LMFDB - Embedded newform 136.3.t.b.65.1

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:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			65.1
Character	$\chi$	$=$	136.65
Dual form			136.3.t.b.113.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10801 + 5.57033i) q^{3} +(-3.32830 + 2.22390i) q^{5} +(-0.387063 - 0.258627i) q^{7} +(-21.4860 - 8.89979i) q^{9} +O(q^{10})$	\(q+(-1.10801 + 5.57033i) q^{3} +(-3.32830 + 2.22390i) q^{5} +(-0.387063 - 0.258627i) q^{7} +(-21.4860 - 8.89979i) q^{9} +(12.6327 - 2.51280i) q^{11} +(-0.187068 - 0.187068i) q^{13} +(-8.70007 - 21.0038i) q^{15} +(-16.5318 - 3.96248i) q^{17} +(-16.4847 + 6.82818i) q^{19} +(1.86951 - 1.86951i) q^{21} +(8.25566 + 41.5040i) q^{23} +(-3.43524 + 8.29340i) q^{25} +(44.9834 - 67.3224i) q^{27} +(23.4648 + 35.1176i) q^{29} +(-9.74589 - 1.93858i) q^{31} +73.1525i q^{33} +1.86342 q^{35} +(-0.185929 + 0.934730i) q^{37} +(1.24930 - 0.834759i) q^{39} +(-40.0098 - 26.7337i) q^{41} +(-2.37066 - 0.981960i) q^{43} +(91.3041 - 18.1615i) q^{45} +(54.0079 + 54.0079i) q^{47} +(-18.6686 - 45.0699i) q^{49} +(40.3896 - 87.6969i) q^{51} +(85.0899 - 35.2454i) q^{53} +(-36.4572 + 36.4572i) q^{55} +(-19.7701 - 99.3909i) q^{57} +(-12.0895 + 29.1867i) q^{59} +(-28.6393 + 42.8617i) q^{61} +(6.01470 + 9.00164i) q^{63} +(1.03864 + 0.206598i) q^{65} +80.1566i q^{67} -240.339 q^{69} +(3.79439 - 19.0757i) q^{71} +(62.4090 - 41.7004i) q^{73} +(-42.3907 - 28.3246i) q^{75} +(-5.53953 - 2.29455i) q^{77} +(38.7103 - 7.69996i) q^{79} +(177.164 + 177.164i) q^{81} +(32.4456 + 78.3305i) q^{83} +(63.8347 - 23.5766i) q^{85} +(-221.616 + 91.7963i) q^{87} +(-28.4107 + 28.4107i) q^{89} +(0.0240262 + 0.120788i) q^{91} +(21.5970 - 52.1399i) q^{93} +(39.6808 - 59.3865i) q^{95} +(-12.5898 - 18.8419i) q^{97} +(-293.790 - 58.4384i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 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} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * 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 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

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
$3$	−1.10801	+	5.57033i	−0.369336	+	1.85678i	0.131614	+	0.991301i	$0.457984\pi$
$3$	−1.10801	+	5.57033i	−0.369336	+	1.85678i	−0.500950	+	0.865476i	$0.667016\pi$
$4$		0			0
$5$	−3.32830	+	2.22390i	−0.665660	+	0.444780i	−0.841948	−	0.539559i	$-0.818591\pi$
$5$	−3.32830	+	2.22390i	−0.665660	+	0.444780i	0.176288	+	0.984339i	$0.443591\pi$
$6$		0			0
$7$	−0.387063	−	0.258627i	−0.0552947	−	0.0369467i	0.527616	−	0.849483i	$-0.323086\pi$
$7$	−0.387063	−	0.258627i	−0.0552947	−	0.0369467i	−0.582910	+	0.812536i	$0.698086\pi$
$8$		0			0
$9$	−21.4860	−	8.89979i	−2.38733	−	0.988866i
$10$		0			0
$11$	12.6327	−	2.51280i	1.14843	−	0.228436i	0.416054	−	0.909340i	$-0.363413\pi$
$11$	12.6327	−	2.51280i	1.14843	−	0.228436i	0.732373	+	0.680903i	$0.238413\pi$
$12$		0			0
$13$	−0.187068	−	0.187068i	−0.0143899	−	0.0143899i	0.699875	−	0.714265i	$-0.253239\pi$
$13$	−0.187068	−	0.187068i	−0.0143899	−	0.0143899i	−0.714265	+	0.699875i	$0.753239\pi$
$14$		0			0
$15$	−8.70007	−	21.0038i	−0.580005	−	1.40025i
$16$		0			0
$17$	−16.5318	−	3.96248i	−0.972456	−	0.233087i
$17$	−16.5318	−	3.96248i	−0.972456	−	0.233087i
$18$		0			0
$19$	−16.4847	+	6.82818i	−0.867615	+	0.359378i	−0.771681	−	0.636010i	$-0.780584\pi$
$19$	−16.4847	+	6.82818i	−0.867615	+	0.359378i	−0.0959342	+	0.995388i	$0.530584\pi$
$20$		0			0
$21$	1.86951	−	1.86951i	0.0890242	−	0.0890242i
$22$		0			0
$23$	8.25566	+	41.5040i	0.358942	+	1.80452i	0.564002	+	0.825774i	$0.309261\pi$
$23$	8.25566	+	41.5040i	0.358942	+	1.80452i	−0.205060	+	0.978749i	$0.565739\pi$
$24$		0			0
$25$	−3.43524	+	8.29340i	−0.137410	+	0.331736i
$26$		0			0
$27$	44.9834	−	67.3224i	1.66605	−	2.49342i
$28$		0			0
$29$	23.4648	+	35.1176i	0.809132	+	1.21095i	0.974426	+	0.224707i	$0.0721424\pi$
$29$	23.4648	+	35.1176i	0.809132	+	1.21095i	−0.165295	+	0.986244i	$0.552858\pi$
$30$		0			0
$31$	−9.74589	−	1.93858i	−0.314384	−	0.0625348i	0.0353766	−	0.999374i	$-0.488737\pi$
$31$	−9.74589	−	1.93858i	−0.314384	−	0.0625348i	−0.349760	+	0.936839i	$0.613737\pi$
$32$		0			0
$33$			73.1525i			2.21674i
$34$		0			0
$35$	1.86342			0.0532406
$36$		0			0
$37$	−0.185929	+	0.934730i	−0.00502512	+	0.0252630i	−0.983216	−	0.182443i	$-0.941600\pi$
$37$	−0.185929	+	0.934730i	−0.00502512	+	0.0252630i	0.978191	+	0.207706i	$0.0665996\pi$
$38$		0			0
$39$	1.24930	−	0.834759i	0.0320335	−	0.0214041i
$40$		0			0
$41$	−40.0098	−	26.7337i	−0.975849	−	0.652042i	−0.0380706	−	0.999275i	$-0.512121\pi$
$41$	−40.0098	−	26.7337i	−0.975849	−	0.652042i	−0.937779	+	0.347233i	$0.887121\pi$
$42$		0			0
$43$	−2.37066	−	0.981960i	−0.0551317	−	0.0228363i	0.354947	−	0.934886i	$-0.384499\pi$
$43$	−2.37066	−	0.981960i	−0.0551317	−	0.0228363i	−0.410079	+	0.912050i	$0.634499\pi$
$44$		0			0
$45$	91.3041	−	18.1615i	2.02898	−	0.403589i
$46$		0			0
$47$	54.0079	+	54.0079i	1.14911	+	1.14911i	0.986729	+	0.162376i	$0.0519158\pi$
$47$	54.0079	+	54.0079i	1.14911	+	1.14911i	0.162376	+	0.986729i	$0.448084\pi$
$48$		0			0
$49$	−18.6686	−	45.0699i	−0.380991	−	0.919794i
$50$		0			0
$51$	40.3896	−	87.6969i	0.791953	−	1.71955i
$52$		0			0
$53$	85.0899	−	35.2454i	1.60547	−	0.665007i	0.613294	−	0.789855i	$-0.289844\pi$
$53$	85.0899	−	35.2454i	1.60547	−	0.665007i	0.992176	+	0.124848i	$0.0398443\pi$
$54$		0			0
$55$	−36.4572	+	36.4572i	−0.662858	+	0.662858i
$56$		0			0
$57$	−19.7701	−	99.3909i	−0.346843	−	1.74370i
$58$		0			0
$59$	−12.0895	+	29.1867i	−0.204907	+	0.494690i	−0.992607	−	0.121369i	$-0.961272\pi$
$59$	−12.0895	+	29.1867i	−0.204907	+	0.494690i	0.787700	+	0.616059i	$0.211272\pi$
$60$		0			0
$61$	−28.6393	+	42.8617i	−0.469496	+	0.702651i	−0.988348	−	0.152213i	$-0.951360\pi$
$61$	−28.6393	+	42.8617i	−0.469496	+	0.702651i	0.518851	+	0.854865i	$0.326360\pi$
$62$		0			0
$63$	6.01470	+	9.00164i	0.0954715	+	0.142883i
$64$		0			0
$65$	1.03864	+	0.206598i	0.0159791	+	0.00317843i
$66$		0			0
$67$			80.1566i			1.19637i	0.801359	+	0.598184i	$0.204111\pi$
$67$			80.1566i			1.19637i	−0.801359	+	0.598184i	$0.795889\pi$
$68$		0			0
$69$	−240.339			−3.48317
$70$		0			0
$71$	3.79439	−	19.0757i	0.0534421	−	0.268672i	−0.944821	−	0.327588i	$-0.893764\pi$
$71$	3.79439	−	19.0757i	0.0534421	−	0.268672i	0.998263	+	0.0589158i	$0.0187644\pi$
$72$		0			0
$73$	62.4090	−	41.7004i	0.854918	−	0.571238i	−0.0490701	−	0.998795i	$-0.515626\pi$
$73$	62.4090	−	41.7004i	0.854918	−	0.571238i	0.903988	+	0.427557i	$0.140626\pi$
$74$		0			0
$75$	−42.3907	−	28.3246i	−0.565209	−	0.377661i
$76$		0			0
$77$	−5.53953	−	2.29455i	−0.0719419	−	0.0297993i
$78$		0			0
$79$	38.7103	−	7.69996i	0.490004	−	0.0974678i	0.0560965	−	0.998425i	$-0.482135\pi$
