LMFDB - Embedded newform 338.4.c.k.191.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(191,338)]

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([4]))

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

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

chi := DirichletCharacter("338.191");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.2
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	338.191
Dual form			338.4.c.k.315.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(1.83244 - 3.17387i) q^{3} +(-2.00000 - 3.46410i) q^{4} +8.53079 q^{5} +(3.66487 + 6.34775i) q^{6} +(2.10052 + 3.63821i) q^{7} +8.00000 q^{8} +(6.78435 + 11.7508i) q^{9} +(-8.53079 + 14.7758i) q^{10} +(32.6863 - 56.6143i) q^{11} -14.6595 q^{12} -8.40209 q^{14} +(15.6321 - 27.0757i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(13.4510 + 23.2977i) q^{17} -27.1374 q^{18} +(6.68648 + 11.5813i) q^{19} +(-17.0616 - 29.5515i) q^{20} +15.3963 q^{21} +(65.3726 + 113.229i) q^{22} +(-79.9645 + 138.503i) q^{23} +(14.6595 - 25.3910i) q^{24} -52.2255 q^{25} +148.679 q^{27} +(8.40209 - 14.5529i) q^{28} +(150.644 - 260.923i) q^{29} +(31.2643 + 54.1513i) q^{30} -73.0232 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-119.791 - 207.484i) q^{33} -53.8038 q^{34} +(17.9191 + 31.0368i) q^{35} +(27.1374 - 47.0033i) q^{36} +(59.3904 - 102.867i) q^{37} -26.7459 q^{38} +68.2464 q^{40} +(216.451 - 374.903i) q^{41} +(-15.3963 + 26.6672i) q^{42} +(178.254 + 308.745i) q^{43} -261.490 q^{44} +(57.8759 + 100.244i) q^{45} +(-159.929 - 277.005i) q^{46} +588.614 q^{47} +(29.3190 + 50.7820i) q^{48} +(162.676 - 281.762i) q^{49} +(52.2255 - 90.4573i) q^{50} +98.5921 q^{51} -269.462 q^{53} +(-148.679 + 257.520i) q^{54} +(278.840 - 482.965i) q^{55} +(16.8042 + 29.1057i) q^{56} +49.0102 q^{57} +(301.288 + 521.846i) q^{58} +(-115.170 - 199.480i) q^{59} -125.057 q^{60} +(190.408 + 329.796i) q^{61} +(73.0232 - 126.480i) q^{62} +(-28.5014 + 49.3658i) q^{63} +64.0000 q^{64} +479.164 q^{66} +(-217.924 + 377.456i) q^{67} +(53.8038 - 93.1909i) q^{68} +(293.060 + 507.595i) q^{69} -71.6765 q^{70} +(-32.9811 - 57.1249i) q^{71} +(54.2748 + 94.0067i) q^{72} +885.517 q^{73} +(118.781 + 205.735i) q^{74} +(-95.7000 + 165.757i) q^{75} +(26.7459 - 46.3253i) q^{76} +274.633 q^{77} -385.463 q^{79} +(-68.2464 + 118.206i) q^{80} +(89.2679 - 154.616i) q^{81} +(432.901 + 749.807i) q^{82} -254.207 q^{83} +(-30.7926 - 53.3344i) q^{84} +(114.747 + 198.748i) q^{85} -713.016 q^{86} +(-552.091 - 956.250i) q^{87} +(261.490 - 452.914i) q^{88} +(186.306 - 322.692i) q^{89} -231.504 q^{90} +639.716 q^{92} +(-133.810 + 231.766i) q^{93} +(-588.614 + 1019.51i) q^{94} +(57.0410 + 98.7979i) q^{95} -117.276 q^{96} +(-656.942 - 1137.86i) q^{97} +(325.351 + 563.525i) q^{98} +887.020 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 12 q^{3} - 12 q^{4} - 24 q^{5} + 24 q^{6} - 27 q^{7} + 48 q^{8} - 9 q^{9} + 24 q^{10} + 82 q^{11} - 96 q^{12} + 108 q^{14} - 90 q^{15} - 48 q^{16} + 90 q^{17} + 36 q^{18} + 130 q^{19} + 48 q^{20}+ \cdots + 4114 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 + 12 * q^3 - 12 * q^4 - 24 * q^5 + 24 * q^6 - 27 * q^7 + 48 * q^8 - 9 * q^9 + 24 * q^10 + 82 * q^11 - 96 * q^12 + 108 * q^14 - 90 * q^15 - 48 * q^16 + 90 * q^17 + 36 * q^18 + 130 * q^19 + 48 * q^20 - 468 * q^21 + 164 * q^22 - 19 * q^23 + 96 * q^24 - 122 * q^25 - 138 * q^27 - 108 * q^28 + 101 * q^29 - 180 * q^30 - 1038 * q^31 - 96 * q^32 - 146 * q^33 - 360 * q^34 + 458 * q^35 - 36 * q^36 + 84 * q^37 - 520 * q^38 - 192 * q^40 + 187 * q^41 + 468 * q^42 + 1205 * q^43 - 656 * q^44 + 645 * q^45 - 38 * q^46 + 1072 * q^47 + 192 * q^48 + 184 * q^49 + 122 * q^50 - 414 * q^51 - 2190 * q^53 + 138 * q^54 + 526 * q^55 - 216 * q^56 + 2818 * q^57 + 202 * q^58 - 1413 * q^59 + 720 * q^60 + 1108 * q^61 + 1038 * q^62 - 1404 * q^63 + 384 * q^64 + 584 * q^66 - 1605 * q^67 + 360 * q^68 + 314 * q^69 - 1832 * q^70 - 909 * q^71 - 72 * q^72 - 574 * q^73 + 168 * q^74 + 505 * q^75 + 520 * q^76 + 960 * q^77 - 3922 * q^79 + 192 * q^80 - 915 * q^81 + 374 * q^82 - 382 * q^83 + 936 * q^84 + 67 * q^85 - 4820 * q^86 - 1636 * q^87 + 656 * q^88 + 1091 * q^89 - 2580 * q^90 + 152 * q^92 - 1614 * q^93 - 1072 * q^94 - 1829 * q^95 - 768 * q^96 - 947 * q^97 + 368 * q^98 + 4114 * q^99

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$2$	−1.00000	+	1.73205i	−0.353553	+	0.612372i
$3$	1.83244	−	3.17387i	0.352653	−	0.610812i	−0.634061	−	0.773283i	$-0.718613\pi$
$3$	1.83244	−	3.17387i	0.352653	−	0.610812i	0.986713	+	0.162471i	$0.0519464\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	8.53079			0.763017			0.381509	−	0.924365i	$-0.375405\pi$
$5$	8.53079			0.763017			0.381509	+	0.924365i	$0.375405\pi$
$6$	3.66487	+	6.34775i	0.249363	+	0.431910i
$7$	2.10052	+	3.63821i	0.113418	+	0.196445i	0.917146	−	0.398551i	$-0.130487\pi$
$7$	2.10052	+	3.63821i	0.113418	+	0.196445i	−0.803729	+	0.594996i	$0.797154\pi$
$8$	8.00000			0.353553
$9$	6.78435	+	11.7508i	0.251272	+	0.435216i
$10$	−8.53079	+	14.7758i	−0.269767	+	0.467251i
$11$	32.6863	−	56.6143i	0.895935	−	1.55180i	0.0632915	−	0.997995i	$-0.479840\pi$
$11$	32.6863	−	56.6143i	0.895935	−	1.55180i	0.832643	−	0.553810i	$-0.186826\pi$
$12$	−14.6595			−0.352653
$13$		0			0
$13$		0			0
$14$	−8.40209			−0.160397
$15$	15.6321	−	27.0757i	0.269080	−	0.466061i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	13.4510	+	23.2977i	0.191902	+	0.332384i	0.945881	−	0.324515i	$-0.105201\pi$
$17$	13.4510	+	23.2977i	0.191902	+	0.332384i	−0.753979	+	0.656899i	$0.771868\pi$
$18$	−27.1374			−0.355352
$19$	6.68648	+	11.5813i	0.0807360	+	0.139839i	0.903566	−	0.428448i	$-0.140940\pi$
$19$	6.68648	+	11.5813i	0.0807360	+	0.139839i	−0.822830	+	0.568287i	$0.807606\pi$
$20$	−17.0616	−	29.5515i	−0.190754	−	0.330396i
$21$	15.3963			0.159988
$22$	65.3726	+	113.229i	0.633522	+	1.09729i
$23$	−79.9645	+	138.503i	−0.724946	+	1.25564i	0.234050	+	0.972225i	$0.424802\pi$
$23$	−79.9645	+	138.503i	−0.724946	+	1.25564i	−0.958996	+	0.283419i	$0.908531\pi$
$24$	14.6595	−	25.3910i	0.124682	−	0.215955i
$25$	−52.2255			−0.417804
$26$		0			0
$27$	148.679			1.05975
$28$	8.40209	−	14.5529i	0.0567088	−	0.0982225i
$29$	150.644	−	260.923i	0.964616	−	1.67076i	0.253973	−	0.967211i	$-0.418262\pi$
$29$	150.644	−	260.923i	0.964616	−	1.67076i	0.710643	−	0.703553i	$-0.248404\pi$
$30$	31.2643	+	54.1513i	0.190268	+	0.329555i
$31$	−73.0232			−0.423076			−0.211538	−	0.977370i	$-0.567847\pi$
$31$	−73.0232			−0.423076			−0.211538	+	0.977370i	$0.567847\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−119.791	−	207.484i	−0.631908	−	1.09450i
$34$	−53.8038			−0.271390
$35$	17.9191	+	31.0368i	0.0865396	+	0.149891i
$36$	27.1374	−	47.0033i	0.125636	−	0.217608i
$37$	59.3904	−	102.867i	0.263885	−	0.457061i	−0.703386	−	0.710808i	$-0.748330\pi$
$37$	59.3904	−	102.867i	0.263885	−	0.457061i	0.967271	+	0.253746i	$0.0816629\pi$
$38$	−26.7459			−0.114178
$39$		0			0
$40$	68.2464			0.269767
$41$	216.451	−	374.903i	0.824486	−	1.42805i	−0.0778262	−	0.996967i	$-0.524798\pi$
$41$	216.451	−	374.903i	0.824486	−	1.42805i	0.902312	−	0.431084i	$-0.141869\pi$
$42$	−15.3963	+	26.6672i	−0.0565643	+	0.0979723i
$43$	178.254	+	308.745i	0.632174	+	1.09496i	0.987106	+	0.160065i	$0.0511704\pi$
$43$	178.254	+	308.745i	0.632174	+	1.09496i	−0.354933	+	0.934892i	$0.615496\pi$
$44$	−261.490			−0.895935
$45$	57.8759	+	100.244i	0.191725	+	0.332078i
$46$	−159.929	−	277.005i	−0.512614	−	0.887874i
$47$	588.614			1.82677			0.913385	−	0.407096i	$-0.133459\pi$
$47$	588.614			1.82677			0.913385	+	0.407096i	$0.133459\pi$
$48$	29.3190	+	50.7820i	0.0881632	+	0.152703i
$49$	162.676	−	281.762i	0.474273	−	0.821465i
$50$	52.2255	−	90.4573i	0.147716	−	0.255852i
$51$	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	$0.613541\pi$
$54$	−148.679	+	257.520i	−0.374679	+	0.648963i
$55$	278.840	−	482.965i	0.683614	−	1.18405i
$56$	16.8042	+	29.1057i	0.0400992	+	0.0694538i
$57$	49.0102			0.113887
$58$	301.288	+	521.846i	0.682087	+	1.18141i
$59$	−115.170	−	199.480i	−0.254133	−	0.440171i	0.710527	−	0.703670i	$-0.248457\pi$
$59$	−115.170	−	199.480i	−0.254133	−	0.440171i	−0.964660	+	0.263499i	$0.915123\pi$
