LMFDB - Embedded newform 1690.2.b.a.339.6

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			339.6
Root			$0.627553 + 1.14620i$ of defining polynomial
Character	$\chi$	$=$	1690.339
Dual form			1690.2.b.a.339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +2.29240i q^{3} -1.00000 q^{4} +(1.14620 - 1.91995i) q^{5} -2.29240 q^{6} -1.25511i q^{7} -1.00000i q^{8} -2.25511 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +2.29240i q^{3} -1.00000 q^{4} +(1.14620 - 1.91995i) q^{5} -2.29240 q^{6} -1.25511i q^{7} -1.00000i q^{8} -2.25511 q^{9} +(1.91995 + 1.14620i) q^{10} -2.00000 q^{11} -2.29240i q^{12} +1.25511 q^{14} +(4.40131 + 2.62755i) q^{15} +1.00000 q^{16} -4.80261i q^{17} -2.25511i q^{18} -5.09501 q^{19} +(-1.14620 + 1.91995i) q^{20} +2.87720 q^{21} -2.00000i q^{22} -2.58480i q^{23} +2.29240 q^{24} +(-2.37245 - 4.40131i) q^{25} +1.70760i q^{27} +1.25511i q^{28} -5.09501 q^{29} +(-2.62755 + 4.40131i) q^{30} -8.58480 q^{31} +1.00000i q^{32} -4.58480i q^{33} +4.80261 q^{34} +(-2.40974 - 1.43860i) q^{35} +2.25511 q^{36} -7.83991i q^{37} -5.09501i q^{38} +(-1.91995 - 1.14620i) q^{40} +9.67982 q^{41} +2.87720i q^{42} -10.8772i q^{43} +2.00000 q^{44} +(-2.58480 + 4.32970i) q^{45} +2.58480 q^{46} -2.74489i q^{47} +2.29240i q^{48} +5.42471 q^{49} +(4.40131 - 2.37245i) q^{50} +11.0095 q^{51} -2.58480i q^{53} -1.70760 q^{54} +(-2.29240 + 3.83991i) q^{55} -1.25511 q^{56} -11.6798i q^{57} -5.09501i q^{58} -5.09501 q^{59} +(-4.40131 - 2.62755i) q^{60} +13.6798 q^{61} -8.58480i q^{62} +2.83039i q^{63} -1.00000 q^{64} +4.58480 q^{66} -8.58480i q^{67} +4.80261i q^{68} +5.92541 q^{69} +(1.43860 - 2.40974i) q^{70} -5.38741 q^{71} +2.25511i q^{72} +6.00000i q^{73} +7.83991 q^{74} +(10.0896 - 5.43860i) q^{75} +5.09501 q^{76} +2.51021i q^{77} -15.0950 q^{79} +(1.14620 - 1.91995i) q^{80} -10.6798 q^{81} +9.67982i q^{82} +11.0950i q^{83} -2.87720 q^{84} +(-9.22079 - 5.50476i) q^{85} +10.8772 q^{86} -11.6798i q^{87} +2.00000i q^{88} +5.09501 q^{89} +(-4.32970 - 2.58480i) q^{90} +2.58480i q^{92} -19.6798i q^{93} +2.74489 q^{94} +(-5.83991 + 9.78219i) q^{95} -2.29240 q^{96} +6.26462i q^{97} +5.42471i q^{98} +4.51021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			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
$5$	1.14620	−	1.91995i	0.512597	−	0.858630i
$5$	1.14620	−	1.91995i	0.512597	−	0.858630i
$6$	−2.29240			−0.935869
$7$		−	1.25511i		−	0.474385i	−0.971463	−	0.237193i	$-0.923773\pi$
$7$		−	1.25511i		−	0.474385i	0.971463	−	0.237193i	$-0.0762272\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−2.25511			−0.751702
$10$	1.91995	+	1.14620i	0.607143	+	0.362461i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		−	2.29240i		−	0.661759i
$13$		0			0
$13$		0			0
$14$	1.25511			0.335441
$15$	4.40131	+	2.62755i	1.13641	+	0.678431i
$16$	1.00000			0.250000
$17$		−	4.80261i		−	1.16480i	−0.812901	−	0.582402i	$-0.802113\pi$
$17$		−	4.80261i		−	1.16480i	0.812901	−	0.582402i	$-0.197887\pi$
$18$		−	2.25511i		−	0.531533i
$19$	−5.09501			−1.16888			−0.584438	−	0.811438i	$-0.698685\pi$
$19$	−5.09501			−1.16888			−0.584438	+	0.811438i	$0.698685\pi$
$20$	−1.14620	+	1.91995i	−0.256298	+	0.429315i
$21$	2.87720			0.627858
$22$		−	2.00000i		−	0.426401i
$23$		−	2.58480i		−	0.538969i	−0.963005	−	0.269484i	$-0.913147\pi$
$23$		−	2.58480i		−	0.538969i	0.963005	−	0.269484i	$-0.0868533\pi$
$24$	2.29240			0.467935
$25$	−2.37245	−	4.40131i	−0.474489	−	0.880261i
$26$		0			0
$27$			1.70760i			0.328627i
$28$			1.25511i			0.237193i
$29$	−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
$31$	−8.58480			−1.54188			−0.770938	−	0.636910i	$-0.780212\pi$
$31$	−8.58480			−1.54188			−0.770938	+	0.636910i	$0.780212\pi$
$32$			1.00000i			0.176777i
$33$		−	4.58480i		−	0.798112i
$34$	4.80261			0.823641
$35$	−2.40974	−	1.43860i	−0.407321	−	0.243168i
$36$	2.25511			0.375851
$37$		−	7.83991i		−	1.28887i	−0.764658	−	0.644436i	$-0.777092\pi$
$37$		−	7.83991i		−	1.28887i	0.764658	−	0.644436i	$-0.222908\pi$
$38$		−	5.09501i		−	0.826520i
$39$		0			0
$40$	−1.91995	−	1.14620i	−0.303571	−	0.181230i
$41$	9.67982			1.51173			0.755867	−	0.654726i	$-0.227216\pi$
$41$	9.67982			1.51173			0.755867	+	0.654726i	$0.227216\pi$
$42$			2.87720i			0.443962i
$43$		−	10.8772i		−	1.65876i	−0.558686	−	0.829379i	$-0.688694\pi$
$43$		−	10.8772i		−	1.65876i	0.558686	−	0.829379i	$-0.311306\pi$
$44$	2.00000			0.301511
$45$	−2.58480	+	4.32970i	−0.385320	+	0.645433i
$46$	2.58480			0.381108
$47$		−	2.74489i		−	0.400384i	−0.979757	−	0.200192i	$-0.935843\pi$
$47$		−	2.74489i		−	0.400384i	0.979757	−	0.200192i	$-0.0641566\pi$
$48$			2.29240i			0.330880i
$49$	5.42471			0.774959
$50$	4.40131	−	2.37245i	0.622439	−	0.335515i
$51$	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	$-0.0568091\pi$
$54$	−1.70760			−0.232375
$55$	−2.29240	+	3.83991i	−0.309107	+	0.517773i
$56$	−1.25511			−0.167720
$57$		−	11.6798i		−	1.54703i
$58$		−	5.09501i		−	0.669008i
$59$	−5.09501			−0.663314			−0.331657	−	0.943400i	$-0.607608\pi$
$59$	−5.09501			−0.663314			−0.331657	+	0.943400i	$0.607608\pi$
$60$	−4.40131	−	2.62755i	−0.568206	−	0.339216i
$61$	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
$63$			2.83039i			0.356596i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.58480			0.564350
$67$		−	8.58480i		−	1.04880i	−0.851472	−	0.524400i	$-0.824290\pi$
$67$		−	8.58480i		−	1.04880i	0.851472	−	0.524400i	$-0.175710\pi$
$68$			4.80261i			0.582402i
$69$	5.92541			0.713335
$70$	1.43860	−	2.40974i	0.171946	−	0.288020i
$71$	−5.38741			−0.639369			−0.319684	−	0.947524i	$-0.603577\pi$
$71$	−5.38741			−0.639369			−0.319684	+	0.947524i	$0.603577\pi$
$72$			2.25511i			0.265767i
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	7.83991			0.911371
$75$	10.0896	−	5.43860i	1.16504	−	0.627996i
$76$	5.09501			0.584438
$77$			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	$0.822892\pi$
$80$	1.14620	−	1.91995i	0.128149	−	0.214657i