$79$	38.7103	−	7.69996i	0.490004	−	0.0974678i	0.433907	+	0.900958i	$0.357135\pi$
$80$		0			0
$81$	177.164	+	177.164i	2.18721	+	2.18721i
$82$		0			0
$83$	32.4456	+	78.3305i	0.390910	+	0.943741i	0.989742	+	0.142866i	$0.0456319\pi$
$83$	32.4456	+	78.3305i	0.390910	+	0.943741i	−0.598831	+	0.800875i	$0.704368\pi$
$84$		0			0
$85$	63.8347	−	23.5766i	0.750997	−	0.277372i
$86$		0			0
$87$	−221.616	+	91.7963i	−2.54731	+	1.05513i
$88$		0			0
$89$	−28.4107	+	28.4107i	−0.319221	+	0.319221i	−0.848468	−	0.529247i	$-0.822475\pi$
$89$	−28.4107	+	28.4107i	−0.319221	+	0.319221i	0.529247	+	0.848468i	$0.322475\pi$
$90$		0			0
$91$	0.0240262	+	0.120788i	0.000264025	+	0.00132734i
$92$		0			0
$93$	21.5970	−	52.1399i	0.232226	−	0.560644i
$94$		0			0
$95$	39.6808	−	59.3865i	0.417693	−	0.625121i
$96$		0			0
$97$	−12.5898	−	18.8419i	−0.129791	−	0.194247i	0.760882	−	0.648890i	$-0.224767\pi$
$97$	−12.5898	−	18.8419i	−0.129791	−	0.194247i	−0.890673	+	0.454644i	$0.849767\pi$
$98$		0			0
$99$	−293.790	−	58.4384i	−2.96757	−	0.590287i
$100$		0			0
$101$			17.5898i			0.174156i	0.996201	+	0.0870782i	$0.0277530\pi$
$101$			17.5898i			0.174156i	−0.996201	+	0.0870782i	$0.972247\pi$
$102$		0			0
$103$	−155.667			−1.51133			−0.755665	−	0.654958i	$-0.772686\pi$
$103$	−155.667			−1.51133			−0.755665	+	0.654958i	$0.772686\pi$
$104$		0			0
$105$	−2.06468	+	10.3799i	−0.0196637	+	0.0988559i
$106$		0			0
$107$	120.956	−	80.8202i	1.13043	−	0.755329i	0.157750	−	0.987479i	$-0.449576\pi$
$107$	120.956	−	80.8202i	1.13043	−	0.755329i	0.972680	+	0.232150i	$0.0745760\pi$
$108$		0			0
$109$	−27.4709	−	18.3554i	−0.252026	−	0.168399i	0.423140	−	0.906064i	$-0.360928\pi$
$109$	−27.4709	−	18.3554i	−0.252026	−	0.168399i	−0.675166	+	0.737666i	$0.735928\pi$
$110$		0			0
$111$	−5.00075	−	2.07138i	−0.0450518	−	0.0186611i
$112$		0			0
$113$	51.5007	−	10.2441i	0.455759	−	0.0906560i	0.0381278	−	0.999273i	$-0.487861\pi$
$113$	51.5007	−	10.2441i	0.455759	−	0.0906560i	0.417631	+	0.908617i	$0.362861\pi$
$114$		0			0
$115$	−119.778	−	119.778i	−1.04155	−	1.04155i
$116$		0			0
$117$	2.35448	+	5.68422i	0.0201238	+	0.0485830i
$118$		0			0
$119$	5.37402	+	5.80929i	0.0451598	+	0.0488175i
$120$		0			0
$121$	41.4815	−	17.1822i	0.342823	−	0.142002i
$122$		0			0
$123$	193.247	−	193.247i	1.57111	−	1.57111i
$124$		0			0
$125$	−26.5334	−	133.392i	−0.212267	−	1.06714i
$126$		0			0
$127$	21.1958	−	51.1712i	0.166896	−	0.402923i	−0.818199	−	0.574936i	$-0.805027\pi$
$127$	21.1958	−	51.1712i	0.166896	−	0.402923i	0.985095	+	0.172013i	$0.0550271\pi$
$128$		0			0
$129$	8.09656	−	12.1174i	0.0627640	−	0.0939330i
$130$		0			0
$131$	66.9816	+	100.245i	0.511310	+	0.765229i	0.993861	−	0.110639i	$-0.0352897\pi$
$131$	66.9816	+	100.245i	0.511310	+	0.765229i	−0.482551	+	0.875868i	$0.660290\pi$
$132$		0			0
$133$	8.14656	+	1.62045i	0.0612524	+	0.0121839i
$134$		0			0
$135$			324.108i			2.40080i
$136$		0			0
$137$	106.964			0.780756			0.390378	−	0.920655i	$-0.372344\pi$
$137$	106.964			0.780756			0.390378	+	0.920655i	$0.372344\pi$
$138$		0			0
$139$	13.7785	−	69.2692i	0.0991259	−	0.498340i	−0.899043	−	0.437859i	$-0.855737\pi$
$139$	13.7785	−	69.2692i	0.0991259	−	0.498340i	0.998169	−	0.0604803i	$-0.0192632\pi$
$140$		0			0
$141$	−360.683	+	241.001i	−2.55804	+	1.70923i
$142$		0			0
$143$	−2.83324	−	1.89311i	−0.0198129	−	0.0132385i
$144$		0			0
$145$	−156.196	−	64.6984i	−1.07721	−	0.446196i
$146$		0			0
$147$	271.739	−	54.0523i	1.84857	−	0.367703i
$148$		0			0
$149$	124.756	+	124.756i	0.837292	+	0.837292i	0.988502	−	0.151210i	$-0.0483170\pi$
$149$	124.756	+	124.756i	0.837292	+	0.837292i	−0.151210	+	0.988502i	$0.548317\pi$
$150$		0			0
$151$	−8.84674	−	21.3579i	−0.0585877	−	0.141443i	0.891875	−	0.452282i	$-0.149390\pi$
$151$	−8.84674	−	21.3579i	−0.0585877	−	0.141443i	−0.950463	+	0.310839i	$0.899390\pi$
$152$		0			0
$153$	319.936	+	232.267i	2.09108	+	1.51808i
$154$		0			0
$155$	36.7484	−	15.2217i	0.237087	−	0.0982045i
$156$		0			0
$157$	83.8512	−	83.8512i	0.534084	−	0.534084i	−0.387701	−	0.921785i	$-0.626731\pi$
$157$	83.8512	−	83.8512i	0.534084	−	0.534084i	0.921785	+	0.387701i	$0.126731\pi$
$158$		0			0
$159$	102.048	+	513.031i	0.641813	+	3.22661i
$160$		0			0
$161$	7.53861	−	18.1998i	0.0468236	−	0.113042i
$162$		0			0
$163$	−14.8151	+	22.1724i	−0.0908902	+	0.136027i	−0.874128	−	0.485695i	$-0.838567\pi$
$163$	−14.8151	+	22.1724i	−0.0908902	+	0.136027i	0.783238	+	0.621722i	$0.213567\pi$
$164$		0			0
$165$	−162.684	−	243.473i	−0.985962	−	1.47560i
$166$		0			0
$167$	291.376	+	57.9582i	1.74476	+	0.347055i	0.961536	−	0.274680i	$-0.0885718\pi$
$167$	291.376	+	57.9582i	1.74476	+	0.347055i	0.783228	+	0.621735i	$0.213572\pi$
$168$		0			0
$169$		−	168.930i		−	0.999586i
$170$		0			0
$171$	414.960			2.42666
$172$		0			0
$173$	14.0020	−	70.3930i	0.0809367	−	0.406896i	−0.918984	−	0.394295i	$-0.870989\pi$
$173$	14.0020	−	70.3930i	0.0809367	−	0.406896i	0.999921	−	0.0126012i	$-0.00401118\pi$
$174$		0			0
$175$	3.47455	−	2.32162i	0.0198546	−	0.0132664i
$176$		0			0
$177$	−149.184	−	99.6818i	−0.842849	−	0.563174i
$178$		0			0
$179$	−256.813	−	106.376i	−1.43471	−	0.594277i	−0.476201	−	0.879336i	$-0.657987\pi$
$179$	−256.813	−	106.376i	−1.43471	−	0.594277i	−0.958510	+	0.285059i	$0.907987\pi$
$180$		0			0
$181$	138.167	−	27.4832i	0.763355	−	0.151841i	0.201966	−	0.979393i	$-0.435267\pi$
$181$	138.167	−	27.4832i	0.763355	−	0.151841i	0.561389	+	0.827552i	$0.310267\pi$
$182$		0			0
$183$	−207.021	−	207.021i	−1.13126	−	1.13126i
$184$		0			0
$185$	−1.45992	−	3.52455i	−0.00789144	−	0.0190516i
$186$		0			0
$187$	−218.798	−	8.51579i	−1.17004	−	0.0455390i
$188$		0			0
$189$	−34.8228	+	14.4241i	−0.184248	+	0.0763179i
$190$		0			0
$191$	62.4391	−	62.4391i	0.326906	−	0.326906i	−0.524503	−	0.851409i	$-0.675749\pi$
$191$	62.4391	−	62.4391i	0.326906	−	0.326906i	0.851409	+	0.524503i	$0.175749\pi$
$192$		0			0
$193$	38.7693	+	194.906i	0.200877	+	1.00988i	0.941257	+	0.337690i	$0.109645\pi$
$193$	38.7693	+	194.906i	0.200877	+	1.00988i	−0.740380	+	0.672188i	$0.765355\pi$
$194$		0			0
$195$	−2.30164	+	5.55665i	−0.0118033	+	0.0284957i
$196$		0			0
$197$	−142.900	+	213.866i	−0.725383	+	1.08561i	0.267153	+	0.963654i	$0.413917\pi$
$197$	−142.900	+	213.866i	−0.725383	+	1.08561i	−0.992535	+	0.121958i	$0.961083\pi$
$198$		0			0
$199$	−56.4918	−	84.5460i	−0.283878	−	0.424854i	0.661937	−	0.749560i	$-0.269735\pi$
$199$	−56.4918	−	84.5460i	−0.283878	−	0.424854i	−0.945815	+	0.324706i	$0.894735\pi$
$200$		0			0
$201$	−446.499	−	88.8142i	−2.22139	−	0.441862i
$202$		0			0
$203$		−	19.6613i		−	0.0968539i
$204$		0			0
$205$	192.618			0.939598
$206$		0			0
$207$	191.996	−	965.229i	0.927517	−	4.66294i
