LMFDB - Embedded newform 338.4.e.h.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not 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:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.5
Root			$-1.07992 + 0.623490i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.4.e.h.147.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(1.83244 + 3.17387i) q^{3} +(2.00000 - 3.46410i) q^{4} +8.53079i q^{5} +(6.34775 + 3.66487i) q^{6} +(-3.63821 - 2.10052i) q^{7} -8.00000i q^{8} +(6.78435 - 11.7508i) q^{9} +(8.53079 + 14.7758i) q^{10} +(56.6143 - 32.6863i) q^{11} +14.6595 q^{12} -8.40209 q^{14} +(-27.0757 + 15.6321i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.4510 + 23.2977i) q^{17} -27.1374i q^{18} +(11.5813 + 6.68648i) q^{19} +(29.5515 + 17.0616i) q^{20} -15.3963i q^{21} +(65.3726 - 113.229i) q^{22} +(79.9645 + 138.503i) q^{23} +(25.3910 - 14.6595i) q^{24} +52.2255 q^{25} +148.679 q^{27} +(-14.5529 + 8.40209i) q^{28} +(150.644 + 260.923i) q^{29} +(-31.2643 + 54.1513i) q^{30} -73.0232i q^{31} +(-27.7128 - 16.0000i) q^{32} +(207.484 + 119.791i) q^{33} +53.8038i q^{34} +(17.9191 - 31.0368i) q^{35} +(-27.1374 - 47.0033i) q^{36} +(102.867 - 59.3904i) q^{37} +26.7459 q^{38} +68.2464 q^{40} +(-374.903 + 216.451i) q^{41} +(-15.3963 - 26.6672i) q^{42} +(-178.254 + 308.745i) q^{43} -261.490i q^{44} +(100.244 + 57.8759i) q^{45} +(277.005 + 159.929i) q^{46} -588.614i q^{47} +(29.3190 - 50.7820i) q^{48} +(-162.676 - 281.762i) q^{49} +(90.4573 - 52.2255i) q^{50} -98.5921 q^{51} -269.462 q^{53} +(257.520 - 148.679i) q^{54} +(278.840 + 482.965i) q^{55} +(-16.8042 + 29.1057i) q^{56} +49.0102i q^{57} +(521.846 + 301.288i) q^{58} +(199.480 + 115.170i) q^{59} +125.057i q^{60} +(190.408 - 329.796i) q^{61} +(-73.0232 - 126.480i) q^{62} +(-49.3658 + 28.5014i) q^{63} -64.0000 q^{64} +479.164 q^{66} +(377.456 - 217.924i) q^{67} +(53.8038 + 93.1909i) q^{68} +(-293.060 + 507.595i) q^{69} -71.6765i q^{70} +(-57.1249 - 32.9811i) q^{71} +(-94.0067 - 54.2748i) q^{72} -885.517i q^{73} +(118.781 - 205.735i) q^{74} +(95.7000 + 165.757i) q^{75} +(46.3253 - 26.7459i) q^{76} -274.633 q^{77} -385.463 q^{79} +(118.206 - 68.2464i) q^{80} +(89.2679 + 154.616i) q^{81} +(-432.901 + 749.807i) q^{82} -254.207i q^{83} +(-53.3344 - 30.7926i) q^{84} +(-198.748 - 114.747i) q^{85} +713.016i q^{86} +(-552.091 + 956.250i) q^{87} +(-261.490 - 452.914i) q^{88} +(322.692 - 186.306i) q^{89} +231.504 q^{90} +639.716 q^{92} +(231.766 - 133.810i) q^{93} +(-588.614 - 1019.51i) q^{94} +(-57.0410 + 98.7979i) q^{95} -117.276i q^{96} +(-1137.86 - 656.942i) q^{97} +(-563.525 - 325.351i) q^{98} -887.020i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) $ 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	1.83244	+	3.17387i	0.352653	+	0.610812i	0.986713	−	0.162471i	$-0.0519464\pi$
$3$	1.83244	+	3.17387i	0.352653	+	0.610812i	−0.634061	+	0.773283i	$0.718613\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			8.53079i			0.763017i	0.924365	+	0.381509i	$0.124595\pi$
$5$			8.53079i			0.763017i	−0.924365	+	0.381509i	$0.875405\pi$
$6$	6.34775	+	3.66487i	0.431910	+	0.249363i
$7$	−3.63821	−	2.10052i	−0.196445	−	0.113418i	0.398551	−	0.917146i	$-0.369513\pi$
$7$	−3.63821	−	2.10052i	−0.196445	−	0.113418i	−0.594996	+	0.803729i	$0.702846\pi$
$8$		−	8.00000i		−	0.353553i
$9$	6.78435	−	11.7508i	0.251272	−	0.435216i
$10$	8.53079	+	14.7758i	0.269767	+	0.467251i
$11$	56.6143	−	32.6863i	1.55180	−	0.895935i	0.553810	−	0.832643i	$-0.313174\pi$
$11$	56.6143	−	32.6863i	1.55180	−	0.895935i	0.997995	−	0.0632915i	$-0.0201598\pi$
$12$	14.6595			0.352653
$13$		0			0
$13$		0			0
$14$	−8.40209			−0.160397
$15$	−27.0757	+	15.6321i	−0.466061	+	0.269080i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−13.4510	+	23.2977i	−0.191902	+	0.332384i	−0.945881	−	0.324515i	$-0.894799\pi$
$17$	−13.4510	+	23.2977i	−0.191902	+	0.332384i	0.753979	+	0.656899i	$0.228132\pi$
$18$		−	27.1374i		−	0.355352i
$19$	11.5813	+	6.68648i	0.139839	+	0.0807360i	0.568287	−	0.822830i	$-0.307606\pi$
$19$	11.5813	+	6.68648i	0.139839	+	0.0807360i	−0.428448	+	0.903566i	$0.640940\pi$
$20$	29.5515	+	17.0616i	0.330396	+	0.190754i
$21$		−	15.3963i		−	0.159988i
$22$	65.3726	−	113.229i	0.633522	−	1.09729i
$23$	79.9645	+	138.503i	0.724946	+	1.25564i	0.958996	+	0.283419i	$0.0914687\pi$
$23$	79.9645	+	138.503i	0.724946	+	1.25564i	−0.234050	+	0.972225i	$0.575198\pi$
$24$	25.3910	−	14.6595i	0.215955	−	0.124682i
$25$	52.2255			0.417804
$26$		0			0
$27$	148.679			1.05975
$28$	−14.5529	+	8.40209i	−0.0982225	+	0.0567088i
$29$	150.644	+	260.923i	0.964616	+	1.67076i	0.710643	+	0.703553i	$0.248404\pi$
$29$	150.644	+	260.923i	0.964616	+	1.67076i	0.253973	+	0.967211i	$0.418262\pi$
$30$	−31.2643	+	54.1513i	−0.190268	+	0.329555i
$31$		−	73.0232i		−	0.423076i	−0.977370	−	0.211538i	$-0.932153\pi$
$31$		−	73.0232i		−	0.423076i	0.977370	−	0.211538i	$-0.0678472\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	207.484	+	119.791i	1.09450	+	0.631908i
$34$			53.8038i			0.271390i
$35$	17.9191	−	31.0368i	0.0865396	−	0.149891i
$36$	−27.1374	−	47.0033i	−0.125636	−	0.217608i
$37$	102.867	−	59.3904i	0.457061	−	0.263885i	−0.253746	−	0.967271i	$-0.581663\pi$
$37$	102.867	−	59.3904i	0.457061	−	0.263885i	0.710808	+	0.703386i	$0.248330\pi$
$38$	26.7459			0.114178
$39$		0			0
$40$	68.2464			0.269767
$41$	−374.903	+	216.451i	−1.42805	+	0.824486i	−0.996967	−	0.0778262i	$-0.975202\pi$
$41$	−374.903	+	216.451i	−1.42805	+	0.824486i	−0.431084	+	0.902312i	$0.641869\pi$
$42$	−15.3963	−	26.6672i	−0.0565643	−	0.0979723i
$43$	−178.254	+	308.745i	−0.632174	+	1.09496i	0.354933	+	0.934892i	$0.384504\pi$
$43$	−178.254	+	308.745i	−0.632174	+	1.09496i	−0.987106	+	0.160065i	$0.948830\pi$
$44$		−	261.490i		−	0.895935i
$45$	100.244	+	57.8759i	0.332078	+	0.191725i
$46$	277.005	+	159.929i	0.887874	+	0.512614i
$47$		−	588.614i		−	1.82677i	−0.407096	−	0.913385i	$-0.633459\pi$
$47$		−	588.614i		−	1.82677i	0.407096	−	0.913385i	$-0.366541\pi$
$48$	29.3190	−	50.7820i	0.0881632	−	0.152703i
$49$	−162.676	−	281.762i	−0.474273	−	0.821465i
$50$	90.4573	−	52.2255i	0.255852	−	0.147716i
$51$	−98.5921			−0.270699
$52$		0			0
$53$	−269.462			−0.698366			−0.349183	−	0.937054i	$-0.613541\pi$
$53$	−269.462			−0.698366			−0.349183	+	0.937054i	$0.613541\pi$
$54$	257.520	−	148.679i	0.648963	−	0.374679i
$55$	278.840	+	482.965i	0.683614	+	1.18405i
$56$	−16.8042	+	29.1057i	−0.0400992	+	0.0694538i
$57$			49.0102i			0.113887i
$58$	521.846	+	301.288i	1.18141	+	0.682087i
$59$	199.480	+	115.170i	0.440171	+	0.254133i	0.703670	−	0.710527i	$-0.251543\pi$
$59$	199.480	+	115.170i	0.440171	+	0.254133i	−0.263499	+	0.964660i	$0.584877\pi$
$60$			125.057i			0.269080i
$61$	190.408	−	329.796i	0.399659	−	0.692230i	−0.594024	−	0.804447i	$-0.702462\pi$
$61$	190.408	−	329.796i	0.399659	−	0.692230i	0.993684	+	0.112217i	$0.0357951\pi$
$62$	−73.0232	−	126.480i	−0.149580	−	0.259080i
$63$	−49.3658	+	28.5014i	−0.0987223	+	0.0569974i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	479.164			0.893652
$67$	377.456	−	217.924i	0.688262	−	0.397368i	−0.114699	−	0.993400i	$-0.536590\pi$
$67$	377.456	−	217.924i	0.688262	−	0.397368i	0.802961	+	0.596032i	$0.203257\pi$
$68$	53.8038	+	93.1909i	0.0959510	+	0.166192i
$69$	−293.060	+	507.595i	−0.511308	+	0.885612i
$70$		−	71.6765i		−	0.122385i
$71$	−57.1249	−	32.9811i	−0.0954857	−	0.0551287i	0.451497	−	0.892273i	$-0.350890\pi$
$71$	−57.1249	−	32.9811i	−0.0954857	−	0.0551287i	−0.546982	+	0.837144i	$0.684224\pi$
$72$	−94.0067	−	54.2748i	−0.153872	−	0.0888381i
$73$		−	885.517i		−	1.41975i	−0.704326	−	0.709876i	$-0.748751\pi$
$73$		−	885.517i		−	1.41975i	0.704326	−	0.709876i	$-0.251249\pi$
$74$	118.781	−	205.735i	0.186595	−	0.323191i
$75$	95.7000	+	165.757i	0.147340	+	0.255200i
$76$	46.3253	−	26.7459i	0.0699194	−	0.0403680i
$77$	−274.633			−0.406459
$78$		0			0
$79$	−385.463			−0.548962			−0.274481	−	0.961592i	$-0.588506\pi$
$79$	−385.463			−0.548962			−0.274481	+	0.961592i	$0.588506\pi$
$80$	118.206	−	68.2464i	0.165198	−	0.0953772i
$81$	89.2679	+	154.616i	0.122452	+	0.212094i