$60$	−125.057			−0.269080
$61$	190.408	+	329.796i	0.399659	+	0.692230i	0.993684	−	0.112217i	$-0.0357951\pi$
$61$	190.408	+	329.796i	0.399659	+	0.692230i	−0.594024	+	0.804447i	$0.702462\pi$
$62$	73.0232	−	126.480i	0.149580	−	0.259080i
$63$	−28.5014	+	49.3658i	−0.0569974	+	0.0987223i
$64$	64.0000			0.125000
$65$		0			0
$66$	479.164			0.893652
$67$	−217.924	+	377.456i	−0.397368	+	0.688262i	−0.993400	−	0.114699i	$-0.963410\pi$
$67$	−217.924	+	377.456i	−0.397368	+	0.688262i	0.596032	+	0.802961i	$0.296743\pi$
$68$	53.8038	−	93.1909i	0.0959510	−	0.166192i
$69$	293.060	+	507.595i	0.511308	+	0.885612i
$70$	−71.6765			−0.122385
$71$	−32.9811	−	57.1249i	−0.0551287	−	0.0954857i	0.837144	−	0.546982i	$-0.184224\pi$
$71$	−32.9811	−	57.1249i	−0.0551287	−	0.0954857i	−0.892273	+	0.451497i	$0.850890\pi$
$72$	54.2748	+	94.0067i	0.0888381	+	0.153872i
$73$	885.517			1.41975			0.709876	−	0.704326i	$-0.248751\pi$
$73$	885.517			1.41975			0.709876	+	0.704326i	$0.248751\pi$
$74$	118.781	+	205.735i	0.186595	+	0.323191i
$75$	−95.7000	+	165.757i	−0.147340	+	0.255200i
$76$	26.7459	−	46.3253i	0.0403680	−	0.0699194i
$77$	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	$0.588506\pi$
$80$	−68.2464	+	118.206i	−0.0953772	+	0.165198i
$81$	89.2679	−	154.616i	0.122452	−	0.212094i
$82$	432.901	+	749.807i	0.582999	+	1.00978i
$83$	−254.207			−0.336179			−0.168089	−	0.985772i	$-0.553760\pi$
$83$	−254.207			−0.336179			−0.168089	+	0.985772i	$0.553760\pi$
$84$	−30.7926	−	53.3344i	−0.0399970	−	0.0692769i
$85$	114.747	+	198.748i	0.146425	+	0.253615i
$86$	−713.016			−0.894029
$87$	−552.091	−	956.250i	−0.680349	−	1.17840i
$88$	261.490	−	452.914i	0.316761	−	0.548646i
$89$	186.306	−	322.692i	0.221892	−	0.384329i	−0.733490	−	0.679700i	$-0.762110\pi$
$89$	186.306	−	322.692i	0.221892	−	0.384329i	0.955383	+	0.295371i	$0.0954433\pi$
$90$	−231.504			−0.271140
$91$		0			0
$92$	639.716			0.724946
$93$	−133.810	+	231.766i	−0.149199	+	0.258420i
$94$	−588.614	+	1019.51i	−0.645861	+	1.11866i
$95$	57.0410	+	98.7979i	0.0616030	+	0.106699i
$96$	−117.276			−0.124682
$97$	−656.942	−	1137.86i	−0.687653	−	1.19105i	−0.972595	−	0.232506i	$-0.925308\pi$
$97$	−656.942	−	1137.86i	−0.687653	−	1.19105i	0.284942	−	0.958545i	$-0.408026\pi$
$98$	325.351	+	563.525i	0.335362	+	0.580863i
$99$	887.020			0.900494
$100$	104.451	+	180.915i	0.104451	+	0.180915i
$101$	−731.861	+	1267.62i	−0.721019	+	1.24884i	0.239573	+	0.970878i	$0.422993\pi$
$101$	−731.861	+	1267.62i	−0.721019	+	1.24884i	−0.960592	+	0.277963i	$0.910341\pi$
$102$	−98.5921	+	170.767i	−0.0957066	+	0.165769i
$103$	210.886			0.201740			0.100870	−	0.994900i	$-0.467837\pi$
$103$	210.886			0.201740			0.100870	+	0.994900i	$0.467837\pi$
$104$		0			0
$105$	131.343			0.122074
$106$	269.462	−	466.722i	0.246910	−	0.427660i
$107$	−195.531	+	338.669i	−0.176660	+	0.305985i	−0.940735	−	0.339144i	$-0.889863\pi$
$107$	−195.531	+	338.669i	−0.176660	+	0.305985i	0.764074	+	0.645128i	$0.223196\pi$
$108$	−297.358	−	515.040i	−0.264938	−	0.458886i
$109$	1331.40			1.16996			0.584978	−	0.811049i	$-0.301103\pi$
$109$	1331.40			1.16996			0.584978	+	0.811049i	$0.301103\pi$
$110$	557.680	+	965.930i	0.483388	+	0.837253i
$111$	−217.658	−	376.996i	−0.186119	−	0.322368i
$112$	−67.2167			−0.0567088
$113$	355.956	+	616.534i	0.296332	+	0.513263i	0.975294	−	0.220911i	$-0.0709031\pi$
$113$	355.956	+	616.534i	0.296332	+	0.513263i	−0.678962	+	0.734174i	$0.737570\pi$
$114$	−49.0102	+	84.8882i	−0.0402652	+	0.0697413i
$115$	−682.161	+	1181.54i	−0.553146	+	0.958078i
$116$	−1205.15			−0.964616
$117$		0			0
$118$	460.679			0.359398
$119$	−56.5081	+	97.8748i	−0.0435301	+	0.0753964i
$120$	125.057	−	216.605i	0.0951342	−	0.164777i
$121$	−1471.29	−	2548.34i	−1.10540	−	1.91461i
$122$	−761.631			−0.565204
$123$	−793.264	−	1373.97i	−0.581514	−	1.00721i
$124$	146.046	+	252.960i	0.105769	+	0.183197i
$125$	−1511.87			−1.08181
$126$	−57.0027	−	98.7316i	−0.0403032	−	0.0698072i
$127$	585.852	−	1014.73i	0.409338	−	0.708995i	−0.585477	−	0.810689i	$-0.699093\pi$
$127$	585.852	−	1014.73i	0.409338	−	0.708995i	0.994816	+	0.101694i	$0.0324262\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	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	$0.622825\pi$
$132$	−479.164	+	829.937i	−0.315954	+	0.547248i
$133$	−28.0902	+	48.6537i	−0.0183138	+	0.0317204i
$134$	−435.848	−	754.911i	−0.280982	−	0.486675i
$135$	1268.35			0.808610
$136$	107.608	+	186.382i	0.0678476	+	0.117516i
$137$	873.967	+	1513.76i	0.545022	+	0.944006i	0.998606	+	0.0527923i	$0.0168121\pi$
$137$	873.967	+	1513.76i	0.545022	+	0.944006i	−0.453583	+	0.891214i	$0.649855\pi$
$138$	−1172.24			−0.723099
$139$	−838.268	−	1451.92i	−0.511518	−	0.885975i	−0.999911	−	0.0133509i	$-0.995750\pi$
$139$	−838.268	−	1451.92i	−0.511518	−	0.885975i	0.488393	−	0.872624i	$-0.337583\pi$
$140$	71.6765	−	124.147i	0.0432698	−	0.0749455i
$141$	1078.60	−	1868.19i	0.644216	−	1.11581i
$142$	131.924			0.0779637
$143$		0			0
$144$	−217.099			−0.125636
$145$	1285.11	−	2225.88i	0.736019	−	1.27482i
$146$	−885.517	+	1533.76i	−0.501958	+	0.869417i
$147$	−596.186	−	1032.62i	−0.334507	−	0.579384i
$148$	−475.124			−0.263885
$149$	448.481	+	776.791i	0.246584	+	0.427095i	0.962576	−	0.271013i	$-0.0873587\pi$
$149$	448.481	+	776.791i	0.246584	+	0.427095i	−0.715992	+	0.698108i	$0.754025\pi$
$150$	−191.400	−	331.515i	−0.104185	−	0.180454i
$151$	−2078.28			−1.12005			−0.560027	−	0.828475i	$-0.689209\pi$
$151$	−2078.28			−1.12005			−0.560027	+	0.828475i	$0.689209\pi$
$152$	53.4918	+	92.6506i	0.0285445	+	0.0494405i
$153$	−182.512	+	316.120i	−0.0964393	+	0.167038i
$154$	−274.633	+	475.679i	−0.143705	+	0.248904i
$155$	−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	$0.848080\pi$
$158$	385.463	−	667.642i	0.194087	−	0.336169i
$159$	−493.772	+	855.238i	−0.246281	+	0.426571i
$160$	−136.493	−	236.412i	−0.0674419	−	0.116813i
$161$	−671.869			−0.328887
$162$	178.536	+	309.233i	0.0865870	+	0.149973i
$163$	225.627	+	390.797i	0.108420	+	0.187789i	0.915130	−	0.403158i	$-0.132088\pi$
$163$	225.627	+	390.797i	0.108420	+	0.187789i	−0.806710	+	0.590947i	$0.798754\pi$
$164$	−1731.61			−0.824486
$165$	−1021.91	−	1770.01i	−0.482157	−	0.835120i
$166$	254.207	−	440.299i	0.118857	−	0.205867i
$167$	−1601.68	+	2774.18i	−0.742164	+	1.28547i	0.209344	+	0.977842i	$0.432867\pi$
$167$	−1601.68	+	2774.18i	−0.742164	+	1.28547i	−0.951508	+	0.307624i	$0.900466\pi$
$168$	123.170			0.0565643
$169$		0			0
$170$	−458.989			−0.207076
$171$	−90.7268	+	157.143i	−0.0405734	+	0.0702752i
$172$	713.016	−	1234.98i	0.316087	−	0.547478i
$173$	−949.691	−	1644.91i	−0.417362	−	0.722893i	0.578311	−	0.815816i	$-0.303712\pi$
$173$	−949.691	−	1644.91i	−0.417362	−	0.722893i	−0.995673	+	0.0929237i	$0.970379\pi$
$174$	2208.36			0.962159
$175$	−109.701	−	190.008i	−0.0473864	−	0.0820756i
$176$	522.980	+	905.829i	0.223984	+	0.387951i
$177$	−844.165			−0.358482
$178$	372.612	+	645.384i	0.156902	+	0.271762i
$179$	−1325.45	+	2295.74i	−0.553455	+	0.958612i	0.444567	+	0.895746i	$0.353358\pi$
$179$	−1325.45	+	2295.74i	−0.553455	+	0.958612i	−0.998022	+	0.0628664i	$0.979976\pi$
$180$	231.504	−	400.976i	0.0958625	−	0.166039i
$181$	−2289.94			−0.940387			−0.470194	−	0.882563i	$-0.655816\pi$
$181$	−2289.94			−0.940387			−0.470194	+	0.882563i	$0.655816\pi$
$182$		0			0
$183$	1395.64			0.563764
$184$	−639.716	+	1108.02i	−0.256307	+	0.443937i
$185$	506.648	−	877.539i	0.201349	−	0.348746i
$186$	−267.621	−	463.533i	−0.105500	−	0.182731i
$187$	1758.65			0.687727
$188$	−1177.23	−	2039.02i	−0.456693	−	0.791015i
$189$	312.304	+	540.926i	0.120195	+	0.208183i
$190$	−228.164			−0.0871198
$191$	169.157	+	292.988i	0.0640825	+	0.110994i	0.896287	−	0.443475i	$-0.146255\pi$
$191$	169.157	+	292.988i	0.0640825	+	0.110994i	−0.832204	+	0.554469i	$0.812921\pi$
$192$	117.276	−	203.128i	0.0440816	−	0.0763515i
$193$	−1342.03	+	2324.46i	−0.500524	+	0.866933i	0.499476	+	0.866328i	$0.333526\pi$
$193$	−1342.03	+	2324.46i	−0.500524	+	0.866933i	−1.00000		0.000605201i	$0.999807\pi$
$194$	2627.77			0.972489
$195$		0			0
$196$	−1301.40			−0.474273
$197$	−948.620	+	1643.06i	−0.343078	+	0.594229i	−0.985003	−	0.172539i	$-0.944803\pi$
