LMFDB - Embedded newform 684.5.y.d.145.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,5,Mod(145,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("684.145");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	684.y (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$70.7050547493$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 2826 x^{12} + 21668 x^{11} + 6144398 x^{10} + 32400228 x^{9} + 4476099452 x^{8} + \cdots + 21\!\cdots\!16 $ x^14 - 2x^13 + 2826x^12 + 21668x^11 + 6144398x^10 + 32400228x^9 + 4476099452x^8 + 1249545344x^7 + 2308151528484x^6 - 2140142598776x^5 + 625358881541536x^4 - 2569874136887808x^3 + 115090576468624800x^2 - 159892348486261824*x + 219826226298839616
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.6
Root			$9.82068 + 17.0099i$ of defining polynomial
Character	$\chi$	$=$	684.145
Dual form			684.5.y.d.217.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.82068 + 15.2779i) q^{5} -52.3606 q^{7} +O(q^{10})$	$q+(8.82068 + 15.2779i) q^{5} -52.3606 q^{7} +204.993 q^{11} +(278.771 + 160.948i) q^{13} +(-194.627 - 337.104i) q^{17} +(-32.1886 + 359.562i) q^{19} +(88.9899 - 154.135i) q^{23} +(156.891 - 271.743i) q^{25} +(-985.695 - 569.091i) q^{29} -263.792i q^{31} +(-461.856 - 799.958i) q^{35} +702.699i q^{37} +(1389.10 - 801.997i) q^{41} +(28.5891 + 49.5177i) q^{43} +(-533.810 + 924.586i) q^{47} +340.633 q^{49} +(2234.27 + 1289.96i) q^{53} +(1808.18 + 3131.86i) q^{55} +(2523.59 - 1456.99i) q^{59} +(-2030.23 + 3516.46i) q^{61} +5678.70i q^{65} +(6206.45 + 3583.29i) q^{67} +(7397.50 - 4270.95i) q^{71} +(4142.65 + 7175.28i) q^{73} -10733.6 q^{77} +(-3143.44 + 1814.86i) q^{79} +1166.31 q^{83} +(3433.49 - 5946.97i) q^{85} +(3702.97 + 2137.91i) q^{89} +(-14596.6 - 8427.35i) q^{91} +(-5777.27 + 2679.81i) q^{95} +(-6202.10 + 3580.78i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) $ 14 * q - 12 * q^5 - 110 * q^7	$ 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) $ 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	8.82068	+	15.2779i	0.352827	+	0.611115i	0.986744	−	0.162287i	$-0.0518870\pi$
$5$	8.82068	+	15.2779i	0.352827	+	0.611115i	−0.633916	+	0.773402i	$0.718554\pi$
$6$		0			0
$7$	−52.3606			−1.06858			−0.534292	−	0.845300i	$-0.679422\pi$
$7$	−52.3606			−1.06858			−0.534292	+	0.845300i	$0.679422\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	204.993			1.69416			0.847079	−	0.531467i	$-0.178359\pi$
$11$	204.993			1.69416			0.847079	+	0.531467i	$0.178359\pi$
$12$		0			0
$13$	278.771	+	160.948i	1.64953	+	0.952357i	0.977258	+	0.212053i	$0.0680151\pi$
$13$	278.771	+	160.948i	1.64953	+	0.952357i	0.672273	+	0.740304i	$0.265318\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−194.627	−	337.104i	−0.673450	−	1.16645i	−0.976919	−	0.213608i	$-0.931478\pi$
$17$	−194.627	−	337.104i	−0.673450	−	1.16645i	0.303469	−	0.952841i	$-0.401855\pi$
$18$		0			0
$19$	−32.1886	+	359.562i	−0.0891650	+	0.996017i
$19$	−32.1886	+	359.562i	−0.0891650	+	0.996017i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	88.9899	−	154.135i	0.168223	−	0.291371i	−0.769572	−	0.638560i	$-0.779530\pi$
$23$	88.9899	−	154.135i	0.168223	−	0.291371i	0.937795	+	0.347189i	$0.112864\pi$
$24$		0			0
$25$	156.891	−	271.743i	0.251026	−	0.434790i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−985.695	−	569.091i	−1.17205	−	0.676684i	−0.217889	−	0.975974i	$-0.569917\pi$
$29$	−985.695	−	569.091i	−1.17205	−	0.676684i	−0.954162	+	0.299289i	$0.903250\pi$
$30$		0			0
$31$		−	263.792i		−	0.274498i	−0.990537	−	0.137249i	$-0.956174\pi$
$31$		−	263.792i		−	0.274498i	0.990537	−	0.137249i	$-0.0438260\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−461.856	−	799.958i	−0.377025	−	0.653027i
$36$		0			0
$37$			702.699i			0.513294i	0.966505	+	0.256647i	$0.0826178\pi$
$37$			702.699i			0.513294i	−0.966505	+	0.256647i	$0.917382\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1389.10	−	801.997i	0.826353	−	0.477095i	−0.0262491	−	0.999655i	$-0.508356\pi$
$41$	1389.10	−	801.997i	0.826353	−	0.477095i	0.852602	+	0.522560i	$0.175023\pi$
$42$		0			0
$43$	28.5891	+	49.5177i	0.0154619	+	0.0267808i	0.873653	−	0.486550i	$-0.161745\pi$
$43$	28.5891	+	49.5177i	0.0154619	+	0.0267808i	−0.858191	+	0.513331i	$0.828411\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−533.810	+	924.586i	−0.241652	+	0.418554i	−0.961185	−	0.275904i	$-0.911023\pi$
$47$	−533.810	+	924.586i	−0.241652	+	0.418554i	0.719533	+	0.694458i	$0.244356\pi$
$48$		0			0
$49$	340.633			0.141871
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2234.27	+	1289.96i	0.795397	+	0.459223i	0.841859	−	0.539697i	$-0.181461\pi$
$53$	2234.27	+	1289.96i	0.795397	+	0.459223i	−0.0464621	+	0.998920i	$0.514795\pi$
$54$		0			0
$55$	1808.18	+	3131.86i	0.597745	+	1.03532i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2523.59	−	1456.99i	0.724961	−	0.418556i	−0.0916151	−	0.995794i	$-0.529203\pi$
$59$	2523.59	−	1456.99i	0.724961	−	0.418556i	0.816576	+	0.577238i	$0.195870\pi$
$60$		0			0
$61$	−2030.23	+	3516.46i	−0.545614	+	0.945032i	0.452954	+	0.891534i	$0.350370\pi$
$61$	−2030.23	+	3516.46i	−0.545614	+	0.945032i	−0.998568	+	0.0534976i	$0.982963\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$			5678.70i			1.34407i
$66$		0			0
$67$	6206.45	+	3583.29i	1.38259	+	0.798239i	0.992466	−	0.122523i	$-0.0390986\pi$
$67$	6206.45	+	3583.29i	1.38259	+	0.798239i	0.390125	+	0.920762i	$0.372432\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	7397.50	−	4270.95i	1.46747	−	0.847243i	0.468130	−	0.883659i	$-0.344928\pi$
$71$	7397.50	−	4270.95i	1.46747	−	0.847243i	0.999337	+	0.0364169i	$0.0115944\pi$
$72$		0			0
$73$	4142.65	+	7175.28i	0.777379	+	1.34646i	0.933448	+	0.358713i	$0.116784\pi$
$73$	4142.65	+	7175.28i	0.777379	+	1.34646i	−0.156069	+	0.987746i	$0.549882\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10733.6			−1.81035
