LMFDB - Embedded newform 136.3.t.a.97.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			97.4
Character	$\chi$	$=$	136.97
Dual form			136.3.t.a.129.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.88082 - 1.92490i) q^{3} +(2.22013 + 0.441611i) q^{5} +(3.75824 - 0.747561i) q^{7} +(1.14971 - 2.77565i) q^{9} +O(q^{10})$	\(q+(2.88082 - 1.92490i) q^{3} +(2.22013 + 0.441611i) q^{5} +(3.75824 - 0.747561i) q^{7} +(1.14971 - 2.77565i) q^{9} +(2.61028 - 3.90656i) q^{11} +(-0.574533 - 0.574533i) q^{13} +(7.24584 - 3.00133i) q^{15} +(-11.8487 - 12.1905i) q^{17} +(2.04898 + 4.94668i) q^{19} +(9.38783 - 9.38783i) q^{21} +(15.0371 + 10.0474i) q^{23} +(-18.3630 - 7.60622i) q^{25} +(4.05268 + 20.3742i) q^{27} +(-0.159543 + 0.802076i) q^{29} +(11.9853 + 17.9372i) q^{31} -16.2786i q^{33} +8.67392 q^{35} +(-14.4014 + 9.62268i) q^{37} +(-2.76104 - 0.549206i) q^{39} +(-54.5733 + 10.8553i) q^{41} +(-15.8921 + 38.3669i) q^{43} +(3.77826 - 5.65457i) q^{45} +(-1.14970 - 1.14970i) q^{47} +(-31.7045 + 13.1325i) q^{49} +(-57.5994 - 12.3110i) q^{51} +(0.621871 + 1.50133i) q^{53} +(7.52035 - 7.52035i) q^{55} +(15.4246 + 10.3064i) q^{57} +(-101.470 - 42.0302i) q^{59} +(16.2663 + 81.7763i) q^{61} +(2.24593 - 11.2910i) q^{63} +(-1.02182 - 1.52926i) q^{65} -3.15904i q^{67} +62.6593 q^{69} +(82.9642 - 55.4349i) q^{71} +(62.2823 + 12.3887i) q^{73} +(-67.5417 + 13.4349i) q^{75} +(6.88968 - 16.6332i) q^{77} +(38.9386 - 58.2757i) q^{79} +(70.0128 + 70.0128i) q^{81} +(46.5535 - 19.2831i) q^{83} +(-20.9222 - 32.2970i) q^{85} +(1.08430 + 2.61774i) q^{87} +(83.0860 - 83.0860i) q^{89} +(-2.58873 - 1.72974i) q^{91} +(69.0547 + 28.6034i) q^{93} +(2.36450 + 11.8871i) q^{95} +(-4.35373 + 21.8877i) q^{97} +(-7.84217 - 11.7366i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{16}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	2.88082	−	1.92490i	0.960272	−	0.641633i	0.0265557	−	0.999647i	$-0.491546\pi$
$3$	2.88082	−	1.92490i	0.960272	−	0.641633i	0.933716	+	0.358014i	$0.116546\pi$
$4$		0			0
$5$	2.22013	+	0.441611i	0.444026	+	0.0883223i	0.412039	−	0.911166i	$-0.364817\pi$
$5$	2.22013	+	0.441611i	0.444026	+	0.0883223i	0.0319866	+	0.999488i	$0.489817\pi$
$6$		0			0
$7$	3.75824	−	0.747561i	0.536892	−	0.106794i	0.0808054	−	0.996730i	$-0.474251\pi$
$7$	3.75824	−	0.747561i	0.536892	−	0.106794i	0.456087	+	0.889935i	$0.349251\pi$
$8$		0			0
$9$	1.14971	−	2.77565i	0.127746	−	0.308405i
$10$		0			0
$11$	2.61028	−	3.90656i	0.237298	−	0.355142i	−0.693638	−	0.720324i	$-0.743993\pi$
$11$	2.61028	−	3.90656i	0.237298	−	0.355142i	0.930936	+	0.365182i	$0.118993\pi$
$12$		0			0
$13$	−0.574533	−	0.574533i	−0.0441949	−	0.0441949i	0.684664	−	0.728859i	$-0.259949\pi$
$13$	−0.574533	−	0.574533i	−0.0441949	−	0.0441949i	−0.728859	+	0.684664i	$0.759949\pi$
$14$		0			0
$15$	7.24584	−	3.00133i	0.483056	−	0.200088i
$16$		0			0
$17$	−11.8487	−	12.1905i	−0.696983	−	0.717088i
$17$	−11.8487	−	12.1905i	−0.696983	−	0.717088i
$18$		0			0
$19$	2.04898	+	4.94668i	0.107841	+	0.260352i	0.968583	−	0.248690i	$-0.0800000\pi$
$19$	2.04898	+	4.94668i	0.107841	+	0.260352i	−0.860742	+	0.509041i	$0.830000\pi$
$20$		0			0
$21$	9.38783	−	9.38783i	0.447039	−	0.447039i
$22$		0			0
$23$	15.0371	+	10.0474i	0.653785	+	0.436845i	0.837725	−	0.546092i	$-0.183885\pi$
$23$	15.0371	+	10.0474i	0.653785	+	0.436845i	−0.183940	+	0.982937i	$0.558885\pi$
$24$		0			0
$25$	−18.3630	−	7.60622i	−0.734521	−	0.304249i
$26$		0			0
$27$	4.05268	+	20.3742i	0.150099	+	0.754599i
$28$		0			0
$29$	−0.159543	+	0.802076i	−0.00550148	+	0.0276578i	−0.983439	−	0.181242i	$-0.941988\pi$
$29$	−0.159543	+	0.802076i	−0.00550148	+	0.0276578i	0.977937	+	0.208900i	$0.0669883\pi$
$30$		0			0
$31$	11.9853	+	17.9372i	0.386622	+	0.578620i	0.972824	−	0.231544i	$-0.0743778\pi$
$31$	11.9853	+	17.9372i	0.386622	+	0.578620i	−0.586203	+	0.810164i	$0.699378\pi$
$32$		0			0
$33$		−	16.2786i		−	0.493292i
$34$		0			0
$35$	8.67392			0.247826
$36$		0			0
$37$	−14.4014	+	9.62268i	−0.389226	+	0.260072i	−0.734751	−	0.678337i	$-0.762701\pi$
$37$	−14.4014	+	9.62268i	−0.389226	+	0.260072i	0.345525	+	0.938410i	$0.387701\pi$
$38$		0			0
$39$	−2.76104	−	0.549206i	−0.0707960	−	0.0140822i
$40$		0			0
$41$	−54.5733	+	10.8553i	−1.33106	+	0.264763i	−0.808829	−	0.588043i	$-0.799898\pi$
$41$	−54.5733	+	10.8553i	−1.33106	+	0.264763i	−0.522226	+	0.852807i	$0.674898\pi$
$42$		0			0
$43$	−15.8921	+	38.3669i	−0.369584	+	0.892254i	0.624235	+	0.781237i	$0.285411\pi$
$43$	−15.8921	+	38.3669i	−0.369584	+	0.892254i	−0.993818	+	0.111017i	$0.964589\pi$
$44$		0			0
$45$	3.77826	−	5.65457i	0.0839614	−	0.125657i
$46$		0			0
$47$	−1.14970	−	1.14970i	−0.0244617	−	0.0244617i	0.694770	−	0.719232i	$-0.255506\pi$
$47$	−1.14970	−	1.14970i	−0.0244617	−	0.0244617i	−0.719232	+	0.694770i	$0.755506\pi$
$48$		0			0
$49$	−31.7045	+	13.1325i	−0.647032	+	0.268009i
$50$		0			0
$51$	−57.5994	−	12.3110i	−1.12940	−	0.241392i
$52$		0			0
$53$	0.621871	+	1.50133i	0.0117334	+	0.0283270i	0.929638	−	0.368475i	$-0.120120\pi$
$53$	0.621871	+	1.50133i	0.0117334	+	0.0283270i	−0.917904	+	0.396802i	$0.870120\pi$
$54$		0			0
$55$	7.52035	−	7.52035i	0.136734	−	0.136734i
$56$		0			0
$57$	15.4246	+	10.3064i	0.270607	+	0.180814i
$58$		0			0
$59$	−101.470	−	42.0302i	−1.71983	−	0.712377i	−0.999831	−	0.0184017i	$-0.994142\pi$
$59$	−101.470	−	42.0302i	−1.71983	−	0.712377i	−0.719999	−	0.693975i	$-0.755858\pi$
$60$		0			0
$61$	16.2663	+	81.7763i	0.266661	+	1.34059i	0.849320	+	0.527878i	$0.177012\pi$
$61$	16.2663	+	81.7763i	0.266661	+	1.34059i	−0.582659	+	0.812717i	$0.697988\pi$
$62$		0			0
$63$	2.24593	−	11.2910i	0.0356496	−	0.179223i
$64$		0			0
$65$	−1.02182	−	1.52926i	−0.0157203	−	0.0235271i
$66$		0			0
$67$		−	3.15904i		−	0.0471499i	−0.999722	−	0.0235749i	$-0.992495\pi$
$67$		−	3.15904i		−	0.0471499i	0.999722	−	0.0235749i	$-0.00750483\pi$
$68$		0			0
$69$	62.6593			0.908106
$70$		0			0
$71$	82.9642	−	55.4349i	1.16851	−	0.780773i	0.188962	−	0.981984i	$-0.439488\pi$
$71$	82.9642	−	55.4349i	1.16851	−	0.780773i	0.979548	+	0.201211i	$0.0644877\pi$
$72$		0			0
$73$	62.2823	+	12.3887i	0.853182	+	0.169709i	0.602261	−	0.798299i	$-0.294267\pi$
$73$	62.2823	+	12.3887i	0.853182	+	0.169709i	0.250921	+	0.968008i	$0.419267\pi$
$74$		0			0
$75$	−67.5417	+	13.4349i	−0.900556	+	0.179132i
$76$		0			0
$77$	6.88968	−	16.6332i	0.0894764	−	0.216015i
$78$		0			0
$79$	38.9386	−	58.2757i	0.492894	−	0.737668i	−0.498740	−	0.866752i	$-0.666204\pi$
$79$	38.9386	−	58.2757i	0.492894	−	0.737668i	0.991634	+	0.129084i	$0.0412037\pi$
$80$		0			0
$81$	70.0128	+	70.0128i	0.864355	+	0.864355i
$82$		0			0
$83$	46.5535	−	19.2831i	0.560885	−	0.232326i	−0.0841842	−	0.996450i	$-0.526828\pi$
