LMFDB - Embedded newform 136.3.t.a.57.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			57.3
Character	$\chi$	$=$	136.57
Dual form			136.3.t.a.105.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35534 - 0.269593i) q^{3} +(4.43942 - 6.64406i) q^{5} +(-5.05024 - 7.55823i) q^{7} +(-6.55066 + 2.71337i) q^{9} +O(q^{10})$	\(q+(1.35534 - 0.269593i) q^{3} +(4.43942 - 6.64406i) q^{5} +(-5.05024 - 7.55823i) q^{7} +(-6.55066 + 2.71337i) q^{9} +(-1.51671 + 7.62503i) q^{11} +(9.47892 - 9.47892i) q^{13} +(4.22571 - 10.2018i) q^{15} +(16.6282 - 3.53575i) q^{17} +(20.4730 + 8.48019i) q^{19} +(-8.88243 - 8.88243i) q^{21} +(-20.1956 - 4.01715i) q^{23} +(-14.8680 - 35.8945i) q^{25} +(-18.4878 + 12.3532i) q^{27} +(24.2626 + 16.2118i) q^{29} +(10.8789 + 54.6917i) q^{31} +10.7434i q^{33} -72.6374 q^{35} +(43.1122 - 8.57555i) q^{37} +(10.2917 - 15.4026i) q^{39} +(9.07242 + 13.5778i) q^{41} +(-39.9878 + 16.5635i) q^{43} +(-11.0533 + 55.5687i) q^{45} +(23.2685 - 23.2685i) q^{47} +(-12.8703 + 31.0717i) q^{49} +(21.5837 - 9.27499i) q^{51} +(-53.2419 - 22.0535i) q^{53} +(43.9278 + 43.9278i) q^{55} +(30.0340 + 5.97413i) q^{57} +(-3.95776 - 9.55489i) q^{59} +(-88.8415 + 59.3620i) q^{61} +(53.5907 + 35.8082i) q^{63} +(-20.8976 - 105.059i) q^{65} -1.75690i q^{67} -28.4548 q^{69} +(21.6696 - 4.31036i) q^{71} +(-64.9241 + 97.1658i) q^{73} +(-29.8280 - 44.6408i) q^{75} +(65.2915 - 27.0446i) q^{77} +(7.36455 - 37.0241i) q^{79} +(23.3960 - 23.3960i) q^{81} +(58.6489 - 141.591i) q^{83} +(50.3280 - 126.176i) q^{85} +(37.2546 + 15.4314i) q^{87} +(24.6554 + 24.6554i) q^{89} +(-119.515 - 23.7729i) q^{91} +(29.4890 + 71.1928i) q^{93} +(147.231 - 98.3766i) q^{95} +(50.5435 + 33.7721i) q^{97} +(-10.7541 - 54.0644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	$ 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{15}{16}\right)$

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
$3$	1.35534	−	0.269593i	0.451779	−	0.0898644i	0.0360439	−	0.999350i	$-0.488524\pi$
$3$	1.35534	−	0.269593i	0.451779	−	0.0898644i	0.415735	+	0.909486i	$0.363524\pi$
$4$		0			0
$5$	4.43942	−	6.64406i	0.887883	−	1.32881i	−0.0559655	−	0.998433i	$-0.517824\pi$
$5$	4.43942	−	6.64406i	0.887883	−	1.32881i	0.943849	−	0.330378i	$-0.107176\pi$
$6$		0			0
$7$	−5.05024	−	7.55823i	−0.721464	−	1.07975i	−0.993091	−	0.117344i	$-0.962562\pi$
$7$	−5.05024	−	7.55823i	−0.721464	−	1.07975i	0.271628	−	0.962402i	$-0.412438\pi$
$8$		0			0
$9$	−6.55066	+	2.71337i	−0.727851	+	0.301486i
$10$		0			0
$11$	−1.51671	+	7.62503i	−0.137883	+	0.693185i	0.848562	+	0.529095i	$0.177469\pi$
$11$	−1.51671	+	7.62503i	−0.137883	+	0.693185i	−0.986445	+	0.164089i	$0.947531\pi$
$12$		0			0
$13$	9.47892	−	9.47892i	0.729147	−	0.729147i	−0.241303	−	0.970450i	$-0.577575\pi$
$13$	9.47892	−	9.47892i	0.729147	−	0.729147i	0.970450	+	0.241303i	$0.0775746\pi$
$14$		0			0
$15$	4.22571	−	10.2018i	0.281714	−	0.680118i
$16$		0			0
$17$	16.6282	−	3.53575i	0.978132	−	0.207985i
$17$	16.6282	−	3.53575i	0.978132	−	0.207985i
$18$		0			0
$19$	20.4730	+	8.48019i	1.07753	+	0.446326i	0.849641	−	0.527362i	$-0.176819\pi$
$19$	20.4730	+	8.48019i	1.07753	+	0.446326i	0.227885	+	0.973688i	$0.426819\pi$
$20$		0			0
$21$	−8.88243	−	8.88243i	−0.422973	−	0.422973i
$22$		0			0
$23$	−20.1956	−	4.01715i	−0.878068	−	0.174659i	−0.264581	−	0.964363i	$-0.585234\pi$
$23$	−20.1956	−	4.01715i	−0.878068	−	0.174659i	−0.613487	+	0.789705i	$0.710234\pi$
$24$		0			0
$25$	−14.8680	−	35.8945i	−0.594719	−	1.43578i
$26$		0			0
$27$	−18.4878	+	12.3532i	−0.684734	+	0.457525i
$28$		0			0
$29$	24.2626	+	16.2118i	0.836642	+	0.559027i	0.898457	−	0.439061i	$-0.144689\pi$
$29$	24.2626	+	16.2118i	0.836642	+	0.559027i	−0.0618148	+	0.998088i	$0.519689\pi$
$30$		0			0
$31$	10.8789	+	54.6917i	0.350931	+	1.76425i	0.604180	+	0.796848i	$0.293501\pi$
$31$	10.8789	+	54.6917i	0.350931	+	1.76425i	−0.253250	+	0.967401i	$0.581499\pi$
$32$		0			0
$33$			10.7434i			0.325557i
$34$		0			0
$35$	−72.6374			−2.07535
$36$		0			0
$37$	43.1122	−	8.57555i	1.16519	−	0.231772i	0.425655	−	0.904885i	$-0.360044\pi$
$37$	43.1122	−	8.57555i	1.16519	−	0.231772i	0.739539	+	0.673114i	$0.235044\pi$
$38$		0			0
$39$	10.2917	−	15.4026i	0.263889	−	0.394938i
$40$		0			0
$41$	9.07242	+	13.5778i	0.221279	+	0.331167i	0.925455	−	0.378859i	$-0.123683\pi$
$41$	9.07242	+	13.5778i	0.221279	+	0.331167i	−0.704176	+	0.710026i	$0.748683\pi$
$42$		0			0
$43$	−39.9878	+	16.5635i	−0.929948	+	0.385197i	−0.795659	−	0.605745i	$-0.792875\pi$
$43$	−39.9878	+	16.5635i	−0.929948	+	0.385197i	−0.134289	+	0.990942i	$0.542875\pi$
$44$		0			0
$45$	−11.0533	+	55.5687i	−0.245629	+	1.23486i
$46$		0			0
$47$	23.2685	−	23.2685i	0.495074	−	0.495074i	−0.414827	−	0.909900i	$-0.636158\pi$
$47$	23.2685	−	23.2685i	0.495074	−	0.495074i	0.909900	+	0.414827i	$0.136158\pi$
$48$		0			0
$49$	−12.8703	+	31.0717i	−0.262659	+	0.634116i
$50$		0			0
$51$	21.5837	−	9.27499i	0.423209	−	0.181863i
$52$		0			0
$53$	−53.2419	−	22.0535i	−1.00457	−	0.416104i	−0.181096	−	0.983465i	$-0.557964\pi$
$53$	−53.2419	−	22.0535i	−1.00457	−	0.416104i	−0.823469	+	0.567361i	$0.807964\pi$
$54$		0			0
$55$	43.9278	+	43.9278i	0.798687	+	0.798687i
$56$		0			0
$57$	30.0340	+	5.97413i	0.526912	+	0.104809i
$58$		0			0
$59$	−3.95776	−	9.55489i	−0.0670807	−	0.161947i	0.886784	−	0.462184i	$-0.152934\pi$
$59$	−3.95776	−	9.55489i	−0.0670807	−	0.161947i	−0.953865	+	0.300237i	$0.902934\pi$
$60$		0			0
$61$	−88.8415	+	59.3620i	−1.45642	+	0.973148i	−0.460060	+	0.887888i	$0.652172\pi$
$61$	−88.8415	+	59.3620i	−1.45642	+	0.973148i	−0.996359	+	0.0852600i	$0.972828\pi$
$62$		0			0
$63$	53.5907	+	35.8082i	0.850646	+	0.568384i
$64$		0			0
$65$	−20.8976	−	105.059i	−0.321501	−	1.61630i
$66$		0			0
$67$		−	1.75690i		−	0.0262224i	−0.999914	−	0.0131112i	$-0.995826\pi$
$67$		−	1.75690i		−	0.0262224i	0.999914	−	0.0131112i	$-0.00417355\pi$
$68$		0			0
$69$	−28.4548			−0.412388
$70$		0			0
$71$	21.6696	−	4.31036i	0.305206	−	0.0607093i	−0.0401114	−	0.999195i	$-0.512771\pi$
$71$	21.6696	−	4.31036i	0.305206	−	0.0607093i	0.345317	+	0.938486i	$0.387771\pi$
$72$		0			0
$73$	−64.9241	+	97.1658i	−0.889371	+	1.33104i	0.0537383	+	0.998555i	$0.482886\pi$
$73$	−64.9241	+	97.1658i	−0.889371	+	1.33104i	−0.943109	+	0.332483i	$0.892114\pi$
$74$		0			0
$75$	−29.8280	−	44.6408i	−0.397707	−	0.595210i
$76$		0			0
$77$	65.2915	−	27.0446i	0.847941	−	0.351229i
$78$		0			0
$79$	7.36455	−	37.0241i	0.0932221	−	0.468659i	−0.905770	−	0.423770i	$-0.860706\pi$
$79$	7.36455	−	37.0241i	0.0932221	−	0.468659i	0.998992	−	0.0448893i	$-0.0142935\pi$
$80$		0			0
$81$	23.3960	−	23.3960i	0.288840	−	0.288840i
$82$		0			0
$83$	58.6489	−	141.591i	0.706613	−	1.70592i	−0.00168139	−	0.999999i	$-0.500535\pi$
$83$	58.6489	−	141.591i	0.706613	−	1.70592i	0.708295	−	0.705917i	$-0.249465\pi$
$84$		0			0
