LMFDB - Embedded newform 117.4.q.d.10.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(10,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("117.10");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.q (of order $6$, degree $2$, 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:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 17x^{2} + 289 $ x^4 - 17*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.2
Root			$3.57071 - 2.06155i$ of defining polynomial
Character	$\chi$	$=$	117.10
Dual form			117.4.q.d.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +O(q^{10})$	\(q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +(-27.7121 - 47.9988i) q^{10} +(35.0707 - 20.2481i) q^{11} +(42.1364 + 20.5310i) q^{13} -129.556 q^{14} +(27.5000 + 47.6314i) q^{16} +(21.5707 - 37.3616i) q^{17} +(23.3636 + 13.4890i) q^{19} +(-104.773 - 60.4906i) q^{20} +(83.4850 - 144.600i) q^{22} +(9.50500 + 16.4631i) q^{23} -55.6971 q^{25} +(192.783 - 13.5562i) q^{26} +(-244.909 + 141.398i) q^{28} +(-77.0557 - 133.464i) q^{29} +308.270i q^{31} +(224.955 + 129.878i) q^{32} -177.877i q^{34} +(-211.192 + 365.796i) q^{35} +(-37.6821 + 21.7558i) q^{37} +111.233 q^{38} -55.4243 q^{40} +(-41.4293 + 23.9192i) q^{41} +(171.061 - 296.286i) q^{43} -364.466i q^{44} +(67.8793 + 39.1901i) q^{46} +133.468i q^{47} +(322.167 + 558.010i) q^{49} +(-198.879 + 114.823i) q^{50} +(349.637 - 236.032i) q^{52} +438.454 q^{53} +(-272.182 - 471.433i) q^{55} +(-64.7779 + 112.199i) q^{56} +(-550.288 - 317.709i) q^{58} +(-511.434 - 295.277i) q^{59} +(270.652 - 468.783i) q^{61} +(635.516 + 1100.75i) q^{62} +631.000 q^{64} +(275.985 - 566.413i) q^{65} +(-199.485 + 115.173i) q^{67} +(-194.136 - 336.254i) q^{68} +1741.54i q^{70} +(389.202 + 224.706i) q^{71} +389.711i q^{73} +(-89.7014 + 155.367i) q^{74} +(210.272 - 121.401i) q^{76} -1272.47 q^{77} -897.820 q^{79} +(640.279 - 369.665i) q^{80} +(-98.6214 + 170.817i) q^{82} +1300.24i q^{83} +(-502.228 - 289.961i) q^{85} -1410.60i q^{86} +(-83.4850 - 144.600i) q^{88} +(-801.113 + 462.523i) q^{89} +(-824.061 - 1220.69i) q^{91} +171.090 q^{92} +(275.151 + 476.575i) q^{94} +(181.324 - 314.062i) q^{95} +(1351.43 + 780.247i) q^{97} +(2300.73 + 1328.33i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) $ 4 * q + 18 * q^4 - 66 * q^7	$ 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) $ 4 * q + 18 * q^4 - 66 * q^7 - 68 * q^10 + 126 * q^11 + 40 * q^13 - 204 * q^14 + 110 * q^16 + 72 * q^17 + 222 * q^19 - 162 * q^20 + 34 * q^22 + 138 * q^23 + 120 * q^25 + 714 * q^26 - 594 * q^28 + 6 * q^29 - 402 * q^35 + 492 * q^37 - 612 * q^38 - 136 * q^40 - 180 * q^41 + 470 * q^43 - 714 * q^46 + 346 * q^49 - 1224 * q^50 - 144 * q^52 + 2268 * q^53 - 446 * q^55 - 102 * q^56 - 2244 * q^58 - 2160 * q^59 - 160 * q^61 + 1428 * q^62 + 2524 * q^64 + 804 * q^65 - 498 * q^67 - 648 * q^68 + 1314 * q^71 - 1530 * q^74 + 1998 * q^76 - 2976 * q^77 + 8 * q^79 + 990 * q^80 + 34 * q^82 - 852 * q^85 - 34 * q^88 + 252 * q^89 - 1668 * q^91 + 2484 * q^92 + 2686 * q^94 + 54 * q^95 - 336 * q^97 + 6732 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	3.57071	−	2.06155i	1.26244	−	0.728869i	0.288892	−	0.957362i	$-0.406713\pi$
$2$	3.57071	−	2.06155i	1.26244	−	0.728869i	0.973546	+	0.228493i	$0.0733797\pi$
$3$		0			0
$3$		0			0
$4$	4.50000	−	7.79423i	0.562500	−	0.974279i
$5$		−	13.4424i		−	1.20232i	−0.799128	−	0.601161i	$-0.794705\pi$
$5$		−	13.4424i		−	1.20232i	0.799128	−	0.601161i	$-0.205295\pi$
$6$		0			0
$7$	−27.2121	−	15.7109i	−1.46932	−	0.848311i	−0.469910	−	0.882715i	$-0.655713\pi$
$7$	−27.2121	−	15.7109i	−1.46932	−	0.848311i	−0.999408	+	0.0344037i	$0.989047\pi$
$8$		−	4.12311i		−	0.182217i
$9$		0			0
$10$	−27.7121	−	47.9988i	−0.876335	−	1.51786i
$11$	35.0707	−	20.2481i	0.961293	−	0.555003i	0.0647219	−	0.997903i	$-0.479384\pi$
$11$	35.0707	−	20.2481i	0.961293	−	0.555003i	0.896571	+	0.442901i	$0.146051\pi$
$12$		0			0
$13$	42.1364	+	20.5310i	0.898965	+	0.438021i
$13$	42.1364	+	20.5310i	0.898965	+	0.438021i
$14$	−129.556			−2.47323
$15$		0			0
$16$	27.5000	+	47.6314i	0.429688	+	0.744241i
$17$	21.5707	−	37.3616i	0.307745	−	0.533030i	−0.670124	−	0.742249i	$-0.733759\pi$
$17$	21.5707	−	37.3616i	0.307745	−	0.533030i	0.977869	+	0.209219i	$0.0670923\pi$
$18$		0			0
$19$	23.3636	+	13.4890i	0.282104	+	0.162873i	0.634375	−	0.773025i	$-0.281257\pi$
$19$	23.3636	+	13.4890i	0.282104	+	0.162873i	−0.352272	+	0.935898i	$0.614591\pi$
$20$	−104.773	−	60.4906i	−1.17140	−	0.676306i
$21$		0			0
$22$	83.4850	−	144.600i	0.809048	−	1.40131i
$23$	9.50500	+	16.4631i	0.0861709	+	0.149252i	0.905890	−	0.423514i	$-0.139204\pi$
$23$	9.50500	+	16.4631i	0.0861709	+	0.149252i	−0.819719	+	0.572766i	$0.805870\pi$
$24$		0			0
$25$	−55.6971			−0.445577
$26$	192.783	−	13.5562i	1.45415	−	0.102253i
$27$		0			0
$28$	−244.909	+	141.398i	−1.65298	+	0.954350i
$29$	−77.0557	−	133.464i	−0.493410	−	0.854611i	0.506561	−	0.862204i	$-0.330916\pi$
$29$	−77.0557	−	133.464i	−0.493410	−	0.854611i	−0.999971	+	0.00759297i	$0.997583\pi$
$30$		0			0
$31$			308.270i			1.78603i	0.450025	+	0.893016i	$0.351415\pi$
$31$			308.270i			1.78603i	−0.450025	+	0.893016i	$0.648585\pi$
$32$	224.955	+	129.878i	1.24271	+	0.717480i
$33$		0			0
$34$		−	177.877i		−	0.897223i
$35$	−211.192	+	365.796i	−1.01994	+	1.76659i
$36$		0			0
$37$	−37.6821	+	21.7558i	−0.167430	+	0.0966657i	−0.581373	−	0.813637i	$-0.697484\pi$
$37$	−37.6821	+	21.7558i	−0.167430	+	0.0966657i	0.413944	+	0.910303i	$0.364151\pi$
$38$	111.233			0.474851
$39$		0			0
$40$	−55.4243			−0.219084
$41$	−41.4293	+	23.9192i	−0.157809	+	0.0911110i	−0.576825	−	0.816868i	$-0.695708\pi$
$41$	−41.4293	+	23.9192i	−0.157809	+	0.0911110i	0.419016	+	0.907979i	$0.362375\pi$
$42$		0			0
$43$	171.061	−	296.286i	0.606663	−	1.05077i	−0.385123	−	0.922865i	$-0.625841\pi$
$43$	171.061	−	296.286i	0.606663	−	1.05077i	0.991786	−	0.127906i	$-0.0408256\pi$
$44$		−	364.466i		−	1.24876i
$45$		0			0
$46$	67.8793	+	39.1901i	0.217571	+	0.125615i
$47$			133.468i			0.414218i	0.978318	+	0.207109i	$0.0664055\pi$
$47$			133.468i			0.414218i	−0.978318	+	0.207109i	$0.933594\pi$
$48$		0			0
$49$	322.167	+	558.010i	0.939263	+	1.62685i
$50$	−198.879	+	114.823i	−0.562514	+	0.324767i
$51$		0			0
$52$	349.637	−	236.032i	0.932422	−	0.629455i
$53$	438.454			1.13635			0.568173	−	0.822909i	$-0.307650\pi$
$53$	438.454			1.13635			0.568173	+	0.822909i	$0.307650\pi$
$54$		0			0
$55$	−272.182	−	471.433i	−0.667291	−	1.15578i
$56$	−64.7779	+	112.199i	−0.154577	+	0.267735i
$57$		0			0
$58$	−550.288	−	317.709i	−1.24580	−	0.719262i
$59$	−511.434	−	295.277i	−1.12853	−	0.651555i	−0.184963	−	0.982746i	$-0.559216\pi$
$59$	−511.434	−	295.277i	−1.12853	−	0.651555i	−0.943564	+	0.331190i	$0.892550\pi$
$60$		0			0
$61$	270.652	−	468.783i	0.568089	−	0.983960i	−0.428665	−	0.903463i	$-0.641016\pi$
$61$	270.652	−	468.783i	0.568089	−	0.983960i	0.996755	−	0.0804965i	$-0.0256506\pi$
$62$	635.516	+	1100.75i	1.30178	+	2.25476i
$63$		0			0
$64$	631.000			1.23242
$65$	275.985	−	566.413i	0.526642	−	1.08084i
$66$		0			0
$67$	−199.485	+	115.173i	−0.363746	+	0.210009i	−0.670723	−	0.741708i	$-0.734016\pi$
$67$	−199.485	+	115.173i	−0.363746	+	0.210009i	0.306977	+	0.951717i	$0.400683\pi$
$68$	−194.136	−	336.254i	−0.346213	−	0.599659i
$69$		0			0
$70$			1741.54i			2.97362i
