LMFDB - Embedded newform 136.3.t.a.129.4

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			129.4
Character	$\chi$	$=$	136.129
Dual form			136.3.t.a.97.4

$q$-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 $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{16}\right)$

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	0.933716	−	0.358014i	$-0.116546\pi$
$3$	2.88082	+	1.92490i	0.960272	+	0.641633i	0.0265557	+	0.999647i	$0.491546\pi$
$4$		0			0
$5$	2.22013	−	0.441611i	0.444026	−	0.0883223i	0.0319866	−	0.999488i	$-0.489817\pi$
$5$	2.22013	−	0.441611i	0.444026	−	0.0883223i	0.412039	+	0.911166i	$0.364817\pi$
$6$		0			0
$7$	3.75824	+	0.747561i	0.536892	+	0.106794i	0.456087	−	0.889935i	$-0.349251\pi$
$7$	3.75824	+	0.747561i	0.536892	+	0.106794i	0.0808054	+	0.996730i	$0.474251\pi$
$8$		0			0
$9$	1.14971	+	2.77565i	0.127746	+	0.308405i
$10$		0			0
$11$	2.61028	+	3.90656i	0.237298	+	0.355142i	0.930936	−	0.365182i	$-0.118993\pi$
$11$	2.61028	+	3.90656i	0.237298	+	0.355142i	−0.693638	+	0.720324i	$0.743993\pi$
$12$		0			0
$13$	−0.574533	+	0.574533i	−0.0441949	+	0.0441949i	−0.728859	−	0.684664i	$-0.759949\pi$
$13$	−0.574533	+	0.574533i	−0.0441949	+	0.0441949i	0.684664	+	0.728859i	$0.259949\pi$
$14$		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	−0.860742	−	0.509041i	$-0.830000\pi$
$19$	2.04898	−	4.94668i	0.107841	−	0.260352i	0.968583	+	0.248690i	$0.0800000\pi$
$20$		0			0
$21$	9.38783	+	9.38783i	0.447039	+	0.447039i
$22$		0			0
$23$	15.0371	−	10.0474i	0.653785	−	0.436845i	−0.183940	−	0.982937i	$-0.558885\pi$
$23$	15.0371	−	10.0474i	0.653785	−	0.436845i	0.837725	+	0.546092i	$0.183885\pi$
$24$		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	0.977937	−	0.208900i	$-0.0669883\pi$
$29$	−0.159543	−	0.802076i	−0.00550148	−	0.0276578i	−0.983439	+	0.181242i	$0.941988\pi$
$30$		0			0
$31$	11.9853	−	17.9372i	0.386622	−	0.578620i	−0.586203	−	0.810164i	$-0.699378\pi$
$31$	11.9853	−	17.9372i	0.386622	−	0.578620i	0.972824	+	0.231544i	$0.0743778\pi$
$32$		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	0.345525	−	0.938410i	$-0.387701\pi$
$37$	−14.4014	−	9.62268i	−0.389226	−	0.260072i	−0.734751	+	0.678337i	$0.762701\pi$
$38$		0			0
$39$	−2.76104	+	0.549206i	−0.0707960	+	0.0140822i
$40$		0			0
$41$	−54.5733	−	10.8553i	−1.33106	−	0.264763i	−0.522226	−	0.852807i	$-0.674898\pi$
$41$	−54.5733	−	10.8553i	−1.33106	−	0.264763i	−0.808829	+	0.588043i	$0.799898\pi$
$42$		0			0
$43$	−15.8921	−	38.3669i	−0.369584	−	0.892254i	−0.993818	−	0.111017i	$-0.964589\pi$
$43$	−15.8921	−	38.3669i	−0.369584	−	0.892254i	0.624235	−	0.781237i	$-0.285411\pi$
$44$		0			0
$45$	3.77826	+	5.65457i	0.0839614	+	0.125657i
$46$		0			0
$47$	−1.14970	+	1.14970i	−0.0244617	+	0.0244617i	−0.719232	−	0.694770i	$-0.755506\pi$
$47$	−1.14970	+	1.14970i	−0.0244617	+	0.0244617i	0.694770	+	0.719232i	$0.255506\pi$
$48$		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	−0.917904	−	0.396802i	$-0.870120\pi$
$53$	0.621871	−	1.50133i	0.0117334	−	0.0283270i	0.929638	+	0.368475i	$0.120120\pi$
$54$		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	−0.719999	+	0.693975i	$0.755858\pi$
$59$	−101.470	+	42.0302i	−1.71983	+	0.712377i	−0.999831	+	0.0184017i	$0.994142\pi$
$60$		0			0
$61$	16.2663	−	81.7763i	0.266661	−	1.34059i	−0.582659	−	0.812717i	$-0.697988\pi$
$61$	16.2663	−	81.7763i	0.266661	−	1.34059i	0.849320	−	0.527878i	$-0.177012\pi$
$62$		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	$0.00750483\pi$
$67$			3.15904i			0.0471499i	−0.999722	+	0.0235749i	$0.992495\pi$
$68$		0			0
$69$	62.6593			0.908106
$70$		0			0
$71$	82.9642	+	55.4349i	1.16851	+	0.780773i	0.979548	−	0.201211i	$-0.0644877\pi$
$71$	82.9642	+	55.4349i	1.16851	+	0.780773i	0.188962	+	0.981984i	$0.439488\pi$
$72$		0			0
$73$	62.2823	−	12.3887i	0.853182	−	0.169709i	0.250921	−	0.968008i	$-0.419267\pi$
