LMFDB - Embedded newform 117.3.p.a.107.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(35,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("117.35");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.p (of order $6$, degree $2$, 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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 32 x^{18} + 690 x^{16} - 7984 x^{14} + 66147 x^{12} - 315440 x^{10} + 1074610 x^{8} + \cdots + 1327104 $ x^20 - 32x^18 + 690x^16 - 7984x^14 + 66147x^12 - 315440x^10 + 1074610x^8 - 2130504x^6 + 3043521x^4 - 2471040*x^2 + 1327104
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.1
Root			$-3.42041 - 1.97477i$ of defining polynomial
Character	$\chi$	$=$	117.107
Dual form			117.3.p.a.35.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.42041 + 1.97477i) q^{2} +(5.79946 - 10.0450i) q^{4} -3.48286i q^{5} +(-3.91511 + 6.78116i) q^{7} +30.0123i q^{8} +(6.87786 + 11.9128i) q^{10} +(-1.34563 + 0.776897i) q^{11} +(-10.1673 + 8.10098i) q^{13} -30.9258i q^{14} +(-36.0696 - 62.4744i) q^{16} +(0.0458820 + 0.0264900i) q^{17} +(-9.50972 + 16.4713i) q^{19} +(-34.9852 - 20.1987i) q^{20} +(3.06839 - 5.31461i) q^{22} +(-24.2254 + 13.9865i) q^{23} +12.8697 q^{25} +(18.7787 - 47.7868i) q^{26} +(45.4110 + 78.6542i) q^{28} +(-19.5861 + 11.3080i) q^{29} -28.9341 q^{31} +(142.780 + 82.4340i) q^{32} -0.209247 q^{34} +(23.6179 + 13.6358i) q^{35} +(-7.55065 - 13.0781i) q^{37} -75.1181i q^{38} +104.529 q^{40} +(-10.8214 + 6.24772i) q^{41} +(-17.8186 + 30.8627i) q^{43} +18.0223i q^{44} +(55.2404 - 95.6792i) q^{46} +25.2020i q^{47} +(-6.15612 - 10.6627i) q^{49} +(-44.0195 + 25.4147i) q^{50} +(22.4091 + 149.111i) q^{52} -20.1527i q^{53} +(2.70583 + 4.68663i) q^{55} +(-203.518 - 117.501i) q^{56} +(44.6616 - 77.3562i) q^{58} +(72.6718 + 41.9571i) q^{59} +(46.1130 - 79.8701i) q^{61} +(98.9665 - 57.1383i) q^{62} -362.597 q^{64} +(28.2146 + 35.4113i) q^{65} +(-8.65002 - 14.9823i) q^{67} +(0.532182 - 0.307255i) q^{68} -107.710 q^{70} +(6.70449 + 3.87084i) q^{71} -60.2339 q^{73} +(51.6526 + 29.8216i) q^{74} +(110.302 + 191.049i) q^{76} -12.1665i q^{77} +59.5786 q^{79} +(-217.590 + 125.625i) q^{80} +(24.6757 - 42.7395i) q^{82} -69.3433i q^{83} +(0.0922610 - 0.159801i) q^{85} -140.751i q^{86} +(-23.3164 - 40.3853i) q^{88} +(7.25951 - 4.19128i) q^{89} +(-15.1280 - 100.662i) q^{91} +324.457i q^{92} +(-49.7683 - 86.2012i) q^{94} +(57.3673 + 33.1210i) q^{95} +(25.0793 - 43.4386i) q^{97} +(42.1129 + 24.3139i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) $ 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−3.42041	+	1.97477i	−1.71020	+	0.987387i	−0.775938	+	0.630809i	$0.782723\pi$
$2$	−3.42041	+	1.97477i	−1.71020	+	0.987387i	−0.934266	+	0.356577i	$0.883944\pi$
$3$		0			0
$3$		0			0
$4$	5.79946	−	10.0450i	1.44986	−	2.51124i
$5$		−	3.48286i		−	0.696572i	−0.937388	−	0.348286i	$-0.886764\pi$
$5$		−	3.48286i		−	0.696572i	0.937388	−	0.348286i	$-0.113236\pi$
$6$		0			0
$7$	−3.91511	+	6.78116i	−0.559301	+	0.968738i	0.438254	+	0.898851i	$0.355597\pi$
$7$	−3.91511	+	6.78116i	−0.559301	+	0.968738i	−0.997555	+	0.0698865i	$0.977736\pi$
$8$			30.0123i			3.75153i
$9$		0			0
$10$	6.87786	+	11.9128i	0.687786	+	1.19128i
$11$	−1.34563	+	0.776897i	−0.122330	+	0.0706270i	−0.559916	−	0.828549i	$-0.689167\pi$
$11$	−1.34563	+	0.776897i	−0.122330	+	0.0706270i	0.437587	+	0.899176i	$0.355833\pi$
$12$		0			0
$13$	−10.1673	+	8.10098i	−0.782101	+	0.623152i
$13$	−10.1673	+	8.10098i	−0.782101	+	0.623152i
$14$		−	30.9258i		−	2.20899i
$15$		0			0
$16$	−36.0696	−	62.4744i	−2.25435	−	3.90465i
$17$	0.0458820	+	0.0264900i	0.00269894	+	0.00155824i	0.501349	−	0.865245i	$-0.332837\pi$
$17$	0.0458820	+	0.0264900i	0.00269894	+	0.00155824i	−0.498650	+	0.866803i	$0.666171\pi$
$18$		0			0
$19$	−9.50972	+	16.4713i	−0.500511	+	0.866911i	0.499488	+	0.866321i	$0.333521\pi$
$19$	−9.50972	+	16.4713i	−0.500511	+	0.866911i	−1.00000		0.000590683i	$0.999812\pi$
$20$	−34.9852	−	20.1987i	−1.74926	−	1.00994i
$21$		0			0
$22$	3.06839	−	5.31461i	0.139472	−	0.241573i
$23$	−24.2254	+	13.9865i	−1.05328	+	0.608110i	−0.923565	−	0.383442i	$-0.874739\pi$
$23$	−24.2254	+	13.9865i	−1.05328	+	0.608110i	−0.129712	+	0.991552i	$0.541405\pi$
$24$		0			0
$25$	12.8697			0.514787
$26$	18.7787	−	47.7868i	0.722259	−	1.83795i
$27$		0			0
$28$	45.4110	+	78.6542i	1.62182	+	2.80908i
$29$	−19.5861	+	11.3080i	−0.675383	+	0.389932i	−0.798113	−	0.602508i	$-0.794168\pi$
$29$	−19.5861	+	11.3080i	−0.675383	+	0.389932i	0.122730	+	0.992440i	$0.460835\pi$
$30$		0			0
$31$	−28.9341			−0.933359			−0.466679	−	0.884427i	$-0.654550\pi$
$31$	−28.9341			−0.933359			−0.466679	+	0.884427i	$0.654550\pi$
$32$	142.780	+	82.4340i	4.46187	+	2.57606i
$33$		0			0
$34$	−0.209247			−0.00615432
$35$	23.6179	+	13.6358i	0.674796	+	0.389594i
$36$		0			0
$37$	−7.55065	−	13.0781i	−0.204072	−	0.353462i	0.745765	−	0.666209i	$-0.232084\pi$
$37$	−7.55065	−	13.0781i	−0.204072	−	0.353462i	−0.949837	+	0.312747i	$0.898751\pi$
$38$		−	75.1181i		−	1.97679i
$39$		0			0
$40$	104.529			2.61321
$41$	−10.8214	+	6.24772i	−0.263936	+	0.152383i	−0.626129	−	0.779720i	$-0.715362\pi$
$41$	−10.8214	+	6.24772i	−0.263936	+	0.152383i	0.362193	+	0.932103i	$0.382028\pi$
$42$		0			0
$43$	−17.8186	+	30.8627i	−0.414385	+	0.717736i	−0.995364	−	0.0961826i	$-0.969337\pi$
$43$	−17.8186	+	30.8627i	−0.414385	+	0.717736i	0.580978	+	0.813919i	$0.302670\pi$
$44$			18.0223i			0.409598i
$45$		0			0
$46$	55.2404	−	95.6792i	1.20088	−	2.07998i
$47$			25.2020i			0.536213i	0.963389	+	0.268107i	$0.0863980\pi$
$47$			25.2020i			0.536213i	−0.963389	+	0.268107i	$0.913602\pi$
$48$		0			0
$49$	−6.15612	−	10.6627i	−0.125635	−	0.217606i
$50$	−44.0195	+	25.4147i	−0.880391	+	0.508294i
$51$		0			0
$52$	22.4091	+	149.111i	0.430944	+	2.86753i
$53$		−	20.1527i		−	0.380240i	−0.981761	−	0.190120i	$-0.939112\pi$
$53$		−	20.1527i		−	0.380240i	0.981761	−	0.190120i	$-0.0608876\pi$
$54$		0			0
$55$	2.70583	+	4.68663i	0.0491968	+	0.0852114i
$56$	−203.518	−	117.501i	−3.63425	−	2.09824i
$57$		0			0
$58$	44.6616	−	77.3562i	0.770028	−	1.33373i
$59$	72.6718	+	41.9571i	1.23173	+	0.711137i	0.967389	−	0.253294i	$-0.0815139\pi$
$59$	72.6718	+	41.9571i	1.23173	+	0.711137i	0.264336	+	0.964431i	$0.414847\pi$
$60$		0			0
$61$	46.1130	−	79.8701i	0.755951	−	1.30935i	−0.188949	−	0.981987i	$-0.560508\pi$
$61$	46.1130	−	79.8701i	0.755951	−	1.30935i	0.944900	−	0.327359i	$-0.106158\pi$
$62$	98.9665	−	57.1383i	1.59623	−	0.921586i
$63$		0			0
$64$	−362.597			−5.66558
$65$	28.2146	+	35.4113i	0.434071	+	0.544790i
$66$		0			0
$67$	−8.65002	−	14.9823i	−0.129105	−	0.223616i	0.794225	−	0.607624i	$-0.207877\pi$
$67$	−8.65002	−	14.9823i	−0.129105	−	0.223616i	−0.923330	+	0.384007i	$0.874544\pi$
$68$	0.532182	−	0.307255i	0.00782620	−	0.00451846i
$69$		0			0
$70$	−107.710			−1.53872
$71$	6.70449	+	3.87084i	0.0944295	+	0.0545189i	0.546471	−	0.837478i	$-0.315971\pi$
$71$	6.70449	+	3.87084i	0.0944295	+	0.0545189i	−0.452042	+	0.891997i	$0.649304\pi$
$72$		0			0
$73$	−60.2339			−0.825122			−0.412561	−	0.910930i	$-0.635366\pi$