$71$	389.202	+	224.706i	0.650561	+	0.375601i	0.788671	−	0.614816i	$-0.210770\pi$
$71$	389.202	+	224.706i	0.650561	+	0.375601i	−0.138110	+	0.990417i	$0.544103\pi$
$72$		0			0
$73$			389.711i			0.624826i	0.949946	+	0.312413i	$0.101137\pi$
$73$			389.711i			0.624826i	−0.949946	+	0.312413i	$0.898863\pi$
$74$	−89.7014	+	155.367i	−0.140913	+	0.244069i
$75$		0			0
$76$	210.272	−	121.401i	0.317367	−	0.183232i
$77$	−1272.47			−1.88326
$78$		0			0
$79$	−897.820			−1.27864			−0.639321	−	0.768940i	$-0.720784\pi$
$79$	−897.820			−1.27864			−0.639321	+	0.768940i	$0.720784\pi$
$80$	640.279	−	369.665i	0.894816	−	0.516623i
$81$		0			0
$82$	−98.6214	+	170.817i	−0.132816	+	0.230044i
$83$			1300.24i			1.71952i	0.510700	+	0.859759i	$0.329386\pi$
$83$			1300.24i			1.71952i	−0.510700	+	0.859759i	$0.670614\pi$
$84$		0			0
$85$	−502.228	−	289.961i	−0.640874	−	0.370009i
$86$		−	1410.60i		−	1.76871i
$87$		0			0
$88$	−83.4850	−	144.600i	−0.101131	−	0.175164i
$89$	−801.113	+	462.523i	−0.954132	+	0.550869i	−0.894362	−	0.447344i	$-0.852370\pi$
$89$	−801.113	+	462.523i	−0.954132	+	0.550869i	−0.0597703	+	0.998212i	$0.519037\pi$
$90$		0			0
$91$	−824.061	−	1220.69i	−0.949287	−	1.40619i
$92$	171.090			0.193884
$93$		0			0
$94$	275.151	+	476.575i	0.301911	+	0.522925i
$95$	181.324	−	314.062i	0.195825	−	0.339179i
$96$		0			0
$97$	1351.43	+	780.247i	1.41460	+	0.816722i	0.995818	−	0.0913623i	$-0.0291221\pi$
$97$	1351.43	+	780.247i	1.41460	+	0.816722i	0.418787	+	0.908085i	$0.362455\pi$
$98$	2300.73	+	1328.33i	2.37152	+	1.36920i
$99$		0			0
$100$	−250.637	+	434.116i	−0.250637	+	0.434116i
$101$	−479.420	−	830.380i	−0.472318	−	0.818078i	0.527181	−	0.849753i	$-0.323249\pi$
$101$	−479.420	−	830.380i	−0.472318	−	0.818078i	−0.999498	+	0.0316752i	$0.989916\pi$
$102$		0			0
$103$	−635.153			−0.607606			−0.303803	−	0.952735i	$-0.598257\pi$
$103$	−635.153			−0.607606			−0.303803	+	0.952735i	$0.598257\pi$
$104$	84.6514	−	173.733i	0.0798150	−	0.163807i
$105$		0			0
$106$	1565.59	−	903.897i	1.43457	−	0.828247i
$107$	−724.162	−	1254.29i	−0.654275	−	1.13324i	−0.982075	−	0.188490i	$-0.939641\pi$
$107$	−724.162	−	1254.29i	−0.654275	−	1.13324i	0.327800	−	0.944747i	$-0.393693\pi$
$108$		0			0
$109$		−	331.084i		−	0.290937i	−0.989363	−	0.145468i	$-0.953531\pi$
$109$		−	331.084i		−	0.290937i	0.989363	−	0.145468i	$-0.0464689\pi$
$110$	−1943.77	−	1122.24i	−1.68483	−	0.972736i
$111$		0			0
$112$		−	1728.20i		−	1.45803i
$113$	347.602	−	602.065i	0.289378	−	0.501217i	−0.684284	−	0.729216i	$-0.739885\pi$
$113$	347.602	−	602.065i	0.289378	−	0.501217i	0.973661	+	0.227999i	$0.0732184\pi$
$114$		0			0
$115$	221.304	−	127.770i	0.179449	−	0.103605i
$116$	−1387.00			−1.11017
$117$		0			0
$118$	−2434.91			−1.89959
$119$	−1173.97	+	677.792i	−0.904351	+	0.522127i
$120$		0			0
$121$	154.470	−	267.550i	0.116056	−	0.201014i
$122$		−	2231.85i		−	1.65625i
$123$		0			0
$124$	2402.73	+	1387.22i	1.74009	+	1.00464i
$125$		−	931.594i		−	0.666595i
$126$		0			0
$127$	123.577	+	214.042i	0.0863441	+	0.149552i	0.905963	−	0.423357i	$-0.139148\pi$
$127$	123.577	+	214.042i	0.0863441	+	0.149552i	−0.819619	+	0.572909i	$0.805815\pi$
$128$	453.481	−	261.817i	0.313144	−	0.180794i
$129$		0			0
$130$	−182.227	−	2591.46i	−0.122941	−	1.74835i
$131$	−472.243			−0.314962			−0.157481	−	0.987522i	$-0.550337\pi$
$131$	−472.243			−0.314962			−0.157481	+	0.987522i	$0.550337\pi$
$132$		0			0
$133$	−423.849	−	734.127i	−0.276333	−	0.478623i
$134$	−474.869	+	822.498i	−0.306138	+	0.530246i
$135$		0			0
$136$	−154.046	−	88.9383i	−0.0971273	−	0.0560765i
$137$	1585.43	+	915.349i	0.988704	+	0.570829i	0.904887	−	0.425652i	$-0.139955\pi$
$137$	1585.43	+	915.349i	0.988704	+	0.570829i	0.0838175	+	0.996481i	$0.473289\pi$
$138$		0			0
$139$	50.0000	−	86.6025i	0.0305104	−	0.0528456i	−0.850367	−	0.526190i	$-0.823620\pi$
$139$	50.0000	−	86.6025i	0.0305104	−	0.0528456i	0.880877	+	0.473344i	$0.156953\pi$
$140$	1900.73	+	3292.16i	1.14744	+	1.98742i
$141$		0			0
$142$	1852.97			1.09506
$143$	1893.47	−	133.146i	1.10727	−	0.0778615i
$144$		0			0
$145$	−1794.08	+	1035.81i	−1.02752	+	0.593237i
$146$	803.411	+	1391.55i	0.455416	+	0.788804i
$147$		0			0
$148$			391.604i			0.217498i
$149$	129.520	+	74.7784i	0.0712127	+	0.0411147i	0.535184	−	0.844736i	$-0.320242\pi$
$149$	129.520	+	74.7784i	0.0712127	+	0.0411147i	−0.463971	+	0.885850i	$0.653576\pi$
$150$		0			0
$151$			800.032i			0.431163i	0.976486	+	0.215582i	$0.0691647\pi$
$151$			800.032i			0.431163i	−0.976486	+	0.215582i	$0.930835\pi$
$152$	55.6164	−	96.3305i	0.0296782	−	0.0514042i
$153$		0			0
$154$	−4543.61	+	2623.26i	−2.37750	+	1.37265i
$155$	4143.88			2.14739
$156$		0			0
$157$	−2706.16			−1.37564			−0.687818	−	0.725884i	$-0.741431\pi$
$157$	−2706.16			−1.37564			−0.687818	+	0.725884i	$0.741431\pi$
$158$	−3205.86	+	1850.90i	−1.61421	+	0.931962i
$159$		0			0
$160$	1745.86	−	3023.93i	0.862642	−	1.49414i
$161$		−	597.330i		−	0.292399i
$162$		0			0
$163$	3185.46	+	1839.12i	1.53070	+	0.883750i	0.999330	+	0.0366108i	$0.0116562\pi$
$163$	3185.46	+	1839.12i	1.53070	+	0.883750i	0.531371	+	0.847139i	$0.321677\pi$
$164$			430.546i			0.205000i
$165$		0			0
$166$	2680.52	+	4642.79i	1.25330	+	2.17079i
$167$	−2791.30	+	1611.56i	−1.29339	+	0.746742i	−0.979254	−	0.202635i	$-0.935050\pi$
$167$	−2791.30	+	1611.56i	−1.29339	+	0.746742i	−0.314140	+	0.949377i	$0.601716\pi$
$168$		0			0
$169$	1353.96	+	1730.20i	0.616275	+	0.787531i
$170$	−2391.08			−1.07875
$171$		0			0
$172$	−1539.55	−	2666.57i	−0.682496	−	1.18212i
$173$	1344.77	−	2329.21i	0.590988	−	1.02362i	−0.403111	−	0.915151i	$-0.632071\pi$
$173$	1344.77	−	2329.21i	0.590988	−	1.02362i	0.994100	−	0.108471i	$-0.0345954\pi$
$174$		0			0
$175$	1515.64	+	875.054i	0.654694	+	0.377988i
$176$	1928.89	+	1113.64i	0.826111	+	0.476955i
$177$		0			0
$178$	−1907.03	+	3303.07i	−0.803022	+	1.39088i
$179$	762.021	+	1319.86i	0.318191	+	0.551122i	0.980111	−	0.198452i	$-0.0635915\pi$
$179$	762.021	+	1319.86i	0.318191	+	0.551122i	−0.661920	+	0.749574i	$0.730258\pi$
$180$		0			0
$181$	−476.881			−0.195836			−0.0979180	−	0.995194i	$-0.531218\pi$
$181$	−476.881			−0.195836			−0.0979180	+	0.995194i	$0.531218\pi$
$182$	−5459.01	−	2659.91i	−2.22335	−	1.08333i
$183$		0			0
$184$	67.8793	−	39.1901i	0.0271963	−	0.0157018i
$185$	292.449	+	506.537i	0.116223	+	0.201305i
$186$		0			0
$187$		−	1747.06i		−	0.683197i
$188$	1040.28	+	600.605i	0.403564	+	0.232998i
$189$		0			0
$190$		−	1495.23i		−	0.570924i
$191$	−684.871	+	1186.23i	−0.259453	+	0.449386i	−0.966096	−	0.258185i	$-0.916876\pi$
$191$	−684.871	+	1186.23i	−0.259453	+	0.449386i	0.706642	+	0.707571i	$0.250209\pi$
$192$		0			0
$193$	1857.38	−	1072.36i	0.692732	−	0.399949i	−0.111903	−	0.993719i	$-0.535695\pi$
$193$	1857.38	−	1072.36i	0.692732	−	0.399949i	0.804635	+	0.593770i	$0.202361\pi$
$194$	6434.08			2.38113
$195$		0			0
$196$	5799.01			2.11334
$197$	207.620	−	119.869i	0.0750879	−	0.0433520i	−0.461986	−	0.886887i	$-0.652863\pi$
$197$	207.620	−	119.869i	0.0750879	−	0.0433520i	0.537074	+	0.843535i	$0.319530\pi$
$198$		0			0
$199$	−794.969	+	1376.93i	−0.283185	+	0.490491i	−0.972167	−	0.234287i	$-0.924724\pi$
$199$	−794.969	+	1376.93i	−0.283185	+	0.490491i	0.688982	+	0.724778i	$0.258058\pi$
$200$			229.645i			0.0811918i
$201$		0			0
$202$	−3423.74	−	1976.70i	−1.19254	−	0.688515i
$203$			4842.47i			1.67426i