$82$	−432.901	+	749.807i	−0.582999	+	1.00978i
$83$		−	254.207i		−	0.336179i	−0.985772	−	0.168089i	$-0.946240\pi$
$83$		−	254.207i		−	0.336179i	0.985772	−	0.168089i	$-0.0537597\pi$
$84$	−53.3344	−	30.7926i	−0.0692769	−	0.0399970i
$85$	−198.748	−	114.747i	−0.253615	−	0.146425i
$86$			713.016i			0.894029i
$87$	−552.091	+	956.250i	−0.680349	+	1.17840i
$88$	−261.490	−	452.914i	−0.316761	−	0.548646i
$89$	322.692	−	186.306i	0.384329	−	0.221892i	−0.295371	−	0.955383i	$-0.595443\pi$
$89$	322.692	−	186.306i	0.384329	−	0.221892i	0.679700	+	0.733490i	$0.262110\pi$
$90$	231.504			0.271140
$91$		0			0
$92$	639.716			0.724946
$93$	231.766	−	133.810i	0.258420	−	0.149199i
$94$	−588.614	−	1019.51i	−0.645861	−	1.11866i
$95$	−57.0410	+	98.7979i	−0.0616030	+	0.106699i
$96$		−	117.276i		−	0.124682i
$97$	−1137.86	−	656.942i	−1.19105	−	0.687653i	−0.232506	−	0.972595i	$-0.574692\pi$
$97$	−1137.86	−	656.942i	−1.19105	−	0.687653i	−0.958545	+	0.284942i	$0.908026\pi$
$98$	−563.525	−	325.351i	−0.580863	−	0.335362i
$99$		−	887.020i		−	0.900494i
$100$	104.451	−	180.915i	0.104451	−	0.180915i
$101$	731.861	+	1267.62i	0.721019	+	1.24884i	0.960592	+	0.277963i	$0.0896592\pi$
$101$	731.861	+	1267.62i	0.721019	+	1.24884i	−0.239573	+	0.970878i	$0.577007\pi$
$102$	−170.767	+	98.5921i	−0.165769	+	0.0957066i
$103$	−210.886			−0.201740			−0.100870	−	0.994900i	$-0.532163\pi$
$103$	−210.886			−0.201740			−0.100870	+	0.994900i	$0.532163\pi$
$104$		0			0
$105$	131.343			0.122074
$106$	−466.722	+	269.462i	−0.427660	+	0.246910i
$107$	−195.531	−	338.669i	−0.176660	−	0.305985i	0.764074	−	0.645128i	$-0.223196\pi$
$107$	−195.531	−	338.669i	−0.176660	−	0.305985i	−0.940735	+	0.339144i	$0.889863\pi$
$108$	297.358	−	515.040i	0.264938	−	0.458886i
$109$			1331.40i			1.16996i	0.811049	+	0.584978i	$0.198897\pi$
$109$			1331.40i			1.16996i	−0.811049	+	0.584978i	$0.801103\pi$
$110$	965.930	+	557.680i	0.837253	+	0.483388i
$111$	376.996	+	217.658i	0.322368	+	0.186119i
$112$			67.2167i			0.0567088i
$113$	355.956	−	616.534i	0.296332	−	0.513263i	−0.678962	−	0.734174i	$-0.737570\pi$
$113$	355.956	−	616.534i	0.296332	−	0.513263i	0.975294	+	0.220911i	$0.0709031\pi$
$114$	49.0102	+	84.8882i	0.0402652	+	0.0697413i
$115$	−1181.54	+	682.161i	−0.958078	+	0.553146i
$116$	1205.15			0.964616
$117$		0			0
$118$	460.679			0.359398
$119$	97.8748	−	56.5081i	0.0753964	−	0.0435301i
$120$	125.057	+	216.605i	0.0951342	+	0.164777i
$121$	1471.29	−	2548.34i	1.10540	−	1.91461i
$122$		−	761.631i		−	0.565204i
$123$	−1373.97	−	793.264i	−1.00721	−	0.581514i
$124$	−252.960	−	146.046i	−0.183197	−	0.105769i
$125$			1511.87i			1.08181i
$126$	−57.0027	+	98.7316i	−0.0403032	+	0.0698072i
$127$	−585.852	−	1014.73i	−0.409338	−	0.708995i	0.585477	−	0.810689i	$-0.300907\pi$
$127$	−585.852	−	1014.73i	−0.409338	−	0.708995i	−0.994816	+	0.101694i	$0.967574\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−1306.56			−0.891751
$130$		0			0
$131$	−1128.61			−0.752726			−0.376363	−	0.926472i	$-0.622825\pi$
$131$	−1128.61			−0.752726			−0.376363	+	0.926472i	$0.622825\pi$
$132$	829.937	−	479.164i	0.547248	−	0.315954i
$133$	−28.0902	−	48.6537i	−0.0183138	−	0.0317204i
$134$	435.848	−	754.911i	0.280982	−	0.486675i
$135$			1268.35i			0.808610i
$136$	186.382	+	107.608i	0.117516	+	0.0678476i
$137$	−1513.76	−	873.967i	−0.944006	−	0.545022i	−0.0527923	−	0.998606i	$-0.516812\pi$
$137$	−1513.76	−	873.967i	−0.944006	−	0.545022i	−0.891214	+	0.453583i	$0.850145\pi$
$138$			1172.24i			0.723099i
$139$	−838.268	+	1451.92i	−0.511518	+	0.885975i	0.488393	+	0.872624i	$0.337583\pi$
$139$	−838.268	+	1451.92i	−0.511518	+	0.885975i	−0.999911	+	0.0133509i	$0.995750\pi$
$140$	−71.6765	−	124.147i	−0.0432698	−	0.0749455i
$141$	1868.19	−	1078.60i	1.11581	−	0.644216i
$142$	−131.924			−0.0779637
$143$		0			0
$144$	−217.099			−0.125636
$145$	−2225.88	+	1285.11i	−1.27482	+	0.736019i
$146$	−885.517	−	1533.76i	−0.501958	−	0.869417i
$147$	596.186	−	1032.62i	0.334507	−	0.579384i
$148$		−	475.124i		−	0.263885i
$149$	776.791	+	448.481i	0.427095	+	0.246584i	0.698108	−	0.715992i	$-0.254025\pi$
$149$	776.791	+	448.481i	0.427095	+	0.246584i	−0.271013	+	0.962576i	$0.587359\pi$
$150$	331.515	+	191.400i	0.180454	+	0.104185i
$151$			2078.28i			1.12005i	0.828475	+	0.560027i	$0.189209\pi$
$151$			2078.28i			1.12005i	−0.828475	+	0.560027i	$0.810791\pi$
$152$	53.4918	−	92.6506i	0.0285445	−	0.0494405i
$153$	182.512	+	316.120i	0.0964393	+	0.167038i
$154$	−475.679	+	274.633i	−0.248904	+	0.143705i
$155$	622.946			0.322814
$156$		0			0
$157$	−3494.75			−1.77650			−0.888252	−	0.459357i	$-0.848080\pi$
$157$	−3494.75			−1.77650			−0.888252	+	0.459357i	$0.848080\pi$
$158$	−667.642	+	385.463i	−0.336169	+	0.194087i
$159$	−493.772	−	855.238i	−0.246281	−	0.426571i
$160$	136.493	−	236.412i	0.0674419	−	0.116813i
$161$		−	671.869i		−	0.328887i
$162$	309.233	+	178.536i	0.149973	+	0.0865870i
$163$	−390.797	−	225.627i	−0.187789	−	0.108420i	0.403158	−	0.915130i	$-0.367912\pi$
$163$	−390.797	−	225.627i	−0.187789	−	0.108420i	−0.590947	+	0.806710i	$0.701246\pi$
$164$			1731.61i			0.824486i
$165$	−1021.91	+	1770.01i	−0.482157	+	0.835120i
$166$	−254.207	−	440.299i	−0.118857	−	0.205867i
$167$	−2774.18	+	1601.68i	−1.28547	+	0.742164i	−0.977842	−	0.209344i	$-0.932867\pi$
$167$	−2774.18	+	1601.68i	−1.28547	+	0.742164i	−0.307624	+	0.951508i	$0.599534\pi$
$168$	−123.170			−0.0565643
$169$		0			0
$170$	−458.989			−0.207076
$171$	157.143	−	90.7268i	0.0702752	−	0.0405734i
$172$	713.016	+	1234.98i	0.316087	+	0.547478i
$173$	949.691	−	1644.91i	0.417362	−	0.722893i	−0.578311	−	0.815816i	$-0.696288\pi$
$173$	949.691	−	1644.91i	0.417362	−	0.722893i	0.995673	+	0.0929237i	$0.0296213\pi$
$174$			2208.36i			0.962159i
$175$	−190.008	−	109.701i	−0.0820756	−	0.0473864i
$176$	−905.829	−	522.980i	−0.387951	−	0.223984i
$177$			844.165i			0.358482i
$178$	372.612	−	645.384i	0.156902	−	0.271762i
$179$	1325.45	+	2295.74i	0.553455	+	0.958612i	0.998022	+	0.0628664i	$0.0200242\pi$
$179$	1325.45	+	2295.74i	0.553455	+	0.958612i	−0.444567	+	0.895746i	$0.646642\pi$
$180$	400.976	−	231.504i	0.166039	−	0.0958625i
$181$	2289.94			0.940387			0.470194	−	0.882563i	$-0.344184\pi$
$181$	2289.94			0.940387			0.470194	+	0.882563i	$0.344184\pi$
$182$		0			0
$183$	1395.64			0.563764
$184$	1108.02	−	639.716i	0.443937	−	0.256307i
$185$	506.648	+	877.539i	0.201349	+	0.348746i
$186$	267.621	−	463.533i	0.105500	−	0.182731i
$187$			1758.65i			0.687727i
$188$	−2039.02	−	1177.23i	−0.791015	−	0.456693i
$189$	−540.926	−	312.304i	−0.208183	−	0.120195i
$190$			228.164i			0.0871198i
$191$	169.157	−	292.988i	0.0640825	−	0.110994i	−0.832204	−	0.554469i	$-0.812921\pi$
$191$	169.157	−	292.988i	0.0640825	−	0.110994i	0.896287	+	0.443475i	$0.146255\pi$
$192$	−117.276	−	203.128i	−0.0440816	−	0.0763515i
$193$	−2324.46	+	1342.03i	−0.866933	+	0.500524i	−0.866328	−	0.499476i	$-0.833526\pi$
$193$	−2324.46	+	1342.03i	−0.866933	+	0.500524i	−0.000605201		1.00000i	$0.500193\pi$
$194$	−2627.77			−0.972489
$195$		0			0
$196$	−1301.40			−0.474273
$197$	1643.06	−	948.620i	0.594229	−	0.343078i	−0.172539	−	0.985003i	$-0.555197\pi$
$197$	1643.06	−	948.620i	0.594229	−	0.343078i	0.766768	+	0.641925i	$0.221864\pi$
$198$	−887.020	−	1536.36i	−0.318373	−	0.551438i
$199$	−1207.80	+	2091.97i	−0.430245	+	0.745207i	−0.996894	−	0.0787527i	$-0.974906\pi$
$199$	−1207.80	+	2091.97i	−0.430245	+	0.745207i	0.566649	+	0.823959i	$0.308240\pi$
$200$		−	417.804i		−	0.147716i
$201$	1383.33	+	798.665i	0.485435	+	0.280266i
$202$	2535.24	+	1463.72i	0.883064	+	0.509837i
$203$		−	1265.72i		−	0.437618i
$204$	−197.184	+	341.533i	−0.0676748	+	0.117216i
$205$	−1846.50	−	3198.22i	−0.629097	−	1.08963i
$206$	−365.265	+	210.886i	−0.123540	+	0.0713258i
$207$	2170.03			0.728635
$208$		0			0
$209$	874.225			0.289337
$210$	227.492	−	131.343i	0.0747546	−	0.0431596i
$211$	−1334.21	−	2310.92i	−0.435312	−	0.753982i	0.562009	−	0.827131i	$-0.310028\pi$
$211$	−1334.21	−	2310.92i	−0.435312	−	0.753982i	−0.997321	+	0.0731491i	$0.976695\pi$
$212$	−538.924	+	933.443i	−0.174592	+	0.302402i
