LMFDB - Embedded newform 147.4.c.a.146.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,4,Mod(146,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("147.146");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, 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:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 29x^{9} + 6x^{8} - 49x^{7} + 1564x^{6} - 441x^{5} + 486x^{4} - 21141x^{3} - 59049x + 531441 $ x^12 - x^11 - 29x^9 + 6x^8 - 49x^7 + 1564x^6 - 441x^5 + 486x^4 - 21141x^3 - 59049x + 531441
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.10
Root			$0.00299931 + 3.00000i$ of defining polynomial
Character	$\chi$	$=$	147.146
Dual form			147.4.c.a.146.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.58741i q^{2} +(2.60257 - 4.49740i) q^{3} +1.30532 q^{4} +16.1181 q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} +O(q^{10})$	\(q+2.58741i q^{2} +(2.60257 - 4.49740i) q^{3} +1.30532 q^{4} +16.1181 q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} +41.7042i q^{10} -35.5990i q^{11} +(3.39719 - 5.87054i) q^{12} -7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} -51.8536 q^{16} +28.9202 q^{17} +(60.5703 - 34.8090i) q^{18} +35.1698i q^{19} +21.0393 q^{20} +92.1090 q^{22} +55.4275i q^{23} +(108.282 + 62.6613i) q^{24} +134.794 q^{25} +19.1683 q^{26} +(-140.295 - 0.420792i) q^{27} -68.1510i q^{29} +(187.560 + 108.538i) q^{30} +178.671i q^{31} +58.4469i q^{32} +(-160.103 - 92.6489i) q^{33} +74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} -233.676 q^{37} -90.9987 q^{38} +(-33.3181 - 19.2807i) q^{39} +388.071i q^{40} +370.068 q^{41} -187.068 q^{43} -46.4680i q^{44} +(-216.841 - 377.320i) q^{45} -143.414 q^{46} +174.745 q^{47} +(-134.953 + 233.206i) q^{48} +348.768i q^{50} +(75.2671 - 130.066i) q^{51} -9.67022i q^{52} +272.180i q^{53} +(1.08876 - 363.002i) q^{54} -573.789i q^{55} +(158.173 + 91.5321i) q^{57} +176.334 q^{58} +96.8709 q^{59} +(54.7564 - 94.6222i) q^{60} -385.534i q^{61} -462.295 q^{62} -566.055 q^{64} -119.408i q^{65} +(239.721 - 414.251i) q^{66} -1018.02 q^{67} +37.7502 q^{68} +(249.280 + 144.254i) q^{69} -125.333i q^{71} +(563.626 - 323.909i) q^{72} -225.566i q^{73} -604.616i q^{74} +(350.812 - 606.223i) q^{75} +45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} -1064.31 q^{79} -835.783 q^{80} +(-367.022 + 629.870i) q^{81} +957.517i q^{82} -601.040 q^{83} +466.140 q^{85} -484.021i q^{86} +(-306.502 - 177.368i) q^{87} +857.104 q^{88} -1505.21 q^{89} +(976.280 - 561.055i) q^{90} +72.3506i q^{92} +(803.556 + 465.005i) q^{93} +452.137i q^{94} +566.872i q^{95} +(262.859 + 152.112i) q^{96} +327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) $ 12 * q - 28 * q^4 + 6 * q^9	$ 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) $ 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$			2.58741i			0.914787i	0.889264	+	0.457393i	$0.151217\pi$
$2$			2.58741i			0.914787i	−0.889264	+	0.457393i	$0.848783\pi$
$3$	2.60257	−	4.49740i	0.500866	−	0.865525i
$3$	2.60257	−	4.49740i	0.500866	−	0.865525i
$4$	1.30532			0.163165
$5$	16.1181			1.44165			0.720825	−	0.693117i	$-0.243763\pi$
$5$	16.1181			1.44165			0.720825	+	0.693117i	$0.243763\pi$
$6$	11.6366	+	6.73392i	0.791771	+	0.458185i
$7$		0			0
$7$		0			0
$8$			24.0767i			1.06405i
$9$	−13.4532	−	23.4096i	−0.498267	−	0.867023i
$10$			41.7042i			1.31880i
$11$		−	35.5990i		−	0.975772i	−0.872907	−	0.487886i	$-0.837768\pi$
$11$		−	35.5990i		−	0.975772i	0.872907	−	0.487886i	$-0.162232\pi$
$12$	3.39719	−	5.87054i	0.0817237	−	0.141223i
$13$		−	7.40831i		−	0.158054i	−0.996872	−	0.0790268i	$-0.974819\pi$
$13$		−	7.40831i		−	0.158054i	0.996872	−	0.0790268i	$-0.0251813\pi$
$14$		0			0
$15$	41.9486	−	72.4897i	0.722073	−	1.24778i
$16$	−51.8536			−0.810212
$17$	28.9202			0.412599			0.206300	−	0.978489i	$-0.433858\pi$
$17$	28.9202			0.412599			0.206300	+	0.978489i	$0.433858\pi$
$18$	60.5703	−	34.8090i	0.793142	−	0.455808i
$19$			35.1698i			0.424659i	0.977198	+	0.212329i	$0.0681050\pi$
$19$			35.1698i			0.424659i	−0.977198	+	0.212329i	$0.931895\pi$
$20$	21.0393			0.235227
$21$		0			0
$22$	92.1090			0.892623
$23$			55.4275i			0.502497i	0.967923	+	0.251249i	$0.0808412\pi$
$23$			55.4275i			0.502497i	−0.967923	+	0.251249i	$0.919159\pi$
$24$	108.282	+	62.6613i	0.920960	+	0.532945i
$25$	134.794			1.07835
$26$	19.1683			0.144585
$27$	−140.295	−	0.420792i	−0.999996	−	0.00299931i
$28$		0			0
$29$		−	68.1510i		−	0.436390i	−0.975905	−	0.218195i	$-0.929983\pi$
$29$		−	68.1510i		−	0.436390i	0.975905	−	0.218195i	$-0.0700169\pi$
$30$	187.560	+	108.538i	1.14146	+	0.660543i
$31$			178.671i			1.03517i	0.855632	+	0.517585i	$0.173169\pi$
$31$			178.671i			1.03517i	−0.855632	+	0.517585i	$0.826831\pi$
$32$			58.4469i			0.322877i
$33$	−160.103	−	92.6489i	−0.844555	−	0.488730i
$34$			74.8285i			0.377440i
$35$		0			0
$36$	−17.5608	−	30.5571i	−0.0812998	−	0.141468i
$37$	−233.676			−1.03827			−0.519137	−	0.854691i	$-0.673747\pi$
$37$	−233.676			−1.03827			−0.519137	+	0.854691i	$0.673747\pi$
$38$	−90.9987			−0.388472
$39$	−33.3181	−	19.2807i	−0.136799	−	0.0791636i
$40$			388.071i			1.53398i
$41$	370.068			1.40963			0.704816	−	0.709390i	$-0.251030\pi$
$41$	370.068			1.40963			0.704816	+	0.709390i	$0.251030\pi$
$42$		0			0
$43$	−187.068			−0.663432			−0.331716	−	0.943379i	$-0.607628\pi$
$43$	−187.068			−0.663432			−0.331716	+	0.943379i	$0.607628\pi$
$44$		−	46.4680i		−	0.159212i
$45$	−216.841	−	377.320i	−0.718327	−	1.24994i
$46$	−143.414			−0.459678
$47$	174.745			0.542324			0.271162	−	0.962534i	$-0.412592\pi$
$47$	174.745			0.542324			0.271162	+	0.962534i	$0.412592\pi$
$48$	−134.953	+	233.206i	−0.405807	+	0.701259i
$49$		0			0
$50$			348.768i			0.986464i
$51$	75.2671	−	130.066i	0.206657	−	0.357115i
$52$		−	9.67022i		−	0.0257888i
$53$			272.180i			0.705412i	0.935734	+	0.352706i	$0.114738\pi$
$53$			272.180i			0.705412i	−0.935734	+	0.352706i	$0.885262\pi$
$54$	1.08876	−	363.002i	0.00274373	−	0.914783i
$55$		−	573.789i		−	1.40672i
$56$		0			0
$57$	158.173	+	91.5321i	0.367553	+	0.212697i
$58$	176.334			0.399204
$59$	96.8709			0.213754			0.106877	−	0.994272i	$-0.465915\pi$
$59$	96.8709			0.213754			0.106877	+	0.994272i	$0.465915\pi$
$60$	54.7564	−	94.6222i	0.117817	−	0.203595i
$61$		−	385.534i		−	0.809223i	−0.914489	−	0.404611i	$-0.867407\pi$
$61$		−	385.534i		−	0.809223i	0.914489	−	0.404611i	$-0.132593\pi$
$62$	−462.295			−0.946960
$63$		0			0
$64$	−566.055			−1.10558
$65$		−	119.408i		−	0.227858i
$66$	239.721	−	414.251i	0.447084	−	0.772588i
$67$	−1018.02			−1.85628			−0.928140	−	0.372231i	$-0.878593\pi$
$67$	−1018.02			−1.85628			−0.928140	+	0.372231i	$0.878593\pi$
$68$	37.7502			0.0673218
$69$	249.280	+	144.254i	0.434924	+	0.251684i
$70$		0			0
$71$		−	125.333i		−	0.209497i	−0.994499	−	0.104749i	$-0.966596\pi$
$71$		−	125.333i		−	0.209497i	0.994499	−	0.104749i	$-0.0334038\pi$
$72$	563.626	−	323.909i	0.922555	−	0.530180i
$73$		−	225.566i		−	0.361651i	−0.983515	−	0.180825i	$-0.942123\pi$
