LMFDB - Embedded newform 110.3.c.b.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,3,Mod(109,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.109"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	110.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.99728290796$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.130897030168576.7
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 18x^{6} + 169x^{4} - 112x^{2} + 1936 $ x^8 + 18x^6 + 169x^4 - 112*x^2 + 1936
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			109.1
Root			$-1.41421 - 3.43731i$ of defining polynomial
Character	$\chi$	$=$	110.109
Dual form			110.3.c.b.109.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421 q^{2} -3.43731i q^{3} +2.00000 q^{4} +(-3.90754 - 3.11948i) q^{5} +4.86108i q^{6} -2.82843 q^{7} -2.82843 q^{8} -2.81507 q^{9} +(5.52609 + 4.41161i) q^{10} +(-7.81507 + 7.74110i) q^{11} -6.87461i q^{12} -3.98111 q^{13} +4.00000 q^{14} +(-10.7226 + 13.4314i) q^{15} +4.00000 q^{16} -23.2571 q^{17} +3.98111 q^{18} -33.1286i q^{19} +(-7.81507 - 6.23896i) q^{20} +9.72217i q^{21} +(11.0522 - 10.9476i) q^{22} -2.16600i q^{23} +9.72217i q^{24} +(5.53768 + 24.3790i) q^{25} +5.63015 q^{26} -21.2595i q^{27} -5.65685 q^{28} -11.5201i q^{29} +(15.1641 - 18.9949i) q^{30} +36.7055 q^{31} -5.65685 q^{32} +(26.6085 + 26.8628i) q^{33} +32.8904 q^{34} +(11.0522 + 8.82322i) q^{35} -5.63015 q^{36} +17.4456i q^{37} +46.8510i q^{38} +13.6843i q^{39} +(11.0522 + 8.82322i) q^{40} -45.0151i q^{41} -13.7492i q^{42} +63.4847 q^{43} +(-15.6301 + 15.4822i) q^{44} +(11.0000 + 8.78157i) q^{45} +3.06319i q^{46} -46.5919i q^{47} -13.7492i q^{48} -41.0000 q^{49} +(-7.83147 - 34.4771i) q^{50} +79.9416i q^{51} -7.96223 q^{52} -11.2066i q^{53} +30.0655i q^{54} +(54.6859 - 5.86966i) q^{55} +8.00000 q^{56} -113.873 q^{57} +16.2918i q^{58} -44.7055 q^{59} +(-21.4452 + 26.8628i) q^{60} -38.8887i q^{61} -51.9094 q^{62} +7.96223 q^{63} +8.00000 q^{64} +(15.5563 + 12.4190i) q^{65} +(-37.6301 - 37.9897i) q^{66} -91.5360i q^{67} -46.5141 q^{68} -7.44522 q^{69} +(-15.6301 - 12.4779i) q^{70} +54.5548 q^{71} +7.96223 q^{72} -56.1521 q^{73} -24.6718i q^{74} +(83.7980 - 19.0347i) q^{75} -66.2573i q^{76} +(22.1044 - 21.8951i) q^{77} -19.3525i q^{78} +101.917i q^{79} +(-15.6301 - 12.4779i) q^{80} -98.4110 q^{81} +63.6609i q^{82} -15.7113 q^{83} +19.4443i q^{84} +(90.8778 + 72.5499i) q^{85} -89.7809 q^{86} -39.5980 q^{87} +(22.1044 - 21.8951i) q^{88} -28.7055 q^{89} +(-15.5563 - 12.4190i) q^{90} +11.2603 q^{91} -4.33201i q^{92} -126.168i q^{93} +65.8909i q^{94} +(-103.344 + 129.451i) q^{95} +19.4443i q^{96} +76.2564i q^{97} +57.9828 q^{98} +(22.0000 - 21.7918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 16 q^{4} - 10 q^{5} + 20 q^{9} - 20 q^{11} + 32 q^{14} - 22 q^{15} + 32 q^{16} - 20 q^{20} - 62 q^{25} - 40 q^{26} - 4 q^{31} + 8 q^{34} + 40 q^{36} - 40 q^{44} + 88 q^{45} - 328 q^{49} + 138 q^{55}+ \cdots + 176 q^{99}+O(q^{100}) $ 8 * q + 16 * q^4 - 10 * q^5 + 20 * q^9 - 20 * q^11 + 32 * q^14 - 22 * q^15 + 32 * q^16 - 20 * q^20 - 62 * q^25 - 40 * q^26 - 4 * q^31 + 8 * q^34 + 40 * q^36 - 40 * q^44 + 88 * q^45 - 328 * q^49 + 138 * q^55 + 64 * q^56 - 60 * q^59 - 44 * q^60 + 64 * q^64 - 216 * q^66 + 68 * q^69 - 40 * q^70 + 564 * q^71 + 394 * q^75 - 40 * q^80 - 192 * q^81 - 208 * q^86 + 68 * q^89 - 80 * q^91 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$		−	3.43731i		−	1.14577i	−0.819636	−	0.572884i	$-0.805824\pi$
$3$		−	3.43731i		−	1.14577i	0.819636	−	0.572884i	$-0.194176\pi$
$4$	2.00000			0.500000
$5$	−3.90754	−	3.11948i	−0.781507	−	0.623896i
$5$	−3.90754	−	3.11948i	−0.781507	−	0.623896i
$6$			4.86108i			0.810181i
$7$	−2.82843			−0.404061			−0.202031	−	0.979379i	$-0.564754\pi$
$7$	−2.82843			−0.404061			−0.202031	+	0.979379i	$0.564754\pi$
$8$	−2.82843			−0.353553
$9$	−2.81507			−0.312786
$10$	5.52609	+	4.41161i	0.552609	+	0.441161i
$11$	−7.81507	+	7.74110i	−0.710461	+	0.703736i
$11$	−7.81507	+	7.74110i	−0.710461	+	0.703736i
$12$		−	6.87461i		−	0.572884i
$13$	−3.98111			−0.306240			−0.153120	−	0.988208i	$-0.548932\pi$
$13$	−3.98111			−0.306240			−0.153120	+	0.988208i	$0.548932\pi$
$14$	4.00000			0.285714
$15$	−10.7226	+	13.4314i	−0.714841	+	0.895427i
$16$	4.00000			0.250000
$17$	−23.2571			−1.36806			−0.684031	−	0.729453i	$-0.739775\pi$
$17$	−23.2571			−1.36806			−0.684031	+	0.729453i	$0.739775\pi$
$18$	3.98111			0.221173
$19$		−	33.1286i		−	1.74361i	−0.489850	−	0.871807i	$-0.662949\pi$
$19$		−	33.1286i		−	1.74361i	0.489850	−	0.871807i	$-0.337051\pi$
$20$	−7.81507	−	6.23896i	−0.390754	−	0.311948i
$21$			9.72217i			0.462960i
$22$	11.0522	−	10.9476i	0.502372	−	0.497617i
$23$		−	2.16600i		−	0.0941741i	−0.998891	−	0.0470870i	$-0.985006\pi$
$23$		−	2.16600i		−	0.0941741i	0.998891	−	0.0470870i	$-0.0149938\pi$
$24$			9.72217i			0.405090i
$25$	5.53768	+	24.3790i	0.221507	+	0.975159i
$26$	5.63015			0.216544
$27$		−	21.2595i		−	0.787388i
$28$	−5.65685			−0.202031
$29$		−	11.5201i		−	0.397244i	−0.980076	−	0.198622i	$-0.936353\pi$
$29$		−	11.5201i		−	0.397244i	0.980076	−	0.198622i	$-0.0636465\pi$
$30$	15.1641	−	18.9949i	0.505469	−	0.633162i
$31$	36.7055			1.18405			0.592024	−	0.805920i	$-0.298329\pi$
$31$	36.7055			1.18405			0.592024	+	0.805920i	$0.298329\pi$
$32$	−5.65685			−0.176777
$33$	26.6085	+	26.8628i	0.806319	+	0.814024i
$34$	32.8904			0.967366
$35$	11.0522	+	8.82322i	0.315777	+	0.252092i
$36$	−5.63015			−0.156393
$37$			17.4456i			0.471502i	0.971813	+	0.235751i	$0.0757550\pi$
$37$			17.4456i			0.471502i	−0.971813	+	0.235751i	$0.924245\pi$
$38$			46.8510i			1.23292i
$39$			13.6843i			0.350880i
$40$	11.0522	+	8.82322i	0.276305	+	0.220581i
$41$		−	45.0151i		−	1.09793i	−0.835846	−	0.548964i	$-0.815022\pi$
$41$		−	45.0151i		−	1.09793i	0.835846	−	0.548964i	$-0.184978\pi$
$42$		−	13.7492i		−	0.327362i
$43$	63.4847			1.47639			0.738194	−	0.674589i	$-0.235679\pi$
$43$	63.4847			1.47639			0.738194	+	0.674589i	$0.235679\pi$
$44$	−15.6301	+	15.4822i	−0.355231	+	0.351868i
$45$	11.0000	+	8.78157i	0.244444	+	0.195146i
$46$			3.06319i			0.0665911i
$47$		−	46.5919i		−	0.991318i	−0.868517	−	0.495659i	$-0.834927\pi$
$47$		−	46.5919i		−	0.991318i	0.868517	−	0.495659i	$-0.165073\pi$
$48$		−	13.7492i		−	0.286442i
$49$	−41.0000			−0.836735
$50$	−7.83147	−	34.4771i	−0.156629	−	0.689541i
$51$			79.9416i			1.56748i
$52$	−7.96223			−0.153120
$53$		−	11.2066i		−	0.211446i	−0.994396	−	0.105723i	$-0.966284\pi$
$53$		−	11.2066i		−	0.211446i	0.994396	−	0.105723i	$-0.0337156\pi$
$54$			30.0655i			0.556768i
$55$	54.6859	−	5.86966i	0.994289	−	0.106721i
$56$	8.00000			0.142857
$57$	−113.873			−1.99778
$58$			16.2918i			0.280894i
$59$	−44.7055			−0.757721			−0.378860	−	0.925454i	$-0.623684\pi$
$59$	−44.7055			−0.757721			−0.378860	+	0.925454i	$0.623684\pi$
$60$	−21.4452	+	26.8628i	−0.357420	+	0.447713i
$61$		−	38.8887i		−	0.637519i	−0.947836	−	0.318760i	$-0.896734\pi$
$61$		−	38.8887i		−	0.637519i	0.947836	−	0.318760i	$-0.103266\pi$
$62$	−51.9094			−0.837249
$63$	7.96223			0.126385
$64$	8.00000			0.125000
$65$	15.5563	+	12.4190i	0.239328	+	0.191062i
$66$	−37.6301	−	37.9897i	−0.570154	−	0.575602i
$67$		−	91.5360i		−	1.36621i	−0.730321	−	0.683104i	$-0.760629\pi$
$67$		−	91.5360i		−	1.36621i	0.730321	−	0.683104i	$-0.239371\pi$
