LMFDB - Embedded newform 136.3.t.b.65.2

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			65.2
Character	$\chi$	$=$	136.65
Dual form			136.3.t.b.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.262425 + 1.31930i) q^{3} +(6.57938 - 4.39620i) q^{5} +(-6.01468 - 4.01888i) q^{7} +(6.64323 + 2.75172i) q^{9} +O(q^{10})$	\(q+(-0.262425 + 1.31930i) q^{3} +(6.57938 - 4.39620i) q^{5} +(-6.01468 - 4.01888i) q^{7} +(6.64323 + 2.75172i) q^{9} +(9.31912 - 1.85369i) q^{11} +(-3.27226 - 3.27226i) q^{13} +(4.07331 + 9.83385i) q^{15} +(14.9745 + 8.04767i) q^{17} +(10.7496 - 4.45261i) q^{19} +(6.88051 - 6.88051i) q^{21} +(3.55492 + 17.8718i) q^{23} +(14.3945 - 34.7515i) q^{25} +(-12.0996 + 18.1083i) q^{27} +(-18.9424 - 28.3493i) q^{29} +(-53.0044 - 10.5432i) q^{31} +12.7812i q^{33} -57.2406 q^{35} +(-11.6728 + 58.6830i) q^{37} +(5.17582 - 3.45837i) q^{39} +(-30.7298 - 20.5330i) q^{41} +(29.7984 + 12.3429i) q^{43} +(55.8054 - 11.1004i) q^{45} +(-2.36241 - 2.36241i) q^{47} +(1.27346 + 3.07440i) q^{49} +(-14.5470 + 17.6439i) q^{51} +(-53.4284 + 22.1308i) q^{53} +(53.1648 - 53.1648i) q^{55} +(3.05338 + 15.3504i) q^{57} +(-37.0677 + 89.4894i) q^{59} +(-7.09476 + 10.6181i) q^{61} +(-28.8981 - 43.2490i) q^{63} +(-35.9150 - 7.14393i) q^{65} +29.4566i q^{67} -24.5112 q^{69} +(25.0641 - 126.006i) q^{71} +(-35.7394 + 23.8803i) q^{73} +(42.0702 + 28.1104i) q^{75} +(-63.5012 - 26.3031i) q^{77} +(130.906 - 26.0388i) q^{79} +(25.0455 + 25.0455i) q^{81} +(-13.1704 - 31.7961i) q^{83} +(133.902 - 12.8821i) q^{85} +(42.3721 - 17.5511i) q^{87} +(18.5018 - 18.5018i) q^{89} +(6.53077 + 32.8324i) q^{91} +(27.8194 - 67.1620i) q^{93} +(51.1508 - 76.5526i) q^{95} +(67.5998 + 101.170i) q^{97} +(67.0099 + 13.3291i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.262425	+	1.31930i	−0.0874750	+	0.439767i	0.912082	+	0.410008i	$0.134474\pi$
$3$	−0.262425	+	1.31930i	−0.0874750	+	0.439767i	−0.999557	+	0.0297590i	$0.990526\pi$
$4$		0			0
$5$	6.57938	−	4.39620i	1.31588	−	0.879240i	0.318243	−	0.948009i	$-0.396907\pi$
$5$	6.57938	−	4.39620i	1.31588	−	0.879240i	0.997633	+	0.0687696i	$0.0219073\pi$
$6$		0			0
$7$	−6.01468	−	4.01888i	−0.859239	−	0.574125i	0.0460412	−	0.998940i	$-0.485339\pi$
$7$	−6.01468	−	4.01888i	−0.859239	−	0.574125i	−0.905281	+	0.424814i	$0.860339\pi$
$8$		0			0
$9$	6.64323	+	2.75172i	0.738137	+	0.305746i
$10$		0			0
$11$	9.31912	−	1.85369i	0.847193	−	0.168517i	0.247640	−	0.968852i	$-0.420345\pi$
$11$	9.31912	−	1.85369i	0.847193	−	0.168517i	0.599553	+	0.800335i	$0.295345\pi$
$12$		0			0
$13$	−3.27226	−	3.27226i	−0.251712	−	0.251712i	0.569960	−	0.821672i	$-0.306959\pi$
$13$	−3.27226	−	3.27226i	−0.251712	−	0.251712i	−0.821672	+	0.569960i	$0.806959\pi$
$14$		0			0
$15$	4.07331	+	9.83385i	0.271554	+	0.655590i
$16$		0			0
$17$	14.9745	+	8.04767i	0.880852	+	0.473393i
$17$	14.9745	+	8.04767i	0.880852	+	0.473393i
$18$		0			0
$19$	10.7496	−	4.45261i	0.565766	−	0.234348i	−0.0814200	−	0.996680i	$-0.525946\pi$
$19$	10.7496	−	4.45261i	0.565766	−	0.234348i	0.647186	+	0.762332i	$0.275946\pi$
$20$		0			0
$21$	6.88051	−	6.88051i	0.327643	−	0.327643i
$22$		0			0
$23$	3.55492	+	17.8718i	0.154562	+	0.777035i	0.977833	+	0.209386i	$0.0671466\pi$
$23$	3.55492	+	17.8718i	0.154562	+	0.777035i	−0.823271	+	0.567648i	$0.807853\pi$
$24$		0			0
$25$	14.3945	−	34.7515i	0.575782	−	1.39006i
$26$		0			0
$27$	−12.0996	+	18.1083i	−0.448133	+	0.670679i
$28$		0			0
$29$	−18.9424	−	28.3493i	−0.653185	−	0.977560i	−0.999226	−	0.0393410i	$-0.987474\pi$
$29$	−18.9424	−	28.3493i	−0.653185	−	0.977560i	0.346041	−	0.938219i	$-0.387526\pi$
$30$		0			0
$31$	−53.0044	−	10.5432i	−1.70982	−	0.340104i	−0.759294	−	0.650748i	$-0.774456\pi$
$31$	−53.0044	−	10.5432i	−1.70982	−	0.340104i	−0.950527	+	0.310643i	$0.899456\pi$
$32$		0			0
$33$			12.7812i			0.387308i
$34$		0			0
$35$	−57.2406			−1.63545
$36$		0			0
$37$	−11.6728	+	58.6830i	−0.315480	+	1.58603i	0.419382	+	0.907810i	$0.362247\pi$
$37$	−11.6728	+	58.6830i	−0.315480	+	1.58603i	−0.734862	+	0.678217i	$0.762753\pi$
$38$		0			0
$39$	5.17582	−	3.45837i	0.132713	−	0.0886762i
$40$		0			0
$41$	−30.7298	−	20.5330i	−0.749507	−	0.500804i	0.121187	−	0.992630i	$-0.461330\pi$
$41$	−30.7298	−	20.5330i	−0.749507	−	0.500804i	−0.870694	+	0.491825i	$0.836330\pi$
$42$		0			0
$43$	29.7984	+	12.3429i	0.692986	+	0.287044i	0.701244	−	0.712922i	$-0.252628\pi$
$43$	29.7984	+	12.3429i	0.692986	+	0.287044i	−0.00825742	+	0.999966i	$0.502628\pi$
$44$		0			0
$45$	55.8054	−	11.1004i	1.24012	−	0.246675i
$46$		0			0
$47$	−2.36241	−	2.36241i	−0.0502640	−	0.0502640i	0.681528	−	0.731792i	$-0.261316\pi$
$47$	−2.36241	−	2.36241i	−0.0502640	−	0.0502640i	−0.731792	+	0.681528i	$0.761316\pi$
$48$		0			0
$49$	1.27346	+	3.07440i	0.0259889	+	0.0627429i
$50$		0			0
$51$	−14.5470	+	17.6439i	−0.285235	+	0.345959i
$52$		0			0
$53$	−53.4284	+	22.1308i	−1.00808	+	0.417562i	−0.824755	−	0.565490i	$-0.808687\pi$
$53$	−53.4284	+	22.1308i	−1.00808	+	0.417562i	−0.183328	+	0.983052i	$0.558687\pi$
$54$		0			0
$55$	53.1648	−	53.1648i	0.966633	−	0.966633i
$56$		0			0
$57$	3.05338	+	15.3504i	0.0535681	+	0.269305i
$58$		0			0
$59$	−37.0677	+	89.4894i	−0.628266	+	1.51677i	0.213509	+	0.976941i	$0.431511\pi$
$59$	−37.0677	+	89.4894i	−0.628266	+	1.51677i	−0.841775	+	0.539828i	$0.818489\pi$
$60$		0			0
$61$	−7.09476	+	10.6181i	−0.116308	+	0.174067i	−0.885056	−	0.465485i	$-0.845880\pi$
$61$	−7.09476	+	10.6181i	−0.116308	+	0.174067i	0.768748	+	0.639552i	$0.220880\pi$
$62$		0			0
$63$	−28.8981	−	43.2490i	−0.458699	−	0.686492i
$64$		0			0
$65$	−35.9150	−	7.14393i	−0.552538	−	0.109907i
$66$		0			0
$67$			29.4566i			0.439651i	0.975539	+	0.219826i	$0.0705488\pi$
$67$			29.4566i			0.439651i	−0.975539	+	0.219826i	$0.929451\pi$
$68$		0			0
$69$	−24.5112			−0.355234
$70$		0			0
$71$	25.0641	−	126.006i	0.353016	−	1.77473i	−0.241251	−	0.970463i	$-0.577558\pi$
$71$	25.0641	−	126.006i	0.353016	−	1.77473i	0.594267	−	0.804268i	$-0.297442\pi$
$72$		0			0
$73$	−35.7394	+	23.8803i	−0.489581	+	0.327128i	−0.775738	−	0.631055i	$-0.782622\pi$
$73$	−35.7394	+	23.8803i	−0.489581	+	0.327128i	0.286157	+	0.958183i	$0.407622\pi$
$74$		0			0
$75$	42.0702	+	28.1104i	0.560936	+	0.374805i
$76$		0			0
$77$	−63.5012	−	26.3031i	−0.824691	−	0.341598i
$78$		0			0
$79$	130.906	−	26.0388i	1.65703	−	0.329605i	0.724112	−	0.689682i	$-0.242250\pi$
$79$	130.906	−	26.0388i	1.65703	−	0.329605i	0.932922	+	0.360077i	$0.117250\pi$
$80$		0			0
$81$	25.0455	+	25.0455i	0.309203	+	0.309203i
$82$		0			0
$83$	−13.1704	−	31.7961i	−0.158679	−	0.383085i	0.824466	−	0.565911i	$-0.191476\pi$
$83$	−13.1704	−	31.7961i	−0.158679	−	0.383085i	−0.983145	+	0.182826i	$0.941476\pi$