$73$	−60.2339			−0.825122			−0.412561	+	0.910930i	$0.635366\pi$
$74$	51.6526	+	29.8216i	0.698008	+	0.402995i
$75$		0			0
$76$	110.302	+	191.049i	1.45135	+	2.51381i
$77$		−	12.1665i		−	0.158007i
$78$		0			0
$79$	59.5786			0.754159			0.377080	−	0.926181i	$-0.376928\pi$
$79$	59.5786			0.754159			0.377080	+	0.926181i	$0.376928\pi$
$80$	−217.590	+	125.625i	−2.71987	+	1.57032i
$81$		0			0
$82$	24.6757	−	42.7395i	0.300923	−	0.521213i
$83$		−	69.3433i		−	0.835461i	−0.908571	−	0.417731i	$-0.862826\pi$
$83$		−	69.3433i		−	0.835461i	0.908571	−	0.417731i	$-0.137174\pi$
$84$		0			0
$85$	0.0922610	−	0.159801i	0.00108542	−	0.00188001i
$86$		−	140.751i		−	1.63663i
$87$		0			0
$88$	−23.3164	−	40.3853i	−0.264960	−	0.458924i
$89$	7.25951	−	4.19128i	0.0815675	−	0.0470930i	−0.458661	−	0.888611i	$-0.651671\pi$
$89$	7.25951	−	4.19128i	0.0815675	−	0.0470930i	0.540229	+	0.841518i	$0.318338\pi$
$90$		0			0
$91$	−15.1280	−	100.662i	−0.166241	−	1.10618i
$92$			324.457i			3.52671i
$93$		0			0
$94$	−49.7683	−	86.2012i	−0.529450	−	0.917034i
$95$	57.3673	+	33.1210i	0.603866	+	0.348642i
$96$		0			0
$97$	25.0793	−	43.4386i	0.258550	−	0.447821i	−0.707304	−	0.706909i	$-0.750089\pi$
$97$	25.0793	−	43.4386i	0.258550	−	0.447821i	0.965854	+	0.259088i	$0.0834221\pi$
$98$	42.1129	+	24.3139i	0.429723	+	0.248101i
$99$		0			0
$100$	74.6371	−	129.275i	0.746371	−	1.29275i
$101$	−150.510	+	86.8971i	−1.49020	+	0.860367i	−0.999937	−	0.0112080i	$-0.996432\pi$
$101$	−150.510	+	86.8971i	−1.49020	+	0.860367i	−0.490262	+	0.871575i	$0.663099\pi$
$102$		0			0
$103$	41.2736			0.400714			0.200357	−	0.979723i	$-0.435790\pi$
$103$	41.2736			0.400714			0.200357	+	0.979723i	$0.435790\pi$
$104$	−243.129	−	305.144i	−2.33778	−	2.93408i
$105$		0			0
$106$	39.7970	+	68.9304i	0.375444	+	0.650287i
$107$	134.548	−	77.6813i	1.25746	−	0.725994i	0.284878	−	0.958564i	$-0.408047\pi$
$107$	134.548	−	77.6813i	1.25746	−	0.725994i	0.972580	+	0.232570i	$0.0747135\pi$
$108$		0			0
$109$	106.118			0.973560			0.486780	−	0.873525i	$-0.338171\pi$
$109$	106.118			0.973560			0.486780	+	0.873525i	$0.338171\pi$
$110$	−18.5101	−	10.6868i	−0.168273	−	0.0971526i
$111$		0			0
$112$	564.865			5.04344
$113$	31.6552	+	18.2761i	0.280134	+	0.161736i	0.633484	−	0.773756i	$-0.281624\pi$
$113$	31.6552	+	18.2761i	0.280134	+	0.161736i	−0.353350	+	0.935491i	$0.614957\pi$
$114$		0			0
$115$	48.7131	+	84.3736i	0.423592	+	0.733684i
$116$			262.322i			2.26140i
$117$		0			0
$118$	−331.423			−2.80867
$119$	−0.359266	+	0.207422i	−0.00301904	+	0.00174305i
$120$		0			0
$121$	−59.2929	+	102.698i	−0.490024	+	0.848746i
$122$			364.251i			2.98566i
$123$		0			0
$124$	−167.802	+	290.642i	−1.35324	+	2.34389i
$125$		−	131.895i		−	1.05516i
$126$		0			0
$127$	59.4737	+	103.011i	0.468297	+	0.811114i	0.999344	−	0.0362288i	$-0.0115345\pi$
$127$	59.4737	+	103.011i	0.468297	+	0.811114i	−0.531047	+	0.847342i	$0.678201\pi$
$128$	669.110	−	386.311i	5.22742	−	3.01805i
$129$		0			0
$130$	−166.435	−	65.4038i	−1.28027	−	0.503106i
$131$			16.9004i			0.129010i	0.997917	+	0.0645052i	$0.0205469\pi$
$131$			16.9004i			0.129010i	−0.997917	+	0.0645052i	$0.979453\pi$
$132$		0			0
$133$	−74.4631	−	128.974i	−0.559873	−	0.969729i
$134$	59.1732	+	34.1637i	0.441591	+	0.254953i
$135$		0			0
$136$	−0.795025	+	1.37702i	−0.00584577	+	0.0101252i
$137$	−129.092	−	74.5312i	−0.942277	−	0.544024i	−0.0516033	−	0.998668i	$-0.516433\pi$
$137$	−129.092	−	74.5312i	−0.942277	−	0.544024i	−0.890673	+	0.454644i	$0.849766\pi$
$138$		0			0
$139$	−12.4281	+	21.5261i	−0.0894109	+	0.154864i	−0.907262	−	0.420565i	$-0.861832\pi$
$139$	−12.4281	+	21.5261i	−0.0894109	+	0.154864i	0.817851	+	0.575429i	$0.195165\pi$
$140$	273.942	−	158.160i	1.95673	−	1.12972i
$141$		0			0
$142$	−30.5761			−0.215325
$143$	7.38776	−	18.7998i	0.0516627	−	0.131467i
$144$		0			0
$145$	39.3843	+	68.2157i	0.271616	+	0.470453i
$146$	206.024	−	118.948i	1.41113	−	0.814714i
$147$		0			0
$148$	−175.159			−1.18350
$149$	−216.107	−	124.769i	−1.45038	−	0.837377i	−0.451877	−	0.892080i	$-0.649245\pi$
$149$	−216.107	−	124.769i	−1.45038	−	0.837377i	−0.998503	+	0.0547033i	$0.982579\pi$
$150$		0			0
$151$	−177.640			−1.17642			−0.588212	−	0.808706i	$-0.700168\pi$
$151$	−177.640			−1.17642			−0.588212	+	0.808706i	$0.700168\pi$
$152$	−494.342	−	285.408i	−3.25225	−	1.87769i
$153$		0			0
$154$	24.0262	+	41.6145i	0.156014	+	0.270224i
$155$			100.774i			0.650152i
$156$		0			0
$157$	15.6911			0.0999435			0.0499717	−	0.998751i	$-0.484087\pi$
$157$	15.6911			0.0999435			0.0499717	+	0.998751i	$0.484087\pi$
$158$	−203.783	+	117.654i	−1.28977	+	0.744647i
$159$		0			0
$160$	287.106	−	497.283i	1.79441	−	3.10802i
$161$		−	219.035i		−	1.36047i
$162$		0			0
$163$	−70.9192	+	122.836i	−0.435087	+	0.753593i	−0.997303	−	0.0733975i	$-0.976616\pi$
$163$	−70.9192	+	122.836i	−0.435087	+	0.753593i	0.562215	+	0.826991i	$0.309949\pi$
$164$			144.934i			0.883741i
$165$		0			0
$166$	136.937	+	237.182i	0.824923	+	1.42881i
$167$	−190.922	+	110.229i	−1.14325	+	0.660054i	−0.947233	−	0.320547i	$-0.896133\pi$
$167$	−190.922	+	110.229i	−1.14325	+	0.660054i	−0.196015	+	0.980601i	$0.562800\pi$
$168$		0			0
$169$	37.7483	−	164.730i	0.223363	−	0.974735i
$170$			0.728778i			0.00428693i
$171$		0			0
$172$	206.676	+	357.973i	1.20161	+	2.08124i
$173$	−209.161	−	120.759i	−1.20902	−	0.698029i	−0.246476	−	0.969149i	$-0.579273\pi$
$173$	−209.161	−	120.759i	−1.20902	−	0.698029i	−0.962546	+	0.271120i	$0.912606\pi$
$174$		0			0
$175$	−50.3861	+	87.2714i	−0.287921	+	0.498694i
$176$	97.0723	+	56.0447i	0.551547	+	0.318436i
$177$		0			0
$178$	−16.5537	+	28.6718i	−0.0929981	+	0.161077i
$179$	124.823	−	72.0666i	0.697335	−	0.402607i	−0.109019	−	0.994040i	$-0.534771\pi$
$179$	124.823	−	72.0666i	0.697335	−	0.402607i	0.806354	+	0.591433i	$0.201438\pi$
$180$		0			0
$181$	177.598			0.981203			0.490601	−	0.871384i	$-0.336777\pi$
$181$	177.598			0.981203			0.490601	+	0.871384i	$0.336777\pi$
$182$	250.529	+	314.432i	1.37653	+	1.72765i
$183$		0			0
$184$	−419.767	−	727.058i	−2.28134	−	3.95140i
$185$	−45.5492	+	26.2979i	−0.246212	+	0.142151i
$186$		0			0
$187$	−0.0823200			−0.000440214
$188$	253.153	+	146.158i	1.34656	+	0.777437i
$189$		0			0
$190$	−261.626			−1.37698
$191$	253.098	+	146.126i	1.32512	+	0.765058i	0.984540	−	0.175158i	$-0.0560436\pi$
$191$	253.098	+	146.126i	1.32512	+	0.765058i	0.340579	+	0.940216i	$0.389377\pi$
$192$		0			0
$193$	127.537	+	220.900i	0.660813	+	1.14456i	0.980402	+	0.197005i	$0.0631216\pi$
$193$	127.537	+	220.900i	0.660813	+	1.14456i	−0.319590	+	0.947556i	$0.603545\pi$
$194$			198.104i			1.02115i
$195$		0			0
$196$	−142.809			−0.728616
$197$	110.874	−	64.0128i	0.562810	−	0.324938i	−0.191463	−	0.981500i	$-0.561323\pi$
$197$	110.874	−	64.0128i	0.562810	−	0.324938i	0.754272	+	0.656562i	$0.227990\pi$
$198$		0			0
$199$	−98.5281	+	170.656i	−0.495116	+	0.857566i	−0.999984	−	0.00563041i	$-0.998208\pi$
$199$	−98.5281	+	170.656i	−0.495116	+	0.857566i	0.504868	+	0.863196i	$0.331541\pi$
$200$			386.248i			1.93124i
$201$		0			0
$202$	343.204	−	594.447i	1.69903	−	2.94281i
$203$		−	177.089i		−	0.872358i
$204$		0			0
$205$	21.7599	+	37.6893i	0.106146	+	0.183850i
