LMFDB - Embedded newform 208.3.bd.g.145.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [208,3,Mod(33,208)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("208.33"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(208, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 0, 11])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	208.bd (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,8,0,-2,0,36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.66758949869$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.44991500544.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 38x^{6} + 555x^{4} - 3674x^{2} + 9409 $ x^8 - 38x^6 + 555x^4 - 3674*x^2 + 9409
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.2
Root			$-3.38852 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	208.145
Dual form			208.3.bd.g.33.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.26125 + 3.91659i) q^{3} +(3.07976 - 3.07976i) q^{5} +(11.8234 - 3.16808i) q^{7} +(-5.72647 + 9.91853i) q^{9} +(0.0486283 - 0.181483i) q^{11} +(-2.24896 - 12.8040i) q^{13} +(19.0263 + 5.09808i) q^{15} +(-11.6675 - 6.73623i) q^{17} +(2.42703 + 9.05781i) q^{19} +(39.1437 + 39.1437i) q^{21} +(-36.0176 + 20.7948i) q^{23} +6.03012i q^{25} -11.0934 q^{27} +(10.2980 + 17.8367i) q^{29} +(-27.0587 + 27.0587i) q^{31} +(0.820756 - 0.219921i) q^{33} +(26.6564 - 46.1703i) q^{35} +(10.7792 - 40.2285i) q^{37} +(45.0626 - 37.7612i) q^{39} +(-41.8319 - 11.2088i) q^{41} +(-58.3471 - 33.6867i) q^{43} +(12.9106 + 48.1829i) q^{45} +(48.6637 + 48.6637i) q^{47} +(87.3214 - 50.4150i) q^{49} -60.9291i q^{51} -19.4689 q^{53} +(-0.409162 - 0.708689i) q^{55} +(-29.9876 + 29.9876i) q^{57} +(-14.4993 + 3.88508i) q^{59} +(16.5150 - 28.6048i) q^{61} +(-36.2838 + 135.413i) q^{63} +(-46.3595 - 32.5070i) q^{65} +(11.2635 + 3.01805i) q^{67} +(-162.889 - 94.0442i) q^{69} +(-30.2048 - 112.726i) q^{71} +(-27.6780 - 27.6780i) q^{73} +(-23.6175 + 13.6356i) q^{75} -2.29981i q^{77} +40.4706 q^{79} +(26.4533 + 45.8185i) q^{81} +(27.7311 - 27.7311i) q^{83} +(-56.6791 + 15.1871i) q^{85} +(-46.5727 + 80.6663i) q^{87} +(-31.1747 + 116.345i) q^{89} +(-67.1544 - 144.262i) q^{91} +(-167.164 - 44.7915i) q^{93} +(35.3706 + 20.4212i) q^{95} +(16.5810 + 61.8810i) q^{97} +(1.52158 + 1.52158i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 2 q^{5} + 36 q^{7} - 22 q^{9} + 24 q^{11} + 26 q^{13} + 76 q^{15} + 42 q^{17} + 18 q^{19} + 42 q^{21} - 48 q^{23} - 244 q^{27} - 36 q^{29} + 16 q^{31} + 18 q^{33} + 6 q^{35} + 112 q^{37}+ \cdots - 576 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 2 * q^5 + 36 * q^7 - 22 * q^9 + 24 * q^11 + 26 * q^13 + 76 * q^15 + 42 * q^17 + 18 * q^19 + 42 * q^21 - 48 * q^23 - 244 * q^27 - 36 * q^29 + 16 * q^31 + 18 * q^33 + 6 * q^35 + 112 * q^37 + 80 * q^39 - 104 * q^41 + 174 * q^43 + 94 * q^45 + 32 * q^47 + 222 * q^49 + 56 * q^53 + 42 * q^55 - 258 * q^57 - 64 * q^59 - 106 * q^61 - 276 * q^63 - 152 * q^65 - 138 * q^67 - 474 * q^69 - 126 * q^71 + 14 * q^73 - 160 * q^79 - 256 * q^81 - 104 * q^83 - 418 * q^85 + 276 * q^87 + 246 * q^89 + 72 * q^91 - 434 * q^93 + 600 * q^95 - 234 * q^97 - 576 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.26125	+	3.91659i	0.753749	+	1.30553i	0.945994	+	0.324184i	$0.105090\pi$
$3$	2.26125	+	3.91659i	0.753749	+	1.30553i	−0.192245	+	0.981347i	$0.561577\pi$
$4$		0			0
$5$	3.07976	−	3.07976i	0.615953	−	0.615953i	−0.328538	−	0.944491i	$-0.606556\pi$
$5$	3.07976	−	3.07976i	0.615953	−	0.615953i	0.944491	+	0.328538i	$0.106556\pi$
$6$		0			0
$7$	11.8234	−	3.16808i	1.68906	−	0.452582i	0.718913	−	0.695100i	$-0.244640\pi$
$7$	11.8234	−	3.16808i	1.68906	−	0.452582i	0.970147	+	0.242517i	$0.0779731\pi$
$8$		0			0
$9$	−5.72647	+	9.91853i	−0.636274	+	1.10206i
$10$		0			0
$11$	0.0486283	−	0.181483i	0.00442075	−	0.0164985i	−0.963680	−	0.267059i	$-0.913948\pi$
$11$	0.0486283	−	0.181483i	0.00442075	−	0.0164985i	0.968101	+	0.250560i	$0.0806149\pi$
$12$		0			0
$13$	−2.24896	−	12.8040i	−0.172997	−	0.984922i
$13$	−2.24896	−	12.8040i	−0.172997	−	0.984922i
$14$		0			0
$15$	19.0263	+	5.09808i	1.26842	+	0.339872i
$16$		0			0
$17$	−11.6675	−	6.73623i	−0.686323	−	0.396249i	0.115910	−	0.993260i	$-0.463022\pi$
$17$	−11.6675	−	6.73623i	−0.686323	−	0.396249i	−0.802233	+	0.597011i	$0.796355\pi$
$18$		0			0
$19$	2.42703	+	9.05781i	0.127739	+	0.476727i	0.999922	−	0.0124514i	$-0.00396351\pi$
$19$	2.42703	+	9.05781i	0.127739	+	0.476727i	−0.872184	+	0.489178i	$0.837297\pi$
$20$		0			0
$21$	39.1437	+	39.1437i	1.86399	+	1.86399i
$22$		0			0
$23$	−36.0176	+	20.7948i	−1.56598	+	0.904120i	−0.569352	+	0.822094i	$0.692806\pi$
$23$	−36.0176	+	20.7948i	−1.56598	+	0.904120i	−0.996630	+	0.0820262i	$0.973861\pi$
$24$		0			0
$25$			6.03012i			0.241205i
$26$		0			0
$27$	−11.0934			−0.410866
$28$		0			0
$29$	10.2980	+	17.8367i	0.355104	+	0.615058i	0.987136	−	0.159884i	$-0.0511121\pi$
$29$	10.2980	+	17.8367i	0.355104	+	0.615058i	−0.632032	+	0.774942i	$0.717779\pi$
$30$		0			0
$31$	−27.0587	+	27.0587i	−0.872861	+	0.872861i	−0.992783	−	0.119923i	$-0.961735\pi$
$31$	−27.0587	+	27.0587i	−0.872861	+	0.872861i	0.119923	+	0.992783i	$0.461735\pi$
$32$		0			0
$33$	0.820756	−	0.219921i	0.0248714	−	0.00666427i
$34$		0			0
$35$	26.6564	−	46.1703i	0.761612	−	1.31915i
$36$		0			0
$37$	10.7792	−	40.2285i	0.291329	−	1.08726i	−0.652760	−	0.757565i	$-0.726389\pi$
$37$	10.7792	−	40.2285i	0.291329	−	1.08726i	0.944089	−	0.329691i	$-0.106944\pi$
$38$		0			0
$39$	45.0626	−	37.7612i	1.15545	−	0.968237i
$40$		0			0
$41$	−41.8319	−	11.2088i	−1.02029	−	0.273386i	−0.290368	−	0.956915i	$-0.593778\pi$
$41$	−41.8319	−	11.2088i	−1.02029	−	0.273386i	−0.729923	+	0.683529i	$0.760444\pi$
$42$		0			0
$43$	−58.3471	−	33.6867i	−1.35691	−	0.783412i	−0.367704	−	0.929943i	$-0.619856\pi$
$43$	−58.3471	−	33.6867i	−1.35691	−	0.783412i	−0.989206	+	0.146531i	$0.953189\pi$
$44$		0			0
$45$	12.9106	+	48.1829i	0.286901	+	1.07073i
$46$		0			0
$47$	48.6637	+	48.6637i	1.03540	+	1.03540i	0.999350	+	0.0360471i	$0.0114766\pi$
$47$	48.6637	+	48.6637i	1.03540	+	1.03540i	0.0360471	+	0.999350i	$0.488523\pi$
$48$		0			0
$49$	87.3214	−	50.4150i	1.78207	−	1.02888i
$50$		0			0
$51$		−	60.9291i		−	1.19469i
$52$		0			0
$53$	−19.4689			−0.367337			−0.183669	−	0.982988i	$-0.558797\pi$
$53$	−19.4689			−0.367337			−0.183669	+	0.982988i	$0.558797\pi$
$54$		0			0
$55$	−0.409162	−	0.708689i	−0.00743930	−	0.0128852i
$56$		0			0
$57$	−29.9876	+	29.9876i	−0.526099	+	0.526099i
$58$		0			0
$59$	−14.4993	+	3.88508i	−0.245751	+	0.0658488i	−0.379592	−	0.925154i	$-0.623936\pi$
$59$	−14.4993	+	3.88508i	−0.245751	+	0.0658488i	0.133841	+	0.991003i	$0.457269\pi$
$60$		0			0
$61$	16.5150	−	28.6048i	0.270737	−	0.468931i	−0.698314	−	0.715792i	$-0.746066\pi$
$61$	16.5150	−	28.6048i	0.270737	−	0.468931i	0.969051	+	0.246861i	$0.0793992\pi$