$84$		0			0
$85$	133.902	−	12.8821i	1.57532	−	0.151554i
$86$		0			0
$87$	42.3721	−	17.5511i	0.487036	−	0.201737i
$88$		0			0
$89$	18.5018	−	18.5018i	0.207886	−	0.207886i	−0.595482	−	0.803368i	$-0.703039\pi$
$89$	18.5018	−	18.5018i	0.207886	−	0.207886i	0.803368	+	0.595482i	$0.203039\pi$
$90$		0			0
$91$	6.53077	+	32.8324i	0.0717668	+	0.360796i
$92$		0			0
$93$	27.8194	−	67.1620i	0.299133	−	0.722172i
$94$		0			0
$95$	51.1508	−	76.5526i	0.538430	−	0.805817i
$96$		0			0
$97$	67.5998	+	101.170i	0.696905	+	1.04299i	0.996051	+	0.0887847i	$0.0282983\pi$
$97$	67.5998	+	101.170i	0.696905	+	1.04299i	−0.299146	+	0.954207i	$0.596702\pi$
$98$		0			0
$99$	67.0099	+	13.3291i	0.676867	+	0.134637i
$100$		0			0
$101$			143.592i			1.42170i	0.703344	+	0.710850i	$0.251689\pi$
$101$			143.592i			1.42170i	−0.703344	+	0.710850i	$0.748311\pi$
$102$		0			0
$103$	18.9182			0.183672			0.0918361	−	0.995774i	$-0.470726\pi$
$103$	18.9182			0.183672			0.0918361	+	0.995774i	$0.470726\pi$
$104$		0			0
$105$	15.0214	−	75.5175i	0.143061	−	0.719215i
$106$		0			0
$107$	−69.6813	+	46.5595i	−0.651227	+	0.435136i	−0.836811	−	0.547493i	$-0.815582\pi$
$107$	−69.6813	+	46.5595i	−0.651227	+	0.435136i	0.185584	+	0.982628i	$0.440582\pi$
$108$		0			0
$109$	−31.2563	−	20.8848i	−0.286755	−	0.191604i	0.403870	−	0.914816i	$-0.367665\pi$
$109$	−31.2563	−	20.8848i	−0.286755	−	0.191604i	−0.690625	+	0.723213i	$0.742665\pi$
$110$		0			0
$111$	−74.3573	−	30.7998i	−0.669885	−	0.277476i
$112$		0			0
$113$	−90.2074	+	17.9434i	−0.798295	+	0.158791i	−0.577351	−	0.816496i	$-0.695914\pi$
$113$	−90.2074	+	17.9434i	−0.798295	+	0.158791i	−0.220944	+	0.975287i	$0.570914\pi$
$114$		0			0
$115$	101.957	+	101.957i	0.886584	+	0.886584i
$116$		0			0
$117$	−12.7341	−	30.7427i	−0.108838	−	0.262758i
$118$		0			0
$119$	−57.7240	−	108.585i	−0.485076	−	0.912477i
$120$		0			0
$121$	−28.3796	+	11.7552i	−0.234542	+	0.0971505i
$122$		0			0
$123$	35.1534	−	35.1534i	0.285800	−	0.285800i
$124$		0			0
$125$	−19.4739	−	97.9018i	−0.155791	−	0.783214i
$126$		0			0
$127$	−3.56829	+	8.61461i	−0.0280968	+	0.0678316i	−0.937305	−	0.348510i	$-0.886688\pi$
$127$	−3.56829	+	8.61461i	−0.0280968	+	0.0678316i	0.909208	+	0.416341i	$0.136688\pi$
$128$		0			0
$129$	−24.1039	+	36.0740i	−0.186852	+	0.279643i
$130$		0			0
$131$	51.5604	+	77.1657i	0.393591	+	0.589051i	0.974354	−	0.225022i	$-0.0722455\pi$
$131$	51.5604	+	77.1657i	0.393591	+	0.589051i	−0.580762	+	0.814073i	$0.697245\pi$
$132$		0			0
$133$	−82.5497	−	16.4201i	−0.620674	−	0.123460i
$134$		0			0
$135$			172.334i			1.27655i
$136$		0			0
$137$	82.2008			0.600006			0.300003	−	0.953938i	$-0.403012\pi$
$137$	82.2008			0.600006			0.300003	+	0.953938i	$0.403012\pi$
$138$		0			0
$139$	47.0833	−	236.704i	0.338729	−	1.70291i	−0.317428	−	0.948282i	$-0.602819\pi$
$139$	47.0833	−	236.704i	0.338729	−	1.70291i	0.656158	−	0.754624i	$-0.272181\pi$
$140$		0			0
$141$	3.73668	−	2.49677i	0.0265013	−	0.0177076i
$142$		0			0
$143$	−36.5604	−	24.4289i	−0.255667	−	0.170831i
$144$		0			0
$145$	−249.258	−	103.246i	−1.71902	−	0.712041i
$146$		0			0
$147$	−4.39025	+	0.873274i	−0.0298656	+	0.00594064i
$148$		0			0
$149$	143.801	+	143.801i	0.965105	+	0.965105i	0.999411	−	0.0343060i	$-0.0109221\pi$
$149$	143.801	+	143.801i	0.965105	+	0.965105i	−0.0343060	+	0.999411i	$0.510922\pi$
$150$		0			0
$151$	61.5945	+	148.702i	0.407911	+	0.984783i	0.985687	+	0.168588i	$0.0539207\pi$
$151$	61.5945	+	148.702i	0.407911	+	0.984783i	−0.577776	+	0.816195i	$0.696079\pi$
$152$		0			0
$153$	77.3340	+	94.6681i	0.505451	+	0.618745i
$154$		0			0
$155$	−395.086	+	163.650i	−2.54894	+	1.05581i
$156$		0			0
$157$	−127.643	+	127.643i	−0.813014	+	0.813014i	−0.985085	−	0.172070i	$-0.944954\pi$
$157$	−127.643	+	127.643i	−0.813014	+	0.813014i	0.172070	+	0.985085i	$0.444954\pi$
$158$		0			0
$159$	−15.1762	−	76.2958i	−0.0954477	−	0.479848i
$160$		0			0
$161$	50.4429	−	121.780i	0.313310	−	0.756397i
$162$		0			0
$163$	37.5410	−	56.1841i	0.230313	−	0.344688i	−0.698256	−	0.715848i	$-0.746040\pi$
$163$	37.5410	−	56.1841i	0.230313	−	0.344688i	0.928569	+	0.371161i	$0.121040\pi$
$164$		0			0
$165$	56.1886	+	84.0921i	0.340537	+	0.509649i
$166$		0			0
$167$	−202.181	−	40.2163i	−1.21066	−	0.240816i	−0.451832	−	0.892103i	$-0.649229\pi$
$167$	−202.181	−	40.2163i	−1.21066	−	0.240816i	−0.758831	+	0.651287i	$0.774229\pi$
$168$		0			0
$169$		−	147.585i		−	0.873282i
$170$		0			0
$171$	83.6641			0.489264
$172$		0			0
$173$	51.2866	−	257.835i	0.296454	−	1.49038i	−0.489451	−	0.872031i	$-0.662803\pi$
$173$	51.2866	−	257.835i	0.296454	−	1.49038i	0.785906	−	0.618346i	$-0.212197\pi$
$174$		0			0
$175$	−226.241	+	151.169i	−1.29280	+	0.863823i
$176$		0			0
$177$	−108.336	−	72.3877i	−0.612067	−	0.408970i
$178$		0			0
$179$	−262.778	−	108.846i	−1.46803	−	0.608079i	−0.501622	−	0.865087i	$-0.667263\pi$
$179$	−262.778	−	108.846i	−1.46803	−	0.608079i	−0.966409	+	0.257008i	$0.917263\pi$
$180$		0			0
$181$	74.7484	−	14.8684i	0.412974	−	0.0821457i	0.0157694	−	0.999876i	$-0.494980\pi$
$181$	74.7484	−	14.8684i	0.412974	−	0.0821457i	0.397205	+	0.917730i	$0.369980\pi$
$182$		0			0
$183$	−12.1466	−	12.1466i	−0.0663747	−	0.0663747i
$184$		0			0
$185$	181.183	+	437.413i	0.979365	+	2.36440i
$186$		0			0
$187$	154.467	+	47.2392i	0.826026	+	0.252616i
$188$		0			0
$189$	145.550	−	60.2889i	0.770108	−	0.318989i
$190$		0			0
$191$	−125.071	+	125.071i	−0.654824	+	0.654824i	−0.954151	−	0.299327i	$-0.903238\pi$
$191$	−125.071	+	125.071i	−0.654824	+	0.654824i	0.299327	+	0.954151i	$0.403238\pi$
$192$		0			0
$193$	−36.1057	−	181.516i	−0.187076	−	0.940497i	−0.954239	−	0.299044i	$-0.903332\pi$
$193$	−36.1057	−	181.516i	−0.187076	−	0.940497i	0.767163	−	0.641452i	$-0.221668\pi$
$194$		0			0
$195$	18.8500	−	45.5079i	0.0966665	−	0.233374i
$196$		0			0
$197$	48.8546	−	73.1160i	0.247993	−	0.371147i	−0.686500	−	0.727130i	$-0.740854\pi$
$197$	48.8546	−	73.1160i	0.247993	−	0.371147i	0.934493	+	0.355983i	$0.115854\pi$
$198$		0			0
$199$	−128.686	−	192.592i	−0.646664	−	0.967800i	−0.999484	−	0.0321095i	$-0.989777\pi$
$199$	−128.686	−	192.592i	−0.646664	−	0.967800i	0.352821	−	0.935691i	$-0.385223\pi$
$200$		0			0
$201$	−38.8621	−	7.73016i	−0.193344	−	0.0384585i
$202$		0			0
$203$			246.639i			1.21497i
$204$		0			0
$205$	−292.450			−1.42658
$206$		0			0
$207$	−25.5619	+	128.509i	−0.123488	+	0.620814i
$208$		0			0
$209$	91.9227	−	61.4208i	0.439822	−	0.293879i
$210$		0			0
$211$	142.064	+	94.9239i	0.673287	+	0.449876i	0.844641	−	0.535333i	$-0.179814\pi$
$211$	142.064	+	94.9239i	0.673287	+	0.449876i	−0.171353	+	0.985210i	$0.554814\pi$
$212$		0			0