$206$	−141.172	+	81.5059i	−0.685303	+	0.395660i
$207$		0			0
$208$	872.834	+	342.997i	4.19632	+	1.64902i
$209$		−	29.5523i		−	0.141399i
$210$		0			0
$211$	−30.3040	−	52.4880i	−0.143621	−	0.248758i	0.785237	−	0.619196i	$-0.212541\pi$
$211$	−30.3040	−	52.4880i	−0.143621	−	0.248758i	−0.928858	+	0.370437i	$0.879208\pi$
$212$	−202.433	−	116.875i	−0.954873	−	0.551296i
$213$		0			0
$214$	−306.806	+	531.404i	−1.43367	+	2.48319i
$215$	107.490	+	62.0596i	0.499955	+	0.288649i
$216$		0			0
$217$	113.280	−	196.207i	0.522028	−	0.904180i
$218$	−362.967	+	209.559i	−1.66499	+	0.961280i
$219$		0			0
$220$	62.7693			0.285315
$221$	−0.681092	+	0.102357i	−0.00308186	+	0.000463155i
$222$		0			0
$223$	72.0887	+	124.861i	0.323268	+	0.559916i	0.981160	−	0.193196i	$-0.0618852\pi$
$223$	72.0887	+	124.861i	0.323268	+	0.559916i	−0.657892	+	0.753112i	$0.728552\pi$
$224$	−1118.00	+	645.476i	−4.99106	+	2.88159i
$225$		0			0
$226$	−144.365			−0.638782
$227$	111.046	+	64.1125i	0.489190	+	0.282434i	0.724238	−	0.689550i	$-0.242192\pi$
$227$	111.046	+	64.1125i	0.489190	+	0.282434i	−0.235048	+	0.971984i	$0.575525\pi$
$228$		0			0
$229$	−286.798			−1.25239			−0.626197	−	0.779665i	$-0.715390\pi$
$229$	−286.798			−1.25239			−0.626197	+	0.779665i	$0.715390\pi$
$230$	−333.238	−	192.395i	−1.44886	−	0.836499i
$231$		0			0
$232$	−339.380	−	587.823i	−1.46284	−	2.53372i
$233$			57.2952i			0.245902i	0.992413	+	0.122951i	$0.0392358\pi$
$233$			57.2952i			0.245902i	−0.992413	+	0.122951i	$0.960764\pi$
$234$		0			0
$235$	87.7752			0.373511
$236$	842.914	−	486.657i	3.57167	−	2.06210i
$237$		0			0
$238$	0.819224	−	1.41894i	0.00344212	−	0.00596192i
$239$		−	190.663i		−	0.797755i	−0.917004	−	0.398878i	$-0.869400\pi$
$239$		−	190.663i		−	0.797755i	0.917004	−	0.398878i	$-0.130600\pi$
$240$		0			0
$241$	195.341	−	338.341i	0.810546	−	1.40391i	−0.101937	−	0.994791i	$-0.532504\pi$
$241$	195.341	−	338.341i	0.810546	−	1.40391i	0.912483	−	0.409115i	$-0.134163\pi$
$242$		−	468.360i		−	1.93537i
$243$		0			0
$244$	−534.861	−	926.406i	−2.19205	−	3.79675i
$245$	−37.1368	+	21.4409i	−0.151579	+	0.0875140i
$246$		0			0
$247$	−36.7455	−	244.507i	−0.148767	−	0.989907i
$248$		−	868.379i		−	3.50153i
$249$		0			0
$250$	260.462	+	451.134i	1.04185	+	1.80454i
$251$	204.609	+	118.131i	0.815177	+	0.470642i	0.848750	−	0.528794i	$-0.177356\pi$
$251$	204.609	+	118.131i	0.815177	+	0.470642i	−0.0335737	+	0.999436i	$0.510689\pi$
$252$		0			0
$253$	21.7322	−	37.6412i	0.0858980	−	0.148780i
$254$	−406.848	−	234.894i	−1.60177	−	0.924780i
$255$		0			0
$256$	−800.559	+	1386.61i	−3.12718	+	5.41644i
$257$	−168.597	+	97.3394i	−0.656018	+	0.378752i	−0.790758	−	0.612129i	$-0.790313\pi$
$257$	−168.597	+	97.3394i	−0.656018	+	0.378752i	0.134740	+	0.990881i	$0.456980\pi$
$258$		0			0
$259$	118.246			0.456550
$260$	519.335	−	78.0478i	1.99744	−	0.300184i
$261$		0			0
$262$	−33.3744	−	57.8061i	−0.127383	−	0.220634i
$263$	−369.214	+	213.166i	−1.40386	+	0.810516i	−0.994786	−	0.101987i	$-0.967480\pi$
$263$	−369.214	+	213.166i	−1.40386	+	0.810516i	−0.409070	+	0.912503i	$0.634147\pi$
$264$		0			0
$265$	−70.1891			−0.264864
$266$	509.388	+	294.096i	1.91499	+	1.10562i
$267$		0			0
$268$	−200.662			−0.748738
$269$	463.435	+	267.564i	1.72281	+	0.994662i	0.912996	+	0.407969i	$0.133763\pi$
$269$	463.435	+	267.564i	1.72281	+	0.994662i	0.809809	+	0.586693i	$0.199571\pi$
$270$		0			0
$271$	−55.6910	−	96.4596i	−0.205502	−	0.355939i	0.744791	−	0.667298i	$-0.232549\pi$
$271$	−55.6910	−	96.4596i	−0.205502	−	0.355939i	−0.950292	+	0.311359i	$0.899216\pi$
$272$		−	3.82193i		−	0.0140512i
$273$		0			0
$274$	588.729			2.14865
$275$	−17.3178	+	9.99841i	−0.0629737	+	0.0363579i
$276$		0			0
$277$	56.3692	−	97.6342i	0.203499	−	0.352470i	−0.746155	−	0.665773i	$-0.768102\pi$
$277$	56.3692	−	97.6342i	0.203499	−	0.352470i	0.949653	+	0.313303i	$0.101435\pi$
$278$		−	98.1708i		−	0.353132i
$279$		0			0
$280$	−409.241	+	708.826i	−1.46157	+	2.53152i
$281$			317.901i			1.13132i	0.824638	+	0.565660i	$0.191379\pi$
$281$			317.901i			1.13132i	−0.824638	+	0.565660i	$0.808621\pi$
$282$		0			0
$283$	195.437	+	338.506i	0.690589	+	1.19614i	0.971645	+	0.236444i	$0.0759820\pi$
$283$	195.437	+	338.506i	0.690589	+	1.19614i	−0.281056	+	0.959691i	$0.590685\pi$
$284$	77.7649	−	44.8976i	0.273820	−	0.158090i
$285$		0			0
$286$	11.8563	+	78.8922i	0.0414555	+	0.275847i
$287$		−	97.8419i		−	0.340913i
$288$		0			0
$289$	−144.499	−	250.279i	−0.499995	−	0.866017i
$290$	−269.421	−	155.550i	−0.929038	−	0.536380i
$291$		0			0
$292$	−349.324	+	605.047i	−1.19631	+	2.07208i
$293$	313.014	+	180.719i	1.06831	+	0.616788i	0.927719	−	0.373280i	$-0.121767\pi$
$293$	313.014	+	180.719i	1.06831	+	0.616788i	0.140589	+	0.990068i	$0.455100\pi$
$294$		0			0
$295$	146.131	−	253.106i	0.495358	−	0.857986i
$296$	392.504	−	226.612i	1.32603	−	0.765581i
$297$		0			0
$298$	985.563			3.30726
$299$	133.002	−	338.455i	0.444824	−	1.13195i
$300$		0			0
$301$	−139.523	−	241.661i	−0.463532	−	0.802861i
$302$	607.602	−	350.799i	2.01193	−	1.16159i
$303$		0			0
$304$	1372.05			4.51331
$305$	−278.176	−	160.605i	−0.912054	−	0.526574i
$306$		0			0
$307$	−442.916			−1.44272			−0.721362	−	0.692558i	$-0.756484\pi$
$307$	−442.916			−1.44272			−0.721362	+	0.692558i	$0.756484\pi$
$308$	−122.212	−	70.5593i	−0.396793	−	0.229089i
$309$		0			0
$310$	−199.005	−	344.687i	−0.641951	−	1.11189i
$311$			546.608i			1.75758i	0.477206	+	0.878792i	$0.341650\pi$
$311$			546.608i			1.75758i	−0.477206	+	0.878792i	$0.658350\pi$
$312$		0			0
$313$	−421.281			−1.34595			−0.672974	−	0.739667i	$-0.734983\pi$
$313$	−421.281			−1.34595			−0.672974	+	0.739667i	$0.734983\pi$
$314$	−53.6700	+	30.9864i	−0.170924	+	0.0986829i
$315$		0			0
$316$	345.523	−	598.464i	1.09343	−	1.89387i
$317$			80.2351i			0.253108i	0.991960	+	0.126554i	$0.0403917\pi$
$317$			80.2351i			0.253108i	−0.991960	+	0.126554i	$0.959608\pi$
$318$		0			0
$319$	17.5704	−	30.4328i	0.0550795	−	0.0954005i
$320$			1262.88i			3.94649i
$321$		0			0
$322$	432.544	+	749.189i	1.34331	+	2.32667i
$323$	−0.872650	+	0.503825i	−0.00270170	+	0.00155983i
$324$		0			0
$325$	−130.850	+	104.257i	−0.402615	+	0.320791i
$326$		−	560.198i		−	1.71840i
$327$		0			0
$328$	−187.508	−	324.774i	−0.571671	−	0.990164i
$329$	−170.899	−	98.6686i	−0.519450	−	0.299905i
$330$		0			0
$331$	−31.8141	+	55.1037i	−0.0961152	+	0.166476i	−0.910073	−	0.414447i	$-0.863975\pi$
$331$	−31.8141	+	55.1037i	−0.0961152	+	0.166476i	0.813958	+	0.580923i	$0.197308\pi$
$332$	−696.550	−	402.153i	−2.09804	−	1.21131i
$333$		0			0
$334$	435.355	−	754.056i	1.30346	−	2.25765i
$335$	−52.1812	+	30.1268i	−0.155765	+	0.0899308i
$336$		0			0
$337$	394.465			1.17052			0.585260	−	0.810846i	$-0.300992\pi$
$337$	394.465			1.17052			0.585260	+	0.810846i	$0.300992\pi$
$338$	196.190	+	637.989i	0.580445	+	1.88754i
$339$		0			0
$340$	−1.07013	−	1.85352i	−0.00314743	−	0.00545152i
$341$	38.9345	−	22.4788i	0.114177	−	0.0659203i
$342$		0			0
$343$	−287.273			−0.837531
$344$	−926.259	−	534.776i	−2.69261	−	1.55458i
$345$		0			0
$346$	953.887			2.75690