$197$	−948.620	+	1643.06i	−0.343078	+	0.594229i	0.641925	+	0.766768i	$0.278136\pi$
$198$	−887.020	+	1536.36i	−0.318373	+	0.551438i
$199$	1207.80	+	2091.97i	0.430245	+	0.745207i	0.996894	−	0.0787527i	$-0.0250937\pi$
$199$	1207.80	+	2091.97i	0.430245	+	0.745207i	−0.566649	+	0.823959i	$0.691760\pi$
$200$	−417.804			−0.147716
$201$	798.665	+	1383.33i	0.280266	+	0.485435i
$202$	−1463.72	−	2535.24i	−0.509837	−	0.883064i
$203$	1265.72			0.437618
$204$	−197.184	−	341.533i	−0.0676748	−	0.117216i
$205$	1846.50	−	3198.22i	0.629097	−	1.08963i
$206$	−210.886	+	365.265i	−0.0713258	+	0.123540i
$207$	−2170.03			−0.728635
$208$		0			0
$209$	874.225			0.289337
$210$	−131.343	+	227.492i	−0.0431596	+	0.0747546i
$211$	−1334.21	+	2310.92i	−0.435312	+	0.753982i	−0.997321	−	0.0731491i	$-0.976695\pi$
$211$	−1334.21	+	2310.92i	−0.435312	+	0.753982i	0.562009	+	0.827131i	$0.310028\pi$
$212$	538.924	+	933.443i	0.174592	+	0.302402i
$213$	−241.743			−0.0777651
$214$	−391.061	−	677.338i	−0.124918	−	0.216364i
$215$	1520.65	+	2633.84i	0.482360	+	0.835471i
$216$	1189.43			0.374679
$217$	−153.387	−	265.674i	−0.0479842	−	0.0831112i
$218$	−1331.40	+	2306.06i	−0.413642	+	0.716449i
$219$	1622.65	−	2810.52i	0.500680	−	0.867202i
$220$	−2230.72			−0.683614
$221$		0			0
$222$	870.634			0.263212
$223$	143.179	−	247.993i	0.0429953	−	0.0744701i	−0.843727	−	0.536773i	$-0.819643\pi$
$223$	143.179	−	247.993i	0.0429953	−	0.0744701i	0.886722	+	0.462303i	$0.152977\pi$
$224$	67.2167	−	116.423i	0.0200496	−	0.0347269i
$225$	−354.316	−	613.694i	−0.104983	−	0.181835i
$226$	−1423.82			−0.419077
$227$	−2600.62	−	4504.41i	−0.760393	−	1.31704i	−0.942648	−	0.333788i	$-0.891673\pi$
$227$	−2600.62	−	4504.41i	−0.760393	−	1.31704i	0.182255	−	0.983251i	$-0.441660\pi$
$228$	−98.0204	−	169.776i	−0.0284718	−	0.0493145i
$229$	890.458			0.256957			0.128478	−	0.991712i	$-0.458991\pi$
$229$	890.458			0.256957			0.128478	+	0.991712i	$0.458991\pi$
$230$	−1364.32	−	2363.08i	−0.391134	−	0.677463i
$231$	503.248	−	871.651i	0.143339	−	0.248270i
$232$	1205.15	−	2087.38i	0.341043	−	0.590704i
$233$	4753.11			1.33642			0.668212	−	0.743971i	$-0.267060\pi$
$233$	4753.11			1.33642			0.668212	+	0.743971i	$0.267060\pi$
$234$		0			0
$235$	5021.35			1.39386
$236$	−460.679	+	797.919i	−0.127066	+	0.220085i
$237$	−706.337	+	1223.41i	−0.193593	+	0.335313i
$238$	−113.016	−	195.750i	−0.0307805	−	0.0533133i
$239$	−2292.62			−0.620491			−0.310245	−	0.950656i	$-0.600411\pi$
$239$	−2292.62			−0.620491			−0.310245	+	0.950656i	$0.600411\pi$
$240$	250.114	+	433.211i	0.0672700	+	0.116515i
$241$	−987.604	−	1710.58i	−0.263972	−	0.457212i	0.703322	−	0.710871i	$-0.251699\pi$
$241$	−987.604	−	1710.58i	−0.263972	−	0.457212i	−0.967294	+	0.253659i	$0.918366\pi$
$242$	5885.14			1.56327
$243$	1680.01	+	2909.87i	0.443510	+	0.768182i
$244$	761.631	−	1319.18i	0.199830	−	0.346115i
$245$	1387.75	−	2403.66i	0.361879	−	0.626792i
$246$	3173.06			0.822385
$247$		0			0
$248$	−584.186			−0.149580
$249$	−465.818	+	806.821i	−0.118554	+	0.205342i
$250$	1511.87	−	2618.64i	0.382477	−	0.662470i
$251$	3732.87	+	6465.52i	0.938711	+	1.62590i	0.767879	+	0.640595i	$0.221312\pi$
$251$	3732.87	+	6465.52i	0.938711	+	1.62590i	0.170833	+	0.985300i	$0.445354\pi$
$252$	228.011			0.0569974
$253$	5227.49	+	9054.27i	1.29901	+	2.24995i
$254$	1171.70	+	2029.45i	0.289446	+	0.501335i
$255$	841.069			0.206548
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	277.483	−	480.615i	0.0673499	−	0.116653i	−0.830384	−	0.557191i	$-0.811879\pi$
$257$	277.483	−	480.615i	0.0673499	−	0.116653i	0.897734	+	0.440538i	$0.145212\pi$
$258$	−1306.56	+	2263.02i	−0.315282	+	0.546084i
$259$	499.004			0.119717
$260$		0			0
$261$	4088.08			0.969525
$262$	1128.61	−	1954.81i	0.266129	−	0.460949i
$263$	996.534	−	1726.05i	0.233646	−	0.404687i	−0.725232	−	0.688504i	$-0.758268\pi$
$263$	996.534	−	1726.05i	0.233646	−	0.404687i	0.958878	+	0.283817i	$0.0916010\pi$
$264$	−958.329	−	1659.87i	−0.223413	−	0.386963i
$265$	−2298.72			−0.532866
$266$	−56.1804	−	97.3074i	−0.0129498	−	0.0224297i
$267$	−682.789	−	1182.63i	−0.156502	−	0.271069i
$268$	1743.39			0.397368
$269$	2603.88	+	4510.06i	0.590191	+	1.02224i	0.994206	+	0.107489i	$0.0342811\pi$
$269$	2603.88	+	4510.06i	0.590191	+	1.02224i	−0.404015	+	0.914752i	$0.632386\pi$
$270$	−1268.35	+	2196.85i	−0.285887	+	0.495170i
$271$	−2042.45	+	3537.63i	−0.457823	+	0.792972i	−0.998846	−	0.0480356i	$-0.984704\pi$
$271$	−2042.45	+	3537.63i	−0.457823	+	0.792972i	0.541023	+	0.841008i	$0.318037\pi$
$272$	−430.430			−0.0959510
$273$		0			0
$274$	−3495.87			−0.770778
$275$	−1707.06	+	2956.71i	−0.374325	+	0.648351i
$276$	1172.24	−	2030.38i	0.255654	−	0.442806i
$277$	−218.996	−	379.313i	−0.0475026	−	0.0822769i	0.841296	−	0.540574i	$-0.181793\pi$
$277$	−218.996	−	379.313i	−0.0475026	−	0.0822769i	−0.888799	+	0.458297i	$0.848460\pi$
$278$	3353.07			0.723395
$279$	−495.415	−	858.083i	−0.106307	−	0.184129i
$280$	143.353	+	248.295i	0.0305964	+	0.0529945i
$281$	5462.34			1.15963			0.579815	−	0.814748i	$-0.303125\pi$
$281$	5462.34			1.15963			0.579815	+	0.814748i	$0.303125\pi$
$282$	2157.20	+	3736.38i	0.455529	+	0.789000i
$283$	398.338	−	689.941i	0.0836704	−	0.144921i	−0.821153	−	0.570707i	$-0.806669\pi$
$283$	398.338	−	689.941i	0.0836704	−	0.144921i	0.904824	+	0.425786i	$0.140002\pi$
$284$	−131.924	+	228.500i	−0.0275643	+	0.0477428i
$285$	418.096			0.0868978
$286$		0			0
$287$	1818.64			0.374045
$288$	217.099	−	376.027i	0.0444191	−	0.0769361i
$289$	2094.64	−	3628.03i	0.426347	−	0.738455i
$290$	2570.22	+	4451.76i	0.520444	+	0.901436i
$291$	−4815.22			−0.970011
$292$	−1771.03	−	3067.52i	−0.354938	−	0.614771i
$293$	−848.662	−	1469.93i	−0.169213	−	0.293085i	0.768931	−	0.639332i	$-0.220789\pi$
$293$	−848.662	−	1469.93i	−0.169213	−	0.293085i	−0.938143	+	0.346247i	$0.887456\pi$
$294$	2384.74			0.473065
$295$	−982.490	−	1701.72i	−0.193908	−	0.335858i
$296$	475.124	−	822.938i	0.0932973	−	0.161596i
$297$	4859.77	−	8417.37i	0.949469	−	1.64453i
$298$	−1793.92			−0.348722
$299$		0			0
$300$	765.600			0.147340
$301$	−748.853	+	1297.05i	−0.143399	+	0.248375i
$302$	2078.28	−	3599.69i	0.395999	−	0.685890i
$303$	2682.18	+	4645.67i	0.508538	+	0.880814i
$304$	−213.967			−0.0403680
$305$	1624.33	+	2813.42i	0.304947	+	0.528184i
$306$	−365.024	−	632.240i	−0.0681929	−	0.118114i
$307$	−9385.86			−1.74488			−0.872442	−	0.488718i	$-0.837465\pi$
$307$	−9385.86			−1.74488			−0.872442	+	0.488718i	$0.837465\pi$
$308$	−549.266	−	951.357i	−0.101615	−	0.176002i
$309$	386.435	−	669.325i	0.0711441	−	0.123225i
$310$	622.946	−	1078.97i	0.114132	−	0.197683i
$311$	−3282.65			−0.598527			−0.299264	−	0.954170i	$-0.596741\pi$
$311$	−3282.65			−0.598527			−0.299264	+	0.954170i	$0.596741\pi$
$312$		0			0
$313$	−5924.67			−1.06991			−0.534955	−	0.844880i	$-0.679672\pi$
$313$	−5924.67			−1.06991			−0.534955	+	0.844880i	$0.679672\pi$
$314$	3494.75	−	6053.08i	0.628089	−	1.08788i
$315$	−243.139	+	421.130i	−0.0434900	+	0.0753269i
$316$	770.927	+	1335.28i	0.137241	+	0.237708i
$317$	−6467.88			−1.14597			−0.572985	−	0.819566i	$-0.694215\pi$
$317$	−6467.88			−1.14597			−0.572985	+	0.819566i	$0.694215\pi$
$318$	−987.544	−	1710.48i	−0.174147	−	0.301631i
$319$	−9847.98	−	17057.2i	−1.72847	−	2.99379i
$320$	545.971			0.0953772
$321$	716.595	+	1241.18i	0.124599	+	0.215813i
$322$	671.869	−	1163.71i	0.116279	−	0.201401i
$323$	−179.879	+	311.560i	−0.0309868	+	0.0536707i
$324$	−714.143			−0.122452
$325$		0			0
$326$	−902.508			−0.153329
$327$	2439.71	−	4225.70i	0.412588	−	0.714624i
$328$	1731.61	−	2999.23i	0.291500	−	0.504892i
$329$	1236.40	+	2141.50i	0.207188	+	0.358860i
$330$	4087.65			0.681872
$331$	1754.62	+	3039.09i	0.291368	+	0.504664i	0.974133	−	0.225974i	$-0.0725563\pi$
$331$	1754.62	+	3039.09i	0.291368	+	0.504664i	−0.682766	+	0.730637i	$0.739223\pi$
$332$	508.414	+	880.599i	0.0840447	+	0.145570i
$333$	1611.70			0.265227
$334$	−3203.35	−	5548.37i	−0.524789	−	0.908962i
$335$	−1859.07	+	3220.00i	−0.303199	+	0.525156i
$336$	−123.170	+	213.337i	−0.0199985	+	0.0346384i
$337$	−1834.82			−0.296584			−0.148292	−	0.988944i	$-0.547378\pi$