$68$	−46.5141			−0.684031
$69$	−7.44522			−0.107902
$70$	−15.6301	−	12.4779i	−0.223288	−	0.178256i
$71$	54.5548			0.768377			0.384189	−	0.923255i	$-0.374481\pi$
$71$	54.5548			0.768377			0.384189	+	0.923255i	$0.374481\pi$
$72$	7.96223			0.110587
$73$	−56.1521			−0.769206			−0.384603	−	0.923082i	$-0.625662\pi$
$73$	−56.1521			−0.769206			−0.384603	+	0.923082i	$0.625662\pi$
$74$		−	24.6718i		−	0.333402i
$75$	83.7980	−	19.0347i	1.11731	−	0.253796i
$76$		−	66.2573i		−	0.871807i
$77$	22.1044	−	21.8951i	0.287070	−	0.284352i
$78$		−	19.3525i		−	0.248109i
$79$			101.917i			1.29008i	0.764148	+	0.645041i	$0.223160\pi$
$79$			101.917i			1.29008i	−0.764148	+	0.645041i	$0.776840\pi$
$80$	−15.6301	−	12.4779i	−0.195377	−	0.155974i
$81$	−98.4110			−1.21495
$82$			63.6609i			0.776353i
$83$	−15.7113			−0.189293			−0.0946463	−	0.995511i	$-0.530172\pi$
$83$	−15.7113			−0.189293			−0.0946463	+	0.995511i	$0.530172\pi$
$84$			19.4443i			0.231480i
$85$	90.8778	+	72.5499i	1.06915	+	0.853528i
$86$	−89.7809			−1.04396
$87$	−39.5980			−0.455149
$88$	22.1044	−	21.8951i	0.251186	−	0.248808i
$89$	−28.7055			−0.322534			−0.161267	−	0.986911i	$-0.551558\pi$
$89$	−28.7055			−0.322534			−0.161267	+	0.986911i	$0.551558\pi$
$90$	−15.5563	−	12.4190i	−0.172848	−	0.137989i
$91$	11.2603			0.123739
$92$		−	4.33201i		−	0.0470870i
$93$		−	126.168i		−	1.35665i
$94$			65.8909i			0.700967i
$95$	−103.344	+	129.451i	−1.08783	+	1.36265i
$96$			19.4443i			0.202545i
$97$			76.2564i			0.786148i	0.919507	+	0.393074i	$0.128588\pi$
$97$			76.2564i			0.786148i	−0.919507	+	0.393074i	$0.871412\pi$
$98$	57.9828			0.591661
$99$	22.0000	−	21.7918i	0.222222	−	0.220119i
$100$	11.0754	+	48.7579i	0.110754	+	0.487579i
$101$			76.7122i			0.759526i	0.925084	+	0.379763i	$0.123995\pi$
$101$			76.7122i			0.759526i	−0.925084	+	0.379763i	$0.876005\pi$
$102$		−	113.054i		−	1.10838i
$103$			113.314i			1.10013i	0.835121	+	0.550066i	$0.185397\pi$
$103$			113.314i			1.10013i	−0.835121	+	0.550066i	$0.814603\pi$
$104$	11.2603			0.108272
$105$	30.3281	−	37.9897i	0.288839	−	0.361807i
$106$			15.8486i			0.149515i
$107$	157.036			1.46763			0.733813	−	0.679352i	$-0.237739\pi$
$107$	157.036			1.46763			0.733813	+	0.679352i	$0.237739\pi$
$108$		−	42.5190i		−	0.393694i
$109$		−	171.403i		−	1.57251i	−0.617904	−	0.786254i	$-0.712018\pi$
$109$		−	171.403i		−	1.57251i	0.617904	−	0.786254i	$-0.287982\pi$
$110$	−77.3375	+	8.30096i	−0.703068	+	0.0754633i
$111$	59.9658			0.540232
$112$	−11.3137			−0.101015
$113$			83.6491i			0.740258i	0.928980	+	0.370129i	$0.120686\pi$
$113$			83.6491i			0.740258i	−0.928980	+	0.370129i	$0.879314\pi$
$114$	161.041			1.41264
$115$	−6.75681	+	8.46374i	−0.0587548	+	0.0735977i
$116$		−	23.0401i		−	0.198622i
$117$	11.2071			0.0957874
$118$	63.2231			0.535789
$119$	65.7809			0.552780
$120$	30.3281	−	37.9897i	0.252734	−	0.316581i
$121$	1.15073	−	120.995i	0.00951016	−	0.999955i
$122$			54.9969i			0.450794i
$123$	−154.731			−1.25797
$124$	73.4110			0.592024
$125$	54.4110	−	112.536i	0.435288	−	0.900291i
$126$	−11.2603			−0.0893674
$127$	132.936			1.04674			0.523370	−	0.852105i	$-0.324674\pi$
$127$	132.936			1.04674			0.523370	+	0.852105i	$0.324674\pi$
$128$	−11.3137			−0.0883883
$129$		−	218.216i		−	1.69160i
$130$	−22.0000	−	17.5631i	−0.169231	−	0.135101i
$131$		−	49.3436i		−	0.376668i	−0.982105	−	0.188334i	$-0.939691\pi$
$131$		−	49.3436i		−	0.376668i	0.982105	−	0.188334i	$-0.0603088\pi$
$132$	53.2171	+	53.7256i	0.403160	+	0.407012i
$133$			93.7020i			0.704526i
$134$			129.451i			0.966055i
$135$	−66.3186	+	83.0722i	−0.491249	+	0.615350i
$136$	65.7809			0.483683
$137$		−	22.2957i		−	0.162742i	−0.996684	−	0.0813711i	$-0.974070\pi$
$137$		−	22.2957i		−	0.162742i	0.996684	−	0.0813711i	$-0.0259299\pi$
$138$	10.5291			0.0762980
$139$		−	261.766i		−	1.88321i	−0.336723	−	0.941604i	$-0.609318\pi$
$139$		−	261.766i		−	1.88321i	0.336723	−	0.941604i	$-0.390682\pi$
$140$	22.1044	+	17.6464i	0.157888	+	0.126046i
$141$	−160.151			−1.13582
$142$	−77.1521			−0.543325
$143$	31.1127	−	30.8182i	0.217571	−	0.215512i
$144$	−11.2603			−0.0781965
$145$	−35.9366	+	45.0151i	−0.247839	+	0.310449i
$146$	79.4110			0.543911
$147$			140.930i			0.958704i
$148$			34.8912i			0.235751i
$149$			266.827i			1.79079i	0.445277	+	0.895393i	$0.353105\pi$
$149$			266.827i			1.79079i	−0.445277	+	0.895393i	$0.646895\pi$
$150$	−118.508	+	26.9191i	−0.790055	+	0.179461i
$151$			123.858i			0.820249i	0.912030	+	0.410125i	$0.134515\pi$
$151$			123.858i			0.820249i	−0.912030	+	0.410125i	$0.865485\pi$
$152$			93.7020i			0.616460i
$153$	65.4703			0.427910
$154$	−31.2603	+	30.9644i	−0.202989	+	0.201068i
$155$	−143.428	−	114.502i	−0.925343	−	0.738723i
$156$			27.3686i			0.175440i
$157$			224.955i			1.43284i	0.697671	+	0.716418i	$0.254220\pi$
$157$			224.955i			1.43284i	−0.697671	+	0.716418i	$0.745780\pi$
$158$		−	144.132i		−	0.912226i
$159$	−38.5206			−0.242268
$160$	22.1044	+	17.6464i	0.138152	+	0.110290i
$161$			6.12638i			0.0380521i
$162$	139.174			0.859100
$163$		−	62.8838i		−	0.385790i	−0.981219	−	0.192895i	$-0.938212\pi$
$163$		−	62.8838i		−	0.385790i	0.981219	−	0.192895i	$-0.0617877\pi$
$164$		−	90.0301i		−	0.548964i
$165$	−20.1758	−	187.972i	−0.122278	−	1.13923i
$166$	22.2191			0.133850
$167$	−104.652			−0.626658			−0.313329	−	0.949645i	$-0.601444\pi$
$167$	−104.652			−0.626658			−0.313329	+	0.949645i	$0.601444\pi$
$168$		−	27.4984i		−	0.163681i
$169$	−153.151			−0.906217
$170$	−128.521	−	102.601i	−0.756003	−	0.603536i
$171$			93.2596i			0.545378i
$172$	126.969			0.738194
$173$	109.059			0.630400			0.315200	−	0.949025i	$-0.397928\pi$
$173$	109.059			0.630400			0.315200	+	0.949025i	$0.397928\pi$
$174$	56.0000			0.321839
$175$	−15.6629	−	68.9541i	−0.0895025	−	0.394024i
$176$	−31.2603	+	30.9644i	−0.177615	+	0.175934i
$177$			153.667i			0.868172i
$178$	40.5957			0.228066
$179$	−98.1165			−0.548137			−0.274069	−	0.961710i	$-0.588370\pi$
$179$	−98.1165			−0.548137			−0.274069	+	0.961710i	$0.588370\pi$
$180$	22.0000	+	17.5631i	0.122222	+	0.0975729i
$181$	357.377			1.97446			0.987229	−	0.159309i	$-0.0509266\pi$
$181$	357.377			1.97446			0.987229	+	0.159309i	$0.0509266\pi$
$182$	−15.9245			−0.0874970
$183$	−133.672			−0.730450
$184$			6.12638i			0.0332956i
$185$	54.4212	−	68.1692i	0.294168	−	0.368482i
$186$			178.429i			0.959294i
$187$	181.756	−	180.035i	0.971955	−	0.962755i
$188$		−	93.1839i		−	0.495659i
$189$			60.1309i			0.318153i
$190$	146.151	−	183.072i	0.769214	−	0.963536i
$191$	164.706			0.862333			0.431166	−	0.902272i	$-0.358102\pi$
$191$	164.706			0.862333			0.431166	+	0.902272i	$0.358102\pi$
$192$		−	27.4984i		−	0.143221i
$193$	−312.919			−1.62134			−0.810671	−	0.585501i	$-0.800898\pi$
$193$	−312.919			−1.62134			−0.810671	+	0.585501i	$0.800898\pi$
$194$		−	107.843i		−	0.555891i
$195$	42.6879	−	53.4719i	0.218912	−	0.274215i
$196$	−82.0000			−0.418367
$197$	−126.436			−0.641809			−0.320905	−	0.947112i	$-0.603987\pi$
$197$	−126.436			−0.641809			−0.320905	+	0.947112i	$0.603987\pi$
$198$	−31.1127	+	30.8182i	−0.157135	+	0.155648i
$199$	−197.411			−0.992015			−0.496008	−	0.868318i	$-0.665201\pi$
$199$	−197.411			−0.992015			−0.496008	+	0.868318i	$0.665201\pi$
$200$	−15.6629	−	68.9541i	−0.0783147	−	0.344771i