$213$	159.662	+	66.1342i	0.749587	+	0.310489i
$214$		0			0
$215$	250.317	−	49.7911i	1.16426	−	0.231587i
$216$		0			0
$217$	276.433	+	276.433i	1.27388	+	1.27388i
$218$		0			0
$219$	−22.1264	−	53.4178i	−0.101034	−	0.243917i
$220$		0			0
$221$	−22.6663	−	75.3345i	−0.102562	−	0.340880i
$222$		0			0
$223$	294.018	−	121.786i	1.31847	−	0.546126i	0.391123	−	0.920339i	$-0.372087\pi$
$223$	294.018	−	121.786i	1.31847	−	0.546126i	0.927343	+	0.374212i	$0.122087\pi$
$224$		0			0
$225$	191.252	−	191.252i	0.850011	−	0.850011i
$226$		0			0
$227$	49.1256	+	246.971i	0.216412	+	1.08798i	0.924304	+	0.381658i	$0.124647\pi$
$227$	49.1256	+	246.971i	0.216412	+	1.08798i	−0.707891	+	0.706321i	$0.750353\pi$
$228$		0			0
$229$	4.08530	−	9.86278i	0.0178397	−	0.0430689i	−0.914709	−	0.404114i	$-0.867580\pi$
$229$	4.08530	−	9.86278i	0.0178397	−	0.0430689i	0.932548	+	0.361045i	$0.117580\pi$
$230$		0			0
$231$	51.3660	−	76.8746i	0.222364	−	0.332790i
$232$		0			0
$233$	−201.488	−	301.548i	−0.864756	−	1.29420i	−0.954493	−	0.298234i	$-0.903602\pi$
$233$	−201.488	−	301.548i	−0.864756	−	1.29420i	0.0897365	−	0.995966i	$-0.471398\pi$
$234$		0			0
$235$	−25.9288	−	5.15756i	−0.110335	−	0.0219470i
$236$		0			0
$237$			179.537i			0.757541i
$238$		0			0
$239$	458.827			1.91978			0.959890	−	0.280379i	$-0.0904600\pi$
$239$	458.827			1.91978			0.959890	+	0.280379i	$0.0904600\pi$
$240$		0			0
$241$	71.7120	−	360.520i	0.297560	−	1.49594i	−0.485636	−	0.874161i	$-0.661412\pi$
$241$	71.7120	−	360.520i	0.297560	−	1.49594i	0.783196	−	0.621774i	$-0.213588\pi$
$242$		0			0
$243$	−202.590	+	135.366i	−0.833704	+	0.557063i
$244$		0			0
$245$	21.8942	+	14.6293i	0.0893642	+	0.0597113i
$246$		0			0
$247$	−49.7455	−	20.6053i	−0.201399	−	0.0834221i
$248$		0			0
$249$	45.4048	−	9.03158i	0.182349	−	0.0362714i
$250$		0			0
$251$	−238.967	−	238.967i	−0.952059	−	0.952059i	0.0468431	−	0.998902i	$-0.485084\pi$
$251$	−238.967	−	238.967i	−0.952059	−	0.952059i	−0.998902	+	0.0468431i	$0.985084\pi$
$252$		0			0
$253$	66.2575	+	159.960i	0.261887	+	0.632252i
$254$		0			0
$255$	−18.1439	+	180.037i	−0.0711524	+	0.706029i
$256$		0			0
$257$	−113.689	+	47.0916i	−0.442370	+	0.183236i	−0.592740	−	0.805394i	$-0.701954\pi$
$257$	−113.689	+	47.0916i	−0.442370	+	0.183236i	0.150369	+	0.988630i	$0.451954\pi$
$258$		0			0
$259$	306.048	−	306.048i	1.18165	−	1.18165i
$260$		0			0
$261$	−47.8294	−	240.455i	−0.183254	−	0.921282i
$262$		0			0
$263$	76.1551	−	183.855i	0.289563	−	0.699067i	−0.710426	−	0.703772i	$-0.751498\pi$
$263$	76.1551	−	183.855i	0.289563	−	0.699067i	0.999989	+	0.00470509i	$0.00149768\pi$
$264$		0			0
$265$	−254.234	+	380.489i	−0.959375	+	1.43581i
$266$		0			0
$267$	19.5541	+	29.2648i	0.0732365	+	0.109606i
$268$		0			0
$269$	−265.477	−	52.8066i	−0.986903	−	0.196307i	−0.324851	−	0.945765i	$-0.605314\pi$
$269$	−265.477	−	52.8066i	−0.986903	−	0.196307i	−0.662052	+	0.749458i	$0.730314\pi$
$270$		0			0
$271$		−	72.5894i		−	0.267858i	−0.990991	−	0.133929i	$-0.957241\pi$
$271$		−	72.5894i		−	0.267858i	0.990991	−	0.133929i	$-0.0427593\pi$
$272$		0			0
$273$	−45.0297			−0.164944
$274$		0			0
$275$	69.7260	−	350.536i	0.253549	−	1.27468i
$276$		0			0
$277$	−157.520	+	105.252i	−0.568665	+	0.379970i	−0.806409	−	0.591358i	$-0.798592\pi$
$277$	−157.520	+	105.252i	−0.568665	+	0.379970i	0.237744	+	0.971328i	$0.423592\pi$
$278$		0			0
$279$	−323.109	−	215.894i	−1.15810	−	0.773815i
$280$		0			0
$281$	393.279	+	162.902i	1.39957	+	0.579721i	0.949640	−	0.313343i	$-0.101449\pi$
$281$	393.279	+	162.902i	1.39957	+	0.579721i	0.449930	+	0.893064i	$0.351449\pi$
$282$		0			0
$283$	385.705	−	76.7214i	1.36291	−	0.271100i	0.541149	−	0.840927i	$-0.317990\pi$
$283$	385.705	−	76.7214i	1.36291	−	0.271100i	0.821765	+	0.569826i	$0.192990\pi$
$284$		0			0
$285$	87.5727	+	87.5727i	0.307272	+	0.307272i
$286$		0			0
$287$	102.310	+	246.998i	0.356481	+	0.860622i
$288$		0			0
$289$	159.470	+	241.019i	0.551799	+	0.833977i
$290$		0			0
$291$	−151.214	+	62.6348i	−0.519635	+	0.215240i
$292$		0			0
$293$	178.249	−	178.249i	0.608357	−	0.608357i	−0.334160	−	0.942516i	$-0.608453\pi$
$293$	178.249	−	178.249i	0.608357	−	0.608357i	0.942516	+	0.334160i	$0.108453\pi$
$294$		0			0
$295$	149.531	+	751.741i	0.506883	+	2.54828i
$296$		0			0
$297$	−79.1904	+	191.183i	−0.266634	+	0.643713i
$298$		0			0
$299$	46.8486	−	70.1138i	0.156684	−	0.234494i
$300$		0			0
$301$	−129.623	−	193.995i	−0.430642	−	0.644501i
$302$		0			0
$303$	−189.441	−	37.6821i	−0.625216	−	0.124363i
$304$		0			0
$305$			101.050i			0.331312i
$306$		0			0
$307$	−155.732			−0.507270			−0.253635	−	0.967300i	$-0.581626\pi$
$307$	−155.732			−0.507270			−0.253635	+	0.967300i	$0.581626\pi$
$308$		0			0
$309$	−4.96462	+	24.9588i	−0.0160667	+	0.0807729i
$310$		0			0
$311$	45.3080	−	30.2739i	0.145685	−	0.0973436i	−0.480592	−	0.876945i	$-0.659578\pi$
$311$	45.3080	−	30.2739i	0.145685	−	0.0973436i	0.626277	+	0.779601i	$0.284578\pi$
$312$		0			0
$313$	88.5195	+	59.1469i	0.282810	+	0.188968i	0.688882	−	0.724873i	$-0.258102\pi$
$313$	88.5195	+	59.1469i	0.282810	+	0.188968i	−0.406072	+	0.913841i	$0.633102\pi$
$314$		0			0
$315$	−380.262	−	157.510i	−1.20718	−	0.500031i
$316$		0			0
$317$	240.610	−	47.8604i	0.759023	−	0.150979i	0.199618	−	0.979874i	$-0.436030\pi$
$317$	240.610	−	47.8604i	0.759023	−	0.150979i	0.559405	+	0.828895i	$0.311030\pi$
$318$		0			0
$319$	−229.077	−	229.077i	−0.718109	−	0.718109i
$320$		0			0
$321$	−43.1399	−	104.149i	−0.134392	−	0.324451i
$322$		0			0
$323$	196.802	+	19.8334i	0.609295	+	0.0614038i
$324$		0			0
$325$	−160.819	+	66.6133i	−0.494827	+	0.204964i
$326$		0			0
$327$	35.7557	−	35.7557i	0.109345	−	0.109345i
$328$		0			0
$329$	4.71489	+	23.7034i	0.0143310	+	0.0720467i
$330$		0			0
$331$	45.8423	−	110.673i	0.138496	−	0.334360i	−0.839380	−	0.543546i	$-0.817081\pi$
$331$	45.8423	−	110.673i	0.138496	−	0.334360i	0.977876	+	0.209186i	$0.0670814\pi$
$332$		0			0
$333$	−239.024	+	357.724i	−0.717789	+	1.07425i
$334$		0			0
$335$	129.497	+	193.806i	0.386559	+	0.578526i
$336$		0			0
$337$	−354.508	−	70.5161i	−1.05195	−	0.209247i	−0.361313	−	0.932445i	$-0.617671\pi$
$337$	−354.508	−	70.5161i	−1.05195	−	0.209247i	−0.690641	+	0.723198i	$0.742671\pi$
$338$		0			0
$339$		−	123.719i		−	0.364954i
$340$		0			0
$341$	−513.499			−1.50586
$342$		0			0
$343$	−64.4547	+	324.036i	−0.187914	+	0.944710i
$344$		0			0
$345$	−161.268	+	107.756i	−0.467444	+	0.312336i
$346$		0			0
$347$	188.399	+	125.884i	0.542937	+	0.362779i	0.796594	−	0.604515i	$-0.206633\pi$
$347$	188.399	+	125.884i	0.542937	+	0.362779i	−0.253656	+	0.967294i	$0.581633\pi$
$348$		0			0