$204$		0			0
$205$	321.531	+	556.908i	0.109545	+	0.189737i
$206$	−2267.95	+	1309.40i	−0.767066	+	0.442866i
$207$		0			0
$208$	180.832	+	2571.62i	0.0602810	+	0.857258i
$209$	1092.50			0.361579
$210$		0			0
$211$	936.427	+	1621.94i	0.305527	+	0.529189i	0.977379	−	0.211497i	$-0.0678339\pi$
$211$	936.427	+	1621.94i	0.305527	+	0.529189i	−0.671851	+	0.740686i	$0.734501\pi$
$212$	1973.04	−	3417.41i	0.639195	−	1.10712i
$213$		0			0
$214$	−5171.55	−	2985.80i	−1.65196	−	0.953761i
$215$	−3982.78	−	2299.46i	−1.26337	−	0.729404i
$216$		0			0
$217$	4843.22	−	8388.70i	1.51511	−	2.62425i
$218$	−682.547	−	1182.21i	−0.212055	−	0.367290i
$219$		0			0
$220$	−4899.28			−1.50141
$221$	1675.98	−	1131.42i	0.510130	−	0.344377i
$222$		0			0
$223$	−48.6085	+	28.0642i	−0.0145967	+	0.00842742i	−0.507281	−	0.861781i	$-0.669349\pi$
$223$	−48.6085	+	28.0642i	−0.0145967	+	0.00842742i	0.492684	+	0.870208i	$0.336016\pi$
$224$	−4081.00	−	7068.51i	−1.21729	−	2.10841i
$225$		0			0
$226$		−	2866.40i		−	0.843673i
$227$	−577.976	−	333.695i	−0.168994	−	0.0975687i	0.413117	−	0.910678i	$-0.364440\pi$
$227$	−577.976	−	333.695i	−0.168994	−	0.0975687i	−0.582111	+	0.813109i	$0.697773\pi$
$228$		0			0
$229$		−	723.299i		−	0.208720i	−0.994540	−	0.104360i	$-0.966721\pi$
$229$		−	723.299i		−	0.208720i	0.994540	−	0.104360i	$-0.0332795\pi$
$230$	526.808	−	912.458i	0.151029	−	0.261590i
$231$		0			0
$232$	−550.288	+	317.709i	−0.155725	+	0.0899078i
$233$	−275.451			−0.0774482			−0.0387241	−	0.999250i	$-0.512329\pi$
$233$	−275.451			−0.0774482			−0.0387241	+	0.999250i	$0.512329\pi$
$234$		0			0
$235$	1794.12			0.498024
$236$	−4602.91	+	2657.49i	−1.26959	+	0.733000i
$237$		0			0
$238$	−2794.61	+	4840.41i	−0.761124	+	1.31831i
$239$			1529.39i			0.413925i	0.978349	+	0.206963i	$0.0663579\pi$
$239$			1529.39i			0.413925i	−0.978349	+	0.206963i	$0.933642\pi$
$240$		0			0
$241$	844.830	+	487.763i	0.225810	+	0.130372i	0.608638	−	0.793448i	$-0.291716\pi$
$241$	844.830	+	487.763i	0.225810	+	0.130372i	−0.382827	+	0.923820i	$0.625050\pi$
$242$		−	1273.79i		−	0.338357i
$243$		0			0
$244$	−2435.87	−	4219.05i	−0.639101	−	1.10695i
$245$	7500.97	−	4330.69i	1.95600	−	1.12930i
$246$		0			0
$247$	707.516	+	1048.05i	0.182260	+	0.269984i
$248$	1271.03			0.325446
$249$		0			0
$250$	−1920.53	−	3326.46i	−0.485860	−	0.841534i
$251$	937.070	−	1623.05i	0.235647	−	0.408152i	−0.723814	−	0.689995i	$-0.757613\pi$
$251$	937.070	−	1623.05i	0.235647	−	0.408152i	0.959460	+	0.281843i	$0.0909458\pi$
$252$		0			0
$253$	666.694	+	384.916i	0.165671	+	0.0956501i
$254$	882.517	+	509.522i	0.218008	+	0.125867i
$255$		0			0
$256$	−1444.50	+	2501.95i	−0.352661	+	0.610827i
$257$	909.094	+	1574.60i	0.220653	+	0.382181i	0.955006	−	0.296586i	$-0.0958480\pi$
$257$	909.094	+	1574.60i	0.220653	+	0.382181i	−0.734354	+	0.678767i	$0.762515\pi$
$258$		0			0
$259$	1367.22			0.328010
$260$	−3172.82	−	4699.95i	−0.756808	−	1.12107i
$261$		0			0
$262$	−1686.24	+	973.554i	−0.397620	+	0.229566i
$263$	336.899	+	583.527i	0.0789890	+	0.136813i	0.902814	−	0.430031i	$-0.141497\pi$
$263$	336.899	+	583.527i	0.0789890	+	0.136813i	−0.823825	+	0.566844i	$0.808164\pi$
$264$		0			0
$265$		−	5893.86i		−	1.36625i
$266$	−3026.88	−	1747.57i	−0.697707	−	0.402822i
$267$		0			0
$268$			2073.11i			0.472520i
$269$	−1678.20	+	2906.73i	−0.380378	+	0.658834i	−0.991116	−	0.132998i	$-0.957540\pi$
$269$	−1678.20	+	2906.73i	−0.380378	+	0.658834i	0.610738	+	0.791833i	$0.290873\pi$
$270$		0			0
$271$	−7721.09	+	4457.77i	−1.73071	+	0.999227i	−0.845699	+	0.533660i	$0.820816\pi$
$271$	−7721.09	+	4457.77i	−1.73071	+	0.999227i	−0.885013	+	0.465567i	$0.845850\pi$
$272$	2372.78			0.528937
$273$		0			0
$274$	7548.16			1.66424
$275$	−1953.34	+	1127.76i	−0.428330	+	0.247296i
$276$		0			0
$277$	2008.65	−	3479.09i	0.435698	−	0.754651i	−0.561654	−	0.827372i	$-0.689835\pi$
$277$	2008.65	−	3479.09i	0.435698	−	0.754651i	0.997352	+	0.0727208i	$0.0231682\pi$
$278$		−	412.311i		−	0.0889523i
$279$		0			0
$280$	1508.21	+	870.768i	0.321904	+	0.185851i
$281$			1841.12i			0.390860i	0.980718	+	0.195430i	$0.0626103\pi$
$281$			1841.12i			0.390860i	−0.980718	+	0.195430i	$0.937390\pi$
$282$		0			0
$283$	2424.70	+	4199.70i	0.509305	+	0.882143i	0.999942	+	0.0107784i	$0.00343094\pi$
$283$	2424.70	+	4199.70i	0.509305	+	0.882143i	−0.490637	+	0.871364i	$0.663236\pi$
$284$	3502.82	−	2022.35i	0.731881	−	0.422551i
$285$		0			0
$286$	6486.55	−	4378.91i	1.34111	−	0.905351i
$287$	1503.17			0.309162
$288$		0			0
$289$	1525.91	+	2642.95i	0.310586	+	0.537951i
$290$	−4270.76	+	7397.17i	−0.864785	+	1.49785i
$291$		0			0
$292$	3037.50	+	1753.70i	0.608754	+	0.351464i
$293$	1224.43	+	706.927i	0.244137	+	0.140953i	0.617077	−	0.786903i	$-0.288317\pi$
$293$	1224.43	+	706.927i	0.244137	+	0.140953i	−0.372940	+	0.927856i	$0.621650\pi$
$294$		0			0
$295$	−3969.22	+	6874.89i	−0.783379	+	1.35685i
$296$	89.7014	+	155.367i	0.0176142	+	0.0305086i
$297$		0			0
$298$	616.639			0.119869
$299$	62.5022	+	888.845i	0.0120889	+	0.171917i
$300$		0			0
$301$	−9309.86	+	5375.05i	−1.78276	+	1.02928i
$302$	1649.31	+	2856.68i	0.314262	+	0.544317i
$303$		0			0
$304$			1483.79i			0.279937i
$305$	−6301.55	−	3638.20i	−1.18304	−	0.683026i
$306$		0			0
$307$			4625.64i			0.859932i	0.902845	+	0.429966i	$0.141474\pi$
$307$			4625.64i			0.859932i	−0.902845	+	0.429966i	$0.858526\pi$
$308$	−5726.10	+	9917.89i	−1.05933	+	1.83482i
$309$		0			0
$310$	14796.6	−	8542.83i	2.71094	−	1.56516i
$311$	−6060.79			−1.10507			−0.552534	−	0.833490i	$-0.686339\pi$
$311$	−6060.79			−1.10507			−0.552534	+	0.833490i	$0.686339\pi$
$312$		0			0
$313$	969.946			0.175158			0.0875792	−	0.996158i	$-0.472087\pi$
$313$	969.946			0.175158			0.0875792	+	0.996158i	$0.472087\pi$
$314$	−9662.91	+	5578.88i	−1.73665	+	1.00266i
$315$		0			0
$316$	−4040.19	+	6997.81i	−0.719236	+	1.24575i
$317$		−	8741.63i		−	1.54883i	−0.632679	−	0.774414i	$-0.718045\pi$
$317$		−	8741.63i		−	1.54883i	0.632679	−	0.774414i	$-0.281955\pi$
$318$		0			0
$319$	−5404.80	−	3120.46i	−0.948623	−	0.547687i
$320$		−	8482.13i		−	1.48177i
$321$		0			0
$322$	−1231.43	−	2132.89i	−0.213120	−	0.369135i
$323$	1007.94	−	581.933i	0.173632	−	0.100247i
$324$		0			0
$325$	−2346.88	−	1143.52i	−0.400558	−	0.195172i
$326$	15165.8			2.57655
$327$		0			0
$328$	98.6214	+	170.817i	0.0166020	+	0.0287555i
$329$	2096.90	−	3631.94i	0.351386	−	0.608618i
$330$		0			0
$331$	−6051.57	−	3493.88i	−1.00491	−	0.580184i	−0.0952114	−	0.995457i	$-0.530353\pi$
$331$	−6051.57	−	3493.88i	−1.00491	−	0.580184i	−0.909697	+	0.415273i	$0.863686\pi$
$332$	10134.4	+	5851.09i	1.67529	+	0.967229i
$333$		0			0
$334$	−6644.61	+	11508.8i	−1.08855	+	1.88543i
$335$	1548.19	+	2681.55i	0.252498	+	0.437339i
$336$		0			0
$337$	4156.59			0.671881			0.335940	−	0.941883i	$-0.390946\pi$
$337$	4156.59			0.671881			0.335940	+	0.941883i	$0.390946\pi$
$338$	8401.50	+	3386.81i	1.35202	+	0.545025i
$339$		0			0
$340$	−4520.05	+	2609.65i	−0.720983	+	0.416260i
$341$	6241.89	+	10811.3i	0.991252	+	1.71690i
$342$		0			0
$343$		−	9468.49i		−	1.49053i
$344$	−1221.62	−	705.301i	−0.191469	−	0.110544i
$345$		0			0
$346$		−	11089.3i		−	1.72301i
$347$	−156.256	+	270.644i	−0.0241737	+	0.0418701i	−0.877859	−	0.478919i	$-0.841029\pi$
$347$	−156.256	+	270.644i	−0.0241737	+	0.0418701i	0.853685	+	0.520789i	$0.174362\pi$
$348$		0			0