$62$		0			0
$63$	−36.2838	+	135.413i	−0.575933	+	2.14941i
$64$		0			0
$65$	−46.3595	−	32.5070i	−0.713223	−	0.500108i
$66$		0			0
$67$	11.2635	+	3.01805i	0.168112	+	0.0450456i	0.341893	−	0.939739i	$-0.388932\pi$
$67$	11.2635	+	3.01805i	0.168112	+	0.0450456i	−0.173781	+	0.984784i	$0.555598\pi$
$68$		0			0
$69$	−162.889	−	94.0442i	−2.36071	−	1.36296i
$70$		0			0
$71$	−30.2048	−	112.726i	−0.425420	−	1.58769i	−0.763004	−	0.646394i	$-0.776276\pi$
$71$	−30.2048	−	112.726i	−0.425420	−	1.58769i	0.337584	−	0.941295i	$-0.390390\pi$
$72$		0			0
$73$	−27.6780	−	27.6780i	−0.379151	−	0.379151i	0.491645	−	0.870796i	$-0.336396\pi$
$73$	−27.6780	−	27.6780i	−0.379151	−	0.379151i	−0.870796	+	0.491645i	$0.836396\pi$
$74$		0			0
$75$	−23.6175	+	13.6356i	−0.314900	+	0.181808i
$76$		0			0
$77$		−	2.29981i		−	0.0298677i
$78$		0			0
$79$	40.4706			0.512286			0.256143	−	0.966639i	$-0.417548\pi$
$79$	40.4706			0.512286			0.256143	+	0.966639i	$0.417548\pi$
$80$		0			0
$81$	26.4533	+	45.8185i	0.326585	+	0.565661i
$82$		0			0
$83$	27.7311	−	27.7311i	0.334109	−	0.334109i	−0.520035	−	0.854145i	$-0.674081\pi$
$83$	27.7311	−	27.7311i	0.334109	−	0.334109i	0.854145	+	0.520035i	$0.174081\pi$
$84$		0			0
$85$	−56.6791	+	15.1871i	−0.666813	+	0.178672i
$86$		0			0
$87$	−46.5727	+	80.6663i	−0.535318	+	0.927199i
$88$		0			0
$89$	−31.1747	+	116.345i	−0.350277	+	1.30725i	0.536048	+	0.844188i	$0.319917\pi$
$89$	−31.1747	+	116.345i	−0.350277	+	1.30725i	−0.886325	+	0.463064i	$0.846750\pi$
$90$		0			0
$91$	−67.1544	−	144.262i	−0.737961	−	1.58530i
$92$		0			0
$93$	−167.164	−	44.7915i	−1.79746	−	0.481629i
$94$		0			0
$95$	35.3706	+	20.4212i	0.372322	+	0.214960i
$96$		0			0
$97$	16.5810	+	61.8810i	0.170938	+	0.637948i	0.997208	+	0.0746745i	$0.0237918\pi$
$97$	16.5810	+	61.8810i	0.170938	+	0.637948i	−0.826270	+	0.563274i	$0.809542\pi$
$98$		0			0
$99$	1.52158	+	1.52158i	0.0153695	+	0.0153695i
$100$		0			0
$101$	9.81546	−	5.66696i	0.0971827	−	0.0561085i	−0.450621	−	0.892715i	$-0.648797\pi$
$101$	9.81546	−	5.66696i	0.0971827	−	0.0561085i	0.547804	+	0.836607i	$0.315464\pi$
$102$		0			0
$103$			101.536i			0.985786i	0.870090	+	0.492893i	$0.164061\pi$
$103$			101.536i			0.985786i	−0.870090	+	0.492893i	$0.835939\pi$
$104$		0			0
$105$	241.107			2.29626
$106$		0			0
$107$	2.20770	+	3.82385i	0.0206327	+	0.0357369i	0.876157	−	0.482025i	$-0.160099\pi$
$107$	2.20770	+	3.82385i	0.0206327	+	0.0357369i	−0.855525	+	0.517762i	$0.826765\pi$
$108$		0			0
$109$	94.5265	−	94.5265i	0.867215	−	0.867215i	−0.124948	−	0.992163i	$-0.539876\pi$
$109$	94.5265	−	94.5265i	0.867215	−	0.867215i	0.992163	+	0.124948i	$0.0398764\pi$
$110$		0			0
$111$	181.933	−	48.7488i	1.63904	−	0.439178i
$112$		0			0
$113$	40.2469	−	69.7097i	0.356167	−	0.616900i	−0.631150	−	0.775661i	$-0.717417\pi$
$113$	40.2469	−	69.7097i	0.356167	−	0.616900i	0.987317	+	0.158761i	$0.0507499\pi$
$114$		0			0
$115$	−46.8827	+	174.969i	−0.407676	+	1.52147i
$116$		0			0
$117$	139.875	+	51.0153i	1.19552	+	0.436028i
$118$		0			0
$119$	−159.291	−	42.6818i	−1.33858	−	0.358670i
$120$		0			0
$121$	104.759	+	60.4823i	0.865773	+	0.499854i
$122$		0			0
$123$	−50.6918	−	189.185i	−0.412129	−	1.53809i
$124$		0			0
$125$	95.5654	+	95.5654i	0.764523	+	0.764523i
$126$		0			0
$127$	75.6956	−	43.7029i	0.596028	−	0.344117i	−0.171449	−	0.985193i	$-0.554845\pi$
$127$	75.6956	−	43.7029i	0.596028	−	0.344117i	0.767478	+	0.641076i	$0.221512\pi$
$128$		0			0
$129$		−	304.696i		−	2.36198i
$130$		0			0
$131$	−100.896			−0.770195			−0.385098	−	0.922876i	$-0.625832\pi$
$131$	−100.896			−0.770195			−0.385098	+	0.922876i	$0.625832\pi$
$132$		0			0
$133$	57.3916	+	99.4053i	0.431516	+	0.747408i
$134$		0			0
$135$	−34.1650	+	34.1650i	−0.253074	+	0.253074i
$136$		0			0
$137$	−156.778	+	42.0086i	−1.14437	+	0.306632i	−0.780706	−	0.624899i	$-0.785140\pi$
$137$	−156.778	+	42.0086i	−1.14437	+	0.306632i	−0.363661	+	0.931531i	$0.618474\pi$
$138$		0			0
$139$	69.9531	−	121.162i	0.503259	−	0.871671i	−0.496734	−	0.867903i	$-0.665467\pi$
$139$	69.9531	−	121.162i	0.503259	−	0.871671i	0.999993	−	0.00376769i	$-0.00119930\pi$
$140$		0			0
$141$	−80.5553	+	300.636i	−0.571314	+	2.13217i
$142$		0			0
$143$	−2.43307	−	0.214488i	−0.0170145	−	0.00149991i
$144$		0			0
$145$	86.6482	+	23.2173i	0.597574	+	0.160119i
$146$		0			0
$147$	394.910	+	228.002i	2.68646	+	1.55103i
$148$		0			0
$149$	−12.1813	−	45.4612i	−0.0817537	−	0.305109i	0.912926	−	0.408125i	$-0.133817\pi$
$149$	−12.1813	−	45.4612i	−0.0817537	−	0.305109i	−0.994680	+	0.103016i	$0.967151\pi$
$150$		0			0
$151$	104.251	+	104.251i	0.690402	+	0.690402i	0.962320	−	0.271918i	$-0.0876580\pi$
$151$	104.251	+	104.251i	0.690402	+	0.690402i	−0.271918	+	0.962320i	$0.587658\pi$
$152$		0			0
$153$	133.627	−	77.1496i	0.873379	−	0.504246i
$154$		0			0
$155$			166.669i			1.07528i
$156$		0			0
$157$	238.111			1.51663			0.758315	−	0.651888i	$-0.226023\pi$
$157$	238.111			1.51663			0.758315	+	0.651888i	$0.226023\pi$
$158$		0			0
$159$	−44.0239	−	76.2516i	−0.276880	−	0.479570i
$160$		0			0
$161$	−359.972	+	359.972i	−2.23585	+	2.23585i
$162$		0			0
$163$	−48.7104	+	13.0519i	−0.298837	+	0.0800730i	−0.405122	−	0.914263i	$-0.632771\pi$
$163$	−48.7104	+	13.0519i	−0.298837	+	0.0800730i	0.106285	+	0.994336i	$0.466104\pi$
$164$		0			0
$165$	1.85043	−	3.20504i	0.0112147	−	0.0194245i
$166$		0			0
$167$	18.2816	−	68.2277i	0.109470	−	0.408549i	−0.889343	−	0.457240i	$-0.848838\pi$
$167$	18.2816	−	68.2277i	0.109470	−	0.408549i	0.998814	+	0.0486905i	$0.0155048\pi$
$168$		0			0
$169$	−158.884	+	57.5913i	−0.940144	+	0.340777i
$170$		0			0
$171$	−103.738	−	27.7966i	−0.606658	−	0.162553i
$172$		0			0
$173$	−46.5968	−	26.9027i	−0.269346	−	0.155507i	0.359245	−	0.933243i	$-0.383034\pi$
$173$	−46.5968	−	26.9027i	−0.269346	−	0.155507i	−0.628590	+	0.777737i	$0.716368\pi$
$174$		0			0
$175$	19.1039	+	71.2967i	0.109165	+	0.407410i
$176$		0			0
$177$	−48.0028	−	48.0028i	−0.271202	−	0.271202i
$178$		0			0
$179$	−161.044	+	92.9788i	−0.899687	+	0.519435i	−0.877099	−	0.480310i	$-0.840524\pi$
$179$	−161.044	+	92.9788i	−0.899687	+	0.519435i	−0.0225884	+	0.999745i	$0.507191\pi$
$180$		0			0
$181$		−	324.686i		−	1.79384i	−0.442190	−	0.896921i	$-0.645798\pi$
$181$		−	324.686i		−	1.79384i	0.442190	−	0.896921i	$-0.354202\pi$
$182$		0			0
$183$	149.378			0.816271
$184$		0			0
$185$	−90.6968	−	157.091i	−0.490253	−	0.849143i
$186$		0			0
$187$	−1.78988	+	1.78988i	−0.00957156	+	0.00957156i
$188$		0			0
$189$	−131.162	+	35.1447i	−0.693977	+	0.185951i
$190$		0			0
$191$	−137.226	+	237.683i	−0.718462	+	1.24441i	0.243146	+	0.969990i	$0.421820\pi$
$191$	−137.226	+	237.683i	−0.718462	+	1.24441i	−0.961609	+	0.274424i	$0.911513\pi$
$192$		0			0
$193$	76.7646	−	286.489i	0.397744	−	1.48440i	−0.419312	−	0.907842i	$-0.637729\pi$
$193$	76.7646	−	286.489i	0.397744	−	1.48440i	0.817056	−	0.576559i	$-0.195605\pi$