$337$	−1834.82			−0.296584			−0.148292	+	0.988944i	$0.547378\pi$
$338$		0			0
$339$	2609.07			0.418010
$340$	458.989	−	794.993i	0.0732123	−	0.126807i
$341$	−2386.86	+	4134.16i	−0.379048	+	0.656531i
$342$	−181.454	−	314.287i	−0.0286897	−	0.0496921i
$343$	2807.77			0.441999
$344$	1426.03	+	2469.96i	0.223507	+	0.387126i
$345$	2500.03	+	4330.19i	0.390137	+	0.675737i
$346$	3798.76			0.590239
$347$	3629.65	+	6286.74i	0.561527	+	0.972593i	0.997364	+	0.0725673i	$0.0231192\pi$
$347$	3629.65	+	6286.74i	0.561527	+	0.972593i	−0.435837	+	0.900026i	$0.643547\pi$
$348$	−2208.36	+	3825.00i	−0.340175	+	0.589200i
$349$	−897.618	+	1554.72i	−0.137674	+	0.238459i	−0.926616	−	0.376009i	$-0.877296\pi$
$349$	−897.618	+	1554.72i	−0.137674	+	0.238459i	0.788942	+	0.614468i	$0.210629\pi$
$350$	438.804			0.0670144
$351$		0			0
$352$	−2091.92			−0.316761
$353$	−2276.19	+	3942.47i	−0.343199	+	0.594438i	−0.985025	−	0.172412i	$-0.944844\pi$
$353$	−2276.19	+	3942.47i	−0.343199	+	0.594438i	0.641826	+	0.766850i	$0.278177\pi$
$354$	844.165	−	1462.14i	0.126743	−	0.219525i
$355$	−281.355	−	487.321i	−0.0420641	−	0.0728572i
$356$	−1490.45			−0.221892
$357$	207.095	+	358.699i	0.0307020	+	0.0531775i
$358$	−2650.89	−	4591.48i	−0.391352	−	0.677841i
$359$	−10165.4			−1.49445			−0.747227	−	0.664569i	$-0.768615\pi$
$359$	−10165.4			−1.49445			−0.747227	+	0.664569i	$0.768615\pi$
$360$	463.007	+	801.952i	0.0677850	+	0.117407i
$361$	3340.08	−	5785.19i	0.486963	−	0.843445i
$362$	2289.94	−	3966.30i	0.332477	−	0.575867i
$363$	−10784.2			−1.55929
$364$		0			0
$365$	7554.16			1.08330
$366$	−1395.64	+	2417.32i	−0.199321	+	0.345233i
$367$	5200.78	−	9008.01i	0.739723	−	1.28124i	−0.212897	−	0.977075i	$-0.568290\pi$
$367$	5200.78	−	9008.01i	0.739723	−	1.28124i	0.952620	−	0.304163i	$-0.0983769\pi$
$368$	−1279.43	−	2216.04i	−0.181237	−	0.313911i
$369$	5873.91			0.828681
$370$	1013.30	+	1755.08i	0.142375	+	0.246601i
$371$	−566.011	−	980.359i	−0.0792070	−	0.137191i
$372$	1070.48			0.149199
$373$	3976.70	+	6887.85i	0.552027	+	0.956138i	0.998128	+	0.0611560i	$0.0194787\pi$
$373$	3976.70	+	6887.85i	0.552027	+	0.956138i	−0.446101	+	0.894982i	$0.647188\pi$
$374$	−1758.65	+	3046.06i	−0.243148	+	0.421145i
$375$	−2770.42	+	4798.50i	−0.381503	+	0.660783i
$376$	4708.91			0.645861
$377$		0			0
$378$	−1249.22			−0.169981
$379$	4507.41	−	7807.06i	0.610897	−	1.05810i	−0.380193	−	0.924907i	$-0.624142\pi$
$379$	4507.41	−	7807.06i	0.610897	−	1.05810i	0.991090	−	0.133197i	$-0.0425243\pi$
$380$	228.164	−	395.192i	0.0308015	−	0.0533497i
$381$	−2147.07	−	3718.84i	−0.288709	−	0.500058i
$382$	−676.627			−0.0906263
$383$	−1248.12	−	2161.81i	−0.166517	−	0.288415i	0.770676	−	0.637227i	$-0.219919\pi$
$383$	−1248.12	−	2161.81i	−0.166517	−	0.288415i	−0.937193	+	0.348812i	$0.886585\pi$
$384$	234.552	+	406.256i	0.0311704	+	0.0539887i
$385$	2342.84			0.310135
$386$	−2684.05	−	4648.91i	−0.353924	−	0.613014i
$387$	−2418.67	+	4189.26i	−0.317695	+	0.550264i
$388$	−2627.77	+	4551.43i	−0.343827	+	0.595525i
$389$	10896.9			1.42029			0.710145	−	0.704056i	$-0.248629\pi$
$389$	10896.9			1.42029			0.710145	+	0.704056i	$0.248629\pi$
$390$		0			0
$391$	−4302.40			−0.556475
$392$	1301.40	−	2254.10i	0.167681	−	0.290432i
$393$	−2068.11	+	3582.07i	−0.265451	+	0.459774i
$394$	−1897.24	−	3286.12i	−0.242593	−	0.420183i
$395$	−3288.31			−0.418868
$396$	−1774.04	−	3072.73i	−0.225123	−	0.389925i
$397$	5443.57	+	9428.55i	0.688174	+	1.19195i	0.972428	+	0.233203i	$0.0749208\pi$
$397$	5443.57	+	9428.55i	0.688174	+	1.19195i	−0.284254	+	0.958749i	$0.591746\pi$
$398$	−4831.21			−0.608459
$399$	102.947	+	178.310i	0.0129168	+	0.0223725i
$400$	417.804	−	723.658i	0.0522255	−	0.0904573i
$401$	4984.38	−	8633.20i	0.620718	−	1.07512i	−0.368634	−	0.929575i	$-0.620174\pi$
$401$	4984.38	−	8633.20i	0.620718	−	1.07512i	0.989352	−	0.145541i	$-0.0464922\pi$
$402$	−3194.66			−0.396356
$403$		0			0
$404$	5854.89			0.721019
$405$	761.526	−	1319.00i	0.0934334	−	0.161831i
$406$	−1265.72	+	2192.30i	−0.154721	+	0.267985i
$407$	−3882.50	−	6724.70i	−0.472847	−	0.818994i
$408$	788.737			0.0957066
$409$	2018.16	+	3495.56i	0.243989	+	0.422602i	0.961847	−	0.273588i	$-0.0882104\pi$
$409$	2018.16	+	3495.56i	0.243989	+	0.422602i	−0.717858	+	0.696190i	$0.754877\pi$
$410$	3692.99	+	6396.45i	0.444839	+	0.770483i
$411$	6405.96			0.768814
$412$	−421.772	−	730.530i	−0.0504350	−	0.0873559i
$413$	483.833	−	838.024i	0.0576462	−	0.0998462i
$414$	2170.03	−	3758.60i	0.257611	−	0.446196i
$415$	−2168.59			−0.256510
$416$		0			0
$417$	−6144.29			−0.721552
$418$	−874.225	+	1514.20i	−0.102296	+	0.177182i
$419$	−7597.43	+	13159.1i	−0.885821	+	1.53429i	−0.0410504	+	0.999157i	$0.513070\pi$
$419$	−7597.43	+	13159.1i	−0.885821	+	1.53429i	−0.844770	+	0.535129i	$0.820263\pi$
$420$	−262.685	−	454.985i	−0.0305184	−	0.0528595i
$421$	−10154.8			−1.17556			−0.587782	−	0.809019i	$-0.699999\pi$
$421$	−10154.8			−1.17556			−0.587782	+	0.809019i	$0.699999\pi$
$422$	−2668.42	−	4621.84i	−0.307812	−	0.533146i
$423$	3993.36	+	6916.71i	0.459017	+	0.795040i
$424$	−2155.69			−0.246910
$425$	−702.483	−	1216.74i	−0.0801775	−	0.138872i
$426$	241.743	−	418.711i	0.0274941	−	0.0476212i
$427$	−799.912	+	1385.49i	−0.0906568	+	0.157022i
$428$	1564.24			0.176660
$429$		0			0
$430$	−6082.59			−0.682159
$431$	−3308.42	+	5730.35i	−0.369747	+	0.640420i	−0.989526	−	0.144356i	$-0.953889\pi$
$431$	−3308.42	+	5730.35i	−0.369747	+	0.640420i	0.619779	+	0.784776i	$0.287222\pi$
$432$	−1189.43	+	2060.16i	−0.132469	+	0.229443i
$433$	−2848.80	−	4934.27i	−0.316177	−	0.547635i	0.663510	−	0.748167i	$-0.269066\pi$
$433$	−2848.80	−	4934.27i	−0.316177	−	0.547635i	−0.979687	+	0.200533i	$0.935733\pi$
$434$	613.548			0.0678600
$435$	−4709.77	−	8157.57i	−0.519118	−	0.899139i
$436$	−2662.81	−	4612.11i	−0.292489	−	0.506606i
$437$	−2138.73			−0.234117
$438$	3245.31	+	5621.04i	0.354034	+	0.613205i
$439$	−218.004	+	377.593i	−0.0237010	+	0.0410513i	−0.877633	−	0.479334i	$-0.840878\pi$
$439$	−218.004	+	377.593i	−0.0237010	+	0.0410513i	0.853932	+	0.520385i	$0.174212\pi$
$440$	2230.72	−	3863.72i	0.241694	−	0.418626i
$441$	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	$0.384673\pi$
$444$	−870.634	+	1507.98i	−0.0930596	+	0.161184i
$445$	1589.34	−	2752.82i	0.169308	−	0.293250i
$446$	286.358	+	495.986i	0.0304023	+	0.0526583i
$447$	3287.25			0.347833
$448$	134.433	+	232.846i	0.0141772	+	0.0245556i
$449$	4007.65	+	6941.46i	0.421231	+	0.729594i	0.996060	−	0.0886795i	$-0.0282647\pi$
$449$	4007.65	+	6941.46i	0.421231	+	0.729594i	−0.574829	+	0.818274i	$0.694931\pi$
$450$	1417.26			0.148468
$451$	−14149.9	−	24508.4i	−1.47737	−	2.55888i
$452$	1423.82	−	2466.14i	0.148166	−	0.256631i
$453$	−3808.32	+	6596.20i	−0.394990	+	0.684142i
$454$	10402.5			1.07536
$455$		0			0
$456$	392.082			0.0402652
$457$	−2253.52	+	3903.21i	−0.230668	+	0.399528i	−0.958005	−	0.286752i	$-0.907424\pi$
$457$	−2253.52	+	3903.21i	−0.230668	+	0.399528i	0.727337	+	0.686280i	$0.240758\pi$
$458$	−890.458	+	1542.32i	−0.0908480	+	0.157353i
$459$	1999.88	+	3463.89i	0.203369	+	0.352245i
$460$	5457.29			0.553146
$461$	1051.78	+	1821.73i	0.106260	+	0.184048i	0.914252	−	0.405145i	$-0.132779\pi$
$461$	1051.78	+	1821.73i	0.106260	+	0.184048i	−0.807992	+	0.589193i	$0.799446\pi$
$462$	1006.50	+	1743.30i	0.101356	+	0.175554i
$463$	−5468.28			−0.548883			−0.274441	−	0.961604i	$-0.588493\pi$
$463$	−5468.28			−0.548883			−0.274441	+	0.961604i	$0.588493\pi$
$464$	2410.30	+	4174.77i	0.241154	+	0.417691i
$465$	−1141.51	+	1977.15i	−0.113841	+	0.197179i
$466$	−4753.11	+	8232.63i	−0.472497	+	0.818389i
$467$	−6043.79			−0.598872			−0.299436	−	0.954116i	$-0.596799\pi$
$467$	−6043.79			−0.598872			−0.299436	+	0.954116i	$0.596799\pi$
$468$		0			0
$469$	−1831.02			−0.180274
$470$	−5021.35	+	8697.23i	−0.492803	+	0.853560i
$471$	−6403.90	+	11091.9i	−0.626489	+	1.08511i
$472$	−921.358	−	1595.84i	−0.0898495	−	0.155624i
$473$	23305.8			2.26555
$474$	−1412.67	−	2446.82i	−0.136891	−	0.237102i
$475$	−349.205	−	604.841i	−0.0337318	−	0.0584253i
$476$	452.065			0.0435301
$477$	−1828.12	−	3166.40i	−0.175480	−	0.303940i
$478$	2292.62	−	3970.94i	0.219377	−	0.379972i