$83$	46.5535	−	19.2831i	0.560885	−	0.232326i	0.645069	+	0.764124i	$0.276828\pi$
$84$		0			0
$85$	−20.9222	−	32.2970i	−0.246144	−	0.379965i
$86$		0			0
$87$	1.08430	+	2.61774i	0.0124632	+	0.0300889i
$88$		0			0
$89$	83.0860	−	83.0860i	0.933551	−	0.933551i	−0.0643752	−	0.997926i	$-0.520505\pi$
$89$	83.0860	−	83.0860i	0.933551	−	0.933551i	0.997926	+	0.0643752i	$0.0205054\pi$
$90$		0			0
$91$	−2.58873	−	1.72974i	−0.0284476	−	0.0190081i
$92$		0			0
$93$	69.0547	+	28.6034i	0.742524	+	0.307564i
$94$		0			0
$95$	2.36450	+	11.8871i	0.0248894	+	0.125128i
$96$		0			0
$97$	−4.35373	+	21.8877i	−0.0448839	+	0.225646i	−0.996716	−	0.0809720i	$-0.974198\pi$
$97$	−4.35373	+	21.8877i	−0.0448839	+	0.225646i	0.951833	+	0.306618i	$0.0991976\pi$
$98$		0			0
$99$	−7.84217	−	11.7366i	−0.0792138	−	0.118552i
$100$		0			0
$101$		−	142.650i		−	1.41238i	−0.708023	−	0.706190i	$-0.750413\pi$
$101$		−	142.650i		−	1.41238i	0.708023	−	0.706190i	$-0.249587\pi$
$102$		0			0
$103$	184.752			1.79371			0.896856	−	0.442322i	$-0.145845\pi$
$103$	184.752			1.79371			0.896856	+	0.442322i	$0.145845\pi$
$104$		0			0
$105$	24.9880	−	16.6964i	0.237981	−	0.159014i
$106$		0			0
$107$	−125.452	−	24.9540i	−1.17245	−	0.233215i	−0.429820	−	0.902914i	$-0.641423\pi$
$107$	−125.452	−	24.9540i	−1.17245	−	0.233215i	−0.742633	+	0.669699i	$0.766423\pi$
$108$		0			0
$109$	−181.676	+	36.1377i	−1.66676	+	0.331539i	−0.936241	−	0.351358i	$-0.885720\pi$
$109$	−181.676	+	36.1377i	−1.66676	+	0.331539i	−0.730515	+	0.682896i	$0.760720\pi$
$110$		0			0
$111$	−22.9650	+	55.4423i	−0.206892	+	0.499481i
$112$		0			0
$113$	54.0591	−	80.9052i	0.478399	−	0.715975i	−0.511258	−	0.859427i	$-0.670820\pi$
$113$	54.0591	−	80.9052i	0.478399	−	0.715975i	0.989657	+	0.143452i	$0.0458203\pi$
$114$		0			0
$115$	28.9472	+	28.9472i	0.251714	+	0.251714i
$116$		0			0
$117$	−2.25525	+	0.934154i	−0.0192756	+	0.00798422i
$118$		0			0
$119$	−53.6435	−	36.9572i	−0.450785	−	0.310565i
$120$		0			0
$121$	37.8570	+	91.3950i	0.312868	+	0.755330i
$122$		0			0
$123$	−136.320	+	136.320i	−1.10829	+	1.10829i
$124$		0			0
$125$	−84.4627	−	56.4362i	−0.675702	−	0.451489i
$126$		0			0
$127$	−55.4283	−	22.9591i	−0.436443	−	0.180781i	0.153634	−	0.988128i	$-0.450902\pi$
$127$	−55.4283	−	22.9591i	−0.436443	−	0.180781i	−0.590077	+	0.807347i	$0.700902\pi$
$128$		0			0
$129$	28.0703	+	141.119i	0.217599	+	1.09394i
$130$		0			0
$131$	35.3510	−	177.722i	0.269855	−	1.35665i	−0.573460	−	0.819234i	$-0.694399\pi$
$131$	35.3510	−	177.722i	0.269855	−	1.35665i	0.843315	−	0.537420i	$-0.180601\pi$
$132$		0			0
$133$	11.3985	+	17.0591i	0.0857032	+	0.128264i
$134$		0			0
$135$			47.0230i			0.348319i
$136$		0			0
$137$	−0.484260			−0.00353475			−0.00176737	−	0.999998i	$-0.500563\pi$
$137$	−0.484260			−0.00353475			−0.00176737	+	0.999998i	$0.500563\pi$
$138$		0			0
$139$	44.5942	−	29.7969i	0.320822	−	0.214366i	−0.384722	−	0.923032i	$-0.625703\pi$
$139$	44.5942	−	29.7969i	0.320822	−	0.214366i	0.705544	+	0.708666i	$0.250703\pi$
$140$		0			0
$141$	−5.52514	−	1.09902i	−0.0391854	−	0.00779445i
$142$		0			0
$143$	−3.74414	+	0.744757i	−0.0261828	+	0.00520809i
$144$		0			0
$145$	−0.708411	+	1.71026i	−0.00488560	+	0.0117949i
$146$		0			0
$147$	−66.0563	+	98.8603i	−0.449363	+	0.672519i
$148$		0			0
$149$	12.2783	+	12.2783i	0.0824049	+	0.0824049i	0.747108	−	0.664703i	$-0.231442\pi$
$149$	12.2783	+	12.2783i	0.0824049	+	0.0824049i	−0.664703	+	0.747108i	$0.731442\pi$
$150$		0			0
$151$	123.044	−	50.9666i	0.814863	−	0.337527i	0.0639703	−	0.997952i	$-0.479624\pi$
$151$	123.044	−	50.9666i	0.814863	−	0.337527i	0.750892	+	0.660425i	$0.229624\pi$
$152$		0			0
$153$	−47.4591	+	18.8723i	−0.310190	+	0.123348i
$154$		0			0
$155$	18.6876	+	45.1158i	0.120565	+	0.291070i
$156$		0			0
$157$	−129.540	+	129.540i	−0.825095	+	0.825095i	−0.986834	−	0.161739i	$-0.948290\pi$
$157$	−129.540	+	129.540i	−0.825095	+	0.825095i	0.161739	+	0.986834i	$0.448290\pi$
$158$		0			0
$159$	4.68140	+	3.12801i	0.0294428	+	0.0196730i
$160$		0			0
$161$	64.0240	+	26.5196i	0.397665	+	0.164718i
$162$		0			0
$163$	17.7460	+	89.2151i	0.108871	+	0.547332i	0.996267	+	0.0863240i	$0.0275120\pi$
$163$	17.7460	+	89.2151i	0.108871	+	0.547332i	−0.887396	+	0.461008i	$0.847488\pi$
$164$		0			0
$165$	7.18882	−	36.1406i	0.0435686	−	0.219034i
$166$		0			0
$167$	−19.1759	−	28.6988i	−0.114826	−	0.171849i	0.769605	−	0.638520i	$-0.220453\pi$
$167$	−19.1759	−	28.6988i	−0.114826	−	0.171849i	−0.884431	+	0.466671i	$0.845453\pi$
$168$		0			0
$169$		−	168.340i		−	0.996094i
$170$		0			0
$171$	16.0860			0.0940700
$172$		0			0
$173$	69.6731	−	46.5541i	0.402734	−	0.269099i	−0.337664	−	0.941267i	$-0.609637\pi$
$173$	69.6731	−	46.5541i	0.402734	−	0.269099i	0.740399	+	0.672168i	$0.234637\pi$
$174$		0			0
$175$	−74.6989	−	14.8585i	−0.426851	−	0.0849059i
$176$		0			0
$177$	−373.220	+	74.2381i	−2.10859	+	0.419424i
$178$		0			0
$179$	−16.2457	+	39.2205i	−0.0907579	+	0.219109i	−0.962740	−	0.270429i	$-0.912835\pi$
$179$	−16.2457	+	39.2205i	−0.0907579	+	0.219109i	0.871982	+	0.489538i	$0.162835\pi$
$180$		0			0
$181$	−64.3336	+	96.2821i	−0.355434	+	0.531945i	−0.965499	−	0.260406i	$-0.916143\pi$
$181$	−64.3336	+	96.2821i	−0.355434	+	0.531945i	0.610065	+	0.792352i	$0.291143\pi$
$182$		0			0
$183$	204.271	+	204.271i	1.11624	+	1.11624i
$184$		0			0
$185$	−36.2224	+	15.0038i	−0.195797	+	0.0811016i
$186$		0			0
$187$	−78.5514	+	14.4671i	−0.420061	+	0.0773641i
$188$		0			0
$189$	30.4619	+	73.5415i	0.161174	+	0.389109i
$190$		0			0
$191$	−189.871	+	189.871i	−0.994089	+	0.994089i	−0.999983	−	0.00589325i	$-0.998124\pi$
$191$	−189.871	+	189.871i	−0.994089	+	0.994089i	0.00589325	+	0.999983i	$0.498124\pi$
$192$		0			0
$193$	−239.619	−	160.108i	−1.24155	−	0.829577i	−0.251168	−	0.967943i	$-0.580815\pi$
$193$	−239.619	−	160.108i	−1.24155	−	0.829577i	−0.990381	+	0.138367i	$0.955815\pi$
$194$		0			0
$195$	−5.88734	−	2.43862i	−0.0301915	−	0.0125057i
$196$		0			0
$197$	−12.7495	−	64.0961i	−0.0647183	−	0.325361i	0.934840	−	0.355068i	$-0.115542\pi$
$197$	−12.7495	−	64.0961i	−0.0647183	−	0.325361i	−0.999559	+	0.0297075i	$0.990542\pi$
$198$		0			0
$199$	61.8179	−	310.780i	0.310643	−	1.56171i	−0.438149	−	0.898902i	$-0.644366\pi$
$199$	61.8179	−	310.780i	0.310643	−	1.56171i	0.748792	−	0.662805i	$-0.230634\pi$
$200$		0			0
$201$	−6.08084	−	9.10061i	−0.0302529	−	0.0452767i
$202$		0			0
$203$			3.13366i			0.0154368i
$204$		0			0
$205$	−125.954			−0.614408
$206$		0			0
$207$	45.1764	−	30.1859i	0.218243	−	0.145826i
$208$		0			0
$209$	24.6730	+	4.90775i	0.118052	+	0.0234821i
$210$		0			0
$211$	202.124	−	40.2050i	0.957935	−	0.190545i	0.308723	−	0.951152i	$-0.400099\pi$