$208$		0			0
$209$	−191.088	+	127.681i	−0.914298	+	0.610915i
$210$		0			0
$211$	236.037	+	157.715i	1.11866	+	0.747464i	0.970404	−	0.241486i	$-0.0776347\pi$
$211$	236.037	+	157.715i	1.11866	+	0.747464i	0.148254	+	0.988949i	$0.452635\pi$
$212$		0			0
$213$	102.054	+	42.2720i	0.479125	+	0.198460i
$214$		0			0
$215$	10.0741	−	2.00385i	0.0468560	−	0.00932025i
$216$		0			0
$217$	3.27090	+	3.27090i	0.0150733	+	0.0150733i
$218$		0			0
$219$	163.135	+	393.843i	0.744910	+	1.79837i
$220$		0			0
$221$	2.35131	+	3.83382i	0.0106394	+	0.0173476i
$222$		0			0
$223$	−233.919	+	96.8925i	−1.04896	+	0.434495i	−0.839522	−	0.543325i	$-0.817165\pi$
$223$	−233.919	+	96.8925i	−1.04896	+	0.434495i	−0.209443	+	0.977821i	$0.567165\pi$
$224$		0			0
$225$	147.619	−	147.619i	0.656085	−	0.656085i
$226$		0			0
$227$	−17.6092	−	88.5277i	−0.0775738	−	0.389990i	−0.999993	−	0.00379915i	$-0.998791\pi$
$227$	−17.6092	−	88.5277i	−0.0775738	−	0.389990i	0.922419	−	0.386191i	$-0.126209\pi$
$228$		0			0
$229$	−32.4673	+	78.3830i	−0.141779	+	0.342284i	−0.978779	−	0.204918i	$-0.934307\pi$
$229$	−32.4673	+	78.3830i	−0.141779	+	0.342284i	0.837000	+	0.547202i	$0.184307\pi$
$230$		0			0
$231$	18.9192	−	28.3146i	0.0819014	−	0.122574i
$232$		0			0
$233$	−15.9274	−	23.8370i	−0.0683579	−	0.102305i	0.795716	−	0.605670i	$-0.207095\pi$
$233$	−15.9274	−	23.8370i	−0.0683579	−	0.102305i	−0.864074	+	0.503365i	$0.832095\pi$
$234$		0			0
$235$	−299.863	−	59.6464i	−1.27601	−	0.253814i
$236$		0			0
$237$			224.161i			0.945826i
$238$		0			0
$239$	−8.04707			−0.0336698			−0.0168349	−	0.999858i	$-0.505359\pi$
$239$	−8.04707			−0.0336698			−0.0168349	+	0.999858i	$0.505359\pi$
$240$		0			0
$241$	−2.50009	+	12.5688i	−0.0103738	+	0.0521527i	−0.985625	−	0.168945i	$-0.945964\pi$
$241$	−2.50009	+	12.5688i	−0.0103738	+	0.0521527i	0.975252	+	0.221098i	$0.0709640\pi$
$242$		0			0
$243$	−577.261	+	385.714i	−2.37556	+	1.58730i
$244$		0			0
$245$	162.365	+	108.489i	0.662716	+	0.442813i
$246$		0			0
$247$	4.36110	+	1.80643i	0.0176563	+	0.00731346i
$248$		0			0
$249$	−472.277	+	93.9417i	−1.89669	+	0.377276i
$250$		0			0
$251$	−49.3901	−	49.3901i	−0.196773	−	0.196773i	0.601842	−	0.798615i	$-0.294434\pi$
$251$	−49.3901	−	49.3901i	−0.196773	−	0.196773i	−0.798615	+	0.601842i	$0.794434\pi$
$252$		0			0
$253$	208.583	+	503.563i	0.824437	+	1.99037i
$254$		0			0
$255$	60.6002	+	381.704i	0.237648	+	1.49688i
$256$		0			0
$257$	−100.045	+	41.4399i	−0.389279	+	0.161245i	−0.568734	−	0.822522i	$-0.692567\pi$
$257$	−100.045	+	41.4399i	−0.389279	+	0.161245i	0.179455	+	0.983766i	$0.442567\pi$
$258$		0			0
$259$	0.313713	−	0.313713i	0.00121125	−	0.00121125i
$260$		0			0
$261$	−191.626	−	963.368i	−0.734199	−	3.69107i
$262$		0			0
$263$	−3.40708	+	8.22541i	−0.0129547	+	0.0312753i	−0.930225	−	0.366991i	$-0.880388\pi$
$263$	−3.40708	+	8.22541i	−0.0129547	+	0.0312753i	0.917270	+	0.398266i	$0.130388\pi$
$264$		0			0
$265$	−204.822	+	306.538i	−0.772915	+	1.15675i
$266$		0			0
$267$	−126.778	−	189.736i	−0.474823	−	0.710622i
$268$		0			0
$269$	310.813	+	61.8245i	1.15544	+	0.229831i	0.735373	−	0.677663i	$-0.237007\pi$
$269$	310.813	+	61.8245i	1.15544	+	0.229831i	0.420066	+	0.907494i	$0.362007\pi$
$270$		0			0
$271$		−	343.293i		−	1.26676i	−0.773840	−	0.633382i	$-0.781666\pi$
$271$		−	343.293i		−	1.26676i	0.773840	−	0.633382i	$-0.218334\pi$
$272$		0			0
$273$	−0.699451			−0.00256209
$274$		0			0
$275$	−22.5567	+	113.400i	−0.0820243	+	0.412364i
$276$		0			0
$277$	240.848	−	160.930i	0.869488	−	0.580973i	−0.0388338	−	0.999246i	$-0.512364\pi$
$277$	240.848	−	160.930i	0.869488	−	0.580973i	0.908322	+	0.418272i	$0.137364\pi$
$278$		0			0
$279$	192.147	+	128.389i	0.688700	+	0.460175i
$280$		0			0
$281$	−367.980	−	152.422i	−1.30954	−	0.542428i	−0.384788	−	0.923005i	$-0.625726\pi$
$281$	−367.980	−	152.422i	−1.30954	−	0.542428i	−0.924749	+	0.380576i	$0.875726\pi$
$282$		0			0
$283$	−58.0886	+	11.5545i	−0.205260	+	0.0408288i	−0.296649	−	0.954986i	$-0.595869\pi$
$283$	−58.0886	+	11.5545i	−0.205260	+	0.0408288i	0.0913892	+	0.995815i	$0.470869\pi$
$284$		0			0
$285$	286.836	+	286.836i	1.00644	+	1.00644i
$286$		0			0
$287$	8.57225	+	20.6952i	0.0298685	+	0.0721089i
$288$		0			0
$289$	257.598	+	131.013i	0.891341	+	0.453333i
$290$		0			0
$291$	118.905	−	49.2522i	0.408609	−	0.169252i
$292$		0			0
$293$	−270.521	+	270.521i	−0.923279	+	0.923279i	−0.997260	−	0.0739808i	$-0.976430\pi$
$293$	−270.521	+	270.521i	−0.923279	+	0.923279i	0.0739808	+	0.997260i	$0.476430\pi$
$294$		0			0
$295$	−24.6707	−	124.028i	−0.0836294	−	0.420434i
$296$		0			0
$297$	399.094	−	963.498i	1.34375	−	3.24410i
$298$		0			0
$299$	6.21971	−	9.30846i	0.0208017	−	0.0311320i
$300$		0			0
$301$	0.663634	+	0.993198i	0.00220476	+	0.00329966i
$302$		0			0
$303$	−97.9810	−	19.4896i	−0.323369	−	0.0643222i
$304$		0			0
$305$		−	206.347i		−	0.676549i
$306$		0			0
$307$	43.7584			0.142535			0.0712677	−	0.997457i	$-0.477296\pi$
$307$	43.7584			0.142535			0.0712677	+	0.997457i	$0.477296\pi$
$308$		0			0
$309$	172.480	−	867.117i	0.558188	−	2.80620i
$310$		0			0
$311$	−297.387	+	198.707i	−0.956227	+	0.638930i	−0.932646	−	0.360792i	$-0.882507\pi$
$311$	−297.387	+	198.707i	−0.956227	+	0.638930i	−0.0235804	+	0.999722i	$0.507507\pi$
$312$		0			0
$313$	−238.487	−	159.352i	−0.761940	−	0.509112i	0.112852	−	0.993612i	$-0.464002\pi$
$313$	−238.487	−	159.352i	−0.761940	−	0.509112i	−0.874791	+	0.484500i	$0.839002\pi$
$314$		0			0
$315$	−40.0375	−	16.5841i	−0.127103	−	0.0526478i
$316$		0			0
$317$	−230.221	+	45.7938i	−0.726249	+	0.144460i	−0.544351	−	0.838858i	$-0.683224\pi$
$317$	−230.221	+	45.7938i	−0.726249	+	0.144460i	−0.181898	+	0.983317i	$0.558224\pi$
$318$		0			0
$319$	384.667	+	384.667i	1.20585	+	1.20585i
$320$		0			0
$321$	316.175	+	763.314i	0.984970	+	2.37793i
$322$		0			0
$323$	299.577	−	47.5616i	0.927484	−	0.147250i
$324$		0			0
$325$	2.19405	−	0.908807i	0.00675094	−	0.00279633i
$326$		0			0
$327$	132.684	−	132.684i	0.405761	−	0.405761i
$328$		0			0
$329$	−6.93655	−	34.8724i	−0.0210837	−	0.105995i
$330$		0			0
$331$	−169.711	+	409.718i	−0.512721	+	1.23782i	0.429573	+	0.903032i	$0.358664\pi$
$331$	−169.711	+	409.718i	−0.512721	+	1.23782i	−0.942294	+	0.334786i	$0.891336\pi$
$332$		0			0
$333$	12.3138	−	18.4289i	0.0369783	−	0.0553420i
$334$		0			0
$335$	−178.260	−	266.785i	−0.532120	−	0.796374i
$336$		0			0
$337$	360.531	+	71.7141i	1.06983	+	0.212801i	0.698434	−	0.715675i	$-0.253881\pi$
$337$	360.531	+	71.7141i	1.06983	+	0.212801i	0.371392	+	0.928476i	$0.378881\pi$
$338$		0			0
$339$			298.227i			0.879725i
$340$		0			0
$341$	−127.988			−0.375332
$342$		0			0
$343$	−8.88046	+	44.6451i	−0.0258906	+	0.130161i
$344$		0			0