$201$	−314.637			−1.56536
$202$		−	108.487i		−	0.537066i
$203$			32.5837i			0.160511i
$204$			159.883i			0.783741i
$205$	−140.424	+	175.898i	−0.684993	+	0.858039i
$206$		−	160.250i		−	0.777910i
$207$			6.09746i			0.0294563i
$208$	−15.9245			−0.0765599
$209$	256.452	+	258.903i	1.22704	+	1.23877i
$210$	−42.8904	+	53.7256i	−0.204240	+	0.255836i
$211$			46.0802i			0.218390i	0.994020	+	0.109195i	$0.0348273\pi$
$211$			46.0802i			0.218390i	−0.994020	+	0.109195i	$0.965173\pi$
$212$		−	22.4132i		−	0.105723i
$213$		−	187.521i		−	0.880383i
$214$	−222.082			−1.03777
$215$	−248.069	−	198.039i	−1.15381	−	0.921112i
$216$			60.1309i			0.278384i
$217$	−103.819			−0.478428
$218$			242.401i			1.11193i
$219$			193.012i			0.881333i
$220$	109.372	−	11.7393i	0.497144	−	0.0533606i
$221$	92.5890			0.418955
$222$	−84.8045			−0.382002
$223$		−	392.748i		−	1.76120i	−0.473860	−	0.880600i	$-0.657140\pi$
$223$		−	392.748i		−	1.76120i	0.473860	−	0.880600i	$-0.342860\pi$
$224$	16.0000			0.0714286
$225$	−15.5890	−	68.6286i	−0.0692844	−	0.305016i
$226$		−	118.298i		−	0.523441i
$227$	268.701			1.18370			0.591851	−	0.806047i	$-0.298397\pi$
$227$	268.701			1.18370			0.591851	+	0.806047i	$0.298397\pi$
$228$	−227.747			−0.998889
$229$	−205.528			−0.897500			−0.448750	−	0.893657i	$-0.648131\pi$
$229$	−205.528			−0.897500			−0.448750	+	0.893657i	$0.648131\pi$
$230$	9.55557	−	11.9695i	0.0415460	−	0.0520415i
$231$	−75.2603	−	75.9795i	−0.325802	−	0.328915i
$232$			32.5837i			0.140447i
$233$	303.698			1.30342			0.651712	−	0.758467i	$-0.274051\pi$
$233$	303.698			1.30342			0.651712	+	0.758467i	$0.274051\pi$
$234$	−15.8493			−0.0677319
$235$	−145.343	+	182.060i	−0.618479	+	0.774722i
$236$	−89.4110			−0.378860
$237$	350.318			1.47814
$238$	−93.0282			−0.390875
$239$		−	186.885i		−	0.781948i	−0.920402	−	0.390974i	$-0.872138\pi$
$239$		−	186.885i		−	0.781948i	0.920402	−	0.390974i	$-0.127862\pi$
$240$	−42.8904	+	53.7256i	−0.178710	+	0.223857i
$241$			20.1770i			0.0837222i	0.999123	+	0.0418611i	$0.0133287\pi$
$241$			20.1770i			0.0837222i	−0.999123	+	0.0418611i	$0.986671\pi$
$242$	−1.62738	+	171.112i	−0.00672470	+	0.707075i
$243$			146.933i			0.604664i
$244$		−	77.7774i		−	0.318760i
$245$	160.209	+	127.899i	0.653914	+	0.522036i
$246$	218.822			0.889520
$247$			131.889i			0.533963i
$248$	−103.819			−0.418624
$249$			54.0045i			0.216886i
$250$	−76.9488	+	159.151i	−0.307795	+	0.636602i
$251$	104.939			0.418082			0.209041	−	0.977907i	$-0.432966\pi$
$251$	104.939			0.418082			0.209041	+	0.977907i	$0.432966\pi$
$252$	15.9245			0.0631923
$253$	16.7673	+	16.9275i	0.0662737	+	0.0669070i
$254$	−188.000			−0.740157
$255$	249.376	−	312.375i	0.977946	−	1.22500i
$256$	16.0000			0.0625000
$257$		−	115.079i		−	0.447778i	−0.974615	−	0.223889i	$-0.928125\pi$
$257$		−	115.079i		−	0.447778i	0.974615	−	0.223889i	$-0.0718753\pi$
$258$			308.604i			1.19614i
$259$		−	49.3436i		−	0.190516i
$260$	31.1127	+	24.8380i	0.119664	+	0.0955308i
$261$			32.4298i			0.124252i
$262$			69.7823i			0.266345i
$263$	229.103			0.871113			0.435556	−	0.900162i	$-0.356552\pi$
$263$	229.103			0.871113			0.435556	+	0.900162i	$0.356552\pi$
$264$	−75.2603	−	75.9795i	−0.285077	−	0.287801i
$265$	−34.9588	+	43.7903i	−0.131920	+	0.165246i
$266$		−	132.515i		−	0.498175i
$267$			98.6696i			0.369549i
$268$		−	183.072i		−	0.683104i
$269$	500.836			1.86184			0.930922	−	0.365218i	$-0.119006\pi$
$269$	500.836			1.86184			0.930922	+	0.365218i	$0.119006\pi$
$270$	93.7886	−	117.482i	0.347365	−	0.435118i
$271$			222.877i			0.822425i	0.911539	+	0.411213i	$0.134895\pi$
$271$			222.877i			0.822425i	−0.911539	+	0.411213i	$0.865105\pi$
$272$	−93.0282			−0.342015
$273$		−	38.7051i		−	0.141777i
$274$			31.5309i			0.115076i
$275$	−231.997	−	147.656i	−0.843627	−	0.536930i
$276$	−14.8904			−0.0539509
$277$	−162.470			−0.586533			−0.293267	−	0.956031i	$-0.594742\pi$
$277$	−162.470			−0.586533			−0.293267	+	0.956031i	$0.594742\pi$
$278$			370.193i			1.33163i
$279$	−103.329			−0.370354
$280$	−31.2603	−	24.9558i	−0.111644	−	0.0891280i
$281$		−	352.861i		−	1.25573i	−0.778321	−	0.627867i	$-0.783928\pi$
$281$		−	352.861i		−	1.25573i	0.778321	−	0.627867i	$-0.216072\pi$
$282$	226.487			0.803147
$283$	−281.390			−0.994311			−0.497155	−	0.867661i	$-0.665622\pi$
$283$	−281.390			−0.994311			−0.497155	+	0.867661i	$0.665622\pi$
$284$	109.110			0.384189
$285$	444.964	+	355.226i	1.56128	+	1.24641i
$286$	−44.0000	+	43.5835i	−0.153846	+	0.152390i
$287$			127.322i			0.443630i
$288$	15.9245			0.0552933
$289$	251.890			0.871593
$290$	50.8220	−	63.6609i	0.175248	−	0.219520i
$291$	262.117			0.900744
$292$	−112.304			−0.384603
$293$	242.422			0.827378			0.413689	−	0.910418i	$-0.364240\pi$
$293$	242.422			0.827378			0.413689	+	0.910418i	$0.364240\pi$
$294$		−	199.304i		−	0.677906i
$295$	174.688	+	139.458i	0.592164	+	0.472739i
$296$		−	49.3436i		−	0.166701i
$297$	164.572	+	166.144i	0.554114	+	0.559409i
$298$		−	377.350i		−	1.26628i
$299$			8.62311i			0.0288398i
$300$	167.596	−	38.0694i	0.558653	−	0.126898i
$301$	−179.562			−0.596551
$302$		−	175.161i		−	0.580004i
$303$	263.683			0.870242
$304$		−	132.515i		−	0.435903i
$305$	−121.312	+	151.959i	−0.397746	+	0.498226i
$306$	−92.5890			−0.302578
$307$	−487.226			−1.58705			−0.793527	−	0.608535i	$-0.791758\pi$
$307$	−487.226			−1.58705			−0.793527	+	0.608535i	$0.791758\pi$
$308$	44.2087	−	43.7903i	0.143535	−	0.142176i
$309$	389.493			1.26050
$310$	202.838	+	161.930i	0.654316	+	0.522356i
$311$	−421.411			−1.35502			−0.677510	−	0.735514i	$-0.736941\pi$
$311$	−421.411			−1.35502			−0.677510	+	0.735514i	$0.736941\pi$
$312$		−	38.7051i		−	0.124055i
$313$		−	502.247i		−	1.60462i	−0.596905	−	0.802312i	$-0.703603\pi$
$313$		−	502.247i		−	1.60462i	0.596905	−	0.802312i	$-0.296397\pi$
$314$		−	318.135i		−	1.01317i
$315$	−31.1127	−	24.8380i	−0.0987705	−	0.0788508i
$316$			203.833i			0.645041i
$317$		−	616.290i		−	1.94413i	−0.234706	−	0.972066i	$-0.575413\pi$
$317$		−	616.290i		−	1.94413i	0.234706	−	0.972066i	$-0.424587\pi$
$318$	54.4763			0.171309
$319$	89.1780	+	90.0301i	0.279555	+	0.282226i
$320$	−31.2603	−	24.9558i	−0.0976884	−	0.0779870i
$321$		−	539.781i		−	1.68156i
$322$		−	8.66402i		−	0.0269069i
$323$			770.475i			2.38537i
$324$	−196.822			−0.607475
$325$	−22.0461	−	97.0555i	−0.0678343	−	0.298632i
$326$			88.9311i			0.272795i
$327$	−589.165			−1.80173
$328$			127.322i			0.388176i
$329$			131.782i			0.400553i
$330$	28.5329	+	265.833i	0.0864634	+	0.805554i
$331$	197.883			0.597835			0.298918	−	0.954279i	$-0.403374\pi$
$331$	197.883			0.597835			0.298918	+	0.954279i	$0.403374\pi$
$332$	−31.4226			−0.0946463
$333$		−	49.1106i		−	0.147479i
$334$	148.000			0.443114
$335$	−285.545	+	357.680i	−0.852372	+	1.06770i
$336$			38.8887i			0.115740i
$337$	375.861			1.11531			0.557657	−	0.830071i	$-0.311700\pi$
$337$	375.861			1.11531			0.557657	+	0.830071i	$0.311700\pi$
$338$	216.588			0.640792
$339$	287.528			0.848164
$340$	181.756	+	145.100i	0.534575	+	0.426764i
$341$	−286.856	+	284.141i	−0.841221	+	0.833258i
$342$		−	131.889i		−	0.385640i
$343$	254.558			0.742153
$344$	−179.562			−0.521982
$345$	29.0925	+	23.2252i	0.0843260	+	0.0673195i
$346$	−154.233			−0.445760
$347$	−310.624			−0.895169			−0.447584	−	0.894242i	$-0.647716\pi$