$85$	50.3280	−	126.176i	0.592094	−	1.48442i
$86$		0			0
$87$	37.2546	+	15.4314i	0.428214	+	0.177372i
$88$		0			0
$89$	24.6554	+	24.6554i	0.277027	+	0.277027i	0.831921	−	0.554894i	$-0.187241\pi$
$89$	24.6554	+	24.6554i	0.277027	+	0.277027i	−0.554894	+	0.831921i	$0.687241\pi$
$90$		0			0
$91$	−119.515	−	23.7729i	−1.31335	−	0.261241i
$92$		0			0
$93$	29.4890	+	71.1928i	0.317086	+	0.765514i
$94$		0			0
$95$	147.231	−	98.3766i	1.54980	−	1.03554i
$96$		0			0
$97$	50.5435	+	33.7721i	0.521067	+	0.348166i	0.788125	−	0.615515i	$-0.211052\pi$
$97$	50.5435	+	33.7721i	0.521067	+	0.348166i	−0.267059	+	0.963680i	$0.586052\pi$
$98$		0			0
$99$	−10.7541	−	54.0644i	−0.108627	−	0.546105i
$100$		0			0
$101$		−	43.7819i		−	0.433484i	−0.976229	−	0.216742i	$-0.930457\pi$
$101$		−	43.7819i		−	0.433484i	0.976229	−	0.216742i	$-0.0695431\pi$
$102$		0			0
$103$	56.2411			0.546030			0.273015	−	0.962010i	$-0.411979\pi$
$103$	56.2411			0.546030			0.273015	+	0.962010i	$0.411979\pi$
$104$		0			0
$105$	−98.4481	+	19.5826i	−0.937601	+	0.186500i
$106$		0			0
$107$	−25.7032	+	38.4676i	−0.240217	+	0.359510i	−0.931915	−	0.362677i	$-0.881863\pi$
$107$	−25.7032	+	38.4676i	−0.240217	+	0.359510i	0.691698	+	0.722187i	$0.256863\pi$
$108$		0			0
$109$	22.2319	+	33.2724i	0.203962	+	0.305251i	0.919323	−	0.393505i	$-0.128737\pi$
$109$	22.2319	+	33.2724i	0.203962	+	0.305251i	−0.715360	+	0.698756i	$0.753737\pi$
$110$		0			0
$111$	56.1196	−	23.2455i	0.505582	−	0.209419i
$112$		0			0
$113$	10.7253	−	53.9198i	0.0949143	−	0.477167i	−0.903867	−	0.427813i	$-0.859284\pi$
$113$	10.7253	−	53.9198i	0.0949143	−	0.477167i	0.998781	−	0.0493531i	$-0.0157160\pi$
$114$		0			0
$115$	−116.347	+	116.347i	−1.01171	+	1.01171i
$116$		0			0
$117$	−36.3733	+	87.8130i	−0.310883	+	0.750538i
$118$		0			0
$119$	−110.701	−	107.824i	−0.930258	−	0.906081i
$120$		0			0
$121$	55.9487	+	23.1747i	0.462386	+	0.191527i
$122$		0			0
$123$	15.9567	+	15.9567i	0.129729	+	0.129729i
$124$		0			0
$125$	−108.560	−	21.5939i	−0.868479	−	0.172751i
$126$		0			0
$127$	27.9314	+	67.4324i	0.219932	+	0.530964i	0.994880	−	0.101061i	$-0.0322238\pi$
$127$	27.9314	+	67.4324i	0.219932	+	0.530964i	−0.774948	+	0.632025i	$0.782224\pi$
$128$		0			0
$129$	−49.7315	+	33.2295i	−0.385515	+	0.257593i
$130$		0			0
$131$	−23.9038	−	15.9720i	−0.182471	−	0.121924i	0.460980	−	0.887411i	$-0.347498\pi$
$131$	−23.9038	−	15.9720i	−0.182471	−	0.121924i	−0.643451	+	0.765487i	$0.722498\pi$
$132$		0			0
$133$	−39.2984	−	197.566i	−0.295477	−	1.48546i
$134$		0			0
$135$			177.675i			1.31611i
$136$		0			0
$137$	−79.3872			−0.579469			−0.289734	−	0.957107i	$-0.593567\pi$
$137$	−79.3872			−0.579469			−0.289734	+	0.957107i	$0.593567\pi$
$138$		0			0
$139$	5.93535	−	1.18061i	0.0427003	−	0.00849362i	−0.173694	−	0.984800i	$-0.555570\pi$
$139$	5.93535	−	1.18061i	0.0427003	−	0.00849362i	0.216394	+	0.976306i	$0.430570\pi$
$140$		0			0
$141$	25.2636	−	37.8096i	0.179174	−	0.268153i
$142$		0			0
$143$	57.9002	+	86.6538i	0.404897	+	0.605971i
$144$		0			0
$145$	215.424	−	89.2315i	1.48568	−	0.615389i
$146$		0			0
$147$	−9.06689	+	45.5823i	−0.0616795	+	0.310084i
$148$		0			0
$149$	−113.603	+	113.603i	−0.762439	+	0.762439i	−0.976763	−	0.214324i	$-0.931245\pi$
$149$	−113.603	+	113.603i	−0.762439	+	0.762439i	0.214324	+	0.976763i	$0.431245\pi$
$150$		0			0
$151$	75.1485	−	181.424i	0.497672	−	1.20149i	−0.453062	−	0.891479i	$-0.649668\pi$
$151$	75.1485	−	181.424i	0.497672	−	1.20149i	0.950734	−	0.310007i	$-0.100332\pi$
$152$		0			0
$153$	−99.3321	+	68.2801i	−0.649230	+	0.446275i
$154$		0			0
$155$	411.670	+	170.519i	2.65594	+	1.10013i
$156$		0			0
$157$	112.609	+	112.609i	0.717255	+	0.717255i	0.968042	−	0.250787i	$-0.0806894\pi$
$157$	112.609	+	112.609i	0.717255	+	0.717255i	−0.250787	+	0.968042i	$0.580689\pi$
$158$		0			0
$159$	−78.1062	−	15.5363i	−0.491234	−	0.0977126i
$160$		0			0
$161$	71.6301	+	172.930i	0.444907	+	1.07410i
$162$		0			0
$163$	−225.620	+	150.755i	−1.38417	+	0.924875i	−0.384175	+	0.923260i	$0.625514\pi$
$163$	−225.620	+	150.755i	−1.38417	+	0.924875i	−0.999999	+	0.00161479i	$0.999486\pi$
$164$		0			0
$165$	71.3796	+	47.6943i	0.432604	+	0.289057i
$166$		0			0
$167$	−64.2091	−	322.801i	−0.384486	−	1.93294i	−0.359200	−	0.933261i	$-0.616950\pi$
$167$	−64.2091	−	322.801i	−0.384486	−	1.93294i	−0.0252863	−	0.999680i	$-0.508050\pi$
$168$		0			0
$169$		−	10.6997i		−	0.0633118i
$170$		0			0
$171$	−157.121			−0.918839
$172$		0			0
$173$	−151.379	+	30.1111i	−0.875023	+	0.174053i	−0.612116	−	0.790768i	$-0.709681\pi$
$173$	−151.379	+	30.1111i	−0.875023	+	0.174053i	−0.262907	+	0.964821i	$0.584681\pi$
$174$		0			0
$175$	−196.212	+	293.651i	−1.12121	+	1.67801i
$176$		0			0
$177$	−7.94003	−	11.8831i	−0.0448589	−	0.0671362i
$178$		0			0
$179$	−225.718	+	93.4953i	−1.26099	+	0.522320i	−0.910214	−	0.414139i	$-0.864083\pi$
$179$	−225.718	+	93.4953i	−1.26099	+	0.522320i	−0.350778	+	0.936459i	$0.614083\pi$
$180$		0			0
$181$	6.38701	−	32.1097i	0.0352873	−	0.177401i	−0.959122	−	0.282992i	$-0.908673\pi$
$181$	6.38701	−	32.1097i	0.0352873	−	0.177401i	0.994410	+	0.105590i	$0.0336731\pi$
$182$		0			0
$183$	−104.407	+	104.407i	−0.570528	+	0.570528i
$184$		0			0
$185$	134.416	−	324.510i	0.726576	−	1.75411i
$186$		0			0
$187$	1.73994	+	132.154i	0.00930450	+	0.706704i
$188$		0			0
$189$	186.736	+	77.3486i	0.988022	+	0.409252i
$190$		0			0
$191$	−190.393	−	190.393i	−0.996824	−	0.996824i	0.00317059	−	0.999995i	$-0.498991\pi$
$191$	−190.393	−	190.393i	−0.996824	−	0.996824i	−0.999995	+	0.00317059i	$0.998991\pi$
$192$		0			0
$193$	−90.4249	−	17.9866i	−0.468523	−	0.0931950i	−0.0448177	−	0.998995i	$-0.514271\pi$
$193$	−90.4249	−	17.9866i	−0.468523	−	0.0931950i	−0.423705	+	0.905800i	$0.639271\pi$
$194$		0			0
$195$	−56.6465	−	136.757i	−0.290495	−	0.701317i
$196$		0			0
$197$	−53.8846	+	36.0045i	−0.273526	+	0.182764i	−0.684766	−	0.728763i	$-0.740096\pi$
$197$	−53.8846	+	36.0045i	−0.273526	+	0.182764i	0.411240	+	0.911527i	$0.365096\pi$
$198$		0			0
$199$	242.793	+	162.229i	1.22006	+	0.815221i	0.987540	−	0.157369i	$-0.0503013\pi$
$199$	242.793	+	162.229i	1.22006	+	0.815221i	0.232525	+	0.972590i	$0.425301\pi$
$200$		0			0
$201$	−0.473649	−	2.38120i	−0.00235646	−	0.0118467i
$202$		0			0
$203$		−	265.256i		−	1.30668i
$204$		0			0
$205$	130.488			0.636528
$206$		0			0
$207$	143.194	−	28.4831i	0.691760	−	0.137600i
$208$		0			0
$209$	−95.7134	+	143.245i	−0.457959	+	0.685384i
$210$		0			0
$211$	48.0414	+	71.8990i	0.227684	+	0.340753i	0.927669	−	0.373405i	$-0.121810\pi$
$211$	48.0414	+	71.8990i	0.227684	+	0.340753i	−0.699984	+	0.714158i	$0.746810\pi$
$212$		0			0
$213$	28.2076	−	11.6840i	0.132430	−	0.0548543i
$214$		0			0
$215$	−67.4737	+	339.213i	−0.313831	+	1.57774i
$216$		0			0
$217$	358.431	−	358.431i	1.65176	−	1.65176i
$218$		0			0