$345$	799.918	−	534.488i	2.31860	−	1.54924i
$346$		0			0
$347$	−184.260	−	123.119i	−0.531009	−	0.354809i	0.260980	−	0.965344i	$-0.415954\pi$
$347$	−184.260	−	123.119i	−0.531009	−	0.354809i	−0.791989	+	0.610535i	$0.790954\pi$
$348$		0			0
$349$	277.517	+	114.951i	0.795178	+	0.329373i	0.743023	−	0.669266i	$-0.233391\pi$
$349$	277.517	+	114.951i	0.795178	+	0.329373i	0.0521546	+	0.998639i	$0.483391\pi$
$350$		0			0
$351$	−21.0088	+	4.17892i	−0.0598543	+	0.0119058i
$352$		0			0
$353$	−252.363	−	252.363i	−0.714910	−	0.714910i	0.252648	−	0.967558i	$-0.418699\pi$
$353$	−252.363	−	252.363i	−0.714910	−	0.714910i	−0.967558	+	0.252648i	$0.918699\pi$
$354$		0			0
$355$	29.7935	+	71.9279i	0.0839254	+	0.202614i
$356$		0			0
$357$	−38.3141	+	23.4984i	−0.107322	+	0.0658217i
$358$		0			0
$359$	131.509	−	54.4726i	0.366319	−	0.151734i	−0.191928	−	0.981409i	$-0.561474\pi$
$359$	131.509	−	54.4726i	0.366319	−	0.151734i	0.558247	+	0.829675i	$0.311474\pi$
$360$		0			0
$361$	−30.1446	+	30.1446i	−0.0835029	+	0.0835029i
$362$		0			0
$363$	49.7488	+	250.104i	0.137049	+	0.688992i
$364$		0			0
$365$	−114.978	+	277.583i	−0.315010	+	0.760500i
$366$		0			0
$367$	−6.13001	+	9.17422i	−0.0167030	+	0.0249979i	−0.839727	−	0.543009i	$-0.817285\pi$
$367$	−6.13001	+	9.17422i	−0.0167030	+	0.0249979i	0.823024	+	0.568006i	$0.192285\pi$
$368$		0			0
$369$	621.727	+	930.480i	1.68490	+	2.52163i
$370$		0			0
$371$	−42.0505	−	8.36437i	−0.113344	−	0.0225455i
$372$		0			0
$373$		−	8.19208i		−	0.0219627i	−0.999940	−	0.0109813i	$-0.996504\pi$
$373$		−	8.19208i		−	0.0219627i	0.999940	−	0.0109813i	$-0.00349554\pi$
$374$		0			0
$375$	772.439			2.05984
$376$		0			0
$377$	2.17986	−	10.9589i	0.00578213	−	0.0290687i
$378$		0			0
$379$	−180.532	+	120.628i	−0.476337	+	0.318278i	−0.770459	−	0.637490i	$-0.779973\pi$
$379$	−180.532	+	120.628i	−0.476337	+	0.318278i	0.294122	+	0.955768i	$0.404973\pi$
$380$		0			0
$381$	261.555	+	174.766i	0.686497	+	0.458703i
$382$		0			0
$383$	−393.790	−	163.113i	−1.02817	−	0.425883i	−0.196121	−	0.980580i	$-0.562834\pi$
$383$	−393.790	−	163.113i	−1.02817	−	0.425883i	−0.832053	+	0.554696i	$0.812834\pi$
$384$		0			0
$385$	23.5400	−	4.68240i	0.0611429	−	0.0121621i
$386$		0			0
$387$	42.1968	+	42.1968i	0.109036	+	0.109036i
$388$		0			0
$389$	−22.8494	−	55.1634i	−0.0587389	−	0.141808i	0.891785	−	0.452459i	$-0.149453\pi$
$389$	−22.8494	−	55.1634i	−0.0587389	−	0.141808i	−0.950524	+	0.310651i	$0.899453\pi$
$390$		0			0
$391$	27.9781	−	718.847i	0.0715553	−	1.83848i
$392$		0			0
$393$	−632.614	+	262.037i	−1.60970	+	0.666761i
$394$		0			0
$395$	−111.715	+	111.715i	−0.282824	+	0.282824i
$396$		0			0
$397$	125.235	+	629.599i	0.315454	+	1.58589i	0.734941	+	0.678131i	$0.237210\pi$
$397$	125.235	+	629.599i	0.315454	+	1.58589i	−0.419488	+	0.907761i	$0.637790\pi$
$398$		0			0
$399$	−18.0529	+	43.5836i	−0.0452454	+	0.109232i
$400$		0			0
$401$	−33.4210	+	50.0181i	−0.0833441	+	0.124733i	−0.870799	−	0.491638i	$-0.836398\pi$
$401$	−33.4210	+	50.0181i	−0.0833441	+	0.124733i	0.787455	+	0.616372i	$0.211398\pi$
$402$		0			0
$403$	1.46050	+	2.18579i	0.00362407	+	0.00542380i
$404$		0			0
$405$	−983.651	−	195.660i	−2.42877	−	0.483112i
$406$		0			0
$407$			12.2754i			0.0301606i
$408$		0			0
$409$	237.804			0.581427			0.290714	−	0.956810i	$-0.406107\pi$
$409$	237.804			0.581427			0.290714	+	0.956810i	$0.406107\pi$
$410$		0			0
$411$	−118.516	+	595.823i	−0.288361	+	1.44969i
$412$		0			0
$413$	12.2279	−	8.17041i	0.0296074	−	0.0197831i
$414$		0			0
$415$	−282.188	−	188.552i	−0.679970	−	0.454342i
$416$		0			0
$417$	370.586	+	153.502i	0.888695	+	0.368110i
$418$		0			0
$419$	694.311	−	138.107i	1.65707	−	0.329611i	0.724133	−	0.689660i	$-0.242240\pi$
$419$	694.311	−	138.107i	1.65707	−	0.329611i	0.932933	+	0.360049i	$0.117240\pi$
$420$		0			0
$421$	−240.976	−	240.976i	−0.572390	−	0.572390i	0.360406	−	0.932796i	$-0.382638\pi$
$421$	−240.976	−	240.976i	−0.572390	−	0.572390i	−0.932796	+	0.360406i	$0.882638\pi$
$422$		0			0
$423$	−679.755	−	1641.07i	−1.60699	−	3.87961i
$424$		0			0
$425$	89.6529	−	123.492i	0.210948	−	0.290570i
$426$		0			0
$427$	22.1704	−	9.18328i	0.0519213	−	0.0215065i
$428$		0			0
$429$	13.6845	−	13.6845i	0.0318986	−	0.0318986i
$430$		0			0
$431$	−4.23372	−	21.2844i	−0.00982302	−	0.0493837i	0.975563	−	0.219720i	$-0.0705145\pi$
$431$	−4.23372	−	21.2844i	−0.00982302	−	0.0493837i	−0.985386	+	0.170337i	$0.945514\pi$
$432$		0			0
$433$	297.878	−	719.141i	0.687940	−	1.66083i	−0.0609509	−	0.998141i	$-0.519413\pi$
$433$	297.878	−	719.141i	0.687940	−	1.66083i	0.748891	−	0.662693i	$-0.230587\pi$
$434$		0			0
$435$	533.458	−	798.376i	1.22634	−	1.83535i
$436$		0			0
$437$	−419.489	−	627.810i	−0.959930	−	1.43664i
$438$		0			0
$439$	514.760	+	102.392i	1.17257	+	0.233239i	0.742684	−	0.669642i	$-0.233553\pi$
$439$	514.760	+	102.392i	1.17257	+	0.233239i	0.429889	+	0.902882i	$0.358553\pi$
$440$		0			0
$441$			1134.52i			2.57260i
$442$		0			0
$443$	−187.416			−0.423060			−0.211530	−	0.977371i	$-0.567845\pi$
$443$	−187.416			−0.423060			−0.211530	+	0.977371i	$0.567845\pi$
$444$		0			0
$445$	31.3768	−	157.742i	0.0705096	−	0.354476i
$446$		0			0
$447$	−833.166	+	556.704i	−1.86391	+	1.24542i
$448$		0			0
$449$	−528.041	−	352.826i	−1.17604	−	0.785803i	−0.195225	−	0.980758i	$-0.562544\pi$
$449$	−528.041	−	352.826i	−1.17604	−	0.785803i	−0.980812	+	0.194955i	$0.937544\pi$
$450$		0			0
$451$	−572.609	−	237.182i	−1.26964	−	0.525903i
$452$		0			0
$453$	128.773	−	25.6145i	0.284267	−	0.0565442i
$454$		0			0
$455$	−0.348587	−	0.348587i	−0.000766125	−	0.000766125i
$456$		0			0
$457$	−195.052	−	470.896i	−0.426809	−	1.03041i	−0.980293	−	0.197548i	$-0.936702\pi$
$457$	−195.052	−	470.896i	−0.426809	−	1.03041i	0.553484	−	0.832860i	$-0.313298\pi$
$458$		0			0
$459$	−1010.42	+	934.712i	−2.20135	+	2.03641i
$460$		0			0
$461$	436.174	−	180.669i	0.946147	−	0.391907i	0.144366	−	0.989524i	$-0.453886\pi$
$461$	436.174	−	180.669i	0.946147	−	0.391907i	0.801781	+	0.597617i	$0.203886\pi$
$462$		0			0
$463$	48.8992	−	48.8992i	0.105614	−	0.105614i	−0.652325	−	0.757939i	$-0.726206\pi$
$463$	48.8992	−	48.8992i	0.105614	−	0.105614i	0.757939	+	0.652325i	$0.226206\pi$
$464$		0			0
$465$	44.0724	+	221.567i	0.0947793	+	0.476488i
$466$		0			0
$467$	−71.2774	+	172.079i	−0.152628	+	0.368477i	−0.981637	−	0.190758i	$-0.938905\pi$
$467$	−71.2774	+	172.079i	−0.152628	+	0.368477i	0.829009	+	0.559236i	$0.188905\pi$
$468$		0			0
$469$	20.7307	−	31.0257i	0.0442019	−	0.0661528i
$470$		0			0
$471$	374.171	+	559.987i	0.794419	+	1.18893i
$472$		0			0
$473$	−32.4153	−	6.44781i	−0.0685314	−	0.0136317i
$474$		0			0
$475$		−	160.171i		−	0.337201i
$476$		0			0
$477$	−2141.92			−4.49039
$478$		0			0