$73$	62.2823	−	12.3887i	0.853182	−	0.169709i	0.602261	+	0.798299i	$0.294267\pi$
$74$		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	0.991634	−	0.129084i	$-0.0412037\pi$
$79$	38.9386	+	58.2757i	0.492894	+	0.737668i	−0.498740	+	0.866752i	$0.666204\pi$
$80$		0			0
$81$	70.0128	−	70.0128i	0.864355	−	0.864355i
$82$		0			0
$83$	46.5535	+	19.2831i	0.560885	+	0.232326i	0.645069	−	0.764124i	$-0.276828\pi$
$83$	46.5535	+	19.2831i	0.560885	+	0.232326i	−0.0841842	+	0.996450i	$0.526828\pi$
$84$		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	0.997926	−	0.0643752i	$-0.0205054\pi$
$89$	83.0860	+	83.0860i	0.933551	+	0.933551i	−0.0643752	+	0.997926i	$0.520505\pi$
$90$		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	0.951833	−	0.306618i	$-0.0991976\pi$
$97$	−4.35373	−	21.8877i	−0.0448839	−	0.225646i	−0.996716	+	0.0809720i	$0.974198\pi$
$98$		0			0
$99$	−7.84217	+	11.7366i	−0.0792138	+	0.118552i
$100$		0			0
$101$			142.650i			1.41238i	0.708023	+	0.706190i	$0.249587\pi$
$101$			142.650i			1.41238i	−0.708023	+	0.706190i	$0.750413\pi$
$102$		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	−0.742633	−	0.669699i	$-0.766423\pi$
$107$	−125.452	+	24.9540i	−1.17245	+	0.233215i	−0.429820	+	0.902914i	$0.641423\pi$
$108$		0			0
$109$	−181.676	−	36.1377i	−1.66676	−	0.331539i	−0.730515	−	0.682896i	$-0.760720\pi$
$109$	−181.676	−	36.1377i	−1.66676	−	0.331539i	−0.936241	+	0.351358i	$0.885720\pi$
$110$		0			0
$111$	−22.9650	−	55.4423i	−0.206892	−	0.499481i
$112$		0			0
$113$	54.0591	+	80.9052i	0.478399	+	0.715975i	0.989657	−	0.143452i	$-0.0458203\pi$
$113$	54.0591	+	80.9052i	0.478399	+	0.715975i	−0.511258	+	0.859427i	$0.670820\pi$
$114$		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	−0.590077	−	0.807347i	$-0.700902\pi$
$127$	−55.4283	+	22.9591i	−0.436443	+	0.180781i	0.153634	+	0.988128i	$0.450902\pi$
$128$		0			0
$129$	28.0703	−	141.119i	0.217599	−	1.09394i
$130$		0			0
$131$	35.3510	+	177.722i	0.269855	+	1.35665i	0.843315	+	0.537420i	$0.180601\pi$
$131$	35.3510	+	177.722i	0.269855	+	1.35665i	−0.573460	+	0.819234i	$0.694399\pi$
$132$		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	0.705544	−	0.708666i	$-0.250703\pi$
$139$	44.5942	+	29.7969i	0.320822	+	0.214366i	−0.384722	+	0.923032i	$0.625703\pi$
$140$		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	−0.664703	−	0.747108i	$-0.731442\pi$
$149$	12.2783	−	12.2783i	0.0824049	−	0.0824049i	0.747108	+	0.664703i	$0.231442\pi$
$150$		0			0
$151$	123.044	+	50.9666i	0.814863	+	0.337527i	0.750892	−	0.660425i	$-0.229624\pi$
$151$	123.044	+	50.9666i	0.814863	+	0.337527i	0.0639703	+	0.997952i	$0.479624\pi$
$152$		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	0.161739	−	0.986834i	$-0.448290\pi$
$157$	−129.540	−	129.540i	−0.825095	−	0.825095i	−0.986834	+	0.161739i	$0.948290\pi$
$158$		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	−0.887396	−	0.461008i	$-0.847488\pi$
$163$	17.7460	−	89.2151i	0.108871	−	0.547332i	0.996267	−	0.0863240i	$-0.0275120\pi$
$164$		0			0
$165$	7.18882	+	36.1406i	0.0435686	+	0.219034i
$166$		0			0
$167$	−19.1759	+	28.6988i	−0.114826	+	0.171849i	−0.884431	−	0.466671i	$-0.845453\pi$
$167$	−19.1759	+	28.6988i	−0.114826	+	0.171849i	0.769605	+	0.638520i	$0.220453\pi$
$168$		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	0.740399	−	0.672168i	$-0.234637\pi$
$173$	69.6731	+	46.5541i	0.402734	+	0.269099i	−0.337664	+	0.941267i	$0.609637\pi$
$174$		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	0.871982	−	0.489538i	$-0.162835\pi$
$179$	−16.2457	−	39.2205i	−0.0907579	−	0.219109i	−0.962740	+	0.270429i	$0.912835\pi$
$180$		0			0
$181$	−64.3336	−	96.2821i	−0.355434	−	0.531945i	0.610065	−	0.792352i	$-0.291143\pi$
$181$	−64.3336	−	96.2821i	−0.355434	−	0.531945i	−0.965499	+	0.260406i	$0.916143\pi$
$182$		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	0.00589325	−	0.999983i	$-0.498124\pi$