$349$	3861.39	−	2229.37i	0.592251	−	0.341936i	−0.173736	−	0.984792i	$-0.555584\pi$
$349$	3861.39	−	2229.37i	0.592251	−	0.341936i	0.765987	+	0.642856i	$0.222251\pi$
$350$	7215.88			1.10201
$351$		0			0
$352$	10519.1			1.59281
$353$	1947.84	−	1124.59i	0.293692	−	0.169563i	−0.345914	−	0.938266i	$-0.612431\pi$
$353$	1947.84	−	1124.59i	0.293692	−	0.169563i	0.639605	+	0.768703i	$0.279098\pi$
$354$		0			0
$355$	3020.58	−	5231.80i	0.451594	−	0.782183i
$356$			8325.41i			1.23945i
$357$		0			0
$358$	5441.92	+	3141.89i	0.803392	+	0.463838i
$359$		−	7842.79i		−	1.15300i	−0.817098	−	0.576499i	$-0.804418\pi$
$359$		−	7842.79i		−	1.15300i	0.817098	−	0.576499i	$-0.195582\pi$
$360$		0			0
$361$	−3065.60	−	5309.77i	−0.446945	−	0.774131i
$362$	−1702.81	+	983.116i	−0.247231	+	0.142739i
$363$		0			0
$364$	−13222.7	+	929.796i	−1.90400	+	0.133886i
$365$	5238.64			0.751241
$366$		0			0
$367$	−3330.12	−	5767.94i	−0.473653	−	0.820392i	0.525892	−	0.850552i	$-0.323732\pi$
$367$	−3330.12	−	5767.94i	−0.473653	−	0.820392i	−0.999545	+	0.0301597i	$0.990398\pi$
$368$	−522.775	+	905.473i	−0.0740531	+	0.128264i
$369$		0			0
$370$	2088.51	+	1205.80i	0.293449	+	0.169423i
$371$	−11931.3	−	6888.53i	−1.66965	−	0.963975i
$372$		0			0
$373$	18.4936	−	32.0319i	0.00256720	−	0.00444651i	−0.864739	−	0.502222i	$-0.832516\pi$
$373$	18.4936	−	32.0319i	0.00256720	−	0.00444651i	0.867306	+	0.497775i	$0.165850\pi$
$374$	−3601.66	−	6238.26i	−0.497961	−	0.862494i
$375$		0			0
$376$	550.301			0.0754777
$377$	−506.696	−	7205.74i	−0.0692207	−	0.984389i
$378$		0			0
$379$	10461.5	−	6039.93i	1.41786	−	0.818603i	0.421751	−	0.906712i	$-0.361416\pi$
$379$	10461.5	−	6039.93i	1.41786	−	0.818603i	0.996111	+	0.0881092i	$0.0280825\pi$
$380$	−1631.91	−	2826.55i	−0.220303	−	0.381577i
$381$		0			0
$382$			5647.59i			0.756429i
$383$	−9151.63	−	5283.69i	−1.22096	−	0.704919i	−0.255835	−	0.966721i	$-0.582350\pi$
$383$	−9151.63	−	5283.69i	−1.22096	−	0.704919i	−0.965122	+	0.261801i	$0.915684\pi$
$384$		0			0
$385$			17104.9i			2.26428i
$386$	4421.45	−	7658.18i	0.583021	−	1.00982i
$387$		0			0
$388$	12162.8	−	7022.22i	1.59143	−	0.918813i
$389$	−9757.49			−1.27179			−0.635893	−	0.771778i	$-0.719368\pi$
$389$	−9757.49			−1.27179			−0.635893	+	0.771778i	$0.719368\pi$
$390$		0			0
$391$	820.119			0.106075
$392$	2300.73	−	1328.33i	0.296440	−	0.171150i
$393$		0			0
$394$	494.234	−	856.039i	0.0631959	−	0.109458i
$395$			12068.8i			1.53734i
$396$		0			0
$397$	−12298.0	−	7100.26i	−1.55471	−	0.897612i	−0.997748	−	0.0670737i	$-0.978634\pi$
$397$	−12298.0	−	7100.26i	−1.55471	−	0.897612i	−0.556962	−	0.830538i	$-0.688033\pi$
$398$			6555.48i			0.825620i
$399$		0			0
$400$	−1531.67	−	2652.93i	−0.191459	−	0.331617i
$401$	−10978.1	+	6338.19i	−1.36713	+	0.789313i	−0.990561	−	0.137076i	$-0.956230\pi$
$401$	−10978.1	+	6338.19i	−1.36713	+	0.789313i	−0.376569	+	0.926389i	$0.622896\pi$
$402$		0			0
$403$	−6329.10	+	12989.4i	−0.782319	+	1.60558i
$404$	−8629.56			−1.06271
$405$		0			0
$406$	9983.01	+	17291.1i	1.22032	+	2.11365i
$407$	−881.026	+	1525.98i	−0.107299	+	0.185848i
$408$		0			0
$409$	−1328.20	−	766.838i	−0.160576	−	0.0927083i	0.417559	−	0.908650i	$-0.362886\pi$
$409$	−1328.20	−	766.838i	−0.160576	−	0.0927083i	−0.578134	+	0.815942i	$0.696219\pi$
$410$	2296.19	+	1325.71i	0.276587	+	0.159688i
$411$		0			0
$412$	−2858.19	+	4950.53i	−0.341779	+	0.591978i
$413$	9278.15	+	16070.2i	1.10544	+	1.91468i
$414$		0			0
$415$	17478.3			2.06741
$416$	6812.28	+	10091.1i	0.802883	+	1.18932i
$417$		0			0
$418$	3901.02	−	2252.25i	0.456471	−	0.263544i
$419$	−1082.95	−	1875.72i	−0.126266	−	0.218699i	0.795961	−	0.605348i	$-0.206966\pi$
$419$	−1082.95	−	1875.72i	−0.126266	−	0.218699i	−0.922227	+	0.386649i	$0.873633\pi$
$420$		0			0
$421$			734.575i			0.0850380i	0.999096	+	0.0425190i	$0.0135383\pi$
$421$			734.575i			0.0850380i	−0.999096	+	0.0425190i	$0.986462\pi$
$422$	6687.43	+	3860.99i	0.771419	+	0.445379i
$423$		0			0
$424$		−	1807.79i		−	0.207062i
$425$	−1201.43	+	2080.93i	−0.137124	+	0.237506i
$426$		0			0
$427$	−14730.0	+	8504.40i	−1.66941	+	0.963833i
$428$	−13034.9			−1.47212
$429$		0			0
$430$	−18961.8			−2.12656
$431$	11872.6	−	6854.66i	1.32688	−	0.766073i	0.342061	−	0.939678i	$-0.388875\pi$
$431$	11872.6	−	6854.66i	1.32688	−	0.766073i	0.984815	+	0.173605i	$0.0555416\pi$
$432$		0			0
$433$	5024.97	−	8703.50i	0.557701	−	0.965967i	−0.439987	−	0.898004i	$-0.645017\pi$
$433$	5024.97	−	8703.50i	0.557701	−	0.965967i	0.997688	−	0.0679624i	$-0.0216498\pi$
$434$		−	39938.2i		−	4.41727i
$435$		0			0
$436$	−2580.54	−	1489.88i	−0.283453	−	0.163652i
$437$			512.850i			0.0561395i
$438$		0			0
$439$	−4066.73	−	7043.79i	−0.442129	−	0.765790i	0.555718	−	0.831371i	$-0.312443\pi$
$439$	−4066.73	−	7043.79i	−0.442129	−	0.765790i	−0.997847	+	0.0655807i	$0.979110\pi$
$440$	−1943.77	+	1122.24i	−0.210604	+	0.121592i
$441$		0			0
$442$	3651.98	−	7495.09i	0.393003	−	0.806572i
$443$	2370.78			0.254264			0.127132	−	0.991886i	$-0.459423\pi$
$443$	2370.78			0.254264			0.127132	+	0.991886i	$0.459423\pi$
$444$		0			0
$445$	6217.40	+	10768.9i	0.662321	+	1.14717i
$446$	−115.711	+	200.418i	−0.0122850	+	0.0212782i
$447$		0			0
$448$	−17170.9	−	9913.60i	−1.81082	−	1.04548i
$449$	−11191.8	−	6461.60i	−1.17634	−	0.679158i	−0.221172	−	0.975235i	$-0.570988\pi$
$449$	−11191.8	−	6461.60i	−1.17634	−	0.679158i	−0.955164	+	0.296077i	$0.904322\pi$
$450$		0			0
$451$	−968.636	+	1677.73i	−0.101134	+	0.175169i
$452$	−3128.42	−	5418.58i	−0.325550	−	0.563869i
$453$		0			0
$454$	−2751.72			−0.284459
$455$	−16409.0	+	11077.3i	−1.69070	+	1.14135i
$456$		0			0
$457$	7275.71	−	4200.63i	0.744734	−	0.429972i	−0.0790543	−	0.996870i	$-0.525190\pi$
$457$	7275.71	−	4200.63i	0.744734	−	0.429972i	0.823788	+	0.566898i	$0.191857\pi$
$458$	−1491.12	−	2582.70i	−0.152130	−	0.263497i
$459$		0			0
$460$		−	2299.85i		−	0.233111i
$461$	15265.7	+	8813.67i	1.54229	+	0.890441i	0.998694	+	0.0510940i	$0.0162708\pi$
$461$	15265.7	+	8813.67i	1.54229	+	0.890441i	0.543596	+	0.839347i	$0.317063\pi$
$462$		0			0
$463$			5461.81i			0.548233i	0.961697	+	0.274116i	$0.0883853\pi$
$463$			5461.81i			0.548233i	−0.961697	+	0.274116i	$0.911615\pi$
$464$	4238.06	−	7340.54i	0.424024	−	0.734431i
$465$		0			0
$466$	−983.558	+	567.858i	−0.0977735	+	0.0564496i
$467$	8262.19			0.818691			0.409345	−	0.912379i	$-0.365757\pi$
$467$	8262.19			0.818691			0.409345	+	0.912379i	$0.365757\pi$
$468$		0			0
$469$	7237.89			0.712611
$470$	6406.29	−	3698.68i	0.628724	−	0.362994i
$471$		0			0
$472$	−1217.46	+	2108.70i	−0.118725	+	0.205637i
$473$		−	13854.6i		−	1.34680i
$474$		0			0
$475$	−1301.28	−	751.297i	−0.125699	−	0.0725723i
$476$			12200.3i			1.17479i
$477$		0			0
$478$	3152.92	+	5461.02i	0.301697	+	0.522555i
$479$	−1364.74	+	787.935i	−0.130181	+	0.0751601i	−0.563676	−	0.825996i	$-0.690613\pi$
$479$	−1364.74	+	787.935i	−0.130181	+	0.0751601i	0.433495	+	0.901156i	$0.357280\pi$
$480$		0			0
$481$	−2034.46	+	143.060i	−0.192855	+	0.0135613i
$482$	4022.20			0.380095
$483$		0			0
$484$	−1390.23	−	2407.95i	−0.130563	−	0.226141i
$485$	10488.4	−	18166.4i	0.981963	−	1.70081i
$486$		0			0
$487$	10908.2	+	6297.84i	1.01498	+	0.586001i	0.912647	−	0.408749i	$-0.134035\pi$
$487$	10908.2	+	6297.84i	1.01498	+	0.586001i	0.102337	+	0.994750i	$0.467368\pi$
$488$	−1932.84	−	1115.93i	−0.179294	−	0.103516i
$489$		0			0