$213$		−	241.743i		−	0.0777651i
$214$	−677.338	−	391.061i	−0.216364	−	0.124918i
$215$	−2633.84	−	1520.65i	−0.835471	−	0.482360i
$216$		−	1189.43i		−	0.374679i
$217$	−153.387	+	265.674i	−0.0479842	+	0.0831112i
$218$	1331.40	+	2306.06i	0.413642	+	0.716449i
$219$	2810.52	−	1622.65i	0.867202	−	0.500680i
$220$	2230.72			0.683614
$221$		0			0
$222$	870.634			0.263212
$223$	−247.993	+	143.179i	−0.0744701	+	0.0429953i	−0.536773	−	0.843727i	$-0.680357\pi$
$223$	−247.993	+	143.179i	−0.0744701	+	0.0429953i	0.462303	+	0.886722i	$0.347023\pi$
$224$	67.2167	+	116.423i	0.0200496	+	0.0347269i
$225$	354.316	−	613.694i	0.104983	−	0.181835i
$226$		−	1423.82i		−	0.419077i
$227$	−4504.41	−	2600.62i	−1.31704	−	0.760393i	−0.333788	−	0.942648i	$-0.608327\pi$
$227$	−4504.41	−	2600.62i	−1.31704	−	0.760393i	−0.983251	+	0.182255i	$0.941660\pi$
$228$	169.776	+	98.0204i	0.0493145	+	0.0284718i
$229$		−	890.458i		−	0.256957i	−0.991712	−	0.128478i	$-0.958991\pi$
$229$		−	890.458i		−	0.256957i	0.991712	−	0.128478i	$-0.0410093\pi$
$230$	−1364.32	+	2363.08i	−0.391134	+	0.677463i
$231$	−503.248	−	871.651i	−0.143339	−	0.248270i
$232$	2087.38	−	1205.15i	0.590704	−	0.341043i
$233$	−4753.11			−1.33642			−0.668212	−	0.743971i	$-0.732940\pi$
$233$	−4753.11			−1.33642			−0.668212	+	0.743971i	$0.732940\pi$
$234$		0			0
$235$	5021.35			1.39386
$236$	797.919	−	460.679i	0.220085	−	0.127066i
$237$	−706.337	−	1223.41i	−0.193593	−	0.335313i
$238$	113.016	−	195.750i	0.0307805	−	0.0533133i
$239$		−	2292.62i		−	0.620491i	−0.950656	−	0.310245i	$-0.899589\pi$
$239$		−	2292.62i		−	0.620491i	0.950656	−	0.310245i	$-0.100411\pi$
$240$	433.211	+	250.114i	0.116515	+	0.0672700i
$241$	1710.58	+	987.604i	0.457212	+	0.263972i	0.710871	−	0.703322i	$-0.248301\pi$
$241$	1710.58	+	987.604i	0.457212	+	0.263972i	−0.253659	+	0.967294i	$0.581634\pi$
$242$		−	5885.14i		−	1.56327i
$243$	1680.01	−	2909.87i	0.443510	−	0.768182i
$244$	−761.631	−	1319.18i	−0.199830	−	0.346115i
$245$	2403.66	−	1387.75i	0.626792	−	0.361879i
$246$	−3173.06			−0.822385
$247$		0			0
$248$	−584.186			−0.149580
$249$	806.821	−	465.818i	0.205342	−	0.118554i
$250$	1511.87	+	2618.64i	0.382477	+	0.662470i
$251$	−3732.87	+	6465.52i	−0.938711	+	1.62590i	−0.170833	+	0.985300i	$0.554646\pi$
$251$	−3732.87	+	6465.52i	−0.938711	+	1.62590i	−0.767879	+	0.640595i	$0.778688\pi$
$252$			228.011i			0.0569974i
$253$	9054.27	+	5227.49i	2.24995	+	1.29901i
$254$	−2029.45	−	1171.70i	−0.501335	−	0.289446i
$255$		−	841.069i		−	0.206548i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−277.483	−	480.615i	−0.0673499	−	0.116653i	0.830384	−	0.557191i	$-0.188121\pi$
$257$	−277.483	−	480.615i	−0.0673499	−	0.116653i	−0.897734	+	0.440538i	$0.854788\pi$
$258$	−2263.02	+	1306.56i	−0.546084	+	0.315282i
$259$	−499.004			−0.119717
$260$		0			0
$261$	4088.08			0.969525
$262$	−1954.81	+	1128.61i	−0.460949	+	0.266129i
$263$	996.534	+	1726.05i	0.233646	+	0.404687i	0.958878	−	0.283817i	$-0.0916010\pi$
$263$	996.534	+	1726.05i	0.233646	+	0.404687i	−0.725232	+	0.688504i	$0.758268\pi$
$264$	958.329	−	1659.87i	0.223413	−	0.386963i
$265$		−	2298.72i		−	0.532866i
$266$	−97.3074	−	56.1804i	−0.0224297	−	0.0129498i
$267$	1182.63	+	682.789i	0.271069	+	0.156502i
$268$		−	1743.39i		−	0.397368i
$269$	2603.88	−	4510.06i	0.590191	−	1.02224i	−0.404015	−	0.914752i	$-0.632386\pi$
$269$	2603.88	−	4510.06i	0.590191	−	1.02224i	0.994206	−	0.107489i	$-0.0342811\pi$
$270$	1268.35	+	2196.85i	0.285887	+	0.495170i
$271$	−3537.63	+	2042.45i	−0.792972	+	0.457823i	−0.841008	−	0.541023i	$-0.818037\pi$
$271$	−3537.63	+	2042.45i	−0.792972	+	0.457823i	0.0480356	+	0.998846i	$0.484704\pi$
$272$	430.430			0.0959510
$273$		0			0
$274$	−3495.87			−0.770778
$275$	2956.71	−	1707.06i	0.648351	−	0.374325i
$276$	1172.24	+	2030.38i	0.255654	+	0.442806i
$277$	218.996	−	379.313i	0.0475026	−	0.0822769i	−0.841296	−	0.540574i	$-0.818207\pi$
$277$	218.996	−	379.313i	0.0475026	−	0.0822769i	0.888799	+	0.458297i	$0.151540\pi$
$278$			3353.07i			0.723395i
$279$	−858.083	−	495.415i	−0.184129	−	0.106307i
$280$	−248.295	−	143.353i	−0.0529945	−	0.0305964i
$281$		−	5462.34i		−	1.15963i	−0.814748	−	0.579815i	$-0.803125\pi$
$281$		−	5462.34i		−	1.15963i	0.814748	−	0.579815i	$-0.196875\pi$
$282$	2157.20	−	3736.38i	0.455529	−	0.789000i
$283$	−398.338	−	689.941i	−0.0836704	−	0.144921i	0.821153	−	0.570707i	$-0.193331\pi$
$283$	−398.338	−	689.941i	−0.0836704	−	0.144921i	−0.904824	+	0.425786i	$0.859998\pi$
$284$	−228.500	+	131.924i	−0.0477428	+	0.0275643i
$285$	−418.096			−0.0868978
$286$		0			0
$287$	1818.64			0.374045
$288$	−376.027	+	217.099i	−0.0769361	+	0.0444191i
$289$	2094.64	+	3628.03i	0.426347	+	0.738455i
$290$	−2570.22	+	4451.76i	−0.520444	+	0.901436i
$291$		−	4815.22i		−	0.970011i
$292$	−3067.52	−	1771.03i	−0.614771	−	0.354938i
$293$	1469.93	+	848.662i	0.293085	+	0.169213i	0.639332	−	0.768931i	$-0.279211\pi$
$293$	1469.93	+	848.662i	0.293085	+	0.169213i	−0.346247	+	0.938143i	$0.612544\pi$
$294$		−	2384.74i		−	0.473065i
$295$	−982.490	+	1701.72i	−0.193908	+	0.335858i
$296$	−475.124	−	822.938i	−0.0932973	−	0.161596i
$297$	8417.37	−	4859.77i	1.64453	−	0.949469i
$298$	1793.92			0.348722
$299$		0			0
$300$	765.600			0.147340
$301$	1297.05	−	748.853i	0.248375	−	0.143399i
$302$	2078.28	+	3599.69i	0.395999	+	0.685890i
$303$	−2682.18	+	4645.67i	−0.508538	+	0.880814i
$304$		−	213.967i		−	0.0403680i
$305$	2813.42	+	1624.33i	0.528184	+	0.304947i
$306$	632.240	+	365.024i	0.118114	+	0.0681929i
$307$			9385.86i			1.74488i	0.488718	+	0.872442i	$0.337465\pi$
$307$			9385.86i			1.74488i	−0.488718	+	0.872442i	$0.662535\pi$
$308$	−549.266	+	951.357i	−0.101615	+	0.176002i
$309$	−386.435	−	669.325i	−0.0711441	−	0.123225i
$310$	1078.97	−	622.946i	0.197683	−	0.114132i
$311$	3282.65			0.598527			0.299264	−	0.954170i	$-0.403259\pi$
$311$	3282.65			0.598527			0.299264	+	0.954170i	$0.403259\pi$
$312$		0			0
$313$	−5924.67			−1.06991			−0.534955	−	0.844880i	$-0.679672\pi$
$313$	−5924.67			−1.06991			−0.534955	+	0.844880i	$0.679672\pi$
$314$	−6053.08	+	3494.75i	−1.08788	+	0.628089i
$315$	−243.139	−	421.130i	−0.0434900	−	0.0753269i
$316$	−770.927	+	1335.28i	−0.137241	+	0.237708i
$317$		−	6467.88i		−	1.14597i	−0.819566	−	0.572985i	$-0.805785\pi$
$317$		−	6467.88i		−	1.14597i	0.819566	−	0.572985i	$-0.194215\pi$
$318$	−1710.48	−	987.544i	−0.301631	−	0.174147i
$319$	17057.2	+	9847.98i	2.99379	+	1.72847i
$320$		−	545.971i		−	0.0953772i
$321$	716.595	−	1241.18i	0.124599	−	0.215813i
$322$	−671.869	−	1163.71i	−0.116279	−	0.201401i
$323$	−311.560	+	179.879i	−0.0536707	+	0.0309868i
$324$	714.143			0.122452
$325$		0			0
$326$	−902.508			−0.153329
$327$	−4225.70	+	2439.71i	−0.714624	+	0.412588i
$328$	1731.61	+	2999.23i	0.291500	+	0.504892i
$329$	−1236.40	+	2141.50i	−0.207188	+	0.358860i
$330$			4087.65i			0.681872i
$331$	3039.09	+	1754.62i	0.504664	+	0.291368i	0.730637	−	0.682766i	$-0.239223\pi$
$331$	3039.09	+	1754.62i	0.504664	+	0.291368i	−0.225974	+	0.974133i	$0.572556\pi$
$332$	−880.599	−	508.414i	−0.145570	−	0.0840447i
$333$		−	1611.70i		−	0.265227i
$334$	−3203.35	+	5548.37i	−0.524789	+	0.908962i
$335$	1859.07	+	3220.00i	0.303199	+	0.525156i
$336$	−213.337	+	123.170i	−0.0346384	+	0.0199985i
$337$	1834.82			0.296584			0.148292	−	0.988944i	$-0.452622\pi$
$337$	1834.82			0.296584			0.148292	+	0.988944i	$0.452622\pi$
$338$		0			0
$339$	2609.07			0.418010
$340$	−794.993	+	458.989i	−0.126807	+	0.0732123i
$341$	−2386.86	−	4134.16i	−0.379048	−	0.656531i
$342$	181.454	−	314.287i	0.0286897	−	0.0496921i
$343$			2807.77i			0.441999i
$344$	2469.96	+	1426.03i	0.387126	+	0.223507i
$345$	−4330.19	−	2500.03i	−0.675737	−	0.390137i
$346$		−	3798.76i		−	0.590239i
$347$	3629.65	−	6286.74i	0.561527	−	0.972593i	−0.435837	−	0.900026i	$-0.643547\pi$
$347$	3629.65	−	6286.74i	0.561527	−	0.972593i	0.997364	−	0.0725673i	$-0.0231192\pi$
$348$	2208.36	+	3825.00i	0.340175	+	0.589200i
$349$	−1554.72	+	897.618i	−0.238459	+	0.137674i	−0.614468	−	0.788942i	$-0.710629\pi$
$349$	−1554.72	+	897.618i	−0.238459	+	0.137674i	0.376009	+	0.926616i	$0.377296\pi$