$211$	202.124	−	40.2050i	0.957935	−	0.190545i	0.649213	+	0.760607i	$0.275099\pi$
$212$		0			0
$213$	132.298	−	319.395i	0.621117	−	1.49951i
$214$		0			0
$215$	−52.2258	+	78.1614i	−0.242911	+	0.363542i
$216$		0			0
$217$	58.4528	+	58.4528i	0.269368	+	0.269368i
$218$		0			0
$219$	203.271	−	84.1976i	0.928178	−	0.384464i
$220$		0			0
$221$	−0.196370	+	13.8113i	−0.000888551	+	0.0624947i
$222$		0			0
$223$	123.566	+	298.315i	0.554107	+	1.33773i	0.914369	+	0.404882i	$0.132687\pi$
$223$	123.566	+	298.315i	0.554107	+	1.33773i	−0.360261	+	0.932851i	$0.617313\pi$
$224$		0			0
$225$	−42.2243	+	42.2243i	−0.187664	+	0.187664i
$226$		0			0
$227$	−66.6363	−	44.5250i	−0.293552	−	0.196145i	0.400070	−	0.916485i	$-0.368986\pi$
$227$	−66.6363	−	44.5250i	−0.293552	−	0.196145i	−0.693622	+	0.720340i	$0.743986\pi$
$228$		0			0
$229$	406.679	+	168.452i	1.77589	+	0.735599i	0.993635	+	0.112643i	$0.0359318\pi$
$229$	406.679	+	168.452i	1.77589	+	0.735599i	0.782257	+	0.622955i	$0.214068\pi$
$230$		0			0
$231$	−12.1693	−	61.1790i	−0.0526808	−	0.264844i
$232$		0			0
$233$	75.6237	−	380.186i	0.324565	−	1.63170i	−0.382077	−	0.924130i	$-0.624791\pi$
$233$	75.6237	−	380.186i	0.324565	−	1.63170i	0.706643	−	0.707570i	$-0.250209\pi$
$234$		0			0
$235$	−2.04476	−	3.06021i	−0.00870113	−	0.0130222i
$236$		0			0
$237$		−	242.835i		−	1.02462i
$238$		0			0
$239$	189.232			0.791765			0.395882	−	0.918301i	$-0.370439\pi$
$239$	189.232			0.791765			0.395882	+	0.918301i	$0.370439\pi$
$240$		0			0
$241$	24.3693	−	16.2830i	0.101117	−	0.0675644i	−0.503984	−	0.863713i	$-0.668133\pi$
$241$	24.3693	−	16.2830i	0.101117	−	0.0675644i	0.605101	+	0.796149i	$0.293133\pi$
$242$		0			0
$243$	153.094	+	30.4522i	0.630015	+	0.125318i
$244$		0			0
$245$	−76.1877	+	15.1547i	−0.310970	+	0.0618558i
$246$		0			0
$247$	1.66482	−	4.01924i	0.00674018	−	0.0162722i
$248$		0			0
$249$	96.9940	−	145.162i	0.389534	−	0.582979i
$250$		0			0
$251$	168.472	+	168.472i	0.671205	+	0.671205i	0.957994	−	0.286789i	$-0.0925879\pi$
$251$	168.472	+	168.472i	0.671205	+	0.671205i	−0.286789	+	0.957994i	$0.592588\pi$
$252$		0			0
$253$	78.5019	−	32.5166i	0.310284	−	0.128524i
$254$		0			0
$255$	−122.441	−	52.7686i	−0.480163	−	0.206936i
$256$		0			0
$257$	68.3241	+	164.949i	0.265852	+	0.641825i	0.999280	−	0.0379431i	$-0.0120806\pi$
$257$	68.3241	+	164.949i	0.265852	+	0.641825i	−0.733427	+	0.679768i	$0.762081\pi$
$258$		0			0
$259$	−46.9303	+	46.9303i	−0.181198	+	0.181198i
$260$		0			0
$261$	2.04285	+	1.36499i	0.00782701	+	0.00522984i
$262$		0			0
$263$	−18.6481	−	7.72429i	−0.0709053	−	0.0293699i	0.346949	−	0.937884i	$-0.387218\pi$
$263$	−18.6481	−	7.72429i	−0.0709053	−	0.0293699i	−0.417854	+	0.908514i	$0.637218\pi$
$264$		0			0
$265$	0.717630	+	3.60777i	0.00270804	+	0.0136142i
$266$		0			0
$267$	79.4233	−	399.288i	0.297465	−	1.49546i
$268$		0			0
$269$	295.705	+	442.553i	1.09927	+	1.64518i	0.670832	+	0.741609i	$0.265937\pi$
$269$	295.705	+	442.553i	1.09927	+	1.64518i	0.428441	+	0.903570i	$0.359063\pi$
$270$		0			0
$271$		−	238.535i		−	0.880205i	−0.897948	−	0.440102i	$-0.854942\pi$
$271$		−	238.535i		−	0.880205i	0.897948	−	0.440102i	$-0.145058\pi$
$272$		0			0
$273$	−10.7872			−0.0395137
$274$		0			0
$275$	−77.6469	+	51.8820i	−0.282352	+	0.188662i
$276$		0			0
$277$	−250.775	−	49.8823i	−0.905327	−	0.180081i	−0.279594	−	0.960118i	$-0.590200\pi$
$277$	−250.775	−	49.8823i	−0.905327	−	0.180081i	−0.625733	+	0.780038i	$0.715200\pi$
$278$		0			0
$279$	63.5670	−	12.6443i	0.227839	−	0.0453199i
$280$		0			0
$281$	100.053	−	241.549i	0.356061	−	0.859606i	−0.639786	−	0.768553i	$-0.720977\pi$
$281$	100.053	−	241.549i	0.356061	−	0.859606i	0.995846	−	0.0910527i	$-0.0290232\pi$
$282$		0			0
$283$	−20.9750	+	31.3912i	−0.0741165	+	0.110923i	−0.866676	−	0.498871i	$-0.833748\pi$
$283$	−20.9750	+	31.3912i	−0.0741165	+	0.110923i	0.792560	+	0.609794i	$0.208748\pi$
$284$		0			0
$285$	29.6932	+	29.6932i	0.104187	+	0.104187i
$286$		0			0
$287$	−196.985	+	81.5937i	−0.686358	+	0.284299i
$288$		0			0
$289$	−8.21636	+	288.883i	−0.0284303	+	0.999596i
$290$		0			0
$291$	29.5893	+	71.4349i	0.101682	+	0.245481i
$292$		0			0
$293$	−56.3438	+	56.3438i	−0.192300	+	0.192300i	−0.796689	−	0.604389i	$-0.793417\pi$
$293$	−56.3438	+	56.3438i	−0.192300	+	0.192300i	0.604389	+	0.796689i	$0.293417\pi$
$294$		0			0
$295$	−206.715	−	138.123i	−0.700730	−	0.468213i
$296$		0			0
$297$	90.1717	+	37.3503i	0.303608	+	0.125759i
$298$		0			0
$299$	−2.86670	−	14.4119i	−0.00958763	−	0.0482003i
$300$		0			0
$301$	−31.0448	+	156.073i	−0.103139	+	0.518514i
$302$		0			0
$303$	−274.587	−	410.949i	−0.906229	−	1.35627i
$304$		0			0
$305$			188.737i			0.618811i
$306$		0			0
$307$	−110.442			−0.359746			−0.179873	−	0.983690i	$-0.557569\pi$
$307$	−110.442			−0.359746			−0.179873	+	0.983690i	$0.557569\pi$
$308$		0			0
$309$	532.238	−	355.630i	1.72245	−	1.15091i
$310$		0			0
$311$	−386.698	−	76.9189i	−1.24340	−	0.247328i	−0.470811	−	0.882234i	$-0.656039\pi$
$311$	−386.698	−	76.9189i	−1.24340	−	0.247328i	−0.772589	+	0.634906i	$0.781039\pi$
$312$		0			0
$313$	−218.122	+	43.3871i	−0.696874	+	0.138617i	−0.530801	−	0.847497i	$-0.678109\pi$
$313$	−218.122	+	43.3871i	−0.696874	+	0.138617i	−0.166073	+	0.986113i	$0.553109\pi$
$314$		0			0
$315$	9.97249	−	24.0757i	0.0316587	−	0.0764309i
$316$		0			0
$317$	−288.913	+	432.388i	−0.911396	+	1.36400i	0.0199253	+	0.999801i	$0.493657\pi$
$317$	−288.913	+	432.388i	−0.911396	+	1.36400i	−0.931321	+	0.364199i	$0.881343\pi$
$318$		0			0
$319$	2.71691	+	2.71691i	0.00851695	+	0.00851695i
$320$		0			0
$321$	−409.440	+	169.595i	−1.27551	+	0.528335i
$322$		0			0
$323$	36.0247	−	83.5899i	0.111532	−	0.258792i
$324$		0			0
$325$	6.18015	+	14.9202i	0.0190158	+	0.0459083i
$326$		0			0
$327$	−453.815	+	453.815i	−1.38781	+	1.38781i
$328$		0			0
$329$	−5.18033	−	3.46139i	−0.0157457	−	0.0105209i
$330$		0			0
$331$	−120.003	−	49.7070i	−0.362548	−	0.150172i	0.193971	−	0.981007i	$-0.437863\pi$
$331$	−120.003	−	49.7070i	−0.362548	−	0.150172i	−0.556519	+	0.830835i	$0.687863\pi$
$332$		0			0
$333$	10.1518	+	51.0364i	0.0304858	+	0.153262i
$334$		0			0
$335$	1.39507	−	7.01348i	0.00416438	−	0.0209358i
$336$		0			0
$337$	94.7420	+	141.791i	0.281134	+	0.420746i	0.944983	−	0.327120i	$-0.106078\pi$
$337$	94.7420	+	141.791i	0.281134	+	0.420746i	−0.663849	+	0.747867i	$0.731078\pi$
$338$		0			0
$339$		−	337.131i		−	0.994488i
$340$		0			0
$341$	101.358			0.297237
$342$		0			0
$343$	−265.454	+	177.371i	−0.773919	+	0.517116i
$344$		0			0
$345$	139.112	+	27.6711i	0.403223	+	0.0802059i
$346$		0			0
$347$	−128.625	+	25.5852i	−0.370678	+	0.0737324i	−0.376914	−	0.926248i	$-0.623015\pi$