$349$	−130.782	−	54.1716i	−0.374733	−	0.155220i	0.187364	−	0.982290i	$-0.440005\pi$
$349$	−130.782	−	54.1716i	−0.374733	−	0.155220i	−0.562098	+	0.827071i	$0.690005\pi$
$350$		0			0
$351$	98.8483	−	19.6621i	0.281619	−	0.0560175i
$352$		0			0
$353$	−338.773	−	338.773i	−0.959698	−	0.959698i	0.0395207	−	0.999219i	$-0.487417\pi$
$353$	−338.773	−	338.773i	−0.959698	−	0.959698i	−0.999219	+	0.0395207i	$0.987417\pi$
$354$		0			0
$355$	−389.040	−	939.227i	−1.09589	−	2.64571i
$356$		0			0
$357$	158.404	−	47.6599i	0.443709	−	0.133501i
$358$		0			0
$359$	−218.947	+	90.6907i	−0.609880	+	0.252620i	−0.666177	−	0.745794i	$-0.732070\pi$
$359$	−218.947	+	90.6907i	−0.609880	+	0.252620i	0.0562974	+	0.998414i	$0.482070\pi$
$360$		0			0
$361$	−159.538	+	159.538i	−0.441934	+	0.441934i
$362$		0			0
$363$	−8.06114	−	40.5261i	−0.0222070	−	0.111642i
$364$		0			0
$365$	−130.160	+	314.235i	−0.356604	+	0.860918i
$366$		0			0
$367$	−137.749	+	206.155i	−0.375337	+	0.561731i	−0.970264	−	0.242048i	$-0.922181\pi$
$367$	−137.749	+	206.155i	−0.375337	+	0.561731i	0.594927	+	0.803779i	$0.297181\pi$
$368$		0			0
$369$	−147.644	−	220.965i	−0.400119	−	0.598821i
$370$		0			0
$371$	410.296	+	81.6129i	1.10592	+	0.219981i
$372$		0			0
$373$		−	105.720i		−	0.283431i	−0.989907	−	0.141715i	$-0.954738\pi$
$373$		−	105.720i		−	0.283431i	0.989907	−	0.141715i	$-0.0452618\pi$
$374$		0			0
$375$	134.272			0.358060
$376$		0			0
$377$	−30.7818	+	154.751i	−0.0816493	+	0.410479i
$378$		0			0
$379$	−22.1514	+	14.8011i	−0.0584471	+	0.0390531i	−0.584451	−	0.811429i	$-0.698690\pi$
$379$	−22.1514	+	14.8011i	−0.0584471	+	0.0390531i	0.526003	+	0.850482i	$0.323690\pi$
$380$		0			0
$381$	−10.4289	−	6.96834i	−0.0273723	−	0.0182896i
$382$		0			0
$383$	−152.830	−	63.3044i	−0.399035	−	0.165286i	0.174136	−	0.984722i	$-0.444287\pi$
$383$	−152.830	−	63.3044i	−0.399035	−	0.165286i	−0.573171	+	0.819436i	$0.694287\pi$
$384$		0			0
$385$	−533.432	+	106.106i	−1.38554	+	0.275601i
$386$		0			0
$387$	163.994	+	163.994i	0.423756	+	0.423756i
$388$		0			0
$389$	227.562	+	549.382i	0.584991	+	1.41229i	0.888239	+	0.459382i	$0.151929\pi$
$389$	227.562	+	549.382i	0.584991	+	1.41229i	−0.303247	+	0.952912i	$0.598071\pi$
$390$		0			0
$391$	−90.5933	+	296.230i	−0.231696	+	0.757620i
$392$		0			0
$393$	−115.335	+	47.7735i	−0.293474	+	0.121561i
$394$		0			0
$395$	746.806	−	746.806i	1.89065	−	1.89065i
$396$		0			0
$397$	−85.4303	−	429.487i	−0.215190	−	1.08183i	−0.925733	−	0.378178i	$-0.876551\pi$
$397$	−85.4303	−	429.487i	−0.215190	−	1.08183i	0.710543	−	0.703653i	$-0.248449\pi$
$398$		0			0
$399$	43.3262	−	104.599i	0.108587	−	0.262152i
$400$		0			0
$401$	105.025	−	157.181i	0.261908	−	0.391973i	−0.677087	−	0.735903i	$-0.736758\pi$
$401$	105.025	−	157.181i	0.261908	−	0.391973i	0.938996	+	0.343929i	$0.111758\pi$
$402$		0			0
$403$	138.944	+	207.945i	0.344775	+	0.515992i
$404$		0			0
$405$	274.889	+	54.6787i	0.678737	+	0.135009i
$406$		0			0
$407$			568.511i			1.39683i
$408$		0			0
$409$	159.169			0.389167			0.194584	−	0.980886i	$-0.437664\pi$
$409$	159.169			0.389167			0.194584	+	0.980886i	$0.437664\pi$
$410$		0			0
$411$	−21.5715	+	108.447i	−0.0524855	+	0.263863i
$412$		0			0
$413$	582.597	−	389.279i	1.41065	−	0.942564i
$414$		0			0
$415$	−226.435	−	151.299i	−0.545626	−	0.364575i
$416$		0			0
$417$	299.928	+	124.234i	0.719251	+	0.297924i
$418$		0			0
$419$	−424.807	+	84.4994i	−1.01386	+	0.201669i	−0.673941	−	0.738785i	$-0.735400\pi$
$419$	−424.807	+	84.4994i	−1.01386	+	0.201669i	−0.339919	+	0.940455i	$0.610400\pi$
$420$		0			0
$421$	382.932	+	382.932i	0.909577	+	0.909577i	0.996238	−	0.0866606i	$-0.0276196\pi$
$421$	382.932	+	382.932i	0.909577	+	0.909577i	−0.0866606	+	0.996238i	$0.527620\pi$
$422$		0			0
$423$	−9.19334	−	22.1947i	−0.0217337	−	0.0524697i
$424$		0			0
$425$	495.219	−	404.543i	1.16522	−	0.951865i
$426$		0			0
$427$	85.3454	−	35.3512i	0.199872	−	0.0827897i
$428$		0			0
$429$	41.8233	−	41.8233i	0.0974903	−	0.0974903i
$430$		0			0
$431$	82.1735	+	413.114i	0.190658	+	0.958501i	0.951050	+	0.309037i	$0.100007\pi$
$431$	82.1735	+	413.114i	0.190658	+	0.958501i	−0.760392	+	0.649464i	$0.774993\pi$
$432$		0			0
$433$	287.575	−	694.267i	0.664145	−	1.60339i	−0.127100	−	0.991890i	$-0.540567\pi$
$433$	287.575	−	694.267i	0.664145	−	1.60339i	0.791245	−	0.611499i	$-0.209433\pi$
$434$		0			0
$435$	201.624	−	301.752i	0.463503	−	0.693682i
$436$		0			0
$437$	117.790	+	176.285i	0.269542	+	0.403399i
$438$		0			0
$439$	−296.527	−	58.9828i	−0.675459	−	0.134357i	−0.154570	−	0.987982i	$-0.549399\pi$
$439$	−296.527	−	58.9828i	−0.675459	−	0.134357i	−0.520889	+	0.853625i	$0.674399\pi$
$440$		0			0
$441$			23.9281i			0.0542588i
$442$		0			0
$443$	134.265			0.303081			0.151540	−	0.988451i	$-0.451577\pi$
$443$	134.265			0.303081			0.151540	+	0.988451i	$0.451577\pi$
$444$		0			0
$445$	40.3928	−	203.068i	0.0907703	−	0.456333i
$446$		0			0
$447$	−227.453	+	151.979i	−0.508844	+	0.339999i
$448$		0			0
$449$	224.570	+	150.053i	0.500155	+	0.334193i	0.779924	−	0.625874i	$-0.215258\pi$
$449$	224.570	+	150.053i	0.500155	+	0.334193i	−0.279769	+	0.960067i	$0.590258\pi$
$450$		0			0
$451$	−324.436	−	134.386i	−0.719371	−	0.297973i
$452$		0			0
$453$	−212.347	+	42.2384i	−0.468757	+	0.0932416i
$454$		0			0
$455$	187.306	+	187.306i	0.411662	+	0.411662i
$456$		0			0
$457$	22.2178	+	53.6385i	0.0486166	+	0.117371i	0.946322	−	0.323225i	$-0.104767\pi$
$457$	22.2178	+	53.6385i	0.0486166	+	0.117371i	−0.897705	+	0.440596i	$0.854767\pi$
$458$		0			0
$459$	−326.915	+	173.789i	−0.712234	+	0.378626i
$460$		0			0
$461$	−33.2424	+	13.7694i	−0.0721092	+	0.0298686i	−0.418447	−	0.908241i	$-0.637425\pi$
$461$	−33.2424	+	13.7694i	−0.0721092	+	0.0298686i	0.346337	+	0.938110i	$0.387425\pi$
$462$		0			0
$463$	−510.130	+	510.130i	−1.10179	+	1.10179i	−0.107599	+	0.994194i	$0.534316\pi$
$463$	−510.130	+	510.130i	−1.10179	+	1.10179i	−0.994194	+	0.107599i	$0.965684\pi$
$464$		0			0
$465$	−112.223	−	564.183i	−0.241340	−	1.21330i
$466$		0			0
$467$	−329.388	+	795.212i	−0.705327	+	1.70281i	0.00603261	+	0.999982i	$0.498080\pi$
$467$	−329.388	+	795.212i	−0.705327	+	1.70281i	−0.711360	+	0.702828i	$0.751920\pi$
$468$		0			0
$469$	118.383	−	177.172i	0.252415	−	0.377766i
$470$		0			0
$471$	−134.903	−	201.897i	−0.286418	−	0.428655i
$472$		0			0
$473$	300.575	+	59.7881i	0.635465	+	0.126402i
$474$		0			0
$475$		−	437.657i		−	0.921383i
$476$		0			0
$477$	−415.835			−0.871772
$478$		0			0
$479$	110.583	−	555.939i	0.230862	−	1.16062i	−0.675251	−	0.737588i	$-0.735965\pi$
$479$	110.583	−	555.939i	0.230862	−	1.16062i	0.906113	−	0.423035i	$-0.139035\pi$
$480$		0			0
$481$	230.223	−	153.830i	0.478633	−	0.319812i