$191$	−189.871	−	189.871i	−0.994089	−	0.994089i	−0.999983	+	0.00589325i	$0.998124\pi$
$192$		0			0
$193$	−239.619	+	160.108i	−1.24155	+	0.829577i	−0.990381	−	0.138367i	$-0.955815\pi$
$193$	−239.619	+	160.108i	−1.24155	+	0.829577i	−0.251168	+	0.967943i	$0.580815\pi$
$194$		0			0
$195$	−5.88734	+	2.43862i	−0.0301915	+	0.0125057i
$196$		0			0
$197$	−12.7495	+	64.0961i	−0.0647183	+	0.325361i	−0.999559	−	0.0297075i	$-0.990542\pi$
$197$	−12.7495	+	64.0961i	−0.0647183	+	0.325361i	0.934840	+	0.355068i	$0.115542\pi$
$198$		0			0
$199$	61.8179	+	310.780i	0.310643	+	1.56171i	0.748792	+	0.662805i	$0.230634\pi$
$199$	61.8179	+	310.780i	0.310643	+	1.56171i	−0.438149	+	0.898902i	$0.644366\pi$
$200$		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	0.649213	−	0.760607i	$-0.275099\pi$
$211$	202.124	+	40.2050i	0.957935	+	0.190545i	0.308723	+	0.951152i	$0.400099\pi$
$212$		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	−0.360261	−	0.932851i	$-0.617313\pi$
$223$	123.566	−	298.315i	0.554107	−	1.33773i	0.914369	−	0.404882i	$-0.132687\pi$
$224$		0			0
$225$	−42.2243	−	42.2243i	−0.187664	−	0.187664i
$226$		0			0
$227$	−66.6363	+	44.5250i	−0.293552	+	0.196145i	−0.693622	−	0.720340i	$-0.743986\pi$
$227$	−66.6363	+	44.5250i	−0.293552	+	0.196145i	0.400070	+	0.916485i	$0.368986\pi$
$228$		0			0
$229$	406.679	−	168.452i	1.77589	−	0.735599i	0.782257	−	0.622955i	$-0.214068\pi$
$229$	406.679	−	168.452i	1.77589	−	0.735599i	0.993635	−	0.112643i	$-0.0359318\pi$
$230$		0			0
$231$	−12.1693	+	61.1790i	−0.0526808	+	0.264844i
$232$		0			0
$233$	75.6237	+	380.186i	0.324565	+	1.63170i	0.706643	+	0.707570i	$0.250209\pi$
$233$	75.6237	+	380.186i	0.324565	+	1.63170i	−0.382077	+	0.924130i	$0.624791\pi$
$234$		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	0.605101	−	0.796149i	$-0.293133\pi$
$241$	24.3693	+	16.2830i	0.101117	+	0.0675644i	−0.503984	+	0.863713i	$0.668133\pi$
$242$		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	−0.286789	−	0.957994i	$-0.592588\pi$
$251$	168.472	−	168.472i	0.671205	−	0.671205i	0.957994	+	0.286789i	$0.0925879\pi$
$252$		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	−0.733427	−	0.679768i	$-0.762081\pi$
$257$	68.3241	−	164.949i	0.265852	−	0.641825i	0.999280	+	0.0379431i	$0.0120806\pi$
$258$		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	−0.417854	−	0.908514i	$-0.637218\pi$
$263$	−18.6481	+	7.72429i	−0.0709053	+	0.0293699i	0.346949	+	0.937884i	$0.387218\pi$
$264$		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	0.428441	−	0.903570i	$-0.359063\pi$
$269$	295.705	−	442.553i	1.09927	−	1.64518i	0.670832	−	0.741609i	$-0.265937\pi$
$270$		0			0
$271$			238.535i			0.880205i	0.897948	+	0.440102i	$0.145058\pi$
$271$			238.535i			0.880205i	−0.897948	+	0.440102i	$0.854942\pi$
$272$		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	−0.625733	−	0.780038i	$-0.715200\pi$
$277$	−250.775	+	49.8823i	−0.905327	+	0.180081i	−0.279594	+	0.960118i	$0.590200\pi$
$278$		0			0
$279$	63.5670	+	12.6443i	0.227839	+	0.0453199i
$280$		0			0
$281$	100.053	+	241.549i	0.356061	+	0.859606i	0.995846	+	0.0910527i	$0.0290232\pi$
$281$	100.053	+	241.549i	0.356061	+	0.859606i	−0.639786	+	0.768553i	$0.720977\pi$
$282$		0			0
$283$	−20.9750	−	31.3912i	−0.0741165	−	0.110923i	0.792560	−	0.609794i	$-0.208748\pi$
$283$	−20.9750	−	31.3912i	−0.0741165	−	0.110923i	−0.866676	+	0.498871i	$0.833748\pi$
$284$		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	0.604389	−	0.796689i	$-0.293417\pi$
$293$	−56.3438	−	56.3438i	−0.192300	−	0.192300i	−0.796689	+	0.604389i	$0.793417\pi$
$294$		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	−0.772589	−	0.634906i	$-0.781039\pi$
$311$	−386.698	+	76.9189i	−1.24340	+	0.247328i	−0.470811	+	0.882234i	$0.656039\pi$
$312$		0			0
$313$	−218.122	−	43.3871i	−0.696874	−	0.138617i	−0.166073	−	0.986113i	$-0.553109\pi$