$347$	−128.625	+	25.5852i	−0.370678	+	0.0737324i	0.00623638	+	0.999981i	$0.498015\pi$
$348$		0			0
$349$	−39.1233	+	94.4519i	−0.112101	+	0.270636i	−0.969967	−	0.243238i	$-0.921790\pi$
$349$	−39.1233	+	94.4519i	−0.112101	+	0.270636i	0.857865	+	0.513874i	$0.171790\pi$
$350$		0			0
$351$	9.37725	−	14.0340i	0.0267158	−	0.0399830i
$352$		0			0
$353$	189.492	+	189.492i	0.536805	+	0.536805i	0.922589	−	0.385784i	$-0.126069\pi$
$353$	189.492	+	189.492i	0.536805	+	0.536805i	−0.385784	+	0.922589i	$0.626069\pi$
$354$		0			0
$355$	208.672	−	86.4348i	0.587808	−	0.243478i
$356$		0			0
$357$	−225.676	−	3.20867i	−0.632145	−	0.00898786i
$358$		0			0
$359$	134.762	+	325.343i	0.375381	+	0.906249i	0.992819	+	0.119629i	$0.0381706\pi$
$359$	134.762	+	325.343i	0.375381	+	0.906249i	−0.617438	+	0.786619i	$0.711829\pi$
$360$		0			0
$361$	234.994	−	234.994i	0.650954	−	0.650954i
$362$		0			0
$363$	284.985	+	190.421i	0.785083	+	0.524576i
$364$		0			0
$365$	132.804	+	55.0091i	0.363846	+	0.150710i
$366$		0			0
$367$	−48.5682	−	244.169i	−0.132338	−	0.665310i	−0.988818	−	0.149129i	$-0.952353\pi$
$367$	−48.5682	−	244.169i	−0.132338	−	0.665310i	0.856480	−	0.516181i	$-0.172647\pi$
$368$		0			0
$369$	−32.6130	+	163.957i	−0.0883821	+	0.444327i
$370$		0			0
$371$	3.45948	+	5.17747i	0.00932473	+	0.0139555i
$372$		0			0
$373$		−	150.922i		−	0.404618i	−0.979322	−	0.202309i	$-0.935156\pi$
$373$		−	150.922i		−	0.404618i	0.979322	−	0.202309i	$-0.0648445\pi$
$374$		0			0
$375$	−351.955			−0.938548
$376$		0			0
$377$	0.552482	−	0.369157i	0.00146547	−	0.000979195i
$378$		0			0
$379$	470.446	+	93.5775i	1.24128	+	0.246906i	0.771702	−	0.635984i	$-0.219406\pi$
$379$	470.446	+	93.5775i	1.24128	+	0.246906i	0.469580	+	0.882890i	$0.344406\pi$
$380$		0			0
$381$	−203.873	+	40.5528i	−0.535099	+	0.106438i
$382$		0			0
$383$	−222.414	+	536.954i	−0.580714	+	1.40197i	0.311452	+	0.950262i	$0.399185\pi$
$383$	−222.414	+	536.954i	−0.580714	+	1.40197i	−0.892166	+	0.451707i	$0.850815\pi$
$384$		0			0
$385$	22.6414	−	33.8852i	0.0588088	−	0.0880136i
$386$		0			0
$387$	88.2217	+	88.2217i	0.227963	+	0.227963i
$388$		0			0
$389$	205.061	−	84.9389i	0.527148	−	0.218352i	−0.103205	−	0.994660i	$-0.532910\pi$
$389$	205.061	−	84.9389i	0.527148	−	0.218352i	0.630354	+	0.776308i	$0.282910\pi$
$390$		0			0
$391$	−55.6864	−	302.358i	−0.142420	−	0.773295i
$392$		0			0
$393$	−240.257	−	580.031i	−0.611340	−	1.47590i
$394$		0			0
$395$	112.184	−	112.184i	0.284010	−	0.284010i
$396$		0			0
$397$	−386.515	−	258.261i	−0.973590	−	0.650532i	−0.0363951	−	0.999337i	$-0.511587\pi$
$397$	−386.515	−	258.261i	−0.973590	−	0.650532i	−0.937195	+	0.348805i	$0.886587\pi$
$398$		0			0
$399$	65.6741	+	27.2031i	0.164597	+	0.0681782i
$400$		0			0
$401$	36.8558	+	185.287i	0.0919097	+	0.462061i	0.999141	+	0.0414300i	$0.0131914\pi$
$401$	36.8558	+	185.287i	0.0919097	+	0.462061i	−0.907232	+	0.420631i	$0.861809\pi$
$402$		0			0
$403$	3.41960	−	17.1915i	0.00848535	−	0.0426587i
$404$		0			0
$405$	124.519	+	186.356i	0.307454	+	0.460138i
$406$		0			0
$407$			81.3777i			0.199945i
$408$		0			0
$409$	609.101			1.48925			0.744623	−	0.667486i	$-0.232629\pi$
$409$	609.101			1.48925			0.744623	+	0.667486i	$0.232629\pi$
$410$		0			0
$411$	−1.39506	+	0.932153i	−0.00339432	+	0.00226801i
$412$		0			0
$413$	−412.769	−	82.1049i	−0.999441	−	0.198801i
$414$		0			0
$415$	111.870	−	22.2524i	0.269567	−	0.0536202i
$416$		0			0
$417$	71.1117	−	171.679i	0.170532	−	0.411700i
$418$		0			0
$419$	25.0740	−	37.5260i	0.0598426	−	0.0895607i	−0.800342	−	0.599544i	$-0.795349\pi$
$419$	25.0740	−	37.5260i	0.0598426	−	0.0895607i	0.860184	+	0.509984i	$0.170349\pi$
$420$		0			0
$421$	−462.980	−	462.980i	−1.09971	−	1.09971i	−0.994444	−	0.105271i	$-0.966429\pi$
$421$	−462.980	−	462.980i	−1.09971	−	1.09971i	−0.105271	−	0.994444i	$-0.533571\pi$
$422$		0			0
$423$	−4.51299	+	1.86934i	−0.0106690	+	0.00441924i
$424$		0			0
$425$	124.855	+	313.978i	0.293776	+	0.738772i
$426$		0			0
$427$	122.266	+	295.175i	0.286336	+	0.691277i
$428$		0			0
$429$	−9.35261	+	9.35261i	−0.0218010	+	0.0218010i
$430$		0			0
$431$	345.981	+	231.177i	0.802741	+	0.536374i	0.887923	−	0.459991i	$-0.152147\pi$
$431$	345.981	+	231.177i	0.802741	+	0.536374i	−0.0851829	+	0.996365i	$0.527147\pi$
$432$		0			0
$433$	−492.518	−	204.007i	−1.13745	−	0.471149i	−0.267146	−	0.963656i	$-0.586080\pi$
$433$	−492.518	−	204.007i	−1.13745	−	0.471149i	−0.870308	+	0.492507i	$0.836080\pi$
$434$		0			0
$435$	1.25127	+	6.29055i	0.00287648	+	0.0144610i
$436$		0			0
$437$	−18.8908	+	94.9706i	−0.0432284	+	0.217324i
$438$		0			0
$439$	−262.658	−	393.095i	−0.598310	−	0.895434i	0.401482	−	0.915867i	$-0.368495\pi$
$439$	−262.658	−	393.095i	−0.598310	−	0.895434i	−0.999791	+	0.0204334i	$0.993495\pi$
$440$		0			0
$441$			103.099i			0.233785i
$442$		0			0
$443$	327.671			0.739663			0.369831	−	0.929099i	$-0.379415\pi$
$443$	327.671			0.739663			0.369831	+	0.929099i	$0.379415\pi$
$444$		0			0
$445$	221.153	−	147.770i	0.496974	−	0.332067i
$446$		0			0
$447$	59.0062	+	11.7371i	0.132005	+	0.0262574i
$448$		0			0
$449$	97.0392	−	19.3023i	0.216123	−	0.0429895i	−0.0858411	−	0.996309i	$-0.527358\pi$
$449$	97.0392	−	19.3023i	0.216123	−	0.0429895i	0.301964	+	0.953319i	$0.402358\pi$
$450$		0			0
$451$	−100.045	+	241.529i	−0.221829	+	0.535542i
$452$		0			0
$453$	256.362	−	383.673i	0.565921	−	0.846961i
$454$		0			0
$455$	−4.98346	−	4.98346i	−0.0109527	−	0.0109527i
$456$		0			0
$457$	−203.871	+	84.4463i	−0.446108	+	0.184784i	−0.594417	−	0.804157i	$-0.702617\pi$
$457$	−203.871	+	84.4463i	−0.446108	+	0.184784i	0.148309	+	0.988941i	$0.452617\pi$
$458$		0			0
$459$	200.352	−	290.812i	0.436498	−	0.633577i
$460$		0			0
$461$	−178.586	−	431.144i	−0.387388	−	0.935236i	−0.990492	−	0.137574i	$-0.956070\pi$
$461$	−178.586	−	431.144i	−0.387388	−	0.935236i	0.603104	−	0.797663i	$-0.293930\pi$
$462$		0			0
$463$	564.768	−	564.768i	1.21980	−	1.21980i	0.252101	−	0.967701i	$-0.418878\pi$
$463$	564.768	−	564.768i	1.21980	−	1.21980i	0.967701	−	0.252101i	$-0.0811216\pi$
$464$		0			0
$465$	140.679	+	93.9986i	0.302535	+	0.202148i
$466$		0			0
$467$	−174.190	−	72.1519i	−0.372998	−	0.154501i	0.188306	−	0.982110i	$-0.439700\pi$
$467$	−174.190	−	72.1519i	−0.372998	−	0.154501i	−0.561304	+	0.827609i	$0.689700\pi$
$468$		0			0
$469$	−2.36158	−	11.8724i	−0.00503534	−	0.0253144i
$470$		0			0
$471$	−123.829	+	622.532i	−0.262907	+	1.32172i
$472$		0			0
$473$	108.400	+	162.232i	0.229175	+	0.342985i
$474$		0			0
$475$		−	106.421i		−	0.224044i
$476$		0			0
$477$	4.88213			0.0102351
$478$		0			0
$479$	−109.311	+	73.0391i	−0.228206	+	0.152482i	−0.664417	−	0.747362i	$-0.731320\pi$