$350$	−438.804			−0.0670144
$351$		0			0
$352$	−2091.92			−0.316761
$353$	3942.47	−	2276.19i	0.594438	−	0.343199i	−0.172412	−	0.985025i	$-0.555156\pi$
$353$	3942.47	−	2276.19i	0.594438	−	0.343199i	0.766850	+	0.641826i	$0.221823\pi$
$354$	844.165	+	1462.14i	0.126743	+	0.219525i
$355$	281.355	−	487.321i	0.0420641	−	0.0728572i
$356$		−	1490.45i		−	0.221892i
$357$	358.699	+	207.095i	0.0531775	+	0.0307020i
$358$	4591.48	+	2650.89i	0.677841	+	0.391352i
$359$			10165.4i			1.49445i	0.664569	+	0.747227i	$0.268615\pi$
$359$			10165.4i			1.49445i	−0.664569	+	0.747227i	$0.731385\pi$
$360$	463.007	−	801.952i	0.0677850	−	0.117407i
$361$	−3340.08	−	5785.19i	−0.486963	−	0.843445i
$362$	3966.30	−	2289.94i	0.575867	−	0.332477i
$363$	10784.2			1.55929
$364$		0			0
$365$	7554.16			1.08330
$366$	2417.32	−	1395.64i	0.345233	−	0.199321i
$367$	5200.78	+	9008.01i	0.739723	+	1.28124i	0.952620	+	0.304163i	$0.0983769\pi$
$367$	5200.78	+	9008.01i	0.739723	+	1.28124i	−0.212897	+	0.977075i	$0.568290\pi$
$368$	1279.43	−	2216.04i	0.181237	−	0.313911i
$369$			5873.91i			0.828681i
$370$	1755.08	+	1013.30i	0.246601	+	0.142375i
$371$	980.359	+	566.011i	0.137191	+	0.0792070i
$372$		−	1070.48i		−	0.149199i
$373$	3976.70	−	6887.85i	0.552027	−	0.956138i	−0.446101	−	0.894982i	$-0.647188\pi$
$373$	3976.70	−	6887.85i	0.552027	−	0.956138i	0.998128	−	0.0611560i	$-0.0194787\pi$
$374$	1758.65	+	3046.06i	0.243148	+	0.421145i
$375$	−4798.50	+	2770.42i	−0.660783	+	0.381503i
$376$	−4708.91			−0.645861
$377$		0			0
$378$	−1249.22			−0.169981
$379$	−7807.06	+	4507.41i	−1.05810	+	0.610897i	−0.924907	−	0.380193i	$-0.875858\pi$
$379$	−7807.06	+	4507.41i	−1.05810	+	0.610897i	−0.133197	+	0.991090i	$0.542524\pi$
$380$	228.164	+	395.192i	0.0308015	+	0.0533497i
$381$	2147.07	−	3718.84i	0.288709	−	0.500058i
$382$		−	676.627i		−	0.0906263i
$383$	−2161.81	−	1248.12i	−0.288415	−	0.166517i	0.348812	−	0.937193i	$-0.386585\pi$
$383$	−2161.81	−	1248.12i	−0.288415	−	0.166517i	−0.637227	+	0.770676i	$0.719919\pi$
$384$	−406.256	−	234.552i	−0.0539887	−	0.0311704i
$385$		−	2342.84i		−	0.310135i
$386$	−2684.05	+	4648.91i	−0.353924	+	0.613014i
$387$	2418.67	+	4189.26i	0.317695	+	0.550264i
$388$	−4551.43	+	2627.77i	−0.595525	+	0.343827i
$389$	−10896.9			−1.42029			−0.710145	−	0.704056i	$-0.751371\pi$
$389$	−10896.9			−1.42029			−0.710145	+	0.704056i	$0.751371\pi$
$390$		0			0
$391$	−4302.40			−0.556475
$392$	−2254.10	+	1301.40i	−0.290432	+	0.167681i
$393$	−2068.11	−	3582.07i	−0.265451	−	0.459774i
$394$	1897.24	−	3286.12i	0.242593	−	0.420183i
$395$		−	3288.31i		−	0.418868i
$396$	−3072.73	−	1774.04i	−0.389925	−	0.225123i
$397$	−9428.55	−	5443.57i	−1.19195	−	0.688174i	−0.233203	−	0.972428i	$-0.574921\pi$
$397$	−9428.55	−	5443.57i	−1.19195	−	0.688174i	−0.958749	+	0.284254i	$0.908254\pi$
$398$			4831.21i			0.608459i
$399$	102.947	−	178.310i	0.0129168	−	0.0223725i
$400$	−417.804	−	723.658i	−0.0522255	−	0.0904573i
$401$	8633.20	−	4984.38i	1.07512	−	0.620718i	0.145541	−	0.989352i	$-0.453508\pi$
$401$	8633.20	−	4984.38i	1.07512	−	0.620718i	0.929575	+	0.368634i	$0.120174\pi$
$402$	3194.66			0.396356
$403$		0			0
$404$	5854.89			0.721019
$405$	−1319.00	+	761.526i	−0.161831	+	0.0934334i
$406$	−1265.72	−	2192.30i	−0.154721	−	0.267985i
$407$	3882.50	−	6724.70i	0.472847	−	0.818994i
$408$			788.737i			0.0957066i
$409$	3495.56	+	2018.16i	0.422602	+	0.243989i	0.696190	−	0.717858i	$-0.254877\pi$
$409$	3495.56	+	2018.16i	0.422602	+	0.243989i	−0.273588	+	0.961847i	$0.588210\pi$
$410$	−6396.45	−	3692.99i	−0.770483	−	0.444839i
$411$		−	6405.96i		−	0.768814i
$412$	−421.772	+	730.530i	−0.0504350	+	0.0873559i
$413$	−483.833	−	838.024i	−0.0576462	−	0.0998462i
$414$	3758.60	−	2170.03i	0.446196	−	0.257611i
$415$	2168.59			0.256510
$416$		0			0
$417$	−6144.29			−0.721552
$418$	1514.20	−	874.225i	0.177182	−	0.102296i
$419$	−7597.43	−	13159.1i	−0.885821	−	1.53429i	−0.844770	−	0.535129i	$-0.820263\pi$
$419$	−7597.43	−	13159.1i	−0.885821	−	1.53429i	−0.0410504	−	0.999157i	$-0.513070\pi$
$420$	262.685	−	454.985i	0.0305184	−	0.0528595i
$421$		−	10154.8i		−	1.17556i	−0.809019	−	0.587782i	$-0.800001\pi$
$421$		−	10154.8i		−	1.17556i	0.809019	−	0.587782i	$-0.199999\pi$
$422$	−4621.84	−	2668.42i	−0.533146	−	0.307812i
$423$	−6916.71	−	3993.36i	−0.795040	−	0.459017i
$424$			2155.69i			0.246910i
$425$	−702.483	+	1216.74i	−0.0801775	+	0.138872i
$426$	−241.743	−	418.711i	−0.0274941	−	0.0476212i
$427$	−1385.49	+	799.912i	−0.157022	+	0.0906568i
$428$	−1564.24			−0.176660
$429$		0			0
$430$	−6082.59			−0.682159
$431$	5730.35	−	3308.42i	0.640420	−	0.369747i	−0.144356	−	0.989526i	$-0.546111\pi$
$431$	5730.35	−	3308.42i	0.640420	−	0.369747i	0.784776	+	0.619779i	$0.212778\pi$
$432$	−1189.43	−	2060.16i	−0.132469	−	0.229443i
$433$	2848.80	−	4934.27i	0.316177	−	0.547635i	−0.663510	−	0.748167i	$-0.730934\pi$
$433$	2848.80	−	4934.27i	0.316177	−	0.547635i	0.979687	+	0.200533i	$0.0642673\pi$
$434$			613.548i			0.0678600i
$435$	−8157.57	−	4709.77i	−0.899139	−	0.519118i
$436$	4612.11	+	2662.81i	0.506606	+	0.292489i
$437$			2138.73i			0.234117i
$438$	3245.31	−	5621.04i	0.354034	−	0.613205i
$439$	218.004	+	377.593i	0.0237010	+	0.0410513i	0.877633	−	0.479334i	$-0.159122\pi$
$439$	218.004	+	377.593i	0.0237010	+	0.0410513i	−0.853932	+	0.520385i	$0.825788\pi$
$440$	3863.72	−	2230.72i	0.418626	−	0.241694i
$441$	−4414.59			−0.476686
$442$		0			0
$443$	6609.58			0.708873			0.354436	−	0.935080i	$-0.384673\pi$
$443$	6609.58			0.708873			0.354436	+	0.935080i	$0.384673\pi$
$444$	1507.98	−	870.634i	0.161184	−	0.0930596i
$445$	1589.34	+	2752.82i	0.169308	+	0.293250i
$446$	−286.358	+	495.986i	−0.0304023	+	0.0526583i
$447$			3287.25i			0.347833i
$448$	232.846	+	134.433i	0.0245556	+	0.0141772i
$449$	−6941.46	−	4007.65i	−0.729594	−	0.421231i	0.0886795	−	0.996060i	$-0.471735\pi$
$449$	−6941.46	−	4007.65i	−0.729594	−	0.421231i	−0.818274	+	0.574829i	$0.805069\pi$
$450$		−	1417.26i		−	0.148468i
$451$	−14149.9	+	24508.4i	−1.47737	+	2.55888i
$452$	−1423.82	−	2466.14i	−0.148166	−	0.256631i
$453$	−6596.20	+	3808.32i	−0.684142	+	0.394990i
$454$	−10402.5			−1.07536
$455$		0			0
$456$	392.082			0.0402652
$457$	3903.21	−	2253.52i	0.399528	−	0.230668i	−0.286752	−	0.958005i	$-0.592576\pi$
$457$	3903.21	−	2253.52i	0.399528	−	0.230668i	0.686280	+	0.727337i	$0.259242\pi$
$458$	−890.458	−	1542.32i	−0.0908480	−	0.157353i
$459$	−1999.88	+	3463.89i	−0.203369	+	0.352245i
$460$			5457.29i			0.553146i
$461$	1821.73	+	1051.78i	0.184048	+	0.106260i	0.589193	−	0.807992i	$-0.299446\pi$
$461$	1821.73	+	1051.78i	0.184048	+	0.106260i	−0.405145	+	0.914252i	$0.632779\pi$
$462$	−1743.30	−	1006.50i	−0.175554	−	0.101356i
$463$			5468.28i			0.548883i	0.961604	+	0.274441i	$0.0884929\pi$
$463$			5468.28i			0.548883i	−0.961604	+	0.274441i	$0.911507\pi$
$464$	2410.30	−	4174.77i	0.241154	−	0.417691i
$465$	1141.51	+	1977.15i	0.113841	+	0.197179i
$466$	−8232.63	+	4753.11i	−0.818389	+	0.472497i
$467$	6043.79			0.598872			0.299436	−	0.954116i	$-0.403201\pi$
$467$	6043.79			0.598872			0.299436	+	0.954116i	$0.403201\pi$
$468$		0			0
$469$	−1831.02			−0.180274
$470$	8697.23	−	5021.35i	0.853560	−	0.492803i
$471$	−6403.90	−	11091.9i	−0.626489	−	1.08511i
$472$	921.358	−	1595.84i	0.0898495	−	0.155624i
$473$			23305.8i			2.26555i
$474$	−2446.82	−	1412.67i	−0.237102	−	0.136891i
$475$	604.841	+	349.205i	0.0584253	+	0.0337318i
$476$		−	452.065i		−	0.0435301i
$477$	−1828.12	+	3166.40i	−0.175480	+	0.303940i
$478$	−2292.62	−	3970.94i	−0.219377	−	0.379972i
$479$	−7345.02	+	4240.65i	−0.700632	+	0.404510i	−0.807583	−	0.589754i	$-0.799225\pi$
$479$	−7345.02	+	4240.65i	−0.700632	+	0.404510i	0.106951	+	0.994264i	$0.465891\pi$
$480$	1000.46			0.0951342
$481$		0			0
$482$	3950.42			0.373312
$483$	2132.43	−	1231.16i	0.200888	−	0.115983i
$484$	−5885.14	−	10193.4i	−0.552699	−	0.957303i
$485$	5604.24	−	9706.83i	0.524691	−	0.908792i
$486$		−	6720.05i		−	0.627218i
$487$	−5735.99	−	3311.68i	−0.533722	−	0.308145i	0.208809	−	0.977957i	$-0.433041\pi$
$487$	−5735.99	−	3311.68i	−0.533722	−	0.308145i	−0.742531	+	0.669812i	$0.766375\pi$