$219$	−61.7988	+	149.195i	−0.282186	+	0.681258i
$220$		0			0
$221$	124.103	−	191.133i	0.561550	−	0.864854i
$222$		0			0
$223$	76.2578	+	31.5870i	0.341963	+	0.141646i	0.547054	−	0.837097i	$-0.315749\pi$
$223$	76.2578	+	31.5870i	0.341963	+	0.141646i	−0.205091	+	0.978743i	$0.565749\pi$
$224$		0			0
$225$	194.790	+	194.790i	0.865733	+	0.865733i
$226$		0			0
$227$	301.870	+	60.0457i	1.32982	+	0.264518i	0.808326	−	0.588735i	$-0.200374\pi$
$227$	301.870	+	60.0457i	1.32982	+	0.264518i	0.521497	+	0.853253i	$0.325374\pi$
$228$		0			0
$229$	−143.928	−	347.474i	−0.628509	−	1.51735i	−0.841476	−	0.540295i	$-0.818313\pi$
$229$	−143.928	−	347.474i	−0.628509	−	1.51735i	0.212967	−	0.977059i	$-0.431687\pi$
$230$		0			0
$231$	81.2009	−	54.2567i	0.351519	−	0.234877i
$232$		0			0
$233$	−295.460	−	197.420i	−1.26807	−	0.847297i	−0.274619	−	0.961553i	$-0.588552\pi$
$233$	−295.460	−	197.420i	−1.26807	−	0.847297i	−0.993451	+	0.114256i	$0.963552\pi$
$234$		0			0
$235$	−51.2986	−	257.895i	−0.218292	−	1.09743i
$236$		0			0
$237$		−	52.1655i		−	0.220108i
$238$		0			0
$239$	−400.442			−1.67549			−0.837744	−	0.546062i	$-0.816126\pi$
$239$	−400.442			−1.67549			−0.837744	+	0.546062i	$0.816126\pi$
$240$		0			0
$241$	−281.402	+	55.9744i	−1.16764	+	0.232259i	−0.740584	−	0.671964i	$-0.765451\pi$
$241$	−281.402	+	55.9744i	−1.16764	+	0.232259i	−0.427061	+	0.904223i	$0.640451\pi$
$242$		0			0
$243$	136.581	−	204.407i	0.562060	−	0.841183i
$244$		0			0
$245$	149.305	+	223.451i	0.609409	+	0.912046i
$246$		0			0
$247$	274.445	−	113.679i	1.11111	−	0.460238i
$248$		0			0
$249$	41.3170	−	207.715i	0.165932	−	0.834196i
$250$		0			0
$251$	218.726	−	218.726i	0.871420	−	0.871420i	−0.121208	−	0.992627i	$-0.538677\pi$
$251$	218.726	−	218.726i	0.871420	−	0.871420i	0.992627	+	0.121208i	$0.0386766\pi$
$252$		0			0
$253$	61.2618	−	147.899i	0.242141	−	0.584581i
$254$		0			0
$255$	34.1952	−	184.579i	0.134099	−	0.723837i
$256$		0			0
$257$	302.258	+	125.200i	1.17610	+	0.487158i	0.883205	−	0.468986i	$-0.155381\pi$
$257$	302.258	+	125.200i	1.17610	+	0.487158i	0.292897	+	0.956144i	$0.405381\pi$
$258$		0			0
$259$	−282.543	−	282.543i	−1.09090	−	1.09090i
$260$		0			0
$261$	−202.925	−	40.3642i	−0.777490	−	0.154652i
$262$		0			0
$263$	19.7552	+	47.6934i	0.0751150	+	0.181344i	0.956977	−	0.290164i	$-0.0937099\pi$
$263$	19.7552	+	47.6934i	0.0751150	+	0.181344i	−0.881862	+	0.471508i	$0.843710\pi$
$264$		0			0
$265$	−382.888	+	255.838i	−1.44486	+	0.965425i
$266$		0			0
$267$	40.0633	+	26.7695i	0.150050	+	0.100260i
$268$		0			0
$269$	−0.0988686	−	0.497046i	−0.000367541	−	0.00184776i	0.980601	−	0.196014i	$-0.0627998\pi$
$269$	−0.0988686	−	0.497046i	−0.000367541	−	0.00184776i	−0.980969	+	0.194166i	$0.937800\pi$
$270$		0			0
$271$			344.175i			1.27002i	0.772504	+	0.635010i	$0.219004\pi$
$271$			344.175i			1.27002i	−0.772504	+	0.635010i	$0.780996\pi$
$272$		0			0
$273$	−168.392			−0.616819
$274$		0			0
$275$	296.247	−	58.9272i	1.07726	−	0.214281i
$276$		0			0
$277$	−168.553	+	252.257i	−0.608493	+	0.910674i	−0.999955	−	0.00952012i	$-0.996970\pi$
$277$	−168.553	+	252.257i	−0.608493	+	0.910674i	0.391462	+	0.920194i	$0.371970\pi$
$278$		0			0
$279$	−219.663	−	328.748i	−0.787321	−	1.17831i
$280$		0			0
$281$	−85.1188	+	35.2574i	−0.302914	+	0.125471i	−0.528963	−	0.848645i	$-0.677419\pi$
$281$	−85.1188	+	35.2574i	−0.302914	+	0.125471i	0.226049	+	0.974116i	$0.427419\pi$
$282$		0			0
$283$	−57.0645	+	286.883i	−0.201641	+	1.01372i	0.738842	+	0.673879i	$0.235373\pi$
$283$	−57.0645	+	286.883i	−0.201641	+	1.01372i	−0.940483	+	0.339840i	$0.889627\pi$
$284$		0			0
$285$	173.026	−	173.026i	0.607108	−	0.607108i
$286$		0			0
$287$	56.8064	−	137.143i	0.197932	−	0.477850i
$288$		0			0
$289$	263.997	−	117.587i	0.913484	−	0.406874i
$290$		0			0
$291$	77.6081	+	32.1463i	0.266695	+	0.110469i
$292$		0			0
$293$	302.622	+	302.622i	1.03284	+	1.03284i	0.999442	+	0.0333983i	$0.0106330\pi$
$293$	302.622	+	302.622i	1.03284	+	1.03284i	0.0333983	+	0.999442i	$0.489367\pi$
$294$		0			0
$295$	−81.0533	−	16.1225i	−0.274757	−	0.0546526i
$296$		0			0
$297$	−66.1526	−	159.707i	−0.222736	−	0.537732i
$298$		0			0
$299$	−229.510	+	153.354i	−0.767593	+	0.512889i
$300$		0			0
$301$	327.139	+	218.587i	1.08684	+	0.726203i
$302$		0			0
$303$	−11.8033	−	59.3392i	−0.0389548	−	0.195839i
$304$		0			0
$305$			853.801i			2.79935i
$306$		0			0
$307$	−50.7050			−0.165163			−0.0825815	−	0.996584i	$-0.526316\pi$
$307$	−50.7050			−0.165163			−0.0825815	+	0.996584i	$0.526316\pi$
$308$		0			0
$309$	76.2256	−	15.1622i	0.246685	−	0.0490687i
$310$		0			0
$311$	−49.8835	+	74.6559i	−0.160397	+	0.240051i	−0.902960	−	0.429726i	$-0.858610\pi$
$311$	−49.8835	+	74.6559i	−0.160397	+	0.240051i	0.742562	+	0.669777i	$0.233610\pi$
$312$		0			0
$313$	−234.155	−	350.437i	−0.748098	−	1.11961i	−0.988835	−	0.149017i	$-0.952389\pi$
$313$	−234.155	−	350.437i	−0.748098	−	1.11961i	0.240737	−	0.970590i	$-0.422611\pi$
$314$		0			0
$315$	475.823	−	197.092i	1.51055	−	0.625690i
$316$		0			0
$317$	53.1677	−	267.292i	0.167721	−	0.843192i	−0.801688	−	0.597743i	$-0.796064\pi$
$317$	53.1677	−	267.292i	0.167721	−	0.843192i	0.969409	−	0.245449i	$-0.0789355\pi$
$318$		0			0
$319$	−160.415	+	160.415i	−0.502867	+	0.502867i
$320$		0			0
$321$	−24.4659	+	59.0660i	−0.0762179	+	0.184006i
$322$		0			0
$323$	370.414	+	68.6232i	1.14679	+	0.212456i
$324$		0			0
$325$	−481.173	−	199.308i	−1.48053	−	0.613256i
$326$		0			0
$327$	39.1017	+	39.1017i	0.119577	+	0.119577i
$328$		0			0
$329$	−293.380	−	58.3569i	−0.891732	−	0.177376i
$330$		0			0
$331$	−14.8057	−	35.7440i	−0.0447301	−	0.107988i	0.899935	−	0.436023i	$-0.143613\pi$
$331$	−14.8057	−	35.7440i	−0.0447301	−	0.107988i	−0.944665	+	0.328035i	$0.893613\pi$
$332$		0			0
$333$	−259.145	+	173.155i	−0.778212	+	0.519985i
$334$		0			0
$335$	−11.6730	−	7.79963i	−0.0348447	−	0.0232825i
$336$		0			0
$337$	94.8348	+	476.767i	0.281409	+	1.41474i	0.820093	+	0.572230i	$0.193922\pi$
$337$	94.8348	+	476.767i	0.281409	+	1.41474i	−0.538684	+	0.842508i	$0.681078\pi$
$338$		0			0
$339$		−	75.9710i		−	0.224103i
$340$		0			0
$341$	−433.526			−1.27134
$342$		0			0
$343$	−137.016	+	27.2542i	−0.399464	+	0.0794584i
$344$		0			0
$345$	−126.323	+	189.055i	−0.366153	+	0.547986i
$346$		0			0
$347$	112.707	+	168.679i	0.324805	+	0.486105i	0.957555	−	0.288251i	$-0.0930738\pi$
$347$	112.707	+	168.679i	0.324805	+	0.486105i	−0.632750	+	0.774356i	$0.718074\pi$
$348$		0			0
$349$	−443.560	+	183.729i	−1.27095	+	0.526443i	−0.913252	−	0.407395i	$-0.866437\pi$
$349$	−443.560	+	183.729i	−1.27095	+	0.526443i	−0.357695	+	0.933839i	$0.616437\pi$
$350$		0			0
$351$	−58.1499	+	292.339i	−0.165669	+	0.832875i
$352$		0			0
$353$	−8.69522	+	8.69522i	−0.0246324	+	0.0246324i	−0.719316	−	0.694683i	$-0.755545\pi$