$81$	−10.6798			−1.18665
$82$			9.67982i			1.06896i
$83$			11.0950i			1.21784i	0.793233	+	0.608918i	$0.208396\pi$
$83$			11.0950i			1.21784i	−0.793233	+	0.608918i	$0.791604\pi$
$84$	−2.87720			−0.313929
$85$	−9.22079	−	5.50476i	−1.00014	−	0.597075i
$86$	10.8772			1.17292
$87$		−	11.6798i		−	1.25221i
$88$			2.00000i			0.213201i
$89$	5.09501			0.540070			0.270035	−	0.962850i	$-0.412965\pi$
$89$	5.09501			0.540070			0.270035	+	0.962850i	$0.412965\pi$
$90$	−4.32970	−	2.58480i	−0.456390	−	0.272462i
$91$		0			0
$92$			2.58480i			0.269484i
$93$		−	19.6798i		−	2.04070i
$94$	2.74489			0.283114
$95$	−5.83991	+	9.78219i	−0.599162	+	1.00363i
$96$	−2.29240			−0.233967
$97$			6.26462i			0.636076i	0.948078	+	0.318038i	$0.103024\pi$
$97$			6.26462i			0.636076i	−0.948078	+	0.318038i	$0.896976\pi$
$98$			5.42471i			0.547979i
$99$	4.51021			0.453293
$100$	2.37245	+	4.40131i	0.237245	+	0.440131i
$101$	−12.6594			−1.25966			−0.629829	−	0.776734i	$-0.716875\pi$
$101$	−12.6594			−1.25966			−0.629829	+	0.776734i	$0.716875\pi$
$102$			11.0095i			1.09010i
$103$			7.60522i			0.749365i	0.927153	+	0.374682i	$0.122248\pi$
$103$			7.60522i			0.749365i	−0.927153	+	0.374682i	$0.877752\pi$
$104$		0			0
$105$	3.29785	−	5.52410i	0.321838	−	0.539097i
$106$	2.58480			0.251058
$107$		−	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
$109$	14.8772			1.42498			0.712489	−	0.701683i	$-0.247568\pi$
$109$	14.8772			1.42498			0.712489	+	0.701683i	$0.247568\pi$
$110$	−3.83991	−	2.29240i	−0.366121	−	0.218572i
$111$	17.9722			1.70585
$112$		−	1.25511i		−	0.118596i
$113$			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
$115$	−4.96270	−	2.96270i	−0.462774	−	0.276274i
$116$	5.09501			0.473060
$117$		0			0
$118$		−	5.09501i		−	0.469034i
$119$	−6.02778			−0.552566
$120$	2.62755	−	4.40131i	0.239862	−	0.401782i
$121$	−7.00000			−0.636364
$122$			13.6798i			1.23851i
$123$			22.1900i			2.00081i
$124$	8.58480			0.770938
$125$	−11.1696	−	0.489790i	−0.999040	−	0.0438081i
$126$	−2.83039			−0.252152
$127$		−	1.41520i		−	0.125578i	−0.998027	−	0.0627892i	$-0.980000\pi$
$127$		−	1.41520i		−	0.125578i	0.998027	−	0.0627892i	$-0.0199996\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	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	$0.340291\pi$
$132$			4.58480i			0.399056i
$133$			6.39478i			0.554497i
$134$	8.58480			0.741614
$135$	3.27851	+	1.95725i	0.282169	+	0.168453i
$136$	−4.80261			−0.411821
$137$			14.5848i			1.24606i	0.782196	+	0.623032i	$0.214099\pi$
$137$			14.5848i			1.24606i	−0.782196	+	0.623032i	$0.785901\pi$
$138$			5.92541i			0.504404i
$139$	−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
$141$	6.29240			0.529916
$142$		−	5.38741i		−	0.452102i
$143$		0			0
$144$	−2.25511			−0.187925
$145$	−5.83991	+	9.78219i	−0.484978	+	0.812367i
$146$	−6.00000			−0.496564
$147$			12.4356i			1.02567i
$148$			7.83991i			0.644436i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	5.43860	+	10.0896i	0.444060	+	0.823809i
$151$	14.5570			1.18463			0.592317	−	0.805705i	$-0.298213\pi$
$151$	14.5570			1.18463			0.592317	+	0.805705i	$0.298213\pi$
$152$			5.09501i			0.413260i
$153$			10.8304i			0.875585i
$154$	−2.51021			−0.202278
$155$	−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	$-0.175018\pi$
$158$		−	15.0950i		−	1.20089i
$159$	5.92541			0.469915
$160$	1.91995	+	1.14620i	0.151786	+	0.0906151i
$161$	−3.24420			−0.255679
$162$		−	10.6798i		−	0.839086i
$163$		−	12.2646i		−	0.960639i	−0.877094	−	0.480320i	$-0.840521\pi$
$163$		−	12.2646i		−	0.960639i	0.877094	−	0.480320i	$-0.159479\pi$
$164$	−9.67982			−0.755867
$165$	−8.80261	−	5.25511i	−0.685282	−	0.409109i
$166$	−11.0950			−0.861140
$167$		−	18.3392i		−	1.41913i	−0.704640	−	0.709565i	$-0.748891\pi$
$167$		−	18.3392i		−	1.41913i	0.704640	−	0.709565i	$-0.251109\pi$
$168$		−	2.87720i		−	0.221981i
$169$		0			0
$170$	5.50476	−	9.22079i	0.422196	−	0.707203i
$171$	11.4898			0.878646
$172$			10.8772i			0.829379i
$173$		−	9.41520i		−	0.715824i	−0.933755	−	0.357912i	$-0.883489\pi$
$173$		−	9.41520i		−	0.715824i	0.933755	−	0.357912i	$-0.116511\pi$
$174$	11.6798			0.885445
$175$	−5.52410	+	2.97767i	−0.417583	+	0.225091i
$176$	−2.00000			−0.150756
$177$		−	11.6798i		−	0.877909i
$178$			5.09501i			0.381887i
$179$	7.32970			0.547847			0.273924	−	0.961751i	$-0.411678\pi$
$179$	7.32970			0.547847			0.273924	+	0.961751i	$0.411678\pi$
$180$	2.58480	−	4.32970i	0.192660	−	0.322717i
$181$	11.7544			0.873698			0.436849	−	0.899535i	$-0.356094\pi$
$181$	11.7544			0.873698			0.436849	+	0.899535i	$0.356094\pi$
$182$		0			0
$183$			31.3596i			2.31817i
$184$	−2.58480			−0.190554
$185$	−15.0523	−	8.98611i	−1.10666	−	0.660672i
$186$	19.6798			1.44299
$187$			9.60522i			0.702403i
$188$			2.74489i			0.200192i
$189$	2.14322			0.155896
$190$	−9.78219	−	5.83991i	−0.709675	−	0.423671i
$191$	−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
$193$			15.7544i			1.13403i	0.823708	+	0.567014i	$0.191901\pi$
$193$			15.7544i			1.13403i	−0.823708	+	0.567014i	$0.808099\pi$
$194$	−6.26462			−0.449773
$195$		0			0
$196$	−5.42471			−0.387479
$197$		−	1.00951i		−	0.0719249i	−0.999353	−	0.0359625i	$-0.988550\pi$
$197$		−	1.00951i		−	0.0719249i	0.999353	−	0.0359625i	$-0.0114497\pi$
$198$			4.51021i			0.320527i
$199$	−0.435617			−0.0308801			−0.0154400	−	0.999881i	$-0.504915\pi$
$199$	−0.435617			−0.0308801			−0.0154400	+	0.999881i	$0.504915\pi$
$200$	−4.40131	+	2.37245i	−0.311219	+	0.167757i
$201$	19.6798			1.38811
$202$		−	12.6594i		−	0.890712i
$203$			6.39478i			0.448825i
$204$	−11.0095			−0.770820
$205$	11.0950	−	18.5848i	0.774909	−	1.29802i
$206$	−7.60522			−0.529881
$207$			5.82900i			0.405144i
$208$		0			0
$209$	10.1900			0.704859
$210$	5.52410	+	3.29785i	0.381199	+	0.227574i
$211$	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
$213$		−	12.3501i		−	0.846216i
$214$	4.58480			0.313411
$215$	−20.8837	−	12.4675i	−1.42426	−	0.850274i