$488$	−2638.37	−	1523.26i	−0.244740	−	0.141301i
$489$		−	1653.79i		−	0.152939i
$490$	2775.50	−	4807.31i	0.255887	−	0.443209i
$491$	8189.68	+	14184.9i	0.752739	+	1.30378i	0.946490	+	0.322732i	$0.104601\pi$
$491$	8189.68	+	14184.9i	0.752739	+	1.30378i	−0.193751	+	0.981051i	$0.562065\pi$
$492$	−5495.90	+	3173.06i	−0.503606	+	0.290757i
$493$	−8105.21			−0.740447
$494$		0			0
$495$	7566.99			0.687093
$496$	−1011.84	+	584.186i	−0.0915986	+	0.0528845i
$497$	138.555	+	239.985i	0.0125051	+	0.0216595i
$498$	931.637	−	1613.64i	0.0838306	−	0.145199i
$499$			7915.70i			0.710131i	0.934841	+	0.355065i	$0.115541\pi$
$499$			7915.70i			0.710131i	−0.934841	+	0.355065i	$0.884459\pi$
$500$	5237.29	+	3023.75i	0.468437	+	0.270452i
$501$	−10167.0	−	5869.94i	−0.906646	−	0.523452i
$502$			14931.5i			1.32754i
$503$	239.755	−	415.269i	0.0212528	−	0.0368110i	−0.855203	−	0.518293i	$-0.826568\pi$
$503$	239.755	−	415.269i	0.0212528	−	0.0368110i	0.876456	+	0.481482i	$0.159901\pi$
$504$	228.011	+	394.926i	0.0201516	+	0.0349036i
$505$	−10813.8	+	6243.36i	−0.952888	+	0.550150i
$506$	20909.9			1.83708
$507$		0			0
$508$	−4686.82			−0.409338
$509$	−1032.59	+	596.164i	−0.0899186	+	0.0519145i	−0.544285	−	0.838900i	$-0.683199\pi$
$509$	−1032.59	+	596.164i	−0.0899186	+	0.0519145i	0.454366	+	0.890815i	$0.349866\pi$
$510$	−841.069	−	1456.77i	−0.0730258	−	0.126484i
$511$	−1860.05	+	3221.70i	−0.161025	+	0.278903i
$512$			512.000i			0.0441942i
$513$	1721.90	+	994.140i	0.148195	+	0.0855602i
$514$	−961.229	−	554.966i	−0.0824864	−	0.0476236i
$515$		−	1799.02i		−	0.153931i
$516$	−2613.11	+	4526.04i	−0.222938	+	0.386140i
$517$	−19239.6	−	33324.0i	−1.63667	−	2.83479i
$518$	−864.300	+	499.004i	−0.0733111	+	0.0423262i
$519$	6961.00			0.588736
$520$		0			0
$521$	−23238.5			−1.95412			−0.977062	−	0.212955i	$-0.931691\pi$
$521$	−23238.5			−1.95412			−0.977062	+	0.212955i	$0.931691\pi$
$522$	7080.77	−	4088.08i	0.593710	−	0.342779i
$523$	5513.14	+	9549.03i	0.460942	+	0.798375i	0.999008	−	0.0445277i	$-0.0141783\pi$
$523$	5513.14	+	9549.03i	0.460942	+	0.798375i	−0.538066	+	0.842903i	$0.680845\pi$
$524$	−2257.22	+	3909.62i	−0.188181	+	0.325940i
$525$		−	804.080i		−	0.0668437i
$526$	3452.10	+	1993.07i	0.286157	+	0.165213i
$527$	1701.27	+	982.231i	0.140624	+	0.0811891i
$528$		−	3833.32i		−	0.315954i
$529$	−6705.15	+	11613.7i	−0.551093	+	0.954522i
$530$	−2298.72	−	3981.51i	−0.188397	−	0.326312i
$531$	2706.68	−	1562.70i	0.221205	−	0.127713i
$532$	−224.722			−0.0183138
$533$		0			0
$534$	2731.16			0.221327
$535$	2889.11	−	1668.03i	0.233472	−	0.134795i
$536$	−1743.39	−	3019.65i	−0.140491	−	0.243337i
$537$	−4857.59	+	8413.59i	−0.390355	+	0.676114i
$538$		−	10415.5i		−	0.834657i
$539$	−18419.5	−	10634.5i	−1.47196	−	0.849835i
$540$	4393.70	+	2536.70i	0.350138	+	0.202152i
$541$			8987.70i			0.714254i	0.934056	+	0.357127i	$0.116244\pi$
$541$			8987.70i			0.714254i	−0.934056	+	0.357127i	$0.883756\pi$
$542$	−4084.90	+	7075.25i	−0.323730	+	0.560716i
$543$	4196.17	+	7267.99i	0.331630	+	0.574400i
$544$	745.527	−	430.430i	0.0587578	−	0.0339238i
$545$	−11357.9			−0.892697
$546$		0			0
$547$	−10734.8			−0.839101			−0.419550	−	0.907732i	$-0.637812\pi$
$547$	−10734.8			−0.839101			−0.419550	+	0.907732i	$0.637812\pi$
$548$	−6055.02	+	3495.87i	−0.472003	+	0.272511i
$549$	−2583.59	−	4474.90i	−0.200847	−	0.347876i
$550$	3414.12	−	5913.42i	0.264688	−	0.458453i
$551$			4029.11i			0.311517i
$552$	4060.76	+	2344.48i	0.313111	+	0.180775i
$553$	1402.40	+	809.675i	0.107841	+	0.0622620i
$554$		−	875.985i		−	0.0671788i
$555$	−1856.80	+	3216.07i	−0.142012	+	0.245972i
$556$	3353.07	+	5807.69i	0.255759	+	0.442987i
$557$	11456.0	−	6614.13i	0.871466	−	0.503141i	0.00363111	−	0.999993i	$-0.498844\pi$
$557$	11456.0	−	6614.13i	0.871466	−	0.503141i	0.867835	+	0.496852i	$0.165511\pi$
$558$	−1981.66			−0.150341
$559$		0			0
$560$	−573.412			−0.0432698
$561$	−5581.72	+	3222.61i	−0.420072	+	0.242529i
$562$	−5462.34	−	9461.06i	−0.409991	−	0.710126i
$563$	5366.98	−	9295.89i	0.401761	−	0.695870i	−0.592178	−	0.805807i	$-0.701732\pi$
$563$	5366.98	−	9295.89i	0.401761	−	0.695870i	0.993939	+	0.109937i	$0.0350649\pi$
$564$		−	8628.79i		−	0.644216i
$565$	5259.53	+	3036.59i	0.391628	+	0.226107i
$566$	−1379.88	−	796.676i	−0.102475	−	0.0591639i
$567$		−	750.037i		−	0.0555531i
$568$	−263.849	+	457.000i	−0.0194909	+	0.0337593i
$569$	2656.73	+	4601.58i	0.195739	+	0.339031i	0.947143	−	0.320813i	$-0.103956\pi$
$569$	2656.73	+	4601.58i	0.195739	+	0.339031i	−0.751403	+	0.659843i	$0.770623\pi$
$570$	−724.164	+	418.096i	−0.0532138	+	0.0307230i
$571$	−4629.37			−0.339287			−0.169644	−	0.985505i	$-0.554262\pi$
$571$	−4629.37			−0.339287			−0.169644	+	0.985505i	$0.554262\pi$
$572$		0			0
$573$	1239.88			0.0903954
$574$	3149.97	−	1818.64i	0.229055	−	0.132245i
$575$	4176.19	+	7233.37i	0.302886	+	0.524613i
$576$	−434.198	+	752.053i	−0.0314090	+	0.0544020i
$577$			504.750i			0.0364177i	0.999834	+	0.0182088i	$0.00579638\pi$
$577$			504.750i			0.0364177i	−0.999834	+	0.0182088i	$0.994204\pi$
$578$	7256.06	+	4189.29i	0.522167	+	0.301473i
$579$	−8518.84	−	4918.36i	−0.611453	−	0.353022i
$580$			10280.9i			0.736019i
$581$	−533.968	+	924.859i	−0.0381286	+	0.0660407i
$582$	−4815.22	−	8340.21i	−0.342951	−	0.594008i
$583$	−15255.4	+	8807.70i	−1.08373	+	0.625691i
$584$	−7084.14			−0.501958
$585$		0			0
$586$	3394.65			0.239303
$587$	−4791.66	+	2766.47i	−0.336922	+	0.194522i	−0.658910	−	0.752222i	$-0.728982\pi$
$587$	−4791.66	+	2766.47i	−0.336922	+	0.194522i	0.321988	+	0.946744i	$0.395649\pi$
$588$	−2384.74	−	4130.50i	−0.167254	−	0.289692i
$589$	488.268	−	845.705i	0.0341575	−	0.0591624i
$590$			3929.96i			0.274227i
$591$	6021.60	+	3476.57i	0.419113	+	0.241975i
$592$	−1645.88	−	950.247i	−0.114265	−	0.0659711i
$593$		−	18079.8i		−	1.25202i	−0.779816	−	0.626009i	$-0.784687\pi$
$593$		−	18079.8i		−	1.25202i	0.779816	−	0.626009i	$-0.215313\pi$
$594$	9719.54	−	16834.7i	0.671376	−	1.16286i
$595$	482.059	+	834.950i	0.0332143	+	0.0575288i
$596$	3107.16	−	1793.92i	0.213548	−	0.123292i
$597$	−8852.88			−0.606909
$598$		0			0
$599$	−1837.55			−0.125342			−0.0626712	−	0.998034i	$-0.519962\pi$
$599$	−1837.55			−0.125342			−0.0626712	+	0.998034i	$0.519962\pi$
$600$	1326.06	−	765.600i	0.0902268	−	0.0520925i
$601$	11743.6	+	20340.6i	0.797060	+	1.38055i	0.921523	+	0.388324i	$0.126946\pi$
$601$	11743.6	+	20340.6i	0.797060	+	1.38055i	−0.124463	+	0.992224i	$0.539721\pi$
$602$	1497.71	−	2594.10i	0.101399	−	0.175627i
$603$		−	5913.89i		−	0.399390i
$604$	7199.37	+	4156.56i	0.484997	+	0.280013i
$605$	21739.4	+	12551.2i	1.46088	+	0.843438i
$606$			10728.7i			0.719182i
$607$	8155.42	−	14125.6i	0.545335	−	0.944548i	−0.453251	−	0.891383i	$-0.649736\pi$
$607$	8155.42	−	14125.6i	0.545335	−	0.944548i	0.998586	−	0.0531648i	$-0.0169309\pi$
$608$	−213.967	−	370.602i	−0.0142722	−	0.0247202i
$609$	4017.25	−	2319.36i	0.267302	−	0.154327i
$610$	6497.32			0.431260
$611$		0			0
$612$	1460.09			0.0964393
$613$	−7320.61	+	4226.56i	−0.482344	+	0.278481i	−0.721393	−	0.692526i	$-0.756498\pi$
$613$	−7320.61	+	4226.56i	−0.482344	+	0.278481i	0.239049	+	0.971008i	$0.423164\pi$
$614$	9385.86	+	16256.8i	0.616910	+	1.06852i
$615$	6767.18	−	11721.1i	0.443705	−	0.768520i
$616$			2197.06i			0.143705i
$617$	−11613.7	−	6705.17i	−0.757779	−	0.437504i	0.0707186	−	0.997496i	$-0.477471\pi$
$617$	−11613.7	−	6705.17i	−0.757779	−	0.437504i	−0.828498	+	0.559992i	$0.810804\pi$
$618$	−1338.65	−	772.870i	−0.0871334	−	0.0503065i
$619$		−	890.135i		−	0.0577990i	−0.999582	−	0.0288995i	$-0.990800\pi$
$619$		−	890.135i		−	0.0577990i	0.999582	−	0.0288995i	$-0.00920027\pi$
$620$	1245.89	−	2157.95i	0.0807036	−	0.139783i
$621$	11889.1	+	20592.5i	0.768263	+	1.33067i
$622$	5685.72	−	3282.65i	0.366522	−	0.211611i
$623$	−1565.36			−0.100666
$624$		0			0
$625$	−6369.30			−0.407635
$626$	−10261.8	+	5924.67i	−0.655184	+	0.378271i
$627$	1601.96	+	2774.68i	0.102035	+	0.176730i
$628$	−6989.49	+	12106.2i	−0.444126	+	0.769249i
$629$			3195.43i			0.202560i
$630$	−842.259	−	486.278i	−0.0532641	−	0.0307521i