$194$		0			0
$195$	22.4864	−	255.078i	0.115315	−	1.30809i
$196$		0			0
$197$	−20.7125	−	5.54991i	−0.105140	−	0.0281721i	0.205866	−	0.978580i	$-0.433999\pi$
$197$	−20.7125	−	5.54991i	−0.105140	−	0.0281721i	−0.311005	+	0.950408i	$0.600666\pi$
$198$		0			0
$199$	−57.6333	−	33.2746i	−0.289615	−	0.167209i	0.348153	−	0.937438i	$-0.386809\pi$
$199$	−57.6333	−	33.2746i	−0.289615	−	0.167209i	−0.637768	+	0.770228i	$0.720142\pi$
$200$		0			0
$201$	13.6491	+	50.9392i	0.0679061	+	0.253429i
$202$		0			0
$203$	178.266	+	178.266i	0.878157	+	0.878157i
$204$		0			0
$205$	−163.353	+	94.3119i	−0.796844	+	0.460058i
$206$		0			0
$207$		−	476.322i		−	2.30107i
$208$		0			0
$209$	1.76186			0.00842996
$210$		0			0
$211$	65.3089	+	113.118i	0.309521	+	0.536106i	0.978258	−	0.207394i	$-0.0664981\pi$
$211$	65.3089	+	113.118i	0.309521	+	0.536106i	−0.668737	+	0.743499i	$0.733165\pi$
$212$		0			0
$213$	373.201	−	373.201i	1.75212	−	1.75212i
$214$		0			0
$215$	−283.442	+	75.9482i	−1.31834	+	0.353247i
$216$		0			0
$217$	−234.202	+	405.650i	−1.07927	+	1.86936i
$218$		0			0
$219$	45.8168	−	170.990i	0.209209	−	0.780778i
$220$		0			0
$221$	−60.0109	+	164.540i	−0.271543	+	0.744525i
$222$		0			0
$223$	26.9675	+	7.22592i	0.120931	+	0.0324032i	0.318777	−	0.947830i	$-0.396728\pi$
$223$	26.9675	+	7.22592i	0.120931	+	0.0324032i	−0.197846	+	0.980233i	$0.563395\pi$
$224$		0			0
$225$	−59.8100	−	34.5313i	−0.265822	−	0.153472i
$226$		0			0
$227$	−3.14269	−	11.7287i	−0.0138444	−	0.0516681i	0.958658	−	0.284561i	$-0.0918477\pi$
$227$	−3.14269	−	11.7287i	−0.0138444	−	0.0516681i	−0.972503	+	0.232892i	$0.925181\pi$
$228$		0			0
$229$	66.5812	+	66.5812i	0.290748	+	0.290748i	0.837376	−	0.546628i	$-0.184089\pi$
$229$	66.5812	+	66.5812i	0.290748	+	0.290748i	−0.546628	+	0.837376i	$0.684089\pi$
$230$		0			0
$231$	9.00742	−	5.20044i	0.0389932	−	0.0225127i
$232$		0			0
$233$		−	20.1428i		−	0.0864498i	−0.999065	−	0.0432249i	$-0.986237\pi$
$233$		−	20.1428i		−	0.0864498i	0.999065	−	0.0432249i	$-0.0137632\pi$
$234$		0			0
$235$	299.745			1.27551
$236$		0			0
$237$	91.5140	+	158.507i	0.386135	+	0.668806i
$238$		0			0
$239$	17.0300	−	17.0300i	0.0712553	−	0.0712553i	−0.670581	−	0.741836i	$-0.733955\pi$
$239$	17.0300	−	17.0300i	0.0712553	−	0.0712553i	0.741836	+	0.670581i	$0.233955\pi$
$240$		0			0
$241$	−158.194	+	42.3879i	−0.656405	+	0.175883i	−0.571623	−	0.820516i	$-0.693686\pi$
$241$	−158.194	+	42.3879i	−0.656405	+	0.175883i	−0.0847820	+	0.996400i	$0.527019\pi$
$242$		0			0
$243$	−169.555	+	293.678i	−0.697758	+	1.20855i
$244$		0			0
$245$	113.663	−	424.196i	0.463930	−	1.73141i
$246$		0			0
$247$	110.518	−	51.4463i	0.447440	−	0.208285i
$248$		0			0
$249$	171.318	+	45.9045i	0.688024	+	0.184356i
$250$		0			0
$251$	114.147	+	65.9026i	0.454768	+	0.262560i	0.709842	−	0.704361i	$-0.248766\pi$
$251$	114.147	+	65.9026i	0.454768	+	0.262560i	−0.255074	+	0.966922i	$0.582100\pi$
$252$		0			0
$253$	2.02243	+	7.54780i	0.00799378	+	0.0298332i
$254$		0			0
$255$	−187.647	−	187.647i	−0.735871	−	0.735871i
$256$		0			0
$257$	141.970	−	81.9664i	0.552412	−	0.318935i	−0.197682	−	0.980266i	$-0.563341\pi$
$257$	141.970	−	81.9664i	0.552412	−	0.318935i	0.750094	+	0.661331i	$0.230008\pi$
$258$		0			0
$259$		−	509.787i		−	1.96829i
$260$		0			0
$261$	−235.885			−0.903774
$262$		0			0
$263$	−139.299	−	241.274i	−0.529656	−	0.917390i	−0.999402	−	0.0345888i	$-0.988988\pi$
$263$	−139.299	−	241.274i	−0.529656	−	0.917390i	0.469746	−	0.882802i	$-0.344345\pi$
$264$		0			0
$265$	−59.9595	+	59.9595i	−0.226262	+	0.226262i
$266$		0			0
$267$	−526.171	+	140.987i	−1.97068	+	0.528042i
$268$		0			0
$269$	−48.2892	+	83.6393i	−0.179514	+	0.310927i	−0.941714	−	0.336414i	$-0.890786\pi$
$269$	−48.2892	+	83.6393i	−0.179514	+	0.310927i	0.762200	+	0.647341i	$0.224119\pi$
$270$		0			0
$271$	22.5559	−	84.1796i	0.0832320	−	0.310626i	−0.911742	−	0.410764i	$-0.865262\pi$
$271$	22.5559	−	84.1796i	0.0832320	−	0.310626i	0.994974	+	0.100138i	$0.0319286\pi$
$272$		0			0
$273$	413.163	−	589.229i	1.51342	−	2.15835i
$274$		0			0
$275$	1.09437	+	0.293234i	0.00397951	+	0.00106631i
$276$		0			0
$277$	297.082	+	171.520i	1.07250	+	0.619206i	0.928862	−	0.370425i	$-0.120788\pi$
$277$	297.082	+	171.520i	1.07250	+	0.619206i	0.143634	+	0.989631i	$0.454121\pi$
$278$		0			0
$279$	−113.432	−	423.333i	−0.406565	−	1.51732i
$280$		0			0
$281$	87.2927	+	87.2927i	0.310650	+	0.310650i	0.845161	−	0.534511i	$-0.179504\pi$
$281$	87.2927	+	87.2927i	0.310650	+	0.310650i	−0.534511	+	0.845161i	$0.679504\pi$
$282$		0			0
$283$	−313.653	+	181.088i	−1.10831	+	0.639886i	−0.938392	−	0.345572i	$-0.887685\pi$
$283$	−313.653	+	181.088i	−1.10831	+	0.639886i	−0.169922	+	0.985457i	$0.554352\pi$
$284$		0			0
$285$			184.710i			0.648104i
$286$		0			0
$287$	−530.107			−1.84706
$288$		0			0
$289$	−53.7464	−	93.0915i	−0.185974	−	0.322116i
$290$		0			0
$291$	−204.869	+	204.869i	−0.704017	+	0.704017i
$292$		0			0
$293$	−106.652	+	28.5772i	−0.363999	+	0.0975332i	−0.436183	−	0.899858i	$-0.643670\pi$
$293$	−106.652	+	28.5772i	−0.363999	+	0.0975332i	0.0721837	+	0.997391i	$0.477003\pi$
$294$		0			0
$295$	−32.6893	+	56.6196i	−0.110811	+	0.191931i
$296$		0			0
$297$	−0.539452	+	2.01326i	−0.00181634	+	0.00677866i
$298$		0			0
$299$	347.258	+	414.402i	1.16140	+	1.38596i
$300$		0			0
$301$	−796.585	−	213.444i	−2.64646	−	0.709117i
$302$		0			0
$303$	44.3903	+	25.6288i	0.146503	+	0.0845834i
$304$		0			0
$305$	−37.2337	−	138.958i	−0.122078	−	0.455600i
$306$		0			0
$307$	−22.2103	−	22.2103i	−0.0723462	−	0.0723462i	0.670008	−	0.742354i	$-0.266291\pi$
$307$	−22.2103	−	22.2103i	−0.0723462	−	0.0723462i	−0.742354	+	0.670008i	$0.766291\pi$
$308$		0			0
$309$	−397.675	+	229.598i	−1.28697	+	0.743035i
$310$		0			0
$311$		−	225.765i		−	0.725932i	−0.931802	−	0.362966i	$-0.881764\pi$
$311$		−	225.765i		−	0.725932i	0.931802	−	0.362966i	$-0.118236\pi$
$312$		0			0
$313$	−161.180			−0.514953			−0.257477	−	0.966285i	$-0.582891\pi$
$313$	−161.180			−0.514953			−0.257477	+	0.966285i	$0.582891\pi$
$314$		0			0
$315$	305.294	+	528.785i	0.969188	+	1.67868i
$316$		0			0
$317$	−18.3223	+	18.3223i	−0.0577991	+	0.0577991i	−0.735416	−	0.677616i	$-0.763013\pi$
$317$	−18.3223	+	18.3223i	−0.0577991	+	0.0577991i	0.677616	+	0.735416i	$0.263013\pi$
$318$		0			0
$319$	3.73783	−	1.00155i	0.0117173	−	0.00313965i
$320$		0			0
$321$	−9.98431	+	17.2933i	−0.0311038	+	0.0538733i
$322$		0			0
$323$	32.6981	−	122.031i	0.101232	−	0.377805i
$324$		0			0
$325$	77.2096	−	13.5615i	0.237568	−	0.0417277i
$326$		0			0
$327$	583.969	+	156.474i	1.78584	+	0.478514i
$328$		0			0
$329$	729.541	+	421.201i	2.21745	+	1.28025i
$330$		0			0
$331$	119.484	+	445.919i	0.360978	+	1.34719i	0.872792	+	0.488092i	$0.162307\pi$
$331$	119.484	+	445.919i	0.360978	+	1.34719i	−0.511814	+	0.859096i	$0.671026\pi$
$332$		0			0