$479$	−109.311	+	73.0391i	−0.228206	+	0.152482i	0.436211	+	0.899844i	$0.356320\pi$
$480$		0			0
$481$	13.8026	+	2.74551i	0.0286957	+	0.00570792i
$482$		0			0
$483$	235.489	−	46.8417i	0.487555	−	0.0969807i
$484$		0			0
$485$	−19.3317	+	46.6709i	−0.0398592	+	0.0962286i
$486$		0			0
$487$	200.121	−	299.502i	0.410926	−	0.614994i	−0.567057	−	0.823678i	$-0.691918\pi$
$487$	200.121	−	299.502i	0.410926	−	0.614994i	0.977983	+	0.208685i	$0.0669183\pi$
$488$		0			0
$489$	222.853	+	222.853i	0.455732	+	0.455732i
$490$		0			0
$491$	626.994	−	259.709i	1.27697	−	0.528939i	0.361896	−	0.932219i	$-0.382130\pi$
$491$	626.994	−	259.709i	1.27697	−	0.528939i	0.915077	+	0.403279i	$0.132130\pi$
$492$		0			0
$493$	11.6681	−	7.55865i	0.0236675	−	0.0153320i
$494$		0			0
$495$	−12.2276	−	29.5200i	−0.0247022	−	0.0596364i
$496$		0			0
$497$	270.359	−	270.359i	0.543981	−	0.543981i
$498$		0			0
$499$	376.667	+	251.681i	0.754844	+	0.504370i	0.872458	−	0.488689i	$-0.162525\pi$
$499$	376.667	+	251.681i	0.754844	+	0.504370i	−0.117614	+	0.993059i	$0.537525\pi$
$500$		0			0
$501$	−110.485	−	45.7643i	−0.220528	−	0.0913458i
$502$		0			0
$503$	116.965	+	588.022i	0.232534	+	1.16903i	0.903847	+	0.427855i	$0.140731\pi$
$503$	116.965	+	588.022i	0.232534	+	1.16903i	−0.671313	+	0.741174i	$0.734269\pi$
$504$		0			0
$505$	62.9960	−	316.702i	0.124745	−	0.627133i
$506$		0			0
$507$	−324.037	−	484.956i	−0.639127	−	0.956521i
$508$		0			0
$509$			723.229i			1.42088i	0.703756	+	0.710441i	$0.251505\pi$
$509$			723.229i			1.42088i	−0.703756	+	0.710441i	$0.748495\pi$
$510$		0			0
$511$	243.333			0.476191
$512$		0			0
$513$	−92.4807	+	61.7937i	−0.180274	+	0.120455i
$514$		0			0
$515$	410.174	+	81.5887i	0.796455	+	0.158425i
$516$		0			0
$517$	−7.49243	+	1.49034i	−0.0144921	+	0.00288266i
$518$		0			0
$519$	111.103	−	268.227i	0.214072	−	0.516816i
$520$		0			0
$521$	268.128	−	401.283i	0.514642	−	0.770216i	−0.479587	−	0.877494i	$-0.659214\pi$
$521$	268.128	−	401.283i	0.514642	−	0.770216i	0.994229	+	0.107278i	$0.0342136\pi$
$522$		0			0
$523$	−122.754	−	122.754i	−0.234711	−	0.234711i	0.579945	−	0.814656i	$-0.303074\pi$
$523$	−122.754	−	122.754i	−0.234711	−	0.234711i	−0.814656	+	0.579945i	$0.803074\pi$
$524$		0			0
$525$	−243.795	+	100.983i	−0.464371	+	0.192349i
$526$		0			0
$527$	76.6537	−	358.639i	0.145453	−	0.680530i
$528$		0			0
$529$	−77.2775	−	186.564i	−0.146082	−	0.352674i
$530$		0			0
$531$	−233.322	+	233.322i	−0.439401	+	0.439401i
$532$		0			0
$533$	37.5909	+	25.1174i	0.0705270	+	0.0471246i
$534$		0			0
$535$	−267.501	−	110.802i	−0.500001	−	0.207107i
$536$		0			0
$537$	28.6948	+	144.258i	0.0534353	+	0.268637i
$538$		0			0
$539$	−31.4551	+	158.135i	−0.0583582	+	0.293386i
$540$		0			0
$541$	268.690	+	402.123i	0.496655	+	0.743296i	0.992115	−	0.125334i	$-0.0400004\pi$
$541$	268.690	+	402.123i	0.496655	+	0.743296i	−0.495460	+	0.868631i	$0.665000\pi$
$542$		0			0
$543$			401.207i			0.738871i
$544$		0			0
$545$	−419.304			−0.769365
$546$		0			0
$547$	−692.085	+	462.437i	−1.26524	+	0.845405i	−0.993148	−	0.116866i	$-0.962715\pi$
$547$	−692.085	+	462.437i	−1.26524	+	0.845405i	−0.272091	+	0.962272i	$0.587715\pi$
$548$		0			0
$549$	245.684	+	48.8695i	0.447511	+	0.0890155i
$550$		0			0
$551$	−4.29451	+	0.854232i	−0.00779404	+	0.00155033i
$552$		0			0
$553$	102.776	−	248.123i	0.185852	−	0.448686i
$554$		0			0
$555$	−75.4692	+	112.948i	−0.135980	+	0.203509i
$556$		0			0
$557$	−692.897	−	692.897i	−1.24398	−	1.24398i	−0.958336	−	0.285644i	$-0.907792\pi$
$557$	−692.897	−	692.897i	−1.24398	−	1.24398i	−0.285644	−	0.958336i	$-0.592208\pi$
$558$		0			0
$559$	31.1736	−	12.9125i	0.0557668	−	0.0230994i
$560$		0			0
$561$	−198.444	+	192.881i	−0.353733	+	0.343816i
$562$		0			0
$563$	−63.0066	−	152.111i	−0.111912	−	0.270180i	0.857994	−	0.513660i	$-0.171711\pi$
$563$	−63.0066	−	152.111i	−0.111912	−	0.270180i	−0.969906	+	0.243480i	$0.921711\pi$
$564$		0			0
$565$	155.747	−	155.747i	0.275658	−	0.275658i
$566$		0			0
$567$	315.464	+	210.786i	0.556374	+	0.371757i
$568$		0			0
$569$	−454.662	−	188.327i	−0.799055	−	0.330979i	−0.0544769	−	0.998515i	$-0.517349\pi$
$569$	−454.662	−	188.327i	−0.799055	−	0.330979i	−0.744578	+	0.667536i	$0.767349\pi$
$570$		0			0
$571$	18.5742	+	93.3786i	0.0325292	+	0.163535i	0.993635	−	0.112644i	$-0.0359318\pi$
$571$	18.5742	+	93.3786i	0.0325292	+	0.163535i	−0.961106	+	0.276179i	$0.910932\pi$
$572$		0			0
$573$	−181.501	+	912.466i	−0.316755	+	1.59244i
$574$		0			0
$575$	−199.703	−	298.877i	−0.347309	−	0.519785i
$576$		0			0
$577$			622.009i			1.07800i	0.842304	+	0.539002i	$0.181199\pi$
$577$			622.009i			1.07800i	−0.842304	+	0.539002i	$0.818801\pi$
$578$		0			0
$579$	−998.491			−1.72451
$580$		0			0
$581$	160.544	−	107.272i	0.276324	−	0.184634i
$582$		0			0
$583$	7.48829	+	1.48951i	0.0128444	+	0.00255491i
$584$		0			0
$585$	−5.41948	+	1.07800i	−0.00926406	+	0.00184274i
$586$		0			0
$587$	−349.968	+	844.899i	−0.596198	+	1.43935i	0.281229	+	0.959641i	$0.409258\pi$
$587$	−349.968	+	844.899i	−0.596198	+	1.43935i	−0.877427	+	0.479710i	$0.840742\pi$
$588$		0			0
$589$	−64.1722	+	96.0404i	−0.108951	+	0.163057i
$590$		0			0
$591$	−160.108	−	160.108i	−0.270910	−	0.270910i
$592$		0			0
$593$	−1001.51	+	414.839i	−1.68889	+	0.699560i	−0.999687	−	0.0250122i	$-0.992038\pi$
$593$	−1001.51	+	414.839i	−1.68889	+	0.699560i	−0.689199	+	0.724572i	$0.742038\pi$
$594$		0			0
$595$	−102.775	−	105.739i	−0.172731	−	0.177713i
$596$		0			0
$597$	−420.134	−	1014.29i	−0.703742	−	1.69898i
$598$		0			0
$599$	363.586	−	363.586i	0.606988	−	0.606988i	−0.335169	−	0.942158i	$-0.608794\pi$
$599$	363.586	−	363.586i	0.606988	−	0.606988i	0.942158	+	0.335169i	$0.108794\pi$
$600$		0			0
$601$	−538.601	−	359.882i	−0.896175	−	0.598805i	0.0199043	−	0.999802i	$-0.493664\pi$
$601$	−538.601	−	359.882i	−0.896175	−	0.598805i	−0.916079	+	0.400997i	$0.868664\pi$
$602$		0			0
$603$	−8.76838	−	3.63198i	−0.0145413	−	0.00602319i
$604$		0			0
$605$	43.6865	+	219.627i	0.0722091	+	0.363019i
$606$		0			0
$607$	−213.837	+	1075.03i	−0.352284	+	1.77105i	0.245500	+	0.969397i	$0.421048\pi$
$607$	−213.837	+	1075.03i	−0.352284	+	1.77105i	−0.597784	+	0.801657i	$0.703952\pi$
$608$		0			0
$609$	6.03199	+	9.02751i	0.00990474	+	0.0148235i
$610$		0			0
$611$			1.32108i			0.00216217i
$612$		0			0
$613$	233.587			0.381055			0.190527	−	0.981682i	$-0.438980\pi$
$613$	233.587			0.381055			0.190527	+	0.981682i	$0.438980\pi$
$614$		0			0
$615$	−362.849	+	242.448i	−0.589998	+	0.394224i
$616$		0			0
$617$	24.3583	+	4.84517i	0.0394786	+	0.00785279i	0.214790	−	0.976660i	$-0.431093\pi$
$617$	24.3583	+	4.84517i	0.0394786	+	0.00785279i	−0.175311	+	0.984513i	$0.556093\pi$
$618$		0			0