$313$	−218.122	−	43.3871i	−0.696874	−	0.138617i	−0.530801	+	0.847497i	$0.678109\pi$
$314$		0			0
$315$	9.97249	+	24.0757i	0.0316587	+	0.0764309i
$316$		0			0
$317$	−288.913	−	432.388i	−0.911396	−	1.36400i	−0.931321	−	0.364199i	$-0.881343\pi$
$317$	−288.913	−	432.388i	−0.911396	−	1.36400i	0.0199253	−	0.999801i	$-0.493657\pi$
$318$		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	−0.556519	−	0.830835i	$-0.687863\pi$
$331$	−120.003	+	49.7070i	−0.362548	+	0.150172i	0.193971	+	0.981007i	$0.437863\pi$
$332$		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	−0.663849	−	0.747867i	$-0.731078\pi$
$337$	94.7420	−	141.791i	0.281134	−	0.420746i	0.944983	+	0.327120i	$0.106078\pi$
$338$		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	0.00623638	−	0.999981i	$-0.498015\pi$
$347$	−128.625	−	25.5852i	−0.370678	−	0.0737324i	−0.376914	+	0.926248i	$0.623015\pi$
$348$		0			0
$349$	−39.1233	−	94.4519i	−0.112101	−	0.270636i	0.857865	−	0.513874i	$-0.171790\pi$
$349$	−39.1233	−	94.4519i	−0.112101	−	0.270636i	−0.969967	+	0.243238i	$0.921790\pi$
$350$		0			0
$351$	9.37725	+	14.0340i	0.0267158	+	0.0399830i
$352$		0			0
$353$	189.492	−	189.492i	0.536805	−	0.536805i	−0.385784	−	0.922589i	$-0.626069\pi$
$353$	189.492	−	189.492i	0.536805	−	0.536805i	0.922589	+	0.385784i	$0.126069\pi$
$354$		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	−0.617438	−	0.786619i	$-0.711829\pi$
$359$	134.762	−	325.343i	0.375381	−	0.906249i	0.992819	−	0.119629i	$-0.0381706\pi$
$360$		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	0.856480	+	0.516181i	$0.172647\pi$
$367$	−48.5682	+	244.169i	−0.132338	+	0.665310i	−0.988818	+	0.149129i	$0.952353\pi$
$368$		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	$0.0648445\pi$
$373$			150.922i			0.404618i	−0.979322	+	0.202309i	$0.935156\pi$
$374$		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	0.469580	−	0.882890i	$-0.344406\pi$
$379$	470.446	−	93.5775i	1.24128	−	0.246906i	0.771702	+	0.635984i	$0.219406\pi$
$380$		0			0
$381$	−203.873	−	40.5528i	−0.535099	−	0.106438i
$382$		0			0
$383$	−222.414	−	536.954i	−0.580714	−	1.40197i	−0.892166	−	0.451707i	$-0.850815\pi$
$383$	−222.414	−	536.954i	−0.580714	−	1.40197i	0.311452	−	0.950262i	$-0.399185\pi$
$384$		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	0.630354	−	0.776308i	$-0.282910\pi$
$389$	205.061	+	84.9389i	0.527148	+	0.218352i	−0.103205	+	0.994660i	$0.532910\pi$
$390$		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	−0.937195	−	0.348805i	$-0.886587\pi$
$397$	−386.515	+	258.261i	−0.973590	+	0.650532i	−0.0363951	+	0.999337i	$0.511587\pi$
$398$		0			0
$399$	65.6741	−	27.2031i	0.164597	−	0.0681782i
$400$		0			0
$401$	36.8558	−	185.287i	0.0919097	−	0.462061i	−0.907232	−	0.420631i	$-0.861809\pi$
$401$	36.8558	−	185.287i	0.0919097	−	0.462061i	0.999141	−	0.0414300i	$-0.0131914\pi$
$402$		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	0.860184	−	0.509984i	$-0.170349\pi$
$419$	25.0740	+	37.5260i	0.0598426	+	0.0895607i	−0.800342	+	0.599544i	$0.795349\pi$
$420$		0			0
$421$	−462.980	+	462.980i	−1.09971	+	1.09971i	−0.105271	+	0.994444i	$0.533571\pi$
$421$	−462.980	+	462.980i	−1.09971	+	1.09971i	−0.994444	+	0.105271i	$0.966429\pi$
$422$		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	−0.0851829	−	0.996365i	$-0.527147\pi$
$431$	345.981	−	231.177i	0.802741	−	0.536374i	0.887923	+	0.459991i	$0.152147\pi$
$432$		0			0
$433$	−492.518	+	204.007i	−1.13745	+	0.471149i	−0.870308	−	0.492507i	$-0.836080\pi$
$433$	−492.518	+	204.007i	−1.13745	+	0.471149i	−0.267146	+	0.963656i	$0.586080\pi$
$434$		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	−0.999791	−	0.0204334i	$-0.993495\pi$
$439$	−262.658	+	393.095i	−0.598310	+	0.895434i	0.401482	+	0.915867i	$0.368495\pi$
$440$		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	0.301964	−	0.953319i	$-0.402358\pi$