$479$	−137.358	+	690.547i	−0.286761	+	1.44164i	0.521718	+	0.853118i	$0.325291\pi$
$479$	−137.358	+	690.547i	−0.286761	+	1.44164i	−0.808479	+	0.588525i	$0.799709\pi$
$480$		0			0
$481$	0.209640	−	0.140077i	0.000435842	−	0.000291220i
$482$		0			0
$483$	93.0261	+	62.1581i	0.192601	+	0.128692i
$484$		0			0
$485$	83.8050	+	34.7132i	0.172794	+	0.0715736i
$486$		0			0
$487$	885.297	−	176.096i	1.81786	−	0.361594i	0.835631	−	0.549291i	$-0.185102\pi$
$487$	885.297	−	176.096i	1.81786	−	0.361594i	0.982227	+	0.187697i	$0.0601022\pi$
$488$		0			0
$489$	−107.092	−	107.092i	−0.219002	−	0.219002i
$490$		0			0
$491$	−201.726	−	487.009i	−0.410847	−	0.991872i	−0.984911	−	0.173062i	$-0.944634\pi$
$491$	−201.726	−	487.009i	−0.410847	−	0.991872i	0.574064	−	0.818810i	$-0.305366\pi$
$492$		0			0
$493$	−248.762	−	673.534i	−0.504588	−	1.36619i
$494$		0			0
$495$	1107.78	−	458.858i	2.23794	−	0.926985i
$496$		0			0
$497$	−6.40216	+	6.40216i	−0.0128816	+	0.0128816i
$498$		0			0
$499$	79.3835	+	399.088i	0.159085	+	0.799775i	0.975104	+	0.221750i	$0.0711767\pi$
$499$	79.3835	+	399.088i	0.159085	+	0.799775i	−0.816018	+	0.578026i	$0.803823\pi$
$500$		0			0
$501$	−645.693	+	1558.84i	−1.28881	+	3.11146i
$502$		0			0
$503$	−258.730	+	387.217i	−0.514374	+	0.769816i	−0.994200	−	0.107548i	$-0.965700\pi$
$503$	−258.730	+	387.217i	−0.514374	+	0.769816i	0.479825	+	0.877364i	$0.340700\pi$
$504$		0			0
$505$	−39.1179	−	58.5441i	−0.0774612	−	0.115929i
$506$		0			0
$507$	940.996	+	187.176i	1.85601	+	0.369183i
$508$		0			0
$509$		−	649.904i		−	1.27682i	−0.769695	−	0.638412i	$-0.779591\pi$
$509$		−	649.904i		−	1.27682i	0.769695	−	0.638412i	$-0.220409\pi$
$510$		0			0
$511$	−34.9411			−0.0683778
$512$		0			0
$513$	−281.848	+	1416.94i	−0.549411	+	2.76207i
$514$		0			0
$515$	518.106	−	346.187i	1.00603	−	0.672209i
$516$		0			0
$517$	817.977	+	546.555i	1.58216	+	1.05717i
$518$		0			0
$519$	376.598	+	155.992i	0.725623	+	0.300563i
$520$		0			0
$521$	50.4526	−	10.0356i	0.0968380	−	0.0192623i	−0.146433	−	0.989221i	$-0.546779\pi$
$521$	50.4526	−	10.0356i	0.0968380	−	0.0192623i	0.243271	+	0.969958i	$0.421779\pi$
$522$		0			0
$523$	351.105	+	351.105i	0.671330	+	0.671330i	0.958023	−	0.286693i	$-0.0925559\pi$
$523$	351.105	+	351.105i	0.671330	+	0.671330i	−0.286693	+	0.958023i	$0.592556\pi$
$524$		0			0
$525$	9.08237	+	21.9268i	0.0172997	+	0.0417653i
$526$		0			0
$527$	153.435	+	70.6659i	0.291148	+	0.134091i
$528$		0			0
$529$	−1165.70	+	482.847i	−2.20358	+	0.912755i
$530$		0			0
$531$	519.511	−	519.511i	0.978364	−	0.978364i
$532$		0			0
$533$	2.48354	+	12.4856i	0.00465955	+	0.0234251i
$534$		0			0
$535$	−222.842	+	537.988i	−0.416527	+	1.00558i
$536$		0			0
$537$	877.098	−	1312.67i	1.63333	−	2.44445i
$538$		0			0
$539$	−349.086	−	522.444i	−0.647655	−	0.969284i
$540$		0			0
$541$	−667.861	−	132.846i	−1.23449	−	0.245556i	−0.465636	−	0.884976i	$-0.654174\pi$
$541$	−667.861	−	132.846i	−1.23449	−	0.245556i	−0.768857	+	0.639421i	$0.779174\pi$
$542$		0			0
$543$			800.089i			1.47346i
$544$		0			0
$545$	132.252			0.242664
$546$		0			0
$547$	−0.923290	+	4.64169i	−0.00168792	+	0.00848572i	−0.981620	−	0.190846i	$-0.938877\pi$
$547$	−0.923290	+	4.64169i	−0.00168792	+	0.00848572i	0.979932	+	0.199331i	$0.0638770\pi$
$548$		0			0
$549$	996.804	−	666.043i	1.81567	−	1.21319i
$550$		0			0
$551$	−626.600	−	418.680i	−1.13720	−	0.759856i
$552$		0			0
$553$	−16.9747	−	7.03116i	−0.0306957	−	0.0127146i
$554$		0			0
$555$	21.2505	−	4.22699i	0.0382892	−	0.00761620i
$556$		0			0
$557$	388.120	+	388.120i	0.696805	+	0.696805i	0.963720	−	0.266915i	$-0.0860043\pi$
$557$	388.120	+	388.120i	0.696805	+	0.696805i	−0.266915	+	0.963720i	$0.586004\pi$
$558$		0			0
$559$	0.259782	+	0.627169i	0.000464726	+	0.00112195i
$560$		0			0
$561$	289.865	−	1209.34i	0.516694	−	2.15569i
$562$		0			0
$563$	−142.529	+	59.0376i	−0.253161	+	0.104863i	−0.505655	−	0.862736i	$-0.668749\pi$
$563$	−142.529	+	59.0376i	−0.253161	+	0.104863i	0.252494	+	0.967598i	$0.418749\pi$
$564$		0			0
$565$	−148.628	+	148.628i	−0.263058	+	0.263058i
$566$		0			0
$567$	−22.7542	−	114.393i	−0.0401309	−	0.201752i
$568$		0			0
$569$	−163.137	+	393.847i	−0.286708	+	0.692174i	−0.999962	−	0.00873155i	$-0.997221\pi$
$569$	−163.137	+	393.847i	−0.286708	+	0.692174i	0.713254	+	0.700906i	$0.247221\pi$
$570$		0			0
$571$	−228.356	+	341.759i	−0.399923	+	0.598527i	−0.975708	−	0.219074i	$-0.929696\pi$
$571$	−228.356	+	341.759i	−0.399923	+	0.598527i	0.575785	+	0.817601i	$0.304696\pi$
$572$		0			0
$573$	278.623	+	416.989i	0.486254	+	0.727730i
$574$		0			0
$575$	−372.570	−	74.1087i	−0.647947	−	0.128885i
$576$		0			0
$577$		−	777.118i		−	1.34682i	−0.739267	−	0.673412i	$-0.764828\pi$
$577$		−	777.118i		−	1.34682i	0.739267	−	0.673412i	$-0.235172\pi$
$578$		0			0
$579$	−1128.65			−1.94931
$580$		0			0
$581$	7.69993	−	38.7101i	0.0132529	−	0.0666267i
$582$		0			0
$583$	986.350	−	659.058i	1.69185	−	1.13046i
$584$		0			0
$585$	−20.4775	−	13.6826i	−0.0350043	−	0.0233891i
$586$		0			0
$587$	−41.5718	−	17.2196i	−0.0708208	−	0.0293349i	0.346992	−	0.937868i	$-0.387203\pi$
$587$	−41.5718	−	17.2196i	−0.0708208	−	0.0293349i	−0.417813	+	0.908533i	$0.637203\pi$
$588$		0			0
$589$	173.895	−	34.5899i	0.295238	−	0.0587264i
$590$		0			0
$591$	−1032.97	−	1032.97i	−1.74783	−	1.74783i
$592$		0			0
$593$	290.327	+	700.911i	0.489590	+	1.18197i	0.954927	+	0.296841i	$0.0959332\pi$
$593$	290.327	+	700.911i	0.489590	+	1.18197i	−0.465337	+	0.885134i	$0.654067\pi$
$594$		0			0
$595$	−30.8056	−	7.38376i	−0.0517741	−	0.0124097i
$596$		0			0
$597$	533.542	−	221.001i	0.893706	−	0.370185i
$598$		0			0
$599$	303.636	−	303.636i	0.506905	−	0.506905i	−0.406670	−	0.913575i	$-0.633310\pi$
$599$	303.636	−	303.636i	0.506905	−	0.506905i	0.913575	+	0.406670i	$0.133310\pi$
$600$		0			0
$601$	−108.360	−	544.764i	−0.180300	−	0.906430i	−0.959941	−	0.280203i	$-0.909598\pi$
$601$	−108.360	−	544.764i	−0.180300	−	0.906430i	0.779641	−	0.626227i	$-0.215402\pi$
$602$		0			0
$603$	713.378	−	1722.25i	1.18305	−	2.85613i
$604$		0			0
$605$	−99.8514	+	149.438i	−0.165044	+	0.247005i
$606$		0			0
$607$	377.738	+	565.324i	0.622302	+	0.931341i	0.999985	+	0.00540638i	$0.00172091\pi$
$607$	377.738	+	565.324i	0.622302	+	0.931341i	−0.377683	+	0.925935i	$0.623279\pi$
$608$		0			0
$609$	109.520	+	21.7849i	0.179836	+	0.0357716i
$610$		0			0
$611$		−	20.2063i		−	0.0330709i
$612$		0			0
$613$	152.767			0.249213			0.124606	−	0.992206i	$-0.460233\pi$
$613$	152.767			0.249213			0.124606	+	0.992206i	$0.460233\pi$
$614$		0			0
$615$	−213.422	+	1072.94i	−0.347027	+	1.74462i
$616$		0			0
$617$	688.306	−	459.911i	1.11557	−	0.745399i	0.145773	−	0.989318i	$-0.453433\pi$
$617$	688.306	−	459.911i	1.11557	−	0.745399i	0.969796	+	0.243919i	$0.0784331\pi$
