i q^{59} +(2.62755 - 4.40131i) q^{60} +13.6798 q^{61} +8.58480i q^{62} -2.83039 q^{63} +1.00000 q^{64} +4.58480 q^{66} -8.58480 q^{67} +4.80261i q^{68} -5.92541 q^{69} +(-2.40974 - 1.43860i) q^{70} +5.38741i q^{71} -2.25511 q^{72} -6.00000 q^{73} +7.83991 q^{74} +(-10.0896 + 5.43860i) q^{75} +5.09501i q^{76} -2.51021i q^{77} -15.0950 q^{79} +(-1.91995 - 1.14620i) q^{80} -10.6798 q^{81} -9.67982i q^{82} +11.0950 q^{83} +2.87720i q^{84} +(5.50476 - 9.22079i) q^{85} +10.8772i q^{86} -11.6798i q^{87} -2.00000i q^{88} +5.09501i q^{89} +(4.32970 + 2.58480i) q^{90} +2.58480i q^{92} -19.6798 q^{93} +2.74489 q^{94} +(5.83991 - 9.78219i) q^{95} +2.29240i q^{96} +6.26462 q^{97} -5.42471 q^{98} +4.51021i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + 4 q^{5} + 4 q^{7} + 6 q^{8} - 10 q^{9} + 4 q^{10} + 4 q^{14} + 14 q^{15} + 6 q^{16} - 10 q^{18} + 4 q^{20} + 16 q^{25} + 4 q^{28} + 4 q^{29} + 14 q^{30} + 6 q^{32} - 6 q^{35} - 10 q^{36}+ \cdots + 26 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + 4 * q^5 + 4 * q^7 + 6 * q^8 - 10 * q^9 + 4 * q^10 + 4 * q^14 + 14 * q^15 + 6 * q^16 - 10 * q^18 + 4 * q^20 + 16 * q^25 + 4 * q^28 + 4 * q^29 + 14 * q^30 + 6 * q^32 - 6 * q^35 - 10 * q^36 + 16 * q^37 + 4 * q^40 + 2 * q^45 + 20 * q^47 + 26 * q^49 + 16 * q^50 + 20 * q^51 + 4 * q^56 - 8 * q^57 + 4 * q^58 + 14 * q^60 + 20 * q^61 - 72 * q^63 + 6 * q^64 - 24 * q^67 - 56 * q^69 - 6 * q^70 - 10 * q^72 - 36 * q^73 + 16 * q^74 + 10 * q^75 - 56 * q^79 + 4 * q^80 - 2 * q^81 + 32 * q^83 - 10 * q^85 + 2 * q^90 - 56 * q^93 + 20 * q^94 + 4 * q^95 - 52 * q^97 + 26 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more