$449$	97.0392	+	19.3023i	0.216123	+	0.0429895i	−0.0858411	+	0.996309i	$0.527358\pi$
$450$		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	0.148309	−	0.988941i	$-0.452617\pi$
$457$	−203.871	−	84.4463i	−0.446108	−	0.184784i	−0.594417	+	0.804157i	$0.702617\pi$
$458$		0			0
$459$	200.352	+	290.812i	0.436498	+	0.633577i
$460$		0			0
$461$	−178.586	+	431.144i	−0.387388	+	0.935236i	0.603104	+	0.797663i	$0.293930\pi$
$461$	−178.586	+	431.144i	−0.387388	+	0.935236i	−0.990492	+	0.137574i	$0.956070\pi$
$462$		0			0
$463$	564.768	+	564.768i	1.21980	+	1.21980i	0.967701	+	0.252101i	$0.0811216\pi$
$463$	564.768	+	564.768i	1.21980	+	1.21980i	0.252101	+	0.967701i	$0.418878\pi$
$464$		0			0
$465$	140.679	−	93.9986i	0.302535	−	0.202148i
$466$		0			0
$467$	−174.190	+	72.1519i	−0.372998	+	0.154501i	−0.561304	−	0.827609i	$-0.689700\pi$
$467$	−174.190	+	72.1519i	−0.372998	+	0.154501i	0.188306	+	0.982110i	$0.439700\pi$
$468$		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	0.436211	−	0.899844i	$-0.356320\pi$
$479$	−109.311	−	73.0391i	−0.228206	−	0.152482i	−0.664417	+	0.747362i	$0.731320\pi$
$480$		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	0.977983	−	0.208685i	$-0.0669183\pi$
$487$	200.121	+	299.502i	0.410926	+	0.614994i	−0.567057	+	0.823678i	$0.691918\pi$
$488$		0			0
$489$	222.853	−	222.853i	0.455732	−	0.455732i
$490$		0			0
$491$	626.994	+	259.709i	1.27697	+	0.528939i	0.915077	−	0.403279i	$-0.132130\pi$
$491$	626.994	+	259.709i	1.27697	+	0.528939i	0.361896	+	0.932219i	$0.382130\pi$
$492$		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	−0.117614	−	0.993059i	$-0.537525\pi$
$499$	376.667	−	251.681i	0.754844	−	0.504370i	0.872458	+	0.488689i	$0.162525\pi$
$500$		0			0
$501$	−110.485	+	45.7643i	−0.220528	+	0.0913458i
$502$		0			0
$503$	116.965	−	588.022i	0.232534	−	1.16903i	−0.671313	−	0.741174i	$-0.734269\pi$
$503$	116.965	−	588.022i	0.232534	−	1.16903i	0.903847	−	0.427855i	$-0.140731\pi$
$504$		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	$-0.748495\pi$
$509$		−	723.229i		−	1.42088i	0.703756	−	0.710441i	$-0.251505\pi$
$510$		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	0.994229	−	0.107278i	$-0.0342136\pi$
$521$	268.128	+	401.283i	0.514642	+	0.770216i	−0.479587	+	0.877494i	$0.659214\pi$
$522$		0			0
$523$	−122.754	+	122.754i	−0.234711	+	0.234711i	−0.814656	−	0.579945i	$-0.803074\pi$
$523$	−122.754	+	122.754i	−0.234711	+	0.234711i	0.579945	+	0.814656i	$0.303074\pi$
$524$		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	−0.495460	−	0.868631i	$-0.665000\pi$
$541$	268.690	−	402.123i	0.496655	−	0.743296i	0.992115	+	0.125334i	$0.0400004\pi$
$542$		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	−0.272091	−	0.962272i	$-0.587715\pi$
$547$	−692.085	−	462.437i	−1.26524	−	0.845405i	−0.993148	+	0.116866i	$0.962715\pi$
$548$		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	−0.285644	+	0.958336i	$0.592208\pi$
$557$	−692.897	+	692.897i	−1.24398	+	1.24398i	−0.958336	+	0.285644i	$0.907792\pi$
$558$		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	−0.969906	−	0.243480i	$-0.921711\pi$
$563$	−63.0066	+	152.111i	−0.111912	+	0.270180i	0.857994	+	0.513660i	$0.171711\pi$
$564$		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	−0.744578	−	0.667536i	$-0.767349\pi$
$569$	−454.662	+	188.327i	−0.799055	+	0.330979i	−0.0544769	+	0.998515i	$0.517349\pi$
$570$		0			0
$571$	18.5742	−	93.3786i	0.0325292	−	0.163535i	−0.961106	−	0.276179i	$-0.910932\pi$
$571$	18.5742	−	93.3786i	0.0325292	−	0.163535i	0.993635	+	0.112644i	$0.0359318\pi$
$572$		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	$-0.818801\pi$
$577$		−	622.009i		−	1.07800i	0.842304	−	0.539002i	$-0.181199\pi$
$578$		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	−0.877427	−	0.479710i	$-0.840742\pi$
$587$	−349.968	−	844.899i	−0.596198	−	1.43935i	0.281229	−	0.959641i	$-0.409258\pi$