$482$		0			0
$483$	147.427	+	98.5074i	0.305231	+	0.203949i
$484$		0			0
$485$	889.529	+	368.455i	1.83408	+	0.759701i
$486$		0			0
$487$	804.425	−	160.010i	1.65180	−	0.328563i	0.720675	−	0.693273i	$-0.243832\pi$
$487$	804.425	−	160.010i	1.65180	−	0.328563i	0.931121	+	0.364711i	$0.118832\pi$
$488$		0			0
$489$	64.2720	+	64.2720i	0.131436	+	0.131436i
$490$		0			0
$491$	−17.6730	−	42.6665i	−0.0359940	−	0.0868972i	0.904860	−	0.425709i	$-0.139975\pi$
$491$	−17.6730	−	42.6665i	−0.0359940	−	0.0868972i	−0.940854	+	0.338811i	$0.889975\pi$
$492$		0			0
$493$	−55.5064	−	576.957i	−0.112589	−	1.17030i
$494$		0			0
$495$	499.480	−	206.892i	1.00905	−	0.417963i
$496$		0			0
$497$	−657.155	+	657.155i	−1.32224	+	1.32224i
$498$		0			0
$499$	−86.6737	−	435.738i	−0.173695	−	0.873223i	−0.965090	−	0.261918i	$-0.915645\pi$
$499$	−86.6737	−	435.738i	−0.173695	−	0.873223i	0.791395	−	0.611305i	$-0.209355\pi$
$500$		0			0
$501$	106.115	−	256.183i	0.211806	−	0.511344i
$502$		0			0
$503$	197.859	−	296.117i	0.393358	−	0.588702i	−0.580945	−	0.813943i	$-0.697317\pi$
$503$	197.859	−	296.117i	0.393358	−	0.588702i	0.974303	+	0.225241i	$0.0723169\pi$
$504$		0			0
$505$	631.257	+	944.743i	1.25001	+	1.87078i
$506$		0			0
$507$	194.708	+	38.7299i	0.384040	+	0.0763904i
$508$		0			0
$509$		−	536.219i		−	1.05348i	−0.850028	−	0.526738i	$-0.823415\pi$
$509$		−	536.219i		−	1.05348i	0.850028	−	0.526738i	$-0.176585\pi$
$510$		0			0
$511$	310.933			0.608480
$512$		0			0
$513$	−49.4360	+	248.532i	−0.0963665	+	0.484467i
$514$		0			0
$515$	124.470	−	83.1683i	0.241690	−	0.161492i
$516$		0			0
$517$	−26.3947	−	17.6364i	−0.0510536	−	0.0341130i
$518$		0			0
$519$	326.703	+	135.325i	0.629486	+	0.260742i
$520$		0			0
$521$	78.1766	−	15.5503i	0.150051	−	0.0298470i	−0.119493	−	0.992835i	$-0.538127\pi$
$521$	78.1766	−	15.5503i	0.150051	−	0.0298470i	0.269544	+	0.962988i	$0.413127\pi$
$522$		0			0
$523$	64.5113	+	64.5113i	0.123348	+	0.123348i	0.766086	−	0.642738i	$-0.222202\pi$
$523$	64.5113	+	64.5113i	0.123348	+	0.123348i	−0.642738	+	0.766086i	$0.722202\pi$
$524$		0			0
$525$	−140.066	−	338.150i	−0.266793	−	0.644095i
$526$		0			0
$527$	−708.865	−	584.442i	−1.34510	−	1.10900i
$528$		0			0
$529$	181.969	−	75.3739i	0.343986	−	0.142484i
$530$		0			0
$531$	−492.499	+	492.499i	−0.927493	+	0.927493i
$532$		0			0
$533$	33.3666	+	167.745i	0.0626015	+	0.314719i
$534$		0			0
$535$	−253.774	+	612.665i	−0.474345	+	1.14517i
$536$		0			0
$537$	212.560	−	318.119i	0.395829	−	0.592400i
$538$		0			0
$539$	17.5665	+	26.2901i	0.0325909	+	0.0487757i
$540$		0			0
$541$	170.429	+	33.9004i	0.315026	+	0.0626625i	0.350071	−	0.936723i	$-0.386157\pi$
$541$	170.429	+	33.9004i	0.315026	+	0.0626625i	−0.0350451	+	0.999386i	$0.511157\pi$
$542$		0			0
$543$			102.517i			0.188798i
$544$		0			0
$545$	−297.461			−0.545799
$546$		0			0
$547$	−189.957	+	954.978i	−0.347270	+	1.74585i	0.273517	+	0.961867i	$0.411813\pi$
$547$	−189.957	+	954.978i	−0.347270	+	1.74585i	−0.620788	+	0.783979i	$0.713187\pi$
$548$		0			0
$549$	−76.3500	+	51.0154i	−0.139071	+	0.0929243i
$550$		0			0
$551$	−329.850	−	220.399i	−0.598640	−	0.399998i
$552$		0			0
$553$	−892.002	−	369.479i	−1.61302	−	0.668136i
$554$		0			0
$555$	−624.626	+	124.246i	−1.12545	+	0.223866i
$556$		0			0
$557$	−278.298	−	278.298i	−0.499637	−	0.499637i	0.411688	−	0.911325i	$-0.364939\pi$
$557$	−278.298	−	278.298i	−0.499637	−	0.499637i	−0.911325	+	0.411688i	$0.864939\pi$
$558$		0			0
$559$	−57.1190	−	137.897i	−0.102181	−	0.246686i
$560$		0			0
$561$	−102.859	+	191.391i	−0.183349	+	0.341161i
$562$		0			0
$563$	51.5199	−	21.3402i	0.0915096	−	0.0379045i	−0.336459	−	0.941698i	$-0.609229\pi$
$563$	51.5199	−	21.3402i	0.0915096	−	0.0379045i	0.427969	+	0.903794i	$0.359229\pi$
$564$		0			0
$565$	−514.626	+	514.626i	−0.910842	+	0.910842i
$566$		0			0
$567$	−49.9857	−	251.295i	−0.0881582	−	0.443201i
$568$		0			0
$569$	176.227	−	425.449i	0.309713	−	0.747713i	−0.690001	−	0.723808i	$-0.742390\pi$
$569$	176.227	−	425.449i	0.309713	−	0.747713i	0.999714	−	0.0239048i	$-0.00760986\pi$
$570$		0			0
$571$	−199.988	+	299.303i	−0.350242	+	0.524174i	−0.964204	−	0.265162i	$-0.914575\pi$
$571$	−199.988	+	299.303i	−0.350242	+	0.524174i	0.613962	+	0.789335i	$0.289575\pi$
$572$		0			0
$573$	−132.185	−	197.829i	−0.230689	−	0.345250i
$574$		0			0
$575$	672.243	+	133.717i	1.16912	+	0.232552i
$576$		0			0
$577$			271.674i			0.470838i	0.971894	+	0.235419i	$0.0756463\pi$
$577$			271.674i			0.470838i	−0.971894	+	0.235419i	$0.924354\pi$
$578$		0			0
$579$	248.949			0.429964
$580$		0			0
$581$	−48.5691	+	244.173i	−0.0835956	+	0.420264i
$582$		0			0
$583$	−456.882	+	305.279i	−0.783675	+	0.523635i
$584$		0			0
$585$	−218.933	−	146.287i	−0.374245	−	0.250062i
$586$		0			0
$587$	−159.517	−	66.0740i	−0.271749	−	0.112562i	0.242648	−	0.970115i	$-0.421984\pi$
$587$	−159.517	−	66.0740i	−0.271749	−	0.112562i	−0.514397	+	0.857552i	$0.671984\pi$
$588$		0			0
$589$	−616.720	+	122.673i	−1.04706	+	0.208274i
$590$		0			0
$591$	83.6413	+	83.6413i	0.141525	+	0.141525i
$592$		0			0
$593$	123.081	+	297.144i	0.207557	+	0.501087i	0.993037	−	0.117800i	$-0.0375841\pi$
$593$	123.081	+	297.144i	0.207557	+	0.501087i	−0.785480	+	0.618886i	$0.787584\pi$
$594$		0			0
$595$	−857.148	−	460.654i	−1.44058	−	0.774208i
$596$		0			0
$597$	287.858	−	119.234i	0.482173	−	0.199723i
$598$		0			0
$599$	−229.272	+	229.272i	−0.382757	+	0.382757i	−0.872095	−	0.489337i	$-0.837239\pi$
$599$	−229.272	+	229.272i	−0.382757	+	0.382757i	0.489337	+	0.872095i	$0.337239\pi$
$600$		0			0
$601$	6.25059	+	31.4238i	0.0104003	+	0.0522859i	0.985637	−	0.168878i	$-0.0540144\pi$
$601$	6.25059	+	31.4238i	0.0104003	+	0.0522859i	−0.975237	+	0.221164i	$0.929014\pi$
$602$		0			0
$603$	−81.0563	+	195.687i	−0.134422	+	0.324523i
$604$		0			0
$605$	−135.042	+	202.104i	−0.223210	+	0.334057i
$606$		0			0
$607$	−380.293	−	569.148i	−0.626512	−	0.937641i	−0.999950	−	0.00998591i	$-0.996821\pi$
$607$	−380.293	−	569.148i	−0.626512	−	0.937641i	0.373439	−	0.927655i	$-0.378179\pi$
$608$		0			0
$609$	−325.390	−	64.7242i	−0.534303	−	0.106279i
$610$		0			0
$611$			15.4608i			0.0253042i
$612$		0			0
$613$	883.158			1.44072			0.720358	−	0.693603i	$-0.243978\pi$
$613$	883.158			1.44072			0.720358	+	0.693603i	$0.243978\pi$
$614$		0			0
$615$	76.7462	−	385.829i	0.124791	−	0.627364i
$616$		0			0
$617$	1019.89	−	681.469i	1.65298	−	1.10449i	0.765787	−	0.643095i	$-0.222350\pi$
$617$	1019.89	−	681.469i	1.65298	−	1.10449i	0.887196	−	0.461393i	$-0.152650\pi$
$618$		0			0
$619$	633.364	+	423.200i	1.02320	+	0.683683i	0.949555	−	0.313601i	$-0.101535\pi$