$333$	337.281	+	337.281i	1.01285	+	1.01285i
$334$		0			0
$335$	43.9839	−	25.3941i	0.131295	−	0.0758033i
$336$		0			0
$337$			293.336i			0.870432i	0.900326	+	0.435216i	$0.143328\pi$
$337$			293.336i			0.870432i	−0.900326	+	0.435216i	$0.856672\pi$
$338$		0			0
$339$	364.033			1.07384
$340$		0			0
$341$	3.59488	+	6.22651i	0.0105422	+	0.0182596i
$342$		0			0
$343$	448.607	−	448.607i	1.30789	−	1.30789i
$344$		0			0
$345$	−791.294	+	212.027i	−2.29361	+	0.614570i
$346$		0			0
$347$	244.551	−	423.575i	0.704758	−	1.22068i	−0.262021	−	0.965062i	$-0.584389\pi$
$347$	244.551	−	423.575i	0.704758	−	1.22068i	0.966779	−	0.255615i	$-0.0822778\pi$
$348$		0			0
$349$	0.364119	−	1.35891i	0.00104332	−	0.00389372i	−0.965402	−	0.260765i	$-0.916025\pi$
$349$	0.364119	−	1.35891i	0.00104332	−	0.00389372i	0.966446	+	0.256872i	$0.0826918\pi$
$350$		0			0
$351$	24.9486	+	142.040i	0.0710785	+	0.404671i
$352$		0			0
$353$	303.026	+	81.1955i	0.858430	+	0.230016i	0.661078	−	0.750317i	$-0.270099\pi$
$353$	303.026	+	81.1955i	0.858430	+	0.230016i	0.197352	+	0.980333i	$0.436766\pi$
$354$		0			0
$355$	−440.193	−	254.145i	−1.23998	−	0.715903i
$356$		0			0
$357$	−193.028	−	720.390i	−0.540695	−	2.01790i
$358$		0			0
$359$	387.119	+	387.119i	1.07833	+	1.07833i	0.996660	+	0.0816660i	$0.0260241\pi$
$359$	387.119	+	387.119i	1.07833	+	1.07833i	0.0816660	+	0.996660i	$0.473976\pi$
$360$		0			0
$361$	236.482	−	136.533i	0.655074	−	0.378207i
$362$		0			0
$363$			547.062i			1.50706i
$364$		0			0
$365$	−170.484			−0.467078
$366$		0			0
$367$	−251.495	−	435.603i	−0.685274	−	1.18693i	−0.973351	−	0.229322i	$-0.926349\pi$
$367$	−251.495	−	435.603i	−0.685274	−	1.18693i	0.288077	−	0.957607i	$-0.406984\pi$
$368$		0			0
$369$	350.724	−	350.724i	0.950472	−	0.950472i
$370$		0			0
$371$	−230.189	+	61.6789i	−0.620455	+	0.166250i
$372$		0			0
$373$	−226.659	+	392.584i	−0.607664	+	1.05250i	0.383960	+	0.923350i	$0.374560\pi$
$373$	−226.659	+	392.584i	−0.607664	+	1.05250i	−0.991624	+	0.129155i	$0.958773\pi$
$374$		0			0
$375$	−158.194	+	590.388i	−0.421850	+	1.57437i
$376$		0			0
$377$	205.221	−	171.970i	0.544353	−	0.456153i
$378$		0			0
$379$	109.480	+	29.3352i	0.288867	+	0.0774016i	0.400343	−	0.916366i	$-0.368891\pi$
$379$	109.480	+	29.3352i	0.288867	+	0.0774016i	−0.111476	+	0.993767i	$0.535558\pi$
$380$		0			0
$381$	342.333	+	197.646i	0.898511	+	0.518756i
$382$		0			0
$383$	56.2995	+	210.113i	0.146996	+	0.548597i	0.999658	+	0.0261344i	$0.00831978\pi$
$383$	56.2995	+	210.113i	0.146996	+	0.548597i	−0.852662	+	0.522462i	$0.825014\pi$
$384$		0			0
$385$	−7.08287	−	7.08287i	−0.0183971	−	0.0183971i
$386$		0			0
$387$	668.246	−	385.812i	1.72673	−	0.996930i
$388$		0			0
$389$		−	642.737i		−	1.65228i	−0.563466	−	0.826140i	$-0.690532\pi$
$389$		−	642.737i		−	1.65228i	0.563466	−	0.826140i	$-0.309468\pi$
$390$		0			0
$391$	560.313			1.43303
$392$		0			0
$393$	−228.150	−	395.167i	−0.580534	−	1.00551i
$394$		0			0
$395$	124.640	−	124.640i	0.315544	−	0.315544i
$396$		0			0
$397$	689.838	−	184.842i	1.73763	−	0.465596i	0.755710	−	0.654906i	$-0.227292\pi$
$397$	689.838	−	184.842i	1.73763	−	0.465596i	0.981917	+	0.189310i	$0.0606252\pi$
$398$		0			0
$399$	−259.553	+	449.559i	−0.650509	+	1.12672i
$400$		0			0
$401$	−157.681	+	588.473i	−0.393219	+	1.46751i	0.431574	+	0.902078i	$0.357958\pi$
$401$	−157.681	+	588.473i	−0.393219	+	1.46751i	−0.824793	+	0.565435i	$0.808708\pi$
$402$		0			0
$403$	407.313	+	285.605i	1.01070	+	0.708698i
$404$		0			0
$405$	222.580	+	59.6402i	0.549581	+	0.147260i
$406$		0			0
$407$	−6.77662	−	3.91248i	−0.0166502	−	0.00961297i
$408$		0			0
$409$	71.7810	+	267.890i	0.175504	+	0.654988i	0.996465	+	0.0840050i	$0.0267712\pi$
$409$	71.7810	+	267.890i	0.175504	+	0.654988i	−0.820962	+	0.570983i	$0.806562\pi$
$410$		0			0
$411$	−519.045	−	519.045i	−1.26288	−	1.26288i
$412$		0			0
$413$	−159.123	+	91.8699i	−0.385287	+	0.222445i
$414$		0			0
$415$		−	170.810i		−	0.411591i
$416$		0			0
$417$	632.724			1.51732
$418$		0			0
$419$	−244.014	−	422.645i	−0.582373	−	1.00870i	−0.995197	−	0.0978890i	$-0.968791\pi$
$419$	−244.014	−	422.645i	−0.582373	−	1.00870i	0.412824	−	0.910811i	$-0.364542\pi$
$420$		0			0
$421$	49.9281	−	49.9281i	0.118594	−	0.118594i	−0.645319	−	0.763913i	$-0.723276\pi$
$421$	49.9281	−	49.9281i	0.118594	−	0.118594i	0.763913	+	0.645319i	$0.223276\pi$
$422$		0			0
$423$	−761.343	+	204.001i	−1.79987	+	0.482272i
$424$		0			0
$425$	40.6203	−	70.3564i	0.0955771	−	0.165544i
$426$		0			0
$427$	104.641	−	390.527i	0.245062	−	0.914583i
$428$		0			0
$429$	−4.66171	−	10.0144i	−0.0108665	−	0.0233435i
$430$		0			0
$431$	−378.478	−	101.413i	−0.878140	−	0.235297i	−0.208535	−	0.978015i	$-0.566870\pi$
$431$	−378.478	−	101.413i	−0.878140	−	0.235297i	−0.669604	+	0.742718i	$0.733536\pi$
$432$		0			0
$433$	−534.485	−	308.585i	−1.23438	−	0.712668i	−0.266438	−	0.963852i	$-0.585847\pi$
$433$	−534.485	−	308.585i	−1.23438	−	0.712668i	−0.967939	+	0.251184i	$0.919180\pi$
$434$		0			0
$435$	105.000	+	391.866i	0.241380	+	0.900841i
$436$		0			0
$437$	−275.771	−	275.771i	−0.631054	−	0.631054i
$438$		0			0
$439$	−81.8276	+	47.2432i	−0.186395	+	0.107615i	−0.590294	−	0.807188i	$-0.700988\pi$
$439$	−81.8276	+	47.2432i	−0.186395	+	0.107615i	0.403899	+	0.914804i	$0.367655\pi$
$440$		0			0
$441$			1154.80i			2.61859i
$442$		0			0
$443$	481.330			1.08652			0.543262	−	0.839563i	$-0.317189\pi$
$443$	481.330			1.08652			0.543262	+	0.839563i	$0.317189\pi$
$444$		0			0
$445$	262.306	+	454.327i	0.589451	+	1.02096i
$446$		0			0
$447$	150.508	−	150.508i	0.336708	−	0.336708i
$448$		0			0
$449$	223.900	−	59.9939i	0.498664	−	0.133617i	−0.000715674	−	1.00000i	$-0.500228\pi$
$449$	223.900	−	59.9939i	0.498664	−	0.133617i	0.499380	+	0.866383i	$0.333561\pi$
$450$		0			0
$451$	−4.06843	+	7.04672i	−0.00902091	+	0.0156247i
$452$		0			0
$453$	−172.571	+	644.044i	−0.380952	+	1.42173i
$454$		0			0
$455$	−651.113	−	237.473i	−1.43102	−	0.521920i
$456$		0			0
$457$	33.8606	+	9.07291i	0.0740931	+	0.0198532i	0.295675	−	0.955289i	$-0.404455\pi$
$457$	33.8606	+	9.07291i	0.0740931	+	0.0198532i	−0.221582	+	0.975142i	$0.571122\pi$
$458$		0			0
$459$	129.432	+	74.7275i	0.281987	+	0.162805i
$460$		0			0
$461$	−63.6288	−	237.466i	−0.138024	−	0.515111i	−0.999967	−	0.00810668i	$-0.997420\pi$
$461$	−63.6288	−	237.466i	−0.138024	−	0.515111i	0.861944	−	0.507004i	$-0.169247\pi$
$462$		0			0
$463$	95.3642	+	95.3642i	0.205970	+	0.205970i	0.802552	−	0.596582i	$-0.203475\pi$
$463$	95.3642	+	95.3642i	0.205970	+	0.205970i	−0.596582	+	0.802552i	$0.703475\pi$
$464$		0			0
$465$	−652.773	+	376.879i	−1.40381	+	0.810492i
$466$		0			0
$467$		−	277.907i		−	0.595090i	−0.954708	−	0.297545i	$-0.903832\pi$
$467$		−	277.907i		−	0.595090i	0.954708	−	0.297545i	$-0.0961679\pi$
$468$		0			0
$469$	142.735			0.304339
$470$		0			0
$471$	538.427	+	932.584i	1.14316	+	1.98001i