$618$		0			0
$619$	161.995	+	108.242i	0.261704	+	0.174865i	0.679499	−	0.733676i	$-0.262197\pi$
$619$	161.995	+	108.242i	0.261704	+	0.174865i	−0.417795	+	0.908541i	$0.637197\pi$
$620$		0			0
$621$	3165.52	+	1311.20i	5.09746	+	2.11144i
$622$		0			0
$623$	18.3445	−	3.64895i	0.0294454	−	0.00585706i
$624$		0			0
$625$	226.275	+	226.275i	0.362040	+	0.362040i
$626$		0			0
$627$	−499.499	−	1205.90i	−0.796649	−	1.92328i
$628$		0			0
$629$	6.77759	−	14.7160i	0.0107752	−	0.0233958i
$630$		0			0
$631$	767.835	−	318.048i	1.21685	−	0.504038i	0.320446	−	0.947267i	$-0.396167\pi$
$631$	767.835	−	318.048i	1.21685	−	0.504038i	0.896408	+	0.443229i	$0.146167\pi$
$632$		0			0
$633$	−1140.05	+	1140.05i	−1.80103	+	1.80103i
$634$		0			0
$635$	43.2536	+	217.450i	0.0681158	+	0.342441i
$636$		0			0
$637$	−4.93885	+	11.9234i	−0.00775329	+	0.0187181i
$638$		0			0
$639$	−251.296	+	376.091i	−0.393264	+	0.588562i
$640$		0			0
$641$	−108.926	−	163.020i	−0.169932	−	0.254321i	0.736722	−	0.676195i	$-0.236372\pi$
$641$	−108.926	−	163.020i	−0.169932	−	0.254321i	−0.906654	+	0.421874i	$0.861372\pi$
$642$		0			0
$643$	696.108	+	138.465i	1.08259	+	0.215341i	0.703985	−	0.710215i	$-0.251402\pi$
$643$	696.108	+	138.465i	1.08259	+	0.215341i	0.378610	+	0.925556i	$0.376402\pi$
$644$		0			0
$645$			58.3361i			0.0904435i
$646$		0			0
$647$	−736.678			−1.13861			−0.569303	−	0.822128i	$-0.692787\pi$
$647$	−736.678			−1.13861			−0.569303	+	0.822128i	$0.692787\pi$
$648$		0			0
$649$	−79.3830	+	399.085i	−0.122316	+	0.614924i
$650$		0			0
$651$	−21.8442	+	14.5958i	−0.0335548	+	0.0224206i
$652$		0			0
$653$	−310.775	−	207.653i	−0.475919	−	0.317999i	0.294373	−	0.955691i	$-0.404889\pi$
$653$	−310.775	−	207.653i	−0.475919	−	0.317999i	−0.770292	+	0.637692i	$0.779889\pi$
$654$		0			0
$655$	−445.869	−	184.685i	−0.680716	−	0.281962i
$656$		0			0
$657$	−1712.05	+	340.547i	−2.60585	+	0.518336i
$658$		0			0
$659$	671.539	+	671.539i	1.01903	+	1.01903i	0.999815	+	0.0192126i	$0.00611593\pi$
$659$	671.539	+	671.539i	1.01903	+	1.01903i	0.0192126	+	0.999815i	$0.493884\pi$
$660$		0			0
$661$	51.0330	+	123.204i	0.0772057	+	0.186391i	0.957770	−	0.287536i	$-0.0928361\pi$
$661$	51.0330	+	123.204i	0.0772057	+	0.186391i	−0.880564	+	0.473927i	$0.842836\pi$
$662$		0			0
$663$	−23.9609	+	8.84968i	−0.0361401	+	0.0133479i
$664$		0			0
$665$	−30.7179	+	12.7238i	−0.0461924	+	0.0191335i
$666$		0			0
$667$	−1263.80	+	1263.80i	−1.89476	+	1.89476i
$668$		0			0
$669$	−280.539	−	1410.37i	−0.419341	−	2.10817i
$670$		0			0
$671$	−254.089	+	613.424i	−0.378671	+	0.914194i
$672$		0			0
$673$	−498.917	+	746.682i	−0.741332	+	1.10948i	0.248691	+	0.968583i	$0.419999\pi$
$673$	−498.917	+	746.682i	−0.741332	+	1.10948i	−0.990024	+	0.140900i	$0.955001\pi$
$674$		0			0
$675$	403.803	+	604.334i	0.598227	+	0.895309i
$676$		0			0
$677$	1139.31	+	226.622i	1.68288	+	0.334745i	0.941671	−	0.336535i	$-0.109255\pi$
$677$	1139.31	+	226.622i	1.68288	+	0.334745i	0.741204	+	0.671279i	$0.234255\pi$
$678$		0			0
$679$			10.5491i			0.0155362i
$680$		0			0
$681$	512.640			0.752775
$682$		0			0
$683$	−91.2983	+	458.987i	−0.133672	+	0.672017i	0.854596	+	0.519293i	$0.173805\pi$
$683$	−91.2983	+	458.987i	−0.133672	+	0.672017i	−0.988269	+	0.152724i	$0.951195\pi$
$684$		0			0
$685$	−356.007	+	237.876i	−0.519718	+	0.347264i
$686$		0			0
$687$	−400.645	−	267.703i	−0.583181	−	0.389669i
$688$		0			0
$689$	−22.5109	−	9.32432i	−0.0326718	−	0.0135331i
$690$		0			0
$691$	−36.6651	+	7.29314i	−0.0530609	+	0.0105545i	−0.221549	−	0.975149i	$-0.571111\pi$
$691$	−36.6651	+	7.29314i	−0.0530609	+	0.0105545i	0.168488	+	0.985704i	$0.446111\pi$
$692$		0			0
$693$	98.6013	+	98.6013i	0.142282	+	0.142282i
$694$		0			0
$695$	108.189	+	261.191i	0.155667	+	0.375814i
$696$		0			0
$697$	555.501	+	600.493i	0.796988	+	0.861539i
$698$		0			0
$699$	150.428	−	62.3093i	0.215204	−	0.0891406i
$700$		0			0
$701$	795.213	−	795.213i	1.13440	−	1.13440i	0.144961	−	0.989437i	$-0.453694\pi$
$701$	795.213	−	795.213i	1.13440	−	1.13440i	0.989437	−	0.144961i	$-0.0463058\pi$
$702$		0			0
$703$	−3.31752	−	16.6783i	−0.00471909	−	0.0237245i
$704$		0			0
$705$	664.500	−	1604.25i	0.942554	−	2.27553i
$706$		0			0
$707$	4.54920	−	6.80835i	0.00643451	−	0.00962992i
$708$		0			0
$709$	−675.741	−	1011.32i	−0.953090	−	1.42640i	−0.903965	−	0.427607i	$-0.859357\pi$
$709$	−675.741	−	1011.32i	−0.953090	−	1.42640i	−0.0491248	−	0.998793i	$-0.515643\pi$
$710$		0			0
$711$	−900.257	−	179.072i	−1.26618	−	0.251860i
$712$		0			0
$713$		−	420.498i		−	0.589759i
$714$		0			0
$715$	13.6400			0.0190769
$716$		0			0
$717$	8.91622	−	44.8249i	0.0124355	−	0.0625172i
$718$		0			0
$719$	−177.768	+	118.781i	−0.247244	+	0.165203i	−0.673017	−	0.739627i	$-0.735002\pi$
$719$	−177.768	+	118.781i	−0.247244	+	0.165203i	0.425774	+	0.904830i	$0.360002\pi$
$720$		0			0
$721$	60.2529	+	40.2597i	0.0835685	+	0.0558387i
$722$		0			0
$723$	−67.2423	−	27.8527i	−0.0930045	−	0.0385237i
$724$		0			0
$725$	−371.851	+	73.9658i	−0.512898	+	0.102022i
$726$		0			0
$727$	12.6160	+	12.6160i	0.0173535	+	0.0173535i	0.715730	−	0.698377i	$-0.246094\pi$
$727$	12.6160	+	12.6160i	0.0173535	+	0.0173535i	−0.698377	+	0.715730i	$0.746094\pi$
$728$		0			0
$729$	−646.017	−	1559.62i	−0.886169	−	2.13940i
$730$		0			0
$731$	35.3002	+	25.6272i	0.0482903	+	0.0350578i
$732$		0			0
$733$	−475.664	+	197.026i	−0.648927	+	0.268795i	−0.682771	−	0.730633i	$-0.739225\pi$
$733$	−475.664	+	197.026i	−0.648927	+	0.268795i	0.0338434	+	0.999427i	$0.489225\pi$
$734$		0			0
$735$	−784.222	+	784.222i	−1.06697	+	1.06697i
$736$		0			0
$737$	201.418	+	1012.59i	0.273294	+	1.37394i
$738$		0			0
$739$	77.4678	−	187.024i	0.104828	−	0.253077i	−0.862759	−	0.505615i	$-0.831265\pi$
$739$	77.4678	−	187.024i	0.104828	−	0.253077i	0.967587	+	0.252539i	$0.0812655\pi$
$740$		0			0
$741$	−14.8945	+	22.2912i	−0.0201006	+	0.0300826i
$742$		0			0
$743$	723.361	+	1082.59i	0.973568	+	1.45705i	0.887527	+	0.460757i	$0.152422\pi$
$743$	723.361	+	1082.59i	0.973568	+	1.45705i	0.0860419	+	0.996292i	$0.472578\pi$
$744$		0			0
$745$	−692.672	−	137.781i	−0.929761	−	0.184941i
$746$		0			0
$747$		−	1971.77i		−	2.63958i
$748$		0			0
$749$	−67.7199			−0.0904137
$750$		0			0
$751$	−49.5624	+	249.167i	−0.0659952	+	0.331780i	−0.999652	−	0.0263892i	$-0.991599\pi$
$751$	−49.5624	+	249.167i	−0.0659952	+	0.331780i	0.933657	+	0.358170i	$0.116599\pi$
$752$		0			0
$753$	329.844	−	220.395i	0.438040	−	0.292689i
$754$		0			0
$755$	76.9424	+	51.4113i	0.101911	+	0.0680944i
$756$		0			0
$757$	−820.591	−	339.900i	−1.08400	−	0.449009i	−0.232092	−	0.972694i	$-0.574557\pi$
$757$	−820.591	−	339.900i	−1.08400	−	0.449009i	−0.851912	+	0.523685i	$0.824557\pi$