$490$	17855.9	−	30927.3i	1.64622	−	2.85133i
$491$	535.606	+	927.697i	0.0492293	+	0.0852676i	0.889590	−	0.456760i	$-0.150990\pi$
$491$	535.606	+	927.697i	0.0492293	+	0.0852676i	−0.840361	+	0.542028i	$0.817657\pi$
$492$		0			0
$493$	−6648.59			−0.607378
$494$	4686.96	+	2283.72i	0.426875	+	0.207995i
$495$		0			0
$496$	−14683.3	+	8477.44i	−1.32924	+	0.767436i
$497$	−7060.68	−	12229.5i	−0.637253	−	1.10376i
$498$		0			0
$499$		−	1422.30i		−	0.127597i	−0.997963	−	0.0637985i	$-0.979678\pi$
$499$		−	1422.30i		−	0.127597i	0.997963	−	0.0637985i	$-0.0203215\pi$
$500$	−7261.06	−	4192.17i	−0.649449	−	0.374959i
$501$		0			0
$502$		−	7727.28i		−	0.687022i
$503$	−4674.67	+	8096.76i	−0.414380	+	0.717727i	−0.995363	−	0.0961884i	$-0.969335\pi$
$503$	−4674.67	+	8096.76i	−0.414380	+	0.717727i	0.580983	+	0.813916i	$0.302668\pi$
$504$		0			0
$505$	−11162.3	+	6444.54i	−0.983593	+	0.567878i
$506$	3174.10			0.278866
$507$		0			0
$508$	2224.39			0.194274
$509$	−11896.0	+	6868.15i	−1.03591	+	0.598086i	−0.918673	−	0.395018i	$-0.870738\pi$
$509$	−11896.0	+	6868.15i	−1.03591	+	0.598086i	−0.117241	+	0.993103i	$0.537405\pi$
$510$		0			0
$511$	6122.73	−	10604.9i	0.530046	−	0.918067i
$512$			16100.7i			1.38976i
$513$		0			0
$514$	6492.23	+	3748.29i	0.557120	+	0.321654i
$515$			8537.96i			0.730538i
$516$		0			0
$517$	2702.47	+	4680.81i	0.229892	+	0.398185i
$518$	4881.94	−	2818.59i	0.414093	−	0.239076i
$519$		0			0
$520$	−2335.38	−	1137.92i	−0.196949	−	0.0959632i
$521$	−11052.3			−0.929386			−0.464693	−	0.885472i	$-0.653835\pi$
$521$	−11052.3			−0.929386			−0.464693	+	0.885472i	$0.653835\pi$
$522$		0			0
$523$	−3238.52	−	5609.28i	−0.270766	−	0.468980i	0.698292	−	0.715813i	$-0.253944\pi$
$523$	−3238.52	−	5609.28i	−0.270766	−	0.468980i	−0.969058	+	0.246832i	$0.920610\pi$
$524$	−2125.09	+	3680.77i	−0.177166	+	0.306861i
$525$		0			0
$526$	2405.94	+	1389.07i	0.199437	+	0.115145i
$527$	11517.5	+	6649.61i	0.952009	+	0.549643i
$528$		0			0
$529$	5902.81	−	10224.0i	0.485149	−	0.840303i
$530$	−12150.5	−	21045.3i	−0.995819	−	1.72481i
$531$		0			0
$532$	−7629.27			−0.621750
$533$	−2236.77	+	157.286i	−0.181773	+	0.0127820i
$534$		0			0
$535$	−16860.6	+	9734.45i	−1.36252	+	0.786649i
$536$	474.869	+	822.498i	0.0382672	+	0.0662808i
$537$		0			0
$538$			13838.8i			1.10898i
$539$	22597.3	+	13046.5i	1.80581	+	1.04259i
$540$		0			0
$541$		−	18341.5i		−	1.45761i	−0.684723	−	0.728803i	$-0.740077\pi$
$541$		−	18341.5i		−	1.45761i	0.684723	−	0.728803i	$-0.259923\pi$
$542$	−18379.9	+	31834.9i	−1.45661	+	2.52292i
$543$		0			0
$544$	9704.88	−	5603.11i	0.764877	−	0.441602i
$545$	−4450.55			−0.349799
$546$		0			0
$547$	−18943.1			−1.48071			−0.740356	−	0.672215i	$-0.765343\pi$
$547$	−18943.1			−1.48071			−0.740356	+	0.672215i	$0.765343\pi$
$548$	14268.9	−	8238.14i	1.11229	−	0.642182i
$549$		0			0
$550$	−4649.88	+	8053.82i	−0.360493	+	0.624393i
$551$		−	4157.61i		−	0.321452i
$552$		0			0
$553$	24431.6	+	14105.6i	1.87873	+	1.08469i
$554$		−	16563.8i		−	1.27027i
$555$		0			0
$556$	−450.000	−	779.423i	−0.0343242	−	0.0594512i
$557$	359.861	−	207.766i	0.0273749	−	0.0158049i	−0.486250	−	0.873820i	$-0.661636\pi$
$557$	359.861	−	207.766i	0.0273749	−	0.0158049i	0.513625	+	0.858015i	$0.328302\pi$
$558$		0			0
$559$	13290.9	−	8972.38i	1.00563	−	0.678875i
$560$	−23231.1			−1.75303
$561$		0			0
$562$	3795.56	+	6574.10i	0.284886	+	0.493437i
$563$	−9145.90	+	15841.2i	−0.684643	+	1.18584i	0.288907	+	0.957357i	$0.406708\pi$
$563$	−9145.90	+	15841.2i	−0.684643	+	1.18584i	−0.973549	+	0.228478i	$0.926625\pi$
$564$		0			0
$565$	−8093.17	−	4672.59i	−0.602623	−	0.347925i
$566$	17315.8	+	9997.29i	1.28593	+	0.742434i
$567$		0			0
$568$	926.486	−	1604.72i	0.0684410	−	0.118543i
$569$	−2173.73	−	3765.02i	−0.160154	−	0.277395i	0.774770	−	0.632244i	$-0.217866\pi$
$569$	−2173.73	−	3765.02i	−0.160154	−	0.277395i	−0.934924	+	0.354848i	$0.884532\pi$
$570$		0			0
$571$	16756.0			1.22805			0.614024	−	0.789288i	$-0.289550\pi$
$571$	16756.0			1.22805			0.614024	+	0.789288i	$0.289550\pi$
$572$	7482.84	−	15357.3i	0.546981	−	1.12259i
$573$		0			0
$574$	5367.40	−	3098.87i	0.390298	−	0.225339i
$575$	−529.401	−	916.950i	−0.0383958	−	0.0665034i
$576$		0			0
$577$			19974.7i			1.44117i	0.693364	+	0.720587i	$0.256128\pi$
$577$			19974.7i			1.44117i	−0.693364	+	0.720587i	$0.743872\pi$
$578$	10897.2	+	6291.48i	0.784191	+	0.452753i
$579$		0			0
$580$			18644.6i			1.33478i
$581$	20428.0	−	35382.4i	1.45869	−	2.52652i
$582$		0			0
$583$	15376.9	−	8877.86i	1.09236	−	0.630675i
$584$	1606.82			0.113854
$585$		0			0
$586$	5829.47			0.410944
$587$	13638.7	−	7874.33i	0.958996	−	0.553677i	0.0631321	−	0.998005i	$-0.479891\pi$
$587$	13638.7	−	7874.33i	0.958996	−	0.553677i	0.895864	+	0.444329i	$0.146558\pi$
$588$		0			0
$589$	−4158.25	+	7202.30i	−0.290896	+	0.503846i
$590$			32731.0i			2.28392i
$591$		0			0
$592$	−2072.52	−	1196.57i	−0.143885	−	0.0830721i
$593$			13318.4i			0.922297i	0.887323	+	0.461148i	$0.152562\pi$
$593$			13318.4i			0.922297i	−0.887323	+	0.461148i	$0.847438\pi$
$594$		0			0
$595$	9111.13	+	15780.9i	0.627765	+	1.08732i
$596$	1165.68	−	673.006i	0.0801143	−	0.0462540i
$597$		0			0
$598$	2055.58	+	3044.96i	0.140567	+	0.208224i
$599$	−2970.80			−0.202644			−0.101322	−	0.994854i	$-0.532307\pi$
$599$	−2970.80			−0.202644			−0.101322	+	0.994854i	$0.532307\pi$
$600$		0			0
$601$	−5316.31	−	9208.13i	−0.360827	−	0.624971i	0.627270	−	0.778802i	$-0.284172\pi$
$601$	−5316.31	−	9208.13i	−0.360827	−	0.624971i	−0.988097	+	0.153831i	$0.950839\pi$
$602$	−22161.9	+	38385.5i	−1.50042	+	2.59880i
$603$		0			0
$604$	6235.63	+	3600.14i	0.420073	+	0.242529i
$605$	−3596.50	−	2076.44i	−0.241684	−	0.139536i
$606$		0			0
$607$	−5793.94	+	10035.4i	−0.387428	+	0.671045i	−0.992103	−	0.125428i	$-0.959970\pi$
$607$	−5793.94	+	10035.4i	−0.387428	+	0.671045i	0.604675	+	0.796472i	$0.293303\pi$
$608$	3503.83	+	6068.82i	0.233716	+	0.404808i
$609$		0			0
$610$	−30001.4			−1.99135
$611$	−2740.22	+	5623.85i	−0.181436	+	0.372368i
$612$		0			0
$613$	18006.7	−	10396.2i	1.18643	−	0.684988i	0.228939	−	0.973441i	$-0.426474\pi$
$613$	18006.7	−	10396.2i	1.18643	−	0.684988i	0.957494	+	0.288453i	$0.0931409\pi$
$614$	9536.00	+	16516.8i	0.626778	+	1.08561i
$615$		0			0
$616$			5246.51i			0.343162i
$617$	−1353.40	−	781.388i	−0.0883079	−	0.0509846i	0.455196	−	0.890391i	$-0.349569\pi$
$617$	−1353.40	−	781.388i	−0.0883079	−	0.0509846i	−0.543504	+	0.839407i	$0.682903\pi$
$618$		0			0
$619$		−	758.406i		−	0.0492454i	−0.999697	−	0.0246227i	$-0.992162\pi$
$619$		−	758.406i		−	0.0492454i	0.999697	−	0.0246227i	$-0.00783844\pi$
$620$	18647.5	−	32298.4i	1.20790	−	2.09215i
$621$		0			0
$622$	−21641.4	+	12494.6i	−1.39508	+	0.805450i
$623$	29066.7			1.86923
$624$		0			0
$625$	−19485.0			−1.24704
$626$	3463.40	−	1999.59i	0.221127	−	0.127668i
$627$		0			0
$628$	−12177.7	+	21092.4i	−0.773795	+	1.34025i
$629$			1877.15i			0.118994i
$630$		0			0
$631$	−12354.0	−	7132.59i	−0.779406	−	0.449990i	0.0568136	−	0.998385i	$-0.481906\pi$
$631$	−12354.0	−	7132.59i	−0.779406	−	0.449990i	−0.836220	+	0.548394i	$0.815239\pi$
$632$			3701.81i			0.232990i
$633$		0			0
$634$	−18021.3	−	31213.9i	−1.12889	−	1.95530i
$635$	2877.23	−	1661.17i	0.179810	−	0.103813i
$636$		0			0
$637$	2118.48	+	30127.0i	0.131770	+	1.87390i
$638$	−25732.0			−1.59677
$639$		0			0