$472$		0			0
$473$	−8.95089	+	8.95089i	−0.0189237	+	0.0189237i
$474$		0			0
$475$	−54.6197	+	14.6353i	−0.114989	+	0.0308111i
$476$		0			0
$477$	111.488	−	193.103i	0.233727	−	0.404827i
$478$		0			0
$479$	36.2003	−	135.101i	0.0755748	−	0.282049i	−0.917788	−	0.397070i	$-0.870027\pi$
$479$	36.2003	−	135.101i	0.0755748	−	0.282049i	0.993363	+	0.115021i	$0.0366936\pi$
$480$		0			0
$481$	−539.327	−	47.5444i	−1.12126	−	0.0988449i
$482$		0			0
$483$	−2223.85	−	595.878i	−4.60424	−	1.23370i
$484$		0			0
$485$	241.644	+	139.513i	0.498236	+	0.287656i
$486$		0			0
$487$	79.1996	+	295.577i	0.162628	+	0.606934i	0.998331	+	0.0577530i	$0.0183936\pi$
$487$	79.1996	+	295.577i	0.162628	+	0.606934i	−0.835703	+	0.549181i	$0.814940\pi$
$488$		0			0
$489$	−161.265	−	161.265i	−0.329785	−	0.329785i
$490$		0			0
$491$	−12.2820	+	7.09101i	−0.0250142	+	0.0144420i	−0.512455	−	0.858714i	$-0.671264\pi$
$491$	−12.2820	+	7.09101i	−0.0250142	+	0.0144420i	0.487441	+	0.873156i	$0.337931\pi$
$492$		0			0
$493$		−	277.479i		−	0.562838i
$494$		0			0
$495$	9.37220			0.0189337
$496$		0			0
$497$	−714.249	−	1237.12i	−1.43712	−	2.48917i
$498$		0			0
$499$	−423.539	+	423.539i	−0.848776	+	0.848776i	−0.989980	−	0.141205i	$-0.954902\pi$
$499$	−423.539	+	423.539i	−0.848776	+	0.848776i	0.141205	+	0.989980i	$0.454902\pi$
$500$		0			0
$501$	308.559	−	82.6782i	0.615887	−	0.165026i
$502$		0			0
$503$	119.024	−	206.156i	0.236629	−	0.409853i	−0.723116	−	0.690726i	$-0.757291\pi$
$503$	119.024	−	206.156i	0.236629	−	0.409853i	0.959745	+	0.280874i	$0.0906242\pi$
$504$		0			0
$505$	12.7764	−	47.6822i	0.0252998	−	0.0944201i
$506$		0			0
$507$	−584.838	−	492.057i	−1.15353	−	0.970527i
$508$		0			0
$509$	517.605	+	138.692i	1.01691	+	0.272479i	0.728512	−	0.685033i	$-0.240212\pi$
$509$	517.605	+	138.692i	1.01691	+	0.272479i	0.288394	+	0.957512i	$0.406879\pi$
$510$		0			0
$511$	−414.935	−	239.563i	−0.812006	−	0.468812i
$512$		0			0
$513$	−26.9240	−	100.482i	−0.0524834	−	0.195871i
$514$		0			0
$515$	312.707	+	312.707i	0.607198	+	0.607198i
$516$		0			0
$517$	11.1981	−	6.46521i	0.0216597	−	0.0125052i
$518$		0			0
$519$		−	243.334i		−	0.468852i
$520$		0			0
$521$	−184.545			−0.354213			−0.177107	−	0.984192i	$-0.556674\pi$
$521$	−184.545			−0.354213			−0.177107	+	0.984192i	$0.556674\pi$
$522$		0			0
$523$	−72.7447	−	125.997i	−0.139091	−	0.240913i	0.788062	−	0.615596i	$-0.211085\pi$
$523$	−72.7447	−	125.997i	−0.139091	−	0.240913i	−0.927153	+	0.374683i	$0.877751\pi$
$524$		0			0
$525$	−236.041	+	236.041i	−0.449603	+	0.449603i
$526$		0			0
$527$	497.980	−	133.433i	0.944934	−	0.253194i
$528$		0			0
$529$	600.344	−	1039.83i	1.13487	−	1.96565i
$530$		0			0
$531$	44.4956	−	166.060i	0.0837958	−	0.312730i
$532$		0			0
$533$	−49.4395	+	560.824i	−0.0927570	+	1.05220i
$534$		0			0
$535$	18.5757	+	4.97735i	0.0347210	+	0.00930347i
$536$		0			0
$537$	−728.320	−	420.496i	−1.35628	−	0.783046i
$538$		0			0
$539$	−4.90319	−	18.2990i	−0.00909683	−	0.0339498i
$540$		0			0
$541$	156.545	+	156.545i	0.289362	+	0.289362i	0.836828	−	0.547466i	$-0.184407\pi$
$541$	156.545	+	156.545i	0.289362	+	0.289362i	−0.547466	+	0.836828i	$0.684407\pi$
$542$		0			0
$543$	1271.66	−	734.194i	2.34192	−	1.35211i
$544$		0			0
$545$		−	582.238i		−	1.06833i
$546$		0			0
$547$	−197.327			−0.360743			−0.180372	−	0.983599i	$-0.557730\pi$
$547$	−197.327			−0.360743			−0.180372	+	0.983599i	$0.557730\pi$
$548$		0			0
$549$	189.145	+	327.609i	0.344526	+	0.596737i
$550$		0			0
$551$	−136.568	+	136.568i	−0.247854	+	0.247854i
$552$		0			0
$553$	478.501	−	128.214i	0.865282	−	0.231852i
$554$		0			0
$555$	410.175	−	710.445i	0.739055	−	1.28008i
$556$		0			0
$557$	51.1767	−	190.994i	0.0918792	−	0.342898i	−0.904649	−	0.426158i	$-0.859867\pi$
$557$	51.1767	−	190.994i	0.0918792	−	0.342898i	0.996528	+	0.0832605i	$0.0265334\pi$
$558$		0			0
$559$	−300.104	+	822.836i	−0.536859	+	1.47198i
$560$		0			0
$561$	−11.0576	−	2.96288i	−0.0197105	−	0.00528142i
$562$		0			0
$563$	549.907	+	317.489i	0.976744	+	0.563923i	0.901285	−	0.433226i	$-0.142625\pi$
$563$	549.907	+	317.489i	0.976744	+	0.563923i	0.0754583	+	0.997149i	$0.475958\pi$
$564$		0			0
$565$	−90.7384	−	338.640i	−0.160599	−	0.599363i
$566$		0			0
$567$	457.926	+	457.926i	0.807629	+	0.807629i
$568$		0			0
$569$	−874.495	+	504.890i	−1.53690	+	0.887328i	−0.537880	+	0.843022i	$0.680775\pi$
$569$	−874.495	+	504.890i	−1.53690	+	0.887328i	−0.999018	+	0.0443066i	$0.985892\pi$
$570$		0			0
$571$			135.312i			0.236973i	0.992956	+	0.118487i	$0.0378043\pi$
$571$			135.312i			0.236973i	−0.992956	+	0.118487i	$0.962196\pi$
$572$		0			0
$573$	−1241.21			−2.16616
$574$		0			0
$575$	−125.395	−	217.190i	−0.218078	−	0.377722i
$576$		0			0
$577$	−572.701	+	572.701i	−0.992549	+	0.992549i	−0.999972	−	0.00742366i	$-0.997637\pi$
$577$	−572.701	+	572.701i	−0.992549	+	0.992549i	0.00742366	+	0.999972i	$0.497637\pi$
$578$		0			0
$579$	1295.65	−	347.167i	2.23773	−	0.599598i
$580$		0			0
$581$	240.022	−	415.730i	0.413119	−	0.715543i
$582$		0			0
$583$	−0.946737	+	3.53327i	−0.00162391	+	0.00606050i
$584$		0			0
$585$	587.898	−	273.668i	1.00495	−	0.467809i
$586$		0			0
$587$	486.142	+	130.261i	0.828181	+	0.221910i	0.647920	−	0.761708i	$-0.275639\pi$
$587$	486.142	+	130.261i	0.828181	+	0.221910i	0.180261	+	0.983619i	$0.442306\pi$
$588$		0			0
$589$	−310.764	−	179.420i	−0.527614	−	0.304618i
$590$		0			0
$591$	−25.0994	−	93.6723i	−0.0424694	−	0.158498i
$592$		0			0
$593$	527.121	+	527.121i	0.888906	+	0.888906i	0.994418	−	0.105512i	$-0.0336482\pi$
$593$	527.121	+	527.121i	0.888906	+	0.888906i	−0.105512	+	0.994418i	$0.533648\pi$
$594$		0			0
$595$	−622.027	+	359.127i	−1.04542	+	0.603576i
$596$		0			0
$597$		−	300.968i		−	0.504135i
$598$		0			0
$599$	191.597			0.319862			0.159931	−	0.987128i	$-0.448873\pi$
$599$	191.597			0.319862			0.159931	+	0.987128i	$0.448873\pi$
$600$		0			0
$601$	74.4437	+	128.940i	0.123866	+	0.214543i	0.921289	−	0.388878i	$-0.127137\pi$
$601$	74.4437	+	128.940i	0.123866	+	0.214543i	−0.797423	+	0.603421i	$0.793804\pi$
$602$		0			0
$603$	−94.4349	+	94.4349i	−0.156608	+	0.156608i
$604$		0			0
$605$	508.903	−	136.360i	0.841161	−	0.225389i
$606$		0			0
$607$	−153.424	+	265.738i	−0.252758	+	0.437789i	−0.964284	−	0.264870i	$-0.914671\pi$
$607$	−153.424	+	265.738i	−0.252758	+	0.437789i	0.711526	+	0.702659i	$0.248004\pi$
$608$		0			0
$609$	−295.092	+	1101.30i	−0.484551	+	1.80837i
$610$		0			0
$611$	513.647	−	732.532i	0.840665	−	1.19891i
$612$		0			0
$613$	−158.519	−	42.4749i	−0.258595	−	0.0692903i	0.127192	−	0.991878i	$-0.459403\pi$
$613$	−158.519	−	42.4749i	−0.258595	−	0.0692903i	−0.385787	+	0.922588i	$0.626070\pi$
$614$		0			0
$615$	−738.762	−	426.525i	−1.20124	−	0.693536i
$616$		0			0
$617$	−78.6264	−	293.438i	−0.127433	−	0.475588i	0.872481	−	0.488647i	$-0.162510\pi$