$347$	−310.624			−0.895169			−0.447584	+	0.894242i	$0.647716\pi$
$348$	−79.1960			−0.227575
$349$			474.256i			1.35890i	0.733722	+	0.679450i	$0.237781\pi$
$349$			474.256i			1.35890i	−0.733722	+	0.679450i	$0.762219\pi$
$350$	22.1507	+	97.5159i	0.0632878	+	0.278617i
$351$			84.6364i			0.241129i
$352$	44.2087	−	43.7903i	0.125593	−	0.124404i
$353$			460.434i			1.30434i	0.758071	+	0.652172i	$0.226142\pi$
$353$			460.434i			1.30434i	−0.758071	+	0.652172i	$0.773858\pi$
$354$		−	217.317i		−	0.613891i
$355$	−213.175	−	170.183i	−0.600492	−	0.479388i
$356$	−57.4110			−0.161267
$357$		−	226.109i		−	0.633359i
$358$	138.758			0.387591
$359$		−	335.649i		−	0.934955i	−0.884005	−	0.467477i	$-0.845163\pi$
$359$		−	335.649i		−	0.934955i	0.884005	−	0.467477i	$-0.154837\pi$
$360$	−31.1127	−	24.8380i	−0.0864242	−	0.0689945i
$361$	−736.507			−2.04019
$362$	−505.407			−1.39615
$363$	−415.895	−	3.95541i	−1.14572	−	0.0108964i
$364$	22.5206			0.0618697
$365$	219.416	+	175.165i	0.601140	+	0.479905i
$366$	189.041			0.516506
$367$		−	175.255i		−	0.477533i	−0.971077	−	0.238767i	$-0.923257\pi$
$367$		−	175.255i		−	0.477533i	0.971077	−	0.238767i	$-0.0767431\pi$
$368$		−	8.66402i		−	0.0235435i
$369$			126.721i			0.343416i
$370$	−76.9631	+	96.4059i	−0.208008	+	0.260556i
$371$			31.6971i			0.0854369i
$372$		−	252.336i		−	0.678323i
$373$	−236.338			−0.633615			−0.316808	−	0.948490i	$-0.602611\pi$
$373$	−236.338			−0.633615			−0.316808	+	0.948490i	$0.602611\pi$
$374$	−257.041	+	254.608i	−0.687276	+	0.680771i
$375$	−386.822	−	187.027i	−1.03153	−	0.498740i
$376$			131.782i			0.350484i
$377$			45.8627i			0.121652i
$378$		−	85.0379i		−	0.224968i
$379$	−416.267			−1.09833			−0.549165	−	0.835714i	$-0.685054\pi$
$379$	−416.267			−1.09833			−0.549165	+	0.835714i	$0.685054\pi$
$380$	−206.688	+	258.903i	−0.543917	+	0.681323i
$381$		−	456.942i		−	1.19932i
$382$	−232.929			−0.609761
$383$		−	166.451i		−	0.434599i	−0.976105	−	0.217299i	$-0.930275\pi$
$383$		−	166.451i		−	0.434599i	0.976105	−	0.217299i	$-0.0697248\pi$
$384$			38.8887i			0.101273i
$385$	−154.675	+	16.6019i	−0.401753	+	0.0431219i
$386$	442.535			1.14646
$387$	−178.714			−0.461793
$388$			152.513i			0.393074i
$389$	−232.939			−0.598814			−0.299407	−	0.954126i	$-0.596789\pi$
$389$	−232.939			−0.598814			−0.299407	+	0.954126i	$0.596789\pi$
$390$	−60.3699	+	75.6207i	−0.154794	+	0.193899i
$391$			50.3749i			0.128836i
$392$	115.966			0.295830
$393$	−169.609			−0.431575
$394$	178.808			0.453828
$395$	317.927	−	398.243i	0.804878	−	1.00821i
$396$	44.0000	−	43.5835i	0.111111	−	0.110059i
$397$		−	705.825i		−	1.77790i	−0.458006	−	0.888949i	$-0.651436\pi$
$397$		−	705.825i		−	1.77790i	0.458006	−	0.888949i	$-0.348564\pi$
$398$	279.181			0.701461
$399$	322.082			0.807224
$400$	22.1507	+	97.5159i	0.0553768	+	0.243790i
$401$	−92.2331			−0.230008			−0.115004	−	0.993365i	$-0.536688\pi$
$401$	−92.2331			−0.230008			−0.115004	+	0.993365i	$0.536688\pi$
$402$	444.964			1.10688
$403$	−146.129			−0.362603
$404$			153.424i			0.379763i
$405$	384.545	+	306.991i	0.949493	+	0.758003i
$406$		−	46.0802i		−	0.113498i
$407$	−135.048	−	136.338i	−0.331813	−	0.334984i
$408$		−	226.109i		−	0.554189i
$409$		−	111.673i		−	0.273038i	−0.990637	−	0.136519i	$-0.956409\pi$
$409$		−	111.673i		−	0.273038i	0.990637	−	0.136519i	$-0.0435915\pi$
$410$	198.589	−	248.757i	0.484363	−	0.606725i
$411$	−76.6371			−0.186465
$412$			226.627i			0.550066i
$413$	126.446			0.306165
$414$		−	8.62311i		−	0.0208288i
$415$	61.3925	+	49.0111i	0.147934	+	0.118099i
$416$	22.5206			0.0541360
$417$	−899.769			−2.15772
$418$	−362.678	−	366.144i	−0.867651	−	0.875942i
$419$	−70.1507			−0.167424			−0.0837121	−	0.996490i	$-0.526678\pi$
$419$	−70.1507			−0.167424			−0.0837121	+	0.996490i	$0.526678\pi$
$420$	60.6562	−	75.9795i	0.144420	−	0.180903i
$421$	299.644			0.711744			0.355872	−	0.934535i	$-0.384184\pi$
$421$	299.644			0.711744			0.355872	+	0.934535i	$0.384184\pi$
$422$		−	65.1673i		−	0.154425i
$423$			131.160i			0.310070i
$424$			31.6971i			0.0747573i
$425$	−128.790	−	566.983i	−0.303036	−	1.33408i
$426$			265.195i			0.622524i
$427$			109.994i			0.257597i
$428$	314.072			0.733813
$429$	−105.932	−	106.944i	−0.246927	−	0.249286i
$430$	350.822	+	280.070i	0.815865	+	0.651325i
$431$			39.5875i			0.0918504i	0.998945	+	0.0459252i	$0.0146236\pi$
$431$			39.5875i			0.0918504i	−0.998945	+	0.0459252i	$0.985376\pi$
$432$		−	85.0379i		−	0.196847i
$433$			387.168i			0.894153i	0.894496	+	0.447076i	$0.147535\pi$
$433$			387.168i			0.894153i	−0.894496	+	0.447076i	$0.852465\pi$
$434$	146.822			0.338300
$435$	154.731	+	123.525i	0.355702	+	0.283966i
$436$		−	342.807i		−	0.786254i
$437$	−71.7568			−0.164203
$438$		−	272.960i		−	0.623196i
$439$		−	84.9689i		−	0.193551i	−0.995306	−	0.0967755i	$-0.969147\pi$
$439$		−	84.9689i		−	0.193551i	0.995306	−	0.0967755i	$-0.0308529\pi$
$440$	−154.675	+	16.6019i	−0.351534	+	0.0377316i
$441$	115.418			0.261719
$442$	−130.941			−0.296246
$443$		−	113.196i		−	0.255521i	−0.991805	−	0.127761i	$-0.959221\pi$
$443$		−	113.196i		−	0.255521i	0.991805	−	0.127761i	$-0.0407790\pi$
$444$	119.932			0.270116
$445$	112.168	+	89.5463i	0.252063	+	0.201228i
$446$			555.429i			1.24536i
$447$	917.166			2.05183
$448$	−22.6274			−0.0505076
$449$	−112.390			−0.250312			−0.125156	−	0.992137i	$-0.539943\pi$
$449$	−112.390			−0.250312			−0.125156	+	0.992137i	$0.539943\pi$
$450$	22.0461	+	97.0555i	0.0489914	+	0.215679i
$451$	348.466	+	351.796i	0.772652	+	0.780035i
$452$			167.298i			0.370129i
$453$	425.737			0.939816
$454$	−380.000			−0.837004
$455$	−44.0000	−	35.1263i	−0.0967033	−	0.0772006i
$456$	322.082			0.706321
$457$	409.705			0.896511			0.448255	−	0.893906i	$-0.352046\pi$
$457$	409.705			0.896511			0.448255	+	0.893906i	$0.352046\pi$
$458$	290.660			0.634628
$459$			494.433i			1.07720i
$460$	−13.5136	+	16.9275i	−0.0293774	+	0.0367989i
$461$		−	80.6404i		−	0.174925i	−0.996168	−	0.0874625i	$-0.972124\pi$
$461$		−	80.6404i		−	0.174925i	0.996168	−	0.0874625i	$-0.0278758\pi$
$462$	106.434	+	107.451i	0.230377	+	0.232578i
$463$		−	112.913i		−	0.243873i	−0.992538	−	0.121936i	$-0.961090\pi$
$463$		−	112.913i		−	0.243873i	0.992538	−	0.121936i	$-0.0389104\pi$
$464$		−	46.0802i		−	0.0993109i
$465$	−393.579	+	493.006i	−0.846406	+	1.06023i
$466$	−429.493			−0.921660
$467$			65.8748i			0.141060i	0.997510	+	0.0705298i	$0.0224690\pi$
$467$			65.8748i			0.141060i	−0.997510	+	0.0705298i	$0.977531\pi$
$468$	22.4143			0.0478937
$469$			258.903i			0.552032i
$470$	205.546	−	257.471i	0.437331	−	0.547811i
$471$	773.240			1.64170
$472$	126.446			0.267895
$473$	−496.137	+	491.441i	−1.04892	+	1.03899i
$474$	−495.425			−1.04520
$475$	807.642	−	183.456i	1.70030	−	0.386223i
$476$	131.562			0.276390
$477$			31.5475i			0.0661372i
$478$			264.296i			0.552920i
$479$			148.397i			0.309806i	0.987930	+	0.154903i	$0.0495065\pi$
$479$			148.397i			0.309806i	−0.987930	+	0.154903i	$0.950494\pi$
$480$	60.6562	−	75.9795i	0.126367	−	0.158291i
$481$		−	69.4529i		−	0.144393i
$482$		−	28.5347i		−	0.0592005i
$483$	21.0583			0.0435989
$484$	2.30146	−	241.989i	0.00475508	−	0.499977i
$485$	237.880	−	297.975i	0.490475	−	0.614381i
$486$		−	207.795i		−	0.427562i
$487$		−	104.062i		−	0.213679i	−0.994276	−	0.106840i	$-0.965927\pi$