$78$		0			0
$79$	−3143.44	+	1814.86i	−0.503675	+	0.290797i	−0.730230	−	0.683201i	$-0.760587\pi$
$79$	−3143.44	+	1814.86i	−0.503675	+	0.290797i	0.226555	+	0.973998i	$0.427254\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1166.31			0.169300			0.0846501	−	0.996411i	$-0.473023\pi$
$83$	1166.31			0.169300			0.0846501	+	0.996411i	$0.473023\pi$
$84$		0			0
$85$	3433.49	−	5946.97i	0.475223	−	0.823110i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3702.97	+	2137.91i	0.467488	+	0.269904i	0.715187	−	0.698933i	$-0.246341\pi$
$89$	3702.97	+	2137.91i	0.467488	+	0.269904i	−0.247700	+	0.968837i	$0.579675\pi$
$90$		0			0
$91$	−14596.6	−	8427.35i	−1.76266	−	1.01767i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−5777.27	+	2679.81i	−0.640140	+	0.296932i
$96$		0			0
$97$	−6202.10	+	3580.78i	−0.659167	+	0.380570i	−0.791959	−	0.610574i	$-0.790939\pi$
$97$	−6202.10	+	3580.78i	−0.659167	+	0.380570i	0.132793	+	0.991144i	$0.457606\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−357.704	+	619.562i	−0.0350656	+	0.0607354i	−0.883026	−	0.469325i	$-0.844497\pi$
$101$	−357.704	+	619.562i	−0.0350656	+	0.0607354i	0.847960	+	0.530060i	$0.177831\pi$
$102$		0			0
$103$		−	11245.1i		−	1.05996i	−0.848011	−	0.529979i	$-0.822200\pi$
$103$		−	11245.1i		−	1.05996i	0.848011	−	0.529979i	$-0.177800\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	6716.00i		−	0.586601i	−0.956020	−	0.293301i	$-0.905246\pi$
$107$		−	6716.00i		−	0.586601i	0.956020	−	0.293301i	$-0.0947537\pi$
$108$		0			0
$109$	−14441.9	+	8338.05i	−1.21555	+	0.701797i	−0.963963	−	0.266038i	$-0.914285\pi$
$109$	−14441.9	+	8338.05i	−1.21555	+	0.701797i	−0.251586	+	0.967835i	$0.580952\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			6301.30i			0.493484i	0.969081	+	0.246742i	$0.0793601\pi$
$113$			6301.30i			0.493484i	−0.969081	+	0.246742i	$0.920640\pi$
$114$		0			0
$115$	3139.81			0.237415
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10190.8	+	17651.0i	0.719638	+	1.24645i
$120$		0			0
$121$	27381.2			1.87017
$122$		0			0
$123$		0			0
$124$		0			0
$125$	16561.4			1.05993
$126$		0			0
$127$	11730.6	+	6772.65i	0.727298	+	0.419905i	0.817433	−	0.576024i	$-0.195397\pi$
$127$	11730.6	+	6772.65i	0.727298	+	0.419905i	−0.0901352	+	0.995930i	$0.528730\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16903.7	+	29278.1i	0.985009	+	1.70609i	0.641898	+	0.766790i	$0.278147\pi$
$131$	16903.7	+	29278.1i	0.985009	+	1.70609i	0.343111	+	0.939295i	$0.388519\pi$
$132$		0			0
$133$	1685.41	−	18826.9i	0.0952803	−	1.06433i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−17977.9	+	31138.7i	−0.957852	+	1.65905i	−0.230149	+	0.973155i	$0.573921\pi$
$137$	−17977.9	+	31138.7i	−0.957852	+	1.65905i	−0.727703	+	0.685892i	$0.759412\pi$
$138$		0			0
$139$	15204.5	−	26334.9i	0.786939	−	1.36302i	−0.140894	−	0.990025i	$-0.544998\pi$
$139$	15204.5	−	26334.9i	0.786939	−	1.36302i	0.927834	−	0.372994i	$-0.121669\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	57146.1	+	32993.3i	2.79457	+	1.61344i
$144$		0			0
$145$		−	20079.1i		−	0.955010i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4322.76	−	7487.25i	−0.194710	−	0.337248i	0.752095	−	0.659054i	$-0.229043\pi$
$149$	−4322.76	−	7487.25i	−0.194710	−	0.337248i	−0.946806	+	0.321806i	$0.895710\pi$
$150$		0			0
$151$			24639.8i			1.08064i	0.841458	+	0.540322i	$0.181698\pi$
$151$			24639.8i			1.08064i	−0.841458	+	0.540322i	$0.818302\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4030.18	−	2326.83i	0.167749	−	0.0968502i
$156$		0			0
$157$	14591.4	+	25273.1i	0.591969	+	1.02532i	0.993967	+	0.109680i	$0.0349825\pi$
$157$	14591.4	+	25273.1i	0.591969	+	1.02532i	−0.401998	+	0.915640i	$0.631684\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4659.57	+	8070.61i	−0.179760	+	0.311354i
$162$		0			0
$163$	7900.08			0.297342			0.148671	−	0.988887i	$-0.452500\pi$
$163$	7900.08			0.297342			0.148671	+	0.988887i	$0.452500\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−14268.1	−	8237.67i	−0.511602	−	0.295374i	0.221890	−	0.975072i	$-0.428777\pi$
$167$	−14268.1	−	8237.67i	−0.511602	−	0.295374i	−0.733492	+	0.679698i	$0.762111\pi$
$168$		0			0
$169$	37528.2	+	65000.8i	1.31397	+	2.27586i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	18603.4	−	10740.7i	0.621586	−	0.358873i	−0.155900	−	0.987773i	$-0.549828\pi$
$173$	18603.4	−	10740.7i	0.621586	−	0.358873i	0.777486	+	0.628900i	$0.216495\pi$
$174$		0			0
$175$	−8214.92	+	14228.7i	−0.268242	+	0.464609i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			18676.5i			0.582893i	0.956587	+	0.291446i	$0.0941365\pi$
$179$			18676.5i			0.582893i	−0.956587	+	0.291446i	$0.905864\pi$
$180$		0			0
$181$	−40612.6	−	23447.7i	−1.23966	−	0.715720i	−0.270638	−	0.962681i	$-0.587235\pi$
$181$	−40612.6	−	23447.7i	−1.23966	−	0.715720i	−0.969025	+	0.246962i	$0.920568\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10735.8	+	6198.29i	−0.313682	+	0.181104i
$186$		0			0
$187$	−39897.2	−	69104.0i	−1.14093	−	1.97615i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	24338.7			0.667161			0.333581	−	0.942722i	$-0.391743\pi$
$191$	24338.7			0.667161			0.333581	+	0.942722i	$0.391743\pi$
$192$		0			0
$193$	−2729.64	+	1575.96i	−0.0732810	+	0.0423088i	−0.536193	−	0.844096i	$-0.680138\pi$
$193$	−2729.64	+	1575.96i	−0.0732810	+	0.0423088i	0.462912	+	0.886404i	$0.346805\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−18748.4			−0.483095			−0.241548	−	0.970389i	$-0.577655\pi$
$197$	−18748.4			−0.483095			−0.241548	+	0.970389i	$0.577655\pi$
$198$		0			0
$199$	−34440.4	+	59652.6i	−0.869686	+	1.50634i	−0.00736868	+	0.999973i	$0.502346\pi$
$199$	−34440.4	+	59652.6i	−0.869686	+	1.50634i	−0.862318	+	0.506368i	$0.830988\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	51611.6	+	29798.0i	1.25243	+	0.723094i
$204$		0			0