$619$	633.364	+	423.200i	1.02320	+	0.683683i	0.0736497	+	0.997284i	$0.476535\pi$
$620$		0			0
$621$	−366.642	−	151.868i	−0.590405	−	0.244554i
$622$		0			0
$623$	−185.639	+	36.9259i	−0.297976	+	0.0592712i
$624$		0			0
$625$	106.419	+	106.419i	0.170271	+	0.170271i
$626$		0			0
$627$	56.9096	+	137.392i	0.0907650	+	0.219126i
$628$		0			0
$629$	−647.055	+	784.808i	−1.02870	+	1.24771i
$630$		0			0
$631$	691.412	−	286.392i	1.09574	−	0.453871i	0.239736	−	0.970838i	$-0.422939\pi$
$631$	691.412	−	286.392i	1.09574	−	0.453871i	0.856005	+	0.516968i	$0.172939\pi$
$632$		0			0
$633$	−162.514	+	162.514i	−0.256736	+	0.256736i
$634$		0			0
$635$	14.3944	+	72.3657i	0.0226684	+	0.113962i
$636$		0			0
$637$	5.89316	−	14.2273i	0.00925142	−	0.0223349i
$638$		0			0
$639$	513.239	−	768.116i	0.803191	−	1.20206i
$640$		0			0
$641$	−104.958	−	157.081i	−0.163742	−	0.245057i	0.740521	−	0.672033i	$-0.234579\pi$
$641$	−104.958	−	157.081i	−0.163742	−	0.245057i	−0.904263	+	0.426976i	$0.859579\pi$
$642$		0			0
$643$	98.0681	+	19.5070i	0.152517	+	0.0303374i	0.270758	−	0.962647i	$-0.412726\pi$
$643$	98.0681	+	19.5070i	0.152517	+	0.0303374i	−0.118241	+	0.992985i	$0.537726\pi$
$644$		0			0
$645$			343.310i			0.532263i
$646$		0			0
$647$	−390.479			−0.603522			−0.301761	−	0.953384i	$-0.597575\pi$
$647$	−390.479			−0.603522			−0.301761	+	0.953384i	$0.597575\pi$
$648$		0			0
$649$	−179.553	+	902.674i	−0.276661	+	1.39087i
$650$		0			0
$651$	−437.240	+	292.155i	−0.671644	+	0.448778i
$652$		0			0
$653$	−373.896	−	249.829i	−0.572582	−	0.382587i	0.235308	−	0.971921i	$-0.424390\pi$
$653$	−373.896	−	249.829i	−0.572582	−	0.382587i	−0.807890	+	0.589334i	$0.799390\pi$
$654$		0			0
$655$	678.471	+	281.032i	1.03583	+	0.429056i
$656$		0			0
$657$	−303.137	+	60.2977i	−0.461396	+	0.0917773i
$658$		0			0
$659$	−336.892	−	336.892i	−0.511217	−	0.511217i	0.403682	−	0.914899i	$-0.367730\pi$
$659$	−336.892	−	336.892i	−0.511217	−	0.511217i	−0.914899	+	0.403682i	$0.867730\pi$
$660$		0			0
$661$	37.7307	+	91.0899i	0.0570812	+	0.137806i	0.949847	−	0.312715i	$-0.101238\pi$
$661$	37.7307	+	91.0899i	0.0570812	+	0.137806i	−0.892766	+	0.450521i	$0.851238\pi$
$662$		0			0
$663$	105.337	−	10.1340i	0.158879	−	0.0152851i
$664$		0			0
$665$	−615.311	+	254.870i	−0.925280	+	0.383264i
$666$		0			0
$667$	439.313	−	439.313i	0.658641	−	0.658641i
$668$		0			0
$669$	83.5149	+	419.858i	0.124835	+	0.627590i
$670$		0			0
$671$	−46.4343	+	112.102i	−0.0692017	+	0.167068i
$672$		0			0
$673$	78.7048	−	117.790i	0.116946	−	0.175022i	−0.768378	−	0.639996i	$-0.778936\pi$
$673$	78.7048	−	117.790i	0.116946	−	0.175022i	0.885325	+	0.464973i	$0.153936\pi$
$674$		0			0
$675$	455.123	+	681.140i	0.674257	+	1.00910i
$676$		0			0
$677$	−532.198	−	105.861i	−0.786112	−	0.156367i	−0.214317	−	0.976764i	$-0.568753\pi$
$677$	−532.198	−	105.861i	−0.786112	−	0.156367i	−0.571795	+	0.820397i	$0.693753\pi$
$678$		0			0
$679$		−	880.182i		−	1.29629i
$680$		0			0
$681$	−338.721			−0.497388
$682$		0			0
$683$	−178.961	+	899.699i	−0.262022	+	1.31728i	0.595719	+	0.803193i	$0.296867\pi$
$683$	−178.961	+	899.699i	−0.262022	+	1.31728i	−0.857741	+	0.514082i	$0.828133\pi$
$684$		0			0
$685$	540.830	−	361.371i	0.789532	−	0.527549i
$686$		0			0
$687$	11.9399	+	7.97797i	0.0173797	+	0.0116128i
$688$		0			0
$689$	247.250	+	102.414i	0.358853	+	0.148642i
$690$		0			0
$691$	982.110	−	195.354i	1.42129	−	0.282712i	0.576186	−	0.817318i	$-0.304540\pi$
$691$	982.110	−	195.354i	1.42129	−	0.282712i	0.845101	+	0.534607i	$0.179540\pi$
$692$		0			0
$693$	−349.475	−	349.475i	−0.504292	−	0.504292i
$694$		0			0
$695$	−730.819	−	1764.35i	−1.05154	−	2.53864i
$696$		0			0
$697$	−294.920	−	554.774i	−0.423127	−	0.795945i
$698$		0			0
$699$	450.709	−	186.690i	0.644790	−	0.267081i
$700$		0			0
$701$	95.2697	−	95.2697i	0.135905	−	0.135905i	−0.635881	−	0.771787i	$-0.719363\pi$
$701$	95.2697	−	95.2697i	0.135905	−	0.135905i	0.771787	+	0.635881i	$0.219363\pi$
$702$		0			0
$703$	135.816	+	682.791i	0.193194	+	0.971253i
$704$		0			0
$705$	13.6087	−	32.8544i	0.0193032	−	0.0466020i
$706$		0			0
$707$	577.077	−	863.657i	0.816234	−	1.22158i
$708$		0			0
$709$	339.627	+	508.287i	0.479022	+	0.716907i	0.989746	−	0.142838i	$-0.0456227\pi$
$709$	339.627	+	508.287i	0.479022	+	0.716907i	−0.510724	+	0.859745i	$0.670623\pi$
$710$		0			0
$711$	941.288	+	187.234i	1.32389	+	0.263339i
$712$		0			0
$713$		−	984.765i		−	1.38116i
$714$		0			0
$715$	−347.938			−0.486627
$716$		0			0
$717$	−120.408	+	605.331i	−0.167933	+	0.844255i
$718$		0			0
$719$	161.443	−	107.872i	0.224538	−	0.150031i	−0.438214	−	0.898871i	$-0.644389\pi$
$719$	161.443	−	107.872i	0.224538	−	0.150031i	0.662751	+	0.748840i	$0.269389\pi$
$720$		0			0
$721$	−113.787	−	76.0301i	−0.157818	−	0.105451i
$722$		0			0
$723$	456.816	+	189.219i	0.631834	+	0.261714i
$724$		0			0
$725$	−1257.85	+	250.201i	−1.73496	+	0.345105i
$726$		0			0
$727$	−661.770	−	661.770i	−0.910275	−	0.910275i	0.0860188	−	0.996294i	$-0.472585\pi$
$727$	−661.770	−	661.770i	−0.910275	−	0.910275i	−0.996294	+	0.0860188i	$0.972585\pi$
$728$		0			0
$729$	−3.43351	−	8.28922i	−0.00470989	−	0.0113707i
$730$		0			0
$731$	346.884	+	424.637i	0.474533	+	0.580898i
$732$		0			0
$733$	−258.578	+	107.107i	−0.352767	+	0.146121i	−0.552028	−	0.833826i	$-0.686146\pi$
$733$	−258.578	+	107.107i	−0.352767	+	0.146121i	0.199261	+	0.979946i	$0.436146\pi$
$734$		0			0
$735$	−25.0460	+	25.0460i	−0.0340762	+	0.0340762i
$736$		0			0
$737$	54.6034	+	274.510i	0.0740888	+	0.372469i
$738$		0			0
$739$	48.5160	−	117.128i	0.0656509	−	0.158495i	−0.887649	−	0.460521i	$-0.847663\pi$
$739$	48.5160	−	117.128i	0.0656509	−	0.158495i	0.953300	+	0.302025i	$0.0976627\pi$
$740$		0			0
$741$	40.2390	−	60.2219i	0.0543037	−	0.0812712i
$742$		0			0
$743$	−54.1875	−	81.0974i	−0.0729307	−	0.109149i	0.793211	−	0.608947i	$-0.208408\pi$
$743$	−54.1875	−	81.0974i	−0.0729307	−	0.109149i	−0.866142	+	0.499798i	$0.833408\pi$
$744$		0			0
$745$	1578.30	+	313.942i	2.11852	+	0.421399i
$746$		0			0
$747$		−	247.470i		−	0.331285i
$748$		0			0
$749$	606.227			0.809382
$750$		0			0
$751$	−15.2436	+	76.6349i	−0.0202978	+	0.102044i	−0.989606	−	0.143804i	$-0.954066\pi$
$751$	−15.2436	+	76.6349i	−0.0202978	+	0.102044i	0.969308	+	0.245848i	$0.0790664\pi$
$752$		0			0
$753$	377.980	−	252.558i	0.501965	−	0.335403i
$754$		0			0
$755$	1058.98	+	707.587i	1.40262	+	0.937201i
$756$		0			0
$757$	1109.73	+	459.666i	1.46596	+	0.607221i	0.965934	−	0.258789i	$-0.0833235\pi$
$757$	1109.73	+	459.666i	1.46596	+	0.607221i	0.500027	+	0.866010i	$0.333324\pi$
$758$		0			0
$759$	−228.422	+	45.4361i	−0.300952	+	0.0598630i
$760$		0			0