$353$	−8.69522	+	8.69522i	−0.0246324	+	0.0246324i	0.694683	+	0.719316i	$0.255545\pi$
$354$		0			0
$355$	67.5622	−	163.110i	0.190316	−	0.459464i
$356$		0			0
$357$	−179.105	−	116.293i	−0.501695	−	0.325751i
$358$		0			0
$359$	−363.078	−	150.392i	−1.01136	−	0.418918i	−0.185408	−	0.982662i	$-0.559361\pi$
$359$	−363.078	−	150.392i	−1.01136	−	0.418918i	−0.825950	+	0.563743i	$0.809361\pi$
$360$		0			0
$361$	91.9641	+	91.9641i	0.254748	+	0.254748i
$362$		0			0
$363$	82.0771	+	16.3262i	0.226108	+	0.0449756i
$364$		0			0
$365$	357.350	+	862.718i	0.979040	+	2.36361i
$366$		0			0
$367$	463.788	−	309.893i	1.26373	−	0.844395i	0.270743	−	0.962652i	$-0.412730\pi$
$367$	463.788	−	309.893i	1.26373	−	0.844395i	0.992983	+	0.118256i	$0.0377305\pi$
$368$		0			0
$369$	−96.2721	−	64.3269i	−0.260900	−	0.174328i
$370$		0			0
$371$	102.199	+	513.790i	0.275470	+	1.38488i
$372$		0			0
$373$		−	201.550i		−	0.540348i	−0.962812	−	0.270174i	$-0.912919\pi$
$373$		−	201.550i		−	0.540348i	0.962812	−	0.270174i	$-0.0870812\pi$
$374$		0			0
$375$	−152.957			−0.407885
$376$		0			0
$377$	383.653	−	76.3134i	1.01765	−	0.202423i
$378$		0			0
$379$	−29.6295	+	44.3437i	−0.0781781	+	0.117002i	−0.868498	−	0.495692i	$-0.834914\pi$
$379$	−29.6295	+	44.3437i	−0.0781781	+	0.117002i	0.790320	+	0.612694i	$0.209914\pi$
$380$		0			0
$381$	56.0358	+	83.8635i	0.147076	+	0.220114i
$382$		0			0
$383$	−21.3817	+	8.85658i	−0.0558268	+	0.0231242i	−0.410422	−	0.911896i	$-0.634619\pi$
$383$	−21.3817	+	8.85658i	−0.0558268	+	0.0231242i	0.354595	+	0.935020i	$0.384619\pi$
$384$		0			0
$385$	110.170	−	553.863i	0.286156	−	1.43860i
$386$		0			0
$387$	217.003	−	217.003i	0.560732	−	0.560732i
$388$		0			0
$389$	−1.66260	+	4.01388i	−0.00427405	+	0.0103185i	−0.926002	−	0.377518i	$-0.876778\pi$
$389$	−1.66260	+	4.01388i	−0.00427405	+	0.0103185i	0.921728	+	0.387837i	$0.126778\pi$
$390$		0			0
$391$	−350.020	+	4.60839i	−0.895193	+	0.0117862i
$392$		0			0
$393$	−36.7036	−	15.2031i	−0.0933933	−	0.0386848i
$394$		0			0
$395$	−213.296	−	213.296i	−0.539989	−	0.539989i
$396$		0			0
$397$	180.832	+	35.9697i	0.455496	+	0.0906038i	0.417506	−	0.908674i	$-0.362904\pi$
$397$	180.832	+	35.9697i	0.455496	+	0.0906038i	0.0379904	+	0.999278i	$0.487904\pi$
$398$		0			0
$399$	−106.525	−	257.174i	−0.266980	−	0.644548i
$400$		0			0
$401$	170.178	−	113.709i	0.424383	−	0.283564i	−0.324982	−	0.945720i	$-0.605358\pi$
$401$	170.178	−	113.709i	0.424383	−	0.283564i	0.749366	+	0.662156i	$0.230358\pi$
$402$		0			0
$403$	621.538	+	415.298i	1.54228	+	1.03052i
$404$		0			0
$405$	−51.5798	−	259.309i	−0.127357	−	0.640269i
$406$		0			0
$407$			341.738i			0.839652i
$408$		0			0
$409$	551.929			1.34946			0.674730	−	0.738065i	$-0.264260\pi$
$409$	551.929			1.34946			0.674730	+	0.738065i	$0.264260\pi$
$410$		0			0
$411$	−107.596	+	21.4022i	−0.261792	+	0.0520736i
$412$		0			0
$413$	−52.2303	+	78.1682i	−0.126466	+	0.189269i
$414$		0			0
$415$	−680.371	−	1018.25i	−1.63945	−	2.45361i
$416$		0			0
$417$	7.72611	−	3.20026i	0.0185278	−	0.00767448i
$418$		0			0
$419$	−101.019	+	507.855i	−0.241095	+	1.21206i	0.650598	+	0.759423i	$0.274518\pi$
$419$	−101.019	+	507.855i	−0.241095	+	1.21206i	−0.891692	+	0.452642i	$0.850482\pi$
$420$		0			0
$421$	186.228	−	186.228i	0.442348	−	0.442348i	−0.450453	−	0.892800i	$-0.648737\pi$
$421$	186.228	−	186.228i	0.442348	−	0.442348i	0.892800	+	0.450453i	$0.148737\pi$
$422$		0			0
$423$	−89.2878	+	215.560i	−0.211082	+	0.509598i
$424$		0			0
$425$	−374.142	−	544.292i	−0.880334	−	1.28069i
$426$		0			0
$427$	897.343	+	371.692i	2.10151	+	0.870472i
$428$		0			0
$429$	101.836	+	101.836i	0.237379	+	0.237379i
$430$		0			0
$431$	−147.366	−	29.3130i	−0.341917	−	0.0680115i	0.0211453	−	0.999776i	$-0.493269\pi$
$431$	−147.366	−	29.3130i	−0.341917	−	0.0680115i	−0.363062	+	0.931765i	$0.618269\pi$
$432$		0			0
$433$	−41.5485	−	100.307i	−0.0959550	−	0.231656i	0.868613	−	0.495492i	$-0.165012\pi$
$433$	−41.5485	−	100.307i	−0.0959550	−	0.231656i	−0.964568	+	0.263836i	$0.915012\pi$
$434$		0			0
$435$	267.916	−	179.015i	0.615898	−	0.411530i
$436$		0			0
$437$	−379.397	−	253.505i	−0.868186	−	0.580104i
$438$		0			0
$439$	−119.772	−	602.135i	−0.272829	−	1.37161i	−0.837566	−	0.546335i	$-0.816022\pi$
$439$	−119.772	−	602.135i	−0.272829	−	1.37161i	0.564737	−	0.825271i	$-0.308978\pi$
$440$		0			0
$441$		−	238.462i		−	0.540730i
$442$		0			0
$443$	−450.347			−1.01659			−0.508293	−	0.861184i	$-0.669723\pi$
$443$	−450.347			−1.01659			−0.508293	+	0.861184i	$0.669723\pi$
$444$		0			0
$445$	273.268	−	54.3563i	0.614084	−	0.122149i
$446$		0			0
$447$	−123.344	+	184.598i	−0.275938	+	0.412970i
$448$		0			0
$449$	462.298	+	691.878i	1.02962	+	1.54093i	0.827417	+	0.561588i	$0.189809\pi$
$449$	462.298	+	691.878i	1.02962	+	1.54093i	0.202200	+	0.979344i	$0.435191\pi$
$450$		0			0
$451$	−117.292	+	48.5838i	−0.260070	+	0.107725i
$452$		0			0
$453$	52.9407	−	266.151i	0.116867	−	0.587529i
$454$		0			0
$455$	−688.524	+	688.524i	−1.51324	+	1.51324i
$456$		0			0
$457$	−10.6885	+	25.8043i	−0.0233884	+	0.0564645i	−0.935142	−	0.354272i	$-0.884729\pi$
$457$	−10.6885	+	25.8043i	−0.0233884	+	0.0564645i	0.911754	+	0.410737i	$0.134729\pi$
$458$		0			0
$459$	−263.742	+	270.780i	−0.574602	+	0.589935i
$460$		0			0
$461$	−490.861	−	203.321i	−1.06477	−	0.441044i	−0.219630	−	0.975583i	$-0.570485\pi$
$461$	−490.861	−	203.321i	−1.06477	−	0.441044i	−0.845144	+	0.534539i	$0.820485\pi$
$462$		0			0
$463$	100.715	+	100.715i	0.217528	+	0.217528i	0.807456	−	0.589928i	$-0.200844\pi$
$463$	100.715	+	100.715i	0.217528	+	0.217528i	−0.589928	+	0.807456i	$0.700844\pi$
$464$		0			0
$465$	603.923	+	120.128i	1.29876	+	0.258339i
$466$		0			0
$467$	−129.160	−	311.819i	−0.276573	−	0.667707i	0.723163	−	0.690677i	$-0.242688\pi$
$467$	−129.160	−	311.819i	−0.276573	−	0.667707i	−0.999736	+	0.0229707i	$0.992688\pi$
$468$		0			0
$469$	−13.2791	+	8.87280i	−0.0283136	+	0.0189185i
$470$		0			0
$471$	182.982	+	122.265i	0.388496	+	0.259585i
$472$		0			0
$473$	−65.6471	−	330.030i	−0.138789	−	0.697738i
$474$		0			0
$475$		−	860.950i		−	1.81253i
$476$		0			0
$477$	408.609			0.856623
$478$		0			0
$479$	302.340	−	60.1392i	0.631190	−	0.125551i	0.130881	−	0.991398i	$-0.458220\pi$
$479$	302.340	−	60.1392i	0.631190	−	0.125551i	0.500309	+	0.865847i	$0.333220\pi$
$480$		0			0
$481$	327.370	−	489.944i	0.680603	−	1.01859i
$482$		0			0
$483$	143.704	+	215.068i	0.297523	+	0.445275i
$484$		0			0
$485$	448.767	−	185.885i	0.925293	−	0.383269i
$486$		0			0
$487$	0.404333	−	2.03272i	0.000830252	−	0.00417396i	−0.980368	−	0.197177i	$-0.936823\pi$
$487$	0.404333	−	2.03272i	0.000830252	−	0.00417396i	0.981198	+	0.193003i	$0.0618227\pi$
$488$		0			0
$489$	−265.149	+	265.149i	−0.542227	+	0.542227i
$490$		0			0
$491$	179.338	−	432.961i	0.365251	−	0.881794i	−0.629263	−	0.777192i	$-0.716643\pi$