$619$	−379.888	+	75.5644i	−0.613712	+	0.122075i	−0.492152	−	0.870509i	$-0.663790\pi$
$619$	−379.888	+	75.5644i	−0.613712	+	0.122075i	−0.121560	+	0.992584i	$0.538790\pi$
$620$		0			0
$621$	−143.768	+	347.087i	−0.231511	+	0.558916i
$622$		0			0
$623$	250.146	−	374.369i	0.401518	−	0.600914i
$624$		0			0
$625$	188.766	+	188.766i	0.302026	+	0.302026i
$626$		0			0
$627$	80.5252	−	33.3546i	0.128429	−	0.0531971i
$628$		0			0
$629$	287.943	+	61.5434i	0.457779	+	0.0978432i
$630$		0			0
$631$	94.0176	+	226.979i	0.148998	+	0.359712i	0.980703	−	0.195506i	$-0.0626348\pi$
$631$	94.0176	+	226.979i	0.148998	+	0.359712i	−0.831705	+	0.555218i	$0.812635\pi$
$632$		0			0
$633$	504.892	−	504.892i	0.797618	−	0.797618i
$634$		0			0
$635$	−112.919	−	75.4500i	−0.177825	−	0.118819i
$636$		0			0
$637$	25.7604	+	10.6703i	0.0404401	+	0.0167508i
$638$		0			0
$639$	−58.4829	−	294.013i	−0.0915225	−	0.460115i
$640$		0			0
$641$	14.8528	−	74.6702i	0.0231713	−	0.116490i	−0.967469	−	0.252991i	$-0.918586\pi$
$641$	14.8528	−	74.6702i	0.0231713	−	0.116490i	0.990640	+	0.136501i	$0.0435857\pi$
$642$		0			0
$643$	163.436	+	244.599i	0.254177	+	0.380402i	0.936511	−	0.350638i	$-0.114035\pi$
$643$	163.436	+	244.599i	0.254177	+	0.380402i	−0.682334	+	0.731040i	$0.739035\pi$
$644$		0			0
$645$			325.698i			0.504958i
$646$		0			0
$647$	−8.49109			−0.0131238			−0.00656189	−	0.999978i	$-0.502089\pi$
$647$	−8.49109			−0.0131238			−0.00656189	+	0.999978i	$0.502089\pi$
$648$		0			0
$649$	−429.059	+	286.688i	−0.661108	+	0.441738i
$650$		0			0
$651$	280.907	+	55.8759i	0.431501	+	0.0858309i
$652$		0			0
$653$	286.117	−	56.9122i	0.438158	−	0.0871550i	0.0289177	−	0.999582i	$-0.490794\pi$
$653$	286.117	−	56.9122i	0.438158	−	0.0871550i	0.409240	+	0.912427i	$0.365794\pi$
$654$		0			0
$655$	156.968	−	378.954i	0.239645	−	0.578555i
$656$		0			0
$657$	105.993	−	158.630i	0.161329	−	0.241446i
$658$		0			0
$659$	−666.417	−	666.417i	−1.01126	−	1.01126i	−0.999936	−	0.0113193i	$-0.996397\pi$
$659$	−666.417	−	666.417i	−1.01126	−	1.01126i	−0.0113193	−	0.999936i	$-0.503603\pi$
$660$		0			0
$661$	998.022	−	413.394i	1.50987	−	0.625407i	0.534336	−	0.845272i	$-0.320562\pi$
$661$	998.022	−	413.394i	1.50987	−	0.625407i	0.975530	+	0.219865i	$0.0705615\pi$
$662$		0			0
$663$	26.0197	+	40.1659i	0.0392454	+	0.0605820i
$664$		0			0
$665$	17.7727	+	42.9071i	0.0267259	+	0.0645220i
$666$		0			0
$667$	−10.4579	+	10.4579i	−0.0156790	+	0.0156790i
$668$		0			0
$669$	930.196	+	621.537i	1.39043	+	0.929054i
$670$		0			0
$671$	361.924	+	149.914i	0.539380	+	0.223418i
$672$		0			0
$673$	−108.421	−	545.069i	−0.161101	−	0.809909i	−0.973832	−	0.227270i	$-0.927020\pi$
$673$	−108.421	−	545.069i	−0.161101	−	0.809909i	0.812731	−	0.582639i	$-0.197980\pi$
$674$		0			0
$675$	80.5510	−	404.957i	0.119335	−	0.599937i
$676$		0			0
$677$	300.657	+	449.965i	0.444102	+	0.664646i	0.984221	−	0.176943i	$-0.0566207\pi$
$677$	300.657	+	449.965i	0.444102	+	0.664646i	−0.540119	+	0.841589i	$0.681621\pi$
$678$		0			0
$679$			85.5140i			0.125941i
$680$		0			0
$681$	−277.673			−0.407743
$682$		0			0
$683$	−199.444	+	133.264i	−0.292012	+	0.195116i	−0.692944	−	0.720992i	$-0.743686\pi$
$683$	−199.444	+	133.264i	−0.292012	+	0.195116i	0.400932	+	0.916108i	$0.368686\pi$
$684$		0			0
$685$	−1.07512	−	0.213855i	−0.00156952	−	0.000312197i
$686$		0			0
$687$	1495.82	−	297.537i	2.17732	−	0.433097i
$688$		0			0
$689$	0.505278	−	1.21985i	0.000733350	−	0.00177046i
$690$		0			0
$691$	−661.944	+	990.669i	−0.957950	+	1.43367i	−0.0576839	+	0.998335i	$0.518372\pi$
$691$	−661.944	+	990.669i	−0.957950	+	1.43367i	−0.900267	+	0.435339i	$0.856628\pi$
$692$		0			0
$693$	−38.2466	−	38.2466i	−0.0551899	−	0.0551899i
$694$		0			0
$695$	112.164	−	46.4597i	0.161387	−	0.0668485i
$696$		0			0
$697$	778.954	+	536.654i	1.11758	+	0.769948i
$698$		0			0
$699$	−513.962	−	1240.81i	−0.735282	−	1.77513i
$700$		0			0
$701$	318.880	−	318.880i	0.454893	−	0.454893i	−0.442081	−	0.896975i	$-0.645760\pi$
$701$	318.880	−	318.880i	0.454893	−	0.454893i	0.896975	+	0.442081i	$0.145760\pi$
$702$		0			0
$703$	−77.1085	−	51.5222i	−0.109685	−	0.0732891i
$704$		0			0
$705$	−11.7812	−	4.87993i	−0.0167109	−	0.00692188i
$706$		0			0
$707$	−106.640	−	536.115i	−0.150834	−	0.758295i
$708$		0			0
$709$	−187.896	+	944.619i	−0.265016	+	1.33233i	0.587330	+	0.809348i	$0.300179\pi$
$709$	−187.896	+	944.619i	−0.265016	+	1.33233i	−0.852346	+	0.522978i	$0.824821\pi$
$710$		0			0
$711$	−116.985	−	175.080i	−0.164535	−	0.246245i
$712$		0			0
$713$			390.144i			0.547187i
$714$		0			0
$715$	−8.64138			−0.0120858
$716$		0			0
$717$	545.142	−	364.252i	0.760309	−	0.508023i
$718$		0			0
$719$	−632.617	−	125.835i	−0.879857	−	0.175014i	−0.265565	−	0.964093i	$-0.585558\pi$
$719$	−632.617	−	125.835i	−0.879857	−	0.175014i	−0.614292	+	0.789079i	$0.710558\pi$
$720$		0			0
$721$	694.344	−	138.114i	0.963030	−	0.191559i
$722$		0			0
$723$	38.8602	−	93.8168i	0.0537485	−	0.129760i
$724$		0			0
$725$	9.03045	−	13.5150i	0.0124558	−	0.0186414i
$726$		0			0
$727$	−433.580	−	433.580i	−0.596397	−	0.596397i	0.342955	−	0.939352i	$-0.388572\pi$
$727$	−433.580	−	433.580i	−0.596397	−	0.596397i	−0.939352	+	0.342955i	$0.888572\pi$
$728$		0			0
$729$	−323.632	+	134.053i	−0.443940	+	0.183886i
$730$		0			0
$731$	656.013	−	260.866i	0.897418	−	0.356862i
$732$		0			0
$733$	277.828	+	670.737i	0.379029	+	0.915057i	0.992148	+	0.125067i	$0.0399145\pi$
$733$	277.828	+	670.737i	0.379029	+	0.915057i	−0.613119	+	0.789990i	$0.710086\pi$
$734$		0			0
$735$	−190.311	+	190.311i	−0.258927	+	0.258927i
$736$		0			0
$737$	−12.3410	−	8.24599i	−0.0167449	−	0.0111886i
$738$		0			0
$739$	−957.941	−	396.792i	−1.29627	−	0.536931i	−0.375420	−	0.926855i	$-0.622501\pi$
$739$	−957.941	−	396.792i	−1.29627	−	0.536931i	−0.920847	+	0.389923i	$0.872501\pi$
$740$		0			0
$741$	−2.94058	−	14.7833i	−0.00396840	−	0.0199505i
$742$		0			0
$743$	111.451	−	560.304i	0.150002	−	0.754110i	−0.830410	−	0.557153i	$-0.811894\pi$
$743$	111.451	−	560.304i	0.150002	−	0.754110i	0.980412	−	0.196958i	$-0.0631062\pi$
$744$		0			0
$745$	21.8372	+	32.6817i	0.0293117	+	0.0438681i
$746$		0			0
$747$		−	151.386i		−	0.202659i
$748$		0			0
$749$	−490.136			−0.654387
$750$		0			0
$751$	174.961	−	116.905i	0.232971	−	0.155666i	−0.433606	−	0.901103i	$-0.642759\pi$
$751$	174.961	−	116.905i	0.232971	−	0.155666i	0.666577	+	0.745436i	$0.267759\pi$
$752$		0			0
$753$	809.630	+	161.045i	1.07521	+	0.213872i
$754$		0			0
$755$	295.682	−	58.8147i	0.391631	−	0.0779003i
$756$		0			0
$757$	330.392	−	797.637i	0.436449	−	1.05368i	−0.540717	−	0.841205i	$-0.681847\pi$
$757$	330.392	−	797.637i	0.436449	−	1.05368i	0.977166	−	0.212477i	$-0.0681530\pi$
$758$		0			0