$640$	−3519.44	−	6095.85i	−0.217372	−	0.376500i
$641$	−1992.82	+	3451.67i	−0.122795	+	0.212688i	−0.920869	−	0.389872i	$-0.872519\pi$
$641$	−1992.82	+	3451.67i	−0.122795	+	0.212688i	0.798074	+	0.602560i	$0.205853\pi$
$642$		0			0
$643$	7063.78	+	4078.28i	0.433232	+	0.250127i	0.700723	−	0.713434i	$-0.252861\pi$
$643$	7063.78	+	4078.28i	0.433232	+	0.250127i	−0.267490	+	0.963561i	$0.586194\pi$
$644$	−4655.73	−	2687.98i	−0.284878	−	0.164474i
$645$		0			0
$646$	2399.37	−	4155.83i	0.146133	−	0.253110i
$647$	−5639.62	−	9768.11i	−0.342684	−	0.593546i	0.642246	−	0.766498i	$-0.278003\pi$
$647$	−5639.62	−	9768.11i	−0.342684	−	0.593546i	−0.984930	+	0.172953i	$0.944669\pi$
$648$		0			0
$649$	−23915.2			−1.44646
$650$	−10737.5	+	755.041i	−0.647935	+	0.0455617i
$651$		0			0
$652$	28669.1	−	16552.1i	1.72204	−	0.994219i
$653$	3282.88	+	5686.11i	0.196736	+	0.340757i	0.947468	−	0.319850i	$-0.103632\pi$
$653$	3282.88	+	5686.11i	0.196736	+	0.340757i	−0.750732	+	0.660607i	$0.770299\pi$
$654$		0			0
$655$			6348.06i			0.378686i
$656$	−2278.61	−	1315.56i	−0.135617	−	0.0782986i
$657$		0			0
$658$		−	17291.5i		−	1.02446i
$659$	2399.67	−	4156.36i	0.141848	−	0.245688i	−0.786344	−	0.617788i	$-0.788029\pi$
$659$	2399.67	−	4156.36i	0.141848	−	0.245688i	0.928193	+	0.372100i	$0.121362\pi$
$660$		0			0
$661$	−13504.5	+	7796.80i	−0.794648	+	0.458790i	−0.841596	−	0.540107i	$-0.818384\pi$
$661$	−13504.5	+	7796.80i	−0.794648	+	0.458790i	0.0469482	+	0.998897i	$0.485050\pi$
$662$	−28811.3			−1.69151
$663$		0			0
$664$	5361.03			0.313326
$665$	−9868.41	+	5697.53i	−0.575459	+	0.332242i
$666$		0			0
$667$	1464.83	−	2537.16i	0.0850351	−	0.147285i
$668$			29008.0i			1.68017i
$669$		0			0
$670$	11056.3	+	6383.37i	0.637526	+	0.368076i
$671$		−	21920.8i		−	1.26116i
$672$		0			0
$673$	−1102.77	−	1910.06i	−0.0631630	−	0.109402i	0.832715	−	0.553702i	$-0.186785\pi$
$673$	−1102.77	−	1910.06i	−0.0631630	−	0.109402i	−0.895878	+	0.444301i	$0.853452\pi$
$674$	14842.0	−	8569.03i	0.848208	−	0.489713i
$675$		0			0
$676$	19578.4	−	2767.13i	1.11393	−	0.157438i
$677$	15046.4			0.854182			0.427091	−	0.904209i	$-0.359538\pi$
$677$	15046.4			0.854182			0.427091	+	0.904209i	$0.359538\pi$
$678$		0			0
$679$	−24516.8	−	42464.4i	−1.38567	−	2.40005i
$680$	−1195.54	+	2070.74i	−0.0674219	+	0.116778i
$681$		0			0
$682$	44576.0	+	25736.0i	2.50279	+	1.44499i
$683$	−26528.5	−	15316.3i	−1.48622	−	0.858068i	−0.486340	−	0.873770i	$-0.661668\pi$
$683$	−26528.5	−	15316.3i	−1.48622	−	0.858068i	−0.999877	+	0.0157020i	$0.995002\pi$
$684$		0			0
$685$	12304.5	−	21311.9i	0.686320	−	1.18874i
$686$	−19519.8	−	33809.3i	−1.08640	−	1.88170i
$687$		0			0
$688$	18816.7			1.04270
$689$	18474.9	+	9001.90i	1.02153	+	0.497743i
$690$		0			0
$691$	1884.22	−	1087.86i	0.103733	−	0.0598901i	−0.447236	−	0.894416i	$-0.647592\pi$
$691$	1884.22	−	1087.86i	0.103733	−	0.0598901i	0.550969	+	0.834526i	$0.314258\pi$
$692$	−12102.9	−	20962.9i	−0.664862	−	1.15157i
$693$		0			0
$694$			1288.52i			0.0704780i
$695$	−1164.14	−	672.118i	−0.0635373	−	0.0366833i
$696$		0			0
$697$			2063.82i			0.112156i
$698$	9191.95	−	15920.9i	0.498453	−	0.863346i
$699$		0			0
$700$	13640.7	−	7875.49i	0.736531	−	0.425236i
$701$	−32718.2			−1.76284			−0.881419	−	0.472335i	$-0.843411\pi$
$701$	−32718.2			−1.76284			−0.881419	+	0.472335i	$0.843411\pi$
$702$		0			0
$703$	−1173.85			−0.0629768
$704$	22129.6	−	12776.5i	1.18472	−	0.683997i
$705$		0			0
$706$	4636.79	−	8031.15i	0.247178	−	0.428125i
$707$			30128.6i			1.60269i
$708$		0			0
$709$	−21840.9	−	12609.8i	−1.15691	−	0.667945i	−0.206352	−	0.978478i	$-0.566159\pi$
$709$	−21840.9	−	12609.8i	−1.15691	−	0.667945i	−0.950563	+	0.310533i	$0.899492\pi$
$710$		−	24908.3i		−	1.31661i
$711$		0			0
$712$	1907.03	+	3303.07i	0.100378	+	0.173859i
$713$	−5075.10	+	2930.11i	−0.266569	+	0.153904i
$714$		0			0
$715$	−1789.79	−	25452.7i	−0.0936146	−	1.33130i
$716$	13716.4			0.715929
$717$		0			0
$718$	−16168.3	−	28004.4i	−0.840385	−	1.45559i
$719$	17733.1	−	30714.6i	0.919796	−	1.59313i	0.120071	−	0.992765i	$-0.461688\pi$
$719$	17733.1	−	30714.6i	0.919796	−	1.59313i	0.799724	−	0.600368i	$-0.204979\pi$
$720$		0			0
$721$	17283.9	+	9978.85i	0.892767	+	0.515439i
$722$	−21892.7	−	12639.8i	−1.12848	−	0.651529i
$723$		0			0
$724$	−2145.97	+	3716.92i	−0.110158	+	0.190799i
$725$	4291.78	+	7433.59i	0.219852	+	0.380795i
$726$		0			0
$727$	14262.2			0.727588			0.363794	−	0.931479i	$-0.381481\pi$
$727$	14262.2			0.727588			0.363794	+	0.931479i	$0.381481\pi$
$728$	−5033.05	+	3397.69i	−0.256233	+	0.172976i
$729$		0			0
$730$	18705.7	−	10799.7i	0.948396	−	0.547557i
$731$	−7379.80	−	12782.2i	−0.373395	−	0.646739i
$732$		0			0
$733$			16022.5i			0.807371i	0.914898	+	0.403685i	$0.132271\pi$
$733$			16022.5i			0.807371i	−0.914898	+	0.403685i	$0.867729\pi$
$734$	−23781.8	−	13730.4i	−1.19592	−	0.690463i
$735$		0			0
$736$			4937.96i			0.247304i
$737$	−4664.05	+	8078.38i	−0.233111	+	0.403760i
$738$		0			0
$739$	−3287.61	+	1898.11i	−0.163649	+	0.0944830i	−0.579588	−	0.814910i	$-0.696786\pi$
$739$	−3287.61	+	1898.11i	−0.163649	+	0.0944830i	0.415939	+	0.909393i	$0.363453\pi$
$740$	5264.09			0.261502
$741$		0			0
$742$	−56804.3			−2.81044
$743$	26266.0	−	15164.7i	1.29691	−	0.748772i	0.317042	−	0.948412i	$-0.397310\pi$
$743$	26266.0	−	15164.7i	1.29691	−	0.748772i	0.979869	+	0.199639i	$0.0639771\pi$
$744$		0			0
$745$	1005.20	−	1741.05i	0.0494331	−	0.0856206i
$746$		−	152.502i		−	0.00748460i
$747$		0			0
$748$	−13617.0	−	7861.78i	−0.665624	−	0.384298i
$749$			45509.1i			2.22011i
$750$		0			0
$751$	10775.9	+	18664.5i	0.523595	+	0.906893i	0.999623	+	0.0274629i	$0.00874280\pi$
$751$	10775.9	+	18664.5i	0.523595	+	0.906893i	−0.476028	+	0.879430i	$0.657924\pi$
$752$	−6357.25	+	3670.36i	−0.308278	+	0.177984i
$753$		0			0
$754$	−16664.3	−	24685.1i	−0.804877	−	1.19228i
$755$	10754.3			0.518397
$756$		0			0
$757$	10208.8	+	17682.2i	0.490153	+	0.848970i	0.999936	−	0.0113335i	$-0.00360764\pi$
$757$	10208.8	+	17682.2i	0.490153	+	0.848970i	−0.509783	+	0.860303i	$0.670274\pi$
$758$	24903.3	−	43133.7i	1.19331	−	2.06687i
$759$		0			0
$760$	−1294.91	−	747.616i	−0.0618043	−	0.0356828i
$761$	27171.9	+	15687.7i	1.29432	+	0.747278i	0.979417	−	0.201845i	$-0.0646937\pi$
$761$	27171.9	+	15687.7i	1.29432	+	0.747278i	0.314906	+	0.949123i	$0.398027\pi$
$762$		0			0
$763$	−5201.64	+	9009.50i	−0.246805	+	0.427478i
$764$	6163.84	+	10676.1i	0.291885	+	0.505559i
$765$		0			0
$766$	−43570.5			−2.05518
$767$	−15487.7	−	22942.2i	−0.729111	−	1.08004i
$768$		0			0
$769$	10784.3	−	6226.33i	0.505712	−	0.291973i	−0.225357	−	0.974276i	$-0.572355\pi$
$769$	10784.3	−	6226.33i	0.505712	−	0.291973i	0.731069	+	0.682303i	$0.239022\pi$
$770$	35262.8	+	61076.9i	1.65037	+	2.85852i
$771$		0			0
$772$		−	19302.5i		−	0.899885i
$773$	−32432.4	−	18724.9i	−1.50907	−	0.871264i	−0.999944	−	0.0105740i	$-0.996634\pi$
$773$	−32432.4	−	18724.9i	−1.50907	−	0.871264i	−0.509129	−	0.860690i	$-0.670033\pi$
$774$		0			0
$775$		−	17169.8i		−	0.795815i
$776$	3217.04	−	5572.08i	0.148821	−	0.257765i
$777$		0			0
$778$	−34841.2	+	20115.6i	−1.60555	+	0.926965i
$779$	−1290.58			−0.0593580
$780$		0			0
$781$	18199.5			0.833839
$782$	2928.41	−	1690.72i	0.133913	−	0.0773145i
$783$		0			0
$784$	−17719.2	+	30690.5i	−0.807179	+	1.39807i
$785$			36377.1i			1.65396i
$786$		0			0