$479$	−4240.65	+	7345.02i	−0.404510	+	0.700632i	−0.994264	−	0.106951i	$-0.965891\pi$
$479$	−4240.65	+	7345.02i	−0.404510	+	0.700632i	0.589754	+	0.807583i	$0.299225\pi$
$480$	−1000.46			−0.0951342
$481$		0			0
$482$	3950.42			0.373312
$483$	−1231.16	+	2132.43i	−0.115983	+	0.200888i
$484$	−5885.14	+	10193.4i	−0.552699	+	0.957303i
$485$	−5604.24	−	9706.83i	−0.524691	−	0.908792i
$486$	−6720.05			−0.627218
$487$	−3311.68	−	5735.99i	−0.308145	−	0.533722i	0.669812	−	0.742531i	$-0.266375\pi$
$487$	−3311.68	−	5735.99i	−0.308145	−	0.533722i	−0.977957	+	0.208809i	$0.933041\pi$
$488$	1523.26	+	2638.37i	0.141301	+	0.244740i
$489$	1653.79			0.152939
$490$	2775.50	+	4807.31i	0.255887	+	0.443209i
$491$	−8189.68	+	14184.9i	−0.752739	+	1.30378i	0.193751	+	0.981051i	$0.437935\pi$
$491$	−8189.68	+	14184.9i	−0.752739	+	1.30378i	−0.946490	+	0.322732i	$0.895399\pi$
$492$	−3173.06	+	5495.90i	−0.290757	+	0.503606i
$493$	8105.21			0.740447
$494$		0			0
$495$	7566.99			0.687093
$496$	584.186	−	1011.84i	0.0528845	−	0.0915986i
$497$	138.555	−	239.985i	0.0125051	−	0.0216595i
$498$	−931.637	−	1613.64i	−0.0838306	−	0.145199i
$499$	7915.70			0.710131			0.355065	−	0.934841i	$-0.384459\pi$
$499$	7915.70			0.710131			0.355065	+	0.934841i	$0.384459\pi$
$500$	3023.75	+	5237.29i	0.270452	+	0.468437i
$501$	5869.94	+	10167.0i	0.523452	+	0.906646i
$502$	−14931.5			−1.32754
$503$	239.755	+	415.269i	0.0212528	+	0.0368110i	0.876456	−	0.481482i	$-0.159901\pi$
$503$	239.755	+	415.269i	0.0212528	+	0.0368110i	−0.855203	+	0.518293i	$0.826568\pi$
$504$	−228.011	+	394.926i	−0.0201516	+	0.0349036i
$505$	−6243.36	+	10813.8i	−0.550150	+	0.952888i
$506$	−20909.9			−1.83708
$507$		0			0
$508$	−4686.82			−0.409338
$509$	596.164	−	1032.59i	0.0519145	−	0.0899186i	−0.838900	−	0.544285i	$-0.816801\pi$
$509$	596.164	−	1032.59i	0.0519145	−	0.0899186i	0.890815	+	0.454366i	$0.150134\pi$
$510$	−841.069	+	1456.77i	−0.0730258	+	0.126484i
$511$	1860.05	+	3221.70i	0.161025	+	0.278903i
$512$	512.000			0.0441942
$513$	994.140	+	1721.90i	0.0855602	+	0.148195i
$514$	554.966	+	961.229i	0.0476236	+	0.0824864i
$515$	1799.02			0.153931
$516$	−2613.11	−	4526.04i	−0.222938	−	0.386140i
$517$	19239.6	−	33324.0i	1.63667	−	2.83479i
$518$	−499.004	+	864.300i	−0.0423262	+	0.0733111i
$519$	−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	$0.931691\pi$
$522$	−4088.08	+	7080.77i	−0.342779	+	0.593710i
$523$	5513.14	−	9549.03i	0.460942	−	0.798375i	−0.538066	−	0.842903i	$-0.680845\pi$
$523$	5513.14	−	9549.03i	0.460942	−	0.798375i	0.999008	+	0.0445277i	$0.0141783\pi$
$524$	2257.22	+	3909.62i	0.188181	+	0.325940i
$525$	−804.080			−0.0668437
$526$	1993.07	+	3452.10i	0.165213	+	0.286157i
$527$	−982.231	−	1701.27i	−0.0811891	−	0.140624i
$528$	3833.32			0.315954
$529$	−6705.15	−	11613.7i	−0.551093	−	0.954522i
$530$	2298.72	−	3981.51i	0.188397	−	0.326312i
$531$	1562.70	−	2706.68i	0.127713	−	0.221205i
$532$	224.722			0.0183138
$533$		0			0
$534$	2731.16			0.221327
$535$	−1668.03	+	2889.11i	−0.134795	+	0.233472i
$536$	−1743.39	+	3019.65i	−0.140491	+	0.243337i
$537$	4857.59	+	8413.59i	0.390355	+	0.676114i
$538$	−10415.5			−0.834657
$539$	−10634.5	−	18419.5i	−0.849835	−	1.47196i
$540$	−2536.70	−	4393.70i	−0.202152	−	0.350138i
$541$	−8987.70			−0.714254			−0.357127	−	0.934056i	$-0.616244\pi$
$541$	−8987.70			−0.714254			−0.357127	+	0.934056i	$0.616244\pi$
$542$	−4084.90	−	7075.25i	−0.323730	−	0.560716i
$543$	−4196.17	+	7267.99i	−0.331630	+	0.574400i
$544$	430.430	−	745.527i	0.0339238	−	0.0587578i
$545$	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	$0.637812\pi$
$548$	3495.87	−	6055.02i	0.272511	−	0.472003i
$549$	−2583.59	+	4474.90i	−0.200847	+	0.347876i
$550$	−3414.12	−	5913.42i	−0.264688	−	0.458453i
$551$	4029.11			0.311517
$552$	2344.48	+	4060.76i	0.180775	+	0.313111i
$553$	−809.675	−	1402.40i	−0.0622620	−	0.107841i
$554$	875.985			0.0671788
$555$	−1856.80	−	3216.07i	−0.142012	−	0.245972i
$556$	−3353.07	+	5807.69i	−0.255759	+	0.442987i
$557$	6614.13	−	11456.0i	0.503141	−	0.871466i	−0.496852	−	0.867835i	$-0.665511\pi$
$557$	6614.13	−	11456.0i	0.503141	−	0.871466i	0.999993	−	0.00363111i	$-0.00115582\pi$
$558$	1981.66			0.150341
$559$		0			0
$560$	−573.412			−0.0432698
$561$	3222.61	−	5581.72i	0.242529	−	0.420072i
$562$	−5462.34	+	9461.06i	−0.409991	+	0.710126i
$563$	−5366.98	−	9295.89i	−0.401761	−	0.695870i	0.592178	−	0.805807i	$-0.298268\pi$
$563$	−5366.98	−	9295.89i	−0.401761	−	0.695870i	−0.993939	+	0.109937i	$0.964935\pi$
$564$	−8628.79			−0.644216
$565$	3036.59	+	5259.53i	0.226107	+	0.391628i
$566$	796.676	+	1379.88i	0.0591639	+	0.102475i
$567$	750.037			0.0555531
$568$	−263.849	−	457.000i	−0.0194909	−	0.0337593i
$569$	−2656.73	+	4601.58i	−0.195739	+	0.339031i	−0.947143	−	0.320813i	$-0.896044\pi$
$569$	−2656.73	+	4601.58i	−0.195739	+	0.339031i	0.751403	+	0.659843i	$0.229377\pi$
$570$	−418.096	+	724.164i	−0.0307230	+	0.0532138i
$571$	4629.37			0.339287			0.169644	−	0.985505i	$-0.445738\pi$
$571$	4629.37			0.339287			0.169644	+	0.985505i	$0.445738\pi$
$572$		0			0
$573$	1239.88			0.0903954
$574$	−1818.64	+	3149.97i	−0.132245	+	0.229055i
$575$	4176.19	−	7233.37i	0.302886	−	0.524613i
$576$	434.198	+	752.053i	0.0314090	+	0.0544020i
$577$	504.750			0.0364177			0.0182088	−	0.999834i	$-0.494204\pi$
$577$	504.750			0.0364177			0.0182088	+	0.999834i	$0.494204\pi$
$578$	4189.29	+	7256.06i	0.301473	+	0.522167i
$579$	4918.36	+	8518.84i	0.353022	+	0.611453i
$580$	−10280.9			−0.736019
$581$	−533.968	−	924.859i	−0.0381286	−	0.0660407i
$582$	4815.22	−	8340.21i	0.342951	−	0.594008i
$583$	−8807.70	+	15255.4i	−0.625691	+	1.08373i
$584$	7084.14			0.501958
$585$		0			0
$586$	3394.65			0.239303
$587$	2766.47	−	4791.66i	0.194522	−	0.336922i	−0.752222	−	0.658910i	$-0.771018\pi$
$587$	2766.47	−	4791.66i	0.194522	−	0.336922i	0.946744	+	0.321988i	$0.104351\pi$
$588$	−2384.74	+	4130.50i	−0.167254	+	0.289692i
$589$	−488.268	−	845.705i	−0.0341575	−	0.0591624i
$590$	3929.96			0.274227
$591$	3476.57	+	6021.60i	0.241975	+	0.419113i
$592$	950.247	+	1645.88i	0.0659711	+	0.114265i
$593$	18079.8			1.25202			0.626009	−	0.779816i	$-0.284687\pi$
$593$	18079.8			1.25202			0.626009	+	0.779816i	$0.284687\pi$
$594$	9719.54	+	16834.7i	0.671376	+	1.16286i
$595$	−482.059	+	834.950i	−0.0332143	+	0.0575288i
$596$	1793.92	−	3107.16i	0.123292	−	0.213548i
$597$	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	$0.519962\pi$
$600$	−765.600	+	1326.06i	−0.0520925	+	0.0902268i
$601$	11743.6	−	20340.6i	0.797060	−	1.38055i	−0.124463	−	0.992224i	$-0.539721\pi$
$601$	11743.6	−	20340.6i	0.797060	−	1.38055i	0.921523	−	0.388324i	$-0.126946\pi$
$602$	−1497.71	−	2594.10i	−0.101399	−	0.175627i
$603$	−5913.89			−0.399390
$604$	4156.56	+	7199.37i	0.280013	+	0.484997i
$605$	−12551.2	−	21739.4i	−0.843438	−	1.46088i
$606$	−10728.7			−0.719182
$607$	8155.42	+	14125.6i	0.545335	+	0.944548i	0.998586	+	0.0531648i	$0.0169309\pi$
$607$	8155.42	+	14125.6i	0.545335	+	0.944548i	−0.453251	+	0.891383i	$0.649736\pi$
$608$	213.967	−	370.602i	0.0142722	−	0.0247202i
$609$	2319.36	−	4017.25i	0.154327	−	0.267302i
$610$	−6497.32			−0.431260
$611$		0			0
$612$	1460.09			0.0964393
$613$	4226.56	−	7320.61i	0.278481	−	0.482344i	−0.692526	−	0.721393i	$-0.743502\pi$
$613$	4226.56	−	7320.61i	0.278481	−	0.482344i	0.971008	+	0.239049i	$0.0768357\pi$
$614$	9385.86	−	16256.8i	0.616910	−	1.06852i
$615$	−6767.18	−	11721.1i	−0.443705	−	0.768520i
$616$	2197.06			0.143705
$617$	−6705.17	−	11613.7i	−0.437504	−	0.757779i	0.559992	−	0.828498i	$-0.310804\pi$
$617$	−6705.17	−	11613.7i	−0.437504	−	0.757779i	−0.997496	+	0.0707186i	$0.977471\pi$
$618$	772.870	+	1338.65i	0.0503065	+	0.0871334i
$619$	890.135			0.0577990			0.0288995	−	0.999582i	$-0.490800\pi$
$619$	890.135			0.0577990			0.0288995	+	0.999582i	$0.490800\pi$
$620$	1245.89	+	2157.95i	0.0807036	+	0.139783i
$621$	−11889.1	+	20592.5i	−0.768263	+	1.33067i
$622$	3282.65	−	5685.72i	0.211611	−	0.366522i
$623$	1565.36			0.100666
$624$		0			0
$625$	−6369.30			−0.407635
$626$	5924.67	−	10261.8i	0.378271	−	0.655184i
$627$	1601.96	−	2774.68i	0.102035	−	0.176730i
$628$	6989.49	+	12106.2i	0.444126	+	0.769249i
$629$	3195.43			0.202560