$216$	1.70760			0.116187
$217$			10.7748i			0.731443i
$218$			14.8772i			1.00761i
$219$	−13.7544			−0.929437
$220$	2.29240	−	3.83991i	0.154554	−	0.258887i
$221$		0			0
$222$			17.9722i			1.20622i
$223$			21.7843i			1.45879i	0.684094	+	0.729394i	$0.260198\pi$
$223$			21.7843i			1.45879i	−0.684094	+	0.729394i	$0.739802\pi$
$224$	1.25511			0.0838602
$225$	5.35012	+	9.92541i	0.356675	+	0.661694i
$226$	−4.00000			−0.266076
$227$		−	9.02042i		−	0.598706i	−0.954142	−	0.299353i	$-0.903229\pi$
$227$		−	9.02042i		−	0.598706i	0.954142	−	0.299353i	$-0.0967709\pi$
$228$			11.6798i			0.773515i
$229$	4.68718			0.309737			0.154869	−	0.987935i	$-0.450505\pi$
$229$	4.68718			0.309737			0.154869	+	0.987935i	$0.450505\pi$
$230$	2.96270	−	4.96270i	0.195355	−	0.327231i
$231$	−5.75441			−0.378612
$232$			5.09501i			0.334504i
$233$			13.5366i			0.886812i	0.896321	+	0.443406i	$0.146230\pi$
$233$			13.5366i			0.886812i	−0.896321	+	0.443406i	$0.853770\pi$
$234$		0			0
$235$	−5.27007	−	3.14620i	−0.343782	−	0.205236i
$236$	5.09501			0.331657
$237$		−	34.6038i		−	2.24776i
$238$		−	6.02778i		−	0.390723i
$239$	3.19739			0.206822			0.103411	−	0.994639i	$-0.467024\pi$
$239$	3.19739			0.206822			0.103411	+	0.994639i	$0.467024\pi$
$240$	4.40131	+	2.62755i	0.284103	+	0.169608i
$241$	−14.1154			−0.909255			−0.454627	−	0.890682i	$-0.650228\pi$
$241$	−14.1154			−0.909255			−0.454627	+	0.890682i	$0.650228\pi$
$242$		−	7.00000i		−	0.449977i
$243$		−	19.3596i		−	1.24192i
$244$	−13.6798			−0.875761
$245$	6.21781	−	10.4152i	0.397241	−	0.665403i
$246$	−22.1900			−1.41478
$247$		0			0
$248$			8.58480i			0.545136i
$249$	−25.4342			−1.61183
$250$	0.489790	−	11.1696i	0.0309770	−	0.706428i
$251$	−21.1696			−1.33621			−0.668107	−	0.744065i	$-0.732895\pi$
$251$	−21.1696			−1.33621			−0.668107	+	0.744065i	$0.732895\pi$
$252$		−	2.83039i		−	0.178298i
$253$			5.16961i			0.325010i
$254$	1.41520			0.0887973
$255$	12.6191	−	21.1378i	0.790240	−	1.32370i
$256$	1.00000			0.0625000
$257$		−	8.21781i		−	0.512613i	−0.966596	−	0.256306i	$-0.917494\pi$
$257$		−	8.21781i		−	0.512613i	0.966596	−	0.256306i	$-0.0825056\pi$
$258$			24.9349i			1.55238i
$259$	−9.83991			−0.611422
$260$		0			0
$261$	11.4898			0.711200
$262$			11.0095i			0.680170i
$263$		−	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
$265$	−4.96270	−	2.96270i	−0.304856	−	0.181997i
$266$	−6.39478			−0.392089
$267$			11.6798i			0.714793i
$268$			8.58480i			0.524400i
$269$	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
$271$	−4.95180			−0.300800			−0.150400	−	0.988625i	$-0.548056\pi$
$271$	−4.95180			−0.300800			−0.150400	+	0.988625i	$0.548056\pi$
$272$		−	4.80261i		−	0.291201i
$273$		0			0
$274$	−14.5848			−0.881100
$275$	4.74489	+	8.80261i	0.286128	+	0.530817i
$276$	−5.92541			−0.356668
$277$		−	19.8698i		−	1.19386i	−0.802292	−	0.596932i	$-0.796386\pi$
$277$		−	19.8698i		−	1.19386i	0.802292	−	0.596932i	$-0.203614\pi$
$278$		−	7.32970i		−	0.439606i
$279$	19.3596			1.15903
$280$	−1.43860	+	2.40974i	−0.0859729	+	0.144010i
$281$	−30.2646			−1.80544			−0.902718	−	0.430233i	$-0.858431\pi$
$281$	−30.2646			−1.80544			−0.902718	+	0.430233i	$0.858431\pi$
$282$			6.29240i			0.374707i
$283$			26.9240i			1.60047i	0.599689	+	0.800233i	$0.295291\pi$
$283$			26.9240i			1.60047i	−0.599689	+	0.800233i	$0.704709\pi$
$284$	5.38741			0.319684
$285$	−22.4247	−	13.3874i	−1.32833	−	0.793002i
$286$		0			0
$287$		−	12.1492i		−	0.717144i
$288$		−	2.25511i		−	0.132883i
$289$	−6.06508			−0.356769
$290$	−9.78219	−	5.83991i	−0.574430	−	0.342931i
$291$	−14.3610			−0.841858
$292$		−	6.00000i		−	0.351123i
$293$		−	5.18051i		−	0.302649i	−0.988484	−	0.151324i	$-0.951646\pi$
$293$		−	5.18051i		−	0.302649i	0.988484	−	0.151324i	$-0.0483538\pi$
$294$	−12.4356			−0.725260
$295$	−5.83991	+	9.78219i	−0.340013	+	0.569541i
$296$	−7.83991			−0.455685
$297$		−	3.41520i		−	0.198170i
$298$		0			0
$299$		0			0
$300$	−10.0896	+	5.43860i	−0.582521	+	0.313998i
$301$	−13.6520			−0.786890
$302$			14.5570i			0.837662i
$303$		−	29.0204i		−	1.66718i
$304$	−5.09501			−0.292219
$305$	15.6798	−	26.2646i	0.897824	−	1.50391i
$306$	−10.8304			−0.619132
$307$		−	0.320184i		−	0.0182738i	−0.999958	−	0.00913692i	$-0.997092\pi$
$307$		−	0.320184i		−	0.0182738i	0.999958	−	0.00913692i	$-0.00290841\pi$
$308$		−	2.51021i		−	0.143032i
$309$	−17.4342			−0.991798
$310$	−16.4824	−	9.83991i	−0.936139	−	0.558869i
$311$	−9.86984			−0.559667			−0.279834	−	0.960048i	$-0.590279\pi$
$311$	−9.86984			−0.559667			−0.279834	+	0.960048i	$0.590279\pi$
$312$		0			0
$313$			10.6126i			0.599859i	0.953961	+	0.299929i	$0.0969631\pi$
$313$			10.6126i			0.599859i	−0.953961	+	0.299929i	$0.903037\pi$
$314$	13.0950			0.738994
$315$	5.43423	+	3.24420i	0.306184	+	0.182790i
$316$	15.0950			0.849161
$317$		−	12.1900i		−	0.684660i	−0.939580	−	0.342330i	$-0.888784\pi$
$317$		−	12.1900i		−	0.684660i	0.939580	−	0.342330i	$-0.111216\pi$
$318$			5.92541i			0.332280i
$319$	10.1900			0.570532
$320$	−1.14620	+	1.91995i	−0.0640746	+	0.107329i
$321$	10.5102			0.586623
$322$		−	3.24420i		−	0.180792i
$323$			24.4694i			1.36151i
$324$	10.6798			0.593323
$325$		0			0
$326$	12.2646			0.679274
$327$			34.1045i			1.88598i
$328$		−	9.67982i		−	0.534478i
$329$	−3.44513			−0.189936
$330$	5.25511	−	8.80261i	0.289284	−	0.484568i
$331$	17.9444			0.986315			0.493158	−	0.869940i	$-0.335843\pi$
$331$	17.9444			0.986315			0.493158	+	0.869940i	$0.335843\pi$
$332$		−	11.0950i		−	0.608918i
$333$			17.6798i			0.968848i
$334$	18.3392			1.00348
$335$	−16.4824	−	9.83991i	−0.900531	−	0.537612i
$336$	2.87720			0.156964
$337$		−	20.9518i		−	1.14132i	−0.821187	−	0.570659i	$-0.806688\pi$
$337$		−	20.9518i		−	1.14132i	0.821187	−	0.570659i	$-0.193312\pi$
$338$		0			0
$339$	−9.16961			−0.498025
$340$	9.22079	+	5.50476i	0.500068	+	0.298537i
$341$	17.1696			0.929786
$342$			11.4898i			0.621297i
$343$		−	15.5943i		−	0.842014i
$344$	−10.8772			−0.586460