$73$		−	225.566i		−	0.361651i	0.983515	−	0.180825i	$-0.0578768\pi$
$74$		−	604.616i		−	0.949800i
$75$	350.812	−	606.223i	0.540110	−	0.933342i
$76$			45.9079i			0.0692894i
$77$		0			0
$78$	49.8870	−	86.2076i	0.0724178	−	0.125142i
$79$	−1064.31			−1.51575			−0.757874	−	0.652401i	$-0.773762\pi$
$79$	−1064.31			−1.51575			−0.757874	+	0.652401i	$0.773762\pi$
$80$	−835.783			−1.16804
$81$	−367.022	+	629.870i	−0.503459	+	0.864019i
$82$			957.517i			1.28951i
$83$	−601.040			−0.794852			−0.397426	−	0.917634i	$-0.630096\pi$
$83$	−601.040			−0.794852			−0.397426	+	0.917634i	$0.630096\pi$
$84$		0			0
$85$	466.140			0.594824
$86$		−	484.021i		−	0.606899i
$87$	−306.502	−	177.368i	−0.377707	−	0.218573i
$88$	857.104			1.03827
$89$	−1505.21			−1.79272			−0.896360	−	0.443327i	$-0.853798\pi$
$89$	−1505.21			−1.79272			−0.896360	+	0.443327i	$0.853798\pi$
$90$	976.280	−	561.055i	1.14343	−	0.657116i
$91$		0			0
$92$			72.3506i			0.0819900i
$93$	803.556	+	465.005i	0.895966	+	0.518481i
$94$			452.137i			0.496111i
$95$			566.872i			0.612209i
$96$	262.859	+	152.112i	0.279458	+	0.161718i
$97$			327.463i			0.342771i	0.985204	+	0.171386i	$0.0548244\pi$
$97$			327.463i			0.342771i	−0.985204	+	0.171386i	$0.945176\pi$
$98$		0			0
$99$	−833.358	+	478.920i	−0.846017	+	0.486195i
$100$	175.949			0.175949
$101$	1095.69			1.07946			0.539729	−	0.841839i	$-0.318527\pi$
$101$	1095.69			1.07946			0.539729	+	0.841839i	$0.318527\pi$
$102$	336.534	+	194.747i	0.326684	+	0.189047i
$103$			207.670i			0.198664i	0.995054	+	0.0993318i	$0.0316705\pi$
$103$			207.670i			0.198664i	−0.995054	+	0.0993318i	$0.968329\pi$
$104$	178.367			0.168177
$105$		0			0
$106$	−704.242			−0.645302
$107$			1802.78i			1.62880i	0.580305	+	0.814399i	$0.302933\pi$
$107$			1802.78i			1.62880i	−0.580305	+	0.814399i	$0.697067\pi$
$108$	−183.130	−	0.549267i	−0.163164	−	0.000489382i
$109$	283.649			0.249254			0.124627	−	0.992204i	$-0.460227\pi$
$109$	283.649			0.249254			0.124627	+	0.992204i	$0.460227\pi$
$110$	1484.63			1.28685
$111$	−608.160	+	1050.94i	−0.520036	+	0.898652i
$112$		0			0
$113$		−	1037.39i		−	0.863627i	−0.901963	−	0.431814i	$-0.857874\pi$
$113$		−	1037.39i		−	0.863627i	0.901963	−	0.431814i	$-0.142126\pi$
$114$	−236.831	+	409.258i	−0.194572	+	0.336232i
$115$			893.388i			0.724425i
$116$		−	88.9588i		−	0.0712036i
$117$	−173.426	+	99.6657i	−0.137036	+	0.0787529i
$118$			250.644i			0.195540i
$119$		0			0
$120$	1745.31	+	1009.98i	1.32770	+	0.768320i
$121$	63.7146			0.0478697
$122$	997.534			0.740266
$123$	963.129	−	1664.34i	0.706036	−	1.22007i
$124$			233.223i			0.168904i
$125$	157.864			0.112958
$126$		0			0
$127$	1645.81			1.14994			0.574968	−	0.818176i	$-0.305015\pi$
$127$	1645.81			1.14994			0.574968	+	0.818176i	$0.305015\pi$
$128$		−	997.039i		−	0.688489i
$129$	−486.858	+	841.319i	−0.332290	+	0.574217i
$130$	308.958			0.208441
$131$	−628.369			−0.419091			−0.209545	−	0.977799i	$-0.567198\pi$
$131$	−628.369			−0.419091			−0.209545	+	0.977799i	$0.567198\pi$
$132$	−208.985	−	120.936i	−0.137802	−	0.0797437i
$133$		0			0
$134$		−	2634.03i		−	1.69810i
$135$	−2261.30	−	6.78237i	−1.44164	−	0.00432395i
$136$			696.303i			0.439026i
$137$		−	498.922i		−	0.311137i	−0.987825	−	0.155569i	$-0.950279\pi$
$137$		−	498.922i		−	0.311137i	0.987825	−	0.155569i	$-0.0497209\pi$
$138$	−373.245	+	644.989i	−0.230237	+	0.397863i
$139$		−	1216.65i		−	0.742410i	−0.928551	−	0.371205i	$-0.878945\pi$
$139$		−	1216.65i		−	0.742410i	0.928551	−	0.371205i	$-0.121055\pi$
$140$		0			0
$141$	454.788	−	785.900i	0.271631	−	0.469395i
$142$	324.288			0.191645
$143$	−263.728			−0.154224
$144$	697.598	+	1213.87i	0.403702	+	0.702473i
$145$		−	1098.47i		−	0.629122i
$146$	583.631			0.330833
$147$		0			0
$148$	−305.022			−0.169410
$149$		−	2321.16i		−	1.27622i	−0.769945	−	0.638111i	$-0.779716\pi$
$149$		−	2321.16i		−	1.27622i	0.769945	−	0.638111i	$-0.220284\pi$
$150$	1568.55	+	907.693i	0.853809	+	0.494086i
$151$	977.451			0.526780			0.263390	−	0.964689i	$-0.415159\pi$
$151$	977.451			0.526780			0.263390	+	0.964689i	$0.415159\pi$
$152$	−846.772			−0.451857
$153$	−389.070	−	677.012i	−0.205585	−	0.357733i
$154$		0			0
$155$			2879.85i			1.49235i
$156$	−43.4908	−	25.1675i	−0.0223209	−	0.0129167i
$157$			165.990i			0.0843786i	0.999110	+	0.0421893i	$0.0134333\pi$
$157$			165.990i			0.0843786i	−0.999110	+	0.0421893i	$0.986567\pi$
$158$		−	2753.80i		−	1.38659i
$159$	1224.10	+	708.369i	0.610552	+	0.353317i
$160$			942.055i			0.465475i
$161$		0			0
$162$	−1629.73	−	949.635i	−0.790393	−	0.460558i
$163$	977.023			0.469487			0.234743	−	0.972057i	$-0.424575\pi$
$163$	977.023			0.469487			0.234743	+	0.972057i	$0.424575\pi$
$164$	483.057			0.230002
$165$	−2580.56	−	1493.33i	−1.21755	−	0.704578i
$166$		−	1555.14i		−	0.727120i
$167$	1.00709			0.000466651			0.000233326	−	1.00000i	$-0.499926\pi$
$167$	1.00709			0.000466651			0.000233326		1.00000i	$0.499926\pi$
$168$		0			0
$169$	2142.12			0.975019
$170$			1206.10i			0.544137i
$171$	823.313	−	473.148i	0.368189	−	0.211594i
$172$	−244.183			−0.108249
$173$	3956.55			1.73879			0.869395	−	0.494117i	$-0.164509\pi$
$173$	3956.55			1.73879			0.869395	+	0.494117i	$0.164509\pi$
$174$	458.923	−	793.046i	0.199948	−	0.345521i
$175$		0			0
$176$			1845.93i			0.790582i
$177$	252.114	−	435.667i	0.107062	−	0.185010i
$178$		−	3894.60i		−	1.63996i
$179$			2798.47i			1.16853i	0.811562	+	0.584266i	$0.198617\pi$
$179$			2798.47i			1.16853i	−0.811562	+	0.584266i	$0.801383\pi$
$180$	−283.046	−	492.523i	−0.117206	−	0.203947i
$181$			1506.74i			0.618758i	0.950939	+	0.309379i	$0.100121\pi$
$181$			1506.74i			0.618758i	−0.950939	+	0.309379i	$0.899879\pi$
$182$		0			0
$183$	−1733.90	−	1003.38i	−0.700403	−	0.405312i
$184$	−1334.51			−0.534681
$185$	−3766.43			−1.49683
$186$	−1203.16	+	2079.13i	−0.474300	+	0.819618i
$187$		−	1029.53i		−	0.402603i
$188$	228.098			0.0884882
$189$		0			0
$190$	−1466.73			−0.560041
$191$			3677.16i			1.39304i	0.717539	+	0.696518i	$0.245268\pi$
$191$			3677.16i			1.39304i	−0.717539	+	0.696518i	$0.754732\pi$
$192$	−1473.20	+	2545.77i	−0.553745	+	0.956903i
$193$	−129.467			−0.0482862			−0.0241431	−	0.999709i	$-0.507686\pi$
$193$	−129.467			−0.0482862			−0.0241431	+	0.999709i	$0.507686\pi$
$194$	−847.280			−0.313563
$195$	−537.026	−	310.769i	−0.197217	−	0.114126i
$196$		0			0
$197$			3044.81i			1.10119i	0.834774	+	0.550593i	$0.185598\pi$
$197$			3044.81i			1.10119i	−0.834774	+	0.550593i	$0.814402\pi$
$198$	−1239.16	−	2156.24i	−0.444765	−	0.773925i
$199$		−	3993.29i		−	1.42250i	−0.702941	−	0.711248i	$-0.748130\pi$
$199$		−	3993.29i		−	1.42250i	0.702941	−	0.711248i	$-0.251870\pi$
$200$			3245.39i			1.14742i
$201$	−2649.47	+	4578.44i	−0.929747	+	1.60666i
$202$			2835.00i			0.987473i
$203$		0			0
$204$	98.2476	−	169.778i	0.0337191	−	0.0582687i
$205$	5964.80			2.03219
$206$	−537.327			−0.181735
$207$	1297.54	−	745.679i	0.435677	−	0.250378i
$208$			384.148i			0.128057i
$209$	1252.01			0.414370
$210$		0			0