$205$	24505.6	+	14148.3i	0.583120	+	0.336664i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6598.44	+	73707.7i	−0.151060	+	1.68741i
$210$		0			0
$211$	53996.5	−	31174.9i	1.21283	−	0.700229i	0.249458	−	0.968386i	$-0.419748\pi$
$211$	53996.5	−	31174.9i	1.21283	−	0.700229i	0.963375	+	0.268156i	$0.0864143\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−504.350	+	873.561i	−0.0109108	+	0.0188980i
$216$		0			0
$217$			13812.3i			0.293324i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	125300.i		−	2.56546i
$222$		0			0
$223$	6721.41	−	3880.61i	0.135161	−	0.0780351i	−0.430895	−	0.902402i	$-0.641802\pi$
$223$	6721.41	−	3880.61i	0.135161	−	0.0780351i	0.566056	+	0.824367i	$0.308469\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$		−	72905.3i		−	1.41484i	−0.706793	−	0.707420i	$-0.749859\pi$
$227$		−	72905.3i		−	1.41484i	0.706793	−	0.707420i	$-0.250141\pi$
$228$		0			0
$229$	−17945.5			−0.342203			−0.171101	−	0.985253i	$-0.554733\pi$
$229$	−17945.5			−0.342203			−0.171101	+	0.985253i	$0.554733\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−13116.4	−	22718.2i	−0.241602	−	0.418468i	0.719568	−	0.694421i	$-0.244340\pi$
$233$	−13116.4	−	22718.2i	−0.241602	−	0.418468i	−0.961171	+	0.275954i	$0.911006\pi$
$234$		0			0
$235$	−18834.3			−0.341046
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−36433.1			−0.637823			−0.318912	−	0.947784i	$-0.603317\pi$
$239$	−36433.1			−0.637823			−0.318912	+	0.947784i	$0.603317\pi$
$240$		0			0
$241$	88892.0	+	51321.8i	1.53048	+	0.883625i	0.999339	+	0.0363436i	$0.0115711\pi$
$241$	88892.0	+	51321.8i	1.53048	+	0.883625i	0.531144	+	0.847281i	$0.321762\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3004.61	+	5204.14i	0.0500560	+	0.0866996i
$246$		0			0
$247$	−66844.2	+	95054.7i	−1.09564	+	1.55804i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7871.02	+	13633.0i	−0.124935	+	0.216394i	−0.921707	−	0.387886i	$-0.873206\pi$
$251$	−7871.02	+	13633.0i	−0.124935	+	0.216394i	0.796773	+	0.604279i	$0.206539\pi$
$252$		0			0
$253$	18242.3	−	31596.6i	0.284996	−	0.493628i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	73340.9	+	42343.4i	1.11040	+	0.641091i	0.938933	−	0.344099i	$-0.111816\pi$
$257$	73340.9	+	42343.4i	1.11040	+	0.641091i	0.171468	+	0.985190i	$0.445149\pi$
$258$		0			0
$259$		−	36793.8i		−	0.548498i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22312.5	−	38646.5i	−0.322580	−	0.558725i	0.658440	−	0.752634i	$-0.271217\pi$
$263$	−22312.5	−	38646.5i	−0.322580	−	0.558725i	−0.981020	+	0.193909i	$0.937883\pi$
$264$		0			0
$265$			45513.2i			0.648105i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−109365.	+	63141.8i	−1.51138	+	0.872594i	−0.511465	+	0.859304i	$0.670897\pi$
$269$	−109365.	+	63141.8i	−1.51138	+	0.872594i	−0.999912	+	0.0132900i	$0.995770\pi$
$270$		0			0
$271$	−2949.17	−	5108.12i	−0.0401571	−	0.0695541i	0.845248	−	0.534374i	$-0.179452\pi$
$271$	−2949.17	−	5108.12i	−0.0401571	−	0.0695541i	−0.885405	+	0.464820i	$0.846119\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	32161.6	−	55705.5i	0.425277	−	0.736602i
$276$		0			0
$277$	−35120.9			−0.457727			−0.228864	−	0.973459i	$-0.573501\pi$
$277$	−35120.9			−0.457727			−0.228864	+	0.973459i	$0.573501\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−80010.0	−	46193.8i	−1.01329	−	0.585021i	−0.101134	−	0.994873i	$-0.532247\pi$
$281$	−80010.0	−	46193.8i	−1.01329	−	0.585021i	−0.912152	+	0.409852i	$0.865580\pi$
$282$		0			0
$283$	29975.7	+	51919.5i	0.374280	+	0.648272i	0.990219	−	0.139522i	$-0.0445565\pi$
$283$	29975.7	+	51919.5i	0.374280	+	0.648272i	−0.615939	+	0.787794i	$0.711223\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−72734.1	+	41993.1i	−0.883028	+	0.509816i
$288$		0			0
$289$	−33998.9	+	58887.8i	−0.407070	+	0.705065i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	74281.6i		−	0.865258i	−0.901572	−	0.432629i	$-0.857586\pi$
$293$		−	74281.6i		−	0.865258i	0.901572	−	0.432629i	$-0.142414\pi$
$294$		0			0
$295$	44519.5	+	25703.4i	0.511572	+	0.295356i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	49615.6	−	28645.6i	0.554978	−	0.320417i
$300$		0			0
$301$	−1496.94	−	2592.78i	−0.0165224	−	0.0286176i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−71632.1			−0.770030
$306$		0			0
$307$	−60415.3	+	34880.8i	−0.641018	+	0.370092i	−0.785007	−	0.619487i	$-0.787341\pi$
$307$	−60415.3	+	34880.8i	−0.641018	+	0.370092i	0.143988	+	0.989579i	$0.454007\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	75175.5			0.777240			0.388620	−	0.921398i	$-0.372952\pi$
$311$	75175.5			0.777240			0.388620	+	0.921398i	$0.372952\pi$
$312$		0			0
$313$	91223.9	−	158004.i	0.931151	−	1.61280i	0.149793	−	0.988717i	$-0.452139\pi$
$313$	91223.9	−	158004.i	0.931151	−	1.61280i	0.781358	−	0.624083i	$-0.214527\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	78686.9	+	45429.9i	0.783040	+	0.452089i	0.837507	−	0.546427i	$-0.184012\pi$
$317$	78686.9	+	45429.9i	0.783040	+	0.452089i	−0.0544664	+	0.998516i	$0.517346\pi$
$318$		0			0
$319$	−202061.	−	116660.i	−1.98564	−	1.14641i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	127475.	−	59129.6i	1.22185	−	0.566761i
$324$		0			0
$325$	87473.3	−	50502.7i	0.828150	−	0.478132i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	27950.6	−	48411.9i	0.258226	−	0.447260i
$330$		0			0
$331$		−	77812.2i		−	0.710218i	−0.934825	−	0.355109i	$-0.884444\pi$
$331$		−	77812.2i		−	0.710218i	0.934825	−	0.355109i	$-0.115556\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			126428.i			1.12656i
$336$		0			0
$337$	3413.20	−	1970.61i	0.0300540	−	0.0173517i	−0.484898	−	0.874571i	$-0.661143\pi$
$337$	3413.20	−	1970.61i	0.0300540	−	0.0173517i	0.514952	+	0.857219i	$0.327810\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	54075.6i		−	0.465042i
$342$		0			0
$343$	107882.			0.916982
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−21576.9	−	37372.3i	−0.179197	−	0.310378i	0.762409	−	0.647095i	$-0.224016\pi$