$588$		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	−0.689199	−	0.724572i	$-0.742038\pi$
$593$	−1001.51	−	414.839i	−1.68889	−	0.699560i	−0.999687	+	0.0250122i	$0.992038\pi$
$594$		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	0.942158	−	0.335169i	$-0.108794\pi$
$599$	363.586	+	363.586i	0.606988	+	0.606988i	−0.335169	+	0.942158i	$0.608794\pi$
$600$		0			0
$601$	−538.601	+	359.882i	−0.896175	+	0.598805i	−0.916079	−	0.400997i	$-0.868664\pi$
$601$	−538.601	+	359.882i	−0.896175	+	0.598805i	0.0199043	+	0.999802i	$0.493664\pi$
$602$		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	−0.597784	−	0.801657i	$-0.703952\pi$
$607$	−213.837	−	1075.03i	−0.352284	−	1.77105i	0.245500	−	0.969397i	$-0.421048\pi$
$608$		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	−0.175311	−	0.984513i	$-0.556093\pi$
$617$	24.3583	−	4.84517i	0.0394786	−	0.00785279i	0.214790	+	0.976660i	$0.431093\pi$
$618$		0			0
$619$	−379.888	−	75.5644i	−0.613712	−	0.122075i	−0.121560	−	0.992584i	$-0.538790\pi$
$619$	−379.888	−	75.5644i	−0.613712	−	0.122075i	−0.492152	+	0.870509i	$0.663790\pi$
$620$		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	−0.831705	−	0.555218i	$-0.812635\pi$
$631$	94.0176	−	226.979i	0.148998	−	0.359712i	0.980703	+	0.195506i	$0.0626348\pi$
$632$		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	0.990640	−	0.136501i	$-0.0435857\pi$
$641$	14.8528	+	74.6702i	0.0231713	+	0.116490i	−0.967469	+	0.252991i	$0.918586\pi$
$642$		0			0
$643$	163.436	−	244.599i	0.254177	−	0.380402i	−0.682334	−	0.731040i	$-0.739035\pi$
$643$	163.436	−	244.599i	0.254177	−	0.380402i	0.936511	+	0.350638i	$0.114035\pi$
$644$		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	0.409240	−	0.912427i	$-0.365794\pi$
$653$	286.117	+	56.9122i	0.438158	+	0.0871550i	0.0289177	+	0.999582i	$0.490794\pi$
$654$		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	−0.0113193	+	0.999936i	$0.503603\pi$
$659$	−666.417	+	666.417i	−1.01126	+	1.01126i	−0.999936	+	0.0113193i	$0.996397\pi$
$660$		0			0
$661$	998.022	+	413.394i	1.50987	+	0.625407i	0.975530	−	0.219865i	$-0.0705615\pi$
$661$	998.022	+	413.394i	1.50987	+	0.625407i	0.534336	+	0.845272i	$0.320562\pi$
$662$		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	0.812731	+	0.582639i	$0.197980\pi$
$673$	−108.421	+	545.069i	−0.161101	+	0.809909i	−0.973832	+	0.227270i	$0.927020\pi$
$674$		0			0
$675$	80.5510	+	404.957i	0.119335	+	0.599937i
$676$		0			0
$677$	300.657	−	449.965i	0.444102	−	0.664646i	−0.540119	−	0.841589i	$-0.681621\pi$
$677$	300.657	−	449.965i	0.444102	−	0.664646i	0.984221	+	0.176943i	$0.0566207\pi$
$678$		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	0.400932	−	0.916108i	$-0.368686\pi$
$683$	−199.444	−	133.264i	−0.292012	−	0.195116i	−0.692944	+	0.720992i	$0.743686\pi$
$684$		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	−0.900267	−	0.435339i	$-0.856628\pi$
$691$	−661.944	−	990.669i	−0.957950	−	1.43367i	−0.0576839	−	0.998335i	$-0.518372\pi$
$692$		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	0.896975	−	0.442081i	$-0.145760\pi$
$701$	318.880	+	318.880i	0.454893	+	0.454893i	−0.442081	+	0.896975i	$0.645760\pi$
$702$		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	−0.852346	−	0.522978i	$-0.824821\pi$
$709$	−187.896	−	944.619i	−0.265016	−	1.33233i	0.587330	−	0.809348i	$-0.300179\pi$
$710$		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	−0.614292	−	0.789079i	$-0.710558\pi$
$719$	−632.617	+	125.835i	−0.879857	+	0.175014i	−0.265565	+	0.964093i	$0.585558\pi$
$720$		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	−0.939352	−	0.342955i	$-0.888572\pi$
$727$	−433.580	+	433.580i	−0.596397	+	0.596397i	0.342955	+	0.939352i	$0.388572\pi$
$728$		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	−0.613119	−	0.789990i	$-0.710086\pi$
$733$	277.828	−	670.737i	0.379029	−	0.915057i	0.992148	−	0.125067i	$-0.0399145\pi$