$630$	−486.278	−	842.259i	−0.0307521	−	0.0532641i
$631$	−5291.22	−	9164.66i	−0.333819	−	0.578192i	0.649438	−	0.760415i	$-0.275004\pi$
$631$	−5291.22	−	9164.66i	−0.333819	−	0.578192i	−0.983257	+	0.182222i	$0.941671\pi$
$632$	−3083.71			−0.194087
$633$	4889.71	+	8469.22i	0.307028	+	0.531787i
$634$	6467.88	−	11202.7i	0.405161	−	0.701760i
$635$	4997.78	−	8656.42i	0.312332	−	0.540975i
$636$	3950.17			0.246281
$637$		0			0
$638$	39391.9			2.44442
$639$	447.510	−	775.111i	0.0277046	−	0.0479858i
$640$	−545.971	+	945.649i	−0.0337209	+	0.0584064i
$641$	−13442.1	−	23282.4i	−0.828286	−	1.43463i	−0.899382	−	0.437164i	$-0.855983\pi$
$641$	−13442.1	−	23282.4i	−0.828286	−	1.43463i	0.0710952	−	0.997470i	$-0.477351\pi$
$642$	−2866.38			−0.176210
$643$	2845.56	+	4928.66i	0.174523	+	0.302282i	0.939996	−	0.341186i	$-0.110828\pi$
$643$	2845.56	+	4928.66i	0.174523	+	0.302282i	−0.765473	+	0.643468i	$0.777495\pi$
$644$	1343.74	+	2327.42i	0.0822216	+	0.142412i
$645$	11146.0			0.680422
$646$	−359.758	−	623.119i	−0.0219110	−	0.0379509i
$647$	−904.896	+	1567.33i	−0.0549847	+	0.0952364i	−0.892208	−	0.451625i	$-0.850844\pi$
$647$	−904.896	+	1567.33i	−0.0549847	+	0.0952364i	0.837223	+	0.546862i	$0.184178\pi$
$648$	714.143	−	1236.93i	0.0432935	−	0.0749865i
$649$	−15057.9			−0.910745
$650$		0			0
$651$	−1124.29			−0.0676871
$652$	902.508	−	1563.19i	0.0542100	−	0.0938945i
$653$	−4729.58	+	8191.88i	−0.283435	+	0.490923i	−0.972228	−	0.234034i	$-0.924807\pi$
$653$	−4729.58	+	8191.88i	−0.283435	+	0.490923i	0.688794	+	0.724957i	$0.258141\pi$
$654$	4879.42	+	8451.41i	0.291744	+	0.505315i
$655$	−9627.94			−0.574343
$656$	3463.21	+	5998.46i	0.206121	+	0.357013i
$657$	6007.66	+	10405.6i	0.356744	+	0.617899i
$658$	−4945.59			−0.293008
$659$	−507.660	−	879.293i	−0.0300085	−	0.0519763i	0.850631	−	0.525763i	$-0.176220\pi$
$659$	−507.660	−	879.293i	−0.0300085	−	0.0519763i	−0.880640	+	0.473787i	$0.842887\pi$
$660$	−4087.65	+	7080.02i	−0.241078	+	0.417560i
$661$	11824.2	−	20480.2i	0.695778	−	1.20512i	−0.274140	−	0.961690i	$-0.588393\pi$
$661$	11824.2	−	20480.2i	0.695778	−	1.20512i	0.969918	−	0.243433i	$-0.0782734\pi$
$662$	−7018.49			−0.412056
$663$		0			0
$664$	−2033.66			−0.118857
$665$	−239.632	+	415.055i	−0.0139737	+	0.0242032i
$666$	−1611.70	+	2791.55i	−0.0937720	+	0.162418i
$667$	24092.3	+	41729.2i	1.39859	+	2.42243i
$668$	12813.4			0.742164
$669$	−524.732	−	908.863i	−0.0303248	−	0.0525242i
$670$	−3718.13	−	6439.99i	−0.214394	−	0.371341i
$671$	24894.9			1.43228
$672$	−246.341	−	426.675i	−0.0141411	−	0.0244931i
$673$	−8873.48	+	15369.3i	−0.508243	+	0.880303i	0.491711	+	0.870758i	$0.336372\pi$
$673$	−8873.48	+	15369.3i	−0.508243	+	0.880303i	−0.999954	+	0.00954455i	$0.996962\pi$
$674$	1834.82	−	3178.00i	0.104858	−	0.181620i
$675$	−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	$0.401258\pi$
$678$	−2609.07	+	4519.04i	−0.147789	+	0.255977i
$679$	2759.84	−	4780.19i	0.155984	−	0.270172i
$680$	917.978	+	1589.99i	0.0517689	+	0.0896664i
$681$	−19061.9			−1.07262
$682$	−4773.71	−	8268.31i	−0.268028	−	0.464238i
$683$	−11990.9	−	20768.8i	−0.671768	−	1.16354i	−0.977402	−	0.211387i	$-0.932202\pi$
$683$	−11990.9	−	20768.8i	−0.671768	−	1.16354i	0.305635	−	0.952149i	$-0.401131\pi$
$684$	725.815			0.0405734
$685$	7455.63	+	12913.5i	0.415862	+	0.720293i
$686$	−2807.77	+	4863.21i	−0.156270	+	0.270668i
$687$	1631.71	−	2826.20i	0.0906166	−	0.156953i
$688$	−5704.13			−0.316087
$689$		0			0
$690$	−10000.1			−0.551737
$691$	14500.7	−	25116.0i	0.798312	−	1.38272i	−0.122403	−	0.992480i	$-0.539060\pi$
$691$	14500.7	−	25116.0i	0.798312	−	1.38272i	0.920715	−	0.390236i	$-0.127607\pi$
$692$	−3798.76	+	6579.65i	−0.208681	+	0.361446i
$693$	1863.21	+	3227.17i	0.102132	+	0.176898i
$694$	−14518.6			−0.794119
$695$	−7151.09	−	12386.1i	−0.390297	−	0.676014i
$696$	−4416.73	−	7650.00i	−0.240540	−	0.416627i
$697$	11645.9			0.632882
$698$	−1795.24	−	3109.44i	−0.0973505	−	0.168616i
$699$	8709.78	−	15085.8i	0.471293	−	0.816304i
$700$	−438.804	+	760.030i	−0.0236932	+	0.0410378i
$701$	−31031.5			−1.67196			−0.835979	−	0.548761i	$-0.815100\pi$
$701$	−31031.5			−1.67196			−0.835979	+	0.548761i	$0.815100\pi$
$702$		0			0
$703$	1588.45			0.0852199
$704$	2091.92	−	3623.31i	0.111992	−	0.193976i
$705$	9201.30	−	15937.1i	0.491548	−	0.851386i
$706$	−4552.38	−	7884.94i	−0.242678	−	0.420331i
$707$	−6149.16			−0.327105
$708$	1688.33	+	2924.27i	0.0896206	+	0.155227i
$709$	−2191.29	−	3795.43i	−0.116073	−	0.201044i	0.802135	−	0.597143i	$-0.203697\pi$
$709$	−2191.29	−	3795.43i	−0.116073	−	0.201044i	−0.918208	+	0.396098i	$0.870364\pi$
$710$	1125.42			0.0594877
$711$	−2615.12	−	4529.52i	−0.137939	−	0.238917i
$712$	1490.45	−	2581.54i	0.0784508	−	0.135881i
$713$	5839.27	−	10113.9i	0.306707	−	0.531232i
$714$	−828.380			−0.0434192
$715$		0			0
$716$	10603.6			0.553455
$717$	−4201.08	+	7276.49i	−0.218818	+	0.379004i
$718$	10165.4	−	17607.0i	0.528369	−	0.915162i
$719$	14382.3	+	24910.9i	0.745994	+	1.29210i	0.949729	+	0.313073i	$0.101358\pi$
$719$	14382.3	+	24910.9i	0.745994	+	1.29210i	−0.203735	+	0.979026i	$0.565308\pi$
$720$	−1852.03			−0.0958625
$721$	442.971	+	767.248i	0.0228808	+	0.0396308i
$722$	6680.16	+	11570.4i	0.344335	+	0.596406i
$723$	−7238.89			−0.372361
$724$	4579.88	+	7932.59i	0.235097	+	0.407200i
$725$	−7867.46	+	13626.8i	−0.403021	+	0.698052i
$726$	10784.2	−	18678.7i	0.551291	−	0.954864i
$727$	25408.5			1.29621			0.648107	−	0.761549i	$-0.275561\pi$
$727$	25408.5			1.29621			0.648107	+	0.761549i	$0.275561\pi$
$728$		0			0
$729$	17134.5			0.870525
$730$	−7554.16	+	13084.2i	−0.383003	+	0.663381i
$731$	−4795.37	+	8305.82i	−0.242631	+	0.420249i
$732$	−2791.28	−	4834.64i	−0.140941	−	0.244117i
$733$	22341.8			1.12580			0.562902	−	0.826524i	$-0.309685\pi$
$733$	22341.8			1.12580			0.562902	+	0.826524i	$0.309685\pi$
$734$	10401.6	+	18016.0i	0.523063	+	0.905972i
$735$	−5085.94	−	8809.10i	−0.255235	−	0.442080i
$736$	5117.73			0.256307
$737$	14246.3	+	24675.2i	0.712032	+	1.23328i
$738$	−5873.91	+	10173.9i	−0.292983	+	0.507461i
$739$	−4105.45	+	7110.84i	−0.204359	+	0.353960i	−0.949928	−	0.312468i	$-0.898844\pi$
$739$	−4105.45	+	7110.84i	−0.204359	+	0.353960i	0.745569	+	0.666428i	$0.232178\pi$
$740$	−4053.18			−0.201349
$741$		0			0
$742$	2264.04			0.112016
$743$	−16376.1	+	28364.3i	−0.808590	+	1.40052i	0.105251	+	0.994446i	$0.466435\pi$
$743$	−16376.1	+	28364.3i	−0.808590	+	1.40052i	−0.913841	+	0.406073i	$0.866898\pi$
$744$	−1070.48	+	1854.13i	−0.0527498	+	0.0913653i
$745$	3825.90	+	6626.65i	0.188148	+	0.325881i
$746$	−15906.8			−0.780684
$747$	−1724.63	−	2987.14i	−0.0844724	−	0.146310i
$748$	−3517.29	−	6092.13i	−0.171932	−	0.297794i
$749$	−1642.87			−0.0801455
$750$	−5540.83	−	9597.00i	−0.269763	−	0.467244i
$751$	−4453.70	+	7714.04i	−0.216402	+	0.374819i	−0.953705	−	0.300742i	$-0.902766\pi$
$751$	−4453.70	+	7714.04i	−0.216402	+	0.374819i	0.737303	+	0.675562i	$0.236099\pi$
$752$	−4708.91	+	8156.08i	−0.228346	+	0.395507i
$753$	27361.0			1.32416
$754$		0			0
$755$	−17729.4			−0.854620
$756$	1249.22	−	2163.71i	0.0600973	−	0.104092i
$757$	5372.32	−	9305.13i	0.257940	−	0.446765i	−0.707750	−	0.706463i	$-0.750290\pi$
$757$	5372.32	−	9305.13i	0.257940	−	0.446765i	0.965690	+	0.259698i	$0.0836231\pi$
$758$	9014.81	+	15614.1i	0.431969	+	0.748193i
$759$	38316.2			1.83240
$760$	456.328	+	790.383i	0.0217799	+	0.0377240i
$761$	−8498.89	−	14720.5i	−0.404841	−	0.701206i	0.589462	−	0.807796i	$-0.299340\pi$
$761$	−8498.89	−	14720.5i	−0.404841	−	0.701206i	−0.994303	+	0.106590i	$0.966007\pi$
$762$	8588.30			0.408296
$763$	2796.64	+	4843.93i	0.132694	+	0.229832i
$764$	676.627	−	1171.95i	0.0320412	−	0.0554970i
$765$	−1556.97	+	2696.75i	−0.0735849	+	0.127453i
$766$	4992.48			0.235490
$767$		0			0
$768$	−938.208			−0.0440816
$769$	9516.21	−	16482.6i	0.446246	−	0.772921i	−0.551892	−	0.833916i	$-0.686094\pi$
$769$	9516.21	−	16482.6i	0.446246	−	0.772921i	0.998138	+	0.0609948i	$0.0194273\pi$
$770$	−2342.84	+	4057.92i	−0.109649	+	0.189918i
$771$	−1016.94	−	1761.39i	−0.0475022	−	0.0822763i
$772$	10736.2			0.500524
$773$	11875.3	+	20568.6i	0.552555	+	0.957053i	0.998089	+	0.0617879i	$0.0196802\pi$