$347$	−21576.9	−	37372.3i	−0.179197	−	0.310378i	−0.941606	+	0.336718i	$0.890683\pi$
$348$		0			0
$349$	20203.8			0.165875			0.0829376	−	0.996555i	$-0.473570\pi$
$349$	20203.8			0.165875			0.0829376	+	0.996555i	$0.473570\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6270.80			0.0503238			0.0251619	−	0.999683i	$-0.491990\pi$
$353$	6270.80			0.0503238			0.0251619	+	0.999683i	$0.491990\pi$
$354$		0			0
$355$	130502.	+	75345.4i	1.03552	+	0.597861i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	38354.3	+	66431.7i	0.297595	+	0.515450i	0.975585	−	0.219621i	$-0.0704821\pi$
$359$	38354.3	+	66431.7i	0.297595	+	0.515450i	−0.677990	+	0.735071i	$0.737149\pi$
$360$		0			0
$361$	−128249.	−	23147.6i	−0.984099	−	0.177620i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−73082.0	+	126582.i	−0.548561	+	0.950135i
$366$		0			0
$367$	3331.05	−	5769.54i	0.0247314	−	0.0428360i	−0.853395	−	0.521265i	$-0.825460\pi$
$367$	3331.05	−	5769.54i	0.0247314	−	0.0428360i	0.878126	+	0.478429i	$0.158794\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−116988.	−	67542.9i	−0.849948	−	0.490718i
$372$		0			0
$373$		−	71997.9i		−	0.517490i	−0.965946	−	0.258745i	$-0.916691\pi$
$373$		−	71997.9i		−	0.517490i	0.965946	−	0.258745i	$-0.0833090\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−183189.	−	317292.i	−1.28889	−	2.23242i
$378$		0			0
$379$			65679.6i			0.457248i	0.973515	+	0.228624i	$0.0734226\pi$
$379$			65679.6i			0.457248i	−0.973515	+	0.228624i	$0.926577\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	42580.8	−	24584.0i	0.290280	−	0.167593i	−0.347788	−	0.937573i	$-0.613067\pi$
$383$	42580.8	−	24584.0i	0.290280	−	0.167593i	0.638068	+	0.769980i	$0.279734\pi$
$384$		0			0
$385$	−94677.3	−	163986.i	−0.638741	−	1.10633i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−133027.	+	230409.i	−0.879101	+	1.52265i	−0.0267730	+	0.999642i	$0.508523\pi$
$389$	−133027.	+	230409.i	−0.879101	+	1.52265i	−0.852328	+	0.523007i	$0.824810\pi$
$390$		0			0
$391$	−69279.4			−0.453159
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−55454.5	−	32016.7i	−0.355421	−	0.205202i
$396$		0			0
$397$	−93519.8	−	161981.i	−0.593366	−	1.02774i	−0.993775	−	0.111404i	$-0.964465\pi$
$397$	−93519.8	−	161981.i	−0.593366	−	1.02774i	0.400409	−	0.916336i	$-0.368868\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	180894.	−	104439.i	1.12496	−	0.649493i	0.182294	−	0.983244i	$-0.441648\pi$
$401$	180894.	−	104439.i	1.12496	−	0.649493i	0.942661	+	0.333751i	$0.108314\pi$
$402$		0			0
$403$	42456.9	−	73537.5i	0.261420	−	0.452792i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			144049.i			0.869601i
$408$		0			0
$409$	−204889.	−	118292.i	−1.22482	−	0.707148i	−0.258876	−	0.965911i	$-0.583352\pi$
$409$	−204889.	−	118292.i	−1.22482	−	0.707148i	−0.965941	+	0.258762i	$0.916685\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−132137.	+	76289.1i	−0.774681	+	0.447262i
$414$		0			0
$415$	10287.6	+	17818.7i	0.0597337	+	0.103462i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−233899.			−1.33230			−0.666149	−	0.745819i	$-0.732058\pi$
$419$	−233899.			−1.33230			−0.666149	+	0.745819i	$0.732058\pi$
$420$		0			0
$421$	−168813.	+	97464.4i	−0.952451	+	0.549898i	−0.893841	−	0.448383i	$-0.852000\pi$
$421$	−168813.	+	97464.4i	−0.952451	+	0.549898i	−0.0586093	+	0.998281i	$0.518667\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−122141.			−0.676213
$426$		0			0
$427$	106304.	−	184124.i	0.583035	−	1.00985i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2424.41	+	1399.74i	0.0130513	+	0.00753515i	0.506511	−	0.862233i	$-0.330935\pi$
$431$	2424.41	+	1399.74i	0.0130513	+	0.00753515i	−0.493460	+	0.869768i	$0.664268\pi$
$432$		0			0
$433$	−112675.	−	65053.2i	−0.600971	−	0.346971i	0.168453	−	0.985710i	$-0.446123\pi$
$433$	−112675.	−	65053.2i	−0.600971	−	0.346971i	−0.769423	+	0.638739i	$0.779456\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	52556.7	+	36958.8i	0.275210	+	0.193533i
$438$		0			0
$439$	4135.23	−	2387.48i	0.0214571	−	0.0123883i	−0.489233	−	0.872153i	$-0.662723\pi$
$439$	4135.23	−	2387.48i	0.0214571	−	0.0123883i	0.510690	+	0.859765i	$0.329390\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−26621.5	+	46109.7i	−0.135651	+	0.234955i	−0.925846	−	0.377901i	$-0.876646\pi$
$443$	−26621.5	+	46109.7i	−0.135651	+	0.234955i	0.790195	+	0.612856i	$0.209979\pi$
$444$		0			0
$445$			75431.3i			0.380918i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	27916.7i		−	0.138475i	−0.997600	−	0.0692376i	$-0.977943\pi$
$449$		−	27916.7i		−	0.138475i	0.997600	−	0.0692376i	$-0.0220566\pi$
$450$		0			0
$451$	284756.	−	164404.i	1.39997	−	0.808275i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	297340.i		−	1.43625i
$456$		0			0
$457$	−77314.4			−0.370193			−0.185096	−	0.982720i	$-0.559260\pi$
$457$	−77314.4			−0.370193			−0.185096	+	0.982720i	$0.559260\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−108272.	−	187533.i	−0.509465	−	0.882419i	−0.999940	−	0.0109637i	$-0.996510\pi$
$461$	−108272.	−	187533.i	−0.509465	−	0.882419i	0.490475	−	0.871455i	$-0.336823\pi$
$462$		0			0
$463$	178453.			0.832457			0.416228	−	0.909260i	$-0.363352\pi$
$463$	178453.			0.832457			0.416228	+	0.909260i	$0.363352\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	165692.			0.759746			0.379873	−	0.925039i	$-0.375968\pi$
$467$	165692.			0.759746			0.379873	+	0.925039i	$0.375968\pi$
$468$		0			0
$469$	−324973.	−	187623.i	−1.47741	−	0.852985i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5860.57	+	10150.8i	0.0261949	+	0.0453709i
$474$		0			0
$475$	92658.5	+	65159.1i	0.410675	+	0.288794i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	196087.	−	339633.i	0.854629	−	1.48026i	−0.0223595	−	0.999750i	$-0.507118\pi$