$758$		0			0
$759$	−3036.13	+	603.923i	−4.00016	+	0.795682i
$760$		0			0
$761$	−867.622	−	867.622i	−1.14011	−	1.14011i	−0.988430	−	0.151678i	$-0.951532\pi$
$761$	−867.622	−	867.622i	−1.14011	−	1.14011i	−0.151678	−	0.988430i	$-0.548468\pi$
$762$		0			0
$763$	5.88573	+	14.2094i	0.00771394	+	0.0186231i
$764$		0			0
$765$	−1581.38	−	61.5487i	−2.06716	−	0.0804558i
$766$		0			0
$767$	7.72147	−	3.19834i	0.0100671	−	0.00416993i
$768$		0			0
$769$	258.697	−	258.697i	0.336408	−	0.336408i	−0.518606	−	0.855013i	$-0.673549\pi$
$769$	258.697	−	258.697i	0.336408	−	0.336408i	0.855013	+	0.518606i	$0.173549\pi$
$770$		0			0
$771$	−119.984	−	603.198i	−0.155621	−	0.782358i
$772$		0			0
$773$	−257.100	+	620.694i	−0.332600	+	0.802968i	0.665784	+	0.746145i	$0.268097\pi$
$773$	−257.100	+	620.694i	−0.332600	+	0.802968i	−0.998384	+	0.0568235i	$0.981903\pi$
$774$		0			0
$775$	49.5568	−	74.1671i	0.0639443	−	0.0956994i
$776$		0			0
$777$	1.39989	+	2.09508i	0.00180166	+	0.00269637i
$778$		0			0
$779$	842.092	+	167.503i	1.08099	+	0.215023i
$780$		0			0
$781$		−	250.512i		−	0.320758i
$782$		0			0
$783$	3419.73			4.36747
$784$		0			0
$785$	−92.6053	+	465.558i	−0.117969	+	0.593068i
$786$		0			0
$787$	305.367	−	204.040i	0.388014	−	0.259263i	−0.346228	−	0.938150i	$-0.612538\pi$
$787$	305.367	−	204.040i	0.388014	−	0.259263i	0.734242	+	0.678888i	$0.237538\pi$
$788$		0			0
$789$	−42.0432	−	28.0924i	−0.0532867	−	0.0356050i
$790$		0			0
$791$	−22.5834	−	9.35436i	−0.0285505	−	0.0118260i
$792$		0			0
$793$	13.3756	−	2.66057i	0.0168670	−	0.00335506i
$794$		0			0
$795$	−1480.58	−	1480.58i	−1.86236	−	1.86236i
$796$		0			0
$797$	499.645	+	1206.25i	0.626907	+	1.51349i	0.843447	+	0.537213i	$0.180523\pi$
$797$	499.645	+	1206.25i	0.626907	+	1.51349i	−0.216540	+	0.976274i	$0.569477\pi$
$798$		0			0
$799$	−678.841	−	1106.85i	−0.849613	−	1.38530i
$800$		0			0
$801$	863.281	−	357.583i	1.07775	−	0.446420i
$802$		0			0
$803$	683.610	−	683.610i	0.851320	−	0.851320i
$804$		0			0
$805$	15.3838	+	77.3395i	0.0191103	+	0.0960739i
$806$		0			0
$807$	−688.766	+	1662.83i	−0.853490	+	2.06051i
$808$		0			0
$809$	171.763	−	257.062i	0.212316	−	0.317753i	−0.709992	−	0.704210i	$-0.751301\pi$
$809$	171.763	−	257.062i	0.212316	−	0.317753i	0.922307	+	0.386457i	$0.126301\pi$
$810$		0			0
$811$	−391.778	−	586.337i	−0.483080	−	0.722980i	0.507237	−	0.861807i	$-0.330667\pi$
$811$	−391.778	−	586.337i	−0.483080	−	0.722980i	−0.990317	+	0.138827i	$0.955667\pi$
$812$		0			0
$813$	1912.25	+	380.371i	2.35210	+	0.467861i
$814$		0			0
$815$		−	106.744i		−	0.130974i
$816$		0			0
$817$	45.7846			0.0560399
$818$		0			0
$819$	0.558761	−	2.80908i	0.000682248	−	0.00342989i
$820$		0			0
$821$	−205.687	+	137.436i	−0.250532	+	0.167400i	−0.674495	−	0.738279i	$-0.735639\pi$
$821$	−205.687	+	137.436i	−0.250532	+	0.167400i	0.423963	+	0.905680i	$0.360639\pi$
$822$		0			0
$823$	434.418	+	290.269i	0.527847	+	0.352696i	0.790763	−	0.612122i	$-0.209684\pi$
$823$	434.418	+	290.269i	0.527847	+	0.352696i	−0.262916	+	0.964819i	$0.584684\pi$
$824$		0			0
$825$	−606.683	−	251.296i	−0.735373	−	0.304602i
$826$		0			0
$827$	612.367	−	121.807i	0.740467	−	0.147288i	0.189577	−	0.981866i	$-0.439288\pi$
$827$	612.367	−	121.807i	0.740467	−	0.147288i	0.550890	+	0.834578i	$0.314288\pi$
$828$		0			0
$829$	−234.759	−	234.759i	−0.283184	−	0.283184i	0.551194	−	0.834377i	$-0.314173\pi$
$829$	−234.759	−	234.759i	−0.283184	−	0.283184i	−0.834377	+	0.551194i	$0.814173\pi$
$830$		0			0
$831$	629.570	+	1519.92i	0.757605	+	1.82902i
$832$		0			0
$833$	130.036	+	819.058i	0.156105	+	0.983263i
$834$		0			0
$835$	−1098.68	+	455.087i	−1.31578	+	0.545015i
$836$		0			0
$837$	−568.913	+	568.913i	−0.679705	+	0.679705i
$838$		0			0
$839$	219.244	+	1102.21i	0.261316	+	1.31372i	0.858993	+	0.511987i	$0.171090\pi$
$839$	219.244	+	1102.21i	0.261316	+	1.31372i	−0.597678	+	0.801737i	$0.703910\pi$
$840$		0			0
$841$	−360.810	+	871.072i	−0.429025	+	1.03576i
$842$		0			0
$843$	1256.77	−	1880.89i	1.49083	−	2.23118i
$844$		0			0
$845$	375.683	+	562.249i	0.444595	+	0.665384i
$846$		0			0
$847$	−20.4997	−	4.07765i	−0.0242028	−	0.00481423i
$848$		0			0
$849$		−	336.375i		−	0.396202i
$850$		0			0
$851$	−40.3300			−0.0473914
$852$		0			0
$853$	177.766	−	893.691i	0.208401	−	1.04770i	−0.724967	−	0.688783i	$-0.758145\pi$
$853$	177.766	−	893.691i	0.208401	−	1.04770i	0.933368	−	0.358920i	$-0.116855\pi$
$854$		0			0
$855$	−1381.11	+	922.828i	−1.61533	+	1.07933i
$856$		0			0
$857$	1378.05	+	920.786i	1.60800	+	1.07443i	0.945628	+	0.325251i	$0.105449\pi$
$857$	1378.05	+	920.786i	1.60800	+	1.07443i	0.662369	+	0.749178i	$0.269551\pi$
$858$		0			0
$859$	−70.5725	−	29.2321i	−0.0821566	−	0.0340304i	0.341227	−	0.939981i	$-0.389158\pi$
$859$	−70.5725	−	29.2321i	−0.0821566	−	0.0340304i	−0.423383	+	0.905951i	$0.639158\pi$
$860$		0			0
$861$	−124.778	+	24.8198i	−0.144922	+	0.0288267i
$862$		0			0
$863$	−765.362	−	765.362i	−0.886862	−	0.886862i	0.107359	−	0.994220i	$-0.465761\pi$
$863$	−765.362	−	765.362i	−0.886862	−	0.886862i	−0.994220	+	0.107359i	$0.965761\pi$
$864$		0			0
$865$	109.944	+	265.428i	0.127103	+	0.306853i
$866$		0			0
$867$	−1015.21	+	1289.74i	−1.17094	+	1.48759i
$868$		0			0
$869$	469.667	−	194.542i	0.540468	−	0.223869i
$870$		0			0
$871$	14.9948	−	14.9948i	0.0172156	−	0.0172156i
$872$		0			0
$873$	102.815	+	516.884i	0.117772	+	0.592078i
$874$		0			0
$875$	−24.2288	+	58.4935i	−0.0276901	+	0.0668497i
$876$		0			0
$877$	−843.775	+	1262.80i	−0.962116	+	1.43991i	−0.0651154	+	0.997878i	$0.520742\pi$
$877$	−843.775	+	1262.80i	−0.962116	+	1.43991i	−0.897000	+	0.442030i	$0.854258\pi$
$878$		0			0
$879$	−1207.15	−	1806.63i	−1.37332	−	2.05532i
$880$		0			0
$881$	1453.42	+	289.103i	1.64974	+	0.328153i	0.930411	−	0.366518i	$-0.119450\pi$
$881$	1453.42	+	289.103i	1.64974	+	0.328153i	0.719328	+	0.694671i	$0.244450\pi$
$882$		0			0
$883$		−	826.926i		−	0.936497i	−0.883597	−	0.468248i	$-0.844885\pi$
$883$		−	826.926i		−	0.936497i	0.883597	−	0.468248i	$-0.155115\pi$
$884$		0			0
$885$	718.212			0.811539
$886$		0			0
$887$	247.286	−	1243.19i	0.278789	−	1.40157i	−0.546785	−	0.837273i	$-0.684149\pi$
$887$	247.286	−	1243.19i	0.278789	−	1.40157i	0.825574	−	0.564294i	$-0.190851\pi$
$888$		0			0
$889$	−21.4384	+	14.3247i	−0.0241151	+	0.0161132i
$890$		0			0
$891$	2683.24	+	1792.88i	3.01149	+	2.01222i
$892$		0			0
$893$	−1259.08	−	521.528i	−1.40994	−	0.584018i
$894$		0			0
$895$	1091.32	−	217.077i	1.21935	−	0.242544i
$896$		0			0
$897$	44.9597	+	44.9597i	0.0501223	+	0.0501223i
$898$		0			0
$899$	−160.607	−	387.740i	−0.178651	−	0.431302i
$900$		0			0
$901$	−1546.34	+	245.501i	−1.71625	+	0.272476i
$902$		0			0
$903$	−6.26775	+	2.59619i	−0.00694103	+	0.00287507i