$347$	263.595	+	152.187i	0.759640	+	0.438578i	0.829166	−	0.559002i	$-0.188816\pi$
$347$	263.595	+	152.187i	0.759640	+	0.438578i	−0.0695266	+	0.997580i	$0.522149\pi$
$348$		0			0
$349$	272.010	+	471.135i	0.779399	+	1.34996i	0.932289	+	0.361715i	$0.117809\pi$
$349$	272.010	+	471.135i	0.779399	+	1.34996i	−0.152890	+	0.988243i	$0.548858\pi$
$350$		−	398.005i		−	1.13716i
$351$		0			0
$352$	−256.171			−0.727758
$353$	−172.625	+	99.6651i	−0.489023	+	0.282337i	−0.724169	−	0.689623i	$-0.757776\pi$
$353$	−172.625	+	99.6651i	−0.489023	+	0.282337i	0.235146	+	0.971960i	$0.424443\pi$
$354$		0			0
$355$	13.4816	−	23.3508i	0.0379764	−	0.0657770i
$356$		−	97.2286i		−	0.273114i
$357$		0			0
$358$	−284.630	+	492.994i	−0.795057	+	1.37708i
$359$		−	113.145i		−	0.315167i	−0.987506	−	0.157584i	$-0.949630\pi$
$359$		−	113.145i		−	0.315167i	0.987506	−	0.157584i	$-0.0503704\pi$
$360$		0			0
$361$	−0.369463	−	0.639928i	−0.00102344	−	0.00177265i
$362$	−607.457	+	350.715i	−1.67806	+	0.968827i
$363$		0			0
$364$	−1098.88	−	431.827i	−3.01891	−	1.18634i
$365$			209.786i			0.574757i
$366$		0			0
$367$	−139.798	−	242.138i	−0.380922	−	0.659777i	0.610272	−	0.792192i	$-0.291060\pi$
$367$	−139.798	−	242.138i	−0.380922	−	0.659777i	−0.991194	+	0.132415i	$0.957727\pi$
$368$	1747.60	+	1008.98i	4.74891	+	2.74178i
$369$		0			0
$370$	103.865	−	179.899i	0.280715	−	0.486213i
$371$	136.659	+	78.9000i	0.368352	+	0.212668i
$372$		0			0
$373$	−133.323	+	230.922i	−0.357435	+	0.619095i	−0.987532	−	0.157421i	$-0.949682\pi$
$373$	−133.323	+	230.922i	−0.357435	+	0.619095i	0.630097	+	0.776517i	$0.283015\pi$
$374$	0.281568	−	0.162563i	0.000752856	−	0.000434661i
$375$		0			0
$376$	−756.370			−2.01162
$377$	107.532	−	273.639i	0.285230	−	0.725833i
$378$		0			0
$379$	257.310	+	445.675i	0.678919	+	1.17592i	0.975307	+	0.220855i	$0.0708847\pi$
$379$	257.310	+	445.675i	0.678919	+	1.17592i	−0.296388	+	0.955068i	$0.595782\pi$
$380$	665.399	−	384.168i	1.75105	−	1.01097i
$381$		0			0
$382$	−1154.26			−3.02163
$383$	−310.787	−	179.433i	−0.811455	−	0.468494i	0.0360060	−	0.999352i	$-0.488536\pi$
$383$	−310.787	−	179.433i	−0.811455	−	0.468494i	−0.847461	+	0.530858i	$0.821870\pi$
$384$		0			0
$385$	−42.3744			−0.110063
$386$	−872.456	−	503.713i	−2.26025	−	1.30496i
$387$		0			0
$388$	−290.893	−	503.841i	−0.749724	−	1.29856i
$389$		−	46.5721i		−	0.119723i	−0.998207	−	0.0598613i	$-0.980934\pi$
$389$		−	46.5721i		−	0.119723i	0.998207	−	0.0598613i	$-0.0190659\pi$
$390$		0			0
$391$	−1.48201			−0.00379031
$392$	320.012	−	184.759i	0.816358	−	0.471324i
$393$		0			0
$394$	−252.822	+	437.900i	−0.641679	+	1.11142i
$395$		−	207.504i		−	0.525326i
$396$		0			0
$397$	−125.251	+	216.942i	−0.315495	+	0.546453i	−0.979543	−	0.201237i	$-0.935504\pi$
$397$	−125.251	+	216.942i	−0.315495	+	0.546453i	0.664048	+	0.747690i	$0.268837\pi$
$398$		−	778.282i		−	1.95548i
$399$		0			0
$400$	−464.204	−	804.025i	−1.16051	−	2.01006i
$401$	352.188	−	203.336i	0.878275	−	0.507072i	0.00818543	−	0.999966i	$-0.497394\pi$
$401$	352.188	−	203.336i	0.878275	−	0.507072i	0.870089	+	0.492894i	$0.164061\pi$
$402$		0			0
$403$	294.182	−	234.395i	0.729980	−	0.581625i
$404$			2015.82i			4.98966i
$405$		0			0
$406$	349.710	+	605.716i	0.861355	+	1.49191i
$407$	20.3207	+	11.7322i	0.0499280	+	0.0288259i
$408$		0			0
$409$	−120.999	+	209.577i	−0.295842	+	0.512413i	−0.975180	−	0.221412i	$-0.928933\pi$
$409$	−120.999	+	209.577i	−0.295842	+	0.512413i	0.679339	+	0.733825i	$0.262267\pi$
$410$	−148.856	−	85.9419i	−0.363063	−	0.209614i
$411$		0			0
$412$	239.364	−	414.591i	0.580981	−	1.00629i
$413$	−569.036	+	328.533i	−1.37781	+	0.795479i
$414$		0			0
$415$	−241.513			−0.581959
$416$	−2119.48	+	318.525i	−5.09491	+	0.765685i
$417$		0			0
$418$	58.3591	+	101.081i	0.139615	+	0.241820i
$419$	−121.143	+	69.9420i	−0.289124	+	0.166926i	−0.637547	−	0.770412i	$-0.720051\pi$
$419$	−121.143	+	69.9420i	−0.289124	+	0.166926i	0.348423	+	0.937338i	$0.386717\pi$
$420$		0			0
$421$	78.3626			0.186135			0.0930673	−	0.995660i	$-0.470333\pi$
$421$	78.3626			0.186135			0.0930673	+	0.995660i	$0.470333\pi$
$422$	207.304	+	119.687i	0.491242	+	0.283618i
$423$		0			0
$424$	604.828			1.42648
$425$	0.590487	+	0.340918i	0.00138938	+	0.000802159i
$426$		0			0
$427$	361.075	+	625.400i	0.845608	+	1.46464i
$428$		−	1802.04i		−	4.21037i
$429$		0			0
$430$	−490.215			−1.14003
$431$	−475.554	+	274.561i	−1.10337	+	0.637033i	−0.937105	−	0.349048i	$-0.886505\pi$
$431$	−475.554	+	274.561i	−1.10337	+	0.637033i	−0.166268	+	0.986081i	$0.553172\pi$
$432$		0			0
$433$	−366.932	+	635.544i	−0.847417	+	1.46777i	0.0360879	+	0.999349i	$0.488510\pi$
$433$	−366.932	+	635.544i	−0.847417	+	1.46777i	−0.883505	+	0.468421i	$0.844823\pi$
$434$			894.811i			2.06178i
$435$		0			0
$436$	615.427	−	1065.95i	1.41153	−	2.44484i
$437$		−	532.032i		−	1.21746i
$438$		0			0
$439$	−243.833	−	422.332i	−0.555429	−	0.962031i	−0.997870	−	0.0652337i	$-0.979221\pi$
$439$	−243.833	−	422.332i	−0.555429	−	0.962031i	0.442441	−	0.896798i	$-0.354113\pi$
$440$	−140.656	+	81.2080i	−0.319673	+	0.184564i
$441$		0			0
$442$	2.12748	−	1.69511i	0.00481330	−	0.00383508i
$443$		−	626.871i		−	1.41506i	−0.706684	−	0.707530i	$-0.749810\pi$
$443$		−	626.871i		−	1.41506i	0.706684	−	0.707530i	$-0.250190\pi$
$444$		0			0
$445$	−14.5977	−	25.2839i	−0.0328037	−	0.0568177i
$446$	−493.146	−	284.718i	−1.10571	−	0.638381i
$447$		0			0
$448$	1419.61	−	2458.83i	3.16876	−	5.48846i
$449$	288.400	+	166.508i	0.642315	+	0.370841i	0.785506	−	0.618854i	$-0.212403\pi$
$449$	288.400	+	166.508i	0.642315	+	0.370841i	−0.143191	+	0.989695i	$0.545736\pi$
$450$		0			0
$451$	9.70767	−	16.8142i	0.0215248	−	0.0372820i
$452$	367.166	−	211.983i	0.812314	−	0.468990i
$453$		0			0
$454$	−506.430			−1.11549
$455$	−350.593	+	52.6886i	−0.770534	+	0.115799i
$456$		0			0
$457$	−178.056	−	308.403i	−0.389620	−	0.674842i	0.602778	−	0.797909i	$-0.294060\pi$
$457$	−178.056	−	308.403i	−0.389620	−	0.674842i	−0.992398	+	0.123067i	$0.960727\pi$
$458$	980.967	−	566.362i	2.14185	−	1.23660i
$459$		0			0
$460$	1130.04			2.45661
$461$	220.638	+	127.385i	0.478607	+	0.276324i	0.719836	−	0.694145i	$-0.244217\pi$
$461$	220.638	+	127.385i	0.478607	+	0.276324i	−0.241229	+	0.970468i	$0.577550\pi$
$462$		0			0
$463$	−292.288			−0.631292			−0.315646	−	0.948877i	$-0.602221\pi$
$463$	−292.288			−0.631292			−0.315646	+	0.948877i	$0.602221\pi$
$464$	1412.93	+	815.753i	3.04510	+	1.75809i
$465$		0			0
$466$	−113.145	−	195.973i	−0.242800	−	0.420543i
$467$			380.785i			0.815385i	0.913119	+	0.407692i	$0.133666\pi$
$467$			380.785i			0.815385i	−0.913119	+	0.407692i	$0.866334\pi$
$468$		0			0
$469$	135.463			0.288834
$470$	−300.227	+	173.336i	−0.638780	+	0.368800i
$471$		0			0
$472$	−1259.23	+	2181.05i	−2.66785	+	4.62086i
$473$		−	55.3728i		−	0.117067i
$474$		0			0
$475$	−122.387	+	211.980i	−0.257657	+	0.446275i
$476$			4.81175i			0.0101087i
$477$		0			0
$478$	376.517	+	652.147i	0.787693	+	1.36432i
$479$	−161.150	+	93.0402i	−0.336431	+	0.194238i	−0.658693	−	0.752412i	$-0.728890\pi$
$479$	−161.150	+	93.0402i	−0.336431	+	0.194238i	0.322262	+	0.946651i	$0.395557\pi$
$480$		0			0