$487$		−	104.062i		−	0.213679i	0.994276	−	0.106840i	$-0.0340731\pi$
$488$			109.994i			0.225397i
$489$	−216.151			−0.442026
$490$	−226.570	−	180.876i	−0.462387	−	0.369135i
$491$		−	330.255i		−	0.672617i	−0.941752	−	0.336309i	$-0.890821\pi$
$491$		−	330.255i		−	0.672617i	0.941752	−	0.336309i	$-0.109179\pi$
$492$	−309.461			−0.628986
$493$			267.923i			0.543454i
$494$		−	186.519i		−	0.377569i
$495$	−153.945	+	16.5235i	−0.311000	+	0.0333809i
$496$	146.822			0.296012
$497$	−154.304			−0.310471
$498$		−	76.3739i		−	0.153361i
$499$	−214.589			−0.430038			−0.215019	−	0.976610i	$-0.568981\pi$
$499$	−214.589			−0.430038			−0.215019	+	0.976610i	$0.568981\pi$
$500$	108.822	−	225.073i	0.217644	−	0.450146i
$501$			359.720i			0.718005i
$502$	−148.406			−0.295629
$503$	848.122			1.68613			0.843063	−	0.537815i	$-0.180750\pi$
$503$	848.122			1.68613			0.843063	+	0.537815i	$0.180750\pi$
$504$	−22.5206			−0.0446837
$505$	239.302	−	299.756i	0.473866	−	0.593575i
$506$	−23.7125	−	23.9391i	−0.0468626	−	0.0473104i
$507$			526.426i			1.03832i
$508$	265.872			0.523370
$509$	130.472			0.256331			0.128165	−	0.991753i	$-0.459091\pi$
$509$	130.472			0.256331			0.128165	+	0.991753i	$0.459091\pi$
$510$	−352.671	+	441.765i	−0.691512	+	0.866205i
$511$	158.822			0.310806
$512$	−22.6274			−0.0441942
$513$	−704.298			−1.37290
$514$			162.746i			0.316627i
$515$	353.479	−	442.777i	0.686368	−	0.859761i
$516$		−	436.432i		−	0.845799i
$517$	360.673	+	364.119i	0.697626	+	0.704293i
$518$			69.7823i			0.134715i
$519$		−	374.870i		−	0.722293i
$520$	−44.0000	−	35.1263i	−0.0846154	−	0.0675505i
$521$	168.939			0.324258			0.162129	−	0.986770i	$-0.448164\pi$
$521$	168.939			0.324258			0.162129	+	0.986770i	$0.448164\pi$
$522$		−	45.8627i		−	0.0878595i
$523$	18.1331			0.0346713			0.0173357	−	0.999850i	$-0.494482\pi$
$523$	18.1331			0.0346713			0.0173357	+	0.999850i	$0.494482\pi$
$524$		−	98.6871i		−	0.188334i
$525$	−237.016	+	53.8383i	−0.451460	+	0.102549i
$526$	−324.000			−0.615970
$527$	−853.662			−1.61985
$528$	106.434	+	107.451i	0.201580	+	0.203506i
$529$	524.308			0.991131
$530$	49.4393	−	61.9288i	0.0932816	−	0.116847i
$531$	125.849			0.237004
$532$			187.404i			0.352263i
$533$			179.210i			0.336229i
$534$		−	139.540i		−	0.261311i
$535$	−613.624	−	489.871i	−1.14696	−	0.915646i
$536$			258.903i			0.483028i
$537$			337.257i			0.628038i
$538$	−708.289			−1.31652
$539$	320.418	−	317.385i	0.594468	−	0.588841i
$540$	−132.637	+	166.144i	−0.245624	+	0.307675i
$541$			98.2869i			0.181676i	0.995866	+	0.0908382i	$0.0289546\pi$
$541$			98.2869i			0.181676i	−0.995866	+	0.0908382i	$0.971045\pi$
$542$		−	315.196i		−	0.581542i
$543$		−	1228.41i		−	2.26227i
$544$	131.562			0.241841
$545$	−534.689	+	669.765i	−0.981081	+	1.22893i
$546$			54.7372i			0.100251i
$547$	207.231			0.378850			0.189425	−	0.981895i	$-0.439338\pi$
$547$	207.231			0.378850			0.189425	+	0.981895i	$0.439338\pi$
$548$		−	44.5914i		−	0.0813711i
$549$			109.474i			0.199407i
$550$	328.094	+	208.817i	0.596534	+	0.379667i
$551$	−381.644			−0.692639
$552$	21.0583			0.0381490
$553$		−	288.264i		−	0.521272i
$554$	229.767			0.414742
$555$	−234.319	−	187.062i	−0.422196	−	0.337049i
$556$		−	523.532i		−	0.941604i
$557$	959.370			1.72239			0.861194	−	0.508277i	$-0.169717\pi$
$557$	959.370			1.72239			0.861194	+	0.508277i	$0.169717\pi$
$558$	146.129			0.261880
$559$	−252.740			−0.452128
$560$	44.2087	+	35.2929i	0.0789442	+	0.0630230i
$561$	−618.836	−	624.749i	−1.10309	−	1.11364i
$562$			499.021i			0.887938i
$563$	−51.7446			−0.0919088			−0.0459544	−	0.998944i	$-0.514633\pi$
$563$	−51.7446			−0.0919088			−0.0459544	+	0.998944i	$0.514633\pi$
$564$	−320.301			−0.567910
$565$	260.942	−	326.862i	0.461844	−	0.578517i
$566$	397.946			0.703084
$567$	278.348			0.490914
$568$	−154.304			−0.271662
$569$			362.183i			0.636526i	0.948003	+	0.318263i	$0.103099\pi$
$569$			362.183i			0.636526i	−0.948003	+	0.318263i	$0.896901\pi$
$570$	−629.274	−	502.365i	−1.10399	−	0.881342i
$571$			698.164i			1.22270i	0.791358	+	0.611352i	$0.209374\pi$
$571$			698.164i			1.22270i	−0.791358	+	0.611352i	$0.790626\pi$
$572$	62.2254	−	61.6364i	0.108786	−	0.107756i
$573$		−	566.143i		−	0.988034i
$574$		−	180.060i		−	0.313694i
$575$	52.8049	−	11.9946i	0.0918347	−	0.0208602i
$576$	−22.5206			−0.0390982
$577$		−	19.2829i		−	0.0334192i	−0.999860	−	0.0167096i	$-0.994681\pi$
$577$		−	19.2829i		−	0.0334192i	0.999860	−	0.0167096i	$-0.00531908\pi$
$578$	−356.227			−0.616309
$579$			1075.60i			1.85768i
$580$	−71.8732	+	90.0301i	−0.123919	+	0.155224i
$581$	44.4383			0.0764858
$582$	−370.689			−0.636922
$583$	86.7516	+	87.5806i	0.148802	+	0.150224i
$584$	158.822			0.271956
$585$	−43.7923	−	34.9604i	−0.0748586	−	0.0597614i
$586$	−342.836			−0.585044
$587$		−	137.281i		−	0.233869i	−0.993140	−	0.116934i	$-0.962693\pi$
$587$		−	137.281i		−	0.233869i	0.993140	−	0.116934i	$-0.0373068\pi$
$588$			281.859i			0.479352i
$589$		−	1216.00i		−	2.06452i
$590$	−247.047	−	197.223i	−0.418723	−	0.334277i
$591$			434.601i			0.735365i
$592$			69.7823i			0.117876i
$593$	307.049			0.517789			0.258895	−	0.965906i	$-0.416642\pi$
$593$	307.049			0.517789			0.258895	+	0.965906i	$0.416642\pi$
$594$	−232.740	−	234.964i	−0.391818	−	0.395562i
$595$	−257.041	−	205.202i	−0.432002	−	0.344878i
$596$			533.654i			0.895393i
$597$			678.562i			1.13662i
$598$		−	12.1949i		−	0.0203928i
$599$	−810.343			−1.35283			−0.676413	−	0.736522i	$-0.736467\pi$
$599$	−810.343			−1.35283			−0.676413	+	0.736522i	$0.736467\pi$
$600$	−237.016	+	53.8383i	−0.395027	+	0.0897305i
$601$			382.095i			0.635766i	0.948130	+	0.317883i	$0.102972\pi$
$601$			382.095i			0.635766i	−0.948130	+	0.317883i	$0.897028\pi$
$602$	253.939			0.421825
$603$			257.680i			0.427331i
$604$			247.715i			0.410125i
$605$	−381.937	+	469.201i	−0.631300	+	0.775539i
$606$	−372.904			−0.615354
$607$	−302.312			−0.498043			−0.249022	−	0.968498i	$-0.580109\pi$
$607$	−302.312			−0.498043			−0.249022	+	0.968498i	$0.580109\pi$
$608$			187.404i			0.308230i
$609$	112.000			0.183908
$610$	171.562	−	214.902i	0.281249	−	0.352299i
$611$			185.488i			0.303581i
$612$	130.941			0.213955
$613$	−520.344			−0.848848			−0.424424	−	0.905464i	$-0.639523\pi$
$613$	−520.344			−0.848848			−0.424424	+	0.905464i	$0.639523\pi$
$614$	689.041			1.12222
$615$	604.615	+	482.679i	0.983114	+	0.784844i
$616$	−62.5206	+	61.9288i	−0.101494	+	0.100534i
$617$		−	1040.89i		−	1.68702i	−0.537113	−	0.843511i	$-0.680485\pi$
$617$		−	1040.89i		−	1.68702i	0.537113	−	0.843511i	$-0.319515\pi$
$618$	−550.827			−0.891305
$619$	1076.13			1.73850			0.869249	−	0.494374i	$-0.164603\pi$
$619$	1076.13			1.73850			0.869249	+	0.494374i	$0.164603\pi$
$620$	−286.856	−	229.004i	−0.462671	−	0.369362i
$621$	−46.0481			−0.0741516
$622$	595.965			0.958143
$623$	81.1914			0.130323
$624$			54.7372i			0.0877199i
$625$	−563.668	+	270.006i	−0.901869	+	0.432010i
$626$			710.285i			1.13464i
$627$	889.928	−	881.505i	1.41934	−	1.40591i
$628$			449.910i			0.716418i
$629$		−	405.733i		−	0.645044i
$630$	44.0000	+	35.1263i	0.0698413	+	0.0557560i
$631$	705.843			1.11861			0.559305	−	0.828962i	$-0.311068\pi$
$631$	705.843			1.11861			0.559305	+	0.828962i	$0.311068\pi$
$632$		−	288.264i		−	0.456113i
$633$	158.392			0.250224