$759$	163.558	−	244.783i	0.215492	−	0.322507i
$760$		0			0
$761$	−283.002	−	283.002i	−0.371882	−	0.371882i	0.496280	−	0.868162i	$-0.334699\pi$
$761$	−283.002	−	283.002i	−0.371882	−	0.371882i	−0.868162	+	0.496280i	$0.834699\pi$
$762$		0			0
$763$	−655.769	+	271.629i	−0.859462	+	0.356001i
$764$		0			0
$765$	−113.700	+	20.9404i	−0.148627	+	0.0273731i
$766$		0			0
$767$	34.1501	+	82.4456i	0.0445243	+	0.107491i
$768$		0			0
$769$	69.1388	−	69.1388i	0.0899074	−	0.0899074i	−0.660723	−	0.750630i	$-0.729750\pi$
$769$	69.1388	−	69.1388i	0.0899074	−	0.0899074i	0.750630	+	0.660723i	$0.229750\pi$
$770$		0			0
$771$	514.339	+	343.670i	0.667107	+	0.445746i
$772$		0			0
$773$	538.198	+	222.929i	0.696246	+	0.288395i	0.702600	−	0.711585i	$-0.252022\pi$
$773$	538.198	+	222.929i	0.696246	+	0.288395i	−0.00635357	+	0.999980i	$0.502022\pi$
$774$		0			0
$775$	−83.6515	−	420.545i	−0.107937	−	0.542638i
$776$		0			0
$777$	−44.8614	+	225.534i	−0.0577367	+	0.290262i
$778$		0			0
$779$	−165.517	−	247.714i	−0.212474	−	0.317990i
$780$		0			0
$781$		−	468.806i		−	0.600263i
$782$		0			0
$783$	−16.9882			−0.0216963
$784$		0			0
$785$	−344.802	+	230.389i	−0.439238	+	0.293489i
$786$		0			0
$787$	430.753	+	85.6821i	0.547336	+	0.108872i	0.461010	−	0.887395i	$-0.347487\pi$
$787$	430.753	+	85.6821i	0.547336	+	0.108872i	0.0863259	+	0.996267i	$0.472487\pi$
$788$		0			0
$789$	−68.5902	+	13.6434i	−0.0869331	+	0.0172921i
$790$		0			0
$791$	142.686	−	344.474i	0.180387	−	0.435492i
$792$		0			0
$793$	37.6377	−	56.3287i	0.0474624	−	0.0710324i
$794$		0			0
$795$	9.01195	+	9.01195i	0.0113358	+	0.0113358i
$796$		0			0
$797$	−125.692	+	52.0632i	−0.157706	+	0.0653239i	−0.460140	−	0.887846i	$-0.652201\pi$
$797$	−125.692	+	52.0632i	−0.157706	+	0.0653239i	0.302434	+	0.953170i	$0.402201\pi$
$798$		0			0
$799$	−0.392957	+	27.6379i	−0.000491811	+	0.0345906i
$800$		0			0
$801$	−135.092	−	326.142i	−0.168655	−	0.407169i
$802$		0			0
$803$	210.972	−	210.972i	0.262729	−	0.262729i
$804$		0			0
$805$	130.430	+	87.1507i	0.162025	+	0.108262i
$806$		0			0
$807$	1703.74	+	705.712i	2.11120	+	0.874489i
$808$		0			0
$809$	−192.774	−	969.138i	−0.238286	−	1.19795i	−0.895784	−	0.444489i	$-0.853385\pi$
$809$	−192.774	−	969.138i	−0.238286	−	1.19795i	0.657498	−	0.753456i	$-0.271615\pi$
$810$		0			0
$811$	−265.414	+	1334.33i	−0.327268	+	1.64529i	0.370404	+	0.928871i	$0.379219\pi$
$811$	−265.414	+	1334.33i	−0.327268	+	1.64529i	−0.697672	+	0.716417i	$0.745781\pi$
$812$		0			0
$813$	−459.157	−	687.177i	−0.564769	−	0.845236i
$814$		0			0
$815$			205.906i			0.252645i
$816$		0			0
$817$	−222.352			−0.272156
$818$		0			0
$819$	−7.77743	+	5.19671i	−0.00949626	+	0.00634520i
$820$		0			0
$821$	−873.104	−	173.671i	−1.06346	−	0.211536i	−0.367801	−	0.929905i	$-0.619889\pi$
$821$	−873.104	−	173.671i	−1.06346	−	0.211536i	−0.695663	+	0.718368i	$0.744889\pi$
$822$		0			0
$823$	1368.75	−	272.262i	1.66313	−	0.330817i	0.728122	−	0.685448i	$-0.240394\pi$
$823$	1368.75	−	272.262i	1.66313	−	0.330817i	0.935006	+	0.354631i	$0.115394\pi$
$824$		0			0
$825$	−123.819	+	298.925i	−0.150083	+	0.362333i
$826$		0			0
$827$	−154.271	+	230.883i	−0.186543	+	0.279181i	−0.912940	−	0.408094i	$-0.866193\pi$
$827$	−154.271	+	230.883i	−0.186543	+	0.279181i	0.726397	+	0.687275i	$0.241193\pi$
$828$		0			0
$829$	−238.145	−	238.145i	−0.287268	−	0.287268i	0.548731	−	0.835999i	$-0.315111\pi$
$829$	−238.145	−	238.145i	−0.287268	−	0.287268i	−0.835999	+	0.548731i	$0.815111\pi$
$830$		0			0
$831$	−818.456	+	339.016i	−0.984905	+	0.407961i
$832$		0			0
$833$	535.749	+	230.892i	0.643156	+	0.277181i
$834$		0			0
$835$	−29.8994	−	72.1834i	−0.0358076	−	0.0864472i
$836$		0			0
$837$	−316.884	+	316.884i	−0.378595	+	0.378595i
$838$		0			0
$839$	−226.405	−	151.279i	−0.269851	−	0.180308i	0.413281	−	0.910603i	$-0.364383\pi$
$839$	−226.405	−	151.279i	−0.269851	−	0.180308i	−0.683132	+	0.730295i	$0.739383\pi$
$840$		0			0
$841$	776.365	+	321.581i	0.923145	+	0.382379i
$842$		0			0
$843$	−176.724	−	888.451i	−0.209637	−	1.05392i
$844$		0			0
$845$	74.3408	−	373.736i	0.0879772	−	0.442291i
$846$		0			0
$847$	210.599	+	315.184i	0.248641	+	0.372118i
$848$		0			0
$849$			130.807i			0.154072i
$850$		0			0
$851$	−313.237			−0.368081
$852$		0			0
$853$	−833.896	+	557.192i	−0.977604	+	0.653214i	−0.938231	−	0.346010i	$-0.887536\pi$
$853$	−833.896	+	557.192i	−0.977604	+	0.653214i	−0.0393734	+	0.999225i	$0.512536\pi$
$854$		0			0
$855$	35.7129	+	7.10375i	0.0417695	+	0.00830848i
$856$		0			0
$857$	845.702	−	168.221i	0.986817	−	0.196290i	0.324803	−	0.945782i	$-0.394702\pi$
$857$	845.702	−	168.221i	0.986817	−	0.196290i	0.662014	+	0.749492i	$0.269702\pi$
$858$		0			0
$859$	−498.385	+	1203.21i	−0.580192	+	1.40071i	0.312448	+	0.949935i	$0.398851\pi$
$859$	−498.385	+	1203.21i	−0.580192	+	1.40071i	−0.892639	+	0.450771i	$0.851149\pi$
$860$		0			0
$861$	−410.417	+	614.232i	−0.476675	+	0.713394i
$862$		0			0
$863$	694.639	+	694.639i	0.804912	+	0.804912i	0.983859	−	0.178947i	$-0.0572690\pi$
$863$	694.639	+	694.639i	0.804912	+	0.804912i	−0.178947	+	0.983859i	$0.557269\pi$
$864$		0			0
$865$	175.242	−	72.5876i	0.202592	−	0.0839163i
$866$		0			0
$867$	532.401	+	848.035i	0.614073	+	0.978126i
$868$		0			0
$869$	−126.017	−	304.232i	−0.145014	−	0.350095i
$870$		0			0
$871$	−1.81497	+	1.81497i	−0.00208378	+	0.00208378i
$872$		0			0
$873$	55.7470	+	37.2489i	0.0638568	+	0.0426677i
$874$		0			0
$875$	−359.621	−	148.960i	−0.410995	−	0.170240i
$876$		0			0
$877$	−202.274	−	1016.90i	−0.230643	−	1.15952i	−0.906408	−	0.422403i	$-0.861187\pi$
$877$	−202.274	−	1016.90i	−0.230643	−	1.15952i	0.675765	−	0.737117i	$-0.263813\pi$
$878$		0			0
$879$	−53.8600	+	270.772i	−0.0612741	+	0.308046i
$880$		0			0
$881$	−578.778	−	866.202i	−0.656955	−	0.983203i	−0.999052	−	0.0435383i	$-0.986137\pi$
$881$	−578.778	−	866.202i	−0.656955	−	0.983203i	0.342096	−	0.939665i	$-0.388863\pi$
$882$		0			0
$883$			764.507i			0.865806i	0.901440	+	0.432903i	$0.142511\pi$
$883$			764.507i			0.865806i	−0.901440	+	0.432903i	$0.857489\pi$
$884$		0			0
$885$	−861.382			−0.973313
$886$		0			0
$887$	194.921	−	130.242i	0.219753	−	0.146834i	−0.440822	−	0.897595i	$-0.645313\pi$
$887$	194.921	−	130.242i	0.219753	−	0.146834i	0.660574	+	0.750761i	$0.270313\pi$
$888$		0			0
$889$	−225.476	−	44.8500i	−0.253629	−	0.0504500i
$890$		0			0
$891$	456.262	−	90.7562i	0.512079	−	0.101859i
$892$		0			0
$893$	3.33149	−	8.04292i	0.00373067	−	0.00900663i
$894$		0			0
$895$	−53.3877	+	79.9003i	−0.0596511	+	0.0892741i
$896$		0			0
$897$	−35.9999	−	35.9999i	−0.0401336	−	0.0401336i
$898$		0			0
$899$	−16.2992	+	6.75134i	−0.0181303	+	0.00750984i
$900$		0			0