$734$		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	−0.920847	−	0.389923i	$-0.872501\pi$
$739$	−957.941	+	396.792i	−1.29627	+	0.536931i	−0.375420	+	0.926855i	$0.622501\pi$
$740$		0			0
$741$	−2.94058	+	14.7833i	−0.00396840	+	0.0199505i
$742$		0			0
$743$	111.451	+	560.304i	0.150002	+	0.754110i	0.980412	+	0.196958i	$0.0631062\pi$
$743$	111.451	+	560.304i	0.150002	+	0.754110i	−0.830410	+	0.557153i	$0.811894\pi$
$744$		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	0.666577	−	0.745436i	$-0.267759\pi$
$751$	174.961	+	116.905i	0.232971	+	0.155666i	−0.433606	+	0.901103i	$0.642759\pi$
$752$		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	0.977166	+	0.212477i	$0.0681530\pi$
$757$	330.392	+	797.637i	0.436449	+	1.05368i	−0.540717	+	0.841205i	$0.681847\pi$
$758$		0			0
$759$	163.558	+	244.783i	0.215492	+	0.322507i
$760$		0			0
$761$	−283.002	+	283.002i	−0.371882	+	0.371882i	−0.868162	−	0.496280i	$-0.834699\pi$
$761$	−283.002	+	283.002i	−0.371882	+	0.371882i	0.496280	+	0.868162i	$0.334699\pi$
$762$		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	0.750630	−	0.660723i	$-0.229750\pi$
$769$	69.1388	+	69.1388i	0.0899074	+	0.0899074i	−0.660723	+	0.750630i	$0.729750\pi$
$770$		0			0
$771$	514.339	−	343.670i	0.667107	−	0.445746i
$772$		0			0
$773$	538.198	−	222.929i	0.696246	−	0.288395i	−0.00635357	−	0.999980i	$-0.502022\pi$
$773$	538.198	−	222.929i	0.696246	−	0.288395i	0.702600	+	0.711585i	$0.252022\pi$
$774$		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	0.0863259	−	0.996267i	$-0.472487\pi$
$787$	430.753	−	85.6821i	0.547336	−	0.108872i	0.461010	+	0.887395i	$0.347487\pi$
$788$		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	0.302434	−	0.953170i	$-0.402201\pi$
$797$	−125.692	−	52.0632i	−0.157706	−	0.0653239i	−0.460140	+	0.887846i	$0.652201\pi$
$798$		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	0.657498	+	0.753456i	$0.271615\pi$
$809$	−192.774	+	969.138i	−0.238286	+	1.19795i	−0.895784	+	0.444489i	$0.853385\pi$
$810$		0			0
$811$	−265.414	−	1334.33i	−0.327268	−	1.64529i	−0.697672	−	0.716417i	$-0.745781\pi$
$811$	−265.414	−	1334.33i	−0.327268	−	1.64529i	0.370404	−	0.928871i	$-0.379219\pi$
$812$		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	−0.695663	−	0.718368i	$-0.744889\pi$
$821$	−873.104	+	173.671i	−1.06346	+	0.211536i	−0.367801	+	0.929905i	$0.619889\pi$
$822$		0			0
$823$	1368.75	+	272.262i	1.66313	+	0.330817i	0.935006	−	0.354631i	$-0.115394\pi$
$823$	1368.75	+	272.262i	1.66313	+	0.330817i	0.728122	+	0.685448i	$0.240394\pi$
$824$		0			0
$825$	−123.819	−	298.925i	−0.150083	−	0.362333i
$826$		0			0
$827$	−154.271	−	230.883i	−0.186543	−	0.279181i	0.726397	−	0.687275i	$-0.241193\pi$
$827$	−154.271	−	230.883i	−0.186543	−	0.279181i	−0.912940	+	0.408094i	$0.866193\pi$
$828$		0			0
$829$	−238.145	+	238.145i	−0.287268	+	0.287268i	−0.835999	−	0.548731i	$-0.815111\pi$
$829$	−238.145	+	238.145i	−0.287268	+	0.287268i	0.548731	+	0.835999i	$0.315111\pi$
$830$		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	−0.683132	−	0.730295i	$-0.739383\pi$
$839$	−226.405	+	151.279i	−0.269851	+	0.180308i	0.413281	+	0.910603i	$0.364383\pi$
$840$		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	−0.0393734	−	0.999225i	$-0.512536\pi$
$853$	−833.896	−	557.192i	−0.977604	−	0.653214i	−0.938231	+	0.346010i	$0.887536\pi$
$854$		0			0
$855$	35.7129	−	7.10375i	0.0417695	−	0.00830848i
$856$		0			0
$857$	845.702	+	168.221i	0.986817	+	0.196290i	0.662014	−	0.749492i	$-0.269702\pi$
$857$	845.702	+	168.221i	0.986817	+	0.196290i	0.324803	+	0.945782i	$0.394702\pi$
$858$		0			0
$859$	−498.385	−	1203.21i	−0.580192	−	1.40071i	−0.892639	−	0.450771i	$-0.851149\pi$
$859$	−498.385	−	1203.21i	−0.580192	−	1.40071i	0.312448	−	0.949935i	$-0.398851\pi$
$860$		0			0
$861$	−410.417	−	614.232i	−0.476675	−	0.713394i