$904$		0			0
$905$	−398.742	+	398.742i	−0.440599	+	0.440599i
$906$		0			0
$907$	31.9741	+	160.744i	0.0352525	+	0.177226i	0.994400	−	0.105679i	$-0.0337017\pi$
$907$	31.9741	+	160.744i	0.0352525	+	0.177226i	−0.959148	+	0.282906i	$0.908702\pi$
$908$		0			0
$909$	156.545	−	377.934i	0.172217	−	0.415769i
$910$		0			0
$911$	−146.484	+	219.229i	−0.160795	+	0.240647i	−0.903115	−	0.429399i	$-0.858725\pi$
$911$	−146.484	+	219.229i	−0.160795	+	0.240647i	0.742320	+	0.670046i	$0.233725\pi$
$912$		0			0
$913$	606.704	+	907.997i	0.664517	+	0.994520i
$914$		0			0
$915$	1149.42	+	228.635i	1.25620	+	0.249874i
$916$		0			0
$917$		−	56.1243i		−	0.0612043i
$918$		0			0
$919$	1273.29			1.38551			0.692756	−	0.721172i	$-0.256396\pi$
$919$	1273.29			1.38551			0.692756	+	0.721172i	$0.256396\pi$
$920$		0			0
$921$	−48.4846	+	243.749i	−0.0526434	+	0.264656i
$922$		0			0
$923$	−4.27827	+	2.85865i	−0.00463517	+	0.00309712i
$924$		0			0
$925$	−7.11338	−	4.75301i	−0.00769014	−	0.00513839i
$926$		0			0
$927$	3344.66	+	1385.40i	3.60805	+	1.49450i
$928$		0			0
$929$	145.007	−	28.8437i	0.156089	−	0.0310481i	−0.116427	−	0.993199i	$-0.537144\pi$
$929$	145.007	−	28.8437i	0.156089	−	0.0310481i	0.272516	+	0.962151i	$0.412144\pi$
$930$		0			0
$931$	615.491	+	615.491i	0.661107	+	0.661107i
$932$		0			0
$933$	−777.359	−	1876.71i	−0.833182	−	2.01148i
$934$		0			0
$935$	747.162	−	458.240i	0.799104	−	0.490097i
$936$		0			0
$937$	1321.18	−	547.249i	1.41001	−	0.584044i	0.457678	−	0.889118i	$-0.348681\pi$
$937$	1321.18	−	547.249i	1.41001	−	0.584044i	0.952329	+	0.305074i	$0.0986812\pi$
$938$		0			0
$939$	1151.89	−	1151.89i	1.22672	−	1.22672i
$940$		0			0
$941$	−307.954	−	1548.19i	−0.327262	−	1.64526i	−0.697693	−	0.716397i	$-0.745790\pi$
$941$	−307.954	−	1548.19i	−0.327262	−	1.64526i	0.370431	−	0.928860i	$-0.379210\pi$
$942$		0			0
$943$	779.249	−	1881.27i	0.826351	−	1.99499i
$944$		0			0
$945$	83.8230	−	125.450i	0.0887016	−	0.132751i
$946$		0			0
$947$	−516.335	−	772.751i	−0.545233	−	0.815998i	0.451869	−	0.892085i	$-0.350758\pi$
$947$	−516.335	−	772.751i	−0.545233	−	0.815998i	−0.997101	+	0.0760861i	$0.975758\pi$
$948$		0			0
$949$	−19.4756	−	3.87393i	−0.0205222	−	0.00408212i
$950$		0			0
$951$		−	1333.15i		−	1.40184i
$952$		0			0
$953$	1846.46			1.93753			0.968763	−	0.247990i	$-0.0797699\pi$
$953$	1846.46			1.93753			0.968763	+	0.247990i	$0.0797699\pi$
$954$		0			0
$955$	−68.9577	+	346.674i	−0.0722070	+	0.363009i
$956$		0			0
$957$	−2568.94	+	1716.51i	−2.68437	+	1.79364i
$958$		0			0
$959$	−41.4016	−	27.6637i	−0.0431717	−	0.0288464i
$960$		0			0
$961$	−796.624	−	329.972i	−0.828953	−	0.343364i
$962$		0			0
$963$	−3318.14	+	660.020i	−3.44563	+	0.685379i
$964$		0			0
$965$	−562.488	−	562.488i	−0.582889	−	0.582889i
$966$		0			0
$967$	−554.928	−	1339.72i	−0.573866	−	1.38543i	−0.898240	−	0.439506i	$-0.855154\pi$
$967$	−554.928	−	1339.72i	−0.573866	−	1.38543i	0.324374	−	0.945929i	$-0.394846\pi$
$968$		0			0
$969$	−67.0001	+	1721.44i	−0.0691435	+	1.77652i
$970$		0			0
$971$	116.696	−	48.3371i	0.120181	−	0.0497807i	−0.321782	−	0.946814i	$-0.604282\pi$
$971$	116.696	−	48.3371i	0.120181	−	0.0497807i	0.441964	+	0.897033i	$0.354282\pi$
$972$		0			0
$973$	−23.2480	+	23.2480i	−0.0238932	+	0.0238932i
$974$		0			0
$975$	2.63133	+	13.2286i	0.00269880	+	0.0135678i
$976$		0			0
$977$	81.5639	−	196.913i	0.0834841	−	0.201548i	−0.876625	−	0.481174i	$-0.840210\pi$
$977$	81.5639	−	196.913i	0.0834841	−	0.201548i	0.960109	+	0.279626i	$0.0902104\pi$
$978$		0			0
$979$	−287.513	+	430.294i	−0.293681	+	0.439524i
$980$		0			0
$981$	426.879	+	638.870i	0.435147	+	0.651244i
$982$		0			0
$983$	−123.390	−	24.5437i	−0.125523	−	0.0249682i	0.131929	−	0.991259i	$-0.457883\pi$
$983$	−123.390	−	24.5437i	−0.125523	−	0.0249682i	−0.257452	+	0.966291i	$0.582883\pi$
$984$		0			0
$985$		−	1029.60i		−	1.04528i
$986$		0			0
$987$	201.936			0.204596
$988$		0			0
$989$	21.1839	−	106.499i	0.0214195	−	0.107683i
$990$		0			0
$991$	344.922	−	230.469i	0.348054	−	0.232562i	−0.369238	−	0.929335i	$-0.620381\pi$
$991$	344.922	−	230.469i	0.348054	−	0.232562i	0.717292	+	0.696772i	$0.245381\pi$
$992$		0			0
$993$	−2094.22	−	1399.32i	−2.10899	−	1.40918i
$994$		0			0
$995$	376.043	+	155.762i	0.377933	+	0.156545i
$996$		0			0
$997$	−181.657	+	36.1339i	−0.182204	+	0.0362426i	−0.285349	−	0.958424i	$-0.592109\pi$
$997$	−181.657	+	36.1339i	−0.182204	+	0.0362426i	0.103145	+	0.994666i	$0.467109\pi$
$998$		0			0
$999$	54.5646	+	54.5646i	0.0546192	+	0.0546192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.65.1	✓	40
4.3	odd	2		272.3.bh.g.65.5		40
17.11	odd	16	inner	136.3.t.b.113.1	yes	40
68.11	even	16		272.3.bh.g.113.5		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.65.1	✓	40	1.1	even	1	trivial
136.3.t.b.113.1	yes	40	17.11	odd	16	inner
272.3.bh.g.65.5		40	4.3	odd	2
272.3.bh.g.113.5		40	68.11	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)

\(f(q)\)	\(=\)	\(q+(-1.10801 + 5.57033i) q^{3} +(-3.32830 + 2.22390i) q^{5} +(-0.387063 - 0.258627i) q^{7} +(-21.4860 - 8.89979i) q^{9} +O(q^{10})\)	\(q+(-1.10801 + 5.57033i) q^{3} +(-3.32830 + 2.22390i) q^{5} +(-0.387063 - 0.258627i) q^{7} +(-21.4860 - 8.89979i) q^{9} +(12.6327 - 2.51280i) q^{11} +(-0.187068 - 0.187068i) q^{13} +(-8.70007 - 21.0038i) q^{15} +(-16.5318 - 3.96248i) q^{17} +(-16.4847 + 6.82818i) q^{19} +(1.86951 - 1.86951i) q^{21} +(8.25566 + 41.5040i) q^{23} +(-3.43524 + 8.29340i) q^{25} +(44.9834 - 67.3224i) q^{27} +(23.4648 + 35.1176i) q^{29} +(-9.74589 - 1.93858i) q^{31} +73.1525i q^{33} +1.86342 q^{35} +(-0.185929 + 0.934730i) q^{37} +(1.24930 - 0.834759i) q^{39} +(-40.0098 - 26.7337i) q^{41} +(-2.37066 - 0.981960i) q^{43} +(91.3041 - 18.1615i) q^{45} +(54.0079 + 54.0079i) q^{47} +(-18.6686 - 45.0699i) q^{49} +(40.3896 - 87.6969i) q^{51} +(85.0899 - 35.2454i) q^{53} +(-36.4572 + 36.4572i) q^{55} +(-19.7701 - 99.3909i) q^{57} +(-12.0895 + 29.1867i) q^{59} +(-28.6393 + 42.8617i) q^{61} +(6.01470 + 9.00164i) q^{63} +(1.03864 + 0.206598i) q^{65} +80.1566i q^{67} -240.339 q^{69} +(3.79439 - 19.0757i) q^{71} +(62.4090 - 41.7004i) q^{73} +(-42.3907 - 28.3246i) q^{75} +(-5.53953 - 2.29455i) q^{77} +(38.7103 - 7.69996i) q^{79} +(177.164 + 177.164i) q^{81} +(32.4456 + 78.3305i) q^{83} +(63.8347 - 23.5766i) q^{85} +(-221.616 + 91.7963i) q^{87} +(-28.4107 + 28.4107i) q^{89} +(0.0240262 + 0.120788i) q^{91} +(21.5970 - 52.1399i) q^{93} +(39.6808 - 59.3865i) q^{95} +(-12.5898 - 18.8419i) q^{97} +(-293.790 - 58.4384i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * 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 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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