$787$	−22915.2	−	13230.1i	−1.03791	−	0.599240i	−0.118672	−	0.992934i	$-0.537864\pi$
$787$	−22915.2	−	13230.1i	−1.03791	−	0.599240i	−0.919242	+	0.393694i	$0.871197\pi$
$788$		−	2157.65i		−	0.0975420i
$789$		0			0
$790$	24880.5	+	43094.3i	1.12052	+	1.94079i
$791$	−18918.0	+	10922.3i	−0.850375	+	0.490964i
$792$		0			0
$793$	21028.9	−	14196.1i	0.941687	−	0.635710i
$794$	−58550.3			−2.61697
$795$		0			0
$796$	7154.72	+	12392.3i	0.318583	+	0.551803i
$797$	−2374.74	+	4113.17i	−0.105543	+	0.182805i	−0.913960	−	0.405805i	$-0.866991\pi$
$797$	−2374.74	+	4113.17i	−0.105543	+	0.182805i	0.808417	+	0.588610i	$0.200325\pi$
$798$		0			0
$799$	4986.56	+	2878.99i	0.220791	+	0.127474i
$800$	−12529.4	−	7233.82i	−0.553724	−	0.319693i
$801$		0			0
$802$	−26133.0	+	45263.8i	−1.15061	+	1.99292i
$803$	7890.91	+	13667.5i	0.346780	+	0.600640i
$804$		0			0
$805$	−8029.53			−0.351557
$806$	4178.97	+	59429.2i	0.182628	+	2.59715i
$807$		0			0
$808$	−3423.74	+	1976.70i	−0.149068	+	0.0860644i
$809$	−2232.02	−	3865.98i	−0.0970009	−	0.168010i	0.813441	−	0.581647i	$-0.197592\pi$
$809$	−2232.02	−	3865.98i	−0.0970009	−	0.168010i	−0.910442	+	0.413637i	$0.864258\pi$
$810$		0			0
$811$		−	20774.6i		−	0.899499i	−0.893155	−	0.449749i	$-0.851513\pi$
$811$		−	20774.6i		−	0.899499i	0.893155	−	0.449749i	$-0.148487\pi$
$812$	37743.3	+	21791.1i	1.63120	+	0.941771i
$813$		0			0
$814$			7265.13i			0.312829i
$815$	24722.2	−	42820.1i	1.06255	−	1.84039i
$816$		0			0
$817$	7993.18	−	4614.86i	0.342284	−	0.197618i
$818$	−6323.51			−0.270289
$819$		0			0
$820$	5787.55			0.246476
$821$	−30977.0	+	17884.6i	−1.31682	+	0.760264i	−0.983215	−	0.182450i	$-0.941597\pi$
$821$	−30977.0	+	17884.6i	−1.31682	+	0.760264i	−0.333601	+	0.942714i	$0.608264\pi$
$822$		0			0
$823$	1472.72	−	2550.83i	0.0623764	−	0.108039i	−0.833151	−	0.553046i	$-0.813465\pi$
$823$	1472.72	−	2550.83i	0.0623764	−	0.108039i	0.895527	+	0.445007i	$0.146799\pi$
$824$			2618.80i			0.110716i
$825$		0			0
$826$	66259.2	+	38254.8i	2.79111	+	1.61145i
$827$			17878.6i			0.751753i	0.926670	+	0.375877i	$0.122658\pi$
$827$			17878.6i			0.751753i	−0.926670	+	0.375877i	$0.877342\pi$
$828$		0			0
$829$	6711.90	+	11625.4i	0.281199	+	0.487051i	0.971680	−	0.236299i	$-0.0759345\pi$
$829$	6711.90	+	11625.4i	0.281199	+	0.487051i	−0.690481	+	0.723350i	$0.742601\pi$
$830$	62410.1	−	36032.5i	2.60998	−	1.50687i
$831$		0			0
$832$	26588.1	+	12955.1i	1.10790	+	0.539827i
$833$	27797.5			1.15621
$834$		0			0
$835$	21663.1	+	37521.6i	0.897824	+	1.55508i
$836$	4916.26	−	8515.22i	0.203388	−	0.352279i
$837$		0			0
$838$	−7733.79	−	4465.11i	−0.318806	−	0.184063i
$839$	−27316.8	−	15771.3i	−1.12405	−	0.648971i	−0.181619	−	0.983369i	$-0.558134\pi$
$839$	−27316.8	−	15771.3i	−1.12405	−	0.648971i	−0.942432	+	0.334398i	$0.891467\pi$
$840$		0			0
$841$	319.334	−	553.103i	0.0130934	−	0.0226784i
$842$	1514.37	+	2622.96i	0.0619816	+	0.107355i
$843$		0			0
$844$	16855.7			0.687437
$845$	23258.0	−	18200.4i	0.946865	−	0.740961i
$846$		0			0
$847$	−8406.92	+	4853.74i	−0.341045	+	0.196902i
$848$	12057.5	+	20884.2i	0.488274	+	0.845715i
$849$		0			0
$850$			9907.22i			0.399782i
$851$	−716.338	−	413.578i	−0.0288552	−	0.0166595i
$852$		0			0
$853$			21810.6i			0.875476i	0.899103	+	0.437738i	$0.144220\pi$
$853$			21810.6i			0.875476i	−0.899103	+	0.437738i	$0.855780\pi$
$854$	−35064.5	+	60733.5i	−1.40502	+	2.43356i
$855$		0			0
$856$	−5171.55	+	2985.80i	−0.206495	+	0.119220i
$857$	33234.6			1.32470			0.662352	−	0.749193i	$-0.269558\pi$
$857$	33234.6			1.32470			0.662352	+	0.749193i	$0.269558\pi$
$858$		0			0
$859$	42697.7			1.69596			0.847978	−	0.530032i	$-0.177820\pi$
$859$	42697.7			1.69596			0.847978	+	0.530032i	$0.177820\pi$
$860$	−35845.0	+	20695.1i	−1.42129	+	0.820580i
$861$		0			0
$862$	28262.5	−	48952.1i	1.11673	−	1.93424i
$863$		−	27419.2i		−	1.08153i	−0.841174	−	0.540765i	$-0.818135\pi$
$863$		−	27419.2i		−	1.08153i	0.841174	−	0.540765i	$-0.181865\pi$
$864$		0			0
$865$	−31310.1	−	18076.9i	−1.23072	−	0.710558i
$866$		−	41437.0i		−	1.62596i
$867$		0			0
$868$	−43589.0	−	75498.3i	−1.70450	−	2.95228i
$869$	−31487.2	+	18179.1i	−1.22915	+	0.709649i
$870$		0			0
$871$	−10770.2	+	757.343i	−0.418983	+	0.0294622i
$872$	−1365.09			−0.0530137
$873$		0			0
$874$	1057.27	+	1831.24i	0.0409183	+	0.0708727i
$875$	−14636.2	+	25350.7i	−0.565479	+	0.979439i
$876$		0			0
$877$	−36896.3	−	21302.1i	−1.42064	−	0.820206i	−0.424285	−	0.905529i	$-0.639475\pi$
$877$	−36896.3	−	21302.1i	−1.42064	−	0.820206i	−0.996353	+	0.0853227i	$0.972808\pi$
$878$	−29042.3	−	16767.6i	−1.11632	−	0.644508i
$879$		0			0
$880$	14970.0	−	25928.8i	0.573454	−	0.993251i
$881$	2349.70	+	4069.80i	0.0898562	+	0.155636i	0.907450	−	0.420160i	$-0.138026\pi$
$881$	2349.70	+	4069.80i	0.0898562	+	0.155636i	−0.817594	+	0.575795i	$0.804693\pi$
$882$		0			0
$883$	−22233.5			−0.847358			−0.423679	−	0.905812i	$-0.639262\pi$
$883$	−22233.5			−0.847358			−0.423679	+	0.905812i	$0.639262\pi$
$884$	−1276.59	−	18154.4i	−0.0485704	−	0.690721i
$885$		0			0
$886$	8465.38	−	4887.49i	0.320993	−	0.185325i
$887$	−4426.23	−	7666.45i	−0.167552	−	0.290208i	0.770007	−	0.638036i	$-0.220253\pi$
$887$	−4426.23	−	7666.45i	−0.167552	−	0.290208i	−0.937558	+	0.347828i	$0.886919\pi$
$888$		0			0
$889$		−	7766.05i		−	0.292986i
$890$	44401.1	+	25635.0i	1.67228	+	0.965491i
$891$		0			0
$892$			505.155i			0.0189617i
$893$	−1800.34	+	3118.28i	−0.0674649	+	0.116853i
$894$		0			0
$895$	17742.0	−	10243.4i	0.662626	−	0.382567i
$896$	−16453.6			−0.613477
$897$		0			0
$898$	−53283.7			−1.98007
$899$	41143.1	−	23754.0i	1.52636	−	0.881246i
$900$		0			0
$901$	9457.77	−	16381.3i	0.349705	−	0.605707i
$902$			7987.58i			0.294853i
$903$		0			0
$904$	−2482.38	−	1433.20i	−0.0913303	−	0.0527296i
$905$			6410.41i			0.235458i
$906$		0			0
$907$	18586.2	+	32192.3i	0.680424	+	1.17853i	0.974851	+	0.222856i	$0.0715378\pi$
$907$	18586.2	+	32192.3i	0.680424	+	1.17853i	−0.294427	+	0.955674i	$0.595129\pi$
$908$	−5201.79	+	3003.25i	−0.190118	+	0.109765i
$909$		0			0
$910$	−35755.4	+	73382.1i	−1.30251	+	2.67318i
$911$	−38035.1			−1.38327			−0.691635	−	0.722247i	$-0.743109\pi$
$911$	−38035.1			−1.38327			−0.691635	+	0.722247i	$0.743109\pi$
$912$		0			0
$913$	26327.4	+	45600.4i	0.954337	+	1.65296i
$914$	17319.6	−	29998.5i	0.626787	−	1.08563i
$915$		0			0
$916$	−5637.56	−	3254.85i	−0.203352	−	0.117405i
$917$	12850.7	+	7419.38i	0.462780	+	0.267186i
$918$		0			0
$919$	4176.14	−	7233.28i	0.149900	−	0.259634i	−0.781290	−	0.624168i	$-0.785438\pi$
$919$	4176.14	−	7233.28i	0.149900	−	0.259634i	0.931190	+	0.364533i	$0.118772\pi$
$920$	−526.808	−	912.458i	−0.0188786	−	0.0326987i
$921$		0			0
$922$	72679.4			2.59606
$923$	11786.2	+	17459.0i	0.420310	+	0.622611i
$924$		0			0
$925$	2098.79	−	1211.74i	0.0746029	−	0.0430720i
$926$	11259.8	+	19502.6i	0.399590	+	0.692110i
$927$		0			0
$928$		−	40031.3i		−	1.41605i
$929$	17521.5	+	10116.0i	0.618796	+	0.357262i	0.776400	−	0.630240i	$-0.217044\pi$
$929$	17521.5	+	10116.0i	0.618796	+	0.357262i	−0.157604	+	0.987502i	$0.550377\pi$
$930$		0			0
$931$			17382.8i			0.611921i
$932$	−1239.53	+	2146.93i	−0.0435646	+	0.0754561i
$933$		0			0
$934$	29501.9	−	17032.9i	1.03355	−	0.596718i
$935$	−23484.7			−0.821423
$936$		0			0
$937$	−27766.9			−0.968095			−0.484048	−	0.875042i	$-0.660834\pi$