$479$	196087.	−	339633.i	0.854629	−	1.48026i	0.876989	−	0.480511i	$-0.159549\pi$
$480$		0			0
$481$	−113098.	+	195892.i	−0.488839	+	0.846694i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−109413.	−	63169.9i	−0.465144	−	0.268551i
$486$		0			0
$487$			307933.i			1.29837i	0.760631	+	0.649184i	$0.224890\pi$
$487$			307933.i			1.29837i	−0.760631	+	0.649184i	$0.775110\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−10705.2	−	18542.0i	−0.0444050	−	0.0769118i	0.842969	−	0.537963i	$-0.180806\pi$
$491$	−10705.2	−	18542.0i	−0.0444050	−	0.0769118i	−0.887374	+	0.461051i	$0.847473\pi$
$492$		0			0
$493$			443042.i			1.82285i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−387338.	+	223629.i	−1.56811	+	0.905350i
$498$		0			0
$499$	−160809.	−	278530.i	−0.645819	−	1.11859i	−0.984112	−	0.177550i	$-0.943183\pi$
$499$	−160809.	−	278530.i	−0.645819	−	1.11859i	0.338293	−	0.941041i	$-0.390150\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	168442.	−	291750.i	0.665755	−	1.15312i	−0.313326	−	0.949646i	$-0.601443\pi$
$503$	168442.	−	291750.i	0.665755	−	1.15312i	0.979080	−	0.203475i	$-0.0652236\pi$
$504$		0			0
$505$	−12620.8			−0.0494884
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−293727.	−	169584.i	−1.13373	−	0.654558i	−0.188858	−	0.982004i	$-0.560479\pi$
$509$	−293727.	−	169584.i	−1.13373	−	0.654558i	−0.944870	+	0.327446i	$0.893812\pi$
$510$		0			0
$511$	−216912.	−	375702.i	−0.830694	−	1.43880i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	171801.	−	99189.5i	0.647756	−	0.373982i
$516$		0			0
$517$	−109427.	+	189534.i	−0.409397	+	0.709097i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			482553.i			1.77775i	0.458155	+	0.888873i	$0.348511\pi$
$521$			482553.i			1.77775i	−0.458155	+	0.888873i	$0.651489\pi$
$522$		0			0
$523$	210353.	+	121448.i	0.769035	+	0.444003i	0.832530	−	0.553979i	$-0.186891\pi$
$523$	210353.	+	121448.i	0.769035	+	0.444003i	−0.0634951	+	0.997982i	$0.520225\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−88925.4	+	51341.1i	−0.320188	+	0.184860i
$528$		0			0
$529$	124082.	+	214916.i	0.443402	+	0.767995i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	516320.			1.81746
$534$		0			0
$535$	102606.	−	59239.7i	0.358481	−	0.206969i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	69827.4			0.240352
$540$		0			0
$541$	−71294.8	+	123486.i	−0.243592	+	0.421914i	−0.961735	−	0.273982i	$-0.911659\pi$
$541$	−71294.8	+	123486.i	−0.243592	+	0.421914i	0.718143	+	0.695896i	$0.244993\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−254775.	−	147095.i	−0.857757	−	0.495226i
$546$		0			0
$547$	231972.	+	133929.i	0.775286	+	0.447611i	0.834757	−	0.550619i	$-0.185608\pi$
$547$	231972.	+	133929.i	0.775286	+	0.447611i	−0.0594713	+	0.998230i	$0.518941\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	236352.	−	336100.i	0.778495	−	1.10705i
$552$		0			0
$553$	164592.	−	95027.4i	0.538219	−	0.310741i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−136176.	+	235863.i	−0.438924	+	0.760239i	−0.997607	−	0.0691426i	$-0.977974\pi$
$557$	−136176.	+	235863.i	−0.438924	+	0.760239i	0.558683	+	0.829382i	$0.311307\pi$
$558$		0			0
$559$			18405.5i			0.0589011i
$560$		0			0
$561$		0			0
$562$		0			0
$563$			409304.i			1.29131i	0.763631	+	0.645653i	$0.223415\pi$
$563$			409304.i			1.29131i	−0.763631	+	0.645653i	$0.776585\pi$
$564$		0			0
$565$	−96270.5	+	55581.8i	−0.301576	+	0.174115i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	211124.i		−	0.652099i	−0.945353	−	0.326050i	$-0.894282\pi$
$569$		−	211124.i		−	0.652099i	0.945353	−	0.326050i	$-0.105718\pi$
$570$		0			0
$571$	−90818.2			−0.278548			−0.139274	−	0.990254i	$-0.544477\pi$
$571$	−90818.2			−0.278548			−0.139274	+	0.990254i	$0.544477\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−27923.5	−	48364.9i	−0.0844566	−	0.146283i
$576$		0			0
$577$	368486.			1.10680			0.553400	−	0.832916i	$-0.313330\pi$
$577$	368486.			1.10680			0.553400	+	0.832916i	$0.313330\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−61068.6			−0.180911
$582$		0			0
$583$	458010.	+	264432.i	1.34753	+	0.777996i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−231505.	−	400978.i	−0.671868	−	1.16371i	−0.977374	−	0.211520i	$-0.932159\pi$
$587$	−231505.	−	400978.i	−0.671868	−	1.16371i	0.305506	−	0.952190i	$-0.401175\pi$
$588$		0			0
$589$	94849.7	+	8491.09i	0.273404	+	0.0244756i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	265418.	−	459718.i	0.754782	−	1.30732i	−0.190701	−	0.981648i	$-0.561076\pi$
$593$	265418.	−	459718.i	0.754782	−	1.30732i	0.945483	−	0.325672i	$-0.105591\pi$
$594$		0			0
$595$	−179779.	+	311387.i	−0.507816	+	0.879562i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	237193.	+	136944.i	0.661072	+	0.381670i	0.792685	−	0.609631i	$-0.208682\pi$
$599$	237193.	+	136944.i	0.661072	+	0.381670i	−0.131613	+	0.991301i	$0.542016\pi$
$600$		0			0
$601$			214512.i			0.593884i	0.954895	+	0.296942i	$0.0959669\pi$
$601$			214512.i			0.593884i	−0.954895	+	0.296942i	$0.904033\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	241521.	+	418326.i	0.659847	+	1.14289i
$606$		0			0
$607$		−	86802.0i		−	0.235588i	−0.993038	−	0.117794i	$-0.962418\pi$
$607$		−	86802.0i		−	0.235588i	0.993038	−	0.117794i	$-0.0375822\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−297621.	+	171832.i	−0.797226	+	0.460279i
$612$		0			0
$613$	−162099.	−	280763.i	−0.431379	−	0.747170i	0.565613	−	0.824670i	$-0.308639\pi$
$613$	−162099.	−	280763.i	−0.431379	−	0.747170i	−0.996992	+	0.0775004i	$0.975306\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24170.1	−	41863.9i	0.0634905	−	0.109969i	−0.832533	−	0.553976i	$-0.813110\pi$
$617$	24170.1	−	41863.9i	0.0634905	−	0.109969i	0.896023	+	0.444007i	$0.146443\pi$
$618$		0			0
$619$	20362.2			0.0531427			0.0265714	−	0.999647i	$-0.491541\pi$