$211$	−4383.67			−1.43026			−0.715129	−	0.698992i	$-0.753632\pi$
$211$	−4383.67			−1.43026			−0.715129	+	0.698992i	$0.753632\pi$
$212$			355.282i			0.115099i
$213$	−563.673	−	326.188i	−0.181325	−	0.104930i
$214$	−4664.53			−1.49000
$215$	−3015.19			−0.956437
$216$	10.1313	−	3377.85i	0.00319141	−	1.06404i
$217$		0			0
$218$			733.916i			0.228014i
$219$	−1014.46	−	587.052i	−0.313018	−	0.181138i
$220$		−	748.978i		−	0.229528i
$221$		−	214.250i		−	0.0652128i
$222$	−2719.20	−	1573.56i	−0.822076	−	0.475722i
$223$		−	4851.53i		−	1.45687i	−0.685114	−	0.728436i	$-0.740247\pi$
$223$		−	4851.53i		−	1.45687i	0.685114	−	0.728436i	$-0.259753\pi$
$224$		0			0
$225$	−1813.42	−	3155.48i	−0.537308	−	0.934958i
$226$	2684.16			0.790035
$227$	2368.10			0.692407			0.346203	−	0.938159i	$-0.387471\pi$
$227$	2368.10			0.692407			0.346203	+	0.938159i	$0.387471\pi$
$228$	206.466	+	119.479i	0.0599717	+	0.0347047i
$229$		−	4315.43i		−	1.24529i	−0.782504	−	0.622646i	$-0.786058\pi$
$229$		−	4315.43i		−	1.24529i	0.782504	−	0.622646i	$-0.213942\pi$
$230$	−2311.56			−0.662695
$231$		0			0
$232$	1640.85			0.464340
$233$		−	5573.72i		−	1.56715i	−0.621296	−	0.783576i	$-0.713393\pi$
$233$		−	5573.72i		−	1.56715i	0.621296	−	0.783576i	$-0.286607\pi$
$234$	−257.876	−	448.724i	−0.0720421	−	0.125359i
$235$	2816.57			0.781841
$236$	126.447			0.0348772
$237$	−2769.94	+	4786.62i	−0.759186	+	1.31192i
$238$		0			0
$239$		−	4683.70i		−	1.26763i	−0.773485	−	0.633814i	$-0.781488\pi$
$239$		−	4683.70i		−	1.26763i	0.773485	−	0.633814i	$-0.218512\pi$
$240$	−2175.19	+	3758.85i	−0.585032	+	1.01097i
$241$			2190.20i			0.585407i	0.956203	+	0.292703i	$0.0945549\pi$
$241$			2190.20i			0.585407i	−0.956203	+	0.292703i	$0.905445\pi$
$242$			164.856i			0.0437906i
$243$	1877.58	+	3289.93i	0.495665	+	0.868514i
$244$		−	503.245i		−	0.132037i
$245$		0			0
$246$	4306.34	+	2492.01i	1.11611	+	0.645872i
$247$	260.549			0.0671188
$248$	−4301.80			−1.10147
$249$	−1564.25	+	2703.12i	−0.398114	+	0.687964i
$250$			408.458i			0.103333i
$251$	2240.70			0.563473			0.281736	−	0.959492i	$-0.409090\pi$
$251$	2240.70			0.563473			0.281736	+	0.959492i	$0.409090\pi$
$252$		0			0
$253$	1973.16			0.490323
$254$			4258.38i			1.05195i
$255$	1213.16	−	2096.42i	0.297927	−	0.514835i
$256$	−1948.69			−0.475754
$257$	1111.57			0.269797			0.134898	−	0.990859i	$-0.456929\pi$
$257$	1111.57			0.269797			0.134898	+	0.990859i	$0.456929\pi$
$258$	−2176.84	−	1259.70i	−0.525287	−	0.303975i
$259$		0			0
$260$		−	155.866i		−	0.0371784i
$261$	−1595.39	+	916.850i	−0.378361	+	0.217439i
$262$		−	1625.85i		−	0.383379i
$263$		−	2058.67i		−	0.482673i	−0.970441	−	0.241337i	$-0.922414\pi$
$263$		−	2058.67i		−	0.482673i	0.970441	−	0.241337i	$-0.0775858\pi$
$264$	2230.68	−	3854.74i	0.520033	−	0.898647i
$265$			4387.04i			1.01696i
$266$		0			0
$267$	−3917.42	+	6769.54i	−0.897912	+	1.55164i
$268$	−1328.84			−0.302880
$269$	4829.24			1.09459			0.547294	−	0.836941i	$-0.315658\pi$
$269$	4829.24			1.09459			0.547294	+	0.836941i	$0.315658\pi$
$270$	17.5488	−	5850.91i	0.00395550	−	1.31880i
$271$		−	221.440i		−	0.0496366i	−0.999692	−	0.0248183i	$-0.992099\pi$
$271$		−	221.440i		−	0.0496366i	0.999692	−	0.0248183i	$-0.00790072\pi$
$272$	−1499.62			−0.334293
$273$		0			0
$274$	1290.91			0.284624
$275$		−	4798.53i		−	1.05223i
$276$	325.390	+	188.298i	0.0709644	+	0.0410660i
$277$	2467.15			0.535151			0.267576	−	0.963537i	$-0.413777\pi$
$277$	2467.15			0.535151			0.267576	+	0.963537i	$0.413777\pi$
$278$	3147.97			0.679147
$279$	4182.63	−	2403.70i	0.897517	−	0.515792i
$280$		0			0
$281$		−	4174.76i		−	0.886282i	−0.896452	−	0.443141i	$-0.853864\pi$
$281$		−	4174.76i		−	0.886282i	0.896452	−	0.443141i	$-0.146136\pi$
$282$	2033.44	+	1176.72i	0.429396	+	0.248485i
$283$			6499.11i			1.36513i	0.730825	+	0.682565i	$0.239136\pi$
$283$			6499.11i			1.36513i	−0.730825	+	0.682565i	$0.760864\pi$
$284$		−	163.600i		−	0.0341826i
$285$	2549.45	+	1475.33i	0.529882	+	0.306634i
$286$		−	682.372i		−	0.141082i
$287$		0			0
$288$	1368.22	−	786.299i	0.279942	−	0.160879i
$289$	−4076.62			−0.829762
$290$	2842.18			0.575512
$291$	1472.73	+	852.247i	0.296677	+	0.171682i
$292$		−	294.436i		−	0.0590087i
$293$	5637.32			1.12401			0.562007	−	0.827133i	$-0.310030\pi$
$293$	5637.32			1.12401			0.562007	+	0.827133i	$0.310030\pi$
$294$		0			0
$295$	1561.38			0.308159
$296$		−	5626.15i		−	1.10477i
$297$	−14.9797	+	4994.37i	−0.00292664	+	0.975767i
$298$	6005.79			1.16747
$299$	410.625			0.0794215
$300$	457.922	−	791.315i	0.0881270	−	0.152289i
$301$		0			0
$302$			2529.06i			0.481892i
$303$	2851.61	−	4927.75i	0.540663	−	0.934297i
$304$		−	1823.68i		−	0.344064i
$305$		−	6214.09i		−	1.16662i
$306$	1751.71	−	1006.68i	0.327250	−	0.188066i
$307$		−	3442.95i		−	0.640064i	−0.947407	−	0.320032i	$-0.896306\pi$
$307$		−	3442.95i		−	0.640064i	0.947407	−	0.320032i	$-0.103694\pi$
$308$		0			0
$309$	933.976	+	540.477i	0.171948	+	0.0995037i
$310$	−7451.33			−1.36519
$311$	151.465			0.0276166			0.0138083	−	0.999905i	$-0.495605\pi$
$311$	151.465			0.0276166			0.0138083	+	0.999905i	$0.495605\pi$
$312$	464.214	−	802.190i	0.0842339	−	0.145561i
$313$			9624.79i			1.73810i	0.494724	+	0.869050i	$0.335269\pi$
$313$			9624.79i			1.73810i	−0.494724	+	0.869050i	$0.664731\pi$
$314$	−429.484			−0.0771885
$315$		0			0
$316$	−1389.26			−0.247317
$317$			9083.95i			1.60948i	0.593627	+	0.804741i	$0.297696\pi$
$317$			9083.95i			1.60948i	−0.593627	+	0.804741i	$0.702304\pi$
$318$	−1832.84	+	3167.26i	−0.323209	+	0.558525i
$319$	−2426.10			−0.425817
$320$	−9123.74			−1.59385
$321$	8107.83	+	4691.87i	1.40977	+	0.815809i
$322$		0			0
$323$			1017.12i			0.175214i
$324$	−479.081	+	822.181i	−0.0821469	+	0.140978i
$325$		−	998.597i		−	0.170438i
$326$			2527.96i			0.429480i
$327$	738.218	−	1275.68i	0.124843	−	0.215735i
$328$			8910.00i			1.49992i
$329$		0			0
$330$	3863.85	−	6676.95i	0.644539	−	1.11380i
$331$	−1405.58			−0.233406			−0.116703	−	0.993167i	$-0.537233\pi$
$331$	−1405.58			−0.233406			−0.116703	+	0.993167i	$0.537233\pi$
$332$	−784.549			−0.129692
$333$	3143.70	+	5470.28i	0.517338	+	0.900208i
$334$			2.60575i			0.000426887i
$335$	−16408.6			−2.67611
$336$		0			0
$337$	7983.35			1.29045			0.645223	−	0.763994i	$-0.276764\pi$
$337$	7983.35			1.29045			0.645223	+	0.763994i	$0.276764\pi$
$338$			5542.53i			0.891935i
$339$	−4665.58	−	2699.90i	−0.747491	−	0.432561i
$340$	608.462			0.0970544
$341$	6360.51			1.01009
$342$	1224.23	+	2130.25i	0.193563	+	0.336815i
$343$		0			0
$344$		−	4503.97i		−	0.705924i
$345$	4017.92	+	2325.11i	0.627008	+	0.362840i
$346$			10237.2i			1.59062i
$347$		−	2619.33i		−	0.405225i	−0.979259	−	0.202612i	$-0.935057\pi$
$347$		−	2619.33i		−	0.405225i	0.979259	−	0.202612i	$-0.0649432\pi$
$348$	−400.083	−	231.522i	−0.0616285	−	0.0356634i
$349$		−	6032.33i		−	0.925224i	−0.886561	−	0.462612i	$-0.846912\pi$
$349$		−	6032.33i		−	0.925224i	0.886561	−	0.462612i	$-0.153088\pi$
$350$		0			0
$351$	−3.11736	+	1039.35i	−0.000474052	+	0.158053i