$491$	179.338	−	432.961i	0.365251	−	0.881794i	0.994514	−	0.104602i	$-0.0333567\pi$
$492$		0			0
$493$	460.766	+	183.787i	0.934616	+	0.372792i
$494$		0			0
$495$	−406.949	−	168.564i	−0.822118	−	0.340533i
$496$		0			0
$497$	−142.016	−	142.016i	−0.285746	−	0.285746i
$498$		0			0
$499$	−512.640	−	101.970i	−1.02734	−	0.204350i	−0.347473	−	0.937690i	$-0.612960\pi$
$499$	−512.640	−	101.970i	−1.02734	−	0.204350i	−0.679862	+	0.733340i	$0.737960\pi$
$500$		0			0
$501$	−174.050	−	420.194i	−0.347405	−	0.838710i
$502$		0			0
$503$	596.413	−	398.511i	1.18571	−	0.792268i	0.203323	−	0.979112i	$-0.434826\pi$
$503$	596.413	−	398.511i	1.18571	−	0.792268i	0.982390	+	0.186844i	$0.0598258\pi$
$504$		0			0
$505$	−290.889	−	194.366i	−0.576018	−	0.384883i
$506$		0			0
$507$	−2.88456	−	14.5017i	−0.00568948	−	0.0286029i
$508$		0			0
$509$		−	408.699i		−	0.802945i	−0.915871	−	0.401473i	$-0.868498\pi$
$509$		−	408.699i		−	0.802945i	0.915871	−	0.401473i	$-0.131502\pi$
$510$		0			0
$511$	1062.28			2.07883
$512$		0			0
$513$	−483.258	+	96.1261i	−0.942024	+	0.187380i
$514$		0			0
$515$	249.678	−	373.669i	0.484811	−	0.725571i
$516$		0			0
$517$	142.131	+	212.714i	0.274915	+	0.411440i
$518$		0			0
$519$	−197.052	+	81.6215i	−0.379676	+	0.157267i
$520$		0			0
$521$	−10.7213	+	53.8997i	−0.0205783	+	0.103454i	−0.989709	−	0.143092i	$-0.954296\pi$
$521$	−10.7213	+	53.8997i	−0.0205783	+	0.103454i	0.969131	+	0.246546i	$0.0792956\pi$
$522$		0			0
$523$	−574.315	+	574.315i	−1.09812	+	1.09812i	−0.103486	+	0.994631i	$0.533000\pi$
$523$	−574.315	+	574.315i	−1.09812	+	1.09812i	−0.994631	+	0.103486i	$0.967000\pi$
$524$		0			0
$525$	−186.766	+	450.894i	−0.355745	+	0.858845i
$526$		0			0
$527$	374.273	+	870.962i	0.710195	+	1.65268i
$528$		0			0
$529$	−97.0087	−	40.1823i	−0.183381	−	0.0759590i
$530$		0			0
$531$	51.8519	+	51.8519i	0.0976496	+	0.0976496i
$532$		0			0
$533$	214.700	+	42.7065i	0.402814	+	0.0801247i
$534$		0			0
$535$	141.474	+	341.548i	0.264437	+	0.638407i
$536$		0			0
$537$	−280.718	+	187.569i	−0.522751	+	0.349291i
$538$		0			0
$539$	−217.402	−	145.263i	−0.403343	−	0.269505i
$540$		0			0
$541$	−10.2219	−	51.3889i	−0.0188944	−	0.0949888i	0.970187	−	0.242356i	$-0.0779201\pi$
$541$	−10.2219	−	51.3889i	−0.0188944	−	0.0949888i	−0.989082	+	0.147367i	$0.952920\pi$
$542$		0			0
$543$		−	45.2413i		−	0.0833173i
$544$		0			0
$545$	319.760			0.586716
$546$		0			0
$547$	−252.841	+	50.2933i	−0.462233	+	0.0919438i	−0.420713	−	0.907194i	$-0.638220\pi$
$547$	−252.841	+	50.2933i	−0.462233	+	0.0919438i	−0.0415199	+	0.999138i	$0.513220\pi$
$548$		0			0
$549$	420.899	−	629.920i	0.766666	−	1.14740i
$550$		0			0
$551$	359.250	+	537.655i	0.651996	+	0.975780i
$552$		0			0
$553$	−317.029	+	131.318i	−0.573290	+	0.237464i
$554$		0			0
$555$	94.6939	−	476.058i	0.170620	−	0.857762i
$556$		0			0
$557$	110.815	−	110.815i	0.198951	−	0.198951i	−0.600599	−	0.799550i	$-0.705071\pi$
$557$	110.815	−	110.815i	0.198951	−	0.198951i	0.799550	+	0.600599i	$0.205071\pi$
$558$		0			0
$559$	−222.037	+	536.044i	−0.397204	+	0.958935i
$560$		0			0
$561$	37.9859	+	178.644i	0.0677111	+	0.318438i
$562$		0			0
$563$	−0.597777	−	0.247607i	−0.00106177	−	0.000439800i	0.382152	−	0.924099i	$-0.375183\pi$
$563$	−0.597777	−	0.247607i	−0.00106177	−	0.000439800i	−0.383214	+	0.923659i	$0.625183\pi$
$564$		0			0
$565$	−310.632	−	310.632i	−0.549791	−	0.549791i
$566$		0			0
$567$	−294.988	−	58.6768i	−0.520261	−	0.103486i
$568$		0			0
$569$	352.633	+	851.331i	0.619741	+	1.49619i	0.852005	+	0.523534i	$0.175387\pi$
$569$	352.633	+	851.331i	0.619741	+	1.49619i	−0.232264	+	0.972653i	$0.574613\pi$
$570$		0			0
$571$	−281.247	+	187.923i	−0.492551	+	0.329112i	−0.776916	−	0.629604i	$-0.783217\pi$
$571$	−281.247	+	187.923i	−0.492551	+	0.329112i	0.284365	+	0.958716i	$0.408217\pi$
$572$		0			0
$573$	−309.376	−	206.718i	−0.539923	−	0.360765i
$574$		0			0
$575$	156.074	+	784.636i	0.271433	+	1.36458i
$576$		0			0
$577$		−	406.466i		−	0.704447i	−0.935916	−	0.352224i	$-0.885426\pi$
$577$		−	406.466i		−	0.704447i	0.935916	−	0.352224i	$-0.114574\pi$
$578$		0			0
$579$	−127.405			−0.220044
$580$		0			0
$581$	−1366.37	+	271.787i	−2.35175	+	0.467793i
$582$		0			0
$583$	248.912	−	372.523i	0.426950	−	0.638975i
$584$		0			0
$585$	421.958	+	631.505i	0.721296	+	1.07950i
$586$		0			0
$587$	−678.270	+	280.949i	−1.15549	+	0.478618i	−0.876369	−	0.481640i	$-0.840041\pi$
$587$	−678.270	+	280.949i	−1.15549	+	0.478618i	−0.279116	+	0.960257i	$0.590041\pi$
$588$		0			0
$589$	−241.073	+	1211.96i	−0.409293	+	2.05765i
$590$		0			0
$591$	−63.3252	+	63.3252i	−0.107149	+	0.107149i
$592$		0			0
$593$	−152.212	+	367.473i	−0.256682	+	0.619685i	−0.998715	−	0.0506783i	$-0.983862\pi$
$593$	−152.212	+	367.473i	−0.256682	+	0.619685i	0.742033	+	0.670363i	$0.233862\pi$
$594$		0			0
$595$	−1207.83	+	256.828i	−2.02997	+	0.431643i
$596$		0			0
$597$	372.802	+	154.420i	0.624459	+	0.258659i
$598$		0			0
$599$	42.3035	+	42.3035i	0.0706236	+	0.0706236i	0.741536	−	0.670913i	$-0.234097\pi$
$599$	42.3035	+	42.3035i	0.0706236	+	0.0706236i	−0.670913	+	0.741536i	$0.734097\pi$
$600$		0			0
$601$	−313.788	−	62.4164i	−0.522110	−	0.103854i	−0.0730025	−	0.997332i	$-0.523258\pi$
$601$	−313.788	−	62.4164i	−0.522110	−	0.103854i	−0.449108	+	0.893478i	$0.648258\pi$
$602$		0			0
$603$	4.76713	+	11.5089i	0.00790569	+	0.0190860i
$604$		0			0
$605$	402.354	−	268.844i	0.665048	−	0.444371i
$606$		0			0
$607$	−904.433	−	604.323i	−1.49001	−	0.995590i	−0.991698	−	0.128589i	$-0.958955\pi$
$607$	−904.433	−	604.323i	−1.49001	−	0.995590i	−0.498307	−	0.867001i	$-0.666045\pi$
$608$		0			0
$609$	−71.5112	−	359.511i	−0.117424	−	0.590330i
$610$		0			0
$611$		−	441.120i		−	0.721963i
$612$		0			0
$613$	−55.3418			−0.0902803			−0.0451402	−	0.998981i	$-0.514373\pi$
$613$	−55.3418			−0.0902803			−0.0451402	+	0.998981i	$0.514373\pi$
$614$		0			0
$615$	176.855	−	35.1787i	0.287570	−	0.0572012i
$616$		0			0
$617$	−78.2957	+	117.178i	−0.126897	+	0.189915i	−0.889478	−	0.456978i	$-0.848932\pi$
$617$	−78.2957	+	117.178i	−0.126897	+	0.189915i	0.762581	+	0.646893i	$0.223932\pi$
$618$		0			0
$619$	67.3147	+	100.744i	0.108747	+	0.162752i	0.881852	−	0.471527i	$-0.156297\pi$
$619$	67.3147	+	100.744i	0.108747	+	0.162752i	−0.773104	+	0.634279i	$0.781297\pi$
$620$		0			0
$621$	422.997	−	175.211i	0.681154	−	0.282143i
$622$		0			0
$623$	61.8353	−	310.867i	0.0992541	−	0.498984i
$624$		0			0
$625$	61.3970	−	61.3970i	0.0982351	−	0.0982351i
$626$		0			0
$627$	−91.1059	+	219.949i	−0.145304	+	0.350796i
$628$		0			0
$629$	686.559	−	295.030i	1.09151	−	0.469046i
$630$		0			0
$631$	880.276	+	364.622i	1.39505	+	0.577849i	0.948462	−	0.316891i	$-0.102639\pi$
$631$	880.276	+	364.622i	1.39505	+	0.577849i	0.446588	+	0.894740i	$0.352639\pi$
$632$		0			0
$633$	84.4957	+	84.4957i	0.133484	+	0.133484i
$634$		0			0