$345$	6.79171	−	11.3765i	0.365653	−	0.612491i
$346$	9.41520			0.506164
$347$			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
$349$	17.8568			0.955852			0.477926	−	0.878400i	$-0.341389\pi$
$349$	17.8568			0.955852			0.477926	+	0.878400i	$0.341389\pi$
$350$	−2.97767	−	5.52410i	−0.159163	−	0.295276i
$351$		0			0
$352$		−	2.00000i		−	0.106600i
$353$		−	36.9240i		−	1.96527i	−0.185557	−	0.982634i	$-0.559409\pi$
$353$		−	36.9240i		−	1.96527i	0.185557	−	0.982634i	$-0.440591\pi$
$354$	11.6798			0.620775
$355$	−6.17506	+	10.3436i	−0.327738	+	0.548981i
$356$	−5.09501			−0.270035
$357$		−	13.8181i		−	0.731331i
$358$			7.32970i			0.387387i
$359$	−6.77483			−0.357562			−0.178781	−	0.983889i	$-0.557215\pi$
$359$	−6.77483			−0.357562			−0.178781	+	0.983889i	$0.557215\pi$
$360$	4.32970	+	2.58480i	0.228195	+	0.136231i
$361$	6.95916			0.366272
$362$			11.7544i			0.617798i
$363$		−	16.0468i		−	0.842239i
$364$		0			0
$365$	11.5197	+	6.87720i	0.602970	+	0.359969i
$366$	−31.3596			−1.63919
$367$		−	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
$369$	−21.8290			−1.13637
$370$	8.98611	−	15.0523i	0.467166	−	0.782530i
$371$	−3.24420			−0.168430
$372$			19.6798i			1.02035i
$373$			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
$375$	1.12280	−	25.6052i	0.0579809	−	1.32225i
$376$	−2.74489			−0.141557
$377$		0			0
$378$			2.14322i			0.110235i
$379$	−16.7748			−0.861665			−0.430833	−	0.902432i	$-0.641780\pi$
$379$	−16.7748			−0.861665			−0.430833	+	0.902432i	$0.641780\pi$
$380$	5.83991	−	9.78219i	0.299581	−	0.501816i
$381$	3.24420			0.166205
$382$		−	1.60522i		−	0.0821304i
$383$		−	16.6147i		−	0.848973i	−0.905434	−	0.424487i	$-0.860455\pi$
$383$		−	16.6147i		−	0.848973i	0.905434	−	0.424487i	$-0.139545\pi$
$384$	2.29240			0.116984
$385$	4.81949	+	2.87720i	0.245624	+	0.146636i
$386$	−15.7544			−0.801878
$387$			24.5292i			1.24689i
$388$		−	6.26462i		−	0.318038i
$389$	−36.7193			−1.86174			−0.930870	−	0.365350i	$-0.880949\pi$
$389$	−36.7193			−1.86174			−0.930870	+	0.365350i	$0.880949\pi$
$390$		0			0
$391$	−12.4138			−0.627793
$392$		−	5.42471i		−	0.273989i
$393$			25.2382i			1.27310i
$394$	1.00951			0.0508586
$395$	−17.3019	+	28.9817i	−0.870554	+	1.45823i
$396$	−4.51021			−0.226647
$397$		−	29.2104i		−	1.46603i	−0.680212	−	0.733015i	$-0.738112\pi$
$397$		−	29.2104i		−	1.46603i	0.680212	−	0.733015i	$-0.261888\pi$
$398$		−	0.435617i		−	0.0218355i
$399$	−14.6594			−0.733888
$400$	−2.37245	−	4.40131i	−0.118622	−	0.220065i
$401$	−15.6052			−0.779288			−0.389644	−	0.920966i	$-0.627402\pi$
$401$	−15.6052			−0.779288			−0.389644	+	0.920966i	$0.627402\pi$
$402$			19.6798i			0.981540i
$403$		0			0
$404$	12.6594			0.629829
$405$	−12.2412	+	20.5048i	−0.608271	+	1.01889i
$406$	−6.39478			−0.317367
$407$			15.6798i			0.777220i
$408$		−	11.0095i		−	0.545052i
$409$	13.7952			0.682131			0.341066	−	0.940039i	$-0.389212\pi$
$409$	13.7952			0.682131			0.341066	+	0.940039i	$0.389212\pi$
$410$	18.5848	+	11.0950i	0.917838	+	0.547944i
$411$	−33.4342			−1.64919
$412$		−	7.60522i		−	0.374682i
$413$			6.39478i			0.314666i
$414$	−5.82900			−0.286480
$415$	21.3019	+	12.7171i	1.04567	+	0.624259i
$416$		0			0
$417$		−	16.8026i		−	0.822827i
$418$			10.1900i			0.498410i
$419$	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
$421$	16.9180			0.824535			0.412268	−	0.911063i	$-0.364737\pi$
$421$	16.9180			0.824535			0.412268	+	0.911063i	$0.364737\pi$
$422$			16.3501i			0.795911i
$423$			6.19003i			0.300969i
$424$	−2.58480			−0.125529
$425$	−21.1378	+	11.3939i	−1.02533	+	0.552687i
$426$	12.3501			0.598365
$427$		−	17.1696i		−	0.830895i
$428$			4.58480i			0.221615i
$429$		0			0
$430$	12.4675	−	20.8837i	0.601234	−	1.00710i
$431$	17.9722			0.865691			0.432846	−	0.901468i	$-0.357510\pi$
$431$	17.9722			0.865691			0.432846	+	0.901468i	$0.357510\pi$
$432$			1.70760i			0.0821569i
$433$		−	2.61259i		−	0.125553i	−0.998028	−	0.0627764i	$-0.980004\pi$
$433$		−	2.61259i		−	0.125553i	0.998028	−	0.0627764i	$-0.0199955\pi$
$434$	−10.7748			−0.517208
$435$	−22.4247	−	13.3874i	−1.07518	−	0.641877i
$436$	−14.8772			−0.712489
$437$			13.1696i			0.629988i
$438$		−	13.7544i		−	0.657211i
$439$	−14.6594			−0.699655			−0.349827	−	0.936814i	$-0.613760\pi$
$439$	−14.6594			−0.699655			−0.349827	+	0.936814i	$0.613760\pi$
$440$	3.83991	+	2.29240i	0.183060	+	0.109286i
$441$	−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	$-0.0634323\pi$
$444$	−17.9722			−0.852924
$445$	5.83991	−	9.78219i	0.276838	−	0.463720i
$446$	−21.7843			−1.03152
$447$		0			0
$448$			1.25511i			0.0592981i
$449$	−4.04084			−0.190699			−0.0953495	−	0.995444i	$-0.530397\pi$
$449$	−4.04084			−0.190699			−0.0953495	+	0.995444i	$0.530397\pi$
$450$	−9.92541	+	5.35012i	−0.467888	+	0.252207i
$451$	−19.3596			−0.911610
$452$		−	4.00000i		−	0.188144i
$453$			33.3705i			1.56788i
$454$	9.02042			0.423349
$455$		0			0
$456$	−11.6798			−0.546958
$457$			0.979580i			0.0458228i	0.999737	+	0.0229114i	$0.00729357\pi$
$457$			0.979580i			0.0458228i	−0.999737	+	0.0229114i	$0.992706\pi$
$458$			4.68718i			0.219017i
$459$	8.20093			0.382787
$460$	4.96270	+	2.96270i	0.231387	+	0.138137i
$461$	−10.7280			−0.499654			−0.249827	−	0.968291i	$-0.580374\pi$
$461$	−10.7280			−0.499654			−0.249827	+	0.968291i	$0.580374\pi$
$462$		−	5.75441i		−	0.267719i
$463$			23.2104i			1.07868i	0.842088	+	0.539340i	$0.181326\pi$
$463$			23.2104i			1.07868i	−0.842088	+	0.539340i	$0.818674\pi$
$464$	−5.09501			−0.236530
$465$	−37.7843	−	22.5570i	−1.75221	−	1.04606i
$466$	−13.5366			−0.627071
$467$			28.5848i			1.32275i	0.750057	+	0.661373i	$0.230026\pi$
$467$			28.5848i			1.32275i	−0.750057	+	0.661373i	$0.769974\pi$
$468$		0			0
$469$	−10.7748			−0.497535
$470$	3.14620	−	5.27007i	0.145123	−	0.243090i
$471$	30.0190			1.38320
$472$			5.09501i			0.234517i
$473$			21.7544i			1.00027i
$474$	34.6038			1.58941
$475$	12.0877	+	22.4247i	0.554619	+	1.02892i
$476$	6.02778			0.276283