$862$		0			0
$863$	694.639	−	694.639i	0.804912	−	0.804912i	−0.178947	−	0.983859i	$-0.557269\pi$
$863$	694.639	−	694.639i	0.804912	−	0.804912i	0.983859	+	0.178947i	$0.0572690\pi$
$864$		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	0.675765	+	0.737117i	$0.263813\pi$
$877$	−202.274	+	1016.90i	−0.230643	+	1.15952i	−0.906408	+	0.422403i	$0.861187\pi$
$878$		0			0
$879$	−53.8600	−	270.772i	−0.0612741	−	0.308046i
$880$		0			0
$881$	−578.778	+	866.202i	−0.656955	+	0.983203i	0.342096	+	0.939665i	$0.388863\pi$
$881$	−578.778	+	866.202i	−0.656955	+	0.983203i	−0.999052	+	0.0435383i	$0.986137\pi$
$882$		0			0
$883$		−	764.507i		−	0.865806i	−0.901440	−	0.432903i	$-0.857489\pi$
$883$		−	764.507i		−	0.865806i	0.901440	−	0.432903i	$-0.142511\pi$
$884$		0			0
$885$	−861.382			−0.973313
$886$		0			0
$887$	194.921	+	130.242i	0.219753	+	0.146834i	0.660574	−	0.750761i	$-0.270313\pi$
$887$	194.921	+	130.242i	0.219753	+	0.146834i	−0.440822	+	0.897595i	$0.645313\pi$
$888$		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	−0.794858	−	0.606795i	$-0.792455\pi$
$907$	−488.357	+	326.310i	−0.538431	+	0.359768i	0.256427	+	0.966564i	$0.417455\pi$
$908$		0			0
$909$	−395.947	+	164.006i	−0.435585	+	0.180425i
$910$		0			0
$911$	−3.07340	+	15.4510i	−0.00337365	+	0.0169605i	−0.982435	−	0.186603i	$-0.940252\pi$
$911$	−3.07340	+	15.4510i	−0.00337365	+	0.0169605i	0.979062	+	0.203563i	$0.0652523\pi$
$912$		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	0.398032	−	0.917372i	$-0.369693\pi$
$929$	−559.100	−	836.752i	−0.601829	−	0.900701i	−0.999861	+	0.0166703i	$0.994693\pi$
$930$		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	−0.521701	−	0.853128i	$-0.674702\pi$
$937$	422.072	−	1018.97i	0.450450	−	1.08748i	0.972151	−	0.234354i	$-0.0752975\pi$
$938$		0			0
$939$	−544.852	−	544.852i	−0.580247	−	0.580247i
$940$		0			0
$941$	−256.065	+	171.097i	−0.272121	+	0.181825i	−0.684142	−	0.729349i	$-0.739823\pi$
$941$	−256.065	+	171.097i	−0.272121	+	0.181825i	0.412021	+	0.911174i	$0.364823\pi$
$942$		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	0.938915	+	0.344150i	$0.111833\pi$
$947$	192.403	+	967.275i	0.203171	+	1.02141i	−0.735744	+	0.677260i	$0.763167\pi$
$948$		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	0.799117	−	0.601175i	$-0.205301\pi$
$967$	908.093	+	376.145i	0.939083	+	0.388981i	0.139966	+	0.990156i	$0.455301\pi$
$968$		0			0
$969$	−57.1216	+	310.151i	−0.0589490	+	0.320073i
$970$		0			0
$971$	−395.974	+	955.965i	−0.407800	+	0.984516i	0.577915	+	0.816097i	$0.303866\pi$
$971$	−395.974	+	955.965i	−0.407800	+	0.984516i	−0.985715	+	0.168419i	$0.946134\pi$
$972$		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	0.282576	−	0.959245i	$-0.408811\pi$
$977$	1133.98	−	469.710i	1.16068	−	0.480768i	0.878100	+	0.478477i	$0.158811\pi$
$978$		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	−0.707603	−	0.706610i	$-0.750224\pi$
$983$	212.335	−	317.782i	0.216007	−	0.323278i	0.923611	+	0.383332i	$0.125224\pi$
$984$		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	−0.838203	−	0.545359i	$-0.816393\pi$
$991$	−1391.27	+	276.740i	−1.40390	+	0.279253i	−0.565699	+	0.824612i	$0.691393\pi$
$992$		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	0.668375	−	0.743825i	$-0.266990\pi$
$997$	−273.782	−	409.743i	−0.274606	−	0.410976i	−0.942980	+	0.332848i	$0.891990\pi$
$998$		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.129.4	yes	32
4.3	odd	2		272.3.bh.f.129.1		32
17.12	odd	16	inner	136.3.t.a.97.4	✓	32
68.63	even	16		272.3.bh.f.97.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.97.4	✓	32	17.12	odd	16	inner
136.3.t.a.129.4	yes	32	1.1	even	1	trivial
272.3.bh.f.97.1		32	68.63	even	16
272.3.bh.f.129.1		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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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