$619$	20362.2			0.0531427			0.0265714	+	0.999647i	$0.491541\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−193890.	−	111942.i	−0.499550	−	0.288415i
$624$		0			0
$625$	48025.9	+	83183.2i	0.122946	+	0.212949i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	236883.	−	136764.i	0.598732	−	0.345678i
$630$		0			0
$631$	68164.6	−	118064.i	0.171199	−	0.296525i	−0.767641	−	0.640881i	$-0.778569\pi$
$631$	68164.6	−	118064.i	0.171199	−	0.296525i	0.938839	+	0.344356i	$0.111903\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$			238958.i			0.592616i
$636$		0			0
$637$	94958.4	+	54824.3i	0.234021	+	0.135112i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−230047.	+	132818.i	−0.559887	+	0.323251i	−0.753100	−	0.657906i	$-0.771442\pi$
$641$	−230047.	+	132818.i	−0.559887	+	0.323251i	0.193213	+	0.981157i	$0.438109\pi$
$642$		0			0
$643$	−45134.6	−	78175.5i	−0.109166	−	0.189081i	0.806267	−	0.591552i	$-0.201485\pi$
$643$	−45134.6	−	78175.5i	−0.109166	−	0.189081i	−0.915433	+	0.402471i	$0.868151\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	826267.			1.97384			0.986920	−	0.161209i	$-0.0515392\pi$
$647$	826267.			1.97384			0.986920	+	0.161209i	$0.0515392\pi$
$648$		0			0
$649$	517318.	−	298674.i	1.22820	−	0.709100i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−157989.			−0.370510			−0.185255	−	0.982690i	$-0.559311\pi$
$653$	−157989.			−0.370510			−0.185255	+	0.982690i	$0.559311\pi$
$654$		0			0
$655$	−298205.	+	516506.i	−0.695076	+	1.20391i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−503444.	−	290663.i	−1.15926	−	0.669298i	−0.208132	−	0.978101i	$-0.566738\pi$
$659$	−503444.	−	290663.i	−1.15926	−	0.669298i	−0.951126	+	0.308803i	$0.900072\pi$
$660$		0			0
$661$	−141709.	−	81815.6i	−0.324335	−	0.187255i	0.328988	−	0.944334i	$-0.393292\pi$
$661$	−141709.	−	81815.6i	−0.324335	−	0.187255i	−0.653323	+	0.757079i	$0.726626\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	302501.	−	140316.i	0.684044	−	0.317297i
$666$		0			0
$667$	−175434.	+	101287.i	−0.394332	+	0.227668i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−416183.	+	720851.i	−0.924357	+	1.60103i
$672$		0			0
$673$		−	346679.i		−	0.765416i	−0.923869	−	0.382708i	$-0.874992\pi$
$673$		−	346679.i		−	0.765416i	0.923869	−	0.382708i	$-0.125008\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$		−	145641.i		−	0.317766i	−0.987297	−	0.158883i	$-0.949211\pi$
$677$		−	145641.i		−	0.317766i	0.987297	−	0.158883i	$-0.0507892\pi$
$678$		0			0
$679$	324746.	−	187492.i	0.704375	−	0.406671i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			583301.i			1.25041i	0.780462	+	0.625203i	$0.214984\pi$
$683$			583301.i			1.25041i	−0.780462	+	0.625203i	$0.785016\pi$
$684$		0			0
$685$	−634310.			−1.35182
$686$		0			0
$687$		0			0
$688$		0			0
$689$	415233.	+	719204.i	0.874688	+	1.51500i
$690$		0			0
$691$	637627.			1.33540			0.667699	−	0.744432i	$-0.267279\pi$
$691$	637627.			1.33540			0.667699	+	0.744432i	$0.267279\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	536455.			1.11061
$696$		0			0
$697$	−540713.	−	312181.i	−1.11302	−	0.642600i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	67477.4	+	116874.i	0.137316	+	0.237839i	0.926480	−	0.376344i	$-0.122819\pi$
$701$	67477.4	+	116874.i	0.137316	+	0.237839i	−0.789164	+	0.614183i	$0.789486\pi$
$702$		0			0
$703$	−252664.	−	22618.9i	−0.511249	−	0.0457679i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	18729.6	−	32440.6i	0.0374705	−	0.0649009i
$708$		0			0
$709$	459182.	−	795327.i	0.913467	−	1.58217i	0.104336	−	0.994542i	$-0.466728\pi$
$709$	459182.	−	795327.i	0.913467	−	1.58217i	0.809130	−	0.587629i	$-0.199939\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−40659.6	−	23474.8i	−0.0799805	−	0.0461768i
$714$		0			0
$715$			1.16409e6i			2.27707i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−195796.	−	339129.i	−0.378744	−	0.656005i	0.612135	−	0.790753i	$-0.290311\pi$
$719$	−195796.	−	339129.i	−0.378744	−	0.656005i	−0.990880	+	0.134748i	$0.956977\pi$
$720$		0			0
$721$			588800.i			1.13265i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−309294.	+	178571.i	−0.588430	+	0.339730i
$726$		0			0
$727$	−410398.	−	710830.i	−0.776490	−	1.34492i	−0.933953	−	0.357396i	$-0.883665\pi$
$727$	−410398.	−	710830.i	−0.776490	−	1.34492i	0.157463	−	0.987525i	$-0.449669\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	11128.4	−	19275.0i	0.0208257	−	0.0360711i
$732$		0			0
$733$	−1.00079e6			−1.86267			−0.931337	−	0.364158i	$-0.881357\pi$
$733$	−1.00079e6			−1.86267			−0.931337	+	0.364158i	$0.881357\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.27228e6	+	734551.i	2.34233	+	1.35234i
$738$		0			0
$739$	−331126.	−	573527.i	−0.606324	−	1.05018i	−0.991841	−	0.127483i	$-0.959310\pi$
$739$	−331126.	−	573527.i	−0.606324	−	1.05018i	0.385517	−	0.922701i	$-0.374023\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−77243.2	+	44596.4i	−0.139921	+	0.0807834i	−0.568326	−	0.822803i	$-0.692409\pi$
$743$	−77243.2	+	44596.4i	−0.139921	+	0.0807834i	0.428405	+	0.903587i	$0.359076\pi$
$744$		0			0
$745$	76259.4	−	132085.i	0.137398	−	0.237981i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			351654.i			0.626833i
$750$		0			0
$751$	591710.	+	341624.i	1.04913	+	0.605715i	0.922405	−	0.386223i	$-0.126221\pi$
$751$	591710.	+	341624.i	1.04913	+	0.605715i	0.126723	+	0.991938i	$0.459554\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−376443.	+	217340.i	−0.660398	+	0.381281i
$756$		0			0
$757$	368128.	+	637616.i	0.642402	+	1.11267i	0.984895	+	0.173152i	$0.0553952\pi$
$757$	368128.	+	637616.i	0.642402	+	1.11267i	−0.342494	+	0.939520i	$0.611272\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	93067.7			0.160705			0.0803526	−	0.996767i	$-0.474395\pi$
$761$	93067.7			0.160705			0.0803526	+	0.996767i	$0.474395\pi$
$762$		0			0
$763$	756188.	−	436585.i	1.29892	−	0.749929i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	938003.			1.59446