$477$			5.82900i			0.266892i
$478$			3.19739i			0.146245i
$479$	−30.4078			−1.38937			−0.694685	−	0.719314i	$-0.744456\pi$
$479$	−30.4078			−1.38937			−0.694685	+	0.719314i	$0.744456\pi$
$480$	−2.62755	+	4.40131i	−0.119931	+	0.200891i
$481$		0			0
$482$		−	14.1154i		−	0.642940i
$483$		−	7.43701i		−	0.338396i
$484$	7.00000			0.318182
$485$	12.0278	+	7.18051i	0.546153	+	0.326050i
$486$	19.3596			0.878171
$487$			8.00000i			0.362515i	0.983436	+	0.181257i	$0.0580167\pi$
$487$			8.00000i			0.362515i	−0.983436	+	0.181257i	$0.941983\pi$
$488$		−	13.6798i		−	0.619256i
$489$	28.1154			1.27142
$490$	10.4152	+	6.21781i	0.470511	+	0.280892i
$491$	22.6893			1.02396			0.511978	−	0.858999i	$-0.328913\pi$
$491$	22.6893			1.02396			0.511978	+	0.858999i	$0.328913\pi$
$492$		−	22.1900i		−	1.00040i
$493$			24.4694i			1.10204i
$494$		0			0
$495$	5.16961	−	8.65940i	0.232357	−	0.389211i
$496$	−8.58480			−0.385469
$497$			6.76177i			0.303307i
$498$		−	25.4342i		−	1.13973i
$499$	31.8698			1.42669			0.713345	−	0.700813i	$-0.247179\pi$
$499$	31.8698			1.42669			0.713345	+	0.700813i	$0.247179\pi$
$500$	11.1696	+	0.489790i	0.499520	+	0.0219041i
$501$	42.0408			1.87825
$502$		−	21.1696i		−	0.944846i
$503$		−	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
$505$	−14.5102	+	24.3055i	−0.645696	+	1.08158i
$506$	−5.16961			−0.229817
$507$		0			0
$508$			1.41520i			0.0627892i
$509$	23.3596			1.03540			0.517699	−	0.855563i	$-0.326789\pi$
$509$	23.3596			1.03540			0.517699	+	0.855563i	$0.326789\pi$
$510$	21.1378	+	12.6191i	0.935996	+	0.558784i
$511$	7.53063			0.333135
$512$			1.00000i			0.0441942i
$513$		−	8.70024i		−	0.384125i
$514$	8.21781			0.362472
$515$	14.6017	+	8.71711i	0.643427	+	0.384122i
$516$	−24.9349			−1.09770
$517$			5.48979i			0.241441i
$518$		−	9.83991i		−	0.432341i
$519$	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	$0.846197\pi$
$522$			11.4898i			0.502894i
$523$			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
$525$	−6.82602	−	12.6635i	−0.297912	−	0.552679i
$526$	4.51021			0.196655
$527$			41.2295i			1.79598i
$528$		−	4.58480i		−	0.199528i
$529$	16.3188			0.709513
$530$	2.96270	−	4.96270i	0.128692	−	0.215566i
$531$	11.4898			0.498614
$532$		−	6.39478i		−	0.277249i
$533$		0			0
$534$	−11.6798			−0.505435
$535$	−8.80261	−	5.25511i	−0.380570	−	0.227198i
$536$	−8.58480			−0.370807
$537$			16.8026i			0.725086i
$538$			8.51021i			0.366901i
$539$	−10.8494			−0.467318
$540$	−3.27851	−	1.95725i	−0.141085	−	0.0842267i
$541$	−26.8772			−1.15554			−0.577771	−	0.816199i	$-0.696077\pi$
$541$	−26.8772			−1.15554			−0.577771	+	0.816199i	$0.696077\pi$
$542$		−	4.95180i		−	0.212698i
$543$			26.9458i			1.15636i
$544$	4.80261			0.205910
$545$	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	$-0.139860\pi$
$548$		−	14.5848i		−	0.623032i
$549$	−30.8494			−1.31662
$550$	−8.80261	+	4.74489i	−0.375345	+	0.202323i
$551$	25.9592			1.10590
$552$		−	5.92541i		−	0.252202i
$553$			18.9458i			0.805659i
$554$	19.8698			0.844189
$555$	20.5998	−	34.5058i	0.874412	−	1.46469i
$556$	7.32970			0.310848
$557$		−	1.50070i		−	0.0635865i	−0.999494	−	0.0317933i	$-0.989878\pi$
$557$		−	1.50070i		−	0.0635865i	0.999494	−	0.0317933i	$-0.0101218\pi$
$558$			19.3596i			0.819559i
$559$		0			0
$560$	−2.40974	−	1.43860i	−0.101830	−	0.0607920i
$561$	−22.0190			−0.929644
$562$		−	30.2646i		−	1.27664i
$563$		−	20.6872i		−	0.871861i	−0.899980	−	0.435930i	$-0.856419\pi$
$563$		−	20.6872i		−	0.871861i	0.899980	−	0.435930i	$-0.143581\pi$
$564$	−6.29240			−0.264958
$565$	7.67982	+	4.58480i	0.323092	+	0.192884i
$566$	−26.9240			−1.13170
$567$			13.4043i			0.562927i
$568$			5.38741i			0.226051i
$569$	6.08550			0.255117			0.127559	−	0.991831i	$-0.459286\pi$
$569$	6.08550			0.255117			0.127559	+	0.991831i	$0.459286\pi$
$570$	13.3874	−	22.4247i	0.560737	−	0.939268i
$571$	−9.98909			−0.418031			−0.209015	−	0.977912i	$-0.567026\pi$
$571$	−9.98909			−0.418031			−0.209015	+	0.977912i	$0.567026\pi$
$572$		0			0
$573$		−	3.67982i		−	0.153727i
$574$	12.1492			0.507097
$575$	−11.3765	+	6.13231i	−0.474433	+	0.255735i
$576$	2.25511			0.0939627
$577$		−	8.33921i		−	0.347166i	−0.984819	−	0.173583i	$-0.944466\pi$
$577$		−	8.33921i		−	0.347166i	0.984819	−	0.173583i	$-0.0555345\pi$
$578$		−	6.06508i		−	0.252274i
$579$	−36.1154			−1.50091
$580$	5.83991	−	9.78219i	0.242489	−	0.406183i
$581$	13.9254			0.577723
$582$		−	14.3610i		−	0.595284i
$583$			5.16961i			0.214103i
$584$	6.00000			0.248282
$585$		0			0
$586$	5.18051			0.214005
$587$		−	23.2442i		−	0.959391i	−0.877435	−	0.479695i	$-0.840747\pi$
$587$		−	23.2442i		−	0.959391i	0.877435	−	0.479695i	$-0.159253\pi$
$588$		−	12.4356i		−	0.512836i
$589$	43.7397			1.80226
$590$	−9.78219	−	5.83991i	−0.402726	−	0.240425i
$591$	2.31421			0.0951940
$592$		−	7.83991i		−	0.322218i
$593$			34.2646i			1.40708i	0.710656	+	0.703540i	$0.248398\pi$
$593$			34.2646i			1.40708i	−0.710656	+	0.703540i	$0.751602\pi$
$594$	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	$0.280106\pi$
$600$	−5.43860	−	10.0896i	−0.222030	−	0.411905i
$601$	−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
$603$			19.3596i			0.788385i
$604$	−14.5570			−0.592317
$605$	−8.02341	+	13.4397i	−0.326198	+	0.546401i
$606$	29.0204			1.17887
$607$			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
$609$	−14.6594			−0.594029
$610$	26.2646	+	15.6798i	1.06342	+	0.634857i
$611$		0			0
$612$		−	10.8304i		−	0.437793i
$613$		−	40.7193i		−	1.64464i	−0.569028	−	0.822318i	$-0.692681\pi$
$613$		−	40.7193i		−	1.64464i	0.569028	−	0.822318i	$-0.307319\pi$
$614$	0.320184			0.0129216
$615$	42.6038	+	25.4342i	1.71795	+	1.02561i
$616$	2.51021			0.101139
$617$			12.6594i			0.509648i	0.966987	+	0.254824i	$0.0820176\pi$
$617$			12.6594i			0.509648i	−0.966987	+	0.254824i	$0.917982\pi$
$618$		−	17.4342i		−	0.701307i
$619$	5.03945			0.202553			0.101276	−	0.994858i	$-0.467707\pi$