$352$	2080.65			0.315054
$353$	5316.31			0.801582			0.400791	−	0.916170i	$-0.368735\pi$
$353$	5316.31			0.801582			0.400791	+	0.916170i	$0.368735\pi$
$354$	1127.25	+	652.321i	0.169245	+	0.0979392i
$355$		−	2020.13i		−	0.302021i
$356$	−1964.78			−0.292509
$357$		0			0
$358$	−7240.77			−1.06896
$359$			1861.96i			0.273735i	0.990589	+	0.136867i	$0.0437034\pi$
$359$			1861.96i			0.273735i	−0.990589	+	0.136867i	$0.956297\pi$
$360$	9084.59	−	5220.80i	1.33000	−	0.764334i
$361$	5622.08			0.819665
$362$	−3898.55			−0.566032
$363$	165.822	−	286.550i	0.0239763	−	0.0414325i
$364$		0			0
$365$		−	3635.70i		−	0.521373i
$366$	2596.16	−	4486.31i	0.370774	−	0.640719i
$367$			1935.15i			0.275242i	0.990485	+	0.137621i	$0.0439456\pi$
$367$			1935.15i			0.275242i	−0.990485	+	0.137621i	$0.956054\pi$
$368$		−	2874.12i		−	0.407130i
$369$	−4978.60	−	8663.15i	−0.702373	−	1.22218i
$370$		−	9745.28i		−	1.36928i
$371$		0			0
$372$	1048.90	+	606.980i	0.146190	+	0.0845980i
$373$	7742.08			1.07472			0.537359	−	0.843354i	$-0.319422\pi$
$373$	7742.08			1.07472			0.537359	+	0.843354i	$0.319422\pi$
$374$	2663.81			0.368296
$375$	410.852	−	709.977i	0.0565768	−	0.0977681i
$376$			4207.28i			0.577059i
$377$	−504.884			−0.0689730
$378$		0			0
$379$	−3722.15			−0.504470			−0.252235	−	0.967666i	$-0.581166\pi$
$379$	−3722.15			−0.504470			−0.252235	+	0.967666i	$0.581166\pi$
$380$			739.949i			0.0998911i
$381$	4283.34	−	7401.86i	0.575963	−	0.995298i
$382$	−9514.31			−1.27433
$383$	−7093.46			−0.946368			−0.473184	−	0.880964i	$-0.656895\pi$
$383$	−7093.46			−0.946368			−0.473184	+	0.880964i	$0.656895\pi$
$384$	−4484.08	−	2594.87i	−0.595905	−	0.344841i
$385$		0			0
$386$		−	334.984i		−	0.0441716i
$387$	2516.67	+	4379.19i	0.330567	+	0.575212i
$388$			427.444i			0.0559283i
$389$			7128.11i			0.929073i	0.885554	+	0.464537i	$0.153779\pi$
$389$			7128.11i			0.929073i	−0.885554	+	0.464537i	$0.846221\pi$
$390$	804.085	−	1389.51i	0.104401	−	0.180411i
$391$			1602.98i			0.207330i
$392$		0			0
$393$	−1635.38	+	2826.03i	−0.209908	+	0.362733i
$394$	−7878.16			−1.00735
$395$	−17154.7			−2.18518
$396$	−1087.80	+	625.144i	−0.138040	+	0.0793300i
$397$			8936.22i			1.12971i	0.825189	+	0.564857i	$0.191068\pi$
$397$			8936.22i			1.12971i	−0.825189	+	0.564857i	$0.808932\pi$
$398$	10332.3			1.30128
$399$		0			0
$400$	−6989.56			−0.873695
$401$		−	8913.83i		−	1.11006i	−0.831829	−	0.555032i	$-0.812706\pi$
$401$		−	8913.83i		−	1.11006i	0.831829	−	0.555032i	$-0.187294\pi$
$402$	−11846.3	−	6855.26i	−1.46975	−	0.850520i
$403$	1323.65			0.163612
$404$	1430.22			0.176130
$405$	−5915.71	+	10152.3i	−0.725812	+	1.24561i
$406$		0			0
$407$			8318.63i			1.01312i
$408$	3131.55	+	1812.18i	0.379988	+	0.219893i
$409$			3094.75i			0.374145i	0.982346	+	0.187073i	$0.0599000\pi$
$409$			3094.75i			0.374145i	−0.982346	+	0.187073i	$0.940100\pi$
$410$			15433.4i			1.85903i
$411$	−2243.85	−	1298.48i	−0.269297	−	0.155838i
$412$			271.076i			0.0324149i
$413$		0			0
$414$	1929.38	+	3357.26i	0.229043	+	0.398552i
$415$	−9687.64			−1.14590
$416$	432.993			0.0510318
$417$	−5471.77	−	3166.42i	−0.642574	−	0.371848i
$418$			3239.46i			0.379060i
$419$	7234.25			0.843476			0.421738	−	0.906718i	$-0.361420\pi$
$419$	7234.25			0.843476			0.421738	+	0.906718i	$0.361420\pi$
$420$		0			0
$421$	406.124			0.0470148			0.0235074	−	0.999724i	$-0.492517\pi$
$421$	406.124			0.0470148			0.0235074	+	0.999724i	$0.492517\pi$
$422$		−	11342.4i		−	1.30838i
$423$	−2350.89	−	4090.72i	−0.270222	−	0.470208i
$424$	−6553.19			−0.750592
$425$	3898.28			0.444928
$426$	843.982	−	1458.45i	0.0959885	−	0.165874i
$427$		0			0
$428$			2353.21i			0.265763i
$429$	−686.372	+	1186.09i	−0.0772456	+	0.133485i
$430$		−	7801.52i		−	0.874936i
$431$		−	12228.7i		−	1.36668i	−0.730102	−	0.683338i	$-0.760528\pi$
$431$		−	12228.7i		−	1.36668i	0.730102	−	0.683338i	$-0.239472\pi$
$432$	7274.82	+	21.8196i	0.810209	+	0.00243008i
$433$		−	3252.79i		−	0.361014i	−0.983574	−	0.180507i	$-0.942226\pi$
$433$		−	3252.79i		−	0.361014i	0.983574	−	0.180507i	$-0.0577738\pi$
$434$		0			0
$435$	−4940.24	−	2858.84i	−0.544521	−	0.315105i
$436$	370.253			0.0406695
$437$	−1949.38			−0.213390
$438$	1518.94	−	2624.82i	0.165703	−	0.286344i
$439$		−	15053.6i		−	1.63661i	−0.574787	−	0.818303i	$-0.694915\pi$
$439$		−	15053.6i		−	1.63661i	0.574787	−	0.818303i	$-0.305085\pi$
$440$	13814.9			1.49682
$441$		0			0
$442$	554.353			0.0596558
$443$			235.990i			0.0253098i	0.999920	+	0.0126549i	$0.00402828\pi$
$443$			235.990i			0.0253098i	−0.999920	+	0.0126549i	$0.995972\pi$
$444$	−793.843	+	1371.81i	−0.0848516	+	0.146629i
$445$	−24261.2			−2.58447
$446$	12552.9			1.33273
$447$	−10439.2	−	6040.99i	−1.10460	−	0.639215i
$448$		0			0
$449$			5874.66i			0.617466i	0.951149	+	0.308733i	$0.0999049\pi$
$449$			5874.66i			0.617466i	−0.951149	+	0.308733i	$0.900095\pi$
$450$	8164.52	−	4692.05i	0.855287	−	0.491523i
$451$		−	13174.0i		−	1.37548i
$452$		−	1354.13i		−	0.140914i
$453$	2543.89	−	4395.99i	0.263846	−	0.455942i
$454$			6127.24i			0.633405i
$455$		0			0
$456$	−2203.79	+	3808.27i	−0.226320	+	0.391094i
$457$	307.766			0.0315026			0.0157513	−	0.999876i	$-0.494986\pi$
$457$	307.766			0.0315026			0.0157513	+	0.999876i	$0.494986\pi$
$458$	11165.8			1.13918
$459$	−4057.38	−	12.1694i	−0.412597	−	0.00123751i
$460$			1166.16i			0.118201i
$461$	−4752.26			−0.480119			−0.240060	−	0.970758i	$-0.577167\pi$
$461$	−4752.26			−0.480119			−0.240060	+	0.970758i	$0.577167\pi$
$462$		0			0
$463$	−9529.43			−0.956523			−0.478261	−	0.878218i	$-0.658733\pi$
$463$	−9529.43			−0.956523			−0.478261	+	0.878218i	$0.658733\pi$
$464$			3533.87i			0.353569i
$465$	12951.8	+	7495.01i	1.29167	+	0.747468i
$466$	14421.5			1.43361
$467$	6538.56			0.647899			0.323949	−	0.946074i	$-0.394989\pi$
$467$	6538.56			0.647899			0.323949	+	0.946074i	$0.394989\pi$
$468$	−226.376	+	130.096i	−0.0223595	+	0.0128497i
$469$		0			0
$470$			7287.61i			0.715218i
$471$	746.524	+	432.001i	0.0730318	+	0.0422624i
$472$			2332.33i			0.227445i
$473$			6659.42i			0.647359i
$474$	−12384.9	−	7166.97i	−1.20013	−	0.694493i
$475$			4740.69i			0.457932i
$476$		0			0
$477$	6371.64	−	3661.70i	0.611609	−	0.351484i
$478$	12118.6			1.15961
$479$	−7342.57			−0.700398			−0.350199	−	0.936675i	$-0.613886\pi$
$479$	−7342.57			−0.700398			−0.350199	+	0.936675i	$0.613886\pi$
$480$	4236.80	+	2451.77i	0.402880	+	0.233140i
$481$			1731.15i			0.164103i
$482$	−5666.94			−0.535523
$483$		0			0
$484$	83.1680			0.00781066
$485$			5278.09i			0.494156i
$486$	−8512.38	+	4858.05i	−0.794505	+	0.453428i
$487$	7017.57			0.652970			0.326485	−	0.945202i	$-0.394136\pi$
$487$	7017.57			0.652970			0.326485	+	0.945202i	$0.394136\pi$
$488$	9282.37			0.861052
$489$	2542.77	−	4394.06i	0.235150	−	0.406352i
$490$		0			0
$491$			224.222i			0.0206089i	0.999947	+	0.0103045i	$0.00328007\pi$
$491$			224.222i			0.0206089i	−0.999947	+	0.0103045i	$0.996720\pi$
$492$	1257.19	−	2172.50i	0.115200	−	0.199073i
$493$		−	1970.94i		−	0.180054i