$773$	11875.3	+	20568.6i	0.552555	+	0.957053i	−0.445535	+	0.895265i	$0.646986\pi$
$774$	−4837.35	−	8378.53i	−0.224644	−	0.389096i
$775$	3813.68			0.176763
$776$	−5255.54	−	9102.86i	−0.243122	−	0.421100i
$777$	914.393	−	1583.78i	0.0422184	−	0.0731244i
$778$	−10896.9	+	18873.9i	−0.502148	+	0.869746i
$779$	5789.17			0.266263
$780$		0			0
$781$	−4312.12			−0.197567
$782$	4302.40	−	7451.97i	0.196743	−	0.340770i
$783$	22397.6	−	38793.8i	1.02225	−	1.77060i
$784$	2602.81	+	4508.20i	0.118568	+	0.205366i
$785$	−29813.0			−1.35550
$786$	−4136.21	−	7164.13i	−0.187702	−	0.325109i
$787$	8912.97	+	15437.7i	0.403702	+	0.699232i	0.994169	−	0.107829i	$-0.0343900\pi$
$787$	8912.97	+	15437.7i	0.403702	+	0.699232i	−0.590468	+	0.807061i	$0.701057\pi$
$788$	7588.96			0.343078
$789$	−3652.17	−	6325.75i	−0.164792	−	0.285428i
$790$	3288.31	−	5695.52i	0.148092	−	0.256503i
$791$	−1495.39	+	2590.09i	−0.0672186	+	0.116426i
$792$	7096.16			0.318373
$793$		0			0
$794$	−21774.3			−0.973225
$795$	−4212.27	+	7295.86i	−0.187917	+	0.325481i
$796$	4831.21	−	8367.90i	0.215123	−	0.372603i
$797$	13230.6	+	22916.1i	0.588020	+	1.01848i	0.994492	+	0.104817i	$0.0334257\pi$
$797$	13230.6	+	22916.1i	0.588020	+	1.01848i	−0.406471	+	0.913663i	$0.633241\pi$
$798$	−411.788			−0.0182671
$799$	7917.42	+	13713.4i	0.350561	+	0.607190i
$800$	835.609	+	1447.32i	0.0369290	+	0.0639630i
$801$	5055.87			0.223021
$802$	9968.76	+	17266.4i	0.438914	+	0.760221i
$803$	28944.3	−	50132.9i	1.27201	−	2.20318i
$804$	3194.66	−	5533.31i	0.140133	−	0.242717i
$805$	−5731.58			−0.250946
$806$		0			0
$807$	19085.8			0.832530
$808$	−5854.89	+	10141.0i	−0.254919	+	0.441532i
$809$	−10936.7	+	18942.9i	−0.475294	+	0.823234i	−0.999600	−	0.0282967i	$-0.990992\pi$
$809$	−10936.7	+	18942.9i	−0.475294	+	0.823234i	0.524305	+	0.851530i	$0.324325\pi$
$810$	1523.05	+	2638.00i	0.0660674	+	0.114432i
$811$	−39113.8			−1.69355			−0.846776	−	0.531949i	$-0.821460\pi$
$811$	−39113.8			−1.69355			−0.846776	+	0.531949i	$0.821460\pi$
$812$	−2531.45	−	4384.60i	−0.109404	−	0.189494i
$813$	7485.32	+	12965.0i	0.322905	+	0.559288i
$814$	15530.0			0.668706
$815$	1924.78	+	3333.81i	0.0827264	+	0.143286i
$816$	−788.737	+	1366.13i	−0.0338374	+	0.0586081i
$817$	−2383.78	+	4128.83i	−0.102078	+	0.176805i
$818$	−8072.65			−0.345053
$819$		0			0
$820$	−14772.0			−0.629097
$821$	−13148.4	+	22773.7i	−0.558931	+	0.968097i	0.438655	+	0.898655i	$0.355455\pi$
$821$	−13148.4	+	22773.7i	−0.558931	+	0.968097i	−0.997586	+	0.0694411i	$0.977878\pi$
$822$	−6405.96	+	11095.4i	−0.271817	+	0.470801i
$823$	−12340.5	−	21374.4i	−0.522678	−	0.905306i	−0.999652	−	0.0263878i	$-0.991600\pi$
$823$	−12340.5	−	21374.4i	−0.522678	−	0.905306i	0.476973	−	0.878918i	$-0.341734\pi$
$824$	1687.09			0.0713258
$825$	6256.15	+	10836.0i	0.264014	+	0.457285i
$826$	967.667	+	1676.05i	0.0407620	+	0.0706019i
$827$	3081.68			0.129578			0.0647888	−	0.997899i	$-0.479363\pi$
$827$	3081.68			0.129578			0.0647888	+	0.997899i	$0.479363\pi$
$828$	4340.06	+	7517.20i	0.182159	+	0.315508i
$829$	4249.27	−	7359.95i	0.178026	−	0.308349i	−0.763179	−	0.646188i	$-0.776362\pi$
$829$	4249.27	−	7359.95i	0.178026	−	0.308349i	0.941204	+	0.337838i	$0.109696\pi$
$830$	2168.59	−	3756.10i	0.0906901	−	0.157080i
$831$	−1605.19			−0.0670076
$832$		0			0
$833$	8752.57			0.364056
$834$	6144.29	−	10642.2i	0.255107	−	0.441859i
$835$	−13663.6	+	23666.0i	−0.566284	+	0.980833i
$836$	−1748.45	−	3028.40i	−0.0723342	−	0.125286i
$837$	−10857.0			−0.448356
$838$	−15194.9	−	26318.3i	−0.626370	−	1.08490i
$839$	9340.06	+	16177.5i	0.384332	+	0.665683i	0.991676	−	0.128756i	$-0.0410984\pi$
$839$	9340.06	+	16177.5i	0.384332	+	0.665683i	−0.607344	+	0.794439i	$0.707765\pi$
$840$	1050.74			0.0431596
$841$	−33192.7	−	57491.4i	−1.36097	−	2.35727i
$842$	10154.8	−	17588.5i	0.415625	−	0.719883i
$843$	10009.4	−	17336.8i	0.408947	−	0.708317i
$844$	10673.7			0.435312
$845$		0			0
$846$	−15973.5			−0.649147
$847$	6180.94	−	10705.7i	0.250743	−	0.434300i
$848$	2155.69	−	3733.77i	0.0872958	−	0.151201i
$849$	−1459.86	−	2528.55i	−0.0590132	−	0.102214i
$850$	2809.93			0.113388
$851$	9498.26	+	16451.5i	0.382604	+	0.662690i
$852$	483.486	+	837.423i	0.0194413	+	0.0336733i
$853$	−24129.9			−0.968574			−0.484287	−	0.874909i	$-0.660921\pi$
$853$	−24129.9			−0.968574			−0.484287	+	0.874909i	$0.660921\pi$
$854$	−1599.82	−	2770.98i	−0.0641040	−	0.111031i
$855$	−773.972	+	1340.56i	−0.0309582	+	0.0536212i
$856$	−1564.24	+	2709.35i	−0.0624588	+	0.108182i
$857$	−7739.30			−0.308482			−0.154241	−	0.988033i	$-0.549293\pi$
$857$	−7739.30			−0.308482			−0.154241	+	0.988033i	$0.549293\pi$
$858$		0			0
$859$	4302.59			0.170899			0.0854496	−	0.996342i	$-0.472767\pi$
$859$	4302.59			0.170899			0.0854496	+	0.996342i	$0.472767\pi$
$860$	6082.59	−	10535.4i	0.241180	−	0.417736i
$861$	3332.54	−	5772.13i	0.131908	−	0.228471i
$862$	−6616.84	−	11460.7i	−0.261451	−	0.452846i
$863$	16253.2			0.641096			0.320548	−	0.947232i	$-0.396133\pi$
$863$	16253.2			0.641096			0.320548	+	0.947232i	$0.396133\pi$
$864$	−2378.87	−	4120.32i	−0.0936698	−	0.162241i
$865$	−8101.62	−	14032.4i	−0.318455	−	0.551580i
$866$	11395.2			0.447142
$867$	−7676.61	−	13296.3i	−0.300705	−	0.520836i
$868$	−613.548	+	1062.70i	−0.0239921	+	0.0415556i
$869$	−12599.4	+	21822.7i	−0.491834	+	0.851882i
$870$	18839.1			0.734144
$871$		0			0
$872$	10651.2			0.413642
$873$	8913.85	−	15439.2i	0.345576	−	0.598556i
$874$	2138.73	−	3704.38i	0.0827728	−	0.143367i
$875$	−3175.73	−	5500.52i	−0.122696	−	0.212516i
$876$	−12981.2			−0.500680
$877$	−4720.67	−	8176.43i	−0.181762	−	0.314822i	0.760718	−	0.649082i	$-0.224847\pi$
$877$	−4720.67	−	8176.43i	−0.181762	−	0.314822i	−0.942481	+	0.334260i	$0.891513\pi$
$878$	−436.007	−	755.186i	−0.0167591	−	0.0290277i
$879$	−6220.48			−0.238693
$880$	4461.44	+	7727.44i	0.170903	+	0.296014i
$881$	5936.22	−	10281.8i	0.227011	−	0.393194i	−0.729910	−	0.683543i	$-0.760438\pi$
$881$	5936.22	−	10281.8i	0.227011	−	0.393194i	0.956921	+	0.290349i	$0.0937714\pi$
$882$	−4414.59	+	7646.30i	−0.168534	+	0.291910i
$883$	−493.891			−0.0188231			−0.00941153	−	0.999956i	$-0.502996\pi$
$883$	−493.891			−0.0188231			−0.00941153	+	0.999956i	$0.502996\pi$
$884$		0			0
$885$	−7201.40			−0.273528
$886$	−6609.58	+	11448.1i	−0.250624	+	0.434094i
$887$	−10271.8	+	17791.3i	−0.388832	+	0.673477i	−0.992293	−	0.123916i	$-0.960455\pi$
$887$	−10271.8	+	17791.3i	−0.388832	+	0.673477i	0.603461	+	0.797393i	$0.293788\pi$
$888$	−1741.27	−	3015.96i	−0.0658031	−	0.113974i
$889$	4922.38			0.185705
$890$	3178.68	+	5505.64i	0.119719	+	0.207359i
$891$	−5835.67	−	10107.7i	−0.219419	−	0.380045i
$892$	−1145.43			−0.0429953
$893$	3935.76	+	6816.93i	0.147486	+	0.255453i
$894$	−3287.25	+	5693.68i	−0.122978	+	0.213004i
$895$	−11307.1	+	19584.5i	−0.422296	+	0.731438i
$896$	−537.734			−0.0200496
$897$		0			0
$898$	−16030.6			−0.595711
$899$	−11000.5	+	19053.4i	−0.408106	+	0.706860i
$900$	−1417.26	+	2454.77i	−0.0524913	+	0.0909176i
$901$	−3624.52	−	6277.85i	−0.134018	−	0.232126i
$902$	56599.7			2.08932
$903$	2744.45	+	4753.53i	0.101140	+	0.175180i
$904$	2847.65	+	4932.27i	0.104769	+	0.181466i
$905$	−19535.0			−0.717532
$906$	−7616.64	−	13192.4i	−0.279300	−	0.483762i
$907$	2693.30	−	4664.94i	0.0985994	−	0.170779i	−0.812506	−	0.582953i	$-0.801897\pi$
$907$	2693.30	−	4664.94i	0.0985994	−	0.170779i	0.911105	+	0.412174i	$0.135230\pi$
$908$	−10402.5	+	18017.6i	−0.380196	+	0.658520i
$909$	−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	$0.303780\pi$
$912$	−392.082	+	679.106i	−0.0142359	+	0.0246573i
$913$	−8309.08	+	14391.8i	−0.301194	+	0.521684i
$914$	−4507.03	−	7806.41i	−0.163107	−	0.282509i
$915$	11905.9			0.430162
$916$	−1780.92	−	3084.64i	−0.0642392	−	0.111266i
$917$	−2370.67	−	4106.12i	−0.0853723	−	0.147869i
$918$	−7999.51			−0.287607
$919$	21495.7	+	37231.6i	0.771575	+	1.33641i	0.936700	+	0.350134i	$0.113864\pi$
$919$	21495.7	+	37231.6i	0.771575	+	1.33641i	−0.165125	+	0.986273i	$0.552803\pi$
$920$	−5457.29	+	9452.30i	−0.195567	+	0.338732i
$921$	−17199.0	+	29789.5i	−0.615338	+	1.06580i
$922$	−4207.10			−0.150275
$923$		0			0
$924$	−4025.98			−0.143339
$925$	−3101.70	+	5372.30i	−0.110252	+	0.190962i