$768$		0			0
$769$	−532516.	+	922345.i	−0.900493	+	1.55970i	−0.0736368	+	0.997285i	$0.523461\pi$
$769$	−532516.	+	922345.i	−0.900493	+	1.55970i	−0.826856	+	0.562414i	$0.809873\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−327488.	−	189075.i	−0.548071	−	0.316429i	0.200273	−	0.979740i	$-0.435817\pi$
$773$	−327488.	−	189075.i	−0.548071	−	0.316429i	−0.748344	+	0.663311i	$0.769151\pi$
$774$		0			0
$775$	−71683.8	−	41386.7i	−0.119349	−	0.0689060i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	243655.	+	525283.i	0.401513	+	0.865602i
$780$		0			0
$781$	1.51644e6	−	875515.i	2.48612	−	1.43536i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−257413.	+	445852.i	−0.417725	+	0.723522i
$786$		0			0
$787$		−	397084.i		−	0.641110i	−0.947230	−	0.320555i	$-0.896131\pi$
$787$		−	397084.i		−	0.641110i	0.947230	−	0.320555i	$-0.103869\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	329940.i		−	0.527329i
$792$		0			0
$793$	−1.13194e6	+	653525.i	−1.80002	+	1.03924i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	187848.i		−	0.295726i	−0.989008	−	0.147863i	$-0.952761\pi$
$797$		−	187848.i		−	0.295726i	0.989008	−	0.147863i	$-0.0472395\pi$
$798$		0			0
$799$	415575.			0.650963
$800$		0			0
$801$		0			0
$802$		0			0
$803$	849215.	+	1.47088e6i	1.31700	+	2.28111i
$804$		0			0
$805$	−164402.			−0.253697
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−337255.			−0.515302			−0.257651	−	0.966238i	$-0.582948\pi$
$809$	−337255.			−0.515302			−0.257651	+	0.966238i	$0.582948\pi$
$810$		0			0
$811$	369719.	+	213458.i	0.562122	+	0.324541i	0.753997	−	0.656878i	$-0.228123\pi$
$811$	369719.	+	213458.i	0.562122	+	0.324541i	−0.191875	+	0.981419i	$0.561457\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	69684.1	+	120696.i	0.104910	+	0.181710i
$816$		0			0
$817$	−18724.9	+	8685.65i	−0.0280528	+	0.0130124i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−331415.	+	574027.i	−0.491683	+	0.851620i	−0.999954	−	0.00957688i	$-0.996952\pi$
$821$	−331415.	+	574027.i	−0.491683	+	0.851620i	0.508271	+	0.861197i	$0.330285\pi$
$822$		0			0
$823$	56997.0	−	98721.8i	0.0841497	−	0.145752i	−0.820879	−	0.571102i	$-0.806516\pi$
$823$	56997.0	−	98721.8i	0.0841497	−	0.145752i	0.905029	+	0.425351i	$0.139849\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	871809.	+	503339.i	1.27471	+	0.735953i	0.975870	−	0.218352i	$-0.0700680\pi$
$827$	871809.	+	503339.i	1.27471	+	0.735953i	0.298837	+	0.954304i	$0.403401\pi$
$828$		0			0
$829$			178899.i			0.260315i	0.991493	+	0.130158i	$0.0415483\pi$
$829$			178899.i			0.260315i	−0.991493	+	0.130158i	$0.958452\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−66296.3	−	114829.i	−0.0955432	−	0.165486i
$834$		0			0
$835$		−	290648.i		−	0.416863i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	456156.	−	263362.i	0.648022	−	0.374136i	−0.139676	−	0.990197i	$-0.544606\pi$
$839$	456156.	−	263362.i	0.648022	−	0.374136i	0.787698	+	0.616062i	$0.211273\pi$
$840$		0			0
$841$	294089.	+	509378.i	0.415803	+	0.720192i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−662049.	+	1.14670e6i	−0.927207	+	1.60597i
$846$		0			0
$847$	−1.43369e6			−1.99843
$848$		0			0
$849$		0			0
$850$		0			0
$851$	108311.	+	62533.2i	0.149559	+	0.0863478i
$852$		0			0
$853$	−85940.6	−	148854.i	−0.118114	−	0.204579i	0.800906	−	0.598790i	$-0.204351\pi$
$853$	−85940.6	−	148854.i	−0.118114	−	0.204579i	−0.919020	+	0.394211i	$0.871018\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	804615.	−	464545.i	1.09554	−	0.632508i	0.160491	−	0.987037i	$-0.448692\pi$
$857$	804615.	−	464545.i	1.09554	−	0.632508i	0.935045	+	0.354530i	$0.115359\pi$
$858$		0			0
$859$	562640.	−	974521.i	0.762508	−	1.32070i	−0.179047	−	0.983841i	$-0.557301\pi$
$859$	562640.	−	974521.i	0.762508	−	1.32070i	0.941554	−	0.336861i	$-0.109365\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	989482.i		−	1.32858i	−0.747477	−	0.664288i	$-0.768735\pi$
$863$		−	989482.i		−	1.32858i	0.747477	−	0.664288i	$-0.231265\pi$
$864$		0			0
$865$	328190.	+	189481.i	0.438625	+	0.253240i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−644383.	+	372035.i	−0.853305	+	0.492656i
$870$		0			0
$871$	1.15345e6	+	1.99783e6i	1.52042	+	2.63344i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−867165.			−1.13262
$876$		0			0
$877$	529245.	−	305560.i	0.688110	−	0.397280i	−0.114794	−	0.993389i	$-0.536621\pi$
$877$	529245.	−	305560.i	0.688110	−	0.397280i	0.802904	+	0.596109i	$0.203287\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−1.22951e6			−1.58409			−0.792044	−	0.610463i	$-0.790983\pi$
$881$	−1.22951e6			−1.58409			−0.792044	+	0.610463i	$0.790983\pi$
$882$		0			0
$883$	381698.	−	661121.i	0.489552	−	0.847929i	−0.510376	−	0.859951i	$-0.670494\pi$
$883$	381698.	−	661121.i	0.489552	−	0.847929i	0.999928	+	0.0120227i	$0.00382704\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.03947e6	+	600140.i	1.32119	+	0.762790i	0.983919	−	0.178617i	$-0.0571622\pi$
$887$	1.03947e6	+	600140.i	1.32119	+	0.762790i	0.337273	+	0.941407i	$0.390496\pi$
$888$		0			0
$889$	−614220.	−	354620.i	−0.777178	−	0.448704i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−315263.	−	221699.i	−0.395340	−	0.278010i
$894$		0			0
$895$	−285337.	+	164739.i	−0.356214	+	0.205660i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−150122.	+	260019.i	−0.185748	+	0.321725i
$900$		0			0
$901$		−	1.00424e6i		−	1.23705i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	827299.i		−	1.01010i
$906$		0			0
$907$	259731.	−	149956.i	0.315725	−	0.182284i	−0.333760	−	0.942658i	$-0.608318\pi$
$907$	259731.	−	149956.i	0.315725	−	0.182284i	0.649486	+	0.760374i	$0.274984\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	1.32860e6i		−	1.60088i	−0.599413	−	0.800440i	$-0.704599\pi$
$911$		−	1.32860e6i		−	1.60088i	0.599413	−	0.800440i	$-0.295401\pi$