$634$			871.566i			1.37471i
$635$	−519.453	−	414.691i	−0.818036	−	0.653057i
$636$	−77.0412			−0.121134
$637$	163.226			0.256241
$638$	−126.117	−	127.322i	−0.197675	−	0.199564i
$639$	−153.576			−0.240338
$640$	44.2087	+	35.2929i	0.0690761	+	0.0551451i
$641$	−530.802			−0.828084			−0.414042	−	0.910258i	$-0.635883\pi$
$641$	−530.802			−0.828084			−0.414042	+	0.910258i	$0.635883\pi$
$642$			763.365i			1.18904i
$643$		−	415.065i		−	0.645513i	−0.946482	−	0.322757i	$-0.895390\pi$
$643$		−	415.065i		−	0.645513i	0.946482	−	0.322757i	$-0.104610\pi$
$644$			12.2528i			0.0190260i
$645$	−680.721	+	852.688i	−1.05538	+	1.32200i
$646$		−	1089.62i		−	1.68671i
$647$			890.968i			1.37708i	0.725201	+	0.688538i	$0.241747\pi$
$647$			890.968i			1.37708i	−0.725201	+	0.688538i	$0.758253\pi$
$648$	278.348			0.429550
$649$	349.377	−	346.070i	0.538331	−	0.533236i
$650$	31.1780	+	137.257i	0.0479661	+	0.211165i
$651$			356.857i			0.548168i
$652$		−	125.768i		−	0.192895i
$653$		−	368.900i		−	0.564931i	−0.959277	−	0.282465i	$-0.908848\pi$
$653$		−	368.900i		−	0.564931i	0.959277	−	0.282465i	$-0.0911522\pi$
$654$	833.206			1.27402
$655$	−153.926	+	192.812i	−0.235002	+	0.294369i
$656$		−	180.060i		−	0.274482i
$657$	158.072			0.240597
$658$		−	186.368i		−	0.283234i
$659$		−	272.221i		−	0.413082i	−0.978438	−	0.206541i	$-0.933779\pi$
$659$		−	272.221i		−	0.413082i	0.978438	−	0.206541i	$-0.0662206\pi$
$660$	−40.3517	−	375.944i	−0.0611389	−	0.569613i
$661$	−784.336			−1.18659			−0.593295	−	0.804985i	$-0.702173\pi$
$661$	−784.336			−1.18659			−0.593295	+	0.804985i	$0.702173\pi$
$662$	−279.849			−0.422733
$663$		−	318.257i		−	0.480025i
$664$	44.4383			0.0669251
$665$	292.301	−	366.144i	0.439551	−	0.550592i
$666$			69.4529i			0.104284i
$667$	−24.9525			−0.0374100
$668$	−209.304			−0.313329
$669$	−1349.99			−2.01793
$670$	403.821	−	505.836i	0.602718	−	0.754979i
$671$	301.041	+	303.918i	0.448646	+	0.452933i
$672$		−	54.9969i		−	0.0818406i
$673$	165.395			0.245758			0.122879	−	0.992422i	$-0.460787\pi$
$673$	165.395			0.245758			0.122879	+	0.992422i	$0.460787\pi$
$674$	−531.548			−0.788647
$675$	518.284	−	117.728i	0.767829	−	0.174412i
$676$	−306.301			−0.453109
$677$	−469.955			−0.694173			−0.347086	−	0.937833i	$-0.612829\pi$
$677$	−469.955			−0.694173			−0.347086	+	0.937833i	$0.612829\pi$
$678$	−406.625			−0.599742
$679$		−	215.686i		−	0.317652i
$680$	−257.041	−	205.202i	−0.378002	−	0.301768i
$681$		−	923.606i		−	1.35625i
$682$	405.676	−	401.836i	0.594833	−	0.589203i
$683$			592.512i			0.867514i	0.901030	+	0.433757i	$0.142812\pi$
$683$			592.512i			0.867514i	−0.901030	+	0.433757i	$0.857188\pi$
$684$			186.519i			0.272689i
$685$	−69.5510	+	87.1212i	−0.101534	+	0.127184i
$686$	−360.000			−0.524781
$687$			706.461i			1.02833i
$688$	253.939			0.369097
$689$			44.6148i			0.0647530i
$690$	−41.1430	−	32.8454i	−0.0596275	−	0.0476020i
$691$	586.418			0.848651			0.424326	−	0.905510i	$-0.360511\pi$
$691$	586.418			0.848651			0.424326	+	0.905510i	$0.360511\pi$
$692$	218.118			0.315200
$693$	−62.2254	+	61.6364i	−0.0897913	+	0.0889414i
$694$	439.288			0.632980
$695$	−816.574	+	1022.86i	−1.17493	+	1.47174i
$696$	112.000			0.160920
$697$			1046.92i			1.50203i
$698$		−	670.699i		−	0.960887i
$699$		−	1043.90i		−	1.49342i
$700$	−31.3259	−	137.908i	−0.0447512	−	0.197012i
$701$		−	1185.11i		−	1.69060i	−0.534296	−	0.845298i	$-0.679423\pi$
$701$		−	1185.11i		−	1.69060i	0.534296	−	0.845298i	$-0.320577\pi$
$702$		−	119.694i		−	0.170504i
$703$	577.949			0.822117
$704$	−62.5206	+	61.9288i	−0.0888076	+	0.0879671i
$705$	625.795	+	499.587i	0.887652	+	0.708634i
$706$		−	651.151i		−	0.922311i
$707$		−	216.975i		−	0.306895i
$708$			307.333i			0.434086i
$709$	230.583			0.325222			0.162611	−	0.986690i	$-0.448008\pi$
$709$	230.583			0.325222			0.162611	+	0.986690i	$0.448008\pi$
$710$	301.475	+	240.675i	0.424612	+	0.338978i
$711$		−	286.902i		−	0.403520i
$712$	81.1914			0.114033
$713$		−	79.5043i		−	0.111507i
$714$			319.766i			0.447852i
$715$	−217.711	+	23.3678i	−0.304491	+	0.0326822i
$716$	−196.233			−0.274069
$717$	−642.383			−0.895931
$718$			474.679i			0.661113i
$719$	647.117			0.900024			0.450012	−	0.893023i	$-0.351420\pi$
$719$	647.117			0.900024			0.450012	+	0.893023i	$0.351420\pi$
$720$	44.0000	+	35.1263i	0.0611111	+	0.0487865i
$721$		−	320.499i		−	0.444520i
$722$	1041.58			1.44263
$723$	69.3547			0.0959263
$724$	714.754			0.987229
$725$	280.847	−	63.7944i	0.387375	−	0.0879923i
$726$	588.165	+	5.59379i	0.810144	+	0.00770495i
$727$			1381.75i			1.90062i	0.311304	+	0.950310i	$0.399234\pi$
$727$			1381.75i			1.90062i	−0.311304	+	0.950310i	$0.600766\pi$
$728$	−31.8489			−0.0437485
$729$	−380.644			−0.522146
$730$	−310.301	−	247.721i	−0.425070	−	0.339344i
$731$	−1476.47			−2.01979
$732$	−267.345			−0.365225
$733$	−354.823			−0.484069			−0.242034	−	0.970268i	$-0.577815\pi$
$733$	−354.823			−0.484069			−0.242034	+	0.970268i	$0.577815\pi$
$734$			247.848i			0.337667i
$735$	439.627	−	550.687i	0.598132	−	0.749234i
$736$			12.2528i			0.0166478i
$737$	708.589	+	715.360i	0.961451	+	0.970638i
$738$		−	179.210i		−	0.242832i
$739$		−	198.704i		−	0.268882i	−0.990922	−	0.134441i	$-0.957076\pi$
$739$		−	198.704i		−	0.268882i	0.990922	−	0.134441i	$-0.0429239\pi$
$740$	108.842	−	136.338i	0.147084	−	0.184241i
$741$	453.343			0.611798
$742$		−	44.8265i		−	0.0604130i
$743$	−1120.12			−1.50756			−0.753779	−	0.657127i	$-0.771771\pi$
$743$	−1120.12			−1.50756			−0.753779	+	0.657127i	$0.771771\pi$
$744$			356.857i			0.479647i
$745$	832.362	−	1042.64i	1.11726	−	1.39951i
$746$	334.233			0.448034
$747$	44.2284			0.0592081
$748$	363.511	−	360.070i	0.485977	−	0.481377i
$749$	−444.165			−0.593010
$750$	547.049	+	264.497i	0.729399	+	0.352662i
$751$	869.405			1.15766			0.578831	−	0.815447i	$-0.303509\pi$
$751$	869.405			1.15766			0.578831	+	0.815447i	$0.303509\pi$
$752$		−	186.368i		−	0.247829i
$753$		−	360.706i		−	0.479025i
$754$		−	64.8596i		−	0.0860207i
$755$	386.371	−	483.978i	0.511750	−	0.641031i
$756$			120.262i			0.159076i
$757$			874.961i			1.15583i	0.816098	+	0.577913i	$0.196133\pi$
$757$			874.961i			1.15583i	−0.816098	+	0.577913i	$0.803867\pi$
$758$	588.691			0.776637
$759$	58.1849	−	57.6342i	0.0766600	−	0.0759344i
$760$	292.301	−	366.144i	0.384607	−	0.481768i
$761$			645.727i			0.848524i	0.905539	+	0.424262i	$0.139466\pi$
$761$			645.727i			0.848524i	−0.905539	+	0.424262i	$0.860534\pi$
$762$			646.214i			0.848049i
$763$			484.802i			0.635389i
$764$	329.411			0.431166
$765$	−255.828	−	204.233i	−0.334415	−	0.266972i
$766$			235.398i			0.307308i
$767$	177.978			0.232044
$768$		−	54.9969i		−	0.0716105i
$769$			670.097i			0.871388i	0.900095	+	0.435694i	$0.143497\pi$
$769$			670.097i			0.871388i	−0.900095	+	0.435694i	$0.856503\pi$
$770$	218.744	−	23.4787i	0.284083	−	0.0304918i
$771$	−395.562			−0.513050
$772$	−625.838			−0.810671
$773$			612.123i			0.791880i	0.918276	+	0.395940i	$0.129581\pi$
$773$			612.123i			0.791880i	−0.918276	+	0.395940i	$0.870419\pi$
$774$	252.740			0.326537
$775$	203.263	+	894.842i	0.262275	+	1.15464i
$776$		−	215.686i		−	0.277945i
$777$	−169.609			−0.218287
$778$	329.425			0.423425
$779$	−1491.29			−1.91436
$780$	85.3759	−	106.944i	0.109456	−	0.137108i
$781$	−426.350	+	422.314i	−0.545902	+	0.540735i