$619$	5.03945			0.202553			0.101276	+	0.994858i	$0.467707\pi$
$620$	9.83991	−	16.4824i	0.395180	−	0.661950i
$621$	4.41381			0.177120
$622$		−	9.86984i		−	0.395745i
$623$		−	6.39478i		−	0.256201i
$624$		0			0
$625$	−13.7430	+	20.8837i	−0.549719	+	0.835349i
$626$	−10.6126			−0.424164
$627$			23.3596i			0.932894i
$628$			13.0950i			0.522548i
$629$	−37.6520			−1.50128
$630$	−3.24420	+	5.43423i	−0.129252	+	0.216505i
$631$	1.00736			0.0401024			0.0200512	−	0.999799i	$-0.493617\pi$
$631$	1.00736			0.0401024			0.0200512	+	0.999799i	$0.493617\pi$
$632$			15.0950i			0.600447i
$633$			37.4810i			1.48974i
$634$	12.1900			0.484128
$635$	−2.71711	−	1.62210i	−0.107825	−	0.0643711i
$636$	−5.92541			−0.234958
$637$		0			0
$638$			10.1900i			0.403427i
$639$	12.1492			0.480614
$640$	−1.91995	−	1.14620i	−0.0758928	−	0.0453076i
$641$	−41.3596			−1.63361			−0.816804	−	0.576916i	$-0.804256\pi$
$641$	−41.3596			−1.63361			−0.816804	+	0.576916i	$0.804256\pi$
$642$			10.5102i			0.414805i
$643$			3.26601i			0.128799i	0.997924	+	0.0643994i	$0.0205132\pi$
$643$			3.26601i			0.128799i	−0.997924	+	0.0643994i	$0.979487\pi$
$644$	3.24420			0.127839
$645$	28.5804	−	47.8739i	1.12535	−	1.88503i
$646$	−24.4694			−0.962734
$647$		−	19.4342i		−	0.764038i	−0.924154	−	0.382019i	$-0.875229\pi$
$647$		−	19.4342i		−	0.764038i	0.924154	−	0.382019i	$-0.124771\pi$
$648$			10.6798i			0.419543i
$649$	10.1900			0.399994
$650$		0			0
$651$	−24.7002			−0.968079
$652$			12.2646i			0.480320i
$653$		−	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
$655$	12.6191	−	21.1378i	0.493070	−	0.825921i
$656$	9.67982			0.377933
$657$		−	13.5306i		−	0.527880i
$658$		−	3.44513i		−	0.134305i
$659$	−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
$661$	24.5292			0.954077			0.477038	−	0.878882i	$-0.341710\pi$
$661$	24.5292			0.954077			0.477038	+	0.878882i	$0.341710\pi$
$662$			17.9444i			0.697430i
$663$		0			0
$664$	11.0950			0.430570
$665$	12.2777	+	7.32970i	0.476108	+	0.284234i
$666$	−17.6798			−0.685079
$667$			13.1696i			0.509929i
$668$			18.3392i			0.709565i
$669$	−49.9385			−1.93073
$670$	9.83991	−	16.4824i	0.380149	−	0.636772i
$671$	−27.3596			−1.05621
$672$			2.87720i			0.110991i
$673$		−	8.95180i		−	0.345066i	−0.985004	−	0.172533i	$-0.944805\pi$
$673$		−	8.95180i		−	0.345066i	0.985004	−	0.172533i	$-0.0551952\pi$
$674$	20.9518			0.807033
$675$	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	$0.784302\pi$
$678$		−	9.16961i		−	0.352157i
$679$	7.86276			0.301745
$680$	−5.50476	+	9.22079i	−0.211098	+	0.353601i
$681$	20.6784			0.792399
$682$			17.1696i			0.657458i
$683$			11.0950i			0.424539i	0.977211	+	0.212269i	$0.0680854\pi$
$683$			11.0950i			0.424539i	−0.977211	+	0.212269i	$0.931915\pi$
$684$	−11.4898			−0.439323
$685$	28.0022	+	16.7171i	1.06991	+	0.638728i
$686$	15.5943			0.595394
$687$			10.7449i			0.409943i
$688$		−	10.8772i		−	0.414690i
$689$		0			0
$690$	11.3765	+	6.79171i	0.433096	+	0.258556i
$691$	13.5306			0.514729			0.257365	−	0.966314i	$-0.417146\pi$
$691$	13.5306			0.514729			0.257365	+	0.966314i	$0.417146\pi$
$692$			9.41520i			0.357912i
$693$		−	5.66079i		−	0.215036i
$694$	−3.51757			−0.133525
$695$	−8.40131	+	14.0727i	−0.318680	+	0.533807i
$696$	−11.6798			−0.442722
$697$		−	46.4884i		−	1.76087i
$698$			17.8568i			0.675889i
$699$	−31.0313			−1.17371
$700$	5.52410	−	2.97767i	0.208791	−	0.112545i
$701$	−48.1345			−1.81801			−0.909007	−	0.416781i	$-0.863158\pi$
$701$	−48.1345			−1.81801			−0.909007	+	0.416781i	$0.863158\pi$
$702$		0			0
$703$			39.9444i			1.50653i
$704$	2.00000			0.0753778
$705$	7.21236	−	12.0811i	0.271633	−	0.455001i
$706$	36.9240			1.38965
$707$			15.8889i			0.597563i
$708$			11.6798i			0.438954i
$709$	16.5292			0.620769			0.310384	−	0.950611i	$-0.399542\pi$
$709$	16.5292			0.620769			0.310384	+	0.950611i	$0.399542\pi$
$710$	−10.3436	−	6.17506i	−0.388188	−	0.231746i
$711$	34.0408			1.27663
$712$		−	5.09501i		−	0.190944i
$713$			22.1900i			0.831023i
$714$	13.8181			0.517129
$715$		0			0
$716$	−7.32970			−0.273924
$717$			7.32970i			0.273733i
$718$		−	6.77483i		−	0.252834i
$719$	6.39478			0.238485			0.119242	−	0.992865i	$-0.461953\pi$
$719$	6.39478			0.238485			0.119242	+	0.992865i	$0.461953\pi$
$720$	−2.58480	+	4.32970i	−0.0963299	+	0.161358i
$721$	9.54535			0.355488
$722$			6.95916i			0.258993i
$723$		−	32.3582i		−	1.20342i
$724$	−11.7544			−0.436849
$725$	12.0877	+	22.4247i	0.448924	+	0.832833i
$726$	16.0468			0.595553
$727$		−	35.0204i		−	1.29884i	−0.760432	−	0.649418i	$-0.775013\pi$
$727$		−	35.0204i		−	1.29884i	0.760432	−	0.649418i	$-0.224987\pi$
$728$		0			0
$729$	12.3406			0.457059
$730$	−6.87720	+	11.5197i	−0.254537	+	0.426364i
$731$	−52.2390			−1.93213
$732$		−	31.3596i		−	1.15909i
$733$			22.6485i			0.836541i	0.908322	+	0.418271i	$0.137364\pi$
$733$			22.6485i			0.836541i	−0.908322	+	0.418271i	$0.862636\pi$
$734$	7.80997			0.288271
$735$	23.8758	+	14.2537i	0.880673	+	0.525756i
$736$	2.58480			0.0952771
$737$			17.1696i			0.632451i
$738$		−	21.8290i		−	0.803537i
$739$	25.0394			0.921091			0.460546	−	0.887636i	$-0.347654\pi$
$739$	25.0394			0.921091			0.460546	+	0.887636i	$0.347654\pi$
$740$	15.0523	+	8.98611i	0.553332	+	0.330336i
$741$		0			0
$742$		−	3.24420i		−	0.119098i
$743$			35.8252i			1.31430i	0.753760	+	0.657149i	$0.228238\pi$
$743$			35.8252i			1.31430i	−0.753760	+	0.657149i	$0.771762\pi$
$744$	−19.6798			−0.721497
$745$		0			0
$746$	−15.8698			−0.581036
$747$		−	25.0204i		−	0.915449i
$748$		−	9.60522i		−	0.351202i
$749$	−5.75441			−0.210262
$750$	25.6052	+	1.12280i	0.934971	+	0.0409987i
$751$	41.6988			1.52161			0.760806	−	0.648979i	$-0.224804\pi$
$751$	41.6988			1.52161			0.760806	+	0.648979i	$0.224804\pi$
$752$		−	2.74489i		−	0.100096i
$753$		−	48.5292i		−	1.76850i
$754$		0			0
$755$	16.6853	−	27.9488i	0.607239	−	1.01716i
$756$	−2.14322			−0.0779480
$757$		−	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
$759$	−11.8508			−0.430157