$635$	572.024	+	113.783i	0.900825	+	0.179185i
$636$		0			0
$637$	172.529	+	416.522i	0.270847	+	0.653881i
$638$		0			0
$639$	−130.255	+	87.0334i	−0.203842	+	0.136203i
$640$		0			0
$641$	296.261	+	197.955i	0.462186	+	0.308823i	0.764774	−	0.644299i	$-0.222851\pi$
$641$	296.261	+	197.955i	0.462186	+	0.308823i	−0.302588	+	0.953121i	$0.597851\pi$
$642$		0			0
$643$	148.006	+	744.076i	0.230180	+	1.15719i	0.907028	+	0.421071i	$0.138346\pi$
$643$	148.006	+	744.076i	0.230180	+	1.15719i	−0.676847	+	0.736123i	$0.736654\pi$
$644$		0			0
$645$			477.938i			0.740990i
$646$		0			0
$647$	593.058			0.916628			0.458314	−	0.888790i	$-0.348454\pi$
$647$	593.058			0.916628			0.458314	+	0.888790i	$0.348454\pi$
$648$		0			0
$649$	78.8591	−	15.6861i	0.121509	−	0.0241696i
$650$		0			0
$651$	389.164	−	582.426i	0.597795	−	0.894663i
$652$		0			0
$653$	25.7736	+	38.5730i	0.0394696	+	0.0590704i	0.850680	−	0.525684i	$-0.176191\pi$
$653$	25.7736	+	38.5730i	0.0394696	+	0.0590704i	−0.811210	+	0.584755i	$0.801191\pi$
$654$		0			0
$655$	−212.237	+	87.9116i	−0.324027	+	0.134216i
$656$		0			0
$657$	161.649	−	812.663i	0.246041	−	1.23693i
$658$		0			0
$659$	534.227	−	534.227i	0.810663	−	0.810663i	−0.174070	−	0.984733i	$-0.555692\pi$
$659$	534.227	−	534.227i	0.810663	−	0.810663i	0.984733	+	0.174070i	$0.0556921\pi$
$660$		0			0
$661$	−291.059	+	702.677i	−0.440331	+	1.06305i	0.535502	+	0.844534i	$0.320122\pi$
$661$	−291.059	+	702.677i	−0.440331	+	1.06305i	−0.975833	+	0.218518i	$0.929878\pi$
$662$		0			0
$663$	116.673	−	292.507i	0.175977	−	0.441186i
$664$		0			0
$665$	−1487.10	−	615.979i	−2.23625	−	0.926284i
$666$		0			0
$667$	−424.873	−	424.873i	−0.636990	−	0.636990i
$668$		0			0
$669$	111.871	+	22.2525i	0.167221	+	0.0332623i
$670$		0			0
$671$	−317.890	−	767.455i	−0.473756	−	1.14375i
$672$		0			0
$673$	−271.228	+	181.229i	−0.403013	+	0.269285i	−0.740515	−	0.672040i	$-0.765418\pi$
$673$	−271.228	+	181.229i	−0.403013	+	0.269285i	0.337501	+	0.941325i	$0.390418\pi$
$674$		0			0
$675$	718.287	+	479.944i	1.06413	+	0.711028i
$676$		0			0
$677$	171.587	+	862.624i	0.253451	+	1.27419i	0.872415	+	0.488766i	$0.162553\pi$
$677$	171.587	+	862.624i	0.253451	+	1.27419i	−0.618963	+	0.785420i	$0.712447\pi$
$678$		0			0
$679$		−	552.576i		−	0.813809i
$680$		0			0
$681$	425.323			0.624557
$682$		0			0
$683$	465.145	−	92.5230i	0.681032	−	0.135466i	0.157561	−	0.987509i	$-0.449637\pi$
$683$	465.145	−	92.5230i	0.681032	−	0.135466i	0.523471	+	0.852044i	$0.324637\pi$
$684$		0			0
$685$	−352.433	+	527.453i	−0.514500	+	0.770004i
$686$		0			0
$687$	−288.748	−	432.142i	−0.420303	−	0.629028i
$688$		0			0
$689$	−713.720	+	295.632i	−1.03588	+	0.429075i
$690$		0			0
$691$	52.1150	−	262.000i	0.0754197	−	0.379160i	−0.924579	−	0.380991i	$-0.875583\pi$
$691$	52.1150	−	262.000i	0.0754197	−	0.379160i	0.999998	+	0.00183097i	$0.000582816\pi$
$692$		0			0
$693$	−354.320	+	354.320i	−0.511284	+	0.511284i
$694$		0			0
$695$	18.5054	−	44.6760i	0.0266265	−	0.0642820i
$696$		0			0
$697$	198.866	+	193.698i	0.285318	+	0.277902i
$698$		0			0
$699$	−453.671	−	187.917i	−0.649029	−	0.268837i
$700$		0			0
$701$	−4.60616	−	4.60616i	−0.00657085	−	0.00657085i	0.703814	−	0.710385i	$-0.251479\pi$
$701$	−4.60616	−	4.60616i	−0.00657085	−	0.00657085i	−0.710385	+	0.703814i	$0.751479\pi$
$702$		0			0
$703$	955.357	+	190.032i	1.35897	+	0.270316i
$704$		0			0
$705$	−139.054	−	335.705i	−0.197239	−	0.476178i
$706$		0			0
$707$	−330.913	+	221.109i	−0.468053	+	0.312743i
$708$		0			0
$709$	−650.630	−	434.737i	−0.917673	−	0.613170i	0.00448201	−	0.999990i	$-0.498573\pi$
$709$	−650.630	−	434.737i	−0.917673	−	0.613170i	−0.922155	+	0.386820i	$0.873573\pi$
$710$		0			0
$711$	52.2175	+	262.515i	0.0734423	+	0.369219i
$712$		0			0
$713$		−	1148.23i		−	1.61042i
$714$		0			0
$715$	832.776			1.16472
$716$		0			0
$717$	−542.733	+	107.956i	−0.756950	+	0.150567i
$718$		0			0
$719$	680.410	−	1018.31i	0.946329	−	1.41628i	0.0374139	−	0.999300i	$-0.488088\pi$
$719$	680.410	−	1018.31i	0.946329	−	1.41628i	0.908915	−	0.416981i	$-0.136912\pi$
$720$		0			0
$721$	−284.031	−	425.083i	−0.393941	−	0.589574i
$722$		0			0
$723$	−366.305	+	151.728i	−0.506645	+	0.209859i
$724$		0			0
$725$	221.177	−	1111.93i	0.305071	−	1.53370i
$726$		0			0
$727$	337.565	−	337.565i	0.464326	−	0.464326i	−0.435745	−	0.900070i	$-0.643515\pi$
$727$	337.565	−	337.565i	0.464326	−	0.464326i	0.900070	+	0.435745i	$0.143515\pi$
$728$		0			0
$729$	16.0494	−	38.7467i	0.0220156	−	0.0531504i
$730$		0			0
$731$	−606.362	+	416.808i	−0.829497	+	0.570189i
$732$		0			0
$733$	−1259.33	−	521.632i	−1.71805	−	0.711640i	−0.999876	−	0.0157780i	$-0.994977\pi$
$733$	−1259.33	−	521.632i	−1.71805	−	0.711640i	−0.718176	−	0.695862i	$-0.755023\pi$
$734$		0			0
$735$	262.600	+	262.600i	0.357279	+	0.357279i
$736$		0			0
$737$	13.3964	+	2.66472i	0.0181770	+	0.00361563i
$738$		0			0
$739$	123.313	+	297.704i	0.166865	+	0.402847i	0.985087	−	0.172054i	$-0.0550405\pi$
$739$	123.313	+	297.704i	0.166865	+	0.402847i	−0.818223	+	0.574901i	$0.805040\pi$
$740$		0			0
$741$	341.318	−	228.061i	0.460618	−	0.307775i
$742$		0			0
$743$	−353.612	−	236.276i	−0.475925	−	0.318003i	0.294369	−	0.955692i	$-0.404891\pi$
$743$	−353.612	−	236.276i	−0.475925	−	0.318003i	−0.770294	+	0.637689i	$0.779891\pi$
$744$		0			0
$745$	250.455	+	1259.12i	0.336181	+	1.69009i
$746$		0			0
$747$			1086.65i			1.45469i
$748$		0			0
$749$	420.555			0.561488
$750$		0			0
$751$	878.270	−	174.699i	1.16947	−	0.232622i	0.428107	−	0.903728i	$-0.359181\pi$
$751$	878.270	−	174.699i	1.16947	−	0.232622i	0.741361	+	0.671107i	$0.234181\pi$
$752$		0			0
$753$	237.481	−	355.415i	0.315379	−	0.471999i
$754$		0			0
$755$	−871.779	−	1304.71i	−1.15467	−	1.72809i
$756$		0			0
$757$	612.760	−	253.814i	0.809459	−	0.335289i	0.0607206	−	0.998155i	$-0.480660\pi$
$757$	612.760	−	253.814i	0.809459	−	0.335289i	0.748738	+	0.662866i	$0.230660\pi$
$758$		0			0
$759$	43.1578	−	216.969i	0.0568613	−	0.285861i
$760$		0			0
$761$	158.270	−	158.270i	0.207977	−	0.207977i	−0.595430	−	0.803407i	$-0.703018\pi$
$761$	158.270	−	158.270i	0.207977	−	0.207977i	0.803407	+	0.595430i	$0.203018\pi$
$762$		0			0
$763$	139.204	−	336.067i	0.182443	−	0.440455i
$764$		0			0
$765$	12.6801	+	963.092i	0.0165753	+	1.25894i
$766$		0			0
$767$	−128.085	−	53.0547i	−0.166995	−	0.0691716i
$768$		0			0
$769$	753.621	+	753.621i	0.980001	+	0.980001i	0.999804	−	0.0198026i	$-0.00630378\pi$
$769$	753.621	+	753.621i	0.980001	+	0.980001i	−0.0198026	+	0.999804i	$0.506304\pi$
$770$		0			0
$771$	443.415	+	88.2007i	0.575116	+	0.114398i
$772$		0			0
$773$	−472.886	−	1141.65i	−0.611755	−	1.47691i	−0.861071	−	0.508485i	$-0.830206\pi$
$773$	−472.886	−	1141.65i	−0.611755	−	1.47691i	0.249316	−	0.968422i	$-0.419794\pi$
$774$		0			0
$775$	1801.38	−	1203.65i	2.32436	−	1.55309i
$776$		0			0