$631$	9164.66	+	5291.22i	0.578192	+	0.333819i	0.760415	−	0.649438i	$-0.224996\pi$
$631$	9164.66	+	5291.22i	0.578192	+	0.333819i	−0.182222	+	0.983257i	$0.558329\pi$
$632$			3083.71i			0.194087i
$633$	4889.71	−	8469.22i	0.307028	−	0.531787i
$634$	−6467.88	−	11202.7i	−0.405161	−	0.701760i
$635$	8656.42	−	4997.78i	0.540975	−	0.312332i
$636$	−3950.17			−0.246281
$637$		0			0
$638$	39391.9			2.44442
$639$	−775.111	+	447.510i	−0.0479858	+	0.0277046i
$640$	−545.971	−	945.649i	−0.0337209	−	0.0584064i
$641$	13442.1	−	23282.4i	0.828286	−	1.43463i	−0.0710952	−	0.997470i	$-0.522649\pi$
$641$	13442.1	−	23282.4i	0.828286	−	1.43463i	0.899382	−	0.437164i	$-0.144017\pi$
$642$		−	2866.38i		−	0.176210i
$643$	4928.66	+	2845.56i	0.302282	+	0.174523i	0.643468	−	0.765473i	$-0.277495\pi$
$643$	4928.66	+	2845.56i	0.302282	+	0.174523i	−0.341186	+	0.939996i	$0.610828\pi$
$644$	−2327.42	−	1343.74i	−0.142412	−	0.0822216i
$645$		−	11146.0i		−	0.680422i
$646$	−359.758	+	623.119i	−0.0219110	+	0.0379509i
$647$	904.896	+	1567.33i	0.0549847	+	0.0952364i	0.892208	−	0.451625i	$-0.149156\pi$
$647$	904.896	+	1567.33i	0.0549847	+	0.0952364i	−0.837223	+	0.546862i	$0.815822\pi$
$648$	1236.93	−	714.143i	0.0749865	−	0.0432935i
$649$	15057.9			0.910745
$650$		0			0
$651$	−1124.29			−0.0676871
$652$	−1563.19	+	902.508i	−0.0938945	+	0.0542100i
$653$	−4729.58	−	8191.88i	−0.283435	−	0.490923i	0.688794	−	0.724957i	$-0.258141\pi$
$653$	−4729.58	−	8191.88i	−0.283435	−	0.490923i	−0.972228	+	0.234034i	$0.924807\pi$
$654$	−4879.42	+	8451.41i	−0.291744	+	0.505315i
$655$		−	9627.94i		−	0.574343i
$656$	5998.46	+	3463.21i	0.357013	+	0.206121i
$657$	−10405.6	−	6007.66i	−0.617899	−	0.356744i
$658$			4945.59i			0.293008i
$659$	−507.660	+	879.293i	−0.0300085	+	0.0519763i	−0.880640	−	0.473787i	$-0.842887\pi$
$659$	−507.660	+	879.293i	−0.0300085	+	0.0519763i	0.850631	+	0.525763i	$0.176220\pi$
$660$	4087.65	+	7080.02i	0.241078	+	0.417560i
$661$	20480.2	−	11824.2i	1.20512	−	0.695778i	0.243433	−	0.969918i	$-0.421727\pi$
$661$	20480.2	−	11824.2i	1.20512	−	0.695778i	0.961690	+	0.274140i	$0.0883932\pi$
$662$	7018.49			0.412056
$663$		0			0
$664$	−2033.66			−0.118857
$665$	415.055	−	239.632i	0.0242032	−	0.0139737i
$666$	−1611.70	−	2791.55i	−0.0937720	−	0.162418i
$667$	−24092.3	+	41729.2i	−1.39859	+	2.42243i
$668$			12813.4i			0.742164i
$669$	−908.863	−	524.732i	−0.0525242	−	0.0303248i
$670$	6439.99	+	3718.13i	0.371341	+	0.214394i
$671$		−	24894.9i		−	1.43228i
$672$	−246.341	+	426.675i	−0.0141411	+	0.0244931i
$673$	8873.48	+	15369.3i	0.508243	+	0.880303i	0.999954	+	0.00954455i	$0.00303817\pi$
$673$	8873.48	+	15369.3i	0.508243	+	0.880303i	−0.491711	+	0.870758i	$0.663628\pi$
$674$	3178.00	−	1834.82i	0.181620	−	0.104858i
$675$	7764.85			0.442769
$676$		0			0
$677$	10754.2			0.610511			0.305256	−	0.952270i	$-0.401258\pi$
$677$	10754.2			0.610511			0.305256	+	0.952270i	$0.401258\pi$
$678$	4519.04	−	2609.07i	0.255977	−	0.147789i
$679$	2759.84	+	4780.19i	0.155984	+	0.270172i
$680$	−917.978	+	1589.99i	−0.0517689	+	0.0896664i
$681$		−	19061.9i		−	1.07262i
$682$	−8268.31	−	4773.71i	−0.464238	−	0.268028i
$683$	20768.8	+	11990.9i	1.16354	+	0.671768i	0.952149	−	0.305635i	$-0.0988687\pi$
$683$	20768.8	+	11990.9i	1.16354	+	0.671768i	0.211387	+	0.977402i	$0.432202\pi$
$684$		−	725.815i		−	0.0405734i
$685$	7455.63	−	12913.5i	0.415862	−	0.720293i
$686$	2807.77	+	4863.21i	0.156270	+	0.270668i
$687$	2826.20	−	1631.71i	0.156953	−	0.0906166i
$688$	5704.13			0.316087
$689$		0			0
$690$	−10000.1			−0.551737
$691$	−25116.0	+	14500.7i	−1.38272	+	0.798312i	−0.992480	−	0.122403i	$-0.960940\pi$
$691$	−25116.0	+	14500.7i	−1.38272	+	0.798312i	−0.390236	+	0.920715i	$0.627607\pi$
$692$	−3798.76	−	6579.65i	−0.208681	−	0.361446i
$693$	−1863.21	+	3227.17i	−0.102132	+	0.176898i
$694$		−	14518.6i		−	0.794119i
$695$	−12386.1	−	7151.09i	−0.676014	−	0.390297i
$696$	7650.00	+	4416.73i	0.416627	+	0.240540i
$697$		−	11645.9i		−	0.632882i
$698$	−1795.24	+	3109.44i	−0.0973505	+	0.168616i
$699$	−8709.78	−	15085.8i	−0.471293	−	0.816304i
$700$	−760.030	+	438.804i	−0.0410378	+	0.0236932i
$701$	31031.5			1.67196			0.835979	−	0.548761i	$-0.184900\pi$
$701$	31031.5			1.67196			0.835979	+	0.548761i	$0.184900\pi$
$702$		0			0
$703$	1588.45			0.0852199
$704$	−3623.31	+	2091.92i	−0.193976	+	0.111992i
$705$	9201.30	+	15937.1i	0.491548	+	0.851386i
$706$	4552.38	−	7884.94i	0.242678	−	0.420331i
$707$		−	6149.16i		−	0.327105i
$708$	2924.27	+	1688.33i	0.155227	+	0.0896206i
$709$	3795.43	+	2191.29i	0.201044	+	0.116073i	0.597143	−	0.802135i	$-0.296303\pi$
$709$	3795.43	+	2191.29i	0.201044	+	0.116073i	−0.396098	+	0.918208i	$0.629636\pi$
$710$		−	1125.42i		−	0.0594877i
$711$	−2615.12	+	4529.52i	−0.137939	+	0.238917i
$712$	−1490.45	−	2581.54i	−0.0784508	−	0.135881i
$713$	10113.9	−	5839.27i	0.531232	−	0.306707i
$714$	828.380			0.0434192
$715$		0			0
$716$	10603.6			0.553455
$717$	7276.49	−	4201.08i	0.379004	−	0.218818i
$718$	10165.4	+	17607.0i	0.528369	+	0.915162i
$719$	−14382.3	+	24910.9i	−0.745994	+	1.29210i	0.203735	+	0.979026i	$0.434692\pi$
$719$	−14382.3	+	24910.9i	−0.745994	+	1.29210i	−0.949729	+	0.313073i	$0.898642\pi$
$720$		−	1852.03i		−	0.0958625i
$721$	767.248	+	442.971i	0.0396308	+	0.0228808i
$722$	−11570.4	−	6680.16i	−0.596406	−	0.344335i
$723$			7238.89i			0.372361i
$724$	4579.88	−	7932.59i	0.235097	−	0.407200i
$725$	7867.46	+	13626.8i	0.403021	+	0.698052i
$726$	18678.7	−	10784.2i	0.954864	−	0.551291i
$727$	−25408.5			−1.29621			−0.648107	−	0.761549i	$-0.724439\pi$
$727$	−25408.5			−1.29621			−0.648107	+	0.761549i	$0.724439\pi$
$728$		0			0
$729$	17134.5			0.870525
$730$	13084.2	−	7554.16i	0.663381	−	0.383003i
$731$	−4795.37	−	8305.82i	−0.242631	−	0.420249i
$732$	2791.28	−	4834.64i	0.140941	−	0.244117i
$733$			22341.8i			1.12580i	0.826524	+	0.562902i	$0.190315\pi$
$733$			22341.8i			1.12580i	−0.826524	+	0.562902i	$0.809685\pi$
$734$	18016.0	+	10401.6i	0.905972	+	0.523063i
$735$	8809.10	+	5085.94i	0.442080	+	0.255235i
$736$		−	5117.73i		−	0.256307i
$737$	14246.3	−	24675.2i	0.712032	−	1.23328i
$738$	5873.91	+	10173.9i	0.292983	+	0.507461i
$739$	−7110.84	+	4105.45i	−0.353960	+	0.204359i	−0.666428	−	0.745569i	$-0.732178\pi$
$739$	−7110.84	+	4105.45i	−0.353960	+	0.204359i	0.312468	+	0.949928i	$0.398844\pi$
$740$	4053.18			0.201349
$741$		0			0
$742$	2264.04			0.112016
$743$	28364.3	−	16376.1i	1.40052	−	0.808590i	0.406073	−	0.913841i	$-0.366898\pi$
$743$	28364.3	−	16376.1i	1.40052	−	0.808590i	0.994446	+	0.105251i	$0.0335646\pi$
$744$	−1070.48	−	1854.13i	−0.0527498	−	0.0913653i
$745$	−3825.90	+	6626.65i	−0.188148	+	0.325881i
$746$		−	15906.8i		−	0.780684i
$747$	−2987.14	−	1724.63i	−0.146310	−	0.0844724i
$748$	6092.13	+	3517.29i	0.297794	+	0.171932i
$749$			1642.87i			0.0801455i
$750$	−5540.83	+	9597.00i	−0.269763	+	0.467244i
$751$	4453.70	+	7714.04i	0.216402	+	0.374819i	0.953705	−	0.300742i	$-0.0972344\pi$
$751$	4453.70	+	7714.04i	0.216402	+	0.374819i	−0.737303	+	0.675562i	$0.763901\pi$
$752$	−8156.08	+	4708.91i	−0.395507	+	0.228346i
$753$	−27361.0			−1.32416
$754$		0			0
$755$	−17729.4			−0.854620
$756$	−2163.71	+	1249.22i	−0.104092	+	0.0600973i
$757$	5372.32	+	9305.13i	0.257940	+	0.446765i	0.965690	−	0.259698i	$-0.0836231\pi$
$757$	5372.32	+	9305.13i	0.257940	+	0.446765i	−0.707750	+	0.706463i	$0.750290\pi$
$758$	−9014.81	+	15614.1i	−0.431969	+	0.748193i
$759$			38316.2i			1.83240i
$760$	790.383	+	456.328i	0.0377240	+	0.0217799i
$761$	14720.5	+	8498.89i	0.701206	+	0.404841i	0.807796	−	0.589462i	$-0.200660\pi$
$761$	14720.5	+	8498.89i	0.701206	+	0.404841i	−0.106590	+	0.994303i	$0.533993\pi$
$762$		−	8588.30i		−	0.408296i
$763$	2796.64	−	4843.93i	0.132694	−	0.229832i
$764$	−676.627	−	1171.95i	−0.0320412	−	0.0554970i
$765$	−2696.75	+	1556.97i	−0.127453	+	0.0735849i
$766$	−4992.48			−0.235490
$767$		0			0
$768$	−938.208			−0.0440816
$769$	−16482.6	+	9516.21i	−0.772921	+	0.446246i	−0.833916	−	0.551892i	$-0.813906\pi$
$769$	−16482.6	+	9516.21i	−0.772921	+	0.446246i	0.0609948	+	0.998138i	$0.480573\pi$
$770$	−2342.84	−	4057.92i	−0.109649	−	0.189918i