$782$		−	71.2408i		−	0.0911008i
$783$	−244.911			−0.312785
$784$	−164.000			−0.209184
$785$	701.744	−	879.021i	0.893941	−	1.11977i
$786$	239.863			0.305169
$787$	1391.41			1.76800			0.883998	−	0.467491i	$-0.154842\pi$
$787$	1391.41			1.76800			0.883998	+	0.467491i	$0.154842\pi$
$788$	−252.873			−0.320905
$789$		−	787.496i		−	0.998093i
$790$	−449.616	+	563.200i	−0.569134	+	0.712912i
$791$		−	236.595i		−	0.299109i
$792$	−62.2254	+	61.6364i	−0.0785674	+	0.0778238i
$793$			154.820i			0.195234i
$794$			998.188i			1.25716i
$795$	150.521	+	120.164i	0.189334	+	0.151150i
$796$	−394.822			−0.496008
$797$			621.140i			0.779348i	0.920953	+	0.389674i	$0.127412\pi$
$797$			621.140i			0.779348i	−0.920953	+	0.389674i	$0.872588\pi$
$798$	−455.493			−0.570793
$799$			1083.59i			1.35618i
$800$	−31.3259	−	137.908i	−0.0391573	−	0.172385i
$801$	80.8081			0.100884
$802$	130.437			0.162640
$803$	438.833	−	434.679i	0.546491	−	0.541319i
$804$	−629.274			−0.782679
$805$	19.1111	−	23.9391i	0.0237405	−	0.0297380i
$806$	206.657			0.256399
$807$		−	1721.53i		−	2.13324i
$808$		−	216.975i		−	0.268533i
$809$			492.303i			0.608532i	0.952587	+	0.304266i	$0.0984112\pi$
$809$			492.303i			0.608532i	−0.952587	+	0.304266i	$0.901589\pi$
$810$	−543.828	−	434.151i	−0.671393	−	0.535989i
$811$		−	581.566i		−	0.717098i	−0.933511	−	0.358549i	$-0.883272\pi$
$811$		−	581.566i		−	0.717098i	0.933511	−	0.358549i	$-0.116728\pi$
$812$			65.1673i			0.0802553i
$813$	766.097			0.942309
$814$	190.987	+	192.812i	0.234627	+	0.236869i
$815$	−196.165	+	245.721i	−0.240693	+	0.301498i
$816$			319.766i			0.391871i
$817$		−	2103.16i		−	2.57425i
$818$			157.929i			0.193067i
$819$	−31.6985			−0.0387040
$820$	−280.847	+	351.796i	−0.342497	+	0.429020i
$821$		−	623.019i		−	0.758854i	−0.925222	−	0.379427i	$-0.876121\pi$
$821$		−	623.019i		−	0.758854i	0.925222	−	0.379427i	$-0.123879\pi$
$822$	108.381			0.131851
$823$		−	1073.90i		−	1.30486i	−0.757849	−	0.652430i	$-0.773750\pi$
$823$		−	1073.90i		−	1.30486i	0.757849	−	0.652430i	$-0.226250\pi$
$824$		−	320.499i		−	0.388955i
$825$	−507.538	+	797.446i	−0.615197	+	0.966601i
$826$	−178.822			−0.216492
$827$	−1446.64			−1.74927			−0.874634	−	0.484784i	$-0.838898\pi$
$827$	−1446.64			−1.74927			−0.874634	+	0.484784i	$0.838898\pi$
$828$			12.1949i			0.0147282i
$829$	−784.117			−0.945858			−0.472929	−	0.881100i	$-0.656803\pi$
$829$	−784.117			−0.945858			−0.472929	+	0.881100i	$0.656803\pi$
$830$	−86.8220	−	69.3121i	−0.104605	−	0.0835086i
$831$			558.458i			0.672032i
$832$	−31.8489			−0.0382799
$833$	953.539			1.14470
$834$	1272.47			1.52574
$835$	408.931	+	326.459i	0.489737	+	0.390969i
$836$	512.904	+	517.806i	0.613522	+	0.619385i
$837$		−	780.340i		−	0.932306i
$838$	99.2081			0.118387
$839$	306.117			0.364859			0.182429	−	0.983219i	$-0.441604\pi$
$839$	306.117			0.364859			0.182429	+	0.983219i	$0.441604\pi$
$840$	−85.7809	+	107.451i	−0.102120	+	0.127918i
$841$	708.288			0.842198
$842$	−423.761			−0.503279
$843$	−1212.89			−1.43878
$844$			92.1605i			0.109195i
$845$	598.442	+	477.751i	0.708215	+	0.565385i
$846$		−	185.488i		−	0.219253i
$847$	−3.25475	+	342.224i	−0.00384268	+	0.404043i
$848$		−	44.8265i		−	0.0528614i
$849$			967.224i			1.13925i
$850$	182.137	+	801.835i	0.214279	+	0.943335i
$851$	37.7872			0.0444033
$852$		−	375.043i		−	0.440191i
$853$	113.883			0.133509			0.0667545	−	0.997769i	$-0.478736\pi$
$853$	113.883			0.133509			0.0667545	+	0.997769i	$0.478736\pi$
$854$		−	155.555i		−	0.182148i
$855$	290.921	−	364.415i	0.340259	−	0.426217i
$856$	−444.165			−0.518884
$857$	−581.910			−0.679008			−0.339504	−	0.940605i	$-0.610259\pi$
$857$	−581.910			−0.679008			−0.339504	+	0.940605i	$0.610259\pi$
$858$	149.810	+	151.241i	0.174604	+	0.176272i
$859$	−118.281			−0.137696			−0.0688482	−	0.997627i	$-0.521932\pi$
$859$	−118.281			−0.137696			−0.0688482	+	0.997627i	$0.521932\pi$
$860$	−496.137	−	396.078i	−0.576904	−	0.460556i
$861$	437.644			0.508297
$862$		−	55.9852i		−	0.0649480i
$863$			1030.51i			1.19410i	0.802203	+	0.597051i	$0.203661\pi$
$863$			1030.51i			1.19410i	−0.802203	+	0.597051i	$0.796339\pi$
$864$			120.262i			0.139192i
$865$	−426.153	−	340.208i	−0.492662	−	0.393304i
$866$		−	547.539i		−	0.632262i
$867$		−	865.825i		−	0.998644i
$868$	−207.638			−0.239214
$869$	−788.946	−	796.485i	−0.907878	−	0.916554i
$870$	−218.822	−	174.691i	−0.251520	−	0.200794i
$871$			364.415i			0.418387i
$872$			484.802i			0.555965i
$873$		−	214.667i		−	0.245896i
$874$	101.479			0.116109
$875$	−153.898	+	318.301i	−0.175883	+	0.363773i
$876$			386.024i			0.440666i
$877$	−378.593			−0.431691			−0.215845	−	0.976428i	$-0.569251\pi$
$877$	−378.593			−0.431691			−0.215845	+	0.976428i	$0.569251\pi$
$878$			120.164i			0.136861i
$879$		−	833.277i		−	0.947983i
$880$	218.744	−	23.4787i	0.248572	−	0.0266803i
$881$	810.076			0.919496			0.459748	−	0.888049i	$-0.347940\pi$
$881$	810.076			0.919496			0.459748	+	0.888049i	$0.347940\pi$
$882$	−163.226			−0.185063
$883$			188.555i			0.213540i	0.994284	+	0.106770i	$0.0340508\pi$
$883$			188.555i			0.213540i	−0.994284	+	0.106770i	$0.965949\pi$
$884$	185.178			0.209477
$885$	479.360	−	600.458i	0.541649	−	0.678483i
$886$			160.083i			0.180681i
$887$	234.430			0.264295			0.132148	−	0.991230i	$-0.457813\pi$
$887$	234.430			0.264295			0.132148	+	0.991230i	$0.457813\pi$
$888$	−169.609			−0.191001
$889$	−376.000			−0.422947
$890$	−158.629	−	126.638i	−0.178235	−	0.142289i
$891$	769.089	−	761.810i	0.863175	−	0.855005i
$892$		−	785.495i		−	0.880600i
$893$	−1543.53			−1.72847
$894$	−1297.07			−1.45086
$895$	383.394	+	306.073i	0.428373	+	0.341981i
$896$	32.0000			0.0357143
$897$	29.6403			0.0330438
$898$	158.944			0.176997
$899$		−	422.850i		−	0.470356i
$900$	−31.1780	−	137.257i	−0.0346422	−	0.152508i
$901$			260.633i			0.289271i
$902$	−492.806	−	497.515i	−0.546348	−	0.551568i
$903$			617.209i			0.683509i
$904$		−	236.595i		−	0.261721i
$905$	−1396.46	−	1114.83i	−1.54305	−	1.23186i
$906$	−602.082			−0.664550
$907$		−	855.676i		−	0.943413i	−0.881756	−	0.471707i	$-0.843638\pi$
$907$		−	855.676i		−	0.943413i	0.881756	−	0.471707i	$-0.156362\pi$
$908$	537.401			0.591851
$909$		−	215.950i		−	0.237569i
$910$	62.2254	+	49.6760i	0.0683796	+	0.0545890i
$911$	−16.2609			−0.0178495			−0.00892477	−	0.999960i	$-0.502841\pi$
$911$	−16.2609			−0.0178495			−0.00892477	+	0.999960i	$0.502841\pi$
$912$	−455.493			−0.499444
$913$	122.785	−	121.623i	0.134485	−	0.133212i
$914$	−579.411			−0.633929
$915$	522.329	+	416.988i	0.570852	+	0.455725i
$916$	−411.055			−0.448750
$917$			139.565i			0.152197i
$918$		−	699.234i		−	0.761693i
$919$			166.342i			0.181003i	0.995896	+	0.0905017i	$0.0288470\pi$
$919$			166.342i			0.181003i	−0.995896	+	0.0905017i	$0.971153\pi$
$920$	19.1111	−	23.9391i	0.0207730	−	0.0260207i
$921$			1674.74i			1.81840i
$922$			114.043i			0.123691i
$923$	−217.189			−0.235307
$924$	−150.521	−	151.959i	−0.162901	−	0.164458i
$925$	−425.305	+	96.6081i	−0.459789	+	0.104441i
$926$			159.683i			0.172444i
$927$		−	318.986i		−	0.344106i
$928$			65.1673i			0.0702234i
$929$	965.712			1.03952			0.519759	−	0.854313i	$-0.326022\pi$
$929$	965.712			1.03952			0.519759	+	0.854313i	$0.326022\pi$
$930$	556.605	−	697.216i	0.598500	−	0.749695i
$931$			1358.27i			1.45894i