$777$	−459.112	−	306.769i	−0.590878	−	0.394812i
$778$		0			0
$779$	70.5969	+	354.915i	0.0906251	+	0.455603i
$780$		0			0
$781$			171.769i			0.219935i
$782$		0			0
$783$	−648.830			−0.828646
$784$		0			0
$785$	1248.10	−	248.262i	1.58994	−	0.316258i
$786$		0			0
$787$	−88.2459	+	132.069i	−0.112129	+	0.167814i	−0.883290	−	0.468827i	$-0.844677\pi$
$787$	−88.2459	+	132.069i	−0.112129	+	0.167814i	0.771160	+	0.636641i	$0.219677\pi$
$788$		0			0
$789$	39.6328	+	59.3147i	0.0502317	+	0.0751771i
$790$		0			0
$791$	−461.704	+	191.244i	−0.583696	+	0.241775i
$792$		0			0
$793$	−279.434	+	1404.81i	−0.352376	+	1.77151i
$794$		0			0
$795$	−449.970	+	449.970i	−0.566000	+	0.566000i
$796$		0			0
$797$	204.585	−	493.912i	0.256694	−	0.619714i	−0.742022	−	0.670375i	$-0.766133\pi$
$797$	204.585	−	493.912i	0.256694	−	0.619714i	0.998716	+	0.0506618i	$0.0161331\pi$
$798$		0			0
$799$	304.642	−	469.185i	0.381279	−	0.587216i
$800$		0			0
$801$	−228.409	−	94.6099i	−0.285154	−	0.118115i
$802$		0			0
$803$	−642.421	−	642.421i	−0.800026	−	0.800026i
$804$		0			0
$805$	1466.95	+	291.795i	1.82230	+	0.362479i
$806$		0			0
$807$	−0.268001	−	0.647010i	−0.000332095	−	0.000801748i
$808$		0			0
$809$	872.647	−	583.084i	1.07867	−	0.720747i	0.116502	−	0.993190i	$-0.462832\pi$
$809$	872.647	−	583.084i	1.07867	−	0.720747i	0.962172	+	0.272444i	$0.0878318\pi$
$810$		0			0
$811$	−368.955	−	246.528i	−0.454938	−	0.303980i	0.306906	−	0.951740i	$-0.400706\pi$
$811$	−368.955	−	246.528i	−0.454938	−	0.303980i	−0.761845	+	0.647760i	$0.775706\pi$
$812$		0			0
$813$	92.7874	+	466.474i	0.114130	+	0.573768i
$814$		0			0
$815$			2168.30i			2.66049i
$816$		0			0
$817$	−959.130			−1.17397
$818$		0			0
$819$	847.404	−	168.559i	1.03468	−	0.205811i
$820$		0			0
$821$	−233.302	+	349.161i	−0.284168	+	0.425288i	−0.945903	−	0.324450i	$-0.894821\pi$
$821$	−233.302	+	349.161i	−0.284168	+	0.425288i	0.661734	+	0.749738i	$0.269821\pi$
$822$		0			0
$823$	278.093	+	416.195i	0.337901	+	0.505705i	0.961041	−	0.276405i	$-0.0891432\pi$
$823$	278.093	+	416.195i	0.337901	+	0.505705i	−0.623140	+	0.782110i	$0.714143\pi$
$824$		0			0
$825$	385.628	−	159.732i	0.467428	−	0.193615i
$826$		0			0
$827$	62.7807	−	315.620i	0.0759138	−	0.381644i	−0.924086	−	0.382184i	$-0.875172\pi$
$827$	62.7807	−	315.620i	0.0759138	−	0.381644i	1.00000		0.000539997i	$0.000171886\pi$
$828$		0			0
$829$	786.907	−	786.907i	0.949225	−	0.949225i	−0.0495471	−	0.998772i	$-0.515778\pi$
$829$	786.907	−	786.907i	0.949225	−	0.949225i	0.998772	+	0.0495471i	$0.0157778\pi$
$830$		0			0
$831$	−160.439	+	387.333i	−0.193067	+	0.466105i
$832$		0			0
$833$	−104.149	+	562.174i	−0.125029	+	0.674878i
$834$		0			0
$835$	−2429.76	−	1006.44i	−2.90989	−	1.20532i
$836$		0			0
$837$	−876.743	−	876.743i	−1.04748	−	1.04748i
$838$		0			0
$839$	−1435.22	−	285.483i	−1.71063	−	0.340265i	−0.759842	−	0.650108i	$-0.774724\pi$
$839$	−1435.22	−	285.483i	−1.71063	−	0.340265i	−0.950788	+	0.309842i	$0.899724\pi$
$840$		0			0
$841$	4.01689	+	9.69764i	0.00477633	+	0.0115311i
$842$		0			0
$843$	−105.860	+	70.7331i	−0.125575	+	0.0839064i
$844$		0			0
$845$	−71.0893	−	47.5004i	−0.0841294	−	0.0562135i
$846$		0			0
$847$	−107.395	−	539.911i	−0.126795	−	0.637439i
$848$		0			0
$849$			404.207i			0.476097i
$850$		0			0
$851$	−905.124			−1.06360
$852$		0			0
$853$	486.833	−	96.8371i	0.570730	−	0.113525i	0.0987152	−	0.995116i	$-0.468527\pi$
$853$	486.833	−	96.8371i	0.570730	−	0.113525i	0.472015	+	0.881590i	$0.343527\pi$
$854$		0			0
$855$	−697.528	+	1043.92i	−0.815822	+	1.22096i
$856$		0			0
$857$	−519.998	−	778.232i	−0.606765	−	0.908088i	0.393170	−	0.919466i	$-0.371378\pi$
$857$	−519.998	−	778.232i	−0.606765	−	0.908088i	−0.999935	+	0.0113775i	$0.996378\pi$
$858$		0			0
$859$	70.6239	−	29.2534i	0.0822164	−	0.0340551i	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	70.6239	−	29.2534i	0.0822164	−	0.0340551i	0.423413	+	0.905937i	$0.360832\pi$
$860$		0			0
$861$	40.0190	−	201.189i	0.0464797	−	0.233669i
$862$		0			0
$863$	930.922	−	930.922i	1.07870	−	1.07870i	0.0820789	−	0.996626i	$-0.473844\pi$
$863$	930.922	−	930.922i	1.07870	−	1.07870i	0.996626	−	0.0820789i	$-0.0261560\pi$
$864$		0			0
$865$	−471.974	+	1139.45i	−0.545635	+	1.31728i
$866$		0			0
$867$	326.104	−	230.541i	0.376129	−	0.265907i
$868$		0			0
$869$	271.140	+	112.310i	0.312014	+	0.129240i
$870$		0			0
$871$	−16.6535	−	16.6535i	−0.0191200	−	0.0191200i
$872$		0			0
$873$	−422.729	−	84.0861i	−0.484226	−	0.0963185i
$874$		0			0
$875$	385.043	+	929.575i	0.440049	+	1.06237i
$876$		0			0
$877$	−207.701	+	138.781i	−0.236831	+	0.158245i	−0.668323	−	0.743872i	$-0.732987\pi$
$877$	−207.701	+	138.781i	−0.236831	+	0.158245i	0.431492	+	0.902117i	$0.357987\pi$
$878$		0			0
$879$	491.740	+	328.570i	0.559431	+	0.373800i
$880$		0			0
$881$	14.6556	+	73.6788i	0.0166352	+	0.0836309i	0.988211	−	0.153097i	$-0.0489249\pi$
$881$	14.6556	+	73.6788i	0.0166352	+	0.0836309i	−0.971576	+	0.236728i	$0.923925\pi$
$882$		0			0
$883$		−	177.030i		−	0.200487i	−0.994963	−	0.100243i	$-0.968038\pi$
$883$		−	177.030i		−	0.200487i	0.994963	−	0.100243i	$-0.0319622\pi$
$884$		0			0
$885$	−114.201			−0.129041
$886$		0			0
$887$	−316.759	+	63.0074i	−0.357113	+	0.0710342i	−0.370387	−	0.928878i	$-0.620775\pi$
$887$	−316.759	+	63.0074i	−0.357113	+	0.0710342i	0.0132734	+	0.999912i	$0.495775\pi$
$888$		0			0
$889$	368.609	−	551.662i	0.414633	−	0.620542i
$890$		0			0
$891$	142.910	+	213.880i	0.160393	+	0.240045i
$892$		0			0
$893$	673.696	−	279.054i	0.754419	−	0.312490i
$894$		0			0
$895$	−380.866	+	1914.74i	−0.425549	+	2.13938i
$896$		0			0
$897$	−269.721	+	269.721i	−0.300692	+	0.300692i
$898$		0			0
$899$	−622.700	+	1503.33i	−0.692658	+	1.67222i
$900$		0			0
$901$	−963.296	−	178.461i	−1.06914	−	0.198070i
$902$		0			0
$903$	502.312	+	208.065i	0.556271	+	0.230415i
$904$		0			0
$905$	−184.984	−	184.984i	−0.204402	−	0.204402i
$906$		0			0
$907$	1482.09	+	294.807i	1.63406	+	0.325035i	0.924958	−	0.380069i	$-0.124100\pi$
$907$	1482.09	+	294.807i	1.63406	+	0.325035i	0.709104	+	0.705104i	$0.249100\pi$
$908$		0			0
$909$	118.797	+	286.800i	0.130689	+	0.315512i
$910$		0			0
$911$	−538.289	+	359.673i	−0.590877	+	0.394812i	−0.814755	−	0.579806i	$-0.803128\pi$
$911$	−538.289	+	359.673i	−0.590877	+	0.394812i	0.223878	+	0.974617i	$0.428128\pi$
$912$		0			0
$913$	990.682	+	661.953i	1.08508	+	0.725030i
$914$		0			0
$915$	230.179	+	1157.19i	0.251562	+	1.26469i
$916$		0			0
$917$			261.332i			0.284986i
$918$		0			0
$919$	1518.30			1.65212			0.826060	−	0.563583i	$-0.190577\pi$
$919$	1518.30			1.65212			0.826060	+	0.563583i	$0.190577\pi$
$920$		0			0
$921$	−68.7224	+	13.6697i	−0.0746171	+	0.0148423i
$922$		0			0
$923$	164.547	−	246.262i	0.178274	−	0.266806i
$924$		0			0
$925$	−948.805	−	1419.99i	−1.02574	−	1.53512i
$926$		0			0