$481$	182.715	+	71.8015i	0.379865	+	0.149275i
$482$			1543.02i			3.20129i
$483$		0			0
$484$	687.733	+	1191.19i	1.42094	+	2.46113i
$485$	−151.291	−	87.3478i	−0.311940	−	0.180098i
$486$		0			0
$487$	286.705	−	496.588i	0.588717	−	1.01969i	−0.405684	−	0.914013i	$-0.632967\pi$
$487$	286.705	−	496.588i	0.588717	−	1.01969i	0.994401	−	0.105674i	$-0.0336999\pi$
$488$	2397.08	+	1383.96i	4.91205	+	2.83598i
$489$		0			0
$490$	84.6819	−	146.673i	0.172820	−	0.299333i
$491$	362.363	−	209.211i	0.738011	−	0.426091i	−0.0833348	−	0.996522i	$-0.526557\pi$
$491$	362.363	−	209.211i	0.738011	−	0.426091i	0.821346	+	0.570431i	$0.193224\pi$
$492$		0			0
$493$	−1.19820			−0.00243043
$494$	608.530	+	763.749i	1.23184	+	1.54605i
$495$		0			0
$496$	1043.64	+	1807.64i	2.10412	+	3.64444i
$497$	−52.4976	+	30.3095i	−0.105629	+	0.0609849i
$498$		0			0
$499$	446.216			0.894221			0.447110	−	0.894479i	$-0.352453\pi$
$499$	446.216			0.894221			0.447110	+	0.894479i	$0.352453\pi$
$500$	−1324.88	−	764.919i	−2.64976	−	1.52984i
$501$		0			0
$502$	−933.130			−1.85882
$503$	−400.438	−	231.193i	−0.796100	−	0.459628i	0.0460057	−	0.998941i	$-0.485351\pi$
$503$	−400.438	−	231.193i	−0.796100	−	0.459628i	−0.842106	+	0.539313i	$0.818684\pi$
$504$		0			0
$505$	302.650	+	524.206i	0.599308	+	1.03803i
$506$			171.665i			0.339258i
$507$		0			0
$508$	1379.66			2.71587
$509$	136.418	−	78.7609i	0.268012	−	0.154737i	−0.359972	−	0.932963i	$-0.617214\pi$
$509$	136.418	−	78.7609i	0.268012	−	0.154737i	0.627984	+	0.778227i	$0.283880\pi$
$510$		0			0
$511$	235.822	−	408.456i	0.461491	−	0.799327i
$512$		−	3233.20i		−	6.31484i
$513$		0			0
$514$	384.446	−	665.881i	0.747950	−	1.29549i
$515$		−	143.750i		−	0.279126i
$516$		0			0
$517$	−19.5794	−	33.9125i	−0.0378711	−	0.0655947i
$518$	−404.451	+	233.510i	−0.780793	+	0.450791i
$519$		0			0
$520$	−1062.77	+	846.784i	−2.04380	+	1.62843i
$521$			110.574i			0.212234i	0.994354	+	0.106117i	$0.0338418\pi$
$521$			110.574i			0.212234i	−0.994354	+	0.106117i	$0.966158\pi$
$522$		0			0
$523$	−172.086	−	298.061i	−0.329036	−	0.569907i	0.653285	−	0.757112i	$-0.273390\pi$
$523$	−172.086	−	298.061i	−0.329036	−	0.569907i	−0.982321	+	0.187205i	$0.940057\pi$
$524$	169.763	+	98.0129i	0.323976	+	0.187047i
$525$		0			0
$526$	841.908	−	1458.23i	1.60059	−	2.77230i
$527$	−1.32756	−	0.766465i	−0.00251908	−	0.00145439i
$528$		0			0
$529$	126.746	−	219.530i	0.239595	−	0.414991i
$530$	240.075	−	138.607i	0.452972	−	0.261524i
$531$		0			0
$532$	−1727.38			−3.24696
$533$	59.4115	−	151.186i	0.111466	−	0.283651i
$534$		0			0
$535$	−270.553	−	468.612i	−0.505707	−	0.875910i
$536$	449.652	−	259.607i	0.838903	−	0.484341i
$537$		0			0
$538$	−2113.51			−3.92846
$539$	16.5677	+	9.56535i	0.0307378	+	0.0177465i
$540$		0			0
$541$	−248.721			−0.459742			−0.229871	−	0.973221i	$-0.573830\pi$
$541$	−248.721			−0.459742			−0.229871	+	0.973221i	$0.573830\pi$
$542$	380.972	+	219.954i	0.702900	+	0.405819i
$543$		0			0
$544$	4.36735	+	7.56448i	0.00802822	+	0.0139053i
$545$		−	369.594i		−	0.678155i
$546$		0			0
$547$	576.229			1.05344			0.526718	−	0.850040i	$-0.323423\pi$
$547$	576.229			1.05344			0.526718	+	0.850040i	$0.323423\pi$
$548$	−1497.33	+	864.482i	−2.73235	+	1.57752i
$549$		0			0
$550$	39.4892	−	68.3973i	0.0717985	−	0.124359i
$551$		−	430.145i		−	0.780663i
$552$		0			0
$553$	−233.256	+	404.012i	−0.421802	+	0.730582i
$554$			445.265i			0.803728i
$555$		0			0
$556$	144.153	+	249.680i	0.259267	+	0.449064i
$557$	593.466	−	342.638i	1.06547	−	0.615149i	0.138529	−	0.990358i	$-0.455763\pi$
$557$	593.466	−	342.638i	1.06547	−	0.615149i	0.926940	+	0.375210i	$0.122429\pi$
$558$		0			0
$559$	−68.8509	−	458.138i	−0.123168	−	0.819567i
$560$		−	1967.35i		−	3.51312i
$561$		0			0
$562$	−627.783	−	1087.35i	−1.11705	−	1.93479i
$563$	−389.054	−	224.620i	−0.691037	−	0.398970i	0.112963	−	0.993599i	$-0.463966\pi$
$563$	−389.054	−	224.620i	−0.691037	−	0.398970i	−0.804000	+	0.594629i	$0.797299\pi$
$564$		0			0
$565$	63.6532	−	110.251i	0.112661	−	0.195134i
$566$	−1336.95	−	771.886i	−2.36210	−	1.36376i
$567$		0			0
$568$	−116.173	+	201.217i	−0.204530	+	0.354255i
$569$	265.734	−	153.422i	0.467019	−	0.269634i	−0.247972	−	0.968767i	$-0.579764\pi$
$569$	265.734	−	153.422i	0.467019	−	0.269634i	0.714991	+	0.699134i	$0.246431\pi$
$570$		0			0
$571$	−207.442			−0.363296			−0.181648	−	0.983364i	$-0.558143\pi$
$571$	−207.442			−0.363296			−0.181648	+	0.983364i	$0.558143\pi$
$572$	−145.999	−	183.239i	−0.255242	−	0.320347i
$573$		0			0
$574$	193.216	+	334.659i	0.336613	+	0.583030i
$575$	−311.773	+	180.002i	−0.542213	+	0.313047i
$576$		0			0
$577$	1016.11			1.76102			0.880508	−	0.474031i	$-0.157201\pi$
$577$	1016.11			1.76102			0.880508	+	0.474031i	$0.157201\pi$
$578$	988.488	+	570.704i	1.71019	+	0.987377i
$579$		0			0
$580$	913.631			1.57523
$581$	470.228	+	271.486i	0.809343	+	0.467274i
$582$		0			0
$583$	15.6566	+	27.1180i	0.0268552	+	0.0465146i
$584$		−	1807.76i		−	3.09547i
$585$		0			0
$586$	−1427.52			−2.43603
$587$	491.007	−	283.483i	0.836469	−	0.482936i	−0.0195935	−	0.999808i	$-0.506237\pi$
$587$	491.007	−	283.483i	0.836469	−	0.482936i	0.856062	+	0.516872i	$0.172904\pi$
$588$		0			0
$589$	275.155	−	476.583i	0.467157	−	0.809139i
$590$			1154.30i			1.95644i
$591$		0			0
$592$	−544.698	+	943.444i	−0.920097	+	1.59366i
$593$			534.041i			0.900575i	0.892884	+	0.450287i	$0.148678\pi$
$593$			534.041i			0.900575i	−0.892884	+	0.450287i	$0.851322\pi$
$594$		0			0
$595$	0.722423	+	1.25127i	0.00121416	+	0.00210298i
$596$	−2506.60	+	1447.19i	−4.20571	+	2.42817i
$597$		0			0
$598$	213.449	+	1420.30i	0.356938	+	2.37509i
$599$			277.715i			0.463631i	0.972760	+	0.231816i	$0.0744666\pi$
$599$			277.715i			0.463631i	−0.972760	+	0.231816i	$0.925533\pi$
$600$		0			0
$601$	−397.687	−	688.814i	−0.661709	−	1.14611i	−0.980166	−	0.198176i	$-0.936498\pi$
$601$	−397.687	−	688.814i	−0.661709	−	1.14611i	0.318458	−	0.947937i	$-0.396835\pi$
$602$	954.452	+	551.053i	1.58547	+	0.915371i
$603$		0			0
$604$	−1030.22	+	1784.39i	−1.70566	+	2.95428i
$605$	357.684	+	206.509i	0.591213	+	0.341337i
$606$		0			0
$607$	−151.132	+	261.768i	−0.248981	+	0.431248i	−0.963243	−	0.268630i	$-0.913429\pi$
$607$	−151.132	+	261.768i	−0.248981	+	0.431248i	0.714262	+	0.699878i	$0.246762\pi$
$608$	−2715.59	+	1567.85i	−4.46644	+	2.57870i
$609$		0			0
$610$	1268.64			2.07973
$611$	−204.161	−	256.237i	−0.334142	−	0.419373i
$612$		0			0
$613$	196.015	+	339.508i	0.319763	+	0.553846i	0.980438	−	0.196826i	$-0.0630633\pi$
$613$	196.015	+	339.508i	0.319763	+	0.553846i	−0.660675	+	0.750672i	$0.729730\pi$
$614$	1514.95	−	874.659i	2.46735	−	1.42453i
$615$		0			0
$616$	365.146			0.592769
$617$	579.136	+	334.364i	0.938632	+	0.541919i	0.889531	−	0.456874i	$-0.151031\pi$
$617$	579.136	+	334.364i	0.938632	+	0.541919i	0.0491007	+	0.998794i	$0.484364\pi$
$618$		0			0
$619$	1111.30			1.79532			0.897661	−	0.440686i	$-0.145265\pi$
$619$	1111.30			1.79532			0.897661	+	0.440686i	$0.145265\pi$
$620$	1012.27	+	584.432i	1.63269	+	0.942632i
$621$		0			0
$622$	−1079.43	−	1869.62i	−1.73541	−	3.00583i
$623$			65.6372i			0.105357i