$932$	607.395			0.651712
$933$			1448.52i			1.55254i
$934$		−	93.1611i		−	0.0997442i
$935$	−1271.83	+	136.511i	−1.36025	+	0.146001i
$936$	−31.6985			−0.0338660
$937$	−842.861			−0.899532			−0.449766	−	0.893146i	$-0.648493\pi$
$937$	−842.861			−0.899532			−0.449766	+	0.893146i	$0.648493\pi$
$938$		−	366.144i		−	0.390345i
$939$	−1726.38			−1.83853
$940$	−290.685	+	364.119i	−0.309240	+	0.387361i
$941$			1467.05i			1.55903i	0.626382	+	0.779517i	$0.284535\pi$
$941$			1467.05i			1.55903i	−0.626382	+	0.779517i	$0.715465\pi$
$942$	−1093.53			−1.16086
$943$	−97.5028			−0.103396
$944$	−178.822			−0.189430
$945$	187.577	−	234.964i	0.198494	−	0.248639i
$946$	701.644	−	695.003i	0.741696	−	0.734675i
$947$			463.518i			0.489460i	0.969591	+	0.244730i	$0.0786993\pi$
$947$			463.518i			0.489460i	−0.969591	+	0.244730i	$0.921301\pi$
$948$	700.637			0.739068
$949$	223.548			0.235561
$950$	−1142.18	+	259.446i	−1.20229	+	0.273101i
$951$	−2118.38			−2.22753
$952$	−186.056			−0.195437
$953$	1260.06			1.32220			0.661099	−	0.750298i	$-0.270090\pi$
$953$	1260.06			1.32220			0.661099	+	0.750298i	$0.270090\pi$
$954$		−	44.6148i		−	0.0467661i
$955$	−643.593	−	513.796i	−0.673919	−	0.538006i
$956$		−	373.771i		−	0.390974i
$957$	309.461	−	306.532i	0.323366	−	0.320305i
$958$		−	209.865i		−	0.219066i
$959$			63.0617i			0.0657578i
$960$	−85.7809	+	107.451i	−0.0893551	+	0.111928i
$961$	386.294			0.401971
$962$			98.2212i			0.102101i
$963$	−442.068			−0.459053
$964$			40.3541i			0.0418611i
$965$	1222.74	+	976.145i	1.26709	+	1.01155i
$966$	−29.7809			−0.0308291
$967$	−857.576			−0.886842			−0.443421	−	0.896314i	$-0.646235\pi$
$967$	−857.576			−0.886842			−0.443421	+	0.896314i	$0.646235\pi$
$968$	−3.25475	+	342.224i	−0.00336235	+	0.353537i
$969$	2648.36			2.73308
$970$	−336.414	+	421.400i	−0.346818	+	0.434433i
$971$	110.816			0.114125			0.0570627	−	0.998371i	$-0.481827\pi$
$971$	110.816			0.114125			0.0570627	+	0.998371i	$0.481827\pi$
$972$			293.867i			0.302332i
$973$			740.386i			0.760931i
$974$			147.166i			0.151094i
$975$	−333.609	+	75.7794i	−0.342163	+	0.0777224i
$976$		−	155.555i		−	0.159380i
$977$		−	687.248i		−	0.703427i	−0.936108	−	0.351713i	$-0.885599\pi$
$977$		−	687.248i		−	0.703427i	0.936108	−	0.351713i	$-0.114401\pi$
$978$	305.683			0.312560
$979$	224.336	−	222.212i	0.229148	−	0.226979i
$980$	320.418	+	255.797i	0.326957	+	0.261018i
$981$			482.513i			0.491858i
$982$			467.051i			0.475612i
$983$			120.258i			0.122338i	0.998127	+	0.0611688i	$0.0194828\pi$
$983$			120.258i			0.122338i	−0.998127	+	0.0611688i	$0.980517\pi$
$984$	437.644			0.444760
$985$	494.055	+	394.416i	0.501579	+	0.400422i
$986$		−	378.900i		−	0.384280i
$987$	452.975			0.458941
$988$			263.778i			0.266982i
$989$		−	137.508i		−	0.139037i
$990$	217.711	−	23.3678i	0.219910	−	0.0236038i
$991$	220.836			0.222842			0.111421	−	0.993773i	$-0.464460\pi$
$991$	220.836			0.222842			0.111421	+	0.993773i	$0.464460\pi$
$992$	−207.638			−0.209312
$993$		−	680.186i		−	0.684981i
$994$	218.219			0.219536
$995$	771.391	+	615.820i	0.775267	+	0.618914i
$996$			108.009i			0.108443i
$997$	−968.398			−0.971312			−0.485656	−	0.874150i	$-0.661419\pi$
$997$	−968.398			−0.971312			−0.485656	+	0.874150i	$0.661419\pi$
$998$	303.475			0.304083
$999$	370.884			0.371255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.3.c.b.109.1	✓	8
3.2	odd	2		990.3.h.b.109.8		8
4.3	odd	2		880.3.i.g.769.8		8
5.2	odd	4		550.3.d.d.351.1		8
5.3	odd	4		550.3.d.d.351.8		8
5.4	even	2	inner	110.3.c.b.109.8	yes	8
11.10	odd	2	inner	110.3.c.b.109.5	yes	8
15.14	odd	2		990.3.h.b.109.3		8
20.19	odd	2		880.3.i.g.769.1		8
33.32	even	2		990.3.h.b.109.4		8
44.43	even	2		880.3.i.g.769.7		8
55.32	even	4		550.3.d.d.351.5		8
55.43	even	4		550.3.d.d.351.4		8
55.54	odd	2	inner	110.3.c.b.109.4	yes	8
165.164	even	2		990.3.h.b.109.7		8
220.219	even	2		880.3.i.g.769.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.3.c.b.109.1	✓	8	1.1	even	1	trivial
110.3.c.b.109.4	yes	8	55.54	odd	2	inner
110.3.c.b.109.5	yes	8	11.10	odd	2	inner
110.3.c.b.109.8	yes	8	5.4	even	2	inner
550.3.d.d.351.1		8	5.2	odd	4
550.3.d.d.351.4		8	55.43	even	4
550.3.d.d.351.5		8	55.32	even	4
550.3.d.d.351.8		8	5.3	odd	4
880.3.i.g.769.1		8	20.19	odd	2
880.3.i.g.769.2		8	220.219	even	2
880.3.i.g.769.7		8	44.43	even	2
880.3.i.g.769.8		8	4.3	odd	2
990.3.h.b.109.3		8	15.14	odd	2
990.3.h.b.109.4		8	33.32	even	2
990.3.h.b.109.7		8	165.164	even	2
990.3.h.b.109.8		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} -3.43731i q^{3} +2.00000 q^{4} +(-3.90754 - 3.11948i) q^{5} +4.86108i q^{6} -2.82843 q^{7} -2.82843 q^{8} -2.81507 q^{9} +(5.52609 + 4.41161i) q^{10} +(-7.81507 + 7.74110i) q^{11} -6.87461i q^{12} -3.98111 q^{13} +4.00000 q^{14} +(-10.7226 + 13.4314i) q^{15} +4.00000 q^{16} -23.2571 q^{17} +3.98111 q^{18} -33.1286i q^{19} +(-7.81507 - 6.23896i) q^{20} +9.72217i q^{21} +(11.0522 - 10.9476i) q^{22} -2.16600i q^{23} +9.72217i q^{24} +(5.53768 + 24.3790i) q^{25} +5.63015 q^{26} -21.2595i q^{27} -5.65685 q^{28} -11.5201i q^{29} +(15.1641 - 18.9949i) q^{30} +36.7055 q^{31} -5.65685 q^{32} +(26.6085 + 26.8628i) q^{33} +32.8904 q^{34} +(11.0522 + 8.82322i) q^{35} -5.63015 q^{36} +17.4456i q^{37} +46.8510i q^{38} +13.6843i q^{39} +(11.0522 + 8.82322i) q^{40} -45.0151i q^{41} -13.7492i q^{42} +63.4847 q^{43} +(-15.6301 + 15.4822i) q^{44} +(11.0000 + 8.78157i) q^{45} +3.06319i q^{46} -46.5919i q^{47} -13.7492i q^{48} -41.0000 q^{49} +(-7.83147 - 34.4771i) q^{50} +79.9416i q^{51} -7.96223 q^{52} -11.2066i q^{53} +30.0655i q^{54} +(54.6859 - 5.86966i) q^{55} +8.00000 q^{56} -113.873 q^{57} +16.2918i q^{58} -44.7055 q^{59} +(-21.4452 + 26.8628i) q^{60} -38.8887i q^{61} -51.9094 q^{62} +7.96223 q^{63} +8.00000 q^{64} +(15.5563 + 12.4190i) q^{65} +(-37.6301 - 37.9897i) q^{66} -91.5360i q^{67} -46.5141 q^{68} -7.44522 q^{69} +(-15.6301 - 12.4779i) q^{70} +54.5548 q^{71} +7.96223 q^{72} -56.1521 q^{73} -24.6718i q^{74} +(83.7980 - 19.0347i) q^{75} -66.2573i q^{76} +(22.1044 - 21.8951i) q^{77} -19.3525i q^{78} +101.917i q^{79} +(-15.6301 - 12.4779i) q^{80} -98.4110 q^{81} +63.6609i q^{82} -15.7113 q^{83} +19.4443i q^{84} +(90.8778 + 72.5499i) q^{85} -89.7809 q^{86} -39.5980 q^{87} +(22.1044 - 21.8951i) q^{88} -28.7055 q^{89} +(-15.5563 - 12.4190i) q^{90} +11.2603 q^{91} -4.33201i q^{92} -126.168i q^{93} +65.8909i q^{94} +(-103.344 + 129.451i) q^{95} +19.4443i q^{96} +76.2564i q^{97} +57.9828 q^{98} +(22.0000 - 21.7918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 16 q^{4} - 10 q^{5} + 20 q^{9} - 20 q^{11} + 32 q^{14} - 22 q^{15} + 32 q^{16} - 20 q^{20} - 62 q^{25} - 40 q^{26} - 4 q^{31} + 8 q^{34} + 40 q^{36} - 40 q^{44} + 88 q^{45} - 328 q^{49} + 138 q^{55}+ \cdots + 176 q^{99}+O(q^{100}) \) 8 * q + 16 * q^4 - 10 * q^5 + 20 * q^9 - 20 * q^11 + 32 * q^14 - 22 * q^15 + 32 * q^16 - 20 * q^20 - 62 * q^25 - 40 * q^26 - 4 * q^31 + 8 * q^34 + 40 * q^36 - 40 * q^44 + 88 * q^45 - 328 * q^49 + 138 * q^55 + 64 * q^56 - 60 * q^59 - 44 * q^60 + 64 * q^64 - 216 * q^66 + 68 * q^69 - 40 * q^70 + 564 * q^71 + 394 * q^75 - 40 * q^80 - 192 * q^81 - 208 * q^86 + 68 * q^89 - 80 * q^91 + 176 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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