$771$	1016.94	−	1761.39i	0.0475022	−	0.0822763i
$772$			10736.2i			0.500524i
$773$	20568.6	+	11875.3i	0.957053	+	0.552555i	0.895265	−	0.445535i	$-0.146986\pi$
$773$	20568.6	+	11875.3i	0.957053	+	0.552555i	0.0617879	+	0.998089i	$0.480320\pi$
$774$	8378.53	+	4837.35i	0.389096	+	0.224644i
$775$		−	3813.68i		−	0.176763i
$776$	−5255.54	+	9102.86i	−0.243122	+	0.421100i
$777$	−914.393	−	1583.78i	−0.0422184	−	0.0731244i
$778$	−18873.9	+	10896.9i	−0.869746	+	0.502148i
$779$	−5789.17			−0.266263
$780$		0			0
$781$	−4312.12			−0.197567
$782$	−7451.97	+	4302.40i	−0.340770	+	0.196743i
$783$	22397.6	+	38793.8i	1.02225	+	1.77060i
$784$	−2602.81	+	4508.20i	−0.118568	+	0.205366i
$785$		−	29813.0i		−	1.35550i
$786$	−7164.13	−	4136.21i	−0.325109	−	0.187702i
$787$	−15437.7	−	8912.97i	−0.699232	−	0.403702i	0.107829	−	0.994169i	$-0.465610\pi$
$787$	−15437.7	−	8912.97i	−0.699232	−	0.403702i	−0.807061	+	0.590468i	$0.798943\pi$
$788$		−	7588.96i		−	0.343078i
$789$	−3652.17	+	6325.75i	−0.164792	+	0.285428i
$790$	−3288.31	−	5695.52i	−0.148092	−	0.256503i
$791$	−2590.09	+	1495.39i	−0.116426	+	0.0672186i
$792$	−7096.16			−0.318373
$793$		0			0
$794$	−21774.3			−0.973225
$795$	7295.86	−	4212.27i	0.325481	−	0.187917i
$796$	4831.21	+	8367.90i	0.215123	+	0.372603i
$797$	−13230.6	+	22916.1i	−0.588020	+	1.01848i	0.406471	+	0.913663i	$0.366759\pi$
$797$	−13230.6	+	22916.1i	−0.588020	+	1.01848i	−0.994492	+	0.104817i	$0.966574\pi$
$798$		−	411.788i		−	0.0182671i
$799$	13713.4	+	7917.42i	0.607190	+	0.350561i
$800$	−1447.32	−	835.609i	−0.0639630	−	0.0369290i
$801$		−	5055.87i		−	0.223021i
$802$	9968.76	−	17266.4i	0.438914	−	0.760221i
$803$	−28944.3	−	50132.9i	−1.27201	−	2.20318i
$804$	5533.31	−	3194.66i	0.242717	−	0.140133i
$805$	5731.58			0.250946
$806$		0			0
$807$	19085.8			0.832530
$808$	10141.0	−	5854.89i	0.441532	−	0.254919i
$809$	−10936.7	−	18942.9i	−0.475294	−	0.823234i	0.524305	−	0.851530i	$-0.324325\pi$
$809$	−10936.7	−	18942.9i	−0.475294	−	0.823234i	−0.999600	+	0.0282967i	$0.990992\pi$
$810$	−1523.05	+	2638.00i	−0.0660674	+	0.114432i
$811$		−	39113.8i		−	1.69355i	−0.531949	−	0.846776i	$-0.678540\pi$
$811$		−	39113.8i		−	1.69355i	0.531949	−	0.846776i	$-0.321460\pi$
$812$	−4384.60	−	2531.45i	−0.189494	−	0.109404i
$813$	−12965.0	−	7485.32i	−0.559288	−	0.322905i
$814$		−	15530.0i		−	0.668706i
$815$	1924.78	−	3333.81i	0.0827264	−	0.143286i
$816$	788.737	+	1366.13i	0.0338374	+	0.0586081i
$817$	−4128.83	+	2383.78i	−0.176805	+	0.102078i
$818$	8072.65			0.345053
$819$		0			0
$820$	−14772.0			−0.629097
$821$	22773.7	−	13148.4i	0.968097	−	0.558931i	0.0694411	−	0.997586i	$-0.477878\pi$
$821$	22773.7	−	13148.4i	0.968097	−	0.558931i	0.898655	+	0.438655i	$0.144545\pi$
$822$	−6405.96	−	11095.4i	−0.271817	−	0.470801i
$823$	12340.5	−	21374.4i	0.522678	−	0.905306i	−0.476973	−	0.878918i	$-0.658266\pi$
$823$	12340.5	−	21374.4i	0.522678	−	0.905306i	0.999652	−	0.0263878i	$-0.00840047\pi$
$824$			1687.09i			0.0713258i
$825$	10836.0	+	6256.15i	0.457285	+	0.264014i
$826$	−1676.05	−	967.667i	−0.0706019	−	0.0407620i
$827$		−	3081.68i		−	0.129578i	−0.997899	−	0.0647888i	$-0.979363\pi$
$827$		−	3081.68i		−	0.129578i	0.997899	−	0.0647888i	$-0.0206374\pi$
$828$	4340.06	−	7517.20i	0.182159	−	0.315508i
$829$	−4249.27	−	7359.95i	−0.178026	−	0.308349i	0.763179	−	0.646188i	$-0.223638\pi$
$829$	−4249.27	−	7359.95i	−0.178026	−	0.308349i	−0.941204	+	0.337838i	$0.890304\pi$
$830$	3756.10	−	2168.59i	0.157080	−	0.0906901i
$831$	1605.19			0.0670076
$832$		0			0
$833$	8752.57			0.364056
$834$	−10642.2	+	6144.29i	−0.441859	+	0.255107i
$835$	−13663.6	−	23666.0i	−0.566284	−	0.980833i
$836$	1748.45	−	3028.40i	0.0723342	−	0.125286i
$837$		−	10857.0i		−	0.448356i
$838$	−26318.3	−	15194.9i	−1.08490	−	0.626370i
$839$	−16177.5	−	9340.06i	−0.665683	−	0.384332i	0.128756	−	0.991676i	$-0.458902\pi$
$839$	−16177.5	−	9340.06i	−0.665683	−	0.384332i	−0.794439	+	0.607344i	$0.792235\pi$
$840$		−	1050.74i		−	0.0431596i
$841$	−33192.7	+	57491.4i	−1.36097	+	2.35727i
$842$	−10154.8	−	17588.5i	−0.415625	−	0.719883i
$843$	17336.8	−	10009.4i	0.708317	−	0.408947i
$844$	−10673.7			−0.435312
$845$		0			0
$846$	−15973.5			−0.649147
$847$	−10705.7	+	6180.94i	−0.434300	+	0.250743i
$848$	2155.69	+	3733.77i	0.0872958	+	0.151201i
$849$	1459.86	−	2528.55i	0.0590132	−	0.102214i
$850$			2809.93i			0.113388i
$851$	16451.5	+	9498.26i	0.662690	+	0.382604i
$852$	−837.423	−	483.486i	−0.0336733	−	0.0194413i
$853$			24129.9i			0.968574i	0.874909	+	0.484287i	$0.160921\pi$
$853$			24129.9i			0.968574i	−0.874909	+	0.484287i	$0.839079\pi$
$854$	−1599.82	+	2770.98i	−0.0641040	+	0.111031i
$855$	773.972	+	1340.56i	0.0309582	+	0.0536212i
$856$	−2709.35	+	1564.24i	−0.108182	+	0.0624588i
$857$	7739.30			0.308482			0.154241	−	0.988033i	$-0.450707\pi$
$857$	7739.30			0.308482			0.154241	+	0.988033i	$0.450707\pi$
$858$		0			0
$859$	4302.59			0.170899			0.0854496	−	0.996342i	$-0.472767\pi$
$859$	4302.59			0.170899			0.0854496	+	0.996342i	$0.472767\pi$
$860$	−10535.4	+	6082.59i	−0.417736	+	0.241180i
$861$	3332.54	+	5772.13i	0.131908	+	0.228471i
$862$	6616.84	−	11460.7i	0.261451	−	0.452846i
$863$			16253.2i			0.641096i	0.947232	+	0.320548i	$0.103867\pi$
$863$			16253.2i			0.641096i	−0.947232	+	0.320548i	$0.896133\pi$
$864$	−4120.32	−	2378.87i	−0.162241	−	0.0936698i
$865$	14032.4	+	8101.62i	0.551580	+	0.318455i
$866$		−	11395.2i		−	0.447142i
$867$	−7676.61	+	13296.3i	−0.300705	+	0.520836i
$868$	613.548	+	1062.70i	0.0239921	+	0.0415556i
$869$	−21822.7	+	12599.4i	−0.851882	+	0.491834i
$870$	−18839.1			−0.734144
$871$		0			0
$872$	10651.2			0.413642
$873$	−15439.2	+	8913.85i	−0.598556	+	0.345576i
$874$	2138.73	+	3704.38i	0.0827728	+	0.143367i
$875$	3175.73	−	5500.52i	0.122696	−	0.212516i
$876$		−	12981.2i		−	0.500680i
$877$	−8176.43	−	4720.67i	−0.314822	−	0.181762i	0.334260	−	0.942481i	$-0.391513\pi$
$877$	−8176.43	−	4720.67i	−0.314822	−	0.181762i	−0.649082	+	0.760718i	$0.724847\pi$
$878$	755.186	+	436.007i	0.0290277	+	0.0167591i
$879$			6220.48i			0.238693i
$880$	4461.44	−	7727.44i	0.170903	−	0.296014i
$881$	−5936.22	−	10281.8i	−0.227011	−	0.393194i	0.729910	−	0.683543i	$-0.239562\pi$
$881$	−5936.22	−	10281.8i	−0.227011	−	0.393194i	−0.956921	+	0.290349i	$0.906229\pi$
$882$	−7646.30	+	4414.59i	−0.291910	+	0.168534i
$883$	493.891			0.0188231			0.00941153	−	0.999956i	$-0.497004\pi$
$883$	493.891			0.0188231			0.00941153	+	0.999956i	$0.497004\pi$
$884$		0			0
$885$	−7201.40			−0.273528
$886$	11448.1	−	6609.58i	0.434094	−	0.250624i
$887$	−10271.8	−	17791.3i	−0.388832	−	0.673477i	0.603461	−	0.797393i	$-0.293788\pi$
$887$	−10271.8	−	17791.3i	−0.388832	−	0.673477i	−0.992293	+	0.123916i	$0.960455\pi$
$888$	1741.27	−	3015.96i	0.0658031	−	0.113974i
$889$			4922.38i			0.185705i
$890$	5505.64	+	3178.68i	0.207359	+	0.119719i
$891$	10107.7	+	5835.67i	0.380045	+	0.219419i
$892$			1145.43i			0.0429953i
$893$	3935.76	−	6816.93i	0.147486	−	0.255453i
$894$	3287.25	+	5693.68i	0.122978	+	0.213004i
$895$	−19584.5	+	11307.1i	−0.731438	+	0.422296i
$896$	537.734			0.0200496
$897$		0			0
$898$	−16030.6			−0.595711
$899$	19053.4	−	11000.5i	0.706860	−	0.408106i
$900$	−1417.26	−	2454.77i	−0.0524913	−	0.0909176i
$901$	3624.52	−	6277.85i	0.134018	−	0.232126i
$902$			56599.7i			2.08932i
$903$	4753.53	+	2744.45i	0.175180	+	0.101140i
$904$	−4932.27	−	2847.65i	−0.181466	−	0.104769i
$905$			19535.0i			0.717532i
$906$	−7616.64	+	13192.4i	−0.279300	+	0.483762i
$907$	−2693.30	−	4664.94i	−0.0985994	−	0.170779i	0.812506	−	0.582953i	$-0.198103\pi$
$907$	−2693.30	−	4664.94i	−0.0985994	−	0.170779i	−0.911105	+	0.412174i	$0.864770\pi$
$908$	−18017.6	+	10402.5i	−0.658520	+	0.380196i
$909$	19860.8			0.724688
$910$		0			0
$911$	31793.5			1.15627			0.578137	−	0.815940i	$-0.303780\pi$
$911$	31793.5			1.15627			0.578137	+	0.815940i	$0.303780\pi$
$912$	679.106	−	392.082i	0.0246573	−	0.0142359i
$913$	−8309.08	−	14391.8i	−0.301194	−	0.521684i
$914$	4507.03	−	7806.41i	0.163107	−	0.282509i
$915$			11905.9i			0.430162i
$916$	−3084.64	−	1780.92i	−0.111266	−	0.0642392i