$624$		0			0
$625$	−137.630			−0.220207
$626$	1440.95	−	831.935i	2.30184	−	1.32897i
$627$		0			0
$628$	91.0000	−	157.617i	0.144905	−	0.250982i
$629$		−	0.800067i		−	0.00127197i
$630$		0			0
$631$	384.366	−	665.742i	0.609138	−	1.05506i	−0.382245	−	0.924061i	$-0.624849\pi$
$631$	384.366	−	665.742i	0.609138	−	1.05506i	0.991383	−	0.130997i	$-0.0418178\pi$
$632$			1788.09i			2.82925i
$633$		0			0
$634$	−158.446	−	274.437i	−0.249915	−	0.432866i
$635$	358.775	−	207.139i	0.564999	−	0.326203i
$636$		0			0
$637$	148.970	+	58.5405i	0.233861	+	0.0919003i
$638$			138.790i			0.217539i
$639$		0			0
$640$	−1345.47	−	2330.42i	−2.10229	−	3.64128i
$641$	651.395	+	376.083i	1.01622	+	0.586713i	0.913006	−	0.407947i	$-0.133755\pi$
$641$	651.395	+	376.083i	1.01622	+	0.586713i	0.103211	+	0.994660i	$0.467088\pi$
$642$		0			0
$643$	−266.402	+	461.421i	−0.414311	+	0.717607i	−0.995356	−	0.0962641i	$-0.969311\pi$
$643$	−266.402	+	461.421i	−0.414311	+	0.717607i	0.581045	+	0.813871i	$0.302644\pi$
$644$	−2200.20	−	1270.28i	−3.41645	−	1.97249i
$645$		0			0
$646$	1.98988	−	3.44657i	0.00308031	−	0.00533525i
$647$	−444.157	+	256.434i	−0.686487	+	0.396343i	−0.802294	−	0.596928i	$-0.796388\pi$
$647$	−444.157	+	256.434i	−0.686487	+	0.396343i	0.115808	+	0.993272i	$0.463054\pi$
$648$		0			0
$649$	−130.385			−0.200902
$650$	241.676	−	615.000i	0.371810	−	0.946154i
$651$		0			0
$652$	822.586	+	1424.76i	1.26164	+	2.18522i
$653$	−265.640	+	153.367i	−0.406799	+	0.234866i	−0.689413	−	0.724368i	$-0.742132\pi$
$653$	−265.640	+	153.367i	−0.406799	+	0.234866i	0.282614	+	0.959234i	$0.408798\pi$
$654$		0			0
$655$	58.8616			0.0898650
$656$	780.645	+	450.705i	1.19001	+	0.687051i
$657$		0			0
$658$	779.393			1.18449
$659$	−220.263	−	127.169i	−0.334239	−	0.192973i	0.323483	−	0.946234i	$-0.395146\pi$
$659$	−220.263	−	127.169i	−0.334239	−	0.192973i	−0.657721	+	0.753261i	$0.728480\pi$
$660$		0			0
$661$	−297.467	−	515.227i	−0.450025	−	0.779466i	0.548362	−	0.836241i	$-0.315252\pi$
$661$	−297.467	−	515.227i	−0.450025	−	0.779466i	−0.998387	+	0.0567747i	$0.981918\pi$
$662$		−	251.303i		−	0.379611i
$663$		0			0
$664$	2081.15			3.13426
$665$	−449.198	+	259.345i	−0.675486	+	0.389992i
$666$		0			0
$667$	316.320	−	547.883i	0.474243	−	0.821414i
$668$			2557.07i			3.82796i
$669$		0			0
$670$	118.987	−	206.092i	0.177593	−	0.307600i
$671$			143.300i			0.213562i
$672$		0			0
$673$	−144.062	−	249.523i	−0.214060	−	0.370762i	0.738922	−	0.673792i	$-0.235335\pi$
$673$	−144.062	−	249.523i	−0.214060	−	0.370762i	−0.952981	+	0.303029i	$0.902002\pi$
$674$	−1349.23	+	778.980i	−2.00183	+	1.15576i
$675$		0			0
$676$	−1435.79	−	1334.53i	−2.12395	−	1.97415i
$677$		−	1095.13i		−	1.61762i	−0.588070	−	0.808810i	$-0.700112\pi$
$677$		−	1095.13i		−	1.61762i	0.588070	−	0.808810i	$-0.299888\pi$
$678$		0			0
$679$	196.376	+	340.134i	0.289214	+	0.500933i
$680$	4.79598	+	2.76896i	0.00705292	+	0.00407200i
$681$		0			0
$682$	−88.7812	+	153.774i	−0.130178	+	0.225474i
$683$	−770.415	−	444.800i	−1.12799	−	0.651244i	−0.184559	−	0.982821i	$-0.559086\pi$
$683$	−770.415	−	444.800i	−1.12799	−	0.651244i	−0.943428	+	0.331578i	$0.892419\pi$
$684$		0			0
$685$	−259.582	+	449.609i	−0.378952	+	0.656364i
$686$	982.591	−	567.299i	1.43235	−	0.826966i
$687$		0			0
$688$	2570.83			3.73668
$689$	163.257	+	204.899i	0.236947	+	0.297386i
$690$		0			0
$691$	268.340	+	464.779i	0.388336	+	0.672617i	0.992226	−	0.124450i	$-0.0397167\pi$
$691$	268.340	+	464.779i	0.388336	+	0.672617i	−0.603890	+	0.797068i	$0.706383\pi$
$692$	−2426.04	+	1400.67i	−3.50584	+	2.02410i
$693$		0			0
$694$	−1202.14			−1.73219
$695$	74.9725	+	43.2854i	0.107874	+	0.0622811i
$696$		0			0
$697$	−0.662008			−0.000949797
$698$	−1860.77	−	1074.32i	−2.66586	−	1.53914i
$699$		0			0
$700$	584.425	+	1012.25i	0.834892	+	1.44608i
$701$			809.935i			1.15540i	0.816250	+	0.577699i	$0.196049\pi$
$701$			809.935i			1.15540i	−0.816250	+	0.577699i	$0.803951\pi$
$702$		0			0
$703$	287.218			0.408561
$704$	487.920	−	281.701i	0.693068	−	0.400143i
$705$		0			0
$706$	393.632	−	681.791i	0.557552	−	0.965709i
$707$		−	1360.85i		−	1.92482i
$708$		0			0
$709$	−225.504	+	390.584i	−0.318059	+	0.550895i	−0.980083	−	0.198588i	$-0.936364\pi$
$709$	−225.504	+	390.584i	−0.318059	+	0.550895i	0.662024	+	0.749483i	$0.269698\pi$
$710$			106.492i			0.149989i
$711$		0			0
$712$	125.790	+	217.874i	0.176671	+	0.306003i
$713$	700.940	−	404.688i	0.983085	−	0.567585i
$714$		0			0
$715$	−65.4772	−	25.7305i	−0.0915765	−	0.0359868i
$716$		−	1671.79i		−	2.33490i
$717$		0			0
$718$	223.436	+	387.002i	0.311192	+	0.539000i
$719$	−352.585	−	203.565i	−0.490382	−	0.283122i	0.234351	−	0.972152i	$-0.424704\pi$
$719$	−352.585	−	203.565i	−0.490382	−	0.283122i	−0.724733	+	0.689030i	$0.758037\pi$
$720$		0			0
$721$	−161.590	+	279.883i	−0.224120	+	0.388187i
$722$	2.52743	+	1.45921i	0.00350059	+	0.00202107i
$723$		0			0
$724$	1029.97	−	1783.96i	1.42261	−	2.46404i
$725$	−252.067	+	145.531i	−0.347678	+	0.200732i
$726$		0			0
$727$	−1100.48			−1.51373			−0.756865	−	0.653572i	$-0.773270\pi$
$727$	−1100.48			−1.51373			−0.756865	+	0.653572i	$0.773270\pi$
$728$	3021.11	−	454.025i	4.14987	−	0.623660i
$729$		0			0
$730$	−414.280	−	717.555i	−0.567507	−	0.982952i
$731$	−1.63510	+	0.944028i	−0.00223680	+	0.00129142i
$732$		0			0
$733$	−342.568			−0.467351			−0.233675	−	0.972315i	$-0.575075\pi$
$733$	−342.568			−0.467351			−0.233675	+	0.972315i	$0.575075\pi$
$734$	956.335	+	552.140i	1.30291	+	0.752235i
$735$		0			0
$736$	−4611.86			−6.26611
$737$	23.2794	+	13.4404i	0.0315867	+	0.0182366i
$738$		0			0
$739$	−478.879	−	829.443i	−0.648009	−	1.12239i	−0.983598	−	0.180376i	$-0.942268\pi$
$739$	−478.879	−	829.443i	−0.648009	−	1.12239i	0.335588	−	0.942009i	$-0.391065\pi$
$740$			610.053i			0.824396i
$741$		0			0
$742$	−623.238			−0.839944
$743$	−15.6101	+	9.01251i	−0.0210096	+	0.0121299i	−0.510468	−	0.859897i	$-0.670528\pi$
$743$	−15.6101	+	9.01251i	−0.0210096	+	0.0121299i	0.489458	+	0.872027i	$0.337194\pi$
$744$		0			0
$745$	−434.554	+	752.669i	−0.583294	+	1.01029i
$746$		−	1053.13i		−	1.41171i
$747$		0			0
$748$	−0.477412	+	0.826901i	−0.000638251	+	0.00110548i
$749$			1216.52i			1.62420i
$750$		0			0
$751$	37.8776	+	65.6059i	0.0504362	+	0.0873580i	0.890141	−	0.455685i	$-0.150606\pi$
$751$	37.8776	+	65.6059i	0.0504362	+	0.0873580i	−0.839705	+	0.543043i	$0.817272\pi$
$752$	1574.48	−	909.027i	2.09372	−	1.20881i
$753$		0			0
$754$	172.573	+	1148.31i	0.228876	+	1.52295i
$755$			618.696i			0.819465i
$756$		0			0
$757$	393.498	+	681.558i	0.519812	+	0.900341i	0.999735	+	0.0230304i	$0.00733145\pi$
$757$	393.498	+	681.558i	0.519812	+	0.900341i	−0.479922	+	0.877311i	$0.659335\pi$
$758$	−1760.21	−	1016.26i	−2.32218	−	1.34071i
$759$		0			0
$760$	−994.037	+	1721.72i	−1.30794	+	2.26543i
$761$	730.995	+	422.040i	0.960571	+	0.554586i	0.896349	−	0.443350i	$-0.146210\pi$
$761$	730.995	+	422.040i	0.960571	+	0.554586i	0.0642223	+	0.997936i	$0.479543\pi$
$762$		0			0
$763$	−415.463	+	719.603i	−0.544513	+	0.943124i
$764$	2935.66	−	1694.90i	3.84249	−	2.21846i
$765$		0			0
$766$	1417.36			1.85034