$901$	10.9336	−	25.3697i	0.0121349	−	0.0281573i
$902$		0			0
$903$	210.990	+	509.374i	0.233654	+	0.564091i
$904$		0			0
$905$	−185.348	+	185.348i	−0.204805	+	0.204805i
$906$		0			0
$907$	−488.357	−	326.310i	−0.538431	−	0.359768i	0.256427	−	0.966564i	$-0.417455\pi$
$907$	−488.357	−	326.310i	−0.538431	−	0.359768i	−0.794858	+	0.606795i	$0.792455\pi$
$908$		0			0
$909$	−395.947	−	164.006i	−0.435585	−	0.180425i
$910$		0			0
$911$	−3.07340	−	15.4510i	−0.00337365	−	0.0169605i	0.979062	−	0.203563i	$-0.0652523\pi$
$911$	−3.07340	−	15.4510i	−0.00337365	−	0.0169605i	−0.982435	+	0.186603i	$0.940252\pi$
$912$		0			0
$913$	46.1871	−	232.198i	0.0505883	−	0.254325i
$914$		0			0
$915$	363.300	+	543.717i	0.397050	+	0.594227i
$916$		0			0
$917$		−	694.348i		−	0.757196i
$918$		0			0
$919$	−207.277			−0.225546			−0.112773	−	0.993621i	$-0.535973\pi$
$919$	−207.277			−0.225546			−0.112773	+	0.993621i	$0.535973\pi$
$920$		0			0
$921$	−318.164	+	212.590i	−0.345454	+	0.230825i
$922$		0			0
$923$	−79.5149	−	15.8165i	−0.0861483	−	0.0171360i
$924$		0			0
$925$	337.645	−	67.1617i	0.365021	−	0.0726073i
$926$		0			0
$927$	212.412	−	512.807i	0.229139	−	0.553190i
$928$		0			0
$929$	−559.100	+	836.752i	−0.601829	+	0.900701i	−0.999861	−	0.0166703i	$-0.994693\pi$
$929$	−559.100	+	836.752i	−0.601829	+	0.900701i	0.398032	+	0.917372i	$0.369693\pi$
$930$		0			0
$931$	−129.924	−	129.924i	−0.139553	−	0.139553i
$932$		0			0
$933$	−1262.07	+	522.765i	−1.35270	+	0.560305i
$934$		0			0
$935$	−180.783	−	2.57038i	−0.193351	−	0.00274907i
$936$		0			0
$937$	422.072	+	1018.97i	0.450450	+	1.08748i	0.972151	+	0.234354i	$0.0752975\pi$
$937$	422.072	+	1018.97i	0.450450	+	1.08748i	−0.521701	+	0.853128i	$0.674702\pi$
$938$		0			0
$939$	−544.852	+	544.852i	−0.580247	+	0.580247i
$940$		0			0
$941$	−256.065	−	171.097i	−0.272121	−	0.181825i	0.412021	−	0.911174i	$-0.364823\pi$
$941$	−256.065	−	171.097i	−0.272121	−	0.181825i	−0.684142	+	0.729349i	$0.739823\pi$
$942$		0			0
$943$	−929.689	−	385.090i	−0.985885	−	0.408367i
$944$		0			0
$945$	35.1526	+	176.724i	0.0371985	+	0.187010i
$946$		0			0
$947$	192.403	−	967.275i	0.203171	−	1.02141i	−0.735744	−	0.677260i	$-0.763167\pi$
$947$	192.403	−	967.275i	0.203171	−	1.02141i	0.938915	−	0.344150i	$-0.111833\pi$
$948$		0			0
$949$	−28.6655	−	42.9010i	−0.0302060	−	0.0452065i
$950$		0			0
$951$			1801.76i			1.89459i
$952$		0			0
$953$	−1420.88			−1.49096			−0.745478	−	0.666530i	$-0.767779\pi$
$953$	−1420.88			−1.49096			−0.745478	+	0.666530i	$0.767779\pi$
$954$		0			0
$955$	−505.388	+	337.689i	−0.529202	+	0.353601i
$956$		0			0
$957$	13.0567	+	2.59714i	0.0136434	+	0.00271383i
$958$		0			0
$959$	−1.81997	+	0.362014i	−0.00189778	+	0.000377491i
$960$		0			0
$961$	189.661	−	457.883i	0.197358	−	0.476465i
$962$		0			0
$963$	−213.498	+	319.522i	−0.221701	+	0.331798i
$964$		0			0
$965$	−461.280	−	461.280i	−0.478010	−	0.478010i
$966$		0			0
$967$	908.093	−	376.145i	0.939083	−	0.388981i	0.139966	−	0.990156i	$-0.455301\pi$
$967$	908.093	−	376.145i	0.939083	−	0.388981i	0.799117	+	0.601175i	$0.205301\pi$
$968$		0			0
$969$	−57.1216	−	310.151i	−0.0589490	−	0.320073i
$970$		0			0
$971$	−395.974	−	955.965i	−0.407800	−	0.984516i	−0.985715	−	0.168419i	$-0.946134\pi$
$971$	−395.974	−	955.965i	−0.407800	−	0.984516i	0.577915	−	0.816097i	$-0.303866\pi$
$972$		0			0
$973$	145.321	−	145.321i	0.149354	−	0.149354i
$974$		0			0
$975$	46.5238	+	31.0862i	0.0477167	+	0.0318833i
$976$		0			0
$977$	1133.98	+	469.710i	1.16068	+	0.480768i	0.878100	−	0.478477i	$-0.158811\pi$
$977$	1133.98	+	469.710i	1.16068	+	0.480768i	0.282576	+	0.959245i	$0.408811\pi$
$978$		0			0
$979$	−107.703	−	541.459i	−0.110013	−	0.553073i
$980$		0			0
$981$	−108.570	+	545.817i	−0.110673	+	0.556389i
$982$		0			0
$983$	212.335	+	317.782i	0.216007	+	0.323278i	0.923611	−	0.383332i	$-0.125224\pi$
$983$	212.335	+	317.782i	0.216007	+	0.323278i	−0.707603	+	0.706610i	$0.750224\pi$
$984$		0			0
$985$		−	147.932i		−	0.150185i
$986$		0			0
$987$	−21.5864			−0.0218707
$988$		0			0
$989$	−624.460	+	417.251i	−0.631405	+	0.421892i
$990$		0			0
$991$	−1391.27	−	276.740i	−1.40390	−	0.279253i	−0.565699	−	0.824612i	$-0.691393\pi$
$991$	−1391.27	−	276.740i	−1.40390	−	0.279253i	−0.838203	+	0.545359i	$0.816393\pi$
$992$		0			0
$993$	−441.389	+	87.7977i	−0.444500	+	0.0884166i
$994$		0			0
$995$	274.488	−	662.672i	0.275867	−	0.666002i
$996$		0			0
$997$	−273.782	+	409.743i	−0.274606	+	0.410976i	−0.942980	−	0.332848i	$-0.891990\pi$
$997$	−273.782	+	409.743i	−0.274606	+	0.410976i	0.668375	+	0.743825i	$0.266990\pi$
$998$		0			0
$999$	−254.418	−	254.418i	−0.254673	−	0.254673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.97.4	✓	32
4.3	odd	2		272.3.bh.f.97.1		32
17.10	odd	16	inner	136.3.t.a.129.4	yes	32
68.27	even	16		272.3.bh.f.129.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.97.4	✓	32	1.1	even	1	trivial
136.3.t.a.129.4	yes	32	17.10	odd	16	inner
272.3.bh.f.97.1		32	4.3	odd	2
272.3.bh.f.129.1		32	68.27	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.88082 - 1.92490i) q^{3} +(2.22013 + 0.441611i) q^{5} +(3.75824 - 0.747561i) q^{7} +(1.14971 - 2.77565i) q^{9} +O(q^{10})\)	\(q+(2.88082 - 1.92490i) q^{3} +(2.22013 + 0.441611i) q^{5} +(3.75824 - 0.747561i) q^{7} +(1.14971 - 2.77565i) q^{9} +(2.61028 - 3.90656i) q^{11} +(-0.574533 - 0.574533i) q^{13} +(7.24584 - 3.00133i) q^{15} +(-11.8487 - 12.1905i) q^{17} +(2.04898 + 4.94668i) q^{19} +(9.38783 - 9.38783i) q^{21} +(15.0371 + 10.0474i) q^{23} +(-18.3630 - 7.60622i) q^{25} +(4.05268 + 20.3742i) q^{27} +(-0.159543 + 0.802076i) q^{29} +(11.9853 + 17.9372i) q^{31} -16.2786i q^{33} +8.67392 q^{35} +(-14.4014 + 9.62268i) q^{37} +(-2.76104 - 0.549206i) q^{39} +(-54.5733 + 10.8553i) q^{41} +(-15.8921 + 38.3669i) q^{43} +(3.77826 - 5.65457i) q^{45} +(-1.14970 - 1.14970i) q^{47} +(-31.7045 + 13.1325i) q^{49} +(-57.5994 - 12.3110i) q^{51} +(0.621871 + 1.50133i) q^{53} +(7.52035 - 7.52035i) q^{55} +(15.4246 + 10.3064i) q^{57} +(-101.470 - 42.0302i) q^{59} +(16.2663 + 81.7763i) q^{61} +(2.24593 - 11.2910i) q^{63} +(-1.02182 - 1.52926i) q^{65} -3.15904i q^{67} +62.6593 q^{69} +(82.9642 - 55.4349i) q^{71} +(62.2823 + 12.3887i) q^{73} +(-67.5417 + 13.4349i) q^{75} +(6.88968 - 16.6332i) q^{77} +(38.9386 - 58.2757i) q^{79} +(70.0128 + 70.0128i) q^{81} +(46.5535 - 19.2831i) q^{83} +(-20.9222 - 32.2970i) q^{85} +(1.08430 + 2.61774i) q^{87} +(83.0860 - 83.0860i) q^{89} +(-2.58873 - 1.72974i) q^{91} +(69.0547 + 28.6034i) q^{93} +(2.36450 + 11.8871i) q^{95} +(-4.35373 + 21.8877i) q^{97} +(-7.84217 - 11.7366i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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