$494$			674.147i			0.0613994i
$495$	−13432.2	+	7719.30i	−1.21966	+	0.700923i
$496$		−	9264.74i		−	0.838708i
$497$		0			0
$498$	−6994.07	−	4047.36i	−0.629341	−	0.364189i
$499$	−20792.2			−1.86530			−0.932651	−	0.360780i	$-0.882510\pi$
$499$	−20792.2			−1.86530			−0.932651	+	0.360780i	$0.882510\pi$
$500$	206.063			0.0184308
$501$	2.62102	−	4.52928i	0.000233730	−	0.000403898i
$502$			5797.60i			0.515458i
$503$	−7341.52			−0.650780			−0.325390	−	0.945580i	$-0.605496\pi$
$503$	−7341.52			−0.650780			−0.325390	+	0.945580i	$0.605496\pi$
$504$		0			0
$505$	17660.5			1.55620
$506$			5105.38i			0.448541i
$507$	5575.02	−	9633.96i	0.488353	−	0.843903i
$508$	2148.31			0.187629
$509$	−19912.2			−1.73398			−0.866988	−	0.498330i	$-0.833947\pi$
$509$	−19912.2			−1.73398			−0.866988	+	0.498330i	$0.833947\pi$
$510$	5424.29	+	3138.95i	0.470964	+	0.272539i
$511$		0			0
$512$		−	13018.4i		−	1.12370i
$513$	14.7992	−	4934.17i	0.00127368	−	0.424657i
$514$			2876.08i			0.246807i
$515$			3347.25i			0.286403i
$516$	−635.506	+	1098.19i	−0.0542182	+	0.0936922i
$517$		−	6220.75i		−	0.529184i
$518$		0			0
$519$	10297.2	−	17794.2i	0.870900	−	1.50497i
$520$	2874.95			0.242452
$521$	−7491.80			−0.629984			−0.314992	−	0.949094i	$-0.602002\pi$
$521$	−7491.80			−0.629984			−0.314992	+	0.949094i	$0.602002\pi$
$522$	−2372.26	−	4127.92i	−0.198910	−	0.346119i
$523$			288.115i			0.0240887i	0.999927	+	0.0120444i	$0.00383393\pi$
$523$			288.115i			0.0240887i	−0.999927	+	0.0120444i	$0.996166\pi$
$524$	−820.223			−0.0683809
$525$		0			0
$526$	5326.62			0.441543
$527$			5167.21i			0.427111i
$528$	8301.90	+	4804.18i	0.684269	+	0.395975i
$529$	9094.79			0.747496
$530$	−11351.1			−0.930299
$531$	−1303.23	−	2267.71i	−0.106507	−	0.185330i
$532$		0			0
$533$		−	2741.58i		−	0.222797i
$534$	−17515.6	−	10136.0i	−1.41942	−	0.821398i
$535$			29057.5i			2.34816i
$536$		−	24510.5i		−	1.97517i
$537$	12585.8	+	7283.21i	1.01139	+	0.585277i
$538$			12495.2i			1.00131i
$539$		0			0
$540$	−2951.72	−	8.85317i	−0.235226	−	0.000705518i
$541$	14801.7			1.17630			0.588149	−	0.808753i	$-0.299857\pi$
$541$	14801.7			1.17630			0.588149	+	0.808753i	$0.299857\pi$
$542$	572.955			0.0454069
$543$	6776.42	+	3921.40i	0.535550	+	0.309915i
$544$			1690.30i			0.133219i
$545$	4571.90			0.359337
$546$		0			0
$547$	−4036.80			−0.315541			−0.157771	−	0.987476i	$-0.550431\pi$
$547$	−4036.80			−0.315541			−0.157771	+	0.987476i	$0.550431\pi$
$548$		−	651.253i		−	0.0507667i
$549$	−9025.21	+	5186.68i	−0.701615	+	0.403209i
$550$	12415.8			0.962563
$551$	2396.86			0.185317
$552$	−3473.16	+	6001.82i	−0.267803	+	0.462780i
$553$		0			0
$554$			6383.53i			0.489549i
$555$	−9802.40	+	16939.1i	−0.749709	+	1.29554i
$556$		−	1588.12i		−	0.121135i
$557$			17194.7i			1.30801i	0.756489	+	0.654007i	$0.226913\pi$
$557$			17194.7i			1.30801i	−0.756489	+	0.654007i	$0.773087\pi$
$558$	6219.36	+	10822.2i	0.471839	+	0.821037i
$559$			1385.86i			0.104858i
$560$		0			0
$561$	−4630.21	−	2679.43i	−0.348463	−	0.201650i
$562$	10801.8			0.810759
$563$	18907.3			1.41536			0.707678	−	0.706535i	$-0.249743\pi$
$563$	18907.3			1.41536			0.707678	+	0.706535i	$0.249743\pi$
$564$	593.643	−	1025.85i	0.0443207	−	0.0765888i
$565$		−	16720.9i		−	1.24505i
$566$	−16815.8			−1.24880
$567$		0			0
$568$	3017.60			0.222915
$569$			7223.31i			0.532191i	0.963947	+	0.266096i	$0.0857337\pi$
$569$			7223.31i			0.532191i	−0.963947	+	0.266096i	$0.914266\pi$
$570$	−3817.27	+	6596.47i	−0.280505	+	0.484729i
$571$	−9930.34			−0.727797			−0.363898	−	0.931439i	$-0.618554\pi$
$571$	−9930.34			−0.727797			−0.363898	+	0.931439i	$0.618554\pi$
$572$	−344.250			−0.0251640
$573$	16537.7	+	9570.08i	1.20571	+	0.697724i
$574$		0			0
$575$			7471.31i			0.541870i
$576$	7615.26	+	13251.1i	0.550872	+	0.958560i
$577$		−	8376.39i		−	0.604356i	−0.953251	−	0.302178i	$-0.902286\pi$
$577$		−	8376.39i		−	0.604356i	0.953251	−	0.302178i	$-0.0977137\pi$
$578$		−	10547.9i		−	0.759055i
$579$	−336.947	+	582.265i	−0.0241849	+	0.0417929i
$580$		−	1433.85i		−	0.102651i
$581$		0			0
$582$	−2205.11	+	3810.56i	−0.157053	+	0.271397i
$583$	9689.33			0.688321
$584$	5430.87			0.384814
$585$	−2795.30	+	1606.42i	−0.197558	+	0.113534i
$586$			14586.1i			1.02823i
$587$	21277.2			1.49609			0.748043	−	0.663650i	$-0.230994\pi$
$587$	21277.2			1.49609			0.748043	+	0.663650i	$0.230994\pi$
$588$		0			0
$589$	−6283.84			−0.439594
$590$			4039.92i			0.281900i
$591$	13693.7	+	7924.34i	0.953104	+	0.551546i
$592$	12117.0			0.841223
$593$	−2848.98			−0.197291			−0.0986454	−	0.995123i	$-0.531451\pi$
$593$	−2848.98			−0.197291			−0.0986454	+	0.995123i	$0.531451\pi$
$594$	−12922.5	−	38.7587i	−0.892619	−	0.00267725i
$595$		0			0
$596$		−	3029.86i		−	0.208235i
$597$	−17959.4	−	10392.8i	−1.23121	−	0.712479i
$598$			1062.45i			0.0726537i
$599$			4439.14i			0.302802i	0.988472	+	0.151401i	$0.0483784\pi$
$599$			4439.14i			0.302802i	−0.988472	+	0.151401i	$0.951622\pi$
$600$	14595.8	+	8446.38i	0.993121	+	0.574703i
$601$			7868.29i			0.534033i	0.963692	+	0.267017i	$0.0860379\pi$
$601$			7868.29i			0.534033i	−0.963692	+	0.267017i	$0.913962\pi$
$602$		0			0
$603$	13695.6	+	23831.4i	0.924924	+	1.60944i
$604$	1275.89			0.0859521
$605$	1026.96			0.0690114
$606$	12750.1	+	7378.28i	0.854683	+	0.494591i
$607$		−	17487.8i		−	1.16937i	−0.811259	−	0.584686i	$-0.801218\pi$
$607$		−	17487.8i		−	1.16937i	0.811259	−	0.584686i	$-0.198782\pi$
$608$	−2055.57			−0.137112
$609$		0			0
$610$	16078.4			1.06720
$611$		−	1294.57i		−	0.0857162i
$612$	−507.861	−	883.717i	−0.0335442	−	0.0583695i
$613$	12844.1			0.846280			0.423140	−	0.906064i	$-0.360928\pi$
$613$	12844.1			0.846280			0.423140	+	0.906064i	$0.360928\pi$
$614$	8908.32			0.585522
$615$	15523.8	−	26826.1i	1.01786	−	1.75892i
$616$		0			0
$617$		−	23625.5i		−	1.54153i	−0.637117	−	0.770767i	$-0.719873\pi$
$617$		−	23625.5i		−	1.54153i	0.637117	−	0.770767i	$-0.280127\pi$
$618$	−1398.43	+	2416.58i	−0.0910247	+	0.157296i
$619$		−	19086.1i		−	1.23931i	−0.784873	−	0.619657i	$-0.787272\pi$
$619$		−	19086.1i		−	1.23931i	0.784873	−	0.619657i	$-0.212728\pi$
$620$			3759.12i			0.243500i
$621$	23.3234	−	7776.23i	0.00150715	−	0.502495i
$622$			391.901i			0.0252633i
$623$		0			0
$624$	1727.67	+	999.772i	0.110836	+	0.0641393i
$625$	−14304.8			−0.915507
$626$	−24903.3			−1.58999
$627$	3258.45	−	5630.79i	0.207544	−	0.358648i
$628$			216.670i			0.0137676i
$629$	−6757.98			−0.428391
$630$		0			0
$631$	32.3893			0.00204342			0.00102171	−	0.999999i	$-0.499675\pi$
$631$	32.3893			0.00204342			0.00102171	+	0.999999i	$0.499675\pi$
$632$		−	25625.0i		−	1.61283i
$633$	−11408.8	+	19715.1i	−0.716367	+	1.23792i
$634$	−23503.9			−1.47233
$635$	26527.3			1.65780
$636$	1597.85	+	924.648i	0.0996207	+	0.0576489i
$637$		0			0
$638$		−	6277.32i		−	0.389532i
$639$	−2934.00	+	1686.13i	−0.181639	+	0.104386i
$640$		−	16070.4i		−	0.992560i
$641$		−	21642.2i		−	1.33357i	−0.745251	−	0.666784i	$-0.767670\pi$
$641$		−	21642.2i		−	1.33357i	0.745251	−	0.666784i	$-0.232330\pi$