$617$	−78.6264	−	293.438i	−0.127433	−	0.475588i	−0.999915	+	0.0130597i	$0.995843\pi$
$618$		0			0
$619$	−461.763	−	461.763i	−0.745982	−	0.745982i	0.227740	−	0.973722i	$-0.426866\pi$
$619$	−461.763	−	461.763i	−0.745982	−	0.745982i	−0.973722	+	0.227740i	$0.926866\pi$
$620$		0			0
$621$	399.557	−	230.684i	0.643409	−	0.371472i
$622$		0			0
$623$			1474.36i			2.36656i
$624$		0			0
$625$	437.885			0.700615
$626$		0			0
$627$	3.98400	+	6.90049i	0.00635407	+	0.0110056i
$628$		0			0
$629$	−396.754	+	396.754i	−0.630770	+	0.630770i
$630$		0			0
$631$	−637.871	+	170.917i	−1.01089	+	0.270867i	−0.726001	−	0.687694i	$-0.758623\pi$
$631$	−637.871	+	170.917i	−1.01089	+	0.270867i	−0.284888	+	0.958561i	$0.591956\pi$
$632$		0			0
$633$	−295.359	+	511.576i	−0.466602	+	0.808178i
$634$		0			0
$635$	98.5300	−	367.719i	0.155165	−	0.579085i
$636$		0			0
$637$	−841.896	−	1004.68i	−1.32166	−	1.57721i
$638$		0			0
$639$	1291.04	+	345.934i	2.02041	+	0.541367i
$640$		0			0
$641$	475.522	+	274.543i	0.741844	+	0.428304i	0.822740	−	0.568419i	$-0.192445\pi$
$641$	475.522	+	274.543i	0.741844	+	0.428304i	−0.0808951	+	0.996723i	$0.525778\pi$
$642$		0			0
$643$	66.7186	+	248.997i	0.103761	+	0.387243i	0.998202	−	0.0599444i	$-0.0190924\pi$
$643$	66.7186	+	248.997i	0.103761	+	0.387243i	−0.894440	+	0.447187i	$0.852426\pi$
$644$		0			0
$645$	−938.391	−	938.391i	−1.45487	−	1.45487i
$646$		0			0
$647$	372.489	−	215.057i	0.575717	−	0.332390i	−0.183713	−	0.982980i	$-0.558812\pi$
$647$	372.489	−	215.057i	0.575717	−	0.332390i	0.759429	+	0.650590i	$0.225478\pi$
$648$		0			0
$649$			2.82031i			0.00434562i
$650$		0			0
$651$	−2118.36			−3.25400
$652$		0			0
$653$	614.781	+	1064.83i	0.941471	+	1.63068i	0.762667	+	0.646791i	$0.223890\pi$
$653$	614.781	+	1064.83i	0.941471	+	1.63068i	0.178804	+	0.983885i	$0.442777\pi$
$654$		0			0
$655$	−310.734	+	310.734i	−0.474404	+	0.474404i
$656$		0			0
$657$	433.023	−	116.028i	0.659091	−	0.176603i
$658$		0			0
$659$	−135.284	+	234.318i	−0.205286	+	0.355566i	−0.950224	−	0.311568i	$-0.899146\pi$
$659$	−135.284	+	234.318i	−0.205286	+	0.355566i	0.744938	+	0.667134i	$0.232479\pi$
$660$		0			0
$661$	−40.7110	+	151.935i	−0.0615900	+	0.229857i	−0.989859	−	0.142052i	$-0.954630\pi$
$661$	−40.7110	+	151.935i	−0.0615900	+	0.229857i	0.928269	+	0.371909i	$0.121297\pi$
$662$		0			0
$663$	−780.136	+	137.027i	−1.17667	+	0.206677i
$664$		0			0
$665$	482.897	+	129.392i	0.726161	+	0.194574i
$666$		0			0
$667$	−741.819	−	428.290i	−1.11217	−	0.642113i
$668$		0			0
$669$	32.6792	+	121.960i	0.0488478	+	0.182302i
$670$		0			0
$671$	−4.38819	−	4.38819i	−0.00653978	−	0.00653978i
$672$		0			0
$673$	923.369	−	533.107i	1.37202	−	0.792136i	0.380837	−	0.924642i	$-0.375636\pi$
$673$	923.369	−	533.107i	1.37202	−	0.792136i	0.991182	+	0.132506i	$0.0423025\pi$
$674$		0			0
$675$		−	66.8944i		−	0.0991028i
$676$		0			0
$677$	931.367			1.37573			0.687864	−	0.725840i	$-0.258549\pi$
$677$	931.367			1.37573			0.687864	+	0.725840i	$0.258549\pi$
$678$		0			0
$679$	392.088	+	679.115i	0.577448	+	1.00017i
$680$		0			0
$681$	38.8300	−	38.8300i	0.0570191	−	0.0570191i
$682$		0			0
$683$	1022.71	−	274.033i	1.49737	−	0.401220i	0.585153	−	0.810923i	$-0.301034\pi$
$683$	1022.71	−	274.033i	1.49737	−	0.401220i	0.912219	+	0.409703i	$0.134368\pi$
$684$		0			0
$685$	−353.463	+	612.217i	−0.516005	+	0.893747i
$686$		0			0
$687$	−110.215	+	411.328i	−0.160429	+	0.598731i
$688$		0			0
$689$	43.7847	+	249.279i	0.0635482	+	0.361799i
$690$		0			0
$691$	486.794	+	130.436i	0.704477	+	0.188764i	0.593235	−	0.805029i	$-0.297850\pi$
$691$	486.794	+	130.436i	0.704477	+	0.188764i	0.111242	+	0.993793i	$0.464517\pi$
$692$		0			0
$693$	22.8107	+	13.1698i	0.0329159	+	0.0190040i
$694$		0			0
$695$	−157.712	−	588.590i	−0.226924	−	0.846892i
$696$		0			0
$697$	412.568	+	412.568i	0.591920	+	0.591920i
$698$		0			0
$699$	78.8912	−	45.5478i	0.112863	−	0.0651614i
$700$		0			0
$701$			184.217i			0.262792i	0.991330	+	0.131396i	$0.0419460\pi$
$701$			184.217i			0.262792i	−0.991330	+	0.131396i	$0.958054\pi$
$702$		0			0
$703$	390.543			0.555538
$704$		0			0
$705$	677.797	+	1173.98i	0.961415	+	1.66522i
$706$		0			0
$707$	98.0989	−	98.0989i	0.138754	−	0.138754i
$708$		0			0
$709$	−30.2515	+	8.10586i	−0.0426678	+	0.0114328i	−0.280090	−	0.959974i	$-0.590364\pi$
$709$	−30.2515	+	8.10586i	−0.0426678	+	0.0114328i	0.237422	+	0.971407i	$0.423698\pi$
$710$		0			0
$711$	−231.754	+	401.409i	−0.325954	+	0.564570i
$712$		0			0
$713$	411.909	−	1537.27i	0.577713	−	2.15605i
$714$		0			0
$715$	−8.15386	+	6.83271i	−0.0114040	+	0.00955624i
$716$		0			0
$717$	105.209	+	28.1906i	0.146735	+	0.0393174i
$718$		0			0
$719$	−1051.54	−	607.107i	−1.46250	−	0.844377i	−0.463378	−	0.886161i	$-0.653363\pi$
$719$	−1051.54	−	607.107i	−1.46250	−	0.844377i	−0.999127	+	0.0417832i	$0.986696\pi$
$720$		0			0
$721$	321.674	+	1200.50i	0.446150	+	1.66505i
$722$		0			0
$723$	−523.731	−	523.731i	−0.724385	−	0.724385i
$724$		0			0
$725$	−107.557	+	62.0983i	−0.148355	+	0.0856528i
$726$		0			0
$727$		−	511.832i		−	0.704032i	−0.935994	−	0.352016i	$-0.885496\pi$
$727$		−	511.832i		−	0.704032i	0.935994	−	0.352016i	$-0.114504\pi$
$728$		0			0
$729$	−1057.46			−1.45057
$730$		0			0
$731$	453.843	+	786.079i	0.620852	+	1.07535i
$732$		0			0
$733$	−497.445	+	497.445i	−0.678642	+	0.678642i	−0.959693	−	0.281051i	$-0.909317\pi$
$733$	−497.445	+	497.445i	−0.678642	+	0.678642i	0.281051	+	0.959693i	$0.409317\pi$
$734$		0			0
$735$	1918.42	−	514.039i	2.61010	−	0.699373i
$736$		0			0
$737$	1.09545	−	1.89738i	0.00148637	−	0.00257446i
$738$		0			0
$739$	−307.807	+	1148.75i	−0.416518	+	1.55447i	0.365257	+	0.930907i	$0.380981\pi$
$739$	−307.807	+	1148.75i	−0.416518	+	1.55447i	−0.781775	+	0.623560i	$0.785686\pi$
$740$		0			0
$741$	451.402	+	316.520i	0.609180	+	0.427153i
$742$		0			0
$743$	776.623	+	208.096i	1.04525	+	0.280075i	0.740289	−	0.672289i	$-0.234689\pi$
$743$	776.623	+	208.096i	1.04525	+	0.280075i	0.304964	+	0.952364i	$0.401355\pi$
$744$		0			0
$745$	−177.525	−	102.494i	−0.238289	−	0.137576i
$746$		0			0
$747$	116.250	+	433.852i	0.155623	+	0.580793i
$748$		0			0
$749$	38.2168	+	38.2168i	0.0510238	+	0.0510238i
$750$		0			0
$751$	−732.120	+	422.690i	−0.974860	+	0.562836i	−0.900714	−	0.434412i	$-0.856956\pi$
$751$	−732.120	+	422.690i	−0.974860	+	0.562836i	−0.0741456	+	0.997247i	$0.523623\pi$
$752$		0			0
$753$			596.088i			0.791618i
$754$		0			0
$755$	642.135			0.850510
$756$		0			0
$757$	−395.660	−	685.304i	−0.522669	−	0.905289i	−0.999652	−	0.0263768i	$-0.991603\pi$
$757$	−395.660	−	685.304i	−0.522669	−	0.905289i	0.476983	−	0.878913i	$-0.341730\pi$
$758$		0			0
$759$	−24.9885	+	24.9885i	−0.0329229	+	0.0329229i
$760$		0			0
$761$	129.902	−	34.8073i	0.170700	−	0.0457388i	−0.172457	−	0.985017i	$-0.555171\pi$
$761$	129.902	−	34.8073i	0.170700	−	0.0457388i	0.343157	+	0.939278i	$0.388504\pi$