$917$	4106.12	+	2370.67i	0.147869	+	0.0853723i
$918$			7999.51i			0.287607i
$919$	21495.7	−	37231.6i	0.771575	−	1.33641i	−0.165125	−	0.986273i	$-0.552803\pi$
$919$	21495.7	−	37231.6i	0.771575	−	1.33641i	0.936700	−	0.350134i	$-0.113864\pi$
$920$	5457.29	+	9452.30i	0.195567	+	0.338732i
$921$	−29789.5	+	17199.0i	−1.06580	+	0.615338i
$922$	4207.10			0.150275
$923$		0			0
$924$	−4025.98			−0.143339
$925$	5372.30	−	3101.70i	0.190962	−	0.110252i
$926$	5468.28	+	9471.34i	0.194059	+	0.336121i
$927$	−1430.72	+	2478.09i	−0.0506916	+	0.0878004i
$928$		−	9641.21i		−	0.341043i
$929$	−35227.0	−	20338.3i	−1.24409	−	0.718277i	−0.274168	−	0.961682i	$-0.588402\pi$
$929$	−35227.0	−	20338.3i	−1.24409	−	0.718277i	−0.969925	+	0.243405i	$0.921736\pi$
$930$	3954.30	+	2283.02i	0.139427	+	0.0804980i
$931$		−	4350.91i		−	0.153164i
$932$	−9506.22	+	16465.3i	−0.334106	+	0.578688i
$933$	6015.25	+	10418.7i	0.211072	+	0.365588i
$934$	10468.2	−	6043.79i	0.366733	−	0.211733i
$935$	−15002.6			−0.524748
$936$		0			0
$937$	21008.3			0.732456			0.366228	−	0.930525i	$-0.380649\pi$
$937$	21008.3			0.732456			0.366228	+	0.930525i	$0.380649\pi$
$938$	−3171.42	+	1831.02i	−0.110395	+	0.0637365i
$939$	−10856.6	−	18804.2i	−0.377307	−	0.653515i
$940$	10042.7	−	17394.5i	0.348465	−	0.603558i
$941$		−	4525.50i		−	0.156777i	−0.996923	−	0.0783885i	$-0.975023\pi$
$941$		−	4525.50i		−	0.156777i	0.996923	−	0.0783885i	$-0.0249775\pi$
$942$	−22183.8	−	12807.8i	−0.767289	−	0.442994i
$943$	−59958.0	−	34616.7i	−2.07052	−	1.19542i
$944$		−	3685.43i		−	0.127066i
$945$	2664.20	−	4614.53i	0.0917106	−	0.158847i
$946$	23305.8	+	40366.9i	0.800991	+	1.38736i
$947$	23730.5	−	13700.8i	0.814295	−	0.470134i	−0.0341499	−	0.999417i	$-0.510872\pi$
$947$	23730.5	−	13700.8i	0.814295	−	0.470134i	0.848445	+	0.529283i	$0.177539\pi$
$948$	−5650.70			−0.193593
$949$		0			0
$950$	1396.82			0.0477040
$951$	20528.2	−	11852.0i	0.699973	−	0.404129i
$952$	−452.065	−	782.999i	−0.0153902	−	0.0266567i
$953$	13113.1	−	22712.6i	0.445725	−	0.772017i	−0.552378	−	0.833594i	$-0.686279\pi$
$953$	13113.1	−	22712.6i	0.445725	−	0.772017i	0.998102	+	0.0615763i	$0.0196128\pi$
$954$			7312.49i			0.248166i
$955$	2499.42	+	1443.04i	0.0846904	+	0.0488960i
$956$	−7941.87	−	4585.24i	−0.268680	−	0.155123i
$957$			72183.2i			2.43819i
$958$	−8481.30	+	14690.0i	−0.286032	+	0.495421i
$959$	3671.58	+	6359.36i	0.123630	+	0.214134i
$960$	1732.84	−	1000.46i	0.0582576	−	0.0336350i
$961$	24458.6			0.821007
$962$		0			0
$963$	−5306.19			−0.177559
$964$	6842.32	−	3950.42i	0.228606	−	0.131986i
$965$	−11448.5	−	19829.5i	−0.381909	−	0.661485i
$966$	2462.32	−	4264.86i	0.0820122	−	0.142049i
$967$			20843.6i			0.693158i	0.938021	+	0.346579i	$0.112657\pi$
$967$			20843.6i			0.693158i	−0.938021	+	0.346579i	$0.887343\pi$
$968$	−20386.7	−	11770.3i	−0.676916	−	0.390817i
$969$	−1141.83	−	659.234i	−0.0378542	−	0.0218552i
$970$		−	22417.0i		−	0.742026i
$971$	−16288.6	+	28212.7i	−0.538339	+	0.932430i	0.460655	+	0.887579i	$0.347615\pi$
$971$	−16288.6	+	28212.7i	−0.538339	+	0.932430i	−0.998994	+	0.0448508i	$0.985719\pi$
$972$	−6720.05	−	11639.5i	−0.221755	−	0.384091i
$973$	6099.59	−	3521.60i	0.200970	−	0.116030i
$974$	−13246.7			−0.435782
$975$		0			0
$976$	−6093.05			−0.199830
$977$	−37987.4	+	21932.0i	−1.24394	+	0.718186i	−0.969893	−	0.243531i	$-0.921694\pi$
$977$	−37987.4	+	21932.0i	−1.24394	+	0.718186i	−0.274042	+	0.961718i	$0.588361\pi$
$978$	−1653.79	−	2864.45i	−0.0540719	−	0.0936553i
$979$	12179.3	−	21095.2i	0.397602	−	0.688667i
$980$		−	11102.0i		−	0.361879i
$981$	15645.1	+	9032.70i	0.509184	+	0.293977i
$982$	28369.9	+	16379.4i	0.921914	+	0.532267i
$983$			14758.8i			0.478875i	0.970912	+	0.239437i	$0.0769630\pi$
$983$			14758.8i			0.478875i	−0.970912	+	0.239437i	$0.923037\pi$
$984$	−6346.12	+	10991.8i	−0.205596	+	0.356103i
$985$	8092.48	+	14016.6i	0.261775	+	0.453407i
$986$	−14038.6	+	8105.21i	−0.453430	+	0.261788i
$987$	−9062.49			−0.292262
$988$		0			0
$989$	−57016.0			−1.83317
$990$	13106.4	−	7566.99i	0.420757	−	0.242924i
$991$	−24311.2	−	42108.2i	−0.779284	−	1.34976i	−0.932355	−	0.361544i	$-0.882250\pi$
$991$	−24311.2	−	42108.2i	−0.779284	−	1.34976i	0.153071	−	0.988215i	$-0.451084\pi$
$992$	−1168.37	+	2023.68i	−0.0373950	+	0.0647700i
$993$			12860.9i			0.411006i
$994$	479.969	+	277.110i	0.0153156	+	0.00884246i
$995$	−17846.2	−	10303.5i	−0.568606	−	0.328285i
$996$		−	3726.55i		−	0.118554i
$997$	9406.17	−	16292.0i	0.298793	−	0.517525i	−0.677067	−	0.735921i	$-0.736749\pi$
$997$	9406.17	−	16292.0i	0.298793	−	0.517525i	0.975860	+	0.218397i	$0.0700827\pi$
$998$	7915.70	+	13710.4i	0.251069	+	0.434865i
$999$	15294.2	−	8830.12i	0.484372	−	0.279652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.h.23.5		12
13.2	odd	12		338.4.a.k.1.2	yes	3
13.3	even	3		338.4.b.f.337.5		6
13.4	even	6	inner	338.4.e.h.147.5		12
13.5	odd	4		338.4.c.k.315.2		6
13.6	odd	12		338.4.c.k.191.2		6
13.7	odd	12		338.4.c.l.191.2		6
13.8	odd	4		338.4.c.l.315.2		6
13.9	even	3	inner	338.4.e.h.147.2		12
13.10	even	6		338.4.b.f.337.2		6
13.11	odd	12		338.4.a.j.1.2	✓	3
13.12	even	2	inner	338.4.e.h.23.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.j.1.2	✓	3	13.11	odd	12
338.4.a.k.1.2	yes	3	13.2	odd	12
338.4.b.f.337.2		6	13.10	even	6
338.4.b.f.337.5		6	13.3	even	3
338.4.c.k.191.2		6	13.6	odd	12
338.4.c.k.315.2		6	13.5	odd	4
338.4.c.l.191.2		6	13.7	odd	12
338.4.c.l.315.2		6	13.8	odd	4
338.4.e.h.23.2		12	13.12	even	2	inner
338.4.e.h.23.5		12	1.1	even	1	trivial
338.4.e.h.147.2		12	13.9	even	3	inner
338.4.e.h.147.5		12	13.4	even	6	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(1.83244 + 3.17387i) q^{3} +(2.00000 - 3.46410i) q^{4} +8.53079i q^{5} +(6.34775 + 3.66487i) q^{6} +(-3.63821 - 2.10052i) q^{7} -8.00000i q^{8} +(6.78435 - 11.7508i) q^{9} +(8.53079 + 14.7758i) q^{10} +(56.6143 - 32.6863i) q^{11} +14.6595 q^{12} -8.40209 q^{14} +(-27.0757 + 15.6321i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-13.4510 + 23.2977i) q^{17} -27.1374i q^{18} +(11.5813 + 6.68648i) q^{19} +(29.5515 + 17.0616i) q^{20} -15.3963i q^{21} +(65.3726 - 113.229i) q^{22} +(79.9645 + 138.503i) q^{23} +(25.3910 - 14.6595i) q^{24} +52.2255 q^{25} +148.679 q^{27} +(-14.5529 + 8.40209i) q^{28} +(150.644 + 260.923i) q^{29} +(-31.2643 + 54.1513i) q^{30} -73.0232i q^{31} +(-27.7128 - 16.0000i) q^{32} +(207.484 + 119.791i) q^{33} +53.8038i q^{34} +(17.9191 - 31.0368i) q^{35} +(-27.1374 - 47.0033i) q^{36} +(102.867 - 59.3904i) q^{37} +26.7459 q^{38} +68.2464 q^{40} +(-374.903 + 216.451i) q^{41} +(-15.3963 - 26.6672i) q^{42} +(-178.254 + 308.745i) q^{43} -261.490i q^{44} +(100.244 + 57.8759i) q^{45} +(277.005 + 159.929i) q^{46} -588.614i q^{47} +(29.3190 - 50.7820i) q^{48} +(-162.676 - 281.762i) q^{49} +(90.4573 - 52.2255i) q^{50} -98.5921 q^{51} -269.462 q^{53} +(257.520 - 148.679i) q^{54} +(278.840 + 482.965i) q^{55} +(-16.8042 + 29.1057i) q^{56} +49.0102i q^{57} +(521.846 + 301.288i) q^{58} +(199.480 + 115.170i) q^{59} +125.057i q^{60} +(190.408 - 329.796i) q^{61} +(-73.0232 - 126.480i) q^{62} +(-49.3658 + 28.5014i) q^{63} -64.0000 q^{64} +479.164 q^{66} +(377.456 - 217.924i) q^{67} +(53.8038 + 93.1909i) q^{68} +(-293.060 + 507.595i) q^{69} -71.6765i q^{70} +(-57.1249 - 32.9811i) q^{71} +(-94.0067 - 54.2748i) q^{72} -885.517i q^{73} +(118.781 - 205.735i) q^{74} +(95.7000 + 165.757i) q^{75} +(46.3253 - 26.7459i) q^{76} -274.633 q^{77} -385.463 q^{79} +(118.206 - 68.2464i) q^{80} +(89.2679 + 154.616i) q^{81} +(-432.901 + 749.807i) q^{82} -254.207i q^{83} +(-53.3344 - 30.7926i) q^{84} +(-198.748 - 114.747i) q^{85} +713.016i q^{86} +(-552.091 + 956.250i) q^{87} +(-261.490 - 452.914i) q^{88} +(322.692 - 186.306i) q^{89} +231.504 q^{90} +639.716 q^{92} +(231.766 - 133.810i) q^{93} +(-588.614 - 1019.51i) q^{94} +(-57.0410 + 98.7979i) q^{95} -117.276i q^{96} +(-1137.86 - 656.942i) q^{97} +(-563.525 - 325.351i) q^{98} -887.020i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) \) 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Introduction

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