$642$	−12139.8	+	20978.3i	−0.746291	+	1.28964i
$643$			19867.3i			1.21849i	0.792982	+	0.609246i	$0.208528\pi$
$643$			19867.3i			1.21849i	−0.792982	+	0.609246i	$0.791472\pi$
$644$		0			0
$645$	−7847.24	+	13560.5i	−0.479046	+	0.827820i
$646$	−2631.71			−0.160283
$647$	22424.4			1.36259			0.681294	−	0.732010i	$-0.261418\pi$
$647$	22424.4			1.36259			0.681294	+	0.732010i	$0.261418\pi$
$648$	−15165.2	−	8836.66i	−0.919358	−	0.535705i
$649$		−	3448.50i		−	0.208576i
$650$	2583.78			0.155914
$651$		0			0
$652$	1275.33			0.0766038
$653$		−	20043.8i		−	1.20119i	−0.799554	−	0.600594i	$-0.794931\pi$
$653$		−	20043.8i		−	1.20119i	0.799554	−	0.600594i	$-0.205069\pi$
$654$	3300.72	+	1910.07i	0.197352	+	0.114204i
$655$	−10128.1			−0.604182
$656$	−19189.3			−1.14210
$657$	−5280.41	+	3034.59i	−0.313559	+	0.180199i
$658$		0			0
$659$		−	13217.9i		−	0.781327i	−0.920533	−	0.390664i	$-0.872246\pi$
$659$		−	13217.9i		−	0.781327i	0.920533	−	0.390664i	$-0.127754\pi$
$660$	−3368.45	−	1949.27i	−0.198662	−	0.114962i
$661$		−	9781.36i		−	0.575568i	−0.957695	−	0.287784i	$-0.907081\pi$
$661$		−	9781.36i		−	0.575568i	0.957695	−	0.287784i	$-0.0929186\pi$
$662$		−	3636.80i		−	0.213517i
$663$	−963.569	−	557.602i	−0.0564433	−	0.0326628i
$664$		−	14471.0i		−	0.845761i
$665$		0			0
$666$	−14153.8	+	8134.03i	−0.823499	+	0.473254i
$667$	3777.44			0.219285
$668$	1.31457			7.61411e−5
$669$	−21819.3	−	12626.5i	−1.26096	−	0.729697i
$670$		−	42455.6i		−	2.44807i
$671$	−13724.6			−0.789617
$672$		0			0
$673$	−4670.73			−0.267524			−0.133762	−	0.991014i	$-0.542706\pi$
$673$	−4670.73			−0.267524			−0.133762	+	0.991014i	$0.542706\pi$
$674$			20656.2i			1.18048i
$675$	−18911.0	−	56.7203i	−1.07835	−	0.00323432i
$676$	2796.15			0.159089
$677$	−27042.0			−1.53517			−0.767584	−	0.640948i	$-0.778541\pi$
$677$	−27042.0			−1.53517			−0.767584	+	0.640948i	$0.778541\pi$
$678$	6985.73	−	12071.8i	0.395701	−	0.683795i
$679$		0			0
$680$			11223.1i			0.632921i
$681$	6163.16	−	10650.3i	0.346803	−	0.599295i
$682$			16457.2i			0.924017i
$683$			13390.9i			0.750203i	0.926984	+	0.375101i	$0.122392\pi$
$683$			13390.9i			0.750203i	−0.926984	+	0.375101i	$0.877608\pi$
$684$	1074.69	−	617.609i	0.0600756	−	0.0345247i
$685$		−	8041.69i		−	0.448551i
$686$		0			0
$687$	−19408.2	−	11231.2i	−1.07783	−	0.623724i
$688$	9700.14			0.537521
$689$	2016.40			0.111493
$690$	−6016.01	+	10396.0i	−0.331921	+	0.573579i
$691$			30989.1i			1.70605i	0.521870	+	0.853025i	$0.325235\pi$
$691$			30989.1i			1.70605i	−0.521870	+	0.853025i	$0.674765\pi$
$692$	5164.56			0.283710
$693$		0			0
$694$	6777.28			0.370694
$695$		−	19610.1i		−	1.07029i
$696$	4270.43	−	7379.55i	0.232572	−	0.401898i
$697$	10702.5			0.581613
$698$	15608.1			0.846383
$699$	−25067.3	−	14506.0i	−1.35641	−	0.784933i
$700$		0			0
$701$		−	2892.67i		−	0.155855i	−0.996959	−	0.0779277i	$-0.975170\pi$
$701$		−	2892.67i		−	0.155855i	0.996959	−	0.0779277i	$-0.0248303\pi$
$702$	−2689.23	−	8.06587i	−0.144585	−	0.000433656i
$703$		−	8218.36i		−	0.440912i
$704$			20151.0i			1.07879i
$705$	7330.33	−	12667.2i	0.391597	−	0.676703i
$706$			13755.5i			0.733277i
$707$		0			0
$708$	329.089	−	568.685i	0.0174688	−	0.0301871i
$709$	15930.4			0.843833			0.421917	−	0.906635i	$-0.361357\pi$
$709$	15930.4			0.843833			0.421917	+	0.906635i	$0.361357\pi$
$710$	5226.91			0.276285
$711$	14318.4	+	24915.1i	0.755248	+	1.31419i
$712$		−	36240.5i		−	1.90754i
$713$	−9903.30			−0.520171
$714$		0			0
$715$	−4250.81			−0.222337
$716$			3652.89i			0.190663i
$717$	−21064.5	−	12189.7i	−1.09716	−	0.634911i
$718$	−4817.66			−0.250409
$719$	−11877.7			−0.616085			−0.308042	−	0.951373i	$-0.599674\pi$
$719$	−11877.7			−0.616085			−0.308042	+	0.951373i	$0.599674\pi$
$720$	11244.0	+	19565.4i	0.581997	+	1.01272i
$721$		0			0
$722$			14546.6i			0.749819i
$723$	9850.20	+	5700.15i	0.506684	+	0.293210i
$724$			1966.78i			0.100960i
$725$		−	9186.35i		−	0.470583i
$726$	741.422	+	429.049i	0.0379019	+	0.0219332i
$727$		−	16795.8i		−	0.856839i	−0.903580	−	0.428419i	$-0.859071\pi$
$727$		−	16795.8i		−	0.856839i	0.903580	−	0.428419i	$-0.140929\pi$
$728$		0			0
$729$	19682.6	+	118.070i	0.999982	+	0.00599859i
$730$	9407.04			0.476945
$731$	−5410.05			−0.273732
$732$	−2263.30	−	1309.73i	−0.114281	−	0.0661327i
$733$			25459.3i			1.28289i	0.767167	+	0.641447i	$0.221666\pi$
$733$			25459.3i			1.28289i	−0.767167	+	0.641447i	$0.778334\pi$
$734$	−5007.02			−0.251788
$735$		0			0
$736$	−3239.57			−0.162245
$737$			36240.4i			1.81131i
$738$	22415.1	−	12881.7i	1.11804	−	0.642522i
$739$	−18639.0			−0.927801			−0.463901	−	0.885887i	$-0.653551\pi$
$739$	−18639.0			−0.927801			−0.463901	+	0.885887i	$0.653551\pi$
$740$	−4916.39			−0.244230
$741$	678.099	−	1171.79i	0.0336175	−	0.0580930i
$742$		0			0
$743$			14043.3i			0.693401i	0.937976	+	0.346700i	$0.112698\pi$
$743$			14043.3i			0.693401i	−0.937976	+	0.346700i	$0.887302\pi$
$744$	−11195.8	+	19346.9i	−0.551689	+	0.953351i
$745$		−	37412.8i		−	1.83986i
$746$			20031.9i			0.983137i
$747$	8085.92	+	14070.1i	0.396049	+	0.689155i
$748$		−	1343.87i		−	0.0656907i
$749$		0			0
$750$	1837.00	+	1063.04i	0.0894370	+	0.0517557i
$751$	16230.3			0.788616			0.394308	−	0.918978i	$-0.370984\pi$
$751$	16230.3			0.788616			0.394308	+	0.918978i	$0.370984\pi$
$752$	−9061.17			−0.439397
$753$	5831.59	−	10077.3i	0.282224	−	0.487700i
$754$		−	1306.34i		−	0.0630956i
$755$	15754.7			0.759433
$756$		0			0
$757$	−33345.7			−1.60102			−0.800508	−	0.599322i	$-0.795437\pi$
$757$	−33345.7			−1.60102			−0.800508	+	0.599322i	$0.795437\pi$
$758$		−	9630.72i		−	0.461482i
$759$	5135.30	−	8874.10i	0.245586	−	0.424387i
$760$	−13648.4			−0.651420
$761$	10788.0			0.513884			0.256942	−	0.966427i	$-0.417285\pi$
$761$	10788.0			0.513884			0.256942	+	0.966427i	$0.417285\pi$
$762$	19151.6	+	11082.7i	0.910486	+	0.526884i
$763$		0			0
$764$			4799.87i			0.227295i
$765$	−6271.09	−	10912.2i	−0.296381	−	0.515726i
$766$		−	18353.7i		−	0.865725i
$767$		−	717.650i		−	0.0337847i
$768$	−5071.61	+	8764.04i	−0.238289	+	0.411777i
$769$			35799.6i			1.67876i	0.543543	+	0.839381i	$0.317082\pi$
$769$			35799.6i			1.67876i	−0.543543	+	0.839381i	$0.682918\pi$
$770$		0			0
$771$	2892.94	−	4999.17i	0.135132	−	0.233516i
$772$	−168.996			−0.00787862
$773$	−36612.6			−1.70358			−0.851788	−	0.523887i	$-0.824481\pi$
$773$	−36612.6			−1.70358			−0.851788	+	0.523887i	$0.824481\pi$
$774$	−11330.8	+	6511.64i	−0.526196	+	0.302398i
$775$			24083.8i			1.11628i
$776$	−7884.22			−0.364725
$777$		0			0
$778$	−18443.3			−0.849904
$779$			13015.2i			0.598612i
$780$	−700.991	−	405.652i	−0.0321789	−	0.0186214i
$781$	−4461.72			−0.204421
$782$	−4147.56			−0.189663
$783$	−28.6773	+	9561.27i	−0.00130887	+	0.436388i
$784$		0			0
$785$			2675.45i			0.121644i
$786$	−7312.09	−	4231.39i	−0.331824	−	0.192021i
$787$			40270.1i			1.82398i	0.410211	+	0.911990i	$0.365455\pi$
$787$			40270.1i			1.82398i	−0.410211	+	0.911990i	$0.634545\pi$
$788$			3974.45i			0.179675i