$927$	−368.416	+	152.603i	−0.397429	+	0.164620i
$928$		0			0
$929$	163.592	−	822.430i	0.176094	−	0.885286i	−0.787171	−	0.616735i	$-0.788455\pi$
$929$	163.592	−	822.430i	0.176094	−	0.885286i	0.963265	−	0.268551i	$-0.0865448\pi$
$930$		0			0
$931$	−526.987	+	526.987i	−0.566045	+	0.566045i
$932$		0			0
$933$	−47.4822	+	114.632i	−0.0508920	+	0.122864i
$934$		0			0
$935$	885.760	+	575.125i	0.947337	+	0.615106i
$936$		0			0
$937$	83.9296	+	34.7648i	0.0895726	+	0.0371022i	0.427020	−	0.904242i	$-0.359563\pi$
$937$	83.9296	+	34.7648i	0.0895726	+	0.0371022i	−0.337447	+	0.941344i	$0.609563\pi$
$938$		0			0
$939$	−411.834	−	411.834i	−0.438588	−	0.438588i
$940$		0			0
$941$	481.021	+	95.6810i	0.511180	+	0.101680i	0.443940	−	0.896057i	$-0.353580\pi$
$941$	481.021	+	95.6810i	0.511180	+	0.101680i	0.0672407	+	0.997737i	$0.478580\pi$
$942$		0			0
$943$	−128.679	−	310.657i	−0.136457	−	0.329435i
$944$		0			0
$945$	1342.91	−	897.302i	1.42107	−	0.949526i
$946$		0			0
$947$	−508.505	−	339.772i	−0.536964	−	0.358788i	0.257328	−	0.966324i	$-0.417158\pi$
$947$	−508.505	−	339.772i	−0.536964	−	0.358788i	−0.794292	+	0.607536i	$0.792158\pi$
$948$		0			0
$949$	305.616	+	1536.44i	0.322040	+	1.61901i
$950$		0			0
$951$		−	376.604i		−	0.396008i
$952$		0			0
$953$	725.282			0.761051			0.380526	−	0.924770i	$-0.375743\pi$
$953$	725.282			0.761051			0.380526	+	0.924770i	$0.375743\pi$
$954$		0			0
$955$	−2110.22	+	419.749i	−2.20965	+	0.439528i
$956$		0			0
$957$	−174.169	+	260.663i	−0.181995	+	0.272375i
$958$		0			0
$959$	400.925	+	600.026i	0.418065	+	0.625679i
$960$		0			0
$961$	−1984.98	+	822.208i	−2.06554	+	0.855575i
$962$		0			0
$963$	63.9962	−	321.731i	0.0664551	−	0.334092i
$964$		0			0
$965$	−520.938	+	520.938i	−0.539832	+	0.539832i
$966$		0			0
$967$	−201.132	+	485.576i	−0.207996	+	0.502147i	−0.993107	−	0.117208i	$-0.962606\pi$
$967$	−201.132	+	485.576i	−0.207996	+	0.502147i	0.785111	+	0.619355i	$0.212606\pi$
$968$		0			0
$969$	520.536	−	6.85340i	0.537188	−	0.00707265i
$970$		0			0
$971$	−871.427	−	360.957i	−0.897453	−	0.371737i	−0.114213	−	0.993456i	$-0.536435\pi$
$971$	−871.427	−	360.957i	−0.897453	−	0.371737i	−0.783240	+	0.621719i	$0.786435\pi$
$972$		0			0
$973$	−38.8983	−	38.8983i	−0.0399777	−	0.0399777i
$974$		0			0
$975$	−705.883	−	140.409i	−0.723983	−	0.144009i
$976$		0			0
$977$	−408.434	−	986.047i	−0.418049	−	1.00926i	−0.982912	−	0.184075i	$-0.941071\pi$
$977$	−408.434	−	986.047i	−0.418049	−	1.00926i	0.564863	−	0.825185i	$-0.308929\pi$
$978$		0			0
$979$	−225.393	+	150.603i	−0.230228	+	0.153834i
$980$		0			0
$981$	−235.914	−	157.633i	−0.240483	−	0.160686i
$982$		0			0
$983$	80.5543	+	404.974i	0.0819474	+	0.411977i	0.999884	+	0.0152496i	$0.00485429\pi$
$983$	80.5543	+	404.974i	0.0819474	+	0.411977i	−0.917936	+	0.396728i	$0.870146\pi$
$984$		0			0
$985$			517.851i			0.525737i
$986$		0			0
$987$	−413.361			−0.418805
$988$		0			0
$989$	874.114	−	173.872i	0.883836	−	0.175806i
$990$		0			0
$991$	192.974	−	288.806i	0.194727	−	0.291429i	−0.721238	−	0.692687i	$-0.756427\pi$
$991$	192.974	−	288.806i	0.194727	−	0.291429i	0.915965	+	0.401258i	$0.131427\pi$
$992$		0			0
$993$	−29.7030	−	44.4537i	−0.0299124	−	0.0447671i
$994$		0			0
$995$	2155.72	−	892.927i	2.16655	−	0.897414i
$996$		0			0
$997$	2.67703	−	13.4583i	0.00268509	−	0.0134988i	−0.979420	−	0.201835i	$-0.935309\pi$
$997$	2.67703	−	13.4583i	0.00268509	−	0.0134988i	0.982105	+	0.188336i	$0.0603095\pi$
$998$		0			0
$999$	−691.115	+	691.115i	−0.691807	+	0.691807i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.a.57.3	✓	32
4.3	odd	2		272.3.bh.f.193.2		32
17.3	odd	16	inner	136.3.t.a.105.3	yes	32
68.3	even	16		272.3.bh.f.241.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.a.57.3	✓	32	1.1	even	1	trivial
136.3.t.a.105.3	yes	32	17.3	odd	16	inner
272.3.bh.f.193.2		32	4.3	odd	2
272.3.bh.f.241.2		32	68.3	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)

\(f(q)\)	\(=\)	\(q+(1.35534 - 0.269593i) q^{3} +(4.43942 - 6.64406i) q^{5} +(-5.05024 - 7.55823i) q^{7} +(-6.55066 + 2.71337i) q^{9} +O(q^{10})\)	\(q+(1.35534 - 0.269593i) q^{3} +(4.43942 - 6.64406i) q^{5} +(-5.05024 - 7.55823i) q^{7} +(-6.55066 + 2.71337i) q^{9} +(-1.51671 + 7.62503i) q^{11} +(9.47892 - 9.47892i) q^{13} +(4.22571 - 10.2018i) q^{15} +(16.6282 - 3.53575i) q^{17} +(20.4730 + 8.48019i) q^{19} +(-8.88243 - 8.88243i) q^{21} +(-20.1956 - 4.01715i) q^{23} +(-14.8680 - 35.8945i) q^{25} +(-18.4878 + 12.3532i) q^{27} +(24.2626 + 16.2118i) q^{29} +(10.8789 + 54.6917i) q^{31} +10.7434i q^{33} -72.6374 q^{35} +(43.1122 - 8.57555i) q^{37} +(10.2917 - 15.4026i) q^{39} +(9.07242 + 13.5778i) q^{41} +(-39.9878 + 16.5635i) q^{43} +(-11.0533 + 55.5687i) q^{45} +(23.2685 - 23.2685i) q^{47} +(-12.8703 + 31.0717i) q^{49} +(21.5837 - 9.27499i) q^{51} +(-53.2419 - 22.0535i) q^{53} +(43.9278 + 43.9278i) q^{55} +(30.0340 + 5.97413i) q^{57} +(-3.95776 - 9.55489i) q^{59} +(-88.8415 + 59.3620i) q^{61} +(53.5907 + 35.8082i) q^{63} +(-20.8976 - 105.059i) q^{65} -1.75690i q^{67} -28.4548 q^{69} +(21.6696 - 4.31036i) q^{71} +(-64.9241 + 97.1658i) q^{73} +(-29.8280 - 44.6408i) q^{75} +(65.2915 - 27.0446i) q^{77} +(7.36455 - 37.0241i) q^{79} +(23.3960 - 23.3960i) q^{81} +(58.6489 - 141.591i) q^{83} +(50.3280 - 126.176i) q^{85} +(37.2546 + 15.4314i) q^{87} +(24.6554 + 24.6554i) q^{89} +(-119.515 - 23.7729i) q^{91} +(29.4890 + 71.1928i) q^{93} +(147.231 - 98.3766i) q^{95} +(50.5435 + 33.7721i) q^{97} +(-10.7541 - 54.0644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9	\( 32 q - 8 q^{3} + 8 q^{7} + 16 q^{9} - 24 q^{11} + 48 q^{13} + 96 q^{15} + 40 q^{19} - 80 q^{21} - 48 q^{23} + 112 q^{25} - 80 q^{27} + 56 q^{29} - 24 q^{31} - 96 q^{35} + 48 q^{37} - 72 q^{39} - 160 q^{41} + 112 q^{43} - 504 q^{45} + 48 q^{47} + 208 q^{49} - 400 q^{51} + 304 q^{53} - 368 q^{55} - 264 q^{57} + 192 q^{59} - 288 q^{61} + 56 q^{63} + 8 q^{65} + 32 q^{69} + 352 q^{71} - 184 q^{73} + 24 q^{75} + 688 q^{77} - 424 q^{79} + 312 q^{81} + 600 q^{83} - 512 q^{85} + 1336 q^{87} - 144 q^{89} - 24 q^{91} + 944 q^{93} - 256 q^{95} + 416 q^{97} + 128 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 8 * q^7 + 16 * q^9 - 24 * q^11 + 48 * q^13 + 96 * q^15 + 40 * q^19 - 80 * q^21 - 48 * q^23 + 112 * q^25 - 80 * q^27 + 56 * q^29 - 24 * q^31 - 96 * q^35 + 48 * q^37 - 72 * q^39 - 160 * q^41 + 112 * q^43 - 504 * q^45 + 48 * q^47 + 208 * q^49 - 400 * q^51 + 304 * q^53 - 368 * q^55 - 264 * q^57 + 192 * q^59 - 288 * q^61 + 56 * q^63 + 8 * q^65 + 32 * q^69 + 352 * q^71 - 184 * q^73 + 24 * q^75 + 688 * q^77 - 424 * q^79 + 312 * q^81 + 600 * q^83 - 512 * q^85 + 1336 * q^87 - 144 * q^89 - 24 * q^91 + 944 * q^93 - 256 * q^95 + 416 * q^97 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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