$767$	−1078.77	+	162.122i	−1.40648	+	0.211372i
$768$		0			0
$769$	−53.2885	−	92.2985i	−0.0692959	−	0.120024i	0.829296	−	0.558810i	$-0.188742\pi$
$769$	−53.2885	−	92.2985i	−0.0692959	−	0.120024i	−0.898592	+	0.438786i	$0.855409\pi$
$770$	144.938	−	83.6798i	0.188231	−	0.108675i
$771$		0			0
$772$	2958.58			3.83236
$773$	−570.104	−	329.150i	−0.737522	−	0.425808i	0.0836459	−	0.996496i	$-0.473344\pi$
$773$	−570.104	−	329.150i	−0.737522	−	0.425808i	−0.821168	+	0.570687i	$0.806677\pi$
$774$		0			0
$775$	−372.373			−0.480481
$776$	1303.69	+	752.687i	1.68002	+	0.969957i
$777$		0			0
$778$	91.9694	+	159.296i	0.118213	+	0.204750i
$779$		−	237.656i		−	0.305079i
$780$		0			0
$781$	−12.0290			−0.0154020
$782$	5.06909	−	2.92664i	0.00648221	−	0.00374250i
$783$		0			0
$784$	−444.098	+	769.200i	−0.566451	+	0.981122i
$785$		−	54.6500i		−	0.0696179i
$786$		0			0
$787$	−85.5172	+	148.120i	−0.108662	+	0.188208i	−0.915229	−	0.402935i	$-0.867990\pi$
$787$	−85.5172	+	148.120i	−0.108662	+	0.188208i	0.806566	+	0.591144i	$0.201323\pi$
$788$		−	1484.96i		−	1.88447i
$789$		0			0
$790$	409.773	+	709.748i	0.518700	+	0.898415i
$791$	−247.867	+	143.106i	−0.313359	+	0.180918i
$792$		0			0
$793$	178.181	+	1185.62i	0.224692	+	1.49511i
$794$		−	989.373i		−	1.24606i
$795$		0			0
$796$	1142.82	+	1979.42i	1.43570	+	2.48671i
$797$	−65.3138	−	37.7089i	−0.0819495	−	0.0473136i	0.458465	−	0.888712i	$-0.348399\pi$
$797$	−65.3138	−	37.7089i	−0.0819495	−	0.0473136i	−0.540415	+	0.841399i	$0.681733\pi$
$798$		0			0
$799$	−0.667602	+	1.15632i	−0.000835547	+	0.00144721i
$800$	1837.53	+	1060.90i	2.29691	+	1.32612i
$801$		0			0
$802$	−803.085	+	1390.98i	−1.00135	+	1.73439i
$803$	81.0523	−	46.7955i	0.100937	−	0.0582759i
$804$		0			0
$805$	−762.868			−0.947663
$806$	−543.346	+	1382.67i	−0.674127	+	1.71547i
$807$		0			0
$808$	−2607.98	−	4517.15i	−3.22770	−	5.59053i
$809$	−911.781	+	526.417i	−1.12705	+	0.650701i	−0.943190	−	0.332252i	$-0.892191\pi$
$809$	−911.781	+	526.417i	−1.12705	+	0.650701i	−0.183856	+	0.982953i	$0.558858\pi$
$810$		0			0
$811$	250.658			0.309073			0.154536	−	0.987987i	$-0.450612\pi$
$811$	250.658			0.309073			0.154536	+	0.987987i	$0.450612\pi$
$812$	−1778.85	−	1027.02i	−2.19070	−	1.26480i
$813$		0			0
$814$	−92.6733			−0.113849
$815$	427.820	+	247.002i	0.524932	+	0.303070i
$816$		0			0
$817$	−338.899	−	586.990i	−0.414809	−	0.718471i
$818$		−	955.784i		−	1.16844i
$819$		0			0
$820$	504.783			0.615590
$821$	410.512	−	237.009i	0.500015	−	0.288684i	−0.228705	−	0.973496i	$-0.573449\pi$
$821$	410.512	−	237.009i	0.500015	−	0.288684i	0.728720	+	0.684812i	$0.240116\pi$
$822$		0			0
$823$	−95.9561	+	166.201i	−0.116593	+	0.201945i	−0.918415	−	0.395617i	$-0.870531\pi$
$823$	−95.9561	+	166.201i	−0.116593	+	0.201945i	0.801822	+	0.597562i	$0.203864\pi$
$824$			1238.71i			1.50329i
$825$		0			0
$826$	1297.56	−	2247.43i	1.57089	−	2.72086i
$827$			921.567i			1.11435i	0.830395	+	0.557175i	$0.188115\pi$
$827$			921.567i			1.11435i	−0.830395	+	0.557175i	$0.811885\pi$
$828$		0			0
$829$	−250.159	−	433.288i	−0.301760	−	0.522664i	0.674775	−	0.738024i	$-0.264241\pi$
$829$	−250.159	−	433.288i	−0.301760	−	0.522664i	−0.976535	+	0.215360i	$0.930907\pi$
$830$	826.073	−	476.933i	0.995269	−	0.574619i
$831$		0			0
$832$	3686.64	−	2937.39i	4.43105	−	3.53052i
$833$		−	0.652303i		−	0.000783077i
$834$		0			0
$835$	383.912	+	664.956i	0.459775	+	0.796354i
$836$	−296.851	−	171.387i	−0.355085	−	0.205009i
$837$		0			0
$838$	276.239	−	478.460i	0.329641	−	0.570955i
$839$	−745.749	−	430.559i	−0.888855	−	0.513181i	−0.0152871	−	0.999883i	$-0.504866\pi$
$839$	−745.749	−	430.559i	−0.888855	−	0.513181i	−0.873568	+	0.486703i	$0.838200\pi$
$840$		0			0
$841$	−164.756	+	285.366i	−0.195905	+	0.339318i
$842$	−268.032	+	154.748i	−0.318328	+	0.183787i
$843$		0			0
$844$	−702.987			−0.832923
$845$	−573.733	−	131.472i	−0.678974	−	0.155588i
$846$		0			0
$847$	−464.276	−	804.149i	−0.548141	−	0.949409i
$848$	−1259.03	+	726.900i	−1.48470	+	0.857193i
$849$		0			0
$850$	−2.69294			−0.00316817
$851$	365.834	+	211.215i	0.429888	+	0.248196i
$852$		0			0
$853$	944.016			1.10670			0.553350	−	0.832949i	$-0.313349\pi$
$853$	944.016			1.10670			0.553350	+	0.832949i	$0.313349\pi$
$854$	−2470.05	−	1426.08i	−2.89232	−	1.66988i
$855$		0			0
$856$	2331.39	+	4038.09i	2.72359	+	4.71740i
$857$		−	616.763i		−	0.719677i	−0.933015	−	0.359838i	$-0.882832\pi$
$857$		−	616.763i		−	0.719677i	0.933015	−	0.359838i	$-0.117168\pi$
$858$		0			0
$859$	−756.640			−0.880838			−0.440419	−	0.897792i	$-0.645170\pi$
$859$	−756.640			−0.880838			−0.440419	+	0.897792i	$0.645170\pi$
$860$	1246.77	−	719.824i	1.44974	−	0.837005i
$861$		0			0
$862$	1084.39	−	1878.22i	1.25799	−	2.17891i
$863$			86.8008i			0.100580i	0.998735	+	0.0502901i	$0.0160146\pi$
$863$			86.8008i			0.100580i	−0.998735	+	0.0502901i	$0.983985\pi$
$864$		0			0
$865$	−420.587	+	728.478i	−0.486228	+	0.842171i
$866$		−	2898.43i		−	3.34691i
$867$		0			0
$868$	−1313.93	−	2275.79i	−1.51374	−	2.62188i
$869$	−80.1704	+	46.2864i	−0.0922560	+	0.0532640i
$870$		0			0
$871$	209.319	+	82.2558i	0.240320	+	0.0944383i
$872$			3184.84i			3.65234i
$873$		0			0
$874$	1050.64	+	1819.76i	1.20211	+	2.08211i
$875$	894.401	+	516.382i	1.02217	+	0.590151i
$876$		0			0
$877$	498.768	−	863.891i	0.568720	−	0.985052i	−0.427973	−	0.903792i	$-0.640772\pi$
$877$	498.768	−	863.891i	0.568720	−	0.985052i	0.996693	−	0.0812606i	$-0.0258946\pi$
$878$	1668.02	+	963.031i	1.89979	+	1.09685i
$879$		0			0
$880$	195.196	−	338.089i	0.221814	−	0.384193i
$881$	171.821	−	99.2009i	0.195030	−	0.112600i	−0.399305	−	0.916818i	$-0.630749\pi$
$881$	171.821	−	99.2009i	0.195030	−	0.112600i	0.594335	+	0.804218i	$0.297415\pi$
$882$		0			0
$883$	56.1693			0.0636119			0.0318059	−	0.999494i	$-0.489874\pi$
$883$	56.1693			0.0636119			0.0318059	+	0.999494i	$0.489874\pi$
$884$	−2.92179	+	7.43515i	−0.00330519	+	0.00841081i
$885$		0			0
$886$	1237.93	+	2144.15i	1.39721	+	2.42004i
$887$	−1231.56	+	711.043i	−1.38846	+	0.801626i	−0.993141	−	0.116919i	$-0.962698\pi$
$887$	−1231.56	+	711.043i	−1.38846	+	0.801626i	−0.395316	+	0.918545i	$0.629365\pi$
$888$		0			0
$889$	−931.383			−1.04768
$890$	99.8598	+	57.6541i	0.112202	+	0.0647799i
$891$		0			0
$892$	1672.30			1.87478
$893$	−415.110	−	239.664i	−0.464849	−	0.268381i
$894$		0			0
$895$	−250.998	−	434.741i	−0.280445	−	0.485744i
$896$			6049.79i			6.75200i
$897$		0			0
$898$	−1315.26			−1.46465
$899$	566.707	−	327.188i	0.630374	−	0.363947i
$900$		0			0
$901$	0.533845	−	0.924647i	0.000592503	−	0.00102625i
$902$			76.6818i			0.0850131i
$903$		0			0
$904$	−548.508	+	950.044i	−0.606757	+	1.05093i
$905$		−	618.548i		−	0.683479i
$906$		0			0
$907$	135.284	+	234.319i	0.149155	+	0.258345i	0.930916	−	0.365234i	$-0.119011\pi$
$907$	135.284	+	234.319i	0.149155	+	0.258345i	−0.781760	+	0.623579i	$0.785678\pi$
$908$	1288.01	−	743.635i	1.41852	−	0.818982i
$909$		0			0
$910$	1095.12	−	872.558i	1.20343	−	0.958855i
$911$			1546.05i			1.69709i	0.529123	+	0.848545i	$0.322521\pi$
$911$			1546.05i			1.69709i	−0.529123	+	0.848545i	$0.677479\pi$
$912$		0			0
$913$	53.8726	+	93.3101i	0.0590061	+	0.102202i