$789$	−9258.66	−	5357.84i	−0.417766	−	0.241754i
$790$		−	44386.1i		−	1.99897i
$791$		0			0
$792$	−11530.8	−	20064.5i	−0.517335	−	0.900203i
$793$	−2856.16			−0.127901
$794$	−23121.7			−1.03345
$795$	19730.3	+	11417.6i	0.880202	+	0.509359i
$796$		−	5212.52i		−	0.232101i
$797$	11444.6			0.508645			0.254323	−	0.967119i	$-0.418148\pi$
$797$	11444.6			0.508645			0.254323	+	0.967119i	$0.418148\pi$
$798$		0			0
$799$	5053.68			0.223762
$800$			7878.30i			0.348175i
$801$	20249.9	+	35236.4i	0.893254	+	1.55433i
$802$	23063.7			1.01547
$803$	−8029.91			−0.352888
$804$	−3458.40	+	5976.32i	−0.151702	+	0.262150i
$805$		0			0
$806$			3424.83i			0.149670i
$807$	12568.5	−	21719.0i	0.548241	−	0.947393i
$808$			26380.5i			1.14859i
$809$		−	3120.99i		−	0.135634i	−0.997698	−	0.0678172i	$-0.978397\pi$
$809$		−	3120.99i		−	0.135634i	0.997698	−	0.0678172i	$-0.0216035\pi$
$810$	−26268.2	−	15306.3i	−1.13947	−	0.663963i
$811$			3571.23i			0.154628i	0.997007	+	0.0773138i	$0.0246343\pi$
$811$			3571.23i			0.154628i	−0.997007	+	0.0773138i	$0.975366\pi$
$812$		0			0
$813$	−995.903	−	576.313i	−0.0429617	−	0.0248612i
$814$	−21523.7			−0.926788
$815$	15747.8			0.676835
$816$	−3902.87	+	6744.38i	−0.167436	+	0.289339i
$817$		−	6579.15i		−	0.281732i
$818$	−8007.37			−0.342263
$819$		0			0
$820$	7785.98			0.331583
$821$		−	28198.2i		−	1.19869i	−0.800492	−	0.599344i	$-0.795428\pi$
$821$		−	28198.2i		−	1.19869i	0.800492	−	0.599344i	$-0.204572\pi$
$822$	3359.70	−	5805.76i	0.142558	−	0.246349i
$823$	−11401.7			−0.482915			−0.241457	−	0.970411i	$-0.577625\pi$
$823$	−11401.7			−0.482915			−0.241457	+	0.970411i	$0.577625\pi$
$824$	−5000.00			−0.211388
$825$	−21580.9	−	12488.5i	−0.910729	−	0.527024i
$826$		0			0
$827$			18948.2i			0.796726i	0.917228	+	0.398363i	$0.130422\pi$
$827$			18948.2i			0.796726i	−0.917228	+	0.398363i	$0.869578\pi$
$828$	1693.70	−	973.349i	0.0710872	−	0.0408529i
$829$		−	765.850i		−	0.0320857i	−0.999871	−	0.0160429i	$-0.994893\pi$
$829$		−	765.850i		−	0.0320857i	0.999871	−	0.0160429i	$-0.00510682\pi$
$830$		−	25065.9i		−	1.04825i
$831$	6420.95	−	11095.8i	0.268039	−	0.463187i
$832$			4193.51i			0.174740i
$833$		0			0
$834$	8192.83	−	14157.7i	0.340161	−	0.587819i
$835$	16.2324			0.000672748
$836$	1634.27			0.0676107
$837$	75.1833	−	25066.8i	0.00310480	−	1.03517i
$838$			18718.0i			0.771600i
$839$	5355.68			0.220380			0.110190	−	0.993911i	$-0.464854\pi$
$839$	5355.68			0.220380			0.110190	+	0.993911i	$0.464854\pi$
$840$		0			0
$841$	19744.4			0.809564
$842$			1050.81i			0.0430086i
$843$	−18775.6	−	10865.1i	−0.767100	−	0.443908i
$844$	−5722.10			−0.233368
$845$	34526.9			1.40564
$846$	10584.4	−	6082.70i	0.430140	−	0.247196i
$847$		0			0
$848$		−	14113.5i		−	0.571533i
$849$	29229.1	+	16914.4i	1.18155	+	0.683747i
$850$			10086.4i			0.407014i
$851$		−	12952.1i		−	0.521730i
$852$	−735.773	−	425.780i	−0.0295859	−	0.0171209i
$853$		−	8591.74i		−	0.344872i	−0.985021	−	0.172436i	$-0.944836\pi$
$853$		−	8591.74i		−	0.344872i	0.985021	−	0.172436i	$-0.0551638\pi$
$854$		0			0
$855$	13270.3	−	7626.26i	0.530800	−	0.305044i
$856$	−43404.9			−1.73312
$857$	40546.7			1.61616			0.808080	−	0.589073i	$-0.200507\pi$
$857$	40546.7			1.61616			0.808080	+	0.589073i	$0.200507\pi$
$858$	−3068.90	−	1775.92i	−0.122110	−	0.0706632i
$859$		−	9645.12i		−	0.383105i	−0.981482	−	0.191553i	$-0.938648\pi$
$859$		−	9645.12i		−	0.383105i	0.981482	−	0.191553i	$-0.0613522\pi$
$860$	−3935.78			−0.156057
$861$		0			0
$862$	31640.7			1.25022
$863$			11490.6i			0.453240i	0.973983	+	0.226620i	$0.0727675\pi$
$863$			11490.6i			0.453240i	−0.973983	+	0.226620i	$0.927232\pi$
$864$	24.5940	−	8199.84i	0.000968407	−	0.322875i
$865$	63772.2			2.50673
$866$	8416.29			0.330251
$867$	−10609.7	+	18334.2i	−0.415599	+	0.718180i
$868$		0			0
$869$			37888.3i			1.47902i
$870$	7396.98	−	12782.4i	0.288254	−	0.498120i
$871$			7541.80i			0.293392i
$872$			6829.33i			0.265218i
$873$	7665.79	−	4405.43i	0.297191	−	0.170792i
$874$		−	5043.84i		−	0.195206i
$875$		0			0
$876$	−1324.19	−	766.290i	−0.0510735	−	0.0295554i
$877$	−29429.4			−1.13314			−0.566568	−	0.824015i	$-0.691729\pi$
$877$	−29429.4			−1.13314			−0.566568	+	0.824015i	$0.691729\pi$
$878$	38949.9			1.49715
$879$	14671.5	−	25353.3i	0.562980	−	0.972862i
$880$			29753.0i			1.13974i
$881$	22330.5			0.853956			0.426978	−	0.904262i	$-0.359578\pi$
$881$	22330.5			0.853956			0.426978	+	0.904262i	$0.359578\pi$
$882$		0			0
$883$	15519.2			0.591463			0.295732	−	0.955271i	$-0.404437\pi$
$883$	15519.2			0.591463			0.295732	+	0.955271i	$0.404437\pi$
$884$		−	279.665i		−	0.0106404i
$885$	4063.60	−	7022.14i	0.154346	−	0.266719i
$886$	−610.602			−0.0231530
$887$	38215.9			1.44663			0.723316	−	0.690517i	$-0.242617\pi$
$887$	38215.9			1.44663			0.723316	+	0.690517i	$0.242617\pi$
$888$	−25303.0	−	14642.5i	−0.956209	−	0.553343i
$889$		0			0
$890$		−	62773.6i		−	2.36424i
$891$	22422.7	+	13065.6i	0.843085	+	0.491261i
$892$		−	6332.80i		−	0.237711i
$893$			6145.77i			0.230303i
$894$	15630.5	−	27010.4i	0.584746	−	1.01047i
$895$			45106.0i			1.68461i
$896$		0			0
$897$	1068.68	−	1846.74i	0.0397795	−	0.0687413i
$898$	−15200.1			−0.564850
$899$	12176.6			0.451738
$900$	−2367.09	−	4118.91i	−0.0876699	−	0.152552i
$901$			7871.52i			0.291053i
$902$	34086.6			1.25827
$903$		0			0
$904$	24977.0			0.918941
$905$			24285.8i			0.892032i
$906$	11374.2	+	6582.08i	0.417089	+	0.241363i
$907$	−8864.60			−0.324525			−0.162262	−	0.986748i	$-0.551879\pi$
$907$	−8864.60			−0.324525			−0.162262	+	0.986748i	$0.551879\pi$
$908$	3091.13			0.112977
$909$	−14740.5	−	25649.7i	−0.537858	−	0.935915i
$910$		0			0
$911$		−	15145.0i		−	0.550798i	−0.961330	−	0.275399i	$-0.911190\pi$
$911$		−	15145.0i		−	0.550798i	0.961330	−	0.275399i	$-0.0888100\pi$
$912$	−8201.83	−	4746.27i	−0.297796	−	0.172330i
$913$			21396.4i			0.775594i
$914$			796.316i			0.0288182i
$915$	−27947.3	−	16172.6i	−1.00974	−	0.584318i
$916$		−	5633.02i		−	0.203188i
$917$		0			0
$918$	31.4872	−	10498.1i	0.00113206	−	0.377439i
$919$	−4488.14			−0.161099			−0.0805495	−	0.996751i	$-0.525668\pi$
$919$	−4488.14			−0.161099			−0.0805495	+	0.996751i	$0.525668\pi$
$920$	−21509.8			−0.770823
$921$	−15484.3	−	8960.53i	−0.553991	−	0.320586i
$922$		−	12296.0i		−	0.439207i
$923$	−928.506			−0.0331118
$924$		0			0
$925$	−31498.2			−1.11963
$926$		−	24656.5i		−	0.875015i
$927$	4861.48	−	2793.83i	0.172246	−	0.0989876i
$928$	3983.21			0.140900
$929$	−17823.9			−0.629475			−0.314737	−	0.949179i	$-0.601916\pi$
$929$	−17823.9			−0.629475			−0.314737	+	0.949179i	$0.601916\pi$
$930$	−19392.6	+	33511.6i	−0.683774	+	1.18160i
$931$		0			0
$932$		−	7275.49i		−	0.255704i
$933$	394.198	−	681.198i	0.0138322	−	0.0239029i
$934$			16917.9i			0.592689i
$935$		−	16594.1i		−	0.580412i
$936$	−2399.62	−	4175.52i	−0.0837969	−	0.145813i
$937$		−	51270.5i		−	1.78755i	−0.448516	−	0.893775i	$-0.648047\pi$
$937$		−	51270.5i		−	1.78755i	0.448516	−	0.893775i	$-0.351953\pi$
$938$		0			0
$939$	43286.5	+	25049.2i	1.50437	+	0.870554i