$760$	9.78219	+	5.83991i	0.354837	+	0.211836i
$761$	−30.2646			−1.09709			−0.548546	−	0.836121i	$-0.684818\pi$
$761$	−30.2646			−1.09709			−0.548546	+	0.836121i	$0.684818\pi$
$762$			3.24420i			0.117525i
$763$		−	18.6725i		−	0.675988i
$764$	1.60522			0.0580749
$765$	20.7939	+	12.4138i	0.751804	+	0.448822i
$766$	16.6147			0.600315
$767$		0			0
$768$			2.29240i			0.0827199i
$769$	24.6594			0.889241			0.444620	−	0.895719i	$-0.353339\pi$
$769$	24.6594			0.889241			0.444620	+	0.895719i	$0.353339\pi$
$770$	−2.87720	+	4.81949i	−0.103687	+	0.173682i
$771$	18.8385			0.678453
$772$		−	15.7544i		−	0.567014i
$773$			30.3501i			1.09162i	0.837910	+	0.545809i	$0.183778\pi$
$773$			30.3501i			1.09162i	−0.837910	+	0.545809i	$0.816222\pi$
$774$	−24.5292			−0.881685
$775$	20.3670	+	37.7843i	0.731604	+	1.35725i
$776$	6.26462			0.224887
$777$		−	22.5570i		−	0.809229i
$778$		−	36.7193i		−	1.31645i
$779$	−49.3188			−1.76703
$780$		0			0
$781$	10.7748			0.385554
$782$		−	12.4138i		−	0.443917i
$783$		−	8.70024i		−	0.310921i
$784$	5.42471			0.193740
$785$	−25.1418	−	15.0095i	−0.897350	−	0.535713i
$786$	−25.2382			−0.900218
$787$		−	11.1288i		−	0.396698i	−0.980131	−	0.198349i	$-0.936442\pi$
$787$		−	11.1288i		−	0.396698i	0.980131	−	0.198349i	$-0.0635579\pi$
$788$			1.00951i			0.0359625i
$789$	10.3392			0.368086
$790$	−28.9817	−	17.3019i	−1.03112	−	0.615575i
$791$	5.02042			0.178506
$792$		−	4.51021i		−	0.160263i
$793$		0			0
$794$	29.2104			1.03664
$795$	6.79171	−	11.3765i	0.240877	−	0.403483i
$796$	0.435617			0.0154400
$797$			46.7939i			1.65752i	0.559602	+	0.828762i	$0.310954\pi$
$797$			46.7939i			1.65752i	−0.559602	+	0.828762i	$0.689046\pi$
$798$		−	14.6594i		−	0.518937i
$799$	−13.1827			−0.466369
$800$	4.40131	−	2.37245i	0.155610	−	0.0838787i
$801$	−11.4898			−0.405972
$802$		−	15.6052i		−	0.551040i
$803$		−	12.0000i		−	0.423471i
$804$	−19.6798			−0.694054
$805$	−3.71850	+	6.22871i	−0.131060	+	0.219533i
$806$		0			0
$807$			19.5088i			0.686743i
$808$			12.6594i			0.445356i
$809$	−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
$811$	36.3991			1.27814			0.639072	−	0.769147i	$-0.279318\pi$
$811$	36.3991			1.27814			0.639072	+	0.769147i	$0.279318\pi$
$812$		−	6.39478i		−	0.224413i
$813$		−	11.3515i		−	0.398115i
$814$	−15.6798			−0.549577
$815$	−23.5475	−	14.0577i	−0.824833	−	0.492420i
$816$	11.0095			0.385410
$817$			55.4195i			1.93888i
$818$			13.7952i			0.482340i
$819$		0			0
$820$	−11.0950	+	18.5848i	−0.387455	+	0.649009i
$821$	6.23684			0.217667			0.108834	−	0.994060i	$-0.465288\pi$
$821$	6.23684			0.217667			0.108834	+	0.994060i	$0.465288\pi$
$822$		−	33.4342i		−	1.16615i
$823$		−	33.7734i		−	1.17727i	−0.808400	−	0.588634i	$-0.799666\pi$
$823$		−	33.7734i		−	1.17727i	0.808400	−	0.588634i	$-0.200334\pi$
$824$	7.60522			0.264941
$825$	−20.1791	+	10.8772i	−0.702547	+	0.378696i
$826$	−6.39478			−0.222503
$827$		−	37.2295i		−	1.29460i	−0.762237	−	0.647298i	$-0.775899\pi$
$827$		−	37.2295i		−	1.29460i	0.762237	−	0.647298i	$-0.224101\pi$
$828$		−	5.82900i		−	0.202572i
$829$	38.2646			1.32899			0.664493	−	0.747295i	$-0.268648\pi$
$829$	38.2646			1.32899			0.664493	+	0.747295i	$0.268648\pi$
$830$	−12.7171	+	21.3019i	−0.441417	+	0.739400i
$831$	45.5497			1.58010
$832$		0			0
$833$		−	26.0528i		−	0.902675i
$834$	16.8026			0.581827
$835$	−35.2104	−	21.0204i	−1.21851	−	0.727442i
$836$	−10.1900			−0.352429
$837$		−	14.6594i		−	0.506703i
$838$			30.6893i			1.06015i
$839$	50.1345			1.73083			0.865417	−	0.501052i	$-0.167054\pi$
$839$	50.1345			1.73083			0.865417	+	0.501052i	$0.167054\pi$
$840$	−5.52410	−	3.29785i	−0.190600	−	0.113787i
$841$	−3.04084			−0.104857
$842$			16.9180i			0.583034i
$843$		−	69.3787i		−	2.38953i
$844$	−16.3501			−0.562794
$845$		0			0
$846$	−6.19003			−0.212817
$847$			8.78574i			0.301881i
$848$		−	2.58480i		−	0.0887625i
$849$	−61.7207			−2.11825
$850$	−11.3939	−	21.1378i	−0.390809	−	0.725019i
$851$	−20.2646			−0.694662
$852$			12.3501i			0.423108i
$853$		−	12.3910i		−	0.424258i	−0.977242	−	0.212129i	$-0.931960\pi$
$853$		−	12.3910i		−	0.424258i	0.977242	−	0.212129i	$-0.0680398\pi$
$854$	17.1696			0.587532
$855$	13.1696	−	22.0599i	0.450391	−	0.754432i
$856$	−4.58480			−0.156705
$857$		−	25.4005i		−	0.867664i	−0.900994	−	0.433832i	$-0.857161\pi$
$857$		−	25.4005i		−	0.867664i	0.900994	−	0.433832i	$-0.142839\pi$
$858$		0			0
$859$	50.1900			1.71246			0.856231	−	0.516593i	$-0.172800\pi$
$859$	50.1900			1.71246			0.856231	+	0.516593i	$0.172800\pi$
$860$	20.8837	+	12.4675i	0.712129	+	0.425137i
$861$	27.8508			0.949153
$862$			17.9722i			0.612136i
$863$		−	43.4451i		−	1.47889i	−0.673217	−	0.739445i	$-0.735088\pi$
$863$		−	43.4451i		−	1.47889i	0.673217	−	0.739445i	$-0.264912\pi$
$864$	−1.70760			−0.0580937
$865$	−18.0767	−	10.7917i	−0.614628	−	0.366929i
$866$	2.61259			0.0887793
$867$		−	13.9036i		−	0.472191i
$868$		−	10.7748i		−	0.365722i
$869$	30.1900			1.02413
$870$	13.3874	−	22.4247i	0.453876	−	0.760269i
$871$		0			0
$872$		−	14.8772i		−	0.503806i
$873$		−	14.1274i		−	0.478139i
$874$	−13.1696			−0.445469
$875$	−0.614738	+	14.0190i	−0.0207819	+	0.473930i
$876$	13.7544			0.464718
$877$			11.6689i			0.394031i	0.980400	+	0.197016i	$0.0631250\pi$
$877$			11.6689i			0.394031i	−0.980400	+	0.197016i	$0.936875\pi$
$878$		−	14.6594i		−	0.494731i
$879$	11.8758			0.400561
$880$	−2.29240	+	3.83991i	−0.0772768	+	0.129443i
$881$	−0.0446585			−0.00150458			−0.000752291	−	1.00000i	$-0.500239\pi$
$881$	−0.0446585			−0.00150458			−0.000752291		1.00000i	$0.500239\pi$
$882$		−	12.2333i		−	0.411916i
$883$		−	24.4269i		−	0.822029i	−0.911629	−	0.411015i	$-0.865174\pi$
$883$		−	24.4269i		−	0.822029i	0.911629	−	0.411015i	$-0.134826\pi$
$884$		0			0
$885$	−22.4247	−	13.3874i	−0.753798	−	0.450013i
$886$	8.33324			0.279961
$887$			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
$889$	−1.77622			−0.0595725
$890$	9.78219	+	5.83991i	0.327900	+	0.195754i