$926$	5468.28	−	9471.34i	0.194059	−	0.336121i
$927$	1430.72	+	2478.09i	0.0506916	+	0.0878004i
$928$	−9641.21			−0.341043
$929$	−20338.3	−	35227.0i	−0.718277	−	1.24409i	−0.961682	−	0.274168i	$-0.911598\pi$
$929$	−20338.3	−	35227.0i	−0.718277	−	1.24409i	0.243405	−	0.969925i	$-0.421736\pi$
$930$	−2283.02	−	3954.30i	−0.0804980	−	0.139427i
$931$	4350.91			0.153164
$932$	−9506.22	−	16465.3i	−0.334106	−	0.578688i
$933$	−6015.25	+	10418.7i	−0.211072	+	0.365588i
$934$	6043.79	−	10468.2i	0.211733	−	0.366733i
$935$	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	$0.380649\pi$
$938$	1831.02	−	3171.42i	0.0637365	−	0.110395i
$939$	−10856.6	+	18804.2i	−0.377307	+	0.653515i
$940$	−10042.7	−	17394.5i	−0.348465	−	0.603558i
$941$	−4525.50			−0.156777			−0.0783885	−	0.996923i	$-0.524977\pi$
$941$	−4525.50			−0.156777			−0.0783885	+	0.996923i	$0.524977\pi$
$942$	−12807.8	−	22183.8i	−0.442994	−	0.767289i
$943$	34616.7	+	59958.0i	1.19542	+	2.07052i
$944$	3685.43			0.127066
$945$	2664.20	+	4614.53i	0.0917106	+	0.158847i
$946$	−23305.8	+	40366.9i	−0.800991	+	1.38736i
$947$	13700.8	−	23730.5i	0.470134	−	0.814295i	−0.529283	−	0.848445i	$-0.677539\pi$
$947$	13700.8	−	23730.5i	0.470134	−	0.814295i	0.999417	+	0.0341499i	$0.0108724\pi$
$948$	5650.70			0.193593
$949$		0			0
$950$	1396.82			0.0477040
$951$	−11852.0	+	20528.2i	−0.404129	+	0.699973i
$952$	−452.065	+	782.999i	−0.0153902	+	0.0266567i
$953$	−13113.1	−	22712.6i	−0.445725	−	0.772017i	0.552378	−	0.833594i	$-0.313721\pi$
$953$	−13113.1	−	22712.6i	−0.445725	−	0.772017i	−0.998102	+	0.0615763i	$0.980387\pi$
$954$	7312.49			0.248166
$955$	1443.04	+	2499.42i	0.0488960	+	0.0846904i
$956$	4585.24	+	7941.87i	0.155123	+	0.268680i
$957$	−72183.2			−2.43819
$958$	−8481.30	−	14690.0i	−0.286032	−	0.495421i
$959$	−3671.58	+	6359.36i	−0.123630	+	0.214134i
$960$	1000.46	−	1732.84i	0.0336350	−	0.0582576i
$961$	−24458.6			−0.821007
$962$		0			0
$963$	−5306.19			−0.177559
$964$	−3950.42	+	6842.32i	−0.131986	+	0.228606i
$965$	−11448.5	+	19829.5i	−0.381909	+	0.661485i
$966$	−2462.32	−	4264.86i	−0.0820122	−	0.142049i
$967$	20843.6			0.693158			0.346579	−	0.938021i	$-0.387343\pi$
$967$	20843.6			0.693158			0.346579	+	0.938021i	$0.387343\pi$
$968$	−11770.3	−	20386.7i	−0.390817	−	0.676916i
$969$	659.234	+	1141.83i	0.0218552	+	0.0378542i
$970$	22417.0			0.742026
$971$	−16288.6	−	28212.7i	−0.538339	−	0.932430i	−0.998994	−	0.0448508i	$-0.985719\pi$
$971$	−16288.6	−	28212.7i	−0.538339	−	0.932430i	0.460655	−	0.887579i	$-0.347615\pi$
$972$	6720.05	−	11639.5i	0.221755	−	0.384091i
$973$	3521.60	−	6099.59i	0.116030	−	0.200970i
$974$	13246.7			0.435782
$975$		0			0
$976$	−6093.05			−0.199830
$977$	21932.0	−	37987.4i	0.718186	−	1.24394i	−0.243531	−	0.969893i	$-0.578306\pi$
$977$	21932.0	−	37987.4i	0.718186	−	1.24394i	0.961718	−	0.274042i	$-0.0883608\pi$
$978$	−1653.79	+	2864.45i	−0.0540719	+	0.0936553i
$979$	−12179.3	−	21095.2i	−0.397602	−	0.688667i
$980$	−11102.0			−0.361879
$981$	9032.70	+	15645.1i	0.293977	+	0.509184i
$982$	−16379.4	−	28369.9i	−0.532267	−	0.921914i
$983$	−14758.8			−0.478875			−0.239437	−	0.970912i	$-0.576963\pi$
$983$	−14758.8			−0.478875			−0.239437	+	0.970912i	$0.576963\pi$
$984$	−6346.12	−	10991.8i	−0.205596	−	0.356103i
$985$	−8092.48	+	14016.6i	−0.261775	+	0.453407i
$986$	−8105.21	+	14038.6i	−0.261788	+	0.453430i
$987$	9062.49			0.292262
$988$		0			0
$989$	−57016.0			−1.83317
$990$	−7566.99	+	13106.4i	−0.242924	+	0.420757i
$991$	−24311.2	+	42108.2i	−0.779284	+	1.34976i	0.153071	+	0.988215i	$0.451084\pi$
$991$	−24311.2	+	42108.2i	−0.779284	+	1.34976i	−0.932355	+	0.361544i	$0.882250\pi$
$992$	1168.37	+	2023.68i	0.0373950	+	0.0647700i
$993$	12860.9			0.411006
$994$	277.110	+	479.969i	0.00884246	+	0.0153156i
$995$	10303.5	+	17846.2i	0.328285	+	0.568606i
$996$	3726.55			0.118554
$997$	9406.17	+	16292.0i	0.298793	+	0.517525i	0.975860	−	0.218397i	$-0.0700827\pi$
$997$	9406.17	+	16292.0i	0.298793	+	0.517525i	−0.677067	+	0.735921i	$0.736749\pi$
$998$	−7915.70	+	13710.4i	−0.251069	+	0.434865i
$999$	8830.12	−	15294.2i	0.279652	−	0.484372i

Twists

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

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

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.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.83244 - 3.17387i) q^{3} +(-2.00000 - 3.46410i) q^{4} +8.53079 q^{5} +(3.66487 + 6.34775i) q^{6} +(2.10052 + 3.63821i) q^{7} +8.00000 q^{8} +(6.78435 + 11.7508i) q^{9} +(-8.53079 + 14.7758i) q^{10} +(32.6863 - 56.6143i) q^{11} -14.6595 q^{12} -8.40209 q^{14} +(15.6321 - 27.0757i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(13.4510 + 23.2977i) q^{17} -27.1374 q^{18} +(6.68648 + 11.5813i) q^{19} +(-17.0616 - 29.5515i) q^{20} +15.3963 q^{21} +(65.3726 + 113.229i) q^{22} +(-79.9645 + 138.503i) q^{23} +(14.6595 - 25.3910i) q^{24} -52.2255 q^{25} +148.679 q^{27} +(8.40209 - 14.5529i) q^{28} +(150.644 - 260.923i) q^{29} +(31.2643 + 54.1513i) q^{30} -73.0232 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-119.791 - 207.484i) q^{33} -53.8038 q^{34} +(17.9191 + 31.0368i) q^{35} +(27.1374 - 47.0033i) q^{36} +(59.3904 - 102.867i) q^{37} -26.7459 q^{38} +68.2464 q^{40} +(216.451 - 374.903i) q^{41} +(-15.3963 + 26.6672i) q^{42} +(178.254 + 308.745i) q^{43} -261.490 q^{44} +(57.8759 + 100.244i) q^{45} +(-159.929 - 277.005i) q^{46} +588.614 q^{47} +(29.3190 + 50.7820i) q^{48} +(162.676 - 281.762i) q^{49} +(52.2255 - 90.4573i) q^{50} +98.5921 q^{51} -269.462 q^{53} +(-148.679 + 257.520i) q^{54} +(278.840 - 482.965i) q^{55} +(16.8042 + 29.1057i) q^{56} +49.0102 q^{57} +(301.288 + 521.846i) q^{58} +(-115.170 - 199.480i) q^{59} -125.057 q^{60} +(190.408 + 329.796i) q^{61} +(73.0232 - 126.480i) q^{62} +(-28.5014 + 49.3658i) q^{63} +64.0000 q^{64} +479.164 q^{66} +(-217.924 + 377.456i) q^{67} +(53.8038 - 93.1909i) q^{68} +(293.060 + 507.595i) q^{69} -71.6765 q^{70} +(-32.9811 - 57.1249i) q^{71} +(54.2748 + 94.0067i) q^{72} +885.517 q^{73} +(118.781 + 205.735i) q^{74} +(-95.7000 + 165.757i) q^{75} +(26.7459 - 46.3253i) q^{76} +274.633 q^{77} -385.463 q^{79} +(-68.2464 + 118.206i) q^{80} +(89.2679 - 154.616i) q^{81} +(432.901 + 749.807i) q^{82} -254.207 q^{83} +(-30.7926 - 53.3344i) q^{84} +(114.747 + 198.748i) q^{85} -713.016 q^{86} +(-552.091 - 956.250i) q^{87} +(261.490 - 452.914i) q^{88} +(186.306 - 322.692i) q^{89} -231.504 q^{90} +639.716 q^{92} +(-133.810 + 231.766i) q^{93} +(-588.614 + 1019.51i) q^{94} +(57.0410 + 98.7979i) q^{95} -117.276 q^{96} +(-656.942 - 1137.86i) q^{97} +(325.351 + 563.525i) q^{98} +887.020 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 12 q^{3} - 12 q^{4} - 24 q^{5} + 24 q^{6} - 27 q^{7} + 48 q^{8} - 9 q^{9} + 24 q^{10} + 82 q^{11} - 96 q^{12} + 108 q^{14} - 90 q^{15} - 48 q^{16} + 90 q^{17} + 36 q^{18} + 130 q^{19} + 48 q^{20}+ \cdots + 4114 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 + 12 * q^3 - 12 * q^4 - 24 * q^5 + 24 * q^6 - 27 * q^7 + 48 * q^8 - 9 * q^9 + 24 * q^10 + 82 * q^11 - 96 * q^12 + 108 * q^14 - 90 * q^15 - 48 * q^16 + 90 * q^17 + 36 * q^18 + 130 * q^19 + 48 * q^20 - 468 * q^21 + 164 * q^22 - 19 * q^23 + 96 * q^24 - 122 * q^25 - 138 * q^27 - 108 * q^28 + 101 * q^29 - 180 * q^30 - 1038 * q^31 - 96 * q^32 - 146 * q^33 - 360 * q^34 + 458 * q^35 - 36 * q^36 + 84 * q^37 - 520 * q^38 - 192 * q^40 + 187 * q^41 + 468 * q^42 + 1205 * q^43 - 656 * q^44 + 645 * q^45 - 38 * q^46 + 1072 * q^47 + 192 * q^48 + 184 * q^49 + 122 * q^50 - 414 * q^51 - 2190 * q^53 + 138 * q^54 + 526 * q^55 - 216 * q^56 + 2818 * q^57 + 202 * q^58 - 1413 * q^59 + 720 * q^60 + 1108 * q^61 + 1038 * q^62 - 1404 * q^63 + 384 * q^64 + 584 * q^66 - 1605 * q^67 + 360 * q^68 + 314 * q^69 - 1832 * q^70 - 909 * q^71 - 72 * q^72 - 574 * q^73 + 168 * q^74 + 505 * q^75 + 520 * q^76 + 960 * q^77 - 3922 * q^79 + 192 * q^80 - 915 * q^81 + 374 * q^82 - 382 * q^83 + 936 * q^84 + 67 * q^85 - 4820 * q^86 - 1636 * q^87 + 656 * q^88 + 1091 * q^89 - 2580 * q^90 + 152 * q^92 - 1614 * q^93 - 1072 * q^94 - 1829 * q^95 - 768 * q^96 - 947 * q^97 + 368 * q^98 + 4114 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more