$762$		0			0
$763$	818.159	−	1417.09i	1.07229	−	1.85727i
$764$		0			0
$765$	173.937	−	649.142i	0.227369	−	0.848552i
$766$		0			0
$767$	82.3529	+	176.912i	0.107370	+	0.230654i
$768$		0			0
$769$	−504.897	−	135.287i	−0.656563	−	0.175926i	−0.0848688	−	0.996392i	$-0.527047\pi$
$769$	−504.897	−	135.287i	−0.656563	−	0.175926i	−0.571695	+	0.820467i	$0.693714\pi$
$770$		0			0
$771$	642.058	+	370.692i	0.832760	+	0.480794i
$772$		0			0
$773$	333.549	+	1244.82i	0.431499	+	1.61038i	0.749307	+	0.662222i	$0.230387\pi$
$773$	333.549	+	1244.82i	0.431499	+	1.61038i	−0.317808	+	0.948155i	$0.602947\pi$
$774$		0			0
$775$	−163.167	−	163.167i	−0.210538	−	0.210538i
$776$		0			0
$777$	1996.63	−	1152.75i	2.56967	−	1.48360i
$778$		0			0
$779$		−	406.110i		−	0.521322i
$780$		0			0
$781$	−21.9267			−0.0280751
$782$		0			0
$783$	−114.240	−	197.869i	−0.145900	−	0.252706i
$784$		0			0
$785$	733.325	−	733.325i	0.934172	−	0.934172i
$786$		0			0
$787$	−759.192	+	203.425i	−0.964666	+	0.258481i	−0.706574	−	0.707639i	$-0.749760\pi$
$787$	−759.192	+	203.425i	−0.964666	+	0.258481i	−0.258092	+	0.966120i	$0.583094\pi$
$788$		0			0
$789$	629.981	−	1091.16i	0.798454	−	1.38296i
$790$		0			0
$791$	255.011	−	951.713i	0.322390	−	1.20318i
$792$		0			0
$793$	−403.397	−	147.127i	−0.508697	−	0.185532i
$794$		0			0
$795$	−370.420	−	99.2538i	−0.465937	−	0.124848i
$796$		0			0
$797$	−986.473	−	569.540i	−1.23773	−	0.714605i	−0.269103	−	0.963112i	$-0.586727\pi$
$797$	−986.473	−	569.540i	−1.23773	−	0.714605i	−0.968630	+	0.248506i	$0.920060\pi$
$798$		0			0
$799$	−239.973	−	895.593i	−0.300342	−	1.12089i
$800$		0			0
$801$	−975.455	−	975.455i	−1.21780	−	1.21780i
$802$		0			0
$803$	−6.36903	+	3.67716i	−0.00793155	+	0.00457928i
$804$		0			0
$805$			2217.26i			2.75435i
$806$		0			0
$807$	−436.775			−0.541233
$808$		0			0
$809$	628.900	+	1089.29i	0.777380	+	1.34646i	0.933447	+	0.358715i	$0.116785\pi$
$809$	628.900	+	1089.29i	0.777380	+	1.34646i	−0.156067	+	0.987746i	$0.549882\pi$
$810$		0			0
$811$	−803.747	+	803.747i	−0.991056	+	0.991056i	−0.999960	−	0.00890417i	$-0.997166\pi$
$811$	−803.747	+	803.747i	−0.991056	+	0.991056i	0.00890417	+	0.999960i	$0.497166\pi$
$812$		0			0
$813$	380.702	−	102.009i	0.468268	−	0.125472i
$814$		0			0
$815$	−109.820	+	190.213i	−0.134748	+	0.233390i
$816$		0			0
$817$	163.518	−	610.256i	0.200144	−	0.746947i
$818$		0			0
$819$	1815.43	+	160.039i	2.21664	+	0.195408i
$820$		0			0
$821$	−768.362	−	205.882i	−0.935885	−	0.250770i	−0.241523	−	0.970395i	$-0.577647\pi$
$821$	−768.362	−	205.882i	−0.935885	−	0.250770i	−0.694363	+	0.719625i	$0.744314\pi$
$822$		0			0
$823$	759.985	+	438.777i	0.923432	+	0.533144i	0.884728	−	0.466107i	$-0.154344\pi$
$823$	759.985	+	438.777i	0.923432	+	0.533144i	0.0387039	+	0.999251i	$0.487677\pi$
$824$		0			0
$825$	1.32615	+	4.94926i	0.00160745	+	0.00599910i
$826$		0			0
$827$	−491.372	−	491.372i	−0.594162	−	0.594162i	0.344591	−	0.938753i	$-0.388018\pi$
$827$	−491.372	−	491.372i	−0.594162	−	0.594162i	−0.938753	+	0.344591i	$0.888018\pi$
$828$		0			0
$829$	703.770	−	406.322i	0.848938	−	0.490135i	−0.0113542	−	0.999936i	$-0.503614\pi$
$829$	703.770	−	406.322i	0.848938	−	0.490135i	0.860292	+	0.509801i	$0.170281\pi$
$830$		0			0
$831$			1551.40i			1.86690i
$832$		0			0
$833$	−1358.43			−1.63077
$834$		0			0
$835$	−153.822	−	266.428i	−0.184218	−	0.319076i
$836$		0			0
$837$	300.172	−	300.172i	0.358629	−	0.358629i
$838$		0			0
$839$	−946.909	+	253.724i	−1.12862	+	0.302412i	−0.774366	−	0.632738i	$-0.781931\pi$
$839$	−946.909	+	253.724i	−1.12862	+	0.302412i	−0.354251	+	0.935150i	$0.615264\pi$
$840$		0			0
$841$	208.402	−	360.962i	0.247802	−	0.429206i
$842$		0			0
$843$	−144.500	+	539.280i	−0.171411	+	0.639715i
$844$		0			0
$845$	−311.959	+	666.694i	−0.369182	+	0.788987i
$846$		0			0
$847$	1430.22	+	383.225i	1.68857	+	0.452450i
$848$		0			0
$849$	−1418.49	−	818.968i	−1.67078	−	0.964626i
$850$		0			0
$851$	448.301	+	1673.08i	0.526793	+	1.96602i
$852$		0			0
$853$	580.816	+	580.816i	0.680909	+	0.680909i	0.960205	−	0.279296i	$-0.0901010\pi$
$853$	580.816	+	580.816i	0.680909	+	0.680909i	−0.279296	+	0.960205i	$0.590101\pi$
$854$		0			0
$855$	−405.097	+	233.883i	−0.473798	+	0.273547i
$856$		0			0
$857$			315.815i			0.368512i	0.982878	+	0.184256i	$0.0589876\pi$
$857$			315.815i			0.368512i	−0.982878	+	0.184256i	$0.941012\pi$
$858$		0			0
$859$	−606.340			−0.705868			−0.352934	−	0.935648i	$-0.614816\pi$
$859$	−606.340			−0.705868			−0.352934	+	0.935648i	$0.614816\pi$
$860$		0			0
$861$	−1198.70	−	2076.21i	−1.39222	−	2.41140i
$862$		0			0
$863$	369.845	−	369.845i	0.428557	−	0.428557i	−0.459580	−	0.888137i	$-0.652000\pi$
$863$	369.845	−	369.845i	0.428557	−	0.428557i	0.888137	+	0.459580i	$0.152000\pi$
$864$		0			0
$865$	−226.361	+	60.6532i	−0.261689	+	0.0701193i
$866$		0			0
$867$	243.068	−	421.006i	0.280355	−	0.485589i
$868$		0			0
$869$	1.96802	−	7.34473i	0.00226469	−	0.00845194i
$870$		0			0
$871$	13.3119	−	151.006i	0.0152835	−	0.173370i
$872$		0			0
$873$	−708.719	−	189.901i	−0.811820	−	0.217527i
$874$		0			0
$875$	1432.67	+	827.152i	1.63734	+	0.945316i
$876$		0			0
$877$	60.3112	+	225.084i	0.0687699	+	0.256653i	0.991749	−	0.128198i	$-0.0409194\pi$
$877$	60.3112	+	225.084i	0.0687699	+	0.256653i	−0.922979	+	0.384851i	$0.874253\pi$
$878$		0			0
$879$	−353.091	−	353.091i	−0.401696	−	0.401696i
$880$		0			0
$881$	−1485.29	+	857.533i	−1.68591	+	0.973363i	−0.728324	+	0.685233i	$0.759700\pi$
$881$	−1485.29	+	857.533i	−1.68591	+	0.973363i	−0.957591	+	0.288130i	$0.906966\pi$
$882$		0			0
$883$		−	1305.91i		−	1.47895i	−0.673186	−	0.739473i	$-0.735075\pi$
$883$		−	1305.91i		−	1.47895i	0.673186	−	0.739473i	$-0.264925\pi$
$884$		0			0
$885$	−295.675			−0.334096
$886$		0			0
$887$	−702.463	−	1216.70i	−0.791954	−	1.37170i	−0.924755	−	0.380562i	$-0.875731\pi$
$887$	−702.463	−	1216.70i	−0.791954	−	1.37170i	0.132801	−	0.991143i	$-0.457603\pi$
$888$		0			0
$889$	756.527	−	756.527i	0.850987	−	0.850987i
$890$		0			0
$891$	9.60168	−	2.57276i	0.0107763	−	0.00288750i
$892$		0			0
$893$	−322.678	+	558.894i	−0.361341	+	0.625861i
$894$		0			0
$895$	−209.625	+	782.330i	−0.234218	+	0.874112i
$896$		0			0
$897$	−837.809	+	2297.13i	−0.934012	+	2.56091i
$898$		0			0
$899$	−761.288	−	203.986i	−0.846816	−	0.226904i
$900$		0			0
$901$	227.153	+	131.147i	0.252112	+	0.145557i
$902$		0			0
$903$	−965.300	−	3602.55i	−1.06899	−	3.98953i
$904$		0			0
$905$	−999.955	−	999.955i	−1.10492	−	1.10492i
$906$		0			0
$907$	−840.882	+	485.483i	−0.927102	+	0.535263i	−0.885894	−	0.463888i	$-0.846454\pi$
$907$	−840.882	+	485.483i	−0.927102	+	0.535263i	−0.0412083	+	0.999151i	$0.513121\pi$
$908$		0			0
$909$			129.807i			0.142801i
$910$		0			0
$911$	−1263.64			−1.38710			−0.693548	−	0.720410i	$-0.743953\pi$
$911$	−1263.64			−1.38710			−0.693548	+	0.720410i	$0.743953\pi$