$891$	21.3596			0.715575
$892$		−	21.7843i		−	0.729394i
$893$			13.9853i			0.467999i
$894$		0			0
$895$	8.40131	−	14.0727i	0.280825	−	0.470398i
$896$	−1.25511			−0.0419301
$897$		0			0
$898$		−	4.04084i		−	0.134845i
$899$	43.7397			1.45880
$900$	−5.35012	−	9.92541i	−0.178337	−	0.330847i
$901$	−12.4138			−0.413564
$902$		−	19.3596i		−	0.644605i
$903$		−	31.2959i		−	1.04146i
$904$	4.00000			0.133038
$905$	13.4729	−	22.5679i	0.447855	−	0.750183i
$906$	−33.3705			−1.10866
$907$			44.7133i			1.48468i	0.670023	+	0.742340i	$0.266284\pi$
$907$			44.7133i			1.48468i	−0.670023	+	0.742340i	$0.733716\pi$
$908$			9.02042i			0.299353i
$909$	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	$0.170153\pi$
$912$		−	11.6798i		−	0.386757i
$913$		−	22.1900i		−	0.734383i
$914$	−0.979580			−0.0324016
$915$	60.2091	+	35.9444i	1.99045	+	1.18829i
$916$	−4.68718			−0.154869
$917$		−	13.8181i		−	0.456314i
$918$			8.20093i			0.270671i
$919$	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
$921$	0.733989			0.0241858
$922$		−	10.7280i		−	0.353308i
$923$		0			0
$924$	5.75441			0.189306
$925$	−34.5058	+	18.5998i	−1.13454	+	0.611557i
$926$	−23.2104			−0.762743
$927$		−	17.1506i		−	0.563299i
$928$		−	5.09501i		−	0.167252i
$929$	−44.1682			−1.44911			−0.724556	−	0.689216i	$-0.757955\pi$
$929$	−44.1682			−1.44911			−0.724556	+	0.689216i	$0.757955\pi$
$930$	22.5570	−	37.7843i	0.739674	−	1.23900i
$931$	−27.6390			−0.905831
$932$		−	13.5366i		−	0.443406i
$933$		−	22.6256i		−	0.740730i
$934$	−28.5848			−0.935323
$935$	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	$0.761493\pi$
$938$		−	10.7748i		−	0.351811i
$939$	−24.3283			−0.793924
$940$	5.27007	+	3.14620i	0.171891	+	0.102618i
$941$	−37.4473			−1.22075			−0.610373	−	0.792114i	$-0.708981\pi$
$941$	−37.4473			−1.22075			−0.610373	+	0.792114i	$0.708981\pi$
$942$			30.0190i			0.978073i
$943$		−	25.0204i		−	0.814777i
$944$	−5.09501			−0.165829
$945$	2.45656	−	4.11488i	0.0799117	−	0.133857i
$946$	−21.7544			−0.707297
$947$		−	11.5644i		−	0.375792i	−0.982189	−	0.187896i	$-0.939833\pi$
$947$		−	11.5644i		−	0.375792i	0.982189	−	0.187896i	$-0.0601668\pi$
$948$			34.6038i			1.12388i
$949$		0			0
$950$	−22.4247	+	12.0877i	−0.727554	+	0.392175i
$951$	27.9444			0.906160
$952$			6.02778i			0.195362i
$953$			53.4810i			1.73242i	0.499680	+	0.866210i	$0.333451\pi$
$953$			53.4810i			1.73242i	−0.499680	+	0.866210i	$0.666549\pi$
$954$	−5.82900			−0.188721
$955$	−1.83991	+	3.08196i	−0.0595380	+	0.0997297i
$956$	−3.19739			−0.103411
$957$			23.3596i			0.755110i
$958$		−	30.4078i		−	0.982433i
$959$	18.3055			0.591114
$960$	−4.40131	−	2.62755i	−0.142052	−	0.0848039i
$961$	42.6988			1.37738
$962$		0			0
$963$			10.3392i			0.333176i
$964$	14.1154			0.454627
$965$	30.2477	+	18.0577i	0.973709	+	0.581298i
$966$	7.43701			0.239282
$967$			34.8941i			1.12212i	0.827776	+	0.561059i	$0.189606\pi$
$967$			34.8941i			1.12212i	−0.827776	+	0.561059i	$0.810394\pi$
$968$			7.00000i			0.224989i
$969$	−56.0936			−1.80199
$970$	−7.18051	+	12.0278i	−0.230552	+	0.386189i
$971$	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
$973$			9.19954i			0.294924i
$974$	−8.00000			−0.256337
$975$		0			0
$976$	13.6798			0.437880
$977$			2.03375i			0.0650655i	0.999471	+	0.0325328i	$0.0103573\pi$
$977$			2.03375i			0.0650655i	−0.999471	+	0.0325328i	$0.989643\pi$
$978$			28.1154i			0.899032i
$979$	−10.1900			−0.325675
$980$	−6.21781	+	10.4152i	−0.198621	+	0.332701i
$981$	−33.5497			−1.07116
$982$			22.6893i			0.724046i
$983$		−	29.4043i		−	0.937851i	−0.883238	−	0.468926i	$-0.844641\pi$
$983$		−	29.4043i		−	0.937851i	0.883238	−	0.468926i	$-0.155359\pi$
$984$	22.1900			0.707392
$985$	−1.93822	−	1.15711i	−0.0617569	−	0.0368685i
$986$	−24.4694			−0.779263
$987$		−	7.89762i		−	0.251384i
$988$		0			0
$989$	−28.1154			−0.894019
$990$	8.65940	+	5.16961i	0.275214	+	0.164301i
$991$	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
$993$			41.1359i			1.30541i
$994$	−6.76177			−0.214470
$995$	−0.499304	+	0.836365i	−0.0158290	+	0.0265145i
$996$	25.4342			0.805914
$997$		−	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
$999$	13.3874			0.423559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1690.2.b.a.339.6		6
5.2	odd	4		8450.2.a.bs.1.3		3
5.3	odd	4		8450.2.a.cc.1.1		3
5.4	even	2	inner	1690.2.b.a.339.1		6
13.5	odd	4		1690.2.c.d.1689.5		6
13.8	odd	4		1690.2.c.a.1689.5		6
13.12	even	2		130.2.b.a.79.3	✓	6
39.38	odd	2		1170.2.e.f.469.6		6
52.51	odd	2		1040.2.d.b.209.2		6
65.12	odd	4		650.2.a.o.1.3		3
65.34	odd	4		1690.2.c.d.1689.2		6
65.38	odd	4		650.2.a.n.1.1		3
65.44	odd	4		1690.2.c.a.1689.2		6
65.64	even	2		130.2.b.a.79.4	yes	6
195.38	even	4		5850.2.a.cs.1.2		3
195.77	even	4		5850.2.a.cp.1.2		3
195.194	odd	2		1170.2.e.f.469.3		6
260.103	even	4		5200.2.a.ce.1.3		3
260.207	even	4		5200.2.a.cf.1.1		3
260.259	odd	2		1040.2.d.b.209.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.b.a.79.3	✓	6	13.12	even	2
130.2.b.a.79.4	yes	6	65.64	even	2
650.2.a.n.1.1		3	65.38	odd	4
650.2.a.o.1.3		3	65.12	odd	4
1040.2.d.b.209.2		6	52.51	odd	2
1040.2.d.b.209.5		6	260.259	odd	2
1170.2.e.f.469.3		6	195.194	odd	2
1170.2.e.f.469.6		6	39.38	odd	2
1690.2.b.a.339.1		6	5.4	even	2	inner
1690.2.b.a.339.6		6	1.1	even	1	trivial
1690.2.c.a.1689.2		6	65.44	odd	4
1690.2.c.a.1689.5		6	13.8	odd	4
1690.2.c.d.1689.2		6	65.34	odd	4
1690.2.c.d.1689.5		6	13.5	odd	4
5200.2.a.ce.1.3		3	260.103	even	4
5200.2.a.cf.1.1		3	260.207	even	4
5850.2.a.cp.1.2		3	195.77	even	4
5850.2.a.cs.1.2		3	195.38	even	4
8450.2.a.bs.1.3		3	5.2	odd	4
8450.2.a.cc.1.1		3	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1690 = 2 \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1690.b (of order \(2\), degree \(1\), minimal)

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

Modular forms

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Database

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