$914$	1218.05	+	703.242i	1.33266	+	0.769411i
$915$		0			0
$916$	−1663.28	+	2880.88i	−1.81580	+	3.14506i
$917$	−114.604	−	66.1667i	−0.124977	−	0.0721556i
$918$		0			0
$919$	−611.934	+	1059.90i	−0.665870	+	1.15332i	0.313179	+	0.949694i	$0.398606\pi$
$919$	−611.934	+	1059.90i	−0.665870	+	1.15332i	−0.979049	+	0.203626i	$0.934727\pi$
$920$	−2532.24	+	1461.99i	−2.75244	+	1.58912i
$921$		0			0
$922$	−1006.23			−1.09135
$923$	−99.5243	+	14.9569i	−0.107827	+	0.0162047i
$924$		0			0
$925$	−97.1744	−	168.311i	−0.105053	−	0.181958i
$926$	999.744	−	577.203i	1.07964	−	0.623329i
$927$		0			0
$928$	−3728.67			−4.01796
$929$	−910.762	−	525.829i	−0.980368	−	0.566016i	−0.0779869	−	0.996954i	$-0.524849\pi$
$929$	−910.762	−	525.829i	−0.980368	−	0.566016i	−0.902381	+	0.430939i	$0.858183\pi$
$930$		0			0
$931$	234.172			0.251527
$932$	575.528	+	332.281i	0.617519	+	0.356525i
$933$		0			0
$934$	−751.963	−	1302.44i	−0.805100	−	1.39447i
$935$			0.286709i			0.000306641i
$936$		0			0
$937$	1042.09			1.11216			0.556078	−	0.831130i	$-0.312305\pi$
$937$	1042.09			1.11216			0.556078	+	0.831130i	$0.312305\pi$
$938$	−463.339	+	267.509i	−0.493965	+	0.285191i
$939$		0			0
$940$	509.048	−	881.698i	0.541541	−	0.937976i
$941$			1592.89i			1.69277i	0.532575	+	0.846383i	$0.321224\pi$
$941$			1592.89i			1.69277i	−0.532575	+	0.846383i	$0.678776\pi$
$942$		0			0
$943$	174.768	−	302.707i	0.185332	−	0.321004i
$944$		−	6053.50i		−	6.41261i
$945$		0			0
$946$	109.349	+	189.397i	0.115591	+	0.200209i
$947$	1342.65	−	775.177i	1.41779	−	0.818561i	0.421685	−	0.906742i	$-0.361439\pi$
$947$	1342.65	−	775.177i	1.41779	−	0.818561i	0.996104	+	0.0881814i	$0.0281055\pi$
$948$		0			0
$949$	612.417	−	487.954i	0.645328	−	0.514177i
$950$		−	966.746i		−	1.01763i
$951$		0			0
$952$	−6.22522	−	10.7824i	−0.00653909	−	0.0113260i
$953$	1598.10	+	922.664i	1.67692	+	0.968168i	0.963609	+	0.267317i	$0.0861371\pi$
$953$	1598.10	+	922.664i	1.67692	+	0.968168i	0.713308	+	0.700851i	$0.247196\pi$
$954$		0			0
$955$	508.937	−	881.505i	0.532918	−	0.923041i
$956$	−1915.21	−	1105.74i	−2.00335	−	1.15664i
$957$		0			0
$958$	367.467	−	636.471i	0.383577	−	0.664374i
$959$	1010.82	−	583.595i	1.05403	−	0.608546i
$960$		0			0
$961$	−123.817			−0.128841
$962$	−766.752	+	115.231i	−0.797039	+	0.119782i
$963$		0			0
$964$	−2265.75	−	3924.39i	−2.35036	−	4.07095i
$965$	769.365	−	444.193i	0.797270	−	0.460304i
$966$		0			0
$967$	1552.78			1.60577			0.802884	−	0.596136i	$-0.203298\pi$
$967$	1552.78			1.60577			0.802884	+	0.596136i	$0.203298\pi$
$968$	−3082.21	−	1779.51i	−3.18410	−	1.83834i
$969$		0			0
$970$	689.968			0.711307
$971$	321.867	+	185.830i	0.331480	+	0.191380i	0.656498	−	0.754328i	$-0.272037\pi$
$971$	321.867	+	185.830i	0.331480	+	0.191380i	−0.325018	+	0.945708i	$0.605370\pi$
$972$		0			0
$973$	−97.3148	−	168.554i	−0.100015	−	0.173231i
$974$			2264.71i			2.32516i
$975$		0			0
$976$	−6653.11			−6.81671
$977$	−212.337	+	122.593i	−0.217336	+	0.125479i	−0.604716	−	0.796441i	$-0.706713\pi$
$977$	−212.337	+	122.593i	−0.217336	+	0.125479i	0.387380	+	0.921920i	$0.373380\pi$
$978$		0			0
$979$	−6.51239	+	11.2798i	−0.00665208	+	0.0115217i
$980$			497.383i			0.507534i
$981$		0			0
$982$	−826.287	+	1431.17i	−0.841433	+	1.45740i
$983$			1242.04i			1.26352i	0.775164	+	0.631761i	$0.217667\pi$
$983$			1242.04i			1.26352i	−0.775164	+	0.631761i	$0.782333\pi$
$984$		0			0
$985$	−222.948	−	386.157i	−0.226343	−	0.392038i
$986$	4.09833	−	2.36617i	0.00415652	−	0.00239977i
$987$		0			0
$988$	−2669.17	−	1048.90i	−2.70158	−	1.06164i
$989$		−	996.879i		−	1.00797i
$990$		0			0
$991$	−454.832	−	787.793i	−0.458963	−	0.794947i	0.539943	−	0.841701i	$-0.318446\pi$
$991$	−454.832	−	787.793i	−0.458963	−	0.794947i	−0.998906	+	0.0467541i	$0.985112\pi$
$992$	−4131.21	−	2385.16i	−4.16453	−	2.40439i
$993$		0			0
$994$	119.709	−	207.342i	0.120431	−	0.208593i
$995$	594.370	+	343.160i	0.597357	+	0.344884i
$996$		0			0
$997$	−174.462	+	302.176i	−0.174987	+	0.303086i	−0.940157	−	0.340743i	$-0.889322\pi$
$997$	−174.462	+	302.176i	−0.174987	+	0.303086i	0.765170	+	0.643828i	$0.222655\pi$
$998$	−1526.24	+	881.176i	−1.52930	+	0.882942i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.p.a.107.1	yes	20
3.2	odd	2	inner	117.3.p.a.107.10	yes	20
13.9	even	3	inner	117.3.p.a.35.10	yes	20
39.35	odd	6	inner	117.3.p.a.35.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.p.a.35.1	✓	20	39.35	odd	6	inner
117.3.p.a.35.10	yes	20	13.9	even	3	inner
117.3.p.a.107.1	yes	20	1.1	even	1	trivial
117.3.p.a.107.10	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.42041 + 1.97477i) q^{2} +(5.79946 - 10.0450i) q^{4} -3.48286i q^{5} +(-3.91511 + 6.78116i) q^{7} +30.0123i q^{8} +(6.87786 + 11.9128i) q^{10} +(-1.34563 + 0.776897i) q^{11} +(-10.1673 + 8.10098i) q^{13} -30.9258i q^{14} +(-36.0696 - 62.4744i) q^{16} +(0.0458820 + 0.0264900i) q^{17} +(-9.50972 + 16.4713i) q^{19} +(-34.9852 - 20.1987i) q^{20} +(3.06839 - 5.31461i) q^{22} +(-24.2254 + 13.9865i) q^{23} +12.8697 q^{25} +(18.7787 - 47.7868i) q^{26} +(45.4110 + 78.6542i) q^{28} +(-19.5861 + 11.3080i) q^{29} -28.9341 q^{31} +(142.780 + 82.4340i) q^{32} -0.209247 q^{34} +(23.6179 + 13.6358i) q^{35} +(-7.55065 - 13.0781i) q^{37} -75.1181i q^{38} +104.529 q^{40} +(-10.8214 + 6.24772i) q^{41} +(-17.8186 + 30.8627i) q^{43} +18.0223i q^{44} +(55.2404 - 95.6792i) q^{46} +25.2020i q^{47} +(-6.15612 - 10.6627i) q^{49} +(-44.0195 + 25.4147i) q^{50} +(22.4091 + 149.111i) q^{52} -20.1527i q^{53} +(2.70583 + 4.68663i) q^{55} +(-203.518 - 117.501i) q^{56} +(44.6616 - 77.3562i) q^{58} +(72.6718 + 41.9571i) q^{59} +(46.1130 - 79.8701i) q^{61} +(98.9665 - 57.1383i) q^{62} -362.597 q^{64} +(28.2146 + 35.4113i) q^{65} +(-8.65002 - 14.9823i) q^{67} +(0.532182 - 0.307255i) q^{68} -107.710 q^{70} +(6.70449 + 3.87084i) q^{71} -60.2339 q^{73} +(51.6526 + 29.8216i) q^{74} +(110.302 + 191.049i) q^{76} -12.1665i q^{77} +59.5786 q^{79} +(-217.590 + 125.625i) q^{80} +(24.6757 - 42.7395i) q^{82} -69.3433i q^{83} +(0.0922610 - 0.159801i) q^{85} -140.751i q^{86} +(-23.3164 - 40.3853i) q^{88} +(7.25951 - 4.19128i) q^{89} +(-15.1280 - 100.662i) q^{91} +324.457i q^{92} +(-49.7683 - 86.2012i) q^{94} +(57.3673 + 33.1210i) q^{95} +(25.0793 - 43.4386i) q^{97} +(42.1129 + 24.3139i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 24 q^{4} - 6 q^{7} + 12 q^{10} - 2 q^{13} - 104 q^{16} - 92 q^{19} + 44 q^{22} - 116 q^{25} + 76 q^{28} - 156 q^{31} + 80 q^{34} + 148 q^{37} + 328 q^{40} + 186 q^{43} + 164 q^{46} + 8 q^{49} + 392 q^{52}+ \cdots - 14 q^{97}+O(q^{100}) \) 20 * q + 24 * q^4 - 6 * q^7 + 12 * q^10 - 2 * q^13 - 104 * q^16 - 92 * q^19 + 44 * q^22 - 116 * q^25 + 76 * q^28 - 156 * q^31 + 80 * q^34 + 148 * q^37 + 328 * q^40 + 186 * q^43 + 164 * q^46 + 8 * q^49 + 392 * q^52 - 208 * q^55 - 236 * q^58 + 210 * q^61 - 1568 * q^64 - 158 * q^67 - 1048 * q^70 + 156 * q^73 + 764 * q^76 - 132 * q^79 + 648 * q^82 + 44 * q^85 + 372 * q^88 + 834 * q^91 - 220 * q^94 - 14 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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