$761$	−581.921	−	581.921i	−0.764679	−	0.764679i	0.212485	−	0.977164i	$-0.431844\pi$
$761$	−581.921	−	581.921i	−0.764679	−	0.764679i	−0.977164	+	0.212485i	$0.931844\pi$
$762$		0			0
$763$	104.063	+	251.230i	0.136387	+	0.329267i
$764$		0			0
$765$	924.989	+	282.881i	1.20914	+	0.369779i
$766$		0			0
$767$	414.128	−	171.537i	0.539932	−	0.223647i
$768$		0			0
$769$	465.814	−	465.814i	0.605740	−	0.605740i	−0.336090	−	0.941830i	$-0.609105\pi$
$769$	465.814	−	465.814i	0.605740	−	0.605740i	0.941830	+	0.336090i	$0.109105\pi$
$770$		0			0
$771$	−32.2930	−	162.348i	−0.0418846	−	0.210568i
$772$		0			0
$773$	−90.3827	+	218.203i	−0.116925	+	0.282281i	−0.971497	−	0.237051i	$-0.923819\pi$
$773$	−90.3827	+	218.203i	−0.116925	+	0.282281i	0.854573	+	0.519332i	$0.173819\pi$
$774$		0			0
$775$	−1129.37	+	1690.22i	−1.45725	+	2.18093i
$776$		0			0
$777$	323.454	+	484.083i	0.416286	+	0.623016i
$778$		0			0
$779$	−421.757	−	83.8927i	−0.541408	−	0.107693i
$780$		0			0
$781$		−	1220.72i		−	1.56303i
$782$		0			0
$783$	742.553			0.948343
$784$		0			0
$785$	−278.668	+	1400.96i	−0.354991	+	1.78466i
$786$		0			0
$787$	705.276	−	471.251i	0.896158	−	0.598794i	−0.0199165	−	0.999802i	$-0.506340\pi$
$787$	705.276	−	471.251i	0.896158	−	0.598794i	0.916075	+	0.401008i	$0.131340\pi$
$788$		0			0
$789$	222.574	+	148.719i	0.282097	+	0.188491i
$790$		0			0
$791$	614.680	+	254.609i	0.777093	+	0.321882i
$792$		0			0
$793$	57.9610	−	11.5292i	0.0730908	−	0.0145387i
$794$		0			0
$795$	−435.261	−	435.261i	−0.547499	−	0.547499i
$796$		0			0
$797$	−138.608	−	334.630i	−0.173912	−	0.419862i	0.812756	−	0.582604i	$-0.197966\pi$
$797$	−138.608	−	334.630i	−0.173912	−	0.419862i	−0.986669	+	0.162742i	$0.947966\pi$
$798$		0			0
$799$	−16.3639	−	54.3877i	−0.0204805	−	0.0680697i
$800$		0			0
$801$	173.824	−	72.0002i	0.217008	−	0.0898878i
$802$		0			0
$803$	−288.793	+	288.793i	−0.359643	+	0.359643i
$804$		0			0
$805$	−203.486	−	1022.99i	−0.252777	−	1.27080i
$806$		0			0
$807$	139.336	−	336.386i	0.172659	−	0.416835i
$808$		0			0
$809$	−743.598	+	1112.87i	−0.919157	+	1.37562i	0.00760720	+	0.999971i	$0.497579\pi$
$809$	−743.598	+	1112.87i	−0.919157	+	1.37562i	−0.926764	+	0.375644i	$0.877421\pi$
$810$		0			0
$811$	−765.166	−	1145.15i	−0.943484	−	1.41202i	−0.910933	−	0.412554i	$-0.864637\pi$
$811$	−765.166	−	1145.15i	−0.943484	−	1.41202i	−0.0325513	−	0.999470i	$-0.510363\pi$
$812$		0			0
$813$	95.7672	+	19.0493i	0.117795	+	0.0234308i
$814$		0			0
$815$		−	534.694i		−	0.656066i
$816$		0			0
$817$	375.278			0.459337
$818$		0			0
$819$	−46.9601	+	236.084i	−0.0573383	+	0.288259i
$820$		0			0
$821$	−546.568	+	365.205i	−0.665734	+	0.444829i	−0.841974	−	0.539518i	$-0.818606\pi$
$821$	−546.568	+	365.205i	−0.665734	+	0.444829i	0.176240	+	0.984347i	$0.443606\pi$
$822$		0			0
$823$	−81.4576	−	54.4282i	−0.0989764	−	0.0661339i	0.505097	−	0.863063i	$-0.331457\pi$
$823$	−81.4576	−	54.4282i	−0.0989764	−	0.0661339i	−0.604074	+	0.796929i	$0.706457\pi$
$824$		0			0
$825$	444.165	+	183.979i	0.538382	+	0.223005i
$826$		0			0
$827$	181.340	−	36.0708i	0.219275	−	0.0436165i	−0.0842302	−	0.996446i	$-0.526843\pi$
$827$	181.340	−	36.0708i	0.219275	−	0.0436165i	0.303505	+	0.952830i	$0.401843\pi$
$828$		0			0
$829$	562.014	+	562.014i	0.677942	+	0.677942i	0.959534	−	0.281592i	$-0.0908625\pi$
$829$	562.014	+	562.014i	0.677942	+	0.677942i	−0.281592	+	0.959534i	$0.590863\pi$
$830$		0			0
$831$	−97.5212	−	235.437i	−0.117354	−	0.283318i
$832$		0			0
$833$	−5.67240	+	56.2859i	−0.00680961	+	0.0675701i
$834$		0			0
$835$	−1507.02	+	624.229i	−1.80482	+	0.747580i
$836$		0			0
$837$	832.253	−	832.253i	0.994329	−	0.994329i
$838$		0			0
$839$	11.4133	+	57.3787i	0.0136035	+	0.0683894i	0.986991	−	0.160777i	$-0.0514000\pi$
$839$	11.4133	+	57.3787i	0.0136035	+	0.0683894i	−0.973387	+	0.229166i	$0.926400\pi$
$840$		0			0
$841$	−123.030	+	297.021i	−0.146290	+	0.353176i
$842$		0			0
$843$	−318.123	+	476.104i	−0.377370	+	0.564773i
$844$		0			0
$845$	−648.811	−	971.015i	−0.767824	−	1.14913i
$846$		0			0
$847$	217.937	+	43.3503i	0.257304	+	0.0511810i
$848$		0			0
$849$			528.994i			0.623079i
$850$		0			0
$851$	−1090.27			−1.28116
$852$		0			0
$853$	167.258	−	840.861i	0.196082	−	0.985769i	−0.749901	−	0.661550i	$-0.769899\pi$
$853$	167.258	−	840.861i	0.196082	−	0.985769i	0.945982	−	0.324218i	$-0.105101\pi$
$854$		0			0
$855$	550.458	−	367.804i	0.643810	−	0.430180i
$856$		0			0
$857$	−1121.65	−	749.460i	−1.30880	−	0.874516i	−0.311672	−	0.950190i	$-0.600889\pi$
$857$	−1121.65	−	749.460i	−1.30880	−	0.874516i	−0.997133	+	0.0756741i	$0.975889\pi$
$858$		0			0
$859$	434.870	+	180.129i	0.506252	+	0.209696i	0.621166	−	0.783679i	$-0.286659\pi$
$859$	434.870	+	180.129i	0.506252	+	0.209696i	−0.114914	+	0.993375i	$0.536659\pi$
$860$		0			0
$861$	−352.714	+	70.1591i	−0.409656	+	0.0814857i
$862$		0			0
$863$	−561.692	−	561.692i	−0.650859	−	0.650859i	0.302341	−	0.953200i	$-0.402232\pi$
$863$	−561.692	−	561.692i	−0.650859	−	0.650859i	−0.953200	+	0.302341i	$0.902232\pi$
$864$		0			0
$865$	−796.061	−	1921.86i	−0.920302	−	2.22180i
$866$		0			0
$867$	−359.826	+	147.139i	−0.415024	+	0.169711i
$868$		0			0
$869$	1171.66	−	485.317i	1.34828	−	0.558477i
$870$		0			0
$871$	96.3898	−	96.3898i	0.110666	−	0.110666i
$872$		0			0
$873$	170.689	+	858.113i	0.195520	+	0.982947i
$874$		0			0
$875$	−276.326	+	667.111i	−0.315802	+	0.762412i
$876$		0			0
$877$	−477.133	+	714.080i	−0.544052	+	0.814231i	−0.997008	−	0.0773020i	$-0.975369\pi$
$877$	−477.133	+	714.080i	−0.544052	+	0.814231i	0.452956	+	0.891533i	$0.350369\pi$
$878$		0			0
$879$	188.386	+	281.940i	0.214319	+	0.320751i
$880$		0			0
$881$	−407.003	−	80.9580i	−0.461979	−	0.0918933i	−0.0413869	−	0.999143i	$-0.513178\pi$
$881$	−407.003	−	80.9580i	−0.461979	−	0.0918933i	−0.420592	+	0.907250i	$0.638178\pi$
$882$		0			0
$883$			151.110i			0.171132i	0.996332	+	0.0855661i	$0.0272699\pi$
$883$			151.110i			0.171132i	−0.996332	+	0.0855661i	$0.972730\pi$
$884$		0			0
$885$	−1031.01			−1.16499
$886$		0			0
$887$	9.42147	−	47.3649i	0.0106217	−	0.0533990i	−0.975111	−	0.221718i	$-0.928834\pi$
$887$	9.42147	−	47.3649i	0.0106217	−	0.0533990i	0.985733	+	0.168319i	$0.0538337\pi$
$888$		0			0
$889$	56.0832	−	37.4736i	0.0630857	−	0.0421525i
$890$		0			0
$891$	279.828	+	186.975i	0.314061	+	0.209849i
$892$		0			0
$893$	−35.9138	−	14.8760i	−0.0402170	−	0.0166584i
$894$		0			0
$895$	−2207.42	+	439.083i	−2.46639	+	0.490596i
$896$		0			0
$897$	80.2070	+	80.2070i	0.0894169	+	0.0894169i
$898$		0			0
$899$	705.136	+	1702.35i	0.784356	+	1.89360i
$900$		0			0
$901$	−978.164	−	98.5778i	−1.08564	−	0.109409i
$902$		0			0
$903$	289.954	−	120.103i	0.321100	−	0.133004i