$912$		0			0
$913$	−3.68421	−	6.38124i	−0.00403528	−	0.00698930i
$914$		0			0
$915$	460.048	−	460.048i	0.502784	−	0.502784i
$916$		0			0
$917$	−1192.93	+	319.645i	−1.30091	+	0.348577i
$918$		0			0
$919$	316.006	−	547.338i	0.343858	−	0.595580i	−0.641287	−	0.767301i	$-0.721599\pi$
$919$	316.006	−	547.338i	0.343858	−	0.595580i	0.985146	+	0.171721i	$0.0549327\pi$
$920$		0			0
$921$	36.7657	−	137.212i	0.0399193	−	0.148981i
$922$		0			0
$923$	−1375.41	+	640.258i	−1.49015	+	0.693671i
$924$		0			0
$925$	242.582	+	64.9998i	0.262251	+	0.0702700i
$926$		0			0
$927$	−1007.09	−	581.443i	−1.08639	−	0.627230i
$928$		0			0
$929$	−294.866	−	1100.45i	−0.317401	−	1.18456i	−0.921733	−	0.387824i	$-0.873227\pi$
$929$	−294.866	−	1100.45i	−0.317401	−	1.18456i	0.604332	−	0.796732i	$-0.293440\pi$
$930$		0			0
$931$	668.581	+	668.581i	0.718132	+	0.718132i
$932$		0			0
$933$	884.230	−	510.510i	0.947727	−	0.547171i
$934$		0			0
$935$			11.0248i			0.0117913i
$936$		0			0
$937$	−474.906			−0.506837			−0.253418	−	0.967357i	$-0.581555\pi$
$937$	−474.906			−0.506837			−0.253418	+	0.967357i	$0.581555\pi$
$938$		0			0
$939$	−364.469	−	631.278i	−0.388145	−	0.672288i
$940$		0			0
$941$	1282.41	−	1282.41i	1.36282	−	1.36282i	0.492516	−	0.870304i	$-0.336077\pi$
$941$	1282.41	−	1282.41i	1.36282	−	1.36282i	0.870304	−	0.492516i	$-0.163923\pi$
$942$		0			0
$943$	1739.77	−	466.170i	1.84493	−	0.494348i
$944$		0			0
$945$	−295.710	+	512.184i	−0.312920	+	0.541994i
$946$		0			0
$947$	177.213	−	661.369i	0.187131	−	0.698383i	−0.807033	−	0.590506i	$-0.798928\pi$
$947$	177.213	−	661.369i	0.187131	−	0.698383i	0.994164	−	0.107877i	$-0.0344052\pi$
$948$		0			0
$949$	−292.143	+	416.636i	−0.307842	+	0.439026i
$950$		0			0
$951$	−113.192	−	30.3298i	−0.119024	−	0.0318925i
$952$		0			0
$953$	341.556	+	197.197i	0.358401	+	0.206923i	0.668379	−	0.743821i	$-0.266988\pi$
$953$	341.556	+	197.197i	0.358401	+	0.206923i	−0.309978	+	0.950744i	$0.600322\pi$
$954$		0			0
$955$	309.383	+	1154.63i	0.323961	+	1.20904i
$956$		0			0
$957$	12.3748	+	12.3748i	0.0129308	+	0.0129308i
$958$		0			0
$959$	−1720.57	+	993.371i	−1.79413	+	1.03584i
$960$		0			0
$961$		−	503.344i		−	0.523771i
$962$		0			0
$963$	−50.5693			−0.0525122
$964$		0			0
$965$	−645.903	−	1118.74i	−0.669329	−	1.15931i
$966$		0			0
$967$	345.208	−	345.208i	0.356989	−	0.356989i	−0.505713	−	0.862702i	$-0.668770\pi$
$967$	345.208	−	345.208i	0.356989	−	0.356989i	0.862702	+	0.505713i	$0.168770\pi$
$968$		0			0
$969$	551.884	−	147.877i	0.569540	−	0.152608i
$970$		0			0
$971$	−18.9265	+	32.7816i	−0.0194917	+	0.0337607i	−0.875607	−	0.483025i	$-0.839538\pi$
$971$	−18.9265	+	32.7816i	−0.0194917	+	0.0337607i	0.856115	+	0.516785i	$0.172871\pi$
$972$		0			0
$973$	443.233	−	1654.17i	0.455533	−	1.70007i
$974$		0			0
$975$	227.705	+	271.733i	0.233543	+	0.278700i
$976$		0			0
$977$	1155.80	+	309.697i	1.18301	+	0.316987i	0.796121	−	0.605137i	$-0.206882\pi$
$977$	1155.80	+	309.697i	1.18301	+	0.316987i	0.386892	+	0.922125i	$0.373548\pi$
$978$		0			0
$979$	19.5988	+	11.3153i	0.0200192	+	0.0115581i
$980$		0			0
$981$	396.261	+	1478.87i	0.403936	+	1.50751i
$982$		0			0
$983$	−434.522	−	434.522i	−0.442036	−	0.442036i	0.450660	−	0.892696i	$-0.351189\pi$
$983$	−434.522	−	434.522i	−0.442036	−	0.442036i	−0.892696	+	0.450660i	$0.851189\pi$
$984$		0			0
$985$	−80.8821	+	46.6973i	−0.0821138	+	0.0474084i
$986$		0			0
$987$			3809.76i			3.85993i
$988$		0			0
$989$	2802.03			2.83320
$990$		0			0
$991$	−836.377	−	1448.65i	−0.843973	−	1.46180i	−0.886511	−	0.462708i	$-0.846878\pi$
$991$	−836.377	−	1448.65i	−0.843973	−	1.46180i	0.0425380	−	0.999095i	$-0.486456\pi$
$992$		0			0
$993$	−1476.30	+	1476.30i	−1.48671	+	1.48671i
$994$		0			0
$995$	−279.975	+	75.0190i	−0.281382	+	0.0753960i
$996$		0			0
$997$	−77.1444	+	133.618i	−0.0773765	+	0.134020i	−0.902117	−	0.431491i	$-0.857988\pi$
$997$	−77.1444	+	133.618i	−0.0773765	+	0.134020i	0.824741	+	0.565511i	$0.191321\pi$
$998$		0			0
$999$	−119.578	+	446.269i	−0.119697	+	0.446716i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.3.bd.g.145.2		8
4.3	odd	2		104.3.v.c.41.1	yes	8
13.7	odd	12	inner	208.3.bd.g.33.2		8
52.7	even	12		104.3.v.c.33.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.3.v.c.33.1	✓	8	52.7	even	12
104.3.v.c.41.1	yes	8	4.3	odd	2
208.3.bd.g.33.2		8	13.7	odd	12	inner
208.3.bd.g.145.2		8	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	208.bd (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26125 + 3.91659i) q^{3} +(3.07976 - 3.07976i) q^{5} +(11.8234 - 3.16808i) q^{7} +(-5.72647 + 9.91853i) q^{9} +(0.0486283 - 0.181483i) q^{11} +(-2.24896 - 12.8040i) q^{13} +(19.0263 + 5.09808i) q^{15} +(-11.6675 - 6.73623i) q^{17} +(2.42703 + 9.05781i) q^{19} +(39.1437 + 39.1437i) q^{21} +(-36.0176 + 20.7948i) q^{23} +6.03012i q^{25} -11.0934 q^{27} +(10.2980 + 17.8367i) q^{29} +(-27.0587 + 27.0587i) q^{31} +(0.820756 - 0.219921i) q^{33} +(26.6564 - 46.1703i) q^{35} +(10.7792 - 40.2285i) q^{37} +(45.0626 - 37.7612i) q^{39} +(-41.8319 - 11.2088i) q^{41} +(-58.3471 - 33.6867i) q^{43} +(12.9106 + 48.1829i) q^{45} +(48.6637 + 48.6637i) q^{47} +(87.3214 - 50.4150i) q^{49} -60.9291i q^{51} -19.4689 q^{53} +(-0.409162 - 0.708689i) q^{55} +(-29.9876 + 29.9876i) q^{57} +(-14.4993 + 3.88508i) q^{59} +(16.5150 - 28.6048i) q^{61} +(-36.2838 + 135.413i) q^{63} +(-46.3595 - 32.5070i) q^{65} +(11.2635 + 3.01805i) q^{67} +(-162.889 - 94.0442i) q^{69} +(-30.2048 - 112.726i) q^{71} +(-27.6780 - 27.6780i) q^{73} +(-23.6175 + 13.6356i) q^{75} -2.29981i q^{77} +40.4706 q^{79} +(26.4533 + 45.8185i) q^{81} +(27.7311 - 27.7311i) q^{83} +(-56.6791 + 15.1871i) q^{85} +(-46.5727 + 80.6663i) q^{87} +(-31.1747 + 116.345i) q^{89} +(-67.1544 - 144.262i) q^{91} +(-167.164 - 44.7915i) q^{93} +(35.3706 + 20.4212i) q^{95} +(16.5810 + 61.8810i) q^{97} +(1.52158 + 1.52158i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 2 q^{5} + 36 q^{7} - 22 q^{9} + 24 q^{11} + 26 q^{13} + 76 q^{15} + 42 q^{17} + 18 q^{19} + 42 q^{21} - 48 q^{23} - 244 q^{27} - 36 q^{29} + 16 q^{31} + 18 q^{33} + 6 q^{35} + 112 q^{37}+ \cdots - 576 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 2 * q^5 + 36 * q^7 - 22 * q^9 + 24 * q^11 + 26 * q^13 + 76 * q^15 + 42 * q^17 + 18 * q^19 + 42 * q^21 - 48 * q^23 - 244 * q^27 - 36 * q^29 + 16 * q^31 + 18 * q^33 + 6 * q^35 + 112 * q^37 + 80 * q^39 - 104 * q^41 + 174 * q^43 + 94 * q^45 + 32 * q^47 + 222 * q^49 + 56 * q^53 + 42 * q^55 - 258 * q^57 - 64 * q^59 - 106 * q^61 - 276 * q^63 - 152 * q^65 - 138 * q^67 - 474 * q^69 - 126 * q^71 + 14 * q^73 - 160 * q^79 - 256 * q^81 - 104 * q^83 - 418 * q^85 + 276 * q^87 + 246 * q^89 + 72 * q^91 - 434 * q^93 + 600 * q^95 - 234 * q^97 - 576 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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