$937$	−27766.9			−0.968095			−0.484048	+	0.875042i	$0.660834\pi$
$938$	25844.4	−	14921.3i	0.899627	−	0.519400i
$939$		0			0
$940$	8073.55	−	13983.8i	0.280138	−	0.485214i
$941$			400.765i			0.0138837i	0.999976	+	0.00694185i	$0.00220968\pi$
$941$			400.765i			0.0138837i	−0.999976	+	0.00694185i	$0.997790\pi$
$942$		0			0
$943$	−787.571	−	454.704i	−0.0271971	−	0.0157022i
$944$		−	32480.4i		−	1.11986i
$945$		0			0
$946$	−28562.0	−	49470.8i	−0.981639	−	1.70025i
$947$	18883.1	−	10902.2i	0.647961	−	0.374101i	−0.139713	−	0.990192i	$-0.544618\pi$
$947$	18883.1	−	10902.2i	0.647961	−	0.374101i	0.787675	+	0.616091i	$0.211285\pi$
$948$		0			0
$949$	−8001.16	+	16421.0i	−0.273687	+	0.561696i
$950$	−6195.35			−0.211583
$951$		0			0
$952$	2794.61	+	4840.41i	0.0951406	+	0.164788i
$953$	−15240.2	+	26396.8i	−0.518026	+	0.897248i	0.481755	+	0.876306i	$0.340000\pi$
$953$	−15240.2	+	26396.8i	−0.518026	+	0.897248i	−0.999781	+	0.0209414i	$0.993334\pi$
$954$		0			0
$955$	15945.8	+	9206.29i	0.540307	+	0.311946i
$956$	11920.4	+	6882.26i	0.403278	+	0.232833i
$957$		0			0
$958$	−3248.74	+	5626.98i	−0.109564	+	0.189770i
$959$	−28762.0	−	49817.2i	−0.968480	−	1.67746i
$960$		0			0
$961$	−65239.6			−2.18991
$962$	−6969.55	+	4704.97i	−0.233583	+	0.157686i
$963$		0			0
$964$	7603.47	−	4389.87i	0.254037	−	0.146668i
$965$	−14415.0	−	24967.6i	−0.480867	−	0.832886i
$966$		0			0
$967$			23864.1i			0.793608i	0.917903	+	0.396804i	$0.129881\pi$
$967$			23864.1i			0.793608i	−0.917903	+	0.396804i	$0.870119\pi$
$968$	−1103.14	−	636.896i	−0.0366283	−	0.0211473i
$969$		0			0
$970$		−	86489.2i		−	2.86289i
$971$	−7005.15	+	12133.3i	−0.231520	+	0.401004i	−0.958256	−	0.285913i	$-0.907703\pi$
$971$	−7005.15	+	12133.3i	−0.231520	+	0.401004i	0.726736	+	0.686917i	$0.241037\pi$
$972$		0			0
$973$	−2721.21	+	1571.09i	−0.0896589	+	0.0517646i
$974$	51933.3			1.70847
$975$		0			0
$976$	29771.7			0.976404
$977$	22038.8	−	12724.1i	0.721681	−	0.416663i	−0.0936898	−	0.995601i	$-0.529866\pi$
$977$	22038.8	−	12724.1i	0.721681	−	0.416663i	0.815371	+	0.578938i	$0.196533\pi$
$978$		0			0
$979$	−18730.4	+	32442.0i	−0.611467	+	1.05909i
$980$		−	77952.4i		−	2.54092i
$981$		0			0
$982$	3824.99	+	2208.36i	0.124298	+	0.0717634i
$983$			52479.9i			1.70280i	0.524519	+	0.851399i	$0.324245\pi$
$983$			52479.9i			1.70280i	−0.524519	+	0.851399i	$0.675755\pi$
$984$		0			0
$985$	−1611.33	−	2790.90i	−0.0521230	−	0.0902798i
$986$	−23740.2	+	13706.4i	−0.766777	+	0.442699i
$987$		0			0
$988$	11352.6	−	798.296i	0.365561	−	0.0257057i
$989$	6503.73			0.209107
$990$		0			0
$991$	−19024.3	−	32951.0i	−0.609814	−	1.05623i	−0.991271	−	0.131842i	$-0.957911\pi$
$991$	−19024.3	−	32951.0i	−0.609814	−	1.05623i	0.381457	−	0.924386i	$-0.375422\pi$
$992$	−40037.5	+	69347.0i	−1.28144	+	2.21952i
$993$		0			0
$994$	−50423.4	−	29111.9i	−1.60899	−	0.928948i
$995$	18509.2	+	10686.3i	0.589728	+	0.340480i
$996$		0			0
$997$	15618.3	−	27051.7i	0.496125	−	0.859314i	−0.503865	−	0.863783i	$-0.668089\pi$
$997$	15618.3	−	27051.7i	0.496125	−	0.859314i	0.999990	+	0.00446833i	$0.00142232\pi$
$998$	−2932.15	−	5078.63i	−0.0930015	−	0.161083i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.q.d.10.2		4
3.2	odd	2		39.4.j.b.10.1	yes	4
12.11	even	2		624.4.bv.c.49.2		4
13.2	odd	12		1521.4.a.z.1.3		4
13.4	even	6	inner	117.4.q.d.82.2		4
13.11	odd	12		1521.4.a.z.1.2		4
39.2	even	12		507.4.a.k.1.2		4
39.11	even	12		507.4.a.k.1.3		4
39.17	odd	6		39.4.j.b.4.1	✓	4
39.23	odd	6		507.4.b.e.337.3		4
39.29	odd	6		507.4.b.e.337.2		4
156.95	even	6		624.4.bv.c.433.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.j.b.4.1	✓	4	39.17	odd	6
39.4.j.b.10.1	yes	4	3.2	odd	2
117.4.q.d.10.2		4	1.1	even	1	trivial
117.4.q.d.82.2		4	13.4	even	6	inner
507.4.a.k.1.2		4	39.2	even	12
507.4.a.k.1.3		4	39.11	even	12
507.4.b.e.337.2		4	39.29	odd	6
507.4.b.e.337.3		4	39.23	odd	6
624.4.bv.c.49.2		4	12.11	even	2
624.4.bv.c.433.1		4	156.95	even	6
1521.4.a.z.1.2		4	13.11	odd	12
1521.4.a.z.1.3		4	13.2	odd	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +O(q^{10})\)	\(q+(3.57071 - 2.06155i) q^{2} +(4.50000 - 7.79423i) q^{4} -13.4424i q^{5} +(-27.2121 - 15.7109i) q^{7} -4.12311i q^{8} +(-27.7121 - 47.9988i) q^{10} +(35.0707 - 20.2481i) q^{11} +(42.1364 + 20.5310i) q^{13} -129.556 q^{14} +(27.5000 + 47.6314i) q^{16} +(21.5707 - 37.3616i) q^{17} +(23.3636 + 13.4890i) q^{19} +(-104.773 - 60.4906i) q^{20} +(83.4850 - 144.600i) q^{22} +(9.50500 + 16.4631i) q^{23} -55.6971 q^{25} +(192.783 - 13.5562i) q^{26} +(-244.909 + 141.398i) q^{28} +(-77.0557 - 133.464i) q^{29} +308.270i q^{31} +(224.955 + 129.878i) q^{32} -177.877i q^{34} +(-211.192 + 365.796i) q^{35} +(-37.6821 + 21.7558i) q^{37} +111.233 q^{38} -55.4243 q^{40} +(-41.4293 + 23.9192i) q^{41} +(171.061 - 296.286i) q^{43} -364.466i q^{44} +(67.8793 + 39.1901i) q^{46} +133.468i q^{47} +(322.167 + 558.010i) q^{49} +(-198.879 + 114.823i) q^{50} +(349.637 - 236.032i) q^{52} +438.454 q^{53} +(-272.182 - 471.433i) q^{55} +(-64.7779 + 112.199i) q^{56} +(-550.288 - 317.709i) q^{58} +(-511.434 - 295.277i) q^{59} +(270.652 - 468.783i) q^{61} +(635.516 + 1100.75i) q^{62} +631.000 q^{64} +(275.985 - 566.413i) q^{65} +(-199.485 + 115.173i) q^{67} +(-194.136 - 336.254i) q^{68} +1741.54i q^{70} +(389.202 + 224.706i) q^{71} +389.711i q^{73} +(-89.7014 + 155.367i) q^{74} +(210.272 - 121.401i) q^{76} -1272.47 q^{77} -897.820 q^{79} +(640.279 - 369.665i) q^{80} +(-98.6214 + 170.817i) q^{82} +1300.24i q^{83} +(-502.228 - 289.961i) q^{85} -1410.60i q^{86} +(-83.4850 - 144.600i) q^{88} +(-801.113 + 462.523i) q^{89} +(-824.061 - 1220.69i) q^{91} +171.090 q^{92} +(275.151 + 476.575i) q^{94} +(181.324 - 314.062i) q^{95} +(1351.43 + 780.247i) q^{97} +(2300.73 + 1328.33i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 18 q^{4} - 66 q^{7}+O(q^{10}) \) 4 * q + 18 * q^4 - 66 * q^7	\( 4 q + 18 q^{4} - 66 q^{7} - 68 q^{10} + 126 q^{11} + 40 q^{13} - 204 q^{14} + 110 q^{16} + 72 q^{17} + 222 q^{19} - 162 q^{20} + 34 q^{22} + 138 q^{23} + 120 q^{25} + 714 q^{26} - 594 q^{28} + 6 q^{29} - 402 q^{35} + 492 q^{37} - 612 q^{38} - 136 q^{40} - 180 q^{41} + 470 q^{43} - 714 q^{46} + 346 q^{49} - 1224 q^{50} - 144 q^{52} + 2268 q^{53} - 446 q^{55} - 102 q^{56} - 2244 q^{58} - 2160 q^{59} - 160 q^{61} + 1428 q^{62} + 2524 q^{64} + 804 q^{65} - 498 q^{67} - 648 q^{68} + 1314 q^{71} - 1530 q^{74} + 1998 q^{76} - 2976 q^{77} + 8 q^{79} + 990 q^{80} + 34 q^{82} - 852 q^{85} - 34 q^{88} + 252 q^{89} - 1668 q^{91} + 2484 q^{92} + 2686 q^{94} + 54 q^{95} - 336 q^{97} + 6732 q^{98}+O(q^{100}) \) 4 * q + 18 * q^4 - 66 * q^7 - 68 * q^10 + 126 * q^11 + 40 * q^13 - 204 * q^14 + 110 * q^16 + 72 * q^17 + 222 * q^19 - 162 * q^20 + 34 * q^22 + 138 * q^23 + 120 * q^25 + 714 * q^26 - 594 * q^28 + 6 * q^29 - 402 * q^35 + 492 * q^37 - 612 * q^38 - 136 * q^40 - 180 * q^41 + 470 * q^43 - 714 * q^46 + 346 * q^49 - 1224 * q^50 - 144 * q^52 + 2268 * q^53 - 446 * q^55 - 102 * q^56 - 2244 * q^58 - 2160 * q^59 - 160 * q^61 + 1428 * q^62 + 2524 * q^64 + 804 * q^65 - 498 * q^67 - 648 * q^68 + 1314 * q^71 - 1530 * q^74 + 1998 * q^76 - 2976 * q^77 + 8 * q^79 + 990 * q^80 + 34 * q^82 - 852 * q^85 - 34 * q^88 + 252 * q^89 - 1668 * q^91 + 2484 * q^92 + 2686 * q^94 + 54 * q^95 - 336 * q^97 + 6732 * q^98

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