$904$		0			0
$905$	426.433	−	426.433i	0.471197	−	0.471197i
$906$		0			0
$907$	31.4369	+	158.044i	0.0346603	+	0.174249i	0.994238	−	0.107195i	$-0.0341868\pi$
$907$	31.4369	+	158.044i	0.0346603	+	0.174249i	−0.959578	+	0.281444i	$0.909187\pi$
$908$		0			0
$909$	−395.123	+	953.912i	−0.434679	+	1.04941i
$910$		0			0
$911$	−375.977	+	562.689i	−0.412708	+	0.617661i	−0.978342	−	0.206995i	$-0.933632\pi$
$911$	−375.977	+	562.689i	−0.412708	+	0.617661i	0.565634	+	0.824656i	$0.308632\pi$
$912$		0			0
$913$	−181.676	−	271.898i	−0.198988	−	0.297807i
$914$		0			0
$915$	−133.316	−	26.5181i	−0.145700	−	0.0289815i
$916$		0			0
$917$		−	671.342i		−	0.732106i
$918$		0			0
$919$	−507.804			−0.552561			−0.276280	−	0.961077i	$-0.589102\pi$
$919$	−507.804			−0.552561			−0.276280	+	0.961077i	$0.589102\pi$
$920$		0			0
$921$	40.8680	−	205.457i	0.0443735	−	0.223081i
$922$		0			0
$923$	−494.341	+	330.308i	−0.535580	+	0.357863i
$924$		0			0
$925$	1871.30	+	1250.36i	2.02302	+	1.35174i
$926$		0			0
$927$	125.678	+	52.0576i	0.135575	+	0.0561571i
$928$		0			0
$929$	−570.066	+	113.393i	−0.613634	+	0.122059i	−0.492116	−	0.870530i	$-0.663776\pi$
$929$	−570.066	+	113.393i	−0.613634	+	0.122059i	−0.121518	+	0.992589i	$0.538776\pi$
$930$		0			0
$931$	27.3782	+	27.3782i	0.0294074	+	0.0294074i
$932$		0			0
$933$	28.0503	+	67.7195i	0.0300647	+	0.0725826i
$934$		0			0
$935$	1223.97	−	368.262i	1.30906	−	0.393863i
$936$		0			0
$937$	77.9736	−	32.2977i	0.0832163	−	0.0344693i	−0.340687	−	0.940177i	$-0.610660\pi$
$937$	77.9736	−	32.2977i	0.0832163	−	0.0344693i	0.423903	+	0.905707i	$0.360660\pi$
$938$		0			0
$939$	−101.262	+	101.262i	−0.107840	+	0.107840i
$940$		0			0
$941$	19.2899	+	96.9769i	0.0204994	+	0.103057i	0.989680	−	0.143292i	$-0.0457689\pi$
$941$	19.2899	+	96.9769i	0.0204994	+	0.103057i	−0.969181	+	0.246349i	$0.920769\pi$
$942$		0			0
$943$	257.719	−	622.189i	0.273297	−	0.659798i
$944$		0			0
$945$	692.588	−	1036.53i	0.732898	−	1.09686i
$946$		0			0
$947$	272.869	+	408.378i	0.288141	+	0.431233i	0.947097	−	0.320948i	$-0.104002\pi$
$947$	272.869	+	408.378i	0.288141	+	0.431233i	−0.658956	+	0.752182i	$0.729002\pi$
$948$		0			0
$949$	195.091	+	38.8061i	0.205576	+	0.0408916i
$950$		0			0
$951$			329.997i			0.347000i
$952$		0			0
$953$	−537.494			−0.564002			−0.282001	−	0.959414i	$-0.590998\pi$
$953$	−537.494			−0.564002			−0.282001	+	0.959414i	$0.590998\pi$
$954$		0			0
$955$	−273.053	+	1372.73i	−0.285919	+	1.43741i
$956$		0			0
$957$	362.337	−	242.106i	0.378617	−	0.252984i
$958$		0			0
$959$	−494.411	−	330.355i	−0.515548	−	0.344478i
$960$		0			0
$961$	1810.46	+	749.918i	1.88394	+	0.780352i
$962$		0			0
$963$	−591.027	+	117.563i	−0.613736	+	0.122080i
$964$		0			0
$965$	−1035.53	−	1035.53i	−1.07309	−	1.07309i
$966$		0			0
$967$	−478.320	−	1154.77i	−0.494643	−	1.19417i	−0.952333	−	0.305062i	$-0.901323\pi$
$967$	−478.320	−	1154.77i	−0.494643	−	1.19417i	0.457690	−	0.889112i	$-0.348677\pi$
$968$		0			0
$969$	−77.8121	+	254.437i	−0.0803014	+	0.262576i
$970$		0			0
$971$	523.919	−	217.015i	0.539567	−	0.223496i	−0.0962207	−	0.995360i	$-0.530675\pi$
$971$	523.919	−	217.015i	0.539567	−	0.223496i	0.635788	+	0.771864i	$0.280675\pi$
$972$		0			0
$973$	−1234.48	+	1234.48i	−1.26873	+	1.26873i
$974$		0			0
$975$	−45.6801	−	229.649i	−0.0468513	−	0.235538i
$976$		0			0
$977$	−207.186	+	500.192i	−0.212064	+	0.511967i	−0.993740	−	0.111717i	$-0.964365\pi$
$977$	−207.186	+	500.192i	−0.212064	+	0.511967i	0.781676	+	0.623684i	$0.214365\pi$
$978$		0			0
$979$	138.124	−	206.718i	0.141087	−	0.211152i
$980$		0			0
$981$	−150.174	−	224.751i	−0.153082	−	0.229104i
$982$		0			0
$983$	731.722	+	145.549i	0.744377	+	0.148066i	0.552686	−	0.833390i	$-0.313603\pi$
$983$	731.722	+	145.549i	0.744377	+	0.148066i	0.191691	+	0.981455i	$0.438603\pi$
$984$		0			0
$985$		−	695.832i		−	0.706428i
$986$		0			0
$987$	−32.5091			−0.0329373
$988$		0			0
$989$	−114.659	+	576.429i	−0.115934	+	0.582840i
$990$		0			0
$991$	679.632	−	454.115i	0.685804	−	0.458240i	−0.163223	−	0.986589i	$-0.552189\pi$
$991$	679.632	−	454.115i	0.685804	−	0.458240i	0.849027	+	0.528350i	$0.177189\pi$
$992$		0			0
$993$	133.981	+	89.5231i	0.134925	+	0.0901542i
$994$		0			0
$995$	−1693.35	−	701.408i	−1.70186	−	0.704932i
$996$		0			0
$997$	1491.53	−	296.685i	1.49602	−	0.297577i	0.621828	−	0.783154i	$-0.286390\pi$
$997$	1491.53	−	296.685i	1.49602	−	0.297577i	0.874194	+	0.485576i	$0.161390\pi$
$998$		0			0
$999$	−921.415	−	921.415i	−0.922338	−	0.922338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.65.2	✓	40
4.3	odd	2		272.3.bh.g.65.4		40
17.11	odd	16	inner	136.3.t.b.113.2	yes	40
68.11	even	16		272.3.bh.g.113.4		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.65.2	✓	40	1.1	even	1	trivial
136.3.t.b.113.2	yes	40	17.11	odd	16	inner
272.3.bh.g.65.4		40	4.3	odd	2
272.3.bh.g.113.4		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)

\(f(q)\)	\(=\)	\(q+(-0.262425 + 1.31930i) q^{3} +(6.57938 - 4.39620i) q^{5} +(-6.01468 - 4.01888i) q^{7} +(6.64323 + 2.75172i) q^{9} +O(q^{10})\)	\(q+(-0.262425 + 1.31930i) q^{3} +(6.57938 - 4.39620i) q^{5} +(-6.01468 - 4.01888i) q^{7} +(6.64323 + 2.75172i) q^{9} +(9.31912 - 1.85369i) q^{11} +(-3.27226 - 3.27226i) q^{13} +(4.07331 + 9.83385i) q^{15} +(14.9745 + 8.04767i) q^{17} +(10.7496 - 4.45261i) q^{19} +(6.88051 - 6.88051i) q^{21} +(3.55492 + 17.8718i) q^{23} +(14.3945 - 34.7515i) q^{25} +(-12.0996 + 18.1083i) q^{27} +(-18.9424 - 28.3493i) q^{29} +(-53.0044 - 10.5432i) q^{31} +12.7812i q^{33} -57.2406 q^{35} +(-11.6728 + 58.6830i) q^{37} +(5.17582 - 3.45837i) q^{39} +(-30.7298 - 20.5330i) q^{41} +(29.7984 + 12.3429i) q^{43} +(55.8054 - 11.1004i) q^{45} +(-2.36241 - 2.36241i) q^{47} +(1.27346 + 3.07440i) q^{49} +(-14.5470 + 17.6439i) q^{51} +(-53.4284 + 22.1308i) q^{53} +(53.1648 - 53.1648i) q^{55} +(3.05338 + 15.3504i) q^{57} +(-37.0677 + 89.4894i) q^{59} +(-7.09476 + 10.6181i) q^{61} +(-28.8981 - 43.2490i) q^{63} +(-35.9150 - 7.14393i) q^{65} +29.4566i q^{67} -24.5112 q^{69} +(25.0641 - 126.006i) q^{71} +(-35.7394 + 23.8803i) q^{73} +(42.0702 + 28.1104i) q^{75} +(-63.5012 - 26.3031i) q^{77} +(130.906 - 26.0388i) q^{79} +(25.0455 + 25.0455i) q^{81} +(-13.1704 - 31.7961i) q^{83} +(133.902 - 12.8821i) q^{85} +(42.3721 - 17.5511i) q^{87} +(18.5018 - 18.5018i) q^{89} +(6.53077 + 32.8324i) q^{91} +(27.8194 - 67.1620i) q^{93} +(51.1508 - 76.5526i) q^{95} +(67.5998 + 101.170i) q^{97} +(67.0099 + 13.3291i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 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

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more