$912$		0			0
$913$	239085.			0.286821
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−885090.	−	1.53302e6i	−1.05256	−	1.82309i
$918$		0			0
$919$	−1.53214e6			−1.81413			−0.907065	−	0.420991i	$-0.861683\pi$
$919$	−1.53214e6			−1.81413			−0.907065	+	0.420991i	$0.861683\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.74961e6			3.22751
$924$		0			0
$925$	190954.	+	110247.i	0.223175	+	0.128850i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	655435.	+	1.13525e6i	0.759448	+	1.31540i	0.943132	+	0.332417i	$0.107864\pi$
$929$	655435.	+	1.13525e6i	0.759448	+	1.31540i	−0.183685	+	0.982985i	$0.558802\pi$
$930$		0			0
$931$	−10964.5	+	122479.i	−0.0126500	+	0.141306i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	703841.	−	1.21909e6i	0.805103	−	1.39448i
$936$		0			0
$937$	588560.	−	1.01942e6i	0.670365	−	1.16111i	−0.307435	−	0.951569i	$-0.599471\pi$
$937$	588560.	−	1.01942e6i	0.670365	−	1.16111i	0.977801	−	0.209538i	$-0.0671960\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−811075.	−	468274.i	−0.915971	−	0.528836i	−0.0336232	−	0.999435i	$-0.510705\pi$
$941$	−811075.	−	468274.i	−0.915971	−	0.528836i	−0.882347	+	0.470599i	$0.844038\pi$
$942$		0			0
$943$		−	285479.i		−	0.321033i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−484545.	−	839257.i	−0.540299	−	0.935826i	−0.998887	−	0.0471764i	$-0.984978\pi$
$947$	−484545.	−	839257.i	−0.540299	−	0.935826i	0.458587	−	0.888649i	$-0.348356\pi$
$948$		0			0
$949$			2.66701e6i			2.96137i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−177487.	+	102472.i	−0.195425	+	0.112829i	−0.594520	−	0.804081i	$-0.702658\pi$
$953$	−177487.	+	102472.i	−0.195425	+	0.112829i	0.399095	+	0.916910i	$0.369325\pi$
$954$		0			0
$955$	214684.	+	371843.i	0.235393	+	0.407712i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	941335.	−	1.63044e6i	1.02354	−	1.77283i
$960$		0			0
$961$	853935.			0.924651
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−48154.6	−	27802.1i	−0.0517111	−	0.0298554i
$966$		0			0
$967$	−292098.	−	505929.i	−0.312375	−	0.541049i	0.666501	−	0.745504i	$-0.267791\pi$
$967$	−292098.	−	505929.i	−0.312375	−	0.541049i	−0.978876	+	0.204455i	$0.934458\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.02153e6	+	589782.i	−1.08346	+	0.625537i	−0.931828	−	0.362900i	$-0.881787\pi$
$971$	−1.02153e6	+	589782.i	−1.08346	+	0.625537i	−0.151634	+	0.988437i	$0.548453\pi$
$972$		0			0
$973$	−796115.	+	1.37891e6i	−0.840911	+	1.45650i
$974$		0			0
$975$		0			0
$976$		0			0
$977$		−	970366.i		−	1.01659i	−0.861183	−	0.508296i	$-0.830276\pi$
$977$		−	970366.i		−	1.01659i	0.861183	−	0.508296i	$-0.169724\pi$
$978$		0			0
$979$	759083.	+	438257.i	0.791998	+	0.457260i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−729695.	+	421290.i	−0.755152	+	0.435987i	−0.827553	−	0.561388i	$-0.810267\pi$
$983$	−729695.	+	421290.i	−0.755152	+	0.435987i	0.0724002	+	0.997376i	$0.476934\pi$
$984$		0			0
$985$	−165374.	−	286436.i	−0.170449	−	0.295227i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	10176.6			0.0104042
$990$		0			0
$991$	−1.04746e6	+	604749.i	−1.06657	+	0.615784i	−0.927242	−	0.374463i	$-0.877827\pi$
$991$	−1.04746e6	+	604749.i	−1.06657	+	0.615784i	−0.139327	+	0.990246i	$0.544494\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−1.21515e6			−1.22740
$996$		0			0
$997$	707195.	−	1.22490e6i	0.711457	−	1.23228i	−0.252853	−	0.967505i	$-0.581369\pi$
$997$	707195.	−	1.22490e6i	0.711457	−	1.23228i	0.964310	−	0.264775i	$-0.0852977\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.5.y.d.145.6		14
3.2	odd	2		228.5.l.b.145.2	✓	14
19.8	odd	6	inner	684.5.y.d.217.6		14
57.8	even	6		228.5.l.b.217.2	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.5.l.b.145.2	✓	14	3.2	odd	2
228.5.l.b.217.2	yes	14	57.8	even	6
684.5.y.d.145.6		14	1.1	even	1	trivial
684.5.y.d.217.6		14	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	684.y (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(8.82068 + 15.2779i) q^{5} -52.3606 q^{7} +O(q^{10})\)	\(q+(8.82068 + 15.2779i) q^{5} -52.3606 q^{7} +204.993 q^{11} +(278.771 + 160.948i) q^{13} +(-194.627 - 337.104i) q^{17} +(-32.1886 + 359.562i) q^{19} +(88.9899 - 154.135i) q^{23} +(156.891 - 271.743i) q^{25} +(-985.695 - 569.091i) q^{29} -263.792i q^{31} +(-461.856 - 799.958i) q^{35} +702.699i q^{37} +(1389.10 - 801.997i) q^{41} +(28.5891 + 49.5177i) q^{43} +(-533.810 + 924.586i) q^{47} +340.633 q^{49} +(2234.27 + 1289.96i) q^{53} +(1808.18 + 3131.86i) q^{55} +(2523.59 - 1456.99i) q^{59} +(-2030.23 + 3516.46i) q^{61} +5678.70i q^{65} +(6206.45 + 3583.29i) q^{67} +(7397.50 - 4270.95i) q^{71} +(4142.65 + 7175.28i) q^{73} -10733.6 q^{77} +(-3143.44 + 1814.86i) q^{79} +1166.31 q^{83} +(3433.49 - 5946.97i) q^{85} +(3702.97 + 2137.91i) q^{89} +(-14596.6 - 8427.35i) q^{91} +(-5777.27 + 2679.81i) q^{95} +(-6202.10 + 3580.78i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 12 q^{5} - 110 q^{7}+O(q^{10}) \) 14 * q - 12 * q^5 - 110 * q^7	\( 14 q - 12 q^{5} - 110 q^{7} + 84 q^{11} + 21 q^{13} - 282 q^{17} + 62 q^{19} + 678 q^{23} - 1293 q^{25} + 774 q^{29} - 228 q^{35} - 5268 q^{41} + 2239 q^{43} - 1674 q^{47} - 1080 q^{49} + 1806 q^{53} + 2204 q^{55} + 11496 q^{59} - 1661 q^{61} + 6957 q^{67} + 11784 q^{71} - 8129 q^{73} - 996 q^{77} - 5907 q^{79} - 24444 q^{83} + 3956 q^{85} - 21648 q^{89} + 13995 q^{91} + 28884 q^{95} - 9408 q^{97}+O(q^{100}) \) 14 * q - 12 * q^5 - 110 * q^7 + 84 * q^11 + 21 * q^13 - 282 * q^17 + 62 * q^19 + 678 * q^23 - 1293 * q^25 + 774 * q^29 - 228 * q^35 - 5268 * q^41 + 2239 * q^43 - 1674 * q^47 - 1080 * q^49 + 1806 * q^53 + 2204 * q^55 + 11496 * q^59 - 1661 * q^61 + 6957 * q^67 + 11784 * q^71 - 8129 * q^73 - 996 * q^77 - 5907 * q^79 - 24444 * q^83 + 3956 * q^85 - 21648 * q^89 + 13995 * q^91 + 28884 * q^95 - 9408 * q^97

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