$940$	3676.52			0.127569
$941$	−10845.0			−0.375702			−0.187851	−	0.982198i	$-0.560152\pi$
$941$	−10845.0			−0.375702			−0.187851	+	0.982198i	$0.560152\pi$
$942$	−1117.76	+	1931.56i	−0.0386610	+	0.0668086i
$943$			20512.0i			0.708336i
$944$	−5023.10			−0.173186
$945$		0			0
$946$	−17230.6			−0.592195
$947$		−	42627.8i		−	1.46274i	−0.681979	−	0.731372i	$-0.738881\pi$
$947$		−	42627.8i		−	1.46274i	0.681979	−	0.731372i	$-0.261119\pi$
$948$	−3615.66	+	6248.07i	−0.123873	+	0.214059i
$949$	−1671.06			−0.0571602
$950$	−12266.1			−0.418910
$951$	40854.2	+	23641.7i	1.39305	+	0.806134i
$952$		0			0
$953$			33229.0i			1.12948i	0.825269	+	0.564739i	$0.191023\pi$
$953$			33229.0i			1.12948i	−0.825269	+	0.564739i	$0.808977\pi$
$954$	9474.31	+	16486.0i	0.321533	+	0.559492i
$955$			59268.9i			2.00827i
$956$		−	6113.72i		−	0.206832i
$957$	−6314.11	+	10911.2i	−0.213277	+	0.368555i
$958$		−	18998.2i		−	0.640715i
$959$		0			0
$960$	−23745.2	+	41033.1i	−0.798306	+	1.37952i
$961$	−2132.38			−0.0715781
$962$	−4479.18			−0.150119
$963$	42202.4	−	24253.2i	1.41221	−	0.811577i
$964$			2858.91i			0.0955179i
$965$	−2086.77			−0.0696118
$966$		0			0
$967$	−16853.4			−0.560464			−0.280232	−	0.959932i	$-0.590411\pi$
$967$	−16853.4			−0.560464			−0.280232	+	0.959932i	$0.590411\pi$
$968$			1534.04i			0.0509357i
$969$	4574.40	+	2647.13i	0.151652	+	0.0877586i
$970$	−13656.6			−0.452048
$971$	1269.65			0.0419618			0.0209809	−	0.999780i	$-0.493321\pi$
$971$	1269.65			0.0419618			0.0209809	+	0.999780i	$0.493321\pi$
$972$	2450.84	+	4294.41i	0.0808751	+	0.141711i
$973$		0			0
$974$			18157.3i			0.597328i
$975$	−4491.09	−	2598.92i	−0.147518	−	0.0853663i
$976$			19991.3i			0.655642i
$977$			57250.6i			1.87473i	0.348351	+	0.937364i	$0.386742\pi$
$977$			57250.6i			1.87473i	−0.348351	+	0.937364i	$0.613258\pi$
$978$	11369.2	+	6579.19i	0.371726	+	0.215112i
$979$			53583.9i			1.74929i
$980$		0			0
$981$	−3816.00	−	6640.13i	−0.124195	−	0.216109i
$982$	−580.153			−0.0188528
$983$	−61467.5			−1.99441			−0.997207	−	0.0746857i	$-0.976205\pi$
$983$	−61467.5			−1.99441			−0.997207	+	0.0746857i	$0.976205\pi$
$984$	40071.8	+	23188.9i	1.29821	+	0.751256i
$985$			49076.6i			1.58752i
$986$	5099.63			0.164711
$987$		0			0
$988$	340.100			0.0109514
$989$		−	10368.7i		−	0.333373i
$990$	−19973.0	−	34754.5i	−0.641195	−	1.11573i
$991$	−51993.1			−1.66662			−0.833308	−	0.552809i	$-0.813556\pi$
$991$	−51993.1			−1.66662			−0.833308	+	0.552809i	$0.813556\pi$
$992$	−10442.8			−0.334232
$993$	−3658.12	+	6321.44i	−0.116905	+	0.202019i
$994$		0			0
$995$		−	64364.3i		−	2.05074i
$996$	−2041.85	+	3528.43i	−0.0649582	+	0.112252i
$997$		−	33968.2i		−	1.07902i	−0.841979	−	0.539510i	$-0.818609\pi$
$997$		−	33968.2i		−	1.07902i	0.841979	−	0.539510i	$-0.181391\pi$
$998$		−	53797.8i		−	1.70635i
$999$	32783.7	+	98.3290i	1.03827	+	0.00311411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.4.c.a.146.10		12
3.2	odd	2	inner	147.4.c.a.146.3		12
7.2	even	3		21.4.g.a.17.5	yes	12
7.3	odd	6		21.4.g.a.5.2	✓	12
7.4	even	3		147.4.g.d.68.2		12
7.5	odd	6		147.4.g.d.80.5		12
7.6	odd	2	inner	147.4.c.a.146.9		12
21.2	odd	6		21.4.g.a.17.2	yes	12
21.5	even	6		147.4.g.d.80.2		12
21.11	odd	6		147.4.g.d.68.5		12
21.17	even	6		21.4.g.a.5.5	yes	12
21.20	even	2	inner	147.4.c.a.146.4		12
28.3	even	6		336.4.bc.d.257.1		12
28.23	odd	6		336.4.bc.d.17.2		12
84.23	even	6		336.4.bc.d.17.1		12
84.59	odd	6		336.4.bc.d.257.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.4.g.a.5.2	✓	12	7.3	odd	6
21.4.g.a.5.5	yes	12	21.17	even	6
21.4.g.a.17.2	yes	12	21.2	odd	6
21.4.g.a.17.5	yes	12	7.2	even	3
147.4.c.a.146.3		12	3.2	odd	2	inner
147.4.c.a.146.4		12	21.20	even	2	inner
147.4.c.a.146.9		12	7.6	odd	2	inner
147.4.c.a.146.10		12	1.1	even	1	trivial
147.4.g.d.68.2		12	7.4	even	3
147.4.g.d.68.5		12	21.11	odd	6
147.4.g.d.80.2		12	21.5	even	6
147.4.g.d.80.5		12	7.5	odd	6
336.4.bc.d.17.1		12	84.23	even	6
336.4.bc.d.17.2		12	28.23	odd	6
336.4.bc.d.257.1		12	28.3	even	6
336.4.bc.d.257.2		12	84.59	odd	6

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.58741i q^{2} +(2.60257 - 4.49740i) q^{3} +1.30532 q^{4} +16.1181 q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} +O(q^{10})\)	\(q+2.58741i q^{2} +(2.60257 - 4.49740i) q^{3} +1.30532 q^{4} +16.1181 q^{5} +(11.6366 + 6.73392i) q^{6} +24.0767i q^{8} +(-13.4532 - 23.4096i) q^{9} +41.7042i q^{10} -35.5990i q^{11} +(3.39719 - 5.87054i) q^{12} -7.40831i q^{13} +(41.9486 - 72.4897i) q^{15} -51.8536 q^{16} +28.9202 q^{17} +(60.5703 - 34.8090i) q^{18} +35.1698i q^{19} +21.0393 q^{20} +92.1090 q^{22} +55.4275i q^{23} +(108.282 + 62.6613i) q^{24} +134.794 q^{25} +19.1683 q^{26} +(-140.295 - 0.420792i) q^{27} -68.1510i q^{29} +(187.560 + 108.538i) q^{30} +178.671i q^{31} +58.4469i q^{32} +(-160.103 - 92.6489i) q^{33} +74.8285i q^{34} +(-17.5608 - 30.5571i) q^{36} -233.676 q^{37} -90.9987 q^{38} +(-33.3181 - 19.2807i) q^{39} +388.071i q^{40} +370.068 q^{41} -187.068 q^{43} -46.4680i q^{44} +(-216.841 - 377.320i) q^{45} -143.414 q^{46} +174.745 q^{47} +(-134.953 + 233.206i) q^{48} +348.768i q^{50} +(75.2671 - 130.066i) q^{51} -9.67022i q^{52} +272.180i q^{53} +(1.08876 - 363.002i) q^{54} -573.789i q^{55} +(158.173 + 91.5321i) q^{57} +176.334 q^{58} +96.8709 q^{59} +(54.7564 - 94.6222i) q^{60} -385.534i q^{61} -462.295 q^{62} -566.055 q^{64} -119.408i q^{65} +(239.721 - 414.251i) q^{66} -1018.02 q^{67} +37.7502 q^{68} +(249.280 + 144.254i) q^{69} -125.333i q^{71} +(563.626 - 323.909i) q^{72} -225.566i q^{73} -604.616i q^{74} +(350.812 - 606.223i) q^{75} +45.9079i q^{76} +(49.8870 - 86.2076i) q^{78} -1064.31 q^{79} -835.783 q^{80} +(-367.022 + 629.870i) q^{81} +957.517i q^{82} -601.040 q^{83} +466.140 q^{85} -484.021i q^{86} +(-306.502 - 177.368i) q^{87} +857.104 q^{88} -1505.21 q^{89} +(976.280 - 561.055i) q^{90} +72.3506i q^{92} +(803.556 + 465.005i) q^{93} +452.137i q^{94} +566.872i q^{95} +(262.859 + 152.112i) q^{96} +327.463i q^{97} +(-833.358 + 478.920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 28 q^{4} + 6 q^{9}+O(q^{10}) \) 12 * q - 28 * q^4 + 6 * q^9	\( 12 q - 28 q^{4} + 6 q^{9} + 6 q^{15} - 268 q^{16} - 132 q^{18} - 268 q^{22} + 84 q^{25} + 1644 q^{30} + 852 q^{36} - 1528 q^{37} + 852 q^{39} - 1012 q^{43} - 1216 q^{46} + 2682 q^{51} + 270 q^{57} - 5740 q^{58} + 1836 q^{60} - 548 q^{64} - 1584 q^{67} + 5424 q^{72} + 4296 q^{78} - 3348 q^{79} - 1674 q^{81} + 348 q^{85} + 1108 q^{88} + 2958 q^{93} - 3354 q^{99}+O(q^{100}) \) 12 * q - 28 * q^4 + 6 * q^9 + 6 * q^15 - 268 * q^16 - 132 * q^18 - 268 * q^22 + 84 * q^25 + 1644 * q^30 + 852 * q^36 - 1528 * q^37 + 852 * q^39 - 1012 * q^43 - 1216 * q^46 + 2682 * q^51 + 270 * q^57 - 5740 * q^58 + 1836 * q^60 - 548 * q^64 - 1584 * q^67 + 5424 * q^72 + 4296 * q^78 - 3348 * q^79 - 1674 * q^81 + 348 * q^85 + 1108 * q^88 + 2958 * q^93 - 3354 * q^99

Introduction

L-functions

Modular forms

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